Klaus Sattler, Hans Jacob Feindt
Thermal Separation Processes
0 VCH Vcrlagsgescllschaft mbH, D-60451 Wcinheim (Federal Rcpuhlic ot Germany). IWS
Distribution:
VCH, P.0. Box 10 1161. D-69451 Weinheim. Federal Kcpublic of Germany
Switzerland: VCH. P.O. Box. CH-4020 Bascl. Switzerland
LJnitcd Kingdom and Ireland: VCH, 8 Wellington Court. Cambridge CBI 1HZ. United Kingdom USA and Canada: VCH, 220 East 23rd Street. New York, NY 10010-4606. USA
Japan: VCH. Eikuw Building, 10-9 Hongo 1-chomc. Bunkya-ku, Tokyo 113. Japan
ISBN 3-527-28622-5
Klaus Sattler, Hans Jacob Feindt
Thermal Separation Processes Principles and Design
Weinheim - New York Base1 - Cambridge - Tokyo
Prof. Dipl.-Ing. Klaus Sattler Fachhochschule fur Technik Speyerer Stral3e 4 D-68163 Mannheim
Dr. Hans Jacob Feindt BASF AG Abteilung Verfahrenstechnik D-67056 Ludwigshafen
This book was carefullyproduced. Nevertheless, authors and publisher donotwarrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Published jointly by VCH Verlagsgesellschaft. Weinheim (Federal Republic of Germany) VCH Publishers. New York. NY (USA)
Editorial Directors: Philomena Ryan-Bugler, Louise Elsam, Karin Sora Production Manager: Claudia Gross1
Library of Congress Card No. applied for A catalogue record for this book is available from the British Library
Die Deutsche Bibliothek - CIP-Einheitsaufnahme Sattler, Klaus: Thermal separation processes : principles and design / Klaus Sattlcr ; Hans Jacob Feindt. - 1. ed. Wcinhcim ; Ncw York ; Bascl ; Cambridge ; Tokyo : VCH, 1995 ISBN 3-527-28622-5 (Weinheim ...) N E : Feindt, Hans Jacob:
0VCH Verlagsgesellschaft m b H , D-69451 Wcinhcim (Federal Rcpublie of Germany), 1995 Printed on acid-free and low-chlorine paper
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form-byphotoprinting,microfilm.or anyother means-nortransmittedartranslated intoamachinelanguage without written permission from the publishers. Registered names, trademarks, etc. used in this book. even when not specifically marked as such, are not to bc considcrcd unprotected by law. Composition: Filmsatz Unger & Sommcr GmbH, D-69469 Weinheim Printing and Bookbinding: Druck haus ,Thomas Muntzer" GnibH, D-99947 Bad Langcnsalza Printed in the Federal Repuhlie of Germany
Foreword
The separation of gaseous and liquid solutions into their components and the drying of wet products have always been an integral part of the manufacture of products in the chemical, petroleum, food, and pharmaceutical industries. As environmental protection has become an increasingly important consideration to industry, separation processes have become more important in direct proportion. This book provides a clear fundamental development of the technology of important separation processes. As indicated by the title the book deals with separation processes in which heat is an input to the complete process of separating the constituents of a mixture. The flow of heat in the process is clear in distillation, crystallization and drying but is not so obvious in absorption, extraction and adsorption, where the heat flow is required to regenerate the solvent or adsorbent.
Each of these six subjects is given thorough coverage in its own chapter. These chapters follow a comprehensive development of the physical chemistry and engineering which provide the principles upon which the separation processes are based. The individual process treatments cover computational algorithms, equipment design criteria and energy conservation. The overall treatment permits the evaluation of competing separations techniques and the choice of the optimal process. This book is intended as a college or university level text for students in chemical engineering and related fields. It is also complete enough and detailed enough in its development of each topic to be useful as a reference for practicing engineers both new to and experienced in the area of separations. CCNY, New York May 1994
Prof. H. Weinstein
Preface
This book, transformed from the original German by Dr. H. J. Feindt, is based on two German editions “Thermische Trennverfahren”, published by Prof. K. Sattler. They have been successfully used as textbooks for university and college students and as reference texts in seminars and training programs for practising engineers in Germany, Austria and Switzerland. The book presents a clear and very practice-oriented overview of thermal separation technologies. An extensive introduction elucidates the physical, physico-chemical, and chemical engineering fundamentals and principles of the different unit operations used to separate homogenous gaseous and liquid mixtures. The introduction is followed by a concise text with many explanatory figures and tables referring to process and basic design, flow-sheets, basic engineering and examples for the application of the unit operations distillation, absorption, adsorption, drying, liquid-liquid and solid-liquid extraction, evaporation and crystallization of solutions, melt crystallization and desublimation. A comprehensive reference list allows follow up of special separation problems. The book enables the reader to choose and evaluate thermal separation processes and to model and design the necessary separation plant equipment.
Chemical and mechanical engineers, chemists, physisists, bio-technologists in research and development, plant design, production, environmental protection and administration and students in engineering and natural sciences will find this treatment of exceptional value and practical use. Due to the quantity of the topics covered exercises could not be included in this book. An additional collection of illustrations with reference to basic engineering and design of the necessary equipment of thermal separation units is available in German (Sattler, K. : Thermische Trennverfahren. Aufgaben und Liisungen, Auslegungsbeispiele) and will be translated into the English language. We are very much obliged to Prof. H. Weinstein, City University of New York for his advice and his Foreword to this book. Many thanks are also given to Philomena Ryan-Bugler, Louise Elsam, Karin Sora and the production team of VCH Verlagsgesellschaft for the accurate lectorship and book production. Special thanks are also given to Paul Fursey, University of Bradford, United Kingdom, for his assistance in copy-editing. Briihl, Ludwigshafen December 1994
K. Sattler H. J. Feindt
Contents
Frequently Used Nomenclature XV
1
Basic Concepts 1
1.1
Principles of Thermal Separation Processes
1.2
Thermal Separation Process Modes
1.3 1.3.1 1.3.2 1.3.3
Mass Balance, Energy Balance, Exergy Balance Mass, Energy and Heat Balances 8 Exergy Balance 12 Calculation of Balance Equations 13
1.4 1.4.1 1.4.1.1
1.4.6
Phase Equilibria 14 Basic Concepts 14 General Differential Equation for the Equilibrium Between Two Phases 17 The Gibbs Phase Rule 18 Liquid-Liquid Equilibrium 19 The Nernst Distribution Law 19 Representation of Liquid-Liquid Phase Equilibrium 23 Vapor-Liquid Equilibrium 28 One Component Systems 28 Two and Multicomponent Systems 30 Henry’s Law, Gas Solubility 44 Boiling Equilibrium of a Solid Solution, Decrease of Vapor Pressure and Increase of Boiling Point 51 Gas-Solid Phase Equilibrium 52 Gas-Solid Phase Equilibrium, Sublimation 52 Gas-Solid Phase Equilibrium with Adsorption/Desorption and Convective Solid Drying (Adsorption Equilibrium) 54 Liquid-Solid Phase Equilibrium 60 Solubility of Solids in Liquid Solvents 60 Melting Pressure Curve 62 Decrease in the Freezing Point 63 State Diagrams of Binary Systems for Solid and Liquid Phase Equilibrium 65 Enthalpy of Phase Changes 65
1.5
Separation Factor and Relative Volatility
1.6
Minimum Separation Work
1.4.1.2 1.4.2 1.4.2.1 1.4.2.2 1.4.3 1.4.3.1 1.4.3.2 1.4.3.3 1.4.3.4 1.4.4 1.4.4.1 1.4.4.2 1.4.5 1.4.5.1 1.4.5.2 1.4.5.3 1.4.5.4
67
1
7
67
8
X
Contents
1.7 1.7.1 1.7.1.1 1.7.1.2 1.7.1.3 1.7.2 1.7.3 1.7.3.1
Mass Transfer Fundamentals 68 Mass Transfer by Molecular Diffusion 69 Steady-State Diffusion 69 Unsteady-State Diffusion 70 Diffusion Coefficient 70 Mass Transfer by Convection 72 Overall Mass Transfer 74 Two Film Theory, Mass Transfer Coefficient and Turbulence Theory
1.8
Steady-State Cocurrent Operation
1.9 1.9.1 1.9.2
1.9.4 1.9.4.1 1.9.4.2
Steady-State Countercurrent Operation 79 Theory of Separation Stages 79 Method to Determine the Number of Theoretical Separation Stages for a Countercurrent Column 82 Calculation for Counterflow Columns 86 Mass Balances 89 Phase Equilibrium Relationship 89 Enthalpy Balances 89 Stoichiometric Conditions for the Sum of the Concentration at Each Equilibrium Stage 90 Kinetic Theory for the Counterflow Separation of a Mixture 90 Two-Directional Mass Transfer Between Phases 91 One-Directional Mass Transfer 92
1.10
Steady-State Crossflow Operation
1.11
General Procedure to Design Equipment for the Thermal Separation of Mixtures 94
2
Distillation and Partial Condensation 101
2.1
Concepts of Simple Distillation, Rectification and Partial Condensation 101
2.2 2.2.1 2.2.2 2.2.3 2.2.4
Discontinuously and Continuously Operated Simple Distillation, Flash Distillation 103 Discontinuously Operated Simple Distillation 103 Continuously Operated Simple Distillation 107 Heat Requirement of Simple Distillation Units 109 Flash Distillation 111
2.3
Carrier Distillation
2.4
Vacuum and Molecular Distillation
2.5 2.5.1 2.5.1.1
Countercurrent Distillation (Rectification) 119 Process Variations of Rectification 119 Continuously Operated Rectification in Rectification Columns with Enriching and Stripping Zones 119 Stripping (Exhausting) Column 120
1.9.3 1.9.3.1 1.9.3.2 1.9.3.3 1.9.3.4
2.5.1.2
75
77
94
113 116
Contents
XI
2.5.4 2.5.5 2.5.6 2.5.6.1 2.5.6.2
Enrichment Column 121 Carrier Rectification 123 Combinations of Different Variations 123 Rectification with an Entrainer 123 Heteroazeotropic Rectification 129 Two Pressure Operation 130 Diffusion Distillation 131 Overpressure, Low Temperature and Vacuum Rectification 132 Continuous Adiabatic Rectification 134 Flow Rates 135 Heat Requirement of a Column 136 Energy Saving Steps 138 Determination of the Number of Separation Stages and Column Height for Heat and Mass Transfer 147 Minimum Reflux Ratio, Optimal Economic Reflux Ratio 157 Feed Stage 157 Discontinuous Adiabatic Rectification 158 Amount of Overhead Product 160 Heat Requirement 161 Still Diameter, Free Vapor Space, Column Diameter 162 McCabe-Thiele Method to Determine the Number of Theoretical Separation Stages 163 Semicontinuous Adiabatic Rectification 163 Determination of the Column Diameter 164 Internals in Rectification Columns 165 Column Trays 167 Random Packing, Packing with Regular Geometry 196
2.6
Choice, Optimization and Control of Rectification Units
2.7
Rectification Units Accessories 218
2.8
Parallel Flow Distillation
2.9
Nonadiabatic Rectification
2.10
Partial Condensation
3
Absorption
3.1 3.1.1 3.1.2
Principle of Absorption and Desorption, Processes and Process Examples 239 Concepts and Process Examples 239 Process Examples 240
3.2
Requirements of the Wash Liquid or Solvent, Solvent Consumption 243
3.3
Enthalpy and Heat Balances
3.4
Cocurrent Phase Flow Absorption
2.5.1.3 2.5.1.4 2.5.1.5 2.5.1.6 2.5.1.7 2.5.1.8 2.5.1.9 2.5,l. 10 2.5.2 2.5.2.1 2.5.2.2 2.5.2.3 2.5.2.4 2.5.2.5 2.5.2.6 2.5.3 2.5.3.1 2.5.3.2 2.5.3.3 2.5.3.4
216
222 222
230
239
246 248
XI1 3.5 3.5.1 3.5.2
Contents
Countercurrent Phase Flow Absorption, Design of Countercurrent Flow Columns 248 Determination of the Column Cross-Sectional Area 248 Determination of the Number of Stages and Column Height for Mass and Heat Transfer 250
3.6
Types of Absorber
3.7
Regeneration of the Solvent, Desorption
4
Adsorption 281
4.1 4.1.1 4.1.2
Principles of Adsorption and Desorption, Processes and Examples 28 1 Concept 281 Processes and Examples 282
4.2 4.2.1 4.2.2 4.2.3
Adsorbents, Selection of Adsorbent 291 Adsorbents 291 Requirements for the Adsorbent, Adsorbent Selection 291 Technical Adsorbents, Characteristic Data of Adsorbents 293
4.3
Adsorption Kinetics
4.4 4.4.1 4.4.2 4.4.3
Variation of Adsorption, Design of Adsorbers 301 Single Stage Adsorption in a Vessel Adsorber with Adsorbent Packing Multistage Adsorption with Cross Flow of Gas and Adsorbent Phases 307 Multistage Countercurrent Adsorption 308
4.5
Adsorber Types 310
4.6
Desorption, Regeneration of Loaded Adsorbent
5
Drying
5.1
Concepts, Processes and Examples
5.2
Characteristics of the Moist Product, Movement of Moisture
5.3
Properties of Wet Gases, h-X Diagram
5.4
Mass and Heat Transfer in Convection Drying
5.5
Drying Kinetics, Course of Drying, Drying Time
5.6 5.6.1 5.6.2 5.6.3
Convection Drying 340 Drying Gas and Heat Requirements in Convection Drying Steps in Energy Saving 343 Variations of Convection Drying 346
5.1
Contact Drying
5.8
Radiation Drying
262 263
293
311
317
349 351
317 320
324 331 335 340
301
Contents
5.9
Dielectric Drying
5.10
Freeze Drying (Sublimation Drying) 355
XI11
352
Design of Dryers 357 Overview of Dryers, Dryer Selection and Design 357 Individual Presentation of Selected Dryer Types with Design Aids 363 Chamber Dryer 363 Tunnel Dryer 364 Belt Dryer 364 Multiple Plate Dryer 364 Rotary Dryer 364 Fluidized Bed Dryer 366 Air-Flow Dryer, Pneumatic (Flash) Dryer 374 Spray Dryer 377 Drum Dryer 381 Thin Film Evaporation Dryer (Vertical and Horizontal Dryer) 381 5.1 1.2.11 Contact-Mixing Dryer 381 5.11.2.12 Contact Dryer with Continuous Product Movement due to Gravity 385 5.11.3 Process Control of Dryers 387 5.11 5.11.1 5.11.2 5.1 1.2.1 5.11.2.2 5.1 1.2.3 5. 11.2.4 5.11.2.5 5.11.2.6 5.11.2.7 5.1 1.2.8 5.11.2.9 5.1 1.2.10
6
Extraction 393
6.1
Basic Concepts and Processes 393
6.2 6.2.1 6.2.2 6.2.3 6.2.3.1 6.2.3.2 6.2.3.3 6.2.3.4 6.2.3.5 6.2.3.6 6.2.4 6.2.4.1 6.2.4.2 6.2.5
Liquid-Liquid Extraction 395 Fields of Application and Process Examples 395 Solvent Requirements, Selection of Solvent 399 Liquid-Liquid Extraction Variations 400 Single Stage Extraction 400 Differential Stagewise Extraction 403 Multistage Cross-Current Extraction 403 Multistage Countercurrent Extraction 407 Countercurrent Extraction with Extract Reflux 421 Countercurrent Distribution 424 Design Forms of Extraction Apparatus 424 Mixer-Settler, Mixer-Settler Cascade 425 Countercurrent Columns with and without Energy Supply 426 Selection and Design of Extraction Apparatus 456
6.3
Solid-Liquid Extraction (Leaching) 458
6.4
High Pressure Extraction (Distraction) 463
XIV
Contents
7
Solvent Evaporation, Crystallization 475
7.1
Basic Concept and Processing Modes of Crystallization
7.2 7.2.1 7.2.1.1 7.2.1.2 7.2.1.3 7.2.1.4 7.2.1.5 7.2.2 7.2.2.1 7.2.2.2 7.2.3 7.2.4 7.2.5 7.2.6 7.2.7
Crystallization from a Solution 484 Concentration of Solutions by Evaporation 485 Single Stage Solution Evaporation 486 Multistage Solution Evaporation 487 Solution Evaporation with Mechanical and Thermal Vapor Compression 492 Multistage Flash Evaporation 498 Types of Evaporators to Concentrate Solutions 500 Balancing of Crystallizers 500 Crystal Product Rate 500 Heat Exchange During Crystallization 506 Crystallization Kinetics, Crystal Seed Formation, Crystal Growth 508 Design of Crystallizers for Mass Crystallization from a Solution 511 Criteria for the Selection and Design of Crystallizers 516 Freezing 519 Fractional Crystallization of a Solution 520
7.3
Crystallization from a Melt
7.4
Crystallization from a Vapor Phase, Sublimation and Desublimation
8
Documentation and Calculation of Physical Characteristics 533
General References 537 Index 539
475
521 524
Frequently Used Nomenclature
A
Area
m2
AQ
Cross sectional area, cross section
m2
D D,D
Diffusion coefficient
m2/h
Vapor; vapor flow rate
kg, kmol; kg/h, kmol/h
E
Enrichment ratio, stage efficiency factor
F
Force
N
F
Loading factor for column trays
m/s
fiF
Feed; feed flow rate
kg, kmol; kg/h, kmol/h
F
Free internal energy
kJ
G, G
Gas; gas flow rate
kg, kmol; kg/h, kmol/h
G
Free enthalpy, Gibbs free energy
kJ
H
Enthalpy
kJ
HE TS
Height equivalent to one theoretical stage
m
HTU
Height of a transfer unit
m
K*
Phase equilibrium constant, distribution coefficient
L, L
Liquid; liquid flow rate
kg, kmol; kg/h, kmol/h
Lc M
Characteristic length
m
Molar mass
kg/kmol
N
Number of stages
NTU
Number of transfer units
Q,Q
Heat; heat flow rate
kJ; kJ/h, W
R, R
Reflux; reflux flow rate
kg, kmol; kg/h, kmol/h
R
Gas constant
kJ/(kmol K)
S
Entropy
k J/K
.
v m
+
=
1/pa
XVI
Frequently Used Nomenclature
T
Absolute temperature
K
U
Internal energy
kJ
V, V
Volume; volumetric flow rate
m3; m3/h
Molar volume
m3/kmol
Work
kJ
Ratio or loading of key component in liquid or heavy phase (moles i/moles inert, kg i/kg carrier (inert))
-
v
W
x
Y
Ratio or loading of key component in vapor or light phase (moles i/moles inert, kg i/kg carrier (inert))
Z
Length or height for heat and mass transfer
a
Activity
a
Specific volumetric area
m2/m3
cp, Cp
Specific heat
kJ/(kg. K), kJ/(kmol. K)
c
Molar concentration
kmol/m3
cw
Resistance coefficient
d
Diameter
m
dP
Particle diameter
m
ds
Sauter diameter
m
f
Fugacity
bar
Specific free internal energy
kJ/kg, kJ/kmol
gravitational acceleration
m/s2
Specific free enthalpy
kJ/kg, kJ/kmol
h,
Specific enthalpy
kJ/kg, kJ/kmol
Ah, A&
Latent heat
kJ/kg, kJ/kmol
k
Overall heat transfer coefficient
W/(m2. K)
k
Overall mass transfer coefficient
m/h
rn, m
Mass; mass flow rate
kg; kg/h
n, n
Number of moles; molar flux
kmol; kmol/h
P
Total pressure
bar, Pa
P,
Partial pressure of component i
bar, Pa
.Lf g g9
E
m
Frequently Used Nomenclature
XVII
Po, i
Saturated vapor pressure of component i
bar, Pa
AP
Pressure drop
mbar, Pa
4
Specific heat requirement
kJ/kg
4
Specific heat flux
kJ/(m2 h), W/m2
r
Radius
m
r
Reaction rate
kmol/(m3 h)
s, s
Specific entropy
kJ/(kg. K), kJ/(kmol K)
S
Characteristic distance (transfer distance)
m
t
Time
h
t,n
Mean residence time
h
u, ii
Specific internal energy
k J/kg, k J/kmol
W
Velocity
m/s
W
Mass fraction, weight fraction of component i
X
Molar fraction, heavy phase
Y
Molar fraction, light phase
Z
Variable distance length or height
Az
Tray spacing
-
m
Greek a
Separation factor
-
a
Heat transfer coefficient
W/(m2. K)
Mass transfer coefficient
m/h
Activity coefficient Film thickness, layer thickness
m
Porosity, void fraction of a bed of solids, fraction of free volume Yield
-
Dynamic viscosity
Pa s
-
Temperature
"C
Slope, gradient angle, inclination
0
Thermal conductivity
W/(m . K)
Chemical potential
k J/kg, kJ/kmol
XVIII
Frequently Used Nomenclature
V
Reflux ratio, solvent ratio, adsorbent ratio
-
V
Kinematic viscosity
m2/s
e
Density
kg/m3
0
Surface tension
N/m
v?
Relative humidity
-
Subscripts
H
Steam
T
Carrier
g is J
Gas phase Component
1
Liquid phase
0
Above, surface
P
Effective, practical
S
Solid phase
t
Theoretical
U
Below
U
Loss
a
Start, entry
0
End, exit
Thermal Separation Processes: Principles and Design Klaus Sattler, Hans Jacob Feindt copyright 0VCH
Verlagsgesellschaft m h H , 1995
Basic Concepts
1.1 Principles of Thermal Separation Processes In a chemical production plant, products are produced by the chemical and physical conversion of raw materials or intermediate products. The production unit is a completely integrated technical operating unit on the site. It is connected with other units on the site by transportation and personnel routes, and pipelines for raw materials, auxiliary substances, products, utilities, and energy. It usually consists of the actual production unit and several off-site facilities, as shown in Fig. 1-1. The main unit contains the unitprocesses and operations, such as separation, combination, division, formulation, heat transfer, conveying, storage, packing. Figure 1-2 shows a general set-up which is independent from the type of process. The combination of unit processes and operations with respect to product properties depends on the product produced. During the chemical conversion of raw materials, homogeneous and heterogeneous mixtures (Figs. 1-2 and 1-3) are generated. Both reactants and products may be found in these mixtures, according to the yield and conversion of the chemical reaction. By means of thermal separation processes these mixtures must be treated to obtain the desired products to a demanded purity and to enable the raw materials to be recycled. Processes to separate physically homogeneous (one phase) and heterogeneous (two or multiphase) mixtures are listed in Table 1-1. The driving force of the separa-
tion process usually forms the criteria for the separation. Homogeneous mixtures with a molecularly dispersed distribution of individual components may only be separated by means of a thermal separation process. Thermal separation processes are mass transfer operations, driven by molecular forces. Mass, and often heat, is exchanged between at least two phases of different composition. The phases are the mixture phase(s) and a selective auxiliary phase. The auxiliary phase is generated by either adding heat and/or by means of an auxiliary substance. The required driving forces, concentration, and temperature gradients, are formed due to the auxiliary phase. In Fig. 1-4 thermal separation processes are listed and are denoted by the phases contributing to mass transfer in Table 1-2. Thermal separations of mixtures are carried out in the following individual steps :
Step 1: An additional phase is generated by supplying energy to the system, or by adding an auxiliary component. - Step 2: Mass, and often simultaneously heat, is exchanged between phases. This is achieved by the addition or removal of energy. - Step 3 : After completion of the interchange process, the phases are separated. Together with the separation of the phases a (partial) separation of the mixture occurs. -
All thermal separation processes follow this order of events. The basic principles of thermal separation processes are now formulated and will be discussed in detail.
2
1 Basic Concepts
Main plant Process consisting of physical and chemical unit operations to produce desired products Off-sites, auxiliary equipment
- process control of the main plant
control room sometimes with a process control computer, control devices for drives, production lab, instrument air station
Inputs Energy
-+
-+
- supply of energy to main plant, generation and distribution
--*
Excess energy
- transport to the process unit of the raw material and auxiliary
-+
materials, transport of the products (roads, rail connections, harbor)
Main products
-+
By-products
+
Waste
of electrical power, heating system for heating media such as
hot water, steam, dyphil, salt melts - provision of auxiliary materials (adjuvants) such as heat
Raw materials Auxiliary materials
-
transfer media, coolants, catalysts, solvents, inerts ~~~
~_~
~~
- storage of raw and auxiliary materials, and products, spare parts, tools and materials for repair work and maintenance
_~
-
__ __
- disposal
treatment of waste gas and wastewater, reprocessing of solid residue and waste disposal
+ Waste gas
Wastewater
- facilities for the operating personnel
Fig. 1-1. General production process set-up.
Raw material
I
metering, preheating
i
Main product ready for storage or shipment
~
Path of raw material or product
Fig. 1-2. Basic flow chart for the main part of a production plant.
1.1 Principles of Thermal Separation Processes
3
Y 1 Y 1 A
Y
r
Reaction mixture
A b : : +
Phases in Cocurrent Flow (Principle of Parallel Flow)
Phases in Countercurrent Flow (Principle of Counterflow)
Phases taking place in mass and heat transfer are guided in cocurrent flow through the separation apparatus. The maximum efficiency of this separation apparatus is the same as that for a single theoretical separation stage.
Phases taking place in mass and heat transfer are guided in countercurrent flow through the separation apparatus. In this case it is important to disperse the phases with the aid of internals, thereby achieving intensive mixing of the phases. Thus the
.............................
............................ I
I
1 I
: I
Rectification (counterflow distillation) counterflow crystallimtion from a melt Counterflow sublimation Counterflow liquid-liquid extraction Fractionating, Counterflow processes
i
1
Partial distillation Partial condensation Absorption Extraction Adsorplion Cristallization from a solution Drying
~
~
phase transformation
Thermal \epnratioii
I_._________..-.....
L
I
Procesres with auxiliary materials
Absorption Adsorption Convective drying Carrier distillarion Extractive distillation Extraction Entrainer gas sublimation
Principle of classification. Distillation Partial condensation Crystallization Drying (except convective drying) Vacuum d h m a t i o n
Fig. 1-4. Summary of thermal separation processes.
,_r -- -- -_,l
Simple phase transfomiation t) fractionating
Auxiliary product: required for separation tf not required tor separation
4
1 Basic Concepts
Table 1-1. Summary of separation processes. Classes of separation processes
Driving force of separation process
Nature of mixture
Separation processes
Mechanical separations
Gravity Centrifugal force Pressure
Heterogeneous
Sorting (s - s) Dense-media separation (s - 1) Flotation (s - 1 - g) Sedimentation (s - 1) Filtration (s - 1) Pressing (s - I) Centrifugation (s - 1) Hydrocyclone separation (s - 1) Classification Sieving (s - s) Air classification (s - g) Hydraulic classification (s - 1)
Membrane separation
Pressure Electrical field Concentration gradient
Heterogeneous Homogeneous
Ultrafiltration (s - 1) Reverse osmosis (hyperfiltration) (s - 1) Dialysis (s - 1) Electrodialysis (s - 1) Electrophoresis ( s - 1) Permeation (1 - 1, g - g) Gas diffusion (g - g)
Electrical separation
Electrical field
Heterogeneous
Electro osmosis (s - 1) Electrical dust removal (s - g)
Magnetic separation
Magnetic field
Homogeneous
Magnetic separation (s - s)
Thermal separation
Concentration gradient Temperature gradient
Homogeneous
Distillation (1 - 1) partial condensation (g - g) Absorption (g - g), (A) Adsorption (g - g, s - I), (A) Chromatography (g - g, 1 - 1) Extraction (s - s, 1 - I), (A) Sublimation (g - g) Crystallization ( s - 1, 1 - 1) Drying (s - 1) Thermal diffusion (g - g, 1 - 1)
~
Abbreviations: s solid, 1 liquid, g gas to characterize the state of the components of the mixture to be separated, (A) thermal separation process with auxilliary component.
maximum possible interfacial area (phase boundary) for mass transfer is obtained and, hence, the highest possible mass transfer coefficient values. Figure 1-5 shows a “separation column” with stages connected in series in which the key component i of a
mixture is exchanged from the heavy phase to the light phase. Both phases may contain all components of the mixture. A closer inspection of stage n shows that the heavy phase, with a mole fraction of x,, is in contact with the light phase with a
5
1.1 Principles of Thermal Separation Processes
Table 1-2. Characteristics of thermal separation processes by the phases in which mass and heat transfer occurs. ~~
Phase Phase All components Not all components are in both phases 1 2 are contained Phase 2 One (several) comin both phases Phase 1 pure pure ponent (s) is (are) in both phases ~
Immiscible phases in contact
Miscible phases in contact
g
1
g
S
Distillation Partial condensation
Concentration of solutions
Gas drying
Counter current sublimation
g
g
1
1
Liquid-liquid extraction
1
S
Crystallization from a melt
S
S
g
g
Thermal diffusion
1
1
Thermal diffusion
S
S
~~
Absorption Desorption by stripping Adsorption Drying
Crystallization from a solution
Solid-liquid extraction (leaching) Adsortpion
-
Abbreviations: g gas phase, 1 liquid phase, s solid phase.
mole fraction of Y , , - ~ .If x, and are not phase equilibrium concentrations, the fed phases of stage n are not in phase equilibrium, and mass and heat transfer take place. The key component i becomes enriched in the light phase up to a final concentration y,, while the heavy phase is reduced in component i from x,,to x , - ~ . With stage n as a theoretical separation stage, the leaving phases are in equilibrium and no further mass or heat transfer is possible. Therefore, y, and x , - ~ are phase equilibrium concentrations. The heavy phase, with concentration x,, - arrives at stage n - 1 and comes into contact with the light phase, with concen-
tration y n P 2 .An exchange, similar to that in stage n, takes place. The discussed example shows that for countercurrent phase flow, single stages are connected in series in one separation apparatus. The light phase leaving a stage is guided to the following stage whereas the heavy phase is guided to the previous stage. A theoretical stage is that part of a separation apparatus where mass or heat transfer take place in which entering phases are not in phase equilibrium, while the leaving phases have reached phase equilibrium (see Chapter 1.4). In a practical separation stage, equilibrium is often not achieved. The efficiency
6
1 Basic Concepts
transfer ratio, depending on whether y is only locally valid or constant across the cross section of the column.
Phases in Cross Flow (Cross Flow Principle)
LP
HP
L-l---r Fig. 1-5. Countercurrent flow of two phases in a separation apparatus. n - 1, n Stages connected in series LP Upflowing light phase HP Downflowing heavy phase Molar fraction of the key component in x the heavy phase Molar fraction of the key component in y the light phase
Phases taking part in mass and heat transfer flow across through the separation apparatus at an angle of 90" to each other. The separation efficiency depends on the equilibrium location and the ratio of the phase fluxes, but is often low in an individual separation stage. To separate a mixture and obtain pure products, several separation stages are connected in series. This is done most effectively with countercurrent phase flow. Phase cross flow and parallel feed of one phase to individual separation stages are sometimes used. However, cocurrent flow is of non importance.
compared with a theoretical stage is ex- ~i~~ Requirement pressed as the stage efficiencyfactor, E (exchange ratio, enrichment ratio, MURPHREE The time needed to separate a mixture in a efficiency) (Fig. 1-5): discontinuous operation is the effective residence time. For continuous operation, it is separation effect of a practical stage the mean residence time t,, of the mixture E= in the separation apparatus: separation effect of a theoretical stage E=
Yn-Yn-1 Yn*-Yn-1
(1-1)
t,
V
=T
V
where
where
y,* - y,-,
possible theoretical enrichment of the key component in the light phase ( y ; phase equilibrium concentration at x, y , - y n p 1 actual enrichment of the key component in the light phase
I/
This often has to be distinguished as a local transfer ratio, as opposed to an overall
Short-, medium- and long-term separation processes can be distinguished depending on the time requirement:
filled volume of the mixture in the separation apparatus (determined by the volume of the apparatus and the degree of filling) effective volumetric flow of the mixture
1.2 Thermal Separation Process Modes
Short-term processes (t, < 30 sec). Examples: Spray drying, gas adsorption, precipitation crystallization. - Medium-term processes (30 sec< t, < 2h). Examples: Absorption, rectification, drum drying, pneumatic-conveyor drying, sublimation, extraction, crystallization, liquid adsorption. - Long-term processes (1 h < t , < 1 d). Examples : Rotary drum drying, vacuum tumbling drying, vacuum freeze drying, fractionation crystallization. -
Energy Supply For the thermal separation of a mixture in an apparatus, energy has to be supplied in the form of: -
Heat, to increase the sensible heat of the flowing masses and to supply latent heat.
-
7
Flow energy, for pressure drops in the ap-
paratus and the connecting pipework. Mechanical energy, for example for dispersing, pulsing, stirring and pump circulation devices. - Work, to operate peripheral machines such as compressors and vacuum pumps. -
1.2 Thermal Separation Process Modes Apparatus for the thermal separation of mixtures may be operated both discontinuously (intermittently, batch production, stagewise operation) and continuously (steady-state). In the following section, the operating modes are briefly illustrated. The advantages and disadvantages are listed in Table 1-3.
Table 1-3. Comparison of continuous and discontinuous operation to achieve the same separation
problem.
Comparison criteria
Operating mode Continuous
Mathematical description of the separation process, modeling Investment cost of separation unit Operating cost of separation unit Operation of separation unit Automatic control of separation process Working stress on unit components Environmental pollution, possibility of accident Operation reliability, flexibility in the case of breakdown of separation unit parts, safety buffer Flexibility to adjust to other mixtures to be separated
Discontinuous
Simpler Less Less Easier Possible with less expense Less Less
Higher Better
8
1 Basic Concepts
Continuous Operation : In continuous operation the mixture being separated is continuously fed to the separation device. It is continuously separated into two or more fractions, which are continuously withdrawn from the separation device. An ideal binary mixture can be separated into almost pure components in a separation column operated continuously with countercurrent flow. To separate a mixture of k components, k - 1 columns connected in series are needed. Discontinuous Operation: With discontinuous operation the mixture being separated is charged to the separation device. During a time period, the “batch period”, the mixture is separated mainly into two fractions of defined different compositions. One fraction is continuously withdrawn from the separation device, while the other remains in the device and is withdrawn at the end of the batch time. Discontinuously operated processes mainly in one stage - allow incomplete separation of a mixture; the obtained fractions are treated in subsequent stages (this is the case for multistage discontinuous separation). Alternating Operation : If in a separation apparatus after a loading process (separation of a mixture) an unloading process (the regeneration of a substance aiding separation) is required, at least two sets of equipment are operated alternately. Therefore, steady separation of the mixture is guaranteed. In the case of the adsorption of a substance from a gas phase in a container adsorber (see Chapter 4), for example, a solid
[
f s u m of amount) entering the system (transport)
+
[
adsorbent adsorbes adsorbate (key component in the gas phase). Adsorption continues to an upper loading limit. After the maximum load has been reached in the first adsorber, operation is switched to the second adsorber. The loaded adsorber is then regenerated by dampening, drying and cooling. After the regeneration cycle is finished, the adsorber is ready for loading again.
1.3 Mass Balance, Energy Balance, Exergy Balance In general, the first step in the design of a separation plant is the balancing of individual apparatuses and parts of the plant. Balances are done with respect to energy and mass fluxes, in connection with a schematic representation of the process (flow diagram).
1.3.1 Mass, Energy and Heat Balances The balancing of chemical engineering systems follows the sequence listed in Fig. 1-6. Of the variables listed for process design, mass and energy (usually in the form of heat, enthalpy, and exergy) are of most interest. These variables may also be used for planning, evaluation of systems, analysis, and synthesis. Based on the laws of conservation of mass, energy and momentum, balance equations are set up [1.1] - [1.5]. For a general open system
f sum of amount ) generated in = the system (transformation)
1
f s u m of amount) leaving the system (transport)
1 f
-k
increase of \ mass stored in the system (accumulation)
1.3 Mass Balance, Energy Balance, Exergy Balance
9
Determination of the balance area of the system by defining real or imaginary boundaries (unit complex, unit, part of the unit, individual apparatus, part of an apparatus, volume element)
Determination of the balance size of measured or valuable system properties (total mass, component mass, atomic mass; state variables such as enthalpy, entropy; momentum; cost)
Process description Flow sheets
4l
Formulation of balance eauation to obtain a list of all balance variables of interest in a quantitative form
1
+
~
Solution of the balance equations
I Optimization
Environmental requirements Safety provision requirements Safety requirements
Dertermination of process --* control equipment
+
Precalculation and economical calculations
Fig. 1-6. Balancing of processes (schematic simplification of the concepts) [1.1].
Depending on the problem or task a integral or differential balance equation is generated : 0
Differential, to investigate a process in a differential volume element or at an interfacial surface element
0
Integral to determine the streams entering and leaving the system
Differential balance equations lead to velocity, concentration, and temperature profiles in the system, or at the boundary surfaces, after solving the corresponding differential equation system with suitable bound-
10
1 Basic Concepts
ary conditions. Integral balance equations give a basis for evaluation of the total system with respect to energy and mass. Results of integral balance equations are often presented in a table or in a flowchart (product and energy scheme, mass and heat flowchart, etc.).
The material balance for an individual component k is
c i
-
-
m i j , * Wi,k,a
c mi,, i
*
m , k =
wi,k,w
+ mS,k
(1-4)
where Mass Balance
mi,a
Material balances (mass or quantity balances) can be general or total material balances over the complete system and must be distinguished from material balances for individual mixture components (Fig. 1-7). Using the terms in Fig. 1-7, for an open system the general integral balance equation is
wi, k, a 9 wi, k, o
c mi,a+ i
mQ =
c i
+ m,
(1-3)
In steady-state operation (continuous feed and withdrawal of material without start up and shut down procedures) the accumulation terms mQ and m, are not required.
m i ,w
rfzp ms, I j z Q , k ,
mass flux i (a feed, o product) mass fraction of component k in stream i ms,k intensity of sources (Q) and sinks (S)inside the balance area generally with respect to component k
m Q , k and m $ k take, for example, chemical reactions involving k into consideration. If k is a reactant in j single reactions taking place simultaneously in the balance area, for steady-state operation,
m l , a ~W l . k , a , '1.a
BA
-BB
-
Fig. 1-7. Balance scheme to derive the balance equations. BB Balance boundary BA Balance area
1.3 Mass Balance, Energy Balance, Exergy Balance
11
the balance area and uj,k is the stoichiometric ratio of k in the reaction j . dnk Instead of mass and mass fractions, it is 'j = (1-6) convenient to use another kind of substance Vj,k * I/. dt flow or concentration units to set up mateis the equivalent reaction rate of the reac- rial balance equations. Useful conversion tion j , V is the volume of reaction mass in relationships are given in Table 1.4. where
Table 1-4. Conversion between concentration scales of a mixture component.
Mass fraction wi
Molar fraction
Partial density
xi
ei
Mole ratio of component i ') x m ,1
Mass fraction m;
wi
Molar fraction
ni x . = __
C.i i
c-M; ei
e
i
Partial density
Wi'
e
ei
xi * Mi M -
e
Molar ratio of component i in the inert or carrier phase
I) Reference is the mass of the remaining mixture excluding component i, expressed as carrier mass m 1
c mi
2,
')
i
Density e = - @ = L e i V i n. Molar ratio carrier load X i = n1
Used variables: mi mass of mixture component i number of moles of mixture component i
ni
M =
_f
c xi Mi mixture mean molar mass of the i
9
V
total volume of the mixture
ml
mass of reference component 1
c mi total mass of the mixture c total number of moles of the mixture i
i
ni
12
1 Basic Concepts
For a complete mass balance over a balance area at steady-state, in which only I physical transformation of matter occurs, an equilibrium system consisting of Eq. I (1-3) and k - 1 equations (1-4) for k active components over the balance area, must be where set up. Due to the valid stoichiometric con- hi,,, hi,, dition, for the individual phases, the kth equation (1-4) gives Q cwk=l
(1-7)
k
Ways to formulate material balances for differential volume elements as the balance area, and methods to solve this differential equation system may be found in, for example [1.1] and [1.3]. Energy and Heat Balances
c Ei,a+ EQ i
= E,
+ c Ei,, + Es
(1-8)
i
where E . . E,,E,
Ei,, EpEs
.
QQ,Qs
specific enthalpy of mass flux ki entering and leaving additional heat flow supplied heat flow lost intensity of heat sources (Q) and sinks ( S ) in the balance area
QQ,Qs account for the exothermic and endothermic nature of phase transformations and chemical reactions under steady-state conditions. If, for example, over the balance area, chemical reactions involving component k occur QQ- Qs = - v * h/r,
Based on the law of conservation of energy, an energy balance analogous to the material balance may be set up for any bounded balance area. Using the terms from Fig. 1-7 for the energetic and materialistic open system, the energy balance becomes Ea+
Qu
(1-9)
includes all energy forms, such as potential and kinetic energy, binding energy, heat energy flow through the system boundary, supplied (a), or removed (0) energy supplied or removed by the mass flux mi intensity of the heat sources or sinks inside the balance area
In process design, a heat balance is often sufficient. From the first law of thermodynamics, for the balance area in Fig. 1-7, the mthalpy or heat balance equation is
- c rj - vj, - hhR, = j
=
- u k Ai;,
*
*
Wi,k,a
(1-10)
i
where AhR,j reaction enthalpy for component k in reactionj AhR the total reaction enthalpy for component k (ALR> 0 for endothermic reactions, Ah;, < 0 for exothermic reaction) U, total conversion of k hfk molar mass of k
1.3.2 Exergy Balance When the economics of plants are considered, the cost of raising primary energy causes a domination of energy costs over investment costs. The optimum cost of a process corresponds to minimum use of energy. Therefore, it is necessary to investigate processes which have high energy consumption in order to optimize energy usage.
1.3 Mass Balance, Energy Balance, Exergy Balance
To evaluate the energy utilization, energetic and exergetic process analyses are used. Since exergetidanergetic flowcharts show local internal and external irreversibilities, the locations and quantities of heat losses may be detected, leading to thermodynamic optimization from the consideration of process energy improvements. According to Fig. 1-7 the exergy balance equation, for a steady-state open system, under isobaric conditions, is
=
GE,w+
c
___
dQ,
+
+
G,,w AG, i
(1-11)
where exergy of input Ea and output E, energy fluxes Gj,a,Gi,w exergy of input Yizi,a and output m;,w mass fluxes Qm heat flow supplied G E , a , GE,@
G; = Yiz; * [(hi - h,) - T, . (s; - s,)]
entropy temperature, enthalpy and entropy, referred to surrounding conditions or to a particular system state reference exergy losses due to irreversibilities
AG,
AG,
(1-12)
=
T, * AS,
(1-13)
More information on energetic and exergetic analysis can be found in the literature [1.6- 1.91. The exergetic analysis of a rectification unit is given as an example in [1.10].
13
1.3.3 Calculation of Balance Equations Calculation of mass, energy and exergy balances for the total separation plant are usually done sequentially from apparatus to apparatus. They are occasionally carried out simultaneously by an iterative method, considering the corresponding equation system for the total separation process. In this case, it is necessary to develop a calculation flowchart with coded interface and ramification. The process structure is conveniently presented graphically. After mathematical formulation of the process, the number and values of the independent system variables are determined. Finally, the balance equations are solved sequentially. To calculate the balance data using a computer [1.1, 1.11-1.161 a flexible programming system is required. The main program controls and organizes by assigning priorities to the calculations via references to the corresponding process steps, mass fluxes, and computation parameters. It organizes the intermediate storage of calculated mass fluxes and state variables, and transfers these as input variables to the following stages. Initial variables for each stage are calculated in subroutines, based on stage specific theoretical and empirical models. By including the graphical methods in the balance, economic optimization by, for example, minimizing the energy flow [1.17] or optimization with respect to complete safe operation of the process can be performed [1.18]. It is often convenient to present the results for a balance over a single piece of equipment, a process unit or total processes, and, if necessary, for combined processes. They can be quickly understood in clearly arranged flowcharts (SANKEYdiagram).
14
1 Basic Concepts
1.4 Phase Equilibria 1.4.1 Basic Concepts With thermal separation of mixtures, usually in open systems, an exchange of heat and mass occurs at the phase interface. When phase equilibrium is reached, no further heat or mass transfer takes place. Basic concepts and equations are now introduced [1.20], in order to describe phase equilibria:
- Thermodynamic Systems: Any quantity
-
-
-
-
-
-
of matter that is separated from its surroundings by rigid or imaginary boundaries and whose properties may be unequivocally and completely described by thermodynamic, macroscopic state variables. Open Systems: Thermodynamic systems in which matter and/or energy may transfer with the surroundings, through the boundaries. Closed Systems: Thermodynamic systems in which only energy may be exchanged with the surroundings. The system is closed, containing constant mass, but is not isolated. Adiabatic (thermally) Isolated Systems: Thermodynamic systems in which no heat or mass transfer with the surroundings takes place, although exchange of energy in other forms, e.g., shaft work, is possible. Closed (isolated) Systems: Thermodynamic systems in which no exchange of energy or matter occurs with the surroundings. Homogeneous Systems: Single phase systems with identical macroscopic properties in each volume element. Heterogeneous Systems: Two or multiphase systems with at least one abrupt change in macroscopic properties at the boundar(y/ies) between the phases.
Phase: A physically homogeneous region of a system, contained within a phase boundary. Each volume element in one phase has identical macroscopic properties. The change of state variables, i. e., those not dependent on mass, such as temperature, pressure, composition, etc., are continuous and time independent (without, for example, a step change). - Dispersed (discontinuous) Phase: A phase consisting of homogeneous matter, which is scattered in space, and dispersed in the continuum of the other mainly coherent phase. - Continuous Phase: A uniform, nondispersed phase. - Free (Gibbs free) Enthalpy (thermodynamicpotential), G : The relationship between the enthalpy H, entropy S and internal energy U is defined as
-
G=H-T.S or G = U + p . V-T-S
(1-14)
Therefore, the Gibbs free enthalpy is that part of the enthalpy which, at a reversible change of state, can be converted into other types of energy. For a closed system (constant mass or for a pure phase), the total differential for the free enthalpy d G is dG =
(z)p (g) - dT+
T
.dp
(1-15)
and, from Eq. (1-14) dG=dU+p*dV+ V*dp-
T-dS-S. dT
(1-16)
For a reversible change of state it follows from the first law of thermodynamics that: d U -tp . dV = T . dS
(1-17)
1.4 Phase Equilibria
(dG), = ,ul dn,
and therefore dG= V-dp-S-dT
(1-18)
With constant mass, the free enthalpy is only a function of pressure and temperature. Comparison of the coefficients in Eq. (1-15) and (1-18) gives:
(g)p= -S
and
(5)
=
V (1-19)
T
For an open system, the free enthalpy is not only a function of pressure and temperature, but also a function of the amount of mass n of each individual component. G = G(T,p,n1,n2,...)
(1-20)
The change of free enthalpy is therefore given by
.dnl +
an2 p,T,n,,n3 ... + (E)
By integrating this equation under the assumption of constant pressure and temperature, the free enthalpy of the system shows a definite dependency on the composition and chemical potential of the components of the mixed phases in the system. G = p l . n , + p 2 - n 2 +...
(1-24)
For a change of chemical potential it follows from Eq. (1-24) that (dc),,, = n1 dp,
+ n2 - dp2 + . . .
(1-25)
and with the requirement of dG = 0 at equilibrium,
n, . dp, + n2 - dp,
+ . .. = 0
(1-26)
or
This is the Gibbs-Duhem equation in two different forms and is of fundamental significance in proving the consistency of precalculated or experimentally determined equilibrium data.
. dn2 + . . .
hence dG = - S . d T + V . d p
(1-23)
(1-27)
d G = - S * d T + Vedp-t p. T , n 2 . . .
+ p 2 . dn, + . . .
15
+ (1-21)
For individual components the isothermal and isobaric change of state is
or by introducing the chemical potential p of the individual components, we can write
Chemical Potential (partial molar free enthaipy): An expression for the change of the free enthalpy of a system, which consists of a mixture, if 1 mole of the mixture component i is added to a n infinite amount of the mixture. Hence,
(1-28)
In a mixture the chemical potential of a component i can be expressed as
16
1 Basic Concepts
where poi is the standard chemical potential, i. e., the chemical potential of the component i at the standard state. For any component of a gas mixture, the standard state is the same as for the standard state of a pure gas component at the temperature and pressure of the system. For any component of a liquid mixture, the standard state is the same as the standard state of a pure liquid component at the temperature and pressure of the mixture. The partial molar free mixing enthalpy A& is
A p i = i ? . T . ln(y,.xi)
(1-30)
-
where y i xi is the activity and yi is the activity coefficient of the component i of the mixture. The activity coefficient here is defined as lim yi = 1
(1-31)
X,'l
Equilibrium: A system is at equilibrium if, in fixed surrounding conditions, no change on a macroscopic scale occurs in the system. Therefore, there is no tendency toward an exchange of matter and energy between the phases. Exchanges of matter and energy between phase boundar(y/ies) of the heterogeneous system are reversible. The equilibrium between the phases (the phase equilibrium) is sensitive to changes in the surrounding conditions. Compositions of the phases at the desired phase equilibrium are independent of time, the amount of material and the direction from which equilibrium is reached. Equilibrium Conditions: Equilibrium between the phases of a heterogeneous system is reached if the following conditions are valid: no local pressure differences exist with respect to time and space (mechanical equilibrium) dp = 0 therefore p1 = prl = . . .
(1-32)
and no local temperature difference exists with respect to time and space (thermal equilibrium) d T = 0 therefore
T, = T,, = . . .
(1-33)
These two conditions meet the requirements to describe an isolated system in a state of equilibrium. The system is stable, when the system entropy reaches a maximum, hence dS = 0
(1-34)
The equilibrium condition for a closed system may be derived from the fact that any infinitesimal change of state at equilibrium is reversible. For example, we have dU=dQ+dW=T*dS-p.dV
(1-35)
or
d H = T -d S i - V* dp
(1-36)
The equilibrium conditions for an adiabatic and isochoric change of state are given by, (dU)v,, = 0
(1-37)
for the adiabatic and isobaric change of state,
(CW),,, =0
(1-38)
for the isothermal and isochoric change of state,
(W" ,=0
(1-39)
and for the isothermal and isobaric change of state,
The internal energy U, the enthalpy H , the free internal energy F, and the free enthalpy G , must be at a minimum for a system to be at equilibrium. This is comparable to a me-
1.4 Phase Equilibria
chanical system where the potential energy is a minimum at equilibrium. Combining Eq. (1-21) and (1-28) gives dG= -S.dT+ V-dp+zpi.dni
(1-41)
The equilibrium condition for an isobaric and isothermal change of state for an open system is (dG),,
=
-
p i dni = 0
(1-42)
At equilibrium, mass transfer between the phases of a system is reversible and a material balance requires (1-43)
dn,,, = -dni,,, and so it follows that p r. , = ~ p. I , I I - Pi,III
=
. ..
(1-44)
Therefore, phase equilibrium is reached when the chemical potential of each chemical species in the system is the same in all phases. For the equilibrium of two phases I and 11 using Eq, (1-291,(1-30) and (1-44) it follows that
Rearrangement defines the “distribution coefficient” (%equilibrium constant’? K:, giving
xi,II= KT * xi,,
(1-46)
and the relationship (1-47) with . - fi or,II . APoi = P or,,
(1-48)
17
Knowledge of the distribution coefficient or the equilibrium relationship = f(xiJ as a function of pressure and temperature is essential for the design of thermal separation processes. The relationship is found in three steps: - Step 1: Evaluation of the activity coefficient yi Of each component in each phase at a different temperature, pressure and composition, measured experimentally or determined from an appropriate correlation. - Step 2 : Determination of the differences in the chemical Potential APoi of each component under the same conditions (see Step 1). - Step 3: Evaluation of KT or the equilibrium relationship x ~ ,=~f ,(xi,,).
1.4.1.1 General Differential Equation for the Equilibrium Between TWO Phases
The criterion for the equilibrium of two phases is p i , , = pi,II or dp,,, - dpi,,, = 0. The general differential equation for the equilibrium of two phases I and I1 may be written:
(1-49) This relationship links the state variables of pressure p , temperature T and molar fraction xi of the component i in both phases I and 11. The enthalpy A ~ Z ~ ,and , , ~ , the volume AK,I,II are partial molar phase transfer quantities. The partial molar quantities of a binary mixture may be determined by graphical method if the appropriate quantities are known as a function of the mixture composition (Fig. 1-8).
18
1 Basic Concepts
q P
vl,p&,p
v
X
Example:
-
Partial molar volume of both mixture components Molar fraction of component 1 Mixture volume
-.Ah;,,,
R *T
R - T2
(1-53)
or dP dT
-
The molar volume Vof a real fluid mixture is
__ -
V = x l . I / , , + x , . T -/ 2 , p = x 1 -. 1 / , p +
where
+ (1 - Xl)
(1-50)
G,p
where q,, and 1/2,p are partial molar volumes of components 1 and 2 of the mixture. The mole fraction x1 of component 1 varies between the limits 0 and 1.
-
q,#=v-x,.=
av
(1-51)
ax1
V + (1 - x,) .
aV ~
ax,
Ah1.1, T -A4.11
Ahi,ii = Ah,,g
AI/,Il =
dp/dT
-
VI
(1-54)
the molar evaporation enthalpy of the components at a given p and T the differences in the molar volumes of the saturated vapor and liquid of the system components, at a given p and T the slope of the vaporpressure curve
(1-52)
In Fig. 1-8 the measured volume of the mixture V is plotted against the molar fraction xl, A tangent from point A of the v(x,)curve gives the points D and E. Points B
1.4.1.2 The Gibbs Phase Rule The Gibbs phase rule describes how many state variables of a muitiphase system may vary independently (degrees of freedom of
19
1.4 Phase Equilibria
the system) without disturbing the systems equilibrium :
P+F=K+2
(1-55)
where
F the degrees of freedom of the system at equilibrium (chosen from the state variables pressure, temperature, concentration of each component in each phase); number of variables describing the state of the system which may be varied independently without disturbing the system equilibrium P number of phases of the heterogeneous system (one gas phase, one or more liquid phases depending on the miscibility of the components, one - at mixed crystal forming - or several solid phases according the number of crystal types) K number of components; the minimum number of components of the system forming the phases which must be independently declared
F = 0 invariant system F = 1 monovariant system F = 2 divariant system, etc. The phase rule is important for thermal separation processes as, if certain process parameters are choosen, it establishes which state variables are cogently fixed at an arbitrarily adjusted phase equilibrium (Table 1-5).
1.4.2 Liquid-Liquid Equilibrium 1.4.2.1 The Nernst Distribution Law
For a dissolved substance S in two nonideal, immiscible, liquid solvents such as T and L at constant pressure and temperature the distribution according to Eq. (1-45) is
pas,, + R . T.ha,,,
=
+ . T . lnczs,II
(1-56)
= pos,II R
where as is the activity of S. For phase equilibrium of two liquid phases, the standard state of both phases is the same (normalized to pure liquid S). It follows that POSJ
(1-57)
= POS,II
and therefore including Eq. (1-56) as,1 = as,II
or
YS,I * *S,I = YSJI
. XS,H
(1-58)
To describe the concentration dependance of the activity coefficients Y , , ~and Y , , ~ ~the , computational methods shown in Table 1-8 may be used, for example the NRTL or UNIQUAC methods. For a substance S distributed in phase I (raffinate R) and phase I1 (extract E) with a small concentration of cS,, and c ~ , the ~, Nernst Distribution Law is an approximation given by
A substance is distributed between two liquid phases so that the same concentration ratio appears in both phases. It is independent of the total amount of phases at constant pressure, constant temperature and similar molecular forms in each phase. For separation by liquid-liquid extraction, the Nernst distribution law describes the equilibrium between raffinate and extract phases if the carrier component T and solvent component L are not miscible (see Chapter 6). Table 1-6 shows additional variations of the Nernst distribution law.
5. Selected thermal separation processes. Examples of the Gibb’s phase rule. separation Phases
on o f binary
Number Type 2 1, g
2
quid n
2
orption
2
orption
3
on of le binary , carrier on of one nt
21 Ig
1, g
s, g
1, 1
Components Number Type 2 Miscible liquids
2
3
3
3
Immiscible liquids
Degrees of freedom 2
1
3
Carrier Key component Solvent
3
Inert gas Adsorbate Adsorbent
3
Inert gas Absorbate Solvent
Process parameters Pressure, concentration o f one component, e.g., in the liquid phase Pressure
Consequences for the remai variables describing the syst explanations Concentration of the second nent in the liquid phase, the tration of both components vapor phase, and the temper all fixed (boiling point diagr Concentrations and tempera strongly fixed, no simple se possible (boiling point diagr
If the concentration of the ponent in the raffinate rema concentration of the extract fixed (distribution equilibriu
Pressure, temperature, concentration of the key component in the liquid phase
Fixed loading of the compo adsorbed in the absorbent ( tion isotherm)
Pressure, temperature, partial pressure o f the absorbate in the gas phase
Concentration of absorbate liquid phase is fixed (absorp isotherm)
Pressure, temperature, partial pressure of the absorbate in the gas phase
. (continued) separation Phases Number Type
Components Number Type
Degrees of freedom
Process parameters
Consequences for the remain variables describing the syste explanations
Components without mixed crystals load
ion
Dissolved substance Solvent
ration and m llization
Concentration of the dissolv substance fixed by the solubi curve
Pressure temperature
Dissolved substance Solvent
zation from n ooling llization
Solid phase concentration an temperature are fixed (solidu liquidus lines)
Pressure, concentration of one component in the liquid phase
Components forming a mixed crystal
ation from
Moisture content of the prod Pressure, temfixed (sorption isotherm, 1st perature, partial pressure of the period) moisture in the gas
Dry product Moisture Dry gas
pic product ng period)
Dry product Moisture Dry gas
on drying groscopic by hot gas g period)
Pressure temperature
Pressure
Temperature
Fixed saturation loading of t product with moisture (sorpt isotherm and 2nd drying per
Boiling point temperature of saturated solution is strongly by the pressure (vapor-press curve of the saturated soluti Temperature determines the pressure of the sublimable c ponents, corresponding to th sublimation pressure curve
tions: s solid phase (solid), 1 liquid phase (liquid), g gas phase (gas).
22
1 Basic Concepts
Table 1-6. Additional formulae of the Nernst distribution law. Correlations and conversion relationships for the distribution coefficient K . 0
Mole fractions x, y are used as the concentration scales for the distributed substances S Y x
-=
0
K?(tP)
Mass fractions w substance S wS. E ~
wS, R 0
= K:(B)
~ and, w~ ~ are, used ~ as the concentration scales for the distributed
(1-61)
.
Molar ratios X , Y are used as the concentration scales for the distributed substance S Y X
- = K$(B) 0
(1-60)
.
(1-62)
.
Relationship between the distribution coefficient
(1-63) 0
Correlation for the distribution coefficient K: [1.21 K$
A , + A z . wS,R
(1-64)
+ A , . w ~ , +R A,. w;,R
Specific substance constants for Eq. (1-64)at tP = 25 "C. System
I
I1 I11
A,
A2
7.1957 0 1.1888 0 1.5569 0
A3
A4
-1022281.0 50722.0 -3.3775 2.0970 - 3.6840 -0.7462
System examples : I Water/toluene/aniline [1.21] 11 Water/benzol/dioxane 111 Watedmethyl isobutyl ketone (4-methyl-2-pentanone)/acetone
Nomenclature used in Eqs. (1-59) to (1-64):
VE
volume of the extract phase nS,R
CS,E = __ nS'E
vE
'S,E
molar concentration of the substance S in the extract phase number of moles of S in the extract phase
C S , R = __ 'R
molar concentration of S in the raffinate phase
IIS,R
number of moles of S in the raffinate phase
VR
volume of the raffinate phase
1.4 Phase Equilibria
23
mole fraction of the substance S i n the raffinate phase mole fraction of the substance S in the extract phase number of moles of extract or raffinate phase weight fraction of S in the extract phase weight fraction of S in the raffinate phase mass of S in extract or raffinate phase mass of extract or raffinate phase mole ratio of S in the raffinate phase number of moles of carrier mole ratio S in the extract phase number of moles of the solvent molar mass of extract and raffinate phase density of extract or raffinate phase A schematic distribution diagram for liquid-liquid extraction is shown in Fig. 1-9. The Y, X distribution diagram is essential for the design of separation apparatus.
1.4.2.2 Representation of Liquid-Liquid Phase Equilibrium
Industrial extraction process systems with three or four liquid components are common. In addition to a vapor phase two or
X-
Fig. 1-9. Schematic presentation of the liquidliquid phase equilibrium, the loading diagram. EC I Equilibrium curve with a constant distribution coefficient EC 11, Equilibrium curve for a concentrationEC I11 dependent distribution coefficient P Plait point Y = X , 45" line AL Mole ratio of S in the extract phase Y Mole ratio of S in the raffinate phase X
three pairs of liquid phases are possible. Now equilibrium of liquid-liquid phases for ternary systems will be discussed in more detail for cases where partial miscibility of carrier liquid and solvent cannot be neglected, and presentation by means of an equilibrium diagram similar to Fig. 1-9 is insufficient. A practical way at constant temperature and pressure to graphically describe the data of phase equilibrium of a ternary system uses an equilateral triangle (Gibbs' triangle). Figure 1-10 shows an equilateral triangle representing a three component mixture. Each apex of the triangle corresponds to one of the pure components T L and S. Any point on the sides TS, TL and LS char-
24
1 Basic Concepts XTXL-
0 0
(1-65)
XS‘l
S
In the case of a liquid-liquid extraction operation, the solvent L must be chosen such that it is very miscible with the solute of the original binary mixture T/S yet immiscible with the carrier liquid 7: Simple extraction processes for a common type of ternary mixture with components T, L, and S are presented in Fig. 1-11. A vapor phase and two liquid phases (in the two phase region) coexist in the heterogeneous system. S is completely soluble in T and L. In the area between A and B, T and L are insoluble in each other. The binary mixture of A and B, x1.l XT= 0 according to point M, will separate into two XL: 0 XLXL- 1 liquid phases of compositions A and B corxs.0 XS‘ 0 XT responding to the mass ratio m/MB. Until for example, the substance S is Fig. 1-10. Equilateral triangle (Gibb’s triangle) for the representation of ternary mixtures. added isothermally to the binary mixture, A Binary mixture state point with molar according to point M, the ratio m M / B fractions of x, = 0.7 and xL = 0.3 will change if the liquid phase with the B,L State points of two ternary mixtures highest concentration of S disappears. Now M State point of a ternary mixture the ternary system is homogeneous. This is resulting from the mixing of B and C xL,xT,xsMolar fractions of L, T, and S in the true at point M’, the saturation point. Similarly, this is valid for points P, P’ and Q, Q‘. ternary mixture at state point M Curve A, M , P’, Q’, B is the line connecting the saturation points or the solubility curve, solubility isotherm or binodal curve acterizes a binary mixture. Point A, for ex- (Fig. 1-11). ample, is a two component mixture with a Below the binodal curve the ternary syscomposition of 0.7 parts of T and 0.3 parts tem is heterogeneous; elsewhere it is a hoof L. Any point within the triangle repre- mogeneous solution of one liquid phase. A sents the composition of a ternary mixture, mixture, such as R in Fig. 1-11 b, below the for example B, C and M; the graphical binodal curve will form two conjugate liqmethod to derive the fractions xT, x, and uid phases, represented by points C and D x, in Fig. 1-10 will now be explained in on the binodal curve. The connecting line more detail. between C and D is the tie line and deIf n, kmol of the ternary mixture at scribes the state of the phase equilibrium of point B is added to n2 kmol of the ternary the conjugate liquid phases. The more submixture at point C, the composition of the stance S the conjugate liquid phases connew mixture lies on the line This is tain, the shorter the tie lines. The equilibshown by means of a material balance. The rium points C and D move toward each location of the mixing point M follows the other on the binodal curve to finally reach lever, or mixture, rule such that the “critical point” P, the plait point.
-
m.
1.4 Phase Equilibria
A 9 z const
a)
b)
25
S=const
A
o'/ I
TA
i
Q
I
i
I
P
\
\
M
BL
Definition of the binodal curve [binode) A Q' P' M' B Binodal curve
Fig. 1-11. Representation of a liquid-liquidphase equilibrium in an equilateral triangle. a) Definition of the binodal curve (binode)
AQ'P'M'B Binodal curve b) Interpolation procedure to determine the tie lines CPD ... Binodal curve CD Tie line PK, K,K3 Conjugation line
If, for example, several tie lines are found experimentally, additional tie lines may be constructed via the interpolation procedure, linking conjugate liquid phases in phase equilibrium, shown in Fig. 1-11b (for additional interpolation methods, see [6.1]). The conjugation line connects the intersecting points that are generated by the lines parallel to the triangle axes TS or E. The starting point occurs at the intersection of the tie lines and the binodal curve. The value of K* for horizontal lines is unity, corresponding to the Nernst Distribution Law and according to Eqs. (1-59)-(1-63). For tie lines inclined to the horizontal the coefficient values are K* > 1 or K* < 1. It is uncommon in extraction processes to find ternary systems of T, L and S where
I Interpolation procedure t o determine the tie lines C P D . . . Binodal curve CD Tie line P K, K, K, Conjugation line
two partially immiscible substance pairs exhibit a miscibility gap at equilibrium as shown in Fig. 1-12. To simplify the procedure of solving extraction problems, equilibrium curves may be transposed from triangular coordinates to rectangular coordinates [0.1, vol. 2, p. 5461. Figure 1-13 shows different graphical methods used to represent the distribution equilibrium. An increase in temperature usually leads to an increase in mutual solubility. The area of heterogeneity under the binodal curve decreases and the tie lines may also change their slopes. This is shown schematically for a liquid-liquid phase equilibrium in Fig. 1-14. The influence of pressure is negligible with regard to technical accuracy.
26
1 Basic Concepts
Closed system with miscibility gap between L and S
Open system with miscibility gap between L and S
Open system with miscibility gap between T and S
System with decomposition of mixture into three phases in region I11
Fig. 1-12. Phase equilibrium of ternary systems with two partially inmiscible substance pairs. I One phase region
I1 Two phase region
111 Three phase region Type A Closed system with miscibility gap between L and S Type B Open system with miscibility gap between L and S Type C Open system with miscibility gap between T and S Type D System with mixture decomposition into three phases in region I11
The liquid-liquid equilibrium data are determined by a straight forward experimental procedure [0.1, vol. 2, p. 5561 or [6.2]. A heterogeneous ternary system is used in the analysis to obtain the tie lines. After intensive mixing, the system is separated isothermally into two conjugate
phases. Both phases are weighed and analyzed and the state points entered on the Cibbs phase diagram. The lever rule for the phases (Eq. 1-65) can be used as a control method. The mixture point R, and the state points of the two conjugate phases C and D form a straight line; the tie line (Fig. 1-11).
1.4 Phase Equilibria al
I
S
27
I
L
X--b
t Y
I
L
Fig. 1-13. Phase equilibrium for a solvent extraction process. a) Closed system of two partially miscible liquids T and L b) Open system of three liquids, T/L and L/S partially miscible R ,,R,, R3 Raffinate phase E l , E2,E3 Extract phase K , , K 2 ,K3 Tie lines BC Binodal curve EC Equilibrium curve P Plait point at K* = 1 Mole fraction of the key component in the raffinate and extract phases x, Y Mole ratio of the key component in the carrier and the solvent X, Y 45" degree line used to transfer equilibrium concentration points x =y
The ratio of the distances CR/m must correspond to the ratio of the mass fractions of the conjugate phases. To determine the binodal curve by the tilration method, the third component must be added slowly to either one of the homogeneous binary mixture, T/S or L / S . If the binodal curve is reached, the mixture becomes cloudy. The analysis gives one point on the binodal curve (point E in Fig. 1-11).
Binodal curves found experimentally may be described by empirical correlations (parabolic approach for system of type C and Hlavaty approach for system of type D in Fig. 1-12 [1.21, 1.221). In the case of a low concentration of S distributed in the raffinate and extract phase, Eq. (1-64) can be used to calculate the distribution coefficient. The activity coefficient in Eq. (1-58) should be calculated according to Table 1-8.
28
1 Basic Concepts 5
S
1
P
L
Fig. 1-14. Temperature effect on ternary liquid equilibria [0.8]. P Plait point T, L, S Components
Data for liquid-liquid equilibria can be found in [1.23-1.301.
1.4.3 Vapor-Liquid Equilibrium 1.4.3.1 One Component Systems The phases of a one component system are usually presented on a p,19diagram. Figure 1-15 shows a p , I9 diagram for water. The diagram is divided into three areas, the solid phase (ice), the liquid phase (water), and the vapor phase (steam). At a higher pressure, due to the existence of additional solid phases, further regions are added (polymorphic). Inside each area the system is divariant; pressure and temperature may be varied independently. The lines separating the regions are the melting or fusion curve, the vaporization
curve and the sublimation curve. These lines generally connect points between the phases at which each of the two coexisting phases are in equilibrium. According to the Gibbs phase rule, a one component system with two phases is monovariant at equilibrium. If the pressure p is changed, then, according to the saturation pressure, the temperature B must also change. The pressure p and temperature 19 are related by the corresponding equilibrium curve. The differential Eq. (1-49) gives the relationship between the two phases at equilibrium. A brief review of the equilibrium conditions, according to Eq. (1-40) gives the following: dgsystem at equilibrium = dgsystem at equilibrium = dgI - dgII =
(1-66)
29
1.4 Phase Equilibria
t I
P 218 Ibarl
From the latent enthalpy of phase transition from I + I I follows
IMC
~
Ah
A S = __
0.987
0.00611
(1-70)
T
Substituting Eq. (1-69), it follows that dp - A h d T T. A V
~
(1-71)
u 0.0075 100
31oc1
37L
Fig. 1-15. p , &Diagram of water. TP Triple point (coexistence of three phases, invariant system) MC Melting or fusion curve (coexistence of solid phase and liquid phase at equilibrium, monovariant system) VC Vaporization curve (coexistence of liquid phase and gas phase (steam) at equilibrium, monovariant system) SC Sublimation curve (coexistence of solid phase and gas phase at equilibrium, monovariant system) C P Critical point p Pressure B Temperature
where dg,, dg,, are the change of free enthalpy in phases I and 11. Substituting into Eq. (1-18), dg1= - S , . d T + q . d p = d g I I = - -311
*
d T + 61. dp
(1-68)
The slope dp/dT of the equilibrium curve between two coexisting phases is therefore
(1-69) where A i is the difference in the molar entropies, and A the difference in molar volumes of phases I and 11.
v
This is the common form of the ClausiusClapeyron equation, also known as the Clapeyron equation. The equation is generally valid and describes all forms of two phase equilibria for one component systems. In the following text, vapor-liquid equilibrium will be discussed. The equilibrium curve is the vaporization line beginning at the triple point and ending at the critical point where the liquid and gas phase are “identical”. Substituting the molar vaporization enthalpy Ah,,g, at the equilibrium temperature T, and the difference of the molar volumes A V of vapor (g) and liquid (I) (TI)into Eq. (1-71), the slope of the vaporization curve is
(6,)
dp
d~
G
-
T.
g
(q,- q)
(1-72)
At a certain distance from the critical point, the molar volume becomes negligible in comparison with GI. Furthermore, if the vapor phase behaves like an ideal gas, may be substituted by RT/p. Eq. (1-72) therefore becomes
q
6,
dlnp ~
dT
Ahl,g %-
R - T2
(1-73)
Upon integration, the following approximation for the vapor-pressure curve is then found :
30
1 Basic Concepts
l n p = - _'his' .R
T
+ const
(1-74)
If Q GI, a plot of Eq. (1-74) as l n p against l/T yields a straight line. This implies the assumption of ideal behavior for the vapor and a vaporization enthalpy independent of temperature and pressure. A better correlation for vapor pressure is as presented by ANTOINE
cal temperature of the components in the mixture. In absorption processes, the temperature is usually higher than the critical temperature of the dissolved gas components. Nevertheless, distillation and absorption processes may be discussed together with respect to relevant phase equilibria. With the equilibrium condition for two phases expressed by Eq. (1-45) or derived from Eq. (1-49), the general equation for gas-liquid phase equilibrium is
(1-75) A, B, and Care substance related constants. Additional methods for computing vapor pressure are listed in [1.58]. If two points on the vapor pressure curve are known, such a s p , , and p z , T,, the vaporization enthalpy may be estimated using the integral form of Eq. (1-73)
1
*
(&
-
":T>
. dp]
P
(1-77)
where mole fraction of component i in the vapor phase pressure of the system at equilibrium p T temperature of the system at equilibrium I? the universal gas constant q,G partial molar volume of component i at pressure p and temperature T yi activity coefficient of i in the liquid phase (see Eq. (1-31)) xi mole fraction of component i in the liquid phase Q L molar volume of liquid component i at temperature T and saturated vapor pressure poi f , fugacity of the pure substance i at temperature T and the corresponding saturated vapor pressure poi yi
(1-76) Methods for computing the vaporization enthalpies are documented and critically examined in [8.1]. Figure 1.16 shows two common presentations of vapor pressure curves for a few different substances. For practical use, vapor pressure data may be found in [8.3, 8.41. 1.4.3.2 Two and Multicomponent Systems The Basic Equation for Vapor-Liquid Equilibrium
The basic equation for the vapor-liquid phase equilibrium forms the major design criteria for apparatus that separate liquid mixtures by distillation or selective absorption. In distillation, the process or actual working temperature is lower than the criti-
The fugacity f , is defined by the chemical potential of a real gas, as postulated by LEWIS:
pi =poi + R . T . lnf,
(1-78)
1.4 Phase Equilibria 1c
[bad
a a’
tP 6
10
[bar] 7 6
5 L
b’
t:
log P
1.c
: 0
0.E
0.7 0.E
0.E 0.4
0.; Fig. 1-16. Vapor-pressure curves of some substances. a) p, T-diagram b) logp, l/T-diagram M Methanol W Water T Toluene E Ethanol B Benzol
31
32
1 Basic Concepts
Fugacity is used to replace the pressure of
an ideal gas pi by a “corrected pressure” A of a real gas i, to produce a universally valid relationship. At zero pressure a real gas behaves like an ideal gas, and fi lim =1 PI’O
(1-79)
Pi
A discussion and derivation of Eq. (1-77) can be found in [0.12, 1.581. Eq. (1-77) is universally valid, and should be applied if real behavior of vapor and liquid phases is to be considered. Considering the influence of pressure on the vapor and liquid properties of a substance, the real saturated vapor pressure p$ is
(1-80)
The molar volume vmay be computed with an appropriate equation of state for v(p,T). Eq. (1-82) can then be integrated. Useful correlations which may be used to calculate state variables are listed in Table 1-7. These equations may be applied to both pure gases and gas mixtures. Most correlations used to calculate the activity coefficients are based on the dependence of the free mixing enthalpy on the activity coefficient for each individual component in the mixture. If two pure components are mixed, the entropy AS, increases. A positive and/or negative change of enthalpy (“heat of mixing”) AH,, and a decrease of the free enthalpy, the free mixing enthalpy AG,, occur. It can be shown that AGM+ T . AS,
AH,=
(1-83)
The free mixing enthalpy Ag,, one kmol of the mixture, is P
Ag, = R . T .
Eq. (1-77) becomes y..p = y;.
xi. p*. 01
(1-81)
AgM = R . T .
For the design of distillation and absorption apparatus, it is necessary to know the equilibrium relationship yi (xi) either as an analytical, homogenous equation, or at least as an equilibrium curve. According to Eq. (1-77), the fugacity or the fugacity coefficients can be calculated or found experimentally to be a function of pressure, temperature and phase composition. An expression for the fugacity is V - E ) . d p
T-
C xi. h a i i
1xi i
*
-
ln(yi x i )
(1-84)
Therefore
Calculation of Vapor-Liquid Equilibrium Data
In- =
=
related to
(1-82)
1xi. lnx, + i
+ E . T.Cxi.lnyi
(1-85)
i
In Eq. (1-85) the first term is the change of enthalpy during the mixing of ideal liquids, a free mixing enthalpy. The second term, change of excess enthalpy AgME, takes into consideration the behavior of real liquids in the mixing process. AgME=R.TCxj*lnyj i
(1-86)
1.4 Phase Equilibria
33
Table 1-7. Method to calculate p, V, T data for real gases and gas mixtures*. Method
Characteristics
Literature
Benedict, Webb, Rubin method ,,BWR equation"
Equation with 8 constants dependent on mixture concentration. Originally developed for light hydrocarbons, but modified and validity region expanded
BENEDICT,M., WEBB,G. B., RUBIN,L. C., .lChem. Phys. 8 (1940) 334. BENDER,E., Habilitationsschrift, Ruhruniversitat Bochum. ORYE,R.V., Znd. Eng. Chem. Des. Dev. 8 (1969) 4, 579.
Redlich-Kwong method
Equation with 2 constants determined by the critical data of a substance, many times extended and improved
Virial equation Wohl method
Correlation for second virial coefficients
WOHL,K., Z. Phys. Chem. 2 (1929) 77
Prausnitz, Gunn method
Correlation for second virial coefficients
PRAUSNITZ, J.M., and GUNN,R.D., AZChE. J. 4(1958) 430.
*
REDLICH,O., and KWONG,J., Chem. Rev.
44 (1949) 223.
Additional methods in [1.70].
Applying a partial mole fraction derivative to Eq. (1-86), the activity coefficients of the components are given by
For example, the activity coefficients of a binary mixture y1 and y2 are
(1-88) and
Some examples for practical use are given in Table 1-8. Each method has been selected and tested on many substances, and their possible applications are given. All of the listed computation methods need not only be used for variables of pure substances, but also for state variables of the mixture. One or more points on the equilibrium curve of a binary system should be found experimentally.
Experimental Investigation of Vapor-Liquid Equilibrium
The procedure to find vapor-liquid equilibrium data by experimentation is as follows: A sample of a liquid mixture, with a known mole ratio in equilibrium with a vaThe methods used to compute A g M L . por phase, is selected and analyzed. Equiincluding Eqs. (1-87)-(1-89), lead to the librium data at constant temperature or methods of VAN LAAR,MARGULES, WOHL, constant pressure can be found. This comREDLICH-KISTER, WILSON, and PRAUSNITPmon procedure is explained in detail by to compute the activity coefficient. HALA,PICKet al. [1.58, 1.591.
34
1 Basic Concepts
Table 1-8. Methods to Calculate Vapor-Liquid Equilibrium Data [1.70, 1.711. Method
Characteristics
Literature
Method of WOHL (VANLAAR,MARGULES,SCATCHARDHAMER)
Effective Volumetric Ratio Polynomial Equation for the excess Gibb's energy, interaction parameters, relatively simple to use
WOHL,K., Trans. Am. Chem. Eng. 42 (1946) 215 [1.13].
Extended Van Laarmethod
For nonpolar binary systems with large dilution in the region up to the critical region
MUIRBROOK, N. K., Dissertation, Univ. of California, Berkeley (1964) CHUEH,P. L., and PRAUSNITZ, J. M., Computer Calculations for HighPressure Vapor Liquid Equilibria. Prentice Hall Inc., 1968.
Scatchard-Hildebrand Solubility parameters and partial Equation, Chaomolar volumes are referred to Seader method 25 "C, suitable for hydrocarbon systems
CHAO,K.C., and SEADER,J.D., AIChE. J 7 (1961) 4, 598.
Wilson equation
Interaction method for the excess Gibb's energy; suitable for totally miscible systems, not applicable for systems with limited miscibility since only the binary parameters are used, applicable to multicomponent systems; only valid for small and medium operating pressures
WILSON,G.M., J. Am. Chem. SOC. 86 (1964) 127.
NRTL equation (non random two liquids)
Method based on the Wilson equation with nonrandomness parameter which can be applied to systems with limited miscibility and nonideal systems; use of binary parameters to calculate multicomponent data; only valid for small and medium operating pressures
J. M., RENON,H., and PRAUSNITZ, AZChE. J 14 (1968) 135. RENON,H., and PRAUSNITZ, J. M., Ind. Eng. Chem. Dev. 8 (1969) 3, 413.
Uniquac equation (universal quasi chemical)
Method based on the principle of the local compositions, similar to the Wilson and NRTL equations, which are derived as special cases; also describes ,,real" liquid phases; only valid for small and medium operating pressures
GMEHLING, J., ANDERSON, T.F., and PRAUSNITZ, J.M., Ind. Eng. Chem. Fund. 17 (1978) 269.
Unifac equation (uniquac functional group activity coefficient)
Contributions of individual functional groups; prediction of the interaction between the activity coefficients of functional groups by interaction parameters, only valid for small and medium operating pressures
J., FREDENSLUND, A., GMEHLING, and RASMUSSEN, P., Vapor-Liquid Equilibria using Unifac. Elsevier Publ. 1977.
1.4 Phase Equilibria
35
n
Fig. 1-17. LABODEST apparatus for the determination of vapor-liquid equilibria. Vacuum, ambient and over pressure operation at temperatures up to 250°C. Presentation according to data of Fischer Labor- und Verfahrenstechnik, Meckenheim near Bonn [1.61]. 1 Flow evaporator with electrical immersion heater Phase mixing chamber to adjust the equilibrium 2 3 Phase contact path 4 Phase separation chamber Solenoid valves to take samples 5 6 Sample take-off, vapor phase 7 Sample take-off, liquid phase 8, 9 Sample take-off, circulation streams 10 Gaseous sampling of vapor phase, i. e., for systems with a miscibility gap
36
1 Basic Concepts
Figure 1-17 shows an experimental apparatus introduced by FISCHER[1.61] to find vapor liquid equilibrium data.
(1-92) In Fig. 1-18, the method used to check consistency is applied to a binary mixture of acetone and trichloromethane. The equilib-
Consistency of Equilibrium Data To check for accuracy, thermodynamic consistency, and lack of contradiction in the equilibrium data found, many methods and criteria using both experimentation and correlations are available t1.62- 1.661. A simple method used to check the consistency of data for a binary system is discussed below: At a constant temperature, it follows from Eqs. (1-21)-(1-26) that (1-90)
a1
I
0
1
10
0.2
x1 0,L
05
0.8
1,O
- 0.1
-0.2
h
- - 0,3
This leads to a simplified Gibbs-Duhem Equation particularly for a binary mixture
The logarithm of the activity coefficients in Eq. (1-91) may be plotted against the mole fraction of component 1. For a consistency check of the values for logy,(x,) and log y 2 (x2)data, the following requirements should be satisfied: Over the complete range of mole fractions the curves should have opposite slopes At the point x1= 0.5 the slope of the curves should be equal but opposite If the curves do not show a minimum or maximum, all y-values should be either larger or smaller than 1 (all data points for both logy(x,) curves should be on the same side of the log y = 0 line) The integral, or rather the area below the log ( y 1 / y 2 )(xI) curve has to be equal to 0
-0.3I Fig. 1-18. Proof of consistency of vapor-liquidequilibrium data for an acetone-trichloromethane system at 1.013 bar. a) log y,,x,-diagram to prove Eq. (1-91) b) log ( y 1 / y 2 ) , x,-diagram to prove Eq. (1-92), 1 Acetone, 2 Trichloromethane
1.4 Phase Equilibria
rium data is supplied by the DECHEMA service for substance properties. The calculation was done with the aid of the Uhde-substance property compiler using the Van-Laar Method. In process engineering the proof of published vapor-liquid equilibrium is of particular interest. In [1.67-1.701 and [1.72-1.851 data collections and bibliographies are listed. Particular attention is given to a collection of vapor-liquid equilibrium data by GMEHLING et a1 and published by DECHEMA [1.72]. Ideal and Real Mixtures
Depending on miscibility and effects resulting from mixing (volume contraction, volume dilation, heat of mixing) of different kinds of liquids, real and ideal mixing behavior and real and ideal mixtures can be distinguished. In an ideal mixture, components are miscible in any mole ratio. The attractive force between different types of molecule, is the same as that between similar types of molecule. During mixing there are no volume effects or heats of mixing. In practice, only approximately ideal behavior is found, for example, in the mixing of substances such as isotopes, optical antipodes, stereo isomers, structural isomers and neighbors in a homologous series. For an ideal mixture, Raoult’s law follows from Eq. (1-81)
y I . p = p . = p O,I. . X i
(1-93)
Definition of Raoult’s law: The partial pressure pi of component i in the vapor phase is at an adjusted equilibrium proportional to the mole fraction xi in the liquid phase. The saturated vapor pressure po,i depends on the equilibrium temperature. For a real mixture the attractive force between different types of molecule is not the same as that between similar types of mole-
37
cule. Molecules are described as similar if they have similar size, structure, and chemical nature. If in a particular mixture, the attractive force between different types of molecule is smaller than that between similar types of molecule, the molecules in the mixture are held together with a smaller force than those in a pure liquid. Thus, the effect during mixing is an endothermic volume expansion and an increase in vapor pressure. There is a positive deviation from Raoult’s law which leads to a pronounced maximum for the vapor pressure, and therefore to a minimum boiling point (for example, ethanol-water mixture). If the attractive force between different types of molecule is larger than that between similar types of molecule, the molecules in the mixture are held together with a stronger force than those in a pure liquid. This results in an exothermic volume contraction during mixing. There is a negative deviation from Raoult’s law, leading to the development of a minimum in the vapor pressure curve, and a maximum boiling point (for example, nitric acid - water mixture). In Table 1-9, different approaches to describe the liquid-vapor (or gas) phase equilibrium are listed. In distillation processes, the operating pressure is usually in the range ca. 0.05-5 bar. It is sufficient to treat the liquid phase as a real liquid, while the vapor phase may be assumed to be ideal. Gas absorption processes are often carried out under relatively high pressure conditions. The real behavior of the vapor phase must be taken into consideration. Representation of the Vapor-Liquid Equilibrium for Binary Mixtures
For the graphical representation of vapor liquid equilibrium of binary mixtures, there
38
1 Basic Concepts
Table 1-9. Gas - liquid equilibrium relationship. Liquid phase Ideal Partial pressure p i of component i in the vapor phase
-
Ideal
PI = Po,1 . XI
Real
1)
-
-
Gas phase
Ideal
PI = Po,1.
Y1
. XI
Real - Real
PI =Po*,[‘ Y1 . XI
Distribution coefficient KT = y ;/x; Relative volatility (separation factor) ai,k Partial pressure p i of the super critical component in the gas phase ’)
Raoult’s Law.
’)
ai,k =
Po. i
Y1 . P0,l Yk’P0.k p I. = H I. . y .l . x l.
ai,k =
Po, k
~
p I. = H I. . x2) 1
~
ai,k =
P,*,i
Yi ~
Yk
*
Po*, k
p I. = p *0,1. . y I. . x I.
Henry’s Law.
are three diagrams of practical importance: the pressure diagram, the boiling diagram, and the equilibrium diagram.
Pressure Diagram: The partial pressures p 1 and p 2 of both components of the mixture, in the vapor phase, and the pressure p, the system or total pressure of the liquid and vapor phase, are plotted against the mole fraction of the liquid phase at constant temperature. Boiling Diagram: The boiling line and dew line are plotted at constant pressure. The boiling line L9(x) connects the bubble points at boiling temperature as a function of the composition of the liquid mixture. The dew line L9(y) shows the condensation temperature Of the saturated vapor mixture as a function of its composition in the vapor. Equilibrium Diagram: For the case of constant operating pressure, the equilibrium composition of the vapor phase is plotted as a function of the liquid phase composition.
Figure 1-19 shows the three diagrams for an ideal binary mixture (for example, a nearly ideal binary system is benzol-toluene). The pressure diagram for an ideal mixture may be described by Raoult’s law. The partial pressures p1(x,), p2(x2)and the overall pressure p(xl) are straight lines. Boiling lines and dew lines for an ideal mixture at a given pressurep may be derived from Dalton’s and Raoult’s laws to give P=CP;
(1-94)
i
and (1-95)
p,I = y 1, .
Therefore, the equation describing the boiling line is
x1(L9,p) =
P - Po,z(d) Po, 1 (8) - Po,2 (19)
(1-96)
and the equation describing the dew line is
1.4 Phase Equilibria
0
x,l%l b)
f
3
100 OC
90
"0
20
XI,
LO
~1160
100
f
-
80 x 1%1
cl
x2
100
8o
Y
[%I 60 Yl
40
20
0'
20
XiLO
60
80
x[%l
-
100
39
Fig. 1-19. Pressure diagram, boiling diagram and equilibrium diagram for the almost ideal mixture benzol-toluene. a) Pressure diagram for a mixture of boiling point temperature 100 "C p 1(xl),p2(x2)Partial pressure lines of benzol and toluene p(xl,xz) Total pressure line X1 Molar fraction of benzol in the liquid phase Molar fraction of toluene in x2 the liquid phase b) Boiling diagram at a total pressure of 1.013 bar I Liquid phase region I1 Steam or vapor phase region 111 Two phase (wet steam) region B Bubble point line D Dew point line L9 Temperature c) Equilibrium diagram at a total pressure of 1.013 bar y Molar fraction of benzol in the vapor x Molar fraction of benzol in the liquid phase -- Conceptional lines to generate the equilibrium diagram from the boiling diagram
Similarly, the equilibrium curve of an ideal mixture may also be derived from Dalton's and Raoult's laws to give Po, 1
yI = P0,l
XI
f
*
XI
(1-98)
P0,2 x 2
The relative volatility a1,2,independent on concentration (see Chapter lS), is (1-99)
Boiling lines and dew lines may be calculated stepwise for a chosen temperature 8. po,l and po,z are the saturated pressures of pure components 1 and 2 corresponding to temperature 8.
y, =
a1,2 * X l
1 + x1 *
@1,2
- 1)
(1-100)
The equilibrium curve may also be developed graphically from the boiling diagram,
40
1 Basic Concepts Fig. 1-20. A schematic of the equilibrium behavior and important thermodynamic functions of a binary system according to Rock [1.861, a) Pressure diagram b) Boiling diagram c) Equilibrium diagram d) Activity coefficient diagram e) Relative volatility diagram f ) Free excess enthalpy of the mixture g) Mixing enthalpy and excess entropy 1st Column: Ideal mixture 2nd Column: Real mixture showing positive deviation from ideal behavior (for example; ethanoltoluene) 3rd Column: Real mixture showing negative deviation from ideal behavior (for example; acetonechloroform)
yressur e diagram
I
x1 Boiling diagram I
bl
0
1
1
0
u XlYl
0
1
P=const
Equilibrium diagram
1 0
1 0
Cl
P =const.S=const
Activity coefficient diagram
dl
Relative volatility diagram
enthalpy Free excess of
dSE
I loo~oc~n
0
the mixture
fl
1oi
/1
__c
Mixing enthalpy and excess entropy
41
x1
3xonst,p=const
O M T-A;, 0
T*AZE
dii
41
1.4 Phase Equilibria
according to the requirement that the system is at thermal equilibrium. In Fig. 1-19 the graphical development of the procedure is shown. This is generally valid and includes real mixtures. Distillation processes are influenced by the working pressure, as shown in Fig. 1-19. With a reduction in pressure, at the same mole fraction x1 in the liquid, the vapor fraction y , increases; hence the separation of the mixture is more efficient at lower pressure. To describe phase equilibria for real binary mixtures, the equations listed in Table 1-9 can be used. Pressure, boiling, and equilibrium diagrams, and other plots showing system behavior characteristics for a real mixture, are given and discussed in Fig. 1-20. According to Raoult's law, and therefore applying to ideal behavior, the activity coefficient can have positive (yi> 1) and negative (yi < 1) deviations. Pressure, boiling, and equilibrium diagrams for the steam distillation of common and important binary mixtures of partial miscibility are shown in Fig. 1-21. Azeotropism An azeotropic point is characterized by the following : 0
0
Pi
X2,ac = Y2,ac
(1-101)
The relative volatility of an azeotropic mixture a,,= 1, therefore (1-102) hence
-
P2
XI
Ylxi
cl
IP iPl
-
iP1 XI
-
YI XI
p=const
-
p=const
t __
x1oc XI
-----c
1
0
-x1oc
x1
I
Fig. 1-21. Pressure diagram (a), boiling diagram (b) and equilibrium diagram (c) of a binary mixture with a miscibility gap over the complete concentration range (left column) and a binary system with a limited miscibility gap (right column). x ~ Azeotropic , ~ ~ concentration B Bubble point line D Dew point line
The equilibrium composition is the same for both vapor and liquid phases X1,ac = Y l , a c
I
P
0
(for an explanation of Eqs. (1-102) and (1-103), see Chapter 1.5) For an azeotropic mixture the isothermal partial pressure curve p 1(xl),p2(x2),the isobaric boiling line t?(xl) and dew line d ( y J and the isobaric equilibrium curve y 1(x,), exhibit maxima/minima (maximum boiling or bubble point and therefore minimum vapor pressure; minimum boiling or bubble point and therefore maximum vapor pressure see Fig. 1-20)
It is not possible to separate an azeotropic mixture by simple distillation. To
42
1 Basic Concepts
t
s,
X-
Fig. 1-22. Influence of the operating pressure on the azeotropic point. A, Azeotropic point at an operating pressure of
PI
A, Azeotropic point at an operating pressure Pll
make separation possible, the position of the azeotropic point must be adjusted. The following steps are required to change the location of the azeotropic point, or to remove if from the diagram: 0
0
If the azeotropic point is restricted only to a certain pressure or temperature range, an increase or decrease in the working pressure can make the azeotropic point disappear (Fig. 1-22) A selected third component may be added to the original binary mixture, causing the azeotropic point to disappear (extractive distillation, Fig. 1-23). The third component is chosen such that it does not form an azeotropic point with either component of the original mixture. Its boiling point should be significantly higher than the highest boiling point of either component of the original mixture and it must be miscible at process conditions with both components of the original mixture
Fig. 1-23. Influence of an auxiliary component on the azeotropic point in an extractive distillation process. Example system: Acetone-trichloro methane Auxilliary component: Methyl isobutyl ketone EC 1 Equilibrium curve without auxilliary component present EC 2 Equilibrium curve with auxilliary component present
0
A selected third component is added to the binary mixture such that, it forms a low-boiling azeotropic mixture with either one of the components of the original mixture. Separation by distillation is now possible (azeotropic distillation, Fig. 1.24). The boiling point of the third component should be in the same range as the components of the binary mixture. At process conditions, the third component should be miscible with both of the original components
Coexistence of the Vapor and Liquid Phases within a Limited Concentration Range It is possible, particularly for distillation processes at high working pressure, for the critical pressure of either one or both components to be lower than the working pres-
1.4 Phase Equilibria
43
With the requirement that C y i = 1 for the vapor phase, the equation needed to compute the boiling or bubble point of a ternary mixture consisting of the components 1, 2, 3, is
x, . P0,l ~
P
P
P
=
1
(1-105)
With the requirement that Exi = 1 for the liquid phase, for a ternary vapor mixture, the computation of the dew points is analogous.
x-
Fig. 1-24. Influence of an auxilliary component on the azeotropic point in an azeotropic distillation process. Example system: Cyclohexane-benzol Auxilliary component : Ethylacetate EC 1 Equilibrium curve without auxilliary component present EC 2 Equilibrium curve with auxilliary component present
sure. Liquid and vapor phases coexist only in a limited concentration range (or mole fraction of the components), as shown in Fig. 1-25. Separation by distillation is only possible within the range of the coexisting phases. If, for example, gas mixtures are condensed under high pressure, low temperature distillation may occur.
Representation of Vapor-Liquid Equilibrium for Ternary Mixtures
For each individual component in an ideal mixture, Raoult’s and Dalton’s laws are valid Po, i x . y . = -. P
+ X z * - Po,2 + x 3 * -
(1-104)
Y , * - P +Y2’--P + y 3 * - - - - 1 Po, 1 Po,2 Po.3
(1-106)
Boiling (or bubble) and dew point curves for ternary mixtures, may be represented by the equilateral triangle discussed in Chapter 1.4.2.2. At constant temperature, the boiling and dew lines, according to Eqs. (1-105) and (1-106), are straight lines within the equilateral triangle. The positions of the lines may be found by an easy graphical procedure if the boiling diagrams for the three binary pairs are given. If the boiling line (liquid isotherm) and dew line (vapor isotherm) are known, the composition of the vapor phase corresponding to a given composition of the liquid phase may be calculated from Eq. (1-104). The positions of the equilibrium lines in the triangle are determined stepwise. For real mixtures, the correlations listed in Table 1-9 may similarly be applied. The liquid and vapor isotherms are curved lines in the triangle diagram. Depending on the behavior of the mixture, the equilibrium or equilibrium distillation lines form one, two or three distillation areas (see [2.1]).
44
1 Basic Concepts bl
a)
Fig. 1-25. Boiling diagram (a) and equilibrium diagrams (b) for a system showing a limited range of coexistance between the vapor and liquid phases. Example system : Carbon dioxide-sulfur dioxide [2.1]. B Bubble point line D Dew point line p r = 40 bar p l , = 91 bar prlr = 62 bar X, 33%, x, = 72.5% Carbon dioxide (At =96 bar, the points A, and A, are the same point for this system, therefore, the bubble point line and dew point line do not show a wet vapor region) Critical point of carbon dioxide: 73.8 bar Critical point of sulfur dioxide: 78.6 bar x Molar fraction of carbon dioxide in the liquid phase y Molar fraction of carbon dioxide in the vapor phase r9 Temperature
Vapor-Liquid Phase Equilibrium of Multicomponent Mixtures
For a mixture consisting of n components, the calculation of the bubble or boiling points including the equilibrium constant (distribution coefficient) K: (defined by Eq. (1-46)) is n
cxi.KT=1
The equilibrium constant K: may be determined from the correlations listed in Table 1-9. Generally K: is dependent on the pressure, temperature and composition of the mixture. For an ideal mixture K: = p0,Jp,hence Eqs. (1-107) and (1-108) are the general form of Eqs. (1-105) and (1-106). Boiling and dew points can be determined iteratively.
(1-107)
1
1.4.3.3 Henry’s Law, Gas Solubility
Similarly, the dew points give
I-= yi
1
Ki*
1
(1-108)
The partial separation of a gas component i (absorptive i) from a gas mixture is usually done using a liquid solvent (absorbent). The
1.4 Phase Equilibria
operating temperature is often higher than the critical temperature of the gas component. During the absorption process the gas component is dissolved or absorbed as a gas without condensation taking place. Under absorption conditions, its liquid state does not exist and the measurement of a saturated vapor pressure is impossible. Describing, for example, the vapor-liquid equilibrium by the expanded Raoult’s law p i = po,i yi. x i , would lead to incorrect results. To find a concept to describe the technical importance of gas solubility, the mixture is assumed to be infinitely dilute, or “an ideally diluted” solution. With a large excess of solvent, when the gas component i is dissolved, the mole fraction xi in the solution tends to 0 (x,-+O). At vapor-liquid equilibrium, Henry’s law for an ideally diluted solution may be applied to the gas solubility of component i in the solvent pi= Hi xi
Lp = const
(1-109)
In an ideally diluted solution, the partial pressure p i of the gas component i is proportional to the mole fraction xi in the solution. The constant of proportionality is Henry’s constant Hi, which is dependent on temperature, pressure, and the respective excess component. Van-der-Waals forces in the solvent bond the gas component i in the solution; the gas component i is physically dissolved. Henry’s and Raoult’s laws are only valid under limited conditions (see Fig. 1-26). Raoult’s law gives an asymptote to the real partial pressure curve p i (xi) where xi 1. Henry’s law gives the tangent of the partial pressure curve at the limit xi -+ 0. Henry’s law is only really valid for gases which are sparingly soluble. A small mole fraction of dissolved gas i leads to a considerable deviation from the linear relationship between the partial pressure p , and the mole fraction xi. For this reason xi is cor+
3 = const
t
/
/
/
/
I’, /
45
KH,I
-HL
Q‘ /
/ Poi
qFig. 1-26. Validity range of Raoult’s law and Henry’s law. pi(xi)Partial pressure curve of i in a real mixture RL Asymptote to the partial pressure curve as xi-+ 1, according to Raoult’s law HL Tangent to the partial pressure curve as xi+ 0 according to Henry’s law K H , i Henry constant Hi pi Partial pressure of component i in the gas phase xi Molar fraction of component iin the liquid phase
rected by the marginal activity coefficient yi,, to give
A comparison of this equation with the corrected Raoult’s law equation gives (1-111)
From this, with the given marginal activity coefficient yi,, and an extrapolated saturated vapor pressure po,;, the Henry’s constant Hi may be estimated. (The dependence of Henry’s constant on pressure is given by
46
1 Basic Concepts
(1-112) where q,Pis the partial molar volume of the dissolved gas i in the liquid phase at infinite dilution.) Normally, the solubility of the gas increases with decreasing operating temperature and increasing pressure (Fig. 1-27). For several gases dissolved in one solute, the solubility increases with increasing boiling temperature. As well as Henry's constant Hi, a measure of the capacity of a liquid to dissolve a gas, are the Bunsen absorption coefficient aBu,iand the Oswald absorption coefficient aos,i,which can be found in tables. The Bunsen absorption coefficient is vNi= a B u , i ' P i
(1-113)
where VN,iis the volume of a gas calculated at standard state, O T , 1.013 bar and dissolved in lm3 of solute. At a partial pressure p i of 1.013 bar of gas i, the Bunsen absorption coefficient aBu,iis the volume at standard state that is dissolved in one unit of solute at a given temperature. The Ostwald absorption coefficient ctOs,; is given by
where cL,;and cG,iare molar concentration of the gas i in the solute (liquid) and gas phase. Therefore the Ostwald absorption coefficient aos,iis the ratio of the concentrations of gas i in the liquid and gas phases. The coefficient is independent of pressure but dependent on temperature. Additional absorption coefficients, such as Kuenen or Raoult absorption coefficients, are listed in [3.1]. These coefficients are seldom used in practice.
tl
6'1
/
xi-
xi-
Xi
+
Fig. 1-27. Sorption isotherms for a gas component i dissolved in a solution in the range of validity of Henry's law. p i Partial pressure of component i in the gas phase x, Molar fraction of component i in the liquid phase yi Molar fraction of component i in the gas phase Molar ratio of component i in the gas phase (loading of carrier gas) XiMolar ratio of component i in the liquid phase (loading of solvent)
1.4 Phase Equilibria
To convert Henry’s constant Hi to the Bunsen absorption coefficient C L ~ , , and ~ the Ostwald absorption coefficient clos,i, the following relationship may be used
47
Eq. (1-116) becomes at absorption equilibrium
-_-.- - Hi 1+y p
Xi l+Xi
L9 = const
(1-117)
where (1-115)
y. ==
moles of component i in the gas phase moles of the remaining inert gas mixture
where Q, is the density and M , the molar mass of the solution. is the loading of i in the gas phase For graphical representation of the gasliquid equilibrium, the “absorption equilibrium”, the partial pressure diagram (pi(xi) moles of component i diagram), and also the equilibrium diagram x.= in the solution yi(xi) or y ( X i ) ,are used. moles of pure solvent If the gas phase is ideal, the solution ideal and diluted, and Henry’s law is valid for the mole fraction of the gas component X i is the loading of i in the liquid phase i, then Figure 1-27 shows the partial pressure lines p i (xi), the equilibrium lines yi (xi) and Hi y.=. x.I L9= const (1-116) y ( X i ) ,the absorption isotherms, at conP stant temperature and physical conditions, (i. e., there are no chemical reactions, and With a solute which is selective to only one the solvent may be described by Henry’s component i of the gas mixture, the solubil- law). Data for practical use giving the solubilities of all the other components of the gas ity of gases in physically and chemically mixture are negligible. During absorption acting solvents, respectively, are found in the remaining gas mixture is inert. Absorp[0.17, 0.21, 1.46-1.561. A method to calcution processes are carried out at low temlate Henry’s constant is given in [1.57]. perature, so vaporization of the solute is Figure 1-28 gives examples of frequently negligible. During the absorption process, the amount of solute and remaining inert used absorption systems. The use of a mixture of pure liquids as a gas are approximately constant. The soluble gas component i in the gas phase may be re- solvent is common in absorption processes. lated to the remaining inert, or insoluble, If, for example, the gas component i is disgas mixture, and in the liquid phase, to the solved in a mixture of two solvents I and 2, solvent. In the gas phase the concentration the Henry’s constant H i , M is, within the of component i is taken as while in the conditions for which it is valid, given by liquid phase it is taken as Xi.Introducing the conversion relationship between the mole fraction and the number of moles of solute in the solvent listed in Table 1-4
48
c 1 Basic Concepts
The solubility of i in the pure solvents 1 and 2, expressed by Henry constant H , , and are required to be known.
i
I
h
1
-
1
-
I
I
1
I
4
Henry's constant for system gas component i-solvent mixture 1 and 2 Henry's constant for system gas component i-solvents 1 and 2, respectively experimentally determined constant (a1,2= 0 for ideal solvent mixture 1 and 2) solvent mixture of 1 and 2 shows a positive deviation from Raoult's law solvent mixture of 1 and 2 shows a negative deviation from Raoult's law mole fraction of solvent 1 and 2 in solution
Gas Solubility with Chemically Active Solvent, Chemisorption
lo-' C2H4
Kr
F Ar
10-2
t0
t I
1 10
I
.J
I
I
1
20
30
I
1
S["Cl
-
I LO
He
50
Fig. 1-28. Solubility of different gases in water. Reference pressure: 1 bar. Representation according to the Linde Report in Jechnik und Wissenschaft". a Absorption coefficient [given in m$t ( m i substance absorbed per t = 1000 kg water)] 19 Temperature
A chemical reaction between the solvent and the gas component i to be separated is called activated absorption or chemisorption. Chemical attractive forces act between the solvent and component i, resulting in high selectivity and solubility. The phase equilibrium becomes a chemical equilibrium. Applying the law of mass action to the chemical equation for chemisorption, the equilibrium constant K: is found. For example, using sodium carbonate solution (Na,CO,) dissolved in water as a solvent for the chemisorption of carbon dioxide (CO,) from a gas mixture, sodium hydrogen carbonate (NaHCO,) is formed according to the chemical equation Na2C0, + CO, 2 NaHCO,
chemisorption
+ H 2 0 ,desorption
(1-119)
1.4 Phase Equilibria
The equilibrium constant KZiis then
tI
49
9 = const
(1-120)
where C N a H C 0 3 ~CNaf203 and cH2C03 are molar concentrations of NaHCO,, Na,CO,, and H,CO,. The maximum solubility of the solvent is limited by the maximum rate of the reaction at equilibrium. According to the Van’tHoff relationships, the equilibrium constant KZi depends on pressure and temperature. Generally, chemisorption processes are more effective at lower temperature and higher pressure. Compared with physical absorption, chemisorption has the following advantages : 0
0
Higher selectivity of the solvent for the separating gas component Higher absorptivity of the solvent and higher rate of absorption
A disadvantage of chemisorption is the fact that the recovery of the solvent might not be effective or even not possible via a reversible reaction. As shown in Fig. 1-29, the positions of the partial pressure lines (absorption isotherms) pi(xi) are different for chemical and physical absorption due to the marginal laws for the partial pressure at pi(xi-,0). According to HAASE[1.87] at the zero point (pi 0, xi 0) the following condition for the partial pressure line pi(xi)applies -+
XI
Fig. 1-29. Partial pressure curves for physical and chemical absorption up < 1 Chemical absorption with association up = 1 Physical absorption up > 1 Chemical absorption with dissociation Partial pressure of the absorbate in the pi gas phase Molar fraction of the absorbed compox, nent i in the liquid phase
where
up number of molecules on the right-hand
K
side of the reaction equation for chemical absorption (in Eq. (1-119) up = 2), if one molecule of sorbate i is dissolved constant (similar to Henry’s constant Hi)
The following cases must be distinguished (see Fig. 1-29): 0
+
0
0
(1-121)
-
up > 1 Chemical absorption including dissociation, a horizontal tangent may be drawn on the partial pressure line at xi = 0. This is a com-
mon case for chemical absorption processes up = 1 Physical absorption, Henry’s law is valid, neither dissociation nor association up < 1 Chemical absorption with association, a vertical tangent may be drawn on the partial pressure line at xi = 0
50
1 Basic Concepts
Fig. 1-30. Determination of the equilibrium curve for adiabatic absorption. a) Balance schematic AB Absorber b) Course of equilibrium curve EC, AB Adiabatic adsorption equilibrium RS Regenerated solvent curve LS Loaded solvent t9,,&, . .. Absorption isotherms FG Feed gas mixture Purified gas mixture, reduced in PG absorbate
Whilst in physical absorption processes the partial pressure p i of the absorbed component i increases approximately proportional to the mole fraction xi in the solution, during chemical absorption when xi is small p i is initially very low (good initial loading capacity of the solvent is the basis of the case up > 1). With increasing xi,p i shows a sharp increase. Absorption is an exothermic process, i. e., during the absorption process heat is released. If this heat cannot be removed, the temperature of the phase streams increases. Since the residence time in the absorber for the gas phase is short and its heat capacity is small at low absorption pressure, the heat of absorption is mainly removed by the liquid phase. In adiabatic absorption processes a significant increase in temperature
of the liquid phase occurs with the consequence of a decreasing loading capacity for the absorptive (absorbant). The course of the equilibrium curve or the operating line for adiabatic absorption at different isothermal states, may be derived using enthalpy balances. For 1 kmol of solvent, the enthalpy balance at constant gas phase temperature, using the notation in Fig. 1-30, is
It follows that the temperature 19 for each kmol solvent loaded with X kmol of absorbed component, is
1.4 Phase Equilibria
Fp, and Cp, are the molar heat capacities of the solvent and absorbed component, respectively, AEAb is the absorption enthalpy (see Chapter 3.3) and dg and 19,are the temperatures of the gas and liquid phase, respectively. For given values of Xi, X 2 , . . the corresponding temperatures I9,, I9, . . . may be calculated using Eq. (1-123). The equilibrium curve for an adiabatic process in the absorber is formed by the intersections of the ordinate parallel lines at Xi, X,, and the corresponding absorption isotherms IP,, d2 (see Fig. 1-30).
tI
a1
.
‘Solubility limit I
/
I
1.4.3.4 Boiling Equilibrium of a Solid Solution, Decrease of Vapor Pressure and Increase of Boiling Point A solid solution consists of surplus solvent and physically soluted, molecularly dispersed, distributed solid. The partial pressure of the solid is generally negligible. Only the pure liquid, in this case the solvent, of the solid solution is vaporized. As the amount of solvent decreases, the solid fraction increases. The boiling equilibrium, (the phase equilibrium of boiling solution and vapor), is of practical interest for the concentration of a solution by vaporization of the solvent. The boiling equilibrium of a solution is characterized by the vapor pressure line p , ( T ) (see Fig. 1-31); this is approximately parallel to the vapor pressure curve po,l( T ) of the pure solvent and may be derived from the equilibrium condition of Eq. (1-49)
(1-124) where ai is the activity of the solvent in the solution and and VII are the molar volumes of the solvent in the liquid and vapor phase.
vI
51
I
v d AT L l n c r e a s e
in bubble point
T-
Fig. 1-31. Vapor pressure curves for a solution and solvent. Mole fraction of dissolved substance x, x2, I < x2,2, etc. Vapor pressure of the solution pL l/T Reciprocal temperature Ap Vapor pressure reduction AT Increase in bubble point P ~ , ~ ( Vapor T) pressure curve of the pure solvent pL Vapor pressure curve of the solution pL,po,l Vapor pressure of the solution and the solvent, respectively Tr Triple point
(n
Integration between the limits of the vapor pressure of the solvent po,iand the vapor pressure of the solution p L gives PL = Po.l
*
a1
(1-125)
or for ideally dilute solutions Raoult’s law PL = P0,l ‘ x1
(1-126)
The vapor pressure p L of the solution is always lower than the vapor pressure of the pure component when they are both at the same temperature. From Eq. (1-126) the reduction of the vapor pressure pa, - pL is
52
1 Basic Concepts
where the expression within the brackets is the ebullioscopic constant kE of the solvent. Ebullioscopic constants for frequently used solvents are listed in Table 1-10. The ebullioscopic constant gives the increase in boiling temperature of the solution if 1 mol If the soluted substances are dissociated in of solid is dissolved in 1 kg solvent. This the solution, the number of moles n2 must may be seen from the dimensions of the be replaced by the number of ions n; in constant kE. Eq. (1-127) For practical use the increase of the boiling point may be quickly and easily approx[l-1281 imated using the nomogram given in [0.17]. n; = n 2 . [I + a . (i - l)]
proportional to the mole fraction x2 (x2= 1 - x l ) of the soluted substance
where a is the degree of dissociation, and i is the number of ions in which 1 mol of soluted substance is dissociated. For example potassium chloride dissociates in water KCl -+K+ + C1-, therefore a = 1 and i = 2. A reduction in the vapor pressure pO,,- p L at constant temperature, corresponds to an increase in the boiling point AT at constant pressure, hence the boiling or bubble point of the solution is higher than that of the pure solvent. For a diluted solution the increase in boiling point A T is
Table 1-10. Ebullioscopic constants for different solvents. Solvent
Boiling point at 1.013 bar ( "C)
Ebullioscopic constant kE (K . kg/mol)
Water Ethanol Diethylether Benzol Acetone Chloroform
100 78.4 34.6 80.1 56.2 61.3
0.51 1.22 2.02 2.53 1.71 3.63
1.4.4 Gas-Solid Phase Equilibrium where T, and q,lare the boiling temperatures of the solution and solvent, respectively, is the vaporization enthalpy of the solvent and x2 is the mole fraction of the dissolved substance (Fig. 1-31). The increase in the boiling temperature is directly proportional to the mole fraction of the substance dissolved in the solution. Instead of using the mole fraction x2 in Eq. (1-129) the molality c, = n2/m, for a dilute solution ( n , B n,) is approximately
1.4.4.1 Gas-Solid Phase Equilibrium, Sublimation
Sublimation is the direct phase change of a substance from the solid into the gas state. Desublimation is the reverse process. In thermal separation processes sublimation is of practical interest in freeze or sublimation drying. Heat transfer into the system causes moisture to sublime directly from the frozen solid into the vapor phase (see Chapter 5.10). Desublimation is important for the separation of gas mixtures; if components of the mixture change directly from the gas into the solid state when heat is removed, these components can be sepa-
1.4 Phase Equilibria
rated from the remaining gas mixture (see Chapter 7.4). The gas-solid phase equilibrium at sublimation or desublimation is described by the generalized CLAUSIUS-CLAPEYRON equation, see Eq. (1.71) and Fig. 1-32 (1-131)
sublimes at atmospheric pressure (“simple sublimation”, Table 1-11). For most substances, in the solid state, however, the triple point pressure is considerably lower than 1.013 bar. Sublimation is then only possible in a vacuum or with the aid of a carrier gas. If steam at a constant pressure is cooled below the triple point, a solid is often not crystallized immediately after passing the sublimation pressure line. Crystallization
where dp/dT is the slope of the sublimation pressure curve at temperature T. FI and 6 are the molar volumes of the substance in the gas and solid states, respectively, and Ah,, is the molar sublimation enthalpy. At the triple point this is the sum of the melting enthalpy and vaporization enthalpy Ah,,,. = Ahs,l -k Ahl,g
(1-132)
For the vapor pressure curve the introduced s and = i?. T/p simplifications are also valid for the sublimation pressure curve. Considering Eq. (I-131), an approximation for the sublimation pressure curve is then
vII v,
vII
(1-133) If the vapor pressure for the solid at the triple point is 1.013 bar or more, the solid
T-
Fig. 1-32. p , T-Diagram of a one-component system. Tr Triple point MC Melting curve VC Vapor curve SC Sublimation curve OC Oversaturation curve S Subcooling point [7.1] p Vapor pressure T Temperature
Table 1-11. Sublimation and melting data of substances which easily sublime [7.1]. Substance
Sublimation temperature (“C) at a sublimation pressure of 1.013 bar
Melting temperature (“C)
Melting pressure (bar)
Acetylene Carbon dioxide Uranium hexafluoride Aluminum chloride Ammonium chloride
-83.6 -78.5 56.4 177.8
- 81.8 - 56.6 69.2 190.0 520.0
5.28 2.03 2.54 35.0
337.8
53
1.18
54
1 Basic Concepts
takes place after passing the surfeiting line, a line parallel to the sublimation curve (desublimation delay, Fig. 1-32). This phenomenon is similar to the supersolubility of a solid dissolving in a solvent (see Chapter 1.4.5).
1.4.4.2 Gas-Solid Phase Equilibrium with Adsorption/Desorption and Convective Solid Drying (Adsorption Equilibrium) Solids with an active interface (adsorbent) can hold on to vapor or gas molecules (udsorbed molecules, adsorbate) at their surface (see Chapter 4). In physical adsorption (physiosorption) the binding forces between the adsorbing surface of the solid and the vapor or gas phase molecules are Van-der-
Waals forces - mostly electrostatic or dispersion forces. In chemical adsorption (chemisorption) the adsorbent and the adsorbed substance, (the adsorbed or bonded form of the adsorbate) have a chemical bond due to valency forces between the molecules. If adsorption equilibrium is reached, no further adsorbate is taken up by the adsorbent. Under these operating conditions of pressure and temperature, the adsorbent is saturated with adsorbed substance. The adsorption equilibrium is characterized by the concentration of the adsorbate in the gas phase and the corresponding equilibrium load of adsorbate adsorbed by the solid. Adsorption equilibrium may be represented by three graphical methods; adsorption isotherms, adsorption isobars and adsorption isosteres (Figs. 1-33 and 1-34):
Fig. 1-33. Adsorption isotherms of water on a Baylith T 144 molecular sieve (Na-form, 3 lo-'' m) and silica gel [4.23]. SG Silica gel BA Baylith X i Mole ratio of water in adsorbent p i Partial pressure of steam 9
1.4 Phase Equilibria a)
55
bl
pi= lOmbar
I
pi= 5 mbar
p, = 2 mbar
I
0
50 S[OCI
-
100
0
Fig. 1-34. Adsorption isobars (a) and adsorption isosteres (b) for water on a Baylith T 144 molecular sieve (Na-form, 3 . lo-'* m) [4.23]. X i Mole ratio of water in adsorbent
t9 Temperature
p i Partial pressure of steam
a
0
a
Adsorption Isotherms: The mole ratio of the adsorbed component in the adsorbent X, is plotted against the partial pressure pi of the adsorbate in the gas phase. Another concentration scale may also be used instead of partial pressure. The partial pressure p i may be replaced by the ratio pi/po,,, which is known in drying technology as the relative humidity pi. (p0,,is the saturated vapor pressure of the adsorbate at the reference temperature 8) Adsorption Isobars: The mole ratio of the adsorbate in the adsorbent Xi is plotted against the temperature at a constant partial pressure of the adsorbate pi Adsorption Isosteres: The temperature is plotted against the partial pressure of the adsorbate pi. The parameter is the mole ratio X i of the adsorbed substance in the adsorbent. (A logarithmic plot of the variables may be more useful)
Figure 1-35 shows characteristic plots of some adsorption isotherms, for different pore systems in the adsorbent and their interactions with the adsorbate. The convective drying of damp solids is characterized by adsorption isotherms. The exchanging adsorbent is the solid and the adsorbate (or adsorbed substance) is the moisture, usually water. A solid is termed hygroscopic if the partial pressure pi of the moisture at equilibrium in the gas space above the solids surface is lower than the saturated vapor pressure p0,; of the moisture at the solids surface temperature. With hygroscopic solids p i is dependent on the temperature and moisture content of the solid. Moisture is bonded by adsorption to the solid and is therefore at a lower energy level than the liquid. To dry a hygroscopic product the specific vaporization enthalpy of the moisture and the bonding energy must be supplied. A solid is not hygro-
56
1 Basic Concepts
Fig. 1-35.Characteristic sorption isotherms. Representation according to KNEULE[5.2]. Form 1 Pure adsorption with mono- or multimolecular layer at the adsorber surface Form 2 Adsorption and capillary condensation Form 3 Adsorption and capillary condensation, nonhygroscopic product behavior at higher product moisture content Form 4 Pure adsorption with low product moisture content, followed by nonhygroscopic product behavior Form 5 Unfavorable course of the adsorption isotherm Form 6 Adsorption to p,, at p, hydrate formation (with water), to pz adsorption and then with cp > cpz capillary condensation
adsorbate in the gas mixture is higher than the partial pressure, corresponding to the adsorbent load X i at equilibrium. Desorption occurs if the concentration of the adsorbate in the light phase is lower than the corresponding equilibrium concentration. If rpi is almost equal 1 condensation of adsorbate takes place. If the structure of the solids consists of a capillary system with small pore sizes, even with pi < 1, capillary condensation of adsorbate with wetting behavior occurs. According to the Gibbs-Kelvin equation (1-134)
where 0
surface tension (N/m)
Mi molar mass of the adsorbate (kg/kmol)
el,; density of the adsorbate in the liquid r
state (kg/m3) radius of curvature (m), negative for wetting (concave surface) and positive for nonwetting- (convex surface) in Eq. (1-134) bl
al
scopic, if the partial pressure p , is equal to the saturated vapor pressure of the adsorbate the partial pressure p iis then only a function of temperature, and only the heat of vaporization is necessary for drying. In practice often low concentrations of the gas phase adsorbate must be handled. The adsorption equilibrium curve is therefore characterized by high loading rates of the adsorbate into the adsorbent at low adsorbate partial pressures in the equilibrium gas phase (approximate vertical tangent of the adsorption isotherm at pi 0, Fig. 1-34). Adsorption takes place when the partial pressure p i or the relative saturation rp, of +
PL
-
t
k
:"i
9-
- - - Capillary condensation
Fig. 1-36. Adsorption isotherm (a), sorption hysteresis (b). Ad Adsorption isotherm De Desorption isotherm X Loading of adsorbent with adsorbate p , Equilibrium partial pressure p Relative humidity
1
35
1
30
25
1/x
20 15 10
5
0 I1
0
0.21 I
01
I I
1.o
106
;
x,y-
08
I
I
I
I
1
I
X
0.6
0.4 0.2
02
I
02
I
01
1
06 x.y
08
1
10
I
I
f 0.8
0
0
04
06
Y-
08
I Adsorption equilibrium data for the system oxygen/nitrogen/active carbon. Presented in a triangular diagram using mass fractions as the concentration scales (8 = - 150"C, p = 1 bar). A,B State points of active carbon loaded with pure oxygen and pure nitrogen, respectively. Curve A.. E.. B Locus of the state points of active carbon loaded with gas mixture. RE Conode TI Adsorption system : Acetylene/ethylene/silica gel ( 8 = 25 "C, p = 1 bar). I11 Adsorption system: Acetylene/ethylene/active carbon (8 = 25"C, p = 1 bar). X Loading of the adsorbent by the key component (adsorbate), in kg key component/kg adsorbent x Molar fraction of acetylene in adsorbate y Molar fraction of acetylene in the gas mixture
58
1 Basic Concepts
1 1
X
0
0
1.0
1.0-
t
1 Y-
Fig. 1-38. Influence of pressure on the course of the adsorption isotherm for the coadsorption of two gases [0.8]. X Loading of the adsorbent by the key component x Molar fraction of the component which is more easily adsorbed in the (key component free) adsorbent y Molar fraction of the more easily adsorbed component in the gas mixture
At the concave surface of a wetting adsorbate in the liquid state, for a capillary of radius r, the adsorbate vapor pressure (po,i ) r is lower than the vapor pressure po,i for a flat surface. For a nonwetting adsorbate, b0Jr > capillary condensation does not occur. Due to capillary condensation, with a monomolecular layer at the adsorbed surface the adsorbate concentration is considerably higher than the saturation concentration X,,, (Fig. 1-36). The adsorption isotherm can be found experimentally using volumetric or gravimetric methods. Special methods to measure proportional properties to detect the change in the occupation of the adsorbate on the surface of the adsorbent are also available (see [1.32, 4.1, 4.21). For the correlation and extrapolation of equilibrium data for adsorption processes with one adsorbate component useful approximations are listed in Table 1-12. Experimentation has shown that different adsorption isotherms are occasionally obtained, for data taken during adsorption or desorption under the same conditions. This hysteresis in the sorption isotherm (Fig. 1-36) must be considered in the design of adsorbers and thermal dryers. The hysteresis phenomena can be explained by capillary condensation. For the adsorption in an adsorbent composed of two components from a gas or vapor mixture, the adsorption equilibrium may be conveniently represented using a triangle. The triangular axes are then l/X, y, and y,x mole fractions or mass fractions. Figure 1-37 shows some practical examples from [0.8]. The effect of the operating pressure of the adsorber can be seen in Fig. 1-38. Published adsorption equilibrium data for binary and ternary mixtures can be found in [1.40]. Adsorption equilibria for two component and multicomponent systems may be calculated using the correlations listed in Table 1-13.
1.4 Phase Equilibria
59
Table 1-12. Correlations and methods for the extrapolation of equilibrium data for one component adsorption. 0
Freundlich equation [1.33] X = k, * pk2
k,, k2 Temperature dependent constant determined experimentally. Freundlich's method is valid for the description of adsorption isotherms of form 5 given in Fig. 1-35. 0
Langmuir equation [1.34] X=
k~ . Xmax . p 1+ k A ' p
kA Adsorption coefficient, Xma,maximum monomolecular layer loading of the adsorbent by the key component (adsorbate).
k System specific adsorption constant (usually k = 1); heat of vaporization of absorbate. AfiAd Adsorption enthalpy, Langmuir equation is valid to the point that the monomolecular layer is saturated. kA and Xma,are experimentally determined. 0
Brunauer, Emmet, Teller equation (,,BET" equation) [1.36] kA*p
x = xma, ' -. 1-p
1 -(n+l).p"+n.p"+'
1 + (kA - 1) * p - kA * p n t '
(In the range 0 < p < 0.35 simplification according to X=
k~ . P (1 - a) . (1 - + kA * Xmax.
and rearranging, gives
-.-
-
1
kA
-1
+ .P Xmax*kA X m a x . k ~
X 1-P the linear relationship in the 1/X. p/(p - l), p diagram. Basis for the determination of the BET surface [4.26]).
n Number of molecular layers of the adsorbed component on the adsorbent (for n = 1 Langmuir equation).
BET equation is valid for multilayer adsorption. Modified BET equation also applicable for systems with capillary condensation [1.36].
0
Dubinin equation i1.371
V Adsorbed volume at the adsorbent
V, Adsorbent saturation volume at p = 1
C Structural factor (depends on the pore structure of the adsorbent)
p Affinity constant, m exponent, characteristic for adsorption system
1 Basic Concepts
60
Table 1-13. Calculation of the adsorption equilibrium of binary and multicomponent systems. 0
Modified Langmuir equation [1.40]:
1
e Experimentally determined adaption parameter X,,,,, Monomolecular layer of component i or of all m components (no uniform fixed value)
k, Adsorption coefficient of the ith component (determined by the adsorption isotherm of i ) 0 0
Modified Dubinin equation [1.41] Ideal Adsorbed Solution Theory (IAST) of MYERSand PRAUSNITZ [1.42], Real Adsorbed Solution Theory o f COSTA et al. [1.43].
1.4.5 Liquid-Solid Phase Equilibrium 1.4.5.1 Solubility of Solids in Liquid Solvents If a solid with an amorphous or crystalline structure is dissolved in a large excess of solvent, the dilute solution gives one homogeneous phase. If more solid is added to the diluted solution, up to the point where the solid can no longer be dissolved, the solution is saturated or at solubility equilibrium. The maximum solubility or the maximum capacity of the solvent to dissolve the solid has then been reached. The solubility of the substance to be dissolved in the solvent depends on the temperature, molar amount of solvent in the crystals, and hence the form of the crystals; the dependence on pressure is only minor. For the same crystal form, solubility usually increases with a higher temperature. If the molar volume of the solid decreases during
dissolution, increasing the pressure also increases the solubility. Figure 1-39 shows a schematic section of the phase diagram for a binary system (solvent - dissolved substance), including the eutecticum. The eutectic of solutions diluted with water is called the cryohydrate. It appears in all solvent - dissolved substance systems. In Fig. 1-39, cooling a solution from point A down to the solubility curve SC, causes crystallization to take place (the case of over solubility will be discussed later). The mass fraction of solvent in the solution thus increases because of partial crystallization of the dissolved solid. During the cooling process, the change of state of the solution moves along the solubility curve SC until the eutectic point E is reached, the solution then freezes completely. If a solution is cooled from B, then the solvent freezes when the ice curve IC is reached. The dissolved substance becomes enriched (the concentration of the solution is increased because the fraction of solvent
1.4 Phase Equilibria
I"C1
W-
Fig. 1-39. Phase diagram for a binary solvent/ dissolved substance system with eutectic point without solvate formation. I Homogeneous solution region I1 Two phase region, solution, and solvent as the bottom layer 111 Two phase region, solution, and solid as the bottom layer I V Region of solid phase, solvent, and eutectic point V Region of solid phase, solute, and solvent IC Ice curve SC Solubility curve E Eutectic point (cryohydrate) ~5 Temperature w Mass fraction of the dissolved substance in the solution Phase. -+ Change of the solution state by cooling from A and B
is decreased by freezing the solvent). During the cooling process, the change of state of the solution moves along the ice curve IC until the eutectic point E is reached; the solution then solidifies. No further separation of solvent or dissolved solid by cooling is possible while passing through the eutectic point E. Therefore, the eutectic temperature is the limit for crystallization by cooling. The closer the
61
system is to the eutectic point the more difficult it becomes to separate the dissolved substance from the solvent. The effect of temperature on the solubility is shown by the solubility curve SC. In crystallization processes, the solubility is expressed as a function of the loading X (kg/kg) of the substance dissolved in the solvent. In the solubility-temperature diagram, the saturation concentration or solubility X i s plotted against the temperature r9, with the result being the theoretical solubility curve or saturation line X ( v )(Fig. 1-40). In Fig. 1-41, if a solution is cooled carefully without a crystallization seed, the following is observed: despite the fact that the saturation line has been crossed no dissolved solid crystallizes. After passing the first oversolubility curve, single crystal seeds may be observed, whilst on passing the second oversolubility curve, small crystals develop spontaneously. The area of the stable, unsaturated solution is followed by the area of the metastable, over-saturated solution between the saturation line and the second over-saturation line. It follows that the area where seeds are spontaneously formed is the area of unstable two- or multiphase systems. The range of practical crystallization processes carried out inside the important metastable area depends upon many process parameters, including solution concentration, intensity of mixing in the crystallizer, cooling rate, initial temperature, number of crystal seeds and the crystallizer shape (surface condition). In order to crystallize an over-saturated solution within the metastable area, inoculate crystals must be present when the solubility curve is crossed. If the crystal seeds are present when the metastable area is entered, the over-saturation of the solution will be reduced; this is because the over-saturation is mainly used by the crystal seeds for growth although a few new crystal seeds are formed. Both crystal growth and seed formation occur and
62
1 Basic Concepts
f
2.
t
%
Ig/lOOgl
Region of unstable solution // 1.
oc oc
k Miers-region) /'
Region of stoble solution (subsatured solution)
Fig. 1-41. Temperature-solubility diagram. SC Theoretical solubility curve (saturation line) 1. O C First super solubility curve 2. OC Second super solubility curve X Solubility r9 Temperature
are dependent upon the over-saturation of the solution (see Chapter 7.2.3). For practical use of crystallization processes, data and references regarding the solubility of solids in solvents can be found in [0.17, 1.46-1.50, 7.21. Calculations of the effect of temperature on solubility can be found in [1.111].
tr-l-l-.-pI \ 2
'0
20
LO
60
80 [ O C ] 100
9-
Fig. 1-40. Temperature-solubility diagram, solubility curves for different salts in water. Representation according to PERRY[0.17]. X Loading of solvent with dissolved substance, g of water-free substance in 100 g water (gA00 g H,O), solubility 6 Temperature
1.4.5.2 Melting Pressure Curve The solid-liquid phase equilibrium of a pure substance is described in the state diagram (see Fig. 1-15) by the melting pressure curve p ( T ) . This curve is formed by the connection of state points, where the liquid and solid phase coexist at phase equilibrium. For crystallization processes which start from the melting point, a knowledge of this curve is important. The melting pressure curve may be given based on the general form of the CLAUSIUSCLAPEYRON equation in a similar manner to the vapor pressure and sublimation curves (Eq. (1-71))
1.4 Phase Equilibria
A&, 1 dP dT T . -
(1-135)
(6 V,)
--
where dp/dT is the slope of the melting pressure curve, Ahs, the melting enthalpy, dependent upon temperature and pressure, and the molar volumes in the liquid and solid state, respectively and T the equilibrium temperature. The molar volumes and are almost the same. It is not allowed to simplify Eq. (1-135) by neglecting <. The difference of the molar volumes A V is given by
6
<
q
Depending on the sign, two cases for the difference of A V have to be distinguished for the course of the melting pressure curve:
63
1.4.5.3 Decrease in the Freezing Point An increase in the boiling point or a decrease in the freezing point of a solution containing a nonvolatile component is compared to pure solvent caused by a reduction in the vapor pressure. The reduction of the freezing point A T of a solution is T, - I; as shown in Fig. 1-42 where To is the freezing point (or melting point) of the pure solvent. At To the vapor pressure is the same for the liquid and solid phases of the solvent. T, is defined by the intersection A of the vapor pressure curve VC and the sublimation pressure curve SC of the solvent. If only pure solvent freezes, the freezing point T of the solution occurs at the intersection B of the vapor pressure curve of the solution VCS and the sublimation pressure curve of the solvent SC. For a dilute solution containing nondissociated, nonassociated and nonvolatile substances the decrease of freezing point is
Case 1: AV>O, 6 > 5, el <@,. From Eq. (1-135) it follows that dT/dp > 0 and the melting temperature increases with increasing pressure. This is common for many substances, especially metals.
c,
Case2: A l / < O , 5 < el >@,. From Eq. (1-135) it follows that dT/dp < 0 and the melting temperature decreases with increasing pressure. For example, this applies to water, gallium, and bismuth. For some substances the sign of A V changes with increasing pressure, (for example with rubidium, caesium and graphite) the sign changes from plus to minus. A maximum temperature for the melting pressure curve then is when A V = 0 or el = e,. Different approximations for the melting pressure curve are discussed in [1.88].
YGas
Solid phase
St-
phase
T-
Fig. 1-42. Lowering of the solution freezing
point.
- T Lowering of freezing point
VC
VCS
SC p
T
Solvent vapor pressure curve Solution vapor pressure curve Solvent sublimation pressure curve Pressure Temperature
64
1 Basic Concepts (1-1 3 7)
where A & , is the melting enthalpy of the pure solvent and x, is the mole fraction of the soluted substance in the solution. Therefore, for an ideal solution, the decrease of the freezing point is proportional to the mole fraction of the solute in the solution. As shown by Eq. (1-128), for solutions, electrolytes, in which dissociation of the solute occurs, the number of molecules n2
t
h
Crystalline phase
t.-i
A
h
x-
B
x-
A
nlB
B+M
AIB-M A/B-M +BlA-M
AiB-M B/A.M A/B M - W A - M
~~
A
x-
0
A
x----t
of solute has to be replaced by the number of ions n;. Replacing the mole fraction x2 of the solute by its molality c, = n2/m,, in Eq. (1-137) gives
=
c,
a
c,
where C, is the cryoscopic constant of the solvent, and is defined within the brackets. C, is the decrease of the freezing point of a
Fig. 1-43. Melting point diagram of some binary systems. Type I Miscibility in the liquid and solid state of components A and B, mixed crystal formation over the entire concentration range. Type I1 Miscibility in the liquid state, immiscible in the solid state, melting point B diagram exhibits eutectic point. Type I11 Miscibility in the liquid state, partial miscibility in the solid state, melting point diagram shows eutectic point and mixed crystal region. Type IV Miscibility in the liquid state, partial miscibility in the solid state, melting L+B/A-M point diagram with peritectic point and mixed crystal region. Miscibility B/A gap reaches temperature region in which mixed crystals are formed. B Type V Compound formation by the components, immiscibility of the solid phases, development of two eutectic points, E, and E,. L Melt Mixed crystals M A/B-M A/B-Mixed crystal (excess of A) B/A-M B/A-Mixed crystal (excess of B) Eutectic point E Peritectic point P Connection A/B VAB Liquidus line LL Solidus line s
65
1.4 Phase Equilibria
solution when 1 kmol of the solute is dissolved in 1 kg of solvent. Table 1-14 shows the cryoscopic constants C, for some solvents. Table 1-14. Cryoscopic constants of several solvents. Solvent
Water Benzol Bromoform Cyclohexane Nitrobenzene Naphthalene Acetic acid
Melting point at 1.013 bar (“C)
Cryoscopic constant C, (K . kg/mol)
0 5.5 7.8 6.5 5.7 80 17
1.86 5.12 14.4 20 6.9 6.8 3.9
In an ideal solution, the increase in the boiling point and the decrease in the freezing point for a chosen solvent is only dependent on the concentration of the dissolved substance, and not the type (colligative properties). The increase in the boiling point and decrease in the freezing point may be used to calculate the molar mass of a soluted substance. 1.4.5.4 State Diagrams of Binary Systems
for Solid and Liquid Phase Equilibrium
For the basic calculation of crystallization starting from a melt, the state diagrams (melting diagrams, 7;x-diagrams) for the partial separation of binary mixtures must be known. A thermal analysis is carried out by the experimental detection of cooling curves. The temperature during cooling is measured as a function of time in solutions of different composition (see, for example, [1.89]). Methods for calculating crystallization equilibrium are presented in [1.112].
Figure 1-43 shows characteristic diagrams for binary systems with explanations given in the caption.
1.4*6 Enthalpy
Of
Phase Changes
For an isobaric phase transition of a substance, the enthalpy change is usually considerable. If a substance is exchanged between two or more phases in a heterogeneous system, a considerable positive or negative heat of evolution is expected. This is because an exchange of substances between phases always has a n associated exchange of heat. The enthalpy change of a substance associated with the isobaric transition from one phase to another at equilibrium may be described analogously to the CLAUSIUSCLAPEYRON equation as dlnZi - Ahi
~
dT
-
_
l?- T 2
_
(1-139)
where Zi is a characteristic quantity for the phase change and is dependent on temperature, the type of substance, and often pressure and concentration. This is explained for important thermal separation processes in Table 1-15. Usually Zi(7‘) is the phase equilibrium curve, or the line that divides the area at the different states of the phases. If, for example, in a one component system, the vapor pressure Zi is equal to the saturation vapor pressure po,i of substance i in the liquid phase, p J T ) is the vapor pressure curve of substance i. Areas of liquid and vapor (gas) phases are separated by the vapor pressure curve; single points on it represent phase equilibria (see Fig. 1-15). If a chemical reaction takes place, in separation apparatus at constant pressure, Z ( 7‘) is the chemical, temperature dependent, equilibrium constant. Eq. (1-139) is
5. Variable Zicharacterizing the phase change and phase change enthalpy Ahi.
nge of substance i between phase 1 and 2 Phase 2 Number of system components 1 S
3, n
1
2, n
g
2, n
g
1
g
2, n
g
1
g
2
1
1 2, n
1 1
Characteristic phase change variable Z j
Phase separation curve (phase equilibrium curve)
Phase c enthalpy
Thermal process
Recrystallization Melting Solidification (crystallization from a melt) Dissolving Liquid-liquid extraction Crystallization from a solution Sublimation Desublimation Adsorption Desorption Drying Evaporation Condensation Distillation Partial condensation Absorption Desorption Liquid-liquid extraction
Recrystallization pressure Melting pressure
Recrystallization pressure curve Melting pressure curve
Recrysta enthalpy Melting
Solidus line Liquids line
Vapor pressure curve
Vapor pressure
Sublima
Sublimation pressure curve Adsorption isotherm Desorption isotherm
Gas load of the solid Moisture load of the solid
Differen solubilit
Saturation curve (solubility curve)
Solid load of the solvent
Sublimation pressure
Partial vapor pressure Henry constant absorption coefficient Gas load of the solvent Distribution equilibrium constant
Bubble point line Dew point line Absorption isotherm
Sorption isotherm
Adsorpti
Evapora Evapora Absorpti
Mixing differenc
tions: s solid phase, 1 liquid phase, g gas phase.
67
1.6 Minimum Separation Work
then the Van-Hoff’s isobar, with reaction enthalpy Ahi. An average value of the differential enthalpy Ahi of the phase change may be assumed, by integrating Eq. (1-139) in the temperature interval T, q.This may be done, if no measured data is available, and the shape of the equilibrium Zi(7‘) is known, using +
Ah, =
R e T, -T2.(lnZi,r,-1nZi,r,)
G-T,
(1-140)
1.5 Separation Factor and Relative Volatility The separation factor a is generally defined as
The separation factor is therefore a direct measure of the separation efficiency of a separation unit or the whole process, and is thus of practical importance. It is usually dependent on pressure, temperature, and phase composition. Large values for the separation factor characterize a process whith a low separation effort. The more a approaches unity, the more difficult the separation. When a = 1 separation is impossible. The separation factor a is the relative volatility in distillation processes. The light phase is the vapor phase and the heavy phase is the liquid phase; the component with the lower boiling point is the “light” component. Taking Dalton’s and Raoult’s laws into account, Eq. (1-142), the relative volatility of the lighter component 1 referred to the heavier component 2, becomes
a1,2 =
Y1 ‘P0,l ~
.
Y2 P0,2
(1-141)
= f (p,
XI,. ..)
(1-144)
For ideal mixtures, Eq. (1-144) becomes where X, is the mole ratio of the key component leaving the separation unit or separation apparatus in the heavy phase, and Y, is the mole ratio of key component leaving the separation unit or separation apparatus in the light phase. Substituting the mole concentration Xl and Y, with the mole fraction x1 and y1 (see Table 1-4) the separation factor a,,2is a1.2 =
Y1 ‘ X 2 ~
Y2 +
x1
(1-142)
where 1 represents the key component and 2 represents the reference component. For a binary mixture Eq. 1-142 becomes (1-143)
a1,2 =
P0,l ~
Po,2
=f(p, T )
(1-145)
In this case, a1,2is dependent only on pressure and temperature and not on the composition of the mixture. A reduction of the working pressure p in distillation processes causes an increase in the relative volatility a and the separation becomes more efficient.
1.6 Minimum Separation Work The mixing of pure substances increases the entropy. The entropy of the mixture is the mixing entropy ASM plus the sum of the
68
1 Basic Concepts
entropies of the pure substances before mixing. Since the entropy increases, the free energy (free internal energy AF, in isochoric processes, free enthalpy AG, in isobaric processes) decreases. Thermal separation operations are isobaric apart from pressure drops which occur in the separation apparatus. During mixing the change of the free enthalpy ACM of the system, the free mixing enthalpy is equal and opposite to the minimum separation work Wmin required to separate the mixture into its pure components. Wmi,
=
(1-146)
-AGM
When k components are mixed to obtain 1 mol of a real mixture, as discussed in Chapter 1.4.1, the free mixing enthalpy AgM, is k
agM= R . T C xi.h a i < 0
(1-147)
i=1
AgM is negative for the entire concentration range, as seen in Eq. (1-147). The minimum separation work required to separate 1 mol of the k component mixture is k
qmin= - E . TCxi.lnai>O
(1-148)
i= 1
Work must be supplied to the system thus values of Wmin are positive. The actual work supplied to separate the mixture is usually higher than the minimum separation work, as given by Eq. (1-148). Additional energy is required to create additional phases if necessary, to divide phases using mechanical means, to mix or to disperse. The energy losses of the separation units, and the pump work necessary to transport the liquid are not considered in Wmin.
For a given mixing enthalpy AH,, the mixing entropy ASM may be derived from the definition of the free mixing enthalpy
(In ideal mixtures the mixing enthalpy AH, = 0; therefore ASM = - AG,/T and therefore ATM = - R . C xi lnxi > 0.) +
1.7 Mass Transfer Fundamentals The basic principles of mass transfer are discussed in detail in [1.95-1.971. Thermal separation processes are actually mass transfer processes; matter is transported between phases and across phase interfaces. Mass transfer is caused by differences in concentration within a phase and by disturbances of the phase equilibrium. The time taken to return to the phase equilibrium depends mainly on mass transfer, but also on heat transfer (heat is transported not only by convection and radiation at higher temperature, but also by mass). For the design of thermal separation processes, along with a knowledge of phase equilibria, it is also important to have a detailed understanding of how equilibrium is reached and the time required, taking into account restrictions in the mass transfer rate. There are two ways in which matter may be transported by the concentration gradient (the driving force):
Molecular Diffusion: Transportation of molecular size matter. Molecular diffusion takes place in solids and phases with no motion or in phase boundaries Convective Diffusion or Convection : Matter is transported in groups of molecules with the concentration gradient as the driving force, along with the free or forced flow. Under the operating condi-
1.7 Mass Transfer Fundamentals
tions chosen in thermal separation processes, convective mass transfer always occurs in liquid and gas phases Heat and mass transfer are analogous processes. Molecular diffusion in homogeneous materials or phases is similar to heat transfer. Convective diffusion or convection in homogeneous materials or phases corresponds to heat transfer by convection. Mass transfer at the phase boundary corresponds to heat conduction. Mass transfer between phases occurs like heat transfer in several chronological steps. The slowest step controls the rate of the entire process. Thus the mathematical descriptions of heat and mass transfer operations are analogous. Calculation methods and approaches to calculate the heat transfer coefficients may similarly be used to calculate mass transfer coefficients. (See Table 1-18 in Chapter 1.7.2 for the analogy of heat and mass transfer.)
1.7.1 Mass Transfer by Molecular Diffusion 1.7.1.1 Steady-State Diffusion Analogous to Newton’s law of momentum transport and Fourier’s law of heat transfer by conduction, Fick’s first law for mass transfer by steady-state equimolar diffusion, is
x
Dj
69
x coordinate of the diffusion space diffusion coefficient of component i in the diffusion space (m2/h)
Introducing the partial pressure of gases as measure of concentration, Fick’s first law becomes
oi.A n 4,x = - _ . R.T or m I., x =
-
apj
oi-M ~A. R.T
(kmol/h)
ax
api *
~
ax
(kg/h)
(1-150)
(1-151)
Fick’s first law describes equimolar diffusion, in which all components of the system may diffuse independent from each other. During thermal separation processes, matter is transported through phase boundaries. If a phase boundary is selectively permeable to one component, only one-directional diffusion is possible (an especially important case for absorption, adsorption, and drying). For one-directional diffusion, STEFAN’S law gives (1-152)
where c is the sum of the molar concentration of all components in the observed phase, and i is the diffusing component. For gases, Eq. (1-152) becomes
where rate of mass flux of substance i in direction x perpendicular to the area A (kmollh) diffusion area (m2) A aci/ax concentration gradient in the direction of the diffusion flux (kmol/ m3/m) Hi,x
where p is the system pressure. The difference in the flow rate fij,x as calculated by Eqs. (1-149) and (1-152), is the factor c/(c - cj), which is due to the additional superseding one-directional diffusion (“Stefan flux”). The amount of mass flux transferred by diffusion is therefore larger
70
1 Basic Concepts
with one-directional diffusion than with equimolar diffusion.
only for simple geometric cases (for example, plate, cylinder, sphere).
1.7.1.2 Unsteady-State Diffusion
1.7.1.3 Diffusion Coefficient
In unsteady-state diffusion processes, the concentration distribution (or concentration gradient) changes with time and position. Fick's second law for unsteady-state diffusion is analogous to the Fourier equation for unsteady heat transfer
The diffusion coefficient D generally depends upon temperature, pressure, the concentrations of the components and the substance mixture components to be diffused. Diffusion coefficients for several systems are listed (see, for example, [1.47, 1.49, 1.90-1.921) or may be calculated empirically [0.8, 8.1, 8.2, 8.16, 8.171. Diffusion coefficients for some systems are shown in Table 1-16 and simple calculation methods are presented in Table 1-17.
(1-154) Solutions of the partial differential equation for given boundary conditions exist
Table 1-16. Diffusion coefficient for different systems [0.1]. Diffusing component
2"d Mixture component (diffusion medium) (solvent)
Pressure
Temperature
(bar)
("C)
100 300 1095 1249 178 428
Gold
Lead
Silicon
a-Iron
Copper
Silver iodide
Benzol Carbon disulfide Methanol
n-Heptane n-Heptane Water
Benzol
Air
1.013
Benzol
Hydrogen
1.013
Benzol
Carbon dioxide
1.013
0
Steam Steam Steam
Air Hydrogen Carbon dioxide
0.981 0.981 0.981
45 0 0 0
25 25 18 0 45 0 45
Concentration
Diffusion coefficient
(m2/h)
4.5 to 7.1
0.83 . 0.54. 0.54. 1.80. lo-' 0.48. lo-' 1.23. lo-'
50 50 0.25
0.89. lo-' 1.28 * lo-' 0.49. lo-'
0.03 to 0.09
0.0270 0.0364 0.1058 0.1437 0.0189 0.0257 0.083 0.278 0.051
1.7 Mass Transfer Fundamentals
71
Table 1-17. Simple calculation methods for the diffusion coefficient. Diffusion in the gas phase The diffusion coefficient D l , 2of gas 1 into gas 2 under moderate pressure may be approximated using the critical data of the gases according to CHENand OTHMER[8.15]
(1-155) Where M I ,M2 Molar mass, kg/kmol Tk, Critical temperature, K J $ 2 Critical molar volumes of gas components 1 and 2, m3/kmol T Absolute reference temperature, K P Reference pressure, bar Dl,2 Diffusion coefficient, m2/s (To convert to different reference conditions and to therefore compute a rough estimate of the diffusion coefficient at different temperatures and pressures, a diagram is given by SLATTERY and BIRD [S.l5]).
5,
0
Diffusion in the liquid phase In large dilution of a solution without dissociation, the diffusion coefficent D l , 2of component 2 in a solvent 1 may be calculated using an equation given by WILKEand CHANG [8.15]
(1-156) Where D l , 2 Diffusion coefficient, cm2/s T Reference temperature, K q1 Dynamic viscosity of solvent, CP M I Molar mass of solvent, kg/kmol & Molar volume of dissolved substance referred to the boiling point at 1.013 bar, cm3/mol C Association factor (C = 2.6 for water, C = 1.9 for methanol, C = 1.5 for ethanol, C = 1.0 for benzol, ether and heptane as a solvent) The temperature dependency of the diffusion coefficient D l , 2 is approximated by the Stokes-Einstein-Term [0.17] (1-157)
The influence of the concentration on Dl,2is discussed, for example, in [0.17].
72
1 Basic Concepts
1.7.2 Mass Transfer by Convection According to the method used to calculate heat transfer by convection, the convective mass transfer under steady state conditions is
PB
I
t
I
,_
Phase I Ci,G
hi = p; * A * ( q k- Cj,G) = A * Ac;
Y
Phase II
L
(1-158)
X-
Fig. 1-44. Illustration of mass transfer.
See also Fig. 1-44, where: convective flow rate of substance i (kmol/h) area of phase boundary (m2) A cLK,c , concentration ~ of substance i in the bulk of the observed fluid Phase and at the phase boundary, respectively (kmol/m3) Pi mass transfer coefficient (m/h) ti;
PB Phase boundary 6 Boundary layer thickness c, Concentration of key component x Space coordinate
matter is only transported by molecular diffusion. Eqs. (1 - 149) and (1 - 158) are then
For gases, Eq. (1-158), gives
ti = I
P;-A -*
R-T
(pi,k
- P I ,G)
=
P,.A
Re T
. Apl (1-159)
where the partial pressures of the gas i, pi,K and pi,Gare those in the bulk of the gas phase and at the phase boundary, respectively. Eq. (1-158) describes generally the transition of a substance from within the bulk fluid to a phase boundary, or from a phase boundary into the bulk fluid (for the latter case, Eq. (1-158) must be appropriately modified). The concentration of the component in the kernel c ~ is , assumed ~ to be constant throughout the fluid. A concentration gradient Aci occurs only in the vicinity of the phase boundary (see Fig. 1-44). Furthermore, it is assumed that a laminar current exists in the boundary layer and that
and the mass transfer coefficient is
p.=-Di
'
s
(1-161)
where 6 is the thickness of the boundary layer. From this equation, the dependency of the mass transfer coefficient Pi on the diffusion coefficient 0; and the boundary layer thickness 6 of the fluid flow, may be seen. The laminar boundary layer and turbulent bulk cannot be distinguished exactly, due to the continous transition; the boundary layer thickness 6 is, therefore, a formal complementary variable. The mass transfer coefficient P depends upon fluid mechanics (free flow, forced flow), the physical characteristics of the exchanging matter system and the properties of the substance in the fluid phase, and may
1.7 Mass Transfer Fundamentals
73
Table 1-18. Analogy between mass and heat transfer. Analogous variable
Heat transfer
Mass transfer
Transfer variable
Heat flux Q (kJ/h)
Mole flux ri (kmol/h) Mass flux m (kg/h)
Driving force
Temperature gradient A 8 ("C)
Concentration gradient Aci (kmol/m3) Partial densitiy gradient Aei (kg/m3) Partial pressure gradient Api (bar)
Thermal conductivity
Diffusion coefficient D (m2/h)
Heat transfer coefficient a (W/(m2. K))
/3 (m/h or kg/(h . m2. bar) or
Transport coefficient Transfer coefficient
1 (W/(m. K))
Mass transfer coefficient
kmol/(h . m2 . bar) ( k is used as overall mass transfer coefficient)
Dimensionsless numbers to consider -
Gr, modified Grashoff number (see [1.31])
free flow Grasshoff number
-
Re
forced flow Reynolds number
=
W.1 ~
V
Reynolds number
- flow
Galilei number
F, Fr=-=-
- flow
w2
Fg
(.g Froud number
- two phase flow
Weber number - two phase flow
Eotvo's number -
physical characteristics
v
pr=-=a
V.Cp'Q
1
Prandtl number [ratio of molecular momentum transfer (friction, or viscosity effect) to molecular heat transfer (heat conduction)]
V
sc = -
D
Schmidt number [ratio of molecular momentum transfer (friction or viscosity effect) to molecular mass transfer (diffusion effect)] (continued next page)
74
1 Basic Concepts
Table 1-18. (continued) Analogous variable Dimensionless numbers used to calculate the transfer coefficients
Heat transfer
Nu=-
Mass transfer
a.1
Sh =
I
p.1 ~
D
Nusset number (ratio of total heat transfer over heat conduction alone)
Sherwood number or second Nusset number (ratio of total mass transfer over molecular mass transfer)
Nu = f ( G r , , P r )
Sh
for free flow
for free flow
Nu = f(Re, Pr,
. ..)
=f
(Grs,Sc)
Sh = f(Re, Sc,
... )
for forced flow
for forced flow
Nomenclature : Fg gravitational force, F, inertial force, Fq viscosity force, F, surface force, I = L , characteristic length, q dynamic viscosity, v kinematic viscosity, I heat conductivity, a temperature conductivity, e fluid density, surface tension of fluid(s), g gravity constant (9.81 m/s2), w flow velocity of fluid, thermal volumetric expansion coefficient of the fluid (for Grashoff number)
known physical characteristics and heat transfer area. In mass transfer, the fluid phases are in contact, and are separated by a phase boundary. The interfacial area depends upon the internals in the apparatus, fluid mechanics, and the properties of the substances making up the phases. Therefore, the dimensions of the surface of the phase boundary are not easily determined. At the phase boundary, equilibrium between the phases is assumed. This equilibrium at the phase boundary must be considered in mass transfer operations.
be calculated in a similar way to the heat transfer coefficient a , by means of dimensionless numbers. The most common dimensionless groups are listed in Table 1-18, including those essential for the calculation of the mass transfer coefficient.
1.7.3 Overall Mass Transfer Overall mass transfer is the transportation of matter through a phase boundary, from one fluid phase into another. Resistance to the mass transfer is analogous to resistance to heat transfer in that it may be considered as being divided into individual resistances; this will be demonstrated later. The main differences between mass transfer and heat transfer are: 0
In heat transfer, the fluid phases are separated by a defined, solid wall with
0
Individual resistances in heat transfer operations may easily be determined by experimentation. In mass transfer operations between two fluid phases, only the total resistance can be found experimentally, and only under complex experimental conditions. During heat transfer the individual resistances are: resistance due to convection in fluid 1, heat conduction
1.7 Mass Transfer Fundamentals
resistance of the wall, and resistance due
to convection in fluid 2. In mass transfer
operations, a mass transfer resistance has to be considered in each phase of the system. Most approaches (two film theory, theory of surface renewal) assume that there is no transfer resistance in the surface of the phase boundary which is not true for every case. For example, surface inhibition occurs at the boundary if active boundary substances are enriched within the boundary. If the substance exists in both phases under different conditions or forms, there may also be surface reactions. The mass transfer may also be considerably influenced by eddies at the boundary (turbulence in the boundary surface layer, Marangoni effect).
75
PB
t u
Fig. 1-45. Illustration of mass transfer, the twofilm theory.
PB Phase boundary (Interfacial area) Concentration of key component x Space coordinate c
where 1.7.3.1 Two Film Theory, Mass Transfer Coefficient and Turbulence Theory
The two film theory [0.4] describes the mass transfer between two adjacent phases. The main resistance occurs in the two boundary layers at either side of the interface. In these laminar boundary layers, matter is only transported by molecular diffusion. With a phase equilibrium at the interface, the interface itself offers no resistance to the mass transfer. Mass transfer is very fast in the bulk of the phase, due to turbulent convection. The concentrations c ~and , cKII ~ are uniform throughout the bulk phase (see Fig. 1-45). As shown in Chapter 1.7.2 and Fig. 1-45, the mass flux from phase I to phase I1 is
ri
mass flux across interface mass transfer coefficient in phase I and phase I1 c ~ , cK,[, ~ , bulk concentration of the substance of interest in the bulk of phase I and phase 11, respectively A interfacial area c ~ cG,II , ~ , concentration of the substance at the interface
P,,PII
The existing phase equilibrium at the interface means that the concentration is (1-164)
CG,I = K * . CGJI
where K* is the equilibrium constant (see Chapter 1.4 and Fig. 1-46). The concentration gradient in phase I is (1-165)
Matter leaving phase I enters phase I1 through the interface and therefore,
and in phase I1 is n
(1-166)
76
1 Basic Concepts
C
Introducing an overall mass transfer coefficient kll, related to the overall mass transfer resistance in phase 11, it follows that 1
1
1
k11
PI1
K * *PI
-=-+-
CII
therefore the molar flux ri is
-
(1-172)
Fig. 1-46. Concentration diagram for mass transfer. BL Balance or operating line
EC Equilibrium curve c1 Concentration of key component in phase I cII Concentration of key component in phase 11
Considering the concentrations cK,I and cK,,, related to the equilibrium concentrations cy and c;"l c K , ~= K " .
~fi
(1-167)
cl*
(1-168)
and
c,,,,
1
=-
K*
(1-171)
Eq. (1-165) may now be written as
where all the variables refer to phase 11. Analogously, referred to phase I 1
1
kl
PI
- _ --
K*
+-
(1-173)
PI1
and
li = k, . A *
(CK,1
- )c:
(1-174)
Eqs. (1-171) and (1-173) Show how the aPpropriate reciprocal value of the mass transfer coefficient is used to calculate the total mass transfer resistance of phases I and 11. When PI1% P, is k, = PI, and the total mass transfer resistance is essentially controlled by the resistance in phase I. When PI % PII is k,, =DI1 and the total mass transfer resistance is essentially controlled by the resistance in phase 11. The ratio (1-175)
combining Eqs. (1-166) and (1-169) gives (1-170) The concentration at the interface cG,1 1 , which is not easily determined experimentally, has been eliminated.
is derived from Eqs. (1-162) and (1-163) and gives the slope of the line connecting PI and Pz in Fig. 1-46. The two film theory is only an approximation of the real mass transfer in thermal separation processes. Nevertheless, it is used for the evaluation of mass transfer measurements. In the thermal separation of mixtures, the interface between phases is usually not
1.8 Steady-State Cocurrent Operation
fixed; it is constantly changed and renewed by the effect of the flow of the phases. More accurate descriptions of mass transfer are shown by HICHBIE[1.93] in his penetration theory and DANCKWERTS [1.94] in his rheory of surface renewal. Both theories take into account the change of the surface of the interface. According to turbulence theory, the mass transfer coefficient /3 is proportional to the square root of the diffusion coefficient D (see Eq. (1-161)).
/3-@
(1-176)
77
(multicomponent) carrier and the component to be exchanged. The total mass balance of the unit (see balance area BAI in Fig. 1-47 and Chapter 1.3) gives the following equation for the exchanged component La * X , - L , . X ,
where . . L a ,L ,
x,, x,
=
Gu . yW - G, . ya (1-177)
entry and exit flux of phase I mole fraction of transferred component at the entry and exit of the unit (phase I) entry and exit flux of phase I1 mole fraction of transferred component at the entry and exit of the unit (phase 11)
1.8 Steady-State Cocurrent Operation
Ga, G, y,, y ,
The cocurrent principle, mentioned in Chapter 1.1, is the basis for the following general discussion of steady-state cocurrent operations. Figure 1-47 shows two immiscible phases Ph I and Ph 11, guided in cocurrent flow through a separation device. Both phases may be mixtures of components, and during the contact of the two phases, one component is transferred from Phase I to Phase 11. Therefore, both phases consist of a
Due to selectivity, only one component is assumed to be transferred between both phases, thus the total flux of each individual phase changes throughout the separation unit. But the flux of the inert components in each phase remains unchanged. Therefore, it is convenient to relate the mole fraction x and y to the inert carrier fluids L, and G, as a mole ratio of component i in
Fig. 1-47. Steady-state cocurrent operation. PhI Phase I PhII Phase I1 BAI Balance area I (Complete separation unit) BAII Balance area I1 (Partial separation apparatus)
78
1 Basic Concepts
the inert (moles i/moles inert). Eq. (1-177) then becomes LT*( X , - Xu) = GT*(Y, - Y,)
tl
(1-178)
In a X X coordinate system, this equation gives a straight line of slope -LT/GT between the points PI (X,, Y,) and P2(X,, Y,) (see Fig. 1-48). Considering only one part of the separation unit (balance area BAII in Fig. 1-47), the mass balance of the exchanged component is L T * ( X , - X ) = G , * ( Y - Y,)
(1-179)
XG
xu x
xu
X----t
Fig. 1-48. Loading diagram for a steady-state cocurrent mass transfer operation from phase I to phase 11. EC Equilibrium curve BL Balance line Y Loading of phase I1 X Loading of phase I
In a K X plot, it also gives a straight line of slope -LT/GT between the points P, (X,, Y,) and P ( X ,Y) (see Fig. 1-48). The line is the balance line, or operating line, of the separation in a steady-state process with cocurrent flow. It is identical to the line given by Eq. (1-178). Points on the balance line represent any chosen cross section of the separation unit, with the corresponding concentration X and Y. P, characterizes the entry cross section into the unit and P2 the exit cross section. (According to Eq. (1-177), if the mole fraction is the concentration scale given by Eq. (1-179), the balance line becomes a curved line. This is also the case if the inert fluxes LT and GT are not constant along x 4 the length of the separation device.) The equilibrium curve Y ( X )of phases I Fig. 1-49. Loading diagram for a steady-state and 11, based on the loading of i, Y and X , cocurrent mass transfer operation from phase I1 is now added to the Y,X diagram in to phase I. Fig. 1-48. The intersection Q(X,, Y,) of EC Equilibrium curve the operating line and the equilibrium curve BL Balance line represents the conditions at the exit cross Y Loading of phase I1 section. This is called a theoretical transfer X Loading of phase I unit, and equilibrium between the phases leaving the transfer unit is reached. If component i is transferred from phase I1 into phase I, the operating line is above ally (for example, cocurrent distillation and the equilibrium line, as shown in Fig. 1-49. cocurrent drying). Countercurrent flow of Cocurrent operation, in thermal separation the phases, which will be discussed in the of homogeneous mixtures is used occasion- following chapter is of more practical use.
tI
1.9 Steady-State Countercurrent Operation
79
1.9 Steady-State Countercurrent Operation a)
Based on the principle of countercurrent flow presented in Chapter 1.1, steady-state countercurrent flow operations are generally discussed in the following section. The separation of a mixture in a single stage does not normally separate the mixture into fractions of the required purity. To increase the separation effect, single stages may be connected to form a cascade (Fig. 1-50). A cascade is a separation device consisting of several similar stages, or several separation units connected in series. If the phases are in countercurrent flow, a serial connection of single stages similar to a countercurrent flow cascade, can be achieved in a countercurrent flow column (Fig. 1-51). This is a practical, simple and economic method of multiplying a single stage separation effect. It is not necessary for countercurrent flow phases to be in stagewise contact (as in tray towers). Constant contact of the phases throughout the length of the column is possible. For the design of countercurrent flow columns, essentially two theories are used,
[ IF M
A
Fig. 1-51. Countercurrent flow column. a) Reflux principle b) Flow through principle F Feed to be separated E Top product A Bottom product I . . .V Separation stages in the countercurrent flow column
the theory of separation stages and the kinetic theory of separation of mixtures in countercurrent flow. The theory applied depends mainly on the type of countercurrent flow process, the internals in the column, the type of mixture to be separated, and its physical and chemical properties.
1.9.1 Theory of Separation Stages
Fig. 1-50. Series connection of individual separation stages (Cascade). I, 11, 111 Equivalent separation stages F. . Feed L , , L,, . . . Individual fraction flows
In separation processes, a common problem is a mixture of a certain composition to be separated into two fractions, where after separation each fraction is of the required composition. If the separation is carried out in a countercurrent flow column, the
80
1
Basic Concepts
necessary height for heat and mass transfer must be determined. The height of the column depends on the number of separation stages connected in series, where each stage represents a single theoretical separation stage (see Chapter 1.1). The actual height of the countercurrent flow column is fixed by the number of theoretical stages and the "stage efficiency factor" (amplification ratio). Determination of the number of required stages is now discussed. Figure 1-52 shows two immiscible phases PhI and PhII flowing countercurrently through a column. Both phases consist of a multicomponent mixture but only one component is transferred from phase 1 to phase I1 during the contact of the phases. Therefore, the phases are composed of a (multicomponent) carrier or solvent and the component to be transferred. Phl PhII
Fig. 1-52. Countercurrent flow column. PhI Phase I PhII Phase I1 BAI Balance area I (total separation column) BAII Balance area I1 (a column section) CC Countercurrent column
Using the notation given for cocurrent flow, a mass balance for the whole separation column (balance area I in Fig. 1-52) for the component to be transferred is
L a .x, + 6,. ya = i, - x, + G, .y ,
(1-180)
where the mole fraction is the concentration scale, or the loading
A mole balance over a section of the column (balance area I1 in Fig. 1-52) with respect to the component to be transferred, gives
and
G,* ( Y - Y,) = i, . (X-X,)
(1-183)
Eqs. (1-181) and (1-183) are plotted on a X X coordinate system and straight lines are produced between the points PI (X,, Y,) and P2(Xa,Y,) and between the points P,(X,, Y,) and P ( X , Y ) .These are the balance lines, or operating lines, with slope LT/GT,the ratio of the flow rates of the carriers. When a component is transferred from phase I into phase 11, the balance line is below the equilibrium line. When a component is transferred from phase I1 into phase I (see Fig. 1-53), the balance line is above the equilibrium line. If the carrier fluxes L, and G , are not constant along the length of the separation device, or other concentration scales are used, the balance line is curved. Points on the balance line link the related mole concentrations X and Y at any cross section of the separation unit. The greater the distance between the balance line and the equilibrium curve, the higher the concentration gradient, i. e. the driving force, for the mass transfer, or the "disturbance from equilibrium". Driving
1.9 Steady-State Countercurrent Operation
Fig. 1-53. Loading, or operating diagram of a countercurrent flow process. BL Balance line EC Equilibrium curve Y Loading of phase I1 X Loading of phase I
forces vary along the column height, as shown in Fig. 1-53. If the balance line touches the equilibrium line, the driving force is zero. The phases in contact at that particular cross-sectional area are in equilibrium, no mass transfer occurs. The separation processes discussed so far consider phase I as a fresh feed into the column. This is important for separation processes such as absorption and extraction. For these processes it is practical to use mole ratio as a concentration scale based on the solvent or inert flux, since the flow remains constant, or will only change negligibly, along the column height. If phase I is generated by phase transition or phase reversal from phase I1 in a heat exchanger on top of a counterflow column, a reflux principle is used instead of the simple flow-through principle (see Fig. 1-51). Phase I is no longer a fresh feed to the column but is the reflux generated by converting phase I1 into phase I; this is the case in countercurrent distillation or rectification. The liquid phase I, the reflux, is generated by partial or total condensation of the
G,y
81
t t
LeX PhII PhI
Fig. 1-54. Reflux principle in a countercurrent flow column.
CC Countercurrent flow column C Condenser BA Balance area PhI Phase I (reflux) PhII Phase I1 (vapor phase)
upflowing vapor phase I1 in a condenser at the top of the column. A mass balance over the upper part of the counterflow column, as shown in Fig. 1-54, at constant vapor flux G and constant reflux with total condensation of phase 11, gives G=L+E
(1-184)
and for the component to be transferred
-
G y
=
i . x + I?.X,
(1-185)
From this, the balance, or operating, line of the rectification column is given by (1-186) where the reflux ratio v is the ratio of the downflowing reflux L = R to the leaving product at the top of the column E
82
1 Basic Concepts
R
(1-187)
V = 7
E
and following from Eq. (1-186)
1.9.2 Method to Determine the Number of Theoretical Separation Stages for a Countercurrent Column
A discussion of a method of determining (1-188) the number of theoretical separation stages v+ 1 required to separate a mixture in a counterflow column follows. Eq. (1-188)is plotted on a y,x diagram (see Fig. 1-55) as a straight line if the slope v/(v + 1) of the balance or operating line is McCabe-Thiele Method constant, or rather if v is constant. A graphical method to determine the theoretical stages of counterflow columns which is easy to use was introduced by MCCABE [1.98]. and BIELE The McCabe-Thiele method is based on the idea of theoretical stages (theoretical separation unit, theoretical tray). From Chapter 1.1, a theoretical stage is that part of a separation apparatus in which heat and/or mass transfer occurs between two phases in contact. Both phases leaving the theoretical separation unit are at phase equilibrium. For a given separation task, the counterFig. 1-55. Operating diagram for a binary system flow column contains the required number EC Equilibrium curve. of theoretical stages in series. To calculate BL Balance or operating line the number of theoretical stages, the x (tan x = v / [ v + I]) Gradient McCabe-Thiele method is applied, for exyo (yo = x E / [ v+ 11) Ordinate intercept ample, to a rectification column for the parx Molar fraction of the low-boiling compotial separation of a binary mixture. In this nent in the liquid phase case, the molar vaporization enthalpies of y Molar fraction of the low-boiling compothe components of the mixture are assumed nent in the vapor phase to be equal and the enthalpy changes of the vapor or the liquid are negligible. Then, the balance line is straight. (A method to calcuWhen, at the phase contact, an equal late a solution to this separation problem amount of matter is converted from phase under different conditions is shown in I (liquid) into phase I1 (vapor) and vice Chapter 2.5.2.4). Fig. 1-56gives a schematic versa the mass fluxes G and L are constant diagram for a rectification column with n along the length of the column. In adiabatic theoretical stages and also the correspondoperation of the column this is only valid if ing y, x diagram according to MCCABEand the components of the mixture have equal BIELE. The vapor flux G leaving the nth stage molar vaporization enthalpies and exhibit with composition yn of the lower-boiling ideal behavior.
y = - . xV+ v+l
XE
1.9 Steady-State Countercurrent Operation
83
Fig. 1-56. Schematic of a rectification
Yn-1
Yn-2
Yn-3
I
I
1 I
&Phase
+Phase
X - - t
I1 (vapor phase) I
(liquid phose. reflux)
component is totally condensed in the condenser. Some of the condensate leaves the top of the column as product E with composition y, = x,. The rest of the condensate, L = G - E, is the reflux at stage n with composition x,. Vapor with composition y , and reflux with composition X , are linked by the balance line given by Eq. (1-188), where in particular y , = x,. The balance line intersects with the y = x line at the point A (xE,yn= xE) in the McCabe-Thiele diagram. For a given reflux ratio v, it follows that yo = x,/(v 1) and therefore point B (O,y,) on the balance line AB is fixed. In general, the balance line combines the mole fraction y,-, and x, of two stages.
+
~
V y,-1 =-. x, + XE v+l v+l ~
(1-189)
Since stage n is a theoretical stage, the vapor leaving the stage yn is in phase equilibrium with the reflux x, leaving stage n. On the McCabeThiele diagram, this gives the point A, with the coordinates x, and y , on
column for the separation of an ideal binary mixture, and the corresponding McCabe-Thiele diagram. C Condenser RC Rectification column n, n - 1,. . . Theoretical separation stage number, indice for the vapor and reflux mole ratio of the low-boiling component EC Equilibrium curve BL Balance or operating line y Molar fraction of the low-boiling component in the vapor x Molar fraction of the low-boiling component in the reflux
the equilibrium curve. The points A,, A,, and A characterize a theoretical stage n. The following stages n - 1, n - 2, etc., can be constructed in the same way, by extending the steps between the balance line and equilibrium curve. For every counterflow separation process, the number of theoretical stages can be found by this simple graphical procedure. Each stage is constructed between the equilibrium curve and balance line, starting with the initial point and finishing at the end point. Obviously in Fig. 1-56 the separation of a binary mixture with the given reflux ratio v gives a top product with composition x, and a bottom product of composition x > xmin. xmi,can only be reached with an infinite number of theoretical stages. Therefore, the reflux ratio v is the minimum reflux ratio for xmi,(see Chapter 2.5.2). If xminshould be reached by the separation, the reflux ratio v has to be raised accordingly (for more details see Chapter 2.5.2). A method similar to the McCabe-Thiele method exists for the graphical determina-
84
1 Basic Concepts
tion of theoretical separation stages for counterflow columns where phase I is not a reflux but a fresh feed phase. The number of theoretical stages is found by the construction of steps between the equilibrium curve and the balance line (see Fig. 1-57). The ratio L T / G T is of particular importance. With practical separation stages installed in counterflow columns, phase equilibrium cannot be reached. Therefore, the efficiency of a practical stage is lower than that of a theoretical stage. For the installation of practical stages in a column, the stage efficiency E (exchange ratio, MURPHREE Efficiency, introduced in Chapter 1.1) is found by a comparison of the number of practical stages and theoretical stages. E may be related to either one of the phases. Relating E to the upflow phase gives
Phl
Egm =
yd yd
- yu - yu,h
(1-190)
or Egm =
yu - yd
'uth - yd
(1-191)
depending on whether the reference component is transferred from phase I into phase I1 or vice versa (see Fig. 1-58). YUthis the mole fraction of the upflow phase for a theoretical separation stage. The method used to determine stage efficiency is demonstrated in Fig. 1-58. The concentrations of the component of interest are experimentally determined in relation to the reference components of the entering and leaving fluxes Xu and xd.For a given
PhII
a)
b)
Fig. 1-57. Schematic of a countercurrent flow column with mass transfer from phase I1 to phase I (a) and an operating diagram to determine graphically the number of theoretical separation stages (b). EC Equilibrium curve BL Balance line n, n - 1,. . . Theoretical separation stages, refer to the loading of the key component in phases I and I1 as indices Y Loading of phase I1 with key component X Loading of phase I with key component
1.9 Steady-State Countercurrent Operation
85
current separation stage
Ph I Ph II a1
bl
Cl
Fig. 1-58. Definition of the stage or Murphree efficiency factor for a countercurrent flow column with the theoretical and practical maximum change in key component loading in a particular stage with mass transfer from phase I1 to phase I and vice versa.
EC Equilibrium curve BL Balance line Y,,, Phase equilibrium loading at X ,
equilibrium curve and balance line, the stage efficiency Egmis the ratio of the distance between these lines. The stage efficiency EI, is related to the downflow phase, and is thus similar to Eqs. (1-190) and (1-191). The stage efficiency varies from stage to stage according to the course of the equilibrium curve and balance line. It is dependent on the design of each separation stage, the process parameters in the column and the properties of the phases in contact. Usually the efficiency is determined experimentally. Empirical approximations may only be used to calculate the stage efficiency factor for a few simple cases. (Due to the nonideal mixture of the phases leaving the separation stage, the stage exchange rate Egmis the mean value of the local exchange rate Eg over the cross section of the stage, see Chapter 2.5.6.1. The latter value can only be calculated if the fluid mechanics of the phases at the cross section are known.) If E,, is the average of all stages, the approximate number of stages Np to be installed in t h e e m n is
Nt
Np = _ _
(1-192)
Egmm
where Nt is the number of theoretical stages, determined by computation or graphically. Where the slopes of the equilibrium curve and balance line are very different this approximation can lead to significant errors. For this case a “pseudo-equilibrium curve” between the equilibrium curve and balance line as shown in Fig. 1-59 may be introduced. Its course is determined by the vertical distances between the equilibrium curve and balance line divided by the stage exchange rate Egnl: a = Egm.b
(1-193)
The number of practical stages Np is determined by constructing steps between the balance line and pseudo-equilibrium curve. In Eq. (1-193), the exchange rate Egmis used repetitively in the interval X , + Xu. If trays are used as internals in a column, the theory of separation stages is particularly important for the determination of the actual column height (see Chapter 2.5.6.1).
1 Basic Concepts
PEC -4
5‘
/
Fig. 1-59. Determination of the number of practical separation stages. EC Equilibrium curve PEC Pseudo-equilibrium curve BL Balance line Y Loading of phase I1 X Loading of phase I
The values of n, and HETS depend on the form of the packing material, the type of packing (or the geometry in general), the operating conditions, and the properties of the two counterflow phases. nt can only be computed in particularly simple cases. The value is usually determined experimentally. If the number of theoretical stages Nt is determined, (for example by the graphical McCabe-Thiele method or by computation), and n, or HETS for the chosen packing are known, the height Z for mass and heat transfer of the packed column can now be calculated with Eqs. (1-194) or (1-195), respectively.
1.9.3 Calculation for Counterflow Columns
Graphical methods for the determination of the required number of theoretical stages discussed so far, are easy to use and are of practical importance for first approximations for separation processes of binary mixtures, or for systems with inert carrier mixtures and a single component to be transferred. If several components are transferred between the phases in contact, the number of separation stages can only be (1-194) calculated with the aid of a computer; graphical methods can only be partially apwhere n, is the number of theoretical plied. stages, which corresponds to the height Z of Methods of calculating the separation of a packed column and Nl is the number of multicomponent mixtures in counterflow theoretical stages that are effective along columns are based on the two “stage-tothe height of the packed column. Therefore, stage” methods by LEWISand MATHESON the reciprocal value HETP = HETS is the [1.99], or THIELE and GEDDES[1.100]. Both height of the packing, which has the same methods are iterative and usually exhibit usage as a theoretical stage (HETP: Height bad convergence, as well as needing a lot of Equivalent to one Theoretical Plate, HETS: computing time and power. Thus, until Height Equivalent to one Theoretical 1960, several approximation methods, or Stage). “short cuts” were developed and modified using simple assumptions to simplify the 1 HETP = (1-195) column design [1.101]. These short cuts are still of practical interest for an estimation nt
Heat and mass transfer in counterflow phases usually only takes place within the area of the trays. The theory of separation stages is also valid for packed columns. Since single stages cannot be distinguished, an evaluation number n, or its reciprocal value HETP or HETS is introduced
1.9 Steady-State Countercurrent Operation
87
been developed. However, a method giving sufficient and rapid convergence for a general design problem does not yet exist. Methods to calculate counterflow columns exactly are based on a column model. The column model gives a system of nonlinear equations, the task of each method is to solve this system. The equation system contains an overall mass balance and also a balance for each component, enthalpy balances, equilibrium relationships and the stoichiometric conditions for the sum of the concentrations for the theoretical stages of a counterflow column (see Fig. 1-60). In the equation system, the following nomenclature is used: Lj
Fig. 1-60. Model of a countercurrent column. i Flow rate of phase I (downflowing phase) SL Flow rate of side stream phase I F Feed 1, .. .j , . . .,n Theoretical separation stages (1 < j < n) j Stage index BA Balance area G Flow rate of phase I1 (upflowing phase) SG Flow rate of side stream phase I1 Q Heat flow
of the design of the column, and as first iteration variables for an exact check. If strong heat effects along the column height or pronounced nonideal behavior of the mixture occur, the short cuts fail. Since 1960, several methods for the exact calculation of a counterflow column have
flow rate of downflow phase leaving the jthstage Gj flow rate of upflow phase leaving the jthstage SLj flow rate of side stream leaving the jthstage (same state as the downflow phase) flow rate of side stream leaving SGj the jthstage (same state as the upflow phase) feed 6 .cj part of feed (same state as the downflow phase) FJ . (1 - c j ) part of feed (same state as the upflow phase) j index, characterizes the actual separation stage; starting at the top of the column, j is counted from 1 to n, from top to bottom heat flow from stage j Qj
6.
The column model in Fig. 1-60 is generally valid for rectification, counterflow absorption, and counterflow extraction. For rectification (see Chapter 2.5.2), the nomenclature used is : stage I (j=1)
condenser at the top of the column
88
1 Basic Concepts
SG, = O with total condensation SG,=O FI * E ] = O valid for normal cases, not F2=0 valid for a stripping column heat flow out of condenser Ql top product flux SL, vapor stream to condenser G reflux from condenser i, heat loss from an actual stage Qj (under approximately adiabatic operating conditions of the column) side stream, vapor SGj side stream, liquid SLj stage n
reboiler
F, =O
valid for normal cases, not valid for an enrichment column
(J =n>
F,+I= O heat supply to the reboiler bottom product flux vapor mixture generated in reboiler
- Qn
SL, Gn
and for counterflow absorption (see Chapter 3.5):
Fl . c1 F,+l
SG] SL,
feed of solvent needed to absorb the key component (washing liquid) (el = 1) feed of gas mixture to be treated ( E , + , = 0) flow rate of treated gas mixture leaving the column flow rate of loaded washing liquid leaving the column
Except for the listed flow rates, all other F,, SGj, SL,, and Qj are virtually zero. In an absorption column operated with an intermediate coolant as the washing liquid, Qj is substantially different than zero. For the case of counterflow liquid-liquid extraction (see Chapter 6.2.3.4)
F,.
E .,
F,+,
feed of heavy phase feed of light phase
SGl L,
s
light phase exit flow rate heavy phase exit flow rate
Usually no side streams are withdrawn ( s L j= 0, s G j = 0 ) and side feeds are not considered (5 = 0). At normal conditions, heat flux Qj through the sides or column walls is negligible. The following approximations are made for the calculation of a counterflow column : The concentration of the phases in one stage (on a tray) are uniform over the cross-sectional area of the column The phases leaving the stage are at phase equilibrium [the stage efficiency coefficient (enriching factor) may be used throughout the calculation] The column is operated at steady-state conditions (an exception being simulation of the start up of the column using dynamic methods; for example see [1.102]) In absorption and extraction processes, the assumption of phase equilibrium of the phases leaving the stage is less valid than in rectification processes. The exact calculation for a counterflow column using the theory of separation stages is generally carried out for rectification processes. The following discussion of a system of nonlinear equations, based on the column model, is particularly valid for rectification, but this may be applied to all other counterflow processes. Before the equation system can be formulated the variables used to describe the state of the counterflow system must be expressed. According to the column model in Fig. 1-60 they are
6
T.F
'.i
SLj s Gj
8;
i';
feed temperature of feed liquid fraction of the feed leaving side stream, liquid leaving side stream, vapor heat flux reflux flow rate
1.9 Steady-State Countercurrent Operation
Gj
T,, Pj x. 1 3 J.y y 1,J .. . z.[ , J.j L ’ z.1J.G
n
vapor stream temperature and pressure of the stages (on the column tray) molar fraction of key component i in the reflux stream L, and the vapor stream Gj molar fraction of the key component i in the liquid and vapor part of feed F j total number of separation stages (trays)
Equations showing the relationships of these variables are given in the following chapters.
1.9.3.1 Mass Balances The overall mass balance over the upper section of the column (see balance area BA in Fig. 1-60) gives J
(F, - SG, - SL,)
+
k=l
+ <+I
*
(1 - ~ j + l + ) Gj+l = Lj
89
If there are rn components in the mixture, rn individual mass balances must be calculated for each separation stage.
1.9.3.2 Phase Equilibrium Relationship For a theoretical separation stagej for each component i, the relationship between the phase equilibria of the leaving phases is
where KC is the equilibrium constant and is dependent on pressure, temperature and concentration. This relationship must be set up for m components and n stages.
(1-196)
where j is the stage number from 1 to n. A mass balance for each individual component i in each theoretical separation stage
1.9.3.3 Enthalpy Balances Enthalpy balances must be set up for each individual stage. For stage j ,
Fig. 1-61. Representation of separation stage j .
90
4
1 Basic Concepts
+ $+I * (1 - & j + I ) ~ , + I , G , F+ + L j p l 6;-1,t + G j + l h j + l , G *
Ej
*
hj,L,F
*
*
*
-(Gj+SGj)
*
hj,,-(Lj+SLj)
*
hj,t-Qj=O
(1-199)
5,,,
where hj+F and are the enthalpies of the liquid and vaporized part of the feed €$,and fij,L and fij,G are the enthalpies of the internal reflux Lj and vapor flow Gj, respectively (see Fig. 1-61).
1.9.3.4 Stoichiometric Conditions for the Sum of the Concentration at Each Equilibrium Stage
From the definition of the mole fraction for mixed phases it follows that rn
rn
Exlj = i
or
i= 1
or
m
m
i= 1
i= 1
C y i , j= 1
1.9.4 Kinetic Theory for the Counterflow Separation of a Mixture
i= 1
(1-200)
This sum is applied to each stage. The equation system is therefore defined by the mass balance, the enthalpy balance, the phase equilibrium relationships and the summation equation for the mole fractions. It contains n m mass balances, n enthalpy balances, n m phase equilibrium relationships and 2 . n summation conditions. Overall this gives n . (2m + 3) equations. Since the enthalpy hj and the equilibrium constant KCj are not linearly dependent on the state variables, particularly pressure and temperature, the equation system is nonlinear. In absorption columns, the number of unknown state variables equals the number of equations. In rectification columns three additional variables must be specified; ex-
-
amples are the reflux ratio at the top of the column and the mass flux of the top product. In extraction columns under normal operating conditions, the temperature profile is of little interest, and enthalpy balances need not be formulated. The solution to the equation system can be obtained using an iterative procedure. An overview and comparison of different iterative procedures are given in [1.102- 1.1041. The solution of the equation system gives the profile of the molar fluxes, the concentration profile and the temperature profile of a counterflow column. Finally the dimensions of the counterflow column need to be determined and the column must be integrated into the separation plant.
If column internals, such as filling or packing material, are used to increase the phase boundary area, then the phases are in constant contact over the column height; this is also true for spray columns. The constant contact of the phases should therefore be considered in column calculations. Instead of the separation stage theory, where the phase contact only takes place within the stages, the kinetic theory for the counterflow separation of a mixture is used. This theory allows the calculation of the actual height of the column where heat and mass transfer occur. The procedure is continuous, does not take single stages into account, and is based on the mass transfer relationships discussed in Chapter 1.7.3. This procedure is also used when the stage efficiency is very small, for example in physical absorption processes.
1.9 Steady-State Countercurrent Operation
1.9.4.1 mo-Directional Mass Transfer Between Phases
Figure 1-62 shows a section of a continuously operated column with two counterflow phases in constant contact. Mass is transferred between both phases, in either direction (for example with rectification). The flow rates of the phases G and L are constant along the column height if the molar vaporization enthalpy of the components is equal, and no side streams appear, no heat losses need to be considered and the mixing enthalpy is negligible. This is approximately true for rectification processes where enriching and stripping sections are treated separately (see Chapter 2.5.2) and no side streams occur. If there are side streams, the column must be calculated in a section wise manner. It follows that for the flow rate dri of the key component in the height element dz, the mass balance is dri = 6 . dy = L . dx
91
tration scale, and the mass transfer coefficient k, is related to the upflow phase. dA is the contact area in height element dz for mass and heat transfer. The specific volumetric surface a of the column packing is the ratio of the surface of the packing to the volume in m2/m3 and AQ is the cross-sectional area of the column. Hence,
dA = q . a . A Q - d z
(1-203)
(Generally, the specific surface a is not completely available for heat and mass transfer; it has to be corrected with an efficiency factor q < 1. q is the ratio of the physical wetted surface a, and the theoretical wetted surface a. q is dependent on the type or method of packing, the properties of the phases in contact, the distribution of the phases across the cross-sectional area of the column and the loading of the cross section by the phases.) From Eqs. (1-201)-(1-203) it follows that
(1-201)
Combining this with Eq. (1-174) dri gives dli=k,*(y-y*).dA
(1-202)
where the mole fraction y is used (instead of the molar concentration c) as the concen-
G Y+
-'
L
X+
d!-. - -~- _ _dx
-.
"+-
G Y
L X
Fig. 1-62. Height Z of a countercurrent column for mass and heat transfer.
Integrating with respect to dz gives the height Z of the column for mass and heat transfer.
If G and k, are not constant along Z , this must be taken into account during the integration. dy is the change of concentration in the upflow phase, in the height element dz, effected by the driving force y - y*. The integral of Eq. (1-205) is, according to CHILTON and COLBURN [1.105] the Number of Transfer Units (NTLr). NTU,, =
dy
Yn ~
yw
Y -Y*
(1-206)
92
1 Basic Concepts
NTU,, gives a number of transfer units describing how often the driving force y - y * is needed in the overall interval ya - y w , and the concentration differences between the entry and exit (z = 0 and z = 2) of the column. The overall mass transfer resistance is considered which is expressed by the index og (overall gas) and is related to the upflowing phase. The Height of a Transfer Unit,HTU,, is given by HTU,,=
G
kg*
Y,l*
a . AQ
= HTU,,
. NTU,,
(1-210)
Z
L
k,*q*a.AQ
= HTU,,.
NTU,,
Z=
LT
dX
(1-214)
(1-208)
(1-209)
=
(1-213)
and
Analogously, with respect to the downflow phase (index 01)
HTU,I
dY
Z=
(1-207)
The height of the column for heat and mass transfer is thus Z
of the key component in the inert part of the fluxes X and Y can thus be used as a concentration scale for the determination of the column height Z . With small concentrations, X and Y are almost equal to the molar fractions x and y. Applying this to the derivative calculated in the previous chapter, gives
(1-211)
At higher concentrations of the key component, the molar fraction may be expressed as
Introducing this expression, Eq. (1-214) becomes
dx
Z = q * LT . -~)~.(,y*-x) a m A Q*x,T k l (1 (1-212)
1.9.4.2 One-Directional Mass lkansfer
In absorption, adsorption, and extraction processes, substances are usually only transported from one phase which carries the key component, into another phase which takes the component. The phase fluxes G and L are not constant along the column height 2, although the inert parts of the phase fluxes G, and L, are constant. The concentration
(1-216)
which may also be applied when the mass transfer coefficient k , is dependent on the concentration. If the balance line and equilibrium curve are parallel, NTU,, and NTU,, are identical. NTU,/ and NTU,, are then equal to the number of theoretical stages determined using a graphical method. It is sufficient with an approximately linear equilibrium curve and balance line to replace the driving force y - y * or x * - x in
1.9 Steady-State Countercurrent Operation bl
a)
t
93
ya
1.
Yl
Fig. 1-63. Graphical determination of the number of transfer units NTU,,. Area under the curve A 1 NTU,, (Eq. 1-213). a) Determination of the driving force Y - Y* b) Graphical evaluation of the integral NTU,, BL Balance line
EC Equilibrium curve
the column. Methods of calculating HTU are given in the discussion of the individual separation processes. Direct experimental determination of k . a, or fi a, under con(Y - Y*), - (Y - r*), (1-217) ditions as close as possible to the operating conditions is often required. (Y - Y*), (The values of the height of a transfer In (Y - Y *), unit HTU,, and HTU,, may be calculated from the mass transfer coefficients fig and and it follows that PI related to the heights HTU, and HTU,. This is analogous to the calculation of the yu dy overall mass transfer coefficient k, based " JO'(1-218) NTU,,= on the mass transfer coefficients P, and PI, y , y - Y* (Y -Y*)/m for example, the height of a transfer unit HTU,, is given by Thus a transfer unit exists if the change of concentration Ay equals the mean driving GT HTU,, = HTU, + m T- HTU, (1-219) force causing the change. LT The integrals NTU,, and NTU,, can simply be evaluated numerically or graphi- with cally, as shown in Fig. 1-63. Graphical GT methods approximating NTU,, and NTU,,, HTU, = (1-220) Pg'r'a'AQ respectively were introduced by BAKER [I .106]. L T The heights of the transfer units HTU,, (1-221) HTU, = and HTU,, largely depend on the mass PI * r . a * A Q transfer coefficients k, and k,, the specific exchange area a and the molar fluxes of the where rn is the slope of the equilibrium phases through the cross-sectional area of curve.) the integral, by the logarithmic mean, ( y - y *),m or (x* - x),~,at both ends of the column. For example for the gas phase,
S --
-
-
-
94
1 Basic Concepts
1.10 Steady-State Crossflow
Operation Figure 1-64 shows a cascade of three stages operated at steady-state in a crosscurrent flow process where heat and mass transfer occur.
ration processes but rarely in solid-liquid and liquid-liquid extraction, drying processes, or adsorption.
t
I
L
Yl v2 Y3
x Fig. 1-64. Steady-state cross-flow operation of 3 stages.
Phase I flows through each stage in turn. Phase I1 is fresh feed to each separation stage. Within the stages, both phases are in cocurrent flow, with mass transfer from phase I into phase 11. A mass balance over the first stage of the crossflow cascade, according to Eq. (1-178) and the notation in Fig. 1-64, gives i T
*
(xa- X I ) = G,
1
*
( 5 - Ya)
(1-222)
For the case of constant inert or carrier fluxes, this equation gives a straight line when plotted on an X, Y graph, of slope - L T / G T , ; this is also true for the other stages. Figure 1-65 shows the operating diagram for the crossflow cascade, including the equilibrium curve and balance line. (The of the balance lines are . slopes . - L T / G T l , - L T / G T z , and -LT/G;7;.3). The crossflow of phases in contact, as shown in Fig. 1-64, is used in thermal sepa-
4
Fig. 1-65. Loading or operating diagram for a steady-state cross-flow cascade consisting of three separation stages. BL,, BL,, BL, Balance lines for stages 1, 2, 3 EC Equilibrium curve Loading of phase I1 by the key Y component Loading of phase I by the key X component
1.11 General Procedure to Design Equipment for the Thermal Separation of Mixtures The design of equipment for the thermal separation of mixtures and its integration into a whole separation unit for a chemical plant follows a certain procedure, shown in Table 1-19. In this book, the chemical engineering aspect of the design of separation equipment is discussed. Literature for stress calculations for parts of the plant may be found in the field of technical mechanics and plant construction [1.107].
1.11 General Procedure to Design Equipment for the Thermal Separation
95
Table 1-19. Planning concepts for thermal separation process units. *
heat transfer by graphical or short-cut methods, Iterative calculations, Correction using Murphree stage efficency coefficients
apparatus length for mass and heat transfer with the help of kinetic
* The order of individual steps in the table does not necessarily mean a chronological order. Generally, according to a time schedule (critical path analysis, Gantt plan) steps are carried out in parallel as much as possible.
96
1 Basic Concepts
References
[ 1.181 SCHILLING, R. : VGB Kraft werkstech. 60
(1980) 9, 695-705. [l. 191 SATTLER,K. : Thermische Trennverfahren. Aufgaben und Losungen. Ausle[1.11 SCHULZE,J., and HASSAN,A.: Methoden gungsbeispiele. Vogel-Verlag, Wiirzburg der Material- und Energiebi~anzierungen 1979. bei der Projektierung von Chemieanla- [ 1.201 Physiochemical fundamentals. gen. Verlag Chemie, Weinheim 1981. [1.21] BENDER,E., BLOCK,U.: VerfahrenstechA.: Grundlai1.21 BENEDEK,P., and L,ASZU~, nik 9 (1975) 3, 106-111. gen des Chemieingenieurwesens. VEB [ 1.221 HLATVA,K. : Collect. Czech. Chem. ComDeutscher Verlag fur Grundstoffindumun. 37 (1972), 4005-4007. strie, Leipzig 1965. [ 1.231 FRANCIS,A. W. : Liquid-liquid-Equili.31 HASSAN,A., Dissertation, TU Berlin briums. Interscience Publishers J. 1979. Wiley&Sons, New York 1967. v.41 KOGL,B., and MOSER,F. : Grundlagen der [1.24] SEIDELL, A., and LINKE,W. F.: Solubility Wrfahrenstechnik. Springer Verlag, Wien of Inorganic and Organic Compounds, 2 1981. Vols. Van Nostrand, Princeton 1958 and [1.51 MULLER,W. H., and MUSCHIK,W.: J 1965. Non Equil. Thermodyn. 8 (1983) 1, [1.25] D'ANs, J., and LAX, E. (eds.): Taschen29-66. buch fur Chemiker und Physiker, Vol. 1. P. : Verfahrenstechnik 13 U.61 GRASSMANN, Springer-Verlag, Berlin 1967. (1979) 1, 28-31. [1.26] STEPHEN,J., and STEPHEN,T. (eds.): So~1.71ARNOLDand BARTMANN:Chem. Ing. lubilities of Inorganic and Organic ComTech. 53 (1981) 7, 497-507. pounds, 2 Vols. Pergamon Press, Oxford W. : Energetische Analyse [ I 3 1 FRATZSCHER, 1964. von Stoffubertragungsprozessen. VEB [I .27] LANDOLT-BORNSTEIN, Vol. 11, part 2b, 2c. Deutscher Verlag fur GrundstoffinduSpringer Verlag, Berlin from 1950. strie, Leipzig 1980. [ 1.281 FRANCIS, A. W. : Handbook for Compo[I .91 SCHAFER,W. : Verfahrenstechnik 4 (1970) nents in Solvent Extraction. Gordon and 8, 352-358. Breach Science Publishers, New York [1.10] WOZNY,G., FETT, F., and CREMER,H.: 1972. Verfahrenstechnik 17 (1983) 6, 375-381 D. M., BRADY,B. L., and [1.29] HIMMELBLAU, and 7, 433-439. MCKETTA,J. J. : Survey of Solubility DiaA. W., HUTCHINSON, H. P. [1.11] WESTERBERG, grams for Ternary and Quaternary LiMOTARD,R. L., and WINTER,P.: Process quid Systems. Bureau of Engineering ReFlowsheeting. Cambridge University search, University of Texas 1959, Special Press 1979. Publication No. 30. T. Verfahrens- [ 1.301 SORENSEN, [1.12] BMAR,L., and PILHOFER, J. M. and ARLT,W. : ,,Liquidtechnik 7 (1973) 2, 53-57. Liquid-Equilibrium Data Collection." [1.13] KAUFMANN, F., HOFFMANN, U., and HOFIn: DECHEMA Chemistry Data Series, 3 MANN,H.: Chem. Ing. Tech. 45 (1973) 7, Vols. Frankfurt from 1979. 450-455. [ 1.311 GRASSMANN, P. : Physikalische Grundla[1.14] FUTTERER,E., and PATTAS,E.: Chem. gen der Verfahrenstechnik. Verlag Salle Ztg. 98 (1974) 9, 438-445. und Sauerlander, FrankfurUMain, Aarau [1.15] PIERUCCI,S. G., BIARDI,G., RANZI,E., 1983. and DENTE,M.: Chim. Ind. Milan 62 [I .32] BEST,R., SPINGLER, E.: Chem. Zng. Tech. 44 (1972) 21, 1222- 1226. (1980) 3, 193-199. [1.16] KETCHUM,R. G.: Chem. Ing. Tech?.44 [1.33] FREUNDLICH, H. : Coffoidand Capillary Chemistry. London 1926. (1972) 7, 457-462. [1.17] LINNHOFF,B., and RJRNER,J.: Chem. [1.34] LANGMUIR,J.: J. Am. Chem. SOC. 38 (1916) 221. Ind. Duesseldorf 104 (1981) 9, 544-550.
References [1.35] BRUNAUER, S., EMMET,H. H., and TELLER, E. : J. Am. Chem. SOC. 60 (1938) 309. [1.36] BRUNAUER, S., DEMING,L. S., DEMING, W. G., and TELLER,E.: .lAm. Chem. SOC. 62 (1940) 1726. [1.37] DUBININ,M. M. : Chem. Rev. 60 (1960) 235-241. [1.38] JUNEEN, H.: Staub Reinhalt. Luft 36 (1976) 7, 281-287. [1.39] MERSMANN, A.: Thermische Erfahrenstechnik. Springer-Verlag, Berlin, Heidelberg 1980. [ 1.401 MERSMANN, A., MUNSTERMANN, U., and SCHADL, J. : Chem. Zng. Tech. 55 (1983) 6, 446-458. [1.41] HOPPE, H. and WORCH,E.: Wiss. Z. Tech. Hochsch. Chem. Carl Schorlemer Leuna Merseburg 23 (1981) 3/4, 418-428. [1.42] MYERS,A. L., and PRAUSNITZ, J. M. : AIChE J. 11 (1965) 1, 121-127. [1.43] COSTA,E., SOTELO,J., CALLEJA, G., and MARRON, C. : AZChE J. 27 (1981) 1, 5- 12. [1.44] KAST,W., and DREHER,H. : Chem. Zng. Tech. 51 (1979) 12, 1245. [1.45] HOPPE,H., and WORCH,E.: Chem. Tech. Leipzig 31 (1979) 9, 464-467. [1.46] SEIDELL, A., and LINKE,W. F. : Solubility of Inorganic and Organic Compounds,2 Vols. Van Nostrand, Princeton 1958 and 1965. [1.47] D'ANs, J., and LAX,E. (Hrsg.): Taschenbuch fur Chemiker und Physiker, Vol. 1. Springer, Berlin 1967. [1.48] STEPHEN H., and STEPHEN,T. (eds): Solubilities of Inorganic and Organic Compounds, 2 Vols. Pergamon Press, Oxford 1964. [1.49] LANDOLT-BORNSTEIN, Vol. 11, 2b, 2c. Springer, Berlin, from 1950. [ 1.501 International Critical Tables. McGrawHill Book Comp., from 1933. [1.51] PRAUSNITZ,J. M., and SHAIR,F. H. : AZChE. J. 7 (1961), 862. [1.52] FRIEND,L., and ADLER,S. B.: Chem. Eng. Prog. 53 (1957) 452. [1.53] BATTINO, R., and CLEVER, H. L., Chem. Rev. 66 (1966) 395. [ 1.541 SEIDEL,A. : Solubilities of Inorganic and Metal-Organic Compounds. Van Nostrand, New York 1958. [1.55] WILHELM, E., and BATTINO,R.: Chem. Rev. 73 (1973) 1.
97
[1.56] WILHELM, E., BATTINO, R., and WILCOCK, R. J.: Chem. Rev. 77 (1977) 219. [1.57] NAKAHARA,T., and HIRATA, M.: J. Chem. Eng. Jpn. 2 (1969) 2, 137-142. [1.58] HALA,E., PICK,J., FRIED,V., and VILIM. 0.: Gieichgewicht Fliissigkeit - DampJ Akademie-Verlag, Berlin 1960. [1.59] HALA,E., PICK,J., FRIED,V., and VILIM, 0.: Vapour-Liquid-Equilibrium.Pergamon Press, Oxford 1967. [1.60] COTTRELL, F, G. : J. A m . Chem. SOC.42 (1919) 721-729. [1.61] Publications of Fischer Labor- und Verfahrenstechnik, Meckenheim. [1.62] NULL,H. R.: Phase Equilibrium in Process Design. Wiley-Interscience J. Wiley and Sons, New York 1970. [ 1.631 KING,M. B. : Phase Equilibrium in Mixtures. Pergamon Press, Oxford 1969. [1.64] PRAUSNITZ, J. M.: Molecular Thermodynamics of Fluid-Phase-Equilibria. Prentice Hall Inc., Englewood Cliffs N.J. 1969. [1.65] PRAUSNITZ, J. M., and ECKERT,C. A. : Computer Calculations for Multicomponent Vapor-Liquid-Equilibria. Prentice Hall Inc. Englewood Cliffs N.J. 1967. [1.66] PRAUSNITZ, J. M., and CHUEH,P. L. : Computer Calculations for High-Pressure Vapor-Liquid-Equilibria. Prentice Hall Inc., Englewood Cliffs N.J. 1968. [ 1.671 CHU, J. C. : Distillation Equilibrium Data. Reinhold Publishing Corp., New York 1950. [ 1.681 CHU, J. C. : Vapor-Liquid Equilibrium Data. J. W. Edwards Publishers Inc. Ann Arbor Mich. 1956. [1.69] KOGAN,V. B., and FRIEDMA", V. M.: Handbuch der DampfFliissigkeitsGleichgewichte. VEB Deutscher Verlag der Wissenschaften, Berlin 1961. [1.70] PRAUSNITZ,J. M., and GMEHLING,J.: Thermische Erfahrenstechnik ' Phasengleichgewichte.Krausskopf-Verlag, Mainz 1980. [1.71] STEPHAN, K.: Chem. Zng. Tech. 52 (1980) 3, 209-218. [1.72] GMEHLING, J., and ONKEN,U.: ,,VaporLiquid Equilibrium Data Collection. " In: DECHEMA-Chemistry Data Series, from 1977.
98
1 Basic Concepts
[I .86] ROCK, H. : Destillation im Laborato[1.73] KOGAN,V. B., FRIEDMAN, V. M., and KArium. Extraktive und azeotrope DestillaEAROV, V. V. : DampjWussigkeifs-Gleichtion. Steinkopff, Darmstadt 1960. gewichte. Verlag Nauka, Moskau 1966. [1.87] HAASE,R. : Thermodynamik der MischI., POLAK,J., and [1.74] HALA,F., WICHTERLE, phasen. Springer, Berlin 1956. BOUBLIK,T. : Vapor-Liquid Equilibrium [1.88] ROWLINSON, J. S.: Nature213 (1967) 440. Data at Normal Pressures. Pergamon [1.89] BARROW, G. M. : Physikalische Chemie, Press, Oxford 1968. part 111: Mischphasenthermodynamik, [ 1.751 Kux, C. : ,,Dampfdriicke von Mischsyste(eds.): Elektrochemie, Reaktionskinetik. Bohrmen. '' In: LANDOLT-BORNSTEIN, mann, Vieweg, Wien 1971. 6th Ed. Vol. 11. part 2a, pp. 336- 767. [1.90] ECKERT,E. R. G., and DRAKER,R. M.: Springer Verlag, Berlin 1960. Analysis of Heat and Mass Transfer. [1.76] STAGE,H., and FALDIX,P.: Fortschritte McGraw-Hill Book Comp. New York der Verfahrenstechnik. Verlag Chemie, 1972. Weinheim, from 1954. [1.91] FULLER,E. N., SCHETTLER, P. D., and [1.77] DELLRICH,I. R., P ~ C K E RU., J., and GIDDINGS,J. C.: Ind. Eng. Chem. 58 KNAPP,H. : Vapor-Liquid Equilibria. A (1966) 5, 19-28. Bibliography of Published Data of Multi[1.92] JOST,W.: Diffusion in Solids, Liquids, component Systems Containing CompoGases, Academic Press, New York 1960. nents with Normal Boiling Points Lower [1.93] HIGHBIE,R.: Trans. Inst. Chem. Eng. 31 than 350 K. (Bibliographie der Veroffent(1935) 365. lichungen seit 1900 bis 1972. Nachweise von 350 Binar-, 90 Ternar- und 30 Mehr[1.94] DANKWERTS, P. V. : Znd. Eng. Chem. 43 (1951) 1460. komponentensystemen). Institut fur [I .95] BRAUER,H. : Stoffaustausch einschlieJThermodynamik. TU Berlin 1973. lich chemischer Reaktionen. Sauerlan[1.78] Dechema material data office. der, Aarau 1971. [ 1.791 RMMERMANS, J. : The Physico-Chemical 11.961 MERSMANN, A. : Stoffubertragung. SprinConstants of Binary Systems in Concenger-Verlag Berlin, Heidelberg 1986. trated Solutions. Interscience Publishers, [ 1.971 SCHLUNDER, E.-U. : Einfuhrung in die New York/London 1960. Stoffubertragung. Thieme-Verlag, Stutt[1.80] CHEMICAL ENGINEERING SOCIETY (JAPAN) gart 1984. (eds.) : Physikalische Konstanten. Maru[1.98] MCCABE,W. L. and ~ I E L E E. , W.: Ind. Zen-Verlag, Japan, from 1963. Eng. Chem. 17 (1925) 605. [1.81] STAGE,H.: Bibliographie von ca. 2000 [I .99] LEWIS,W. K., and MATHESON, G. L.: Binursystemen. Destillationstechnik Dr. Ind. Eng. Chem. 24 (1932) 494. H. Stage, Koln-Niehl. R. L.: Ind. (1.821 HORSLEY, I. H.: ,,Aceotropic Data." In: [I .I001 ~ I E L EE., W., and GEDDES, Eng. Chem. 25 (1933) 289. Advances in Chemistry; Series Vol. 6 and 35. American Chemical Society. Wash- [1.101] FENSKE,M. R.: Ind. Eng. Chem. 24 (1932) 482. UNDERWOOD, A. J. V.: ington 1952 and 1962. Chem. Eng. Prog. 44 (1948) 8, 603-614. [1.83] OGORODNIKOV, S. K., LESTEVA, T. M., GILLILAND, E. R.:Ind. Eng. Chem. 32 KOGAN,V, B.: Azeotrope Gemische, Ver(1940) 1220. lag Chemie, Leningrad 1971. [1.84] BUSCH,A.: ,,Binare Systeme - azeo- [l. 1021 KETCHUM,R. G. : Chem. Ing. Tech. 43 (1971) 5, 264-269. trope Gemische." In: Landolt-BornEDULJEE,H . E.: Hydrocarbon Process. stein (eds.): 6th Ed. Vol. 2, part 2a, 54 (1975) 9, 120-122. pp. 663/711. Springer-Verlag, Berlin ERBAR,R. C. JOYNER,R. S., and MAD1960. DOX, R. N.: PetroKhem Eng. 33 (1961) 11.851 WICHTERLE, I., LINEK,J., and HALA,E. : 3, C 19-C 22. Vapor-Liquid Equilibrium Data BiblioWINN, F. W.: Pet. Refiner 40 (1961) 4, graphy. Elsevier Scientific Publishing ~ . . Comp., Amsterdam 1973. 153- 155.
References [1.103] GELBE, H., and NOMINE,H.: Verfahrenstechnik 5 (1971) 10, 429-435. [1.104] NEUMANN, K. K.: Erdoel, Kohle, Erdgas, Petrochem. Brennst. Chem. 26 (1973) 4, 198-202. [I .lo51 CHILTON,R. H., and COLBURN, A. P. : Ind. Eng. Chem. 27 (1935) 255. [1.106] BAKER,T. C.: Ind. Eng. Chem. 27 (1935) 977. [I. 1071 KLAPP,E. : Apparate und Anlagentechnik. Springer-Verlag, Berlin, Heidelberg 1980. SCHWAIGERER,S. ; Festigkeitsberechnung im Dampfkessel-, Behalter- und Rohrleitungsbau. Springer-Verlag, Berlin 1979. BTZE, H. : Elemente des Apparatebaus. Springer, Berlin 1967. AD-Merkblattter der Arbeitsgemeinschaft Druckbehaltec VdTUV, Essen. RABALD,E., and BRETSCHNEIDER, H.: DECHEMA-Werkstofftabelle.Verlag Chemie, Weinheim, from 1954. PIATTI,L. : Werkstoffeder chemischen Technik. Sauerlander, Aarau.
99
WAGNER,W. : Apparate- und Rohrleitungsbau. Vogel-Buchverlag, Wiirzburg 1984. [ 1.1081 JORDAN, D. G. : Chemical Process Development, 2 Vols. Interscience Publishers, J. Wiley & Sons, New York 1968. [1.109] MACH, E.: Planung und Einrichtung chemischer Fabriken. Sauerlander, Aarau 1972. BERNECKER, G. : Planung und Bau verfahrenstechnischer Anlagen. VDI-Verlag, Diisseldorf 1984. ULLRICH, H. : Anlagenbau. Georg Thieme-Verlag, Stuttgart 1983. [ 1.1101 LUDWIG,E. E. : Applied Process Design for Chemical and Petrochemical Plants, 3 Vols. Gulf Publishing Comp., Houston 1965. [1.111] WEHDE, K.-H., and STICHLMAIR,J.: Chem. Zng. Tech. 57 (1985) 4, 348-349. H.: Chem. Ing. Tech. 55 [1.112] HORMEYER, (1983) 1, 54-55. [ 1.1131 WETZLER,H. : Kennzahlen der Wrfahrenstechnik. Hiithig-Verlag, Heidelberg 1985.
Thermal Separation Processes: Principles and Design Klaus Sattler, Hans Jacob Feindt copyright 0VCH
Verlagsgesellschaft m h H , 1995
2 Distillation and Partial Condensation
2.1 Concepts of Simple Distillation, Rectification and Partial Condensation Distillation is a process for the thermal separation of liquid mixtures. The process may be used when the boiling points of the components in the mixture are significantly different, provided the substances are thermally stable under the operating conditions. The following is typical for a distillation process: by supplying heat, approximately isobarically, some of the liquid mixture is vaporized. The vapor is then distilled off and condensed after separation from the remaining liquid mixture, forming a second phase, the vapor phase. The low-boiling substances of the mixture are enriched in the vapor phase (case: relative volatility ai,j > 1). The “selective” vapor phase generally has a different composition to the liquid phase (an exception being an azeotropic mixture). By separating the vapor phase from the remaining liquid mixture a partial separation is carried out and since the vapor phase is enriched with the more volatile components, the less volatile components are concentrated in the distillation residue. In the process of partial condensation some of the vapor mixture is condensed by the removal of heat. Low-boiling components are therefore enriched in the remaining vapor, while the condensate of the additional “selective” phase contains the
higher-boiling components of the original vapor mixture. Figure 2-1 shows the effects of partial distillation and partial condensation on a binary mixture in a bubble point temperature diagram. Heating this mixture, which has a mole fraction x,, of the lower-boiling component and a temperature t9,, to the temperature dBC gives a liquid and a vapor phase which are in equilibrium. B is the state point of the remaining liquid phase, which is reduced in the lower-boiling component (xB < x,). The distillate (point C, yc > x ,) is enriched with lower-boiling component. At the point where boiling begins, (state point S, boiling point temperature rSS) the change of state follows the bubble point curve from S to B. Cooling the
xB
xA
x.y
-
YC xE
YO
YF
Fig. 2-1. Partial distillation and condensation in a bubble point temperature diagram. BC Boiling point curve DC Dew point curve
102
2 Distillation and Partial Condensation
vapor mixture, by means of partial condensation and at phase equilibrium, (from dD to L9E,F) gives a partial condensate containing less lower-boiling component than the original vapor (point El x, < yo), while the remaining vapor (point F, y, > yo) is enriched with the lower-boiling component. This change of state follows the dew point curve from D to F. In contrast to the evaporation of solutions, where only the solvent vaporizes and the partial pressure of the soluted substance is negligible, in distillation processes all components found in the liquid phase are also present in the vapor phase. The fraction of each component in the vapor phase depends upon the “effort” required to escape from the liquid into the vapor phase. The relative volatility is a measure of this “effort”, the separability of a mixture by distillation (discussed in Chapter 1.5). Since the relative volatility increases with decreasing pressure, the separation efficiency of a distillation process is increased by decreasing the operating pressure. Distillation processes may be operated continuously or batchwise. The operating pressure may be low (10’ Pa-100 Pa), medium (10 Pa-0.1 Pa) or even high vacuum (0.1 Pa- l o p 3 Pa) (molecular distillation) to avoid thermal damage to the mixture, or to increase efficiency. Special types of distillation are equilibrium or flash distillation (flash evaporation) and carrier distillation processes. A simple single distillation stage gives an imperfect separation of liquid mixtures. The single distillation stage is repeated in a counterflow distillation process, or rectification, to give separate components of the desired purity. In rectification processes the generated vapor is guided through the rectifying column in counterflow to parts of its condensate (Fig. 2-2). If the relative volatility a > 1, at the intensive contact of the counterflow phases
.I
ss
Fig. 2-2. Continuous countercurrent distillation unit. RC Rectifying column ES Enriching section, rectifying column SS Stripping section, exhausting column C Condenser DC Distillate cooler DR Distillate receiver R Reboiler RC Residue cooler RR Residue receiver F Feed Sidestream G Vapor to condenser Overhead product, light ends R Reflux A Bottom product, residue, heavy ends LC Lower boiling component H C Higher boiling component
s
2.2 Discontinuously and Continuously Operated Simple Distillation
(vapor and reflux) heat and mass transfer occurs. In binary processes, the less volatile component of the vapor condenses into the liquid phase. In adiabatic operation of the column, the heat released during condensation is used to vaporize the more volatile components from the reflux. Thus, the vapor flow up the column is enriched with the more volatile components, whilst the reflux is enriched with the less volatile components from top to bottom. For example, when a nonazeotropic binary mixture is rectified, the vapor leaving the top of the column will be nearly pure lower-boiling component, whereas at the bottom of the column, the liquid leaving will be nearly pure heavy boiling component. Heat and mass transfer can be intensified inside the column by using internal elements, such as trays and packing. These internals increase the contact time between the phases and the interfacial area. A separation by rectification of a multicomponent mixture cannot be completely carried out in a single column. Several columns connected in series are required to give a “pure” product for each component. For example, for m components without an azeotropic point, m-1 columns are required to give complete separation. Rectification processes may be operated continuously and discontinuously. Under adiabatic conditions the process can be operated at normal pressure, underpressure, and overpressure. Azeotropic mixtures are treated using azeotropic or extractive rectification. For special cases nonadiabatic, thermal rectification is used. The operation conditions and the type of internals used in the rectification column depend on the behavior of the mixture during separation and the properties of the components present.
103
2.2 Discontinuously and Continuously Operated Simple Distillation, Flash Distillation 2.2.1 Discontinuously Operated Simple Distillation In discontinuous simple open distillation (discontinuous partial distillation, Rayleigh Distillation) the distillation still is charged with a liquid mixture. Slow heating to the boiling point partially vaporizes the liquid. The vapor becomes enriched with the more volatile components and is withdrawn from the distillation still. After condensing in a condenser the distillate is stored in a distillate receiver (Fig. 2-3).
DR
Y Fig. 2-3. Batch distillation unit.
DS Distillation still Distillate condenser cooler DR Distillate receivers C
If the distillate is collected in several different distillate receivers, over a time period, the process is known as fractional simple distillation. The distillate is subdivided into several different batches, called cuts, of different purities. The fraction of the less volatile components in the batches
104
2 Distillation and Partial Condensation
increases with time, whilst the fraction of the more volatile component remaining reduces. Fractional simple distillation is therefore only used for partial separation of multicomponent mixtures. During discontinuous simple distillation, the concentration in the still, the distillate concentration and the temperature all change as the process proceeds. Figure 2-4 shows these changes as a function of time.
t
d
Fig. 2-4. Concentrations and temperatures at discontinuous distillation as a function of distillation time f. xn Still concentration x, Distillate concentration 8, Still temperature d D Distillate temperature
Masses and mass fractions may be used in place of moles and mole fractions. It is thus only possible to state xQm if B,, xBa, and xBw and the distillation residue B, are known. A differential mathematical approach must be used to obtain B,, this is discussed as follows. During the distillation, at any time, the molar content of the distillation still is B with mole fraction x of the key component. After distilling a partial amount d B with mole fraction y of the key component, the residue in the still becomes B - d B with mole fraction x - dx. Neglecting the product dB . dx and separating the variables x and y in the mass balance, a differential equation for the discontinuous simple distillation is derived. This equation was first introduced by LQRDRAYLEICH and is called the Rayleigh equation dB - dx B y-x Integration between the limits B,, B,, on the left-hand side of Eq. (2-2) and with the limits x,,, x, on the right-hand side (2-3)
The integral in Eq. (2-3) can only be evaluated if the vapor concentration y ( x ) is The liquid mixture being separated B, known as a function of the concentration x, with a molar fraction x, of the more volain the still during the distillation period. tile component (key component), is distilled Numerical results from experiments are during a period of time to obtain a distillagenerally used. tion residue B , with x , ~ . In the distillate Assuming phase equilibrium between the receiver the number of mols of distillate is liquid and the vapor in the still, the vapor D = B, - B, with a mean fraction x ~of , concentration ~ y ( x ) is described by the equithe key component. From an overall matelibrium curve. The integral in Eq. (2-3) can rial balance of the distillation unit the mean now be evaluated using numerical or graphdistillation concentration is ical means (Fig. 2-5). The assumption of phase equilibrium between vapor and liquid in the still is improved when the contents of the still are intensively agitated, and when
2.2 Discontinuously and Continuously Operated Simple Distillation
:1-
I
k
1 Yl-xl
xBw
x1
105
Fig. 2-5. Determination of the definite integral in Eq. (2-3). a) Equilibrium diagram b) Graphical integration method EC Equilibrium curve y Molar fraction of the key component in the vapor x Molar fraction of the key component in the liquid
XBa
a)
less distillate compared with the contents of the still, is distilled during a period of time. A special case occurs when the relative volatility 01 is constant in the concentration range of interest, xBa> x > xBw. Provided that there is phase equilibrium between the contents of the still and the distillate vapor, the amount of distillate D can be expressed as
-.
(2-4)
For a binary mixture the mean distillate concentration of the lower-boiling component is then
(2-5)
In order to assess the volume of the distillation still the following time periods must be considered: the time required to charge and
discharge the still, the time required to heat the still contents to the boiling point, the distillation time, the time to cool the distillate residue, and if necessary, the time required to form the vacuum and to bring the apparatus back to atmospheric pressure. If the distillation unit is part of a continuous chemical plant, an additional buffer is also required. The minimum size of the distillation still and buffer depends on the liquid volume fed from the previous units of the plant during the total time period required to operate the distillation unit. Free vapor space must be added to the fixed volume of the distillation still and an extra safety margin to the buffer volume. Therefore, the minimum volume V of the still is
where
v, tg
VD
volumetric flow rate of the feed mixture at its boiling (m3/h) overall batch time volume of the free vapor space
Distillation and Partial Condensation
molar mass and density (with
where
diameter and height of the free vapor space of the still
C
xB, at L9,) of the fed mixture
eg, e, density of the distillate vapor and
The diameter d of the distillation still is then calculated from the relationship d=
-1 ~
n: a3600
eg*w
(2-7)
Z , is the minimum height of the vapor space (see Fig. 2-3)
where diameter of the distillation still maximum flow of distillate vapor during the distillation period (kmol/h) Mg molar mass of the distillate vapor eg density of the distillate vapor w maximum rising velocity of the vapor (m/s)
d
d,,,
Entrained liquid droplets must be eliminated, so that the vapor leaving the still is dry. Therefore, the rising vapor should not exceed a maximum velocity w. Otherwise, liquid droplets will be carried out of the still and mechanical mist eliminators must be used, for example, 0 0
0
simple or finned baffles radial mist eliminators (spinning body with guide vanes) demister (separation mat made of wire or plastic gauze of thickness 100-500 mm and, for the special case of separating small droplets out of a fog, 300-600 mm)
A higher vapor rise velocity w and a decreased free vapor space can then be employed compared with those units without mist eliminators. The vapor rise velocity w is el - e g
liquid mixture empirically evaluated constant, which depends on the type of mist eliminator (C = 0.036 m/s for stills without separation aids, [2.6], C = 0.107 m/s for demisters in regular process operation in columns and stills [2.7])
(2-8)
4 . Dmax. Mg
z,= 71
*
d2
- e,
*
VZ
(2-9)
with vz = 500 +
40
zA5 + 0.01
(2-10)
where vz is the maximum steam space load (m3/(m3 h) and Mg the molar mass of the vapor (vz as given in Eq. (2-10) is valid for stills without a mist eliminator [2.8]). In the distillation period the heat required to heat the contents of the still B, to the boiling point, and the actual heat Q required for the distillation, are provided by the heating system of the still:
where
Qvw, QD heat required to heat the contents of the still and for the distillation process, respectively hBa,hs enthalpy of the still contents B, after charging and at boiling conditions, respectively Ah,, enthalpy of vaporization of the distillate
2.2 Discontinuously and Continuously Operated Simple Distillation
In practice there are different types of heating device available for use on the still [2.9], for example, steam jacket or heating coils of round or half-round tubes welded on the still (since the surface to volume ratio of the still is inversely proportional to the still diameter, this heating system is only used for small heat fluxes or small still diameters) heating coils in the still (mainly for long tubes and large still sizes, although contamination and incrustation possible) heating tube bundle in the still, finned if necessary, (compared with heating coils: less tube length and smaller stills, but still a danger of contamination and incrustation) external reboiler with pump recirculation direct firing Figure 2-6 shows the technical construction of a distillation still, including the steam jacket and the necessary connections.
IV
'1'
VI
Fig. 2-6. Jacketed still. I Adapter, agitator I1 Man hole, sight glass
111 Outlet, distillate vapor
IV V VI VII
Inlet, liquid mixture
Inlet, heating agent Outlet, heating agent Outlet, residue
II
107
2.2.2 Continuously Operated Simple Distillation With continuously operated simple open distillation processes, a continuously fed liquid mixture is partially vaporized by supplying heat to the system. The vapor and residue generated are continuously withdrawn from the distillation unit. Similar distillation devices include vaporizers, which are used for concentrating solutions (see Chapter 7.2.1): circulating evaporator - which has a large liquid holdup and a correspondingly long residence time in the vaporization area; continuous flow evaporator - which has little liquid contents and a short residence time, and therefore offer gentle thermal treatment of the liquid mixture. Continuously operated simple distillation is similar to discontinuous distillation in that it is only of technical interest with large relative volatility values. It is used for mixtures which easily are separated due to large differences in the boiling points of the components of the mixture, but only then the yield of the separation is satisfactory. Continuous distillation is particularly suitable for the separation of small concentrations of low-boiling components from highboiling components, or for the separation of small concentrations of high-boiling components in low-boiling components. Distillation devices are usually continuous flow evaporators. In rectification processes, continuously operated vaporizers are used as simple continuous distillation devices. The vaporizer, usually a circulating evaporator, forms the first practical separation stage of the stripping zone of the rectification column. A mathematical description of continuous simple distillation gives equations similar to those describing discontinuous simple distillation. The concentrations of the liquid mixture and the distillate vapor depend
108
2 Distillation and Partial Condensation
in discontinuous distillation on distillation time, in continuous distillation they are functions of the heat transfer area (see Figs. 2-4 and 2-7). For example, for continuous distillation of a binary mixture, as shown in Fig. 2-8,
the continuous flow evaporator is considered to be a film, or falling film evaporator. The mean distillate concentration along the length of the evaporator tube y D = x, is derived from the mass balance of the vaporizer (2-12) where . . Fa, F, Xa,
I
Z
Evaporator tube length z-
Fig. 2-7. Liquid concentration x, distillate concentration y , liquid temperature tYF and distillate temperature tYD as a function of the evaporator tube length z. Key component of x and y is the low-boiling component (see also Fig. 2-9).
t
xlu
Fa - Fu
=
d
feed and outlet flow rate of the liquid mixture mole fraction of the lowerboiling key component in the liquid phase of feed and outlet flow rate distillate flow rate generated along the length Z of the evaporator tube
The differential equation describing simple continuous distillation is derived from a mass balance for a length element dz of the evaporator tube (Fig. 2-8), giving
d F- d x F y-x TW
(2-13)
Integrating gives
(2-14) l
z
Fig. 2-8. Film evaporation or falling film evaporation in an evaporation tube. HM Heating medium side TW Evaporator tube wall LF Liquid film 0 d Inner diameter of evaporator tube DD Distillate vapors
This is similar to the method already discussed for discontinuous simple distillation. All the assumptions made are also valid. (Under the same conditions, the relationships given by Eqs. (2-4) and (2-5) may also be applied.) The heat flux, dQ, supplied by the surface area element dA = d n dz is
-
e
2.2 Discontinuously and Continuously Operated Simple Distillation
where k is the heat transfer coefficient, and AV the driving temperature gradient between the heating medium and the boiling liquid mixture in the interval of the evaporator tube z and z + dz. (The temperature difference AV is approximately linear if saturated steam is used as the heating medium. If the heat transfer medium is, for example, liquid diphyl, then Ad is the logarithmic mean value.) The heat flux d Q required to vaporize the distillate vapor (with flow rate &) from the boiling liquid film is given by (2-16) where is the vaporization enthalpy of the liquid mixture with respect to concentration and operating pressure at dA. Combining Eqs. (2-13)-(2-16), the required length of the heat evaporator tube 2 is
tors and head or bottom product vapor compression are also discussed. Thin film distillation and rectification may be combined in such a way that the thin film evaporator is connected to a column with both an enrichment and a stripping zone, or just an enrichment zone [2.17]. Such a combination is particularly useful for separation of sensitive mixtures in a vacuum.
2.2.3 Heat Requirement of Simple Distillation Units The heat requirement of a separation unit follows from the energy balance as shown in Chapter 1.3.1. For a simple distillation unit the heat flux may be derived, as shown in Fig. 2-9. An energy balance of the distillation unit under isobaric operation gives Q = D . fiD + F w . fiw - F a
ha = = Ij (fib - hw)+ Fa (Ew - ha) (2-18) *
(2-17) Z is the length of the evaporator tubes required to generate the distillate flux B. If the feed mixture is at a lower temperature than the boiling temperature, a preheating zone is additionally required. For the design of distillation facilities, it is generally sufficient to use A&,,, k and At9 averaged over the length 2 in Eq. (2-17). Methods of calculating the heat transfer coefficient k are found in [2.10]. Applications of thin film and falling film evaporators in film distillation are reported in [2.14], together with the achieved separa-
109
*
*
The specific heat requirement, which is the required heat flux for each kmol distillate vaporized, is Feed Fa,x a
2.
1r
h,
A Distillate vapor D,yo=xh.3o.ho
* * -+
d_
<
Heat supp~y
* -+ -c
F,,
X,,3,.hw
v Outlet,
distillation residue
110
2 Distillation and Partial Condensation Component 1 Mixing unit
(2-19) The specific heat requirement 4 can then be calculated after integration of Eq. (2-14). With the aid of the enthalpy-concentration diagram q arises graphically. MERKEL and PONCHON introduced the caloric enthalpy-concentration diagram. The enthalpy h of a binary mixture is plotted against the mixture composition w with temperature as a parameter. The h, w diagram is shown in Fig. 2-10. If, at a temperature Lp, w kg of component 1 is isothermally mixed with (1 - w)kg of component 2, in a mixing vessel, the enthalpy of mixing Ah, is released. Depending on the temperature and the components in the mixture, the mixing enthalpy may be positive or negative, (i. e., exothermic or endothermic). It is also a function of the composition of the mixture and can change its sign in the concentration range 0 Iw I1. In the MERKELand PONCHON h, w diagram, if the values of the enthalpies h , and 11, of each individual component and the mixing enthalpy AhMhave been found experimentally, the enthalpy of the mixture h can be found from
Component 2 1- w I kg),9, h
*
Mixing enthalpy
Fig. 2-10. Enthalpy-concentration diagram of MERKELand PONCHON. h Enthalpy of the binary mixture w Mass fraction of the key component in the binary mixture
D. Point C is the point on the dew line of composition yo. If the mixture is fed at its boiling temperature, points A and E have the same position and clearly the heat reh ( w ) = w * h, + (1 - W ) . h2 f Ah, (2-20) quired to reach the bubble point temperature is zero. The specific heat requirement 4 for disRepeating the procedure at different temperatures gives a set of isotherms h(w,Lp). continuous simple distillation is derived by The distillation process can be discussed a method similar to that used to determine with the aid of a h, w or h, x diagram. The the heat requirement for continuous simple distillate vapor enthalpies are based on the distillation. For the exact determination of dew line, and the liquid mixture enthalpies 4, the amount of distillation vapor as a are based on the bubble point line of the bi- function of the concentration of the still nary mixture, as shown in Fig. 2-11. The contents and distillates must be considered. specific heat requirement q is therefore the Discontinuous distillation may therefore be distance CDin the 6, x diagram shown in looked upon as a number of differential disFig. 2-12. This line constructed by using tillation processes connected in series. q Eq. (2-19), and by extrapolating the line FA may be graphically determined using the fi, back to the intercept with y,, giving point x diagram [2.11].
2.2 Discontinuously and Continuously Operated Simple Distillation const.
p
p = const
111
I
,Bubble point line
Xw
x.y
3
Liquid phase region
bl
x1
x2 Y1
$01
Xa
YO
__c
Fig. 2-12. Graphical determination of the specific heat requirement q for a continuous simple distillation. A State point of feed B State point of distillation residue C State point of saturated distillate vapor specific heat requirement qv for Line heating the mixture to the bubble point Line specific heat requirement q
Y2
Mole fraction of the low boiling component in the liquid and vapor phase x,y-
Fig. 2-11. fi, x-Diagram of a binary mixture including liquid phase and vapor phase (a). Construction of bubble point line and dew point line in the 6, x-diagram using a boiling diagram (b). A , , A2 and B,, B, state points of liquid phase and vapor phase in equilibrium. 6 Enthalpy x, y Mole fraction of the low-boiling component in the liquid phase and vapor phase Ly Temperature
2.2.4 Flash Distillation In flash distillation, a liquid mixture Fa at its boiling temperature (under pressure) is released into a vapor-liquid separator or a rectification column. No heat is added or removed (isenthalpic throttling, see Fig. 2-13). The liquid mixture may, for example, come from a reaction unit operated at high pressure. It also may be preheated to its boiling temperature in a preheater, operated at a higher pressure than the following separator. Alternatively, the liquid mixture may be heated in a tube heater in which some vapor is generated. The vapor and remaining liquid are in constant contact (“closed simple distillation”).
112
2 Distillation and Partial Condensation
residue
Fig. 2-13. Flash distillation unit. P Preheater S Vapor liquid separator “Expansion or flash evaporator” C Condenser
When a > 1 the released vapor generated under pressure contains a higher concentration of low-boiling components than the mixture introduced into the separator. In flash operation processes, therefore, a partial separation of the feed occurs in which the separator can at best only act as one theoretical separation stage. A mass balance for the separator gives the ratio FJD with the nomenclature as explained in Fig. 2-13. With yo = x,, Fu - x D - x a
D
xa-xx,
x w xa X+
Fig. 2-14. Working diagram for flash distillation. EC Equilibrium curve OL Operating line of slope K (tanx = --FW/B) y Molar fraction of the low-boiling component in the vapor x Molar fraction of the low-boiling component in the liquid
(2-21)
this ratio gives the operating line for a flash distillation, as seen in Chapter 1.8. For a binary mixture, this is shown in Fig. 2-14. If for a given mixture flow rate Fu with mole fraction xu, a vapor flow rate Ij is generated, the operating line can be determined using the operating diagram
(Fig. 2-14). B is the intersection of the equilibrium curve with the line of slope F J D starting at point A, xu. The distillate concentration yo = x, and distillate residue concentration x,, are simply the coordinates of B. Provided that the released vapor and distillation residue are in phase equilibrium, this is approximately true in practice.
2.3 Carrier Distillation
A heat balance over the separator gives the amount of distillate generated during the flash operation.
113
2.3 Carrier Distillation
In carrier distillation, the boiling behavior of liquid mixtures is influenced positively (with respect to a separation effect), by the addition of a n auxiliary component as a vaThis is only worth considering for large por. Figure 1-21 shows the boiling diagram amounts of feed Fa or when the pressure for two immiscible components over the differences on release are large. whole concentration range. Each compoIf some of the distillation residue is recy- nent behaves as though it exists alone; the cled back into the preheater, with flow K, partial pressure in the vapor phase is the then the amount of distillate dkis saturation pressure of each component at the boiling temperature of the mixture and thus the operating pressure is the sum of the (2-23) saturation pressures of each of the components. Due to the immiscibility, the boiling point of the mixture is lower than the boil(In Fig. 2-13, K is the nomenclature used ing points of the pure components at the for the recycle.) operating pressure. For example, the boiling From an energy balance applied to the point of pure o-xylene is 144°C at 1 bar, preheater the heat Q, required in the whereas a mixture of water and o-xylene preheater is boils at 95 "C. The vapor generated during the distillation has a constant composition, which is independent of the composition of the liquid and is an azeotropic mixture. Carrier distillation is used to gently separate nonvolatile impurities from high-boiling substances. Saturated or overheated vapor is blown through the impure liquid in a still. The carrier and the product liquid are The diameter d of the separator can then be immiscible in liquid phase, for example a calculated using Eq. (2-7). The required higher fatty acid-water system. The carrier minimum height ZD of the free vapor space vapor is used firstly as a heat transfer mecan be found using Eq. (2-9), in which vz is dium, heating the contents of the still to the the maximum vapor space loading chosen boiling point and providing the heat for the distillation. Secondly, it is used as a carrier such that for the substance being distilled. The vapor mixture composition corresponds to the vz = 3600 m3/(m3 . h ) (2-25) aceotropic composition. A discontinuously operated carrier distilIn practice, flash distillation is rarely used lation unit is shown in Fig. 2-15. Neglecting as a single separation stage; more often it is the heat due to the nonvolatile impurities, used in combination with other distillation the heat balance over the distillation still, processes without a preheater to arise the gives the required amount of carrier, mostly flash effect. steam DH blown into the still.
(2-22)
114
2 Distillation and Partial Condensation
Fig. 2-15. Steam distillation. DB Still C Condenser cooler PS Phase separator LIC Level indication, control SH Supplementary heating
A = D,Po, B
Po, w
(2-26) where
B
DH fiB ~
AD
b S
quantity of substance to be purified (kmol) total quantity of auxiliary steam (kmol) molar enthalpy of still contents before heating enthalpy of the carrier steam (related to the steam pressure PD) enthalpy of the auxiliary substance at the boiling point (related to the boiling point 19, of the mixture) enthalpy of the vapor of the substance to be purified at Po, B enthalpy of the vapor of the auxiliary substance at po,
W distillation residue saturated vapor pressure of the substance to be purified (related to the boiling point rS, of the mixture) saturated vapor pressure of the auxiliary substance (related to the boiling point t9,)
The boiling point rSs of the mixture can easily be determined graphically using the vapor pressure curves, as shown in Fig. 2-16. The sum of the saturated vapor pressures of both components po,Band po, gives the operating pressure p. P = Po,B -k Po, W
(2-27)
For the azeotropic composition of the distillate, it follows that YE =
Po, B P
(2-28)
~
and the ratio YB --Po,B
--~
w
Yw
Po, w
(2-29)
2.3 Carrier Distillation I-.
2
Q
%P
Operating pressure p
Q
i Pow
d
-1
1
3s
D
115
Fig. 2-16. Determination of the boiling point LS, and the composition of the azeotropic mixture. po,B(19)Vapor-pressure curve of the substance to be purified p-po,w (8) Vapor-pressure curve of the auxiliary substance, substracted from the total pressure p p Total pressure po Saturation pressure c9 Temperature
C
Fig. 2-17. Steam distillation unit with heat recovery by mechanical vapor compression [2.12]. Representation according to the data of GEA Wiegand GmbH. 1 Still 2 Steam converter (inclined tube heat exchanger with vapor condensation in the tubes) 3 Condensate separator 4 Steam compressor (reciprocating compressor with speed regulated direct current motor) 5 Steam saturator A Live steam B Contaminated vapor C Contaminated condensate D Condensatelfeed water E Low-pressure steam F Recovered steam
Data of the presented unit: Steam mass flow feed Steam feed overpressure Performance coefficient (evaporation energy of generated steam feed/electrical power consumption of the compressor)
6.1 t/h
3 bar I
I16
2 Distillation and Partial Condensation
The saturated vapor pressures po,B and p o , w of the substance to be purified and that of the auxiliary substance can be obtained from Fig. 2-16. The dimensions of the still can be determined according to the description in Chapter 2.2. Carrier distillation using water vapor as the carrier is common in the oil and fat industry. In the oil and petrochemical industries, carrier distillation is used to strip loaded solvent from absorption units, using water vapor or an inert carrier in continuous counterflow columns. A carrier distillation unit designed to save energy is shown in Fig. 2-17 [2.12]. Solvent is discontinuously removed from the contents of a distillation still (1) by blowing water vapor into the still. The impure vapor is condensed in a steam converter (a tube heat exchanger (2), slightly inclined). The condensate is fed to a regeneration unit for further treatment. Pure steam generated at the jacket during vapor condensation is compressed to the injection pressure in a steam compressor (4) and is simultaneously superheated. The superheat is removed in a saturator (5) by the injection of condensate or water and the saturated steam is injected into the distillation unit (1). A general discussion of the economic efficiency of mechanical vapor compression is found in [2.13]. The use of vapor compressors is already of economic benefit if
15Yo of the primary energy is saved. For example, the heat recovery, by vapor compression of live steam at a pressure of 5 bar gives a primary energy saving of up to 22 Yo, as illustrated by a diagram in [2.13].
2.4 Vacuum and Molecular Distillation Vacuum distillation is suitable for the separation of thermally sensitive liquids, being a gentle distillation process which operates at low pressure. Due to the reduced operating pressure, the boiling point of the mixture is also reduced. A low residence time and a narrow residence time distribution are maintained, by careful selection of the distillation unit to be used. The advantages of vacuum distillation over ordinary distillation at normal or higher pressure are listed in Table 2-1. Different vacuum ranges, including the vacuum forming device are discussed in Table 2-2. Common distillation units are also shown. Molecular Distillation Molecular distillation is used to separate very temperature sensitive liquid mixtures at absolute operating pressures in the range 0.1 -0.001 Pa.
Table 2-1. Advantages of vacuum distillation over normal pressure distillation.
0 0
A lower and only short-term heating is nessecary due to the lower boiling point of the mixture to be separated Increase of selectivity due to the increasing relative volatility with decreasing operating pressure A favorable influence on the azeotropic point of a n azeotropic mixture under lowered operation pressure Usage of cheaper heating medium due to a lower temperature level of the process
117
2.4 Vacuum and Molecular Distillation
Table 2-2. Vacuum range, vacuum forming device, distillation process and features of distillation units.
Vacuum range
Vacuum forming device
Distillation process
Distillation unit
Low vacuum (1 bar1 mbar)
Positive displacement Pump Booster diffusion vacuum pump (particularly steam jet pumps)
Low vacuum distillation
Vacuum circulation evaporator Continuous evaporator with falling or wiped film Rotary evaporator
Medium vacuum (1 mbar0.1 Pa)
Pump combination for example: positive displacement pump+ booster diffusion pump (oil ejector)
Medium vacuum distillation
Continuous evaporator with agitated film (film evaporator with fixed or swinging wipers, film evaporator with brushes or rolls) Rotary evaporator
High vacuum (0.1 Paca. 0.001 Pa)
Pump combination for example: two stage positive displacement pump + diffusion pump or single stage positive displacement pump +oil ejector +diffusion pump
Molecular distillation (open path, short path distillation)
Cup molecular distillator Rotary molecular distillator Film molecular distillator Centrifugal molecular distillator
The maximum evaporation rate is obtained if all molecules distil from the liquid into the vapor space and reach the condensation unit without collision with other molecules. After condensation the liquid is withdrawn from the unit. Distillation without recondensation effects, such as reflection of vapor molecules back to the liquid phase, or time delays due to collision with other molecules on the way to the condensation unit, is the aim of molecular distillation. The mean free path of the molecules at a pressure of 0.1 to 0.001 Pa is a few centimeters, then the distance between the vapor-
ization surface and the condensation surface should be less or approximately this mean free path of the molecules in the distillation unit. Vaporization from the surface occurs without vigorous agitation of bubbles, unlike the case of nucleate boiling, where bubbles are formed and agitated at the heating surface. The liquid mixture spreads over the heating surface becoming a thin film of constant thickness. The rate of the distilled vapor flow is derived from the kinetic theory of gases. this According to KNUDSENand LANGMUIR, flow rate is
aA
2 Distillation and Partial Condensation
118
dA= E
*
1.577 . lo6 -p0,;
vzT
(2-30)
where p0,;is the saturated vapor pressure (given in bars), i is the substance to be distilled at temperature T with molar mass Mi. dAis obtained in kg/(m2 h). E is the effectiveness factor, E 5 1. Its value increases the fewer vapor molecules diffuse back, and the better the renewal of the active liquid film surface. With ordinary distillation the relative volatility is given by Eq. (1-144). For the pressure range of molecular distillation, not only are the saturation pressures p , ; and po,jimportant, but also the molar masses of the components i a n d j . The relative volatility is thus
.I
-
-.,I
.
.
(2-31)
During equilibrium distillation each component vaporizes proportionally to its partial pressure p i ,pJ, etc. During molecular distillation each component is vaporized proportionally t o p , / pJ / v M J , . . The composition of the distillate X i , for component i, distilled from a binary mixture of components i and j , is given by
mL,
-5
B
4, 4 7
Fig. 2-18. Agitated film evaporator for molecular distillation. 1 Agitator with rolls or brushes to circulate the
film 2 Feed 3 To vacuum pumps 4 Heating jacket; heating agent in, out 5 Condenser (inlined) 6 Cooling agent in, out 7 Distillate
8 Residue
(2-32) Investigation and operating costs make molecular distillation an expensive separation method. It is used mainly in the pharmaceutical industry to treat high-grade substances such as vitamins, hormone concentrations, fats, oil, and waxes. Agitated thin-film evaporators with a falling, revolving liquid film (Fig. 2-18) are often used in molecular distillation. The film is 0.1-1 mm thick, with a mean residence time ranging from 10 s-10 min and a
throughput rate of up to 1 t/h. A further device is the centrifugal molecular distillation still (Fig. 2-19). It has a film thickness of 0.03-0.001 mm depending on the number of revolutions of the rotor. A typical throughput is 1 t/h, with a mean residence time of 0.1-0.001 s [2.15, 2.16, 2.18-2.20, 2.1401.
2.5 Countercurrent Distillation (Rectification) 5
6
Fig. - 2-19. Centrifugal - molecular distillation still. Rotating evaporator with liquid film forming and mixing due to the effect of centrifugal force Electrical radiant heater Condenser with cup surface and drainage to collect the distillate (aerofoil condenser with self-pumping effect for distillate) Cooling agent for condenser Distillate discharge To vacuum pumps Feed Residue discharge
2.5 Countercurrent Distillation (Rectification) Countercurrent distillation or rectification was introduced as a special countercurrent distillation process in Chapter 2.1. With the requirement of high quality thermal separation, the reflux flows down while vapor flows up the rectification column, thereby ensuring intensive contact of the phases. Intermediate products from, for example, a reaction unit, usually need treatment in an energy intensive thermal separation process to obtain the desired purity of the final product. 60 to 80% of the energy used in the chemical industry is spent for this purpose [2.21]. An energy intensive rectification process for thermal separation is of-
119
ten employed, and thus the required rectification columns are designed and linked to recover and save as much energy as possible. An analysis and optimization procedure for the energy usage in each individual unit and the entire plant, as introduced by Linhoff [2.21 a] is often used. In the following sections, different rectification processes and methods for the design of rectification columns are discussed. Energy saving possibilities are highlighted.
2.5.1 Process Variations of Rectification A number of variations of the rectification process have been developed and adapted to suit certain rectification problems during the decades of distillation usage. Substantial adaptations are due to the properties of the mixture and its thermal behavior, the mode of operation, the required operating conditions, the economic efficiency, the flexibility, and the safety of the operation. Several important process variations are now presented and briefly discussed. 2.5.1.1 Continuously Operated Rectification in Rectification Columns with Enriching and Stripping Zones
Figure 2-2 shows the most common process in rectification practice. It can give a good separation efficiency for nonazeotropic mixtures, depending on the number of separation stages and the reflux ratio. It is possible to almost completely separate a nonazeotropic binary mixture into its pure components in a column including enriching and stripping zones. To separate a multicomponent mixture, several columns must be linked. For a nonazeotropic mixture with k components in the mixture, the
120
2 Distillation and Partial Condensation
For example, to separate a mixture of four components, 10 different separation tasks for 10 different mixture streams with 5 different column arrangements in which each arrangement contains 3 rectification columns are possible (Fig. 2-20). During optimization of the separation process (minimizing the energy and fixed costs), additional variations of Z,, may be included, as shown for a ternary mixture in Fig. 2-21 [2.24, 2.251.
required number of columns is k - 1. The possible number of different connections of the columns, Z, (variations of separation) is given in [2.22, 2.231. Provided each column performs only one separation task with no side streams, recycle, and circulation - l)] ! z,= [2k ! (k (k-l)! *
(2-33)
-
*
The number of mixture streams is
z,=-k2
(2-34)
* ( k +1)
and the number of separations Z, (separation tasks) of the mixture streams is
z,= k6 . (2- 1)
(2-35)
-
2.5.1.2 Stripping (Exhausting) Column Figure 2-22 shows a stripping column operated without an enrichment zone and without reflux. In this variation, a good purity of bottom product can be achieved with a small throughput. This variation is of interest for small amounts of overhead product,
iu C)
L
3
2
4
L
3
Fig. 2-20. Different methods of connecting three columns in a quaternary mixture distillation unit. a)-d) Serial connections of columns e) Parallel connection F Feed 1, 2, 3, 4 Components in the order of increasing boiling points
2.5 Countercurrent Distillation (Rectification)
$i2
121
3
’ 3
or for the recycling of overhead product, or for further treatment of column sidestreams (Fig. 2-25 shows sidestream strippers for a crude oil column). Since the number of separation stages is fixed the only operation parameters are the bottom temperature and the vapor loading, which is ad-
-
Fig. 2-21. Methods of connecting columns in a ternary mixture distillation unit, without vapor recompression. (Representation according to SCHLUTER and SCHMIDT [2.24], and BDDER [2.25]).
justed by the heat transfer per unit surface area in the vaporizer.
2.5.1.3 Enrichment Column Figure 2-23 shows an enrichment column in which no reboiler is used. The feed to C
A
Fig. 2-22. Charge reflux fractionator (stripping section only). SC Stripping column R Reboiler C Condenser F Feed, liquid E Overhead product A Bottom product
Fig. 2-23. Charge reboiler fractionator (enrichment section only). RC Rectifying column C Condenser F Feed, saturated vapor or wet vapor E Overhead product R Reflux A Bottom product
122
2 Distillation and Partial Condensation
C)
K P H
PS &A I
E --GLS
T
o-& T
% /jc
the bottom must therefore be saturated vapor, or at least wet vapor, with a small fraction of the liquid phase. With a small throughput, the overhead product is of good purity. With a fixed number of separation stages, the reflux ratio is the only operating parameter. A column operating only in the enrichment mode is used with carrier distillation in crude-oil distillation
Fig. 2-24. Carrier distillation, “steam distillation”. a)-c) Different types of steam distillation d), e) Regeneration of loaded solvent from an absorption stage, stripping RC Rectifying column SC Stripper C Condenser R Reboiler PS Phase separator GLS Gas-liquid separator PH Preheater CC Condenser cooler F Feed B i Rich oil, solvent + absorbent E Overhead product i‘ Carrier, water T b Vaporous carrier, steam or inert gas, stripping in solvent regeneration A Bottom product RL Recovered solvent, lean oil
processes. This variation may also be used if the feed mixture shows a tendency to form a scale (incrustation), or if small streams of heavy boiling components are diverted in repeated rectification stages. The enrichment column now used with a circulating evaporator and a receiver is operated in the “endless circulation” experimental rectification process.
2.5 Countercurrent Distillation (Rectification)
2.5.1.4 Carrier Rectification Carrier rectification can be used with different variations, to gently separate highboiling substances from a mixture, as shown in Fig. 2-24. Carrier steam which is immiscible with the components in the mixture is introduced into the column. Since the partial pressure of the components of the mixture is reduced by the additional vapor component (steam), the boiling point of the mixture is reduced. The carrier steam can also be used as heating medium (see Chapter 2.3). 2.5.1.5 Combinations of Different Variations The discussed variations may be combined, depending on the number of mixture components and their boiling behavior, to form rectification units consisting of many individual columns, the aim being optimum economic efficiency. Figure 2-25 shows a
123
crude-oil column with sidestream strippers; the first column, an enrichment column, is used to separate the crude-oil, with carrier rectification used in the sidestream strippers. The sidestream strippers act only as stripping columns, recycling the overhead product back to the main column. 2.5.1.6 Rectification with an Entrainer
More theoretical stages, and a reflux ratio which increases with time, are needed to separate a liquid mixture by rectification the closer the relative volatility ai,, approaches to unity. A simple separation is not possible if ai,j= 1. According to COLBURN and SCHOENBORN the number of theoretical stages required is 4 / ( a , ,- 1) for a 99% separation. For ai,j = 1.05 80 theoretical stages are required, while for ai,j = 1.1 under the same operating conditions only 40 are required. An entrainer or auxiliary component must be added to mixtures with small dif-
w
Fig. 2-25. Crude-oil distilla-
CG
C
tion unit. AC Atmospheric column vc Vacuum column HE Crude-oil heater, directly fired C Condenser PS Phase separator ss Sidestream stripper 0 Crude oil Steam w Water CG Crude gasoline K Kerosene G Gas oil H Heavy oil v Vacuum gas oil R Residue
s
124
2 Distillation and Partial Condensation
ferences in the components’ boiling points (ca. a < 1.04) and to azeotropic mixtures to influence the liquid phase volatility behavior, and to shift the location of the azeotropic point (see also azeotropy in Chapter 1.4.3.2). Using an entrainer for distillation is only economically efficient for mixtures with nonisomeric components. Azeotropic rectification or extractive rectification is used depending on the behavior of the mixture. An extractive rectification (Distex-process, distillation extraction) can be used to separate substances with similar chemical properties and small differences in boiling points. By reducing the partial pressure or the volatility of one of the components, the adjuvant increases the relative volatility of the original binary mixture over the entire concentration range. Azeotropic rectification can be used where there is a low concentration of the key component in the feed. Entrainer and key component are discharged as overhead product. Since the quantity of the entrainer is small, the additional energy required due to its presence is small. The entrainer is chosen such that it forms an azeotropic mixture with
either one of the mixture components, having a minimum boiling point due to the partial miscibility in the liquid phase. (A comparison of the economic efficiency of rectification processes, including auxiliary substances, can be found in [2.26].) Choosing the entrainer to separate a certain mixture is a substantial problem. Properties of mainly polar entrainers (used in azeotropic and extractive rectification) are given in Table 2-3. Of the possible interacting forces between the liquid molecules of the mixture, hydrogen bonds are most important. A classification of important groups of substances with respect to the occurrence and strength of the hydrogen bonds has been done by BERG[2.27]. These groups are listed in Table 2-4. A general overview of expected deviations from Raoult’s law for mixture substances is given in Table 2-5, in the classes I-V. Thus first pointers toward choosing a rectification entrainer are given. Experiments with different entrainers are necessary to make a final choice. The selectivity S C j is the decisive factor
Table 2-3. Required properties of an entrainer to be used in azeotropic or extractive rectification. 0 0 0
0 0 0 0
0 0 0
Suitability to cause a change in the relative volatility ai,j of the original mixture components i, j High efficiency and selectivity (a small amount of entrainer should cause a suitable change in a l j ) Total miscibility with the mixture components at the operating temperature with extractive rectification, and with azeotropic rectification formation of a miscibility gap and a minimum-boiling azeotropic Easily separable from the mixture components Low evaporation enthalpy Thermal stability No toxicity, low environmental pollution Favorable physical-chemical properties (e. g., boiling point, melting point, viscosity, surface tension, density) Noncorrosive Good availability, low price
2.5 Countercurrent Distillation (Rectification)
125
Table 2-4. Classification of important groups of substances. Liquids which form a three-dimensional network of strong hydrogen bonds, *, ** Examples : water, polyhydric alcohol, aminoalcohol, hydroxylamines, hydroxyacids (oxyacid), amides, polyphenol I1 Liquids whose molecules contain active hydrogen atoms as well as donor atoms (oxygen, nitrogen, fluorine) *, ** Examples: alcohols, acids, phenols, amines, oximes, ammonium, nitro compounds with a-state hydrogen 111 Liquids whose molecules contain donor atoms but no active hydrogen atoms** Examples: ethers, ketones, aldehydes, esters, tertiary amines, nitro compounds without a-state hydrogen, nitriles IV Liquids whose molecules contain active hydrogen, but no donor atoms Examples : chloroform, dichloroethane V All other liquids Examples: hydrocarbons, carbon disulfide, sulfides, mercaptan
Class 1 Class
Class Class Class I
* **
Associated liquids covered by class I and 11. Water-soluble liquids covered by class I and 111.
where is the relative volatility, K?and K? are the equilibrium constants of the key components i and j , with activity coefficients yi and y j , respectively. p and a indicate whether the adjuvant is present or not. The larger the value of the selectivity Si,j the better the efficiency of the adjuvant in the rectification process. Table 2-6 gives an explanation of how the adjuvant normally functions and how it affects the relative volatility as a result of this. Azeotropic Rectification
In azeotropic rectification, the otherwise unwanted formation of an azeotrope is used to simplify the separation by distillation of a mixture with a narrow range of boiling points, or azeotropic mixtures. An auxiliary
component chosen to form an azeotropic point (in mixtures with a narrow range of boiling points) or to change the azeotropic point (of azeotropic boiling mixtures) is added to the mixture. Since the newly formed azeotrope is low-boiling, it can be easily withdrawn from the column as an overhead product. In contrast to extractive rectification, the boiling point of the entrainer should be similar to those of the components of the mixture (temperature range 35°C). Entrainers forming a heteroazeotrope are preferred, as they are easily separated mechanically. Azeotropic rectification processes using adjuvants to form a homogeneous azeotrope are not of economic interest, since distillation is not easy. Therefore, other separation processes are employed. Figure 2-26 shows an azeotropic distillation unit [2.5, 2.28-2.301 for a binary mixture. In an azeotropic column, a binary mixture is separated into an almost pure bottom product component 1, and a low-boiling ternary mixture as an azeotropic over-
*
126
2 Distillation and Partial Condensation
Table 2-5. Deviation from Raoult’s law of mixtures classified in Table 2-4. Liquid mixtures of classes
Deviation from Raoult’s law
I+V
I1 + v
Positive (at I + V often miscibility gap)
I11
Negative
+ IV
I + IV I1 + IV
Positive (at I + IV often miscibility gap)
I+I I + I1 I + 111 I1 + I1
Usually positive, sometimes negative formation of an aceotropic with maximum boiling point
111 + I11
Almost ideal behavior, non- or only small positive deviation, seldom formation of an azeotropic with minimum boiling point
I1 + 111
I11 + v IV + IV IV + v
v+v
Table 2-6. Effect of entrainer on the mixture behavior. Effect of entrainer
Consequence
Formation of a complex or a hydrogen bond with the key component i
Lowering of the vapor pressure of component i Decrease of the relative volatility ai,j
Complex dissolving of components i, j or dissolving of associates of similar molecules
Increase of the relative volatility
Formation of an easily separable azeotrope with key component i
Influence on the relative volatility ai,j
head product. After condensation of the overhead product, two immiscible phases form which are decanted in the phase separator. The light phase, with a high concentration of the entrainer 3, is the reflux to the azeotropic column. The heavy phase is separated into an almost pure component 2 and the entrainer in the entrainer recovery column, which is operated as a stripping column.
Other columns arrangements than those shown in Fig. 2-26 are possible in azeotropic rectification processes. The column arrangement and the locations of the outlets for the components of the mixture and the entrainer, depend on the state and behavior of the mixture. Examples of practical azeotropic rectification are listed in Table 2-7.
2.5 Countercurrent Distillation (Rectification)
MC
,
RC
Fig. MC RC R C PS F 3
$3
127
2-26. Azeotropic distillation unit. Azeotrope tower (main column) Entrainer recovery tower Reboiler Condenser Phase separator Mixture feed of components 1 and 2 Entrainer Entrainer make-up
Table 2-7. Examples of a practical azeotropic rectification process. Mixture to be separated
Entrainer
Ethanol - Water (homogenuous azeotrope)
Benzol, Trichlorethylene
Water - Acetic acid (not an azeotropic mixture although costly distillative separation without an entrainer)
Ethylene dichloride, n-Propyl acetate, n-Butyl acetate
Acetone
- Methanol
Aromatic-rich fraction in crude oil rectification (separation of the remaining paraffines)
Extractive Rectification
Extractive rectification (Distex-process) [2.28, 2.29, 2.35, 2.361 is a distillation process which separates homogeneous, narrow boiling, or azeotropic liquid mixtures by the aid of an added substance of low volatility. The boiling point of the entrainer must be substantially higher than the boiling points of the components of the mixture. The less volatile component of the mixture selectively bonds to the entrainer, due to interactive forces. The vapor pressure of the less volatile component is therefore reduced and
Methylene chloride Methylene ethyl ketone
hence the relative volatility of all the other components are increased. Separation of the lower-boiling components thereby becomes easier. The activity coefficient, and hence the partial pressure and volatility, of only one component should be changed by the adjuvant. For example, adding aniline to a mixture of benzol and cyclohexane reduces the volatility of benzol. This gives the equilibrium curve a more favorable position with respect to separation efficiency. A high selectivity, or effectiveness of the entrainer leads to large heats of mixing (of
128
2 Distillation and Partial Condensation
either sign) in the mixture. Gas chromatography may also be used to evaluate the selectivity, and the behavior of the components in the mixture in the presence of the added component [2.31]. A methodical procedure to choose the component to be added is given in [2.37]. This is based on the Unifac method, which derives the phase equilibrium behavior of the mixture from the molecular structure of the mixture components. Figure 2-27 shows a setup of an extractive distillation unit. The adjuvant 3 is added at the top of the extraction column and withdrawn with the less volatile component 2. Both compromise the bottom product. This is then separated into the more volatile component 2 and the adjuvant 3 in a solvent stripper. This is then recycled back to the extraction tower. Table 2-8 lists some examples of practical extractive distillation processes. For the separation of a narrow boiling or azeotropic binary mixture as in azeotropic
Fig. MC RC C R F 3 83
2-27. Extractive distillation unit. Extraction tower (main column) Solvent stripper to recover entrainer 3 Condenser Reboiler Feed of components 1 and 2 Solvent entrainer Solvent make-up (entrainer make-up)
Table 2-8. Examples of practical extractive rectification processes. Mixture to be separated
Entrainer
Benzol - Cyclohexane
Aniline
Methylcyclohexane
- Toluene
Aniline
Hydrochloric acid - Water
Concentrated sulfuric acid
Nitric acid - Water
Concentrated sulfuric acid
C,-Fraction
Furfurol, dimethyl formamide N-methyl pyrolidine N-methyl pyrolidine (NMP) (Distapexprocess, Lurgi [2.33]) N-formyl morpholine (NFM) (Morphylane-process), Morphylex process including a combination of extractive rectification and liquidliquid extraction, Krupp-Koppers t2.341
Pyrolisis benzene, reforming products and other aliphatic/ aromatic mixtures (aromatic substance production [ 2 . 3 2 ] )
2.5 Countercurrent Distillation (Rectification)
rectification two columns are required for extractive distillations. The same arguments also apply to investment and operating costs. The application of these processes therefore always depends on the result of the efficiency calculation. A liquid-liquid extraction process with downstream solvent recovery is frequently an alternative process. The azeotropic mixture of tetrahydrofuradwater is processed by extractive rectification with glycol as the third component; whilst with furan as a third component, it is processed by azeotropic rectification and with glycerine as a third component it is processed by liquid-liquid extraction. Figure 2-28 shows the DISTAPEX-process [2.33] as an applied example of extractive rectification used to separate a mixture of aromatic and nonaromatic substances.
-
129
2.5.1.7 Heteroazeotropic Rectification [2.381 An azeotropic mixture with a widemiscibility gap can be separated by distillation without using a third component. Figure 2-29 shows the separation of a binary mixture with a miscibility gap. In the first column, the feed is separated into an almost pure less volatile component 2 as the bottom product, and into a mixture of nearly azeotropic composition as the overhead product. After condensation, the overhead product decays into two liquid phases by phase separation. According to the miscibility gap, the composition of the phases is xF, and xF2. Phase I, of composition x, is the reflux in the first column, while phase
