Advances in comminution

ADVANCES IN COMMINUTION

Published by the Society for Mining, Metallurgy, and Exploration, Inc.

Society for Mining, Metallurgy, and Exploration, Inc. (SME) 8307 Shaffer Parkway Littleton, Colorado, USA 80127 (303) 973-9550 / (800) 763-3132 www.smenet.org SME advances the worldwide mining and minerals community through information exchange and professional development. SME is the world’s largest association of mining and minerals professionals. Copyright ” 2006 Society for Mining, Metallurgy, and Exploration, Inc. All Rights Reserved. Printed in the United States of America. Information contained in this work has been obtained by SME, Inc., from sources believed to be reliable. However, neither SME nor its authors guarantee the accuracy or completeness of any information published herein, and neither SME nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that SME and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Any statement or views presented here are those of the author and are not necessarily those of SME. The mention of trade names for commercial products does not imply the approval or endorsement of SME. ISBN-13: 978-0-87335-246-8 ISBN-10: 0-87335-246-7

Library of Congress Cataloging-in-Publication Data Advances in comminution / edited by S. Komar Kawatra. p. cm. Includes bibliographical references and index. ISBN-13: *978-0-87335-246-8 ISBN-10: 0-87335-246-7 1. Stone and ore breakers--Technological innovations. 2. Crushing machinery--Technological innovations. 3. Mining engineering--Technological innovations. I. Kawatra, S. K. TN510.A38 2006 622'.73--dc22 2005057533

Preface This third international symposium and proceedings, Advances in Comminution, have come at a critical time. Because of rapidly rising energy prices, it is important that the latest information be made available for improving the efficiency of highly energy-intensive comminution processes. The contributors and topics for this third international symposium have been carefully selected to provide a balance between academic and industrial practice so that the reader can readily find information on current best practices and evaluate future industry trends. Two previous symposiums, also organized by the Society for Mining, Metallurgy, and Exploration, were great successes. The first conference was held in 1992, at a time when there was much discussion about switching from traditional rod mill and ball mill circuits to autogenous grinding. The second comminution symposium, held in 1997, focused on initial installations of high pressure grinding rolls (HPGRs). Now, in 2006, the HPGRs are becoming part of hard-rock grinding circuits. They have proven to be a very economical addition to many comminution processes because of lower energy consumption and easy integration into existing conventional systems. The 2006 conference focuses on the dilemma of needing to grind materials to everfiner sizes while maintaining reasonable energy costs. The selection and sizing of stirred mills for regrinding and ultrafine grinding applications do not lend themselves to conventional methodologies; therefore, new approaches are being developed. There is also a great deal of activity directed toward improving ore characterization to predict AG/ SAG mill energy requirements, as well as developing improved models and instrumentation for optimization and control of comminution circuits. Instrumentation, modeling, and control functions in particular have benefited from rapidly advancing computer technology, with calculations that were formerly extremely time-consuming becoming rapid and routine. These advances will keep energy waste to a minimum and will provide the increased energy efficiency needed to maintain ongoing industry success. It is hoped that the symposium and these proceedings will be useful to those who are working toward major advances in industrial practice. Appreciation is extended to members of the organizing committee, who were instrumental in acquiring high-quality papers and reviewing them on very short notice, and to the SME staff, particularly Ms. Tara Davis and Ms. Jane Olivier, for their assistance in organizing the third international symposium and publishing these proceedings.

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Contents EDITORIAL BOARD PREFACE PART 1

v

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ADVANCED COMMINUTION TECHNOLOGIES

1

High-Pressure Grinding Rolls—Characterising and Defining Process Performance for Engineers

PART 2

PART 3

3

High-Pressure Grinding Rolls—A Technology Review

15

Some Basics on High-Pressure Grinding Rolls

41

High-Pressure Grinding Rolls for Gold/Copper Applications

51

Selection and Sizing of Ultrafine and Stirred Grinding Mills

69

Effects of Bead Size on Ultrafine Grinding in a Stirred Bead Mill

87

Specific Energy Consumption, Stress Energy, and Power Draw of Stirred Media Mills and Their Effect on the Production Rate

99

AG/SAG Mill Circuit Grinding Energy Requirement—How to Predict It from Small-Diameter Drill Core Samples Using the SMC Test

115

COMMINUTION PRACTICES

129

Causes and Significance of Inflections in Hydrocyclone Efficiency Curves

131

Simulation-Based Performance Improvements in the Ispat Inland Minorca Plant Grinding Circuit

149

Determining Relevant Inputs for SAG Mill Power Draw Modeling

161

Cement Clinker Grinding Practice and Technology

169

Extended Semiautogenous Milling: Smooth Operations and Extended Availability at C.M. Doña Ines de Collahuasi SCM, Chile

181

LIBERATION AND BREAKAGE

191

Shell and Pulp Lifter Study at the Cortez Gold Mines SAG Mill

193

Breakage and Damage of Particles by Impact

205

The Rationale behind the Development of One Model Describing the Size Reduction/Liberation of Ores

225

Influence of Slurry Rheology on Stirred Media Milling of Limestone

243

iii

Experimental Evaluation of a Mineral Exposure Model for Crushed Copper Ores

261

Linking Discrete Element Modeling to Breakage in a Pilot-Scale AG/SAG Mill 269

PART 4

Significance of the Particle-Size Distribution in the Quality of Cements with Fly Ash Additive

285

Modeling Attrition in Stirred Mills Applying Statistical Physics

293

MILL DESIGN

307

Design of Iron Ore Comminution Circuits to Minimize Overgrinding

309

Evaluation of Larger-Diameter Hydrocyclone Performance in a Desliming Application

321

Selection and Design of Mill Liners

331

The Importance of Liner Geometry and Wear in Crushing

377

Bond’s Method for Selection of Ball Mills

385

Developments in SAG Mill Liner Design

399

The Gearless Mill Drive—The Workhorse for SAG and Ball Mills 413 Optimizing Hydrocyclone Separation in Closed-Circuit Grinding PART 5

INSTRUMENTATION, MODELING, AND SIMULATION

435

445

Use of Multiphysics Models for the Optimization of Comminution Operations

447

Batu Hijau Model for Throughput Forecast, Mining and Milling Optimization, and Expansion Studies

461

The Use of Process Simulation Methodology in Process Design Where Time and Performance Are Critical

481

Modeling and Simulation of Comminution Circuits with USIM PAC

495

Remote and Distributed Expert Control in Grinding Plants

513

Developments in Sensor Technology for Tumbling Mills

527

Ball Mill Circuit Models for Improving Plant Performance

539

INDEX

547

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PART 1

Advanced Comminution Technologies

1

High-Pressure Grinding Rolls— Characterising and Defining Process Performance for Engineers Richard Bearman*

ABSTRACT

High-pressure grinding rolls (HPGRs) are increasingly becoming a part of the hard-rock processing picture through their energy efficiency, the ability to induce microcracks and preferential liberation, coupled with high throughput and high reduction ratio. Given that the machine is still not regarded by many as an off-the-shelf piece of process equipment, there is work required to define guidelines for its use and to provide engineers with tools they can use. This paper examines the current knowledge around the HPGR process performance and explores key relationships available to engineers, whilst considering current approaches to simulation. INTRODUCTION

High-pressure grinding rolls (HPGRs) have struggled for acceptance into the hard-rock mining sector. Many of the issues that restricted their widespread use have now been conquered, but it is still regarded as an “immature” technology. Why is this the case? In contemplating an answer to the issue of the “immaturity,” the status of other accepted technologies must be examined. As an example, the traditional compressionstyle cone-gyratory crushers can be considered. When a plant design is being assembled, every well-equipped engineer will be able to turn to numerous rules of thumb associated with these crushers—even without reference to textbooks or suppliers. The types of rules referenced above include ƒ Product-size distribution will be approximately 80% passing the closed-side setting—

with poor applications dropping to 50%. ƒ Centralized and circumferentially distributed feed is required to extract the best

performance. ƒ Profile and condition of the crushing liners is critical to deliver the best distribu-

tion of energy into the crushing chamber. ƒ Low-bulk-density feeds reduce throughput. ƒ Maximum product bulk density is 1.9 to 2.1 t/m3 for average limestone feedstock. ƒ Secondary applications are power driven, whilst tertiary duties are pressure driven. * Rio Tinto Technical Services, Perth, Western Australia 3

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ƒ Mostly 5%–10% of the feed-size distribution is the maximum less than the closed-

side setting—except with modern cones that are trying to generate interparticle crushing. ƒ Maximum feed size should not exceed 80% of the open-side feed opening. ƒ Feed moistures >4% should be avoided.

Given this type of knowledge, it is easy for the designer to determine the position within the flowsheet and to then calculate the feed rates, type of feed arrangement, and the pre- and postclassification required. Why do these rules of thumb, or guidelines, not exist for HPGRs? There are several reasons for this lack of clarity, namely: ƒ Number and type of applications ƒ Genesis of the HPGR concept ƒ Industry position on technology ƒ Existence of process models

First, there are very few actual, or operating, applications in hard-rock duties. The only hard-rock applications that have been in existence for any length of time are restricted to the diamond and iron ore (pellet-feed) sectors. Another consideration is that the HPGR is a very rare breed of machine, in that its development stemmed from fundamental research. Given the types and focus of early publications, much was made of the nature of the interparticle breakage at the heart of the technology. Obviously, given the ground-breaking nature of the invention, this focus was fully justified, but it led—unfairly—to the HPGR being regarded as an academic device searching for an industry application. The language used about the HPGR, and unfamiliar terms such as “m-dot” (denoting specific throughput), further led to an air of mystique around the HPGR. Was it a crusher or a mill? Its place in the world was unclear. Another element restricting the rate of application was the lack of process models. Simulation is a large part of the flowsheet design exercise and this inevitably requires process models to exist for each piece of equipment. In the case of the HPGR, much of the effort was placed in scale-up procedures. Several organisations did produce process models of HPGRs, but they have been fragmented in their acceptance. Currently, the most complete model approach is that reported by Daniel and Morrell (2004), who have developed an approach from the earlier model of Tondo (1997). It is interesting to note that the Tondo model came out of the first major process study of HPGRs, namely the AMIRA P428 that was completed in 1997. If these points above are added to the naturally conservative stance of the mining industry, this provides a view of why, even after mechanical/wear issues have been overcome, there is still a slow rate of acceptance. As of today, the situation has changed. The features and benefits have become clear to many practitioners, including ƒ Energy efficiency ƒ Preferential liberation at natural grain boundaries ƒ Microcracking and enhanced extraction ƒ Small footprint in terms of throughput and size reduction ƒ Minimal vibration from machine into drive mechanisms and support structure

Of increasing importance is the energy-efficiency issue. It was not too long ago that the mining industry regarded energy consumption as somewhat of a side issue. The Kyoto Protocol and the greenhouse debate changed this view forever (Ruben 2002).

HPGRS—CHARACTERISING AND DEFINING PROCESS PERFORMANCE

5

CRITICAL HPGR PARAMETER S

HPGR roll diameters typically range from 0.5 m to 2.8 m, depending on the supplies, and roll widths vary from 0.2 m to 1.8 m. The aspect ratio of the rolls also varies as a function of manufacturer. Typical HPGR throughput rates range from 20 to 3,000 tph, with installed motor power as high as 3,000 kW per roll. The roll surface is protected with wear-resistant materials, and it has been these that have traditionally stymied HPGR acceptance, but solutions are now in place (Maxton, Morley, and Bearman 2004). When operating an HPGR, the two most important operating parameters are ƒ Operating pressure ƒ Roll speed

The two key operating parameters are inherently linked to the following: ƒ Specific throughput ƒ Specific pressing force ƒ Maximum pressure between the rolls ƒ Specific energy input

Detailed descriptions of the derivation and formulation of the parameters are given in numerous texts, and as such, the following section provides only a précis of the critical formulas, with some examples of actual relationships from testwork. Specific Throughput

The specific throughput, m-dot, is regarded by many as the key parameter for sizing the rolls. Specific throughput is defined as the throughput (tph), divided by the roll diameter (m), roll width (m), and the peripheral roll speed (m/s). For the purposes of brevity, only the equations for this parameter are reported here. Further details are provided in earlier works. (Schönert 1991). Part of its importance is that the equation allows comparison between any size of rolls providing that the surfaces are the same. m• = M/(D u L u u) where M D L u m•

= = = = =

(EQ 1)

throughput rate (tph) roll diameter (m) roll width (m) roll speed (m/s) specific throughput (ts/hm3)

The throughput can also be calculated from the continuity equation as follows: M = L u s u u u Uc u 3.6

(EQ 2)

where s = operating gap (mm) Uc = density of the product cake (t/m3) Combining equations (1) and (2), one obtains: m• = (s/D) u Uc u 3.6

(EQ 3)

For a given material and operating conditions, the gap scales linearly with the diameter of the rolls, and hence the specific throughput can be assumed to be constant.

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250 30 Bar 38 Bar 52 Bar

m-dot, ts/hm 3

230

210

190

170

150 1.40

1.45

1.50

1.55

1.60

1.65

1.70

1.75

Bulk Density, t/m 3

FIGURE 1 Variation in specific throughput as a function of feed-bulk density for various operating pressures using a pilot-scale HPGR

It should be noted that recent work by Daniel (2005) has examined the determination of an equivalent diameter for piston press tests. Daniel proposes D = (Ucf u xc u xd) / ((Ucf u xc ) – (xg u Ug )) where Ucf xc xd xg Ug

= = = = =

(EQ 4)

feed bulk density, lightly compacted initial bed height in piston press displacement of piston final bed height (i.e., operating gap) density of product flake

This relationship has potential to assist in translating piston press results to engineering parameters. Variation in Throughput with Key Variables

Figure 1 shows the variation in the specific throughput as a function of the feed bulk density. The relationship appears to be linear over the range of feeds tested. Given that the specific gravity of the feed material is 2.85 t/m3, it would be unlikely that the loose feed bulk density would exceed 1.8 t/m3; therefore, this graph suggests that the relationship is relevant over a vast majority of cases. It should be noted that throughput is highest at the lowest pressure, with larger changes associated with the all-in (high bulk density) feed types. Figure 2 shows the type of linear increase in specific throughput associated with increasing operating gap. Figure 3 shows a plot of all tests versus the specific energy (power) consumed. It is interesting to note that the data appear in two distinct clusters. The right-hand cluster consists purely of the all-in feed types with no truncation of the feed-size distribution at the lower end, whilst the left-hand cluster is formed from feeds with fines truncation.

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HPGRS—CHARACTERISING AND DEFINING PROCESS PERFORMANCE

250 240 230

m-dot, ts/hm 3

220 210 200 190 180 170 160 150 15

16

17

18

19

20

21

Operating Gap, mm

FIGURE 2 Variation in specific throughput as a function of operating gap using a pilot-scale HPGR at an operating pressure of 38 bar

60 58 56

m-dot, ts/hm 3

54 52 50 48 46 44 42 40 40

90

140

190

240

290

Power, kW

Variation in specific throughput as a function of operating gap using a pilot-scale HPGR

FIGURE 3

Specific Pressing Force

The specific pressing force is defined as the grinding force applied to the rolls (kN), divided by the diameter (m) and width (m) of the rolls (Schönert 1988). The specific pressing force has the unit of N/mm2. Fsp = F/(1,000 u D u L) where Fsp F D L

= = = =

specific pressing force (N/mm2) applied grinding force (kN) roll diameter (m) roll width (m)

(EQ 5)

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Ranges for specific pressing force vary considerably in the range 1–9 N/mm2, with studded machines normally restricted to 5 N/mm2 maximum pressure. Specific pressing force is a key parameter used in scale-up and for comparison purposes between different machine sizes. Maximum Pressure between Rolls

The maximum pressure applied to the material between the rolls has been estimated by several workers, and it is generally assumed to be in the range of 40 to 60 times the specific pressing force. It is generally accepted that the following equation (Schönert 1988) holds true: Pmax = F/(1,000 u D u L u k u D ip ) where Pmax F D L k D ip

= = = = = =

(EQ 6)

maximum pressure (MPa) applied grinding force (kN) roll diameter (m) roll width (m) material constant (0.18–0.23) compression angle (6–10 degrees)

The parameter D ip can be calculated from the operating gap, with a detailed description being given by Schönert and Lubjuhn (1990). Specific Energy Input

The specific energy consumption of an HPGR is a familiar quantity to process engineers. As with all other instances of the parameter, it is calculated from the net power input to the rolls divided by the ore throughput rate. It is important to note that specific energy input (kWh/t) is proportional to the specific pressure applied to the rolls. Typical specific energy values for studded rolls range from 1 to 3 kWh/t. As with all direct comminution devices, harder material will absorb more energy compared to a softer material, for a given size reduction. A rule of thumb is that the ratio of specific pressing force to specific energy input is 1.8–3:1, with this ratio decreasing towards 1.0 for finer comminution. Figure 4 shows the type of response mentioned. In this case, the slope of the graph indicates a ratio of 1.5:1. Specific energy consumption is markedly impacted by the feed-size distribution, as illustrated in Figure 5. As the feed distribution lengthens (i.e., the bulk density increases), the specific energy consumption drops. The major impact of specific energy input is the product fineness. As with all comminution equipment, a point of diminishing returns will occur where extra energy does not generate a commensurate increase in fineness. Figure 6 shows a range of energies and fines generation. At the levels displayed in Figure 6, the point of diminishing returns has not been reached. SIMULATION OF HPGR PERFOR MANCE

As with all modeling and simulation of process equipment, there is a sliding scale from the simplest spreadsheet-based feed-product transfer function at one end, through empirical representations, to mechanistic models, and finally to detailed fundamental descriptions. The key process issues that need to be estimated, or predicted, during the design phase of a process plant are

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HPGRS—CHARACTERISING AND DEFINING PROCESS PERFORMANCE

Specific Energy Consumption kWh/t

2.1 1.9 1.7 1.5 1.3 1.1 0.9 0.7 0.5 1.0

1.5

2.0

2.5

3.0

3.5

4.0

Specific Pressing Force, MPa

FIGURE 4 Relation between specific energy consumption and specific pressing force using a pilot-scale HPGR

Specific Energy Consumption kWh/t

2.1 30 Bar 38 Bar 52 Bar

1.9 1.7 1.5 1.3 1.1 0.9 0.7 0.5 1.40

1.45

1.50

1.55

1.60

Feed Bulk Density, t/m

1.65

1.70

1.75

3

FIGURE 5 Relation between specific energy consumption and feed bulk density using a pilot-scale HPGR, at various operating pressures

ƒ Throughput ƒ Size reduction (product and oversize) ƒ Power consumption (energy efficiency) ƒ Required hydraulic stiffness ƒ Target gap and operating pressure

Using these parameters, it is then possible to insert the HPGR into a flowsheet and make sensible comparisons against other types of equipment and flowsheet configurations. The additional benefits of preferential liberation and enhanced extraction must be assessed via laboratory tests and incorporated with the full analysis.

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35

Net –1 18 mm Generation

33 31 29 27 25 23 21 19 17 15 0.5

1.0

1.5

2.0

Specific Energy Consumption, kWh/t

FIGURE 6 HPGR

Relation between specific energy consumption and fines generation using a pilot-scale

Piston Press Testing and Ore Characterisation

The main ore characterisation tests for HPGR modeling are the piston-press and dropweight procedures. The drop-weight test is the Julius Kruttschnitt Mineral Research Centre (JKMRC) -developed, single-particle test and is used to examine areas in the HPGR where the breakage is of a single-particle nature. The piston-press test is for characterisation of the packed-bed breakage zone in the HPGR. The purpose of the piston-press test is to generate an appearance function as per the drop-weight test, but for packed-bed breakage. Hence, the piston-press appearance function is used to characterise the predominant breakage action in the HPGR. The piston press can be used in an analogous manner to the traditional drop-weight test (i.e., breakage parameters and an appearance function can be determined). In terms of the breakage characteristics, Table 1 provides an example of the comparison of the “b” parameters from the drop-weight and piston-press tests for material from Argyle Diamonds. The immediate observation regarding the data in Table 1 is that the piston press “b” parameters are higher than the single-particle test, with the inference being that the material appears softer in a packed-bed environment. Given the mode of compression (i.e., slow interparticle versus transient compression), Table 1 could represent an efficiency factor relating the two forms of breakage. Of more practical importance is that the use of the packed-bed, piston-style test is critical to the formation of a representative model of HPGR performance. Application of Piston Press to Provide Conceptual-Level HPGR Performance Estimates

A variety of workers are now using piston-press tests to research the action of HPGRs. The press arrangement at Freiberg University has recently been used to test a copper ore supplied by Rio Tinto. The aim of the tests is to determine the amenability of the ore to HPGR treatment and to examine the use of the piston press for conceptual-level evaluations. A series of tests at pressures from 80 to 320 MPa were undertaken with the results presented in Table 2. The maximum pressures reported in Table 2 were chosen to mimic those seen in the HPGR pilot tests, and the results appear to be good approximations to those obtained

HPGRS—CHARACTERISING AND DEFINING PROCESS PERFORMANCE

TABLE 1

Single-particle breakage parameters

Sample Unweathered lamproite Siliceous waste

TABLE 2

11

Single-Particle Test

Packed-Bed Test

b 0.44 0.40

b 0.940 0.703

Flake density results from piston-press tests Maximum Pressure, MPa

Flake Density, t/m3

77.24 157.29 230.53 310.98

2.14 2.32 2.32 2.38

from pilot-scale HPGR work. Given this agreement, it is suggested that the piston press be used to provide a conceptual-level envelope of performance. The suggested sequence is 1. Estimate m-dot value from Equation (3), by substitution of the product flake

density, operating gap (final bed depth from piston press), and use of Equation (4) to determine D. 2. Estimate throughput from the rearranged Equation (1), with assumed values for

roll diameter (D), roll width (L), and roll speed (u) relating to the desired scale of equipment. These values can be determined in association with manufacturers. It should be noted that the scale independence of m-dot, due to the linearity of operating gap versus roll diameter, is a major assumption in this step. 3. Calculate the specific pressing force (Fsp) from Equation (5) using the applied

grinding force from the piston press and the D and L values used above. With these key parameters, it is possible to ensure that the size of rolls and the bearing selection is correct. To estimate comminution performance: ƒ Determine the specific energy consumption from assumed relationship with spe-

cific pressing force. Values for the ratio Fsp:Wsp can be assumed to vary from 1:1 for very fine comminution through to 3:1 for very coarse duties. A value of 1.5:1, as shown in Figure 5, is a good general value for moderate comminution of hard ores. Care should be taken—although particle-size distribution is a major part of the bulk properties that dictate the relationship between Fsp and Wsp, other factors also influence the bulk behaviour including ore hardness, friction, and moisture (M.J. Daniel, personal communication, 2005). ƒ Specific energy consumption is inherently linked to product-size distribution via the

traditional breakage and appearance type mapping employed in single-particle dropweight tests. Using the A and b parameters from the piston-press test, these along with the specific energy consumption can be substituted into the following equation: t10 = A(1 – e–b. Ecs) where t10 = percentage passing one tenth of the feed size A and b = breakage characteristics from piston-press tests Ecs = specific energy consumption (kWh/t)

(EQ 7)

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ADVANCED COMMINUTION TECHNOLOGIES

Using the standard single-particle relationships between t10 and the other size distribution markers (i.e., t2, t4, t25, t50, t75), the entire size distribution of the product can be generated. Theoretically, this is a combination of packed- and singlebed approaches, but, as Tondo (1997) showed, the packed-bed t10 versus tn relationship underestimates size reduction in coarse sizes, compared to single-particle tests. Given that the variable edge effect generates coarser products, it is likely that any underestimation from the packed-bed parameters is simply an approximation to the coarser edge comminution. This approach is backed up by the fact that various workers have chosen to deal with this in different ways, whilst still obtaining satisfactory results. Tondo (1997) used both single-particle and packedbed A and b parameters with separate appearance functions in his work, whilst Daniel (2002) assumes a 10% split to edge and uses the single-particle function for all breakage with a t10 of 30. This conceptual-level approach, although not rigorous, helps engineers to obtain a “feel” for HPGR performance and at least obtain a quick, first-pass estimate of the operational envelope. It should be noted that no account is taken of precrush or edge effects. Analysis of this technique suggests that both throughput and product fineness are overstated, but as the scale of machine increases, the discrepancy lessens. This reduction in error with scale can probably be assigned to the decreasing proportion of machine performance impacted by edge effects. Detailed HPGR Modeling

For a more complete treatment of performance estimation in a modeling sense, true models are required. The work of Daniel and Morrell (2004) represents the most complete current description. The basis for their work is shown schematically in Figure 7. Daniel and Morrell outline information required for modeling, as shown in Table 3. To undertake the simulation, there are a variety of parameters relating to the breakage and classification of material in the three different zones as defined in Figure 7. The main parameters are listed in Table 4. This extremely comprehensive treatment is then used in a verification and scale-up scheme procedure; full details can be found in works by Daniel and Morrell (2004). CONCLUSIONS

There is an increasing body of knowledge around the application of HPGRs in hard-rock duties. In terms of selection and sizing, much has already been written, particularly by the suppliers. For process performance, the increasing application is allowing the development of some rules and shortcuts that can allow a first-pass evaluation of HPGRs for flowsheet purposes—a critical element on the pathway to engineering acceptance. In many ways, this paper seeks to provide a pragmatic engineering basis for the assessment of HPGR performance. This message was also the theme expressed by Klymowsky and Liu (1996), where they sought a Bond work-index analogy for HPGRs. There is no doubt that a standardized, accepted HPGR “work index” would be a great boost to HPGR acceptance. Beyond these engineering views of HPGRs, the detailed modeling and simulation of HPGR process performance is finding common ground, and workers have developed comprehensive approaches that provide the required accuracy and resolution. Assimilation of this understanding within the industry, along with simpler measures and guidelines, will accelerate HPGR implementation, particularly now that mechanical issues are predominantly of historical interest only.

HPGRS—CHARACTERISING AND DEFINING PROCESS PERFORMANCE

13

Feed to HPGR

Entry Zone Single-Particle Breakage

Centre Zone Packed-Bed Breakage

Edge Effect SingleParticle Breakage

Product from HPGR

After Tondo 1997.

FIGURE 7

TABLE 3

Schematic representation of Daniel and Morrell model

Model inputs and outputs Measured Input

Sample mass Roll diameter (D) Roll width (L) Roll speed (U) Bulk “compacted” density (qc) Feed-size distribution

Measured Output

Calculated Output

Working gap (xg) Flake thickness (xgf ) Flake density (qg) Product-size distribution (measured) Batch process time Working pressure (pw), power (kW)

Measured throughput (Qm) Calculated throughput (Qcalc) Specific energy (Ecs) Specific force (Fsp) Critical gap (xc) Product-size distribution

Source: Daniel and Morrell 2004.

TABLE 4

Model parameters Fixed Default Parameters

t10p, t10e—breakage for edge and precrusher K1p, K2p, K3p—precrusher model parameter K1e, K2, K3—edge-crusher model parameter K1h, K2h, K3h—compression zone parameter Split factor (c) Kp(edge)—power coefficient (edge)

Critical Model Parameters

Kp(HPGR)—power coefficient (compression zone) t10h—breakage for compression zone crusher

Source: Daniel and Morrell 2004.

ACKNOWLEDGMENTS

The author gratefully acknowledges all practitioners in the field of HPGR technology that have contributed to this paper through discussions. In particular, the discussions and advice from Mike Daniels, JKMRC, showed that a considerable amount of effort is still being applied to the issue of HPGR application.

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REFERENCES

Daniel, M.J. 2002. HPGR model verification and scale-up. Master’s thesis. Brisbane, Australia: Julius Kruttschnitt Mineral Research Centre, Department of Mining and Metallurgical Engineering, University of Queensland. ———. 2005. Paper submitted to Randol Pacific Gold Forum, Perth, Australia. Daniel, M.J., and S. Morrell. 2004. HPGR model verification and scale-up. Minerals Engineering 17:1149–1161. Klymowsky, I.B., and J. Liu. 1996. Towards the development of a work index for the roller press. In Comminution Practices, SME Symposium 1996. S.99/105. Maxton, D., C. Morley, and R. Bearman. 2004. A quantification of the benefits of high pressure rolls crushing in an operating environment. Minerals Engineering 16:827–838. Ruben, E.S. 2002. Learning our way to zero emissions technologies. IEA Zero Emission Technologies Strategies Workshop, Washington, DC, March 19. Schönert, K. 1988. A first survey of grinding with high-compression roller mills. International Journal of Mineral Processing 22:401–412. ———. 1991. Advances in comminution fundamental, and impacts on technology. Pages 1–21 in Proceedings of the XVII International Mineral Processing Congress. Volume 1. K. Schöenert, ed. Ljubijana, Yugoslavia. Schönert, K., and U. Lubjuhn. 1990. Throughput of high compression roller mills with plain and corrugated rollers. Pages 213–217 in 7th European Symposium on Comminution. Tondo, L.A. 1997. Phenomenological modelling of a high pressure grinding roll mill. Master’s thesis. Brisbane, Australia: Julius Kruttschnitt Mineral Research Centre, Department of Mining and Metallurgical Engineering, University of Queensland.

High-Pressure Grinding Rolls— A Technology Review* Chris Morley†

ABSTRACT

The development of high-pressure grinding rolls (HPGRs) technology is reviewed, with an emphasis on aspects relevant to hard-rock comminution. Case histories are investigated and lessons learned are discussed in the particular context of the application of the device as a supplement to, or replacement for, conventional crushing and semiautogenous milling circuits. The potential for the more widespread use of this technology as a comminution method in hard-rock processing is examined. The use of the technology as a metallurgical tool is addressed, and future flowsheet concepts are introduced that make progressively greater use of the energy efficiency of HPGRs. INTRODUCTION

High-pressure grinding roll (HPGR) technology has its genesis in coal briquetting in the early twentieth century, but it was not until the mid-1980s that it was adopted for comminution applications, when it was applied in the cement industry to treat relatively easily crushed materials. Since then, it has been applied to progressively harder, tougher, and more abrasive materials, generally successfully, but as would be expected, not without some developmental problems. Machines are now also in use in the following applications: ƒ Kimberlites in secondary, tertiary, and recrush roles ƒ Iron ores for coarse crushing, autogenous mill pebble crushing, regrinding, pre-

pelletising, and briquetting ƒ Limestone crushing ƒ Concentrates fine grinding ƒ Gold ore crushing

Other prospective applications include phosphates, gypsum, titanium slag, copper and tin ores, mill scale, and coal. Hard-rock operations that use HPGRs as an alternative or supplement to conventional comminution devices include Argyle, Diavik, Premier, Kimberley, Jwaneng, Venetia and

* Updated from the original paper, “HPGR in Hard Rock Applications,” published in Mining Magazine, September 2003, www.miningmagazine.com † Fluor, Australia 15

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Courtesy of Köppern.

FIGURE 1

Coal briquetting press—early twentieth century

Ekati (diamonds), CMH-Los Colorados, CVRD, Empire and Kudremukh (iron ore), and Suchoj Log (gold ore). Hard-rock operations to have considered using HPGR and conducted pilot testing include Mt. Todd, Boddington, and KCGM, all in Australia. A full plant trial of an HPGR was conducted on a particularly arduous duty at Cyprus Sierrita between 1995 and 1996; and, more recently, HPGR has been piloted at Lone Tree, Nevada, in the United States, and Amplats Potgietersrus in South Africa. Currently, HPGR-based comminution plants are under construction at Bendigo, Australia (gold), and Cerro Verde, Peru (copper), and at final feasibility study stage for the Soledad Mountain, California (heap leach gold/silver), and Boddington, Australia (gold/copper), projects. There are currently three recognised manufacturers of HPGR machines, namely Polysius (a Thyssen Krupp company), KHD Humboldt Wedag AG, and Köppern, all based in Germany. T H E TE C H N O L O G Y

Machine Design

The HPGR machine comprises a pair of counterrotating rolls mounted in a sturdy frame. One roll is fixed in the frame, while the other is allowed to float on rails and is positioned using pneumohydraulic springs. The feed is introduced to the gap between the rolls and is crushed by the mechanism of interparticle breakage. The pressure exerted by the hydraulic system on the floating roll largely determines comminution performance. Typically, operating pressures are in the range of 5–10 MPa, but can be as high as 18 MPa. For the largest machines, this translates to forces of up to 25,000 kN. The rolls are protected with wear-resistant surfaces, and the ore is contained at the roll edges by cheek plates. Technology Motivators

Generally, the primary motivation for the use of the HPGR as a comminution alternative is its energy efficiency when compared to conventional crushers and mills. This improved

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Courtesy of KHD Humboldt Wedag AG.

FIGURE 2

HPGR machine

efficiency is due to the determinate and relatively uniform loading of the material in the HPGR compression zone, whereas the loading in conventional crushers and (particularly) tumbling mills is random and highly variable, and therefore inefficient. The most energy-efficient method of breakage is the slow application of pressure to individual particles to cause structural failure, such that the energy lost as heat and noise is minimised. However, until a device is invented that can perform this task on a commercial scale, the HPGR remains the most energy-efficient comminution technology available. A major operating cost in conventional semiautogenous-based comminution circuits treating hard and abrasive ores is that of grinding media. One effect of the use of HPGRbased circuits is that semiautogenous mill grinding media is eliminated, and while ballmill media costs typically are slightly greater (due to the increased transfer size from HPGRs), the overall media savings are typically of the same order of magnitude as the energy savings. In addition to its energy and media benefits, the HPGR may be regarded as a metallurgical tool offering improved gravity, flotation and leach recoveries, and enhanced thickening, filtration, and residue deposition performance. These effects can be attributed to the phenomenon of microcracking of individual progeny particles due to the very high stresses present in the HPGR compression zone. Microcracking occurs predominantly at grain boundaries and so increases liberation and lixiviant penetration, while the effective reduction in milling work index caused by microcracking reduces overgrinding and slimes generation. In addition to being ore dependent, the extent of microcracking is a direct function of the operating pressure—and therefore energy input—of the HPGR, and in any given operation, the benefits of microcracking must be weighed against the incremental power required to achieve those benefits. The HPGR’s mechanism of interparticle breakage is particularly beneficial in the processing of diamond-bearing kimberlites, which undergo a form of differential comminution

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Courtesy of Polysius AG.

FIGURE 3

Cone crusher product particle (conventional crushing)

Courtesy of Polysius AG.

FIGURE 4

HPGR product particle (internal microfractures after Polycom treatment)

whereby the host rock is shattered while the diamonds are liberated undamaged—provided, of course, that the diamonds are smaller than the operating gap of the HPGR. This effect is also of benefit in the treatment of gold ores containing coarse gravity-recoverable gold grains, which would be flattened in conventional tumbling mills and rendered more difficult to recover. Technology Status

The HPGR, considered a mature technology in the cement industry, is now the norm rather than the exception in modern diamond plant design and is becoming common in iron ore processing, particularly in the field of pellet feed preparation. However, although some of the current diamond and iron ore applications can be regarded as hard-rock duties, HPGR is regarded by many as unproven in true hard-rock mining, and this perception is reinforced by the experience at Cyprus Sierrita in 1995– 1996. This application is widely considered to have been unsuccessful because it did not lead to a commercial sale; however, the fact that the comminution performance of the machine was impressive is not in dispute. The difficulties experienced related to the behaviour of the wear surfaces, and many valuable lessons were learned from this operation regarding the precautions necessary in circuit design and unit operation for the protection of the studded roll surfaces and the successful application of HPGR technology.

HIGH-PRESSURE GRINDING ROLLS—A TECHNOLOGY REVIEW

FIGURE 5

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Cyprus Sierrita installation

The following is a summary of the more important issues arising from observations of the HPGR operation at Cyprus Sierrita and elsewhere: ƒ The technology is approaching a level of maturity allowing it to be seriously con-

sidered for hard-rock applications. ƒ HPGRs are sensitive to segregation and tramp metal in the feed. ƒ Mechanical availability of HPGRs is relatively high, and loss of machine utilisation

in hard-rock applications is predominantly wear related. ƒ The smooth and profiled hard-metal roll surfaces commonly used in the cement

sector are unsuitable for hard abrasive ores. Instead, the more recently introduced autogenous wear layer concept should be used, in which crushed ore is captured in the interstices between metal carbide studs or tiles. ƒ On hard-rock applications in particular, HPGRs are sensitive to feed top size,

which ideally should not exceed the roll operating gap. Oversize material in the feed can lead to stud breakage. ƒ Roll wear surfaces may be formed as segments or as cylindrical sleeves or tyres.

Segments may be used for softer ores and lower operating pressures, while tyres are recommended for hard-rock duties and higher pressures as they present a uniform, uninterrupted wear surface to the ore and thereby avoid the preferential wear that occurs at segment boundaries. In addition, tyres are easier to fabricate than segments and so are less expensive. ƒ Tyres involve long change-out times due to the need to remove the roll assemblies

from the mainframe, while segments can be changed in situ. Some machine designs aim to minimise change-out times for tyres by allowing roll assembly removal without the need for dismantling of the feed system and superstructure. ƒ Wear of the roll edges and cheek plates (the static wear plates used to contain the

ore at the roll edges) remains an issue, and development in this area is ongoing. A

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few operations use rock boxes (chutes at the edges of the rolls) instead of cheek plates, allowing part of the feed material to flow around the rolls and so relieve the pressure on, and wear of, the roll edges. This does, however, introduce the disadvantage of passing uncrushed feed to product. Technology Hindrances

Hindrances to the adoption of HPGRs in hard-rock processing include ƒ The generally conservative nature of the mining industry ƒ A perception of high cost, particularly of the replacement wear parts in abrasive

applications ƒ Uncertainties regarding the reliability of modeling and scale-up from laboratory

or pilot operations to commercial installations ƒ A lack of definition of the requirements for robust flowsheet design of an HPGR-

based comminution circuit. Of these, it is generally acknowledged that high wear rates constitute the major obstacle to the ready acceptance of the technology in hard-rock applications. However, the HPGR can prove a cost-effective comminution device, even when the high cost and frequency of replacement of wear surfaces in highly abrasive duties are considered. Scale-up procedures have been the subject of many technical publications and should now be considered reliable. They are mentioned here only briefly for the sake of completeness. The characteristics of HPGRs that have a significant impact on flowsheet design will be considered as the main emphasis of this analysis. SCALE OF OPERATION

A common perception is that a project must be of relatively large scale before the use of HPGRs can be justified. However, HPGR units of almost any size can be produced (up to the current practical unit capacity limit of about 2,200 t/h), and this technology deserves serious consideration over a much wider range of plant capacities than might initially be imagined. Ultimately, HPGRs can be justified if they offer benefits to metallurgical performance and/or project economics, and the potential for such benefits can usually be assessed at the prefeasibility study phase by conducting preliminary tests. The manufacturers have test facilities in Germany, and small-scale laboratory facilities are available at various locations globally. Pilot-scale machines are available at several research facilities in Perth, Western Australia, and a Polysius mobile pilot unit used for trials at an operation in North America in 2003 was subsequently relocated to South Africa for evaluation on a hard-rock mining operation. THE MANUFACTURERS AND THEIR DESIGNS

Polysius, KHD, and Köppern are widely represented globally, but the machines are manufactured exclusively at their respective facilities in Germany. Polysius favours a high-aspect-ratio design—large diameter, small width—while KHD and Köppern prefer a low-aspect ratio. The high-aspect-ratio design is inherently more expensive but also offers an intrinsically longer wear life for a given application, as the operating gap is larger and the roll surfaces are exposed to a correspondingly smaller proportion of the material processed. The high-aspect-ratio design also produces a coarser product due to the greater influence of the edge effect; however, this difference is relatively slight, particularly with larger units. Nevertheless, for closed-circuit applications,

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ATWAL

REGRO LABWAL Data of Test Units: Diameter of Rolls: Width of Rolls: Speed of Rolls: Top Feed Size:

0.71 m 0.21 m 0.29–1.10 m/s 16–35 mm

Diameter of Rolls: Width of Rolls: Speed of Rolls: Top Feed Size:

0.30 m 0.07 m 0.2–0.9 m/s 8–12 mm

Courtesy of Polysius AG.

FIGURE 6

Polysius test facility

this additional coarseness does increase the circulating load and tends to offset the wear life benefits, as a higher total throughput is required for the same net product. The use of tungsten carbide studs to create an autogenous wear layer on the roll surface is covered by a patent held by KHD, from whom this technology is available under license. Both Polysius and KHD have experience with minerals applications and studded roll technology, and are able to supply machines with capacities of up to about 2,200 t/h. Although Köppern has limited minerals experience, their HPGRs are successfully operating in the cement industry. For highly abrasive materials, Köppern recommends HPGRs fitted with their Hexadur wear protection. The Hexadur surface comprises hexagonal tiles of a proprietary abrasion-resistant material set into a softer matrix, which wears preferentially in operation, allowing the formation of an autogenous wear protection layer at the tile joints. The tiles and matrix material are fully bonded together and to the substrate in a high-temperature, high-pressure furnace. By contrast, KHD’s studs are inserted into drilled holes. As a result, the tiles are inherently stronger and more resistant to breakage due to oversize ore or tramp metal. Köppern supplies patterned and profiled surfaces in both segment and tyre format, whereas Hexadur is generally available only in tyre format due to the dimensional control difficulties inherent in the fabrication and furnace treatment of segments. However, research into the commercial production of Hexadur segments is ongoing. Meanwhile, the maximum Hexadur roll diameter available currently (and for the foreseeable future) is 1.5 m, constrained by furnace dimensions. This constraint limits Köppern’s unit capacity to about 1,000 t/h for hard-rock comminution applications using Hexadur. However, Köppern also offers machines with studded roll surfaces supplied by KHD, effectively lifting this capacity constraint.

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Courtesy of KHD Humboldt Wedag AG.

FIGURE 7

Studded roll wear surface

Courtesy of Köppern.

FIGURE 8

Hexadur wear surface for hard-ore comminution

Köppern has an established design in which the ends of the mainframe hinge outwards to allow the roll assemblies to be removed without disturbing the feed system and superstructure. This allows roll change-out times for tyre replacement of about the same duration as for in-situ segment change-out. Polysius also offers a design that allows rapid roll assembly removal, but without the need for a hinged frame design. In more recent developments, KHD has unveiled a rapid change-out concept to be offered on new

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Courtesy of Köppern.

FIGURE 9

Köppern HPGR

Courtesy of Köppern.

FIGURE 10

Köppern hinged frame

machines and which can be retrofitted to existing units, and Köppern has introduced their “C-frame” design that allows the removal of both roll assemblies from one end of the frame, so offering a maintenance advantage over their earlier design. KHD uses cylindrical roller bearings that allow the choice of grease or circulating oil lubrication systems, as there is no relative movement between the bearings and seals. Polysius and Köppern use grease-lubricated, self-aligning spherical roller bearings. OPERATING CHARACTERISTICS

There are many factors to be considered when specifying an HPGR and selecting an appropriate flowsheet for a given application. The following subsections summarize the more important issues.

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Ore Characteristics

The compressive strength of the material to be crushed determines the amount of useful energy that can be absorbed by the material, which in turn dictates the bearing and motor sizes required for a given duty. With studded roll wear surfaces, the compressive strength of the ore, in combination with the feed particle top size and operating pressure, will largely determine the probability of stud damage—the higher the values of each of these variables, particularly when they occur together, the higher the likelihood of incurring stud damage. Ongoing development of stud technology is aimed at reducing the sensitivity of the studs to these variables. The abrasion index of the material being crushed will determine the wear rate (as distinct from the breakage rate) of the studs, as well as that of the substrate metal. For example, the wear life at the iron ore operations at Los Colorados and Empire are about 14,000 and 10,000 hours, respectively, while those at the Argyle and Ekati diamond mines were about 4,000 hours initially, but increased to 6,000–8,000 hours and beyond with ongoing development of stud and edge protection configurations. HPGRs are not generally suitable for the treatment of highly weathered ores or feeds containing a large proportion of fines. (This of course does not apply to applications where all the feed material is fine, such as fine grinding of concentrates.) Fine and weathered material tends to cushion the action of the rolls and so reduces the efficiency of comminution of the larger feed particles. For example, Argyle bypasses its primary HPGRs when very fine ore is being mined. On these ore types, the fine or weathered material should be removed by prescreening if HPGR treatment of the coarser component is required. HPGRs are not generally suitable for comminution of feeds containing excessive moisture, which tends to cause washout of the autogenous layer on studded rolls and increases slippage on smooth rolls. In both cases, accelerated wear is the result. For example, Ekati bypasses the –4+1 mm feed fraction around the HPGR when the prevailing ore type results in inherently high moistures. Specific Pressure

The specific pressure (specific press force) is the force (Newtons) divided by the apparent (or projected) area of the roll—that is, the product of roll diameter and length: specific pressure (N/mm2) = force (N)/(D (mm) u L (mm)) Typical practical operating values are in the range of 1–4.5 N/mm2 for studded roll surfaces and up to 6 N/mm2 for Hexadur. The required specific pressure determined in tests is used for scale-up of the required operating hydraulic pressure for the commercial unit. Specific Energy Input

The specific energy input (SEI) is the net power draw per unit of throughput: specific energy input (kWh/t) = net power (kW)/throughput (dry t/h) Typical operating values are in the range of 1–3 kWh/t. In general, a given ore will absorb energy up to a point beyond which little additional useful work (i.e., size reduction) is achieved—a zone of diminishing returns is approached. For equivalent size reduction, a hard, competent ore of high compressive strength will result in a higher SEI than a softer ore of low compressive strength. The energy input is governed by the hydraulic pressure, of which it is a roughly linear function. Generally, specific energy input in coarse crushing applications is numerically

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about one half to one third of the specific pressure, so that a specific pressure in the typical operating range of 3–4.5 N/mm2 can be expected to correspond to a specific energy input of 1–2.5 kWh/t. In fine-grinding duties, this ratio is typically higher—for example, a ratio of 1.05 applies at the Kudremukh pellet feed operation. The best method of determining the optimum specific energy is to conduct tests to derive a graph of product fineness against specific energy. The graph generally displays an initial steep slope that flattens out to approach the horizontal at high SEI values (e.g., 3.5–4.5 kWh/t). The optimum SEI can then be selected. Microcracking

Although the size reduction graph frequently enters an area of diminishing returns with increasing specific energy, it has been demonstrated on some ores that the reduction in effective work index due to microcracking (also known as microfracturing or microfissuring) does not always display the same tendency. As a result, it may be beneficial from an overall comminution energy perspective to operate at a higher specific energy than corresponds to the optimum for size reduction in the HPGR stage, to maximise the benefits of microcracking. In this regard, the final grind size must also be taken into account, as the effects of microcracking are felt more in the coarser fractions, so that an application with a coarse grind will benefit more than one with a fine grind. It is important to conduct sufficient tests to quantify the optimum point of increased fines generation and reduced product work index, to ensure an HPGR is specified that is capable of transmitting the necessary power. Feed Top Size

For hard-rock applications, the feed top size is a critical variable in the successful operation of an HPGR crusher. For smooth rolls, too large a top size results in reduced nip efficiency, slippage, and accelerated wear; for studded rolls, tangential forces at the roll surface due to early nipping—effectively causing single-particle breakage by direct contact with the roll surfaces—can cause stud breakage. Constraints on feed top size have been related in the literature both to roll diameter and to operating gap. Figures of up to 7% of roll diameter and three times the gap have been quoted as appropriate limits on feed top size, even though the latter ratio implies some direct contact of the larger particles with the surfaces of both rolls, leading to singleparticle breakage. These figures are now considered much too optimistic in hard-rock applications, and it is generally accepted that, to minimise the likelihood of stud breakage, feed top size should not exceed the expected operating gap. This will normally demand a closedcircuit crushing operation upstream to ensure this top size is positively controlled. For softer materials, this rule can be relaxed—for example, some kimberlite operations successfully treat open-circuit secondary crushed products with top size–gap ratios of about 1.8–2.0 using studded rolls. By interpolation, ratios of around 1.3–1.5:1 are tolerable when treating ores of moderate hardness. Where uncertainty exists regarding ore hardness categorisation, it is considered prudent to adopt a ratio of close to 1:1 initially, and then relax this incrementally if and when it is established that stud breakage is not an issue. As a guide, the direct-contact nip angle (for single-particle breakage and possible stud damage) is normally in the range of 10˚ to 13˚ while interparticle breakage commences at angles of 5˚ to 7˚. By using a scale diagram of an HPGR unit of a given roll diameter, and showing these angles and an appropriate operating gap, estimates can be made of the particle size above which single-particle breakage is likely to occur and below which interparticle breakage commences.

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Unit Capacity

The capacity of an HPGR is fundamentally a function of the ore characteristics. Capacity is generally expressed in terms of specific throughput mx (m-dot), which is a function of the roll diameter, length, and peripheral speed: mx (t·s/m3·h) = throughput (t/h)/(diameter (m) u length (m) u speed (m/s)) The value of mx is determined in pilot tests and used in scale-up to the commercial unit, taking into account the change in the relative proportions of product from the centre of the rolls and from the edges where poorer comminution occurs (the “edge effect”), and also whether the commercial unit is to be operated with cheek plates or rock boxes for roll edge protection. In addition to its fundamental relationship to the ore characteristics, the value of mx is a function of many variables. The following should be regarded as general trends for the majority of ores, rather than as statements of universal fact—there will always be the exception that proves the rule: ƒ Ore hardness—mx increases with ore hardness. ƒ Specific pressure—mx decreases slightly with increasing pressure. ƒ Roll surface—mx increases with increasing “texture” of the roll surface, due to the

reduced slip (increased kinetic friction) and improved nip between the rolls. Thus, smooth rolls give the lowest values, with profiled surfaces in the mid-range, and studded surfaces the highest (typically about 50% higher than for smooth rolls). ƒ Roll speed—for smooth rolls, mx decreases with roll peripheral speed, so that

actual throughput increases with increasing speed but at a progressively diminishing rate due to increased slippage. The effect is much reduced with profiled or studded rolls due to the inherently higher kinetic friction of these surfaces. ƒ Feed top size—the available evidence is not conclusive, but it appears that mx

might increase slightly with an increase in feed top size. ƒ Feed bottom size—mx decreases significantly as feed bottom size is increased.

Thus, the highest value of mx occurs with a full-fines feed, and this value decreases progressively as the fines cut-off or truncation size is increased. This is due to the increased voidage in the truncated feeds, which results in a lower back pressure on the rolls and a consequent reduction in the operating gap. ƒ Feed moisture—for moisture levels greater than about 1%, mx decreases with

increasing moisture due to the replacement of solids with water in the compacted product flake; higher moisture levels can result in excessive slippage and ultimately to washout of the autogenous layer on studded rolls. Below 1% moisture, there is some evidence of reduced m• values with studded rolls due to the difficulty in generating and maintaining a competent autogenous wear layer with very dry feeds, as the crushed product is too friable to form a compacted layer between the studs. Operating Gap

The operating gap is directly related to the unit capacity, all else being equal, so “gap” can be interchanged with mx in the above analysis. Depending on the application, the ratio of operating gap to roll diameter will normally lie in the range of 0.010 to 0.028. Circuit Capacity

The capacity of an HPGR circuit, as distinct from the unit capacity discussed above, is obviously a function of the circuit design. Of the above variables, the feed bottom size

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is particularly relevant in this regard, as a truncated feed necessarily implies the presence of a screen or other classification device upstream of the HPGR. It has been noted that capacity decreases with truncated feeds; however, the capacity of the circuit would increase if the amount of fines removed from the HPGR feed exceeded the reduction in HPGR unit capacity. Whether this occurs in practice remains the subject of some debate (and in any event is probably ore specific), but recent modeling of pilot test data for two prospective applications indicates that this is the case, and this is supported by the limited evidence available in the literature. However, an increase in circuit throughput achieved in this way may be offset by a decrease in product fineness and/or reduced microcracking such that, depending on the downstream processing route, a full-fines HPGR feed may be preferable to a truncated feed. For any given application, the more efficient flowsheet can be determined only by comprehensive tests and modeling, but where doubt exists, the circuit should, if possible, be designed with the flexibility to operate with full fines or truncated feed to allow circuit performance to be optimised. This flexibility normally comprises the prescreening of the feed and a facility to recycle to HPGR feed a portion of either the HPGR product or, where the HPGR operates in closed circuit with a screen, the screen undersize. Product Sizing

As noted earlier, product fineness increases with operating pressure (and therefore power), generally up to a point of diminishing returns. It has been observed elsewhere that it is more energy efficient to operate an HPGR at low pressures and in closed circuit with a screen, so that less energy is wasted on compacting the product. However, this generally would require more or larger HPGRs to handle the increased circulating load. Also, it is not clear whether the analysis included the cost of conveying the increased circulating load of screen oversize. Product fineness generally decreases with increasing “texture” of the roll surface; so smooth rolls give the finest product, with profiled surfaces in the mid-range and studded surfaces the coarsest. This is due to the reduced slip between the rolls and the ore, giving a higher throughput for a given power draw. For the same product fineness, therefore, a studded or profiled roll machine would have to be operated at higher pressures than a smooth roll unit. However, the effect is relatively small, and the benefits of profiled or studded rolls usually outweigh the reduced product fineness. Furthermore, the effect appears to be ore specific, and some operations (e.g., Jwaneng) have recorded an increase in fineness with studded rolls compared to smooth rolls. Increasing roll speed leads to a reduced product top size and improved F50/P50 reduction ratio, without significantly changing the fine end of the sizing spectrum. A slight mismatch or differential in roll speeds has been found to enhance grinding performance, and though this could be considered intuitively plausible, it might also be expected that adopting this as a deliberate control strategy could lead to increased roll surface wear rates due to this imposed speed differential. This effect is therefore regarded as being of academic interest rather than practical significance. Product sizing is largely independent of feed moisture. Product sizing is a function of roll aspect ratio. A high aspect ratio gives an inherently coarser product for the following reasons: ƒ The proportion of edge material in the product is greater. ƒ The pressure peak in the compression zone is lower (for a given specific pressure).

However, the overall effect is generally fairly modest. The shape of the HPGR product sizing curve is dissimilar to that of conventional crushers, so that for products with nominally the same P80, the HPGR product contains

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considerably more fines below this size than from a conventional crusher. The implications of this are that, where the product is delivered to, for example, a ball milling operation, mill capacity will be greater when treating HPGR product than predicted by the standard Bond equation. Milling power requirements are thus reduced by both the sizing of the HPGR product and the microcracking of the product particles, and are therefore best determined by pilot testing. Roll Surface Wear

Increasing roll speed increases turbulence in the feed material and slip of feed against the roll surfaces, leading to elevated wear rates. This should generally be a concern only at the top end of the practical speed range. In this respect, Polysius traditionally uses a rule of thumb to the effect that the peripheral speed of the rolls (in meters per second) should not exceed roll diameter (in meters), although Köppern does not support this view and regularly nominates speed–diameter ratios of up to 1.3. KHD also uses these higher ratios for their smaller-diameter machines but generally uses <1.0 for larger units and on coarse crushing applications. More recently, Polysius has proposed that it is the angular velocity rather than peripheral speed that should be used as the roll speed selection criterion, and that maximum speed should be in the range of 18 to 20 rpm for finegrinding applications and 20 to 22 rpm for typical hard-rock coarse crushing duties. High moisture levels lead to significant increases in wear. It is believed that this could be due to a combined erosion/corrosion effect analogous to that observed in Nordberg WaterFlush cone crushers. In recent studies involving tough, abrasive ores, it was found that wear rates were significantly higher with truncated feeds than with full fines or untruncated feeds, to the extent that wear life considerations heavily outweighed the energy efficiency advantages that had previously been established for these ores using truncated feeds. This illustrates the importance of conducting comprehensive tests to ensure that decisions made on flowsheet selection are well informed. Roll surface wear rates for studded rolls can vary as the operating life of the wear surface progresses. In one application, the wear rate was observed to increase with time from 0.006 Pm/t after 200 operating hours to 0.015 Pm/t after 1,000 hours, after which a plateau was established in the wear-rate curve. It is believed that this effect is due to an initial imbalance in the wear rates of the studs and the substrate. In the case in point, it would appear that the stud protrusion above the new roll surface was too small for this particular duty, so that the substrate initially wore more rapidly than the studs. Presumably, had the stud protrusion instead been too great, then stud wear would have been more rapid initially and declined thereafter. This, however, was not demonstrated. In either case, overall wear rate stabilises when the two components of wear—stud and substrate—are in equilibrium. The important point is that roll surface wear life should not be computed from initial wear rates. The wear-rate curve must be plotted and the equilibrium plateau established before wear-life predictions are made. The “bathtub” effect is a well-documented phenomenon whereby the central zone of the rolls wears at a greater rate than the edges, forming a concave wear pattern. For smooth rolls, this can lead to a requirement for regular grinding of the edges to maintain parallel roll surfaces and avoid touching of the rolls at the edges with the correct nominal gap in the central zone. For studded rolls, harder studs can be used in the central zone to give a more uniform wear pattern across the roll surface. However, harder studs are also more brittle, and stud breakage, as distinct from stud wear, can become a problem. The optimum combination of stud hardness levels for the central and edge studs in a given application must be established by trial and error. Normally, studs of lower hardness are

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60

ATWAL Wear Rate, g/t

50 40 30 20 10 0 Truncated

50% Truncated

Full Feed

MATERIAL 1

FIGURE 11

Truncated

50% Truncated

Full Feed

MATERIAL 2

Impact of feed truncation on roll wear

selected for the initial setup to minimise the incidence of stud breakage, which is more difficult to accommodate than stud wear. After evaluating initial performance, adjustments to stud hardness may be made. Several iterations might be needed to achieve the optimum configuration. Ekati and Argyle have both achieved significantly improved results using this approach. The differential wear-rate effect is also well documented—it appears that the floating roll typically wears at a slightly higher rate than the fixed roll, though the reasons for this have not been fully investigated. It is believed that the effect is caused by the additional applied kinetic forces imparted to the floating roll. However, recent experience at a pilot operation has shown the reverse trend. In any event, the effect is small and of little practical significance. In a recently commissioned installation, a more irregular wear pattern was observed on the fixed roll relative to the floating roll, although the overall wear rate for the floating roll was higher. The reasons for this comparatively irregular wear pattern are not clear, but it is suspected that it is due to the effect of the presence of a feed-regulating gate, which presents the feed stream preferentially towards the fixed roll. This may result in an increased level of turbulence in the vicinity of the feed gate tip. The need for the gate at this operation is not proven (as the variable-speed drives provide adequate turndown), and it is to be removed as a trial, during which any change in wear patterns will be recorded. Tramp Steel

Theoretically, the HPGR is equipped to handle tramp steel in that the bearing arrangement allows skewing of the floating roll and the hydraulic system is able to relieve excessive pressures. However, particularly with larger units, the inertia of the rolls and their very brief exposure to tramp metal in the compression zone generally results in damage to the roll surface instead of, or as well as, the relieving action of the floating roll. Repair of roll damage can be expensive and operationally disruptive, and flowsheet design should endeavour to locate the HPGR in an intrinsically noncontaminated flow stream, or ensure that a comprehensive and practical tramp metal detection and removal system is included. Such a system should preferably be automatic, with contaminated ore bypassed around the HPGR or rejected from the circuit. It is important to minimise the need for operator intervention and process interruption.

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Extrusion

Extrusion is a phenomenon whereby the HPGR product stream emerges from the compression zone at a speed greater than that of the roll surface. This is similar to the wellknown extrusion effect observed in metal rolling and occurs when the product flake expands as it leaves the compression zone and the applied pressure reduces to zero. This expansion is typically in the order of 2% to 5%, and the resultant slippage can be the cause of increased roll wear. Extrusion has generally been observed to increase with roll diameter, but also has been recorded with pilot-sized machines. Extrusion also increases with applied pressure and feed moisture, and the evidence available suggests the effect is most pronounced at a roll peripheral speed of about 1.5 m/s. It is most noticeable with smooth rolls, and decreases markedly with studded or profiled surfaces. Product Flake Formation and Treatment

The HPGR product emerges from the compression zone as a compacted cake or flake. The coherence of the flake is a function primarily of the ore type and moisture content, and also of the operating pressure of the machine. Generally, competent flakes are produced with softer materials or those with a high clay or moisture content—kimberlites, for example—while hard, primary ores tend to produce fragile flakes, even at relatively high moistures and pressures. Depending on flake competency and downstream processing requirements, a dedicated unit operation for deagglomeration of the flake product could be required, and this is a significant consideration in flowsheet development. Kimberlite flakes normally must be intensively deagglomerated in wet rotary-drum scrubbers, and then screened to ensure efficient removal of fines before downstream processing, usually in a heavy media separation operation. By contrast, the flake in a hard, primary-ore application might require no separate deagglomeration, being adequately broken down by handling in chutes and bins and on conveyors, so that acceptable efficiencies are achieved in normal screening. The need for, and nature of, a dedicated deagglomeration step in the comminution flowsheet can normally be assessed by testing. KHD has developed a standard flake competency test specifically designed to determine whether separate deagglomeration is required ahead of further processing. FLOWSHEET OPTIONS

The flowsheet for a given ore is driven by the requirements of the process and consideration of the above HPGR characteristics. In particular, the possible need for a controlled feed top size, fines recycling, and separate deagglomeration will have a significant effect on the formulation of a practical and robust flowsheet. It is important that the appropriate amount of testing be conducted to determine flowsheet design requirements. Alternatively, in the absence of adequate tests, a conservative approach must be taken to flowsheet design—that is, it must be assumed that topsize control, fines recycling, and deagglomeration will all be needed. This of course has the potential to impose significant and possibly unnecessary cost penalties on any project, and a comprehensive test programme generally represents excellent value for the money in this context. The selection of flowsheets considered here focuses on alternatives to conventional hard-rock crushing, screening, and milling circuits, either as greenfield projects or as retrofits to existing operations for the purposes of debottlenecking or plant expansion. HPGR may also be considered as a beneficial metallurgical tool in heap-leach applications.

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Primary Crushing

Secondary Crushing

Screen

O/S

U/S HPGR

Semiautogenous Milling

Screen

O/S

Pebble Crushing

U/S Cyclone

U/F

Ball Milling

O/F

FIGURE 12

SAG mill precrushing to SAG mill feed

SAG Mill Precrushing

In this circuit, a portion of the semiautogenous grinding (SAG) mill feed is precrushed in a secondary crusher followed by an HPGR (with prescreening for top-size control, if necessary) before rejoining the main SAG mill feed stream. The total SAG mill feed is therefore correspondingly finer while some coarse particles are retained in the mill feed as media. This is suitable for both new and existing operations and has the potential to increase mill throughput by 50% or more. (The Troilus gold operation in Canada introduced a screen on the SAG mill feed stream and recorded a circuit capacity increase of about 35% using only a secondary crusher to precrush the –125+25 mm middlings fraction.) An alternative to this arrangement is to deliver the HPGR product to the SAG mill discharge screen, so that finished product and material of ball mill feed size bypasses the SAG mill. These circuits are flexible in that milling can continue (albeit at reduced rates) with the precrushing circuit out of service. Also, if an HPGR bypass facility is provided, the secondary crushing component of the precrushing circuit can continue to operate when the HPGR is inactive. SAG Mill Pebble Crushing

Further size reduction of the pebble fraction in an SABC (semiautogenous-ball-crusher) circuit can be achieved by passing the pebble crusher product through an HPGR, thus increasing circuit capacity. Alternatively, the conventional cone crusher may be replaced entirely by an HPGR, provided the pebble top size is small enough. In a variation, the pebble crusher and HPGR can be operated in closed circuit with the screen undersize delivered to the ball milling circuit. This circuit can be used to open-circuit the SAG mill when this is the circuit bottleneck.

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Primary Crushing

Secondary Crushing

Screen

O/S

U/S HPGR

Semiautogenous Milling

Screen

O/S

Pebble Crushing

U/S Cyclone

U/F

Ball Milling

O/F

FIGURE 13

SAG mill precrushing to ball mill feed

These circuits have the disadvantage of exposure of the HPGR to tramp steel in the SAG mill discharge. Also, the use of HPGR in the pebble-crushing circuit can usually be justified only when pebble arisings are a relatively large proportion of SAG mill new feed. Multistage Crushing and Ball Milling

In this circuit, the HPGR is used in the tertiary crushing stage immediately ahead of the ball mills. This can be applied in new projects or as a retrofit to increase crushing capacity. However, for hard rock, it is important that the secondary crushing stage be operated in closed circuit to control HPGR feed top size, and this must be borne in mind when considering this circuit as a retrofit. Depending on whether deagglomeration is indicated, the HPGR product screens may be operated dry (no deagglomeration required) or wet (mild deagglomeration). In the latter case, the dilute screen undersize slurry must be delivered to the mill sump rather than mill feed. Where intensive deagglomeration is required, the entire HPGR product is delivered to the mill, the mill discharge screened, and the screen oversize returned to the HPGR. In this case, it may be preferable to adopt a two-stage milling circuit, with the primary mill designed to minimise pebble generation, so minimising the return of moist material to the HPGR. This is inherently less efficient than delivering a controlled feed top size to the milling circuit, and it might be more efficient to use a dry deagglomerator on the HPGR product, such as a hammer mill or vertical impactor, followed by conventional dry screening. Open-Circuit HPGR with Edge Recycle

This option obviates the need for fine screening of the HPGR product and instead uses a dividing chute below the HPGR to separate the highly reduced centre product from the

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Primary Crushing

HPGR U/S O/S

Semiautogenous Milling

Screen

O/S

Screen

Pebble Crushing

U/S Cyclone

U/F

Ball Milling

O/F

FIGURE 14

SAG mill pebble crushing

Primary Crushing

HPGR Middlings Semiautogenous Milling

Screen

O/S

O/S

Screen

U/S

Pebble Crushing

U/S Cyclone

U/F

Ball Milling

O/F

FIGURE 15

Open-circuit SAG mill

coarser “edge” material, as typically practised on test units and at a few commercial operations. The centre product is delivered to downstream processing, while the edge material is returned to HPGR feed. This arrangement would typically be used where energy efficiency was not of paramount importance, such as heap-leach applications. A N A L Y S I S O F TE C H N O L O G Y B E N E F I T S

The metallurgical benefits of HPGRs have been discussed earlier in a qualitative sense. These are highly ore-specific and should be determined by the appropriate tests.

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Primary Crushing

Secondary Crushing

O/S

Screen

Middlings

HPGR

U/S Ball Milling

Cyclone

U/F

O/F

FIGURE 16

Three-stage crushing, closed-circuit HPGR

Primary Crushing

Secondary Crushing

O/S

Screen U/S HPGR

Primary Ball Mill

Screen

O/S

U/S Cyclone

U/F

Secondary Ball Mill

O/F

FIGURE 17

Three-stage crushing, open-circuit HPGR

Likewise, the energy benefits of HPGRs must be properly quantified to allow a realistic assessment of HPGR-based circuit options, as comminution energy generally is a major component of operating costs in hard-rock applications. In a recent study, a comparison was drawn between a high-capacity conventional SABC circuit and a three-stage crushing/single-stage ball milling circuit with both secondary and tertiary crushing stages operating in closed circuit and with the HPGR as the tertiary step. As part of the analysis, various intermediate circuits were also evaluated in which the HPGR played a progressively greater role.

HIGH-PRESSURE GRINDING ROLLS—A TECHNOLOGY REVIEW

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Primary Crushing

O/S

Screen

Secondary Crushing

U/S HPGR

Cement and Water Edge

Centre

Heap

FIGURE 18

Open-circuit HPGR with edge recycle

The comparison showed the following conclusions: ƒ The energy efficiency of the circuit increased with the proportion of comminution

performed by the HPGR. ƒ The specific capital cost (i.e., cost per unit capacity) of the HPGR/ball mill circuit

was 26% lower than that of the SABC circuit. (However, the capacity of the HPGR-based circuit in this example was higher than that of the SABC base-case circuit, so this differential figure would be lower in a direct comparison. This has been supported in subsequent studies on various projects in which the capital costs of an HPGR-based circuit were found to be about the same or slightly greater than for the equivalent SAG-based circuit of the same capacity.) ƒ The HPGR/ball mill circuit was 28% more energy efficient than the SABC circuit. ƒ Overall operating costs for the HPGR/ball mill circuit and downstream plant were

22% lower than for the SABC circuit. ƒ Project implementation time was significantly reduced for the HPGR option due

to the removal of the long-delivery SAG mill. As a result of these conclusions, project viability was considerably enhanced—in fact, it was determined that, in the absence of HPGR in some part of the comminution circuit, project viability was at best marginal. A sensitivity analysis was conducted in which the wear life of the HPGR roll surfaces was reduced from the 4,000 hours predicted by the manufacturers to a very conservative figure of 2,000 hours. This had the effect of increasing overall operating costs by only 5%, meaning that the HPGR-circuit operating costs were still 17% lower than those of the SABC circuit. C O M P A R I S O N W I T H C O N V E N T I O N A L TE C H N O L O G I E S

Autogenous grinding (AG) and SAG technologies displaced multistage crushing and rod/ ball milling circuits as they were simpler and offered lower capital and overall operating costs, even though they were often demonstrably less efficient in the use of comminution energy. AG and SAG mills were also ideal for handling wet, sticky, clay-rich, and oxidised

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ores, allowing the elimination of the traditional washing plant normally required for such materials. With the progressive global depletion of easily treated ores, harder, tougher, and more abrasive primary ores are being targeted for treatment, and energy efficiency will become steadily more important from both economic and environmental perspectives. These ores may be well suited to SAG mill treatment in the context of media competency, but this treatment path is grossly inefficient in the application of energy for size reduction. The circuit developed in the study referred to above represents a return to the traditional multistage crushing/ball milling circuit. The difference now is that, with HPGR in the tertiary crushing step, energy efficiencies are elevated to such a degree that overall operating costs are much lower than for the equivalent SAG mill circuit. When the potential for lower specific capital costs also is considered, the additional circuit complexity of the HPGR-based plant can more readily be justified. Just as the traditional multistage crushing/ball milling circuit has survived in selected applications, semiautogenous milling will of course also survive and remain the appropriate choice for some ores. It is believed, however, that HPGR circuits represent the next generation of hard-rock comminution plant design, as semiautogenous milling did several decades ago. VISION FOR THE FUTURE

The HPGR is the most energy-efficient comminution device currently available to the minerals processing plant designer, and the focus must be on the development of both machine and flowsheet to maximise the proportion of total comminution performed by the HPGR. The initial objective must be to minimise the top size of ball mill feed by reducing HPGR product screen aperture and recirculating progressively more material to the HPGR. This will entail changing to wet screening as the separation size falls below about 6 mm, and this in turn will impact circuit design philosophies, as there will be no opportunity to stockpile mill feed. As the mill feed top size falls, there might be some merit in operating tertiary HPGRs in open circuit and introducing quaternary HPGR crushing to handle screen oversize. The associated moisture would, however, be detrimental to this process, and some form of blending with dry material might be necessary. Ultimately, with very fine mill feeds, the number and size of conventional wet screens will become unmanageable, while the ball mills will trend ever smaller. The next step is to abandon screens and ball mills entirely and operate HPGRs in closed circuit with air separators, with the final product repulped and fed directly to flotation or other downstream processes. The technology for this type of circuit already exists and is in operation. An example is the use in Europe of KHD HPGRs and air separators for the production of dry-ground limestone for use in a flue-gas desulphurisation process. Typical air-separator performance in this type of application is 90 Pm P90, while the finest separation is claimed to be around 20 Pm P90. Product size is adjustable, and the P80 grind sizes of 75 to 150 Pm common in minerals processing should be readily achievable. CONCLUSION

HPGR technology holds the promise of significant improvements in comminution energy efficiency in hard-rock applications when compared to SAG-based circuits. Properly designed HPGR-based circuits offer the potential of significant savings in comminution energy requirements and overall operating costs when compared to SAG-based circuits. Further energy savings are envisioned as progressively more of the comminution load is

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performed by HPGR, culminating in the generation of final ground product by air classification of HPGR product and the elimination of ball milling. ACKNOWLEDGMENTS

In addition to the technical papers listed in the bibliography, from which much of this material is drawn, the sourcing of study information and operational data from Boddington Gold Mine and Argyle Diamonds, respectively, is gratefully acknowledged, as are the contributions from the manufacturers, Polysius, KHD, and Köppern. BIBLIOGRAPHY

AMIRA Project P428. 1996. Application of High Pressure Grinding Rolls in Mineral Processing (Overview). Report P428/11. Austin, L.G. 1990. Ball Mills, Semi-Autogenous Mills and High Pressure Grinding Rolls. University Park, PA: Penn State University Press. Austin, L.G., Trubeljal, M.P., and von Seebach. 1995. Capacity of high-pressure grinding rolls. Minerals and Metallurgical Processing (May): 65–73. Baum, W. 1998. HPGR as a processing tool for gold & copper leaching, flotation and gravity separation. Paper presented at Raw Material Technology Seminar, Tucson, AZ. Baum, W., and Knecht, J. 1994. Optimizing refractory and oxide gold ore operations with high pressure grinding rolls. Paper presented at SME Annual Meeting, Albuquerque, NM, February 14–17. ———. 2000. HPGR as a processing tool for gold and copper leaching, flotation and gravity separation. Paper presented at 2nd Annual Crushing and Grinding in Mining Conference, Johannesburg. Baum, W., Patzelt, N., and Knecht, J. 1996. The Use of High Pressure Grinding for Optimisation of Copper Leaching, SME, Phoenix, AZ, March. ———. 1997. Metallurgical benefits of high pressure roll grinding for gold and copper recovery. Paper presented at SME Comminution Practices Symposium, Denver, CO. Bleifuss, R.L., Goetzman, H.E., Benner, B.R. and Zhong, S. 1997. Evaluation of a high pressure roller press for taconite comminution. Paper presented at SME Comminution Practices Symposium, Denver, CO. Brachthäuser, M., and Kellerwessel, H. 1988. High pressure comminution with roller presses in mineral processing. Pages 209–219 in Reprints XVI International Mineral Processing Congress. Bruce, R. 1992. Practical experience gathered with new segmented liners. KHD Humboldt Wedag Symposium. Burchardt, E. 1998. HPGR: A metallurgical tool for the diamond industry. Paper presented at Proceedings, Randol Diamond Focus, Vancouver, BC, November. Dunne, R., Goulsbra, A., and Dunlop, I. 1996. High pressure grinding rolls and the effect on liberation: Comparative test results. Paper presented at Randol Gold Forum ’96, Olympic Valley, CA. Fischer-Helwig, F. 1992. Current state of roller press design. KHD Humboldt Wedag Symposium. Fuerstenau, D.W., and Asoke, D.E. 1997. Energy Optimisation in High Pressure Roll/Ball Mill Hybrid Grinding Systems. Pages 115–128 in Proceedings of XX IMPC. Volume 2. Aachen, Germany.

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Fuerstenau, D.W., Shukla, A., and Kapur, P.C. 1991. Energy consumption and product size distributions in choke-fed high-compression roll mills. International Journal of Mineral Processing 32:59–79. Kellerwessel, A.M. 1996. High pressure particle bed comminution—state of the art, application, recent developments. Engineering and Mining Journal (February): 45–52. Kellerwessel, H. 1993. High Pressure Particle Bed Comminution—Principles, Application, Testing and Scale-Up, Details of Equipment Design. Germany: KHD Humboldt Wedag AG. Kellerwessel, H., and Oberheuser, G. 1995. Scale-up of roller presses. Pages 67–70 in Proceedings of 19th International Mineral Processing Congress. Klymowsky, I.B., and Liu, J. 1997a. Modelling of comminution in a roller press. Pages 141– 154 in Proceedings of XX IMPC. Volume 2. Aachen, Germany. ———. 1997b. Towards the development of a work index for the roller press. Paper presented at SME Comminution Practices Symposium, Denver, CO. Klymowsky, R. 1998. Roller press installations in iron ore. World Mining Equipment (April). ———. 2003. High Pressure Grinding Rolls for Minerals. McGill Presentation. Klymowsky, R., and Cordes, H. 1999. The modern roller press—practical applications in the ore and minerals industry. Aufbereitungs Technik 40(Nr 8). Klymowsky, R., Patzelt, N., Burchardt, E., and Knecht, J. 2002. Selection and sizing of high pressure grinding rolls. Pages 636–668 in Mineral Processing Plant Design. Proceedings, Volume I. Edited by A. Mular, D. Halbe, and D. Barratt. Littleton, CO: SME. Klymowsky, R., and van der Meer, F. 1999. Roller press grinding—new applications for the iron ore industry and updates on the latest developments. Paper presented at 5th Annual Iron Ore and Steel Summit, Sydney, Australia, February 22–23. Lim, W.I.L., Campbell, J.J., and Tondo, L.A. 1996a. The effect of rolls speed and rolls surface pattern on high pressure grinding rolls performance. Minerals Engineering 10:401–419. ———. 1996b. Extrusion effects in the high pressure grinding rolls. Paper presented at SME Comminution Practices Symposium, Denver, CO. Lubjuhn, U., and Schoenert, K. 1993. Material flow in the acceleration zone and throughput of high pressure roller mills. Pages 161–168 in XVIII International Mineral Processing Congress. Maxton, D. 2003. Argyle Breaks Down HPRC Barriers. Australia’s Mining Monthly (July). Maxton, D., Morley, C., and Bearman, R. 2002. Recrush HPRC Project—The benefits of high pressure rolls crushing, crushing and grinding. Kalgoorlie, Australia, October 30–November 1. ———. 2003. A quantification of the benefits of high pressure rolls crushing in an operating environment. Minerals Engineering 16(9). McIvor, R.E. 1997. High pressure grinding rolls—a review. Paper presented at SME Comminution Practices Symposium, Denver, CO. McIvor, R.E., Dowling, E.C., Korpi, P.A., and Rose, D.J. 2001. Application of high pressure grinding rolls in an autogenous-pebble milling circuit. Pages 194–201 in Proceedings SAG 2001. Volume III. Morrell, S., Lim, W., Shi, F., and Tondo, L. 1997. Modelling of the HPGR crusher. Paper presented at SME Comminution Practices Symposium, Denver, CO. Mörsky, P., Klemetti, M., and Knuutinen, T. 1995. A comparison of high pressure roller mill and conventional grinding. Pages 55–58 in Proceedings of 19th IMPC.

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Murilo Mourão, J., and Schwalm, T. Pelletizing at CVRD—three decades of Brazilian German cooperation. MPT International 3:36–45. Norgate, T., and Weller, K.R. 1991. Options for incorporating high pressure grinding rolls into comminution circuits. Pages 19–24 in Fourth Mill Operators’ Conference. Norgate, T.N., and Weller, K.R. 1994. Selection and operation of high pressure rolls circuits for minimum energy consumption. Minerals Engineering 7(10):1253–1267. Parker, B., Rowe, P., Lane, G., and Morrell, S. 2001. The decision to opt for high pressure grinding rolls for the Boddington expansion. SAG 2001, Vancouver, BC. Patzelt, N., Klymowsky, R., Burchardt, E., and Knecht, J. 2001. High pressure grinding rolls in AG/SAG mill circuits. Pages 107–123 in Proceedings SAG 2001. Volume III. Patzelt, N., Knecht, H., and Baum, W. 1995. Case made for high-pressure roll-grinding in gold plants. Mining Engineering (June): 524–529. Patzelt, N., Knecht, J., Burchardt, E., and Klymowsky, R. 2000. Challenges for high pressure grinding in the new millennium. Pages 47–55 in 7th Mill Operators Conference. Pietsch, W. 1995. Roller presses—versatile equipment for mineral processing. Pages 59–66 in Proceedings of 19th International Mineral Processing Congress. Schönert, K. 1979. Energetische Aspekte des Zerkleinerns spröder Stoffe. ZKG 32:1–9. ———. 1988. A survey of grinding with high pressure roller mills. International Journal of Mineral Processing 22:401–412. Schönert, K., and Flügel, F. 1980. Zerkleinerung spröder minerale im hochkomprimierten gutbett. European Symposium of Particle Technology. Schwechten, D., and Milburn, G.H. 1990. Experiences in dry grinding with high pressure compression roller mills for end product quality below 20 microns. Minerals Engineering 3(1–2):24–34. Sotillo, F., and Finch, E. 1998. On the beneficiation of high dolomitic pebbles: Exploring the use of a high pressure roll mill. SME Preprint 98-91. Littleton, CO: SME. Strasser, S. 1992. Current state of roller press technology. KHD Humboldt Wedag Symposium. Thomsen, L.G. 1997. Operational performance of grinding rolls at Cyprus Sierrita Corporation. Chapter 15 in Comminution Practices. Edited by K.S. Kawatra. Littleton, CO: SME. Thurat, B., and Wolter, A. 1989. Roller presses for fine grinding of cement raw meal, coal and lime. (Reprint). Zement, Kalk, Gips Journal 6: 278–285. Van der Meer, F.P. 1997. Roller press grinding of pellet feed—experiences of KHD in the iron ore industry. AusIMM Conference on Iron Ore Resources and Reserves Estimation, Perth, Australia, September. Van der Meer, F.P., and Schnabel, H.G. 1997. The effect of roller press grinding on ball mill energy. Erzmetall 50(Nr 9). Weller, K.R. 1995. New grinding technologies. Pages 17–26 in Randol Gold Forum. Weller, K.R., and Norgate, T.E. 1989. The place of high pressure rolls grinding in fine comminution. Paper presented at Sagsem ’89, Murdoch University and AusIMM, Perth, Australia. Weller, K.R., Norgate, T.E., Sterns, U.J., and Housley A.G. 1990. The response of some Australian ores to high pressure rolls grinding. Pages 821–835 in 7th European Symposium on Comminution. Westermeyer, C.P., and Cordes, H. 2000. Operating experience with a roller press at the Los Colorados ore dressing plant in Chile. Aufbereitungs Technik 41(Nr 11):497–505.

Some Basics on High-Pressure Grinding Rolls Eberhard W. Neumann*

ABSTRACT

High-pressure grinding roll (HPGR) technology was first introduced on an industrial scale in the mid-1980s for the grinding of clinker and raw material in cement making. Notwithstanding early difficulties as would be expected with any new technology, HPGRs quickly proved to be a very economical addition for comminution processes because of lower energy consumption and easy integration into existing conventional systems for capacity enhancement. Subsequent to successes in cement making, HPGRs soon began to be utilized in a variety of applications in the mining industry to reduce power consumption, increase product yield, and add production capacity in existing milling systems. With regard to abrasive wear, material properties, and selection of process parameters, the natural materials used in mining pose much greater challenges as compared to the relatively constant artificial product, cement clinker. This paper describes the principle of comminution in a compacted material bed, pressure application to the packed bed, power draw, energy density in the compression zone, and technical solutions to particular HPGR requirements. The paper will also reflect on typical process flowsheets with HPGR integration in mining applications. T H E VE R Y B A S I C S

Any rotating machine, from the ancient grain mill (G. Gudat, personal communication) (Figure 1) to modern high-pressure grinding rolls (HPGRs), draws this amount of power: v P = T u Z = F u L u ----c R where P T Ȧ F L Ȟc R

= = = = = = =

power (kW) torque (kNm) angular velocity (sec–1) force F (kN) lever length (m) circumferential speed (m/sec) radius (m)

* Köppern Equipment Inc., Charlotte, North Carolina 41

(EQ 1)

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FIGURE 1

ADVANCED COMMINUTION TECHNOLOGIES

Ancient packed-bed pressure grinding mill

This, of course, is true for all unit systems. Using, however, N (Newton) for force, m (meter) for length, and sec (second) as the time unit gives the power directly in watts: Nm watt = -------sec Our ancestors in the desert already knew that one particle could be cracked by applying pressure. If our desert mill were to grind more, it either had to grind longer or the donkey had to run faster. If it ran faster, it increased the Ȧ, thereby increasing power because the radius stayed the same. If the grind was to be finer, they had to use a heavier stone and the donkey would have noticed because he would have had to pull harder, thereby increasing F, and also power, if he could maintain his speed. The Principle of High-Pressure Grinding

This paper presents one type of machine that accomplishes this purpose, the high-pressure grinding roll, or HPGR. An HPGR consists of two counterrotating rolls (Figure 2), one of which is in a fixed location while the other one, a moving roll, is supported off hydraulic cylinders acting against a hydropneumatic spring that allows horizontal movement of the moving roll. The material to be ground is fed into the gap between the rolls. A small feed hopper, which always contains material, is installed above the rolls. The surfaces of the rotating rolls grip the material and pull it into and through the roll gap. For a certain arc length the material will slip on the roll surfaces until it reaches a point where the circumferential velocity and the material velocity are equal. This is called the nip zone. Because the horizontal distance between two locations on the roll surfaces decreases, the material is exposed to an increasing pressure. As it moves down, it reaches the maximum pressure approximately in the narrowest gap at the rolls’ centerlines. This pressure is so high that the material particles fracture. The majority of the feed particles are smaller than the narrowest gap. The maximum pressure pmax is therefore exerted on a material bed rather than on single particles. This effect is called interparticle or packed-bed comminution. Not every particle that fractures need come into contact with the roll surfaces.

SOME BASICS ON HIGH-PRESSURE GRINDING ROLLS

43

Feed Material

pmax

Nip

Slip

Grinding Roll

PRE

Grinding Roll Cake

FIGURE 2

High-pressure grinding—material slip and nip between the rolls

Some Formulas

The specific throughput (O. Knobloch, personal communication) m· is independent of machine size and allows up- or downscaling for a given feed material and roll surface: M· m· = ----------------------D u L u vc

(EQ 2)

where M· = throughput D = roll diameter L = roll length The total throughput M· in mass or weight per time unit is M· = s u L u v c u U c

(EQ 3)

where s = working gap ȡc = cake density The maximum pressure pmax (K. Schoenert, personal communication) is F p max = c -----s

(EQ 4)

where c is a constant depending upon machine and material parameters. The required pmax to achieve a certain comminution result needs to be determined for each material. Typical values range from 140 to 300 MPa.

44

ADVANCES IN COMMINUTION

ADVANCED COMMINUTION TECHNOLOGIES

F Fu

Fn

Fu

Grinding Roll

Grinding Roll

R

FIGURE 3

Force diagram, force acting angle ȕ

Figure 3 shows the force diagram for the grinding force F, the normal force Fn, and the tangential force Fu. The intersection of the three forces is located inside the nip zone. The total power draw at both roll shafts is P = 2F u v c u sin E

(EQ 5)

with the force acting angle E (K. Schoenert, personal communication). THE HPGR BONUS

The HPGR bonus describes the ability of the HPGR to replace or supplement kilowatts or kilowatt-hours per ton supplied by the reference mill, typically a tube mill, with HPGR kW or kWh/t: Wspec mill B = --------------------------Wspec HPGR

(EQ 6)

If WspecHPGR < Wspecmill, then B > 1. When the HPGR is added to an existing mill circuit the bonus becomes Wspec millbefore – Wspec millafter B = ------------------------------------------------------------------------Wspec HPGR

(EQ 7)

Wspecmill is the kilowatt-hours per ton for the existing mill before and after adding the HPGR. The energetic advantage of the HPGR is that the bonus is greater than 1, which means that 1 HPGR kW or kWh/t will do more grinding work than 1 mill kW or kWh/t. In other words, adding an HPGR to an existing mill circuit will reduce specific energy

SOME BASICS ON HIGH-PRESSURE GRINDING ROLLS

45

consumption and increase production. The savings in specific power consumption at the mill main drives is 'P = Wspec millbefore –  Wspec millafter + Wspec HPGR

(EQ 8)

The overall system savings are somewhat lower because of added equipment, such as conveying or screening. Bonus values depend mainly upon feed material, circuit configuration, and reference mill. Some typical values (from Köppern operating and test data) are ƒ Cement clinker

1.8–2.5

ƒ Blast furnace slag

2.5–3.8

ƒ Limestone

1.7–2.0

ƒ Kimberlite

1.6–2.0

The Machine Design

Figure 4 views an HPGR from the side where the hydraulic system is located. The two grinding rolls are suspended with self-aligning roller bearings in bearing blocks, which are mounted in the machine frame. Each roll has its own drive train with planetary gear reducers. Torque arms are provided to neutralize the countertorques generated by the drives. This particular machine design features a hinged frame that swings open for easy roll exchange. The machine has the following characteristics: Roll diameter Roll length Circumferential speed Installed power Installed grinding force Throughput Bonus achieved

2,140 mm 1,300 mm variable, max. 1.58 m/sec 2 u 1,300 kW 19,500 kN 850 tph cement clinker 2.1

The energy density in the nip zone is quite high, about 400 times compared to a ball mill. Correspondingly high are the loads and stresses on the rolls, especially on the roll surfaces. Figure 5 shows three basic roll designs. The roll surfaces are of particular importance not only from the wear aspect but also for their capability to draw in the material. Figure 6 shows a studded roll surface (according to sources at KHD Humboldt Wedag, Cologne, Germany) where material builds up between the studs, thereby forming an autogenous wear protection and providing a rough surface for good friction. Figure 7a shows a worn, welded hard surface, and Figure 7b shows metallurgical powder-based wear elements applied by a hot isostatic pressure process. These are just three examples; there are several others that have been developed over the years. HPGR Applications in Mining

Figures 8 through 11 show some typical applications for HPGRs to increase throughput and lower specific energy consumption of a grinding circuit. Figure 8 shows the HPGR after a semiautogenous grinding (SAG) mill for pebble grinding. The HPGR product is returned either to the SAG mill or to the screen. In Figure 9, the HPGR is located after the secondary crusher. The HPGR product is screened, and the oversize is returned to the HPGR. Figure 10 has the HPGR as single-pass pregrinder in front of the milling plant.

46

ADVANCES IN COMMINUTION

Hinged Frame

FIGURE 4

1

2

Roll

Hydraulic System

Torque Arms

Gear Reducers

HPGR assembly at the workshop (view from the hydraulic side)

Grinding Surface

3

Bearing Journal

(a) Solid Roller

FIGURE 5

ADVANCED COMMINUTION TECHNOLOGIES

1

Roller Core

4

1

Roller Core

5

Segments

2 (b) Tire-Shaft Roller

(c) Segments

Press tools

The HPGR can apply about 2.3 kWh/t to the feed material. At a bonus of, for example, 1.8, it would add 2.3 u 1.8 = 4.14 kWh/t ball-mill equivalent to the grinding circuit. The HPGR can also be located after heavy-media separation (HMS) with or without a crusher grinding the wet oversize (Figure 11). The best HPGR location for a given mine needs to be decided for each case; bottleneck identification, space availability, conveying distances, power grid, and other conditions must be considered. CONCLUSIONS

Versatility and efficient energy utilization have made high-pressure grinding an established comminution technology in the minerals processing industries. Relatively simple formulae can be used to describe and understand the underlying mechanics of HPGRs. Careful consideration must be given to the overall grinding process in order to take full advantage of the special features offered by high-pressure comminution.

SOME BASICS ON HIGH-PRESSURE GRINDING ROLLS

Tungsten Carbide Studs

FIGURE 6

Studded roll surface

Circumferential Wear Grooves

(a) Worn Surface Welding

FIGURE 7

Autogenous Wear Protection

Roll surface examples

Hexadur Tiles

Softer Interstice Material

(b) Hexadur Roll Surface

47

48

ADVANCES IN COMMINUTION

ADVANCED COMMINUTION TECHNOLOGIES

Run-of-Mine Ore

Primary Crusher

SAG Mill

Screen

Crusher

Grinding Circuit

HPGR

Sorting Section

FIGURE 8

HPGR after SAG mill for pebbles grinding

Run-of-Mine Ore

Primary Crusher

Intermediate Stockpile

Double-Deck Screen Secondary Crusher

HPGR

Screen

Concentration Section

FIGURE 9

HPGR after secondary crusher with screen

SOME BASICS ON HIGH-PRESSURE GRINDING ROLLS

Concentrate Stockpile

Storage Bin

HPGR

Grinding Circuit

Pelletizing Plant

FIGURE 10

HPGR in single-pass grinding before milling plant

Ore Storage

Screen

HMS Float Sink HPGR Final Concentration

Screen

HMS Float Sink Crusher Final Concentration HPGR

Final Concentration

Screen Fines

Tailings

FIGURE 11

HPGR grinding wet oversize

49

High-Pressure Grinding Rolls for Gold/Copper Applications Norbert Patzelt,* Rene I.B. Klymowsky,* Johann Knecht,* and Egbert Burchardt*

ABSTRACT

Successful pilot-plant demonstrations carried out in 2003 and 2004 have proven the operational reliability of high-pressure grinding rolls (HPGRs) in hard-rock applications. As a result of these breakthroughs, six HPGRs will be commissioned in two copper concentrators in 2006. INTRODUCTION

High-pressure grinding rolls (HPGRs) are well established in the diamond and iron ore industries. Process advantages of HPGRs had been recognised by the minerals industry for many years. However, unresolved issues pertaining to wear have made the industry reluctant to adopt this technology. Starting in 2003, a successful pilot-plant demonstration on an exceptionally hard and abrasive gold ore proved that the wear issues could be resolved by the design of an appropriate wear-protection system, and availabilities in excess of 90% could be achieved. The pilot-plant results built up confidence in the minerals industry and a second pilot-plant trial was conducted on another extremely hard ore with the aim of determining if anything could break the machine. The machine demonstrated even higher availabilities than in the previous case. A commercial breakthrough then came when one of the world’s leading copper producers decided to build a new concentrator in South America based on HPGR technology. Four Polycoms, 24/16 in size, each equipped with two 2,500-kW motors, will be used in tertiary crushing duty in closed circuit with wet screens. Shortly thereafter, a second major copper producer ordered two large Polycom 20/15 units for an existing copper concentrator in Indonesia. In both cases, it was the energy savings and low operating costs of the HPGRs that attracted the producers. This paper examines the conditions (such as the press force necessary) that lead to energy savings, lower operating costs, and the optimum performance of the HPGRs. Wide variations occur in ores, even within one deposit. These variations, insofar as they affect the performance of an HPGR, need to be quantified with meaningful HPGR indices. Two such indices are the ATWAL Wear Index (ATWI) for wear due to abrasion and the Polycom Grinding Index (PGI) for quantifying the fines production.

* Polysius AG, Neubeckum, Germany 51

52

ADVANCES IN COMMINUTION

FIGURE 1

ADVANCED COMMINUTION TECHNOLOGIES

Installation of an HPGR in a copper concentrator in the United States in 1994

A laboratory ball mill test, the Labmill test, is described to overcome the uncertainty about the energy required for ball milling after an HPGR. The test is aimed to deal specifically with the special features of an HPGR product (i.e., microcracking and the high amount of fines in the product). EXPERIENCES WITH HPGRS IN HARD-ROCK APPLICATIONS

Cyprus Sierrita

The first serious application of HPGRs in the hard-rock mining industry was the installation of an HPGR in a copper concentrator in the United States in 1994 (Figure 1). The expected performance in terms of throughput, fines production, and energy consumption was met. However, the hardness and abrasiveness of the ore was by far higher than that of ores treated in HPGRs previously. It soon became apparent that the wear protection of HPGRs, in particular, the stud technology, was not advanced enough at that time to allow for a smooth and easy transition into continuous operation. Different stud qualities had to be tested and changed in order to suit the requirements of the ore. The change-outs were facilitated by having the rolls equipped with segments; however, these also contributed to wear problems. Finally, stud qualities were found that provided a reasonable lifetime at low cost (~0.10 to 0.15 US$/t) even under these difficult circumstances. In the end, the unit was decommissioned after treating more than 7,000,000 t of ore when the initial investment plans for the mine were abandoned. Despite the positive operating results, this installation was widely viewed by the industry as a failure of HPGR technology, and its acceptance was set back for years. Newmont Gold, Lone Tree (Nevada)

Following the Cyprus Sierrita demonstration, there was little progress made towards improving the technology or improving the wear protection for hard-rock applications. The next milestone in HPGR development came in April 2003, when Newmont Mining Corporation began a 3-month trial of a pilot-sized HPGR. Polysius designed a new roll surface specifically for the grinding of hard and abrasive copper and gold ores (Figure 2). The new roll surface consisted of a replaceable shrink-fitted tyre, armed with a new design of tungsten carbide studs, and a new edge-protection system intended to eliminate

HIGH-PRESSURE GRINDING ROLLS FOR GOLD/COPPER APPLICATIONS

FIGURE 2

TABLE 1

53

A pilot-sized HPGR equipped with a new roll surface designed by Polysius

Material data of Lone Tree ore Ball Mill Work Index, Wi (BM) Unconfined compressive strength Silica content Bond Abrasion Index, Ai ATWAL Wear Index, ATWI

20 kWh/t 200 MPa 78%–84% 0.64 >40 g/t

repair welding of the roll edges. The rolls were also provided with cheek plates to contain the material within the gap. The roll dimensions were 950 mm diameter u 350 mm width. Each roll was driven by a 160-kW motor and was operated at a speed of 21 rpm. The capacity of the unit was about 80 tph. The unit was run in closed circuit with an 8-mm square-mesh screen, and was protected from tramp metal by an overhead magnet and a metal detector on the main conveyor belt. The machine was operated 24 hours a day, 7 days a week, for a period of 87 days with no mechanical downtimes. The initial operational availability of the unit was 89% due to a programming glitch, which occurred after startup, after which a 92% availability was achieved. The properties of the feed are specified in Table 1. The Lone Tree trial was a true milestone, as no other pilot unit previously had been operated continuously on a 24/7 basis, and no mechanical or welding repairs had been required. The operators and maintenance staff were encouraged by the operation of the HPGR. No stud failures occurred during the more than 1,600 operating hours of the demonstration trial. In a commercial-scale application on a similar hard, abrasive ore, an HPGR would have achieved more than 3,000 hours of service and run considerably longer on a less competent and less abrasive ore. Relationships between wear and particle-size distribution were obtained that will improve future understanding of wear and wear life, benefiting the industry as a whole. The Polysius ATWAL laboratory abrasion test accurately predicted the wear rate in the trial. Individual tests, conducted over the course of 1 year on several representative samples obtained prior, during, and after the trial, were found to be reproducible within 10% of each other, validating the method used for determining and predicting wear in larger units.

54

ADVANCES IN COMMINUTION

ADVANCED COMMINUTION TECHNOLOGIES

Anglo American Platinum, Potgietersrust Platinum Mine

In October 2004, a pilot-plant unit was commissioned in the Potgietersrust platinum mine. This was a further step forward and the first approach of HPGR technology to the platinum industry. The HPGR was again operated in closed circuit with 8-mm screens. The feed material was prepared by two-stage crushing. Feed size was initially –25 mm but was increased to –35 mm for extended operating periods. The HPGR treated a total of 188,000 tph, resulting in 115,000 tph of final product until it was decommissioned in April 2005. The operating time was in excess of 3,000 hours. The ore was even tougher than that used in the previous application, which is reflected in the Bond Work Index (BWI) of 22 kWh/t, and in the operational problems experienced at the crushers. The HPGR was equipped with the latest wear protection. Results from abrasion testing indicated low abrasion, which was confirmed in the field. Availabilities as high as 97% were achieved. The test installation was declared a success by the operator who, in his words, “had tried very hard to break the machine.” IMPLEMENTATION OF HPGRS IN GRINDING CIRCUITS

In greenfield installations, HPGRs will have their place as the tertiary crushing stage in front of ball mills. Even this commitment still leads to many different flowsheet configurations. One possible flowsheet is shown in Figure 3. The secondary crusher and the HPGR, which replaces conventional tertiary crushers, are operated in closed circuit with dry screens. The product of the crushing circuit is stockpiled. In this configuration, the crushing circuit and the ball mill circuit are decoupled, allowing both circuits to be operated at a different utilisation. However, this decoupling has two implications. First, an additional stockpile is required. Stockpiling of the HPGR product, which contains a lot of fines, remains a challenge and requires extensive dust suppression. Second, screening of the HPGR product has to be done dry because a wetscreen undersize cannot be stockpiled. This entails a coarser product. Wet screening of the HPGR discharge may provide significant improvements. It is advantageous from the point of energy efficiency to shift as much grinding work as possible to the HPGR and feed the ball mills with a finer product. This approach requires a finer mesh size for the screen, 4 to 6 mm. Fine screening usually has a lower efficiency, especially if the discharge from the HPGR is in the form of highly compacted flakes. Wet screening will address the disagglomeration of the HPGR discharge and will definitely improve screening efficiency. It also will facilitate wetting of the material. A flowsheet illustrating a wet-screen arrangement for an HPGR is shown in Figure 4. The HPGR and ball mill circuits are combined, whereas the secondary crusher is decoupled. Alternatively, if the circuit consists of multiple crushing and grinding units, all three can be combined, eliminating the stockpile by oversizing the equipment. This arrangement allows for the lower availability of the crushers, whereas the HPGR availability is expected to be high enough for in-line operation with the ball mills. OPTIMUM HPGR PERFOR MANCE IN CLOSED-CIRCUIT OPERATION

In tertiary applications, HPGRs have to be operated in closed circuit. Consequently, the ball mill feed is not the “discharge” of the HPGR but is the product of the size distribution of the HPGR discharge and the mesh size of the closing screen. This raises two questions: first, what influence do HPGR operating parameters have on the feed-size distribution to the ball mill; and secondly, what is the most efficient way to operate an HPGR? In open circuit, the operating parameter that manifests the most influence on the particle-size distribution is the press force applied to the rolls. The energy absorbed by the material has been shown to be proportional to the applied press force.

HIGH-PRESSURE GRINDING ROLLS FOR GOLD/COPPER APPLICATIONS

FIGURE 3

55

HPGR in closed circuit with dry screens

Optional

FIGURE 4

HPGR in closed circuit with wet screens

In a closed circuit, however, the influence of the press force on the product size of the circuit is lost. This is demonstrated with two examples, one taken from tests on a semi-industrial scale unit and the other from tests on a laboratory-scale HPGR (Figure 5). Results were taken from single-pass tests on these units, in order to prove that the findings were independent of the machine size. The press forces applied were in the range of 2.7 to 4.3 N/mm2 on the semi-industrial unit, and from 2.3 N/mm2 to a higher value of 8.4 N/mm2 on the laboratory-scale unit. The impact of the press force on the throughput and energy consumption of the circuit are also shown. A screen undersize, representing the circuit product, was calculated on the basis of 100% screen efficiency from the discharge. Cut sizes were 4 mm for the semi-industrial circuit and 1 mm for the laboratory-scale circuit. It was assumed that the recirculation of screen oversize did not affect the size reduction in the HPGR significantly. On this basis,

56

ADVANCES IN COMMINUTION

ADVANCED COMMINUTION TECHNOLOGIES

2.5 Feed 1 Feed 2

Specific Energy, kWh/t

2.0

1.5

1.0

0.5

0.0 0

1

2

3

4

5

Specific Press Force, N/mm 2

FIGURE 5

Absorbed specific energy versus press force

a projection of the circuit performance in terms of throughput and energy consumption was also made. This approach may be considered simplistic but is adequate to explain some of the principles. Figure 6 shows discharge size distributions of a copper ore treated in a semi-industrial test unit. The grinding force was steadily increased from test R4 to R6, resulting in a finer discharge. The circuit product of an HPGR with a 4-mm classifying screen was calculated on the basis of 100% screening efficiency. Figure 7 shows discharge size distributions of a platinum ore treated in a lab-scale test unit. The grinding force was steadily increased from test L1 to L4, resulting in a finer discharge. The circuit product of an HPGR with a 1-mm classifying screen was calculated on the basis of 100% screening efficiency. The conclusions drawn from Figures 6 and 7 were that the size distribution of the final circuit product did not vary much, no matter if the HPGR discharge was finer or not. The fineness of the circuit product was largely determined by the mesh size of the closing screen. However, the applied press force had a strong influence on the circulating load and the circuit throughput with an HPGR of given size, as well as on the energy consumption, as shown in Figures 8 and 9. In Figure 8, the specific energy input was increased by 30% while the throughput of the closed circuit increased by only 10%. In Figure 9, the specific grinding energy was increased even further by 100% to 8.2 N/mm2, whereas the throughput of the closed circuit only increased by 40%. These examples show that operation at high specific press forces, 8 N/mm2, reduces energy efficiency drastically. The following general conclusions were drawn with regard to optimum operation of HPGRs in closed circuit: 1. The product-size distribution of an HPGR in closed circuit with screens is not

influenced by the applied press force. 2. The applied press force determines the circulating load and the energy consump-

tion of the HPGR circuit.

HIGH-PRESSURE GRINDING ROLLS FOR GOLD/COPPER APPLICATIONS

100 Feed R4 Discharge R4 S/U R5 Discharge R5 S/U R6 Discharge R6 S/U

Fineness Cumulative Passing, %

80

60

40

20

0 0.01

0.10

1.00

10.00

100.00

Particle Size, mm NOTES: Discharge denotes the HPGR discharge from respective tests. S/U denotes the screen undersize from respective tests.

FIGURE 6

Semi-industrial HPGR test with copper ore

100 Feed L1 – D L1 – S/U L3 – D L3 – S/U L4 – D L4 – S/U

Fineness Cumulative Passing, %

80

60

40

20

0 0.01

0.10

1.00

10.00

Particle Size, mm NOTES: D denotes the HPGR discharge from respective tests. S/U denotes the screen undersize from respective tests.

FIGURE 7

Lab-scale HPGR tests with platinum ore

100.00

57

58

ADVANCES IN COMMINUTION

ADVANCED COMMINUTION TECHNOLOGIES

4

80

60

3

40

2

20

1

0

Specific Energy Input w(sp), kWh/t

Throughput M, tph

M w(sp)

0 3

2

4

5

6

2

Specific Grinding Force ϕ, N/mm

FIGURE 8

Semi-industrial circuit projection (copper ore <4-mm product)

8

8

6

6

4

4

2

2

0 0

2

4

6

8

Specific Energy Input w(sp), kWh/t

Throughput M, tph

M w(sp)

0 10

2

Specific Grinding Force ϕ, N/mm

FIGURE 9

Lab-scale circuit projection (platinum ore <1-mm product)

– For harder ores, increasing the press force increases the circuit throughput, but the increase in energy consumption is disproportionately higher. – For softer ores, increasing the press force may even decrease the circuit throughput. The additional fines produced do not compensate for the loss in specific throughput of soft ores resulting from the reduction in the operating gap. 3. Optimum grinding forces are material specific. Specific grinding forces up to

8 N/mm2, such as those applied in cement grinding, are unsuitable for minerals applications where the final product fineness is substantially coarser. 4. Circuit throughput can be adjusted by varying the applied press force. The

increase in the energy consumption, however, is often disproportionate to the

HIGH-PRESSURE GRINDING ROLLS FOR GOLD/COPPER APPLICATIONS

59

increase in throughput, and varying the roll speed is a far more efficient means of adjusting the circuit throughput. These considerations still leave open the question as to what impact the application of higher press forces may have on the energy requirements in downstream ball milling. This issue is addressed in the next section. BALL MILL ENERGY REQUIREMENTS

Significant savings in grinding energy can be expected on feeding a ball mill with an HPGR product. The increased grindability can be used to expand the throughput of existing plants or to produce a finer grind if required by the recovery process. In new plants, ball mills can be sized smaller as compared to a plant where the ball mills receive feed prepared by conventional crushers. The reduced energy demand of ball mills fed with HPGR products has been proven in numerous trials. In ball mill pilot-plant tests conducted after the HPGR trials at Kalgoorlie Consolidated Gold Mines PTY Ltd., a reduction in energy consumption of 20% was observed on HPGR centre product, and a reduction of 16% was obtained on HPGR total discharge, as compared to a tertiary crushed product. Similar results have been reported from tests on Boddington ore, and have also been confirmed in practice on iron ore in Chile. The energy consumption in a ball mill (w(sp)) is often expressed as a function of a Bond Work Index (BWI), the product size (P80), and the feed size (F80): w(sp) = BWI u (10/ P80 – 10/ P80 )

(EQ 1)

This method is widely used. However, the limitation of the Bond theory is that it does not consider the feed-size distribution and only refers to a single point on the distribution, the F80 size. In particular, the Bond theory does not consider any variations in the amount of fines that may be in the ball mill feed. Figure 10 shows product-size distributions from crusher and HPGR circuits. It is obvious that the “HPGR circuit” product contains far more fines than the conventional “crushed” product, although the P80 values may be similar (see “fine crushed” material in Figure 10). This higher amount of fines will result in a reduced energy consumption (w(sp)) in subsequent ball milling, even if potential microcracks are ignored and the BWI of the fine crushed and HPGR circuit samples are found to be identical. According to Bond, the mills would require the same energy. The two energy-reducing features of a “polycomized” product, microcracks and higher fines content, will not necessarily be reflected in the BWI. The BWI seems to be material specific and is not affected by how the sample was prepared. Only in a few cases have Bond tests revealed differences of 10%–18% between conventional crushed and polycomized products. Only a grinding test based on the actual feed size distribution that does not require any further size reduction—which could eliminate microcracks—can provide a realistic comparison of the ball mill energy required for materials with different size distributions. Polysius has used the Labmill for decades in order to determine the energy requirements in ball milling. The test is a dry, open-circuit grinding test, but it can provide information on the relative energy requirements for different materials and for different feed-size distributions in wet milling as well. Typical results from Labmill tests are shown in Figures 11 and 12. In these figures, feed with different size distributions are compared. The tests were conducted on a “conventional crushed” material and on HPGR “discharge” and “centre” products with different size distributions.

60

ADVANCES IN COMMINUTION

ADVANCED COMMINUTION TECHNOLOGIES

100

Fineness Cumulative Passing, %

80

Crushed Fine Crushed HPGR Circuit

60

40

20

0 0.01

0.10

1.00

10.00

100.00

Particle Size, mm

FIGURE 10

Conventional crusher products and polycomized product of an HPGR circuit

The graph in Figure 12 shows the product fineness at 90 and 200 Pm as a linear function of the energy applied according to the following equation: F90 Pm = a90 Pm * E + b90 Pm F90 Pm

: fineness (cumulative % passing at 90 Pm)

E

: energy index or consumption at F90 Pm

(EQ 2)

where b90 Pm corresponds to the amount of 90-Pm material in the feed (F90 Pm,feed), and a90 Pm is the slope showing the rate of increase in the 90-Pm material produced per kilowatt-hour per ton. Reference to Figures 11 and 12 shows that the a90 Pm value is very similar for all feedsize distributions, no matter how the feed material was prepared or how many fines were present in the feed. The a90 Pm value (or a200 Pm) reflects the grindability of an ore in the Labmill and is ore specific similar to the BWI. It is referred to as the Labmill Grinding Index. The “b” parameter reflects the amount of fines in the feed. Equation (2) can be rewritten by substituting b90 Pm for F90 Pm,feed as follows: E (F90 Pm) = (F90 Pm – F90 Pm,feed) / a90 Pm

(EQ 3)

This approach allows one to correct the energy requirements for grinding to a certain fineness according to the feed-size distribution. The relative energy requirements for the different feed-size distributions tested are summarised in Table 2. Looking at the 80% <200 Pm size, the difference in the energy index from the HPGR centre material to the crushed material is 33%, and at 90 Pm, the corresponding difference in the energy index is 25%. Another series of Labmill tests were conducted on a platinum ore with a high BWI of 22.2 kWh/t. Bond testing showed no difference in the BWI between an HPGR product

HIGH-PRESSURE GRINDING ROLLS FOR GOLD/COPPER APPLICATIONS

100 Crushed HPGR Discharge HPGR Centre

Fineness Cumulative Passing, %

80

60

40

20

0 0.01

0.10

1.00

10.00

100.00

Particle Size, mm

FIGURE 11

Feed-size distribution of Labmill test samples (gold ore)

.6

.6

98

7.

x

87

+

x

y=

7. = y

5.4

5.7

18

.33

3

2.8

1 x+

9

y=

x+

2

4.

+

47

20

28 + x 22 = y

y

Fineness Cumulative Passing, %

=

8.

80

.45

2

9

100

y=

x .41

+2

5

60

40 Crushed: % < 90 μm % < 200 μm HPGR Discharge: % < 90 μm % < 200 μm HPGR Centre: % < 90 μm % < 200 μm

20

0 0

5

10 Energy Index, kWh/t

FIGURE 12

Results from Labmill test with gold ore samples

15

20

61

62

ADVANCES IN COMMINUTION

TABLE 2

ADVANCED COMMINUTION TECHNOLOGIES

Energy requirements in Labmill tests for different feed-size distributions

Variable

Bond Work Index Relative Energy index from Labmill 80% <90 μm Relative 80% <200 μm Relative

Coefficient

Crushed

HPGR Discharge

HPGR Centre

kWh/t %

19.2 100

n.d. n.d.

18.0 94

kWh/t % kWh/t %

14.4 100 9.4 100

12.3 85 7.7 82

10.8 75 6.3 67

and a conventionally crushed product. Labmill tests were conducted to investigate if the application with higher press forces in an HPGR would have an effect on the energy requirements in subsequent ball milling. In the preparation of the samples for the Labmill, two of the samples were pressed in a laboratory HPGR, and one was crushed conventionally (Figure 13). The specific press forces applied in HPGR tests were 2.2 N/mm2 and 8.4 N/mm2, respectively. Figure 14 shows the differences in the energy requirements to grind these samples to a P80 of 90, and 200 Pm. The results suggest that the main reason for these differences was the varying amounts of fines <90 and <200 Pm produced in the feed. The Labmill grindability indices (LGIs) did not appear to be affected by the application of different press forces. The a90 Pm was nearly the same for all the samples, between 4.23 and 4.47. Also the a200 Pm was steady between 6.24 and 6.38. Closed-circuit operation of the HPGRs at these different pressures would provide product-size distributions that would be nearly the same as shown before. Therefore, the energy requirements in a subsequent ball mill may be expected to be the same for products of the high and low press forces. The overall energy balance for the circuit shows that the application of extremely high press forces is a waste of energy (refer to Figure 9). To recapitulate, in a first instance the Labmill test serves as a means of comparing mill power requirements for feed materials with differences in preparation and fineness. The test may also be used to provide correction factors to the conventional Bond sizing considering the particular properties of a high-pressure-rolls product. O R E C H A R A C T E R I S A T I O N F O R H P G R TR E A T M E N T

Several tests have been developed in order to quantify the behaviour of different ores in the various crushing and grinding applications. Indices like the Bond work ball and rod mill index, Bond Abrasion Index, and compressive strength data have a long history. More recent are tests that refer to autogenous or semiautogenous milling, include the JK Drop Weight Test and the semiautogenous grinding (SAG) Power Index (SPI) (MinnovEX). However, none of these tests can be applied to high-pressure grinding. Of greatest importance to HPGRs is 1. Fines production 2. Abrasiveness of an ore

These parameters determine the investment and operating costs of a high-pressure grinding circuit. The more fines that are produced in one pass through the rolls, the lower the circulating load. Low circulating loads mean small equipment size and lower capital costs as well as low energy consumption. The abrasiveness of an ore directly correlates with availability and wear cost.

HIGH-PRESSURE GRINDING ROLLS FOR GOLD/COPPER APPLICATIONS

100 Crushed HPGR (ϕ = 2.2 N/mm2) HPGR (ϕ = 8.2 N/mm2)

Fineness Cumulative Passing, %

80

60

40

20

0 0.010

0.10

1.00

10.00

100.00

Particle Size, mm

FIGURE 13

Feed-size distribution of Labmill test samples (platinum ore)

100 7

.6

+ 8x

y=

Fineness Cumulative Passing, %

80

35

4x

y=

2 6.

+

. 21

y=

x+

27

6.

5

3.7

3

.5

18

3 6.

11

y=

x .23

x .41

0

3.9

+1

4 y= 6 .2 +6 7x

4

y=

+2

4.4

60

40 Crushed % < 90 μm % < 200 μm HPGR (ϕ = 2.2 N/mm2) % < 90 μm % < 200 μm HPGR (ϕ = 8.2 N/mm2) % < 90 μm % < 200 μm

20

0 0

5

10 Energy Index, kWh/t

FIGURE 14

Results from Labmill test with platinum ore samples

15

20

63

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100 y = 72.967x0.1483 R2 = 0.2406

Fineness Cumulative Passing, %

80

60 y = 28.787x0.3479 R2 = 0.2788 40 y = 20.35x0.3031 R2 = 0.1374 20 % < 250 μm % < 1 mm % < 8 mm 0 0

2

4

6

8

Specific Grinding Force, N/mm 2

FIGURE 15

Product fineness as a function of the grinding force for different ores

The achievable product fineness in one single pass for a particular ore depends on the applied grinding force (Figure 15). The fineness at the same grinding forces varies vastly for different ores, however. The properties of an ore have a far greater impact on the achievable fines production than the grinding force. Also, wear rates of gold and copper ores vary extremely in a range from 2 to 50 g/t. Two indices have been defined in order to characterise the behaviour of an ore in the high-pressure grinding process (i.e., the PGI and the Polycom Abrasion Index [ATWI]). Polycom Grinding Index

The PGI is the amount of tons less than 250 Pm and 1 mm that are produced in 1 hour with a standardised HPGR having rolls of 1-m diameter and 1-m width and being operated at a speed of 1 m/s. The fines production is referred to a constant specific grinding force of 3.5 N/mm2. The PGI is calculated from test results. PGI (1 mm) [t/h] = F (1 mm) / 100% u m F (1 mm) [%]

(EQ 4)

: net production of –1 mm material

m [t u s/(m3 u h)] : specific throughput rate of HPGR The higher the PGI, the higher the fines production and the amenability of an ore to the HPGR process. Polycom Abrasion Index

The abrasiveness of ores varies widely with the physical properties of the material and the operating conditions. Several abrasion tests are available in the minerals industry. However, none are based on high pressure as the principle for comminution and therefore cannot be used for reliably predicting wear rates in an HPGR. Inclusion of this principle in the test procedure is a precondition for determining the abrasiveness in an HPGR.

HIGH-PRESSURE GRINDING ROLLS FOR GOLD/COPPER APPLICATIONS

FIGURE 16

65

Wear testing HPGR

50

High Abrasive, Low Fines Production

High Abrasive, High Fines Production

ATWI

2

3

25

1

4

Low Abrasive, Low Fines Production

0 20

Low Abrasive, High Fines Production

70

120

PGI (1 mm)

FIGURE 17

PGI and ATWI

The ATWAL wear-testing, high-pressure grinding unit is shown in Figure 16. The rolls are 100 mm diameter u 30 mm wide. The unit can be equipped with tyres made of different wear materials. The tyres are weighed before and after a test run. The wear rate is calculated from the weight loss divided by the amount of material treated and is expressed in grams per ton, as a wear index designated by the name ATWI. Typically, 100 kg is sufficient for a test run. Ore Categorisation

Test data collected on a semi-industrial unit and the wear testing unit ATWAL are included in Figure 17. The PGI (1 mm) and the ATWI are independent. The diagram is divided into four quadrants. Ores best suited for high-pressure grinding are located in quadrant 4. These ores are low abrasive and produce a lot of fines. Most difficult ores are

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found in quadrant 2. This location indicates that these ores are highly abrasive and produce only a low amount of fines. Test work for PGI testing will be conducted on a lab-scale HPGR in the future in order to reduce the amount of material required for testing. The PGI and ATWI allow different ores to be easily compared with respect to their behaviour in the high-pressure grinding process. They permit a basic comparison of installations treating different ores. A model is under development based on the PGI that would allow prediction of how much the throughput may be expected to vary in existing HPGR grinding circuits, if different ores types have to be treated. CONCLUSIONS

A milestone in HPGR development was reached in April of 2003, when Newmont Mining Corporation began a 3-month trial on an HPGR equipped with a new wear-protection system designed by Polysius specifically for the grinding of hard and abrasive copper and gold ores. The new wear-protection system proved itself in the field and was accepted by the operators. Nevertheless, liner development for HPGRs did not stop there. In the meantime, more than 10 HPGRs in South African diamond mines have been converted from tyres with a hard facing to a studded design. These installations provide a valuable source of information on wear behaviour and the suitability of different wear-protection systems. Experience flowing back from the field ensures further progress in the future. HPGRs can be operated in closed circuit with either dry or wet screens. Dry screening allows the crushing section to be decoupled from the ball mills by the interposition of a stockpile. However, wet screening allows for the implementation of finer cut sizes in the HPGR circuit, thus producing a finer feed to the ball mills. In addition, wet screening may be expected to be more efficient than dry screening. A finer HPGR product and more efficient screening can improve the energy efficiency of a crushing and grinding circuit. The press force applied to high-pressure rolls determines the circulating load and the energy consumption of the HPGR circuit but has no influence on the product-size distribution of a closed circuit. For harder ores, the throughput can be increased by the application of higher press forces, but the increase in energy consumption will be disproportionately higher. For softer ores, circuit throughput may even decrease at higher press forces. Optimum press forces are material specific. Specific press forces up to 8 N/mm2, such as those applied in cement grinding, are unsuitable for minerals applications where the required product fineness in tertiary crushing applications is quite coarse. The overall energy balance for the circuit shows that the application of high press forces is a waste of energy. Speed control is a more efficient means of controlling circuit throughput than trying to adjust the roll gap by varying the applied press force. Ball mill testing in the Labmill provides an ore-specific LGI that is comparable to the BWI. Feed up to 30 mm in size can be tested directly in the mill without adjustments for top size, which may alter any properties inherent in the coarser sizes. The Labmill test can serve as a means of comparing the mill power requirements for feed materials with differences in preparation and fines content. The test may also provide correction factors to the conventional Bond sizing considering the particular properties of a high-pressure-rolls product. In the future, the power requirements of wet-grinding ball mills could be also determined by the Labmill test. This approach may allow prediction of the energy requirements for wet grinding in ball mills according to the actual feed conditions (i.e., feed size and potentially any microcracks). This approach may be more precise than conventional Bond sizing, which was developed long before HPGRs came on the scene.

HIGH-PRESSURE GRINDING ROLLS FOR GOLD/COPPER APPLICATIONS

67

Two indices have been defined in order to characterise the behaviour of an ore in the high-pressure grinding process (i.e., the ATWI and the PGI). These indices allow different ores to be easily compared with regard to their behaviour in HPGRs and to benchmark them with existing installations. BIBLIOGRAPHY

Baum, W. 1993. Case made for high pressure grinding in gold plants. Mining Engineering (June): 524–529. Baum, W., and J. Knecht. 2000. HPGR as a processing tool for gold & copper leaching, flotation and gravity separation. 2nd Annual Crushing and Grinding in Mining Conference, Johannesburg. Baum W., N. Patzelt, and J. Knecht. 1996. The use of high pressure grinding for optimization of copper leaching. SME Preprint 96-68. Littleton, CO: SME. Burchardt, E. 1998. HPGR: A metallurgical tool for the diamond industry. Proceedings, Randol Diamond Focus 98. Vancouver, BC, November. Dunne, R., A. Goulsbra, and I. Dunlop. 1996. High pressure grinding rolls and the effect on liberation. Comparative test results. Pages 46–54 in Proceedings, Randol Gold Forum, Olympic Valley, CA, April. Klymowsky, I.B., and J. Liu. 1997a. Modelling of the comminution in a roller press. Pages 141–154 in Proceedings of the XX IMPC. Volume 2. Aachen, IMPC, September. ———. 1997b. Towards the development of a work index for the roller press. Chapter 14 in Comminution Practices. Edited by S.K. Kawatra. Littleton, CO: SME. Klymowsky, R., and T.C. Logan. 2005. HPGR demonstration at Newmont’s Lone Tree mine. Pages 325–334 in Proceedings of the Canadian Mineral Processors. Ottawa, ON: CIMM. Klymowsky R., N. Patzelt, E. Burchardt, and J. Knecht. 2002. Selection and sizing of high pressure grinding rolls. Pages 636–668 in Mineral Processing Plant Design. Proceedings, Volume I. Edited by A.L. Mular, D.N. Halbe, and D.J. Barratt. Littleton, CO: SME. Patzelt, N., R. Klymowsky, E. Burchardt, and J. Knecht. 2001. High pressure grinding rolls in AG/SAG mill circuits. Pages 107–123 in Proceedings, SAG 2001. Volume III, Mining and Minerals Process Engineering, University of British Columbia, Vancouver. Rowe, P., B. Parker, G. Lane, and S. Morell. 2001. The decision to opt for high pressure grinding rolls for the Boddington expansion. Pages 93–106 in Proceedings, SAG 2001. Volume III, Mining and Minerals Process Engineering, University of British Columbia, Vancouver. Thompsen, L.G. 1997. Operational performance of grinding rolls at Cyprus Sierrita Corporation. Chapter 15 in Comminution Practices. Edited by S.K. Kawatra. Littleton, CO: SME. Watson, S., and M. Brooks. 1994. KCGM evaluation of high pressure grinding roll technology. Pages 69–83 in Proceedings of the Fifth Mill Operators Conference. The Australian Institute of Mining and Metallurgy, October. Westermeyer, C.P., and H. Cordes. 2000. Operating experience with a roller press at the Los Colorados ore dressing plant in Chile. Aufbereitungs Technik 41(11):497–505.

Selection and Sizing of Ultrafine and Stirred Grinding Mills Jens K.H. Lichter* and Graham Davey†

ABSRACT

The selection and sizing of mills for regrind and ultrafine grinding applications do not lend themselves to conventional methodologies. A more holistic approach is required, one that considers not only the mill but also the application of the mill within the process. The selection of stirred mills for ultrafine milling requires unique approaches to answer questions related to selection of the circuit configuration, type of mill, media, and operating conditions. Further considerations required for the selection of mills are the inherent difficulties of particle-size measurement and an accurate definition of the product size required. INTRODUCTION

Minerals with fine particle intergrowth, either with other metallic minerals or gangue, are being increasingly mined. These ores have provided new challenges in concentrator design, requiring fine and ultrafine grinding in order to obtain acceptable grades and recoveries. The advancement of flotation technologies now permits effective flotation in the sub-10-Pm size range, making it possible to separate finely disseminated minerals from gangue. Similarly, the ability to produce ultrafine feed for various leaching processes, including bio-leach and low-pressure oxidation, often requires fine or ultrafine grinding to improve reaction kinetics to the level at which these processes become commercially viable. Economic ultrafine grinding processes also make it feasible to direct leach refractory gold ores, rather than the more conventional roasting or high-pressure autoclave routes. The relationship between energy required and product size is not a proportional one. Theoretically, the energy required (per unit mass) to break a particle to 1/100th of its size is 4,000 times greater. As we strive for ever-finer grinds, the need to optimize the comminution process becomes self-evident. In order to achieve the required improvements, changes in milling technologies are needed, as well as a better understanding of the variables that affect them. The media in a mill generates a particular energy spectrum, which is best defined as a frequency/magnitude plot of the energy delivered by the mill. It is possible to substantially alter this relationship for a mill by changing the operating conditions. Different mill designs will, however, differ in the range of energy spectra they can generate. The better that a mill’s energy spectra matches the breakage requirements of an application, * Metso Minerals Optimization Services, Colorado Springs, Colorado † Metso Minerals Industries Inc.–Grinding, York, Pennsylvania 69

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100

Tumbling Mills Stirred Media Mills 10

1 0

50

100

150

200

250

Specific Energy, kW-hr/t

FIGURE 1

Relative performance of tumbling ball mills versus stirred media mills

the more efficient the system will be. Jankovic (2001) has demonstrated this where clear optimum operating points could be determined for a mill by changing the operating characteristics. THE SELECTION OF MILLS—EQUIPMENT OPTIONS

Time and innovation have resulted in numerous different mill designs capable of producing fine and ultrafine products. This paper will concentrate on the few that have seen mainstream commercial application in the mineral processing industry. In many cases, these mills are of a unique and proprietary design, do not have generic names, and are known only by their commercial trademarked names. Mills for fine and ultrafine grinding fall into four primary categories: 1. Ball mills 2. Stirred media mills 3. Centrifugal mills 4. Jet mills

The first two categories make up the bulk of the fine and ultrafine grinding duty. Ball mills still see extensive use for the production of fine powders; however, these tend to be predominantly dry applications in specific industries. Industrial minerals applications make extensive use of dry ball mills, often using ceramic grinding media (to avoid metal contamination of the product) for the production of fine and ultrafine powders. Ball mills in these applications are typically operated in closed circuit with dynamic classifiers. Long tube mills (length-to-diameter ratios in excess of 3 to 1) and batch mills are also used. For wet minerals applications, the application of tumbling ball mills is declining and limited primarily to very large tonnage applications and relatively coarse grinds. The efficiency advantages of stirred media mills over ball mills have largely seen the fine and ultrafine applications move away from conventional tumbling ball mills. Figure 1 shows a typical relationship for specific energy versus grind for a ball mill and a stirred media mill. At coarser grinds, the stirred media mill requires approximately 30% less

SELECTION AND SIZING OF ULTRAFINE AND STIRRED GRINDING MILLS

71

energy than a ball mill. For ultrafine grinds, this advantage increases to more than 50%. The data shown in this example are comparative data from closed-circuit pilot milling campaigns using a conventional ball mill and a Vertimill. Media size and feed were identical for both mills. These relationships hold for full-size mills and are typical of the relative performance of stirred media mills in general when compared to conventional ball mills. Stirred media mills can be applied to relatively coarse feeds and grinds, with feeds up to 6 mm and products as coarse as 300 Pm possible from some of the available mills. These do, however, represent extremes in the range, and, more typically, feed sizes will range from 300 Pm down to 50 Pm. Products typically range from 50 Pm down to 5 Pm. The definition for ultrafine products is not an industry standard, but for the purposes of this paper, it is defined as sub-15 Pm. Stirred media mills can be classified into a number of different subcategories predominantly defined by the speed, geometry, and orientation of the media agitator or stirrer. The mill orientation can be either horizontal or vertical. The media agitator can consist of a shaft fitted with a spiral screw, pins, or discs, and the media can be either agitated or fluidized. Although the basic appearance of the mills is often similar, the operating regime and performance can be very different. There are two fundamentally different classes of stirred media mills. The first class includes the Vertimill or Tower Mill and conventional pin mills. In these mills the agitator “stirs” the media with the fluid, having limited effect on the interaction of the media with itself. In the second class, typified by the stirred media detritor (SMD) and the Netzsch/IsaMill, the media size is very fine, and the speed of the impellor is high enough to effectively fluidize the media. The media becomes highly mobile and takes on the flow pattern of a viscous fluid. Stirred media mills such as pin mills or the Vertimill, which use larger media, are more efficient with coarse, hard feeds. Fluidized media mills using low-density silica or ceramic media have the advantage for ultrafine milling with fine feeds. One commonly quoted characteristic of stirred mills, the energy intensity, does not have a strong influence on the relative performance of the mills. Mills such as the Vertimill and Tower Mill with low energy intensities operate as efficiently as mills, such as the SMD and the Netzsch/IsaMill, which have very high energy intensities. The key is correct media selection. The various mills are described briefly in the following sections. Vertimill or Tower Mill

This is a stirred media mill consisting of a vertical cylinder with a relatively slow-speed screw media agitator (see Figure 2). The Vertimill/Tower Mill is most often used for concentrate regrind applications with a typical feed size of around 100 to 300 Pm and typical products of 100 to 15 Pm. Finer products are possible with the use of suitable media. These mills predominantly use steel ball media ranging in size from 40 mm to 6 mm, and are also capable of using cast pebble media such as “cylpebs” or “power pebs,” which become economically attractive for media sizes less then 25 mm. The low impellor speed aids in reducing component wear but results in a large mill size and volume. These mills are predominantly wet mills. The finest grinds in commercial applications grind down to approximately 80% passing 12 Pm, but with suitable media, sub-5-Pm grinds have been obtained in pilot installations at comparable efficiencies to other stirred media mills. Pin Mill

Pin mills have a vertical shaft impellor fitted with pins. The mill body is filled with spherical media, typically steel or ceramic, in the size range of 3 to 12 mm. Pebble or autogenous media can also be used. These mills are capable of operating either wet or dry. The preferred feed size is <300 Pm, and sub-10-Pm grinds are achievable. Relatively high

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ADVANCES IN COMMINUTION

FIGURE 2

General view of a Vertimill

ADVANCED COMMINUTION TECHNOLOGIES

FIGURE 3

General view of a Metprotech mill

impeller speeds often result in wear issues with these mills, and they are most suitable for nonabrasive feeds. Figure 3 shows a cutaway view of a Metprotech mill. Stirred Media Detritor or Sand Grinder

This mill utilizes a vertical shaft pin agitator. Media is typically high-grade alluvial silica sand or ceramic spheres in the range of 1 to 3 mm in diameter (see Figure 4). The agitator speed is high enough to fluidize the media. Screens fitted to the upper circumference of the mill body allow product to leave the mill while retaining the media. These screens do not act as a classifier but function only to retain the media. Feed size is typically in the range of 100 Pm down to 15 Pm, and products as fine as 98% passing 2 Pm are achievable. Typical applications in the metalliferous industry have products down to 80% passing 6 Pm. Figure 4 shows the Metso SMD. Netzsch or IsaMill

This mill utilizes a horizontal shaft media agitator most commonly fitted with discs. Media utilized ranges from prepared fine slag media through sand media and ceramic media in the 1-to-3-mm size range. In the case of the IsaMill, the mill is fitted with an internal centrifugal screen fitted to the impellor for media retention. The application range is similar to the SMD (see Figure 5). Centrifugal Mill

This category of mills generates high energy intensity inside the mill by moving the mill body around a central axis at high speed. It is, therefore, possible to create forces well in excess of the 1-g force available to tumbling ball mills. These mills can be operated with conventional media or autogenously, and will operate wet or dry. One example is the HiCom nutating mill. This mill swings the mill body in a nutating motion. These mills will accept coarse feeds (limited by the throat diameter) and are capable of grinding below 10 Pm. Media retention can be an issue when small media is required (see Figure 6). Jet Mill or Fluid Energy Mill

This is a stationary mill that uses the energy contained in a fast-moving fluid to produce particle-size reduction by impact or abrasion of the particles. Two main types are in use— either the parallel type where the air is introduced to a circular grinding chamber or the opposed jet where two opposing fluid streams are impacted. The fluid used to carry the feed solids is normally compressed air, an inert gas, or steam. No media is used in fluid energy mills, the feed material and fluid providing the breakage forces.

SELECTION AND SIZING OF ULTRAFINE AND STIRRED GRINDING MILLS

FIGURE 4 detritor

General view of a stirred media

FIGURE 6

Cutaway view of the HiCom nutating mill

FIGURE 5

73

General view of a Netzsch/IsaMill

PRODUCT DEFINITION

The selection of type and size of mill for an ultrafine grinding application has to start with a thorough understanding of the duty. A mill is not there to provide a product of a particular size specification, but to provide a product with the desired liberation characteristics. To amplify on this statement, different mill characteristics and operating conditions will affect the type of comminution that takes place in a mill and will vary the balance between the fracture, attrition, and abrasion components. This in turn affects the size distribution, liberation, and surface characteristics of the product. It is important to consider these points when developing pilot-plant flowsheets. It is not advisable to utilize a conveniently available mill for the generation of feed to a pilot concentrator plant. The mill product characteristics, and therefore the grade and recovery performance of the plant, are closely related to the type of mill used. It is important to at least stay within similar classes of mills. If different types of mills are to be considered, then due cognizance is required of the differences between the mill products and their effect on plant performance. At the very least, whole-size distributions should be compared and evaluated for their recovery characteristics. Defining Product Size

It is a common practice in the minerals processing industry to define the product size of a slurry by the particle size at which 80% of the particles by mass are smaller than that

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particle size (the P80.) This does not give a true picture of the mill product-size distribution. Many industrial minerals producers (e.g., the paper filler suppliers) have long moved away from such “loose” product definitions. Multipoint product-size distributions with very tight specifications (sometimes defining the required 99.9% passing size) are commonplace. Such stringent restrictions are not necessary in most minerals applications and are often not achievable for wet applications. It would, however, be advantageous to move away from the customary 80% passing size specification. In many mineral concentration systems, the P95 or the P10, rather than the P80, will define more accurately the grade and recovery possible with that product stream. As an example, consider the typical flotation grade/recovery characteristics. Recovery of particles below a threshold size are severely impacted by limitations in the physical chemistry of the system (e.g., the ability to depress ultrafine gangue or collect mineralized particles). Similarly, coarse particles will result in poor liberation affecting both grade and recovery. Recovery losses in most leach processes (e.g., a cyanide gold leach) are largely determined by the coarse tail. It is therefore important to consider the whole mill product distribution curve in relation to the optimum-grade recovery requirements of the downstream concentration stage. Consider the decision to mill in open circuit or in closed circuit. Figure 7 shows the grind versus specific energy characteristics of a Vertimill application. The data depict the relationship between the grind and the specific energy required for open- and closed-circuit configuration. The grind and energy relationships are shown as functions of the P80 and the P95. Assume that open-circuit pilot tests preceded leaching tests and a P80 of 10 Pm was defined as the correct product size for optimum grade/recovery economics. This would equate to a specific energy requirement of 54 kW-hr/t milled. In closed circuit, the specific energy required to the same grind would be 37 kW-hr/t. This is a reduction of approximately 30%. Considering the cost differences between an open and a closed milling circuit at these product sizes (both capital and operating), the additional specific energy required might be considered reasonable. If this were a milling circuit preparing feed for a leach circuit, then the key recovery criteria would probably be a P95 of 22 Pm. Based on this assessment, an open milling circuit would require 54 kW-hr/t, but a closed milling circuit would require only 18 kW-hr/t. If the selection criterion were a P95 rather than a P80, the energy reduction from open- to closed-circuit milling would then be 67%. Reaction kinetics will reduce the difference by a margin, but the basis for a decision would still be substantially different. An equally important criterion is the product size specified. In the ultrafine product range, the relationship between the specific energy required and the product size is very flat. Significant increases in specific energy are required to produce moderate improvements in the grind. Figure 8 shows a typical specific energy versus grind relationship for a stirred media mill. A change in the product specification from 80% passing 7 Pm to 80% passing 6 Pm would require an additional 50% specific energy. In this environment it is important to be precise as to the required product specification. Particle-Size Measurement

The definition of the product size also warrants consideration as ultrafine milling adds an additional level of complication. Unlike typical grinds down to 38 Pm, where screening is commonly employed, there are no “absolute” standards with which to measure ultrafine particle-size distributions. Current particle-size measurement methods include laser diffraction, settling, cycloning, optical, and so forth. The most common units are the Malvern Mastersizer, Microtrac, Cyclosizer, Coulter Counter, and the Sedigraph. Each of these methods has distinct characteristics and is affected differently by shape, density, and translucence among other particle properties. For the industrial minerals

SELECTION AND SIZING OF ULTRAFINE AND STIRRED GRINDING MILLS

75

100

10

Open Circuit P80 Open Circuit P95 Closed Circuit P80 Closed Circuit P95 1 0

10

20

30

40

50

60

70

80

90

100

110

120

Specific Energy, kW-hr/t

FIGURE 7

Grind versus specific energy—comparison of open- and closed-circuit performance

100

10

1 0

10

20

30

40

50

60

70

80

90

Specific Energy, kW-hr/t

FIGURE 8

Typical specific energy versus grind relationship for a stirred media mill

and pharmaceutical industries that have always worked in these fine size ranges, common industry standards are employed. That is not the case in the metalliferous industry where many different methods are still used. Table 1 shows comparative results between different particle-size measurement methods for eight samples over a range of product sizes. It should be noted that the relative trends (i.e., which machine reports a finer size) are not always consistent for all powders. The particle characteristics, predominantly shape, have a strong influence. The discrepancies tend to be more pronounced at the finer sizes, where machine limitations begin to be encountered.

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ADVANCES IN COMMINUTION

TABLE 1

ADVANCED COMMINUTION TECHNOLOGIES

Particle-size distributions reported by different size-measurement techniques

Sample

Screen P80, μm

Microtrac P80, μm

Malvern P80, μm

1 2 3 4 5 6 7 8

64.3 49.7

80.6 61.8 13.5 7.4 4.1

13.6 10.2 6.5

Malvern P50, μm

Sedigraph P50, μm

3.6 5.6 7.9

0.83 4.1 4.7

In addition to potentially large differences in the product sizes “measured” by the different methodologies, machines of the same type and brand can give significantly different results. Even if the type and model of particle-size analyzer has been standardized, machine setup, maintenance, standard operating procedures, and operator skill all have significant effects. Agglomeration of particles during measurement is also a concern, and the use of dispersants adds an additional level to the potential error. If different milling technologies are being compared, using pilot or batch milling tests in different locations, it is important to be aware that the particle-size measurement will be different, and probably by more than the potential difference between the different milling technologies. This would be true even if the same model particle-size-measurement device were used. The only reliable comparisons can be made if the products from both tests are tested on the same particle-size analyzer using the same technician. Failing that, normal measurement errors may be too high to make meaningful comparisons. Where the same particle-size analyzer cannot be used, it is essential to at least use similar model machines and employ the same operating procedures. Comparisons made using dissimilar particle-size-measurement techniques are not very meaningful. Similarly, it must be remembered that the particle-size-measurement method must be similar to that employed when originally determining the grind requirement for optimum liberation. There are no easy solutions. The key is to exercise caution, and rigorously work according to best-known practice. Be realistic about the reliability and accuracy of the methods used for sizing and comparing equipment. DETERMINATION OF THE SPECIFIC ENERGY REQUIRED

Stirred media mill designs are generally unique, and mill selection is often based on manufacturers’ testing, or alternatively, on tests run in third-party laboratories using lab-scale versions of the mills being considered. Empirical methods, such as the Bond method, are largely unsuccessful in determining power draw requirements for ultrafine grinds and are unsuitable for stirred media mills. The Bond method, for example, incorporates a correction factor (EF5) for fine product sizes. This correction factor was specifically intended to correct for the inefficiency of ball mills using conventional media sizes when producing very fine products. With stirred media mills, the media size limitation is largely overcome and milling efficiencies are dramatically improved. Specific energies derived from the Bond equations would be unacceptably conservative. It is not possible to determine Bond Work Indices for the majority of fine and ultrafine grinding applications, as the feed size would not meet the test requirements. There is also considerable activity in the development of population balance models (PBMs) for stirred media mills. The primary challenge is to accurately define the breakage rates and the effects of operating parameters and media on the breakage parameters. It

SELECTION AND SIZING OF ULTRAFINE AND STIRRED GRINDING MILLS

77

is unlikely that these techniques will be used for mill sizing in the foreseeable future, as the challenges are considerable. One benefit of the finer feed size typical of ultrafine grinding applications is that an accurate laboratory test is possible. To accurately size a semiautogenous grinding (SAG) mill, a minimum sample size of 100 kg is required for a laboratory test, and 20–100 t for a pilot test due to the large feed particle size. Statistical relevance requires significantly larger samples. For stirred mills, the feed top size is generally <200 Pm, and therefore a sample mass of 100 g is sufficient for statistical reproducibility. The only reliable method currently available for the selection of mills for ultrafine grinding is a well-planned and executed lab- or pilot-scale test regime. The test program should include an evaluation of all the primary operating parameters (listed in the section on Media Considerations). Small sample size and relative ease of testwork make the evaluation of multiple operating parameters feasible. The primary data generated with such a laboratory- or pilot-scale test involve the relationship between specific energy and grind. Depending on the type of mill being evaluated, the net specific energy generated by the test mill can either be used directly without any correction factors or will need to be adjusted. This task is currently best left to the supplier of the equipment being evaluated or to the laboratory where the tests are being executed. Media Considerations

Use of the correct media is important for all grinding applications, but in the case of ultrafine grinding in stirred media mills, it becomes the most important variable. Media parameters that need to be considered include ƒ Size ƒ Type ƒ Competency ƒ Hardness

Stirred media mills use a wide variety of media from 25-mm-to-6-mm steel balls and cylpebs commonly used in mills such as the Vertimill and Tower Mill to 1-mm-to-5-mm high-grade alumina and sand media used in mills such as the SMD and the Netzsch/ IsaMill. Media can affect the specific energy required for an application by an excess of 30%. Any laboratory-scale testwork should therefore include a range of different medias. Media availability is often regional, and transport costs are a significant contributor to the total cost. When undertaking laboratory or pilot milling regimes, both local and known media types should be tested. Cost and performance are the primary considerations. The cost of conventional steel media increases rapidly as the size decreases below 25 mm. This has largely restricted the use of small steel media in mills such as the Vertimill, Tower Mill, and pin mills. These restrictions are now largely eliminated due to the recent availability of cast media and steel shot. Size limitations no longer exist, but there are still questions regarding the media consumption and influence of iron (from the media) on some concentration processes. Material and sphericity are the strongest influencing factors for the 1-mm-to-3-mm media commonly used in “fluidized” media mills. Choice of media for laboratory and pilot milling tests should reflect the reasonable choices available for the proposed plant. Using 2 kg of high-alumina ceramic media at US$70/kg may be acceptable for a pilot mill but would be wholly undesirable for a commercial installation requiring 10 t of media. Similarly, using low-cost local media may provide acceptable specific energies for the application, but media breakage and wear of mill components (which are not readily measurable in batch laboratory tests) may make

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the media unacceptable for a commercial application. Higher quality media could also reduce equipment size. Comparisons between different types of mills should consider media costs and, where reasonable, use similar media. It is advisable to always include at least one commercially available media of known quality in a test regime. Media Size. Media size has a significant impact on the performance of mills in fine and ultrafine grinding applications. It is often the primary limitation of the fineness of grind possible from a type of mill. As feed and product sizes decrease, the energy required to break a particle also decreases, and the frequency of the breakages per unit mass increases. Excess energy from breakage events is largely converted to heat and does not contribute to the grinding process. The most effective way to increase the frequency of the grinding events and decrease the energy per event is to reduce the media size. Consider the relationship between media size and the number of balls (or other media shapes). Table 2 shows the relationship between the media size and the number of balls per unit mass (or volume). The number of media per unit volume increases by the inverse ratio of the media size to the third power. As the number of breakage events in a mill is proportional to the number of media, dramatic improvements are possible through the selection of the correct media size. Because of the need to focus energy on ever-increasing numbers of smaller particles, media above a certain size may become completely ineffective in producing ultrafine particles. A typical media size, specific energy plot for a Vertimill is given in Figure 9. Significant reductions in the specific energy required to achieve a grind can be obtained from the use of smaller media. The specific energy required to achieve a grind of 15 Pm is more than 50% greater with 10-mm media than it is with 5-mm media. A 15-Pm grind was not achieved with the 18-mm media over the range of specific energy tested. Similar effects are found with the media used in “fluidized” media mills. Figure 10 shows the effect of media size on an SMD. In this particular case, the trend between energy required and media size reflected in the Vertimill data is reversed. In this example, the mill requires over 50% more energy to the same grind with the 1-mm media than is required with the 2-mm media. The 1-mm media is too small to effectively break down the larger feed particles. A finer, or softer, feed might see this trend reversed. Also evident from the data is that the use of seasoned media charge is a requirement when generating design data. Monosized media will not give a true reflection of the eventual performance of an operation. Media Type. Media type and shape also affect mill performance. Media can be either ferrous or nonferrous. Nonferrous media includes high-grade alumina balls and beads, lower-grade mullite ceramic beads, and silica sand. There is a large variety of exotic medias available for highly specialized industrial applications where contamination, and not cost, is the primary consideration. These medias are not normally suitable for high-tonnage applications. Table 3 shows some typical medias, as well as examples of cost and relative wear (where applicable). Steel media is most commonly used in ball mills, vertical mills with screw agitators, and pin mills. Fluidized media mills most often use small ceramic beads or silica sand. One consideration in the selection of a suitable milling technology for an application is the effect of steel media on flotation recovery characteristics. In ultrafine grinding applications, iron in solution from the media can contaminate sulphide mineral surfaces with iron oxide, thereby affecting the grade and recovery characteristics of the flotation plant. Iron in solution will also consume oxygen and affect some downstream processes. Under these conditions, a nonferrous media may be preferred. Ball mills and stirred mills draw less power with nonferrous media of a lower density than steel, and the mill sizes must therefore be increased. Although fluidized media mills can be operated with ferrous

SELECTION AND SIZING OF ULTRAFINE AND STIRRED GRINDING MILLS

Relationship between media size and the number of balls per unit mass

TABLE 2

Ball Size, mm

Surface Area, m2/t

Number of Balls, per t

Number of Balls, normalized

20 15 10 5 3 2

83.3 111.1 166.7 333.3 555.6 833.3

66,315 157,190 530,516 4,144,132 19,648,758 66,314,560

1 2.4 8 62 296 1,000

100

10

18-mm Steel Media 10-mm Steel Media 5-mm Steel Media 1 0

10

20

30

40

50

Specific Energy, kW-hr/t

Effect of media size on mill efficiency (typical results for a Vertimill)

FIGURE 9 100

10

100% 2-mm Media 100% 1-mm Media 50/50 2-mm and 1-mm Media 1 0

10

20

30

40

50

60

70

80

90

Specific Energy, kW-hr/t

FIGURE 10

Effect of media size on mill efficiency (typical results for an SMD)

100

110

79

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TABLE 3

ADVANCED COMMINUTION TECHNOLOGIES

Media characteristics Type

Steel media Attrition sand Mullite ceramic Glass beads Alumina ceramic Zirconium silicate Yttrium-stabilized zirconia oxide

Main Components

Price, US$/kg

Approximate Consumption, kg/kW-hr

Fe/Cr Quartz Kaolin Quartz Aluminum oxide Zircon Zircon

0.4–1.5 0.2 0.8 3 15 18 70

0.02–0.01 0.02 0.01 0.01 0.005 0.005 0.001

media, they are generally designed to operate only with nonferrous media. Design modifications would be required, and as such, this is not typically an option. Mullite ceramic beads have supplemented high-grade alumina medias. These beads are typically kaolin based and, while being hard and having good media properties, are significantly more affordable than more traditional alumina media. This class of media is seeing increasing application for use in ultrafine grinding. Sand media should be near spherical, and aspect ratios better than 1:1.1 can be obtained. With all stirred media mills, the way that media moves over itself affects the energy utilization. Spherical media moves over itself relatively easily, whereas nonspherical shapes will have an increasing tendency to “lock up,” thereby consuming energy. This effect is most readily seen with “fluidized media” mills. Figure 11 shows a specific energy relationship for an SMD using sand and ceramic media. The ceramic media has advantages in both the specific gravity of the media, the hardness, and the sphericity. For this particular application, the use of ceramic media would reduce the energy required by almost 50% over the use of sand media. Use of ceramic media for this application would almost halve the milling capacity required, as well as the energy consumed. This would need to be factored against the media consumption and cost differences between the two media types. This level of improvement is not always found and is dependent on the feed size, hardness, and grind required. Media Competency. Of particular importance with sand media used in “fluidized media” mills is the competency. The typical commercial sand media used in “fluidized” media mills is normally used for filtration or other duties. Mechanical strength is not specified. Ideal sand media is alluvial sand with rounded edges and is free of flaws. A common problem associated with low-grade sand media is that it has internal flaws and is not able to withstand the forces associated with milling. Flawed media tends to break up rapidly, degrading the media shape and size. Breakage increases media consumption. Broken media also presents sharp edges, which increase the wear of the impeller and wear liners in a mill. These faults are not typically evident during batch laboratory tests. Care is required therefore when designing a plant based on the use of such media in batch or pilot milling tests. Media Hardness. One aspect sometimes not considered is the media hardness. With steel media, hardness does not affect mill performance, only media consumption. This is not the case where nonferrous media is used. Consider the environment inside a typical “fluidized media” mill using sand or other nonferrous media. If the mineral being ground is harder than the media itself, then the media will in effect be subject to comminution, and size reduction of the feed will be reduced (Krause and Pickering 1998). These data depict the product-size distributions for a fluidized media mill grinding quartz feed. These are batch grinds for the same duration. Quartz has a Mohs hardness of approximately 7. The data show dramatically different results for media that is softer

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81

70 Sand Media Ceramic Media

60

50

40

30

20

10

0 0

10

20

30

40

50

60

70

80

90

Specific Energy, kW-hr/t

FIGURE 11

Effect of media type on performance of an SMD

Product, Cumulative % Passing

100

3.56 Specific Gravity - 8+ Mohs 3.27 Specific Gravity - 8+ Mohs 2.71 Specific Gravity - 7+ Mohs 2.68 Specific Gravity - 6+ Mohs 10 1

10

100

Size,

FIGURE 12

Effect of media hardness

or harder than the feed. There is also a density effect, but this is primarily due to higher absorbed powers with the higher specific gravity media. The primary variable is the media hardness. Whereas sand media may be acceptable for soft minerals, when hard minerals are encountered, higher-grade-alumina media may be necessary. Figure 12 shows the product-size distributions for the various runs. Operating Parameters. Outside of the effect of media selection on the performance of stirred mills, the strongest influencing variable is the slurry percent solids, or viscosity. Vertimills, Tower Mills, and pin mills are less sensitive to slurry viscosity than

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“fluidized media” mills. The former category of mills is able to operate over a reasonably wide range of percent solids. Fluidized media mills require more careful analysis of the effect of percent solids. Two sets of trends are presented in Figures 13 and 14, showing typical relationships between the grind and specific energy at various percent solids. The figures show the effect of slurry percent solids. As can be seen, the effect of slurry percent solids on the performance of the mills is significant and trends are not always consistent. Lab or pilot milling tests over a range of operating conditions are essential in order to determine the optimum operating conditions of the selected mill and, therefore, the correct mill selection. CIRCUIT CONSIDERATIONS

Classification

The primary options are open- or closed-circuit milling, with the possibility to prescalp the feed ahead of milling. Scalping can be either in dedicated classifiers or, alternatively, by introducing the new feed to the mill discharge sump. Fine and ultrafine grinding circuits benefit from classification in much the same way that conventional grinding circuits do. Use of a classifier will reduce fines generation, produce a tighter product specification, and reduce the overall energy requirements to achieve a specific grind. These benefits have to be weighed against the cost, both capital and operating, of classification circuits. For dry grinding circuits, the most commonly used classifiers are dynamic “whizzer” type units. The primary type of wet classifier for fine and ultrafine classification is the hydrocyclone. As grinds become finer, cyclone sizes need to be reduced, and the percent solids in the cyclone feed reduced. For sub-10-Pm grinds, cyclone sizes are around 25 mm to 50 mm. In addition, the product is very dilute, typically no more than 15% solids w/w. The downstream circuit determines whether this dilution is prohibitive or not. As an example, where a mill is used to regrind a concentrate, if the concentrate is reintroduced to the bulk float cell feed, then the dilution may not be an issue. If, however, the mill product were treated in dedicated float cells, then the dilute feed would not be acceptable. Added dewatering costs need to be factored into the overall economic evaluation. Another consideration is the slurry percent solids requirement for the mill feed. A typical concentrate from flotation cells would be too dilute to be used as mill feed for an open-circuit mill. Good control of the feed density is essential to efficient operation. A scalping cyclone would be required for this duty. The cyclone would have the combined benefit of removing finished product in the feed, thereby improving milling efficiency and producing a tighter product specification, as well as increasing the density of the mill feed. As the milling circuit is open circuit, the total flow to the cyclones, and therefore the number, is reasonable, and the cyclone overflow is recombined with the higher density mill discharge, and further dilution can be limited. Number of Mills

Milling circuits are always designed for maximum duty. These circuits rarely operate at these values. During startup of greenfield plants, extended operating periods with significantly reduced feed rates can last for up to 1 or 2 years. Also, where mills are included in concentration circuits, feed rate to the mill will be affected by both the normal total circuit feed fluctuations due to the hardness of the ore, as well as swings due to the grade of the ore. In tough applications, these tonnage swings can be on the order of 100% to 200%. Under these conditions, the turndown ratio (the minimum power at which the mill can operate) of the selected mills must be considered. Mills installed in fine and ultrafine

SELECTION AND SIZING OF ULTRAFINE AND STIRRED GRINDING MILLS

83

100

10

30% Solids 40% Solids 50% Solids 1 0

10

20

30

40

50

60

70

Specific Energy, kW-hr/t

FIGURE 13

Effect of slurry percent solids on fluidised media mill performance (trend 1)

100

10

30% Solids 40% Solids 50% Solids 1 0

10

20

30

40

50

Specific Energy, kW-hr/t

FIGURE 14

Effect of slurry percent solids on fluidised media mill performance (trend 2)

regrind duties are normally constant speed and, therefore, constant power machines. Ball mills and some stirred mills, such as the screw-agitated mill and the pin-agitated mill, can operate at reduced ball levels and, therefore, power draws. These changes in ball charge can be used to minimize overgrinding during known periods of reduced throughput, such as startup periods, but typically cannot follow the normal capacity swings resulting from short-term changes in the feed rate. Fluidized media mills have very limited turndown and should be operated at their design power if severe wear problems are to be avoided.

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What this means is that if the feed rate should drop below the design values, the mills will continue to input the full power, and the product will be ground significantly finer than required. This would be more of a problem for flotation circuits than leach circuits, but the effect on the filters and thickeners in the plant must still be considered. The most effective method to control overgrinding is with the use of multiple units fed from a common source. Individual mills can be brought into service, or taken out, as required. Caution should be exercised when specifying a single mill for an application if feed-rate variations are expected to be a problem. Vertical mills with screw agitators do have a measure of control over this problem. The mills include an internal recycle loop that controls the uprising velocity of slurry in the mill. On specification, product can be removed from the mill and presented to classification, thereby reducing overgrinding. In some cases, specifications on the allowed coarse material in the product require the installation of two mills in series (where open-circuit milling is required). EXAMPLES

Ziniflex Century Ultrafine Milling Circuit

The Ziniflex Century lead–zinc deposit is a massive fine-grained ore body located in the northwestern region of Queensland, Australia. Minable reserves are approximately 100 Mt at an average grade of 1.7% lead and 12.5% zinc. The flotation plant has a design throughput of 5 Mtpy, and the first ore was introduced to the plant in November 1999 (Barnham and Kirby 2001). The deposit was originally identified by Conzinc Riotinto of Australia (CRA) in 1990, who conducted the definitive feasibility study during 1994 and 1995. Rio Tinto Zinc Corporation (RTZ) sold the project to Pasminco after the RTZ merger with CRA during 1997. The main process problem with the Century ore is that the sphalerite, which is the main zinc mineral, is very finely interspersed with silica (Hookham and Sutherland 1999). Ultrafine grinding to a P80 of 6.5 Pm followed by flotation was considered the most cost-effective and practical solution. Fifteen Metso 355-kW SMDs were installed at Century to produce the desired product size with an additional six units in a zinc regrind duty (Figure 15). As mentioned previously, small media, smaller than 5 mm, is generally more energy efficient than coarser media when the material feed size is greater than 100 Pm. This accounts for the relatively low work input values to mill to a P80 of 6.5 Pm. Century uses a sand media with a mean size around 2 mm. Current operating conditions for the zinc ultrafine grinding SMDs are shown in Table 4. Individual SMD performance is monitored constantly, and mass flow rates and the number of SMDs operating is adjusted continually to allow for the varying flotation mass pull. This minimizes over- and undergrinding in the zinc circuit. One limitation of all fine and ultrafine grinding circuits is the lack of a reliable industrial on-line particle-size analyzer capable of measuring sub-20-Pm particles. Overall, it was found that the laboratory and pilot studies conducted before the construction of the final mineral processing plant provided accurate plant sizing data to the engineering company charged with designing the plant and Metso process engineers. This was aided by the quality of the original test samples, a combined effect of the quantity of samples mined and processed.

SELECTION AND SIZING OF ULTRAFINE AND STIRRED GRINDING MILLS

FIGURE 15

TABLE 4

85

Photograph of 355-kW SMD at Century

Century ultrafine milling data Operating Parameter

Units

Value

Mill power draw Feed rate Feed density Feed size Product size Sand media consumption Mill-specific energy

kW tph % solids w/w F80 μm P80 μm kg/kW-hr kW-hr/t

310 8.6 50 35 6.5 0.07 36

REFERENCES

Barnham, M., and E. Kirby. 2001. The design and commissioning of the Pasminco Century process plant. SME Annual Meeting, Littleton, CO. Hookham, M., and G. Sutherland. 1999. Century grinds its way to saleability. Australian Mining Monthly (May). Jankovic, A. 2001. Scale-Up of Tower Mill Performance Using Modelling and Simulation. JKMRC/Amira P9M project. Third Progress Report. Melbourne, Australia: Amira International. Krause, C., and M. Pickering. 1998. Evaluation of ultrafine wet mineral milling using carboceramics proppant products for attrition grinding media. Colorado Springs, CO: Metso Minerals Optimization Services.

Effects of Bead Size on Ultrafine Grinding in a Stirred Bead Mill J. Yue* and B. Klein*

ABSTRACT

The effects of bead size and composition on particle breakage rate, product size, and size distribution, as well as the mill power consumption in a stirred mill are investigated and evaluated. The results confirm that monosized beads produce better milling performance than bimodal beads as far as media wear is concerned. There exist optimum bead sizes for certain feed sizes with respect to particle breakage rate, product size, and size distribution. The optimum ratio of bead size to feed size is confirmed at about 20:1. INTRODUCTION

Stirred bead mills are used widely for ultrafine grinding minerals and other materials to particle sizes below a few micrometers. The energy needed for breakage is transferred through the grinding media to the particles. For a given particle size, mineral type, and specific energy input, the bead size plays a very important role in the comminution process, particularly with respect to the stress intensity (SI) and the stress number (SN) (Kwade 1999). From a physical–mechanical point of view, two conditions need to be satisfied for breaking particles in a grinding mill: the grinding media must exert sufficient SI to the particles, and there must be direct contact between the media and the particles. For fine grinding, it has been recognized (Stehr, Mehte, and Herbst 1987; Kwade 1999) that the specific energy consumption by stirred balls is less than that of tumbling mills. Due to the high-media volumetric loading in stirred bead mills, the SI and SN per unit volume acting on particles is higher than in tumbling mills. For brittle particles, massive fracture occurs when the overall stress acting on a particle exceeds a critical value, resulting in particle disintegration and creating a large number of fragments. Attrition is associated with smaller stresses exerted on particle edges causing a continuous but slow loss of particle mass. It is understood that massive fracture of brittle solids results in a faster particle breakage rate than attrition. Kwade and others (Kwade 1999; Kwade and Schwedes 2002) assumed that the SI is proportional to the kinetic energy of grinding media, and thus showed that it is proportional to both stirrer speed and bead size. The SN is also proportional to stirrer speed as well as to the number of beads in the mill. Kwade (1999) presented the following expressions for SI and SN (Equations 1 and 2), which demonstrate these relationships:

* Mining and Mineral Process Engineering, University of British Columbia, Vancouver, Canada 87

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2

SI v SI GM = d GM U GM v t

(EQ 1)

SN = NCPS/NP

(EQ 2)

where GM is the grinding media; d is the bead diameter; ȡ is the bead density; vt is the bead tangential velocity; NC is the media contact number; PS is the probability that a particle is caught and stressed sufficiently by the media; and NP is the number of product particles inside the mill. Blecher and Schwedes (1996) studied the motion of grinding media with disc stirrers. They showed that a high tangential velocity gradient exists near the surfaces of the discs and at the grinding chamber wall. At these areas, they suggested that the power density is much higher than the mean value for the mill and that more intensive collisions take place. These high-intensity collisions are believed to account for most of the particle breakage in the mill. The size of grinding balls is known to play a very important role in grinding in tumbling mills. In particular, small balls are important for effective compression and attrition of fine particles. The motion of mixture of beads, mineral particles, and water in a stirred mill chamber occurs at a very high speed, but it is not clear if this is also the same scenario. So far, rheological concepts have been applied to the aqueous mineral suspension. These concepts may be applied to the entire mixture within the mill as well. For aqueous mineral suspensions, the relative viscosity Kr increases with solid volume fraction ) (Bicerano, Douglas, and Brune 1999; Chong, Christiansen, and Baer 1971), and increasing particle size d (Clarke 1967). Similarly, Wang and Forssberg (1997) observed that increasing bead volumetric loading ()) causes the power draw to intensify greatly. Also, Herbst (1978) showed that increasing the bead size (d) increases the power draw. Both of these results demonstrate that the volume content and size of grinding media affect power in a similar manner to how particles affect rheology. The changes in the physical properties of suspension that cause the viscosity to decrease correspond to changes in bead composition that lead to a reduction in power requirements. Therefore, testing was carried out to demonstrate the effect of bead size on grinding in stirred mills with respect to breakage kinetics, product size, size distribution, and power consumption. Research on the rheology of mineral suspensions has demonstrated that selected compositions of bimodal particle-size distributions produce a “minimum” viscosity (Chong, Christiansen, and Baer 1971). This bimodal size distribution is also characterized by a maximum particle-packing fraction. A study was conducted to assess the effect of bimodal bead-size distribution on power usage, grinding rate, and product-size distribution. EXPERIMENTAL PROCEDURES

A Netzsch LME 4 horizontal stirred bead mill was used for the study. The mill is 400 mm in length, 173 mm in diameter, and has a volume of 2.48 L. The stirrer has eight polyethylene discs. A loading charge of 80% of the mill volume was maintained using steel-shot grinding media with the diameters of 3, 2, 1, and 0.5 mm. The mill is equipped with a digital control panel on which operating conditions were set and output parameters were displayed, including temperature, pressure, and power. For tests with bimodal bead sizes, 2-mm and 0.5-mm beads were used. Grinding tests were performed on suspensions of quartz particles with feed sizes (F80) of 83 Pm and 32 Pm (Figure 1). The feed slurry solids content was maintained at 35% solids by weight. Detailed test conditions are shown in Table 1. The slurry feed rate

EFFECTS OF BEAD SIZE ON ULTRAFINE GRINDING IN A STIRRED BEAD MILL

89

Cumulative Undersize, %

100.0

10.0

1.0

0.1

0.0 0

FIGURE 1

TABLE 1

1

10

100

1,000

Feed-size distributions

Test program for evaluating grinding bead effects on a stirred bead mill

Test No.

Feed Size F80, μm

Agitator Speed, rpm

Pump Flow Rate, L/min

Agitator Power, kW

Bead Size, mm

8 9 10 11 12

30 83 30 83 83

1,500 — — 1,500 —

3.1 3.1 3.1 3.1 3.1

— 3.7 3.7 — 3.7

0.5, 1, 2, 3 0.5, 1, 2, 3 0.5, 1, 2, 3 0.5+2 0.5+2

was kept constant at 3.1 L/min. For tests with constant agitator speed (1,500 rpm), the power usage was recorded as a response. For tests with constant power, the agitator speed was adjusted to maintain this constant power and recorded. For tests with bimodal bead sizes, a series of tests were performed using varying proportions of small beads (0%–100%). Particle-size analyses were performed using a Malvern Mastersizer 2000 laserdiffraction particle-size analyzer (PSA). The Rosin-Rammler equation was fit to the data to characterize the particle-size distributions. RESULTS AND DISCUSSION

Monosized Grinding Beads

The ultrafine grinding tests were conducted to evaluate the effects of bead size on particle breakage rate, product size, size distribution, as well as agitator power consumption. The bead size, agitator speed, and feed size were varied, whereas the pulp density was kept constant during the tests. Figure 2 shows how the specific breakage rate varies with bead size. At a constant agitator speed, the specific breakage rate increased almost linearly with bead size. When the mill power was kept constant, the specific breakage rate was highest at a bead size of 2 mm, and the rates were lower when using smaller and larger beads. Although the “maximum” breakage rate at a bead size of approximately 2 mm was observed for both

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0.09 0.08

Specific Breakage Rate

0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0

1

2

3

4

Bead Size, mm

FIGURE 2

Specific breakage rate versus bead size

feed materials (F80 32 Pm and F80 83 Pm), it cannot be concluded that this bead size is optimum for coarser or finer feed materials. The significance of bead size was more pronounced for the coarser feed material. When changing the bead size from 2 mm to 3 mm, the corresponding decrease in agitator speed had a greater impact on breakage rate than the increase in bead size. Using a smaller bead size caused a decrease in breakage rate implying a lower SI and a less effective use of power. There is insufficient information available to make conclusions about the reasons for the “optimum” bead size. Factors such as SI and SN likely play a role. However, the results of this study reveal that an optimum bead size can be selected. Figure 3 shows how bead size affects product fineness (P80). At constant agitator speed, increasing the bead size caused the product to become finer. However, when grinding power was kept constant, there was an optimum bead size. For the 32-Pm feed, the product size was finest when using a bead size of 1 mm. For the 83-Pm feed, the 2-mm bead size produced the finest product. In this case, when larger beads were used, the agitator speed had to be decreased to maintain a constant power. Conversely, when smaller beads were used, a higher agitator speed was required. The bead size also affects product-size distributions. Figure 4 is a plot of the RosinRammler particle-size distribution coefficient, b, versus bead size; a high value of b corresponds to a narrow size distribution. The product-size distributions were characterized using the distribution coefficient from the fitted Rosin-Rammler equation. At constant power, larger beads produced a narrower size distribution. The results agreed with those obtained by Wang and Forssberg (1997). Larger beads have higher kinetic energy, therefore, they have greater potential to cause massive fracture, producing narrower product distribution. The smaller beads produce a wide size distribution, possibly due to the lower SI promoting attrition over massive fracture. For mineral processing, a narrower particle-size distribution is usually preferred as it benefits downstream flotation and dewatering. If the goal is to produce a narrow productsize distribution, the results presented in Figure 4 suggest that there is an optimum bead size.

EFFECTS OF BEAD SIZE ON ULTRAFINE GRINDING IN A STIRRED BEAD MILL

91

60

50

40

30

20

10

0 0

1

2

3

4

Bead Size, mm

FIGURE 3

P80 versus grinding bead size

Particle-Size Distribution Coefficient, b

2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0

1

2

3

4

Bead Size, mm

FIGURE 4

Particle-size distribution modulus versus bead size

Figure 5 shows the relationship between bead size and agitator power draw (agitator speed was kept constant). Tests were performed with and without slurry to demonstrate the background effect of the grinding beads. Increasing the bead size causes the power draw to increase. In the presence of slurry, the power draw increases more sharply than without slurry. Such a relationship also can be interpreted by rheological concepts. Researchers (Chong, Christiansen, and Baer 1971; Clarke 1967) found that slurry viscosity is lowest at an intermediate particle size and increases above and below this particle size.

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6

5

Power, kW

4

3

2

1

0 0.0

With Load of Slurries Without Load of Slurries 0.5

1.0

1.5

2.0

25

Bead Size, mm

FIGURE 5

Agitator power versus bead sizes

These results show that adding coarser beads increases the power draw, which implies an increased viscosity. The particles are filled into the bead voids and nipped, causing a strong shearing resistance that needs to be overcome by bead kinetic energy. The experiments showed that at constant agitator speed, increasing the bead size gave the following results: ƒ Increased breakage rate ƒ Finer product size ƒ Narrower product-size distribution ƒ Increased power usage

These results are supported by Equation 1, which shows that using larger beads will increase the SI. These results demonstrate that factors that increase the SI will increase grinding kinetics and produce a finer product. However, there is a trade-off, as these factors also cause an increase in power usage. In practice, mills are operated near the upper power limit. It is, therefore, important to understand how to “optimize” grinding at this constant upper power limit. The results reveal that at constant power draw, there was an optimum bead size with respect to a high breakage rate, fineness of the product, and narrow size distribution. The reasons for the optimum bead sizes cannot be readily explained by Equations 1 and 2. Mankosa, Adel, and Yoon (1986) suggested that the optimum size ratio between beads and particles (mean size) is 20:1. Fadhel and Frances (2001) believed the ratio lies between 20:1 and 200:1. Figure 6 is a schematic diagram in which the ideal geometric dimensions of both beads and particles are assumed. Figure 6a shows there is one particle nipped by beads; Figure 6b shows four to five particles are captured in the bead void for optimum breakage. The results calculated in Table 2 confirm that the “optimum” ratio between bead and particle is close to 20:1. The test data shown in Figures 2, 3, and 4 support Mankosa, Adel, and Yoon’s conclusion. In fact, the maximum breakage rate occurs when particles are large enough to have a high probability of contacting beads but are small enough to be effectively caught and broken by the media. Above this limit, the breakage kinetics and size-reduction ratio decrease. This decrease can be explained by geometric aspects of particle “nipping” or by a lower SN (in Equation 2, PS decreases and NP increases simultaneously), although the SI is kept constant.

EFFECTS OF BEAD SIZE ON ULTRAFINE GRINDING IN A STIRRED BEAD MILL

93

R r

(a)

FIGURE 6

(b)

Schematic diagram of beads and particles in a stirred mill

TABLE 2 Relationship between bead diameter (D) and maximum particle size (d) based on geometries shown in Figure 6 where d = 2(R/cos 30 – R) D, mm (a) d, mm (b) d, mm

3 0.46 0.15

(a)

FIGURE 7

2 0.3 0.1

(b)

1 0.15 0.05

0.5 0.076 0.025

(c)

Schematic diagram of impact and compression breakage mechanism

Figure 7 presents the possible scenarios for impact and compression breakage in stirred bead mills. Figure 7a shows collision between a particle and a bead. Figure 7b shows that particles captured in the void between beads are impacted indirectly by another bead. Figure 7b illustrates particles being “roll-crushed” between beads. For Figure 7a, massive fracture occurs when the bead impacts the particle, but the probability of this impact is relatively low due to the vast size difference between beads and particles. Figure 7b demonstrates the collision as balls hit the bed, in which impact energy is transferred through beads to particles indirectly, resulting in particle fracture. This is perhaps responsible for most of the particle breakage in stirred mills. The probability of Figure 7c is also quite high. In this case, compression occurs between beads, which act as numerous tiny roll-crushers working in a mill. If particle sizes are too small, compression may be replaced by attrition. Bead-Size Distribution

There is the theoretical possibility of increasing charge mass load while keeping load volume constant by selecting the bead-size distribution. In particular, the packing density of

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grinding media can be increased by filling the voids between the largest beads with smaller beads, producing a bimodal bead-size distribution. The maximum packing density for a bimodal distribution is achieved when the ratio of particle sizes (small to large) is less than about 0.1 and when approximately 30% of the total volume is comprised of the smaller particles (Furnas and Anderegg 1931). Chong, Christiansen, and Baer (1971) found that the viscosity of suspensions at a fixed solids concentration was at a minimum when using this bimodal size distribution. The implication is that a bimodal bead-size distribution would correspond to a minimum power draw. For stirred mill grinding, the grinding media typically occupies about 80% of the mill volume. Introducing fine beads into a bed of coarse beads would theoretically increase the volume of solid fraction of beads by 24%, from about 60% to about 84%. Therefore, adding small beads has the potential to increase the charge mass by 40% (24/60) while maintaining a constant charge volume. There likely would be a consequence of increasing the charge mass to grinding rate and power usage; however, there are practical limitations to maintaining such a bead-size distribution during operation of an industrial mill. In practice, there is a distribution of bead sizes in grinding mills. During grinding, the beads wear, reducing their size, and they eventually pass through the mill product screen and are rejected. There is a trade-off between optimizing bead size with respect to grinding (size reduction, power usage, and product-size distribution) and costs associated with media consumption. It is therefore critical to determine the appropriate screen aperture to satisfy both of these criteria. A set of experiments was conducted to assess the effect of changing the bead-size distribution by increasing the proportion of fine beads. In particular, grinding tests were conducted using mixtures of 2-mm and 0.5-mm beads with compositions that varied from 100% coarse beads/0% fine beads to 0% coarse beads/100% fine beads. In order to maintain a constant charge volume for all experiments, the bulk densities of mixtures were determined (Figure 8). The graph shows that as the proportion of fine beads is increased, the bulk density increases; this result can be explained by the packing theory described above. However, there is an unusual dip in the bulk-density curve corresponding to fine fractions between 30% and 80%. It is suggested that this dip is a result of imperfect mixing that prevented optimum packing of the beads. Since optimum mixing likely would not be achieved in an operating mill, the measured bulk densities were used to prepare media compositions for the study. The experimental work was aimed at evaluating the effect of media wear. Tests were conducted using increasing proportions of fine media and determining the specific breakage rate, product particle size, size distribution, and power consumption. The results are shown in Figures 9–12. Under conditions of maintaining constant mill power or maintaining constant agitator speed, the specific breakage rate decreases as fine bead fraction increases (Figure 9). The decrease in breakage rate corresponds to an increase in product size (Figure 10). It is interesting to note that the product-size distribution becomes wider by increasing the media fineness. The trend towards a wider size distribution and slower grinding rate can be interpreted as a change in grinding mechanisms from primarily massive fracture for the coarse media to attrition for the finer media. Figure 12 shows that the total power draw and net power draw decreased as the bead size became smaller. Results from Figures 9, 10, and 11 show that the existence of fine beads affects milling performance greatly with respect to particle breakage rate, product size, and size distribution, even when the power input is kept constant. Figure 12 shows that replacing fine beads with coarse ones results in a decrease in power usage. The consequence of the buildup of fine media is that energy is not efficiently used and mills are not operated under “optimum” conditions.

EFFECTS OF BEAD SIZE ON ULTRAFINE GRINDING IN A STIRRED BEAD MILL

95

5.2

Bulk Density, g/cm 3

5.1

5.0

4.9

4.8

4.7

4.6 0

20

40

60

80

100

Fine Fraction, %

FIGURE 8

Bead bulk density versus fine fraction of bimodal beads

0.16 Agitator Power 3 7 kW Agitator Speed 1,500 rpm

Specific Breakage Rate

0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0

20

40

60

80

100

Fine Bead Fraction (0.5 mm), %

FIGURE 9

Specific breakage rate versus percent fine bead

All these results confirmed that the fine beads existing in grinding media have negative effects in particle breakage rate, product size, and size distribution, and are not optimal for grinding efficiency in stirred mills. The trends can be attributed to the lack of sufficient SI in stirred mills when the beads become too fine. In a ball mill used as secondary grinding, for example, even small balls have sufficient energy to break particles through tumbling or rolling due to their relatively large diameter and heavy mass. However, it is the bead kinetic energy (high speed with a necessary mass) that breaks particles in a stirred mill. Where the mass of fine bead is low, it may not exert sufficient SI onto particles at a certain circumference speed. On the other hand, the mill power draw (bead viscosity) decreases due to the existence of small beads, as explained by “the ball-bearing effects” theory. This suggests that Chong, Christiansen, and Baer’s (1971) findings for bimodal suspension apply to grinding beads in a

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90 80 70 60 50 40 30 20 Agitator Power 3 7 kW Agitator Speed 1,500 rpm

10 0 0

20

40

60

80

100

80

100

Fine Bead Fraction (0.5 mm), %

FIGURE 10

Product size P80 versus grinding bead size

Particle-Size Distribution Coefficient, b

1.50 1.40 1.30 1.20 1.10 1.00 0.90 0.80 0

20

40

60

Fine Bead Fraction (0.5 mm), %

FIGURE 11

Particle distribution modulus versus percent fine bead

stirred mill. When beads move at a high speed, the fine beads behave as bearings and can alter the directions of coarser ones adjacent to them, thus buffering and lowering the kinetic energy of coarse beads. The consequence is that the impact and compression force for breaking down particles from larger beads is weakened, and likely accounts for the main breakage mechanisms in stirred mills. CONCLUSIONS

Monosized and bimodal bead distributions are studied in a stirred bead mill for grinding quartz suspensions. The effects of bead size and composition on particle breakage rate, product size, and size distribution, as well as the mill power consumption are investigated and evaluated.

EFFECTS OF BEAD SIZE ON ULTRAFINE GRINDING IN A STIRRED BEAD MILL

97

6.0 5.5

Net Power on Slurries Total Power on the Shaft Power on Beads Only

5.0

Power Draw, kW

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0

20

40

60

80

100

Fine Bead Fraction (0.5 mm), %

FIGURE 12

Agitator power versus percent fine bead

At a constant agitator speed for monosized grinding beads, increasing bead size increases mill power consumption and thus results in a fast particle breakage rate, fine product size, and narrow size distribution. When the mill power draw is kept constant, there exist optimum bead sizes for certain feed sizes with respect to particle breakage rate, product size, and size distribution. The optimum ratio of bead size to feed size is confirmed at about 20:1. Similar to suspensions, bimodal bead viscosity (power consumption) is lower than monosized beads. The fine beads existing in grinding media have negative effects in particle breakage rate, product size, and size distribution due to ball-bearing effects and are not in favor of grinding efficiency for stirred mills. REFERENCES

Bicerano, J., J. Douglas, and D. Brune. 1999. Model for the viscosity of particle dispersions. Journal of Macromolecular Science Reviews C39:561–642. Blecher, L., and J. Schwedes. 1996. Energy distribution and particle trajectories in a grinding chamber of a stirred ball mill. International Journal of Mineral Processing 44–45:617–627. Chong, J.S., E.B. Christiansen, and A.D. Baer. 1971. Rheology of concentrated suspensions. Journal of Applied Polymer Science 15:2007–2021. Clarke, B. 1967. Rheology of coarse settling suspensions. Transactions of the Institute of Chemical Engineering 45:T251–T256. Fadhel, H.B., and C. Frances. 2001. Wet batch grinding of alumina hydrate in a stirred bead mill. Powder Technology 119(2–3):257–268. Furnas, C.C. 1929. Pages 75–79 in Flow of Gases through Beds of Broken Solid. Bulletin 307. Washington, DC: U.S. Bureau of Mines. Furnas, C.C., and F.O. Anderegg. 1931. Grading aggregates. Industrial and Engineering Chemistry 23(9):1052–1064.

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Herbst, J.A. 1978. Fundamentals of fine and ultrafine grinding in a stirred ball mill. Pages 452–470 in Proceedings of the International Powder and Bulk Solids Handling Conference. Chicago, IL: Industrial and Scientific Conference Management. Kwade, A. 1999. Wet comminution in stirred media mills—research and its practical application. Powder Technology 105:14–20. Kwade, A., and J. Schwedes. 2002. Breaking characteristics of different materials and their effect on stress intensity and stress number in stirred media mills. Powder Technology 122:109–121. Mankosa, M.J., G.T. Adel, and R.H. Yoon. 1986. Effect of media size in stirred ball mill grinding of coal. Powder Technology 49(1):75–82. Stehr, N., R.K. Mehte, and J.A. Herbst. 1987. Comparison of energy requirement for conventional and stirred ball milling of coal-water slurries. Coal Preparation 4:209–226. Wang, Y., and E. Forssberg. 1997. Ultra-fine grinding and classification of minerals. Pages 203–214 in Comminution Practices. Edited by S.K. Kawatra. Littleton, CO: SME.

Specific Energy Consumption, Stress Energy, and Power Draw of Stirred Media Mills and Their Effect on the Production Rate Arno Kwade*

ABSTRACT

Stirred media mills are capable of grinding various products down to sizes in the nanometer range. The specific energy required to achieve a certain product quality mainly depends upon the stress energy and can be predicted for different sets of operating parameters using a stress model and grinding tests. Moreover, the effect of several operating parameters on the power draw of stirred media mills can be described by the relation between the power number and the Reynolds number. By combining the relations for specific energy and power draw, the influence of important operating parameters on production rate can be predicted. Moreover, the production rate of the grinding process can be increased and maximized. Examples will show that, depending upon the product and the formulation, different operating parameters are important for increasing the production rate of the grinding process. INTRODUCTION

Currently, the selection, design, and sizing of grinding and dispersion processes are based mainly on practical experience and empirical relations. For determining optimum operating parameters and the related production rate of a mill, usually several grinding or dispersing tests have to be carried out. But still production capacity cannot be determined precisely for operating conditions not tested previously. A stirred media mill is used most economically if the required product quality is produced with maximum production rate at the lowest possible operating costs. The main parameters influencing the production rate m· P are given by the following expression: P GC m P,Ch m· P = ------------ = -------t Ch Em

(EQ 1)

where mP,Ch is the solids mass or pigment mass of the charge; tCh is the grinding or dispersion time of the charge; PGC is the power consumed inside the grinding chamber (motor power minus no-load power); and Em is the specific energy required for a certain product quality. The production rate is proportional to the power consumed inside the * Institute for Particle Technology, Technical University of Braunschweig, Germany 99

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grinding chamber of the stirred media mill and is inversely proportional to the specific energy, which is necessary to produce the required product quality. The power consumed inside the grinding chamber is the overall power draw decreased by the no-load power. The maximum production rate is gained if the following are true: ƒ The power draw has a maximum value. ƒ The needed specific energy for the production of the required product quality is

minimal. In order to increase the production rate efficiently, it has to be known which operating parameters have the greatest effects on production rate. To derive a relation between the production rate and the operating parameters, it must be known how the power draw and the specific energy requirement for the production of a certain product quality are affected by the different operating parameters. The power draw of a certain operation condition can be determined by applying the power characteristics of the stirred media mill (i.e., the relation between power number and Reynolds number). The dependency of the specific energy on important operating parameters can be determined using a so-called stress model, which focuses on the elementary processes taking place in grinding and dispersion processes. MODEL OF STRESSING PAR TICLES IN A MILL

A so-called “stress model” was developed that describes the physical processes in mills (e.g., the stressing and grinding of particles). Generally, there are two perspectives from which stressing and grinding of particles can be observed (Kwade 2002; Kwade 2004). One perspective is from the view of the product particle (i.e., how intensively and how often the particle is stressed). The other perspective is from the view of the mill (i.e., how strongly and how frequently the mill can stress particles). The basic principle of the product-related stress model is that for a given feed particle, the product quality and fineness achieved in a grinding or dispersing process is determined by ƒ Type of stress event including particle configuration (e.g., compression and shear,

impact) ƒ How often each feed particle and its resulting fragments are stressed and, thus, by

the number of stress events of a feed particle, SNF ƒ How high the specific energy or specific force at each stress event is and, thus, by the

stress intensity at each stress event, SI In actual comminution processes, the feed particles and the resulting fragments are not stressed equally often with the same stress intensity; the number of stress events and the intensity of these stress events is different for each feed particle. Thus, the number of stress events and the stress intensity can only be characterized by distributions, not by single numbers. Both distributions, particularly the magnitude of SNF and SI, depend on the operating parameters. The width of the distribution of the stress number is determined primarily by the residence time distribution of the particles in the mill. The width of the distribution of the stress intensity depends mainly on how the stress energies differ locally over time. The exact determination of these distributions is difficult but should be possible using numerical methods in the future. For an engineering approach, in most cases it is sufficient to use a characteristic value of the stress intensity instead of an entire distribution (Kwade, Blecher, and Schwedes 1996; Kwade 1996, 1998, 1999). It could be shown that as long as the following are true—only one particle is sufficiently stressed; the tangential velocity of the grinding media are proportional to the tip speed of the discs; the viscosity of the suspension is not too high; the young modulus of the product

Specific Surface ΔS m, m 2/g Disintegration Degree, %

ENERGY CONSUMPTION, STRESS ENERGY, AND POWER DRAW OF STIRRED MEDIA MILLS

101

n inutio omm

lC Rea

Disagglomeration and Disintegration

0.1

1

10

100

Relative Stress Intensity SI/SIopt [–]

FIGURE 1

Specific surface and disintegration degree as function of relative stress intensity

material is low compared to the young modulus of the grinding media; and the geometry and size of the mill is not changed—then the stress intensity in stirred media mills can be described by the following expression called stress energy of the grinding media, SEGM: 3

2

SE v SE GM = d GM ˜ v t ˜ U GM

(EQ 2)

where dGM is the grinding media size; vt is the stirrer tip speed; and UGM is the grinding media density. The stress energy of the grinding media, SEGM , is a measure for the maximum stress energy inside the grinding chamber. As long as the geometry and size of the grinding chamber are constant and, thus, the stress energy distribution does not change, it is also a measure for the mean stress energy inside the grinding chamber. If the geometry and/or the size of the grinding chamber changes, the change in the stress energy distribution has to be taken into account (Stender, Kwade, and Schwedes 2002). The stress intensity determines how effective the specific energy transferred to the product at one stress event is transposed into product quality and product fineness. The relationship between increase in product quality and stress intensity depends on the breakage characteristics of the grinding material. The principal effect of the stress intensity on the product quality follows from Figure 1 for the case that single particles are stressed. In Figure 1, the product quality (e.g., specific surface) is depicted as the function of the relative stress intensity. The relative stress intensity is defined as the ratio of stress intensity SI to the optimum stress intensity SIopt . The stress intensity has an optimum value and the energy utilization, a maximum value EUmax , when the energy is just sufficient to break a particle, to disagglomerate agglomerate or to disintegrate a microorganism. If the stress intensity is smaller (SI/SIopt < 1), the product fineness increases with the stress

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intensity for all three applications (with different slopes). The slope of the curve depends on the material under investigation. However, if the stress intensity is larger (SI/SIopt > 1), there are obvious differences. In a so-called “ideal disagglomeration” process, the agglomerates are initially broken to their primary particles at a certain stress intensity. By “ideal disagglomeration,” agglomerates can also be disagglomerated by abrasion of single primary particles from the agglomerate. In the case of ideal disagglomeration, the product quality is constant because the agglomerate is already fully disagglomerated at the stress intensity, called optimum stress intensity in this paper. The same holds true for the disintegration of microorganisms if all microorganisms were already disintegrated at optimum stress intensity. During grinding crystalline materials or during “nonideal” disagglomeration, the specific surface will further increase with increasing stress intensity, but usually at a lower slope because the energy utilization is less than at the optimum stress intensity. The more difficult the feed material is to grind, the greater the slope of the curve. Therefore, two boundary cases can be defined: 1. The upper limit can be assumed to be the case when the product quality (e.g.,

new surface area) increases proportionally to the stress intensity. In this case, the slope of the curve is 1. 2. The lower limit is equal to an ideal disagglomeration process, in which the size of

the fragments does not depend on the stress intensity, as long as the stress intensity is higher than the optimum stress intensity. In this case, the slope of the curve and the value of exponent is 0. For SI > SIopt , the following equation can be stated: SI a 'S m, A v § ----------- · © SI opt ¹

(EQ 3)

with a = 0 for ideal disagglomeration/disintegration 0 < a < 1 for grinding crystalline materials If the energy utilization (EU) is used to characterize the effect of the stress intensity, Figure 2 follows from Figure 1. The EU is defined as the ratio of the newly produced specific surface ǻSm to the specific energy Em required to produce ǻSm. In general, the energy utilization also can be considered as the ratio of increase in product quality to the specific energy required to produce the increase in product quality. If a single particle is stressed once, the stress intensity corresponds to the specific energy for stressing the particle, so that in this case, the energy utilization is equal to ǻSm/SI. At the optimum stress intensity SIopt, the energy utilization has its maximum value EUmax at which a certain specific surface can be produced with a minimum of specific energy. In Figure 2 the relative energy utilization EU/EUmax is plotted versus the relative stress intensity SI/SIopt. At the optimum, both ratios are 1. To the left of the optimum, the energy utilization increases with increasing stress intensity for all three applications in a similar, but not equal, mode. To the right of the optimum, the relative energy utilization decreases. In the case of disagglomeration and disintegration, the slope of the curve is –1, because the stress intensity or specific energy, respectively, added to the optimum stress intensity is not used at all and does not affect the product fineness or the disintegration rate. Therefore, the energy utilization is inversely proportional to the specific energy of a single stress event and, thus, to the stress intensity. If a single crystalline particle is stressed to the right of the optimum stress intensity, the relative increase in product quality is smaller than the corresponding relative

ENERGY CONSUMPTION, STRESS ENERGY, AND POWER DRAW OF STIRRED MEDIA MILLS

103

Relative Energy Utilization EU/EUmax [–]

4

1 Rea l Co

mm

Di

sa

gg lom

er at ion

inut ion

an

d

Di

sin

0.1

te

gr at

ion

0.01 0.1

1

10

100

Relative Stress Intensity SI/SIopt [–]

FIGURE 2

Relative energy utilization as a function of the relative stress intensity

increase in stress intensity, so that the EU decreases to the right of the optimum. The more difficult the feed material is to be ground, the smaller the decrease in energy utilization. The upper limit is probable if the energy utilization stays constant while the stress intensity increases. Thus, for SI > SIopt, the following can be stated: EU SI a–1 --------------- v § ---------- · © EU max SI opt ¹

(EQ 4)

with a = 0 for disagglomeration action /cell disruption 0 < a < 1 for real-time grinding R E L A T I O N B E T W E E N S P E C I F I C E N E R G Y, S T R E S S E N E R G Y, AND STRESS NUMBER

The total energy transferred to the product particles can be determined by the summation of all stress energies SEi of the individual stress events. The stress energy is a measure for the stress intensity and independent of the mass of the product stressed between two grinding media. The sum of all stress energies is again equal to the product of the number of stress events and a mean stress energy. The specific energy, Em,P, actually transferred to the product particles is obtained by relating the total energy to the total mass of the product. Due to friction and other losses, the specific energy consumed by the comminution device or mill, Em,M, is not equal but proportional to the specific energy, Em,P, transferred to the product particles. If the losses are taken into account by an energy transfer factor, QE , the two characteristic numbers SNM = tC · SFM and SE can be related to the specific energy consumed by the mill, as shown in the following:

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SN M

¦ SEi

SN M ˜ SE i=1 --------------- = ---------------------- = E m P = Q E ˜ E m M m P tot m P tot

(EQ 5)

where SEi is the stress energy at stress event i; SNM is the total number of stress events to achieve a certain product quality; Em,P is the specific energy transferred to the product particles; QE is the energy transfer factor of the mill; and Em,M is the total specific energy consumption of the mill. The specific energy transferred to the product Em,P is also named effective specific energy. This specific energy is the part of the total energy consumption of the mill, which is actually used for stressing the particles. Under the assumption of a constant shape of the stress frequency distribution and the stress energy distribution based on Equation (1), the product quality of a certain product mass mP is already fixed if two of the three parameters—total number of stress events, SNM, mean stress energy, SE , and specific energy transferred to the product, Em,P—are set. Thereby Em,P is fully determined if the energy transfer factor, QE, and the specific energy consumed by the mill, Em,M, are known. The energy transfer factor is among others proportional to the filling ratio of the grinding media, MGM because the portion of the energy that can be used for comminution and dispersing inside the grinding chamber is proportional to the part of the volume filled with grinding media (Kwade 2002, 2004). In addition, the ratio of surface area to grinding chamber volume affects the energy transfer factor (Stender, Kwade, and Schwedes 2002) because energy is lost at the grinding chamber wall due to friction between the grinding media and the wall. APPLICATION OF THE STRESS MODEL

In order to verify the stress model, batch grinding tests with limestone (median size approximately 60 Pm) in a stirred media mill with disc-stirrer geometry (see Figure 3) under different operational conditions (different sizes and densities of the grinding media as well as different tip speeds) were carried out (Kwade, Blecher, and Schwedes 1996; Kwade 1996; Kwade and Schwedes 1997). In Figure 4, the specific energy used to produce a median size of 2 Pm is shown as function of the stress intensity of the grinding media, SEGM, for different sets of operating parameters. The grinding media size varied from 399 Pm to 4,000 Pm, the stirrer tip speed from 6.4 to 12.8 m/s, and the grinding media density from 2,894 kg/m3 to 7,550 kg/m3. It can be seen that the relation between specific energy required to obtain a median size of 2 Pm and stress energy can be described by one fitted curve. Thus, the characteristic number SEGM can be used to describe the effect of the operating parameters’ diameter and density of the grinding media as well as stirrer tip speed on the specific energy required to obtain a certain product fineness (here, x50 = 2 Pm) in a combined form. From the curve, an optimum stress energy can be ascertained at which a certain product quality can be achieved with a minimum of specific energy. If the operating parameters’ size and density of the grinding media as well as stirrer tip speed are chosen in a way that results in optimum stress energy, the specific energy requirement for a certain grinding task is the lowest. As Figure 5 shows, the influence of stirrer tip speed as well as size and material of the grinding media on the result of different comminution processes can be described well by two of the three parameters—stress number, stress intensity, and specific energy. The relations among product quality (fineness or disintegration rate), stress intensity, and specific energy depend on the breakage behavior of the material. If the relations among product quality, stress intensity, and specific energy are known, statements regarding the breakage characteristics and comminution behavior of the material can be made.

ENERGY CONSUMPTION, STRESS ENERGY, AND POWER DRAW OF STIRRED MEDIA MILLS

FIGURE 3

105

Schematic drawing of a stirred media mill with disc-stirrer geometry

1,000 ρGM [kg/m3] = 2,894 7,550 vt [m/s] = 6.4 vt [m/s] = 9.6 vt [m/s] = 12.8 dGM [μm] = 399–4,000

kJ/kg

800

600

400

200 x50 = 2 μm ϕGM = 0.8 cm = 0.4

00 0.002

0.01

0.1

1

Stress Intensity SIGM [10–3 Nm]

FIGURE 4 Specific energy required for a median size of 2 μm as a function of stress energy (limestone)

10

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100

Em / Em,min [–]

Pigments [1] Yeast Cells SiO2 Aggregates Water-based Ink [17] Printing Ink Limestone Al2O3

x50 = 1 μm A = 60% x50 = 2 μm Cl = 140% T = 80% x50 = 2 μm x50 = 2 μm

10

1 0.8 0.5

1

100

10

1,000

SE/SEopt [–]

FIGURE 5 Specific energy related to the minimum specific energy as a function of the stress energy related to the optimum stress energy (constant product fineness or constant disintegration rate)

These relationships are illustrated by comparing comminution results of the following seven different materials: pigments (Stadler et al. 1990), yeast cells (Bunge 1992), synthetically produced SiO2 aggregates (median size of feed particles about 22 ȝm), water-based ink (Vock 1997), printing ink, limestone, and fused alumina (median size of feed particles about 33 ȝm; Becker, Kwade, and Schwedes 2001). The comminution behavior of the seven materials can be compared by looking at the influence of the stress intensity on the specific energy required for a certain product quality. Thus, in Figure 5, the ratio of the specific energy required for a certain product quality to the minimum specific energy required for the same product quality is presented as a function of the stress energy related to the optimum stress energy in a log–log diagram. The ratio SE/SEopt is equal to the ratio SI/SIopt since the mass of the product stressed at on stress event is eliminated by dividing the stress intensity by the optimum stress intensity. In Figure 5, only the results of measurements are shown, at which the stress intensity is approximately equal to or greater than the optimum stress intensity. The measurement values for the different materials can be described by different approximation curves, so that the specific energy required for a certain product quality depends more or less strongly on the stress intensity. The greatest influence of the stress intensity on the specific energy exists for the disagglomeration and the disintegration processes, where the measurement values can be described in a first approximation by a straight line with a slope of nearly 1. Therefore, above all, for a disagglomeration and a disintegration process, it is advisable that the stress intensity lie in the optimum range. For these two materials, the result of a single stress event is independent of the stress intensity as long as the stress intensity is higher than the optimum stress intensity. At a constant product quality, the stress number stays constant with increasing stress intensity, therefore, the specific energy consumption increases proportionally to the stress intensity.

ENERGY CONSUMPTION, STRESS ENERGY, AND POWER DRAW OF STIRRED MEDIA MILLS

TABLE 1

107

Values of exponent “a”

Material

Pigments

Yeast Cells

Synthetic SiO2

Waterbased Ink

Printing Ink

Limestone

Fused Alumina

1–a [–] a [–]

|1 0

1 0

0.77 0.23

|0.4 0.60

0.37 0.63

0.33 0.67

0.26 0.74

In the case of the synthetically produced SiO2 aggregates from SiO2, the slope of the straight line is slightly smaller than 1, so that the stress intensity already has a slight effect on the result of a stress event. Therefore, with increasing stress intensity, the aggregate is decomposed in smaller agglomerates or primary particles. The smallest slopes can be found for grinding limestone and fused alumina. In the case of these two materials, finer fragments are produced with increasing stress intensity. This effect is somewhat more distinct for fused alumina than for limestone, but the slope of the approximation curve is clearly greater than 0. For alumina, an increase in stress intensity is more effective regarding an increase in product quality than for the other materials. The relationships between the ratio of specific energy and minimum specific energy and the ratio of stress intensity and optimum stress intensity can be derived from Equations (2) and (3), if the product quality and, thus, the produced specific surface is set constant. At a constant specific surface, the ratio EU/EUmax corresponds to Em,min/Em, so that the following relation can be given for SE > SEopt: Em SE 1–a ---------------v § ------------- · E m min © SE opt ¹

(EQ 6)

with a = 0 for disagglomeration/disintegration 0 < a < 1 for grinding crystalline materials Therefore, the specific energy required for a certain product quality is a function of the stress energy, SE. From Figure 5, the values of exponent “a” can be found for the seven investigated materials. Exponent “a” determines the slope of the curves shown in Figures 1 and 2. The values are shown in Table 1. It can be seen that the value of exponent “a” increases with the grinding resistance of the material. Summing up the results in Figure 5 and in Table 1 shows that, depending upon the feed material, the specific energy required for a certain product quality relies more or less on the stress energy. The strongest influence of the stress energy on the specific energy exist for pure disagglomeration and disintegration. In the case of disagglomeration and disintegration, attention should be given to an optimum setting of the stress energy, because otherwise the specific energy requirement becomes needlessly high and, thus, at constant power input, the production capacity becomes needlessly low. DETER MINATION OF POWER DRAW

The power draw can be determined by simple empirical equations or by a relation between dimensionless numbers. For stirred media mills, the relation between power number and Reynolds number will be used to determine the power draw as a function of the most important operating parameters: The exact description of the three-dimensional fluidflow field in the grinding chamber of a stirred media mill is currently impossible due to the complexity of fluid–mechanical equations. Thus, the power draw is estimated by suitable models developed in stirring technology. The basis of this model is the transfer of power draw behavior of geometrically similar stirring systems (in this case, stirred

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103

d/D = 0.8 L/D = 2.5 Z =8 102

1

Ne =

101

2

100

3

10–1 100

101

102

105

104

103

106

Re =

FIGURE 6

Relation between Newton number and Reynolds number without grinding media

102 ϕGM = 0.90

Grinding Media: Glass dGM = 1 mm

ϕGM = 0.65

Ne =

101

100

ϕGM = 0.35

ϕGM = 0.0

10–1

102

103

104

105

106

Re =

FIGURE 7 Relation between power number and Reynolds number of stirrer for different filling ratios of grinding media

ENERGY CONSUMPTION, STRESS ENERGY, AND POWER DRAW OF STIRRED MEDIA MILLS

TABLE 2

109

Calculation of power number Flow Region

Reynolds Number

Power Number

Laminar region Lower transition region Upper transition region Lower turbulent region Upper turbulent region

ReR < 1.2 · 102 1.2 · 102 < ReR < 8 · 103 8 · 103 < ReR < 3.5 · 104 3.5 · 104 < ReR < 2 · 105 ReR > 2 · 105

Ne0 = Klaminar · ReR–1 Ne0 = Ktransition,A · ReR–0.5 Ne0 = Ktransition,B · ReR–0.3 Ne0 = Kturbulent,A · ReR–0.2 Ne0 = Kturbulent,B

media mills) by means of two characteristic numbers: the power number, sometimes called the Newton number, Ne; and the Reynolds number, ReS. The power number and Reynolds number are defined as follows: Power number:

P GC Ne = ----------------------------5 3 d R n U product

Reynolds number:

nd U product Re S = -------------------------K product

(EQ 7)

2

(EQ 8)

where PGC is the power consumed inside the grinding chamber; d is the diameter of stirrer discs; n is the number of revolutions; Uproduct is the density of product slurry; and Kproduct is the kinematic viscosity of the product slurry. In analogy to stirring technology, it is assumed that the power number only depends on the Reynolds number. Tests with a Newtonian fluid and grinding media were carried out in a stirred media mill with disc-stirrer geometry to obtain a theoretical relation between the Newton number and the Reynolds number (Stehr 1982; Weit 1987). The results are shown in Figure 6. In the case of an operation with grinding media, the question arises as to whether the grinding media belongs to the suspension or to the mill itself. If the grinding media belongs to the suspension, for the physical characteristics of the density and the viscosity, the values of the grinding media–product suspension must be used. In this case, the relationship between the power and Reynolds numbers shown in Figure 6 is also valid if the mill is operated with grinding media. If the grinding media are considered to be part of the mill (like baffles in a stirred vessel), the physical characteristics of the product suspension can be taken for the suspension density and the suspension viscosity. In this case, for each filling ratio of the grinding media, for each grinding media density, and for each grinding media size, a different relationship between the Newton and Reynolds numbers exist. Figure 7 shows the power number as function of the Reynolds number for a mill with disc stirrer which was operated without grinding media (continuous line) and with three different filling ratios of grinding media. As described previously, for each filling ratio of the grinding media, a different relationship between the power number and the Reynolds number exists. At a constant power number, the Newton number is the greater because of the higher filling ratio of the grinding media. In detail it can be seen that the curves for the operation with grinding media can be distinguished into five regions, each with a different slope instead of into three regions as in the operation without grinding media (see Table 2). If the equations for the power and the Reynolds numbers are put in the equations given in Table 3 (right column), for each region of the Reynolds number, a different relationship arises between the power draw and the parameter number of revolution or stirrer

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TABLE 3

ADVANCED COMMINUTION TECHNOLOGIES

Exponents to determine power draw as a function of important operating parameters

Influencing parameter Exponent Low number of revolutions, high viscosity (ReR < 105) High number of revolutions, low viscosity (ReR > 105)

MGM X 2.8 2.2

vt 3+Y 2.5 3

Y –0.5 0

USusp 1+Y 0.5 1

KSusp –Y 0.5 0

dS 2+Y 1.5 2

dGM Z d0 t0

tip speed, density of the product suspension, viscosity of the product suspension, and stirrer diameter: 2

§ n ˜ d S ˜ U Susp· P GC --------------------------------¸ v ¨ ----------------------------3 5 K Susp ¹ d S ˜ n ˜ U Susp © Ÿ P GC v n

3+Y

5+2Y

˜ dS

1+Y

–Y

3+Y

˜ U Susp ˜ K Susp v v t

Y

(EQ 9)

2+Y

˜ dS

1+Y

–Y

˜ U Susp ˜ K Susp

where Y Y Y Y Y

= = = = =

–1 for ReS < 1,2 · 102 –0.5 for 1.2 · 102 < ReS < 8 · 103 –0.3 for 8 · 103 < ReS < 3.5 · 104 –0.2 for 3.5 · 104 < ReS < 2 · 105 0 for ReS > 2 · 105

In the following paragraphs, the relationships between the power consumption and the operating parameters’ filling ratio of the grinding media, MGM, stirrer tip speed, vt, density of the product suspension, UP, viscosity of the product suspension, KSusp, viscosity of the product suspension, KP, and the stirrer diameter, ds, are discussed individually. The symbol of the exponents comes from the following equation: X

3+Y

P GC v M GM ˜ v t

1+Y

–Y

2+Y

˜ U Susp ˜ K Susp ˜ d S

Z

˜ d GM

(EQ 10)

The exponent Y depends on the Reynolds number and results from the relation between the power number and Reynolds number. The exponents X and Z can only be estimated from experimental results. The effect of the filling ratio of grinding media on the relation between power number and Reynolds number is shown in Figure 7, in which the filling ratio was varied from 0 to 0.9. The density and viscosity of the pure Newtonian fluid were used to calculate the power and Reynolds numbers. Thus, the analog to baffles in stirred vessels in the grinding media are considered to be part of the grinding chamber. If the grinding media are considered to be part of the suspension, the exact influence of the filling ratio of the suspension viscosity must be known, which currently is not possible. The power number, and thus the power draw, increases with increasing filling ratio of grinding media for a constant Reynolds number. All curves look similar. The curves approach a horizontal line in the turbulent region. This indicates that the power draw does not change in the turbulent region. From the shape of the curve and the above equations, it follows that depending on the number of revolutions and the product viscosity, the exponent X of the filling ratio MGM is in the range of 2.8 for lower Reynolds numbers and 2.2 for higher Reynolds numbers. The values for the exponent are valid for mills with a disc-stirrer geometry. Eventually, other mill geometries may have other values for the exponents.

ENERGY CONSUMPTION, STRESS ENERGY, AND POWER DRAW OF STIRRED MEDIA MILLS

111

Practical experiences show that the influence of grinding media size on power draw is not uniform. The power draw remains either constant, decreases, or increases when the media size is changed (Weit 1987). For low Reynolds numbers (low turbulences, high viscosity), the power draw is higher for smaller grinding media. An explanation for this behavior can be different mechanisms of power transfer from the stirrer to the grinding media. For example, at low Reynolds numbers, the power draw is determined mainly by the effect of the media size on the viscosity of the grinding media–product suspension, which increases with smaller media sizes. At high Reynolds numbers, the hits between the grinding media are more important for the power consumption of the mill. Therefore, in principle, the exponent is less than 0 at low Reynolds numbers and greater than 0 at high Reynolds numbers. The dependency of the power draw PGC on the operating parameters can be summarized by Equation (10) and Table 3. Exponent values for Reynolds numbers range between 8 · 103 and 2 · 105, and thus values for medium stirrer tip speeds as well as for high tip speeds and simultaneously high viscosities are between the values given in Table 3. In the case of low stirrer tip speeds and very high viscosities, the exponent values can also lie outside the range given in the table (i.e., –1 < Y < –0.5). The actual value of the exponent Z for the grinding media size dGM must be determined experimentally. The tendency is for the exponent to be negative at small Reynolds numbers (especially in the laminar region) and positive at higher Reynolds numbers. The simplest way is to carry out two or three grinding tests with different grinding media sizes. All other parameters have to be held constant. Grinding tests with different grinding media sizes are needed for the determination of the optimum grinding media size and, thus, should always be carried out. DETERMINATION OF PRODUCTION RATE

As described in the introduction to this paper, stirred media mills are used most economically if the required product quality is produced at the maximum production rate and lowest possible operating costs. The relation between the production capacity and production rate, respectively, m· P , is given by the following relation (see Equation [1]): P GC m P Ch m· P = ------------- = -------t Ch Em

(EQ 11)

The production capacity is proportional to the power consumed inside the grinding chamber of the stirred media mill and inversely proportional to the specific energy that is needed to produce the required product quality. The relation between the power draw and important operating parameters is given by Equation (10). The dependency of the specific energy on the most important operating parameters can be achieved by rearranging Equation (6): E m min - ˜ SE 1 – a E m = --------------1 –a SE opt

(EQ 12)

The quotient Em,min/SEopt1–a is only constant and, thus, is independent of all operating parameters if the energy transfer coefficient QE is constant. If the energy transfer coefficient QE changes, the minimum specific energy Em,min that is transferred into the grinding chamber also changes. Therefore, it is advantageous to use the ratio Em,P,min/QE instead of the specific energy Em,min that is transferred into the grinding chamber. The

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minimum specific energy Em,P,min is the minimum specific energy that is actually transferred to the product particles and, thus, can be considered to be constant even at different operating conditions. By the energy transfer factor, QE, the effect of operating parameters, such as the filling ratio of the grinding media on the production capacity, can be considered: The energy transfer coefficient is proportional to the filling ratio of the grinding media (Kwade 2004). Therefore, the relation for the specific energy transferred to the grinding chamber results if the stress energy of the grinding media, SEGM (see Equation [2]), is used as a measure for the stress energy: 3

Em

1 –a

2

1 –a E m P min SE 1 –a  d GM ˜ v t ˜ U GM SE - ˜ ------------- = C ˜ ------------= ------------------v ---------------------------------------------1 –a Q Q M GM E E SE opt

(EQ 13)

The dependency of the production capacity on the most important operating parameters results if Equation (13) and Equation (10) are inserted into Equation (1): X

3+Y

1+Y

–Y

2+Y

Z

P–P M GM ˜ v t ˜ U Susp ˜ K Susp ˜ d S ˜ d GM m· P = --------------0 v ---------------------------------------------------------------------------------------1 –a 3 2 Em  d GM ˜ v t ˜ U GM

(EQ 14)

Equation (14) is the basic equation for determining the effect of the most important operating parameters on the grinding result. How much the influence of the operating parameters on the production capacity is affected by the product and formulation of the grinding or dispersion process is shown by the following two examples. Example 1: Dispersion of an agglomerate at a high viscosity and relatively low stirrer tip speed in a mill with disc-stirrer geometry. In the case of a high viscosity and relatively low stirrer speed, it can be concluded that the mill is operated in the lower transition region. Moreover, it is assumed that the grinding media size has no effect on the power draw in this flow regime. The exponent “a” is 0 in case of disagglomeration. Therefore, the variables in Equation (14) have the values shown in Table 4. 2.8+1

2.5

0.5

0.5

1.5

0

0.5

M GM ˜ v t ˜ U Susp ˜ K Susp ˜ d S ˜ d GM 3.8 0.5 U Susp 0.5 1.5 –3 m· P v ----------------------------------------------------------------------------------------= M GM ˜ v t ˜ ----------˜ K Susp ˜ d S ˜ d GM (EQ 15) 1–0 3 2 U GM  d GM ˜ v t ˜ U GM Therefore, in the case of dispersing an agglomerate at high viscosity and relatively low stirrer tip speed, in addition to a change in the filling ratio of the grinding media, a change in the grinding media size has the greatest effect on the production capacity. Thus, the production capacity can be increased most effectively by changing the filling ratio and the size of the grinding media. Therefore, the stirrer tip speed has only a minor effect on the production capacity. If the viscosity would be very high and, thus, the mill would be operated in the laminar flow regime, there would be nearly no effect of the stirrer tip speed on the production capacity. Example 2: Real grinding of a hard ceramic raw material at low viscosity and relatively high stirrer tip speed in a mill with disc-stirrer geometry. In the case of a low viscosity and relatively high stirrer speed, it can be concluded that the mill is operated in the turbulent flow regime. Moreover, it is assumed that the power draw is proportional to the grinding media size with a power of 0.5, so that the exponent Z is equal to 0.5. The exponent “a” is assumed to be 0.75, which is close to the value of the 0.74 found for fused alumina. Therefore, the variables in Equation (14) have the values shown in Table 5.

ENERGY CONSUMPTION, STRESS ENERGY, AND POWER DRAW OF STIRRED MEDIA MILLS

TABLE 4

Values of the exponents for disagglomeration at high viscosities and low stirrer speed

Variable/exponent Operating parameters affected Value

TABLE 5

113

X MGM 2.8

Y vt, USusp, KSusp, dS –0.5

Z dGM 0

a dGM, vt, UGM 0

Values of the exponents for disagglomeration at high viscosities and low stirrer speed

Variable/exponent Operating parameters affected Value

2.2+1

3

1

X MGM 2.2

0

2

Y vt, USusp, KSusp, dS 0

Z dGM 0.5

a dGM, vt, UGM 0.75

0.5

M GM ˜ v t ˜ U Susp ˜ K Susp ˜ d S ˜ d GM 3.2 2.5 U Susp 2 – 0.25 m· P v ---------------------------------------------------------------------------------= M GM ˜ v t ˜ ----------˜ d S ˜ d GM 1–0.75 0.25 3 2 U GM  d GM ˜ v t ˜ U GM

(EQ 16)

Therefore, in the case of grinding a raw ceramic material at low viscosity and relatively high stirrer tip speed, in addition to a change in the filling ratio of the grinding media, a change in the stirrer tip speed has the greatest effect on the production capacity. Thus, the production capacity can be increased most effectively by changing the filling ratio of the grinding media and the stirrer tip speed. Therefore, the grinding media size has only a minor effect on the production capacity. If the resistance against grinding would be even higher (i.e., exponent “a” would be in the range of 0.8), there would be nearly no effect of grinding media size on the production capacity. The two examples show how different the effects of the various operating parameters on the production capacity and on the power draw can be. This is particularly valid for the effect of the stirrer tip speed and the grinding media size. How the different operating parameters affect the production capacity is always a function of the product and formulation of the grinding or dispersion process under consideration. Therefore, it is not surprising that the influences of the parameters’ stirrer tip speed and grinding media size on the grinding time and mean residence time can be described very differently among the various literature. The effect of the filling ratio of the grinding media is always the only independent factor on the product and formulation of the grinding or dispersion process. CONCLUSIONS

The effect of the important operating parameters on the production rate of stirred media mills can be determined by using models for stressing the particles and for the power draw of the mill. For different products and formulations, the relation between the production rate and the different operating parameters show how sensitive the operating parameters are regarding the production rate: Two examples of different products and formulations reveal that the different operating parameters can have totally different effects: In the case of dispersing agglomerates at high viscosities and low tip speeds, in addition to the filling ratio of the grinding media, the grinding media size has a great effect of the production rate, whereas the stirrer tip speed has only a small effect. Therefore, in the case of real grinding of a hard ceramic raw material, in addition to the filling ratio of the grinding media, the stirrer tip speed is very important, whereas the grinding media size has only a minor effect.

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Moreover, using the relations for the determination of the specific energy, the power draw and the production rate of the mill performance for operating conditions that were not tested before can be determined as long as the stress energy is greater than the optimum stress energy. By that, the production rate can be optimized so that the capacity is as high as possible. REFERENCES

Becker, M., A. Kwade, and J. Schwedes. 2001. Stress intensity in stirred media mills and its effect on specific energy requirement. International Journal of Mineral Processing 61:189–208. Bunge. 1992. Mechanischer Zellaufschluß in Rührwerkskugelmühlen. Ph.D. dissertation. Braunschweig, Germany: Technical University of Braunschweig. Kwade, A. 1996. Autogenzerkleinerung von Kalkstein in Rührwerkmühlen. Ph.D. dissertation. Braunschweig, Germany: Technical University of Braunschweig. ———. 1998. Wet comminution in stirred media mills—research and its practical application. Pages 23–32 in Preprints 9th European Symposium on Comminution, Albi, France. Frankfurt, Germany: European Federation of Chemical Engineering. ———. 1999. Wet comminution in stirred media mills—research and its practical application. Powder Technology 105:14–20. ———. 2002. Mill selection and process optimization using a physical grinding model. In Preprints 10th European Symposium on Comminution, Heidelberg, Germany. Frankfurt, Germany: European Federation of Chemical Engineering. ———. 2004. Mill selection and process optimization using a physical grinding model. International Journal of Mineral Processing 74S:93–101. Kwade, A., L. Blecher, and J. Schwedes. 1996. Motion and stress intensity of grinding beads in a stirred media mill. Part II: Stress intensity and its effect on comminution. Powder Technology 86(1):69–76. Kwade, A., and J. Schwedes. 1997. Wet comminution in stirred media mills. KONA 15:91–101. Stadler, N., R. Polke, J. Schwedes, and F. Vock. 1990. Naßmahlung in Rührwerksmühlen. Chemie-Ingenieur-Technik 62(11):907–915. Stehr, N. 1982. Zerkleinerung und Materialtransport in einer Rührwerkskugelmühle, Ph.D., dissertation. Braunschweig, Germany: Technical University of Braunschweig. Stender, H.H., A. Kwade, and J. Schwedes. 2002. Stress energy distribution in different stirred media mill geometries. In Preprints 10th European Symposium on Comminution, Heidelberg, Germany. Frankfurt, Germany: European Federation of Chemical Engineering. Vock, F. 1997. Lackherstellung. Termen, Switzerland: Verlag CC Press. Weit, H. 1987. Betriebsverhalten und Maßstabsvergrößerung von Rührwerkskugelmühlen, Ph.D., dissertation. Braunschweig, Germany: Technical University of Braunschweig.

AG/SAG Mill Circuit Grinding Energy Requirement—How to Predict It from Small-Diameter Drill Core Samples Using the SMC Test Stephen Morrell*

ABSTRACT

The SMC (semiautogenous mill comminution) test has been developed to provide a rockbreakage description that can be used to predict autogenous grinding (AG) and semiautogenous grinding (SAG) mill performance. The test has been specifically designed to be usable in situations where only limited quantities of rock samples are available (e.g., small-diameter core). The test generates a Drop-Weight Index (DWi ) that can be used to estimate the throughput of AG and SAG circuits through a combination of power-based and model-based approaches. The model-based approach makes use of the direct relationship between the DWi and the JKTech drop-weight test rock-breakage parameters A and b. The power-based route uses correlations that have been developed between the DWi and the specific energies of a very wide range of operating AG and SAG circuits. Its usefulness is also shown to extend to rock mass characterisation in mining applications, as it also is correlated with the point load index/UCS (unconfined compressive strength). It is therefore ideally suited for mine-tomill studies where it can be simultaneously used to predict comminution circuit performance and to augment input to blast-fragmentation models. This makes it a valuable tool for ore-body profiling in greenfield, brownfield, and established operations. Recent investigations have shown that the DWi is also strongly related to high-pressure grinding roll (HPGR) performance. The ability of the test and associated equations to predict AG/SAG circuit-specific energy is demonstrated using a wide range of industrial data. This approach is compared to more traditional ones such as that of Bond, which is also reviewed in the context of its ability to predict AG/SAG circuit-specific energy and energy utilisation efficiency. INTRODUCTION

As little as 10 years ago, a “conventional” comminution circuit in the minds of many metallurgists would have conjured up pictures of crushing–ball mill or rod mill–ball mill circuits. Today, it is not common to find such circuits in operation, let alone being built. AG and SAG mills now dominate circuit design in gold and base metals applications and can rightfully lay claim to being conventional, leaving technologies such as high-pressure grinding rolls (HPRGs) the title of “new.” Regardless of how one categorises these technologies, * SMCC Pty. Ltd., Queensland, Australia 115

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today a much wider spectrum of proven equipment is available to the circuit designer than, say, 25 to 30 years ago. Although such choice may be seen as an improvement, it provides a particular challenge in terms of assessing which circuit is the most energy efficient and how in the first place the ore type should be meaningfully described in terms of its breakage characteristics. For ball milling, Bond’s ball work indices and equations have become the standard for describing grindability and efficiency. However, to date, there is no universal equivalent for autogenous/semiautogenous milling. The Julius Kruttschnitt Mineral Research Centre (JKMRC) drop-weight test parameters, A and b, have become popular when characterising rock for autogenous/semiautogenous milling, but they are specifically for use in autogenous/semiautogenous modeling and cannot be used for power-based calculations. In addition, the JK (JKTech) parameters are obtained from breaking relatively large quantities of material and hence cannot be obtained from small samples such as those provided by drill core. The recently developed Drop-Weight Index (DWi) may provide the solution. In this paper, the DWi will be reviewed in terms of how it relates to AG/SAG mill specific energy as well as to traditional strength measurements and the JK A,b parameters. The test used to determine the DWi (SMC test) is also described. In the course of this review, traditional ways of determining AG/SAG specific energy will be analysed. TR A D I T I O N A L A P P R O A C H T O C I R C U I T S E L E C T I O N

For AG/SAG mill circuit selection, piloting is still regarded as being the best option for estimating what the performance of the full-scale circuit will be. Tests are normally conducted under a range of conditions, the choice of circuit then being made on the basis of a number of criteria, which normally include factors such as minimum specific energy and/or maximum power utilisation efficiency. The specific energy is easy to determine as it is unambiguously defined as the power draw divided by the throughput, with different operating conditions (e.g., ball load and speed) and circuit configurations (e.g., open circuit, closed circuit, with or without pebble crusher, etc.) resulting in different specific energies. However, product grind size from each also varies, leaving the designer with the problem of determining which is the most energy efficient. Historically, this has often been done by applying Bond’s equation to determine the operating work index, which is considered by some to be indicative of the efficiency of the circuit. This has been recently challenged on the basis that the Bond equation is fundamentally flawed and hence any conclusions regarding energy efficiency based on its use are likely to be erroneous (Morrell 2004a). A further problem is that, whereas the piloting may provide sufficient information to select the best circuit, it may only apply to the ore that was tested during the programme. Many deposits have highly variable comminution characteristics leaving unanswered the very important question: “Will the chosen circuit work as well on other ore types?” When pilot testing is not carried out at all, this problem is exacerbated as the circuit design has to rely entirely on laboratory-scale ore characterisation data. A N A L Y S I S O F A G / S A G C I R C U I T E N E R G Y E F F I C I E N C Y U S I N G B O N D ’S EQUATION

As mentioned in the previous section, a common choice is to use the Bond equation to calculate the Bond operating work indices to compare the efficiencies of different circuits. This equation is written as W OW i = -------------------------------§ 1 · 1 10 ¨ ------- – ------¸ F¹ © P

(EQ 1)

AG/SAG MILL CIRCUIT GRINDING ENERGY REQUIREMENT

where W OWi P F

= = = =

117

specific energy operating work index 80% passing size for the product 80% passing size for the feed

By way of example to illustrate its use, data from a pilot programme are given in Figure 1 and show a systematic trend in the specific energy as ball charge is varied. It is pointed out that the AG mill runs were conducted with a pebble crusher in circuit whilst the SAG mill runs were not. The data indicate that the worst condition (highest specific energy) is when about 4% of steel balls are used. When the Bond operating work indices are calculated, a very different picture is obtained, as shown in Figure 2. From these data, the 4% case is indicated to give the best power utilisation efficiency (lowest OWi). Closer analysis of the data shows that there is also a similar relationship between the ball charge and the P80 (Figure 3), indicating that the underlying relationship is in fact one that links operating work index to P80. This is confirmed in Figure 4 where a strong correlation between the Bond operating work index and the product P80 is seen. This trend, which is found in many data sets, shows a decreasing operating work index as the grind becomes finer and is counterintuitive. The expected result would be one in which either the operating work index remained constant (indicating constant energy efficiency and constant material properties) or it increased as product size decreased (i.e., the rock became harder as the product size became smaller and/or the mill became less efficient at producing a finer grind). This result points to a potential error in the Bond equation and puts into question the conclusion regarding maximum power efficiency with 4% balls. Researchers such as Hukki (1962) have challenged the validity of Bond’s equation, at least outside the range of feed and product sizes treated in ball mills. Recently, an alternative equation to Bond’s has been proposed (Morrell 2004a). This has the form: f  x2

W = Mi K  x 2 where W Mi K x2 x1

= = = = =

f  x1

– x1



(EQ 2)

specific energy (kWh/t) index related to the breakage property of an ore (kWh/t) constant chosen to balance the units of the equation 80% passing size for the product 80% passing size for the feed f  x = – a + x b

(EQ 3)

where a,b = constants x = 80% passing size The parameters a and b in Equation (3) have been estimated from analysing a wide range of size reduction data from industrial grinding mills. Equation (2) can therefore be used provided Mi is known. Alternatively, for analysing circuit performance, the equation can be rearranged such that an operating value for Mi can be calculated using plant data. This is the equivalent of the Bond operating work index. When this is done using the data from Figure 4, the results given in Figure 5 are obtained and show that the operating work index is in fact largely constant with respect to product size, and hence there is no indicated difference in power utilisation efficiency between the different operating conditions.

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20 18

Specific Energy, kWh/t

16

14

12

10

8

6

4 With Pebble Crusher Without Pebble Crusher

2

0

0

2

4

6

8

10

12

14

10

12

14

Ball Charge, %

FIGURE 1

Trends in pilot SAG mill specific energy

8 7

Bond OWi, kWh/t

6

5

4

3

2

1

0

0

2

4

6

8

Ball Charge, %

FIGURE 2

Trends in Bond operating work index

EFFICIENCY OF AG/SAG AND BALL MILL CIRCUITS

Given that the use of Equation (2) indicates that there is little or no difference between the power utilisation efficiencies of the different modes of AG/SAG mill operation, the question arises as to whether the equation indicates differences in efficiency between AG/SAG and ball milling in general. Data from 18 different operations were analysed to answer this question. The data comprised throughput and power draws as well as feed, transfer, and ball mill cyclone overflow sizings from each circuit. Initially, Bond operating work indices were calculated for each circuit. These are plotted for each circuit and shown in Figure 6. The ball mill values largely followed the Bond laboratory work index results, which were also obtained for each ore type. The AG/SAG operating work indices

AG/SAG MILL CIRCUIT GRINDING ENERGY REQUIREMENT

119

1.8 1.6

Product P80, mm

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

0

2

4

6

8

10

12

14

5

6

7

Ball Charge, %

FIGURE 3

Relationship between ball charge and product P80

80 70

Bond OWi, kWh/t

60

50

40

30

20

10

0

0

1

2

3

4

Product P80, mm

FIGURE 4

Trend in Bond operating work index with product P80

show their usual elevated levels compared to those from the ball mill circuit. This has often resulted in conclusions concerning lower energy efficiencies of AG/SAG mill circuits compared to ball mills. The correlation between the AG/SAG and ball mill circuit data is also very poor. Use of Equation (2) shows a very different picture, the results being illustrated in Figure 7. This shows that on average the “M” operating work indices of AG/SAG and ball mill circuits are very similar, and hence energy utilisation efficiencies are similar. Also, the AG/SAG and ball mill circuit operating work indices are highly correlated. The conclusion that AG/SAG circuits have, on average, a similar power utilisation efficiency to ball mill circuits may run counter to much “conventional wisdom.” However, controlled experiments in which very different crushing and grinding circuits have

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70

60

Morrell OWi, kWh/t

50

40

30

20

10

0

0

1

2

3

4

5

6

7

Product P80, mm

FIGURE 5

Trend in SMCC operating work index with product P80

60 AG/SAG Ball

Bond OWi, kWh/t

50

40

30

20

10

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

Data Set

FIGURE 6

Bond operating work indices for AG/SAG and ball mill circuits

been run using identical ores have shown little difference in the energy required to reach a target grind from a given feed size (Larsen, Cooper, and Trusiak 2001; Morrell, Johnson, and Revy 1991). The analyses provided in this paper support these results and lead to the assertion that in many cases, regardless of the processing route, the energy required to grind an ore from a specific feed size to a specific product size will be similar, at least to within r5%. It can be concluded from this argument that, at least from an energy utilisation efficiency viewpoint, all circuits work equally well regardless of ore type when they are fully optimised. Of course, that is not to say that from a capital cost, operating cost, and operability standpoint, all circuits are the same—far from it. Ultimately, circuit choice should be made on financial grounds. However, differences in overall power efficiency should not necessarily play a prominent role in decision making as, when analysed correctly, data show that few differences exist between circuit power

AG/SAG MILL CIRCUIT GRINDING ENERGY REQUIREMENT

121

60 AG/SAG Ball

Morrell OWi, kWh/t

50

40

30

20

10

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

Data Set

FIGURE 7

“M” operating work indices for AG/SAG and ball mill circuits

efficiencies. These arguments relate to conventional crushing and tumbling mill circuits. The use of HPGRs, however, appears to provide a genuine reduction in power requirements (Parker et al. 2001). NEW APPROACH TO PREDICTING AG/SAG SPECIFIC ENERGY

The previous sections have indicated that AG/SAG mill circuit power utilisation efficiencies are largely similar, regardless of the circuit configuration and operating conditions such as ball charge, speed, and so forth. If this is the case, then it should be possible to predict the AG/SAG specific energy of all types of circuits without making any assumptions and/or corrections concerning energy utilisation efficiency. The choice of an appropriate measure of the ore breakage characteristics and an associated technique for predicting the specific energy is obviously very important for this approach to work. A potential appropriate measure of an ore’s breakage characteristics is the so-called DWi, which is a parameter derived from the SMC test (Morrell 2004b). The difficulty in determining whether such a relationship exists is that the specific energy of AG/SAG mills does not just depend on ore competence but also factors such as feed size, ball load, aspect ratio, whether the mill has a pebble crusher or not, and whether the mill is in closed circuit or not. An equation was therefore developed for use with the DWi for predicting specific energy and has the following form: a

b

S = K ˜ F 80 ˜ DW i ˜  1 + c  1 – e –dJ –1 ˜ I e ˜ f  A r

(EQ 4)

where S F80 DWi J I f(Ar) a,b,c,d,e K

= = = = = = = =

specific energy (kWh/t) 80% passing size of the feed strength index volume of balls (%) mill speed (% of critical) function of mill aspect ratio (length/diameter) constants function whose value is dependent upon whether a pebble crusher is in circuit

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A companion equation was also developed for predicting transfer size, as follows, and works on the basis that the more energy that is input to the mill in relation to the hardness of the ore, the finer will be the transfer size. g˜S T 80 = f – ----------b DW i

(EQ 5)

where S = specific energy (kWh/t) b,f,g = constants A combination of the two equations gives the AG/SAG specific energy as well as the transfer size, such that the “M” operating work index from Equation (2) remains fairly static regardless of autogenous/semiautogenous operating conditions. To develop the approach, 46 data sets from 30 different operations were used. AG/SAG specific energy and ball mill specific energy were predicted using DWi and Bond ball laboratory work indices. Ore types represented in the database were from Al, Au, Pt, Cu, Ni, and Pb/Zn operations. The range of conditions covered is given in Table 1. The results are shown in Figure 8, indicating a reasonable correlation between observed and predicted specific energies, the standard deviation of the relative error (precision) being 8.5%. S M C TE S T D E S C R I P T I O N

The SMC test, from which the DWi is derived, was originally developed to make use of relatively small samples, both in terms of quantity and particle size, and to be versatile so as to make as much use as possible of whatever sample(s) is available for testing. As a result, the test is able to accommodate a wide range of particle sizes, either in core or crushed form. The test is applied to particles of a particular size, the size being chosen depending on the type and quantity of sample available. The particle sizes that can be used in the SMC test are –45+37.5, –31.5+26.5, –22.4+19, and –16+13.2 mm. Sample sources can be from core sizes as large as PQ (85 mm) and as small as AQ (27 mm). Mostly, either the 31.5+26.5 mm or –22.4+19 mm sizes are chosen because these are easily extractable from HQ and NQ cores, respectively, and these tend to be the most popular choice of core sizes. When sample availability is very limited, quartered (slivered) core samples are cut using a diamond saw (Figure 9). This results in sample mass requirements as low as 2–2.5 kg in total. However, where core is available in sufficient quantity (10–15 kg), it can be crushed instead and the appropriate size fraction extracted. Once the core has been cut or crushed/sized into the chosen particle size range, 100 specimens are chosen and divided into five equal lots. Each lot is then broken in an impact device using a range of closely controlled energies. A suitable impact device is JKMRC’s drop-weight tester (Napier-Munn et al. 1996). After breakage, the products are collected and sized on a sieve whose aperture is related to the original particle size. The percentage of undersize from sieving the broken products is plotted against the input energy. A typical plot from a test is given in Figure 10 and shows the expected trend of an increasing amount of undersize as the input energy is increased. The slope of this plot is related to the strength of the rock, a slope with a larger gradient being indicative of a weaker rock. The gradient of the slope is used to generate a so-called drop-weight index (DWi). The DWi has the units of kWh/m3, which in turn has the same dimensions as strength, and hence it is not surprising that the DWi is correlated with direct strength measurements such as the point load index (discussed later in this paper). The high degree of control imposed on both the size of particles and the energies used to break them means that the SMC test is very precise and is largely free of the

AG/SAG MILL CIRCUIT GRINDING ENERGY REQUIREMENT

TABLE 1

123

Range of Variables in the Database Variable

Maximum

Minimum

JK – A JK – b Specific gravity DWi Bond ball working index, kWh/t F80, μm P80, μm Diameter, m Length, m Ball load, % Speed, % Aspect ratio, L/D SAG, kWh/t

81.3 2.56 4.63 14.2 26 176,000 600 12 8.3 25 86 1.5 29.2

48 0.25 2.5 1.8 9.4 19,400 54 3.94 1.65 0 68 0.3 2.4

35

30

Observed kW

25

20

15

10

5

AG/SAG Circuit Only Total Circuit

0 0

5

10

15

20

25

30

35

Predicted kWh/t

FIGURE 8

Predicted AG/SAG and total circuit specific energy

repeatability problems that plague tumbling-mill rock characterisation tests (Angove and Dunne 1997; Kaya 2001). Such tests usually suffer from variations in feed size, which is often not closely controlled, as well as energy input per mill revolution, which is often assumed to be constant but in practice can be highly variable (Levin 1989). The standard JK drop-weight test normally needs about 75 kg of raw material, and hence its use is normally precluded for small drill-core samples. However, the DWi is highly correlated with the A and b parameters and therefore can be used to estimate their values with a high degree of accuracy. Figure 11 illustrates this using data from 40 different ore types. The scatter apparent in the figure has an associated standard deviation of 6.5%. This is related to the differences in the variation of strength with particle size that different rocks exhibit. This scatter can be reduced by carrying out full dropweight tests on selected samples from the ore body in question to better define the sizeby-size relationship and hence refine the DWi – A,b correlation. Such drop-weight tests

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Sample pieces cut from 50-mm quartered core

FIGURE 9

60

50

% Undersize

40

30

20

10

0 0

50

100

150

200

250

Energy, Joules

FIGURE 10

Typical raw results from an SMC test

are usually referred to as SMC test “calibrations,” though they can be dispensed with if the 6.5% precision of the database correlation is deemed to be acceptable. USE OF DWi IN MODELING

AG and SAG Mill Circuits

The use of modeling and simulation has become routine in the design and optimisation of AG and SAG mill circuits. One of the most widely used models for this purpose is the so-called “variable rates” model (Morrell and Morrison 1996). A more up-to-date version has also been developed with enhanced predictive capabilities (Morrell 2004c). This uses a two-parameter description of rock breakage that is developed from data obtained

AG/SAG MILL CIRCUIT GRINDING ENERGY REQUIREMENT

125

160

140

Predicted A × b

120

100

80

60

40

20

0 0

20

40

60

80

100

120

140

160

Observed A × b

FIGURE 11

Observed versus predicted values of A × b using the DWi

from a drop-weight test (Napier-Munn et al. 1996). The two parameters (A and b) are ore specific and are generated as part of the SMC test via their correlation with the DWi. They relate the t10 (a size distribution index) to the applied specific energy (Ecs). The equation used for describing the relationship between the t10 and Ecs is t 10 = A  1 – e –b·Ecs

(EQ 6)

The specific comminution energy (Ecs) has the units kWh/t and is the energy applied during impact breakage. As the impact energy is varied, so is the t10 . Higher impact energies produce higher values of t10 , which are reflected in products with finer size distributions. The A and b parameters, in conjunction with Equation (6), are used in AG/SAG mill modeling for predicting how rock breaks inside the mill. From this description, the model can predict what the throughput, power draw, and product size distribution will be. Apart from being able to predict throughput and power draw of AG/SAG mills, modeling and simulation also enables a detailed flowsheet to be built up of the comminution circuit response to changes in ore type. It also enables optimisation strategies to be developed to overcome any deleterious changes in circuit performance that are predicted. This is particularly useful during the design stage because the chosen circuit can be tested under a range of conditions to see whether the circuit will meet its production targets. Strategies can then be developed to overcome any potential problems. These can include both changes to how mills are operated (e.g., ball load, speed, etc.) but also changes to feed-size distribution through modification to blasting practices and primary crusher operation—the so-called mine-to-mill approach. Mine-to-Mill Applications

The feed size to AG and SAG mill circuits has been demonstrated to have a significant impact on throughput. Modifying blast design and primary crusher operation can significantly influence AG/SAG mill feed size, hence giving a potentially cost-effective way to increase comminution circuit throughput. Trial-and-error experimentation in this field, however, can be very costly, and thus it is usual to rely on blast-fragmentation modeling and grinding-circuit simulations to determine what the optimum blast design should be.

126

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14

Point Load Strength, MPa

12

10

8

6

4

2 0 0

2

4

6

8

10

12

DWi

FIGURE 12

Correlation between point load strength and the DWi for a copper ore

This will vary with ore type, and hence it is important not only to have appropriate blast models but also rock-breakage descriptions. Blasting models require information on rock mass competence such as provided by the point load strength (Scott, Morrell, and Clark 2002). The DWi is correlated with the point load strength (Figure 12) and hence also can be used in blast-fragmentation modeling where direct measurements of point load strength are not available or are very limited. Conversely, where a significant database of point load tests are available, these can be used to augment the comminution description of the ore body by using the correlation from Figure 12 in reverse. High-Pressure Grinding Rolls

Although HPGR technology has become commonplace in the cement and diamond mining industries and of late has been making significant inroads in the processing of iron ore, it has yet to make a major impact in the gold, platinum, and base metals sectors. However, interest in the technology is now such that the general expectations are that rapidly increasing numbers of HPGR machines are likely to find their way into these sectors. Due to the operation of HPGRs, the more established techniques for breakage characterisation, design, and scale-up that have been developed on the basis of tumbling mills are not applicable. Simulation has helped in this regard, and JKSimMet software contains a model that has been shown to have good scale-up capabilities (Morrell, Shi, and Tondo 1997; Daniel and Morrell 2004). This model needs HPGR data to calibrate it, and although it has been shown that laboratory-scale HPGR results are suitable, separate tests need to be conducted on every different ore type, as the size reduction and throughput parameters of the model are machine and ore dependent. Ore characterisation therefore remains a problem, though it is being currently researched in the AMIRA P9 project. The DWi may provide at least part of the answer, as it has been found that it is correlated with the operating work index of HPGRs as Figure 13 indicates. The data in this figure have been obtained from 13 different ore types. It is valid for machines operating with a working pressure in the range of 2.5 to 3 N/mm2. The correlation in Figure 13 is not intended for design purposes but can be used in conjunction with pilot- and/or laboratory-scale HPGR test results to predict the specific energy requirement of rock samples that cannot be tested in an HPGR. Its value for ore-body

AG/SAG MILL CIRCUIT GRINDING ENERGY REQUIREMENT

127

25

HPGR OWi, kWh/t

20

15

10

5

0 0

2

4

6

8

10

DW i

FIGURE 13

DWi versus HPGR operating work index

profiling is obvious. Also, the fact that the DWi is both applicable to AG/SAG and HPGR circuits makes the SMC test particularly attractive in greenfield design projects, as its use for characterising drill core does not compromise the ability of the designer when subsequently evaluating the response of AG/SAG and HPGR circuits to changes in ore type. CONCLUSIONS

The SMC rock-breakage characterisation test has been developed to make use of very small quantities of sample, such as quartered drill core. The test generates a strength index (DWi) which, via modeling and/or power-based techniques, can be used to predict the specific energy of AG and SAG mills as well as HPGR circuits. Its applicability for modeling stems from its correlation with the JK rock-breakage parameters (A and b). For power-based calculations, an equation has been developed that relates it and operating variables such as feed size, ball load, and speed to AG/SAG mill specific energy with a precision of 8.5% (1 standard deviation). The usefulness of the DWi also extends to rock mass characterisation in mining applications, as it is correlated with the point load index/UCS. It is therefore ideally suited for mine-to-mill studies as it can be simultaneously used as an input to both comminution circuit and blast-fragmentation models where independent point load/UCS measurements are not available. BIBLIOGRAPHY

Angove, J.E., and Dunne, R.C. 1997. A review of standard physical ore property determinations. World Gold Conference, Singapore, September 1–3. Daniel, M.J., and Morrell, S. 2004. HPGR model verification and scale-up. Minerals Engineering 17(11–12):1149–1161. Hart, S., Valery, W., Clements, B., Reed, M., Song, M., and Dunne, R. 2001. Optimisation of the Cadia Hill SAG mill circuit. Pages 11–30 in Proceedings of the International Conference on Autogenous and Semi-Autogenous Grinding Technology. Volume 1. Vancouver, BC: University of British Columbia.

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Hukki, R.T. 1962. Proposal for a solomnic settlement between the theories of von Rittinger, Kick and Bond. AIME Transactions 223:403–408. Kaya, E. 2001. Evaluation of bond grindability testing. Pages 339–347 in Proceedings of the International Conference on Autogenous and Semi-Autogenous Grinding Technology. Volume 1. Vancouver, BC: University of British Columbia. Larsen, C., Cooper, M., and Trusiak, A. 2001. Design and operation of Brunswick’s AG/ SAG Circuit. Pages 350–367 in Proceedings of the International Conference on Autogenous and Semi-Autogenous Grinding Technology. Volume IV. Vancouver, BC: University of British Columbia. Levin, J. 1989. Observation on the Bond standard grindability test, and a proposal for a standard grindability test for fine materials. South African Institute of Mining and Metallurgy 89(1):13–21. Morrell, S. 1996. Power draw of wet tumbling mills and its relationship to charge dynamics—Part 1: A continuum approach to mathematical modelling of mill power draw. Transactions of the Institution of Mining and Metallurgy 105:C43–53. ———. 2004a. An alternative energy-size relationship to that proposed by Bond for the design and optimisation of grinding circuits. International Journal of Mineral Processing 74:133–141. ———. 2004b. Predicting the specific energy of autogenous and semi-autogenous mills from small diameter drill core samples. Minerals Engineering 17(3):447–451. ———. 2004c. A new autogenous and semi-autogenous mill model for scale-up, design and optimisation. Minerals Engineering 17(3):437–445. Morrell, S., Johnson, G., and Revy, T. 1991. A comparison through observation and simulation of the power utilisation and performance of two dissimilar comminution plants. Pages 157–160 in Fourth Mill Operators’ Conference, Australasian Institute of Mining and Metallurgy, Burnie, Tasmania, March. Morrell, S., and Morrison, R.D. 1996. AG and SAG mill circuit selection and design by simulation. Pages 769–790 in Proceedings SAG 96. Volume 2. Vancouver, BC: University of British Columbia. Morrell, S., Shi, F., and Tondo, L.A. 1997. Modelling and scale-up of high pressure grinding rolls. In Proceedings of the XX International Mineral Processing Congress (IMPC), Aachen, Germany, September 1997. Napier-Munn, T.J., Morrell, S., Morrison, R.D., and Kojovic, T. 1996. Mineral Comminution Circuits: Their Operation and Optimisation. JKMRC Monograph Series. Brisbane, Australia: Julius Kruttschnitt Mineral Research Centre. Parker, B., Rowe, P., Lane, G., and Morrell, S. 2001. The decision to opt for high pressure grinding rolls for the Boddington expansion. Pages 93–106 in Proceedings of the International Conference on Autogenous and Semi-Autogenous Grinding Technology. Volume III. Vancouver, BC: University of British Columbia. Scott, A., Morrell, S., and Clark, D. 2002. Tracking and quantifying value from “Mine to Mill.” In Proceedings of the Value Tracking Symposium. Melbourne, Australia: AusIMM.

PART 2

Comminution Practices

129

Causes and Significance of Inflections in Hydrocyclone Efficiency Curves S.K. Kawatra* and T.C. Eisele*

ABSTRACT

Deviations of the shape of hydrocyclone efficiency curves from the ideal “S” shape have long been reported, appearing as changes in slope, or inflections. These inflections can be divided into two categories: “coarse” inflections, which are caused by differences in density of the minerals being separated, and “fine” inflections, for which there are a number of competing hypotheses concerning their cause. The existing literature addresses either the fine inflection or the coarse inflection, but no papers have reported both types of inflection occurring at once. This paper presents hydrocyclone results from both in-plant studies and laboratory experiments that show both coarse and fine inflections, and the industrial significance of both types of inflections are discussed. INTRODUCTION

The performance of hydrocyclone classifiers is determined using efficiency curves, which show the probability of a particle reporting to the hydrocyclone underflow as a function of its size. This is expressed using selectivity functions, S(d), which represent the fraction of the feed material in size fraction d that reports to the hydrocyclone underflow. This is normally divided into (1) a bypass fraction that is taken to be equal to the value of the water split, Rf, and represents the material that does not undergo classification; and (2) a classification function, C(d), which has a smooth “S” shape, starting at 100% at the coarse end and decreasing to zero at the fine end, as shown in Figure 1. The classification function can be expressed closely by equations such as (Plitt 1976) Cd = 1 – e

m d – 0.693 § ------------ · © d50c ¹

(EQ 1)

or (Lynch and Rao 1968) d D § ------------ · © ¹

e d50c – 1 C  d = --------------------------------------e

d D § ------------ · © d50c ¹

+ eD – 2

* Department of Chemical Engineering, Michigan Technological University, Houghton, Michigan 131

(EQ 2)

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ADVANCES IN COMMINUTION

COMMINUTION PRACTICES

Fraction of Size to Underflow

1.0

0.5

d50c Size

0

FIGURE 1

Shape of an ideal corrected hydrocyclone efficiency curve

where C (d) = classification function for particles of size d after correcting for particles that bypass classification; d = particle size (Pm); d50c = particle size that has equal probability of reporting to the overflow or the underflow, after correcting for the particles that bypass classification; and m, Į = measures of the sharpness of separation. If a hydrocyclone is expected to produce a standard S-shaped efficiency curve, then it is possible to predict the corrected d50 size using a relationship such as the one shown in Equation (3) (Plitt 1976): 0.46

0.6

1.21

50.5D c D i D o exp  0.063I d50 c = -------------------------------------------------------------------------------0.5 0.71 0.38 0.45 Du h Q  US – U

(EQ 3)

where d50c = corrected d50 (Pm); Dc = cyclone diameter (cm); Di = inlet diameter (cm); Do = overflow diameter (cm); I = volumetric fraction of solids in feed; Du = underflow diameter (cm); h = free vortex height (cm); Q = volumetric flow rate of feed (L/min); Us = solid density (g/cm3); and U = liquid density (g/cm3). However, there are a number of cases where the efficiency curve does not follow this uniform, easily modeled shape. The curve can show inflections where the slope changes abruptly, and in extreme cases the curve can reverse direction, as shown in Figure 2. This is commonly referred to as a “fishhook” in the literature. The term comes from the fact that when the smallest size measured corresponds to the portion where the curve is rising, it resembles a hook. A number of possible causes of efficiency curve inflections have been proposed in the literature. Laplante and Finch (1984) explained the coarse inflection as being a result of a combination of density and size distribution effects. The causes of the fine inflection are less clear, and a variety of agglomeration, heavy media, entrainment, and fines recirculation mechanisms have been proposed (Heiskanen 1993). To date, no investigators have reported observing both the coarse inflection and the fine inflection in a single

INFLECTIONS IN HYDROCYCLONE EFFICIENCY CURVES

133

Fraction of Size to Underflow

1.0

Coarse Inflection

Fine Inflection 0

FIGURE 2 A hydrocyclone efficiency curve showing two inflections, one at the coarse end and one at the fine end

efficiency curve, which has tended to contribute to confusion as to which type of inflection is being addressed in any given paper. When inflections occur at either coarse or fine sizes, it can be difficult to unambiguously determine the d50c size for the hydrocyclone, which greatly complicates efforts to accurately model comminution circuits that incorporate hydrocyclones. Coarse Inflections

From Equation (3), it is evident that the cut size is a function of the particle density. The higher the density of a material, the smaller the d50 (Lynch and Rao 1968). With a heterogeneous feed containing particles that vary in density, each feed component follows the appropriate efficiency curve for particles of its density. The effect of this on a synthetic mixture of low-density and high-density particles is exemplified in Figure 3, which includes the efficiency curves for pyrite (specific gravity = 5.0) and nonsulfides (specific gravity 2.7), as well as the combined bulk efficiency curve for the mixture. Both of the pure components clearly follow portions of classic S-shaped efficiency curves, but the combined curve deviates markedly from an S shape. In order for the differences in particle density to produce a non-S-shaped efficiency curve, the particles must not only differ in density, but also must differ in size distribution, with the heavier mineral being concentrated in the finer size fractions (Laplante and Finch 1984). This results in the bulk efficiency curve following the shape of the lowdensity component at the coarser sizes, and then switching to following the high-density component at the finer sizes. If the relative percentages of high-density particles and low-density particles in each size fraction are known, then it is possible to calculate the bulk efficiency curve based on the weighted averages according to the respective weight percentages of dense and light components contained in the feed stream (Heiskanen 1993). This is calculated as shown in the following equation (Napier-Munn et al. 1996):

134

ADVANCES IN COMMINUTION

COMMINUTION PRACTICES

100 90

% Feed to Hydroclone Underflow

80 70 60 50 40 30 20 Pyrite Feed Bulk Feed Nonsulfide Feed

10 0 10

100

1,000

After Laplante and Finch 1984.

FIGURE 3 Example of an inflection at the coarse end of a hydrocyclone efficiency curve due to the presence of particles of very different densities

S(d) = fL(d)SL(d) + [1 – fL(d)]SH(d)

(EQ 4)

where S(d) = bulk efficiency curve value for size fraction d; fL(d) = weight fraction that is the light feed component for size fraction d; SL(d) = efficiency curve value of light feed component for size fraction d; SH(d) = efficiency curve value of heavy (dense) feed component for size fraction d; and d = particle size (Pm) The degree to which this effect occurs depends upon the difference in density between types of particles. The most extreme case is reported by Banisi, Laplante, and Marois (1991), where metallic gold particles in a silicate ore produce a pronounced inflection at an unusually fine size, due to the extremely high density of gold (19.3 g/cm3). Fine Inflections

Efficiency curve inflections at the coarser sizes are satisfactorily explained by differences in particle density and size distribution; however, the inflections at the finer sizes are a completely different phenomenon that has resisted reliable measurement or modeling. In the case of the fine inflections, there are numerous possible proposed mechanisms that have not been conclusively demonstrated. It has also not been demonstrated whether the fine inflection is a significant consideration, because it occurs at the very fine particle sizes where there is often only a very small fraction of the total material present. It has even been proposed that the phenomenon of fine inflections does not even exist, and that its appearance is due mainly to the difficulty of accurately measuring particle sizes and weights at very fine sizes. The effect is sometimes elusive, and some authors have not observed the fine inflection even after extensive experiments (Coelho and Medronho 2001). The fine inflection is well known in air classifiers and can be expressed mathematically as the result of internal recycling and reclassification of material in the classifier

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135

(Luckie and Austin 1975). However, air classifiers have a significantly different design than hydrocyclones, with areas that clearly can be identified as producing two stages of classification. It is the interaction of these two stages that leads to the inflection in air classifier efficiency curves. This analysis, therefore, does not apply directly to hydrocyclones, which lack the internal structures needed to produce multiple stages of classification within a single unit. A fine inflection can be modeled by assuming that it is due to fines entrainment in the hydrocyclone underflow (Finch 1983; Del Villar and Finch 1992; Kelly 1991). The model based on this assumption becomes S(d) = C(d) + a(d)

(EQ 5)

where C(d) = fraction of the feed of size d that is recovered to the underflow as a result of classification forces only, and a(d) = fraction of the feed of size d that is carried to the underflow independently of the classification. The bypass function a(d) is normally calculated from the water bypass fraction, Rf, as follows: a(d) = Rf(1 – C(d))

(EQ 6)

If it is assumed that, instead, the value of a(d) instead increases linearly with decreasing values of d, and becomes equal to the water bypass fraction (Rf ) when d = 0, then the Plitt equation for the uncorrected efficiency curve becomes

Sd = 1 – e

m d – 0.693 § ------------ · © d50c ¹

d 0–d· + Rf § --------© d0 ¹

(EQ 7)

where S(d) = selectivity function for particles of size d, uncorrected for the bypass fraction; Rf = fraction of the water entering with the feed that reports to the hydrocyclone underflow; and d0 = maximum particle size that is entrained by the water flow into the underflow while bypassing classification. This model does predict a small inflection in the efficiency curve as long as the value of d0 is quite fine, as shown by the example curve given in Figure 4. It is consistent with the observation that, in many cases, the fine inflection is most pronounced when the value of Rf is quite high (Pasquier and Cilliers 2000). However, the model does not predict two features that are sometimes reported for the fine inflection: (1) It does not allow the value of S(d) for the small particles to exceed the value of Rf; and (2) it does not account for cases where S(d) for the fine particles first rises and then falls again. A frequently proposed mechanism for the fine inflection is fines agglomerating to the coarse solids, which are preferentially carried to the underflow, as shown in Figure 5 (Heiskanen 1993; Finch 1983). This mechanism is quite plausible; however, it is difficult to conclusively prove and even more difficult to reliably model. In any case, the fine inflection has been observed even in cases where measures have been taken to ensure thorough dispersion (Rouse, Clayton, and Brookes 1987). Therefore, while fines agglomeration may be a contributing factor in many cases, it is unlikely to be the cause of all observed cases of the fine inflection. It would be expected that the fine inflection would be most pronounced when there are many coarse particles and few fine particles, as then there would be significant surface area available to carry the fines. It also would be expected that the magnitude of the fine inflection would vary depending on the properties of the coarse particles that could lead to agglomeration. Another possible mechanism is based on fine particles being entrained in the wake behind coarser particles, as shown in Figure 6 (Neesse, Dueck, and Minkov 2004;

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1.0 0.9 0.8

Fraction to Underflow

0.7 0.6 0.5 0.4 0.3 S(d) Observed S(d) Calculated C(d) a(d)

0.2 0.1 0 10

60

110

After Finch 1983.

FIGURE 4 Selectivity curve for a 25-cm hydrocyclone, sized by microsieving to 25 μm, and modeled using Equation (7) with the following parameters: d50c = 70 μm; m = 3.2; d0 = 100 μm, Rf = 0.47. In addition to the selectivity function S(d), the entrainment function a(d) and the classification function C(d) are also shown.

Agglomerated Fines

Particle Motion

Coarse Particle

Fluid Flow

FIGURE 5 Schematic of the fines agglomeration effect, with a coarse particle carrying fines that are attached to its surface

INFLECTIONS IN HYDROCYCLONE EFFICIENCY CURVES

137

Coarse Particle

Fine Particles Trapped in Wake of Coarse Particle

FIGURE 6 Fine particles trapped in the wake of a coarse particle, carried along by it to the hydrocyclone underflow

Kraipech et al. 2002). This is supported by the observation that when particles of different sizes are settling together, the settling rate of the finer particles is increased compared to their settling rate when no coarse particles are present. This effect can be quantified, and models based on it can show a quite pronounced fine inflection. It is reported that this effect becomes experimentally noticeable at particle sizes <3.5 ȝm for lime particles, glass beads, and dusts suspended in water (Kraipech et al. 2002). The quantity of fines that could be carried to the underflow would depend on the volume of coarse particle wakes, and would therefore increase as the number of coarse particles increased. It also would be expected that there would be relatively little dependence on the coarse particle properties, and the effect would depend only on the size and settling velocity of the coarse particles. The objective of this paper is to examine the effects leading to non-S-shaped efficiency curves from a practical standpoint, and to determine what the presence of these inflections tells us about the performance of hydrocyclones and the comminution circuits that contain them. This is accomplished both by examining the results of analyses of plant samples and by conducting controlled laboratory experiments to confirm these results. PLANT SAMPLING STUDIES

The plant examined was a magnetite concentrator located in the Lake Superior iron ore district. This type of plant was selected both because iron ore is one of the most highvolume metallic ores produced and is therefore of considerable practical importance, and because the feed processed contains approximately equal quantities of a high-density mineral (magnetite, ȡ = 5.18) and a low-density mineral (silica, ȡ = 2.65), ensuring that the shape of efficiency curves from the hydrocyclones would be equally affected by the behavior of both minerals. The hydrocyclones sampled were part of a standard hydrocyclone/pebble mill circuit, as shown in Figure 7. The circuit normally operated with 14 cyclones, with 2 additional cyclones available as spares. Samples were collected from the cyclone feed, cyclone underflow, and circuit product as part of an overall survey of the plant performance. Size analyses of the samples were carried out by three methods:

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Circuit Product (COF)

Cyclone Underflow (CUF)

Cyclone Feed

Circuit New Feed (CNF)

Sump

Krebs 15-in. (38.1-cm) Cyclone 16 Total, 2 Stand-By OF: 5.25 in. (13.3 cm); UF: 3 in. (7.6 cm)

Pebbles

Pebble Mill 15.5 ft x 32.5 ft (4.7 m x 9.9 m) 2,650 hp (1,976 kW)

Chip Removal Screen Pebble Chips

Pebble Mill Discharge (PMD); Recirculating Load = 250% NOTES: The total flow rates of the various streams for the particular circuit sampled were as follows: Circuit New Feed: 120.6 ltph (long tons of dry solids per hour) or 122.5 tph (metric tons per hour); Cyclone underflow: 299.3 ltph (304 tph); Pebble mill discharge: 306.9 ltph (312 tph); Circuit product: 128.1 ltph (130.1 tph). The hydroclone feed was 13.2% solids.

FIGURE 7

Configuration of the hydrocyclone/pebble mill circuit sampled for this study

1. Wet sieving at 25 ȝm using a woven-wire test sieve, followed by dry sieving of

the +25-ȝm particles using woven-wire test sieves in a Ro-Tap sieve shaker 2. Microsieving of dry powders using electroformed nickel-foil sieves in a Sonic

Sifter apparatus, which allowed sieving down to 10-ȝm particle size 3. Microtrac laser diffraction particle-size analysis to measure particle sizes down

to 1 ȝm, primarily as a check on the accuracy of the sieve analyses For the sieved samples, each individual size fraction was assayed using a dichromate titration method to determine the iron assay for every sieved size fraction for each stream. The size distribution and assay data were then mass balanced, and the magnetite concentration in each size fraction was calculated from the iron assays. Sampling Results

A summary of the results from plant sampling around the hydrocyclones is shown in Table 1. Note that the –500 mesh fraction of the cyclone underflow product is highly enriched in magnetite relative to the cyclone overflow. This indicates that the magnetite is being retained in the grinding circuit until it is ground to a finer size than the silicate gangue, and as a result is being significantly concentrated into the finer size fractions. The size analyses of the individual components (magnetite and quartz) were then used to calculate the hydrocyclone efficiency curves for the magnetite phase, the quartz phase, and the overall combined result. These efficiency curves are shown in Figure 8. Discussion—Plant Sampling

The efficiency curves in Figure 8 illustrate the effect of the different mineral densities on the hydrocyclone separation size. While the hydrocyclone begins to remove quartz from the circuit at a fairly coarse size (d50 = 39 Pm), it does not remove the magnetite until a

INFLECTIONS IN HYDROCYCLONE EFFICIENCY CURVES

139

TABLE 1 Flow rates for total solids, magnetics, and nonmagnetics for the material entering and leaving the hydrocyclones* Total

+500 Mesh Fraction

–500 Mesh Fraction

Stream

Overall

Magnetic

Nonmagnetic

Overall

Magnetic

Nonmagnetic

Overall

Magnetic

Nonmagnetic

Cyclone feed

427.5

257.7 (60.3%)

169.8 (39.7%)

226.9

122.0 (53.8%)

104.9 (46.2%)

200.6

135.7 (67.6%)

64.9 (32.4%)

Cyclone overflow

128.1

73.5 (57.4%)

54.6 (42.6%)

16.1

7.0 (43.5%)

9.1 (56.5%)

112

66.5 (59.4%)

45.5 (40.6%)

Cyclone underflow

299.3

201.4 (67.3%)

97.9 (32.7%)

207.1

115.8 (55.9%)

91.3 (44.1%)

85.6 (92.8%)

6.6 (7.2%)

92.2

* Flow rates are in long tons per hour. Percentages are relative to the overall flow rate for the corresponding size fraction. Note that the cyclone underflow, particularly the –500 mesh fraction, is considerably enriched in magnetite compared to the cyclone feed and overflow.

1.0 0.9

Fraction of Size to Underflow

0.8 0.7 0.6 0.5

Inflection

0.4 0.3 0.2 0.1 0.0 10

Magnetics Nonmagnetics Overall 100

FIGURE 8 Hydrocyclone efficiency curves determined from overflow and underflow samples collected from an operating hydrocyclone in the magnetite concentrator studied

significantly finer size (d50 = 20 Pm) is reached. The hydrocyclone underflow between approximately 20 Pm and 39 Pm is therefore predominantly magnetite. This material is then returned to the grinding circuit and reground until it finally becomes fine enough to be removed. This results in a substantial accumulation of magnetite in the hydrocyclone underflow in this size range, as shown in Figure 9. The effect of this retention of the higher density fraction in the circuit is seen in the overall efficiency curve of Figure 8. The magnetite and quartz efficiency curves are very close to the ideal S shape, however, the overall curve shows an inflection. This is a direct result of the fact that the cyclone feed consists of approximately equal quantities of magnetite and quartz at sizes coarser than 39 Pm; but at finer sizes, it is primarily composed

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40 Magnetics Nonmagnetics

% of Total Hydrocyclone Underlfow

35

30

25

20

15

10

5

0 10

100

1,000

FIGURE 9 Quantities of magnetite and quartz by size fraction in the hydrocyclone underflow collected from an operating hydrocyclone in a magnetite concentrator plant. The particles larger than 20 μm and smaller than 39 μm were primarily magnetite.

of magnetite. As a result, the overall efficiency curve is initially the average of the magnetite and quartz efficiency curves, but then rapidly switches to follow the overall efficiency curve once it reaches sizes where the quartz has been removed from the circuit. The result is an inflection in the overall efficiency curve. The practical significance is that such an inflection only occurs when the cyclone feed has become enriched in the denser mineral in the fine sizes. If the high-density and low-density minerals have the same size distribution, then the overall bulk efficiency curve will simply be the average of the curves for the high- and low-density minerals. The inflection can only be seen when the overall curve switches from following the lowdensity curve to following the high-density curve, which can only happen if there is a difference in size distributions between the two minerals. LABORATOR Y STUDIES

In order to more closely examine the coarse inflection phenomenon, and to determine how the relative size distributions affect the degree of the inflection, a series of laboratory experiments were carried out using controlled size distributions for the hydrocyclone feed. Also, the plant sampling was unable to determine whether a fine inflection was occurring, so the laboratory experiments were designed to be able to detect the fine inflection. Equipment

A 10.2-cm-diameter Krebs hydrocyclone was used, mounted on a test rig with a variablespeed pump, pressure gauge, ultrasonic flowmeter, and sampling mechanism for collecting simultaneous overflow and underflow samples. The hydrocyclone dimensions were ƒ Feed inlet: 3.5 cm

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141

ƒ Vortex finder diameter: 3.18 cm ƒ Spigot diameter: 1.59 cm

The hydrocyclone test rig consisted of a sump with a variable-speed centrifugal pump circulating material continuously through the hydrocyclone. An oil-filled pressure gauge was used to monitor hydrocyclone inlet pressure. Flow rates in the hydrocyclone test rig were monitored using an ultrasonic Doppler flowmeter. Samples were collected using a specially designed sample cutter that simultaneously collected samples from both the cyclone overflow and underflow, so that the relative flow rates of the two streams could be accurately measured. Particle-size distributions were determined using a Leeds and Northrup Microtrac laser diffraction particle-size analyzer. Materials and Procedures

Materials used were finely ground quartz sand and magnetite concentrate. Experiments were first conducted using magnetite alone and quartz alone, followed by experiments with mixtures of magnetite and quartz. All samples were collected in triplicate at each hydrocyclone operating condition, and each of the triplicate samples were analyzed separately to determine the random variations from test to test. In all experiments, the random variation in the fraction of each size reporting to the underflow was less than r0.01 units. This is smaller than the magnitude of the inflections that were observed, demonstrating that the inflections were actually present and not simply due to experimental error. Experiments with Single Minerals. For experiments using magnetite alone and using quartz alone, the size distributions of the hydrocyclone feeds are shown in Figure 10. For these experiments, the size distributions of magnetite and quartz were reasonably similar, and in particular they had similar quantities of particles finer than 10 ȝm. This made it possible to determine whether there were differences in the fine inflections for the two minerals that could be attributed to differences in the mineral properties. Experiments were run at three different percent solids for each mineral (2.5%, 5.5%, and 16.5% solids for the magnetite; 2.3%, 8.4%, and 16.9% solids for the quartz). At each percent solids, the cyclone inlet pressure was varied over the range of 5 to 20 psi to alter the hydrocyclone flow rate. Experiments with Magnetite/Quartz Mixtures. Additional experiments were conducted with 50:50 mixtures by weight of magnetite and quartz. Two sets of these experiments were conducted, with the size distributions of the quartz and magnetite being very different. This was done in order to produce the maximum coarse inflection. In the first set of experiments, the quartz was the underflow (coarse) product from the cyclone experiments using quartz alone, while the magnetite was the overflow (fine) product from the cyclone experiments using magnetite alone. This resulted in a moderate amount of overlap between the magnetite and quartz size distributions, as can be seen in Figure 11. The second set of 50:50 magnetite–quartz experiments used quartz that had been further processed by sedimentation to remove the finest particles, and magnetite that had been processed by sedimentation to remove the coarsest particles, with the coarse magnetite particles then being ground using an attrition mill and added back to produce a finer magnetite size distribution. This resulted in much less overlap between the magnetite and quartz size distributions, and the magnetite being significantly finer than in the first set of experiments (as shown in Figure 11). For these experiments, the percent solids was varied from as high as 30% solids to as low as 2.5% solids, and the cyclone operating pressure was varied from 7 to 20 psi to alter the flow rates.

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100 90 80

Cumulative % Passing

70 60 50 40 30 20 Magnetite Quartz

10 0 10

10

100

1,000

FIGURE 10 Magnetite and quartz size distributions used in laboratory hydrocyclone experiments using magnetite alone and quartz alone

100 90 80

Overlap between Magnetite and Quartz Size Distributions

Cumulative % Passing

70 60 50 40 30 Quartz Set 1 Quartz Set 2 Magnetite Set 1 Magnetite Set 2

20 10 0 10

10

100

1,000

FIGURE 11 Magnetite and quartz size distributions used for experiments with a 50:50 mixture by weight. Two sets of experiments were run, with the second set having less material in the “overlap” region than did the first set.

INFLECTIONS IN HYDROCYCLONE EFFICIENCY CURVES

Results and Discussion Individual Mineral Results.

143

The results for the individual minerals did not show a coarse inflection, due to the feed being composed of minerals of a single density. However, both the quartz and magnetite did show a fine inflection. For quartz, the fine inflection was relatively small, as shown by the example curves in Figure 12, but was still much larger than the random variations between triplicate samples, demonstrating that it was a real effect and not due to random error. The fine inflection was only slightly affected by percent solids, and was completely unaffected by flow rate, although the d50 size for the remainder of the curve varied, as predicted by Equation (3). For pure magnetite, however, the fine inflection shown in Figure 13 was much more pronounced than the fine inflection for silica shown in Figure 12. The magnetite feed had a size distribution similar to the quartz feed, and so the magnitude of the fine inflection would be expected to be similar in both cases if the same mechanism was responsible for the fine inflection. This very large difference between the quartz and the magnetite, and the fact that the magnetite is much more sensitive to flow rate and percent solids, clearly indicates that different mechanisms are responsible in each case. Mineral Mixture Results. Experiments with mixtures of minerals were able to show both the coarse inflection and the fine inflection. In the first set of experiments, with a relatively large overlap of the magnetite and quartz particle sizes, the coarse inflection in the efficiency curves was not observed, although the fine inflection was present, as shown in Figure 14. The second set of experiments, with very little overlap between the magnetite and quartz size distributions, showed a very visible coarse inflection at the lower values of the percent solids, as can be seen in Figure 15. This coarse inflection was clearly visible in all three of the triplicate samples in each of the experiments where it appeared, and was significantly larger than the random variations between triplicates, indicating that it is a real effect and not due to random errors. In these experiments, it can be seen that as the percent solids increased, the d50 also increased as would be expected from Equation (3). This caused the efficiency curve to sweep through the size where the feed changes from being entirely quartz to being entirely magnetite. As a result, the inflection occurs near the top of the curve at the lowest percent solids, and the inflection moves down the curve as the percent solids increases and the d50 size coarsens. Note that the coarse inflection is most easily visible near the top of the curve; however, it is difficult to distinguish at all when it is near the middle or bottom of the curve, as it simply appears to be a decrease in the sharpness of separation. The fine inflection also can be seen in the results shown in both Figure 14 and Figure 15. It is very interesting to note that, even though all of the material producing the fine inflection in these experiments is magnetite, the behavior is much more similar to that of the pure quartz curve (Figure 12) than the pure magnetite curve (Figure 13). This shows that the magnitude of the fine inflection is controlled by the nature of the coarse particles, not by the nature of the fine particles. This is not consistent with the entrainment model for the fine inflection (Finch 1983), as in that case the fine inflection would be controlled entirely by the characteristics of the fine particles. Also, the behavior of the fine inflection is not entirely consistent with the hydrodynamic model (Neesse, Dueck, and Minkov 2004), as this model would not predict such a large alteration in behavior simply by changing the density of the coarse particles. The result is much more consistent with agglomeration of fine particles onto the coarse surfaces. In this particular system, there is potential for magnetic agglomeration of fine magnetite particles onto the coarse magnetite, which would account for the much higher value of the fine inflection for pure magnetite than for pure quartz. When there is no coarse magnetite

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1.0 17.5% Solids 8.1% Solids 2.5% Solids

0.9

Fraction of Size to Underflow

0.8 0.7 0.6 0.5 0.4 0.3

Fine Inflection

0.2 0.1 0.0 1

10

100

FIGURE 12 Efficiency curves for pure silica as a function of percent solids at a fixed flow rate (110 L/min). At each percent solids, samples were collected in triplicate and analyzed independently to ensure reproducible results.

1.0 202 L/m 157 L/m 109 L/m

0.9

Fraction of Size to Underflow

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1

10

NOTES: Flow rate was varied from 109 L/m to 202 L/m, at a constant percent solids of 5.5%. The fine inflection for pure magnetite was significantly affected by flow rate.

FIGURE 13

Efficiency curves for pure magnetite as a function of flow rate

100

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145

1.0 31% Solids 14% Solids 5.1% Solids 2.4% Solids

0.9

Fraction of Size to Underflow

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1

10

100

NOTES: Inlet pressure was 12 psi, providing a flow rate of approximately 200 L/m, and the percent solids was varied as indicated. For each experiment, samples were collected and analyzed in triplicate to ensure reproducible results. The coarse inflection is difficult to see because of the relatively large overlap in the quartz and magnetite size distributions, but the fine inflection is prominent.

FIGURE 14

Representative efficiency curves for the first set of mixed-mineral experiments

present to carry the fine magnetite particles and only nonmagnetic quartz particles are present, then the behavior of the fine magnetite becomes much more similar to that of the fine quartz. An additional phenomenon that was noted with the mixed-mineral experiments is that when the magnetite was made finer and the quantity of material in the particle size range from 1 to 5 Pm increased, the magnitude of the fine inflection was reduced. This can be seen by comparing Figure 14 (which had a smaller amount of material in the fine fraction and exhibited a large fine inflection) with Figure 15 (which had a larger amount of material in the fine fraction and exhibited a small fine inflection). This indicates that only a portion of the fine material can follow the fine inflection, with the remainder behaving as would be predicted by conventional classification theory. If the fine inflection is being caused by the fine particles agglomerating onto the coarser particles, then there is a limited amount of fine material that can be recovered before all of the available coarse-particle surface area is used up. Similarly, if the fine inflection is caused by fine particles being carried in the wakes of the coarse particles, there is a limited amount of wake volume available to carry the particles. As a result, the fine inflection is only significant when there is relatively little material present in the finest size range. As the material in the finest sizes increases, the behavior of the fines that are not being transported by coarse particles swamps the effects of the fines being carried by the coarse particles, and the fine inflection becomes negligible. In the results reported here, even when there is a very large fine inflection, the size distributions shown in Figures 10 and 11 reveal that less than 10% of the total weight of the feed was affected, and so the fine inflection has a minimal effect on the actual composition of the bulk cyclone products.

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1.0 27% Solids 21.7% Solids 9.7% Solids 5.8% Solids

0.9

Fraction of Size to Underflow

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1

10

100

NOTES: For each experiment, samples were collected and analyzed in triplicate to ensure reproducible results. The coarse inflection is only easily seen at the two lowest percent solids. The increased quantity of magnetite in the fine fraction also resulted in a smaller fine inflection than was seen in the experimental results shown in Figure 14.

FIGURE 15 Variations in efficiency curves for a quartz/magnetite mixture with very little overlap between the magnetite and quartz size distributions as the percent solids in the cyclone feed changes

CONCLUSIONS

There are two distinct phenomena that lead to inflections in hydrocyclone efficiency curves. The coarse inflection is caused by the presence of fine, high-density particles combined with coarser, low-density particles in the cyclone feed. This results in the efficiency curve being dominated by low-density materials at the coarser sizes and high-density materials at the finer sizes, with the inflection occurring when the curve switches from one to the other. In a comminution circuit, such an inflection is an indicator that highdensity particles are being preferentially retained in the grinding circuit and are being overground. As overgrinding is a significant waste of energy and can cause losses of valuable minerals, the appearance of a coarse inflection in a hydrocyclone efficiency curve in a plant is a sign that there is a problem that needs to be corrected. The fine inflection, on the other hand, has been explained by a number of theories, many of which do not fully account for the behavior seen in the results reported here. The observed behavior is most consistent with an agglomeration mechanism, where fine particles agglomerate onto coarse particles and are carried into the cyclone underflow. This mechanism can only carry a limited quantity of fines, and so when there are very large quantities of fine particles present, the majority of them follow the theoretical curve because there is insufficient coarse particle surface to carry them all. As a result, the fine inflection does not appear likely to be of much industrial significance, as it is only clearly seen in cases where there is very little of the cyclone feed at the affected sizes.

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ACKNOWLEDGMENTS

This project was partially supported by the U.S. Department of Energy under Grant No. DE-FC26-01NT41062. The support of the Cleveland-Cliffs Iron Co. is also gratefully acknowledged. The authors would also like to thank Ted Weldum, Todd Davis, Gary Rajala, and Ron Mariani for their considerable advice and assistance in carrying out this work. Laboratory experiments were conducted by H.J. Walqui and J.G. Jelsma. REFERENCES

Banisi, S., Laplante, A.R., and Marois, J. 1991. The behavior of gold in Hemlo Mines Ltd. grinding circuit. CIM Bulletin 84(955):72–78. Coelho, M.A.Z., and Medronho, R.A. 2001. A model for performance prediction of hydrocyclones. Chemical Engineering Journal 84(1):7–14. Del Villar, R., and Finch, J.A. 1992. Modelling the cyclone performance with a size dependent entrainment factor. Minerals Engineering 5(6):661–669. Finch, J.A. 1983. Modelling a fish-hook in hydrocyclone selectivity curves. Powder Technology 36:127–129. Heiskanen, K. 1993. Pages 59–60, 87, 264–272 in Particle Classification. 1st edition. London: Chapman and Hall. Kelly, E.G. 1991. The significance of by-pass in mineral separators. Minerals Engineering 4(1):1–7. Kraipech, W., Chen, W., Parma, F.J., and Dyakowski, T. 2002. Modelling the fish-hook effect of the flow within hydrocyclones. International Journal of Mineral Processing 66:49–65. Laplante, A.R., and Finch, J.A. 1984. The origin of unusual cyclone performance curves. International Journal of Mineral Processing 13:1–11. Luckie, P.T., and Austin, L.G. 1975. Mathematical analysis of mechanical air separator selectivity curves. Transactions of the Institute of Mining and Metallurgy 84:C253–C255. Lynch, A.J., and Rao, T.C. 1968. The operating characteristics of hydrocyclone classifiers. Indian Journal of Technology 6:106. Napier-Munn, T.J., Morrell, S., Morrison, R.D., and Kojovic, T. 1996. Pages 326–327 in Mineral Comminution Circuits: Their Operation and Optimisation. Brisbane, Australia: JKMRC, University of Queensland. Neesse, Th., Dueck, J., and Minkov, L. 2004. Separation of finest particles in hydrocyclones. Minerals Engineering 17:689–696. Pasquier, S., and Cilliers, J.J. 2000. Sub-micron particle dewatering using hydrocyclones. Chemical Engineering Journal 80(1–3):283–288. Plitt, A.J. 1976. A mathematical model of the hydrocyclone classifier. CIM Bulletin 69(776):115–123. Rouse, B.D., Clayton, J.S., and Brookes, G.F. 1987. Confirmation of modelling techniques for small diameter cyclones. Pages 7–20 in Proceedings of the 3rd International Conference on Hydrocyclones. Edited by P. Wood. Amsterdam: Elsevier.

Simulation-Based Performance Improvements in the Ispat Inland Minorca Plant Grinding Circuit S. Ersayin,* W.M. Bond,† R. Strukel,† J. Arola,† and B. Kettunen‡

ABSTRACT

This study was initiated by plant sampling. Raw data generated by sample analysis were mass balanced and used for performance assessment and model fitting. Evaluation of massbalanced data indicated that the ball mill circuit at the Ispat Inland Minorca plant was the bottleneck limiting throughput. A team of engineers developed performance improvement ideas to alleviate the load around the circuit. These included modifications that have a direct effect on the circuit, such as makeup ball size, volumetric ball charge, critical speed, percent solids in the mill, more efficient hydrocyclones, and replacing of hydrocyclones with stack sizers. Other modifications that have indirect effects—namely, dry cobbing, improved fine screening, and separate grinding of fine screen oversize—were also simulated. Simulations were carried out using an improved version of Usim Pac mineral processing simulation software. Improvements included incorporation of magnetic separator, hydroseparator, and fine screen models into the software. Although the simulations were aimed at reducing the load around the ball mill, complete plant simulations were carried out to determine the effects of modifications on downstream flows and to simulate the upstream effects of increased feed rates. Results of simulations indicated that all the modifications would provide some degree of benefit to the circuit/plant performance. However, the most promising and feasible alternative was the use of finer makeup balls with more efficient hydrocyclones. The finer makeup ball size modification was immediately implemented in the plant, and substantial improvements in throughput were obtained. Plant sampling was repeated to quantify benefits from this modification. Mass-balanced data indicated a very good fit between actual and predicted performances. As a result of simulation-based modifications at the plant, throughput was increased more than 10%. Further improvements are expected following replacement of existing 15-in. cyclones by more efficient 20-in. units. INTRODUCTION

The Ispat Inland plant annually processes approximately 9 Mt of crude magnetite-bearing iron ore (taconite) to produce 2.8 Mt of final concentrate containing less than 4% silica. * University of Minnesota, Coleraine Minerals Research Laboratories, Coleraine, Minnesota † Mittal Steel, Minorca Mine (formerly Ispat Inland Mining Co.), Virginia, Minnesota ‡ Noramco Engineering, Hibbing, Minnesota 149

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The plant consists of magnetic separation and flotation circuits. The magnetic separation circuit has three parallel lines and produces magnetic concentrate containing 6%–7% silica. The flowsheet of the magnetic separation circuit is shown in Figure 1. Fine ore (–25 mm) coming from the crushing plant goes through two stages of grinding and three stages of magnetic separation. Magnetic concentrate from all three lines is combined and fed to a flotation circuit floating silica using amine as a collector. Flotation is carried out in two stages: rougher cells produce a final magnetite concentrate, whereas rougher floats (tails) are further treated in scavenger cells to recover magnetite carried into the tail stream (Ersayin et al. 2005). The final product from the plant is fired iron ore pellets. Final concentrate from concentration circuits goes through filtering, balling, and induration steps to produce the final product. The pellet plant has ample capacity. Therefore, pellet production is concentrate limited. It is estimated that the pellet plant could easily process 3 Mt of concentrate annually. This created an incentive for plant engineers to search for improved concentrator performance that could increase the throughput by 10%. The integrated size reduction and concentration nature of iron ore processing and lack of reliable models for magnetic separation and other unit operations specific to iron ore processing had prevented iron ore processing plants from making full use of mineral processing simulation techniques. Triggered by impressive performance improvements in the National Steel Pellet Company’s plant through a combination of modeling and a pilot-scale testing study (Wennen, Nordstrom, and Murr 1995), the iron ore producers on the Iron Range in northern Minnesota decided to establish the Concentrator Modeling Center to develop mathematical models needed for reliable simulation of their plants and to provide simulation-based services. The Iron Ore Cooperative Research Program of the Minnesota Department of Natural Resources provided funding for the center, which was established within the Coleraine Minerals Research Laboratory (CMRL), University of Minnesota. Following the development of basic models for magnetic separators, hydroseparators, and fine screens, the center was ready to carry out reliable simulations of taconite plants. In 2002, the U.S. Department of Energy provided major funding for the project to demonstrate how mineral processing simulation can reliably be used for improving performance of iron ore processing plants. This paper summarizes a large portion of this study aimed at improving ball mill grinding circuit efficiency. SIMULATION-BASED STUDY

The study was initiated by plant sampling and followed typical steps of efficiency improvement plans, including sample analysis, mass balancing, performance evaluation, development of alternatives for improved performance, modeling and plant simulation, selection of most feasible alternatives, plant implementation, and validation of simulation results. Details of these steps are described in the following subsections. Plant Sampling and Sample Analysis

Prior to sampling, operating conditions were checked to ensure that the plant was operating under steady-state conditions. All the streams in one of the magnetic separation circuit lines from rod mill feed to magnetic concentrate were sampled. Stream sampling was repeated at hourly intervals during an entire shift. Although plant sampling also included the flotation circuit to assess potential effects of modifications in the magnetic circuit on flotation performance, this portion of the study was excluded from this paper due to its focus on the grinding circuit. Details of flotation circuit study can be found elsewhere (Ersayin et al. 2005). Plant sampling was repeated for the second ore blend that is processed during a different period in the year. However, only the data for the first

SIMULATION-BASED PERFORMANCE IMPROVEMENTS

Roughers

Ball Mill

Rod Mill Feed

151

Cyclones

Cobbers Hydroseparator Fine Screens

Finishers

Tails Thickener Coarse Tails

FIGURE 1

O/F

Magnetic Concentrate

Fine Tails

Existing flowsheet of the Ispat Inland plant magnetic circuit

blend are presented in this paper because plant data indicated that the circuit was operating at its limiting (maximum) capacity during sampling of this particular blend. Such plant data formed a good basis for comparison with simulations aimed at alleviating bottlenecks. Stream samples were immediately filtered and dried at the plant. Then they were transferred to the CMRL for sample analysis work, which included size analysis, size-bysize total iron, Satmagan iron, and silica analysis. Bond ball mill grindability tests were also carried out to assess the efficiency of the ball mill grinding circuit and to have a reference point for future plant sampling data. In these tests, cobber magnetic separator concentrates, which were the fresh feed to ball mill in the circuit, were used. Mass Balancing and Performance Evaluation

Raw size and chemistry data generated by sample analysis were mass balanced using the mass-balancing algorithm of Usim Pac (BRGM, Orleans, France) mineral processing software. Based on a measured rod mill feed rate of 350 tph, all the flow rates within the circuit were calculated. In general, mass-balanced data provided a very good fit to raw data, indicating quality of sampling. The only node that created a minor mass-balancing problem was the cobber magnetic separators, due to difficulty in obtaining a representative sample from a large volume and coarse-sized stream of rod mill discharge. Mass-balanced data for major streams are summarized in Table 1. From mass-balanced data and flow rates, magnetic iron losses in tailing streams and recovery in magnetic concentrate were calculated (Table 2). The circuit had a high magnetic iron recovery of 96.2%, with much of the losses occurring in cobber and rougher tails. The circulating load ratio (hydrocyclone underflow to overflow) around the ball mill circuit was 380%. Plant data also showed that existing hydrocyclones were performing poorly (i.e., they had a bypass of more than 40%; Figure 2). A smaller fraction of the circulating loads was coming from the fine screens. Due to density effect, bypassing fines were low-silica fractions unnecessarily circulated back to the ball mill. Plant data showed that hydrocyclone underflow contained approximately 25% concentrate quality material (Table 3). As shown in Figure 2, fine screening was not particularly efficient. These devices also act as a concentration device separating coarse silica, so that screening efficiency

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TABLE 1

COMMINUTION PRACTICES

Mass-balanced data for major streams

Stream

Feed Cobber concentrate Ball mill discharge Cyclone feed Cyclone overflow Hydroseparator underflow Fine screen undersize Magnetic concentrate

Flow Rate, tph

Magnetic Iron, %

Silica, %

350 237 1,536 1,454 303 290 142 135

25.8 37.5 48.0 50.6 54.0 56.4 63.6 64.5

45.5 33.9 23.9 21.3 16.9 14.6 9.6 6.96

TABLE 2 Relative flow rates and magnetic iron recovery in tailing streams and magnetic concentrate Stream

Flow Rate, %

Recovery, %

32.5 23.4 3.7 1.9 38.6

1.9 1.3 0.2 0.4 96.2

Cobber tails Rougher tails Hydroseparator overflow Finisher tails Magnetic concentrate

100 90

Partition Coefficient, %

80 70 60 50 40 30 20

Hydrocyclones Fine Screens

10 0 10

100

1,000

FIGURE 2 Partition curves of existing hydrocyclones and fine screens. The curves represent the actual operation with no correction for water bypass to underflow.

was compromised to obtain low silica in the magnetic concentrate. Operating them at high feed percent-solids results in a finer product containing lower silica, which also creates high bypass. Identifying Bottlenecks. The objective was to increase plant throughput, therefore, identification of circuit bottlenecks that limit capacity was crucial. Discussion involving team members and control room operators identified the existence of three criteria that control the rod mill feed rate: (1) pumping capacity of hydrocyclone feed pump; (2) processing capacity of fine screens; and (3) flotation concentrate silica. Massbalanced data corresponded to the maximum limits for the first two items, which were

SIMULATION-BASED PERFORMANCE IMPROVEMENTS

TABLE 3

153

Silica content of size fractions in hydrocyclone underflow stream Size, μm

Weight, %

Silica, %

150 105 75 53 38 25 –25

42.4 15.2 14.2 12.6 5.5 2.5 7.6

36.9 23.5 12.2 5.0 4.1 3.0 4.8

1,450–1,500 tph at 45% solids and 300 tph (or 1,600 gpm) at 55% solids, respectively. Flotation concentrate silica is primarily controlled by adjusting amine rates. However, when this type of control fails to provide the desired level of silica, the rod mill feed rate is reduced. Alternatives for Improved Performance

Performance evaluation indicated that the ball mill grinding circuit was the major bottleneck limiting plant throughput. In order to increase throughput, the circulating load needed to be reduced. This could be achieved through improved grinding, hydrocyclone classification, and/or, to a lesser degree, fine screening. Several alternatives were considered for improved grinding efficiency. Existing electric motors driving ball mills had ample power. This could create an opportunity to increase power draw of the mills by increasing ball load in the mill and/or critical speed. Analysis of ball mill data indicated that the existing makeup ball charge was too coarse. Use of finer balls could increase the rate of fines production, thereby reducing circulating loads. Another option for grinding efficiency was to increase feed percent-solids. Increased feed percent-solids would increase retention time in the mill and result in improved grinding efficiency. However, this was a variable that was difficult to control because it required control of percent-solids in all streams feeding the ball mill (i.e., cobber concentrate, hydrocyclone underflow, and fine screen oversize). Nevertheless, plant operators could try to keep feed percent-solids high, if substantial benefits could be obtained by such a strategy. For improved classification efficiency, the primary option was double hydrocycloning (Figure 3), which implied a secondary separation of fines in the existing hydrocyclone underflow by a secondary set of hydrocyclones. Later, several other alternatives emerged: retrofitting existing 15-in. cyclones to improve their efficiencies; use of 20-in. more-efficient cyclones; and replacing hydrocyclones with more-efficient size-separation devices, known as stack sizers. One of the hydrocyclone manufacturers claimed that the efficiency of the existing cyclones could be improved by retrofitting, which involved converting the existing constant angle conical part to two conical sections with two different angles. It also was suggested that a new set of larger-diameter cyclones with two conical parts could provide further improvements in terms of efficiency. A radical solution to the inefficiency problem would be the use of stack sizers, which are essentially high-capacity screens with durable screen panels (Valine and Wennen 2002). In recent years, they have emerged as an alternative to hydrocyclones and are very efficient size-separation devices. Other alternatives for improved efficiency were dry cobbing, separate grinding of fine screen oversize, and fine screen feed dilution. Dry cobbing involves magnetic separation of low-grade, near-barren material from the ore before it is fed to a plant. Typically, rod mill feed would be treated by dry magnetic drums, and only the magnetic fraction would

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COMMINUTION PRACTICES

Roughers

Ball Mill

Rod Mill Feed

Cobbers

Primary Cyclones

Secondary Cyclones

Hydroseparator Finishers

Tails Thickener Coarse Tails

FIGURE 3

O/F

Fine Screens Magnetic Concentrate

Fine Tails

Modified flowsheet for the simulated alternative of double hydrocycloning

be fed to the plant (Wu 1997). This would not have a direct impact on the grinding circuit, but it had a potential to increase concentrate production by eliminating a substantial portion of silica-bearing particles from the plant feed. As a result, feed grade would be higher and grinding energy would be better spent on particles that could easily be beneficiated. As fine screen oversize is relatively fine material, it is not expected to go through an efficient grinding and liberation process when it is circulated back to the ball mill, which is designed for a much coarser feed. An alternative is to have a separate grinding circuit for this stream (Figure 4). Vertical mills are successfully used in these types of applications, and substantial improvements in throughput have been reported (Benner 1998). Such a modification would directly reduce the load on the ball mill circuit. Although it is known that diluting fine screen feed would increase the magnetic concentrate silica, this could decrease the load on the ball mill by reducing the fine screen oversize rate as a result of lower bypass and increased cut size. A small increase in silica could be handled by the subsequent flotation process, if benefits prove to be reasonably high. Modeling and Plant Simulation

An enhanced version of Usim Pac software was used for simulations. Improvements included magnetic separator, hydroseparator, and fine screen models developed at the CMRL (Ersayin 2003, 2004; Pletka 2004). For simulation of dry cobbing, data from a pilot-scale test were used to calculate rod mill feed characteristics for this option (Wu 1997). For double cycloning, hydrocyclone retrofitting, and 20-in. cyclones, expected performance and equipment data provided by a hydrocyclone vendor are used to modify model parameters of the Plitt model available in Usim Pac (BRGM 2003). A similar approach was used for stack sizer modeling; Derrick Corporation provided test data for the screen mesh (0.15 mm) to be used in the study. Test data were converted to partition curves for each component. These curves formed the mathematical basis for the simulations. For rod and ball mill modeling, Usim Pac uses a kinetic model combined with an energetic approach. The model adjusts grinding rates in line with the variations in power draw, which could arise due to changes in operating conditions (BRGM 2003). However, this model does not have the capability to simulate the effect of makeup ball size. To

SIMULATION-BASED PERFORMANCE IMPROVEMENTS

Roughers

Ball Mill

Rod Mill Feed

Cobbers

155

Cyclones

Hydroseparator

Fine Screens

Cyclones

Finishers

Tails Thickener Coarse Tails

FIGURE 4 oversize

O/F

Magnetic Concentrate

Vertmill

Fine Tails

Modified flowsheet for the simulated alternative of separate grinding of fine screen

overcome this deficiency, size distributions for different makeup ball sizes generated by the JKTech ball mill model (Napier-Munn et al. 1996) were used to devise a coupling for such an effect. For the screen oversize grinding, a ball mill model with similar grinding parameters as the (primary) ball mill was used. The objective of this particular simulation was to have a size distribution from this separate circuit similar to the magnetic circuit. The number of hydrocyclones and their geometry were adjusted until the objective was achieved. For simulation purposes, it was assumed that the ore consisted of two components, namely, magnetite and gangue. Mass-balanced magnetic iron grades were converted to magnetite on the basis of atomic weights, dividing by 0.7236. The remainder was considered gangue. Eventually, empirical equations developed using mass-balanced data were employed to calculate silica in each stream after magnetite–gangue-based simulations were performed. As a first step, the current operation was simulated. Initially, the best-fit model parameters for each unit were calculated individually. Then, model parameters were fine-tuned to obtain a satisfactory fit between simulated and actual flow rates, grades, and size distributions. Fine tuning was a major task around the ball mill to match operating data with simulated data, due to a number of circulating streams. Finally, an excellent fit to all three types of data was obtained. As a summary, the list of simulations carried out is presented: ƒ Dry Cobbing ƒ Hydrocyclone Efficiency Improvements

– Double Cycloning – Retrofitting the Existing Cyclones – 20-in. Cyclones – Stack Sizers Replacing Hydrocyclones ƒ Ball Mill Efficiency Improvements

– Makeup Ball Size—1.75 and 1.5 in.

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– Increased Ball Charge – Increased Critical Speed – Feed Percent-Solids ƒ Fine Screen Feed Dilution ƒ Fine Screen Oversize Grinding

For each alternative, complete plant simulations were carried out. To simplify comparisons, existing operating conditions were kept constant for the rest of the plant. The effect was then measured by three criteria: ball mill discharge rate, magnetic iron recovery, and silica in magnetic concentrate. Results of Simulations, Selection of Most-Feasible Alternatives, and Plant Implementation

Results of the simulation study are summarized in Table 4. Several simulations were carried out to quantify the effects of increased ball charge, critical speed and feed percentsolids in ball milling, and feed dilution in fine screens, which had existing values of 34%, 0.667, 68.5%, and 56.5%, respectively. For these variables, only one set of simulation results is presented in Table 4. They correspond to 38% ball charge, 0.75 critical speed, 72% solids in feed to ball mill, and 52% solids in feed to fine screens. In general, all alternatives had a certain degree of potential to reduce the circulating loads around the ball mill, thus creating room for increased throughput. For the dry cobbing alternative, rod mill feed rate had to be reduced to 330 tph to maintain the existing level of circulating load, due to a higher-grade feed. As the bottleneck was in the ball milling process, separation of silica gangue by dry cobbing did not substantially alleviate the loads around the ball mill. Nevertheless, simulations showed that dry cobbing would increase the rate of concentrate production as a result of increased feed grade to the rod mill. Increasing ball mill power draw by increased ball load or critical speed would produce similar benefit. However, increased ball load would require narrowing the diameter of the discharge ring because the ball mill had a tendency to discharge balls when ball charge exceeded 35%. The other option required replacement of the pinion shaft. Benefits of increased feed percent-solids would be relatively small, with the risk of increasing viscosity beyond a point that could create grinding inefficiency. The most significant benefits would be obtained by simply changing ball size from 2 in. to 1.5 in. Of the three hydrocyclone efficiency improvement alternatives, double hydrocycloning produced a benefit similar to retrofitting. It was found that 20-in. cyclones would produce more-efficient hydrocycloning. It would reduce the ball mill load appreciably and create enough room for increased throughput. Although stack sizers showed a very large decrease in the ball mill load, detailed data indicated that downstream flow rates would be almost doubled even with a rod mill feed rate of 350 tph. A cut size coarser than the existing meant higher downstream flow rates. Implications were that this alternative requires not only the replacement of hydrocyclones with stack sizers, but also doubling of the downstream equipment sizes. Diluting fine screen feed generated relatively small benefits with increased silica in the magnetic concentrate, indicating that it might be used as a relief when the circuit is overloaded. Separate grinding of fine screen oversize appeared to have a large potential to increase plant throughput. Use of 1.5-in. makeup balls appeared to be the most feasible alternative to implement at the plant. It had a large potential to increase throughput. Although finer balls were more expensive, benefits would easily pay for the additional cost. This alternative also had several advantages: it did not require a capital investment; it would not increase the power draw; no downstream problem was expected; and it was easy to implement.

SIMULATION-BASED PERFORMANCE IMPROVEMENTS

TABLE 4

157

Summary of simulation results

Performance Improvement Alternative

Current Dry cobbing Double hydrocycloning Hydrocyclone retrofit 20-in. hydrocyclones Stack sizers (0.15 mm) 1.75-in. makeup balls 1.5-in. makeup balls Increased ball charge (38%) Increased critical speed (0.75) Ball mill feed % solids (72%) Fine screen feed dilution (52%) Separate grinding of fine screen oversize

Magnetic Concentrate

Ball Mill Discharge Rate, tph

Recovery, %

Silica, %

1,536 1,542 1,245 1,296 1,149 1,039 1,299 1,085 1,395 1,282 1,386 1,382 835

96.2 96.6 96.1 96.1 96.0 96.2 96.2 96.2 96.3 96.3 96.3 96.2 96.2

6.96 6.92 7.35 7.31 7.65 7.24 6.93 7.00 6.99 7.00 6.99 7.28 6.53

Consequently, this option was primarily selected for plant implementation. It was also concluded that the current hydrocyclones should be replaced by more-efficient ones. After the alternative was selected, a number of simulations were carried out to examine the sensitivity of the modified plant to feed grade, feed size distributions, and increased feed rate to flotation circuit. Simulation data indicated that a 10% increase in throughput was an achievable target, even with moderate variations observed in feed grade, feed rate, and coarseness of the feed. Validation of Simulation Results

As a precautionary move, initially one of the lines was partially (30%) converted to 1.5-in. makeup ball size. After running for a period of 4 months without any upsets in the line, it was decided to carry out limited plant sampling to examine if such a modification were producing expected benefits. Mass-balanced flow rates and size distributions were used to simulate the ball mill with a 30% 1.5-in. makeup ball charge. A very good fit between actual and simulated size distributions was observed (Figure 5). Bond tests indicated that there has not been any significant change in ball mill grindability of the ore despite a 3-year difference between the two sampling periods. Encouraged by the observed throughput increase in this particular line, it was decided to convert all three lines at the plant to use 1.5-in. makeup balls. Final plant sampling was carried out after the plant had operated with 1.5-in. makeup balls for approximately 1 year. During this period, plant throughput measurements clearly indicated that more than a 10% increase in throughput was achieved. This increase resulted in a decrease in energy used per ton of concentrate production. However, it also became apparent that upstream unit operation would have problems in supplying the increased ore demand by the plant. Unfortunately, plant sampling had to be carried out during such a period. The line was running with a rod mill feed rate of 360 tph. Nevertheless, plant data could still validate the simulation no matter what the feed rate was. Plant sampling and sample analysis followed the same procedures as the initial sampling. Operating conditions were recorded and raw data were mass balanced. Plant sampling conditions were simulated using model parameters determined from the original data. The following data representing the new conditions were modified: rod mill feed rate, rod mill feed size distribution, rod and ball mill charge levels, and hydrocyclone and fine

158

ADVANCES IN COMMINUTION

COMMINUTION PRACTICES

100

Cumulative Passing, %

80

60

40

20

0 10

Simulated Actual 100

1,000

10,000

FIGURE 5 Ball mill discharge size distributions: Simulated versus actual after 30% 1.5-in. makeup ball charge

screen feed percent-solids. Mill charge levels were not directly measured. Instead, they were adjusted for the recorded power draws. As shown in Table 5, this simulation provided a very good fit to mass-balanced data in terms of flow rates, grades, and recovery, thereby validating the findings of the original simulations. Comparison of simulated and actual data was also carried out for individual pieces of equipment. Only the magnetic separators showed unsatisfactory deviations from the simulated data, probably due to the variations in liberation characteristics and/or the way that separators are currently operated. There had been a 4-year difference between the two plant sampling surveys. Each piece of equipment was individually simulated and simulated size distributions of major streams were compared to actual streams (Figure 6). Particularly, the simulated size distribution of the ball mill discharge provided an excellent fit to the actual distribution. Other simulated and actual parameters corresponded well, all validating the simulation results. CURRENT STATUS

Replacement of 15-in. cyclones with more-efficient 20-in. cyclones has been completed. Optimization of plant operation with the new cyclones is being carried out. As pointed out previously, after the modifications, several upstream problems became apparent. Decisions already have been made to solve these problems. Replacement of existing cobber magnetic separators by higher-capacity 4-ft magnetic separators has been initiated to enable the circuit to process increased throughputs. Modifications in the crushing plant are being made. The capacity of mining equipment to deliver the increased ore demand is being examined. FUTURE PLANS

The next step is to develop a control strategy to optimize circuit efficiency. Steady-state simulations will be used to develop such a strategy. Preliminary simulations prior to hydrocyclone replacement showed that the simulator had excellent capability to mimic circuit operation. However, the existing hydrocyclone model failed to simulate the newly designed 20-in. cyclones after their installation. Therefore, it became necessary to modify

SIMULATION-BASED PERFORMANCE IMPROVEMENTS

159

TABLE 5 Comparison of simulated and actual performance of magnetic circuit after modifications were implemented at the plant Performance Criteria

Simulated

Actual

Feed rate, tph Ball mill discharge rate, tph Hydrocyclone pressure, psi Fine screen feed rate, gpm Magnetic concentrate 80% passing size, μm Magnetic iron, % Recovery, %

360 1,228 20.2 1,363

360 1,239 20 1,351

44 65.0 96.0

45 65.3 95.2

100 90 80

Cumulative Passing, %

70 60 50 40 Rod Mill Discharge: Simulated Rod Mill Discharge: Actual Ball Mill Discharge: Simulated Ball Mill Discharge: Actual Cyclone O/F: Simulated Cyclone O/F: Actual Magnetic Concentrate: Simulated Magnetic Concentrate: Actual

30 20 10 0 10

100

1,000

10,000

100,000

FIGURE 6 Simulated and actual size distributions of major streams in the circuit after implementation of 100% 1.5-in. makeup ball size modification

the current hydrocyclone model to gain the capability of simulating these new hydrocyclones. After such work is completed, a simulation-based control strategy will be developed by carrying out a number of offline simulations. Eventually, this strategy will be tested in the plant. CONCLUSION

Simulation has been successfully used to improve performance of the grinding circuit at the Ispat Inland plant. A large number of simulations were carried out to quantify the potential benefits from performance improvement ideas. Eventually, it was found that replacement of current 2-in. makeup balls with 1.5-in. balls would provide more-efficient grinding and would increase plant throughput by more than 10%. This appeared to be the most feasible option, and it was also easy to implement. Further improvements were

160

ADVANCES IN COMMINUTION

COMMINUTION PRACTICES

expected by additional replacement of existing hydrocyclones with more-efficient ones. As a result of simulation-assisted modifications that have been implemented at the plant, a throughput increase of more than 10% has been achieved. Other performance improvement options are still being pursued. ACKNOWLEDGMENTS

The authors would like to express their thanks to the U.S. Department of Energy, the Iron Ore Cooperative Research Program of the Minnesota Department of Natural Resources, and the Permanent University Trust Fund of the University of Minnesota for their funding of this project. REFERENCES

Benner, R.B. 1998. The Application of Vertimill to the Fine Grinding of Taconite. Technical Report CMRL/TR-98-28. Coleraine, MN: Coleraine Minerals Research Laboratory, University of Minnesota. BRGM. 2003. Usim Pac 3.0: Unit Operation Model Guide. Orleans, France: BRGM. Ersayin, S. 2003. Iron Ore Processing Improvements through Process Modeling and Computer Simulation—2003. Technical Report CMRL/TR-03-08. Coleraine, MN: Coleraine Minerals Research Laboratory, University of Minnesota. ———. 2004. Low intensity magnetic separator modelling: A pseudo liberation approach. Mineral Processing and Extractive Metallurgy 113:C167–C174. Ersayin, S., W.M. Bond, J. Arola, and B. Kettunen. 2005. Simulation of flotation feed preclassification. In Proceedings of the Centenary of Flotation 2005 Symposium. Brisbane, Australia: AUSIMM. Napier-Munn, T.J., S. Morrell, R.D. Morrison, and T. Kojovic. 1996. Page 413 in Mineral Comminution Circuits: Their Operation and Optimization. Indooroopilly, Australia: JKMRC. Pletka, J. 2004. Development of a Mathematical Model for Fine Screening. Technical Report NRRI/TR-2004/15. Coleraine, MN: Coleraine Minerals Research Laboratory, University of Minnesota. Valine, S.B., and J.E. Wennen. 2002. Fine screening in mineral processing operations. Pages 225–236 in Mineral Processing Plant Design, Practice, and Control. Edited by A.L. Mular, D.N. Halbe, and D.J. Barratt. Littleton, CO: SME. Wennen, J.E., W.J. Nordstrom, and D.L. Murr. 1995. National Steel Pellet Company’s secondary grinding circuit modifications. Pages 19–25 in Comminution Practices. Edited by S.K. Kawatra. Littleton, CO: SME. Wu, C. 1997. Dry Cobbing Test on Rod Mill Feeds Inland Steel Minorca Mine Crushed Fine Ores. Technical Report CMRL/TR-97-04. Coleraine, MN: Coleraine Minerals Research Laboratory, University of Minnesota.

Determining Relevant Inputs for SAG Mill Power Draw Modeling Rajive Ganguli,* Sridhar Dutta,† and Sukumar Bandopadhyay‡

ABSTRACT

Recurrent neural network models were developed to model semiautogenous grinding (SAG) mill power draw. This paper demonstrates how sometimes seemingly relevant inputs have no effect on the parameter being modeled. Initially, six inputs (SAG density, bearing pressure, revolutions per minute, noise, recycle, and feed rate) were used to model power draw. Model predictions had a high R2 (0.87), with 90% of the predictions being within 5%. However, a closer inspection revealed certain deficiencies. When the number of inputs was reduced to three (revolutions per minute, recycle, and feed rate), the prediction R2 improved to 0.91, and the number of predictions within 5% increased to 96.2%. INTRODUCTION

SAG mills are a major component within mining. Given their impact on important mining parameters such as throughput and power consumption, it is not surprising that they receive a lot of attention. In order to improve efficiencies, efforts are constantly being made to understand and control them better (Austin 1990; Galan, Barton, and Romagnoli 2002; McCaffery, Katom, and Craven 2002). PROBLEM

Effective control requires that the various factors that influence a process be identified and their impact on the process quantified. Identifying factors that affect a process may not be simple necessarily. Sometimes factors that should logically impact a process do not have any significant bearing, thereby making them a poor choice as a control parameter. Quantifying the impact of the various factors is even more difficult. Many choose to use empirical equations to relate/obtain process values. Among those are Galan, Barton, and Romagnoli (2002), who, for example, modeled the SAG mill power draw using the following equation: power draw (kW) = 25.9(WE + WL) – 2064.5 where WE and WL represent the empty and loaded mill weights in tons.

* Associate Professor of Mining Engineering, University of Alaska Fairbanks † Doctoral Candidate, University of Alaska Fairbanks ‡ Professor of Mining Engineering, University of Alaska Fairbanks 161

(EQ 1)

162

ADVANCES IN COMMINUTION

COMMINUTION PRACTICES

13,700.0 y = –35.932x + 41263 R2 = 0.8036

13,680.0

Horsepower

13,660.0 13,640.0 13,620.0 13,600.0 13,580.0 13,560.0 13,540.0 13,520.0 768.0

768.5

769.0

769.5

770.0

770.5

771.0

771.5

772.0

Bearing Pressure, psi (a) Horsepower Decreasing with Bearing Pressure

13,950.0

Horsepower

13,900.0

y = 58.849x – 31574 R2 = 0.5622

13,850.0 13,800.0 13,750.0 13,700.0 13,650.0 770.0

770.5

771.0

771.5

772.0

772.5

773.0

Bearing Pressure, psi (b) Horsepower Increasing with Bearing Pressure

FIGURE 1 Contrasting relationship between horsepower and bearing pressure of the SAG mill, within minutes of each other

A possible complaint about Equation (1) is that it imposes a fixed linear relationship between the mill power draw and mill weights. This may not be reflective of real-time operating characteristics of a SAG mill. This is demonstrated in Figure 1, which plots the relationship between the bearing pressure and horsepower for the SAG mill considered in this paper. A SAG mill’s bearing pressure is dependent on the weight and, therefore, Figure 1 plots a relationship between factors similar to those given in Equation (1). However, as can be seen, within a short period of time (the two were plotted a few minutes apart), the relationship between the two factors reverses, rather than remaining constant, as implied by Equation (1). Additionally, the recurrent network model does not consider other factors, such as rotation of the SAG mill, in determining the power draw. Yet, SAG rotation does affect power draw. For example, after a certain point, when the rotation is increased, more material inside the mill remains mid-air, thereby reducing power draw. B A C K G R O U N D T O T H E C U R R E N T WO R K

Many SAG mills operate at the limit of their power draws; therefore, this study was designed around power draw (i.e., to understand the various factors that impact power

INPUTS FOR SAG MILL POWER DRAW MODELING

163

draw and to quantify their impact). The intent was to develop real-time models that reflect the dynamic nature of SAG mills, with relationships among factors changing, such as ore type and other operating parameters. Some researchers have used expert systems for SAG control (McCaffery, Katom, and Craven 2002). Essentially, rules (fuzzy or otherwise) based on human experiences are tied to the controller, who applies them as situations change. As a limitation of this approach, only relationships that are easily understood and captured by humans become incorporated. Additionally, trends often are not caught early. This paper builds a recurrent neural network (RNN) model (rather than imposes rules) for horsepower based on the various factors that affect it. Initially, six relevant factors to modeling the horsepower are used as inputs. Subsequently, an effort is made to reduce the number of inputs. As the ultimate intent of the modeling exercise was to determine the control parameters for horsepower, reducing the number of inputs (and hence the number of control parameters) was worthwhile. Control parameters are those factors which, when manipulated, impact the power draw (i.e., horsepower) in a known way. This paper does not present work on horsepower control. RECURRENT NEURAL NETWORK

RNNs are a type of neural network where outputs depend not only upon the current inputs but also upon the previous inputs. This is unlike regular neural networks where outputs depend only upon the current inputs. RNNs are preferred when process parameters have temporal relationships. State–space concepts are often used in describing RNNs. The dynamic behavior of a state–space model is described by the following equations: x(n + 1) = M (x(n), u(n))

(EQ 2)

y(n) = C x(n)

(EQ 3)

where x(n) is the current state vector at time n; u(n) is the input vector; y(n) is the desired output vector; C is a matrix of weights characterizing the output layer; and M is a nonlinear function. In an RNN (Figure 2), the hidden layer defines the state. In Figure 2: x1 x = x2 x3

u =

u1 u2

SAG MILL MODELING

The SAG mill (at a surface gold mine) that was modeled is typically run at 2,000 st/hr, with a peak power draw of 13 MW. Information from OSIsoft’s PI System (www.osisoft.com, San Leandro, California) was used for the modeling. Table 1 shows a snapshot of the SAG-related data from the plant. Initially, six parameters that affected the power draw were considered: SAG revolutions per minute, discharge end bearing pressure, SAG density (percent solids), noise, recycle (tons per hour), and feed rate (tons per hour). The model, therefore, had six inputs and one output, and 20,120 minutes of data (20,120 rows) was used for the modeling. The first 10,000 rows were used for training, while the next 5,000 rows were used for calibration. The final 5,120 rows were used to test the model. Note that for an RNN, selection for training, calibration, and prediction subsets cannot be random because the

164

ADVANCES IN COMMINUTION

COMMINUTION PRACTICES

z–1 z–1 z–1

x1(n)

x1(n + 1)

z–1

y(n)

x2(n) x2(n + 1) x3(n) x3(n + 1)

Bias

u1(n) z–1 = Unit Delay

u2(n)

FIGURE 2

TABLE 1

A fully connected two-input RNN, with two hidden neurons and one output neuron

A snapshot of the real-time database (May 14, 2004)

SAG, rpm

SAG Discharge End Bearing Pressure, psig

SAG Density, % solids

Average Noise, Knox units

New Feed, tph

SAG Power, hp

Pebble Crusher Motor Current, amps

Recycle, tph

SAG Ball Charge, % volume

Mill Tonnage Constraint

6:30

10.4

768.6

73.9

40.7

6:31

10.4

768.4

73.9

40.8

206.5

1848.8

13692.3

29.8

8.7

SAG

203.0

1843.5

13665.9

29.8

8.7

6:32

10.4

768.6

73.9

SAG

40.9

200.0

1907.3

13643.0

28.9

8.7

6:33

10.4

768.9

SAG

73.9

40.9

207.0

1833.7

13626.3

29.4

8.7

6:34

10.4

SAG

769.2

73.9

41.0

206.4

1827.7

13610.8

29.8

8.7

6:35

SAG

10.4

769.4

73.9

41.1

203.8

1850.9

13592.8

29.7

8.7

SAG

6:36

10.4

769.7

73.9

41.2

206.7

1804.6

13584.9

29.9

8.7

SAG

6:37

10.4

770.0

73.9

41.3

202.4

1844.8

13595.6

29.8

8.7

SAG

6:38

10.4

770.2

73.9

41.4

196.0

1865.3

13591.9

29.1

8.7

SAG

6:39

10.4

770.5

73.8

41.5

189.8

1841.5

13577.5

28.7

8.7

SAG

6:40

10.4

770.7

73.8

41.6

192.2

1843.1

13562.9

28.7

8.7

SAG

6:41

10.4

770.8

73.8

41.6

195.0

1865.0

13548.4

28.9

8.7

SAG

6:42

10.4

770.9

73.7

41.7

197.2

1841.7

13539.4

29.1

8.7

Ball mill

6:43

10.4

771.0

73.7

41.8

199.3

1823.8

13541.5

29.2

8.7

Ball mill

6:44

10.4

771.2

73.7

41.9

199.0

1779.2

13544.0

28.7

8.7

Ball mill

6:45

10.4

771.3

73.7

42.0

198.0

1852.1

13548.4

29.1

8.7

Ball mill

6:46

10.4

771.4

73.7

42.2

196.3

1862.8

13559.6

29.2

8.7

Ball mill

6:47

10.4

771.4

73.7

42.8

194.5

1781.0

13571.5

29.2

8.7

Ball mill

6:48

10.4

771.3

73.8

43.4

192.4

1848.2

13577.3

29.2

8.7

Ball mill

6:49

10.4

771.2

73.9

44.0

189.1

1769.8

13567.2

28.6

8.7

Ball mill

6:50

10.4

771.0

74.0

44.7

191.5

1823.4

13556.3

28.4

8.7

Ball mill

6:51

10.4

770.9

74.1

45.0

193.6

1764.7

13553.2

28.7

8.7

Ball mill

6:52

10.4

770.8

74.1

44.6

192.5

1766.8

13559.1

28.6

8.7

Ball mill

6:53

10.4

770.8

74.1

44.3

191.2

1791.7

13569.9

28.6

8.7

Ball mill

Approx. 1-min. Intervals

INPUTS FOR SAG MILL POWER DRAW MODELING

165

14,000 13,500

Horsepower

13,000 12,500

True Predicted

12,000 11,500 11,000 10,500

5055

4789

4523

4257

3991

3725

3459

3193

2927

2661

2395

2129

1863

1597

1331

1065

799

533

267

1

10,000

Time, min

FIGURE 3

True versus predicted horsepower values for RNN modeled with six inputs

model has to be exposed to and depends upon the temporal relationships within the data. All subsets have to be continuous in time domain. Quick stop training (Yu et al. 2004) was followed to ensure network generalization. RESULTS

Neuroshell (Ward Systems, Inc., Frederick, Maryland) was used for RNN modeling. The R2 for the prediction subset was 0.87, with 90% of the predictions being within 5% of the true values. At first glance, the results seem impressive. However, a closer inspection (Figure 3) highlights the deficiencies (lending credence to those who consider R2 to be a poor judge of performance). The model shown in Figure 3 seems to be treading the middle in the first half of the plot, and has difficulty adjusting when the horsepower changes to a different level (on the right-hand side). Additionally, it never entirely tracks the extreme values in horsepower. Therefore, the mean absolute error is relatively high, 348 hp (another model deficiency). Model residual analysis reveals that the R2 between the residuals (true minus predicted) and true values is a somewhat high (0.23). However, this is simply an artifact of the model not adjusting quickly to the swings in horsepower, especially on the right side of plot (Figure 3), where it never quite caught up to the true horsepower. Note that many RNN models fit the data and the model reported here is simply representative. The above performance could be thought of as the general performance of RNNs on the data set. Reduced Number of Inputs

The next part of the project explored if all the inputs were relevant to the model. Noise and SAG density were removed as inputs either because their measurement quality or their relationship to horsepower consumption was deemed questionable. The bearing pressure is primarily dependent on feed rate, recycle, and SAG empty weight. The empty weight of SAG is essentially constant, therefore, any trend in bearing pressure is entirely dependent on feed rate and recycle. Bearing pressure becomes redundant once the feed rate and recycle are used as inputs. Therefore, in the next phase, the model only had three inputs (feed rate, recycle, and revolutions per minute). The rest of the modeling procedure remained the same. The R2 of the prediction subset increased to 0.91, with 96.5% of the predictions being within 5%. The mean absolute error was much better at 189 hp. The residual R2

166

ADVANCES IN COMMINUTION

COMMINUTION PRACTICES

was lower (i.e., better) at 0.1. Thus, elimination of some inputs seemed to have only improved the model. Using the three-input model shown in Figure 4, the R2 for the entire data set (including the prediction subset) was 0.97, with 96.2% of the predictions within 5%. The mean absolute error was 188 hp. Figure 5 gives the line plot of predictions for the entire data set. Further reduction in inputs hurt the model (not presented here). From Figure 4, it is apparent that the three-input model tracks the true horsepower significantly better than the earlier model. However, as seen also in Figure 5, it fails to adequately model the steady regions. For example, in the right half of Figure 4, while the horsepower oscillates in the 13,500–14,000 range, the model predictions simply stay in the middle, with changes in predictions being minor. Ultimately, the steady-state regions are the most important. DISCUSSIONS

The results indicate that predictability did not suffer when the number of inputs was reduced. This could be due to ƒ Lack of quality of certain inputs (not all sensors have robust first principles of

measurement) ƒ The impact of certain inputs on the output being subtle compared to the scale of

observation ƒ Interrelationship between inputs, deeming some of them irrelevant ƒ Some inputs simply not having an impact on the output ƒ Some inputs distracting the relationship between other inputs and the output;

this results in model improvement when the distracting inputs are removed In any modeling exercise, parsimony of parameters, especially inputs, is desired because it reduces the errors of estimation. When the goal of the modeling exercise is control (such as here, even though power draw control is not presented here), reduction in inputs implies reduction in control parameters. Control can only be effective if the selected control parameters truly have an impact on the output. In this paper, it became evident that despite many inputs initially deemed relevant, only three were ultimately sufficient to model power draw. The failure of recurrent models to accurately model the power draw (the high R2 notwithstanding) is partly due to the lack of all information necessary to model the power draw. For example, no information was present on ore hardness. Although determining hardness is difficult in real time, an indirect measure of hardness, such as particle size analysis, could be used. Cameras (and image processing software) installed above the feed belt could provide this information. A criticism of the work presented here would be that the model was not adaptive. The training subset (10,000 rows) consisted of almost 7 days of data. The final prediction subset was 3.5 days long. In other words, during the prediction phase, while the SAG underwent various stages of operation, the model did not change. An improvement may exist in incorporating very short term or adaptive modeling (spanning minutes rather than days), where numerical models are automatically fit to a recent history of process information. This may also solve the problem of the model not being able to predict steady/oscillating horsepower.

INPUTS FOR SAG MILL POWER DRAW MODELING

167

14,000 13,500

Horsepower

13,000 12,500

True Predicted

12,000 11,500 11,000 10,500

5083

4582

4621

4390

4159

3928

3697

3466

3235

3004

2773

2542

2311

2080

1849

1618

1387

925

1156

694

463

1

232

10,000

Time, min

FIGURE 4

True versus predicted horsepower values for RNN modeled with three inputs

15,000 14,500 14,000 Horsepower

13,500 13,000 12,500 True Predicted

12,000 11,500 11,000 10,500

20224

19475

18726

17977

17228

16479

15730

14981

14232

13483

11985

12734

11236

10487

9738

8989

8240

7491

6742

5993

5244

4495

3746

2997

2248

1499

1

750

10,000

Time, min

FIGURE 5

Plot comparing the true and predicted values for the final model for the entire data set

CONCLUSIONS

The power draw of a SAG mill was modeled using RNNs. Initially, power draw estimation was based on six inputs. It was found that when three of the inputs were eliminated, power draw estimation did not suffer. In other words, fewer inputs—SAG density, noise, and bearing pressure—were as adequate for evaluating power draw as more inputs (SAG revolutions per minute, feed rate, and recycle). RNN modeling yielded a high R2 of prediction. However, closer inspection revealed that they did not model the steady/oscillating regions very well. Possible improvements to modeling power draw could include additional relevant data (especially on particle size distribution) and adaptive modeling.

168

ADVANCES IN COMMINUTION

COMMINUTION PRACTICES

REFERENCES

Austin, L. 1990. A mill power equation for SAG mills. Minerals and Metallurgical Processing (February): 57–62. Galan, O., Barton, G.W., and Romagnoli, J.A. 2002. Robust control of a SAG mill. Powder Technology 124:264–271. Haykin, S. 1999. Neural Networks: A Comprehensive Foundation. 2nd edition. Englewood Cliffs, NJ: Prentice Hall. McCaffery, K.M., Katom, M., and Craven, J.W. 2002. Ongoing evolution of advanced SAG mill control at Ok Tedi. Minerals and Metallurgical Processing (May): 72–80. Yu, S., Ganguli, R., Walsh, D.E., Bandopadhyay, S., and Patil, S.L. 2004. Calibration of on-line analyzers using neural networks. Mining Engineering 56(9):99–102.

Cement Clinker Grinding Practice and Technology Hakan Benzer,* Alex Jankovic,† and Levent Ergun*

ABSTRACT

The current world consumption of cement is close to 2 billion tpa and is increasing by about 1% per annum. Conventional cement grinding circuits consist of two-compartment tube mills and air separators. Alternative mills such as high-pressure grinding rolls (HPRGs), vertical roller mills, and Horomills have been applied in recent times to improve grinding efficiency. Air separators play a crucial role in improving the overall energy efficiency of a cement grinding circuit, and their design has been improving continuously over the decades. The introduction of a clinker precrushing stage can significantly improve cement grinding energy efficiency. Due to the relatively low capital cost associated with installation of a Barmac crusher, it is proving an attractive upgrade option. Hybrid grinding circuits with HPGRs are being widely used, primarily to increase energy efficiency, with specific energy consumption reduced to almost 50% compared to some conventional circuits. INTRODUCTION

The current world consumption of cement is close to 2 billion tpa. During the last 10 years, cement production has increased by 38%. Different types of portland cement are manufactured to meet different physical and chemical specifications. The American Society for Testing and Materials (ASTM) has designated five types of portland cement, the characteristics of which are outlined in Table 1. Portland cement is made from exact proportions of materials containing calcium, silica, alumina, and iron. Approximately 1.5 t of raw materials are required to produce 1 t of finished cement. Grinding is an important operation in the cement making process, occurring at the beginning and end of the production cycle. The last stage in the process of manufacturing portland cement is the finish grinding of clinker together with small amounts of gypsum and some admixtures. The principal objectives of clinker grinding are to promote the hydration of cement and to ensure complete coating of inert aggregates. The fineness of the cement affects the placeability, strength, and permeability of the concrete properties. The finer the grind, the more reactive the finished cement. Therefore, every type of cement must exhibit a particular degree of fineness to meet its quality specification. In Figure 1, the particle-size distribution of the different cement types are presented.

* Hacettepe University, Ankara, Turkey † Metso Minerals Process Technology (Asia Pacific), Brisbane, Australia 169

170

ADVANCES IN COMMINUTION

COMMINUTION PRACTICES

Portland cement classification with its constituents and fineness

TABLE 1 Types

Clinker, %

Admixture, %

Minor Component, %

Fineness +45 μm, %

CEM I CEM II CEM III CEM IV CEM V

95–100 80–94 35–64 65–89 40–64

— 6–20 36–65 11–35 18–30

0–5 0–5 0–5 0–5 0–5

11.4 14.2 5.9 11.6 17.0

100 90

Cumulative % Passing

80 70 60 50 40 CEM I CEM II CEM III CEM IV CEM V

30 20 10 0 0.001

0.01

0.1

1

Particle Size, mm

FIGURE 1

Size distribution of different cement types

The electrical energy consumed in the conventional cement making process is in the order of 110 kWh/t, about 30% of which is used for raw materials preparation and 40% of which is used during final cement production by cement clinker grinding. Figure 2 shows the consumption of electrical energy by the different processes in a typical cement production plant (Fujimoto 1993). Minimizing production costs and increasing environmental concerns have emphasized the need to use less energy and therefore promoted the development of more-energy-efficient machines for grinding and classification. EQUIPMENT USED FOR CLINKER GRINDING

Tube Ball Mill

The continuous ball mill has been used for more than 100 years and is still the most widely installed grinding equipment for this application. Cement is ground in tube ball mills operating either in open or closed circuit. The tube mills are characterized by their length/diameter (L/D) ratio with a ratio of 3 found to be best to minimize energy expenditure (Schnatz and Knobloch 2000). The tube ball mills can be operated with one, two, or three compartments, and the length of each compartment should be designed to achieve optimum size distribution variation from feed to the discharge end. Special diaphragms divide the cylinders of multicompartment mills. The diaphragms are primarily designed to prevent loss of the balls to the next compartment

CEMENT CLINKER GRINDING PRACTICE AND TECHNOLOGY

171

Quarry Crushing and Pre-Homogenization, 5%

Raw Material Grinding, 24% Finish Cement Grinding, 38%

Feed Homogenization, 6% Conveying, Packing, and Loading, 5%

Burning and Cooling, 22%

FIGURE 2

Energy consumption for different stages of cement production

FIGURE 3

Example of mill liners in the first and second compartment of a cement ball mill

while allowing the flow of ground material through the mill. The design of the diaphragm influences the fineness of the ground material (Duda 1985). Various shapes of mill liners have been developed for cement mills (see Figure 3). The classifying liners for clinker grinding have a specific design. This lining causes a classification of the grinding ball sizes down the length of the mill. The grooved liner is usually used in the second or third compartment of the cement mill to produce a cascading motion which promotes abrasion breakage. Operation of the tube ball mills is relatively well understood with several design and operating parameters of the ball milling operation affecting the mill efficiency and the quality of the cement produced (Gouda 1981). Vertical Roller Mill

Vertical roller mills (VRMs) have been used for limestone and coal grinding in the cement industry for many years due to their high drying capacity, low energy consumption, compactness, and reliability in operation. The largest mill in operation has an installed power of 6 MW and grinds 840 t/h of lump feed down to 85% passing 90 Pm. Cement grinding by a VRM has found applications in pregrinding systems, advanced pregrinding systems, and finish grinding systems (Shimoide 1996).

172

ADVANCES IN COMMINUTION

COMMINUTION PRACTICES

In a VRM, the interparticle comminution takes place in a material filled gap between the rotating table and the grinding rollers. The mill feed is charged to the center of the table and moves, affected by centrifugal forces and friction, toward the table’s edge. On its way, it is nipped by two, three, four, or six conical rollers installed at the outside rim of the table. The rollers are attached to hydraulic cylinders that provide the grinding force for comminution of the material. The ground particles leave with the airstream and are taken up by the separator incorporated into the casing of the mill. The fine product reports to the mill discharge, and the coarse reject of the separator falls back onto the table as a recirculating load. The VRM was first used in a commercial operation to finish-grind cement in 1984 (Shimoide 1996). Since then, however, further applications of this technology in the industry have been relatively limited. One reason is that a portion of the power savings achieved in the VRM (because of higher grinding efficiency) is lost due to additional power consumption by the fan. In addition, the VRM suffers from roller wear problems. Recent plant trials, however, have indicated that the problem can be reduced with new roller designs. The wear rate and the throughput of the system depends very heavily on the consistency of the materials being ground (Nobis 2001). Effective comminution largely depends upon the formation of a stable grinding bed between the rollers and the grinding table. The main operational bottleneck of the VRM is its high circulating load from the separator back to the table. This causes inefficient grinding operation because of the high load accumulation inside the mill. To overcome this problem, the roller mills can be operated with external material circulation. It has been reported that the specific power consumption involved in producing portland cement with external material circulation was 30% less than for producing these cements in tube mills (Feige 1981). The Kawasaki Inc. CKP mill is an example of this type of machine and was developed based on the proven technology of VRMs (Sutoh et al. 1992). In CKP systems, material is fed through a central chute. A centrifugal force, produced by rotation of the table, distributes the product over the table surface. After grinding, which is carried out between the table and rollers, the material is extracted from the CKP by gravity with the assistance of scrapers (Miranda et al. 1998). CKP mills are generally used as pregrinders, and the grinding energy efficiency of these mills as a pregrinder has resulted in grinding energy savings of 17% (Dupuis and Rhin 2003). Horizontal Roller Mill

The horizontal roller mill (Horomill) consists of a horizontal cylinder supported on slideshoe bearings and driven through an open gear train. Terms used to describe the principles of operation of a Horomill include a bed material compression mill, a multi-compression mill, and a high-capacity mill (Cornille 1999). A simplified diagram outlining the principles of operation is shown in Figure 4. The material passes into the mill at one end of the cylinder and, because of the centrifugal effect caused by operating the cylinder above the critical speed, is carried as a uniformly distributed layer of material on its inner surface. The finished product is collected in a dust filter, while the coarse particles are recycled to the mill. The grinding force is transmitted to the roller by hydraulic cylinders. Internal fittings are provided to control the material recirculation. It’s been reported that the grinding process based on multiple compressions gives the machine a high stability, and also the recirculating load can be adjusted to suit the quality target (Cordonnier 1994). Compared to a ball mill, the Horomill operates with a larger grinding bed thickness and moderate pressures that lead to energy savings of 35% to 40% when used for cement grinding. In operation, the specific costs related to the liner and wear parts are

CEMENT CLINKER GRINDING PRACTICE AND TECHNOLOGY

173

Horomill Tube Inlet

F

F

Rotation of Horomill Tube F

Scraper Forward Plate

Material Outlet Material Inlet

Roller

Shoe Bearing

Grinding Force

Outlet

FIGURE 4

Comminution principle in a Horomill

higher than in an equivalent ball mill (Brunelli 2001). Mechanical problems with a Horomill have been reported in a Konya cement plant in Turkey (Fochardiere 1999). High-Pressure Grinding Roll

The high-pressure grinding rolls (HPGRs) developed by Professor Schoenert have been offered as a comminution technology with claims of improved performance when compared to conventional grinding technology. In particular, it has been claimed that the HPRG has a lower specific energy consumption (Schoenert 1979). The material to be ground in an HPGR is compressed in a gap between two counterrotating grinding rolls (see Figure 5) with circumferential speed of 1 to 1.8 m/sec. The product from the HPGR is a compacted cake that contains fine particles and coarser particles with a large number of incipient cracks and weak points that greatly reduce the energy expenditure during further comminution (Ellerbrock 1994). An HPGR can be used at different stages in the cement grinding process: precrushed, finish grinding, hybrid grinding, and semifinish grinding. When an HPGR has been used in the precrushed stage, 20% reductions in overall energy consumption have been achieved (Kellerwessel 1996). Hybrid grinding involves splitting the coarse fraction from the air classifier to the HPRGs and ball mill, respectively. In the semifinish grinding application, the HPRG is operated in closed circuit with the air classifier, and the fines from the separator are finally ground in a tube mill circuit. In the finish-grinding application, the HPRGs operate with an air classifier in closed circuit. Using this finish-grinding configuration, the potential energy savings can be as high as 50% (Kellerwessel 1996), but the water requirements in the subsequent mortar production process are significantly higher due to the narrow size distribution produced (Roseman 1989; Odler and Chen 1995). Air Classifier

Classification in the clinker grinding circuits is achieved using the air classifiers. Development of the air classifier was based on the operating principles of two devices, the simple expansion chamber and the Mumford and Mood separator, patented in 1885 (Klumpar, Currier, and Ring 1986). There are two types of air classifiers, dynamic and static. Static air classifiers are an old technology without moving parts. Classification is achieved by changes in air velocity and direction. The principle of operation is shown in Figure 6a. The airstream carrying the particles is converted from a directional flow through the outer cone into a rotating flow by guide vanes. The particles are subject to a centrifugal force—the coarse particles moving to the outer wall of the inner cone and collected in a bin, while the fine particles leave with the air and are sent to a dust collector. The product size can be altered to some

174

ADVANCES IN COMMINUTION

COMMINUTION PRACTICES

Nitrogen cylinder

Feed

Oil Cylinders

Moveable Roll

Fixed Roll

Product

FIGURE 5

The principle of operation of HPGRs

Fines Adjustable Blades

Particle Feed

Immersion Tube

Direction of Rotation

fC fD fG

To Coarse Particle Cone

Tailings

T

R

To Fine-Particle Chamber (a)

(b)

FIGURE 6 (a) Schematic of the static air classifier; and (b) separation mechanism in a dynamic air classifier

extent by changing the angle of the vanes, but the efficiency is low and static classifiers can be regarded more as grit separators than efficient classifiers. Dynamic classifiers have both moving and fixed internal parts. The dynamic air classifiers utilize a distribution plate to disperse the feed material into the separation zone. Thus a particle of material is subjected to three forces: centrifugal force from the distribution plate, uplift from the air current, and gravity. Figure 6b indicates the forces acting on a particle in a dynamic air classifier. Dynamic classifiers have evolved through three generations, each being significantly better than its predecessor. The first-generation classifier had a distributor plate, and the air circulation in the classifier was provided by a vertically supported rotor. The main problems with the first-generation classifiers were that the circulating air became very hot, fine particles were not removed from the recycling air, and the control of the product was very difficult. Figure 7a shows a simplified sketch of a first-generation air separator. The second-generation classifier (see Figure 7b) is based on the same operating principles as the first but an external fan is used to circulate the air and a cyclone is used

CEMENT CLINKER GRINDING PRACTICE AND TECHNOLOGY

175

Closed Circuiting A c

d

Fresh Air

Feed

b

Exhaust

a Cyclone

Distribution Table

e

Recycling Fan

Fines

Return Air Vanes Rejects

G F (a)

(b)

FIGURE 7 (a) First-generation dynamic air separator; and (b) second-generation dynamic air separator

to remove fine particles. Greater product control is possible due to the ability to adjust the rotor speed and air velocity separately. The third-generation separators are highly efficient separator devices (see Figure 8). The feed material to the separator is delivered as a dispersed curtain of particles, and the horizontal air flow to the separator results in uniform separation performance across the unit. The fine particles pass through a rotating cage before going to the fine product. The bars of the cage assist in the performance of the separator. CIRCUIT CONFIGURATION FOR IMPROVED ENERGY EFFICIENCY

For most of the twentieth century, the common dry-grinding circuits for the production of finished cement from cement clinker consisted of two-compartment tube mills with or without the air separators. The advantage of this circuit is its simplicity and ease of operation; however, the energy consumption is high, especially for open-circuit operation. One of the reasons that the two-compartment tube mill circuit has limited energy efficiency is due to the high reduction ratio that must be achieved in the single comminution/ classification step. Clinker feed size can vary from F80 = 10–40 mm and the final product size from P80 = 35–40 ȝm with the size reduction ratio being in the order of 250–1,000. Large balls (up to 100 mm) are required in the first compartment of the tube mill to crush the coarse clinker. Ball mill grinding efficiency for feed sizes larger than F80 = 2–3 mm is particularly poor, and it should therefore be more energy efficient to precrush the clinker. Recent work indicates that introduction of the Barmac crusher for clinker precrushing can increase the cement circuit throughput on the order of 10%–20%. Alternatively, the total energy consumption of the circuit can be reduced on the order of 5%–10% (Jankovic, Valery, and Davis 2004). This is an attractive upgrade option due to the relatively low capital investment involved in the installation of a Barmac crusher. Clinker precrushing can be carried out with a variety of different crushers. Figure 9 shows the product size distributions from a Barmac and, alternatively, a high-performance (HP) cone crusher in closed circuit with a 4.75-mm screen at 2.3 kWh/t specific energy input. Although the 80% passing size for the HP cone crusher is finer, the Barmac product is potentially more favorable due to its higher content of fines. This advantage, however, is

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Shaft Fines Plus Air

Plate Blade Vane Annular Space

Feed Plus Air Inlet

Volute Spoke

Tertiary Air

FIGURE 8

Coarse

Schematic of a third-generation dynamic air separator

100 HP Cone, 2.3 kWh/t, Product Barmac, 2.3 kWh/t, Product HP Cone Feed Barmac Feed

90 80

Cumulative % Passing

70 60 50 40 30 20 10 0 0.01

0.1

1

10

100

Size, mm

FIGURE 9

Product size distribution from the closed Barmac and HP cone crusher circuit

not crucial for the selection, as the clinker feed size, hardness, and abrasivity, as well as the required capacity, will have an effect on the particular crusher best suited to the particular application. In order to obtain the most efficient breakage in the first compartment of the ball mill after introduction of the precrushing stage, the ball size distribution should be changed to suit the new particle-size distribution of the material fed to the mill. An example of the measured particle-size distribution of the combined ball mill feed (new feed + 150% recycle) with raw and precrushed clinker is shown in Figure 10. A significant fraction of the material in the feed containing the raw clinker is coarser than 5 mm. To effectively

CEMENT CLINKER GRINDING PRACTICE AND TECHNOLOGY

FIGURE 10

TABLE 2

Optimum Ball Size, mm 142 116 101 90 71 50 36 25 18 13 9 6 / / / / / /

Precrushed Raw Clinker, Clinker, % Retained % Retained 0.20 0 0.53 0 3.71 0 6.30 0 4.15 0 10.28 0.40 7.50 9.65 2.86 11.26 0.94 4.74 4.63 4.40 3.821 6.83 13.92 16.12 9.82 9.89 8.17 8.63 3.41 3.84 3.97 4.60 8.27 9.53 7.49 10.10

18 16

Raw Clinker Precrushed Clinker

14 12

% Retained

Particle Size, mm 37.5 25 19 13.7 9.5 4.75 2.36 1.18 0.6 0.3 0.15 0.075 0.053 0.038 0.032 0.025 0.01 0

177

10 8 6 4 2 0 0.01

0.1

1

10

100

Size, mm

Combined ball mill feed-size distribution when processing raw and precrushed clinker

Specific energy consumption in different cement grinding circuits utilizing HPGRs

Cement Grinding Circuit Description

Open-circuit HPGR, closed-circuit ball mill Open-circuit HPGR with partial recycling, closed-circuit ball mill Hybrid grinding Closed-circuit HPGR, closed-circuit ball mill Semifinish grinding

HPGR Specific Energy Consumption, kWh/t

Circuit Overall Specific Energy Consumption, kWh/t

4.05 8.9

34.2 29.6

— 8.0 9.8

29.9 21.7 23.0

grind this sized feed, the calculated top ball size required (using the Bond formula) would be 90–100 mm. For precrushed feed, the top ball size would be 35–40 mm due to the absence of coarse particles. With precrushed feed, the optimum ratio in length between the first and second compartment would also be affected. Design of the transfer grate, mill liners, and sweep air velocity should also be reviewed to suit the new reduced ball size and provide efficient removal of fine particles. In the last 20 years, HPGRs have been used extensively in cement grinding circuits due, primarily, to their higher grinding efficiency compared to the conventional twocompartment tube mills. HPGRs can be used for precrushing, finish grinding, hybrid grinding, and semifinish grinding. Table 2 shows the energy consumption of five cement-grinding circuits employing HPGR units in different applications (Aydo÷an, Ergün, and Benzer 2004). It can be observed that the overall circuit specific energy consumption decreases when a large portion of the size reduction (higher HPGR kWh/t) is performed by the HPGR. Circuits that employ HPGR mills can achieve in excess of 40% improvements in grinding energy efficiency, providing that the circuit is optimized and automated process control is employed. In order to assess the performance of a particular cement-grinding circuit and to compare efficiency of different circuit configurations, complete audits are required. The audit includes monitoring and sampling of different circuit streams during steady-state operation, as well as mill inspection and sampling after a crash-stop. Based on information obtained from the audit, a mass balance can be carried out to determine material

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flows (solids and air) around the circuit. Using this information, the performance of the circuit and individual pieces of equipment can be assessed and potential bottlenecks identified. To assist with circuit optimization, site and equipment-specific models are calibrated based on the results from the audit. Models can be then used to simulate different operating conditions and circuit scenarios (Benzer et al. 2001, 2003). CONCLUSION

The current world consumption of cement is close to 2 billion tpa and is increasing at about 1% per annum. The electrical energy consumed in the conventional cement-making process is approximately 110 kWh/t, and around 40% of this energy is consumed for clinker grinding. For most of the twentieth century, the dry-grinding circuits for the production of finished cement from cement clinker consisted of two-compartment tube mills and air separators. Alternative mills such as the HPGRs, VRMs, and the Horomill have been applied in recent times to improve the grinding efficiency. Significant energy savings are reported in applications that utilize these mills, the HPGR being the most widely used. During this period, the design of the air separators has evolved from the very inefficient static separators to the highly efficient dynamic separators. These separators play a crucial role in improving the overall energy efficiency of the cement-grinding circuits. The increasing demand for “finer cement” products, and the need for a reduction in energy consumption and greenhouse gas emissions, increases the importance of grinding optimization. In the last two decades, significant progress has been achieved through improved equipment design and the use of new circuit configurations. Introduction of a clinker precrushing stage can significantly improve the energy efficiency. Barmac crusher installation, due to its relatively low capital cost, is an attractive upgrade option. Hybrid grinding circuits incorporating HPGR units are being used widely, primarily to achieve higher energy efficiency, with specific energy consumption reduced by almost 50% compared to that achieved in some conventional circuits. In order to optimize a grinding circuit, a detailed knowledge of circuit operation is required. Modeling and simulation techniques can be effectively utilized to assist in this process optimization exercise. BIBLIOGRAPHY

Aydo÷an, N., Ergün, ù.L., and Benzer, H. 2004. HPGR applications in the cement industry. Pages 33–48 in JKMRC International Student Conference 2004, 6–7 September. Brisbane, Australia: JKMRC. Benzer, H., Ergün, L., Lynch, A.J., and Öner, M. 2003. Case studies of models of tube mill and air separator grinding circuits. Pages 1524–1533 in Proceedings: XXII International Mineral Processing Congress. Edited by L. Lorenzen and D.J. Bradshaw. Cape Town, South Africa: African Institute of Mining & Metallurgy. Benzer, H., Ergün, L., Oner, M., and Lynch, A.J. 2001. Simulation of open circuit clinker grinding. Minerals Engineering 14(7):701–710. Brunelli, G. 2001. A proven partnership. International Cement Review (February): 37–40. Buzzi, S. 1997. The Horomill. ZKG International 3:127–138. Cordonnier, A. 1994. The Horomill—a new finish grinding mill. ZKG 11:643–647. Cornille, J.P. 1999. Pages 21.1–21.2 in Horomill: Latest Developments and Results. European Cement Conference Proceedings. Surrey, UK: Pro Publications International.

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Duda, W.H. 1985. Cement Data Book—International Process Engineering in the Cement Industry. 3rd edition. Bauwerlag: GMBH. Dupuis, J., and Rhin, C. 2003. Increased grinding capacity at R.A.K. World Cement (February): 79–83. Ellerbrock, H.G. 1994. High pressure grinding rolls. ZKG 4:1047–1100. Feige, F. 1981. Cement grinding in a roller mill with external material circulation. ZKG 11(81):560–562. Fochardiere, R. 1999. Horomill: One year’s operating experience. World Cement (September): 98–104. Fujimoto, S. 1993. Reducing specific power usage in cement plants. World Cement 7:25–35. Gouda, G.R. 1981. Technical aspects of comminution in the cement industry. Part 1. World Cement Technology (April): 112–122. Jankovic, A., Valery, W. Jr., and Davis, E. 2004. Cement grinding optimisation. Minerals Engineering Journal 17(11–12). Kellerwessel, H.A.M. 1996. High pressure particle bed comminution. State of the art, application, recent developments. Engineering and Mining Journal (February): 45–52. Klumpar, I., Currier, F., and Ring, T.A. 1986. Air classifiers. Chemical Engineering (March): 77–92. Marchal, G. 1995. FCB breaks into Asian market with Horomill. World Cement (September): 23–25. Miranda, R.F., Minas, I., Yamana, W.T., Pirapora, S., Cimentos, V., and Tete, P. 1998. Brazilian progress in grinding. World Cement (May): 40–42. Namik, A.A., Levent, E., and Benzer, H. 2004. High pressure grinding rolls (HPGR) application in the cement industry. Presented at JKMRC International Conference, Brisbane, Australia. Nobis, E. 2001. Experience with grinding slag and clinker in a Loesche mill. ZKG 54(4):196–204. Odler, I., and Chen, Y. 1995. Influence of the method of comminution on the properties of the cement. ZKG 48(9):496–500. Roseman, H. 1989. Investigations on a high pressure grinding roll mill used for cement grinding. ZKG 42(6):142–144. Schnatz, R., and Knobloch, O. 2000. Influence of the Ball Filling Factor on the Power Consumption and Throughput of Ball Mills in Combined Grinding Plants. ZKG 8(53):438. Schoenert, K. 1979. Verfahren zur Fein und Feinstzerkleinerung von Materialien sproden Stoffverhaltens. German Patent DP 2708053. Shimoide, K. 1996. Cement grinding by vertical roller mill. World Cement (September): 68–74. Sutoh, K., Murata, M., Hashimoto, S., Hashimoto, I., Sawamura, S., and Ueda, H. 1992. Current report on preliminary grinding of clinker and raw material using the CKP system. ZKG 3:94–96.

Extended Semiautogenous Milling: Smooth Operations and Extended Availability at C.M. Doña Ines de Collahuasi SCM, Chile F. Romero,* L. Yacher,† and O.A. Bascur‡

ABSTRACT

Comminution circuits represent one of the largest operating costs in mineral processing. The current state-of-the-art plant information systems enable the use of a wide range of supervision techniques. The use of a real-time plant information system has derived major economic benefits. Semiautogenous milling operations are supervised in real time for any substandard or abnormal conditions. Furthermore, the use of advanced statistical technologies allows for an increased potential of plant performance. The use of semiautogenous milling operations have been made easier, and major economic benefits can be obtained, by extending mill operating time and reducing maintenance costs. INTRODUCTION

Comminution circuits represent one of the largest operating costs in mineral processing plants. These circuits are highly multivariable and their analysis and optimization are difficult. Compañia Minera Doña Ines de Collahuasi SCM, Chile, has implemented a RealTime Performance Management (RtPM) system powered by OSIsoft’s PI System to integrate and capture data and events of their processes and metallurgical information. This RtPM system is used to extract, analyze, provide context, distribute, and display information. Operators and managers can act quickly and with confidence in their decisionmaking. The RtPM infrastructure provides an environment for transforming real-time and historical information into action. Under RtPM integration infrastructure, many valuable applications can be designed by customers and third parties (Bascur and Kennedy 2000, 2004). This paper presents an example of adding an advanced statistical analysis tool to a basic platform. The operation of semiautogenous mill grinding circuits is multivariable and dynamic. The process variables involved in mineral processing plants show strong interaction. It is difficult to identify the cause and effect between process variables and ore mineralogy. There are nonlinearities and delays in the interaction of many different process variables, equipment wear characteristics, slurry rheology, mineral composition, and operator behavior. * C.M. Doña Ines de Collahuasi SCM, Iquique, Chile † Contac Ingenieros LTDA., Santiago, Chile ‡ OSIsoft, Inc., Houston, Texas 181

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Analysis of the process history allows for defining critical process patterns (models) that can be put to work online, using the RtPM calculation engine. Specific models can be developed to help operations with early alerts of pattern deviations, estimation of projected process variables, and their influence on specific targets, among others. The RtPM tools simplify the implementation of continuous improvement strategies. It can be challenging to estimate the liner wear in large machines. Both increasing the availability of the equipment and improving metallurgical performance are key for optimal operations. Mineral composition plays a very important role in overall metallurgical performance, flotation recovery and thickener, and pipeline performance. Changes in specific gravity of the ore can increase viscosity, and these changes affect the hydrodynamic conditions of the process. To deal with this complex scenario, advanced multivariable statistical techniques have demonstrated a great application potential for characterizing variable relationships and the development of performance models in operations. This paper highlights some of the findings in applying multivariate analysis to semiautogenous grinding (SAG) mill operations. It will discuss the basic findings in predicting liner wear and detection, the effect of stockpile in metallurgical performance, and the effect of iron content in feed. RESULTS FOR PATTER N RECOGNITION IN SAG MILL OPERATION

To analyze the behavior of complex systems, one can add known facts to the data, such as complying with mass balance constraints. This is a typical use of data reconciliation to identify how close the data are to satisfying mass balance constraints. Romero, Suarez, and Bascur (2004) have presented such a case (Bascur and Linares 2005). When no structure is available to relate the patterns of a complex system, principal component analysis (PCA) is now a well-known method for multivariate data analysis. PCA has been discussed by several authors in the mineral processing and metals industry (MacGregor et al. 1991; MacGregor and Kourti 1998; Hodouin et al. 1993; Dudzic 1998; Vaculik and Smyth 2003; Romero, Orchard, and Yacher 2003). The multivariable statistical analyses use two basic concepts. One is the variability factor analysis or “VFA,” also known as PCA. Information technology evaluates the predominant sources of variability in a data set. The procedure consists of a data reduction of the original data-set space by selecting the vectors where the variability is maximized. Thus, it is possible to represent the process by only analyzing these new projections structures called variability factors (VFs), a reduced set of calculated variables that represent the variability of the operations (Rodriguez and Tobias 2001). The second most important concept is the projection to latent structures (PLS), a valuable tool for model identification around an operating point. PLS generates latent vectors for the statistically normalized input and output variables for which simplified output versus input models can be generated for real-time relationships evaluation. PLS models can be used in several ways; the most common are variable estimators and soft sensors. Recent works (mostly in machine surveillance) have demonstrated potential for early detection of pattern deviations (a pattern being defined as “normal,” “desired operating region,” among others, depending upon the model), and for the offline and online evaluation of the relative influence of model variables. In the case of SAG mill circuits, the VFA approach detects time instances when the SAG mill’s operation adjusts to a recommended performance, generating an operation pattern for the process. The process is captured by the PI System and analyzed using PI DataLink (OSIsoft). Afterward, the pattern is analyzed with the statistical tests included

EXTENDED SEMIAUTOGENOUS MILLING

183

To Flotation

SAG Mill (2) 32 ft × 15 ft, 8 [MW]

Pebbles Crusher (2) To Stockpile

Sump (2)

Hydrocyclones Battery (4) 12xDS26 Ball Mill (2) 22 ft × 36 ft, 9.7 [MW]

Hydrocyclones Pump (4)

From Stockpile

FIGURE 1

SAG mill circuit process diagram

FIGURE 2

Raw data set in Excel using PI Datalink and SCAN add-ins

in SCAN software (Contac Ingenieros, L. Yacher). SCAN is used to obtain the reduction in the representation of the data and evaluates the contributions of the data. It also provides the tools to develop a predictive model and the necessary code to run it online in OSIsoft’s PI ACE (advanced computing engine). As a result, the main sources for process variability are identified, and the principal components for the data set are determined (Figure 1). Figure 2 shows a typical set of real-time information that is used to further analyze the data to find structure or relationships for detecting pattern changes based on normal condition model characterizations. PI DataLink is used to extract filtered data to construct the basic data set. Figure 2 shows the offline data analysis using Excel with PI Datalink and SCAN addins. All the process variables are extracted to the spreadsheet for further multivariable analysis using SCAN offline. As the process consists of two mill lines, first a comparison between each line performance is needed to define a single normal operation pattern, which is shown in Figure 3. From Figures 3 and 4, it is clear that each SAG mill (operating at the same conditions) was affected by an unmeasured disturbance. A conclusion of the analysis, taking into account the maintenance records, the process history, and the operator’s experience, estimates the unmeasured variable affecting

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20

15

10

VF2

5

0

–5

–10

–15

–20 –20

–15

–10

–5

0

5

10

15

20

VF1

FIGURE 3

Influences of liner wear in SAG mill 1 data variance

8

6

4

VF4

2

0

–2

–4

–6

–8 –10

–8

–6

–4

–2

0

2

VF3

FIGURE 4

Influence of liner wear in SAG mill 2 data variance

4

6

8

10

EXTENDED SEMIAUTOGENOUS MILLING

185

the SAG mill’s performance was the liner wear. The final analysis considered the existence of two main operation patterns, one of them when the SAG mill’s liners were new and the other when they were worn. The process variables included in the analysis are ore and water feed, mill speed, motor power (two motors for each SAG mill), pressures (feed and discharge), and pebble mass flow. SAG Mill Variability Patterns (New Liners)

From the VFA loading maps (Hodouin et al. 1993), the following conclusions can be stated: ƒ The main sources of variability are the mill speed, bearing oil pressures, and the

motor’s power. ƒ Ore feed, water feed, and pebble flow give additional and complementary infor-

mation about the mill’s operation. ƒ There is more residual variability in the discharge pressure than in the feed pressure. ƒ A powerful correlation is seen between the ore and water feed loops. ƒ Any unusual increment of variability in the mill speed or in pebble flow can be

considered an important disturbance. SAG Mill Variability Patterns (Worn Liners)

Four variability factors need adequate supervision for each SAG mill. The factors are approximately 97% of the total dispersion of the pattern data set. In this case, only 3% of the remaining variance is related to the typical noise of the process. ƒ Ore feed, water feed, and pebble flow still give additional and complementary

information about the mill operation. ƒ There is more residual variability in pebble flow than in the previous condition. ƒ There is less correlation between the ore and water feed loops than that appreci-

ated in the previous condition. ƒ There exists less residual variance in the mill’s power.

As in the previous case, the adequate variability range for both SAG mill lines 1 and 2 have been characterized through the same control ellipses. The axis of these ellipses has been calculated to obtain a 95% and 99% of confidence for normal operation, as long as the scores are inside them (Figure 5). The created geometric areas inside the score map for the mentioned VFs ease the visualization of the actual mill’s behavior and the earlier detection of abnormalities according to the position of the score cloud versus time. Figure 6 shows the regions which have been identified from the data analysis to detect when liners become ineffective. The online identification of this state has importance for the online and offline process performance monitoring and analysis of the grinding circuit. As such, the circuit has been able to extend the availability of the circuit for more than 2 months. After the inferential model is defined, an online calculation can be programmed using PI ACE for online alert detection of the state of the SAG mill circuits. This new inferred variable or soft sensor can be used for additional knowledge monitoring of the system. Figure 7 shows a simplified data flow as the PI System collects the data, the analysis step used to identify the process patterns, and generation of the online calculations using SCAN. SCAN provides the necessary contribution plots for analysis of the data. Online calculations are processed by the PI ACE to generate soft sensors and alerts to avoid deterioration of the SAG mill equipment and also prevent overloading the mill.

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Variability factor results

FIGURE 5

20

15 Pressure’s Increment

10 Strong Power’s Decrement

Possible Typical Overwhelm

VF3

5

0

–5 Power and Pressure Increments –10

Pressure’s Decrement

Strong Power’s Increment

–15

–20 –25

–20

–15

–10

–5

0

5

10

15

20

25

VF1

FIGURE 6

SAG mill’s nonsecure operation areas

Figure 8 shows a PI ProcessBook with the weight of the variables as it is calculated online by the SCAN-inferred multivariable data set. Several additional historical data analyses have been done to evaluate the effect other disturbances in the SAG mill circuits. Example: Iron Content in SAG Mill Feed

The analysis of the influence of the size distribution and the effect of iron content on the SAG mill total feed was made. The PLS model used the different size fraction as inputs to check the effect on total tonnage. The results show the model weight factors are shifted from low iron content to higher iron content. This is due to the change in specific gravity

EXTENDED SEMIAUTOGENOUS MILLING

Offline Analysis

PI System

Embedding

SCAN

Calculation Engine

Process Models

Online Analysis

PI Visualization Tools

FIGURE 7

Data analysis flow of offline and online processes

FIGURE 8

PI ProcessBook with the derived multivariate weights of all mills

187

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0.38–0.5 0.75–1.0

(b)

2.5–3.0

0.25–0.38 0.5–0.75 1.0–1.5

2.0–2.5

0.38–0.5 0.75–1.0 1.5–2.0 4.0–8.0

< 0.25

0.25–0.38 0.5–0.75 1.0–1.5

3.0–4.0

2.5–3.0

2.0–2.5

4.0–8.0

< 0.25 Desplazamiento de distribucion

Contributions plots of (a) low and (b) high iron content at several size fractions

FIGURE 9

Predicted Data

3,680.5

Real Data 3,480.5 3,280.5 3,080.5 2,880.5 2,680.5 2,480.5 2,280.5 2,080.5 1,880.5 1,680.5 26

36

46

56

66

76

86

96

106

116

126

136

146

156

166

176

Time

FIGURE 10

PLS model for SAG mill behavior

of the ore, which changes the rheology of the pulp. The slurry transport in the mill is affected and the tonnage is reduced. Figure 9 shows a shift of the weight factors revealing the effect of the iron content in the size distribution. Example: Effect of Stockpile Level

The stockpile minimum level has been a source of discussion for some time. In the test plant, the typical limits are 100,000 to 600,000 t. A long period of SAG mill operational time was analyzed and a PLS model was developed, as shown in Figure 10. The model weight for stockpile was particularly high, and a detailed analysis of the process PI history showed a decay of the plant throughput whenever the stockpile was below 150,000 t. There is a penalty of 12 t in reduction of feed due to segregation of the material when the stockpile is below 150,000 t. It was advised to maintain a minimum level to increase overall production and minimize SAG mill disturbances due to changes in feed size distribution. Figure 10 shows the PLS model for SAG mill behavior. Up to this point, the stockpile level influence was “embedded” in the rest of the process variable values. The ability to isolate individual influences was key to obtaining these results. As a conclusion of the study, a process operation policy was made to reflect this restriction.

EXTENDED SEMIAUTOGENOUS MILLING

189

2.5

2.0

1.5

1.0

0.5

0

–0.5

–1.0

–1.5

–2.0 0

FIGURE 11

50

100

150

Copper concentrate grade prediction

FUTURE APPLICATIONS

The obtained results for the multivariate SAG mill analysis promoted further investigation for other process areas where statistical testing and modeling procedures available in SCAN software can be applied. A broader application includes the consideration of the flotation plant where dynamic linear and nonlinear modeling modules are applied in order to obtain a prediction for the copper concentrate grade as a function of process measurable variables. A close adjustment of the model allows for the online estimation of the individual “weights” or relative influences of each of the manipulated variables, giving the operator a guideline for the most effective ones at given times. The analysis is based on latent structures in order to reduce model complexity. Thus, a NIPALS (Nonlinear Iterative Partial Least Squares) algorithm is used to find the structures of the process variable matrix X, which are more correlated with the actual concentrate grade. However, inner linear and nonlinear relationships are being used to explain the variations of the predicted variable (copper concentrate grade) around an operation point. Figure 11 shows the obtained results for variable prediction over 750 minutes considering a 5-minute sample time. CONCLUSIONS

The availability of RtPM infrastructure simplifies the addition of specialized data analysis tools. The ease of collection adds context and helps filter the data to simplify the data reconciliation, multivariate data analysis, and the development of online pattern detection models. Multivariate analysis has demonstrated the ability to identify variability sources that were not initially considered in the characterization of the operation’s behavior. Specifically,

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the software detected the influence of the SAG mill liner’s state in its operation and identified the established relationships between the main variability sources. The knowledge acquired in the pattern identification procedures can be successfully incorporated in the online process supervision in order to detect and predict plant disturbances. In the presented cases, the implemented methodology helped define the reference operation’s patterns, and main variability sources aided in the identification and definition of the existent correlation structures for the controlled process. Future applications should demonstrate a decisive potential in operation improvement, not only for the SAG mill liner but also in other important production areas, including the flotation plant. Therefore, the use of information obtained through statistical multivariate analysis and from the operator’s knowledge for the continuous improvement of process control and maintenance are shown to be important factors for future evaluation. SCAN, which is developed by Contac Ingenieros, uses PI Datalink and PI ACE from OSISoft as the basic tools for implementation. BIBLIOGRAPHY

Bascur, O.A., and Kennedy, J.P. 2000. Pages 115–121 in Web Enabled Industrial Desktop to Increase Overall Process Effectiveness in Metallurgical Plants. IFAC Workshop, Finland, August 22–24. ———. 2004. Are you really using your information to increase the effectiveness of your assets and people? Improving and optimizing operations: Things that actually work! In Proceedings Plant Operators Forum. Edited by E.C. Dowling and J. Marsden. Littleton, CO: SME. Bascur, O.A., and Linares, R. 2005. Grade Recovery Optimization Using Data Unification and Real-time Gross Error Detection. Centenary Flotation Symposium, Brisbane Australia, June 6–9. Edited by G. Jameson and R.H. Yoon. Littleton, CO: SME. Dudzic, M. 1998. The use of advanced multivariate statistical tecnologies (chemometrics) at Dofasco. AISE Conference, MIT, Cambridge, MA, July. Hodouin, D., MacGregor, J.F., Hou, M., and Franklin, M. 1993. Multivariate statistical analysis of mineral processing plant data. CIM Bulletin 23–34. MacGregor, J.F., and Kourti, T. 1998. Pages 31–41 in Multivariable Statistical Treatment of Historical Data for Productivity and Quality Improvements. FOCAP0 98. Volume 94. AIChE Symposium Series 320. Edited by J.F. Pekny and G.E. Blau. Chelsea, MI: Ann Arbor Press. MacGregor, J.F., Marlin, T.E., Kresta, J., and Skagerberg, B. 1991. Multivariate statistical methods in process analysis and control. AIChE Publication P-67. Pages 17–22 in Proceedings of the CPC-IV. AIChE Symposium. Edited by Y. Arkun and W.H. Ray. Rodriguez, R., and Tobias, R. 2001. Multivariate methods for process knowledge discovery: The power to know your process. Pages 252–26 in Statistics, Data Analysis, and Data Mining. Romero, F., Orchard, M., and Yacher, L. 2003. Statistical multivariate analysis for improved plant control at C.M. Doña Ines de Collahuasi SCM, Chile. 2003 SME Annual Meeting, Cincinnati, OH. Romero, F., Suarez, M., and Bascur, O.A. 2004. Improving metallurgical performance at Collahuasi. SME Annual Meeting, Denver, CO. Vaculik, V., and Smyth, A. 2003. Dofasco’s enhanced monitoring system. OSIsoft PI Users Conference, San Francisco, May 13.

PART 3

Liberation and Breakage

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Shell and Pulp Lifter Study at the Cortez Gold Mines SAG Mill Raj. K. Rajamani,* Sanjeeva Latchireddi,* and Julius Stieger†

ABSTRACT

The energy efficiency of certain high-throughput grinding mills can be attributed to the field of breakage and slurry transport. The charge motion and breakage of particles inside the mill depends upon the shell lifter design, whereas the discharge of ground particles is controlled by the grate and the pulp lifters. The design of these mill components has been largely based on trial and error and hence varies considerably among manufacturers. This paper discusses the use of two state-of-the-art design tools—MillSoft and FlowMod. MillSoft is an effective tool to design the shell lifters and optimize charge motion, whereas FlowMod simulates the slurry discharge system to design grate and pulp lifters. A study done at the Cortez Gold Mines semiautogenous grinding (SAG) mill shows how the redesign of the shell lifter brings about a reduction in energy consumption when slurry transport through the mill is adequate. INTRODUCTION

There are a number of SAG mills in operation around the world with diameters reaching up to 40 ft. These operations continually invest in new technologies to improve their energy efficiency and capacity in their SAG circuit. Commercial SAG mill performance is determined by a large number of variables, both mine-site variables and mill variables. In many cases these variables dictate production capacity seemingly randomly. Therefore, a number of operating philosophies, each specific to a plant, have arisen. In almost all concentrators, the SAG operation is continually evolving. Every year, ways and means are sought to increase capacity, decrease energy consumption, and prolong lifter and liner life. Ore blending, newer designs of lifters, recycle crushing, and redesign of grates and trommel screens are a few routes taken at considerable expense. Operation of SAG Mills

The processing capability of a SAG mill is greatly affected by ore geology and operating variables within the mill. The key issues broadly can be classified into two categories: field of breakage and charge motion, and flow through the grate and pulp lifters. The field of breakage and charge motion are affected primarily by the design of shell lifters and mill speed. Once the ore is ground to a size that can pass through the grate holes, the slurry flows into the pulp lifter chamber that transports it into the discharge trunnion. These components of the SAG mill are schematically shown in Figure 1. * Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah † Cortez Gold Mines, Crescent Valley, Nevada 193

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Feed Trunnion

FIGURE 1

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Mill Shell

Grate

Pulp Lifter

Discharge Trunnion

Schematic of a typical SAG mill

Once the slurry has made its way via the grinding media charge, its first stage of discharge is via the grate. Hence, in the absence of any subsequent restriction, the maximum flow capacity that can be obtained for a given mill is determined by the grate design. Here, the design variables are the open area and radial distribution of slots. The driving force for slurry transport from the mill shell through the grate holes is the difference in pressure head across the grate. Field of Breakage. The motion of charge or rocks and balls in SAG mills can be viewed as a field of breakage generated as a result of the internal profile of the lifters and the rotational speed of the mill shell. The ore entering through the feed port is ground by this field and, after being sufficiently ground to the grate slot size, the slurry leaves through the slots in the grate. The field of breakage influences the rock mass in the SAG mill. Should the incoming ore be harder and the field of breakage insufficient to reduce the size, the ore stays in the mill longer because it is unable to pass through the grate. The net effect is an increase in rock mass, and the feed rate to the mill must be decreased appropriately to maintain rock-to-ball ratio. On the other hand, when the ore is soft, the field of breakage reduces the ore size rapidly, and hence the rock mass decreases. To sustain a set rock mass, the feed rate must be increased. The complicating factor is that the incoming ore feed itself determines the breakage field. Flow through the Grate and Pulp Lifters. Discharge grates and pulp lifters play an important role in performance of the autogenous and semiautogenous mills (Latchireddi 2002). The performance of the pulp lifters in conjunction with grate design determines the flow capacity of these mills. The function of the pulp lifters is simply to transport the slurry passing through the discharge grate into the discharge trunnion. Its performance depends on the mill size and design, the grate design, and mill operating conditions, such as mill speed and charge level. The difficulties associated with slurry transportation from SAG mills have become more apparent in recent years with the increasing trend to build larger-diameter mills for grinding high tonnages. This is particularly noticeable when SAG mills are run in closed circuit with classifiers such as fine screens or hydrocyclones. The performance analysis of conventional pulp-lifter designs shows that a large amount of slurry flows back from the pulp lifter into the mill (Latchireddi and Morrell 1997, 2003a,b; Rajamani et al. 2002). The backflow depends on the size and design of the pulp lifters. The back face of the pulp lifter is the grate itself, so that the slurry readily flows back into the mill. Subsequently, the field of breakage diminishes when excessive slurry builds in the mill.

SHELL AND PULP LIFTER STUDY

195

Charge Motion. In a concentrator, all of the auxiliary equipment (i.e., pumps, conveyers, screens, and hydrocyclones) and two primary resources (i.e., steel and electricity) primarily serve to maintain grinding action in the belly of the SAG mill. It is this action that dictates capacity. Therefore, this grinding action should be observed continuously from the control room so that the necessary steps can be taken to keep the grinding field at its highest potential. Unfortunately, the grinding environment within the mill shell is very severe, and none of the online instrumentation developed so far is able to survive the continuous impact of large steel balls. Direct observation is impractical, therefore, the next available option is a simulation of the grinding field to gauge the intensity of grinding or the lack of intensity of grinding. Mill Power Draft. The field of breakage and flow through the grate and pulp lifter influence each other, and the net effect is the buildup of a holdup level in the mill, which draws a certain power, and this power draft is clearly linked with mill throughput. If the interaction can be understood, then mill capacity can be determined much more clearly. Then the expectation of increasing capacity at the same level of power draft by one means or another can be safely evaluated. The power draft of a SAG mill and its consequences are illustrated in Figure 2, wherein 5 days of operating data in a 32u14-ft SAG mill is plotted. The power draft of the mill is held between 6 and 7 MW, whereas tons per hour (tph) of ore feed to the mill shows wide variations between 1,000 and 1,600 tph. Figure 2 shows that the feed rate drops whenever the power draft shows an increasing trend, whereas intuitive reasoning would suggest that feed rate should be proportional to power draft. The data show that the specific energy consumption (kWh/t) of ore is not steady, as one would expect for a typical ore body. Even within a 24-hour time frame, where the feed ore hardness may be assumed constant, the variation in feed rate is dramatic. The internal dynamics within the SAG mill, as exemplified by the three broad concepts, are causing wide fluctuations in grinding rate, which in turn is reflected as capacity. SAG Mill Efficiency

The energy efficiency of tumbling mills can be examined directly by looking at the motion of ore and grinding balls inside the mill. The makeup of the charge and the lifter bars attached to the inside of the mill shell can be designed particularly to maximize the mass of ore fractured per unit of energy spent. At the same time, the unnecessary collisions of steel balls against the mill shell can be reduced. Furthermore, the cascading charge flow can be altered in such a way as to maximize grinding efficiency. First, the shell lifters are designed in such a way that the motion is fully cascading and that part of cataracting motion is made to strike in the vicinity of the toe. In such a charge motion regime, both shearing action and impacts are fully utilized in grinding the ore. The shell lifters are usually replaced once or twice a year. Pulp lifters survive for 2 or 3 years. The design of these two important mill components has been based largely on trial and error and hence varies considerably among manufacturers. However, over the years, important tools such as MillSoft and FlowMod have begun to help the designers analyze and understand the influence of the internal components of SAG mills—shell lifters, grates, and pulp lifters, respectively. The following sections discuss the basic principles and application of these two simulators. MillSoft—Discrete Element Simulation of SAG Mills. The SAG mill is made up of a cylindrical shell with two conical shells attached on both ends. Lifter elements are attached in both the cylindrical and conical shell sections. As the SAG mill rotates, typically around 10 rpm, the internal flat walls of the lifter and shell impart momentum to the balls and rocks. The momentum is transferred primarily to particles in direct contact with the plate elements (Villouta 2001). These particles, in turn, impart their momentum

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FIGURE 2 Five days of plant operating data: 32×14-ft SAG circuit (fresh feed rate in tons per hour, mill power in megawatts)

to adjacent layers of particles. In this manner the motion of the entire charge evolves, resulting in what is commonly referred to as cascading and cataracting charge. The discrete element method embedded in MillSoft replicates the evolution of charge motion as described above. In the simulation, the exact dimensions of lifters, plates, and balls are used. MillSoft can be used effectively to show the effects of different lifter configurations, mill loading, mill speed, and other operating conditions. Unlike single-particle trajectory programs that show only the outermost particle path, MillSoft takes into account the entire charge; one can effectively see the “kidney” shape of the charge, the dead zone, toe and shoulder of the charge, and areas of high impact on the mill lifters. MillSoft also can be used to follow lifter wear, shell plate wear, and particle breakage. Most importantly, the location and the intensity of impacts on lifter bars can be recorded computationally, and a corresponding metal abrasion at that location can be worked out. In a like manner, the energy of impact can be used to fragment the rock particles in the simulation. However, the distribution and number of fragments produced overwhelm the computational task, and hence, this computational path is rarely followed. Shell Lifter Design and Charge Motion Analysis with MillSoft. A typical example of charge motion analysis with MillSoft is described in this section. The SAG mill under consideration is a 38u24-ft mill drilled for 60 rows of shell lifters. Therefore, the mill can be fitted with a set of 30 high and 30 low lifters or a total of 60 high lifters. The total charge is 27% with 15% balls. The mill is expected to draw 15–18 MW power. The mill speed is set at 76% critical speed. The snapshots of the charge motion at different conditions are shown in Figure 3. Figure 3a shows the SAG mill fitted with traditional lifters. The high lifters are the top-hat type with a 7˚ release angle. The velocity vectors are superimposed on the balls and the rock particles. The central region reveals where grinding action is minimum. Due to the small release angle, a considerable amount of rock and ball particles are thrown against the mill shell. The ball-to-liner strike zone extends as high as the nine

SHELL AND PULP LIFTER STUDY

(a) Top Hat (7˚)

FIGURE 3

(b) 25˚ Release Angle

197

(c) 35˚ Release Angle

Snapshots of charge motion

o’clock mark. The mill may not reach design capacity, especially with a hard ore type. Furthermore, considerable damage to liners is imminent within 4 months of operation. Next, we consider the same mill fitted with 30 high lifters and 30 low lifters of a 25˚ release angle. Figure 3b shows the snapshot of charge animation. Here, ball strikes on liners are seen nearly up to the eight o’clock position, a considerable improvement over that shown in Figure 3a. This lifter is suitable for maintaining a moderately aggressive charge motion at the expense of shorter lifter wear life. Next, the release angle is increased to 35˚ with 30 high lifters, as shown in Figure 3c. The cataracting charge lands within the toe of the charge. This type of charge motion is ideal for SAG mills in order to preserve the life of shell lifters. The mill speed may be increased without fear of damaging liners. The Alumbrera mines exploited this concept to increase production. With such lifters, Alumbrera even used 150-mm top ball size. SAG Mill Study at Cortez Gold Mines

The aforementioned analysis of shell and pulp lifters is illustrated with the work done at Cortez Gold Mines, Crescent Valley, Nevada (Stieger et al. 2005). The grinding circuit consists of a 26u13-ft SAG mill in closed circuit with a pebble crusher. The discharge of the SAG mill is screened on a 0.75-in. screen, and the oversize material is fed to the cone crusher. The undersize is sent to the ball milling circuit. The typical SAG mill feed is 400 stph, which varies anywhere between 250 and 550 stph, depending on the ore type. At least five different ore types are encountered at this mine site. During the course of many years, the SAG shell lifter has evolved to a high–low pattern with a typical high-lifter dimension of a 7-in. height, 5-in. top width, and 17˚ face angles on both sides. The low-lifter dimensions are 5-in. height, 5-in. top width, and 17˚ face angles on both sides. The mill shell has been drilled for 52 rows of shell lifters. The open area of the grate is 7% with the typical 2.75-in.2 opening. The plant operating work index (Wio) depicted in Figure 4 shows an average of 15 kWh/st in the year 2004 until the liner change, since then decreasing to about 13 kWh/st. This reflects the efficient usage of energy in the SAG mill as well as the ball mill operation, which is probably getting a relatively finer feed. Grate and Pulp Lifters. First, a review of the grate plate and pulp lifter showed that an open area of 7% was adequate for handling the daily-targeted tonnage. In fact, the grate openings were found to be free of balls or rocks during many inspections. The discharge capacity of the grate is 482 m3/h of slurry. However, FlowMod calculations indicated that the pulp lifter diminished this flow to 382 m3/h as a result of backflow phenomena. However, this flow rate is adequate to handle current daily tonnage. Also,

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FIGURE 4

Monthly record of plant operating work index

the radial distribution of grate opening in the mill periphery indicated that some advantages could be gained by redistributing the open area in the most optimal flow regime. The recommendation was implemented in a subsequent grate redesign. In summary, the grate and pulp lifter combination was operating more than satisfactorily, although there is always room for further increase in the pulp discharge capability of the mill. Figure 5 shows discharge flow rate as a function of fractional slurry holdup. At the current operating conditions, increasing the open area to 9% and redistributing the slots radially may increase the discharge flow rate to 450 m3/h. It is very critical that the pulp transport capacity of the mill be set at its maximum value before changing shell lifters. The shell lifters may increase the production of fines, but there must be the capacity to discharge these fines. High–Low Shell-Lifter Experience. The high–low shell-lifter design leaves a gap of 10 in. between the lifters. As a result, caking between lifters was very severe, as shown in Figure 6. Due to cake buildup, the effective height of the high lifter over the base is a mere 2 in. Figure 6 shows the MillSoft simulation of charge motion with the high lifters. The 17˚ lead face angle causes cataracting between the eight o’ clock and nine o’ clock positions of the mill circle. With the use of 5-in. grinding balls and exposed shell plates, the cataracting caused consistent and moderate-level damage to the mill shell. Some of the lifters were broken, and in other places there was severe peening. As a result, the mine experienced unscheduled SAG mill–related downtime every month. Figure 7 shows the unscheduled downtime for a 2-year period. It can be seen that though the lifter is in the last 4 months of operation leading up to September 2004, there is downtime due to lifter damage. A crash stop done during this period shows cake buildup between lifters and a fair amount of slurry retention within the mill (see Figure 6). Shell-Lifter Redesign. A decision was made to reduce downtime and increase energy efficiency with a new design of lifters. In particular, it was decided to bring the 5-in. ball trajectory to the toe of the charge by correct choice of the leading face angle. Furthermore, it was decided to eliminate every other lifter row to minimize packing and

SHELL AND PULP LIFTER STUDY

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Slurry Flow Rate, m /h Slurry Removal Efficiency of Pump Lifters = 382.65/481.88 = 79.4%

FIGURE 5

FlowMod analysis of slurry flow rate through the SAG mill

Packing

Slurry Pooling

FIGURE 6

Charge motion simulation and crash-stop picture with high–low shell lifters

maximize lift as well as to increase mill volume. Figure 8 shows a MillSoft simulation of the new design (9-in. height, 5-in. top width, with 28˚ leading and trailing face angles). As anticipated, the cataracting charge lands near the toe of the charge at around the seven o’clock position of the mill circle. The simulated power draw was consistent with operating power draw. This type of liner with the leading face inclined at a steep angle (22˚–35˚) has been well documented in the literature. A number of mine sites, including Alumbrera (Sherman 2001), Collahuasi (Villouta 2001), Candelaria, Los Pelambres, and others (Bird et al. 2001), have had success with these types of lifters. In addition to the design criteria for optimal trajectories for 5-in. grinding balls, a number of other

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FIGURE 7

Summary of SAG mill unscheduled downtime

FIGURE 8

Charge motion simulation and crash-stop picture with new shell lifters

issues—such as safety of liner handling, safety of mill noise, inching drive capability, load on the mill motor, and mill startup—were addressed and taken care off. Slurry Transport and Load Buildup in the Mill. Slurry transport out of the mill plays an important role in determining SAG capacity. Figure 9 shows the cyclical behavior of the SAG circuit 3 weeks after changeover to the new lifter design. In particular, the feed to the SAG mill cycles up and down every 2 hours. Mill bearing pressure exhibits similar behavior. The cyclical behavior is primarily due to the pulp lifter returning part of the slurry passing through the grate back into the mill. In other words, backflow in the pulp lifter returns part of the slurry to the mill. As a result, the mill slurry holdup increases and the controller cuts the feed to the SAG mill. This cyclical behavior points out that the circuit capacity can be improved by a proper choice of pulp lifters. Impact on Power Draw and Energy Consumption. The energy efficiency of the SAG mill is the main focus of this section. Figure 10 shows the SAG throughput before and after installation of a new shell lifter. The SAG circuit maintains more or less the

FIGURE 10

Time

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same throughput after lifter installation. Because ore type is changing from day to day, it will take more than 4 months to encounter all the different ore types. The major advantage gained with the new lifter design is shown in Figure 10. The fact that the mill bearing pressure stays at a steady value both before and after the lifter change implies that the mill load is unaffected by the design of the new lifters. However, the mill feed rate steadily increased after the lifter change. These two observations imply that the new lifter design is bringing about an efficient breakage of ore particles. Thus, the mill throughput increases while maintaining the same load. The critical impact of the new lifter design is illustrated in Figure 11. The SAG mill exhibits a very definite reduction in power draft. It is estimated that the power decreases in the 230–370-kW range. Hence, energy consumption per ton of ore milled decreases by 0.3–1.3 kWh/t. This energy savings is in the 10% range. Furthermore, a 1%–10% reduction in recirculation to the cone crusher was noticed due to efficient impact breakage of critical size material. All of these results amount to a significant reduction in operating costs. A more efficient ball trajectory or charge motion means that there is less direct impact of grinding balls on shell plates and lifters. As a result, grinding ball consumption and steel loss in lifter wear must be impacted. At the Cortez Gold Mines operation, grinding ball consumption could not be tracked via a digital control system; however, it was noticed that during 16 weeks of operation, only 2.5 in. of lifter height was lost due to wear. It was estimated that the new design results in 57 kg/day in steel loss compared to 84 kg/day for the previously installed lifter, a 47% savings in steel loss. Furthermore, in the 9 months of operation leading up to June 2005, the mill did not experience any downtime due to cracked shell plates, severely peened lifters, broken lifters, or leaky bolts. Thus, we find that proper design of shell lifters leads to a decrease in energy consumption per ton of ore. CONCLUSIONS

The design of both the shell lifters and the grate–pulp lifter assembly are crucial for optimal performance of a SAG mill. The design of shell lifters, which control the charge motion and thus the breakage field, can be optimized using MillSoft—a discrete element numerical method. FlowMod, a steady-state simulator, can be used to optimize the design of grate and pulp lifters to handle the given flow through the mill. It estimates the slurry holdup inside the mill and shows its dynamic surface at any mill operating condition. These two tools were employed in the study of the SAG mill at Cortez Gold Mines. First, the flow or discharge capacity of the grate and pulp lifter were analyzed, and it was found that the capacity was adequate for meeting daily tonnage. Next, the redesign of shell lifters readily resulted in a 230–370-kW reduction in mill power draw while maintaining the same throughput level. The SAG mill circuit exhibited cyclic loading behavior, indicating that there was room for further increase in capacity via pulp lifter redesign. ACKNOWLEDGMENTS

The authors from the University of Utah would like to thank the U.S. Department of Energy, Industries of the Future Program, for support of this study through contract DE-FC26-03NT-41786. The authors also thank Cortez Gold Mines management for participating in this study.

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SAG mill power data

BIBLIOGRAPHY

Bird, S., A.E. Lamb, W. Lamb, and D.W. Partridge. 2001. Evolution of SAG mill liner design at Kennecott Utah Copper Concentrator. Pages 256–259 in International Autogenous and Semiautogenous Grinding Technology. Volume III. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Vancouver, BC: University of British Columbia, Department of Mining and Mineral Process Engineering. Denis, N., S. Morrell, B. Chapman, and S. Latchireddi. 2001. The development and installation of the twin chamber pulp lifter at Alcoa. In Proceedings SAG ’01, Vancouver, BC. Latchireddi, S.R. 2002. Modeling the performance of grates and pulp lifters in autogenous and semiautogenous mills. Ph.D. thesis. Brisbane, Australia: University of Queensland. Latchireddi, S.R., and S. Morrell. 1997. A new design of pulp lifter for grate discharge mills. Pages 57–61 in 6th Mill Operators Conference, Madang, Papua New Guinea, October. ———. 2003a. Slurry flow in mills: Grate-only discharge mechanism, part 1. Minerals Engineering 16(7):625–633. ———. 2003b. Slurry flow in mills: Grate–Pulp lifter discharge mechanism, part 2. Minerals Engineering 16(7):635–642. Mishra, B.K., and R.K. Rajamani. 1994a. Simulation of charge motion in ball mills. Part 1: Experimental verifications. International Journal of Mineral Processing 40:171–176. ———. 1994b. Simulation of charge motion in ball mills. Part 2: Numerical simulations. International Journal of Mineral Processing 40:187–197.

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Moys, M.H. 1986. The effect of grate design on the behavior of grate discharge mills. International Journal of Mineral Processing 18:85–105. Rajamani, R.K. 1997. Slurry transport through the dynamic porosity of the ball mill. Transactions of the Indian Institute of Metals 50(5):337–347. Rajamani, R.K., and B.K. Mishra. 1996. Dynamics of ball and rock charge in SAG mills. Pages 700–712 in International Autogenous and Semiautogenous Grinding Technology. Volume 2. Edited by A.L. Mular, D.J. Barratt, and D.A. Knight. Vancouver, BC: University of British Columbia, Department of Mining and Mineral Process Engineering. Rajamani, R.K., B.K. Mishra, A. Joshi, and J. Park. 2002. Two and three dimensional simulation of ball and rock charge motion in large tumbling mills. In DEM Numerical Modelling of Discontinua. Geotechnical Special Publication 117. Edited by B.K. Cook and R.P. Jensen. Reno, VA: American Society of Civil Engineers. Rajamani, R.K., B.K. Mishra, and P. Songfack. 1997. The modeling of rock and ball charge motion in SAG mills. Pages 195–200 in Comminution Practices. Edited by S.K. Kawatra. Littleton, CO: SME. Sherman, M. 2001. Optimisation of the Alumbrera SAG mills. Pages I59–I75 in SAG 2001, Vancouver. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Vancouver, BC: University of British Columbia, Department of Mining and Mineral Process Engineering. Stieger, J., D. Plummer, S. Latchireddi, and R. Rajamani. 2005. SAG mill operation at Cortez: Evolution of liner design. SME Annual Conference, Salt Lake City, UT, February 28–March 2. Villouta, R.M. 2001. Collahuasi: After two years of operation. Pages I31–I42 in SAG 2001, Vancouver. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Vancouver, BC: University of British Columbia, Department of Mining and Mineral Process Engineering.

Breakage and Damage of Particles by Impact L.M. Tavares,* L.G. Austin,† and R.P. King‡

ABSTRACT

Measurements of forces resulting from impacts of 3u3-mm cylindrical pellets fired at a constant velocity against a target mounted on a rapid-response load cell showed that the maximum force generated at each impact was not constant. The measured distribution of maximum force was used to calculate a distribution of energy utilization factors. The results indicated that measurements of the distribution of strengths calculated, assuming that the specific impact energy defines strength, are in error for nonspherical particles. Drop-weight impact tests on roughly spherical mineral particles mounted on an impact load cell showed that the distribution of force required to produce fracture was dependent on the distribution of existing damage as indexed by initial stiffness factor, that of the damage accumulation coefficient, and that of the critical deformation at fracture. Knowledge of the distribution of strength alone is not sufficient to define the fracture behavior of the particles under known impact conditions, especially for repeated low-level impacts where damage accumulates. INTRODUCTION

The two most important types of grinding mills in terms of the tons ground per year around the world are tumbling media mills (mainly for rocks and ores) and ball-race/ roll-race mills (mainly for pulverized coal for electricity generation). The traditional laboratory-scale tests used to determine the required size of these mills for different feed materials are the Bond test and the Hardgrove test, respectively. These tests use standardized test mills that are small-scale versions of the full-scale mills, and each test delivers a single number that compares the “ease of grindability” of different materials: the Bond Work Index (Bond 1960) and the Hardgrove Grindability Index. Although the breakage actions are quite different between the two mill types, the two indices have a reasonable empirical intercorrelation (Austin and Aplan 1998): a material that is predicted by the Bond test to be easy (or hard) to grind is also predicted to be easy (or hard) to grind by the Hardgrove test. The actual use of these empirical indices for mill design is based on many years of industrial experience with each type of mill on a range of different feed materials. These two indices are not useful generally either for the design of the many other types of grinding mills of importance or for predicting performance of new types of mills. Thus, there is a clear need for a more fundamental approach to describe those properties of a given material that make it easy or difficult to comminute in any given * Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil † The Pennsylvania State University, University Park, Pennsylvania ‡ University of Utah, Salt Lake City, Utah 205

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type of device. Recognition of this need in the past led to a substantial amount of effort in this area, with little apparent success. However, recent years have seen a renewed interest in characterizing the breakage properties of particles under specified stressing conditions, using new techniques and ideas. It is hardly worth the effort to try to extract data from the older literature because the reported test results—from drop-weight tests, for example—lack important information. On the other hand, certainly a number of important concepts were discovered. For example, the cracking and eventual collapse of cubes of coal subjected to repeated light impacts was described (Bond 1954), which is an example of the damage accumulation that will be discussed later in the paper. Similarly, Austin and co-workers (Austin, Shoji, and Everell 1973) postulated that if the distribution of “strengths” of a given size of particle were known, and the distribution and frequency of applied forces were known, then the two distributions could be convoluted to give rates of breakage. The problems of applying such ideas, of course, included the need for the development of suitable test procedures for (1) the determination of strength, and (2) the determination of the suite of forces in an operating machine. In addition, there was no formal structure to describe and measure the process of damage accumulation. This chapter will present briefly the background relevant to the recent work done in this field, with special reference to solving the problem of describing and measuring damage accumulation. I D E A L I Z E D S T R E S S D I S T R I B U T I O N S A N D FR A C T U R E M E C H A N I C S IN IMPACTED SPHERES

Figure 1 shows idealized diagrams of how a sphere of homogenous material appears when it is impacted between smooth, rigid anvils or fired to impact against an anvil. The Hertzian solutions for these impacts are known (Goldsmith 1960), and the resulting equations are summarized in Appendix A. For example, the equation for the maximum force produced by the perpendicular impact of a sphere (of diameter d, material of density ȡ, and stiffness factor kp—also called particle stiffness) on a flat surface (of stiffness ks) at velocity v is (Equation A9) 2

2e5

F m = 0.757d K e

2 3e5

 Uv

(EQ 1)

where Ke = kp ks /(kp + ks ), k = Y/(1 – P2), Y is the Young’s modulus, and P is the Poisson ratio. This maximum occurs at the instant when the kinetic energy is converted completely to the strain energy of compression and when the relative velocity of sphere to surface is zero (before rebound). The solutions also show that the compression caused by the impact produces a maximum in tensile stress acting around the perimeters of the contact circles. Griffith (1921) showed that a small defect (a Griffith flaw) in a brittle solid leads to concentration of the stress field around the flaw, and that a large flaw suitably aligned in a region of high tensile stress can act to initiate an expanding crack. If the stressing conditions are appropriate, the crack can propagate rapidly, bifurcate at other flaws, and lead to a disintegrative failure. For spheres, then, the cracks would be expected to propagate from flaws in the rim of the contact circle, and the rest of the stress field would drive the cracks to produce fracture into rough segments. This type of behavior has been observed (Schönert 1986). Appendix A shows that the tensile stress ıT in the perimeter of the contact circle is proportional to the (mass) specific impact energy E1/5 (Equation A11): 4e5

V T = 0.32  1 – 2P K e

 UE

1e5

(EQ 2)

BREAKAGE AND DAMAGE OF PARTICLES BY IMPACT

Contact Circle

207

v

v Contact Circle

(a)

FIGURE 1

(b)

Spheres impacted (a) against an anvil and (b) between anvils

Thus, there will be a critical, specific impact energy that will make ıT sufficient to cause disintegrative fracture of the sphere. Similarly, another method of defining the strength is given by (Hiramatsu and Oka 1966) 2.8F V P = -------------c 2 Sd

(EQ 3)

where Vp was called “particle fracture strength” (Tavares and King 1998). Fc is the critical value of Fm at which failure occurs. It can be shown that this is proportional to the specific impact energy E3/5 for the case of one-point contact (n = 1 in Equation A12): 2e5

V P = 1.56K e

 UE

3e5

(EQ 4)

Equations 2 and 4 show that “strength” can be defined as the critical ıT, or as ıp, or by the critical, specific impact energy. The strength is a function of the basic bond strength of the material and of the size, density, and alignment of the flaws. The application of the definition of strength as the “critical, specific impact energy required to produce fracture” requires the measurement of the mass fraction of spheres that are broken when a reasonably large number of the spheres (of a chosen size) are impacted with a known specific impact energy. Repeating (with a fresh sample) at higher and higher specific impact energies gives larger and larger fractions broken. In this way, a curve or vector of “cumulative fraction broken versus specific impact energy” is constructed. This is the “distribution of strengths” of the spheres of that size. With respect to the variation of strength with sphere size, Weichert (1992) and Vogel and Peukert (2003) have treated the length of the perimeter of the contact circle as if it were a chain length in the “weakest link” concept (Weibull 1939). It can be shown that smaller spheres have a lower probability of having weak flaws in the contact circle perimeter and thus will be stronger than larger spheres. This is in agreement with experimental evidence. However, if it is considered that smaller particles have been produced by breakage of larger particles, then it is possible that the population of flaws for smaller particles has a different strength distribution than that for larger particles, having a smaller fraction of the larger, weaker flaws. Whether this effect is significant or negligible

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depends on the flaw density; if the density is high, many steps of breakage can occur without significant reduction of the density of larger, weaker flaws, and vice versa. A MORE REALISTIC PICTURE OF THE IMPACT BREAKAGE OF NONSPHERICAL PAR TICLES

Examination of the shapes of particles of interest, such as crushed or ground rocks, ores, coals, and so forth, shows a wide variety of shapes for a given material and size, including sharp angles, flat faces, and projections, with very few particles approximating a spherical shape. It cannot be expected that the equations for ideal spheres can be applied directly to irregular-shaped particles, except as a guide to the form of the descriptive equations. A major advance was made (Vervoorn and Scarlett 1990) with the construction of a device to fire cylindrical pellets against a rigid target fitted with a force transducer that produced force–time curves for the impact. The pellets (catalytic cracker pellets of sintered Al2O3) were 3 mm in diameter by 3 mm in length, 30 to 39 mg in weight, and were tested over impact velocities of 6 to 24 m/sec. It was found (Vervoorn 1986) that, contrary to expectations, the maximum impact force measured from the graphical output of the transducer was not constant at a given impact velocity but varied over a range with a ratio of about 1:5. The assumption that the mass and velocity of the impact determined the maximum force of impact was not correct. This finding invalidates much of the earlier work on the measurement of strength distributions for nonspherical particles. The impact process was found to be much more complex than that expected from spheres. In some impacts, a single major impact peak occurred over a time period of about 10 Psec, which is consistent with the expectation from Hertzian theory. Smaller peaks followed, presumably due to fragments broken from the pellet also striking the transducer. However, in many cases a double impact occurs as the pellet hits, twists, and strikes again, giving a much smaller maximum force. Later analysis (Vervoorn and Austin 1990) showed that the range of measured maximum force Fm at a given velocity could be normalized to the median value Fm50 and fitted to a log-logistic function: 1 G  F m = -------------------------------------5 1 +  F m50 e F m

(EQ 5)

where G(Fm) is the fraction of impacts that produces a maximum force d Fm, G(Fm50) = 0.5. This curve fitted the data reasonably well for all the test impact velocities. The values of Fm50 varied with impact velocity according to Fm50 = 3.03v6/5

Newtons, v in m/sec

(EQ 6)

A cylinder of equal diameter and length is not much different than a sphere in geometry, but it is different enough to give maximum impact forces that vary considerably from the idealized treatment for spheres given previously. It must be expected that the same result would be found for irregular particles that can also twist and dissipate impact energy as several small impacts instead of one large one. The result will be a proportion of impacts that do not break at a given impact velocity because the force is not as high as calculated from the mass and velocity. This will make the strengths in the measured strength distribution versus velocity (or versus calculated specific impact energy) appear stronger than the real particle strengths.

BREAKAGE AND DAMAGE OF PARTICLES BY IMPACT

209

To proceed further, it was necessary to have an independent estimate of the distribution of strengths and an estimate of the modulus of rigidity of the pellets. This was done (Austin, Trubelja, and Scarlett 1993) by fracturing 100 of the pellets, one by one, using slow compression in a universal testing machine, with the pellet orientation in the Brazilian mode of test. With this type of test there can be no twisting of the pellets, and the initial region of the output curve of the tester can be used to estimate the Young’s modulus during the pellet compression. The “strength” in this test is the load P required to produce a disintegrative fracture. The distribution of strengths by this definition could be fitted with reasonable accuracy by a log-logistic function: 1 cumulative fraction broken at loads d P = -------------------------------41 +  P 50 e P

(EQ 7)

where P50 was 48 N. However, it also was found that the measured Young’s modulus was not constant but had a wide distribution. The variation of the modulus did not correlate with the strength. This was an important finding because the modulus of rigidity affects the maximum force obtained by an impact of a given specific energy. Thus, part of the distribution of impact forces seen in the impact tests (Equation 5) would be due to the variation in modulus in addition to the effect of variation in the orientation of the impact. The distribution of the modulus could be fitted approximately by 1 cumulative fraction of pellets with modulus below Y = ----------------------------------3.4 1 +  Y 50 e Y

(EQ 8)

where Y50 was 1.3 GPa. The equation relating the maximum impact force to the impact velocity for perpendicular impact of a sphere against a (much more) rigid target is (Equation 1, with K e # k p ) 2 2e5

2 3e5

F m = 0.757d k p  Uv

(EQ 9)

Equation 9 predicts that the maximum impact force varies with the 6/5 power of the impact velocity (as found in Equation 6 for Fm50), and that a higher modulus of rigidity increases the maximum force at a given velocity. Equation 9 can be used to estimate the expected maximum forces for the pellet impacts. At a given set of conditions, the only variable is kp, so all the other values can be 2e5 combined into a new constant, F m = const.k p . Substituting kp for Y in Equation 8 and 5/2 using kp = (Fm/const.) gives 1 G  F m = ----------------------------------------------------3.4  5 e 2 1 +  F m50 e F m 2e5

(EQ 10)

where F m50 = const.k p50 . Thus, the distribution of the impact forces predicted solely from the distribution of Young’s modulus is also a log-logistic function, but with an exponent of 8.5. This can be compared with Equation 5, where the exponent was found to be 5. This means that the measured force distribution is much wider about Fm50 than expected from the variation of Young’s modulus alone (a higher value of the exponent in the loglogistic function gives a narrower distribution), showing that the effect of pellet orientation on impact force is significant. It is clearly invalid to assume that an impact at velocity v produces a unique force on the pellet.

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This can be illustrated by using Equation 9, taking d as the equivalent spherical diameter corresponding to the pellet volume, (2.73)10–3 m, a median value of Young’s modulus of (1.3)109 Pa, and a pellet density of (1.4)103 kg/m3 corresponding to a pellet porosity of about 55%. At this porosity, the Poisson ratio can be taken as 0.25 (Jaeger and Cook 1969). Then Fm50 = 4.5v6/5

Newtons, v in m/sec

(EQ 11)

Figure 2 shows the values of G(Fm) predicted from Equations 10 and 11, at an impact velocity of 10 m/sec, for comparison with the experimentally determined values of Equation 5. It can be seen that the upper limit of impact forces predicted from treating the impacts of the pellets as if the pellets were spheres agrees with those found experimentally, providing the variation in the Young’s modulus found in compressive tests is included. However, the experimentally determined impact forces are otherwise much lower; compare (a) and (b) in Figure 2. This is in agreement with the concept that a few of the impacts will be full impacts, but many will give lower force values due to the impact energy being spread over two or more partial impacts. The theoretical estimates of maximum force are too high; therefore, the measured values of “cumulative fraction broken at force Fm (or specific impact energy E)” are for a much lower force, so the particles are actually much weaker. An energy utilization factor U can be defined as the fraction of specific impact energy that is actually used in the production of the largest Fm in a multiple-impact sequence. This factor will generally lie between 0 and 1. Equation 9 is now modified to 2 2e5

2 3e5

F m = 0.757d k p  UUv

*2 e 5

= Ck p

U

*3 e 5

(EQ 12) 2

*

2 3e5

where k p and U* are values normalized to the median values, and C = 0.757d  Uv 2e5

3e5

k p50 U 50 . It was assumed that the distribution of U, F (U), can be fitted with a modified loglogistic function: 1 * F  U = -----------------------------O- , * 1 + 1 e U = 1,

U1 U = 1

(EQ 13)

where U* = U/U50. Appendix B shows how the effect of orientation can be extracted from the data, using convolution of the distributions (Gardner and Austin 1975). A search was made for the values of U50 and O that made the predicted distribution of forces agree as closely as possible with the experimental values of Equation 5, and reasonable agreement was obtained with U50 = 0.51 and O = 3.65. This result is also shown in Figure 2. Figure 3 shows the cumulative fraction of impacts with an energy utilization factor less than or equal to U. It is seen that the percentage of impacts with U = 1 is about 7 and that more than 50% of the impacts have a U value of less than half a percent, meaning that calculation of impact forces (and strengths) from the specific energy of impact, assuming that U is 1, will give substantial errors. In fact, the values of U also contain the errors generated by assuming that the impacts are comparable to those of equivalent spheres.

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211

1.0

(a) (b) (c)

Cumulative Number of Impacts ≤ Force Fm

0.8

0.6

0.4

0.2

0.0

0

50

100

150

Maximum Impact Force Fm, N

FIGURE 2

Comparison of distributions of force

THE ORIENTATION EFFECT IN REPEATED IMPACTS

The discussion in the previous section described the impact forces, but the test results also included the fraction of pellets broken after 1 impact and after 10 impacts, at several impact velocities (Vervoorn and Austin 1990). In the traditional viewpoint, a strong particle is always strong (except for damage accumulation), and the strength distribution is of the strengths between particles. Vervoorn and Austin tried a different type of analysis by assuming the opposite extreme; that is, the distribution of strengths was within each particle due to different strengths in different impact orientations. In this viewpoint, a particle that does not break in one impact at a given velocity has the chance to break in the next impact of the same velocity. The equation that results (for a sufficiently large number of impacted particles of a given size) is w  N = w  0 exp  – SN  w  0 = 1 N = 1 2 3 }

(EQ 14)

where w(N) is the fraction left unbroken after N impacts, and S is the equivalent to a specific rate of breakage, with units of fraction broken per impact event. The decrease in the amount remaining unbroken at each step is given by the factor exp(–S) applied to the previous value. It seems much more likely that there is a distribution of strengths between the pellets plus a distribution of strengths within each pellet due to the orientation effect. This would apply to any system in which random orientations of irregularly shaped particles can occur in repeated impacts. Thus, the theoretical investigation (Austin 2004) of grinding kinetics in a batch system was invalid because it did not include the orientation effect. Further work is required in this area.

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1.0

Cumulative Fraction of Impacts ≤ U

0.8

0.6

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Energy Utilization Factor U (–) –

FIGURE 3

The distribution of the energy utilization factor, as predicted by Equation 13

The important points to note are (1) that the usual methods of determining the “distribution of strengths” do not differentiate between the two distributions but give a combined effect; and (2) the two different distributions will give entirely different results in a mill model, so it is necessary to determine which one is applicable and to measure both if they are relevant. I M P A C T TE S T S A N D T H E K I N G - TA V A R E S TE S T

There are two major types of tests that have been used in recent years to measure the distribution of strengths of particles to impact. The first type consists of firing a stream of the particles at a target at known velocity, or of hitting suspended (sized) particles or a stream of falling particles by a hammer moving at a known velocity (Vogel and Peukert 2003). The test is repeated at higher velocities to generate a distribution of strength defined by the calculated specific impact energy. This type of test has again the advantage of rapid testing of a large number of particles, but if the particles are not spheres, the calculated impact energies are not correct due to the orientation effect discussed above. The second type of test is impact by a drop weight on a single particle using an instrumented apparatus called a rapid-response impact load cell (King and Bourgeois 1993). The test particle is laid resting flat on the end of a vertical steel rod (that acts as the anvil) and can be held in place by a thin film of grease in order to limit relocation during contact. The theory of wave propagation along a rigid cylinder is used to get a measure of the force–time curve produced by the impact and, hence, the force–deformation curve (Tavares and King 1998). This type of tester is capable of recording impacts of duration in the range of tenths and hundredths of microseconds. The impact produces a

BREAKAGE AND DAMAGE OF PARTICLES BY IMPACT

213

140

120

100

Force, N

80 Starting κ0 60

40

20

0 0

100

200

300

400

500

(Deformation, μm)3/2

FIGURE 4 Force–deformation curves produced by repeated impacts on a particle, without fracture. Model parameters: d = 4.4 mm, N0 = 17 GPa, Dc = 70 μm, J = 9, and impact energy = 1.4 mJ.

plane-compressive wave that moves down the rod at high speed and is detected by fastresponse strain gauges placed far enough away from the contact surface to allow the development of the plane wave. The output of the strain gauges is taken to a digital storage oscilloscope and later processed in order to give the force–deformation curve (Tavares 1997). Rounded or very regular particles of a given material and particle size were hand selected for the test, as these shapes of particles conform closest to the assumptions in data analysis, enabling the most accurate measurements of rigidity modulus and damage accumulation coefficients (discussed later in this paper). An advantage of a single-particle test of this kind is that the impact energy can be made low enough to produce deformation without fracture, and then the particle can be impacted again. Figure 4 presents the simulated results of such a test, which show that the force–deformation curve is not reversible but returns to give a lower starting stiffness modulus for the curve produced by the next impact. Two important conclusions can be made. First, the stiffness factor decreases as the particle is compressed by the impact. This is attributed to microcracking in the solid that leaves the outline of the solid unchanged after the stress is removed. Second, the ability of the solid to compress more readily (lower stiffness) is permanent. These two factors require a reexamination of the theories of deformation and fracture. The equation relating force and deformation for a sphere between anvils is, for a constant stiffness modulus (particle stiffness) kp (Equation A6 with n = 2),

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1e2 kp ks · 3 e 2 d § ---------------¸ D F = ---------- ¨ k 3 © p + ks ¹

(EQ 15)

where ks is the stiffness of the anvil, which in the case of steel is about 230 GPa. The force–deformation curves of Figure 4 show that kp is not constant, so an apparent mean value of kp for the rising part of a curve, N, can be defined in Equation 15 by replacing kp with N. The degree of “damage” was defined as a measure of the degradation of particle stiffness (Kachanov 1958; Tavares and King 2002) as D = 1 – N e N0

(EQ 16)

where N0 is the initial value at the start of the curve. The variation of N with deformation D was fitted by the empirical equation J

N = N0 > 1 – Dc  D e Dc @

(EQ 17)

where DC is the critical deformation at the point of fracture, Dc is the critical damage, and J is the “damage accumulation coefficient.” A large value of this coefficient means that damage accumulation is small until the deformation approaches the critical value, whereas low values give large increases of damage as the deformation increases. Rewriting Equation 15 as to allow for the variation of the stiffness factor (Equation 16) and also considering that the stiffness of the anvil is typically reasonably higher than that of the particle ( N 0  1 – D + k s # N 0 + k s ) gives 1e2 d § ks N0 · D- · J 3 e 2 § ---1 D – D F = ---------- ¨ ---------------¸ c © Dc ¹ 3 © ks + N0 ¹

(EQ 18)

where Dc corresponds to the value of damage for which the derivative of Equation 18 is equal to zero, giving Dc = 3/(2J + 3). The critical force to produce fracture is approximately given by 1e2

d ks N0 > 1 – Dc @ 3 e 2 - Dc F c = ----------------------------------------3  ks + N0

(EQ 19)

Figure 5 shows the force–deformation curves predicted by this equation up to the point of fracture, for a single impact of sufficient energy to produce fracture. Several important conclusions can be made from Figure 5. If the response curve of the impact of a weight falling on a particle follows this pattern, then the values of the three parameters N0 , Dc , and J can be determined from the curve. The N0 is not necessarily an exact value because it is a spherical equivalent value, but it is the variation of the value that is important. The experimental value of the force required to produce disintegrative fracture (when the value of stiffness factor tends to zero) can be predicted by the parameters. It is not necessary to make the assumption (generally erroneous) that an impact of a known specific energy can be used to predict the force. Thus, the “strength” of the particle can be defined explicitly by this critical force. Alternatively, it is common to use “strength” as the “specific impact energy required to produce fracture,” which appears to be due to much of the work being done by mineral process engineers who are familiar with kilowatt-hours per ton as an index of the difficulty of size reduction, or to

BREAKAGE AND DAMAGE OF PARTICLES BY IMPACT

215

240 Fracture γ = 90 200 Fracture γ=9

Force, N

160

Starting κ0

120

80

40 3/2

αc 0 0

100

200

300

400

500

600

700

800

(Deformation, μm)3/2

FIGURE 5 The force–deformation curves predicted for impact on a sphere of 4.4-mm diameter, N0 = 17 GPa, Dc = 70 μm

the use of experimental techniques where the actual force cannot be measured directly. The relationship between the deformation and the specific strain energy E is obtained by integrating Equation 18, which gives 3  1–n e 2 1 e 2

d ks N0 2 2 D J - -- – D c §----- · a 5 e 2 E = ------------------------------------------© Dc ¹ 3m p  k s + N 0 5

(EQ 20)

where mp is the particle weight, and n the number of contact points (1 or 2). In this test there is no orientation effect because the particle cannot twist and re-impact during impact. It is only necessary to test enough particles to encompass different shapes and measure the actual fracture force each time. Of course, the equipment is complex, and testing particles one at a time is very time consuming, but the results are far more informative than those from other types of tests. It will be noted from Equation 18 that the influence of the damage accumulation coefficient on the critical force (strength) becomes small for large values of the coefficient as 3/(2J + 3) becomes small compared to 1. However, if an impact is not sufficient to cause disintegrative fracture, then the particle is damaged and will be weaker for another impact. Tavares and King (2002) show that the calculation of the decreasing strength with each impact depends on the value of J, and it is essential to know this value, even if each amount of damage is small, in order to estimate how many impacts will cause disintegrative fracture.

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EXPERIMENTAL RESULTS

Table 1 shows a set of data for a material that is damaged relatively easily (low J), with the data presented in the order of decreasing strength. There are several important conclusions. It might be argued that the distribution of stiffness factor seen in the pellet tests discussed previously is due to variability in the manufacture of the pellets by pressing and sintering. However, the particle data also show a wide distribution of the factor. This can be interpreted as a combination of natural material variability and the damage sustained as the test particles are produced (usually by crushing). A given size of particle can originate from a single breakage or it might result from a sequence of breakages, so the damage prehistory will be different. A particle that starts with a low value of N will reach N tending to zero sooner in a compression, other factors being equal. On the other hand, particles with a high value of J will resist further damage and appear stronger. Any “theoretical” treatment that assumes that particles have a single value for the mechanical properties is clearly incorrect. The data also show that there is little correlation between the initial N values and the J values. This implies that the prehistory of the particles controls the starting stiffness factor, whereas further damage occurs independently of the existing damage. For this set of data, it can be shown that there is a weak and scattered relation between the critical deformation and the starting stiffness factor. It appears that lower stiffness is associated with a larger critical deformation, so that some degree of damage enables the material to deform more before it breaks. Equation 20 shows that the strength is affected by each of the three parameters. There is an important finding that results when a particular value of strength can arise from different combinations of the three parameters (if they are not strongly correlated and are almost independent of one another). When such particles are repeatedly impacted, they will behave differently, and a given number of impacts at a given specific impact energy may break some of the particles and not others, even though they have the same strength to start (Tavares and King 2002). This invalidates treatments (e.g., Austin 2004) that assume that particles of the same strength behave identically when repeatedly impacted. The damage accumulation coefficient acts in two ways. If it is relatively small, the damage accumulates gradually during the impact and the critical force (or specific impact energy) that is required to produce fracture depends on the value. If the value is large, there is little effect until the deformation approaches the critical value, and the value of the critical force has a negligible dependence on the damage accumulation coefficient. Thus the most accurate way of determining J when it is large is by analyzing results from repeated low-energy impacts (Tavares and King 2002), although this is a time-consuming test compared to the single-impact test. The results from data similar to those in Table 1 are shown in Table 2 for different mineral particles. The cumulative distribution of J was fitted approximately to the loglogistic function: 1 F  J = -------------------------------O 1 +  J 50 e J O

(EQ 21)

where J50 is the median value. Although there is no strong correlation between J and N0 seen in the individual data sets, because each particle has its own starting stiffness factor, Figure 6 shows that J50 is strongly correlated with Fm50. Material that is strong on the average is more difficult to damage on the average. However, it must be remembered that individual particles have their own J values, to be calculated from J50 and Fm50.

BREAKAGE AND DAMAGE OF PARTICLES BY IMPACT

TABLE 1

217

King-Tavares test data for marble (4.0–4.75 mm)

Maximum Impact Force Fm, N

Initial Stiffness Factor N0 , GPa

Damage Accumulation Coefficient J (–)

Critical Deformation Dc , μm

190 186 171 170 164 161 160 152 144 129 125 123 123 110 89 87 85 78 67 60

34 26 31 28 26 21 21 21 25 23 20 18 20 16 15 14 11 9.5 7.5 8.2

12 20 10 11 6.5 11 10 9.0 8.0 6.5 7.0 8.5 9.0 7.0 6.0 9.0 9.5 6.0 5.0 7.7

47.6 53.4 47.3 49.5 54.9 57.7 58.7 55.6 49.2 51.8 51.5 54.4 49.9 54.6 50.5 49.9 57.6 63.5 69.4 57.7

TABLE 2

Results from the King-Tavares test on particles with size 4.00–4.75 mm

Material

Median Impact Force Fm50, N

Median Damage Accumulation Coefficient J50 (–)

Damage Accumulation Distribution Factor OJ (–)

Heat-treated quartz Marble Iron ore Limestone Cement clinker Quartz

105 125 180 185 360 540

10.0 8.5 15.0 31.5 45.0 68.0

2.6 6.0 2.6 2.4 2.35 1.65

Additionally, a comparison can be made between the distribution of strengths from impact load cell tests (n = 2) (Tavares 1997) and impact on a target (n = 1) (Vogel and Peukert 2003) on irregularly shaped particles. It shows that the target impact data give distributions that have consistently higher maximum strengths than the impact load cell tests, which is in agreement with what we have argued previously. FR A G M E N T D I S T R I B U T I O N S

It is well understood that the description of the strength behavior of a collection of particles is not generally sufficient for the purposes of predicting mill performance because it is also necessary to describe the distribution of fragments formed on the breakage. This is easily done in those tests where many particles are broken and the collected fines can be sized. However, it is clear that the result will be the mean of many different types of breakage and it will be difficult to predict the values for other breakage processes. It is possible to collect and analyze the fragments from (automatically well-characterized)

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600

Median Impact Force, N

500

400

300

200

100

0

0

10

20

30

40

50

60

70

80

Median Damage Accumulation Coefficient

FIGURE 6 Correlation of median damage coefficient with median force required to cause fracture (data from Table 2)

individual particle breakage in the King-Tavares test, but only for large particles. The test work is tedious and has not yet been done in sufficient detail to describe the laws controlling the fragment distribution. There is also an additional complication. When the impact energy is greater than that required to cause the primary disintegrative fracture, then the remaining energy may, under some circumstances, be used to break the resulting fragments. It has been suggested (Austin 2002) that this can be treated as a repetitive breakage process, and the appropriate algorithm has been formulated, but the assumptions involved have not been rigorously tested. C O N C L U S I O N S A N D F U T U R E WO R K

The brittle breakage model based on the damage mechanical theory has two extremes. At low values of the damage accumulation coefficient, a particle undergoes irreversible damage by microcracking (the stiffness factor decreases) as the particle is compressed by the impact. At a critical value of deformation, the accumulated damage makes the particle so weak (the stiffness factor tends to zero) that the particle disintegrates. On the other hand, at high values of the damage accumulation constant, the particle suffers little damage until the critical deformation is approached and the stiffness factor drops suddenly to zero. This second extreme is close to the conventional theory of brittle fracture, with the critical deformation producing crack propagation from a Griffith flaw with a critical tensile stress. In both cases, repeated impact at levels too low to give fracture will produce weaker and weaker particles until fracture occurs. In general, it is necessary to know the initial stiffness factor, the critical deformation, and the damage accumulation coefficient in order to define the failure properties of any given particle. In an assemblage of closely sized particles of natural materials such as

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219

mineral ores, coals, and so forth, there will be distributions of these three controlling parameters, which will vary with particle size. Knowing these parameters enables the distribution of strengths to be calculated and the failure behavior of the assemblage under specified impact conditions, including repeated impacts, to be predicted. There are no mathematical difficulties in the calculations. Tests that measure only the distribution of strengths are of limited use because the distributions of the three controlling parameters cannot be deduced from that information alone. Future advances in understanding will come only from tests that use appropriate load cells to measure the fundamental material properties. It is not yet clear whether the damage accumulation coefficient derived from a single destructive impact is the same as that derived from repeated small impacts. In repeated impacts, the compressive stress is relieved after each impact, and this could lead to increased damage by microcrack extension. The Hertzian solutions for ideal impact of spheres can be used to guide the research, but they must be used with caution. Impacts of nonspherical particles can occur with an inefficient transfer of the impact energy to the primary breakage, so calculations based on the specific energy of impact must allow for the energy utilization factors described in this paper. It is difficult to imagine the concept of contact circle of impact applying with exactitude to the variety of impacts of irregular-shaped mineral particles. This paper has attempted to define the problems to be solved rather than to present detailed investigations of specific systems. It is clear that a great deal of work remains to be done, involving accurate and detailed investigations of different sizes of different materials. REFERENCES

Austin, L.G. 2002. A treatment of impact breakage of particles. Powder Technology 126: 85–90. ———. 2004. The effect of damage on breakage kinetics. Powder Technology 143–144: 151–159. Austin, L.G., and F.F. Aplan. 1998. The powder technology of standard grinding tests: Part I, ball milling and roller-race milling. In Fine Powder Processing Technology. Edited by R. Hogg, R. Cornwall, and C.C. Huang. University Park, PA: Pennsylvania State University. Austin, L.G., K. Shoji, and M.D. Everell. 1973. An explanation of abnormal breakage of large particle sizes in laboratory mills. Powder Technology 7(1):3–7. Austin, L.G., P.M. Trubelja, and B. Scarlett. 1993. A study of the fracture of pellets fired against a target. Particle and Particle Systems Characterization 10:347–352. Bond, F.C. 1954. A two-dimensional phenomenon in the breakage of coal. Fuel 33(2):249. ———. 1960. Crushing and grinding calculations. British Chemical Engineering 6:378–391, 543–548. Gardner, R.P., and L.G. Austin. 1975. The applicability of the first-order grinding law to particles having a distribution of strengths. Powder Technology 12(1):65–69. Goldsmith, W. 1960. Impact: The Theory and Physical Behavior of Colliding Solids. London: Edward Arnold. Griffith, A.A. 1921. The phenomena of rupture and flow in solids. Series A. Philosophical Transactions of the Royal Society 221:163–198.

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Hiramatsu, Y., and Y. Oka. 1966. Determination of the tensile strength of rock by a compression test of an irregular test piece. International Journal of Rock Mechanics and Mining Sciences 3:89–99. Jaeger, J.C., and N.G.W. Cook. 1969. Fundamentals of Rock Mechanics. 1st edition. London: Methuen. Kachanov, L.M. 1958. Time of the rupture process under creep conditions (in Russian). Izv. Akad. Nauk AN SSSR 8:26–31. King, R.P., and F.S. Bourgeois. 1993. Measurement of fracture energy during singleparticle fracture. Minerals Engineering 6:353–368. Schönert, K. 1986. Advances in the physical fundamentals of comminution. Pages 19–32 in Advances in Mineral Processing. Edited by P. Somasundaran. Littleton, CO: SME. Tavares, L.M. 1997. Microscale investigation of particle breakage applied to the study of thermal and mechanical predamage. Ph.D. dissertation, Salt Lake City, UT: University of Utah. Tavares, L.M., and R.P. King. 1998. Single-particle fracture under impact loading. International Journal of Mineral Processing 54:1–28. ———. 2002. Modeling of particle breakage by repeated impacts using continuum damage mechanics. Powder Technology 123:138–146. Vervoorn, P.M.M. 1986. Particle Attrition. International Fine Particle Research Institute Final Report FRR 13.01. Netherlands: Delft University of Technology. Vervoorn, P.M.M., and L.G. Austin. 1990. The analysis of repeated breakage events as an equivalent rate process. Powder Technology 63:141–147. Vervoorn, P.M.M., and B. Scarlett. 1990. Particle impact testing. Pages 195–204 in Proceedings 7th European Symposium Comminution. Ljubljana, Yugoslavia. Vogel, L., and W. Peukert. 2003. Breakage behavior of different materials—construction of a mastercurve for the breakage probability. Powder Technology 129:101–110. Weibull, W.A. 1939. A statistical theory of the strength of materials. Ingvetenskakad Handl 151:5–45. Weichert, R. 1992. Application of defect statistics and fracture mechanics for describing comminution processes. Zement-Kalk-Gips 45:51–57.

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APPENDIX A

Hertzian Solutions for Impact of Spheres From the potential theory (Goldsmith 1960) the pressure distribution in the surface of contact of two curved bodies is given by 2 2 2· K § D r a –r p  r = -----e ¨ – -------------------- + -------------------------- – --------------------¸ Kg ¸ S¨ 2 2 2 2 Kg a – r a –r © ¹

(EQ A1)

where D represents the decrease under pressure of the distance along the normal from the center of the sphere through the center of the contact circle to a point in the anvil distant from the contact, and r is the radial distance from the center of the contact circle. The value of D is 2

a D = ----Kg

(EQ A2)

Substituting Equation A2 in Equation A1 gives 2K 2 2 p  r = – ---------e a – r SK g

(EQ A3)

The radius of the contact circle, a, is obtained from 3

4a K F = ---------------e 3K g

(EQ A4)

where F is the applied load. Substituting Equation A2 in Equation A4 4 1e2 3e2 F = -- K e K g D 3

(EQ A5)

This is the constitutive equation describing one-point contact of curved surfaces. Note that Hertzian contact theory predicts a nonlinear relationship between load and deformation, which is the result of the fact that the contact area changes continuously with the applied load. For the case of two contact points (such as that of a sphere compressed between two platens), D must be halved in Equation A5. Therefore, the general constitutive equation from the Hertz theory that describes the impact of a sphere against a target (n = 1) or the impact of a sphere between anvils (n = 2) is 3  1–n e 2

2 1e2 3e2 F = ---------------------- d K e D 3 with Ke = kpks(kp + ks) and Kg = d/2.

(EQ A6)

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Integrating Equation A6 up to a given deformation, D, gives the elastic energy stored 3  1–n e 2 +1

2 1e2 5e2 elastic strain energy = -------------------------- d K e D 15

(EQ A7)

The relationship between the mass-specific elastic strain energy stored in the spherical particle and the force is given by substituting Equation A6 in Equation A7 is F = 0.90 ˜ 2

3  1–n e 5

2e5 3e5 2

Ke

E

d

(EQ A8)

Further, the relationship between the maximum force and the impact velocity at one-point contact (n = 1 in Figure 1) is given by 2

2e5

F m = 0.757d K e

2 3e5

 Uv

(EQ A9)

given that E = v2/2. The maximum tensile stress occurs at the circular boundary of the surface of contact (r/a = 1) 2 – 4P F K 2 V T = ---------------- -- § -----e · S 9© d ¹

1e3

(EQ A10)

This can be rewritten as a function of specific impact energy (E) as V T = 0.32  1 – 2P  2

1 – n e 5

4e5

K e

 UE

1e5

(EQ A11)

From the definition of particle strength (Equation 3), it is possible to show that V p = 0.678  2

32 – n e 5

2e5

K e

 UE

3e5

(EQ A12)

BREAKAGE AND DAMAGE OF PARTICLES BY IMPACT

223

APPENDIX B

Allowance for Energy Utilization Factors The distribution of stiffness can be described by (from Equation 8) * 1 F 1  k p = -----------------------------* O1 1 +  1 e kp

(EQ B1)

*

Differentiating with respect to k p *

O1 dF 1  k p ------------------- = ---------------------------------------------* * – O 1 2 *1 + O 1 dk p  1 + kp kp

(EQ B2)

*

*

*

*

Consider a particular value of Fm. For k p in the range k p to k p + dk p all impacts with *2 e 5

§ k p C· -¸ U d ¨ ---------------© Fm ¹

5e3

*

(EQ B3)

will give maximum force d Fm. As U* has a maximum of 1/U50 when U = 1, the maximum * k p for this condition is F * k m = § -----m-· © C¹

5e2

1 · § -------© U 50 ¹

(EQ B4)

Then the total fraction of impacts with maximum force d Fm is *

km

G  Fm =

*

dF 1  k p * * - F 2  U dk p ³ -----------------* dk p

(EQ B5)

0

Equation 14 gives the distribution of U*. Using this and Equations B2, B3, and B4 in Equation B5 becomes, *

km

G  Fm =

§

O1

1

·

1

*

-¸ -------------------------------O- dk p - ¨ ------------------------³ ----------------------------*1 + O *–O 2 *2 e 3 ©1 + k ¹ 0

 1 + kp

1



1

p

(EQ B6)

§ kp · 1 + ¨ ------------¸ © F m e C¹

This integral can be calculated numerically for any value of Fm, with U50 and O as adjustable constants, since kp50 and O1 are known and values of d, U, and v are necessary to define the impact conditions.

The Rationale behind the Development of One Model Describing the Size Reduction/Liberation of Ores Ronald L. Wiegel*

ABSTRACT

A.M. Gaudin espoused the use of the Rubik’s-cube arrangement of mineral grains to conceptually describe binary mineral liberation. That idealized concept has been examined, modified, tested, and extended over the past 40 years, resulting in a useful quantitative model for describing the liberation of medium-grade ores. This paper describes the background and rationale for accepting this approach for modeling mineral liberation as part of an overall mineral process simulation capability. As much of the size reduction used for liberation is aimed at lower-grade mineral deposits, comments have been included concerning extending the approach to low-grade ores. INTRODUCTION

A Visualization of Mineral Liberation Due to Size Reduction

In his 1939 text, Principles of Mineral Dressing, A.M. Gaudin described a conceptual model for mineral liberation caused by the three-dimensional geometric effects of size reduction in a binary mineral system (Gaudin 1939). This idealized conceptual model is admittedly an extreme simplification of a real mineral system, as it assumed that the mineral grains of both mineral species were of the same uniform cubic shape and were aligned adjacent to each other, such that the eight corners of the cube were touching other cubes’ corners. This then provides intimate surface-to-surface, edge-to-edge, and corner-to-corner contacts, similar to what has more recently become known as a Rubik’scube arrangement. Further, when Gaudin’s binary mineral grain assemblage was broken in a size reduction event, the resultant fracture plains ran parallel to the mineral grain surfaces and produced uniformly sized cubic particles. The composition of the individual resultant particles depends upon whether the grain fragments that constitute it are all of the same mineral species or are of different species. In the first case, there would be liberated particles of either waste or value, and in the second, there would be locked middling particles of a wide range of compositions. The author believes the original purpose of Gaudin’s conceptual model was to convey the ideas that help one to understand qualitatively how the composition of the particles produced by size reduction relate to the original mineral grain size, the particle size, and * Mineral Processing Consultant, Lakeland, Florida 225

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ADVANCES IN COMMINUTION

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the location of similar or dissimilar grains adjacent to one another in the original grain assemblage being broken. There were some quantitative relationships provided with Gaudin’s description, but because special situations were required to cause these relationships to be valid, little attention was paid to their possible use. R EV I EW O F P R EV I O U S WO R K O N T H E G A U D I N M O D E L

Converting a Qualitative Model to a Quantitative One The Fully Liberated Minerals. The Gaudin liberation model was reviewed and

revived in the 1960s (Wiegel 1964, 1965; Wiegel and Li 1967) with the purpose of developing more general quantitative relationships to describe the liberation effects of size reduction. Although the same idealized conceptual model was used, the idea of a random location of the two ordered mineral grain species was introduced and was defined by binary probability concepts. It also was assumed that the uniformly spaced fracture planes, which run parallel to the mineral grain surfaces, are equally likely to occur at any position in the mineral grain. This then permitted the derivation of the following fairly complex relationships, which are valid over the entire size spectrum, for the proportion of liberated waste particles (Equation 1), liberated values particles (Equation 2), and locked waste and values particles (Equation 3) as a function of the mineral grain size, particle size, and the original ore’s volumetric fraction of values (feed grade). At that time, the newly termed Gaudin Random Liberation Model (GRLM) was still a mathematical curiosity, with no proven usefulness. It defined the analytical relationships for an idealized binary mineral system among the quantities of liberated and locked minerals and two liberation parameters, the volumetric proportion of value in the ore and the ratio of mineral grain size to particle size. A plot of these liberation relationships for the case where the original ore contains 0.25 volume fraction of values is shown in Figure 1. 3

PA =  1 – H VA

 t+1

3

2

2

+ 3H  1 – H VA 3

PA =  1 – H VB 2

 t+1

= = = = = = = = = =

 t+1  t+2

2

3

2

+ 3H  1 – H VB  t+1  t+2

 t+1  t+2

+ H VA

3

+ 3H  1 – H VB

where PA H VA t PB VB PAB E D K

2

+ 3H  1 – H VA

2

3

 t+2

2

 t+1  t+2

+ H VB

(EQ 1)

3

 t+2

(EQ 2)

3

PAB = 1 – PA – PB

(EQ 3)

E/D = t + e = 1/K

(EQ 4)

fraction of particles by volume of liberated waste mineral fractional remainder in ratio E/D volume fraction of waste mineral in original feed largest integer in ratio E/D fraction of particles by volume of liberated values mineral volume fraction of values in original feed fraction of particles by volume of locked values and waste particle size (linear dimension) mineral grain size (linear dimension) grain size–particle size ratio

Conceptually, when carrying out the GRLM calculations, there is only one particle size into which the mineral grain aggregate is broken. In reality, there is an entire distribution

RATIONALE FOR ONE MODEL DESCRIBING THE SIZE REDUCTION/LIBERATION OF ORES

227

1.0 Liberated Values

Cumulative Fraction by Volume

0.8 Locked Values and Waste 0.6 Liberated Waste 0.4

0.2

0.0 0.1

1

10

100

Grain to Particle Size Ratio

FIGURE 1 Fraction locked and liberated particles versus grain size–particle size ratio for an ore with 0.25 fraction values

of particle sizes resulting from size reduction. The way the GRLM has been used in simulations is to calculate liberation results for the log mean particle size for each individual screen fraction. One is therefore making the assumption that the particles in a resultant narrow size range have a composition distribution spectrum similar to the uniform, cubic particles generated by the GRLM calculations. Comparison of the Model with Reality—Magnetic Iron Formations. The underlying reason for developing more quantitative liberation relationships was due to an interest in better explanations and possible control of the rejection of waste by magnetic separation following the several stages of size reduction in the magnetic taconite process, which was receiving a great deal of process engineering interest at that time. To see if the GRLM had a potential quantitative use, despite its many idealized assumptions, a suite of crude magnetic iron ore samples were collected of the feed and product from the initial size-reduction step in 12 magnetite concentrators operating around the world (Wiegel 1975; Lynch 1977). These individual product samples were screened into closely sized fractions and concentrated in laboratory-use Davis tube separations, with the weighed concentrate and tail products subjected to Satmagan measurements for magnetite, specific gravity measurements, and wet chemical analyses for gangue components. It should be pointed out that the Davis tube, when used on small quantities (10–20 g) of closely sized particles for reasonable testing times (10–20 min), is an extremely efficient separator of particles containing magnetite from those that are nonmagnetic. The relatively close particle size all but eliminates the tendency for strings of magnetic particles to entrap nonmagnetic particles, such as that which happens routinely in commercial magnetic separators, where particle-size distributions are wide and separation time is minimal. The Davis tube results are therefore a very good indication of the quantity of particles containing magnetite (liberated magnetite and locked magnetite and waste) versus those that have no magnetite (liberated waste).

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A comparison of the shape of the concentrate-grade versus particle-size results for the Davis tube—with GRLM calculations assuming total capture of magnetite-containing particles in the concentrate and total rejection of nonmagnetite particles in the tailing when converted to weight units—provided support for the potential use of the GRLM as a quantitative tool for the explanation of liberation, at least for magnetic taconites. It also was possible to obtain an estimate of the “effective” mineral grain size for each magnetite iron ore source by best fitting the calculated GRLM plots to the experimental separation data. Concentrate-grade data typical of these samples are shown in Figure 2, versus those calculated using the GRLM. The concentrate quantity versus particle-size results for these tests were not as encouraging; they were somewhat distorted by the tendency for the magnetite and the gangue minerals to grind at different rates. Gradual Liberation by Batch Grinding. An examination of the use of the GRLM in describing the gradual size reduction/liberation of an ore was made (Wiegel 1976a) when a series of laboratory-batch grinds were carried out on a coarse-grained magnetic iron formation sample, with the product size fractions subjected to Davis tube separations and analyses. A portion of these concentrate-grade and quantity results are shown in Figures 3 and 4, for grinds of 0, 1, 2, 5, 10, and 20 minutes’ duration. In this case, there was an indication that some differences existed in the grinding rates of the waste and values species, as evidenced by trends in magnetite content increasing with smaller particle size, indicating that the magnetite was ground more rapidly than the waste. A useful concept that also came out of this batch-grinding study was the definition of a directional coefficient, which described the proportion of material that started in a specific size/composition location and proceeded as a result of size reduction to a finer size/ composition location. This concept is useful in tracing what happens to particles when modeling simultaneous size reduction and mineral liberation.

¦ V  I J Q  I II J

= V  II J + 1

(EQ 5)

I

¦ Q  I II J

= 1

(EQ 6)

II

where V(I, J) Q(I, II, J) I II

= = = =

quantity of particles of size J, composition I directional coefficient, going from composition I to II composition index in beginning particle size range, J composition index in next finer particle size range, J + 1

The GRLM was incorporated into an early simulation program for a magnetic taconite concentrator (Wiegel 1976b, 1979), which included models for hydrocycloning, fine screening, closed-circuit grinding, and multidrum magnetic separation. Expansion of the Gaudin Random Liberation Model

For some 20 years (1980 to 2000), there was little interest shown in the use of the GRLM, and no attempts were made to pull more information from the potential quantitative aspects of the model. There were also no further efforts to develop liberation information from the Davis tube separation of magnetite ores, despite the advantage of an almost perfect separation of magnetic from nonmagnetic particles. Rather, the general emphasis of liberation studies shifted to an interest in ores, where liberation information was determined from image-analysis-related techniques (Barbery 1991; Schneider 1995).

RATIONALE FOR ONE MODEL DESCRIBING THE SIZE REDUCTION/LIBERATION OF ORES

229

75 GRLM Plot

Davis Tube Concentrate Grade, % mag Fe by wt

70 65

Sample 6

60

Effective Grain Size: 1,200 μm Feed Grade: 45%

55 50 45

Sample 8

40

Effective Grain Size: 32 μm Feed Grade: 30%

GRLM Plot

35 30 25 20 10

1

100

1,000

10,000

100,000

Particle Size, μm

FIGURE 2

Davis tube concentrate grade versus particle size

100

Davis Tube Concentrate Grade, % Fe3O4 by vol.

Coarse-Grained Magnetite

90 Liberation Parameters: Effective Grain Size: 1,200 μm Mineralized Ore: 30% Fe3O4 Additional: 25% Barren Dilution

80 70 60 50 40 30 20 10 0 10

0 min 1 min 2 min 5 min 10 min 20 min GRLM 100

1,000

10,000

Particle Size, μm

FIGURE 3

Davis tube concentrate grade for ground samples

In the mid-1990s, a renewed interest in iron ore mineral process modeling and simulation was underscored by the success of one magnetic taconite concentrator in achieving a 34% increase in capacity and a 26% reduction in grinding energy consumption per unit of production (Wennen, Nordstrom, and Murr 1997). This improvement was attributed to significant, but not extraordinary, process changes resulting from a combination of small-scale pilot testing, computer modeling of portions of the concentrator flow scheme, and critical evaluation and analysis of the test results.

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Davis Tube Concentrate Quantity, % Feed vol.

90 80 70 60 50 40 0 min 1 min 2 min 5 min 10 min 20 min GRLM

30 20 10 0 10

100

1,000

10,000

Particle Size, μm

FIGURE 4

Davis tube concentrate quantity versus particle size

Measuring Liberation Parameters. The mineral process modeling and simulation software packages, which had entered the marketplace in the late 1980s, did not have either a mineral liberation or magnetic separation modeling capability, so efforts began at the University of Minnesota’s Coleraine Minerals Research Laboratory to determine what might fill these gaps. As a result of the earlier encouragement provided by the GRLM, a new and more detailed look was taken at what additional information could be gleaned from the idealized system. As mentioned above, with an appropriate choice of “effective” mineral grain size, the GRLM provided a quantitative estimate of the amount of either liberated waste or liberated values, with the remainder being locked particles covering the entire range of compositions. As a step towards obtaining better quantitative measures of those parameters directly affecting mineral liberation, a least-squares computer program was written to obtain a best fit of the already recognized variables of “effective mineral grain size” and original mineralized crude ore feed grade. It also was realized that an additional parameter of barren waste dilution provided a significant reduction in the residual errors. This dilution, which was assumed to be of the same composition as the waste mineral, could be visualized either as a true dilution that takes place during mining or as a mathematical adjustment for the fact that—at least in the case of many iron formations—the iron oxide mineral is layered into higher- and lowergrade bands (Wiegel 1999a). The GRLM information displayed in Figures 3 and 4 use three liberation parameters: volume fraction of values in the mineralized ore, effective mineral grain size, and barren waste dilution. Quantifying Locked Particles. It was found that a computer simulation of the breakage of the assemblage of cubic grains of the binary mineral aggregate in the GRLM, with a proper randomized manipulation of the spacing of the breakage grid, could be used to generate information on the quantity and composition of the locked and liberated particles for a specific mineral grain size–particle size ratio and original ore grade (Wiegel 1999b). These breakage simulations for a particular product size were carried out with a minimum of 200,000 particles being created, to ensure reasonable statistical

RATIONALE FOR ONE MODEL DESCRIBING THE SIZE REDUCTION/LIBERATION OF ORES

231

confidence while not requiring excessive simulation time. The particle composition spectrum was divided into 12 volume classes: liberated waste at 0% values, 10 locked particle classes with ranges increasing in 10% increments, and liberated values at 100% values. Each particle created by the simulation was placed in its appropriate composition slot. For a given volumetric feed grade, separate simulations were carried out for grain size– particle size ratios in the range of 0.125 to 32, with size ratios increasing by a factor of the fourth root of 2 (1.189), providing roughly 30 sets of observations for each feed grade. Similar sets of simulations were carried out for feed grades of 5%, 15%, 25%, 35%, and 45% values by volume. The higher feed-grade results can be calculated from these due to the symmetry introduced by having only two mineral components, values and waste. The composition range midpoint was chosen as a reasonable approximation to the mean particle composition for each of the ranges resulting from the breakage simulations. The detailed simulation results for the GRLM provide an improved mathematical or statistical insight into how quantities of locked particles behave as they experience sizereduction-induced mineral liberation. It has hitherto proven difficult to visualize, let alone quantify, the gradual change that takes place in composition as the particle’s dimensions are broken to finer and finer sizes. Although some appreciation can be gained by examining microscopic images before and after breakage, there are so many variables that can affect imaging results for a specific sample that it is impossible to gain a quantitative understanding of the overall subject. As an example of the additional information provided by these locked particle breakage simulations, the GRLM-calculated results related to complete liberation of values and waste, as presented in Figure 1, are complemented by the inclusion of the comparable locked particle quantity and composition information as shown in Figure 5. The mineral grain aggregate starts out containing 0.25 volume fraction of values at a particle size, which contains in excess of 700 grains and grain fragments of values and waste. As the linear size dimension is reduced from 8 grains to 4, to 2, there is a very gradual disappearance of the original feed particles in the 0.2–0.3 composition range and a gradual appearance of 0.1–0.2 and 0.3–0.4 particles. It is not until the particles approach the size of a single grain that a measurable quantity of liberated waste appears, and it is not until particles reach about one tenth of the grain size that there is appreciable liberation of both values and waste. This particle size approximates the situation of one grain being broken into about one thousand particles. As an initial approximation, it seemed reasonable to assume that the same distribution of particle compositions would be generated by breakage from a specific size/composition range to a finer specific size, regardless of how the particles had entered into that starting size/composition range. That, in essence, states that the particles’ progeny is only dependent on the particles’ size and composition and not on the particles’ previous history. GRLM locked-particle simulation results have provided a way for one to approach quantitatively, an explanation of the process that takes place when achieving gradual liberation as a result of size reduction. Although volumetric balances dictate the requirement for conservation of overall volume and of the two individual mineral components’ volumes, in passing from one particle size into the next smaller particle size, it is still not possible to calculate directly the portion of the volume in a specific composition range that moves to each composition range in the next finer particle size. Only in the case of the breakage of liberated values and waste particles do we know which composition slots they fit into, as particles that are once liberated stay liberated. One Approach to Solving the Distribution Problem for Locked Particle Breakage. The use of the total-volume and component-volume balances in Equations 5 and 8, together with the use of the earlier mentioned directional coefficients of Equation 6, permit one to create a linear programming (LP) problem of this distribution phenomena (Wiegel

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1.0 1.0 Liberated Values

Cumulative Fraction by Volume

0.8

0.4

0.3 0.6 Liberated Waste 0.2 0.4 0.1

0.0

0.2

0.0 0.1

1

10

100

Grain-to-Particle-Size Ratio

FIGURE 5 Fraction liberated and locked particles with compositions versus grain size–particle size ratio for an ore with 0.25 fraction values

2000). Although, in LP there are many more unknowns (directional coefficients) than linear equations, it is frequently possible to obtain a solution that satisfies a stated objective criteria, which in this case was the maximization of the directional coefficients that retain material in the same composition class as particle size is reduced, shown by Equation 7. The relationships for the LP are as follows: Objective criteria:

¦ Q  I I J

= maximum

I

From Equation 5, total volume balances for II = 1 to 12

¦ V  I J Q  I II J

= V  II J + 1

I

From Equation 6, directional coefficient balances for I = 1 to 12:

¦ Q  I II J

= 1

II

Values volume balances for I = 1 to 12: V  I J ¦ Q  I II J MV  II = V  I J MV  I II

where MV(I) = mean value of a composition range I.

(EQ 7)

RATIONALE FOR ONE MODEL DESCRIBING THE SIZE REDUCTION/LIBERATION OF ORES

233

Or simplified:

¦ Q  I II J MV  II

= MV  I

(EQ 8)

II

In addition, there are 24 directional coefficients with values that are restricted to 1 or 0, by the fact that once a particle is liberated, it will remain liberated through all subsequent size-reduction steps. The remaining directional coefficients must have values between 0 and 1. In summary, for each size-reduction step, this provides a total of 36 equations with 120 unknown directional coefficients to be evaluated. Fortuitously, the solution to this particular series of LP problems indicated that only three non-zero directional coefficients were required, out of a possible twelve, for each locked-particle composition range in a particle-size-reduction step. This then gives a total of 30 non-zero directional coefficients for each size step problem. All of the variables in Equations 5, through 8, except the values of the directional coefficients, were known and obtained from the locked-particle breakage simulations for the GRLM. It was also noted that there was a pattern in the occurrence of the non-zero directional coefficients that permitted the distribution relationships to be grouped into five regions of the grain size–particle size ratio: K < 18, 18 < K < 12, 12 < K < 1, 1 < K < 22.6, and K > 22.6. Additional detail is presented in other literature (Wiegel 2000). Breakage of a particular narrow locked-particle composition range from one specific particle-size range to a smaller specific size range, with the GRLM, is treated as a series of size-reduction steps. A demonstration of the calculation is shown in Table 1, how the distribution of composition classes is handled by the GRLM simulation. In this case, the demo starts with an ore with a 0.25 volume fraction of values, and for the sake of simplicity, the directional coefficients that describe the retention of material in their initial composition ranges are assumed to be 0.50 for all but the totally liberated composition ranges, which are by definition unity. Again for simplicity, the demo is based on that material which does change from one composition class to another, moving to the nearest neighbors, both higher and lower in composition. The quantity that moves in each direction is calculated by the one feed–two product formula, based on the mean composition of the composition ranges involved. In this example, the barren waste dilution is 0, but if it were other than 0, it would appear as additional liberated waste, passing from size to size as portions of it were broken in size-reduction steps. If the original mineralized ore had a 0.23 volume fraction of values, this would be simulated by starting with 80% of the feed volume in the 0.20–0.30 values range (0.25 mean) and 20% in the 0.10– 0.20 values range (0.15 mean). The actual GRLM simulation results for a crude ore with a 0.25 volume fraction of values are shown in Table 2 for the grain size–particle size ratio range of 18 to 8 in a progression of the square root of 2. Incorporation into a Size Reduction/Mineral Liberation Simulation Program. The directional coefficient approach and the values obtained from the LP solutions for a range of original ore feed grades were then converted to regression relationships and used as a basis to construct a computer program to simultaneously simulate tumbling mill size reduction and the resultant progressive liberation for a binary mineral system (Wiegel 2000). This BASIC program’s use was demonstrated for the simulation of the batch grinding of the coarse-grained magnetite ore, described previously, and the closed-circuit grinding, hydrocycloning, and magnetic separation of a magnetic taconite ore (Wiegel 2002). One interesting aspect of this simulation capability is the possibility of recognizing and incorporating different grinding rates for the values and waste constituents, and likewise, by volumetric weighting of the locked particles. The size reduction/ mineral liberation portion of the program has since been translated into FORTRAN for

234

Demonstration of calculation of quantity in each composition range when simulating three individual size-reduction steps K = 0.177

Composition Composition Index Mean

0

0

1

0.05

2

0.15 0.25

4

0.35

5

0.45

6

0.55

7

0.65

8

0.75

9

0.85

10

0.95

11

1

Total quantity Total composition

K = 0.149 Step 1/3

Step 2/2

Step 2/3

Step 2/4

Step 2 Total

Step 3/1

Step 3/2

Step 3/3

Step 3/4

Step 3/5

2.08

2.08 6.25

100.00

25.00

12.50

50.00

6.25

25.00

12.50

Step 3 Total

9.38

6.25

3.12

6.25

25.00

1.04

12.50

9.38

6.25

18.75

6.25

9.38

12.50

1.56

23.44

6.25

3.12

9.38

1.56

1.56

25.00

6.25

37.50

12.50

12.50

25.00

6.25

6.25

22.92 31.25

100.00

100.00

25.00

50.00

25.00

100.00

6.25

25.00

37.50

25.00

6.25

100.00

0.25

0.25

0.15

0.25

0.35

0.25

0.05

0.15

0.25

0.35

0.45

0.25

LIBERATION AND BREAKAGE

3

K = 0.125 Original

K = 0.210

ADVANCES IN COMMINUTION

TABLE 1

TABLE 2

GRLM simulation results for an ore grade with a 0.25 volume fraction of values for grain size–particle size ratio range of 1/8 to 8

0

0

1

0.05

2

0.15

3

0.25

100.00

K = 1.00

K = 1.41

K = 2.00

K = 2.83

K = 4.00

K = 5.66

K = 8.00

0.04

4.31

13.02

31.75

44.91

54.00

60.28

64.63

67.67

1.76

11.46

20.76

25.86

16.32

10.02

6.25

4.00

2.63

1.76

2.96

15.65

24.93

25.32

22.83

14.13

9.51

6.54

4.46

3.03

2.07

1.43

94.08

68.70

48.42

32.15

17.82

12.67

7.96

5.59

3.98

2.84

2.03

1.46

2.96

15.65

4

0.35

21.47

18.64

11.06

8.83

6.93

4.99

3.58

2.57

1.84

1.32

5

0.45

3.28

8.37

11.58

8.09

6.54

4.90

3.65

2.70

1.99

1.45

6

0.55

0.14

3.22

7.65

6.55

5.28

4.18

3.21

2.41

1.78

1.30

7

0.65

0.73

2.72

4.44

4.96

4.21

3.35

2.57

1.93

1.42

8

0.75

0.07

0.72

3.59

3.66

3.36

2.81

2.22

1.69

1.25

9

0.85

0.48

1.79

3.05

3.64

3.33

2.69

2.03

1.48

10

0.95

0.07

0.89

2.24

2.75

2.70

2.32

1.84

1.38

11

1

0.14

1.80

4.91

8.68

12.37

15.54

18.08

Total quantity Total composition

100.00

100.00

100.00

100.00

100.00

100.00

100.00

100.00

100.00

100.00

100.00

100.00

100.00

0.25

0.25

0.25

0.25

0.25

0.25

0.25

0.25

0.25

0.25

0.25

0.25

0.25

RATIONALE FOR ONE MODEL DESCRIBING THE SIZE REDUCTION/LIBERATION OF ORES

Composition Composition Index Mean K = 0.125 K = 0.177 K = 0.250 K = 0.354 K = 0.500 K = 0.707

235

236

ADVANCES IN COMMINUTION

LIBERATION AND BREAKAGE

eventual inclusion in one of the mineral process modeling and simulation packages now on the market. This approach appears to be adequate for its original intended target—the simulation of magnetic taconite size reduction/liberation—but the author’s opinion is that it is limited to original ore feed grades in the range of 15% to 85% values by volume. The magnetic taconite is usually in the 20% to 40% by volume range and therefore fits the suitability criteria. EXTENSION OF THE DIRECTIONAL COEFFICIENT APPROACH TO LOW-GRADE ORE

Much of the interest in size reduction/liberation, however, is related to the processing of low-grade, hard-rock ores in the one-half to several percent values range, for which this current program is not suitable. The limitation relates to the choice of ten evenly spaced ranges to represent the locked particle composition spectrum for medium-grade ores. This results in the lowest composition range of 0% to 10% values having a mean of 5%, which serves no purpose when attempting to represent an ore with, say, 2% values by volume. There is no reason to believe, however, that the approach used for mediumgrade ores cannot be applied to the low-grade ores. That is, the quantitative information on composition distribution could be generated by locked particle breakage simulations using the GRLM, and the directional coefficients could be obtained by setting up and solving a similar set of LP problems. At this point, serious thought has been given to the differences between the two problems, and several items become obvious: ƒ It will be necessary to expand the number of composition ranges significantly to

adequately cover low-grade ore. ƒ It is probably appropriate to look at something akin to logarithmic composition

ranges in the low fraction values region, and in the high values region as well, because of the symmetry due to a binary mineral system. ƒ When the number of composition ranges is increased, it may be necessary to look

at smaller grain-to-particle-size ratios than the 18 value limit used with the medium-grade simulations. ƒ The number of directional coefficients is related to the square of the number of

composition ranges, and the problem of solving for their values becomes significantly more difficult—already for the medium-grade ore there were 120 unknown values. ƒ Although an increase in the number of composition ranges will increase the quan-

tity of variable storage and the program execution time in the simulation program, this is probably of minor concern. ƒ The interest in low-grade ores frequently coincides with an interest in an ore

more complex than binary, but the GRLM can be used to generate locked particle breakage information for such an ore, recognizing that the underlying mineral grain size, shape, and breakage assumptions for the GRLM are now being extended even further. Expanding the Number of Composition Ranges

As a starting point, a series of locked particle breakage simulations for the GRLM was carried out for a 0.015 fraction values ore, in which the number of composition ranges was increased from the current 12 to 30. The single 0–0.1 range was expanded to ten: 0–0.0001, 0.0001–0.0002, 0.0002–0.0005, 0.0005–0.001, 0.001–0.002, 0.002–0.005, 0.005–0.01, 0.01–0.02, 0.02–0.05, and 0.05–0.1. There was a complementary expansion

RATIONALE FOR ONE MODEL DESCRIBING THE SIZE REDUCTION/LIBERATION OF ORES

237

at the upper end as well. A summary of the results is presented in Table 3, expressed as the number of particles out of a total of one million that were broken. It is interesting to note how very few particles occur in the composition region of 0.9995–1.0 fraction values over the entire size ratio range of 116 to 64. In the lower-composition region of 0–0.0005 fraction values, a maximum of about 2.5% of the total number of particles occur. The author’s opinion is that the increased complexity and difficulty in obtaining directional coefficients for these additional six composition classes, three at both the low- and highcomposition ends, would outweigh the marginal benefit that might be provided. The plan is therefore to proceed with the development of information based on 24 composition ranges, recognizing that the calculation of even these directional coefficients may in itself be a Herculean task. Solitary Grain Model Representation of a Low-Grade Ore

As a part of the original work aimed at deriving quantitative liberation relationships from Gaudin’s conceptual model, it was recognized that a set of analytical equations could be obtained to describe the distribution of locked particles for a low-grade ore, where some complexities of the GRLM become negligible (Wiegel and Li 1967). This model was termed the Solitary Grain Model (SGM) and can be visualized as a solitary cubic grain of valuable mineral completely surrounded by grains of waste mineral. The same form of cubic fracture lattice is imposed on this assemblage of grains, but because there is no chance of having adjacent valuable-mineral grains, many of the terms in Equations 1 and 2 disappear or can be simplified. When one considers the breakage of the solitary grain of values to particles smaller than the grain size (K > 1), the number of liberated particles of values is given by Equation 9, whereas the locked particles are of three types as given by Equation 10: those located along the six surfaces of the cubic valuable-mineral grain, which are composed of two grain fragments; those located along the 12 edges of the valuable-mineral grain, which are composed of four grain fragments; and those located at the eight corners of the valuable-mineral grain, which are composed of eight grain fragments. The remaining particles are liberated waste mineral (Equation 11). PB = VB(K – 1)3/K3

(EQ 9)

PAB = VB[6(K – 1)2 + 12(K – 1) + 8]/K3

(EQ 10)

PA = 1 – VB(K + 1)3/K3

(EQ 11)

For this model, with particle size larger than grain size (K < 1), there are no liberated values, but there is a maximum values particle composition, which occurs when a full grain of valuable mineral is contained in a particle, and is given by Equation 13. The liberated waste continues to follow Equation 11, but there is a size ratio at which the approximation to the amount of liberated waste mineral becomes zero, as shown in Equation 14. The quantity of locked particles is now given by Equation 15. PB = 0

(EQ 12)

VBMAX = (DE 3= K3

(EQ 13)

K(@ PA = 0) = 1/((1/VB)1/3 – 1)

(EQ 14)

PAB = VB(K + 1)3/K3

(EQ 15)

Summary of particle breakage simulation for liberation of ore with a 0.015 volume fraction of values for size ratio of 1/16 to 64

238

TABLE 3

0.125

0.25

0.5

1

2

4

8

16

32

64

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4580 993275 2145 0 0 0 0 0 0 0 0.01508 1000000

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 160127 678329 148912 11921 480 125 50 20 20 16 0.01694 1000000

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20 16301 278479 296679 111079 74322 29873 17581 12607 4929 6938 151192 0.01658 1000000

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 40 1693 43826 74265 82920 44884 31673 25900 12149 7280 5368 2222 2846 664934 0.01651 1000000

0 0 0 0 0 0 0 0 1 5 28 198 580 1228 2269 4033 6836 11667 21231 19204 18904 9858 6581 5423 2363 1388 1135 362 591 886115 0.01531 1000000

1959 2 1 4 6 10 33 58 106 395 647 1518 1846 2254 2755 3411 4241 5612 7927 5778 4982 2261 1391 1060 433 255 179 68 83 950725 0.015079 1000000

6423 4 1 1 6 13 36 67 126 392 656 1393 1510 1631 1787 1986 2228 2568 3151 1960 1499 617 368 263 102 55 38 15 22 971082 0.01502 1000000

10113 0 3 2 1 7 23 45 92 256 436 891 922 960 999 1054 1118 1201 1344 772 525 216 118 72 27 13 9 4 3 978774 0.01500 1000000

12397 0 0 1 1 5 16 26 48 146 248 499 506 516 527 542 556 578 614 334 214 76 43 28 10 4 2 1 1 982061 0.01500 1000000

13657 0 1 0 1 3 8 11 30 72 135 263 265 268 270 274 277 284 292 156 89 37 16 11 3 2 1 0 1 983573 0.01500 1000000

14318 0 0 1 1 1 3 7 14 40 68 134 136 136 137 138 138 140 143 72 45 16 8 3 2 1 1 0 0 984297 0.01500 1000000

LIBERATION AND BREAKAGE

0.0625

1 0.99995 0.99985 0.99965 0.99925 0.9985 0.9965 0.9925 0.985 0.965 0.925 0.85 0.75 0.65 0.55 0.45 0.35 0.25 0.15 0.075 0.035 0.015 0.0075 0.0035 0.0015 0.00075 0.00035 0.00015 0.00005 0 Calculated VB Calculated volume

ADVANCES IN COMMINUTION

VB Average/K

RATIONALE FOR ONE MODEL DESCRIBING THE SIZE REDUCTION/LIBERATION OF ORES

239

1 0.00 Values 0.01 Values

Liberated Waste

Cumulative Fraction by Volume

0.1 0.10 Values

0.01

0.50 Values 0.001 Liberated Values

Solitary Grain Model Open Symbols and Curve

0.0001

GRLM Filled Symbols 0.90 Values 0.99 and 1.00 Values 0.00001 0.1

1

10

100

Grain to Particle Size Ratio

FIGURE 6 of values

Comparison of GRLM results with SGM calculations for ore with 0.015 volume fraction

There are SGM analytical relationships for the quantity of locked particles expressed as a function of the size ratio and linear and logarithmic functions of locked particle composition (Wiegel and Li 1967). Although repeating these relationships is not warranted here, they are quantitative approximations for low-grade ore which, because they are in an analytical form, may prove of value in extending the modeling and simulation capability of size reduction and liberation. A comparison of data obtained from the SGM and the GRLM are shown in Figure 6 for an ore containing 0.015 volume fraction of valuable mineral. SUMMAR Y AND CONCLUSIONS

Mineral liberation is an extremely important phenomenon to understand and to be able to quantitatively model, as it is this liberation that permits subsequent mineral separations to be carried out and simulated effectively. The development of the GRLM began with the work of Gaudin in the 1930s, as a conceptual understanding of how size reduction affects the liberation of an idealized binary mineral system. In the 1960s, the Gaudin conceptual model was modified by the application of binary probability concepts, and as a result it could be quantified for the entire range of ore feed grades and particle sizes. Since then, over a 40-year period, there has been a gradual collection of experimental data to provide support for the quantitative model. Additional efforts have been made more recently to extend both its qualitative and quantitative usefulness by tapping some of its more intricate features, such as information on the gradual change in the compositional distribution of locked particles as particle size is reduced and mineral liberation proceeds. With the expected inclusion of the GRLM into a popular mineral processing simulation package, it is now ready for a rigorous test of its applicability to the simulation of real mineral systems. With the capability of incorporating mineral liberation into the suite of unit operation models available to the process engineer, it will no longer be

240

ADVANCES IN COMMINUTION

LIBERATION AND BREAKAGE

necessary to assume either complete homogeneity or complete liberation in flow-scheme simulations, but rather it should be possible to better simulate the “entire real process.” Unfortunately, one current restriction on the use of the model is its applicability only to intermediate- or medium-grade ores, in the range of 15% to 85% by volume of valuable mineral. However, there is no reason to believe that the GRLM concept and the approach used to apply it to the medium-grade binary ores cannot be extended to cover the low-grade, multicomponent ores as well. To that end, work has begun on extending the current 12 composition ranges of the GRLM to 24. The author invites anyone interested to apply their own ingenuity to this task, and would be happy to share with such industrious individuals any unpublished ideas and special programs that have been developed for generating the locked particle composition distributions from particle breakage simulations. Virtually all of the published experimental verification of the applicability of the GRLM to real mineral systems has been for magnetic iron ores. The GRLM is not limited to this application; but rather this situation is due first to the author’s professional career being focused on the Minnesota and Northern Michigan iron ore industry and the Florida phosphate rock industry where there are no mineral liberation problems; and second, to the usefulness of the Davis tube as an efficient, simple, and inexpensive laboratory technique that ensures an almost perfect separation of magnetics from nonmagnetics. Information comparable to the Davis tube could be collected from flotation or gravity separation samples, where the individual concentrate and tailing samples from the plant or laboratory test are screened into narrow size fractions and subjected to analytical measurements to obtain the required mineral liberation information, recognizing that some separation inefficiencies will necessarily be present. REFERENCES

Barbery, G. 1991. Mineral Liberation—Measurement, Simulation and Practical Use in Mineral Processing. Quebec, Canada: Editions GB. Gaudin, A.M. 1939. Pages 70–91 in Principles of Mineral Dressing. New York: McGraw-Hill. Lynch, A.J. 1977. Mathematical model of mineral liberation. Pages 187–202 in Mineral Crushing and Grinding Circuits, Their Simulation, Optimisation, Design and Control. New York: Elsevier Scientific Publishing. Schneider, C.L. 1995. Measurement and calculation of liberation in continuous milling circuits. Ph.D. dissertation. Salt Lake City, UT: University of Utah. Wennen, J.E., W.J. Nordstrom, and D.L. Murr. 1997. National Steel Pellet Company’s secondary grinding circuit modifications. Pages 19–25 in Comminution Practices. Edited by S.K. Kawatra. Littleton, CO: SME. Wiegel, R.L. 1964. A mathematical model for mineral liberation by size reduction. Master’s paper, Pittsburgh, PA: Carnegie Mellon University, Chemical Engineering Department. ———. 1965. A quantitative approach to mineral liberation. Pages 3–9 in VII International Mineral Processing Congress. Volume I. Edited by N. Arbiter. New York: Gordon and Breach. ———. 1975. Liberation of magnetite iron formations. AIME Transactions 258(3):247–256. ———. 1976a. Integrated size reduction-mineral liberation model. AIME Transactions 260(2):147–152. ———. 1976b. Simulation of magnetic taconite concentration processes. Ph.D. dissertation. Brisbane, Australia: University of Queensland.

RATIONALE FOR ONE MODEL DESCRIBING THE SIZE REDUCTION/LIBERATION OF ORES

241

———. 1979. Application of process modeling to taconite. AIME Transactions 266:1863–1876. ———. 1999a. Fitting of Liberation Model Parameters to Davis Tube Test Data. Technical Report CMRL/TR-99-13. Duluth, MN: University of Minnesota–Duluth, Coleraine Minerals Research Laboratory. ———. 1999b. Magnetic Taconite Concentration Modeling. Technical Report CMRL/TR-99-12. Duluth, MN: University of Minnesota–Duluth, Coleraine Minerals Research Laboratory. ———. 2000. Development of an Approach to the Simulation of Size Reduction/Mineral Liberation for Magnetic Taconite Ore in Tumbling Mills, and Its Implementation in a Basic Computer Program. Technical Report. CMRL/TR-00-16. Duluth, MN: University of Minnesota–Duluth, Coleraine Minerals Research Laboratory. ———. 2002. Size reduction/mineral liberation simulation for a magnetic taconite concentrator. Mineral and Metallurgical Processing 19(3):113–122. Wiegel, R.L., and K. Li. 1967. A random model for mineral liberation by size reduction. AIME Transactions 238:179–189.

Influence of Slurry Rheology on Stirred Media Milling of Limestone Mingzhao He* and Eric Forssberg*

ABSTRACT

This paper reviews the influences of solids concentrations and dispersants with a range of molecular weights on the flowability of limestone slurries as well as the effects on wet ultrafine grinding in order to reduce energy cost and increase the fineness of a product. Sodium polyacrylate with a molecular weight of 5,500 (i.e., Dispersant S40) appears most effective for the grinding due to the effective reduction of apparent viscosities and the maintenance of steady flowability. Optimal solids concentration exists at a certain beads load for the effective wet ultrafine grinding of limestone, and a rheological explanation is presented. INTRODUCTION

Due to some advanced properties of ultrafine powders—such as surface chemistry, packing characteristics, strength, optical properties and reaction kinetics, and an increasing demand for ultrafine powders for industries—wet ultrafine grinding has found increased use in many fields (He, Wang, and Forssberg 2005). Most of the mills used in wet ultrafine grinding are stirred media mills due to their high unit outputs and high-energy efficiencies (Bernhardt, Reinsch, and Husemann 1999; Kapur et al. 1996; Blecher, Kwade, and Schwedes 1996). The stirred media mills are equipped with a stationary grinding chamber and a high-speed stirrer (disks or pins) fixed on a drive shaft. The grinding chamber is filled with small grinding media (normally spherical annealed glass, steel, or ceramic beads) at a high beads load. By stirring a slurry–bead mixture at a high stirring speed, a characteristic flow pattern and a grinding action are generated in the chamber. The respective kind of flow determines the spatial distribution of zones with high grinding intensities and the predominant types of grinding mechanisms as well as their composition (Blecher, Kwade, and Schwedes 1996; Kwade, Blecher, and Schwedes 1996). Thus, the predominant grinding mechanisms in stirred media mills are dependent upon compressional, shear, and torsional stresses, which are invoked by stirring the slurry–bead mixture at a very high velocity (Blecher, Kwade, and Schwedes 1996; Kwade, Blecher, and Schwedes 1996; Kwade 1999a,b). The effective grinding motions of the mixture are correlated to its flowability in the grinding chamber. From a diagnostic point of view, the rheological behavior of a mineral slurry is indicative of the level of interparticle interaction or aggregation in the slurry. Therefore, it is a useful variable to be controlled in industrial processes such as transportation of slurries, dewatering, and wet grinding (Muster and Prestidge 1995). Physical and chemical * Division of Mineral Processing, Luleå University of Technology, Luleå, Sweden 243

244

ADVANCES IN COMMINUTION

LIBERATION AND BREAKAGE

properties of a slurry—such as solids concentration, use of dispersants, particle size and distribution, particle shape, pH value, shear rate, and slurry temperature—have a significant influence on the slurry rheology due to the change or modification in surface property (He, Wang, and Forssberg 2004). Product fineness significantly increases with grinding time in a wet ultrafine grinding operation characterized by a high solids concentration and the presence of excessive fines; therefore, the surface properties tend to predominate in the system (Bernhardt, Reinsch, and Husemann 1999; Klimpel 1999; Gao and Forssberg 1993b). Interparticle forces such as van der Waals forces (Greenwood et al. 2002; Reinisch, Bernhardt, and Husemann 2001) and electrostatic forces (Bernhardt, Reinsch, and Husemann 1999; Muster and Prestidge 1995) lead to the formation of agglomeration and aggregation. This results in changes in rheological property in wet ultrafine grinding operations. The effect of slurry flowability or slurry rheology in wet ultrafine grinding becomes particularly important. The optimization of the rheological behavior of a ground slurry can enhance the energy efficiency and throughput in wet ultrafine grinding operations. For instance, the addition of an optimum dispersant to a given feed slurry can result in a drastic reduction or even the elimination of yield stress and permits a higher solids concentration of the ground slurry (Kapur et al. 1996; Klimpel 1999; Greenwood et al. 2002; Reinisch, Bernhardt, and Husemann 2001). In the absence of any dispersant, the typical maximum percentage solids by weight in a slurry is approximately 50% for the feed of ultrafine grinding in stirred media mills, whereas an upper limitation of solids concentration is up to 80 wt % in the presence of an optimal dispersant (Greenwood et al. 2002). Therefore, the improvement of rheological behaviors of a feed slurry with the addition of a suitable dispersant can enhance the productivity and throughput for wet ultrafine grinding. Many studies related to slurry rheology in conventional tumbling ball mills have been published, but there is still little understanding of slurry rheology relevant to wet ultrafine grinding characterized by a very fine product size and a high slurry concentration; this is due to the complex slurry rheological behaviors in stirred media mills (Gao and Forssberg 1993b; Blecher and Schwedes 1996). Also, findings from tumbling ball mills involving the role of slurry rheology on the grinding results cannot be completely applicable to the stirred media milling case due to their different breakage mechanisms (Kwade 1999a,b; Gao and Weller 1993; Austin, Klimpel, and Luckie 1984). Therefore, it is necessary for scientific understanding and industrial application to systematically investigate slurry rheology and its effect on wet ultrafine grinding performance. The objective of this paper is to investigate the influences of solids concentration and dispersants on the rheological behavior of limestone slurry, and its effect on wet ultrafine grinding performance in order to reduce the energy cost and increase the throughput and the fineness of a product. The grinding results are evaluated by energy efficiency and the median size of a ground product with respect to specific energy consumption. MATERIALS AND EXPERIMENTAL METHODS

Materials

A limestone powder provided by SMA Karbonater AB, Sweden, was used for experiments in this study. Figure 1 presents the particle-size distribution of the powder. The chemical analysis and physical characteristics of the limestone powder are listed in Tables 1 and 2, respectively. Sodium polyacrylates with a range of molecular weights such as BCX-476, Dispersant S40, and BCX-552 obtained from CDM AB, Sweden, were selected as dispersants. Table 3 shows the physical and chemical properties of the sodium polyacrylates,

INFLUENCE OF SLURRY RHEOLOGY ON STIRRED MEDIA MILLING OF LIMESTONE

245

Cumulative Mass Finer, %

100

80

60

40

20

0

FIGURE 1

TABLE 1

TABLE 2

1

10

100

1,000

Particle-size distribution of limestone powder

Chemical analysis of limestone composition Main Chemical Composition

Percent

Standard Deviation

CaO total CaO ASTM C602 CaCO3 ASTM C602 MgO Fe2O3 SiO2 Al2O3 MnO P2O5 Loss on ignition Moisture

50 52.5 93.7 4.50 0.70 3.50 0.85 0.15 0.01 40 0.2

1.0 0.7 1.3 1.0 0.2 1.0 0.2 0.03 0.6

Physical characteristics of limestone

Real Density, kg/m3

Volume Density, kg/m3

Mohs Hardness

Whiteness (ISO 457), %

pH

Particle Shape

Specific surface area, m2/g

2,700

1,000

3

77

9

Nodular

1.174

TABLE 3

Physical and chemical properties of three sodium polyacrylates

Physical and Chemical Properties

Solid content, wt % Active content, wt % pH Density at 20°C Molecular weight* Sodium polyacrylate content, wt % Water content, wt % Solubility (in water)

BCX-476

Dispersant S40

BCX-552

45 40 7.5 1.30 2,000 40 55 Very soluble

45 40 7.5 1.30 5,500 40 55 Very soluble

30 26 7.5 1.315 85,000 26 70 Very soluble

* Molecular weight determined by gel permeation chromatography (GPC).

246

ADVANCES IN COMMINUTION

LIBERATION AND BREAKAGE

including their molecular weights. In this investigation, the additive amount of a dispersant is the percentage of the pure dispersant (i.e., active content) by weight relative to the weight of solids in a limestone slurry. Experimental Methods Mix-up. A limestone–water slurry was prepared at a predetermined solids con-

centration by the addition of 40 to 50 kg of limestone powder into a certain amount of water to make up about 35 L of the slurry. The slurry was stirred as the limestone powder was added to the water, and the stirring continued for 15 min after the completion of adding the limestone powder to make the slurry uniform. If a given dispersant was necessary, the slurry was stirred again for 15 min after its addition to make the chemical disperse uniformly in the slurry. About 200 mL of slurry was taken for each sample, which was used to analyze the particle size and distribution and to measure the rheological behavior of the slurry. The rest of the limestone slurry was used for grinding experiments. Stirred Media Milling. A stirred media mill utilized for the grinding experiments is the PMH 5 TEX Drais mill (Draiswerk GmbH, Germany). It consists of a )150u420-mm stainless-steel cylinder chamber (5.6 L of net grinding chamber volume) and a stirrer with six )120u10 perforated discs installed on a horizontal-driven shaft. The grinding chamber is equipped with a water jacket for cooling. The discs rotate at 1,808 rpm (corresponding to a peripheral speed of 11.36 m/sec). The flow rate of a feed slurry in this study was controlled by a feeding pump at 1.5 L/min. The discharge of a product was facilitated by means of two specially designed screen cartridges inserted at the end of the cylinder. Zircon beads with diameters of 1.6–2.0 mm and a density of 3,700 kg/m3 were used as grinding media. The grinding operation in the PMH 5 TEX is the mode of circulation pass by pass. Fifteen of the 35 L of slurry were fed through the mill first and then thrown away in order to attain a steady milling state with respect to solids concentration. The remaining ~20 L of slurry was circulated through the mill for several passes. About 200 mL of slurry sample was taken after each pass. The samples were then analyzed for particle size, rheological property, and specific surface area, respectively. Viscometer. A rotational viscometer called a Bohlin Visco 88 BV (Bohlin Reologi UK Ltd., United Kingdom) was used for the determination of slurry viscosities and shear stress–shear rate curves. It employs a concentric cylinder geometry with a rotating inner cylinder and a stationary outer cylinder. In this study, all samples were measured by the use of C30 system (C30 DIN), which has a gap width of 1.5 mm between the inner and outer cylinders and can provide a viscosity range of 0.007 to 6.18 Pa·sec. The inner cylinder has 8 different rotation speeds, from 20 to 1,000 rpm, corresponding to a shear-rate range of 4 to 1,200 sec–1. The torque developed on the inner cylinder due to a sample is directly related to the sample viscosity and should be in the range of 0.5 to 9.5 mN·m for accuracy. A thermal jacket allows the use of an external fluid circulator to control or regulate the temperature of a sample measured. The viscometer employs a so-called “viscosoft” computation program so the digital readings, or measurement parameters, such as shear rate, shear stress, viscosity, and torque, are directly displayed on the screen of the viscometer. The viscometer exhibits good reproducibility with a rather small standard deviation for all the measurement parameters and accurately gives a resolution of 0.001 Pa·sec at a torque >0.5 (He, Wang, and Forssberg 2005). Slurry samples were aged for 4 hours and then were shaken at an intensity of 225 min–1 (TH-30 shaker from Edmund Bühler, Germany) for 1 hr to redisperse the samples prior to the rheological measurement. Each slurry sample was first presheared for 3 min at the highest shear rate of the viscometer (i.e., 1,200 sec–1) prior to measurement; then the measurement started from this highest shear rate. The shear rate was stepped down one by one until the torque reading was less than 0.5 mN·m. The digital

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247

readings (viscosity, shear rate, shear stress, and torque) were recorded at each shear rate. About 25 mL of slurry sample was required for each measurement. Each sample was measured three times, and the mean values of shear stress, shear rate, and viscosity were used for analysis. In addition, the extrapolated Bingham yield stress, WB, was utilized, which was obtained by fitting the experimental data into the Bingham model (Gao and Forssberg 1993b; Prestidge 1997; Muster and Prestidge 1995): W = W B + K pl J

(EQ 1)

where W is the shear stress, Kpl is the plastic viscosity, and J is the shear rate. Energy Consumption. The energy consumed by the mill was measured by an electrical meter called a Micro VIP (Elcontrol Co., Italy). In this study, only the active power (kilowatts) was recorded and used by considering the power factor. The active power of the mill is sensitive to the current change at all levels up to the rated power of the motor. An active power reading was recorded every minute during each grinding pass, and about 10 readings were taken for each pass. The mean active power of each pass is regarded as its real one. The mean active power, Pmn (kW), of the nth pass for a grinding experiment was determined by m

¦ Pni

i=1 P mn = ------------m

(EQ 2)

where Pni is the ith discrete power reading of the nth pass, and m is the number of readings of the nth pass. The milling energy of the nth pass was calculated by taking away the idle power draw of the mill, P0 (kW) (without grinding media or ground material) from the mean active power, Pmn (kW) at the given rotation speed of 1,808 rpm. Only the power adsorbed by the mill chamber was accounted for in all the tests in this study. In order to evaluate the net energy consumption of the Drais mill, the mass specific energy consumption, Em (kWh/t), was determined by (Stehr and Weyand 1990): P mn – P 0 E m = -------------------3.6M p C

(EQ 3)

where Mp (kg/sec) is the mass flow rate of a slurry suspension fed to a mill, and C is the solids concentration by weight. Due to the volume flow rate of a limestone slurry being controlled and measured in this study, Equation 3 is modified as P mn – P 0 E m = ------------------------------3,600M v C v U

(EQ 4)

where Mv (m3/sec) is the volume flow rate of the slurry suspension fed to the mill, C v is the volume concentration of the slurry suspension, and ȡ (kg/m3) is the density of solid. Specific Surface Area. The specific surface area of a sample was measured by a Flow Sorb ÉÉ 2300 (Micromeritics Co., Ltd., United States), which is an instrument designed to take the measurements on bone-dried powders by N2 gas adsorption and desorption in liquid nitrogen temperature and room temperature (Brunauer-EmmetTeller [BET] method), respectively. A representative amount of sample was taken from each sample, and then was dried in an oven at 110˚C for 24 hours in order to remove the residual moisture of the sample prior to the measurement. The mean value

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of the adsorption and desorption specific surface areas of a sample was regarded as its real one. Calculation of Energy Efficiency. Energy efficiency or energy utilization, Ef (m2/Wh), which is defined as the increment of specific surface area per unit of specific energy consumption (Gao and Forssberg 1993a), was calculated by E f = 1,000'S ---------------------Em

(EQ 5)

where 'S = S – S0; S and S0 are the specific surface areas (m2/g) of a ground product and its feed by BET, respectively. Particle Size and Distribution. An x-ray sedimentometer SediGraph 5100D (Micromeritics) was used to analyze the particle size and distribution of samples. It measures particle size ranges from 0.1 to 300 Pm, which is suitable for the samples in this study. A representative amount of sample was directly dispersed in aqueous solution of 0.1 wt % of Calgon for the measurement. RESULTS AND DISCUSSION

Effect of Molecular Weight of a Dispersant

The effect of the concentration of sodium polyacrylates with various molecular weights on the rheological behavior of the limestone slurry at 75 wt % of solids concentration appears similar. Figure 2 shows the effect of the concentration of the Dispersant S40 sodium polyacrylate on the flowability of the slurry. The apparent viscosity of the slurry first increases, then decreases, and reverts after reaching a minimum. The slurry with less than 0.01 wt % of BCX-476 or Dispersant S40, or 0.015 wt % of BCX-552 shows a pseudoplastic characteristic with a yield stress and possesses a higher apparent viscosity than that without dispersant at a given shear rate. The reason is that an insufficient dispersant causes the flocculation of particles in the slurry by bridging attraction forces, leading to larger flow units (Zhou, Scales, and Boger 2001; Johnson et al. 2000). At the additive amount of a dispersant up to 0.015 wt % for BCX-476 or Dispersant S40, and 0.02 wt % for BCX-552, the apparent viscosity of the slurry is lower than that without dispersant, and the slurry still exhibits pseudoplastic flowabilities with an evident yield stress. At the additive level of 0.03 wt %, the slurry shows different rheological properties with different molecular weights of dispersants. For Dispersant S40, the slurry is transformed into a dilatant flow (Figure 2), whereas the slurry presents a pseudoplastic property with an insignificant yield stress for BCX-476 or BCX-552. The gradual increase in the additive amount of a dispersant leads to a complete transition to a weakly dilatant flow and a further slight decrease of the apparent viscosity in the range of shear rates investigated, and to a minimum at an additive level of 0.2 wt % for BCX-476 or 0.1 wt % for Dispersant S40, or 0.04 wt % for BCX-552. In these cases, the saturation adsorption of the dispersants on the particle surface has been attained, and electrostatic and steric stabilizations (electrosteric stabilizations) occur. By further adding the dispersants, the apparent viscosity at a given shear rate insignificantly reverts for BCX-476 and Dispersant S40, but evidently returns for BCX-552. In the case of BCX-476 or Dispersant S40, the excessive dispersant above the adsorption saturation exists in the slurry but does not adsorb onto the suspended particles, and causes a depletion flocculation (Papo, Piani, and Ricceri 2002; Zhou, Scales, and Boger 2001; Johnson et al. 2000). In addition, the excessive dispersant can increase the ion strength of the slurry, resulting in a compression of the electrical double layers around the particles and a reduction of the range and magnitude of the electrostatic repulsive force between the

INFLUENCE OF SLURRY RHEOLOGY ON STIRRED MEDIA MILLING OF LIMESTONE

249

120 0 0.01 wt % 0.02 wt % 0.04 wt % 0.2 wt % 0.6 wt %

100

0.004 wt % 0.015 wt % 0.03 wt % 0.1 wt % 0.4 wt %

Shear Stress, Pa

80

60

40

20 (a) 0

0

500

1,000

1,500

Shear Rate, L/sec

Apparent Viscosity, Pa·sec

1 0 0.01 wt % 0.02 wt % 0.04 wt % 0.2 wt % 0.6 wt %

0.004 wt % 0.015 wt % 0.03 wt % 0.1 wt % 0.4 wt %

0.1

(b) 0.01

0

500

1,000

1,500

Shear Rate, L/sec

FIGURE 2 Flowability of 75 wt % of solids concentration with various dosages of Dispersant S40 at 25 ± 0.2°C

particles, that is, the electrosteric forces are decreased (Papo, Piani, and Ricceri 2002; Zhou, Scales, and Boger 2001; Banash and Croll 1999; Ewais, Zaman, and Sigmund 2002). In the case of BCX-552, it possesses a larger molecular weight (i.e., 85,000) with a longer molecular chain, so the depletion flocculation is more significant, in addition to the reduction of electrosteric force (Banash and Croll 1999). Therefore, above the adsorption saturation, a further addition of BCX-552 evidently raises the apparent viscosity of the slurry at a given shear rate. Figure 3 shows the results. Clearly, the yield stress is eliminated when the additive amount of dispersants with three different molecular weights exceeds 0.03 wt %. In the case of 75 wt % of the limestone slurry, the apparent

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Extrapolated Bingham Yield Stress, Pa

30 (a) 25 20 15 10 BCX-476 Dispersant S40 BCX-552

5 0 0.0

0.01

0.02

0.03

0.04

0.05

Addition of Dispersants with Various Molecular Weights, wt %

Apparent Viscosity at the Shear Rate of 663 sec–1, Pa·sec

0.12 (b) 0.10 0.08 0.06 0.04 BCX-476 Dispersant S40 BCX-552

0.02 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Addition of Dispersants with Various Molecular Weights, wt %

FIGURE 3 Change in rheological behaviors of 75 wt % of solids concentration with the addition of dispersants with different molecular weights at 25 ± 0.2°C: (a) extrapolated Bingham yield stress; (b) apparent viscosity at the shear rate of 663 sec–1

viscosity of the slurry at a given shear rate stays constant in a wider range of the concentration of dispersant (about 0.1–0.6 wt %) for BCX-476 than that (0.1–0.2 wt %) for Dispersant S40. Similar phenomena were observed for kaolin suspensions with sodium tripolyphosphate and sodium polyphosphate (Papo, Piani, and Ricceri 2002) and zirconia slurries with triammonium citrate (Ewais, Zaman, and Sigmund 2002). For 70 wt % of the limestone slurry, a similar phenomenon was also observed. The apparent viscosity of 70 wt % of the limestone slurry reaches a minimum at an additive level of 0.1 wt % for BCX-476 or Dispersant S40, and 0.04 wt % for BCX-552. Figure 4 shows the accessible minimum viscosity for 70 wt % of the limestone slurry with a given additive amount for each dispersant. In the case of the reduction of viscosity of the limestone slurry, Dispersant S40 and BCX-476 are better than BCX-552. Dispersant S40 and BCX-476 present almost the same effect for 70 wt % of the limestone slurry (Figure 4), while the former is better than the latter for 75 wt % of the slurry (Figure 3). This is because Dispersant S40 gives a better steric stabilization than BCX-476 in a denser limestone slurry due to its relatively larger molecular weight with respect to BCX-476.

INFLUENCE OF SLURRY RHEOLOGY ON STIRRED MEDIA MILLING OF LIMESTONE

251

Apparent Viscosity, Pa·sec

0.03

0.02

0.01 BCX-476: 0.1 wt % Dispersant S40: 0.1 wt % BCX-552: 0.04 wt % 0 0

500

1,000

1,500

Shear Rate, L/sec

FIGURE 4 Accessible minimum viscosity for 70 wt % of solids concentration in the presence of three chemicals with a certain addition at 25 ± 0.2°C

Thus, the use of sodium polyacrylates with a range of molecular weights as grinding aids can change the surface nature of particles in a ground limestone slurry, resulting in interparticle forces being entirely repulsive to improve the slurry flowability by decreasing the viscosity and by eliminating the Bingham yield stress. This can increase the energy efficiency and the fineness of a product for wet ultrafine grinding. To clarify the effect of the molecular weights of sodium polyacrylates used as grinding aids on the wet ultrafine grinding of limestone through the improvement of slurry rheology, Figure 5 shows the grinding results for three sodium polyacrylates with different molecular weights at 75 wt % of solids concentration with 0.2 wt % of each dispersant. Clearly, Dispersant S40 with a molecular weight of 5,500 gives the better grinding results (i.e., a higher energy efficiency and a smaller median size) in the wet ultrafine grinding of limestone when other operation conditions are kept constant. The reason is that Dispersant S40 maintains a lower viscosity during the grinding (Figure 6). Clearly, the feed of 75 wt % of solids concentration with BCX-552 exhibits higher viscosities in the shear rate range studied (Figure 6a). This gives a lower energy efficiency and a larger median size during pass 1. The feeds of 75 wt % of solids concentration with BCX-476 and Dispersant S40 display almost the same rheological property in the shear rate range and produce an insignificant difference in grinding results during pass 1. After pass 1, the better grinding results are obtained for 75 wt % of solids concentration with Dispersant S40 due to its lower viscosities in the shear rate range. However, whatever dispersants exist at 75 wt % of solids concentration, the grinding operation is forced to automatically stop due to high pressure inside the mill chamber by a safety control device when a ground slurry presents a pseudoplastic flow with a definite extrapolated Bingham yield stress (Figures 6d and 7). The pseudoplastic slurry with a yield stress could be the reason because the more viscous the slurry, the more power is needed to make the slurry flow when the slurry is circulated through the mill by a pump. This increases the pressure in the mill up to the limit. In addition, for 75 wt % of solids concentration with 0.2 wt % of BCX-552, the grinding process can only run for one pass but can run for three passes for BCX-476 or Dispersant S40. Consistent results were also obtained in the case of 70 wt % of solids concentration with the three dispersants.

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Cumulative Energy Efficiency, m 2/Wh

70 (a) 65

60

55 BCX-476 Dispersant S40 BCX-552

50

45 0

50

100

150

Cumulative Specific Energy Input, kWh/t 5.5 (b)

5.0 4.5 4.0 3.5 3.0 2.5

BCX-476 Dispersant S40 BCX-552

2.0 1.5 0

50

100

150

Cumulative Specific Energy Input, kWh/t

FIGURE 5 Effect of chemicals with various molecular weights at the additive level of 0.2 wt % on the grinding results for 75 wt % of solids concentration at 74 vol. % of beads load

Effect of Solids Concentration

The influence of solids concentration on slurry rheology is significant because various ranges of solids concentrations can lead to different types of flows, as shown in Figure 8. The results show the rheological properties of seven solids concentrations of limestone slurries without dispersant at 25 r 0.2˚C. The slurry rheological behavior is transformed from a weakly dilatant characteristic to an evidently pseudoplastic one with a yield stress when the solids concentration is increased from 60 wt % (35.71 vol. %) to 78.5 wt % (57.49 vol. %). At a solids concentration d65 wt % (40.75 vol. %), the slurry appears to be a weakly dilatant flow. This is because in a dilute slurry (i.e., d65 wt % or 40.75 vol. %), the interparticle distance is so large that the limestone particles in the slurry are not subjected to the attractive forces between the particles but are free to move as individuals. At lower shear rates, the particles have enough opportunities to slip over each other. At higher shear rates, the shearing process becomes increasingly rapid, causing restricted movement of the particles. The local accumulation of solid particles causes the slurry to behave like a solid system. In a dilatant system, however, this state is not stable. As long as the external force is removed, the particles without any tendency to adhere are distributed more uniformly in the suspension. At solids concentrations up

253

INFLUENCE OF SLURRY RHEOLOGY ON STIRRED MEDIA MILLING OF LIMESTONE

0.15

0.08 (a)

(b) 0.06

0.10 0.04

Apparent Viscosity, Pa·sec

0.05 BCX-476 Dispersant S40 BCX-552

0 0

500

1,000

0.02

0

1,500

0.08

BCX-476 Dispersant S40 BCX-552 0

500

1,000

1,500

1.6 (c)

(d)

0.06

1.2

0.04

0.8

0.02

0.4

BCX-476 Dispersant S40 BCX-552

BCX-476 Dispersant S40 0

0 0

500

1,000

1,500

0

500

1,000

1,500

Shear Rate, L/sec

FIGURE 6 Change of rheological behaviors for 75 wt % of solids concentration with various molecular-weight chemicals at the additive level of 0.2 wt % with pass number (grinding time) increasing at 74 vol. % of beads load: (a) feed; (b) after pass 1; (c) after pass 2; and (d) where grinding is forced to stop automatically

Extrapolated Bingham Yield Stress, Pa

70 60 50 40 30 20 10 0 BCX-476

Dispersant S40

BCX-552

Chemicals with Different Molecular Weights

FIGURE 7 Extrapolated Bingham yield stress where the grinding process is forced to automatically stop for 75 wt % of solids concentration with various molecular-weight chemicals at the additive level of 0.2 wt % at 74 vol. % of beads load

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100 90

60 wt % 65 wt % 67 wt % 70 wt % 75 wt % 77 wt % 78.5 wt %

Shear Stress, Pa

80 70 60 50 40 30 20 10

(a)

0 0

500

1,000

1,500

Shear Rate, L/sec

Apparent Viscosity, Pa·sec

10 60 wt % (35.71 vol. %) 65 wt % (40.75 vol. %) 67 wt % (42.92 vol. %) 70 wt % (46.36 vol. %) 75 wt % (52.63 vol. %) 77 wt % (55.36 vol. %) 78.5 wt % (57.49 vol. %)

1

0.1

(b) 0.01 0

500

1,000

1,500

Shear Rate, L/sec

FIGURE 8 Effect of solids concentration on the rheological properties of the limestone slurry in the absence of chemicals at 25 ± 0.2°C

to 67 wt % or 42.92 vol. %, the flowability of the slurry exhibits a pseudoplastic characteristic without a definite yield stress at shear rates <663 sec–1 and a weakly dilatant one at shear rates >663 sec–1. This indicates that in a lower range of shear rates, the interparticle attractive forces are predominant over the hydrodynamic forces exerted by a flow field at 67 wt % of solids concentration, as opposed to shear rates >663 sec–1. With further increases in the solids concentration, to 70 wt % (i.e., 46.36 vol. %) or more, the slurry rheology is changed into a pseudoplastic flow with an evident shear yield stress at shear rates <362 sec–1, followed by a transition to a Bingham plastic flow (with a higher extrapolated Bingham yield stress) at shear rates >362 sec–1. Furthermore, the degree of pseudoplasticity and the shear yield stress increase with increasing solids concentration when the solids concentration is >70 wt % (Figure 8a). Similar phenomena were observed for various slurries of materials such as coal and quartz (Tangsathitkulchai and Austin 1988), galena (Prestidge 1997), and sphalerite (Muster and Prestidge 1995). The effect of solids concentration on the apparent viscosity at a given shear rate and the extrapolated Bingham yield stress for the slurries is shown in Figure 9. The viscosity and the yield stress increase rather sharply in exponential and power-law forms with increasing solids concentration when the solids concentration is >70 wt % (i.e., 46.36 vol. %),

INFLUENCE OF SLURRY RHEOLOGY ON STIRRED MEDIA MILLING OF LIMESTONE

255

Apparent Viscosity, Pa·sec

0.35 0.30 0.25

663 L/sec 362 L/sec 194 L/sec

0.20 0.15 0.10 0.05 (a) 0 55

60

65

70

75

80

85

Solids Concentration, wt %

Extrapolated Bingham Yield Stress, Pa

20

15

10

5

(b) 0 55

60

65

70

75

80

85

Solids Concentration, wt %

FIGURE 9 Effect of solids concentration on (a) the apparent viscosity and (b) the extrapolated yield stress at 25 ± 0.2°C

respectively. This is similar to a previous conclusion (Tseng and Chen 2003); indicating that there are strong interactions between the particles to hold the particles together in the slurry and form loosely packed flocs, immobilizing some water within them, which is indispensable to flow. This is due to a smaller interparticle distance in a denser slurry, producing an increased attraction potential and a larger probability of collisions between the particles, resulting in more particles attracting each other. A shearing force over a certain shear yield stress has to be exerted on the slurry to overcome the internal friction among the particles constituting the flocs and to make it flow again. Once the slurry flows, the flocs are broken down into smaller flow units, and the water entrapped within them is gradually released with increasing shear rate. This facilitates the slurry to flow and leads to a decrease of the slurry viscosity. A small addition of a suitable dispersant is indispensable for the wet ultrafine grinding of limestone at a higher solids concentration (>70 wt %) due to the rapid increase in the viscosity and the yield stress, which results in an increase in the energy consumption for wet ultrafine grinding and even makes the operation impossible. In order to investigate the effect of the difference in slurry rheology resulting from different solids concentrations on the wet ultrafine grinding, Dispersant S40 (molecular weight 5,500) is selected as a grinding aid on the basis of the previous results. Figure 10 shows the grinding

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Cumulative Energy Efficiency, m 2/Wh

75 (a)

70 65 60 55 50 45

65 wt % 70 wt % 75 wt %

40 35 0

50

100

150

200

Cumulative Specific Energy Input, kWh/t 5.5 (b)

5.0 4.5 4.0 3.5 3.0 2.5 65 wt % 70 wt % 75 wt %

2.0 1.5 1.0 0

50

100

150

200

Cumulative Specific Energy Input, kWh/t

FIGURE 10 Effect of various solids concentrations with 0.2 wt % of Dispersant S40 on the grinding results at 74 vol. % of beads load

results of limestone slurries with three different solids concentrations with 0.2 wt % of Dispersant S40 at 74 vol. % of beads load. The cumulative energy efficiency increases first and then decreases with increasing solids concentration from 65 wt % to 75 wt % at a given specific energy input. The median size of the product varies with solids concentration in an opposite way from the cumulative energy efficiency. This is in agreement with a previous conclusion (Bernhardt, Reinsch, and Husemann 1999). The best grinding results are obtained at 70 wt % of solids concentration with 0.2 wt % of Dispersant S40 at 74 vol. % of beads load. The reason for this is that the slurry of 70 wt % of solids concentration with 0.2 wt % of the dispersant exhibits proper viscosities in a wide range of shear rate (Figure 11) and produces better stress conditions (i.e., a higher stress intensity and a larger average number of stress events for each particle). In the case of 65 wt % of solids concentration with 0.2 wt % of the dispersant, a lower viscosity and a larger average interparticle distance make grinding beads difficult to effectively capture particles. This increases the possibility of the direct collision between the beads, resulting in higher energy loss. A higher solids concentration (i.e., 75 wt %) gives a smaller average interparticle distance, which leads to a larger average number of stress events of each particle. However, at 75 wt % of solids concentration, the larger viscosity damps the motion of the grinding beads in the mill

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INFLUENCE OF SLURRY RHEOLOGY ON STIRRED MEDIA MILLING OF LIMESTONE

0.05

0.06 (a)

(b) 0.05

0.04

0.04 0.03 0.03 0.02 Apparent Viscosity, Pa·sec

0.02 65 wt % 70 wt % 75 wt %

0.01 0

65 wt % 70 wt % 75 wt %

0.01 0

0

500

1,000

1,500

0

500

1,000

1,500

1 65 wt % 70 wt % 75 wt %

0.08

65 wt % 70 wt % 75 wt %

(c) 0.8

(d)

0.06 0.6 0.04

0.4

0.02

0.2

0

0 0

500

1,000

1,500

0

500

1,000

1,500

Shear Rate, L/sec

FIGURE 11 Change of rheological behaviors of three different solids concentrations with 0.2 wt % of Dispersant S40 with pass number (grinding time) increasing at 74 vol. % of beads load: (a) feed; (b) after pass 1; (c) after pass 3; and (d) where grinding is forced to stop

and significantly increases the attenuation of the velocity and kinetic energy of the beads, which bring about lower stress intensities of collisions among the beads, particles, and chamber inner wall. The decrease in stress intensity is dominant, compared with the increase in the number of stress events. Therefore, the captured particles cannot be effectively ground, which causes an ineffective milling operation. However, the grinding operation at a solids concentration from 65 to 75 wt % with a given amount of Dispersant S40 (i.e., 0.2 wt %) automatically ceases when a ground slurry exhibits a pseudoplastic flow with an evident extrapolated Bingham yield stress (Figures 11d and 12). CONCLUSIONS

The influences of dispersants with different molecular weights and solids concentration on the flowability of limestone slurries as well as their effect on wet ultrafine grinding have been investigated in order to reduce energy cost and increase the fineness of a product. The effect of sodium polyacrylate salts with a range of molecular weights on the rheological behaviors appears similar for a given solids concentration of limestone slurry. With the additive amount increasing, the apparent viscosity of the slurry at a given shear rate first increases, then decreases, and reverts after reaching a minimum. Also, the yield stress is eliminated when the additive amount exceeds a certain value. Sodium polyacrylate with a molecular weight of 5,500 (i.e., Dispersant S40) appears to be more effective for the reduction of apparent viscosity and the maintenance of steady flowability. Thus, Dispersant S40 as a grinding aid gives better grinding results (i.e., a

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Extrapolated Bingham Yield Stress, Pa

35 30 25 20 15 10 5 0 65 wt %

70 wt %

75 wt %

Solids Concentration by Weight, wt %

FIGURE 12 Extrapolated Bingham yield stress where the grinding process is forced to automatically stop for three solids concentrations with 0.2 wt % of Dispersant S40 at 74 vol. % of beads load

higher energy efficiency and a smaller median size). The rheological behavior of limestone slurry is transformed from a weakly dilatant characteristic to a pseudoplastic one with a yield stress when the solids concentration is increased from 60 wt % (35.71 vol. %) to 78.5 wt % (57.49 vol. %). The apparent viscosity and the extrapolated Bingham yield stress increase in exponential and power-law forms with increasing solids concentration, respectively, when the solids concentration of the slurry is greater than 70 wt % (i.e., 46.36 vol. %). A small addition of a suitable dispersant is indispensable for the wet ultrafine grinding of limestone at a higher solids concentration (>70 wt %) due to the rapid increases in the viscosity and the yield stress. An optimal solids concentration exists at a certain beads load for the effective wet ultrafine grinding of limestone. ACKNOWLEDGMENTS

The financial support from the Swedish National Energy Administration and Hesselmanska Stiftelsen in Sweden (MinFo’s Process Technology Program) is acknowledged. Professor Anders Sellgren and Yanmin Wang at the Luleå University of Technology are appreciated for their helpful comments. The authors are grateful to Britt-Marie Antti at the paper mill in Piteå (Kappa Kraftliner Piteå, Sweden) for her kind help in the slurry viscosity measurements. REFERENCES

ASTM (American Society for Testing and Materials). 1996. C602-95a. Standard specification for agricultural liming materials. Pages 306–308 in Annual Book of ASTM Standards. Volume 04.01. West Conshohocken, PA: ASTM International. Austin, L.G., R.R. Klimpel, and P.T. Luckie. 1984. Process engineering of size reduction: Ball milling. New York: SME-AIME. Banash, M.A., and S.G. Croll. 1999. A quantitative study of polymeric dispersant adsorption onto oxide-coated titania pigments. Progress in Organic Coatings 35:37–44. Bernhardt, C., E. Reinsch, and K. Husemann. 1999. The influence of suspension properties on ultra-fine grinding in stirred ball mills. Powder Technology 105:357–361.

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Blecher, L., A. Kwade, and J. Schwedes. 1996. Motion and stress intensity of grinding beads in a stirred media mill. Part 1: Energy density distribution and motion of single grinding beads. Powder Technology 86:59–68. Blecher, L., and J. Schwedes. 1996. Energy distribution and particle trajectories in a grinding chamber of a stirred ball mill. International Journal of Mineral Processing 44–45:617–627. Ewais, E., A.A. Zaman, and W. Sigmund. 2002. Temperature induced forming of zirconia from aqueous slurries: Mechanism and rheology. Journal of the European Ceramic Society 22:2805–2812. Gao, M., and E. Forssberg. 1993a. A study on the effect of parameters in stirred ball milling. International Journal of Mineral Processing 37:45–59. ———. 1993b. The influence of slurry rheology on ultra-fine grinding in a stirred ball mill. Pages 237–244 in Proceedings of XVIII International Mineral Processing Congress. Volume 2. Sydney, Australia. Gao, M., and K. Weller. 1993. Fine grinding in mineral processing using stirred ball mills. Chemical Engineering in Australia 18(2):8–12. Greenwood, R., N. Rowson, S. Kingman, and G. Brown. 2002. A new method for determining the optimum dispersant concentration in aqueous grinding. Powder Technology 123:199–207. He, M., Y. Wang, and E. Forssberg. 2004. Slurry rheology in wet ultrafine grinding of industrial minerals: A review. Powder Technology 147:94–112. ———. 2005. Parameter studies on rheology of limestone slurries. International Journal of Mineral Processing. In press. ISO (International Organization for Standardization). 1983. ISO 457. Soaps—Determination of Chloride Content—Titrimetric Method. Geneva, Switzerland: ISO. Johnson, S.B., G.V. Franks, P.J. Scales, D.V. Boger, and T.W. Headly. 2000. Surface chemistry—rheology relationships in concentrated mineral suspensions. International Journal of Mineral Processing 58:267–304. Kapur, P.C., T.W. Healy, P.J. Scales, D.V. Boger, and D. Wilson. 1996. Role of dispersants in kinetics and energetics of stirred ball mill grinding. International Journal of Mineral Processing 47:141–152. Klimpel, R.R. 1999. The selection of wet grinding chemical additives based on slurry rheology control. Powder Technology 105:430–435. Kwade, A. 1999a. Determination of the most important grinding mechanism in stirred media mills by calculating stress intensity and stress number. Powder Technology 105:382–388. ———. 1999b. Wet comminution in stirred media mills—research and its practical application. Powder Technology 105:14–20. Kwade, A., L. Blecher, and J. Schwedes. 1996. Motion and stress intensity of grinding beads in a stirred media mill. Part 2: Stress intensity and its effect on comminution. Powder Technology 86:69–76. Muster, T.H., and C.A. Prestidge. 1995. Rheological investigations of sulphide mineral slurries. Minerals Engineering 8:1541–1555. Papo, A., L. Piani, and R. Ricceri. 2002. Sodium tripolyphosphate and polyphosphate as dispersing agents for kaolin suspensions: Rheological characterization. Colloids and Surfaces A: Physicochemical Engineering Aspects 201:219–230.

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Prestidge, C.A. 1997. Rheological investigations of ultra-fine galena particle slurries under flotation-related conditions. International Journal of Mineral Processing 51:241–254. Reinisch, E., C. Bernhardt, and K. Husemann. 2001. The influence of additives during wet ultra-fine grinding in agitator bead mills. Part 1: General principles and experimental. Ceramic Forum International: Berichte der Deutschen Keramischen Gesellschaft 78(3):E38–E42. Stehr, N., and C. Weyand. 1990. Control System for Agitated Media Mills. Pages 681–695 in 7th European Symposium of Comminution, Ljubljana, Yugoslavia. Volume 2. Edited by K. Schönert. Tangsathitkulchai, C., and L.G. Austin. 1988. Rheology of concentrated slurries of particles of natural size distribution produced by grinding. Powder Technology 56:293–299. Tseng, W.J., and C.N. Chen. 2003. Effect of polymeric dispersant on rheological behaviour of nickel-terpineol suspensions. Materials Science and Engineering A347:145–153. Zhou, Z., P.J. Scales, and D.V. Boger. 2001. Chemical and physical control of the rheology of concentrated metal oxide suspensions. Chemical Engineering Science 56:2901–2920.

Experimental Evaluation of a Mineral Exposure Model for Crushed Copper Ores D. Garcia,* C.L. Lin,* and J.D. Miller*

ABSTRACT

Copper mineral inclusions dispersed in crushed ore particles have a certain size distribution (grain-size distribution). For efficient heap leaching processes, the crushing plant should be designed and operated to crush the ore to an appropriate particle-size distribution so that copper mineral grains are exposed and can be leached. In this regard, based on the approach of Hsih, Wen, and Kuan (1995), a mineral exposure model has been evaluated to describe the extent of grain exposure as a function of particle size. Experimental evaluation of the mineral exposure model for different copper ores has been accomplished by 3D analysis of crushed ore particles using cone beam x-ray microtomography. The model evaluation with micro-CT data suggests that the extent of preferential grain boundary breakage varies both with ore type and with particle size for a given ore type. INTRODUCTION

In the copper heap leaching process, inclusions of copper mineral grains (copper-bearing minerals) are to be dissolved from ore particles. The copper-bearing minerals have some unknown grain-size distribution, texture/exposure, and spatial distribution in the ore particles. The procedure is to crush the ore so that the copper mineral grains are exposed and can be dissolved during the heap leaching process. If the relationship between the percentage of the exposed copper mineral grains and the particle size for a given ore type can be determined, then the practical recovery in the heap leaching process can be predicted for a specific particle-size distribution. It is, therefore, extremely important to determine the percentage of exposed copper mineral grains for a given ore as a function of particle size. X-ray microtomography (XMT) is currently the only direct measurement technique available for such mineral exposure analysis. In this regard, XMT has been used to determine the copper mineral grain-size distribution and extent of exposure for a given particle-size distribution. For the approach used in traditional mineral processing, comminuted particles can be classified as either free particles or locked particles. In the case of hydrometallurgy, the fraction of grain exposure determines the extent of leaching. Thus, both liberated and exposed grains will respond to chemical attack during leaching. The unexposed grains that remain as inclusions in the gangue particles are not dissolved easily during the leaching operation.

* Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah 261

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According to generally accepted terms, “grain” pertains to the crystalline and intimately mixed mineral phases with well-defined boundaries, composed of distinctive crystal chemistry and microstructure, whereas “particle” refers to crushed single and multiphase particles, generally composed of heterogeneous crystal chemistry and texture/structure. “Free particles” are particles of ore consisting of a single mineral. “Locked particles” are particles of ore consisting of two or more minerals. “Degree of liberation” is the fraction of a specific mineral in the form of free particles relative to that of both free and locked particles. “Exposed grains” are grains exposed at the surface of locked particles, whereas “unexposed grains” are grains enclosed within other host mineral, the gangue. The ratio of the volume of exposed valuable grains to the total volume of both exposed and unexposed grains in the comminuted particle is defined as “the degree of exposure” and is analogous to “the degree of liberation” for comminuted particles as used in particle separation processes. Thus, as the degree of liberation defines the limits to recovery in particle separation processes, so the degree of exposure defines the extent of leaching that may be expected in a reasonable time. THEOR Y

The concept of Hsih, Wen, and Kuan’s (HWK’s; 1995) exposure model is based on a liberation theory developed by Gaudin (1939). In this model, the mineral grain-size distribution is related to the crushed particle-size distribution, using an intergranular fracturing factor, P. The intergranular fracturing factor is primarily controlled by the mineralogical characteristics of the particular feed material (P = 1 for pure intergranular fracture, preferential grain boundary fracture, and P = 0 for pure transgranular fracture). The derivation of the exposure model follows the approach used by Gaudin. In the case of a fixed grain size (d), the fractional exposure (FE ) is given for a specific particle size (D) as follows: 3

3

3

3

K – K – 2 K – K – 1 - +  1 – P ------------------------------F E  K = P ------------------------------3 3 K K

K = D --d

In order to derive the model, the following assumptions are made: ƒ The ore consists of a scarce phase of valuable mineral and an abundant phase of

gangue. ƒ Both mineral and gangue have the same uniform size of cubic grains d. ƒ The grains are aligned in the ore so that the grain surfaces form continuous

planes. ƒ Grains of the two species are randomly located throughout the ore. ƒ The ore is broken into uniformly sized particles D, according to a cubic fracture

lattice either randomly or nonrandomly superimposed on the ore parallel to the grain surfaces. ƒ P is the probability of fractures occurring at the grain boundary, which is a real

number between 0 and 1; (1 – P) is the probability of fracture occurring as random, transgranular breakage events during which event interfacial area is conserved. ƒ The crushed particle is invariably larger than the size of the grain.

Although these assumptions represent no actual conditions, they provide a reasonable foundation for initial study.

MINERAL EXPOSURE MODEL FOR CRUSHED COPPER ORES

FIGURE 1

263

The cone beam XMT system at the University of Utah

M I N E R A L E X P O S U R E A N A L YS I S

The advanced XMT system at the University of Utah was designed and assembled to obtain 2,048 u 2,048 pixel reconstruction over a 10-mm diameter, while allowing for the 3D imaging of somewhat larger (40 mm) objects (Lin and Miller 2002). Specifically, the specimen-positioning stage system can be manually mounted at one of three different locations, providing system magnifications of 5, 2, or 1.25, and spheres of reconstruction with respective diameters of 10, 25, or 40 mm. Also, the system has been designed to be capable of handling high-density materials, even materials having a density as high as 8.0 g/cm3. A photograph of the cone beam XMT system is shown in Figure 1. Particle-Size Distribution for Heap Leaching

Copper mineral inclusions have a certain size distribution (grain-size distribution), N(X), where N is the weight fraction of grains for particle size X (Miller et al. 2003). The heap leaching process should be designed to crush the ore so that the copper mineral grains are exposed and can be leached. Figures 2 to 4 present the grain-size distribution for various particle size classes for Composite 2 (rhyolite/sulfide), Composite 4 (andesite/sulfide), and Composite 6 (andesite/oxide) samples. In this regard, a 3D connected components labeling technique was used to label and classify each individual grain volume (number of volume elements, voxels). In this way, then, the grain size is defined as the cube root of the grain volume. There is evidence that the copper mineral grain-size distribution is bimodal for particle sizes greater than 1.7 mm, as revealed in the grain-sizes distribution presented in Figures 2, 3, and 4. RESULTS AND DISCUSSION

In the case of Composites 2 and 6 (Figures 5 and 6, respectively) it seems that for particles greater than 10 mm in size the predominant mechanism of breakage is intergranular fracture. In contrast, for Composite 4 (Figure 7), the predominant mechanism of breakage appears to be transgranular fracture for particles greater than 10 mm in size. One possible explanation for this behavior, in the case of Composite 4, is that the grain sizes

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70 60

40 30

Weight, %

50

20 10 0.15 × 0.075 0.425 × 0.15 1.7 × 0.425 Pa 3.18 × 1.7 r tic le 6.3 × 3.18 Siz 9.5 × 6.3 eC las 12.7 × 9.5 s, mm 19.0 × 12.7 25.4 × 19.0

FIGURE 2

25,400 6,300 1,680 420 105 37

Overall grain-size distributions of Composite 2 for different particle size classes

70 60

40 30

Weight, %

50

20 10 0.15 × 0.075 0.425 × 0.15 1.7 × 0.425 Pa r tic 3.18 × 1.7 le 6.3 × 3.18 Siz eC 9.5 × 6.3 las 12.7 × 9.5 s, mm 19.0 × 12.7 25.4 × 19.0

FIGURE 3

25,400 6,300 1,680 420 105 37

Overall grain-size distributions of Composite 4 for different particle size classes

are much larger than the grain sizes for Composites 2 and 6, hence a possible difference in fracture mechanism. For particles smaller than 5 mm in size, there is no predominant mechanism of fracture for Composite 2; it appears that both transgranular and intergranular mechanisms are present. Composite 4 appears to exhibit mainly intergranular fracture and Composite 6 transgranular fracture. There is no evident explanation for this difference in behavior between these three samples. Analysis of the fracture mechanism requires more detailed

265

MINERAL EXPOSURE MODEL FOR CRUSHED COPPER ORES

70 60

40 30

Weight, %

50

20 10 0.15 × 0.075 0.425 × 0.15 1.7 × 0.425 Pa 3.18 × 1.7 r tic le 6.3 × 3.18 Siz 9.5 × 6.3 eC las 12.7 × 9.5 s, 19.0 × 12.7 mm 25.4 × 19.0

FIGURE 4

25,400 6,300 1,680 420 105 37

Overall grain-size distributions of Composite 6 for different particle size classes

100

80

Exposure, %

XMT 60

40

P = 0.9 P = 0.5 P = 0.1

20

0

0

5

10 15 Particle Size, mm

20

25

FIGURE 5 Exposure for Composite 2 given by XMT, model using P = 0.1 (mainly transgranular fracture), P = 0.9 (mainly intergranular fracture) and P = 0.5 (equal probability for transgranular and intergranular fracture)

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100

80 XMT

Exposure, %

60

40 P = 0.9 P = 0.5 P = 0.1 20

0

0

5

10 15 Particle Size, mm

20

25

FIGURE 6 Exposure for Composite 6 given by XMT, model using P = 0.1 (mainly transgranular fracture), P = 0.9 (mainly intergranular fracture) and P = 0.5 (equal probability for transgranular and intergranular fracture)

100

80

Exposure, %

XMT 60

P = 0.9 40

P = 0.5 P = 0.1

20

0 0

5

10 15 Particle Size, mm

20

25

FIGURE 7 Exposure for Composite 4 given by XMT, model using P = 0.1 (mainly transgranular fracture), P = 0.9 (mainly intergranular fracture) and P = 0.5 (equal probability for transgranular and intergranular fracture)

MINERAL EXPOSURE MODEL FOR CRUSHED COPPER ORES

267

Interface

A

B

Mineral “A”

Mineral “B”

Binary AB Case 2 M

in

er al

A

M

ine

ra l

Binary AB Case 1

V1

B

V2 Vi

Source: Bradt et al. 1995.

FIGURE 8 Top: Schematic representation of binary mineral particle, AB; Bottom: Schematic representation of conditions for liberation by preferential interfacial breakage of a hypothetical binary particle

measurements of interfacial area to determine the extent of preferential breakage of multiphase particles for different sizes. With these data, further arguments can be developed regarding the breakage mechanism. Such research is now in progress. Thus, the mineral exposure model is limited to a fixed fraction of grain boundary breakage independent of particle size. It seems from the results of these crushing experiments that the significance of grain boundary fracture (preferential breakage) varies not only with ore type but also with particle size. For example, in the case of Composites 2 and 6 (coarse grain-size distributions as described in Figures 2 and 4), the data best fit the model with a grain boundary fracture probability of 0.9 for coarse particle sizes. On the other hand at finer particle sizes, the data best fit the model with a grain boundary fracture probability of 0.1, indicating that random transgranular fracture predominates. These results are particularly interesting because they substantiate earlier research that suggested that for a given ore type, there may be a critical size at which the breakage mechanism for multiphase particles changes from transgranluar fracture to intergranular fracture (Bradt et al. 1995). Specifically, the previous results for the breakage of single, multiphase particles defined this critical size concept as revealed in Figure 8. This figure shows the case for which a pure particle of mineral B is stronger than a pure particle of mineral A for all sizes (volumes) considered. Both pure minerals increase in strength

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with decreasing particle size as observed by statistical analysis of experimental results from the fracture of brittle solids and as expected from Weibull fracture statistics. In Figure 8, case 1, the strength of the interface of the binary particle is weaker than either of its components at a volume size (particle size) of less than V1. As shown in Figure 7 for Composite 4, preferential fracture occurs for a particle size of less than 3.2 mm. On the other hand, for Composite 6 (Figure 6), most of the fracture mechanism is transgranular for a particle size of less than 6.3 mm. SUMMAR Y

Based on XMT-measured grain-size distributions, the percentage of exposure was calculated from HWK’s exposure model and the calculated results compared with experimental XMT exposure data. In general, the exposure measurements from XMT data can be explained from the HWK exposure model. These results are particularly interesting because they substantiate earlier research that suggested that for a given ore type there may be a critical size at which the breakage mechanism for multiphase particles changes from transgranular fracture to intergranular fracture (Bradt et al. 1995). REFERENCES

Bradt, R.C., C.L. Lin, J.D. Miller, and G. Chi. 1995. Interfacial fracture of multiphase particles and its influence on liberation phenomena. Minerals Engineering 8(4–5):359–366. Gaudin, A.M. 1939. Pages 70–91 in Principles of Mineral Dressing. New York: McGraw-Hill. Hsih, C.S., S.B. Wen, and C.C. Kuan. 1995. An exposure model for valuable components in comminuted particles. International Journal of Mineral Processing 43:145–165. Lin, C.L., and J.D. Miller. 2002. Cone beam x-ray microtomography—a new facility for three-dimensional analysis of multiphase materials. Minerals and Metallurgical Processing 19:65–71. Miller, J.D., C.L. Lin, C. Garcia, and H. Arias. 2003. Ultimate recovery in heap leaching operations as established from mineral exposure analysis by x-ray microtomography. International Journal of Mineral Processing 72:331–340.

Linking Discrete Element Modeling to Breakage in a Pilot-Scale AG/SAG Mill R. Morrison,* B. Loveday,† N. Djordjevic,* P. Cleary,‡ and P. Owen‡

ABSTRACT

One of the more challenging areas in comminution is to link ore characterisation techniques with computationally intensive modeling techniques, such as discrete element modeling (DEM). Julius Kruttschnitt Mineral Research Centre (JKMRC) drop-weight tester characteristics have been shown to be suitable for the prediction of single-event breakage in impact and conventional crushers. However, the prediction of particle breakage in a tumbling mill environment is a continuing challenge because it seems very likely that breakage occurs as a result of several mechanisms and often involves multiple events. A range of small, well-instrumented mills have been developed at the University of KwaZulu-Natal. These mills allow the rate of generation of fine material to be measured in close to real time for autogenous grinding (AG) and semiautogenous grinding (SAG) mill charges. This paper reports on the application of discrete element modeling techniques to the power draw and charge motion within a 1.2-m diameter u 300-mm long pilot-scale mill. Data from a series of experiments were analysed, in which rocks ranging in size from 70 to 150 mm were tumbled at different charge levels. An earlier regression model for the rate of attrition of the rocks is compared with a DEM-based model, which relates the attrition rate to the rock-on-rock impacts. The DEM outputs are also used to predict charge motion within the pilot mill. The DEM-model predictions support the idea of an approximately constant wear rate for 20–180-mm particles for any particular load configuration after the initial particle rounding process is completed. INTRODUCTION

The purpose of this work is to compare three-dimensional (3D) DEM results with experimental measurements of the power draw and the self-abrasion of well-worn rocks in a pilot-scale AG mill (Loveday 2004) in order to enhance the interpretation of the experimental results. Earlier work (Loveday and Naidoo 1997; Loveday and Whiten 2002) concluded that the self-abrasion rate could be considered as an approximately constant surface wear rate over a range of particle sizes. The pilot-mill experimental work (Luckan and Pillay 2004) was undertaken to further test this idea using a larger-diameter test mill. The particle wear rates were related to operating conditions by regression modeling (Luckan and Pillay 2004). * Julius Kruttschnitt Mineral Research Centre, University of Queensland, Australia † School of Chemical Engineering, University of KwaZulu-Natal, Durban, South Africa ‡ CSIRO Division of Mathematics and Information Sciences, Clayton, Victoria, Australia 269

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The DEM work reported in this paper was undertaken to see if a simple link could be made between the DEM collision histories for each particle size and the measured rates of wear. In other words, did the DEM model provide any insight into why the surface wear rate should be approximately constant? The results from two of the measured data sets were apparently anomalous, and it was hoped that the DEM model might offer some insight into possible reasons. P I L O T - M I L L E X P E R I M E N T A L WO R K A N D R E S U L T S

The pilot-mill experiments were performed on quartzite rock from a quarry in the Durban area, South Africa. These experiments were performed using a rubber-lined mill with an inside diameter of 1.19 m and length of 0.31 m. The mill was fitted with 14 square, metal lifters with heights of 40 mm. The rotational velocity of the mill was 3.14 rad/sec (77% of critical speed). Two sizes of rocks were used in these tests: “large” defined as 100–130 mm; and “small” defined as 70–100 mm. The small and large rock categories have one important difference—relative to the mill lifters, the centre of mass of the small rocks should be less than the mill lifter height while the centre of mass of the large rocks will be greater. Figures 1 and 2 show realisations of the pilot mill and its rock charge made using Particle Flow Code 3D (PFC3D; Itasca 1999) and CSIRO-MIS DEM codes (Cleary 2001; Morrison and Cleary 2004), respectively. Size reduction within AG mills is based on progressive wear of the larger rocks in the charge. This rock wear, defined in general terms, could be due to impacts, compression, shearing, chipping, or attrition. Initially, size reduction is rapid as asperities are removed and the rocks become rounded. Further size reduction is much slower. The rocks used in the test program had already been subjected to the period of rapid wear. Each rock was weighed before and after each test and the total weight loss compared with the total weight of recovered fines. The program of AG test work and the results are summarised in Table 1. Tests 9–15 were for SAG mill operation and will be reported in a later paper. The energy consumption per ton of product is a number that is well known to operators of AG/SAG mills. The energy per ton of “fines” produced from rocks is an indication of the efficiency of size reduction by abrasion/chipping in these mills. This is directly linked to the specific wear rate (Rs) and the holdup of rocks in the mill as follows: Pu = P/(Rs u M) where Pu P Rs M

= = = =

(EQ 1)

power utilisation net power (gross power less empty running power) measured specific wear rate of rock mass of rock in the mill

Pu can be calculated from the wear rate, gross power consumption, and difference in fragment mass between the start and finish of each test and average power utilisation (Loveday 2004). Table 1 shows that the experimental program covered a reasonable range of operating conditions in terms of Pu while the Rs is approximately constant over a reasonable range of mill load masses and size distributions. However, the average values for small rocks alone and large rocks alone are given in Table 2 and do appear to be significantly different. The detailed data for each rock also support at least some degree of size dependence.

LINKING DISCRETE ELEMENT MODELING TO BREAKAGE IN A PILOT-SCALE AG/SAG MILL

FIGURE 1

3D DEM model of the AG test mill created by PFC3D code

FIGURE 2

3D DEM model of the AG test mill created by CSIRO-MIS DEM code

271

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TABLE 1

LIBERATION AND BREAKAGE

Pilot-mill AG test runs and results

Run No.

Mill Loading, %

Rock Size

Specific Wear Rate Rs, 1/h*

Gross Power, W

'M, kg

Pu, kWh/t

1 2 3 4 5 6 7 8 16 17

30 20 20 30 20 30 20 25 25 25

Large Large Small Small Large Mixture Mixture Mixture Large Small

0.204 0.223 0.241 0.227 0.223 0.202 0.219 0.211 0.215 0.235

833 684 709 895 701

7.149 7.856 3.317 5.539 9.477

571.5 390.0 888.2 712.4 330.8

694 801

3.531 6.712

897.9 564.8

798

7.476

453.9

Source: After Luckan and Pillay 2004. * The specific wear rate (Rs) of the rocks was defined as the rate of loss of mass (per unit of time) per unit of initial mass of the particle. The dimension of this specific wear rate is inverse time (1/time).

TABLE 2

Average rock wear rates for large and small particles

Rock Size

Specific Wear Rate, 1/h

Average Power Utilisation, kWh/t

Small Large

0.234 ± 0.007 0.216 ± 0.009

684.8 ± 218.5 430.8 ± 125.9

If the rock wear rate is a material “constant” that can be determined from testing, it potentially offers a very simple model that might relate mill feed size distribution and feed rate to mill load size distribution and mass (from calculated or modeled power draw) and the mass of material leaving the mill. Obviously, a reasonable balance will be required for stable model or mill operation. Loveday and Whiten (2002) tested this model against several data sets from a much smaller test mill with encouraging results. MODELING APPROACH

The computing power of modern desktop computers presents an opportunity to use DEM for mill modeling (Mishra and Rajamani 1994). In this case, the modeling has been performed using PFC3D (Itasca 1999) and CSIRO-MIS DEM (Cleary 2001; Morrison and Cleary 2004) codes. Both codes in this case simulated the behaviour of spherical particles. The particles were enclosed by the mill, which was modeled by finite volume elements (PFC3D) or triangular surface mesh elements (CSIRO-MIS DEM). Both codes keep a record of individual particles and update any contact with other particles or walls. Each calculation step includes application of the laws of motion to a particle, a forcedisplacement law to each contact, and constant updating of wall position (Cundall and Strack 1979). The modeling is based on the assumption that the individual particles (balls) are treated as stiff bodies. At contacts, rigid particles can overlap. The magnitude of the overlap is related to the contact force. The overlaps are small relative to the size of the particles. Individual particles can also be bonded to form clusters to mimic rock shape and strength. During contact, the behaviour of a material is simulated using a linear contact model. The contact force vector between two balls or ball and wall is composed of normal and shear components. The normal contact force vector is calculated using the following formula:

LINKING DISCRETE ELEMENT MODELING TO BREAKAGE IN A PILOT-SCALE AG/SAG MILL

Fn = Kn u Un u ni where Fn Kn Un ni

= = = =

273

(EQ 2)

normal force at contact normal stiffness at the contact relative contact displacement in the normal direction unit normal vector

The incremental shear force is calculated using the following formula: 'Fs = –Ks u 'Us

(EQ 3)

where 'Fs = incremental shear force Ks = shear stiffness at contact 'Us = incremental shear displacement at contact Each DEM code also includes a slip model. The slip model is defined by the friction coefficient at the contact, where the active relevant friction coefficient is taken to be the minimum friction coefficient of the two contacting entities. Each contact is checked for slip conditions by calculating the maximum allowable shear contact force: Fs (max) = P u abs (Fn) where Fs P abs Fn

= = = =

(EQ 4)

shear component of the contact force friction coefficient absolute value of (the normal force) normal force

The energy state of the entire set of particles can be examined by recording various forms of energy. Frictional work is defined as the total cumulative energy dissipated by frictional sliding at all contacts. Considering that the shape of the model particles is spherical, the calculated frictional energy is probably more similar to the slower size reduction of rounded particles. The model of the mill is composed of a number of weightless walls that represent liner and lifters as well as rock and steel “balls” which represent the mill charge. The power of the mill is calculated for each instant of time by summing products of the moments that are applied to the mill liner and lifters and the rotational velocity of the mill. A critical aspect of DEM is the selection of material parameters. Parameters such as material stiffness, coefficient of friction, and damping ratio may not only affect the value of the power draw but also the required computational time. Considering that realistic full-3D modeling of a tumbling mill may require many thousands of particles, the ability to produce a modeling result within a reasonable time is of great practical significance. Previous DEM tumbling mill studies (Djordjevic 2003; Djordjevic, Shi, and Morrison 2004; Morrison, Cleary, and Valery 2001) have shown that a full-sized mill can be reliably represented by a vertical slice of sufficient thickness. These studies also showed that in terms of power draw, the DEM code model power is consistent with the power draw predicted using empirical models, even when the stiffness of the modeled material is much lower than the measured stiffness of the rock or the steel media and mill liners. The material parameters used for PFC3D modeling are provided in Table 3.

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TABLE 3

LIBERATION AND BREAKAGE

Material parameters used for PFC3D models Density Normal contact stiffness Shear contact stiffness Coefficient of friction Damping coefficient (normal and shear direction)

2,650 kg/m3 Kn = 4e5 N/m Ks = 3e5 N/m 0.5 0.5

y = 6.8606x + 102.18

1,800

R2 = 0.9887

1,600 1,400

Power Draw, W

1,200 1,000 800 600 400 200 0 0

50

100

150

200

250

Mass, kg

From data reported by Luckan and Pillay 2004.

FIGURE 3 Measured power draw of the pilot experimental mill as a function of the measured charge mass

COMPARISON OF MEASURED AND MODELED PILOT-MILL POWER DRAW

Before comparing modeled power with measured power draw, it is necessary to distinguish between the measured gross power draw and net power draw consumed by the motion of the charge. The pilot mill was provided with a torque arm for accurate measurement of power consumed. However, from Figure 3, the power consumed still has a significant zero offset of about 105 W at an extrapolated charge mass of zero. The net mill power draw (measured – zero offset) has been used for comparison with the power draw predicted by DEM modelling as shown in Figure 4. The results calculated by PFC3D show good agreement with the measured net power of the small AG mill, as shown in Figure 4. The average relative error for all of the AG tests is 3.65%. CSIRO-MIS DEM performed similar modeling and achieved a slightly better prediction (average error of 3.08%), as shown in Figure 5. P R E D I C T I O N O F R O C K WE A R R A T E S

As the milling environment in this case seems likely to provide predominantly frictional interaction, modeled frictional power (the power that corresponds with the energy consumed as friction between particles or between particles and mill liners and lifters) was compared with the empirical parameter Pu devised for average power utilisation (Loveday 2004; Loveday and Naidoo 1997) as defined by Equation 4.

LINKING DISCRETE ELEMENT MODELING TO BREAKAGE IN A PILOT-SCALE AG/SAG MILL

275

900 Measured Net Modeled Net

800

Power, W

700 600 500 400 300 200 100 0 1

FIGURE 4

2

3

4 5 Run No.

7

8

17

Modeled power (PFC3D) and measured net power draw of the experimental AG mill

900 Measured Net Modeled Net

800

Power Draw, W

700 600 500 400 300 200 100 0 1

2

3

4

5

7

8

17

Run No.

FIGURE 5

Modeled (CSIRO) and measured net power draw of the experimental AG mill

This comparison is presented in Figure 6 and shows a good correlation between modeled frictional power and measured Pu. For the two measurements, which are not on the trend line, it is possible that either the rock type varied or there might have been an experimental error. However, these two results were also anomalies in the regression model. The result shown in Figure 6 suggests that an increase in the energy consumed through friction will result in an increase of particle abrasion in a predictable manner. As the frictional power can be estimated for each individual particle, it offers a much more detailed correlation than the empirical parameter, which depends on the measured power of the mill—that is, the power drawn by all of the rocks. However, it should be remembered that this frictional calculation is based on a simple model for collisions between spheres. Loveday and Naidoo (1997) monitored the mass of individual rocks within a small test mill (0.6 m diameter) and noted that rapid rounding of the rocks occurred initially, including failure along obvious planes of weakness. This is followed by slow but reproducible

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Measured Average Power Utilisation, kWh/t

1,000 800 600 400 200 0 0

200

400

600

800

1,000

Modeled Frictional Power, W

FIGURE 6

Modeled frictional power versus power utilisation parameter Pu

removal of the surface material. Loveday and Whiten (2002) have shown that if the actual rate of wear of the rocks, per unit mass, remains relatively constant over the size range 20 mm to 180 mm, a simple mathematical model can be applied to estimate mill load and size distribution of coarse particles based on a mill feed rate and size distribution. Given that the mass of a particle is proportional to the cube of its diameter, the specific rate of abrasion can be expressed as Rs = 3K/D

(EQ 5)

where Rs = specific rate of abrasion (loss of rock mass per unit of mass) K = rate of diameter reduction (m/h) D = particle diameter (m) Equation 5 assumes that all particles will undergo a similar degree of relative size reduction, regardless of their size. This implies that the rate of diameter reduction is a rock-specific “constant,” not a function of the particle diameter. However, a more detailed examination of the DEM results shows that smaller particles exhibit a different pattern of motion from that exhibited by larger particles. As noted earlier, the key difference is most likely the relationship between particle size and lifter height. For a constant lifter size and shape, smaller particles will be lifted more efficiently than larger ones, which will result in higher potential/kinetic energy and impact velocities for smaller particles. Previous work at JKMRC (Djordjevic, Shi, and Morrison 2004) has indicated that the effect of particle diameter on the modeled power draw is insignificant when the ratio of the lifter height to particle diameter is kept constant under otherwise identical simulation conditions. Therefore, the effectively constant surface wear rate observed by Loveday and Whiten (2002) may occur as a result of two opposite trends: First, that the smaller particles will be exposed to higher impact forces, which will increase their propensity for size reduction; and second, that smaller particles (with smaller actual surface areas) will be less prone than larger particles to size reduction due to abrasion. These two trends will tend to cancel each other, resulting in a wear rate of rock that is relatively constant over particle size range of 20 to 180 mm. The DEM results also indicate that the energy consumed through shear loading at particle contacts (opposite from normal loading) is a function of the particle size. The smaller particles experienced an increase in the amount of net power consumed through

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277

1.8

Specific Shear Power, W/kg , 102

1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0

02

0.4

06

0.8

1.0

Time, sec , 101

FIGURE 7 PFC3D estimates of specific shear power for small particles (upper curve) and large particles (lower curve) versus time from mill startup

TABLE 4 Energy consumed by collision type at various mill volume loads for CSIRO-MIS DEM models Energy Consumed by Collision Type, % of total input energy All Collisions

Rock–Rock Collisions

Rock–Liner Collisions

Mill Volume Load, %

Normal

Shear

Total

Normal

Shear

Total

Normal

Shear

Total

20 25 30

58 54 54

42 46 46

100 100 100

22 24 25

21 24 25

43 48 50

36 31 29

22 21 21

57 52 50

shear motion at particle contacts—as shown in Figure 7. This result is in qualitative agreement with experimental results (Table 2), which show that small particles lose mass a little faster than large particles. Table 4 shows the energy consumed, predicted using the CSIRO-MIS DEM code, for each collision type (all collisions, rock–rock collisions, and rock–liner collisions) for various mill volume loads. This table indicates that for increasing mill volume loading: (1) the shear energy consumed in rock–liner collisions remains steady at about 21%; (2) the normal energy consumed in rock–liner collisions decreases from 36% to 29%; (3) the shear energy consumed in rock–rock collisions increases from 21% to 25%; and (4) the normal energy consumed in rock–rock collisions increases from 22% to 25%. At higher mill loadings there are more rocks in the mill, and, as expected, the normal and shear energy consumed in rock–rock collisions make up a higher proportion of the total energy consumed. At 20% mill loading, only a few rocks cascade from the shoulder; most are cataracted and impact the liner near the toe region. At higher mill loadings, more rocks cascade down the mill, producing a thicker protective layer for the liner. So, as expected,

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TABLE 5

LIBERATION AND BREAKAGE

Energy consumed by collision type for various rock sizes for CSIRO-MIS DEM models Energy Consumed by Collision Type, % of total input energy All Collisions

Rock–Rock Collisions

Rock–Liner Collisions

Rock Size Class

Normal

Shear

Total

Normal

Shear

Total

Normal

Shear

Total

Small Mix Large

54 55 57

46 45 43

100 100 100

24 24 22

26 24 21

50 47 43

29 31 35

20 21 22

50 53 57

the normal energy consumed in rock–liner collisions makes up a reduced proportion of the total energy consumed. Table 5 shows the energy consumed, which was predicted using the CSIRO-MIS DEM code, for each collision type (all collisions, rock–rock collisions, and rock–liner collisions) for the various rock size classes. This tables indicates that for increasing rock sizes in the mill load: (1) the shear energy consumed in rock–liner collisions increases slightly from 20% to 22%; (2) the normal energy consumed in rock–liner collisions increases from 29% to 35%; (3) the shear energy consumed in rock–rock collisions decreases from 26% to 21%; and (4) the normal energy consumed in rock–rock collisions is approximately constant at about 24%. The CSIRO-MIS DEM results also show that the shear energy consumed in rock–rock collisions is a function of the particle size. The smaller particles that are involved in rock–rock collisions show a higher proportion of the total energy. For increasing particle size, the increase in the normal energy consumed in rock–liner collisions is directly related to the increase in the kinetic energy of the cataracting stream of particles. DISCUSSION OF DEM PREDICTIONS OF DETAILED CHARGE MOTION

Considering the detailed estimates of the motion of one large and one small (randomly selected) particle within a mixed-size mill charge illustrates plausible reasons for the variations in behaviour. As shown in Figure 8, the translational velocity of the smaller particle (mass of 1.155 kg) is significantly higher than that of the larger particle (mass of 4.478 kg). As mentioned previously, this is most likely due to the centre of mass of the larger particle being significantly larger than lifter height. Hence, the lifters will be unable to lift it as far as the smaller particle. In contrast, the rotational velocities of the large and small particles are approximately the same, as shown in Figure 9. The larger particle will not be lifted as efficiently as the smaller one, which is clearly visible from the particle pattern of motion in the vertical plane of the mill, as shown in Figures 10 and 11. Due to its higher drop-off point, the smaller particle has a higher maximum velocity at each moment of impact, as well as a higher residual velocity after impact. This discussion also can be considered in terms of the empirical model developed by Luckan and Pillay (2004). The overall particle wear rate was regressed against feed sizing, mill loading, and percentage of steel in the charge. This regression model suggested slightly higher specific wear rates for the smaller particles than the larger—which is consistent with the previous discussion. This empirical approach is not well suited to the mixed-size mill charges. This difference in trajectories provides a plausible rationale for the quite different levels of specific shear power per unit of mass and per unit of surface area to be 98 W/kg and 4,071 W/m2 for the small particle and 18.9 W/kg and 1,260 W/m2 for the large particle. The spatial distribution of shear forces was divided into three ranges—10 to 100 N, 100 to 1,000 N, and >1,000 N—and plotted in Figures 12 to 14. These figures show that

LINKING DISCRETE ELEMENT MODELING TO BREAKAGE IN A PILOT-SCALE AG/SAG MILL

279

4.5 4.0

Translational Velocity, m/s

3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0

0.2

0.4

0.6

0.8

1.0

Time, sec , 101

FIGURE 8 PFC3D estimates of the time history of the translational velocity of a small particle (black—higher maxima) and a large particle (gray)

8.0 7.5 7.0 6.5

Rotational Velocity, rad/s, 101

6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0

0.2

0.4

0.6

0.8

1.0

Time, sec , 101

FIGURE 9 PFC3D estimates of the time history of the rotational velocity of a small particle (black) and large particle (gray) showing minimal difference

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6.0 5.0 4.0

Vertical Coordinate, m, ×10–1

3.0 2.0 1.0 0.0 –1.0 –2.0 –3.0 –4.0 –5.0 –6.0 –6.0

–4.0

–2.0

0.0

2.0

4.0

6.0

Horizontal Coordinate, m, ×10–1

FIGURE 10 Spatial pattern of motion in the vertical plane of a randomly selected single small particle in a mixed size charge in the PFC3D model

6.0 5.0

Vertical Coordinate, , m, ×10–1

4.0 3.0 2.0 1.0 0.0 –1.0 –2.0 –3.0 –4.0 –5.0 –6.0 –6.0

–4.0

–2.0

0.0

2.0

4.0

6.0

Horizontal Coordinate, m, ×10–1

FIGURE 11 Spatial pattern of motion in the vertical plane of a randomly selected single large particle in a mixed size charge in the PFC3D model

LINKING DISCRETE ELEMENT MODELING TO BREAKAGE IN A PILOT-SCALE AG/SAG MILL

281

6.0 5.0 4.0

Vertical Coordinate, m, ×10–1

3.0 2.0 1.0 0.0 –1.0 –2.0 –3.0 –4.0 –5.0 –6.0 –6.0

–4.0

–2.0

0.0

2.0

4.0

6.0

Horizontal Coordinate, m, ×10–1

FIGURE 12

Spatial pattern in the vertical plane of shear contact forces of 10 to 100 N

6.0 5.0 4.0

Vertical Coordinate, m, ×10–1

3.0 2.0 1.0 0.0 –1.0 –2.0 –3.0 –4.0 –5.0 –6.0 –6.0

–4.0

–2.0

0.0

2.0

4.0

6.0

Horizontal Coordinate, m, ×10–1

FIGURE 13 1,000 N

Spatial pattern in the vertical plane of shear contact forces with intensities of 100 to

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6.0 5.0 4.0

Vertical Coordinate, m, ×10–1

3.0 2.0 1.0 0.0 –1.0 –2.0 –3.0 –4.0 –5.0 –6.0 –6.0

–4.0

–2.0

0.0

2.0

4.0

6.0

Horizontal Coordinate, m, ×10–1

FIGURE 14

Spatial pattern in the vertical plane of shear contact forces >1,000 N

low- and medium-intensity shear forces occur predominantly within the charge, whereas strong shear forces occur during freefall and at the resultant impact. Significantly higher intensity shear forces also occur in the base of the mill charge at the interface between the mill liners and the particles. CONCLUSIONS

Based on the results presented, 3D DEM can accurately predict net power draw of the pilot experimental AG mill. This success does not necessarily imply similar accuracy in prediction of power draw in operating mills, because only a small quantity of ore fines and water are present in this pilot mill. As the no-load power of the larger AG mills can be predicted with sufficient accuracy using established empirical models (Napier-Munn et al. 1996), the DEM model may well be capable of accurate prediction of total mill power draw if slurry behaviour can be included. A strong correlation exists between the observed power utilisation and modeled net frictional power consumed within the mill charge. Therefore, subject to further validation of DEM, the modeled net-frictional power may be able to be used in a similar manner to the empirical power utilisation parameter for optimisation of performance of industrialscale AG mills. The insight offered into the interactions between lifter height and particle size goes well beyond liner damage caused by excessive liner height and offers the possibility of liner design for maximum production. The DEM results provide a rationale for the approximately constant rock-wear rate reported in the literature—even though there are significant differences due to the interaction with the mill lifters by different sized particles. Hence, there is also a strong possibility that a single, measurable characteristic may be used to model this type of rock wear when combined with a DEM model.

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283

ACKNOWLEDGMENTS

The DEM modeling work reported in this paper has been partially funded by the Centre for Sustainable Resource Processing. REFERENCES

Cleary, P.W. 2001. Recent Advances in DEM Modelling of tumbling mills. Minerals Engineering 14:1295–1319. Cundall, P.A., and O.D.L. Strack. 1979. A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65. Djordjevic, N. 2003. Discrete element modelling of the influence of lifters on power draw of tumbling mills. Minerals Engineering 16(4):331–336. Djordjevic, N., F.N. Shi, and R.D. Morrison. 2004. Determination of lifter design, speed and filling effects in AG mills by 3D DEM. Minerals Engineering 17(11–12):1135–1142. Itasca Consulting Group. 1999. PFC3D (Particle Flow Code in 3 Dimensions). Minneapolis, MN: Itasca Consulting Group. Loveday, B.K. 2004. The use of FAG and SAG batch tests for measurement of abrasion rates of full-size rocks. Minerals Engineering 17(11–12):1093–1098. Loveday, B.K., and D. Naidoo. 1997. Rock abrasion in autogenous milling. Minerals Engineering 10(6):603–612. Loveday, B.K., and W.J. Whiten. 2002. Application of a rock abrasion model to pilot-plant and plant data for fully and semi-autogenous grinding. Transactions of the Institution of Mining and Metallurgy 111:C39–C43. Luckan, P.I., and K. Pillay. 2004. The development of an autogenous model for quartzite by using semi-batch laboratory-scale milling. Laboratory Project 2004 DNC4IP1. Durban, South Africa: University of KwaZulu-Natal. Unpublished. Mishra, B.K., and R.K. Rajamani. 1994. Simulation of charge motion in ball mills. Part 1: Experimental verifications. International Journal of Mineral Processing 40(3–4): 171–186. Morrison, R., and P.W. Cleary. 2004. Using DEM to model ore breakage within a pilot scale SAG mill. Mineral Engineering 17:1117–1124. Morrison, R., P.W. Cleary, and W. Valery. 2001. Comparing power and performance trends from DEM and JK modelling. Pages 284–300 in SAG 2001. Volume IV. Vancouver, BC: University of British Columbia, Department of Mining and Mineral Process Engineering. Napier-Munn, T.J., S. Morrell, R.D. Morrison, and T. Kojovic. 1996. Mineral Comminution Circuits: Their Operation and Optimisation. Brisbane, Australia: Julius Kruttschnitt Mineral Research Centre.

Significance of the Particle-Size Distribution in the Quality of Cements with Fly Ash Additive Viktória Gável* and Ludmilla Opoczky*

ABSTRACT

The fineness of fly ash used as a cement additive influences the quality of the cement. The cement industry characterizes fineness based on the Blaine surface area. However, according to our investigations, the Blaine surface does not reflect exactly the actual fineness and particlesize distribution of fly ash or cements with fly ash added. Cements with fly ash added are characterized by “coarser” and “narrower” particle-size distributions than cements without fly ash added, but both types of cement typically have approximately the same Blaine surface area. The value of specific surface area calculated from the particle-size distribution of fly ash, using the exponential approximation method, gives a better estimate of its real fineness. Given this knowledge, the fineness and, therefore, the quality of cements with fly ash additive can be influenced favorably during cement production. INTRODUCTION

Fly ash—the by-product of coal powder–fired thermal power stations—has been utilized as an additive to cement for several decades. Recently, several problems concerning the production of composite cements that contain fly ash were raised regarding the technology of grinding and the analysis of particle size. The most important issues were (1) the role of the fineness (specific surface and particle-size distribution) of fly ash in the development of the cement quality; and (2) the revision and improvement of methods used for characterization and testing of the fineness (Opoczky and Juhász 1990). This paper presents the principal results of our investigations that were carried out in this field. EXPERIMENTAL MATERIALS AND METHODS

To conduct the experiments, we used various types of cements produced in Hungarian cement plants, as well as fly ash from two Hungarian power stations. The quality of the materials investigated (strength, water demand, pozzolanic activity, etc.) was tested according to the related European and Hungarian standards. Particle composition of the ground products was determined by a Cilas (Marcoussis, France) Model 715 laser granulometer. For the characterization of the particle-size * Research & Development Ltd. for the Cement Industry (CEMKUT Ltd.), Budapest, Hungary 285

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distribution, we used two parameters from the Rosin-Rammler-Sperling-Bennett (RRSB) equation: the fineness number ( x ) and the uniformity coefficient (n). Uniformity coefficient n characterizes the dispersion (width) of the particle-size distribution curve (i.e., the lower the value of n, the “wider” [more disperse] the particle-size distribution). Fineness number x characterizes the fineness of the ground product (i.e., the smaller the value of x , the finer the ground product; Beke 1981).

Rx = e

x – § --· © x¹

(EQ 1)

where R(x) = oversize x = particle size x = fineness number Fineness and degree of dispersion of the initial materials and the ground products were characterized by their specific surface, as determined by the widely used Blaine apparatus (based on measuring the permeability of a packed bed of powder). This is commonly referred to as the “Blaine surface” (S), as it is generally taken to be related to the specific surface area of the particles. Fineness was also calculated from the particlesize distribution data using an exponential approximation method referred to as “calculated surface.” The essence of this calculation is that the individual particles are assumed to be spherical, which is similar to the laser granulometric analysis where the apparatus expresses the size of the particles through the diameter values of the equivalent spheres. In this way, the specific surface area, Smg, for the assembly consisting of different continuous spheres of various sizes can be expressed as x max

S mg

6 = ----- ˜ US

³

1 --- ˜ f  x dx x

(EQ 2)

x min

where x = particle size (i.e., the diameter of the equivalent sphere) f(x) = function describing the particle-size distribution (frequency curve) A single function seldom describes the size distribution exactly; therefore, approximations were made for the individual sections of the curve using either the same type of functions with various parameters or using different types of functions. Additionally, the definite integrals were summarized by sections. Knowing that the smallest particles play a decisive role in constituting the specific surface, and that the individual particle classes are usually not sufficiently narrow as compared to the size of the particles, a more exact result was achieved when using an exponential approximation to the distribution function. The specific surface by particle classes could be calculated using the following formula: mi F F i–1 · - ˜ § ----i – -------'S mgi = -------------m i – 1 © x i x i–1 ¹

(EQ 3)

The exponent of the power function by particle classes also could be calculated as follows:

PARTICLE-SIZE DISTRIBUTION IN THE QUALITY OF CEMENTS WITH FLY ASH ADDITIVE

lg  F i e F i–1 m i = --------------------------lg  x i e x i–1

287

(EQ 4)

where mi = exponent of the power function for the given particle class Fi = cumulative distribution function for the given particle class RESULTS AND DISCUSSION

The degree of dispersion, or fineness, of fly ash used as an additive to cement has a significant influence on the quality of the fly ash and that of the composite cements with fly ash additive (Opoczky 1996; Opoczky and Tamás 2002). The fineness of fly ash is characterized in the cement industry by the Blaine surface, and the fly ash is also qualified by this value. According to our investigations, assessment by the Blaine surface value does not provide adequate information on the actual particle composition or fineness of the fly ash (Opoczky 2001; Gável 2003). This is shown in Figure 1 and Table 1 where the particle-size distribution of two products of about the same Blaine surface, ground clinker and fly ash, are illustrated in the RRSB system of coordinates (DIN [German Institute for Standardization] 66145), accepted in both the European and Hungarian practice. Particle-size distribution of the fly ash that had about the same Blaine surface (~3,500 cm2/g) when characterized by the fineness number ( x = 60 Pm) proved to be much more coarse than that of the ground clinker ( x = 18 Pm). In order to approach the particle-size distribution of the clinker, fly ash had to be ground to a Blaine surface of 2 ~6,000 cm /g. A similar conclusion also resulted in the case of fly ash and cement(s) when the Blaine surface values were compared with those calculated from particle-size distribution measurements data using the exponential approximation method (calculated surfaces) (Table 2). In the case of cement(s) with no additive, the calculated surface values (arrived at from the particle-size distribution measurements data using the exponential approximation method) do not differ significantly from the Blaine surface determined by the permeability method. However, in the cases of fly ash and of cements with fly ash additive, the difference between the Blaine surface value and the calculated surface value is significant. The difference between the Blaine surface values of cement and fly ash can be explained, on the one hand, by a significant difference in their particle-size distribution and, on the other hand, by the fact that the fly ash always contains—in addition to relatively coarse particles—very fine particles of elementary carbon, the presence of which significantly increase the Blaine surface value. The particle-size distribution of fly ash plays an essential role in the quality of composite cements containing fly ash additive. According to our investigations, there is a definite relationship between the uniformity coefficient, n, of composite cements and their water demand. Cements of higher uniformity coefficient (n)—that is, of more “narrow” particle-size distribution—usually require more water. The more narrow the particle-size distribution, the less tightly the particles can pack together, and so more water is required to fill the pores and gaps (Opoczky and Tamás 2002). As the fly ash has more narrow particle-size distribution than the cements, it increases the uniformity coefficient (n) of the cements and simultaneously increases its water demand when being added to the cement (Figure 2). This adversely affects the

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1 10

99 90 75 50

Oversize, %

36.8 75

25

90

10

95

5

99

Clinker, 3,500 cm2/g Fly ash, 6,600 cm2/g Fly ash, 3,500 cm2/g 1

10

100

Undersize, %

288

1

1,000

Particle Size, µm

FIGURE 1

TABLE 1

Particle-size distribution

Particle-size distribution and Blaine surface Parameters of the RRSB Equation

Denomination of Materials Investigated

Blaine Surface, cm2/g

Ground clinker Original fly ash Ground fly ash

~3,500 ~3,500 ~6,000

TABLE 2

Fraction Composition, %

Fineness Number, μm

n Uniformity Coefficient

0–3 μm

3–32 μm

32–192 μm

~18 ~60 ~19

0.9013 1.0870 1.0835

15.90 3.70 13.20

64.00 34.70 67.70

20.10 61.60 19.10

x

Fineness characteristics of fly ash and cements with fly ash additive Parameters of the RRSB Equation

Denomination of Materials Investigated

Original fly ash* Ground fly ash CEM I 42.5N* CEM II/A-V 42.5N* CEM II/A-V 32.5R* CEM II/B-V 32.5N*

Fly Ash Content, m/m %

Fineness Number, μm

n Uniformity Coefficient

Blaine Surface, cm2/g

Calculated Surface, cm2/g

100 100 0 20 20 35

95 48 19 21 25 24

1.0237 1.0342 0.9953 0.9555 0.9575 1.0249

3,460 3,840 3,570 3,750 3,590 3,340

1,940 3,230 3,620 3,640 3,420 3,190

x

* European Standard: EN 197-1.

strength, workability, and other application properties of the cements and mortars or concretes made of such cements. By applying an adequate fine grinding, the particle-size distribution of the fly ash can be influenced favorably. Interrelations between the fineness number ( x ) and Blaine surface value of fly ash are shown in Figures 3 and 4. From Figures 3 and 4 one can determine what Blaine surface value the fly ash should be ground to in order for its fineness and particle-size distribution ( x – fineness number, calculated surface) to approach the fineness characteristics of the cement without fly ash additive. For example, in order to achieve a fineness number x , 2 ~25 Pm the fly ash should be ground to a Blaine surface value of at least 5,500 cm /g.

289

PARTICLE-SIZE DISTRIBUTION IN THE QUALITY OF CEMENTS WITH FLY ASH ADDITIVE

36 34

1.00

32 30

0.95

28 n Wd

26

0.90

24 0 100

10 90

Fly Ash Clinker

20 80

m/ % m

35 65

FIGURE 2 Change of the uniformity coefficient (n) and water demand (Wd) of the cement, depending on the fly ash content

Fineness Number (x), µm

80 70 60 50 40 30 20 10 0 2,000

3,000

4,000

5,000

6,000

7,000

2

Blaine Surface (S), cm /g

FIGURE 3

Connection between the fineness number and Blaine surface of ground fly ash

4,500 Calculated Surface, cm 2/g

4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 0 2,000

3,000

4,000

5,000

6,000

7,000

2

Blaine Surface (S), cm /g

FIGURE 4

Connection between the calculated surface and Blaine surface of ground fly ash

Water Demand (Wd), m/m %

Uniformity Coefficient (n)

1.05

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Blaine surface (S) of cement with fly ash content in cm2/g

60

3,000 3,500 4,000

Compressive Strength, N/mm 2

50

40

30

20

10

0 0 10 20 35

3

28 7 Days

m

Fly Ash Content, /m %

FIGURE 5 Change of compressive strength of cement, depending on fly ash content and fineness of cement (co-grinding)

Other examples of this connection are ƒ It is possible to reduce the adverse effect of the fly ash additive on the strength—

particularly the initial strength—of the cement, as shown in Figure 5. ƒ It is possible to reduce the adverse effect of the fly ash additive on the water-

retaining capability of the cement (Figure 6). ƒ It is possible to reduce sulfate-caused expansion of the cement or to produce

cements of increased sulfate resistance (Figure 7). CONCLUSIONS

The fineness of fly ash used as a cement additive has a significant influence on the quality of composite cements containing fly ash. In the cement industry, the fineness of fly ash is characterized through the Blaine surface, which is determined by a permeability method. According to our investigations, the Blaine surface value does not provide adequate information on the actual particle composition of the fly ash. Namely, in the case of having approximately the same Blaine-specific surface value, fly ash is usually characterized by coarser and narrower particle-size distribution ( x = fineness number, n = uniformity coefficient) than cements without additives. We arrived at a similar conclusion when comparing the Blaine-surface and calculatedsurface values of fly ash and cements. Knowing the correlations between particle-size distribution, calculated surface, and Blaine surface of the fly ash, one can establish to what Blaine surface value the fly ash should be ground in order for its fineness and particle-size distribution to approach the fineness characteristics of the cement.

PARTICLE-SIZE DISTRIBUTION IN THE QUALITY OF CEMENTS WITH FLY ASH ADDITIVE

291

Water-Retaining Capability, m/m %

100

90

80

70

60

50 3,200 Cement

2,200 Fly Ash

3,000 Fly Ash

4,000 Fly Ash

Blaine Surface (S), cm 2/g

FIGURE 6

Water-retaining capability of cements with 20% different fineness of fly ash

Fly Ash SBlaine, ~6,000 cm2/g

Fly Ash SBlaine, cm 2/g 1.2

0.5 ~4,000

Expansion, mm/m

Expansion, mm/m

~3,000

0.8

0.4

0

0.4

0.3

0.2 CEM I 42.5

10 Fly Ash Content, m/m %

FIGURE 7

15

S-54 Cement

10

15

Fly Ash Content, m/m %

Effect of different fineness of fly ash on the sulfate resistance of cements in 28 days

Through the proper adjustment of the particle-size distribution of the fly ash, the properties (water demand, water retaining capability, strength, sulfate resistance, etc.) of fly ash containing composite cements can be influenced favorably. REFERENCES

Beke, B. 1981. The Process of Fine Grinding. Volume 1. Developments in Mineral Science and Engineering series. Budapest, Hungary: Akadémiai Kiadó and Martinus Nijhoff/ Dr. W. Junk Publishers. Gável, V. 2003. Description of grinding fineness of fly-ash and cements with fly-ash (in Hungarian). Paper presented at the 20th Cementipari Konferencia, HortobágyMáta, Hungary, October 13–15.

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Opoczky, L. 1996. Grinding technical questions of producing composite cement. International Journal of Mineral Processing 44–45:395–404. ———. 2001. Silicate-chemical properties of fly-ashes. Pages 255–262 in Oilfield Chemistry. Volume 3. Edited by I. Lakatos. Budapest, Hungary: Akadémiai Kiadó. Opoczky, L., and A.Z. Juhász. 1990. Mechanical Activation of Minerals by Grinding: Pulverizing and Morphology of Particles. Budapest, Hungary: Akadémiai Kiadó and Ellis Horwood Publishers. Opoczky, L. and F. Tamás. 2002. Multicomponent composite cements. Pages 559–594 in Advances in Cement Technology: Chemistry, Manufacture and Testing. 2nd edition. Edited by S.N. Gosh. New Delhi, India: Technical Books International.

Modeling Attrition in Stirred Mills Applying Statistical Physics Thomas Neesse,* Johann Dück,* and Friedrich Schaaff*

ABSTRACT

Grinding attrition is a new purification process that can be used for mineral residues. It can be applied to efficiently remove surface-adsorbed contaminants in the particle size range <100 P m. The process is a special case in comminution technology to be performed in conventional stirred mills. The operating parameters are selected so as to avoid particle breakage. For this process, a mathematical model was developed, which describes the kinetics of the grinding attrition on the basis of the microprocess (i.e., the attrition at an individual particle). In a next step, the model was extended to the macroprocess, applying principles of statistical physics for the entire milling chamber. The model was validated on the basis of experimental data. INTRODUCTION

Grinding attrition is a newly developed purification process for fine particles of contaminated soils and mineral residues, where the contamination is fixed adsorptively at the particle surface (Schricker, Dueck, and Neesse 1998). Prior to grinding attrition, the sandy feed material is deslimed at about 20 Pm. Subsequently, the particle outer layer is abraded and collected in a highly contaminated fines fraction <10 Pm, which is then removed in hydrocyclones. In grinding attrition, normally conventional stirred mills, as used in comminution technology, are utilized. To prevent particle breakage, special process conditions must be selected. Typical process conditions are grinding media size/maximum particle size ~1.5–2.0; solids concentration of the feed suspension 0.5–0.56 vol. %; and specific energy input ~20–30 kWh/t. Specific knowledge of grinding attrition from laboratory up to the industrial scale (Tiefel, Schricker, and Neesse 1999) is now available. This paper deals with the physical modeling of grinding attrition, which can be understood as a special case of comminution in stirred mills. LAB-SCALE EXPERIMENTS

Lab-scale grinding attrition tests were performed with the test setup shown in Figure 1. It consisted of a 1.5-L and a 3.0-L laboratory mill with a vertical attritor shaft. The test material was quartz sand with a mean particle diameter of 92 Pm. Selected experimental conditions to be used to validate the model are listed in Table 1. During the discontinuous tests, both the temporal change of the torque of the attritor shaft and the change of the particle-size distribution of the feed suspension (i.e., fines * Friedrich-Alexander University, Erlangen-Nuremberg, Germany 293

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ADVANCES IN COMMINUTION

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Variable n Measured Value: M

PC

Speed-Controlled Drive

Water, Attrition Material, Grinding Media

Ring-Type Stirrer

Sampling

Particle-Size Analysis

Water Cooling Attrition Container

Water Cooling

FIGURE 1

TABLE 1

Test rig for grinding attrition

Experimental conditions

Parameters and Experimental Conditions

Number of shaft revolutions (min–1) Grinding media (size dGM = 200–400 μm) Volume ratio of grinding media to the contaminated feed particle (–) Solids volume concentration (grinding media + attrition material) of suspension (–) Initial value of the torque (Nm)

Case 1

Case 2

Case 3

1,400 Steel spheres 1

1,600 Glass spheres 1

1,200 Steel spheres 1

0.54

0.56

0.56

0.704

0.434

0.678

generation as a result of attrition) were determined. The total mill volume was almost ideally mixed and samples were taken at different positions, showing fluctuations of the particle-size distribution of <1%. The total error was determined by fluctuations of the feed size distribution and amounted to ~3%. The current status of the process was evaluated by taking two samples of ~3 g after interrupting the process. MODELING OF THE GRINDING ATTRITION MICROPROCESS

Within comminution, the modeling of the grinding attrition is comparatively simple because only one fine fraction is produced, as demonstrated in Figure 2.

MODELING ATTRITION IN STIRRED MILLS APPLYING STATISTICAL PHYSICS

Particle-Size Distribution

dAM Particle-Size Distribution after the Attrition

Particle-Size Distribution of the Generated Fines

Particle-Size Distribution before the Attrition

295

dGM

Particle-Size Distribution of the Grinding Media

dr

Particle Diameter

Changes of the particle-size distribution during attrition (schematically)

FIGURE 2

The following simplifying assumptions are made for process modeling: 1. All grinding media are of the same size. 2. The particle-size distribution of the attrition material can be described by a mean

particle diameter. 3. The particle-size distribution of the attrition material remains approximately

constant during attrition. 4. The fine particles produced have a narrow size distribution and also are charac-

terized by a mean particle diameter. 5. The fines result only from friction impact between the grinding media and the

particles of the attrition material. 6. The mass ratio between the grinding media and the attrited particles remains

approximately constant during the process because the produced fines fraction is less than 0.1. The starting point for the analysis of the grinding attrition is the statement (Joost and Schwedes 1996) that, in microgrinding, two parameters are the deciding factors: the stress intensity and the stress number. For single particles of the attrition material, analogous proceedings should be applied: Mt e ges  t = h ˜ e = Zt ˜ ----------N tot where eges t h e Z M Ntot

= = = = = = =

(EQ 1)

entire energy transfer to a particle in respect to a grinding body (J/particle) attrition time (sec) stress frequency of a particle (–) stress intensity (J/particle) stress number of a particle respectively a grinding ball (L/sec) torque of the shaft, (J) total number of the particles and grinding media, (–)

More simply stated, it is assumed that the energy input is evenly distributed between all impact partners Ntot. This is justified because grinding media and the attrition material are close in size.

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The special conditions of grinding attrition are characterized by the facts that only one fines fraction is produced by abrasion and that the stress intensity of the attrition material decreases with the increasing fraction of the fines generated (Schricker 1999). This decrease in friction between the particles due to fine particle layers is shown schematically in Figure 3. The fines form a cushion between the impact partners, which attenuates the stress intensity. The reduction of the measured torque of the agitator with increasing fines fraction mf is shown in Figure 4. The obvious proportionality can be written as follows: e  t =  1 – Dm  t M  t - = ------------------f e0 M0

(EQ 2)

where M0 = torque at t = 0 (Nm) mf = mass ratio of the fines at time t (–) e0 = stress intensity of the particles at t = 0 on condition that mf = 0 (J) D is a measure for the attenuation of the particle impact due to the produced fines. It can be taken from the slope of the straight line from Figure 4. On the basis of Equation 1, Equation 3 then applies: e  t =  1 – Dm f e 0

(EQ 3)

In the following discussion, the microprocess of the friction impact between a grinding ball and a particle is studied. In the attrition mill, the grinding media/particle filling exhibits a pseudo-turbulent movement, obeying statistic laws. Thus, the stress intensity of a particle is a fluctuating value. This means that the necessary energy barrier sufficient for abrasion can only be exceeded at a limited number of impacts. This is schematically shown in Figure 5. Simplifying, it was assumed that there is no stochastic oscillation of the critical intensity. The probability that a particle is stressed so much during grinding attrition by a friction impact that a fine particle of the size df is formed can be formulated according to statistic physics as follows (Levich 1997): 2

eA df · 2 w  e >>  e A d f = exp § – ----------© e ¹

(EQ 4)

where w = probability for a successful friction impact (–) eA = specific surface energy formed by attrition (J/m2) df = size of the fine particle produced (m) Equation 4 expresses that the attrition result is connected with the increase of the specific surface energy by the value eA df2. The kinetics of fines production by grinding attrition can now be formulated by the following kinetic equation: 2

dm f eA df --------- = Z ˜ w = Z exp – ---------------------------------dt  1 – Dm f ˜ e 0 where mf = mass ratio of fines at time t Z = stress number (L/sec)

(EQ 5)

MODELING ATTRITION IN STIRRED MILLS APPLYING STATISTICAL PHYSICS

Grinding Media

Grinding Media

Attrition Material

FIGURE 3

Grinding Media

Attrition Material

One Impact Full Attrition

297

Attrition Material

i-th Impact Reduced Attritiion

n-th Impact No Attrition

Microprocess of the grinding attrition

1.000 Case 1 Case 2 Case 3 Regression

M/M0 (–)

0.875

0.750

0.625 Case 1: M/M 0 = –1.57 m + 1.03 Case 2: M/M 0 = –2.02 m + 1.05 Case 3: M/M 0 = –1.67 m + 1.03 0.500 0

0.05

0.10

0.15

0.20

0.25

0.30

mf (–)

FIGURE 4

Relation between torque of the attritor agitator and produced fines mf

It should be noted that in accordance with the assumption in Equation 5, the mass of the stressed particles is not considered (which is not usual in comminution kinetics). Equation 5 applies initially to the attrition process of one particle of the attrition material. Assuming the same initial conditions for all particles, however, this relationship also describes the overall process. The approximate integration of the Equation 5 leads to the following relationship: 2

 1 – Dm f0 t· - ln § 1 + --m f = m f0 + ----------------------------© DE tc ¹

(EQ 6)

ADVANCES IN COMMINUTION

LIBERATION AND BREAKAGE

Oscillating of Stress Intensity

298

Stress Intensity Critical Intensity for Abrasion Time

FIGURE 5

Oscillating stress intensity of a particle in the attrition mill (schematic)

with 2

eA df E = ----------e0

(EQ 7)

and 2

 1 – Dm f0 E exp § ---------------------- · t c = ----------------------------© 1 – Dm f0 ¹ D˜E˜Z

(EQ 8)

where E is a measure for the free surface energy produced under certain stress intensities, and tc is a characteristic attrition time. Furthermore, on the condition t > tc, the following is obtained: 2

 1 – Dm f0 t ln § ---- · m f = m f0 + ----------------------------© tc ¹ DE

(EQ 9)

With this equation, the parameters D, E, and tc can be determined using experimental data. The total quantity of the produced fines 'mf during attrition can be determined on the basis of Equations 5 and 8, according to which the increase in the fine particles diminishes over time. The production rate can be calculated according to the following relationship: dm dm f --------- = ---------f dt dt

t=0

1 ------------------1 + t e tc

(EQ 10)

Here a process duration tp is to be defined, at which the production rate of the fines decreases on 0.01. This corresponds to a time interval of tp = 99 tc and is at the same time the interpretation of the parameter tc.

MODELING ATTRITION IN STIRRED MILLS APPLYING STATISTICAL PHYSICS

299

For the total fines production 'mf, the following results from Equation 6: 2

 1 – Dm f0 'm f = 4.6 ----------------------------DE

(EQ 11)

Figure 6 shows the measured fines fraction over ln t for three experimental data sets. The linear progression of this dependence confirms the validity of Equation 9. The parameters of the process equation for the three experiments are listed in Table 2. Equation 5 is thus the result of a physically based model of the attrition process, proceeding from a statistic distribution of the stress intensity in the milling chamber. With this model, it is possible to present the fines production in the form of a dimensionless equation with three parameters. These parameters D, E, and tc must be experimentally determined. MACROPROCESS OF THE GRINDING ATTRITION

In the previous section, grinding attrition was studied as a microprocess. Figure 7 illustrates the model of the macroprocess referring to the entire milling chamber and considering the main process parameters. These are ƒ Size and density of the grinding media dGM, UGM, and the particles of the attrition

material dAM, UAM ƒ Volume ratio of grinding media/attrition material VGM/VAM ƒ Volume fraction of water cv in the milling chamber ƒ Specific mechanical energy input Em referred to as the mass of the attrition material

The modeling of the macroprocess is again based on the assumption of a stochastic movement of the grinding media and the particles. Blecher (1993) showed that energy dissipates in two main portions, one portion at the tip of the stirrer and another one at the inner surface of the mill. Contrary to real comminution in stirred mills, for grinding attrition, there are not any zones with a high local energy dissipation. Due to a high solids content and a moderate energy input, the energy dissipation of the grinding media occurs in an equidistributed manner in the mill chamber. The Reynolds number of the movement in the mill is very high and indicates a turbulent regime. Turbulence in the stirred mill is also the basis of the investigations of Theuerkauf and Schwedes (1999) modeling the movement of the filling of stirred media mills. The turbulent movement is statistically recordable as a random walk of the turbulence elements in all three directions in space. Thus, turbulence is responsible for the impacts between particles and grinding media. In the following discussion, grinding attrition is characterized by a homogeneous turbulence with the mean velocity v' 2 = v . To model the macroprocess, the relations of the mean free path length O with respect to the mean impact time W in the milling chamber must be found. STRESS NUMBER

The macromodel is based on determining the stress numbers for one particle and one grinding body per unit of time. According to Figure 8, a cylindrical cell with the cross-sectional area (rGM + rAM)2 and the length O = v ˜ 't is observed, where a particle moves through with the velocity v during 't. The mean impact number in this volume results from the contact number of the particle and the grinding media, whose central point is located in the cell observed. Here, it should be noted that the impact partners (particle and grinding media) have different sizes.

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Case 1 Case 2 Case 3 Regression

0.28

Δmf

0.24

0.20

0.16 Case 1: Δmf = 0.0399 In t + 0.1498 Case 2: Δmf = 0.0542 In t + 0.0591 Case 3: Δmf = 0.0438 In t + 0.1153 0.12 1

2

3

4

5

In t

FIGURE 6 TABLE 2

Comparison of the nonlinear model with the experimental data Values of the parameters according to Equation 9 for the experimental data Case 1

Case 2

Case 3

D = 1.57 E = 14.8 tc = 0.024 min

D = 2.02 E = 8.22 tc = 0.34 min

D = 1.67 E = 12.6 tc = 0.072 min

The time W between two impacts is W = O --v

(EQ 12)

Z = 1 --W

(EQ 13)

and the impact frequency Z is

The mean free path length of one particle can now be determined in analogy to gas molecules, considering different sizes of particle and grinding media: 1 O = --------------------------------------------2 S  r AM + r GM c GM where rAM = radius of attrited material rGM = radius of grinding media cGM = volume concentration of grinding media

(EQ 14)

MODELING ATTRITION IN STIRRED MILLS APPLYING STATISTICAL PHYSICS

Diameter of the Ring-Type Stirrer Solids Concentration (attrition material + grinding media + water)

Revolution Number

Filling Volume

Size and Density of Particles and Grinding Media

Volume Ratio of Particles and Grinding Media

FIGURE 7

Volume Element for Determining the Stress Number

Scheme of the macroprocess, including the main process parameters

Particle Does Not Hit Grinding Medium

r = rGM + rAM

>r
rAM
=r

rGM

Particle Hits Grinding Media

According to Atkins 2001.

FIGURE 8

Observed volume element to calculate the mean free path

301

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ADVANCES IN COMMINUTION

LIBERATION AND BREAKAGE

The impact frequency of one particle with the grinding media yields 2

Z = vS  r AM + r GM c GM

(EQ 15)

Further, the impact frequency : of all particles in the above cylindrical volume is 2

: = vS  r AM + r GM c AM ˜ c GM

(EQ 16)

For the volume concentration cGM of the grinding media, one may assume the following: V GM V S 1 V GM V GM 1 N GM 1 - ---------- = --------- ----- --------- = --------- c V --------c GM = ---------= --------3 3 3 V V V V V S S d GM d GM d GM NGM VGM V dGM VS cV

= = = = = =

(EQ 17)

number of grinding media particles volume of grinding media volume of milling chamber size of grinding media volume of solids volume fraction of water in the milling chamber

Analogously, for the volume concentration cAM of the particles of the attrited material, the following equation is valid: V AM 1- c --------c AM = --------VS v d3

(EQ 18)

GM

Assuming v ~ nD, the impact frequency :A for the total volume of the apparatus can be determined as follows: V GM --------- d AM + d GM 2 V AM - c v ---------------------------: A a V A nD --------------------------------3 3 2 GM · d AM d GM §1 + V --------© V AM ¹ 2

(EQ 19)

where VA = mill volume (m3) cv = solids concentration of the suspension containing the attrition material and the grinding media (–) Specific Energy Input

The specific energy input transferred from the attritor shaft to the grinding material with the mass mg is computed according to the following: 3

3

§ N GM U GM d GM 2 N AM U AM d AM 2 · E 0 = ¨ -------------------------------¢ v GM² + ------------------------------¢ v ²¸ N + N N GM + N AM AM ¹ AM © GM where ¢ v GM² = turbulent velocity of the grinding media (m/sec) UGM = density of the grinding media (kg/m3)

(EQ 20)

MODELING ATTRITION IN STIRRED MILLS APPLYING STATISTICAL PHYSICS

303

¢ v AM² = turbulent velocity of the attrition material (m/sec) UAM = density of the attrition material (kg/m3) Equations 19 and 20 apply, however, only to the initial phase of the grinding attrition, provided that no attenuation has begun as a result of the fines production. As a further simplification, it is to be assumed that the mean velocity of all particles and grinding media is equal: ¢ v 2² = ¢ v 2GM² = ¢ v 2AM² . Thus, Equation 20 becomes § N GM U GM d 3GM N AM U AM d 3AM· 2 2 –1 + -------------------------------¸ n D ˜ m G E 0 a ¨ -------------------------------N GM + N AM ¹ © N GM + N AM

(EQ 21)

Considering the appropriate volumes of the grinding media VGM and the attrition material VAM, depending upon the reference values, the following is obtained: U AM V AM · § ¨ 1 + ---------- ---------- ¸ U GM V GM ¹ 3 © –1 2 2 E 0 = kn D U GM d GM ------------------------------------˜ mG 3 d GM V AM · § - ---------- ¸ ¨ 1 + --------3 d V GM ¹ ©

(EQ 22)

AM

U GM V GM · § ¨ 1 + ---------- ---------- ¸ U AM V AM ¹ 2 2 3 © –1 = kn D U GM d GM ------------------------------------˜ mG 3 d AM V GM · § - ---------- ¸ ¨ 1 + --------3 d V AM ¹ © GM

where k is a numerical constant. Implementing now the microprocess from Equation 11 and Equation 7, the following is obtained with E0 instead of e0: U GM V GM · § --------- ---------- ¸ 3 ¨1 + U  1 – Dm f0 n D U AM d AM © AM V AM ¹ ------------------------------------4.6k ----------------------------- --------------------------------2 3 D EA df d AM V GM · § - ---------- ¸ ¨ 1 + --------3 d GM V AM ¹ © 2

'm f =

2

2

(EQ 23)

Further, the energy input E0 will be related to the produced fines mf which results in

M0 E mf = 2Sn  1 – Dm 0 ---------------------------- exp U AM V AM : A

U GM V GM · § ¨ 1 + ---------- ---------- ¸ 2 U AM V AM ¹ df EA © ----------------------------------------------------------------------------------------------2 2 3 3  1 – Dm 0 n D U AM d AM § d AM V GM · - ---------- ¸ ¨ 1 + --------3 d GM V AM ¹ ©

(EQ 24)

For a better survey and to enable scale-up considerations, the process Equation 24 is modified, introducing the following dimensionless numbers:

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ADVANCES IN COMMINUTION

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0.18 Calculated n = 1,600 n = 1,600 1/min Calculated n = 1,200 1/min n = 1,200 1/min Calculated n = 1,000 n = 1,000 1/min

0.16 0.14 0.12 0.10

t = 16 min cv = 0.56 VGM/VAM = 1 VA = 1.51

0.08 0.06 0.04 0.02 0 0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

Density of Grinding Media, kg/m 3

FIGURE 9

Influence of density of grinding media on fines production

2 Va ˜ D 1 V GM d AM U GM df EA - ----T = --------- ; ' = --------; ) = --------- ; 3 = ----------------------------------------------------------- ; < = ------------4 4 2 2 3 V AM d GM U AM d GM '  1 – Dm 0 n D U AM d AM

With these dimensionless numbers, Equations 23 and 24 can be transformed to  1 – Dm f0 1  1 + )T - ---- ----------------------'m f = 4.6k -------------------------D 3  1 + '3 T

(EQ 25)

and 2

 1 + )T 1 + T - exp 3 ----------------------Eˆ mf = --------------------------------------------2 3 k< ˜ '  1 + ' c v T 1 + ' T

(EQ 26)

The correction constant k serves to adapt the model equation to the experimental values. M O D E L VA L I D A T I O N

To validate Equations 25 and 26, attrition experiments in a 1.5-L cell were conducted. The attrition material was hard limestone in the particle size range between 100 and 150 Pm. Figures 9–12 present the comparison of experimental data and curves calculated using the model equations. Obviously, the model satisfactorily reflects the influence of grinding body size and density on fines production. The same can be concluded for the dependency of specific energy input on the circumferential stirrer speed. The constant k was determined as k | 550. Especially remarkable is the dependency of fines production on circumferential stirrer speed measured in three mills of different sizes—1, 3, and 6 L. According to Figure 12, making a scaleup of the attrition in stirred mills seems to be justified.

MODELING ATTRITION IN STIRRED MILLS APPLYING STATISTICAL PHYSICS

305

0.12 Calculated n = 1,600 n = 1,600 (1/min) Calculated n = 1,000 n = 1,000 (1/min) Calculated n = 800 n = 800 (1/min)

0.10

0.08

t = 16 min cv = 0.56 ρGM = 2.5 kg/L VGM/VAM = 1 VA = 1.51

0.06

0.04

0.02

0 0

200

400

600

800

1,000

1,200

1,400

Diameter of Grinding Media dGM,

FIGURE 10 Influence of grinding media size on fines production at different revolution numbers of the agitator

8,000 dGM = 750 μm Calculated dGM = 750 μm dGM = 350 μm Calculated dGM = 350 μm dGM = 250 μm Calculated dGM = 250 μm

Specific Energy Input Emf, J/kg

7,000 6,000 5,000

t = 16 min cv = 0.56 ρGM = 2.5 kg/L VGM/VAM = 1 VA = 1.51

4,000 3,000 2,000 1,000 0 0

500

1,000

1,500

2,000

Revolution Number n, 1/min

FIGURE 11 Influence of agitator revolution number on specific energy input at different grinding media sizes

CONCLUSIONS

The presented macromodel of grinding attrition can substantially reduce experimental expenditure for the optimization of the attrition conditions. First, it is necessary for the parameters of the kinetic equation to be determined in very few tests. The influence of fluctuating process conditions can then be simulated with Equations 9 and 5. Comparisons with experimental data show that the developed kinetic model can be used for a prediction of the fines production under certain process conditions. Further investigations are required to improve the model’s applicability to ensure that experimental expenditures to define process conditions can be minimized.

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0.18 Calculated Horizontal Mill 31 Horizontal Mill 31 Calculated Vertical Mill 11 Vertical Mill 11 Calculated Vertical Mill 61 Vertical Mill 61

0.16

Δmf < 10 μm (–)

0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0

500

1,000

1,500

2,000

Revolution Number n, 1/min

FIGURE 12

Fines production for three different mill sizes at different agitator revolution numbers

REFERENCES

Atkins, P.W. 2001. Physikalische Chemie. Weinheim: Wiley-VCH. Blecher, L. 1993. Strömungsvorgänge in Rührwerkskugelmühlen (Flow pattern in stirred mills). Ph.D. dissertation. Braunschweig: Technische Universitat. Joost, B., and J. Schwedes. 1996. Comminution of white fused alumina and wear of grinding beads in stirred media mills. Part II: Effect of operational parameters, grinding chamber geometry and beads hardness on the wear of grinding beads. Ceramic Forum International 73:69–76. Levich, B.G. 1997. Theoretical Physics. Amsterdam: North-Holland. Schricker, B. 1999. Intensivierung der Attrition bei der physikalisch-chemischen Sanierung kontaminierter mineralischer Abfallstoffe (Intensifying the attrition with physicalchemical cleanup of contaminated, mineral waste material). Ph.D. dissertation. Nurnberg: Universität Erlangen. Schricker, B., J. Dueck, and T. Neesse. 1998. Grinding-attrition for treatment of contaminated mineral residues. In Proceedings of the Third World Congress on Particle Technology, Brighton, Great Britain. Warwickshire: Institution of Chemical Engineers. Theuerkauf, J., and J. Schwedes. 1999. Theoretical and experimental investigation on particle and fluid motion in stirred media mills. Powder Technology 105:406–412. Tiefel, H., B. Schricker, and Th. Neesse. 1999. Hochleistungsattrition zur mechanischen Reinigung von mineralischen Roh und Reststoffen (High performance attrition for mechanical cleaning of mineral raw materials and residues). Aufbereitungs Technik 40(4):160–164.

PART 4

Mill Design

307

Design of Iron Ore Comminution Circuits to Minimize Overgrinding T.C. Eisele* and S.K. Kawatra*

ABSTRACT

Overgrinding is a major concern in grinding circuits because it (1) wastes energy, and (2) can result in valuable minerals being ground to such fine sizes that they are difficult to process. Overgrinding can be particularly severe in grinding circuits that are processing mixtures of minerals of different densities while using classifiers for size control. This results in the highdensity minerals that have already reached the target size being retained in the circuit and ground to a finer size than the low-density minerals. While this problem could, in principle, be solved by the use of screens for size control, in practice, screening costs become excessive for fine grinding due to high maintenance and low screening efficiency. A novel approach is to redesign the circuit so that the particles that are very close to the target size can be separated out and handled differently than particles that are definitely coarser than the target size. Simulations of this type of approach are presented. For the circuit simulated in this paper, the circulating load was reduced from 250% to only 42.5% without sacrificing quality, resulting in a 50% increase in grinding circuit throughput. INTRODUCTION

In grinding circuits, energy is wasted when particles are ground to a size finer than is necessary. Such overgrinding can be caused when particles are retained in the circuit for too long and continue to be ground even after they have reached the target product size of the circuit. There are two factors that contribute heavily to overgrinding: (1) inefficient classification returning a large fraction of the finest particles to the circuit; and (2) excessive mill retention times causing particles to be broken multiple times before they are discharged. It is normally expected that there is a trade-off between overgrinding and the presence of locked particles. If the circuit product size is made coarser to reduce the overgrinding, this typically leads to an increase in the top size of the product as well, with the top size particles being poorly liberated. This reduces the grade that can be produced in the processing that follows comminution. In order to reduce this trade-off, it is necessary to determine how to change the grinding circuit to produce a narrower size distribution, which will reduce overgrinding while simultaneously controlling the quantity of coarse locked particles leaving the circuit. A significant cause of overgrinding is when an ore contains minerals of different densities, and a hydrocyclone or other classifier is used to control product size from the * Department of Chemical Engineering, Michigan Technological University, Houghton, Michigan 309

310

ADVANCES IN COMMINUTION

MILL DESIGN

circuit grinding the ore. The most important case of this is iron ore grinding, where the iron oxides have densities of approximately 5 g/cm3 whereas the gangue minerals are less than 3 g/cm3, and the iron oxides make up a large fraction of the mass of the raw ore. As classifiers separate based on both size and density, the higher-density iron oxides continue to report to the classifier coarse product even when they are already finer than the lower-density gangue particles that report to the classifier fine product. This results in the iron oxides being ground to a much finer size than necessary. To illustrate the extent of this problem, the results of plant sampling studies are presented in the next section. PLANT SAMPLING STUDIES

The plant examined was a magnetite concentrator located in the Lake Superior iron ore district. The flowsheet was a pebble mill circuit, as shown in Figure 1. This type of plant was selected because iron ore is one of the most high-volume metallic ores produced and is therefore of considerable practical importance. Sampling and sample analysis were conducted by plant personnel. Size analyses were carried out by three methods: 1. Wet sieving at 25 Pm using a woven-wire test sieve, followed by dry sieving of

the +25-Pm particles using woven-wire test sieves in a Ro-Tap sieve shaker 2. Microsieving of dry powders using electroformed nickel-foil sieves in a Sonic

Sifter apparatus, which allowed sieving down to 10-Pm particle size 3. Microtrac laser diffraction particle size analysis to measure particle sizes down to

1 Pm For the sieved samples, each individual size fraction was assayed using a dichromate titration method (ASTM 2001) by plant personnel to determine the iron assay of each sieved size fraction for each stream mentioned above. The size distribution and assay data were then mass balanced, and the magnetite concentration in each size fraction was calculated from the iron assays. The results for the pebble mill circuit were as shown in Table 1. It should be noted that the –25-Pm fraction of the cyclone underflow/mill feed is 30.8% of the material being returned to the pebble mill for grinding, even though it is already finer than the target grind size of 25 Pm. Further, this fraction of the pebble mill feed is unusually enriched in magnetite and consists of 92.9% magnetic material. From this information, it is clear that a great deal of the pebble mill feed consists of fine magnetite that is being retained in the circuit by the hydrocyclones and, as a result, is being overground. This is a very large contribution to the circulating load, which is 250% of the circuit new feed. The Bond equation can be used to estimate the energy wasted in overgrinding the fine magnetite. The target size was 80% passing 25 Pm, but size analysis of the magnetite product from the circuit showed that it was 80% passing 20 Pm. Given that the average work index of the ore was 11.6 kW-hr/t, the energy wasted can be calculated as § 10 10 · W = 11.6 ¨ ---------- – ----------¸ = 2.74 kW-hr/t 25¹ © 20

(EQ 1)

As the overall circuit product was 57.4% magnetite, thus, the energy wasted per ton of total circuit feed was (0.57)(2.74) = 1.57 kW-hr/t. The plant grinds approximately 15 Mt of ore per year, and so the overgrinding losses from this source are 23 million kW-hr/ year, or 2.4 u 1011 Btu/year for a single plant.

DESIGN OF IRON ORE COMMINUTION CIRCUITS TO MINIMIZE OVERGRINDING

Chips

–½ in. + 1 mm Back to Primary Mill

COF

Cobbers Magnetic Separator (3) 36 in. (d) × 10 ft (l)

Krebs 15 in. Cyclone 16 Total, 2 Standby Vortex: 5¼ in. Apex: 3 in. Pressure: 20–30 psi

Pebbles (–2½ in. + ½ in.)

CUF

Primary Mill (1) 32 ft × 16.5 ft 8,500 hp

Excess Pebble Crusher Nordber 200 hp Short-Head Cone 350 hp

CNF

Cobber Tails to Tailings Dam

Chips Cyclones Feed and Sump

Pebble Mill (1) 15.5 ft × 32.5 ft 2,650 hp

Pebble Mill Discharge

Vibrating Screen Top Deck: ½ in. Bottom Deck: 1 mm

Cobbers Magnetic Separator (3) 36 in. (d) × 10 ft (l)

CNF

Cobber Tails to Tailings Dam Cobbers Feed and Sump

Crushed Pebbles

311

Roll Press KHD RP 7.0 1,400 mm (d) × 800 mm (l) Feed: 67% – ½ in. Production: 84% – ¼ in.

COF Krebs 15 in. Cyclone 16 Total, 2 Standby Vortex: 5¼ in. Apex: 3 in. Pressure: 20–30 psi

Pebbles (–2½ in. + ½ in.)

CUF

Chips Cyclones Feed and Sump

Pebble Mill (1) 15.5 ft × 32.5 ft 2,650 hp

Pebble Mill Discharge

NOTES: CNF = circuit new feed; COF = cyclone overflow; CUF = cyclone underflow.

FIGURE 1 Configuration of the base grinding circuit sampled for this study. The paired pebble mills were the primary area of interest.

TABLE 1

Results of plant sampling

Stream

Circuit new feed—122.5 metric tons per hour (tph)

Size Fraction

Overall*

Magnetic†

Nonmagnetic†

+25 μm

89.3 tph 72.9% 33.2 tph 27.1%

46.1 tph 51.7% 29.0 tph 87.4%

43.2 tph 48.3% 4.2 tph 12.6%

210.4 tph 69.2% 93.7 tph 30.8%

117.6 tph 55.9% 87.0 tph 92.9%

92.8 tph 44.1% 6.7 tph 7.1%

141.2 tph 45.3% 170.6 tph 54.7%

77.8 tph 55.1% 108.8 tph 63.8%

63.4 tph 44.9% 61.8 tph 36.2%

16.4 tph 12.6% 113.8 tph 87.4%

7.1 tph 43.5% 67.6 tph 59.4%

9.2 tph 56.5% 46.2 tph 40.6%

–25 μm Cyclone underflow/mill feed— 304.1 tph

+25 μm –25 μm

Pebble mill discharge— 311.8 tph

+25 μm –25 μm

Cyclone overflow/circuit product—130.1 tph

+25 μm –25 μm

* Overall percentages are the percentage of each size fraction in the stream, with the sum of + 25-μm and –25-μm values equaling 100%. † Magnetic and nonmagnetic percentages are the assays for each size fraction.

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These results show that there is a significant benefit to be gained if the plant can be redesigned to prevent overgrinding. This is an ideal situation for simulation studies, as it is necessary to consider radical rearrangements of the circuit that would not be feasible to conduct on a speculative basis in actual plant studies. CIRCUIT SIMULATION

Base Circuit Simulations

In order to simulate the pebble mill portion of the grinding circuit, a pebble mill model and hydrocyclone model were needed. Both of these models were implemented using USIM-PAC 3.0 simulation software (BRGM 2004). The pebble mill model used was based on the following mill characteristics. Number of mills in parallel: Mill diameter inside shell (m): Length–diameter ratio: Fraction of critical speed: Mill discharge: Filling of the mill (%): Reference size for the wear function (mm): Wear coefficient (0 = surface; 1 = volume): Wear rate of pebbles (1/hr): Reference size class for the selection function:

1 4 2.1 0.8785 Overflow 43 15.875 0 3.45 10

The forms of the selection and breakage functions used in the model were based on work by Austin and Herbst (BRGM 2004; Austin, Manacho, and Pearcy 1987; Kinneberg and Herbst 1984). Breakage function: J

B ij = )  x i–1 e x j +  1 – )  x i–1 e x j

E

(EQ 2)

where Bij is the fraction of the mass of broken particles from size fraction i that reports to size fraction j; and xi is the top size limit of size fraction i. The breakage function parameters that were found to give the best fit to plant data were ) E J

0.096 3.93 0.608

Selection function: E

2

S i = S 1 exp > a 1 ln  d i e d i  ref + a 2  ln  d i e d i  ref @

(EQ 3)

where Si is the fraction of particles in size fraction i that are broken; di is the geometric mean particle diameter of size fraction i; and di(ref) is the reference particle size class.

DESIGN OF IRON ORE COMMINUTION CIRCUITS TO MINIMIZE OVERGRINDING

313

The selection function parameters that were found to give the best fit to plant data were E

S 1 0.75 a1 –1.5 a2 –0.5 The simulations did not incorporate a liberation model. The proportions of magnetite and quartz by size were determined by chemical analysis of sieve fractions collected from the plant, and it was assumed that as the target grind size was being held constant, the degree of liberation at each size would also be essentially constant and would therefore not have a major effect on the predictions of the model. By using these parameters to simulate the pebble mill, the results shown in Figure 2 were obtained, which show an excellent match between the predicted and measured mill discharge. Several different sets of data from the same plant at different flow rates were used to validate the model parameters, with similar results. The hydrocyclone model used was that developed by Plitt (1976), which performed adequately in predicting the cyclone performance in this circuit.

Cd = 1 – e

d m – 0.693 § -------------· © d50c¹

(EQ 4)

where C(d) = classification function for particles of size d after correcting for particles that bypass classification d = particle size, in micrometers d50c = particle size that has equal probability of reporting to the overflow or the underflow, after correcting for the particles that bypass classification m = measure of the sharpness of separation

The corrected d50 size was calculated using the following formula: 0.46

0.6

1.21

50.5D c D i D o exp  0.063I d50c = -------------------------------------------------------------------------------0.5 0.71 0.38 0.45 Du h Q  Us – U where d50c I Dc h Di Q Do Us Du U

= = = = = = = = = =

(EQ 5)

corrected d50 (Pm) volumetric fraction of solids in feed cyclone diameter (cm) free vortex height (cm) inlet diameter (cm) volumetric flow rate of feed (L/min) overflow diameter (cm) solid density (g/cm3) underflow diameter (cm) liquid density (g/cm3)

Simulations of the overall pebble mill/hydrocyclone circuit reproduced the tendency of the circuit to retain fine magnetite in the pebble mill feed, as can be seen in Figure 3. Here, it can be seen that the nonmagnetic material was much coarser than the magnetics,

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100 90

Cumulative % Passing

80 70 60 50 40 30 20

Feed Measured Mill Discharge Predicted Mill Discharge

10 0 1

10

100

1,000

10,000

FIGURE 2 Simulation results for the pebble mill model as compared with actual grinding mill performance

and the overall size distribution of the mill feed was dominated by the presence of fine magnetite that was being returned to the mill and overground. It is particularly noteworthy that the magnetics are concentrated in the size range of 25 to 50 Pm. If this size fraction could be segregated into a separate process stream to be managed separately, it would allow the particles coarser than 50 Pm to be ground without excessive production of overground material. Modified Circuit Simulations

The results for the unmodified circuit suggested a novel approach to the problem of overgrinding the magnetite fines, shown in Figure 4. If the particles that are near the target size are separated from the rest of the pebble mill feed by using two-stage cycloning, then they will be prevented from being trapped in the circulating load, allowing the first pebble mill to concentrate on grinding the particles that are definitely coarse enough to require vigorous grinding. Two-stage classification has been used in the past to improve the performance of classifiers (Dahlstrom and Kam 1987; Hukki, Karhunen, and Lindsberg 1977). The most effective applications of two-stage classification have been in cases where the bypass fraction of a single-stage classifier is large, allowing a large quantity of the fine particles to bypass classification and be returned to the grinding circuit. With a two-stage cyclone circuit of proper configuration and water additions, the fine-particle bypass can be decreased, resulting in lower circulating loads and the possibility of higher feed capacity (Peterson and Herbst 1984). However, this approach is of little effect if the hydrocyclones are already being operated with a very low bypass fraction, as is often the case in iron ore concentrators (T. Weldum, personal communication, 2003). When fine, high-density particles are, in fact, undergoing classification and not bypassing classification, they are then classified into the coarse product due to their density. The settling rate of fine, dense particles is the same as that of coarser, less dense particles, so that the fine magnetite tends to concentrate in the hydrocyclone underflow as a direct result of correct operation of the hydrocyclone. In this situation, the reduction of

DESIGN OF IRON ORE COMMINUTION CIRCUITS TO MINIMIZE OVERGRINDING

315

100 90

Cumulative % Passing

80 70 60 50 40 30 20

Overall Magnetics Nonmagnetics

10 0 1

10

100

1,000

10,000

FIGURE 3 Size distributions of the magnetic and nonmagnetic material in the hydrocyclone underflow/mill feed, as calculated by simulations. These results were consistent with the observed performance of the grinding circuit.

Chips

–½ in. + 1 mm Back to Primary Mill

Primary Mill (1) 32 ft × 16.5 ft 8,500 hp

Cobbers Magnetic Separator (3) 36 in. (d) × 10 ft (l)

COF Dewatering Cobber

Cobber Tails to Tailings Dam

Pebbles (–2½ in. + ½ in.)

CUF Excess Pebble Crusher Nordber 200 hp Short-Head Cone 350 hp

Vibrating Screen Top Deck: ½ in. Bottom Deck: 1 mm

Chips

Cobbers Magnetic Separator (3) 36 in. (d) × 10 ft (l)

CNF

Open-Circuit Pebble Mill (1) 15.5 ft × 32.5 ft Pebbles (–2½ in. + ½ in.)

CUF

Cobber Tails to Tailings Dam

Crushed Pebbles

Cobbers Feed and Sump Roll Press KHD RP 7.0 1,400 mm (d) × 800 mm (l) Feed: 67% – ½ in. Production: 84% – ¼ in.

Mill Product

Chips Cyclones Feed and Sump Closed-Circuit Pebble Mill (1) 15.5 ft × 32.5 ft Pebble Mill Discharge

FIGURE 4 Modified circuit that was produced from the circuit shown in Figure 1. This is largely a rearrangement of existing equipment, with the only major added unit being the dewatering cobber for the open-circuit pebble mill.

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the bypass fraction will not cause these particles to be removed from the coarse product, and an attempt to use two-stage classification will simply result in a stream of trapped, narrowly sized high-density particles continuously circulating between the two hydrocyclone classifiers. This stream of near-size particles then continuously increases in volume until the hydrocyclones become overloaded (T. Weldum, personal communication, 2003). If the near-size particles can be separated as a sufficiently narrow size distribution, the possibility arises of grinding this stream from two-stage cycloning in an open-circuit mill. This would eliminate the possibility of near-size particles being trapped in the circulating load and overground. Normally, open-circuit grinding will produce a broad size distribution due to the lack of particle size control (Kinneberg and Herbst 1984). However, it is also normal for the feed to an open-circuit mill to itself have a broad size distribution, which would broaden still further during open-circuit grinding. In previous work in this plant (T. Weldum, personal communication, 2003), it had been determined that the use of two-stage cycloning could produce one stream with a very narrow size distribution. If such a closely sized feed were ground in open circuit, the size distribution would be expected to remain moderately narrow. In addition, it is normal for the coarsest particles to have a higher probability of breaking than the finer particles in a tumbling-media mill (Teke et al. 2002), and so a pass through an open-circuit mill would be expected to preferentially break the coarsest particles. Based on these considerations, a new circuit was developed and simulated, as shown in Figure 4. The primary considerations in this circuit were ƒ Use two-stage cycloning to produce three product streams: (1) coarse particles for

grinding in a closed-circuit mill; (2) fine particles that are definitely fine enough to be removed from the grinding circuit as product; and (3) near-size particles that are only slightly coarser than the target product size, and that have an extremely narrow size distribution. ƒ Use open-circuit grinding to reduce the top size of the near-size particle stream.

Material only makes a single pass through this mill, so there is no opportunity to continuously recycle and regrind high-density particles. The narrow size distribution of the near-size particle stream will allow the open-circuit mill to produce a moderately closely sized product. ƒ As far as possible, use only equipment that is already present in the existing circuit.

By reconfiguring the mills and existing cyclones, it would be possible to implement the circuit shown in Figure 4 directly from the circuit shown in Figure 1, with the only major equipment addition being the dewatering cobber added to remove excess water from the open-circuit mill feed. The product size of an open-circuit mill is quite sensitive to the feed rate (Teke et al. 2002); therefore, it was first necessary to ensure that an appropriate amount of material was sent to this mill by the two hydrocyclones. It was determined that, in order to produce the target feed size distribution, the open-circuit mill needed to receive 81 tph of feed. In order to produce this quantity of material, the hydrocyclones were operated with the efficiency curves shown in Figure 5. The two mill feed products produced by the two-stage cyclone processing are shown in Figure 6. The feed to the closed-circuit mill is much coarser than it had been for the unmodified circuit (compare with the size distributions shown in Figure 3 for the unmodified circuit). In addition, the difference between the magnetite and quartz size distributions is greatly reduced, so that there is much less tendency to overgrind the magnetite while reducing the size of the nonmagnetic quartz. For the feed to the opencircuit mill, the hydrocyclones are successfully producing a very narrowly sized stream

DESIGN OF IRON ORE COMMINUTION CIRCUITS TO MINIMIZE OVERGRINDING

317

100 90

% of Size to Underflow

80 70 60 50 40 30 20

Two-Stage Primary Cyclone Two-Stage Secondary Cyclone Single-Stage Cyclone

10 0 1

10

100

1,000

FIGURE 5 Efficiency curves for the two-stage cyclones used in the combined closed-circuit/ open-circuit flowsheet, including a comparison with the efficiency curve for the single stage of cycloning used in the original, unmodified circuit. The close spacing between the efficiency curves ensured a very sharp size distribution in the feed to the open-circuit mill, while still providing the 81 tph of solids needed to produce the desired size distribution.

100 90

Cumulative % Passing

80 70 60 50 40 CC Feed Overall CC Feed Magnetics CC Feed Nonmagnetics OC Feed Overall OC Feed Magnetics OC Feed Nonmagnetics

30 20 10 0 1

10

100

1,000

10,000

FIGURE 6 Size distributions of the feed streams produced by the two-stage cyclone arrangement for the closed-circuit (CC) mill and the open-circuit (OC) mill shown in Figure 4

where the size distributions for the magnetite and quartz are very similar. Again, this similarity of the size distribution will help to prevent overgrinding of the magnetite. Two products are produced by the two-stage circuit: a primary cyclone overflow stream and an open circuit mill discharge stream. The size distributions predicted by the simulation for these streams are shown in Figure 7, along with the sum of the two product streams, and the size distribution of the final product of the original single-stage circuit

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120

Cumulative % Passing

100

80

60

40 Primary Cyclone Overflow Open-Circuit Mill Discharge Total Two-Stage Product Single-Stage Product

20

0 1

10

100

1,000

10,000

FIGURE 7 Size distributions for the two products produced by the two-stage open/closed-circuit grinding simulation, compared with the product from the original single-stage closed-circuit grinding process

for comparison. The open-circuit mill discharge stream can be seen to be maintaining a narrow size distribution, due to the fact that the mill feed consisted of closely sized particles. It should be noted that the size distribution of the open-circuit mill feed was considerably finer than the plant feeds that were originally available for use in determining and validating the model parameters. The model is therefore not fully validated for the opencircuit mill conditions, and it is possible that the predicted size distribution from the simulation will not be identical to the actual size distribution that would be produced in the plant. However, as there is no circulating load from the open-circuit mill, any errors from this portion of the circuit simulation will not propagate back to the rest of the circuit. When the two products from the two-stage mill are added together, the size distribution predicted is nearly identical to that produced by the original single-stage grinding circuit. This indicates that the two-stage grinding circuit is fully capable of reaching the target grind size. The main benefit is seen when the relative flow rates of material through the circuit are compared, as shown in Table 2. The use of the two-stage circuit allows the circulating load to be drastically reduced, from a 253% circulating load to only 42.5%. This makes available a great deal of extra hydrocyclone and grinding mill capacity, allowing the capacity of the circuit to be increased by 50%. This reduction in circulating load is a direct result of the large reduction in the recirculation and overgrinding of the fine, high-density magnetite particles. It should be noted that the “circulating load” and “primary cyclone feed” streams for the two-stage circuit contained, respectively, only 66.0% and 64.5% magnetite, compared to 89.2% and 82.0% magnetite for the corresponding streams in the single-stage closed grinding circuit. This shows that the two-stage open/closed grinding circuit was removing the near-size magnetite from the circulating load and diverting it to the open-circuit mill feed for removal from the circuit.

DESIGN OF IRON ORE COMMINUTION CIRCUITS TO MINIMIZE OVERGRINDING

319

TABLE 2 Solids flow rates and percent magnetite of process streams in the simulated two-stage open/closed grinding circuit, as compared to the two single-stage closed grinding circuits that it would replace Process Stream

Circuit feed Circulating load Primary cyclone feed Open-circuit mill feed Primary cyclone overflow

Pair of Single-Stage Closed Grinding Circuits

Two-Stage Open/Closed Grinding Circuit

240 tph solids 63.9% magnetite 606 tph solids (253%) 89.2% magnetite 846 tph solids 82.0% magnetite —

360 tph solids 63.9% magnetite 153 tph solids (42.5%) 66.0% magnetite 513 tph solids 64.5% magnetite 81 tph solids 86.5% magnetite 273 tph solids 58.4% magnetite

240 tph solids 63.8% magnetite

CONCLUSIONS

Overgrinding of valuable minerals is often caused by the tendency of hydrocyclones to retain dense minerals in a closed grinding circuit until they are ground to an excessively fine size. This is a particular problem for iron ore concentrators, where a large fraction of the mass of the ore consists of the higher-density iron oxide minerals. The classical solution to this problem is to use screens for product size control rather than classifiers, but this is not practical when the target size is very fine due to limited screen capacity and high maintenance costs. Simulations of a magnetite ore grinding circuit indicated that a reconfiguration of the circuit could greatly reduce the overgrinding problem. The use of two-stage hydrocycloning can concentrate the near-size high-density magnetite particles into a closely sized single stream that requires only a very small amount of grinding to reach the target size. Open-circuit grinding of this stream is predicted to preferentially grind the coarsest particles, leaving a product that has the necessary size distribution to be a finished project. This introduction of open-circuit grinding greatly reduced the circulating load of the grinding circuit (from 253% to only 42.5%) because the fine magnetite was no longer being continuously returned to the mill for repeated regrinding. The simulations indicated that this change would increase the circuit capacity by as much as 50% while still making the target grind specification. ACKNOWLEDGMENTS

This project was partially supported by the U.S. Department of Energy under Grant No. DE-FC26-01NT41062. The support of the Cleveland-Cliffs Iron Co. is also gratefully acknowledged. The authors would also like to thank Ted Weldum, Todd Davis, Gary Rajala, and Ron Mariani for their considerable advice and assistance in carrying out this work, and B.K. Mishra of IIT for his useful suggestions. Parameters for the pebble mill simulation model were determined by H.J. Walqui and J.G. Jelsma. REFERENCES

ASTM (American Society for Testing and Materials). 2001. Standard test methods for determination of iron in iron ores and related materials by dichromate titration. In Annual Book of ASTM Standards. Standard Designation E246-01. West Conshohocken, PA: ASTM International.

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Austin, L.G., J.M. Menacho, and F. Pearcy. 1987. A general model for semi-autogenous and autogenous milling. Pages 107–126 in Proceedings of APCOM 1987. Volume 2. Johannesburg: South African Institute of Mining and Metallurgy. BRGM. 2004. USIM PAC 3.0 Unit Operation Model Guide. Version 3.0.7.0. Caspeo, 3 Avenue Claude Guillemin—BP 6009, 45060 Orleans Cedex 2, France. Dahlstrom, D.A., and W.P. Kam. 1987. Potential energy savings in comminution by twostage classification. International Journal of Mineral Processing 22(1–4):239–250. Hukki, R.T., J. Karhunen, and R. Lindsberg. 1977. Research on two-stage classification. Zement-Kalk-Gips 30(7):314–22. Kinneberg, D.J., and J.A. Herbst. 1984. A comparison of linear and nonlinear models for open-circuit ball mill grinding. International Journal of Mineral Processing 13:143–165. Peterson, R.D., and J.A. Herbst. 1984. Effects of two-stage hydrocyclone classification on mineral processing plant performance. Canadian Metallurgical Quarterly 23(4): 383–391. Plitt, A.J. 1976. A mathematical model of the hydrocyclone classifier. CIM Bulletin 69 776:115–123. Teke, E., M. Yekler, U. Ulusoy, and M. Canbazoglu. 2002. Kinetics of dry grinding of industrial minerals: Calcite and barite. International Journal of Mineral Processing 67:29–42.

Evaluation of Larger-Diameter Hydrocyclone Performance in a Desliming Application J.J. Campbell,* R. Zhu,* J.M. Young,* and P.T. Nielsen*

ABSTRACT

The drive for continuous improvement and lower operating and capital costs for mineral processing operations is of increasing importance to industry. Therefore, an assessment of the feasibility of using larger-diameter hydrocyclones in fine ore desliming applications was conducted. The work focused on developing and implementing a systematic methodology for comparing the performance of a standard-diameter (100 mm) and a larger-diameter (250 mm) hydrocyclone in a desliming application. The results show that in terms of the performance criteria, similar metallurgical performance was obtained from the larger-diameter hydrocyclone compared with a standard-diameter unit but at significantly higher throughput. The results indicate that the larger-diameter units would be suitable in this application and should lead to simpler and more cost-effective desliming circuit performance. INTRODUCTION

Previous investigations of hydrocyclones in classification applications looked at the influence of vortex finders and spigot sizes (Chu, Chen, and Lee 2000, 2001), cylindrical height (Kraipech et al. 2002), viscosity and pulp density (Kawatra, Bakshi, and Rusesky 1996), and hydrocyclone diameter coupled with other parameter changes (Lynch and Rao 1975). In this work, a wide-ranging test program was conducted to establish the optimum conditions for primary and secondary hydrocyclone desliming of a fine iron ore. This ore contained high proportions of gangue components in the finer fractions (<10 Pm). Desliming processes separate the fine fractions to the overflow and provide products with higher iron and lower gangue content at minimal loss of iron units. A range of hydrocyclone types were assessed at the standard diameter (100 mm), and tests were also conducted to compare the performance of a larger-diameter (250 mm) unit against the optimum standard-diameter performance. The standard-diameter unit is in current industrial use for the desliming processes. There was interest in whether the diameter of the hydrocyclone could be enlarged to increase throughput without signficant detriment to performance. This paper presents the performance comparisons between standard- and larger-diameter units for both primary and secondary hydrocyclone desliming. The purpose of the program was to obtain actual operating data, as * CSIRO Minerals, Kenmore, Queensland, Australia 321

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opposed to results from simulations, to allow an objective assessment of both operational and metallurgical performances. The ultimate outcome of the work was to assess whether the larger-diameter unit was appropriate in this application. EXPERIMENTAL APPROACH

Feed Preparation

A bulk sample of –0.5-mm iron ore was used for the testwork. Representative splits (from a rotary splitter) of the feed were used to conduct the various test runs. Hydrocyclone Rig and Sampling System

The key to accurate assessment of hydrocyclone performance is high-quality sampling. To ensure this, CSIRO designed a purpose-built, fully transportable, computer-controlled hydrocyclone rig (Figure 1) with on-line monitoring and control of process parameters. A notable feature of the rig is a special splitter box that collects simultaneous cuts of the hydrocyclone underflow (U/F) and overflow (O/F) streams (Figure 2). Test Conditions

The objective of the hydrocyclone testwork was to determine appropriate operating conditions that achieved target performance, which were defined as ƒ Corrected cut point of d10 Pm ƒ High-quality separation, as evidenced by a low partition imperfection (<0.5) ƒ Hydrocyclone U/F density of >55% solids by weight ƒ High mass recovery to underflow (>85%) ƒ High throughput

The experimental approach was to test each variable in turn while the others were held constant. The variables tested were ƒ Hydrocyclone type and design ƒ Vortex finder and spigot sizes ƒ Hydrocylone pressure ƒ Feed density

Hydrocyclone Type and Design. A key aim of the testwork was to quantify the comparative performance of different types of hydrocyclones (Types 1 and 2). Type 1 is currently used at a number of Australian iron ore operations and was nominally a shortcone design of the standard 100-mm diameter (Figure 3). However, it did have the option of adding an extra cylindrical section to increase body length, which was in place for all test results reported in this paper. The Type 2 unit was a standard-diameter longcone design. For comparison to the larger scale, the two different types were available with a 250-mm diameter (Figure 4), and a similar program of tests were conducted on these units. Vortex Finder and Spigot Sizes. The project assessed the performance of various vortex finder and spigot combinations to quantify the effect of the changes on cut-point, imperfection, and capacity. However, in this paper, the only results examined are from tests conducted when the vortex-finder-to-spigot-area ratio was kept constant at approximately 2.5, because this ratio corresponded most closely to the performance criteria (particularly that of the d50c). This ratio was determined from the Plitt (1976) formula: 0.46

d 50c = 14.8D c

0.6

1.21

Di Do

0.71 0.38

exp  0.063V e  D u

h

Q

0.45

S – L

0.5



(EQ 1)

LARGER-DIAMETER HYDROCYCLONE PERFORMANCE IN A DESLIMING APPLICATION

323

Hydrocyclone

Sample Cutters

Control Room

Feed Tank

FIGURE 1

CSIRO hydrocyclone test rig

Q = 0.021P

0.56

0.21

Dc

0.53 0.16

Di

h

2

2 0.49

 Du + Do

e  exp  0.0031V

(EQ 2)

where d50c = corrected d50 (Pm) Dc, Di, Do, Du = internal diameters of the hydrocyclone, inlet, vortex finder, and spigot, respectively (cm) V = volumetric percentage solids in the feed h = distance from the bottom of the vortex finder to the top of the spigot (cm) Q = flow rate of the feed slurry (m3/hr) S = density of solids (t/m3) L = density of liquid (t/m3) P = pressure (kPa) Hydrocyclone Pressure. Previous testing and commissioning testwork at CSIRO on the hydrocyclone rig on similar samples indicated hydrocyclone pressures around 180 kPa would be required to achieve target performance in this application. In this program, three operating pressures were used from 120 to 240 kPa. The wide pressure

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Hydrocyclone Discharge

Pneumatic Rams

Sample Containers Sample Cutters

FIGURE 2

Sampling rams and cutters

range was chosen to quantify performance over a range that simulated a plant being required to operate at significantly variable tonnages. Feed Density. Following a range of preliminary tests, it became evident that at feed pulp densities of less than 20% solids, the U/F density could only reach approximately 40% solids. Hence, the feed pulp densities of 25%, 30%, and 35% solids were tested so that an acceptable U/F density could be achieved and an optimum determined by interpolation. Feed densities higher than 35% solids would achieve the target U/F density; however, the Plitt calculation indicated that performance in terms of cut size and imperfection would fail to achieve target levels. The feed density was measured on-line using an Amdel nucleonic density gauge with manual cross-checks conducted using a Marcy scale. Measurements were also made on all samples by calculating the feed density from wet and dry sample weights. Analysis Procedures

Samples collected during the test program were sized and prepared for further analysis according to the following processing procedures. Feed and U/F samples: ƒ Wet screening at 38 Pm ƒ Dry screening of the +38-Pm fractions into a root-two size series using a Ro-Tap

sieve shaker ƒ Laser sizing of the –38-Pm fractions

Laser sizing was used for each O/F sample. In order to speed up the sizing analysis process, laser sizings were used for the –38-Pm fractions of all test products. Cyclosizing of –38-Pm fractions was only used when samples were required for assay and image analysis. The laser sizer made the assumption that all particles were spherical, and therefore calculated the particle-size distribution on that basis. When the material was examined under a light microscope, the majority of the particles had elongated shapes. Therefore,

LARGER-DIAMETER HYDROCYCLONE PERFORMANCE IN A DESLIMING APPLICATION

325

Ø61

Ø40 260

Ø100 Ø240 145

Ø62

255

Ø98 Ø256 320

250 Ø143

Ø98

360

200

Ø114

Ø47

360 405 Ø75

360 Ø25

Ø38

FIGURE 3 Schematic of the Type 1 100-mm hydrocyclone (not to scale; dimensions in mm)

FIGURE 4 Schematic of the Type 2 250-mm hydrocyclone (not to scale; dimensions in mm)

the spherical size distribution obtained from the laser sizer was “converted” to a cylindrical shape with an aspect ratio of 2:1. This correction also ensured that when the sizing results from screening and laser sizer were combined for the feed and U/F samples, no discontinuity in the curve was present. This correction was used for all laser-sized results. The sizing correction of a typical result is shown in Figure 5. RESULTS

Quality of Separation

The basis for comparing the separation efficiency in this work is the separation imperfection (I) given by I = (d75c – d25c) / 2 u d50c

(EQ 3)

where the d75c, d25c, and d50c are the corrected d75, d25, and d50 (in Pm), respectively.

326

ADVANCES IN COMMINUTION

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100

Cumulative % Passing

10

1

Screen Laser Corrected

0.1

0.0 0.1

1

10

100

1,000

Size, mm

FIGURE 5

Comparison of original and corrected sizing results

Table 1 shows that the data from the initial tests on each hydrocyclone revealed that the Type 2 hydrocyclone would satisfy the separation efficiency criteria, which were a partition imperfection of less than 0.5 and a cut-point d50c of approximately 10 Pm. The larger-diameter Type 1 hydrocyclone performed well in terms of separation efficiency but at some cost to capacity, as will be shown later. However, the smaller-diameter Type 1 unit struggled to achieve the criteria in terms of cut-point. Lower feed density lowered the cut-point to the desirable range; however, this resulted in borderline U/F density (55.6% solids) and unacceptably high imperfections (0.56). Hydrocyclone U/F Density

The intentional similarity of vortex finder–spigot area ratios across the various hydrocyclone types allowed feed density to be the primary influence on hydrocyclone U/F density. Figure 6 shows a typical result of the effect of feed density on U/F density. Feed densities >30% solids were required to produce the target U/F density of >55% solids. Pressure variation had little influence on U/F density. Table 2 shows the typical U/F densities produced by different hydrocyclones at the same feed density. Note that both of the Type 1 hydrocyclones produced higher U/F densities than the Type 2s at equivalent conditions. Mass Recovery to Underflow

Table 2 also shows that mass recoveries to underflow were somewhat different for the different units, indicating the influence of hydrocyclone geometry (long cylinder versus long cone). Across the pressure range tested, only the standard-diameter Type 1 hydrocyclone failed to achieve the target recovery. Also notable was the performance of the standarddiameter Type 2 unit, which exhibited mass recoveries to underflow of around 90%.

LARGER-DIAMETER HYDROCYCLONE PERFORMANCE IN A DESLIMING APPLICATION

327

Typical separation performance

TABLE 1

Type (diameter)

VF,* mm

Sp,* mm

Press, kPa

Density, %

I

d50c

1 (100 mm) 2 (100 mm) 1 (250 mm) 2 (250 mm)

40 41 60 61

25 26 40 38

180 180 180 180

30 30 30 30

0.50 0.38 0.28 0.41

12.57 9.74 10.61 10.73

* VF = vortex finder; Sp = spigot diameter.

70 35% Solids Primary 30% Solids Primary 25% Solids Primary 65

U/F Density, % Solids

60

55

50

45

40 100

150

200

250

Pressure, kPa

FIGURE 6

TABLE 2

Hydrocyclone pressure versus U/F density

U/F density and mass recoveries to underflow for each make (feed density 30% w/w)

Type (Diameter)

Pressure, kPa

VF, mm

Sp, mm

U/F density, % w/w

Mass Recovery to Underflow, %

1 (100 mm)

120 180 240 120 180 240 120 180 240 120 180 240

40 40 40 41 41 41 60 60 60 61 61 61

25 25 25 26 26 26 40 40 40 38 38 38

56.59 60.62 60.99 55.08 53.74 52.38 60.42 60.48 60.38 56.10 54.77 56.89

83.46 79.74 82.91 90.33 90.83 91.04 85.55 84.05 84.32 84.77 82.61 85.09

2 (100 mm)

1 (250 mm)

2 (250 mm)

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ADVANCES IN COMMINUTION

TABLE 3

MILL DESIGN

Change in cut-point with pressure (30 wt % solids)

Type (Diameter)

Pressure, kPa

VF, mm

Sp, mm

Area Ratio

d50c

1 (100 mm)

120 180 240 120 180 240 120 180 240 120 180 240

40 40 40 41 41 41 60 60 60 61 61 61

25 25 25 26 26 26 40 40 40 38 38 38

2.56 2.56 2.56 2.49 2.49 2.49 2.25 2.25 2.25 2.58 2.58 2.58

12.90 12.57 10.83 9.98 9.74 9.26 11.74 10.61 9.52 11.23 10.73 9.46

2 (100 mm)

1 (250 mm)

2 (250 mm)

Cut-point d50c

As with tests manipulating the feed density, the vortex finder–spigot area ratio was held as constant as possible to highlight the effects of different pressures on the measured cut-point. In all cases, the corrected cut-point decreased as pressure increased. However, the impact of the shorter cone length for the 100-mm-diameter Type 1 was evident in that it failed to achieve the target cut-point of 10 Pm at any of the pressure settings tested. Both makes of 250-mm-diameter hydrocyclones achieved the target within the pressure range tested. Table 3 shows typical results for each unit. Hydrocyclone Throughput/Flow Rate

It was expected that the hydrocyclone flow rate and, hence, throughput would increase with increased hydrocyclone diameter. Table 4 shows that this was true. However, there are higher reported flow rates for the Type 2 units compared with the Type 1 units of the same diameter. This result quantifies the extra capacity of the long-cone units. As expected, Figure 7 shows that the differences in flow rate translated into similar differences in dry throughput as a function of pressure. The results presented in Table 4 and Figure 7 highlight some interesting differences among the hydrocyclones types. As noted earlier, the 100-mm Type 1 hydrocyclone was a long-cylinder unit, whereas the 100-mm Type 2 unit was a long-cone unit. Note that while the intention with the additional cylinder length in the Type 1 unit was to provide similar capacity to a long-cone unit, the results show that the long-cone unit achieved consistently higher flow rate and throughputs at equivalent conditions. The contrast is even more dramatic for the larger-diameter units. It is important to note that the 250-mm Type 1 unit was not fitted with the extra cylinder, so it was of a conventional short-cone design. Clearly, the results on the 250-mm-diameter units show the substantially higher capacity for the long-cone unit. Secondary hydrocycloning tests were also conducted for both types of hydrocyclones using primary hydrocyclone underflow as feed, and the trends in the results were consistent with those described above. A final comparison was conducted at optimum conditions for secondary hydrocycloning. In terms of the cone length, given that only the Type 2 hydrocyclones were directly comparable, it is this comparison that is shown in Table 5. Clearly, both units satisfy all criteria for this assessment; however, in all measures, it is the larger-diameter unit that provided superior performance.

LARGER-DIAMETER HYDROCYCLONE PERFORMANCE IN A DESLIMING APPLICATION

329

Flow rates for different operating pressures (30 wt % solids)

TABLE 4

Type (Diameter)

VF, mm

Sp, mm

Pressure, kPa

Flow Rate, L/sec

1 (100 mm)

40 40 40 41 41 41 60 60 60 61 61 61

25 25 25 26 26 26 40 40 40 38 38 38

120 180 240 120 180 240 120 180 240 120 180 240

3.94 5.04 6.19 4.34 6.56 7.79 11.30 15.50 19.12 14.40 18.20 22.74

2 (100 mm)

1 (250 mm)

2 (250 mm)

40

35

Throughput, tph

30

250-mm Type 2 250-mm Type 1 100-mm Type 2 100-mm Type 1

25 20 15

10 5 0 100

120

140

160

180

200

220

240

260

Pressure, kPa

FIGURE 7

Throughput performance for the units tested

TABLE 5 Comparison of the performance of the Type 2 hydrocyclones (secondary hydrocyclone optimum) Performance Characteristics

Pressure, kPa Feed density, % I Dry throughput, tph U/F density, % Recovery to underflow, % d50c , mm

Type 2 (100 mm) VF 41 mm, Sp 26 mm

Type 2 (250 mm) VF 61 mm, Sp 38 mm

180 33 0.37 10.2 56 88 10.1

180 33 0.34 32.4 65 93 8.1

330

ADVANCES IN COMMINUTION

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CONCLUSIONS

The results achieved in this assessment demonstrate that larger-diameter hydrocyclones may be used in fine desliming applications provided that careful attention is paid to setting appropriate operating conditions. In this work, the performance of larger-diameter (250 mm) units at least equaled—and in the optimum secondary hydrocycloning case, exceeded—that of the smaller-diameter (100 mm) standard unit in terms of the performance criteria, namely corrected cut-point of d10 Pm; high-quality separation, as evidenced by a low partition imperfection (<0.5); hydrocyclone U/F density of >55% solids by weight; high mass recovery to underflow (>85%); and high throughput/capacity. These results illustrate the opportunity to realize significant potential gains in circuit capacity, lower circuit footprint, and simpler operating configuration, and hence, lower costs with no loss of metallurgical performance by the use of larger and fewer hydrocyclones in this application. REFERENCES

Chu, L-Y., M-W. Chen, and X-L. Lee. 2000. Effect of structural modification on hydrocyclone performance. Separation and Purification Technology 21:71–86. ———. 2001. Effects of geometric and operating parameters and feed characters on the motion of solid particles in hydrocyclones. Separation and Purification Technology 26:237–246. Kawatra, S.K., A.K. Bakshi, and M.T. Rusesky. 1996. Effect of viscosity on the cut (d50) size of hydrocyclone classifiers. Minerals Engineering 9(8):881–891. Kraipech, W., W. Chen, F.J. Parma, and T. Dyakowski. 2002. Modelling the fish-hook effect of the flow within hydrocyclones. International Journal of Mineral Processing 66:49–65. Lynch, A.J., and T.C. Rao. 1975. Modelling and scale-up of hydrocyclone classifiers. Pages 9–25 in Proceedings 11th International Mineral Processing Congress, Cagliari, Italy. Plitt, L.R. 1976. A mathematical model of the hydrocyclone classifier. CIM Bulletin 69:114.

Selection and Design of Mill Liners Malcolm Powell,* Ian Smit,† Peter Radziszewski,‡ Paul Cleary,§ Bruce Rattray,** Klas-Goran Eriksson,†† and Leon Schaeffer‡‡

ABSTRACT

Dramatic shortcomings of mill liner designs, especially of large semiautogenous grinding (SAG) mills—such as rapid failure, mill shell damage arising from the charge impacting directly on the liner, and unsuitable spacing of lifter bars yielding unfavourable compromises between lifter bar height and liner life — highlight the significance of correct mill liner selection. Liners protect the mill shell from wear and transfer energy to the grinding charge. A careful balance is required to optimise these conflicting requirements. This review serves to highlight these problems and addresses logical and often inexpensive resolutions by considering charge trajectories and liner spacing criteria, in conjunction with liner wear monitoring. An overview of the principal types and materials of liner construction is given, with a focus on liner design based on the best technology available, combined with experience and logical engineering practice. Methods of monitoring the progressive wear of liners and their relation to the performance of the mill are presented. The value of wear monitoring in ongoing liner optimisation and cost saving, through balancing the longevity of the lifters and shell plates and providing reliable comparative data for testing different liner materials and designs, is explained. Wear-testing techniques and their drawbacks and limitations are discussed, along with new tests that are under development. The contribution of advanced computation techniques, such as the Discrete Element Method (DEM), to predict the wear profiles of liners and integrate this information into optimising the overall performance of the mill from a production and cost perspective are considered in some detail. This takes into account the change of the charge trajectories, energy transfer, and milling efficiency as the mill liner wears and the profile changes. It is hoped that this review will enable mill operators to select suitable mill liners, with a view toward decreasing production costs while maintaining mill performance near optimal levels. INTRODUCTION

Poor liner design has a detrimental effect on milling performance and on liner life (Powell 1991a), which can result in a loss of revenue and increased operational costs. Reduced * Mineral Processing Research Unit, University of Cape Town, Cape Town, South Africa † Anglo Research, Johannesburg, South Africa ‡ Department of Mechanical Engineering, McGill University, Montreal, Canada § CSIRO Mathematics and Information Sciences, Clayton, Victoria, Australia ** Castech Solutions, South Fremantle, Perth, Australia †† Mill Linings Systems/Technical Support, Metso Minerals, Ersmark, Sweden ‡‡ Mill Linings, Weir Rubber Engineering, Salt Lake City, Utah 331

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ADVANCES IN COMMINUTION

MILL DESIGN

milling efficiency can cause excess power usage and decreased recovery of valuable minerals. Excess liner wear results in exorbitant liner materials costs and excessive downtime, which reduces mill availability and impacts on plant throughput. For a plant with a number of mills, this also entails the employment of extra mill relining staff and the risks and costs associated with frequent relining. Optimised liner design can be used to strike the best economic balance between liner life and mill grinding performance, thus enhancing the profitability of a mining operation. Protection of the mill shell from the aggressive impacting and abrasive environment inside a mill is the primary purpose of mill liners. Generally, the care of liners came under the maintenance and engineering department, where the objective was to utilise a liner that lasted as long as possible, or was as inexpensive as possible, or, preferably both. Liners were treated merely as a cost overhead and a cause of downtime, and the maintenance approach has been to reduce the cost while remaining within acceptable downtime constraints. Cost savings led to the development of profile liners and lifter bars, as these dramatically increase the life of the liner. The downtime constraints and high stresses in large SAG mills helped to drive the development of greatly improved liner materials. However, this cost-engineering approach ignored the mill performance and overlooked the other key function of mill liners. The second critical function of a liner is to transfer rotary motion of the mill to the grinding media and charge. After all, the liner is the interface between the mill and the grinding charge. Although literature on the grinding action in mills has been published for 100 years (White 1905; Davis 1919), the first publication on the influence of liner design on the charge motion appeared about 70 years later (McIvor 1983). With the advent in the 1980s of larger SAG mills running in single-stream circuits, it became apparent to the operating staff that the liner was having a significant influence on mill performance. This had been hidden previously by the regular changing of liners over a number of mills in the older plants that had many mills in parallel function. In fact, this is generally still the case in the multistream plants, where mill liner design and selection is only tackled on a cost-consumables basis. However, the gains to be had through good liner design and selection are just as great as on the large SAG mills. This paper discusses recognising problems in liner design and selection in existing operations and reviews liner selection for new applications. TY P E S O F L I N E R S

Design and Structure

The design of a liner is driven by the material of construction and the application, and is limited by casting, moulding, and handling constraints. For large mills with wide inlet trunnions in excess of 1.5 m, liner handling machines are now in common use, and this has allowed the evolution of large integral liner blocks, each weighing up to 1.5 t (Figure 1). This holds great advantage for minimising relining time, as there are fewer blocks to handle. For example, at the Kalgoorlie Consolidated Gold Mines (Western Australia), the number of outer head liners in a 36-ft SAG mill was reduced from 36 to 18 pieces, and in doing so, the time to replace them was reduced by 9 hours at a cost-downtime savings of about US$25,000/hr. In this case, the liners sections are 3.5 t each. For smaller mills, the liners have to be handled and installed manually, so smaller blocks with removable lifter bars are generally favoured (Figure 2). Following is a list of the primary types of liners, including comments on their application, advantages, and disadvantages:

SELECTION AND DESIGN OF MILL LINERS

FIGURE 1

Solid steel liners with integral lifter bars

FIGURE 2

Removable lifter bars

333

1. Solid liners: These types of liners have an integral lifter and liner, as shown in

Figure 1. They have fewer pieces and are easier to install, but they tend to have a high scrap weight, as once the lifter section is worn down, liner performance drops and necessitates change-out. 2. Removable lifter: In a liner with a removable lifter, the lifter can be changed

rather than the complete liner (Figure 2), thereby maximising liner life and assisting in manually relined mills. The drawback is that there are more pieces to be installed, and the liners can move during relining. If they are not well secured against the backing liner, the lifter can shift and work loose; this is especially a problem if the bolts begin to stretch. 3. Grid liners: Pocketed grid liners is a system (that appears to be unique to South-

ern Africa) where the grinding media packs in the grid structure and forms an integral part of the liner (Figure 3). Often the liners have a flat profile, suited to the high speeds (85% to 90% of critical) at which most of the older mills operate. These liners have been demonstrated to be economically unbeatable for highly abrasive ores in small- to medium-size mills (Powell 1991a). They are lightweight and make use of the grinding media hardness to provide an effective wear material. They must be manufactured in manganese steel to wedge the steel balls, but the manganese steel spreads on impact and can make removal difficult. Safety

334

ADVANCES IN COMMINUTION

FIGURE 3

MILL DESIGN

Austenitic manganese steel grid liners

FIGURE 4 Single-direction top-hat liners: an integral liner (left), and bidirectional liners with removable lifters (right)

aspects should be considered because of the risk of balls dislodging when the mill is entered for inspection or relining. The liners require a thorough hosing down to prevent this. 4. Wedged liners: Wedged liners were common in the first half of the last century

but are dangerous to install and no longer used. Liner blocks are now wedged in by bolted lifter bars, which allows simple castings of the liner blocks. 5. Integral wave blocks: These are commonly used in ball mills, and the profile of

the liners has become sufficiently sophisticated to enable the liner profile to be maintained as the liner wears. 6. Uni-direction profiled liners: The lifter has different leading and trailing profiles

(Figure 4). The profile can be better customised to suit mill speed and filling and therefore optimise performance. It allows more material in the lifter for a given base width, but the mill must only run in one direction. 7. High–low double-wave ball mill liners: These liners are a refinement of the wave

liner (Figure 5). This was applied to Cadia Hill gold mine through evaluation of their existing wear profile and wear rate, and it provided a more consistent wear profile through the liner’s working life. The correct wave face angle needs to be calculated and applied because an incorrect angle can lead to ball segregation and loss of grind. An indication of our limited ability to accurately “design” liner profiles is that few liners are optimal at original installation or in the post-commissioning set, and it is imperative as a user to vigorously pursue improvement of the design to get the most out of the liners.

SELECTION AND DESIGN OF MILL LINERS

FIGURE 5

335

High–low wave ball mill liner

Materials

The selection of the construction material is a function of the application, abrasivity of ore, size of mill, corrosion environment, size of balls, mill speed, and so forth. Liner design and material of construction are integral and cannot be chosen out of context. Following is a list of the primary materials of construction, including particular uses and strengths. 1. Austenitic manganese steel (AMS): AMS is used for grid liners generally, in

smaller mills. Its great advantage is that it hardens under stress, yet the substrate remains tough and can withstand extreme impacting without fracture. Its primary disadvantage is that it spreads with impact, so solid liners begin to squeeze together and become extremely difficult to remove, and can damage a mill shell if the stress is allowed to build to an extreme level. 2. Low-carbon chrome moly steel (300 to 370 BHN [Brinell hardness number]):

Generally used for mill liners (autogenous grinding [AG], SAG, and ball) prior to the movement to higher-carbon-content steels. It has excellent wear characteristics with some impact resistance and is generally used for discharge grates where slightly better impact resistance is required, compared to the higher carbon chrome moly steels or for thinner section liners. 3. High carbon chrome moly steel (325 to 380 BHN): This steel is now considered

the main material used for SAG mill liners. There are a number of variations with either different carbon or chrome contents. The variations tend to have a bearing on the size of the liner and its section thickness. There is ongoing development within this area as the size of the liners are outstripping the properties provided by the standard high chrome moly steels. 4. Nihard iron (550 BHN): The use of this type of material generally began with rod

mills and ball mills, where impacts were considered low enough for this brittle yet highly abrasive-resistant wear material to perform well. However, it is considered obsolete in light of the use of high chrome irons and chrome moly white iron.

336

ADVANCES IN COMMINUTION

FIGURE 6

MILL DESIGN

Rubber lining in a ball mill and feed head metal-capped lifter

5. High chrome irons (+600 BHN) chromium iron: This iron is considered to have

superior wear-abrasion characteristics, and it is generally used in rod and ball mills. It is more cost-competitive and more brittle than chrome moly white irons. 6. Chrome moly white irons (600 to 700 BHN): This cast material is considered to

be the ultimate and was developed and used to date for abrasion resistance in milling. It is commonly used in cement mills and in some of the largest ball mills in the world, and where performance has not been improved to date. Rubber Liners

The interplay of a material and its configuration are especially significant in rubber liners. During the last half century, rubber mill linings have been used successfully in secondary and regrind milling applications and are specified today for these new applications (Figure 6). However, now with improved materials and computer-aideddesign programs, they are being used more and more in primary grinding applications. In addition to their abrasion resistance, they also are resistant to most chemicals (Schnarr, Schaeffer, and Weinand 2002). The more technical term for rubber is “elastomer.” A good elastomer for a mill liner would have an elongation of 500% to 600%, which means that it can be stretched five to six times its length without damaging it. In addition, the tensile strength should be around 20.68 MPa (3,000 psi). The third important physical characteristic is hardness, and this should be between 55 and 70 durometer on the A scale. The material used for a rubber mill liner usually consists of a blend of a natural and synthetic rubber. In some applications, the material may be all synthetic. The mixture of the rubber and synthetic materials plus various chemicals and fillers is called a “compound.” Each rubber mill-lining manufacturer has their own recipes for their compounds, as well as their own designation. In designing a rubber lining, the same computer tools as described elsewhere in this paper are used. Whether the lining material is metal or rubber, the same type of comminution is required in the charge; therefore, the same simulation tools can be used with some adjustments for the lining material. For maximum life, rubber performs best with a 90˚ impact, so this is taken into consideration when designing. Many improvements in

SELECTION AND DESIGN OF MILL LINERS

FIGURE 7

337

Configurations of metal-capped rubber liners

rubber compounds have been made over the years, but current research and development is providing nanotechnology, which should further improve wear life in the future. Rubber and Steel Composites. Rubber and steel have been used successfully in many applications. In some cases, the rubber and metal can be separate components (i.e., metal lifter bars and rubber plates). During the last two decades more emphasis has been placed on metal-capped rubber lifter bars (Figures 6 and 7). The material used for a metal cap is similar to that used for a metal lining, but a hardened steel plate can also be used. The joining of the metal and rubber has to be with a chemical bond plus a mechanical type of attachment to ensure a positive fastening of the two materials for the life of the component. With the use of computer simulations and careful inspection of the existing wear profile, a greatly improved liner design can be generated. Thus, all high, or high–low, or lower-sloped lifters are recommended for different applications, as illustrated in Figure 7. Rubber is one-seventh the weight of metal, and in many countries the cost is less, so it is very beneficial to utilise rubber wherever possible. By strategically placing the metal cap material with the minimal amount of metal, the best economy can be obtained. Some applications require a metal leading face only. Others require a metal face and top protection (Figure 7). An important feature of combination linings for ball mills is the configuration of the lining, where the lifting action is transferred to the charge, and therefore will remain constant throughout the life of the lining; whereas solid linings will wear more on the lifting portion and become smoother with less lifting action as the lining wears down. The different wear characteristics of the two materials in Skega Poly-Met (Mill Linings Systems, Metso Minerals, Ersmark, Sweden) make it possible to design a lining that will maintain its profile throughout its life, as illustrated in Figure 8. Magnetic Liners

The lining system in magnetic liners consists of permanent magnets embedded in a rubber moulding. The powerful magnets keep the lining in place without liner bolts and ensure that the lining attracts magnetically susceptible material available in the mill (Figure 9). The particles attracted to the surface of the magnetic lining form a thin, continuous layer in a wave profile. The total thickness of the magnetic lining, including the wear layer, is much less than that of a conventional lining. The mill will thus have a larger effective diameter. The lining configuration is ideal for fine grinding, giving an efficient grinding performance in

ADVANCES IN COMMINUTION

MILL DESIGN

90

60

338

FIGURE 8

Designing steel-capped liners for even wear

Homogeneous Bed of Fine Magnetic Material Coarser Bed of Small Pieces of Magnetic Material Fluid Bed of Fine and Coarse Magnetic Material

S

N

N

S Rubber

FIGURE 9

Steel Shell

Permanent Magnet

Magnetic liner (Metso OreBed)

these applications. A combination of the previously described features has resulted in higher throughput (or lower energy consumption) and, in several cases, a lowering of media consumption by at least 10%. Because of the complicated manufacturing process, the magnetic liner elements are much more expensive than conventional rubber lining, but in an ideal application, the wear on the lining is almost negligible and therefore can give years of trouble-free operation. The limitation for this lining concept is that the magnets are not very resistant to impact because they are brittle. They are suitable in mills of t12 ft diameter using maximum 1-in. balls, and in mills d12 ft in diameter using maximum 112-in. balls. Magnetic liners have been utilised successfully in vertical stirred mills. An example of the application of the Metso OreBed lining is at the LKAB Kiruna iron ore operation in Sweden (K. Tano, personal communication, 2005). A test on the primary ball mill showed that the conventional Poly-Met lining slightly outperformed the OreBed lining in terms of a 0.5-tph higher throughput, so the plant remained with PolyMet. However, they installed the OreBed lining in all their pebble mills, where they have successfully operated for more than 10 years without any maintenance or replacement. Figure 10 shows the liner with the coating of magnetite ore and slurry. It was concluded at the site that the magnetic lining works well for secondary grinding, where abrasion is more important than impact.

SELECTION AND DESIGN OF MILL LINERS

FIGURE 10

339

OreBed liner in secondary ball mill, and a single panel

HOW GOOD IS CURRENT DESIGN?

Liner installations have resulted in variable performance, from outstanding to disastrous. This range indicates the potential of good design and application, as well as the potential for poor installations. In this section, a few case studies will highlight this range, what was identified as the cause, and the lessons learned. Good Examples

Two examples of successful liner design applications that highlight key design aspects are as follows: ƒ Cadia Hill gold mine 40-ft SAG mill—reduced rows: The primary objective was to

reduce the packing of material between the existing high–low liner design. A twothirds row design was installed, which allowed for increased spacing between lifters and thus the use of a larger release angle. Packing was eliminated and the mill was able to run at a higher speed, thereby increasing grinding performance and reducing ball breakage. ƒ Codelco Andina 20-ft ball mill—high–low ball mill liners (white iron): The objec-

tive was to increase liner life, thereby increasing plant availability and reducing running costs. The high–low wave profile liner developed at Cadia was installed in chrome moly white iron. The mill operating performance was not hampered, yet liner life increased by more than 50% over the previous sets of double-wave liners that had been in use. Bad Examples

Some disasters with the emphasis on cause, and the lessons learned, are presented: ƒ Large-diameter SAG mill in South America—pulp lifter design: The outer pulp

lifter had not been designed correctly to allow for ease of removal without the need to remove the shell liners adjacent to it. This arose from a lack of knowledge of how relines are carried out and the importance of timely removal during shutdowns. This highlights the need to discuss liner design changes or new concepts with the maintenance crews and reliners so as to detect design retailing flaws.

340

ADVANCES IN COMMINUTION

FIGURE 11

Bolt-hole cracking

FIGURE 12

Heavily dimpled, peened, and cracked liners

MILL DESIGN

ƒ Large ball mill—white iron liners: The existing liner design had always been con-

structed from high carbon chrome moly steel; however, to increase liner life, the move was made to use chrome moly white iron. However, the liners cracked severely during installation. Bolt-hole details had remained unchanged, but on close examination, the bolt-hole profile was found to not be a tight fit with the liner bolt. This allowed pinpoint loading to occur, which acted like a guillotine, cracking the liners down the bolt-hole centre line, as illustrated in Figure 11. This demonstrates the need for a full reevaluation of the liner design, with close attention to fit faces (curves, angles, etc.), clamping face, lifting lugs, and bolt-hole shape when changing liner material. ƒ Dimpled, peened, and cracked SAG liner: Examples of dimpled, peened, and

cracked SAG liners in a 24-ft SAG mill are shown in Figure 12. The mill was found to have the correct lifter profile and filling, but the feed was excessively diluted (to assist in flushing feed through a poorly designed feed chute). From listening carefully to the mill (in the absence of a proper microphone system), it was concluded that the angle of repose of the charge was abnormally steep, resulting in the toe being very low in the mill. The dilute charge also significantly removed the padding influence of the charge contents. The feed chute had to be reconstructed before this problem could be resolved.

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It is difficult to comprehend, given the number of SAG mills in operation globally, that the design of SAG mill liners is still largely troublesome. A number of papers from the SAG 2001 conference (CIM 2001) refer to the following problems: ƒ Candelaria: “Liner design progressed from 72 lifter rail type design, with aggres-

sive face angle, to 36 lifter design with 35 degree face angle. Mill throughput increased by 15%.” ƒ Alumbrera: “Three years worth of trials have been conducted to optimise lifter

geometry. Liner progression from 72 to 48 to 36 rows of lifter bars. Could originally not operate SAG mill at speeds in excess of 70% of critical because of impact on the shell. Operation at reduced speed resulted in low power draw and reduced throughput.” ƒ Los Pelambres: “SAG mill liner progression from 72 rows with 8 degree face angle

to 36 rows with less aggressive 30 degree face angle. Changes allowed for the mills to be operated safely at higher steel loads without increased risk of liner damage. Increased power draw resulted in increased primary mill throughput.” ƒ Collahuasi: “The original SAG mill liner design, Hi-Hi with a 6 degree contact

angle, was changed to a 17 degree angle and later to 30 degree angle. An 11% increase in mill throughput was achieved.” It is common practice to rely on the mill vendor to supply the liner design. This is quite often a contractual requirement with respect to the vendor guaranteeing the performance of the mill. When the mill does not achieve the required throughput rate— because it has to be operated differently from that originally intended in order to prevent liner damage—most vendors appear to adopt a trial-and-error approach, leading to the iterations such as those referred to previously. The net result is a lengthy ramp-up time and loss of production. SYMPTOMS OF POOR LINER DESIGN

When liners are performing to expectations, they are usually left as is. It is usually only when they suffer from premature failure, or come under the cost spotlight, that they are assessed and their performance scrutinised. This section of the paper provides basic guidelines to assessing whether the liners may require reevaluation and identifies possible causes of problems in liners that are known to be problematic. Noisy Mill

A distinct impact rattling indicates that the grinding media is impacting directly on the liner, rather than on the toe of the grinding charge. The consequences of balls impacting on the liner are 1. Greatly accelerated liner wear due to high-energy impacts on the liner. For a 5-m-

diameter mill, these will be in excess of 8 m·s–1; for a 10-m-diameter mill, these exceed 12 m·s–1. This causes high chrome liners to spall and crack, and they may even fracture. This can reduce liner life from a year to less than a few months. Rubber liners can split and tear under these excessive stresses, especially when worn to partial thickness. 2. Reduced milling efficiency from the highest impact collisions occurring against

the liner instead of on the toe of the charge—where effective work can take place 3. Lowered power draw from dilation of the mill charge and the balls returning

energy to the mill shell rather than to the mill charge

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4. Ball fracture from the high-velocity impacts directly onto steel—an impulse force

that many balls cannot withstand. This results in a loss of top-size grinding media and reduced milling efficiency, plus increased ball addition costs. 5. Loosening of liner bolts arising from high stress on the liners stretching the bolts.

The damage consequences of rocks impacting the liner are essentially the same as for ball impact, but the impact forces are lower and less detrimental. Autogenous milling takes place when the larger rocks land on smaller rocks and transfer their large energy to the smaller rocks, which can then be sufficient to fracture them (Napier-Munn et al. 1996). As the high-energy collisions are occurring on the liner rather than on the rocks in the toe of the charge, the milling efficiency is reduced. Mill Listening Devices. It is of great advantage to monitor the sound of impacts on the mill shell to warn of direct impacting. This has recently taken a step beyond simple decibel monitoring to full Fourier analysis of the frequency spectrum in research work conducted at the Julius Kruttschnitt Mineral Research Centre (JKMRC; Pax 2001). Broken Liners

Broken liners can result from media impacting directly on the liner, and this is particularly severe for large AG/SAG mills. A high incidence of fracture of lifter bars without corresponding evidence of porosity or casting faults generally indicates impact breakage. Excessive Liner Wear

If the liners have a low or flat profile, this generally indicates excessive slip of the grinding media on the liner. Consequences of excessive slip are as follows: ƒ Liner wear increases substantially and can show evidence of circumferential

grooving of the lining. ƒ There is a substantial loss of energy transfer to the mill. Although a small fraction

of grinding may take place at the liner–ball interface, a 10% loss in energy due to slip results in about a 10% loss of energy transfer to the grinding media. ƒ Reduced mill throughput results from reduced milling efficiency.

Often a lining wears through a favourable profile regime. This can occur in a number of different manners: ƒ Mill throughput drops markedly when new liners are installed. This can indicate

an unfavourable new profile, or an excessively thick new lining—to counteract excessive wear from poor liner design. ƒ Mill throughput peaks during the liner life, usually at the end of the life of the

liner. This is often a symptom of oversized lifter bars, or lifters with too vertical a face angle. ƒ Mill throughput decreases towards the end of the liner life, and the liner has a

flattened profile—a sign of excessive slip, and the liner should be replaced sooner. An incorrect mill product size can result from the incorrect tumbling action within the mill: ƒ Primary mills require a vigorous action with high-energy impacts to fracture the

ore. If the action is primarily gentle cascading, then a fine product and low throughput would result.

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Rate of Production of Fines for Different Liner Configurations at Two Mill Speeds 0.80 80% 90%

0.78

0.75 0.70 0.71

0.64

0.64

0.55

0.57 0.55

0.60

0.60

70 mm, 90˚

0.60

70 mm, 50˚

Rate, kg/min

0.65

0.56

0.50 0.45

FIGURE 13

40 mm, 50˚

Grids

Smooth

70 mm, 70˚

40 mm, 70˚

Grids

Smooth

0.40

Influence of liner profile on mill performance

ƒ Regrind mills require a cascading action to maximise the frequency of abrasion

interactions. High-energy impacting wastes energy, reduces the rate of abrasion interactions, and reduces the grinding pressure, thus reducing the ability of the mill to produce fines. This can result in a high recirculating load of oversized particles and a reduced mill throughput, as limited by the required product size. P I L O T TE S T S O F T H E I N F L U E N C E O F L I N E R D E S I G N

It can be difficult to assess the influence of liner design upon mill performance in a production environment, as it tends to be a small influence superimposed upon a number of operational variations, especially in semiautogenous milling. Standard pilot tests do not account for the liner design; they use a standard liner profile for all testwork, generally designed to give adequate lift to the charge at standard mill operating conditions—75% of critical speed and 25% filling for autogenous/semiautogenous milling. In this section, a test procedure is presented that can be applied to batch pilot milling. To assess the direct influence of liner design on mill efficiency, a 1.8-m-diameter pilot mill was utilised (Powell and Vermeulen 1994). The use of batch milling meant that reasonable size samples (<2 t) of the ore under consideration could be used to provide a rapid test (a few days) of a number of liner profiles. The mill was operated in batch mode, and the rate of production of final product— minus 75 Pm, in this instance—was measured when the charge size distribution was seasoned and the slurry percent solids was at the equilibrium conditions found in a continuous mill. The results showed a substantial influence of liner profile on the performance of the mill, as illustrated in Figure 13. Differences of up to 30% in the rate of production of fines were measured.

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Protective Strip

MILL DESIGN

Sample Hard Facing

3.00 Relative Life

2.50

Clamping Wedge

1.50 1.00 0.50 Martensitic Manganese Steel Bainitic Manganese Steel

High Cr White Iron

Austenitic Manganese Steel

Mill Shell

Mild Steel

0.00

Clamping Bolt

FIGURE 14

2.00

Wear testing mill and results of relative wear rates

The test results were sensitive to when the sample was taken. The rate of production of fines dropped in time as a normal charge size distribution and slurry density were attained, and this occurred at a different time for each type of liner. In followup work (Powell 1993), the technique was refined to sample during the period when a desired slurry density was reached. The particular exploratory technique described in the works by Powell (1993) can be improved upon in a number of aspects but, nevertheless, showed the clear influence of liner profile on milling efficiency. The test requires direct correlation studies with production mills to provide a quantitative correlation with the influence in a production mill. TE S T I N G L I N E R W E A R R A T E S

Tests used to predict the wear rate of production liners are notoriously inaccurate, to such an extent that they are misleading rather than informative. The fundamental problem besetting all these tests is reproducing the wear modes present in production mills. The contact pressure, rates of relative movement, and abrasive material properties all play a large role in determining the resultant wear rate. A poorly conceived test can easily be in error by an order of magnitude and, additionally, will not rank a range of materials in the correct order. Considering one extreme, a low-pressure sliding abrasion test can invert the ranking of tested materials relative to an application under high impact. A predictive wear test must be tuned to the application; a single standard test cannot possibly predict the liner (or ball) wear for a whole host of very different types and sizes of mills. This is a fundamental problem of the Bond wear test, also known as the Pennsylvania abrasion test. It was established for, and correlated to, a limited range of similar mills yet is now expected to provide meaningful results for large SAG mills, well beyond its scope of application. Near-Field-Condition Testing

Near-field-condition testing attempts to reproduce the overall action and forces encountered in the application. A test developed by Powell (Powell and Cornelius 1992) utilised the same 1.8-m batch mill as used for liner profile testing. This could reasonably simulate the wear modes observed on liners in the 5-m-diameter mills being tested. Small blocks of the material, 200 u 40 u 80 mm, were clamped onto the top of custombuilt lifter bars (Figure 14). A limited, and accurately controlled, surface area was allowed to protrude and be exposed to wear. The rate of wear could then be precisely monitored by progressive mass loss over a period of a test lasting a few days and requiring less than 2 t of ore. The test was not designed to produce an absolute wear rate but

SELECTION AND DESIGN OF MILL LINERS

(a)

345

(b) Fg2 Fg1 Fg3 Fgq–1

Fc3

Fgq Fcp

FIGURE 15

Fc1 Fc2

Fcp–1

(a) Ball charge forces acting on mill liner, and (b) bevelled liner profile wear simulation

rather a relative wear rate against a standard sample—usually the current production liner—used in the test. Once this sample had been calibrated in a production environment, the results could be converted to absolute wear rates. Advantages of this test are ƒ Small samples of test material are required (<1 kg). ƒ Up to six different materials can be tested simultaneously. ƒ Short test period (a few days) ƒ Simple sample geometry (rectangles) ƒ Accurate wear rate figures ƒ Specific to the ore under consideration ƒ Ball load determines the degree and force of impact wear.

Laboratory Tests

As mentioned previously, laboratory tests tend to give misleading results. However, a new test is being developed as part of the AMIRA P9 collaborative research project (Radziszewski 2001). The advance of this work over previous techniques lies in the investigator’s emphasis on duplicating the forces and wear modes found in a production mill. The measurement and isolation of the forces in a mill have long been a stumbling block to this approach, but with the advent of DEM techniques and their application to milling (Mishra and Rajamani 1994a, b; Cleary 1998; Inoue and Okaya 1996; Radziszewski 1986; Radziszewski and Tarasiewicz 1989; Radziszewski and Morrell 1998; Herbst and Nordell 2001; Zhang and Whiten 1998), the tools are now available to mathematically derive the required forces. Radziszewski has utilised this computational capability to guide the design of a comprehensive test that accounts for impact and abrasion, utilising the forces derived from computational mathematical derivations. He also incorporates corrosion, thus addressing the three main known causes of material wear (Rajagopal and et Iwasaki 1992). This test is still in the developmental stage and is currently being expanded from grinding media to liner wear testing. Initial outcomes should be available from Radziszewski by the end of 2006. Background. Charge motion models also can determine the forces acting on mill liners (Figure 15a), which can be used together with wear models to determine liner wear (Figure 15b; Radziszewski and Tarasiewicz 1993; Radziszewski 1997). In the case of liner wear, the main contribution comes from abrasion wear. Abrasive wear, or the volume of material removed, is a function of the applied force, F, and the

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Abrasive Grain 2r

F

θ

Volume Removed

h

Bearing Surface

x

Source: Rabinowicz 1996.

FIGURE 16

Abrasion wear description

distance slid, x, and is described using an abrasive grain represented by angle T, as illustrated in Figure 16. An abrasive wheel is used to simulate this mode of wear. The relationship between wear and energy can be described by Equation 1, where mabr represents metal loss per liner; the energy Eabr is dissipated in grinding on one liner; Hr and Uare metal hardness and density, respectively; and T is the abrasion grain angle (Rabinowicz 1996). tan  T m abr = U ----------------- E abr SH r

(EQ 1)

Coupling an abrasive wear model to the abrasive forces and energies acting on a mill liner is the basis for all DEM liner wear models. The model parameters are back-calculated from operating data of observed liner wear behaviour. These calibrated liner wear models can then be used to simulate the effect of wear on modified liner profiles where the liner material is of the same material as the original. The challenge is to determine these wear parameters from laboratory tests and correlate them to operating data. This will develop the capacity to predict the effect of changes of liner materials on liner wear as well as predict the liner wear in greenfield applications. Abrasion Test Development. The standard abrasion wheel (Figure 17; Misra and Finnie 1980) has been extensively used to investigate abrasive wear under varying conditions, materials, and abrasives. Gore and Gates (1997) first investigated the substitution of the rubber-lined wheel with a steel wheel that used an abrasion force between 45 and 130 N. Radziszewski (1997, 2001) introduced the use of mineral ore as the abrasive. In these initial tests, it was shown that the abrasion grain angle was a function of the applied force. These tests led to the development of a test capable of applying forces up to 1,000 N. The evolving design of the abrasion experiment has incorporated measurement of the torque acting on the abrasion wheel. The net power consumed by the abrasion wheel is the product of the torque acting on the abrasion wheel and the wheel rotation speed expressed in radians per second. The torque can be used to determine the friction coefficient P. Modifying the relationship of Equation 1 to include both the abrasion grain angle function and friction leads to Equation 2. The product PFx describes the energy lost in abrasion or net energy consumed by the abrasion wheel. tan  T  F m abr = U ------------------------- PFx SH r

(EQ 2)

Initial test results confirm the need to generate forces applied in abrasion that approach those found in real mills. Figure 18 shows that the wear rates can be significantly

SELECTION AND DESIGN OF MILL LINERS

347

Abrasive Hopper

½ in. × ½ in. Chlorobutyl Tire

8 in. Dia. Wheel

Abrasive

Weight

Test Specimen

(a) General Set-Up

(b) Initial Test Apparatus

Source: Misra and Finnie 1980.

FIGURE 17

Abrasion wheel set-up

1.0 0.9

Mass Worn, mg/s

0.8 0.7 0.6 0.5 0.4

a-a b-b c-c d-d e-e

0.3 0.2 0.1 0.0 0

500

1,000

1,500

2,000

Energy Rate, J/s

FIGURE 18

Mass worn differences for similar energy rates (1045 steel, Ottawa foundry sand)

different for tests at similar energies—force multiplied by the sliding distance for a given time—but with a range of applied forces that give rise to different energy rates. As the objective is to predict the abrasive wear contributions to liner wear, it becomes important to apply forces representing those found in real mills; hence, the critical importance of linking this to realistic DEM simulations of mill forces. Future Directions. With the evolution of the abrasion test, promising results should contribute to a better understanding of the parameters affecting wear in tumbling mills. Future work should address the contribution of impact wear, both to work hardening of mill liners and media as well as the effects of ore breakage on liner wear. The sophisticated outputs of DEM simulations (discussed elsewhere in this paper), when

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linked with wear experiments that can reproduce the simulated wear modes, is undoubtedly the best available technique for development of a truly predictive wear-testing methodology. Plant Trials

Plant trials can be used effectively to select the liner material and design most suited to an application. They do, however, suffer from a number of drawbacks: ƒ They take a long time—usually more than a year—to yield results. ƒ The tests are expensive—the cost of a set of liners that may or may not perform

well is no trivial matter. ƒ There is downtime involved in installing and monitoring the liners. ƒ Results can be inconclusive as plant conditions vary with time.

Monitoring of the installation and removal masses, and recording dates of individually marked and located liner blocks comprise the best approach for obtaining reliable results. Monitoring liner wear throughout the test is also a vital component to meaningful comparison. Monitoring two identical mills in tandem before and during the test is a useful technique, as used in assessing a mill with a new liner design (Powell 1991a) in which a 5% change in throughput was measured. An alternative method of conducting field trials is to test a number of materials simultaneously in one mill. This gives a direct comparison but requires sensible test design and wear monitoring to provide useful data. Such a trial was conducted by Powell (1991a) and provided conclusive data on the wear life, wear rate, and liner cost per ton milled for six very disparate materials—white iron, high chrome white iron, solid manganese steel, manganese grid liners, rubber, and mild steel. Historic Data. In the absence of a reliable test, production mill wear data from similar applications are possibly the most useful data to use for assessing the wear rates of liners in a new mill. Keep in mind the following points when “looking over the fence”: ƒ The ore must be similar. ƒ The applications must be similar: AG, SAG, total mill load, mill speed. ƒ Obtain data on new and fully worn masses and thicknesses to obtain the actual

wear rates, and compare different materials and sites, which have different fully worn dimensions. INFLUENCE OF LIFTER BAR HEIGHT ON LINER LIFE

It is well known that the height of the lifter bar directly influences the life of the liner block as a whole—the higher the lifter bar, the lower the wear rate of the liner. The tradeoff is in mill production, which drops as the lifter bar height is increased above an optimal height. In assessing the wear of a liner, it is useful to monitor the wear of the backing block relative to the height of the lifter bar. This can be used to assess the useful operating height of the lifter bar. In work conducted on monitoring the wear of liners, this measure provided a direct correlation between lifter height and liner wear (Powell 1991a). This is illustrated in Figure 19, which shows a drop of >40% in liner wear rate when the lifters were renewed from 35 mm to 80 mm in height. This dramatic change clearly showed that the lifters were being left in for too long, and the economy of extending the life of the lifter bars was imposing a more expensive penalty of accelerated wear of the backing liner. The data also show how different materials respond differently to the degree of protection.

SELECTION AND DESIGN OF MILL LINERS

349

200 Mild Steel High-Chromium White Iron White Iron Rubber AMS Grids

Wear Rate, mm/Mt of Feed

180 160 140 120 100 80 60 40 0.0

0.1

0.2

0.3

0.4

0.5

Mass of Feed Treated, Mt

Source: Powell 1991a.

FIGURE 19

Liner wear rate after lifter bar renewal

The onset of accelerated liner wear also can be used to give a reliable indication of when slip of the charge on the liner begins to occur, with the resultant reduction in milling efficiency. For this testwork, the wear rate had risen rapidly during the wear of the first set of lifter bars, levelling out when the lifters were about 50 mm high (0.17 Mt point). A further output of thorough liner wear monitoring is the ability to balance the life of the lifter bar with that of the backing liner. Whether the lifter bar is removable or integral to the liner, this is an essential piece of information in optimising the life and cost of liners. Ideally the lifter bar and backing plate should wear to minimum productivity height and safe thickness simultaneously. This prevents the scrapping of excess unworn liner and losses in mill throughput while the maintenance manager tries to maximise liner life. The technique also can be used to allow for uneven wear along a mill by designing lifters of different heights along the length of the mill, so as to enable a single change-out routine. Monitoring the full profile of a liner as it wears is useful in providing the input for calculating the changing charge trajectories as the profile wears. This information can be used to change the operating window of a mill, such as minimum filling and maximum speed. The trajectories and safe operating window are illustrated, and the monitoring techniques are presented, in the Utilising Charge Trajectory Predictions subsection in this paper. OPTIMISING LINER DESIGN

It is not necessary to select either a long liner life or a high mill throughput; the two can be optimised simultaneously with suitable liner selection. There are a number of tools available for guiding the design of liners so as to help optimise the profile to suit a particular application. The benefits can be substantial, with dramatic changes in liner life, downtime, and liner cost. At the same time, mill productivity can be held around the optimum if the interplay of liner design and mill operation is understood. Tuning liners to an application has many potential benefits: 1. AG/SAG maximises media drop height to maximise impact grinding 2. Ensures a cascading action for regrind mills

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3. Avoids impact on the mill shell 4. Maximises liner life by providing sufficient protection with lifter bars 5. Prevents ball breakage by avoiding impacts directly onto the shell 6. Maximises mill throughput with the correct spacing and height of lifter bars—an

essential factor in liner design 7. Balances liner life and mill throughput with a protective profile of the lining

while retaining the correct charge motion of the grinding media Successful Applications of Improved Liner Design

There are many cases of successful changes to liner designs that have greatly increased the liner life and economy; a few examples follow. At Deelkraal mine of Goldfields Ltd. (Powell 1991a), a wave profile liner in a primary single-stage run-of-mine mill had been modified by placing a 100-mm lifter bar in the recess. This was a poor design option, as the lifter protruded too little and left the main portion of the liner exposed to maximum wear. The liners were replaced with simple flatprofile grids, with 100-mm lifter bars. This increased liner life sevenfold, equating to savings in liner costs of more than R300,000 Rands and downtime of 100 hours per annum. At Kloof gold mine, liner monitoring (Powell 1991a) indicated that the shell backing plate thickness could be reduced to match one liner plate to two sets of lifter bars, and this yielded a 5% improvement in mill throughput. At Rustenburg Platinum Amandelbult Merensky section, closely spaced rows of rectangular lifters in the primary SAG mills were resulting in a loss of mill throughput. The correct lifter face angle was calculated, and the spacing of the lifters was corrected by installing alternating high and low lifters; this design is still in use since installation in 1993. Lifter bars with a low 50˚ face angle were installed over flat grid liners in a primary run-of-mine mill operating at 90% of critical speed at Lindum Reefs gold mine (Powell 1994). This increased liner life more than fivefold while maintaining mill production. At Freeport Indonesia, the new 34-ft SAG mill suffered severe liner wear and obvious impact on the liners. Morrison (R.D. Morrison, personal communication, 2001) examined the problem by applying the MillTraj trajectory equations were used to verify the source of the problem—overly high lifters with almost no relief angle—and to assess a range of alternative configurations. In the short term, Freeport staff overcame the problem by fitting an available set of low–low lifters (Coleman and Veloo 1996). In notable cases (generally unpublished), liner life and mill performance have been dramatically improved once inappropriate liner design has been corrected. U T I L I S I N G O U T E R C H A R G E TR A J E C T O R I E S T O D E S I G N L I N E R P R O F I L E S

A detailed study of the trajectories of the outermost layer of charge in a mill was conducted and used to test a mathematical model of the trajectories relative to lifter bar height and angle (Powell 1991b). Based on this validated theory, the MillTraj software program (supplied by Liner Design Services) was developed for use in conducting design simulations (Powell 2000). The program predicts the trajectory of the outermost layer of charge, which forms the envelope within which the rest of the charge cascades or cataracts downwards. The primary design criterion is to ensure that the media impacts on the toe of the charge rather than on the mill lining. As discussed earlier, direct impacts on the liner are wasted energy and cause accelerated liner wear. By ensuring that the grinding media lands on the toe of the charge, the drop height and energy transfer can be maximised, which is ideal for a SAG mill.

SELECTION AND DESIGN OF MILL LINERS

351

B A

Relative Energy Consumption

Relative Capacity

Capacity

kWh

0

1

2

3

4

Valid for 75% of Nc Range

FIGURE 20

5

6 Proportion A/B

The Skega A/B ratio related to mill capacity and throughput

MillTraj software predicts the likely position of the toe of the charge, even though it is not possible to predict this with great accuracy, as it is heavily dependent upon the type of ore, slurry percent solids, ball filling, and other bulk media properties. Therefore, a 10˚ range is given that forms a safe area to impact upon. The position of the toe is most strongly dependent upon the mill filling, so selection of a suitable liner design must be according to the operating filling range of the mill. The other important design criterion for mill liners is the spacing to height (S/H) ratio of the lifter bars. This is to ensure sufficient wear resistance, while at the same time not allow packing of the charge into a dead area between lifters. This is applicable to AG/SAG mills and primary ball mills; it is less important for secondary ball mills and does not apply to wave linings. The S/H ratio is strongly dependent upon mill speed. Skega developed an empirical formula for this ratio (called A/B), which is still widely used (Moller and Brough 1989). The relationship of mill capacity and power draw to liner spacing is illustrated in Figure 20. The S/H ratio varies as the liner wears, so it should start with a low value and finish with a high value when the liner is replaced; a range of ideal S/H r1 is considered reasonable. If a suitable S/H ratio cannot be achieved with the number of rows of liners, it is sometimes necessary to resort to a high–low liner profile, so as to achieve a quasi wider lifter bar spacing. Utilising Charge Trajectory Predictions

Presenting the results in graphical form best illustrates the influence of liner design. The trajectories are shown as a stream of ball positions at equal time intervals. The trajectories for a range of different liner designs can be simulated and shown as separate ball paths on one plot for direct comparison. The calculated toe position is used as a reference from which to select a suitable liner design.

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ADVANCES IN COMMINUTION

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Lifter Bar Face Angle. The lifter bar face angle is a crucial aspect of liner design and, if neglected, can lead to premature liner failure and loss of mill throughput. The angle is quoted from the base of the lifter, so a rectangular lifter has a face angle of 90˚. Figure 21 shows how trajectories vary with lifter face angle for an 8-m-diameter mill, with 30% charge filling, running at 75% of critical speed. Each trajectory is for a progressively lower angle from 90˚ (rectangular) down to 60˚. The impact point is sensitive to the lifter angle, indicating that this is an important liner design criterion. The position of the toe is shown, and trajectories that impact above this are considered unsuitable. For this application the ideal angle is 65˚, shallower than may otherwise be selected. Lifter Bar Height. The ideal S/H ratio at 75% of the critical speed is 4.0, giving an ideal lifter height of 95 mm. For a ball size of 125 mm, the lifter should not be allowed to wear <60 mm, otherwise slip and accelerated wear begin to occur. If a 170-mm lifter is chosen, the midpoint of the lifter is about 115 mm. The lifter has an increasing rate of wear as it is worn down, so the half-life is likely to be >120 mm. The 95-mm height will be reached after three fourths of the liner life. So for the first half of the liner life, the lifters will be unsuitably high for this speed and spacing. This leads to packing between the lifters in the region from toe to shoulder of the charge, the degree of which is dependent upon the stickiness of the ore, resulting in reduced mill throughput. To span the ideal spacing range, the new height of the lifter should be no more than 125 mm, so alternating rows of high and low lifters would be recommended to ensure a lifter height that is adequate for liner life. High–Low Lifters. In the given example, the new lifters could be 170 mm, and worn low lifters, 90 mm. When the lifters have worn to about 120 mm and 60 mm, the spacing will be in the ideal range. When the high lifters are worn down to 90 mm, the low ones will be down in the sub-40-mm range. If the lifters are removable, then just the alternating rows of worn low lifters can be replaced with high lifters to repeat the cycle. Although this sounds attractive, relining teams generally opt for the easier routine of replacing all the lifters less frequently. For integral liners it is not feasible to replace alternate rows, so a larger scrap mass will result from removing the higher liners that still have a lot of life left in them. The authors contend that the use of high–low lifters is not ideal. Although necessary for many existing applications, new mills should not be designed to require this high– low system but should require even rows of lifters. Mill Drilling. Mill drilling is generally determined by the mill manufacturer on the following conventional formula

rows of drill holes = mill diameter (in ft) u 2

(EQ 3)

or the Skega modification of subtracting 2 from the conventional formula. These relationships were developed more than 20 years ago on much smaller mills than those being installed currently, and the Skega formula already indicated a nonlinear relationship. As mill size has increased, it has been found from practical experience that these formulae are no longer applicable. A far wider spacing is required to ensure optimal mill performance. It is proposed that it is more rigorous to select mill bolt-hole spacing based on liner requirements than upon a mill size formula. The following example illustrates this approach. A lifter bar height and liner shell plate thickness are selected to yield a desired liner life. These height calculations are based on manufacturers’ databases and plant data, or (in the future) proven pilot and laboratory tests. For the current example, the liner supplier may recommend that a lifter wear thickness of 100 mm is required to last a year, with a backing plate wear of 50 mm being sufficient to last the same period of time.

SELECTION AND DESIGN OF MILL LINERS

FIGURE 21

353

Trajectories for different angled lifter bars

For a minimum lifter height of 70 mm, this yields a new height of 170 mm. The base width of the lifter may be recommended as 160 mm to support this height. The average half-life height of the lifters may be about 125 mm, so this is used as the ideal height for calculating lifter spacing. Allowing for the sloping face of the lifter increasing the effective spacing, the ideal number of rows is 36. This is considerably fewer than the 52 rows that would be recommended by the conventional formula. The issue of hole spacing has received considerable attention, and a number of mills have undergone dramatic changes in liner spacing during the past 5 years. For practical purposes of installation without having to redrill the mills, these have gone to fitting two lifters over three bolt holes (i.e., two thirds of the original spacing). Thus, at Cadia the spacing in this 40-ft mill was reduced from 78 rows to 52 (Rattray 2000) after simulation work that included the use of the MillTraj software (Radziszewski and Valery 1999). This has been operating successfully since December 1998, with two liner changes that have included adjustments to the lifter bar angle, from 78˚ down to 60˚ (Hart et al. 2001). These changes have eliminated packing and ball breakage, and have allowed an increase in power draw and throughput. Similar circumstances hold for KCGM, Alcoa, and MIM operations, with all the liners successfully in place for a few years. At the Alumbrera mine, the spacing was increased to every second row, which resulted in a dramatic reduction in liner life, showing that this was too far apart. They then moved to the 2/3 configuration, which has been in place since 2000. These instances illustrate that the simple conventional formula is inadequate. These mills now have a number of lifter rows of 1.3 times the diameter, in feet. These were by force of circumstance, and multipliers in the range of 1.4 to 1.6 seem to be a more appropriate guideline. The wider spacing between lifter bars has given rise to a new problem in some installations. The backing plates have been suffering from peening and spreading, arising from less protection from the lifters, which leaves them exposed to increased impacting. Thus the materials of construction may have to advance with these design changes. Mill Speed. The trajectory of the media is strongly influenced by the mill speed (Figure 22). If this mill had a variable-speed drive, then operating at speeds of more than 75% of critical for the given load of 30% filling would result in direct impacts on the mill

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SAG Mill 8-m Diameter 46 Rows 30% Filling 125-mm Balls

90%

80%

75%

65%

FIGURE 22

70%

Influence of mill speed on ball trajectory

liner. The liner profile can be selected to suit the mill speed, or provide the best compromise for a variable-speed mill. Final Liner Selection. The final liner profile and height selection can be based around the desired operating window of the mill. Figure 23 shows how this was used for a gold mine SAG mill. The lines give the safe upper operating mill speed as a function of lifter bar face angle, for new (215 mm) and fully worn (62 mm) lifters, and for the upper and lower range of mill filling (25% to 30%). Figure 23 shows how the mill operating speed can be increased from 70% up to 80% of critical as the lifter angle wears down from 72˚ to 55˚. Mill Control. Understanding the charge trajectories in a mill can provide control guidelines to mill operators, to keep the mill in the correct operating regime and, possibly, more importantly, out of the undesirable regimes. A control window was set up for an open-pit gold mine (Figure 24). A control rule is especially useful in preventing liner damage in the early stages of mining if soft oxidised ore is received, which results in low loading conditions. A control rule can ensure that the mill speed is lowered, feed rate pushed up, and if necessary the mill stopped to protect the liners. For new high and aggressive liners, it was determined that the maximum speed was 75% of critical for the maximum mill filling. Only when the liners were worn in could the speed be increased, while remaining in a safe operating window. Such a control strategy if implemented at startup of a SAG mill, can prevent the severe liner pounding that the mill liners tend to receive with subsequent liner failures, and even mill damage and major shutdown and repair periods. As absolute load is a function of ball filling for a given mill, filling the derived curves is subject to recalibration, which should be a standard function of mill maintenance.

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85 62 mm, 30% Fill 62 mm, 25% Fill 215 mm, 30% Fill 215 mm, 25% Fill

Mill Speed, % Critical

80

75

70

65 50

55

60

65

70

75

Lifter Angle

FIGURE 23 mill filling

Safe operating window of a mill as a function of speed, lifter angle, lifter height, and

76 75

Safe Maximum

Mill Speed, % Critical

74 73 72 71 Line calibrated at 2% ball charge. 5,385 kW, 267 t, 30.3% filling update calibration if ball load changes indicated by power, load cell, and filling correlation.

70 69 68 67 200

72˚ Lifter 220

240

260

280

300

Load Cell, t

FIGURE 24 Safe operating range as a function of mill speed and filling for an example mill with new high lifters with an aggressive face angle

Summary of Optimising Liner Design

Liners can be tuned to suit the application of each particular mill. A primary input to this is the profile of the liners, which can be selected to provide a suitable grinding action throughout the life of the liner and to enhance liner life. One does not have to select either a good liner life or a high mill throughput; the two can be optimised simultaneously with suitable liner selection. The direct influence of liner design on mill efficiency was studied in a 1.8-m-diameter pilot mill (Powell and Vermeulen 1994), in which a difference of up to 10% in the rate of production of fines was measured. Design guidelines are summarised as follows:

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1. Maximise media drop height for primary AG and SAG to maximise impact grinding. 2. Ensure a cascading action for regrind mills. 3. Avoid impact on the mill shell by ensuring that the balls and rocks land on the

toe of the grinding media. 4. Maximise liner life by providing sufficient protection with lifter bars or an inte-

gral liner profile. 5. Prevent ball breakage by promoting the correct cascading action and avoiding

impacts directly onto the shell. 6. Maximise mill throughput with the correct spacing and height of lifter bars, an

essential factor in liner design. 7. Balance liner life and mill throughput by maximising the protective profile of the

lining while retaining the correct charge motion of the grinding media. F U L L C H A R G E TR A J E C T O R I E S — D E M M O D E L I N G

The Discrete Element Method (DEM) is a numerical tool for modeling the behaviour of discontinuous and particulate systems. The recent advent of affordable high-speed desktop computers has made the simulation of complex systems feasible, and hence the increased interest shown by the mining industry to simulate various applications. The general DEM methodology and its variants are well established and are described in review articles (Campbell 1990; Barker 1994; Walton 1994), and its uses in mineral processing are described by a number of authors (Cleary 1998b; Inoue and Okaya 1996; Mishra and Rajamani 1994b; Powell, McBride, and Govender 2003). The behaviour of the rock and ball charge within a tumbling mill is of express interest, as a fundamental understanding of these systems is hard to gain purely from operational experience and small-scale laboratory experiments. An important aspect is prediction of equipment wear and its effect on process performance. In this section we describe the process of prediction of liner wear using the DEM. Of particular interest for the holistic design of mills is the effect of lifter wear on the performance of a mill and the rate at which this wear occurs. Lifter wear results in the charge motion changing over time. The lifter design needs to take the wear factor into account to ensure that the worn lifter profile produces a reasonable charge motion for the purpose of grinding while still minimising damage to the shell over the lifetime of the lifter. The effect of wear on charge motion can be directly observed using DEM simulations. Consider the series of DEM simulations of a laboratory mill shown in Figure 25; the first three images show the effect of increasing the mill speed on the charge motion. The change in ball trajectories, for a fixed mill speed, from the third image to the fourth image shows the dramatic effect of varying the face angle of the lifter on the charge motion. A 0.5-m slice of a full-size industrial mill is simulated next to demonstrate the capability of the DEM in contributing to greatly improved liner design. An example of a full-mill simulation has been published by Cleary (2004). The mill modeled here is a traditional 36-ft SAG mill running at 78% of critical speed with 72 rows of symmetric, close-packed, steep face-angle lifters (7˚ from the face), loaded to 30% by volume with a 10% ball charge. Representative SAG mill ball and rock size distributions are used—modeled as spheres—and total 185,000 particles of +25 mm.* * The coefficient of restitution used 0.3 for rock–rock collisions, 0.5 for rock–steel collisions, and 0.8 for steel–steel collisions. The friction coefficient used was 0.5 for all materials. Using a standard spring stiffness of 106 gives a timestep of 3.4 u 10–5 s.

SELECTION AND DESIGN OF MILL LINERS

Face Angle = 45˚ Speed = 50% Critical

Face Angle = 45˚ Speed = 70% Critical

Face Angle = 45˚ Speed = 90% Critical

357

Face Angle = 90˚ Speed = 90% Critical

Rendered DEM Snapshot

FIGURE 25

Example of DEM charge motion predictions

(a) Particle Sizes (dark = fines, light = coarse)

FIGURE 26

(b) Particle Velocity (dark = fast, light = slow)

Slice model of a 36-ft SAG mill

Charge Motion

Figure 26 shows two snapshots of the 36-ft SAG mill, with the particles shaded by diameter and velocity. The particles near the mill shell rotate with the liner rotation and at moderate speed from the toe position around and up to the shoulder position. The particles between the lifters are thrown in a high dilute cataracting stream, which impacts on the liner at around the three o’clock position. The cataracting particles accelerate to more than 13 m/s. The impact region of the cataracting stream is well above the toe, even though the mill speed is only 78% of critical. This occurs because the lifters have steep face angles. The majority of the charge avalanches down the steep free surface. The effects of radial segregation are clear with a concentration of fine particles against the mill shell and in the upper part of the cataracting stream. The bulk of the lower part of the cataracting stream consists of larger rocks and balls. Segregation happens to be useful in this scenario, as the balls in the cataracting stream are at least on the shallower trajectories and lead to less damaging impacts with the liner. It should be noted that mill speed is a strong driver in determining the type and severity of segregation.

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Liner Stresses

Stress and wear data are collected on a high-resolution triangular mesh that covers the mill liner. The average element edge length is 20 mm, which is half the size of the smallest particles in the simulation, giving good spatial information about the stress and wear distributions. The contribution of every particle collision with the mill liner is accumulated in the triangular elements in which the collisions occur. These raw data are then aggregated across the depth of the mill slice and spatially smoothed to remove noise on the scale of the particle size. Figure 27 shows a section of the liner shaded by the stress components. These distributions are easier to analyse when presented as a line plot following the surface of the lifter/liner starting from the bottom of the front face, moving up across the top surface and down the back of the lifter, and then finally across the liner plate. Figure 28 shows the normal and shear stress distributions along the liner for the SAG mill simulated in Figure 27. In the plot, each section of the lifter/liner stress is separated by a vertical line. The normal and shear stresses have very similar spatial distributions, but the normal stress is around three times higher than the shear stress. The stress is zero at the base of the lifter (because no particles can make contact with this part of the lifter) and rises steadily along the front of the lifter to a peak occurring near the top corner. This reflects the force transmitted to the front of the lifter as it pushes into and then lifts up the charge. The highest stresses for this new liner actually occur exactly at the corners, but these are not shown in Figure 28 because the magnitudes are much higher and any amount of rounding of the corner by wear will substantially reduce these peaks. The stress along the top of the lifter is relatively constant and is about half the level of that at the top of the face. The stress on the back of the lifter is low, at about half the level of the top of the lifter. This reflects the fact that only a small proportion of the charge is supported by the backs of the lifters. The stress on the liner plate is higher and increases as the front of the next lifter is approached. Note that there are small, well-defined peaks near the front and back of each lifter. These occur 18 mm from the corners and correspond closely to the average radius of the particle when trapped against the lifter. The ability to capture such features demonstrates the spatial accuracy possible using DEM simulation. Liner Wear Distributions

To predict the impact damage on the liner, two measures were used (Cleary 1998a, b). The first was the energy dissipated in the normal direction during collisions between the particles and the liner. The second was a measure of excess kinetic energy of impact. Low-speed collisions (<0.1 m/s), which are large in number but of limited importance for damage, make no contribution to the damage estimateʊbut high-speed collisions do much more damage because of the quadratic dependence on speed. The impact damage measure is shown on the surface of the liner in Figure 29a, and as a line plot in Figure 30 for both impact measures. The distributions are quite different than those of the normal stress distributions. In particular, the wear is substantially higher across the entire top of the lifter, with peaks near the corners. There is little impact damage on either front or back faces because they are protected from the cataracting stream by the steep face angles and close lifter spacing. There is some moderately higher wear on the upper part of the leading face produced when the lifters crash into the charge in the toe region. The wear on the liner plate is peaked in the middle in the plate. This damage is produced by the penetration of the cataracting stream (and particularly balls) between the lifters where they impact the middle of the liner, which is clearly more exposed to impact and so has the highest predicted impact wear rate.

SELECTION AND DESIGN OF MILL LINERS

Normal Stress, N/m2

Shear Stress, N/m2

50,000.0

5,000.0

40,000.0

4,000.0

30,000.0

3,000.0

20,000.0

2,000.0

10,000.0

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(a) Normal Stress

359

(b) Shear Stress

Stress distributions on the SAG liner (dark = high magnitudes; light = low)

FIGURE 27

60,000 50,000 N/m2

40,000 30,000 20,000 10,000 0 0

200

400

600

800

600

800

Distance along Surface, mm (a) Normal Stress, N/m2 20,000

N/m2

15,000 10,000 5,000 0 0

200

400 Distance along Surface, mm (b) Shear Stress, N/m2

FIGURE 28 Normal and shear stresses along the lifter and liner plate. The distance is measured from the base of the lifter front. Each region (lifter front, top, and rear; and finally the liner plate) is separated by a vertical line.

The abrasive wear is also estimated using two measures (Cleary 1998a, b). The first is the shear work, which is the energy dissipated by sliding (tangential) interactions between particles and the liner. The second uses the kinetic energy of each collision with the inclusion of a strong angular dependence. This takes into account the fact that collisions at around 22˚ produce significantly more scouring/abrasion damage than particles sliding directly along the boundary or impacting in the normal direction. Figure 29b

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MILL DESIGN Impact Damage

Abrasion

2,000.0

600.0

1,500.0

450.0

1,000.0

300.0

500.0

150.0

0.0

0.0

(a) Impact Damage

FIGURE 29

(b) Abrasion Damage

Wear distributions on the SAG liner (dark = high magnitudes; light = low)

Joules

1,500

1,000

500

0 0

200

400

600

800

600

800

Distance along Surface, mm (a) Normal Work, J 400

Joules

300 200 100 0 0

200

400 Distance along Surface, mm (b) Impact Damage

FIGURE 30 Impact wear rate along the lifter and liner plate as given by the normal work rate and an impact damage measure

shows the abrasion damage prediction on the surface of the liner and Figure 31 shows both the abrasive wear distributions as line plots. These are, again, both quite different from the stress and impact damage distributions shown previously. The highest abrasive wear occurs on the front face of the lifter with the wear rate increasing with height up the lifter. This wear will lead to steadily increasing lifter face angle (as one would expect). There is also significant abrasive erosion from the top surface of the lifter, which one would expect to lead to steadily decreasing lifter height. The abrasion on the back of the

SELECTION AND DESIGN OF MILL LINERS

361

800 600 400 200 0 0

200

400

600

800

600

800

Distance along Surface, mm

J

(a) Shear Work, J

140 120 100 80 60 40 20 0 0

200

400 Distance along Surface, mm (b) Abrasion

FIGURE 31 Abrasive wear rate along the lifter and liner plate as given by the shear work rate and an angular-dependent abrasion measure

lifter and the liner plate predicted by the shear work is relatively even and is approximately one third of the magnitude on the lifter top. The second abrasion measure gives similar predictions to the shear work for the front and top faces but predicts much lower wear on the liner and the rear face. The lower prediction arises from the much lower weighting given to the many low-speed contacts sliding directly along these surfaces. They dissipate a reasonable amount of energy, but this is likely to be an overestimate, as shown by the second measure. The second measure suggests that the wear will decrease with height down the back face, which is reasonable because most oblique impacts will occur during the filling of the space between lifters as they pass through the toe region. There is a peak in the abrasion in the middle of the liner for similar reasons. The rate of normal work is around double the rate of shear work. This might cause one to conclude that the dominant erosion mechanism is from impact rather than abrasion. The actual erosion rates, however, also must be dependent upon the material properties of the liner and its resistance to impact and abrasion damage. High-quality steel might be expected to be very resistant to impact and erode predominantly by abrasion. The Cleary CSIRO DEM code currently has the capability to evolve the shape of the liner in accordance with the wear rates predicted. However, it is not clear which of these wear rates or which combinations should be used in order to obtain the best quantitative predictions of the wear behaviour. Ultimately, it will be a combination of an impact and an abrasion measure weighted by the resistance of the liner material to each damage mechanism. Effect of Liner Height on Abrasive Wear

Figure 32 shows the rate of abrasive wear (using the shear energy absorption) on the liner of a 36-ft SAG mill as the lifter height is decreased in 50-mm increments. Initially

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(a) 200 mm

(b) 150 mm

Shear Power

Shear Power

1,500.0

1,500.0

1,125.0

1,125.0

750.0

750.0

375.0

375.0

0.0

0.0

(c) 100 mm

(d) 50 mm

Shear Power

Shear Power

1,500.0

1,500.0

1,125.0

1,125.0

750.0

750.0

375.0

375.0

0.0

0.0

FIGURE 32 Rate of shear energy (abrasive wear) on the liner as the lifter height is decreased in 50-mm increments

(for the original 200-mm lifter shown in Figure 32a), the wear is high across the top surface of the lifter with the peak abrasion occurring on the outer parts of the top surface. There is reasonable abrasion on the front face, which decreases with distance down the front face. There is little sign of abrasion on the liner plate, as it is protected by the lifter. This distribution is consistent with the line plot shown in Figure 31. When the lifter height is decreased to 150 mm (Figure 32b) (either as a design change or as a crude representation of the liner wear), there is a significant reduction in the abrasive wear rate on its top surface. The wear is now more concentrated on the front half of the top surface, and the peak abrasion rate is reduced by approximately 25%. There is also a marked reduction in the rate of wear on the front face. The distribution along the front face, though, remains similar with decreasing magnitude as the liner plate is approached. There is little change to the wear on the liner plate. This indicates that the wear rate of the lifters are higher for new 200-mm lifters and decrease once their height has been reduced. When the lifter height is decreased to 100 mm (Figure 32c), there is little change to the abrasive wear pattern or the magnitudes compared to the 150-mm case. The wear on the top surface is still weighted towards the front corner of the lifter, and the magnitude is similar or perhaps slightly lower than for the 150-mm lifter. There is now a small amount of wear observed on the liner plate, with the higher wear concentrated on the right side, just in front of the next lifter. The similarity of the wear for the 100- and 150-mm

SELECTION AND DESIGN OF MILL LINERS

363

cases indicates that the wear behaviour of a liner can be fairly constant throughout the middle parts of the lifter life span. If the lifter height is decreased further to 50 mm (Figure 32d), then there is a sharp change in the abrasive wear patterns and the rate of wear. The abrasion remains highest on the top surface of the lifter and is strongest on the front half of the top surface. The magnitude of the peak wear has risen back to the original level observed for the 200-mm liner. The wear on the liner plate has also increased sharply, with the peak values found immediately before the next advancing lifter at around 40% of the overall maximum wear on the top surface. This means that the 50-mm lifter experiences significantly higher wear than the 100- and 150-mm lifters. This can be understood geometrically because the median size of the rocks in the mill is 50 mm, meaning that half the rocks are now taller than the lifter and the lifter is no longer able to properly lock into and lift the charge. The charge now slides much more readily over the liner, leading to much enhanced abrasive wear on the front face and the front half of the top of the lifter. This behaviour of accelerating wear near the end of the lifter life span is often reported anecdotally and is demonstrated in Figure 19. The effect is both reproducible and explainable using DEM simulation. Summary of DEM Potential

The DEM can be used to predict the charge behaviour and performance of the mill over the life span of the lifter. This allows the liner profile and material to be optimised in a more holistic manner by taking into consideration mill performance and liner cost as an integrated objective function. When linked with a meaningful wear-testing technique that can reproduce the wear modes found in the mill, the DEM can be used to predict liner wear and profile evolution. This can be used for fast-tracking of liner selection, assessing new designs and materials, and deriving an optimal balance of liner life and mill performance. Additionally, the time between relining can be calculated. MILL LINER MANAGEMENT

The lining in a mill serves a dual purpose. It not only protects the shell of the mill from impact and abrasive-related wear, but it also transfers the energy to the charge where it is required for breakage. The performance and the cost-effectiveness of a mill are thus largely dependant on both the design and care of the mill lining. Given that the lining normally constitutes a large portion of the operating cost of the mill, it is not commonplace to keep a spare set of liners on site, as these are seen as a form of “dead capital.” The lead time on procuring a set of liners is also normally in the order of months. Damaging a set of liners can thus be a very expensive exercise when the downtime that could result is taken into consideration. Despite these risks, the importance of proper liner management is often underestimated. The lining in a mill can be damaged severely in the time period between even weekly liner inspections. Most operations only conduct liner inspections on a biweekly to monthly cycle. It is thus very important that mill operators understand and manage risks by conducting proper mill liner inspections and by placing sufficient emphasis on the safe operation of the mill. Liner Wear Measurement

As with most processes, optimisation does not come without measurement. By monitoring the change in the liner profile with time, valuable information regarding the wear rates of the different facets of the lining allow for the refinement of the liner design. Given that the lining in a SAG mill could last for 12 to 18 months, the optimisation of the

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liner profile for a particular mill could take a number of years. A dedicated and ongoing measurement effort is thus required in order to achieve success in this regard. The challenge of obtaining a measure of the profile of a liner is easily overcome with the use of the simple yet highly effective mechanical gauge (Figure 33). By measuring the length of the rods that are displaced when an imprint of the liner profile is taken, it is possible to present the liner wear data graphically. The change to the profile of a lifter bar with time, in a large SAG mill, is shown in Figure 34. An electronic gauge has been developed at the University of Cape Town, capable of measuring six positions along three liners in less than 10 minutes. The data are automatically logged and transferred to a liner profile and wear-monitoring program. PERI Associates supplies an automated electronic gauge driven by a worm-gear motor. Metso has a full mill liner profile gauge, which is inserted down the centre of the mill and within hours can collect a detailed profile along the entire length of the mill. Tools of this nature can be used to collect accurate, reproducible, and reliable data on a regular basis, so as to build up an accurate history of the wear profile of liners. A critical measurement—in addition to the profile—is the liner thickness at each end of the profile, which is used to calculate the absolute liner thickness along the profiles. The measurement of the thickness of the liner plate can present considerable difficulties. One of the authors has been on site where the mill reliners overpredicted the liner life by months, based on incorrect liner thickness estimates. This mistake led to catastrophic failure and extensive mill downtime. For rubber liners, the accepted technique is to hammer a nail through the liner and measure the length of the protruding section. This can be done at the joint between steel liners, but it is slow; it is difficult to find a clear spot in the joints, which are packed with steel slivers and slurry, through which the nail must penetrate. It is all too easy to take incorrect readings, as it is not obvious whether the nail has penetrated to the mill shell. Even careful measurement of internal mill diameter can lead to inaccurate liner thickness calculations, as a small number is being calculated from the difference between two large numbers (diameters inside the shell and inside the liner). An ultrasonic thickness gauge can be used, but its effectiveness is dependent upon the structure of the steel. The signal is seriously attenuated by any porosity, which can result in plausible but incorrect readings, and an expensive high-penetration gauge is required to penetrate 100 mm of steel. Based on the expense and unreliability of this route, it has been deemed unsuitable. In response to this situation, a measurement indicator that is installed with the liners, and is accurate to 1 mm, is being developed at the University of Cape Town. It is best to collect data from a consistent set of liners, and in the same place each time, so as to obtain accurate and consistent wear data. Selecting three rows of liners and taking five to six profiles along each row should be sufficient. Observing the change in the lifter profile over a period of time not only provides an indication as to when to change the direction of rotation of the mill, in the case of a bidirectional mill, but also provides information as to the relative wear rates of the different liner components. It can be seen in Figure 34, for example, that the base section of the liner is wearing at a much lower rate than that of the lifter bar itself. It may therefore be possible to design the next set of liners with a slightly thinner base section that would effectively lead to an increase in mill diameter, which could possibly have a positive effect on mill throughput. Also, by optimising the distribution of the steel across the profile of a liner, by making observations such as those mentioned previously, it is possible to derive the maximum wear benefit out of a casting and to minimise scrap at the end of the life of the lining. This can only be made possible through the implementation of a liner wear measurement program.

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SELECTION AND DESIGN OF MILL LINERS

FIGURE 33

Mill liner profile measurement

32.0 30.0

16-01-2001 05-04-2001 12-04-2001 18-04-2001 09-05-2001 07-06-2001 16-06-2001 21-06-2001 19-07-2001 26-07-2001

28.0 26.0 24.0 22.0

centimeters

20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0

50.0

48.0

46.0

44.0

42.0

40.0

38.0

36.0

34.0

32.0

30.0

28.0

26.0

24.0

22.0

20.0

18.0

16.0

14.0

12.0

8.0

10.0

6.0

4.0

2.0

0.0

–2.0

–2.0

centimeters

FIGURE 34

The changing profile of a lifter bar in a 24-ft-diameter SAG mill

Mill Liner Inspections

It is good practice to schedule mill liner inspections rather than to conduct them on an ad-hoc basis. Other routine mill maintenance, such as cyclone maintenance for example, also can be conducted during this period. When conducting mill liner inspections, it is also important to look for the following: ƒ Signs of cracks in the castings resulting from ball impacts ƒ Raceways or abnormal wear patterns ƒ Signs of damage around liner bolt holes ƒ Edge spreading as a result of impact ƒ Pegging of the discharge grates

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ƒ Presence of freshly broken steel balls ƒ Smallest surviving ball diameter ƒ Shape of the grinding media ƒ Presence of excess steel scats ƒ Loose discharge grates ƒ Loose liner bolts

Cracks in the castings, dimpled impact marks, and peening of liner edges indicate excessive impacting on the liner, as shown in Figure 12. Freshly broken balls are normally indicative of severe ball-on-liner impact. If any of these conditions are observed, it is imperative that the operation of the mill be addressed so as to prevent any further liner damage. Loose liner bolts, normally identified by wet patches on the shell of the mill while it is in operation, are also indicative of shell impacts. Abnormal wear patterns in liners normally suggest abnormal mill operating conditions. The operation of a mill with too dilute a slurry charge, for example, can result in severe slippage between the charge and the lining and lead to accelerated wear. An example of this phenomenon is shown in Figure 35 for a wave-type liner design in a 6-MW ball mill. This mill had been in operation for only a number of weeks. It is good practice during liner inspections to inch the mill periodically in order to obtain a view of all of the liners in the mill. It is not necessary to inspect each liner with a great deal of detail, but it is important to glance over each casting to identify any obvious defects. When measuring liner wear profiles, it is important that the same liners are measured each time that the mill is stopped. LINER DESIGN DETAILING

There are many practical issues that should be taken into consideration when detailing liner design. Seemingly small details in design can be the difference between durability and reliability, and a disastrous liner. Some guidelines for consideration in liner detailing are listed: 1. Understand clearly what the mill operator wants from the mill performance,

durability versus performance considerations, downtime intervals and extent, variability in ore, mill filling, mill speed, ball loading, etc. 2. Discuss potential liner designs with the relining and maintenance crews. Their

input and buy-in can make a significant difference to the performance of a liner. 3. The liner designs must be tailored to the materials liners from which they are to

be manufactured. For example, a high carbon chrome moly steel has different liner design requirements than those of a chrome moly white iron. 4. Proper calculation of lifter wear height versus liner plate thickness is required.

This wear ratio needs to be either known or estimated so as to prevent premature failure of either the lifter or the backing plate; failure to do so would leave a lot of expensive scrap and a reduced liner life. 5. Liner handler capacity and clamping capability must be taken into accountʊthese

control maximum liner mass, size, and the positioning of handling lugs. 6. Consider designing the mill drill pattern to be flexible so as to allow the row spacing

to be varied over a limited range, so that the optimal row spacing can be selected. 7. Allow sufficient (if not more) pulp lifter depth in the liner assembly of AG/SAG mills.

Many of these mills have been found to have inadequate discharge capacity over their full range of operation, especially as throughput is forced up over the years.

SELECTION AND DESIGN OF MILL LINERS

367

FIGURE 35 Raceways and accelerated “pocketing” resulting from the operation of a ball mill with too dilute a slurry charge

8. Design criteria should include ease of removal of worn liners. It should be

assumed that liners could flow together if not protected, and this should be taken into account. 9. It is generally prudent to base designs and materials on known current working

trends. Although it is not necessary to be too conservative, any changes should be properly assessed in light of current experience with operational liner designs and materials. Further insights into design detailing are given by Rattray (Rattray 2000). COMMISSIONING

The commissioning period of a liner often presents abnormal operating conditions for a liner, and this should be taken into account when designing the first set of liners for a new mill, especially a SAG mill. It is often not appreciated by the mill operators that the mill should be kept within a certain window of reasonably normal operation during the commissioning period, so as to prevent damage to, and possible premature failure of, the liners. The challenges facing the commissioning metallurgist often include softer than normal run-of-mine ores, aggressive mill liner profiles, uncalibrated instrumentation/control systems, and inexperienced operators. In addition, the time frame allowed to overcome some of these issues is normally limited, owing to an eagerness/pressure to start producing. The commissioning of SAG mills is thus not without risk, but with proper planning and preparation, the risk can be managed. Feed Preparation

The early stages of the life of an open-pit mine are normally characterised by large volumes of soft overburden or oxide ore. This material is often grade bearing and cannot be discarded. It is important that this is taken into consideration during the design phase of the milling circuit. If it is not possible during the commissioning of the operation to obtain material that is competent enough to establish a load in the SAG mill, it may be necessary to bypass the SAG mill altogether and process this material in the ball mill until such time that the ore competency increases. AngloGold Ashanti’s Morila circuit was started up in this manner with the feed diverted from the SAG mill feed conveyor head pulley to a temporary ball mill feed hopper located some short distance away. Converting back to a two-stage circuit required a few chute changes and was completed in a matter of hours. The circuit was operated in

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this manner for a number of weeks until the competency of the ore increased sufficiently in order to warrant semiautogenous milling. This approach is considered to be good practice in terms of reducing the risk of SAG mill liner damage during commissioning. Safe Operating Window

Identifying the safe operating window with respect to mill filling and speed is a vital part of the commissioning of large-diameter SAG mills. The same applies to the operation of any SAG mill with a new liner profile. It is often assumed that the newly installed liner is capable of catering to the entire speed range of the mill. Experience has shown that often this is not the case, particularly because it is difficult to design a liner profile to accommodate wide speed ranges. Most SAG mills, on commissioning, need to be operated at reduced speeds and higher volumetric fillings than those stipulated in the design specifications. From a charge motion point of view, mill liners are at their most aggressive when newly installed. In most cases, it is not possible to operate the mill within the upper speed region of the mill speed range until such time that the lifters have been subjected to a certain amount of wear. Trajectory studies are very useful in defining the safe operating window of an AG/SAG mill with respect to mill filling and volumetric loading. For example, one such study demonstrated that the speed of a particular 6-m-diameter SAG mill should initially be limited to the 65%–70% of critical speed (Nc) range and that the mill filling should be in the range of 30% to 33%. It was predicted that the operation of the mill at fillings of below 25%, even at the lowest speed setting, would result in direct impact of the charge on the mill shell. This was converted into chord measurement figures, so that the operating staff could relate the operating window directly to their raw measured data (Figure 36). Load Calibration

To control the load in a SAG mill to a known volumetric filling, it is necessary to calibrate some measure of the load mass to that of volumetric filling. The majority of mills are either mounted on load cells or have some measure of slipper pad hydraulic pressure that can be related to the mass of the charge in the mill. The volumetric filling in the mill is measured by “crash-stopping” the mill, locking it out, and measuring the width of the chord along the charge surface, or the height from the charge surface to the “roof” of the mill. The height measurement is a more accurate method of determining the mill filling, and it has been found that an industrial surveying laser distance meter with a rugged, water-resistant casing and 100-m range accurate to 1 mm, is eminently suited to this, allowing quick and accurate height measurements to be taken in any size mill (Figure 37). By observing the indicated load-cell reading, or bearing backpressure, it is possible to determine a relationship between mill volumetric filling and mass or pressure. This relationship is obviously dependant on the bulk density of the material in the mill. As the steel loading in the mill fluctuates over time, it is necessary to calibrate the mass–volume relationship fairly frequently by recording the indicated mass reading and measuring the charge volume during routine mill stoppages. The load calibration curves measured during the commissioning of a 30-ft mill operating without a steel load are shown in Figure 38. The shaded rectangular area indicates the safe operating window for the operation of the mill at 68% of critical speed. The trends shown in Figure 38a contain many data points. It is normally not necessary to obtain as many points to determine the mass–pressure versus volumetric filling relationship. In this particular example, a great deal of signal noise was observed, and hence many points were obtained in order to determine a better average. Figure 38b

SELECTION AND DESIGN OF MILL LINERS

369

790 780 Chord Width along Charge Surface (S)

770 760

S

750 740 S, cm

730 720 Safe Operating Speed 65% Nc

710

Safe Operating Range 65%–70% Nc

Safe 70%–75% Nc

Load Running in Trunnion

700 690 680

Liner Damage Even at Lowest Speed

670 660 650 20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

Volumetric Filling, %

FIGURE 36

Example of defined safe operating window for a 6-m SAG mill with new liners

Laser Tape Measure

Support Pole Resting on Charge

FIGURE 37

Measuring the mill filling with a laser tape measure

shows the relationship for a nonlinear bearing-pressure response, and Figure 38c shows the linear relationship between a load-cell reading and mill filling. Once the mass–pressure versus filling relationship has been obtained, limits should be placed on these to define the safe operating window of the mill. It is important that mill operators gain an understanding of this process, as they will be relied upon to conduct the necessary calibrations in the future.

ADVANCES IN COMMINUTION

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Load Calibration Curves Mass

400 390 380 370 360 350 340 330 320 310 300 290 280 270 260 250 240 230 220

34 32 30 28 26 24 22 20 10.0

Mass Filling Relationship 2

y = –0.0102x + 0.8732x + 13.023

“Mass” Calibration Points

15.0

20.0

800.0

25.0

30.0

35.0

40.0

45.0

% Filling

(b)

AG Mill — Load vs. Filling

700.0 SCADA Mass SCADA Pressure Linear (SCADA Pressure) Linear (SCADA Mass)

600.0 Load, t

Mass (tons) or Pressure (bar)

370

y = 13.549x + 43.284

500.0

400.0

300.0 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Volumetric Filling, %

(c)

(a)

FIGURE 38

200.0 25.0

30.0

35.0

40.0

45.0

50.0

Filling, %

Relating load cell and pad backpressure to mill volumetric filling

A set point for the mill mass is normally then chosen for the operation of the mill. It is good practice to vary the feed rate in accordance with the indicated mill mass in order to maintain this mass set point. This can be accomplished with the use of a properly tuned proportional/integral/derivative (PID) controller, or a system if it is already operational. Operator vigilance is still required to ensure that the mill load is maintained within the safe operating window. It is good practice to define a lower mass limit and to incorporate this into an alarm function in the control software. Some operators apply a rule/interlock in the software that automatically stops the mill should the lower load limit be breached for a certain period of time. This prevents liner damage if there are problems associated with the delivery of feed to the mill, as in the case of a blocked feed chute, for example. Using a Power Model

At the time of commissioning a SAG mill, the steel consumption rate is largely an unknown. The equilibrium steel addition rate or the rate that results in an essentially constant steel loading in the mill is normally found through trial and error. The initial steel load is normally known, as this is usually measured out in terms of the numbers of drums of steel required for the intended startup steel load. After only a few hours of operation, the steel load in the mill is likely to change, as the initial steel addition rate is seldom that of the desired equilibrium rate. The main challenge facing the operator is determining what the ongoing steel load in the mill is in order to make decisions regarding the addition rate. This is quite often determined by conducting grind-outs, by stopping the feed and allowing the rock charge to grind out until only the steel load remains. This practice accelerates liner wear and, in the case of large-diameter SAG mills, the chance of damaging the lining is always a concern. A SAG mill power model can be used in the determination of the volumetric steel loading in a mill. By observing the power draw of the mill, prior to crash stopping the mill to measure the charge volume, the steel content can be back-calculated from a model. An example of the relationship between mill power and the steel content of a 30-ft SAG mill, at a total mill volumetric filling of 30%, is shown in Figure 39, derived from the Morrell SAG power model (Morrell 1996a,b). Separate lines are given for a set of mill speeds.

Gross Power, kW

SELECTION AND DESIGN OF MILL LINERS

8,250 8,000 7,750 7,500 7,250 7,000 6,750 6,500 6,250 6,000 5,750 5,500 5,250 5,000 4,750 4,500

371

Increasing Speed

68% Critical 70% Critical 72% Critical 74% Critical 75% Critical 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Steel Load, %

FIGURE 39

Mill power versus steel loading for a 30-ft mill at 30% total volumetric filling

Mill power draw is a strong function of both mill speed and filling. A SAG mill power model can be used to estimate mill filling at a certain speed by comparison of the indicated mill power draw and the prediction of mill power by the model. This is particularly useful when the steel loading in the mill is known, or has already been determined, and is often used during commissioning to verify the load calibration relationship. The estimated filling for the 30-ft SAG mill used in the example, operating with an observed power draw of 5,000 kW and at 74% of critical speed, is slightly more than 30% according to the model prediction. Startup SAG Mill Steel Load

Many operators choose to commission their SAG mills without an initial steel charge to allow for the commissioning and calibration of the necessary systems that are required to control the mill load. This also provides the operators with an opportunity to familiarise themselves with the systems and operate the mill without the threat of liner damage. The throughput of the mill is then ramped up with the addition of the first steel charge, and by knowing the mass of steel being added to the mill, it is possible to calculate the new mass set point that would correspond to the desired total volumetric filling. The set point is then verified by measuring the charge volume in the manner described previously, and the safe operating limits must be adjusted accordingly. Ball Mill Steel Load

Given that the commissioning of the SAG mill may be an incremental affair with respect to the addition of steel to the mill, charging the ball mill to that of the maximum, or even design, operating steel load may initially lead to overgrinding and high steel/liner wear rates. The startup steel load in a ball mill should be at least 20% and should be ramped up fairly rapidly in accordance with the observed circulating load. It is easier to add steel to a ball mill than to remove steel. Observation of the sand load in the mill on crash-stopping the ball mill is also a means of determining whether the optimum steel load has been achieved or not. By dipping a hand or stick through the water layer down to the surface of the balls, the solids level above the balls can be determined. A small solids sand layer of <100 mm above the level of the grinding media should be observed. “Islands” of sand

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in the mill indicate too low a steel charge and will normally be accompanied by a high circulating load and a coarse product grind when the mill is in operation. The steel load in a ball mill should be adjusted to typically maintain a circulating load of between 200% and 300%. Summary of Commissioning Guidelines

A new mill in a new operation with unreliable delivery and often soft oxide ore is at extremely high risk of liner damage, especially cracking and peening, leading to reduced liner life and possible mill damage. More than one mill has been literally split open by heavily peened liners inexorably spreading and forcing the shell apart. This is clearly catastrophic and must be guarded against at all costs. It is therefore necessary to take this information into account in the design and material specifications of the first set of liners. Thus, the initial set can seldom be the final optimised material and design; they need to be tougher, and consequently less wear resistant, and have a conservative liner profile, which also reduces liner life. It is important that the supplier, plant metallurgist, and purchasing department are aware of this, otherwise the plant may continue to order suboptimal liners. Management has been known to use an inferior supplier to provide replacement liners where the supplier mimicked the commissioning set of liners, at a high eventual cost to the plant. The operators also need to be acutely aware of the risk that they expose to the liner and mill if they allow the mill charge to run down. Strict lower limits must be placed on mill load, and the mill must be stopped if feed rate or ore incompetence lead to the mill charge grinding out and exposing the liners to direct impact. Charge trajectory simulations linked to calibration of the load measurement and power draw with mill filling and ball load can provide an effective safe operating window within which the operator can run the mill. D E S I G N TR E N D S

Where is liner design heading, how are liners likely to evolve, and what drives the trends? Customised design that is optimised for the individual site, operation, and ore types will be the emphasis for the future. These will be driven by new techniques (such as rapid laser scanning) used in the measurement of the liner wear pattern and rates. By using the data from these scans and combining them with the power of DEM simulations and realistic wear-testing techniques, liner profiles can be optimised more expertly to provide a more effective and efficient liner profile throughout the life of the liner. There will be a continued shift to the use of larger liner pieces. This will only be limited or directed by the speed and safe installation with the type of liner handler being designed and implemented. CONCLUSIONS

There are many instances of marked improvements in liner life and/or mill performance as a result of liner reconfigurations. In most instances, these appear to be found by trial and error, or in response to a successful change. That such substantial improvements can be gained indicates a deficiency in design and selection of liners, most likely based on poor understanding of their action in the mill. It is considered inadequate to rely on the rule-of-thumb relationships used by suppliers to select lifter bar heights, angles, and spacing. There are sufficient decisive examples in the industry to show that these do not hold out, especially for large SAG mills. It is proposed that the heights of lifter bars should be determined by the size of the grinding media and the desired wear life, balanced against the spacing that gives optimal

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mill performance. The face angles of the lifters can be determined by simulation to give the desired point of impact on the toe of the charge. The final selection of liner profile can be determined to give the widest operating window for the load and speed conditions that the mill is expected to run under. This safe operating window can then be used as an operator guide and can be fine-tuned once the mill is in operation. Sensible and controlled management of new liners, using straightforward techniques that are currently available when commissioning mills, can protect them from damage that can be catastrophic. The sophisticated outputs of DEM simulations, such as charge behaviour, and stresses and forces imparted on liners, when linked with wear experiments that can reproduce the simulated wear modes, is undoubtedly the best available technique for development of a truly predictive wear-testing methodology. The DEM can be used to predict the charge behaviour and performance of the mill over the life span of the lifter. This will allow the liner profile and material to be optimised in a more holistic manner, by taking into consideration mill performance and liner cost as an integrated objective function. BIBLIOGRAPHY

Barker, G.C. 1994. Computer simulations of granular materials. In Granular Matter: An Interdisciplinary Approach. Edited by Anita Mehta. New York: Springer-Verlag. Bird, S., A.E. Lamb, W. Lamb, and D.W. Partridge. 2001. Evolution of SAG mill shell liner design at Kennecott Utah Copper’s Copperton Concentrator. Pages 256–269 in Proceedings International Autogenous and Semiautogenous Grinding Technology 2001, September 30–October 3. Volume III. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Canadian Institute of Mining, Metallurgy and Petroleum. Campbell, C.S. 1990. Rapid granular flows. Annual Review of Fluid Mechanics 22:57–92. CIM (Canadian Institute of Mining, Metallurgy and Petroleum). 2001. Proceedings International Autogenous and Semiautogenous Grinding Technology 2001, September 30– October 3. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Canadian Institute of Mining, Metallurgy and Petroleum. Cleary, P.W. 1998a. Discrete element modelling of industrial granular flow applications. TASK. Quarterly—Scientific Bulletin 2:385–416. ———. 1998b. Predicting charge motion, power draft, segregation, wear and particle breakage in tumbling mills using discrete element methods. Minerals Engineering 11:1061–1080. ———. 2001a. Charge behaviour and power consumption in ball mills: Sensitivity to mill operating conditions, liner geometry and charge composition. International Journal of Mineral Processing 63:79–114. ———. 2001b. Modelling comminution devices using DEM. International Journal for Numerical and Analytical Methods in Geomechanics 25:83–105. ———. 2004. Large scale industrial DEM modelling. Engineering Computations 21:169–204. Cleary, P.W., R. Morrison, and S. Morrell. 2003. Comparison of DEM and experiment for a scale model SAG mill. International Journal of Mineral Processing 68:129–165. Coleman, R., and C. Veloo. 1996. Freeport Indonesia Concentrator expansion. SME Preprint 96–161. Proceedings SME Annual Meeting, Phoenix, AZ, March 11–14. Littleton, CO: SME. Davis, E.W. 1919. Fine crushing in ball mills. AIME Transactions 61:250–296.

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Gore, G.J., and J.D. Gates. 1997. Effect of hardness on three very different forms of wear. WEAR 203–204:544–563. Hart, S., W. Valery, B. Clements, M. Reed, M. Song, and R. Dunne. 2001. Optimisation of the Cadia Hill SAG mill circuit. Pages 11–30 in Proceedings International Autogenous and Semiautogenous Grinding Technology 2001, September 30–October 3. Volume 1. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Canadian Institute of Mining, Metallurgy and Petroleum. Herbst, J.A., and L.K. Nordell. 2001. Optimization of the design of SAG mill internals using high fidelity simulation. Pages 150–164 in Proceedings International Autogenous and Semiautogenous Grinding Technology 2001, September 30–October 3. Volume IV. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Canadian Institute of Mining, Metallurgy and Petroleum. Inoue, T., and K. Okaya. 1996. Grinding mechanism of centrifugal mills—a batch ball mill simulator. International Journal of Mineral Processing 44–45:425–435. Kendrick, M.J., and J.O. Marsden. 2001. Candelaria post expansion evolution of SAG mill liner design and milling performance, 1998 to 2001. Pages 270–287 in Proceedings International Autogenous and Semiautogenous Grinding Technology 2001, September 30–October 3. Volume III. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Canadian Institute of Mining, Metallurgy and Petroleum. McIvor, R.E. 1983. Effects of speed and liner configuration on ball mill performance. Mining Engineering (June): 617–622. Meekell, W., A. Adams, and K. Hanna. Mill liner development at Highland Valley Copper. Pages 224–239 in Proceedings International Autogenous and Semiautogenous Grinding Technology 2001, September 30–October 3. Volume III. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Canadian Institute of Mining, Metallurgy and Petroleum. Mishra, B.K., and R.K. Rajamani. 1994a. Simulation of charge motion in ball mills, Part 1: Experimental verifications. International Journal of Mineral Processing 40:171–186. ———. 1994b. Simulation of charge motion in ball mills, Part 2: Numerical simulations. International Journal of Mineral Processing 40:187–197. Misra, A., and I. Finnie. 1980. A classification of three-body abrasive wear and design of a new tester. WEAR 60:111–121. Moller, T.K., and R. Brough. 1989. Optimising the performance of a rubber-lined mill. Mining Engineering (August): 849–853. Morrell, S. 1996a. Power Draw of wet tumbling mills and its relationship to charge dynamics— Part 1: a continuum approach to mathematical modelling of power draw. Transactions of the Institution of Mining and Metallurgy 105:C43–C53. ———. 1996b. Power Draw of wet tumbling mills and its relationship to charge dynamics—Part 2: an empirical approach to modelling of mill power draw. Transactions of the Institution of Mining and Metallurgy 105:C54–C62. Napier-Munn, T.J., S. Morrell, R.D. Morrison, and T. Kojovic. 1996. Mineral Comminution Circuits—Their Operation and Optimisation. Brisbane, Australia: University of Queensland, JKMRC. Nesbit, P.Q., and H.M. Moys. 1998. Load behaviour in the HiCom nutating mill. Minerals Engineering 10:979–988.

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Pax, R.A. 2001. Non-contact acoustic measurement of in-mill variables of a SAG mill. Pages 386–393 in Proceedings International Autogenous and Semiautogenous Grinding Technology 2001, September 30–October 3. Volume II. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Canadian Institute of Mining, Metallurgy and Petroleum. Powell, M.S. 1991a. The design of rotary-mill liners, and their backing materials. Journal of the South African Institute of Mining and Metallurgy 91(2):63–75. ———. 1991b. The effect of liner design on the motion of the outer grinding media in a rotary mill. International Journal of Mineral Processing 31:163–193. ———. 1993. A study of charge motion in rotary mills, with particular reference to the grinding action. Ph.D. dissertation. Cape Town, South Africa: University of Cape Town. ———. 1994. Lifter bars save costs for Lindum. Mintek Bulletin 77 (October). ———. 2000. MillTraj—liner design software. JKTech Application Papers. Brisbane, Australia: University of Queensland: JKMRC. ———. 2001. Liner selection—a key issue for large SAG mills. Pages 307–322 in Proceedings International Autogenous and Semiautogenous Grinding Technology 2001, September 30– October 3. Volume III. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Canadian Institute of Mining, Metallurgy and Petroleum. Powell, M.S., and F.S. Cornelius. 1992. A test for the realistic simulation of coarse abrasive wear. Prep. Tribology ’92, SAIT, Pretoria, September 15–17. Powell, M.S., A.T. McBride, and I. Govender. 2003. Application of DEM outputs to refining applied SAG mill models. Pages 307–316 in Proceedings of the IMPC 2003 Conference, Cape Town, South Africa, 28 September–3 October. Powell, M.S., and G.N. Nurick. 1996a. A study of charge motion in rotary mills. Part 1: Extension of the theory. Minerals Engineering 9(2):259–268. ———. 1996b. A study of charge motion in rotary mills. Part 2: Experimental work. Minerals Engineering 9(3):343–350. ———. 1996c. A study of charge motion in rotary mills. Part 3: Analysis of results. Minerals Engineering 9(4):399–418. Powell, M.S., and L.A. Vermeulen. 1994. The influence of liner design on the rate of production of fines in a rotary mill. Minerals Engineering 7(2–3):169–183. Rabinowicz, E. 1996. Friction and Wear of Materials. 2nd edition. Toronto, ON: John Wiley & Sons. Radziszewski, P. 1986. Modeling comminution as a function of crushing, tumbling and grinding in a ball mill (in French). Master’s thesis. Quebec, Canada: Universite Laval. ———. 1997. Predictive model for ball mill wear. Canadian Metallurgical Quarterly 36(2):87–93. ———. 2001. Determining impact, abrasive, and corrosive contributions to total media wear. Pages 252–259 in Proceedings International Autogenous and Semiautogenous Grinding Technology 2001, September 30–October 3. Volume IV. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Canadian Institute of Mining, Metallurgy and Petroleum. Radziszewski, P., and S. Morrell. 1998. Fundamental discrete element charge motion model validation. Minerals Engineering 11(12):1161–1178.

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Radziszewski, P., and S. Tarasiewicz. 1989. Ball mill simulation: Part II—numerical solution to ball charge model. Transactions of the Society of Computer Simulations 6(2):75–88. ———. 1993. Simulation of ball charge and liner wear. International Journal on Wear, Friction and Lubrication 169:77–85. Radziszewski, P., and W. Valery. 1999. Cadia SAG mill simulated charge behaviour. Pages 267–283 in Proceedings 31st Annual Meeting of the Canadian Mineral Processors, Ottawa, Canada, January. Rajagopal, V., and I. et Iwasaki. 1992. Grinding media selection criteria for wear resistance and flotation performance. Pages 181–200 in Comminution—Theory and Practice. Littleton, CO: SME. Rattray, B. 2000. Mill liner evolutions in recent times. Pages 57–62 in Proceedings of Seventh Mill Operators Conference, Kalgoorlie, Australia, October 12–14. Australasian Institute of Mining and Metallurgy. Schäfer, J., S. Dippel, and D.E. Wolf. 1996. Force schemes in simulation of granular material. Journal de Physique I France 6(5). Schnarr, P., L.E. Schaeffer, and H.J. Weinand. 2002. Elastomers in the Mineral Processing Industry. Section 16, construction materials for equipment and plants, in Mineral Processing Plant Design, Practice, and Control. Littleton, CO: SME. Walton, O.R. 1994. Numerical simulation of inelastic frictional particle–particle interaction. Pages 884–911 in Particulate Two-Phase Flow. Edited by M.C. Roco. Boston: Butterworth-Heinemann. White, H.A. 1905. The theory of the tube mill. The Journal of the Chemical, Metallurgical, and Mining Society of South Africa (May): 290–305. Zhang, D., and B. Whiten. 1998. An efficient calculation method for particle motion in discrete element simulations. Powder Technology 98(3):223–230.

The Importance of Liner Geometry and Wear in Crushing Persio P. Rosario,*† Robert A. Hall,† and Daan M. Maijer†

ABSTRACT

Optimization of crushing processes provides a significant opportunity to enhance the overall efficiency in mining operations. This paper presents some results and conclusions from a collaborative research project between the University of British Columbia and Highland Valley Copper (HVC), which was conducted for the purpose of understanding gyratory crusher liner wear in the overall context of the crushing process. Significant outcomes from this project were the enhancement of product quality and the reduction of liner and maintenance costs at HVC. This case study highlights the potential benefits realizable by a proper assessment of crusher liner geometry and material. INTRODUCTION

Crushing and grinding together are responsible for the consumption of approximately 3% of all electric power generated in the world mainly due to the low level of energy efficiency of comminution processes (Fuerstenau 1992). Thus, there is a valuable opportunity to save energy consumption and reduce operational costs in mining operations around the world through the optimization of comminution processes. Canadian open-pit mines are seeking high throughput and significant operational efficiencies to remain competitive with higher grade and lower labor cost operations around the world. HVC, a Teck Cominco operation located in Logan Lake (approximately 350 km from Vancouver, British Columbia), is one of the largest open-pit copper (Cu) mines in the world. At HVC, on average, 137,000 t of ore with grades lower than 0.5% Cu are processed per day. The primary comminution equipment consists of three 60u89-in. Metso gyratory crushers and five grinding lines (three semiautogenous grinding [SAG] and two autogenous grinding [AG] mills). HVC has been closely analyzing the parameters involved in the comminution process as a whole and has been very active in assessing the relationship between the mine and the mill operations. Experiments conducted at HVC served to confirm that finer mill feed increases mill throughput. They also revealed that finer primary crushing and blasting should be managed concurrently in order to achieve the desirable mill feed quality (Dance 2001). In the early 2000s, after improving blasting practices and implementing automatic control at the primary crushers for finer size reduction, HVC started to experience higher * Fluor Mining & Minerals, Vancouver, British Columbia, Canada † University of British Columbia, Vancouver, British Columbia, Canada 377

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milling throughputs. However, the reliability of crusher major components dropped and crushing power consumption increased. In addition, adverse wear patterns were observed on the inner liner (mantle), which considerably decreased the life of the liners. HVC’s recognition of the importance of the primary crushers in the overall comminution process and the relevance of liner wear in their performance led to the acquisition of a prototype laser-based device to measure liner profile. This also led to the development of a collaborative research project with the University of British Columbia. The primary objective of the research project was to improve the understanding of liner wear in primary gyratory crushers (i.e., how chamber geometries and their modification impact crushing capacity and product quality). In pursuit of the primary objective, the following secondary objectives were targeted: ƒ The assessment of the prototype laser-based device to establish an efficient meth-

odology to monitor liner profile wear over time ƒ The development of a database of wear information linked to other monitored

crushing parameters, such as current draw, product size distribution, and production rate ƒ The evaluation of the liner profiles available at the mine and, if necessary, the

development of new profile designs ƒ The concurrent enhancement of crushing performance and the extension of the

lives of the liners and the other major components of the crusher BACKGROUND

During crushing, rock particles are in rolling, impact, and sliding contact with the liners of the machine (Moshgbar, Parkin, and Bearman 1994). Hence the wear of the liners is inevitable and is caused by gouging/ploughing (Bearman and Briggs 1998). As liner wear directly impacts the gap dimension and the chamber profile, it is an important variable in the overall crushing operation as it is closely related to product quality (size consistency and throughput) and cost (Svensson and Steer 1990). The rate of wear and its distribution among the different regions of the chamber results in profile modifications affecting liner life and crusher performance. Chamber profile has been considered a key parameter in crushing performance by both the manufacturers and users of cone and gyratory crushers (Gaudin 1939; Burkhardt 1982). In addition, some of them also claim that with the right liner design, wear may be minimized and made more uniform along the profile (Bearman and Briggs 1998; Svensson and Steer 1990). The design of curved concaves, known as nonchoking concaves, serves to minimize excessive levels of stress at the bottom of the chamber, which is responsible for localized and rapid liner wear in this region (Westerfeld 1985). Even though the importance of chamber profile and its deterioration over time is known, no effective method exists to assess liner wear rate in the field. Not only is it difficult to measure liner characteristics during crusher operation, but even within scheduled shutdown periods, it historically has been quite onerous. HVC acquired a new prototype device in an effort to address the issues in measuring crusher wear and the chamber shape; the equipment is known as a laser profiler device (LPD) and was purchased from Conveyor Dynamics, Inc. (CDI, Bellingham, Washington). It should be noted that the LPD was the first of its kind for this application. Figure 1 shows the major components of the LPD, which is comprised of ƒ A support structure to mount it to the crusher ƒ A track for the laser to run on

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Motor Drive

Track

Laser Mirror

FIGURE 1

Major components of the LPD

ƒ An actuator motor to drive the laser up and down the track ƒ A time-of-flight laser with a mirror for reversing the target direction ƒ Software and a computer to collect and process the measurement data (not

shown in the figure) The research project involved the implementation and refinement of the testing methodology using the LPD. The work included improvements in the device’s mechanical systems and software and in the reduction of the original setup time by redesigning and constructing an alternative support structure (Rosario, Hall, and Maijer 2004b). The LPD provides an Excel (Microsoft Corporation, Redmond, Washington) spreadsheet for each test performed. The Excel file contains data representing several points from the surface of each liner given as pairs of coordinates. The Excel file can be imported into a computer-aided design (CAD) package allowing the overlaying of measurement profiles on the original liner drawings for visual assessment of the condition of the worn liners. Figure 2 gives examples of measurement profiles for liners used for short periods of time (concaves, 6 weeks; mantle, 2 weeks). A N A L YS I S A N D R E S U L T S

During the period of the research project, from May 2001 to October 2003, periodic measurements of the crushing chamber were conducted. In addition, a methodology to analyze the geometry of the crushing chamber using LPD’s data was developed. This methodology applied a slicing technique for the calculation of chamber volumetric changes occurring over time and liner wear-rate per liner region; it was used to quantify the chamber nonchoking status (Rosario, Hall, and Maijer 2004b). During the first 2 years, approximately 40 sets of measurements were taken, corresponding to four concave-life periods, two for each crusher. In addition to the data

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Crusher Liner Profile

Mantle

FIGURE 2

Concave

Example of measured profiles aligned with the original liner drawings

generated from these measurements, crushing operational data were extracted from the digital control system. As a result, three types of data were collected, as follows: ƒ Chamber profiles measured using the LPD ƒ Information about the different types and sizes of liners used within this period,

such as liner material and profile type ƒ Crushing operational data extracted from the Citect (Citect Corporation,

Alpharetta, Georgia) process control system used at HVC. Data included product size distribution (monitored with an image analysis system) and power draw. After collection, the crushing operational data, liner information, and measurement dates were grouped and plotted in four graphs, each graph corresponding to a period of one concave life (Rosario 2003). The graphical analysis allowed the observation of a series of interesting relationships between the parameters plotted and resulted in the identification of key periods for cross-reference with the information provided by the wear measurements. Through the graphical analysis, it was possible to correlate chamber volume characteristics with distinct operation periods, including the periods when overload conditions appeared (i.e., unstable current draw as well as high-amplitude maximum current values [power spikes]), and other selected periods when not only the current draw remained stable but also the product quality and mantle tonnage were the highest. From the assessment, it was clear that the chambers that provided the best results were closer to a

THE IMPORTANCE OF LINER GEOMETRY AND WEAR IN CRUSHING

381

nonchoking type and the ones providing poor results were closer to a straight type (Rosario, Hall, and Maijer 2004a). In addition, on several occasions when overload conditions appeared, the concaves had been running for more than 7 Mt on average (during the period of the research, HVC was achieving an average total life of 11 Mt). Although several different types of mantles containing different profiles were used during the periods of concave life after 7 Mt, none of them achieved a substantial cumulative production. Actually, most of the lowest-tonnage-per-mantle results appeared in these periods. In general, product quality had significant variation during the research project. Only a few occasions were observed where reasonable product quality, smooth operation, and normal product rate occurred simultaneously for considerable time periods. These rare events happened approximately within 2.0 and 5.5 Mt of concave life and repeatedly with the same profile type and liner material (HVC used 10 different mantleprofile types and two different materials during the study period). The issues related to the final life period of the concaves plus the variations in mantle use suggested that the liner replacement policies at HVC should be changed in order to improve crushing performance. The first suggested modification to the usual replacement schedule was the reduction of concave life from ~11.3 to ~7.8 Mt. Second, after an evaluation of all different mantle sizes and profiles available, it was concluded that to achieve the chamber characteristics compatible with adequate crushing performance (during the entire concave life), and to ensure a consistent life span for the mantles, the design of new mantle profiles was required. The design of two new mantle profiles resulted from the cooperative project. The essential parameters in designing the new mantle profile were the nonchoking characteristic of the chamber and allowance for vertical adjustment of the mantle position during operation (25.4 mm). A proper nonchoking condition and a close side setting (CSS) mantle position relationship that provides a long life for the mantle were the design targets (Rosario, Hall, and Maijer 2004a). Considering that under optimal circumstances mantle lives exceeded 3 Mt, and adhering to HVC’s maintenance schedule with a 3-week shutdown pattern (~950,000 t of production), the expected useful lives for the mantles were designed as follows: ƒ 1st mantle, 9 weeks (~2,900,000 t) ƒ 2nd mantle, 9 weeks (~2,900,000 t) ƒ 3rd mantle, 6 weeks (~1,950,000 t)

The application of the new mantle designs and the suggested management policy for the replacement of the liners were expected to result in better operational conditions and increased average product quality. A cost analysis was performed, which indicated that the suggested policy had the potential for a reduction of approximately 13% over the total annual liner cost (parts, rebuilds, and installations), and the cost associated for the amount of downtime involved in the replacements also was expected to drop as the average annual downtime would decline by 15%. CURRENT SITUATION AT THE MINE

After receiving the new mantles and commissioning the proposed liner management, HVC decided it would be beneficial to set the concave lives to approximately 8.4 Mt, thus fixing their replacement schedule to twice a year. The decision was taken to avoid concave replacements during winter days. As a consequence of this change in the proposed

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maintenance schedule, four mantles are being used instead of three. Therefore, one undersize, two standards, and one oversize mantle type are being used per concave life (undersize, 9 weeks; standards, 6 weeks each; and oversize for 5–7 weeks, depending on concave replacement schedule; A. Adams, personal communication, 2005). The new schedule represents a significant change from the unpredictable liner usage that occurred previously. For instance, during 2001 and 2002, the number of mantles used per concave oscillated between 6 and 11 mantles per concave. In addition, significant reductions in total annual liner cost and maintenance downtime for liner replacements are being realized. The crushers are operating regularly with stable current draw, and normal power consumption is observed. The overall crusher product quality has increased, and fine feed for the mills can be supplied. In addition, mantle tonnage has been reached as scheduled. The LPD has been used only occasionally when abnormal operation of the crushers is required for various reasons. For example, if one of the crushers is down for a long period of time and the operating crusher is used for high tonnage, the wear pattern is assessed with the laser. CONCLUSIONS

The use of a new LPD to measure the crusher chamber was implemented at HVC, and improvements were made to the original measurement procedure. Calculations and graphical analysis techniques were developed and integrated in a new software tool to facilitate data analysis. The data analyses conducted provided an understanding of crushing chamber characteristics and their impact in crushing performance. In addition, wear rate as a function of production was determined for the concaves, which enabled wear prediction for the bottom part of the concave. The knowledge gained from the analyses helped in the evaluation of the current liner management policy. The evaluation resulted in a revised maintenance schedule based on the use of two new mantle profiles designed for this application. The proposed liner management policy was put in place, and after the trial period, it was accepted with minor adjustments. The new policy reduced overall liner costs and, most importantly, enhanced crushing performance. Thus, a concrete and significant increase in the profitability of the operations was gained with this work. F U T U R E WO R K

The development of a comprehensive gyratory crusher liner wear model to be used in dynamic modeling for this type of crusher would be very beneficial to the mining industry. This enhanced model might be a more realistic tool for an effective simulation for design or optimization of primary crushing systems as the inevitable wear factor is added to such studies. Further development of the laser-based prototype or the development of other profiler devices based on different technologies also would be important to facilitate similar studies as those conducted at HVC. ACKNOWLEDGMENTS

The authors are grateful to HVC for all their support for the work presented in this paper and also to the Natural Sciences and Engineering Research Council of Canada for their financial support. The support given by Fluor for the presentation in the Comminution Symposium is also much appreciated.

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REFERENCES

Bearman, R.A., and C.A. Briggs. 1998. The active use of crushers to control product requirements. Minerals Engineering 11(9):849–859. Burkhardt, E.S. 1982. Primary crushers factors that affect capacity. Pages 387–392 in Design and Installation of Comminution Circuits. Volume II. Edited by A.L. Mular and G.V. Jergensen. New York: SME-AIME. Dance, A. 2001. The importance of primary crushing in mill feed size optimisation. Pages 189–202 in Proceedings of the SAG Conference, Vancouver, BC, September 30– October 3. Volume I. Edited by D.J. Barratt, M.J. Allan, and A.L. Mular. Canadian Institute of Mining, Metallurgy and Petroleum. Fuerstenau, D.W. 1992. Comminution: Past developments, current innovation and future challenges. Pages 15–21 in Proceedings of the International Conference on Extractive Metallurgy of Gold and Base Metals, Kalgoorlie, Australia. Gaudin, A.M. 1939. Crushers. Pages 25–50 in Principles of Mineral Dressing. New York: McGraw-Hill. Moshgbar, M., R.M. Parkin, and R.A. Bearman. 1994. The compensation of liner wear for optimum control of cone crushers: Progress in mineral processing technology. Pages 549–555 in Proceedings 5th International Mineral Processing Symposium, Cappadocia, Turkey, September 6–8. Edited by H. Demirel and S. Ersayin. Rosario, P.P. 2003. Optimization of primary gyratory crushing at Highland Valley Copper. Master’s thesis, Vancouver, BC: University of British Columbia. Rosario, P.P., R.A. Hall, and D.M. Maijer. 2004a. Improved gyratory crushing operation by the assessment of liner wear and mantle profile redesign. Minerals Engineering 17(11–12):1083–1092. ———. 2004b. Liner wear and performance investigation of primary gyratory crushers. Minerals Engineering 17(11–12):1241–1254. Svensson, A., and J.F. Steer. 1990. New cone crusher technology and developments in comminution circuits. Minerals Engineering 3(1–2):83–103. Westerfeld, S.C. 1985. Gyratory crushers. Pages 27–46 in SME Mineral Processing Handbook. Edited by N.L. Weiss. New York: SME-AIME.

Bond’s Method for Selection of Ball Mills Chester A. Rowland*

ABSTRACT

Although it was developed nearly 50 years ago, Bond’s method is still useful for calculating necessary mill sizes and power consumption for ball and rod mills. This paper discusses the basic development of the Bond method, the determination of the efficiency correction factors based on mill dimensions and feed characteristics, and the application of the results to designing grinding circuits. INTRODUCTION

The development of the ball mill during the twentieth century has been described as the most significant development in the machinery for performing the grinding of ores (Lynch and Rowland 2006). A key part of the implementation of ball mills was the development of the ability to predict their performance in the plant based upon grindability data from standardized tests performed in small-diameter laboratory mills. Early in the twentieth century, ball mill manufacturers and other research laboratories developed proprietary batch-grinding tests to measure the resistance of metallic mineral ores, industrial mineral ores, cement raw materials, cement clinkers, and related materials being ground to fine sizes in rod and ball mills. These tests, called grindability tests, were needed to help determine the energy required to grind these materials from a coarse-sized feed to the desired product size. During the first half of the century, none of these test methods could be used to directly determine the energy needed for grinding at plant size capacity. If grinding tests for direct determination of the energy required were needed, pilot-plant tests in small-diameter continuous operating ball mills were run. Pilot-plant grinding data always had to be adjusted for scale-up factors to larger-diameter mills. In 1930, Allis-Chalmers hired Fred Bond to design and build a laboratory for testing ores and grains, for minerals processing and flour milling, and to conduct research for processes for the treatment of ores and grains. Bond’s first developments for grinding ores and rocks are now known as the Bond rod milling and ball milling grindability tests. The grindability results from these tests are still reported as “net grams produced per revolution of the test mill.” Bond carried out two studies using his grindability tests: 1. The first study was to determine if either of the two existing theories of commi-

nution—the Rittenger theory or the Kick theory—were correct. Bond concluded that neither was correct. He developed a theory that the energy required for comminution was a function of the difference in the square root of the size of the * Consultant, Comminution Systems, Milwaukee, Wisconsin 385

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particles in the feed and in the product of the material being comminuted. This is known as Bond’s third theory of comminution. 2. The second study was used to develop a correlation between ball mill operating

data and grindability test data. This was based on the Work Index concept. From this concept came two equations: (a) the equation to determine the Work Index from Bond grindability tests, and (b) the Bond equation, which uses the Work Index to determine the energy needed for grinding. When Bond introduced the Work Index concept (Bond 1952), he introduced a new method for determining the energy required for grinding ores and outlined a mathematical method for using the Work Index to design grinding circuits. Though it is an empirical procedure, even at this time, there is little prospect that the Work Index will be replaced as a tool for determining the energy required to grind a mineral or ore. Numerical examples of the use of the Work Index are given in this paper. The calculations are based upon measurements giving the amount of the size reduction by the difference in the size distributions of the feed (F ) and the product (P). PAR TICLE-SIZE DISTRIBUTIONS

The traditional method of measuring the size distribution of a broken product is to shake a representative sample of the material through a set of sieves where the apertures decrease by a constant ratio, normally 2 (which is 1.414). When plotted on a logarithmic scale, the intervals between successive apertures having a constant geometric ratio are equally spaced. This makes the logarithmic plot a convenient method for representing very wide ranges of particle size. Also, when using this ratio, the area of the openings in screen n is half the area of the openings in screen (n – 1). Tyler screens are frequently used to measure sizings, with the screen mesh numbers and corresponding aperture sizes as shown in Table 1. Dry sizing is suitable for particles >0.05 mm, but smaller particles tend to agglomerate and should be washed on the smallest screen used for sizing. The coarse fraction is then sized when it is dry, without interference from the highly agglomerating fines. The practical limit of screens is about 0.030 mm, and as a result, they are inadequate to assess the performance of processes that require most of the particles to be ground to <0.030 mm. Other methods of sizing are used for very small particles based on physical characteristics such as ƒ Settling rates in air or water (e.g., the Infrasizer or the Cyclosizer) ƒ Volume measurement (Coulter counter) ƒ Laser diffraction (various instrumentation)

These techniques all have practical upper-size limits of a few millimeters. They all give a relative measure of the proportion of particles in a sample that fall in progressively smaller size fractions. The problem is that they measure different physical characteristics of particles, so measurements at the same nominal size (often determined with glass spheres) do not coincide. Consequently, sizing of distributions determinations upon a single material using different techniques varies, with the variations depending on physical properties of the particles. Therefore, there is no method of unifying them. It is important to consistently use a single sizing technique at all times when a specific sizedistribution problem is being investigated. Sizing distributions are most informative when shown as graphs, as in Figure 1. Particle size (or the number indicating the size designation of a sieve in a series of sieves selected to have a constant geometric ratio) is plotted on a logarithmic scale on the x axis, and the cumulative percent passing each size is plotted on the y axis. The y axis may be arithmetic,

BOND’S METHOD FOR SELECTION OF BALL MILLS

TABLE 1

387

The link between the Tyler screen number and the aperture size Tyler Mesh Size

Aperture, mm

4 6 8 10 14 20 28 35 48 65 100 150 200 270 325 400

4.75 3.35 2.36 1.70 1.18 0.85 0.60 0.425 0.300 0.212 0.150 0.106 0.075 0.053 0.045 0.038

Screen Analysis Chart 100 90 80 70 Cumulative % Passing

60 50 40 30

20

10 200

150

100

65

48

36

28

20

14

10

8

6

Size, Tyler Sieve Number

FIGURE 1 The type of log–log plot used by Bond in developing the third theory of comminution. The values on the x axis are Tyler sieve numbers. The range from 6 to 200 mesh represents a size range from 3.35 to 0.075 mm, as indicated in Table 1.

logarithmic, or by the Rosin-Rammler scale, according to preference. Bond noted that the plot from a log–log plot of a natural particle-size distribution and the cumulative percent passing the particle size gave a relatively straight line between 80% passing and 20% passing sizes. Bond selected the 80% passing size as the representative size to designate the size of the mill feed and the mill product. With closed ball mill grinding circuits, the mill product with a natural particle-size distribution is the fines from the classifier.

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D E T E R M I N I N G G R I N D I N G P O W E R U S I N G B O N D ’S E Q U A T I O N

Bond was able to develop a procedure for determining the energy needed for grinding by correlating the results from his grindability test with plant operating data for the samples he had tested. The procedure includes the following: ƒ Work Index concept ƒ Bond’s third theory of comminution ƒ Bond Work Index equation ƒ An equation to determine Work Index from grams per revolution obtained from

Bond grindability tests In Bond’s studies during the late 1930s and 1940s, most of the operating data and samples came from ore concentrators using 8-ft-diameter rod and ball mills. After using the Bond method, it was determined that the grinding power calculated using Work Indices from Bond grindability tests fit very specific conditions: ƒ The Work Indices determined from Bond rod mill grindability tests are for wet

grinding, open-circuit, 8-ft-diameter, inside liners rod mills. ƒ The Work Indices determined from Bond ball mill grindability tests are for wet

grinding, closed-circuit, 8-ft-diameter, inside liners ball mills. Variations from these standards required the development of correction factors (Bond 1961; Rowland 1973). The methods to determine the multipliers for eight efficiency factors have been previously published (Rowland 2002) and are applied to the energy calculated for grinding using the Bond equation. Following the energy calculations for rod mill–ball mills circuits, the factors to determine the efficiency factors are given. The definition of Work Index is “the total energy required to comminute a material from an infinite feed size to 80% passing 100 microns.” Bond proposed that the energy required to crush or grind a material is the total energy required to produce the product from an infinite size, minus the energy used to produce the feed from an infinite size. The equation that Bond developed for this calculation was 100 ˜ Wi – ------------------------100 ˜ Wi W = ------------------------P F where W Wi 100 P, F

= = = =

(EQ 1)

predicted mill energy consumption, in kWh/st Work Index, in kWh/st 100 Pm, which is the product size in the definition of Work Index 80% passing sizes, in Pm of the feed (F ) and product (P)

This equation is also commonly written as 1 – -----1- · W = 10 ˜ Wi § -----© P F¹

(EQ 2)

The Bond equation has become an accepted means to calculate the energy required for grinding. It should be noted that the power calculated by the Bond equation is the power that should be delivered to the mill and does not include motor or drive-train losses. It is a simple tool for use in ƒ Determining the power required for crushing and grinding by crushers and grind-

ing mills ƒ Calculating the efficiency of crushers and grinding mills

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389

ƒ Comparing crushing and grinding circuits with the same feed to the same product

sizes and the same Work Index based upon laboratory crushability and grindability tests NUMERICAL EXAMPLE

Work Indices for an ore determined from bench-scale laboratory data are ƒ Bond impact crushing, 11.5 ƒ Bond Rod Mill Grindability Test at 10 mesh, 13.2 ƒ Bond Ball Mill Grindability Test at 65 mesh, 11.7 ƒ Bond Ball Mill Grindability Test at 100 mesh, 12.1

Examples are given to calculate the grinding power required for grinding this ore in the following circuits: ƒ Rod mill–ball mill ƒ Single-stage ball mill ROD MILL–BALL MILL CIRCUIT EXAMPLE

Rod mill: F = 18,000 Pm; P = 1,200 Pm; Wi = 13.2 kWh/st 1 1 · = 2.83 kWh/st W = 10 ˜ 13.2 § -----------------– --------------------© 1,200 18,000 ¹ Ball mill: F = 1,200 Pm; P = 175 Pm; Wi = 11.7 kWh/st 1 – -----------------1 · = 5.47 kWh/st W = 10 ˜ 11.7 § ------------© 175 1,200 ¹ rod mill 2.83 + ball mill 5.47 = total 8.30 kWh/st To convert power per short ton to power per metric ton, multiply power per short ton by 1.102. Efficiency Factors

To determine the grinding power for the specified capacity, multiply each of the power figures by the specified hourly feed rate. As some of the efficiency factors are sensitive to mill diameter, refer to published tables or information from the grinding mill manufacturers to make preliminary selections for the mill sizes to use. Then apply the relevant efficiency factors to determine the grinding power for the desired capacity, and make any changes needed to the mill sizes selected. The efficiency factors (EFs) are given in a 1973 paper (Rowland 1973, 2002). They are discussed in the following subsections. EF1—Dry Grinding. For the same range of size reduction, dry grinding in both rod mills and ball mills requires 1.3 times as much power as wet grinding. EF2—Open-Circuit Grinding. When grinding in open-circuit ball mills, the amount of extra power required, compared to closed-circuit grinding, is a function of the degree of control required for the product to be produced. With open-circuit grinding, the

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TABLE 2

MILL DESIGN

Open-circuit inefficiency factors Product Size Control Reference, % Passing

Inefficiency Multiplier (EF2)

50 60 70 80 90 92 95 98

1.035 1.05 1.10 1.20 1.40 1.46 1.57 1.70

desired product is specified as a percent plus a mesh size allowed in the product. The inefficiency factors given in Table 2 are based upon the percent plus a mesh size allowed in the product. The percentage of the mesh size allowed in the grinding mill product is the mill product size control. From the specified product size distribution, the 80% passing size has to be determined to calculate the necessary grinding energy. Then the efficiency factor from Table 2 is applied to the calculated power. The smaller the required percentage passing control point, the more efficient the operation. For example, if the specified grind is 50% passing a particular mesh size, the grinding is easier to obtain than if the grinding is specified as 90% passing the same mesh size. EF3—Diameter Efficiency Factor. Using the base mill diameter of 2.44 m (8 ft) inside liners, the diameter efficiency factor can be calculated using the following equation: EF3 = (2.44/D)0.2 when D is in meters

(EQ 3)

EF3 = (8/D)0.2 when D is in feet

(EQ 3a)

As the mill diameter inside liners exceed 2.44 m (8 ft), there is a tendency to neglect the EF3 factor and let it be a safety factor. The increase in ball milling efficiency does not continue in mills diameter inside liners greater than 3.81 m (12.5 ft). The diameter efficiency factor of 0.914 applies to all mills larger than this size. For further discussion, please refer to the Ball Mill Size Scale-up section in this paper. EF4—Oversized Feed. The oversized feed factor applies when a grinding mill is to grind a feed that is coarser than the optimum size of feed (Fo ). The oversized feed inefficiency factor applies to both rod milling and ball milling, and is a function of the Work Index of the ore and of the desired reduction ratio. Fo (for rod milling) = 16,000 (13/Wi)0.5

(EQ 4)

Fo (for ball milling) = 4,000 (13/Wi)0.5

(EQ 5)

ratio of reduction (Rr ) = F/P

(EQ 6)

 F – Fo R r +  Wi – 7 -----------------Fo EF4 = ---------------------------------------------------Rr

(EQ 7)

In Equation 4, use the Wi from a rod mill grindability test. In Equation 5, use the Wi from a ball milling grindability test.

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391

EF5—Fineness of Grind Factor. Fineness of grind applies to fine grinding when the 80% passing size of the product is finer than 75 Pm (200 mesh). The equation to determine this is

P + 10.3 EF5 = -------------------1.145P

(EQ 8)

EF6—High or Low Ratio of Reduction Rod Milling. Use of this factor is based on the mill constant Rro, as determined from the following equation:

R ro = 8 + 5L -----D

(EQ 9)

where L = rod length D = mill diameter The equation for this efficiency factor is 2

 R r – R ro EF6 = 1 + -------------------------150

(EQ 10)

When the difference (Rr – Rro ) is between +2 and –2, this multiplier becomes insignificant and does not have to be used. It should, however, be used whenever the Wi from the rod mill grindability test is greater than 7. EF7—Low Ratio of Reduction Ball Milling. The need to use this factor does not occur very often. It only applies to ball milling when the ratio of reduction is less than 6. The equation for determining this factor is 2  R r – 1.35 + 0.26 EF7 = -----------------------------------------------2  R r – 1.35

(EQ 11)

EF8—Rod Milling. A study of rod milling operations showed that rod mill performance is affected by the attention given to the preparation of the feed and feeding a uniform top size to the mill, as well as to the care given to removing broken rods from the mill. The effect of these issues varies with the attention given to condition of the rods and the mill operation, so it is individual for each installation. The following guidelines for estimating the rod milling factor are recommended when selecting rod mills based on power calculated from grindability tests: 1. When calculating rod mill power for a rod-milling-only application, use an ineffi-

ciency factor of 1.4 when the feed is prepared with open-circuit crushing, and 1.2 when the feed is prepared with closed-circuit crushing. The mill diameter, low or high ratio of reduction, and oversized feed factors should also be applied to the calculated grinding power. 2. To calculate the energy for rod milling for a rod mill–ball mill circuit when the

rod mill feed is produced with open-circuit crushing, use a rod mill inefficiency factor of 1.2. When the rod mill feed will be consistently uniform, such as that produced by closed-circuit crushing, do not apply any inefficiency factor. The mill diameter, low or high ratio of reduction, and oversized feed factors should also be applied to the calculated rod milling grinding energy.

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NOTE: In the previous discussion of EF8 (Rowland 1973, 2002), the directions for rod mill–ball mill circuit gave the following instruction: “Do not use the improvement in the performance of the ball mill due to its receiving rod mill product.” Before Bond’s work was published, some of the reports on rod mill–ball mill circuits indicated that there was an improved grinding efficiency of up to 10% in the ball milling stage. This was probably a result of the difference in the grindability of the ore for rod milling and for ball milling. This difference is covered by Bond grindability tests and energy calculations using the Bond equation and therefore did not apply after the Bond method was introduced. This instruction was given to avoid an error by using the factor when it no longer applied. SINGLE-STAGE BALL MILL CIRCUIT EXAMPLE

Consider a single-stage ball mill receiving a feed that is 100% passing 0.5 in. (12,500 Pm). This normally corresponds to an 80% passing size of 9,400 Pm. As the feed to the standard Bond Ball Mill Grindability Test is –6 mesh, which is 80% passing 2,100 Pm, the ball mill grindability value does not include the grindability of the –0.5 in./+6 mesh material. However, the standard feed to the Bond Rod Mill Grindability Test is –0.5 in., which is the same as the feed to our example single-stage ball mill. To obtain the complete Work Index profile of the feed to a single-stage ball mill, it is recommended that two Bond grindability tests be run. A Bond rod milling grindability test at 6 mesh should be performed on a sample of minus 12-inch ore and a Bond ball milling grindability test at the specified product size should be performed on a sample of –6 mesh ore. Both samples to be tested should contain the natural size distribution finer than the coarsest size in the specified feed size for the grindability test. If there is a difference in the Work Indices obtained from the rod mill and ball mill grindability tests, and the rod milling Work Index is greater than the ball milling Work Index, a two-stage calculation should be made to determine the grinding power for a ball mill grinding crusher product. The first stage of the calculation will be to reduce the feed size to a product size of 80% passing 2,100 Pm (100% passing 6 mesh) using the Work Index from the rod mill grindability test. This covers any hard size fraction in the singlestage ball mill feed. The ball mill grindability value is then used for calculating the energy needed to reduce the particles from 80% passing 2,100 Pm to the final desired 80% passing size of the desired product size. The specifications for the single-stage ball mill feed are as follows: F = 80% passing 9,400 Pm; P = 80% passing 175 Pm rod mill, Wi = 13.2; ball mill, Wi = 11.7 Step 1: Reduce to 80% passing 2,100 Pm. 132 – -----------------132 = 1.52 kWh/st W = -----------------2,100 9,400 Step 2: Reduce to final product size. 117 117 W = ------------- – ------------------ = 6.29 kWh/st 175 2,100 total energy required = 7.81 kWh/st

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393

To convert power per short ton to power per metric ton, multiply power per short ton by 1.102. To determine the grinding power for the specified capacity, multiply the total power per ton by the specified hourly feed rate. Some of the efficiency factors are sensitive to mill diameter. Use either published tables (Rowland 2002) or information from the grinding mill manufacturers to preselect the mill size; then apply the efficiency factors pertinent to the circuit to determine the grinding power for the desired capacity; then make any changes needed to the mill size selected. PRIMAR Y SAG MILLS

There are no bench-scale grinding tests that are used to directly determine the Work Index of the feed to primary semiautogenous grinding (SAG) mills (Rowland 1989). The MacPherson test (MacPherson 1976) is performed in a small, fully autogenous drygrinding mill with the mill operating in closed circuit with a 14-mesh screen. The feed to the MacPherson test mill is either ore or drill cores crushed to –32 mm. This feed size distribution may miss any critical or hard coarse size fractions in the feed. The results of the test are specified as a corrected Autogenous Index (Ai). The Ai results from this test are determined from the operating Work Index (Wio) for the test circuit and can be used in the Bond equation to determine the grinding power for a primary SAG mill. There are impact and compression tests that are used to determine the crushability of the coarse fractions in a SAG mill feed. When the results of these crushing tests are available as Work Index values, the Bond equation can be used in the power calculations for primary SAG mills. A rule of thumb is that a primary SAG mill in a SAG mill–ball mill circuit requires 25% more energy than crushers and rod mills doing the same work. When pilot-plant primary SAG mill operating data are available, using the power, feed, and product size distribution data, an operating Work Index can be determined from the pilot-plant data then used in the Bond equation to determine the grinding power required for a primary SAG mill. BALL MILL SIZE SCALE-UP

Operating Work Indices for wet-grinding overflow ball mills 4.88 m (16.0 ft) diameter, inside liners, and larger have shown that some large-diameter ball mills are operating inefficiently. Grindability tests on the feed to these mills had Work Indices of <10, the specified grind was coarser than 80% passing 65 mesh (212 Pm), and the liberation of the minerals was acceptable at coarser grinds. These conditions made for a low power per ton for grinding the ore. This allowed for high feed rates that developed high circulating loads, which resulted in fast slurry flow rates through the mill and very short retention time for the ore in the mill. In some mills the grinding media was thrown out of the mill with the slurry. The cause for these conditions was found in the factors involved in the scale-up from small-diameter ball mills to large-diameter ball mills. The scale-up factors are in the equation that Bond developed for determining the power that a ball mill should draw. The equations are given in the following paragraphs (Rowland 2002). KW b = 4.879D where KWb D Vp Cs Ss

= = = = =

0.3

0.1 · + S  3.2 – 3V p C s § 1 – ---------------s 9–10C s ¹ © 2

kilowatts per metric ton of balls (1,000 kg [2,204 lb]) mill diameter inside liners, in m fraction of mill volume occupied by balls, in % fraction of critical speed, in % ball size factor (see Equation 13)

(EQ 12)

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ADVANCES IN COMMINUTION

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For mill diameters, in feet, and the power per short ton (2,000 lb [908 kg]), Equation 12 becomes KW b = 3.1D

0.3

0.1  3.2 – 3V p C s § 1 – ---------------- · + S s 9–10C s ¹ © 2

(EQ 12a)

For overflow ball mills larger than 3.3 m (10 ft) in diameter, the top size of the grinding balls used could affect the power drawn by the mill. This is called the ball size factor (Ss). The equation to determine Ss in terms of power per metric ton of balls is B – 12.5D S s = 1.102 § ------------------------ · © 50.8 ¹

(EQ 13)

where B = diameter of the largest size ball, in mm D = mill diameter inside liners, in m For Ss in terms of power per short ton of balls (2,000 lb [908 kg]), ball size in inches, and mill diameter in feet, the Ss equation is 3D § B – ------20 ¨ S s = ----------------¨ 2 ©

· ¸ ¸ ¹

(EQ 13a)

The total power that a wet-grinding overflow ball mill should draw is then KW = KWb u Vp u L u ȡB / WB where KWb L Vp ȡB WB

= = = = =

(EQ 14)

kilowatt per ton of balls, either st or t, per foot of mill length mill length fraction of mill volume occupied by balls, in % bulk density of ball charge weight of balls in the mill charge, in st (or t)

To scale-up the size of a wet-grinding overflow ball mill keeping Vp, Cs, and L constant, KWb scales up as the ratio of the mill diameters raised to the 0.3 exponent. The volume of the mill increases at the ratio of the diameters squared. To determine the power of the scaled-up mill, as KWb and mill volume are multiplied in the determination of total power, mill power draw varies as the ratio of the diameters raised to the 2.3 exponent. Mill power draw is a measure of the potential capacity of the mill, so potential capacity increases as the ratio of the diameters raised to the 2.3 exponent. The volume of the mill only increases as the diameter squared. Therefore, as the diameter of mills increases, the available volume per ton of feed is reduced. As a result, the velocity of flow of the slurry through the mill has to increase, and the retention time of the ore in the mill decreases. One of the effects of this is an increase in the amount of the circulating load of ore not ground to the desired fineness that is returned to the mill to be ground further. As a result, the amount of solids that are fed to the mill increases, further increasing slurry velocity flow through the mill and reducing the retention time of the ore in the mill. The symptoms of a lack of retention time are a coarser grind with the same power per ton consumption required for the desired fineness of grind, combined with an increase in the circulating load (classifier oversize) being returned to the mill for further grinding. The

BOND’S METHOD FOR SELECTION OF BALL MILLS

395

symptoms of too high a slurry velocity are balls being carried out of the mill by the slurry, and the slurry and balls coming over the discharge trunnion liner at a sufficient velocity to be thrown out of the mill. Some of the first authorities on grinding in ball and pebble mills indicated that the retention time of the ore in a ball mill and the flow rate of the slurry through the mill were factors to be considered. However, as the diameter of ball mills kept increasing—up to 4.88 m (16.0 ft) in diameter—there were no obvious indications of any serious efficiency problems. One question that developed was that since the increase in efficiency as mill diameters increased stopped at 3.8 m (12.5 ft), was there a diameter at which the ball mill would become less efficient? The efficiency of ball mills is determined by comparing operating Work Indices with the Work Indices from the Bond ball milling grindability test on samples of mill feed from which the Wio was calculated (Rowland 1973, 2002). The only way to accurately determine an acceptable minimum retention time and a maximum slurry velocity for ball milling a specific ore is to run tests in the size of mill to be used. Because of their small size and design, bench-scale tests in a batch-type ball mill cannot be used to test for retention time and slurry flow rates. Pilot-plant ball mills normally are too small in diameter to be affected by the retention and slurry flow that occur in large-diameter mills because the volume available per unit of feed rate is more than adequate. It has been proposed that “A general guideline is 1.2 to 1.4 minutes for the minimum retention time and 6 meters per minute for the maximum slurry velocity” (Rowland 1988). This recommendation was based upon studies of operating conditions in 4.88-m (16.0-ft) and 5.33-m (17.5-ft) diameter, inside liners, wet-grinding overflow ball mills. The proposed minimum retention time applies to the total solids in the mill, which includes new feed and circulating load. The maximum slurry applies to the total slurry flow consisting of the solids in the new feed, the solids in the circulating load, and all the water in the feed, circulating load, and separately added to the mill. Large-diameter overflow ball mills are operated with a ball loading between 30% and 35% of the mill volume while maintaining the overflow opening in the discharge trunnion at a 40% volumetric loading level. This reduces mill power, mill throughput, and slurry flow rate through the mill and increases retention time of the ore to overcome the inefficiency problems caused by too short a retention time and too fast a slurry flow. Other factors that change with each mill diameter are 1. The percentage of mill volume loaded with balls is constant. The weight and

number of balls in the mill is a function of the mill volume, so the number of balls per unit weight of the feed decreases as the mill diameter increases. This decreases the number of ball-to-ore contacts. 2. The percentage of critical speed is constant, but as the mill diameter increases,

the critical speed decreases. Critical speed for a ball mill is determined by a constant divided by the square root of the mill diameter. As the diameter of ball mills increases, the mill speed in revolutions per minute decreases so that the number of times the balls are lifted per minute decreases again, reducing the number of ball-to-ore contacts. 3. Whereas the mill speed in revolutions per minute decreases with increasing mill

diameter, the mill speed in distance per minute at the inner surface of the shell liners increases with increases in mill diameter. This is based upon the increase in the circumference of the mill (SD). Peripheral speed is a factor in estimating the wear on shell and end liners. 4. Once the scale-up calculation is completed, mill power and/or volume can be

changed by changing the mill length. For the same mill diameter, mill volume

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ADVANCES IN COMMINUTION

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and power are directly proportional to changes in the effective grinding length of the grinding chamber. 5. Ball mill power is not directly proportional to the percentage of volumetric load-

ing. The curve for this is shown in work by Rowland (2002). The maximum power draw is between 40% and 55% of the mill volume occupied by media charge. For small-diameter mills, the maximum power draw is between 50% and 55% volumetric loading; for middle-sized mills, it is between 45% and 48%; and for mills with the largest diameters, it is between 42% and 45%. 6. Field studies have shown that while mill power draw increases as the percentage

of critical speed increases, there is an increase in the power per unit of capacity consumed. The more efficient grinding in wet-grinding ball mills comes at mill speeds between 68% and 75% of critical speed. 7. Although grate-discharge ball mills have been used, grate maintenance problems

and blinding of the slots in the grates with broken ball chips, large ore chips, and worn balls reduce the availability of the mill and the flow of slurry through the mill. These problems have discouraged the use of large-diameter, grate-discharge ball mills. Dry-grinding ball mills either have grate dischargers or are discharged by air sweeping. 8. For the same fraction of mill volume occupied by balls (Vp), the ratio of the mill

diameter inside liners divided by the diameter of the largest size of grinding ball used increases as the mill diameter increases, which means the number of balls near the center of gravity of the ball charge, which is the least-active portion of the charge, increases. This reduces the intensity of the grinding action. OBSER VATIONS

There is no way to scale-up a ball mill and have a larger duplicate of the original mill because of the difference in the scale-up factors. The use of a mathematical computer for the simulation of smaller mills into larger mills is gaining interest in selecting large ball mills. For accurate simulation, it will be necessary to include the scale-up factors and compensate for the negative effects of scale-up. The fact that each diameter of ball mill is different than any other diameter ball mill could also be the reason that selection and breakage functions in large-diameter mills cannot be duplicated in bench-scale and small-diameter pilot-plant ball mills. The factors that are used to determine selection and breakage functions change with each mill diameter. Bond’s additions to the technology of comminution should, for the foreseeable future, continue to be the basis for further studies of comminution and the machinery being developed for comminution. This report gives a general review on Bond’s additions for ball milling. For more detailed discussions of the information given in this review, please refer to the references listed herein and other papers, articles, and books where comminution is discussed. REFERENCES

Bond, F.C. 1952. Third theory of comminution. AIME Transactions 193:484. ———. 1961. Crushing and grinding calculations. [Revised by Allis-Chalmers, January 1961. A-C publication 07R9235B.] British Chemical Engineering (June 1960).

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Lynch, A.J., and C.A. Rowland. 2005. The History of Grinding. Littleton, CO: SME. MacPherson, A.R. 1976. A simple method to predict the autogenous mill requirements for processing ore from a new deposit. SME Preprint No. 76-B-327. Littleton, CO: SME. Rowland, C.A. 1973. Comparison of work indices calculated from operating data with those from laboratory test data. Page 47 in Proceedings of the Tenth International Mineral Processing Congress. London, England: Institution of Mining and Metallurgy. ———. 1988. Large ball mills—length and diameter. Part A. Page 281 in Proceedings of the XVI International Mineral Processing Congress, Stockholm, Sweden, June 5–10. Edited by K.S. Eric Forssberg. Amsterdam: Elsevier Science. ———. 1989. Testing for selection of autogenous and semi-autogenous grinding mills and circuits. Page 47 in Advances in Autogenous and Semi-Autogenous Technology. Volume 1. Edited by A.L. Mular and G.E. Agar. Vancouver, BC: University of British Columbia. ———. 2002. Selection of rod mills, ball mills and regrind mills. Page 710 in Mineral Processing Plant Design, Practice and Control. Edited by A.L. Mular, D.N. Halbe, and D.J. Barratt. Littleton, CO: SME.

Developments in SAG Mill Liner Design David Royston*

ABSTRACT

This paper presents an overview of current practical approaches to semiautogenous grinding (SAG) mill liner designs as they affect long-term liner performance, mill performance, and the interaction between grinding media and the mill charge. INTRODUCTION

Mill liners provide the wear-resistant surface within grinding mills; they also impart motion on the mill charge (i.e. the grinding process) by providing the key between the charge and mill shell. As SAG mills have grown in sizeʊnow more than 12 m in diameter and drawing around 20 MW of powerʊthe significance of the process aspects of liner design on mill performance have become particularly important. Liners discussed in this overview include the shell liner lifters (that dictate charge motion) and mill-end liners, especially the discharge-end liners that function to empty the mill of ground product. This paper provides a practical background on mill liners in SAG mill operations. SHELL LIFTERS

Current Experience—Wide-Space and Large-Angle Shell Lifters

Changing the face angles of shell lifters alters grinding ball trajectories in SAG mills. From the experimental work of McPherson (using traditional blunt-faced shell lifters), spacing between such lifters affects mill performance (McIvor 1983). The former can be used to reduce ball and liner breakage and improve mill performance by directing balls towards the toe of the charge (i.e., away from the liners and to where milling action is most vigorous). Computer-program trajectory tools that illustrate this point have been available for some time. Wider lifter spacing (with fewer lifters) increases the “bucket” size between the lifters and also reduces or eliminates packing, resulting, potentially, in more lift of the charge per rotation of the mill. More lift then results in more thrown balls and charge, and may increase the participation rate of grinding media in impacts at the toe of the charge. Discrete element modeling (DEM) has provided detailed illustration and articulation of these two concepts, and claims have been made that significant improvements in mill performance should result from changes to wider-spacing and large lifter face angles. However, practical experience in recent years has demonstrated that such changes could also lead to charge slippage, increased shell liner wear, and degraded overall mill performance. * Royston Process Technology Pty. Ltd., Brisbane, Queensland, Australia 399

400

ADVANCES IN COMMINUTION

MILL DESIGN

A review of SAG mills that had changed to wider-spaced shell lifters and large face angles showed, in most cases, that the changes were driven principally by (1) packing between lifters or (2) damage in the liners and balls (Royston 2003b, 2004). Wider spacing could eliminate packing, and larger face angles could reduce damaging ball-on-mill impacts. With the alleviation of these immediate issues, mill performance improved. In addition, and almost inevitably with new and expanding operations, other changes occurred in the circuit and in the ore feed at the same time as changes to liner configuration. All such changes would have affected mill performance; particularly changes in ore hardness, which has a dominating effect on mill performance. In that review, it was difficult to assign significant increases in mill performance simply to changes in lifter angle or spacing alone. Where mills did not suffer packing and/or breakage, because of changes in liner design (using the guidelines mentioned), at best, there were modest claims for increases in mill performance. The most recent development has been to introduce a form of the traditional “HiLo” lifter system (where high lifters alternate with low around the mill shell) with, in this new development, “Hi” lifters considerably larger than the practice to date. The “Lo” lifter is kept to a height similar to the Hi in a prior “HiHi” arrangement. The objectives are to increase lifting rate and to influence the grinding action at the toe, while preserving the ball-impact resistance and wear life of the original HiHi lifter set. The practical outcomes of changes to wide-spaced, large face-angle shell lifters are as follows: ƒ In most cases there were immediate issues, such as packing and lifter/ball break-

age, particularly in large mills (36+ ft in diameter), that limited mill performance with traditional “2 u mill diameter”* blunt-faced HiLo lifters. ƒ The practical reaction was to space out the lifters (to reduce packing) and/or

change lifter angle (to direct ball throws into the charge, not the shell, for charge levels >30%). This resulted directly in improvements to mill performance due to the elimination of packing and breakage. ƒ Short-term, early benefits could be gained in using large lifter face angles. They

help a newly lined mill come on grind quickly. But such lifters are also likely to wear out more quickly, so the gains at the beginning may be offset by issues of reduced wear life or lowered throughput at the end of liner life, especially if mills are operated at a fixed speed. ƒ For mills without packing (or other limiting issues such as breakage), DEM out-

puts have indicated potential improved outcomes for wide-spacing and large angles. But significant sustained improvements—solely due to such changes—have been difficult to identify, and are certainly not on the scale of some claims. Shell Liner Design and Mill Performance

Trajectory and charge level tools can be used together with engineering design to investigate the practical mill operating situation, as well as to interpret the output from DEM. The following discusses aspects of this approach. Figure 1 shows the trajectories of an array of balls from a 33-ft-diameter SAG mill using a traditional blunt-faced lifter in HiHi configuration. Figure 2 shows the same configuration but with half-worn shell lifters. Figure 3 shows similar output for a wide-spaced, large face-angle lifter. Figure 4 is a version of Figure 3, but with a higher charge level.

*

In conventional designs, the number of rows of shell lifters is twice the number of feet in the mill diameter.

DEVELOPMENTS IN SAG MILL LINER DESIGN

401

Input Data Mill Diameter Mill Speed Lifter Height from Shell Lining Height from Shell Lining to Transition Plate Thickness Lifter Top Width, Total Lifter Top Width, Leading Lifter Top Width, Trailing Lifter Base Width Corner Radius Lifter Angle Top, Leading Lifter Angle Top, Trailing Lifter Angle Base, Leading Lifter Angle Base, Trailing Ball Diameter Number of Lifter Rows Number of Bolt Hole Rows Shell Liner Length, Overall Liner Wear Plate Wear Packing Fill Level

FIGURE 1

mm rpm mm mm mm mm mm mm mm mm degrees degrees degrees degrees mm # # mm mm mm mm %

10,058.4 10.40 310 175 100 150 75 75 217 0 9 9 9 9 125 66 66 4,627 0 0 0 25.00

33 ft % Nc 78.00 12.20 in. 6.89 in. 3.94 in. 5.90 in. 2.95 in. 2.95 in. 8.52 in. 0.00 in.

4.92 in.

Belly 5,029.2 mm 0.1734 rps and 5.48 m/sec

8.02 kg

182.16 in. 0.00 in. 0.00 in. 0.00 in.

Ball – Lifter Ball Triangle – Second Ball Cross – Late Ball Box Cross – Plate Ball Curve Model Effective McPherson Ratio A:B 1.42 Unpacked Lift Volume 17.52 m3 Lifting Rate 3.04 m3/sec

New blunt-faced shell lifter ball trajectories

Input Data Mill Diameter Mill Speed Lifter Height from Shell Lining Height from Shell Lining to Transition Plate Thickness Lifter Top Width, Total Lifter Top Width, Leading Lifter Top Width, Trailing Lifter Base Width Corner Radius Lifter Angle Top, Leading Lifter Angle Top, Trailing Lifter Angle Base, Leading Lifter Angle Base, Trailing Ball Diameter Number of Lifter Rows Number of Bolt Hole Rows Shell Liner Length, Overall Liner Wear Plate Wear Packing Fill Level

FIGURE 2

mm rpm mm mm mm mm mm mm mm mm degrees degrees degrees degrees mm # # mm mm mm mm %

10,058.4 10.40 310 175 100 150 75 75 217 0 9 9 9 9 125 66 66 4,627 0 0 0 25.00

33 ft % Nc 78.00 12.20 in. 6.89 in. 3.94 in. 5.90 in. 2.95 in. 2.95 in. 8.52 in. 0.00 in.

4.92 in.

Belly 5,029.2 mm 0.1734 rps and 5.48 m/sec

8.02 kg

182.16 in. 0.00 in. 0.00 in. 0.00 in.

Ball – Lifter Ball Triangle – Second Ball Cross – Late Ball Box Cross – Plate Ball Curve Model Effective McPherson Ratio A:B 2.97 Unpacked Lift Volume 9.00 m3 Lifting Rate 1.56 m3/sec

Worn blunt-faced shell lifter ball trajectories

In Figures 1 and 2, the lifter spacing may allow only the “lifter ball,” and balls above it in the bucket, to be lifted. In Figures 3 and 4, more balls sit on the plate and come into play (see Royston 2001). In Figure 1, the lifter ball hits the mill shell, then rebounds and enters the toe region of the charge with high speed and energy (outputs are from trajectory calculations based on simple collision physics). The balls that are higher in the bucket also fall towards the toe end of the charge. As the lifter wears, the same effect continues (i.e., balls continue to rebound and enter the toe of the charge with high energy [Figure 2]). In Figures 3 and 4, the large lifter face angle directs the lifter ball towards the toe of the charge. In Figure 3, the lifter ball still “overthrows,” or rebounds off the shell, into the charge but lower in the shell entering the charge at a lower speed than the equivalent in

402

ADVANCES IN COMMINUTION

MILL DESIGN

Input Data Mill Diameter Mill Speed Lifter Height from Shell Lining Height from Shell Lining to Transition Plate Thickness Lifter Top Width, Total Lifter Top Width, Leading Lifter Top Width, Trailing Lifter Base Width Corner Radius Lifter Angle Top, Leading Lifter Angle Top, Trailing Lifter Angle Base, Leading Lifter Angle Base, Trailing Ball Diameter Number of Lifter Rows Number of Bolt Hole Rows Shell Liner Length, Overall Liner Wear Plate Wear Packing Fill Level

FIGURE 3

mm rpm mm mm mm mm mm mm mm mm degrees degrees degrees degrees mm # # mm mm mm mm %

10,058.4 10.40 310 175 100 150 75 75 346 0 25 25 25 25 125 44 66 4,627 0 0 0 25.00

33 ft % Nc 78.00 12.20 in. 6.89 in. 3.94 in. 5.90 in. 2.95 in. 2.95 in. 13.62 in. 0.00 in.

4.92 in.

Belly 5,029.2 mm 0.1734 rps and 5.48 m/sec

8.02 kg

182.16 in. 0.00 in. 0.00 in. 0.00 in.

Ball – Lifter Ball Triangle – Second Ball Cross – Late Ball Box Cross – Plate Ball Curve Model Effective McPherson Ratio A:B 2.49 Unpacked Lift Volume 18.67 m3 Lifting Rate 3.24 m3/sec

Large-angle-face and wide-spaced shell lifter ball trajectory outputs (low charge level)

Input Data Mill Diameter Mill Speed Lifter Height from Shell Lining Height from Shell Lining to Transition Plate Thickness Lifter Top Width, Total Lifter Top Width, Leading Lifter Top Width, Trailing Lifter Base Width Corner Radius Lifter Angle Top, Leading Lifter Angle Top, Trailing Lifter Angle Base, Leading Lifter Angle Base, Trailing Ball Diameter Number of Lifter Rows Number of Bolt Hole Rows Shell Liner Length, Overall Liner Wear Plate Wear Packing Fill Level

FIGURE 4

mm rpm mm mm mm mm mm mm mm mm degrees degrees degrees degrees mm # # mm mm mm mm %

10,058.4 10.40 310 175 100 150 75 75 346 0 25 25 25 25 125 44 66 4,627 0 0 0 30.00

33 ft % Nc 78.00 12.20 in. 6.89 in. 3.94 in. 5.90 in. 2.95 in. 2.95 in. 13.62 in. 0.00 in.

4.92 in.

Belly 5,029.2 mm 0.1734 rps and 5.48 m/sec

8.02 kg

182.16 in. 0.00 in. 0.00 in. 0.00 in.

Ball – Lifter Ball Triangle – Second Ball Cross – Late Ball Box Cross – Plate Ball Curve Model Effective McPherson Ratio A:B 2.49 Unpacked Lift Volume 18.67 m3 Lifting Rate 3.24 m3/sec

Large-angle-face and wide-spaced shell lifter ball trajectory outputs (high charge level)

Figure 1. In Figure 4, with a higher charge level*, the ball plunges directly into the charge with full energy transfer, potentially more than in the Figure 1 rebound case. These singleparticle models track a limited array of the most significant balls; some move together as a “train,” yet others peel off to separate trajectories. Note in both Figures 3 and 4 that the “late” and “plate” balls (the other balls in the bucket that sit on the plate) rebound off the mill shell before entering the charge, whereas the “second balls” (and others higher in the bucket) fall well short (i.e., they contribute more to attrition than to crushing). We could expect (at constant mill speed) that the trajectories should degrade with time as the lifter heights wear down. For lifters with some overthrow, they should “comeon” to grind (e.g., the situation in Figure 3), then fall away; for those impacting the toe initially (e.g., Figure 4), we could expect only a fall-off in performance. * A similar outcome could be achieved by lowering the mill speed.

DEVELOPMENTS IN SAG MILL LINER DESIGN

403

Increasing mill speeds increases throw and could compensate for lifter wear to maintain grind. The general characteristics mentioned previously would be preserved initially in the wearing lifters; however, with time, any special benefits from new initial lifter profiles (unless of substantial size) are lost, especially at high levels of wear. Practical observations from this engineering analysis, general experience, and computerbased trajectory tools are as follows: ƒ Conventional lifters (those not suffering from packing or breakage) deliver

energy effectively into the toe of the charge through rebound. This could be sustained through a cycle of wear. (But such lifters could also suffer from packing [reduced by wider lifter spacing] and/or ball/liner breakage [reduced by larger lifter face angles].) ƒ Large face-angle lifters need to direct balls into the toe, or the rebounding balls

will be less effective that in the conventional case. ƒ Wide spacing should result in increased lifting rate and participation of balls in

the milling action, but the energy in the lifted material may be dissipated through rebounds or by falling short of the toe. ƒ With large face angles and wide spacing, performance could improve through

“grind-in,” but is likely to degrade through balls undershooting the toe as wear increases. ƒ Any initial advantages in particular initial lifter profiles may be lost with time due

to wear. ƒ Current, new liner designs often adopt large face angles (typically 22˚ but up to,

say, 30˚) with sufficient spacing to overcome packing. ƒ For large mills using 125-mm feed ball size, typical new lifter-liner dimensions are

~300–350 mm overall height above the shell, ~100-mm plate thickness, and ~150-mm top width; detailed design depends on individual mill circumstances. ƒ Mill speed is increased over the lifter life to maintain throw at a “sweet spot” of mill performance; yet as mill speeds increase to greater than 78% of critical speed, pulp lifter efficiencies could fall and affect overall mill performance. Figures 5a and 5b show similar trajectories superimposed on simple DEM output cases (Royston 2001). The trajectory outputs, in effect, provide illustrative tracks of individual balls within the array of discharge shown by DEM. DEM provides similar information to the trajectory analysis but in more detail. Note, for example, the detail of discharge from the “bucket”—the wide-spaced bucket discharges such that part of its contents (in this example) fall well short of the toe of the charge. With more charge information, especially with the evolving 3D and multishape particle versions of DEM, much more impressive detail should be available from DEM (and CFD, computational fluid dynamics). However, the output requires interpretation according to the previously mentioned guidelines before translation into liner designs. Mill Charge Levels

Having hit the charge, grinding balls have to transfer their impact energy effectively to the rock charge. Balls also have to transfer energy to rocks via attrition and abrasion through other aspects of charge motion in the mill (i.e., the lifter-induced swirl at the toe, the nonthrown cascading action, and the relative motion of the rising charge). Together, these are aspects of “ball-charge participation.” Charge participation is a function of the number ratio of balls to candidate rocks. In a practical engineering analysis, the volumetric ratio of balls to “free rocks” could be

404

ADVANCES IN COMMINUTION

MILL DESIGN

Source: Royston 2001.

FIGURE 5a Trajectory model outputs superimposed on DEM outputs

used as an indication of the number ratio. Free rock is the rock sized greater than that present in the fluid pulp. Some years ago, it became a common practice for SAG mills to be run with low charge levels at maximum ball charge levels to improve throughput. Generally, such mills had limits on the total charge mass and/or motor capacity (and the resulting low charge levels often resulted in increased liner damage, and ball and bolt breakage). With newer mills with higher load capacities, high ball charge levels (say, up to 18%) have been used. In both approaches, the objective was to increase ball-charge participation through increasing the ball-to-rock ratio, while drawing maximum power at the maximum allowable total charge mass. This approach is illustrated in Figures 6 and 7, which are derived from a charge tool (based on charge mass balance, and charge and mill geometry) that includes power calculations. Both outputs are for similar charge mass and the same power draft; Figure 7 has the higher ball-to-rock ratio. Note that Figure 7 also has the lower charge level; hence, in that mode, the mill lining is more vulnerable to impact damage. It could be anticipated that more detailed and localized modeling of the DEM type would provide detailed output on the significance of ball-to-rock ratios and to articulate better the arguments mentioned previously. However, as noted, DEM output does need interpretation in the light of experience and is best used in support of engineering judgment in liner design.

DEVELOPMENTS IN SAG MILL LINER DESIGN

Source: Royston 2001.

FIGURE 5b Trajectory model outputs superimposed on DEM outputs

Input Data Mill Diameter Mill Belly Length Flange to Flange Total Shell Liner Length DE to FE Rubber Lining Depth Trunnion Diameter Trunnion Rubber Number of Pulp Lifters Cone Angle Ball Density Mill Speed Solids through Grate Water through Grate Grate % Open Area Depth Center to Solid Charge Charge Mass

mm mm mm mm mm mm # degrees t/m3 rpm tph tph % mm tons

10,058 5,029.2 4,626.9 6 2,514.6 80 33 15 7.84 10.40 710.9 177.72 10 1,450 412

78 %Nc

New Shell Liners

Composition Mass, t

% Mill Vol. % Mill Vol. Net Bulk

Total

412.00

29.97

29.97

Free Rock Total Pulp Pulp Water Pulp Rock Steel Balls

161.17 78.57 17.29 61.29 172.26

14.53 9.89 4.36 5.53 5.55

21.69 0.00

FIGURE 6

33.0 ft 16.5 ft 15.2 ft 0.24 ft 8.3 ft 3.15

8.28

Mill charge, composition, and power draft (low ball participation)

405

406

ADVANCES IN COMMINUTION

MILL DESIGN

END LINERS AND GRATES

The overall charge level in the mill affects both the wear patterns on the end liners and the transfer efficiency of the grate (through the degree of exposure of the grate openings to the charge). Ball trajectories together with charge level (especially low levels) affect end-liner design through the nature of ball impacts on these end liners and grates. End Liner Design/Life Issues

With feed-end (FE) liners, the trend in recent years has been towards FE lifters with angled leading faces and an outer taper designed to shed (i.e., avoid throwing) balls and to even-out the wear along the lifter. One-part lifter liners are favored for larger mills. The position of maximum wear on the FE lifters is around the “eye line” (i.e., the circumferential line “drawn” on the mill end by the “stationary” eye of the charge). Practical issues for FE liners are ƒ Ensure good fit of FE parts with the conical mill head (and mount on sound back-

ing rubber); poor fit could lead to bolt failure and plate cracking. ƒ Limit exposure of parts to radial incoming ball impacts (i.e., avoid exposed ends,

protrusions, and large bolt-hole openings that provide ball impact points that could lead [through persistent impacts] to metal flow and/or fracture). ƒ Avoid mixing new with old parts in ways that expose new parts to impact damage. ƒ Sequence change-out of FE with shell lifters; this avoids wear on old shell lifters

caused by new FE lifters. With the discharge end (DE), most large mills have adopted cantilever grates, usually with a large open area; inter-grate gaps; and a large proportion of pebble ports to promote pebble recycle for pebble crushing. Nevertheless, there are mills with restricted grates that aim to limit rock outflows to promote a fine grind size and other mills that use a return-trumpet system and have to limit the opening size of grate slots to allow steel media to be returned into the mill by the jet. The general structural principles outlined for FE liners apply also to the DE—noting for grates and plates that the fit has to be a match with the underlying pulp lifter (discussed later in this paper). Grate performance as a liner in terms of charge transfer is affected by the following issues: ƒ Peening: Check the impact situation, material of construction, slot opening size,

and wear rates across the surface of the grate. ƒ Pegging, especially ball pegging: Check the reverse taper, pebble ports, in-mill

ball-charge management, ball type, and rock fracture at pegging size; avoid recycling worn balls. ƒ Reverse side outer grate damage: Check the ball throw; grate lifter throw; plate

thickness; edge support; casting integrity, especially at the extremities of the grate; web thickness; web support; and wear-relief rates across plate. ƒ Inner end grate damage: Check the ball throw trajectory, especially if using large

face-angle lifters near the head end; local sources of plunging balls; protection provided by inner plate and [worn?] lifters; metal flow between grate and inner plate; charge levels; casting integrity; web thickness; wear-relief rates across plate, and glacis (protective ramp) on inner plate.

DEVELOPMENTS IN SAG MILL LINER DESIGN

407

DISCHARGE FROM PULP LIFTERS

Pulp lifters serve both to discharge material from the SAG mill and to control the contents in the mill. The interpretation of flow inside the pulp lifter came out of an integration of practical experience (of wear patterns in and discharge from pulp lifters) into a flow mechanism based on the engineering physics of single-particle motion in a rotating channel (Denlay, Woods, and Royston 1997). A single-particle model was developed to describe flow in both straight-radial and curved pulp lifters (and to demonstrate the advantages of the latter; Royston and Denlay 1999, Royston 2000a); followed by a full “engineering design” approach to both grates and pulp lifters (Royston 2000b). More recently, in a fresh approach to the issue of flow in pulp lifters, especially in the discharge cone, a single-particle computer-program motion tool has been developed that covers the full flow path, including that in the discharge cone (Royston 2003a). Outputs from this tool are shown in Figures 8 and 9, for the same mill speed. They illustrate the earlier arrival of the particle at the trunnion in the curved pulp lifter case, hence why curved pulp lifters could be expected to discharge earlier (thus, perform better) than straight-radial pulp lifters. Figure 10 extends this output to cover the single-particle tracks at the discharge cone where up to four channels converge into a single discharging channel. NOTE: For straight-radial pulp lifters, particles from higher, shorter channels fall to the lowest channel wall and in these examples would fail to discharge. These tracks are reflected in the wear patterns observed in discharge cones and help to explain when and how backflow (of undischarged rocks down the pulp lifter) occurs. The velocity data from these outputs show that the discharge channels themselves do not choke (i.e., fill with normal outflowing charge) to prevent outflow. “Backflow rocks” that restrict pulp lifter outflow also prefill and reduce pulp-lifter capacity, as shown in Figure 11. A partial solution, as supported by practical experience and the engineering analysis mentioned previously, is to increase the pulp lifter depth from front to back and/or to increase the depth of the pulp lifter channel towards the center of the mill. In this way, the depth of the blockage caused by the burden of backflowing rocks is reduced, which helps the overall discharge of pulp and rocks. Curved pulp lifters provide a better solution by discharging rocks much sooner and more completely; however, they do require a commitment to unidirectional rotation of the mill. Curved pulp lifters continue in successful application. Their long wear lives provide proof of their “elimination” of backflow as an issue (Royston 2003a, 2005). Flow through a pulp lifter is complex, even more so if the grate–pulp lifter interaction flow and flow in the discharge cone discussed above are taken into account. DEM-type illustrative outputs have been presented on pulp lifter and grate flows and used to support the use of curved pulp lifters at Cadia (Hart et al. 2001; Figure 12), and have also been used to illustrate pulp lifter flows and backflow (Rajamani, Latchireddi, and Mishra 2003). LINER SIZE AND MATERIALS

There is a developing trend towards large liner sizes, especially in larger mills. There is some pull and push in this development. The pull is the need to reduce downtimes and simplify change-outs. The push is the availability of large-capacity liner-handling machines and associated bolt-removal impulse hammers (as well as other equipment aimed to mechanize and at the same time improve the safety of change-outs). “Double-wide” parts are increasingly common for end liners, grates, and now shell liners, and foundries are directing efforts to supply such parts. Important issues in moving to double-wide parts are to ensure full fit, and for grates not to overlap joints in the pulp lifters (i.e., one-on-one fit is required); otherwise, there is a risk of breakage at or near the joint. “Chrome-moly” alloy steel is still the dominant material of construction and choice for SAG mill liners, with white iron being the material of choice for nonimpact abrasive

408

ADVANCES IN COMMINUTION

MILL DESIGN

Input Data Mill Diameter Mill Belly Length Flange to Flange Total Shell Liner Length DE to FE Rubber Lining Depth Trunnion Diameter Trunnion Rubber Number of Pulp Lifters Cone Angle Ball Density Mill Speed Solids through Grate Water through Grate Grate % Open Area Depth Center to Solid Charge Charge Mass

mm mm mm mm mm mm # degrees t/m3 rpm tph tph % mm tons

10,058 5,029.2 4,626.9 6 2,514.6 80 33 15 7.84 10.40 710.9 177.72 10 1,839.6 418.7

78 %Nc

New Shell Liners

Composition Mass, t

% Mill Vol. % Mill Vol. Net Bulk

Total

418.70

25.00

29.97

Free Rock Total Pulp Pulp Water Pulp Rock Steel Balls

92.75 65.54 14.42 51.12 260.41

8.36 8.25 3.64 4.61 8.39

12.48 0.00

FIGURE 7

33.0 ft 16.5 ft 15.2 ft 0.24 ft 8.3 ft 3.15

12.52

Mill charge, composition, and power draft (high ball participation)

05 0.4 0.3 0.2 0.1

–0.5 –0.4 –0.3 –0.2 –0.1 –0.1

0.1

0.2

0.3

0.4

0.5

–0.2 –0.3 –0.4 –0.5

FIGURE 8

Straight-radial pulp lifter particle track

wear zones. Specialized formulations around the chrome-moly type of materials are being promoted; these are based on changing microstructures and through-hardness, and are claimed to provide improved wear resistance in certain applications, especially abrasion-prone parts of SAG mills. Other liner suppliers claim harder versions of their “standard” products give similar outcomes. One interesting new development is that of bimetallic liners using white-iron inserts that could give increased wear life in lowimpact abrasion-prone locations in the mill such as in end liners.

DEVELOPMENTS IN SAG MILL LINER DESIGN

409

0.5 0.4 0.3 0.2 0.1

–0.5 –0.4 –0.3 –0.2 –0.1 –0.1

0.1

0.2

0.3

0.4

0.5

–0.2 –0.3 –0.4 –0.5

FIGURE 9

Curved pulp lifter particle track

02

0 25

02

0 15

0 15

01 01

0 05 0 05

0 15 02

0 15

01

0 05

0 05

01

0 15

02

0 25

02

0 05 01

0 05

01

0 15

02

0 25

0 05

0 05

01

01 0 15

0 15 02

02

0 25

Source: Hart et al. 2001.

FIGURE 10

Particle tracks in discharge cone: (a) top channel entry, and (b) middle channel entry

REFERENCES

Denlay, D.R., R.J. Woods, and D. Royston. 1997. Development of the ANI Bradken vortex pulp lifter and spherical head bolt mill liner fastener system. Pages 67–71 in Proceedings 6th Mill Operators’ Conference, Australasian Institute of Mining and Metallurgy, Madang, Papua New Guinea, October 6–8. Hart, S., W. Valery, B. Clements, M. Reed, M. Song, and R. Dunne. 2001. Optimisation of the Cadia Hill SAG mill circuit. Pages 11–30 in Proceedings International Conference on Autogenous and Semiautogenous Grinding Technology. Volume 1. SAG 2001, Vancouver, BC, 30 September–3 October.

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ADVANCES IN COMMINUTION

MILL DESIGN

Source: Hart et al. 2001.

FIGURE 11

Pulp lifter rocks

Straight Radial Lifter

Curved Radial Lifter

Source: Hart et al. 2001.

FIGURE 12

Pulp lifter discharge

McIvor, R. 1983. Effects of speed and liner configuration on ball mill performance. Mining Engineering (June): 617–622. Rajamani, R.K., S. Latchireddi, and B.K. Mishra. 2003. Discrete element simulation of ball and rock charge and slurry flow through grate and pulp lifters. SME Annual Meeting, Cincinnati, OH, February 24–26. SME Preprint 03-108. Littleton, CO: SME. Royston, D. 2000a. Curved pulp lifters for AG and SAG mills. SME Annual Meeting, Salt Lake City, UT, 28 February–1 March. SME Preprint 00-14. Littleton, CO: SME. ———. 2000b. Grate-pulp lifter interaction in SAG/AG Mills. Pages 63–67 in Proceedings 7th Mill Operators’ Conference. Australasian Institute of Mining and Metallurgy, Kalgoorlie, Western Australia, October 12–14. ———. 2001. Interpretation of charge throw and impact using multiple trajectory models. Pages 115–123 in Proceedings International Conference on Autogenous and Semiautogenous Grinding Technology, SAG 2001. Volume 4. Vancouver, BC. 30 September– 3 October.

DEVELOPMENTS IN SAG MILL LINER DESIGN

411

———. 2003a. Current experience with curved pulp lifters. SME Annual Meeting, Cincinnati, OH, February 24–26. SME Preprint 03-055. Littleton, CO: SME. ———. 2003b. A review of recent experience with large-angle wide-spaced shell lifter-liners. SME Annual Meeting, Cincinnati, OH, February 24–26. SME Preprint 03-056. Littleton, CO: SME. ———. 2004. Charge flow in pulp lifters. In Proceedings of Metallurgical Plant Design and Operating Strategies. Australasian Institute of Mining and Metallurgy, Perth, Australia, September 6–7. ———. 2005. SAG mill pulp lifter design, discharge and backflow. SME Annual Meeting, Salt Lake City, UT, 28 February–2 March. SME Preprint 05-049. Littleton, CO: SME. Royston, D., and D.R. Denlay. 1999. Design and performance of curved SAG mill pulp lifters. SME Annual Meeting, March 1–3, Denver, CO. SME Preprint 99-52. Littleton, CO: SME.

The Gearless Mill Drive—The Workhorse for SAG and Ball Mills Reinhold A. Errath*

ABSTRACT

The Antamina concentrator plant was one of the first plants in the world to install 60 MW in milling power. It was also one of the first plants to have both semiautogenous grinding (SAG) mills and the ball mills powered by gearless mill drives (GMDs). As a result of the use of GMDs, the speed of the mills is adjustable, allowing the operators to react to the different ore grades in order to achieve the best results in terms of milling efficiency. Antamina was also the first plant to operate with a power requirement of more than 100 MW on a network that had, under other operating circumstances, a very weak fault level (<300 MVA). The GMD has the capability to operate in such a condition. Since the Antamina installation in 1999, several other similar plants, with even greater power, have been installed and are operating successfully. It is time to look more closely at the installation, design, and operation of the GMD and to make its advantages apparent. The paper describes in detail the basic design of a GMD—its construction, manufacturing facilities, transport, installation, and its function. It should provide enough insight to understand why GMDs are so reliable, the usefulness of their adjustable-speed drive, and why they have the highest efficiency of all drive systems. It also describes the overload capabilities, the reaction to the network, and the reason why the maintenance of the drive system is less consequential. Additionally, it should make clear why the GMD is called a “workhorse.” B A S I C D A T A A N D P HYS I C A L L AYO U T

Antamina’s concentrator plant is situated in northern Peru, in the mine of Yanacancha, at an altitude of 4,300 m. The grinding circuit consists of one SAG mill and three ball mills with an enormous pure grinding power of 72,000 hp for an average design throughput of 70,000 tpd. The mine produces mainly copper and zinc concentrate. The concentrate is pumped through a 302-km pipeline to Antamina’s port facility at Huarmey, where the concentrate is dewatered and shipped overseas. The SAG mill shown in Figure 1 has the following characteristics: ƒ Mill diameter of 38 ft ƒ Mill length of 19 ft ƒ Nominal power of 27,000 hp ƒ Nominal torque of 20 MN·m

* ABB Schweiz AG, Switzerland 413

414

ADVANCES IN COMMINUTION

FIGURE 1

MILL DESIGN

SAG mill driven with a GMD

ƒ Mill maximum speed of 10 rpm ƒ Mill operating range between 9 and 10 rpm ƒ Drive train designed for 130% starting torque

The SAG mill discharge is distributed to the three ball mill circuits through a splitter box. The ball mills shown in Figure 2 have the following characteristics: ƒ Mill diameter of 24 ft ƒ Mill length of 35.5 ft ƒ Nominal power of 15,000 hp each ƒ Nominal torque of 8.2 MN·m ƒ Mill maximum speed of 13 rpm ƒ Mill operating range between 10.5 and 13 rpm ƒ Drive train designed for 130% starting torque THE HISTOR Y OF THE GEARLESS MILL DRIVE

The first GMD with a power of 6,500 kW was installed in 1969 in a cement plant in Le Havre, France. In the first few years, the GMD was only used in the cement industry. The GMD is known also as a wraparound and a ringmotor. Almost 20 years later, the first GMD with 6 MW of power and 17.2 rpm was installed in the minerals industry. Since then, numerous GMDs for SAG mills have been installed in the minerals industry for several reasons: ƒ The GMD is adjustable in speed, which can meet the requirements for a range of

minerals for SAG mills. ƒ The GMD does not need any gearbox and ring gear. ƒ In terms of power, there are really no design limits in the upper range—not on the

electrical part and not in terms of mechanical considerations.

THE GEARLESS MILL DRIVE—THE WORKHORSE FOR SAG AND BALL MILLS

FIGURE 2

415

Three ball mills driven with GMDs

Antamina was the first plant in the world where all the mills—the SAG and ball mills—have been equipped with GMDs. A drive with a huge power requirement—such as in ball and SAG mills with between 10 and 20 MW—has a certain complexity. The GMD should not be considered a single drive anymore but rather a drive system. The challenge on the one hand, and the big advantage on the other, is that the drive itself covers all the operational needs to run the mill properly. The GMD system includes not only the motor and drive regulation algorithm, the transformer, and the drive and motor protections, but it also includes the control and supervision of the hydraulic and lubrication equipment for the mill bearings, the mechanical mill break control, and the visualization of all parts of the drive system. Figure 3 shows all the involved equipment for a GMD. Not only is it a driveʊit is a drive system. THE MOTOR

The GMD, obviously, is a drive system without any gears. The transmission of the torque between the motor and the mill is realized in the magnetic air gap between the motor stator and the motor rotor. The idea to drive the mill this way is simple, based on the fact that the mill body is used as the rotor, onto which the poles are mounted. Around the mill/poles, the stator is erected. This simple and ingenious design results in the fact that the motor does not have a rotor by itself, and consequently, no bearings for the rotor are needed. Only the mill needs bearings, which it already has. Rotor Installation

Figure 4 shows the mill body with the flange for pole mounting. The first step in mounting the mill and the motor is to put the mill body in position. The motor is synchronous with a separate excitation. The number of poles is based on the required speed of the mill. Generally, the bigger the mill diameter, the lower the mill operating speed and critical speed. Consequently, the number of poles will tend to increase; therefore, the bigger the diameter of the mill and the lower the critical speed, the higher the number of motor poles. This explains the different quantity of poles in past installations in which the mill speed has varied between 15 rpm in smaller mills and 9.8 rpm in larger SAG mills.

416

ADVANCES IN COMMINUTION

FIGURE 3

Schematic of equipment in a GMD

FIGURE 4

Mill body with flange for pole mounting

MILL DESIGN

THE GEARLESS MILL DRIVE—THE WORKHORSE FOR SAG AND BALL MILLS

417

Figure 5 shows a number of single poles before the impregnation process. The pole support plate has three holes, of which the outer two are prepared to fit the eccentric bushings. The fixing of the poles on the mill flange is made by pure friction, no-shear forces. The poles are made with laminated sheets, and the whole construction is compacted together with press plates. The winding layers are separated from one layer group to the other to allow the cooling air to pass through it. Consequently, this means that usually the configuration varies from 48 to 72 poles. The weight of one single pole is about 2 t. The motor operates with a typical frequency form zero to about 6 Hz. The poles will be transported loose, as single units, to the site. The mill body in the pole mounting process is shown in Figure 6. Before the pole mounting starts, the dimension and tolerances of the mill flange have to be checked in both directions, radially and axially. The mill shell has to be in the exact position and must be able to turn. For safety reasons during the erection of the poles and the resulting temporary unbalanced load conditions, the mill shell must be secured. Each pole is fixed to the mill flange with one center bolt and two eccentric bushings. The torque transfer from the poles to the mill flange is realized purely by friction; no shear forces are applied. With the eccentric bushings, a perfect run-out of the poles can be achieved. Tolerances of the mill flange can be compensated for with this system. The exact run-out is needed to reduce the risk of unbalanced magnetic pulls around the circumference. After the erection of the first pole, the mill is turned 180˚, and the second pole then mounted in order to keep the mill balanced. This procedure will continue until all poles are mounted. Figure 7 shows all the poles and the slip rings mounted on the mill shell. After mounting the poles, the tolerance for the run-out over the complete circumference is within 0.5 mm. Taking this 0.5 mm in relation to the outside diameter of the rotor— which can be up to 12 m or more, depending on the mill diameter—the precision is similar to that of a Swiss watch. The GMD motor is, by design, a synchronous motor. Synchronous motors need an excitation to build up a magnetic field. The excitation power is fed via carbon brushes to the two slip rings and then distributed to the single poles. Excitation power is dependent on the mill power, between 250 and 450 kW. ABB has evaluated a series of copper alloys for the slip rings, but the best results and performance, in terms of carbon brush consumption, lifetime of the slip rings, and the ohmic resistances between the carbon brushes and the slip rings, were achieved with slip rings made with pure electrolytic copper. Stator

The stator is built with the capability to be shifted. Part of the erection is done in the shifted position, which allows work activity with the rotor and the stator to proceed in tandem. When the installation of the stator is finished, it will be shifted to the position over the rotor. In order to allow stator shifting, the base plate of the stator is elongated. Stator Design

Depending upon the mill diameter, the stator will be either a foot-mounted or pedestalmounted design. Foot-mounted designs are used mainly with mills having a smaller diameter of ~25 ft or less. This means the foot-mounted design is reserved generally for ball mills up to the mentioned diameter. The reasons for this are the mechanical stability of the stator construction, as well as the thermal expansion. As the foot-mounted design can expand only in one direction—upwards—it can result in an undesirable change in the air-gap distance between the stator and the rotor. On the lower position of the stator, the air gap would have the tendency to decrease, and on the upper side of the stator, the air gap would have the tendency to increase, thus creating an undesirable, unbalanced magnetic pull.

418

ADVANCES IN COMMINUTION

FIGURE 5

Single poles before the impregnation process

FIGURE 6

Mill body in the pole mounting process

FIGURE 7

Poles and slip rings mounted on the mill shell

MILL DESIGN

THE GEARLESS MILL DRIVE—THE WORKHORSE FOR SAG AND BALL MILLS

419

The basic design of a GMD with a foot-mounted design is shown in Figure 8. The stator is built and delivered in three pieces for smaller ball mills and in four pieces for larger ball mills. The individual stator quarters are mounted together on-site. The reason for the multiple-piece design is not only for ease in transporting the huge pieces, but also because of the weight, which would be too heavy to lift and handle as a single unit. The stator as a single unit would have a weight of about 300 to 400 t. The stator is affixed only at its base. The joints for the four stator quarters are located at the three-, six-, nine-, and twelve-o’clock positions. Lateral Forces

To withstand the lateral forces (i.e., to keep the motor stator in its position) that are created during normal operation as well as during failures, several structural factors and methods are used to maintain the GMD position, including: ƒ 20 screws M56, 20% ƒ Dowel pins, 59% ƒ Retention blocks, 18% ƒ Stator’s own weight, 3% with a friction factor of 0.15

The basic design of a GMD with a pedestal-mounted design is shown in Figure 9. An important design parameter is the thermal expansion of the stator construction. When the stator expands thermally, it can expand in both directions, from the stator fixing point “up” as well as “down” below the fixing point. Because SAG mills are usually larger in diameter than ball mills, the pedestal-mounted design will often be used. With this method, the center line of the rotor will remain independent of the magnitude of the thermal expansion, always in the center position. The stator is affixed at the three- and nine-o’clock positions. The safety factor between the possible lateral forces created and the ability to withstand damages is between 1.5 and 2. The worst-case scenario in the creation of lateral forces is the situation of an unbalanced two-phase short circuit. This unbalanced short circuit is not an operational condition, but the design of the stator must be able to withstand it. Stator Installation

The stator is delivered in four stator quarters. The stator quarter joints are located at the three-, six-, nine-, and twelve-o’clock positions. The stator segments are equipped with lifting lugs, and for safe handling, the center of gravity is indicated on the segments as well. Installation of the lower quarter of a stator is shown in Figure 10. The stator lower quarters are installed after the mill body is in its final position. The stator quarters are delivered fully assembled with the impregnated windings and wedges attached. At the joints, the windings and wedges have to be installed and finished on-site after the segments are screwed and bolted together. At both ends, the windings and wedges are not inserted into the slots until the assembly of each stator segment. Movement of the segments to the required position is a challenge, because the space available to allow handling of the 70-to-90-t segment is restricted. On one side of the pile is the concrete construction of the pedestal, and on the other side of the mill body. The segment lowering is done with the help of a high-capacity overhead or mobile crane. Inserting into the final position below the mill is accomplished with one or two manually operated rope power pullers called come-alongs. Once in the correct position, the segment will rest on a temporary support until it is screwed and bolted together with the second lower quarter. After installation is complete, the temporary support will be removed in order to give the stator room to thermally

420

ADVANCES IN COMMINUTION

FIGURE 8

FIGURE 10

GMD with a foot-mounted design

MILL DESIGN

FIGURE 9 design

A GMD with a pedestal-mounted

Installation of a stator’s lower quarter

expand in the down direction once the stator reaches its operating temperature. Joining the windings of one segment with the other will be completed when the mechanical stator erection is finished. The installation of the stator’s upper quarter is not as challenging as the lower quarter, because the positioning of the segment is much easier, due to the free access to the final segment position (Figure 11). The same procedure followed in the lower segment must be repeated with the upper segment, giving the segment a temporary support, before the second upper quarter is placed. After installation of all four segments, and after the segments are screwed and bolted together, the rest of the windings on the joints of the segments can be installed. These windings are delivered already formed in the correct shape. After inserting the winding bars into the slots (Figure 12), the electrical interconnection has to be made by brazing them together. The brazing will be done by specialized local workers using inductive heating. The brazing equipment operation is based on a medium-frequency inductive coil. The alloy used is a silver/copper composition. After the brazing process, the winding bars will be isolated with multilayer hot-applied epoxy tape and a one-layer glass tape. Then, this part will be impregnated and, after drying, the impregnation will be painted and high voltage tested. All of these activities can be done concurrently to the rotor pole mounting, because the stator is shifted out of the rotor position.

THE GEARLESS MILL DRIVE—THE WORKHORSE FOR SAG AND BALL MILLS

FIGURE 11

Installation of a stator’s upper quarter

FIGURE 12

Brazing of the inserted winding bars

421

Sealing System

The GMD must be protected from the hostile environment in which it operates. To fulfill this requirement, an axially operated greaseless sealing system was developed by ABB especially for this purpose and has been used for many years. This sealing system protects the inside of the motor from both of the following ambient conditions: ƒ Wet (moisture- and water-containing particles) ƒ Dry (dust-containing particles)

422

ADVANCES IN COMMINUTION

MILL DESIGN

Rotor Cover Mill Side Protector

Motor Side Rubber Gasket

Rubber Profile

PTFE Rings

Spring

FIGURE 13

Stator Cover

Schematic of a greaseless sealing system

In order to prevent contamination inside the motor, makeup fans produce a positive pressure inside the motor. Buildup of a positive pressure is only possible if the sealing system is operating properly. A greaseless sealing system is shown in Figure 13. The ABB sealing system contains several sealing elements. All the sealing elements are at the static part of the system. The main sealing function will be achieved by ƒ Two polytetrafluoroethylene (PTFE)–bronze rings ƒ Two rubber profiles ƒ Rubber gasket protection cover ƒ Spring-loading system

To ensure that the PTFE rings will always be in close contact with the rotating part, a spring-loading system is applied. This ensures that there’s always a proper sealing, independent of the condition of the PTFE–bronze rings, whether new, half worn, or 10% life remaining. The use of the materials previously mentioned makes the system unique in the sense that it does not need to be greased to fulfil its function. In this sense, it not only fulfils its purpose, but it is also environmentally friendly. The PTFE–bronze-to-metal seal has an extremely long service life. Depending on the local operating conditions, its operating life is between 25,000 and 60,000 hours before it has to be changed. This time frame means a change of the seal is needed sometime between 3 and 8 years. The sealing tracks are easily inspected through access inspection boards. Provisions are incorporated for sealing monitoring, to know when the sealing is wearing out. The sealing height sensor supervision creates an alarm signal about 2,000 hours before the sealing gets to the end of its service life. The maintenance department has, with this 2,000 hours left, enough time to plan a stop of the mill, to order the new sealing material and arrange for the personnel to change it. If change of the sealing system is made with the premanufactured sealing elements (Figure 14), the work can be completed in less than a day.

THE GEARLESS MILL DRIVE—THE WORKHORSE FOR SAG AND BALL MILLS

FIGURE 14

423

Premanufactured sealing system elements

In order to prevent grooving in the rotating metal part, the sealing rings are slightly oval shaped. With this design, the effect of grooving will be largely eliminated, because the PTFE–bronze rings are not touching the rotating part along the circumference at the same place. Cooling System

The GMD system is recognized for its high efficiency, which can be achieved only if the losses are kept to a minimum. The main losses in the motor are resistive heating in the windings (I2R losses). One method for keeping these losses low is to lower the resistance of the windings by implementing larger-diameter current conductors, which means putting more copper inside the windings. Another method that helps to reduce the losses is to increase the voltage of the motor and thereby reduce the current, resulting in lower I2R losses. Both measures are implemented with the ABB GMD design. Additionally, the cooling of the motor is very important to achieve high efficiency of the system. The lower the operational winding temperature, the lower the losses. The motor cooling system in the ABB GMD is designed to achieve the lowest possible operating temperature in the windings. The Primary Cooling Circuit

The water supply can come from a closed, chilled water system or from fresh water. Usually the solution with chilled water will be used only if the ambient water temperature is too high or if water is not available in a freshwater quality. The feedback water from the hot side of the heat exchanger can be used for process purposes. The motor cooling system consists of two independent cooling circuits (Figure 15), a primary water circuit, and a secondary air circuit. The motor itself is cooled by two independent air-cooling systems, one system for the left-hand side and one system for the right-hand side. The Secondary Cooling Circuit

The cooling system of the motor consists of two closed air-cooling systems, one for the left side of the motor and one for the right side. Makeup fans are installed to obtain a positive pressure in the closed cooling system. The reconditioning of the warm feedback air from the motor is accomplished with two water-to-air heat exchanger units, one for each side of the motor.

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ADVANCES IN COMMINUTION

MILL DESIGN

Motor Left Side Air Fan

Motor Right Side Air Fan

Water

Water

Water/Air Heat Exchanger

FIGURE 15

Water/Air Heat Exchanger

Basic design of a motor cooling circuit

The cold air from the heat exchanger is distributed along half of one motor from the base to the top. The cooling effect is very efficient, because the cooling system is not only surface cooling, but also is based on core cooling (Figure 16). The injected cooling air passes through the stator lamination core, which contains cooling holes. Also, on the rotor poles, the winding layers are separated from each other in order to circulate the cooling air and keep the windings cool from within. Hot-spot temperatures can be eliminated in this way and efficiency improved. Equal Distribution of Cooling Air

It is the nature of air transportation that a pressure drop occurs along the cooling air ducts. In order to get an equal distribution of the cooling air quantity, the number of cooling holes, which allow the cooling air to move through the stator laminations, is inversely proportional to the pressure drop. The highest pressure in the cooling circuit occurs near the fans, in the water-to-air heat exchanger in the lower part of the motor. The lowest pressure is found in the top of the motor. Consequently, the lowest number of holes, where the air moves through, is in the lower part of the stator, and the highest number of holes is in the upper part of the motor. With this method, an equal distribution of cooling air quantity can be achieved. Water-to-Air Heat Exchanger

As previously discussed, the motor has two internal cooling circuits, one for the left side of the motor and one for the right, which also include two water-to-air heat exchangers. Generally, the weak point of heat exchangers is their ability to operate with different coolant or water qualities. In most cases, potable water quality is required. The heat exchangers included in the GMD are of an advanced design in this regard; even seawater or heavily contaminated water is suitable. The only required condition is that the temperature of the coolant liquid should be lower than 32˚C. The heat exchanger module consists of the heat exchanger plates and two to four fans, depending on the size of the motor and the heat developed. The design of the number of fans applied is such that the cooling system can operate if one fan is out of commission. The module is mounted below the motor and does not have any direct screwed on or fixed contact to the motor frame. It is attached to the motor frame by a rubber tube or an inflatable tube (Figure 17). This kind of construction was selected so that the eventual vibrations from the motor stator body to the heat exchanger would not be transmitted. Heat exchangers are sensitive to vibration, because vibration can accelerate the aging speed of the water tube joints, resulting in breaks in the tubes and subsequent water leakage.

THE GEARLESS MILL DRIVE—THE WORKHORSE FOR SAG AND BALL MILLS

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FIGURE 16

Cooling principle of the motor-cooling secondary circuit

FIGURE 17

Water-to-air heat exchanger attached to the motor stator body by an inflatable tube

Summarizing the configuration of the heat exchanger modules, there are five valid advantages with the GMD motor cooling design: 1. Eventual vibration of the motor stator body cannot be transmitted to the heat

exchanger modules. 2. The system is operable even if one cooler fan fails. 3. There are no water tubes and heat exchangers at the level of the motor stator

and therefore no danger of water penetrating into the motor in case of a water leakage. 4. The cooling air quantity is equally distributed in the motor stator and rotor poles. 5. Due to the fact that the heat exchanger is on the motor’s lowest position, an

eventual water leak can be detected with a water leakage detector. Air-Gap Monitoring

The air gap is the distance between the rotor poles and the stator. The distance of the air gap on the complete circumference should be kept equal to avoid unbalanced pulling between the rotor and the stator. The pull between the rotor and the stator is inversely

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ADVANCES IN COMMINUTION

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proportional to its distance. Large distances lead to reduced pulling and small distances to increased pulling. The air gap of the GMD is quite large, between 15 and 18 mm, depending on the mill size. Therefore, the system is not sensitive to small misalignments between the stator and the rotor. However, it is a common engineering and protection practice to monitor and supervise the air gap from generators and motors of larger sizes. In the application of a GMD, knowledge about the air-gap condition is vital and must be regarded as a critical matter. Contrary to a standard motor where the stator and the rotor form one unit, in the GMD design, the stator and the rotor each have their own foundations, which are the foundations of the mill bearings on the mill feed and mill discharge ends. Both foundations do not necessarily have a common base foundation. The air-gap detection system detects problems mainly in the following situations: ƒ Settling or moving of only one foundation on the feed or discharge end in

earthquake-prone zones, or in zones with a soft soil ƒ When the mill body forms a banana shape, which is sometimes caused when a

charged mill remains stationary for a long time ƒ Any change in the stator structure like collapsing of the stator, or the rotor struc-

ture like the mill body becoming oval shaped The Principle of the Air-Gap Measurement

The air-gap measurement is designed with noncontact, capacitive probes. The family of VM capacitive sensors (Vibrosyst M, Longueuil, Quebec, Canada) is designed for various measuring ranges from 1 to 50 mm with customization possibilities. The sensors are glued on to the stator wall and linked to a signal conditioner. The conditioner provides an analog output signal of 4–20 mA, which is proportional to the air gap. It is factorycalibrated to the required sensor type and the length of the cable. The air-gap system provides direct and safe access to true and precise air-gap values and helps determine the type and location of anomalies around the stator/rotor. The measuring accuracy is r2% and can operate in an ambient temperature up to 125˚C. Physical Arrangement

The positioning of one air-gap probe on the stator is shown in Figure 18. The air-gap probe is extremely flat with dimensions of 120 u 90 u 2 mm. The total number of air-gap probes installed is nine. The position of the air-gap probes are ƒ Three air-gaps probes on the lower part of the stator in the range of five- to seven

o’clock ƒ Two air-gap probes on the left-hand side of the stator in the range of eight- to nine

o’clock ƒ One air-gap probe on the upper part of the stator in the range of twelve o’clock ƒ Three air-gap probes on the right-hand side of the stator in the range of two- to

four o’clock The probes are positioned, and signals from them are processed in such a way that the air-gap probes do not show an error when the rotor is turning and the air-gap probe is positioned between two poles.

THE GEARLESS MILL DRIVE—THE WORKHORSE FOR SAG AND BALL MILLS

FIGURE 18

427

Photo showing the positioning of one air-gap probe on the stator

Signal Processing and Fault Handling

In normal conditions, the air gap is 16 mm. If the rotor is out of center for ƒ r4 mm, an alarm signal will be generated ƒ r5 mm, a trip signal will be generated

As the GMD does not have a tachometer or a position sensor, the position of the rotor is not known. The air-gap signals are used to determine what position the rotor is in at any moment. Every time a pole passes the probe, a signal is created. Between the poles, the probe will show definitive distances. A counter will record the number of poles passed in front of the probe. This signal serves for rotor positioning purposes and also for the position identification for the dropping charge protection. THE HOUSE

In order to operate in harmful, dusty areas, all the electrical equipment is installed in an air-conditioned and containerized electrical house (E house; Figure 19). The container provides adequate protection against ingress of dust and water and contains all electrical main and auxiliary electrical equipment such as ƒ Cycloconverter, three-phase with all its protective elements for the motor stator ƒ Direct-current (dc) excitation equipment for the motor rotor with all its protective

elements ƒ Motor control centers (MCCs) for all motor and external auxiliary equipment,

including hydraulic and lubrication systems and the brakes ƒ Programmable logic controller (PLC) for the control of the auxiliary equipment,

including lubrication and hydraulic units ƒ Programmable high-speed regulator (PSR) for the motor control and regulation

algorithm ƒ Converter transformer protection relays ƒ Excitation transformer protection relays ƒ Fire-fighting system ƒ Uninterrupted power supply (UPS) for the PSR and the PLC ƒ Visualization of the complete drive system with the video maintenance system (VMS)

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ADVANCES IN COMMINUTION

FIGURE 19

MILL DESIGN

Air-conditioned, containerized E house with IP 55 protection

The E house comes on-site completely assembled, internally cabled, and factoryfunctionally tested. Therefore, installation and subsequent commissioning on-site requires only the connection of external cables and checking of external signals. Consequently, only a very short commissioning time is required. The Cycloconverter Design and Principle.

The cycloconverter is a frequency changer that converts a polyphase voltage with the frequency f1 into a single or polyphase voltage with a different, lower frequency f2. Energy can be transferred in either direction directly without a dc link. Consequently, the cycloconverter is classified in the group of line-commutated converters. If the output current of such a converter is controlled to obtain a sinusoidal shape with a given frequency, as shown on Figure 20, the arrangement acts as a frequency converter and is called a cycloconverter. By virtue of its design, the cycloconverter consists of reversible, usually suppressed, half-thyristor converters used for years with dc drives. The basic unit is generally a threephase bridge with which a three-phase voltage can be converted into a direct voltage. In this way, the converter output is a positive, rectified voltage in rectifier operation, or a negative, rectified voltage in inverter operation. Figure 21 shows the principal design of a six-pulse cycloconverter. By means of phase-angle control, this voltage can be continuously varied from zero to roughly the maximum phase-to-phase ac voltage, both in the positive and the negative polarity. Figure 22 shows the operating range of a cycloconverter for one phase. The reactive power of commutation required for the current transfer between the individual legs of each bridge is obtained from the power system. Only one of the antiparallel bridges is in operation at a time, so that circulating currents are entirely excluded. When the current reverses (i.e., when the current commutates to the antiparallel bridge), a short dead time is observed before this antiparallel bridge is fired. Methods of Controlling the Cycloconverter/Motor. Two different modes of operation are used to control the entire speed range (i.e., frequency range) of the drive: 1. Sinusoidal operation (see Figure 20): The sinusoidal operating range is from the

starting point up to the drive operational range. In this range, the output has a constant torque capability with varying power. The network power factor in this mode is from about 0.2 up to 0.8. This mode is used just for startup.

THE GEARLESS MILL DRIVE—THE WORKHORSE FOR SAG AND BALL MILLS

2

429

1

u+

u–

i+

A B

i–

FIGURE 20

Output voltage of a cycloconverter for one phase in the sinusoidal mode of operation

f1 S

T2

n2

T1

T1

T1

n1 B i– A i+

FIGURE 21

= Circuit-breaker = Output Current and Voltage = Converter Transformer = Six-pulse Stator Converter = Excitation Current = Excitation Converter = Stator Currents = Synchronous Motor = Stator Voltages = Three-phase Bridges Connected in Antiparallel f1 = Mains Frequency f2 = Frequency of Synchronous Motor

u+ u

iR ie

S i+, i–, u+, u– T1, T2 n1 ie n2 iR, iS, iT SM uR, uS, uT A, B

uR

iS uS SM 3

iT uT f2

Principal design of a six-pulse cycloconverter

id

M IV

a

I

Vd

id n III

M = Torque n = Speed

FIGURE 22

Vd

Operating range of a cycloconverter for one phase

II

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ADVANCES IN COMMINUTION

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2. Trapezoidal operation (see Figure 23): The trapezoidal operating range is for the

entire mill operating range. In this range, the output has a constant power capability with varying torque. It is operating in the field-weakening range. The longer the converters are operated with a full firing angle over one cycle of the machine frequency f2, the better the main power factor. The slopes of the trapezoidal characteristic do have a certain limit. The network power factor in this mode is about 0.82. Figure 23 shows the output voltage of a cycloconverter for one phase in the trapezoidal mode of operation. As the output frequency of the cycloconverter is derived from the main frequency, it must be lower than that frequency. In practice, the output frequency f2 can be continuously varied from zero to about 50% of the system frequency. The maximum speed attainable by the drive thus amounts to nearly half the synchronous speed referred to as the system frequency. That means in a 50-Hz network, nearly 25 Hz could be reached. In the case of the application for the GMDs, the operational output frequency is from 0.3 Hz up to about 6 Hz. In view of this physical limitation, the cycloconverter is used for low-speed drives typically found in SAG and ball mills. Physical Design of the Cycloconverter. The construction of the thyristor is made in a so-called “stack method.” The thyristors are put together in a sandwich formation and are water cooled. Each stack contained six thyristors with their respective firing pulse transformers. For each motor phase, there are 24 thyristors needed; for three phases, a total of 72 thyristors are installed. There are no parallel thyristors used. The system is a fuseless design, and the thyristors are dimensioned to withstand a possible short circuit for about 100 msec. To enhance troubleshooting, each thyristor leg is supervised for its correct function (Figure 24). A feedback signal from each leg is transmitted by a fiber-optics cable back to the PSR. It indicates the proper function during the thyristor firing and conducting period or it indicates which one of the 72 thyristors is not operating correctly. The thyristor bridges are equipped with self-protecting elements. Snubber circuits and overvoltage protection from both the network side and the motor side are installed. THE NETWORK

About 60% of plant power used is milling power. The relationship between the linear load and the nonlinear load when fixed-speed drives were applied was 95% linear and 5% nonlinear. Today, this relationship is almost reversed, with about 70% to 80% of the load being nonlinear and only 20% to 30% linear. Two more facts were also observed in the last two decades: (1) Plants are being built in remote areas, resulting in long overhead lines to the plant; and (2) the quality standards for the power supply network—for instance IEEE 519—and their fulfillment, are much more strict. The relationships among the fault level of the network, power required from the network, linear load, and nonlinear load are changing, with negative implications. Long Transmission Lines and Their Associated Effects

Two important criteria for the transmission of electrical power and the amount of power that can be used at the end of the line are the overhead line length and the short-circuit power at the source. The values are not related in a linear function but rather in an exponential function. Inrush Current Effects of Switching On the Converter Transformers

When switching on transformers or saturatable inductances, in general, harmonic emissions effects can be noted.

THE GEARLESS MILL DRIVE—THE WORKHORSE FOR SAG AND BALL MILLS

3

2

431

1

u+

u– i+ A

B

i–

FIGURE 23

Output voltage of a cycloconverter for one phase in the trapezoidal mode of operation

FIGURE 24

One leg of a thyristor configuration

The inrush current of transformers and ac machines depends on the phase angle of the switching instant and the remnant magnetization of the active iron parts. The inrush current contains all integer low-order harmonics including zero order for dc components. The harmonic components decay with a time constant between several seconds on low-power transformers and a few minutes on high-power transformers. Consequently, heavy distortion of the network by creating mainly the strong second harmonic will occur. Due to the fact that the second harmonic is normally not expected in plants, the potential to create negative effects is very high. The damping of a second harmonic with a filter is costly. In cases where networks are weak, and consequently the network natural parallel resonance is low, potential danger to hit the network with its low parallel resonance during

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the transformer switch-on period is high, and damage to equipment is likely if counteractions are not taken. Danger of Low Parallel Resonance

If the parallel resonance of the network comes too close to the fundamental frequency, no damping is possible anymore and network instabilities will result. These can lead to oscillation of the network voltage. Harmonic Generation Sources

All electrical equipment consuming nonsinusoidal currents from the supplying line has to be considered as a source of harmonic currents. Strictly speaking, only actual linear loads—resistive, capacitive, and inductive (without iron-core)—do not produce harmonics. All others, such as transformers and ac motors, contribute to the harmonic pollution of the networks. The impact can be more or less severe depending upon both the amplitude and the frequency of the harmonic currents. Solution for Weak Networks, the Synchronous Condenser

The synchronous condenser has played a major role in voltage and reactive power control for many years. Synchronous condensers have been connected at both subtransmission and transmission voltage levels to improve stability and maintain the voltage within desired limits under varying load conditionsʊbut they have been used mainly to supply a portion of the converter reactive-power requirements and provide necessary system reinforcement. Synchronous condensers have an inherent advantage over capacitors for emergency voltage support in maintaining or increasing their output at reduced voltage. Functionally, a synchronous condenser is a synchronous machine that is synchronized to the power system. The field is controlled to either generate or absorb reactive power. The improvement of the short-circuit level at the connection point of the condenser is about 100 MVA, with a condenser rating of 15 MVA. The synchronous condenser brings up the short-circuit power, and as a result of this also the network’s parallel resonance. Another strong argument for a rotating synchronous condenser is its ability to ride through small disturbances in the network because of its large accelerated masses. The performance of a synchronous condenser in terms of efficiency is rather good, because the total full-load losses of the condenser, including its auxiliary systems, is in the order of 1% of the condenser rating. About two-thirds are in function of loading condition. DRIVE CHARACTERISTICS

GMD Starting Characteristic

The GMD as an adjustable-speed drive is known for its extremely soft start. In the starting procedure, no inrush current can be noted. The current increase from zero to the maximum current required for starting takes between 7 and 10 seconds. All ABB GMDs are equipped with a dropping charge protection. Therefore, the ramp-up for the starting is defined and preset until the material starts to cascade. A typical starting procedure is as follows: 1. Ramp up to about 1 rpm in about 1 second. 2. Keep the speed at 1 rpm until the material is cascading. (This happens after 7 to

10 seconds at an angle of mill rotation from 40˚ to 50˚.) 3. As soon as the material is cascading, the current will reduce significantly. At this

stage, the speed can be ramped up.

THE GEARLESS MILL DRIVE—THE WORKHORSE FOR SAG AND BALL MILLS

433

Speed about 1.5 rpm

Mill Starts Current Material is Cascading; Increasing in 7 seconds Current is Decreasing

FIGURE 25

Starting characteristic of a GMD

4. If the material is not cascading after a certain mill angle motion, it is obvious that

the material is frozen, and the drive will stop automatically. Figure 25 shows the starting characteristic of a GMD. In this case, the material is starting to cascade at 41˚, which corresponds to a normal operating condition. DESIGN CONDITIONS

GMDs have to cope with several technical and construction challenges, including: ƒ Operation under weak network conditions:

– The relationship between the total power of all adjustable-speed drive systems (in megawatts) to the network short-circuit level in MVA should be ideally 1 to 10. In concrete values for Antamina, this would mean that for about 80 MW for adjustable-drive systems installed, the short-circuit level should be ideally 800 MVA. In this case, a relatively simple filter and compensation unit will fulfil the requirements. – In most of the actual cases in the last years, a relationship of 1:6 has been found (80 MW/480 MVA). For all these cases, operationally it only requires a special design of the filter and compensation units. – In Antamina, the relationship was initially about 1:3 (80 MW/240 MVA), which is unusually low. It did need a very special filter and compensation design with an additional static voltage compensator (SVC) on the utility level, and two synchronous condensers to push the short-circuit power up. ƒ Operation in high altitude. For high altitude, several aspects had to be considered

such as – The reduced creeping distance, requiring that the voltage level utilization had to be reduced to about 75%. Therefore, for the utilization of 415 V, equipment with 500 V had to be used.

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ADVANCES IN COMMINUTION

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– For operation in high altitudes, the air-cooling capability is significantly reduced; therefore, larger fans had to be installed. ƒ Relation from linear load to nonlinear load is unfavorable. Linear load is only

about 25% of the total plant load, with 75% of the load being nonlinear such as milling, transporting, and pumping power. ƒ Operation in active and violent earthquake-prone zone D R I V E S YS T E M E F F I C I E N C Y

The definition of the efficiency of a drive system is only correct if the overall efficiency of the drive system is defined. The overall efficiency takes into account all individual losses, such as for the following: ƒ Converter transformer ƒ Excitation transformer ƒ Cycloconverter ƒ Excitation converter ƒ Motor ventilating ƒ E house air conditioning ƒ Motor I2R ƒ Motor excitation ƒ Motor core and stray load losses

The overall efficiency for the entire GMD system is around 95% and greater, depending on the size of the motor and the winding configuration. No other adjustablespeed drive system for SAG and ball mills achieves this high an efficiency. CONCLUSIONS

The paper described in detail the basic design of a GMD—its construction, manufacturing facilities, transport, installation, and its function, leading to an understanding of why GMDs are so reliable and used as an adjustable-speed drive, and why they have the highest efficiency of all drive systems. Additionally, it described the overload capabilities, the reaction to the network, the reason why the maintenance of the drive system proves to be a lesser issue, and why the gearless mill drive is called a workhorse.

Optimizing Hydrocyclone Separation in Closed-Circuit Grinding Thomas Neesse,* Valeriy Golyk,* and Fred Donhauser†

ABSTRACT

Hydrocyclones used for closed-circuit grinding can be operated with either the rope or the spray discharge of the underflow. Each of these operating states presents advantages and disadvantages. Optimum separation results as to solids recovery and solids content are achieved at the transition point between the rope and spray discharges. This is confirmed by experiments performed with a 150-mm hydrocyclone. To stabilize separation at the transition state, a hydrocyclone control system is required. The new control concept is based on overflow throttling for volume split regulation and varying the pump speed. INTRODUCTION

In closed-circuit grinding applied in mineral processing systems, the hydrocyclone overflow is discharged and directed to the subsequent sorting process, preferably to flotation. Size distribution and solids content of the flotation feed determine the effect of mineral beneficiation. Therefore, these properties should be stabilized and optimized at the hydrocyclone overflow. Unfortunately, hydrocyclone separation itself is influenced by the feed conditions, which fluctuate because of changing hardness of the material. A harder mill feed results in coarser mill discharge and hydrocyclone feed, as well as a higher circulating load—which means that changing feed properties must be compensated by a hydrocyclone control system. CONTROL CONCEPT

A new control concept (Neesse, Schneider, et al. 2001) is shown in Figure 1. The control is based on hydrocyclone monitoring that delivers the command variable for process optimization and stabilization. Fluctuating feed conditions regarding solids content and particle-size distribution result in varying operating conditions characterized by ƒ Sediment mass stored in the hydrocyclone ƒ Different air core formation in the hydrocyclone center ƒ Shape of the underflow discharge

* Friedrich-Alexander University, Erlangen-Nuremberg, Germany † AKW Apparate und Verfahren GmbH, Hirschau, Germany 435

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ADVANCES IN COMMINUTION

MILL DESIGN

p2

p1

Control Valve V Sensor Overflow

Underflow Control Unit

p n

FIGURE 1 Hydrocyclone control using overflow throttling (n = feed pump speed; p = pressure drop; p1 = inlet pressure; p2 = overflow outlet pressure; V = volumetric flux)

These operating characteristics can be detected by applying the following principles (Neesse, Schneider, et al. 2004b): ƒ Detecting the shape of the underflow discharge using

– Dielectric properties of the underflow with a capacitance probe as the direct contact sensor – Optical pattern identification via infrared or with a laser beam ƒ Measuring the internal process state of the hydrocyclone utilizing

– Gravimetric determination of the hydrocyclone weight using a weighing cell, and – Measurement of the hydrocyclone oscillations by an acoustic sensor These signals indicating the process status are transmitted to the computer, along with the values for the pump power input, the pressure in the feed, and in the overflow where a control valve is installed. Large hydrocyclones with a nominal diameter of >500 mm are equipped with monitoring sensors and control valves at every cyclone. Smaller hydrocyclones use the situation as shown in Figure 2. In Figure 2, the hydrocyclone assembly consists of a number of single hydrocyclones connected in parallel in a round battery. The overflows of all hydrocyclones are collected in a special pressure chamber with a collecting discharge pipe where a control valve is installed. The system is controlled by adjusting the throttle valve and the feed pump speed. The control mechanism actuated by stepwise throttling intensifies the pressure inside the hydrocyclone. Consequently, the underflow discharge increases until the point where breakthrough of the air core is reached. Then the sensor detects the spray discharge and opens the control valve for a short time. After that, a new control interval starts.

OPTIMIZING HYDROCYCLONE SEPARATION IN CLOSED-CIRCUIT GRINDING

Control Valve

437

Overflow

Pressure Chamber P

V

Sensor

Hydrocyclone(s)

Underflow

PC P

n

Feed Pump

Feed

FIGURE 2 Computer-controlled hydrocyclone battery (n = feed pump speed; p = pressure drop; PC = process control computer; V = volumetric flux)

H Y D R O C Y C L O N E O P E R A T I O N A T T H E TR A N S I T I O N P O I N T R O P E / SPRAY DISCHARGE

Three different operating states are shown in Figure 3 (Neesse, Golyk, et al. 2004). In dense flow separation (Figure 3a), more solids are stored in the conical part of the hydrocyclone and partly forced to the overflow, consequently reducing solids recovery to the underflow. The air core does not extend up to the apex yet oscillates intensively. The discharge assumes the shape of a rope and is characterized by high solids content and less fines, which is the advantage of this operating state. In dilute flow separation (Figure 3c) with its typical spray discharge, a continuous, uninterrupted air core can be observed that extends down to the underflow. The separation presents high solids recoveries as an advantage but low solids concentrations in the underflow, which results in more fines being swept into the underflow. In existing hydrocyclone plants of closed-circuit grinding, this is the preferred operating state. A disadvantage of this method is that the fines in the underflow result in overgrinding of the material. On the other hand, a discharge of oversized particles to the overflow is avoided, which would lead to difficulties in the flotation cells. The transition state (Figure 3b) between dense flow and dilute flow separations is an unstable state with rapid changes between the two discharge types. Given the remarkable separation effects reached in the transition state, operating the hydrocyclone at this point is of special interest (Neesse, Schneider, et al. 2004a).

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Suspension

Suspension

Sediment Residue

Much Sediment

FIGURE 3

Suspension Developed Air Core

Unstable Air Core

Less Sediment

Rope Discharge

Combined Discharge

Spray Discharge

(a) Dense Flow Separation

(b) Transition State

(c) Dilute Flow Separation

Hydrocyclone operating states

EXPERIMENTS WITH A 150-mm HYDROCYCLONE

A more detailed description of the transitional discharge range is presented in Figure 4. The beginning of rope dispersion is signaled by a lateral deflection of the rope. Subsequently, the real transition state starts, characterized by quick changes between rope and spray discharges. Finally, the spray with a small discharge angle (<10˚) can be assigned to the transitional range. This transitional operating state is the most appropriate for hydrocyclones in closed-circuit grinding. All these hydrocyclone states have been studied by operating a 150-mm hydrocyclone with the parameters given in Table 1. SEPARATION CUR VES

Figure 5 demonstrates the control behavior of the 150-mm hydrocyclone, where the change of the separation curves measured for increasing overflow throttling can be seen. The maximum throttling with the cross section being opened by 30% corresponds to a pressure of 0.5 bar in the overflow. At the same time, the hydrocyclone throughput is stabilized by increasing the feed pump speed. For stable feed solids contents Cs,in 350 g/L, it is shown that the curves are shifted towards finer separation. The sharpness of separation remains approximately stable. Of course, the starting point of the curves at low particle sizes must increase due to the higher solids recovery in the underflow. The separation behavior of the controlled hydrocyclone with increasing solids feed content is demonstrated in Figure 6. As can be seen, the high cut size for rope discharge drops rapidly to about 50 Pm. This value does not decrease further with spray discharge. SOLIDS CONTENT AND SOLIDS RECOVER Y

Figure 7 shows the solids content in the underflow at different discharge types, resulting from increasing overflow throttling. As can be seen, a high solids content >1,200 g/L is obtained up to the transitional state, characterized by quick changes between rope and spray discharges. After that, at spray discharge, the solids content drops to about 800 g/L.

OPTIMIZING HYDROCYCLONE SEPARATION IN CLOSED-CIRCUIT GRINDING

Rope

Transitional State Lateral Deflection of the Rope

FIGURE 4

TABLE 1

Quick Change Rope/Spray

439

Spray Spray with Small Discharge Angle

Discharge types of the hydrocyclone underflow

The hydrocyclone and feed parameters for the experiments Hydrocyclone diameter Inlet nozzle Vortex finder Depth of the vortex finder Spigot diameter Length of the spigot Height of the cylindrical section Cone angle Feed pressure Solids concentration of the feed Material: quartz

150 mm 25 × 80 mm 72 mm 100 mm 38 mm 150 mm 350 mm 18° 1 bar 100–400 g/L <1 mm 55% <100 μm 5% <12 μm 40% <1 μm

This behavior is stable even at a relatively low feed solids content of 200 g/L. The corresponding values for solids recovery can be derived from Figure 8. It starts with relatively low recoveries at rope discharge and indicates the dependency on feed solids content. Low feed contents result in higher solids recoveries. Approaching the transitional state, the recovery increases markedly and reaches, at the transition state, approximately the maximum values occurring at spray discharge. This maximum is almost independent of the feed content. OPTIMIZATION CRITERION

In most practical applications of hydrocyclone separation, both solids content cs,u and solids recovery in the underflow Rm,U should assume high values. Therefore, the product cs,u · Rm,U can be taken as optimization criterion. As can be determined from Figure 9, this criterion indicates a maximum at the transitional point rope/spray. This point unifies the advantages of rope discharge (high solids content) and spray discharge (high solids recovery). Therefore, the control strategy will focus on stabilizing the hydrocyclone operation at this point.

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ADVANCES IN COMMINUTION

Overflow Throttling

100

100% 50% 45% 40% 30%

80

Separation Function T, %

MILL DESIGN

60

40

20

Cs,in = 350 g/L Du = 29 mm 0 1

10

100

1,000

FIGURE 5 Separation functions of the controlled hydrocyclone with increasing overflow throttling, giving the opening of the cross section in % (feed solids content Cs,in = 350 g/L; apex diameter Du = 29 mm)

400 350 300 250 200 200 g/L 250 g/L 350 g/L

150 100 50 0 1

2

3

4

5

Discharge Type

FIGURE 6 Cut sizes of the controlled hydrocyclones for feed solids contents Cs,in of 200, 250, and 350 g/L

OPTIMIZING HYDROCYCLONE SEPARATION IN CLOSED-CIRCUIT GRINDING

1,400

Solids Content in the Underflow Cs,in, g/L

1,200

1,000

800

600

Cs,in = 200 g/L 400 1,400

Solids Content in the Underflow Cs,in, g/L

1,200

1,000

800

600

Cs,in = 250 g/L 400 1,400

Solids Content in the Underflow Cs,in, g/L

1,200

1,000

800

600

Cs,in = 350 g/L 400 1

2

3

4

5

Discharge Type Increasing Throttling

Du = 29 mm

Du = 35 mm

FIGURE 7 Underflow solids content of the controlled 150-mm hydrocyclone at different feed solids contents Cs,in and apex diameter Du

441

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Solids Recovery in the Underflow Rm,G, [–]

0.8

0.6

0.4

Cs,in = 200 g/L 0.2

Solids Recovery in the Underflow Rm,G, [–]

0.8

0.6

0.4

Cs,in = 250 g/L 0.2

Solids Recovery in the Underflow Rm,G, [–]

0.8

0.6

0.4

Cs,in = 350 g/L 0.2 1

3

2

4

5

Discharge Type Increasing Throttling

Du = 29 mm

Du = 35 mm

FIGURE 8 Solids recovery in the underflow of the 150-mm hydrocyclone at different feed solids content Cs,in and apex diameter Du

OPTIMIZING HYDROCYCLONE SEPARATION IN CLOSED-CIRCUIT GRINDING

443

Optimisation Criterion Rm,G × Cs,u [–]

0.25

0.20

0.15

pin = 1,1 Bar Cs,in = 350 g/L 0.10 1

2

3

4

5

Discharge Type

Du = 29 mm

FIGURE 9

Du = 35 mm

Optimization criterion of the 150-mm hydrocyclone

CONCLUSIONS

In existing plants of closed-circuit grinding, hydrocyclones in most cases are operated with spray discharge. This guarantees maximum solids recoveries in the underflow and avoids the undesired discharge of coarse particles to the overflow. The relatively low solids content, however, transports more fines to the underflow that leads to overgrinding. The transition point between rope and spray discharges presents optimal separation effects concerning solids recovery and solids content in the underflow. This necessitates a control system using an overflow throttling for volume split regulation. REFERENCES

Neesse, Th., V. Golyk, P. Kaniut, and V. Reinsch. 2004. Hydrocyclone control in grinding circuits. Minerals Engineering 17:1237–1240. Neesse, Th., M. Schneider, F. Donhauser, and B. Schricker. 2001. Computer controlled hydrocyclone battery. Paper presented at the Congress of the American Filtration Separation Society. Volume 15, Session 32. Tampa: Advances in Filtration and Separation Technology. Neesse, Th., M. Schneider, J. Dueck, V. Golyk, S. Buntenbach, and H. Tiefel. 2004a. Hydrocyclone operation at the transition point rope-spray discharge. Minerals Engineering 17:733–737. Neesse, Th., M. Schneider, V. Golyk, and H. Tiefelb. 2004b. Measuring the operation state of the hydrocyclone. Minerals Engineering 17:697–703.

PART 5

Instrumentation, Modeling, and Simulation

445

Use of Multiphysics Models for the Optimization of Comminution Operations J.A. Herbst* and J.K. Lichter*

ABSTRACT

Recent developments in multiphysics models are providing new opportunities for the optimization of crushing and grinding equipment and their operation. Combinations of discrete element methods (DEMs), discrete grain breakage (DGB) modeling, and multiphase flow (MPF) modeling are allowing interactions between breakage, fluid flow, equipment design features, and wear processes to be predicted accurately. Therefore, a new era of microscale optimization is beginning for comminution. The dream of integrated optimization of comminution equipment design and process operation should soon be realized. In this paper, several areas that may benefit from this type of optimization are identified. Examples for crushing, tumbling mill grinding, and stirred milling are presented. INTRODUCTION

Historical evidence points to the fact that effective process optimization requires the use of good mathematical models. This is true because accurate interpolation and extrapolation (only possible with a good model) are required for all types of optimization searches, whether empirical or analytical. Figure 1 shows the progression in comminution models and modeling accuracy that has occurred during the last few decades. Empirical models at the base of the triangle in Figure 1 are epitomized by the Bond equation (Bond 1952). Phenomenological models get their form from theory, but model constants must be determined experimentally. This model type is epitomized by population balance models (PBMs) (Hulburt and Katz 1964). The highest level of modeling is physics based, where the model constants are calculated from fundamental material properties and actual equipment geometry and mechanical motion. The generally accepted levels of prediction accuracy for comminution equipment capacity are on the order of r10% for the empirical level, r5% for the phenomenological levels, and r2% for the current models at the physics-based level. By the turn of the century, a collection of tools termed high-fidelity simulation (HFS) tools had emerged. The HFS tools consist of DEMs, MPF, and DGB with a strong tie back to the PBM (Herbst and Nordell 2001). Each of these tools is described briefly in the following paragraphs.

* Metso Minerals Optimization Services, Colorado Springs, Colorado 447

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MPF

Circa 2005

on sC sic hy gP sin rea

DEM Physics Based

Population Balance Models Phenomenological Single-Parameter Models Empirical

Circa 1972

cy

Inc

DGB

ra ccu gA sin rea Inc

te n

t

Microscale

Circa 1952

Macroscale

FIGURE 1

Evolution of modeling tools for comminution system simulation

DEM simulations focus on discrete “particles” by solving Newton’s second law of motion applied to a particle of mass mi moving with velocity vi when it is acted upon by a collection of forces fij, including gravitational forces and particle–particle, particle–fluid, and particle–boundary interactive forces: D  mi vi ------------------- = Dt

¦ fij

(EQ 1)

MPF simulations focus on continuous flow behavior of fluids and slurries modeled as pseudofluids by solving the full Navier-Stokes equation with a term for interactions between particles and fluid: 1 Dv 2 U ------ = – ’P + K’ v + Ug + § ----------- · f i ©1 – H ¹ Dt

(EQ 2)

where ȡ is the fluid density, v is the velocity vector, P is the pressure, g is the gravitational force constant, İ is the local solid fraction, and fi is the particle–fluid interaction force. DGB simulations focus on discrete particles in the same way that DEMs do, except in this case, each physical particle is made up of a set of discrete grains into which strain energy can be stored/released and cracks can propagate along their boundaries, governed by the energy conservation equation that governs the crack extension force, G: 1 Gu G = ----- -----2t Ga

(EQ 3)

where t is the crack width, u is the stored strain energy around the crack, and a is the crack length. These physics-based models have been found to be useful in comminution equipment design and most recently have been determined to be extremely valuable for comminution system optimization. The fundamentals of the multiphysics models are presented briefly in the next section. The balance of this paper deals with the application of the models to optimizing comminution operations.

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449

Start

Search for Contacts

Calculate Contact Forces

Integrate Equations of Motion

End

FIGURE 2

Flowchart of a typical “soft particle” DEM simulation

F U N D A M E N T A L S O F H I G H - F I D E L I T Y S I M U L A T I O N TO O L S

DEM is a numerical technique developed for particle-flow simulation. Unlike continuous numerical approaches, such as the finite element method or finite volume (FV) method, the DEM does not involve the integration of the equation of motion of the continuous medium. Instead, the progress over time of every particle in the simulated system is followed by integration of the equations of motion for that particle. In this approach, virtually everything is known about every particle in the system at every moment during the simulation. The continuous parameters (bulk density, bulk particle velocity, etc.) are obtained by spatial and temporal averaging of the parameters of the motion of DEM particles. In this sense, the DEM is closer to the experiment than to a continuous simulation technique; some investigators (Campbell 1997), therefore, prefer to use the term “numerical experiment” instead of “simulation.” The basic steps of a DEM simulation are presented in Figure 2. After the initialization of the simulation, three basic steps are repeated at every simulation time step: (1) search for the particle–particle and particle–boundary contacts; (2) calculation of contact forces; and (3) integration of equations of motion (spatial advance of particles). At the start of the simulation, information about position and characteristics (velocities, sizes, shapes, etc.) of every particle in the simulation as well as parameters of the simulation boundaries (geometries, motion parameters, etc.) must be supplied. Preprocessing programs usually generate all these values. In order for the basic DEM program to simulate the flow of nonbreakable particles, the boundaries have to be triangulated in three dimensions or be subdivided into straight-line segments in two dimensions; these triangles and straight lines are basic shapes for the calculation of the particle–boundary contact forces. One can use a variety of particle shapes, depending upon the characteristics of material to be simulated. The next step in the DEM simulation process is to search for particle–particle and particle–boundary contacts. This step is probably the most important in determining the efficiency and speed of the DEM software because the two remaining steps (force calculation and integration of the equations of motion) are relatively easy to program efficiently. One can always simply search for the contacts of every particle against every other particle and boundary element in the simulated system, but this approach creates

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an algorithm that is tremendously inefficient for the simulation of large numbers of particles. The authors believe that the DEM programs they use involve a local search routine that is one of the best available in the world at the present time. The second cyclic (repeated at every time step) process of the DEM simulation is the contact force calculation. Two basic approaches are used; the first one is used for nonbreakable particle simulations. In this approach, the normal force acting on the particle contact is the sum of viscous and elastic components. The elastic component is proportional to the particle–particle or particle–boundary distance of overlap with a constant coefficient of proportionality (normal stiffness). The viscous normal force is proportional to the relative normal velocity of the contacting members, also with constant coefficient of proportionality (contact viscosity). One can demonstrate that for this type of contact force, the coefficient of restitution of the simulated particles is a velocity-independent value that depends upon particle mass and normal stiffness as well as contact viscosity. The tangential force on the contact is proportional to the relative displacement at the contact point from the origination of the contact with a constant coefficient of proportionality (tangential stiffness) up to the limit of equal normal force multiplied by the friction coefficient of the simulated material. The second basic approach for the contact force calculation is used for breakable particle simulations with the DGB technique. In this approach, the contacts are subdivided into two categories: the so-called “glued” and “collisional” contacts. The glued contacts can withstand tensile stresses; these contacts are responsible for holding elementary particles together. One can think about this contact as a set of elastic fibers connecting together the sides of elementary triangles or tetrahedrons (Potapov, Hopkins, and Campbell 1995; Potapov and Campbell 1996). These fibers have specified normal and tangential stiffness and can be broken (eliminated) once specified stress is reached in the fiber. The collisional contacts still exist once the glued contacts are broken, as well as those between different fragments or between fragments and boundaries. These contacts cannot withstand tensile forces. The normal force on these contacts is viscous–elastic; the elastic component is proportional to the area or volume of particle overlap, and the viscous component is proportional to the rate of change of this area or volume. The tangential contact force is elastic with a frictional limit similar to the nonbreakable DEM approach. The end result of such a model is that a brittle–elastic material with predictable elastic and breakage properties is created (Potapov, Hopkins, and Campbell 1995; Potapov and Campbell 1996). In addition to the contact forces, some noncontact forces are normally added to the particles in the DEM simulation. These forces can include fluid drag forces in multiphase simulations, forces of gravity, and so on. The calculation of these forces is usually straightforward except for the case of two-way, solid–fluid coupling. This two-way coupling requires simulation of the fluid motion together with DEM simulation of the particles. To simulate the motion of the fluid, the standard FV technique, or in some instances, the smooth particle hydrodynamics technique, is employed. To achieve geometric flexibility, an unstructured grid (triangular in two dimensions and tetrahedral in three dimensions) can be used. It has been found by direct comparison with a structured grid that the computational time overhead associated with an unstructured grid with respect to the structured grid is minimal. Free surfaces of the fluid in a piece of equipment are traced by an extension of the volume of fluid (VOF) technique (see description in works by Ferzinger and Peric [1997]). The authors and their co-workers have developed a version of the VOF technique that has virtually no numerical diffusion. To achieve greater numerical stability and to be able to employ larger time steps, the implicit pressure-correction approach based on the simple algorithm has been utilized.

MULTIPHYSICS MODELS FOR THE OPTIMIZATION OF COMMINUTION OPERATIONS

451

Several ways of coupling of fluid and solid particle motion are described in the scientific and engineering literature. The most exact one is to simulate the flow of the fluid around every particle. This technique requires several tens of fluid cells per solid particle; it is also necessary to change the fluid mesh at every time step. At the present time, this technique can deal with, at most, tens of solid particles and thus has been found not to be useful for most mineral processing simulations. The authors and their colleagues have programs of this type based on meshless, smooth particle hydrodynamics and particlein-cell techniques that are also used to establish the formulas for fluid–solid interaction terms. However, for the large-scale mill simulation, the approach based on the work of Di Felice (1994) is used. It has been established by analyzing the experimentally obtained solid–fluid interaction terms (Ergun 1952; Richardson and Zaki 1954; Foscolo, Gibilaro, and Waldram 1983) that one can describe the effect of the fluid surrounding the solid particles simply by the summation of drag and pressure forces. The pressure force term is simply the local pressure gradient multiplied by particle volume, and the drag force depends only on the local solid fraction and the Reynolds number based on particle size. Thus, in our program, we simulate the motion of the fluid through the FV technique, taking into account change of the local solid fraction in the pressure-correction equation and adding solid–fluid interaction force to the momentum equation. We simulate motion of the solid particles using the DEM technique with additional pressure and solid–fluid interaction forces applied to the particles. This allows us to implement the two-way solid–fluid interaction accurately and inexpensively in terms of computational time. This approach is also fully conservative in terms of mass and momentum. Finally, the last step in the cyclic process (and probably the simplest one) is numerical integration of the equations of motion of the particles. The numerical integration is performed for both translational and rotational components of motion of every particle in the simulation. There are several possibilities for numerically integrating the equations of motion. Several integration techniques of different orders of accuracy in time can be applied. However, we found that a very simple first-order Euler integration is normally sufficient for the simulation purposes. We usually use this technique unless there are specific requirements for a higher-order integration approach. A few comments on computational requirements/limitations are in order at this point. There are no inherent limitations on particle size, size range, or number of size fractions. However, irregularity in shape and a wide range of sizes require more computational time than monosize spheres. Current practical limits on the number of particles modeled is about 1 million. Simulations presented in this paper were carried out on multiprocessor computers with computation times varying between a few hours and a few weeks. To take full advantage of the multiphysics models for optimization, it is necessary to capture the main features of these microscale simulations in another macroscopic simulator that can compute at many times real time. This has been accomplished through an energy-based coupling of HFS results to more traditional PBMs. This coupling has occurred within the framework of MinOOcad, Metso’s dynamic flowsheet simulator, which can run entire mine-to-mill simulations at 200–400 times real time. Because of this link between HFSs and PBMs, a large number of scenarios can be evaluated quickly as an optimizing search is being conducted. RECENT APPLICATIONS OF THE HFS TO COMMINUTION S YS T E M O P T I M I Z A T I O N

During the last 3 years, the authors and their co-workers have applied HFS tools to the modeling of a wide variety of comminution operations including crushing, tumbling mill

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grinding, and stirred mill grinding (Herbst and Potapov 2003). A few recent examples are described in the following paragraphs. Optimizing Crushers

The application of multiphysics modeling to crusher optimization is an emerging field with considerable potential. One primary difference between the application of multiphysics modeling for crushers as compared to more typical applications for mill design is that the use of breakage modeling, or DGB, is necessitated. Flow of material through a crusher cannot be achieved unless there is size reduction. The combined use of DEM/ DGB modeling permits the evaluation of any of the process parameters of a crusher and will provide information on capacity, crusher power draw, product size gradation, and localized forces on the wear components. Parameters that can be evaluated include, but are not limited to ƒ Crusher chamber (wear liner) profile ƒ Crusher speed ƒ Crusher throw ƒ Open side settings (or closed side settings)

HFS allows a search over the parameter space to allow the determination of the optimum operating parameters. Applications to date have successfully predicted the effect of crusher chamber design on crusher capacity and product gradation for jaw crushers and cone crushers. Figure 3 shows one such data set for a cone crusher. Simulated and predicted size distributions are shown. Breakage modeling is a core element of crusher performance simulations, therefore, the starting point is characterization of the breakage properties of the ore, and the development of ore-specific DGB particles for the crusher feed. The ore breakage characterization is a two-stage process. The ore is first tested using a drop-weight tester (Figure 4). The drop-weight test is then repeated as a DGB experiment and the ore-specific crack propagation energy is determined, which results in the same product size distribution as that measured in the drop-weight test. This single ore breakage characteristic is typically constant across all particle sizes and energy levels that would be simulated. Once the ore breakage characteristics have been defined, the crusher can be modeled. Given the design of the crusher and the wear liners, the effect of crusher operating parameters—namely, speed and throw—and the closed side setting can be predicted. The current challenge lies in the prediction of wear rates of the wear liners and the resultant crushing chamber profile (e.g., the mantle and the concave liners in a gyratory crusher). The interest in multiphysics modeling for these applications is twofold: to assist in the correct selection of wear materials and for the prediction of liner life and the performance of the crusher as the liners wear. DEM/DGB is likely to become a vital link in the development of a methodology to select high-performance wear materials for crusher liners. Current activities include the development of a test methodology that will evaluate the performance of various wear materials based on a series of laboratory tests. Metal samples are subjected to a series of tests that determine a material’s resistance to abrasive wear and cutting or ploughing. A key component in this testing is a knowledge of the magnitude and frequency of the forces applied to the wear material. A DEM/DGB experiment can provide those data for any configuration of a crusher, and is sensitive to the ore properties. Forces generated with soft ores will therefore be less than those generated for hard ores. Figure 5 shows a representation of the different wear mechanisms expressed as a function of surface loading

MULTIPHYSICS MODELS FOR THE OPTIMIZATION OF COMMINUTION OPERATIONS

453

120 Feed—Measured Feed—Simulated Output—Measured Output—Simulated

Time = 3.03 sec

Cumulative % Passing

100 80 60 40 20 0 1

10

100

Particle Size, mm

FIGURE 3

Comparison of simulated (DGB) and measured size distributions for a cone crusher

Translational Velocity, m/sec 5

4

3

2

1

0

FIGURE 4

Drop-weight tester (left) and DGB simulation of test (right)

and distance of movement. The insert (top right) shows a laser measurement of a cut resulting from a high-load, long-glide-distance wear event. Basic measurements plus DGB modeling can soon be used for optimal wear material property selection in crushers. OPTIMIZING SAG AND BALL MILLS

Optimization of tumbling mill performance at the microscale involves controlling impacts and particle transport processes. In practice, this is accomplished by manipulating mill

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5

1,000 18.6

0 mm y

Severe Microcutting (Gouging)

Minimal Wear

Light Pressure Abrasion (Grinding)

15˚

x

–0.1 –5

–0.6

0 mm

–18.8 0.6

Surface Load, MPa

Microfatigue Microcracking

z

100 Gliding Distance

FIGURE 5

Wear mechanisms as a function of surface loading and distance of movement

speed, media size and density, mill filling (ore and media), and the character of mill internals (liners and discharge systems). The first case study presented here is for the optimization of throughput for a 34u15.25-ft semiautogenous grinding (SAG) mill at Kinross’s Fort Knox operations (Hollow and Herbst, in press). An adhoc team of four Metso Minerals Optimization Services (MMOS) specialists and members from the Fort Knox Process Improvement team joined together to execute this project and to evaluate the results. The manipulated variables explored were liner design and mill speed. A base case was established for a medium hardness ore (based on plant sampling and drop-weight tests) for a traditional liner design (66 lifter, rail liners) with a fraction of critical speed equal to 81% and a filling composed of 17.4% ore and 12.6% ball by volume in the mill. HFSs were performed to see the effect of lifter spacing, lifter face angle, lifter height, and plate thickness on wear and throughput using a methodology described in previous publications (Herbst and Nordell 2001, 2002; Qiu et al. 2001). The optimum liner profile was selected based on identifying a balance between high throughput and long wear life. A Metso “Natural Shape” design was chosen, which promised significant benefits from increased lifter spacing (with protection to the plate) and a more open but variable lifter face angle. The prediction for the Natural Shape liner chosen was 6.1% higher throughput with about the same wear life for the base case ore. The analysis of breakage and transport (including HFS modeling of the mill discharge system; Figure 6) using the MinOOcad circuit simulator (Figure 7) suggested that both the new and the old liner designs could benefit from a reduced operating speed. Model predictions and experimental data on capacity versus speed are shown for the new liner design in Figure 8. The net result of changing liner design and speed was about an 8% increase in throughput. The second tumbling mill case study was designed to determine optimum lifter profiles, pulp densities, and ball sizes for 13.5u28-ft ball mills at Iron Ore Company of Canada

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MULTIPHYSICS MODELS FOR THE OPTIMIZATION OF COMMINUTION OPERATIONS

150

160

170 180 190

200

210 220

140 130

230

120

240

110

Translational Velocity, m/sec

Translational Velocity, m/sec

10

10

9

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1

0

0

250

100

260 270

90

280

80

290

70 60

300 50

310 40

320 30

20

10

0

350

340

330

FIGURE 6 Simulation of charge motion (balls and particles) in the mill (left) and particle motion in the SAG discharger (right)

FIGURE 7

MinOOcad simulation SAG circuit performance with new liners

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1.15

Relative Throughput

1.10

1.05

1.00

0.95

0.90

0.85 60

Plant Data Model 65

70

75

80

85

Rotation Speed, % of Critical

FIGURE 8 SAG throughput for HFS-designed liners relative to base case as a function of percentage of critical speed of mill rotation

Impact Power, x250 Watt 0.0008

0.0006

0.0004

0.0002

0

FIGURE 9

Laboratory mill and associated DEM simulation snapshot

in Labrador City. Microscale breakage parameters were extracted from a combination of laboratory tests and DEM simulations, as shown in Figure 9 (Herbst 2002). These parameters were in turn used along with full-scale DEM simulations to predict plant behavior with Metso’s MinOOcad package for different liners and operating conditions, as shown in Figure 10. These predictions were verified by plant tests. In Figure 11, a comparison is made between predicted and measured size distributions for two liner configurations investigated. The liner chosen was found to produce about a 5% increase in the amount of fines <44 Pm at the same energy consumption. Optimum operating levels for liner design, mill speed, and percent solids were projected by DEM/PBM simulations. Predicted performance improvements (on the order of 25%) were verified after implementation in the plant.

MULTIPHYSICS MODELS FOR THE OPTIMIZATION OF COMMINUTION OPERATIONS

FIGURE 10

457

DEM/PBM simulations of 13×28-ft mills for two liner configurations

OPTIMIZING STIRRED MILL

Multiphysics modeling has also been applied to the fundamental design evaluation and equipment scaling of stirred mills. One example is the evaluation of the media movement in the mill and the resultant forces being brought to bear on the comminution process. Figure 12 shows a snapshot of a VertiMill DEM simulation depicting the magnitude of the shear forces developed between media. The resultant energy spectra (Figure 13) provides a detailed account of the comminution environment within the mill. An understanding of the interrelationship between screw design, media selection, and operating parameters can ultimately lead to a methodology to optimize the performance of VertiMills for a specific application. Similarly, a detailed analysis of shear work on the screw can be used to show the areas and mechanisms for screw liner wear and can be used to evaluate the effect of screw design and mill operation on the wear of the liners. CONCLUSIONS

Physics-based models are now available to optimize predictions of crushing and grinding operations with a high level of accuracy. The HFS tools described herein have been applied to crushing, tumbling mill grinding, and stirred milling with confirmed success. Benefits on the order of 5% to 25% increases in throughput have been reported by users of this technology. It is expected that these physics-based models will play an increasing role in the comminution optimization process. Links to PBMs are expected to be strengthened to allow circuit, full plant, and even mine-to-mill optimization in the near future.

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100

% Passing

80

60

40 Predicted Microscale Mill 7 Measured Ball Mill 7 Feed Predicted Microscale Mill 8 Measured Ball Mill 8

20

0 10

100

1,000

FIGURE 11 Comparison of size distributions measured in plant tests for mills with two different liner configurations and those predicted from DEM/PBM simulations

ACKNOWLEDGMENTS

The authors thank Iron Ore Company of Canada, Metso Minerals (Mineral Processing and Wear Protection business lines), and Kinross Fort Knox for allowing these results to be published. The support of several of our colleagues from MMOS is also gratefully acknowledged.

MULTIPHYSICS MODELS FOR THE OPTIMIZATION OF COMMINUTION OPERATIONS

FIGURE 12

459

Shear Power, Watts

Shear Power, Watts

5.0

5.0

4.5

4.5

4.0

4.0

3.5

3.5

3.0

3.0

2.5

2.5

2.0

2.0

1.5

1.5

1.0

1.0

0.5

0.5

0.0

0.0

Sectional side view and top view of a DEM simulation of a VertiMill (model VTM 1250)

2.0 At the Wall All Balls

1.8

Total Shear Energy, J/kg

1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.001

0.01

0.1

1

10

100

1,000

Single Collision Energy, J/kg

FIGURE 13 Simulated shear energy dissipation at the wall and on the surface of balls as a function of the intensity of events

REFERENCES

Bond, F.C. 1952. The third theory of comminution. AIME Transactions 193:484–494. Campbell, C.S. 1997. Computer simulation of powder flows. Pages 777–793 in Powder Technology Handbook. 2nd edition. Edited by K. Gotoh, H. Masuda, and K. Higashitani. New York: Marcel Dekker. Di Felice, R. 1994. The voidage function for fluid-particle interaction systems. International Journal of Multiphase Flow 20(1):153–159. Ergun, S. 1952. Fluid flows through packed columns. Chemical Engineering Progress 48:89–94. Ferzinger, J.H., and M. Peric. 1997. Computational Methods for Fluid Dynamics. Berlin: Springer-Verlag.

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Foscolo, P.U., L.G. Gibilaro, and S.P. Waldram. 1983. A unified model for particulate expansion of fluidized beds and flow in fixed porous media. Chemical Engineering Science 38:1251–1260. Herbst, J., and L. Nordell. 2001. Optimization of the design of SAG mill internals using high fidelity simulation. Pages 1–5 in SAG 2001 Conference, Vancouver, BC. Herbst, J.A. 2002. A microscale look at tumbling mill scale-up using high fidelity simulation. European Comminution Symposium, Heidelberg, Germany. Herbst, J.A., and L.K. Nordell. 2002. Emergence of HFS as a design tool in mineral processing. Plant Design Symposium, Vancouver, BC. Herbst, J.A., and A.K. Potapov. 2003. Radical innovations in mineral processing simulation. Mineral and Metallurgical Processing (October). Hollow, J., and J. Herbst. In press. Attempting to quantify improvements in SAG liner performance in a constantly changing ore environment. SAG 2006. Vancouver, BC. Hulburt, H.M., and S. Katz. 1964. Some problems in particle technology—a statistical mechanical formulation. Chemical Engineering Science 19:555–574. Potapov, A.V., and C.S. Campbell. 1996. A three-dimensional simulation of brittle solid fracture. International Journal of Modern Physics C 7:717–729. Potapov, A.V., M.A. Hopkins, and C.S. Campbell. 1995. A two-dimensional dynamic simulation of solid fracture. Part I: Description of the model. International Journal of Modern Physics C 6:371–398. Qiu, X., A. Potapov, M. Song, and L. Nordell. 2001. Prediction of wear of mill lifters using discrete element method. SAG 2001 Conference, Vancouver, BC. Richardson, J.F., and W.N. Zaki. 1954. Sedimentation and fluidization: Part I. Transactions of the Institution of Chemical Engineers 42:35–53.

Batu Hijau Model for Throughput Forecast, Mining and Milling Optimization, and Expansion Studies Ben Burger,* Karen McCaffery,† Ian McGaffin,† Alex Jankovic,‡ Walter Valery,‡ and David La Rosa‡

ABSTRACT

PT Newmont Nusa Tenggara (PTNNT) Batu Hijau and Metso Minerals Process Technology (Asia Pacific) (MMPT-AP) have developed a comprehensive model for forecasting and optimizing throughput at the Batu Hijau operation. The model is based on mechanistic models of blast fragmentation, crushing, milling, and classification. The model inputs are the proportions and main characteristics of the defined ore domains (e.g., rock quality designation [RQD], Point Load Index [PLI], Bond Work Index, lithology, design, and operating conditions). The final model is able to predict monthly throughputs with a 95% accuracy and is also being used for optimization of the entire mining and milling processes and for expansion studies. MMPT-AP has developed a stand-alone program to encapsulate the final throughput model with a user-friendly interface. This is used to input ore delivery information with blend composition and key model parameters and to output the model predictions (throughput, circuit performance, and product-size distributions from the run-of-mine [ROM] ore to the final grinding product). The intent is to give users in the mine and plant a simple interface to run simulations and allow geology, mining, processing, and management the ability to predict unblended throughputs for each of the defined ore domains as well as final blend throughput. INTRODUCTION

The Batu Hijau ore body is a copper and gold porphyry deposit located in southwest Sumbawa, in the province of Nusa Tenggara Barat, Indonesia. The process plant was designed to treat 120,000 tpd of ore through two semiautogenous–ball–crusher (SABC) grinding circuits to produce a copper–gold concentrate. Concentrator operations started in September 1999 and have been subject to continuous improvements to increase mine and mill production rates. Major improvements in mill availability, flowsheet changes to the SABC pebble crushing circuit in 2002 and 2003, plus miscellaneous de-bottlenecking projects increased mill production rates by * Newmont Mining Corporation, Perth, Australia † PT Newmont Nusa Tenggara, Sumbawa, Indonesia ‡ Metso Minerals Process Technology (Asia Pacific), Brisbane, Australia 461

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>10% since 2001. Improvements in mine blasting practices increased fragmentation of harder ores and improved mill throughput by 2%–7% since late 2003. Average flotation feed grind size increased from 200 to 240 Pm as a result of the throughput increases, with only minor penalty to flotation recovery. Mill throughput rates are highly variable with daily throughput rates ranging from 4,500 to 7,300 tph. The effect of mill feed size and hardness on throughput rate is apparent with feed size F80 ranging from 40 to 95 mm. Several years of record-low commodity prices immediately after startup at Batu Hijau placed pressure on the mine to produce higher-grade ore to feed the mill and on the mill to maximize throughput for the operation to remain economically viable. Hence, corporate management required an accurate (r5% tpa) mill throughput model for strategic planning to ensure life-of-mine (LOM) economics. It was also recognized that optimization of ore delivery on a revenue-per-mill-runhour basis could offer economic benefits by maximizing metal production and could provide a basis for ore blending. Revenue per mill run-hour could be determined by including the mill throughput rate in the traditional mine-revenue-per-ton model (grade x recovery minus smelter charges). ORE CHARACTERIZATION AND MILL THROUGHPUT MODELING

Semiautogenous grinding (SAG) mill throughput rates are dependent on ore hardness or breakage rates in the mill and mill feed size distribution. If both breakage rates and mill feed size can be measured or modeled for an ore, a JKSimMet (JKTech Pty. Ltd., Brisbane, Queensland, Australia) model can accurately predict SAG mill performance. Breakage rates are dependent on rock strength whereas mill feed size is dependent on in-situ rock structure, rock strength, blast intensity, and primary crushing. The first step in producing an accurate mill throughput model is to develop an understanding of geological parameters that define rock strength and rock structure. In a collaborative effort through 2004, the Batu Hijau mine-to-mill team and MMPT-AP conducted a comprehensive review of ore hardness and fragmentation in the Batu Hijau ore body to define mill throughput domains. MMPT-AP provided a modeling process for each domain that utilized blast fragmentation and primary crusher models to predict SAG mill feed size and produce a more accurate mill throughput model. HISTORICAL ORE CHARACTERIZATION

This section summarizes the post-startup ore domain definitions used at Batu Hijau. Ore domains used for design of the Batu Hijau grinding circuit are not discussed. Initial ore characterization for mill throughput prediction was based on lithology and RQD* (Table 1). An RQD cutoff of 50% was used to differentiate hard from soft ore. Process operating experience in 2003 indicated that lowering the RQD cutoff to 40% provided better definition by equalizing the tonnage of ore in the plus- and minus-RQD fractions of each major lithology. N E W TE C H N I Q U E F O R O R E D O M A I N D E F I N I T I O N

Recognition that both SAG mill feed size and ore hardness/breakage rates dictate SAG mill throughput rates allows geological indicators for both to be used to define ore domains for mill throughput prediction. * RQD%, or rock quality designation, is defined as the cumulative length of core pieces longer than 10 cm in a core run, divided by the total length of the core run, including all lost core sections and excluding mechanical breaks caused by the drilling process. RQD% is a measure of in-situ block size.

BATU HIJAU MODEL FOR FORECAST, OPTIMIZATION, AND EXPANSION

TABLE 1

TABLE 2

463

Batu Hijau ore definition Ore Definition 2000–2003

Ore Definition 2003–2004 (2nd quarter)

Faulted Volcanic RQD <50% Volcanic RQD >50% Diorite RQD <50% Diorite RQD >50% Intermediate tonalite RQD <50% Intermediate tonalite RQD >50% Young tonalite Undifferentiated (stockpile rehandle)

Volcanic RQD <40% Volcanic RQD >40% Diorite RQD <40% Diorite RQD >40% Intermediate tonalite RQD <40% Intermediate tonalite RQD >40% Young tonalite RQD <40% Young tonalite RQD >40% Undifferentiated (stockpile rehandle)

Geological database summary

Copper (Cu) grade RQD Rock Mass Rating (RMR) PLI Bond Crusher Work Index (WiC) Bond Rod Mill Work Index (WiRM) Bond Ball Mill Work Index (WiBM) Bond Abrasion Index (Ai) A×b

Average Ore 2004 Life of Mine

Units

No. of Samples

0.59 44 55 5.4 8.1 14.90 11.2 0.24 55

% Cu % % N/mm2 kWh/t kWh/t kWh/t — —

>50,000 >70,000 >70,000 >12,000 265 287 287 287 39

The geological model developed by exploration geologists at Batu Hijau is extensive and is testament to their efforts in core logging and rock characterization. Table 2 shows the number of measurements utilized in the geological model. Definition of ore hardness domains depends upon correlations between the relatively few metallurgical comminution tests and the statistically representative measurements, such as grade, RQD, and PLI. In-situ rock structure, as indicated by block size, in combination with a blast powder factor will dictate ROM fragmentation size and hence SAG mill feed size distribution. Ore hardness and hence breakage in the SAG mill can be correlated to rock strength measurements, such as unconfined compressive strength (UCS) and PLI. SAG Mill Feed Size

Figure 1 shows process plant operating data (4-day averages) from November 2003 to April 2004, which confirms the following relationships: ƒ SAG mill feed rate decreases as feed size F80 from Split-OnLine (Split Engineering,

Tuscon, Arizona) measurements increases. ƒ SAG mill feed size increases as RQD increases.

Thus, SAG mill feed size and throughput rate is related to RQD, but size can be modified with blast designs to influence mill throughput. Ore Hardness

Mill throughput modeling using JKSimMet software requires ore breakage properties to be derived from the JKTech drop-weight test procedure in combination with SAG mill feed and product size distribution.

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ADVANCES IN COMMINUTION

INSTRUMENTATION, MODELING, AND SIMULATION

7,000

80

6,500 70 6,000 60

5,000

50

RQD, %

Total SAG, tph

5,500

4,500 40 4,000 30 3,500 SAG tph RQD 3,000 50

55

60

65

70

20 75

SAG Feed Size F80, mm

FIGURE 1

RQD effect on SAG feed size and SAG throughput

The JK drop-weight test is expensive and time consuming and requires large samples, but it provides an accurate measurement of the breakage distribution function of the ore in a SAG mill. By early 2004, drop-weight tests had been conducted on 39 samples of Batu Hijau ore taken from in-fill drill programs in 2002 and 2003. The results indicated significant variability in ore hardness with the Aub results ranging from 23 to 107. The bulk of results ranged from 35 to 65, indicating that the average ore is amenable to semiautogenous milling. A mechanism was required to model the SAG breakage function through the whole ore body (1.3 billion t). A relationship between drop-weight Aub and PLI, as a measure of rock strength, has been identified for many different ore bodies (Morrell 2000). The point load test is a low-cost, quick test on a small sample of drill core. More than 12,000 tests have been performed on Batu Hijau drill cores, providing sufficient data density to define ore hardness domains. Low-PLI and high-Aub values indicate low resistance to breakage (i.e., high breakage rates) and hence higher mill throughput rates. Figure 2 shows the PLI and Aub measurements from the Batu Hijau drop-weight tests, which demonstrate a similar relationship observed for other ores, but each lithology has a unique PLI-versus-Aub relationship. NOTE: Aub results were adjusted by dividing by ore density (~2.62 t/m3 for Batu Hijau). Using the PLI to “map” ore-body hardness is an efficient approach for throughput modeling and forecasting. It provides a high sample density within the ore body at no extra cost to the mine as the test is done routinely for geomechanical classification. Use of other tests (JKMRC drop-weight, SMCC, SPI tests) is limited to much lower sample density due to the significant cost involved to obtain drill core samples and conduct the tests. To map the ore body for 4 years of production at Escondida, only 978 SPI tests were carried out, which was insufficient to achieve the required mapping precision. PLI was used to improve the interpolation procedure (Flores 2005).

465

BATU HIJAU MODEL FOR FORECAST, OPTIMIZATION, AND EXPANSION

120 Diorite All Tonalites Volcanics Tonalite (MMPT Database) Volcanics Best Fit Diorite Best Fit MMPT Database

A×b Adjusted, m3/kWh

100

80

60

40

20

0 0

2

4

6

8

10

12

14

PLI (Is(50)), MPa

FIGURE 2

PLI versus JKMRC drop-weight test result for Batu Hijau ore and MMPT database

PLI Database Corrections. While reviewing Batu Hijau data in 2004, MMPT identified significant errors in the PLI database in the Batu Hijau exploration block model. These errors were due to two factors: 1. Poor data collection/measurement for one in-fill drill campaign from year 2002.

These data were removed from the database in March 2004. 2. Incorrect calculation of PLI. This issue was resolved in May 2004 using the stan-

dardized PLI (Is(50)) calculation from the raw data. The formula for calculating size-corrected PLI (Is(50)) is

Is  50

§D · = 1,000 ¨ -----e- ¸ © 50 ¹

0.45

§ P · ¨ -----2- ¸ , (MPa) © De ¹

(EQ 1)

where P = force applied at failure (N) De = equivalent core diameter (mm) 2

D e = D2 (diametral) 2

D e = 4A/ʌ (for axial, block, and irregular lump) where A is the minimum cross-sectional area of a plane, through the platen contact points. Ore Domain Definition

Definition of mill throughput domains on the basis of ore hardness and mill feed size can be achieved using both RQD to infer size and PLI to infer ore hardness.

466

ADVANCES IN COMMINUTION RQD 2004 - LOM

2.5%

2.0% 1.5% 1.0% 0.5% 0.0%

PLI 2004 - LOM

2.5%

% of Total Mill Feed, t

% of Total Mill Feed, t

INSTRUMENTATION, MODELING, AND SIMULATION

% of Total Mill Tons Volcanics = 49% Diorite = 28% Int. Tonalite = 21% Young Tonalite = 1.4%

2.0% 1.5% 1.0% 0.5% 0.0%

0

10 20 30 40 50 60 70 80 90 100

0

10 20 30 40 50 60 70 80 90 100

RQD, % Volcanics Diorite

FIGURE 3

Intermediate Tonalite Young Tonalite

PLI, MPa Volcanics Diorite

Intermediate Tonalite Young Tonalite

Selected RQD and PLI ranges

A review of RQD and PLI distributions at Batu Hijau indicated that three ranges of RQD and PLI could be used to define a matrix of nine mill throughput domains, as shown in Figure 3. The ranges were selected to evenly divide the ore body tons into each domain. Each domain was categorized into soft, medium, or hard on the basis of ore hardness or fragmentation size expected within the domain as shown in Figure 4. Batu Hijau mine engineers developed a drill and blast “cookbook” based on the 9-domain matrix to define drill and blast parameters for use in ore shots, as shown in Figure 5. The design information was collated from historical performance data and blast trial results. Ore Hardness with 16 Domains

The 9-domain ore hardness matrix, based on RQD and PLI, was applied to each of the four major ore lithologies to produce 36 ore domains. Review of the ore delivery quantities in 36 domains immediately identified 15 domains that contained <1% of the ore body tons and hence could be eliminated. Spatial analysis of the remaining domains indicated spatial associations could be used to combine some smaller “halo” domains with a larger neighboring domain. The resultant 16 domains shown in Figure 6 each contain 5%–10% of the ore-body tons. The domains are identified according to the following list: C = coarse fragmentation (i.e., very high RQD) D = diorite F = fine fragmentation (i.e., low RQD) H = hard (high PLI) IT = intermediate tonalite M = medium fragmentation or hardness S = soft (low PLI) V = volcanic YT = young tonalite Plotting the 16 domains in the geological model illustrated high variability for mill throughput within the deposit. Figure 7 shows a plan view of the 16 ore domains relative

BATU HIJAU MODEL FOR FORECAST, OPTIMIZATION, AND EXPANSION

467

9 Medium

Hard

Very Hard

Soft

Hard

Hard – Very Hard

Very Soft

Medium

Hard

PLI, MPa

6

3

0 0

30

60

90

RQD, %

Ore hardness matrix

PLI

FIGURE 4

Type = 3 >6 40 m/hr Type = 2 3–6

8x8–7m 70:30 0.34 kg/dmt* 9 x 10 – 8 m 70:30 0.21 kg/dmt

Type = 6

16.5 m/hr Type = 5

6 x 7 – 6.5 m 70:30 0.54 kg/dmt 6 x 7 – 6.5 m 70:30 0.54 kg/dmt

Type = 9

11 m/hr Type = 8

55 m/hr

16.5 m/hr

11 m/hr

Type = 1

Type = 4

Type = 7

0–3 55 m/hr

10 x 10 – 8 m 50:50 0.22 kg/dmt

40 m/hr

0–30

30–60

Type = 5 Hole Spacing EP:AN (Emulsion:ANFO) Drill Penetration Rate

8x8–7m 70:30 0.34 kg/dmt

16.5 m/hr

6 x 7 – 6.5 m 70:30 0.54 kg/dmt

16.5 m/hr

6 x 7 – 6.5 m 70:30 0.54 kg/dmt 6 x 7 – 6.5 m 70:30 0.54 kg/dmt

6 x 7 – 6.5 m 70:30 0.54 kg/dmt > 60

RQD

Stemming Length

Powder Factor

* dmt = dry metric tons

FIGURE 5

Drill and blast “cookbook” for mill feed ore

to the average high- and low-grade ore boundaries. The figure shows that most of the harder ores (high RQD and PLI) are located in the center, south, and west sections of the ore body. Significant faulting has produced a low RQD in most of the north and eastern sections of the ore body; major faults strike northwest to southeast. MILL THROUGHPUT MODELS

This section summarizes the post-startup throughput modeling experience at Batu Hijau. Modeling conducted for design of the Batu Hijau grinding circuit is not discussed.

468

ADVANCES IN COMMINUTION

Volcanic

Diorite

Intermediate Tonalite Young Tonalite

FIGURE 6

PLI 0–3 PLI 3–6 PLI >6 PLI 0–3 PLI 3–6 PLI >6 PLI 0–3 PLI 3–6 PLI >6 PLI 0–3 PLI 3–6 PLI >6

INSTRUMENTATION, MODELING, AND SIMULATION

RQD 0–30 V-FS V-FH D-FS D-FM

RQD 30–60 RQD >60 V-CS V-MM V-CM V-MH V-CH D-CS D-CM D-CH

IT-MM

IT-CH IT-MH YT-CH

Sixteen ore-hardness domains

High Grade Medium Grade Low Grade Young Tonalite Intermediate Tonalite Diorite Ultimate Pit V-FS V-FH V-CS V-MM V-MH V-CM V-CH D-FS D-FM D-CS D-CM D-CH IT-MM IT-MH IT-CH YT-CH

FIGURE 7

Batu Hijau ore body description in 16 ore hardness domains

Historical Models

Several mill throughput models were developed from 2001 to 2004, using the techniques outlined in the following subsections. Simple Regression Modeling (2002). Basic multiple linear regression models were generated by fitting several months of historical mill throughput data to daily proportions of each ore domain. Initial models were based on simple lithology separation and later subdivided as RQD was used to further delineate lithology. The models generated provided reasonable throughput indicators; however, they did not account for throughput variations resulting from differences in mill feed size distribution. Bond Work Index Modeling (2002). Bond Work Index–based modeling was used to determine mill power as a function of work index:

BATU HIJAU MODEL FOR FORECAST, OPTIMIZATION, AND EXPANSION

469

mill power = fn(WiC) + fn(Wirm) + fn(Wibm) where WiC = Bond Crusher Work Index WiRM = Bond Rod Mill Index WiBM = Bond Ball Mill Index This model places the greatest emphasis on ball mill power and assumes fixed feed size to the SAG mill for all ore types. Throughput predictions produced were significantly different to actual plant performance. This was particularly true for tonalite ores, which have the lowest actual mill throughput rates and also the lowest Bond rod and ball mill work indices. The tonalite ores are generally much coarser than the other lithologies, as demonstrated by their inherently higher RQD. This modeling method was similar to models used to design the Batu Hijau grinding circuit. Figure 8 shows that the Bond Work Index modeling approach is not valid for modeling SAG mill throughput rates as it does not describe SAG mill breakage rates or account for variations in feed size to the mill. BOCCOST Empirical Modeling (early 2003). BOCCOST, or blasting optimization crushing conveying optimizing SAG throughput, is a database that captures approximately 200 variables from blasting, mining, and milling operations and assigns them to a common point in space in the geological model in real time (Pontin and Setiawan 2002). The intention was that the relationships between these variables should be determined with a view to optimize the overall blasting, blending, and crushing process to maximize mill throughput. Interpretative analysis of about fifteen variables from the BOCCOST database was used to model the following: ƒ The relationship between size of material delivered to the primary crusher and pit

geology and blasting practices ƒ The relationship between SAG mill feed rate, pit geology, and blasting practices

Again, essentially basic multiple linear regression analysis was used over three defined ore-body zones. The zones were differentiated broadly based on major differences in faulting and lithology that corresponded with perceived mill throughput zones. Initial data screening was used to isolate the variables that had the most impact on mill throughput and blasted rock size. Model output was used as a tool to assist short- and medium-term mine planning. Prediction of blasted rock size from BOCCOST was viewed to be more accurate than the throughput predictions. JKSimMet Modeling (early 2003). JKSimMet modeling, based on mill surveys and nine drop-weight results across RQD and lithology-defined ore domains, used the JKSimMet ta estimation of mill feed size P80. This model produced similar results to the simple linear regression model. JKSimMet Modeling (late 2003). JKSimMet modeling used mill feed size estimation from the BOCCOST empirical blast fragmentation model. JKSimMet modeling from early 2003 was used to generate throughput versus mill feed F80 relationships for “hard,” “medium,” and “soft” hardness ores of the following form: throughput = M u SAG F80b

470

ADVANCES IN COMMINUTION

INSTRUMENTATION, MODELING, AND SIMULATION

Empirical Ore Delivery Method JKSimMet Model (early 2003) Bond Work Index Model

8,000 7,000

Mill Throughput, tph

6,000 5,000 4,000 3,000 2,000 1,000

FIGURE 8

Volcanic RQD >50

Volcanic

Diorite RQD >50

Diorite

Young Tonalite RQD >50

Young Tonalite

Tonalite RQD >50

Tonalite

0

Mill throughput predictions

The constants M and b were determined based on functions of RQD for each ore hardness. SAG feed F80 was estimated from a simple log fit of historical measured SAG F80 and BOCCOST blasted rock P80. This relationship is very robust, as demonstrated in Figure 9. Throughput prediction from this method was an improvement over previous modeling attempts in that it allowed for variable mill feed size distribution; however, it still lacked adequate accuracy for incorporation into the ore block model revenue calculation. INTEGRATED MILL THROUGHPUT MODELING

In early 2004, Batu Hijau contracted MMPT-AP to assist with ore characterization and produce domain-specific mill throughput models for use in long-term production forecasting and evaluation of mill expansion options. Revised models were required due to pebble circuit flowsheet changes in August 2003, which produced a step change improvement in mill performance, such that previous throughput models were no longer valid. MMPT-AP conducted modeling of the full comminution process using blasting, crushing, and grinding models to calculate SAG mill feed size, throughput rate, and flotation feed grind size (Jankovic et al. 2004). The simplified model is presented in Figure 10. This model consists of the following combined mechanistic models: ƒ Blast fragmentation model ƒ Primary crusher model ƒ Milling circuit model (SAG mill, ball mill, and cyclone models, pebble crusher in

closed circuit) The results of the simulations combining the blast fragmentation model, the primary crusher model, and the complete SAG/ball/pebble/screen models were divided into coarse/hard, mean, and fine/soft for each lithology. The inputs to these models were ƒ The rock mass data consisting of RQD, which was used to estimate the volumetric

joint distribution and then converted into a mean in-situ block size ƒ UCS inferred from PLI data ƒ Drop-weight test data and their correlations to PLI

BATU HIJAU MODEL FOR FORECAST, OPTIMIZATION, AND EXPANSION

471

85

SAG Feed F80, mm

80 75 70 65 60 55 50 45 17-Jun-05

8-May-05

29-Mar-05

17-Feb-05

8-Jan-05

29-Nov-04

20-Oct-04

10-Sep-04

1-Aug-04

22-Jun-04

13-May-04

3-Apr-04

23-Feb-04

14-Jan-04

40

Date Average SAG F80 mm Predicted SAG F80 Based on BOCCOST Shovel P80 7 per Moving Average (Average SAG F80 mm) 7 per Moving Average (Predicted SAG F80 Based on BOCCOST Shovel P80)

FIGURE 9

Actual and predicted SAG F80 and BOCCOST model P80 comparison

Ore Characterization

Blast Design

MMPT Blast Fragmentation Model

Lithology Zones Rock Strength - PLI - DWi, A×b, ta - WiC, WiBM, WiRM, Ai Rock Structure - RQD, Mapping

ROM Ore Size Distribution

Primary Crusher Model (JKSimMet/MMPT)

SAG Feed Size Distribution

Grinding Circuit Model (JKSimMet)

tph

FIGURE 10

P80

Schematic of the modeling approach

The blast fragmentation model assumed a blast design with bench heights of 15 m, using blast-hole diameters of 311 mm, and a burden and spacing of 7 and 6 m, respectively. The polygon and shovel P80s were used to validate the model predictions. The envelopes of ROM size distributions (soft/fine, mean, hard/coarse) were obtained using Monte Carlo sampling followed by model simulation. Monte Carlo sampling refers to the traditional technique for using random or pseudo-random numbers to sample from a probability distribution. These techniques are applied to a wide variety of complex problems involving random behavior. Each Monte Carlo iteration involves obtaining an estimate of each of the input variables to the model based on their mean value and standard deviation.

472

ADVANCES IN COMMINUTION

INSTRUMENTATION, MODELING, AND SIMULATION

The ROM size distribution is calculated using the model and these randomly created input variable parameter estimates. This process is repeated 1,000 times to obtain an envelope of possible ROM size distributions based on the variation in the input data. The coarse, mean, and fine ROM size distributions are the upper, mean, and lower size distributions based on the 5% and 95% confidence intervals. The ROM fragmentation is used as input to the primary crusher model to predict the feed size for SAG mills. Simulations were conducted with a crusher closed side setting of 125 mm. The primary crusher product size distributions were used as feed to the SAG mill model, and simulations of the entire grinding circuit were conducted. The resulting simulated throughputs for each ore type were “blended” according to the reported oreblending information and compared to the actual average daily throughput. Preliminary Models for Ore Characterization

Metso modeling was conducted on three different sets of ore domains to determine the level of detail required to produce a representative and accurate mill throughput model. The models were validated and compared to daily production information: ƒ Eight ore domains used historically based on four lithologies and two ranges of

RQD (<40%, >40%) ƒ Nine ore-hardness domains (matrix) based on three ranges of RQD and PLI but

not lithology ƒ Twenty-four domains based on four lithologies, two ranges of RQD (<40%,

>40%), and three ranges of PLI (<3, 3–6, >6) Model prediction compared to actual production is shown in Figure 11. The 24domain model produced the best fit, indicating that a combination of lithology, RQD, and PLI was required to accurately model mill throughput rates. The 9-domain model results show poor sensitivity to high and low throughput rates. Overall, the results indicated the need to retain lithology as a parameter in ore domain definition. The results of this work led to the application of three RQD and three PLI ranges to each of the four lithologies to produce 36 domains. Spatial and quantitative ore characterization reduced the 36 domains to 16 domains, as shown in Figure 6. Predicting Mill Throughput for Varied Blast Designs

The Metso modeling approach was applied to the 16 ore domains shown in Figure 6, using two different drill and blast regimes: ƒ Historical powder factor, little variation between ore types (0.25–0.35 kg/t) ƒ Drill and blast cookbook, high powder factors in harder ores (up to 0.54 kg/t)

Blast-fragmentation simulations indicate a large variation in ROM fragmentation for each lithology as a consequence of different rock strength (PLI), RQD, and blast design. Figure 12 shows the simulated ROM for volcanic lithology. Intense blast designs were implemented in mine operations in 2004. The resultant improvement in ROM fragmentation size in harder ores is shown in Figure 13. The points plotted are annual averages for each of the 16 ore domains. The reduction in variability of primary crusher feed size improved crusher operation and increased average power draw for harder ores as the crusher can be operated consistently at the target closed side setting of 120 mm. The primary crusher product (SAG mill feed) was obtained by “passing” the ROM ore through the primary crusher model. This approach produced a SAG mill feed size distribution for each of the 16 ore domains (and two blast designs).

BATU HIJAU MODEL FOR FORECAST, OPTIMIZATION, AND EXPANSION

473

7,000

6,500

Model, tph

6,000

5,500

5,000 8-Domain R2 = 0.16 24-Domain R2 = 0.33 9-Domain R2 = 0.35 4,500 4,500

5,000

5,500

6,000

6,500

7,000

Actual, tph

FIGURE 11 Preliminary Metso models versus actual November 2003–March 2004 mill production (4-day moving average composites)

100 90

Cumulative % Passing

80 70

V-CHc V-CMc V-MHc V-MMc V-FHc V-FSc V-FS hb V-CSc V-CS hb V-MM hb V-MH hb V-CM hb V-CH hb

60 50 40 30 20 10 0 1

10

100

1,000

Size, mm

FIGURE 12

ROM volcanic (hb = blast designs from the cookbook; c = old blast design)

10,000

474

ADVANCES IN COMMINUTION

INSTRUMENTATION, MODELING, AND SIMULATION

400 Year 2003, Low Powder Factor Blast Designs Year 2004, Intense Blast Designs

ROM Fragmentation F80, mm

350

300

250

200

150

100 0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Powder Factor, kt/t

FIGURE 13

Actual ROM fragmentation improvement from intense blast designs

Domain-specific ore breakage parameters for input to a SAG mill model were obtained using the JKTech drop-weight test Aub result versus point load index (Is50) relationships from Figure 2. This approach allowed evaluation of the variability of breakage rates and indicated a “possible throughput range” for each domain and blast design (powder factor) simulated. Additionally, the “average throughput” for each domain and blasting powder factor was determined based on “best fit” to actual daily throughput. The average-throughput results presented in Figure 14 show that a 10%–15% mill throughput rate increase could be expected in the harder ore types with more intense blasting. Model Validation

The 16-domain model mill throughput rates were applied to the daily ore delivery blends for year 2004 and compare well on a monthly/annual basis, as shown in Figure 15. Model prediction errors were estimated using a sum-of-squared-error method, weighted for total tons milled in each time interval. The results shown in Table 3 and Figure 16 indicate that estimation of mill throughput for weekly ore delivery could be utilized to optimize short-term mine plans. The daily mill throughput prediction is inherently inaccurate as the daily mine ore delivery will not match average RQD, PLI, and powder factor used to predict the average throughput rate for each domain. Additional external effects, such as the particle size segregation on mill feed stockpiles and the nonlinear effect of ore blending on mill throughput, cannot be accounted for in the model, thus, further increasing the error of estimate for shorter time periods. APPLICATION OF THE MODEL

The 16-domain model was integrated with the ore control block model to assign a mill throughput rate factor as “mill run time required to process each ore block” (tons per

BATU HIJAU MODEL FOR FORECAST, OPTIMIZATION, AND EXPANSION 8,000

475

1.2

1.0 Mill tph (Metso Model)

6,000 0.8

5,000

4,000

0.6

3,000 0.4

2,000 0.2

Drill and Blast Powder Factor, kg/t

7,000

1,000 Volcanic

Diorite

Tonalite

0

Historical Mill tph Historical Powder Factor

FIGURE 14

YT-CH

IT-CH

IT-MH

IT-MM

D-CH

D-CM

D-CS

D-FM

D-FS

V-CH

V-CM

V-MH

V-MM

V-CS

V-FH

V-FS

0.0

Intense Blast Mill tph Intense Blast Powder Factor

Effect of blast powder factor on mill throughput

8,000

Total Mill Throughput Rate, tph

7,000 6,000 5,000 4,000 3,000 2,000 Actual Daily Production 16-Domain Model Prediction

1,000 0 1-Jan-04

FIGURE 15

1-Apr-04

1-Jul-04

30-Sep-04

31-Dec-04

Actual mill throughput for 16-domain model predictions for 2004

block/mill tons per hour). This mine scheduling was simplified to selection of sufficient ore blocks to match forecast mill run-hours for a time period. This approach also enables optimization of ore delivery on the basis of both payable metal content (dollar index) and production rates. The 16-domain model was also used to evaluate mill throughput rates during a recent mill expansion study based on the properties of the incremental ore added to the ore delivery plans to feed the expanded plant.

476

ADVANCES IN COMMINUTION

TABLE 3

INSTRUMENTATION, MODELING, AND SIMULATION

Sixteen-domain model predictions for 2004 Average, tph

Actual production Annual model prediction Monthly Weekly Daily

Average Error, tph

Average Error, %

9 258 401 578

0 4 7 10

6,062 6,070

8,000

+10%

7,000

Model, tph

–10%

6,000

5,000

Daily Weekly Monthly Annual 4,000 4,000

5,000

6,000

7,000

8,000

Actual, tph

FIGURE 16

Model predictive performance

CONTINUOUS THROUGHPUT MODEL

The 16-domain mill throughput model is useful for monthly and annual throughput forecasting as the average properties of the ore delivered over these longer time periods is generally close to the average RQD and PLI within each domain. The model output of an average throughput rate per domain does not account for throughput variability within the domains; hence, significant step changes in throughput prediction occur at the domain boundaries. To be able to improve the accuracy of the mill throughput predictions on a shorter time scale, a continuous model was required that could accept any combination of RQD, PLI, and blast powder factor per domain to reflect ore blocks delivered on a daily basis.

BATU HIJAU MODEL FOR FORECAST, OPTIMIZATION, AND EXPANSION

FIGURE 17

Continuous model user interface

16-Domain Model

Continuous Model

8,000

8,000

7,000

7,000

6,000

6,000

5,000

5,000

Mill tph

Mill tph

477

4,000 3,000

4,000 3,000 2,000

2,000 1,000

0–30 30–60 RQD

0 0–3

3–6

>60 >6

PLI

FIGURE 18

1,000 0

1.5

3

4.5

6

7.5

75

45 60

15 30 RQD

PLI

Sixteen-domain model and continuous model for volcanic ore lithology

Metso conducted more than 40 complete model runs to generate multiple fragmentation and mill throughput predictions per domain and converted the results into a userfriendly software package, as shown in Figure 17. The user can input any combination of RQD, PLI, and powder factor per domain to reflect specific ore parcels. Figure 18 illustrates the difference in the prediction resolution between the 16-domain model using a single throughput value per domain and the continuous model. Batu Hijau engineers have found the continuous model to be informative but not entirely practical for monitoring of long time periods (monthly/annual), as the model is coded into the software developed by Metso and hence cannot be integrated into a spreadsheet calculation. FUTURE MODEL REFINEMENTS

The path forward for refinement of ore domain characterization and mill throughput modeling includes additional comminution testwork on drill cores, updates to the geological model from in-fill drilling, and revisions to the mill throughput models based on the revised geology. Future refinement possibilities are as follows: ƒ Development of a continuous function equation for each ore domain that can be

used in a spreadsheet rather than using the continuous model program. Some work has started in this area to allow throughput prediction based on variation in RQD within each ore domain.

478

ADVANCES IN COMMINUTION

INSTRUMENTATION, MODELING, AND SIMULATION

ƒ Refinement of the model for periods where peaks and dips are not picked up.

More than 80 additional modified drop-weight tests on 2004 and 2005 in-fill drill samples will be conducted in 2005 to boost model integrity. ƒ Modeling of ball mill and pebble crusher limiting ore—requires additional ball

mill work index tests to produce a spatially representative ball mill work index model. Some lower-grade ores appear to have a significantly higher ball mill work index based on plant performance and testing of grabs samples. The geological model is not complete in low-grade ores. ƒ Development of a blend model to describe the nonlinear impact of blending on

the throughput rate estimates from each ore source. ƒ Determination of the impact of mill throughput on flotation feed size distribution

and consequently on flotation recovery. Increasing grind size with throughput has variable impact for Batu Hijau ore, and significant losses can be incurred in some of the softer ore types. This will enable an improved revenue cutoff relationship to be determined to truly optimize blending and ore delivery strategy for maximizing revenue. CONCLUSIONS

An ore-characterization and mine-to-mill throughput modeling approach has been successfully applied at Batu Hijau. This has produced significantly better mill throughput rate predictions than previous modeling has allowed. The ore domain definition and modeling approach relies on definition of ore domains based on ore lithology, rock structure (RQD), and rock strength (PLI) and takes the in-situ ore through blasting, crushing, and milling models to produce an accurate prediction of mill throughput for medium- to long-term production forecasting. Short-term predictions are influenced by external factors, such as particle-size segregation and residence time on process surge piles, and the nonlinear impact of blending. Improved ore definition and understanding of the Batu Hijau resource has resulted in the following benefits: ƒ Enormous improvement in communications between the mine and the mill at

Batu Hijau. Mine engineering, operations, and geology personnel understand the variables that drive mill throughput. The mine and the mill work with a common purpose. ƒ Development of a blasting “cookbook” for generation of an optimum product size

for feed to the mill ƒ Accurate prediction of blast fragmentation size, which is the key to accurate pre-

diction of SAG mill feed size (F80) ƒ Generation of a throughput model that has superior accuracy for annual and

monthly throughput budgeting purposes and evaluation of mill expansion options ACKNOWLEDGMENTS

The authors would like to thank the PT Newmont Nusa Tenggara engineering, operations, and management team at Batu Hijau for their efforts and continued support of this program, and for their permission to publish this paper. BIBLIOGRAPHY

Butcher, A., and W. Valery Jr. 2005. Establishing the links between ore characteristics and crushing and grinding performance. Paper presented at SME 2005 Conference, Salt Lake City, UT, 28 February–2 March.

BATU HIJAU MODEL FOR FORECAST, OPTIMIZATION, AND EXPANSION

479

Flores, L. 2005. Hardness model and reconciliation of throughput models to plant results at Minera Escondida LTDA, Chile. Paper 16 in Proceedings of Canadian Minerals Processors, 2005. The Canadian Institute of Mining, Metallurgy and Petroleum, ISBN 1-894475-47-X. Grundstrom, C., S. Kanchibotla, A. Jankovic, and D. Thornton. 2001. Blast fragmentation for maximising the grinding circuit throughput at Porgera gold mine. Pages 383– 399 in Proceedings of the 27th Annual Conference on Explosives and Blasting Technique. Orlando, FL: International Society of Explosives Engineers. Hart, S., W. Valery Jr., B. Clements, M. Reed, S. Ming, and R. Dunne. 2001. Optimisation of the Cadia Hill SAG mill circuit. SAG2001: International Conference on Autogenous and Semiautogenous Grinding Technology, Vancouver, BC. Jankovic, A., D. La Rosa, W. Valery Jr., and Y. Tai. 2004. Throughput Model for Forecasting Production at Batu Hijau. Final report to PT Newmont Nusa Tenggara. Asia Pacific, Australia: Metso Minerals Process Technology. Kanchibotla, S.S., W. Valery Jr., and S. Morrell. 1999. Modelling fines in blast fragmentation and its impact on crushing and grinding. Explo’99 Conference, Kalgoorlie, Western Australia. Lam, M., A. Jankovic, W. Valery Jr., and S. Kanchibotla. 2001. Increasing SAG mill circuit throughput at Porgera gold mine by optimising blast fragmentation. SAG2001: International Conference on Autogenous and Semiautogenous Grinding Technology, Vancouver, BC. Morrell, S. 2000. Point load/drop-weight test correlation. Progress Report JKMRC/ AMIRA. Project D438 A, confidential to sponsors. Australian Mining Industry Research Association, Melbourne. Morrell, S., and W. Valery Jr. 2001. Influence of feed size on AG/SAG mill performance. SAG2001: International Conference on Autogenous and Semiautogenous Grinding Technology, Vancouver, BC. Morrell, S., W. Valery Jr., G. Banini, and S. Latchireddi. 2001. Developments in AG/SAG mill modelling. SAG2001: International Conference on Autogenous and Semiautogenous Grinding Technology, Vancouver, BC. Pontin, D., and L.E. Setiawan. 2002. BOCCOST modelling—tracking and relating mine and mill performance indicators in real time to increase SAG mill throughput. Value Tracking Symposium AusIMM (October). Valery, W., Jr. 1997. A model for dynamic and steady-state simulation of autogenous and semi-autogenous mills. Ph.D. dissertation. Brisbane, Australia: JKMRC, University of Queensland. ———. 2004. Process integration and optimisation in aggregates production. Paper presented at the 2nd International Seminar on Construction Aggregates. Campinas, Brazil, October 25–28. Valery, W., Jr., et al. 2001. Mine to mill optimisation and case studies. Paper presented at VI Southern Hemisphere Conference on Minerals Technology, Rio de Janeiro, Brazil, May 27–30. Valery, W., Jr., D. La Rosa, and A. Jankovic. 2004. Mining and milling process integration and optimisation. Paper presented at SME 2004 Conference, Denver, CO, February 23–25.

The Use of Process Simulation Methodology in Process Design Where Time and Performance Are Critical Kent T. Tano,*† Bertil I. Pålsson,† Johanna Alatalo,* Lars Lindqvist‡

ABSTRACT

In 2004, LKAB started a basic engineering study to expand its existing production lines at the Malmberget mine site. Current limitations in the underground mine capacity require the use of ore from other mine sites, which results in varying ore properties regarding grindability and chemical composition. It was necessary to determine if the required particle size from an agglomeration point of view could be obtained with extreme ore types by design in a robust process and proper control strategy. In addition, project time constraints forced a decision on final design of the ore beneficiation process to be based on a combination of pilot-scale campaigns and process simulations. Steady-state simulations using ModSim software are used extensively to study process performance for different ore-type feed and different design parameters, such as mill dimensions and varying feed particle size. Population balance models of the ball mills are combined with simple flowsheet models of magnetic separation. Model parameters are derived from pilot-plant data and, when possible, from existing circuits. Dynamic process simulation (Dymola) based on ModSim data is used to evaluate necessary instrumentation as this called for early decisions in the ongoing project. The dynamic simulator will be used to parameterize the progressive, integration and derivative (PID) function controllers and also as a tool in the education of production personnel. The final goal is to facilitate and minimize startup of the plant and to reach design capacity rapidly. INTRODUCTION

The iron ore market is expected to grow in the coming years, mostly due to the tremendous growth in China. Most steel producers in the blast furnace industry, as well as those in the direct reduction route of iron making, have decided to invest in capacity expansions or plan to do so. To maintain market share, LKAB must increase its pelletizing capacity. Existing plants are run at their maximums, and investment in new pellet capacity is a necessity. As a first step, a decision was made in November 2004 to invest in a new pellet plant at Malmberget. The application for an environmental permit at this site has already been approved by the authorities, thus, actual startup production near the * LKAB, Research and Development, Malmberget, Sweden † Luleå University of Technology, Division of Mineral Processing, Luleå, Sweden ‡ Optimation AB, Luleå, Sweden 481

482

ADVANCES IN COMMINUTION

INSTRUMENTATION, MODELING, AND SIMULATION

end of 2006 is promising. The total production capacity of pellet and sinter fines at the Malmberget operation is today limited by the production system for run-of-mine ore. An immediate increase in pellet production without dropping the production of sinter fines will therefore need ore transported from LKAB’s other mine site (Kiruna), approximately 100 km away. This situation will most likely last for only a few years until present bottlenecks at the Malmberget mine are eliminated. This must be taken into account in designing the beneficiation process. The differences in ore mineralogy and chemical composition for the Malmberget and Kiruna ore will put extra control demands on the grinding and mixing of pellet feed concentrates. The ore from Kiruna has to be ground to a finer size for liberation, approximately 80% <45 Pm, which can be compared with 68% <45 Pm for the Malmberget ore. A variation in the mixing ratio of fine and coarse concentrate will give rise to variations in the dewatering and the subsequent green ball production (agglomeration). At the same time, chemical differences in concentrates also will set constraints on mixing ratio. Balancing these two criteria will be necessary to fulfill customer demands. To manage all project criteria, ranging from process performance to product quality issues within the given time constraints, a strategy used early in the project was to extensively use modeling and simulation methods. A further objective, more strategic in nature, was to strengthen in-house competence on simulation tools. During the process design work, the steady-state ModSim simulator (King 2001) was used and simulated results formed the basis for equipment sizing and the general process layout. This kind of steady-state simulation tool is valuable in matters related to mineral process issues but is of less help in process control. To complement managing control aspects, a dynamic simulation tool (Dymola 2004) was used. Generated data from ModSim, such as residence time, and so on, provided input data to the dynamic simulator, and different scenarios of process events were then possible to simulate. Added benefits of using dynamic simulation are the education of operators and early testing of the control system, which hopefully will result in a problem-free startup. STEADY-STATE SIMULATIONS

Parameter Estimation from Pilot Mills Description of Feed Material. A major problem in all simulations is that even for a

well-known process and ore, the basic parameters needed for the simulation do not exist, at least not in the way required by a simulation program. Often, only the feed particlesize distribution is known to some extent, although not very well because it is not easy to sample coarse ore feeds accurately. The amount of mineral interlocking in various size ranges is seldom known. With luck, one may find the element content of the size ranges. With this in mind, simulations and scale-up proceeded very carefully, with checks and validations for every step of the process. The Malmberget raw feed used in the pilot tests had a particle-size distribution according to data presented in Table 1. A simple limitation is that the material is assumed to consist of only two components: 1. Magnetic with 99% magnetite (corresponding to 71% Fe), density 5.0 g/cm3 2. Gangue with 7% magnetite (corresponding to 5% Fe), density 3.1 g/cm3

The reason for this assumption is merely that there are no data on the frequency of mixed particles, the implication being that it is not possible to simulate the liberation of particles in the comminution process.

USE OF PROCESS SIMULATION METHODOLOGY IN PROCESS DESIGN

TABLE 1

Feed particle-size distribution in pilot tests (maximum particle size, 18 mm)

Sieve, mm

Cumulative % Finer

Sieve, mm

Cumulative % Finer

Sieve, mm

Cumulative % Finer

16.0 12.5 10.0 5.0 2.8

97.41 90.62 85.53 72.51 66.94

2.000 1.400 1.000 0.710 0.500

63.66 59.79 54.17 46.37 36.33

0.355 0.250 0.180 0.125 0.090

28.09 20.57 14.57 9.98 6.22

TABLE 2

483

Composition of feed material Fraction, mm

Magnetic, %

Gangue, %

>6.68 4.7–6.68 3.33–4.7 1.65–3.33 0.59–1.65 0.30–0.59 0.15–0.30 0.07–0.15 <0.07

85.00 92.70 90.75 90.75 91.80 91.75 93.70 94.30 88.35

15.00 7.30 9.25 9.25 8.20 8.25 6.30 5.70 11.65

The composition of the feed material in the fines range (<6.68 mm) is known to some extent (compare to Table 2) and the composition in the coarsest fraction is inferred from visual examination of it. Flowsheet. In the pilot runs, the throughput was kept at 1.5 tph. A flowsheet indicating typical flows and grades from simulation is shown in Figure 1. The flowsheet shows that ~10 wt % of the feed to the grinding section goes to tailings, and with it ~1% of the iron content. Though this may sound extremely good, one must keep in mind that the feed is not run-of-mine material; it is a product from the drycobbing plant. As the primary ore mineral is magnetite, the flowsheet becomes very simple; wet low-intensity magnetic separator (LIMS) and ball mill grinding involve three consecutive steps. The major reason for the three steps is the need to grind fine to liberate gangue minerals, and to produce a pellet feed with sufficiently large surface area. In the simulation work, the main effort was to model the grinding steps. The models for the magnetic separation steps were adjusted just enough to give a fair description of the solids, water, and iron split over them. All LIMS steps were modeled with ModSim’s WDM2 model with slightly different parameters for each step (compare to Table 3). The concentrate from the wet-cobbing step went to a primary ball mill ‡ 1.0 u 1.5 m with inner dimensions ‡ 0.911 u 1.330 m. Grinding bodies are 60-mm steel balls. Installed motor power is 15 kW, of which ~10.5 kW is used. The mill was run at volumetric filling 0.26 and with speed nc 0.75. Desired dilution was 70% by weight. Grinding in the primary mill was simulated with ModSim’s GMSU model, which uses the standard Austin breakage and selection function. Selecting proper values for the breakage parameters and selection parameters was a somewhat hands-on approach. After extensive trial and error, the best combination found was to use the default values for the breakage parameters, but with the fraction of fine breakage (I5) lowered to 0.3, while the selection function achieved the standard values for taconite (ModSim 2003). The GMSU

484

ADVANCES IN COMMINUTION

1 50 0.0152 1

99.0 65.2 9

0. 2 23

INSTRUMENTATION, MODELING, AND SIMULATION

0. 0. 0.152

13 12 Wet Cobbing 21 16 11 17 1

0.

18

10

0. 2.01

0.

14

6

0. 0.0630

3 1.41 0.450

75.7 69.2

1.41 0.602

70.0 69.2

2

5

12

22 19

0. 0. 2 60 6

3

0.

7

15 0. 0. 0.00912

7

0.0950 1.80

4

5.01 6.57

0.0404 2.09

1 90 7.13

1.36 0.522

72 3 71.0

0.141 6 50

2.13 6 71

70.0 71.0

0.00602 0.230 6.02 8 2.61

8

2

1 36 0 585

23 4

10

13

1 36 0 573

20

70 3 71 3

TABLE 3

11

1.36 0.582

9

tph 3 m /hr

FIGURE 1

5

70.0 71 3

% Sol % Fe

Pilot flowsheet for Malmberget pellet feed production

Parameter values in each LIMS step used by ModSim model WDM2 LIMS Step

Sharpness index Grade of mineral 2 that has 50% recovery Small size limit of short-circuit to nonmagnetics, mm Exponential coefficient to reduce bypass as size increases Water split to tail stream Set solids content in the LIMS, wt %

Wet Cobbing

Primary Separation

Secondary Separation

0.70 0.15 0.050 20

0.85 0.15 0.010 40

0.99 0.40 0.001 99

0.80 40

0.80 35

0.82 30

model simulates the mill with three mixers in a row. The relative retention times are assumed to be 0.05, 0.10, and 0.85 with transport model PM PM (PM,CL). The pilot mill was a grate-discharge mill that was simulated by the model’s postclassification routine and the Exponential Sum function with D50 of 3 mm (half of the shortest grate dimension) and separation efficiency 3. The GMSU model input form with all parameter values for the primary mill is shown in Figure 2. Secondary pilot ball mill grinding was done in a grate-discharge mill ‡ 1.5 u 1.7 m with inner dimensions ‡ 1.414 u 1.574 m. Installed motor power is 2 u 30 kW. The mill was run at volumetric filling 0.13, speed nc 0.73, and a power draw of ~20.5 kW. It was simulated with the GMSU model with the following changes compared to the primary mill: postclassification with D50 of 4 mm (shortest grate dimension, 8 mm) and grinding balls, 30 mm. As the Malmberget ore has a large grinding resistance in the secondary and tertiary grinding steps, the fraction of fine breakage (I5) was lowered to 0. Concentrate from the secondary LIMS step reports to the tertiary ball mill, which is identical to the secondary mill. The tertiary mill was run with volumetric filling 0.13, speed nc 0.70, and power draw ~17 kW. Dilution was 70% by weight. This mill was also modeled with the GMSU routine, and the only difference from the secondary mill was the use of 25-mm grinding balls.

USE OF PROCESS SIMULATION METHODOLOGY IN PROCESS DESIGN

FIGURE 2

485

GMSU model input form for the primary pilot ball mill

Results from the Pilot Circuit. The most important particle-size distributions are plotted in Figure 3. The primary ball mill is simulated to grind a particle to fine, compared to observed values, but the fit is very good for the secondary and tertiary mills. The simulated sieve data for the wet-cobbing concentrate are on top of the circuit feed. This means that either the wet cobbing does not show any significant classification (which is unlikely) or that the amount of wet-cobbing tailings is so low that it hardly influences the concentrate particle-size distribution. The latter is more likely. The simulations also provided estimates of net power according to Morrell (1996) and estimates of the average residence times in the mills (compare to Table 4). The simulated net power shown in Table 4 is the sum of the Morrell net power and the so-called no-load power (King 2001; Morrell 1996), which is the power needed to turn an empty mill. Comparing the simulated net power and the observed electrical power, a discrepancy is seen, attributed to mechanical losses on the order of 10%–20%, which is fairly normal for small-scale pilot mills. Validation against Full-scale Circuit

To validate the simulations, results from a sampling campaign in March 2002 over section 5 (one of the existing grinding lines, number 5) was used. Section 5 is a full-scale circuit in the existing concentrator that treats ~250 tph. A comparison of measured particle-size distributions in the pilot circuit and section 5 is shown in Figure 4. The feed for the pilot campaign was coarser than in the validation run, but the difference is within normal feed fluctuation. It is also clear, from looking at the particle-size distributions from the pilot- and the full-scale circuit, that there is consistency in the progression of the grinding work. The more gradual distributions from

486

ADVANCES IN COMMINUTION

11 to Tertiary Separator 1 Feed

INSTRUMENTATION, MODELING, AND SIMULATION

9 Total Tailings 18 Discharge Primary Ball Mill

16 Wet Cobbing Concentrate 6 Discharge Secondary Ball Mill

100 90 80

Cumulative % Smaller

70 60 50 40 30 20 10 0 100

FIGURE 3

TABLE 4

101

102

103

104

105

Particle-size distributions from the pilot circuit (lines simulated, markers observed)

Pilot mill powers and residence times

Mill

Primary grate-discharge, Ø60-mm ball Secondary grate-discharge, Ø30-mm ball Tertiary grate-discharge, Ø25-mm ball

Installed Power, kW

Observed Gross Power, kW

Simulated Net Power, kW

Simulated Residence Time, min

15

10.5

7.84

4.59

2 × 30

20.5

16.88

6.85

2 × 30

17.0

16.12

6.90

the full-scale circuit, most noticeable in secondary and tertiary grinding, are probably caused by the full-scale mills being trunnion overflows. In the validation, the material description is kept the same as for the pilot circuit, except for a change in the increased throughput. The mills replicate the dimensions of section 5. In the GMSU model, the postclassification is removed because the full-scale mills are trunnion overflow mills. After trial and error, it was found that to compensate for the postclassification, the value for fine breakage in the breakage function could be the same (I5 = 0.3) for all the mills. The primary mill in the full-scale circuit is a trunnion overflow ball mill ‡ 4.15 u 5.4 m, with inner dimensions ‡ 3.95 u 5.2 m. Installed power is 1,800 kW, of which ~1,450 kW is used. It is run at volumetric filling level 0.42, speed nc 0.75, and 70% solids by weight. The ball charge consists of 60-mm steel balls. The secondary and tertiary mills are equal in dimensions. They are trunnion overflow ball mills ‡ 4.9 u 5.7 m, with inner dimensions ‡ 4.77 u 5.4 m. Installed power is

USE OF PROCESS SIMULATION METHODOLOGY IN PROCESS DESIGN

487

100

Cumulative % Finer

80

60

Feed Pilot Feed S5 March 2002

40

Discharge Primary Pilot Discharge Kv001 S5 Discharge Secondary Pilot

20

Discharge Kv002 S5 Discharge Tertiary Pilot Discharge Kv003 S5

0 10

FIGURE 4

100

1,000

10,000

100,000

Particle-size distributions from pilot- and full-scale circuit

3,600 kW for each mill. Both are run at volumetric filling 0.42, speed nc 0.76, and 72% solids by weight. The secondary mill uses 30-mm steel balls and the tertiary, 25-mm steel balls. Observed power draw was 2,550 kW and 2,450 kW in secondary and tertiary grinding, respectively. With the changed mill dimensions and for the validation throughput of 262.1 tph, a new simulation was run. It resulted in the flowsheet shown in Figure 5. As for the pilot circuit, ~10% of the solid feed goes to the tailings. The simulated particle-size distribution of the discharge from the primary mill is slightly coarser than measured values (compare to Figure 6). The agreement is better for the secondary and tertiary mills. Note that the wet-cobbing concentrate is simulated to be finer than the actual mill product. This means that the simulation slightly underestimates the true grinding capability in the full-scale circuit. The simulation estimated net power according to Morrell (1996) and estimated the average residence times in the mills (compare to Table 5). A key finding of the simulation work was that it showed the difficulty in achieving the desired throughput and particle fineness with a new grinding section identical to the present section 5. Therefore, with increased confidence in the procedures, the simulation and scale-up continued with larger mills. Comparison with Traditional Scaling Procedures

The simulation and scale-up based on population balance models was a new in-house approach for LKAB. Therefore it was necessary to check what traditional scaling procedures would predict for a new grinding section; that is, to rely on energy requirements and calculation of a conditional Bond Work Index and an apparent grindability expressed in kilograms of newly produced material <45 Pm pro kWh [kg <45 Pm/kWh]. A condensed compilation for Malmberget feed material is shown in Table 6, where the expected grindabilities have been used to calculate the particle size key numbers for a new section 6, similar to the present one running at 250 tph.

488

ADVANCES IN COMMINUTION

262.1 2.65 1

99.0 0. 65.5 390.6 13 9

0. 0. 26.8

12 Wet cobbing 1

INSTRUMENTATION, MODELING, AND SIMULATION

21 16 11 17

0.

18

10

0. 351.5 14

6

0. 1.70

3 246.1 78.6

75.8 69.3

246.1 105.4

70.0 69.3

0.

22 12 19 5

2

0. 0. 465.5 6

3

0.

7

15 0. 3.33

7

16.0 314.5

4

4.85 8.10

6.69 365.4

1.80 7.55

239.4 91.4

23.7 1149.1

2.02 7.90

239.4 93.1

72.0 71.0

1.00 8 469.1

8

2

72.4 71.0

0.213 6.87

4

10

23 13 20

238.4 89.4

72.7 71.3

m3/hr

11

238.4 92.7

9

tph

FIGURE 5

5

0.

72.0 71.3

% Sol % Fe

Validation flowsheet for Malmberget pellet feed production

11 to Tertiary Separator 1 Feed

9 Total Tailings 18 Discharge Primary Ball Mill

16 Wet Cobbing Concentrate 6 Discharge Secondary Ball Mill

100 90 80

Cumulative % Smaller

70 60 50 40 30 20 10 0 100

FIGURE 6

101

102

103

104

105

Particle-size distributions from the full-scale circuit (lines simulated, markers observed)

One observation from applying traditional scaling procedures is that a better use of the grindability concept is for predicting product sizes suitable for pellet feed. Conditional work indices do not give consistent results <100 Pm, which is not surprising as the Bond Work Index is defined for grinding down to that size. The traditional scaling gave more or less the same general result as the simulation. It showed the possibility of achieving the desired product fineness for Malmberget feed alone, but that the final product size would be too coarse in any combination with Kiruna material.

USE OF PROCESS SIMULATION METHODOLOGY IN PROCESS DESIGN

489

Full-scale mill powers and residence times

TABLE 5

Mill

Installed Power, kW

Observed Gross Power, kW

Simulated Net Power, kW

Simulated Residence Time, min

1,800

1,450

1,312

3.07

3,600

2,550

2,240

4.93

3,600

2,450

2,241

4.96

Primary overflow, Ø60-mm ball Secondary overflow, Ø30-mm ball Tertiary overflow, Ø25-mm ball

TABLE 6

Predicted grindabilities and product sizes Predicted Grindability Primary

Secondary

Section 6 Product

Tertiary

kg <45 μm/kWh

Fineness, % <45 μm

Final d80, μm

Operation

Section 5, March 2002

28.5

28.7

17.9

70

67

27.3 24.7

25.1 26.5

19.5 19.6

67 73

57 54

Pilot 2004 for MK3

MA-feed, test 1 Kiruna 55% + MA 45%, test 3

Scaling to Full Circuit—Section 6

Duplication of any of today’s grinding sections would not meet the demands for throughput and particle fineness; therefore, up-scaling and simulation have continued with consideration of larger mills. It also became obvious, for other reasons, that a much larger average throughput was desired. The new circuit would have to have a capacity of 480 tph when running Malmberget ore, and 325 tph if fed with only Kiruna material. The final design also abolished the wet-cobbing step. After bidding from several manufacturers, a line of mills with dimensions according to Table 7 was selected. Residence times are calculated for 480 tph fresh feed, which is a worst-case scenario. The new section will have nearly twice the capacity as one of the existing sections, and this will add flexibility in producing special products. A flowsheet for the final design is shown in Figure 7. A consequence of the eliminated wet-cobbing step is the higher flow through the primary mill. This will call for careful design of the grate to avoid blockage and added flow resistance. Another effect is that the total tailings become much finer (compare to Figure 8). In addition to finer total tailings, another feature of the large circuit is a redistribution of the grinding energy so that the primary particle-size distribution will be coarser. Also, a new fineness aim with Malmberget ore feed is to have 65% <45 Pm. These changes have a potential negative impact in a higher amount of mixed particles in the >100-Pm range. Therefore, provisions have been made to include a classification step around the secondary grinding step. DYNAMIC PROCESS SIMULATION

Process Model Description

The object-oriented dynamic process simulator (Dymola 2004) has been used thus far for the development and evaluation of the control system, with only limited sections of

490

ADVANCES IN COMMINUTION

TABLE 7

INSTRUMENTATION, MODELING, AND SIMULATION

Section 6 final mill data, Malmberget feed Mill

Type Dimensions Volumetric filling Mill speed, nc Simulated net power Simulated residence time

Primary

Secondary

Tertiary

Grate-discharge, 70-mm ball Ø 4.6 × 6.5* m, coned mill ends 0.33 0.75 1,974 kW 1.86 min

Overflow, 30-mm balls Ø 5.5 × 8.0 m, flat mill ends 0.33 0.75 3,919 kW 3.89 min

Overflow, 25-mm balls Ø 5.5 × 8.0 m, flat mill ends 0.33 0.75 3,919 kW 3.98 min

* Belly length.

479.9 4.85 1

99.0 65.2 8

0. 200.8

0.

0. 514.4

17 20 10

13

5

14

9

0. 27.7

2 479.9 205.7

70.0 65.2

0.

11

1 4

11 18 15

0. 0. 648.0

2

5

0. 6

12 0. 21.8

6 3 38.6 576.0

6.28 5.57

75.4 70.4

441.4 171.6

72.0 70.4

5.85 7 672.1

7 44.5 3.44 1248.1 5.56

441.4 144.0

0.863 5.54

3

9

19 12 16

435.6 147.6

FIGURE 7

10

4

74.7 71.3

435.6 169.4

8

tph m3/hr

0.

72.0 71.3

% Sol % Fe

New section 6 when treating Malmberget ore at maximum capacity

the process simulated. An initial process control description has been completed and will be updated continuously according to results obtained from simulations. In this early stage, a simple grinding model—feed as input and product fineness measured by the percentage of particles finer than 45 Pm as output variable—has been implemented in the dynamic simulator. Other elements are described by simpler models, such as single mixers for tanks and pure delays for pipes. Calibration data for the grinding model are based on pilot mill experiments and ModSim simulations. Model parameters and a comparison of measured and predicted output is shown in Figure 9. The accuracy of the model is expected to be appropriate to represent the dynamics of the grinding circuit and to be of use in the continuing control system development. Simulation of Process Upsets

The simulated process layout is shown in Figure 10. The pellet product coming from both plants (BUV and MK 3) should be of the same quality; therefore, the pellet feed properties (fineness and chemical composition) must be the same. Variation in fineness will influence green ball productivity, and the allowable range of variation is less than r2% in the amount of particles <45 Pm. The accepted variation in phosphorous grade is less than 0.005%. The main variable to manipulate is the ore feed rate, which influences particle size and, to some extent, the chemistry. To a lesser extent, it is also possible to manipulate the ratio of Malmberget ore (PAR) and Kiruna (B2) and the mixing ratio of slurry concentrates (MPCO and MPCO 2). The two latter control actions are limited by

USE OF PROCESS SIMULATION METHODOLOGY IN PROCESS DESIGN

8 Total Tailings 14 Discharge Primary Ball Mill

10 to Tertiary Separator 1 Feed

491

5 Discharge Secondary Ball Mill

100 90 80

Cumulative % Smaller

70 60 50 40 30 20 10 0 100

101

102

103

104

105

FIGURE 8 Particle-size distributions for new section 6 while treating Malmberget ore (lines simulated, markers observed in validation circuit)

71 70 %-44U

69

Model: Kp/(T*s + 1) L = 450 Kp = –2.141954132 T = 888

68 67 66 65 64 6,000

7,000

8,000

9,000

10,000

11,000

Time, sec

FIGURE 9

Step response of grinding modelʊoutput value is the amount of particles finer than 45 μm

the size of buffers in the process. Furthermore, the amount of additives (olivine) must be kept at a target value, while the addition of hematite can vary in the range of 8%–12% of total feed. The interest in this phase of the project is to study the dynamic behavior when process upsets occur and also the sensitivity of the process to quality variations in chemical composition in the feed ore, especially the ore from Kiruna, marked B2 in Figure 10. Figure 11 shows the response in P-grade when a process upset occurs at the existing grinding line no. 5; in this case, a complete stop at line no. 5 is simulated. The control actions taken in the simulated scenario are, first, to adapt feed rates to keep the target product size within limits; and second, to use the possibility to increase the ratio of PAR to B2

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PAR

PAR Olivin Sek 4

Sek 5

Hem.

Sek 6

B2

MPC 2 MPC

Hermatit

MPCO

MPCO 2

BUV

MK3

BUV

FIGURE 10

MK3

Computation diagram for dynamic simulation of the new production system

P_IN_BUV.value P_IN_MK3.value MixingTanks3_1.P_OUT_BUV.value MixingTanks3_1.P_OUT_MK3.value POUT.value

.0148 .0144 .0140

%P in buffer tank MK3 due to changed ratio of PAR and B2.

Process Disturbance

P-grade, %

.0136 .0132 .0128 .0124 .0120

After approximately 14 hours in the buffer tank MK3 empty and %P reaches its maximum.

%P in buffer tank BUV increase due to increased ratio of hematite.

.0116 .0112

Target %P

.0108 .0104 .0100

%P to the pellet plants increase due to increased slurry flow from the buffer tank MK3.

.0096 .0092 .0088 .0084 0.00E0

2.50E4

5.00E4

7.50E4

1.00E5

1.25E5

1.50E5

Time, sec

FIGURE 11

Process response to a shutdown of the grinding line no. 5

1.75E5

2.00E6

USE OF PROCESS SIMULATION METHODOLOGY IN PROCESS DESIGN

493

and also to increase the hematite ratio to grinding line no. 4. Both actions help keep the production level as high as possible. The simulation result shows that within the first 14 hours P-grade will be well within limits and cause no loss of production. CONCLUSIONS

The simulation work done is based on population balance models and shows that this type of modeling works in practice. Model parameters are mainly default values within ModSim, but some parts are fine-tuned from pilot experiments. The obtained models were scaled up and validated against an existing process line. The agreement is satisfactory, and the simulation result slightly underestimates the true grinding capability in the full-scale circuit. A comparison with traditional scaling procedures also was performed, which showed more or less the same general result as the simulation. The combination of few pilot experiments and extensive process simulation has shown to be both cost- and time-effective. The final process layout will nearly double the capacity as that of the existing grinding sections. Extra information gained using modeling tools (e.g., residence time data for the mills, slope, and shape of particle-size distribution) is of great value to pinpoint potential process bottlenecks. An observation made from simulations is that slurry flow through the primary mill is very high, which calls for careful grate-design consideration. Moreover, the primary particle-size distribution will be coarser, which results in preparation for a possible classification step around the secondary mill. Data obtained from the static simulation have been used in dynamic modeling to study the effect of day-by-day variation. Results show that the proposed process design in combination with proper control actions will be able to manage expected variation in ore feed and “normal” process shutdowns. The implemented process description in the dynamic simulator will be used in the next phase as a process simulator for operator training. REFERENCES

Dymola–Dynamic Modeling Laboratory. 2004. User Manual Version 5.3a. Dynasim AB, Research Park Ideon. Lund, Sweden: Dymola–Dynamic Modeling Laboratory. King, R.P. 2001. Modeling and Simulation of Mineral Processing Systems. Oxford, UK: Butterworth-Heinemann. ModSim. 2003. ModSim Ver. 3.6.12 Program and User Manual. Salt Lake City, UT: Mineral Technologies International. Morrell, S. 1996. Power draw of wet tumbling mills and its relationship to charge dynamics. Part 2: An empirical approach to modeling of mill power draw. Section C, Mineral Processing and Extractive Metallurgy Review. Transactions of the Institution of Mining and Metallurgy 105:C54–C62.

Modeling and Simulation of Comminution Circuits with USIM PAC S. Brochot,* R.L. Wiegel,† S. Ersayin,‡ and S. Touze§

ABSTRACT

Modeling and simulation techniques now are used widely for the design and optimization of comminution circuits. The choice of mathematical models used for various unit operations existing in a comminution circuit depends upon the objective of the simulation study (preliminary design, advanced design, unit sizing, plant survey, or plant optimization) and on available data. Another significant task is the description of the material flowing in the streams. The selection of the material characteristics also depends upon the objective of the study and available data. It should take into account the material properties used in the different unit operation models and allow for the links among them. USIM PAC is a powerful software tool providing various mathematical models for each unit operation. The models are classified into different levels depending upon their complexity. They can be used for (1) the evaluation of all streams in an ideal case using only performance parameters; (2) the unit size calculation based on an energetic approach; and (3) circuit optimization using plant data and a population balance approach. In the latter case, there are various possible descriptions: simple size reduction, selective grinding, or mineral liberation. This paper briefly describes the comminution models available in USIM PAC and illustrates their use through the example of an iron ore grinding circuit using mineral liberation data. INTRODUCTION

The performance of a given comminution circuit is evaluated through several measurements, such as size distributions at various streams, reduction ratio, energy consumption, and/or partition curves. The main objective of a mathematical model is to reproduce performance by simulation, providing satisfactory fit to observed data. This reproduction is very important to improve the understanding of the process. Another advantage of a mathematical model is its ability to predict the behavior when some variables are modified (e.g., flowsheet, equipment sizes and settings, and/or material characteristics). Simulation can then be used for plant design and optimization. A mathematical model is a representation of the real world using mathematical equations from general knowledge about observed phenomena. The equations can be classified as one of three types: (1) equations derived from general physics theories (e.g., * † ‡ §

Caspeo, Orléans, France Mineral Processing Consultant, Lakeland, Florida University of Minnesota, Coleraine Minerals Research Laboratories, Coleraine, Minnesota Bureau de Recherches Géologiques et Minières (BRGM), Orléans, France 495

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Newtonian equation) using constants and parameters available in tables and/or that are directly measurable; (2) equations derived from general physical theories, but including model-fitting parameters that are not directly measurable; or (3) empirical equations derived from experimental work and using adjustment parameters. The parameters types in items 2 and 3 compensate for the lack of knowledge that occurs as a gap between general theory and observation. Therefore, a mathematical model is only an approximation of the real world limited by knowledge. Various theories with different levels of description can be used for a model. The choice of the theory is decided by the following points: (1) its ability to reproduce observations (i.e., fit to an existing set of data); (2) its observability (i.e., the one-to-one relation between observations and adjustment parameters); and (3) its adequacy with the objectives of use of the model. These points will be discussed in the following sections. The frequently used model for continuous processes is a graph representation of material flows (more or less representing the plant flowsheet), consisting of nodes and oriented arcs. Each arc represents a stream characterized by a set of data describing the material flowing at this stage (quantity, size distribution, mineral or chemical composition, etc.). Each node represents a unit of equipment characterized by a unit operation model that groups a set of equations linking data of the input and output streams with other parameters (size, settings, adjustment parameters, etc.). The USIM PAC software package is based on the above-mentioned model structure. It was developed by BRGM and has been in use since 1986 (Broussaud 1988; Durance et al. 1993, 1994; Guillaneau et al. 1997; Brochot et al. 2002). It is a user-friendly, steadystate simulator that allows mineral processing engineers and scientists to model plant operations using available experimental data and to determine the optimal plant configuration that meets production targets. The simulator can also assist plant designers with sizing of unit operations required to achieve given circuit objectives. The unit operation models available in USIM PAC for size reduction (Blot et al. 1991; Villeneuve et al. 1996) and classification devices are described in sections that follow. The Phase Modeling section is dedicated to the material description called “phase model” and its link with the unit operation models. The Flowsheet Simulation section presents an example and discusses the relationship between the choice of models and the objective of simulation. SIZE-REDUCTION MODELING

Modeling of a comminution device can be tackled at different levels (Herbst, Lo, and Flintoff 2003). For each level, the focus is on a system or a subsystem with a description of the phenomena occurring under external stress. Table 1 summarizes this approach. External stress influences the behavior of the system, which can be translated into external stress applied to the subsystem of the lower level. Conversely, the behavior of a subsystem will affect the behavior of the system in the upper level. Such a complex model, which takes into account all physical phenomena and interactions at different levels, seems difficult to build today. Another limitation is the usability of the general model for process design and optimization. For these reasons, available models in USIM PAC are based only on some parts of the general model with simplification hypotheses. Nevertheless, to increase model predictivity, it is important to separate the effect of the material properties from the effect of the comminution device as much as possible.

MODELING AND SIMULATION OF COMMINUTION CIRCUITS WITH USIM PAC

TABLE 1

497

Breakage phenomena at the different levels

System

Scale

Mineral

<1 μm

Particle

1 μm to 10 mm

Particle bed

1 mm to 10 cm

Equipment

0.1 m to 10 m

System Description

Strength of materials Mineral interface Crack and fragmentation Movement Elastic and plastic distortion Finer particle progeny Mineral liberation Fluid dynamics Grinding kinetics Population balance Transport Grinding media movement Material balance Size reduction

External Stress

Compression Shear Particle–particle, particle–grinding media, particle–fluid interactions Bed–grinding media, bed–fluid interactions Geometry Dynamics Available energy

Size Distribution

Size distribution of the material is the first element of a comminution model. Its definition and its mathematical representation have to be coherent with the method of measurement and the comminution theory used. There are many definitions for the size of a particle (Kelly and Spottiswood 1982; Hogg 2003), including geometrical definitions, depending on the shape and composition of the particles, and a measurement definition, depending on the device used. The size of a particle is then defined as the sphere equivalent diameter d. The cumulative size distribution F(d) is defined as the mass proportion of particles having a sphere equivalent diameter less than d. The size distribution measurement provides a limited number of points defining this function, F(di), corresponding to the proportion of particles passing the sieve aperture di. A size class is then defined as the interval [di+1 ; di], and the individual size fraction is given by fi = F(di) – F(di+1). Sometimes, an analytical form is used in place of this set of size fractions. The one commonly used in USIM PAC is the Rosin-Rammler distribution:

Fd = 1 – e

d m – § ------· © d*¹

(EQ 1)

where d* gives the fineness and m the size dispersion (slope of the size distribution curve). The fineness of the material is generally characterized using d80. Size Reduction

As the d80 characterizes the material fineness, many size-reduction models are based on the calculation of the product d80. The Bond formula links the product fineness (P80) with the feed fineness (F80) and the specific energy available for grinding (W): § 1 1 · W = 10W I ¨ ------------ – -----------¸ © P 80 F 80¹

(EQ 2)

where WI is the Bond Work Index obtained by a standard test. The d80 gives only one point of the size distribution. The entire size distribution can be obtained using an analytical form of the size distribution such as the Rosin-Rammler

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distribution. In that case, the size dispersion can be obtained by measurement of typical product size distributions or by simply using the same size dispersion as that of the feed. Population Balance

The previous approach considers the particles as a whole without taking into account the size effect of the particle behavior. The population balance approach divides the particles into size classes and writes the equations governing their transformation during breakage events and the mass transfer from one size class to the finer ones. It improves the description of the breakage phenomena. Considering the size class i, grouping the particles having a diameter in the interval [di+1 ; di], only a mass proportion pi will be subject to breakage events leading to the transformation of the particles into smaller particles reporting to other size classes. Defining bij as the mass proportion of the broken particles in the size class j reporting to the size class i ( j < i), the mass balance of size class i is given by i–1

m Pi =  1 – p m Fi + ¦ b ij p j m Fj

(EQ 3)

j=1

where mFi and mPi are the masses in size class i in the feed and the product, respectively. The breakage matrix (or function) b is linked to the size distribution of progeny fragments after one breakage event and mainly depends upon the material. The breakage probability p is linked to the breakage event probability distribution and mainly depends upon the comminution device. Breakage Matrix

The breakage matrix is generally given in its cumulative form describing the mass proportion of the broken particles in size class j reporting to size class i and finer (d = di): B ij =

¦ bkj

(EQ 4)

kti

This is the cumulative size distribution of the undersize product after grinding of a calibrated material. In the case of a tumbling mill, this size distribution follows a double Gaudin-Schuhmann form: J

§d · §d · B ij = I j ¨ ----i ¸ +  1 – I j ¨ ----i ¸ d © j¹ © dj ¹

E

(EQ 5)

where Ij is a size-dependent parameter relative to a reference size dr: §d · I j = I r ¨ ----j ¸ © dr ¹

–G

(EQ 6)

The parameters J, E, Ir , and G are back-calculated by fitting the size distribution obtained from specific laboratory tests for breakage matrix determination. This analytical form is only an approximation of the system, but compared to the (n – 1)(n – 2)/2 independent elements of the breakage matrix where n is the number of size classes, the previous four parameters allow a better observability of the model.

MODELING AND SIMULATION OF COMMINUTION CIRCUITS WITH USIM PAC

499

In the case of jaw or cone crushers, a Rosin-Rammler form can be used for the breakage function of the particles coarser than the closed side setting s:

B is = 1 – e

d m – § ------i-· © k·s¹

(EQ 7)

where the parameters k and m have different values for different ranges of the ratio of di/s. A particular case of Equation 5 is used for the hammer crusher. In that case, E = G = 0 and Ir is a constant. The matrix element is limited to 1. The fine product generated as a result of attrition of rocks in a semiautogenous grinding/autogenous grinding (SAG/AG) mill is distributed using Equation 5 where dj is replaced by a reference size corresponding to the maximum size of that product. Selection Function

In the case of crushers, the breakage probability can be directly obtained by simply considering the breakage events conducted by the particle size. The simplest model used for jaw and cone crushers considers a probability of 1 for the particles having a diameter greater than the closed side setting and 0 for the others. In the case of a hammer crusher, the probability is less than 1 for particles having a diameter greater than a reference size and 0 for the others. Another model for the cone crusher considers a probability of 1 for particles larger than a maximum size dmax = E·s + J, 0 for particles smaller than a minimum size dmin = D·s, and the following probability in the interval: d max – d i · k p i = 1 – § -------------------------© d max – d min¹

(EQ 8)

In the case of tumbling mills, a breakage event occurs if there exist a particle and an impact of the grinding media with sufficient energy in the same time and at the same place. As the mean number of such impacts per second is constant in the mill, the probability of a particle to be broken is proportional to its residence time in the mill. In addition, the number of breakage events is proportional to the number of particles. The breakage phenomenon is equivalent to a first-order kinetics with the breakage rate: dm ---------i = – S i m i dt where mi is the mass of particles of size class i in the mill and S is the selection function. This kinetic equation can be completed with source terms provided from the progeny of the upper size classes: i–1 dm ---------i = – S i m i + ¦ b ij S j m j dt

(EQ 9)

j=1

If the transport model is a perfect mixer with a mean residence time W, the integrated equation on the residence-time distribution becomes: i–1

m Pi  1 + WS i = m Fi + W § ¦ b ij S j m Pj· © ¹ j=1

(EQ 10)

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Equation 10 is equivalent to Equation 3. As for the breakage matrix, an analytical form of the selection function allows reduction of the n – 1 elements of the selection function to three parameters—S1, D1, and D2:

Si = S1 e

d di 2 D 1 ln -----i + D 2 § ln -----· © d 1¹ d1

(EQ 11)

Equation 11 gives the size dependence of the selection function. The breakage rate S1 only depends on the delivered energy P and the mass of material (holdup) in the mill H: EP S 1 = S 1 ---H

(EQ 12)

E

The specific breakage rate S 1 can be back-calculated from observation. It depends on the Bond Work Index and is valid for a given material. In some cases, the compensation hypothesis can be applied, simplifying the system of equations and reducing the number of model parameters:

B ij S j = K i =

EP K 1 --- e

d di 2 D 1 ln -----i + D 2 § ln -----· © d 1¹ d1

H

(EQ 13)

Wear Rate

The wear rate is mainly used in the SAG/AG mill model to reproduce the wear (attrition grinding) of the rocks. It can also be used to simulate the ball wear. The diameter of particles is decreasing by abrasion, and the mass of fine particles produced per unit of time is 2+' dm ------- = 4Sr UV dt

(EQ 14)

where r is the radius of the worn particle, U is the specific gravity of the material, V is the wear rate, and ' ranges from 0 if the wear is proportional to the particle surface to 1 if the wear is proportional to its volume. The mass balance equation of the worn particles in size class i takes into account the mass of particles coming from the upper size class i – 1 and the mass of particles going to the lower size class i + 1 by radius reduction:

Q Pi

ri · 3 § m § ------· i–1 © ¨ ¸ mi r i–1 ¹ = Q Fi +  1 – ' V ¨ --------------------------- – -------------------------¸ 1–' 1–' 1–' 1–' ¨ r i–1 – r i r i – r i+1 ¸ © ¹

(EQ 15)

QP and QF are the product and feed mass flow rates, respectively. The repartition of fine product in the finest classes is given by modified Equation 5. Available Energy

The breakage rate is linked to the delivered energy. This energy is a function of the equipment sizes and settings. For each type of tumbling mill, a different equation is proposed:

MODELING AND SIMULATION OF COMMINUTION CIRCUITS WITH USIM PAC

501

1

Rod mill:

S 2 + --3P = 1.752 --- D L.0.8.T c U b  6.3 – 5.4T c V r 4

(EQ 16)

Ball mill:

S 2.3 0.1 P = 4.879 --- D L.0.6.T c U b  3.2 – 3T c V r 1 – ---------------9–10V r 4 2

(EQ 17)

SAG mill:

P = 10.6D

2.5

U L  1 – 1.03T l §  1 – H ----s T l + © cs

(EQ 18)

U 0.1 · 0.6T c § U b – ----s· · V r § 1 – ---------------9–10V r ¹ © cs ¹ ¹ © 2 Pebble mill:

S 2.3 0.1 - · P = 10 sin D --- D LU c T c  3.2 – 3T c V r § 1 – ---------------9–10V r ¹ © 4 2

(EQ 19)

where P D L Vr Tc

= = = = =

H Ub Us cs Tl D

= = = = = =

power consumed (kW) inside mill diameter (m) inside mill length (m) rotation speed expressed as a fraction of the critical speed loading fraction: fraction of mill volume occupied by grinding media (bulk volume) bulk porosity of the load: 0.3 specific gravity of the grinding media (t/m3) mean specific gravity of rocks (t/m3) weight fraction of solids in pulp loading fraction: fraction of mill volume occupied by balls, rocks, and pulp angle of repose of the mill load

Equation 2 can also be used with introduction of an adjustment parameter B, which can be back-calculated from test data (Q is the mass feed rate): § 1 1 · P = 10BW i Q ¨ ----------– ----------¸ © P 80 F 80¹

(EQ 20)

In the case of ball and rod mills, B is the product of the efficiency factors (Rowland and Kjos 1978). A similar equation by Magdalinovic and others (1990) introduces two adjustment parameters, A and n: § 1 A 1 · P = ------10W i Q ¨ ----------- – -----------¸ n © P 80 F 80¹ P 80

(EQ 21)

Residence-Time Distribution

The residence-time distribution is a transport model. It gives the probability density of a particle to dwell for a time t in the mill. The simplest model is the perfect mixer model,

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where the mean residence time W is the ratio of the mass of material in the mill divided by the mass feed rate: – tW

e f  t = -----W

(EQ 22)

This model is well adapted for many kinds of tumbling mills. For a long mill or vertical mill, a set of n identical perfect mixers in series can be used: n n–1

nt – ----W

n t e f  t = § -- · ------------------© W ¹  n – 1 !

(EQ 23)

For the bi-conical ball mill, a set of three different perfect mixers is used. Unit Operation Models in USIM PAC

The mathematical models used in USIM PAC (see Table 2) are classified into different levels: ƒ Level 0 models enable the user to specify directly the performance of the units.

For example, the performance of a comminution unit can be modeled by the product size distribution for which the user specifies the d80 and the slope of the Rosin-Rammler distribution. Such models are good for developing flowsheets that do not take into account any sizing parameters. During the simulation, the performance of the unit will be independent of its dimensions and the flow rate of the ore feeding it. ƒ Level 1 models take dimensional parameters into account. They require few

(sometimes no) experimental data. A typical example is a ball mill model, which uses, in addition to the mill dimension and settings, the Bond Work Index as its single experimental parameter. If no data are available, it is even possible to estimate the Work Index. Obviously, the precision of such models is limited, but they are simple to use. ƒ Models of a higher level are more accurate, but they require the estimation of

some of their parameters. This estimation can be carried out either on the basis of experimental data obtained from the continuous operation of the unit (Level 2 models) or from such data supplemented by information obtained from specific tests, generally carried out in the laboratory (Level 3 models). SIZE CLASSIFICATION MODELING

Size classification units appear in a comminution circuit as soon as a closed circuit is required. The partition function (or partition curve) characterizes the size classification performance. It gives the proportion Y(d) of particles with diameter d reporting to the coarse product. Mathematical models for size classification (see Table 3) are generally based on an analytical form, such as the Rosin-Rammler function: d § – § --------- · © d 50c ¹ ¨ = + Yd S 1 – S 1 – 2 ¨ ©

m

· ¸ ¸ ¹

(EQ 24)

MODELING AND SIMULATION OF COMMINUTION CIRCUITS WITH USIM PAC

TABLE 2

503

Main comminution models in USIM PAC

Level and Name

Equations

Level 0 Crusher from database

Interpolation of typical product size distributions for different settings. Eqs. 20, 21, power consumption.

Level 0 Jaw crusher, Symons cone crusher Level 0 Gyratory crusher Level 0 Mill 0A Level 0 Mill 0B Level 1 Rod mill

Eq. 7 Eqs. 20, 21, power consumption. Eq. 7 Eqs. 20, 21, power consumption. Eq. 1 with the same distribution slope in feed and product. Size distribution given size by size. Eqs. 16 and 20 with efficiency factors. Eq. 1 with the same distribution slope in feed and product. Eqs. 17 and 20 with efficiency factors. Eq. 1 with the same distribution slope in feed and product. Eq. 5 with E = G = 0 and Ir constant.

Level 1 Ball mill Level 2 Crusher Level 2 Cone crusher Level 2 Rod mill Level 2 Ball mill Level 2 SAG/AG mill

Eqs. 5 and 8.

Comment and Use

Database containing typical size distributions and capacity chart. It can be updated by the user. Design + optimization Calibrated by the equipment provider. Flowsheeting + design + optimization Calibrated by the equipment provider. Flowsheeting + design + optimization Flowsheeting Flowsheeting No prediction of the whole size distribution. Design + sizing No prediction of the whole size distribution. Design + sizing Well adapted for hammer crusher. Design + optimization Design + optimization

Eqs. 10, 13, and 16.

Calibrated using operating data. Design + optimization Eqs. 10, 13, and 17. Calibrated using operating data. Design + optimization Eq. 15 for rock wear and modified Eq. 5 Partition curve for the extraction of for distribution of fines. pebbles and extraction of ore. Eqs. 18 and 13 for ore. Design + optimization Simplified Eq. 10 and modified Eq. 11. (Guillaneau et al. 1995) Design + optimization Eqs. 10, 5, 6, 11, 12, and 16. Design + advanced optimization

Level 2 Sala Agitated Mill Level 3 Rod mill Level 3 Ball mill Level 3 SAG/AG mill

Eqs. 10, 5, 6, 11, 12, and 17.

Design + advanced optimization

Eq. 9 with terms for feed rate, Design + advanced optimization discharge rate, and rock breakage rate. Modified Eq. 17. Eqs. 10, 5, 6, 11, and 19. Eq. 14 for pebble wear.

Level 3 Pebble mill

where S is the short circuit of fines, d50c the cut size of the corrected partition function, and m the slope linked to the partition imperfection by 1em

ln 3- · 2 – § 2 – -------© d 75c – d 25c ln 2 ¹ I = ------------------------- = --------------------------------------------------2d 50c 2 1em

(EQ 25)

PHASE MODELING

In USIM PAC, the phase model describes the set of data used to characterize the material flowing through the circuit (Brochot et al. 1995). It is based on the material properties

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ADVANCES IN COMMINUTION

TABLE 3

INSTRUMENTATION, MODELING, AND SIMULATION

Main classification models in USIM PAC

Level and Name

Level 0 Classifier 0A Level 0 Classifier 0B Level 0 Classifier 0C Level 0 Partition curve per component Level 0 Perfect classifier Level 0 Screen Level 1 Screen 1A Level 1 Screen 1B

Equations

Comment and Use

Eqs. 24 and 25.

Flowsheeting

Eqs. 24 and 25.

d50c calculated to reach the d80 of fines. Flowsheeting + design Flowsheeting + design

Modified Eq. 24 to take into account the fishhook effect. Eqs. 24 and 25 with partition curve parameters defined for each component. Y(d < do) = 0 and Y(d > do) = 1.

Simulates density-dependent classification. Flowsheeting + design Flowsheeting

Y(d > SO) = 1 (SO = screen opening), Y(d < dmin) = S, log-linear interpolation between. Based on probability of particle jump.

Based on screen efficiency. Flowsheeting + design

Eq. 24.

d50c calculated to reach the screen efficiency using standard screen sizing method. Design + sizing d50c calculated using equilibrium between gravity and drag forces. Design + sizing Design + sizing

Level 1 Spiral and rake classifier

Eq. 24 with m = 1.5 + 40d50c.

Level 1 Hydrocyclone Level 2 Hydrocyclone

Eq. 24 and Plitt model (Plitt 1976). Eq. 24 and Plitt model with roping effect.

Design + sizing

Design + sizing

(particle size, particle density, chemical content) called “criteria,” and the way to classify the material successively using these criteria (size distribution, density distribution, assays per size class, mineral composition, liberation data, etc.) called “description hierarchies.” Size Distribution

As shown in the previous sections, the comminution models are mainly based on the particle-size distribution of the ore. This material property is easily obtained by direct measurement (sieving) or indirect measurement (cyclosizer, laser diffraction, sedimentation). If the interpretation of this measurement does not cause a problem for coarse particles (>1 mm) due to the quasi-sphericity of the particles and the systematic use of sieving, it is a key point for very fine particles (<10 Pm). In that case, different methods can give very different size distributions. The choice of the measurement method has to match the definition of the size distribution in the theory used for the unit operation model (e.g., use a sedimentation method when the size classification is based on drag force). It is then important to use the same method for the description of the different streams of the circuit, but also for all measurements occurring during experimental tests in the laboratory or in a pilot plant. Another key point is the choice of the size classes: sieve series, finest mesh. This will influence the observability and the predictivity of the model. A few size classes are sufficient for a preliminary design using Level 1 models. This number must increase to be able to observe different breakage phenomena and to back-calculate the associated population

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balance parameters. It can be useful to have many coarse size classes for the rocks in a SAG/AG mill to observe the wear rate and adjust the model. Density Distribution

The density distribution is necessary as soon as there is a particle density effect, such as in hydraulic classification. In addition, density separation units can be included in the grinding circuit (gold recovery by gravity or dense medium separation for coal recovery). In the case of LIMS (low-intensity magnetic separation) of iron ore, the elimination of nonmagnetic particles in the cobber stage is also linked to the density distribution due to the magnetite content. In USIM PAC, various density classes can be defined to describe the material using the density distribution per size class. The predictivity of the comminution circuit is improved by this fine description: better estimate of the circulating load in quantity and quality (size distribution and composition), and it is the only way to evaluate the advantage to introduce density separation within a grinding circuit. Chemical and Mineral Composition per Size Class

The chemical composition is obtained directly by laboratory analysis and assaying. Process modeling generally works on a mineral basis, however. The chemical composition is used for metallurgical accounting and can be converted to the mineral composition when the transformation is possible. If this is not the case, some assumptions can be made to solve the problem. The comminution, classification, and separation stages process the minerals, not the chemical elements. The selective grindability, the densitydependent classification, the magnetic separation, or the particle flotation are based on the minerals. In addition, the same chemical element can appear in various forms (minerals) with very different behavior during processing. In the case of gold, for example, the Au element can appear in the electrum phase as nuggets recoverable by gravity, which can report systematically to the underflow of the hydrocyclone; or as fine flakes recoverable by cyanidation, which can be free-flowing in water or attached to various other minerals and having the same behavior; or as refractory gold inside the matrix of specific minerals. Only such fine size-by-size description allows the prediction of the behavior of gold in a grinding circuit (circulating load) and the evaluation of introducing a gravity separation stage. The main issue is the measurement of the distribution of total gold in the different phases. In the field of iron ore, only a description in terms of minerals allows a predictive simulation of the grinding circuit including magnetic separation. In that case, the measurement of magnetic iron is required to identify magnetite and other iron minerals. Due to the size effect in the magnetic separation stage, a mineral composition per size class is necessary. Mineral Liberation Data

To clarify the previous section, “the comminution, classification, and separation stages process the particles, not the minerals, nor the chemical elements.” Particles are generally a mixture of various minerals. The mineral composition of the particles can be measured by image analysis. The density distribution measurement can be used when only two minerals with very different specific gravities occur, such as coal–ash association. Concerning magnetite-bearing iron ore, the Davis tube tests combined with magnetic iron measurements can be used to derive liberation characteristics. The composite particles can be classified in line with their mineral composition. In the case of only two phases (e.g., valuable mineral and gangue; coal and ash; magnetics and nonmagnetics), the composite particle classes are defined by a range of first-phase

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content or a mean content. For n phases, the number of such defined classes increases as n!. For more than three phases, it is necessary to use another classification. Due to mineral liberation, the composite particle distribution (proportion of particles in each composite particle class) is very much dependent on particle size. The coarser particles are mainly in the composite particle classes around the mean mineral composition of the massive rock. The finer particles are mainly in the liberated particle classes (with phase content of 100% or 0%). The transition between these two extreme distributions occurs around the liberation size (as illustrated later in Figure 2). In USIM PAC, such composite particle classes can be defined with their mineral and chemical compositions. The composite particle distribution by size class is given for each stream, allowing the calculation of the mineral and chemical compositions per size class and globally. Generally, composite particle distribution cannot be directly obtained from the listed measurements but necessitates a liberation model for interpretation. The Gaudin Random Liberation Model

Conceptually, the Gaudin Random Liberation Model (GRLM) is based on starting with an infinitely large portion of hard-rock ore, which on a microscale consists of an ordered arrangement of uniformly sized cubic mineral grains, aligned side by side, edge to edge, and corner to corner, similar in appearance to a Rubik’s cube puzzle. In the simplest case, the grains are of two types, valuable mineral and waste mineral. A breakage grid is superimposed on the grains in a direction that is parallel to the grain surfaces and which produces uniformly sized cubic particles. Depending on the size and location of this breakage grid, the resultant particles may consist of 1. Assemblages of whole and partial fragments of many dissimilar grains—when

particle size is much larger than mineral grain size and very little mineral liberation is obtained. 2. Combined fragments of several dissimilar grains and some liberated particles

made up of combined fragments of adjacent similar grain species—when particle size approximates mineral grain size and some liberation, especially of the more abundant mineral species, is achieved. 3. Many separate, individual fragments generated by breakage from within single

grains and some grain fragment composite particles that may be locked or liberated depending on the composition of the original adjacent mineral grains— when particle size is much smaller than mineral grain size and liberation of the two species is quite significant. Liberation is a three-dimensional geometric phenomenon; therefore, the primary calculations for the GRLM are based on volumetric quantities. The calculation is carried out individually for each particle size fraction that is a part of the size distribution of interest. Admittedly, this concept of an ore and its breakage is very much idealized, and might be dismissed as being too simple by those metallurgists and mineralogists who are experienced in viewing the extreme complexities of real mineral systems. When developing mathematical models of the real world, however, it is essential to recognize the importance of retaining simplicity in approach wherever possible, while incorporating the complexities that are necessary to fulfill the purpose of the model. In this particular case, the GRLM conceptual model does lend itself to the development of reasonable and understandable mathematical derivations, calculations, and simulations, while retaining many of the more important complexities of a real mineral system.

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In the development of the use of the GRLM for magnetic taconite size reductionliberation simulation, several other simplifications were made. In describing the composition spectrum, use was made of the twelve common mineral composition classes, consisting of the two end members of liberated waste (0%) and values (100%), and the ten locked particle classes, each with a 10% composition range. In addition, it was assumed that each composition class could be adequately approximated by its midpoint composition (e.g., the 20% to 30% values range has a composition of 25% values). The particlesize spectrum was represented by the normal logarithmic sieve series, with a specific size fraction approximated by the geometric mean of the upper and lower linear screen openings. From a liberation standpoint, the important size parameter is the dimensionless ratio of “effective” mineral grain size to particle size, represented by the variable k. For a given ore, as particle size decreases, the value of this ratio increases and the amount of liberation increases for both values and waste. Further, it seemed reasonable that when one breaks the contents of a particular composition range from a specific k value to a slightly larger specific k value, it would yield the same distribution of particle compositions, regardless of how the particles had gotten into that initial composition range. A longstanding deterrent to the development of a useful and readily accepted liberation model has been development of the quantitative mathematical description of particle composition changes that occur as particle size is decreased. It has been possible to generate particle size-composition information for the GRLM by a combination of analytical mathematics and simulation. This information has been used in a linear programming problem formulation to determine a relatively simple solution for this composition distribution problem. In this solution, the product from an individual locked composition range is distributed to only three composition ranges of a finer particle size. A portion of the broken material stays in the same composition range; one portion goes to a lowergrade composition range and another portion enters a higher-grade composition range. These portions were calculated for each logarithmic step in the size ratio and are termed directional coefficients. Regression relationships defining the directional coefficients as a function of the size ratio then are used to describe the behavior of each composition range as particle size is decreased, and therefore become the basis on which the effect of size reduction on liberation is modeled. Details of this have been presented elsewhere (Wiegel 2000, 2006). The application of the GRLM to the size reduction-liberation modeling of an ore requires the specification of three liberation parameters. Conceptually, these parameters represent the “effective” mineral grain size; the grade (% magnetite) of the mineralized crude ore in the feed, which has not experienced previous concentration; and the amount of barren waste dilution, which is included with that feed. In the case of magnetic taconite, the three parameters are determined using a least-squares fitting of the concentration data from the Davis tube separation of individual size fractions of the ground crude ore. The data required include weights and magnetite assays of the Davis tube concentrate (magnetics) and tailing (nonmagnetics), and specific gravities of the magnetite and waste minerals. The current GRLM formulation is suitable for mineralized ore grades of 15% to 85% values by volume. This liberation model is coupled with the Level 3 ball mill model to produce a comminution model with mineral liberation. For size class i and composite particle class k, Equation 10 becomes i–1 12

m Pik  1 + WS ik = m Fik + W ¦

¦ bijl qikjl Sjl mPjl

j=1 l=1

(EQ 26)

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Phase model selection Criteria

Description Hierarchies

Size classes

Size distribution

Size classes, density classes Size classes, chemical elements Size classes, minerals (chemical elements)

Size distribution; density distribution per size class Size distribution; chemical analysis (per size class) Size distribution; mineral content per size class (chemical analysis per mineral)

Size classes, composite particle classes, minerals (chemical elements)

Size distribution; composite distribution per size class; mineral content per composite particle (chemical analysis per mineral)

Objective

Grinding circuit for size reduction only. Preliminary design. Grinding circuit with density effect in classification or density separation. Grinding circuit for size reduction only with metal accounting. Preliminary design. Grinding circuit with density effect in classification, density separation, magnetic separation, or flotation. Metal accounting. Grinding circuit with mineral liberation affecting classification and separation. Metal accounting.

The breakage matrix and selection function are given by composite class to simulate the selectivity. Choice of the Phase Model

Almost all comminution and size classification models are able to work with the different phase models. The choice of the phase model is driven by the objective of the modeling and simulation study and the available data (see Table 4). FLOWSHEET SIMULATION

This section presents an example of the use of the size reduction-liberation simulation for the magnetic iron ore grinding, classification, and LIMS circuit. In this case, three configurations were simulated, in which the magnetic separation was located alternatively on the cyclone feed (CFE), the cyclone overflow (COF), or the cyclone underflow (CUF). The COF configuration is shown in Figure 1. In Figure 1, Unit 1 is a feeder associated with a mathematical model generating the composite particle distribution per size class using the GRLM, the specific liberation parameters, and the measured size distribution. Unit 2 is a ball mill associated with the Level 3 ball mill model coupled with GRLM. Figure 2 shows the size reduction and mineral liberation effect on the distribution of composite particles per size class for the COF configuration. Unit 4 is a set of hydrocyclones associated with the Plitt (1976) model, taking into account the density of the composite particles. Unit 5 is a magnetic separator associated with a Level 0 separator model for which the weight recovery is given for each composite particle in each size class in order to take into account the size and degree of liberation effects. Figure 3 shows the recovery of magnetite and waste versus particle size in the concentrate for the three configurations with the same set of model parameters. Figure 3 demonstrates the importance of a description in terms of composite particles to be able to simulate the LIMS with the same model wherever the unit is placed in the circuit. Indeed, it is impossible to obtain the same results with only the mineral (magnetite and waste) distribution per size class. In that case, to compensate for the lack of information, it is necessary to define the mineral recovery for each LIMS stage (Ersayin 2004).

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COF

1

Circuit Feed

Mill Product

509

Mag Concentrate

Cyclone Feed 6

8 5

2

3

9

4

Tails

1 2 CUF

7

4 5

COF configuration of the iron ore grinding circuit

10

9

9

8

8

7

7

6

6

% Mass

10

5 4

0 5 15 25 35 45 55 65 75 85 95 100

3 2 1 0 Volum e

Mag

FIGURE 2

1,664 9 832.45 416 22 208.11 104.06 52.03 26.01

Conte

nt, %

5 4 3 2 1 0 0 5 15 25 35 45 55 65 75 85 95 100

FIGURE 1

% Mass

3

Volum e

Mag

1,664.9 832.45 416.22 208.11 104.06 52.03 26.01

Conte

nt, %

Distribution of mixed particles per size class in mill feed (left) and product (right)

100

Recovery, %

80

60

40

Magnetite COF Waste COF Magnetite CFE Waste CFE Magnetite CUF Waste CUF

20

0 10

FIGURE 3

100

1,000

1,000

Magnetite and waste recovery for the three circuit configurations (COF, CFE, CUF)

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CONCLUSION

An example was used to highlight the different levels of modeling for a comminution circuit (from the simple size reduction for a preliminary design to the mineral liberation model for plant optimization) and the advantages of each level relative to the study objectives. USIM PAC offers such flexibility for modeling and simulation. Ongoing developments in the field of modeling and simulation of comminution circuits provide regular improvements to the software. REFERENCES

Blot, P., E. Oblad, J.A. Herbst, J. Villeneuve, and J.C. Guillaneau. 1991. Integrating and using an advanced SAG/AG mill model in the USIM PAC mineral processing simulator. Pages 439–449 in Proceedings of the Conference on the Computer Applications in the Mineral Industry “Software of the 90’s for the Mineral Industry.” Vancouver, BC. Brochot, S., M.V. Durance, G. Fourniguet, J.C. Guillaneau, and J. Villeneuve. 1995. Modelling of the minerals diversity: A challenge for ore processing simulation. Pages 861– 866 in Proceedings EUROSIM’95 Conference. Vienna, Austria, September 1995. Brochot, S., J. Villeneuve, J.C. Guillaneau, M.V. Durance, and F. Bourgeois. 2002. USIM PAC 3: Design and optimization of mineral processing plants from crushing to refining. Pages 479–494 in Mineral Processing Plant Design, Practice, and Control. Edited by A.L. Mular, D.N. Halbe, and D.J. Barratt. Littleton, CO: SME. Broussaud, A. 1988. Advanced computer methods for mineral processing: Their functions and potential impact on engineering practices. Pages 17–44 in Proceedings XVIth International Mineral Processing Congress. Stockholm, Sweden, June 5–10. Durance, M.V., J.C. Guillaneau, J. Villeneuve, S. Brochot, and G. Fourniguet. 1994. USIM PAC 2 for Windows: Advanced simulation of mineral processes. Pages 539–547 in Proceedings of the 5th International Mineral Processing Symposium. Cappadocia, Turkey, September. Durance, M.V., J.C. Guillaneau, J. Villeneuve, G. Fourniguet, and S. Brochot. 1993. Computer simulation of mineral and hydrometallurgical processes: USIM PAC 2.0, a single software from design to optimization. Pages 109–121 in Proceedings of the International Symposium on Modelling, Simulation and Control of Hydrometallurgical Processes. Québec, Canada, August 24–September 2. Ersayin, S. 2004. Low intensity magnetic separator modelling: A pseudo liberation approach. Mineral Processing and Extractive Metallurgy. Transactions of the Institution of Mining and Metallurgy 113:C167–C174. Guillaneau, J.C., O. Olofsson, M.V. Durance, and J. Villeneuve. 1995. Modelling the SAM (Sala Agitated Mill) using BRGM pilot plant data. Pages 325–331 in Proceedings of the APCOM XXV 1995 Conference. Brisbane, Australia. Guillaneau, J.C., J. Villeneuve, M.V. Durance, S. Brochot, G. Fourniguet, and H. Durand. 1997. A range of software for process analysis. SME Annual Meeting. SME Preprint 97-202. Littleton, CO: SME. Herbst, J.A., Y.C. Lo, and B. Flintoff. 2003. Size reduction and liberation. Pages 61–118 in Principles of Mineral Processing. Edited by M.C. Fuerstenau and K.N. Han. Littleton, CO: SME. Hogg, R. 2003. Particle characterization. Pages 9–60 in Principles of Mineral Processing. Edited by M.C. Fuerstenau and K.N. Han. Littleton, CO: SME. Kelly, E.G., and D.J. Spottiswood. 1982. Introduction to Mineral Processing. New York: John Wiley & Sons.

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Magdalinovic, N., M. Grbovic, I. Budic, A. Jancovic, Z. Markovic, and Z. Mitrovic. 1990. Mathematical model for the determination of an optimal crusher product size. Aufbereitungs Technik 31(5):277–279. Plitt, L.R. 1976. A mathematical model of the hydrocyclone classifier. CIM Bulletin (December). Rowland, C.A., and D.M. Kjos. 1978. Rod and ball mills. Pages 239–278 in Mineral Processing Plant Design. Edited by A.L. Mular and R.B. Bhappu. Littleton, CO: SME. Villeneuve, J., J.-C. Guillaneau, M.-A. Soares Martin, and G.S. Lopes. 1996. SAG mill modelling in USIM PAC 2: Example of the CVRD Igarapé Bahia circuit. In Proceedings of the International Autogenous and Semi Autogenous Grinding Technology 1996 Conference (SAG’96). Vancouver, BC. Wiegel, R.L. 2000. Development of an Approach to the Simulation of Size Reduction/Mineral Liberation for Magnetic Taconite Ore In Tumbling Mills and Its Implementation in a BASIC Program. Technical Report CMRL/TR-0016. Coleraine Minerals Research Laboratory. Duluth, MN: University of Minnesota. ———. 2006. The rationale behind the development of one model describing the size reduction/liberation of ores. In Advances in Comminution. Edited by S.K. Kawatra. Littleton, CO: SME.

Remote and Distributed Expert Control in Grinding Plants Lynn B. Hales* and Michael L. Hales*

ABSTRACT

Since the first experiments with computerized expert control of grinding plants in the early 1970s, expert control has steadily progressed in the minerals industry to be very advanced, including not only many artificial intelligence methodologies but also advanced computing and measurement systems. In this paper, a 1970s expert system is compared with the latest systems used in the industry, along with performance comparisons. The most advanced systems today use real-time image systems as well as acoustic systems that listen to the grinding process within the mill to further understand the process of grinding in large mills. EXPER T COMPUTER CONTROL IN THE 1970S

Computer-based control in the 1970s was an experiment. Debate centered on whether or not direct computer control (DCC) was advisable or foolish. Distributed control systems (DCSs) were new on the scene, and most grinding plants were still controlled through relay panels and single-loop analog controllers. Computers were expensive with operating systems that were complex and not necessarily designed for real-time applications. Databases were monolithic and only existed on “mainframe” computers. Artificial intelligence remained deeply buried in the research areas of a few universities and was still a fanciful dream of fiction writers. Grinding plants were small by today’s standards and included two and three stages of crushing, primary ball milling, and secondary rod milling. Semiautogenous grinding (SAG) mills were in the development stage, and debate raged over all aspects of their utilization. These facts were only technical details, however, to those studying grinding—its costs and the benefits of improving its efficiency and the capacity of existing grinding lines. At the time, it was believed that the energy efficiency of ball mill grinding was as low as 3%–5%, which provided plenty of impetus for experimentation with installing computers in mineral processing plants and then writing supervisory control programs that would monitor the performance of the grinding plant, then calculate new process set points and send them out to the underlying control system for implementation. RAY MINES EXAMPLE

In the 1970s, Kennecott Utah Corporation owned multiple mineral processing plants in the United States and maintained a world-class process technology center. One of the * KnowledgeScape, Salt Lake City, Utah 513

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chartered responsibilities at the Process Technology Center was to understand, develop, and implement world-class process control systems and strategies at each of its operations. The group’s cutting-edge skills with computers made it very natural to install a computer with a real-time operating system at Ray Mines and begin the process of interfacing it to the underlying control system. Grinding line five was selected because it had installed one of the very first particle-size analyzers manufactured by Autometrics. The original program written to monitor the state, or performance, of the grinding line was written in BASIC programming language, and data collected by the system were actually stored in digital format on a portable cassette tape recorder. This was somewhat rudimentary yet innovative and effective. The computer itself was housed in a wooden cabinet and connected to a custom interface set of electronics to ultimately interact with Foxboro single-loop analog controllers, as is shown in Figures 1 and 2. OPERATOR MIMIC

The phrase “operator mimic” was selected as the title of the computer control program that was written to monitor the grinding line and then calculate new process set points to be automatically implemented by the single-loop controllers. The control objective was to maximize the throughput rate and minimize the final particle size. Experiments were run to determine the best underlying control loops to supervise—for example, to control size with water addition to the cyclone feed sump, or by adjusting the new feed rate or by the feed density to the cyclones. The cyclone feed pumps were variable speed, which was also somewhat unique for the time period. Once the basic stabilizing control loops were selected, the operator mimic expert’s strategy was implemented and performance was documented with on–off testing and statistical analysis of the results. Figure 3 shows the terse output of the system that kept the operators informed about the decisions being made and the new set points being sent to the controllers. In the example, we see that the condition of the circuit was deemed to be “low ore,” suggesting that feed rate could not be maximized but that the grind size could be minimized. The ball mill circulating load was being monitored and the particle size set point was being changed when mill conditions permitted. Despite the difficult computing environment and rudimentary sensors, the strategy was very successful. The on–off testing proved what was possible before the experiment began; that the average throughput rate could be increased while decreasing the average grind size. One interesting finding was that the actual specific energy of the mill decreased, which suggested that the actual grinding efficiency increased as a result of the control strategy. Figure 4 shows the throughput histograms for the grinding line under the preexisting operator-controlled approach versus the operator mimic expert control strategy. The improvement was at the high end of the types of improvements that have been achieved over the years. The plots also clearly show a bimodal data set, suggesting that there were probably two different ore types routinely being processed. PHENOMENOLOGICAL MODELING—POPULATION BALANCE MODELS

Parallel to the emerging efforts to program computers to monitor and calculate process set points was the academic development of first-principle models of the grinding process. At the forefront of this work was Professor John Herbst, then at the University of Utah. Professor Herbst’s graduate studies at University of California, Berkeley, under Professor Douglas Fuerstenau, centered on what became known as the population balance grinding model (Herbst 1968). The basis of the modeling methodology was the concept that rocks or particles in a grinding mill have a certain probability of being

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FIGURE 1

Supervisory control computer in a wooden box (circa 1978)

FIGURE 2

Rudimentary single-loop analog controllers installed on milling floor next to grinding mills

selected for a breakage phenomenon, either with other rocks or the grinding media itself. Once selected for breakage, the result was a distribution of daughter fragments or particles produced by the event. Mathematically, this concept of the grinding process was represented in a mass balance construct that only needed to have model parameters determined to represent the grinding process. Estimation of these model parameters was made by applying Kalman filtering to the process in real time (Rajamani 1979). The value, of course, of real-time process modeling lies within the ability to look ahead, or to predict the future state of the grinding circuit, thereby allowing possible future states of the mill to be taken into account along with the past and current state to determine, based upon expert knowledge, what changes to the process set points will push the mill to more closely achieve the optimization objectives of the circuit. Accurate real-time predictive models expand the possibilities of control to include asking the model—given

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STRATEGY I TELEPRINTER OUTPUT

TAPE DUMP 257 6 32 15 LOW ORE CONTROL PSSP= 23.5939 PS= 24.1492 CL= 58.377 @ 6 36 23 257 OFFSET= .137956 SLOPE= -.447284 B4= .309328 NO ACTION LOW ORE CONTROL PSSP= 23.5939 PS= 23.7331 CL= 62.8788 @ 6 44 30 257 OFFSET= .244697 SLOPE= 1.40856 B4= 1.65326 INCREASE PSSP 257 6 44 30 22.3633 25.3863 28 LOW ORE CONTROL PSSP= 25.3863 PS= 25.6098 CL= 63.30966 @ 6 52 39 257 OFFSET= .332064 SLOPE= 1.17905 B4= 1.51111 INCREASE PSSP 257 6 52 39 22.3633 27.121 28

FIGURE 3

Minimal system output from a thermal printer for the operator mimic strategy

Rod/Ball Milling Comparison (Actual Plant Data)

Frequency

Operator Expert

Throughput

FIGURE 4

On–off testing results of the 1978 operator mimic expert control strategy

where we are (current set points) and our operational objectives—what are the best new set points that could be implemented to improve our state in the near future?” Now, instead of circuit optimization by way of heuristic expert rules, we have the opportunity for optimization based on model predictions. Incidentally, if either the structure or the parameters of the models are adjusted dynamically, then instead of a static expert control system, we now have an adaptive one that changes over time or adjusts over time, thereby reflecting ore changes or equipment changes.

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These population balance models were implemented in the 1980s in a number of plants around the world with fair success. The Kalman filter mathematics are not trivial and require substantial skill and experience to implement, which certainly was a barrier to widespread use, as was the fact that these models were all programmed in traditional computer programming languages in custom-designed programs that suffered from the maintenance problems. AR TIFICIAL INTELLIGENCE MEETS MINERALS PROCESSING—EXPER T SYSTEM SHELLS

Expert system shells that began to appear at universities around the world in the early 1980s are computer programs that have two specific and unique features: (1) the ability to write rules about a specific domain of knowledge in linguistic terms, and (2) the ability to infer or draw conclusions about new information, given the domain rules of the system. The ability to record domain knowledge in linguistic terms was a great advancement for the industry, because historically there have been many supervisory computer programs written in a variety of programming languages that were successfully implemented in mineral processing plants, yet they fell into disuse after the original creators moved on to new positions or new plants. It is difficult for one person to understand the big picture and subtle nuances of a sophisticated computer program that has been written by another individual. Program documentation is an art that is not practiced by many. With the formalization of expert system shells, several possibilities for overcoming the shortcomings of hard-coded, operator mimic–type, supervisory control programs loomed on the horizon. The most immediate problem to be overcome was the fact that the expert system shells that were appearing were not designed to be connected to realtime processes where they would continually cycle through sets of rules to calculate new set points on a second-by-second basis. Two of the companies that emerged first to address this problem had their roots in metallurgical engineering and minerals processing— Pyramid Resources, now known as KnowledgeScape; and Comdale, which ultimately failed as a business and was subsequently purchased by ABB. Another entrepreneurial startup company, Gensym, recognized the opportunity for a real-time expert system and ultimately created a system known as G2. There were others along the way, but these were first in the minerals industry. As an interesting note, the first real-time expert system created by Pyramid Resources was known as RTX. RTX had connections to NASA and its Cerberus program, which had been created to analyze Landsat photographs. Cerberus was not designed for real-time analysis or control purposes, so Pyramid’s work to create RTX from some of the underlying technologies in Cerberus was unique. Three minerals plants are still running RTX systems that were installed in the early 1990s. CRISP RULES

Examples of mineral processing domain knowledge written in linguistic terms are shown in Figure 5. Careful examination of the rules suggests that they are associated with ascertaining whether or not a mill is in a classic overload condition or not, where overload is generally defined as a rising bearing pressure or load in the mill at the same time the power to turn the mill is decreasing. These types of rules are designed to draw conclusions about the condition of a system. Certainly, the person writing such rules needs be knowledgeable about grinding mills to be able to formulate these types of rules. Another set of rules that also require “expert” knowledge are those that assess the condition of a grinding system, and then,

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FIGURE 5

INSTRUMENTATION, MODELING, AND SIMULATION

Crisp rules to infer a classic mill overload

given a set of control objectives, determine new set points that are deemed by the expert to operate the grinding mill in a better way. For example, it is quite common for mill operators to want to maximize throughput rate, given physical, metallurgical, and economic constraints. Rules that reflect this objective and expert knowledge about grinding are shown in Figure 6. A term given to these various examples of rules is “crisp rules.” They are called “crisp” because of the unequivocal nature of the operators’ terminology—less than, equal to, greater than, and the singular numeric constants in the rule. In other words, the rule is either entirely true or it is false. The expert systems of the 1980s only utilized crisp rules. FUZZY LOGIC

Fuzzy logic is an approach to computing based on “degrees of truth” rather than the usual “true or false” (1 or 0) Boolean logic on which the modern computer is based. Dr. Lotfi Zadeh of the University of California, Berkeley, first advanced the idea of fuzzy logic in the 1960s. Dr. Zadeh (1965, 1973) was working on the problem of computer understanding of natural language. Natural language (like most other activities in life and indeed the universe) is not easily translated into the absolute terms of 0 and 1. Fuzzy logic includes 0 and 1 as extreme cases of truth, or “the state of matters” or “fact,” but also includes the various states of truth in between so that, for example, the result of a comparison between two things could be not “tall” or “short” but “0.38 of tallness.” Fuzzy logic seems closer to the way that our brains work. We aggregate data and form a number of partial truths that we aggregate further into higher truths, which in turn, when certain thresholds are exceeded, cause certain further results such as motor reaction. It may help to see fuzzy logic as the way that reasoning really works, and binary or Boolean logic as simply a special case of it (Whatis.com 2001).

REMOTE AND DISTRIBUTED EXPERT CONTROL IN GRINDING PLANTS

FIGURE 6

519

Optimization of feed-rate rule

A mill power example is shown in Figures 7 and 8. For these examples, mill power is defined in the fuzzy terms of “very low,” “low,” “average,” “high,” and “very high.” An example concept that uses these fuzzy values is shown in Figure 9. NEURAL NETWORK MODELS

The advent of the population balance grinding model created a lot of hope and expectation regarding on-line adaptive modeling of grinding mills. Its complexity and the nature or lumping of an unknown phenomenon into the error function and the complexity of the model parameter adaptation proved to be quite challenging in a practical sense. After the advent of this modeling approach, several first-principle modeling approaches were made for the flotation process (Bascur 1982). Again, some success was achieved in actual plant trials, but widespread industrial utilization was not achieved. These difficulties left a void for a generalized nonlinear modeling technique that was suitable for minerals processing unit operations yet was flexible and understandable for a wider audience. The artificial neural networks (ANNs) (or just neural network [NN]) have proven to be one such modeling process. The origin of the science of NNs can be traced back to ancient times, but the real investigations started with the work of McCulloch and Pitts (1943). Wikipedia.com (2005) defines an ANN as an interconnected group of artificial neurons that uses a mathematical or computational model for information processing based on a connectionist approach to computation. There is no precise agreed-upon definition among researchers as to what an NN is, but most would agree that it involves a network of relatively simple processing elements where the global behavior is determined by the connections between the processing elements and element parameters. The original inspiration for the technique was from examination of bioelectrical networks in the brain formed by neurons and their synapses. In an NN model, simple nodes (called variously

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FIGURE 7

A fuzzy set for SAG mill power

FIGURE 8

Fuzzy rules utilizing the fuzzy representation of power

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Input Neurons

Process Variable One Output Neurons or Predicted Value of Process Variables of Three OneTime Increments into the Future

Process Variable Two

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FIGURE 9

Neural network concepts

“neurons,” “neurodes,” “PEs” [processing elements], or “units”) are connected together to form a network of nodes—hence, the term “neural network.” Like the brain, an ANN is a massively parallel collection of small and simple processing units where the interconnections form a large part of the network’s intelligence. ANNs, however, are quite different from the brain in terms of structure. For example, an NN is much smaller than the brain. Also, the units used in an NN are typically far simpler than neurons. Nevertheless, certain functions that seem exclusive to the brain, such as learning, have been replicated on a simpler scale with NNs. These concepts are shown in Figure 9, where the concept of modeling the future state from the recent past is shown. This is precisely how NNs are used in grinding applications.

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MODERN EXPER T CONTROL OF A LARGE GRINDING CIRCUIT

Expert control systems in modern SAG mill plants have evolved into robust, stable, and highly available systems. They tightly integrate all of the unit operations into a plantwide control strategy that continuously stabilizes the process, and then searches for optimum set points based on metallurgical principles and best practices. Most modern expert system shells employ an object-oriented approach. Object-oriented programming is a software development paradigm that has become popular in recent years; it allows software representation of a better model of the domain and of the problem to be solved. Rather than create a program that is a monolithic set of instructions for the computer, the developer can create a system of objects, which can contain both state and behavior. These objects represent real-world entities and interact with one another. This allows the expert strategy developer to program intelligence into the software representation of each piece of equipment. The equipment can then look after itself, searching for the best operating conditions. When a certain piece of equipment or circuit becomes a bottleneck for the process, it can signal upstream equipment or circuits that then react accordingly to remedy the situation. The modern expert system in a mineral processing plant will integrate all of the unit operations in a manner that achieves the financial objectives of the plant. This profit optimization provides tremendous value to the plant with little associated cost. An example copper sulfides plant will be analyzed. A modern copper plant would include one or more lines of SAG mills, each feeding two ball mills. The ball mills operate in closed circuit, with cyclone overflow feeding a flotation plant. The diagram in Figure 10 illustrates the plant layout. The overall goal of the plant is maximum copper production at acceptable concentrate grades. The result is a combination of feed rate and the recovery and cleaning ability of the flotation circuit. Experience has shown that the best way to achieve the plantwide goal is to allow the unit operations to work independently towards their specific goal and interact when necessary. When those unit operations cannot maintain a certain level of production, they may communicate with upstream processes to find a joint solution. In this example plant, the unit goals can be broken down as follows: ƒ SAG mill—maximum throughput ƒ Ball mill—target grind size ƒ Rougher—maximum recovery ƒ Cleaner—target concentrate grade ƒ Scavenger—maximum recovery

When allowed to work towards these individual goals, the plantwide goals may be achieved. If one of the units cannot achieve a minimum requirement, it may then signal upstream processes to help. For example, a ball mill circuit strategy will try to maintain a target grind size. The strategy will adjust sump water, underflow water, cyclone pressure, and pump speed to maintain the grind size. When all of the control actions are exhausted, the ball mill circuit will signal the SAG mill circuit that it is overloaded, and the SAG mill strategy will react properly. It will change its operating parameters to provide more attrition grinding and alleviate the overload of the ball mill circuit. If the overload is not reduced, then the total feed rate will be reduced. Another example would be in the flotation circuit. A set of columns would adjust their air, pulp level, and wash-water settings to obtain the target concentrate grade. If the minimum grade is not achieved after making all possible changes, the cleaner circuit

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FIGURE 10

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Pictorial representation of a modern grinding and flotation plant

can then communicate with the rougher circuit to negotiate a solution. The response of the rougher may be to make changes in its settings to increase its own concentrate grade, facilitating the cleaner circuit to achieve its minimum requirements. This system of interaction between units allows for the highest level of plant optimization. In the unit operations’ individual strategies, all of the previously described technology is implemented as necessary. This may include rules, fuzzy logic, NN models, and optimizers. The implementer will use all of the technology available to achieve the goals of the plant. An example of this would be the integration of technologies in the SAG mill strategy. The SAG plant may have a set of rules designed to react to emergency situations like mill overloads, high mill power, or excessive recycle rates. These may be implemented using crisp logic. If no emergency conditions exist, the strategy may try to maintain stable operating conditions while trying to gradually move the mill to its most-efficient operating conditions. This is accomplished by changing the mill feed water and the mill speed. Fuzzy logic could be used to provide a smooth control response while taking into account multiple variables. At the same time, NN models may be running to help select the best possible set points and limits using modern sensors like microphones and image analysis that provide valuable information but are hard to write direct rules for. In the modern expert system, we use many forms of artificial intelligence tools to build individual unit strategies, and the object-oriented interaction of those strategies provides a robust global optimization strategy for the plant. This provides significant benefits for the plants using them and gives a framework for control that will endure for many years to come. When running correctly, the control system will ensure that the plant is running at its full potential and is only constrained by actual physical bottlenecks. Over time, these bottlenecks can be identified and addressed, and a continuous cycle of plant improvement can be achieved. INDUSTR Y CHALLENGES—THREE PROBLEMS

Three problems have plagued the minerals industry since the inception of using computers to monitor and calculate process set points. The first, process understanding, seems

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counterintuitive as we are all process professionals (i.e., metallurgical engineers, mineral processors, and experienced mill operators). The problem is that our education isolates mineral processing into individual pieces where cause and effect can be neatly delineated, whereas the reality of plant production is a complex multivariable, everchanging environment where nothing exists in isolation from all other elements of the process, ore conditions, and equipment conditions. Mineral processors are not conversant with modern artificial intelligence theory and practice. Neural networks, genetic algorithms, swarm optimization, induction rule tree discovery, fuzzy logic, for example, are not even understood generally by the mineral processing engineer. Additionally, the personnel problem is complicated by the relatively remote locations of minerals processing plants throughout the world and the fact that drawing qualified people to these remote locations for extended periods of time has been and will continue to be a challenge. The second problem is that minerals processing professionals are mobile, moving somewhat frequently from one employer or position within the organization to another, which is compounded by the constantly expressed opinion that most processing facilities are understaffed. It is not uncommon for one or more plant team members, from management to implementer, to leave or new members to join during the design and implementation of an advanced expert control project, not to mention the problems created from changeover of personnel regarding maintenance and use of the technology over the long-term life of the project. The third problem is that computer control, programming, computer operating systems, networking, and so on, are so complex that traditional educational training barely touches on these essential areas. This problem is compounded by the fact that with too few professionals in our plants, there are even fewer who are proficient in both the complex reality of mineral processing and the complex reality of modern computing hardware and software. These problems have been present ever since the inception of expert control. There is an inherent need for improved processing efficiencies, as well as improved coordination between all the plant entities, and new technology is slowly being introduced to further transform the monitoring and control of mineral processing plants. DISTRIBUTED AND REMOTE CONTROL

Long-range connection to expert control systems has been done routinely since the earliest days of experimentation and installation. Telephone modems were used for many years. Of course, communication speeds and greatly varying telephone line quality throughout the world greatly hampered the functionality and success of this methodology. With the advent of the Internet and the emerging widespread speed increases of this technology, it is now possible to connect to plant expert systems via cyberspace at greater and greater speeds. This has opened up a whole new possibility to further improve the performance of expert control systems as well as to minimize the impact of the three problems just discussed. T H E N E A R - TE R M F U T U R E — L O N G - R A N G E D I S T R I B U T E D C O N T R O L

In their advertising, Sun Microsystems coined the phrase “The Network Is The Computer.” This embodies the concept that we believe will become prevalent in the near future; that is, long-distance extensions to the plant expert control system to a “virtual control room” located remotely in a convenient city, with ample personnel resources. In this remote location, a subtle shortcoming of many minerals plant expert systems will also be improved. That is, many expert systems are somewhat static in nature. Once they are designed, installed, tested, and adjusted, they are left “as is” for long periods of time.

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The problem is that additional improvements are always possible if there is a process in place to measure performance, analyze data, and further design improvements. Visualizing the shape of a normal distribution or the “bell curve,” the bulk of most grinding expert systems naturally and appropriately centers around the mean, represented by ore and equipment conditions. In total, there are still substantial gains to be found and mined on both sides of the distribution of conditions. With newer, affordable, higher-speed Internet connection technology, remote expansion of the plant expert control system will facilitate the next generation of plant performance improvements. This next wave of development and improvement will require a different type of trust to be developed between plant operations and the remote locations. This will be accomplished because of the sound business issues driving continued improvement and a recognition of the barriers that prevent continued improvement that are limited to plant site only. The establishment of remote virtual control rooms will allow a newer technology, “data mining,” to enter into use and be applied to further improve mineral plant performance. Vast quantities of process data accumulated via the real-time expert control systems are, by and large, not used with defined processes to further improve expert systems once they are up and running. Simply put, data mining is the “mechanized process of identifying or discovering useful structure in data” (Bascur 1982). The objective is the knowledge discovery associated with the process of analyzing large collections of process data, cleaning and filtering the data, organizing the data, and then statistically analyzing them to reveal and explore any deep and potentially profitable relationships that were not previously identified or understood. CONCLUSIONS

There has been a steady march to improve control of the complex grinding processes used in minerals processing. Each new sensor, computing, analysis, and visualization methodology has found its way into the mix of tools to better understand and control grinding. The result of this is the tightly integrated control of grinding using many of the artificial intelligence tools available today. There remains, however, much more to do. With each new implementation, we learn that we can do better and that there are still many shortcomings. As technology continues to progress at astounding rates, the “human factor” becomes the rate-limiting factor for continuous improvement of control in the plant. Continuous remote monitoring and assessment of performance by a cadre of qualified engineers utilizing high-speed data-mining methodologies will surely be one of the next steps used to identify additional improvements that can be achieved in the grinding process. BIBLIOGRAPHY

AbsoluteAstronomy.com. 2005. http://www.absoluteastronomy.com/encyclopedia/n/ne/ neural_network.htm. Accessed October 10, 2005. Bascur, A. 1982. Modeling and computer control of a flotation cell. Ph.D. dissertation. Salt Lake City, UT: University of Utah, Department of Metallurgy and Metallurgical Engineering. Herbst, J. 1968. Batch ball mill simulation: A new method for estimating selection and breakage parameters. Master’s thesis. Berkeley. CA: University of California–Berkeley. McCulloch, W., and W. Pitts. 1943. A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5:115–133.

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Rajamani, K. 1979. Optimal control of closed circuit ball mill grinding. Ph.D. dissertation. Salt Lake City, UT: University of Utah, Department of Metallurgy and Metallurgical Engineering. Usama, F., G.G. Grinstein, and A. Wierse. 2002. Information Visualization in Data Mining and Knowledge Discovery. New York: Academic Press. Whatis.com. 2005. http://whatis.techtarget.com/definition/0,289893,sid9_gci212172,00.html. Accessed October 11, 2005. Wikipedia.com. 2005. http://en.wikipedia.org/wiki/Artificial_neural_network. Accessed October 11, 2005. Zadeh, L. 1965. Fuzzy sets. Pages 338–353 in Information and Control. Volume 8. New York: Academic Press. ———. 1973. Outline of a new approach to the analysis of complex systems and decision process. IEEE Transactions on Systems, Man and Cybernetics 3:28–44.

Developments in Sensor Technology for Tumbling Mills B.K. Mishra,* Raj. K. Rajamani,† Vishal Duriseti,† and Sanjeeva Latchireddi†

ABSTRACT

Monitoring grinding operations in tumbling mills has been the focus of research in academia and industry for several decades due to the expectation of high throughput and low operating costs. Sensors form one of the main components of a successful monitoring system. These come in a wide variety that can be categorized as direct, indirect, and soft sensors. For example, the strain gauges that are used as direct sensors are typically mounted inside the lifters and liners of the tumbling mill to measure the stress intensity on the mill shell. Indirect sensors, which include acoustic sensors (noncontact type), are used to predict the state of grinding, wear of liners, and so on. In this paper, a survey of the sensor technologies that have been implemented to monitor tumbling mills (ball and semiautogenous grinding [SAG] mills) is presented. The force spectrum measured in a laboratory-scale mill is shown. Then, through a case study, it is demonstrated that by proper interpretation of vibration signature of tumbling mills, it is possible to predict the extent of liner wear. INTRODUCTION

Tumbling mills have been used in the minerals industry for more than a century. Although the design has changed very little, the size of these mills, particularly SAG mills, has increased significantly. Today 12.9-m (40-ft) diameter SAG mills with motor powers of up to 20 MW and ball mills with a diameter of 7.3 m (24 ft) and a corresponding motor power of more than 11 MW are in operation. The overall energy efficiency of size reduction in grinding mills is still less than 1%–2% (Fuerstenau and Abouzeid 2002). It is estimated that proper monitoring and optimization of the operating conditions with the help of sensor technology can increase the energy efficiency of grinding mills by 10%. The success of a monitoring system depends upon the type, suitability, and reliability of information captured by the sensors. Many different types of sensors have been commercially available. In milling systems, sensors are typically used to monitor ore hardness, particle-size distribution, solid and liquid flow, mill noise, power draft, and so on. The main idea is to integrate both off-line and on-line measurements related to the process to assess the state of grinding and general performance. This paper briefly describes the most commonly used sensors for monitoring of tumbling mills. It presents the result of a case study on a 10.6-m (32-ft) diameter SAG mill where the wear of liners * Indian Institute of Technology, Kanpur, India † University of Utah, Salt Lake City, Utah 527

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inside the mill has been monitored to produce a status signal for the mill operator on a continuous basis. Also, a sensor package for direct measurement of impact spectrum in grinding mills is presented. S E N S O R S F O R TU M B L I N G M I L L S

The primary objective of tumbling mills is to grind material at a desired rate and maintain a specific grind size. For maximum throughput, the rate of grinding must be maintained at the highest level at all times, and the fine product slurry must be removed from the mill by efficient grate and pulp lifers. The key variables that are fundamentally important from an optimization point of view are ƒ Feed ore characteristics, which include ore competency (hard to soft classification)

and feed size distribution ƒ The field of breakage, which relates to energy intensity inside the mill and is

largely a consequence of mill speed and filling, lifter configuration, and ball-toore ratio ƒ Transport or discharge of the fine slurry and pebbles through grate and pulp lifters

Furthermore, these parameters must be amenable to measurement. For example, one should be able to measure what is being delivered to the mill in terms of feed ore characteristics and monitor the effects of changes in rock size and how it affects mill throughput. In modern mineral processing plants, sensors are placed externally to the mill (Sams, Naranjo, and Kemmerer 2003). The measurement systems monitor particle-size distribution of the feed, feed rate, total mill load, power drawn by the mill, discharge specific gravity, and so forth. However, it long has been believed that success in grinding lies in predicting the motion of the charge, which in turn is responsible for grinding. If the motion of the grinding media were not controlled, then a greater fraction of energy would be wasted in impacts, which do not break particles, or consumed in the generation of unwanted product sizes such as ultrafines. Therefore, in order to improve energy utilization, it is essential to estimate the intensity of the tumbling charge that directly relates to its energy. However, it is extremely difficult to ascertain the behavior of the charge in real time during operation. Several methods have been tried by many researchers with limited success; they are briefly reviewed here. Direct Sensors

Direct sensors typically are designed for direct measurement of unknown process parameters of interest. Examples include mechanical sensors that rely on magnetoelastic effects such as strain and force, torque sensors, and displacement sensors. Power. Monitoring power consumption represents one of the simplest methods of monitoring grinding efficiency. Power data have been successfully interpreted to correlate with mill capacity, but the main drawback is that in the case of large industrial mills, small changes in the load or capacity cannot be detected through variations in a power draw pattern. Nevertheless, the standard practice is to maximize mill power for maximum throughput. In many operations, maximizing mill power for maximum throughput works because it is believed that the greater the energy spent per unit mass, the greater is the capacity or the smaller is the product size. In several situations, this idea fails because the ore hardness changes too often. For example, when a harder ore is fed to the mill, desired grinding is not achieved and material builds up inside the mill. As a result, the power draw increases as grinding progresses. The operating data over a 5-day period of a 32u14-ft SAG mill are shown in Figure 1. The power draft of the mill is held between

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FIGURE 1 Five days of plant operating data: 32u14-ft SAG circuit (fresh feed rate in tph; mill power in MW)

6 and 7 MW, whereas ton per hour (tph) of mill feed shows wide variations between 1,000 and 1,600 tph. On close examination, Figure 1 shows that the feed rate drops whenever the power draft shows an increasing trend. The load buildup in the mill is due to insufficient capacity of the pulp lifter, which is the primary reason for this reversal in power. Particle-Size Distribution. It has been recognized in the mineral processing industry that on-line monitoring of particle-size distributions can provide crucial information for mill control. Unfortunately, due to the difficulties in handling large tonnages, it is not possible to perform on-line analysis from process streams, such as the feed and recycle streams in a SAG mill, or from crusher product streams using traditional sizing methods. Lately, on-line digital size analysis using video input has made it possible to monitor and even control the feed size to the mill. Commercially available sensors include the On-Line Particle Size Analyzer, or OPSA (Lin, Yen, and Miller 2000), and Split-Online (Split Engineering, Tucson, Arizona; http://www.spliteng.com). The procedure for the determination of rock size distribution on a conveyor that feeds the mill involves several stages of image processing. The first stage is digital image generation and segmentation, which involves distinguishing the foreground particles from the background. In this way, a binary image can be created by thresholding. A particular threshold value of intensity is chosen and all the pixels having intensities less than the threshold value are made black and the remainder white or vice versa. The next step is edge detection where an edge is defined by a discontinuity in the gray level values. Once the images are prepared (i.e., the segregated particles are visualized), the next step is the measurement of chord lengths, which is calculated by the mean intercept method. Horizontal lines are drawn on the image, and the intercept on each particle is measured. Analysis of the chord length distribution gives an estimate of the size distribution of the particles. Finally, the two-dimensional data of chord length distribution are transformed to three dimensions to obtain an estimate for the rock size. Kernel functions are used to obtain the actual size of the particles from the chord length.

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Charge Motion. In the last decade, much has been learned about charge motion in tumbling mills. With the help of the discrete element method (DEM), the effect of operating variables on the overall motion of the charge is fairly well understood (Mishra 2003). The relationship between impact spectra and breakage in the mill is evolving (Datta and Rajamani 2001; Herbst and Potapov 2005). Much has been learned also about redesigning of liners and lifters. However, in SAG mills there is an ever-pressing demand for on-line prediction of charge dynamics, charge constitution, and impact energy spectra. In this context, the research work on instrumented balls and lifters holds much promise (Rolf and Vongluekiet 1984; Rothkegel 1992; Moys and Skorupa 1993). Instrumented balls with embedded force sensors could measure the impact energy spectra in tumbling mills. Figure 2 shows a typical set of results that can be obtained with the help of a set of instrumented balls. In the figure, variation in the number of impacts (N) of a specific impact intensity is plotted against the mill speed. For example, the uppermost curve corresponds to all impacts >100 mJ. The number of impacts corresponding to all impact energy categories shows a maximum around 90% of critical speed where the power draw also is expected to be maximized. In this way, it is possible to assess the impact energy distribution and subsequently correlate the same to the charge profile. Powell and Nurick (1996) traced the trajectory of a single ball that contained a radioactive source and filmed its path with a gamma-ray camera. These individual ball trajectories led to an understanding of charge interaction, charge segregation, and the influence of lifters. In a more ambitious approach, Rajamani and colleagues (1996) photographed the motion of the charge in a pilot-scale mill. A camera was placed on a mechanically driven trolley that was periodically introduced from the feed end to capture an image of the charge. Figure 3 shows the camera location with respect to the feeding chute and a snapshot of the charge in motion. Several such snapshots can be processed to determine the ratio of the amount of ball to rock. However, to date, this technology has not evolved into a commercial application. Indirect Measurement Acoustic Emission Sensor.

Acoustic emission (AE) sensors are used in several mineral processing plants. It is considered to be one of the most practical technologies to use for monitoring mill operations, and AE sensors have been particularly effective in SAG mill operations. Major conditions to be monitored and detected are intensity and type of impacts (i.e., ball–ball and ball–liner). For practical applications in impact monitoring, the first problem to be solved is how the sensor should be mounted on the mill. These sensors (one to four) are located roughly around the eight o’clock position of a counterclockwise rotating mill. Thus, action is taken to increase the mill sound up to a level beyond which actual cataracting or direct ball strikes on the shell is occurring. In practice, analysis of frequency peaks is made to discriminate between attrition and impact events. For this reason, acoustic signal analysis is difficult and subjective at best. Most operations use sound level as a way of controlling mill speed and/or feed rate. Force Sensor. Force measurement is based on the determination of a displacement subject to loading. Strain gauges have been used primarily to analyze forces, but lately, piezoelectric transducers are becoming more popular for the measurement of forces. In tumbling mills, the forces on the lifter bars are quite sensitive to impact and collision. Hence, instrumented lifters incorporating force sensors have been used to monitor the performance of tumbling mills. These types of sensors are particularly useful to investigate the fluctuations in the load in SAG mills and identify extreme conditions that can lead to shutdowns. Numerical Results. To highlight the potential of force sensors to monitor the load behavior in tumbling mills, a numerical exercise was carried out using the DEM-based

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FIGURE 2 Variation in the number of impacts of a specific impact energy with mill speed (charge profile corresponding to various mill speeds)

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FIGURE 3 Arrangement of camera for scoping charge motion in a SAG mill (left) and a photograph of charge motion inside a pilot-scale mill (right)

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Millsoft software (Raj K. Rajamani, Department of Metallurgical Engineering, The University of Utah, Salt Lake City, Utah). A 10.2-m diameter SAG mill fitted with 24 rows of lifters was simulated. In the simulation, 24 equally spaced stationary sensors were used around the mill shell. During the simulation, the number of normal impacts on the lifter and the corresponding impact intensity were recorded. Because the impact locations are known, all the impacts were mapped to the corresponding sensors. After every revolution, the cumulative data were analyzed and the simulation was stopped when a steadystate pattern was obtained. Figure 4a shows the numerical identity of the sensors and its location with respect to the charge. Figure 4b shows the variation in the impact force around the mill shell. It is observed that maximum impact intensity is shared by the 7th through 9th lifters. The spectrum will be greatly influenced by the wear of the lifters and the makeup of the charge mass. By comparing the spectrum with that obtained during best operating conditions, it is possible to take control actions in order to keep the mill at its highest throughput rate. Preliminary Experimental Results. The instrumented lifter concept also was used successfully to measure the impact spectrum of an operating mill. The sensing system is comprised of two main parts—a strain gauge mounted on the mill shell that sends out a continuous voltage signal and a computer for data acquisition and signal analysis. The voltage signal from the sensor was amplified to prevent attenuation of the signal. This was achieved by using an in-line amplifier, which in addition to amplifying the signal also gave the power required for the sensor to operate. The signal from the sensor is sampled at a rate of 100 kHz and transmitted from the mill to an analog-to-digital converter, from which it is sent to the computer for analysis. At this sampling rate, each impact was individually measured and recorded. Several experiments were performed in an 8.5u9-in. laboratory-scale ball mill. A ball size of 1.28 in. was used at 28% mill filling. The mill was run for 4, 8, 12, 16, and 20 minutes at 60%, 70%, and 80% of critical speed. The data were collected on a continuous basis, and a force spectrum and force histogram were generated for each run. A typical force spectrum and a force histogram are as shown in Figures 5 and 6, respectively. A force spectrum is the plot of force in newtons on the y axis against a number of revolutions or time on the x axis. Each rise and fall in the spectrum corresponds to an individual impact that the sensor experiences due to the balls. It easily can be interpreted from the force spectrum that at any given point in time, the number of low-force impacts is much higher than the number of high-force impacts. Force spectrum also paves the path for the force histogram. The force histogram represents the number of impacts per revolution corresponding to a mean force. The maximum number of impacts in this lab mill is around 300 N. Figure 7 shows the compilation of force histogram in 4, 8, 12, 16, and 20 minutes. It seems the impact signature of the mill could be captured in as little as 4 minutes or 288 revolutions. Figure 8 shows the number of impacts observed in the experiment as a function of critical speed. In particular, the impacts are collected only in the range of 0 to 600 N. As this is a low-level force, the number of impacts in this range decreases as the critical speed increase from 60% to 80%. Similar to Figure 8, Figure 9 shows the number of impacts per 1,000 revolutions versus critical speed in the force range of 4,200 to 4,800 N. In this high-force range, it can be seen that as the critical speed increases from 60% to 80%, the number of impacts also increase. As the mill speed increases, the charge motion slowly shifts from cascading to cataracting, and cataracting implies high-force impacts. Thus, the result previously obtained

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agrees with the theory that as critical speed is approached, the number of low-force impacts would decrease and the number of impacts with higher force would increase. Vibration Sensor. Vibration signals of tumbling mills contain a vast amount of information pertaining to charge dynamics. Accelerometers have been a popular choice for vibration monitoring. These sensors are rugged, compact, and lightweight with a wide frequency-response range. These are typically attached to the outer surface of bearings or gear sets where the vibration due to mechanical grinding is transmitted. The traditional way of observing these signals is to view them in the time domain. The time domain is a record of fluctuations in the amplitude of vibration of the mill versus time. If any waveform that exists in the real world in the time domain can be generated by adding up sine waves, then these sine waves in turn can be processed to reproduce the complex wave in the frequency domain. In the context of mill vibration, the relative

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Comparison of force histogram for different run times at 80% of critical speed

amplitudes of these sine waves of different frequencies contain information directly related to the operating state of grinding (see Zeng and Forssberg 1993). Typically, the time domain waveforms are transformed into frequency domain by the fast Fourier transform (FFT) technique; standard software packages are available for this purpose. V I B R A T I O N A N A L YS I S O F A S AG M I L L — A C A S E S T U D Y

Vibration signals that are emitted by SAG mills as a direct outcome of tumbling charge behavior can be felt all around the mill. These signals can be interpreted for diagnostic

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45 No. of Impacts per Revolution

44 43 42 41 40 39 60

70

80

Critical Speed

FIGURE 8

Number of impacts with force ranging from 0 to 600 N versus critical speed

No. of Impacts per 1,000 Revolutions

10 8 6 4 2 0 60

70

80

Critical Speed

FIGURE 9

Number of impacts with force ranging from 4,200 to 4,800 N versus critical speed

purposes. To illustrate, the results of a case study on a 10.6-m (32-ft) diameter SAG mill are presented. The mill is located in an iron ore mine at Kudremukh in Chickmagalore District in Karnataka, India. A primary gyratory crusher receives run-of-mine ore and after size reduction, the product is conveyed to a coarse ore stockpile. The ore is withdrawn from the stockpile and is fed to four 10.6-m (32-ft) diameter SAG mills, which discharge through a screen to a mill sump. Screen oversize is conveyed to the SAG mill feed, while the undersize is pumped to the ball mill sump. The mill is fitted with 48 lifters and operated at 25% filling with 6%–8% ball load and a mill speed of 10.4 rpm. Forged-steel grinding balls of 90-mm diameter are used for grinding in the SAG mills. Two out of the four mills were subjected to vibration analysis to predict the amount of liner wear. Liner wear is a very complex phenomenon because it results from several complicated processes that occur simultaneously. The liner hardness and design, size distribution of the charge, mill speed, ore abrasion index, forces on media and liners, and the extent of corrosion all influence the wear rate. In this study, an attempt was made to predict the liner life through interpretation of vibration data. For this purpose, one ultrasensitive accelerometer was latched to the surface of the gearbox. Figure 10 shows the mill and the location of the sensor on the gearbox. Continuous vibration signals were obtained over a period of 3 days. The vibration data must be analyzed in the frequency domain, and for this reason, all the data in time domain were transformed to the frequency domain. A typical vibration signature of the mill is shown in Figure 11. The vibration signature basically contains

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Picture of the SAG mill and location of the sensor

FIGURE 10

0.12 126 Hz 49 Hz

0.10

Amplitude, m/s 2

0.08

0.06

0.04

0.02

0 0

300

600

900

1,200

Frequency, Hz

FIGURE 11

Typical vibration spectra of the SAG mill

various frequencies of mill vibration, but it may also contain spurious data. As should be expected, the characteristic frequency of the vibration spectra must correspond to the dynamics of the charge; any other source of vibration is assumed to be negligible in comparison. Through careful analysis of vibration data, it was determined that several individual peaks always are present in the vibration spectra and they do respond to the changes in mill operating parameters. For example, in Figure 11 it is easy to identify the 49- and the 126-Hz peaks. Also, as with all the data, the vibration spectra also show three humps (at 90, 300, and 570 Hz) in the frequency spectra. During operation, these humps do change but could not be related to mill operation due to lack of sensitivity. The variation in 49- and 126-Hz peaks were monitored for two different SAG mills. One of those mills had newly installed liners, and the other one was operating with worn liners (more than half the estimated liner life). Statistical analysis of data (49- and 126-Hz peaks) from these two mills showed that the intensities of both peaks were higher in the case of the newly lined mill as compared to the worn-out mill.

DEVELOPMENTS IN SENSOR TECHNOLOGY FOR TUMBLING MILLS

(a)

Amplitude, m/s 2

0.03

537

(b)

0.02

0.01

0

0

150

300

450

600

750

Frequency, Hz

FIGURE 12

900 1,050 1,200

0

150

300

450

600

750

900 1,050 1,200

Frequency, Hz

Vibration spectra of the SAG mills: (a) new liner; (b) worn liner

The whole spectrum was analyzed, rather than the individual peaks. Figure 12 shows a comparison between the FFT spectra of the newly lined and the worn-out mills. Interestingly, one very important feature, which is characteristic of the liner profile, is evident. Figure 12a shows three distinct humps when the mill operates with new liners. However, Figure 12b, which corresponds to the vibration spectra of the worn-out mill, shows no sign of the third hump. This was encouraging because both mills were identical in dimensions and were being operated under similar conditions. In this way, it was possible to correlate the loss in the height (amplitude of vibration) of the humps and elimination of distinct patterns/features in the vibration signal to wear characteristic of the liners. In short, with the vibration spectra, one is able to indicate qualitatively the liner state. DISCUSSION

This paper has presented a survey of some of the relevant sensor technologies that have been implemented in research and industry relating to grinding systems. Both the direct and the indirect sensors that are commonly used for monitoring of tumbling mills are presented. Another class of sensor, known as “soft sensors” that encompass artificial intelligence techniques are not discussed here. However, the main issues of on-line monitoring of charge dynamics in tumbling mills are addressed. Also, a force sensor package installed in a laboratory-scale mill was discussed. The force spectrum and force histogram were shown. The paper also focused on the scope of vibration monitoring for tumbling mills. It was demonstrated by means of a case study on a 10.6-m (32-ft) diameter SAG mill, that mill dynamics and liner wear can be monitored by interpretation of continuous vibration signals of the mill. Today, many new sensing technologies are utilized, and most of these technologies have claimed reasonable success in research and industry. It is believed that the main trend in sensor technology is expected to be in the following areas: ƒ The availability of low-cost wireless technology that has the potential to make the

industrial implementation of sensors, particularly in the milling environment, easier and less expensive. ƒ Nanotechnology has the potential to provide miniaturized and embedded sensors

that can be contained within a ball for mapping the impact-energy spectra. ƒ Calibration of some of the advanced sensors could easily exceed the cost of the

actual hardware. Therefore self-calibrating sensors can provide a lower-cost option.

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Finally, with the emerging electronic and material technologies, it is expected that new miniaturized sensors with broad capabilities will become available soon. This will solve many process-engineering problems related to comminution circuits. ACKNOWLEDGMENTS

The University of Utah authors would like to thank the support of the U.S. Department of Energy, Industries of the Future Program’s award under contract DE-FC26-04NT42088. REFERENCES

Datta, A., and R.K. Rajamani. 2001. A direct approach of modeling batch grinding in ball mills using population balance principles and impact energy. International Journal of Mineral Processing 64(4):181–200. Fuerstenau, D.W., and A.Z.M. Abouzeid. 2002. The energy efficiency of ball milling in comminution. International Journal of Mineral Processing 67(1–4):161–185. Herbst, J., and A. Potapov. 2005. High fidelity simulation of the mineral liberation process. In Innovations in Natural Resource Processing. Edited by C.A. Young, J.J. Kellar, M.L. Free, J. Drelich, and R.P. King. Littleton, CO: SME. Lin, C.L., Y.K. Yen, and J.D. Miller. 2000. Plant-site evaluations of the OPSA system for on-line particle size measurement from moving belt conveyors. Minerals Engineering 13(8):897–909. Mishra, B.K. 2003. A review of computer simulation of tumbling mills by DEM. Part I: Contact mechanics. Part II: Practical applications. International Journal of Mineral Processing 71(1–4):73–93. Moys, M.H., and J. Skorupa. 1993. Measurement of the forces exerted by the load on a liner in a ball mill, as a function of liner profile, load volume and mill speed. International Journal of Mineral Processing 37:239–256. Powell, M.S., and G.N. Nurick. 1996. A study of charge motion in rotary mills. Parts 1, 2, and 3. Minerals Engineering 9(3–4):259–268, 343–350, 399–418. Rajamani, R., and S. Latchireddi. 2005. Online SAG mill grinding pulse measurement— preliminary studies. In Innovations in Natural Resource Processing. Edited by C.A. Young, J.J. Kellar, M.L. Free, J. Drelich, and R.P. King. Littleton, CO: SME. Rajamani, R., P. Songfack, and B.K. Mishra. 1996. Project report on mill charge motion videography. Salt Lake City, UT: University of Utah. Rolf, L., and T. Vongluekiet. 1984. Measurement of energy distribution in ball mills. German Chemical Engineering Journal 7:287–292. Rothkegel, B. 1992. Oertliche Stossverteilungen in einer Modelkugelmuhle. Ph.D. dissertation. Berlin, Germany: Technische Universitat Berlin. Sams, C.M., G. Naranjo, and J. Kemmerer. 2003. New performance enhancement technologies for the milling industry. Workshop, SAG 2003, Chile. Zeng, Y., and E. Forssberg. 1993. Application of vibration signals to monitoring crashing parameters. Powder Technology 76:247–252.

Ball Mill Circuit Models for Improving Plant Performance Robert E. McIvor*

ABSTRACT

The “Work Index Analysis” method, developed by Fred C. Bond and Chester A. Rowland Jr., provides the means for quantitatively characterizing the overall efficiency of a ball (or pebble) milling circuit. “Population Balance Computer Modeling” provides a means to mathematically characterize the grinding circuit in great detail, at a very high level of complexity. The “Functional Performance Equation” demonstrates that overall ball mill circuit performance is determined by two specific circuit inputs, and two separate and distinct efficiencies that are at work in the grinding circuit. These three ball mill circuit steady-state “models” each display strengths and weaknesses, but when used in an appropriate fashion collectively, a path to higher plant grinding efficiency is clearly visible. INTRODUCTION

In order to be meaningful for plant performance analysis, any definition of grinding efficiency must incorporate the following fundamentals: 1. Energy input 2. Tonnage ground 3. Feed and product sizing 4. Ore resistance to breakage

WO R K I N D E X A N A L YS I S

The work index equation, developed by F.C. Bond (1952), relates rod or ball mill grinding circuit feed and product sizing (F80 and P80) to circuit-specific energy input (kWh/t). By also comparing plant energy consumption to laboratory grindability measurements made over the same size reduction range (again, F80 to P80), the scale-up relationship between the laboratory and plant scale equipment, for the purpose of mill sizing/selection for new installations, was also established (Bond 1961). Given the scale-up factor of 1.0 (after certain correction factors), that is, the plant operating work index should equal that obtained from the Bond work index test. A comparison between the two, therefore, provides a global circuit efficiency measurement (Rowland 1976). “Work index efficiency” provides us with a very useful tool. It is a quantitative measure of overall circuit efficiency. Having defined the statistical confidence limits of measurements * Metcom Consulting, LLC, Ishpeming, Michigan 539

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taken in a given circuit (Laplante, McIvor, and Finch 1988; McIvor 1988), it can be used to quantify changes in grinding circuit efficiency. It is recognized internationally as the standard for general comparisons of circuit performance, as well as ore grinding resistance. It is simple to calculate, and it relates directly to the two factors that dominate grinding costs, energy, and media consumption, providing the important link to processing economics. But as a simple, overall ball mill circuit efficiency measurement, what work index efficiency does not provide is any detailed understanding of relationships between circuit inputs and outputs. The strategy of making trial-and-error circuit changes while monitoring the corresponding changes in work index efficiency can fail because of complex circuit interactions. For example, a change in mill water addition rate could affect both how effectively the mill grinds, as well as the separation performance of the cyclones, with any improvement in one location potentially being overcome by a loss in the other. As well, the method is not generally useful for regrind circuits, and requires some adjustments for use with ball mills following autogenous or semiautogenous grinding. POPULATION BALANCE COMPUTER MODELING

The advent of powerful computing capabilities brought with it the opportunity of representing complex processes with correspondingly complex mathematical modeling systems. A well-known example of this methodology applied to ball milling circuits in steady state is provided by Austin, Klimpel, and Luckie (1984). The wet grinding ball mill circuit is comprised of a grinding mill and a hydrocyclone model. The mill model is comprised of three functions: (1) the “selection for breakage” or “breakage rate” for each particle size class; (2) the “breakage” function, describing the size distribution created by the breakage of each particle; and (3) the residence time characteristic of particles as they pass through the mill. Then, given a mill feed size distribution along with the above three functions, a mill product size distribution is calculated. The ball mill model construction process works back from measured plant data, along with lab measured “breakage” function(s) or certain assumptions, to fit the plant ball mill feed and product size distribution data to three sets of equations for “selection,” “breakage,” and “residence time distribution.” The cyclone is represented by size recovery to underflow. The equations describing the performance of the mill and cyclones, usually of a semiempirical nature, are themselves related to design and operating variables from experimentation and/or observation, either from the lab or in the field. The power of this method of circuit modeling derives from two major advantages. First, there is almost no limit to the complexity of the processes, or the mathematics describing them, that can be readily handled with evenly modestly capable computers, by today’s standards. Second, it provides for off-line experimentation, importantly with no experimental error. This means that even the tiniest change in an output (a circuit product size distribution, for example) can be computed with absolute certainty, and it can be applied to ball milling in all types of circuits. However, as a tool for improving the performance of ore grinding circuits, this method has serious disadvantages. It is mathematically complex beyond all but the most intimately involved specialist. Although off-line experimentation results contain no experimental error, it says nothing about model inaccuracies, which abound (McIvor 1988). There is no term for, or measurement of, grinding “efficiency,” the ore grinding resistance (or “grindability”) needed to calculate it being a glaring exclusion. The lack of ore grindability also means that plant tests conducted to check the outcome of a change in a design or operating variable are always fundamentally in doubt (the exception being

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541

a clinker grinding circuit, or the like, where the feedstock is physically consistent). This led one group of researchers (Kelsall and Stewart 1971) to entirely discount the method as a means of measuring the changes in plant performance, whereas others (Meloy, Williams, and Kapur 1990) have challenged its viability on the grounds that one data set can provide an infinite number of model solutions. By the writer’s count, as many attempts to use the method to improve plant performance have failed as have been claimed to succeed. And many of the “successes” are based on the unverified assumption that the ore did not change. In conclusion, as a stand-alone approach to ball mill circuit steady-state optimization in a mineral processing plant, the method is seriously (or depending on the intended use, fatally) flawed. THE FUNCTIONAL PERFOR MANCE EQUATION

The ball mill circuit Functional Performance Equation for ball milling circuits was first proposed by McIvor in 1988, published in 1992 (McIvor et al. 1992), and most recently re-presented with a series of plant case studies in 2005 (McIvor 2005). This equation relates the production rate of the circuit of new product size material (PRNP) to four factors: the total power draw of the mill (TMP); the batch grindability of the mill feed (or alternatively the locked cycle grindability of the circuit feed, either designated as LabGr); and two active and distinct efficiencies at work in the grinding circuit—first the classification system efficiency (CSEff), which is the percentage of the mill power being applied to “coarse” or target size material; and finally, the ball mill grinding efficiency (BMGEff), the ratio between the plant mill energy-specific grinding rate of coarse particles and the lab grindability. PRNP = TMP u CSEff u LabGr u BMGEff The advantages of using this equation for plant ball mill circuit, steady-state optimization are numerous. It is simple to understand and can be used by plant personnel at all levels. The data are readily generated from a plant survey, and the statistical confidence level of each factor can be determined (McIvor et al. 2000). A term for overall circuit efficiency can be determined by grouping the two efficiency terms on one side of the equation. But most importantly, it defines two separate and active efficiencies, decoupling them from each other and overall circuit efficiency. The maximization of each, and both, provides the optimization criteria for the circuit. Specific design and operating variables are clearly related to each efficiency term. For example, pumping and cycloning are related to CSEff, and media sizing and mill percent solids to BMGEff. As each efficiency term is linear with overall circuit efficiency, it provides a link to primary grinding circuit operating costs, those for energy and media. Unlike work index efficiency, which uses the measured 80% passing size of the product, whatever it happens to be, functional performance analysis penalizes circuit performance when grinding to too fine a product size compared to the target because, in such a case, CSEff is negatively impacted. As well, it penalizes overgrinding, the waste of energy on particles that have already reached desired product size (usually defined by the target P80) or finer. Downstream processes sensitive to particle sizing, like flotation, clearly benefit when CSEff is maximized. It can be applied to all types of ball milling circuits. What the functional performance equation does not provide is a way to predict the outcome of changes to circuit design and operating variables, for which it must generally rely on heuristic guidelines (e.g., for media sizing; McIvor 1997), or some separately established engineering method (e.g., adjusting the cyclone cut size to change circulating load ratio or to improve the water balance; McIvor 1984). It provides no widely recognized standard of performance, as provided by work index analysis.

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C O M B I N I N G C I R C U I T M O D E L I N G S YS T E M S

The relative advantages and disadvantages of each of the previously-described ball mill circuit modeling methods, when used alone, are as described above. It is the recommendation and practice of the writer to use all three of these tools together for plant ball mill circuit optimization work. Doing so creates a synergy that very positively impacts the effectiveness of such project work, to which the following discussion attests. Work index analysis provides the standard, and a reference benchmark, for comparison with other ball milling circuits anywhere in the world. It is simple and statistically quantifiable. It also provides a direct link to major operating costs, those for energy and grinding media. Functional performance analysis is simple and practical. Each term is readily measured from plant survey/audit data and is statistically quantifiable. It decouples circuit efficiency into classification system and ball mill grinding efficiencies. Each can readily be related to specific design and operating variables, which in turn can be manipulated in efforts to maximize both efficiencies. Repeat surveys are then used to measure the effect of changes in design and operating variables on circuit performance, and thus validate efficiency gains. A population balance circuit model, with all the circuit size distributions, can be created on the computer from plant survey data. A particularly useful approach is a slightly modified version of that provided by Laplante, Finch, and del Villar (1986), which is simple and very easy to use, and also eliminates many of the more complex ball mill model issues. The design and operating variables affecting classification system efficiency, specifically the cyclones and the feed to them provided by the pump, can be manipulated in this circuit modeling system. Maximization of the classification system efficiency, from functional performance analysis, is the optimization objective. This computation provides a prediction of the improvement in circuit efficiency achievable with pump/cyclone adjustments. The outcome of such an analysis is essentially unaffected by the assumption that the ore and the performance of the ball mill did not change, and thus is valid as long as the plant data from which the model was constructed are typical. Reasonably sized batch mill grinding tests that include power measurements and are run under similar conditions (media sizing and percent solids) as the plant mill, can (but do not always) replicate plant mill grinding rates (i.e., the Laplante selection function). When direct scale-up can be verified from plant data, the test mill conditions (e.g., media sizing) can be optimized to achieve different (i.e., higher) grinding rates, and the new values entered into the circuit model to predict the level of improved plant circuit performance. Use of such a ball mill model to optimize mill conditions in a computer circuit modeling system continues to be developed by the writer at this time. EXAMPLE CASE STUDIES

Optimization of the conventional A-2 ball mill circuit at Les Mines Selbaie, Joutel, Quebec, Canada, was undertaken (McIvor 1988). Initial detailed grinding circuit surveys were conducted following detailed planning and preparations. The results of the first survey conducted without the influx of fines from the crushing plant are summarized in Table 1. The work index efficiency of the circuit (i.e., the Bond lab test work index divided by the uncorrected circuit operating work index) was calculated to be 101%. The functional performance equation was used to calculate a classification system efficiency of 71% at 106 Pm, and a relative ball mill grinding efficiency value of 38.8 (kg/kWh)/(g/rev), using the grindability measured during the Bond work index test on the circuit feed sample. Error analysis showed the latter calculations to be accurate to (the 95% confidence interval of approximately) r4%, relative. Classification system efficiencies, being calculated

BALL MILL CIRCUIT MODELS FOR IMPROVING PLANT PERFORMANCE

TABLE 1

543

Les Mines Selbaie ball mill circuit survey data summary

Circuit feed rate (t/h) F80 (μm) % –106 μm Bond test work index (kWh/t) Grindability (g/rev) Circuit product P80 (μm) % –106 μm Ball mill feed (% –106 μm) Discharge (% –106 μm) % solids Temperature, °C Mill power draw Operating W.I. (kWh/t) W.I. efficiency test/operating (%) 106 μm production rate (t/h) Class system efficiency (%) Mill grinding efficiency (kg/kwh)/(g/rev)

November 13, 1985

November 23, 1988

Cast-Iron Cones

Forged-Steel Balls

70.3 1,160 30.3 11.8 2.31 115 77.6 21.8 36.1 74.3 13 523 kW

71.3 1,640 26.3 12.7 1.98 116 77.5 20.5 35.1 75.1 13 549 kW

11.7 101 33.3 71.0 38.8

11.3 112 36.5 72.2 46.5

from only the mill feed and discharge size distributions, were determined to be much more accurate, approximately r1% to 2% relative. The A-1 circuit survey data were also used to construct a steady-state circuit computer model. Having noted at the time its limitations for assessing mill grinding conditions, the circuit model was used to conduct off-line tests on the possible effects of making cyclone adjustments. Running a variety of changes indicated that the set up of the pump and cyclones was already near optimum, the exception being if additional water could be used to affect the water balance, that is to reduce the bypass fraction. However, this was limited by the need to maintain flotation feed percent solids. Subsequently, with the support of a media vendor, Magatteaux Canada, a series of grinding media tests were undertaken (McIvor, Duval, and Leclercq 1991). The mill had been charged with 38-mm cast iron, conically shaped grinding slugs. It was proposed that different grinding media could increase the relative breakage rates. Lacking good quantitative predictive capability of the circuit model for this purpose, it was decided to experiment in the plant using work index and functional performance as the performance analysis tools. Mill charges were also dumped and sized as part of these studies. After the mill was charged with 38-mm forged steel grinding balls for a sufficient period for the charge to reach size equilibrium, another survey was conducted, also as summarized in Table 1. The work index efficiency had increased to 112%, and the ball mill grinding efficiency to 46.6 (kg/kWh)/(g/rev). The functional performance equations for the two surveys are as follows: PRNP = TMP u CSEff u LabGr u BMGEff For the first: 33,300 kg/h = 523 kW u 71.0% u 2.31 g/rev u 38.8 (kg/kWh)/(g/rev) For the second: 35, 500 kg/h = 549 kW u 71.5% u 1.98 g/rev u 46.5 (kg/kWh)/(g/rev) From the first to the second survey, the relative mill grinding efficiency increased by approximately 20%. As prescribed in the introduction to this paper, these measurements

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take into account changes in energy input, tonnage ground, feed and product sizing, and ore grindability. They also account for the different proportion of the mill energy expended on +106 ȝm size particles during the two surveys, the relative classification system efficiencies. The calculated work index efficiency for the circuit also increased measurably, by approximately 10%. Fundamental differences in these two models mean that they will not necessarily agree quantitatively. For example, whereas the ore grindability, which factors directly into the functional performance mill grinding efficiency, decreased by about 17%, the ore work index, which factors into the work index efficiency, increased by only 8%. They both, nevertheless, showed a measurable increase in circuit efficiency. Work index analysis could not pinpoint the source of the improved efficiency, which could have come from a change in classification conditions. However, through functional performance analysis, the improvement in circuit efficiency was attributed to the mill grinding efficiency and, by implication, the match of the particular grinding media with the prevalent ore conditions. As the grindability of the ore decreased substantially, the media alone cannot be said to have necessarily caused the change in efficiency. But it can be concluded that the media being used was a far better match with the ore being ground during the second survey. Given the significant effect of media selection on circuit efficiency, either with Bond work index or functional performance analysis, the overall economics of the media selection process, also accounting for cost and consumption rate, lead to the same conclusion. At the time of the initial Selbaie work, a simultaneous study was being conducted at Kidd Creek Mines Limited, Timmins, Ontario, Canada (McIvor 1988). Once again, following rigorous preparations, two baseline surveys were conducted on rod milling, firststage ball milling through rougher copper flotation, and secondary ball milling. The circuit work index and functional performance parameters were calculated from each survey. Survey no. 1 was used as the basis for more detailed circuit-modeling calculations, particularly cyclone performance, as described below. It was noted that the primary ball milling circulating load ratio during the two surveys was quite high—430% and 490%, respectively. It was suggested that this, and the relative coarseness of the rod mill discharge, were contributing to what were considered to be excessively high cyclone feed pump maintenance costs. Because any rougher copper flotation losses would be made up in subsequent flotation stages, an investigation of the potential benefit of lowering the circulating load ratio was undertaken. The economic model used traded-off direct ball milling costs, taken to be proportional to work index efficiency and dominated by mill energy and grinding media consumption, against pumping costs, dominated by pump energy consumption and maintenance. The results are summarized in Table 2. In each circuit simulation, the circuit P80 was held constant, as follows. Cyclone parameters (the d50c, bypass fraction, and m, the slope of the reduced separation performance curve) were adjusted until the water, solids, and size distribution data all matched and conformed with the cyclone general model (Plitt 1976). The ore and ball mill interactions were not touched. The relative circuit efficiency was then determined by the tonnage that was achieved to the common circuit P80. Now, because all circuit efficiency calculation parameters except the tonnage were unchanged, the change in classification system efficiency equaled the total change in circuit efficiency by functional performance analysis and as measured by work index efficiency. As shown in Table 2, a reduced circulating load was shown to be more favorable. As a result of this analysis, the cyclone dimensions were altered and the pump speed was reduced to achieve a target circulating load ratio of 350%.

BALL MILL CIRCUIT MODELS FOR IMPROVING PLANT PERFORMANCE

TABLE 2

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Circulating Load Ratio, %

Class System Efficiency @150 μm, %

Relative Circuit Efficiency, %

Operating Costs, ¢/t Milling

Pumping

Total

250 350 450 (base) 550

53.4 56.1 57.2 58.6

93.4 98.1 100.0 102.4

57.4 54.6 53.6 52.3

5.2 6.7 8.2 9.7

62.6 61.3 61.8 62.0

CONCLUSION

Plant data collection for the purposes of characterizing and improving ball mill circuit performance readily accommodates all three types of analyses described here. Numerous examples of the combined use of work index and functional performance analysis of ball milling are provided in the references and, in turn, in their references. Many examples of the use of population balance computer modeling to predict the effect of grinding circuit changes on grinding performance are also available in the literature. When used in isolation, the methods can be seen to have both strengths and, often, severe limitations. But when used collectively, in conjunction with sound data collection methods, the path to improved plant grinding circuit performance becomes evident. REFERENCES

Austin, L.G., Klimpel, R.R., and Luckie, P.T. 1984. Process Engineering of Size Reduction: Ball Milling. New York: American Institute of Mining, Metallurgical, and Petroleum Engineers. Bond, F.C. 1952. The third theory of comminution. AIME Transactions 193:484–494. ———. 1961. Crushing and grinding calculations. British Chemical Engineering (June): 378–385; (August): 543–548. Kelsall, D.F., and Stewart, P.S.B. 1971. A critical review of applications of models of grinding and flotation. Pages 213–232 in Proceedings of Australasian IMM Symposium on Automatic Control. Laplante, A.R., Finch, J.A., and del Villar, R. 1986. Simplification of the grinding equation for plant simulation. CIM Meeting, Montreal. Laplante, A.R., McIvor, R.E., and Finch, J.A. 1988. Error analysis for bond work index determinations. Part 1: Accuracy and reproducibility. Minerals Engineering 2(2):113–125. McIvor, R.E. 1984. A material balance calculation procedure for grinding circuit hydrocyclone selection. CIM Bulletin (December): 50–53. ———. 1988. Technoeconomic analysis of plant grinding operations. Ph.D. thesis. Montreal, PQ: McGill University. ———. 1997. The effect of media sizing on ball milling efficiency. Chapter 35 in Comminution Practices. Edited by S.K. Kawatra. Littleton, CO: SME. ———. 2005. Industrial validation of the functional performance equation: A breakthrough tool for improving plant grinding performance. SME Annual Meeting. SME Preprint No. 05–31. Littleton, CO: SME.

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McIvor, R.E., Duval, L., and Leclercq, L. 1991. The use of functional performance analysis for plant grinding media testing and selection. Pages 145–155 in Copper ’91. Volume 2. New York: Pergamon Press. McIvor, R.E., Lavallee, M.L., Wood, K.R., Blythe, P.M., and Finch, J.A. 1992. Functional performance characteristics of ball milling. Mining Engineering (March): 269–276. McIvor, R.E., Weldum, T.P., Mahoski, B.J., and Rasmussen, R.S. 2000. Systems approach to grinding improvements at the Tilden Concentrator. Mining Engineering (February): 41–47. Meloy, T.P., Williams, M.C., and Kapur, P.C. 1990. Problems inherent in using the population balance model for wet grinding in ball mills. Pages 31–40 in Advances in Fine Particle Processing. Edited by J. Hanna and Y. Attia. New York: Elsevier. Plitt, L.R. 1976. A mathematical model of the hydrocyclone classifier. CIM Bulletin (December): 114–123. Rowland, C.A. 1976. The Tools of Power Power: The Bond Work Index, a Tool to Measure Grinding Efficiency. AIME Meeting, Denver, Colorado.

INDEX NOTE: f. indicates figure; t. indicates table.

Index Terms

Links

A Acoustic emission sensors

342

530

534

AG/SAG mills. See SAG mills AG/SAG pilot-scale mill study linking DEM to breakage

269

experimental work and results

270

modeling approach

272

power draw comparisons

274

275f.

predicting detailed charge motion with DEM

278

predicting rock wear rates

274

software CSIRO-MI DEM

22

270

276

270

274t.

277f.

software PFC3D Air classifiers

279

173

See also dynamic air separators Anglo American Platinum, Potgietersrust Platinum Mine Artificial neural networks (ANNs) ATWAL Wear Index (ATWI)

54 519

521

51

64

ATWI. See ATWAL Wear Index (ATWI)

B Ball mill circuit models for improving plant performance. See modeling improved plant performance

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Ball mill selection using Bond’s method. See Bond’s method Ball mills

70

optimizing using multiphysics models Barmac crushers

454

456

457f.

458f.

175

Batu Hijau model for throughput forecast, mining and milling optimization, and expansion studies

461

application of the Metso 16-domain model

474

background

461

blast fragmentation model

471

BOCCOST empirical modeling

469

470

Bond Work Index modeling

468

470f.

future model refinements

477

JKSimMet modeling

469

471f.

mill feed size

463

464f.

462

476

mill throughput (continuous throughput model) mill throughput modeling (integrated)

470

mill throughput models (historical)

467

modeling progression

468

ore characterization (historical)

462

463t.

ore characterization models

472

473f.

ore domain definition

462

465

467f.

ore hardness

463

465f.

466

simple regression modeling

468

Blaine surface value inadequacy regarding fly ash

468f.

287 290

Blasting optimization crushing conveying optimizing SAG throughput (BOCCOST), modeling

469

470

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

BOCCOST. See blasting optimization crushing conveying optimizing SAG throughput (BOCCOST) Bond wear test, limitations Bond Work Index (BWI)

344 59

205

386

Bond’s equation

310

386

388

alternative

117

empirical model

447

limitations

115

388

See also Work index analysis

Bond’s method for selection of ball mills ball mill size scale-up

118f.

385 393

determining grinding power using Bond’s equation

388

diameter efficiency factor

390

dry grinding factor

389

efficiency factors

389

fineness of grind factor

391

high or low ratio of reduction rod milling factor

391

low ratio of reduction ball milling factor

391

numerical example

389

observations

396

open-circuit grinding factor

389

oversized feed factor

390

particle-size distributions

386

primary SAG mills

393

rod mill-ball mill circuit example

389

rod milling factor

391

single-stage ball mill circuit example

392

Bond’s third theory of comminution

385

387t.

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Breakage and damage of particles by impact

205

Allowance for Energy Utilization Factors

223

background information

205

experimental results

216

fragment distributions

217

Hertzian Solutions for Impact of Spheres

221

impact and King-Tavares tests

212

non-spherical particles data

208

repeated impacts orientation effect

211

spherical particles data

206

218f.

BWI. See Bond Work Index (BWI)

C Cement clinker grinding practice and technology

169

air classifiers

173

Barmac crushers

175

176f.

circuit configuration for improved efficiency

175

dynamic air separators

175

176f.

high-pressure grinding rolls (HPGRs)

173

174f.

horizontal roller mill (Horomill)

172

(HP) cone crusher

175

176f.

170f.

170t.

177

Portland cement classifications and particle size distributions specific energy consumption with HPGRs

177f.

tube ball mill

170

vertical roller mill (VRM)

171

Cement quality, effect of particle-size distribution in cements with fly ash. See particle-size distribution This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Centrifugal mill

72

Classification, two-stage Classification circuits Classifiers (air)

73f.

314 82 173

176f.

C.M. Doña Ines de Collahuasi SCM, Chile plant (real-time plant information system study)

181

Comprehensive mine/mill throughput model. See Batu Hijau Computer control. See expert control Cone crushers

175

176f.

Control. See expert control Cortez Gold Mines, shell and pulp lifter study

193

Cyprus Sierrita mine

52

D Daniel and Morrell model

12

126

227

229f.

230f.

448

450

Davis tube, in magnetic taconite separations DEM. See discrete element methods (DEM) DGB. See discrete grain breakage (DGB) Directional coefficient definition

228

Discrete element methods (DEM). See models. See also modeling Discrete grain breakage (DGB), simulations

447

452

Drives. See gearless mill drive (GMD) Drop-Weight Index (DWi) correlation with JK drop-weight test A,b parameters measuring ore breakage characteristics

123 121

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Drop-Weight Index (DWi) (Cont.) predicting specific energy from small samples

115

predicting specific energy using DWi

121

usage in circuit modeling

124

Drop-weight tester

123f.

452

453f.

175

176f.

DWi. See Drop-Weight Index (DWi) Dynamic air separators See also air classifiers

E Expert control (remote and distributed) in grinding plants

513

artificial intelligence + minerals processing = expert system shells

517

crisp rules

517

data mining

525

distributed and remote control

524

expert computer control in the 1970s

513

fuzzy logic

518

industry challenges—three problems

523

long-range distributed control

524

519f.

520f.

modern expert control of a large grinding circuit

522

neural network models

519

object-oriented programming

522

operator mimic

514

516f.

phenomenological modeling—population balance models

514

population balance models

519

Ray Mines example

513

515f.

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

F Finite volume (FV)

450

451

Fly ash additive effect of particle-size distribution on cement quality

285

experimental materials and methods

285

results and discussion

287

291f.

Force sensors

530

534f.

Future work

382

535f.

FV. See finite volume (FV)

G Gaudin Random Liberation Model (GRLM), as used with USIM PAC software

506

Gaudin Random Liberation Model (GRLM): the rationale behind the development of one model describing the size reduction/liberation of ores

225

comparing the model with reality— magnetic iron formations

227

converting a qualitative model to a quantitative one

226

expanding the number of composition ranges

236

expansion of the Gaudin Random Liberation Model

228

extension of the directional coefficient approach to low-grade ore

236

the fully liberated minerals

226

gradual liberation by batch grinding

228

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Gaudin Random Liberation Model (GRLM): (Cont.) incorporation into a size reduction/ mineral liberation simulation program measuring liberation parameters

233 230

one approach to solving the distribution problem for locked particle breakage quantifying locked particles

231 230

Solitary Grain Model (SGM) representation of a low-grade ore

237

visualizing mineral liberation via size reduction

225

Gauges to measure liner wear

364

Gearless mill drive (GMD)—the workhorse for SAG and ball mills

413

air-gap measurement principle

426

air-gap monitoring

425

basic data and physical layout

413

415f.

423

424

cycloconverter design and principle

428

429f.

cycloconverter/motor control methods

428

431f.

cycloconverter physical design

430

431f.

danger of low parallel resonance

432

design conditions

433

drive characteristics

432

drive system efficiency

434

GMD starting characteristics

432

harmonic generation sources

432

history of the GMD

414

the house (electrical house) (E house)

427

cooling system and equal distribution of cooling air

416f.

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Gearless mill drive (GMD)—the workhorse for SAG and ball mills (Cont.) inrush current effects of switching on the converter transformers lateral forces

430 419

420f.

long transmission lines and their associated effects

430

the motor

415

the network

430

physical arrangement

426

427f.

primary cooling circuit

423

424f.

rotor installation

415

416f.

sealing system (greaseless)

421

secondary cooling circuit

423

signal processing and fault handling

427

stator design

417

419

stator installation

419

421f.

synchronous condenser

432

water-to-air heat exchanger

424

417

418f.

425f.

420f.

Grinding attrition, new purification process for mineral residue

293

lab-scale experiments

293

macroprocess of the grinding attrition

299

301f.

model validation

304

305f.

306f.

modeling of the microprocess

294

300f.

300t.

specific energy input

302

stress number

299

Grinding efficiency fundamentals

539

GRLM. See Gaudin Random Liberation Model (GRLM)

This page has been reformatted by Knovel to provide easier navigation.

Index Terms Gyratory crushers, liner geometry and wear

Links 377

analysis and results

379

background

378

chamber profile

378

current situation at the mine

381

Excel spreadsheet

379

future work

382

laser profiler device (LPD)

378

liner replacement schedule

381

382

measuring crusher wear and chamber shape

378

new mantle profiles

381

H Hardgrove Grindability Index

205

HFS. See high-fidelity simulation (HFS) HiCom nutating mill High-fidelity simulation (HFS) tools High-pressure grinding rolls (HPGRs)

72

73f.

447

449

3

15

41

51

45

52

173

174f.

45

48f.

54

Anglo American Platinum, Potgietersrust Platinum Mine applications

54 15 177

ATWAL wear-testing HPGR

65

ball mill energy requirements

59

circuit capacity

26

circuit design considerations

30

65f.

34

54 comparison with conventional technologies

35

critical HPGR parameters

4

Cyprus Sierrita

52

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

High-pressure grinding rolls (HPGRs) (Cont.) Daniel and Morrell model DWi usage in ore characterization

12

126

126

energy efficiency

4

16

59

equivalent diameter for piston press tests

6

feed bulk density

6

6f.

9f.

feed moisture

24

26

27

feed size

19

25

26

flowsheet options

30 18

51

54

67

45

history

3

the HPGR bonus

44

indices

51

53

m-dot

5

26

16

17f.

20

17

18f.

25

6

8

13f.

machine design maximum pressure between rolls microcracking modeling and simulation

177

8

13t.

43

62

126

126 multistage crushing and ball milling

32

Newmont Gold, Lone Tree (Nevada)

52

operating characteristics

4

23

7f.

25

operating parameters

4

23

ore characterisation

10

24

Polycom Abrasion Index

64

Polycom Grinding Index

64

product extrusion

30

product flake

11

product sizing

27

roll diameters

5

operating gap

roll edges and cheek plates

19

roll speed

26

26

26

30

52

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

High-pressure grinding rolls (HPGRs) (Cont.) roll surface wear

27

roll surfaces

19

21

22f.

26

45

47f.

52

66

31

33f.

27

SAG mill pebble crushing and precrushing scale of operation

20

specific energy input

6

8

9f.

10f.

24

specific pressure

7

9f.

24

26

27

33

44

54 specific throughput

5

26

16

41

technology benefits

4

16

technology hindrances

3

20

technology basics

technology status

18

testing (ball mills fed with HPGR)

59

testing (closed-circuit)

54

testing (Labmill)

54

59

6

10

testing (piston-press) tramp steel

29

unit capacity

26

variation in throughput with key variables vision for the future

6

7f.

36

Horizontal roller mills (Horomills)

172

HP cone crushers

175

176f.

131

321

324

326f.

HPGR. See high-pressure grinding rolls (HPGRs) Hydrocyclones analysis procedures

435

causes and significance of inflections in efficiency curves

131

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Hydrocyclones (Cont.) control concept (new)

435

437f.

cut point

328

328f.

efficiency curve background

131

efficiency curve coarse inflections

133

146

efficiency curve fine inflections

134

146

efficiency curve laboratory studies

140

146f.

efficiency curve plant sampling studies

137

experimental approach

322

experiments with a 150mm hydrocyclone

438

feed density

324

feed preparation

322

hydrocyclone type and design

322

laser sizing of fractions

324

mass recovery to underflow

326

327t.

transition point

437

438f.

optimization criterion

439

443f.

439f.

439t.

325f.

operation at the rope/spray discharge

optimizing hydrocyclone separation in closed-circuit grinding

435

performance evaluation of larger-size units in a desliming operation

321

Plitt formula

322

pressure

323

quality of separation

325

results

325

rig and sampling system

322

323f.

separation curves

438

440f.

solids content and solids recovery

438

441f.

442f.

test conditions

322

throughput/flow rate

328

329f.

329t.

327t.

324f.

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Hydrocyclones (Cont.) U/F density

326

vortex finder and spigot sizes

322

327t.

I Impact breakage. See breakage and damage of particles by impact IsaMill

72

73f.

Ispat Inland Minorca Plant grinding circuit improvements (simulation-based study)

149

J Jet mill JK drop-weight test

72 463

correlation with DWi test

123

limitations

116

K Kalman filter

515

517

L Labmill grindability indices (LGI)

54

LGI. See Labmill grindability indices (LGI) Liberation. See mineral liberation Liners. See mill liners Linking discrete element modeling to breakage in a pilot-scale AG/SAG mill. See AG/SAG pilot scale mill study LKAB Malmberget mine, time/performancecritical process design

481

This page has been reformatted by Knovel to provide easier navigation.

Index Terms Lone Tree (Nevada) mine

Links 52

M Mathematical model, defined and explained

495

Metso Minerals Process Technology (Asia Pacific) (MMPT-AP) Microcracking

461

462

213

219

331

399

474

Mill drives (gearless). See Gearless Mill Drive (GMD) Mill liners (SAG), selection and design development abrasion test development

346

ball mill steel load

371

bolt hole spacing

353

broken liners

342

charge motion

357

commissioning

367

DEM modeling

399

400

401f.

402f.

404f.

405f.

408f.

409f.

357f.

DEM modeling of full charge trajectories

356

DEM potential (summary)

363

DEM techniques

345

356

design and structure

332

335f.

design (current) how good is it?

339

design trends

372

end liner design/life issues

406

end liners and grates

406

excessive liner wear

342

feed preparation

367

future directions

347

historic data

348

This page has been reformatted by Knovel to provide easier navigation.

404

Index Terms

Links

Mill liners (SAG), selection and design development (Cont.) lab test background

345

laboratory tests

345

lifter bar face angle

352

lifter bar height

352

lifter bar height (influence on liner life)

348

lifter wear (effect on performance)

356

lifters (high-low)

352

lifters (shell)

399

lifters (shell) wide-space and large-angle

399

liner design detailing

366

liner design (optimizing)

349

liner design (pilot tests of influence of)

343

liner design (shell) and mill performance

400

liner height (effect on abrasive wear)

361

liner selection (final)

354

liner size and materials

337

339f.

liner stresses

358

359f.

liner wear distributions

358

liner wear measurement

363

liner wear rates (testing)

344

liners (magnetic)

337

liners (rubber)

336

liners (rubber and steel composites)

337

liners (steel and iron)

335

liners (types of)

332

load calibration

368

materials

335

mill charge levels

403

405f.

406

mill control

341

354

355f.

mill drilling

352

353f.

407

365f.

339f.

338f.

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Mill liners (SAG), selection and design development (Cont.) mill liner inspections

365

367f.

mill liner management

363

mill listening devices

342

mill speed

353

MilTraj software

350

near-field-condition testing

344

noisy mill

341

plant trials

348

pulp lifters discharge

406

409f.

410f.

safe operating window

368

369f.

370

startup SAG mill steel load

371

353

successful applications of improved liner design

350

summary of commissioning guidelines

372

summary of optimising liner design

355

symptoms of poor liner design

341

using a power model

370

utilising charge trajectory predictions

351

utilizing outer charge trajectories to design liner profiles Mill listening devices

350 342

534

Mineral exposure in crushed copper ores (model evaluation)

261

mineral exposure analysis

263

model theory

262

particle-size distribution for heap leaching

263

preferential breakage

267

results and discussion

263

264f.

265f.

265f.

266f.

267

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Mineral liberation by size reduction per the GRLM model

225

Davis tube separations

227

229f.

directional coefficients

228

230

extending the model for low-grade ore

236

genesis of the model

225

locked particle breakage simulation

230

results of batch grinding study

228

review of previous work on the model

225

simulation program possibilities

230

230f.

solitary grain model (SGM) for low-grade ore

237

239

Modeling and simulation of comminution circuits with USIM PAC

495

available energy

500

breakage matrix

498

chemical and mineral composition per size class

505

choice of phase model

508

density distribution

505

flowsheet simulatin

508

Gaudin Random Liberation Model

506

main comminution models in USIM PAC

509f.

503t.

mathematical model defined/explained

495

mineral liberation data

505

phase modeling

503

population balance

498

residence-time distribution

501

selection function

499

size classification modeling

502

504t.

size distribution

497

504

size reduction

497

509f.

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Modeling and simulation of comminution circuits with USIM PAC (Cont.) size-reduction modeling

496

unit operation models in USIM PAC

502

USIM PAC history

496

wear rate

500

503t.

Modeling grinding attrition by applying statistical physics

293

lab-scale experiments

293

macroprocess of the grinding attrition

299

301f.

model validation

304

305f.

306f.

microprocess

294

300f.

300t.

specific energy input

302

stress number

299

modeling of the grinding attrition

Modeling improved plant performance by combining ball mill circuit models

539

combining circuit modeling systems

542

example case studies

542

545t.

functional performance equation

541

542

grinding efficiency fundamentals

539

population balance computer modeling

540

542

work index analysis

539

542

Modeling preparation, determining relevant inputs for SAG mill power draw modeling

161

Models artificial neural networks (ANNs)

519

Batu Hijau model for throughput forecast, mining and milling optimization, and expansion studies Bond’s method for selection of ball mills

461 385

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Models (Cont.) combining ball mill circuit models for improving plant performance DEM

539 345

356

449

530

357f.

447

450

452

DEM/DGB methodology in crusher liner material selection

452

DEM linked to breakage in a pilot-scale AG/SAG mill DEM modeling of full charge trajectories

269 356

discrete grain breakage (DGB) simulations

447

448

evolution of modeling tools

447

448f.

finite volume (FV) technique

450

451

functional performance equation

541

542

grinding attrition of surface-adsorbed contaminants high-fidelity simulation (HFS) tools

293 447

449

liberation of ores by size reduction (GRLM)

225

mineral exposure in crushed copper ores

261

multiphase flow (MPF) simulations

447

448

multiphysics models for optimizing comminution operations

447

population balance (PBMs)

447

451

540

542

projection to latent structures (PLS)

182

186

188

188f.

recurrent neural network (RNN)

163

165

167f.

237

239

solitary grain model (SGM), for lowgrade ore stress (describes physical processes in mills)

99

This page has been reformatted by Knovel to provide easier navigation.

448

Index Terms

Links

Models (Cont.) volume of fluid (VOF) technique

450

work index analysis

539

542

447

448

MPF. See multiphase flow (MPF) Multiphase flow (MPF), simulations Multiphysics models usage in the optimization of comminution operations

447

breakage modeling

452

evolution of modeling tools

447

fundamentals of high-fidelity simulation tools

449

optimizing crushers

452

454f.

optimizing SAG and ball mills

453

457f.

458f.

recent applications of HFS to comminution system optimization

451

Multivariable statistical analyses, in SAG mill smooth operation and extended availability

181

N Netzsch mill

72

Newmont Gold, Lone Tree (Nevada) mine

52

73f.

Newton number. See power number NIPALS (Nonlinear Iterative Partial Least Squares) algorithm

189

NN (neural networks). See artificial neural networks (ANNs) Nutating mill

72

73f.

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

O Optimizing comminution operations using multiphysics models

447

breakage modeling

452

evolution of modeling tools

447

fundamentals of high-fidelity simulation tools

449

optimizing crushers

452

454f.

optimizing SAG and ball mills

453

457f.

458f.

recent applications of HFS to comminution system optimization

451

Ore characterization, linking discrete element modeling to breakage in a pilot-scale AG/SAG mill Ore domain definition

269 462

Overgrinding minimization by circuit design in iron ore comminution

309

base circuit simulations

312

Bond equation

310

circuit simulation

312

modified circuit simulations

314

overgrinding factors

309

plant sampling studies

310

two-stage classification

314

two-stage open/closed grinding circuit

316

USIM-PAC 3.0 software

312

315f.

319t.

319t.

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

P Particle-size distribution significance (in the quality of cements with fly ash additive) Blaine surface area

285 286

287

compressive strength of cements with fly ash additive

290f.

elementary carbon

287

experimental materials and methods

285

results and discussion

287

291f.

water demand

287

289f.

71

72f.

291f.

PBM. See population balance model (PBM) Performance improvements. See simulationbased performance improvements PGI. See Polycom Grinding Index (PGI) PID controller. See proportional/integral/ derivative (PID) controller Pin mill Plant information systems, real-time

181

PLI. See point load index (PLI) Point load index (PLI)

464

Point load test

464

Polycom Abrasion Index. See ATWAL Wear Index (ATWI) Polycom Grinding Index (PGI) Population balance model (PBM) Potgietersrust Platinum Mine Power number (Newton number)

51

64

447

451

498

540

54 108f.

109

Predicting grinding energy requirements from small-diameter drill core samples using the SMC test

115

This page has been reformatted by Knovel to provide easier navigation.

542

Index Terms

Links

Principal component analysis (PCA)

182

Process simulation methodology in process design. See simulation-based process design Proportional/integral/derivative (PID) controller

370

Pulp lifter and shell lifter study (Cortez Gold Mines)

193

Purification process for mineral residues. See grinding attrition

R Rapid-response impact load cell

212

Real-time performance management (RtPM) system

181

evaluating disturbances in circuits using PLS models

186

example: effect of stockpile level

188

example: iron content in SAG mill feed

186

Excel (Microsoft)

183

future applications

189

liner wear (analyzing in real time)

183

PI ACE (OSIsoft)

183

PI DataLink (OSIsoft)

182

PI ProcessBook

186

187f.

PI System (OSIsoft)

181

182

189

principal component analysis (PCA)

182

projection to latent structures (PLS)

182

186

188

181

185

182

189

188

185

188f.

Real-Time Performance Management (RtPM) system results for pattern recognition in SAG mill operation

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Real-time performance management (RtPM) system (Cont.) SCAN (Contac Ingenieros, L.Yacher)

183

185

186

189

variability factor analysis (VEA)

182

variability patterns with new liners

185

variability patterns with worn liners

185

Recurrent neural network (RNN) model

163

164f.

165

167f.

108f.

109

462

463

464f.

466

115

161

181

193

195

197f.

119f.

120f.

Remote control in grinding plants. See expert control Reynolds number Rheology. See slurry rheology RNN. See recurrent neural network (RNN) Rock quality designation (RQD) RQD. See rock quality designation (RQD)

S SAG mills charge motion circuit efficiency compared with ball mills

118

circuit energy efficiency analysis using Bond’s equation

116

118f.

circuit grinding energy requirement prediction from small-diameter drill core samples using SMC test

115

circuit modeling using DWi

124

circuit selection (traditional approach)

116

determining relevant inputs for power draw modeling

161

DWi usage in modeling

124

energy efficiency of SAG mills

195

This page has been reformatted by Knovel to provide easier navigation.

269

Index Terms

Links

SAG mills (Cont.) evaluating disturbances in circuits using PLS models

186

example: effect of stockpile level

188

example: iron content in SAG mill feed

186

Excel (Microsoft)

183

field of breakage

194

flow through grate and pulp lifters

194

FlowMod calculations

197

future applications

189

grate and pulp lifters

197

high-low shell lifter experience

198

188

199f.

202

198

199

impact of new lifters on power draw and energy consumption

200

liner selection and design

331

liner wear (analyzing in real time)

183

linking discrete element modeling (DEM) to breakage in a pilot-scale AG/SAG mill

269

measuring ore breakage characteristics with DWi

121

mill performance (optimizing with multiphysics models)

453

mill performance (predicting with SMC test)

115

mill power draft

195

MillSoft-Discrete Element simulation

195

199f.

202 modeling AG and SAG mill circuits using DWi

124

modeling HPGR circuits with help from DWi

126

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200f.

Index Terms

Links

SAG mills (Cont.) modeling mine to mill applications using DWi

125

Neuroshell software (for RNN modeling)

165

operation of SAG mills

193

ore characterization (linking discrete element modeling to breakage in a pilot-scale AG/SAG mill)

269

PI ACE (OSIsoft)

183

185

PI DataLink (OSIsoft)

182

PI ProcessBook

186

187f.

PI System (OSIsoft)

181

182

189

power draw modeling problem

161

164f.

165

principal component analysis (PCA)

182

projection to latent structures (PLS)

182

186

188

188f.

181

185

164f.

165

167f.

185

186

189

Real-Time Performance Management (RtPM) system real-time plant information systems

181

recurrent neural network

163

results for pattern recognition in SAG mill operation SCAN (Contac Ingenieros, L.Yacher)

182 183

shell lifter and pulp lifter study at Cortez Gold Mines

197

shell lifter design and charge motion analysis with MillSoft shell lifter redesign

196 198

slurry transport and load buildup in the mill

200

SMC test description

122

specific energy prediction using DWi

121

variability factor analysis (VEA)

182

123f.

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Index Terms

Links

SAG mills (Cont.) variability patterns with new liners

185

variability patterns with worn liners

185

See also AG/SAG pilot-scale mill study; mill liners Sand grinder

72

73f.

Scale-up JKSimMet software model

126

simulation vs. traditional methods

385

487

Semiautogenous mill comminution (SMC) test predicting grinding energy requirement using small-diameter drill core samples rock breakage characterization

115 122

127

Sensor technology for tumbling mills: developments in

527

acoustic emission sensor

530

background

527

charge motion

530

direct sensors

528

discussion

537

fast Fourier transform (FFT) technique

342

534

force sensor

530

534f.

indirect measurement

530

Millsoft software

532

particle-size distribution

529

power consumption

528

sensors for tumbling mills

528

531f.

535f.

vibration analysis of a SAG mill (case study) vibration sensor

534 533

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

SGM. See Solitary Grain Model (SGM) Shell lifter and pulp lifter study (Cortez Gold Mines SAG mill)

193

Significance of the particle-size distribution in the quality of cements with fly ash additive

285

Simulation-based performance improvements in the grinding circuit (Ispat Inland Minorca plant)

149

alternatives for improved performance

153

current status and future plans

158

identifying bottlenecks

152

mass balancing and performance evaluation

151

modeling and plant simulation

154

plant sampling and sample analysis

150

results, selection of alternatives, and plant implementation validation of simulation results

156 157

Simulation-based process design where time and performance are critical Bond Work Index

481 487

488

487

489t.

Dymola 2004

481

482

dynamic process simulation

489

feed material description

482

flowsheet

483

low-intensity magnetic separator (LIMS)

483

ModSim 2003

483

490

ModSim’s GMSU model

483

484

ModSim’s WDM2 model

483

comparison with traditional scaling procedures

489

485f.

486

This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Simulation-based process design where time and performance are critical (Cont.) parameter estimation from pilot mills

482

pilot circuit results

485

population balance models

487

process model description

489

491f.

scaling to full circuit

489

490f.

490t.

simulation of process upsets

490

492f.

493

steady-state simulations

482

validation against full-scale circuit

485

488f.

489t.

253f.

486f.

486t.

491f.

Size reduction/liberation of ores. See Gaudin Random Liberation Model (GRLM) Slurry rheology influence on stirred media milling of limestone

243

background

243

calculation of energy efficiency

248

effect of molecular weight of dispersant

248

252f.

effect of solids concentration

252

258f.

energy consumption

247

experimental methods

246

materials

244

mix-up

246

particle size distribution

248

specific surface area

247

stirred media milling

246

viscometer

246

Small-diameter drill core samples and the SMC test (in predicting AG/SAG mill circuit grinding energy requirement)

115

SMC test. See semiautogenous mill comminution (SMC) test This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

Software CSIRO-MI DEM codes

22

270

276

481

482

489

202

Dymola 2004 (dynamic process simulation) Excel

183

fast Fourier transform (FFT) technique

534

FlowMod (steady state simulator)

197

199f.

462

463

195

198

202

532

451

454

ModSim (simulator)

482

490

Nuroshell (Ward Systems Inc.)

165

object-oriented programming

522

Particle Flow Code 3D (PFC3D)

270

274t.

PI ACE (OSIsoft)

183

185

PI Datalink (OSIsoft)

182

183

PI ProcessBook (OSIsoft)

186

187f.

PI System (OSIsoft)

163

181

185

(RtPM) system

181

182

189

scale-up (JKSimMet model)

126

SCAN (Contac Ingenieros, L. Yacher)

183

185

186

189

151

154

312

495

Solitary Grain Model (SGM)

237

239

Stack sizers

153

156

72

73f.

JKSimMet (JKTech Pty.Ltd., Brisbane, Australia) MillSoft (discrete element simulation)

199

199f.

MinOOcad (Metso) (dynamic flowsheet simulator)

456

277f.

279

Real-Time Performance Management

size reduction/mineral liberation modeling possibilities

230

Usim Pac (BRGM, Orleans, France) mineral processing simulation

Stirred media detritor

This page has been reformatted by Knovel to provide easier navigation.

200f.

Index Terms Stirred media mills

Links 69

87

applications experience

84

85f.

bead study experimental procedures

88

bimodal bead-size distribution

93

circuit classification

82

circuit number of mills

82

effect of bead size on ultrafine grinding

87

equipment options

70

flowsheet design considerations

73

99

243

grinding attrition purification process for mineral residue

293

influence of slurry rheology on stirred media milling of limestone

243

lab-scale experiments

293

macroprocess of the grinding attrition

299

301f.

media competency

80

media considerations

77

media hardness

80

81f.

media size

78

79f.

media type

78

80f.

81f.

mill selection criteria

76

305f.

306f.

300f.

300t.

model of stressing particles in a mill

100

model validation

304

modeling attrition in stirred mills applying statistical physics modeling of the microprocess

293 294

monosized grinding beads

89

Netzsch or IsaMill

72

number of mills required

82

operating parameters

81

83f.

457

459f.

73f.

optimizing performance using DEM simulation

This page has been reformatted by Knovel to provide easier navigation.

293

Index Terms

Links

Stirred media mills (Cont.) optimum bead size

92

overgrinding

84

particle size measurement

74

performance vs. tumbling ball mills

70f.

pin mill

71

population balance models (PBMs)

76

power draw determination product size definition production rate determination

72f.

107 73

75f.

111

removal of surface-adsorbed contaminants results and discussion (bead study)

293 89

selection and sizing of ultrafine and stirred grinding mills specific energy

69 70f.

75f.

specific energy consumption, stress energy, and power draw of stirred media mills and their effect on the production rate

99

specific energy determination using lab or pilot scale tests specific energy input

76 302

specific energy/stress energy/stress number relationship

103

stirred media detritor (sand grinder)

72

73f.

stress model application

104

stress number

299

technologies

70

73f.

Vertimill/Tower Mill

71

72f.

Ziniflex Century ultrafine milling circuit

84

85f.

See also slurry rheology This page has been reformatted by Knovel to provide easier navigation.

Index Terms

Links

T Throughput, comprehensive mine/mill model. See Batu Hijau Time/performance-critical process design using simulation (LKAB Malmberget mine) Tower mill Tube ball mills

481 71

72f.

170

Tumbling mills, developments in sensor technology

527

Ultrafine grinding

69

U

circuit considerations

82

equipment options

70

flowsheet design considerations

73

product definition

73

specific energy determination

76

Ziniflex Century ultrafine milling circuit

84

85f.

V Variability factor analysis (VFA). See principal component analysis (PCA) Vertical roller mills (VRMs) Vertimill Vibration sensors

171 71

72f.

533

534

VOF. See volume of fluid (VOF) Volume of fluid (VOF)

450

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Index Terms

Links

W Work index analysis

539

542

See also Bond Work Index (BWI)

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