Electrochemical Water Processing
Scrivener Publishing 3 Winter Street, Suite 3 Salem, MA 01970 Scrivener Publishing Collections Editors James E. R. Couper Richard Erdlac Pradip Khaladkar Norman Lieberman W. Kent Muhlbauer S. A. Sherif
Ken Dragoon Rafiq Islam Vitthal Kulkarni Peter Martin Andrew Y. C. Nee James G. Speight
Publishers at Scrivener Martin Scrivener (
[email protected]) Phillip Carmical (
[email protected])
Electrochemical Water Processing
Ralph Zito
Scrivener
WILEY
Copyright © 2011 by Scrivener Publishing LLC. All rights reserved. Co-published by John Wiley & Sons, Inc. Hoboken, New Jersey, and Scrivener Publishing LLC, Salem, Massachusetts. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., Ill River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. For more information about Scrivener products please visit www.scrivenerpublishing.com.
Library of Congress Cataloging-in-Publication ISBN 978-1-118-09871-4
Printed in the United States of America 10
9 8 7 6 5 4 3 2 1
Data:
Contents Preface Acknowledgements Introduction
xi xvii xix
1. Water Contaminants and Their Removal 1.1 Introduction 1.2 Technology, History, and Background 1.3 Application Areas: Electrochemical Technology Water Processing
10
2. Basic Electrochemical and Physical Principles 2.1 Introduction 2.2 Acidity and Alkalinity, pH 2.3 Activity and Activity Coefficients 2.4 Equilibrium and Dissociation Constants 2.4.1 Degree or Percentage Dissociation 2.5 Electrode, or Half Cell Potential 2.6 Chemical Potential Definition 2.7 Concentration Potential 2.8 Equivalent Conductance 2.9 Free Energy and Equilibrium 2.10 Dissociation Constants 2.11 Ionic Conductance and Mobility 2.12 Osmotic Pressure 2.13 Diffusion (Flick's Law)
15 15 17 19 19 20 20 21 22 23 23 24 24 26 26
3. Systems Description: General Outlines of Basic Approaches 3.1 Electrodialysis 3.1.1 Performance Characteristics 3.1.2 General Purpose Processor 3.1.3 Additional Details for Appropriate Application - Desalinator for Small Boats v
1 1 9
29 29 31 33 36
vi
CONTENTS
3.2 pH Control: Analytic Development 3.2.1 Introduction 3.2.2 Some Technical Background 3.2.3 Sample Processes for pH Control 3.2.4 Application Possibilities 3.2.4.1 Swimming Pool Water 3.2.4.2 Cooling Towers 3.2.4.3 Regeneration of Ion Exchange Resins 3.2.5 Current and Electrical Energy Requirements 3.2.6 Shielded (Limited Ion Access) Positive Electrode Operation 3.2.6.1 Double Barrier 3.2.6.2 Close Spacing 3.2.6.3 Porous Barrier Design 3.2.6.4 Etched Electrode Surfaces 3.3 Biociding Technology 3.3.1 Electrolytic Production of Free Halogens 3.3.2 Chlorination Process Description 3.3.3 Bromination Process Description 3.4 Ion Exchange Resin Regeneration System 3.4.1 General 3.4.1.1 Present Regeneration Methods 3.4.1.2 Electrochemical Regeneration Method 3.4.2 Equipment Comparison 3.4.2.1 Performance Characteristics Comparisons 3.5 Metals Reclamation 3.5.1 Electrochemical Process for the Removal of Iron in Acid Baths 3.5.2 Technical Approaches 3.5.3 Technical Approaches 3.5.4 Laboratory Feasibility & Data Study Suggestions
39 39 39 42 45 46 46 46 50 51 51 52 52 52 55 55 57 61 62 62 63 65 65 66 71 71 72 73 76
CONTENTS
3.5.5 3.5.6
Experimental Methods 3.5.5.1 Approach B Tests 3.5.5.2 Approach A Conclusions & Recommendations
Mathematical Analysis & Modeling Electrodialysis Systems 4.1 Electrodialysis: Descriptions and Definitions 4.2 Basic Assumptions and Operating Parameters 4.2.1 Electrolytic Conductivity 4.2.2 Solute Concentration & Electrical Conduction 4.2.3 Electric Charge Equivalence 4.2.4 Coulombic Efficiency 4.2.5 Coefficients of Performance 4.3 Parametric Analysis: Flow-Through Configuration 4.3.1 Performance Analysis of Electro-dialytic Systems, Part I 4.3.1.1 First Approximation 4.3.1.2 Design Assumptions 4.3.1.3 Equation Development 4.3.1.4 Resistance of a Cell 4.3.2 Further Definition Of Terms 4.3.2.1 Average Current Density 4.3.2.2 Entrance & Exit Current Densities 4.3.2.3 Water Flow Rate in Processed Chamber 4.3.2.4 Solute Concentration Along the Length of the Cell 4.3.2.5 Figure of Merit 4.3.3 Numerical Evaluation Program 4.3.3.1 Second Approximation, Part II 4.3.4 Multiple Cells in Parallel
vii
76 79 81 91 95 95 102 102 106 108 109 109 110 110 110 111 111 112 114 114 115 115 116 121 122 123 127
viii
CONTENTS
4.3.5 4.3.6
4.4
4.5
4.6
4.7
4.8
General Characteristics Total Electric Current through the Electrodes and Membranes 4.3.7 Coulombic Efficiency Variation 4.3.8 Further Considerations Flow-Through Design Exercises 4.4.1 Exercise #1 4.4.2 Exercise #2 4.4.2.1 Predetermined Independent Variables 4.4.3 Exercise #3 4.4.4 TDS Removal Rate Capacity 4.4.5 Stacked Cell Configuration 4.4.6 Expanded Analysis Batch Process Analysis: Re-Circulating or Static Water Processing System 4.5.1 Coulombic Efficiency 4.5.2 Single Cell Analysis 4.5.3 Single Cell - Special Case 4.5.3.1 Ohmic Energy loss and Water Temperature Rise Design Exercises for Water Re-Circulation Systems 4.6.1 Exercise #1 4.6.2 Exercise #2 Cell Potential and Membrane Resistance Contributions 4.7.1 Membranes 4.7.2 Electrodes 4.7.3 Opposing Voltages Diffusion Losses of Ions and Molecules Across Membranes
System Design Exercises & Examples 5.1 Electrolytic Generation of Bromine and Chlorine: Design Procedures 5.1.1 Design Geometry Comments 5.1.1.1 Example
127 127 130 138 138 140 142 142 144 145 146 146 149 154 155 157 158 160 161 162 163 164 164 169 171 177 177 184 188
CONTENTS
5.2 5.3
Simple Estimate of Capital Equipment and Operating Cost of Electrochemical Desalination Apparatus Cost Estimates Outline for an Electrodialysis De-ionizing System
Applications Discussion 6.1 Demineralizer: Electrodialysis 6.1.1 Advantages of Electrodialysis 6.1.1.1 General Characteristics 6.1.2 Desalination System - Module Specifications 6.1.3 Performance Characteristics 6.1.4 Cost Factors 6.2 Reseidentialwater Softener 6.2.1 Product Design Description 6.2.2 Physical Description of the System 6.2.3 Operation 6.2.4 Design Example 6.2.5 Competitive Methods 6.3 Electrical Water Processor Portable Design 6.3.1 Present Solutions 6.3.2 Operation of an ED System 6.3.3 Design Prototype 6.3.4 Description
ix
189 191 195 195 196 196 196 199 201 202 202 203 205 205 210 211 211 212 212 214
Appendix A: Some Physical Constants and Conversion Factors
217
Appendix B: Conductance and Solubility B.l KC1 Ionization Constants
219 219
Appendix C: Feeder Tube and Common Manifolding Losses
225
Appendix D: Variable Current Density D.l Current Density Variation
231 231
x
CONTENTS
Appendix E: Mathematical Analysis: Water pH Control Cell and Ion Exchange Resin Regeneration E.l Analytic Approach E.2 Special Case Evaluation - No Resins Present in System E.2.1 Non-Constant Electrochemical Generation Rates for H + and OH" E.2.2 Dimensions and Units E.2.3 Variable Electric Current Densities E.3 Estimation of Resin Constants E.4 Electrolytic Resistance of the System Water E.5 Solution of the Simultaneous System Equations E.6 Sample Solution of Operating System
235 238 248 250 254 256 257 261 263 268
Appendix F: Industrial Chlorination and Bromination Equipment Cost Estimates E l Bromination Equipment List F.2 Capital Cost Analysis E3 Operating Cost Analysis F.4 Conclusions and Comments
271 275 277 280 281
Appendix G: Design Mathematics in Computer Format G.l Case A G.2 Case B G.3 Case C
285 286 294 299
Appendix H: Mathematics for Simple Electrochemical Biociding
303
Bibliography Index Also of Interest
309 311 313
Preface In recent years, the awareness of water needs and processing requirement has become an increasingly important topic. As the earth's population increases the demand for "clean" water has become an even larger factor in residential as well as industrial and commercial costs. There are now almost no natural water sources that do not require some purification of one form or another to render them potable sources. If the water impurities are ionic in nature, i.e., inorganic salts such as sodium chloride, calcium chloride, or iron sulfate, or inorganic acids such as sulfuric and hydrochloric etc., then the most effective method of moving these components about is by electrochemical means. Most substances dissolved in water do not lend themselves to be removed by filtration, as usually such ionic materials have been leached out of the ground supply. If the contaminants are non-ionized organic substances in solution, then there must be other means for their removal, and we will not treat the subject of their removal by chemical, distillation or filtration means. The technology that will be described here is well known but it is hoped that some of the quantitative and systems fabrication aspects covered here will contribute to the increasing practicality of electrochemical methods in water treatment applications. Much of the methods discussed here are a direct outgrowth of our research and development work in energy storage. Electrode design and construction methods for single and multiple cell devices were first addressed in the development of energy storage cells and multi-cell modules.
XI
xii
PREFACE
As the title of this book indicates, the following pages represent a summary of the results of a number of years of R&D effort directed to a better understanding of some basic processes for water treatment as well as the development of practical methods for design of useful hardware. The information contained herein is presented in an informal manner, in much the same fashion that it was generated in the laboratory studies. It is sincerely hoped that this compendium of technical notes will add meaningfully to the body of information associated with electrochemical approaches to water treatment, and will encourage others to pursue these avenues more intensively. Except for the review of some very basic mathematical relationships associated with chemical and physical processes, involving electric potential, molecular diffusion and solution pH, all of the material presented in this book is original. The major purpose of this book is the presentation of a body of analytical and design information that the reader may find useful in the exploration of electrochemical technology as applied to water processing. Hopefully, the contents of this text will encourage and promote further development of electrochemical processing systems for consumer as well as industrial and commercial applications. In our attempt to accomplish this end, the book has been organized into three main sections. They are: 1. General description of electrochemical processing and their application areas 2. Mathematical analysis of operating systems for design and optimization purposes 3. Design examples and procedures. Most of the experimental work on various water treatment projects was done at GEL/TRL during the period between 1978 and 1988. A short introduction to some very important and basic concepts is included at the beginning of the book and
PREFACE
xiii
in Chapter 2 as a convenient review for the reader. The Appendices are also offered for some additional analytical and ancillary application information, without disrupting the arguments and descriptions in the main portion of the text. The thread of the discussions to follow is to first identify the nature of the technology and to describe its various formats and uses. Then the book proceeds to develop an approach to mathematically treat the essential parameters associated with the principle mechanisms of ionic transport, electrolysis and diffusion. These developed mathematical tools are then applied to the preliminary design of a number of systems, serving as exercises for those that wish to carry on with their application in practical water processing problem-solving. The fundamental equations that evolve in the analyses are listed in a reasonably convenient and accessible form so that the reader can place them into appropriate computer software programs for easy solution and graphing of data. I have tried to establish an obvious rationale throughout the book to minimize confusion and the obscuring of direction and purpose. The Technology Research Laboratories, Inc. sponsored most of the analytical and experimental developments presented in the following pages. Some of the laboratory hardware and prototype systems were part of development projects funded by other industrial organizations for evaluation purposes. Our purpose in writing this book is to present sufficient basic applications and information about electrodialysis so that the reader is able to develop his own designs and approaches to solving water management problems. We will treat a number of forms of electrochemical water treatment from pH control to desalination along with their many application potentials. This book is concerned with the development of the basic principles and engineering design aspects of electrochemical
xiv
PREFACE
water processing. The intent in writing this volume is to serve as handbooks for the further development of related products. It should provide most of the necessary physical and chemical background to enable the reader to proceed with his own mathematical computations and engineering designs and mathematical computations. He should be able to arrive at sizes, performance characteristics and some preliminary cost factors on the basis of the information presented in this volume. No attempt is made in this book at covering the entire field of water treatment or reviewing the various competitive technologies associated with these methods. There are many excellent texts that have treated these subjects extensively, and have reviewed and summarized the work of numerous other investigators. There have been many texts that present excellent reviews of the state of the art in electrodialysis, reverse osmosis, filtration and distillation systems. Some of the specific terms and physical constants employed in the analytic approaches are covered in Chapter 2. However, it is assumed that the reader is familiar with the basic concepts of physical chemistry and elementary inorganic chemistry. For those who are not so well versed in these scientific disciplines, the resultant equations developed in Chapter 4 and elsewhere in the book are still useable for purposes of calculating the design parameters for the water processing devices under discussion. TRL, Inc. has performed the background work, a portion of which is covered by this book, over a ten-year period. The author, with over 35 years of research and development experience in related technical areas, has been principle investigator in most of the work represented in these pages. Water treatment with the minimal use of chemical reagents will increasingly become the goal of most systems in the future. In some instances, the elimination entirely of chemical agents is possible.
PREFACE
XV
A family of systems that provide means for controlling pH, biocide level and dissolved solids concentration in water have been studied as a result of the many years of electrochemical developments in the energy storage area at TRL. A larger portion of our attention here is devoted to the direct removal of dissolved, ionized materials in water via electrochemical (electrodialysis) separation. As a final comment, it is important to note that this book is concerned primarily with methodology rather than the specifics of any one design or system configuration. Very little empirical data or materials' properties information is contained herein. The specifics of component characteristics such as membranes, electrodes, and materials properties will be treated in another reference that is presently in preparation. This future text will also contain some empirical data on system performance as well as design and fabrication methods. Many application possibilities are still available that are eminently suitable to electrochemical techniques. I would like to express my sincere appreciation to Donald Morris, who performed many of the experiments and prototype design and fabrication, and for his invaluable assistance in organizing this information. Much of the discussion on biociding processes, and especially the sections that treat large-scale industrial water cooling systems was prepared by Catherine Middelberg as part of an application study at TRL, Inc. Special gratitude is due to my wife, Min, for her encouragement and endurance with the labors of organizing the technical material for these volumes. Ralph Zito Port Orange, FL January, 2011
Acknowledgements The work represented as a summary of laboratory investigations, as well as the design, building and field testing of potentially viable and useful water treatment products took place over a period of a few years at TRL, Inc. in Durham, NC. A number of different talents of various individuals participated in critical manners to bring about the net results contained in this book. Only a few of these people can be credited here. It required not only some scientific perceptivity, but also engineering and fabrication knowhow to persistently pursue these projects. It is hoped that some of these developments and knowledge gained by the activities of these people will be useful to others in the commercializing of systems in the future. Generally, water must be treated in some manner due to the many problems that beset its use in applications where "uncontaminated water" is critical to our civilization. Among the numerous contributors to this project, I would like to particularly cite Dale Jones for his steadfast support in overcoming some difficult situations, Don Morris for his unparalleled contributions to design and hardware fabrication. And many thanks to Patricia Pearson and Sara Tortora who provided order to the laboratory; orderly enough to maintain the necessary continuity for any work to succeed with a staff of usually over a dozen individual contributors. Also, without their imposed discipline and encouragement we almost certainly would not have completed these tasks.
XVll
Introduction Water has been in plentiful supply on this planet since it long ago cooled down and the oceans were formed. Despite the fact that over 70% of the Earth's surface is covered by water, the water needed for various life sustaining purposes is either unavailable at the required locations, or it is too contaminated for practical use. Obtaining fresh water is almost invariably a costly endeavor. The natural pools and lakes have gone to a great extent, relatively free of contaminants, and scattered everywhere in the communities of this country. High population densities coupled with increased demands and pollution by industry and residents have left these idyllic scenes far behind us. Now, we must either transport water from a few remaining sources at higher elevations such as melting snow on mountains or lakes at or near mountaintops.
Roman cross country aqueduct. XIX
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INTRODUCTION
The ancient Romans took advantage of such sources in Europe by building aqueducts (viaducts) to provide water to remote farms and villages by gravity feed. They spanned obstructions and valleys with gradually diminishing height to sustain the driving force of the mass of water being transported. There was little expense beyond the initial capital investment of the masonry, and of course, some continuing maintenance costs. These facilities were durable and had very long lives, as is evidenced by their existence today as functioning water lines. Today, we must resort to other transportation mechanisms other than gravity. Now, pipelines with water pumps are more common, but trucking and shipping is even used in some areas where water is critical. Such means of provision are quite costly. The only alternative to transporting water of good quality to other places of need is a purification or decontamination process of some sort. These methods, too, are costly depending upon the extent of processing necessary and the source of materials and energy As in the case of transportation, energy for separation is necessary to produce useable water from contaminated sources. There are only a limited number of mechanisms that can be employed to remove unwanted substances from water, whether they are dissolved or simply as particulate matter in suspension. In the latter case, filtration of one form or another or sedimentation can solve these problems. For those materials that are in solution, other methods must be employed, such as reverse osmosis, electrodialysis, or the old standby, distillation. Both distillation and RO will remove all solid matter in solution regardless of whether they are organic in nature, or inorganic, ionic materials. Distillation is the oldest method in existence, but it can be quite inefficient in terms of energy required per unit quantity of condensed water produced. Maintenance of boilers and evaporators can also be costly because of the solids left behind. The same is
INTRODUCTION
xxi
true for ED systems whose micro-porous membranes can become clogged with solid matter. ED is a cleaner system in the sense that no solids are collected as such, but the process will only remove substances that produce ions when dissolved so that they will respond to electrical forces for the separation process. Hence, ED is limited to removing only inorganic materials. Depending upon the nature of the situation one or more of these systems might be employed in treating a single body of water. It should be kept in mind that a minimum amount of energy is required to extract dissolved materials at the very least equivalent to their heats of solution. However, in practical systems that amount of energy is usually quite small compared to the dissipative factors of electrical resistance in ED devices, and mechanical resistances of RO devices. Desalination of sea water presents the greatest of all problems because of the very high concentrations of salt involved. Depending upon the form of energy available at a particular location where the fresh water supply is a problem, one of the preceding approaches is usually employed. If, for example, solar energy or cheap fuels are in great supply, distillation may very well be the method used in that location. Desalination should be receiving greater attention as a means of providing "fresh water" especially because seawater is so plentiful, and the demands are increasing so rapidly. The future will undoubtedly bring more conservation measures, but we may still be hard-pressed for better solutions to this ever-increasing problem. In recent years, especially, many devices and gadgets have been offered for sale on the open market, claiming to be capable of "purifying" water for drinking and cooking purposes. Some of these offered products are, indeed, genuine and perform as advertised. Products such as those based upon the use of ion exchange resins and distillation are based upon real science.
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INTRODUCTION
However, numerous electrical devices on the market do not perform the tasks of which vendors claim they are capable. For example, ineffective devices include those that supposedly operate on the basis of some sort of magnetic field imposed on the water system via coils of wires that "polarize" or otherwise change the character of ionic species. These products are not based upon any known mechanism that would, in fact, separate unwanted materials in the water supply, or prevent mineral deposits from accumulating on the insides of pipes or hot water tanks in home or industrial water systems. There are some simple rules that one can follow to determine whether these proffered products do indeed operate. One should consider the amount of energy required to remove a given quantity of maters, i.e., dissolved substances, from a given volume of water. Generally one can employ such simple estimates to determine the probability of successful operation. Most of these important issues are covered thoroughly in the text to follow. There isn't much question about the importance of water in every facet of our lives, specifically the necessity for good quality water. The issues covered here are largely concerned with the removal of unwanted dissolved substances in water—substances that are ionic and are usually inorganic salts, acids and bases of soluble materials. The most common of these is salt, i.e. sodium chloride, because of its abundance and global availability. Various competing methods for removing materials of this nature are reviewed, but the main emphasis is electrochemical approaches such as electrodialysis. Much of the book is an analysis of the performance, efficiency and configurations of these types of systems. Some information is provided about the materials of construction, but the main theme of the book is analytic in format.
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
1 Water Contaminants and Their Removal 1.1
Introduction
This book is intended both as a tutorial presentation of basic principles of electrochemical water processing as well as a short working manual for the design and operation of electrochemical deposition cells and for electrodialysis devices. Water quality for direct and indirect human uses has always been an important concern in the past, and continues on into the future. With the ever-increasing concentrations of population centers and the demands of the industry, that concern is growing continuously throughout the world. The conditions that determine acceptable water quality are very dependent upon the use to which the water is intended. The factors involved are numerous, to say the least, and range from one high purity extreme to non-potable irrigation water. Water intended for farm 1
2
ELECTROCHEMICAL WATER PROCESSING
irrigation, for example, can contain a high level of foreign substances at the level of thousands of parts per million as long as these are not damaging to crops. At the other end of the water spectrum is the need for super pure, or "polished" demineralized water for pharmaceutical or semiconductor production uses. Among the more common types of foreign materials present that determine the "purity level" of water are listed below. Their removal from the body of water for each type is identified. 1. Solid matter in agitation or suspension Removal by: filtration, decanting 2. Dissolved organic substances Removal by: distillation, adsorption 3. Dissolved inorganic, ionic substances Removal by: distillation, reverse osmosis (RO), ion exchange resins, electrodialysis (ED) 4. Bacteria and other living organism contaminants Removal by: reverse osmosis, chemical addition, heating 5. Gasses present, in solution or otherwise Removal by: heating, ED, RO, adsorption 6. Other liquids miscible or non-soluble Removal by: fractional distillation, adsorption, RO,ED The removal method selected depends upon the economics of the situation for the intended applications, the specifics of the contaminants, and other unwanted substances present in the water. In the future, water treatment with minimal use of chemical reagents will become the goal of most processing systems. This approach is stimulated by the desire to minimally disturb the existing chemical conditions in water, and to reduce the amount of chemical correction needed as one introduces a reagent to fix one problem, only creating
WATER CONTAMINANTS AND THEIR REMOVAL
3
another problem. In some water conditioning instances, the elimination of all chemical agents is possible. A family of systems is possible, which will provide means for controlling pH, biocide level and dissolved solids concentration in water. One such form of technology is the direct removal of dissolved, ionized materials in water via electrochemical, (electrodialysis), separation. In the ensuing pages, one such class of processes will be described in some considerable engineering detail. In some instances the need to introduce bulk chemical agents to the water system can be eliminated entirely. This system removes dissolved substances such as salts, mineral compounds, acids and alkalis through the application of an electric field impressed across an array of electrodes and ion selective membranes. An electric power source is only required as input to the water. No chemicals or consumable materials are introduced into the water system. Dissolved substances that are removed from the main body or mainstream of water are carried over into a waste water stream and eventually discarded. A maximum of only a small percent of the incoming water is "wasted" in this manner, and no materials are put back into the drainage that were not present initially. The waste- water just has a higher concentration of the same dissolved materials than it had when first introduced into the systems. There are only a limited number of other methods, which can be employed to perform this task. They are: 1. 2. 3. •
Distillation Reverse osmosis, RO Ion exchange resin beds Distillation is simply the evaporation of solvent from solids and other contaminants present in the original body of water. The disadvantages are the life of equipment, relatively high maintenance in cleaning residues
4
ELECTROCHEMICAL WATER PROCESSING
from evaporating surfaces (heat exchangers), and high temperatures and high-energy consumption. • Ion exchange resins operate on the basis of the displacement of one ionic species for another as a function of relative concentrations. A mixed resin bed (cation and anion), regenerated in the hydrogen and hydroxide forms, respectively, will remove all other species of ions upon passing through the bed, and replace them with hydrogen and hydroxide (water as net product). High quality water can be obtained via this method. However, problems include high cost of regeneration and contamination. Usually this process is suitable for bringing good quality input water to high quality (polished, ultra pure) water for pharmaceutical and semiconductor uses. • During osmosis, solvent passes through a semipermeable membrane separating two solutions. Solvent—or water in this case—passes from the dilute solute side to the more concentrated side. This migration of solvent molecules to the concentrated side will continue until the solute concentrations are equal on both sides of the membrane. Reverse osmosis or migration of solvent to the dilute side can occur if a sufficiently large hydraulic pressure differential is established across the membrane in the appropriate direction (see Chapter-2, Section 2-12). RO is a system in which the water (solvent) is forced through the membrane, leaving behind ionized solutes as well as solids and organic materials. This filtration aspect of the process is an advantage in terms of ridding the water of most of the unwanted contaminants. However, the problems of membrane damage and clogging or blocking and fouling are significantly increased.
WATER CONTAMINANTS AND THEIR REMOVAL
5
The electrodialysis, (ED), method offers some distinct advantages over all three of the above alternative methods. A comparison of attributes shows these to be some of the distinct benefits in practical use. Problem areas with Distillation a. b. c. d.
Costly in energy consumption Small systems are usually very inefficient Maintenance and scale accumulation problems Low production rate of water
Problem areas with Reverse Osmosis a. Fouling of membranes b. High pressure requirements for high TDS differences and their potential hazards. c. Costly systems d. Large size systems for large water flow rates make them impractical for many consumer applications Problem areas with Ion-Exchange Resins a. Resins are costly b. Need for regeneration is inconvenient and costly c. Two resin bed systems require use of hazardous acids and alkalis for regeneration d. Practical considerations of these de-ionize systems render them impractical for consumer and many commercial applications Problems and Limitations of ED Methods 1. No filtration provided for particulate matter 2. ED will separate out only ionized chemical species, no organic 3. Possible corruption of membrane by crystallizing materials within the membrane structure
6
ELECTROCHEMICAL WATER PROCESSING
The ED system employs long-term, inexpensive electrodes in conjunction with durable membranes that make for a low capital cost apparatus. The equipment operates at standard conditions of temperature and pressure, and requires no special precautions regarding quality of incoming water. The system can be designed to handle a full flow of water on a "once through" basis or it can be made very small and used in conjunction with a storage tank as a batch processor. Because the system is very simple in structure and operates through direct input of electric power, it can be made very small for portable applications. Surprisingly, ED is not employed in many areas where its applicability has distinct advantages. For various reasons of cost, unavailability of durable ion exchange membranes, and perhaps complex manufacturing requirements in the past, ED is not as popular for desalination and demineralizing as reverse osmosis, RO, systems. In a similar fashion, RO and cation exchange resin bed methods have been preferred for performing the tasks of water softening. Residential water softening presents an interesting example of a use where one method almost exclusively predominates the field. Cation resin bed devices have become the primary choice of the industry. RO and ED are competing systems that offer dramatic advantages with regard to the condition of the emergent, treated water over cation resins for softening water. Neither RO nor ED requires the consumption of sodium chloride for its operation resulting in brine waste water effluents into the ground water table. Softening by cation resins results in virtually the same concentration of dissolved substances in the treated water, except that sodium ions have been substituted for the unwanted "hardening cations" such as calcium and iron. RO and ED systems soften and demineralize input water by the removal of both cations and anions, thus
WATER CONTAMINANTS AND THEIR REMOVAL
7
lowering the total dissolved solids concentration without ionic substitutions. RO devices are presently available as small units for residential applications, processing a few gallons per day. A full-scale unit that has the capacity to handle peak flows of 2 to 10 gallons per minute, without storage tanks, would be too large, impractical, complex and costly for individual home use. However, ED systems can be fabricated with high flow rate capacities that would be relatively simple and low cost. It is the intention here to review the operation of ED systems and show how economically practical ED water treatment systems might be designed to solve more problems than they are presently employed. Perhaps we can encourage a closer examination of the salient features and applicability of ED and electrochemical methods in general. The main attractiveness of the ED approach to water treatment is its inherent simplicity and compatibility with ambient conditions of standard temperature and pressures. This simplicity of hardware is illustrated in the photograph below (Figure 1.1) of an early field test prototype water demineralizer. The principle component parts of the system shown in Figure 1.1 are listed below. Processing Module (ED stack of electrodes and membranes) Processed water reservoir Waste water reservoir DC electric power supply Circulation pumps (two) We hope to accomplish our goals by going through numerous design exercises, and by establishing straightforward analytical methods, as well as describing some approaches to the practical problems of equipment life, manufacturing designs and costs.
8
ELECTROCHEMICAL WATER PROCESSING
Figure 1.1 Water demineralizer system components.
We are concerned in this book only with electrochemical processes for the control of water quality. Filtration, active carbon adsorption, and reverse osmosis systems are not the subjects of this text. Our primary purpose is to present the results of research and development conducted and some of the resultant engineering prototypes, along with some useful analytic methods for the design and performance optimization of an array of electrochemical systems. These potential systems range in function from that of demineralizing and desalting streams or bodies of water to the generation, in situ, of oxidizing agents for biocide purposes. The latter would eliminate the need for introduction of biocides from external sources. Some basic physical chemical principles and electrochemistry are briefly reviewed in Chapter 2 to provide a convenient reference for the reader when going through the analytic portions of this book. For a thorough understanding or tutorial presentation of the physics and
WATER CONTAMINANTS AND THEIR REMOVAL
9
thermodynamics of the relationships employed in the parametric developments, it is suggested that the reader consult any of the numerous and excellent texts on the subject matter. Some suggested sources are given in the accompanying Bibliography section. ED systems can be designed to handle full flow of water on a "once through" basis or they can be made quite small and used in conjunction with a storage tank. Many portable applications are also possible due to the relative simplicity of its construction and the absence of any need for non-standard ambient conditions, including high pressures or temperatures. 1.2
Technology, History, and Background
TRL, Inc. is an independent Research & Development company. It was formed in Cambridge, Massachusetts in 1971 for the purpose of developing its own proprietary technology in energy conversion and storage; energy storage for utility load leveling and standby power. Most of the laboratory work over the years has been in the area of electrochemical processes, electrode development for Redox and halogen batteries, along with research in the physics of surfaces and transport phenomena. During the 25 years of applied research and prototype designing, a body of electrochemical technology was developed that lends itself to many applications totally unrelated to energy storage, batteries or fuel cells. Figure 1.2 shows a typical test set up for evaluating single cell electrodialysis systems for either pH control or de-ionization applications. Pictured are power supplies, timers, TDS and pH meters along with small fluid pumps and data acquisition connections for computer filing. A resulting potential application for some of the developmental work at TRL is in the field of water processing.
10
ELECTROCHEMICAL WATER PROCESSING
Figure 1.2 Laboratory test stand for water electrochemical studies.
Water treatment via non-hazardous methods afforded by electrochemical processes is an attractive and sensible product area possibility. The laboratory proceeded to develop, field test and engineer a class of new products for pool and spa use (labeled SimPool systems), and manufactured systems for field testing over a year. Over that time period, systems were developed and successfully installed in over 100 pools and spas in various geographic areas of the United States. 1.3
Application Areas: Electrochemical Technology Water Processing
The following is a list of some immediate areas of application, which are possible with ED and electrochemical
WATER CONTAMINANTS AND THEIR REMOVAL
11
technology. These product applications would make use of well-established hardware designs and know-how. 1. Electrochemical Generation of Free Halogen (chlorine or bromine) in "salted" water for the purpose of disinfection. Product types are: 1. Swimming pool and spa halogenators 2. Water cooling tower processing 3. Potable water supply treatment 2. Free Halogen, Hypochlorous or Hypobromous Acid Injection Electrochemical generation of halogens and halogen acids via concentrated salt solution are injected into electrode reaction chambers. "Salting" an entire body of water to be treated is thus avoided. This method is particularly suited to large bodies of water and in evaporative cooling water systems, which require frequent "blow-down". 3. pH Control of bodies of water without the addition of acids or bases from an external chemical source. Only electrical power input is required to perform the conversion process instead of introducing additional chemical species. Handling, transporting, and storing corrosive and hazardous chemicals is eliminated. This is suitable for: 1. Swimming pools and spas 2. Industrial water supplies for the industry 3. Cooling water for machinery 4. Reverse osmosis system pH control
process
4. Water Softening 1. Residential and commercial water softening systems use the precipitation of dissolved minerals as scale on the negative electrode surfaces.
12
ELECTROCHEMICAL WATER PROCESSING
A system employing a membrane separator will perform this function without the introduction of sodium ions into the water stream, as is presently done. 2. A counter top version of this system is possible, which would "purify" a small quantity of water at a time (perhaps 1 qt. to 1 gal.)- The design may resemble that of a typical drip-type coffee maker. 5. Oxygénation Oxygen bubbles can be generated for the purpose of replenishing the supply in relatively confined and stagnant bodies of water, including aquariums. Such a unit would have no moving parts, generate no noise or vibrations, last indefinitely and be quite inexpensive. Electrolysis of the water produces the needed oxygen. "Starved" electrode designs would have to be employed in this instance to guard against production of free halogens. 6. Ion Exchange Resin Regeneration 1. Regeneration of resin beds normally employed in residential and commercial water softeners requires the periodic replenishment of salt (sodium chloride) in a reservoir. Frequently unwanted sodium ions are then substituted for the heavy, hardness producing metals, which are removed from the water. An ED system can be substituted for the salt reservoir and hydrogen ions used to regenerate the resin instead of sodium. Electrolysis of the water through an ED unit produces the H + ions. Normal pH is restored by the proper use of the staged electrolytic unit. In this approach, no salt is needed and no sodium ions are produced in the water.
WATER CONTAMINANTS AND THEIR REMOVAL
13
2. Regeneration of de-ionizer resin beds at the operating site via electrochemical means. This would eliminate the need to remove equipment and transport it to service depots. Costs would be reduced and operational interruption minimized; plus, there would be no handling of hazardous chemicals, such as concentrated acids and alkalis. 7. Organic Contaminant Control In some cases where unwanted organic molecular structures can be altered and rendered acceptable via high acid or alkali exposure, a pH control cell may provide a "local" environment to achieve the needed reaction without the introduction of chemical reagents.
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
2 Basic Electrochemical and Physical Principles 2.1
Introduction
There are innumerable excellent texts available that cover the various subjects of thermodynamics, physical chemistry, and physics for students and researchers in the physical sciences. No attempt will be made here to present in a tutorial fashion any of these disciplines. Instead, we will outline and summarize some of the more pertinent concepts and mathematical artifacts that are basic to the design of the mathematics of operating electrochemical systems. These principles are the foundations of all of the calculations and performance assessments we make, whether or not they are consciously employed. In order to benefit from the design information presented here, and to be able to maximize the use of the associated mathematical developments, it is recommended that the reader have a general background in physical chemistry and college level calculus. 15
16
ELECTROCHEMICAL WATER PROCESSING
When generating the design parameters for an electrodialysis system, or for any other electrochemical process that is related to the subject matter in this text, the descriptions of the systems are in terms of these concepts and physical parameters. The major question here is simply "what are we interested in knowing about the operation and performance of an electrochemical system so that we can optimize designs and make effective use of the system?" The primary issues are the following: 1. Statement of the water treatment problem to properly identify the method of solution 2. Effectiveness of the system as applied to the problem in terms of function 3. Cost of initial capital equipment 4. Operating costs including life of equipment, labor, maintenance, and power. 5. Secondary problems that must be addressed as a result of the electrochemical system application, such as waste water disposal. 6. Physical size of system 7. "Efficiency" of operation 8. Reliability of apparatus To answer these questions, it is necessary to go through a design procedure that addresses the specific problem under consideration. The design process involves performing numerous calculations and making certain assumptions and technical decisions, again, in terms of the particular application needs. The procedures compiled in this book are the results of a series of analytical approaches in conjunction with empirical data available from much experience with related electrochemical processes, as well as the vast resources in the general scientific literature of materials properties data. Certain basic physics and chemistry tools are needed to make use of this information.
BASIC ELECTROCHEMICAL AND PHYSICAL PRINCIPLES
17
What follows is a very brief review of the background concepts that underlie much of the work that has been directed toward these water treatment application processes. • Chemical potentials at surfaces of electrodes and membranes • Diffusion and transport of molecular and ionic species • Electronic and electrolytic conduction processes • Acidity or alkalinity of water solutions, pH • Chemicals produced at the electrodes Some of the tools and concepts employed in the development of the information contained in this book are summarized in this chapter. We will review some of the chemical and thermodynamic properties and concepts that are particular to those employed in the analyses developed here. They are: Ionic equilibrium
pH
and dissociation Activity coefficients
Ohm's Law
Ionic mobility
Coulombic equivalents
Chemical potential
Figure of merit
Oxidation and reduction 2.2
Acidity and Alkalinity, p H
The concept of pH was first introduced by Sorensen in 1909, and provides a convenient measure of the level of acidity of aqueous solutions. The term is defined as the logarithm or exponent to the base 10 of the activity, aH+. Thus, 10"PH = a„. M
or (
pH =-log
aH+=
log
1^
vVy
(2.1)
18
ELECTROCHEMICAL WATER PROCESSING
The activity, a, of ions as employed in electrochemical theory is the ratio or percentage of the active (effective) concentration for reaction participation versus the total ionic specie concentration present in solution. In order to develop the necessary relationships for design and analysis of operating system parameters, it is necessary to define and qualify certain other basic concepts such as free energy, equilibrium constant and ionic mobility. The following relationships and concepts can be found in innumerable texts on electrochemistry or physical chemistry. For the sake of convenience, these are the basic tools needed to quantify the performance of electrolytic processes having to do with H+ and OH~ ion production or ion transport in general. The purpose of this exercise is to establish the relationships necessary to estimate the amount of electrical current flow or electrical power to change an aqueous solution by a pH point—thus, the relationships between pH, electrode potential and concentration of hydrogen or hydroxyl ions. Pertinent to the subject matter of this book is the ability to estimate the concentration of H+ ions. In very dilute solutions the activities are equal to the ionic concentrations. In term of ionic concentrations scale, pH can be expressed as üH = - l o g | H + | = l o g r ^ - T
(2.2)
where \H+1 is the concentration of hydrogen ions. The scale is from near zero to 14. On this scale, 7 is neutral (equal numbers of OH~ and H+ ions), with 14 being maximum alkalinity or minimum H+ ion concentration. For example, a pH of 2.5 would correspond to a hydrogen ion concentration of log|H + | = -2.5 \H+1 = 3.16 x 10"3 gram-ions/liter
(2.3)
BASIC ELECTROCHEMICAL AND PHYSICAL PRINCIPLES
19
2.3 Activity and Activity Coefficients The term activity as introduced by G.N. Lewis was directed at measuring the escaping (vaporizing) tendency of a volatile liquid. The activity term, a, is defined by the equation (2.4)
AF = FA-F°A=RT\naA
for a solvent substance, A, with a dissolved solute present. In this case, a= p / p o , where p o is the vapor pressure of the pure solvent and p is the depressed vapor pressure of the solvent with a dissolved substance present. In the case of ions in solution, the activity is defined as the effective concentration of solutes. Ideally, the activity and actual concentration are equal. And indeed, as the dilution becomes infinite, they become equal. In an infinite dilution situation the expression
X = M^ = 1
(Z5)
a means a = activity of the solute molecule.
Activity coefficient, y, is defined as the activity divided by the molarity, m, of the specific ion, or a
(2.6)
r=— m
2.4 Equilibrium and Dissociation Constants For a binary electrolyte, i.e. a single solute consisting of two ionic components, A and B, the reaction AB^A+
+ B~
(2.7)
is the dissociation of the molecule into its oppositely charged ions. The equilibrium, or dissociation constant, K, is expressed in terms of the activity coefficients as B
K=^
-
a
AB
(2.8)
20
ELECTROCHEMICAL WATER PROCESSING
2.4.1
Degree or Percentage Dissociation
A more directly useful parameter for calculating performance of equipment is the degree of dissociation, ß, of an ionic solute. That would also enable us to better estimate pH values of solutions 2 . ß is defined as the ratio of the concentrations of the ionized solute species to the total solute concentration, or
__[£] +[ £ ] _ ß=
[AB]+[A+]
+
[B-]
a 9 )
In dilute solutions the activity coefficients can be approximated by aM~[AB] = c(l-ß) ~[A+] = cß
A+A+
a
a„-
(2.10)
[B~] = cß
where c = total concentration of the solute of ionic as well as undissociated molecules. Continuing on, we may see how the pH of a dilute solution can be approximated as pH = - l o g [ A + ] = - l o g [ H + ] = -log[cß]
(2.11)
on the basis of calculations made from the equivalent conductance, Ao, of completely ionized pure water. 2.5
Electrode, or Half Cell P o t e n t i a l
The electrical potential, E, of an electrochemical cell is simply stated as AF = -nß
(2.12)
where n = electric charge transfer per ion and f = faraday's number, 96,000 coulombs per gram, the equivalent weight of monovalent charge transfer.
BASIC ELECTROCHEMICAL AND PHYSICAL PRINCIPLES
2.6
21
C h e m i c a l Potential D e f i n i t i o n
In order to appreciate the origin and definition of the term chemical potential as a mathematical concept, other energetic relationships associated with chemical processes are outlined below. Internal energy, E, of a system is usually a measure of its energy state in terms of its thermal energy content and chemical or physical configuration. Or, simply the change, AE, in internal energy in going from one condition to another is AE = E 2 - E 1
(2.13)
Next is the concept of enthalpy, which is the sum of internal energy change and any change in volume or pressure of a system during some energetic transition by either internal means or input or extraction of energy by means external to the system. This is described as AH = AE + Apv
(2.14)
The free energy, F, of the system is another useful parameter employed in calculating chemical potentials of electrochemical cells. It is the sum F = E + pv-TS = H-TS
(2.15)
where S = entropy and T = absolute temperature. The concept of entropy is best described mathematical as ,_ CdT dS = , or T S=\ ^
(2.16)
where C is the appropriate specific heat of the system (substance), and Q is the quantity of heat transfer absorbed or expelled by the system.
22
ELECTROCHEMICAL WATER PROCESSING
Willard Gibbs introduced the concept of chemical potential as a means of identifying chemical energy changes in multi-component systems. The internal energy of a system with n-components is then described as dE - TdS - pdv + Hydnx + jL^d^ +
+ ^dnn
(2.17)
and *
K^aJ
2.7
(2.18) S,V,n
C o n c e n t r a t i o n Potential
If the standard electric potential, Eo, of a cell is defined as that potential when all reactants are at unit concentration, (activities are all unity), then RT E0=—InK
nf
(2.19)
and K is the quotient of the reaction products multiplied together, divided by the reactant concentrations product. This ratio of products is defined by the above as the equilibrium constant, and Eo can be considered the "half cell" potential of an electrode in equilibrium with that electrolyte. If two electrolytes, separated for example by a porous barrier, contain the same chemical species but at different concentrations, a potential is realized between two electrodes, each immersed in opposite solutions. That net potential, A£, is given as RT A£ = — - [(In K - In Q, ) - (in K - In Q2 )] nj
(2.20)
BASIC ELECTROCHEMICAL AND PHYSICAL PRINCIPLES
23
Simplifying we obtain "/
Oi
And, most frequently this can be further related to a difference in concentration of the reactant specie in the two electrolytes, or RT, c, AE = — I n 2 nf cx 2.8
(2.21)
Equivalent Conductance
This is employed for determining electrical conductivity (or resistivity) of working solutions of electrolytes in the processes associated with the ED treatment of water. The term equivalent conductance refers to the electrical conductance of an equivalent weight of electrolyte. It is found by multiplying the specific conductance, L, (mho- cm 4 ) by the solution volume, V, that contains 1 gram equivalent of solute, or A = VL = \000L/c
(2.22)
and c is the solute concentration in the actual situation. Units of specific conductance are usually cm2 equiv 1 ohm-1. These are useful in determining actual conductivity or resistivity for very highly diluted electrolytes. 2.9
Free Energy a n d E q u i l i b r i u m
The free energy change, AF in any process may also be represented as AF = nRT In K
(2.23)
The equilibrium constant, K, for a process described between two reagents and two reactants A + B-+C + D
(2.24)
24
ELECTROCHEMICAL WATER PROCESSING
can be given as KAK = KAB=^-
lAllB ! , or as \C\\D\ (2.25) acaD
The terms \A\, and |ß|, etc. are concentrations of the respective components, or the expression employing activities may be used. 2.10
Dissociation Constants
The dissociation constant, K d , of a solute electrolyte can be given as
«£^c (l-a)c
A \-a
(226)
where a is the fraction dissociated of the solute, and c is the stoichiometric concentration of the electrolyte. These terms are employed to compute equilibrium conditions for electrolyte systems.
2.11 Ionic Conductance and Mobility The movement of ions through a solution under the influence of an electric field is the basis of all of the subject matter in this book. Electrodialysis processes, pH control, electrodepostion of materials, transport of ionic and molecular species across porous and ion-exchange barriers are all results of moving ionic substances in an electrolyte by means of electric charge conduction. The mobility, u, of an ion in a conductive solution is defined as follows.
BASIC ELECTROCHEMICAL AND PHYSICAL PRINCIPLES
25
(2.27)
u = x\t-—\ dx
where x is the distance an ion moves per unit time, t, under an electric field gradient, d E / d x , of volts per unit distance. The specific conductance, L, of an electrolyte is certainly dependent upon mobility, concentration of ions (or charge carriers), or in general, (2.28)
L = k-u-Ni
where k is some constant of proportionality, and N. is the population density of that specific ion in terms of numbers per unit volume of solution. The conductance in terms of mobilities of cations and anions in solution is represented as follows. L = f(caua + ccuc)/1000
(2.29)
The terms c, above, are concentrations of anions and cations respectively. The equivalent conductance, A, also discussed above, can be related to the specific conductance as follows. A = f(ua + uc)
(2.30)
Transference numbers through electrolytes or membranes for the anions and cations are simply n = —-— na + n=l
and (2.31)
if the concentrations do not change significantly with time as the ions are transported out of an electrolyte region.
26
ELECTROCHEMICAL WATER PROCESSING
2.12
O s m o t i c Pressure
When a semi-permeable membrane separates two fluids with different concentrations of the same solute, the solvent transports itself across the membrane from the dilute to the concentrated side until the concentrations of the solute are equalized. The pressure necessary to prevent this migration of solvent applied higher on the concentrated side is known as the osmotic pressure. This is an important phenomenon to be considered under some circumstances in the design and operation of an electrodialysis cell because large differences in water solution concentrations are established during its operation. Conventionally the osmotic pressure is represented by the symbol %. The value of this pressure is given as 7c=mRT
(2.32)
where m = molarity of the solution. For dilute solutions, solution volume is essentially the same as the solvent volume. Hence, the relationship may be written in the form nRT n=^± = CRT
(2.33)
so!«
where C = concentration of the solute in moles per liter. 2.13
D i f f u s i o n (Flick's Law)
Diffusion because of thermal motion or agitation (random collisions) of molecules can be quantified by applying Ficks's law in the form described below. The number of molecules passing through or across an area, A, normal to the path of molecular migration is given as D = -QLaTAC
(2.34)
BASIC ELECTROCHEMICAL AND PHYSICAL PRINCIPLES
27
The terms in the above equation are: D = diffusion coefficient (specific diffusion rate) 1 = diffusion distance through the area, A AC = concentration change over the distance, 1 t = time interval over which the diffusion is measured Another form of the expression is simply ^
= D-A-^
(2.35)
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
3 Systems Description: General Outlines of Basic Approaches 3.1 Electrodialysis Electrodialysis as a water processing mechanism has applications ranging from separation of ionic species in industrial processes to the production of potable water from sea water and demineralizing water sources. The principles of operation are quite simple and straightforward to comprehend, apply and manipulate for the purposes of achieving certain application criteria. In essence, a dialysis cell consists of four basic components: two electrodes and two membranes. Electrodes are, of course, opposite in electrical polarity, and the membranes have ion-selective properties. The positive ion selective, which permits (+) ions to be transported more easily than negative ones, is usually fabricated of carboxylic group, or sulfonic acid compounds, and is referred to as a cation membrane. 29
30
ELECTROCHEMICAL WATER PROCESSING
The negative ion selective, which permits (-) ions to be transported more readily than positive ones, is usually an amine structure or styrene-quaternary ammonium base material, and it is referred to as the anion membrane. A cell is comprised of these three compartments. The middle compartment is the "processed water" compartment. Ionic materials are removed from the middle chamber to the two sides adjacent to the electrodes. The cation membrane is on the side of the (-) electrode, and similarly, the anion membrane is adjacent to the positive electrode. This general configuration is shown in Figure 3.1. A cell can be designed specifically as a desalinator to produce potable water from concentrated saline solutions such as
Cation membrane
Anion membrane
Positive electrode
Negative electrode Na+
cr
Waste water
Waste water
Processed water Figure 3.1 Single cell electrodialysis.
GENERAL OUTLINES OF BASIC APPROACHES
31
seawater. Such a unit may also be used to process hard water from ground sources as a demineralizer (water softener). TDS of water at 40,000 ppm is reduced to 50 ppm or less within one hour of operation at the rate of 10 gallons per hour. An ED system is usually comprised of a series of electrodialysis cells that separates dissolved ionic materials from processed water compartments into waste water sections by means of selective transfer through ion exchange membranes. The ions are transported across these membranes by passage of electric current from a dc power supply. The process of ion transfer is shown in a single cell of Figure 3.1. Sodium and chloride ions move out of the middle compartment into the two waste water chambers where they are expelled as effluents. Over a period of time, the center (processed water) chamber is relieved of most of the ionic materials in solution and eventually becomes drinkable water. Module waste water is returned to the sea. Water is desalinated in a "batch process" manner. The time required for the desalination is dependent upon the volume of the processed water reservoir. The process takes place without application of internal high pressures or high temperatures as in Reverse Osmosis and Distillation systems, respectively. Life of components is long and maintenance is low. Electric pumps circulate the water through water reservoirs (tanks). By means of a controlled, variable voltage power supply, dissolved substances in the water are reduced by a factor of 1000 to 1 per hour of operation. 3.1.1
Performance Characteristics
Some typical performance data and time dependence of desalination are shown in Figure 3.2 presented here on the basis of a 10 gallon reservoir. The system is a recirculation configuration in which the processed water is
32
ELECTROCHEMICAL WATER PROCESSING
Controlled, variable stack voltage 10 cell stack, 120 volts DC max
Figure 3.2 Recirculating water system small boat desalinator.
a predetermined volume and is circulated many times through the processor in the desalting operation. A typical application for this size system is for small boat water processing. Power input to the unit is variable and dependent upon the TDS concentration of the processed water volume at that time during the cycle. Operation involves filling the 10 gallon reservoir with sea water at the beginning of a cycle. The graph shows the manner in which the TDS of a 10 gallon reservoir of processed water diminishes with time. Initially, the input power level is highest because that is when the electrical conductivity of the processed water has the maximum values. As the TDS is lowered, the electrical current drawn from the Power Supply also diminishes and eventually approaches zero power consumption. This occurs when the TDS arrives at the level of high quality potable water. The power level is about 2 KW initially and rapidly sinks to only a few watts within 30 to 40 minutes under normal
GENERAL OUTLINES OF BASIC APPROACHES
33
circumstances. The total energy consumed during the entire time for desalinating 10 gallons of sea water is less than 1 KWH. Depending upon the source of electric energy, the operating cost for desalinating can be less than $0.01 per gallon. 3.1.2
General Purpose Processor
To provide the reader with some notion of the size and configuration of ED systems and their performance capabilities, the following example is offered. The unit in Figure 3.3 is a general purpose system capable of processing 10 gallons of water from 1,000 ppm TDS to 50 ppm within one hour. Electric pumps circulate the water through water reservoirs (tanks). Dissolved substances in the water are reduced by a factor of 10 to 1 per hour of operation. Depending upon the concentration of minerals in the water initially and the power supply capacity, the rate of purification can be greater even than 10 to 1.
Figure 3.3 Operational schematic diagram.
34
ELECTROCHEMICAL WATER PROCESSING
The ED system consists of four major components. They are: Processor Module DC voltage Power Supply Processed Water and Waste water Reservoirs Two Circulation Pumps Assembly of a working system on a platform can be accomplished within an hour if no special installation requirements are encountered. In Figure 3.3, the principle components of the ED system are shown connected in an operational manner. In this arrangement, water is introduced from a source into both reservoirs. After the tanks are filled, the pumps are switched on, and water is circulated through filters into the module. Table 3.1 gives some typical values for the weight and volume contributions of the different system components shown in Figure 3.3. Because the water flow is over the surfaces of the membranes, and not through them as in a reverse osmosis device, no filtering of particulate matter is involved in the ED systems as part of their operation. Hence, separate filters must be provided to perform that task, if needed. Filters-A
Table 3.1 ED component weight & size. Component
Weight
Size
Processor Module
22 lbs
20"h x 6"w x 4"d
Power Supply
12 lbs
5"h x 12"w x 6" d
Reservoir Tanks(s)
10 lbs
1.5 cubic feet
Circulation Pumps
8 lbs
Power Input
10 to 500 watts
10 to 50 watts
GENERAL OUTLINES OF BASIC APPROACHES
35
are mechanically porous solids gatherers to prevent accumulation of materials in the module and reservoirs. Adsorption type filters can be provided if necessary to remove unwanted odor- and taste-producing organic substances from the body of processed water. Water processed in this manner results in the equivalent of de-mineralized (desalted) water approaching the purity of distilled water. The graph below, Figure 3.4, shows the manner in which both the TDS and power input varies with time at constant 50 volts operation from the power supply. At $0.10 per KWH as the cost of electrical energy, the cost per gallon of processed water is less than half a cent per gallon. The system is self-regulating, as seen here, because the electrical resistance of the processed water rises toward the end of the cycle, shutting off any electrical current from the power supply.
TRL electric demineralizer performance standard configuration
1
I 30 Volts constant stack voltage operation 5 cell stack, 200 sq in electrodes
Figure 3.4 Performance data. Module has five series cells and operates at 50 volts.
36
ELECTROCHEMICAL WATER PROCESSING
Some of the pertinent system data are: Cell stack Stack voltage Maximum Power supply rating TDS readout Hydraulic connections 3.1.3
5 cells in series electrically and in parallel hydraulically 30 volts 500 watts (for 1000 ppm input water) meter & indicator light polyethylene or Tygon for maximum versatility
Additional Details for Appropriate Application - Desalinator for Small Boats
An eminently applicable area for ED is for desalination in the small and medium boat sizes. Technology Research Laboratories, Inc. has explored these possibilities and has designed and prototyped some systems specifically for this application. Figure 3.5 is a photograph of an early desalinator prototype. This unit will produce up to 10 gallons per hour of potable water in the range of 50 ppm of salt from seawater at 40,000 ppm. ED water desalination designed specifically for small boats offers a number of significant advantages. These are: • • • • • • • •
Self Contained No High Pressures (RO) Noiseless, No Vibration No Boiling Water Low Maintenance No Installation Economical Operation Portable
It operates at standard temperature and pressure conditions. There are no high pressure pumps, clogged membranes, or noise and vibrations with which to contend
GENERAL OUTLINES OF BASIC APPROACHES
37
Figure 3.5 TRL Processor.
as in an RO unit. The main components of a desalinator are shown schematically in Figure 3.6, and are listed as: Processor Module Power Supply Processed Water Reservoir Circulation Pumps Initially water is drawn from the sea and pumped into the reservoir as shown until filled to the level desired, and then both pumps circulate water. Processed water is circulated through the module numerous times during any one period of desalination. Waste water is slowly expelled back into the sea as the processing takes place. Filters are provided at the inputs to the module to extract any solids from the original water. If desired, the filter in the processed water tank circuit can be an adsorption unit for the removal of undesirable microorganisms or other organic substances.
38
ELECTROCHEMICAL WATER PROCESSING To the dc voltage power supply
^
Filters
Sea water Pumps
Figure 3.6 Electrolytic desalination system schematic diagram.
Table 3.2 Weight and size of system components. Component
Weight
Size
Power Input
Processor Module
50 lbs
28"hxl4"wxl0"d
10 to 2,000 watts
Power Supply
30 lbs
8"h x 12"w x 10"d
10 to 2,000 watts
Reservoir Tank
12 lbs
1.5 cubic feet
Circulation Pumps
10 lbs each
25 to 50 watts
A convenient size tank for most applications is probably about ten gallons, requiring about one hour of processing to produce less than 50 ppm potable water from the initial 35,000+ ppm source water. The table 3.2 lists the salient features of the system in terms of size and weight.
GENERAL OUTLINES OF BASIC APPROACHES
39
There are many other examples of ED hardware application, some of which will be discussed in some detail later in this text.
3.2 pH Control: Analytic Development 3.2.1
Introduction
The control and maintenance of pH of aqueous solutions is another important consideration in water treatment of virtually all bodies of water for industrial, commercial or personal use. The pH of water in industrial processes will determine reaction types and rates. In cooling systems, low pH will frequently result in unwanted corrosion of metal parts and heat exchange surfaces. Skin irritation of promotion of bacterial growth may be encountered depending upon the level of pH in swimming pool water. High pH tends to promote growth of algae and other microorganisms detrimental to health. High pH will also result in scale accumulation and microorganism deposits on working parts of chemical treatment systems or heat transfer surfaces. A method of controlling pH levels in aqueous systems is described herein and depends upon electrochemical reactions. This approach substitutes the introduction of electrical energy to the water system to generate and inject the H+ and OH' needed instead of the chemical addition of an acid or base. No external supply of chemicals are required or added to the controlled body of water. 3.2.2
Some Technical Background
Returning to our definition of pH (see Chapter 2, Section 2.1), we have pH = log
1 a +,
V H
(3.1) J
40
ELECTROCHEMICAL WATER PROCESSING
The activity, a, of ions as it is employed in electrochemical disciplines is the ratio or percentage of the active (effective) concentration for reaction participants versus the total ionic specie concentration in solution. The free energy of reaction, F, is represented in terms of activity as F = F0 + RT In (aA)
(3.2)
or substance, A, undergoing a change from its standard state to another. The Debye-Huckel theory provides for a relationship between activity coefficient, y, and ionic strength, u. This is expressed as log ft =0.51zi VM for a solution, y+ = 0.51z + z_ Vw = ^y+Y-,
(3.3)
where u = sum of the products of concentration of each ionic specie in solution times the square of their electric charge. Or,
u = y^cxz\
+ c2zf +
)
(3.4)
Now, since it has been established that for all cases a
=1(T 14 ,
-a +
H
and water dissociates as
OH"
H20-+H+
(3.5)
'
+ OH-,
(3.6)
the equilibrium constant, K, is represented as K=
\H+ OH~
(3.7)
HiO
and because the concentration of water is nearly constant: K
w = \H+
OR-
i4 l(T-14
(3.8)
GENERAL OUTLINES OF BASIC APPROACHES
41
Reference electrodes are employed experimentally to obtain values of pH from measurable electric potentials. The standard hydrogen electrode, with high purity H2 gas at 1.0 atmospheres on a platinum probe and surrounded by H+ ions with unit activity, is assigned a potential of 0.00 volts. This reaction is simply
Y2H2^H+ + e-.
(3.9)
A commonly employed pH measurement apparatus is the glass electrode. A solution of constant pH next to an Ag-AgCl electrode with a glass membrane separates the solution. The observed potential is measured between the glass electrode and the reference calomel, (Hg2Cl2) electrode. The voltage measured between these two electrodes will vary in accordance with pH or activity of H+ ions in the intervening solution. About 0.59 volts per pH unit is obtained at 25° C. It must be remembered that the pH is a measure only of the activity concentration and not the total available hydrogen ion concentration in solution. The latter value can be obtained by direct titration with a base or acid as the case may be with low or high solution pH, respectively. In some instances it is possible to work backwards from the pH measurements (if sufficient a priori information is available), to the values of aH+ and fl0H- and y+ and y_. Concentration, m, of the electrolyte could be estimated then from the equation, log y- -0.51-v/m - bm,
(3.10)
where b = some constant. Similarly, for dilute solutions, the concentrations, cT and c2, for a "two ion kind" electrolyte such as HC1, H 2 S0 4 , etc. may be evaluated from the above formula where
42
ELECTROCHEMICAL WATER PROCESSING
log y= log J ^ _ = log
{m^âl)
z 1 +c 2 z 2 + ...) 3.2.3
(3.11)
Sample Processes for p H Control
Alkalinity and acidity of a test body of water can be controlled via a single electrochemical cell with a separating membrane between electrodes as shown in Figure 3.7. In the illustrations that follow the membrane is a microporous structure (semi-permeable) that has no ionic transport preference. The H+ ions and the OH' ions are supplied by the water. However, other anions and cations must be supplied from some solute, which will enable a balance of charge on either side of the membrane. One excellent choice of solutes for this purpose is sodium sulfate, Na2SOA. Na2SOA is very soluble, and the sulfate radical will not be decomposed at the positive electrode. No chemical other than oxygen will be evolved at the (+) electrode. Effluent at high pH OH" ions
Low pH output H+ ions
*G-
Main water supply input Figure 3.7 pH control cell.
Oxygen
Hydrogen
S0 4 =
Na+
OH-
H+
-►
■€>'
GENERAL OUTLINES OF BASIC APPROACHES
43
Water is electrolyzed at the electrode surfaces, and the principle reaction at the negative and positive electrodes, showing the unaltered salt ionic components as charge carriers: Negative side - basic: Na+ + H20 + e~ ^Na++OH~+y2H2
(pHup)
(3.12)
Positive side - acid: SOl + H20^2H++SOl+y202
+ 2e-
(pHdown) (3.13)
The decomposition of water with the accompanying evolution of hydrogen and oxygen is essential to the generation of hydrogen and hydroxide ions in the pH down and up chambers, respectively. OH~ ions are generated on the negative side of the membrane with the attendant rise in pH. H+ ions are produced in the positive side, and pH is driven downward. Depending upon the function desired, the main test body of water is directed through the appropriate side of the cell, or more specifically, the electrical polarity of the electrodes is established on the basis of pH drive direction needed. For example, if we wish to drive the pH downward in the main body of water, the hydraulic system configuration shown in Figure 3.8 would be employed. Sulfuric acid, H2S04, would be produced in the positive (+) cell side along with the evolution of oxygen being expelled into the water stream and vents. The generated H2S04 enters the main tank and the pH is consequently lowered. A corresponding amount of base is generated in the negative (-) side, in this case as NaOH, and it is slowly discarded from the main water body in order to keep the net pH change in the downward direction. Because the membranes are not ion selective in the configurations discussed here, there is significant loss of the generated H+ and
44
ELECTROCHEMICAL WATER PROCESSING Filter
ItTW Switch H 2 S0 4 H 2 0
pH Cell
Jr-n-
'Til
H+ ion injection main body of water
-O
V
V
Water pump
€f
Power H supply
Figure 3.8 Single cell control - pH down.
OH~ ions by diffusion and transport via electric field across the membrane. These processes are outlined and analyzed in some detail in Appendix D. Loss of sodium (as basic NaOH), in this case, is replenished by make-up water impurities added to the system. Scale and heavy metal deposits on electrodes are removed by periodic electric polarity reversal at the electrodes, and are then subsequently eliminated in the drain. A simple switching and valving via timer circuit controls the polarity reversal and periodic discharge. A second example is shown in Figure 3.9 where the pH is driven upward in the main water system. Main flow is directed through the negative side of the cell, which is actually the same physical side of the cell is utilized, but the operating voltage polarity is opposite that of the first case above in Figure 3.8. Sodium hydroxide, NaOH, is produced in the negative compartment, and
GENERAL OUTLINES OF BASIC APPROACHES
45
Filter
Î
1
Hydraulic switch NaOH + H 2 0 pH cell
*
H 2 S0 4 + H 2 0
A
OH" ion injection
-O
Main body of water
V
V
Water pump
& Power supply
Figure 3.9 Single cell control - pH up.
H2 gas is evolved. NaOH entering the stream raises the pH of the water system. As in the above first case, to maintain a net upward change in pH, the acidic solution in the positive side of the cell is expelled as unwanted low pH effluent. Some provision must also be made for cleaning scale off the negative electrodes and out of the (-) cell compartments. The solid effluents must then also be filtered out of the main water stream. The filter shown in Figures 3.8 and 3.9 is connected through a manual application of an electrically actuated hydraulic switch, permitting periodic filter back-flushing and rinsing. 3.2.4
Application Possibilities
Of the various applications possible, the following are listed as the more obvious candidates. Some configurations will be offered that are appropriate for pH control.
46
ELECTROCHEMICAL WATER PROCESSING
3.2.4.1
Swimming Pool Water
Pool water is usually treated with a strong oxidizer such as CaClö3 as disinfectant and for prevention of growth of algae, etc. Continual addition of such agents results in everincreasing pH, and necessitates periodic addition of acid to lower pH to acceptable levels. Loss of Cl2 and Br2 from the pool water, with the corresponding increase of Ca(OH)2 and NaOH will push pH upwards and encourage further water haziness and promote scale accumulation. However, in some instances it may be necessary to raise the pH due to the natural water source conditions and acid rainfall. 3.2.4.2
Cooling Towers
Mineral deposits that accumulate in commercial watercooling towers as a result of addition of hard water to make up for evaporation losses in the cooling process will tend to increase pH of the system and further promote the deposition of scale and solid matter on the heat exchanger surfaces. 3.2.4.3 Regeneration of Ion Exchange Resins Regeneration of resin beds for de-ionizers, ion exchange apparatus and water softener systems is another important area of application. Figure 3.10 shows a schematic of a proposed system for a single ion (cation) resin bed regeneration process. Instead of the normal or conventional brine reservoir employed to recharge the Na+ ions for Ca+, Mg+2, Fe+3, Cu+2, etc.ions during the recharging cycle, a source of hydrogen ions may be provided. These H+ ions are supplied electrically from a pH cell as described in Figures 3.7 and 3.8. Initial H2SOA may be introduced into the water stream to initiate the process and supply charge carriers.
GENERAL OUTLINES OF BASIC APPROACHES Softened output for use
47
R Regenerative mode position N Normal operation mode position Mechanically coupled valves
Input from water supply source
Trickle drain of un-needed NaOH
Figure 3.10 Cation regeneration without effluent recycling hydraulic circuit ■ water softener.
As the regeneration cycle proceeds, some portion of the effluent from the resin bed that is rich in Na+, Ca+1, etc. ions is permitted to recycle through the pH cell to lower the electrical resistance and then supply positive ions for migration to the negative electrode for OH~ ion production charge balance. Make-up water added during recycling will also contain a significant amount of minerals as charge carriers, thus assisting the electrical conduction. Let us review the principle mechanisms of the process as follows: When the resin bed is "depleted", the cation sites are largely occupied by the unwanted heavy metal ions that were extracted from solution during the working or softening portion of the cycle. Step 1 - Regeneration mode is established by turning off the two-way valves to the main water so that the main supply is shut off and no longer flows through the resin
48
ELECTROCHEMICAL WATER PROCESSING
bed. Instead, water is caused to flow through the pH cell and resin bed as shown in Figure 3.10. Step 2 - Electric power, dc current, is applied to the pH cell with the electric polarity as shown. Step 3 - H+ ions (H2S04, etc., acids) are generated in the positive compartment and fed through the resin bed resulting in substitution of H+ ions for the Ca+, Mg+2, Fe+3, Cu+2, etc. ions, which at this time occupy the loaded sites. Step 4 - These re-dissolved minerals are flushed as drainage from the system. However, some portion may be re-circulated through the pH cell to provide charge carriers for generation of additional H+ ions. Most of the heavy metals passing through the pH cell will migrate to the negative side and be discarded as shown. Step 5 - As the process continues most of the cation sites will be occupied by H+ ions and the bed will be regenerated and made ready for the normal work mode wherein A and B are switched to open the main water lines and close off the lines to and from the pH cell. Step 6 - If the negative electrode has much scale accumulation the power supply, polarity can be reversed for a period of time between regeneration cycles to de-plate the scale and discharge the solids through the pH drain. Actually, the de-plating operation may take place during the regular regeneration cycle by having the electric current reverse for a period of time long enough to perform the needed clean-up action, but for a period that is still so much shorter than the standard regeneration length of time that the net effect on the total regeneration process is negligible. Another configuration is shown in Figure 3.11 in which both outputs from the pH cell flow through the resin beds. The anion resin bed is supplied with base, OH' ions, to regenerate the sites from Cr,CO^,SOÏ,etc. which were removed during the normal water treatment mode.
GENERAL OUTLINES OF BASIC APPROACHES Processed and de-ionized water for use
N
N
Cation resin bed Drain during regeneration
49
Anion resin bed NaOH
HoSO,
*®«-|
$>Note:
Input from water supply source
-e
u
pH cell
Figure 3.11 De-Ionizer system regeneration without effluent recycling hydraulic circuit.
Operation of the water system shown in Figure 3.11 is virtually identical to that of Figure 3.10, except for the existence of two regeneration loops, each through their respective resin beds. An electrode or "scale clean-up" mode may also be utilized as before, by voltage polarity reversal for brief periods of time. Application to a de-ionization system takes better advantage of the attributes of the pH control cell because both streams are directly utilized instead of using only the acidic side as in the water softener set-up. Also, residential, as well as commercial use possibilities for de-ionizers, are opened up due to the simplicity and low cost of on-site regeneration via electrolysis—without the necessity of obtaining and handling bulk acids and bases. Those areas where low sodium water is needed can be served very effectively by the de-ionizer systems in a low cost manner.
50
ELECTROCHEMICAL WATER PROCESSING
3.2.5
Current and Electrical Energy Requirements
To compute typical electrical energy requirements for the creation of a 0.001 N acid solution in 1,000 gallons of water, the following estimates can be made. According to the Faraday equivalent, about 96,500 coulombs, or 26 amp-hours of electrical charge will produce lgram equivalent weight of product. In a 1,000 gallon volume of water, a 0.001N solution of acid has a total of about 4 equivalent weights of acid. That would correspond to about a 100 amp-hour of electric charge, or about 500 to 1,000 watt-hours of energy if the electrolysis took place at a potential of 5 to 10 volts per cell. If the regeneration cycle takes place within a period of one hour, then a power source of about 1 kw is needed to perform the task; assuming 100% coulombic efficiencies. Let us now also examine what this total energy input to a water softener resin system would do in terms of its effectiveness at replacing heavy metal cations. If 4 equivalent weights of CaC0 3 or FeCl3, etc. were replaced at an average equivalent weight of 100 grams per molecule, then 100 ppm in 1,000 gallons of water is 0.8 lbs of mineral compounds, or about 4,000 grams. This amount is about a 4 gram equivalent weight of the materials. To displace the heavy metal ions in the resin bed by means of an acid wash would require at least a 4 gram equivalent weight of the acid or H+ ions. Generation of such an amount of acid as calculated earlier requires about 1 kwH of energy if the coulombic efficiencies are between 50% and 100%. Most residential water softeners will handle much less than the 1,000 gallons between regenerations. Hence, less than 1 kwH of energy is needed for most home use situations for the regeneration cycle.
GENERAL OUTLINES OF BASIC APPROACHES
3.2.6
51
Shielded (Limited Ion Access) Positive Electrode Operation
In many instances the water stream may contain a fairly high concentration of anions, such as chlorides and bromides that will produce chemical species other than oxygen at the (+) electrode when electrolyzed. These cited anions, for example, will result in free chlorine or bromine, respectively, at the inert (+) electrode surface under most electrolysis conditions. Operation of the pH control cell may necessitate minimizing these reactions that are dissipating to raising pH levels by decomposition of water and subsequent evolution of oxygen, e.g. 2Cr -> C/2 + 2e~ and
2Br~ -> Br2 + 2e~
(3.14)
because they will reduce coulombic efficiency for generation of H+ ions. Oxygen evolution is necessary for the production of H+ ions in the positive compartment. A method developed at TRL that has proven quite effective is the intentional "starvation of the positive electrode". To achieve this end, a means of inhibiting the flow or diffusion is always present from the dissociation of water, hence the availability of Cl~ and Br~ ions in favor of the OH'. These methods are listed below. 3.2.6.2
Double Barrier
This is an extra or second separator between the cell that compartmentalizes membrane and the positive electrode. A relatively stagnant region of electrolyte is established in which the Cl~ and Br~ ions are depleted and remain in low concentration. Hence, their availability for oxidation to their elemental forms at the positive electrode would be considerably more limited. Ion membrane or micro-porous membranes may also be employed as shown in Figure 3.12.
52
ELECTROCHEMICAL WATER PROCESSING
H+ ¡on, acidic output
OH" ion, alkaline output Membranes
+
-O
G-
Input water
Slow flow .
Normal flow rates
Figure 3.12 Starved posode pH control cell double barrier configuration.
3.2.6.2
Close Spacing
The space between the positive electrode and the cell membrane can be made very small. Low fluid circulation in this intervening space of low availability of specific ions can be achieved. See Figure 3.13. 3.2.6.3 Porous Barrier Design A diffusion-limiting barrier in intimate contact with the positive electrode can also be used to create a stagnant electrolyte region to achieve specie starvation conditions. Thick, almost sponge-like nonconductive polypropylene, unwoven fiber structure placed against the electrode will impede the availability of dissolved anions in preference to OH' ions provided by the water. See Figure 3.14. 3.2.6.4
Etched Electrode Surfaces
Use of carbon-polymer composites as electrode structures provides the opportunity to develop limited electrolyte availability conductive surfaces. The surfaces of the carbon composites are cavities whose walls are largely
GENERAL OUTLINES OF BASIC APPROACHES H+ ions acidic output
53
OH" ions alkaline output
Membrane
+
Electrodes
o
-0' Slow flow
Input water
Normal flow
Figure 3.13 Starved posode pH control cell double barrier configuration.
H+ ion, acidic output
OH ion, alkaline output
Electrodes
'©-
-©'
Porous layer Membranes
Input water
Figure 3.14 Starved posode pH control cell double barrier configuration.
non-conductive polymer materials with conductive carbon located deep within the cavities. This configuration results in recessed regions of electrolytic conduction into which migration of Or and Br~ ions is severely restricted. Their slow diffusion from the main electrolyte volume renders them less available as compared to the ever-present OH~ ions. This is illustrated in Figure 3.15.
54
ELECTROCHEMICAL WATER PROCESSING
Figure 3.15 Starved posode pH control cell etched posode configuration.
The rate of generation of Or, for example, at the positive electrode surface is not only dependent upon current density, but also upon Or availability at the electric current density demand rate. Thus, if the current density is high and the obstruction to Or migration to that electrode is also great, then the electrode will be starved for those ions, and more 0 2 will be generated via the electrolytic decomposition of water as the preferred reaction. Current efficiencies are greatly dependent upon population density of the specific ion in the immediate vicinity of the electrode. Experience with carbon-plastic electrodes has shown that the efficiency of C/2 and Br2 production on these electrodes diminished to very low values as the surface erosion (spallation of carbon particles) proceeded with the generation of oxygen during cell operation. The drawing of Figure 3.15 illustrates this effect by showing caverns of non-conductive plastic walls with conductive carbon bases at the bottom of the caverns and as the working surface of the electrode. Availability of 0~ ions from the moderate concentration in the surrounding solution is severely limited within these caverns.
GENERAL OUTLINES OF BASIC APPROACHES
55
hr ions OH ions
Posilyte line
+
&
K
Negalyte line
-€>"
-
Porous barriers
Input from the water reservoir Figure 3.16 Series bipolar array - separate manifolding.
An interesting illustration of acid/alkali generation is shown in Figure 3.16. This is an array of cells specifically designed to produce pH effluents of wide separation. 3.3 3.3.1
Biociding Technology Electrolytic Production of Free Halogens
Production of strong oxidants such as free chlorine and bromine by means of electrolytic processes is well known and has been employed for over two hundred years. In fact, an early method of producing sodium hypochlorite, NaClO, a strong bleaching agent, was by electrolysis of NaCl. The use of elemental chlorine and bromine as a biocide is widespread. At present the most popular method for chlorination of pools is the use of Ca(ClÖ)2 (calcium hypochlorite, HTH trade name) as a source of available chlorine for sanitization. Cost of the product is over $1.00 per pound.
56
ELECTROCHEMICAL WATER PROCESSING
Because the available chlorine is about 50% by weight, the cost of the biocide is over $2.00 per pound. This is a reliable standard of cost comparison for sanitizing small bodies of water. Larger water volumes such as cooling water for utilities, municipal supplies and commercial pool employ elemental chlorine in the form of compressed gas. In most instances, these reagents are produced in a manufacturing plant and transported to the use on site as elemental substances with all the attendant hazards and associated costs. However, it is possible to produce these substances at the end point of use by electrolytic means. The electrolysis process that takes place in a brominator electrode assembly is described as follows. Direct current flow through the electrodes and electrolyte with NaBr salt in solution generates these net chemical reactions at the electrode surfaces (see Figure 3.17).
Figure 3.17
o,
H,
Br-
Na*
OH-
H*
GENERAL OUTLINES OF BASIC APPROACHES
57
At the negative electrode: 2H++2e~ ^ H
2
t
(3.15)
At the positive electrode: 2Br~-^Br2 + 2e~
(3.16)
The total chemical reaction in the water is 2NaBr + 2H20 -> 2NaOH + Br2 + H21
(3.17)
Hence, free bromine is produced at the positive electrode and becomes solubilized in the water stream. Meanwhile, NaOH is generated at the negative electrode and slightly raises the pH level of the body of water. If the electrode separation is wide and the water flow rate between the electrode plates is sufficiently rapid, there are very few immediate secondary reactions. However, prolonged interaction of sodium hydroxide and bromine will produce the hypobromite, NaBrO, or 2NaOH + Br2 -> NaBrO + H20 + NaBr
(3.18)
resulting in an immediate 50% loss of Br2 back to the original NaBr compound. The hypobromite is as effective as free bromine for germicidal purposes. About 0.5 to 2.0 ppm of Br2 is adequate to ensure useable water condition. For a quantitative assessment of design procedures in constructing electrolytic halogen generators see Chapter 5, Section 5.1. This approach offers opportunities for sanitizing water at significantly lower costs. 3.3.2
Chlorination Process Description
Water disinfection through chlorination is practiced in industrial, municipal and private water supplies to destroy harmful water-borne organisms. In private and municipal waters, disinfection processes have been employed to mainly eliminate pathogenic organisms, while industrial
58
ELECTROCHEMICAL WATER PROCESSING
processes require the destruction of fouling, and sometimes corrosive, micro-and macro-organisms inhabiting their water systems. Though water disinfection can be accomplished through physical or chemical means, chlorination has achieved wide acceptance because of its low cost and adaptability in water treatment operations. This section will review chlorination and an alternative chemical treatment method of disinfection—bromination. It will also compare the capital and operating costs in a specific industrial application of open, re-circulating water systems. Bromine disinfection has been successfully employed in the private sector for pools and spas since the 1940s1, utilizing the organic compound, l-bromo-3-chloro-5dimethyhydantoin, known commercially as Aquabrom or Dihalo. More recently, industrial cooling water treatment with this biocide has shown the advantages of bromination over chlorination, though the operating costs were reported to be significantly higher 2 . This is attributed to the cost differential between chlorine gas and Aquabrom. However, when chlorine is not an acceptable treatment method because of safety and high maintenance costs, l-bromo-3chloro-5-dimethylhydroin has proved to be a cost effective treatment method as compared to other available or current technologies. Other combined forms of bromine and the chemical oxidizing agents necessary to produce available bromine residuals in water have been evaluated as disinfection treatment alternatives. These include chlorine—or persulfate-activated bromine salts. Each of these activation methods has limitations that hinder its use on a wide scale. However, more recently, TRL, Inc. has developed and fieldtested a bromination system based upon electro-chemical
See1,2 Appendix F references on page 283.
GENERAL OUTLINES OF BASIC APPROACHES
59
decomposition of bromine salts to produce free bromine residuals. For over two decades, the TRL involvement in bromine technology and electrochemical research in the form of zinc/bromine and redox batteries has initiated interest in similar processes for water treatment. As an outgrowth of this experience in halogen chemistry, a series of successful electrochemical disinfection devices have been constructed for swimming pools and spas. The following is a description of the economic and safety considerations and attributes that an electrochemical bromination system offers the water treatment field over conventional chlorination practices. Many industrial operations require cooling water to reduce process heat, such as in petroleum refining, power and steam generation chemical production, metals recovery and refining, air conditioning and refrigeration. Whenever water is used in a cooling system, microorganisms, plants and animals will reproduce and inhibit the rate of heat transfer through fouling, and decrease process flow rates as well as corrode process equipment. The goal of chlorination is to minimize microbial and macro-organism growth to avoid expensive system shutdowns for cleaning, repair and maintenance. Liquid chlorine is stored in this facility in a single chlorine tank car, and is unloaded through a flexible metal connection to the process piping under its own pressure. If necessary, air padding is provided to deliver the chlorine from the storage tank to the chlorination equipment. When a tank has been emptied, air purging for safe inspection and repair is also required. The system piping has both a liquid and gas header— one for gas withdrawal and one for liquid. Both headers feed the evaporator and are provided with expansion tanks in the event of liquid chlorine vaporization or hydrostatic pressure build-up in the supply line.
60
ELECTROCHEMICAL WATER PROCESSING
Liquid chlorine enters the evaporator, which is essentially a water-jacketed pressure vessel equipped with electric immersion heaters. The liquid chlorine absorbs heat through the vessel walls from the hot water until it boils at its vaporization temperature. The chlorine gas absorbs superheat as it is withdrawn from the evaporator through contact with the hot upper walls of the evaporator vessel. This prevents liquefaction in the process lines. The gas passes from the evaporator through a gas filter to remove impurities. The chlorine pressure-reducing valve is downstream of the filter, which further reduces the liquefaction temperature by reducing the chlorine gas pressure. This valve also serves as a safety device to automatically shut off the chlorine supply to the evaporator in the event that the water bath temperature falls below the set point. Downstream from the relief valve, the gas is drawn through the chlorinator, which is the flow metering and control equipment for the supply system. The components of this piece of equipment include an inlet gas pressurereducing valve, a rotameter, a metering orifice, a vacuum differential-regulating valve, a pressure-vacuum relief valve and an injector. The injector creates a vacuum, which draws the gas through the equipment and ultimately mixes the chlorine with water to supply the required dosage to the cooling water circuit. The inlet gas-regulating valve controls the density and velocity of the gas entering the chlorinator. The variable orifice meter controls the chlorine feed rate and is controlled automatically through chlorine residual feedback control. The rotameter is a local feed rate indicator. Because of the possible chlorine supply failure, vacuum relief valves are provided within the chlorinator to allow air to enter the system and prevent "suck-back" of water from the injector into the chlorine supply lines and to prevent a high vacuum rise within the chlorinator. As previously described, the injector mixes the chlorine gas with a water stream to provide the dosage required by the treatment system. From the injector, the chlorine
GENERAL OUTLINES OF BASIC APPROACHES
61
solution is applied at the designated points near the heat exchanger equipment and in the tower basin. 3.3.3
Bromination Process Description
It has been reported that bromine disinfection efficiency is lower than that achieved with chlorination. When tested under standard methods of disinfection evaluation, bromine, at 1.0 ppm was as effective as 0.6 ppm of available chlorine to control the bacteria (see E. Coli). This can be attributed to the higher oxidation potential of chlorine. However, one must be careful in its correlating ppm between chlorine and bromine by weight because the molecular weight of bromine is twice that of chlorine. Also, bromamines, formed when bromine reacts with nitrogenous compounds, are superior disinfectants in comparison with the corresponding chloramines. The dissociation constant, pK, for hypobromous acid is approximately one pH unit higher than the pK for hypochlorous acid. This is significant in systems operating over a wider pH range of 7 to 8.5. Recent field trials with Aquabrom (a bromine biocide) in open, re-circulating water-cooling systems have demonstrated bacteriological, algae and slime control, while minimizing the maintenance and safety hazards encountered with contemporary chlorination practices. While the only disadvantage to current bromination practices is chemical costs, TRL has developed an industrial bromination process with operating costs equivalent to or less than a chlorination process. The bromine vehicle to the process is the salt, sodium bromide (NaBr), which is stored in a feed bin. Capacities and sizes have been equated with a chlorination system to compare costs. The NaBr salt is intermittently metered to the solution tank and dissolved to a concentration of about 31b per gallon of water. This concentrated solution is metered to the cooling water circuit to maintain the salt at
62
ELECTROCHEMICAL WATER PROCESSING
about 1,000 ppm. Due to windage losses, it is estimated that a make-up of 50 lbs per hour of NaBr will be required, or approximately 15 gallons per hour of salt solution. Control of salt feed rate is maintained by the volumetric, vibrating feeder and bin load cell. Cooling water is re-circulated to the heat exchanger equipment or other points with the cooling tower recirculation pump(s). Though it is common to employ several pumps, it has been assumed that one pump will handle the entire flow of 100,000 gallons per minute. On the downstream side of the pump, the flow will pass through the bromination tank, equipped with 12 modules of ten cells each, with a five square foot cell area. Though 600 square feet of cell area is provided, only 500 square feet are required to maintain 2 ppm bromine residual. The cells are arranged so that 2 spare modules are available should a failure occur. Power to the cells is provided by a 150 amp, 240 volt supply. Current density to the cells is 100 ma per sq. in. From the bromination tank, the cooling water is distributed to its specific application points. Because the bromination tank is a pressure vessel, modules cannot be removed or repaired without bypassing the tank. For this reason the spare modules have been added.
3.4 Ion Exchange Resin Regeneration System 3.4.1 General Of the various processes employed in water treatment, e.g. reverse osmosis, dialysis, ion-exchange, direct chemical treatment, filtration, etc., the ion-exchange process offers the highest purity water in terms of de-ionized content, especially the mixed bed version. Cation and anion exchange resins such as those produced by Rhom & Haas, Diamond Shamrock, and Dow are employed to remove the respective ions from solution. In a
GENERAL OUTLINES OF BASIC APPROACHES
63
de-ionization apparatus there are either two separate beds of ion-exchange resins (one cation and one anion) or a single mixed resin bed. Our attention is directed here to the two separate resin bed system. Input water to be treated is first passed through the cation stack wherein most unwanted cations such as Ca++, Mn++, Fe+3, Mg++, etc. are removed and replaced by H + ions. Subsequent passage of the water through the second stack (anion resin) removes the negative ions such as C0 3 ~ 2 , Cl~, S 0 4 2 , etc., which are replaced by OH" ions. Thus, dissolved solids are removed from solution and replaced by water as the resultant product. After some usage, the resin sites become increasingly occupied by the removed ions in place of the H + and OH" in the cation and anion beds, respectively. As this replacement proceeds, the resin becomes less effective in removing the above ionic species dissolved in the input water and it must be "regenerated". Regeneration entails exposing the cation resin to a concentration of H+ ions (acid bath) and the anion resin to a concentration of OH" ions (alkali bath). Water processed in this manner is used for various industrial and science laboratory purposes as well as for potable water in some instances. Some of the reasons for removal of these dissolved solids include: • Improve taste characteristics • Reduce hardness and accumulation of scale • Remove coloration and staining properties of the water • Remove salt where low sodium levels are required in potable water 3.4.2.1
Present Regeneration Methods
Regeneration of resin stacks is presently accomplished by treating with appropriate chemical solutions (see Figure 3.18).
64
ELECTROCHEMICAL WATER PROCESSING Treated water Cation resin
Anion resin
Input water In use mode Input water
Acid
Cation
Anion
Waste
Water
Base
Regeneration mode
Figure 3.18 Functional block diagram conventional deionizer - on site regeneration.
Cation resins are washed in a 1 N H 2 S0 4 or HCl (sulfuric or hydrochloric acid) solution. Anion resins are washed in a 1 NaOH (sodium hydroxide) solution. These standard solutions are obtained by diluting much more concentrated reagents (30% to 50% concentration) purchased in bulk quantities. Regeneration is either performed at the water treatment site or at some regeneration station as a service to the user. In the first case, it is periodically necessary to transport the acids and alkalis to the water-processing site. In the latter case, transportation of resin tanks and dismantling and reinstallation operations are necessary. Transportation and handling of chemical reagents also involves the required procedures for hazardous materials and their disposal.
GENERAL OUTLINES OF BASIC APPROACHES
3.4.1.2
65
Electrochemical Regeneration Method
Resins can be regenerated electrochemically and on site or at established regeneration depots. The needed H + ions (acid) and OH" ions (base) are produced from the waste via the electric charge carriers within the resins as they are replaced by H + and OH - via electrolysis. Water is electrolyzed with the accompanying evolution of hydrogen and oxygen gasses to produce acid and alkali on opposite sides of an ion conductive membrane. This regeneration process can be implemented in numerous ways. They include: • Regeneration of resins during no-use times • Regeneration of a standby stack, which is made ready for interchanging at the appropriate times The acid and alkali electrochemically generated in the electrode assembly (conversion reactor) are circulated through the respective resin stacks during the regeneration cycle period. 3.4.2
Equipment Comparison
Component parts of the currently employed regeneration method are compared with the electrochemical system in Table 3.3. In conventional, on site regeneration, concentrated solutions are diluted and introduced into the resin stacks via eductor units. Because no concentrated reagents are employed in an electrochemical regenerator, no eductor, controller or programmer circuitry is needed as presently found in bulk chemical agent methods. Instead, a solenoid actuated hydraulic switching apparatus is employed. A timer or a water conductivity sensor can control the switching. Dilute acid and base are produced electrochemically in a hydraulic circuit in which the standby (resin stack being
66
ELECTROCHEMICAL WATER PROCESSING
Table 3.3 Conventional System
Electrochemical Regeneration
1 Cation Resin Bed
2 Cation Resin Beds
1 Anion Resin Bed
2 Anion Resin Beds
Controller Circuitry
Timer and / o r Sensor Switching
Eductor Heads
Manifold Assembly
Acid Reservoir
none
Alkali Reservoir
none
none
Electrolytic Unit
none
D.C. Power Supply
none
2 Circulation Pumps
regenerated) is situated. Input water is slowly passed through the regeneration circuit during the reprocessing. The water consumption rate can be significantly reduced in the regeneration loop by employing a recirculation circuit (2 optional pumps). 3.4.2.1 Performance Characteristics Comparisons There are a number of significant differences in the performance characteristics between the more conventional systems and an ECR approach. These are simply represented in the list of attributes given below. • • • • •
Reprocessing waste water is minimized Lower capital equipment costs Lower operating costs Reduction in maintenance and personnel time Less complex apparatus—greater unattended reliability • Minimum chemical hazard • No chemical reagents to purchase or transport
GENERAL OUTLINES OF BASIC APPROACHES
67
• No objectionable fumes or stored chemicals • No addition of chemical reagents to effluent Electric energy is the substitute for chemical reagents in an Electrochemical Regeneration (ECR) system. Hence, the consumption of electrical energy is greater in the ECR approach then in present systems. Two overall design versions of an ECR system will be briefly described here. They are: 1. Self contained regeneration configuration within the resin bed, (in situ regen system) (see Figure 3.19). 2. External regeneration system, which employs a physically separate electrochemical reprocessing unit (see Figure 3.20).
Processed water
Input water Cation
&
In use unit
anion
"l
(
r
'r
i
Cation
&
Power supply controller
anion
Standby (regen) unit
—►
■4
Waste
Waste No valvlng and switching show
Figure 3.19 Functional block diagram system A: normal operating configuration.
68
ELECTROCHEMICAL WATER PROCESSING Input water
Cation resin
Anion resin
In use water
y
Input water
Electrolytic regenerator
Power supply
J~L Cation resin
Input . water
13 Anion resin
Standby units version A
£5
0
Standby units version B
rft Cation resin
Anion resin
Waste
0
Waste
Power supply Figure 3.20 Functional block design system B: normal operating configuration.
In the first design, A, the entire resin bed configuration is revamped. Electrode assemblies, separator membranes and fluid manifolds all become an integral part of one total unit. This design necessitates a completely new system, and would make use of only some ancillary control devices of present de-ionizer systems. Design B necessitates only the replacement of the regeneration portion of present systems, which have an on site regeneration capability. The approach could also serve as a substitute method for regeneration stations in service companies where chemical handling problems need to be eliminated. Performance of the above two approaches are outlined below. System-A Two pairs of resin beds are employed. A resin pair for processing input water and a pair undergoing a slow electrochemical regeneration process. The regeneration time available could be a minimum of 20 hours or
GENERAL OUTLINES OF BASIC APPROACHES
69
as long as 100 hours. The reactor processor and the power supply are sized by the dissolved solids removal capacity of the system and the time available for regeneration. At the end of the "use" time, a simple switching of the in-useresin beds to the newly regenerated beds takes place, and the overall processes continues with minimal interruption. During regeneration of the "standby stacks" the necessary washing and back-flushing operations are carried out as they are normally conducted at present. Provision is made to exhaust the generated H 2 and 0 2 gasses. In most cases these gasses are discharged along with the waste water during the regeneration mode. A single pair resin tank system could be employed. However, unless there is a large non-use period of time available, the required regeneration equipment can become quite large and expensive. System-B This approach enables the use of most of the equipment presently employed in de-ionizers except for eductor heads, chemical reagent tanks and some of the controller and valving specially designed for the chemical treatment. The significant advantage of this design is its high degree of compatibility with existing ion-exchange hardware. Three versions of design B are possible. They are: 1. Recirculation of water through resin beds during regeneration via a small reservoir and circulation pump (see Figure 3.21). 2. Once through water flow with no recirculation (see Figure 3.21). 3. Only one pair of resin stacks is needed if the acid and alkali are electrochemically generated continually and stored in reservoir tanks for treatment of the resin bed during regeneration. In this manner, the equivalent of the present system is available wherein the regeneration process occurs periodically and may take only
70
ELECTROCHEMICAL WATER PROCESSING
Cation resin
Use mode
Anion resin
Processed water
Input water Cation
Anion
Ï—€ Acid tank
^
Regeneration mode Alkali tank
Power supply
_©
Figure 3.21 System B, Version 1.
Deionized water output
Valve
Deionizer in use
Water input
Deionizer in regen. mode
T^ Drain
Figure 3.22 System B, Version 2.
the standard time of about 1 hour. Circulation pumps and reagent storage tanks are required in this case (see Figure 3.22).
GENERAL OUTLINES OF BASIC APPROACHES
71
In the first of the above versions, water economy is maximized, and in the second version, the equipment is somewhat simplified, but the water consumption rate is considerably higher. The third case is essentially a direct replacement of the acid /alkali wash without the necessity of supplying, handling, diluting and chemically feeding reagents from an external source. All of the above designs use the same regeneration power supply and electrochemical capacity. As in the system A design, the H 2 and 0 2 gasses produced during the regeneration as a result of the electrolytic decomposition of water in design versions 1 and 2 are expelled with the waste water. Special provision must be made for discharging the gasses in design version 3 because there is no waste discharge or drain during the electrolytic production mode of acid and base in the reservoirs. The real potential merit of the ECR approach is in the reduction of materials handling labor and administrative costs along with the attractiveness of a cleaner facility. 3.5 3.5.1
Metals Reclamation Electrochemical Process for the Removal of Iron in Acid Baths
In this section we will explore the practicality of removing iron and other heavy metals from solutions such as "spent" pickling baths by electrochemical means. There are, in fact, a few electrochemical approaches to achieve a low cost and safe method with minimal associated pollution hazards. As a test case we will explore some of these means of continuously removing iron from sulfuric acid solutions. All the proposed methods are electrochemical processes and they require special ion exchange membranes and electrodes for their practical operation. The membranes need to be chemically resistant to the acidic and somewhat oxidizing environment. They must have adequate selectivity
72
ELECTROCHEMICAL WATER PROCESSING
and not be "fouled" by iron or other heavy metals, as well as have low permeability for the prevention of excessive molecular (thermal) diffusion. Electrodes must be chemically inert, inexpensive enough and have a long operating life to make them useable in practical systems. As the iron accumulates within the pickling bath during a stripping process, the pickling solution capability diminishes. Eventually, the solution must be replaced with fresh sulfuric acid solution. The problem that exists is the disposition of the "spent" pickling solution. Ideally, the continuous restoration of the bath via a method not requiring either the discarding or the re-supply of toxic or hazardous chemicals is desired. We will briefly explore the possibility of removing dissolved iron in the form of ferrous and ferric sulfate from the bath as a solid. The acid level in the bath is controlled solely by means of an electrochemical process. The technical goal is creating circumstances in which no chemical reagents, other than iron and iron compounds (Fe(OH)2, Fe(OH)3) in solid form, are brought to or removed, respectively, from the pickling process. 3.5.2
Technical Approaches
Three different electrochemical cell configurations, identified as A, B & C, are identified as potential solutions. Approach B as the first for this study. Cell design B appears to be the most attractive because it might result in the most current efficient method, if other parameters prove practical. Approach A, another very likely possibility, has been selected as a close alternative method. Approach C is a strong contender, but probably more complex in structure and operational management. One additional approach to removing heavy metals in solution from a water stream is one in which insoluble
GENERAL OUTLINES OF BASIC APPROACHES
73
compounds are precipitated out of solution into a collection chamber, or in which the metal(s) are electrodeposited onto a negative electrode. Passage of soluble iron compounds such as the sulfates through a cation membrane into an electrode cell chamber in which the pH is maintained high by means of electrolysis, for example, will result in removal of these metals as solid hydroxide and oxide compounds. As an example of a realistic problem that may be solved, we will select the following. We will assume a pickling bath is a 10% H 2 S 0 4 / H 2 0 solution with Fe2(S04)3 at levels up to 5% in concentration. It is desired to remove the iron component from the bath, or at least reduce the level significantly for bath reuse, and return the bath solution to its original 10% acid concentration. To achieve a practical and workable approach, it is necessary that this entirely electrochemical method of iron removal and acid level restoration of the pickling bath have certain characteristics. They include: a. Reasonably high coulombic efficiencies of separation b. Long life of components (estimates) c. Acceptable membrane transport number and conductivity values d. High percentage removal of iron, and low loss factors for sulfate ion 3.5.3
Technical Approaches
There are three basic approaches outlined as possible contenders. These are described below. Approach A. Figure 3.23 is a very simple cell schematic showing the type of process to be investigated. The membrane is an anion structure with excellent iron compatibility. Modified RAI cation membranes have yielded very encouraging properties in terms of iron transport numbers (Lee, Zito, and D'Agostino).
74
ELECTROCHEMICAL WATER PROCESSING
H 2 S0 4
Filtered OHNa+ so;
H+ Fe+3
ÍJ*
H
Fe2(S04)3 Na 2 S0 4
(+)
Anion membrane
H 2 S0 4 Fe2(S04)3
Figure 3.23 Approach A.
Depleted bath solution is circulated through the negative side of the cell and iron is plated out and iron oxides are formed in the increasingly basic environment. Iron compounds are precipitated out of solution and collected for discarding. Sulfate ions are pulled through the membrane to the positive side and sulfuric acid is generated as the new, reconstituted pickling bath. Disadvantages: Higher coulombic need for moving S0 4 = ions across the cell to generate acid. An auxiliary stage of cells may be of assistance in further restoration of acid level. Approach B Figure 3.24 is a simple cell diagram showing the operation of a device employing cation membranes. In this case the iron is being transported for removal from the main bath rather than the sulfate to form acid. As the iron is accumulated in the negative side (basic), it will be precipitated out of solution as oxide-hydroxide compounds. The sulfuric acid solution will also be reconstituted to its original concentration via loss of Fe+3 ions and replacement
GENERAL OUTLINES OF BASIC APPROACHES
75
Fe ' Solid ! «= ! Fe(OH)2 ;
1
1 1 i
MaHH
i
OHNa+
!
■H*r'rrr-
1
A
; Cation Membrane
1
H+
Fe+3
1
|1
i
(+)
|
H 2 S0 4 ' Fe 2 (S0 4 ) 3
Figure 3.24 Approach B.
of H + ions with the evolution of oxygen gas at the positive electrode. Disadvantages: Some loss of S0 4 = ions from the (+) side due to membrane diffusion, and coulombic loss due to H + ions transport from (+) to (-) side. Advantages: Better coulombic efficiency due to the fact that Fe is being removed from the bath rather than removing the larger quantity of sulfuric acid to another solution. Investigate: Membrane performance, electrode life and sludge removal. Approach C Another possibility is the use of membranes, which do "foul" in the presence of iron ions. There may be an opportunity to preferentially remove hydrogen ions from solution. Figure 3.25 shows the type of process contemplated as a means of separating iron from the acid solution. Each of the above has limitations and certain advantages. The optimum choice would depend greatly upon the nature of the problem to be solved as well as the properties of the electrode and membrane components available.
76
ELECTROCHEMICAL WATER PROCESSING
o,
Neg
Pos
Cation
Anion
Figure 3.25 Approach C.
Another possible cell design that could be a practical solution to removal of iron and other heavy metals would entail a modified pH control cell wherein the cations to be removed are transported into a region of high pH in the (-) compartment of a control cell. These ionic substances would be either plated out onto the (-) electrode or precipitated as hydroxides and oxides. 3.5.4
Laboratory Feasibility & Data Study Suggestions
All the proposed methods are not only electrochemical processes, but they also require special ion exchange membranes and electrodes. The membranes need to be resistant chemically to the acidic and somewhat oxidizing environment. As was stated earlier, they must have adequate selectivity—not be "fouled" by iron—and have low permeability to prevent excessive molecular (thermal) diffusion. 3.5.5
Experimental Methods
In order to conduct the necessary series of experiments, data collection and quantitative evaluations,
GENERAL OUTLINES OF BASIC APPROACHES
77
appropriate tests were designed. Apparatus, chemical analysis equipment and electrical circuits must be available, while demountable electrochemical cells need to be constructed. Electrodes with carbon polymer compositions and external wire connections were fabricated to accommodate the test cells. Ion exchange membranes from various sources were assembled, and some membranes were modified for ferrous and ferric ion transfer. Figure 3.26 shows a simple circuit employed in the experiments. A constant current power supply was used to simplify computation of total amp-hours transferred. A coulometer in series with the cell was employed. Wet chemistry analysis was employed to determine the concentrations of ferric and ferrous ions, and the level of acidity (normality) of the solutions at different periods during cell operation.
Constant current power supply
/»
\._
Ammeter
1 ^ 1 I / 1 Voltmeter
Electrochemical cell
Figure 3.26 Electric circuit cell operation.
Coulometer
78
ELECTROCHEMICAL WATER PROCESSING
The chemical methods employed for these measurements are identified below. 1. Acidity determination - Titration with a 1 normal solution of NaOH and with phenolpthlalein as indicator. 2. Ferric concentration - Oxidation of iodide method. A solution of Nal is used with a starch indicator. Titration is accomplished with a 0.10 N solution of sodium thiosulfate. 3. Ferrous concentration-An ortho-phenanthroline ferrous complex is used as indicator, (changing color from red to faint blue when ferrous is oxidized to ferric), with a 0.1 N solution of ferric sulfate as titrant. Figure 3.27 is a diagram of the type of open top test cells that were made for and employed in these experiments. The cell is constructed of rigid PVC in two half sections. Each section contains an electrode and a flat rim around the frame. The two half-cell sections are clamped together with a membrane sandwiched between the frames. RTV is used as a liquid gasket to make a water-tight seal.
(+)
Carbon composite electrode
Cell container
Figure 3.27 Basic test cell construction box, electrode, & membrane.
GENERAL OUTLINES OF BASIC APPROACHES
79
3.5.5.1 Approach B Tests A cation membrane, SYBRON lonac, was placed in the cell shown in Figure 3.23. Solutions of sulfuric acid and ferric sulfate mix were prepared to anticipate a worst-case condition for pickling baths. The first solution is as follows: 100 ml of 66 Baume H 2 S0 4 50 grams of Fe 2 (S0 4 ) 3 5H 2 0 Total volume of solution is 1200 cc Titration of the mix gives the net concentrations below. 1.9 ml of thiosulfate per 2 ml of bath sample = 0.095 N ferric salt, or approximately 4% by weight solution of ferric sulfate. 7.1 ml of NaOH solution per 2 ml sample = 3.55 N sulfuric acid, or approximately 16% by weight solution. The first cell tested employed a SYBRON cation membrane, and was configured as cation| (+) 0.095 N F e + 3 + 3.35 N acid membrane 210 ml
0.10 N NaOH
(-)
210 ml
with 7.5 square inch active area electrodes in the cell. The cell operation and planned ion transfer are shown in Figure 3.24. Ferric ions are to migrate from the (+) side to the (-) side with an increase in pH. They precipitate as hydroxides, or come out as iron plating. The cell ran for 2 hour intervals at 1.5 amps on five separate occasions with no measurable net transfer of Fe+3 out of the positive (+) side compartment. It appeared that all the charge transfer was via H + ions.
80
ELECTROCHEMICAL WATER PROCESSING
Other similar series of tests were conducted employing cation membranes. Membranes'were tested from a variety of sources such as HCI, Ionics, and DuPont, NAFION types. The same results of very little or no significant Fe+ ion transfer were obtained. An ESC (RAI) homogeneous polyethylene membrane was converted from the normal Na form to the Fe+3 form at TRL and tested in similar circumstances. The short Table 3.4 below gives typical results. Let us review the magnitude of the Fe+3 concentration change we should expect from this charge transfer if the mechanism was entirely attributed to iron transport. A200 ml volume of 0.095 N Fe+3 solution in the cell chemically configured above would have these electrode reactions: (+) side ... 3(S04"2) +3 H 2 0 = 3H 2 S0 4 +3/2 0 2 + 6e" (-) side ... 2Fe+3 + 3H 2 0 + 6e~ = Fe(OH)3 + 3/2 H 2 Six electrons are drawn from the external circuit per two Fe ions, or about 78 amp-hours of charge are needed to +3
Table 3.4 Iron Form ESC membrane test (2 ml test sample sizes). Time, hrs
Volts
Amps
Thiosulf ate, ml
0
10.7
0.64
1.8
0.2
10.7
1.73
1.7
0.4
4.7
1.5
1.8
0.6
4.7
1.6
1.7
0.8
4.7
1.6
1.7
1.0
5.4
1.9
1.7
1.5
5.4
1.9
1.65
2.0
5.4
1.9
1.6
2.5
5.4
1.9
1.65
3.0
5.4
1.9
1.65
GENERAL OUTLINES OF BASIC APPROACHES
81
transfer iron from the (+) to the (-) side at 100% coulombic efficiency. If the coulombic efficiency were 100%, total transfer of iron from 200 ml of 0.095 N Fe+3 solution would require about 1.5 amp-hours of charge. In the experiments above, more than 1.5 AH of charge flowed with no measurable net transfer of iron. In the case of the ESC membrane, its coloration after conversion to the iron form was brown. Its normally colorless dry and white when wet. During operation of the cell, the membrane became white, showing that it had reconverted to the hydrogen form via displacement of iron by H + ion migration through the membrane as the sole charge carrier in the cell. A quick look at the relative specific ion conductivities of H + and Fe+3 at infinite dilution will show the significant preferential nature of the processes in the cell. H+ l/3Fe + 3 OHNa + 1/2SO; 2
320 mho-cm" Vmilli-equiv. 50 172 44 68
And, because the concentration of the H + ions is 3.55 N, or 35 times as great as that of the iron, one can expect the transport numbers for these ions to be at least 100 times greater for hydrogen. It appears that the only way in which the cation membrane configuration of Approach B, shown in Figure 3.24 can be useful is in very much more dilute acid solutions. The competition for hydrogen transport over iron is not as pronounced in lower acid concentrations. 3.5.5.2 Approach A The results of the experiments of method B were not very promising, so it was decided to explore the possibilities of approach A. The configuration is essentially the same as in
82
ELECTROCHEMICAL WATER PROCESSING
B except that an anion membrane was employed and the principle ion for transfer is the sulfate radical. Figure 3.24 shows the principle processes involved. S04~2 ions are transferred from the (-) side to the (+) side with no net movement of iron, sodium or hydroxide ions. SYBRON anion membranes were employed in all these tests. The approach involves the idea that as the bath circulates through the (+) side of the cell, its H 2 S0 4 content rises because of the transfer of S04~2 ions from the (-) side of the cell, and the liberation of oxygen at the (+) electrode. Meanwhile, hydrogen is evolved at the (-) electrode with the continuous formation of hydroxide ions for the precipitation of insoluble iron compounds. Some iron also comes off as plating on the (-) electrode. These solid materials are removed as sludge or by filtration in a continuously moving bath. Various tests show the behavior of this system, and provide some quantitative data for further design purposes. A series of tests with solutions of composition listed below were made. (+) side ... 16% H 2 S0 4 solution, about 3.35 N concentration. 4% Fe+3 solution, about 0.10 N concentration. (-) side ... 2% Na 2 S0 4 solution initially, 0.3 N Concentration. The cell was operated at 2 amps with an electrode effective area of 7.5 in2. A 2 ml sample was withdrawn from the solutions periodically and analyzed for reagent concentrations. Table 3.5 shows a typical run. The purpose of these experiments is to determine if the acidity in the (+) side can be increased at the expense of S04~2 ions from the (-) side, and if the ferric and ferrous ion concentrations move in the direction desired. The acidity in the (+) side increases steadily to that of the (-) side initial value.
GENERAL OUTLINES OF BASIC APPROACHES
83
Table 3.5
Time-hrs 0
(+) side
(+) side
(-) side
1.0 N NaOH
Fe+3
Fe+2
1.9
0
Volts
Amps
Titration
6.56
2
0.05
0
0.05
0.08
0.15
0.16
0.15
0.33
0.25
0.67
0.60
1.5
4.8
2
1.7
2.16 2.67
1.3
3.56
2
0.05 3.3
1.95
The Fe+3 concentration diminishes and the Fe+2 concentration increases as the iron is reduced at the (-) electrode. A quantitative assessment of the transfer yields the following information. 1.95 ml of a 1 N N a O H / 2 ml sample corresponds to a concentration of 1.0 N acid transfer in 2.67 hrs. via 2 amps x 2.67 hrs = 5.34 AH input. Only 5 AH are needed to do transfer for 200 ml of 1.0 N for 100% coulombic efficiency. Figure 3.28 is a graph of this data, and shows how close the cell performance is to the maximum. Another new experiment was devised to explore the possibility of introducing small quantities of Fe+3 from pickling bath into the (-) side to maintain a steady flow of freed solution back into the increased acidity bath of increasing acidity as a continuous restoration process. The following composition was prepared as the initial solutions, and a
84
ELECTROCHEMICAL WATER PROCESSING Approach A Data from table I 120
0.25
I
I
0.15
c a 0.05
3 LU
2
3 4 Amp-hour input
■ Actual equivalents
Theoretical Max. Equiv.
- Coulombic efficiency Equivalents of sulfate in 200 ml volume Figure 3.28
small quantity of depleted pickling bath was introduced periodically into the (-) side for iron removal. (+) side ... 200 ml 3.35 N H 2 S0 4 + 0.095 N Fe2(S04)3 (-) side ... 200 ml H 2 0 + 5 ml of (+) side composition solution The (-) side is plain water with a very small quantity of the pickling solution to provide for initial conductivity to get the cell started. The approach contemplated here is that while the main body of the pickling bath circulates through the (+) side, a small percentage is introduced slowly into the (-) side. The (-) side is at a much higher pH, enabling the iron to be removed as filterable solids. The liquid from the (-) side is then returned to the main bath as essentially a Na 2 S0 4 water solution. The pH in the (+) side is continuously being lowered due to acid regeneration via S04~2 ion transfer from the (-) side.
G E N E R A L O U T L I N E S OF B A S I C A P P R O A C H E S
85
All these observations are made in the tests conducted with these cells. If the pH in the (-) side is kept above 7, there is little Fe+2 or Fe+3 in solution. Table 3.6 below lists some typical data obtained from such a cell. Plots of this data are presented in Figure 3.29.
Table 3.6 Hydrogen ion concentration figures are given as ml NaOH titration data. Time, hrs
Volts
Amps
0
0
0.08
14.6
2
0.16
16.2
1.68
0.25
16.4
1.24
0.33
16.1
0.97
0.42
16.1
0.60
0
(+)H +
(+) Fe+2
0.4
0.05
0.5
0.05
(-) side Fe+
3
0.3 0.1
0.3 0.2
precipitate noted in (-) side, reddish brown iron 0.5
16.1
0.40
introduced 2 ml of pickling, (+) side solution, into (-) side 0.59
13.1
2
0.1
0.67
16.1
1.3
0.2
0.75
16.1
0.61
0.25
orange colored ppt. in (-) side appeared again 0.83
16.1
0.41
added 3 grams Na 2 S0 4 salt to (-) side 0.92
8.3
2
1
7.6
2
1.08
8.3
2
0.3
(-) side H+
86
ELECTROCHEMICAL WATER PROCESSING
Table 3.6 (cont.) Hydrogen ion concentration figures are given as ml NaOH titration data. Time, hrs
Volts
Amps
(+)H +
8.4
2
0.4
1.13 1.25
0.45
added 2 ml 1.28
7.8
2
added 2 ml 1.72 added 2 ml 1.8
0.8
added 2 ml 2.0 2.04
0.95
2 ml 2.25
1.15
2.42
1.25
2 ml 2.52
1.25
2 ml 2.72
1.4
2 ml 2.83
1.5
2 ml 3.13
1.6
2 ml 3.83
1.9
(+) Fe+2
(-) side Fe+3
(-) side H+
GENERAL OUTLINES OF BASIC APPROACHES
87
Table 3.6 (cont.) Hydrogen ion concentration figures are given as ml NaOH titration data. Time, hrs
Volts
Amps
(+)H +
(+) Fe+2
(-) side Fe+3
(-) side H+
12 ml 4.08
2.0
4.27
2.25
10 ml 2.35
4.45 4.55 4.68
5.6
2
2.45
Some simple calculations and general observations follow. • Every time the pH of the (-) side became basic, a large quantity of brown-orange precipitates were seen. • Coulombic efficiency for generating acid in the (+) side can be estimated as: ° Constant current @ 2 Amp for 4.2 hrs is 8.4 AH charge transfer ° Acidity change in that time is 0.3 to 2.45 ml = 2.15 ml/sample, or about 1.1 N acid in vol. of 200 ml giving about 1/5 equivalent S04~2 transported to (+) side. At 100% coulombic efficiency, about 5 AH are needed, giving the cell a current efficiency of 5/8.4 = 60%. Considering the very low concentration of S04~2 present in the (-) side during the processing, this efficiency is quite surprising. • To estimate the efficiency of maintaining a basic environment in the (-) side, we may take the
88
ELECTROCHEMICAL WATER PROCESSING
readings between 1.72 and 2.0 hrs. This provides the following: 2.0-1.72 = 0.28 hrs, @ 2 Amps the charge is 0.56 AH 4 ml @ 4.2 N contains 0.0168 equiv. weights of acid 26 x 0.0168 = 0.44 AH required @ 100% eff. to transport SO~ Coulombic efficiency of conversion to precipitates is the found as 0.44/0.56 = 79%. Figure 3.29 is a graph of the salient data from Table 3.6. A different composition batch of test solution was prepared that may better represent the spent pickling bath. Experiments were established to observe the behavior of the cell when initially at the condition where the solution on both sides is the same.
Approach A Data from table I
0.25 to
o u
■o 0)
er
0.15
0.05 -
LU
2
3
4
Amp-hour input - Actual equivalents -Coulombic efficiency Equivalents of sulfate in 200 ml volume
Figure 3.29
Theoretical Max. Equiv.
GENERAL OUTLINES OF BASIC APPROACHES
89
The composition of the synthesized pickling bath is: 50 ml of 66 Baume suifuric acid + 14 grams of Fe2(S04)3-5 H 2 0 + 15 grams of Na 2 S0 4 salt to a total volume of water solution = 800 ml. Titration and analysis give the following concentrations: H 2 S0 4 2.25N(requires4.6mloflNNaOH/2ml sample) Fe 2 (SO 4 ) 3 ....0.80N(requires0.8mlof0.1NThios/2ml sample) Na 2 S0 4 0.26 N (estimated via weights & degree of dilution) The cell is modified to provide for larger electrodes. The electrode active area is about 13 square inches, affording higher operating current for accelerated testing. Solution volume per side is about 200 ml initially. Samples of 2 ml are taken periodically from the cell do diminish the total working fluid volume in time. Table 3.7 shows characteristic data obtained in cell operation. Table 3.7 Time, hrs
Volts
0
3.37
Amps
(+) side
(-) side
Fe+3
H+
Fe+3
H+
0.9
4.6
0.8
4.6
0.2
0.5
4.15
0.27
0.8
4.25
0.38
0.65
4.6
0.35
3.8
0.63
0.7
4.7
0.2
4.05
1.03
0.7
4.7
0.1
4.3
1.43
0.9
5.05
0.05
3.85
2
0.13
90
ELECTROCHEMICAL WATER PROCESSING
Table 3.7 (cont.) Time, hrs
Volts
1.63
4.1
Amps
(+) side Fe+
3
(-) side
H+
Fe+
3
H+
4
1.88
0.8
5.5
0.0
3.7
2.2
0.9
5.45
0.0
3.5
2.47
0.95
5.7
0.0
3.35
2.87
0.8
5.8
0.0
2.5
3.22
6.2
0.0
2.5
3.47
7.0
2.25
6.4
2.6.
3.55
4.4
4
0.8
3.89
2.5
4.47
2.0
5.05
1.7
5.64
1.4
6.55 6.8
8.2 5.7
1.5
4
6.92 7.55
0.55 7.2
4
9.35
7.80 8.02 8.14
7.6
4
10.1
0.5
0.25
0.5
0.1
0.5 0.45
Some general observations & comments follow. • Efficiency of generation of acid in the (+) side is: Change in concentration over 8.14 hours is (10.14.6)/2 =2.8 N, a 200 ml vol. has gained 2.8/5
GENERAL OUTLINES OF BASIC APPROACHES
91
Equiv. requiring 14.3 AH for transfer. About 4 x 8.14 = 32.6 AH was involved, giving an averaged coulombic efficiency for the process of about 14/32.6 = 43%. The transport of H + ions at these high acid levels most likely contributed to the lowering of charge efficiencies. Figures 3.30 and 3.31 show the above information graphically. They are plots of the acidity change in the (+) and (-) sides, respectively. 3.5.6
Conclusions & Recommendations
The results of this brief empirical study and the ensuing analysis of the data lead us to these conclusions and suggestions for further work. Figure 3.32 shows a suggested design. The pickling bath is circulated through the positive side of the electrolyte :ic Approach A Data from table 3.7 for (+) side
120 - 100
3 4 Amp-hour input Actual equivalents Coulombic efficiency Equivalents of sulfate in 200 ml volume Figure 3.30
5
Theoretical Max. Equiv.
}
92
ELECTROCHEMICAL WATER PROCESSING Approach A Data from table 3.7 for (-) side 120 - 100
j
3 4 Amp-hour input - Actual equivalents
Theoretical Max. Equiv.
- Coulombic efficiency Equivalents of sulfate in 200 ml volume Figure 3.31 Neutral LowpH Iron solids «artremoval
Filter
^MrPickling bath reservoir
(-)
side
(+) side
Figure 3.32 Design schematic proposed system.
removal system, and through the (-) side at a much lower flow rate. In effect, the bath is also bypassed through the negative side of the system and through a series filter for
GENERAL OUTLINES OF BASIC APPROACHES
93
iron withdrawal. The (-) side is always kept at a relatively higher pH in order to precipitate the iron compounds. The (+) side bath has its pH lowered directly and continuously in passing through the systems. 1. Coulombic efficiencies of at least 50% for the removal of iron (+3) from pickling acid baths is easily attainable with this technology. 2. Operating cell potentials of between 2 and 2.5 volts are expected. 3. With these figures, we estimate that about 150 amp-hours of charge and about 600 watt-hours of energy are required to remove one pound of ferric sulfate salt from solution. In terms of elemental iron (Fe), about 2 KWH are needed to remove 1 lb. At an energy cost of $0.05/KWH, the cost of elemental iron removal is about $0.10 per pound. 4. Electric current densities should be kept down below 0.10 amps per square inch at present for long life electrode operation. At this level, at least 10 ft2 of electrode and membrane are needed for a removal rate of 1 lb of ferric sulfate per hour. At a cost of approximately $5/ft 2 of system, the capital equipment cost appears to be about $50 for a system, with removal rate capacity of 1 lb of salt per hour of operation.
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
4 Mathematical Analysis & Modeling Electrodialysis Systems 4.1 Electrodialysis: Descriptions and Definitions Dialysis is described as the process of selective or fractional diffusion, separation, of dissolved substances and substances in colloidal suspension across a porous membrane. There is a clear distinction between such processes and osmotic mechanisms. In the case of dialysis, both solvent and solutes pass through the porous membranes, leaving behind large colloidal molecules and structures. Thus, ionic solutes may be separated from colloids by this type of diffusion through microporous membranes. Figure 4.1 shows the simple configuration of such a cell. If fresh water with low concentrations of dissolved substances is flushed through the outer compartments, 95
96
ELECTROCHEMICAL WATER PROCESSING
Solute diffusion
Colloid plus solution
Microporous membrane
Wash water flow Figure 4.1 Single cell dialysis.
the separation process is accelerated and more complete because of better concentration gradient maintenance. The diffusion of unwanted dissolved materials back into the colloid-containing compartment is greatly reduced. When an electric field is also impressed across a dialysis cell, or chamber, further separation of ionic species is possible depending upon the type of membranes and electric charge configurations. With strictly microporous membranes that have no electric charge characteristics of their own, the ion migrations are accelerated into the outer compartments by attracting oppositely charged electrodes. However, care must be taken in maintaining low ionic concentrations in the electrode compartments to minimize migration of ionic species back into the colloid compartment by the electric field. Figure 4.2 illustrates these processes. Transport is assisted by electric field, keeping very low concentration of ions in wash water, which reduces "back diffusion" and transport into the colloid region. In recent years, practical ion exchange membranes with high transport number ratios have been developed and are available at low enough costs to make electro-dialysis applicable for other, larger scale applications. The principle working parts of an ED cell are shown in Figure 4.3.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
97
Electrode
Wash water flow Figure 4.2 Electrodialysis. Demineralized output water
Electrode
Wash water
Anion membrane
Cation membrane
Waste water
Input water
Figure 4.3 Single cell electrodialysis.
They are: Anion transfer membrane Cation transfer membrane Two chemically inert electrodes The ionic selectivity of the membranes makes it possible to perform a broader range of separation operations. Ionic substances in solution can be removed from a body of water quite efficiently.
98
ELECTROCHEMICAL WATER PROCESSING
Referring to Figure 4.3, negative ions are shown migrating through the anion membrane toward the (+), positive electrode. The positive ions are shown migrating toward the (-) electrode. As the transport of ions progresses, the concentration of dissolved ionic materials in the middle chamber becomes more dilute. Eventually, most of the ionic species are transported to the outer chambers, while the middle chamber is "de-ionized". As the processing continues, the electrical resistance of the center chamber water increases, and the current flow is reduced if a constant potential is kept across the electrodes. Gradually, the amount of dissolved solids removed per unit time will diminish as the processed water is de-ionized. An example that illustrates the processes between the membranes and also at the electrodes is that of removing a single ionic compound in solution from the water to be processed. A most common solute is sodium chloride, NaCl. Figure 4.4 shows the specific ion migration directions and the ensuing oxidation and reduction reactions taking place at the anode, (+) electrode, and cathode, (-) electrode, respectively. Sodium ions are removed from the mid-chamber through the cation membrane toward the (+) electrode. Reduction of H + ions to H 2 gas takes place at that electrode, and NaOH ;CI2
CI
Na
OH"
Anion membrane
Figure 4.4
H20
Cation membrane
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
99
is formed. Chloride ions are transferred through the anion membrane to the (+) electrode and are oxidized to Cl2 and evolve as gas. If the concentration of Cl" ions is very low, then oxygen will also be produced at the (-) electrode, and HC1 is generated. These two end chamber solutions become alkaline and acidic, respectively. In some instances it may be practical to separate the electrode regions from the waste water compartments by additional membranes, porous or ion-selective to prevent evolved gas from entering the discarded waste streams. This concern is even more important in large multiple cell assemblies. In laboratory cell studies, provisions permit generated gasses to either escape or to be collected and analyzed. Concentrations of dissolved salts and pH levels are monitored easily within the reservoirs of the circulating solutions. Larger multiple stacks of dialysis cells prove much more effective and economical for practical systems. These cells are in series electrically and in parallel hydraulically. Figure 4.5 shows the essence of the "sandwich" construction of an array, where the ion exchange membranes are kept separate by plastic screening or mesh that provides mechanical support, but still permits necessary flow of water with minimum increase of hydraulic pressure requirements.
Waste water compartments Figure 4.5
/
\
Processed water compartments
100
ELECTROCHEMICAL WATER PROCESSING
Figure 4.6 shows a particular and rather commonly employed hydraulic configuration. Input water is from a common source, and exit streams are separated by two manifold arrangements. The waste water is either discarded into the original water source reservoir or conducted elsewhere for further treatment or reclamation. The two electrode end compartments are treated separately because gasses and other generated chemical products are included. The exact treatment of these effluents will depend upon operating conditions at the electrodialysis site or the application. The ratio of processed water to waste- water volumes is a critical factor in determining operating costs and practicality. In most ED systems, that ratio is at least 10:1 and as high as 100:1 in some designs. There are numerous benefits derived from stacking large numbers of cells in a single array. They include: a. Reduction in electrode size and cost; particularly when precious metals are employed in their structure.
uuuuuuuu UÜUÜUÜUUUÜUÜL Negative
Input solutions
Positive
Cation membrane Anion membrane Low TDS effluent
n
DP DD
nanDÛ na
DÛ
Alkaline effluent
Acidic effluent Figure 4.6 Ten cell array. Hydraulically in parallel - Electrically in series.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
101
b. Less gas generation per unit weight of solutes removed from the processed water stream. c. More compact geometry is achieved than single cells with very large areas. d. Construction costs are less for larger cell arrays versus a greater number of smaller arrays to achieve the same performance end result. Electrodes for these types of ED systems are usually fabricated, platinized or ruthenized fabricated from titanium sheet metal, or are simple carbon structures that have been impregnated with a polyolefin or fluorocarbon materials to reduce porosity. Carbon structures are less costly, but usually have less operating life at higher current densities. Flat plate designs are by far the more common geometries employed in dialysis cells. This type of construction offers the greatest versatility, compactness and simplicity, as well as the lowest cost over any other hardware design approach. All of the analyses presented here are for parallel, flat plate constructions. Cation membranes are usually sulfonated copolymers of styrene and divinylbenzene, and are generally more stable than the anion membrane materials of the quaternary ammonium anion membrane materials. The fluorocarbon polymer membranes are generally more stable and superior properties of selectivity, diffusion inhibition and electrical conductivity. However, these membranes, such as the DuPont products known as NAFION, are usually too expensive to be used in large scale ED systems. Application for ED systems ranges from desalination and demineralizing to reclamation of critical or contaminating elements from industrial waste streams. Production of acids and bases from neutral bodies of water as a means of "chemical" pH control is another application that is becoming increasingly widespread.
102
ELECTROCHEMICAL WATER PROCESSING
Basic problem areas that continuously plague ED systems are: 1. Chemical attack of membranes 2. Fouling and poisoning of membranes by some heavy metal ions and large organic species in transported into anion membranes 3. Life of electrodes versus current densities 4. Insulation of cathodes by deposition of metal compounds such as carbonates, hydroxides and oxides onto the surface during operation in an alkaline solution 5. Handling of evolved gasses at the electrodes— usually oxygen, hydrogen and chlorine
4.2
Basic Assumptions and Operating Parameters
It is important to make clear not only the definitions employed here, but also their quantitative values and their inter-relationships. 4.2.1
Electrolytic Conductivity
Bulk electrical properties of materials are conventionally defined as follows. The specific conductivity and resistivity of substances have the dimensional characteristics -1
1 , or mho-in" ,
<7= specific conductivity, mho-cm and p = specific resistivity, ohm-cm
(4 1)
and, in the case of electrolytes, it is important to know the amount of electrically conducting components—solutes—
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
103
present per unit volume of solution or liquid. This term is identified here as c = concentration by weight of solutes, ppm
(4.2)
Electric conduction—charge transport—in electrolytes takes place by the migration of ions as charge carriers across an imposed electric potential. The mobility of each species of ion through the water solution medium is expressed quantitatively as specific ion conductivity. Specific conductivities for most of the common ions have been measured and are available from numerous reference sources such as Handbook of Chemistry & Physics (CRC Press). Some values from Smithsonian Physical Tables for the specific conductance of ions at infinite dilution are given below. Specific conductivity at infinite dilution is the limiting, maximum value for the compound or ion where the concentration is so low that ionic interaction is negligible and where ionic dissociation is complete. The specific ion conductance is in units of (reciprocalohm-cm 2 ) if concentrations of solutions are represented as milli-equivalents per liter. Table 4.1 lists values of a few more common ions at various temperatures. As illustrated, the dependence of conductance upon temperature is quite great. In order to calculate the conductance of a particular ion or ionic compound, its equivalent conductance value must be multiplied by the concentration of the ionic specie in solution. Concentration, in this instance, must be in terms of milli equivalents per liter. With the exception of the hydrogen and hydroxyl ions, the conductance at infinite dilution are all remarkably close in values. The specific conductance of substances in solution is more useful for practical evaluation of the performance of an electrochemical device. As an example of the necessary
104
E L E C T R O C H E M I C A L W A T E R PROCESSING
Table 4.1 Equivalent conductance of the separate ions at different temperatures. ION
0°C
K+
40.4
74.5
159
26
50.9
116
NH/
40.2
74.5
159
Ag+
32.9
63.5
143
l/2Ca + +
30
60
142
240
350
565
Na
+
H+
25°C
75°C
ci-
41.1
75.5
160
NO3-
40.4
70.6
140
1/2SO; 2
41
79
177
105
192
360
OH-
steps to estimate specific conductance of an ionic compound in solution, we can examine two typical salts that have concentrations to reduce: sodium chloride and sodium sulfate, which both may be present in a body of water. The equivalent conductance of the separate ions should be added together to obtain the equivalent conductance of a compound. From Table 4.1, the specific conductance of NaCl becomes aNaCi= 50.9+ 75.5
= 126.4 mho-cm 2 times the equivalents per 1000 cm 3 Or,
aNaCl = A ^ l N 1000
mho-cm"1
(4.3)
where N = solution normality, i.e. equivalents of solute dissolved in one liter of solution, and where A = equivalent conductance in cm2 equiv"1 ohm-1.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
105
The equivalent conductance for most strong electrolytes such as NaCl, KCl, HC1, Na 2 S0 4 , etc., remains reasonably constant over a wide range of concentrations and at a constant temperature. The range extends from almost infinite dilution to close to one normal solution. It should be noted that the stronger electrolytes retain a more constant equivalent conductance as concentration is increased more than the weaker ones. Table 4.2 gives some equivalent conductance for five compounds at 18° C at different concentrations. It is necessary to multiply the above by the concentration of the solute, NaCl, to obtain the specific conductivity of the electrolyte in the familiar units below. Let us assume that the concentration of NaCl is 0.10 normal, or 100 milli-equivalents per liter. Then _ 92 mho - cm2 -0.10 equiv.^NaCl ~
cm
lÖÖÖ
-mho-cm
-i
= 0.0092 mho -cm'1
(4.4)
In terms of specific resistivity, p
d
of the solution (4.5)
108.7ohm -cm
J
NaCl
Table 4.2 Aqueous solutions equival ent milli-ec uivalents per liter. Compound Ca(N0 3 ) 2
0
2
70.4
66.5
50
80
55.6
100 51.9
HC1
379
373.6
353
350.6
KCl
130.1
126.3
113.5
112
NaCl
100
105.6
93.5
92
H 2 S0 4
383
353.9
253.5
233.3
106
ELECTROCHEMICAL WATER PROCESSING
This resistivity is that of a volume of electrolyte 1 cm3 with faces of 1 cm2 in area. Electrical conduction is between two opposite faces of the centimeter cube. 4.2.2
Solute Concentration & Electrical Conduction
When designing and assessing the performance of electrodialysis systems it is frequently convenient to perform the associated calculations in terms of dissolved solids concentrations, or "Total Dissolved Solids" (TDS) numbers. TDS is normally expressed as the portion of solids present in solution as parts per million of the weight of the total solution. Obviously, in the usually encountered low concentrations, the total weight of the solution is essentially that of the solvent— water. An examination of the range of values of specific conductivities at the same concentration for various common solutes show that there is no single TDS-to-a conversion constant, (p, applicable to all dissolved compounds. Table 4.3 shows a few such proportionalities, or conversion factors for the salts discussed so far. They are obtained by merely dividing the specific resistivity, p mho-cm -1 , by the mass, m grams, of substance in solution in one-liter volume. ç=m (gm/L) -cr(millimho-cm"1)
(4.6)
And, putting the above in terms of more widely used units, ç= m (milligrams/L) • cr(micro-mho-cm _1 )
(4.7)
It is readily seen from even the limited table of ratios above that there is a wide spread in values of (p, ranging over more than just an order of magnitude. Conductivities of the compounds depend upon ion mobility, degree of dissociation and charge configuration. Strong electrolytes produce
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
107
Table 4.3 Ratio of conductivity-to-TDS at 18°C and 0.10 normality. Compound
TDS, p p m
(xmhos-cm 1
I^mhos-cm^-ppm" 1
JCL
35,000
3,600
9.7
NaOH
20,000
4,000
5.0
KC1
11,200
7,400
1.51
NaCl
9,200
5,800
1.59
K 2 S0 4
9,500
13,700
0.69
NaC 2 H 3 0 2
6,000
8,200
0.73
Ca(NO s ) 2
5,200
10,200
0.74
values of (p in the order of 10 at near room temperature, and weak electrolytes have (p as low as 0.50 urnhos-cm~ 1 -ppnr 1 . Unfortunately it is not possible to find a universal value of (p for all compounds of interest in solution. The generalized equation that can be employed for expressing specific conductivity, a, in terms of ppm concentration (TDS) is o = ç- c pmhos-cm_1
(4.8)
Or, in terms of resistivity, p, we have p=
1 ç-c
ohm-cm
(4.9)
And for a rectangular volume of conductor with a path length L and with a cross-sectional area A, the resistance, R, is R=p \ A
(4.10)
If one wishes to place the ensuing mathematical relationships in terms of solute concentration rather than solution
108
ELECTROCHEMICAL WATER PROCESSING
resistivity, the value of cp appropriate to the composition of the electrolyte must be determined. Referring to Table 4.3 again, we see that in the case of alkali halide solutes such as NaCl and KC1, cp is in the vicinity of 1.5 at ambient conditions. Some commercial TDS meters employ fixed ratio scales between TDS and conductivity. Frequently, the scale conversion factor for dissolved species in ppm, and conductance is about 1.5 to 2.0 x 10~6 mhos-cm -1 per ppm. If we take the factor for cp at 1.5, then its value in equation (4.4) ms cp = 66.7x104 ohm-cm per ppm concentration. For units in the English system, cp = 26xl0 4 ohm-in. For example, a widely employed laboratory TDS/Conductivity meter (Fisher Scientific Co., Auto Temp, compensated, digital output) has a built-in conversion factor of 1.5. Proceeding now with the development of the mathematics of electrodialysis performance, we may later identify the conversion factor. 4.2.3
Electric Charge Equivalence
Another concept necessary to the computation of energy and coulombic efficiencies of system operation is the equivalency between electric charge transfer and materials transported. The Faraday equivalent of total charge transfer during electric current flow in terms of quantity of ionic materials transported is: 1 Faraday = 96,500 coulombs = 96,500 amp-sec per gram equivalent weight = 26.8 amp-hours/GEW Conduction of 26.8 AH through an electrolyte will result in the transport, electro-deposition, or generation of 1 gram equivalent weight of ionic specie.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
109
Most solutes encountered in ground water or seawater sources have equivalent weights between 50 and 80. A reasonable average equivalent weight of these dissolved materials of interest to us could be set at about 60 for purposes of arithmetical simplification. That average E.W. results in about 2.3 gm of dissolved material per AH conducted. As particular examples, the equivalent weights of these compounds are: CaCl2 NaCl KC1 CaCOs Ca(N03)2 CaS04
56 E.W. 58 74 50 82 68
Dividing an average gram equivalent weight of 60 grams by 26.8 AH/G.E.W., we get the figure of 2.3 gm/AH. 4.2.4
Coulombic Efficiency
Current efficiency, r\, is defined here as the ratio of materials transported across the membranes as dictated by Faradays Law, and what is actually removed. In the initial representations, the coulombic efficiency is set at 100%. That is an unrealistic figure. A value of 50% is closer to actuality. In fact, r| does not stay constant; it will decrease as the TDS in the processed water compartments becomes smaller. Its actual values need to be determined experimentally for a given set of operating conditions and membrane types. 4.2.5
Coefficients of Performance
Figures of Merit and operating coefficients of performance can be arbitrarily defined relationships. They serve the purpose of assessing the effectiveness of an operating system in terms of energy consumption rate, for example, versus the dissolved solids removal rate.
110
ELECTROCHEMICAL WATER PROCESSING
The definition of these types of defining relationships will be left to Appendix G and H. 4.3 4.3.1
Parametric A n a l y s i s : F l o w - T h r o u g h Configuration Performance Analysis of Electro-dialytic Systems, Part I
4.3.1.1 First Approximation The following is a performance study and engineering design analysis of an electrodialysis (ED) water processing system. This first part is based upon simple, initial assumptions that will be described in some detail. As the modeling progresses in later sections, these assumptions will be modified to reflect more realistic situations. The intent of the ensuing analysis is the construction of a generalized body of mathematical relationships that can serve as a foundation for the design optimization of ED systems for a wide range of applications. The goals of this analysis are the development of mathematical relationships that will provide a means of rapidly estimating the output ppm of a water processing system of a particular design as a function of the many independent parameters, such as stack voltage, water flow rates a n d / o r quantity of water to be processed. These all are evaluated on the basis of the specifics of module dimensions and number of cells per stack, as well as in terms of the operating energy efficiency. A first step in this presentation is the establishment of basic physical constants, and the definition of terms employed in the analysis. We have tried to identify all important assumptions and simplifications made at this first stage in the parametric analysis. To establish a first approximation, or beginning analysis, some simplifying approaches are taken. Whenever
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
111
the reader has doubts about the validity or questions the realistic representation of these assessments, he will be able to trace these assumptions and resultant mathematics and perhaps make changes and modifications of his own. In those cases where some disagreements may arise or operational conditions be sufficiently different than those assumed here, identify whatever changes may be necessary to modify the parameters or equations in these analyses to suit a new set of conditions. 4.3.1.2
Design Assumptions
Numerous assumptions have been made in our initial treatment of the parameters of electrolytic systems for extracting dissolved solids. Most are realistic and quite close to actual conditions. Coulombic efficiency is treated as constant, and for the sake of simplicity, is given a numerical value of 100%. None of the assumptions are considered to significantly alter the nature of the basic processes described here. These initial assumptions are: 1. Flow of water through the unit is uniform without mixing or turbulence. 2. Transport of water is assumed to be negligible 3. Transport of H + and OH" are generally accounted for as a lowering of coulombic efficiency. 4. All processes are assumed to be Steady State. No start-up or transient analyses are performed here. 5. All the voltage across a cell is due solely to the ohmic losses through the electrolyte. 4.3.1.3
Equation Development
A series of mathematical expressions will be developed to describe the operation of an electrodialysis unit. We will proceed from rather fundamental concepts and then apply them to the specifics of an operating ED cell, and eventually to an array or cells connected together electrically in series.
112
ELECTROCHEMICAL WATER PROCESSING
We can accomplish this by identifying and solving each of the parameters of critical interest to us when assessing performance of different cell designs. 4.3.1.4
Resistance of a Cell
A single cell is defined as an operational assembly consisting of two electrodes, an anion and a cation membrane, with spacing and dimensions as shown in Figure 4.7 The cell area is defined as the useful or working area of electrodes and membranes. In the cell illustrated in Figure 4.7, the working cell area is L-W, where L is the length and W is the width of each electrode. Membrane areas are assumed equal to those of the electrodes. Because the membranes and electrodes are in series electrically, the effective working area of the cell is simply the area of one electrode or one membrane. Electrolyte, membranes and electrodes all contribute to the total electrical resistance. With the exception of the electronic resistance of the electrode structure themselves, all other resistance terms are result of ionic transport through solutions and membranes. The electrode resistance (resistance of the electrode material) is generally so much lower
Cation membrane
Anion membrane
Figure 4.7 ED cell dimensions.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
113
than any of the other contributors that it will be ignored as a factor in determining cell currents and voltages. Each cell component in the series circuit contributes its own electrical resistance to that of the complete cell. The sum of these resistances plus any opposing cell potentials are the important factors in determining power level required to operate the cell. One of the first steps in evaluating cell performance is the identification of all resistance terms. Total resistance, R^ of the cell is the sum of the following factors: RT = 2R1 + Rw + Rp + Rm. + Rm+
(4.11)
where: R.
i
R mR R
m+ w
Rr
= electrode-to-water interface resistance resistance through the anion membrane resistance through the cation membrane resistance through the waste water compartment resistance through the processed water compartment (4.12)
In this first analysis, we will ignore the contributions of membranes and interface resistance to the total as a first approximation, because the spacing and resistance of the low TDS-treated water are quite large in these first examples. Also, in cell designs operating with low waste water to processed water flow rate ratio, the resistance of the waste water compartments will be negligibly small. This is a consequence of the much higher concentration of dissolved substances in the waste water compartments (usually anywhere between 10:1 to 100:1), producing much lower electrical resistances than that of the low processed water concentrations.
114
ELECTROCHEMICAL WATER PROCESSING
Membrane resistance is generally much smaller than that of the processed water compartments. Even relatively high resistance membranes such as the SYBRON Ionac and Dupont NAFION types have specific resistivity much lower than the electrolytes at low concentrations. Since R «R , the maior contributor is R . Thus, as a simple first setup we let RT~R to approximate the electrical characteristics of the cell and, we get for the processed water compartment resistance, r , per unit area (per square inch), rp = (p-v—, r = 26xl0 4 • £ ohm-in 2 , v c[ppmj c
(4.13)
where p = spacing (distance between membranes) in the processed (low TDS) compartment. Membrane contributions to cell resistance will be taken into account in a second approximation approach further in this chapter. 4.3.2
Further Definition of Terms
4.3.2.1 Average Current Density A linear dependence of current density upon solute concentration is assumed. In other words, (p is constant over the whole range of operating concentrations for the cell. Refer to equations (4.6) and (4.7) for definitions of (p. If it is also assumed that the gradient of TDS within the processed water compartments along the length of the cell is uniform, the TDS is highest at the entrance with the input water, and decreases linearly along the length of the electrodes to its minimum value at the exit of the cell. Then the average electric current density, 1 , is ia = (io+i L )/2 amps/in 2 ,
(4.14)
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
115
However, as we shall later see, this is not necessarily the case in real situations. Because most dimensioning of mechanical parts and plumbing structures in the US are still in English units, the quantities are expressed accordingly in the subsequent computations. The assumption that TDS varies linearly with the path length is reasonable if there is no turbulent water flow through the cell. Certainly, for simplicity this is a desirable condition to assume in a first approximation. 4.3.2.2
Entrance & Exit Current Densities
The expressions for the two end current densities are simply, i0 = entrance current density VOltS ppm =E-c0^= amps/in 2 ,
and (4.15)
Equations (4.15) relate to a constant flow through a constant inter-electrode spacing cell with a length, L, as shown in Figure 4.7. 4.3.2.3
Water Flow Rate in Processed Chamber
Another important relationship to define in establishing the parametric analysis is the fluid speed, v, through the cell. A cell with a fixed dc voltage impressed across its electrodes will conduct more current at higher water flow rates because the emergent and the average water TDS will be higher than those of slower flow rates. The water speed in terms of distance per unit time may be expressed in terms of volume of water flow rate and cell geometry.
116
ELECTROCHEMICAL WATER PROCESSING
Specific relationships can be derived to express the volumetric flow in terms of fluid speed. One form of this relationship in the English system of units, which will be employed here, is described as follows. Because 1 gallon has a volume of about 231 cubic inches, the speed of a unit volume of water flowing through a cell can be determined by v =F
231 (W-p)
in/min
(4.16)
where W = width of the cell, and p = spacing between membranes as shown in Figure 4.7 4.3.2.4
Solute Concentration Along the Length of the Cell
Now, we can estimate the TDS, cx, within the processed chambers at any point, x, along the flow path. The equation is derived as follows. In Figure 4.8, we show the volume of water that is passing through the cell between the cation and anion membranes. The direction of water flow is in the x-direction, and electric (ionic) current flow is perpendicular to the x direction as shown. Figure 4.8 illustrates that the net change in solute concentration along the length of a cell is due to the extraction by electro-dialytic migration from both faces all along the length of the processed water cell section. Solute ion extraction
Flow in
Figure 4.8 Section of processed water compartment.
Flow out
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
117
Let us now examine the manner in which the quantity of solutes changes as the stream of solution progresses down the length of the cell. The amount of solute, Qf, that passes into (enters) any section, p-W-dx, from the more concentrated upstream regions of the cell whose cross section is W-p, and at some distance, x, from the entrance, and over a time interval, dt, can be expressed as Q f =W-p-v-/?-c x -if
(4.17)
The multiplier, ß, in Equation 4.17 is the density of the solution flowing through the cell. Even though ß will change with either time or distance down the cell length, it will be treated as constant in these analyses. Low concentrations of solutes encountered in most water processing tasks make the densities of the solutions about equal to that of pure water. When making more accurate performance estimates for seawater desalinators, one may wish to account for the higher densities and for the change in density along the cell length. However, it would appear to be an unnecessary complication in the mathematics for a first performance approximation. The quantity of solute change, dQ f , or lost from the flow stream is now dQ f =W-p-v-/?-dc x -d£,
(4.18)
or, more appropriately, (à&) =W-p-v-ß-dcx \ dt Jt
in2- —-^-ppm3 min in
rr
(4.19)
If we stay with the English system, the terms above are expressed dimensionally in units of p v c
in in/min ppm
118
ELECTROCHEMICAL WATER PROCESSING
W Q
in in 3 -ppm/min
Now, we must examine the rate of which the solutes are leaving that same region or volume of cell by mechanism of electrodialysis. Equation (4.19) is now related to the rate of which the dissolved solids are leaving the stream via dialysis through the membrane walls. The current flow, Ix, through the element of area W • dx is I x = i x - W - d x —¿--in-in (4 20) in If a constant, X, that is a conversion factor for electric charge to quantity of solids transported is introduced then Equation 4.3.8 may be rewritten later in the form of charge transfer. And, the rate with which dissolved solids, (dQ/dt) d , are removed by the electrodialysis process from the region volume W-p-dx, whose length in the flow direction is dx, and whose area is W • dx, is represented by — 1 =i x -77-W-dx-A g m / u n i t t i m e , V dt Jd
(4.21)
The constant, X, is in units of grams per unit time per amp. The term, n, is the coulombic efficiency of solute transfer through the membranes. Referring again to the Faraday equivalent, and using the average gram molecular weight, GMW, of the solids that we identified earlier as 60 gm, we can assign a numerical value to X. About 60 grams of solute should be displaced by 26.8 amp-hr or 1 amp hr should produce about 2.3 gms at 100% coulombic efficiency. Dividing the 2.3 g m / h r figure by 60 to convert from hours to minutes, the conversion factor becomes A= 0.038gms/amp - min
(4.22)
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
119
In order to rapidly arrive at quantitative solutions to the mathematical relationships of this first approximation, some major assumptions made so far are: 1. Non turbulent flow 2. Equivalent conductance of solutes remain essentially constant with concentration 3. Equivalent weights of solutes is averaged at 60 The equations can be kept more general and in shorter form by retaining the symbols instead of numerical substitutions for some quantities such (p and X. Returning to the two rates of change of quantity of solutes as represented by Equations (4.19) and (4.21), we must now equate the removal rate of dissolved substances that enter the region in question to the rate of which the solutes are entering the region, p-W-dx, in order for steady state conditions to be established. To solve for cx in the cell, Equation (4.19) must be set equal to the negative of Equation (4.21).
ÉQ)=-\*Q.\ dt i,
(4.23)
\ dt
In order to equate and evaluate the two expressions, it is necessary to put them into the same units. If in Equation (4.19) ß is in units of grams/in 3 , and if the right side of Equation (4.18) is multiplied by 10~6to convert concentration from ppm to fractional ratio, the two relationships in question can be equated. Equating, we obtain W-p-v-dcx-ß-10-6=ix-i]-W-dx-A where cx continues to be expressed in ppm.
(4.24)
120
ELECTROCHEMICAL WATER PROCESSING
We now want to put the variable, i , in terms of the variable, cx, which we wish to solve. If the applied voltage, E, is constant all along the cell length the following expression becomes simple to solve exactly. Substituting for ix in the above net expression, as was shown in Equations (4.15), we have Ec
(4.25)
and
X
p-v-dc x -ß-l(r 6 =
77-A-dx.
(4.26)
Transposing terms, and solving the differential equation, dc x
-E • r¡- X
v
. i
ln(c x ) =
(4.27)
(pp2v-ß
cx
EriÀx
=
+ K(const), or
2
(p-p -v-ß
(4.28)
cx =K-e" M x , and the constant, K, is evaluated as co from the limiting condition that at x = 0, c = c . Then c finally becomes '
X
O
J
X
c„e
E-ifA-x p2vß
(4.29)
The total current, I, passing t h r o u g h the cell is 1= W- \ix- dx. Substituting from Equations 4.25 a n d 4.28 for i a n d cx a n d performing the integration, w e get l
1=
(P-P
■\e
E-1J-2.-X
^Vßdx
(4.30)
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
121
Equation (4.30) has the form L
I = A-¡e~Bxdx,
(4.31)
0
and when the integration is carried out, has the final form I = -~[e-BL-l]
(4.32)
By re-substituting the polynomials for A and B, the expression for I is W-v-
ß-p-c0 TJÀ,
(4.33)
For many initial estimations of performance, we will let ß = 16.4 gms/in 3 for dilute solution density, and we will use the previously estimated value for À, of 0.038 gms/amp-min. 4.3.2.5
Figure of Merit
Introducing the idea of a coefficient of performance—or figure of merit—facilitates performance comparisons of operating ED systems. Among the characteristics of an ED system such as size, life and cost, perhaps the most important parameter is that of the "effectiveness" of operation in terms of amount of power required to remove a given quantity of dissolved solids per unit time from the input water stream. Let us define a figure of merit, FM, simply as ™ . Quantity removed unit time FM = Power Input _ gallons per minute x ppm change input watts = F-(C0-CL) = F-(C0-CL) power I•E
(4 34)
122
ELECTROCHEMICAL WATER PROCESSING
Such a relationship enables us to compare various design trade-off in an even more meaningful fashion. 4.3.3
Numerical Evaluation Program
Numerous and popular personal computer software programs can find the solution of the above equations in a simultaneous manner. A convenient means of solving a series of simultaneous equations is afforded by a basic program called FORMULA ONE published by Alloy Computer Products, Inc., and MathCad by Mathsoft, Inc. Computations made by means of these programs have been rapid and quite straightforward. All of the relationships developed so far are sufficient to perform a first approximation of the performance of a flow-through type of ED water processor. The system of simultaneous relationships have been collected together and conveniently listed below as Equations 4.35. r
*
cx
= 26-10 4 -^-lE-]-x-2.8-W-3/p2-v)
y
V
= c0-e = F-231/W-p
h
= E-c o /26-10 4 -p
h
=
I
»
E-cL/26-104-p c0-W-v-ß-p
C
L
h
= ia-L-W
Q Q
= 10-/.-/
= F-(c0-cL) power = I-E
1-
e
ErjXL (f>-v2vß
(4.35)
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
123
For a series of examples and the implementation of numerical computations based upon the set of equations in (4.35), refer to Chapter 4, Section 4.4 and Appendix G. 4.3.3.1
Second Approximation, Part II
In the preceding analysis, a number of assumptions were made that do not entirely represent actual operating conditions or take into account the fact that both current density and coulombic efficiency vary along the length of the cells in the direction of water flow. Examples of the manner in which the current density varies with distance along the fluid flow path are shown in Figures 4.9 through 4.14. These are graphs showing the manner in which both the concentration, TDS, of solutes and electric current density vary along the length of a cell as flow rate, F, and voltage, E, are changed. Since the current density is directly
Figure 4.9 Single cell performance factors. For F = 0.10 gal/min, E = 10 volts.
124
ELECTROCHEMICAL WATER PROCESSING
proportional to the TDS concentration, it is seen to vary in shape in the same manner as concentration. Figures 4.9 and 4.10 clearly show how both current density and TDS are non-linear with distance at 10 volts as cell potential. If the cell potential is reduced to 2 volts, the curves become more straight lines. Similarly, Figures 4.11 and 4.12 show how the shape of the curves for current density and concentration versus distance along the cell length is less non-linear at the higher flow rate of 0.50 gal/min, and becomes even more linear at the lower cell potential of 2 volts. These charts show the differences in the two curves if the flow rate is increased from 0.10 to 0.50 gal/min at the two voltage values. The last two graphs, Figures 4.13 and 4.14, show the relative effects of increasing cell potential to 20 volts at 0.50 gal/min, and changing to an even higher flow rate of 1.0 gal/min at 10 volts potential.
Figure 4.10 Single cell performance factors. For F = 0.10 gal/min, E = 2 volts.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
125
The graphs show that as impressed voltage is increased or asflowrate is decreased for any particular cell configuration, the curves become more pronouncedly non-linear.
Figure 4.11 Single cell performance factors. For F = 0.50 gal/min, E = 10 volts.
Figure 4.12 Single cell performance factors. For F = 0.50 gal/min, E = 2 volts.
126
ELECTROCHEMICAL WATER PROCESSING
Figure 4.13 Single cell performance factors. For 0.5 gal/min, E = 20 volts.
Figure 4.14 Single cell performance factors. For 1 gal/min, E = 10 volts.
Averaging the entrance and exit current densities are not reasonable approximations.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
4.3.4
127
Multiple Cells in Parallel
Different characteristics of performance can be achieved by placing more than one cell in either series or parallel connection hydraulically. We will now proceed to evaluate the advantages and limitations of such design variations. 4.3.5
General Characteristics
The amount of solids removed from a stream of water per unit time flowing through a cell is solely a function of the following parameter: 4.3.6
Total Electric Current through the Electrodes and Membranes
For constant voltage operation, the change in concentration in the water stream between input and output values is also dependent upon the flow rate through the cell. At constant voltage, if the flow rate is lower, the net change in ppm is greater because the water spends more time in the processing chamber. The total quantity removed per unit of time is constant and directly proportional to the total electric current. Let us now examine some of the trade-off factors between design parameters in the construction of a single cell unit. The design goal is to provide for the needed dissolved solids removal rate at minimum capital cost and minimum power cost, while maintaining an electric current density below some prescribed level. Referring to the set of Equations (4.35) developed so far, we can now proceed with an exploration of the parameter interdependencies that lead to design optimization. We need to view both the flexibility and constraints associated with the basic cell operation. A specific set of design criteria
128
ELECTROCHEMICAL WATER PROCESSING
serves as an initial example to demonstrate a performance analysis approach. • The quantity of dissolved solids to be removed per unit of time determines the total electric current required in the cell, regardless of the length and width of a cell and the flow rate of water. • The procedure in establishing the design parameters is as follows; Let us define a set of performance requirements. For example: a. Total volumetric flow rate = 0.50 gal./min. b. Input TDS = 200 ppm c. Desired output TDS = 2.0 ppm This defines the set of criteria that must be met by the unit. For further details on computer formatting, see Appendix G. However, there are numerous other considerations to be taken into account before hardware design can be finalized. Some of these considerations are: • • • •
Maximum allowable current density Materials and component costs Aspect ratio of packaging Volt-amp ratio
A file (see Appendix G) has been set up to compute the results of various design inputs. If we set the above criteria as input values and set some maximum value of current density to between 0.05 and 0.20 amp/in 2 , along with a cell width of 6 inches, we can evaluate the voltage, length, and power requirements for a single cell. We let F be such that the cell will produce water at 2 ppm from 200 ppm entrance at 0.50 gal/min flow volume. The removal rate of solutes at the 0.5 gal/min and 198 ppm change is 99 gal-ppm/min.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
129
The Table 4.4 below illustrates the range of dependent variable values obtained. As the current density is raised from 0.05 to 0.20 amps/in 2 the cell potential must be increased accordingly and the length of cell is less to achieve the removal of 198 ppm from the water flow-through. We see that the only changes are the length of the cell and the voltage needed to extract solutes at the 99 gal-ppm/ min rate. As the input current is increased, the power level increases accordingly because the cell length had been reduced proportionately with the consequent increase in cell internal resistance, necessitating a rise in voltage to maintain the ppm difference at input and output. Note that the total current, I, is constant. Thus, it is evident that in order to increase "power efficiency" for any removal rate, keeping all other parameters constant, current density should be reduced with the consequent increase in cell length. Now, let us examine a multiple cell arrangement with the same general parameters of spacing, cell widths, 0.5 gal/min flow, and input-output concentrations. Another computer file described in Appendix G addresses the mathematics relating to a stacked series of n cells. Again, for purposes of illustration, let us set the number of cells in the stack at an arbitrary figure of n=10. The Table 4.4 Sample computation for a single cell. E
L
I
Power
0.05 A/in 2
13 volts
92 in.
9.9 amps
128 watts
0.10
26
45.9
9.9
256
0.20
52
23
9.9
513
i
0
130
ELECTROCHEMICAL WATER PROCESSING
Table 4.5 Sample computation for a 10 cell array. i
E
L
I
Power
16.3 volts
15.3 in.
0.99 amps
160 watts
o
0.05 A/in
2
0.10
32.5
7.7
0.99
320
0.20
65
3.8
0.99
641
data calculated by the parametric analysis are given in the Table 4.5 above. As in the case of the single cell, the only parameters that have changed in moving to higher current densities are the stack voltage and stack cell length. Some power consumption sacrifice is made in stacking the cells, but a gain is achieved in compactness of design. The question now is why does one wish to stack up these ED cells at all? The resulting multi-cell configuration has little effect on performance. The main benefits of a multiple cell design over a single cell is more practical module dimensions of length and width, and the avoidance of very high currents and low voltages if the cells are connected in series electrically. Lower current power supplies along with more practical configurations and system packaging will also tend to lower capital costs of manufacture. The configuration of a stacked module versus a thin and rather long single cell is undoubtedly a more practical design for most applications. 4.3.7
Coulombic Efficiency Variation
So far, coulombic efficiency has been treated as constant throughout the range of the operation of ED cells and at all TDS values and current densities. In actuality, the coulombic efficiency, r\c, does, indeed, depend upon many factors such as concentration availability of the specific ions, current density, pH range, membrane properties and even the characteristics of the ions.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
131
The probability that any one ion in solution with other ionic species will be the charge carrier across a membrane is proportional to its mobility and availability (or concentration), as compared to that of other similarly charged ionic species. Another factor influencing the selectivity of one ion over another in the transfer process is their relative mobility. We can show what general form the relationships would probably take. Taking the transport process for cations, and more specifically, for sodium ions as an example of how the development of a relationship between population density of ions and coulombic efficiency may proceed, we will define the following variables. QN QH V /i+ t+
= = = =
quantity of Na + ions quantity of H + ions volume of electrolyte solution ion mobility of cation transport number ratio for cation through membrance
The rate at which a specific cation is leaving an electrolyte volume, V, is directly proportional to the concentration ratio of that ion to those of all other available (+) ions in the volume. The dependency is further modified by the relative values of the mobility of each ion and their relative transport numbers through the membrane. To abbreviate the necessary mathematical characters that will be manipulated, the constants, a and b, are given as composites, or products of the mobility and transport number. In other words, a = ßjN-tN b = fjH-tH
and (4.36)
where the constants, jo, and t, are mobilities and transport numbers for sodium and hydrogen ions, respectively.
132
ELECTROCHEMICAL WATER PROCESSING
Based upon the probability of transfer of specific ions, the rates can be represented as follows: aQ ^^-i-A-, " , , and dt (aQN+bQH) bQ ^-=-i-A-, " x dt (aQN+bQH)
(4.37)
Achieving the solution of these equations can be made simple for the sake of illustration by assuming that the concentration of hydrogen ions in solution is constant. This assumption is not entirely unreasonable because the H + ion concentration is very low due to ionization of mid pH range water, and reasonably constant because they are being replenished by continuous ionization of water as dialysis proceeds. Treating Q H as constant, we solve the first differential equation for Q N by direct integration in the manner shown below. aQ
N
^
+
bQ
N
^=-i-AQ
N
,
or multiplying through by dt, and dividing by b • Q H • dQ N we get dQw bQ H
+
¿ Q N
=
QN
.jA.d bQ H
t
(4.38)
Integration, and re-arrangement of terms yields •Q N + l n Q N = - ^ ¿ — t + K,or bQ H ^ ^ bQ H i-At
QN
b H
QN-e °
=Ke"
bQH
(4.39)
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
133
Boundary conditions are such that when t=0, Q N is some maximum value, N. And K = N • e1*2", thus the equation for Q N becomes N-Q N
(4.40)
Ut
Q N =N-e b Q « -e"bQH Differentiating the last expression, with respect to t to obtain the rate of change of sodium ions with time, N-Q N
J_C[QN_ = gbQ H
N
dt
U-t
.g bQH dQ f dt bQ H +
iX bQ H
moving terms to solve for dQ N /dt .-
dQ N
dt
. .. 1
N
N-Q N
1A
bQH
e
bQfl
,
.
l
bQH
e
Ut
• e bQH
N-Q N Ut b< 2 H . e bQ H
(4.41)
We are primarily interested at this juncture in seeing how the coulombic efficiency depends upon the variables at any time, t. The coulombic efficiency, r¡c, is defined as the ratio of the rate of equivalent ion transfer to electric current flow over, and may be represented as dQ > 7 77c
a
dt
(4.42)
Without pursuing the mathematical manipulations further, one can see that the form taken by the expression for r/c is that of an exponential with Q N appearing in the exponent.
134
ELECTROCHEMICAL WATER PROCESSING
As an approximation, and as a first compensation for the variation in r¡c, we will consider only the effect of ion concentration. In general, as the concentration or availability of specific ions to be transported across membranes becomes lower, the coulombic efficiency for transporting that specific ion will diminish. The decrease in 77c is simply due to the fact that the competition of H + and OH" ions becomes greater because their availability as charge carriers becomes proportionately greater than the less populous ions. Hence, the functional dependence of r¡c upon concentration, cx, at some point x within a cell must be determined. A simplified, but useful, form of the functional dependence that could be taken would be the exponential relationship i% = (l-e^),
(4.43)
where \]/ has a value such that the coulombic efficiency is nearly unity when cx was at some level where the competition for transport by other ions was negligibly small. Such values of cx can be determined experimentally. To define the function completely, at least one empirical data point is needed. Some simple measurements should be made for each of the membranes to be employed at more than one concentration of dissolved substances. We have graphed Equation (4.43) to show how coulombic efficiency varies with concentration for different values of the constant, \\f. Empirical data provides the information needed to quantify \\f. To properly account for the dependency of r¡c upon cx it is necessary to insert the expression for r¡c into the preceding formulas for cx and ix as seen in Equations (4.31) and (4.35). Because of the additional variable terms, the resultant expression becomes more complex mathematically when accounting for a non-constant r¡c. For example, the solute concentration takes the form
ANALYSIS «fe MODELING ELECTRODIALYSIS SYSTEMS
pvdcx/? =
Ec
X
r¡- À- dx
135
(4.44)
substituting for r/c from the equation rç = ( l - e ^ ) ,
(4.45)
E-c,
(4.46)
and we get p-v-dcx-ß:
(l-e-^)-A-dx,
Rearranging Equation (4.46), and putting it into a form for solution of c , dc v cx(l-e^)
-El •dx
(4.47)
A graphical approach to an approximation of solute concentration may be taken by simply assuming values of \j/, and multiplying the concentration step-by-step along the cell length by the adjusted values of r¡c. A program (anal-1. wk3) was devised to accomplish this series of calculations to explore the effect upon cell performance by a varying coulombic efficiency. The next four graphs show the dependence of r¡c upon TDS for two different values, 0.01 and 0.10, of the coefficient \|/, along with their effect upon the variation of cx along the length of the cell. Figure 4.15 and Figure 4.16 show both coulombic efficiency and TDS data for \j/=0.01. Figure 4.16 shows that the manner in which the TDS varies with distance is more pronounced by assuming a constant (r¡c, represented by the letter, J, in these LOTUS plotted graphs) than it does with a variable r¡c and similarly Figures 4.17 and 4.18 for y=0.10. The TDS change calculations with distance along the cell with an assumption of either variable or constant r¡c.
136
ELECTROCHEMICAL WATER PROCESSING
Figure 4.15 Coulombic efficiency versus solute concentration. y/= 0.01.
Figure 4.16 TDS versus distance.
y/=0M.
The value of y must be determined prior to more accurate evaluation of coulombic efficiencies at lower TDS. This can be simply accomplished by performing a series of measurements of sodium ion transport numbers with the specific
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS Exponential approximation (1-exp(-cx*p)) for P = 0.1
1.2
s
137
1
x
g- 0 - 8 £ 0.6 | 0.4 ° 0.2 0
0
50
100
150
200
250
Concentration PPM Figure 4.17 Coulombic efficiency versus solute concentration. \f/= 0.10.
Figure 4.18 TDS versus distance. \¡/=Q.\Q.
cation membrane needed. These measurements should be performed at different concentrations of sodium salt on the transfer source side. Experiments to make these measurements are straightforward to implement.
138
ELECTROCHEMICAL WATER PROCESSING
4.3.8
Further Considerations
All of the preceding analyses have been performed with many assumptions in mind, and by ignoring some important factors. In our continuing development of design mathematics, we will need to account for many of these factors. These include: a. b. c. d. e. f. g.
Membrane resistance Resistance of the waste water compartments Electrode potentials and polarization effects Concentration potentials across membranes Variable coulombic efficiencies Heat dissipation and effects on cell resistance Electrical losses by conduction through common water manifolds
In the next section we will treat those systems with either static solutions in waste and processing compartments, or with a limited volume of fluids in continuous re-circulation.
4.4
Flow-Through Design Exercises
In this section, we will go through a few design variations with the mathematical developments of Section 4.3. All of the following exercises are for a system in which the water passes through the electrode assembly only once. First, let us quickly review the overall status of the analysis at this point in its development. The design types based upon these assumptions and equations will be called Designs-A. These are the basic assumptions made so far. 1. Uniform, non-turbulent flow of processed water through cells 2. One pass through cells for total processing 3. Constant equivalent conductance of solutions—hence resistance is directly proportional to concentration
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
139
4. No losses due to diffusion or fluid interconnections 5. No opposing electrical potentials 6. All electrical resistance is due only to processed water solutions 7. Coulombic efficiency, n, is constant The last assumption is maintained here even though some thought was devoted to exploring variable, current density dependent functions for n. Since all ED extraction of dissolved solids takes place in one flow-through operation, the equations employed at this point for a design exercise are those developed in Section 4.3. The salient parameters for this design approach are listed below. Through our approach to the design exercise, we will determine which parameters are independent and which are treated as dependent variables. For additional detailed performance estimates, see Appendix G. The variables and constants employed alomg with their abbreviations are defined in Table 4.6. Some results of these computations are given below as examples of the type of performance expected from a cell operating within the envelope of the above assumptions. The important issue to resolve at this time is the establishment of a methodology to arrive at the specifics of design for any particular application. In other words, how does one go about designing an assembly of electrodes and membranes along with the needed power supply requirements to meet the needs of an application, and in a reasonably optimized fashion? The first step is to define the performance needs in terms of input TDS, desired output TDS, and flow rate of water to be processed—or the quantity of processed water output required per unit time. Immediately after that determination, it is necessary to define certain operating limits of the cell components, such as maximum allowable current density, practical maximum length of the electrodes, number of
140
ELECTROCHEMICAL WATER PROCESSING Table 4.6 Abbreviations for the various parameters. Definition
Dimensions
io
entrance current density
amps/in 2
iL
exit current density
amps/in 2
ri
coulombic efficiency
%/100
P
cell spacing
in
c
o
entering TDS
ppm
E
cell potential
volts
V
flow speed
in /min
F
volume now rate
gal/min
C
exit TDS
ppm
L
cell length
in
W
electrode width
in
I
total current
amps
power
power input
watts
Quantity
L
cells in a series stack, and acceptable physical dimensions of the stack module(s) for a specific application. In general, the practical constraints placed upon the hardware design must be clearly identified. For illustrative purposes, we assign the somewhat unrealistic, but convenient value of 100% for r|, along with values for some of the other cell parameters. Now, we can proceed with a sample design. 4.4.1
Exercise #1
Let us take a single cell structure, and calculate the cell parameters necessary to produce a water treatment capacity of 0.50 gallons per minute flow rate (see Appendix G).
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
141
We also wish to have a 10:1 reduction ratio between the input and output water TDS. The maximum sustained current density for extended life of electrodes is about 0.10 amps/sq. in. The first step in estimating the design configuration is the determination of the cell area needed to accomplish this task. When we insert the values of input TDS, co, and output TDS, cL, to solve for cell width and length, these physical dimensions of the cell will determine the ratio cjch at a specific flow rate independent of the magnitude of the concentration of salts in the input water, if the voltage applied to the cell is kept constant. Only the power input requirement will be affected. A more practical restriction for cell operation is to limit the current density. If the maximum current density, i , is made constant at a specific value of perhaps 0.10 amp/sq, then the ratio cJcL is linearly dependent upon the total cell area. If we let the input TDS = 200 ppm, then the output TDS is 20 ppm. The data computes to the following values for cell operation: co = 200 ppm cL = 20 ppm Ae = 730 sq in
Input Power = 320 watts F = 0.50 gal/min I = 10 amps
To determine the voltage necessary from an external power supply to the cell, it is necessary to decide upon cell spacing, p, (distance from membrane to membrane and membrane to electrode). We will assume all spacing to be the same, and for this exercise, we will let p = 0.25 in. Then the dc power supply potential, E, is 32 volts, and the power is 320 watts. Further examination of some of these parameters shows that if either the spacing or maximum input current were to be changed, the power required and the power supply voltage would also change. For example, if the spacing were reduced to 0.12 in., the power would decrease to 160 watts, and the driving cell potential would then need to
142
ELECTROCHEMICAL WATER PROCESSING
be only 16 volts instead of the 32 volts to provide 10 amps through the cell. These changes all occur because of the lower cell internal resistance at the smaller spacing. However, the engineering trade-off in this last instance is the greater difficulty in fabricating and controlling uniform water flow as cell spacing is made smaller. Lower operating cost for the cell in terms of electric energy per processed gallon may also entail a lower degree of reliability of cell operation. Another interesting trade-off is between current density, operating cost and equipment size. If the maximum current density, io, is lowered, for example, to 0.05 a m p / s q in, the power is reduced from 320 watts to 160 watts for the 0.25 in. spacing cell. In essence, the energy efficiency is doubled, and the operating life of electrodes is extended, but the cell becomes twice the size and twice the cost of the materials. One must decide what set of values provides the best overall cell performance and lowest total cost. To further illustrate the various combinations of parameter values in the design and operation of single cells, the following additional short examples are offered. Again, the following are some results obtainable from the system of Equations 4.35, when other values are selected for cell geometry, current density and flow rates. There is a wide range of choices in assigning dependent and independent variables. 4.4.2
Exercise #2
For example, if we select cell dimensions and electric current densities as the independent values 4.4.2.1 Predetermined Independent Variables L = 100 in. W = 10in. i o = 0.10 amp/in 2
r¡ = 1.0
p = 0.25 co = 200ppm F = 1.0 gal./min.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
143
Then, we may solve for these variables as dependent ones, and their values become, I = 19.8 amps E = 32.5 volts
Power = 644 watts cL = 41 ppm
Another calculated term can be introduced here that we will refer to as the Figure of Merit, FM. It is defined as FM = F/(co/cL). FM is a measure of the quantity of material removed from the water stream per unit time for the power input required. FM is in units of gal-ppm/watt-min., and it enables us to conveniently assess and compare the effectiveness of one design to another. The figure of Merit for the case above is FM = 0.246 gal-ppm/watt-min Cell voltage, E, and entrance current density, io, can be interchanged as dependent-independent variables. If it is desirable to establish a maximum current density because of electrode life considerations, then io is chosen as independent. Note: The value 0.10 amp/in 2 was selected from the data developed in laboratory studies with carbon electrode structures snowing carbon electrode erosion rate versus current density in dilute solutions. If the current density exceeded 0.10 amps/in 2 for most of the carbon types employed in these tests, the life of electrodes began to diminish rapidly. If, on the other hand, one limits the operating voltages to some maximum value for safety reasons, then E may become the independent selection. Similarly for all the other parameters of the cell, one may select and make any combination of the parameter independent as long as the conditions of sufficient independent equations matches the number of parameters left as dependent ones (see Appendix G). In the above solutions, we see that the potential necessary to provide a maximum current density of 0.10 amp/in 2
144
ELECTROCHEMICAL WATER PROCESSING
is 32.5 volts, and the emerging solute concentration in the processed water chamber is 20 or more ppm. If the ppm level of the input water were to be either increased or decreased, only the operating voltage would be affected either upward or downward, respectively, and the ratio of the ppm of the input water to that of the output water would remain constant. 4.4.3
Exercise #3
If we wish to change the ratio of input to output ppm, it is necessary either to change the maximum permissible value of current density, io, or the cell geometry. As another example, if the length of the cell is shortened to 50 inches, and all other independent parameters of the above circumstances are kept the same, these are the operating results. Calculated Values iL = 0.021 amp/in 2 v = 46.2 in/min E = 32.5 volts I = 9.9 amps
r x = 445 ohm-in. cx = 146 gms c* = 41.4 ppm power = 322 watts
Even though the emerging processed water from the 50 inch long cell is at a measurably higher TDS level, the power level, total current and operating voltage are all essentially unaltered. There is no sacrifice in the figure of merit with the shortened cell length. The current density at a point 50 inches down the length of a 100 inch long cell is 0.021 amps/in 2 , the same as the current density, cL, at the exit of the 50 inch long cell. In other words, the processed water has no knowledge at any point in its path of the total length of the cell. Valuable design exercises such as the one above can be performed rapidly to explore the engineering, cost and performance trade-off possibilities.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
145
We will see later that the most effective way to increase the FM of operation is by the reduction of internal cell resistance. Due to overcoming the ohmic loss through a cell, the only manner available to increase the FM at this point in the presentation is by the reduction of electrical path length through the cell, or smaller spacing, p. Reducing the spacing will result in improvements in FM because less voltage will be required to conduct the same current through the cell. 4.4.4
TDS Removal Rate Capacity
A useful quantity describing the overall performance of an ED unit is the rate with which the dissolved solids are removed as a function of other independent variables. A meaningful numerical dimension for this rate, C, is in terms of gallons-ppm per minute. To obtain the total weight removed per unit time, multiply C by the density of the water solution. With any given set of fixed design factors, such as cell dimensions and operating current, the quantity of dissolved solids removed per unit time will be constant. However, as the flow rate is increased or decreased through the unit, the change in ppm, (or TDS), of the incoming to outgoing water will vary. Thus, the importance of C as a factor that characterizes the unit under all flow conditions. The removal rate, C, is defined simply as C- F-(c0-cL)
gallons-ppm/min.
(4.48)
If we look at the computations performed above, the values for removal rates are For L = 100 in., For L = 50 in.,
C = 96 gal-ppm/min, and C = 79 gal-ppm/min
146
4.4.5
ELECTROCHEMICAL WATER PROCESSING
Stacked Cell Configuration
We can now take the next analytical step to easily determine performance for units (modules) in which a number of cells are stacked in an array. The most meaningful array configuration is a number of cells through which the water flow is in parallel, and that are connected electrically in series. This has been developed in more detail as Case-A.wk3 in Appendix G.
4.4.6
Expanded Analysis
The expanded analysis shows that the number of cells, n, in series modified the final performance figures. Total voltage, for example, across the stack of n cells in parallel is nE. If the total water flow through the stack is F, then the removal capacity is still C. The terms employed in these expanded equations are listed in Table 4.7. Table 4.7 Operating parameters for designs-A. Dimensions
Symbol
Description
V
in/min
Water Speed
F
gal/min
Total Flow Rate
W
in
Cell Width
P
in
Cell Spacing
i
a m p / s q in
Exit Current Density
E
volts
Cell Volts
c
ppm
TDS at distance x
260000 ohm-in/ppm
Resistivity factor
X
X
Coulombic Efficiency
il X
in
Distance from entrance along cell
c
ppm
Input TDS
0
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
147
Table 4.7 (cont.) Operating parameters for designs-A. Dimensions
Symbol
Description
I
amps
Total Stack Current
i
amps/sq in
Input Current Density
watts
Total DC Electrical Power Input
0
Power
Number of Cells
n A A
sqin e
Area per Electrode Area per Membrane
m
Size
cu in
Module Volume
nE
volts
Stack or Module Volts
Thickness
in
Stack Thickness
CompCost
$
Electrode & Membrane Cost
FM
gal/watt-min
Figure of Merit Coefficient of Performance
COP EnergyGal
wh/gal
Energy per Processed Gallon
We can now pursue another example of performance based upon the general conditions stipulated above for single and multiple cells. Costs of electrode and membrane components are treated in Appendix G. Maintaining the same values as in the first example, a stack of n cells in series electrically, but with parallel water flow through all the cells, will produce n-times as much processed water for the same current densities as a single cell of the same length, L. Taking the cell design of Exercise #1, n such cells will perform as follows. co = 200 ppm cL = 20 ppm Ae = 730 sq in
Input Power = nE x I watts nF = 0.50 x n gal/min I = 10 amps
148
ELECTROCHEMICAL WATER PROCESSING
Thus, the total voltage impressed across the stack is nE, and the power is greater proportionately. If the number, n, of cells is 10, then the quantity of processed water flowing through the stack would be 10 x 0.50 = 5 gallons per minute; the stack voltage is 320 volts and the power supplied is 3200 watts. The Figure of Merit would be unaltered. The same performance in terms of 5 gallons per minute can be achieved by placing 10 such cells in parallel electrically. Then the power supply would have to provide the same 3200 watts in the form of 100 amps at 32 volts. The trade-off in such design considerations is strictly a matter of the economics of electrical characteristics most convenient for the user in terms of higher voltages and lower current versus the opposite. The economic considerations concern dc power supply costs for different ranges of volt-amp relationships, as well as the increase in electrode costs for a parallel electrical construction. In both single cell, and in a series array of cells, the electrode area (2 per stack) is the same. If cells are in parallel electrically, there would need to be (n+1) electrodes for the necessary electrical connections. With electrically parallel stacks, there are a correspondingly greater number of waste water compartments, (n+1), in which electrolysis is taking place versus just 2 for a series stack. The larger number of waste water compartments would also give rise to more hydrogen and oxygen generation by electrolysis, accompanied by a correspondingly greater stack voltage requirement. There are many possible combinations of series and parallel designs, such as placing two or more series stacks in parallel hydraulically to lessen the hydraulic impedance to water flow. In general, it is desirable to make the cell spacing and width large and the cell length small to reduce the pressure needed for water flow. However, in doing so, the necessary stack becomes larger, and the power required is increased, consequently lowering of the Figure of Merit.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
149
4.5 Batch Process Analysis: Re-Circulating or Static Water Processing System In some applications, it is desirable to have a water purification system not function in a "once through" manner. Examples of such requirements are those cases where only a small or limited quantity of processed water is required over an extended period of time, and the need for immediate and continuous peak quantities of water delivery are absent. In these instances, a much more economical design may be that of a re-circulated water system with a processed water storage tank, or reservoir. In these cases, the water processor unit, the ED stack, can be made much smaller in size and with significantly lower costs in parts and materials. Figure 4.19 is a schematic illustration of such a configuration in which both the waste and processed water are circulated around through the ED module and back into the reservoirs. An analysis of the performance of such a design can be made on the basis of a simplifying assumption that the water circulates many times in any one processing cycle,
Waste water reservoir Volume = V„
Processed water reservoir Module
0
Pump
Figure 4.19 Constant volume system batch processing.
Volume = Vn
_© Pump
150
ELECTROCHEMICAL WATER PROCESSING
and that complete mixing of the water takes place continuously in the reservoirs. In that manner, the TDS of each of the two quantities of water throughout the module and reservoirs is uniform and constant at any moment in time. In a fashion similar to the preceding computations, we will first identify the system parameters and the system constants, and then establish their mathematical relationship. The total resistance, R, of a stack of n cells is (ignoring the membrane resistance for the present), R = R(waste water) + R(processed water) = R w + Rp
(4.49)
If the TDS is the same all along the length of the cells at any time, t, the rate with which the ionic species are being transported across the membranes is represented by ^=i-n-A-W-L-77 dt
(4.50)
where the terms are identified as, i = current density, amps/in 2 , rj - coulombic efficiency, W = width of cells, in., L = length of cells, in., À = 0.038 gm/amp-min., conversion factor, and n = number of cells in series electrically In order to compute the dependence of Q upon time, the current density, i, must be represented in terms of Q. Electric current density, i, in a stack is i
=
* = ^ = -**-. R n-R R w +R p
(4.51)
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
151
As a means of simplifying the analyses at this time, we will let the thickness of the waste water and processed water compartments be the same. Also, we will approximate the ratio of the number of processed water to waste water chambers to be unity, i.e., there are the equal numbers of compartment types. In actuality, there are (n+1) waste water compartments, if n = number of stacked cells. The resistance terms in the last equation must now be replaced as functions of the solute concentrations, C w andC . p
From our earlier assessments we found that the resistivities, r, are; r
=26xl04-£-,and
rp = 26xl0 4 -£- ohm-in 2 ,
(4.52)
p
where C w and C are the concentrations in units of ppm of the waste water and processed water volumes respectively. In general, the relationship between TDS in ppm and the quantity, (mass), of solutes is A Q „ i n 3J xlO = A p p m = AC, V where V is the volume in liters, and Q is in grams. It is also undertood that
jf*-*2
(4.53)
152
ELECTROCHEMICAL WATER PROCESSING
Substituting the expressions for the resistances into the equation for i, we obtain, i =
|
Cp
E„ C
W
C
(4.54)
d
QJXTQ.103
p
(4.55)
v„
The (+) sign in the Q w equation accounts for the fact that solutes are being transported into the waste water region, pWdx, by the flowing water stream, and the (-) sign in the Q equation is due to the fact that an equivalent amount is being removed by electrical transport from the processed water during operation of the ED stack. Now, the above may be substituted in the differential equation for Q so that there is only one dependent variable, Q, and one independent variable, t. Qwo+Q i =
10
3 , Qpo-Q
v„
V. (PP
1Q3
(Q po -Q)(Q wo +Q) VV p
w
,or 6
10
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
V,.
-+-
v„
Q Dpo0 -Q
■ io3
153
(4.56)
Inserting this expression (4.56) for i into the equation (4.50) for d Q / d t , we obtain, dQ , ECWL V,. v + —-- =n-A-77-—Q w o +Q Q p o - Q dt (pp n-EcWLA^ cpp
•10 3 ,or
Vw(Qpo-Q)+Vp(Qwo-Q) (Q wo +Q)(Q po -Q)
■103
(4.57) Rearranging terms to solve the differential Equation (4.57) becomes dQ
V,.
-+-
Qwo+Q
V Q P o-Q
above,
n - A - 7 7 - E c ' W ' L - 1 0 3 - d t . (4.58) (PP
If the coulombic efficiency is treated as constant throughout the range of TDS concentrations, then we can integrate and solve the above directly and simply as follows: Vw-ln(Qwo+Q)-Vp-ln(Qpo-Q) = n-A-7?-Ec'W'L-103-t + K
(4.59)
K is a constant to be evaluated from boundary conditions. These limits are: when t=0, Q=0. Thus, the constant, K, is found as K = V w -lnQ w o -V p .lnQ p o
(4.60)
154
ELECTROCHEMICAL WATER PROCESSING
It is now possible to plot the change in TDS of both the waste and processed water volumes as a function of elapsed time. However, before performing the evaluation, it is necessary to decide upon the electrical mode of operation—constant voltage or constant current. If constant voltage is chosen, one must exercise some precautions in the design of the power supply. In order to make the removal rate of solutes reasonable toward the end of a cycle, the impressed voltage will have to be quite high. That same cell potential at the beginning of a processing cycle can produce extremely high currents if not limited in some manner. Thus, it would seem that some control on the maximum current available from the power supply would be necessary to avoid inordinately high power dissipation at the beginning phase of a constant voltage design system. One can eliminate the problem by limiting the system current or self-regulating, regardless of the solute concentration at any time of operation. 4.5.1
Coulombic Efficiency
An improvement in accuracy of process description can be achieved by modifying the preceding analysis to account for non-constant coulombic efficiency. Changes in coulombic efficiency during system operation as a function of the concentration changes of solutes in the processed water volume decreases during system operation are taken into account. As before, r\ may have the form ^(l-e^")
(4.61)
and it may be substituted for the constant efficiency term in the expression for Q versus t. Quite obviously that would lead to significantly increased complications and greater difficulties in arriving at mathematical solutions in closed form. Another approximate approach to the problem of compensating for variable coulombic efficiency is to adopt a linear dependence of n upon C for the region where rj begins to change quickly. That relationship can be as simple as
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
155
(4.62)
v=r-cv
where y is a proportionality coefficient applicable to the region of concentration where r\ is changing rapidly. That would necessitate solving two separate equations for Q. Each equation would cover different ranges of values of C . A bit of manipulation would be needed to determine where these equation boundaries lie. 4.5.2
Single Cell Analysis
The simplest configuration of the system to fabricate is a single cell. Such a reduced configuration eliminates the necessity of making a manifolding arrangement, and simplifies the stacking problems. In order to account for different chamber thicknesses, p and p , and the fact that a single cell has two waste water chambers and one processed water chamber, the analysis is modified as follows. The resistances become: r w =2ç>-^-, and P
(4.63)
vc
Because the current density, i, is merely the cell voltage divided by the total resistance per unit area, we have
E„
>[2p w C p +C wPp ]
(p
2pwCp+CwPF
c c
(4.64)
156
ELECTROCHEMICAL WATER PROCESSING
Substituting the expressions for concentrations in terms of quantities of solutes, as before, we obtain Q w o + Q Qpo-Q
V,.
y
Q P o-Q ^
IO3+PF
i=-
2p v
v
V
P
1Q6
Qwo+Q •IO3
j V
v
w
2pwvw(Qpo-Q)+Ppvp(Qwo+Q)
A
• IO 3
(Q W O +Q)-(Q P O -Q)
2pwVw , P P V P Q W o+Q Q PO DO -Q
■ io3
(4.65)
Now, from the expression for the rate of change of solute concentration in the processed w a t e r side, w e obtain this as the modified, single cell, differential equation:
dQ-
2p w V w , P P V P Qwo+Q
Qppo0 -Q
=A-W-L-77-^-103-dt
(4.66)
Still treating the coulombic efficiency as constant, the above expression is integrated w i t h respect to Q a n d t. 2-Pw-Vw-ln(Qwo+Q) - Pp-Vp-ln(Qpo-Q) (4.67)
The constant, K, is evaluated as before b y the fact that at t=0 a n d Q=0. Thus, K = 2-Pw-Vw-ln(Qwo)
-pp-Vp-ln(Qpo)
(4.68)
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
4.5.3
157
Single Cell - Special Case
In the generalized situations where the waste and processed water volumes are not the same, and where the cell spacing is not necessarily the same, the mathematics becomes a bit complex and more difficult to evaluate. For example, explicit evaluation of Q versus time, as expressed above, is not easily accomplished directly. A simultaneous equation solving program, such as MathCad or Formula-One, enables such computations to be made, but with some difficulty. If we assign equal values to the two volumes (waste water and processed water, Vw and V ), and cell compartment spacings, p w and p , the mathematics is significantly simplified without great sacrifice to actual hardware design parameters or performance evaluation. Hence, we will proceed on the basis of Pp=Pw=P>and V w =V p =V
(4.69)
The reservoir volumes are presumably adjusted to give equal total fluid volumes. Now we may solve for Q explicitly as follows: ln(Q w o + Q) - l n ( Q p o - Q ) = A-77-Ec'W'L-103-t + K p-p-V
(4.70)
Raising both sides to the exponents of the natural logarithm, we obtain this resultant equation of the form
Qpo-Q
=KeMt
(4.71)
158
ELECTROCHEMICAL WATER PROCESSING
Transposing terms, and solving for Q, N-2wo+^
Q-po DO -Q
TX „Mt =K • e Mt , becomes
Q w o + Q= (Q p o - Q ) • K • e M t , a n d the final expression is
QpoK-e--Qwo U
K-eMt+l
^/Z)
Where the terms, M, and K are ..
.
ECWL
M = À-TJ-— ç-p-V
in3
10
K=lnQ w o -lnQ p o
(4.73)
By substituting Equations (4.73) for M and K into Equation (4.72) for Q, we can solve for Q explicitly. This relationship can then easily be placed into a spreadsheet type of format to be numerically evaluated. Graphical representations can also be plotted for different independent variables to quickly and conveniently observe how Q changes with time as any one or more of other parameters such as L, V, W, p, etc. are changed. 4.5.3.1
Ohmic Energy loss and Water Temperature Rise
A straightforward method of assessing the highest temperature rise in both the processed and waste-water volumes is outlined as follows. The worst-case situation, or maximum temperature attained upon sustained operation, is the main interest. This worst-case situation would occur if the following conditions were true: a. The process is adiabatic (perfect thermal insulation to the outside)
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
159
b. All electrical input power is dissipated as ohmic heating (very little voltage drop due to ion transport across concentration gradients). That assumes that there are no voltage gradients across membranes, and that no energy is required for the oxidation/reduction reactions at the electrodes. c. Heating of all water compartments is equal, or thermal energy distribution throughout the internal structure is immediate and uniform). The total volume, VT, of a water processing system operating in a batch mode is simply Vw+Vp=VT
(4.74)
If the volumes are given in terms of Liters, then the mass, M, of the water in grams is 1000xV r Because 1 joule = 1 amp-sec =1/4.18 calorie, the temperature rise, AT, of the volume of water is watt-sec input - — = AT • M • C, where 4.18 C = specific heat of water = 1 deg C/gram-calorie (4.75) The energy input over some operating period of time, t, from the electrical power supply is t
Energy (watt-minute input) = j i • L • W • E c dt
(4.76)
Thus, the final expression for AT is A T =
Energy-60 MC-4.18
These values are easily implemented also by numerical integration in a LOTUS spreadsheet. The temperature
160
ELECTROCHEMICAL WATER PROCESSING
rise can also be computed by insertion of the analytical expression for i as given in Equation (4.51) into (4.77) for the total energy input to the systems. Direct integration of Equation (4.77) for the energy simply gives Q = n-A-W-L-77-Ji-di
(4.78)
Substituting for ¡i ■ dt into Equation 4.79, we obtain for the electrical energy input based upon our assumptions of constant voltage and total conversion of power input to the system as heat Energy = - ^ - ^ -
(4.79)
n-À-rj
Substituting again into Equation 4.77, we are able to estimate the highest possible temperature attainable by operating the system over any time period. 4.6
D e s i g n Exercises for Water Re-Circulation S y s t e m s
The following are some examples of design trade-off calculations for an electrodialysis system in which the processed water is re-circulated from a reservoir many times through the electrolytic module. These are based upon the analysis and series of mathematical relationships developed in Chapter 4, Section 4.5. As was done in Section 4.4, we will select some operating and design characteristics that typify actual application performance requirements. Let us suppose that we want to process 500 gallons in a period of one day, (24 hours). Also assume that the input water supply is quite hard at 400 ppm concentration, and that we wish to low that level to at least 40 ppm at the processed water output from the ED processing
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
161
system. By doing a series of number substitutions in the set of equations developed in Section 4.5, it is possible to arrive at a system configuration with electrical inputs that are acceptable on the basis of practical considerations. There are two methods of electrically controlling the processor cell, or module. They are either by constant current or by constant voltage dc sources. 4.6.1
Exercise #1
A constant current mode of operation is our first example. Let us take a configuration with the following dimensions and input/output goals, and limit the current to 0.05 amp/sq. in. to afford extended electrode life. L=10in. W = 20 in.,
co=400ppm c° = 40 ppm
The total current is then established as 10 amps constant. Table 4.8 gives some values of reservoir ppm, c , at various times after startup of the equipment. In the first single cell, the case where n = 1, the water is not processed to the 50 ppm level within the 24 hours with the current limitation at 0.05 a m p / s q in, and with a Table 4.8 Constant current. n=l
Time, hours
E
n=5 C
E
C
p
p
0
9
400
45
400
1
9.2
387
52.5
336
5
10.5
3366
200
83
10
12.7
273
815
20
20
23
147
162
ELECTROCHEMICAL WATER PROCESSING
total cell area of L x W = 200 sq in. Hence, it is necessary to either increase the cell area or the current density. The former would generally be more practical In the case of the five stack array, n = 5, the water ppm is achieved well within the 24 hours, but the voltages and power requirements are much too high to be practical. A more practical arrangement would be to have a near-constant current power source in which the current is maintained constant up to some maximum output voltage. After that maximum potential is reached, the current diminishes as the cell stack resistance goes up with lowering TDS. A current limiting power supply would be appropriate for this type of operation. 4.6.2
Exercise #2
A second manner in which the cells or array of cells can be operated is on a constant voltage basis. In general, that sort of operation more closely matches the characteristics of a simple power supply circuit. If we take the dimensions of the cell in exercise #1 as an illustration of such a system, the conditions of operation are listed in the table below. We have listed four different modes of operation, and one of which is for a five-cell stack shown in Table 4.9. Table 4.9 Constant voltage. Time Hours
E=10 volts n=l
I
C p
E=50 n=5
E=25
I
C p
E=50 n=l
I
C p
I
C p
0
400
11.2
400
11.1
400
28
400
56
1
385
10.8
329
9.4
362
25.6
329
47
5
329
9.4
151
4.5
246
17.8
151
22
10
271
7.8
57
1.7
151
11.2
20
183
5.4
8
0.25
57
4.3
8.6 8
57 1.2
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
163
As shown in Tables 4.8 and 4.9, single cells, or multiple cells operated at a constant voltages do not process the water to the low values of TDS within the same amount of time. Again, there are innumerable variations on designs and types of power inputs to the units that can be devised to achieve the same end performance of reducing a quantity of water time from one TDS level to another within a specific period of time. For more details about the sets of equations, list of variables, and methods of making the computations see Appendix G.
4.7 Cell Potential and Membrane Resistance Contributions In the development of the previous equations for an operating dialysis cell, we did not take into account the contribution of membrane resistance and back-emf factors. Even though they were identified as parameters, they were ignored in the mathematical development. For those wishing to be somewhat more precise in their estimates of cell behavior, these terms should be taken into account. The importance of these factors as contributions to the overall potential required from a d.c. power supply will depend largely upon these issues: • Membrane-electrode and inter-membrane spacing • Membrane type and its resistivity • Average concentration of water solutions being processed • Type of electrodes employed and their surface properties As spacing between the electrodes and membranes, and between membranes, is made larger, the contribution of
164
ELECTROCHEMICAL WATER PROCESSING
electrolyte (water solutions) becomes larger, and becomes a greater fraction of the total cell resistance. The lowest resistance of electrolyte in any situation would be encountered in a desalination unit at the very start of its operation when all compartments are filled with sea water. This salt concentrated condition would give a specific conductivity of the solution in the range of 0.10 mho-cm -1 , or about 10 ohm-cm. 4.7.1
Membranes
Let us examine the above as the condition where cell membranes may have their largest contribution. Using relatively small spacing between cell components of 1/8 inch, or about 0.32 cm, the resistance per square centimeter area of a three-compartment cell filled with seawater is about 10 ohm-cm x 0.32 cm x 3/1 cm 2 = 9.6 ohms.
(4.80)
The highest membrane specific resistivity that we have employed in ED cells is in the range of 5+ ohm-cm 2 . These values would indicate that a large portion of cell resistance is due to the membranes in such a limiting situation. In those cases where salt concentration is less than seawater by a factor of a hundred or greater, as in the case or water softeners and demineralizers, where the TDS of the input water is in the range of 200 to 1,000 ppm, solution resistances are about 100 to 200 or more ohms for a one square centimeter of cell area. That is considerably higher than the contributions of even the high resistance membranes above, which may have specific resistivities of 10+ ohm-cm 2 at these lower TDS ranges. 4.7.2
Electrodes
Many different electronically conductive materials have been extensively studied and evaluated for application to water electrochemistry. Metals lend themselves to mechanical handling and shape configurations better than carbon.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
165
They are generally much more malleable and electrical connections are more easily made to external circuitry. However, those few metals, such as platinum as rubidium, that will withstand chemical attack as electrodes— especially when made the negative terminal—are very costly and tend to be in scarce supply. Their high costs make them rather impractical as electrode components for application in moderately priced consumer products. In many instances, other "base' metals with thin deposited coatings of platinum or ruthenium have been used for such purposes. The coatings withstand attack and erosion for a prolonged period of use. However, a base metal such as titanium is usually employed so that when the surfacing is consumed and the base conductor is exposed, it will not be attacked very rapidly. The exposed titanium is not directly useful as a positive electrode, where oxidation takes place because its oxidized surface ceases to conduct electrical current. Hence, we resort to carbon as the principal electrode material. Composite structures of polymer (plastic) bonded carbon particles have been attempted with little success. The carbon particles are rather rapidly eroded away at the positive electrode surface by the gasses generated within the structures, leaving behind only the supporting, nonconductive polymer binder, and the electrode eventually acquires too high a resistance for practical use. Fused carbon plates give the most satisfactory results because as they erode, they present the same surface to the electrolyte. Their relatively low cost enables us to tolerate the gradual loss of carbon from the plate electrodes. Low conduction of these plates as compared to metals is of little concern because in most applications the ionic concentration is low, giving rise to generally high resistivity electrolyte. This subject is covered a bit more, later in this text. Electronic resistance of electrodes as current carriers is completely negligible because of the vast difference in specific resistivity of metallic conductors (carbon included) and
166
ELECTROCHEMICAL WATER PROCESSING
those of electrolytes. In most instances, the bulk resistivity ratio between metallic resistivities, pM, and electrolytic resistivities, pe, for conduction through the materials is in the order of ^<10"4 Pe
(4.81)
However, the interface resistance encountered between the electrode surfaces and the electrolyte can be significant. In a single cell, that contribution to total resistance is greatest because there are two such interfaces per cell. In multiple cell arrays, that resistance is amortized over the number of cells. There are only two electrodes in a series stack per n number of cells. Typical interface resistance for carbon composite electrodes of the type employed in most of the hardware designs are in the range of 0.05 and 0.10 ohm-cm 2 for two electrodes. With desalinators operating with entering seawater, the contributions of both electrode and membrane resistances are not negligible. Even though the electrode interface resistances are not constant over the entire range of TDS from 40,000 to 100 ppm, the variations are not very large. Referring to Equation (4.11), RT=2R,+Rœ
+ RD + R _+K + ,
the total resistance of an array of n-cells becomes RT in) = 2R¿ +(n +1) R +nR+nR
_+nR
+
(4.82)
As n becomes greater, the contribution of R, interface resistance becomes smaller. Equation (4.82) should be substituted for (4.11) to be more rigorous in the analyses. However, the approximations made in the previous sections are certainly valid for dialysis systems operating as demineralizers with ten or more cells in series.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
167
To see how the various elements contribute to the total array resistance, some values may be inserted into Equation (4.82). If we take n = 10 for a desalinator array, cell spacing of 0.60 cm, sea water in all cells, and electrode-water interface resistance as 0.05 ohms, the total resistance per square centimeter of the area of such an array is Rt(n) = 2- (0.05) + (2w + l)-10-0.60 + 2n(5) = 0.10 + 126 + 100 = 226.1 ohms
(4.83)
The resistance for the processed and waste water sides (initial condition at the start of operation) are equal. Almost half of the total resistance is due to membranes in this case. If the array was being used to demineralize water from about 200 ppm of salt to less than 10 ppm, then the ratios would change drastically. For example, the same 10 cells would have a resistivity per square centimeter of area in the order of the following: R. = 0.10 ohms R1 = R = 200 x 0.60 ohms w
p
m
m
R = R + = 10 ohms and the total resistance becomes R((n) = 2-(0.10) + (2n + l)-200-0.60 + 2n-10 = 0.20+ 2100+ 200 = 2300.2 ohms
(4.84)
Now, the contribution of the membranes to the total resistance is quite small. In actuality, the interface and membrane resistance are functions of solute concentrations in the water, but introducing such terms would further complicate the mathematics of analysis. If we return to the analyses in Section 4.3, we can insert these resistance terms easily as constants into the overall relationships to account for their contributions. Equation (4.83) assumed that the waste water compartment resistances were very small compared with the far
168
ELECTROCHEMICAL WATER PROCESSING
more dilute processed water compartments in a cell or array of cells. And, it neglected the contributions of the membranes and electrode interfaces. Instead of employing the simplified expression for r , we can take into account all of the terms above and have as the expression for an array equation (4.82). In those cases where the ppm of the processed water is low, membrane and interface resistance can be ignored. When a unit has been operating for a period of time sufficient to increase the level of TDS in the waste water side to 10 times or greater that of the processed water chambers, the contribution of the waste water to total resistance is also negligible and may be ignored. Then Equation (4.83) is a reasonable expression to use. However, if these conditions are not true, then use the full expression in (4.82). In general, however, it is reasonable to discard the interface term, R, from the expressions because of its very small magnitude. In fact, the anion and cation membrane electrical properties are sufficiently close together to enable us to conveniently lump them together, and the net expression for cell resistance can be Rt=Rp + 2Rm
(4.85)
after steady state is achieved wherein RW({R ■ Substituting this expression for the total resistance into the subsequent relationships of section (4.7.2), we have rt=rp
+
2rm=££
+ 2rm
(4.86)
And, the current density becomes . _£_
n
E ^
+
2r.
Ec, ç-p + 2rm/cx
(4.87)
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
169
Returning to equation (4.24), we can substitute Equation (4.85) for ix, and we get -E-e, rj-A-dx (p-p + 2rm/cx
p-v-dcx ■ ß-10-6
(4.88)
Again, transposing terms and solving the differential Equation (4.83), we obtain
r
c,-
*w;
-ErjA, p-v-ß-lQ-
-dx
(4.89)
Integrating Equation (4.87), the expression for the concentration of solutes in the processed water side at some point x is found as [çj-pln
C
—TC
_2
T=
-E-TJÀX
p-v-ß-10'6
(4.90)
where the boundary conditions are the same as in Section 4.3, proceeding with the solution of Equation (4.88)
-EÎ]ÀX
p-v-ß-lQ-6
■x+ç-p\nc0-rmcf
(4.91)
The remainder of the mathematics follows the same guidelines as in the earlier section to arrive at expressions for the total electric current, while taking into account the membrane resistance contributions. 4.7.3
Opposing Voltages
There are two sources of voltages opposing that of the external power supply driving electric current through a series of cells. They are: concentration potentials and
170
ELECTROCHEMICAL WATER PROCESSING
decomposition potentials at the electrodes where electrolysis is taking place. The half-cell potentials at the respective electrodes are primarily due to the decomposition of water at the negative electrode, and, depending upon the materials in solution in the waste water compartments, the production of elemental chlorine a n d / o r oxygen at the positive electrode. The solution in the (-) side will become alkaline with the production of H 2 and OH" The principle reaction is 2H20 + 2e~ -> H 2 + 20H~
(4.92)
At the positive electrode the reactions are variously 2Cl~ -» Cl2 + 2e~ @ -1.36 volts, and 2H20 -+02 + 4H + + Ae~ @ -1.23 volts
(4.93)
The potential resulting from electrolysis that is opposing the input voltage from a dc power source is in the order of 3 volts. Concentration potentials across membranes all cancel out across the array of cells in series because they have alternatively opposite polarities, due to the differences in solute concentrations between waste and processed water. The expressions 4.15 and 4.25 in Section 4.3 for the current density at some point x along the cell length, should be replaced by the following modified equation V
ej_^
( 4 9 4 )
where Ee is the opposing emf due to electrolysis at the electrode surfaces. One can see how the mathematical relationships for cx and ix grow more complex as we account for more variable parameters.
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
171
4.8 Diffusion Losses of Ions and Molecules Across Membranes Many secondary transport processes are taking place during the operation of an ED cell. Among these are: • • • •
Osmotic transport Water molecules of hydration transport Molecular (thermal) diffusion of solutes Negative ions back transfer through cation membranes • Positive ion back transfer through anion membranes • Transport of hydrogen ions into waste sides • Transport of hydroxyl ions into waste sides
Some of these effects are most pronounced at the latter stages of processing, where the processed water is very dilute with solutes, and the concentration difference is greatest between waste and processing chambers. Of all the above secondary processes, the diffusion of solutes back into the dilute chamber of the cell has, perhaps, the largest negative effect on overall ED performance. Osmotic pressure differences result in water loss only, and do not actually detract much from cell performance. Water molecules being transported as attached to ionic clusters from one compartment to another is also not a significant factor except for some slight water loss. Depending upon the ionic transport number ratio for membranes that are employed, the back transfer of ions through these membranes can also be quite small. This last degradation in performance can easily be handled analytically by slight modification in the mathematics as either additional transport terms, or more easily within the efficiency factor, n. For the present analyses, we will ignore these factors except for the thermal diffusion of solutes as undissociated components back into the processed water cell chamber.
172
ELECTROCHEMICAL WATER PROCESSING
In the continuous flow through the configuration of an ED processor, the gradient of concentration of processed water along the length of the cells results in a changing rate of back diffusion of species through the membrane. This rate of diffusion is not constant along the length of the cell. The following is a modification of the expressions for concentration of exiting processed water from an operating cell. We must return to the mathematical developments earlier in this chapter to account for this back diffusion and modify the expressions accordingly. Equations 4.19 and 4.23 need to include an additional term for the diffusion factor. As was proposed in Section 4.3, the loss rate, (dQ/dt)d, of dissolved ionic species in the water stream passing through the processed water chamber is due to the electro-dialytic effect of electric current passing through the membranes. This was described as (see Equation 4.21): ^ =ix.^W.dx-A^/ dt )A min
(4.95)
It is now necessary to add a new term due to molecular diffusion of the solute-bearing water back through the membranes to the processed water chamber because of concentration difference of solutes. That new term can be represented as (dQ/dt)m, the quantity diffusing back into the dilute side through membrane area of 2Wdx. Because the processed water chamber has two membrane walls, the area term must be multiplied by two. The amount diffusing out of the two walls of an element of cell whose area is Wdx, according to Fick's Law, is fê5") V ut Jw dx
=
*" ' A C ' a r m = kmic0-cxyW-dx
(4.96)
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
173
where km = molecular diffusion constant peculiar to the membrane co = input as well as the waste water concentration Then the relationship for the net transport of solutes from the processed water chambers to the waste water sides in steady state conditions is Input rate of solutes from water flow + molecular diffusion into the pWdx space = electrical removal rate of ions and can be expressed as dQ^ _ dt 'w,dx
(dQA^dQ^ dt v dt
(4.97)
for an area of Wdx. Equation (4.97) then would essentially replace Equation (4.21). The ensuing mathematics must be modified now for the additional diffusion factor. We now have the resultant equation to manipulate where W-p-v-dcx-ß-10~6 = -ix-rj-W-dx-A
+ km-(c0-cx)-W-dx-ß-10-6
(4.98)
Then the mathematics can be developed to account for the losses by thermal diffusion. We can modify the relationship as follows: pvdcx/M0 E c x r]-A-dx+k (c -c )-ß-dx m 0 x (P-P
(4.99)
The equations retain the same format, but become a bit more complex in the sense that more terms are in the
174
ELECTROCHEMICAL WATER PROCESSING
expressions. If one wishes to compensate for the thermal diffusion back into the purified water, these modifications must be followed through in the same fashion as they were in 4.8.3. In a very similar manner the expression for cx becomes, dcv
p-v-ß-10'
■ = dx, or
~^ft^+ka(c0-cxy (P-P dc cx\km-ß-W-6
ß-io-^
+ V-Ä~ + kmc0ß-W W
dx pvß-10~ (4.100)
Direct integration to solve for cx as a function of distance, x, yields 1 kJ-W
-In
kj-l^
+ rjX
pvß-lCT
+ nk— +fcmco/M0-6
■ + constant
(4.101)
Applying the boundary conditions of cx - co when x = 0, the constant is Const. 1
kj-w^
+ v^-
-ln co\kmß-\0-6 + VÄ—
+kmc0ß-10-6
ANALYSIS & MODELING ELECTRODIALYSIS SYSTEMS
175
w e find the final expression containing cx becomes
1
-ln cx\kmßlO-6
6
V
kmß-W- + VÄ-
+ VX—
W)
+kmcoß-10-
1 Íb
. ., E
fcm/MO- +77A pvß-lQ-
-In
kmß.lO-6 + r1X— +fc m c o /M0- 6 V
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
5 System Design Exercises & Examples 5.1 Electrolytic Generation of Bromine and Chlorine: Design Procedures Design procedures of electrolysis devices for the production of free bromine are relatively straightforward, and easily lend themselves to implementation as mathematical programs. The electrolytic processes that take place in the "brominator" electrode array, as shown in Figure 3.17, are described in Chapter 3. In this section, we will address the rates of the processes and the analytical development of the methods to determine appropriate electrode areas, inter-electrode spacing and numbers of electrodes in an array. Voltages and currents needed to achieve the type of performance desired are also considered in the following. There are a number of factors that influence the behavior of an electrolytic bromine generator. In order to design an 177
178
ELECTROCHEMICAL WATER PROCESSING
operating system, it is necessary to identify, and quantify each parameter. These are: Coulombic efficiency for Br2 production Driving electrode potential Electrolyte (water) specific resistivity
r| E p
With these three basic materials parameters, it is possible to calculate the electrode areas, spacing and electric power input to the electrodes needed to produce a given amount of bromine per unit time. However, the coulombic efficiency must be explored in a bit more detail before we are able to proceed with some degree of rigor. The efficiency of the production of free bromine at the (+) electrode surface is dependent upon the concentration of bromide ions at the electrode surface, the nature of the electrode surface and the electric current density (per unit area of electrode). The competing process is the generation of oxygen from the available OH' ions. Thus, ri = (/>{CBr_,i,)
(5.1)
some function, (j), of current density, i, and bromide ion, CBr_, is the concentration for a particular electrode structure. In general, n will decrease with increasing i and decreasing CBr_. As was stated before, the maximum value of r| is 0.50 due to the recombination of bromine and NaOH to reform NaBr, the original salt that is decomposed to produce free bromine at the beginning of the reactions. Let us proceed with setting up a series of equations to establish a design process for electrode configurations and electric power supply specifications to produce bromine at a given rate. The amount of molecular bromine, B, produced per unit time per unit area of electrode by electrolysis is simply d
ydt
= i-î]-A-y/
(5.2)
SYSTEM DESIGN EXERCISES & EXAMPLES
179
where dB/dt = rate of production of elemental bromine = gm/sec = 8.56-10-4-z'v4-77 A = total working area of a single cell, square inch, *F= conversion constant = 1.07xl0~5 gm-equiv-wt/amp-sec = 8.56x1o-4 gms/amp-sec i = amp/in 2 The voltage, E, needed to produce the necessary total current for a single cell is given as (5.3)
E = Ec + i-A-Rc
where Ec = electrochemical cell potential for the couple 2Br + 2H20 -> 2 0 H ' + H 2 + Br2 P' S
Rr = cell resistance = —— A and s = cell spacing (distance between electrodes)
(5.4)
Cell voltages (back, or opposing emf), encountered with chloride and bromide salts are in the order of 2+ volts. It is difficult to be exact because so much depends upon the flow rate of solution passing over the electrode, polarization effects, concentration of solute, etc. For purposes of illustration, we will use a value of 2.0 volts. Let us now perform a calculation to estimate the power input, current requirements, and electrode size for producing a given amount of bromine per unit time. For example, we will select a body of water of 20,000 gallons (a small swimming pool volume) to be provided with 1 ppm of free bromine per hour. This is a strictly arbitrary situation, but it is within the realm of actual circumstances.
180
ELECTROCHEMICAL WATER PROCESSING
The equivalent conductance, A+, and A of the separate ions, Na+, and Br, are 50 and 78 cm^equiv^-ohm" 1 respectively (see Section 4.2). A typical concentration of salt, NaBr, in a pool that would be well below the taste threshold and metal corrosion level is in the order of 1,000 ppm. The equivalent conductance, A, for the salt in dilute solutions is A = A + + A - = 128,
(5.5)
and the specific resistivity is given as 1000
« ^
. (5.6) NA A convenient conversion factor for putting normality of NaBr solution in terms of ppm is as follows. Normality, N, is 1N=GEW/1000 gm, and since the GEW of NaBr is 103 gm, the conversion factor for this salt is p= F
ppm = 103xl0 3 N
(5.7)
Given these basic facts, and assuming, for the moment, a coulombic efficiency, n, of 0.50, we can proceed to estimate the size of the hardware and the electric power input. The drawing in Figure 5.1 shows the dimensions of an electrode array to produce the necessary rate of bromine. If the total working area of a single cell is A, regardless of whether that cell is comprised of two electrodes or n-number of electrodes connected in parallel electrically, and if the spacing between the electrodes is s, as shown in Figure 5.1, the electrolytic resistance of the cell is R =
S
nA
=
1000 nA NA S
(5.8)
We can now set some values to the independent parameters to calculate the electrode area needed to generate the 1 ppm of bromine per hour of operation. In order to do so, we
SYSTEM DESIGN EXERCISES & EXAMPLES
181
^ 2
Figure 5.1 Brominator electrode array.
must decide an acceptable current density at the electrodes. Again, we will be somewhat arbitrary and set that value at 0.10 amp/in 2 . The units implicit in the above equations are in metric values, or cgs. Hence, s and A must be in centimeters. Generation of 1 p p m / h r in a volume of 20,000 gallons, or about 160,000 lbs of water is 0.16 lbs, or 72.6 gm of bromine per hour. Because 8.56xl0"4 gm of Br2 are produced per second at one amp current, (or about 3.08 g m / h r at one amp), a current of 47.2 amps is necessary for that generation rate of bromine with a coulombic efficiency = 0.50. Returning to the remainder of the design problem, we see that an area of 472 square inches of electrodes is necessary to keep the current density at the 0.10 amp/in 2 , and if the spacing, s, is set at a mechanically and hydraulically convenient value of 0.25 inches, the voltages are: E = E +23.6
0.25-2.54 l-236-(2.54) 2
1000 pptn •128 103xl0 3
(5.9)
Carrying out the arithmetic, and putting in the value of 2.0 volts for Ec, and 1000 for the NaBr ppm, we obtain
182
ELECTROCHEMICAL WATER PROCESSING
the following for the dc potential needed from an external power supply: E = 2.0+ 15.6 volts.
,cim (5.10)
It is now straightforward to establish a system of equations to assess and optimize design parameters in terms of cost, current density, physical size and shape, energy consumption, etc. We can solve the following system of simultaneous equations by substituting various values for independent parameters, and one can even decide which parameters will be dependent and independent. As in many computations before, solution of these relationships can be implemented within a number of computer software programs, such as MathCad, and Formula One. Because LOTUS and EXCEL do not permit simultaneous solutions, these equations must be rearranged so that their solutions are accomplished in a sequential fashion. There are many engineering trade-off possibilities that affect capital equipment operating life, cost, efficiency and energy consumption, as well as practical considerations such as geometry. The relationships and definition of terms are listed below. t
*B/,. = i-rj-A-y/= grams/hr E = Ec + i-A-Rc = volts
1000 p= """" = o ohm-cm ppm =
3; l03xWN
Rrc = —— = ohms A The units of the constants are: y/-1.07xl0~5gew/amp-sec, = 3.08 gms/hr-amp
and for bromine
A = 128 cm2 - equiv : - ohm"1, for bromine
(5.11) (5.12)
SYSTEM DESIGN EXERCISES & EXAMPLES
183
In addition to these relationships that have been described earlier, we may wish to identify the following in our optimization calculations: Power Input = P = i- A- E
(5.13)
And defining a measure of bromine output against input power as COP, we have Coefficient of Performance = COP =
1
âVi
P àt
=
(Ri)
P
(5.14)
Costs and specifics of device and system design will be discussed in some detail in a later volume on the same subject, but dealing with empirical data and fabrication methods. Costs will vary with design. For example, if the current density is lowered, then the electrode area must be increased for the same bromine yield. However, resistive losses are lower and the power supply cost will be reduced, thus compensating for the greater electrode array size. In addition, the electrode life will be extended at the lower current densities. An increase in coulombic efficiency due to lower electrode starvation and lower polarization effects will also be realized at lower current densities. Similarly, the amount of salt in solution will influence the power requirements by determining solution resistance, as well as coulombic efficiency. Some examples of design trade-off opportunities independent of cost changes are presented here by employing the above set of equations as simultaneous relationships. In these computations, n is treated as having a constant value, even though in reality it will depend upon current density and salt concentration. If the current density is reduced, the required power supply voltage decreases as well as the power input level, and the COP is increased. Examples are listed below in Table 5.1.
184
ELECTROCHEMICAL WATER PROCESSING
Table 5.1 cm2
volts
watts
Electrode Area
Cell Potential
Power Input
0.05
9433
4.5
212
0.34
0.01
4716
7.0
332
0.22
0.15
3144
9.5
450
0.16
0.20
2358
570
0.13
amps/cm 2
5.1.1
12
COP
D e s i g n Geometry Comments
Practical designs of the this type of oxidizer-producing electrode stack may need to be installed in high pressure water systems such as those in residential and commercial water lines. Pumped circulation systems for pool filtration are usually at fairly high pressure as well. Pressures encountered can be as high as 100 psi. A cylindrical or near spherical housing configuration would be best as pressure vessel containers for electrode assemblies. If cylindrical housing is selected, for example, one would want to achieve maximum space utilization of the inside of the cylinder for the electrode array as a design goal. A short analysis is given below of such a design, where a stack of parallel plate electrodes is inserted into a cylindrical container as the outside housing. Figure 5.2 shows an end view of a stack of electrodes in a cylinder with a set of dimensions as indicated. • • • • • • •
Number of electrodes in parallel = n Width of stack = b Stack thickness = a Electrode thickness = u Interelectrode spacing = s Cylinder inside radius = R Stack length = L
SYSTEM DESIGN EXERCISES & EXAMPLES
185
Figure 5.2 Electrode stack.
We are now ready to estimate the optimum design for any given total area, A, needed for proper electrochemical operation as determined by the preceding set of equations. The total electrode area of the stack above is A = La(n-l)
(5.15)
If the electrodes are to be sized such that the end ones are in contact with the cylinder wall as shown, the relationships between the stack parameters and the cylinder radius are b-n(u + s)-s
HííiS
(5.16)
Figures 5.3 and 5.4 are photographs of an electrode stack inserted in a cylindrical housing in process of fabrication. The electrical wires and connections to the carbon plates are through an epoxy casting surrounding the edges of the plates as well as encapsulating the electrical connections
186
ELECTROCHEMICAL WATER PROCESSING
Figure 5.3
Figure 5.4
themselves. Water flow is parallel to the electrodes and goes from one end of the cylinder to the other via entrance and exit pipes in the end-caps. The computations for A, or any three of the parameters in the above three equations (5.15 to 5.17) may be performed after deciding upon the other variables. For example, if we wish to solve for L, a and n while keeping all other
SYSTEM DESIGN EXERCISES & EXAMPLES
187
parameters fixed at some pre-determined value, the results are obtainable as a variety of choices. Maximum utilization of space within the cylinder can be derived by maximizing A in the above system of equations to determine the optimum relationship between R, a and b as a function of the rest of the parameters of s, u and n. The optimum expression is found by setting the derivative of A with respect to either a or b to zero. Substituting for a and n in equation in Equation (5.15), we obtain: b+s u+s
A=L
[4R2-b2f2, or
(u + s)A = Lb(AR2 -b2)Á
-Lu(4R2 -b2)A
(5.18)
Differentiating A with respect to b, we get
(u + sy — = db
L(AR2-b2)y2-Lb2(AR2-b2yV2
+ Lub(4R2-b2yV2
(5.19)
Setting dA/db = 0 to find the maximum of A, and multiplying Equation (5.19) through by UR2 -b2\2 /(u + s), t n e result is 0 = L(4R2 -b2)-Lb2 2b2-ub-4R2
=0
+ hub, or more simply (5.20)
Calculations can now proceed with that these equations to arrive at the best value of a, b, and n to obtain maximum area, A of an electrode stack.
188
ELECTROCHEMICAL WATER PROCESSING
5.1.1.1
Example
Our reference are Equations (5.3). Calculations can now proceed with these equations to arrive at the best value of a, b, and n to obtain maximum area, A of an electrode stack. We can now assume some operating criteria, and based upon them, find out how the trade-off factors are interrelated quantitatively, and perhaps find some optimum combinations of size, initial cost, and electrical power requirements. It is known that the life of an electrode assembly is directly related to the electrical current density. However, it is important to also be aware of the improvement realized in long term operating costs of an electrode array by reducing its replacement frequency. For equation setup and computation procedures, refer to Appendix H. An interesting investigation made during 1983 to 1988 was the design and implementation of a number of complete systems for field-testing in residential and commercial pools. The photographs in Figures 5.5 and 5.6 are of some of these experimental systems. They show the programmed power supply and connections to the pool pump
Figure 5.5
SYSTEM DESIGN EXERCISES & EXAMPLES
189
Figure 5.6
and reservoir. These chlorinator/brominator units were operated continuously, in some installations for over three years. A Chlorine or bromine salt, i.e., NaCl or NaBr, was added to the pool water to bring the concentration up to between 600 to 1000 parts per million. The devices demonstrated their ability to maintain clear water conditions without increasing hardness or requiring the addition of other chemical agents.
5.2 Simple Estimate of Capital Equipment and Operating Cost of Electrochemical Desalination Apparatus The following is a preliminary cost estimation of a sea water/potable water system. The cost of membranes is set at the high value of $5/ft 2 and electrodes are also $5 to $10 per ft2. Input water is taken as 30,000 ppm (3% by weight salt) and the output is set at 300 ppm, a reasonable level for general potability.
190
ELECTROCHEMICAL WATER PROCESSING
Two stages of the water processing system are employed. Each stage is capable of reducing the TDS to 10% of the input at a flow rate of 10 gallons per minute. The first stage brings the sea water down to 3,000 ppm, and the second stage to 300 ppm. The accompanying data and calculation sheets show the dependence of power consumption and initial capital equipment investment versus the number of stages of cells in the stack. Let us take 60 cells as the figure for a good compromise between power consumption and capital cost. This gives the following figures for the cost of the system and cost of operation on a per gallon basis: Stage 1 Equipment cost = $5177 (materials) Power consumption = 48 KW Power cost @ $0.05/KWH = $2.40/hr = $0.004/gal. Stage 2 Equipment cost = $5177 (materials) Power consumption = 5 KW Power cost @ $0.05/KWH = $0.25/hr = $0.0004/gal As one can see, there is a trade-off between energy efficiency and initial capital equipment cost. There are many engineering design parameters that can be varied to further optimize the system performance, such as spacing and construction materials. Now, let us look at the amortization of capital equipment costs. If the apparatus lasts only one year of continuous operation without significant repair or replacements of parts, then we have 365 days x 24 hrs/day x 600 gal/hr = 5.256 x 106 gal/year
SYSTEM DESIGN EXERCISES & EXAMPLES
191
processed by the system. At an initial cost of $10,354 for the two stage equipment, the cost per gallon is $10,354 / 5,256,000 gal, or $.002/gal of processed water. Our guess at this time is that the equipment should have a life between 5 and 10 years of continuous use. Hence, the capital equipment costs would be about 10% of the total cost of processed seawater. It appears that the cost of producing potable water from seawater is in the range of 0.5 cents per gallon with the ED approach. When we are able to employ lower cost membranes and electrodes in the near future, the total system cost will be markedly reduced. Membranes that cost $1.00/ft2 would reduce the equipment cost from the $5177 figure to $1180 in terms of materials alone. With additional engineering development and testing, the system seems more than competitive with RO or distillation.
5.3
Cost Estimates Outline for an Electrodialysis De-ionizing System
The following is a brief summary of cost factors in the design and manufacture of an electrochemical de-ionizing unit recently configured at TRL. Costs of a system are essentially proportional to the quantity of dissolved matter removed per unit time from a water stream (flow through) or a reservoir of water (recirculation system). The quantity of dissolved substance removed per unit time from the water, d Q / d t , is directly proportional to the electric current flow, or R = d Q / d t = ni (rate of dissolved matter removal), where r) = coulombic efficiency.
192
ELECTROCHEMICAL WATER PROCESSING
Convenient units for R are: • • • •
ppm-gallons/min. grains/min. grams/min. lbs/min.
Coulombic efficiencies are generally between 70% and 90% in a practical system. A 70% figure is quite conservative. Values of n = 70% to 90% have been regularly obtained at "higher" current densities. Generally, when the TDS drops down to low values, i.e. 1 to 20 ppm, the efficiency, r\, falls off to 70% or less. Some useful conversion figures are provided below. 1 gal = 3.79 liters 1 gram = 15.4 grains 1 gm/liter = 8.35 x 10"3 lb/gal 100 ppm = 0.1 gm/liter = 0.379 gm/gal. = 1.54 grain/liter = 5.85 grain/gal. At 100% coulombic efficiency, approximately 26 amp-hours remove one gram equivalent weight of dissolved substances. If we set 1 equiv. wt. = 60, then 1 amp-hour is equivalent to about 60/26 gram of dissolved solids. Thus, the passage of 1 amp-minute is equivalent to 1/26 gram, or about 0.04 gm of DS. Normalizing the above to grains per minute, or ppm-gal/min, we obtain for a single cell: • 1 amp removes 0.62 grains per min. • 1 amp removes 10 ppm-gal per min. Now, we must relate this to electrode and membrane area, device size, and power supply specifications to estimate manufacturing materials costs.
SYSTEM DESIGN EXERCISES & EXAMPLES
193
Continuous current densities in the order of 0.04 to 0.05 amps/in 2 are acceptable with present electrodes and result in reasonably low erosion rates. Hence, taking i = 0.05 amp/in 2 as an operating current density, we find that 20 in2 area are required for removal rate of 10 ppm gal/min. Current densities at peak water flow of 0.10 amp/in 2 or more are acceptable, as well. If a system were to be designed that was capable of the peak performance, below, as a once through flow, or • 350 ppm input water - to - 50 ppm output water • 10 gal/min. maximum flow rate, then the effective area for the system would be: Total area = 2 in 2 /ppm-gal/min x 300 ppm x 10 gal/min = 6,000 in2 = 40 ft2 This design is equivalent to a removal rate of 1800 grains per minute. Ion exchange membranes employed presently cost about $5/ft 2 in moderate quantities. Electrodes presently utilized are also about $5 /ft2. Future costs may come down to $l/ft 2 for membranes and $0.20 to $0.50/ft2 for electrodes with some further development. The ratio of electrode area to membrane area will range between 1:2 to 1:20 depending upon series/ parallel design specifics. The volume of the system described above would be about 5 to 6 ft3 with 1/4 in. inter-electrode spacing, or about 2.5 to 3.0 ft3 with 1/8 in. spacing. The plastic encapsulation volume with manifolding, etc., would probably be about an additional 0.4 to 0.5 ft3 in volume. External housing, if any, to withstand the 100+ psi line pressures is not estimated here. At an average voltage of 3 volts/cell, and a total of 3000 amps-cell, a power supply with about 10 KW
194
ELECTROCHEMICAL WATER PROCESSING
output is required. Power supply is a simple, non-regulated, non-filtered dc source with no special requirements other than overload protection. The following is a cost summary for the full-scale system, capable of producing 10 gal of water per minute with a TDS change of 300 ppm from input to output. Table 5.2 Factory cost summary for 1800 grain/min. system. Present
Future Production
Cost
Size
Cost
$200
40 ft2
$40 to $80
Electrodes
$5 to $10
5 ft2
$1 to $5
Structure (Plastic)
$10+
4 ft3
$5 to $10
?
5 to 7 ft3
?
Power Supply
$300+
10 KW Peak
$200
Total Cost
$515+
Membranes
Housing
$245 to $295
It should be noted that the above figures are merely estimates. They do not account for possible volume production cost reductions, direct labor or overhead. A system of 1/10 the above size with a holding tank of perhaps 50 gallons may be a more practical design for residential applications, where water usage is intermittent and peak flow has usually very short duration. In that case, virtually all the above costs would be reduced by a factor of 10, but the cost of the tank reservoir plus any necessary controls would need to be added.
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
6 Applications Discussion 6.1
Demineralizer: Electrodialysis
ED water processing systems can be produced in a wide range of sizes. The process lends itself readily to designs and product configurations ranging from small, hand held, portable units to large-scale systems for industrial and municipal uses. Units can be stacked easily to handle large quantities of water, or to increase purity levels of output. Electrodialysis can be used to convert salt water (seawater) to drinkable water by removing salts from input water to potable concentration levels. The system will also sanitize (disinfect) the water if configured to do so. Electrical injection of strong oxidizers generated from the sea water at the start of processing would destroy any micro-organisms that might be present. Seawater normally contains salt at a concentration of 3 to 3.5% by weight, or about 35,000 ppm. Water composition from drinking wells is often at 200 to 400 ppm levels. Water from city or municipal reservoirs is usually between 80 to 150 ppm, and is considered soft for washing purposes. 195
196
ELECTROCHEMICAL WATER PROCESSING
Depending upon the length of operating time (duration of processing), the purity of the water emerging from an ED system may exceed that of reservoir water. 6.1.1
Advantages of Electrodialysis
The method uses an entirely electrical process (electrochemical) that requires only a source of a.c. or d.c. power to operate. Some of the attendant advantages are outlined below. 6.1.1.1 General Characteristics Silent operation No mechanically moving parts Operates at standard temperature and pressure Low power consumption, efficient Self regulating, needs no on-off switching Made entirely of plastic - no corrosion or maintenance No vibration, sturdy and abuse resistant Small waste water ratio Not affected by impurities usually found in water Operates over wide range of power inputs No maintenance service required Additional features: • Units can be portable to sites such as camps, motor homes, etc. • Modular construction enables multiple unit systems 6.1.2
Desalination System - Module Specifications
The drawing below shows the simple system with its essential parts. The power converter is an integral component of the module.
APPLICATIONS DISCUSSION
197
To 120 volts
Figure 6.1 Electrolyte desalt system.
A basic unit consists of the following parts: a. b. c. d. e.
ED module (Desalter) Power limited & water condition indicator Flexible plastic lines for water input and outputs Two circulation pumps Line cord adapter for operation from 12 volts d.c.
An example of a practical design is outlined below. The desalt module has these specifications: Weight Size Maximum output rate Maximum input power Internal water capacity
30 lbs 7" x 8" x 22" 1 gallon per hour 500 watts 0.7 gallons (2.6 liters)
The photograph Figure 6.2 is a laboratory size module showing a direct current power supply and the pump
198
ELECTROCHEMICAL WATER PROCESSING
Figure 6.2 Module.
needed for water circulation. Depending upon the hydraulic configuration that is set up, it may be employed as a water softener, a demineralizers, or even a desalination system. Figure 6.3 graphically shows the performance of the above module as a demineralizer when operated at about 120 volts d.c. over a two hour period. The electric current falls off quite rapidly as the salt (mineral) concentration in the processed water compartments is reduced by the electrolytic transport of ions to the seawater side of the system. A simple version of such a system would involve only connection to a 120 volt a.c, or a 12 volt d.c. source, and connection of the hydraulic lines, as shown in the above drawing for its operation. Water purification rate would be dependent upon the applied voltage and consequent electric current.
APPLICATIONS DISCUSSION
199
• c
»,
a» o
-£
«
§
0.
Figure 6.3 DeSalt module performance. (Same as shown in Figure 6.6 when starting as desalina tor).
The waste water line is connected either to the primary water source tank, or directly into the ocean by a submersible pump. Processed water lines connect to a body of water, usually a reservoir containing an initial quantity of sea water to be desalted. After the unit has been operating for the specified design time, a conductivity meter could provide the output signal to indicate that the processed water is sufficiently desalted to be usable for cooking, drinking or washing purposes. The length of time required to process the water depends upon the amount of water initially in the reservoir and power input level. 6.1.3
Performance Characteristics
The curves below show the type of performance one can expect from this size unit. The graphs in Figures 6.4, 6.5 and 6.6 are plots of power level and salt level in the processed water reservoirs as a function of time. The data is presented in three graphs because they are divided inrto three ranges of initial salt
200
ELECTROCHEMICAL WATER PROCESSING
Figure 6.4 DeSalt module performance. (High salt levels).
Figure 6.5 DeSalt module performance. (Medium salt levels).
concentrations. Actually, the process is continuous, but it is shown in the form of three separate processes in order to change scales to make the data more easily visible, especially at the low end of salt concentrations.
APPLICATIONS DISCUSSION
201
Figure 6.6 DeSalt module performance. (Low salt levels).
Output ppm and power consumption versus operating time are plotted for a 2 gallon-size reservoir of processed water when the module is powered from a rectified 120 volt a.c. line. Electrical power from a current limited supply, (5 amps), increases to a maximum of 500 watts as salt content in the processed water diminishes. Then, as the processed water becomes more purified, power consumption decreases to low wattage. If the fresh water (processed water) reservoir has a 10 gallon capacity, the processing time would be 15 hours instead of the 3 hours shown in the graphs for 2 gallons. Between 15 and 20 gallons can be processed from seawater per day of operation. 6.1.4
Cost Factors
Initial equipment cost of the system is continually being assessed. A factory cost is anticipated for the system of between $500 and $700, depending upon production rate and features embodied in the system. Operating costs
202
ELECTROCHEMICAL WATER PROCESSING
for electrical energy are estimated based on $0.10 per kilowatt-hour. Such a small unit requires about 500 watthours to produce 2 gallons of desalted water. Electrical energy costs are about $0.02 to $0.03 per gallon of potable water.
6.2 6.2.1
R e s i d e n t i a l Water S o f t e n e r Product D e s i g n Description
To illustrate the possibilities of developing and manufacturing small water softening systems employing electrodialysis principles, a design exercise is offered in the following pages of this section. The design goal is a system to non-selectively remove all ionized and dissolved substances from the input water stream into a home or any small establishment where the peak water flow demand is 10 gallons per minute or less. Input water could originate from any primary source, such as wells or reservoirs. Water entering the unit is "softened" and "de-ionized" in the sense that the total dissolved solids, TDS, is lowered as it passes through the system. Electric current passing across ion-selective membranes within the device separates all electrically charged substances from the main water stream and into a waste water outlet. This waste water contains minerals, etc. removed from the main stream in concentrated form, and is discarded or drained back into the soil (its original source). Thus, water leaving the unit would normally have 90% or more of its original dissolved materials removed. If water of 500 ppm TDS (quite hard) is the source concentration, for example, the system would deliver between 5 and 50 ppm TDS to the home, depending upon the demand rate for water by the user.
APPLICATIONS DISCUSSION
203
Some of the types of materials, (mostly inorganic compounds), which would be removed by an ED system are listed below. Cations
Anions
Others
Sodium Potassium Calcium Magnesium Manganese Lead Copper Iron Mercury
Carbonates Chlorides Bromides Sulfates Nitrates Sulfides Phosphates Borates Citrates Acetates
Acids Alkalis Hydrogen Sulfide
However, virtually no organic substances are removed from the processed stream. Un-ionized materials such as sugar, alcohols and solvents are unaffected. In order to remove or decrease the concentration of such non-ionic materials, filters a n d / o r adsorbent charcoal beds would be required. 6.2.2
Physical Description of the System
Figure 6.7 shows the general configuration of a proposed system for residential application. Dimensions and hydraulic connections are schematically outlined. The component parts are identified below. 1. Control Unit is a valve device that switches on the flow of waste water through the processor when the mainstream water flow is initiated by house demands from faucets. 2. Power Supply is a D.C. source at 120 volts, and a maximum power level of 4 KW to process up to 1,000 ppm input water. A timer circuit
204
ELECTROCHEMICAL WATER PROCESSING Processed water output
Power line input
Figure 6.7 ED Residential Water Processing System.
switches electrical polarity periodically, and briefly, to clear scale build-up from the negative electrode. 3. Electrochemical Processor is an assembly of cells (membrane/electrode stack) connected hydraulically in parallel, and electrically in series. Current flow causes dissolved solids to be continuously removed from the main water stream during usage. When the water flow is stopped, the electric current quickly diminishes to zero because of the high electrical resistance of the main body de-ionized water. Hence, the power supply and module are self regulating, eliminating the need for switching during times of zero or low water flow. The module is shown as a plastic cylinder of about 50 inches in length, and 8 inches in diameter. The structure is designed to withstand 300 psi. Pressures as high as 100 psi may be encountered in some water input lines.
APPLICATIONS DISCUSSION
6.2.3
205
Operation
Water from the primary source, (wells, etc.), enters the system via the flow controller. When a water demand is made, the flow controller permits flow of water through the waste channels. Waste water ratio is less than 5% of the total. The power supply is continuously on-line and supplies current when there is some water flow. Electric power is self-regulatory, and will supply current as needed, continuously and smoothly varying in accordance with flow rates and input TDS. No external switching is necessary. 6.2.4
D e s i g n Example
An ED system can be sized for residential application in a very direct manner. Cost, simplicity and physical dimensions are among the critical factors that determine its practicality. A geometry and size was selected for this design exercise that seems to be in the range of economic and performance criteria for applicability to typical home water supply needs. Cylindrical configuration for outer case structures is generally more suitable as pressure containers for on-line installations. This aspect of construction has been discussed to some extent in Chapter 5. The dimensions and operating conditions selected as a proposed initial design approximation are as follows. First, it is important to try to minimize the quantity of materials and number of components in this first design draft. If a plastic cylinder is selected as the pressure bearing outer shell for the stack of ED cells, then we should seek the smallest diameter possible to minimize cost of the cylinder. As the cylinder diameter increases, its walls will need to become thicker to sustain the pressure differential, and generally cost increases non-linearly with diameter of pipes and cylinders because of increased manufacturing difficulties.
206
ELECTROCHEMICAL WATER PROCESSING
Also, we need to bear in mind that there is a maximum practical length to the module, or cell stack, especially if it is to be placed indoors and perhaps installed with its long axis in a vertical position. Four to five feet in length seems to be about the upper limit for a unit to be readily installed in most residences. There are some instances where much longer units could be used installed horizontally, but there are other problems of fabrication that are encountered when electrodes and membranes become very narrow and very long. With these considerations in mind, let us select a cylinder with inside diameter of about 12 inches and a working length of 50 inches, and then explore the performance and costs of such a configuration. The following graphs show the performance that may be expected from the design described in Figure 6.8. In Figure 6.8, the power input requirements are plotted against the flow rate for different Input Water TDS Values. Particulars of the design, in addition the container diameter and length, are: Inter-membrane spacing Cell width Cell length Number of cell Total stack potential
0.10 inch 8 inches 50 inches 40 120 volts
The estimated cost of components and materials on limited production basis for this module design is between $300 and $500 depending upon pricing of membranes and production levels. Coulombic efficiency is assumed to be 100%, not a realistic figure, but it will serve as an initial and convenient starting point. It will be noted in Figure 6.8 that the power level is much lower at the lower flow rates water TDS because the average resistance of the processed water is higher.
APPLICATIONS DISCUSSION
207
Figure 6.8 For different flow rates and input water TDS. Power input requirements.
Since the unit is operated at constant voltage, electric current drawn from the power supply is considerably less at low TDS values. Figure 6.9 shows the change in output TDS as flow rate is increased with three different input TDS values of 1000, 500 and 200 ppm. This graph is correlated with Figure 6.8. Most problem residential groundwater sources that are not from municipal reservoirs have TDS values ranging from 200 ppm to 500 ppm. Higher values than 500 ppm are not rare, but probably much smaller in number. Hence, it would seem that the design center of operation for a "water softener" system intended for this application would be in the regions shown in both of the above graphs. Also, most water discharge rates for home use are between 2 and 4 gallons per minute or less. Rarely are flows of 10 gallons per minute encountered in normal, single residence buildings. Figures 6.8, 6.9 and 6.10 are performance data for electrode lengths of 50 inches.
208
ELECTROCHEMICAL WATER PROCESSING
Figure 6.9 For different flow rates and input water TDS. Output water TDS.
Figure 6.10 For different flow rates and input water TDS. Energy per gallon output.
If these are indeed the circumstances, then we see that the unit described above has been somewhat over-designed for this application. The TDS output is much lower than necessary at the peak flow rates of 2 to 6 gallons per minute.
APPLICATIONS DISCUSSION
209
A level of 50 or more ppm is generally acceptable for most potable use. There are two directions that a design modification can take to raise the output TDS level. They are: decrease voltage and current from the power supply, or reduce the physical size of the module. The latter is the more attractive direction because power consumption costs per gallon of output water, as shown in Figure 6.10 are very small. In fact, they are almost negligible, and would be even less for smaller sized units operated under the same 120 volts. If the length of the module is reduced to 25 inches, half the power is needed, but much more importantly, the cost is reduced by a factor almost two, and the output TDS of processed water in the flow rate and input TDS range commonly encountered will still be acceptable, good quality water. Figure 6.11 and Figure 6.12 show the dependence of Power requirements and output TDS upon flow rates with the shorter length unit.
Figure 6.11 For different flow rates and input water TDS. Power input requirements.
210
ELECTROCHEMICAL WATER PROCESSING
Figure 6.12 For different flow rates and input water TDS. Output water TDS.
Life expectancy of hardware should be between five and ten years. Amortizing capital equipment costs of $500 over a five-year period would be less than $10 per month for hardware replacement. The average household uses over 10,000 gallons per month. Dividing the numbers gives a cost per gallon of less than $0.001 per gallon of processed (softened) water. It would seem that application of ED to commercial and consumer water softening problems could be a very attractive and a sound subject for serious investigation and development. Among the many benefits that ED offers is the absence of regeneration cycles and the elimination of need to introduce salt to the systems as is done presently for cation resin bed softeners. 6.2.5
Competitive Methods
Conventional water softeners, employing cation resins with automatic features for regeneration, cost between $1,000 and $2,000. Salt (sodium chloride) consumption costs will vary depending upon hardness, efficiency of operation and
APPLICATIONS DISCUSSION
211
the price of salt. The utilization factor for the salt in terms of cation displacement is generally very poor. Usually salt cost per gallon of water, if the initial hardness is in the range of 500 ppm, will be greater than $0.001 to $0.02. Reverse osmosis systems are too slow in operation and too costly to be employed as practical, in-line water demineralizers. An RO unit capable of delivering 4 to 6 gallons per minute peak demand without storage tanks would be quite large and costly.
6.3
Electrical Water Processor Portable Design
Many areas of the U.S. and other countries have water with unacceptable levels of dissolved substances, salts, acids, alkalis, etc. The potability of such water is very limited. Water is either not drinkable or is at least very distasteful. There are only a limited number of ways in which to treat the problem on a small, decentralized scale. Other than introducing improved large-scale, municipal water treatment systems, some alternative options are listed below. 6.3.1
Present Solutions
1. Bottled water - distilled or de-ionized. Cost is high and convenience factor low because of necessity to transport large bulk. 2. Water softener (home type) - replaces dissolved solids with unwanted sodium salts, and requires purchase and handing of salt. 3. De-ionization - Expensive two resin bed systems that are generally not available because of cost and hazard problems associated with regeneration chemicals. 4. Reverse osmosis - High quality water output, but requires high-pressure pumps. Maintenance is significant, equipment cost is high and portability is low.
212
ELECTROCHEMICAL WATER PROCESSING
Another possibility, electrodialysis processing, is an alternative. Inexpensive, table-top batch processing can be achieved with self-contained reservoirs for both waste water and processed water. Two chambers configured to electrically concentrate the dissolved solids into one set of compartments while the other, central chamber, is freed of dissolved materials to a wide range of desired levels. The water in the waste chambers is discarded. No chemicals other than the initial water are needed. The unit does not have to be monitored during operation since the process is self-limiting. The device works well with almost any level of dissolved solids. Heavy concentrations of solutes will not block or contaminate the system. In necessary cases, the unit could be employed as a desalinator (seawater to fresh water converter). 6.3.2
Operation of an ED System
1. 2. 3. 4.
Check to close both drains Fill all chambers from the top Connect unit into wall outlet or (power supply) When indicator shows very low current drain processed water into container. 5. Discard water from the waste water chamber 6. Repeat steps 1 through 5. 6.3.3
D e s i g n Prototype
On the basis of the above operational description, we will briefly outline an early version of a portable processor designed to treat a small quantity of water for personal use. Purification of small quantities of water in a batch process manner for drinking, cooking, washing or other generalpurpose use, such as refilling storage batteries, steam irons, etc., is desirable on frequent occasions. No chemical agents are employed; only electric power is required.
APPLICATIONS DISCUSSION
213
Figure 6.13 shows a small portable unit with a connector mounted at the top, an opening on the top lid for pouring water into the processing chambers, and a release valve at the bottom of the unit from which the processed water is drained into a separate container for later use. At the end of a processing cycle, and after the processed water has been drained out, the waste water is removed from the unit by pouring out of the top opening. Water processed by this device is essentially de-ionized. The device will lower the total dissolved solids (TDS) of the input water to a few parts per million, (1 to 10 ppm). The resultant output will have the properties of relatively high quality distilled or de-ionized water, which is frequently purchased at stores as bottled potable water.
Figure 6.13 Portable demineralizer with static fluids.
214
ELECTROCHEMICAL WATER PROCESSING
Water with dissolved solids as high as 1,000 to 10,000 ppm can be treated with the apparatus above. 6.3.4
Description
The device can have a variety of configurations depending upon the use for which it is intended. As a counter top product for home use, a simple two component system would probably be most appropriate. 1. Power supply (probably wall-plug mounted type) 2. Water processor housing Capacity: 1/2 to 1 gal per processing Processing: 20 minutes to 1 hour depending upon hardness of water and level of purification desired Configuration: Rectangular container with filler holes/ pouring spouts; compact and placed directly on counter. Maintenance: Other than periodic cleaning and washing, there are no other special maintenance requirements that are known at this time. General Characteristics Voltage Current Size Power Input Useful Life Manufacturing Costs Materials:
between 12 and 40 volts d.c. depending upon design 0.25 to 1 amp d.c. depending upon size of unit 1 pint to 2 quarts 10 to 50 watts 3 to 5 years minimum continuous use (very approximate, & dependent upon size) $5 to $12
APPLICATIONS DISCUSSION
Parts: Labor:
215
$3 to $5 $2 to $5
There are no known difficult manufacturing operations involved in the production of the apparatus, nor are there any expensive, rare or strategic materials of construction. • No heating during normal operation because the system is not a thermal process, distillation apparatus. • No moving parts • Water pH can also be controlled • Compact versions of the apparatus make it available to traveling and military applications. • Low salt aspects of the output water make it attractive for health reasons. • Almost maintenance free operation • Safe handling, and low voltage permits easy UL approval.
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
Appendix A: Some Physical Constants and Conversion Factors Useful conversions from one system of units to another are listed below. 1 gram = 15.432 grains 1 once = 28.35 gm. 1 newton = 0.224 lb. 1 pound = 445,000 dynes 1 atmosphere = 14.7 l b / in2 1 joule = 107 ergs 1 calorie = 4.186 joules 1 in2 = 6.45 sq. cm. 1 sq. ft. = 929 sq. cm. 1 cu. in. = 16.39 cu. cm. 1 gallon = 3.785 liters 1 gallon = 231 cu. in. 1 pound = 453.6 gm. 1 kilogram = 2.205 lb. 217
218
ELECTROCHEMICAL WATER PROCESSING
1 slug = 14.6 kgm. 1 foot-pound = 1.355 joules 1 B.T.U. = 252 calories 1 B.T.U. = 778 ft-lb. 1 horse power = 746 watts Some pertinent Physical-Chemical constants are presented for convenience below. Avogadro constant
N
Gas Constant
R
Boltzmann constant
k=R/N
Electronic charge
e=F/N
Absolute Temperature T of the 0° C point o Coulomb q Faraday constant F
6.0238 x 1023 molecules/ mole 1.987 cal/deg-mole 82.06 cm3 atm/deg-mole 0.08205 1 atm /deg-mole 8.31 joules/deg-mole 1.38 xlO 1 6 erg/ deg-molecule 1.602 x 1019 coulombs 273.2° K 1 amp-sec. 96,493 coulombs/ equivalent 26.8 amp-hours
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
Appendix B: Conductance and Solubility The following tables provide the reader with some of the more common and readily available materials properties of specific ions and compounds. A commonly used inorganic salt for electrolytic experiments and in conjunction with reference electrodes is potassium chloride, KC1. Some data for this compound in relatively dilute solutions are presented below, where the equilibrium constant for salt dissociation, K, is defined as
K+
B.l
cr
KC1 Ionization Constants Normality N 0.0001 0.001 0.01
K 0.0075 0.035 0.132 219
220
ELECTROCHEMICAL WATER PROCESSING
Normality, N 0.10 1.0
K 0.495 2.22
As a helpful guide to calculating conductance and corresponding resistivity, the Table B.l below provides some additional related data for the salt KC1. To further provide the reader with typical properties data for some of the more common solutes, Table B.2 below lists some equivalent conductance at different concentrations. Limiting ion mobilities are significant factors for making assessments of conductance and ionization coefficients. The term limiting mobility refers to the value at infinite dilution, i.e., conditions in which interaction with other ionic components is minimum. Some values of the more common ions are listed in Table B.3 below. An extremely useful table to have available for calculating equivalent weights, etc., is a copy of the International Atomic Weights of the Elements (Table B.4).
Table B.l Equiv. per Liter
Dilution ml per Equiv.
Specific Conductance
Equivalent Conductance
1
103
0.1119
111.9
0.1
104
0.0129
128.9
0.01
105
0.00141
141.3
0.001
106
0.000147
146.9
0.0000149
148.9
0.0001
7
10
APPENDIX B: CONDUCTANCE AND SOLUBILITY
221
Table B.2 Equivalent conductance at 298 Deg. K.
c
NaCl
KC1
NaOH
KN03
HC1
HN03
1/2H 2 S0 4
0.0005
125
148
246
143
423
416
413
0.0010
124
147
245
142
421
415
400
0.0020
123
146
141
419
413
390
0.0050
121
144
241
139
416
409
365
0.010
119
141
238
136
412
405
336
0.020
116
138
227
132
407
401
308
0.050
111
134
221
126
399
393
273
0.100
107
129
120
391
384
251
0.200
102
124
113
380
374
234
0.500
93
117
101
359
357
223
333
333
1.00
112
Table B.3 Limiting ion mobilities cm2 /volt-sec. Ion
/ixl0s
Li+
40
ci-
Na+
52
K+
76
H+
363
Ion
//xlO 5
Ion
/ixlO5
79
Ca ++
62
Br
81
Ba++
66
r
80
so4=
83
205
NO-
74
OH
121.8
9 209 10.8 79.9 112.4 40.1 12 140.1 132.9
51
18
33
56
4
82
5
35
48
20
6
58
55
Sb
A
AS
Ba
Be
Bi
B
Br
Cd
Ca
C
Ce
Cs
Antimony
Argon
Arsenic
Barium
Berylium
Bismuth
Boron
Bromine
Cadmium
Calcium
Carbon
Cerium
Cesium
137.4
74.9
40
26.97
13
Al
Aluminum
Atomic Wt.
Atomic No.
Element
Symbol
Table B.4 Atomic weights and numbers.
Mo Nd
Molybdenum Neodymium
Radium
Protactinium
Praseodymium
Potassium
Platinum
Phosphorous
Palladium
195.2 39.1
78 19
Pt K
Ra
Pa
88
91
226
231
140.9
30.98
15 P
59
106.7
46 Pd
Pr
16
8
O
Oxygen
190.2
76
Os
14
7
N
Nitrogen Osmium
58.7
28
Ni
Nickel
144.3
60
20.18
96
42
10
Atomic Wt.
Atomic No.
Ne
Neon
Symbol
Element
o
h-1
on
!» Tl sa O n a
>
H tu
n >
a
n
O
n
M
r
m 1
178.6 4.00
72
2
Hf
He
Helium
Tellurium
Tantalum
Te
Ta
S
Hafnium
197.2
Sulfur
79
Au
Gold
162.5
63.6
92.9
58.9
52
72
16
127.6
180.9
32
87 38
Sr
Strontium
72.6
32
Ge
Germanium
23
11 Na
Sodium
69.7
31
Ga
Galium
107.9
47 Ag
Silver
156.9
64
Gd
Gadolinium
28
14
Si
Silicon
19
9
F
Fluorine
79
34
Se
Selenium
152
63
Eu
Europium
45.1
21
Sc
Scandium
167.2
68
Er
Erbium
150.4
62
Sm
Samarium
66
Dy
Dysprosium
44
Ru
Ruthenium
29
Cu
101.7
Copper
85.5
37
Rb
Rubidium
41
Cb
Columbium
102.9
45
Rh
Rhodium
27
Co
Cobalt
186.3
75
Re
Rhenium
52
24
Cr
Chromium
222
86
Rn
Radon
35.5
17
Cl
Chlorine
z
H
t->
> a (X) o
M
d
a o Z n
Z
o
n
ça
X
o
M
>
Thallium Thorium
Uranium vanadium
1.01 114.8 126.9 193.1 55.9 83.7 138.9 207.2 6.9 174.9 24.32 54.9 200.6
1
49
53
77
26
36
57
82
3
71
12
25
80
H
In
I
Ir
Fe
Kr
La
Pb
Li
Lu
Mg
Mn
Hg
Hydrogen
Indium
Iodine
Iridium
Iron
Krypton
Lanthanum
Lead
Litium
Lutecium
Magnesium
Manganese
Mercury
Zirconium
Zinc
Yttrium
Ytterbium
Xenon
Tungsten
Titanium
Tin
Thullium
Terbium
164.9
67
Holmium
Ho
Element
Atomic Wt.
Symbol
Element
Atomic No.
Table B.4 (cont.) Atomic weights and numbers.
232.1 169.4 118.7 47.9
90 69 50 22
Th Tm Sn
131.3
54
Zr
40
30
39
Y Zn
70
Yb
Xe
51
23
V
91.2
65.4
88.9
173
238.1
92
u
183.9 74
W
Ti
204.4
81
Tl
159.2
65
Tb
Atomic Wt.
Atomic No.
Symbol
o
z
on
ta
o n
ta TI
5
>
ñ
g
M
n
O
!«
H
n
M
r1
m
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
Appendix C: Feeder Tube and Common Manifolding Losses In designing an array of cells, there are many additional factors to consider for the purposes of optimization. Among these are such considerations as the shape and size, manner in which cost changes with geometry, electrical power supply requirements and electrical current losses encountered in the common manifolding of cells that are supplied with water from a common source. Cells are interconnected by common manifolds that are so large in cross-sectional area that they present little electrical resistance to short circuiting currents. The only significant resistances to the common connections are those in the smaller diameter, longer length feeder tubes. In electrodialysis systems, there are four such circuits in parallel electrically. Two manifolds and corresponding feeder tubes for the entering water, and two manifolds for the separate exiting water processed and waste water 225
226
ELECTROCHEMICAL WATER PROCESSING
channels. This situation is true regardless of the specifics of the design geometry and manufacturing methods of module construction. Figure C.l shows the general configuration with only two of the four alternate manifolds illustrated. Manifold cross sectional area is much larger than the individual feeder tubes for the individual cells. The following is the development of the equations describing the common loop current losses, (parasitic currents), that an ED array experiences. Figure C.2 shows the simple mesh current model that represents the leakage paths through the parallel hydraulic circuits model employed in arriving at the expressions and consequent estimates of coulombic losses. In other words, electrical current that does not contribute to the separation of dissolved substances from the processed water stream. Each cell is represented as a voltage source, E, and the electrical resistance path due to the feeder tubes or channels from each cell to the common manifold is represented as the constant, R. If all the fluid supply channels are the Exit manifold
Electrodes Membranes
Feeder tubes
Entrance manifold Figure C.l Manifold configuration.
FEEDER TUBE AND COMMON MANIFOLDING LOSSES
R:
R -I E
^
E
227
R:
Hh E
-I E
Figure C.2 Equivalent circuit for common manifold.
E
E
E
Figure C.3 Single manifold - Equivalent manifold.
same in construction the resistances, R, are all equal and constant. There are a number of ways in which the analysis of the electrical current losses can be determined. Simple application of Kirchoffs Law enables us to calculate the dissipative current through any cell in an array. Figure C.3 shows the loop currents assumed in the series of circuits of the array of cells. Each small loop is treated as an independent circuit except for the interconnectivity due to currents flowing in the adjacent resistances from other loops. After establishing the basic relationships, we can construct a series of simultaneous, linear equations to be solved for calculating the currents. The form of these equations is as follows. For any one loop in the circuit array the expression has the form of equation C.l. Tracing the potential around the nth loop results in the sum of all current producing voltages passing through the respective feeder tube resistances equals the voltage of that particular cell produced by current flow through the cell. The cell voltage, E, is that expressed in Equations (4.25) and (4.87).
228
ELECTROCHEMICAL WATER PROCESSING
2i n -R = E + i n . 1 -R + i n+1 -R
(C.1)
where n =1 to N, if there are N number of cells in the array. The current passing through the n t n cell due to the common manifold circuit is i n . A sample calculation of the above solution can be made by taking a 10 cell array, and solving for the currents in each cell. The equations are: 2irR = E + i2-R 2i2-R = E + irR + i3-R (C.2) 2i9R = E + i 8 R + i10R 2i10R = E + i 9 R If we assign some values to both R and E that are typically in the range of operating ED systems, we can solve for the currents to obtain an idea of the dissipation current distribution. Also, in order to see what the shape and the magnitudes of the dissipation currents are we must settle upon values for the geometry of the feeder channels from the manifold to the cells. Let E = 1 volt, and the electrolyte resistivity be in the order of 200 ohm-in., and the length, 1, and diameters, d, of the feeder channels can be about 0.10 in. and 1 in., respectively. The solution of the equations above give the calculated values for the currents through cells one through ten as follows. For p=200 ohm-in.
For p=2 ohm-in.
ii = 1.96x10""4 amps \ = 3.53 i3 = 4.7 \ = 5-5 \ = 5.89
0.0196 amps 0.0353 0.047 0.055 0.0589
FEEDER TUBE AND COMMON MANIFOLDING LOSSES
For p=200 ohm-in.
For p=2 ohm-in.
\ = 5.89 \ = 5.5 i = 4.7 \ = 3.53 i10 = 1.96
0.0589 0.55 0.47 0.353 0.0196
229
Dissipation currents are highest in the middle cells, and diminish toward either end cell. The solution concentration in the waste water channels can be between 10 and 100 times greater than in the processed water side. In fact, if the ratio of waste water to processed water is to be as high as practical, these could very well be the range of concentrations encountered in any operating ED systems. The values above are, for most water demineralizing applications, quite high. Significant coulombic losses can certainly be encountered in desalination ED systems where the salt water conductivities are high. The two entering water concentrations will be the same, and at the level of the initial input water source. However, one of the manifold systems at the exit will be at the concentration of the waste water, and will be the major contributor of any parasitic current losses. Figure C.4 is a plot of the two values of currents from the above table. As is readily seen, the most severe dissipative current, or coulombic losses are in the inner most, or middle cells of an array. Another current calculation that results in the same answers as derived by the preceding calculations is shown in Figure C.4. Here, the loop currents are taken differently. Instead of independent for each small circuit in the series, the currents are assumed as all originating from the first cell and circulating through each of the succeeding circuits in turn. Thus, the first current, iv passes through only the first cell, and the second current, i , passes from the first resistance, R, and then through around through the third resistor, R, and then through the two cell sources, E.
230
ELECTROCHEMICAL WATER PROCESSING Ten cell array 0.07 0.06
E
0.05
< 0.04 "'<
' ■
0.03 O
/
!
0.02 0.01 n
4
5 6 7 Cell number 200 ohm-in 2 ohm-in
10
11
Feeder tube diameter = 0.10 in. Figure C.4 Dissipative current per cell in an array. Consecutive and cumulative current loop analysis
E
E
E
E
E
Figure C.5 Consecutive and cumulative current loop analysis.
The relationships that describe the above current flows again are a series of N simultaneous equations having the form: N
X(inR) + inR = nE
(C.3)
The dissipative current, i n , passing through the n*" cell is given as N
in = X i n ' R
(C.4)
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
Appendix D: Variable Current Density D.l
Current Density Variation
The equations for the non-linear change in current density along the length of an ED cell with continuous and constant water flow were developed in Chapter 4. However, another, somewhat more detailed derivation is present below. For a better estimation of cell performance, we will treat the variation of current density along the flow path in closer approximation of reality. In Figure D.l the area current density is shown as the current conducted through an area of unit width and length, dx. Because the current density is constant in any direction normal to the cell length, or the x-direction, the current element taken for integration is ixW. The electric current density, ix, at any point at distance, x, from the entrance is (see Figure D.l)
231
232
ELECTROCHEMICAL WATER PROCESSING Current element, 1x Water flow direction
Figure D.l Area current density.
i x =E-c x /0-p
or
E-TJX-X
i
2 ° , Pe ^P ' -v-,
=
(D.l)
0-P
Because the current density is assumed constant along any path normal to the water flow, we can represent the electric current element, px, of width, W, as (D.2)
Px =i x -W
To calculate the total current flow across the electrode area, WL, we must integrate the above expression, or J px ■ dx = I,
the total current
(D.3)
By substitution, we obtain the complete expression for the current density as
px = w ^ ^ d x
WEcc 0-p
•e-Mxdx
(D.4)
This has the following general form, and for the sake of convenient shorthand we will temporarily substitute the symbols M and N for the respective polynomials. j"oLpx • dx = j*LNe"Mxdx = I
(D.5)
APPENDIX D: VARIABLE CURRENT DENSITY
233
Integrating directly for I, between the limits L and 0,
2i- e -M-x
NÍ L e" M x dx
M
Jo
+ constant
(D.6)
Boundary conditions are when x=0, 1=0, Thus the constant is evaluated, and the solution is
I=[l-e"ML] 21 M
(D.7)
Replacing terms into the equation for I for quantitative evaluation, we obtain E-77-A
l_e
Wc0pvyg
(D.8)
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
Appendix E: Mathematical Analysis: Water pH Control Cell and Ion Exchange Resin Regeneration The purpose of presenting the following analyses and proposed hardware configurations is to stimulate further thought in these directions, and promote development of practical systems for the many application needs that exist in the industrial and commercial world. To facilitate the design of an electrochemical system for the regeneration of resin stacks in water treatment devices, the following analysis has been performed. This mathematical treatment is independent of the analyses to follow in the other appendices, and it is specifically directed at the issue of generating hydroxyl and hydrogen ions for pH control purposes. This study of the processes involved in the operation of a pH control cell will be of assistance in the selection 235
236
ELECTROCHEMICAL WATER PROCESSING
of materials combinations, components and cell stack geometry for multiple cell arrays. The types of considerations entering into the design engineering of a total, self-regenerating system include these items: 1. Ion transfer membrane thickness and type of material including such parameters as ion diffusion, water transfer, and electrolytic conductivity 2. Inter-electrode spacing for optimum performance 3. Resin properties and size of beads 4. Electrode area 5. Electric current densities. The analysis that ensues was conducted on the basis of minimum initial assumptions in deriving the first series of expressions. This text is directed toward developing a series of equations along with their solutions that results in a quantitative relationship for the concentration of H + (hydrogen) ions a n d / o r OH" (hydroxide) ions in either the resins or in the water as functions of time. These concentrations are given in terms of the various physical parameters of the operating system in question. An important assumption made in these first derivations is that the generation rates by electrolysis of H + and OH" ions are constant, i.e. independent of specific ion concentrations at any point in time- In other words, the supply of appropriate ions is essentially unaltered during the cell operation, and there are no competing electrode processes such as deposition of metals at the (-) electrode, or generation of halogens at the (+) electrode. Figure E.l shows the general configuration employed in which the regeneration electrodes are an integral part of the deionization stacks. The resin beads are stacked between the membrane and their respective electrode. The cation exchange resin is contained in the "positive" compartment,
APPENDIX E: MATHEMATICAL ANALYSIS
Cation Resin
Cation membrane
Input water
237
Anion resin
Anion membrane
Deionized water output
Figure E.l Three chambered - Continously operating cell basics.
and the anion exchange resin in the "negative" compartment of a cell. The membrane is held rigidly in the center of the cell by suitable plastic screen spacers. During operation, water (electrolyte) flows into the positive, (+), side of the cell, and thence out and into the negative, (-), side. The exiting fluid is the de-ionized water. During regeneration, water is stagnant in the cell and provision is made for venting the H 2 and the 0 2 gas by product. Cell volumes and final salt levels are then estimated to determine the practicality of regeneration with a non-flowing water configuration. Non-flowing-fluid situation during regeneration would simplify the valving and switching requirements. Flow through during regeneration would necessitate the introduction of additional hydraulic circuits to convert from one configuration to another when operating modes are changed. Flow during operation of the system as a deionizer is serial. If flow were to be needed during regeneration, a parallel path would have to be provided through the two cell compartments. Some tests were run with a two-cell configuration in which the resins were integral with the electrode/membrane
238
ELECTROCHEMICAL WATER PROCESSING
assembly. Among the critical factors in the assembly design are: • • • •
Coulombic efficiency Resin capacity Resin void volume ratio time allowed for regeneration
For example, if we set the coulombic efficiency at 50% and the resin capacity at 12,000 grains per cubic foot volume of resin, resin void volume percentage at 30%, and regeneration time at 5 hours, the second set of numbers in Table I gives the current densities needed as the electrode spacing is increased. Current densities range from 0.011 to 0.18 amps/sq in, and the max concentration is constant at 1.43 normal. Equations and derivations for table E.l are given in Appendix A.
E.l
Analytic Approach
Figure E.2 is an illustration of the basic processes in a regeneration cell that contains no resins. This cell would function Hydrogen & hydroxyl ion injection system - symmetrical Low pH input
Effluent @ high pH
H+ Ions
+
a
Main water supply input Figure E.2 p H control cell.
OH" Ions
l
K
.so:
No+
.OH"
H+
-o'
APPENDIX E: MATHEMATICAL ANALYSIS
239
strictly as a pH control device in which acid and base are produced from salts initially present in the water. As shown in Figure E.2, the various ionic species and the rate processes associated with them are listed below. It must be remembered that all densities, concentrations, etc. are normalized on the basis of per square inch of electrode area. Table E.l provides a listing of these processes and the ions present in the two sides of the cell. Now, let us take each one of the above rates and ion specie concentrations and describe them in terms of the system Table E.l Rate process. Symbol
General Description on a per Square Inch Basis
RH(G)
Rate of H + ion generation via electrolysis
ROH(G)
Rate of OH" ion generation via electrolysis
RH(TD)
Rate of H + ion trans-barrier thermal diffusion
ROH(TD)
Rate of OH" trans-barrier thermal diffusion
RH(ED)
Rate of H + transfer via electric current
ROH(ED)
Rate of OH" transfer via electric current
RC(TD)
Rate of cation, Na+,Ca++, etc thermal diff.
RC(ED)
Rate of cation transfer in electric field
RA(TD)
Rate of Anion, Cl", S0 4 = , etc thermal diff.
RA(ED)
Rate of Anion transfer in electric field
If ion exchange resins are present, These are additional terms must be taken into account RR(H)
Rate of Cation Resin H + concentration change
RR(C)
Rate of Cation Resin cation concentration, change
RR(OH)
Rate of Anion Resin OH" concentration change
RR(A)
Rate of Anion Resin anion concentration change
240
ELECTROCHEMICAL WATER PROCESSING
Table E.l (cont.) Rate process. Quantity Symbol
General Description
Qc
Cation resin cation concentration, GEW per cu. in.
QA
Anion Resin anion concentration
QH
Cation Resin H + concentration.
QOH
Anion Resin OH" concentration.
q+c
Cation concentration, in Positive (+) Side
qH
H + concentration, in (+) side
q+A
Anion concentration, in (+) side
q.c
Cation concentration, in Negative (-) Side
qOH
OH" concentration, in (-) side
q.A
Anion concentration, in (-) side
Q0
Initial resin cation concentration., full regeneration.
q0
Initial salt concentration in water
operating parameters. It is possible now to relate these various parameters to each other in a quantitative manner. Taking each of the rate quantities and relating them to the electric current density and the relevant ion concentrations, we obtain the following. Rate of generation of H+ ions is directly proportional to the electric current. Since all computations are performed per unit area of electrode, the relationship is RH(G) = ia (at the negative electrode) where the constant, a, is the faraday equivalent, F, times the coulombic efficiency. The units are: i = amps/in 2 F = 26 amp-hours/gm equiv. wt. RH(G) = gm equiv. wt./in 2 -hour
APPENDIX E: MATHEMATICAL ANALYSIS
241
(The above also assumes negligible metallic plating on the negative electrode) Rate of hydroxide ion generation is similarly defined, if there are no competing reactions in the electrochemistry at the positive electrode. If we assume no generation of free halogens, essentially the only reaction possible is e + H20==OH- + l / 2 0 2 , and the expression is identical to that for RH(G). Thus ROH(G) = RH(G) = ai RH(TD) is the net rate of H + ion migration across the barrier membrane from one cell compartment to another, this diffusion is due to thermal phenomena only and is independent of any electric current flow and charge carrier transport process. The rate is given as RH(TD) = k ^ gm equiv. wt./in 2 -hr where qH is in gm equiv wt per in3 There are no H + ions on the negative side. ROH(TD) is described in the same fashion as RH(TD), and is ROH(TD) = k2qOH There are no OH" ions in the positive side. RH(ED) is the rate with which H + ions are transported from the (+) to the (-) side as part of the charge carriers in the conduction of electric current. This is a loss factor of the generated H + on the (+) side. The rate is proportional to the product of the electric current flow times the H + concentration, and is represented as RH(ED) = ibqH
242
ELECTROCHEMICAL WATER PROCESSING
R„„(ED) is the rate of electric field induced flow of hydroxide ions across the membrane, and has the same form as all "(ED)" processes. Since there are no OH" ions in the (+) side, the net expression is ROH(ED) = icqOH RC(TD) is similar functionally to RH(TD). It is the diffusion due to the concentration difference in the (+) and (-) sides of the cell. Generally, the cations will be produced in the (+) side due to the displacement of cations in the (+) side resin by the H + ions in solutions and generated electrochemically. Diffusion is from the (+) to the (-) side. RC(TD) = k3q+c - k4q.c RC(ED) is the rate due to the conduction of electric current through the cell, and since cations have a (+) charge, the migration is toward the negative side, and expressed as RC(ED) = irq+c RA(TD) = k5q_A-k6q+A Flow usually from the (-) to the (+) side. RA(ED) = isq.A In the case where there are ion exchange resins present in the cell compartments, these additional rates are involved; RR(H) is proportional to the quantity per unit volume, or concentration of cations in the (+) side resin multiplied by the concentration of H + ions in the surrounding water, or RR(H) = eq+cQHW2v Similarly, RR(C) = fqHQcW2v
APPENDIX E: MATHEMATICAL ANALYSIS
243
RR(OH) = gq.AQOHWV RR(A) = hqOHQAW2v The next step is the establishing of equations for solving. The purpose is a final expression which will give the concentration H + or OH" or cations or anions in either the water or in the resin stack as a function of time, and in terms of the various system and materials constants. The equations are as follows. Table E.l shows the various rate process directions. The total cations in the system is Q o + 2qo (if the volumes of water and resin on the (+) and (-) sides are equal.
Qo + 2qo = qc-q-c + Qc
<E.D
The balance of ions on the (+) side, q+c + qH = qA (no OH" in (+) side, pH>7)
(E.2)
The balance of ions on the (-) side, q.c = qOH + q.A (no H + in (-) side, pH<7)
(E.3)
The cation resin ion balance, QC = Q O - Q H
(E.4)
Total anion balance in the system, Qo + 2q0 = qA + q.A+ Q A
Œ-s)
Anion resin ion balance, QA = Q0-QOH
(E.6)
The rate, dq H /dt, with which the concentration of H + ions is changing in the ('+) side is the sum of some of the above rates, and is given below.
244
ELECTROCHEMICAL WATER PROCESSING
d q H / d t = RH(G) - RH(TD) - RH(ED) - ROH(TD) -R OH (ED) + R R (H)-R R (C)
(E.7)
Similarly, the rate of change of OH" ion concentration in the (-) side is, dq O H /dt = ROH(G) - RH(TD) - RH(ED) - ROH(TD) - ROH(ED) + RR(OH) - RR(A)
(E.8)
Other relationships that can be written are the necessary charge balance of total ion migration across the membrane. Thermal diffusion of ions across the membrane must result in zero net charge transfer. Hence, we have RH(TD) - ROH(TD) + R(TD) - RA(TD) = 0
(E.9)
Electric field gradient induced diffusion, (charge transport for electric current flow support), must result in the faraday equivalent of charge transport across the membrane corresponding to the net electric current density, i. RH(ED) + ROH(ED) + R(ED) + RA(ED) = iF
(E.10)
where F = faraday equivalent. The above rates in equation (E.10) are all "loss terms" with respect to their side of origination, and hence are additive as shown. Rate of loss and gain of ionic species within the two ion exchange resins are expressed below. As a convenient shorthand notation for the first derivative of a variable we will use the "pounds". symbol, or # = d/dt. In the cation resin, W#Q c = dQ c /dt = -dQ H /dt = RR(C) - RR(H)
APPENDIX E: MATHEMATICAL ANALYSIS
W#Q c = (fqHQc -eq_cQH)W2v
245
(E.ll)
In the anion resin, W#Q A = d Q A / d t = -dQ O H /dt = RR(A) - RR(OH) W#Q A = (hqOHQA - gq A Q OH )W^
(E.12)
Remember, all q terms are concentrations, and we are performing all calculations on the basis of 1 in2 of electrode surface area. Some additional relationships that will be needed to solve the total transport problem are discussed below. Since there are no sources or sinks for anions in the (+) side, the only gain or loss mechanism in that region for anions is the diffusion from the (-) side, or #q+A = dq + A /dt = isq.A
(E.13)
Also, since there are no sources or sinks for cations in the (-) side, changes in cation concentration in the (-) side can be due only to trans-compartment diffusion, or #q_c = dq_ c /dt = irq+c
(E.14)
NOTE: The thermal diffusion rates are assumed, for the sake of greater simplicity, to be very much smaller than those resulting from current flow. Henceforth, in this analysis, the (TD) terms will be dropped. To further simplify the nomenclature employed here, and to make it more readily usable in computer math programs, we will substitute more abbreviated symbols for the system variables. Taking inventory of the various parameters and equations also enables us to assess the status of our analysis.
246
ELECTROCHEMICAL WATER PROCESSING
Let us substitute the following for the various ionic quantities identified earlier. A
=qH B=q. c C=q+C D=Qc I =QoH
E = q+A L = q-A G= q O H H = QH
J
= QA
There are ten variables, the solution of which requires ten independent equations. Also, we let Q o = Q, and qo = q. The equations now become, Q + 2q = B + C +D
(E.l)
A+C=E
(E.2)
B=G +L
(E.3).
D=Q-H
(E.4)
Q + 2q = E + L + J
(E.5)
J = Q-I
(E.6)
#A = ia - ibA - icG + eCH - fAD = irC + isL + #Qc (E.7) #G = ia -ibA - icG + gLI - hGJ = irC + isL + #QA (E.8) F = bA + rC + cG + sL
(E.9)
#Q c = eCH - fAD
(E.10)
#QA = gLI-hGJ
(E.11)
#E = isL
(E.12)
APPENDIX E: MATHEMATICAL ANALYSIS
#B = irC
247
(E.13)
If we choose to solve for qH as a function of time, equations (E.l) through (E.7) and equation (E.9) provide eight of the ten needed relationships. The two additional equations may be obtained as follows. Differentiating equation (E.3), we obtain, #B = #G + #L Substituting for #B via equation (E.13), for #G via equation (E.8), and for #L via the derivative of equation (E.5), 0 = #E + #L + #J The ensuing operations are shown below. dq_ c /dt = dq O H /dt + dq_ A /dt = dq O H /dt + (-dq +A /dt - dQ A /dt) #B = #G + #L = #G + ( #E - #J) Substituting irq+c = (ia - icqOH -ibqH + QA) + (-isq.A - QA) the above becomes ir
q +c + isq.A = ig - ic q OH - i b q H
or rC + sL = a -cG -bA
(E.14)
The tenth equation, shown at the bottom of page 244, may be obtained by substituting from equations (E.l2) and (E.13) into equation (E.9), and solving for dq H /dt. F = bA + r(E - A) + cG + s(B - G)
248
ELECTROCHEMICAL WATER PROCESSING
differentiating, we obtain 0 = b#A + r(#E - #A) + c#G + s(#B - #G) = #A(b - r) + #Er + #G(c - s) + s#B = #A(b - r) + isrL + #G(c - s) + irsC 0 = (ia - icG - ibA + #Qc)(c - s) + #A(b - r) + isrL + irsC
(E.15)
E.2 Special Case Evaluation - No Resins Present in System A first approximate solution to a special configuration is of interest here. The simple analysis that follows is for a cell that contains no resins on either side of the membrane. It will operate strictly as a pH control or acid/base-generating cell. Some fraction of the salts initially present in the cell water will be converted to acids and alkalis. The following assumptions are made: • Constant electric current density • Only H 2 and 0 2 are evolved at the electrodes. Now equations (E.7) and (E.8) become, dq O H /dt = ia - icqOH - ibqH, and d q H / d t = ia - icqOH - ibqH.
(E.16) (E.17)
Obviously dq O H /dt = dq H /dt. Also, since there are no sinks or sources for H+ and OH ions on the (-) and (+) sides, respectively, of the membrane other than their diffusion across the membrane, and also because diffusion of H + into the (-) side and diffusion of OH" into the positive side cancels out with the the formation of water,
APPENDIX E: MATHEMATICAL ANALYSIS
249
The diffusion coefficients, b and c, do not necessarily have the same value. The resultant equation for #qH, (dq H /dt), is #qH = ia - iqH(b +c)
(E.18)
Transposing terms to solve for this first-degree differential equation dqH
i a - i q H ( b + c)
-=dt
vu \ J t -i(b+c)dq H or, -i(b +c)dt = -^Lia-iqH(b+c) Direct integration yields ln(ia - iqH(b + c)) = -i(b + c)t + const. ia -iqH(b + c) = K^xpHO) + c)t) + K2
(E.19)
To evaluate the constants the following limits are employed. When t = 0; When t = infinity. When t = 0
qH = 0 dqH/dt = 0 d q H / d t = ig
The constants are evaluated as, ia - i(0) = Kjexp (0) - K2, , „ u . .„ v -Kiexp(-it(b + c)) - K2 - ig and #qH = ia - i(b + c) x ^~ 4 i(b + c)
250
ELECTROCHEMICAL WATER PROCESSING
The constants are, K1 = ia, K2 = 0 And the final expression is, qH =
a - a.exp(-it(b + c))
*7d
m
_m
(E 20)
'
NOTE: All of the above assumes that the supply of cations on the (+) side and the supply of anions on the (-) side are inexhaustible for the duration of a regeneration run. Hence, we find that all generation rates for ions are such that the increase in the ions is a constant term minus an exponential. Another important consideration in these relationships is the need to distinguish between quantities of materials transported or in solution and concentration of the same material. In all of the above equations involving rate processes the terms involving rates are quantities per unit time per unit area, because all computations are performed on the basis of normalized electrode and membrane area of one in2 Hence, the foregoing equations must be modified to reflect this issue as follows. Returning to equations (E.16) and (E.17), we have, dq O H /dt = 1/w (ia - icq OH - ibqH) = d q H / d t
(E.21)
The term, w, is the thickness of the cell compartments, i.e. the distance from electrode to membrane, and is assumed the same on both sides of the cell. Since the rate term is in dimensions of GEW/in 2 of electrode, dividing by cell half width only is necessary for the specific volume correction. E.2.1
Non-Constant Electrochemical Generation Rates for H + and OH
If we introduce the fact that the availability of cation and anion species will become increasing limited as they
APPENDIX E: MATHEMATICAL ANALYSIS
251
are depleted in their respective cell compartments, and that coulombic efficiency will diminish accordingly, the following modifications in the equations are made. The constant generation term, ia, on page 241 for the rates RH(G) and ROH(G) is replaced by trans-barrier diffusion terms. Since the production and net increase of a H + ion in the (+) side must be accompanied a loss of a cation or gain of an anion in that side, the generation rate may be more appropriately represented by RH(G) = irq+c + isq.A. Similarly, the net gain of a OH" ion on the (-) side is due to either the loss of an anion or gain of a cation to the (-) side. Hence ROH(G) = irq+c + isq.A, and RH(G) = ROH(G). With these new generation terms equations (E.7) and (E.8) become, d q H / d t = #qH = irC + isL - ibA - icG + eCH - fAD
(E.7a)
dq O H /dt = #qOH = irC + isL - ibA - icG +gLI -hGJ
(E.8a)
As before, we may now proceed to find the needed ninth and tenth equations. The first eight equations are (E.l) through (E.6) and (E.7a) and (E.9). Differentiation of equation (E.3) gives #B = #G + #L
(E.22)
252
ELECTROCHEMICAL WATER PROCESSING
Equation (E.22) says dq c / d t = dq O H /dt _ dq A / d t = dq O H /dt + (dq + A /dt - dQ A /dt) Because #B = irC, and #G = irC + isL - ib A - icG + QA and #L - - #E - #J from the derivative of equation (E.5), we have by substitution into equation (E.22), irC = (irC + isL - ibA - icG +QA) -isL - QA The above reduces to, bA = sG.
(E.14a)
The tenth equation may be extracted from equation (E.9) and its derivative. Substituting equation (E.14a) into (E.9), F = 2bA + rC + sL.
(E.23)
Differentiating equation (E.9) gives, 0 = 2b#A + r#C + s#L.
(E.24)
In order to substitute for #C and #L in the above equation, we must return to equations (E.7a) and (E.8a) as well as (E.2) and (E.3). Differentiating (E.2) and (E.3), we obtain
#L = #B - #G, and
(E.25)
#C = #E - #A.
(E.26)
equations (E.12) and (E.13), #L = irC - #G, and
(E.27)
#C = isL - #A.
(E.28)
APPENDIX E: MATHEMATICAL ANALYSIS
253
Substitution of values for #G and #A from equations (E.7a) and (E.8a), we find #L = ibA + icG - isL - QA, and
(E.29)
#C = ibA + icG - irC - Qc.
(E.30)
Now we can return to the derivative of equation (E.9) again and complete the algebraic manipulations. 0 = 2b#A + r(ibA + icG - irC - #Qc) + s(ibA + icG -isL should be isL
(E.31)
It is further necessary now to substitute for #Q c and #Q A in the above expression. 0 = 2b#A + irbA + ircG -ir2C - r(eCH - fAD) + isbA + iscG - is2L -s(gLI - hGJ).
(E.15a)
Solution of the preceding resultant equations is obviously quite laborious. They are complex expressions with many terms. Ultimate solution of the time dependence relationships for qH, Q H , etc. necessitates the solution of the net differential equation which one extracts from the above and which contains only the constants and is entirely in terms of the one dependent variable and time, t. The above has been performed with the solution of A, or qH, in terms of time in mind. The equations can, of course be manipulated such that the final, resultant expression is in terms of any one of the other dependent variables versus time. Solution of these equations would be greatly facilitated in the sense of reduction of the number of terms if numerical values for the constants can be substituted. Even with that advantage the expressions are cumbersome enough to suggest the use of a symbolic mathematics program to assist with the algebra and substitutions. A program known
254
ELECTROCHEMICAL WATER PROCESSING
as MuMath (Microsoft) has been employed to significant advantage. Continuation of these calculations should be done with computer assistance. E.2.2
D i m e n s i o n s and Units
Diffusion processes are generally described by the Fick's Law relationship that has the form
jp=-kfA-
(E.32)
dt dx The quantity of material, Q, which diffuses or migrates through a medium is directly proportional to the product of the concentration gradient of that material in the medium and the cross sectional area of the path. The dimensions of the terms are; Q C x A k
= quantity of material, grams, moles, etc. = quantity of material per unit volume, gm/in 2 ,... = length, cm, in.,... = area, cm2, in 2 ,... = reciprocal (time)(length), cm-1 sec 1 ,...
In setting up the equations for this electrochemical/ ion-exchange process, the units of the q quantities are "normals/in 2 ", or "gram-equivalent-weights per square inch" of electrode area. Thus the constant terms appearing in the equations would have to contain the specific volume values of the cell components or additional provision must be made to normalize the expressions dimensionally. Reviewing the equations and normalizing for specific volumes, we have: Cell volume/in 2 = 2W, since W is the distance from the membrane to either electrode, (equal spacing in (+) and (-) side. The void volume ratio for the resins is v, and vW gives the void volume available for water.
APPENDIX E: MATHEMATICAL ANALYSIS
255
The previous equations are modified accordingly and listed below. Qo + 2q0 = qc + q-c + Q c
OE-D
Q + 2q = B + C + D same A + C = E
(E.2)
same B = G + L
(E.3)
same D = Q - H
(E.4)
Qo + 2q0 = q+A + q . A + Q c
<E-5)
Q + 2q = E + L + J same J = Q -1
(E.6)
vWdq H /dt = vWia - ibA - icG + (eCH - fAD)W2v
(E.7)
vWdq H /dt = irC + isL - ibA - icG + (eCH - fAD)W2v
(E.7a)
vWdq O H /dt = vWia - ibA - icG +(eCH - fAD)W2v
(E.8)
vWdq O H /dt = irC + isL -ibA - icG + (gLI - hGJ)W2v
(E.8a)
vWF = bA + rC +cG + sL
(E.9)
rC + sL = avW - cG - bA
(E.14)
samebA=sG
(E.14a)
0 = (iavW - icG - ibA + #QcvW)(c - s) + #A(b - r)
(E.15)
0 = 2b#A + irbA + ircG - ir2C - (eCH - fAD)rvW + isbA + iscG -is2L - (gLI - hGJ)svW
(E.15a)
256
E.2.3
ELECTROCHEMICAL WATER PROCESSING
Variable Electric Current Densities
Unless constant current supplies are employed in the electrochemical regeneration mode, a more realistic set of electrical circumstances would involve current density dependence upon dissolved solids level in the water. As regeneration proceeds, the concentration of acid and dissolved salts will increase in the (+) side, and alkali and dissolved solids will increase in the (-) side. With this increase in solute content the electrical conduction rises. If a constant voltage supply were employed then the d.c. current through the cell would increase directly as the specific conductivity of the water rose. The following is another simplification of probably real circumstances, but it more closely approaches actual conditions than the previous assumption of constant current throughout the regeneration process. The salt concentration will increase from some few hundreds parts per million level to perhaps tens of thousands of parts per million toward the end of regeneration. That is quite a large spread in concentration and conductivity. The conductivity, P, of the water may be expressed as P = P(q+C + q H ) / W ' or P = p(q.A + q OH )/W, or P = p(q +A )/W, or P = p(q_c)/W, if the concentrations on either side is at about the same level, and if the spacings on either side are equal. P is in units of ohm 1 in"1, and p is a proportionality factor having the dimensions of ohm 1 in2 GEW. If there is a great disparity in total ionic concentrations between the (+) and (-) sides, then an expression of the form below might be employed as an averaged value of conduction. p = p(q+c + qH + q-A + qoH)/2w.
Œ.33)
APPENDIX E: MATHEMATICAL ANALYSIS
257
The electric current density, i, is then represented at anytime as, i = EP
(E.34)
where E is the applied electric potential in volts d.c.
E.3 Estimation of Resin Constants The constant coefficients, e, f, g, and h, which determine the rates with which the various ions are displaced at the resin sites must be inserted in the balance equations. These coefficients may be approximated for the present from general information regarding resin bed regeneration via standard acid and alkali washes. There is no question that the time constants or reaction rates are dependent upon the size of resin beads and the state of regeneration of the resin as well as the flow pattern or "film depth" of the water medium surrounding the beads. A concentration of 1 normal HC1 or H 2 S0 4 will regenerate a resin bed within 1 hour, and the solution undergoes a depression in concentration of about 50%. Thus we may represent, as an averaged expression, the decay in ionic concentration as the following. The diffusion relationship has the form; vWdQ c /dt = (eCH - fAD)vW2 = K[CH - AD]vW2
(E.35)
Integrating, and letting e = f = K, indicating that the resin has no greater or lesser preference for H + than for other cations, we obtain; «Q= . . * _ dQc vW(eq+cQH - fqHQc) K[q+cQH - qHQc]vW
258
ELECTROCHEMICAL WATER PROCESSING
Now, during the period of regeneration we will set the following conditions as a trial; Qc goes from Q o to 0.05Qo qH = constant qc = constant
qVqH = lN QH = Q O - Q C
But, we must first solve the above equation to evaluate K. The above equation becomes, after substituting for Q H , vWdQ c /dt = K[qc(Qo - Qc) - qHQc]vW = -K[Qc(qH + q c )-q c Q o ]vW
(E.37)
Transposing terms and factoring for integration,
= "K d t ( ^ + qH)vW
(E.38)
ln[(qc + qH)Qc - qcQo] = -Kt(qc + qH)vW + Kl
(E.39)
[(qc + qH)Qc - qcQo] = Kl exp(-Kt(qc +qH)vW)
(E.40)
(qC + dQc u[(qc + q HVn ) Q c - ni qcQ0]
Integrating, we get;
Or,
To solve for the value of the coefficient, Kl, the constant of integration we set the limits, when t - 0, Qc = Q o , which describe the initial conditions of the resin at the start of the regeneration process. (This initial condition should reflect more accurately the level or extent of regeneration of the resin beds due to the electrochemical process).
APPENDIX E: MATHEMATICAL ANALYSIS
259
Substitution of the above conditions yield Kl = q H Q 0 .
(E.41)
Inserting that value of Kl into the main equation gives Kqc + qH)Qc - qcQ0] = qHQD ex P (-Kt(q c + qH)vW)
(E.42)
Based upon general data regarding performance and chemical regeneration of resins in present systems, it seems that these are reasonable conditions to impose for the evaluation of K. Apparently a cation resin bed can be regenerated within one hour by passing a 1 normal solution of HCl over the bed. The concentration of the emergent acid is in the range of 0.7 to 0.6 N after removal of the cations, and the remainder is 0.3 to 0.4 N cation solution. The regenerated resin is evidently 90%, or greater, regenerated in the process. Thus it is reasonable to set these as additional boundary conditions in assessing the material constant, K. When t = 1 hour, Qc = 0.05Qo, from an initial value of Q o . Substitution again gives 0.05qH - 0.95qc = qH exp(-K(qc +qH)vW)
(E.43)
Qo cancels out of both sides of the equation. Now for the various constants of the materials and system! If an ion bed has the capability of removing 17,000 grains per cubic foot, then this corresponds to 1130 grams per cu. ft., or 0.65 grams/in 3 . At an average of 50 grams per gram equivalent weight of most inorganic dissolved substances, the capacity of the resin then is 1.31xl0-2 GEW per in3 of bulk resin volume. It is interesting to note here that the values of K exist over a limited range for the conditions imposed in the above. If e = f = g = h = K, we see that K has values not greatly dependent upon qc, qH, or percentage of regeneration. Examination
260
ELECTROCHEMICAL WATER PROCESSING
of the table below shows the variation in K over a range of values of concentrations of emergent acid and cations. NOTE: The q values are given in terms of GEW per in3. 0.05qH - 0.95qc = qH exp(-K(qH + qc)vW)
qH 0.016 GEW/in 3 0.0155 0.0154 0.0153
KvW
—
0 0.00048 0.00064 0.00072
187 in 3 /Hr-GEW 242 285 328
0.10qH -0.90qc = qH exp(-K(qH + qc)vW) 0.0152 0.0147 0.0146
0.0008 0.0013 0.00144
0.0024
0.0131
0.00288
0.004 0.0046
(E.46)
177 232
0.30qH - 0.70qc = qH exp(-K(qH + qc)vW) 0.012 0.0114
(E.45)
184 239 281
0.20qH - 0.80qc = qH exp(-K(qH + q > W ) 0.0136
(E.44)
(E.47)
169 266
It can be seen that the value of K ranges from about 160 as a minimum to 330 as a maximum over the allowable spread of qH and qc concentrations. If the acid concentration is too low the resin cannot be regenerated to the preset percentage of full capacity.
APPENDIX E: MATHEMATICAL ANALYSIS
261
E.4 Electrolytic Resistance of the System Water When evaluating the expressions for quantitative relationships it becomes necessary to specify the constants for the transport terms due to electric current flow. The RA(ED), RC(ED), RH(ED) and ROH(ED) terms are electric current dependent. Equations E.7(a), E.8(a), E.14(a) and E.15(a) on pages 197 and 198 all contain R(ED), or current terms. The constants b, c, r and s are equivalent resistance (reciprocal equivalent conductance) terms. Appendix B gives a table of some specific ion values of conductance. These resistance values are inversely proportional to the ion mobilities for that specific ion. If the equivalent conductance of a substance is M, and its solution concentration is S, in GEW per liter, then: Conductance = SM/1000, or Resistivity, R = 1000/SM ohm-cm. Equivalent Conductance, M, is given as mho/cm-equiv. Converting to the English system, R = 1000/2.54SM = 400/SM ohm-in Now, the electric current is V/R, where V is the voltage drop along the path of flow of the specific, subject ion. The units would be amperes. To convert to equivalent weights transported per unit time, we need to change dimensions. Since 26 amp-hr corresponds to about 1 gram equivalent weight of substance, The above equation becomes d q / d t = V/26R GEW per hour.
(E.48)
If we are interested in the quantity, d q / d t , transported per hour per square inch of electrode area in a particular cell, the inter-electrode or electrode-membrane spacing, W, must be taken into account, and d q / d t becomes V/26RW.
(E.49)
262
ELECTROCHEMICAL WATER PROCESSING
Since the q terms in the system expressions are in units of GEW per in3, it is necessary to normalize them in terms of GEW per liter. Hence, the expression d q / d t = V/26RW = V/26(400/SM)W = VSM/10400W,
(E.50)
becomes d q / d t = 60VqM/10400W = VqM/173W.
(E.51)
Typical values of M at low concentrations are: MH+ 340 mho/cm-equiv. MOH.190 M Na+ 44 M r 60 Ca M
C1-
6 5
MS04 75 Now, we may insert numerical values for the constants, b, c, r, and s as follows. b = M H+ /173W = 2/W + mho/equiv.
(E.52)
c = M OH ./173W = 1.1/W
(E.53)
r = M c+ /173W = 0.29/W +
(E.54)
s = MA_/173W = 0.40/W
(E.55)
A potential problem exists in determining the value of voltage to use in the rate equations since the division of the cell potential from the membrane to the electrodes will depend upon the ratio of the resistances. For example, if the resistance on the positive side is R+ and that of the negative side is R, then the potential drop, V , (driving voltage) on the (-) side of the cell is
APPENDIX E: MATHEMATICAL ANALYSIS
V = VR./(R + R+),
263
(E.56)
and similarly for the positive side voltage, V+ = VR + /(R + R+).
(E.57)
The R's are obviously obtained by taking the reciprocal of the sum of all the conductances due to the various ionic species in either side of the cell. For example, R=(l/ROH. + l / R A + l / R / = ([SM]OH_/400W + [SMIA/400W_ + [SM]_C/400W)"1 (E.58) and similarly for the positive side, R+ = (l/R H +
+
l/R+A+l/R+c)-i
= ([SM]H+/400W+ + [SM]+A/400W+ + [SM]+C/400W+)-1 (E.59) A reasonable first approximation which may be employed in the computations associated with the rate processes is to let the total resistance on either side of the membrane be equal then the driving potential for the specific ions will be 1/2V. In most designs the spacing in the (-) and (+) cell compartments will be about equal also, or W = W+ = W.
E.5 Solution of the Simultaneous System Equations The series of equations that were described earlier now assume the forms given below. These are the modified forms of equations (E.l), (E.2), (E.3), (E.4), (E.5), (E.6), (E.7a), (E.8a), E.9, (E.14a) and (E.15a) in light of the further definitions provided the coefficients. The q and Q terms have been substituted in the following equations as shown on page 9 for the sake of brevity
264
ELECTROCHEMICAL WATER PROCESSING
of use of symbols, and in order to make the nomenclature more adaptable to MuMath for symbolic manipulations, FORMULA ONE and LOTUS for numerical evaluations. Q + 2q = B + C + D
(E.60)
A+C =E
(E.61)
B=G +L
(E.62)
D = Q-H
(E.63)
Q + 2q = E + L + J
(E.64)
J = Q-I
(E.65)
v W d A / d t =: V+rC + V sL - V+bA - V cG + (eCH - fAD)W2v
(E.66)
v W d G / d t == VrC + VsL - V bA +
- V cG + (gLI - hGJ)W2v EvWF/Rj. := V+bA + V+rC + V cG + V sL VbA=VsG
(E.67) (E.68) (E.69)
0 = 2V + bdA/dt + V+r(V+bA + VcG - V+rC - (eCH - fAD)W2v) + V s(V+bA + V cG - VsL - (gLI - hGJ)W2v)
(E.70)
NOTE: The quantity, Rp, appearing in equation (E.68) is the total electrical resistance of the cell, or Rj. = R + R+ Since H + ions do not exist in the negative cell side, and because OH" ions do not survive in the positive side, current is carried by these ions only in their respective sides of origination. Hence the driving potential for these ions is that of the half-cell side, or V+ for the H + ions, and V for the OH" ions.
APPENDIX E: MATHEMATICAL ANALYSIS
265
The conduction process is due to all ion migration on both sides of the membrane. Hence, the total resistance is found as follows. The conductance on the positive side is the sum of all charge carriers, or l/R + = b A + r C + sE
(E.71)
l / R = c G + rB + sL
(E.72)
Since Rj. = R+ + R, the final expression for the total resistance becomes; RT = 1
bA + rC + sE
+
cG + rB + sL
(E.73)
The above value for the total resistance must then be substituted into equation (E.68) for Rj, Equation (E.70) has the form above only if Rj, is treated as constant in equation (E.68). Since it is in fact not constant, equation (E.70) must be modified accordingly to reflect this fact. Differentiating equation (E.68) as before is now a very complex operation. There are some approximations that are allowed while still preserving the basic relationships of interest. For example, the resistance on both sides of the membrane will probably be about equal throughout the operation of the system. Thus, one may let the total resistance be equal to twice that of either side, or R =2R+ = T
+
bA + rC + sE
(E.74)
Substitution of (E.74) into (E.68) gives, VvWF[bA +rC +sE]/2 = VbA/2 +VrC +VcG/2 +VsL (E.75)
266
ELECTROCHEMICAL WATER PROCESSING
Eliminating both C and L from equation (E.75) by substituting from (E.61) and (E.62) gives VvWF(bA +r(E-A)+ sE)/2 = VbA/2 + Vr(E - A)/2 +VcG/2 + Vs(B - G)/2
(E.76)
Differentiating equation (E.76) with respect to time yields vWF(bdA/dt + r(dE/dt - d A / d t ) + sdE/dt) = b d A / d t + r(dE/dt -dA/dt) + cdG/dt + s(dB/dt - dG/dt)
(E.77)
Now we can substitute again for the derivatives d E / d t and d G / d t and dB/dt from equations (E.12), (E.8a) and (E.13), respectively. vWF(bdA/dt + r(VsL/2 - dA/dt) +Vs2L/2) = bdA/dt + r(VsL/2 - dA/dt) + cdG/dt + s(VrC/2 - VrC/2 - VsL/2 + VbA/2 + VcG/2 -dQ A /dt) (E.78) dA/dt(bvWF - rvWF - b + r) + vVWFrsL/2 + vVWFs 2 L/2 = VrsL/2 + sVrC/2 - rsVC/2 - Vs 2 L/2 + VsbA/2 + VscG/2 - sdQ A /dt + VrcC/2 + VscL/2 - VbcA/2 + Vc 2 G/2 - cdQ A /dt Equation (E.78) becomes the new version of equation (E.70), and equation (E.68) has the form of equation (E.75). Thus, the new series of relationships are equations (E.60), (E.61), (E.62), (E.63), (E.64), (E.65), (E.66), (E.67), (E.75), (E.69) and (E.78). We may now proceed with the solution of these equations in generalized form and then in terms of specific values of the system constants.
APPENDIX E: MATHEMATICAL ANALYSIS
267
Equations (E.60) through (E.65) and equation (E.75) are solved as a series of linear, simultaneous algebraic relations. Their solutions for the variables B, C, D, E, G, H and I in terms of the variables A, J and L are listed below. B = (AvWsF + AvWbF - ab + 2vqWrF + 2vqWsF + vHWrF + vHWsF -2qr - Ls + Lc - H r ) / (-r + c + vWrF + vWsF)
(E.79)
C = (-AvWsF - AvWbF + Ab + 2qc + Ls - Lc +Hc)/ (-r + c + vWrF + vWsF) D = Q-H
(E.80) (E.81)
E = (AvWrF - AvWbF - Ar + Ab + Ac + 2qc + Ls - Lc + He)/ (-r + c + vWrF + vWsF)
(E.82)
I = (AvWrF - AvWbF - Ar + Ab + Ac - 2vqWrF - 2vqWsF + vLWrF + vLWsF + 2qr - Lr + Ls + He)/ (-r + c + vWrF + vWsF)
(E.83)
J = (-AvWrf + AvWbF + Ar - Ab - Ac + vQWrF + 2vqWrF + 2vqWsF - vLWrF - vLWsF - Qr + Qc - 2qr + Lr - Ls -He)/ (-r + c + vWrF + vWsF)
(E.84)
G = (AvWscA2F + AvWbc A 2F -Abc A 2 - 2vqWrc A 2F + 2vqsWc A 2F - vLWrcA2F - vLWscA2F + vHWrc A 2F + vHWsc A 2F - 2qrc A 2 + Lrc A 2 - LscA2 - Hrc A 2)/ (vWrcA2F + vWsc A 2F - rc A 2 + cA3)
(E.85)
268
ELECTROCHEMICAL WATER PROCESSING
These are employed in conjunction with equations (E.66), (E.75) and (E.78) to totally evaluate A, (as it is set up at present), as a function of time. To accomplish this end the first order differential equation, d A / d t , must be solved. The relationships rapidly become extremely complex and lengthy. Hence, it serves simplicity to insert numerical values wherever possible and as early as practical to shorten the lengths of these expressions. E.6
S a m p l e S o l u t i o n of O p e r a t i n g S y s t e m
It seems that the initially most interesting relationships from which to obtain quantitative information and to graph are the following: • Time dependence of qH and Q H for different values of V, W, and perhaps v. • Maximum level of regeneration achievable in the resin for a particular set of conditions • Coulombic efficiency versus time, V, W, and v. • Different resin properties will affect the performance as well Let us now insert the first series of numerical values for the system constants as a test for the type of analytic information afforded here. The values for e,f,g and h are set to K = 200/vW in 3 / hr-GEW The values of the remainder are: b = 2 / W mho/equiv c = l.l/W r = 0.29/W s = 0.40/W V = about 10 volts, but is one of the variables
APPENDIX E: MATHEMATICAL ANALYSIS
269
W = W+ = W_ = about 1 inch, but is one of the variables Q o = Q = 1.3xl0 2 GEW/in 3 for 15,000 grain/ft 3 resins qo = q = 1.3x10-* GEW/in 3 for 400 ppm input water If we substitute the above values for the constants, the equations are: B = 2.7A + 2.137xl0 4 + 0.113L +0.822H C = -2.7A + 0.436xl0"4 - 0.113L + 0.177H D = 1.3xl0- 2 -H E = -1.7A + 0.436xl0 4 - 0.113L + 0.177H I = -1.7A - 2.137xl0 4 + 0.886L + 0.177H J = 1.7A + 1.3xl0-2 + 2.137xl0"4 - 0.886L - 0.177H G = 2.7A + 2.137x1o4 - 0.886L + 0.822H and 0.3dA/dt = - 20A + 2.9C - 11G + 4L -200AD + 200CH 2A = 0.4G 10.764L + 11.628dA/dt = -7A + 1.595C + 8.25G + 1.98L +300GJ -300LI If we leave in the parameters W and V as indeterminate, the expressions are; B = (-0.00007 - 2A + 0.7L - 0.29H + 18.72AW + 0.00139W + 5.382HW)/(0.81 +5.382W) C = (0.0002 + 2A- 0.7L + 1.1H - 18.72AW)/(0.81 + 5.382W)
270
ELECTROCHEMICAL WATER PROCESSING
D-0.013-H E = (0.0002 + 2A- 0.7L +1.1H - 13.338AW)/(o.81 + 5.382W) I = (0.00007 + 2.81 A + O.llL + I.IH - 0.00139W - 13.338AW + 5.382LW)/(0.81 + 5.382W) J = (0.01045 - 2.81 A - O.llL - I.IH + 0.07136W + 13.338AW - 5.382LW)/(0.81 + 5.382W) G = (-0.00009 - 2.42A - 0.1331L - 0.3509H + 0.00169W + 22.6512AW - 6.51222LW + 6.51222HW)/ (0.9801 + 6.51222W) 0.3dA/dt = -200ADW -AV + 200CHW + 0.29CV -1.1GV +0.4LV 2A = 0.4G -1.71dA/dt + 1.0764LWV + 13.338WdA/dt = -0.7AV + 0.1595CV + 300GJ +0.825GV -300LI + 0.198LV The above equations can now be solved for A as f(t) for different voltage ranges and cell widths.
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
Appendix H: Mathematics for Simple Electrochemical Biociding In Chapter 5, Section 5.1 we outlined the salient factors in the design of an electrochemical bromine generator. The assembly of electrodes is designed to accomplish a particular bromination task, and hence require electrodes of sufficient size along with a dc power supply for the necessary current flow. The first of the following two sets of equations quantitatively relates the geometry of an array of electrodes, and voltages necessary to production of a given amount of bromine per unit time. This set of equations is named Figure H.l. The parameters in the above equations are identified and defined as follows. Bt Ec
Bromine generation rate, g m / h r Cell potential, volts 303
304
ELECTROCHEMICAL WATER PROCESSING Bt= i■ tj ■ Ae-3.08 Ec= Er+ i ■ Ae- Rc
p=1000/(/V-JJ
ppm = 103- 10 3 -/V R^s-pKN-AJ COP=Bt/P ppmBr= Bt- 106/(454 ■ V ■ 8) l=i-Ae P=l-Ec
Figure H.l Bromine generator array.
E r A
e
Î1
ppmBr
ppm N R c p n P s COP V
J
Electrode reaction potential, volts Working electrode area, sq in Coulombic efficiency Bromine concentration rate, p p m / m i n ppm of NaBr salt NaBr solution normality Cell resistance, ohms Power Input (electrical), watts Number of cells (electrodes) in parallel Specific resistivity, ohm-in Inter-electrode spacing, in. Coefficient of performance, gm of Br/ hr-watt Gallons of water being brominated, Equivalent conductance, 130 cm 2 / equiv-ohm
The second set of equations, Figure H.2, concerns the geometrical arrangement for housing an array of electrodes of a brominator. The simplest, least costly and most effective manner of housing an array to withstand high hydraulic pressures normally encountered in most application settings, is a cylinder. As was described in Section 5.1, the relationship is between the dimensions of electrodes and cylinder diameter to give the largest utilization of available space within the cylinder to the greatest total electrode area.
MATHEMATICS FOR SIMPLE ELECTROCHEMICAL BIOCIDING
305
The short set of such relationships is £>= n2 ■ u ■ sAe=L-W-n-L-W
s
4 f i 2 = W2+b2 2b2- u ■ b -4R2=0
Figure H.2 Cylindrical configuration.
The above relates the maximum area, A , and the inside radius of the cylindrical housing. The parameters are identified as follows: b n Ae L W R u s
Stack thickness, in. Number of plates (electrodes) Operating electrode area, sq in Plate length, in Plate width, in Cylinder radius, in. Plate thickness Inter-electrode spacing, in.
To illustrate the usefulness of establishing these equations into a suitable mathematics program, the following is offered as a typical computation for a convenient size of "reactor module", or array of cells needed to supply sufficient bromine for a body of water with a volume of 40,000 gallons - a large swimming pool. Strictly as a matter of illustration, let us specify that about 1 ppm of bromine must be provided to this body of water when electrolyzing a water solution of about 1000 ppm of sodium bromide. That concentration of NaBr is a 0.0097 normal solution. If the above equations are entered into either a MathCad type or spreadsheet program and solved for various lengths of electrodes and diameter of cylindrical housings, we can manipulate the variables to arrive at a maximally acceptable configuration of electrode array.
306
ELECTROCHEMICAL WATER PROCESSING
Let us see what the physical dimensions and electrical power requirements estimates are for the following set of operating conditions. These electrodes are assumed to be all connected electrically in parallel making a single cell with a multiplicity of electrodes. uirements: Single cell r, = l ppm = 1000 ppm ppm-Br = 1 p p m / h r
E =3 s i = 0.10 amp/in 2 = 0.016 amp/cm 2 s = 0.25 in = 0.625 cm V = 40,000 gal.
From equations in Figure H.l, the values of the dependent variables are found to be, Bt = 145 gm/hr, A = 2950 cm2 = 461 in2 E = 11.2 volts, I = 47 amps, and P = 530 watts regardless of the number of cells or specific geometry of the unit as long as the electrode spacing, s, is kept the same. Now, in order to decide upon the actual number of cells and size and shape of the unit, we make use of the set of equations in Figure H.2. The only actual choice we have in placing an electrode assembly into a cylinder is the inside radius of the housing. The equations are set up to provide the values of L and W, and n for the maximum area in the shortest stack length, L. We will select two values of R to complete the illustrative computations, and to provide the reader with an idea of the size and power required to produce electrolytically 1 p p m / h r of bromine in 40,000 gallons of water at a coulombic efficiency of 100%.
MATHEMATICS FOR SIMPLE ELECTROCHEMICAL BIOCIDING
For R = 4 in: n = 17 plates
L = 5.1 in
W = 5.6 in For R = 2 in: n = 9 plates W = 2.8 in.
L = 21 in
307
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
Appendix F: Industrial Chlorination and Bromination Equipment Cost Estimates The processes and cost information described here are based upon current practices and available information. Equipment cost figures was estimated from engineering experience and cost figures was estimated from 1992 dollars using the Engineering News Record Construction and Cost Indexes (CCI). This feasibility study has produced an order-of-magnitude investment and operating cost estimate for a proposed bromination circuit. Both the chlorination and bromination water treatment processes have been sized to treat a three million gallon industrial water supply in an open, re-circulating system. It has been assumed that a recirculation rate of 100,000 gallons per minute (gpm) occurs in an induced-draft cooling tower.
271
272
ELECTROCHEMICAL WATER PROCESSING
Table E l summarizes the design and operating conditions chosen for this analysis and systems comparison. No forced blow-down in the bromination process design was assumed because of the water softening capabilities of the unit. Though no specific calculations or field tests have been conducted on this assumption, the experience with operating these types of devices supports this contention. Zero forced blow-down also minimizes bromide salt make-up requirements. Chemical storage facilities for chlorine gas and bromide salt have been provided to accommodate one tanker or truckload delivery of the gas or solid, respectively. No building storage or shelter, other than that indicated on the equipment list, was considered. Chlorine demand Table El Water treatment design assumptions and operating conditions. Chlorination
Bromination
Recirculation Rate - gpm
100,000
100,000
Turnover Rate - min
30
30
Tower Load - F
20
20
Evaporation - gpm
2,000
2,000
Windage Loss - gpm
100
100
Forced Blowdown - gpm
400
-
Total Blowdown - gpm
500
100
Total Makeup - gpm
2,500
2,100
Cycles of Concentration
5
21
Chemical Disinfectant
chlorine (g)
bromine (s)
Chemical Demand - ppm
3
2
Chemical Demand - lb / d a y
6,000
1,200*
*Expressed as sodium bromide.
EQUIPMENT COST ESTIMATES
273
was calculated based on average ranges reported and the industry's published "rules-of-thumb" for processes with no product contamination. 3 Bromine demand was assumed based on experience at TRL, Inc. The brominator module and power supply were sized assuming a bromine loss rate of 1 ppm per hour, requiring the generation of 25 lbs per hour of bromine. The efficiency (coulombic) of bromine generation was assumed at 50%, and the current density applied was 0.10 amps per square inch of cell area. All cells were connected in series at 5 volts per cell. The process demand is approximately 75 to 80% of the equipment design capacity. The following is a major equipment list for a chlorination circuit, which will supply 6,000 lbs/day of chlorine to an open, re-circulating cooling water system with a recirculation rate of 100,000 gallons per minute. Table F.2 is an Table F.2 Chlorination system equipment list. Equipment
Specification
Materials of Construction
Cost-1992
Cl2 Gas Storage Tank & Shield
4,800 gallons
MS
$25,000 E
Weigh Platform
30 ton
mf g std
23,900
Storage Tank Eductor
2 in. air oper.
mf g std
1,000
Air • • •
50 SCFM at 125 psi 50 hp
mfg std
32,200
Flexible Tank Connections 2 required
10 ft. L
Monel
2,000
Padding System air compressor air dryer aftercoolers receiver • air filter • moisture indicator
274
ELECTROCHEMICAL WATER PROCESSING
Table F.2 (cont.) Chlorination system equipment list. Equipment
Specification
Materials of Construction
Cost -1992
Expansion Tanks
20% header volume
MS
600
Injector
25 in. Hg vacuum
titanium
Chlorinator • inlet reducing valve • retameter • oriface meter • regulating valve • relief valve
8,000 lb/day
mfg std
Injector Pump
150 gpm 150 ft. 15 hp
Iron
2,100
Evaporator • temperature alarms • level & pressure switch
8,000 lb/day 12 KW
mfg std
57,900 E.
Residual Controller/ Analyzer / Monitor
-
mfg std
5,000
Safety Equipment • Cl 2 Leak Detector • Breathing Apparatus • Container Kits • Floor Level Fans (2)
10 hp @ 2500 acfm
mfg std frp
7,000
Total Erected E q u i p m e n t
$82, 900
Total Non-erected E q u i p m e n t
$86,600
EQUIPMENT COST ESTIMATES
275
equipment, materials listing along with their estimated costs. Below is a glossary of abbreviations found in the equipment list. dia frp hP lb gpm rpm sqft MS RL mfg std E El
diameter fiber-reinforced polyester horsepower pound, avoirdupois gallons per minute revolutions per minute square feet mild steel rubber lined manufacturers standard field erected
B r o m i n a t i o n E q u i p m e n t List
The following table is a major equipment list for a bromination circuit which will supply 1,200 lb/day of sodium bromide salt to the cooling tower system, and maintain a bromine concentration of 2 ppm to effect slime, algae and bacteriological control. The system has been specified Table F.3 Bromination system. Equipment
Specification
Materials of Construction
Cost -1992
NaBr Feed Bin w / load cell
45,000 lb
MS,RL
$24,600
NaBr Vibrating Feeder
8,000 lb/hr, 1/4 hp
MS, RL
2,900
NaBr Discharge
-
MS,RL
800
NaBr Solution Tank
4,000 gallon, 9 ft dia, 10 ft deep
MS,RL
17,000
276
ELECTROCHEMICAL WATER PROCESSING
Table F.3 (cont.) Bromination system. Equipment
Specification
Materials of Construction
Cost -1992
NaBr Mixing Agitator
32 in dia impeller 5 hp,125 rpm
MS,RL
5,500
Feed Water Pump
100gpm-30 ft 4hp
RL
7,400
Solution Feed Pump
variable gpm50ft,l/2hp
mfg std
2,800
Pneumatic Conveyor System
5 ton/hr capacity
mfg std
14,700
Bromination Channel Tank
3 ft x 2 1/2 ft xl9ft
frp
6,100
Bromination Modules • 12 modules/10 cells per • 1200 sq ft plates
5 sq ft per plate
carbon plates copper bus
7,500
Residual Analyzer/ Recorder /Monitor pH Analyzer Power Supply
5,000 " 150 amps 240 volts 36 KW
mfg std
Total Erected E q u i p m e n t
$24,600
Total Non-erected E q u i p m e n t
$79,700
10,000
EQUIPMENT COST ESTIMATES
277
for an open, re-circulating cooling water system with a recirculation rate of 100,000 gpm. F.2
Capital Cost A n a l y s i s
Capital costs were developed from the major equipment lists and preliminary capital cost estimating techniques and factors. Installation labor costs were estimated based upon purchased equipment costs. Installed instrumentation and control costs were based upon equipment and process type; 30% of the purchased equipment costs for the chlorination system and 20% of the purchased equipment costs for the bromination system. This cost difference is required when the safety precautions necessary in the chlorine supply, handling and metering system are examined. Because the chlorine is handled as a liquid and gas in duplicate header systems in the storage area, and as a gas in the metering system, the piping costs associated with the chlorination process are greater; 40% of purchased equipment costs, versus 30% for the bromination circuit. Electrical costs are estimated at 10% of equipment costs for the bromination circuit, and 5% of equipment costs for the chlorination costs. Because of the complexity of the power supply and circuitry associated with brominator modules, it is estimated that the electrical installation costs for the bromination circuit would be a significant cost. Services and platform construction is necessary for both processes, and include lighting, site preparation and access platforms to the storage facilities. Both costs are approximately 30% of the purchased equipment costs. All of the above costs, plus the equipment costs, make up the total construction costs'4-5'. As a check against estimating techniques developed in this treatment, the construction costs figures published by the US EPA in January 1978 for chlorine storage and feed systems were referenced. Escalated to 1992 dollars, the construction cost for an 8,000 lb / d a y capacity chlorine system
278
ELECTROCHEMICAL WATER PROCESSING
was approximately $332,0006. The total construction costs estimated for this exercise is approximately $363,000. Because the proposed bromination system is a new treatment method for industrial water systems, there are no construction data available for comparison. Indirect costs, such as engineering and supervision, construction expenses and profit, administration and legal fees, and contingency were taken as percentages of the total construction costs usually associated with water treatment facilities6. In the bromination circuit, an initial charge of bromide salt was included in the indirect costs as a one-time fee. The interest charges were calculated based on estimated construction times and an 8% interest rate. For the chlorination system, the fixed-capital investment is estimated at $607,500. The bromination system is estimated to cost $375,000, approximately 60% of the chlorine circuit. The following tables (F.4 and F.5) list the individual cost components and charges for each system.
Table F.4 Chlorination system fixed capital summary. Total Non-erected Equipment
$86,000
Total Erected Equipment
82,900
Installation Labor
13,100
Instrumentation & Controls (installed)
50,700
Freight & Site Handling
3,400
Piping (installed)
67,600
Electrical
8,400
Service, Platforms
50,700
Total Construction Costs (TIC)
362,800
Contingency @15% TCC
54,400
EQUIPMENT COST ESTIMATES
Table F.4 (cont.) Chiorination system fixed capital summary. Contractor Overhead & Profit @ 20% TCC
43,500
Engineering @ 13% TCC
47,200
Legal, Fiscal & Administrative @ 20% TCC
72,600
Subtotal
580,500
Interest During Construction @ 8%
27,000
Fixed Capital Investment
607,500
Table F.5 Bromination system fixed-capital summary. Total Non-Erected Equipment
$79,700
Total Erected equipment
24,600
Installation Labor
13,000
Instrumentation & Controls (installed)
20,900
Freight & Site Handling
2,000
Piping (installed)
33,000
Electrical
10,600
Service, Platforms
33,000
Total Construction Costs (TCC)
216,800
Contingency @ 15% TCC
32,500
Contractor Overhead & Profit @ 12% TCC
26,000
Engineering @ 13% TCC
28,200
Legal, Fiscal & Administrative @ 20% TCC
43,400
Sodium Bromide Initial Charge, delivered 27,000 lb
16,200
Subtotal
363,100
Interest During Construction @ 8%
12,000
Fixed-Capital Investment
375,100
279
280
F.3
ELECTROCHEMICAL WATER PROCESSING
O p e r a t i n g Cost A n a l y s i s
Operating costs were calculated based on factored estimates delivered from the fixed capital investment. Percentages typical of water treatment facilities were utilized for plant life and depreciation, maintenance and insurance. Raw material costs were restricted to bromide and chloride salts for each respective process. Corrosion inhibitors, chemical cleaners and flocculants were not included. Connect hp and make-up water requirements from evaporation, windage and forced blow-down estimates were used to calculate utility charges. Administrative charges include office and laboratory labor, and operation charges include labor and engineering. The following operating cost summary in Table F.6 indicates no appreciable operating cost difference between chlorination or bromination under the design basis and assumptions outlined earlier. Because of safety considerations and maintenance and insurance increases possibly Table F.6 System o Derating cost comparison. Bromination Usage/yr Depreciation @ 10% TFI
$/yr
-
60,700
1050 tons
210,000
Chlorination Usage/yr
$/yr
-
37,500
210 tons
252,000
Maintenance @ 4% TFI Insurance @ 2% TFI Chemicals (delivered) • Chlorine® $0.10/lb • Sodium Bromide @ $0.60/lb
EQUIPMENT COST ESTIMATES
281
Table F.6 (cont.) System operating cost comparison. Bromination Usage/yr
$/yr
Utilities • Cooling 1,260 MM Gal 88,200 water @ $0.07/ 1,000 gal • Electricity® 0.30 MM 15,000 KWH $0.05/KWH Labor • Administrative • Operation Total Operating Cost
-
37,800 109,200
Chlorination Usage/yr
$/yr
1,058 MM Gal 74,100
0.36 MM KWH
-
$557,300
18,200
37,800 89,600 $531,700
associated with the storage and handling of chlorine, a possible operating cost increase in the estimate of $35,000 to $40,000 would not be unreasonable. However, this would not be a significant difference in the operating cost comparison for this order of magnitude estimate.
F.4 Conclusions and Comments The preliminary capital investment and operating cost estimates have indicated that the bromination system for disinfection and control of micro-organisms, algae, and slime growths in re-circulating water systems is a cost effective alternative to chlorination. A capital savings of approximately 40% is realized with the installation of the bromination process versus the chlorination equivalent. The assumptions for the design of the brominator and power supply were chosen to provide a severe duty estimate for equipment selection. Because of the water-softening action, iron, manganese and other dissolved metal removal
282
ELECTROCHEMICAL WATER PROCESSING
achieved by the brominator unit, it is assumed no forced blow-down will be required in this system. This assumption significantly decreases make-up bromide salt requirements, but needs to be verified in an actual operating system. When demineralized water is used for tower make-up, the tower cycles are limited only by windage losses, and the assumption of zero forced blow-down would be completely valid for both operations. There are many significant advantages to bromination over chlorination in water treatment applications. In the past, use of bromine biocides were limited to uses where chlorine disinfection was unacceptable because of higher chemical costs of bromine, and the oxidizing agents needed to produce the bromine residuals. With an electrolytic bromination system, based upon electrochemical "activation" of the bromide salts, the higher operating costs of bromination have essentially been eliminated. Because bromine is supplied in relatively inert salt form as sodium bromide, the storage and handling hazards associated with elemental halogens do not exist in this system. Operator safety training, control and safety equipment, system maintenance, leak detection apparatus are not required in the storage of bromide salts. The use of this system should also favorably impact insurance costs because of reduced safety hazards to operating personnel. Producers of bromine chemicals, such as l-bromo-3chloro-5, 5 dimethylhydantoin (Aquabrome), are actively pursuing industrial cooling water applications of bromine disinfection. References in the following describe the results of field tests and operations in several water-cooling water facilities. Another bromine biocide, 2.2-dibromo-3-nitrilo proprionamide (DBNPA), found to be an effective disinfectant, with no environmental toxicity because of it accelerated decomposition upon the application of heat or the increase in pH (78) . The data taken with these compounds have shown the effectiveness and advantages of bromine disinfection in open, re-circulating water systems.
EQUIPMENT C O S T ESTIMATES
283
Table F.7 Industrial re-circulating water rates. Industry
Recirculation Rate
200 MW Power Station
120,000 gpm
900 MW Power Station
405,000
200,000 MTPY Lead Production Hydrometallurgical Process Ammonia Production Facility (Capacity Unknown) Aquitance Refinery (Capacity Unknown)
5,300 36,000 292,000
Due to environmental regulations concerning toxicity and thermal pollution, cooling systems are being built by industry in an effort to meet government standards. In the power industry, two thirds of the fuel supplied must be dissipated as waste heat, requiring large cooling systems, and many of which have recirculation rates over 200,000 gpm. Cooling water requirements and quantities vary greatly, depending upon the industry. Table F.7 outlines several industrial systems cooling tower recirculation rates and production capacities.
References 1. White, George C , Handbook of Chlorination, page 712, Van Nostrand Reinhold Co., New York, 1972 2. Colturi, T. F, and Kozelski, K.J., "Corrosion and Biofouling Control in a Cooling Tower System", Material Performance, Vol. 23, No. 8, pages 43-47, August 1984. 3. White, pages 557-558. 4. White, pages 711-712. 5. Peters, Max S., and Timmerhaus, Klaus D., Plant Design and Economics for Chemical Engineers, pages 100 -141.
284
ELECTROCHEMICAL WATER PROCESSING
6. Montgomery, J.J., Water Treatment Principles and Design, pages 656-673. 7. Colyuri, pages 43-47. 8. Cappeline, G.A., and Carroll, J.G., "Enhance Your Cooling Systems's Performance Through Proper Use of Microbiocides," Power, Vol. 121, No. 10, pages 56-61, October 1977.
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
Appendix G: Design Mathematics in Computer Format The groups of mathematical equations developed in Chapter 4 are listed here, along with their corresponding lists of variables (basic parameters), for the convenience of those readers that wish to perform design estimates of operating ED systems. The information contained here is also useful is their implementation into computer files and programs. Because all the mathematical derivations and assumptions upon which they are based are to be found in the text, the reader can modify these expressions to reflect other analytical approaches or to allow other assumptions to be made. Three basic analyses will be given in this appendix. They are based upon these types of configurations: Case-A Once through, multiple cell array Case-B Re-circulation array with constant current Case-B Re-circulation array with constant voltage 285
286
ELECTROCHEMICAL WATER PROCESSING
In the first case, A, the idea of either constant current or constant voltage is not relevant in the analysis since the composition of the water flowing through the cells remains constant after steady state conditions are met. The dc power supply will merely provide whatever the current demand is at the impressed cell or stack voltage - after steady state is achieved. The analysis is set up such that the cell voltage or cell current at the input end can be set to a predetermined value. For the derivation of the following listed equations for Case-A refer to Chapter 4, Sections 4.2 and 4.3. The set of relationships employed here are direct results of those developed earlier and listed in Equations (4.35). In the re-circulating configurations, B and C, the mathematical representation is quite different, and the composition, TDS, of the re-circulating water changes with time. Hence, one must decide whether to establish a constant current, constant voltage, constant current or voltage limited, etc. system before the analysis and numerical computations can begin.
G.l
Case A
A continuous water flow-through configuration through a module establishes a set of mathematical expressions that were developed in Section 4.3, and are listed below. These relationships in the form given in Table G.l are set up for simultaneous solution in programs with the capability of performing such computations. The variables and constants employed throughout are identified and defined below in Table G.2. Let us examine the set of variables and constants in Table G.2. The last two columns in the table list the typical options of either initially setting a value for a parameter such as width of membranes or stack voltage, or setting some other parameter and solving for that particular one.
APPENDIX G: DESIGN MATHEMATICS IN COMPUTER FORMAT
287
Table G.l Equation group for case-A. Once flow-through design. v = 23\-F/W-p-n x =Vc;e/V-P
{
i-Ec-ri-ix/
x~co'e
i0 = co-Ec/
l-e
cp-p2-v-ß-10~6
Power = I ■ Ec ■ n Ae = W-x A-m = \ ' 2 ' n Size = W-x-p-n/l728 Compnts = 5 • \2Ae + Am J A 44 Thick = p ■ (l + 2nj FM = F ■ Í c0 - cx \j Power COP =
(c0-cxyc0
Energy = Power/F ■ 60 Es = n-Ec
Ignoring the last nine items beginning with Power in Table G.2, there are basically nine variables that can be handled as either independent or dependent ones. Almost invariably the single most important parameter we wish to either solve for or control is the TDS, cL, of the emerging water from a cell or a stack of cells in an array (module). The variables that we would usually most wish
288
ELECTROCHEMICAL WATER PROCESSING
Table G.2 Parameter
Definition total current
I
Units Dimensions amps 2
Value
LOTUS Symbol
cale
I
input
io
entrance current density
amps /in
i
exit current density
amps/in 2
cale
ix
conversion factor
ohm-in-ppm
26X10A
D
ß
water density
gm/in 3
16.4
B
X
conversion factor
gm/amp-min.
0.038
A
TI
coulombic efficiency
%/100
input
J
P
cell spacing
in
input
P
c
entering TDS
ppm
input
CO
E
cell potential
volts
cale
Ec
V
flow speed
in/min
cale
V
F
volume flow rate
gal/min
input
F
W
electrode width
in
cale or input
W
n
number of stacked cells
input
n
X
distance from entrance
in
select
x
r
process side resistivity
ohm/in2
cale
rx
TDS at point x, or at exit
ppm
cale
ex
i
o
X
o c
c
X
APPENDIX G: DESIGN MATHEMATICS IN COMPUTER FORMAT
289
Table G.2 (cont.) Parameter
Definition
Units Dimensions
Value
LOTUS Symbol
E
stack voltage
volts
cale or input
Es
power
power input
watts
cale
Power
COP
coefficient performance
cale
COP
FM
figure of merit
cale
FM
Energy
energy per gallon out
wh/gallon
cale
Energy
Thick
stack thickness
in.
cale
Thick
Compnts
elect. & memb cost
$
cale
Compnts
Size
module volume
ft3
cale
Size
A
electrode area
in2
cale
A
2
cale
A
s
A
e m
membrane area
in
e m
to control are the dimensions of a stack and the number of cells as well as the electrical input. Of these nine variables, only six independent equations are available. Hence, three of the nine variables must have their values predetermined in order to solve for the remaining six dependent variables. Which variables are established as independent and dependent is strictly optional. These nine variables are ix, p, F, cx, n, W, n, x, and Es. Of the above parameters, (f> and r| are constants. Usually the TDS, co, of the entering water is known, or is determined by outside conditions over which we have little control. Either the flow speed, v, or the volume flow rate, F, is also usually a given condition or requirement for a specific
290
ELECTROCHEMICAL WATER PROCESSING
application. That then leaves us with the module configuration to manipulate in terms of membrane area and cell spacing. The number of cells in a stack is relevant only to the resultant volt-amp characteristics of an operating array. The amount of processing that is accomplished is strictly determined by the total electric current through the unit or the current density times the membrane area, if the area is taken as the total of all cells in series. To further illustrate the position of these various parameters the variables have been shaded in Table G.2 to indicate their normal placement. The lightly shaded areas identify those parameters that are usually given some initial values (becoming independent variables), and the more heavily shaded ones are the variables (dependent ones) that are of most interest and for which the program provides solutions. The parameters that are left unshaded are also dependent variables and are solved as part of the process. The cost outlines are based upon $5 per square foot of membrane and electrode components, and can be changed at any time to new, more realistic values. Cell spacing is almost always set at some minimum practical value that will permit ease of fabrication and minimal chance of obstruction of cell passages, while still affording a low cell electrical resistance. Most of our experience and design estimates have been with spacing, p, of between 0.10 to 0.20 inches. For example, one may wish to determine the membrane area necessary for processing a given quantity of water, F, per unit time through a module of cells with a given spacing, p, and a maximum allowable current density, i o , at the input to the module. If the input TDS, co, is stipulated as one of the conditions for that particular application, then it becomes quite simple to calculate the total membrane area needed to process that flow of input water to some specified output TDS, cx.
APPENDIX G: DESIGN MATHEMATICS IN COMPUTER FORMAT
291
Performing the computations in the manner of a series of simultaneous equations offers a better opportunity for optimization of parameters to satisfy any specific set of requirements. Because of the manner in which the set of equations is structured, it is necessary to set a convenient value of W as a trial computation, and then pick a value of x, the length of the cell for a preliminary calculation to be performed. The number of cells, n, can be arbitrarily set at any value, usually n=l for a start since n only determines the voltage needed and the length and thickness of the stack. For example, if we let W = 10 inches, F = 1 gal/min, p = 0.20 inch, io.= 0.10 amp/in 2 , and an input TDS of 1,000 ppm, we can then proceed to see what the exit TDS would be for different lengths of the cell, or what length of cell is needed to attain a predetermined exit TDS. If the value of io is specified, then the cell voltage, Ec, must not be fixed. It will be calculated for the value of voltage necessary under the other fixed parameters. The equation solving for the above conditions gives the following output information. Tables G.3 and G.4 list the values for the independent variables with n = 1, and n = 5, respectively. The stack voltage is given, in the case of n = 1, E =E. c
s
We note that the only difference between the two configurations is that the impressed voltage is higher for the Table G.3 W = 10 in, F = 1 gal/min, p = 0.20 in, io.= 0.10 amp/in 2 , co = 1000 ppm, ri = 1.0 for n =1. c TDS
E Volts
I Amps
Power, Watts
10
904
5.2
9.5
49
20
818
18
94
50
605
39
204
100
366
63
328
200
134
86
450
X
X
S
292
ELECTROCHEMICAL WATER PROCESSING
Table G.4 For n = 5. 10
605
20 40
7.9
204
366
12.6
328
134
17
450
26
stacked five cells. Power, efficiency, etc. are all unaltered in going from a single cell to a multiple cell array as long as the total area is kept constant. The only way in which the COP (coefficient of performance), or FM (figure of merit), can be improved is to reduce the cell spacing - unfortunately with the attendant increase in mechanical design and reliability problems. An example of the manner in which these equations can be arranged in a spreadsheet program to afford ease of computation and plotting various variables against each other for comparison and optimization purposes is show in the graph, Figure G.I. As the title indicates, this is a plot of exiting TDS and power input as a function of the length of the cell stack. Power increases and TDS decreases as the length becomes greater. This graph was done for fixed values of p, F, io, co, W, n, tj. The values can be changed at will within a spreadsheet to produce the corresponding graph. In fact, the basic equations can be rearranged to enable one to calculate the value of x, or W, etc. that will result in a predetermined value of cx. That would entail, for example, reformatting the equation for cx by taking the log of each side and then solving for perhaps x or W for any given set value of cx. The worksheet (spreadsheet) from which graphs can be plotted have standard forms containing mathematical expressions (formulas) for the evaluation of the dependent variables. An example of such a worksheet is shown below
APPENDIX G: DESIGN MATHEMATICS IN COMPUTER FORMAT
293
as Table G.5. In this table the values of the p a r a m e t e r s are those found represented in Figure G.I.
Output TDS and input power versus cell stack length 1200 1000 IB
Q. CL CO
Q
s
800
0)
600
I
¡400
a
n
200 10
20 30 40 Stack length, Inches - Exit TDS
50
60
■ Power
W = 10, n = 5, F = 1, p = 0.2, co = 1000, ¡o = 0.1, J = 1 Figure G.l Flow-through configuration case-A.
Table G.5 Spreadsheet form for Lotus or Excel. CASE-A output TDS and power input change with cell length. Independent Variables with Pre-set Values io = 0.04
D = 260000.00 B = 16.40
p = 0.20
co = 200.00 F = 0.10
A = 0.04
W =6
J = 1.00
n=l
v = 19.25
Ec = 10.4
294
ELECTROCHEMICAL WATER PROCESSING
Table G.5 (cont.) Spreadsheet form for Lotus or Excel. CASE-A output TDS and power input change with cell length.
Calculated Values of the Dependent Variables Formulas TDS@ ex
i amps
FM
0.00
200.00
0.00
2.00
157.21
4.00
COP
E
#DIV/0!
0.00
volts 10.40
0.00
0.43
0.96
0.21
10.40
4.44
123.57
0.76
0.96
0.38
10.40
7.92
6.00
97.14
1.03
0.96
0.51
10.40
10.67
8.00
76.35
1.23
0.96
0.62
10.40
12.82
10.00
60.02
1.40
0.96
0.70
10.40
14.51
12.00
47.18
1.52
0.96
0.76
10.40
15.85
14.00
37.08
1.62
0.96
0.81
10.40
16.89
16.00
29.15
1.70
0.96
0.85
10.40
17.71
18.00
22.91
1.77
0.96
0.89
10.40
18.36
20.00
18.01
1.81
0.96
0.91
10.40
18.87
25.00
9.87
1.90
0.96
0.95
10.40
19.71
30.00
5.40
1.94
0.96
0.97
10.40
20.18
35.00
2.96
1.96
0.96
0.99
10.40
20.43
40.00
1.62
1.98
0.96
0.99
10.40
20.57
45.00
0.89
1.99
0.96
1.00
10.40
20.64
50.00
0.49
1.99
0.96
1.00
10.40
20.69
X
G.2
s
Power watts
Case B
The second operating configuration, labeled Case-B, for a water processor in which the processed water is re-circulated many times before the entire quantity of water
APPENDIX G: DESIGN MATHEMATICS IN COMPUTER FORMAT
295
is processed to the desired level of TDS. This design is a batch process system in which a quantity of the processed water is stored in a reservoir or tank. The waste water may also be so stored in a separate reservoir, or made to pass slowly through the waste water compartments only once. For the derivation of the mathematics refer to Chapter 4, Section 4.5. The additional quantities included in the set of expressions below provide some preliminary means of assessing costs of components and polymeric case. Somewhat arbitrarily establishing case thicknesses and borders determines the dimensions and volumes of the case. These values are set, for illustrative purposes only, at Top and bottom case thickness = 1.0 in. Vertical edge case thickness = 0.50 in. Case face thickness = 0.25 in. Electrode thickness is 0.25 inch, and cell spacing in both the waste water and processed water compartments are the same. The electrode cost is set at $10 per square foot, and polymer cost at $0.12 per cubic inch. Membrane cost is estimated at about $8 per square foot of area. Also, a means for approximating temperature rise of the processed water from joule heating is provided. Hence, we arrive at the additional quantities as shown in Table G.5. As before, two constants appearing in the equations are: X = 0.038 gm/amp-minute ç - 26.104 phm-in-ppm The set of equations applicable to this situation wherein the electric current is kept constant is as follows.
296
ELECTROCHEMICAL WATER PROCESSING
Table G.6 Term
Description
Calories
Thermal energy generated by ohmic losses
Temprise
Rise in processed water temperature
V
Volume of processed water in its reservoir p
ModVol
Volume of module inner components
MembCost
Membrane cost- $/sq ft
ElectCost
Cost of electrodes - $/sq ft
EpoxyCost
Cost of polymer - $/cu in
EpoxyVol
Volume of the outer polymer case or shell - cu in
CaseCost
Cost of polymer case
ModuleCost
Total Cost of basic module materials
ModWt
Total weight of the Hence the additional termsmodule
ElectWt
Weight of the two end electrodes
T
Depth, or thickness of the module
EpoxyWt
Weight of the outer polymer shell
In a fashion similar to the one for Case A, the mathematics may be set up in either a spreadsheet form, or other math program to actually perform the computations and plot graphs of the change in values for the dependent parameters as a selected independent one is varied. An example of a simple computation for Case B is given below. To illustrate the behavior of a constant current, re-circulating water system we will choose some values for the necessary parameters, and solve for the ones we will make independent here employing the relationships shown in Table G.7. We may choose, for example, values for the independent variables as shown in Table G.8.
APPENDIX G: DESIGN MATHEMATICS IN COMPUTER FORMAT
297
Table G.7 Equation group for case B. Batch process - constant current. E
c
RW
= i R
[ w
=
+ R
p)
(
P-P/CW
Rp =
=
i-r¡-W-L-n-A-t
I = i-WL Power = i2 ■ (RW +
Rp)-n-L-W
Calories = Power ■ 60/4.1 Temprise = Calories/V„ • 10 ModVol = L-W -n-p/60 ts = n ■ tc MembCost = 8 ■ L • W ■ 2n/l44 ElectCost = 2- L-W -10/144 EpoxyCost = 0.12 EpoxyVo/ = 2-(W + l)-(T + l)-(0.25 + l) + 2 - ( r + l) ■(L + l)-(0.25 + l) + 2-(W-L) •0.50 CaseCost = EpoxyCost ■ EpoxyVol T = n-(p + p) + p + 2-0.25 ModuleCost = CaseCost + ElectCost + MembCost ModWt = 16 • 2 • (L • W ■ 0.25) ■ 2/454 +1.1 EpoxyVol-16/454 ElectWt = 16 ■ 2 • (L • W ■ 0.25) • 2/454 EpoxyWt = 1.1 • EpoxyVol ■ 16/454
And, then we obtain the results shown in Table G.9 for the dependent variables from the equations of state listed in Table G.7.
298
ELECTROCHEMICAL WATER PROCESSING
Table G.8 Independent parameters. i = 0.10 amps
V =50 liters
p = 0.20 in.
W = 10 in
cw = 10,000 ppm
L = 20 in.
c o = 1000 ppm
n=l
p
Table G.9 De rendent & calculated parameters versus time. t, Min.
E , Volts c'
C ,TDS
Power Watts
I, Amps 20
p'
0
5.72
1000
114
10
6.56
848
133
20
8
696
159
30
10
544
201
40
13.8
392
276
50
22
240
444
60
59.6
88
1192
Total current, I, is a constant 20 amps. As can readily be seen, the power and cell voltage begin increasing very rapidly as the TDS of the processed water becomes low. At some point the power supply will be required to deliver impractically high powers. Thus, a current limited power supply would most likely be employed in such configurations wherein the voltage would reach some maximum level and remain there as current begins to diminish with increasing water resistance as the processing goes on. This latter stage of operation would place the system into a "constant voltage" mode of operation, or into Case C situation. A further example of the computational possibilities afforded by the mathematical relationships when employed
APPENDIX G: DESIGN MATHEMATICS IN COMPUTER FORMAT
299
2500
2000
s
Q. 0. 1500 (A
I I
a g. 1000
500 <» 0 0 0 0 <
10
20 30 40 Elapsed time - Minutes -Output TDS
50
60
■ Input power
co = 1000, p = 0.2, W = 5, L = 40,Vp = 40, n = 1, i = 0.10 Figure G.2 Case-B constant current batch process.
in a spreadsheet program is offered in the graph, Figure G.2. In this instance the fixed parameters are L, W, n, r|=l, I, and co. The value assigned to cw is ten times that of the initial c = co because the processed water ratio to waste water volumes is at least 10 to 1.
G.3 Case C Operating an electrodialysis system from a constant voltage power supply is probably more practical, and would be the form most taken in the future. The distinct disadvantage of such a dc source is the need for limiting current because initial water resistance can be quite low for high TDS sources. The set of equations for this third version, Case C constant voltage configuration is presented below (Table G.10). The relationships are different from the previous two cases, and need to be handled accordingly. For derivations and design exercises of constant voltage systems refer to Chapter 4, Sections 4.5 and 4.6.
300
ELECTROCHEMICAL WATER PROCESSING
Table G.10 Equation group for case-C. Batch process - constant voltage. i = E C / (Rw + Rp ) c
Rw =
w
Rp = (p-V p c
p ' *p
3 po ' *p - Q - 1 0
= c
Y = n-X ■T]-Ec-L-W-103/((p3 po '*p - Q - 1 0
c
—c
po ' *p ' e
P) -Y-t/Vp)
Power = i-Ec-n- L-W Calories = Power 60/4.1 temprise = Calories/(vp J = L-W ^s
=
10 3 )
■i
^c n
The term, Y, in the above set is merely a convenient shorthand notation for a group of variables, and it has no physical significance. The analysis is performed with the assumption that the minimum ratio of TDS, c w /c po , is 10 since the waste water loss is certainly less than 10% of the total input. Each initial batch of processing will have an initial input TDS of the water to be processed represented as c . In reality, the waste water TDS will be at least 100 times that of the initial water input as the number of batches increases. If a waste water reservoir is employed instead of permitting the waste water to slowly drain directly out of the processor back into its original source, a small portion of the waste water is drained off with each batch to control the TDS level in the waste reservoir.
APPENDIX G: DESIGN MATHEMATICS IN COMPUTER FORMAT
301
We will give another simple example of the performance and associated computations for a constant voltage operating system. As before, a series of parameters must be selected and assigned some values to begin any computations. The following should illustrate the major characteristics of this mode of operation. As was done before. Then the values that result from the independent selections made in Table G.ll for the dependednt variables is shown in Table G.12. In order to approach the performance of Case-B employing constant current, the initial current density of this last, constant voltage configuration is up to 0.17 amp/in 2 versus the 0.10 amp/in 2 for Case-B. Table G.ll Independent parameters. E = 10 volts
c o=1000ppm
Vp =50 liters
p = 0.20 in.
cw = 10000 ppm
L = 20 in.
n=l
W = 10 in.
c
Table G.12 Dependent & calculated parameters versus time. t, Minutes
c
p
i , Amps/in 2
I , Amps
Power, Watts
0
1000
0.17
35
350
10
747
0.134
26.7
267
20
557
0.101
20.3
154203
30
416
0.077
15.4
154
40
310
0.058
11.6
116
50
231
0.044
8.7
87
60
173
0.033
6.5
65
80
96
0.018
3.68
36.8
302
ELECTROCHEMICAL WATER PROCESSING
20
30
40
50
60
70
Elapsed time - Minutes -Output TDS
■ Input power
co = 1000, p = 0.2, W = 5, L = 40,Vp = 40, n = 4, Ec = 4, J = 1 Figure G.3 Case-C constant voltage operation, batch process.
These equations are set up as a series of simultaneous relationships, and can be solved within a number of mathematical programs capable of manipulating, and solving simultaneous equations by iterative processes. A spreadsheet computation result of variation of processed water TDS and input power with time is illustrated in the graph below, Figure G.3.
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
Bibliography The following is a list of texts, collections of papers and books that either provide pertinent background material in the related scientific disciplines, or treat the subjects of electrodialysis and electrochemical water conditioning processes. Baker, Walter K.; Rapier, Pascal M.; Weiner, Susan A., Experimental Study of some Basic Parameters in Electrodialysis, Richmond, University of California, Sea Water Conversion Laboratory, 1963 Balaban, Miriam, Desalination and Water Re-use: Proceedings of the twelfth International Symposium (Rugby, UK). Institution of Chemical Engineers; NY, Hemisphere Publishing Corp. 1991 Belfort, Georges, Synthetic Membrane Processes: Fundamentals & Water Applications, Orlando, Florida, Academic Press, 1984 Brev, Jr., Wallace S., Principles of Physical Chemistry, Appleton-CenturyCrofts, Inc., New York, 1958 Eisenman, John L.; Smith, J. Douglas, Electrodialysis in Advanced Waste Treatment, Cincinnati Water Research laboratory; Federal Water Pollution Administration, 1967 Farrington, Daniels; Alberty, Robert A., Physical Chemistry, John Wiley & Sons, New York, 1959 Fletcher, Derek, A First Course in Electrode Processes, The Electrochemical Consultancy, P.O. Box 430, East Amhurst, New York 14051, USA, 1991 Harrington, Joseph J.; Pryun, Kenneth T.; Smith, J. Douglas, Mathematical Model of the Electrodialysis Process, Cincinnati, Ohio: Advanced Waste Treatment Research Laboratory; Washington, D.C. : U.S. document, U.S.G.P.O., 1969 Koryta, J.; Dvorak, J.; Bohackova, V, Electrochemistry, Methuen & Co., London, 1970 Latimer, Wendell M., Prentice-Hall, New Jersey, second edition, 1952 Lacey, Robert E.; Huffman, Everett L., Demineralization of Waste Water by the Transport-depletion Process; Washington, D.C, US EPA, 1971 Pletcher, Derek, Electrode Processes, A First Course, The Electrochemical Consultancy, UK, 1991 Pletcher, Derek; Walsh, Frank C , Industrial Electrochemistry, Blackie Academic & Professional, (an imprint of Chapman & hall), second edition, UK, 1990 309
310
BIBLIOGRAPHY
Walsh, Frank C , A First Course in Electrochemical Engineering, The Electrochemical Consultancy, P.O. Box 430, East Amhurst, New York 14051, USA, 1993 Walsh, Frank C , Electrochemical Engineering, A First Course, The Electrochemical Consultancy, UK, 1993 Weissberger, Arnold, Heating and Cooling, Mixing, Centrifuging, Extraction and Distribution, Dialysis and Electrodialysis, Crystallization and Re-crystallization, Filtration, Solvent Removal, Evaporation and Drying, Inter science, New York, 1950 Wilson, J. R., Demineralization by Electrodialysis, London, Butterworths Publications, 1960
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
Index Acidity control 17,42, 77,83, 91 Alkalinity control 17,42 Applications xi, xvii, 5, 7,9,149, 197,199,201, 282, 309 Batch processing 6,88,149, 212, 295,297,300 Biociding 55,303, 305 Bromine 11,51, 61,177,272,282, 303, 304 Chemical potential 17, 21, 69 Chemical treatment 39, 58, 63 Chlorine 11, 54-61,102,170,177, 189,273,272, 277, 282 Constant current operation 77, 87,129,154,161,256,285, 299, 301 Constant voltage operation 127, 302 Coulombic efficiency 84, 88, 91, 123,140,150 Cylindrical configurations 184, 305 Desalination xxi, 6,21, 31,102, 164,189,196, 309, Design schematic 100,110, 111, 92,127-145,177 et. Seq. Dialysis 29, 62, 95,96,97, 99,101, 102, 310 Dissipation currents 228,229 Dissociation constants 19, 24 Distillation xi, xiv, xx, xxii, 2,3, 5, 31,191,215
Electrode potential 5,18, 138,178 Electrodes 3, 6,17,22,29, 36,41, 54,56,71,97-102,112,127, 164,181,187,189,248, 305 Electro-dialysis 2, 6,11,14, 24, 32, 36, 99,102,107,124,167,197, 201,218,A4,A69 Equivalent conduction 23,103, 180, 220,261 Fick's Law 172,254 Flow through solutions 110,138, 237, 293 Free energy 18,21 23,40 Ion membranes 73, 83,101,116, 171,226 Membrane resistance 114,138, 150,163 Membranes xv, xxi, 3, 5, 6,17,23, 51, 71, 73, 80, 95, 99,112,127, 163,171, Metals reclamation 73 Microporous membrane 95,96,97 Molecular diffusion 172,173 Once through design 6, 9, 69,149, 193,285 Osmotic pressure 26,171, Parametric analysis 110,115,130 pH control 9,13,24, 39, 42, 51, 76, 235,238
311
312
INDEX
Portable processor 212 Processor module 34, 37, 38, Recirculation design 31, 62, 69, 191,271,277 Residential water softening 6,11, 49,184,194, 202, 205 Resin regeneration 12, 62, 235 Reverse Osmosis 2-8, 31, 62,211
Sedimentation xx Single cell performance 124 -127 Static solutions 138 Swimming pool 11, 39,46, 59, 179,305 Table of elements 222 - 224 Test cell 77, 78 TRL, Inc. xiv, xvii, 9, 58,273
Electrochemical Water Processing by Ralph Zito Copyright © 2011 Scrivener Publishing LLC.
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