COMPUTER SIMULATION OF STRONGACID CATION AND WEAK BASE ANION-

EXCHANGE RESINS

A thesis submitted to the University of Surrey for the degree of Doctor of Philosophy in the Faculty of Biological and Chemical Sciences.

ByDEREK C. HOLLIDAY

Department of Chemistry University of Surrey GUILDFORD MARCH 1978

ProQuest Number: 11012660

All rights reserved

INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted.

In the unlikely event that the author did not send a com p le te manuscript and there are missing pages, these will be noted. Also, if material had to be removed,

a note will indicate the deletion.

uestProQuest 11012660

Published by ProQuest LLC(2018). Copyright of the Dissertation is held by the Author.

All rights reserved.This work is protected against unauthorized copying under Title 17, United States C ode

Microform Edition © ProQuest LLC.

ProQuest LLC.789 East Eisenhower Parkway

P.O. Box 1346 Ann Arbor, Ml 48106- 1346

CONTENTS

SUMMARYACKNOWLEDGEMENTSINTRODUCTIONCHAPTER 1 : REVIEW OF METHODS OF WATER TREATMENT

Water and its impufities Ion-Exchange Electrodialysis Reverse Osmosis

CHAPTER 2 ; ION EXCHANGE RESINS AND THEIRCHARACTERISTICS

MANUFACTURE OF ION EXCHANGE RESINSStrong Acid Cation ResinsResin CrosslinkingWeak Acid Cation ResinsAnion ResinsType of Ion Exchange Resins Resin Characteristics COLUMN OPERATION THEORETICAL CONCEPTS EQUILIBRIAIon Exchange Isotherm Separation Factor Selectivity Co-efficient KINETICS Column KineticsFactors affecting the Operating Capacity

of Ion ExchangeResins in Columns Donnan Exclusion

3k

711

15 18 20 21

23 2k 2 6 30 30 323233 3k 38

39k7

CHAPTER 3

. CHAPTER 4

STRONG ACID CATION RESINSBASE EXCHANGE SOFTENING 48Packing of Resin Beads 49Experimental Work on the Effects of Particle Size, Water Regain, and Regeneration Level and Time on the Regeneration Efficiency 50The Method used to measure the Regeneration Efficiency 50Results 52Discussion of Results 60Regeneration of Strong Acid Cation Resins (H+ - Metal) 63Interpretation of Regeneration Results 73Loading Stage of Strong AcidCation Resins 74Effect' of Particle Size 75Effect of Bed Depth 77Effect of Flow Rate 79Effect of Inlet Concentration 79Regeneration Level 80Sharpness of the Ion Exchange Profile 80Conclusion 81COMPUTER MODELS 82Results from Computer Models 86Working Capacity 88Conclusions - Particle size and Industrial Applications 90MIXED BASE 'ANION RESINSIntroduction 91Working Capacity 93Factors which affect the Working Capacity 94Initial Modelling of the Capacity of Mixed Base Resins 98EMA Determination 102Modelling of Column Behaviour 105Final Model 108

Effect of Carbonic Acid 110Diffusipn Rates 111Program — Computer Model 112Conclusions I - Mixed Base Resins 124Conclusions II- Strong Base Resins 127

CHAPTER 5 : COMPUTING 130Variable Names used in the Programs 131

BIBLIOGRAPHY 134APPENDIX 1 : GLOSSARY OF TERMS 137

ABBREVIATIONS AND SYMBOLS 1 40APPENDIX 2 : Listing of Computer Programs 141APPENDIX 3 • Standard Zerolit Test Methods for

Ion Exchange ResinsAPPENDIX 4 : Paper presented to the Society of

Chemical Industry; Continuous Ion Exchange: Design and T Development.

SUMMARY

Ion exchange and its industrial applications to water treatment are briefly reviewed. The emphasis has been placed on column operation and the performance of strong acid cation, and mixed base anion, resins.

A new approach to explain the complicated behaviour of mixed base resins is reported, which is based on diffusion kinetics and equilibria. A computer program has been developed to evaluate a model incorporating these parameters, by comparing the results of calculation against existing and .new experimental data. Because of the number of variables which affect the performance of mixed base resins, a satisfactory quantitative approach to this problem has not been made hitherto. In the course of this work the 1sulphate/bisulphate’ explanation for the increased capacity of resins for sulphate ions as compared with chloride ions has been shown to be generally invalid. Two alternative explanations, one for weak and mixed base resins, the other for strong base resins, are proposed.

A quantitative study of some of the variables affecting the regeneration of strong acid cation resins is reported,.and optimum values for these variables are suggested. Some of this information has been available qualitatively but has not previously been published in detail.

Part of this work was reported in a paper presented at the Society of Chemical Industry1s International Conference on Ion Exchange held in Cambridge (31 )•

Also, D.L. Robinson of Permutit-Boby gave a paper based on this material to the National Iranian Oil Company at their Rey Research Centre.

Work on Continuous Ion Exchange, referred to in this thesis has been published (see Appendix 4).

Some of these results have been used by Zerolit Limited, e.g. in choosing the particle size of Zerolit 525 resin.

ACKNOWLEDGEMENTS

The work carried out in this thesis was done in the Portals Water Treatment Limited laboratories (now partly Diamond Shamrock - Zerolit), Isleworth, and the Physical Chemistry Department and the Computing Unit of Surrey University.

Sincere thanks are due to Dr. T.R.E. Kressman (retired),Mr. J.G. Grantham and Mr J. Irving of Diamond Shamrock-Zerolit Limited, Mr D. Bird of Permutit-Boby Limited, and to Dr W.H. Lee, Mr R. Fortescue and Mr B. Deaville of the University of Surrey for their assistance and encouragement.

Use has also been made of literature from Diamond Shamrock- Zerolit Limited, Rohm and Haas (UK) Limited, Dia-Prosim Limite’d and Bayer A.G.

During the course of this work there have been various changes in the organisation of the companies involved. Permutit Limited, part of the Portals Group, was reorganised underPortals Water Treatment Limited being divided into Permutit-Boby Limited (dealing with industrial plant), Zerolit (resin; manufacture) and other companies., Zerolit was sold to Diamond Shamrock Polymers in December 1976. Diamond Shamrock manufacture Duolite resins in the U.S.A., and, as Dia-Prosim, in France.

The author was originally employed in the Technical Development .Department of the Permutit Company Limited, before transferring to Permutit-Boby, firstly in the Process Department and at present in the U.K. Projects Department. • Colleagues who have helped with items in this thesis, as acknowledged in the appropriate sections, have worked for various companies in the Portals Water Treatment Group; some are now employed by Diamond Shamrock-Zerolit Limited.

M ATERIAL REDACTED AT REQUEST OF UNIVERSITY

INTRODUCTIONIon exchange has been studied for many years, since the original discovery of base exchange in soils in 1850. (1). Synthetic Zeolite ion exchangers were prepared by fusing Kaolin, quartz and soda ash in 1903 by Harm and Rimpler (2). The major breakthrough came in 1935 when Adams and Holmes discovered synthetic organic ion exchangers (3), It is from the.development of these that the ion exchange materials of today have evolved.

Almost all the ion exchange resins manufactured today 099$) are used for the purification of water, but there are numerous other small scale uses. The majority of research deals with processes other than water treatment, especially hydrometallurgy where it is hoped that ion exchange can improve or complement some of the solvent extraction processes.

The common cations present in Natural1 water are calcium, magnesium and sodium but the titles of published papers show that barium, strontium, potassium, copper etc., have received a disproportionately greater amount of study than their importance would suggest; this is partly due to the use of potassium rather than sodium in laboratory reagents. The usual need for water treatment in this country is to produce boiler feed water; modern power stations operating at 160 bar pressure require water which is 99*9999^ pure. An example of a large water treatment plant producing water of this

- 2 -

quality by ion exchange is illustrated in Plate 1; this is a Permutit-Boby cation, degas, anion, mixed bed plant installed at CEGB Drakelow Power Station.

Although much research has been carried out, the field is so large that there are many gaps in our knowledge.Another problem is that a large amount of data has been obtained on ion exchange resin performance but little has been done, except on a very superficial basis, to give scientific reasons for, and to find the relationships between, the many different parameters involved.

This thesis has concentrated on two areas:

1. strong acid cation resins, where there is a wealth of information, although it is sometimes conflicting; and

2. mixed base anion resins, whose performance is affected by many variables; no satisfactory wayof predicting the effects of the inter-relationships of these variables has yet been derived.

This investigation has been made partly by experimental work, but mainly by studying published data and trying to predict performance in terms of equations based on kinetic and equilibrium data. The aid of a computer has been sought for evaluating models.

CHAPTER ONE: REVIEW OF METHODS OF WATER TREATMENT

Water and its impurities

Water can be obtained from many sources such as rivers, lakes and boreholes. Depending on the environment the water has passed through, it dissolves and/or suspends various substances. Bacteria also grow in the water, but only dissolved inorganic chemical substances are considered in this thesis.

The dissolved material of interest forms cations and anions. The cations usually found in water are sodium (Na+), calcium (Ca2+), magnesium (Mg2+) and potassium (K+). Occasionally trace elements such as cobalt, aluminium, manganese and most commonly, iron, are present. Ammonia (NH^) is also found in polluted waters. The calcium and magnesium content is called the 'hardness* as their salts (e.g. CaCo^ and CaSo^) form scale on boiling and evaporation.

The corresponding anions are chloride (Cl~), nitrate (NO^"5’),2sulphate (SO^ ’), carbonate (CO^ “) and bicarbonate (HCO^“).

Also found occasionally in trace quantities are phosphate (PO^ ), fluoride (F ) and nitrite (N02“). Nitrate is now occurring in some sources e.g. the River Lea, in levels up to 50 mg/1 and is causing concern as this is above the level recommended by the World Health Organisation. It can cause methaemoglobinaemia (blue baby disease) in infants. The chloride, nitrate, nitrite and sulphate constitute the ’equivalent mineral acidity’ (EMA) and the carbonate

- k -

and bicarbonate the Alkalinity1. Silica is often also present, sometimes in a non-ionic form.

Organic matter is found in many waters and gives rise to colour. This is especially noticeable in Scottish surface waters. It is formed variously by the decay of leaf and other plant material, but can also originate from sewage effluent and industrial wastes. The River Aire is highly coloured but this is mainly due to less than 1 mg/l of a dye from an industrial effluent.

There is often suspended matter present, which may be siliceous or organic and is removed by filtration alone or by coagulation and filtration.

Demineralisation

The method of removal of dissolved solids in water varies according to the concentration. Below 600-800 m g/l ion-exchange is usual ; above this concentration electrodialysis or reverse osmosis is often used. At very high concentrations, such as are present in sea-water, evaporation is used.

Ion-Exchange

There are several ion exchange processes used to make the water more suitable for industrial and domestic use.

- 5 -

s . .

Base-exchange softening is the oldest process, and originally employed natural zeolites and greensands before ion-exchange resins were developed. This is a neutral reaction; no acids or bases are involved.

2R - Na+ + Ca2+ + 2Cl” ^ 2R2""- Ca2+ + 2Na+ + 2Cl“

R is used throughout as an abbreviation for resin.

The resin is regenerated by passing a concentrated solution of a sodium salt (;2r3M), usually NaCl, through the resin. This is a very useful exchange process and is very efficient chemically. The high efficiency is obtained because the selectivity of the resin is affected by the solution concentration - divalent ions being preferred by the resin in contact with dilute solutions (see Chapter 2), and monovalent ions at high (> 1M) solution concentrations.This is exactly what is required as the divalent ions present in waters to be softened are at low concentration and the regenerant, NaCl is usually dissolved from solid to form a concentrated solution. If the selectivity were the other way round such that a dilute regenerant solution was necessary, then very large quantities of waste water would be produced and the amount of product from a given volume of raw water would be unacceptably low. At least 95$ conversion of the raw water to product is obtained in softening.

- 6 -

However, softening does not reduce the total dissolved solids (T.D.S.) in the water; it merely replaces the less soluble calcium and magnesium ions by sodium ions in order to prevent precipitation and scale formation when the water is heated or evaporated.

The following processes reduce the T.D.S. and make use of acid or alkali regenerants, i.e., containing H+ or OH , the constituents of water.

Dealkalisation is the removal of metal ions associated with the alkalinity in the water. The alkalinity is usually due to bicarbonate, sometimes with carbonate in addition. The resins used for this purpose contain carboxylic active groups (-COOH) which are only slightly ionised in neutral solution, but exchange H+fairly readily with metal ions in alkaline solutions. There is a high affinity for divalent ions at the low concentration of the solutions usually treated, but not for monovalent ions. This is unimportant in practice as there are very few waters where the alkalinity is greater than the total hardness, so that normally only calcium and magnesium ions are removed:

2R~ - H+ + M2+ + 2HC03~ — R2 - M2+ + 2H2CC>3, ,2 + .... 2+ n 2+M = Mg or Ca

The carbonic acid produced can easily be removed in a degassing tower. In the tower the water flows down over

- 7 -

packed rings to give a large wetted surface area for contact with the air which is blown countercurrent to the water, thus removing the carbon dioxide.

A mineral acid is used to regenerate the resin, and an approximately stoichiometric quantity of the acid is required.

For complete demineralisation, water is passed through a strong acid cation resin followed by a strong base anion resin. The reactions for the removal of Na+Cl” are :

R“- H+ + Na+ + Cl” r* R~- Na+ + H+ + Cl"

R+- OH" + Cl" + H+— » R+- Cl” + H20

The cation resin is regenerated with a mineral acid and the anion resin usually with sodium hydroxide. Sodium carbonate or ammonia are sometimes used for regeneration, but being less basic than sodium hydroxide they are not so effective.

Electrodialysis

In electrodialysis water is processed by passing it between selective membranes and electrodes as shown in Fig. 1.1. Electrodialysis will remove all types of cationst and anions, but not dissolved gases.

- tt

+ ve electrode

- v eelectrode

C

^ c r

NaX

Na1

A

£ f

-C f.c T

Concentrate ? \ JC o n e s * ) \ r& te»

chluate.

Fig, 1.1. Electrodialysis cells

The cation- and anion- selective membranes allow only cations and anions respectively to pass through, and are substantially impermeable to water.

In a cell, illustrated in fig. 1.1. the cations movetowards the cathode, passing through the cationselective membrane but being held by the anion selectivemembrane. Similarly the anions move in the opposite direction.The net result is that the concentration falls in thecentre section and increases in the sections oneither side. An industrial unit would have many pairsof membranes giving alternate concentrate and diluatestreams.

- 9 -

In normal operation the cell resistance is determined by the ionic concentrations in the diluate and concentrate streams; the higher the concentration the lower the resistance. The concentrate thus has a lower resistance than the diluate, whose ionic concentration is related to the required water quality.The cell voltage is determined by the total resistance and the maximum current density.

It is easy to reduce high concentrations to medium concentrations but to reduce the concentration still further ( <1250 mg/l) is difficult, as the resistance of the dilute streams increases significantly and the process becomes uneconomic.

It is often necessary to Condition* the water by treatment with an acid to reduce the carbonate concentration, or by softening to prevent precipitation of calcium carbonate or sulphate in the concentrate.

The process is more tolerant to fouling of the membranes than is reverse osmosis, especially because of the advantage of using the membranes in both directions by polarity reversal.

A photograph of an electrodialysis stack is shown in Fig. 1.2.

M ATERIAL REDACTED AT REQUEST OF UNIVERSITY

- 11 -

Reverse Osmosis ( R. 0. )

The principle of* R. 0. is very simple. When a pressure in excess of* the natural osmotic pressure is applied to a solution in contact with a semi-permeable membrane, pure water will flow through the membranes. This continues until the osmotic pressure (which increases as the concentration increases) matches the applied pressure.

There is often a limit to the percentage of the inlet water which can be converted to product water and a typical figure is 75 °/o . This is lower than the percentage which should be obtained theoretically at the applied pressure, because of the low solubility product of the ions (especially of calcium salts) remaining in the concentrate stream. Calgon (sodium hexametaphosphate) and/or acid are usually added to inhibit precipitation and increase the °/o conversion. The acid converts carbonate to CO^ which passes through the membrane and Calgon inhibits precipitation of CaSO^.

The main problems in designing R. 0. equipment are inits engineering. High pressures, usually in the range28-40 bars, are used with their attendant problems, especiallyas plastics are often used in R„ 0. assemblies to avoidcorrosion problems. The other main requirement isto get a large surface area of membrane into a smallcontainer.

- ± d -

The membrane systems so far developed Include the Du Pont Permasep hollow - fibre technique, the Ajax spiral wound system and the PCI system of rods.The hollow fibre system is based on polyamide whilst most other systems use cellulose acetate membranes. The hollow fibres are about as thick as a human hair and so a large number can be packed into a container. A section is shown in Fig. 1.3* whilst Fig. 1.4 is a phcfcograph of a small unit with 16 permeators showing the controls and high pressure pump.

The advantage of polyamide over cellulose acetate asthe membrane is its higher permissible operating temperatureand this is very important as the potential market existsmainly in hot climates such as the Middle East. Athigh temperatures ( ^ 30OC) the cellulose acetate hydrolysesat too rapid a rate for economic replacement.

A problem which occurs more in this country than in the Middle East or America is that of colloidal organic matter fouling the membranes; this means that pretreatment is often required, especially for the hollow-fibre system, to prevent fouling of the very narrow channels.

The membranes will typically reject 90°/o of NaCl at1500 mg/l concentration. The rejection of different ions variesbut divalent ions are rejected to a greater extent

M ATERIAL REDACTED AT REQUEST OF UNIVERSITY

CHAPTER 2: ION EXCHANGE RESINS AND THEIR CHARACTERISTICS

Ion exchange resins are polymeric organic products; there is a growing, although at present mainly academic, interest in insoluble gel structures. The majority of organic ion exchange resins are based on styrene;,a few exchangers are based on acrylic resins. They fall into two major categories - cation and anion exchangers -

» and these are further subdivided into strong and weak acid or base.

MANUFACTURE OF ION EXCHANGE RESINS

Strong Acid Cation Resins

These are formed by sulphonation of the styrene matrix; however, since linear polystyrene sulphonic acid is solubl in water, it is unsuitable as an ion exchange resin.This solubility is easily overcome by copolymerising the styrene with divinyl benzene to form a cross-linked matrix (see Fig. 2.1). The copolymerisation is carried out in a stirred heated reactor as a suspension and this gives the characteristic spherical beads. "When the beads are sulphonated, by refluxing with concentrated sulphuric acid the product swells in water but does not dissolve. The amount of crosslinking affects the extent of swelling in water; a typical swollen resin contains approximately 50°/o by weight of water.

- 1 6 -

c h = ch2

Heatcatalyst

Styrene

CH — CH2— CH — CH2— CH— CH2— CH

Divinyl benzene

Linear polystyrene

CH2 CH CH2-

CHCH CH2 CH CH2 CH— CH2

Crosslinked polystyrene

H2SO4CH CH2 — CH--------CH2 — CH — CH2-

H+

H+SOJ

CH CH2 CH'S03

CH— CH2-ch2-

H+' H+

SO3 'SO3

Cation exchange resin

Preparation o f sulphonic cation exchange resin

i i

Fig. 2.1. Preparation of sulphonic cation exchange resin

- 17 -

Typical resins of this type are Zerolit 225 > Amberlite IR 120

and Duolite C 20. Figure 2.2. is a photograph of ZerolI t 225 resin beads at x 15 magnification.

Fig.2.2. Zerolit 225 magnification x 15

- 18 -

Resin Crosslinking

The resin is crosslinked by the divinyl benzene (DVB) across the polystyrene chains, and at a low precentage of DVB the percentage crosslinking is the same as that of the DVB. These percentages are on a molar basis. However, as the percentage of DVB increases there will be some DVB-DVB links formed instead of DVB-Styrene links. Xt is therefore necessary to measure the water regain to obtain accurately the percentage crosslinking. It is slightly more accurate to use the specific water regain (STO) which takes into account the sulphonation of the benzene rings. The relationship between SWR and percentage crosslinking, for both H+ and Na+ forms of resin, is shown in fig. 2.3 (10).

In the following chapter, reference will be made to nominal crosslinking based on °/o DVB and actual crosslinking derived from specific water regain measurement.

PIC V\

SPECIFIC. WATER

ff.ECAIN

v CROSSLINKINCj

ZER.OLIT

2.15

- 19 -

- «A

<r'>

WUOd ^ N - N lV W * m V/M SldttSdS

SPEC

IFIC

W

ATER

. RE

CAIN

-H

TFO

R.M

- 20 -

Weak Acid cation resins

Another type of resin is the weak acid cation resin, which contains carboxylic rather than sulphonic groups. There are several ways of making this, a typical route being via the copolymerisation of acrylic acid or methacrylic acid with divinyl benzene (see Fig.2.4). Resins of this type are Zerolit 236, Amberlite IRC 84 and Duolite CC3-

ch3I

c = ch2

COOH

Methacrylic acid

CH=CH2

c h= ch2Divinyl benzene

CH3

— C -— CH2 — CH— CH2 —IC00H

CH3

— c- CH2 —CH— CH2-

CO OH

CH3

c—ICOOH

c —

COOH

Fig.2.4. Preparation of carboxylic cation exchange resins.

- 21 -

Anion Resins

These often have the same hydrocarbon bead as the cation resin for the starting point but then the beads are subjected to chloromethylation and amination instead of sulphonation (Fig. 2.5*) If a tertiary amine is used (typically trimethylamine) a quaternary ammonium compound with a high basic strength is formed e.g, Zerolit FF, Amberlite IRA 400, Duolite Al* 101. These are called Type 1 strong base anion resins. A similar, but slightly less basic resin is obtained if dimethylethanolamine is used; this is called a Type 2 strong base resin e.g. Zerolit N, Amberlite IRA 410, Duolite A102. When a primary or secondary amine is used, the resulting secondary or tertiary ammonium resin is weakly basic in nature. There are many amines available and therefore a variety of resins can be made, which differ only in capacity and reaction rate. The uses of these different types are described later.

- 22 -

CH2Cl

CH30CH2CI

c h 2

C ross linked po lystyrene

N(CH3)3 NHICH3},

CH2-N (C H3)3 Cl

CH2Ct

'CH2NH(CH3)zCr

y

(a)CH2-N(CH3) lC l ‘ch2nh(ch3)2 cr

(b)

Preparation o f anion exchange resins (a) Strongly basic anion exchange resin (b) Weakly basic (tertiary amine) anion exchange resins

F i g , 2 . 5 .

- 23 -

Types of Ion Exchange Resins

Both, cation and anion resins can have either a macroporous or a gel structure; this only alters slightly the exchange characteristics, affecting the diffusion rates but not usually the selectivity.Because of their larger pores, macroporous resins usually have a lower total chloride capacity (T.C.C.)The main advantage of macroporous resins is their superior mechanical strength. Cation resins are physically stronger than anion resins and so macroporous cation resins are not usually required.

The macroporosity is formed by including a non aqueous- solvent (e.g, heptane) during the polymerisation which is subsequently removed. This has the effect of forming a number of relatively large pores inside the beads.

At the present time there are two main types of cation resins - strong acid and weak acid. Formerly there was a mixed type containing both strong (-SO^H) and weak (-COOH) acid groups but this is now very rarely used. Strong acid cation resins will exchange hydrogen ions for the metal ions in a neutral solution, but weak acid cation resins will only remove metal ions in relationship to the alkalinity in the water - they will exchange only a very small quantity of hydrogen ions for metal ions in a neutral solution.

- 2 k -

There are also strong base, weak base and mixed base anion exchange resins. There are very few completely weakly basic anion exchange resins because in practice, when making a weak base anion exchange resin, usually between 5°/o and 20^ strong base groups are formed at the same time. The strong base groups help to maintain the structure of the resin and to reduce the extent of swelling on exhaustion, which would result in gradual disintegration of the resin beads. Strong base anion resins are of two types, referred to as type 1 and type 2. A type 1. resin will have a lower regeneration efficiency than a type 2 resin, but will remove silica and carbon dioxide to a lower leakage level. The characteristics of mixed base resins will be described in detail in Chapter 4.

Resin Characteristics

In designing a Water Treatment plant the leakage and capacity of a resin, as a function of its regeneration level and the ionic composition of the water to be treated, are required.

Most manufacturers produce data giving values for these properties. These data are obtained from laboratory experiments under ideal conditions and it is usual to subtract 10°Jo or 15°/° from the capacity as a plant design factor. There is very little difference in the performance of resins of the same type from different manufacturers,

- 25 -

especially in the case of the strong acid cation resins - indeed it would be almost impossible to differentiate between samples of Zerolit 225» Amberlite IR 120 and Duolite C 20 by chemical or physical means.

There is possibly a larger variation between batches from each manufacturer than there is between those of different manufacturers. One would therefore expect the capacity and leakage data provided by the manufacturers to agree reasonably closely; however, there are some noticeable differences in these quoted characteristics, particularly as a function of solution composition. Some of the published data from different manufacturers, and some data obtained from laboratory work at Zerolit are given in the Appendices. It is hoped that a model of a strong acid cation resin will demonstrate which data are more accurate.

Resins can be used in a batch system or in a column. The batch method is used mainly in laboratories for obtaining equilibrium and kinetic data. Industrial plants use the column method, as a greater utilisation of the resin is achieved with a lower consumption of regenerant. To enable plant to be designed, laboratory tests are also carried out in columns. Such laboratory columns are often:', similar in height to, but very much smaller in diameter than, industrial plant; the usual dimensions are 25mm.diameter arid 500-2000mm height of resin whereas industrial plants are commonly built with diameters up to 3600mm and heights of 1000-3000mm.

- 2 6 -

COLUMN OPERATION

The usual sequence of operations of a column containing either a cation or an anion resin (a unit sometimes has two types of cation or anion resin, or both cation and anion resins, in it) is exhaustion, backwash to remove any accumulated solid matter, or 'crud', from the bed, regeneration, and rinsing; the cycle is then repeated.

A unit may sometimes contain both a cation and an anion resin; this is called a mixed bed unit. The regeneration sequence of this unit differs because the resins must first be separated before they can be regenerated, and then after regeneration and partial rinsing, they are re-mixed with air and given a final rinse. The mixed bed gives a product a higher purity than a cation unit followed by an anion unit, but has a higher regenerant consumption.

The regeneration of a column may be either co-flow or counter-flow; the latter is often abbreviated to CFR (counter-flow) or CCR (countercurrent) regeneration.

regenerantrawwater

rawwater

resin

regenerantCCRCo-flow

- 27 -

The reason for using countercurrent regeneration is that the quality of the subsequently treated water is very much better, and there is sometimes also an increase in the resin capacity. The 'leakage1 of a coflow -unit, treating a water containing only NaCl at a regeneration level of 80kg/m , would be h0°/o i.e., for 200 mg/l Na in the feed there would be 80 mg/l Na in the product. However for a countercurrent regenerated unit operating under the same conditions the leakage would be less than .1 mg/l. Nevertheless, many plants are still built with coflow regeneration because they are cheaper.

There are many techniques of performing countercurrent regeneration. It is usual to operate the service cycle downflow as shown, so that regeneration is in the upflow direction; this operation is designed to prevent fluidisation> and hence mixing, of the resin bed, as this results in a loss of capacity and a reduction in quality of the treated water.It is sometimes possible to use a low regeneration flowrate (e.g. 8°/o hydrochloric acid regenerant at a low regeneration level); usually, however, because a higher flowrate is used, (otherwise the time required would be prohibitive) it is necessary to hold the resin bed in place. This has been done in many ways but the commonest techniques emplo}?- either air, water or regenerant, which is put into the top of the-unit, and comes out together with the regenerant passed up from the bottom, through a collecting system buried a short way below the top of the bed.

- 28 -

Sometimes even better quality water than can be obtained with CCR is needed, and to achieve this, co-flow or countercurrent treatment is followed by treatment in a mixed bed unit. The conductivity of the water from a cation-anion system is usually 2-5y Siemen/cm, but after treatment with a mixed bed unit the conductivity may be less than 0.1jiSiemen/cm.

For softening, adequate quality of the treated water can usually be achieved with co-flow regeneration and therefore CCR softening units are uncommon.

Another technique employed is continuous ion exchange; this involves separate columns for regeneration and exhaustion. In the operation of these units the resin is slightly mixed during its transfer from one column to the other, so that the treated water quality is somewhere between that of the CCR unit and the co-flow unit, generally nearer to that of the former. A photograph of the Permutit-Boby continuous ion exchange unit at SSEB Longannet Power Station, in which the two columns can be seen, is shown in Fig. 2.6. A more detailed description of this process is given in the paper 'Continuous Ion Exchange; Design and Development' (Appendix 4) and some of the work reported in this thesis was done in order to provide information to optimise the design and performance of these units.

M ATERIAL REDACTED AT REQUEST OF UNIVERSITY

- 'JU -

THEORETICAL CONCEPTS

There are two main areas of concern - Equilibria and Kinetics. The former determines how far the reactions could go under ideal conditions and the latter the extent to which these reactions proceed in the time available.

Without changing the active group on the resin little can be done to alter its equilibrium characteristics but there are a number of changes that can be made to alter the kinetics or their effect on a process, e.g. resin particle size and extent of crosslinking.

EQUILIBRIA

Ion exchange equilibrium can be characterised by the ion exchange isotherm. This is a graphical representation which, in principle, covers all possible experimental conditions at a given temperature. Any set of experimental conditions (e.g. solution concentration, and ratio of the counter ion concentrations) is given by a point on the appropriate isotherm : See fig. 2.7» The lines a - d represent different solution normalities.

y ca

- 3 1 -

Fig. 2

x — Equiv. ionic fraction in solution v = Equiv. ionic fraction in resin a (0 025), b (0-1), c (0-6), d (1 0)

2+ +.7 Ion exchange isotherm for C% - Na with Zerolit 225 resin for different normality solutions.

Equilibrium may also be described by the selectivity coefficient, and by the separation factor. Considerable confusion has arisen from inadequate definitions and loos usage of these terms; the system adopted here is based on that used by Helfferich^^ in his definitive work on ion exchange.

Ion Exchange Isotherm

This is usually shown by plotting the’ equivalent ionic fraction, X ^ } of the counter ion a in the ion exchanger as a function of the equivalent ionic fraction, X& , in the solution, whilst the other variables are kept constant

: t

The equivalent ionic fraction is defined by:

v z mX = a aa -----« z . m .1 1 1Summation is over all ionic species present, of charge z .r 1molality m ..J i

Separation FactorThe preference of an ion exchanger for one of two counter ions a and b is often expressed, by the separation factor

where m. is the molal concentrationi

x. ” ” ionic fractioni

c . M n molar concentrationi

If the resin preferentially sorbs ion a then ©£ a ^ 1.b

The numerical value of the (dimensionless) separation factor is not affected by the choice of concentration units. It is not a constant, but depends on the total concentration of the solution, the temperature and the equivalent ionic fraction x& .

Selectivity Coefficient

This is sometimes used instead of the separation factor. The molal selectivity coefficient is defined as

- lZbl MK a = ma * mbb ------------- :----

= I N . . . I N

th.where z. is the ionic charge of the i ion.iThe selectivity coefficient can also be defined in molarunits or in equivalent ionic fractions; the coefficientsare denoted by K a and a respectively.

b b

If the ions are of equal valence, then

K a = K a. = NK a = (<* a) (z = z)b b b ib a b

For counter ions of different valence the choice of concentration units affects the' numerical value of the selectivity coefficient0

For a univalent exchange e.g. Na* - H .

K Na+ = m . m = NaH+ Na+ H+ H+

+

mH+ * mNa+

+ 2+for a univalent-divalent exchange e.g., Na - Ca

K 2+ (”w + ^ = «< Ca2+ . mNaNa Ca . Na --Na/ “ \ 2 2+ ( m.T + ) rnv Na 7 . Ca

m.XTNa

KINETICS

The ion exchange reaction, in which M+ in solution replace N'+ in the resin, follows the following steps1. diffusion of M in the bulk solution to the resin

bead surface2. diffusion of M+ into the resin bead

«|»3. the exchange reaction M fr>N4. diffusion of N+ out of the resin bead

- 35 -

5. diffusion of N+ away from the resin bead surfaceinto the bulk solution.

The rate-determining step is usually either a combination of 1 and 5 or of 2 and 4. In the former case the rate is said to be film-diffusion controlled, in the latter case particle-diffusion controlled.

Except in certain cases, e.g., the adsorption of acids on a weak base ion exchange resin, ion exchange is essentially a stoichiometric process. Any counter ions which leave the resin bead are replaced by an equivalent amount of other counter ions. The total number of ionic charges must remain constant because of the electroneutrality requirement. Minor discrepancies are caused by electrolyte sorption and desorption where both co- and counter-ions are sorbed. The amounts depend on the electrolytes and their concentrations.

The co-ion has little direct effect on the rate as it does not take part in the reaction, but it can have considerable indirect effect by altering the position of equilibrium. The classic example in water treatment is the difference which the alkalinity (i.e. HCO~), as contrasted with EMA, has on the removalof metal ions in hydrogen ion exchange.

- 3 6 -

This is because the hydrogen ion released in the exchange -reaction combines with the bicarbonate to form the largely undissociated carbonic acid and thereby stops the back reaction.

R - H+ + Na+ + C1“ ^ R - Na+ + H+ + C1

R - H+ + Na+ + HCO^— $R - Na+ + ^ 0 0 ^

Because of the electroneutrality requirement the diffusionrates in and out of the resin bead are not independent;when ion A diffuses away from the resin bead faster thanion B diffuses towards the bead an electric potentialgradient is set up which slows down ion A and acceleratesion B. Diffusion rates are therefore expressed asinterdiffusion rates of A and B. To understand themechanism of film diffusion it is necessary to introducethe concept of the diffusion layer originally developed

(11)by Nernst and usually named after him v '.

ConcentrationConcentration

Flow rate Flow rate

Space coordinate0

L a m in a r flow Turbu len t f low

The Nernst diffusion layer. The diagrams show the actual and the idealized concentration profiles (solid and broken lines, respectively) of a dissolved species which reacts instantaneously at the solid surface. The idealized profile is the tangent of the actual profile at the surface. In addition, the actual flow rates of the solutions are shown.

- 37 -

The bulk of the solution has a uniform concentration and this changes in the 'film* to zero at the resin bead surface. In the idealised Nernst film the concentration gradient is linear and predictions based on this compare favourably with actual results.

The ffilm thickness1, &, is an imaginary quantity and therefore cannot be measured directly. Its magnitude can

fitbe estimated from hydrodynamic or kinetic measurements and- 2 - 1is usually of the order of 10 to 10 mm. For columns

(23)with spherical ion exchange beads, Gillilandv 7 gives the empirical relationS- 0. 1r R and Glueckauf givesS*0.2ro/ 0 + 70rQv) for low flow rates and Cjt0.0029/v for high flow rates.

"Where Re, the Reynolds number, = 2vrQ/yv = velocity of the solution,y = kinetic viscosity rQ= particle radius

Whether a reaction is film - or particle - diffusion controlled depends on the interdiffusion coefficients in the resin, D,

and in the solution, D,the solution concentration, C,the bead radiusthe resin concentration of fixed groups, X, the film thickness, &

and the separation factorocA.B

A factor relating to these is Y :

Y = XD S (5 + 2<«A)CDr ‘ Bo

- 38 - •if* Y^Cl particle diffusion controls the rate, if Y » 1 then film diffusion controls. In the intermediate range Y ^ 1 then both mechanisms have an effect upon the rate of the exchange.

in the regeneration part of the operating cycle of the resins, the solution concentration is high ( > IN) and part-idle diffusion dominates, whereas in the loading cycle film diffusion usually controls.

Fields first law of diffusion is : J. = -D grad C. where J.1 1 iisT the flux (in moles per unit time and unit cross section) of ion i, where is its concentration (moles per unitvolume) and D is the diffusion coefficient. This law holds for both film-and particle— diffusion control with appropriate values in the equation.

Column Kinetics

The underlying principles are understood and have been briefly described but a quantitative treatment from first principles is very difficult. The problem has been solved for a few ideal limiting cases in batch operations - usually a single bead in a stirred solution - but no general and rigorous quantitative theory yet exists for column kinetics.

- j y -

Various theories based on drastic simplifications or on asemi-empirical approach have been fairly successful,and a simplified approach has been adopted in this thesis.

Factors affecting the Operating Capacity of Ion Exchange Resins in Columns

The operating characteristics of all cation and anion resins containing at least a proportion of strongly acidic or strongly basic groups are affected by the regeneration technique used (i.e. whether coflow, countercurrent or mixing prior to regeneration). The operation of completely weakly acidic or weakly basic resins is not affected in this way, as they regenerate to approximately 100^ efficiency (i.e. stoichiometric quantities of regenerant are sufficient to give full capacity) and in practice they are usually regenerated by the coflow technique. "Whichever method is used, regeneration must be carried out at near optimal conditions with respect to parameters such as regenerant concentration and specific flow rate of regenerant.

The choice of regenerant can have an effect depending on the process. This choice is determined by economic considerations. In base exchange softening, sodium chloride is the almost universally used regenerant, as it is very cheap; however, any monovalent salt is suitable. In hydrogen ion exchange, sulphuric acid and hydrochloric

- ko -

acid are used for regeneration. Sulphuric acid is cheaper than other acids in the United Kingdom whilst hydrochloric acid is the cheapest acid in Europe. Nitric acid is used in a very few plants where it is being manufactured on site.It is occasionally necessary to store the regenerant as a solid and some units, usually on ships, are therefore regenerated with sulphamic acid (NH^SO^H). In anion exchange, sodium hydroxide is usually used but ammonia and sodium carbonate are sometimes used, although these may be less efficient as they are less basic.

For strong acid/base resins the regeneration level affects the capacity. An excess of regenerant is required and the chemical efficiency decreases with increasing regeneration level. Each increment of regenerant has less effect, as is predicted by the law of mass action. The situation is complicated when more than two ions are considered. This relationship is studied in more detail in Chapter 3»

The bed depth can also affect the capacity. Usually deep beds are chemically more efficient than shallow beds, but there are limitations, especially with anion resins, because of the physical strength of the resins and the volume changes (see table 2.1) between different ionic forms. The pressure loss increases proportionally to the bed depth, so that athigh service flow rates this consideration may limit the maximum bed depth.

Table 2.1 Resin volume changes related to ionic form

Type of Resin Form Volume Form Volume Form Volume

Zerolit 225 Na+ 100 H+ 111 Ca2+ 103(strong acid cation)

Zerolit 236 Na+ 199 H+ 100 Ca2+ 120(weak acid cation)

Zerolit FF Cl" 100 0H~ 121(strong base anion

type l)

Zerolit N Cl” 100 OH" 111(strong base anion

type 2)

Zerolit H Cl" 100 Free 89(mixed base anion) base

These figures are related to the resin volume in pure water or in a dilute solution; however during regeneration, the resin is osmotically shrunk by the high concentration of regenerant.. The volume returns to its normal value on rinsing.

The bed depth also can alter the shape of profile after regeneration - examples of deep and shallow beds are shown in figs. 2.8 & 2.9 which were obtained in the course ofthis work.

Iul%

I t£ . Ul2 *

' o . o4CO • •01 ul

.9 2u. Ul

IA31K

in

z01 UlzulUula.

zg

§UlZjulvJm•£.

arfultdH><5

o |

5

§zin*1v3OWwN

dluift

Ul*£o *—-Qin --

u1ifU1—o Ul_J

o> _SaZ UldlUl3If1-

CD

«Q

•O

o o -OCO b> i

- 42 -

CO

LUM

N

LSNC

.TH

ftM

HESIN

Ze

eotlT

ZZS

Na+

POBM

HB

CENE

IUTI

OIM

6S

g/l

WITH

E%

H}S

6a

fttiiM

V

OLU

ME

; Sh

8 m

is

^TU

BE

»IA\

\ETE

ft I

V HE

qENE

EATI

ON

EFFIC

IENC

Y I Bi

•? »/.

pic a-q

clu5A (Jit u

2O O*r* <qf 9 O o

ST

o oCO o oooo o

1 XI

vrZui

z£D_ joVJ

I,I

- '43 -

The service specific flow rate affects the ion exchange profile (see Glossary) - the higher the flow rate, the longer the profile and the less the useful capacity obtained. A high specific flow rate gives a high Reynolds number and hence a thin N e m s t film, making diffusion faster, and this is made use of in continuous ion exchange systems

\ 2+ ^(see Appendix 4.). For Ca - Na exchange the profile was found to follow a power law with respect to flow rate with a co-efficient of 0.4 - see Chapter 3.

The concentration of ions to be removed - the counter ions - may affect the working capacity, but unless the

Oconcentration is very low ( K 25g/m ) or very highO( ^ 500 g/m ) this effect can be ignored.

The composition of the ions to be removed is very important, and affects both the leakage and the capacity. This is because of the different diffusion rates of the ions and the differing selectivities of the resin for the ions.

The composition of the co-ions is also important in certain cases; for example, in cation exchange the alkalinity to E.M.A. ratio is important. This is because with alkalinity

-

the product of* the exchange is removed and the reactionbecomes irreversible, e.g. at a regenerant level of*

O80 kg/m (H^SO^) the capacity and leakage of an !all sodium* water vary as follows

°/o Alkalinity 0 °/o 60 °/o 90 °/oocapacity kg/m ' 40.5 44.5 54

leakage °/o 40 16 4

An increase in the temperature of the water increases the diffusion rate and makes a large difference in the capacity of weak acid ion exchange resins ( see fig. 2.10) but has only a small effect on strong acid and strong base resins.

The acceptable leakage determines the start and finish of the service cycle. The higher the leakage that can be accepted the higher is the useful capacity when regenerating coflow ,but there is little effect with OCR.

Organic matter in the feed water may cause fouling of anion resins which in turn would necessitate regeneration levels higher than those required from capacity considerations, to ensure adequate removal of organic matter adsorbed by the resin. If the level of organic matter would cause fouling it is necessary to use a coagulation and filtration process prior to the ion exchange treatment.

Du<laI VJz<IoXu l

zo

f£ba5

sUlULao

(AUl

UUC*o!tain§LbiHaot iidULtLjUl

Zo

£

AO

<Ul£

43iCoJOl- * * 0

* 8

U*c4

O

O■o

UV

IIV

oCDiO •/,

TEM

PERA

TURE

OP

FEED

W

ATER

- <+Y -

Donnan Exclusion

If* an ion exchange resin is put into a dilute solutionof a strong electrolyte, considerable concentration

(12)differences are set up between the two phases.v ' If one considers a cation exchange resin, the cation concentration is larger in the ion exchanger whereas, the (mobile) anion concentration is larger in the solution. If the ions carried no electric charges then these concentration differences would become equalised by diffusion.

However, diffusion of cations out of the exchanger andOneIinto the solutionAof anions in the reverse direction

gives a positive charge to the solution and a negativecharge to the ion exchanger. The first few ions whichdiffuse therefore build up a static electric, potentialdifference between the two phases. This is called the1 Donnan potential1, after FjG.Donnan who applied thisapproach to membranes^^. It was applied to ion

(17)exchangers by Mattson in 1929 but was not universallyaccepted for twenty years. ( 18, 19* 20, 21)

The Donnan potential tends to pull cations back into the exchanger and anions back into the solution. Thus a static electric field balances the diffusion gradient, thereby maintaining in the ion exchanger a much higher counter - ion concentration, and in the solution a higher co-ion concentration. The situation with anion exchangers is analagous with the Donnan potential having the appointed sign,

CHAPTER THREE : STRONG ACID CATION RESINS

BASE EXCHANGE SOFTENING

Tills is the easiest system to study and a considerable amount of work has been done already; however, there are a number of gaps in our knowledge, particularly in respect of column operation. This thesis is mainly concerned with column work in both the loading and regeneration parts of the cycle. Before one can study the loading part of the cycle it is necessary to make sure that the column has been regenerated at near optimal conditions.

There are a number of factors which affect the regeneration efficiency - the concentration and type of regenerant, the contact time with the resin bed, the configuration of the resin bed and the physical characteristics of the resin. The temperature of the exchange is not critical and in most plant and laboratory work the temperature is ambient, usually within the range 5°C to 25°C.

The regenerant used in "the softening process is sodium(2 2 )chloride, and from work by JR Millar' 7 it was established

that the optimum regeneration concentration is between \y/o and 17°/o w/v. At low regeneration levels (< 100g/l ) the concentration was less significant. The concentration used in the experimental work reported here was 13°/o w/v, and this is the figure usually recommended.

**y

The diameter and depth of the resin bed can alter theefficiency of regeneration, but only at extreme values,see figures 2.8 and 2.9. Providing the ratio of tubediameter to bead diameter is greater than 25 : 1 andsolution distribution is adequate, wall effects can be

(5)ignored.v 7 Tests were done in glass columns of small diameter, 25mm and 150mm, and the results compared with those from 2500mm diameter plant columns; they were found to be in good agreement. With the high efficiency of regeneration obtained in base exchange softening, the effect of increasing the bed depth beyond 300mm was very small, and most experimental work was done with bed depths of 400mm.This depth corresponds, in a 25mm diameter column, to 200ml of resin, which was the volume used for most of this type of test work in the Permutit laboratories. The effects of regenerant injection time, regeneration level and resin characteristics were investigated and are discussed in detail below.

Packing of Resin Beads

To obtain consistent quantities of resin, the resin volume was measured after vibrating to give the maximum packing density, This does not always give the same quantity for different particle distributions, but it seems to be the most practical method, and has been used in our laboratories for many years. The dry weight of resin (g) per 100ml of wet resin was measured for three different conditions, as follows:

Vibrated coarse resin 50*&5gLoose packed coarse resin ^8.76gVibrated standard grade

- -

One would not expect large differences in packingdensities of spheres and this is seen to be true. In

(8 )fact according to Hicksv , mixtures of spheres of differing radii have a higher packing density than those of uniform size but probably because of the gradual variation in size this was not realised.

Experimental ¥ork on the Effects of Particle Size,Water Regain.and Regeneration Level and Time, on the Regeneration Efficiency

Several series of experiments were done on strong acidcation resins, manufactured by Zerolit Limited. The resinwas usually wet sieved, using B.S. sieves, into close -tolerance particle gradings, although some runswere carried out on unsieved materials. All the resins

4- 2+were found to have the same Na - Ca equilibriumOcharacteristics within experimental error (+ 1.0 kg/m )

This value was obtained by mixing a known quantity of24-resin in the Ca form with a constant quantity of regenerant,

gently agitating for 2 or 3 days, filtering off the resin, and then rinsing and measuring the amount of calcium eluted by titration.

The method used to measure the Regeneration Efficiency

200ml samples of resin, wet screened to give the required particle size where necessary, were put into a 25mm diameter glass column. This gave an approximate bed depth of 400mm.The resin was then completely exhausted by passing town mains

- 51 -

water through the bed until the hardness in the waterequalled the hardness in the output from the column. Xngeneral the columns were run past the exhaustion point.The column was then backwashed and rinsed with mixed bed

2+ 2+water until the effluent was free from Ca and Mg , and then regenerated with different volumes of 15°/o NaCl solution - the time for the regenerant to drain to bed level being recorded as the regeneration time. The regenerant flowed by gravity, the flow being controlled at the outlet of the column. When the regenerant drained to the level of the resin, mixed bed water was introduced as the rinse, initially at the same flow rate as the regenerant had passed through the column. The spent regenerant and rinse were collected until the total volume was 1 litre.

The resulting solution was titrated against standard N/50 E.D.T.A. solution using eriochrome black indicator. .This

2 + 2-i-gives the total concentration of Ca and Mg ions, and therefore the regeneration efficiency can be calculated.

The water regain and dry weight capacity (D.W.C) of each size and type of resin were measured using the method given in Appendix 3» During the course of the work it was found that for large size beads in the calcium form the original method gave low values for the D.W.C. An investigation was carried out and the quantity of acid required for this measurement in the standard test method was increased by k times for large beads in the calcium form and doubled for large beads in the sodium form.

- 52 -

Results

Resin sieved from a standard batch was used for the first two series of tests. A finer particle size than the median was used for the first and a coarser one for the second.

Series 1

Zerolit 225 - nominal 8°/o divinyl benzene (DVB)Particle Size - 30 + 36 mesh.

ORegeneration level 60 kg NaCl/m resin.Water Regain (w.R.) 1.0 g/gDry weight capacity (D.W.C.) 4.91 meq/g dry resin

Time (ks) Regeneration efficiency (°/o)

2.52

0.180.400.60

2.16

1 .001.55

68.780.686.588.488.588.486.5

7.50 82.0216.00 39.9 (equilibrium)

- -

Series 2

Zerolit 225 (8°/o DVB)Particle size - 1 8 + 2 2 mesh

ORegeneration level 60 kg NaCl/m resin W.R. 1.01 g/gD.W.C. 5«00 meq/g dry resin Specific W.R. 0.202 gH^O/meq

Time (ks) Regeneration efficiency (° /o )

0.17 58.00.39 67.1O .65 71.40.90 73.01.25 72.4I .67 72.52.75 70.59.00 70.0

216 40.2 (equilibrium)

- 54 -

Series 3

To obtain very large diameter beads, Zerolit 225 (8°/o DVB) which had been rejected as being too coarse was used for the third series - this was soft and badly cracked as is usual with very large beads, because it is very difficult to make strong uncracked beads larger than 14 mesh.

Particle Size - 10 + 12 mesh Regeneration level 60 kg NaCl/m resin W.R. 1.0 g/gD.W.C. 5-0 meq/g dry resin Specific W.R. 0.2 gH^O/meq.

Time (ks) 0.10

Regeneration e35.0

fficiency (°/o)

0.35 41 .81.03 49.41.48 49.43.60 48.4

216 41.2 (equilibrium)

- DD -

Series 4

To see the effect of changes in crosslinking a batch of nominal 4\°/o DVB resin was used for this series. To obtain a direct comparison the same particle size and resin as in Series 2 was used. This lower crosslinked resin is usually used for treating sugar solutions.

Nominal 4\°/o DVB resin Particle size - 1 8 + 2 2 mesh

QRegeneration level 60 kg NaCl/m resin W.R. 1.54 g/gD.W.C. 5.06 meq/g dry resin Specific W.R. 0.304 gH^O/meq

o .NaCl Value 82.6 kg/m Na form resin

Time (ks) Regeneration efficiency (%}

0.12 54.5O .36 62.80.91 67.51.78 68.94.20 66.0

216 39.2 (equilibrium)

- 5 6 -

Series 5

This series uses a resin of slightly higher crosslinking than the standard Zerolit 225*

Zerolit 325 (nominal 10°/o DVB)Particle size - 1 8 + 2 2 mesh ORegeneration level 60 kg NaCl/m resin W.R. 0.72 g/gD.W.C. 4.91 meq/g dry resinSpecific W.R. 0.146 gHp/meq

3 +NaCl value 105 kg/m Na form resin

Time Regeneration efficiency {°/o)0 .34 64.60.93 72.52.19 74.0

equilibrium 43*2

- 57 -

Series 6

At the time of this test, Zerolit 525 was a very coarse grade of the standard 8°/o DVB material. As a result of these tests, it was decided that this grading was too coarse and the specification has since changed several times. The aim was to produce a material that would easily separate in mixed and layer bed plants, and would also have a low head loss.

Zerolit 525 (8°/> DVB) Batch 199 Particle size (dry) + 18 68, 2°/o

- 1 8 + 2 2 23.0 - 2 2 + 2 5 7.6- 2 5 1.21 .2ORegeneration level 60 kg NaCl/m resin

W.R. 0.95 s / sD.W.C. 5.16 meq/g dry resin

Time(ks ) Regeneration efficiency0.10 O.36 1 .48 1 .87

37.1 45.357.1 56.8

- 58 -

Series 7

A batch of special resin, again sieved to -18 + 22 mesh of a high level of crosslinking, was used to study the effect of having a high available capacity (NaCl value) but a smaller pore size. As DVB is more expensive than styrene, it is usual to keep the DVB level down for economic reasons, so that resins containing a high percentage of DVB are uncommon.

Nominal '\6°/o DVB resin Particle size - 1 8 + 2 2 mesh ORegeneration level 60 kg NaCl/m resin W.R. 0.58 g/gD.W.C. 4.56 meq/g dry resinSpecific W.R. 0.127 S H 0/meq

3 +NaCl value 112.3 kg/m Na form resin

Regeneration efficiency (°/o)41.659.058.541.0

Time (ks)0 . 16 0.84 2.56

equilibrium

- 59 -

Series 8

Series 8 and 9 used the same resin as Series 2 but at higher regeneration levels.All details as for series 2 but at a regeneration level of 100 kg/m^.

Time (ks) Regeneration efficiency (°/o)

0.35 49.01.80 65.8

11.0 59.0equilibrium 36.0

Series 9

All details as for series 2 at a regeneration level of 160 kg/m^

Time (ks) Regeneration efficiency (°/o)

0.37 1.35 4.56

18.0equilibrium

37.048.75-1.249.228.2

- 6 0 -

Discussion of Results

a.) Time

The first topic considered is the effect of time on the efficiency of regeneration, As expressed graphically, see figures 3*1 / 3*3? 3*6, the result was always similar - the efficiency of regeneration increases with time to a maximum value and then slowly decreases to the equilibrium value. It is possible that, with very large diameter and highly cross-linked beads, this maximum value, which is greater than the equilibrium value, would not be observed. The regeneration efficiency would gradually increase with time to the equilibrium valuer

b) Particle Size

Fig. 3.1 shows the regeneration efficiency versus time for three different particle sizes. The wet screened sizes were:

through 30 held on 36 mesh (B.S.S.)through 18 held on 22 mesh (B.S.S.)through 10 held on 12 mesh (B.S.S.)

OThe regeneration level was 60 kg/m .

The percentage efficiency is adequate for comparison in this case as all the particle sizes have similar equilibrium

- 6 1 -

values. As is predicted from the kinetics, which are particle diffusion controlled, the smaller diameter beads regenerate more efficiently; for any given contact time, the smaller the bead the higher the efficiency.The maximum values of the ratio capacity/equilibrium capacity for the different particle sizes were 1.25>1.85 and 2.22 in order of decreasing size; see fig. 3*2.At 100^ efficiency the value would be approximately 2.5*

It is also apparent that the time required to reach the maximum value increases with particle size; therefore with a typical resin it is not possible to give each bead the optimum conditions. However, the curves are fairly flat in this region, so there should be little difference in performance over a range of times and in practice the shorter time is usually chosen.

c) Regeneration Level

Three different regeneration levels (60, 100 ando160 kg/m ) were used with the -18 + 22 mesh resin. The

higher the regeneration level, the greater the available capacity and the lower the efficiency. The efficiency versus time curves are shown in fig. 3»3»

However, the higher regeneration level corresponds to a higher equilibrium value, and so the ratio of capacity/ equilibrium capacity is very similar for the three regeneration levels, falling slightly from about 1.83 to 1.80 as the regeneration level increases. See fig. 3»^«

- 6 2 -

The time required to give the maximum efficiency increaseswith regeneration level but the curves of efficiencyversus time are very flat at the maxima, making accuratedetermination difficult. For the experimental conditions

-3 -1the optimum rate is approximately 170 kg NaCl m h ; see fig. 3*5* The range of the maxima is indicated for each regeneration level by the longitudinal lines.

d) Percentage Crosslinking

Four different pereentage-crosslinked resins were used (nominally 8, 10 and '\6 °/o DVB, actual crosslinking4.4, 7*4, 10.8 and 13*2) in the experiments. Lower crosslinked resins make diffusion easier because they swell more (i.e. they have a higher water regain) but this gives a lower total capacity in a given volume of swollen resin.Low DVB resins are physically weak and for most commercial applications a minimum of 8°/o DVB is used.

The nominal 8°/o and 10^ DVB resins give similar results.When plotted as regeneration efficiency the 8 - 10^ gave the highest values and the 16°/o the lowest (fig. 3*6), but if the ratio of capacity/NaCl value is used, to allowfor the lower number of sites available in the lower cross- linked resins, the order becomes 4°/o9 8 - 10^ and 16^(Fig. 3.7).

If one considers capacity versus crosslinking, the optimum is 8 - 10^ crosslinking (fig. 3*8).

- OJ -

This corresponds to the value usually used for commercial resins. Fig. 3*9 shows the capacity divided by the NaCl value for three different regeneration times, plotted against the specific water regain (SWR) on a log scale.These are all good approximations to a straight line. Regeneration of Strong Acid Cation Resins (H+ - Metal)

Some further experiments were carried out to see the effects of particle size and of regeneration time on H+ - Na+ and H+ - Ca^+ exchange.

A coarse batch of resin (97°/o held on 25 mesh sieve dry grading) and a standard grade resin, were tested similarly to the Na - Ca experiments but with 80 kg/m hydrochloric Acid (59 w/v) as regenerant; at 32 minutes regeneration time they gave:

standard 35°/o efficiencycoarse . k j°/o efficiency

The same resin exhausted with NaCl and then regeneratedOwith y/o Sulphuric Acid (96 kg/m ) gave:

standard (15 min) 73*9°/o efficiencycoarse (15 min) 71*1^ efficiencycoarse (30 min) 72.0°/o efficiency

Efficiency

-v—

time

for

Varying

Particle

Size

s

fa QN faH £m fafafa fafa oo wH fafa fa< 3:fa '—'

vo

o<r\

— O

|A# AONaiOI^a • N3D3H

to•Hfa

REGENERATION

TIME

(sec

onds

)

CAPA

CITY

/EQU

ILIB

RIUM

CAPACITY

-v-

TIME

FOR

VARYING

PARTICLE

SIZE

S- 65 -

-o

— X

o

rO

CM<T\

6D•H

03TJSOOCD03

WSH

gHC«W§owPS

•4 oCf co ' ♦

xxiovdvo wniHamnba/xiiovdvo

cn n n

o.

VO©IfX

# A0N3I0I333 * N3D3H

REGENERATION

TIME

(seconds)

Fig. 3.3

o~\ n n

in

o

>> ■

-Q

<■ X . NAxiovdvo wniHaninba/AXiovdvo

- DO -

\

4}'6

o4) J 4» ^ d*10 UN cui/3-y[ qaACCT *NCK)3H

OPTIMUM

REGEN. TIME

Ks.

Fig. 3.5

• *0

- — «

I- o

o

1Ao\

— o

>Q

G•Hu0>uo<H

0s•HI>I0GH0>HO0z

*pHO0fr0 -*0

rJ

•amyA #toU n / Axiovdvo

REGENERATION

TIME

FiS*

3.7

ca

•H

lA \Q

L.

<0

o55HISHcoCOoao

in

o Q«*\ ocJ.ui/Sx XXIOVdVO

- r---------------------- 1............. ......— t- :------------ 1 o^ ef\ o| *o o o °^fhavrf T fiB M /T T .T W J V ^

- 73 -

Interpretation of Regeneration Results

From the results it is concluded that the rate-determining step in the regeneration is the diffusion of metal ions in the resin bead. "When calcium is the ion in the bead this limits the efficiency obtainable, especially at the larger bead diameters and higher crosslinking. This is true for both acid and salt regeneration;.

The diffusion of sodium is however much faster, and particlesize has only a small effect. Also the efficiency obtainable

Hh •{• 2 "J*is very much higher for H - Na exchange than for H - Ca

The diffusion effect with calcium is affected by the structure of the resin and the lower crosslinked resins show a faster diffusion rate, as would be expected by their more open structure; this rate falls off considerably as the DVB increases above 10°/o.

The efficiency increases with regenerant contact time, as is predicted for particle diffusion, but reaches a maximum and then decreases. This decrease is due to the back diffusion of the exchange products into the fresh regenerant at a rate approaching the flow rate through the column, which is very low at long contact times, and the system eventually corresponds to a batch equilibrium reaction.

- l h -

Loading Stage of Strong Acid Cation Resins

In column work this is best studied by means of the ’ion- exchange zone’ concept described by Michaels (6). This is the depth of the bed in which a given extent of exchange, usually from 5-"9^C/ot 1-99^ of the inlet ,concentration, takes place. The extentof exchange is not taken as 0-100^ but a lower range to allow for experimental error in measurements, and for the ’leakage1• In some cases the leakage could be greater than 5°/o, and then other ranges about a. 50°/o mean can be taken.

In these earlier studies (6,7)3 it was assumed that:-a) exchange took place within a zone of constant

depth,b) this zone descended through the bed at a constant

rate, determined by the operating conditions and the extent of regeneration of the resin,

c) the zone length was quickly established, and d) the particle size was uniform.

These assumptions do not apply to industrial* fixed-bed plant regenerated either co-flow or counter-flow, but would apply reasonably well to a continuous ion exchange plant.In a fixed-bed plant both the regeneration level and the particle size vary considerably-between the top and bottom of the resin bed. Backwashing grades the bed, with the finer particles at the top and the coarse particles at the bottom.

- 75 -

Depending on the type of regeneration, either the top of the column is highly regenerated and the bottom only partly so, or vice versa.

However, with most continuous systems, close tolerance gradings of resin are used; the resin is transferred in small quantities and will undergo some mixing during transfer, resulting in a fairly constant extent of regeneration.

The zone length increases with;a) increasing particle sizeb) increasing bed depthc) increasing flowrated) increasing inlet concentratione) decreasing regeneration level

The zone length can also be affected by the composition of the co-ions and counter-ions as these affect both the equilibria and the kinetics. In H - metal exchange, alkalinity present in the influent gives a much shorter zone length than EMA because the reaction product H^O or H^CO^ is removed, making the exchange effectively an irreversible reaction and hence controlled only by kinetics and not by equilibrium.

Particle Size

This affects the surface area of the beads available for exchange. The smaller the diameter the smaller is the surface area of the bead but the number of beads in a given volume increases to give a greater total surface area.

- 76 -

Bead diameter cm 0.032Bead surface area cm 0.00283 . bNumber of beads in 1cm 4.2.10

0.0078 0.02 0.0319.5.103 2.4.103 1.2.10^

0.05 0.08 0.1

Total surface area cm in 1cm^in 1 cm 120 7b.6 b&.2 37.7

The effective surface area decreases with increasing flow because of the formation of eddies around the back of the bead. The contact with other beads also reduces the area and the other beads may also cause ’dead spots’ and eddies.

For standard grade resins the effective surface area would 2 3be about 50 cm per cm , and for the coarse grade used in

2some zone length experiments, about 30cm .

These figures imply that particle size will have a considerable effect on the zone length as the surface area changes considerably. There will also be an effect caused by the influence of the particle size on the interstitial pores and hence the Reynolds number of the water flowing through the bed.

As mentioned on page lb, the zone length should change throughout a graded bed. This was confirmed using a column of standard grade STerolit 225 regenerated at 65g/l and backwashed. The first run was in the direction from coarse beads t fine and the second run the reverse way round. The bed depth

- 77 -

was 1 .04m and the specific flowrate 90m/h.

Direction of flowOCapacity (kg/m ) to

Breakthrough Saturation 1-99^ Zone Leng'Coarse to fine 40.7 226mmFine to coarse 37.2 45.0 340mm

The majority of work (part of which is reported here) waswith the same particle size and so insufficient data was produced to derive a relationship between particle size and zone length. However, the results agree reasonably well with

Effect of Bed Depth

That bed depth affects the zone length is contrary to the assumption of a steady state used by most workers in the derivation of mass transfer equations. Similar relationships:

where C = 0.34, 0.26 and 0.33 respectively, were found, by Michaels (6), Baddour (23) and Mois on (7), respectively.

those of Moison (7) who gives the relationship

zone 1 ength<£(particle diameter ^

zone length>£(bed depth)

- 78 -Only a few experiments were carried out at different bed depths with other variables constant and these did not provide a good correlation.

If the zone length did continue to increase with increasing bed depth, there would be problems with some continuous ion exchange units where freshly-regenerated resin is frequently added to the outlet end of the bed, and exhausted resin taken from the inlet end, thus giving the equivalent of an infinitely long bed.

The suggested reason given by Moison for the effect of bed depth on zone length is longitudinal mixing (or axial dispersbn) resulting from the non-piston type flow in packed beds.

Jefferson (26) while considering heat transfer data for columns of spheres suggests 1 that fluid particle transfer correlations in fact may include their own axial dispersion corrections. It seems that the effects of axial ’dispersion* cannot be separated from those of fluid-particle transfer experimentally.’ When comparing some data of Handley and Heggs (27) a correction' factor of 3k °/o at low flows (Re = 100) was found by Jefferson; this factor decreased to 10°/o at the higher Reynold’s number of 4000.

It is possible that the reason for the effects observed isthat the -zone length takes a significant time and hencedistance to become established, especially if the 1-99 zonelength is considered. Most of the previous workers used5-95°/o zones and/or short bed depths. By using deep (>1m)beds and 1-99^ zones the effect may be less significant if indeedit does exist.

- 79 -

Effect of Flow Rate

As the flow rate increases the contact time between the fluid and the particle, and hence the time for the diffusion across the film, is decreased. However, the increasing flow rate also reduces the thickness of the film and therefore the overall effect is diminished but still results in an increase of the zone length. Michaels (6) found that the zone length was proportional to the flow rate to the power 0.5; this work was entirely in the streamline region at low Reynolds numbers. Moison (7) obtained a similar relation­ship but with the power 0.4, which is the same as results obtained by the author in the Permutit laboratories. If the two shortest zone lengths (from Michael’s work), corresponding to the very low flow rates are ignored, his graph would also fit a line with the power 0.4. The work carriedout at Permutit has always been in the turbulent region,

3 2usually with flow rates in the range, of 30 - 9 0 m /h.m • Toconvert these rates to actual linear velocities past the resinbead they must be multiplied by a factor of 2.5* as the voidvolume is approximately 40$ . The flow in normally sized

3 2resin beds tends to be streamlined below 11m /h.m . and3 2turbulent above 20m /h.m , with a transitional stage between

these two limits.

Effect of Inlet ConcentrationIncreasing the inlet concentration increases the number of transfer units required to reduce this concentration to the normal effluent level, and hence the zone length is also

- 80 -

increased. Further, in the case of univalent-divalent exchange, the selectivity coefficient is reduced, further increasing the zone length. As the solution concentration increases above 0.1N, particle diffusion as well as film diffusion can become significant. However, such high concentrations are not normally met with in water treatment.In all the work considered here, the loading cycle has been controlled by film diffusion, and only the regeneration part of the cycle has been under particle diffusion control.

Regeneration LevelIncreasing the regeneration level increases the number of sites available for exchange and reduces the leakage level in the loading part of the cycle. However, its main effect is to shorten the ion exchange zone when the quantity of ions which could be exchanged, based upon diffusion rates, is greater than the number of sites available; this only occurs at the trailing edge of the profile. The shape of the leading edge is determined by the film diffusion kinetics.

A high regeneration level, and hence a large available capacity, increases the throughput before either breakthrough or saturation occurs.

Sharpness of the Ion Exchange Profile

The sharpness of the boundary depends primarily on the equilibrium or the separation factor. (29) The more favourable the equilibrium the sharper will be the zone profile. Ions in the resin not yet exchanged, in the area behind the boundary

- 81 -

are preferentially exchanged into the solution and thus catch up with the boundary, whilst ions to be exchanged from the solution which has moved ahead of the boundary are . preferentially exchanged into the resin until the boundary catches up. Thus the boundary remains relatively sharp.

With favourable equilibrium, the sharpening effect of the equilibrium and the spreading effects of any disturbances counteract one another. The boundary reaches a steady state, and should remain unchanged as it moves down the column.This is called a self-sharpening boundary, and occurs in the loading stage of softening. On the other hand the regeneration stage produces a non-sharpening boundary, and such disturbances as eddy dispersion or effects due to density difference (regenerants usually have a significantly higher density than the loading fluid) tend to lengthen the boundary.

Conclusion

From the previous discussions it is concluded that the zone length is proportional to

( f l o w r a t e ^ x (particle d i a m e t e r ^ x (bed depth)^**^ x (inlet concentration)3, x (regeneration level )-^

- 82 -

COMPUTER MODELS

2+ +Several programs have been developed to model the Ca -Na exchange in a column of* strong acid cation resins. ProgramCW^B models the loading and regeneration cycles as theywould be performed in the laboratory. This starts with fullyregenerated resin, and repeats exhaustion and regenerationcycles until the same working capacity is found on

osuccessive runs, to an acceptable tolerance; a 1 kg/m tolerance is usually acceptable for laboratory work, and has been used in the program. Program CW^E models the ion exchange zone profile for a column with a constant regeneration level throughout the resin. This is similar to the experiments described on page 7 b (6, 7)«

The programs written in Fortran IV are iterative in nature; they compute what happens to slugs of solution passed through the column, which is divided into segments. Typically the column is divided into 100 segments each 10mm long, and the time interval for the exchange is one minute. The flow through the column is considered as specific flowrate in m/h; different rates of flow are considered.

Calculation of the Equilibrium Solution Composition For a given Resin Composition

The equilibrium relationship for a univalent-divalent exchange is given on p.3^ in terms of molal quantities. When expressed in terms of ionic fractions the total solution molality, M, also appears in the equation because the solution term on the top line is a squared term. This means that for exchanges

- 83 -

between ions of different valencies the solution concentration affects the equilibrium.

The relationship becomes in terms of upper case symbols K42 i= X4r x X2S2 x M

X2R2 x X4S (i)where X is the mole fraction,

S the solution phase R the resin phase K the equilibrium constant 2 represents sodium 4 represents calcium

also with only 2 components,X4S = 1 - X2S (ii)

substituting (ii) in (i) gives -K42 = M x X4R x (1 - X4S)2

X4S x X2R2 (iii)rearranging in terms of X4S

(M x x4r) x X4S2 - (k42 x X2R2 +2 x M x X4r) x X4S+ M x X4R = 0 (iv)

Let F = (K42 x X2R2) +2(M x X4R) (v )

then, X4S = F-\/fF2 - k) (vi)2

As 0^;X4S^:1 and 2 and K42, X4R and M are all positive the negative sign must be taken.The equilibrium composition X4SE at section J of the column and at the time, I, is given by

X4SE = 0.5 x (F - SQRT (F2 - 4)) where F = 2 + K42 x X2R2 ( j , I - 1)/(M x X4r ( j , I - 1))

- 84 -

Having calculated the extent of exchange which would occur to reach equilibrium, this is compared with the maximum exchange which could occur based on the diffusion co-efficient and the related conditions in the column. The lower value of these extents of exchange is then used for further calculations.

The maximum exchange based on diffusion, DIFMAX, is a function of:

(a) the effective surface area of the beads,A, given on p.76.

(b) The time interval I between iterations (in the programme I has been taken as 60 seconds).

(c) the concentration difference - film diffusion has been taken as the limiting factor, so that the bulk solution concentration has been used as this difference.

(d) the 'effective film thickness'£ cm, which was given on p.37* According to Glueckauf (24)

.0029/flow (in cm/sec) or 4. 2 x10”"2/f low (in m^/h) .O t *(e) the inter-diffusion co-efficient, D, for Ca - Na ;

the diffusion coefficient (at 25°C) for Ca2+ is7.9 x 10 cm2/s and for Na+ 1.32 x 10” cm2/s, therefore the interdiffusion coefficient is taken as 1.0 x 10"^ cm2/s.

For standard grading of resin this givesDIFMAX-=2=.0 . 71 x Flow x solution concentration

(m^/h) (mg/l)For coarse grading of resin this gives

DIFMAX =£= 0.43 x Flow x solution concentration

- 85 -

It was sometimes found that the extent of exchange was sufficiently large for the equilibrium between the resin and the inlet solution to be exceeded.

composition which would be in equilibrium with the incoming solution, and to limit the extent of exchange accordingly.

Calculation of the Equilibrium Resin Composition For a given Solution Composition_________________

For the regeneration stage it is the equilibrium resin concentration X2RE which is required. This is obtained in a similar fashion to the equilibrium solution composition in the preceding paragraphs.

By rearranging (i) and substituting (vii)

XkBE = 0.5 x (F1 - SQRT(F12 - 4))F1 = 2 + (M x X2S(J - 1)2/(K42 x X4s(j - 1))

(vii ) (viii)

A check was added as shown, (vii, viii). to calculate the resin

we obtainand letting

X^R = 1 - X2R (vii)G = (X2S2 x M)/(K42 x Xks)

X2R2 = G x X2R - G = 0

- 86 -

to keep^O X2R^1 the positive sign must be taken.• p. . X2R = 0.5 x (-G + SQRT (G + 4g ))

It has been found necessary to put in a number of statements to check that the mole fractions are always in the range 0 to 1.0 and to avoid divisions by zero when the mole fraction is zero, as is the case with the pure regenerant.

Results from Computer Models

These computer models have not proved very satisfactory.CW^B, which models the laboratory method of evaluating resins, reaches a consistent capacity in about three cycles as is found in the Permutit laboratory experiments, and by Dodds (28).The effects due to solution composition and regeneration technique are modelled quite well but quantitatively the effects of flowrate and regeneration level are unsatisfactory except with respect to leakage, as shown in Table 3«1*

It was decided.to concentrate work mainly on the mixed base resin model described in the next chapter, as it would be necessary to obtain more laboratory data before these models of strong acid cation resin exchange could be satisfactorily developed.

- 87 -

Table 3.1 Some Computer Model ResultsN.B. These are various results not all obtained with thesame constants and program.

a) Capacity: counter current regeneration - regeneration levels

various

Flow = 20m /hInlet = 500 mg/l Ca

Regeneration Level(kg/m3)

Computer Predicted Capacity (kg/m3j

Zerolit Published Capacity Leakage (kg/mj) (mg/l) Notes

30 23.7 22 0 Leakage alright but60 47.0 42 0 capacity too high at90 71.3 33 0 higher regeneration

levels•b) Capacity: effect of inlet concentration•jCounter current regeneration 100 kg/m

Flow = 10m /hInlet Sodium

(mg/l)Calcium(mg/l).

Capacity(kg/m3) Notes

50 300 70.3 Capacities high but show1000 1000 63.3 1 ®°/o reduction for higher

inlet concentration whichagrees with Zerolit data.

c) Leakage — effect of inlet concentration and extent ofregeneration.

Inlet Sodium (mg/l)

Calcium(mg/l)

Mole fraction Resin in Na form

Leakage(mg/l)

300 0.4 7.6- 300 0.6 2.1

1000 1000 0.99 0.42000 2000 0.99 . 2.31000 3000 0.99 2.3Results are of the right pattern and order but may be slightly low.

Working Capacity

This is a function of bo.th the regeneration efficiency and the ion exchange zone length.

For binary exchange (Ca^ - Na+ and Na+ - H+) it has*been possible to fit the capacity (for co-flow regeneration) with an equation based on the law of mass action.

_ OFor softening the capacity (Kg m as CaCO^) =100 x (1 - exp (-0.009 x Reg)),where Reg = regeneration level (kg m NaCl). (fig. 3.10)

+ +For Na - H exchanges the capacity =100 x (1 - exp (-0.0101 x Reg)),

-3where Reg is expressed in kg m H^SO^-3100 kg m is the total capacity of the resin and hence the

limiting value in these equations.

+ 2+For the exchange of H with either Ca or a mixture of2+ +Ca and Na it has not been possible to fit this type of

equation without altering.the initial constant to below 100;this means that although a fit is obtained for the usual range of regeneration (30 - 160kg m ) the maximum value is less than that obtainable with a vast excess of acid.

CAPACITY

-v-

REGENERATION

LEVEL

FOR

SOFTENING

- PREDICTED

AND

EXPERIMENTAL

DATA

- “oT—<r\

.3 £

O<r

5h ft

C/355HOO > Ph55 w ■tfft- £ JH O <5OH Q 55ft ft ftft 8-* Sft O HH*>© Q ftO ft pHO ><!H P< ft

oto

o

ocl\

\\ \ a

HOd55

<T\O sK \to ■ «

o•Q

L oi (A

►J>355OHhCtf55ftC5ft

X

0

~roo o olrv o* QC«v^00^0 SV •JLXIOVdVO

- 90 -

CONCLUSIONS

Particle Size and Industrial Applications

Particle size is mainly important in the regeneration stage when divalent ions are present. The effect on the loading stage, or on regeneration if only monovalent ions are present is very small. Hence for the mixed bed units which are treating waters containing only monovalent cations, a coarse grade of strong acid cation resin can be used without loss of performance, and this ensures a very good separation of the cation resin from the anion resin during backwashing prior to regeneration. Another advantage of coarse resin is the lower headloss and hence reduced pumping cost. For cation layered bed units where the permanent hardness is low, a coarse grade resin may also be used to help separation.

When treating divalent ions the effects of particle size on headloss, ease of separation and capacity must be balanced. This is particularly important with continuous ion exchange units which operate at high specific flow rates. The best solution for continuous iori exchange plants seems to be a closely graded resin without coarse or fine beads,

-16 + 30 mesh.

CHAPTER FOUR : MIXED BASE ANION RESINS

Introduction

Whereas both strong acid and weak acid cation resins are made, weak base anion resins are seldom made. This is because weak base anion resins are relatively weak physically and undergo a large volume change on exhaustion. To reduce the volume change, a proportion of* strong base groups, typically 10-20^is introduced. These reduce the amount of swelling but also reduce the capacity. The proportion of strong base groups formed depends on the reaction conditions. Formation of, weakly basic groups during amination may be represented:

and formation of a strongly basic group when two sites react with one molecule of dimethylamine:

H ClR.CH2C1 + (CH3)2NH-^R.CH2 - N+- CH^

c h3

r .c h2ci R.CH CH+ Cl + HC1

r .c h2ci 2 3

This is similar to a type II strong base group.

Table ^.1 lists the mixed base anion resins commonly available in this country with some of their characteristics relevant to this study.

a r O a O !> i> s> N N N N0 0 P p P 3 3 3 0 0 0 0* 3 o o o 0* a* O' 4 4 4 4P P H H H 0 0 0 0 o O od d- H* ■H* H- 4 4 4 H H H H aH* H* d- d- d- H H H* H- H* H* 0C+- d- 0 0 0 H* H* H* d- d- d* d- 0

d- d- d- H*S s > > S> 0 0 0 £ ffi - * • a - a P►c* 43 03 03 03 43 X NO NOON ON ON ON ON H H H tP■P" to NO 00 00 » 03 43 -»■ 43

a p> > W 'O s—' 4W NO NO ■P" 0 0

•P" 03 -O d-CO

s £ £ £ £ £ £ ■ £p P P P P P P Q P o d Qo O o o o o o 0 o 0 0 0 oj4 4 4 4 4 4 4 H 4 H H H 43O o 0 O o O O O 0

O0P

CO oX «! >-<! 3 «! >< 2 ! 12| 0 Q0 0 0 0 0 0 P 0 0 0 o o P O01 0 0 0 0 0 H 0 0 0 d- to

H1 4 IOp IPd- 143p. ipO IO

. P 1H-1 d-

1 0COI0

< a o i p .X X k ! X lz! • X *J p p - 10

0 0 0 0 0 0 O a 0 0 0 0 d- H-w 0 0 0 0 0 p 0 0 0 0 h* a id -

4 O S IH -> l< !

0 10111 d-IO

aH

CO CO 0«! >•<! * i 3 3 X- «! 30 0 0 0 0 P P 0 0 0 0 . 0K 0 0 0 0 H H 0 0 0 0 0 a

H H pd-0

to —i O — i — i to 03 ■P- pOx to o OX o 03 o Ox o o o 0 CO

0 d-1 1 1 1 1 1 4

Q Oto — 1 I\3 to 03 4 P03 o Ox o Ox Ox O (ft

Pa0

^ ? r o o ^ON ON Njt ON 00 ox Ox —i On ON ON ON q 0x5 p fr* o■p* Ol Or Or Ox Ox -a Ox O O Ox H \ a H d-o 3 P O p

i 1 1 a 030 4 HO H- H-

ON ON ON 4 d- aO O OX 3 Oj 0

a a <ia 4 oa 0 h

+ + + + + + + + + + + + 4 0 P3

-a to to to Ox to ro —i —i o a 0o -p- o Ox O to 03 00 w to o to a pH 0 O0 0 a4 P

■ H* d- pCL O (ftffi 0

COMPARISON OF

MIXED BASE

ANION RESINS

- 9 3 -

Zerolit call their mixed base resins type H; their initial version of H had a very high percentage of strong base groups. This percentage was reduced and the resin was then called HX; however, it was found to be prone to breakdown in industrial use, and so in late 1973 they reverted to a resin which was again called H but is in fact intermediate in type between the original H and *HX.These have therefore been listed as H pre-1971 and H post- 1973* A similar but mAcroporous mixed base resin, MPH is now produced,

Duolite have a family of three resins with graded changes in their properties, Rohm and Haas have IRA 93* but this has some breakdown problems when treating waters of high sulphate concentration, so that IRA 9 -S was developed and this is recommended for use with these high-sulphate waters. The kinetics of predominantly weak base resins tend to be particle-diffusion controlled, so that the contact time between the resin and solution is important.

Working Capacity

The working capacity usually depends on both the regeneration and loading stages. However in the case of weak or mixed base resins with only a small proportion of strong base groups (^20^) the regeneration is chemically very efficient, and is similar for the three main anionic species, Cl“,N03 “ and S0^“.

- 9 h -

This regeneration efficiency was shown by experiments similar to the loading kinetics studies described on p.106, but using sodium hydroxide to regenerate the resin in the chloride, nitrate or sulphate form; except for slight kinetic differences, all these forms reached the same equilibrium position in less than 30 minutes.

The loading part of the cycle is therefore the important consideration which directly affects the working capacity.

Factors which affect the Working Capacity

The working capacity of mixed base anion resins is usually a function of the following variables:1) The specific flowrate (m/h) of the water being

treated. This is expressed alternatively as bed volumes per hour or exhaustion time by different workers. However, neither alternative is specific,as bed volumes per hour does not take into account the configuration of the column; as was shown in the previous chapter, the exhaustion time is a factor of both ionic concentration and flowrate, and these have different effects on the ion exchange zone profile.

2) The free mineral acid (FMA) concentration, (mg/l asCaCO^) of the water being treated, especially at low levels (less than 100 mg/l).

- 5*5 -

3) The carbon dioxide (CO^) concentration of the water being treated; this is more important for waters rich in chloride than for those containing sulphate.

4) The ratio of divalent anions to the FMA.

5) The temperature and particle size of the resin; these are considered constant for the purpose of this discussion. Both an increase of temperature and a decrease of particle size would increase the working capacity of the resin because of the faster diffusion rate..

It was found that the working capacity was not a function of these factors as independent variables; there were inter­relationships between them. For example, a water having a low CO^ concentration, with chloride as the only anion present at a low concentration, which is passed through the resin at a high flow rate, gives a lower capacity than would be predicted from the cumulative effect of these variables from other conditions.

None of the manufacturers has yet devised a completely satisfactory method of calculating the working capacity as a function of all these variables. The difficulties arise usually in the areas of combinations of extreme values of the variables, when the inter-relationships

- yo -

have a large effect; the predictions are acceptable for the majority of natural waters encountered. The weak base groups will only take up strong acids, and not neutral salts or weak acids such as carbonic acid-. • However at the beginning of the run, when there are some strong base groups in the resin in the OH.form, weak acids present will be exchanged. These weak acids are then displaced as the run proceeds. The outlet carbon dioxide concentration, pH and conductivity as a further function of run length are shown in the graph 4.2.

The initial explanation for these effects was that the rateof the reaction, e.g:

RN: + H+C1~ — ► RNH+Cl”is dependent on the pH of the solution in contact with theresin and on the pK value of the resin. Therefore, inathe model, logarithmic terms were used for the FMA and CO^ concentrations.

A factor which affects all the resins, except IRA93* is the ratio of divalent anions (i.e. sulphate, being the only divalent strong anion normally met with in water treatment) to the FMA. Apart from this exception, the resins have a higher working capacity for sulphate than for monovalent ions; this also applies to strong base anion resins. The explanation usually given for this is that the sulphate goes on to the resin as bisulphate. However, this widely held view seems untenable for the following reasons:

-d-ON

oV)

( O T Y 9 T B O S \ n/3m A.11 lAHOUDUOn

- 98 -

a) The working capacity when treating a water where the FMA is entirely sulphuric acid under optimum conditions (ie. low flow rate, high CO^ and FMA concentrations) never exceeds the total exchange capacity of the resin quoted in terms of the sulphate ion.

b) The K value for the bisulphate ion equilibrium2L- + 2— —2HSO^ H SO^ is 1.2 x 10 , but under normal

operating conditions the pH of the water beingtreated is seldom below 2 and so the concentrationof bisulphate ion present is very small. Of course,if a sulphuric acid solution is used of concentrationsuch that the pH is less than the pK value (1.-92)athen it is possible for the bisulphate ion to exchange and for the total capacity of the resin, as quoted in terms of the sulphate ion, to be exceeded. This concentration of acid, however, is not met with in normal water treatment.

Initial Modelling of the Capacity of Mixed Base Resins

33From laboratory test data on Zerolit HX, an attempt was made to find a satisfactory correlation of the variables. Initial work, using a desk top calculator, suggested that it might be possible to fit the data using the following relationship:

- 99 -

Capacity = K x “IT (1 - exp ))Where K, a. are constants1 i

t. are variablesi

This gave the following equation where c_ are weighting constants, which were initially taken as unity:

c c cK x ( 1-exp(-a.jt.|) ) 1x( 1-exp(-a2t2) ) 2x(l-expf-a^t^)) -

C^.1)K, a^, a^i a^, c^, c^, c^ are constants 1/flow rate in m/h1/In (concentration of CO^ in mg/l)1/ln (concentration of FMA in mg/l)

This equation was evaluated against the laboratory data for all-chloride waters as these showed larger effects than all-sulphate waters with changes in EMA, CO^ concentration and flow rate.

The first trial did not give an adequate reduction of capacity for low CO^ concentration, with high flow rates, and so an extra term based on the Dia-Prosim formula (30) was added

' ' c.(1 - exp (-a^t^))

Where t^ = CO^ concentration in mg/l FMA x (Flowrate)^

Working Capacity =

Where

— | \JKJ —

03 ro io —1 —»O Ox O Ox O Ox Ox O Ox IO

O O O O o o o o o o o o0 0 0 0-00

o o o o o o o oo o o o o oo o o o o o o oIO IO IO IO

ox 00 —I .p- 00 VO • « • • • •IO Ox 03 “<I JO O O 00 00 ovo

to

03 05 03 jr* jr* 4?- Ox -<l VO J\3 Os VO

05 03 ON OX - i 00 00 03 00 00 4 -OX

—> H H OO h* H

ON 3 00 oo-o ro ro on ox —a 00 Ox VO Ox 4 o ON

COMPARISON BETWEEN

PREDICTED AND

EXPERIMENTAL DATA

FOR HX

- 101-

o P w <H - H - P

II HII II P

0o — A oo co• Ox — 4.03 • oVO 03 Hj-P-

oo o

O • p• o CO03 Ox d -

O P— * - 3 PVI Ss d -

COON

• • PON VO CO-0 ON 0Va P.

__L ro H-• • Pro -P-ON 00 0

O,X •

•p-o •

4P- — 1>

-p-oj oo ro ro —* o Ox o Ox o Ox

o o o o o . o • • • • • •o o o o o oro ro ro ro jo roOx Ox Ox Ox Ox Ox

o o o o o o « « • • • •o o o o o oo o o o o oro ro ro ro ro ro

ro —1 —1 O Ox O Ox

o o o o

o o o o • • • •o o o o o o o oIO IO IO IO

ro io —1 1Ox O Ox O Ox

o o o o o• • I • •

o o o o o • • • • •o o o o oOx Ox ox Ox Ox

3 oKpd-0

>

£03

ooIO

03

—x —». ro ro io03 ON VO IO 03 03• • • • • •ro vo ro —1 ox oo

— —1 —>• ro ro io ro ox oo 03 ox • • • • • •-O Ox Ox 4 VO 00 ON -* -p-VO O

I I I O ^ O O O I O • • • • • ••P" 03 ON ON -P" O -P-VO ON-* 0-0

-* IO 03 03 00 Ox —* ON • • • •O O O IO

03 03 03 -p- -p- -* OX VO 03 ON • • • • •IO IO O O ON

IO IO 03 03 —* -0 03 ON • • • ••P* O ON ONVO IO

03 03 03 -P* -P* 4 ON VO IO OX • • • • •-p"Ox JO Ox vo IO VO ’-VI

O IO IO o • ♦ • •vo O On p on ro .p--o

i i03 h* O O O • • • • •IO 03 ro 4- ON ro vo -0 ON 03

od-P;pK

IO IP rd

►CJIP 4 IO 0 IH* JOild- H-M O Id~k“''0 i<r aic13I 03

«H-H)H)040PO0

A computer programme for optimising the constants to fit the data was available at the National Physical Laboratory (NPL) and was used to find values of the constants. It was

ohoped to keep K at about 50 kg/m , being the maximum working capacity of the resin, but it increased in value during the optimisation. The term for CO^ would not converge and had to be constrained.

The fit found is given in Table 4.2 and is similar to the more detailed graphical methods so far produced in the manufacturers* literature.

EMA determination

The method used for determining the EMA is based on titration of 100 ml sample with N/50 NaOH to screened methyl orange end point ( pH 4.3)*. To bring this to pH7,0 an extra 8 mis of N/50 NaOH (equivalent to 8mg/l) would be required; so it could be argued that the EMA values used in the experiments should be increased by 8mg/l. Using the same constants as before, the capacity values were calculated on this basis and the results obtained are shown in Table 4.3* There has been an improvement in some predictions and a worsening of others. Some slightly . different constants were tried but a significantly better fit was not found.

*pH 4.3 is the value in BS.1427 on water examination and is chosen so that CO^ does not interfere with the titration.

'oJH\ o V 3

\j> ro ro -»■o Vn o Vn O Vn

o o o oo o o o o o o oo o o o o oro ro ro roUr Ur Ur Onoo oo- oo oo

ro ro ro roOn Ur On Onoo oo oo ooO O O O O O00 00 00 00 00 oo

0 0 0-0o o o o • • • •o o o o o o o oro ho ro ro

o o o oO' O O 0 . 0 o

-p- -P-Vn Vno -1 • # • ••p-VO -p--<J

VO 4T- 4r- .p-Vn Vn oo -p* oo ro roO O N O M \3 o v o

VO -P* -P" -P*Vn Vn -ropco-iM VO-p- 00 Vn VJ Vn 00 -V! -pr-<i VO 3 Vn V0 -<2 O 00 00 pr

oi-vi o p o ro vn vo vo ro p- —1 vo o oo ro ov

COMPARISON BETWEEN

PREDICTED &

EXPERIMENTAL DATA

FOR HX

WITH ADJUSTED

FMA VALUES

- 104 -

P*00 U M W -» O Or O On O Ur

O O O O O O • • • • • •o o o o o oVjO 00 00 00 00 00 OO VjO VO VjO 00 US

o o o o o o • • • • • •o o o o o o o o o o o o ro ro ro ro ro ro

ro -k -k O On O On

O O O O • • • •o o o o00 00 00 00

o o o o • • • •o o o o o o o o ro ro ro ro

ro ro -k -k On O On O On

O O O O O • • • • •o o o o o00 00 00 00 00

o o o o o • • • • •o o o o oOn On On On On

3 HOO0F w3 PIOd-0

s>

oOIO

OConcentration

k^/m

ro ro ro oo oj —4 ro oo oo VO 00 -p- 4P0n >-3 ro on oo —i —‘ vo oa .vo oo oo ro on o o• • • • • • • • • • • • • • d-p-oo p i o o p ■p O0n -k -VI O -k 'p-VO c op P■d

poH*d-

fc*ftd 3"-* -k ro ro oo oo io ro oj -P* •P* P* P*0n On 4 00ro on-* o m o cv o vo 00 o O P 00 -k ro 0• • • • • • • • • * ' * • • • • avo on ro -vi p- oo On 00 -p- -P- -0 p-0O P*-3 H--3 00 -k On On On vo 00 vo 00 Ov 00 O -vi On O-VOO -VI 00 oo VO - k V O O ^ 00 P- P- 00 -k d-0P.

1 1 1 1 Op-Vn P- IO —k On -* M p-k -VI ON ON On ro • H*

H5p--0 -k P P P -k 00 vo 00 o p- ro o p- H>./TVIO -k 00 p-0n On vo 00 vo 00 ON 00 O -Vi On ivwvo io oo ro oo vo -k vo O -VI 00 pr P- 00 -k 0

po0

- 105 -

Modelling of column behaviour

Although an empirical relationship has been produced, it was felt that this did not lend itself to an interpretation of the processes occurring, and a different approach was tried.

The aim of this approach is to model the behaviour of the resin during the service cycle to breakthrough and then to integrate the quantity of sorbed ions down the length of the column to give the working capacity.

The column is considered as a number of sections orequilibrium stages, and the effect of passing the waterthrough each stage is calculated. The first model was based

_ 2 —on equilibria between the Cl /SO^ ions and the resin, together with the difference between the P&a of* the resin and the pH of the solution. The greater affinity for divalent ions as described in Chapter 3 should favour the sulphate ions and give a higher working capacity.

A number of computer runs were carried out with this model, but these were abandoned after studying the following results of some laboratory work which had been initiated to obtain data for this model.

J. Irving of Diamond Shamrock-Zerolit was asked to investigate the uptake of hydrochloric acid and sulphuric acid on MPH (p. 106) resin to obtain data for the model.

- 106 -

The outline of the experiments was suggested and, as the results of the experiments would also be of interest to Zerolit, they were carried out. The results have not yet been formally reported, and are taken from the experimenter's notebook and interpreted in the following section.

The first experiment was to compare the extent of sorption - • of hydrochloric and sulphuric acids at a given concentration. The solution volume (ll) and concentration (800 mg/l as CaCO^) and 8ml of resin were chosen to give approximately equivalent quantities of acid and free base resin. The volume of resin was large enough to be measured with sufficient accuracy and the volume of solution adequate to sample without affecting the equilibrium.

Complementary to the equilibrium experiment it was decided to obtain kinetic information from the same investigation.

A quantity of resin was converted to the free base form with: it 300g NaOH/l of resin using a 5°/o NaOH solution and then rinsedwith mixed bed water. The resin was dried in a Buchner funnel and portions were weighed (5»528g being the equivalent to 8ml).

The portion of resin was added to a beaker containing 11 of acid and stirred continuously. Samples were taken at known intervals and titrated with N/50 NaOH. In some later experiments the pH was also measured.

107

I O

'COio

o

£P h£>i k TJ

3 *H £ O ft 03

H'

o o

<r\: h 'o

- 108 -

The results of the first test are shora in fig. 4.3*The amount of acid taken up was the same for both acidsbut the rate of uptake of the sulphuric acid was aboutfour times that_ of the hydrochloric acid. This was

(1 3)surprising as, according to Helferrich v ', the interdiffusion coefficient for the sulphate ion is lower than that for the chloride ion. This result has been obtained with a strong base anion resin.

This experimental result was not predicted by either the bisulphate hypothesis or the comparison with divalent cation exchange. However if the faster kinetics for sulphuric acid are accepted as correct, a simple explanation of the capacity data is possible in terms of kinetics andequilibria. The equilibrium is not between the resin and the sulphate and chloride ions but between the resin and the hydrogen ions from the corresponding acids.

Work on the equilibrium model was stopped and a new model formulated on the above result.

Final Model

As the strong base groups exchange anions for OH ions which then react with the H ions to form water, thereby removing the reaction product, no equilibrium is set up and all the strong base groups that have been regenerated will be exchanged.

O OThis corresponds to about 0.2 kg/m of the total 0.3 kg/m strong base sites. This is a similar ratio to that obtained with type II strong base resins.

- 109 -

r -o h“ + h + + A^-?R±A“ + H20

For the reaction of the weak base groups, where HA represents a mineral acid and R-N: the weak base site,

R-N: + H+ + A~*->R-NH+A~

the equilibrium is given by

K = (H+) (R-N:)a _____(r -n h+)

However, this equilibrium is based on the H+ concentration inside the resin and not in the external solution. The H+ concentration is greater in the solution because of the Donnan exclusion principle (P.^7)»

Because of the effect of the Donnan exclusion, and theinability to measure the activity coefficients in the resin,

»it was decided to use a pseudo equilibrium constant K inclterms of the solution H+ activity, which can be measured,

rThe value of K from the experiments and capacity data isa . ■•■-'■■■•■vapproximately 0.0009 (p&a = 3*05) • According to Helferrich

- 110 -

Ihe pK value of* a weak base resin is usually about 5 orSL

6 .

According to the equilibrium equation, increasing the EMAshould give a higher capacity and this has been found. Alsoif the pK of the resin is above 5 the carbonic acid in the asolution, which at the low pH (<5) is largely undissociated can diffuse into the resin, as the Donnan exclusion is only applicable to ionised species. However since the pH in the resin is nearer to 7*0/ the H^CO^ can dissociate to give a higher H+ concentration, and hence capacity for a given solution EMA concentration. The effect of this on the working capacity would be more pronounced at low solution EMA values.

Effect of Carbonic Acid

It will be seen from the capacity data that carbonic acid increases the capacity for both hydrochloric and sulphuric acids but the increase is most noticeable for low concentrations of hydrochloric acid. There are two reasons for this effect.

The first reason is that already mentioned, in that by changing the equilibrium position at low concentrations the capacity for both HC1 and H^SO^ is increased. However it would seem that above a hydrogen ion concentration of 135 mg/l this effect stops, presumably because this corresponds to a pH in the

- 1 1 1 -

resin when further carbonic acid does not dissociate.This is illustrated by the capacities showing a maximum

oof just over 50 kg/m . It is probable that if the capacity were measured with a 250 mg/l H^SO^ water a slightly higher figure would be found.

Lewatit in their published data show no increase in the capacity of MP62 for CO^ concentrations above 80mg/l; this is considered to be a generalisation and is not true for all waters. The limiting value would depend on the pKcLof the resin, and this is probably different for MP62 and HX.

The second reason is kinetic. The hydrochloric acid diffusion rate seems faster in hie presence of 00^.

Diffusion Rates

It has been shown experimentally that the diffusion of sulphuric acid is much faster than that of hydrochloric acid in MPH. It is assumed that this also applies to HX and other mixed base resins. A possible explanation for this unexpectedly high mobility of the sulphuric acid in the resin could be a similar effect to the well known proton-jump motion of the hydrogen ion in water. The resin sorbs the sulphuric acid on two sites but then the sulphate ion can pivot and move into the resin, thereby giving an extra means of movement besides simple diffusion.

- 112 -

The carbonic acid allows the movement of HC1 through the bead at a faster rate but the mechanism for this is unknown, it may be similar to that proposed for sulphuric acid. An. alternate reason is that the carbonic acid having dissociated inside the bead would react with some of the unionised sites to form an ionised site and the chloride could then exchange with the bicarbonate ion. Early attempts with this model allowed for the carbon dioxide to increase the diffusion rate of the sulphuric acid, but this was found not to/^produce the data. The increased capacity, even at high flow rates, is due to the fast diffusion of the sulphuric acid and to the carbon dioxide driving the reaction even when the EMA concentration is low, making a very short ion exchange zone length.

Program - Computer Model

A program was written based on the relationships and data described in the previous section, and is given in Appendix 2. This was to evaluate the experimental laboratory data not only for all-chloride waters but also for all-sulphate waters and for the combination found in MWB water - H^SO^ 73mg/l*HC1 67mg/l. It could be applied to other combinations but there is no experimental data with which to compare the results.

The following variables when given values as shown produced the results given, in figures 4.4 to 4.9:

AK

WBCRMO

RM5FICK 6

&FICK 8

Limiting

pseudo equilibrium constant 0.0009 (see p . 109)

o1.1keq/m - (measured value)rsregenerated strong base sites: 0.2keq/m

except for low capacity results (<25kg/m ) where running for several cycles would give a much higher effective regeneration level for the strong base sites, and thisOvalue was increased to 0 .25keq/m .

ORegenerated weak base sites 1,09keq/m

Are diffusion-related reaction' coefficients, the 6 referring to HC1 and the 8 to H^SO^.A variety of values were tried for these and the graphs are based on the following values:FICK 6 = (100 x 00^ concentration (molar)

+ 0.22) divided by the flowrate (m3/h)

FICK 8 = 2.0 divided by the flowrate (m^/h)concentration of C0^ affecting the equilibrium:

135<ng/l.

The effect of varying these constants is discussed in the following paragraphs.

- 114 -

AK

The pseudo equilibrium constant directly effects the maximum capacity obtainable and with RM5 = 1.09*C02= 2mg/l.

EMA AK=.00Q8 .0009 .00125 ' .412100 .790 .763 .738144 .856 .832 .811250 .948 .932 .917

The value of 0.0009 was used for the majority of the work and this seems to be accurate to at least - .0001• But evensmall differences in AK can have large effects, upon thecapacity, especially at low EMA values.

Limiting Value to effect of C0^ on Equilibrium

This was taken as 0.0027 (molar) for the majority of thework. One run was tried at .0016, corresponding to Bayer’s 80mg/l limit for MP62 but this was too low for the HX data. Although .0027 may be too high, the results indicate that 0.002 is the lower limit.

- 115 -

FICK 6

This is made up of two terms, one relating to the CO^ concentration and the other being a constant. FICK 6 = a x SM9 + b .

The effect on the capacity of varying the constant b on a water containing 100mg/l hydrochloric acid and 2mg/l CO^ at various flowrates ( m^/h ) is shown below with AK = .0009.

CAPACITY (kg/m3)b

CapacityFlow=5 15 20

0.2 35.83 20.0 17.130.22 36.98 21.35 18.000.25 38.50 23.65 19.330.35 41 .07 28 • 80

From the results it is estimated that b = 0.22 -O.^and this value was used in figs• 4.4, 4.5* 4.6 and 4.9.

The term in FICK 6 for CO^ was the molar concentration, SM9, times a constant. Values of this constant, a, between 50 and 500 were used but often with a ;change in the constant, b, as well.For SC6 = 100, AK = .0009, Flow = 15.

CAPACITY (kg/m3) a SM9=.001 .002100 39.8 44.8550 37.75 42.95

— 116 —

The value of a = 100 was used but is not entirely satisfactory. This makes a similar contribution to the diffusion rate at CO^ = 100mg/l, as does the basic constant b. Another run using SC6 x SM9 was made and this made some points better and some worse. It will probably be necessary to include in the model for the adsorption and replacement of the CO^ on the strong base sites and hence its variable concentration before the exact solution can be found.

FICK 8

This was, at first, made up of two terms - one for 00^, the other a constant. However as the constant is much larger than b in FICK 6 the term for CO^ was less significant and was left out. It is thought that the CO^ does not increase the rate of diffusion of the sulphuric acid but only that of hyclrochloric acid which is much slower.

The effect of differing values of FICK 8 is shown below for FloW = 20, SC8 = 100 and AK = .0009

FICK 8 Capacity (SC9=2) Capacity (SC9=100)1.8 42.472.0 43.00 49.202.3 43.67 49.40

From all the results considered it is estimated that FICK 8 2.0 - 0.2 and this value is used in figs. 4.7 to 4.9*

Fig

. k,

k

117 -

cnOo cm cd O o ocn (o cd cd

£ £ m cmC\i

•rlOcd

o•rluOH£ooU•dXK

fl-p o•H -P O O ft *H T3 H 0 cd Jh-P0£

ft

0 •H -P ?!0 ft ft £ X O H O1 IX ©

m

ocn•rl cn o £>cd £ido M

Exhaustion

Time

(hours)

- 1 1 8 -

cmo o

ca cmo CUB Oo £ Ocd oo o

r— r-)cncd I Cud

© £iH ii O

>; u-\ttf) Pi es -P 0o ’H ? jo •H -P i 1! jT“ o o

f t -H. n CM

T3 TJj4 O

•H i—1 CD OO cdcd ■p ft tH

C ’£UDo o k

•rl £ 0 1 £u •H +3 CM0 PSrH 0 ft£ ft £ ! 0O X O0 ft OuT3 1 1 i

) iw ><5 © !

<b

4a4t

o■it

iACA

JDCA

x

\

0

-1ACM

H0cm

flo•H-Pcn3cd£ft

x©-4A

I

\ C5> V- 0k . x. •Si m

A• ✓--V

J* H CAo £•

tic ft ClD•rl <! ft!ft o v— '

o1A

o-cf OCA

OCM

Time

(hours)

- 119 -

\o-d-•rlft

fl-P O

rrv & 'HCn .H 43o O Oo H 0 0

fclDE0 m01

-p ft fl•H -PU S 0 ft ft £ X O ft o

H « I{Xj ®

£-1 -"-VHen o E<!> ft ElO< 1 MO'W

-©

-PEx

haus

tion

Time

(hou

rs)

- 120 -

cn

&•rlft

H ' ' Hen o S

ooocn ca

tcDs

CMOo-p

H

£UD£cv

•H -Po o ft-HTlH 0

-P ft

•H -P

ft S X 0 ft o

- m

o

ftC X O'—

Exha

usti

on

Time

(hou

rs)

CAPA

CITY

- 121 -

£cn -p oo £ •rl

o •H -P© 0 Oo ft•rl

T5CO iH ©© © £+3 ftH £© ££i0 £ ©S •rl -Po £ £o © ftT— ft s

0(3 Oo

CO 1 icmffi ><! ©

-1

o-J

p<

nn

r\

,n

-Dcv

-A

-D

00-ct.-j

th

Cn oin O-3- ocn ocvbQr*

Exha

usti

on

Time

(hou

rs)

- 122 -

P 0 cno

•H P o0 O ©A *H o

T3H © wa u aP Acl© Cl HE 0

t»D•H P H3

f»oE

© A t -A S S C“-K OH O VO -3"

o1 l rH

Wm

O CMX © w tn

CMoO

fcUDS+

oo

X

\

?ncn

!ocn

noicvt

-O.’CM

Jo

in

CN

fd•Hfa

XH cn o s< >Ph tlD<! -MO w

Om o-d* ocn oCM

Exhaustion

Time

(hours)

- 123 -

An improved fit could be found using slightly different values for these constants, but the fit as shown in Fig.4.4 to 4.9 is usually within experimental error of the data. The iterative method of evaluation uses a large amount of computer time, and further refinement is not justified.

As well as normal errors in obtaining laboratory data, other differences could be due to the following factors:

1) Some runs were carried out with different batchesof resin, having slightly different characteristics.

2) The particle size distribution down the column could vary between runs depending on the efficiency of the backwashing; as the particle size is very important in particle diffusion controlled kinetics, this can affect the zone length and hence the capacity to breakthrough.

3) The capacities should be obtained at constant flowrates, but since some runs are extended overnight and were therefore unattended, the flowrate may have varied during the run. If the flowrate had fallen considerably and was then speeded up, a lower capacity would be recorded than would be expected for the exhaustion time.

4) At low flowrates'i.e., long exhaustion times, there may be problems due to channelling through the column, giving early apparent exhaustion.

Figs. 4.4 to 4.6 show the computer model predictions for different concentrations of hydrochloric acid with different carbon dioxide concentrations. These show a different shape of curve to that drawn when the data were originally obtained.

- 124 -

A curve rising sharply to a plateau had been expected and the original curves were drawn through the points to give this shape (Fig.4.10)

However, the model predicts a much flatter curve, whichone would expect from studying the uptake curve infig.4.3* This flatter curve can also be drawn satisfactorilyto compare with the experimental data.

The model for both sulphuric acid, (figs. 4.7 and 4.8) and MWB water fig.4.9* agrees well with the data. These curves do rise more steeply and have a similar shape to fig.4.10 but with a slightly rising curve instead of the completely flat plateau.

Conclusions I ; Mixed Base Resins

The model based on -

1) rapid and complete exhaustion of the regenerated strong base sites.

2) slower diffusion and equilibrium controlled, exhaustion of the weak base sites.

3) a very much faster diffusion rate for sulphuric acid than for hydrochloric acid.

4) an increase in the hydrochloric acid diffusion rate if carbon dioxide is present.

- 125 -

octfoCQ

soo'd•HO(tfo•rluOrHA-ooUTi!>»W CMOO

OO

CMOO«H H \ \bQ £»D S SO)A

CMOO

*10ECM -Ocn

! x* i

— IT\ Oi

-rOCM

m

o

hQ•rlfa

>1HOf a<O

cn£uD O

\*\

oJ: Ocn

\X "m

ocm

Exhaustion

Time

(hours)

- 126 -

5) di ssociation of* any carbon dioxide present, up to a limiting H concentration, keeping the equilibrium favourable within the bead.

is qualitatively and quantitatively sound although the exact way in which the effects the diffusion has notbeen fully resolved.

The values used for the constants are only approximate, but their expected limits are also given.

The success of this approach should confirm the invalidity of the bisulphate theory and present a basis for future work.

It should be possible to use this model with appropriate constants for all mixed and weak base resins. Values of the weak and strong base capacities'are known for most of these types of resins but it should be emphasised that they vary from batch to batch within each type of resin.

However the diffusion rate constants, the limiting CO^ value andthe equilibrium constant would have to be evaluated from sufficient experimental data. It should also be pointed out that the diffusion-related constants FICK6 and FICK8 are dependent on particle size. The values later in this work were related to experimental work carried out with standard production resin of -16 + 52 mesh.

- 127 -

Conclusions II; Strong Base Resins

The following explanation, which was originally thought to apply to both weak - and strong - base anion resins, has been shown in the preceding section not to apply to weak base resins. However it offers a more logical reason for the increased capacity for sulphate ions apparent with strong base resins than the bisulphate theory.

The separation factor for divalent-monovalent exchange is(14)related to the solution concentrationv Divalent ions

are preferred with increasing dilution of the solution; this is the reason why base exchange softening is so successful a process. This same principle should apply to the divalent sulphate ion. A possible reason why this comparison with the exchange of sulphate has not been made in the past is that calcium gives a lower working capacity than sodium when used in the hydrogen exchange cycle.However, this is because during regeneration the calcium is removed very slowly from the resin, since the interdiffusion coefficient for calcium is at least an order of magnitude lower than that for sodium. Hence, after regeneration with

oan economic amount of acid (e.g. 65 kg H^SO^/m resin) onlyo20kg/m of the resin would be converted to the H+ form from2+ 3 +the Ca form, but 60kg/nv would be converted from the Na

form. Therefore, because the available working capacityof the resin is low, even though during the service cyclethe calcium is taken up readily, the actual capacity obtainedis low.

- 128 -

However, with sulphate the situation is different, because the sulphate ion, having an inter-diffusion coefficient approximately half that of the chloride ion (13)? is replaced much more readily in relation to the chloride than the calcium is in relation to sodium. Thus a large number of sites are available for the service cycle, and therefore, a high working capacity for sulphate exchange can be achieved.

The uptake of sulphuric acid, nitric acid and hydrochloric acids is shown in fig.4.11. The method used was similar to that for MPH but with 2 litres of acid solution at 400mg/l as CaCO^ instead of 1 litre at 800mg/l. This shows that the equilibrium value is the same for nitric and hydrochloric acids, but considerably different for sulphuric acid at the same concentration. However, the rate of uptake for all the acids is an order of magnitude faster than for weak base resins. This means that the capacity of strong base resins is less time dependent, and provided there is a minimum of eight hours exhaustion time the capacity is independent of time.

- 130 -CHAPTER 5 : COMPUTING

The computing reported here has been carried out with the University of Surrey1s ICL 1905F and Control Data Corporation CDC 76OO of the Regional Computing Service at the University of London Computing Centre (ULCC) via the Surrey University Remote Job Entry Link.

It was originally intended that much of the work would use a continuous simulation language, and several of these were tried. The first was SLANG, a language developed by Hawker Siddeley for rocket trajectory simulation. This was available on the 1903 F machine but was not very sophisticated, and a change was made to MIMIC, a CDC language which was available at ULCC. ICL then introduced SLAM which became available on the 1905 F whilst still being developed by ICL.Both the MIMIC and SLAM languages are supersets of FORTRAN, translating the user’s programme and adding their own routines to produce a FORTRAN program.

As some problems were encountered in using these simulation languages, and as the computing staff had little experience with them, it was decided to use FORTRAN IV which, although not designed for this application, was well documented and familiar. Some use was also made of ALGOL 60.

- 131 -

Another problem has been the difficulty in programdevelopment caused by operating in batch mode, not being on site. The change to FORTRAN meant that some program development could be carried out using the interactive ’MAXIMOP’ system.This was useful for fault detection and elimination but the iterative nature of the simulation meant that run times were long, and full results could only be obtained in batch mode.

VARIABLE NAMES USED IN THE PROGRAMS

FORTRAN accepts strings of characters, up to six in length, starting with a letter. Unless specified otherwise at the start of a program the variable is stored as an INTEGER if the first letter is I, J, K, L, M or N, otherwise it is stored as REAL.Only upper-case letters are used. Variable arrays are formed by adding a subscript list in parentheses after the variable name and must be declared at the beginning of the program, so that a suitable amount of core storage is allocated to them.

To make the understanding and writing of the programs easier, variable-names have been used which are related to their significance. '

Some of the variable names are made up of several letters and numbers as follows:

- 132 -

c Concentration in mg/l as CaCOD "DifferenceE At equilibriumK Coefficient or constantM Molar concentrationR Resin phase or a ratioS Solution phaseX Mole fraction

Numbers has been used to refer to the ionic species concerned -

0 Hydroxide ion1 Hydrogen ion2 Sodium ion3 Magnesium ionk Calcium ion5 Free base form (weak base resin only)6 Chloride ion7 Nitrate ion8 Sulphate ion9 Carbon dioxide or carbonic acid

A few examples will illustrate this use:-

X^-SE is the mole fraction (x) of calcium ions in the solution phase (s) at equilibrium (e).

- 1 33-

K^2 is the selectivity coefficient (k ) of thecalcium ion (4) to the sodium ion (2).

RM6 is the molal concentration (m ) of the chlorideion (6) in the resin phase (r ).

FICK6 is the diffusion coefficient for the chlorideion (6).

EMA however is used for the Equivalent MineralAcidity.

- 134 - BIBLIOGRAPHY

1 Way, J.T., J. Roy. Agr.Soc.Engl., (1830), 3132 Harm, F. and Rumpler, A,. 3th Intern. Congr.Pure

Appl. Chem. (1903), 593 Adams, B.A., and Holmes, E.L., J.Soc. Chem Ind. (1935),

5i+ 14 Teasdale L, Miller J.R. , and Holliday D.C., (l971)

Internal Permutit Memoranda.5 Perry, J.H. Ed., ’Chemical Engineer’s Handbook’, (1950),

McGraw Hill, N.Y. p3946 Michaels, A.S., Ind.Eng.Chem., (1952), kk, 19227 Moison, R.L. and O ’Hern, H.A.Jr. Chem.Eng.Progr. Symp.

(1959)i Ser.No. 2k 33, 718 Hicks, R.E., Ind.Eng.Chem. Fundamentals. (197Q)> 9_, 3, 5009 Kressman, T.R.E., and Miller, J.R., Chem. and Ind.

1833, (1961),

10 Helferrich, F. ’Ion Exchange’, (1962), McGraw Hill P152

, N.Y.

11 ibid, p25312 ibid, p 13^13 ibid, p30914 ibid, P 13715 ibid, p8616 Donnan, F.G., Z.Elektrochem. , (1911), .17, 57217 Mattson S, Soil Sci., (1929), 28, 17918 Bauman, W.C. and Eichorn J, J.Am.Chem. Soc . , ( 1947) , §2 , 283019 Boyd, G.E. et al, J. Am. Chem. Soc. , (1947), 69,, 281820 Gregor, H.P., J.Am.Chem.Soc., (19^8), 70* 1293;

(1951), 73, 64221 Glueckauf E, Proc.Roy. Soc.(London), (1952), A214, 20722 Miller, J.R., Internal Permutit Memoranda, (i960)23 Gilliland, E.R. and Baddour R.F., Ind.Eng.Chem.,

(1953), 33024 Glueckauf, E. in 'Ion Exchange and its Applications',

(1955), The Society of Chemical Industry, London, p3 -25 Arden, T.V., 'Water Purification by Ion Exchange’,

Butterworths. London, p20(1968),

26 Handley, D., and Heggs P.J., Trans.I .Chem.Eng. 46, (1968), T251

- 135 -

27 Jefferson, C.P., Am.I•Chem.Eng. Journal (1972), 18,2, 409-420

28 Dodds, J.A. and Tondeur, D., Chem.Eng.Sci.(1972),27, 1267-81

29 Helfferich, F., Angew.Chem. internat Edit. Vol.I (1962), No.8, 440ff

30 - Dia Prosim bulletin for A368PR (1973)31 Lee, W.H., and Holliday, D.C., 'The Theory and Practice

of Ion Exchange'. Society of Chemical Industry,London. (1976)

32 Internal Permuifcit Memoranda (1971/72)33 Internal. Tisb L a b tm io ^ ft&pot-Js on M X

Evulaainon 0^71) *

- 136 -

List of Resin Manufacturers1 Bulletins Used in this Work

ManufacturerZerolit

ResinH

HXMPH225M

Date PrintedMarch 1968, March 1972 1976April 1970 197^, 1975 May 1970, 197^May 1969

Rohm & Haas IR 120IRA45IRA47IRA93IRA94S

March 1967 February 1971

December 1971

Dia-Prosim (Duolite)

C20 A368 • A368PRA369

March 1971

September 1973

Lewatit S100MP62MP64

September 1969 February 19^9

- 137 -

APPENDIX ONE

GLOSSARY OF TERMS

Capacity(a) Working capacity - units Kg as CaCO^/m ;or keq/m .

The mass or equivalent weight of ions which the resin will remove at a given regeneration level to a given leakage endpoint. This is lower than the total capacity of the resin.

O(b) Total capacity - units Kg as CaCO^/m : or meq/lThis is exchange capacity of the resin from thefully regenerated to the fully exhausted state. Foranion resins it is measured as the total chloridecapacity (TCC) and as the NaCl value (9) for thecation resins.

Dry weight capacity (DWC) - meq/g5 i.e.,the total exchange capacity of the resin in meq/g.of dried resin.

Ion Exchange ProfileThis is usually represented by a curve showing the percentage conversion of the resin.

direction of flow y of solution

distance along .ion exchange columnl \

+ /

H+

(c)

0 100°/oU+

- 138 -

Ion Exchange Zone

The part of the ion exchange resin bed in which the exchange is taking place.

Leakage

The concentration of the ions to be extracted which passes through the ion. exchange column and appears in the treated water.

Regeneration

That part of the cycle in which the resin is returned to the appropriate form for treating the water e.g., the Na form for softening, H form for cation-and OH form for anion-exchange.

Regeneration Efficiency

The quantity of ions removed in the service cycle divided by the quantity of regenerant. This is usually quoted as the percentage, both terms being in equivalent units. Another way of expressing this is as a percentage of the stoichiometric^ requirement.N.B. 5Q°/o efficiency S' 200°/o of stoichiometric requirement.

Regeneration Level

The ratio of the weight of regenerant to the volume of resin;ousually expressed as Kg (regenerant - as is )/m resin.

- 139 -

RinseThe flushing out of the regenerant from the column after regeneration before returning the ion exchange resin to service.

Service/Loading/SorptionThese are difference names for that part of the cycle of operation during which the resin is removing ions from the solution being treated.

Specific Flowrate3 2This is the flow rate per unit area, e.g. m /h. m . (m/h).

This is not the same as the actual flow rate because the resin occupies approximately 60°/o of the volume of the column - the linear flow rate past the resin beads is therefore 2y times the specific flow rate.

Metropolitan Water Board (MWB)This supply was used for a large proportion of the test work. A typical analysis in terms of mg/las CaCO^

Calcium 280 Alkalinity 192Magnesium 20 Chloride 52Sodium & Sulphate 71Potassium 38 ,T. , _l. -J Nitrate 22.5

Water Regain (WR)This is the ratio of the weight of water contained in a wet swollen bead to the dry weight of the bead, g H^O/g resin.

Specific Water Regain (SWR)This is the value of the water regain divided by the dry weight capacity. g H^O/meq.

- 141 -ABBREVIATIONS AND SYMBOLS

Concentration of species i in moles per unit volume of solution, sometimes expressed in terms of the calcium carbonate convention, mg/l as CaCO^.

nn Concentration of species in moles per kg of solvent(molality).Equivalent ionic fraction of counter ion i.

A bar above a quantity, e.g. X^, refers to the resin phase.H+ will be used instead of the more correct H^0+ for the

hydrogen ion in aqueous solution.FMA Free mineral acidity is the concentration of mineral

acids expressed as CaCO^.EMA Equivalent mineral acidity; this becomes the free

mineral acidity after exchanging the metal ions for hydrogen ions.

CCR Counter current regeneration )) These have the same

CFR Counter flow regeneration ) meaningCIX Continuous ion exchangeb.v. Bed volumeWR Water regainSWR Specific water regainDWC Dry weight capacity

\TCC Total chloride capacityK The selectivity coefficient is defined on p. 33*

The separation factor is defined on p.32.

- 142 -

APPENDIX 2

Flowcharts and listings of computer programs, together with some typical output:

CW4B - Cation exchange (softening) exhaustion and regeneration model

CW4E - Ion Exchange Zone model (softening)

C¥4e - Mixed base anion exchange exhaustion model.

An explanation of the variable names is given on pages 131-133•

simulation of Calc2.um~Sodium exchange in a column,- ^

START

READ IRTYPZ/

READ FLOW

JriHiAD LsiiR .

B

'^EAD CA-S,C2S\ /

D O L L - 1 , 5

VREGEN=30*LL

VDO L=1,101

V

X2R(L,1)=0.6

\/

X tf " < 4. <101 Yes >

ATifVr-r?\, WRITE REGEN,IRTYPEj

WRITE CkS, C2S, LEAK, FLOW

VjCAPAC=100

PRECAP=0'•V

A,

A

A

M2S=C2S/50000|. jY

M^S=C*fS/500001i

V _______ ^REGT=6*HSGEN/17

, y ,IN=1+REGT j

__________ i

f

FL0HR=HEGEN*O. 4/IN

\ / ■ f

CALL SUN

/ ' IF "v f(CAPAC- PSECAP)|

........ t jPRECAP=CAPAC | I— r — J y

STOP

Subroutine RUN

START

DO L=1,101 - y ______BO K=1,2 |-

X2H(L,K)=AX2R(L,K)

M/ 5 Yes.... K < 2 / -------

<-

No\/

/"IF/ L<101 "-.Yes /

NoV

DRATER=0,5 i

DRATE=0•95

- ^ tM=M*fS+M2S

KR= ( M * FLOW ) /1 • 2

IF FLAG , TRUENo

\/

K42=2.6

Yes jKR=KR*2

<-

S/

V headings

r t \

..... ■ -"-IMH0W=1 !

NR0W=2■V

I 11=0

IJ=0•

DO 1=2,NV

I

| ; jx2S(1)=M2S/m|

X4S(1)=M^S/MV

]DO J=2,101 ~1[' i

IF \NOT x > X e s . FLAG /

No

-Ye > [xXsE=0

F=2+K4-2*X2R( J.MHOW)* *2/(M*Xj!f5( J.MROW) ) I I! I|xisE=. 5 * (F-SQRT( F* *2-k)) f V

IF X4SE<1

/ / I F \ 1w r ( j ,m h o w ) \ x < 1E-5

J.-T f

VDIFF4=X4SE-X45(J-l) I

DI FF4=D I FF4 * DRATEV

DIFMAX=FL0W*X4S(J-1 ) *m !

Yes

No

X4R ( J , NROW )=X4R(J, MROW ) -DIFF4 * KR!

No

" IF \X4R ( J , NROW)> -

d i f f4=d i f m a x

F1 =2+(M*X2S( J-1 ) * *2 )/(K42 *X4S ( J-1 ) )

X4RE=.5*(F1-SqRT(F1**2-4))

' IF -> — X4R ( J , NROW) =X4REX4R(J,NROW)

X4RE

L

IF \X -3 ( J-1) \ Yes ■>---1 X2RE=1■/

NoV

G=(X2S( J-1 )**2*M)/(K4-2*XzfS( J-1)) I

X2RE=.5 *(-G+SQRT(G**2+4*G))

-4-

X2R(J,NROW)=X2R(J,MROW) +DRATER*(X2 RE-X2R(J, MROW))

X^R ( J , NROW )=1 -»X2R( J , NROW )

v!/"/

X2R(J ,NROW)=1-X^R(J ,NROW)

V<

X4S( J )=X4s(J-1 )-1 /K3»(X4R(J ,NROW)-X4R(J ,MEOW) )

./llN ij < 5 Ye i

Ye

No

X2S(J)=1-X*fS(J)

> M

/"1T\

NBUF=N3UF+1

V— !•BUF1 ( N5UF ) =X4H (J , NROW ) j

BUF2 ( NBUF) =X4S ( J ) *11*50000

V

IJ = 0

NBUF <20

15sths^O'])* 50000

Yes

Yes

11=11+1

IX < 3 0

11=0

y.’/RITE I,BUFy

NoV

CAP AC=M^ S * FLOW * I * 5/6 1

1 CAPAC=i =CAFAC*2 j

i

\ t

\ WRITE I,BUFl7}i1

\ WRITE I,BUF2/‘V!

yvRITE CAPAC j

. ' IF IRTYPE

=1\ Yes DO L=1,101

NoDO K=1,2

DO L=2,101.X2R( L , K ) =X2R(L, K )

AX2R(L,1 )=X2R(103-L,1 )|

TV2 X Y e s

IF ^ L < 101 NoYes

NoIF -

L < 101Yes

No

- 152 -

c A <•t* S( ■*; ■x I A A .. i T p w r. ^ Go :> U :? C i: * *V ;J3 r f a C U i F

r G G A•1 T G ? r ? ' L L A 7 t I 0 i P / C HA :‘ uE c ■) 1 u yr > C c 7 F. •1 I K G ; I U * MI c • n ;•/ •X CH Ax- G £c AS J J < A ‘ I r c f P£ > T Xl T * '2■; U 7 I n n i ’ y i c g y a y T i T f cp •'* \ 7 C f T 7.i 1 1 1 1 ,V L I T P ■J WA LG ALL I 0 3 C AFf i t S S t :a 1 -1 ■?r, / L A S C Ai y 70 2 = N 5 » As r AL ■J. IA C J L I >' N- p E F 7 H • r { s T I M • •:r A P •' A Tg S I \ ,S PC R 1 1. UT s G X ■# A h 0 P. r j , £ P 0 vC 7 t 0 A

S L A L <■ 4 > iA f > X F r 1 f 2 ~ , >t. 4 3F i: A L L £ 4 «.C I A ? \ 5 I r ,\ X ?. £ ( 1 0 1 , 2 \

r l-Gvsm; - s i I S 7 L ' F Ar-> 3 c ') 1 u ‘1 M CGr-tP a c c u g j-C A U 1 F C

CGU t I N£ ' * 3 C A! / A 1 i X£ s

?■»r, K s 4 nF £

a g G £ N A r* ( 5 #

g R A T I C G )

! r n

I F i

■f M

t V

0p

? 1 r n? CO F L •>y , ,•■) FOR c c J

c hc 5 r S p e c i f i c i-C W TN M HO ' 1RF ^ A G ( 3 / 1 fC ) F I 0 ■

S s G c e

£n C p C a n < a f

I N 7I C O

L FAL E

/ i G : x ‘ • -• i ' 1/ I

V/ 3 £ A G I A LET C C K C ‘ 7 \ t i a •ISs c A >: ( b , 1 c- C ) C ^ s . c 2 3

c C A t C G L 3 T E C A F a C I 7 V F 0 R p T j- ?: F RE n T H g 0 P *N ff :? 3 T I 0 N l £cc J 7 L l .=1 >

t

F£ G g \ 3 3 r * L-• • I.c I >« [ T I A. i. I .3 E C’C L:i... M A r C ‘-i 0 [ T I 0 A3

CG 10 1 : M C 1X < R ( |, / 1 isc; ff

1 c r c n r i M * f

u R I T g ( c / 1 c X ) F g r. P N , ? f} T Y ■? c U * I r i ( 6 , 1 C 1 ) ' C 4 f C » , L 5 a K , F L ( W

c A p 4 c = 1 O'C ’

c S E s V i R s i ’ ,

'■ N i 3 z C £ 5 / 5 C C C 0 *

?/ A S s C 4 S / H C C (J j C ! = : C ( ] : i T J C T T H p

K E fi r s 6 , * R fc G E N / 1 » .

T N z 1 + R E r. T

F L - J w R = « E G E N * n , 4 ■' I A

C C a l l S l g R C l T ^ E T O C a I c U L A T E L O ^ O i ’-jG S T a G E

* 0 C . A l i R W \ < * 2 $ , S O . I f l , L E A * r I p T Y . , e , F t g W # C A ' p A C , , t ^ i E . )c T e s t i c . c . a c ^ . c i T Y M i s H o u I U h h i a t i= p

I F ( $ ^ S C c & P a C F R “ C A P ) . i- E - 1 • G ‘3 f 1 rs "tF r t f c C A ? s C A P ^ C

C G 4 | 3 I S A C !, 7 I K F T0 G A [ f !v ] A t f R F 0 G R A T { . >,j ^ 7 A G e

3 1 ' r a u t H M 4 , 5 * > M , 0 . T * 0 . E R , 1 P r Y S , p L R , C , . F A 13 c _ )G; C T 3 3 C

1 ; i Q F C R jV a T ( ? f G G • 0 )

-I w 1 F C R v f l r < 1 x # f C 4 S = * , F « . 0 , J5 V , ’ C 2 S S ’ , F S * 0 , 3 X , * L 5 t K A G r. = ’ * F 5 . 2 * 3 x '1 f F L G U 8 * T E = l » F 5 , 1 )

1u « F C R.v A T ( 1 y , ? F F G H J . U \l E C = * , F 4 , U , • T - M v p E s • , J 2 )

a / c c N r I - 1 . r-

S T 0 p

F N f)

- 153 -

u :j I T N £ T( C a L C 1: 1. J T > rK. .• 0 .1 >’* '-> '? r T I Li 11s !_ 1 C t;T T \ F S i M ; ‘ S i.v 4 s / ■! » L E A K / I rs t k K F f X 5 ; M .d i i P A . v / 7 fi r A c;iv w.S i r a 1. ? L A (■I c ^ [C A L F t A G 14- •1 = N S I r A x k ( i ^ 1 9 y 1AM c \ S I r >. X 4 S H 11 ) t \ 2 ,*> V1 (! 1 ) , r A ^ C1a U F i f -»4 •:) / £ l. F 2 ( 5 0 )

c wMvC / p i / A J Pc C 1 I - ■ / 1C 1C 0 1 K 5 1 t IX y R ( L < X ) r a X 2 M I , * )c U »N r T N I rC a 1 T E as * •At, NA T F = c Qv 5 k s + N >:sk R-3 ( w ■f F LCU ) / 1 , 2r r < f I A G ) K R. = K R •* T .K 6 A ^ 2 . 6•a P I f c ( 2 , 1 C S 5u R I t E ( 6 , 1 C A )\ 3 J r s 0u «M p C. A I s T C T A \ pj f?F p Q c n i. U MMS U ha T i n E t k t: s t c p , g g r «? M i N I MI S E DV ROUr 1

II I S A c C I N 1 t H 1 0 Ui R I r p 0 M !.. V £ V u I* vn=0

I j I 5 : C C L N 1 £ k lo u « I r c 0 u i_ Y p v fc R vT J -nC 13 I = 2? N * 4 S ( 1 ) a v '2 S / r -K 1 ( ■] ) "V;iS / ?’CC S3 J = 2 , 1 C 1 > ( j # 1 ) S 1 f " Y 4 '1 ; J I 1 }I F ( . n G T . f L ^ G ) u ,) T 0 7 0 1 F ( x 4 R ( I * t V. > , . 1 ~ “ 5 n o T 0 b dF = 2 . 4 K. <; - * > g K ( j / m p rrj} * * 2 M * Y R I j , X '< 3 S = , 5 * ( F « s 0 H T { p * * ? * 4 , ) ) I F c x 4 S E . G E , 1 , C ) y U 5 ~ s 1 , 0 G C T c 6 C

a S > 4 3 c = 0 . nU Cl FP4=X4SE'-*

0 I F ? 4 = C I F M *C t F v X = F (_ C U *1 f c i I pf./, . c-e tX M R ( J » N 5C'U ).;T F C < 4, R ( j , N h - QT F ' !< 4 R C j * N R' C F 1 “ ? . + ( v * > 4 S ^1F=,3WF1- I F U / , R < J

C o ■' .--j c o t L? v **; U [ T H r H r » ~ A 5 I 0 T ( M fR £ . F L ) l.J ' C A R A 0 , p L a G )

1 j 1 » d 1 * \ »? R C t y I > ? v /

r> A T ;\ SO IH.vT Cni-V- T U 0 a ° C AFED' -D

r H I R T I u T H I T g p , T I 0 N

P I F TH ;? TA 3 p

•'in j))

o . n

4 S ( . f - l )D F A r hX S r j - 1 ) *M n I ? ■*« 4 X ) 0 I F £ /i = P I F M A .>'■!< K ( J / M ;? 0 ^ n I F F 4 * < .?**■ * L F * 0 . o ) y £ R ( J » N R "»w ) sW ) . f-; p . 1 . 0 ) R t .j , N R -w > s 1 . 0( J "*'! ) + * 3 ) / C<j^2*.'<4SC |-1 ) )SG R r < F-1 ,r*2-a ) )t ) . <; t . x . - r e ) x /4 r c j .? o > - : <4R e

- 1 5 -

(c

t i

( 1 X 4 S ( .1 ) “ X 4 S ( J «• 1 - 1 , f v. o ’t ( ' m ( j , *-i A ;■* y j - .< 4 p ( j , j y h y > ’t

30 4

3 ■)

06 1 J 2 1 u 31 0 ** 1 G 3

Xd" < J / N:-C!0 = 1 , - X 40 : J , j •: n )H T . / IJ F ( ,< 4 *5 ( - V) s I. F 1 . g - O G : T'j r 20 s C y s 3 C j - 'l ) * ■* < ■a: O / ( 4 0 ^ -s 4 0 V , J •» j ^ )^ ^ = 0 ^ ■»T C G ' * ? + .■ * 5 'i ^G CT ■' 4 3x < '■’• c = 1 ,r c ' t i •' i fx h i ( j / ;> n c u ) s x i ■i c j , r 4 1 ('A?xA 0 ( J » \wC^ ) s 1 1 * >- X y R =; J * - J ! n \ )^ S ( J ) = U S ( J - 1 ) -1 , / y ( u C J f r-i X : ’ y JT F ( v 4 3 ( ,J ) t 1 i- i . :T ) A 4 S ( J *, = o 0X * 3 ( J ) s 1 . 1‘ - * i 5 ( 1) ■I J = r .! + 11 ? < I j • I T , 5 ) <K *#:) 3 3I J - n *i ' B i f i I S 4 wfc r 0 0 0 TO W■/ I T £ RE.'i i L TX 5 U s = N 3 I f 4 13 L F j { N & i c ; = > 4 S < ! ,t S: A 0 X )£ L F -j ( G 3 L £ ) = X 4 3 V i ) H 0 0 o G .I F ( 5 i j P |_ t « c 0 j G 0 T J 55 3l F ( X - 4 3 ( i o 1 ) * 5 l .T0 0 . * ' -. G K I, c 4 ’/ 'j 5 OT0S i! U f : 0N X Ox = i * 1 S-C Uw S 0 , - i t .v s; C '■*i i a r i +1T F C U . l T . i r ; )fiC TO S 31 1=0US I r 5 € <5,1- C 6 > I , I i ! F 1u « I t c ( 2 ( 1 c 3 ) I , 0 IF?c c m r i m i pC 5 3 1 C = t* .i, s * r I C ’* r + 5 , / * .C A o U = C C * ? ,U * t T ? ( 6 , 1 C £ ) I ' A C 1

3 ! C -»XTU X I r ? ( £ , 1 C H } CA-5 4 CI F ( I R T V i- E E. C 1 ) G0 T y 55N1 h N T I C P E-'V E P 3 F C 0 L :J V N 5 T A G f» (.0 JC-C C 3 L = '? »1 C ii X '0 A < I / i )• = x 2 S < I r3 - L /1 )r C ;s T T N L FC'CTo 56C c 2 L a 1 ,1 c 1CC 2 Ka i , 2*S X 2 'J ( L f % ) ” X H ( LC C N f I N I ca E 1 v. R Np C R v A T (1 v / 5 r a r- AA G 1 T y = * , P5 . 1 / * K 0 / i .F 4 S v /5 T (1 x > ! 4 , 1 '<• 0 0 S3 - 1 )FC ^ v a T C ^ / ' S F S I •i CO j cFOTXAT I ON is • )pCR- vATci x# f S C Lu r T 0 \l r 0 ^ r p h J a f\ T i •VISF C S y T ( 1 X / U , 1 1>\ , ? 0 F 5 . 3 )F N D

T I 0 N S pOy rC

- 155 -

o zo /—a X) © Xj o 70 © © 2C © 70 3 © O_» _> —» —a m Ja* -r» 2* ~n > TV D> -n x> r r 2» —> —a —k -n 3 'tDD~3 s , J~ 'V ■O © ON 'S> 'aO © © -Vi O ' Oai •S'. X3 _k ■Xt "Q ~o O' S'. *o — -o 3 V j S' rvi nD © On rs> oo 3 3> o _k _k _> ---k —a II T 1> _k _k —k — D> no — 2* —k _k —i. — > no — 2* O —a —> _k —k —1■—a II 3

3 2 © © © 2 © 2 © z p - ~ r_> _» _. _a —k a — _k —a ■© —> -a © —a _> —a —1—a ■ ,T

—i . . . a a a —J —1. • .© —1a © —1> • * © -1 » •3 • • ■ • 3 Z-< 3 © o © © © © -c. © © © ' -< © © -< © © o ©> -c 3 o -<r © o o 3 © © © .**" 3i i 3 © o © © >•» rn II o © © II 2 II © © o II —* z II o © © © © © 2 on 3

3 o © p ; © © © © © © © o © © o © X - © © © © 3 © © 3 © < 3o r _> _k —* —k *n © T ! r v _k —k —k © © .01■VJ —k —k r r © ■*n on —k —k —k —k —k -n «33. <TnD r— aaM • a a Z ■© a ox • a • z o a sz © • 1 • a a * z a r~ Xn

< © o © 3 © © II a © © © —j • © —a a © © o —1a o - * a 3 © © © © © — i II ©S j 3 © 3 3 © © •C ~vj © © © X - © DC X -V! o © o © © Cs- 3T -v j © 3 © © © © 70

o o © © © © x» © © © © > LN D> o © o 2* 'X> © © © © © 3 2> On

■X. _k —> _k _> —» _k .© © © _k — © © — i © —> _k —a © 3 3 © —k _> - * —k —1—k •H 3 ©. • . a a a -a r v • S . a a a a—. ■ a— a a — ■a a~> V a a ■ a a a * a— no a

i i © 3 ■ : 3 © © f_T; — ? © © © © rs nsj -© _2© © o DD >x> D © © 3 © © © DD O'. ■—aOn o o © o © © z II x> la/aj o © z laAa _ k z Ox © © o 7T. 0M —k z ON © © © © © 3 2 II 70

© © © © © © —» © © © y : Do V5 ©> © o S) DO S) © © © © © © ' -T_» _» _a - * © < _> —A _k © ’ \ ~ _»

p -<

5 © © © _£v m © On © © ‘wX © © © © © XV 3,© © © 3 © © 11 © © © © © © Ca- ■o © o © 3 © © II z■3o © © o © .a—- © © _k © © w © © © © © © © 0_> —k _> — — -** © -a-a _ i © _k ’ —» © —> _t> — <3 © ©a 1 > a a > a a a a • a a * a » a • a a a a ■ rs© © © © © X* © © © O l © © o S' © © © 3 3 3

o o © 3 © © © © © © -a—S © o > © © © © © © 3© ■ © © © © © © On © © o no 3 © © © © xO."_k _k _k _k © a— _> _k - k —> - k —* © _> _> —k _ k © XS

. a a a a ,T* a a a a » a • • • a • a a rn 3o o © © © X*- > © ■© ©a -Vl o © o -V j © © O © © xs D >3 3> © © © © © © © © © w - © © © W © © © x:

o © © © © w >> © © © ■o © © © 0c © © © © © © >_» _k _k _k © © © _k _k ---k © —k _k © —k ~k —k © © ©. 1 a a a a m a a a a a a « a a a ■ • a • a ,3o © © 3 XS XS II © O © DC o © o c c © © © © Xs II*© © © © ■© © © © © —k © © o —k © © 3 © © ©o © © © ’ > © © © o CO © o o -Vl © 3 © © cs 3- On_k _k _k _ k © © ’ a _ k _k _k © —k _k © _ k _ k —k —k © © a a •a a a a a © a a a • • a • • a a a * a a ©© o © X * xs © © © © 0C © © © -DO © © © © ■X" XS O 3© © © © © © © © © •o © © w ■o © © © © 3 © 3o o © © © © © © © no © © o —k © © © © © © ©-1 _ k -_k © © _k _k —k © _» —k © _ k —k —k —k © .3 ©, a a a a a T ! a a a a ■ ' a • a a a a a a a 3o o © o X** xs r - © © © •o © © o © © © 3 3 XS C-a '3 ©© © © © © © O © © © «aN © o o ox © © © © © O O Zo o © © © © © © © XD © © o •© © © © © © © 3—a —k —k © © © _k _ k _k © _k —k © —k _k © 3 © 70- ©a a a 1 a a ■> a a a a a a - a a a a a a a S> ono o © 00 X - xs —I © © © -© © © o © © © 3 c o XS XS -4 Vo 3- © x» © © *n © © © ■> ©» © o > © i © • ©■ © 3 rn ©o o © "Vl © © ll © © © © i © © o -Va © © © -o © © 11 ON_k _k -k © © © —k —Jl © —k —k © —> —k —k © © © s .• a a a a a i\ j a a a • a a • • a a a a a a PO “VIo o © XS XS xs © © ' © © © © w © © © o > X> © Dco o © © © © a © © © 00 o © © 00 © © © © © © ao o © © © © © © © © ox © © © ox © © © © © © © 2>—k _ k - » © © © _k —* —k © —k _ k O —k —k © © © —*a a a a a a a a a a a a ■ a a a a a a ao o © X^ XS xs © © © © © © o © © o © X - X " +s noo © © © © © © © © •© © © w © © © © © © © ©o © © © © © © © © —k © © o —k © © © © © ©_» _k _k 3 © © —k _k © —k —k © _> —k —k © © © noa > a a a . a a a a a a « a a ' a a a a a xs3 © © XS x s © © © © © © © © ■© 3 XS XS xso © © © © © © © © -c © © o © © © © 3> © ■©3 © © © © © © © © ■> © © o o © © © © 3 ©_k © ©

T© - * _k _k o —k

- * © _k “ * © © © po © X - X-- X - © © © © © © © © 3 © X^ X - X^ xso © 3 © o © © © © © © © 3 © © 3 3 © ©© © © © © © © © © DO © © o cc © © © © © ©—k —* © © © © _k —k © _k —k -J* © - k —k © © © ©a a a a a a a a a a a a • • a a a a a ao © xs XS XS x> © © © © © © o © © © X - XS X->o © o © © {© © © © © © i© o © © © © © © '—N

o © © © ' © © © © © © © © o © © © © © © ©—k —* © © © © —k —k _k _ k —k _k —k —k © © © ©a a a a a a a a a a a a • a a a a a a a© © x s xs X" XS o © © © © o o © © X - XS XS XSo © © © © © © © © © © © o © © © © © © 3o © © © © © © © © © © © o © © © © © © ©_a

T' - • © © _k _k © k —k *3 —k _k © © p3 XS xn XS xs XS o © © © - > © 3 Xs X - xs XN XN

o © © © © a*K © © DC © © © © © <3© © © ©© no o © © © © © - k © © © 00 © © no 3 3 © ©- * © © © © © © _k _k _ k © © p ©

o XS XN XS X * X> © r a —k © © o -A © © X n XS XS x^ £*»© © © © © © O © © © © © 3 © © © © © © ©© © © © © © © © o © © © -V l o © © © © © ©

- * © — © © © © _ k - * © - * 3 © © p

© x> XS XS xs © © - o © © 3 XS X - x^o © © © © © © © rv; © © © © © © © © ©o © © © © © © © no © o o OaI © © © © © ©o © © © © © O © © —k © © © _k © © © *2* ©

xs £s X " XS xs XS © o © © o a*1 3 XS xs xs xs xs—* © © 3 © a*. _ k © © © 'O © © o _ k © © © 3 3

— - —4 © © o © © © o © © © xs © © © © ©

-0 © 3 © X ' © 3 © TJ 3 x: X, t ;■ !V no _> —* —k rr- > D> —* _> —k •N-i s r r S» —k -r. x> rr- > —A rr - p

—k _k DC on no C 3 —0 on © ON ON ’Si 3 V i S' no © 3 on DO 3 3 xs .V •C On y : 3 ,V "O r \ j O ■ 0 s- 'Si 00 «N;■ X> _k —> © _ k _> _k _a —a 2» ON _k —a > © —k —k _> —a _k —a II © X» —k —k _k _a —k -a © oN > —> A A -J* —• 0> *%S* —

2 O z a© 2 Z © 2 3 2 n roi —a _ k —a _> —> _ © 3 —a _ * _k _» _> _> —a —> —a — — --i —a © a.> —» A —A V—. O

. . a a . . a a 3 —1 a • 0 —a • • • a • • O — • • • ■ 3 —1a ro • « • • • 0 i *3 © © © O © © © 3 -<r © 3 0 < © © 3 © 3 '— O © -< 3 © 3 © © 3 < © O < O O o - .3* -<r O ' —s

© © © o © 3 "3© Z II © © :z II © © © O 3 © Z on © II O O © © 3 2 II 3 11 O 0 O O 0 2: u O '© o © © 3 3> © 2 ' 3 © 3 © 3 © O 3 © ’ © © 3 < O '3 3 3 © 3 3 O c O 00 0 0 0

j _> —k _> _> _k —> _k —k m © O r r on _k _k _k —k _k —k r r 3 © Xs —> —k —k —a —k 3 3 m —> -A -A -A ' ."T. 0 ;*r» a . . a a a a a 2 0 > a 3 nD a a a • a a z a :— ©1 • a a a a Z 3 a *1 "**“v • « • • • 0 • Z

© 3* 3 © O © 3 3 —1 ■ © 3 -a • © © 3 © © -n II © 3 3 3 © —1 ' 3 —a O O O O O -H * 0 O4 N o 3 © 3 O © © © © 3 ©1 © © 3 © © © •O 3 3 © 3 3 ’© X 3 3 ~x > 0 O O O c * O X ' nO 0 TC-

o © © o © 3 © 3 > ■*; © 3 > 7K 3 © O © © DD 2> c 2: © © © © 3 7* _k 7 O O O 0 O 0> a«A 0>_k —k —k —k _k _k _k —k —. 3 © © —i 3 —> _ k —> —> —> —a © 0 3 _> —> —> _k _k —a © 3 —4 ■T- -A «-•> -A —1 0 O —1

>— — a • »—a V no a © • . a • a N». • r - ' « • • * —e \ •© © © 3 3 © © 3 2 © 3 N—• ”TT 3 © © 3 , © 3 O s. — ‘2 3 3 © 3 © 2 2 N*a» d - O Zj O O ' or* 0 0 1 O 00

f o © © 3 © © © © ,2 ON © 2 On © © O *—-* © © 2 11 vN © r j © © 2 On O 1^. O O 0 0 7* Ov O 20© © © © 3 3 © © ■jo © 3 y> 3 3 © © © 3 DO —a © © 3 © yn wT v~ O O O 0 V ) wH—> _k _k - * _k —k _a _k © © -*■ - * _k —k —1 P < - * _k _a O _> -*■ A - *

O © © 3 3 '3 © .a*- © 3 © 3 . •3 JS .© O © © ■3 O O O O O 0 - O3 o © © © © 3 © 3 3 3 © 3 © © © II 3 © 3 3 © —* O p : D 0 0 -A

o © © © © © © 3 3 —k © 3 O © 3 3 © © 3 © 3 -c c> O - O 0 0 O_> -_k _> — 3- 3 _X _> _> c O - _k _> Ok — — A -A A «A O

O © © © © '© ' © 3 © © © © © JS O 3 3 © O O O O© © O © © ©1 © 3 © 3 © © © © © © © © © © O O O O O • T© 3 3 © 3 © © © no no © 3 3 © © 3 3 © 3 © 3 INJ c 0^ O O O A_> _k - * - * - * _> _k 3 —k _k _k

p r~ - * _> _k _k — A ■O

© o © © © © © © © © © © © 3 © Xs 3> ' © © © © © 1 a 0 0 O O O 1a

3 © © © © O 3 3 3 ©■■ © © © —\ © 3 2T ■© 3 3 3 3 0 0 O Oo © © 3 © O © 3 © Dc O 3 © 3 © © > © 3 © O 3 c 0 0 O O O CC-—» _k —k —k _ k _k —a 3 © O —k —> —k —k © 3 © —k ^k —k —k _k •w -A A -A 0

• • • a ' a a a a a * a a * a a ‘ m a a a a a • • * • • * •© 3 © CD 3 © 3 ON © © © © © © xs it © © © 3 3 O O O O C : A© © © 3 © O O ■© —k _k © O © © © © 3 © 3 O 3 O O O O O nC© © © © • © 3 © _n ND © © O © O © ON © © © © © X ) w O ' ro O O- * _ k —k —k —k - * © © © _k _k _ k © p * - * - k —* —k 0 «A A •A A CO

© © © © © © 3 On © © O © © '©> XS 3 © O 0 3 0 pvj O O -w O O ro© © © © © O © oN JS © © © © © 3 © © © © 3 O O O O O 0© 3 © © © © © © ON no © © © © © © © © © © 3 "Nj O O O O O on_k —k _k _k _k _k —k © 3 3 _k _k _k —a © © _k _k —k -k *-> —> -A —A -A w

• • ■ a a a a a a a a a a a a a ■ *n a a a a a • ■ • « • • *© © © © © ©■ © no © © © 3 © © JS Xn © © © © © O O O O Xv© © © © © © © © *s l © © © © © O O © © © © O O O O O O —A

© © © © © 3 © on Ji 00 © © © © © © £ •3 3 © 3* 3 '■J* •tO- 0> O CO 00" A_k —> _k —k -J . —• © 3 © 3 —k _ k —A © © 3 00 _k _> _» _k _k —* A _ > O. • • a a a a a a a a a a » a a X * a a a a a « a * • ■ * *© © © © © 3 —k —k _k _ k © © © Do xs XN -4 O © © © © O 0 O O 0 O l© © © © © O XN XS 3 ON © © 3 xs © 3 m O © © © 3 Vsf t> 0 C* O 0 ro© © © © 3 © on XS CO © © © © s i © 3 II © © © © © O O O O 0 Co—k _ k —k —k - k © © © © —k —k __k © © . —k _ k _k _ k O —A -A -A —A O ■

a « • • • • • a a a a • a a a a ro • ' a a a a * * a • • •

© © © © © © 3 —k —k © © © Xs © 3 3 © . © © O O O O O 0 O© © © © © © DC DC 3 3 © © © © © 3 a © © © © 3 O O O * O 0 On

© © © 3 © © DO CO O 0 0 © © © © © © © O © © © © O O O O O 0 •v j—k —k —k —k © © © © © _ k —» —k © © 0 —k —* —» _k © O A A -A 0 O

• • a a a a a a a a 1 a a a a a a a a a a • * • • » * •© © © © © © © 3 r v r o © © © XN XS xs © 3 © © ON % O O O O •M© © 3 © © 'on X n XS XN 00 © © © © © © © 3 © © 3 O O O O •0© © 3 © 3 _ k DO Do ON © © © © © © © © 3 © 3 © O O O O -A ro_k —k

- * - * p © - p 3 _k —k ~k p_k _> _k __k •A p —

© 3 © 3 3 * 3 © ON ON © 3 . 3 . Xs xs XS 3 3 3 .3 fV Do O 05 O ro Oc© 3 © 3 © ro rv rv no - 0 © © © 3 © © © © © on aJl O O O O •*r O© © 3 © © x> ON O 3 © 3 3 © •© © © 3 3 3 ■V O O O O O_k _k

- * © © © © ■aa A _k © © © © _k —k p -Ja p A _Ar

O

© © © © © © © © X n x s © © XS Xs XS XS © O © © 1 * CC O O O O 1 a Co3 © © 3 rv —» —k © ro © © 3 © • © © © 3 © © © on O O O O DT >© © © © 3 3 3 vO —k o r © © © © © 3 © O © © © O O O O on <5—k _ k —k —k © © © 3 © © _k © © © © _k —k —k © © 0 -■aaA —* -ifc O 0 0• • • a ■ a a a a a a a a • • a a a a a a ' a « « • • • *© 3 © © © © © © on on © © XS XN xs XS © © © © © •O O O O O 0 c -© © © © 3 © © © —k on © © © © © O 3 O © co oc O O O DC DC© 3 © © ON ON ON ON ON DO © © © © © 3 3 © © _k © O O O -A 0 ro- k —k —k © © © © © © © _k —k © © © s _k —k —k © © O —> -A -A O 0 0• i • a a a a a a a a a a a a a a a a a a • • • • « • «© © © © © © 3 3 -> © © Xn XN XS xs 3 © © © © O O O O 0© © © —k 3 © © © 3 X n © © © © © © © © © ON ON O O O uv XV© 3 3 © _> —k —k —k tv © © © © 3 © 3 © 3 ON ON O O O_k —k ■3 © . 3 © © 3 3 .

p O 3 -=* © ' 3 p J' — — O

3 © *3 © © 3 3 *© © -v j *3. XS XS XN JS XN 3 3 3 © !;• O O O 0 O© © © 3 © © © 3 DO n j © © O © © © © 3 _a _k _k > 0 O A >© © © © © © © 3 ON no O no © © 3 3 © 3 —k © O vH O O 0 on_ k _k © 3 © © © 3 © © p © © © © © “ * © © © O -A O O 0 0

© © © © © © © © ©1 © i © XS X n Xs XS XS 3 © © © © 'O O O S A O 0 nC© 3 «bA © © © © 3 on CO © © © © © 3 © O © © 3 O O 0> O 0 -V i© 3 -c © © © © © on co © © © © © © © © IV IV V O O O ro ro fO Co_k _k © © © © 3 © © - * © © © CO .3 © 3 p © O - * O sO 'aO 0 OD

o © o 3 3 3 DO Or 3 X n JS Xn 3 3 C C: O O 0 ■c© 3 © © © © © © _k X>» © © © © © © 3 3 © © © OC O O 0 O 0 Oc© © 3 .3 3 © © © XS ON 3 3 © © © © O —k © © O •v i O —A 0 O 0 •v i© © © © © © 3 © © 3 © © © © © © O © © © © O O O 0 O 0 O

On © © O © © © © 0 0 00 XS xs XS Xs XS XN IV © © © © >C 1 a O 0 O 0 O© —k © 3 3 © © © ce -k 3 3 © 3 © ON 3 © 3 3 O 0 O 0 ODO •o © © © © © 3 oN © Xs © © © © © r v © © © © O 0 O 0 <\>

V5 ■c •V._V — a © Cc —> _3 —£S ■VI c © •Do ro — -V V tv c_> _k _k _k -* “ ON ON 5 © _s -*2 :s/1 2 z 1 V* _■ ■V _ V V s/1 V

©Ss© o © © © © _} tv ■2 “ © © ©• • a • • iV ■ • • • •© o o © © s“> PS­ sAJ © © © © ©2 Is/1 's/I 2 V © 'S- o V V V V© o o ©■ © z ON V © © © ©

o o © © © — Do © © © © ©• a • • -r • • ■© • • • ••© © .© © © —i © © © ©2 2 2 VI V — 1 + —i Vi /. V V© 3 o © ■© x — xn -C © © o ©© s-> ■© © © -> rv £— z> © © © ©• ■ > * • —1 Xs • — i * • ■• ■© © © © © — < o © — * © © ■••s ©2 2 2 V V 3 V * o V V V V3 © © © © ZD V —* o © © ©© © © © © z V) © © ©a . . - • sC s/1 • • * >© o o 3 > © 3b VI © © © ©.3 's/1 ■s/i b2 V —b • ■s/i V V V© o o © © -Ni © © © ■©© o © © © © © © © ©. • • • • tv V « • • ■© o © © © XN rv © ©- -© ©z 2 s/1 V V -c •0 V s/1 V V© 3 © © © a DO © © •©© © © © © * © ■© © ©• • • • • *■ rv * * • ’o o o © © * © -© © ©2 1s/1 s/1 V? ro —k V V V V© o © © © -Vi _k © © © y s© © © y—N © o o © © ©a . » • • ‘V © • » • •© © o © © *vj v> © S3 © ©2 s/1 2 VI VI • • VI ./I V V©» © © © © © > © © © ©© o © © © * © © © ©• • * * * v • • • •© o © © © _* o © © ©2 ■s/I ■s/1 2 Vi V V. V VO o © © © © o © © ©© S3 © © S© © © © © ©© 3 © © *© ©■ O © S3 o

2 's/I ■v VI * V V Vo o © © © -vl © © © Vo o © © © -> © © © o

o o © © © © © © © Js2 2 2 VI rv V VI V© o © © © « © © ©o © © © © © © © © V• * • • a * • • • •© © © © © JN © © © —»2 2 V/1 VI 00 V VI Vo © © © JN © © ©© © © © ON © © © rv• •« • • • l s • • • •© © © © _k • © © ©2 ’s/I is/ —» V V V.o' © © © * © ry. ■©o o © © © © © ! © ■V» • • * • vl ♦ * • •o o © © © rv © © ©2 •s/I s/1 VI ■V on V© © © © ■DC <“V ©o © © © © • © © rv rv• • • a • • • • •o © c> © Xn * -© © _>2 s/1 z -vJ V Vo © © •v © ©o © © © © •© ©• • • • • -V • • * •o © © rv iV 00 © © —» —>2 's/I 2 « V V© © © VI © ©o © © © © * © © .V• • • a • © • • • •© © © _k —* © © © ->z 2 -pv V© © -pv ©

© © © -jrip

rv ■V .Vo L* © © O rv _>1»2 2 5f Vo © —* ©o © © o © © © rv v rv• • • • ■ © • > • •o © © © © © © —* —» —»2 -v Vo ©• ©o © —. © © • © ■V ■V• • • • * rv • • •S3 —* © © © 3b © _> —»

©vO © © © © © Vi .V ro V• • > • • rv • • • •ON © © ■© © V —» -*V

Ov*_1-A•sn

—- C * 3 3> a 3 _> —k —k 3© . On — © i © a— ■ / - i — -Nj © On — V - i ~Va V t v ■C © 'ON ©—> —* © —» —» —» 3 3*- V © _v _k —k © 3b V 3 o _k —k _> —k —k 3 3

— —A —1 ~a»-< _k — : —: 7DV V — V V — v V .2 — 's i ■3b —a V V z z z z — T

© © 7T © © © *3. © © © © © © -k 3 © © © © © © 3 —1• « • • * -> ON a a • Xn © a • a • a a© © © © © © '/» “1 © '© © © On Xs © © —s © © © © ■©. ©V V © V V v-n » • 3 V V V © • • ■3 V sZ v . V . 2 V © 3© © © . © •© O .2: Sa 2 . © © © o 3s © © ■© © © © © X -© © © © © o >- 3 © © © © o *■ © © © © © © © © ©• < rr • a * m —* V rr. • < • r ) —• V © a • a ' - a ■•Ti© © © © © © z fNj Cc 3 © © © © V Dr- © © © © © © ©v . V —< V V . vyr —- V V ‘Z z —i DC 'C —a V . z '2 z Z z —i

© © © © © • V I X © © © X —* o ~ © © © © © © X© S3 > © © O > a > ©■ ~s © > ■-N a > © © © © c - ©■ D>• . —, • » ■-* —i . a • —i © ■Co —1 a • » a a • —•© © —s © © © >— • 3b —a © i © © — • —> © © © © © © —aV -s. V V c? PsJ 3 sZ V O V V .-~b V V z z z 13© © © © © *• V z. © © © .2 3b V 2 © © © © © ©: N© V © © © —> c Si © © © —k -O Z © © © © © r v z« • • • ro o a V _k • * • a • ©■© —i © © © Js © © o Co © © © © © © —k ©V V V . —* . 'V •v _> * 'Z z z z .3

© © © © - \ i •C © © © -v i -Vi © © © © 0 3© ro © © © —» •+ © © © _k *- © © © © © V — 1» • • a • • />■ « ■ a ■ • Xs > a a a • • O© © © ■© On © © © - IV On © © © © © -k 3V V V s/: >(■ 00 'V on V * 0 0 on V 2 z 2 Xs© © © © —i -s i © © © _k —k © © © © © ©

© ■V © © © JV 'O © © © r v V © © © ■s—a ■—s V• > « a • DO a a « ■ ' Do a ♦ a • a a a© © © © —k © © © - v © © © •© © —k

V V . j i © If V - 'S. on ■o V z Z z© © © ■© © © © © ■© o © © © ©

r v ro © © © a Qs © © ■© a > © o © © r v r v* • • a * —k a a a © © a a a a • aV - * © © © * —k © © © * © © © © © z -A

V I V . U i —k NO V . _ k © V l V z z aa© © © V a © © © V a © © © -3

r v t v © © © oc © © © © cc V © © © © r v V 1---• • • a ■ —k li­ a a « _k 3b a a . a a a a ©—» —» © © © o ce © © © •sC DC © © © © _k —k O

s/> 'V ■s/I >D0V V s on DC V V - 2 2 z r v© © 3 • Co © © © a © • © © © 0

V r v © © © V l © © © © XN DO © © ■© © r v r v 3• < • a s © • a • X- —k • a a a a 2—» —a © © © • _ k a O © © —k a © © © © —k —k

V 'V U1 r v on V V V . r v a 'Z on OZ ©© © o 00 3b © © © ■DC © © © V Z

t v (V © © © r v _ k © © © no —k © © © SO r v IV ■ s• • • • • © © a a a ■© © • a - a a a a ■©—» © S © IV —k © © © r o © © © © X n _k —1 ON

on v/1 a o V - V 'a sO on 2 z • Ns© © © r v sC © © o IV Cc © © o -s i

V r v © © -> o © © V © © © V t v r v ■CO• « • • • a a • a a a a a a • a

© © © © © © © V I © © © —k —» —k 3>v/1 V v/1 3f V V . V * on v 2 -H© © 3 _k © © © —k © © ©

r v V © © © —k © o © _k © © © . r v .V V r v* • • » • a a a —k a a a a a a ©—X —» © © © CC © © © -s i © © © —k —k —k •

V V * /! ON V V V V V V Z t v© © o ON © © © © © © © XN

V V © © .© a © © © a © ©■ 3> V •V iV• « « * V a • DO a • • a—» _1 © © * © © © *• © © © —k —k -A

V Z ! V w _k V z© © © —k © © © —k S ©

t v r v © © '© CO © © o 0 0 © © • (V V r v r v• • • • » - v a a a - 0 a a a a a a

sJk © © sC © © © ^s © © _k —k —k —kV l Z1 co V V V I _k V . z© © © a © © © a © ©

V r v © © © v k © © © V © © t v V r v t v• i • • • Sf a a a * a a a a a a—» © © © _k © © © _ k © © —» —k —» —k

V I Z I V V I V V V V . z© © © ON © © © V © ©

iV V © © © © © © © sC © © t v .V r v r v> > • • 1 V • a a ■o a a a a a a

—» © © © c © © © XN © © —k _k —k —*•s/1 a V V a V

© © X ) © © © V © ©V V © © *- © © © *• © .V V V V V. < a • • —k a a a _k a a a a a a_k —k © © o IV © © XN V © r v —k _k _k -A

s/1 V V V on on© o XN © © Ss. ©

V V © © o © © © © X n o r v ? v V r v r v• • • « « XN a a a ON a a a a a a—» —k © © Osl a © © ON > © _k _k _k —k

on V V V _k V© © * © © ■J>- ©

V ©■ © 3 —i © © © _k © .V rv- V V V■ t a • » r v a a a V a a a a a a— s —> © © © © © © © o © —» _k —k _k —k

Cc -vJ© 0 c

r v t v o © XN © •O ON V r v r v t v t v

1 * r v © 3 V NO © © -s i _ k I k __k _ k _k*. 3b

_ k _ kr v r v-Nj >J2 2o o-vi -»

21 A

S 00

. 05

00 - O

rM)t>. OS

00 .()*'0

0. 0^

00. 05

00. 05

00. 0*^00

. 0

30

0. 0

50

0. 0

50

0. 0^00

. 050

0. 05

00. 05

00

. 03

00 . 0

50

0. 05()0

. 0

?^'

J-JKJ -

vj + 73rv _i —a © O C •© -*—» © VJ rv c 3 A r~ V Vm DC a .— sj—» —* -k _k —k —» _X ~ © VJ VJ — O

c rv —vj V V V V V 'V — VJ V — V© © ©* © © © a© z ©i © PO © 'Z ©• « . • . • • *• . > « •— © © © © © © © © —* <©. © ©V V 'VJ V, V V VJ © © © © V!o © © © © © © z rv V. ©o © © © © © © n -* © © © © ©• • » • • • • ~n VJ • Si » © •o O © © © © o Z —k V j ■CO © © ©x V ■ V V VJ V —! • • —• ’V© © © © © © © CC © © CC ©© © © © © ©• © © *- *• Sj ©« . • . • < . —< _X —k ♦ “1 •© © "G © © © k—k © V _k Si — < ©V3 V VJ V VJ x. v> o Co -J» o 'V© © © © © © © rz X Vi 3 V © ©■© © © © © © © V! — VJ si © v: ©• • * • • • * cc -a _k * *o © © © © © © * ■ .Jv • ■Si oVl V V V V VJ V? v — a 'S' r* '■ V© © © © © © © VJ rv ©© © © © © © © DC o ©© © © © © © .£». Ik ©X v VI V V •v V V Si !v© © © © © © © -S- > ©o © © © © © o -O v ©o © © © © © © rv © ©'■V VI 'V 'V VI V *■ if VJ© © © © © © — X rv ©© © © © © rv © ©» ■ • • • ■• ■ • © _k .o © © © © © -k -V ©Vi wi VI V « . VJO © © © © © O _k ©© © © © o —k * * ©• « • • • • ■ VI -> •o © © © © © ■C ©'VJ 'VI V V V. V ■v V-o © © © © © sj VJ ©o © © © © © © • • ©• • i * • « • 'VJ rv •© © © © o © Vi + * ©Vi 'V V V V o DC ■Vl© © © © © 00 VJ ©© © © © © © © VJ p* ©• • • • • • • © O •o © © © © JS • • ©w 'VI V V SJ © Vl© © © © © * )J- ©© © © © © © © —k —k o. • • • . • • rv •© © © © © SJ rv © ©v< w VI VI rv _k v:o © © © 03 •DO ©© © © © © © O' * • ©. • . • ■ . • • V ■JS •© © © © Si _k -k * *. ©v- V V V —k rv V© © © —a 'C rv ©© © © © © © © _k si ©* • • * • « VC rv .© © © © © © © 4S © .

v» VVI • . VI© © © © V! ©© o © © © © * * o• • • • • • • si VJ •© © © —k © © o cc V ovt VJ VJ rv © ‘V© © o VJ VJ ©© © © © © © © ■Si Cc ©• • . . . • . • . .© © © © © © © VJ -Si ©VI V * * ■v© c V j is ©© o —* © © o © 00 VJ ©• • • • • ■ • s! © «© o SJ © © © © ■o V ©VJ \S<- CO > V©. o • . ©© o © © © © © ■c si ©■• • • • « • • * *. .© o © © © © © V VJ ©VI © VJ VIo VJ 00 ©o —* © © © © © rv © ©* ■ . • • • . Ov •© /V) © © © © © • » ©VI © ©o * + ©© o © © © © © •> > ©• • . • • • • rv si •© 0 0 © © o © _k co ©

oo SiJS CO—k © © © © © © • • VJ

• • • . ■ • • rv JS *Si © © © © © © * ■J- —»

■siVJ ©s i VVJ oSr ; jj

V V a V 3o _> - * 3 3

V •Sj ■C V .— J*- rv c © vS — V S r -_i - * _k _k © _> _k - * — - s VJ 3

S'. V VJ V 'V - ■_ _ r V* V _ V _© © © © © © © © © © © 3 c© ■© © © © z. © © o © z _k V z* • • a • . • a a a iSJ a© © © © © s © O © © © V © ©v s V V •V © V V V V V 3 '■C 3© © © © © © © © © © Z Cc V z© © © © © © © © © © © o S i > ©■ • • ' • . rr . a . . a rn a m© o © G © o © ■ k ©< © 3 S i o zV s. V V i V —< ■X V V V X —a *- CS —

© © © © © CC © © © © © CC — cc© © © © © > © © o V - © r> V -IS >• . » • a 1• a a a j>k 1 —H© © © © © —a - k © © © © i—« © V —•s V V V © V 'V V V V 3 © i x- 3© © © © © ©„ © o © © 2 3 —* 3© © c © rv 73 © © © :© © V a• . • • a • a • • 2o >© © © © —» © © © © G * VJV V v .; V V VJ V : V . V —k *© © © © © © © © • © S ' . SJ© © © © r v © © © © © .> =»■• . « • • • a • • V V© © © © _ k © © © ■© © s aTJ•V! V V V V V V V V _k VJ© © © © © o © © © >© © © © r v © o © G © V a« * a • a ' a a > • a ■a- ©*—k © © © —» © © © © © —» *VJ V . V V V V V V S i —k

© © © © © © © © s j —k© © G V S i © © © © © © SJ• • a a a a a a a a s j S i© © © V —k © © © © © . COV V . V V V V V V a a© © © © © © © © s© © ©< r v (V © © o © © *■ • a • • . a a a a V© © o _k —k o ■© © © © —kVJ V X. V V V V X . V I© © © G © © G © VJo © G r v V © .— © © © ■ s i

© ■ s _k Ik © © © © © ©VJ V V V V V V *© © iV © © © © © VJ© © o * v r v © © © © ©• a a • a . a a a a —k© o .J*. —k —k 1 © © © © oVJ VJ V V V V V S i■© G © © G <a~a © a© G r v r v S i •© © © © © is• • « a • a a a a a *•© —> —k . —k © © © © ©

V l V V V V cc© © © © © ©

© r v r v r v © © © •© V ■C• • a • a a a a -a a 'VJ© © —» _k —k © © © © r v a

V V V V V V ©© G © G © G *■© © . rv V V © © © © © ©

■ * • a a ' ‘vJ© © _> —k —k © © © © ■o S i

V V V V —k© © © © © •DC© r v r v r v r v © © © © © a• • a a a a a a a • _k© — k — k _k _k © © © © 4S JjaV I V V V S i

© © © o •DO© r v r v r v S i © © © © © ©. • a a a • • • « • __k© —> _k _k —k © © © S J S i ©V I V V V a

© © © © ©© rv r v r v V © © © © © *• • • « a a a a a a

© _k - 1 — a © © © — k —* ©v. vj O© G -n

rv ■V V rv V o Va

rv La Ik Ik Ik 3 *© La © 'V■VJ VJ if© © — k

rv rv V Si V © © o o © ©a a 1 a a « ■ a I • _k— k — k — k _k — k G © © G © —k

VI X

© ©s V IV V s © © © © © aa • a a a a a a a a ©— k _k _k — k —k o _ k © © © 5f

— X

_ k ©rv V .V V rv -JS G © © © ~ <2a a a a a a a a • a VJ_ k _k _ k — k —k sj © © © © O

Vi

VI*

bi.nuls.tion of ion exchange zone length exDeriments for Calcium*Sodium exchange in a column.

( \

B

START

K4-2=2.6L=2200 !

> KK= 1,5 I

\ HEAD C23, Cksf

|VALUE=C^-S*.05l— -j DO JJ=30,90,30

,OW=JJaF

FLAG=•.TRUE.

DO K=1,51

£2R(K, 1 )=0.6

Yes

/inITS C^S,C2S,FLCw“\

BRATS=1,0-FL0W/200i

M2S=C2S/50000!

|M43=C4S/50000f - I' — \M=M2S+M^S|

NBTJFsO

KR=M*FL0W/2.*f

X4R(J,1)=1-X2R(J,1) ]

FIFF^f=DIFF4 *DRATE

DIFMAX=FL0¥*X4s(J-1 )

IF x"FV'h>FEAX

Yes

No

X*fH( J, RtR0W)=X4R( J, HR0V/)-DIFF4*KR

X4SE=. 5 * (F-SQRT(F**2-4))

F=2-t-K42 *X2R(J, MROW) * *2/( M*a4R(J , MROW) )

......... i

FI=2+(H«X2S(J-l)«»2)/(Kk2*XkS(J-1))

:>_! X4R(J,K30W)=X43E jW'X4R(J,N30¥) ' \ > X4RE

1X23 ( J , NROW)=1.0-X4R ( J , NROW)

iX4s(J)=X4s(J-1 ) -1 /KR *(X4R(J, NROW )-X4R(J, MROW )

.. IF'-.X4S(J) • Yes\ n >--- 1X4SCJ)=0.0\ V 0 '---------■»--

No

|X2S(J)=1-X4s(J)

/

/ I F \ "J<51

No!j\v

Yes

NROW=3-N?!0¥ I\/

KROW=3-MEOW

->

/

X .IFFLAG TRUE

xes > VOLB= 1-1

NoV<-

FLAG=FALSE

V!nbufsNbuf+i

XBUF1(NBUF)=X4s (51)*M*50000

:f\> '\X££L

X*fS(1)*.95 X

No

>

X NK

\■' IF \ Yes I <5000

Xwo\K

>

S F = .5 !

VOLS = 1-1

DIFVCL=VOLS-VOLE\k

|Z0NE=L*DIFV0L/(V0LB+F*DIFV0L)V

\ UNITE ZONE/__________ N|/\5ilTE 1-1,BUF1/

V

STOP

- 164 -

* * * * * * I ft p !j T F r 0 M f* s n s j ij C f* * * * * * *M 3 7 p R r u 4- FP « C G F A;.' T C S I K L ^ T p I0r4 F X r H A N G E 4o.*je p X P F R I ?' E *J 7 S T O S A T U R A T I O N 'a & •/ {• P a R A f ^ F T f c P ^ C M = N C L ■* 7 U H ~ A S £ W 4 ?

« fc A L * 4 2 * * R * v ' M7S f ai *SC i ? n S I C K * 4 $ < 3 1 > * X,?S ( 3 i ) * X 4 R O 1 , ? > , X ? R ( 5 1 * 2 > M c f T O n )L C G t C A L K ^ 2 c 2 * 6

l I S L c K G T h ( F f C L -J v v-i - t v M m

L = «£•.? C Gr: C 5 4 K k- = 1 o R E A { 5 # 1 0 c > r X S , c A s

S 1:1 (’' A X L f 5 k .7* C 5 p F R C L: ^ 1 n F I N! P L U - ?g V A i„j . E = C h S * f L 5 C C 3 A J .j = 2 G * 9 C > i n F L 0 u = J J F L A •; = . 7 ;; I E ,c t ? K s T , 5 1X t R ( k * 1 ) = C Mc c N 7 I M FU R I i E ( 6 , 1 1 1 3 Lc * A 7 F = 1 C M L O* * S r C 2 S / 5 (J 0 C0 ,r/ A 5 - C 4 S / 5 C C t o 1v s M; $ * v a SX " ~v* F L-CU / 2 , AK H•= X F. / 2 . 21 f'N p Uf = 0

ARO'* r2X 2 5 (1 > _ >j ? S /.*X A 3 d > Z W 4, S / Nc c '5 3 I = 2 * 5- (. Oi'n o > *S J : 2 * 5 1X A R ( J ' 1 ) = 1 * r - y 2 ( j M )F = 2 . 4 K a ; * X 2 F < J f •« d 0 M ) * * 2 / ( m * y a R C ! , A’ 0 ) )X *')r>n c = • 5 * ( F - S C F T ( p * * ,5 - A . > )C I F p L = X '■ S E " > A S <% j-1 )n 1>• p A = 1 1F F 4 * E R A r pn 1r V A X. = F L C u * y.A s ( J - 1 ) * M , _ ?I F ( I I F > E . d F ’ f- A ) n I F F A = n i F M A < .X A 3 ( J ' N ? C U ) = X A 3 (.1 * / C vv ) - D i f F / ?! F c x A R ( J t h H ( U ) , 1 c . 1 . n ) •' A -' ( J , i v H ; "> U ) =1 . 0F ! r 7 . 4 (A, * X 2 S i J 1 ) * * y ) / ( y A 2 4 x A S C 1- 1 MA A r r* •• 3 * ( M ' S C "7 r ( F 1 * * 2- A ) )I r ( X 4 ft (,l * N R C u ) , g i . x a r e ) y a r c j * v ? 0 5 = :< a r 17V r? ( J 1S. F C M = 1 f -f V /» p j , <1 p 0 )/ M X ( v' > r V A S ( j -1 ) " 1 . / < p * ( y a R < j » K * > w ) - X 4 P ( JI F ( y 4 5 (j 5 . L E , I t•1 > X 4 7 ( J ) = 0 . 0X c A ( J > s 1 / - > A > ( f 15 c c T T N I H

- 165 -

A *5 U = 3 “ **. F C w|V * 0 U = 3 " R C *

■ I E ( x A s ( F 1 ) * ★ 3 0 •'' 0 0 . . I E . v A IU F ) Q-3t OC ' c L R I 55 v C i L f-' E T1 .j 3 f A fr T H 3 r> U 0 H

! I E ( = t. A G ) V C L » s I - -ji p L A s s . f a l s e ,K a U F = N B L F 4 1r E F -) ( P L F ) s >• 4 - ( ” 1 ) * ■4 * 3 0 0 0 1 .I E C ;< A S ( 5 1 ) , G E , X i c. ( l ) * . 9 s V G 0 T 3 s 6

3 3 C C N 7 I V U HC E ,S ^ L An r Tc -THi- ^ : , p E r< F THE 2 0 kjE

5 1? F= . 5C V.r { ? IS VC. j l .Ef -TC .'<?ATU-jAT;inw

V C L S = I - 1r I f j C L r V C I S - V C La

c; ,&Q .4 F T t t H F I c K t X r H A ■, f 2 ^ N E ' L fc *3 t H I H 7 0 >i t: - L * r 1 F V C L / ( ,/ r 1 n + F * D T F V 0 L )* * J T t 6 * ^A ? 0 « F

C c u 1 P t 7 ■■ t ?.* £ F R C p I T r R a T T p ;m S AT S A 1 u J A T i g m A^jD. C q n c H rJ T K A T ? 0 U S 3 R £ A * ™ R nU! C T ui 5 a T U $ A T J c \ ' . . :

u H l T F ( 6 f - i c 2 5 1 " ‘J F 13 A C C M t I f. 1 5-'

Slop1 uc F C 3 v t> I (.< r E C , 0 )-j ;-h ' Fl^'A T < - V # » c A'2 ’ ,rfi, ' *:?x ' 1 A - 1 , F 8 . 0 # 3 X r * F I CERATE* < ,F 5 . n ' 1 ,J*3 /H

1 * )1 U 2 F L R ,yA T (1 V , I A , 1 X , * n F ;V. 1 )-j a A c C R v A 1 (1 x , «.2 C N E = » # F .< 2 , » M M ‘ )

E N W

RESULTS

FROM

CW^E

- 1 6 6 -

o•ooofA - •oONCO•NAONLA

ONVO-d-NA

OOO

OOOOJ

rA«

CNIAOJ

votNOIN

IA O O IN O. • « • •OJ O O OJ COOD O O ON IN00 O O r- NAT— OJ OJ

ON CO IA LAOJ • « • •

• IN Ol CO -d--d- O -d- vo OJON O -d- r~ NAIN r-

O IN VO ON VO• « • • •OD 0J 0 O INNA ON LA OJ vo.1 ■ fi -4- & VO *— *—

s e s E sE OD g r - E IN

rH IA ON H 'C~ O OJ H O OD O «H IN IN rH NA IA'NCO • IN « "N IA -d - • \ O OJ . \ V r - «

&0 r - IA to . OJ 60 • VO to IA IA tOLA VOS • II ON S ON II OJ s T~ II ON S • II IN ' E • II s—

'T~ OJ OJ OJ ON OJ •d- OO VO CO X i 0 T- X 0 r - X O IN X I O ON X!to to to to toII II d II II d II II d II II d If II d

O IN 0 IA 0 r- 0 OJ 0 NACD d • CD d « CD d • CD d • CD d •d x : LA d r| IA d X IA d O d X NA

cd 0 -p IA ro 0 ft O ro 0 -p -d- ro 0 ft LA ro 0 ft Onf t tS3 ft! ft IN} u V* ft IS3 ft! v~ f t n m ft td m

0 ro ro ro roCD CD 0 CD CDd • « d • • d •• d • « d ••

X r—I X rH X rH X H X H\ \

O fc3 O to O to O to 0 tof t e f t -E f t S f t B ft Eto ro to ro to ro to ro 10 ro

H d 0 rH d 0 rH d 0 rH d 0 rH d 00 0 0 \ 0 0to x •H 0 to x •H CD bOX •H 0 to X •H CD to X •rl CD

S \ +> h S v. f t rH g f t H S \ f t rH S N . ft HNA ro •H tA ro NA ro •H IA ro •H NA ro •H

O fi d f t O E d f t O E d f t 0 s d f t 0 s d f tO O 0 O 0 O O CD O O 0 O O CD OO O -P d O O -P d O O ft d O O -p d O O f t doj rA •H f t 00 vo •H f t OJ ON •H f t v- rA •rl f t v vo •ri f tli n Cj_i -P 11 II f t -P II II ft f t II II f t ft 11 II ft ftO O 0 CD O CD O CD O CD

rH H +> H £ H *5 HO . -P O • f t O • f t O • f t O . ftCu f—I O d ro H 0 d ro iH O d cd rH O d ro h O dO ft 1 0 0 ft ft 0 0 ft fft 0 O ft r-tO 0 ft 0 Ga

= 1000

Tmg/l

Na

= 0 mg/l

Flow

= 90

mJ/h

Zone

= 172.07 ram

No, of

iterations to

breakthrough

= 93

Outlet profile

Ca mg/l:

60.9

103.8

137.5

229.9

339.8

99.

816.7

1000

- 167IN LA Ph o• • • •

A _ri- IN pj-_L. CN LA ON

A LA CO

r~

A• • • • •

AJ CO LA Ph A*3* A VO LA A

OJ

LA IN LA -t-

<c—

O• • • • •

r~ VO O LA APh OJ LA IA A

OJ

co Ph O COr-

T“ • A« • « • • vo •

O VO co vo A Ph IN-3- o LA-S' LA A r—

OJ

OJ LA

Oj

OJ r-CN

LA •

r-

ON• « • • • O •

O IN V“ ON LA r- APh IN LA A pf* A O

CN LA

OJ

CO ONVO

LA •

'T'

V-• • « • • LA •

APh IN-S* LA VO AAPh OJ CO LA T— A

T~

r- A

v~

O coLA

A • A• « • • • VO •

C7\ A vo IN On A OLA r- OJ A A r- CO

r~

APh

V*

O PhCN

LA • O'* « • • • Ph •

CO O LA 00 VO A IN(A ON OJ O A v- VO

Ph O

r-

Ph LA A LA LA VO• « • • • • • •

tN-ri* Ph A A On VO tNLA IN OJ ON A r- A A-

VO V O O

v -

LA CN

P

pf CN* • • • • • • •

LA LA Ph vO pj- vo VO PhLA VO oj co OJ r* -S' A

p f ON vo o O ON

Ph

A A« • • • • • • •

CO LA LA OJ Ph LA CO AA LA OJ CO A t- LA t-

T— ph

-cr t-. £ r- CN £ v- O PT AS CO • * £ • • £ • • rH £ • •£ vo LA t— CO A On A r* CO \ . £ A t~

H O OJ LA H CO LA OJ EN H VO VO A ON hO A A VO\ A v \ LA A \ CO LA £ r- ph A£0 LA hO • hD • CO£ • II vo co £ O II LA A £ O II A A O • II A O

VO • * o • • LA • • O VO • •O LA & co IN O r co CO O t J3VOVO A CO 43 A A

cO r- -rf- bO v- O- hOr- IN hO A ONll ii p II li p II II p 11 II P A

o O O Oo P on ph O P ON OJ 0 p vo a 0 P ACOfi i-P • * C Jp • • £« HM • • P ,P • •

cd O -P _ri- LA cd O -P LA CN (S o 42 A LA cd o -p vo oS t s l ^ r r i - ' S N M v - CN S N & r- VO P M £ A Ph

cd cd cd cd Ao 0 0 0p •• P •• P •• P ••,0 H .a H & H A H

\o ha O hO o ha o t o-p £ -p E -p g •P £

CO Cd K Cd CO cd c cdfi o P O p o P o

i—! O H 0 H o rH O*N jq *h o \ X I -H 0 'N ,P »h 0 \ X i -H 0fcO \ -P H h 0 \ -P H fcO \ -p H hON 43 |— |£ LA cd *H £ LA cd *H £ LA d •H £ A cj -H

£ P <H £ P ch £ P £ P «HO O O o a> O O C) o O 0 OLA O -P Li LA O -P p LA O -P p O O -P PCM LA -H Pi A VO -H Pi AO N *ri Pi A A *H Pi

11 II tn P II II ch -P It II «H -P II II <H +>O 0 O 0 o 0 O 0

P H 5 i—1 |3 rH P rHO • -P O • -P o • +> O • -P

cd H o p a h o p cd H o P Cd rH O pO In ^ O O Ph s o O h 5 o O P P O

- 168 - FLOWCHART FOR PROGRAM CW*fH

Simulation of Mixed Base Anion resin column performance

? START

WBC = 'l.l

c y

D

AK = 0*0b09i

.READ LEAK/

DO K = 1,13

\READ SC6^~SC8, SC9/

. . . vDO KK =5,25,5| vFLOW-= KK

-IF K = 1 Yes --FLOW = FLOW/2!

IF K > 8

No

Yes -4flow=flow+i 0

v ■ IF

K > 11 Yes -4flow=flow+i 0]

NoV

■DOL = 1,101

RM0(L,1)=.2- V .

ian5(i.D = 1.09

RM6(L,1 )=.01!

169 -0-V-

EM8(L,1) = 0!

©A

L < 101

No '

R = FL0W/60

Yes

KR=Rx 100.

\WRITE FLOW, LEAK /

I II\ = 0\

1 NBUF = 0 ]Vf

IJ = 0 'y

MROW = 1J L

NROW = 2

\WRITE SC6, SC8, SC9/i

--------- ;----- )h— -----------\WRITE RESIN CONCENTRATIONS/

vyLgM9=SC9/50000. j

FICK6 = (100 * SM9+.2 2)/FLOWv

FICa8= 2.0/FL0W

-©DO 1=2,5000

I SM6(l)=SC6/50000

ISM8(1)=SC8/50000

0 - 170 -

\k jDO J = 2,101 |

IEMA=SM6(J-1)+SM8(I-1)

IF EMA ' • . Yes 1.E-6/

No

IF■RM0(J,MR0W) RKO(J,NROW)=RMO(J.MROW)

NoDIFFO=EMA*KRj

IFDIFFO■ \ RMO( J.MROVJ ). .j DIFFQsRMQ ( J, MROW )

Ho f---|RMO ( J, NROW ) =RMO ( J . MROW ) -DIFFO

\• - \/Jsm6( J-1 )=SM6(J-1 )-DIFF0*SM6( J-1 )/(ema*k r )

±;sm8(j-i)=:sm8 (j-1 )-diffo*sm8 (j-1)/(em a*k r )

j EMA=EMA-DIFFO/KR

Y/ I F ' les EM.< 1 .E-6>-----

V

No

\ /IASM9 = SM9

Y

/ IF ' . — ¥EMA> ,0027^ - ■/y

NoV

.-'IF \ /FMA+SM9 ' ' Yei ' . >.0027

\ /No

V «■!SM1 = EMA+ASM9 I

> jASM9 = ,0027-EHAj

SM1 EQ=AK* (WBC-RM5 ( J,MROW) )/RM5 (J ,MROW) V ______________

DRM6=FICK6 *SM6(J-1 ) *(SM1-SM1EQ )/EMA

vIF

^DRM6 ^ SM6(J-1)

Yes DRM6=SM6(J-1)

No I¥

$=FICK8 * SM8 ( J-1) * ( SM1-SM1EQ )/EMA

DRM8=SM8(J-1)!

Nov

- 1RM6 ( J. NROW )=RM6 (J, MROW ) + DRM6*KR

.. y ______ ___________ _[rm8 ( J,TSow=RM8 (J, MROW) +d rm8*kr*- ■ - . . ■■■■:

- 172 -

RMO(J,NROW)=RMO(J,MROW)

/\RIvi6 ( J, NROW ) =RM6 ( J, MROW ) |

/RM8(J,MR0W)

_|SM6(J)sSM6(J-1)\

sm8(j )=sm8(j-i2J

V

>

[ RMT=RM6 (J, NROW ) +RM8 (J, NROW)X

RM5(J,NROW)sWBC-RMT

VIF

RM5(J,NROW)< ° . x

Yes RM5 ( J t NROW ) =0

No\ V----- -<-------

CLEAK=50000 *(SM6(J)+SM8(J)V

i f""'"-. Yes

No 1 V_IJ=0V

- 173

NBUF=NBUF=ITBNF+1

BUF1(NBTJF)=BMT

BUF2 ( NBTJF ) =CLEAK

/ IF \ NBUF < 20 Yes

No

Yes

No

11=11+1

YesXI < 50

NoJ,

11=0

CAPAO=(SC6 +SC8 )*FLOW*1/60000V

\Y7>TTE I,BUF1 /\/

\wHITE!

I,BUF2/\/

\wRITE /CAPAC /

/ IF Yes<\ k k < 25\ /"

No

No

STOP

- ± Y 5

r -j S : ! . i 'JTu-i .5 ' - ■< ? U A- ii

<•s \ •/ T r S I L L A 7 r’ * ^ / Y r v 6 0 p. 4 S * ■MI ON R FS I - CCl ‘ iH M0 n Ll 7 I t* \ p V- A E -j r' T- : ' Y 5 ’> T •; •? ii ASs * I •; C •) n 0 5 ; f * A r t u M \ ''i ' ‘ r, / L , ,v r m 0 iL ■>f 1 T S h VC £ G 0 9 :; 13 r Y L 0 r i 0 a t -4 I s 3U L N V M P , 9 TP C A P A 0 • j D T • ‘ X f 0 t:r 1'' E I N ?- I M 7 z : , .) T c C > ! j j Y :■! 0 fc 3th r 0 CO

P c A LE \ k / ^ aT * 1- \ 5 ! r \ ^ fo M •) 1 / ^ » , R M ( 7 0 1 1A J , ,1J •3 c 101 , 0 J , .** 0 < 1 /) "1 ) # t ? 1101 3fi f '4(' K3 I \ E;L ? 1 ( 3 0 ) « M; F 1(20)

r 1 **? \ 3 1r'k x r c < 1 VI 0 )i u h A f ‘ ii ? E CA P A 0 t T V O t o / f*. i

Uu c " 1 . 1 Ay* >; fCU r 1. 7 A H3 T L 9 . r 0 q T A N r

A ,X '** f GO /1Cr' I s fc \ rPC I M L A X \ fJA c. Aj <9 f 1 C G ) Lb A t\C C 3 ^ k z 1 * 2H »i \ C0 7 r c m : e m 0 N SQ c A1 \5 * n o ?Cq . S C -3 , S C 9

f-0 t 0 1 r F ii R0 7. S 5 E 0 ? P I C p L 0 Y G I JJ \t 5 / MCUqC C X X , 9 G * 1 s? L 0 !.A “* •< X

H I ;* U I 1 L i 7 Cc • 0 ^ 7 O T I 0 M 3 US t L ow rr L 0 wT r ( N s f.Q ■2 ' r L L -V= f l o n. / 1 2

I :j n I A1 T S E A * R \ yS 0 r 2 c P ! N CU ■.<( EMT >?A T I ) MS .C 0 1 L s •4 , 1 C 1Rf'* j t L , 1 ) = *•*, 255 v (t , 1 >= 1 , C 95^-5 ( L ,1 = L , G 1P iv 8 C I ' 1 ) = t’ , CC C N T I M ? r = ? 1 C W / a (_: .5 1 T I C f? r. 7;I- F 6 N 5 3 f N A -i 0 ‘> 0 L ;j r • 0 9 Q U a N T I 7'<«= a * 1 c ,k ? ~ 4 c< * 2 _' * * 1 T 5 <6 »1CS) ' K i I O L e a K ■11\ * u = s yi j = oU K;) U = 1KH0XV2u * J r ? ( 6 /1 c 1 ■} -SC/S / > C a , S C 9U R I f E O i ^ C ^ )U*It-E<2,TC5) c ?' 9 _ 9 C 9 / 5 C C C 0 ,

i s A n T f F C S r L N r; 0 £ p F I C I £ N T p I C K 6 = ( S C fc * S r*9 + . p 5 ) / P L 0v*F I C < .« = 1 . £ / F L C u

r r S

1 = I , 5 C 0 1s ?/ 6 (1 ) 5 ? C t / 3 0 C 0 0J v O ' i Y M C 8 / ' j 0 t 0 9 !C u 5 3 J = 2. 11 0 1 E f# 4 .? S y 6 ' j - 1 ) + S M 4 ( j - 1 >T f * ( S ^ A , L F . 1 , 6 - 5 ) SO r 0 5 9I c 4 7 C r A l c L L A u* S 0 O p T n N A V S T ?? n \! G q A S g S I r F s I r :< >v 0 C -I 1 6 C U ) . l c . 1 . p “ 6 ) vj U T 0 j j0 I F p C = E V A * * ii1 H c I F F 0 , G £ , {??•• 0 (,1 , M >f! W ) > 0 1 p F 0 “ 3 m w ( j , tf ROu )* * 0 ( J # N H C1* ) = p N 0 ( J , M {? c Ai) ~ D 16 F 0S 6 ( J -1 ) = S N‘ t ( J - 1 ) • D T F F 0 * S* 6 ( J ** 1 > / ( E M A * '< R )

( J - 1 ) = SN‘ <? ( j - 1 ) - D J p F 0 -.v s 3 f J " 1 ) / ( E v a * K r )E jv A 3 E r< A - c I F F H / 3 I F ( P v A . l £ , 1 f E - 6 ) G 0 r C 5 5<3 C T 0 5 8 RvO<J iNRC^ysSi

- i y b -

T g '•“ T v e r a a f3 C N C I L i ' n = '-CF 3 r T 0 T 0 r 4 H F Ia ‘ S-.v 9 - S- 9

7 M - (v a , '• E • C , <:• { ~\■’ ) G.i t O 11

TP ( ' : v i + " N! 9 , Gr- i •1 n 3 2 ■? y < Rs-9 =0 , 0 7 j! 7 - p 4G CT: 12

1 1 4 5 >10 = 0 ,'! 7 5 .v i - p ,v a -» S l-

3 C C f j C N TC r a L C i- l.P T 3 n ■>a r I 3 *; ay t \ x xi % a eS M 3 G = * s; * { U m' c - 'A ■'3 ( J , v RO': ) ) / 0 C ! . a . - j )C f< M = F I C * 6 * 3 a- ( 1 - 1 ) , (S y ! - s m i j=0 ) J p • -*AT F ( * R v 6 , -■ • t *-■v c K J _ 1 ) . D0 ‘ 6 = 3v M J . i )C N >' A ; F I C. X 8 * Sn .* < 1 __1 > > ( 3 »11 - s M 1 p y ) / p MAI F ( £ B * S .. (51 f s.V ’c \ 1 IX.1 ) 1 0 0 :< .a = C J -1 .H r O i J / Np r U ) = R >“o < J / m c y ) ? n « M f, ★ (( N

,N F C * ) * ST- 3 V J , ■,< ’5 r bj ) 4 n k w p * K ^S ?' 6 ( J ) s 3 8 8 ( J *» ! ) «• 0 R M aS'- 'i ( J ) S SP-E CJ ) - n R M 1G C T r; 5 6

A 9 1 'v 0 ( J » K b C u 5 = Pf/ 0 ' J 9 fi? ’r| f! Wy*>3 F > ; 5 J ' N? C u > 3 PN 6 G ,! # a j c y )

S d ( j ■ # Ns c u ) 3 R(v l- J • M 3 c w) *' 6 ( J ) a •:>•'{!( ,! »1 )

> H ( J ) a FN' 8 < J )5-0 S N* T „ p ,v a• • -4 * V ( J * N F c - ) -R M8 , J ; o - o o )

F 3 f J » N c C u )•• s ua c — tiy t vI F C 0 V 5 <.1 1 N F- c O i C , 0 . 0 ) >' y 3 G j , o H - i y ) " 0 . 0C L £ i K = 5 OGCC, * ( 3 -j A ( j ) + s O0 ( j ) )

T J IS A CCl N T e R TO ■3 R I N 7 5 9 p Rv PI f T:m : 0 t U M N ferricN

I i

3 6

1 u C1 m 1

1 u0 1 u 'iI U.31 u 61 ii <*

IJ * I J +1J F C r J . I, t , 5 > tfCT.o 5‘5 T J - 0 B i j ? S (v 8 ! F + 1

3 L F -| ( O 3 L F ) s R K T 3 I F ) ( N 8 L F ) a C L £ A >•'I. M \ B L F . i T f - 0 J r. r . T 0iKctE^.ee., n ?) g, y y \ s i " n h: c '*K F J * s 3 “ N R C ^NdUp;0

r ? a r 0 1 \ T E F T C ;■? p d 0

i i = r i + iI F ( M . I, T , 5 c ) C OTC j 3 u a I r g (t f 1 c s > I *-1 ! f i U * I T E ( 2 ,1 C £ ) I , -? I j F 2 I 1 = 1c C N T I N L FCfl°4C=(SC6+SCfc)*FL0-J*I/^ 0 0 0 o . C/»3aC = CAP*C*;?!

■U M I t 6 (6 ,1 C 3 ) I , 1 P 1 " I ’ a < 2 , 1 C 6 5 I / 3 y F 2 f i r f (6 ,1 (, "i) c \ ■? a c

C C N r J ,\ t F cc NT I M p S T 0 cF C 3 iV a T ( 2 r 0 C , (j)

L I N 5 S O F ■' n U T P u r

cC Rv 4 T (1 X F C 3 v A T ( 1 V F C R,v 4 I (1 X C C R y 4 T ( 1 X F C R v A T ( i X F C R v a T ( i x F C 9 v J T ( 1 V END

• s c e = ! , p * . 0 , :5 x , ' 3 0 8 = ’ , F 4 . 0 , 3 X , ‘ 3 C ° S ’ , * 4 . 0 ) f C A F A 0 I j Y - ' , F . 2 / i ^ G / * * 3 » ;I 4 , 1 X , ? 0 F 3 . ?)! F S I j C 0 ---j r £ N r r A T T 0 N 3 > )1 3 G L U T | 0 N C O ^ ^ e o T ^ N r ^ ^ J S , )

* 1 1 X * ? 0 c 5 , 1 ) f 6 L c / c j , 1 ? I X # 1 L E A < 3 » , F 4 . 1 )

- 177 -

sOM—— — — — —— — — — ———Hr— T3X0 "'T 5*XiX*<X«C*<i"O2 5? ’-O •■£ 03 OSvjV4O'' O;XiCT X3X XiXi'O Mi——• <3 ."5!0 ‘'0i5 OINN J1 J* £-*-5- XiX*t o ’ "in '■tjosj-xst-so "J"- 02 j o z xiox ons; rS : z xn3 it .z .u i.v o r - s o s n s : x ~ z c j i x n z o r 2 cn z x n z x o z x r z ‘J’ 2 x i z x i xijc- z.

■—• itro I!----------------------------------------'-------------------------------------------------------:--------------------:-------------' 7 p

— < - j r ^ t r » i # i i » i » » » ♦ i ♦ » » • m « i I j » ♦ t i » i i » * » i i r « i » » » » • * i ? n s

TO -C \C X- X X X X X- ’C X X X C X X X- X X £ X X C :C X X ' C X X X X X' X X X CO OS '-v O'- X -X Xi 1—• T Q* rO X XI —n; Xi vi-XiXi X X X X X* X ‘X X -X X X —X -X-v- X X XXi Xi 'X Xi -X -X:X v>* 'J X X w‘ X X *■ XJ- *

_v_ . 1, X.- - --- - a-s£ -rj

-x'-' ] * ■ » » ■ " ■ * » • • • • • * ■ * • • * • • • * • ■ • • • • ■ • • ZTL*» bj-'OO X -C -O X X X X X VO X x - C X O O X -X X X X C X X X X X X C X X X X ‘X X X J3 ViO • - j ' X X X M — S. TO — v>|» *XfX-Xi X ‘ 'XiX- X ’X-' X X ’X X X *X X X X X X ‘ X v>* X X X X X X --v.-XiXX.Z*‘ X 'X OrO ‘-UvlV< X’ 00 X ‘X X 5 vJ ■.*; X'~— - *—^X50M \> X -Q M X ->JXM Xryj rp ■ O X X M A j-Q m X X X X M M > 0 M M M M M M — -O — -O X X vXQs r~ vi 03 — - J- M X >j I ? ^Toroi . —i >\T' » ? i > ♦ i » » ♦ » » I » ♦ » i » j » » » i # » * » * » » r i » * # » ♦ » ♦ # » * » * » • > * » H ^x. ";jX X 'X X X X X X X X X X X X X X X X X X 'X X -OX X X X X X X X X X X X i XXiM X1-XX50—— 2 2 X -2Cj X Mst * x* X ’X *x x<xi *x x x x x x x x x Cxi ’X x xi x i xj x x i ‘j* x ;X x x x*rx xj-v*to x c?» v *■ —* —<*x x ro roro m ro :o ro rc *o rx m m ro ro- roroMforo.M ro rx x ro rp ro ro ro x x —x — x — rx — x= x '^i rx *o cr x x

LT' • * * • * » * * •*»#••«*»•*•• ****** ***** a ««•»•******<*•X X r ~'£j V 1 j *-- '- - -i** 1 1 x x x x o x x : x > x : - x x x - j x i

j<! L*+ CaJ 1~J X X X-' CJ j-i X ..oi Xi >X C/w X* C*» X> X.1 L»i Oi Cw C*i '_*i Xi C>»' C-fO X -N0 i. v"S. X X • "Nj -O .\3 Xi / i X’ —*■ *■ —* —■*>x " j ••■> x --Q x ro x x ~o x :o ;o .x ro ro x x x ro x ~o ,x m ro m m ‘C >. x . x-* ro o;— vi — x v s i s s a

t t i t > * t t 1X ’x X X X X X X X X X X X X X X X X X X X X X X X X 'X X X X X N.' X X" C.V X. Xi V— — X X 3 Z- X X X '“. X* ;Xi Xi Xi V>i Xi Xi Xi Xi Xi Xi Xi X‘ iX «*■* X' Xi Xi Xi Xi Xi Xi Xi Xi X Xi X : O —* C X X' Vi ,"X 3i -*d *0 X Oi Tv VJ Xi —* — — * — “*~ fo TJ M TO ro TO TQ -V- ~Q M M M ro M M j\> M ro :\> M *Q ~Q V- M ^ -Q \ x \ j ■.?, Vi y; X: -X vi vi X. 3 ~X X -■*? •-: XiMi■.y*~ ) Q £ ■£> O iC O O O O -O £ '-D £ £> X -£ -0:0 O OO’C C O v O S V V T n J ' x. Xii\i M — X X S Ti 'X 3 'V Si X 55 X S® Tji V i \>i - A‘ V i »y» sAl i i j i ' v ivi iAi >>i'X v »A i T J ’'' X -.A V ’ V t ' *'w* i-A - __J. II A - _ f ' '** ' *” ' _ ' ' I-s M M M M M M ^ X L X M L X i y n ^ x n N > x Xi XSXi-X; Z~X 5 X X x ~X .XX Z.,M‘.

» » * M M M M t I » » M > > » > f M » » J M f » f ^ » M » M » » * M » •

C £ -£ J ’£ j ' 0 - 0 'C £ - C ' £ £ ' £ - :£ ~ 0 ■££>'■£'■£ 02 *< O ' ‘T X iM M — T£TX -Z Z X X Z X Z Z Z X X X* ■ X X X X X X X X X X X X X X X X X X X X X TO “ vii—• Xi Xi CJ”! 3" O M vi Z* \5 — ‘ ■ * ■ - —» —• ——a .—a-v.

■XX K> M \ ) -O ~V) -MM MM M \) V \ - M V V \) V M V S X PO TX vi Xi X X X. X V> Xi M Z \ ) M Z X X x S 3 3 ' ; > S 3 Z Z Mi

^ 0 0 0 0 0 - 0 0 - 0 0 0 z x > o o o -O O O O i T C N O-. xn X . X X TO —* — Z X X X Xi 'XJ Xi Xi XIXX CX -X Xi XX Xi Xi Xi Xi Xi X X'j X- ST — O X O’! O- ViCT o — X C3 TO VI X»'—■ “ M.MM-OMMMMMM MM MMMMM — v; Vi— ^ 3:?

ji X ‘X V S5 Sv ^ i

O C ' C O O O ’■ O - o O O O O O O O O O O -53 V i O': O'.- Ti! X X i TO — — ».3 :-i ; XJ X i X i X i X i X i X i X i X i X i X i X i X i X i X i M M -55 o ;to O S " 3 .\3 X i O O O JX - M - - J M M M V ) M -VS TO \ 3 M M TO — O TO TO V i O V | TO CO Z 0 3 O - X O

TO''F * * ......... . . . . . . . . . . . . i i . .........!5jvC O O -O O o O O O -O O O O O O X 00 V i O XT ^ X i M V — — 25 S5 S5 Z S i Z Z

zho ro m m ~3 ~o M ~o to to ro t q s j sj — o — o> o t>j -o> - j og ro o a s :a z • :x z z z z z z z s- z z 2 z z ..z z

~i o o • o o o o - o 0 o o o o o : cs v i o o x ; x j t o —— z s s z z z i s s z z z ^ s ^ r z s s- z .> z z x z • jxi x x x x* x o«i x x x to — csx» Xi O) o .v j os z -x»i vjro vj x i — •i— —* ———* ——*■'•—— . —* — -v.z-p. > M M M M M M — v*. TT. -OS.fX Xi;-** ■; r^ v ts -os p.— -rx— * ,Z Z Z Z Z Z Z Z Z Z Z SXS.. Z. Z Z V Z Z

0 0 0 O O O O O O OS 02 Vi o XT! XT X X J M — — Z Z Z Z Z Z Z S’ X i X i X i X* Xki X i X i TO TO O XH OS O O £ Z — X i -XT O X ’ ’-CO -X — —* — *-*— —a i MrV>TO\5MA0*-A O— OX Z SXS>— XliMO.iivVivJXiZ c c s o a .

*3 Z TO Z S3 Z Z Si s»W»l -'A |S » - A ||-V| '. - j I Iiarf 11-—

TO

O O O O O 0 -0 .C U O V i O ' X S X X * M M ----- - Z Z Z Z Z .XI Xi Xi Xi Xi TO S ivrz—M'OXi'-T CO — ■ O’ -Si •'X — — — —- - ■Q TOM — Z x.00 Z x -TO X o Q £ ) < - Xi -X — O' o> z z z :

3T323QSS'

^ -3' *: » 3 7v.3

a

MX»

•O O O O 32 0 0 v» XT v"i-£* -Xi X* \ J — ■— Z Z Z 3 Z 3 Z \ O O Z -Z Z X Z Z Z 3 X 3 ^ j i S S X Z . 3 X 2 v , ^ ^X t X / M — C O .M Z J I O O ' 0 2 Z X iV i .— O'- TO — — — — — — — — — — — — — — — — — *------ *r— )—— a 7i v Vi .- XiOSO' - X X J - Vi O OS 3 3 3 3 3 a 3 3 X 3 3 .3 a 3 3 0 0 0 3 X 3 '3 3 Z Z 3 S> 3 3 3 3

OCO'-»viOiCT.O».*.Xi.TO — ■— O 3 30 30 : — o vj 00 00 O ZTCX^OO X' 00 .Ok— — — — ' •on O'. 33 X r o V i X . VJ 3 . O aO C X X . 3 . 3 3 3 S 1

3 CSOOSSOZ X 3-3 S3 -3 — Z 3 33 Z S353Z ZZ 00 Z 3 Z■I— • “ — • ■— . — — — m —— — A * —A I— • .-»!— * •—

O v j V i 0^ o n X- X« ,\3 \ 3 ’ 50 SO 3 X 2 " 2 .2 S3 2 2 2 2 2 TO 2 2 2 2 2 -.0 2 2 2 2 2 O S 2 2 O 2 2 0 2 2 2 2 2« Vjr-iA!— *f\} X X ! V i 50 X . OCJ! — — — — — — I i*|-.»^(-->.l A — A ..A I- A I. A ) V ...V. !-*,-** * M h * W i - * A * W > A W H * U W WX4Xi— 2. ,Z:Z.S.Z,SLZ.ZJ0LZ.3:3i . ^-AS.ZZZZ2 0.0 2 2 Z Z 0 2,2 X 3Z XJ3 ,

o>Xion 2XOTJ-- 2 05 *3 50 Z 2 Z Z ST 2 0 3 00 30 SO 2 : * 1*0 - X V i C \ ' "O'. — O l M — — — ■— — f - A * l - * r * w w w v ( — .

3 0 0 3 3 3 3 3 ‘X

■TO - 0 X0 Vi»03 '0-:X J0' X” 00 3 0 30 0 2 2 10 50 50 2> X D’ 2 :3 ■ 53 X- f^ j . . • • • • • • • • * • . « • • • * • • • • • • * • « • • • • • • • • • • • • « • • • • • • • •xj'O’O — — 2 Z Z 2 2 2 2 2 -Z 2 2 Z Z Z Z Z 2 2 2 2 Z 2 Z 2 2 X 2 2 2 3 3 3 3 0 3 2.2 3 S Z v Z D 2 2 <Vi OS X . 03 -O V i 3 S3 I S O Z Z . 2 2 55 2 2 2 3 3 3 3 0 2 2 2 2 2 2 ~3 2 S3 2 2 Z X 2 2 Z 2 2 50 v 2 2 2 2

V«|—>Z £3 Z Z -Z S O S 2 S Z 52 Z '2 72 S .-52 Z Z Z Z :C0 T "2 Z 53 -.Z Z Z 2 -S Si.oO-52 Z X X "Z-ii* '.3 X S i '2 Z S3 52

Ocjx X O X 2 3 Z 2 3 3 S 3 S Z TOT O O O S S S 2 :2 X Z " Z X 5« 3 3 3 2 3 2 ^ S S S O S S O S S S S— I---------------------------------------------:------------------°L' • • • • »..••-• *••••»-•*»•»* v , v v-CjX Z Z 3 X 3 ?. 3 3 3 Z 3 3 3 S 3 S 2 3 3 IT 2 u ‘3 3 2* c» j.- ^ ^ :3 v iv j * 0 X ..*• v -a* v X V

M ATERIAL REDACTED AT REQUEST OF UNIVERSITY