Electrochemical Water Processing

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

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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

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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

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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.

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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

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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.

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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

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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

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output is required. Power supply is a simpl