[a._g._d._emerson]_quantitative_forecasting_of_pro(booksee.org).pdf

British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center,Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required fromthe publisher.

ISBN 981-238-184-8

All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic ormechanical, including photocopying, recording or any information storage and retrieval system now known or tobe invented, without written permission from the Publisher.

Copyright 2003 by World Scientific Publishing Co. Pte. Ltd.

Published by

World Scientific Publishing Co. Pte. Ltd.5 Toh Tuck Link, Singapore 596224USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

Printed in Singapore.

QUANTITATIVE FORECASTING OF PROBLEMS IN INDUSTRIAL WATER SYSTEMS

FOREWORD

Some calculations in Sections 1.2.1, 1.3.1, 1.5.2, 3.3, 3.4, 4.1.1, 4.4.4, 4.4.6,4.4.7, and 5.1.4 require the use of tables published in an earlier work cited asRef. [8] in the References.

Readers will therefore need to have a copy of that earlier work to handbefore using this book.

Unfortunately, after this book had been drafted, the publishers of Ref. [8]stated that this earlier work was now out of print. Readers may therefore havedifficulty in obtaining a copy.

To overcome this situation Ref. [8] has been reprinted as a Supplement atthe end of this book. Readers will therefore have all the tables needed, bothfrom this book and from the supplement, available under one cover.

vii

Qfpiws-2Foreword.p65 02/17/2003, 5:17 PM7

SYNOPSIS

The operating problems most likely to be encountered in industrialwater systems are:

Fouling by calcium carbonate.Fouling by calcium sulphate.Fouling by calcium phosphate.Corrosion of mild steel.Corrosion of copper.

Methods are described for calculating the amount of fouling likely to occur,and the rate at which corrosion is likely to proceed.

These data enable a quantitative forecast to be made of the problems likelyto be encountered in an industrial water system, while the project is still at thedesign stage. The information will also be of assistance in investigating problemsexperienced in existing systems.

The data are presented in the form of tables to assist operators who areworking on site with portable testing equipment.

The methods described introduce new concepts for the saturation indices ofcalcium carbonate, calcium sulphate, and calcium phosphate; for buffer capacity;and the pitting propensity index.

ix

Qfpiws-3Synopsis.p65 02/17/2003, 5:17 PM9

NOMENCLATURE

( ) Thermodynamic activities, expressed as mol/l.[ ] Stoichiometric concentrations, expressed as mol/l.

a Fraction of molecules remaining after precipitation.Alk Total alkalinity expressed as

Alkalinity to Methyl Orange mg/l in termsAlkalinity to pH 4.5 of CaCO3.

b Fraction of molecules remaining after precipitation.B Buffer CapacityC Total carbon dioxide expressed as mg/l in terms of CaCO3.C/ Corrosion rate

Ca Calcium hardness expressed as mg/l in terms of CaCO3.ClR Chlorine residual expressed as mg/l Cl2.DS Dissolved solids expressed as mg/l as such.exp Exponential exp (a) = ea.

E Summation of equilibrium constants.E/ Constant for Suzukis equation.f Activity coefficient.I Calcium carbonate saturation index. (Langelier Index)

IL Copper pitting propensity index. (Lucey Index)Ip Calcium phosphate saturation index.IS Calcium sulphate saturation index.K Thermodynamic equilibrium constants.

K Stoichiometric equilibrium constants.ln Logarithm to base e.

log Logarithm to base 10.n Number of concentrations.p Negative log.

pHs Equilibrium pH.Phos Total phosphate expressed as mg/l in terms of PO4.

Q Weight of calcium carbonate expressed as mg CaCO3.R Ryznar Index.

xi

Qfpiws-4Nomenclature.p65 02/17/2003, 5:17 PM11

xii Quantitative Forecasting of Problems in Industrial Water Systems

SO4 Sulphate expressed as mg/l in terms of Na2SO4.T Temperature C. Ionic strength.V Vectors.W Weight of calcium carbonate expressed as mg/l CaCO3.Z Valency.

Qfpiws-4Nomenclature.p65 02/17/2003, 5:17 PM12

INTRODUCTION

This book has been written as a contribution to changing the attitude of mindwhen considering problems in industrial water systems. The need for such achange has been brought about by changes in prevailing economic conditions.

Industrial systems using water for heating or cooling purposes frequentlyencounter problems which are associated with the quality of water used. Informer times, when both labour and materials were cheap, it was a relativelysimple matter to discard a system that had encountered problems and build anew one designed in the light of the experience gained from an old system: inthis way it was hoped to avoid the difficulties previously experienced.

If discarding the system was not considered necessary, some form of chemicaltreatment and monitoring might be introduced. If this was not entirely satisfactorythen, with cheap labour available, it was, again, a relatively simple matter toarrange for periodic manual cleaning of the system to make good the deficienciesof the treatment. In fact some operators used to boast of the quantity of depositremoved during such manual cleaning operations. As though it was a matter ofpride, instead of a reflection on the manner in which the system had beencontrolled and operated.

But under present day ecomomic conditions such a leisurely approach is nolonger feasible. In the design and operation of industrial water systems it isimportant to know in advance what problems are likely to be encountered, andto be able to give a forecast in quantitative terms.

For one type of system, the steaming boiler, the problem is not too difficult.For example, a boiler feed water contains X mg/1 of hardness salts: since all thewater entering the boiler is evaporated as steam, all the hardness salts mustremain behind to form scale. Therefore X mg of scale will be formed for eachlitre of water evaporated. Expressing the problem in quantitative terms is thereforea matter of simple arithmetric. For this reason steaming boilers have beenexcluded from the discussions in this book.

But for systems involving heat-exchangers (whether for heating or cooling) amore complex situation exists, depending on the chemical reactions taking placein the water at various temperatures. The study in this book has been restrictedto heat exchange systems where there is no loss of water by evaporation, or

xiii

Qfpiws-5Introduction.p65 02/17/2003, 5:17 PM13

xiv Quantitative Forecasting of Problems in Industrial Water Systems

other means, unless specifically mentioned in special cases. It is also assumedthat there is no change in the chemical characteristics of the water by accidentalingress of contaminants, or by the loss of dissolved gases by venting toatmosphere, unless addition of chemicals or loss of gases are specificallymentioned in special cases. Changes in the chemical characteristics of the waterare limited to those induced by a change of temperature.

The problems most likely to be encountered in the types of systems outlinedabove are fouling and corrosion. Fouling is caused by:

Deposition of calcium carbonate.Deposition of calcium sulphate.Deposition of calcium phosphate.

These are studied by physical-chemistry methods.It is appreciated that some fouling may occur by the formation of organic

slimes, which may act as binders for the inorganic deposits mentioned above.But organic slimes have been excluded from the discussion as their formation isnot amenable to physical-chemistry methods.

The metals of construction most likely to be used in industrial water systemsare mild steel and copper: their rates of corrosion have therefore been includedin the discussion. Other metals may be used from time to time, but mild steeland copper are regarded as basic: other (often more expensive) metals areintroduced when justified on technical and economic grounds by the operatingconditions existing in an individual system.

Manufacturers of special alloys are sometimes able to indicate how the rateof corrosion of their materials compare with mild steel or copper under givenoperating conditions. Thus, a knowledge of the probable rate of corrosion of thebasic metals can be of assistance in selecting special alloys.

The purpose of the data offered in this book is to enable quantitative forecaststo be made of the fouling or corrosion likely to be encountered in an industrialwater system, while the project is still at the design stage. A decision can thenbe made on the type of water treatment to be adopted, commensurated with thepurpose for which the system is to be used, and its life expectancy.

A discussion on the various types of water treatment that might be consideredis beyond the terms of reference of this book. It is a diagnostic tool utilising thebasic physical-chemistry of water supplies. Water treatment methods may changefrom time to time, but the basic physical-chemistry remains unchanged.

However, a forecast of probable operating problems may be used to influencethe choice of a water supply, if several alternatives are available on any givensite.


Introduction xv

In the case of a small project, or one handling a low grade product, a forecastof problems as outlined in this book may suffice. But for a large project, or onehandling a sophisticated and expensive product, a trial run on a scale modelmay be undertaken before final design details are settled. In such a case aninitial forecast of the problems will enable the trial run to focus on the mostcritical conditions likely to be encountered.

In addition, to work at the design stage of a project, the methods describedin this book may be used to assist operators in investigating problems on anexisting system. As this often involves working with portable testing equipment,the data are presented in the form of tables to facilitate site work.


v This page has been reformatted by Knovel to provide easier navigation.

Contents

Foreword .......................................................................................... vii

Synopsis ........................................................................................... ix

Nomenclature ................................................................................... xi

Introduction ....................................................................................... xiii

1. Calcium Carbonate Fouling ..................................................... 1 1.1 The Ryznar Index .............................................................................. 1

1.1.1 Origin of Ryznars Work .................................................... 1 1.1.2 Emergence of the Ryznar Index ........................................ 3 1.1.3 Revised Evaluation of the Ryznar Index ............................ 7 1.1.4 Experimental Errors .......................................................... 9

1.2 New Data ........................................................................................... 11 1.2.1 Use in the Field ................................................................. 13 1.2.2 Margin of Error .................................................................. 16

1.3 The Langelier Index .......................................................................... 17 1.3.1 Use in the Field ................................................................. 19 1.3.2 Margin of Error .................................................................. 21

1.4 Choice Between Langelier and Ryznar ............................................ 22 1.5 The Special Case of Recirculating Systems .................................... 23

1.5.1 Closed Recirculating Systems ........................................... 23 1.5.2 Open Recirculating Systems ............................................. 23

2. Calcium Sulphate Fouling ........................................................ 27 2.1 Calcium Sulphate Saturation Index .................................................. 27 2.2 Calculating the Weight of Calcium Sulphate .................................... 28

vi Contents

This page has been reformatted by Knovel to provide easier navigation.

2.3 Use in the Field ................................................................................. 31 2.4 The Special Case of Recirculating Systems .................................... 32

3. Calcium Phosphate Fouling ..................................................... 37 3.1 Calcium Phosphate Saturation Index ............................................... 37 3.2 Calculating the Weight of Calcium Phosphate ................................. 41 3.3 Use in the Field ................................................................................. 44 3.4 The Special Case of Recirculating Systems .................................... 48

4. Corrosion of Mild Steel ............................................................. 53 4.1 The Ryznar Index .............................................................................. 53

4.1.1 Use in the Field ................................................................. 57 4.1.2 The Special Case of the Recirculating System .................. 59

4.2 The Langelier Index .......................................................................... 60 4.2.1 Use in the Field ................................................................. 62 4.2.2 The Special Case of the Recirculating System .................. 64

4.3 Comparison Between the Ryznar Index and Langelier Index .......... 65 4.4 Buffer Capacity .................................................................................. 65

4.4.1 Description of Buffer Effect ............................................... 66 4.4.2 Definition of Buffer Capacity .............................................. 66 4.4.3 Water Analyses and Buffer Capacity ................................. 67 4.4.4 Evaluation of Buffer Capacity ............................................ 70 4.4.5 Buffer Capacity and Corrosion Rate .................................. 73 4.4.6 Use in the Field ................................................................. 73 4.4.7 The Special Case of the Recirculating System .................. 75

5. Corrosion of Copper ................................................................. 77 5.1 Cold Water Systems ......................................................................... 77

5.1.1 The Lucey Index ............................................................... 78 5.1.2 An Alternative Approach ................................................... 80 5.1.3 Data Required ................................................................... 80 5.1.4 Effect of Concentration ..................................................... 81 5.1.5 Calculating the Index ........................................................ 82 5.1.6 Time Scale ........................................................................ 84

Contents vii

This page has been reformatted by Knovel to provide easier navigation.

5.2 Hot Water Systems ........................................................................... 90 5.2.1 Data on Water Chemistry .................................................. 90 5.2.2 The Role of Residual Chlorine .......................................... 95 5.2.3 Time Scale ........................................................................ 95

References ...................................................................................... 99

Tables .............................................................................................. 101

Index ................................................................................................ 193

Supplement (Reprint of Ref. 8) ...................................................... 197

Chapter 1

CALCIUM CARBONATE FOULING

The starting point for a study of calcium carbonate fouling is the need for amethod possessing the thermodynamic integrity of physical-chemistry; a methodwhich is easily applied and will allow the amount of calcium carbonate depositedto be estimated, or forecast, from an inspection of the chemical analysis of awater supply.

At present, the literature offers only one parameter linking water analysisand the amount of calcium carbonate deposited: that parameter is the RyznarIndex. A study of that Index is, therefore, the logical starting point for thedevelopment of methods for forecasting fouling by calcium carbonate.

1.1. THE RYZNAR INDEX

The Ryznar Index [1] is formally defined as:

pH2pHS =R (1)

where pHS is the equilibrium pH described by Langelier [2].But to understand the significance of the Ryznar Index in relation to the

amount of calcium carbonate deposited, it is necessary to go back to the originof Ryznars work and make a reappraisal in the light of recent information thatwas not available to him.

1.1.1. Origin of Ryznars Work

Ryznar was investigating, in the laboratories of the National AluminateCorporation, Chicago, the effect of scaling inhibitors in reducing, or preventing,calcium carbonate deposits in industrial water systems. The work involved theuse of a test rig described by Thompson and Ryznar [3]. The basis of the testrig is shown in Fig. 1. A sample of water to be tested is contained in the headertank. A fixed volume of water is allowed to flow at a fixed rate through the coilin the heater tank, which is controlled at any desired temperature. The coil isdetached from the test rig and weighed before and after each run. In this way,

1

Qfpiws-chap1.p65 02/17/2003, 5:17 PM1

2 Quantitative Forecasting of Problems in Industrial Water Systems

the weight of calcium carbonate deposited is determined, at any selectedtemperature, under fixed operating conditions.

At this point it must be emphasised that the conditions existing in the testrig restricts the application of Ryznars work to those industrial water systemsin which similar conditions apply. That is, once-through, closed systems in whichwater enters, passes through to drain, and is subjected only to a temperaturerise. Apart from deposition of calcium carbonate there are no other changes: forexample, incidental ingress of chemicals by contamination, or loss of dissolvedgases by venting to atmosphere. The only chemical changes permitted are thoseresulting from the deliberate addition of known reagents to the header tankbefore the run starts.

These restrictions apply to all the discussions which follow in this book,unless there is a direct statement to the contrary.

Using the procedure outlined above, Ryznar determined the weight of calciumcarbonate deposited by a sample of raw water, and compared it with the samewater treated with various inhibitors. In this way he was able to list the inhibitors

Fig. 1. Basis of ThompsonRyznar test rig.

Qfpiws-chap1.p65 02/17/2003, 5:17 PM2

Calcium Carbonate Fouling 3

in their order of merit. By repeating the process for different raw waters Ryznarwas able to provide a more extensive and more informative list of merit for arange of inhibitors.

Because Ryznars method required only comparative weights of calciumcarbonate, and each experiment was run under fixed conditions, his data recordsonly the weights of calcium carbonate deposited and not the volume of waterfrom which they were produced.

Another important point to be taken into account is Ryznars method ofpreparing water samples. In the earlier stages of his work he found that theexperimental runs had to be extended over a protracted time, and use largevolumes of water, in order to deposit sufficient calcium carbonate in the coil toproduce a significant weight change.

In order to reduce the time of each run to a manageable length, Ryznarincreased the scaling potential of the waters by increasing their alkalinity. Sodiumcarbonate or sodium bicarbonate was added for this purpose. The significanceof this step is discussed later. See Sec. 1.1.4.

1.1.2. Emergence of the Ryznar Index

In the procedures followed by Ryznar it would be an advantage to be able toforecast, or estimate, from an inspection of the chemical analysis of the water,the weight of calcium carbonate deposited from a given volume of water at agiven temperature. This information would facilitate the preparation of raw watersamples that would yield a weight of deposit within a range required for aspecific sector of Ryznars investigations.

In pursuit of this objective Ryznar prepared 21 raw water samples whichwere passed through the ThompsonRyznar test rig and the weights of calciumcarbonate deposits recorded. The results are set out in Table 1.

The chemical analyses of the water samples were made at atmospherictemperature (assumed to be a nominal 15 C). From these data Ryznar calculated,for the temperature (T) in the test rig the equilibrium pH (pHS) as described byLangelier (loc.cit.).

The equilibrium pH is defined as:'

S'

22

S ppp[Alk]]p[Ca pH KK + ++= (2)

]HCO[]CO][H[

where3

23'

2

++

=K (3)

][CO Ca and 232'S + ][=K (4)pHS was evaluated from tables by Larson and Buswell [4].

Qfpiws-chap1.p65 02/17/2003, 5:17 PM3


From the values of pHS (at T) and the values of pH (at 15 C) Ryznarcalculated the values of the calcium carbonate saturation index, described byLangelier (loc.cit.).

I = pH pHS (5)The calculated parameters are set out in Table 2.Because the values of pHS had been adjusted to (T), the temperature in the

test rig, but the values of pH had not (being recorded for 15 C) Ryznar hadbroken thermodynamic integrity. But he had no choice since in 1944 there wasno published method for adjusting pH for temperature changes.

In this present reappraisal of Ryznars original work, Eq. (2) has been usedin the modified form:

/100(DS)ppp[Alk]]p[CapH 0.5S22S +++= + KK (6)described by Emerson [5].

)(HCO))(CO(H

Where3

23

2

+

=K (7)

))(CO(Caand 23S +2=K (8)Values of p[Ca2+] and p[Alk] have been taken from tables by Manning [6]

and values of pK2 and pKS from tables on pp. 416 and 424 of Hamer et. al. [7].For this reason the values of pHS, I, and R in Tables 2 and 3 may differ

slightly from those in Ryznars original paper.A plot of the values of calcium carbonate saturation index (I) against weight

of calcium carbonate (Q) from Table 2 is shown in Fig. 2.The plot shows a ragged scattering of points with no apparent relationship

between the two quantities. The scattered pattern may be due to:

(i) Absence of any fundamental relationship between I and Q.(ii) Errors introduced by Ryznar breaking thermodynamic integrity.

(iii) Experimental errors in the test rig.(iv) A combination of two or more (i) to (iii).

These matters are discussed later in Secs. 1.1.3 and 1.1.4. But Ryznar assumedthat only (i) was applicable. He abandoned any further investigation of arelationship between I and Q and began to search for a new, empirical indexthat was directly linked to the weight of calcium carbonate deposited. Ryznarsfurther investigations produced an empirical index:

R = 2pHS pH (1)

Qfpiws-chap1.p65 02/17/2003, 5:17 PM4


Fig. 2. Plot of Langelier index(I)-v-weight of calcium carbonate(Q).

Qfpiws-chap1.p65 02/17/2003, 5:17 PM5


Fig. 3. Plot of Ryznar index(R)-v-weight of calcium carbonate(Q).

Qfpiws-chap1.p65 02/17/2003, 5:17 PM6


The data in Table 2 has been rearranged to show values of R and the newparameters are set out in Table 3.

A plot of the values of the Ryznar Index (R) against the weight of calciumcarbonate (Q) from Table 3 is shown in Fig. 3. It will be seen that a smoothcurve can be drawn through the plot to give a neutral point (zero deposit) atR = 6.2. Ryznars original graph gave the neutral point as R = 6.0. The slightdifference is due to the difference in evaluation mentioned earlier in this section.

A number of proprietary water treatment suppliers have accepted the criterium(R = 6.0) as a basis for the routine control of systems using their treatment.

There is still a moderate amount of scattering of points in Fig. 3 which maybe due to:

(v) Ryznar breaking thermodynamic integrity.(vi) Experimental errors in the test rig.(vii) A combination of both.

Ryznar did not proceed beyond Fig. 3. Having established that a smooth curvecould be drawn linking R and Q, and that a neutral point existed at R = 6.0, heallowed the matter to rest. He did not, for example, publish any further work onmethods of forecasting, or estimating, the weight of calcium carbonate depositedusing calculations based on his index R.

The objective of this section of this book is to provide methods of forecasting,or estimating, the weight of calcium carbonate deposited in systems: then clearlyfurther work must be done on the Ryznar Index if it is to be included in themethods which follow in this book. It is therefore important to investigate, andif possible eliminate, errors which may be arising from (v) and (vi) above.

1.1.3 Revised Evaluation of the Ryznar Index

The first step in a revised evaluation of the Ryznar Index is to restore, as far aspossible, the thermodynamic integrity. This can be achieved by using values ofpHS and pH that have both been adjusted to the temperature (T) in the test rig.

The values of pHS have already been adjusted. The values of pH at 15 Cin Tables 13 are converted to temperature T using the method described byEmerson on pp. 2021 of Ref. [8]. The new values of pH are set out in Table 4,which is a revised version of Table 3.

A plot of the revised data in Table 4 is shown in Fig. 4. It will be seen thata smooth curve can be drawn through the plot. This curve is very similar to thatobtained in Fig. 3 (which has been inserted in Fig. 4 as a dotted line forcomparison) but has been displaced to the right in the diagram to give a newneutral point at R = 7.5.

Qfpiws-chap1.p65 02/17/2003, 5:17 PM7


Fig. 4. Plot of revised Ryznar index(R)-v-weight of calcium carbonate(Q).

Qfpiws-chap1.p65 02/17/2003, 5:17 PM8


It will be a matter for individual water treatment suppliers and plant operatorsto decide whether to accept the thermodynamically improved neutral point ofR = 7.5 as a basis for plant control instead of the older, more familiar R = 6.0discussed in Sec. 1.1.2.

There is still a moderate amount of scattering of points in Fig. 4. In thisrespect, Fig. 4 offers no improvement over Fig. 3. This leads to the conclusionthat the scattering is not due to the thermodynamic status of the data. If thethermodynamic status was a significant explanation there would have been amarked improvement in the closeness of the fit of the points to the curve onmoving from Fig. 3 to Fig. 4. This conclusion is not altogether unexpected sincethe Ryznar Index in Eq. (1) is empirically derived and not the result of a rigidthermodynamic calculation.

Leading on from this conclusion the next logical step is to consider possibleexperimental errors in the test rig.

1.1.4 Experimental Errors

It is considered possible for experimental errors to arise in the test rig for thefollowing reasons:

(viii) In Sec. 1.1.1, it was explained that Ryznar increased the alkalinity of watersamples by the addition of alkali (sodium carbonate or sodium bicarbonate).Following such additions time will be required for the ionic speciescontributing to the alkalinity and pH of the water to undergo internalrearrangement and achieve equilibrium. Very little is known about thistime interval, but it introduces the possibility of the onset of precipitationbeing delayed. This delay could vary from one water to another and thusintroduces an error when comparing results. Thus the fixed conditionsof the test runs may, in fact, be open to some variation.

(ix) When a water is treated with alkali, to increase the scaling potential,it passes through a metastable stage where actual precipitation does nottake place. This metastable stage continues until the water is disturbedand passes into a labile (precipitating) stage by an increase in alkalinityand/or temperature. Here again, the onset of precipitation may be delayedleading to a variation in the conditions of the test run. The existence ofthe metastable stage is demonstrated in many natural occurring waters,which have a positive calcium carbonate saturation index (scaling) butremain stable without precipitation over long periods until the temperatureis raised.

Qfpiws-chap1.p65 02/17/2003, 5:17 PM9


(x) The precipitation of calcium carbonate when water is heated takes placein the bulk of the water. Some precipitate then becomes attached to theheat exchange surface. (This is in direct contrast, for example, to calciumsulphate which crystallises on the heat exchange surface). Under theseconditions some of the precipitate may be carried forward with the flowof water and pass to drain. Thus some of the precipitated calcium carbonatemay be lost and not recorded when the test coil is weighed. Variations inthe recorded weight of calcium carbonate for the reasons just discussedmay be small. But they are significant in comparison with the recordedweights which amount to a modest number of milligrams.

It may be argued that items (viii), (ix), and (x) are only hypotheses, and posethe question Can errors of this type actually arise?. The short answer is Yes.Edwards [9], working in the laboratories of Imperial Chemical Industries Ltd,.in London, was carrying out investigations very similar to Ryznar using a verysimilar test rig. He found that the reproductivity of results was poor. Samples ofwater, prepared to the same specification, and put through the test rig onsuccessive days, gave variable weights of calcium carbonate. It was necessaryto run 5 or 6 tests and take a mean value in order to obtain meaningful results.

Again, a sample of water, treated with inhibitors A, B, C and D, gave resultsindicating an order of merit:

ABCD

but on subsequent runs the order changed:

B A AA B CC D B

etc.

D C D

Again, it was necessary to run 5 or 6 tests and take mean values in order toobtain meaningful results.

It will be seen from Edwards results that the use of the test rig provides ascreening test capable of indicating broad trends in the amount of calciumcarbonate precipitated (and its reduction by using various inhibitors). But theresults are not sufficiently finely tuned to match parameters calculated on anaccurate thermodynamic basis.

Qfpiws-chap1.p65 02/17/2003, 5:17 PM10


To overcome this difficulty the next logical step is to investigate a method forcalculating the weight of calcium carbonate deposited on a thermodynamic basis.

1.2. NEW DATA

The discussions in Sec. 1.1 have extracted from Ryznars work with the test rigall the information likely to be of value in estimating calcium carbonatedeposition. The next step forward is to provide a method of calculating theweight of calcium carbonate deposited, instead of using weights obtained froma test rig. Such a method was not available to Ryznar or Edwards, but is availablenow. It has been applied in the following way:

Ten water analyses have been selected which are typical of the raw waterslikely to be available from natural sources, or municipal supplies, for industrialuse. The analyses are set out in Table 5.

The analyses cover the same broad characteristics as the waters used byRyznar, with one important exception. Because Ryznar increased the alkalinityof his waters, his pH values are high (in the 8.0 to 9.0 range, with a fewexceptions). These pH values are higher than those normally found in the naturalwaters and municipal supplies available to industry. Therefore in Table 5 a lowerpH range (7.0 to 7.9) has been used.

In the original Ryznar test rig waters were maintained at a temperature of95 C in 13 cases, at 70 C in 3 cases, and at 50 C in 5 cases. This range oftemperatures is too narrow to cover the range likely to be encountered in actualplant practice. Therefore in this discussion a temperature range of:

30 C 40 C 50 C 60 C 70 C 80 C

has been selected.For each of the ten waters at each of the six temperatures the values of pHS,

pH, I, and R have been calculated as described in Secs. 1.1.2 and 1.1.3. Fromthe values of I, the weights of calcium carbonate (W) have been calculated bythe method described by Emerson on p. 26 of Ref. [8].

W is expressed as mg/1, a unit which is more useful than the original Q(in mg). Values of W allow weights of calcium carbonate deposits to be calculatedfor any volume throughput of water. The results of the above calculations areset out in Table 6.

In order to obtain a preliminary insight into the relationship between R andW a plot of values at 30 C, 50 C, and 80 C was made in Fig. 5. It will beseen that a smooth curve can be drawn for each temperature, and the wholetemperature range covered by a family of curves. It is therefore worthwhile

Qfpiws-chap1.p65 02/17/2003, 5:17 PM11


Fig. 5. Plot of revised Ryznar index(R)-v-weight of calcium carbonate(W).

Qfpiws-chap1.p65 02/17/2003, 5:17 PM12


exploring the mathematics of Table 6 in further detail. It can be shown by adetailed mathematical analysis of Table 6 that the relationship between R and Wcan be expressed as:

W = exp(AR + B) (9)and that for individual temperatures the best fit equations are:

30 C W = exp(1.75R + 14.79) (10)40 C W = exp(1.66R + 13.80) (11)50 C W = exp(1.47R + 12.54) (12)60 C W = exp(1.13R + 10.28) (13)70 C W = exp(1.17R + 10.33) (14)80 C W = exp(1.24R + 10.65) (15)

A further examination of Eqs. (10) to (15) shows that the values of A arelinear in relation to temperature and the best fit equation is:

A = 0.015T 2.22 (16)Similarly, the values of B are linear in relation to temperature and the best

fit equation is:

B = 0.11T + 18.21 (17)Substituting Eqs. (16) and (17) in Eq. (9) gives a universal equation:

W = exp[(0.015T 2.22)R 0.11T + 18.21] (18)For practical purposes it may be easier to use Eq. (18) in the logarithmic

form:

lnW = (0.015T 2.22)R 0.11T + 18.21 (19)or logW = (0.007 0.97)R 0.048T + 7.92 (20)

1.2.1. Use in the Field

When applied to practical problems in the field, Eqs. (18) or (19) or (20) willgive the best value of W calculated on the basis of R. The calculated value of Wis the maximum weight of calcium carbonate that can be deposited from 1 litre

Qfpiws-chap1.p65 02/17/2003, 5:17 PM13


of water. But in practice in an actual system it could be less for the followingreasons.

(xi) If the water velocity is high, the retention time in the system may be toolow to allow all deposition to be completed within the system.

(xii) Because the precipitation of calcium carbonate takes place in the bulk ofthe water (rather than on the heat exchange surfaces) precipitated calciumcarbonate may be carried out of the system by the flow of water.

(xiii) Retention of precipitated calcium carbonate can be influenced by theroughness of the metal surfaces, and the geometry of the system (e.g. sharpbends).

(xiv) There may be temperature variations within the system, so that some partsmay not be as high as T. In these lower temperature regions precipitationwill be reduced.

Having listed these points it may be stated that the calculated value of Wrepresents the highest weight of calcium carbonate that can be deposited, andthus represents the maximum fouling likely to be encountered.

Another practical aspect that must be considered is the speed and ease withwhich Eq. (18), or (19), or (20) can be used by a water technologist. Whetherthe technologist is advising a design team on the choice between several possiblewater supplies, or carrying out site tests with portable analytical equipment, theability to produce a quick answer has obvious advantages. To assist in this, atable giving values of W against R is set out in Table 7. It is used as follows:

(xv) From a water analysis at atmospheric temperature (15 C) take the valuesof Ca, Alk, and DS. Use them to calculate the value of pHS at T byusing Eq. (6) evaluated as described in Sec. 1.1.2. To assist in thisevaluation values of:

p[Ca2+] are given in Table 8p[Alk] in Table 9

pK2 and pKS in Table 10.

Values of (DS)0.5/100 are calculated by simple arithmetic.(xvi) From a water analysis at atmospheric temperature (15 C) take the values

of pH and Alk and use them to convert pH to the pH at T, using themethod described by Emerson on p. 20 of Ref. [8].

(xvii) From (xv) and (xvi) calculate the Ryznar Index at T.R = 2pHS pH (1)

Qfpiws-chap1.p65 02/17/2003, 5:17 PM14


(xviii) In Table 7, locate the sector containing the value of R obtained in (xvii).Scan the sector heading horizontally and locate the column headed withthe value of R.

(xix) At the left hand edge of the table scan vertically to find T. Now scanhorizontally to meet the column selected in (xviii).

(xx) Where the two intersect is the value of W.

ExampleWater analysis at 15 C

Ca = 300 mg/l CaCO3Alk = 250 mg/l CaCO3DS = 450 mg/l as suchpH = 7.8.

Temperature in system = 60 C.Evaluate Eq. (6) as:

[email protected]

21.0100

)DS()[email protected](40.1pp

9Tablefrom30.2]Alk[p8Tablefrom53.2]Ca[p

S

5.0S2

2

o

o

=

=

=

=

=+

KK

From Table 20 at 15 C in Ref. [8]Alk = 250 gives C = 520.pH = 7.8.

From Table 74 at 60 C in Ref. [8]Alk = 250 gives pH = 7.6 @ 60 C.C = 520

Evaluate Eq. (1) as:R = 2pHS pH = 2 6.44 7.6 = 12.88 7.6

= 5.28 @ 60 C.

In Table 7, locate the sector headed R 5.0 to 5.9.

Qfpiws-chap1.p65 02/17/2003, 5:17 PM15


Select the column headed 5.3.At the left hand edge find T = 60 C.The vertical column and horizontal line meet at W = 101 mg/l CaCO3.

This figure may be multiplied by the rate of water flow and the time theplant is on load to give total calcium carbonate fouling.

1.2.2. Margin of Error

Before concluding the discussion of the use of Table 7 it will be useful to try toaccess the margin of error likely to be encountered

To make this assessment five waters from Table 5 have been selected asrepresentative of the range of waters examined. They are Nos: 22, 25, 26, 29and 30.

Similarly, three temperatures from Table 6 have been selected as representativeof the range of temperatures examined. They are 30 C, 60 C, and 80 C.

Combining these two pieces of data, the values of R and W as recorded inTable 6 have been listed. The corresponding values of W from Table 7 havebeen added alongside. The difference between corresponding values of W havebeen listed and expressed as a percentage. The details are set out in Table 11.

In setting up Table 11 the values of W from Table 6 have been taken as thetrue value, since they were calculated direct from individual water analyses ona sound thermodynamic basis.

It will be seen from Table 11 that the errors vary between +50% and 27%.In an ideal situation the error should be zero. How do the errors arise and whatis their significance?

Equation (18), on which Table 7 is based, is a best fit derived fromEqs. (10) to (17) which are themselves a best fit to a set of data. Therefore,there will be cases where the value of a parameter calculated from one of theequations will be different from the true value.

The errors may be positive or negative, and they will also be cumalativebecause any error arising from Eqs. (10) to (15) will be combined with anyerrors arising from Eqs. (16) and (17).

It can be shown that the error of +50% mentioned above can be caused byon error of 0.2 in the value of R, and the error of 27% caused by an error of+0.5 in the value of R. Errors of this magnitude can be caused by errors of theorder of 0.15 in the values of pHS and pH: errors which are within the toleranceapplicable to normal plant practice.

To assess the significance of the errors in Table 11 it is necessary to comparethem with errors which arise from variations in water analyses due to natural

Qfpiws-chap1.p65 02/17/2003, 5:17 PM16


causes. To investigate this aspect, water analyses from two different locationshave been selected. Each water supply possesses characteristics that are likelyto lead to scaling. For each supply, the mean, maximum and minimum analyseshave been recorded. During the progress of any project the normal procedure isto base calculations for design, operation, and control of a system on the meanwater analysis. But during the working life of the system it will receive watervarying between the minimum and maximum analyses.

To represent these real-life conditions W has been calculated at 30 C, 50 C,and 80 C for the mean, maximum, and minimum analyses of both supplies. Thedifference in values between mean and maximum analyses, and between mean andminimum analyses have been recorded as errors. The results are set out in Table 12.

It will be seen that the errors recorded in Table 12 vary between +190% and95%. This range is much greater than those recorded in Table 11. ThereforeTable 7 may be used as a useful working estimate since any errors it mayproduce will be far outweighed from those arising from natural causes.

1.3. THE LANGELIER INDEX

It was stated earlier in Sec. 1.1.2 that Ryznar had investigated a possible relation-ship between Q and I, but had abandoned this line of investigation. In view ofthe relationship between R and W subsequently produced in Sec. 1.2 the questionarises Is it possible to produce a similar relationship between I and W?

To explore this possibility a plot of values for I and W at 30 C, 50 C, and80 C (as recorded in Table 6) was made in Fig. 6. It will be seen from the plotin Fig. 6 that a smooth curve can be drawn for each temperature, and that thewhole range can be covered by a family of curves. It is therefore worth exploringthe mathematics of the relationship between I and W in further detail.

It can be shown by a detailed mathematical analysis that the relationshipbetween I and W can be expressed as:

W = exp(YI + Z) (21)and that for individual temperatures the best fit equations are:

30 C W = exp(4.30I + 0.71) (22)40 C W = exp(3.73I + 0.69) (23)50 C W = exp(3.50I + 0.69) (24)60 C W = exp(2.23I + 1.70) (25)70 C W = exp(2.92I + 0.69) (26)80 C W = exp(2.97I + 0.37) (27)

Qfpiws-chap1.p65 02/17/2003, 5:17 PM17


Fig. 6. Plot of Langelier index(I)-v-weight of calcium carbonate(W).

Qfpiws-chap1.p65 02/17/2003, 5:17 PM18


A further examination of Eqs. (22) to (27) shows that the values of Y arelinear in relation to temperature and the best fit equation is:

Y = 0.03T + 5.17 (28)Similarly, the values of Z are linear in relation to temperature and the best

fit equation is:

Z = 0.0004T + 0.714 (29)Substituting Eqs. (28) and (29) in Eq. (21) gives a universal equation:

W = exp[(0.03T + 5.17)I 0.0004T + 0.714] (30)For practical purposes it may be easier to use Eq. (30) in the logarithmic

form:

lnW = (0.03T + 5.17)I 0.0004T + 0.714 (31)

or logW = (0.014T + 2.41)I 0.0002T + 0.333 (32)

1.3.1. Use in the Field

When applied to practical problems in the field Eq. (30), (31), or (32) will givethe best values of W calculated on the basis of I. The calculated value of W isthe maximum weight of calcium carbonate that can be deposited from 1 litre ofwater.

But in practice, in a actual system it could be less for the reasons alreadygiven in items (xi) to (xiv) in Sec. 1.2.1.

Also, as in Sec. 1.2.1, there is a need for a fast and easy method for evaluatingEq. (30), or (31), or (32). To assist in this, a table giving values of W against Iis set out in Table 13. It is used as follows:

(xxi) From a water analysis at atmospheric temperature (15 C) take the valuesof Ca, Alk, and DS. Use them to calculate the value of pHS at T asalready described in item (xv) of Sec. 1.2.1.

(xxii) From a water analysis at atmospheric temperature (15 C) take the valuesof Alk and pH and use them to convert the pH to the value at T asalready described in item (xvi) of Sec. 1.2.1.

(xxiii) From (xxi) and (xxii) calculate the Langelier index at T.

I = pH pHS (5)

Qfpiws-chap1.p65 02/17/2003, 5:17 PM19


(xxiv) In Table 13, locate the sector containing the value of I obtained in (xxiii).Scan the sector heading horizontally and locate the column headed bythe value of I.

(xxv) At the left hand edge of the table scan vertically to find T. Now scanthis line horizontally to meet the column selected in (xxiv).

(xxvi) Where the two intersect is the value of W.

ExampleWater analysis at 15 C

Ca = 300 mg/l CaCO3Alk = 250 mg/l CaCO3DS = 450 mg/l as suchpH = 7.8.

Temperature in system = 60 C.Evaluate Eq. (6) as:

)[email protected](40.1pp9Tablefrom30.2]Alk[p8Tablefrom53.2]Ca[p

S2

2

o

=

=

=+

KK

21.0100

)DS( 5.0=

[email protected] o=

From Table 20 at 15 C in Ref. [8]

Alk = 250 gives C = 520.pH = 7.8

From Table 74 at 60 C in Ref. [8]

Alk = 250gives pH = 7.6 @ 60 C.C = 520

Evaluate Eq. (5) as:

I = 7.6 6.44 = 1.16.

Qfpiws-chap1.p65 02/17/2003, 5:17 PM20


In Table 13, find the sector headed 1.1 to 2.0 and select the column headed1.2. At the left hand edge find T = 60 C The vertical column and horizontalline meet at:

W = 114 mg/l CaCO3.

This number, multiplied by the rate of water flow and the time the plant ison load, will give the total calcium carbonate fouling.

1.3.2. Margin of Error

Before concluding the discussion on the use of Table 13, it will be useful to tryto assess the margin of error likely to be encountered. To make this assessmentthe proceedure already described in Sec. 1.2.2 has been adopted. Analyses Nos.22, 25, 26, 29 and 30 from Table 5 have been taken and temperatures 30 C,50 C, and 80 C from Table 6.

Combining these two pieces of data, the values of I and W as recorded inTable 6 were listed. The corresponding values of W from Table 13 were addedalongside. The difference between corresponding values of W were then listedand expressed as a percentage. The details are set out in Table 14.

In setting up Table 14 the values from Table 6 were regarded as the truevalues, since they were calculated direct from individual water analyses on asound thermodynamic basis.

It will be seen from Table 14 that the error varies between +36% and 26%.This is a narrower range than that exhibited by R in Sec. 1.2.2. How do theseerrors arise and what is their significance?

The discussion in Sec. 1.2.2 concerning Eqs. (10) to (18), Table 7, and theerrors recorded in Table 11, also apply here concerning Eqs. (21) to (30),Table 13, and the errors recorded in Table 14. It can be shown that the errors of+36% and 26% mentioned above, can be caused by errors of 0.04 and +0.06in the evaluation of I. These errors can arise from errors of the order of 0.03 inthe values of pH and pHS: errors which are well within the tolerance applicableto the evaluation of these parameters.

As already stated in Sec. 1.2.2 this is an important point which must not beoverlooked when considering the magnitude of errors in the value of W, as ameans of assessing the magnitude of errors in the procedure under discussion.

To assess the significance of errors in Table 14 the procedure already describedin Sec. 1.2.2 has been adopted. The same two waters listed in Table 12 havebeen used again and the values of W for values of I at 30 C, 50 C, and 80 Care recorded. The results are set out in Table 15.

Qfpiws-chap1.p65 02/17/2003, 5:17 PM21


It will be seen that the errors recorded in Table 15 vary between + 463% and100%. This range is much greater than the range recorded in Table 14. Thereforethe errors arising from Table 13 can be ignored as likely to be outweighed byerrors arising from natural causes.

1.4. CHOICE BETWEEN LANGELIER AND RYZNAR

In this book two methods have been developed for estimating the weight ofcalcium carbonate deposited in a system. One method is based on the RyznarIndex (R) and the other on the Langelier Index (I). The existence of two possiblemethods of estimation at once raises the question, Which one shall be used?for any specific problem.

To assist in answering this question selected values of W, based on R andderived from Table 7, and selected values of W, based on I and derivedfrom Table 13, are set out together in Table 16. The values based on I havebeen taken as the standard: the difference between the values based on R andthe values based on I have been recorded in Table 16 and expressed as apercentage.

As already stated in Sec. 1.3.1 values of W based on I are considered to besuperior to values based on R. Calculations based on I have a higherthermodynamic integrity than those based on R. (R is an empirically derivedparameter, and this is considered to be a weak point). Thus values based on I(Langelier) is the preferred method.

But some water treatment technologists and plant operators may have alreadyestablished methods of treatment and control based on R, and would prefer tocontinue using R as a basis for estimating W. If this preference is followed, itwill be seen from Table 16 that errors between +38% and 25% may beencountered. But these degrees of error are small compared with errors likely tobe introduced by natural causes. See Secs. 1.2.2 and 1.3.2.

The final decision will depend on the degree of tolerance that can be acceptedwhen making a forecast for any given installation.

In the case of a small project, or one handling a low grade product, atolerance between +38% and 25% may be acceptable. A calculation for Wbased on the value of R would be attractive to a technologist or operatorwho already has embedded in his methods of treatment and control calculationsbased on R.

But for a large project, or one handling a sophisticated and expensive product,a more accurate value for W, based on the value for I, will be required.

Qfpiws-chap1.p65 02/17/2003, 5:17 PM22


1.5. THE SPECIAL CASE OF RECIRCULATING SYSTEMS

Under the proviso stated in Sec. 1.1.1 the whole of the work discussed up tothis point is restricted to once-through, closed systems. However, as industrialinstallations often include recirculating systems, they must now be considered.

1.5.1. Closed Recirculating Systems

Some industrial cooling systems take the form of a primary closed ring in whichwater continuously recirculates. Heat, which needs to be dissipated, is absorbedby the water in a heat-exchanger and then discharged from the water by a secondheat-exchanger which itself is cooled by a secondary cooling system.

In the primary system the volume of water used for the initial filling (or re-filling after draining for maintenance) will deposit an initial quantity of calciumcarbonate according to the temperature rise experienced. Once this initialprecipitation has taken place, no more calcium carbonate will be deposited.

The quantity of calcium carbonate can be estimated by the methods alreadydescribed, from the analysis of the water and the temperature in the system. Inthe calculation, the volume of water in the closed system replaces the flow ratefor a once-through system.

1.5.2. Open Recirculating Systems

The open recirculating cooling system, incorporating an evaporative coolingtower, is widely used in industry. A special feature of this type of system is theincrease in the concentration of dissolved salts in the recirculating water.

The normal procedure for this type of system is to operate with a pre-determined number of concentrations in the recirculating water (by controlledpurging from the system) coupled with treatment with an inhibitor. Eachinhibitor varies in the quantity of calcium carbonate it can hold in solutionbefore precipitation occurs. This factor determines the optimum number of con-centrations to be maintained in the recirculating water. Therefore the numberof concentrations and the dosage of inhibitor are usually given to the plantoperator by the water treatment supplier.

In this context, it will be useful to estimate the weight of calcium carbonatethat will be deposited by a given water in a given plant at a given temperatureif the system is operated at various number of concentrations. This informationwill assist in selecting the most appropriate treatment to inhibit fouling, andthe number of concentrations compatible with the selected treatment. Also, this

Qfpiws-chap1.p65 02/17/2003, 5:17 PM23


information can be used to justify the cost of treatment by giving an indicationof the loss of thermal efficiency if the system is operated without treatment.

In order to estimate the fouling (whether on the basis of Table 7 or on thebasis of Table 13) it is necessary to modify the methods previously describedfor calculating pHS and pH.

pHSThe value of pHS for the make-up water at T, the temperature in the system isfirst calculated as in (xv) in Sec. 1.2.1. If the system is to operate with nconcentrations in the recirculating water, the value of pHS in the make-up wateris converted to pHS in the recirculating water by means of the equation describedby Emerson [5]:

)upmake(.)recirc(100

DS)1(log2pHpH5.0

5.0SS

+= nn

(33)

pHThe value of pH in the recirculating water at T, the temperature in the system,at n concentrations is calculated from the alkalinity of the make-up waterusing the method described on p. 27 of Ref. [8].

With the new values of pHS and pH new values of R or I can be calculatedand a new value for W read off from Table 7 or Table 13.

ExampleMake-up water analysis at 15 C

Ca = 120 mg/l CaCO3Alk = 80 mg/l CaCO3DS = 180 mg/l as such.

Temperature in system = 40 C.Number of concentrations in system = 3.From Eq. (6)

)10TablefromC 40at52.822.10(70.1pp9Tablefrom80.2]Alk[p8Tablefrom92.2]Ca[p

S2

2

=

=

=+

oKK

13.0100

)DS( 5.0=

.55.7pHS =

Qfpiws-chap1.p65 02/17/2003, 5:17 PM24


Convert to recirculating water

pHS = 7.55 2 log 3 + 0.13(30.5 1)= 7.55 0.95 + 0.13(1.73 1)= 7.55 0.95 + 0.09= 6.69.

Alk in make-up water = 80.In circulating water = 3 80 = 240.From p. 27 of Ref. [8]C = 2Alk = 2 240 = 480.From Table 63 of Ref. [8]pH = 8.2

R = 2pHS pH = 2 6.69 8.2 = 13.38 8.2 = 5.18.

From Table 7

W = 159 mg/l CaCO3 for water in system= 159/3 = 53 mg/l CaCO3 for make-up water.

Alternatively:

I = pH pHS = 8.2 6.69 = 1.51.

From Table 13

W = 490 mg/l CaCO3 for water in system= 490/3 = 163 mg/l CaCO3 for make-up water.

The values of W in the make-up water may be multiplied by the rate ofadding water to the system and the time that the plant is on load to give thetotal calcium carbonate fouling.

In considering the values of W above, the comments in Sec. 1.4 are stillapplicable.

Qfpiws-chap1.p65 02/17/2003, 5:17 PM25

Chapter 2

CALCIUM SULPHATE FOULING

The need for discussing calcium sulphate fouling may not, at first, be apparent.It is therefore useful to outline the circumstances in which calcium sulphatefouling may be anticipated.

The fouling may be anticipated with water supplies which are high in sulphate.Typical examples are deep well waters, or saline waters. A similar, but notidentical source, is treated effluent which is offered for industrial coolingpurposes, especially if effluent has been derived from a process involving theuse of sulphuric acid or sulphates.

Waters high in calcium hardness and alkalinity may be treated with sulphuricacid in order to reduce the alkalinity to a level which will not promotecalcium carbonate fouling. But in doing so, the natural sulphate of the watermay be artificially boosted to a point which will now promote calcium sulphatefouling.

A similar difficulty may be encountered with waters which will not promotecalcium sulphate fouling in their natural state, but if used in a recirculatingcooling tower (where a concentration effect operates) may be artificially boostedto a point which will now promote calcium sulphate fouling in the circulatingwater.

In the light of the above discussion it is strongly recommended that, whenevera new system is being designed, or problems in an existing system is underinvestigation, the possibility of calcium sulphate fouling should be included. Itshould not be assumed, merely by visual inspection of water analyses, that suchfouling will not arise.

2.1. CALCIUM SULPHATE SATURATION INDEX

The calcium sulphate saturation index (IS) is defined by Emerson [10] as:

++= +50

)DS(]SO[p]Ca[pp5.0

24

2KIS (34)

.mequilibriuat ))(SO(CaWhere 242 +=K (35)

27

Qfpiws-chap2.p65 02/17/2003, 5:17 PM27


Equation (34) may be evaluated by taking values of:pK from Table 17 (which is based on solubility data for calcium sulphate

by Seidell [11] and Booth and Bidwell [12])p[Ca2+] from Table 8p[SO24 ] from Table 18.

Values of (DS)0.5/50 are calculated by simple arithmetic.

ExampleCa = 1000 mg/l CaCO3SO4 = 1700 mg/l Na2SO4DS = 2800 mg/l as such

Temperature = 90 C.

98.406.192.100.2

50)DS(

]p[SO81TableFrom]p[Ca8TableFrom02.5C90@p17TableFrom

5.0

24

2

=

=

==

+oK

IS = 5.02 4.98 = +0.04.

The positive value of I indicates a water supersaturated to calcium sulphate,which will cause fouling. If the value was negative there would be no depositionof calcium sulphate.

Having established a method for calculating IS it may now be utilised tocalculate the weight of calcium sulphate deposited to cause fouling.

2.2. CALCULATING THE WEIGHT OFCALCIUM SULPHATE

For any given water at any given temperature:

Let initial calcium = A mg/l as CaCO3 (36)Let initial sulphate = B mg/l as Na2SO4. (37)

After precipitation of calcium sulphate:

Let fraction of calcium remaining = a (38)Let fraction of sulphate remaining = b. (39)

Qfpiws-chap2.p65 02/17/2003, 5:17 PM28

Calcium Sulphate Fouling 29

Thus:

Final calcium = aA mg/l as CaCO3 (40)Final sulphate = bB mg/l as Na2SO4. (41)

From Eqs. (36) and (40):

Loss of calcium = A aA = A(1a) mg/l as CaCO3 (42)

4CaSOas1/mg)1(100136

aA = (42a)

= 1.36 A(1a) mg/l as CaSO4 (42b)From Eqs. (37) and (41)

Losss of sulphate = B bB = B(1b) mg/l as Na2SO4 (43)

4CaSOas1/mg)1(142136 bB = (43a)

= 0.96 B(1b) mg/l as CaSO4. (43b)

Since loss of calcium must be equal to loss of sulphate when both areexpressed in the same unit:

From Eqs. (42b) and (43b):

.)1()1(42.1)1()1(

96.036.1

)1(96.0)1(36.1

a

bBA

a

bBA

bBaA

=

=

=

For the initial water, the calcium sulphate saturation index may be obtainedby substituting Eqs. (36) and (37) in Eq. (34):

++=50

DSppp5.0

BAKIS (45)

For the final water (i.e. after precipitation of calcium sulphate) the saturationindex may be obtained by substituting Eqs. (40) and (41) in Eq. (34):

++=50

DSppp5.0

bBaAKIS (46)

(44a)

(44)

(44b)

Qfpiws-chap2.p65 02/17/2003, 5:17 PM29


But since the water has already precipitated calcium sulphate, and thereforereached a state of equilibrium, IS has become zero. Thus,

)pp(50

DSppp

50DSppp0

5.0

5.0

baBAK

bBaAK

+

++=

++=

Substituting Eq. (45) in Eq. (46b) gives:

ba

abIab

abIabI

baI

I

I

S

S

1010

)log()log(

)(p)pp(0

S

S

S

S

=

=

=

+=

=

+=

(The calculation set out above assumes that the loss of DS by the precipitationof calcium sulphate does not make a significant difference in the value of 50

DS 5.0 ).Substituting Eq. (44b) in Eq. (47e) gives:

0)10(42.1142.1

)10(42.1)(42.1

)1()10(42.1)10(

)1(

)01()1(

b101

)1(42.1

S

S

S

S

S

S

2

2

2

=

+

=

==

=

=

=

BA

BAbb

bbB

AB

bA

bbbbB

bAb

bbb

bb

bB

A

I

I

I

I

I

I

(46a)

(46b)

(47)(47a)(47b)(47c)(47d)

(47e)

(48)

(48a)

(48b)

(48c)

(48d)

(48e)

Qfpiws-chap2.p65 02/17/2003, 5:17 PM30


Expressed in more general terms Eq. (48e) becomes:

0)10(SO

Ca42.11SO

Ca42.1S

44

2=

+ Ibb (49)

By substituting values for 4SOCa

and IS into Eq. (49), it can be solved for valuesof b. Only real, positive values are retained for use: negative or imaginaryvalues have no physical significance.

The value of b is then substituted in Eq. (43b) to give the loss of calciumsulphate. The value of b can also be substituted in Eq. (47e) to give a valuefor a, which, in turn, can be substituted in Eq. (42b) to give an alternativefigure for the loss of calcium sulphate. Ideally, the two figures for the loss ofcalcium sulphate should be identical.

To avoid the time and labour required to solve Eq. (43b), Table 19 has beenprepared from which values of b can be read off for various values of

4SOCa

andIS. This offers a procedure suitable for field use.

2.3. USE IN THE FIELD

The procedure outlined below yields a calculated figure for the maximum weightof calcium sulphate precipitated to cause fouling. In practice, the figure may belower due to the effect of restrictions similar to those described in items (xi),(xiii) and (xiv) in Sec. 1.2.1.

(xxvii). From a water analysis at atmospheric temperature take the values ofCa, SO4 and DS. Use them to calculate the ratio 4SO

Ca, and the value of IS at T

as described in Sec. 2.1. If IS is negative there will be no fouling and furthercalculation is unnecessary.

(xxviii) In Table 19, run down the left hand edge to find the value of4SO

Ca.

If the value calculated from the water analysis does not exactly fit the values inthe tables, use the nearest value.

(xxix) Follow that line horizontally across the tables (through 19/1, 19/2,etc.) to find the column headed with the value of IS. Where the horizontal lineand vertical column meet is the value of b.

Example

Ca = 1000 mg/l CaCO34SO

Ca ratio = 17001000

SO4 = 1700 mg/l Na2SO4 = 0.59DS = 2800 mg/l as suchT = 90 C

Qfpiws-chap2.p65 02/17/2003, 5:17 PM31


From Table 17 From Table 8pK @ 90 C = 5.02 p[Ca2+] = 2.00

From Table 18p[SO24 ] = 1.92

50)DS( 5.0 = 1.06

4.98

IS = 5.02 4.98 = +0.04.

As the index is positive, the water will deposit calcium sulphate at 90 C.In Table 19, find

4SOCa

= 0.6 (the nearest value to 0.59). Scan right tofind IS = 0.04 in Table 19/1. The horizontal line and vertical column meet atb = 0.96.

From Eq. (43b)Loss of sulphate = 0.96 1700 (10.96)

= 0.96 1700 0.04 = 65 mg/l CaSO4

From Eq. (47e)95.0

96.091.0

96.010 04.0

===

a

From Eq. (42b)Loss of calcium = 1.36 1000 (10.95)

= 1.36 1000 0.05 = 68 mg/l CaSO4

Ideally the two loss figures should be identical, since they are both expressedin terms of CaSO4. The difference is due to assuming that the change in DSon precipitation of calcium sulphate made no significant difference to the valueof 50

DS 5.0 (as discussed in Sec. 2.1) and to the values of b in Table 19 beingrounded off to two places of decimals.

For all practical plant purposes the two values are sufficiently close to alloweither value to be used for design or performance forecast purposes.

This value may be multiplied by the rate of water flow through the systemand the time the plant is on load, to estimate the total calcium sulphate fouling.

2.4. THE SPECIAL CASE OF RECIRCULATING SYSTEMS

The comments made in Sec. 1.5 concerning recirculating systems also applyhere. The only item that needs to be discussed in detail is the effect of

Qfpiws-chap2.p65 02/17/2003, 5:17 PM32


concentration, in open recirculating systems, on the calcium sulphate saturationindex.

For any given water at any given temperature the calcium sulphate saturationindex is given by Eq. (34):

++= +50

)DS(]SO[p]Ca[pp5.0

24

2S KI

If the water is now allowed to concentrate n times in an open recirculatingsystem, the conditions for the circulating water become:

50)DS()1(log2

50)DS()1(p2

50)DS()1(p2(

50)DS(]SO[p]Ca[pp

,

50)DS(p2]SO[p]Ca[pp)(

50)DS(]SO[p]Ca[pp)(

5.05.0

S

5.05.0

S

5.05.0

5.024

2

5.024

2S

5.024

2S

+=

=

+

++=

+++=

++=

+

+

+

nnI

nnI

nnK

nnKI

nnnKI

n

n

The use of Eq. (50d) is illustrated in the following example:

ExampleInitial water analysis:

Calcium = 1500 mg/l CaCO3 4SO

Ca ratio

Alkalinity = 500 mg/l CaCO3 83.018001500

==

Sulphate = 1800 mg/l Na2SO4Dissolved Solids = 2800 mg/l as such.

This water is to be treated with sulphuric acid to reduce the alkalinity to 20mg/l CaCO3, and then used as make-up to a recirculating cooling system at atemperature of 60 C and operating at a concentration factor of 6.0.

The following changes take place:

Loss of alkalinity = 50020 = 480 mg/l CaCO3Corresponding gain in sulphate = 480 1.42 = 682 mg/l Na2SO4 New sulphate = 1800 + 682 = 2482 mg/l Na2SO4.

(50)

(50a)

(50b)

(50c)

(50d)

(34)

Qfpiws-chap2.p65 02/17/2003, 5:17 PM33


Loss of dissolved solids due to loss of alkalinity = 480 mg/l CaCO3Gain of dissolved solids due to gain of sulphate = 682 mg/l Na2SO4 Nett gain in dissolved solids = 682 480 = 202 mg/l as such New dissolved solids = 2800 + 202 = 3002 mg/l as such.

The make-up water to the system therefore becomes:

Calcium = 1500 mg/l CaCO34SO

Ca ratio

Alkalinity = 20 mg/l CaCO3 60.024821500

==

Sulphate = 2482 mg/l Na2SO4Dissolved Solids = 3002 mg/l as such

From Table 17

pK @ 60 C = 4.74 From Table 8p[Ca2+] = 1.82From Table 18p[SO24 ] = 1.76

50)DS( 5.0

= 1.10

4.68

For the make-up water IS = 4.74 4.68 = +0.06For the recirculating water, Eq. (50d) applies:

02.060.162.1

)10.1()45.1(56.106.050

79.54)145.2(78.0206.050

3022)16(6log206.0)(5.0

5.0

+=

+=

++=

++=

++=nSI

From Table 19/1

98.0gives02.0)(and60.0SOCa

4=+== bI nS

Qfpiws-chap2.p65 02/17/2003, 5:17 PM34


From Eq. (43b)Loss of sulphate = 0.96 6 2482 (1-0.98)

= 0.96 6 2482 0.02= 286 mg/l CaSO4

This is equivalent to 6286

= 48 mg CaSO4 for each litre of water entering thesystem.

An alternative calculation using Eq. (47e) gives:

98.098.096.0

98.01010 02.0)(

====

ba

nSI

Loss of calcium = 1.36 6 1500 (10.98)= 1.36 6 1500 0.02= 245 mg/l CaSO4.

This is equivalent to 245/6 = 41 mg CaSO4 for each litre of water enteringthe system.

The reason for the differences between the two calculated values for calciumsulphate fouling has already been discussed in Sec. 2.3. For practical plantpurposes the two values are sufficiently close to allow either value to be usedfor design or performance forecast purposes.

Since the fouling has been expressed in terms of water entering the system,the question may be raised as to why calculations have not been based on thesaturation index of the make-up water and then simply multiplied by 6 (thevalue of n).

It will be seen in the Example already worked out that IS = +0.06 forthe make-up water and

4SOCa

= 0.60. Using these values in Table 19/1 givesa value of b = 0.94.

On this basis, the loss of sulphate = 0.96 2482 (10.94)= 143 mg CaSO4 per litre.

The alternative calculation gives a = 94.010 06.0

= 0.93and loss of calcium = 1.36 1500 (10.93)

= 142 mg CaSO4 per litre.

This appears to be very good agreement. But it cannot be accepted becausecalculations based on the make-up water do not allow the full influence ofdissolved solids to be exercised on the ionic equilibria involved in the circulatingwater. This leads to loss of thermodynamic integrity, and therefore, the methodcannot be accepted.

Qfpiws-chap2.p65 02/17/2003, 5:17 PM35

Chapter 3

CALCIUM PHOSPHATE FOULING

The need for discussing calcium phosphate fouling arises from the fact thatthere has been an increase in the phosphate content of water supplies and hencean increase in the risk of calcium phosphate fouling in industrial water systems.

The increased use of phosphate fertilisers in agriculture has led to an increasein phosphate in waterways. Following heavy rain, fertiliser is washed from thesurface of fields into adjoining streams, which in turn feed rivers from whichpublic water supplies are drawn. This introduction of phosphate into generalwater supplies is seasonal, since fertilisers are more usually applied to fields inSpring, when seed is sown and new crops planted out.

There is also a meteorological factor since the coincidence of heavy Springrains with agricultural planting provides a means of washing the surface offields at the time fertiliser has been applied.

The use of phosphates in industrial processes and the inclusion of phosphatesin detergents is another source of phosphate entering industrial systems. Effluentsfrom such processes, which have been treated on site and accepted by a RiversAuthority for discharge into a stream, will still carry some phosphate. Similarly,effluent which has been accepted by a local sewage work for treatment, andsubsequently offered to industry for cooling purposes will still carry somephosphate.

Although step are being taken to reduce the amount of phosphate in watersupplies, complete freedom from phosphate cannot be assumed. It is thereforerecommended that whenever a new system is being designed, or a problem inan existing system investigated, an assessment of calcium phosphate foulingshould be included. Mere visual inspection of water analysis should not beaccepted as sufficient.

3.1. CALCIUM PHOSPHATE SATURATION INDEX

Following the basis of the definition of the saturation index for calcium sulphategiven in Sec. 2.1, the saturation index for calcium phosphate may be similarly

37

Qfpiws-chap3.p65 02/17/2003, 5:17 PM37


defined as:

)]PO(p2)Ca(p3[KpI 342Sp + += (51)where

234

32S )PO()Ca( +=K (52)

at equilibrium.In evaluating Eq. (51) values for calcium can be obtained from a water

analysis, but values for phosphate cannot be obtained so easily. The analyticaltest for phosphate gives phosphates in all forms present in the water, whereasEq. (51) requires only that portion of the total phosphate present as theorthophosphate ion. Clearly, some form of conversion is needed.

The necessary conversion has been provided by Green and Holmes [13].Starting with the equations:

.)POH()POH()HPO()PO()Phos()HPO(

)PO()H(

)POH()HPO()H(

)POH()POH()H(

434224

34

24

34

3

42

24

2

43

421

+++=

=

=

=

+

+

+

K

K

K

These were re-arranged to give:

.)H()H()H()Phos()PO( 321212133213

4 KKKKKKKKK

+++=

+++ (57)

Because the expression containing the equilibrium constants is long andcumbersome it has, in this book, been replaced by the abbreviation:

.)H()H()H( 32121213321

KKKKKKKKKE

+++=

+++ (58)

Substituting Eq. (58) in Eq. (57) gives:.))(Phos()PO( 34 E= (59)

Substituting Eq. (59) in Eq. (51) gives:

.)](p2)Phos(p2)Ca(p3[p 2Sp EKI ++= + (60)

(56)

(55)

(54)

(53)

Qfpiws-chap3.p65 02/17/2003, 5:17 PM38

Calcium Phosphate Fouling 39

For any given water at any given temperature at equilibrium Ip becomes zeroand, for these conditions, Eq. (60) can be written as:

.)(p2p)Phos(p2)Ca(p3 S2 EK =++ (61)

Taking values for calcium and Phos from water analyses, and values of KSfrom the literature, Green and Holmes calculated values of (E) at equlibriumconditions. Using these values, and values of K1, K2, and K3 from the literaturein Eq. (58), they then calculated the value of (H+) at equilibrium and henceobtained pHS. Green and Holmes did not proceed beyond this point as theirmain interest was to establish a method for determining the values of pHS as anaid to controlling phosphate treatments of boiler feed waters.

To facilitate these calculations Green and Holmes set up tables to allowvalues of pHS at various temperatures to be read off from analytical values ofcalcium and Phos.

In setting up their tables Green and Holmes used values for pK1 based onNims [16], values for pK2 based on Bates and Acree [17], and values for pK3based on Bjerrum and Unmack [18]. The values are set out in Table 20. Therewas, however, a problem in evaluating pKS. The literature gave values varyingbetween 25 and 31. After a review of the literature Green and Holmes selecteda value by Kuyper [19], which they modified in the light of data by Sendroyand Hastings [20] to give a value of 29.3. This value refers to a temperature of38 C: there are no experimental data available (nor reliable theoretical data) toindicate the effect of temperature variations on the selected value of 29.3.

Having to operate with a fixed value for pKS obviously is a weak point inthe procedure.

In establishing Eq. (60) calcium and Phos have both been expressed in termsof thermodynamic activity. This will lead to an error (usually slight) becauseanalytical results yield values expressed in terms of stoichiometric concentrations.Green and Holmes made no correction on this account: they considered sucha correction to be unwarranted in view of the uncertainty over the valuefor pKS.

However, it is considered that the necessary corrections should be incorporatedinto Eq. (60) in order to preserve thermodynamic integrity. If, and when, newand improved values for pKS over a range of temperatures become available,then Eq. (60) will be in a form to use and benefit from the new data.

The corrections may be introduced by applying the theories of Debye andHuckel [14] and Bronstead and LaMer [15].

]Ca[)Ca( 2Ca2 ++ = f (62)

Qfpiws-chap3.p65 02/17/2003, 5:17 PM39


]Ca[pp)Ca(p 2Ca2 ++ += f (63)]Ca[)(5.0 25.02Ca ++= pz (63a)]Ca[p)(25.0 25.02 ++= (63b)

.]Ca[p)(2 250 ++= . (63c)

A similar treatment may be applied to (Phos) by using the valency (z) forPO34 since the analytical tests for Phos are expressed in terms of PO4.

]Phos[)Phos( 4POf= (64)]Phos[pp)Phos(p 4PO += f (65)

]Phos[p)(PO5.0 5.042 += z (65a)]Phos[p)(35.0 5.02 += (65b)

.]Phos[p)(5.4 5.0 += (65c)Substituting Eqs. (63c) and (65c) in Eq. (60) gives:

)}(2)(9]Phos[p2)(6]Ca[p3{p 5.05.02Sp EpKI ++++= + (66).})(15)(p2]Phos[p2]Ca[p3{p 5.02S +++= + EK (66a)

Using the Langelier [2] evaluation:

mg/l) in expressed is DS(where40000

DS=

})DS(075.0)(p2]Phos[p2]Ca[p3{p 5.02Sp +++= + EKI (67)

To evaluate Eq. (67) pKS has already been assigned the fixed value of 29.3:values of p[Ca2+] are given in Table 8: values of p[Phos] are given in Table 21:values of p(E) are given in Table 22. The value of 0.075(DS)0.5 may be calculatedby simple arithmetic.

Example

Ca = 250 mg/l CaCO3Phos = 50 mg/l PO4DS = 300 mg/l as suchpH = 7.8T = 20 C

Qfpiws-chap3.p65 02/17/2003, 5:17 PM40


pKS = 29.3 From Table 8 p[Ca] = 2.603p[Ca] = 7.80

From Table 21 p[Phos] = 3.282p[Phos] = 6.56

From Table 22 p(E) = 4.732p(E) = 9.46

DS = 3000.075(DS)0.5 = 1.30

25.12Ip = 29.3 25.12 = + 4.18.

As the index is positive, the water will deposit calcium phosphate. Had theindex been zero or negative the water would not deposit calcium phosphate.

At this stage, a word of caution on the interpretation of the index is necessary.In their original paper Green and Holmes [13] used Eq. (61) to calculate theequilibrium pH (pHS) for calcium phosphate. If pHS is less than the actual pH,then precipitation of calcium phosphate will occur. But if pHS is equal to, orgreater than, the actual pH there will be no precipitation of calcium phosphate.

Using the difference between pHS and pH is a useful indicator, and servedthe purpose of Green and Holmes, but it is not mathematically identical withthe true saturation index as defined by Eq. (67). The confusion arises because,in the original concept of a saturation index pioneered by Langelier [2] forcalcium carbonate, the value of I = pH pHS is mathematically identical withI = pKS (p(Ca) + p(CO3)). But this is not universally true for all molecules.Thus, although the value of I = pH pHS has been used as a basis for calculationsin Sec. 1.3, it cannot now be used for calculations in this section.

Having established a method for calculating Ip it may now be utilised tocalculate the weight of calcium phosphate deposited to cause fouling.

3.2. CALCULATING THE WEIGHT OFCALCIUM PHOSPHATE

For any given water at any given temperature:

3CaCO as mg/lcalcium initialLet A= (68). POas mg/l PhosinitialLet 4B= (69)

After precipitation of calcium phosphate:

a=remaining calcium of fractionLet (70).remaining Phosof fractionLet b= (71)

Qfpiws-chap3.p65 02/17/2003, 5:17 PM41


Thus:3CaCO mg/l calcium Final aA= (72)

. POmg/l PhosFinal 4bB= (73)From Eqs. (68) and (72):

.)(POCa as mg/l)1(03.1)(POCa as mg/l)1(

300310

CaCO as mg/l)1(calcium of Loss

243

243

3

aA

aA

aAaAA

=

=

==

From Eqs. (69) and (73):

.)(POCa as mg/l)1(63.1)(POCa as mg/l)1(

190310

PO as mg/l)1(Phos of Loss

243

243

4

bB

bB

bBbBB

=

=

==

Since loss of calcium must be equal to loss of Phos, when both are expressedin the same unit:

From Eqs. (74b) and (75b):)1(63.1)1(03.1 bBaA = (76)

.

63.063.103.1

)1()1(

BA

BA

a

b==

(76a)

For the initial water the calcium phosphate saturation index may be obtainedby substituting Eqs. (68) and (69) in Eq. (67):

))DS(075.0)(p2p2p3(p 5.0Sp +++= EBAKI (77)For the final water (i.e. after precipitation of calcium phosphate) the saturation

index may be obtained by substituting Eqs. (72) and (73) in Eq. (67):))DS(075.0)(p2p2p3(p 5.0Sp +++= EbBaAKI (78)

))DS(075.0)(p2p2p2p3p3(p 5.0S +++++= EBbAaK (78a).)p2p3())DS(075.0)(p2p2p3(p 5.0S baEBAK ++++= (78b)

Because the final water will be in equilibrium with precipitated calciumphosphate Ip must be zero. Thus:

)p2p3())DS(075.0)(p2p2p3(p0 5.0S baEBAK ++++= (79)

(74a)(74b)

(74)

(75a)(75b)

(75)

Qfpiws-chap3.p65 02/17/2003, 5:17 PM42


Substituting Eq. (77) in Eq. (79) gives:)p2p3(0 p baI += (80))pp( 23p baI += (80a)

23p loglog baI ++= (80b)

23p log baI += (80c)

23p log baI = (80d)

23log10log p baI = (80e)23p10 baI = (81)

23

p10b

aI

= (81a)33.0

2

p10

=

ba

I(81b)

(neglecting negative or imaginary roots).Substituting Eq. (81b) in Eq. (76a) gives:

BA

b

bI

63.0

101

)1(33.0

2

p

=

(82)

BA

b

bI

63.0)10(1

)1(

67.0

33.0p=

(82a)

BA

bb

bI

63.0))10((

)1(

67.0

33.067.0 p=

(82b)

BA

bbb

I63.0

})10({)1(

33.067.0

67.0

p=

(82c)

33.067.067.167.0 )10(63.063.0 pIB

AbB

Abb

= (82d)

.0)10(63.0163.0 33.067.067.1 p =

+ I

BA

BAbb (82e)

Qfpiws-chap3.p65 02/17/2003, 5:17 PM43


The discussion covering the development of Eq. (78) through to Eq. (82e)assumes that the change in DS due to the precipitation of calcium phosphatewill not make a significant difference in the value of 0.075(DS)0.5.

The discussion also assumes that there will be no change in pH to alter thevalue of (E). This assumption is justified because the precipitation takes placein an environment in which the pH is dominated by the relationship betweenthe alkalinity of the water and the total carbon dioxide content. Since neitheralkalinity nor carbon dioxide are involved in the precipitation of calciumphosphate, the pH of the water will be buffered to the initial pH.

To utilise Eq. (82e), values of A and B can be obtained from a wateranalysis and the value of Ip obtained from Eq. (77) by the method alreadydescribed earlier in this section. Equation (82e) may then be solved for bwhich can be inserted in Eq. (75b) to give the loss of calcium phosphate.

As Eq. (82e) is complex, Table 23 has been set up to allow values of b tobe read-off from values of Ip and the ratio B

A ; or in more general terms the ratioCaCO3/PO4.

An alternative approach would be to obtain from Eq. (81) an evaluation ofb in terms of a. This evaluation could then be used in a process similar tothat used for Eqs. (82) to (82e) to produce an equation similar to (82e) butexpressed in terms of a.

It can be shown that the equation would read:

.0)10(63.0163.0 5.05.15.2 p =

+

IaB

Aa

BA (83)

This equation, like (82e), is complex and would need a new table (similar toTable 23) to allow Eq. (83) to be evaluated. As Table 23 is already in existenceit is considered that the work involved in preparing a new table for Eq. (83) isnot justified.

3.3. USE IN THE FIELD

The procedure outlined below yields a calculated figure for the maximum weightof calcium phosphate precipitated to cause fouling. In practice, the figure maybe lower due to the effect of restrictions similar to those described in items (xi),(xiii), and (xiv) in Sec. 1.2.1.

(xxx) From a water analysis at atmospheric temperature take the values ofCa, Alk, PO4, DS and pH. Use them to calculate the ratio CaCO3/PO4: to convertthe pH to the value for the temperature in the system (if different fromatmospheric) using the method on p. 20 of Ref. [8]: to calculate the value of Ip

Qfpiws-chap3.p65 02/17/2003, 5:17 PM44


using Eq. (67); for the temperature in the system. (If Ip is zero or negative therewill be no precipitation).

(xxxi) In Table 23, find the section containing the value of Ip. Run down theleft-hand edge of the first table in the section to find the value of Ip. (If thevalues displayed to not exactly fit the value calculated from Eq. (67) select thenearest).

(xxxii) Follow the selected value horizontally across the table, proceedingfrom table to table in strict numerical order, until the value for CaCO3/PO4 isfound. (If the exact figure is not recorded, select the nearest).

(xxxiii) At the head of the column located in (xxxii) the value of b isgiven. Use this to calculate the calcium phosphate precipitated from Eq. (75b).(Multiply by the rate of flow, and the time the system is on load to give thetotal fouling).

(xxxiv) Having precipitated calcium phosphate the water may still be capableof depositing calcium carbonate to give a mixed fouling. This should now bechecked.

(xxxv) Take the result from (xxxiii) and multiply by 310300

= 0.97 to give thedeposit in terms of CaCO3. Deduct this from the original Ca figure to give anamended value. Use this, together with the values for Alk, DS, and pH at thesystem temperature to calculate I at the system temperature, as described inSec. 1.3.1.

(xxxvi) Use the value of I from (xxxv) to read-off the weight of calciumcarbonate deposited from Table 13.

Example

Ca = 250 mg/l CaCO3Phos = 50 mg/l PO4Alk = 150 mg/l CaCO3DS = 300 mg/l as suchpH = 7.8 @ 15 C.

What is the fouling at 40 C?

At 15 C At 40 CAlk = 150 mg/l CaCO3 Alk = 150 mg/l CaCO3pH = 7.8 C = 312 mg/l CaCO3C = 312 mg/l CaCO3 pH = 7.7From Table 20 of Ref. [8] From Table 50 of Ref. [8]

Qfpiws-chap3.p65 02/17/2003, 5:17 PM45


pKs = 29.3 From Table 8 p[Ca2+] = 2.603p[Ca2+] = 7.80

From Table 21 p[Phos] = 3.282p[Phos] = 6.56

From Table 22 p[E] = 4.552p[E] = 9.10

DS = 3000.075(DS)0.5 = 1.30

24.76Ip = 29.3 24.76 = + 4.54

.0.550250

POCa

4==

From Table 23 b = 0.01

Final phosphate = 50 0.01 = 0.5 mg/l PO4Loss of phosphate = 50 0.5 = 49.5 mg/l PO4

= 49.5 190310

= 81 mg/l Ca3 (PO4)2 .

Loss of calcium = 81 mg/l Ca3 (PO4)2= 81

310300

= 78 mg/l CaCO3.

Residual calcium = 250 78 = 172 mg/l CaCO3.Residual dissolved solids = 300 81 = 220 mg/l as such

p[Ca2+] = 2.76 from Table 8p[Alk] = 2.52 from Table 9pK2 pKS = 1.70 (10.22 8.52 from Table 10) @ 40 CDS0.5/100 = 0.15pHS = 7.13

pHS = 7.13pH = 7.70I = + 0.57 @ 40 CFrom Table 13 W = 20 mg/l CaCO3 (by interpolation)Total Fouling 81 mg/l Ca3(PO4)2

20 mg/l CaCO3.

Qfpiws-c

[a._g._d._emerson]_quantitative_forecasting_of_pro(booksee.org).pdf

Documents

calcium sulphate

calcium phosphate

earlier work

terms of caco3

corrosion of copper

form of tables

methyl orange mgl

usa office