Quantitative Forecasting of Problems in Industrial Water Systems (Chemical Engineering)

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Author: A. G. D. Emerson

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

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

QUANTITATIVE FORECASTING OF PROBLEMS IN INDUSTRIAL WATER SYSTEMS Copyright © 2003 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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 from the publisher.

ISBN 981-238-184-8

Printed in Singapore.

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 as Ref. [8] in the References. Readers will therefore need to have a copy of that earlier work to hand before 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 have difficulty in obtaining a copy. To overcome this situation Ref. [8] has been reprinted as a Supplement at the end of this book. Readers will therefore have all the tables needed, both from this book and from the supplement, available under one cover.

vii

SYNOPSIS

The operating problems most likely to be encountered in industrial water 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 likely to be encountered in an industrial water system, while the project is still at the design stage. The information will also be of assistance in investigating problems experienced in existing systems. The data are presented in the form of tables to assist operators who are working on site with portable testing equipment. The methods described introduce new concepts for the saturation indices of calcium carbonate, calcium sulphate, and calcium phosphate; for buffer capacity; and the pitting propensity index.

ix

NOMENCLATURE

( ) [ ] a Alk

Thermodynamic activities, expressed as mol/l. Stoichiometric concentrations, expressed as mol/l. Fraction of molecules remaining after precipitation. Total alkalinity  expressed as Alkalinity to Methyl Orange  mg/l in terms  of CaCO3. Alkalinity to pH 4.5 b Fraction of molecules remaining after precipitation. B Buffer Capacity C 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 Suzuki’s 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

xii Quantitative Forecasting of Problems in Industrial Water Systems

SO4 T µ

V W Z

Sulphate expressed as mg/l in terms of Na2SO4. Temperature °C. Ionic strength. Vectors. Weight of calcium carbonate expressed as mg/l CaCO3. Valency.

INTRODUCTION

This book has been written as a contribution to changing the attitude of mind when considering problems in industrial water systems. The need for such a change has been brought about by changes in prevailing economic conditions. Industrial systems using water for heating or cooling purposes frequently encounter problems which are associated with the quality of water used. In former times, when both labour and materials were cheap, it was a relatively simple matter to discard a system that had encountered problems and build a new one designed in the light of the experience gained from an old system: in this way it was hoped to avoid the difficulties previously experienced. If discarding the system was not considered necessary, some form of chemical treatment and monitoring might be introduced. If this was not entirely satisfactory then, with cheap labour available, it was, again, a relatively simple matter to arrange for periodic manual cleaning of the system to make good the deficiencies of the treatment. In fact some operators used to boast of the quantity of deposit removed during such manual cleaning operations. As though it was a matter of pride, instead of a reflection on the manner in which the system had been controlled and operated. But under present day ecomomic conditions such a leisurely approach is no longer feasible. In the design and operation of industrial water systems it is important to know in advance what problems are likely to be encountered, and to 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 the water entering the boiler is evaporated as steam, all the hardness salts must remain behind to form scale. Therefore X mg of scale will be formed for each litre of water evaporated. Expressing the problem in quantitative terms is therefore a matter of simple arithmetric. For this reason steaming boilers have been excluded from the discussions in this book. But for systems involving heat-exchangers (whether for heating or cooling) a more complex situation exists, depending on the chemical reactions taking place in the water at various temperatures. The study in this book has been restricted to heat exchange systems where there is no loss of water by evaporation, or xiii

xiv

Quantitative Forecasting of Problems in Industrial Water Systems

other means, unless specifically mentioned in special cases. It is also assumed that there is no change in the chemical characteristics of the water by accidental ingress of contaminants, or by the loss of dissolved gases by venting to atmosphere, unless addition of chemicals or loss of gases are specifically mentioned in special cases. Changes in the chemical characteristics of the water are limited to those induced by a change of temperature. The problems most likely to be encountered in the types of systems outlined above 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 is not amenable to physical-chemistry methods. The metals of construction most likely to be used in industrial water systems are mild steel and copper: their rates of corrosion have therefore been included in the discussion. Other metals may be used from time to time, but mild steel and copper are regarded as basic: other (often more expensive) metals are introduced when justified on technical and economic grounds by the operating conditions existing in an individual system. Manufacturers of special alloys are sometimes able to indicate how the rate of corrosion of their materials compare with mild steel or copper under given operating conditions. Thus, a knowledge of the probable rate of corrosion of the basic metals can be of assistance in selecting special alloys. The purpose of the data offered in this book is to enable quantitative forecasts to be made of the fouling or corrosion likely to be encountered in an industrial water system, while the project is still at the design stage. A decision can then be made on the type of water treatment to be adopted, commensurated with the purpose for which the system is to be used, and its life expectancy. A discussion on the various types of water treatment that might be considered is beyond the terms of reference of this book. It is a diagnostic tool utilising the basic physical-chemistry of water supplies. Water treatment methods may change from time to time, but the basic physical-chemistry remains unchanged. However, a forecast of probable operating problems may be used to influence the choice of a water supply, if several alternatives are available on any given site.

Introduction

xv

In the case of a small project, or one handling a low grade product, a forecast of problems as outlined in this book may suffice. But for a large project, or one handling a sophisticated and expensive product, a trial run on a scale model may be undertaken before final design details are settled. In such a case an initial forecast of the problems will enable the trial run to focus on the most critical conditions likely to be encountered. In addition, to work at the design stage of a project, the methods described in this book may be used to assist operators in investigating problems on an existing system. As this often involves working with portable testing equipment, the data are presented in the form of tables to facilitate site work.

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 Ryznar’s 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

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

v

vi

Contents 2.3 Use in the Field .................................................................................

31


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


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


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


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

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 a method possessing the thermodynamic integrity of physical-chemistry; a method which is easily applied and will allow the amount of calcium carbonate deposited to be estimated, or forecast, from an inspection of the chemical analysis of a water supply. At present, the literature offers only one parameter linking water analysis and the amount of calcium carbonate deposited: that parameter is the Ryznar Index. A study of that Index is, therefore, the logical starting point for the development of methods for forecasting fouling by calcium carbonate.

1.1. THE RYZNAR INDEX The Ryznar Index [1] is formally defined as:

R = 2pH S − pH

(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 origin of Ryznar’s work and make a reappraisal in the light of recent information that was not available to him.

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

2


Fig. 1. Basis of Thompson–Ryznar test rig.

the weight of calcium carbonate deposited is determined, at any selected temperature, under fixed operating conditions. At this point it must be emphasised that the conditions existing in the test rig restricts the application of Ryznar’s work to those industrial water systems in which similar conditions apply. That is, once-through, closed systems in which water enters, passes through to drain, and is subjected only to a temperature rise. Apart from deposition of calcium carbonate there are no other changes: for example, incidental ingress of chemicals by contamination, or loss of dissolved gases by venting to atmosphere. The only chemical changes permitted are those resulting from the deliberate addition of known reagents to the header tank before 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 calcium carbonate deposited by a sample of raw water, and compared it with the same water treated with various inhibitors. In this way he was able to list the inhibitors

Calcium Carbonate Fouling

3

in their order of merit. By repeating the process for different raw waters Ryznar was able to provide a more extensive and more informative list of merit for a range of inhibitors. Because Ryznar’s method required only comparative weights of calcium carbonate, and each experiment was run under fixed conditions, his data records only the weights of calcium carbonate deposited and not the volume of water from which they were produced. Another important point to be taken into account is Ryznar’s method of preparing water samples. In the earlier stages of his work he found that the experimental runs had to be extended over a protracted time, and use large volumes of water, in order to deposit sufficient calcium carbonate in the coil to produce a significant weight change. In order to reduce the time of each run to a manageable length, Ryznar increased the scaling potential of the waters by increasing their alkalinity. Sodium carbonate or sodium bicarbonate was added for this purpose. The significance of 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 to forecast, 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 a given temperature. This information would facilitate the preparation of raw water samples that would yield a weight of deposit within a range required for a specific sector of Ryznar’s investigations. In pursuit of this objective Ryznar prepared 21 raw water samples which were passed through the Thompson–Ryznar test rig and the weights of calcium carbonate deposits recorded. The results are set out in Table 1. The chemical analyses of the water samples were made at atmospheric temperature (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 by Langelier (loc.cit.). The equilibrium pH is defined as: pH S = p[Ca 2+ ] + p[Alk] + pK 2' − pK S' where

and

K 2' =

[ H + ][CO32+ ] [ HCO3− ]

KS' = [Ca 2+ ] [CO 32− ]

pHS was evaluated from tables by Larson and Buswell [4].

(2) (3) (4)

4


From the values of pHS (at T) and the values of pH (at 15 °C) Ryznar calculated the values of the calcium carbonate saturation index, described by Langelier (loc.cit.). (5) I = pH − pHS 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 had broken thermodynamic integrity. But he had no choice since in 1944 there was no published method for adjusting pH for temperature changes. In this present reappraisal of Ryznar’s original work, Eq. (2) has been used in the modified form: pH S = p[Ca 2+ ] + p[Alk] + pK 2 − pK S + (DS) 0.5 /100

(6)

described by Emerson [5]. Where

and

(H + )(CO32− ) (HCO3− )

(7)

K S = (Ca 2+ )(CO 23− )

(8)

K2 =

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 Ryznar’s 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) (ii) (iii) (iv)

Absence of any fundamental relationship between I and Q. Errors introduced by Ryznar breaking thermodynamic integrity. Experimental errors in the test rig. 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 assumed that only (i) was applicable. He abandoned any further investigation of a relationship between I and Q and began to search for a new, empirical index that was directly linked to the weight of calcium carbonate deposited. Ryznar’s further investigations produced an empirical index: R = 2pHS − pH

(1)


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

5

6


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


7

The data in Table 2 has been rearranged to show values of R and the new parameters are set out in Table 3. A plot of the values of the Ryznar Index (R) against the weight of calcium carbonate (Q) from Table 3 is shown in Fig. 3. It will be seen that a smooth curve can be drawn through the plot to give a neutral point (zero deposit) at R = 6.2. Ryznar’s original graph gave the neutral point as R = 6.0. The slight difference 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 may be 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 curve could be drawn linking R and Q, and that a neutral point existed at R = 6.0, he allowed the matter to rest. He did not, for example, publish any further work on methods of forecasting, or estimating, the weight of calcium carbonate deposited using 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 clearly further work must be done on the Ryznar Index if it is to be included in the methods which follow in this book. It is therefore important to investigate, and if 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 as possible, the thermodynamic integrity. This can be achieved by using values of pHS 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 °C in Tables 1–3 are converted to temperature T using the method described by Emerson on pp. 20–21 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 that a smooth curve can be drawn through the plot. This curve is very similar to that obtained in Fig. 3 (which has been inserted in Fig. 4 as a dotted line for comparison) but has been displaced to the right in the diagram to give a new neutral point at R = 7.5.

8


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


9

It will be a matter for individual water treatment suppliers and plant operators to decide whether to accept the thermodynamically improved neutral point of R = 7.5 as a basis for plant control instead of the older, more familiar R = 6.0 discussed in Sec. 1.1.2. There is still a moderate amount of scattering of points in Fig. 4. In this respect, Fig. 4 offers no improvement over Fig. 3. This leads to the conclusion that the scattering is not due to the thermodynamic status of the data. If the thermodynamic status was a significant explanation there would have been a marked improvement in the closeness of the “fit” of the points to the curve on moving from Fig. 3 to Fig. 4. This conclusion is not altogether unexpected since the Ryznar Index in Eq. (1) is empirically derived and not the result of a rigid thermodynamic calculation. Leading on from this conclusion the next logical step is to consider possible experimental errors in the test rig.

1.1.4 Experimental Errors It is considered possible for experimental errors to arise in the test rig for the following reasons: (viii) In Sec. 1.1.1, it was explained that Ryznar increased the alkalinity of water samples by the addition of alkali (sodium carbonate or sodium bicarbonate). Following such additions time will be required for the ionic species contributing to the alkalinity and pH of the water to undergo internal rearrangement and achieve equilibrium. Very little is known about this time interval, but it introduces the possibility of the onset of precipitation being delayed. This delay could vary from one water to another and thus introduces an error when comparing results. Thus the “fixed” conditions of 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 not take place. This metastable stage continues until the water is disturbed and passes into a labile (precipitating) stage by an increase in alkalinity and/or temperature. Here again, the onset of precipitation may be delayed leading to a variation in the conditions of the test run. The existence of the metastable stage is demonstrated in many natural occurring waters, which have a positive calcium carbonate saturation index (scaling) but remain stable without precipitation over long periods until the temperature is raised.

10


(x) The precipitation of calcium carbonate when water is heated takes place in the bulk of the water. Some precipitate then becomes attached to the heat exchange surface. (This is in direct contrast, for example, to calcium sulphate which crystallises on the heat exchange surface). Under these conditions some of the precipitate may be carried forward with the flow of water and pass to drain. Thus some of the precipitated calcium carbonate may be lost and not recorded when the test coil is weighed. Variations in the recorded weight of calcium carbonate for the reasons just discussed may be small. But they are significant in comparison with the recorded weights which amount to a modest number of milligrams. It may be argued that items (viii), (ix), and (x) are only hypotheses, and pose the 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 very similar test rig. He found that the reproductivity of results was poor. Samples of water, prepared to the same specification, and put through the test rig on successive days, gave variable weights of calcium carbonate. It was necessary to 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 results indicating an order of merit: A B C D but on subsequent runs the order changed: B A C D

A B D C

A C B D

etc.

Again, it was necessary to run 5 or 6 tests and take mean values in order to obtain meaningful results. It will be seen from Edwards results that the use of the test rig provides a screening test capable of indicating broad trends in the amount of calcium carbonate precipitated (and its reduction by using various inhibitors). But the results are not sufficiently finely tuned to match parameters calculated on an accurate thermodynamic basis.


11

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

1.2. NEW DATA The discussions in Sec. 1.1 have extracted from Ryznar’s work with the test rig all the information likely to be of value in estimating calcium carbonate deposition. The next step forward is to provide a method of calculating the weight of calcium carbonate deposited, instead of using weights obtained from a test rig. Such a method was not available to Ryznar or Edwards, but is available now. It has been applied in the following way: Ten water analyses have been selected which are typical of the raw waters likely to be available from natural sources, or municipal supplies, for industrial use. The analyses are set out in Table 5. The analyses cover the same broad characteristics as the waters used by Ryznar, with one important exception. Because Ryznar increased the alkalinity of his waters, his pH values are high (in the 8.0 to 9.0 range, with a few exceptions). These pH values are higher than those normally found in the natural waters and municipal supplies available to industry. Therefore in Table 5 a lower pH range (7.0 to 7.9) has been used. In the original Ryznar test rig waters were maintained at a temperature of 95 °C in 13 cases, at 70 °C in 3 cases, and at 50 °C in 5 cases. This range of temperatures is too narrow to cover the range likely to be encountered in actual plant 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. From the values of I, the weights of calcium carbonate (W) have been calculated by the 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 calculated for any volume throughput of water. The results of the above calculations are set out in Table 6. In order to obtain a preliminary insight into the relationship between R and W a plot of values at 30 °C, 50 °C, and 80 °C was made in Fig. 5. It will be seen that a smooth curve can be drawn for each temperature, and the whole temperature range covered by a family of curves. It is therefore worthwhile

12


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


13

exploring the mathematics of Table 6 in further detail. It can be shown by a detailed mathematical analysis of Table 6 that the relationship between R and W can 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 are linear 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:

or

lnW = (0.015T − 2.22)R − 0.11T + 18.21

(19)

logW = (0.007Τ − 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) will give the best value of W calculated on the basis of R. The calculated value of W is the maximum weight of calcium carbonate that can be deposited from 1 litre

14


of water. But in practice in an actual system it could be less for the following reasons. (xi) If the water velocity is high, the retention time in the system may be too low to allow all deposition to be completed within the system. (xii) Because the precipitation of calcium carbonate takes place in the bulk of the water (rather than on the heat exchange surfaces) precipitated calcium carbonate may be carried out of the system by the flow of water. (xiii) Retention of precipitated calcium carbonate can be influenced by the roughness of the metal surfaces, and the geometry of the system (e.g. sharp bends). (xiv) There may be temperature variations within the system, so that some parts may not be as high as T. In these lower temperature regions precipitation will be reduced. Having listed these points it may be stated that the calculated value of W represents the highest weight of calcium carbonate that can be deposited, and thus represents the maximum fouling likely to be encountered. Another practical aspect that must be considered is the speed and ease with which Eq. (18), or (19), or (20) can be used by a water technologist. Whether the technologist is advising a design team on the choice between several possible water supplies, or carrying out site tests with portable analytical equipment, the ability to produce a quick answer has obvious advantages. To assist in this, a table 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 values of Ca, Alk, and DS. Use them to calculate the value of pHS at T by using Eq. (6) evaluated as described in Sec. 1.1.2. To assist in this evaluation values of: p[Ca2+] are given in Table 8 p[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 the method described by Emerson on p. 20 of Ref. [8]. (xvii) From (xv) and (xvi) calculate the Ryznar Index at T. R = 2pHS − pH

(1)


15

(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 with the value of R. (xix) At the left hand edge of the table scan vertically to find T. Now scan horizontally to meet the column selected in (xviii). (xx) Where the two intersect is the value of W. Example Water analysis at 15 °C Ca = 300 mg/l CaCO3 Alk = 250 mg/l CaCO3 DS = 450 mg/l as such pH = 7.8. Temperature in system = 60 °C. Evaluate Eq. (6) as:

p[Ca 2+ ]

= 2.53 from Table 8

p[ Alk ]

= 2.30 from Table 9

pK 2 − pK S = 1.40 (10.14 − 8.74 @ 60 o C from Table 10) ( DS) 0.5 = 0.21 100 pH S = 6.44 @ 60 o C From Table 20 at 15 °C in Ref. [8] Alk = 250 pH = 7.8.

gives C = 520.

From Table 74 at 60 °C in Ref. [8] Alk = 250 C

= 520

gives pH = 7.6 @ 60 °C.

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.

16


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 the plant 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 to access the margin of error likely to be encountered To make this assessment five waters from Table 5 have been selected as representative of the range of waters examined. They are Nos: 22, 25, 26, 29 and 30. Similarly, three temperatures from Table 6 have been selected as representative of 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 in Table 6 have been listed. The corresponding values of W from Table 7 have been added alongside. The difference between corresponding values of W have been 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 the true value, since they were calculated direct from individual water analyses on a 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 what is their significance? Equation (18), on which Table 7 is based, is a “best fit” derived from Eqs. (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 the equations will be different from the true value. The errors may be positive or negative, and they will also be cumalative because any error arising from Eqs. (10) to (15) will be combined with any errors arising from Eqs. (16) and (17). It can be shown that the error of +50% mentioned above can be caused by on 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 the order of 0.15 in the values of pHS and pH: errors which are within the tolerance applicable to normal plant practice. To assess the significance of the errors in Table 11 it is necessary to compare them with errors which arise from variations in water analyses due to natural


17

causes. To investigate this aspect, water analyses from two different locations have been selected. Each water supply possesses characteristics that are likely to lead to scaling. For each supply, the mean, maximum and minimum analyses have been recorded. During the progress of any project the normal procedure is to base calculations for design, operation, and control of a system on the mean water analysis. But during the working life of the system it will receive water varying 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. The difference in values between mean and maximum analyses, and between mean and minimum 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% and −95%. This range is much greater than those recorded in Table 11. Therefore Table 7 may be used as a useful working estimate since any errors it may produce 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 relationship between Q and I, but had abandoned this line of investigation. In view of the relationship between R and W subsequently produced in Sec. 1.2 the question arises “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, and 80 °C (as recorded in Table 6) was made in Fig. 6. It will be seen from the plot in Fig. 6 that a smooth curve can be drawn for each temperature, and that the whole range can be covered by a family of curves. It is therefore worth exploring the mathematics of the relationship between I and W in further detail. It can be shown by a detailed mathematical analysis that the relationship between 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)

18


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


19

A further examination of Eqs. (22) to (27) shows that the values of Y are linear 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:

or

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

(31)

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 give the best values of W calculated on the basis of I. The calculated value of W is the maximum weight of calcium carbonate that can be deposited from 1 litre of water. But in practice, in a actual system it could be less for the reasons already given 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 evaluating Eq. (30), or (31), or (32). To assist in this, a table giving values of W against I is set out in Table 13. It is used as follows: (xxi) From a water analysis at atmospheric temperature (15 °C) take the values of Ca, Alk, and DS. Use them to calculate the value of pHS at T as already described in item (xv) of Sec. 1.2.1. (xxii) From a water analysis at atmospheric temperature (15 °C) take the values of Alk and pH and use them to convert the pH to the value at T as already described in item (xvi) of Sec. 1.2.1. (xxiii) From (xxi) and (xxii) calculate the Langelier index at T. I = pH − pHS

(5)

20


(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 by the value of I. (xxv) At the left hand edge of the table scan vertically to find T. Now scan this line horizontally to meet the column selected in (xxiv). (xxvi) Where the two intersect is the value of W. Example Water analysis at 15 °C Ca = 300 mg/l CaCO3 Alk = 250 mg/l CaCO3 DS = 450 mg/l as such pH = 7.8. Temperature in system = 60 °C. Evaluate Eq. (6) as:

p[Ca 2+ ]

= 2.53 from Table 8

p[ Alk ]

= 2.30 from Table 9

pK 2 − pK S = 1.40 (10.14 − 8.74 @ 60 o C from Table 10)

( DS) 0.5 100

= 0.21

pH S

= 6.44 @ 60 o C

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

gives C = 520.

From Table 74 at 60 °C in Ref. [8] Alk = 250 C

= 520

gives pH = 7.6 @ 60 °C.

Evaluate Eq. (5) as: I = 7.6 − 6.44 = 1.16.


21

In Table 13, find the sector headed 1.1 to 2.0 and select the column headed 1.2. At the left hand edge find T = 60 °C The vertical column and horizontal line meet at: W = 114 mg/l CaCO3. This number, multiplied by the rate of water flow and the time the plant is on 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 try to assess the margin of error likely to be encountered. To make this assessment the 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 in Table 6 were listed. The corresponding values of W from Table 13 were added alongside. The difference between corresponding values of W were then listed and 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 true values, since they were calculated direct from individual water analyses on a sound 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 these errors arise and what is their significance? The discussion in Sec. 1.2.2 concerning Eqs. (10) to (18), Table 7, and the errors 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 +0.06 in the evaluation of I. These errors can arise from errors of the order of 0.03 in the values of pH and pHS: errors which are well within the tolerance applicable to the evaluation of these parameters. As already stated in Sec. 1.2.2 this is an important point which must not be overlooked when considering the magnitude of errors in the value of W, as a means of assessing the magnitude of errors in the procedure under discussion. To assess the significance of errors in Table 14 the procedure already described in Sec. 1.2.2 has been adopted. The same two waters listed in Table 12 have been used again and the values of W for values of I at 30 °C, 50 °C, and 80 °C are recorded. The results are set out in Table 15.

22


It will be seen that the errors recorded in Table 15 vary between + 463% and −100%. This range is much greater than the range recorded in Table 14. Therefore the errors arising from Table 13 can be ignored as likely to be outweighed by errors arising from natural causes.

1.4. CHOICE BETWEEN LANGELIER AND RYZNAR In this book two methods have been developed for estimating the weight of calcium carbonate deposited in a system. One method is based on the Ryznar Index (R) and the other on the Langelier Index (I). The existence of two possible methods 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 and derived from Table 7, and selected values of W, based on I and derived from Table 13, are set out together in Table 16. The values based on I have been taken as the standard: the difference between the values based on R and the values based on I have been recorded in Table 16 and expressed as a percentage. As already stated in Sec. 1.3.1 values of W based on I are considered to be superior to values based on R. Calculations based on I have a higher thermodynamic integrity than those based on R. (R is an empirically derived parameter, 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 already established methods of treatment and control based on R, and would prefer to continue using R as a basis for estimating W. If this preference is followed, it will be seen from Table 16 that errors between +38% and −25% may be encountered. But these degrees of error are small compared with errors likely to be 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 accepted when making a forecast for any given installation. In the case of a small project, or one handling a low grade product, a tolerance between +38% and −25% may be acceptable. A calculation for W based on the value of R would be attractive to a technologist or operator who already has embedded in his methods of treatment and control calculations based 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.


23

1.5. THE SPECIAL CASE OF RECIRCULATING SYSTEMS Under the proviso stated in Sec. 1.1.1 the whole of the work discussed up to this point is restricted to once-through, closed systems. However, as industrial installations 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 which water continuously recirculates. Heat, which needs to be dissipated, is absorbed by the water in a heat-exchanger and then discharged from the water by a second heat-exchanger which itself is cooled by a secondary cooling system. In the primary system the volume of water used for the initial filling (or refilling after draining for maintenance) will deposit an initial quantity of calcium carbonate according to the temperature rise experienced. Once this initial precipitation has taken place, no more calcium carbonate will be deposited. The quantity of calcium carbonate can be estimated by the methods already described, from the analysis of the water and the temperature in the system. In the calculation, the volume of water in the closed system replaces the flow rate for a once-through system.

1.5.2. Open Recirculating Systems The open recirculating cooling system, incorporating an evaporative cooling tower, is widely used in industry. A special feature of this type of system is the increase in the concentration of dissolved salts in the recirculating water. The normal procedure for this type of system is to operate with a predetermined number of concentrations in the recirculating water (by controlled purging from the system) coupled with treatment with an inhibitor. Each inhibitor varies in the quantity of calcium carbonate it can hold in solution before precipitation occurs. This factor determines the optimum number of concentrations to be maintained in the recirculating water. Therefore the number of concentrations and the dosage of inhibitor are usually given to the plant operator by the water treatment supplier. In this context, it will be useful to estimate the weight of calcium carbonate that will be deposited by a given water in a given plant at a given temperature if the system is operated at various number of concentrations. This information will assist in selecting the most appropriate treatment to inhibit fouling, and the number of concentrations compatible with the selected treatment. Also, this

24


information can be used to justify the cost of treatment by giving an indication of 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 the basis of Table 13) it is necessary to modify the methods previously described for calculating pHS and pH. pHS The value of pHS for the make-up water at T, the temperature in the system is first calculated as in (xv) in Sec. 1.2.1. If the system is to operate with “n” concentrations in the recirculating water, the value of pHS in the make-up water is converted to pHS in the recirculating water by means of the equation described by Emerson [5]:

pHS

= pHS − 2 log n + ( n 0.5 − 1)

( recirc.)

DS0.5 100

( make − up )

(33)

pH The 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 water using 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 calculated and a new value for W read off from Table 7 or Table 13. Example Make-up water analysis at 15 °C Ca = 120 mg/l CaCO3 Alk = 80 mg/l CaCO3 DS = 180 mg/l as such. Temperature in system = 40 °C. Number of concentrations in system = 3. From Eq. (6)

p[Ca 2+ ] = 2.92 from Table 8 p[ Alk ] = 2.80 from Table 9 pK 2 − pKS = 1.70 (10.22 − 8.52 at 40 oC from Table 10) ( DS)0.5 = 0.13 100 pH S

= 7.55 .


25

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 = 2 Alk = 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 of adding water to the system and the time that the plant is on load to give the total calcium carbonate fouling. In considering the values of W above, the comments in Sec. 1.4 are still applicable.

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 sulphate fouling 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 not identical source, is treated effluent which is offered for industrial cooling purposes, especially if effluent has been derived from a process involving the use of sulphuric acid or sulphates. Waters high in calcium hardness and alkalinity may be treated with sulphuric acid in order to reduce the alkalinity to a level which will not promote calcium carbonate fouling. But in doing so, the natural sulphate of the water may be artificially boosted to a point which will now promote calcium sulphate fouling. A similar difficulty may be encountered with waters which will not promote calcium sulphate fouling in their natural state, but if used in a recirculating cooling tower (where a concentration effect operates) may be artificially boosted to a point which will now promote calcium sulphate fouling in the circulating water. In the light of the above discussion it is strongly recommended that, whenever a new system is being designed, or problems in an existing system is under investigation, the possibility of calcium sulphate fouling should be included. It should not be assumed, merely by visual inspection of water analyses, that such fouling will not arise.

2.1. CALCIUM SULPHATE SATURATION INDEX The calcium sulphate saturation index (IS) is defined by Emerson [10] as:  ( DS)0.5   I S = pK −  p[Ca 2 + ] + p[SO 24− ] + 50  

Where

K = (Ca 2+ )(SO 24− ) at equilibrium . 27

(34) (35)

28


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]) 2+ p[Ca ] from Table 8 p[SO2− 4 ] from Table 18. Values of (DS)0.5/50 are calculated by simple arithmetic. Example Ca

= 1000 mg/l CaCO3

SO4 = 1700 mg/l Na2SO4 DS = 2800 mg/l as such Temperature = 90 °C. 2+ From Table 17 pK @ 90 o C = 5.02 From Table 8 p[Ca ] = 2.00 From Table 18 p[SO 24− ] = 1.92 ( DS) 0.5 = 1.06 50 4.98

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

2.2. CALCULATING THE WEIGHT OF CALCIUM 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)

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(1−a) mg/l as CaCO3 136 A(1 − a ) mg /1 as CaSO 4 = 100 = 1.36 A(1−a) mg/l as CaSO4

(42) (42a) (42b)

From Eqs. (37) and (41) Losss of sulphate = B − bB = B(1−b) mg/l as Na2SO4 136 B(1 − b) mg /1 as CaSO 4 = 142 = 0.96 B(1−b) mg/l as CaSO4.

(43) (43a) (43b)

Since loss of calcium must be equal to loss of sulphate when both are expressed in the same unit: From Eqs. (42b) and (43b):

1.36 A (1 − a ) = 0.96 B (1 − b) 1.36 A = 0.96 B A 1.42 = B

(1 − b) (1 − a ) (1 − b) . (1 − a )

(44) (44a) (44b)

For the initial water, the calcium sulphate saturation index may be obtained by substituting Eqs. (36) and (37) in Eq. (34):  DS0.5   I S = pK −  pA + pB + 50  

(45)

For the final water (i.e. after precipitation of calcium sulphate) the saturation index may be obtained by substituting Eqs. (40) and (41) in Eq. (34):  DS0.5   I S = pK −  paA + pbB + 50  

(46)

30


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

 DS 0.5   0 = pK −  paA + pbB + 50    DS 0.5   − ( pa + pb) = pK −  pA + pB + 50  

(46a) (46b)

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

0 = I S − ( pa + pb ) = I S − p( ab)

(47) (47a)

= I S + log(ab)

(47b)

log(ab) = − I S

(47c)

ab = 10− IS a=

(47d)

10− IS b

(47e)

(The calculation set out above assumes that the loss of DS by the precipitation 0 .5 of calcium sulphate does not make a significant difference in the value of DS50 ). Substituting Eq. (44b) in Eq. (47e) gives:

1.42 A (1 − b) = B  10− IS  1 −  b   (1 − b) =  ( b − 10 − I S )    b   (1 − b)b = (b − 10− IS ) 1.42 A(b − 10− IS ) = (1 − b)b = b − b2 B 1.42 A(b) 1.42 A(10− IS ) − = b − b2 B B  1.42 A − 1  1.42 A(10− IS ) =0 b 2 + b − B B  

(48)

(48a)

(48b)

(48c) (48d) (48e)


31

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

 1.42Ca  1.42Ca b 2 + b (10−IS ) = 0 − 1 − SO4  SO4 

(49)

Ca

By substituting values for SO4 and IS into Eq. (49), it can be solved for values of “b”. Only real, positive values are retained for use: negative or imaginary values have no physical significance. The value of “b” is then substituted in Eq. (43b) to give the loss of calcium sulphate. The value of “b” can also be substituted in Eq. (47e) to give a value for “a”, which, in turn, can be substituted in Eq. (42b) to give an alternative figure for the loss of calcium sulphate. Ideally, the two figures for the loss of calcium sulphate should be identical. To avoid the time and labour required to solve Eq. (43b), Table 19 has been Ca prepared from which values of “b” can be read off for various values of SO4 and IS. 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 weight of calcium sulphate precipitated to cause fouling. In practice, the figure may be lower 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 of Ca Ca, SO4 and DS. Use them to calculate the ratio SO4 , and the value of IS at T as described in Sec. 2.1. If IS is negative there will be no fouling and further calculation is unnecessary. Ca (xxviii) In Table 19, run down the left hand edge to find the value of SO 4 . If the value calculated from the water analysis does not exactly fit the values in the 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 line and vertical column meet is the value of “b”. Example Ca = 1000 mg/l CaCO3 SO4 = 1700 mg/l Na2SO4 DS = 2800 mg/l as such T

= 90 °C

Ca ratio = 1000 1700 SO 4 = 0.59

32


From Table 17

From Table 8

pK @ 90 °C = 5.02

p[Ca2+]

= 2.00

From Table 18 p[SO2− 4 ]

= 1.92

( DS)0.5

= 1.06

50

4.98

IS = 5.02 − 4.98 = +0.04. As the index is positive, the water will deposit calcium sulphate at 90 °C. Ca In Table 19, find SO4 = 0.6 (the nearest value to 0.59). Scan right to find IS = 0.04 in Table 19/1. The horizontal line and vertical column meet at ‘b’ = 0.96. From Eq. (43b) Loss of sulphate = 0.96 × 1700 (1−0.96) = 0.96 × 1700 × 0.04 = 65 mg/l CaSO4 From Eq. (47e)

a=

10 −0.04 0.91 = = 0.95 0.96 0.96

From Eq. (42b) Loss of calcium = 1.36 × 1000 (1−0.95) = 1.36 × 1000 × 0.05 = 68 mg/l CaSO4 Ideally the two loss figures should be identical, since they are both expressed in terms of CaSO4. The difference is due to assuming that the change in DS on precipitation of calcium sulphate made no significant difference to the value 0 .5 of DS50 (as discussed in Sec. 2.1) and to the values of “b” in Table 19 being rounded off to two places of decimals. For all practical plant purposes the two values are sufficiently close to allow either value to be used for design or performance forecast purposes. This value may be multiplied by the rate of water flow through the system and 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 apply here. The only item that needs to be discussed in detail is the effect of


33

concentration, in open recirculating systems, on the calcium sulphate saturation index. For any given water at any given temperature the calcium sulphate saturation index is given by Eq. (34):  ( DS)0.5  (34)  I S = pK −  p[Ca 2+ ] + p[SO 24− ] + 50   If the water is now allowed to concentrate “n” times in an open recirculating system, the conditions for the circulating water become:

 ( nDS) 0.5  (50) ( I S ) n = pK −  pn[Ca 2+ ] + pn[SO 24− ] +  50    ( nDS) 0.5  (50a) ( I S ) n = pK −  p[Ca 2+ ] + p[SO 24− ] + 2pn +  , 50   0 . 5   ( DS) ( DS) 0.5   = pK −  p[Ca 2+ ] + p[SO 24− ] + −  ( 2pn + ( n 0.5 − 1)   (50b) 50 50     ( DS) 0.5 50 ( DS) 0.5 = I S + 2 log n − ( n 0.5 − 1) 50 = I S − 2pn − ( n 0.5 − 1)

(50c) (50d)

The use of Eq. (50d) is illustrated in the following example: Example Initial water analysis: Calcium = 1500 mg/l CaCO3 Alkalinity = 500 mg/l CaCO3

Ca ratio SO 4 =

1500 = 0.83 1800

Sulphate = 1800 mg/l Na2SO4 Dissolved Solids = 2800 mg/l as such. This water is to be treated with sulphuric acid to reduce the alkalinity to 20 mg/l CaCO3, and then used as make-up to a recirculating cooling system at a temperature of 60 °C and operating at a concentration factor of 6.0. The following changes take place: Loss of alkalinity = 500−20 = 480 mg/l CaCO3 Corresponding gain in sulphate = 480 × 1.42 = 682 mg/l Na2SO4 ∴ New sulphate = 1800 + 682 = 2482 mg/l Na2SO4 .

34


Loss of dissolved solids due to loss of alkalinity = 480 mg/l CaCO3 Gain 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 CaCO3

Ca ratio SO 4

Alkalinity = 20 mg/l CaCO3

=

1500 = 0.60 2482

Sulphate = 2482 mg/l Na2SO4 Dissolved Solids = 3002 mg/l as such From Table 17 pK @ 60 °C = 4.74

From Table 8 p[Ca2+]

= 1.82

From Table 18 p[SO2− 4 ]

= 1.76

( DS)0.5 50

= 1.10 4.68

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

30220.5 50 54.79 = +0.06 + 2 × 0.78 − (2.45 − 1) 50 = +0.06 + 1.56 − (1.45) (1.10) = +1.62 − 1.60 = +0.02

( I S )n = +0.06 + 2 log 6 − (60.5 − 1)

From Table 19/1 Ca = 0.60 and ( I S )n = +0.02 gives b = 0.98 SO4


35

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 286 = 48 mg CaSO4 for each litre of water entering the 6 system. An alternative calculation using Eq. (47e) gives:

a=

10 −( I S )n 10 −0.02 0.96 = = = 0.98 0.98 0.98 b

Loss of calcium = 1.36 × 6 × 1500 × (1−0.98) = 1.36 × 6 × 1500 × 0.02 = 245 mg/l CaSO4. This is equivalent to 245/6 = 41 mg CaSO4 for each litre of water entering the system. The reason for the differences between the two calculated values for calcium sulphate fouling has already been discussed in Sec. 2.3. For practical plant purposes the two values are sufficiently close to allow either value to be used for 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 the saturation index of the make-up water and then simply multiplied by 6 (the value of “n”). It will be seen in the Example already worked out that IS = +0.06 for Ca the make-up water and SO = 0.60. Using these values in Table 19/1 gives 4 a value of “b” = 0.94. On this basis, the loss of sulphate = 0.96 × 2482 × (1−0.94) = 143 mg CaSO4 per litre. The alternative calculation gives a =

10 −0.06 0.94

= 0.93

and loss of calcium = 1.36 × 1500 (1−0.93) = 142 mg CaSO4 per litre. This appears to be very good agreement. But it cannot be accepted because calculations based on the make-up water do not allow the full influence of dissolved solids to be exercised on the ionic equilibria involved in the circulating water. This leads to loss of thermodynamic integrity, and therefore, the method cannot be accepted.

Chapter 3

CALCIUM PHOSPHATE FOULING

The need for discussing calcium phosphate fouling arises from the fact that there has been an increase in the phosphate content of water supplies and hence an increase in the risk of calcium phosphate fouling in industrial water systems. The increased use of phosphate fertilisers in agriculture has led to an increase in phosphate in waterways. Following heavy rain, fertiliser is washed from the surface of fields into adjoining streams, which in turn feed rivers from which public water supplies are drawn. This introduction of phosphate into general water supplies is seasonal, since fertilisers are more usually applied to fields in Spring, when seed is sown and new crops planted out. There is also a meteorological factor since the coincidence of heavy Spring rains with agricultural planting provides a means of washing the surface of fields at the time fertiliser has been applied. The use of phosphates in industrial processes and the inclusion of phosphates in detergents is another source of phosphate entering industrial systems. Effluents from such processes, which have been treated on site and accepted by a Rivers Authority for discharge into a stream, will still carry some phosphate. Similarly, effluent which has been accepted by a local sewage work for treatment, and subsequently offered to industry for cooling purposes will still carry some phosphate. Although step are being taken to reduce the amount of phosphate in water supplies, complete freedom from phosphate cannot be assumed. It is therefore recommended that whenever a new system is being designed, or a problem in an existing system investigated, an assessment of calcium phosphate fouling should be included. Mere visual inspection of water analysis should not be accepted as sufficient.

3.1. CALCIUM PHOSPHATE SATURATION INDEX Following the basis of the definition of the saturation index for calcium sulphate given in Sec. 2.1, the saturation index for calcium phosphate may be similarly 37

38


defined as: I p = pKS − [3p(Ca 2+ ) + 2p( PO34− )]

(51)

K S = (Ca 2+ ) 3 ( PO 34− ) 2

(52)

where

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 analytical test for phosphate gives phosphates in all forms present in the water, whereas Eq. (51) requires only that portion of the total phosphate present as the orthophosphate ion. Clearly, some form of conversion is needed. The necessary conversion has been provided by Green and Holmes [13]. Starting with the equations: K1 = ( H + )

( H 2 PO 4− ) ( H 3PO 4 )

(53)

K2 = (H + )

( HPO 24− ) ( H 2 PO 4− )

(54)

K3 = ( H + )

( PO 34− ) ( HPO 24− )

(55)

( Phos ) = ( PO 34− ) + ( HPO 24− ) + ( H 2 PO 4− ) + ( H 3PO 4 ) .

(56)

These were re-arranged to give:

( PO34− ) = ( Phos)

( H + )3

+ K1

K1K 2 K3 . + K1K 2 ( H + ) + K1K 2 K 3

( H + )2

(57)

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

E=

( H + )3

+ K1

K1K 2 K 3 . + K1K 2 ( H + ) + K1K 2 K 3

( H + )2

(58)

Substituting Eq. (58) in Eq. (57) gives:

( PO 34− ) = ( Phos)( E ) .

(59)

Substituting Eq. (59) in Eq. (51) gives: I p = pKS − [3p(Ca 2+ ) + 2p( Phos) + 2p( E )].

(60)

Calcium Phosphate Fouling

39

For any given water at any given temperature at equilibrium Ip becomes zero and, for these conditions, Eq. (60) can be written as: 3p(Ca 2 + ) + 2p( Phos) = pK S − 2p( E ) .

(61)

Taking values for calcium and Phos from water analyses, and values of KS from the literature, Green and Holmes calculated values of (E) at equlibrium conditions. Using these values, and values of K1, K2, and K3 from the literature in Eq. (58), they then calculated the value of (H+) at equilibrium and hence obtained pHS. Green and Holmes did not proceed beyond this point as their main interest was to establish a method for determining the values of pHS as an aid to controlling phosphate treatments of boiler feed waters. To facilitate these calculations Green and Holmes set up tables to allow values of pHS at various temperatures to be read off from analytical values of calcium and Phos. In setting up their tables Green and Holmes used values for pK1 based on Nims [16], values for pK2 based on Bates and Acree [17], and values for pK3 based on Bjerrum and Unmack [18]. The values are set out in Table 20. There was, however, a problem in evaluating pKS. The literature gave values varying between 25 and 31. After a review of the literature Green and Holmes selected a value by Kuyper [19], which they modified in the light of data by Sendroy and Hastings [20] to give a value of 29.3. This value refers to a temperature of 38 °C: there are no experimental data available (nor reliable theoretical data) to indicate 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 in the procedure. In establishing Eq. (60) calcium and Phos have both been expressed in terms of thermodynamic activity. This will lead to an error (usually slight) because analytical results yield values expressed in terms of stoichiometric concentrations. Green and Holmes made no correction on this account: they considered such a correction to be unwarranted in view of the uncertainty over the value for pKS. However, it is considered that the necessary corrections should be incorporated into Eq. (60) in order to preserve thermodynamic integrity. If, and when, new and 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 and Huckel [14] and Bronstead and LaMer [15]. (Ca 2 + ) = f Ca [Ca 2 + ]

(62)

40


p(Ca 2 + ) = pf Ca + p[Ca 2 + ]

(63)

2 ( µ ) 0.5 + p[Ca 2 + ] = 0.5zCa

(63a)

= 0.5 × 2 2 ( µ ) 0.5 + p[Ca 2 + ]

(63b)

=

2( µ ) 0 .5

+ p[Ca 2 + ].

(63c)

A similar treatment may be applied to (Phos) by using the valency (z) for PO3− 4 since the analytical tests for Phos are expressed “in terms of PO4”. ( Phos) = f PO 4 [ Phos]

(64)

p( Phos) = pf PO 4 + p[ Phos ] = 0.5z 2 PO 4 ( µ ) 0.5 + p[ Phos] =

0 . 5 × 3 2 ( µ ) 0. 5

+ p[ Phos]

= 4.5( µ ) 0.5 + p[ Phos ].

(65) (65a) (65b) (65c)

Substituting Eqs. (63c) and (65c) in Eq. (60) gives: I p = pKS − {3p[Ca 2+ ] + 6( µ )0.5 + 2p[ Phos] + 9( µ )0.5 + 2 p( E )}

= pKS − {3p[Ca 2+ ] + 2 p[ Phos] + 2 p( E ) + 15( µ )0.5}.

(66) (66a)

Using the Langelier [2] evaluation:

µ=

DS (where DS is expressed in mg/l) 40000

I p = pKS − {3p[Ca 2+ ] + 2p[ Phos] + 2p( E ) + 0.075( DS)0.5 }

(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 calculated by simple arithmetic. Example Ca

= 250 mg/l CaCO3

Phos = 50 mg/l PO4 DS

= 300 mg/l as such

pH

= 7.8

T

= 20 °C


pKS = 29.3

41

p[Ca] = 2.60 3p[Ca] = 7.80 From Table 21 p[Phos] = 3.28 2p[Phos] = 6.56 From Table 22 p(E) = 4.73 2p(E) = 9.46 DS = 300 = 1.30 0.075(DS)0.5 25.12 From Table 8

Ip = 29.3 − 25.12 = + 4.18. As the index is positive, the water will deposit calcium phosphate. Had the index 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 the equilibrium 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, or greater than, the actual pH there will be no precipitation of calcium phosphate. Using the difference between pHS and pH is a useful indicator, and served the purpose of Green and Holmes, but it is not mathematically identical with the true saturation index as defined by Eq. (67). The confusion arises because, in the original concept of a saturation index pioneered by Langelier [2] for calcium carbonate, the value of I = pH − pHS is mathematically identical with I = 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 calculations in 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 to calculate the weight of calcium phosphate deposited to cause fouling.

3.2. CALCULATING THE WEIGHT OF CALCIUM PHOSPHATE For any given water at any given temperature:

Let initial calcium = A mg/l as CaCO3

(68)

Let initial Phos = B mg/l as PO 4 .

(69)

After precipitation of calcium phosphate:

Let fraction of calcium remaining = a

(70)

Let fraction of Phos remaining = b .

(71)

42


Thus:

Final calcium = aA mg/l CaCO3

(72)

Final Phos = bB mg/l PO 4 .

(73)

From Eqs. (68) and (72): Loss of calcium = A − aA = A(1 − a ) mg/l as CaCO3 310 = A(1 − a ) mg/l as Ca 3 (PO4 ) 2 300 = 1.03 A(1 − a ) mg/l as Ca 3 (PO4 ) 2 .

(74) (74a) (74b)

From Eqs. (69) and (73): Loss of Phos = B − bB = B(1 − b) mg/l as PO4 310 B(1 − b) mg/l as Ca 3 (PO4 ) 2 190 = 1.63 B(1 − b) mg/l as Ca 3 (PO4 )2 . =

(75) (75a) (75b)

Since loss of calcium must be equal to loss of Phos, when both are expressed in the same unit: From Eqs. (74b) and (75b):

1.03 A(1 − a ) = 1.63 B (1 − b) (1 − b) 1.03 A 0.63 A = = . (1 − a ) 1.63B B

(76) (76a)

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

I p = pK S − (3pA + 2 pB + 2 p( E ) + 0.075( DS) 0.5 )

(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):

I p = pK S − (3paA + 2pbB + 2p( E ) + 0.075( DS) 0.5 )

(78)

= pKS − (3pa + 3pA + 2pb + 2pB + 2p( E ) + 0.075( DS )0.5 )

(78a)

= pK S − (3pA + 2 pB + 2 p( E ) + 0.075( DS) 0.5 ) − (3pa + 2pb) .

(78b)

Because the final water will be in equilibrium with precipitated calcium phosphate Ip must be zero. Thus: 0 = pK S − (3pA + 2pB + 2p( E ) + 0.075( DS) 0.5 ) − (3pa + 2 pb)

(79)


43

Substituting Eq. (77) in Eq. (79) gives: 0 = I p − (3pa + 2pb)

(80)

= I p − ( pa 3 + pb 2 )

(80a)

= I p + log a 3 + log b 2

(80b)

= I p + log a 3b 2

(80c)

− I p = log a 3b 2

(80d)

log10 − I p = log a 3b 2

(80e)

10− I p = a 3b 2

(81)

10 − I p b2

(81a)

a3 =

 10 − I p a =  2  b

   

0.33

(81b)

(neglecting negative or imaginary roots). Substituting Eq. (81b) in Eq. (76a) gives: (1 − b )   10 − I p   1 −  2   b

   

0.33 

0.63 A B

=

  

(1 − b )  (10 − I p )0.33  1 −  b0.67  

(82) =

0.63 A B

(1 − b)  (b0.67 − (10 − I p )0.33 )   

b0.67

 

=

0.63 A B

(1 − b) b0.67 0.63 A = B {b0.67 − (10 − I p )0.33}  0.63 A  0.67  0.63 A  − b 0.67 − b1.67 =  b  (10 − I p )0.33  B   B 

 0.63 A  0.63 A −I p 0.33 (10 ) = 0. − 1 − b1.67 + b 0.67  B  B 

(82a)

(82b)

(82c) (82d) (82e)

44


The discussion covering the development of Eq. (78) through to Eq. (82e) assumes that the change in DS due to the precipitation of calcium phosphate will 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 the value of (E). This assumption is justified because the precipitation takes place in an environment in which the pH is dominated by the relationship between the alkalinity of the water and the total carbon dioxide content. Since neither alkalinity nor carbon dioxide are involved in the precipitation of calcium phosphate, 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 water analysis and the value of Ip obtained from Eq. (77) by the method already described earlier in this section. Equation (82e) may then be solved for “b” which 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” to be read-off from values of Ip and the ratio BA ; or in more general terms the ratio CaCO3/PO4. An alternative approach would be to obtain from Eq. (81) an evaluation of “b” in terms of “a”. This evaluation could then be used in a process similar to that used for Eqs. (82) to (82e) to produce an equation similar to (82e) but expressed in terms of “a”. It can be shown that the equation would read:  0.63 A  2.5  0.63 A  1.5 −I  a − (10 p ) 0.5 = 0 .   a + 1 − B B    

(83)

This equation, like (82e), is complex and would need a new table (similar to Table 23) to allow Eq. (83) to be evaluated. As Table 23 is already in existence it is considered that the work involved in preparing a new table for Eq. (83) is not justified.

3.3. USE IN THE FIELD The procedure outlined below yields a calculated figure for the maximum weight of calcium phosphate precipitated to cause fouling. In practice, the figure may be 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 of Ca, Alk, PO4, DS and pH. Use them to calculate the ratio CaCO3/PO4: to convert the pH to the value for the temperature in the system (if different from atmospheric) using the method on p. 20 of Ref. [8]: to calculate the value of Ip


45

using Eq. (67); for the temperature in the system. (If Ip is zero or negative there will be no precipitation). (xxxi) In Table 23, find the section containing the value of Ip. Run down the left-hand edge of the first table in the section to find the value of Ip. (If the values displayed to not exactly fit the value calculated from Eq. (67) select the nearest). (xxxii) Follow the selected value horizontally across the table, proceeding from table to table in strict numerical order, until the value for CaCO3/PO4 is found. (If the exact figure is not recorded, select the nearest). (xxxiii) At the head of the column located in (xxxii) the value of “b” is given. 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 the total fouling). (xxxiv) Having precipitated calcium phosphate the water may still be capable of depositing calcium carbonate to give a mixed fouling. This should now be checked. = 0.97 to give the (xxxv) Take the result from (xxxiii) and multiply by 300 310 deposit in terms of CaCO3. Deduct this from the original Ca figure to give an amended value. Use this, together with the values for Alk, DS, and pH at the system temperature to calculate I at the system temperature, as described in Sec. 1.3.1. (xxxvi) Use the value of I from (xxxv) to read-off the weight of calcium carbonate deposited from Table 13. Example Ca

= 250 mg/l CaCO3

Phos = 50 mg/l PO4 Alk = 150 mg/l CaCO3 DS

= 300 mg/l as such

pH

= 7.8 @ 15 °C.

What is the fouling at 40 °C? At 15 °C

At 40 °C

Alk = 150 mg/l CaCO3

Alk = 150 mg/l CaCO3

pH = 7.8

C = 312 mg/l CaCO3

C = 312 mg/l CaCO3

pH = 7.7

From Table 20 of Ref. [8]


46


pKs = 29.3

p[Ca2+] = 2+ 3p[Ca ] = From Table 21 p[Phos] = 3.28 2p[Phos] = From Table 22 p[E] = 4.55 2p[E] = DS = 300 0.075(DS)0.5 =

From Table 8

2.60 7.80 6.56 9.10 1.30 24.76

Ip = 29.3 − 24.76 = + 4.54

Ca 250 = = 5.0. PO 4 50 b = 0.01

From Table 23

Final phosphate = 50 × 0.01 = 0.5 mg/l PO4 Loss of phosphate = 50 − 0.5 = 49.5 mg/l PO4 310 = 49.5 × = 81 mg/l Ca3 (PO4)2 . 190 Loss of calcium = 81 mg/l Ca3 (PO4)2 300 = 81 × = 78 mg/l CaCO3. 310 Residual calcium = 250 − 78 = 172 mg/l CaCO3. Residual dissolved solids = 300 − 81 = 220 mg/l as such p[Ca2+]

= 2.76 from Table 8

p[Alk]

= 2.52 from Table 9

pK2 − pKS = 1.70 (10.22 − 8.52 from Table 10) @ 40 °C DS0.5/100 = 0.15 pHS

= 7.13

pHS

=

7.13

pH

=

7.70

I

= + 0.57 @ 40 °C

From Table 13 Total Fouling

W = 20 mg/l CaCO3 (by interpolation) 81 mg/l Ca3(PO4)2 20 mg/l CaCO3.


Example Ca

= 30 mg/l CaCO3

Phos = 80 mg/l PO4 Alk = 60 mg/l CaCO3 DS

= 100 mg/l as such

pH

= 8.2 @ 15 °C.

What is the fouling at 60 °C? At 15 °C

At 60 °C

Alk = 60 mg/l CaCO3

Alk = 60 mg/l CaCO3

pH = 8.2

C = 121 mg/l CaCO3

C = 121 mg/l CaCO3

pH = 8.0



pKS = 29.3

p[Ca2+] = 3.53 = 10.59 3p[Ca2+] From Table 21 p[Phos] = 3.08 2p[Phos] = 6.16 From Table 22 p[E] = 3.95 2p[E] = 7.90 DS = 100

From Table 8

0.075(DS)0.5

=

0.75 25.40

Ip = 29.3 − 25.40 = + 3.90 Ca 30 = = 0.38 . PO 4 80

From Table 23

b = 0.78

Final phosphate = 80 × 0.78 = 62 mg/l PO4 Loss of phosphate = 80 − 62 = 18 mg/l PO4 310 = 18 × = 29 mg/l Ca3(PO4)2 190 300 Loss of calcium = 29 × = 28 mg/l CaCO3 310 Residual calcium = 30 − 28 = 2 mg/l CaCO3. Residual dissolved solids = 100 − 29 = 71 mg/l as such

47

48


p[Ca2+]

=

4.70 from Table 8

p[Alk]

=

2.92 from Table 9

pK2 − pKS =

DS0.5

1.40 (10.14 − 8.74 from Table 10) @ 60 °C

=

0.08

=

9.10

pH

=

8.00

I

= − 1.10.

100 pHS

As I is negative there will be no precipitation of calcium carbonate. Fouling = 29 mg/l Ca3(PO4)2 only.

3.4. THE SPECIAL CASE OF RECIRCULATING SYSTEMS The comments made in Sec. 1.5 concerning recirculating systems also apply here. The only item that needs to be discussed in detail is the effect of concentration, in open recirculating systems, on the calcium phosphate saturation index. For any given water at any given temperature, the calcium phosphate saturation index is given by the Eq. (67): I p = pKS − {3p[Ca 2+ ] + 2p[ Phos] + 2p[ E ] + 0.075( DS)0.5 }.

(67)

If the water is now allowed to concentrate “n” times in an open recirculating system the condition for the circulating water becomes: ( I p )n = pKS − {3pn[Ca 2+ ] + 2pn[ Phos] + 2p[ E ] + 0.075( nDS)0.5 } = pKS − {3pn + 3p[Ca 2+ ] + 2 pn + 2 p[ Phos] + 2p[ E ] + 0.075( nDS)0.5 } = pKS

− {3p[Ca 2+ ] + 2 p[ Phos] + 2p[ E ] + 0.075( nDS)0.5

+ 5pn}

= pKS − {3p[Ca 2+ ] + 2 p[ Phos] + 2p[ E ] + 0.075( nDS)0.5 − 5 log n}.

(84) (84a) (84b) (84c)

The equation cannot be developed beyond this stage, because of the changes in the pH of the water as it passes round the open recirculating system. Firstly, there is the change in pH due to the temperature rising from atmospheric to the ambient temperature in the system. Secondly, there is the change in pH as the circulating water establishes an equilibrium with the atmosphere. Thus, the final pH will be different from that resulting solely from a temperature rise in the system and therefore a different value of p[E] will be needed to evaluate Eq. (84c).


The use of Eq. (84c) is illustrated in the following example. Example Calcium = 80 mg/l CaCO3 Phos

= 40 mg/l PO4

Alk

= 70 mg/l CaCO3

DS

= 200 mg/l as such

pH

= 7.2 @ 15 °C

Temperature in system = 45 °C. Number of concentrations = 3. At 15 °C

At 45 °C and n = 3

Alk = 70 mg/l CaCO3

Alk = 3 × 70 = 210 mg/l CaCO3

pH = 7.2

C = 2 × Alk = 2 × 210 = 420 mg/l CaCO3 From p. 27 of Ref. [8] pH = 8.2 From Table 57 of Ref. [8].

pKS = 29.3

p[Ca2+] = 3.10 3p[Ca2+] = From Table 21 p[Phos] = 3.38 2p[Phos] = From Table 22 p[E] = 3.90 2p[E] = DS = 200 0.075 (3 × 200)0.5 =

From Table 8

n = 3 log n = 0.45 5 log n Ip = 29.3 − 23.45 = 5.85 Ca 80 = = 2 .0 . PO 4 40

From Table 23/6

b = 0.015 (by interpolation).

Final phosphate in system = 3 × 40 × 0.015 = 1.8 mg/l PO4.

=

9.30 6.76 7.80 1.84 25.70 2.25 23.45

49

50


Loss of phosphate = 3 × 40 − 1.8 = 118 mg/l PO4 310 = 118 × 190 = 192 mg/l Ca3 (PO4)2. Equivalent to as make-up.

192 3

= 64 mg Ca3(PO4)2 for each litre of water entering the system

Loss of calcium in system = 192 mg/l Ca3(PO4)2 300 = 192 × 310 = 186 mg/l CaCO3. Residual calcium in system = 3 × 80 − 186 = 240 − 186 = 54 mg/l CaCO3. Residual dissolved solids in system = 3 × 200 − 192 = 600 − 192 = 408 mg/l as such. Alkalinity in system (unchanged) = 3 × 70 = 210 mg/l CaCO3. p[Ca2+]

= 3.27 from Table 8

p[Alk]

= 2.38 from Table 9

pK2 − pKS = 1.63 (10.20 − 8.57) from Table 10 @ 45 °C DS0.5/100 = 0.20 pHS

= 7.48

pH

= 8.20

I = pH − pHS = 8.20 − 7.48 = + 1.72. From Table 13 the value of I = + 1.72 at 45 °C falls outside the range of the table and would appear to indicate calcium carbonate deposited in excess of 620 mg/l. But this is impossible with a residual calcium in the system of only 54 mg/l. The anomoly arises from the fact that the Alk/Ca ratio is very high for the water under discussion. Clearly, the true value for calcium carbonate deposited will be of the order of 50 mg/l. A value may be calculated by the method of iteration.


51

If, by way of illustration, it is assumed that there is a nominal precipitation of 40 mg/l CaCO3, then the final water in the system will contain: Ca = 14 mg/l CaCO3 Alk = 170 mg/l CaCO3 DS = 368 mg/l as such p[Ca2+]

= 3.85 from Table 8

p[Alk]

= 2.47 from Table 9

pK2 − pKS = 1.63 (10.20 − 8.57) from Table 10 @ 45 °C DS0.5/100 = 0.19 = 8.14 pHS pH I

= 8.20 = pH − pHS = 8.20 − 8.14 = + 0.04.

This value is close enough to the, theoretical, zero for all practical, plant purposes and therefore 40 mg/l can be accepted as the deposited calcium carbonate in the system. = 13 mg/1. In the make-up water the corresponding figure is 40 3 Total fouling

64 mg Ca3(PO)4 13 mg CaCO3 for each litre of water entering the system as make-up.

Chapter 4

CORROSION OF MILD STEEL

4.1. THE RYZNAR INDEX At the beginning of this book, under the discussion of fouling by calcium carbonate, the Ryznar Index was introduced. It was pointed out that Ryznar had produced his Index as an empirical relationship linking the chemical characteristics of a water and the weight of calcium carbonate that it would precipitate under given conditions. It was also pointed out that Ryznar did not extend his investigations beyond this area. He did not take (what would appear to be the next logical step) of investigating a possible relationship between his Index and the rate of corrosion of steel in water. That gap has now been filled by Finan et al. [21]. Their work involved the use of a cooling tower test rig, the basis of which is shown in Fig. 7. Water from the sump is pumped through an electric heat-exchanger in order to obtain a controlled rise in temperature. The water then passes through a test coupon chamber in which mild steel and cast iron test coupons are suspended. Weighing the coupons before and after a test run gives the weight loss due to corrosion during the duration of the run, and hence the corrosion rate is calculated. Water leaving the test coupon chamber next passes down a cooling tower where it is cooled by an upward current of air. Some evaporation losses occur here, causing an increase in the concentration of salts dissolved in the water. The degree of concentration is controlled by adjustment of the purge bled from the sump and the make-up water added. Using this procedure Finan et al. were able to study the corrosion rates for a range of natural waters over a range of concentration factors. The results of this study were not published in the form of tables, giving details of each test run, but were summarised in the form of a graph. The graph makes no distinction between cast iron and mild steel. That graph is reproduced in Fig. 8. Mathematical analysis of the graph shows that the “best fit” equation corresponding to the curve is: C/ = 0.774 exp (0.458R) 53

(85)

54


Fig. 7. Basis of cooling tower test rig.

Corrosion of Mild Steel

Fig. 8. Plot of Ryznar index(R)-v-corrosion rate(C/ ) mild steel.

55

56


which may be converted to the logarithmic form as: In C/ = 0.458R + In 0.774 = 0.458R − 0.256.

(86) (86a)

For practical use it will probably be more convenient to use common logarithms. The conversion is: 2.303 log C/ = 0.458R − 0.256

(87)

log C/ = 0.199R − 0.111.

(87a)

In Fig. 8, the corrosion rate is expressed in terms of mpy (mils per year = in × 10−3 per year). It is preferred to work in the corresponding SI unit (mm per year = mm.y−1). The conversion is: log (C/ × 39.3) = 0.199R − 0.111

(88)

log C/ + log 39.3 = 0.199R − 0.111

(88a)

log C/ + 1.594 = 0.199R − 0.111

(88b)

log C/ = 0.199R − 1.705

(88c)

Before Eq. (88c) can be used in the field, attention must be given to the temperature at which the values of C/ and R were determined in order to construct the graph in Fig. 8. The values for R were based on the analyses of samples of water taken from the test rig and analysed on the bench at atmospheric temperature. (A nominal 15 °C). The values of C/ represent the corrosion rates of mild steel test coupons maintained at the ambient water temperature in the test rig. This temperature has not been stated. However, elsewhere in their report, Finan et al. give a temperature rise of 9 °C for a typical industrial cooling system. This figure is in line with general experience for this type of system. It may reasonably be assumed that the test rig was set to reproduce conditions existing in typical industrial systems and therefore the ambient water temperature would be of the order of 9 °C above atmospheric temperature. For the purpose of evaluating Eq. (88c) a nominal system temperature of (25 °C) has been assumed. Therefore, before Eq. (88c) is used the value of C/ must be converted from that for 25 °C to that for 15 °C. Ison and Butler [22] give the temperature coefficient for the corrosion rate of mild steel in water as: C/ T°C = C/ t°C (1 + 0.05 (T − t)).

(89)


57

A similar coefficient is indicated by Large [23]. For a 10 °C rise from 15 °C to 25 °C: C/ 25 °C = C/ 15 °C (1 + 0.05 × 10).

= C/ 15 °C (1.5).

(90) (90a)

Inserting this value in Eq. (88c) gives: log 1.5C/ 15 °C = 0.199R − 1.705

(91)

log 1.5 + log C/ 15 °C = 0.199R − 1.705

(91a)

0.176 + logC/ 15 °C = 0.199R − 1.705

(91b)

log C/ 15 °C = 0.199R − 1.881.

(91c)

For general plant use, the equation may be written: log C/ = 0.2R − 1.9.

(92)

4.1.1. Use in the Field To apply Eq. (92) in the field, the following procedure may be used: (xxxvii) From a water analysis at atmospheric temperature (15 °C) take the values of Ca, Alk, and DS. Use them to calculate the value of pHS at temperature T (the temperature in the system) using Eq. (6) in Sec. 1.1.2 and following paragraph (xv) in Sec. 1.2.1. (xxxviii) From a water analysis at atmospheric temperature (15 °C) take the values of pH and Alk and use them to convert to the pH at T, as described by Emerson on p. 20 of Ref. [8]. (xxxix) From (xxxvii) and (xxxviii) calculate the Ryznar Index at T. R = 2pH S − pH

(1)

(xl) Use the value of R in Eq. (92) to obtain a value of C/ . (xli) This value of C/ assumes that the relationship between R and C/ is the same for all temperatures: but this is not so and C/ must be adjusted for the temperature in the system (T) using Eq. (89). Example Calcium = 80 mg/l CaCO3. Alkalinity = 60 mg/l CaCO3. Dissolved Solids = 150 mg/l as such pH = 7.2.

58


Temperature in system = 50 °C p[Ca2+] = 3.10

from Table 8

p[Alk] = 2.92

from Table 9

pK2 − pKS = 1.54 @ 50 ° (10.17 − 8.63) from Table 10

DS0.5 = 0.12 100 pHS = 7.68 @ 50 °C. At 15 °C

At 50 °C

Alk = 60 mg/l CaCO3

Alk = 60 mg/l CaCO3

pH = 7.2

C = 140 mg/l CaCo3

C = 140 mg/l CaCO3

pH = 7.1

from Table 20 of Ref. [8]

from Table 62 of Ref. [8]

R = 2pHS − pH = 2 × 7.68 − 7.1 = 8.26 @ 50 °C log C/ = 0.2 × 8.26 − 1.9 (from Eq. 92) = 1.65 − 1.9 = −0.25 C/ = 0.56 mm.y−1 @ 15 °C value. Convert to 50 °C C/ = = = =

0.56 0.56 0.56 0.56

(1 + 0.05 (50 − 15)) (1 + 0.05 × 35) (1 + 1.75) × 2.75 = 1.54 mm.y−1.

If the system was constructed from mild steel of 5 mm thickness, failure by penetration of the metal by corrosion would be anticipated in approximately 3 years ( 1.554 = 3.25). An alternative way of obtaining the corrosion rate is to read it off from Table 24. Locate the section of the table containing the values of R between 8.0 and 8.9. This is found in Table 24/3. Locate the column headed R = 8.3 (the nearest value to R = 8.26). At the left-hand edge of the table locate the temperature in the system (50 °C). Scan this line horizontally until it meets the column headed R = 8.3. The figure at the intersection is the corrosion rate (1.60). This gives the same failure time for the system. ( 1.561 = 3.13 years)


59

These corrosion rates should be regarded as estimates. The original rates used by Finan et al. [21] were obtained experimentally from test plates, and are therefore empirical. Also, they were related to the Ryznar Index, which is itself an empirical parameter. There is no direct thermodynamic relationship between the corrosion rate and the Ryznar Index.

4.1.2. The Special Case of the Recirculating System The discussion so far has been based on once-through system. If a closed system is employed, utilising a heat-exchanger to shed heat, and IF THE SYSTEM IS HERMETICALLY SEALED, the water will be maintained out of contact with oxygen. Any initial corrosion will be stifled. This situation is unusual and most, so called, closed systems have some access from atmospheric oxygen via a feed/expansion tank or venting valves which allow contact with the atmosphere. Under these conditions, with oxygen available to the system, corrosion will proceed at a similar rate to that already described. However, different conditions exist in the open recirculating system using a cooling tower. In this type of system there is a concentration of dissolved salts in the circulating water. This modifies the value of pHS as described in Eq. (33) in Sec. 1.5.2. Also, intimate contact between the circulating water and atmospheric air in the cooling tower modifies the pH, as described on p. 27 of Ref. [8]. These modified values must be used to calculate the value of R to be used in Eq. (92). Example Calcium = 80 mg/l CaCO3. Alkalinity = 60 mg/l CaCO3. Dissolved solids = 150 mg/l as such. pH = 7.2. Temperature in system = 50 °C. Number of concentrations in system = 2 from Table 8 p[Ca2+] = 3.10 p[Alk] = 2.92 from Table 9 pK2 − pKS = 1.54 @ 50 °C (10.17 − 8.63) from Table 10

DS0.5 = 0.12 100 pHS = 7.68 for make-up water @ 50 °C.

60


In system with n = 2 from Eq. (33)

DS0.5 100 = 7.68 − 2 × 0.30 + (1.41 − 1) 0.12 = 7.68 − 0.60 + 0.05 = 7.1 .

pHS = 7.68 − 2 log 2 + (20.5 − 1)

Make-up @ 15 °C Alk = 60 mg/l CaCO3 pH = 7.2 C = 140 mg/l CaCO3 from Table 20 of Ref. [8]

System @ 50 °C and n = 2 Alk = 2 × 60 = 120 mg/l CaCO3 C = 2 × 120 = 240 mg/l CaCO3 from page 27 of Ref. [8] pH = 8.2 from Table 63 of Ref. [8]

R = 2pHS − pH = 2 × 7.1 − 8.2 = 14.2 − 8.2 = 6.0. From Table 24/1 C/ = 0.55 mm.y−1 and failure for 5 mm mild steel = 9 years.

4.2. THE LANGELIER INDEX At the beginning of this book the relationship between the Ryznar Index and calcium carbonate fouling was discussed in Secs. 1.1 and 1.2. The discussion was then extended to establish a similar relationship between the Langelier Index and calcium carbonate fouling in Sec. 1.3. In the preceeding Sec. 4.1, the relationship between the Ryznar Index and the corrosion rate for mild steel has been discussed, following the work of Finan et al. The next logical step appears to be to investigate the possibility of a relationship between the Langelier Index and the corrosion rate for mild steel. In order to carry out this next stage of investigation, ten water analyses have been selected, which cover a reasonably wide range of industrial water supplies. The Ryznar Index and Langelier Index have been calculated for each water and, using the Ryznar Index, the corrosion rate for mild steel calculated from Eq. (92). The relationship between the corrosion rates and the values for the Langelier Index is then investigated. The water analyses and associated data are set out in Table 25. The relationship between the Langelier Index (I) and the Corrosion Rate (C/ ) at 15 °C is shown by the curve in Fig. 9. It will be seen that the general characteristics of this curve are very similar to those shown in Fig. 8 for the Ryznar Index.


Fig. 9. Plot of Langelier index(I)-v-corrosion rate(C/ ) mild steel.

61

62


Mathematical analysis of Fig. 9 shows that the “best fit” equation corresponding to the curve is: C/ = exp (−0.767 I ) × 0.359.

(93)

It will probably be more convenient to use this equation in the logarithmic form: In C/ = −0.767 I − 1.024

(94)

or using common logarithms: 2.303 log C/ = −0.767 I − 1.024 log C/ = −0.333 I − 0.455.

(95) (95a)

4.2.1. Use in the Field To apply Eq. (95a) in the field, the following procedure may be used: (xlii) From a water analysis at atmospheric temperature (15 °C) take the values of Ca, Alk, DS. Use them to calculate the value of pHS at temperature T (the temperature in the system) using Eq. (6) in Sec. 1.1.2 and following paragraph (xv) in Sec. 1.2.1. (xliii) From a water analysis at atmospheric temperature (15 °C) take the values of Alk and pH and use them to convert to the pH at T, as described by Emerson on p. 20 of Ref. [8]. (xliv) From (xlii) and (xliii) calculate the Langelier Index: I = pH − pHS

(5)

(xlv) Use the value of I to calculate the value of C/ from Eq. (95a). (xlvi) This value of C/ assumes that the relationship between I and C/ is the same for all temperatures: but this is not so and C/ must be adjusted for the temperature in the system (T) using Eq. (89). Example Calcium = 80 mg/l CaCO3. Alkalinity = 60mg/l CaCO3. Dissolved Solids = 150 mg/l as such. pH = 7.2. Temperature in system = 50 °C.


63

p[Ca2+] = 3.10 from Table 8 p[Alk] = 2.29 from Table 9 pK2 − pKS = 1.54 @ 50 °C (10.17 − 8.63) from Table 10 DS0.5 = 0.12 100 pHS = 7.68 @ 50 °C. At 15 °C Alk = 60 mg/l CaCO3 pH = 7.2 C = 140 mg/l CaCO3 From Table 20 of Ref. [8]

At 50 °C Alk = 60 mg/l CaCO3 C = 140 mg/l CaCO3 pH = 7.1. From Table 62 of Ref. [8]

I = 7.1 − 7.68 = −0.58 @ 50 °C log C/ = −0.333(−0.58) − 0.455 (from Eq. (95a)) = 0.193 − 0.445 = −0.252 C/ = 0.56 mm.y−1 @ 15 °C value. Convert to 50 °C C/ = 0.56 (1 + 0.05(50 − 15)) = 0.56 (1 + 0.05 × 35) = 0.56 (1 + 1.75) = 0.56 × 2.75 = 1.54 mm.y−1. If the system was constructed from mild steel of 5 mm thickness, failure by penetration of the metal by corrosion would be anticipated in approximately 3 years. ( 1.554 = 3.25). An alternative method of calculating the corrosion rate is to read it off from Table 26. Locate the section of the table containing the values of I between −0.1 and −1.0. This is found in Table 26/1. Locate the column headed I = −0.6 (the nearest value to −0.58). At the left-hand edge of the table, locate the temperature in the system (50 °C). Scan this line horizontally until it meets the column headed I = −0.6. The figure at the intersection is the corrosion rate (1.57). This gives the same failure time for the system ( 1.557 = 3.18). These corrosion rates should be regarded as estimates. Although the Langelier Index is derived by thermodynamic calculations, its calibration to corrosion rates still depends on the empirical values of Finan.

64


4.2.2. The Special Case of the Recirculating System The comments made in Sec. 4.1.2 also apply here. Therefore, it is only necessary to consider the open recirculating system incorporating a cooling tower. Again, as already stated is Sec. 4.1.2, the values of pHS must be adjusted to take account of the concentration factor in the system and before using Eq. (95a). Example Calcium = 80 mg/l CaCO3. Alkalinity = 60 mg/l CaCO3. Dissolved Solids = 150 mg/l as such. pH = 7.2. Temperature in System = 50 °C. Number of concentrations in system = 2 p[Ca2+] = 3.10 from Table 8 p[AlK] = 2.92 from Table 9 pK2 − pKS = 1.54 @ 50 °C (10.17 − 8.63) from Table 10

DS0.5 = 0.12 100 pHS = 7.68 for make-up water @ 50 °C In system with n = 2 from Eq. (33)

DS0.5 100 = 7.68 − 2 × 0.30 + (1.41 − 1) 0.12 = 7.68 − 0.60 + 0.05 = 7.1.

pHS = 7.68 − 2 log 2 + (20.5 − 1)

Make-up @ 15 °C Alk = 60 mg/l CaCO3 pH = 7.2 C = 140 mg/l CaCO3 from Table 20 of Ref. [8].

System @ 50 °C and n = 2 Alk = 2 × 60 = 120 mg/l CaCO3 C = 2 × 120 = 240 mg/l CaCO3 from p. 27 of Ref. [8] pH = 8.2 from Table 63 of Ref. [8]. I = pH − pHS = 8.2 − 7.1 = 1.1.

Under the operating conditions of the system the water has now achieved a positive Langelier Index and converted to a scale-forming water. Corrosion (if any) will be negligible.


65

Before moving on to the next section, it will be interesting to make a comparison between the values of C/ obtained from the Ryznar Index and the Langelier Index.

4.3. COMPARISON BETWEEN THE RYZNAR INDEX AND THE LANGELIER INDEX In order to make a comparison between the results obtained from the Ryznar Index and the Langelier Index, four different pairs of values for pHS and pH and four different temperatures have been selected. The values of R and I have been calculated for each pair and the values of C/ read off from Tables 24 and 26 respectively. The results are set out in Table 27/1. It will be seen that there is a difference between the two values of C/ in each case. The difference increases and becomes more significant as temperatures increase. It is considered that the explanation lies in the basic characteristics of R and I. Five pairs of values for pHS and pH have been selected and the corresponding values of R and I calculated. The results are set out in Table 27/2. (No temperature has been recorded as it is not relevant in this case). It will be seen that the values of I vary over a fairly wide range, whereas values of R are constant at 8.0–8.1. This is an indication that I is a more regularly calibrated parameter than R, and therefore the use of I is preferred. Additionally, I has the advantage of being obtained by direct thermodynamic calculations, whereas R is empirically derived. Some plant operators may prefer to work with R since the values of C/ obtained from Table 24 are generally higher than corresponding values from Table 26 based on I. The use of R therefore provides an extra “margin of safety”. However, using a higher value for C/ may lead to extra or more expensive corrective treatment and thereby result in a condition of “over-kill”. A final decision can only be taken after a careful consideration of the local conditions prevailing at each plant.

4.4. BUFFER CAPACITY In the preceding sections, two parameters have been considered for providing a quantitative forecast of the rate of corrosion for mild steel. The two parameters, the Ryznar Index and the Langelier Index, both involve the use of the equilibrium pH (pHS) as defined in Eq. (2). This equation contains a term related to the concentration of calcium ions in the water.

66


Calculations involving the concentration of calcium ions in the water cease to be applicable when this item is missing. This state of affairs arises where the water has been softened by the base-exchange process, or less frequently, has been softened naturally by the original raw water passing through a layer of natural zeolite (green sand) in the strata of the ground through which the water has passed. An alternative parameter which may be considered for these conditions is the buffer capacity (sometimes referred to as the buffer value). Large [23] and Stumm [24] both show that there is a qualitative relationship between the buffer capacity of a water and the rate of corrosion of cast iron (the lower the buffer capacity the higher the corrosion rate) but neither worker investigated a quantitative relationship. Before investigating any possible quantitative relationship further, it may be helpful to describe buffer effect and buffer capacity.

4.4.1. Description of Buffer Effect The buffer effect is well known and is described in chemical text books. For the purpose of this discussion it may be summarised, in general terms, as follows. When a strong electrolyte is dissolved in water it is completely dissociated into cations and anions. The change in the alkalinity of the solution on adding a strong acid/strong base can easily be determined by a simple stoichiometric calculation. Similarly, the corresponding change in the pH of the solution can easily be determined by a simple logarithmic calculation. But when the salt of a weak acid is dissolved in water the anion produced on dissociation undergoes a secondary reaction with water to form a partially dissociated anion. This form of anion has the ability to resist or restrict changes in pH. Thus, while the change in alkalinity following the addition of a strong acid/strong base remains easily determined by a simple stoichiometric calculation, the corresponding change in pH can no longer be determined by a simple logarithmic calculation, because of the anions ability to resist or restrict changes in pH.

4.4.2. Definition of Buffer Capacity If was proposed by Van Slyke [25] that the qualitative effect described in the previous section should be quantified in the following manner. Original Solution Add acid

Original pH pH0 New pH = pHa

Original alkalinity Alk0 New Alkalinity = Alka.


67

A change (decrease) in pH = pHa − pH0 = d(pH) has produced a change (decrease) in alkalinity = Alka − Alk0 = d(Alk) Hence a change (decrease) in pH = d ( Alk ) in alkalinity = d ( pH ) .

d ( pH ) d ( pH )

Original Solution Add base

Original alkalinity Alk0 New Alkalinity = Alkb.

Original pH pH0 New pH = pHb

= 1 will produce a change (decrease)

A change (increase) in pH = pHb − pH0 = d(pH) has produced a change (increase) in alkalinity = Alkb − Alk0 = d(Alk). Hence a change (increase) in pH = in alkalinity = d ( Alk ) .

d ( pH ) d ( pH )

= 1 will produce a change (increase)

d ( pH ) d ( Alk ) d ( pH ) is

The ratio termed the buffer capacity and is defined as the change in alkalinity per change of 1 unit of pH. As pH is a logarithm (a pure number) it has no dimensions: but Alk will be expressed in whatever unit alkalinity is measured. (Mole per litre: equivalent per litre: mg CaCO3 per litre: etc.). Thus the buffer capacity will be expressed (for example) as mg CaCO3/litre per unit of pH. Having developed Van Slyke’s concept of buffer capacity to this point it is now possible to move on to its application to water analyses.

4.4.3. Water Analyses and Buffer Capacity The relationship between water analyses and buffer capacity can best be followed graphically by means of Fig. 10. Any given water at any given temperature will have an original alkalinity (Alk0) and an original pH (pH0) represented by the point 0 in Fig. 10. If a strong base is now added to the water the alkalinity/pH relationship will follow the curve 0B. Similarly, if a strong acid is added the alkalinity/pH relationship will follow the curve 0A. d ( Alk ) The buffer capacity is defined as d ( pH ) which, in the differential calculus notation, is the slope of the curve A0B at the point 0 and represented by the tangent X0Y. If the equation of the curve A0B was known, the slope at point 0 could be calculated. Unfortunately, this equation will not be known and its experimental determination (especially at elevated temperatures) will be timeconsuming, difficult, and therefore impractical.

68


Fig. 10. Plot of water analyses and buffer capacity.

One way round this difficulty has been offered by Stumm [24] who has produced the equation:

 ( H + )( Alk )  ( H + )   K  +  + ( H + ) + (OH − ) . + + 2 B = 2.3  +  ( H ) + 2K 2  ( H ) + K1 ( H ) + K 2  

(96)

In this equation, (Alk) is expressed as equivalents per litre while K1 and K2 are the first and second dissociation constants respectively for carbonic acid.


69

Thus Eq. (96) will give values of B expressed as equivalents per litre per 1 unit of pH. Stumm offered Eq. (96) as a means of representing the Van Slyke concept in terms of water analyses. But there was no detailed mathematical description showing how Eq. (96) had been deduced. On first inspection the form and style of Eq. (96) is consistent with it having been thermodynamically deduced. But it contains a mathematical anomoly. d ( Alk )

By definition B = d ( pH ) and therefore Eq. (96) is a differential equation representing changes in alkalinity relative to changes in pH. Such an equation cannot also contain a term for alkalinity (Alk) on the right hand side. This point is clearly illustrated by refering to the equation produced by Dye [26].  K   (H + ) K2   (H + )       + + 1 (C ) =  ( Alk ) − W ( H + )   ( H + ) + 2 K 2  ( H + )   K1 

(97)

which can be rearranged to give:

( Alk ) =

 (H + )

  K1

K (C ) + W . + K2   (H )  (H + )  + 1 + +   + ( H )   ( H ) + 2 K 2 

(97a)

Equation (97a) is a complex expression yielding values of (Alk) in terms of (C) K1 K2 and (H+). If the equation is now differentiated to give values of d ( Alk ) it will yield another complex expression in terms of (C) K1 K2 and (H+). d ( pH ) But in no way will it contain a term for (Alk) on the right hand side. It is for this reason that, in the absence of any details of its derivation, Eq. (96) is considered to contain a mathematical anomoly. On this basis Eq. (96) is considered to lack thermodynamic integrity, but is retained as an empirical equation since it was used by both Large [23] and Stumm [24] in establishing a relationship between buffer capacity and the rate of corrosion of cast iron. In a later section (Sec. 4.4.5) there is a comparison of these results with the corrosion rate obtained by another method. Therefore it is important to know the status of Eq. (96) in order to make such a comparison meaningful. Evaluating B from Eq. (96) is time-consuming rather than difficult. This will obviously be a disadvantage if a large number of calculations have to be made. One method of overcoming the difficulty would be to prepare a series of tables from which the value of B could be read off for a wide range of alkalinities, pH values and temperatures. To cover the full range of conditions likely to be

70


encountered in industrial water systems the tables would need to embrace: Alkalinity pH Temperature

10 mg to 500 mg CaCO3 per litre in steps of 10 mg. 6.0 to 11.9 in steps of 0.2 0 °C to 100 °C in steps of 5 °C.

This range will require a total of 126 tables. Fortunately, there is no need to prepare these tables. A method is available for the value of B to be read off from existing tables in Ref. [8].

4.4.4. Evaluation of Buffer Capacity The method of evaluating buffer capacity can be best described graphically using Fig. 11. In this graph the curve A0B is identical with that used in Fig. 10. Any water at any temperature has an original alkalinity (Alk0) and an original pH (pH0) represented by the point 0. A strong base is added to increase the pH by 0.1 unit to pH b. The corresponding change in alkalinity is an increase to Alkb. A strong acid is added to decrease the pH by 0.1 unit to pHa. The corresponding change in alkalinity is a decrease to Alka. Thus: Total change in alkalinity = d(Alk) = Alkb − Alka. Total change in pH = d(pH) = pHb − pHa. = pH0 + 0.1 − (pH0 − 0.1) = 0.1 + 0.1 = 0.2 d ( Alk ) d ( pH ) ( Alk b − Alk a ) = 0.2 = 5(Alkb − Alka).

Buffer capacity = B =

Since Alkb and Alka can be read off direct from the tables in Ref. [8], B is easily calculated. In the three examples which follow the value of B is calculated by the method described above and, for a comparison, the value calculated from Eq. (96) is also shown. The difference between the two values may be explained by the fact that Eq. (96) is an empirical equation (as explained in Sec. 4.4.3) whereas


71

Fig. 11. Plot of evaluation of buffer capacity.

the thermodynamic integrity of the tables in Ref. [8] have already been established in the text of that work. However, the values calculated from Eq. (96) are of the same order of magnitude as those obtained from the method described above. Hence the comparison of corrosion values in Sec. 4.4.5 with those obtained from values of B from Eq. (96) is acceptable.

72


Example pH = 7.0

Alk = 100 mg CaCO3/l From Table 20 of Ref. [8] At pH = 7.1

T = 15 °C

C = 253 mg CaCO3/l

and C = 253

Alkb = 105 mg CaCO3/l (by interpolation)

From Table 19 of Ref. [8] Alka = 95 mg CaCO3/l (by interpolation) B = 5(Alkb − Alka) = 5(105 − 95) = 5 × 10 = 50 mg CaCO3/l per unit of pH (From Eq. (96a) B = 64). At pH = 6.9

and C = 253

Example pH = 8.0


T = 15 °C

C = 511 mg CaCO3/l

and C = 511

Alkb = 252 mg CaCO3/l (by interpolation)

From Table 20 of Ref. [8] Alka = 248 mg CaCO3/l (by interpolation) B = 5(Alkb − Alka) = 5(252 − 248) = 5 × 4 = 20 mg CaCO3/l per unit of pH (From Eq. (96a) B = 17). At pH = 7.9

and C = 511

Example pH = 7.5


T = 40 °C

C = 318 mg CaCO3/l

and C = 318

Alkb = 153 mg CaCO3/l (by interpolation) At pH = 7.4 and C = 318 Alka = 148 mg CaCO3/l (by interpolation) B = 5(Alkb − Alka) = 5(153 − 148) = 5 × 5 = 25 mg CaCO3/l per unit of pH (From Eq. (96a) B = 21).


73

4.4.5. Buffer Capacity and Corrosion Rate In order to establish a relationship between buffer capacity and corrosion rate for base-exchange waters, the ten water analyses in Table 25 have been converted to the analyses that would be obtained following base-exchange treatment. Although it is often assumed that base-exchange treatment produced a water with zero hardness, this is not the case. There is an equilibrium between the water and the base-exchange resin which leaves a trace of residual hardness in the water. In the present discussion a nominal residual hardness of 2 mg CaCO3/l has been assigned to each water. The new analyses are set out in Table 28. In the same table, new values for pHS and I have been calculated and the corresponding values of C/ taken from Table 26. Also recorded are the values for buffer capacity, calculated according to Sec. 4.4.4. It will be noted in Table 28 that the lower the value of the buffer capacity, the higher is the value of the corrosion rate. This is in agreement with the observations of Large [23] and Stumm [24], as already stated at the beginning of Sec. 4.4. Exploration of the values recorded in Table 28 shows that a linear relationship exists between C/ and B/Alk. This is shown in Fig. 12, which indicated a “best fit” relationship of: C/ = 3.89 B / Alk + 0.96.

(100)

For pratical plant purpose this may be rounded-off to: C/ = 4 B / Alk + 1.

(100a)

This is for base-exchange waters @ 15 °C. Equations (100) and (100a) provide an empirical relationship and therefore, are of the same status as the Ryznar Index.

4.4.6. Use in the Field Equation (100a) may be used in the field as follows: (xlvii) From an analysis of a base-exchange water at atmospheric temperature (nominal 15 °C) select the alkalinity and pH value. (xlviii) From Tables 19 to 24 in Ref. [8] read off the value of C. (xlix) Move to the tables in Ref. [8] covering the temperature in the system. Using the alkalinity of the water and the value of C from (xlviii) read off the new pH.

74


Fig. 12. Plot of corrosion rate(C/ )-v-buffer capacity/alkalinity base exchange water and mild steel.


75

(l) Increase the pH by 0.1 and with the value of C as above read off the value of Alkb. Similarly, reduce the pH by 0.1 and read the value of Alka. (li) Calculate the buffer capacity(B) as 5(Alkb − Alka). (lii) Using the value of B and the alkalinity calculate the value of B/Alk and then use this in equation (100a) to calculate the corrosion rate (C/ ). (liii) The value of C/ obtained from (lii) assumes that the corrosion rate at the temperature in the system is the same as at 15 °C, which is not the case. (liv) Apply a temperature correction to convert the value of C/ at 15 °C to the temperature) of the system by using Eq. (89) from Sec. 4.1. Example Alkalinity = 200 mg CaCO3/l System temperature = 40 °C.

pH = 7.5 @ 15 °C.

At 15 °C From Table 20 of Ref. [8] C = 433

At 40 °C From Table 50 of Ref. [8] pH = 7.4.

Increase pH to 7.5 C = 433 Alkb = 205 (by interpolation)

Reduce pH to 7.3 C = 433 Alka = 197 (by interpolation).

B = 5(Alkb − Alka) = 5(205 − 197) = 5 × 8 = 40 40 B / Alk = = 0.2 200 C/ = 4 × 0.2 + 1 = 1.8 mm/yr @ 15 °C rating. Convert to 40 °C C/ = 1.8 (1 + 0.05 (40 − 15) = 1.8(1 + 0.05 × 25) = 1.8 (1 + 1.3) = 1.8 × 2.3 = 4.1 mm/yr @ 40 °C. An alternative method is to use Table 29. In Table 29/1 find the column headed B/Alk = 0.2. At the left hand edge find T = 40 °C. Where this line meets the column above read off C/ = 4.05 mm/yr.

4.4.7. The Special Case of the Recirculating System The comments made in Sec. 4.1.2 also apply here and, therefore, it is only necessary to consider a recirculating cooling system incorporating a cooling tower.

76


The following procedure may be used. (lv) From the water analysis select the alkalinity of the make-up water @ 15 °C. (lvi) Multiply by the number of concentrations (n) to be carried in the system to obtain the alkalinity of the system water (nAlk). (lvii) From p. 28 of Ref. [8] calculate C for the system water as twice the alkalinity (C = 2nAlk). (lviii) From the tables in Ref. [8], using the values from (lvi) and (lvii) read off the pH for the system temperature. (lix) Using this pH value, repeat steps (l) to (liv). Example Alkalinity of make-up = 150 mg CaCO3/l System temperature = 30 °C. Number of concentrations = 3.0. Alkalinity in system = 3 × 150 = 450 C in system = 2 Alk = 2 × 450 = 900. From Table 39 of Ref. [8] pH = 8.3. Increase to pH = 8.4 to obtain Alkb = 452. Decrease to pH = 8.2 to obtain Alka = 448. B = 5(452 − 448) = 5 × 4 = 20. B / Alk = 20/450 = 0.04. C/ = 4 × B / Alk + 1 = 4 × 0.04 + 1 = 1.16 @ 15 °C rating Convert to 30 °C = 1.16 (1 + 0.05 (30 − 15)) = 1.16(1 + 0.05 × 15) = 1.16(1 + 0.75) = 1.16 × 1.75 = 2 mm/yr. From Table 29/1 the value of B / Alk falls off the left-hand edge of the table. C/ will therefore be less than 2 mm/yr.

Chapter 5

CORROSION OF COPPER

Copper is widely used for pipelines in a variety of industrial systems. Because of this wide use it is generally assumed that copper is inert and stable with all types of water likely to be encountered in such systems. But this is not the case. Under appropriate conditions copper can suffer corrosion. The track record of this metal shows that it can suffer two forms of corrosion. One form is designated Type 1 and occurs in cold water systems. The other form is designated Type 2 and occurs in hot water systems.

5.1. COLD WATER SYSTEMS Copper used for pipelines in industrial water systems is usually in the “halfhard” (annealed) state. The conditions under which this class of copper suffers corrosion in cold water has been described by Campbell [27] and Lucey [28]. These conditions may be summarised as follows: — The copper must carry an ingrained carbon film, due to imperfections in the annealing process. — The chemical composition of the water must fall within the range that is capable of initiating corrosion in copper with an ingrained film. — Both conditions must exist together. From a water-treatment view point it is necessary to be able to forecast whether any given water falls within the specific range and, if so, to forecast a time-scale for the progress of the corrosion. Where a water is found to be within the specific range the plant operator should be warned that the possibility of corrosion exists, if the copper carries an ingrained carbon film. But this will not be known in advance as it is impractical to metallurgically examine every piece of pipework before installation. Any future preventive action will depend on the local conditions prevailing in the system. If the time-scale for the progress of the corrosion is very long no further action may be needed. The probable working life of the system may be shorter than the time for corrosion to become apparent. However, if corrosion is likely to become apparent during the working life of the system, the system should be 77

78


kept under observation. (If an ingrained film is not present in the metal, corrosion will not be initiated). However, if corrosion does appear, the affected pipelines should be replaced. Complete pipe-runs should be replaced (not merely cutting out short pipe lengths). In this situation it may be possible to obtain some compensation from the original pipe supplier (since the carbon film will have formed during the annealing process). Details of invoices, batch numbers, etc., issued at the time of the original purchase should, therefore, be retained. If the operating conditions of the water system are critical, and no risk of possible corrosion can be tolerated, then the system should be given an initial treatment with oxalic acid to remove any ingrained film. This may be achieved by arranging with the supplier to carry out the acid wash before pipelines are delivered. It will be clear from the foregoing discussion that the ability to forecast the corrosion potential of any water is crucial. A method of making this forecast has been described by Lucey [29]. He described a procedure for calculating the Pitting Propensity Index (Lucey Index). If the index is positive, the water is capable of initiating copper corrosion in the presence of an ingrained film. The higher the value of the index, the shorter the time-scale. If the index is negative, corrosion will not be initiated.

5.1.1. The Lucey Index Lucey’s method for calculating the Pitting Propensity Index is based on the study of a large number of case histories. It is, therefore, an empirical method. Lucey presented his method in the form of a nomogram. This is shown in skeleton form in Fig. 13. It will be seen that the nomogram is a complex structure, involving reading off six “vectors” on fixed scales and the ruling in of a further eight variable “vectors” in order to obtain the final index. At this point it must be stressed that the Lucey Index is the best method available at present for forecasting copper corrosion in cold systems. There is no reason why the original nomogram should not be used by anyone wishing to work from the original Lucey paper. However, experience in using the nomogram shows that the following difficulties may be encountered: (a) The original nomogram was published on a sheet measuring 21 cm × 30 cm. Accurate working is somewhat difficult on a diagram of this size. (b) An improvement may be obtained (where full drawing office facilities exist) by taking an enlarged copy of the original nomogram. But this facility will

Corrosion of Copper 79

Fig. 13. Lucey nomogram for pitting propensity index (IL) skeleton layout.

80


not be available to a technologist working on site with portable testing equipment. (c) In any project it is essential to keep a “Work Sheet” recording all calculations in case checking is needed. With nomograms (of whatever size) it is necessary to provide spare copies of the diagrams and rule in the “vectors”. In the light of these difficulties it is considered that a case exists for trying to find an alternative approach. A method which suggests itself is converting each vector in the Lucey nomogram to an algebraic form. This would yield a series of equations which could be evaluated by conventional algebra, or allow for values to be read off from prepared tables. In either case the calculations could be easily recorded by a normal typewriter, while the use of tables would be of considerable assistance to a technologist working on site.

5.1.2. An Alternative Approach Arising from the foregoing discussion an alternative approach is offered below. At this point it is stressed that the alternative approach in no way denigrates or devalues Lucey’s original method. Starting from the same data it seeks to provide an alternative, algebraic, path to the same end point.

5.1.3. Data Required pH As cold systems operate at ambient atmospheric temperature the pH recorded by a bench test will be the same as that obtaining in the system. There is no need for a temperature correction of the pH. Sulphate expressed as SO4 mg/l If expressed in other terms use the following conversion factors: S Na2SO4

× 3.00 × 0.68

Sodium expressed as Na mg/l If expressed in other terms use the following conversion factors: Na2O Na2SO4 NaCl

× 0.74 × 0.32 × 0.39

NaNO3 NaHCO3 CaCO3

× 0.27 × 0.27 × 0.45


Nitrate expressed as NO3 mg/l If expressed in other terms use the following conversion factors: N NaNO3

× 4.42 × 0.72

Chloride expressed as Cl mg/l If expressed in other terms use the following conversion factors: NaCl CaCO3

× 0.61 × 0.71

Dissolved Oxygen expressed as O2 mg/l If a dissolved oxygen figure is available by direct analysis it may be used. But for industrial systems, dissolved oxygen is not often included in routine water analyses. In such case, the dissolved oxygen may be calculated from the water temperature. In industrial systems it is rare for water to be pumped direct from a main into a system. In the UK, it is not permitted and some form of break tank between the main and the system is mandatory. Therefore water entering the system will have been held in a river, or a reservoir, or a feed and expansion tank. In all cases the water will have been exposed to the atmosphere and the dissolved oxygen will be in equilibrium with the oxygen in the air at ambient atmospheric temperature. The dissolved oxygen figure may therefore be taken from data by Truesdale et al. [30] which, for temperatures up to 40 °C corresponds to the equation: O 2 = ( 24 − 0.2T )3 × 10 −3 + 0.07T − 0.462 .

(101)

Alternatively, the values may be read off from Table 30.

5.1.4. Effect of Concentration In most cases, the water will pass direct through the system without undergoing a concentration effect. This will also be true for closed recirculating systems. However, a concentration effect will be experienced if the water is recirculated via an open spray pond or an open evaporative cooling tower. In these cases the values of the items listed above must be adjusted before calculating the Lucey Index. If the system is operating with a concentration factor of “n” the values

82


for calculation become: SO4 Na NO3 Cl

becomes becomes becomes becomes

nSO4 nNa nNO3 nCl

Dissolved oxygen does not change because the recirculating water, in the form of a fine spray, is in continual contact with the air and therefore dissolved oxygen remains constant. A change in pH is required in an open recirculating system. To calculate the change a value for the alkalinity of the water is needed and the procedure is described on pp. 27 to 29 of Ref. [8]. However, it will be seen from those pages that for an open recirculating system, operating in clean air and without chemical additions, the pH will stabilise at 8.3. This value of pH may be used to calculate the Lucey Index where the above conditions obtain.

5.1.5. Calculating the Index The method of calculating the Lucey Index which follows, involves evaluating a series of algebraic expressions (which are termed “Vectors”) and which correspond to the geometric steps in the original Lucey nomogram. Vectors are indicated by the letter “V” and individual vectors are indicated by a number. Thus, (V1) (V2) etc. The procedure is as follows: (lx) Calculate (V1) from sodium as 0.167 Na. (lxi) Calculate (V2) from nitrate for various values of sulphate as: Sulphate 0–7.9 SO4 8–19.9 SO4 20–39.9 SO4 40 and over SO4

(V2) 0.083 0.1 0.125 0.167

NO3 NO3 NO3 NO3

(lxii) Calculate (V3) = (V1) − (V2) (lxiii) Calculate (V4) from sulphate and (V3) as:

( V4 ) = 0.25(SO 4 ) + {(10.2 − 1.07(SO 4 )}( V3 ) + 25 Alternatively, read off values of (V4) from Table 31.


(lxiv) Calculate (V5) from chloride as:

(V5 ) =

(Cl) 2.196 . 106.66

Alternatively, read off values of (V5) from Table 32. (lxv) Calculate (V6) from dissolved oxygen as:

( V6 ) = 126 (1 − log O2 ). Alternatively, read off values of (V6) from Table 33. (lxvi) Calculate (V7) = (V4) − (V6). (lxvii) Calculate (V8) as:

(V8 ) =

(V7 ) . (V5 ) + 55

Alternatively, read off values of (V8) from Table 34. (lxviii) Calculate (V9) as:

(V9 ) =

1.852(V6 ) + 246.298(V8 ) . 1.852 + (V8 )

Alternatively, read off values of (V9) from Table 35. (lxix) Calculate the Lucey Index (IL) from pH as follows:

I L = 0.154(V9 ) −

(pH − 7) 0.33 − 2. 0.15

Alternatively, read off values of IL from Table 36. Positive values of IL indicate pitting and negative values non-pitting. In working through the procedure described above, it will be noted that two of the tables (Tables 35 and 36) have been abridged. Only limited values for (V9) and IL have been displayed. If these two tables had been completely filled it would have led to values of IL being obtained which far exceeded the range produced by Lucey’s original nomogram. This was considered to be undersirable, since the purpose of the alternative approach is to follow Lucey’s original nomogram as closely as possible. Tables 35 and 36 have therefore been deliberately abridged in order to keep results within the same range as the original nomogram.

84


Examples In order to provide some examples of the calculation of the Lucey Index, five waters have been selected from Lucey’s original paper. They represent a reasonably wide spectrum of values for IL. Each water has been put through the “vector” process described above. The results are set out in Table 37. When making these calculations the values to be used at any stage do not always fit exactly to the values shown in the tables. In such cases, the nearest value is usually selected. However, in a few cases the interval between successive values is sufficiently wide to require interpolation to be used. It will be seen from Table 37 that the non-pitting waters (Cases 16 and 47) show some variance between the “vector” process and the original nomogram. This is not considered to be of any practical significance. Having determined that a water was non-pitting Lucey did not proceed with any further calculations concerning its behaviour in an industrial water system. Case 14 is a neutral water representing border-line conditions. This will be considered later when discussing the time-factor for pitting attack. In the case of the pitting waters (Cases 10 and 8) there is reasonably good agreement between the “vectors” and the nomogram. As already stated at the start of this section, when a positive (pitting) index has been established it is necessary to calculate a time-scale for the progress of the attack. This is needed to serve as a warning to the plant operators in case any given system carries the ingrained carbon film that can initiate pitting.

5.1.6. Time Scale In setting up a time-scale, Lucey picked three time intervals: Threshold Time:

The time after a system had started up for the threshold of attack to commence.

Awareness Time:

The time after a system had started up for the first physical awareness that attack was in progress. (e.g. the first signs of pin-hole leaks).

Established Time: The time after a system had started up for the attack to be well established. (e.g. the system approaching total failure due to many leaks). Lucey’s method for calculating time-scales is based on the study of a large number of case histories. It is, therefore, an empirical method.


Fig. 14. Lucey nomogram for time scale skeleton layout.

Lucey presented his method in the form of a nomogram. This is shown in skeleton form in Fig. 14. It will be seen that the nomogram contains three guidelines: one for “threshold” time; one for “awareness” time; and one for “established” time. For any given positive value of IL a vertical projection strikes each of the guidelines in turn to give three corresponding intercepts on the ordinate axis of the diagram.

86


Continuing the “vector” notation used in Sec. 5.1.5 these ordinates are designated as “Vector 10” (V10). Mathematical analysis of the original Lucey diagram yields the following results: Threshold (V10) = 98 − 19(IL). Awareness (V10) = 161 − 19(IL). Established (V10) = 212 − 19(IL). For each given value of (V10) a horizontal projection strikes the curve in the nomogram to give an intercept. A vertical projection from each intercept strikes the time scale to give the corresponding times. These times are represented by the letters T, A, and E in Fig. 14. Mathematical analysis of the original Lucey diagram yields the following result for the curve: Time ( years ) = {( V10 )2 /( 2460 − 11.24 ( V10))}.

Using the vectors described above, the three time-scales may be calculated for any given positive value of IL. Alternatively, the time-scales my be read off from Table 38 in which all the above vectors have been combined. Examples In Table 37, the example from the original Lucey Case 10 gave a calculated value for IL of 6.3. Table 38/1 gives time-scales for this value as: Threshold

Less than 0.1 year.

Awareness

0.9 year (interpolated).

Established

6.0 years (interpolated).

On this basis, the plant operator would be warned to look out for pin-hole leaks during the first year of operation, with probable complete failure within 6 years. The original Lucey value was 7.0, which corresponds to time-scales of: Threshold

Less than 0.1 year.

Awareness

0.4 year.

Established

4.0 years.

These values are of the same order of magnitude as those given above and would lead to the plant operator being given warnings in similar terms to those expressed above.


The margin of error between the two sets of values is acceptable for results derived from two empirical calculations applied to an industrial system. In Table 37, the example from the original Lucey Case 8 gave a calculated value for IL of 3.0. The original Lucey value was identical. Table 38/1 gives the time-scales as: Threshold

0.8 year.

Awareness

8.4 years.

Established

33.5 years.

On this basis, the plant operator would be warned to look out for pin-hole leaks after about 8 years and to expect complete failure in approximately 30 years. In Table 37, the example from the Lucey Case 14 gave a calculated value for IL of 0.4. Table 38/1 gives the time scales as: Threshold

5.7 years.

Awareness

3.2 years.

Established

257.0 years.

On this basis, the plant operator would be advised that it was unlikely that any leakage would be noticed for approximately 30 years. This time would probably exceed the working life of the system, so a trouble-free life would be expected. The original Lucey value was zero, which would also indicate a probable trouble-free life for the system. Before leaving the discussion on time-scales it may be of interest to record an actual case history. Case history A building, fitted with copper cold water systems, carrying mains water from the local water authority, had experienced no operating difficulties for some 10 years. It was decided to build an extension to the main building. In view of the past satisfactory experience with copper systems it was decided to use copper again in the extension to carry local mains water. However, as a precaution, the consulting engineer responsible for the design of building services approached the local water authority and enquired if copper would be a suitable material to use with the local mains water. He was assured that copper would be satisfactory.

88


Unfortunately, after the construction of the extension had been completed, and the new building had been in use for some 2 to 3 years, pin-hole leaks began to appear in the copper systems. On investigation it was found that the copper pipework carried ingrained carbon films. This was traced back to a sub-contractor using sub-standard copper pipes in an attempt to save costs by using a cheaper material. When the problem was referred back to the local water authority it was stated that, during the period of construction of the extension, there had been a change in the water supplied through the local mains. In order to meet demands another water supply had been imported into the area and a mixture of old and imported water now formed the supply to the building. The local water authority had also noted that, following this change, complaints had begun to reach them of leakage in copper systems. The local water authority were unable to offer any further comment at that time. The chemical composition of the water supplies involved in this incident are as follows: Original Supply

Imported Supply

Mixed Supply

300

190

288

12

33

32

Total hardness (mg/l CaCO3)

312

223

310

Total alkalinity (mg/l CaCO3)

250

130

260

Chloride (mg/l CaCO3)

17

81

37

9

74

17

Nitrate (mg/l NaNO3)

30

3

22

Sulphate (mg/l Na2SO4)

25

260

53

Calcium hardness (mg/l CaCO3) Magnesium hardness (mg/l CaCO3)

Sodium (mg/l Na)


Dissolved solids (mg/l as such) pH

355

500

7.2

370

7.4

7.3

Carrying out the “vector” procedures on these analyses gave the following results: Lucey Index

1.5

2.0

2.4

Threshold time (years)

3.0

2.0

1.5

Awareness time (years)

18

14

11.5

Established time (years)

85

60

47

The first thing to note about the above analyses is that it is not possible to make a forecast of the Lucey Index merely by scanning the figures. A full calculation must be made. The second thing to note is that the Lucey Index of the mixed supply is not intermediate between the values for the two component waters, but is greater than either. The crucial figures in the above lists are those for the Lucey Index and the “times” for the mixed supply. It is clear that with a positive Lucey Index, and the presence of ingrained carbon films, conditions were favourable for attack on the copper leading to pin-hole leakage. But it is surprising to find that the onset of the attack was very much shorter than the “times” predicted from Table 38. Why this anomoly? In the copper systems joints between lengths of pipes, angles and T-joints were formed by inserting the ends of pipes into outer sleeves which were then sealed with a ring of solder. Examination of the systems revealed that in a number of places the soldering had left flux trails on the internal surfaces of the pipes, and that the incidence of pin-holes was more concentrated in areas adjacent to the flux trails. A more detailed examination of these areas was not possible, and the chemical characteristics of the flux trails are not known. But it may reasonably be assumed that some substance or substances had been leached from the flux trails by the flow of water and resulted in the water in the immediate vicinity acquiring a higher, positive, Lucey Index than the bulk of the supply. This would account for the aggrevated attack and the “awareness” of pin-holes after only 2 to 3 years instead of 11 years as predicted. It is considered that the quantity of leachate need not be very high to produce the observed effects. For instance, if the leachate was acidic in character, and

90


resulted in a lowering of alkalinity and pH in the immediate vicinity, it can be shown that a reduction of only 25 mg/l in the alkalinity of the mixed supply would result in a lowering of the pH to 7.0, with a corresponding reduction of the “awareness” time to approximately 1 year. This illustration is not offered as a definite explanation of the anomoly encountered, but it does serve to show that only very modest leaching from the flux trails may be required. The case history recorded above points up the need for: Calculating the Lucey Index of the water supply at the design stage of any project. Ensuring that copper pipework used is of the highest (carbon film free) approved standard. Ensuring a high standard of workmanship in making joints (with a preference for compression fittings in order to eliminate flux trails).

5.2. HOT WATER SYSTEMS Copper used for pipelines in industrial water systems is usually in the “half-hard” (annealed) state. But is some countries, particularly Scandinavia, “hard-drawn” copper is used. Copper corrosion in hot water systems is designated Type 2 which has been described by Campbell [27] and Lucey [28]. The attack is associated with the presence of an ingrained carbon film in the metal but the process by which the corrosion proceeds is different from that of Type 1 in cold water systems. Data on the water chemistry associated with Type 2 corrosion is less than the corresponding data for Type 1.

5.2.1. Data on Water Chemistry Much of the data on the water chemistry of Type 2 corrosion in copper systems has been obtained from the study of domestic hot water systems, or laboratory experiments which simulate domestic systems. Any parameters which are offered for the forecasting of copper corrosion in hot water systems are therefore empirical. Investigations by Mattsson and Fredriksson [31] into the failures in Sweden in hot water systems incorporating “hard-drawn” copper show that pitting occurs when the following water characteristics exist in the system.


The pH value lies between 5.0 and 7.0. The bicarbonate concentration is 100 mg/l HCO3− or less. (This corresponds to a total alkalinity of 83 mg/l CaCO3 or less for the pH range given above.) The ratio of [HCO3−] : [SO2− 4 ] is less than 1.0. (This corresponds to a ratio of mg/l CaCO3 : mg/l Na2SO4 less than 1.16.) The investigations make no reference to water temperatures in the systems. Therefore it must be assumed that all systems operated at the temperature commonly used in domestic systems, namely, 60 °C (140 °F). Further work by Mattsson [32] shows that even waters which are rated as non-pitting on the basis of the parameters above, can suffer an erosion effect and lose their immunity if the linear rate of flow is too high. Recommended limiting flow rates are given below. If pipework is easily accessible, so that it can easily be exchanged when damaged, higher flow rates are permitted. Type of System

Accessibility

Mains

Exchangeable Not exchangeable

Branch pipes

Exchangeable Not exchangeable

Continuous flow

Flow Rate (m/s) at T 10

50

70

90

4.0 2.0

3.0 1.5

2.5 1.3

2.0 1.0

16.0 12.0 10.0 4.0 3.0 2.5

8.0 2.0

2.0

1.5

1.3

1.0

Industrial heat-exchange systems, whether once-through or recirculating, would be included under continuous flow systems. Systems with an evaporative cooling tower are excluded. Their operating pH value is likely to be of the order of 8.0. which is outside the range specified by Mattsson. It should be noted that the temperatures given in the table above refer only to the selection and control of linear flow rates. They have no influence on the water parameters specified by Mattsson earlier in this section. Investigations by Adeloju and Hughes [33] into the corrosion of copper hot water systems using Perth (Australia) town supply, gave the analyses for this

92


supply as follows: Min

Max

pH

6.5

7.5

7.0

Calcium (mg/l Ca2+)

2

5

4

Chloride (mg/l Cl−)

44

105

75

8

15

12

24

88

56

3

9

6

Bicarbonate (mg/l HCO3−) Sodium (mg/l Na+) Sulphate (mg/l SO2− 4 )

Calculated Mean

Taking the mean analysis, and converting the bicarbonate figure to total alkalinity as CaCO3 gives 10 mg/l, while converting the sulphate figure to Na2SO4 gives 9 mg/l. Hence the alkalinity : sulphate ratio is 1.11. With the mean pH as 7.0 these figures all fall within the Mattsson parameters for a water which will cause pitting. Although the type of copper pipework used in Perth is not defined, it would appear from the agreement between the Mattsson parameters and the occurence of pitting, that the use of the parameters is not necessarily restricted to “hard-drawn” copper. In their report on the investigation, Adeloju and Hughes include a review of four other sites, worldwide, where copper corrosion in hot water systems has been experienced. Only the briefest details of water analyses are given, and therefore it is not possible to make any detailed study of any relationship between water characteristics and the onset of copper corrosion. However, at all the other four sites, the pH values are greater than 7.0, which suggests that it may be possible to extend the pH term in the Mattsson parameters beyond the stated maximum of 7.0. It is not possible to offer any firm explanation for this, apparent, anomoly: but one explanation which comes to mind is the possibility that in the cases cited by Adeloju and Hughes the pipework was fabricated from “half-hard” copper instead of the “hard-drawn” in the Mattsson systems. On this basis there would be a metallurgical difference between the systems. In their report, Adeloju and Hughes describe the Perth town water as being “high in chlorides”. But in the text of the report they indicate that the concentration of the chloride ion did not have a significant effect on the progress of the corrosion mechanism. In the four other sites, mentioned earlier, two have chloride ion concentrations of the same order of magnitude as the Perth water, but the other two are


definitely lower. It will be recalled that chloride ion concentration is not included in the Mattsson parameters. Investigations by Al-Kharafi et al. [34] into the corrosion of copper in hot water systems in Kuwait indicate that the presence of an ingrained carbon film and/or a phosphate film (derived from the water treatment programme in Kuwait) on the surface of the pipework is necessary for the corrosion to proceed. The Kuwait water supply consists of a blend of desalinated water and brackish water (approximately 7%) with pH adjusted to the range 7.6 to 8.7. An average analysis is: pH

8.1

Conductivity (mS/m)

35.0

Total alkalinity (mg/l CaCO3)

12.5

Bicarbonate (mg/l HCO3−)

15.0

Total hardness (mg/l CaCO3)

93.0

Calcium hardness (mg/l CaCO3)

59.0

Magnesium hardness (mg/lMgCO3)

33.0

Cl−)

51.8

Chloride (mg/l

Sulphate (mg/l SO2− 4 ) Silica (mg/l SiO2)

75.0 4.0.

The total alkalinity of 12.5 is less than the value of 82 in the Mattsson parameters. Making the necessary conversions gives the bicarbonate/sulphate .5 CaCO3 as 12 ratio in terms of Na 111 = 0.11 which is less than the maximum of 1.16 2SO4 in the Mattsson parameters. The pH range for Kuwait water is higher than the maximum specified in the Mattsson parameters. This again is support for the suggestion that the pH range in the Mattsson parameters should be extended when accessing the potential of a water to cause copper corrosion in hot water systems. The chloride ion concentration in Kuwait water is of the same order of magnitude as that for Perth water, but again there is no indication that the chloride ion plays a significant part in the corrosion mechanism. Investigations into the corrosion of copper in hot water systems using Tokyo town supply are covered by four papers: Sato [35] and Baba et al. [36–38]. Sato [35] reports that pitting is not dependant on the presence of an ingrained carbon film on the surface of the metal.

94


Baba et al. [36, 37] with a synthetic water containing: Bicarbonate (mg/l HCO3−)

36.6

Chloride (mg/l Cl−)

42.6

Sulphate (mg/l SO2− 4 )

76.8

pH

7.0 to 7.8

produced no corrosion at 60 °C. The bicarbonate figure converts to 30 mg/l CaCO3 (which is below the Mattsson figure of 83) while the sulphate figure converts to 114 mg/l Na2SO4 giving a bicarbonate:sulphate ratio of 0.72 (which is below the Mattsson ratio of 1.16). The pH is within the extended Mattsson range which has been suggested earlier in this section. Therefore the water would be expected to show pitting. However, when the water was chlorinated, to provide a residual chlorine of 2–3 mg/l rapid pitting was observed. In a further series of experiments, Baba et al. [38] took Tokyo tap water as their basic raw water and then made chemical adjustments to produce four “experimental” waters. The analyses are shown in Table 39; the “experimental” waters are designated A, B, C, D in the table. The pH values are within the Mattsson parameter, except for water C, but from the work described earlier in this section some extension of pH above 7.0 appears to be capable of allowing corrosion to proceed. The total alkalinities are below the limit of the Mattsson parameter, except for water D, which is marginally higher by only 3 mg/l. The bicarbontate : sulphate ratios are below the limit of the Mattsson parameter, except for water D. On this evidence it is expected that the “experimental” waters would produce pitting at elevated temperatures, with the exception of water D. However, in a series of experiments; conducted at 60 °C; using both “hard-drawn” and “half-hard” copper tubes; maintaining the residual chlorine at the original value of 1 mg/l; no pitting was observed. But when the chlorine residual was increased to the range 2–3 mg/l pitting was observed. It was noted that the presence or absence of an ingrained carbon film had no significant effect on the progress of the pitting, and no difference was reported between “hard-drawn” and “half-hard” tubes. The conclusion from these experiments is that residual chlorine is the critical factor controlling the progress of the pitting.


5.2.2. The Role of Residual Chlorine The sterilisation of water supplies is usually achieved by adding chlorine gas, or hypochloride solution, in sufficient quantity to oxidise all the organic matter present and leave a residual of free chlorine. The free chlorine undergoes the following reactions: Cl2 + H2O = H+ + Cl− + HOCl 2HOCl = 2H+ + Cl− + ClO2− (chlorite) HOCl + ClO2− = H+ + Cl− + ClO3− (chlorate). In a series of laboratory experiments Suzuki et al. [39] have demonstrated that the chlorite ion is the aggressive species which promotes pitting of copper in hot water systems.

5.2.3. Time Scale In a further series of experiments Suzuki [40] described a method for estimating the time for pitting to be initiated by the chlorite ion. His experiments were made at a fixed temperature of 65 °C. Suzuki expressed his results in the form of an equation: Time =

Constant ( E/ ) . Chlorine residual (Cl R )

The constant (E/ ) is a function of: Temperature pH (which covered the range 5.5 to 7.5) Concentration of total anions (Cl− + HCO−3 + SO2− 4 ). It can be shown that, for all practical plant purposes, the total anions can be expressed as 0.65 (dissolved solids). Mathematical analysis of Suzuki’s results indicate a relationship: E/ = g (DS)h where the values of g and h are dependant on pH.

(103)

96


If the time is expressed as days, and the dissolved solids as mg/l, the smoothed values of g and h are: pH 5.5 6.0 6.5 7.0 7.5 *8.0 *8.5

g

h

3.9 3.3 2.7 2.1 1.5 0.9 0.3

0.69 0.75 0.82 0.88 0.94 1.00 1.07

* The table has been extrapolated to 8.5 in order to cover the same pH range as used by Lucey [29] for cold water systems in Sec. 5.1. It is considered that the values listed are sufficiently accurate for a prediction procedure under practical, plant conditions. Using the values listed above, the value of E/ can be calculated for given values of pH and DS using Eq. (103). If this result is then divided by the chlorine residual (ClR), expressed as mg/l Cl2, the time (in days) to initiate pitting is obtained. Further to the work discussed above, Suzuki visited 9 sites in Japan where pitting had occurred in hot water systems. He recorded the time taken for failure of the systems by pitting and compared it with the calculated time for pitting to be initiated. He was thus able to obtain a ratio: Failure Time : Initiating Time The results of this investigation are: Site NO. 1 2 3 4 5 6 7 8 9

pH 7.2 7.0 7.2 6.0 6.8 6.8 6.1 7.0 6.7

Initiation Failure Time (years) Time (years) 1.2 1.3 1.9 1.0 0.7 1.7 0.5 1.1 1.0

2.1 2.4 3.0 2.0 7.5 5.0 2.0 3.2 4.0

Ratio 1.75 1.85 1.58 2.00 10.71 2.94 4.00 2.91 4.00


Mathematical analysis of these results indicate a linear result between pH and the “ratio” except for Sites No. 5 and 7 which are out of line from the remainder. Excluding these two sites, the remainder indicate a relationship: Ratio = −2.28pH + 18.38.

(104)

As Eq. (104) is a ratio it is independent of the time units used to express the initiation and failure times. Having calculated an initiation time, using Eq. (103) it is now possible also to calculate a failure time from Eq. (104). The work discussed in this section is summarised in Table 40 which enables initiation time and failure time to be read off from values of pH, dissolved solids, and chlorine residual. Example pH = 7.5 DS = 150 Initiation Time = 167 days

Chlorine Residual = 1.0 Failure Time = 376 days

From the work described in this section, the following empirical guidelines are offered in order to assess the probability of pitting attack in the copper pipework of hot water systems. An ingrained carbon film on the inner surface of the pipe is required. Some workers claim that a phosphate deposit (derived from the treatment of the water) is necessary while other workers claim that pitting can occur in the absence of any surface film. But the balance of opinion appears to be slightly in favour of the carbon film. Therefore high standard, film free, pipework should be selected. There appears to be no evidence to diffentiate between “hard-drawn” and “half-hard” copper in the risk of pitting. The chemical characteristics of the water in the system must fall within the Mattsson parameters. However, there is evidence to suggest that the pH value may exceed the range originally specified by Mattsson. The risk of pitting is aggrievated if the linear flow rate of the water exceeds the values recommended by Mattsson. The presence of free residual chlorine in the water is necessary for pitting to occur. The work described in this section has been carried out at temperatures in the region of 60 °C. At higher temperatures the rate of attack would be expected to be quicker, and at lower temperatures slower. More work is needed over a reasonably wide range of temperatures to improve the accuracy of forecasting pitting in industrial systems.

98


The work described has been limited to the water supplies of a few localities (e.g. Perth, Tokyo) or to synthetic waters which are similar to these supplies. More work over a wider range of water characteristics is needed to improve the accuracy of forecasting. Once-through water systems, or closed recirculating systems, serving industrial heat exchangers are sufficiently close to domestic hot water systems to allow the methods described in the section to be used. However, in domestic systems some residual free chlorine is usually present from the sterilisation of potable supplies. In industrial systems, free residual chlorine can be avoided since other chemicals can be used to combat organic pollution; chemicals which are not permitted for potable water supplies. Systems incorporating an open cooling tower are excluded. The temperature of the water in these systems is much lower than in closed systems. And also, if any form of chlorination is applied, the residual chlorine is stripped from the water during passage through the tower.

REFERENCES

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

[24] [25] [26] [27]

Ryznar, J. Amer. Waterworks Assoc. 1944, 36, 472. Langelier, J. Amer. Waterworks Assoc. 1936, 28, 1500. Thompson & Ryznar, Combustion 1942, 14(5), 41. Larson & Buswell, J. Amer. Waterworks Assoc. 1942, 34, 1667. Emerson, J. Soc. Chem. Ind. 1945, 64, 335. Manning, Upublished I. C. I. Report R93/62/2 (1944). Hamer, Thurston & Jackson, Industrial Water Treatment Practice Butterworths, London, 1961. Emerson, Alkalinity-pH Changes with Temperature for Waters in Industrial Systems Ellis Horwood, Chichester, 1986. Edwards, Unpublished I. C. I. Report R628/23/5 (1944). Emerson, Unpublished I. C. I. Report R93/7/29 (1961). Seidell, Solubilities of Inorganic and Metal Organic Compounds Van Nostrand, New York, 1940 and 1952. Booth & Bidwell, J. Amer. Chem. Soc. 1950, 72, 2567. Green & Holmes, J. Amer. Waterworks Assoc. 1947, 39, 1098. Debye & Huckel, Physic. Z. 1923, 24, 285 and 334. Bronstead & LaMer, J. Amer. Chem. Soc. 1924, 46, 555. Nims, J. Amer. Chem. Soc. 1934, 56, 1110. Bates & Acree, J. Res. Nat. Bur. Stds. 1943, 34, 373. Bjerrum & Unmack, Kgl. Danske Videnskab. Selskab. Matfys. Medd. 1929, 9, 5. Kuyper, J. Biol. Chem. 1945, 159, 417. Sendroy & Hastings, J. Biol. Chem. 1927, 71, 783 and 797. Finan, Harris & Marshall, Materials Performance 1098, 19, Part 3, 24–29. Ison & Butler, Corrosion and Its Prevention in Waters Leonard Hill, London, 1966. Large, Symposium Internal Corrosion of Iron Mains and Copper Services Inst. Water Eng. & Scientist (Scientific Sect.) London 22 April 1962. Paper No. 2 pp. 17–29. Stumm, Proc. Am. Soc. Corr. Eng. (J. San. Eng. Div.) Nov. 1960 Sect. SA6. Paper No. 2657 pp. 27–45. Van Slyke, J. Biol. Chem. 1922, 52, 525. Dye, J. Amer. Waterworks Assoc. 1952, 44, 356. Campbell, J. Inst. Metals 1950, 77, 345. 99

100


[28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40]

Lucey, Br. Corr. J. 1967, 3, 175. Lucey, Brit. NonFerrous Metals Res. Assoc. Res. Report. No. A1838, Dec. 1972. Truesdale, Downing & Lowden, J. Appl. Chem. 1955, 5, 53. Mattsson & Frederiksson, Br. Corr. J. 1968, 3, 246. Mattsson, Br. Corr. J. 1980, 15, 6. Adeloju & Hughes, J. Inst. Corr. Sc. Tech. 1986, 26, 851. El-Alkharafi, Shalaby & Gouda, Br. Corr. J. 1989, 24, 284. Sato, Corr. Eng. Japan 1982, 31, 3. Baba, Kodama, Fujii, Hisamatsu & Ishikawa, Corr. Eng. Japan 1982, 30, 113. Baba, Kodama, Fujii & Hisamatsu, Corr. Eng. Japan 1981, 30, 161. Fujii, Kodama & Baba, J. Inst. Corr. Sc. Tech. 1984, 24, 901. Suzuki, Ishikawa & Hisamatsu, J. Inst. Corr. Sc. Tech. 1983, 23, 1095. Suzuki, J. Inst. Corr. Sc. Tech. 1984, 24, 429.

SUPPLEMENT (Reprint of Ref. 8)

ALKALINITY — pH CHANGES WITH TEMPERATURE FOR WATERS IN INDUSTRIAL SYSTEMS

197

ERRATA TO SUPPLEMENT

Page 12 Line 24 to read: - - - - - the temperature change of pH to the temperature change of pK2 - - - - Page 16 Equation (19) to read:

 K  (H + ) K   (H + )  + 1 + 2+  ×  + C = ( Alk ) − W+  ×   ( H )   K1 (H )   ( H ) + 2K 2   Page 17 Equation (24) to read:

  10 −( pH )  K K   10 − ( pH ) + 1 + −(2pH )  ×  −( pH ) C × 10 −5 = 2 M × 10 −5 − −(WpH )  ×   + 2K 2  10 10    K1  10 Equation (25) to read:

   10 −( pH ) K K   10 − ( pH ) +5 C = 2 M × 10 −5 − −(WpH )  ×  + 1 + −(2pH )  ×  −( pH )  × 10 10 10 10 2 K K +    1 2   Page 22 Line 16 to read: - - - - - loss of accuracy to make an easier calculation - - - - -

199

200


Table 66 M

pH 11.0

11.1

11.2

280 290 300

7 18 28

310 320 330 340 350

39 50 60 72 82

6

360 370 380 390 400

92 103 114 125 135

17 27 38 48 59

410 420 430 440 450

140 157 167 178 189

69 80 90 101 112

7 17

460 470 480 490 500

199 210 221 231 242

122 133 143 154 164

28 38 49 59 70

This section of the table should not be in the “grey” area, but in the “clear white” area, since the values listed are all real positive values

Errata to Supplement 201

Table 76 M 10/ pH 9.4 The listed value of − 4 should be in the “grey” area. Table 78 M 490/ pH 11.0 should read 10 (no minus sign) M 500/ pH 11.0 should read 20 (no minus sign) and both be in the “clear white” area. Table 82 M 40/ pH 9.7 The listed value of 12 should be in the “clear white” area. Table 113 The whole of the “grey” area should be labelled “No real, positive, values in this area” Table 116 M 150/ pH 7.9 listed value should read 306 M 200/ pH 7.6 listed value should read 428 Table 117 M 180/ pH 8.5 listed value should read 342

TABLES

Table 1. Ryznar’s original data.

No

Ca

Alk

DS

pH

T

Q

No

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

72 72 72 72 70 70 150 150 150 133 133 301 301 301 301 301 301 66 61 68 137

103 132 183 68 169 264 246 280 324 130 322 350 472 535 470 470 550 135 137 142 280

163 190 240 160 380 490 380 420 460 410 760 550 630 690 630 630 700 170 170 185 390

7.90 9.10 9.50 6.70 9.70 9.00 8.90 9.20 9.10 7.65 9.70 7.25 8.65 8.90 8.60 8.55 8.90 8.75 8.70 8.70 8.55

95 95 95 95 95 95 95 95 70 95 95 95 95 95 70 50 50 50 50 70 50

nil 36 105 nil 95 147 117 130 66 4 183 55 325 405 119 74 93 93 4 15 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

101

102


Table 2. Ryznar’s calculated parameters. No

pH @ 15 °C

pHS @ T

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

7.90 9.10 9.50 6.70 9.70 9.90 8.90 9.20 9.10 7.65 9.70 7.25 8.65 8.90 8.60 8.55 8.90 8.75 8.70 8.70 8.55

6.92 6.83 6.69 7.11 6.78 6.52 6.29 6.24 6.47 6.63 6.32 5.89 5.78 5.74 6.06 6.35 6.29 7.42 7.45 7.11 6.89

I = pH − pHS 0.98 2.27 2.81 −0.41 2.92 3.38 2.61 2.96 2.63 1.02 3.38 1.36 2.87 3.16 2.54 2.20 2.61 1.33 1.25 1.59 1.69

Q

No

nil 36 105 nil 95 147 117 130 66 4 183 55 325 405 119 74 93 53 4 15 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Tables

Table 3. Ryznar’s index data. No

pH @ 15 °C

pHS @ T

R = 2pHs − pH

Q

No

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

7.90 9.10 9.50 6.70 9.70 9.90 8.90 9.20 9.10 7.65 9.70 7.25 8.65 8.90 8.60 8.55 8.90 8.75 8.70 8.70 8.55

6.92 6.83 6.69 7.11 6.78 6.52 6.29 6.24 6.47 6.63 6.32 5.89 5.78 5.74 6.06 6.35 6.29 7.42 7.45 7.11 6.89

5.94 4.56 3.88 7.52 3.86 3.14 3.68 3.23 3.84 5.61 2.94 4.53 2.91 2.58 3.52 4.15 3.68 6.09 6.20 5.52 5.17

nil 36 105 nil 95 147 117 130 66 4 183 55 325 405 119 74 93 53 4 15 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

103

104


Table 4. Revised data Ryznar Index. No

pH @ T

pHS @ T

R = 2pHS − pH

Q

No

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

7.90 8.40 8.80 6.80 9.00 9.20 8.40 8.60 8.70 7.70 9.10 7.30 8.30 8.40 8.40 8.40 8.10 8.60 8.50 8.40 8.30

6.92 6.85 6.69 7.11 6.78 6.52 6.29 6.24 6.47 6.63 6.32 5.89 5.78 5.74 6.06 6.35 6.29 7.42 7.45 7.11 6.86

5.94 5.26 4.58 7.42 4.56 3.84 4.18 3.88 4.14 5.56 3.54 4.48 3.26 3.08 3.72 4.30 4.48 6.24 6.40 5.82 5.42

nil 36 105 nil 95 147 117 130 66 4 183 55 325 405 119 74 93 53 4 15 35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Table 5. Water analyses for new data. AT TEMPERATURE 15°C No

Ca

Alk

DS

pH

No

22

150

120

225

8.00

22

23

150

180

270

7.90

23

24

200

160

300

7.90

24

25

200

246

360

7.80

25

26

250

200

375

7.80

26

27

250

300

450

7.70

27

28

300

240

450

7.80

28

29

300

360

540

7.70

29

30

350

280

525

7.80

30

31

350

420

630

7.70

31

Tables

Table 6. Calculated weights of calcium carbonate. No

pHS

pH

R = 2pHS − pH

I = pH − pHS

W

No

0.43 0.50 0.55 0.61 0.63 0.68 0.76 0.82 0.88 0.93

10 20 20 35 30 50 50 80 70 110

22 23 24 25 26 27 28 29 30 31

0.61 0.68 0.68 0.79 0.81 0.76 0.94 1.00 1.06 1.11

15 20 25 40 40 70 60 100 80 130

22 23 24 25 26 27 28 29 30 31

0.71 0.73 0.75 0.94 0.91 1.01 1.09 1.15 1.11 1.21

20 30 30 50 50 80 70 120 90 145

22 23 24 25 26 27 28 29 30 31

TEMPERATURE 30 °C 22 23 24 25 26 27 28 29 30 31

7.47 7.30 7.25 7.09 7.07 6.92 6.94 6.78 6.82 6.67

7.90 7.80 7.80 7.70 7.70 7.60 7.70 7.60 7.70 7.60

7.04 6.80 6.70 6.48 6.40 6.24 6.18 5.96 5.94 5.74 TEMPERATURE 40 °C

22 23 24 25 26 27 28 29 30 31

7.29 7.12 7.07 6.91 6.89 6.74 6.76 6.60 6.64 6.49

7.90 7.80 7.75 7.70 7.70 7.50 7.70 7.60 7.70 7.60

6.68 6.94 6.39 6.12 6.08 5.98 5.82 5.60 5.58 5.38 TEMPERATURE 50 °C

22 23 24 25 26 27 28 29 30 31

7.14 6.97 6.92 6.76 6.74 6.59 6.61 6.45 6.49 6.34

7.85 7.70 7.70 7.70 7.65 7.60 7.70 7.60 7.60 7.55

6.43 6.24 6.14 5.82 5.83 5.58 5.52 5.30 5.38 5.13

105

106


Table 6 (Continued) No

pHS

pH

R = 2pHS − pH

I = pH − pHS

W

No

0.85 0.87 0.92 1.08 1.05 1.15 1.23 1.09 1.35 1.40

25 35 40 65 60 95 85 130 90 100

22 23 24 25 26 27 28 29 30 31

1.10 1.08 1.08 1.24 1.26 1.31 1.39 1.45 1.57 1.56

30 50 50 80 75 115 115 155 125 190

22 23 24 25 26 27 28 29 30 31

1.13 1.25 1.28 1.34 1.38 1.43 1.51 1.57 1.63 1.68

35 60 60 90 85 130 115 170 140 210

22 23 24 25 26 27 28 29 30 31

TEMPERATURE 60 °C 22 23 24 25 26 27 28 29 30 31

7.00 6.83 6.78 6.62 6.60 6.45 6.47 6.31 6.35 6.20

7.85 7.70 7.70 7.70 7.65 7.60 7.70 7.40 7.70 7.60

6.15 5.96 5.86 5.54 5.55 5.30 5.24 5.22 5.00 4.80 TEMPERATURE 70 °C

22 23 24 25 26 27 28 29 30 31

6.84 6.67 6.62 6.46 6.44 6.29 6.31 6.15 6.19 6.04

7.85 7.75 7.70 7.70 7.70 7.60 7.70 7.60 7.70 7.60

5.83 5.50 5.54 5.22 5.18 4.98 4.92 4.70 4.68 4.48 TEMPERATURE 80 °C

22 23 24 25 26 27 28 29 30 31

6.72 6.55 6.52 6.36 6.32 6.17 6.19 6.03 6.07 5.92

7.85 7.80 7.80 7.70 7.70 7.60 7.70 7.60 7.70 7.60

5.59 5.30 5.24 5.02 4.94 4.74 4.68 4.48 4.44 4.24

Tables

107

Table 7. Weight of calcium carbonate deposit (W) from R. VALUE OF R @ T T

4.0

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

T

30 35 40 45 50 55 60 65 70 75 80

2515 1920 1525 1164 925 706 561 428 340 260 206

2107 1620 1297 997 799 614 492 378 303 233 186

1765 1367 1103 954 690 634 431 334 269 209 168

1479 1153 938 731 595 464 378 294 240 187 152

1239 973 798 626 514 403 331 260 213 167 137

1038 821 679 536 444 351 290 229 190 150 124

870 692 577 459 383 305 254 202 169 134 112

729 584 491 393 331 265 223 179 150 120 101

610 493 417 337 285 228 195 158 133 108 91

511 416 355 289 246 200 171 139 119 97 82

30 35 40 45 50 55 60 65 70 75 80

5.0

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

428 350 302 247 213 174 150 123 106 86 74

359 296 257 212 184 151 131 108 94 77 67

301 250 218 181 159 132 115 96 84 69 61

252 211 186 155 137 114 101 84 74 62 55

211 177 158 133 118 99 88 74 66 56 50

177 150 134 114 102 86 77 66 59 50 45

148 126 114 98 88 75 68 58 52 45 40

124 107 97 84 76 65 60 51 47 40 36

104 90 83 72 66 57 52 45 41 36 33

87 76 70 61 57 49 46 40 37 32 30

6.0

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

73 64 60 52 49 43 40 35 33 29 27

61 54 51 45 42 37 35 31 29 26 24

51 46 43 38 36 32 31 27 26 23 22

43 38 37 33 31 28 27 24 23 21 20

36 32 31 28 27 25 24 21 21 19 18

30 27 27 24 23 21 21 19 18 17 16

25 23 23 21 20 19 18 17 16 15 15

21 19 19 18 17 16 16 15 14 13 13

18 16 16 15 15 14 14 13 13 12 12

15 14 14 13 13 12 12 11 11 11 11

30 35 40 45 50 55 60 65 70 75 80

30 35 40 45 50 55 60 65 70 75 80

30 35 40 45 50 55 60 65 70 75 80

30 35 40 45 50 55 60 65 70 75 80

108


Table 8. Values of p[Ca2+] from Ca.

0 10 20 30 40 50 60 70 80 90

100 200 300 400 500 600 700 800 900

1000 2000

4.00 3.70 3.53 3.40 3.30 3.22 3.15 3.10 3.05

3.00 2.70 2.53 2.40 2.30 2.22 2.15 2.10 2.05

2.00 1.70

1

2

3

4

5

6

7

8

9

5.00 3.96 3.68 3.51 3.39 3.29 3.21 3.15 3.09 3.04

4.70 3.92 3.66 3.50 3.38 3.28 3.20 3.14 3.09 3.04

4.53 3.89 3.64 3.48 3.37 3.28 3.20 3.14 3.08 3.03

4.40 3.85 3.62 3.47 3.36 3.27 3.19 3.14 3.08 3.03

4.30 3.82 3.60 3.46 3.35 3.26 3.19 3.13 3.07 3.02

4.22 3.80 3.58 3.44 3.34 3.25 3.18 3.12 3.07 3.02

4.15 3.77 3.57 3.43 3.33 3.24 3.17 3.11 306 3.01

4.10 3.74 3.55 3.42 3.32 3.23 3.17 3.11 3.06 3.01

4.05 3.72 3.54 3.41 3.31 3.22 3.16 3.10 3.05 3.00

10

20

30

40

50

60

70

80

90

2.96 2.68 2.51 2.39 2.29 2.21 2.15 2.09 2.04

2.92 2.66 2.50 2.38 2.28 2.20 2.14 2.09 2.04

2.89 2.64 2.48 2.37 2.28 2.20 2.14 2.08 2.03

2.85 2.62 2.47 2.36 2.27 2.19 2.13 2.08 2.03

2.82 2.60 2.46 2.35 2.26 2.19 2.13 2.07 2.02

2.80 2.58 2.44 2.34 2.25 2.18 2.12 2.07 2.02

2.76 2.57 2.43 2.33 2.24 2.17 2.11 2.06 2.01

2.74 2.55 2.42 2.32 2.23 2.17 2.11 2.06 2.01

2.72 2.54 2.41 2.31 2.22 2.16 2.10 2.05 2.00

100

200

300

400

500

600

700

800

900

1.96 1.68

1.92 1.66

1.89 1.64

1.85 1.62

1.82 1.60

1.80 1.58

1.76 1.57

1.74 1.55

1.72 1.54

Tables

109

Table 9. Values of p[Alk] from Alk.

10 20 30 40 50 60 70 80 90

100 200 300 400 500 600 700 800 900

3.70 3.40 3.23 3.10 3.00 2.92 2.85 2.80 2.75

2.70 2.40 2.23 2.10 2.00 1.92 1.85 1.80 1.75

1

2

3

4

5

6

7

8

9

3.66 3.38 3.21 3.09 2.99 2.91 2.85 2.79 2.74

3.62 3.36 3.20 3.08 2.98 2.90 2.84 2.79 2.74

3.59 3.34 3.18 3.07 2.98 2.90 2.84 2.78 2.73

3.55 3.32 3.17 3.06 2.97 2.89 2.83 2.78 2.73

3.52 3.30 3.16 3.05 2.96 2.89 2.83 2.77 2.72

3.50 3.28 3.14 3.04 2.95 2.88 2.82 2.77 2.72

3.47 3.27 3.13 3.03 2.94 2.87 2.81 2.76 2.71

3.44 3.25 3.12 3.02 2.93 2.87 2.97 2.81 2.76 2.71

3.42 3.24 3.11 3.01 2.92 2.86 2.80 2.75 2.70

10

20

30

40

50

60

70

80

90

2.66 2.38 2.21 2.09 1.99 1.91 1.85 1.79 1.74

2.62 2.36 2.20 2.08 1.98 1.90 1.84 1.79 1.74

2.59 2.34 2.18 2.07 1.98 1.90 1.84 1.78 1.73

2.55 2.32 2.17 2.06 1.97 1.89 1.83 1.78 1.73

2.52 2.30 2.16 2.05 1.96 1.89 1.83 1.77 1.72

2.50 2.28 2.14 2.04 1.95 1.88 1.82 1.77 1.72

2.47 2.27 2.13 2.03 1.94 1.87 1.81 1.76 1.71

2.44 2.25 2.12 2.02 1.93 1.87 1.81 1.76 1.71

2.42 2.24 2.11 2.01 1.92 1.86 1.80 1.75 1.70

Table 10. Values of pK2 for Eq. (7) and pKS for Eq. (8).

T

PK2

pKS

0 10 20 30 40 50 60 70 80

10.63 10.49 10.38 10.29 10.22 10.17 10.14 10.12 10.12

8.02 8.15 8.28 8.41 8.52 8.63 8.74 8.87 8.99

110


Table 11. Assessment of margin of error (from R). ERRORS

W No

T

R

Table 6

Table 7

(Table 7)–(Table 6)

No

22

30 50 80

7.04 6.43 5.59

10 20 35

15 27 40

+5 (+50%) +7 (+35%) +5 (+14%)

22

25

30 50 80

6.48 5.82 5.02

35 50 90

30 66 74

−5 (−14%) +16 (+32%) −16 (−18%)

25

26

30 50 80

6.44 5.83 4.92

30 50 85

36 66 82

+6 (+20%) +16 (+32%) −3 (−4%)

26

29

30 50 80

5.96 5.30 4.46

80 120 170

73 137 124

−7 (−9%) +17 (+14%) −46 (−27%)

29

30

30 50 80

5.94 5.38 4.49

70 90 140

87 118 124

+17 (+26%) +28 (+31%) −16 (−11%)

30

Tables

Table 12. Errors for two water supplies (from R). WATER ANALYSES T

MEAN

MAX

ERRORS MIN

(MAX)-(MEAN)

(MIN)-(MEAN)

NORTHAMPTON (PITSFORD) 15

30

50

80

Ca Alk DS pH pHS pH R W pHS pH R W pHS pH R W

210 124 386 8.10 7.37 8.00 6.74 21 7.04 7.90 6.18 36 6.62 7.90 5.34 55

230 140 466 8.40 7.24 8.30 6.28 43 6.69 6.20 6.72 76 6.27 8.10 4.44 137

Ca Alk DS pH pHS pH R W pHS pH R W pHS pH R W

270 186 435 7.60 7.09 7.50 6.68 21 6.76 7.50 6.02 49 6.34 7.50 5.18 61

310 222 505 7.90 6.97 7.80 6.14 61 6.64 7.70 5.58 88 6.22 7.80 4.64 112

183 96 290 7.90 7.50 7.90 7.10 15 7.17 7.80 6.54 23 6.76 7.80 5.70 3

+22 (+105%)

−6 (−29%)

+40 (111%)

−13 (−36%)

+82 (+149%)

−52 (−95%)

OXFORD (SWINFORD) 15

30

50

80

240 113 365 7.10 7.53 6.90 7.16 2 7.02 6.90 7.14 9 6.50 7.00 6.00 27

+40 (+190%)

−19 (−90%)

+39 (+50%)

−40 (−82%)

+51 (+82%)

−34 (−56%)

111

112

Quantitative Forecasting of Problems in Industrial Water Systems Table 13. Weight of calcium carbonate (W) from I. VALUE OF I @ T T

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

T

30 35 40 45 50 55 60 65 70 75 80

3 3 3 3 3 3 3 3 3 3 3

5 5 4 4 4 4 4 4 4 4 3

7 7 7 6 6 6 5 5 5 5 5

11 10 10 9 9 8 8 7 7 6 6

17 16 15 14 12 12 11 10 9 8 8

26 24 22 20 18 17 15 14 13 11 10

40 36 32 29 26 24 21 19 17 15 14

62 54 48 43 38 34 30 26 23 20 18

94 82 72 63 54 48 41 36 32 27 24

145 124 107 92 78 68 58 50 43 37 32

30 35 40 45 50 55 60 65 70 75 80

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

222 187 159 135 113 97 81 69 58 49 42

340 283 236 197 163 138 114 95 79 66 55

521 427 351 289 235 196 159 131 108 88 72

644 522 423 340 278 202 181 147 118 95

30 35 40 45 50 55 60 65 70 75 80

620 490 395 313 250 199 158 126

707 562 438 344 271 211 166

613 475 308 283 219

655 501 378 289

506 381

502

30 35 40 45 50 55 60 65 70 75 80

Tables Table 14. Assessment of Margin of Error (from I ).

W No

T

I

22

30 50 80

0.43 0.71 1.13

25

30 50 80

26

(Table 6)

ERRORS

No

(Table 13)

(Table 13)−(Table 6)

10 20 35

11 26 42

+1 (+10%) +6 (+30%) +7 (+20%)

22

0.61 0.94 1.34

35 50 90

26 54 72

−9 (−26%) +4 (+8%) −12 (−20%)

25

30 50 80

0.63 0.91 1.38

30 50 85

26 54 95

−4 (−13%) +4 (+8%) +10 (+12%)

26

29

30 50 80

0.82 1.15 1.57

80 120 170

62 163 166

−18 (−23%) +43 (+36%) −4 (−2%)

29

30

30 50 80

0.88 1.11 1.63

87 118 124

94 113 166

+7 (+5%) −5 (−4%) +42 (+34%)

30

113

114

Quantitative Forecasting of Problems in Industrial Water Systems Table 15. Errors for two water supplies (from I ).

WATER ANALYSES T

MEAN

MAX

ERRORS MIN

(MAX)−(MEAN)

(MIN)−(MEAN)

NORTHAMPTON (PITSFORD) 15

Ca Alk DS pH

210 124 386 8.1

230 140 466 8.4

183 96 290 7.9

30

pHS pH RI W

7.37 8.00 0.63 26

7.29 8.30 1.01 145

7.50 7.90 0.40 11

+119 (+82%)

−15 (−58%)

pHS PH I W

7.04 7.90 0.86 54

6.96 8.20 1.24 163

7.17 7.80 0.63 18

+109 (+202%)

−36 (−67%)

pHS pH I W

6.62 7.90 1.28 72

6.27 8.10 1.83 289

6.75 7.80 1.05 42

+217 (+300%)

−30 (−42%)

50

80

OXFORD (SWINFORD) 15

Ca Alk DS pH

270 186 435 7.6

310 222 505 7.9

240 113 365 7.1

30

pHS pH I W

7.09 7.50 0.41 11

6.97 7.80 0.83 62

7.35 6.90 −0.45 nil

+51 (+463%)

−11 (−100%)

pHS PH I W

6.76 7.50 0.74 26

6.64 7.70 1.06 113

7.02 6.90 −0.12 nil

+87 (+335%)

−26 (−100%)

pHS pH I W

6.34 7.50 1.16 55

6.22 7.80 1.58 116

6.60 7.00 0.40 6

+111 (+201%)

−49 (−89%)

50

80

Tables Table 16. Comparison between Langelier and Ryznar.

VALUES OF W No

T

22

30 50 80 30 50 80 30 50 80 30 50 80 30 50 80

25

26

29

30

FROM R (TABLE 7) 15 27 40 30 66 74 36 66 82 73 137 124 87 118 124

FROM I (TABLE 13)

ERRORS

No

11 26 42 26 54 72 26 54 95 62 163 166 94 113 166

+4 (+36%) +1 (+4%) +2 (−5%) +4 (+15%) +12 (+22%) +2 (+3%) +10 (+38%) +12 (+22%) −13 (−14%) +11 (+18%) −26 (−16%) −42 (−25%) −7 (−7%) +5 (+4%) −42 (−25%)

22

Table 17. Values of pK for Eq. (34). T

pK

0 10 20 30 40 50 60 70 80 90

4.62 4.57 4.54 4.52 4.54 4.64 4.74 4.82 4.92 5.02

25

26

29

30

115

116

Quantitative Forecasting of Problems in Industrial Water Systems Table 18. Values of p[SO2− 4 ] from SO4.

0 10 20 30 40 50 60 70 80 90

100 200 300 400 500 600 700 800 900

1000 2000

4.15 3.85 3.68 3.55 3.46 3.38 3.31 3.25 3.20

3.15 2.85 2.68 2.55 2.46 2.38 2.31 2.25 2.20

2.15 1.85

1

2

3

4

5

6

7

8

9

5.15 4.11 3.82 3.66 3.54 3.44 3.37 3.30 3.24 3.19

4.85 4.07 3.81 3.65 3.53 3.43 3.36 3.29 3.23 3.19

4.68 4.04 3.80 3.64 3.53 3.43 3.36 3.29 3.23 3.18

4.55 4.00 3.77 3.62 3.51 3.42 3.35 3.28 3.22 3.18

4.46 3.98 3.76 3.61 3.50 3.41 3.34 3.28 3.22 3.17

4.38 3.96 3.74 3.60 3.49 3.40 3.33 3.28 3.21 3.17

4.31 3.92 3.72 3.58 3.48 3.40 3.33 3.27 3.21 3.17

4.25 3.91 3.70 3.57 3.47 3.39 3.32 3.26 3.20 3.16

4.20 3.87 3.69 3.56 3.46 3.38 3.31 3.25 3.20 3.15

10

20

30

40

50

60

70

80

90

3.11 2.82 2.66 2.54 2.44 2.37 2.30 2.24 2.19

3.07 2.81 2.65 2.53 2.43 2.36 2.29 2.23 2.19

3.04 2.80 2.64 2.53 2.43 2.36 2.29 2.23 2.18

3.00 2.77 2.62 2.51 2.42 2.35 2.28 2.22 2.18

2.98 2.76 2.61 2.50 2.41 2.34 2.28 2.22 2.17

2.96 2.74 2.60 2.49 2.40 2.33 2.28 2.21 2.17

2.92 2.72 2.58 2.48 2.40 2.33 2.27 2.21 2.17

2.91 2.70 2.57 2.47 2.39 2.32 2.26 2.20 2.17

2.87 2.69 2.56 2.46 2.38 2.31 2.25 2.20 2.15

100

200

300

400

500

600

700

800

900

2.11 1.82

2.07 1.81

2.04 1.81

2.00 1.77

1.98 1.76

1.96 1.74

1.92 1.72

1.91 1.70

1.87 1.69

Tables

117

Table 19 Values of “b” from Eq. (49). Table 19/1 Ca/SO4

VALUES OF IS

(Range 0.01 to 0.10)

Ca/SO4

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.2 0.4 0.6 0.8 1.0

0.99 0.99 0.99 0.99 0.99

0.99 0.98 0.98 0.98 0.97

0.99 0.98 0.97 0.96 0.96

0.98 0.97 0.96 0.95 0.95

0.98 0.96 0.95 0.94 0.93

0.97 0.95 0.94 0.93 0.92

0.97 0.94 0.93 0.92 0.91

0.96 0.94 0.92 0.91 0.90

0.96 0.93 0.91 0.90 0.89

0.95 0.92 0.90 0.88 0.87

0.2 0.4 0.6 0.8 1.0

1.2 1.4 1.6 1.8 2.0

0.99 0.99 0.98 0.98 0.98

0.97 0.97 0.97 0.97 0.97

0.96 0.96 0.95 0.95 0.95

0.94 0.94 0.94 0.94 0.93

0.93 0.93 0.92 0.92 0.92

0.92 0.91 0.91 0.91 0.90

0.90 0.90 0.89 0.89 0.89

0.90 0.88 0.88 0.87 0.87

0.88 0.87 0.86 0.86 0.86

0.87 0.86 0.85 0.85 0.84

1.2 1.4 1.6 1.8 2.0

2.2 2.4 2.6 2.8 3.0

0.98 0.98 0.98 0.98 0.98

0.97 0.97 0.96 0.96 0.96

0.95 0.95 0.95 0.95 0.95

0.93 0.93 0.93 0.93 0.93

0.92 0.91 0.91 0.91 0.91

0.90 0.90 0.90 0.90 0.89

0.88 0.88 0.88 0.88 0.88

0.87 0.87 0.86 0.86 0.86

0.85 0.85 0.85 0.85 0.84

0.84 0.84 0.83 0.83 0.83

2.2 2.4 2.6 2.8 3.0

3.2 3.4 3.6 3.8 4.0

0.98 0.98 0.98 0.98 0.98

0.96 0.96 0.96 0.96 0.96

0.95 0.94 0.94 0.94 0.94

0.93 0.93 0.93 0.93 0.92

0.91 0.91 0.91 0.91 0.91

0.89 0.89 0.89 0.89 0.89

0.88 0.87 0.87 0.87 0.87

0.86 0.86 0.86 0.86 0.85

0.84 0.84 0.84 0.84 0.84

0.83 0.82 0.82 0.82 0.82

3.2 3.4 3.6 3.8 4.0

4.2 4.4 4.6 4.8 5.0

0.98 0.98 0.98 0.98 0.98

0.96 0.96 0.96 0.96 0.96

0.94 0.94 0.94 0.94 0.94

0.92 0.92 0.92 0.92 0.92

0.91 0.91 0.90 0.90 0.90

0.89 0.89 0.89 0.89 0.89

0.87 0.87 0.87 0.87 0.87

0.85 0.85 0.85 0.85 0.85

0.84 0.84 0.83 0.83 0.83

0.82 0.82 0.82 0.82 0.82

4.2 4.4 4.6 4.8 5.0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

Ca/SO4

VALUES OF IS

(Range 0.01 to 0.10)

Ca/SO4

118

Quantitative Forecasting of Problems in Industrial Water Systems Table 19/2

Ca/SO4

VALUES OF IS

(Range 0.11 to 0.20)

Ca/SO4

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.20

0.2 0.4 0.6 0.8 1.0

0.95 0.91 0.89 0.87 0.86

0.94 0.91 0.88 0.86 0.85

0.94 0.90 0.87 0.85 0.84

0.94 0.89 0.86 0.84 0.83

0.93 0.89 0.85 0.83 0.81

0.93 0.88 0.85 0.82 0.80

0.92 0.87 0.84 0.81 0.79

0.92 0.87 0.83 0.80 0.78

0.92 0.86 0.82 0.79 0.77

0.91 0.85 0.82 0.78 0.76

0.2 0.4 0.6 0.8 1.0

1.2 1.4 1.6 1.8 2.0

0.85 0.84 0.84 0.83 0.83

0.84 0.83 0.82 0.82 0.81

0.83 0.82 0.81 0.80 0.80

0.81 0.80 0.80 0.79 0.78

0.80 0.79 0.78 0.78 0.77

0.79 0.78 0.77 0.76 0.76

0.78 0.77 0.76 0.75 0.74

0.77 0.75 0.74 0.74 0.73

0.75 0.74 0.73 0.72 0.72

0.75 0.73 0.72 0.71 0.71

1.2 1.4 1.6 1.8 2.0

2.2 2.4 2.6 2.8 3.0

0.82 0.82 0.82 0.81 0.81

0.81 0.81 0.80 0.80 0.80

0.79 0.79 0.79 0.78 0.78

0.78 0.78 0.77 0.77 0.77

0.77 0.76 0.76 0.75 0.75

0.75 0.75 0.74 0.74 0.74

0.74 0.73 0.73 0.73 0.72

0.73 0.72 0.72 0.71 0.71

0.71 0.71 0.70 0.70 0.70

0.70 0.69 0.69 0.69 0.68

2.2 2.4 2.6 2.8 3.0

3.2 3.4 3.6 3.8 4.0

0.81 0.81 0.81 0.81 0.80

0.80 0.79 0.79 0.79 0.79

0.78 0.78 0.78 0.77 0.77

0.76 0.76 0.76 0.76 0.76

0.75 0.75 0.75 0.74 0.74

0.74 0.73 0.73 0.73 0.73

0.72 0.72 0.72 0.71 0.71

0.71 0.70 0.70 0.70 0.70

0.69 0.69 0.69 0.69 0.68

0.68 0.68 0.67 0.67 0.67

3.2 3.4 3.6 3.8 4.0

4.2 4.4 4.6 4.8 5.0

0.80 0.80 0.80 0.80 0.80

0.79 0.79 0.78 0.78 0.78

0.77 0.77 0.77 0.77 0.77

0.76 0.75 0.75 0.75 0.75

0.74 0.74 0.74 0.74 0.74

0.73 0.72 0.72 0.72 0.72

0.71 0.71 0.71 0.71 0.71

0.70 0.70 0.70 0.69 0.69

0.68 0.68 0.68 0.68 0.68

0.67 0.67 0.67 0.67 0.66

4.2 4.4 4.6 4.8 5.0

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.20

Ca/SO4

VALUES OF IS

(Range 0.11 to 0.20)

Ca/SO4

Tables

119

Table 19/3 Ca/SO4

VALUES OF IS

(Range 0.21 to 0.30)

Ca/SO4

0.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.30

0.2 0.4 0.6 0.8 1.0

0.91 0.85 0.80 0.77 0.75

0.91 0.84 0.79 0.76 0.74

0.90 0.83 0.79 0.75 0.73

0.90 0.83 0.78 0.74 0.72

0.90 0.82 0.77 0.73 0.71

0.89 0.82 0.76 0.73 0.70

0.89 0.81 0.75 0.72 0.69

0.89 0.81 0.75 0.71 0.68

0.88 0.80 0.74 0.70 0.67

0.88 0.79 0.73 0.69 0.66

0.2 0.4 0.6 0.8 1.0

1.2 1.4 1.6 1.8 2.0

0.73 0.72 0.71 0.70 0.69

0.72 0.71 0.70 0.69 0.68

0.71 0.70 0.68 0.68 0.67

0.70 0.68 0.67 0.66 0.66

0.69 0.67 0.66 0.65 0.64

0.68 0.66 0.65 0.64 0.63

0.67 0.65 0.64 0.63 0.62

0.66 0.64 0.63 0.62 0.61

0.65 0.63 0.62 0.61 0.60

0.64 0.62 0.61 0.60 0.59

1.2 1.4 1.6 1.8 2.0

2.2 2.4 2.6 2.8 3.0

0.69 0.68 0.68 0.67 0.67

0.67 0.67 0.67 0.66 0.66

0.66 0.66 0.65 0.65 0.64

0.65 0.64 0.64 0.63 0.63

0.64 0.63 0.63 0.62 0.62

0.63 0.62 0.61 0.61 0.61

0.61 0.61 0.60 0.60 0.59

0.60 0.60 0.59 0.59 0.58

0.60 0.58 0.58 0.57 0.57

0.58 0.57 0.57 0.56 0.56

2.2 2.4 2.6 2.8 3.0

3.2 3.4 3.6 3.8 4.0

0.67 0.66 0.66 0.66 0.66

0.65 0.65 0.65 0.65 0.64

0.64 0.64 0.63 0.63 0.63

0.63 0.63 0.62 0.62 0.62

0.61 0.61 0.61 0.61 0.60

0.60 0.60 0.60 0.59 0.59

0.59 0.59 0.59 0.58 0.58

0.58 0.58 0.57 0.57 0.57

0.57 0.57 0.56 0.56 0.56

0.56 0.56 0.55 0.55 0.54

3.2 3.4 3.6 3.8 4.0

4.2 4.4 4.6 4.8 5.0

0.66 0.65 0.65 0.65 0.65

0.64 0.64 0.64 0.64 0.64

0.63 0.63 0.63 0.62 0.62

0.62 0.61 0.61 0.61 0.61

0.60 0.60 0.60 0.60 0.60

0.59 0.59 0.59 0.59 0.58

0.58 0.58 0.57 0.57 0.57

0.57 0.56 0.56 0.56 0.56

0.55 0.55 0.55 0.55 0.55

0.54 0.54 0.54 0.54 0.54

4.2 4.4 4.6 4.8 5.0

0.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.30

Ca/SO4

VALUES OF IS

(Range 0.21 to 0.30)

Ca/SO4

120


Ca/SO4

VALUES OF IS

(Range 0.31 to 0.40)

Ca/SO4

0.31

0.32

0.33

0.34

0.35

0.36

0.37

0.38

0.39

0.40

0.2 0.4 0.6 0.8 1.0

0.88 0.79 0.72 0.68 0.65

0.87 0.78 0.72 0.67 0.64

0.87 0.78 0.71 0.67 0.63

0.87 0.77 0.70 0.66 0.62

0.86 0.76 0.70 0.65 0.61

0.86 0.76 0.69 0.64 0.61

0.86 0.75 0.68 0.63 0.60

0.86 0.75 0.68 0.62 0.59

0.85 0.74 0.67 0.62 0.58

0.85 0.74 0.66 0.61 0.57

0.2 0.4 0.6 0.8 1.0

1.2 1.4 1.6 1.8 2.0

0.63 0.61 0.60 0.59 0.58

0.62 0.60 0.59 0.57 0.57

0.61 0.59 0.58 0.56 0.56

0.60 0.58 0.57 0.55 0.54

0.59 0.57 0.56 0.54 0.53

0.58 0.56 0.55 0.53 0.52

0.57 0.55 0.54 0.52 0.52

0.56 0.54 0.53 0.52 0.51

0.55 0.53 0.52 0.51 0.50

0.54 0.52 0.51 0.50 0.49

1.2 1.4 1.6 1.8 2.0

2.2 2.4 2.6 2.8 3.0

0.57 0.56 0.56 0.55 0.55

0.56 0.55 0.55 0.54 0.54

0.55 0.54 0.54 0.53 0.53

0.54 0.53 0.53 0.52 0.52

0.53 0.52 0.51 0.51 0.51

0.52 0.51 0.50 0.50 0.50

0.51 0.50 0.49 0.49 0.49

0.50 0.49 0.49 0.48 0.48

0.49 0.48 0.48 0.47 0.47

0.48 0.47 0.47 0.46 0.46

2.2 2.4 2.6 2.8 3.0

3.2 3.4 3.6 3.8 4.0

0.54 0.54 0.54 0.54 0.53

0.53 0.53 0.53 0.53 0.52

0.52 0.52 0.52 0.51 0.51

0.51 0.51 0.51 0.50 0.50

0.50 0.50 0.50 0.49 0.49

0.49 0.49 0.49 0.48 0.48

0.48 0.48 0.48 0.47 0.47

0.47 0.47 0.47 0.46 0.46

0.46 0.46 0.46 0.45 0.45

0.45 0.45 0.45 0.44 0.44

3.2 3.4 3.6 3.8 4.0

4.2 4.4 4.6 4.8 5.0

0.53 0.53 0.53 0.53 0.53

0.52 0.52 0.52 0.52 0.51

0.51 0.51 0.51 0.50 0.50

0.50 0.50 0.50 0.49 0.49

0.49 0.49 0.49 0.48 0.48

0.48 0.48 0.48 0.47 0.47

0.47 0.47 0.47 0.46 0.46

0.46 0.46 0.46 0.45 0.45

0.45 0.45 0.45 0.44 0.44

0.44 0.44 0.44 0.43 0.43

4.2 4.4 4.6 4.8 5.0

0.31

0.32

0.33

0.34

0.35

0.36

0.37

0.38

0.39

0.40

Ca/SO4

VALUES OF IS

(Range 0.31 to 0.40)

Ca/SO4

Tables Table 20. Values of pK1 pK2 pK3 for Eq. (58). T

pK1

pK2

pK3

10 20 30 40 50 60 70 80

2.07 2.10 2.15 2.20 2.26 2.33 2.40 2.47

7.25 7.21 7.19 7.18 7.18 7.19 7.21 7.24

12.56 12.41 12.26 12.13 12.00 11.88 11.77 11.67

Table 21. Values of p[Phos] from Phos.

0 10 20 30 40 50 60 70 80 90

100 200

3.98 3.68 3.50 3.38 3.28 3.20 3.13 3.08 3.03

2.98 2.68

1

2

3

4

5

6

7

8

9

4.98 3.94 3.66 3.49 3.37 3.27 3.19 3.13 3.07 3.02

4.68 3.90 3.64 3.47 3.36 3.26 3.19 3.12 307 3.02

4.50 3.87 3.62 3.46 3.35 3.26 3.18 3.12 3.06 3.01

4.38 3.83 3.60 3.45 3.34 3.25 3.17 3.11 3.06 3.01

4.28 3.80 3.58 3.44 3.33 3.24 3.17 3.10 3.05 3.00

4.20 3.78 3.57 3.42 3.32 3.23 3.16 3.10 3.05 3.00

4.13 3.75 3.55 3.41 3.31 3.22 3.15 3.09 3.04 2.99

4.08 3.72 3.53 3.40 3.30 3.22 3.15 3.09 3.04 2.99

4.03 3.70 3.52 3.39 3.29 3.21 3.14 3.08 3.03 2.98

10

20

30

40

50

60

70

80

90

2.94 2.66

2.90 2.64

2.87 2.62

2.83 2.60

2.80 2.58

2.78 2.57

2.75 2.55

2.72 2.52

2.70 2.52

121

122

Quantitative Forecasting of Problems in Industrial Water Systems Table 22. Values of p(E) for Eq. (67) TEMPERATURE

pH @ T

10

20

30

40

50

60

70

80

6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9

7.83 7.64 7.60 7.26 7.08 6.89 6.70 6.53 6.36 6.18

7.65 7.46 7.27 7.09 6.90 6.72 6.53 6.35 6.18 6.01

7.49 7.31 7.12 6.93 6.74 6.56 6.39 6.21 6.04 5.87

7.33 7.14 6.96 6.78 6.58 6.40 6.21 6.03 5.85 5.69

7.22 6.93 6.70 6.50 6.31 6.13 5.96 5.80 5.65 5.50

7.13 6.87 6.63 6.42 6.28 6.06 5.87 5.71 5.56 5.41

7.00 6.81 6.63 6.43 6.25 6.05 5.85 5.70 5.53 5.35

6.94 6.75 6.55 6.37 6.18 5.99 5.80 5.62 5.45 5.29

7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9

6.00 5.84 5.68 5.53 5.38 5.24 5.10 4.96 4.84 4.72

5.85 5.64 5.54 5.39 5.25 5.11 4.98 4.85 4.73 4.61

5.69 5.53 5.37 5.22 5.09 4.95 4.82 4.69 4.57 4.45

5.53 5.37 5.22 5.08 4.94 4.80 4.67 4.55 4.43 4.31

5.36 5.21 5.06 4.93 4.79 4.67 4.54 4.42 4.31 4.19

5.26 5.11 4.97 4.82 4.68 4.55 4.42 4.30 4.18 4.06

5.19 5.03 4.87 4.72 4.57 4.43 4.30 4.17 4.05 3.94

5.12 4.95 4.80 4.65 4.50 4.37 4.23 4.10 3.98 3.86

8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9

4.65 4.49 4.38 4.27 4.17 4.06 3.96 3.85 3.75 3.65

4.49 4.38 4.27 4.16 4.06 3.95 3.84 3.74 3.63 3.53

4.33 4.22 4.11 4.01 3.90 3.79 3.68 3.58 3.47 3.37

4.19 4.08 3.97 3.86 3.76 3.65 3.54 3.44 3.34 3.24

4.07 3.97 3.86 3.75 3.64 3.54 3.43 3.32 3.22 3.11

3.95 3.88 3.72 3.62 3.51 3.40 3.30 3.20 3.10 3.00

3.82 3.71 3.59 3.49 3.38 3.28 3.17 3.07 2.97 2.87

3.75 3.64 3.53 3.42 3.31 3.20 3.10 3.00 2.90 2.79

Tables

123

Table 22 (Continued) TEMPERATURE pH @ T

10

20

30

40

50

60

70

80

9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9

3.55 3.44 3.33 3.23 3.13 3.03 2.93 2.83 2.72 2.62

3.42 3.32 3.22 3.12 3.02 2.92 2.82 2.72 2.62 2.52

3.27 3.17 3.07 2.97 2.87 2.77 2.67 2.57 2.47 2.37

3.14 3.02 2.92 2.82 3.72 2.62 2.52 2.43 2.33 2.23

3.01 2.91 2.81 2.70 2.60 2.50 2.40 2.30 2.20 2.10

2.89 2.80 2.69 2.59 2.49 2.38 2.28 2.18 2.08 1.98

2.77 2.67 2.57 2.47 2.37 2.28 2.18 2.08 1.99 1.89

2.69 2.59 2.49 2.39 2.28 2.19 2.09 1.99 1.89 1.80

10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9

2.52 2.43 2.33 2.23 2.14 2.04 1.94 1.84 1.74 1.65

2.42 2.32 2.22 2.18 2.03 1.93 1.83 1.73 1.64 1.54

2.27 2.17 2.08 1.98 1.88 1.79 1.69 1.59 1.49 1.40

2.13 2.04 1.94 1.84 1.74 1.65 1.55 1.45 1.36 1.26

2.00 1.90 1.80 1.71 1.61 1.51 1.42 1.33 1.24 1.15

1.89 1.79 1.69 1.59 1.49 1.40 1.31 1.21 1.12 1.03

1.80 1.71 1.62 1.53 1.43 1.34 1.25 1.16 1.07 0.98

1.70 1.60 1.51 1.41 1.32 1.23 1.13 1.04 0.94 0.85

124

Quantitative Forecasting of Problems in Industrial Water Systems Table 23. Values of CaCO3/PO4 for selection of values of “b” from Eq. (82). Table 23/1 Ip RANGE 0.1 to 1.9 VALUES OF b (RANGE 0.10 to 0.19)

Ip

0.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

Ip

0.1

0.1

0.2 0.3 0.4 0.5

0.2 0.3 0.4 0.5

0.6 0.7 0.8 0.9 1.0

0.6 0.7 0.8 0.9 1.0

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

42.10

70.43 16.00

20.33 10.45

34.33 12.58 8.03

130.10 16.25 9.08 6.50

26.75 11.15 7.30 5.58

199.48

32.38

1.1 1.2 1.3 1.4 1.5

14.78 8.30 5.95 4.75

11.08 7.13 5.40 4.43

1.6 1.7 1.8 1.9

Tables

125

Table 23/2 VALUES OF b (RANGE 0.20 to 0.38) Ip

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

Ip

0.1

0.1

0.2 0.3 0.4 0.5

0.2 0.3 0.4 0.5

0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

8.58

20.33 7.03

25.68 10.50 6.70

52.70 12.18 7.30 5.28

6.80 5.53 4.88 4.50

6.20 4.83 4.00 3.48

4.93 4.03 3.45 3.05

4.13 3.50 3.05 2.75

125.30

22.00

102.00 12.15

21.35 8.40

0.6 0.7 0.8 0.9 1.0

16.18 8.10 5.65 4.38

26.00 9.88 6.18 4.65 3.78

12.85 7.15 5.00 3.98 3.33

8.73 5.70 4.25 3.50 2.98

6.63 4.73 3.70 3.10 2.70

5.35 4.03 3.28 2.80 2.48

1.1 1.2 1.3 1.4 1.5

3.58 3.10 2.75 2.53

3.18 2.80 2.53 2.33

2.85 2.55 2.33 2.15

2.60 2.33 2.15 2.00

2.38 2.18 2.00 1.88

2.20 2.03 1.88 1.78

1.6 1.7 1.8 1.9

126

Quantitative Forecasting of Problems in Industrial Water Systems Table 23/3 VALUES OF b (RANGE 0.40 to 0.58)

Ip

0.40

0.42

0.44

0.46

0.48

0.50

0.52

0.54

0.56

0.58

Ip

0.1

0.1

0.2 0.3 0.4 0.5

32.85

0.2 0.3 0.4 0.5

0.6 0.7 0.8 0.9 1.0

13.78 6.63 4.48

42.25 9.23 5.33 3.85

17.30 6.98 4.48 3.38

10.78 5.58 3.85 3.00

30.58 7.78 4.63 3.35 2.68

15.00 6.08 3.93 2.98 2.43

9.80 4.95 3.40 2.65 2.20

7.18 4.15 2.98 2.38 2.00

0.6 0.7 0.8 0.9 1.0

256.58 12.23 6.50

25.63 8.55 5.28

1.1 1.2 1.3 1.4 1.5

4.50 3.55 2.93 2.55 2.28

3.88 3.15 2.65 2.35 2.10

3.43 2.83 2.43 2.15 1.95

3.03 2.55 2.23 2.00 1.83

2.83 2.33 2.05 1.85 1.70

2.48 2.15 1.90 1.73 1.58

2.25 1.98 1.75 1.60 1.48

2.05 1.83 1.63 1.50 1.40

1.88 1.68 1.50 1.40 1.30

1.73 1.55 1.40 1.30 1.23

1.1 1.2 1.3 1.4 1.5

1.6 1.7 1.8 1.9

2.05 1.88 1.78 1.68

1.90 1.78 1.65 1.58

1.78 1.65 1.58 1.48

1.68 1.55 1.48 1.40

1.58 1.48 1.40 1.33

1.48 1.38 1.33 1.25

1.38 1.30 1.25 1.18

1.30 1.23 1.18 1.13

1.23 1.15 1.10 1.05

1.15 1.08 1.05 1.00

1.6 1.7 1.8 1.9

Tables

127


0.60

0.62

0.64

0.66

0.68

0.70

0.72

0.74

0.76

0.78

0.1

Ip 0.1

0.2 0.3 0.4 0.5

7.15 3.48

39.35 5.28 2.90

13.95 4.08 2.45

8.08 3.25 2.08

5.53 2.65 1.78

0.2 0.3 0.4 0.5

14.93

9.45

60.18 6.80

18.45 5.28

10.53 4.23

0.6 0.7 0.8 0.9 1.0

5.60 3.53 2.63 2.13 1.83

4.53 3.05 2.35 1.93 1.68

3.75 2.65 2.08 1.75 1.50

3.20 2.33 1.88 1.58 1.38

2.75 2.05 1.68 1.43 1.25

2.38 1.83 1.50 1.30 1.15

2.05 1.63 1.35 1.18 1.05

1.80 1.43 1.20 1.05 0.95

1.55 1.28 1.08 0.95 0.85

1.35 1.13 0.95 0.85 0.78

0.6 0.7 0.8 0.9 1.0

1.1 1.2 1.3 1.4 1.5

1.60 1.43 1.30 1.23 1.13

1.45 1.33 1.20 1.13 1.05

1.35 1.23 1.13 1.05 1.00

1.23 1.13 1.05 0.98 0.93

1.13 1.05 0.95 0.90 0.85

1.03 0.95 0.88 0.80 0.80

0.95 0.88 0.83 0.78 0.73

0.85 0.80 0.75 0.70 0.68

0.78 0.73 0.68 0.65 0.60

0.70 0.65 0.63 0.58 0.55

1.1 1.2 1.3 1.4 1.5

1.6 1.7 1.8 1.9

1.08 1.03 0.98 0.85

1.00 0.95 0.93 0.88

0.93 0.90 0.85 0.83

0.88 0.83 0.80 0.78

0.80 0.78 0.75 0.73

0.75 0.73 0.70 0.68

0.70 0.68 0.65 0.63

0.63 0.60 0.60 0.58

0.58 0.55 0.55 0.53

0.53 0.50 0.50 0.48

1.6 1.7 1.8 1.9

128


VALUES OF b (RANGE 0.80 to 0.98) Ip

0.82

0.84

0.86

0.88

24.48

5.95

2.68

1.30

0.50

0.1

0.2 0.3 0.4 0.5

4.00 2.15 1.50

13.80 3.03 1.78 1.28

7.00 2.33 1.45 1.08

4.33 1.80 1.18 0.90

2.90 1.40 0.95 0.73

1.98 1.08 0.75 0.58

1.35 0.78 0.58 0.45

0.90 0.55 0.40 0.33

0.53 0.35 0.25 0.20

0.25 0.15 0.13 0.10

0.2 0.3 0.4 0.5

0.6 0.7 0.8 0.9 1.0

1.18 0.98 0.85 0.75 0.68

1.03 0.85 0.75 0.65 0.60

0.88 0.73 0.65 0.58 0.53

0.73 0.63 0.55 0.50 0.45

0.60 0.53 0.45 0.43 0.38

0.50 0.43 0.38 0.35 0.33

0.38 0.33 0.30 0.28 0.25

0.28 0.25 0.23 0.20 0.18

0.18 0.15 0.15 0.13 0.13

0.08 0.08 0.08 0.08 0.05

0.6 0.7 0.8 0.9 1.0

1.1 1.2 1.3 1.4 1.5

0.63 0.58 0.55 0.53 0.50

0.55 0.53 0.50 0.48 0.45

0.48 0.45 0.43 0.40 0.40

0.43 0.40 0.38 0.35 0.35

0.35 0.33 0.33 0.30 0.30

0.30 0.28 0.25 0.25 0.25

0.23 0.23 0.20 0.20 0.20

0.18 0.15 0.15 0.15 0.15

0.13 0.10 0.10 0.10 0.10

0.05 0.05 0.05 0.05 0.05

1.1 1.2 1.3 1.4 1.5

1.6 1.7 1.8 1.9

0.48 0.45 0.45 0.43

0.43 0.40 0.40 0.38

0.38 0.35 0.35 0.35

0.33 0.33 0.30 0.30

0.28 0.28 0.25 0.25

0.23 0.23 0.23 0.20

0.18 0.18 0.18 0.18

0.13 0.13 0.13 0.13

0.10 0.08 0.08 0.08

0.05 0.05 0.05 0.05

1.6 1.7 1.8 1.9

0.1

0.90

0.92

0.94

0.96

0.98

Ip

0.80

Tables

129

Table 23/6

Ip RANGE 2.0 to 5.8 VALUES OF b (RANGE 0.01 to 0.09) Ip

0.01

0.02

0.03

0.04

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8

0.05

0.06

0.07

0.08

0.09

Ip

10.70

6.30

4.70

3.90

3.43

2.0 2.2 2.4 2.6 2.8

10.38 5.70

13.48 6.45 4.35 3.45

10.40 8.70 4.13 3.28 2.80

5.65 4.08 3.28 2.80 2.48

4.28 3.38 2.88 2.53 2.30

3.55 2.98 2.60 2.33 2.15

3.13 2.70 2.40 2.20 2.05

2.85 2.50 2.28 2.10 1.95

3.0 3.2 3.4 3.6 3.8

4.0 4.2 4.4 4.6 4.8

35.88 11.95 5.98 4.23 3.43

3.80 3.35 2.85 2.55 2.33

2.80 2.60 2.35 2.18 2.05

2.43 2.30 2.13 2.00 1.98

2.20 2.13 2.00 1.90 1.83

2.01 2.00 1.90 1.83 1.78

1.98 1.93 1.83 1.78 1.73

1.90 1.85 1.78 1.73 1.68

1.83 1.80 1.73 1.68 1.63

4.0 4.2 4.4 4.6 4.8

5.0 5.2 5.4 5.6 5.8

3.00 2.55 2.40 2.26 2.10

2.20 2.05 1.98 1.90 1.86

1.98 1.88 1.83 1.78 1.75

1.85 1.78 1.75 1.73 1.68

1.78 1.75 1.70 1.68 1.65

1.73 1.68 1.65 1.63 1.60

1.68 1.65 1.63 1.60 1.58

1.65 1.60 1.58 1.58 1.55

1.58 1.58 1.55 1.55 1.53

5.0 5.2 5.4 5.6 5.8

130



0.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

Ip

2.0 2.2 2.4 2.6 2.8

304.98 10.15 5.35 3.85 3.10

20.15 7.18 4.48 3.43 2.85

11.63 5.80 3.95 3.15 2.68

8.20 4.90 3.55 2.90 2.53

6.53 4.30 3.28 2.73 2.40

5.55 3.90 3.05 2.58 2.30

4.83 3.55 2.85 2.45 2.20

4.33 3.30 2.70 2.35 2.10

3.93 3.08 2.55 2.25 2.05

3.63 2.90 2.45 2.18 1.98

2.0 2.2 2.4 2.6 2.8

3.0 3.2 3.4 3.6 3.8

2.65 2.38 2.15 2.00 1.90

2.48 2.25 2.08 1.93 1.83

2.35 2.15 2.00 1.88 1.78

2.25 2.05 1.93 1.83 1.73

2.15 2.00 1.88 1.78 1.70

2.08 1.98 1.83 1.73 1.65

2.00 1.88 1.78 1.68 1.63

1.95 1.83 1.73 1.65 1.58

1.88 1.78 1.68 1.60 1.55

1.83 1.75 1.65 1.58 1.53

3.0 3.2 3.4 3.6 3.8

4.0 4.2 4.4 4.6 4.8

1.78 1.75 1.68 1.65 1.60

1.73 1.70 1.65 1.60 1.58

1.70 1.65 1.60 1.58 1.55

1.65 1.63 1.58 1.55 1.53

1.63 1.60 1.55 1.53 1.50

1.58 1.55 1.53 1.50 1.48

1.55 1.53 1.50 1.48 1.45

1.53 1.50 1.48 1.45 1.43

1.50 1.48 1.45 1.43 1.40

1.48 1.45 1.43 1.40 1.38

4.0 4.2 4.4 4.6 4.8

5.0 5.2 5.4 5.6 5.8

1.58 1.55 1.53 1.53 1.50

1.55 1.53 1.50 1.50 1.48

1.53 1.50 1.48 1.48 1.45

1.50 1.48 1.45 1.45 1.43

1.48 1.45 1.45 1.43 1.43

1.45 1.43 1.43 1.40 1.40

1.43 1.40 1.40 1.40 1.38

1.40 1.40 1.38 1.38 1.35

1.38 1.38 1.35 1.35 1.35

1.38 1.35 1.35 1.33 1.33

5.0 5.2 5.4 5.6 5.8

Tables

131

Table 23/8


0.20

0.22

0.24

0.26

0.29

0.30

0.32

0.34

0.36

0.38

Ip

2.0 2.2 2.4 2.6 2.8

3.38 2.75 2.35 2.10 1.93

2.98 2.50 2.18 1.95 1.80

2.68 2.30 2.03 1.85 1.73

2.45 2.13 1.90 1.75 1.63

2.28 2.00 1.80 1.65 1.55

2.10 1.88 1.70 1.58 1.50

1.98 1.78 1.63 1.50 1.43

1.85 1.68 1.55 1.45 1.38

1.75 1.60 1.48 1.38 1.30

1.65 1.50 1.40 1.33 1.25

2.0 2.2 2.4 2.6 2.8

3.0 3.2 3.4 3.6 3.8

1.78 1.68 1.60 1.55 1.50

1.70 1.60 1.55 1.48 1.45

1.63 1.55 1.48 1.43 1.40

1.55 1.48 1.43 1.38 1.35

1.48 1.43 1.38 1.33 1.30

1.43 1.38 1.33 1.28 1.25

1.35 1.30 1.28 1.25 1.20

1.30 1.25 1.23 1.20 1.18

1.25 1.23 1.13 1.15 1.13

1.20 1.18 1.13 1.10 1.10

3.0 3.2 3.4 3.6 3.8

4.0 4.2 4.4 4.6 4.8

1.45 1.43 1.40 1.38 1.35

1.40 1.38 1.35 1.33 1.33

1.35 1.33 1.33 1.30 1.28

1.30 1.30 1.28 1.28 1.25

1.28 1.25 1.23 1.23 1.20

1.23 1.20 1.20 1.18 1.18

1.18 1.18 1.15 1.15 1.13

1.15 1.13 1.13 1.10 1.10

1.10 1.10 1.08 1.08 1.05

1.08 1.05 1.05 1.03 1.03

4.0 4.2 4.4 4.6 4.8

5.0 5.2 5.4 5.6 5.8

1.35 1.33 1.33 1.33 1.30

1.30 1.30 1.28 1.28 1.25

1.28 1.25 1.25 1.25 1.23

1.23 1.23 1.23 1.20 1.20

1.20 1.18 1.18 1.18 1.18

1.15 1.15 1.15 1.15 1.13

1.13 1.13 1.10 1.10 1.10

1.10 1.08 1.08 1.08 1.08

1.05 1.05 1.05 1.03 1.03

1.03 1.00 1.00 1.00 1.00

5.0 5.2 5.4 5.6 5.8

132



0.40

0.42

0.44

0.46

0.48

0.50

0.52

0.54

0.56

0.58

Ip

2.0 2.2 2.4 2.6 2.8

1.55 1.43 1.33 1.25 1.20

1.48 1.38 1.28 1.20 1.15

1.40 1.30 1.15 1.10 1.10

1.33 1.23 1.15 1.10 1.05

1.25 1.18 1.10 1.05 1.00

1.20 1.13 1.05 1.00 0.98

1.18 1.10 1.05 1.00 0.95

1.08 1.00 0.95 0.90 0.88

1.00 0.95 0.90 0.88 0.88

0.95 0.90 0.85 0.83 0.80

2.0 2.2 2.4 2.6 2.8

3.0 3.2 3.4 3.6 3.8

1.15 1.13 1.10 1.08 1.05

1.10 1.08 1.05 1.03 1.00

1.08 1.03 1.00 1.00 1.00

1.03 1.00 0.98 0.95 0.93

0.98 0.95 0.93 0.93 0.90

0.95 0.90 0.90 0.88 0.85

0.93 0.90 0.90 0.88 0.85

0.85 0.83 0.83 0.80 0.80

0.83 0.80 0.78 0.78 0.75

0.78 0.75 0.75 0.73 0.73

3.0 3.2 3.4 3.6 3.8

4.0 4.2 4.4 4.6 4.8

1.03 1.03 1.00 1.00 1.00

1.00 0.98 0.98 0.98 0.95

0.95 0.95 0.93 0.93 0.93

0.93 0.90 0.90 0.90 0.90

0.88 0.88 0.88 0.85 0.85

0.85 0.85 0.83 0.83 0.83

0.85 0.85 0.83 0.83 0.83

0.78 0.78 0.78 0.75 0.75

0.75 0.73 0.73 0.73 0.73

0.70 0.70 0.70 0.70 0.68

4.0 4.2 4.4 4.6 4.8

5.0 5.2 5.4 5.6 5.8

0.98 0.98 0.98 0.98 0.98

0.95 0.95 0.95 0.93 0.93

0.93 0.90 0.90 0.90 0.90

0.88 0.88 0.88 0.88 0.88

0.85 0.85 0.85 0.83 0.83

0.83 0.80 0.80 0.80 0.80

0.83 0.80 0.80 0.80 0.80

0.75 0.75 0.75 0.75 0.75

0.73 0.70 0.70 0.70 0.70

0.68 0.68 0.68 0.68 0.68

5.0 5.2 5.4 5.6 5.8

Tables

133

Table 23/10


0.60

0.62

0.64

0.66

0.68

0.70

0.72

0.74

0.76

0.78

Ip

2.0 2.2 2.4 2.6 2.8

0.90 0.85 0.80 0.78 0.75

0.85 0.80 0.78 0.73 0.73

0.80 0.75 0.73 0.70 0.68

0.75 0.70 0.68 0.65 0.63

0.70 0.68 0.63 0.60 0.60

0.65 0.63 0.60 0.58 0.55

0.60 0.58 0.55 0.53 0.53

0.55 0.53 0.50 0.50 0.48

0.50 0.48 0.48 0.45 0.45

0.48 0.45 0.43 0.43 0.40

2.0 2.2 2.4 2.6 2.8

3.0 3.2 3.4 3.6 3.8

0.73 0.73 0.70 0.70 0.68

0.70 0.68 0.68 0.65 0.65

0.65 0.65 0.63 0.63 0.60

0.63 0.60 0.60 0.58 0.58

0.58 0.58 0.55 0.55 0.55

0.55 0.58 0.53 0.53 0.50

0.50 0.50 0.48 0.48 0.48

0.48 0.45 0.45 0.45 0.45

0.43 0.43 0.43 0.40 0.40

0.40 0.38 0.38 0.38 0.38

3.0 3.2 3.4 3.6 3.8

4.0 4.2 4.4 4.6 4.8

0.68 0.68 0.65 0.65 0.65

0.63 0.63 0.63 0.63 0.63

0.60 0.60 0.60 0.60 0.58

0.58 0.58 0.55 0.55 0.55

0.53 0.53 0.53 0.53 0.53

0.50 0.50 0.50 0.50 0.50

0.48 0.48 0.45 0.45 0.45

0.43 0.43 0.43 0.43 0.43

0.40 0.40 0.40 0.40 0.40

0.38 0.38 0.35 0.35 0.35

4.0 4.2 4.4 4.6 4.8

5.0 5.2 5.4 5.6 5.8

0.65 0.65 0.65 0.65 0.65

0.63 0.63 0.60 0.60 0.60

0.58 0.58 0.58 0.58 0.58

0.55 0.55 0.55 0.55 0.55

0.53 0.53 0.53 0.53 0.50

0.48 0.48 0.48 0.48 0.48

0.45 0.45 0.45 0.45 0.45

0.43 0.43 0.43 0.43 0.43

0.40 0.38 0.38 0.38 0.38

0.35 0.35 0.35 0.35 0.35

5.0 5.2 5.4 5.6 5.8

134



0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

Ip

2.0 2.2 2.4 2.6 2.8

0.43 0.40 0.38 0.38 0.38

0.38 0.35 0.35 0.33 0.33

0.33 0.33 0.30 0.30 0.30

0.30 0.28 0.28 0.25 0.25

0.25 0.23 0.23 0.23 0.23

0.20 0.20 0.18 0.18 0.18

0.18 0.15 0.15 0.15 0.15

0.13 0.13 0.13 0.10 0.10

0.08 0.08 0.08 0.08 0.08

0.05 0.05 0.05 0.03 0.03

2.0 2.2 2.4 2.6 2.8

3.0 3.2 3.4 3.6 3.8

0.35 0.35 0.35 0.35 0.33

0.33 0.33 0.30 0.30 0.30

0.28 0.28 0.28 0.28 0.28

0.25 0.25 0.25 0.23 0.23

0.20 0.20 0.20 0.20 0.20

0.18 0.18 0.18 0.18 0.18

0.15 0.15 0.13 0.13 0.13

0.10 0.10 0.10 0.10 0.10

0.08 0.08 0.08 0.08 0.08

0.03 0.03 0.03 0.03 0.03

3.0 3.2 3.4 3.6 3.8

4.0 4.2 4.4 4.6 4.8

0.33 0.33 0.33 0.33 0.33

0.30 0.30 0.30 0.30 0.30

0.28 0.28 0.25 0.25 0.25

0.23 0.23 0.23 0.23 0.23

0.20 0.20 0.20 0.20 0.20

0.18 0.18 0.18 0.18 0.15

0.13 0.13 0.13 0.13 0.13

0.10 0.10 0.10 0.10 0.10

0.08 0.08 0.08 0.08 0.08

0.03 0.03 0.03 0.03 0.03

4.0 4.2 4.4 4.6 4.8

5.0 5.2 5.4 5.6 5.8

0.33 0.33 0.33 0.33 0.33

0.30 0.30 0.30 0.30 0.28

0.25 0.25 0.25 0.25 0.25

0.23 0.23 0.23 0.23 0.23

0.20 0.20 0.20 0.20 0.20

0.15 0.15 0.15 0.15 0.15

0.13 0.13 0.13 0.13 0.13

0.10 0.10 0.10 0.10 0.10

0.08 0.08 0.08 0.08 0.08

0.03 0.03 0.03 0.03 0.03

5.0 5.2 5.4 5.6 5.8

Tables

135

Table 23/12

Ip RANGE 6.0 to 9.8 VALUES OF b (RANGE 0.01 to 0.09) Ip

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Ip

6.0 6.2 6.4 6.6 6.8

2.00 1.95 1.85 1.80 1.75

1.73 1.75 1.70 1.68 1.65

1.70 1.68 1.65 1.63 1.60

1.65 1.65 1.60 1.60 1.58

1.63 1.60 1.58 1.58 1.55

1.58 1.58 1.55 1.55 1.53

1.55 1.55 1.53 1.53 1.50

1.53 1.53 1.50 1.50 1.50

1.50 1.50 1.48 1.48 1.48

6.0 6.2 6.4 6.6 6.8

7.0 7.2 7.4 7.6 7.8

1.75 1.70 1.63 1.68 1.68

1.65 1.63 1.60 1.60 1.60

1.60 1.60 1.58 1.58 1.58

1.58 1.58 1.55 1.58 1.55

1.55 1.55 1.53 1.53 1.53

1.53 1.53 1.50 1.50 1.50

1.50 1.50 1.50 1.50 1.50

1.50 1.48 1.48 1.48 1.48

1.48 1.45 1.45 1.45 1.45

7.0 7.2 7.4 7.6 7.8

8.0 8.2 8.4 8.6 8.8

1.63 1.63 1.63 1.60 1.60

1.58 1.58 1.58 1.58 1.58

1.55 1.55 1.55 1.55 1.55

1.55 1.55 1.55 1.53 1.53

1.53 1.53 1.53 1.50 1.50

1.50 1.50 1.50 1.50 1.50

1.48 1.48 1.48 1.48 1.48

1.48 1.48 1.48 1.45 1.45

1.45 1.45 1.45 1.45 1.45

8.0 8.2 8.4 8.6 8.8

9.0 9.2 9.4 9.6 9.8

1.60 1.60 1.58 1.58 1.58

1.58 1.58 1.55 1.55 1.55

1.55 1.55 1.55 1.53 1.53

1.53 1.53 1.53 1.53 1.53

1.50 1.50 1.50 1.50 1.50

1.50 1.50 1.48 1.48 1.48

1.48 1.48 1.48 1.48 1.48

1.45 1.45 1.45 1.45 1.45

1.45 1.45 1.45 1.45 1.43

9.0 9.2 9.4 9.6 9.8

136



0.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

Ip

6.0 6.2 6.4 6.6 6.8

1.48 1.48 1.48 1.45 1.45

1.48 1.45 1.45 1.45 1.43

1.45 1.45 1.43 1.43 1.43

1.43 1.43 1.40 1.40 1.40

1.40 1.40 1.40 1.38 1.38

1.40 1.38 1.38 1.38 1.38

1.38 1.38 1.35 1.35 1.35

1.35 1.35 1.35 1.33 1.33

1.33 1.33 1.33 1.33 1.30

1.33 1.30 1.30 1.30 1.30

6.0 6.2 6.4 6.6 6.8

7.0 7.2 7.4 7.6 7.8

1.45 1.45 1.45 1.45 1.45

1.43 1.43 1.43 1.43 1.43

1.43 1.40 1.40 1.40 1.40

1.40 1.40 1.38 1.38 1.38

1.38 1.38 1.35 1.38 1.38

1.38 1.35 1.35 1.35 1.35

1.35 1.35 1.33 1.33 1.33

1.33 1.33 1.33 1.33 1.33

1.30 1.30 1.30 1.30 1.30

1.30 1.30 1.28 1.28 1.28

7.0 7.2 7.4 7.6 7.8

8.0 8.2 8.4 8.6 8.8

1.43 1.43 1.43 1.43 1.43

1.43 1.43 1.43 1.40 1.40

1.40 1.40 1.40 1.40 1.40

1.38 1.38 1.38 1.38 1.38

1.38 1.38 1.38 1.35 1.35

1.35 1.35 1.35 1.35 1.35

1.33 1.33 1.33 1.33 1.33

1.33 1.33 1.33 1.30 1.30

1.30 1.30 1.30 1.30 1.30

1.28 1.28 1.28 1.28 1.28

8.0 8.2 8.4 8.6 8.8

9.0 9.2 9.4 9.6 9.8

1.43 1.43 1.43 1.43 1.43

1.40 1.40 1.40 1.40 1.40

1.40 1.40 1.40 1.40 1.40

1.38 1.38 1.38 1.38 1.38

1.35 1.35 1.35 1.35 1.35

1.35 1.35 1.35 1.35 1.35

1.33 1.33 1.33 1.33 1.33

1.30 1.30 1.30 1.30 1.30

1.30 1.30 1.30 1.30 1.30

1.28 1.28 1.28 1.28 1.28

9.0 9.2 9.4 9.6 9.8

Tables

137

Table 23/14


0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

Ip

6.0 6.2 6.4 6.6 6.8

1.30 1.30 1.28 1.28 1.28

1.28 1.28 1.28 1.25 1.25

1.23 1.23 1.23 1.23 1.23

1.20 1.20 1.18 1.18 1.18

1.15 1.15 1.15 1.15 1.15

1.13 1.13 1.13 1.13 1.13

1.10 1.10 1.08 1.08 1.08

1.05 1.05 1.05 1.05 1.05

1.03 1.03 1.03 1.03 1.03

1.00 1.00 1.00 1.00 0.98

6.0 6.2 6.4 6.6 6.8

7.0 7.2 7.4 7.6 7.8

1.28 1.28 1.28 1.28 1.28

1.25 1.25 1.25 1.25 1.25

1.23 1.20 1.20 1.20 1.20

1.18 1.18 1.18 1.18 1.18

1.15 1.15 1.15 1.15 1.15

1.13 1.10 1.10 1.10 1.10

1.08 1.08 1.08 1.08 1.08

1.05 1.05 1.05 1.05 1.05

1.03 1.03 1.03 1.03 1.03

0.98 0.98 0.98 0.98 0.98

7.0 7.2 7.4 7.6 7.8

8.0 8.2 8.4 8.6 8.8

1.28 1.28 1.28 1.28 1.28

1.23 1.23 1.23 1.23 1.23

1.20 1.20 1.20 1.20 1.20

1.18 1.18 1.18 1.18 1.18

1.15 1.15 1.15 1.13 1.13

1.10 1.10 1.10 1.10 1.10

1.08 1.08 1.08 1.08 1.08

1.05 1.05 1.05 1.05 1.05

1.00 1.00 1.00 1.00 1.00

0.98 0.98 0.98 0.98 0.98

8.0 8.2 8.4 8.6 8.8

9.0 9.2 9.4 9.6 9.8

1.28 1.28 1.28 1.25 1.25

1.23 1.23 1.23 1.23 1.23

1.20 1.20 1.20 1.20 1.20

1.18 1.18 1.18 1.18 1.18

1.13 1.13 1.13 1.13 1.13

1.10 1.10 1.10 1.10 1.10

1.08 1.08 1.08 1.08 1.08

1.05 1.05 1.05 1.05 1.05

1.00 1.00 1.00 1.00 1.00

0.98 0.98 0.98 0.98 0.98

9.0 9.2 9.4 9.6 9.8

138

Quantitative Forecasting of Problems in Industrial Water Systems Table 23/15 VALUES OF b (RANGE 0.40 to 0.58)

Ip

0.40

0.42

0.44

0.46

0.48

0.50

0.52

0.54

0.56

0.58

Ip

6.0 6.2 6.4 6.6 6.8

0.98 0.95 0.95 0.95 0.95

0.93 0.93 0.93 0.93 0.93

0.90 0.90 0.90 0.90 0.90

0.88 0.88 0.85 0.85 0.85

0.83 0.83 0.83 0.83 0.83

0.80 0.80 0.80 0.80 0.80

0.78 0.78 0.78 0.78 0.75

0.73 0.73 0.73 0.73 0.73

0.70 0.70 0.70 0.70 0.70

0.68 0.68 0.68 0.68 0.68

6.0 6.2 6.4 6.6 6.8

7.0 7.2 7.4 7.6 7.8

0.95 0.95 0.95 0.95 0.95

0.93 0.93 0.93 0.93 0.93

0.90 0.90 0.88 0.88 0.88

0.85 0.85 0.85 0.85 0.85

0.83 0.83 0.83 0.83 0.83

0.80 0.80 0.80 0.80 0.80

0.75 0.75 0.75 0.75 0.75

0.73 0.73 0.73 0.73 0.73

0.70 0.70 0.70 0.70 0.70

0.68 0.68 0.68 0.68 0.68

7.0 7.2 7.4 7.6 7.8

8.0 8.2 8.4 8.6 8.8

0.95 0.95 0.95 0.95 0.95

0.93 0.93 0.93 0.93 0.93

0.88 0.88 0.88 0.88 0.88

0.85 0.85 0.85 0.85 0.85

0.83 0.83 0.83 0.83 0.83

0.80 0.80 0.80 0.80 0.80

0.75 0.75 0.75 0.75 0.75

0.73 0.73 0.73 0.73 0.73

0.70 0.70 0.70 0.70 0.70

0.68 0.68 0.68 0.65 0.65

8.0 8.2 8.4 8.6 8.8

9.0 9.2 9.4 9.6 9.8

0.95 0.95 0.95 0.95 0.95

0.93 0.93 0.93 0.93 0.93

0.88 0.88 0.88 0.88 0.88

0.85 0.85 0.85 0.85 0.85

0.83 0.83 0.83 0.83 0.83

0.80 0.80 0.80 0.80 0.80

0.75 0.75 0.75 0.75 0.75

0.73 0.73 0.73 0.73 0.73

0.70 0.70 0.70 0.70 0.70

0.65 0.65 0.65 0.65 0.65

9.0 9.2 9.4 9.6 9.8

Tables

139


0.60

0.62

0.64

0.66

0.68

0.70

0.72

0.74

0.76

0.78

Ip

6.0 6.2 6.4 6.6 6.8

0.65 0.65 0.63 0.63 0.63

0.60 0.60 0.60 0.60 0.60

0.58 0.58 0.58 0.58 0.58

0.55 0.55 0.55 0.55 0.55

0.50 0.50 0.50 0.50 0.50

0.48 0.48 0.48 0.48 0.48

0.45 0.45 0.45 0.45 0.45

0.43 0.43 0.43 0.43 0.40

0.38 0.38 0.38 0.38 0.38

0.35 0.35 0.35 0.35 0.35

6.0 6.2 6.4 6.6 6.8

7.0 7.2 7.4 7.6 7.8

0.63 0.63 0.63 0.63 0.63

0.60 0.60 0.60 0.60 0.60

0.58 0.58 0.58 0.58 0.58

0.55 0.55 0.55 0.55 0.55

0.50 0.50 0.50 0.50 0.50

0.48 0.48 0.48 0.48 0.48

0.45 0.45 0.45 0.45 0.45

0.40 0.40 0.40 0.40 0.40

0.38 0.38 0.38 0.38 0.38

0.35 0.35 0.35 0.35 0.35

7.0 7.2 7.4 7.6 7.8

8.0 8.2 8.4 8.6 8.8

0.63 0.63 0.63 0.63 0.63

0.60 0.60 0.60 0.60 0.60

0.58 0.58 0.58 0.58 0.58

0.53 0.53 0.53 0.53 0.53

0.50 0.50 0.50 0.50 0.50

0.48 0.48 0.48 0.48 0.48

0.45 0.45 0.45 0.45 0.45

0.40 0.40 0.40 0.40 0.40

0.38 0.38 0.38 0.38 0.38

0.35 0.35 0.35 0.35 0.35

8.0 8.2 8.4 8.6 8.8

9.0 9.2 9.4 9.6 9.8

0.63 0.63 0.63 0.63 0.63

0.60 0.60 0.60 0.60 0.60

0.58 0.58 0.58 0.58 0.58

0.53 0.53 0.53 0.53 0.53

0.50 0.50 0.50 0.50 0.50

0.48 0.48 0.48 0.48 0.48

0.45 0.45 0.45 0.45 0.45

0.40 0.40 0.40 0.40 0.40

0.38 0.38 0.38 0.38 0.38

0.35 0.35 0.35 0.35 0.35

9.0 9.2 9.4 9.6 9.8

140



0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

Ip

6.0 6.2 6.4 6.6 6.8

0.33 0.33 0.33 0.33 0.33

0.28 0.28 0.28 0.28 0.28

0.25 0.25 0.25 0.25 0.25

0.23 0.23 0.23 0.23 0.23

0.20 0.20 0.20 0.20 0.20

0.15 0.15 0.15 0.15 0.15

0.13 0.13 0.13 0.13 0.13

0.10 0.10 0.10 0.10 0.10

0.08 0.08 0.08 0.08 0.08

0.03 0.03 0.03 0.03 0.03

6.0 6.2 6.4 6.6 6.8

7.0 7.2 7.4 7.6 7.8

0.33 0.33 0.33 0.33 0.33

0.28 0.28 0.28 0.28 0.28

0.25 0.25 0.25 0.25 0.25

0.23 0.23 0.23 0.23 0.23

0.20 0.20 0.20 0.20 0.20

0.15 0.15 0.15 0.15 0.15

0.13 0.13 0.13 0.13 0.13

0.10 0.10 0.10 0.10 0.10

0.08 0.08 0.08 0.08 0.08

0.03 0.03 0.03 0.03 0.03

7.0 7.2 7.4 7.6 7.8

8.0 8.2 8.4 8.6 8.8

0.33 0.33 0.33 0.33 0.33

0.28 0.28 0.28 0.28 0.28

0.25 0.25 0.25 0.25 0.25

0.23 0.23 0.23 0.23 0.23

0.20 0.20 0.20 0.20 0.20

0.15 0.15 0.15 0.15 0.15

0.13 0.13 0.13 0.13 0.13

0.10 0.10 0.10 0.10 0.10

0.08 0.08 0.08 0.08 0.08

0.03 0.03 0.03 0.03 0.03

8.0 8.2 8.4 8.6 8.8

9.0 9.2 9.4 9.6 9.8

0.33 0.33 0.33 0.33 0.33

0.28 0.28 0.28 0.28 0.28

0.25 0.25 0.25 0.25 0.25

0.23 0.23 0.23 0.23 0.23

0.20 0.20 0.20 0.20 0.20

0.15 0.15 0.15 0.15 0.15

0.13 0.13 0.13 0.13 0.13

0.10 0.10 0.10 0.10 0.10

0.08 0.08 0.08 0.08 0.08

0.03 0.03 0.03 0.03 0.03

9.0 9.2 9.4 9.6 9.8

Tables

141

Table 24. Corrosion rate (C/ ) as mm.y−1 for mild steel from R. Table 24/1 VALUES OF R @ T

(Range 6.0 to 6.9)

T

6.0

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

T

5 10 15 20

0.10 0.15 0.20 0.25

0.11 0.16 0.21 0.26

0.11 0.17 0.22 0.28

0.12 0.17 0.23 0.29

0.12 0.18 0.24 0.30

0.13 0.19 0.25 0.31

0.13 0.20 0.26 0.33

0.14 0.21 0.28 0.35

0.15 0.22 0.29 0.36

0.15 0.23 0.30 0.38

5 10 15 20

25 30 35 40

0.30 0.35 0.40 0.45

0.32 0.37 0.42 0.47

0.33 0.39 0.44 0.50

0.35 0.40 0.46 0.52

0.36 0.42 0.48 0.54

0.38 0.44 0.50 0.56

0.39 0.46 0.52 0.59

0.42 0.49 0.56 0.63

0.44 0.51 0.58 0.65

0.45 0.53 0.60 0.68

25 30 35 40

45 50 55 60

0.50 0.55 0.60 0.65

0.53 0.58 0.63 0.68

0.55 0.61 0.66 0.72

0.58 0.63 0.69 0.75

0.60 0.66 0.72 0.78

0.63 0.69 0.75 0.81

0.65 0.72 0.78 0.85

0.70 0.77 0.84 0.91

0.73 0.80 0.87 0.94

0.75 0.83 0.90 0.98

45 50 55 60

65 70 75 80

0.70 0.75 0.80 0.85

0.74 0.79 0.84 0.89

0.77 0.83 0.88 0.94

0.81 0.86 0.92 0.98

0.84 0.90 0.96 1.02

0.88 0.94 1.00 1.06

0.91 0.98 1.04 1.11

0.98 1.05 1.12 1.19

1.02 1.09 1.16 1.23

1.05 1.13 1.20 1.28

65 70 75 80

T

6.0

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

T

VALUES OF R @ T

(Range 6.0 to 6.9)

142

Quantitative Forecasting of Problems in Industrial Water Systems Table 24/2 VALUES OF R @ T

(Range 7.0 to 7.9)

T

7.0

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

T

5 10 15 20

0.16 0.24 0.32 0.40

0.17 0.25 0.33 0.41

0.18 0.26 0.35 0.44

0.18 0.27 0.36 0.45

0.19 0.29 0.36 0.48

0.20 0.30 0.40 0.50

0.21 0.32 0.42 0.53

0.22 0.33 0.44 0.55

0.23 0.35 0.46 0.58

0.24 0.36 0.48 0.60

5 10 15 20

25 30 35 40

0.48 0.56 0.64 0.72

0.50 0.58 0.66 0.74

0.53 0.61 0.70 0.79

0.54 0.63 0.72 0.81

0.57 0.67 0.76 0.86

0.60 0.70 0.80 0.90

0.63 0.74 0.84 0.95

0.66 0.77 0.88 0.99

0.69 0.81 0.92 1.04

0.72 0.84 0.96 1.08

25 30 35 40

45 50 55 60

0.80 0.88 0.96 1.04

0.83 0.91 0.99 1.07

0.88 0.96 1.05 1.14

0.90 0.99 1.08 1.17

0.95 1.05 1.14 1.24

1.00 1.10 1.20 1.30

1.05 1.16 1.26 1.37

1.10 1.21 1.32 1.43

1.15 1.27 1.38 1.50

1.20 1.32 1.44 1.56

45 50 55 60

65 70 75 80

1.12 1.20 1.28 1.36

1.16 1.24 1.32 1.40

1.23 1.31 1.40 1.49

1.26 1.35 1.44 1.53

1.33 1.43 1.52 1.62

1.40 1.50 1.60 1.70

1.47 1.58 1.68 1.79

1.54 1.65 1.76 1.87

1.61 1.73 1.84 1.96

1.66 1.80 1.92 2.04

65 70 75 80

T

7.0

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

T

VALUES OF R @ T

(Range 7.0 to 7.9)

Tables

143

Table 24/3 VALUES OF R @ T

(Range 8.0 to 8.9)

T

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

T

5 10 15 20

0.25 0.38 0.50 0.63

0.26 0.39 0.52 0.65

0.28 0.41 0.55 0.69

0.29 0.44 0.58 0.73

0.30 0.45 0.60 0.75

0.32 0.47 0.53 0.79

0.33 0.50 0.66 0.83

0.35 0.52 0.69 0.86

0.36 0.54 0.72 0.90

0.38 0.57 0.76 0.95

5 10 15 20

25 30 35 40

0.75 0.88 1.00 1.13

0.78 0.91 1.04 1.17

0.83 0.96 1.10 1.24

0.87 1.02 1.16 1.31

0.90 1.05 1.20 1.35

0.95 1.10 1.26 1.42

0.99 1.16 1.32 1.49

1.04 1.21 1.38 1.55

1.08 1.26 1.44 1.62

1.14 1.33 1.52 1.71

25 30 35 40

45 50 55 60

1.25 1.38 1.50 1.63

1.30 1.43 1.56 1.69

1.38 1.51 1.65 1.79

1.45 1.60 1.74 1.89

1.50 1.65 1.80 1.95

1.58 1.73 1.89 2.05

1.65 1.82 1.98 2.15

1.73 1.90 2.07 2.24

1.80 1.98 2.16 2.34

1.90 2.09 2.28 2.47

45 50 55 60

65 70 75 80

1.75 1.88 2.00 2.13

1.82 1.95 2.08 2.21

1.93 2.06 2.20 2.34

2.03 2.18 2.32 2.47

2.10 2.25 2.40 2.55

2.21 2.36 2.52 2.68

2.31 2.48 2.64 2.81

2.42 2.59 2.76 2.93

2.52 2.70 2.88 3.06

2.66 2.85 3.04 3.28

65 60 75 80

T

8.0

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

T

VALUES OF R @ T

(Range 8.0 to 8.9)

144


VALUES OF R @ T

(Range 9.0 to 9.0)

T

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

T

5 10 15 20

0.40 0.58 0.79 0.99

0.42 0.62 0.83 1.04

0.44 0.65 0.87 1.09

0.46 0.68 0.91 1.14

0.48 0.71 0.95 1.19

0.50 0.75 1.00 1.25

0.53 0.79 1.05 1.30

0.55 0.83 1.10 1.38

0.58 0.86 1.15 1.44

0.60 0.90 1.20 1.50

5 10 15 20

25 30 35 40

1.19 1.38 1.58 1.78

1.25 1.45 1.66 1.87

1.31 1.52 1.74 1.96

1.37 1.59 1.82 2.05

1.43 1.66 1.90 2.14

1.50 1.75 2.00 2.25

1.58 1.84 2.10 2.36

1.65 1.93 2.20 2.48

1.73 2.01 2.30 2.59

1.80 2.10 2.40 2.70

25 30 35 40

45 50 55 60

1.98 2.17 2.37 2.57

2.08 2.28 2.49 2.70

2.18 2.39 2.61 2.83

2.28 2.50 2.73 2.96

2.38 2.61 2.85 3.09

2.50 2.75 3.00 3.25

2.63 2.89 3.15 3.41

2.75 3.03 3.30 3.58

2.88 3.16 3.45 3.74

3.00 3.30 3.60 3.90

45 50 55 60

65 70 75 80

2.77 2.96 3.16 3.36

2.91 3.11 3.32 3.53

3.05 3.26 3.48 3.70

3.19 3.41 3.64 3.87

3.33 3.56 3.80 4.04

3.50 3.75 4.00 4.25

3.68 3.94 4.20 4.46

3.85 4.12 4.40 4.68

4.03 4.31 4.60 4.89

4.20 4.50 4.80 5.10

65 70 75 80

T

9.0

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

T

VALUES OF R @ T

(Range 9.0 to 9.9)

Tables

145

Table 24/5 VALUES OF R @ T

(Range 10.0 to 10.9)

T

10.0

10.1

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

T

5 10 15 20

0.63 0.95 1.26 1.58

0.66 0.99 1.32 1.65

0.69 1.04 1.38 1.73

0.73 1.09 1.45 1.81

0.76 1.13 1.51 1.89

0.79 1.19 1.58 1.98

0.83 1.25 1.66 2.08

0.87 1.31 1.74 2.18

0.91 1.37 1.82 2.28

0.96 1.43 1.91 2.39

5 10 15 20

25 30 35 40

1.89 2.21 2.52 2.84

1.98 2.31 2.64 2.97

2.07 2.42 2.76 3.11

2.18 2.54 2.90 3.26

2.27 2.64 3.02 3.40

2.37 2.77 3.16 3.56

2.49 2.91 3.22 3.74

2.61 3.05 3.48 3.92

2.73 3.19 3.64 4.10

2.87 3.34 3.82 4.30

25 30 35 40

45 50 55 60

3.15 3.47 3.78 4.10

3.30 3.63 3.96 4.29

3.45 3.80 4.14 4.49

3.63 3.99 4.35 4.71

3.78 4.15 4.53 4.91

3.95 4.35 4.74 5.14

4.15 4.57 4.98 5.40

4.35 4.79 5.22 5.66

4.55 5.01 5.46 5.92

4.78 5.25 5.73 6.21

45 50 55 60

65 70 75 80

4.41 4.73 5.04 5.36

4.62 4.95 5.28 5.61

4.83 5.18 5.52 5.87

5.08 5.44 5.80 6.16

5.29 5.66 6.04 6.42

5.53 5.93 6.32 6.72

5.81 6.23 6.64 7.06

6.09 6.53 6.96 7.40

6.37 6.83 7.28 7.74

6.69 7.16 7.64 8.12

65 70 75 80

T

10.0

10.1

10.2

10.3

10.4

10.5

10.6

10.7

10.8

10.9

T

VALUES OF R @ T

(Range 10.0 to 10.9)

146

Quantitative Forecasting of Problems in Industrial Water Systems Table 24/6 VALUES OF R @ T

T

11.0

11.1

11.2

11.3

5 10 15 20

1.00 1.50 2.00 2.50

1.05 1.57 2.09 2.61

1.10 1.64 2.19 2.74

1.15 1.72 2.29 2.86

25 30 35 40

3.00 3.50 4.00 4.50

3.14 3.66 4.18 4.70

3.29 3.83 4.38 4.93

45 50 55 60

5.00 5.50 6.00 6.50

5.23 5.75 6.27 6.79

65 70 75 80

7.00 7.50 8.00 8.50

T

11.0

11.4

(Range 11.0 to 11.9) 11.5

11.6

11.7

11.8

11.9

T

1.20 1.80 2.40 3.00

1.26 1.88 2.51 3.14

1.32 1.97 2.63 3.29

1.38 2.06 2.75 3.44

1.44 2.16 2.88 3.60

1.51 2.27 3.02 3.78

5 10 15 20

3.44 4.01 4.58 5.15

3.60 4.20 4.80 5.40

3.77 4.39 5.02 5.65

3.95 4.60 5.26 5.92

4.13 4.81 5.50 6.19

4.32 5.04 5.76 6.48

4.53 5.29 6.04 6.80

25 30 35 40

5.48 6.02 6.57 7.12

5.73 6.30 6.87 7.44

6.00 6.60 7.20 7.80

6.28 6.90 7.53 8.16

6.58 7.23 7.89 8.55

6.88 7.56 8.25 8.94

7.20 7.92 8.64 9.36

7.55 8.31 9.06 9.52

45 50 55 60

7.32 7.84 8.36 8.88

7.67 8.21 8.76 9.31

8.02 8.59 9.16 9.73

8.40 9.00 9.60 10.20

8.79 9.41 10.04 10.67

9.21 9.86 10.52 11.18

9.63 10.31 11.00 11.69

10.08 10.80 11.52 12.24

10.57 11.33 12.08 12.84

65 70 75 80

11.1

11.2

11.3

11.4

11.5

11.6

11.7

11.8

11.9

T

VALUES OF R @ T

(Range 11.0 to 11.9)

Tables

147

Table 24/7

VALUES OF R @ T T

12.0

12.1

12.2

12.3

12.4

(Range 12.0 to 12.9) 12.5

12.6

12.7

12.8

12.9

T

5 10 15 20

1.58 2.37 3.16 3.95

1.66 2.48 3.31 4.14

1.74 2.60 3.47 4.34

1.82 2.72 3.63 4.54

1.90 2.85 3.80 4.75

1.99 2.99 3.98 4.98

2.09 3.13 4.17 5.21

2.19 3.28 4.37 5.46

2.29 3.43 4.57 5.71

2.40 3.59 4.79 5.90

5 10 15 20

25 30 35 40

4.74 5.53 6.32 7.11

4.97 5.79 6.62 7.45

5.21 6.07 6.94 7.81

5.45 6.35 7.26 8.17

5.70 6.65 7.60 8.55

5.97 6.97 7.96 8.96

6.26 7.30 8.34 9.38

6.56 7.65 8.74 9.83

6.86 8.00 9.14 10.28

7.19 8.38 9.58 10.78

25 30 35 40

45 50 55 60

7.90 8.69 9.48 10.27

8.28 9.10 9.93 10.76

8.68 9.54 10.41 11.28

9.08 9.98 10.89 11.80

9.50 10.45 11.40 12.35

9.95 10.95 11.94 12.94

10.43 11.47 12.51 13.55

10.93 12.02 13.11 14.20

11.43 12.57 13.71 14.85

11.98 13.17 14.37 15.57

45 50 55 60

65 70 75 80

11.06 11.55 12.64 13.43

11.59 12.41 13.24 14.07

12.15 13.01 13.88 14.75

12.71 13.61 14.52 15.43

13.30 14.25 15.20 16.15

13.93 14.93 15.92 16.92

14.60 15.64 16.68 17.72

15.30 16.39 17.48 18.57

16.00 17.14 18.28 19.42

16.77 17.96 19.16 20.36

65 70 75 80

T

12.0

12.1

12.2

12.3

12.4

12.5

12.6

12.7

12.8

12.9

T

VALUES OF R @ T

(Range 12.0 to 12.9)

Table 25. Water analyses for Langelier index/corrosion relationship for mild steel. No

Ca

Alk

DS

pH

pHS @ 15°C (Eq. 6)

R @ 15°C (Eq. 1)

I @ 15°C (Eq. 5)

C/ @ 15°C (Eq. 92)

32 33 34 35 36 37 38 39 40 41

50 50 100 100 150 150 200 200 250 250

30 70 60 140 100 200 140 260 180 320

120 180 240 360 375 525 510 690 645 855

6.50 6.60 6.80 6.90 7.10 7.00 7.20 7.10 7.30 7.20

8.86 8.50 8.29 7.96 7.93 7.67 7.70 7.46 7.51 7.31

11.22 10.40 9.78 9.02 8.76 8.34 8.20 7.82 7.72 7.42

−2.36 −1.90 −1.49 −1.06 −0.83 −0.67 −0.50 −0.36 −0.21 −0.11

2.21 1.51 1.14 0.80 0.71 0.59 0.54 0.46 0.44 0.38

148

Quantitative Forecasting of Problems in Industrial Water Systems Table 26. Corrosion rate (C/) as mm.y−1 for mild steel from I. Table 26/1 (Range −0.1 to −1.0)

VALUES OF I @ T T

−0.1

−0.2

−0.3

−0.4

−0.5

−0.6

−0.7

−0.8

−0.9

−1.0

T

5 10 15 20

0.20 0.29 0.39 0.49

0.21 0.32 0.42 0.53

0.23 0.34 0.45 0.56

0.25 0.37 0.49 0.61

0.27 0.40 0.53 0.66

0.29 0.43 0.57 0.71

0.31 0.46 0.61 0.76

0.33 0.50 0.66 0.83

0.36 0.54 0.72 0.90

0.39 0.58 0.77 0.96

5 10 15 20

25 30 35 40

0.59 0.68 0.78 0.88

0.63 0.74 0.84 0.95

0.68 0.79 0.90 1.01

0.74 0.86 0.98 1.10

0.80 0.93 1.06 1.19

0.86 1.00 1.14 1.28

0.92 1.07 1.22 1.37

0.99 1.16 1.32 1.49

1.08 1.26 1.44 1.62

1.16 1.35 1.54 1.73

25 30 35 40

45 50 55 60

0.98 1.07 1.17 1.27

1.05 1.10 1.26 1.37

1.13 1.24 1.35 1.46

1.23 1.35 1.47 1.59

1.33 1.46 1.59 1.72

1.43 1.57 1.71 1.85

1.53 1.68 1.83 1.98

1.65 1.82 1.98 2.15

1.80 1.98 2.16 2.34

1.93 2.12 2.31 2.50

45 50 55 60

65 70 75 80

1.37 1.46 1.56 1.66

1.47 1.58 1.68 1.79

1.58 1.60 1.80 1.91

1.72 1.84 1.96 2.08

1.86 1.99 2.12 2.25

2.00 2.14 2.28 2.42

2.14 2.29 2.44 2.59

2.31 2.48 2.64 2.81

2.52 2.70 2.88 3.06

2.70 2.89 3.08 3.27

65 70 75 80

T

−0.1

−0.2

−0.3

−0.4

−0.5

−0.6

−0.7

−0.8

−0.9

−1.0

T

VALUES OF I @ T

(Range −0.1 to −1.0)

Tables

149

Table 26/2 (Range −1.1 to −2.0)

VALUES OF I @ T T

−1.1

−1.2

−1.3

−1.4

−1.5

−1.6

−1.7

−1.8

−1.9

−2.0

T

5 10 15 20

0.42 0.62 0.83 1.04

0.45 0.68 0.90 1.13

0.49 0.73 0.97 1.21

0.53 0.79 1.05 1.31

0.57 0.85 1.13 1.41

0.61 0.92 1.22 1.53

0.66 0.99 1.32 1.65

0.72 1.07 1.43 1.79

0.77 1.16 1.54 1.93

0.88 1.25 1.66 2.08

5 10 15 20

25 30 35 40

1.25 1.45 1.66 1.87

1.35 1.58 1.80 2.02

1.46 1.70 1.94 2.18

1.58 1.84 2.10 2.36

1.70 1.98 2.26 2.54

1.83 2.14 2.44 2.75

1.98 2.31 2.64 2.97

2.15 2.50 2.86 3.22

2.31 2.70 3.08 3.47

2.49 2.91 3.32 3.74

25 30 35 40

45 50 55 60

2.08 2.28 2.49 2.70

2.25 2.48 2.70 2.93

2.43 2.67 2.91 3.15

2.63 2.89 3.15 3.41

2.83 3.11 3.39 3.67

3.05 3.36 3.66 3.97

3.30 3.63 3.96 4.29

3.58 3.93 4.09 4.65

3.85 4.24 4.62 5.01

4.15 4.57 4.96 5.49

45 50 55 60

65 70 75 80

2.91 3.11 3.32 3.53

3.15 3.38 3.60 3.83

3.40 3.64 3.88 4.12

3.68 3.94 4.20 4.46

3.96 4.24 4.52 4.80

4.27 4.58 4.88 5.19

4.62 4.95 5.28 5.61

5.01 5.36 5.72 6.08

5.39 5.78 6.16 6.55

5.81 6.23 6.64 7.06

65 70 75 80

T

−1.1

−1.2

−1.3

−1.4

−1.5

−1.6

−1.7

−1.8

−1.9

−2.0

T

VALUES OF I @ T

(Range −1.1 to −2.0)

150

Quantitative Forecasting of Problems in Industrial Water Systems Table 26/3 VALUES OF I @ T

(Range −2.1 to −3.0)

T

−2.1

−2.2

−2.3

−2.4

−2.5

−2.6

5 10 15 20

0.90 1.35 1.80 2.25

0.97 1.45 1.93 2.41

1.05 1.57 2.09 2.61

1.13 1.70 2.26 2.83

1.22 1.83 2.44 3.05

1.32 1.98 2.64 3.30

25 30 35 40

2.70 3.15 3.60 4.05

2.90 3.38 3.88 4.34

3.14 3.66 4.18 4.70

3.39 3.96 4.52 5.09

3.66 4.27 4.88 5.49

45 50 55 60

4.50 4.95 5.40 5.85

4.83 5.31 5.79 6.27

5.23 5.75 6.27 6.79

5.65 6.22 6.78 7.35

65 70 75 80

6.30 6.75 7.20 7.65

6.76 7.24 7.72 8.20

7.32 7.84 8.36 8.88

T

−2.1

−2.2

−2.3

−2.8

−2.9

−3.0

T

1.43 2.14 2.85 3.56

1.54 2.30 3.07 3.84

1.66 2.49 3.32 4.15

1.79 2.69 3.58 4.48

5 10 15 20

3.96 4.62 5.28 5.94

4.28 4.99 5.70 6.41

4.61 5.37 6.14 6.91

4.98 5.81 6.64 7.47

5.37 6.27 7.16 8.06

25 30 35 40

6.10 6.71 7.32 7.93

6.60 7.26 7.92 8.58

7.13 7.84 8.55 9.26

7.68 8.44 9.21 9.98

8.30 9.13 9.96 10.79

8.95 9.85 10.74 11.64

45 50 55 60

7.91 8.48 9.04 9.61

8.54 9.15 9.76 10.37

9.24 9.90 10.56 11.22

9.98 10.69 11.40 12.11

10.75 11.51 12.28 13.05

11.62 12.45 13.28 14.11

12.53 13.42 14.32 15.22

65 70 75 80

−2.4

−2.5

−2.6

−2.7

−2.8

−2.9

−3.0

T

VALUES OF I @ T

−2.7

(Range −2.1 to −3.0)

Tables

151

Table 26/4 VALUES OF I @ T

(Range −3.1 to −4.0)

T

−3.1

−3.2

−3.3

−3.4

−3.5

−3.6

−3.7

−3.8

−3.9

−4.0

T

5 10 15 20

1.94 2.90 3.87 4.84

2.09 3.13 4.17 5.23

2.25 3.38 4.50 5.62

2.44 3.65 4.87 6.09

2.63 3.94 5.25 6.56

2.84 4.25 5.67 7.09

3.06 4.59 6.12 7.65

3.30 4.95 6.60 8.25

3.57 5.36 7.14 8.93

3.86 5.78 7.71 9.64

5 10 15 20

25 30 35 40

5.81 6.77 7.74 8.71

6.26 7.30 8.34 9.38

6.75 7.88 9.00 10.13

7.31 8.52 9.74 10.96

7.88 9.19 10.50 11.81

8.51 9.92 11.43 12.76

9.18 10.71 12.24 13.77

9.90 11.55 13.20 14.85

10.71 12.50 14.28 16.07

11.57 13.49 15.42 17.35

25 30 35 40

45 50 55 60

9.68 10.64 11.61 12.58

10.43 11.47 12.51 13.55

11.25 12.38 13.50 14.63

12.18 13.39 14.61 15.83

13.13 14.44 15.75 17.06

14.18 15.59 17.01 18.43

15.30 16.83 18.36 19.89

16.50 18.15 19.80 21.45

17.85 19.64 21.42 23.21

19.28 21.20 23.13 25.06

45 50 55 60

65 70 75 80

13.55 14.51 15.48 16.45

14.60 15.64 16.68 17.72

15.75 16.88 18.00 19.13

17.05 18.26 19.48 20.70

18.38 19.69 21.00 22.31

19.85 21.26 22.68 24.01

21.42 22.95 24.48 26.01

23.10 24.75 26.40 28.05

24.90 26.78 28.56 30.35

26.99 28.91 30.84 32.77

65 70 75 80

T

−3.1

−3.2

−3.3

−3.4

−3.5

−3.6

−3.7

−3.8

−3.9

−4.0

T

VALUES OF I @ T

(Range −3.1 to −4.0)

Table 27. Comparison between Ryznar and Langelier. Table 27/1 T

pHS @ T

pH @ T

R@T

C/ from Table 24

I@T

C/ from Table 26

20 30 40 50

7.0 8.5 9.6 10.2

6.5 7.2 7.8 8.0

7.5 9.8 11.4 12.4

0.50 2.01 5.40 10.45

−0.5 −1.3 −1.8 −2.2

0.66 1.70 3.22 5.31

152

Quantitative Forecasting of Problems in Industrial Water Systems Table 27/2. pHS

pH

I

R

7.5 7.8 8.0 7.3 7.0

7.0 7.5 8.0 6.5 6.0

−0.5 −0.3 0 −0.8 −1.0

8.0 8.1 8.0 8.1 8.0

Table 28. Water analyses for buffer capacity/corrosion relationship for mild steel. No

Ca

Alk

DS

pH

pHS @ 15°C (Eq. 6)

I @ 15°C (Eq. 3)

C/ @ 15°C (Eq. 26)

Alkb 4.4.4

Alka 4.4.4

B 4.4.4

No

42 43 44 45 46 47 48 49 50 51

2 2 2 2 2 2 2 2 2 2

30 70 60 140 100 200 140 260 180 120

120 180 240 360 375 525 510 690 645 855

6.50 6.60 6.80 6.90 7.10 7.00 7.20 7.10 7.30 7.20

10.26 9.90 9.99 9.66 9.81 9.55 9.70 9.46 9.61 9.41

−3.76 −3.30 −3.19 −2.76 −2.71 −2.55 −2.50 −2.36 −2.31 −2.21

6.36 4.50 4.17 2.95 2.85 2.54 2.44 2.17 2.09 1.93

33 76 65 150 105 210 145 270 185 330

25 63 55 133 95 190 135 250 175 310

40 65 50 85 50 50 50 100 50 100

42 43 44 45 46 47 48 49 50 51

Tables

153

Table 29. Corrosion rate (C/) as mm.y−1 for mild steel in base exchange waters from B/Alk. Table 29/1 B/Alk @ T

(Range 0.1 to 1.0)

T

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

5 10 15 20

0.70 1.05 1.40 1.75

0.90 1.35 1.80 2.25

1.10 1.65 2.20 2.75

1.30 1.95 2.60 3.25

1.50 2.25 3.00 3.75

1.70 2.55 3.40 4.25

1.90 2.85 3.80 4.75

2.10 3.15 4.20 5.25

2.30 3.45 4.60 5.75

2.50 3.75 5.00 6.25

5 10 15 20

25 30 35 40

2.10 2.45 2.80 3.15

2.70 3.15 3.60 4.05

3.30 3.85 4.40 4.95

3.90 4.55 5.20 5.85

4.50 5.25 6.00 6.75

5.10 5.95 6.80 7.65

5.70 6.65 7.60 8.55

6.30 7.35 8.40 9.45

6.90 8.05 9.20 10.35

7.50 8.75 10.00 11.25

25 30 35 40

45 50 55 60

3.50 3.85 4.20 4.55

4.50 4.95 5.40 5.85

5.50 6.05 6.60 7.15

6.50 7.15 7.80 8.45

7.50 8.25 9.00 9.75

8.50 9.35 10.20 11.05

9.50 10.45 11.40 12.35

10.50 11.55 12.60 13.65

11.50 12.65 13.80 14.95

12.50 13.75 15.00 16.25

45 50 55 60

65 70 75 80

4.90 5.25 5.60 5.95

6.30 6.75 7.20 7.65

7.70 8.25 8.80 9.35

9.10 9.75 10.40 11.05

10.50 11.25 12.00 12.75

11.90 12.75 13.60 14.45

13.30 14.25 15.20 16.15

14.70 15.75 16.80 17.85

16.10 17.25 18.40 19.55

17.50 18.75 20.00 21.25

65 70 75 80

T

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

T

B/Alk @ T

(Range 0.1 to 1.0)

T

154

Quantitative Forecasting of Problems in Industrial Water Systems Table 29/2 B/Alk @ T

(Range 1.1 to 2.0)

T

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

T

5 10 15 20

2.70 4.05 5.40 6.75

2.90 4.35 5.80 7.25

3.10 4.65 6.20 7.75

3.30 4.95 6.60 8.25

3.50 5.25 7.00 8.75

3.70 5.55 7.40 9.25

3.90 5.85 7.80 9.75

4.10 6.15 8.20 10.25

4.30 6.45 8.60 10.75

4.50 6.75 9.00 11.25

5 10 15 20

25 30 35 40

8.10 9.45 10.80 12.15

8.70 10.15 11.60 13.05

9.30 10.85 12.40 13.95

9.90 11.55 13.20 14.85

10.50 12.25 14.00 15.75

11.10 12.95 14.80 16.65

11.70 13.65 15.60 17.55

12.30 14.35 16.40 18.45

12.90 15.05 17.20 19.35

13.50 15.75 18.00 20.25

25 30 35 40

45 50 55 60

13.50 14.85 16.20 17.55

14.50 15.95 17.40 18.85

15.50 17.05 18.60 20.15

16.50 18.15 19.80 21.45

17.50 19.25 21.00 22.75

18.50 20.35 22.20 24.05

19.50 21.45 23.40 25.35

20.50 22.55 24.60 26.65

21.50 23.65 25.80 27.95

22.50 24.75 27.00 29.25

45 50 55 60

65 70 75 80

18.90 20.25 21.60 22.95

20.30 21.75 23.20 24.65

21.70 23.25 24.80 26.35

23.10 24.75 26.40 28.05

24.50 26.25 28.00 29.75

25.90 27.75 29.60 31.45

27.30 29.25 31.20 33.15

28.70 30.75 32.80 34.85

30.10 32.25 34.40 36.55

31.50 33.75 36.00 38.25

65 70 75 80

T

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

T

B/Alk @ T

(Range 1.1 to 2.0)

Tables

155

Table 29/3 B/Alk @ T

(Range 2.1 to 3.0)

T

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

T

5 10 15 20

4.70 7.05 9.40 11.75

4.90 7.35 9.80 12.25

5.10 7.65 10.20 12.75

5.30 7.95 10.60 13.25

5.50 8.25 11.00 13.75

5.70 8.55 11.40 14.25

5.90 8.85 11.80 14.75

6.10 9.15 12.20 15.25

6.30 9.45 12.60 15.75

6.50 9.75 13.00 16.25

5 10 15 20

25 30 35 40

14.10 16.45 18.80 21.15

14.70 17.15 19.60 22.05

15.30 17.85 20.40 22.95

15.90 18.55 21.20 23.85

16.50 19.25 22.00 24.75

17.10 19.95 22.80 25.65

17.70 20.15 23.60 26.55

18.30 21.35 24.40 27.45

18.90 22.05 25.20 28.35

19.50 22.75 26.00 29.25

25 30 35 40

45 50 55 60

23.50 25.85 28.20 30.35

24.50 26.95 29.40 31.85

25.50 28.05 30.60 33.15

26.50 29.15 31.80 34.45

27.50 30.25 33.00 35.75

28.50 31.35 34.20 37.05

29.50 32.45 35.40 38.35

30.50 33.55 36.60 39.65

31.30 34.65 37.80 40.95

32.50 35.75 39.00 42.25

45 50 55 60

65 70 75 80

32.90 33.25 37.60 39.95

34.30 36.75 39.20 41.65

35.70 38.25 40.80 43.35

37.10 39.75 42.40 45.05

38.50 41.25 44.00 46.75

39.90 42.75 45.60 48.45

41.30 44.25 47.20 50.15

42.70 45.75 48.80 52.85

44.10 47.25 50.40 53.55

45.50 48.75 52.00 55.25

65 70 75 80

T

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

T

B/Alk @ T

(Range 2.1 to 3.0)

Table 30. Dissolved oxygen (O2 mg/l) for water in equilibrium with atmospheric air.

Temperature (T °C) 0 5 10 15 20 25 30 35 40

Dissolved Oxygen (O2 mg/1) 14.16 12.37 10.89 9.61 8.82 8.09 7.50 7.00 6.54

156

Quantitative Forecasting of Problems in Industrial Water Systems Table 31. Values of vector 4 (V4) from (V3) and SO4 Table 31/1 VALUES OF (V3)

(Range 10.0 to 5.5)

SO4

10.0

9.5

9.0

8.5

8.0

7.5

7.0

6.5

6.0

5.5

SO4

10

28.80

28.73

28.67

28.60

28.54

28.47

28.41

28.34

28.27

28.21

10

20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

31.07 33.43 35.83 38.26 40.70 43.16 45.62 48.08 50.55 53.03 55.51 57.99 60.47 62.95 65.44 67.92 70.41 72.90 75.39

31.01 33.38 35.79 38.22 40.67 43.12 45.48 48.05 50.53 53.00 55.48 57.96 60.44 62.93 65.41 67.90 70.39 72.88 75.37

30.96 33.34 35.75 38.18 40.63 43.09 45.56 48.03 50.50 52.98 55.46 57.94 60.42 62.91 65.39 67.88 70.37 72.86 75.35

30.91 33.29 35.71 38.15 40.60 43.06 45.52 48.00 50.47 52.95 55.43 57.91 60.40 62.88 65.37 67.86 70.35 72.84 75.33

30.85 33.24 35.76 38.11 40.56 43.03 45.49 47.97 50.44 52.92 55.40 57.89 60.37 62.86 65.35 67.84 70.33 72.82 75.31

30.80 33.20 36.63 38.07 40.53 42.99 45.46 47.94 50.42 52.90 55.38 57.86 60.35 62.84 65.33 67.82 70.31 72.80 75.29

30.74 33.15 35.68 38.03 40.49 42.96 45.43 47.91 50.39 52.87 55.35 57.84 60.33 62.82 65.31 67.80 70.29 72.78 75.27

30.69 33.10 35.54 37.99 40.46 42.93 45.40 47.88 50.36 52.84 55.35 57.82 60.30 62.79 65.28 67.77 70.27 72.76 75.25

30.64 33.06 35.50 37.96 40.42 42.89 45.37 47.85 50.33 52.82 55.30 57.79 60.28 62.77 65.26 67.75 70.25 72.74 75.23

30.59 33.01 35.36 37.92 40.39 42.86 45.34 47.82 50.30 52.79 55.28 57.77 60.26 62.75 65.24 67.73 70.23 72.72 75.21

20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

SO4

10.0

9.5

9.0

8.5

8.0

7.5

7.0

6.5

6.0

5.5

SO4

VALUES OF (V3)

(Range 10.0 to 5.5)

Tables

157

Table 31/2

VALUES OF (V3)

(Range 5.0 to 0.5)

SO4

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

SO4

10

28.14

28.08

28.02

27.95

27.89

27.82

27.75

27.69

27.62

27.56

10

20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

30.53 32.97 30.97

65.22 67.71 70.20 72.70 75.19

30.48 32.92 35.38 37.84 40.32 42.80 45.28 47.76 50.25 52.74 55.23 57.72 60.21 62.70 65.20 67.69 70.18 72.68 75.17

30.43 32.87 35.33 37.80 40.28 42.76 45.25 47.73 50.22 52.71 55.20 57.69 60.19 62.68 65.17 67.67 70.16 72.66 75.15

30.37 32.83 35.29 37.77 40.25 42.73 45.22 47.70 50.19 52.69 55.18 57.67 60.16 62.66 65.15 67.65 70.14 72.64 75.14

30.32 32.78 35.25 37.73 40.21 42.70 45.19 47.68 50.17 52.66 55.15 57.65 60.14 62.64 65.13 67.63 70.12 72.62 75.12

30.27 32.73 35.21 37.69 40.18 42.66 45.15 47.65 50.14 52.63 55.13 57.62 60.12 62.61 65.11 67.61 70.10 72.60 75.10

30.21 32.69 35.17 37.65 40.14 42.63 45.12 47.62 50.11 52.61 55.10 57.60 60.09 62.59 65.09 67.58 70.08 72.58 75.08

30.16 32.64 35.13 37.61 40.11 42.60 45.09 47.59 50.08 52.58 55.08 57.57 60.07 62.57 65.07 67.56 70.06 72.56 75.06

30.11 32.59 35.08 37.58 40.07 42.57 45.06 47.56 50.06 52.55 55.05 57.55 60.05 62.55 65.04 67.54 70.04 72.54 75.04

30.05 32.55 35.04 37.54 40.04 42.53 45.03 47.53 50.03 52.53 55.03 57.72 60.02 62.52 65.02 67.52 70.02 72.52 75.02

20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

SO4

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

SO4

35.42 37.88 40.35 42.83 45.31 47.79 50.28 52.76 55.25 57.74 60.23 62.73 63.73

VALUES OF (V3)

(Range 5.0 to 0.5)

158

Quantitative Forecasting of Problems in Industrial Water Systems Table 31/3 (Range 0 to −5.0)

VALUES OF (V3) SO4

0

− 0.5

− 1.0

− 1.5

− 2.0

− 2.5

− 3.0

− 3.5

− 4.0

− 4.5

− 5.0

SO4

10

27.50

27.44

27.37

27.31

27.24

27.18

27.11

27.05

26.98

26.92

26.85

10

20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

30.00 32.50 35.00 37.50 40.00 42.50 45.00 47.50 50.00 52.50 55.00 57.50 60.00 62.50 65.00 67.50 70.00 72.50 75.00

29.95 32.45 34.96 37.46 39.96 42.47 44.97 47.47 49.97 52.47 54.97 57.48 59.98 62.48 64.98 67.48 69.98 72.48 74.98

29.89 32.41 34.92 37.42 39.93 42.43 44.94 47.44 47.94 52.45 54.95 57.45 59.95 62.45 64.96 67.46 69.96 72.46 74.96

29.84 32.36 34.87 37.39 39.89 42.40 44.91 47.41 49.92 52.42 54.92 57.43 59.93 62.43 64.93 67.44 69.94 72.44 74.94

29.79 32.31 34.83 37.35 39.86 42.37 44.88 47.38 49.89 52.39 54.90 57.40 59.91 62.41 64.91 67.42 69.92 72.42 74.92 74.42

29.73 32.27 34.79 37.31 39.82 42.34 44.84 47.35 49.86 52.37 54.87 57.38 59.88 62.39 64.89 67.39 69.90 72.40 74.90

29.68 32.22 34.75 37.27 39.79 42.30 44.81 47.32 49.83 52.34 54.85 57.35 59.86 62.36 64.87 67.37 69.88 72.38 74.88

29.63 32.17 34.71 37.23 39.75 42.27 44.78 47.30 49.81 52.31 84.82 57.33 59.84 62.34 64.85 67.35 69.86 72.36 74.86

29.57 32.13 34.67 37.20 39.72 42.24 44.75 47.27 49.78 52.29 54.80 57.32 59.81 62.32 64.83 67.33 69.84 72.34 74.85

29.52 32.08 34.62 37.16 39.68 42.20 44.72 47.24 49.75 52.26 54.77 57.28 59.79 62.30 64.80 67.31 69.82 72.32 74.83

29.47 32.03 34.58 37.12 39.65 42.17 44.69 47.21 49.72 52.24 54.75 57.26 59.77 62.27 64.78 67.29 69.80 72.30 74.81

20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

SO4

0

− 0.5

− 1.0

− 1.5

− 2.0

− 2.5

− 3.0

− 3.5

− 4.0

− 4.5

− 5.0

SO4

VALUES OF (V3)

(Range 0 to −5.0)

Tables

159

Table 31/4 (Range − 5.5 to − 10.0)

VALUES OF (V3) SO4

− 5.5

− 6.0

− 6.5

− 7.0

− 7.5

− 8.0

− 8.5

− 9.0

− 9.5

− 10.0

SO4

10

26.79

26.72

26.66

26.59

26.53

26.46

26.40

26.33

26.27

26.20

10

20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

29.41 31.99 34.54 37.08 39.61 42.14 44.66 47.18 49.70 52.21 54.72 57.23 59.74 62.25 64.76 67.27 69.77 72.28 74.79

29.36 31.94 34.50 37.04 39.58 42.11 44.63 47.15 49.67 52.18 54.70 57.21 59.72 62.23 64.74 67.25 69.75 72.26 74.77

29.31 31.90 34.46 37.01 39.54 42.07 44.60 47.12 49.64 52.16 54.67 57.18 59.70 62.21 64.72 67.23 69.73 72.24 74.75

29.25 31.85 34.42 36.97 39.51 42.04 44.57 47.09 49.61 52.13 54.65 57.16 59.67 62.18 64.69 67.20 69.71 72.22 74.73

29.20 31.80 34.37 36.93 39.47 42.00 44.54 47.06 49.58 52.10 54.62 57.14 59.65 62.16 64.67 67.18 69.69 72.20 74.71

29.15 31.76 34.33 36.89 39.44 41.97 44.51 47.03 49.56 52.08 54.60 57.11 59.63 62.14 64.65 67.16 69.67 72.18 74.69

29.09 31.71 34.29 36.85 39.40 41.94 44.48 47.00 49.53 52.05 54.57 57.09 59.60 62.12 64.63 67.14 69.65 72.16 74.67

29.04 31.66 34.25 36.82 39.37 41.91 44.44 46.97 49.50 52.02 54.54 57.06 59.58 62.09 64.61 67.12 69.63 72.14 74.65

28.99 31.62 34.21 36.78 39.33 41.88 44.41 46.95 49.47 52.00 54.52 57.04 59.56 62.07 64.59 67.10 69.61 72.12 74.63

28.93 31.57 34.17 36.74 39.30 41.84 44.33 46.92 49.45 51.97 54.49 57.01 59.53 62.05 64.56 67.08 69.59 72.10 74.61

20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

SO4

− 5.5

− 6.0

− 6.5

− 7.0

− 7.5

− 8.0

− 8.5

− 9.0

− 9.5

− 10.0

SO4

VALUES OF (V3)

(Range − 5.5 to − 10.0)

160

Quantitative Forecasting of Problems in Industrial Water Systems Table 32. Values of vector 5 (V5) from Cl. Chloride (Cl mg/1) 5 10 15 20 25 30 35 40 45 50 55 60

Vector 5 (V5) 0.32 1.47 3.59 6.75 11.01 16.43 23.06 30.91 40.04 51.46 62.21 75.30

Table 33. Values of vector 6 (V6) from O2. Dissolved Oxygen (mg/1) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Vector 6 (V6) 126.00 88.07 65.88 50.14 37.93 27.95 19.52 12.21 5.77 0.00 −5.22 −9.98 −14.36 −18.41 −22.19

Tables

161

Table 34. Values of vector 8 (V8) from (V5) and (V7). Table 34/1 VALUES OF (V7)

(Range 100 to 55)

(V5)

100

95

90

85

80

75

70

65

60

55

(V5)

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0

1.82 1.81 1.81 1.80 1.79 1.79 1.78 1.78 1.77 1.76 1.75 1.74 1.72 1.71 1.69 1.68 1.67 1.64 1.61 1.59 1.56 1.54 1.43 1.33 1.25 1.15 1.11 1.05 1.00 0.95 0.91 0.87 0.83

1.73 1.72 1.71 1.71 1.70 1.70 1.69 1.69 1.68 1.67 1.67 1.65 1.64 1.62 1.61 1.60 1.58 1.56 1.53 1.51 1.48 1.46 1.36 1.27 1.19 1.12 1.06 1.00 0.95 0.90 0.86 0.83 0.79

1.64 1.63 1.62 1.62 1.61 1.61 1.60 1.60 1.59 1.58 1.58 1.57 1.55 1.54 1.53 1.51 1.50 1.48 1.45 1.43 1.41 1.38 1.29 1.20 1.13 1.06 1.00 0.95 0.90 0.86 0.82 0.78 0.75

1.55 1.54 1.53 1.53 1.52 1.52 1.51 1.51 1.50 1.50 1.49 1.48 1.47 1.45 1.44 1.43 1.42 1.39 1.37 1.35 1.33 1.31 1.21 1.13 1.06 1.00 0.94 0.89 0.85 0.81 0.77 0.74 0.71

1.45 1.45 1.44 1.44 1.43 1.43 1.42 1.42 1.41 1.41 1.40 1.39 1.38 1.37 1.36 1.34 1.33 1.31 1.29 1.27 1.25 1.23 1.14 1.07 1.00 0.94 0.89 0.84 0.80 0.76 0.73 0.70 0.67

1.36 1.36 1.35 1.35 1.34 1.34 1.33 1.33 1.33 1.32 1.32 1.30 1.29 1.28 1.27 1.26 1.25 1.23 1.21 1.19 1.17 1.15 1.07 1.00 0.94 0.88 0.83 0.79 0.75 0.71 0.68 0.65 0.63

1.27 1.27 1.26 1.26 1.25 1.25 1.25 1.25 1.24 1.23 1.23 1.22 1.21 1.20 1.19 1.18 1.17 1.15 1.13 1.11 1.09 1.08 1.00 0.93 0.88 0.82 0.78 0.74 0.70 0.75 0.67 0.64 0.61 0.58

1.18 1.18 1.17 1.17 1.16 1.16 1.16 1.16 1.15 1.14 1.14 1.13 1.12 1.11 1.10 1.09 1.08 1.07 1.05 1.03 1.02 1.00 0.93 0.87 0.81 0.76 0.72 0.68 0.65 0.70 0.62 0.59 0.56 0.54

1.09 1.09 1.08 1.08 1.08 1.07 1.07 1.07 1.06 1.06 1.05 1.04 1.03 1.03 1.02 1.01 1.00 0.98 0.97 0.95 0.94 0.92 0.86 0.80 0.75 0.71 0.67 0.63 0.60 0.65 0.57 0.55 0.52 0.50

1.00 1.00 0.99 0.99 0.99 0.98 0.98 0.98 0.97 0.97 0.96 0.96 0.95 0.94 0.93 0.92 0.92 0.90 0.89 0.87 0.86 0.85 0.79 0.73 0.69 0.65 0.61 0.58 0.55 0.60 0.52 0.50 0.48 0.46

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0

(V5)

100

95

90

85

80

75

70

65

60

55

(V5)

VALUES OF (V7)

(Range 100 to 55)

162

Quantitative Forecasting of Problems in Industrial Water Systems Table 34/2 VALUES OF (V7)

(Range 50 to 0)

(V5)

50

45

40

35

30

25

20

15

10

5

0

(V5)

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0

0.91 0.91 0.90 0.90 0.90 0.89 0.89 0.89 0.88 0.88 0.88 0.87 0.86 0.85 0.85 0.84 0.83 0.82 0.81 0.79 0.78 0.77 0.71 0.67 0.63 0.59 0.56 0.53 0.50 0.48 0.45 0.43 0.42

0.82 0.82 0.81 0.81 0.81 0.80 0.80 0.80 0.80 0.79 0.79 0.78 0.78 0.77 0.76 0.76 0.75 0.74 0.73 0.71 0.70 0.69 0.64 0.60 0.56 0.53 0.50 0.47 0.45 0.43 0.41 0.39 0.38

0.73 0.72 0.72 0.72 0.72 0.71 0.71 0.71 0.71 0.71 0.70 0.70 0.70 0.68 0.68 0.67 0.67 0.66 0.65 0.63 0.63 0.62 0.57 0.27 0.53 0.50 0.47 0.44 0.42 0.40 0.38 0.36 0.35 0.33

0.64 0.63 0.63 0.63 0.63 0.63 0.62 0.62 0.62 0.62 0.61 0.61 0.60 0.60 0.59 0.59 0.58 0.57 0.56 0.56 0.55 0.54 0.50 0.47 0.44 0.41 0.39 0.37 0.35 0.33 0.32 0.30 0.29

0.55 0.54 0.54 0.54 0.54 0.54 0.53 0.53 0.53 0.53 0.53 0.52 0.52 0.51 0.51 0.50 0.50 0.49 0.48 0.48 0.47 0.46 0.43 0.40 0.38 0.35 0.33 0.32 0.30 0.29 0.27 0.26 0.25

0.45 0.45 0.45 0.45 0.45 0.45 0.44 0.44 0.44 0.44 0.44 0.43 0.43 0.43 0.42 0.42 0.42 0.41 0.40 0.40 0.39 0.38 0.36 0.33 0.31 0.29 0.28 0.26 0.25 0.24 0.23 0.22 0.21

0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.35 0.35 0.35 0.35 0.34 0.34 0.34 0.34 0.33 0.33 0.32 0.32 0.31 0.31 0.29 0.27 0.25 0.24 0.22 0.21 0.20 0.19 0.18 0.17 0.17

0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.27 0.26 0.26 0.26 0.26 0.26 0.25 0.25 0.25 0.25 0.24 0.24 0.23 0.23 0.21 0.20 0.19 0.18 0.17 0.16 0.15 0.14 0.14 0.13 0.13

0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.17 0.17 0.17 0.17 0.17 0.17 0.16 0.16 0.16 0.16 0.15 0.14 0.13 0.13 0.12 0.11 0.11 0.10 0.10 0.09 0.09 0.08

0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.07 0.07 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.04 0.04

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0

(V5)

50

45

40

35

30

25

20

15

10

5

0

(V5)

VALUES OF (V7)

(Range 50 to 0)

Tables

163

Table 34/3 VALUES OF (V7)

(Range −5 to −50)

(V5)

−5

−10

−15

−20

−25

−30

−35

−40

−45

−50

(V5)

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0

−0.09 −0.09 −0.09 −0.09 −0.09 −0.09 −0.09 −0.09 −0.09 −0.09 −0.09 −0.09 −0.09 −0.09 −0.08 −0.08 −0.08 −0.08 −0.08 −0.08 −0.08 −0.08 −0.07 −0.07 −0.06 −0.06 −0.06 −0.05 −0.05 −0.05 −0.05 −0.04 −0.04

−0.18 −0.18 −0.18 −0.18 −0.18 −0.18 −0.18 −0.18 −0.18 −0.18 −0.18 −0.17 −0.17 −0.17 −0.17 −0.17 −0.17 −0.16 −0.16 −0.16 −0.16 −0.15 −0.14 −0.13 −0.13 −0.12 −0.11 −0.11 −0.10 −0.10 −0.09 −0.09 −0.08

−0.27 −0.27 −0.27 −0.27 −0.27 −0.27 −0.27 −0.27 −0.27 −0.26 −0.26 −0.26 −0.26 −0.26 −0.25 −0.25 −0.25 −0.25 −0.24 −0.24 −0.23 −0.23 −0.21 −0.20 −0.19 −0.18 −0.17 −0.16 −0.15 −0.14 −0.14 −0.13 −0.13

−0.36 −0.36 −0.36 −0.36 −0.36 −0.36 −0.36 −0.36 −0.35 −0.35 −0.35 −0.35 −0.34 −0.34 −0.34 −0.34 −0.33 −0.33 −0.32 −0.32 −0.31 −0.31 −0.29 −0.27 −0.25 −0.24 −0.22 −0.21 −0.20 −0.19 −0.18 −0.17 −0.17

−0.45 −0.45 −0.45 −0.45 −0.45 −0.45 −0.44 −0.44 −0.44 −0.44 −0.44 −0.43 −0.43 −0.43 −0.42 −0.42 −0.42 −0.41 −0.40 −0.40 −0.39 −0.38 −0.36 −0.33 −0.31 −0.29 −0.28 −0.26 −0.25 −0.24 −0.23 −0.22 −0.21

−0.55 −0.54 −0.54 −0.54 −0.54 −0.54 −0.53 −0.53 −0.53 −0.53 −0.53 −0.52 −0.51 −0.51 −0.51 −0.50 −0.50 −0.49 −0.48 −0.48 −0.47 −0.46 −0.43 −0.40 −0.38 −0.35 −0.33 −0.32 −0.30 −0.29 −0.27 −0.26 −0.25

−0.64 −0.63 −0.63 −0.63 −0.63 −0.63 −0.62 −0.62 −0.62 −0.62 −0.61 −0.61 −0.60 −0.60 −0.59 −0.59 −0.59 −0.57 −0.56 −0.56 −0.55 −0.54 −0.50 −0.47 −0.44 −0.41 −0.39 −0.37 −0.35 −0.33 −0.32 −0.30 −0.29

−0.73 −0.72 −0.72 −0.72 −0.72 −0.71 −0.71 −0.71 −0.71 −0.70 −0.70 −0.70 −0.69 −0.68 −0.68 −0.67 −0.67 −0.66 −0.65 −0.63 −0.63 −0.62 −0.57 −0.53 −0.50 −0.47 −0.44 −0.42 −0.40 −0.38 −0.36 −0.35 −0.33

−0.82 −0.82 −0.81 −0.81 −0.81 −0.80 −0.80 −0.80 −0.80 −0.79 −0.79 −0.78 −0.78 −0.77 −0.76 −0.76 −0.75 −0.74 −0.73 −0.71 −0.70 −0.69 −0.64 −0.60 −0.56 −0.53 −0.50 −0.47 −0.45 −0.43 −0.41 −0.39 −0.38

−0.91 −0.91 −0.90 −0.90 −0.90 −0.89 −0.89 −0.89 −0.88 −0.88 −0.88 −0.87 −0.86 −0.85 −0.85 −0.84 −0.83 −0.82 −0.81 −0.79 −0.78 −0.77 −0.71 −0.67 −0.63 −0.59 −0.56 −0.53 −0.50 −0.48 −0.45 −0.43 −0.42

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0

(V5)

−5

−10

−15

−20

−25

−30

−35

−40

−45

−50

(V5)

VALUES OF (V7)

(Range −5 to −50)

164

Quantitative Forecasting of Problems in Industrial Water Systems Table 34/4 (Range −55 to −100)

VALUES OF (V7) (V5)

−55

−60

−65

−70

−75

−80

−85

−90

−85

−100

(V5)

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0

−1.00 −1.00 −0.99 −0.99 −0.99 −0.98 −0.98 −0.98 −0.97 −0.97 −0.96 −0.96 −0.95 −0.94 −0.93 −0.92 −0.92 −0.90 −0.89 −0.89 −0.86 −0.85 −0.79 −0.73 −0.69 −0.65 −0.61 −0.58 −0.55 −0.52 −0.50 −0.48 −0.46

−1.09 −1.09 −1.08 −1.08 −1.08 −1.07 −1.07 −1.07 −1.06 −1.06 −1.05 −1.04 −1.03 −1.03 −1.02 −1.01 −1.00 −0.98 −0.97 −0.85 −0.94 −0.92 −0.86 −0.80 −0.75 −0.71 −0.67 −0.63 −0.60 −0.57 −0.55 −0.52 −0.50

−1.18 −1.18 −1.17 −1.17 −1.16 −1.16 −1.16 −1.16 −1.15 −1.14 −1.14 −1.13 −1.12 −1.11 −1.10 −1.09 −1.08 −1.07 −1.05 −1.03 −1.02 −1.00 −0.93 −0.87 −0.81 −0.76 −0.72 −0.68 −0.65 −0.62 −0.59 −0.57 −0.54

−1.27 −1.27 −1.26 −1.26 −1.25 −1.25 −1.25 −1.25 −1.24 −1.23 −1.23 −1.22 −1.21 −1.20 −1.19 −1.18 −1.17 −1.15 −1.13 −1.11 −1.09 −1.08 −1.00 −0.93 −0.88 −0.82 −0.78 −0.74 −0.70 −0.67 −0.64 −0.61 −0.58

−1.36 −1.36 −1.35 −1.35 −1.34 −1.34 −1.33 −1.33 −1.33 −1.32 −1.32 −1.30 −1.29 −1.28 −1.27 −1.26 −1.25 −1.23 −1.21 −1.19 −1.17 −1.15 −1.07 −1.00 −0.94 −0.88 −0.83 −0.79 −0.75 −0.71 −0.68 −0.65 −0.63

−1.45 −1.45 −1.44 −1.44 −1.43 −1.43 −1.42 −1.42 −1.41 −1.41 −1.40 −1.39 −1.38 −1.37 −1.36 −1.34 −1.33 −1.31 −1.29 −1.27 −1.25 −1.23 −1.14 −1.07 −1.00 −0.94 −0.89 −0.84 −0.80 −0.76 −0.73 −0.70 −0.67

−1.54 −1.54 −1.53 −1.53 −1.52 −1.52 −1.51 −1.51 −1.50 −1.50 −1.49 −1.48 −1.47 −1.45 −1.44 −1.43 −1.42 −1.39 −1.37 −1.35 −1.33 −1.31 −1.21 −1.13 −1.06 −1.00 −0.94 −0.89 −0.85 −0.81 −0.77 −0.74 −0.71

−1.64 −1.63 −1.62 −1.62 −1.61 −1.61 −1.60 −1.60 −1.59 −1.58 −1.58 −1.57 −1.55 −1.54 −1.53 −1.51 −1.50 −1.48 −1.45 −1.43 −1.41 −1.38 −1.29 −1.20 −1.13 −1.06 −1.00 −0.95 −0.90 −0.86 −0.82 −0.78 −0.75

−1.73 −1.72 −1.71 −1.71 −1.70 −1.70 −1.69 −1.69 −1.68 −1.67 −1.67 −1.65 −1.64 −1.62 −1.61 −1.60 −1.58 −1.56 −1.53 −1.50 −1.48 −1.46 −1.36 −1.27 −1.19 −1.12 −1.06 −1.00 −0.95 −0.90 −0.86 −0.83 −0.79

−1.82 −1.81 −1.81 −1.80 −1.79 −1.79 −1.78 −1.78 −1.77 −1.76 −1.75 −1.74 −1.72 −1.71 −1.69 −1.68 −1.67 −1.64 −1.61 −1.59 −1.56 −1.54 −1.43 −1.33 −1.25 −1.18 −1.11 −1.05 −1.00 −0.95 −0.91 −0.87 −0.83

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0

(V5)

−55

−60

−65

−70

−75

−80

−85

−90

−85

−100

(V5)

VALUES OF (V7)

(Range −55 to −100)

Tables Table 35. Values of vector 9 (V9) from (V6) and (V8). Table 35/1 VALUES OF (V8)

(Rangel 1.85 to 1.40)

(V6)

1.85

1.80

1.75

1.70

1.65

1.60

1.55

1.50

1.45

1.40

(V6)

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

111 113 116 118 121 123 126 128 131 133 136 138 141 143 146 148

109 111 114 116 119 121 122 126 129 132 134 137 139 142 144 147

107 109 112 115 117 120 121 125 127 130 133 135 138 140 143 145 148

105 107 110 113 115 118 119 123 126 128 131 134 136 139 141 144 147

103 105 108 111 113 116 117 121 123 126 129 132 135 137 140 143 145 148

101 103 106 109 111 114 115 120 122 125 128 130 133 136 138 141 144 146

99 101 104 107 109 112 113 118 120 123 126 129 131 134 137 139 142 145 148

96 99 102 105 107 110 112 116 119 121 124 127 130 132 135 138 141 143 146

94 97 100 103 105 108 109 114 117 119 122 125 128 131 133 136 139 142 145 147

92 95 97 100 103 106 107 112 115 117 120 123 126 129 132 135 137 140 143 146

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

(V6)

1.85

1.45

1.40

(V6)

Values of (V9) in this area lead to very high, positive, values of IL which fall outside the original Lucey nomogram and indicate conditions favourable to intense pitting.

1.80

1.75

1.70

VALUES OF (V8)

1.65

1.60

1.55

1.50

(Rangel 1.85 to 1.40)

165

166


VALUES OF (V8)

(Range 1.35 to 0.90)

(V6)

1.35

1.30

1.25

1.20

1.15

1.10

1.05

1.00

0.95

0.90

(V6)

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

89 92 95 98 101 103 107 110 113 115 118 121 124 127 130 133 136 139 141 144 147

87 90 93 96 99 102 105 107 110 113 116 119 122 125 128 131 134 137 140 143 146

84 87 90 93 96 99 102 105 108 111 114 117 120 123 126 129 132 135 138 141 144 147

82 85 88 91 94 97 100 103 106 109 112 115 118 121 124 127 130 133 136 139 142 145 148

79 82 85 88 91 94 97 101 104 107 110 113 116 119 122 125 128 131 134 138 141 144 147

77 79 82 86 88 92 95 98 101 104 107 111 114 117 120 123 126 129 133 136 139 142 145 148

73 76 79 83 86 89 92 96 99 102 105 108 111 115 118 121 124 127 131 134 137 140 143 147

70 73 77 80 83 86 90 93 96 99 103 106 109 112 116 118 122 125 129 132 135 138 142 145 148

67 70 74 77 80 84 87 90 93 97 100 103 106 110 113 117 120 123 126 130 132 136 140 143 146

64 67 70 74 77 81 84 88 92 94 97 101 104 107 111 114 118 121 124 128 131 134 138 141 144 148

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

(V96)

1.35

0.90

(V96)

Values of (V9) in this Area lead to very high, positive, Values of IL which fall outside the original Lucey nomogram and indicate conditions favourable To intense pitting.

1.30

1.25

1.20

VALUES OF (V8)

1.15

1.10

1.05

1.00

(Range 1.35 to 0.90)

0.95

Tables Table 35/3 VALUES OF (V8) (V6) −25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 (V6)

0.85

0.60

0.55

0.50

0.45

0.40

(V6)

60 57 53 49 45 41 64 60 57 53 49 45 67 64 60 57 53 49 71 67 64 60 57 53 74 71 67 64 60 56 77 74 71 68 64 60 81 78 75 71 68 64 84 81 78 74 71 68 88 85 82 78 75 72 91 88 85 82 79 75 95 92 89 86 82 79 98 95 92 89 86 83 101 99 96 93 90 87 105 102 99 97 94 90 108 106 103 100 97 94 112 109 107 104 101 98 115 113 110 107 105 102 119 116 114 111 108 106 122 120 117 115 112 109 125 123 121 118 116 113 129 127 125 122 120 117 132 130 128 126 123 121 136 134 131 129 127 124 139 137 135 133 131 128 143 141 139 137 134 132 146 144 142 140 138 136 Values of 146 144 142 140 149 147 145 143 (V9) in this area lead to very high 149 147 positive values of IL which fall outside the original Lucey nomogram and indicate conditions favourable to intense pitting.

37 41 45 49 53 56 60 64 70 72 75 80 83 87 91 95 99 103 107 110 114 118 122 126 130 135 137 141 145 149

33 37 41 49 48 53 56 60 64 68 72 76 80 84 88 92 96 100 104 107 111 115 119 123 127 131 135 139 143 147

28 32 36 40 24 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 113 117 121 125 129 133 136 141 145

23 27 31 36 40 44 48 52 56 60 64 68 73 77 81 85 89 93 97 101 105 110 114 118 122 126 130 134 138 142

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120

149

147

125

0.45

0.40

(V6)

0.85

0.80

0.80

0.75

0.75

0.70

(Range 0.85 to 0.40)

0.70

VALUES OF (V8)

0.65

0.65

0.60

0.55

(Range 0.85 to 0.40)

0.50

167

168


VALUES OF (V8)

(Range 0.35 to 0.00)

(V6)

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

(V6)

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

18 22 27 31 35 39 43 48 32 56 60 64 69 73 77 81 85 90 94 98 102 106 111 115 119 123 127 132 136 140 144

13 17 21 26 30 34 39 42 47 52 56 60 64 69 73 77 82 86 90 95 99 103 107 112 116 120 125 129 133 138 142

7 12 16 20 25 29 34 38 43 47 51 56 60 65 69 73 78 82 87 91 95 100 104 109 113 117 122 126 131 135 139

1 6 10 15 20 24 29 33 38 42 47 51 56 60 65 69 74 78 83 87 92 96 101 105 110 114 119 123 128 132 137

−5 0 5 9 14 18 23 28 32 37 42 46 51 55 60 65 69 74 79 83 88 92 97 102 106 111 116 120 125 129 134

−11 −6 −2 3 8 13 17 22 27 32 36 41 46 51 55 60 65 70 74 79 84 89 93 98 103 108 112 117 122 126 131

−18 −13 −8 -3 2 7 11 16 21 26 31 36 41 45 50 55 60 65 70 75 80 84 89 94 99 104 109 114 118 123 128

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

(V6)

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

(V6)

VALUES OF (V8)

(Range 0.35 to 0.00)

Tables

169

Table 35/5 (Range 0.00 to −0.45)

VALUES OF (V8) (V6)

0.00

−0.05

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

−25 −20 −15 −10 −5 −0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

−33 −27 −22 −17 −12 −7 −2 3 9 14 19 24 29 34 40 46 50 55 60 65 70 75 81 86 92 96 101 106 111 116 122

(V6)

0.00

−0.05

−0.10 −0.15 −0.20 −40 −35 −30 −25 −19 −14 −9 −3 2 7 12 18 23 28 34 39 44 49 55 60 65 71 76 81 87 92 97 102 108 113 118

−49 −43 −38 −33 −27 −22 −16 −11 −5 0 5 11 16 22 27 33 38 44 49 54 60 65 71 76 83 87 93 98 103 109 114

−0.25

−58 −52 −47 −41 −35 −30 −24 −19 −13 −7 −2 4 9 15 21 26 32 37 43 49 54 60 65 71 78 82 88 93 99 105 110

−67 −62 −56 −50 −44 −38 −33 −27 −21 −15 −10 −4 2 8 14 19 25 31 37 42 48 54 60 66 73 77 83 89 95 100 106

−0.10 −0.15 −0.20

−0.25

VALUES OF (V8)

−0.30 −0.35

−0.40

−0.45

(V6)

−88 −82 −76 −70 −64 −57 −51 −45 −39 −33 −27 −20 −14 −8 −2 4 10 17 23 29 35 41 47 54 61 66 72 78 84 91 97

−100 −93 −87 −81 −74 −68 −61 −55 −49 −42 −36 −30 −23 −17 −10 −4 2 9 15 21 28 34 41 47 55 60 66 72 79 86 92

−105 −99 −92 −87 −79 −72 −67 −59 −53 −46 −39 −33 −26 −20 −13 −6 0 7 13 20 27 33 40 48 53 60 66 73 79 86

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

−0.30 −0.35

−0.40

−0.45

(V6)

−77 −71 −66 −60 −54 −48 −42 −37 −30 −24 −18 −12 −6 0 6 12 18 24 30 36 42 48 54 60 67 72 78 84 90 96 102

(Range 0.00 to −0.45)

170

Quantitative Forecasting of Problems in Industrial Water Systems Table 35/6 (Range −0.50 to −0.95)

VALUES OF (V8) (V6)

−0.50 −0.55

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

−105 −98 −91 −84 −77 −71 −64 −57 −50 −43 −36 −29 −23 −16 −9 −2 5 12 18 25 32 39 46 53 60 66 73 80

(V6)

−0.50 −0.55

−0.60 −0.65

−0.70

−0.75

−0.80

−0.85

−0.90

−0.95

(V6)

−102 −95 −87 −101 −79 −93 −72 −85 −64 −77 −56 −69 −48 −61 −41 −53 −33 −45 −25 −37 −18 −29 −10 −21 −2 −13 5 −5 13 3 21 11 29 19 36 27 44 35 52 43 59 51

−100 −92 −84 −75 −67 −58 −50 −42 −33 −25 −16 −8 0 9 17 26 34 42

−99 −90 −82 −73 −64 −55 −46 −38 −29 −20 −11 −2 6 15 24 33

−107 −98 −89 −80 −70 −61 −52 −43 −33 −24 −15 −6 4 13 22

−106 −97 −87 −77 −67 −58 −48 −38 −29 −19 −9 −1 10

−105 −95 −85 −75 −64 −54 −44 −34 −23 −13 −3

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

−0.60 −0.65 −0.70

−0.75

−0.80

−0.85

−0.90

−0.95

(V6)

Values of (V9) in this area lead to very high negative values of IL which fall outside the original Lucy nomogram and indicate conditions favourable to non-pitting −104 −97 −90 −83 −76 −68 −61 −54 −47 −40 −33 −26 −19 −12 −5 3 10 17 24 31 38 45 52 60 67 74

−103 −96 −88 −81 −74 −66 −59 −51 −44 −37 −29 −22 14 −14 −77 0 8 15 22 30 37 45 52 59 67

VALUES OF (V8)

(Range −0.50 to −0.95)

Tables

171

Table 35/7 (Range −1.00 to −1.45)

VALUES OF (V8) (V6)

−1.00

−1.05

−1.10

−1.15

−1.20

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

−104 −93 −83 −72 −61 −50 −39 −28 −17

−103 −92 −80 −68 −57 −45 −34

−102 −89 −77 −65 −52

−100 −87 −74

−98

(V6)

−1.00

−1.05

−1.10

−1.15

−1.20

−1.25

−1.30

−1.35

−1.40

−1.45

−25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125

Values of (V9) in this area lead to very high negative values of IL which fall outside the original Lucey nomogram and indicate conditions favourable to non-pitting.

VALUES OF (V8)

−1.25

−1.30

(V6)

−1.35

(Range −1.00 to –1.45)

−1.40

−1.45

(V6)

172

Quantitative Forecasting of Problems in Industrial Water Systems Table 36. Values of Lucey index (IL) from (V9) and pH. Table 36/1

VALUES OF (V9) pH

150

148

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 pH

146

144

(Range 150 to 132) 142

140

138

136

134

132

pH

13.0 12.7 12.4 12.2 11.9 11.7 11.5 11.3 11.2 11.0

13.0 12.7 12.3 12.0 11.9 11.6 11.4 11.2 11.0 10.9 10.6

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

143

132

pH

High, positve positivevalues valuesof ofIILLininthis thisarea areafall fall outside the original Lucey nomogram and indicate conditions favourable to intense pitting.

150

148

12.9

12.9 12.8 12.6

13.0 12.8 12.6 12.5 12.3

12.9 12.7 12.5 12.3 12.2 12.0

12.9 12.6 12.4 12.2 12.0 11.9 11.7

13.0 12.7 12.5 12.2 12.0 11.8 11.6 11.5 11.3

146

144

142

140

138

136

VALUES OF (V9)

(Range 150 to 132)

Tables Table 36/2 (Range 130 to 112)

VALUES OF (V9) pH 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 pH

130

128

126

124

122

120

118

116

114

112

pH

12.6 12.0 11.6 11.2 10.9 10.6 10.3 10.1 9.8 9.6 9.4 9.2 9.1 8.9

12.3 11.7 11.3 10.9 10.6 10.3 10.0 9.8 9.5 9.3 9.1 8.9 8.8 8.6

12.8 12.0 11.4 11.0 10.6 10.3 10.0 9.7 9.5 9.2 9.0 8.8 8.6 8.5 8.3

12.5 11.7 11.1 10.7 10.3 10.0 9.7 9.4 9.2 8.9 8.7 8.5 8.3 8.2 8.0

12.1 11.3 10.7 10.3 9.9 9.6 9.3 9.0 8.8 8.5 8.3 8.1 7.9 7.8 7.6

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

120

118

116

114

112

pH

High, positive values of IL in thia area fall outside the original Lucey nomogram and indicate conditions favourable to intense pitting.

12.7 12.4 12.1 11.8 11.6 11.3 11.1 10.9 10.7 10.6 10.4

12.8 12.4 12.1 11.8 11.5 11.3 11.0 10.8 10.6 10.4 10.3 10.1

12.9 12.5 12.1 11.8 11.5 11.2 11.0 10.7 10.5 10.3 10.1 10.0 9.8

12.6 12.2 11.8 11.5 11.2 10.9 10.7 10.4 10.2 10.0 9.8 9.7 9.5

12.9 12.3 11.9 11.5 11.2 10.9 10.6 10.4 10.1 9.9 9.7 9.5 9.4 9.2

130

128

126

124

122

VALUES OF (V9)

(Range 130 to 112)

173

174

Quantitative Forecasting of Problems in Industrial Water Systems Table 36/3 (Range 110 to 92)

VALUES OF (V9) pH 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 pH

110

108

106

104

102

100

98

96

94

92

pH

11.5 10.7 10.1 9.7 9.3 9.0 8.7 8.4 8.2 7.9 7.7 7.5 7.3 7.2 7.0

11.2 10.4 9.8 9.4 9.0 8.7 8.4 8.1 7.9 7.6 7.4 7.2 7.0 6.9 6.7

10.9 10.1 9.5 9.1 8.7 8.4 8.1 7.8 7.6 7.3 7.1 6.9 6.7 6.6 6.4

10.6 9.8 9.2 8.8 8.4 8.1 7.8 7.5 7.3 7.0 6.8 6.6 6.4 6.3 6.1

10.3 9.5 8.9 8.5 8.1 7.8 7.5 7.2 7.0 6.7 6.5 6.3 6.1 6.0 5.8

10.0 9.2 8.6 8.2 7.8 7.5 7.2 6.9 6.7 6.4 6.2 6.0 5.8 5.7 5.5

12.8 9.7 8.9 8.3 7.9 7.5 7.2 6.9 6.6 6.4 6.1 5.9 5.7 5.5 5.4 5.2

12.5 9.4 8.6 8.0 7.6 7.2 6.9 6.6 6.3 6.1 5.8 5.6 5.4 5.2 5.1 4.9

12.2 9.1 8.3 7.7 7.3 6.9 6.6 6.3 6.0 5.8 5.5 5.3 5.1 4.9 4.8 4.6

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

108

106

104

102

100

98

96

94

92

pH


11.8 11.0 10.4 10.0 9.6 9.3 9.0 8.7 8.5 8.2 8.0 7.8 7.6 7.5 7.3 110

VALUES OF (V9)

(Range 110 to 92)

Tables Table 36/4 (Range 110 to 92)

VALUES OF (V9) pH

90

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 11.9 7.1 8.8 7.2 8.0 7.3 7.4 7.4 7.0 7.5 6.6 7.6 6.3 7.7 6.0 7.8 5.7 7.9 5.5 8.0 5.2 8.1 5.0 8.2 4.8 8.3 4.6 8.4 4.5 8.5 4.3 pH

90

88

86

84

82

80

78

76

74

72

pH

12.5 9.4 6.3 5.5 4.9 4.5 4.1 3.8 3.5 3.2 3.0 2.7 2.5 2.3 2.1 2.0 1.8

13.0 12.2 9.1 6.0 5.2 4.6 4.2 3.8 3.5 3.2 2.9 2.7 2.4 2.2 2.0 1.8 1.7 1.5

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

74

72

pH


11.6 8.5 7.7 7.1 6.7 6.3 6.0 5.7 5.4 5.2 4.9 4.7 4.5 4.3 4.2 4.0

11.2 8.1 7.3 6.7 6.3 5.9 5.6 5.3 5.0 4.8 4.5 4.3 4.1 3.9 3.8 3.6

10.9 7.8 7.0 6.4 6.0 5.6 5.3 5.0 4.7 4.5 4.2 4.0 3.8 3.6 3.5 3.3

10.6 7.5 6.7 6.1 5.7 5.3 5.0 4.7 4.4 4.2 3.9 3.7 3.5 3.3 3.2 3.0

10.3 7.2 6.4 5.8 5.4 5.0 4.7 4.4 4.1 3.9 3.6 3.4 3.2 3.0 2.9 2.7

10.0 6.9 6.1 5.5 5.1 4.7 4.4 4.1 3.8 3.6 3.3 3.1 2.9 2.7 2.6 2.4

12.8 9.7 6.6 5.8 5.2 4.8 4.4 4.1 3.8 3.5 3.3 3.0 2.8 2.6 2.4 2.3 2.1

88

86

84

82

80

78

76

VALUES OF (V9)

(Range 90 to 72)

175

176


(Range 70 to 52)

VALUES OF (V9) pH 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 pH

70

68

66

64

62

60

58


13.0 12.7 12.4 11.9 11.6 8.5 83.8 8.8 5.7 5.4 4.9 4.6 4.3 4.0 3.9 3.6 3.5 3.2 3.2 2.9 2.9 2.6 2.6 2.3 2.4 2.1 2.1 1.8 1.9 1.6 1.7 1.4 1.5 1.2 1.4 1.1 1.2 0.9 70

68

12.7 12.1 11.3 8.2 5.1 4.3 3.7 3.3 2.9 2.6 2.3 2.0 1.8 1.5 1.3 1.1 0.9 0.8 0.6

12.8 12.4 11.8 11.0 7.9 4.8 3.9 3.4 3.0 2.6 2.3 2.0 1.7 1.5 1.2 1.0 0.8 0.6 0.5 0.3

12.8 12.4 12.0 11.4 10.6 7.5 4.4 3.6 3.0 2.6 2.2 1.9 1.6 1.3 1.1 0.8 0.6 0.4 0.2 0.1 −0.1

12.8 12.5 12.1 11.7 11.1 10.3 7.2 4.1 3.3 2.7 2.3 1.9 1.6 1.3 1.0 0.8 0.5 0.3 0.1 −0.1 −0.2 −0.4

66

64

62

60

VALUES OF (V9)

56

12.8 12.5 12.2 11.8 11.4 10.8 10.0 6.9 3.8 3.0 2.4 2.0 1.6 1.3 1.0 0.7 0.5 0.2 0.3 0 −0.2 −0.4 −0.5 −0.7

13.0 12.8 12.5 12.2 11.9 11.5 11.1 10.5 9.7 6.6 3.5 2.7 2.1 1.7 1.3 1.0 0.7 0.4 0.2 −0.1 −0.3 −0.5 −0.7 −0.8 −1.0

58

56

(Range 70 to 52)

54

52

pH

12.9 12.7 12.5 12.2 11.9 11.6 11.2 10.8 10.2 9.4 6.3 3.2 2.4 1.8 1.4 1.0 0.7 0.4 0.1 −0.1 −0.4 −0.6 −0.8 −1.0 −1.1 −1.3

12.8 12.7 12.4 12.0 11.9 11.6 11.3 10.9 10.5 9.9 9.1 6.0 2.9 2.1 1.5 1.1 0.9 0.4 0.1 −0.2 −0.4 −0.7 −0.9 −1.1 −1.8 −1.4 −1.6

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

54

52

pH

Tables Table 36/6 VALUES OF (V9) pH

(Range 50 to 32)

50

48

46

44

42

40

38

36

34

32

pH

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

13.0 12.7 12.6 12.4 12.1 11.9 11.6 11.3 11.0 10.6 10.2 9.6 8.8 5.7 2.6 1.8 1.2 0.8 0.4 0.1 −0.2 −0.5 −0.7 −1.0 −1.2 −1.4 −1.6 −1.7 −1.9

13.0 12.8 12.7 12.5 12.3 12.1 11.8 11.6 11.3 11.0 10.7 10.3 9.9 9.3 8.5 5.4 2.3 1.5 0.9 0.5 0.1 −0.2 −0.5 −0.8 −1.0 −1.3 −1.5 −1.7 −1.9 −2.0 −2.2

12.7 12.5 12.4 12.2 12.0 11.8 11.5 11.3 11.0 10.7 10.4 10.0 9.6 9.0 8.2 5.1 2.0 1.2 0.6 0.2 −0.2 −0.5 −0.8 −1.1 −1.3 −1.6 −1.8 −2.0 −2.2 −2.3 −2.5

12.4 12.2 12.1 11.9 11.7 11.5 11.2 11.0 10.7 10.4 10.1 9.7 9.3 8.7 7.9 4.8 1.7 0.9 0.3 −0.1 −0.5 −0.8 −1.1 −1.4 −1.6 −1.9 −2.1 −2.3 −2.5 −2.6 −2.8

12.1 11.9 11.8 11.6 11.4 11.2 10.9 10.7 10.4 10.1 9.8 9.4 9.0 8.4 7.6 4.5 1.4 0.6 0 −0.4 −0.8 −1.1 −1.4 −1.7 −1.9 −2.2 −2.4 −2.6 −2.8 −2.9 −3.1

11.8 11.6 11.5 11.3 11.1 10.9 10.6 10.4 10.1 9.8 9.5 9.1 8.7 8.1 7.3 4.2 1.1 0.3 −0.3 −0.7 −1.1 −1.4 −1.7 −2.0 −2.2 −2.5 −2.7 −2.9 −3.1 −3.2 −3.4

11.5 11.3 11.2 11.0 10.8 10.6 10.3 10.1 9.8 9.5 9.2 8.8 8.4 7.8 7.0 3.9 0.8 0 −0.6 −1.0 −1.4 −1.7 −2.0 −2.3 −2.5 −2.8 −3.0 −3.2 −3.4 −3.5 −3.7

11.1 10.9 10.8 10.6 10.4 10.2 9.9 9.8 9.4 9.1 8.8 8.4 8.0 7.4 6.6 3.5 0.4 −0.4 −1.0 −1.4 −1.8 −2.1 −2.4 −2.7 −2.9 −3.2 −3.4 −3.6 −3.8 −3.9 −4.1

10.8 10.6 10.5 10.3 10.1 9.9 9.6 9.4 9.1 8.8 8.5 8.1 7.7 7.1 6.3 3.2 0.1 −0.7 −1.3 −1.7 −2.1 −2.4 −2.7 −3.0 −3.2 −3.5 −3.7 −3.9 −4.1 −4.2 −4.4

10.5 10.3 10.2 10.0 9.8 9.6 9.3 9.1 8.8 8.5 8.2 7.8 7.4 6.8 6.0 2.9 −0.2 −1.0 −1.6 −2.0 −2.4 −2.7 −3.0 −3.3 −3.5 −3.8 −4.0 −4.2 −4.4 −4.5 −4.7

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

pH

50

48

46

44

42

40

38

36

34

32

pH

VALUES OF (V9)

(Range 50 to 32)

177

178

Quantitative Forecasting of Problems in Industrial Water Systems Table 36/7 VALUES OF (V9)

(Range 30 to 12)

pH

30

28

26

24

22

20

18

16

14

12

pH

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

10.2 10.0 9.9 9.7 9.5 9.3 9.0 8.8 8.5 8.2 7.9 7.5 7.1 6.5 5.7 2.6 −0.5 −1.3 −1.9 −2.3 −2.7 −3.0 −3.3 −3.6 −3.8 −4.1 −4.3 −4.5 −4.7 −4.8 −5.0

9.9 9.7 9.6 9.4 9.2 9.0 8.7 8.5 8.2 7.9 7.6 7.2 6.8 6.2 5.4 2.3 −0.8 −1.6 −2.2 −2.6 −3.0 −3.3 −3.6 −3.9 −4.1 −4.4 −4.6 −4.8 −5.0 −5.1 5.3

9.6 9.4 9.3 9.1 8.9 8.7 8.4 8.2 7.9 7.6 7.3 6.9 6.5 5.9 5.1 2.0 −1.1 −1.9 −2.5 −2.9 −3.3 −3.6 −3.9 −4.2 −4.4 −4.7 −4.9 −5.1 −5.3 −5.4 −5.6

9.3 9.1 9.0 8.8 8.6 8.4 8.1 7.9 7.6 7.3 7.0 6.6 6.2 5.6 4.8 1.7 −1.4 −2.2 −2.8 −3.2 −3.6 −3.9 −4.2 −4.5 −4.7 −5.0 −5.2 −5.4 −5.6 −5.7 −5.9

9.0 8.8 8.7 8.5 8.3 8.1 7.8 7.6 7.3 7.0 6.7 6.3 5.9 5.3 4.5 1.4 −1.7 −2.5 −3.1 −3.5 −3.9 −4.2 −4.5 −4.8 −5.0 −5.3 −5.5 −5.7 −5.9 −6.0 −6.2

8.7 8.5 8.4 8.2 8.0 7.8 7.5 7.3 7.0 6.7 6.4 6.0 5.6 5.0 4.2 1.1 −2.0 −2.8 −3.4 −3.8 −4.2 −4.5 −4.8 −5.1 −5.3 −5.6 −5.8 −6.0 −6.2 −6.3 −6.5

8.4 8.2 8.1 7.9 7.7 7.5 7.2 7.0 6.7 6.4 6.1 5.7 5.3 4.7 3.9 0.8 −2.3 −3.1 −3.7 −4.1 −4.5 −4.8 −5.1 −5.4 −5.6 −5.9 −6.2 −6.3 −6.5 −6.6 −6.8

8.1 7.9 7.8 7.6 7.4 7.2 6.9 6.7 6.4 6.1 5.8 5.4 5.0 4.4 3.6 0.5 −2.6 −3.4 −4.0 −4.4 −4.8 −5.1 −5.4 −5.7 −5.9 −6.2 −6.4 −6.6 −6.8 −6.9 −7.1

7.8 7.6 7.5 7.3 7.1 6.9 6.6 6.4 6.1 5.8 5.5 5.1 4.7 4.1 3.3 0.2 −2.9 −3.7 −4.3 −4.7 −5.1 −5.4 −5.7 −6.0 −6.2 −6.5 −6.7 −6.9 −7.1 −7.2 −7.4

7.4 7.2 7.1 6.9 6.7 6.5 6.2 6.0 5.7 5.4 5.1 4.7 4.3 3.7 2.0 −0.2 3.3 −4.1 −4.7 −5.4 −5.5 −5.8 −6.1 −6.4 −6.6 −6.9 −7.1 −7.3 −7.5 −7.6 −7.8

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

pH

30

2.8

26

24

22

20

18

16

14

12

pH

VALUES OF (V9)

(Range 30 to 12)

Tables Table 36/8 (Range 10 to −8)

VALUES OF (V9) pH

10

8

6

4

2

0

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

7.1 6.9 6.8 6.6 6.4 6.2 5.9 5.7 5.4 5.1 4.8 4.4 4.0 3.4 2.6 −0.5 −3.6 −4.4 −5.0 −5.4 −5.8 −6.1 −6.4 −6.7 −6.9 −7.2 −7.4 −7.6 −7.8 −7.9 −8.1

6.8 6.6 6.5 6.3 6.1 5.9 5.6 5.4 5.1 4.8 4.5 4.1 3.7 3.1 2.3 −0.8 −3.9 −4.7 −5.3 −5.1 −5.7 −6.1 −6.4 −6.7 −7.0 −7.2 −7.5 −7.7 −7.9 −8.1 −8.2 −8.4

6.5 6.3 6.2 6.0 5.8 5.6 5.3 5.1 4.8 4.5 4.2 3.8 3.4 2.8 2.0 −1.1 −4.2 −5.0 −5.6 −6.0 −6.4 −6.7 −7.0 −7.3 −7.5 −7.8 −8.0 −8.2 −8.4 −8.5 −8.7

6.2 6.0 5.9 5.7 5.5 5.3 5.0 4.8 4.5 4.2 3.9 3.5 3.1 2.5 1.7 −1.4 −4.5 −5.3 −5.9 −6.3 −6.7 −7.0 −7.3 −7.6 −7.8 −8.1 −8.3 −8.5 −8.7 −8.8 −9.0

5.9 5.7 5.6 5.4 5.2 5.0 4.7 4.5 4.2 3.9 3.6 3.2 2.8 2.2 1.4 −1.7 −4.8 −5.6 −6.2 −6.6 −7.0 −7.3 −7.6 −7.9 −8.1 −8.4 −8.6 −8.8 −9.0 −9.1 −9.3

5.6 5.4 5.3 5.1 4.9 4.7 4.4 4.2 3.9 3.6 3.3 2.9 2.5 1.9 1.1 −2.0 −5.1 −5.9 −6.5 −6.9 −7.3 −7.6 −7.9 −8.2 −8.4 −8.7 −8.9 −9.1 −9.3 −9.4 −9.6

pH

10

8

6

4

2

0

VALUES OF (V9)

−2

−4

−6

−8

pH

5.3 5.0 5.1 4.8 5.0 4.7 4.8 4.5 4.6 4.3 4.4 4.1 4.1 3.8 3.9 3.6 3.6 3.3 3.3 3.0 3.0 2.7 2.6 2.3 2.2 1.9 1.6 1.3 0.8 0.5 −2.3 −2.6 −5.4 −5.7 −6.2 −6.5 −6.8 −7.1 −7.2 −7.5 −7.6 −7.9 −7.9 −8.2 −8.2 −8.5 −8.5 −8.8 −8.7 −9.0 −9.0 −9.3 −9.2 −9.5 −9.4 −9.7 −9.6 −9.9 −9.7 −10.0 −9.9 −10.2

4.7 4.5 4.4 4.2 4.0 3.8 3.5 3.3 3.0 2.7 2.4 2.0 1.6 1.0 0.2 −2.9 −6.0 −6.8 −7.4 −7.8 −8.2 −8.5 −8.8 −9.1 −9.3 −9.6 −9.8 −10.0 −10.2 −10.3 −10.5

4.4 4.2 4.1 3.9 3.7 3.5 3.2 3.0 2.7 2.4 2.1 1.7 1.3 0.7 0.1 −3.2 −6.3 −7.1 −7.7 −8.1 −8.5 −8.8 −9.1 −9.4 −9.6 −9.9 −10.1 −10.3 −10.5 −10.6 −10.8

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

−6

−8

pH

−2

−4

(Range 10 to −8)

179

180


(Range −10 to −28)

VALUES OF (V9) pH

−10

−12

−14

−16

−18

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

4.1 3.9 3.8 3.6 3.4 3.2 2.9 2.7 2.4 2.1 1.8 1.4 1.0 0.4 −0.4 −3.5 −6.6 −7.4 −8.0 −8.4 −8.8 −9.1 −9.4 −9.7 −9.9 −10.2 −10.4 −10.6 −10.8 −10.9

3.8 3.6 3.5 3.3 3.1 2.9 2.6 2.4 2.1 1.8 1.5 1.1 0.7 0.1 −0.7 −3.8 −6.9 −7.7 −8.3 −8.7 −9.1 −9.4 −9.7 −10.0 −10.2 −10.5 −10.7 −10.9

3.4 3.2 3.1 2.9 2.7 2.5 2.2 2.0 1.7 1.4 1.1 0.7 0.3 −0.3 −1.1 −4.2 −7.3 −8.1 −8.7 −9.1 −9.5 −9.8 −10.1 −10.4 −10.6 −10.9

3.1 2.9 2.8 2.6 2.4 2.2 1.9 1.7 1.4 1.1 0.8 0.4 0 −0.6 −1.4 −4.5 −7.6 −8.4 −9.0 −9.4 −9.8 −10.1 −10.4 −10.7 −10.9

2.8 2.6 2.5 2.3 2.1 1.9 1.6 1.4 1.1 0.8 0.5 0.1 −0.3 −0.9 −1.7 −4.8 −7.9 −8.7 −9.3 −9.7 −10.1 −10.4 −10.7 −11.0

pH

−10

−12

−14

−16

−20

−22

−24

−26

−28

pH

2.5 2.2 1.9 1.6 1.3 2.3 2.0 1.7 1.4 1.1 2.2 1.9 1.6 1.3 1.0 2.0 1.7 1.4 1.1 0.8 1.8 1.5 1.2 0.9 0.6 1.6 1.3 1.0 0.7 0.4 1.3 1.0 0.7 0.4 0.1 1.1 0.8 0.5 0.2 −0.1 0.8 0.5 0.2 −0.1 −0.4 0.5 0.2 −0.1 −0.4 −0.7 .2 0.1 −0.4 −0.7 −1.0 0.2 −0.2 −0.5 −0.8 −1.1 −1.4 −0.6 −0.9 −1.2 −1.5 −1.8 −1.2 −1.5 −1.8 −2.1 −2.4 −2.0 −2.3 −2.6 −2.9 −3.2 −5.1 −5.4 −5.7 −6.0 −6.3 −8.2 −8.5 −8.8 −9.1 −9.4 −9.0 −9.3 −9.6 −9.9 −10.2 −9.6 −9.9 −10.2 −10.5 −10.8 −10.0 −10.3 −10.6 −10.9 −10.4 −10.7 −11.0 −10.7 −11.0 −11.0

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

High, negative values of IL in thia area fall outside the original Lucey nomogram and indicate conditions favourable to non-pitting.

−18

VALUES OF (V9)

−20

−22

−24

−26

(Range −10 to −28)

−28

pH

Tables Table 36/10 (Range −30 to −48)

VALUES OF (V9)

−48

pH

5.5 1.0 0.7 0.4 0.1 −0.3 −0.6 −0.9 −1.2 −1.5 −1.8 5.6 0.8 0.5 0.2 −0.1 −0.5 −0.8 −1.1 −1.4 −1.7 −2.0 5.7 0.7 0.4 0.1 −0.2 −0.6 −0.9 −1.2 −1.5 −1.8 −2.1 5.8 0.5 0.2 −0.1 −0.4 −0.8 −1.1 −1.4 −1.7 −2.0 −2.3 5.9 0.3 0 −0.3 −0.6 −1.0 −1.3 −1.6 −1.9 −2.2 −2.5 6.0 0.1 −0.2 −0.5 −0.8 −1.2 −1.5 −1.8 −2.1 −2.4 −2.7 6.1 −0.2 −0.5 −0.8 −1.1 −1.5 −1.8 −2.1 −2.4 −2.7 −3.0 6.2 −0.4 −0.7 −1.0 −1.3 −1.7 −2.0 −2.3 −2.6 −2.9 −3.2 6.3 −0.7 −1.0 −1.3 −1.6 −2.0 −2.3 −2.6 −2.9 −3.2 −3.5 6.4 −1.0 −1.3 −1.6 −1.9 −2.3 −2.6 −2.9 −3.2 −3.5 −3.8 6.5 −1.3 −1.6 −1.9 −2.2 −2.6 −2.9 −3.2 −3.5 −3.8 −4.1 6.6 −1.7 −2.0 −2.3 −2.6 −3.0 −3.3 −3.6 −3.9 −4.2 −4.5 6.7 −2.1 −2.4 −2.7 −3.0 −3.4 −3.8 −4.0 −4.3 −4.6 −4.9 6.8 −2.7 −3.0 −3.3 −3.6 −4.0 −4.3 −4.6 −4.9 −5.2 −5.5 6.9 −3.5 −3.8 −4.1 −4.4 −4.8 −5.1 −5.4 −5.7 −6.0 −6.3 7.0 −6.6 −6.9 −7.2 −7.5 −7.9 −8.2 −8.5 −8.8 −9.1 −9.4 7.1 −9.7 −10.0 −10.3 −10.6 −11.0 7.2 −10.5 −10.8 7.3 7.4 7.5 High, negative values of IL in thia area 7.6 fall outside the original Lucey nomogram 7.7 and indicate conditions favourable to 7.8 non-pitting. 7.9 8.0 8.1 8.2 8.3 8.4 8.5

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

pH

pH

−30

−30

−32

−32

−34

−34

−36

−36

VALUES OF (V9)

−38

−38

−40

−40

−42

−42

−44

−44

−46

−46

(Range −30 to −48)

−48

pH

181

182


VALUES OF (V9) pH

−50

−52

−54

−56

−58

−60

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

−2.1 −2.4 −2.7 −3.0 −3.3 −2.3 −2.6 −2.9 −3.2 −3.5 −2.4 −2.7 −3.0 −3.3 −3.6 −2.6 −2.9 −3.2 −3.5 −3.8 −2.8 −3.1 −3.4 −3.7 −4.0 −3.0 −3.3 −3.6 −3.9 −4.2 −3.3 −3.6 −3.9 −4.2 −4.5 −3.5 −3.8 −4.1 −4.4 −4.7 −3.8 −4.1 −4.4 −4.7 −5.0 −4.1 −4.4 −4.7 −5.0 −5.3 −4.4 −4.7 −5.0 −5.3 −5.6 −4.8 −5.1 −5.4 −5.7 −6.0 −5.2 −5.5 −5.8 −6.1 −6.4 −5.8 −6.1 −6.4 −6.7 −7.0 −6.7 −6.9 −7.2 −7.5 −7.8 −9.7 −10.0 −10.3 −10.6 −10.9

−3.6 −3.8 −3.9 −4.1 −4.3 −4.5 −4.8 −5.0 −5.3 −5.6 −5.9 −6.3 −6.7 −7.3 −8.1

pH

−50

−62 −3.9 −4.1 −4.2 −4.4 −4.6 −4.8 −5.1 −5.3 −5.6 −5.9 −6.2 −6.6 −7.0 −7.6 −8.4

−64 −4.3 −4.5 −4.6 −4.8 −5.0 −5.2 −5.5 −5.7 −6.0 −6.3 −6.6 −7.0 −7.4 −8.0 −8.8

−66 −4.6 −4.8 −4.9 −5.1 −5.3 −5.5 −5.8 −6.0 −6.3 −6.6 −6.8 −7.3 −7.7 −8.3 −9.1

High, negative, values of IL in thia area fall outside the original Lucey nomogram and indicate conditions favourable to non-pitting.

−52

−54

−56

VALUES OF (V9)

−58

−60

−62

−64

−66

(Range −50 to −68)

−68 pH −4.9 −5.1 −5.2 −5.4 −5.6 −5.8 −6.1 −6.3 −6.6 −6.9 −7.2 −7.6 −8.0 −8.6 −9.4

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

−68 pH

Tables Table 36/12

(Range −70 to −88)

VALUES OF (V9) pH

−70

−72

−74

−76

−78

−80

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

−5.2 −5.5 −5.8 −6.1 −6.4 −6.7 −5.4 −5.7 −6.0 −6.3 −6.6 −6.9 −5.5 −5.8 −6.1 −6.4 −6.7 −7.0 −5.7 −6.0 −6.3 −6.6 −6.9 −7.2 −5.9 −6.2 −6.5 −6.8 −7.1 −7.4 −6.1 −6.4 −6.7 −7.0 −7.3 −7.6 −6.4 −6.7 −7.0 −7.3 −7.6 −7.9 −6.6 −6.9 −7.2 −7.5 −7.8 −8.1 −6.9 −7.2 −7.5 −7.8 −8.1 −8.4 −7.2 −7.5 −7.8 −8.1 −8.4 −8.7 −7.5 −7.8 −8.1 −8.4 −8.7 −9.0 −7.9 −8.2 −8.5 −8.8 −9.1 −9.4 −8.3 −8.6 −8.9 −9.2 −9.5 −9.8 −8.9 −9.2 −9.5 −9.8 −10.1 −10.4 −9.7 −10.0 −10.3 −10.6 −10.9

pH

−70

−82

−84

−7.0 −7.3 −7.2 −7.5 −7.3 −7.6 −7.5 −7.8 −7.7 −8.0 −7.9 −8.2 −8.2 −8.5 −8.4 −8.7 −8.7 −9.0 −9.0 −9.3 −9.3 −9.6 −9.7 −10.0 −10.1 −10.4 −10.7 −11.0

−86

−88

pH

−7.6 −8.0 −7.8 −8.2 −7.9 −8.3 −8.1 −8.5 −8.3 −8.7 −8.5 −8.9 −8.8 −9.2 −9.0 −9.4 −9.3 −9.7 −9.6 −10.0 −10.0 −10.3 −10.3 −10.7 −10.7

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5


−72

−74

−76

−78

VALUES OF (V9)

−80

−82

−84

−86

(Range −70 to −88)

−88

pH

183

184


VALUES OF (V9) pH

−90

−92

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5

−8.3 −8.5 −8.6 −8.8 −9.0 −9.2 −9.5 −9.7 −10.0 −10.3 −10.6 −11.0

−8.6 −8.8 −8.9 −9.1 −9.3 −9.5 −9.8 −10.0 −10.3 −10.6 −10.9

pH

−90

−94

−96

−98

−100

−102 −104

−106 −108

pH

−8.9 −9.2 −9.5 −9.1 −9.4 −9.7 −9.2 −9.5 −9.8 −9.4 −9.7 −10.0 −9.6 −9.9 −10.2 −9.8 −10.1 −10.4 −10.1 −10.4 −10.7 −10.3 −10.6 −10.9 −10.6 −10.9 −10.9

−9.8 −10.0 −10.1 −10.3 −10.5 −10.7 −11.0

−10.1 −10.3 −10.4 −10.6 −10.9 −11.0

−10.4 −10.6 −11.0 −10.6 −10.9 −10.7 −11.0 −10.9

5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5


−92

−94

−96

VALUES OF (V9)

−98

−100

−102

−104

−106

(Range −90 to −108)

−108

pH

Table 37. Examples of calculating Lucey index (IL).

ORIGINAL LUCEY CASE NO:

10

8

14

16

47

pH

7.7

7.3

7.8

8.0

7.5

SULPHATE mg/l SO4

190

61

99

58

18

SODIUM mg/l Na

18

15

37

22

11

NITRATE mg/l NO3

nil

37

28

37

37

CHLORIDE mg/l Cl

22

23

42

37

22

OXYGEN mg/l O2

7.5

9.4

7.0

14.0

7.2

(V1) 0.167 Na

0.167 × 18 3.01

0.167 × 15 2.51

0.167 × 37 6.18

0.167 × 22 3.67

0.167 × 11 1.84

For SO4 190 0.167 NO3 0.167 × 0 nil

For SO4 61 0.167 NO3 0.167 × 37 6.18

For SO4 99 0.167 NO3 0.167 × 28 4.68

For SO4 58 0.167 NO3 0.167 × 37 6.18

For SO4 18 0.1 NO3 0.1 × 37 3.7

(V2)

Tables 185

186

Table 37. (Continued)

10

8

14

16

47

3.01 − 0 3.01

2.51 − 6.18 −3.67

6.18 − 4.68 1.5

3.67 − 6.18 −2.51

1.84 − 3.7 −1.86

(V4) Table 31

Table 31/2 72.62

Table 31/3 39.75

Table 31/2 50.08

Table 31/3 39.82

Table 31/3 29.79

(V5) Table 32

8.88

8.88

35.48

27.00

8.88

(V6) Table 33

15.71

2.89

19.52

−18.41

10.27

72.62 − 15.71 56.91

39.75 − 2.89 36.86

50.08 − 19.52 30.56

39.82 − (−18.41) 39.82 + 18.41 58.23

29.79 − 19.52 10.27

(V8) Table 34

Table 34/1 0.90

Table 34/2 0.59

Table 34/2 0.33

Table 34/1 0.71

Table 34/2 0.16

(V9) Table 35

Table 35/2 92

Table 35/3 62

Table 35/4 56

Table 35/3 55

Table 35/4 37

IL

Table 36/3 6.3 Pitting

Table 36/5 3.0 Pitting

Table 36/5 0.4 Slight Pitting

Table 36/5 −0.3 Non Pitting

Table 36/6 −1.6 Non Pitting

7.0 Pitting

3.0 Pitting

zero Non Pitting

−1.0 Non Pitting

−3.0 Non Pitting

(V3) (V1) − (V2)

(V7) (V4) − (V6)

Table 36 Original Lucey Nomogram


ORIGINAL LUCEY CASE NO:

Tables Table 38. Time-scales from values of (IL). Table 38/1 TIME-SCALES (Years) IL

THRESHOLD

AWARENESS

ESABLISHED

IL

0.2 0.4 0.6 0.8 1.0

6.3 5.7 5.0 4.5 4.6

35.7 32.0 28.7 25.9 23.3

361.7 257.0 196.0 156.2 128.1

0.2 0.4 0.6 0.8 1.0

1.2 1.4 1.6 1.8 2.0

3.5 3.1 2.7 2.3 2.0

21.1 19.0 17.2 15.5 14.0

107.4 91.4 78.7 68.5 60.0

1.2 1.4 1.6 1.8 2.0

2.2 2.4 2.6 2.8 3.0

1.7 1.5 1.2 1.0 0.8

12.7 11.5 10.3 9.3 8.4

53.0 47.0 14.8 37.4 33.5

2.2 2.4 2.6 2.8 3.0

3.2 3.4 3.6 3.8 4.0

0.7 0.5 0.4 0.3 0.2

7.5 6.8 6.0 5.4 4.8

30.0 27.0 24.4 22.0 19.9

3.2 3.4 3.6 3.8 4.0

4.2 4.4 4.6 4.8 5.0

0.1 0.1

4.3 3.8 3.3 2.9 2.5

17.9 16.2 14.6 13.2 12.0

4.2 4.4 4.6 4.8 5.0

2.2 1.9 1.6 1.4 1.1

10.8 9.7 8.8 7.9 7.1

5.2 5.4 5.6 5.8 6.0

1.0 0.8 0.6 0.5 0.4

6.3 5.7 5.0 4.5 4.0

6.2 6.4 6.6 6.8 7.0

5.2 5.4 5.6 5.8 6.0

Values in this area are less than 0.1 years

6.2 6.4 6.6 6.8 7.0 IL

THRESHOLD

AWARENESS

ESABLISHED

TIME-SCALES (Years)

IL

187

188

Quantitative Forecasting of Problems in Industrial Water Systems Table 38/2 TIME-SCALES (Years) IL

THRESHOLD

AWARENESS

ESABLISHED

IL

0.3 0.2 0.1 0.1

3.5 3.1 2.7 2.3 2.1

7.2 7.4 7.6 7.8 8.0

8.2 8.4 8.6 8.8 9.0

1.7 1.5 1.2 1.0 0.8

8.2 8.4 8.6 8.8 9.0

9.2 9.4 9.6 9.8 10.0

0.7 0.5 0.4 0.3 0.2

9.2 9.4 9.6 9.8 10.0

10.2 10.4 10.6 10.8 11.0

0.1 0.1

10.2 10.4 10.6 10.8 11.0

7.2 7.4 7.6 7.8 8.0

Values in these areas are all less than 0.1 years

11.2 11.4 11.6 11.8 12.0

11.2 11.4 11.6 11.8 12.0

12.2 12.4 12.6 12.8 13.0

12.2 12.4 12.6 12.8 13.0

IL

THRESHOLD

AWARENESS

ESABLISHED

TIME-SCALES (Years)

IL

Tables Table 39. Water analyses for Tokyo corrosion experiments.

Tokyo Tap Water (ex.R.Tone)

Experimental Waters A

B

C

D

pH Total alkalinity (mg/l CaCO3) Total hardness (mg/l CaCO3) Calcium hardness (mg/l CaCO3) Magnesium hardness (mg/l CaCO3) Chloride (mg/l Cl− ) Sulphate (mg/l SO42− ) Residual chlorine (mg/l Cl−1 )

7.0 40.8 67.6 48.4 18.8 19.2 37.9 1

7.0 25.0 64.6 51.4 13.2 39.9 76.2 3

6.9 33.9 67.8 48.8 19.0 26.2 39.3 2

7.9 52.0 68.2 48.8 19.4 163.1 38.0 3

6.9 85.1 68.2 49.0 19.2 32.0 37.1 3

Bicarbonate : Sulphate

0.73

0.22

0.58

0.92

1.55

Ratio mg/l CaCO3 mg/l Na2SO4

Table 40. Time-scales for copper pitting in hot systems. Table 40/1

RESIDUAL CHLORINE mg/l Cl2 0.5

1.0

1.5

2.0

TIME (days) TIME (days) TIME (days) TIME (days) pH

DS

INIT

FAIL INIT FAIL INIT FAIL INIT FAIL

DS

pH

5.5

20 40 60 80 100 150 200 250 300 350 400 450 500

62 100 132 160 188 248 302 352 400 444 486 528 568

362 584 771 934 1098 1148 1764 2056 2336 2593 2838 3083 3317

20 40 60 80 100 150 200 250 300 350 400 450 500

5.5

pH

DS

INIT

FAIL INIT FAIL INIT FAIL INIT FAIL

pH

DS

31 50 66 80 94 124 151 176 200 222 243 264 284

281 292 385 467 549 724 882 1028 1168 1296 1419 1542 1659

21 123 33 293 44 257 53 310 63 368 83 485 101 590 117 683 133 777 148 864 162 946 176 1028 189 1104

16 25 33 40 47 62 76 88 100 110 122 132 142

93 146 193 234 275 362 444 514 584 648 712 771 829

TIME (days) TIME (days) TIME (days) TIME (days) 0.5

1.0

1.5

RESIDUAL CHLORINE mg/l Cl2

2.0

189

190

Quantitative Forecasting of Problems in Industrial Water Systems Table 40/2 RESIDUAL CHLORINE mg/l Cl2 0.5

1.0

1.5

2.0


DS

INIT FAIL INIT FAIL INIT FAIL INIT FAIL

DS

pH

6.0

20 40 60 80 100 150 200 250 300 350 400 450 500

62 104 142 176 208 282 352 414 476 534 590 644 698

291 489 667 827 978 1325 1654 1940 2237 2510 2773 3027 3250

31 52 71 88 104 141 176 207 238 267 295 322 349

146 244 334 414 489 663 827 973 1119 1255 1387 1513 1640

21 35 47 59 69 94 117 138 159 178 197 215 233

99 165 221 277 324 442 550 649 747 837 926 1011 1095

16 26 36 44 52 71 88 104 119 134 148 161 175

75 122 169 207 244 334 414 489 559 630 696 752 823

20 40 60 80 100 150 200 250 300 350 400 450 500

6.0

6.5

20 40 60 80 100 150 200 250 300 350 400 450 500

62 112 156 196 236 328 416 500 580 658 734 810 882

221 399 555 698 840 1168 1481 1780 2065 2342 2613 2884 3140

31 56 78 98 118 164 208 250 290 329 367 405 441

110 199 278 349 420 584 740 890 1032 1171 1307 1442 1570

21 37 52 65 79 109 139 167 193 219 245 270 294

75 132 185 231 281 388 495 595 687 780 872 961 1047

16 28 39 49 59 82 104 125 145 165 184 203 221

57 97 139 174 210 292 370 445 516 587 655 723 797

20 40 60 80 100 150 200 250 300 350 400 450 500

6.5

pH

DS

INIT FAIL INIT FAIL INIT FAIL INIT FAIL

pH

DS


1.0

1.5


2.0

Tables Table 40/3 RESIDUAL CHLORINE mg/1 Cl2 0.5

1.0

1.5

2.0


DS

INIT FAIL

INIT FAIL INIT FAIL INIT FAIL

DS

pH

7.0

20 40 60 80 100 150 200 250 300 350 400 450 500

68 108 154 148 142 346 444 542 636 728 818 908 996

140 261 373 479 586 817 1074 1311 1539 1762 1980 2197 2410

29 54 77 99 121 173 222 271 318 364 409 454 498

70 131 186 240 293 419 537 656 770 881 990 1099 1205

19 36 51 66 81 115 148 181 212 243 273 303 332

46 87 123 160 196 278 358 438 513 588 661 733 803

15 27 39 50 61 87 111 136 159 182 205 227 249

36 65 94 121 148 211 269 329 385 440 496 532 603

20 40 60 80 100 150 200 250 300 350 400 450 500

7.0

7.5

20 40 60 80 100 150 200 250 300 350 400 450 500

50 96 140 184 278 334 436 538 640 738 838 936 1034

113 216 315 414 513 752 981 1210 1440 1661 1886 2106 2327

25 48 70 92 114 167 218 269 320 369 419 468 517

56 108 158 207 257 376 491 605 720 830 943 1053 1163

17 32 47 61 76 111 145 179 213 246 279 312 345

38 72 106 137 171 250 326 403 479 554 628 702 776

13 24 35 46 57 84 109 135 160 185 210 234 259

29 54 79 104 128 189 245 304 360 416 473 527 588

20 40 60 80 100 150 200 250 300 350 400 450 500

7.5

pH

DS

INIT FAIL

INIT FAIL INIT FAIL INIT FAIL DS

pH


1.0

1.5

2.0

RESIDUAL CHLORINE mg/1 Cl2

191

192

Quantitative Forecasting of Problems in Industrial Water Systems Table 40/4 RESIDUAL CHLORINE mg/l Cl2 0.5

1.0

1.5

2.0

TIME (days)

TIME (days)

TIME (days) TIME (days) INIT FAIL INIT FAIL

DS

PH

pH

DS

INIT FAIL

INIT

FAIL

8.0

20 40 60 80 100 150 200 250 300 350 400 450 500

36 72 108 144 180 270 360 450 540 630 720 810 900

72 144 216 288 360 540 720 900 1080 1260 1440 1620 1800

18 36 54 72 90 135 180 225 270 315 360 405 450

36 72 108 144 180 270 360 450 540 630 720 810 900

12 24 36 48 60 90 120 150 180 210 240 270 300 600

24 48 72 96 120 180 240 300 360 420 480 540 600 300

9 18 27 36 45 68 90 118 135 158 180 203 225 600

18 36 54 72 90 136 180 226 270 316 360 406 450 225

20 40 60 80 100 150 200 250 300 350 400 450 500

8.0

8.5

20 40 60 80 100 150 200 250 300 350 400 450 500

14 32 48 66 82 128 174 220 268 316 366 414 464

25 56 84 116 144 224 305 385 469 553 641 725 812

7 16 24 33 41 64 87 110 134 158 183 207 232

12 28 42 58 72 112 152 193 235 277 320 362 406

5 11 16 22 27 43 58 73 89 105 122 138 155

9 19 28 39 47 75 102 128 156 184 214 242 271

4 8 12 17 21 32 44 55 67 79 92 104 116

7 14 21 30 37 56 77 96 117 138 161 182 203

20 40 60 80 100 150 200 250 300 350 400 450 500

8.5

pH

DS

INIT FAIL

INIT

FAIL

INIT FAIL INIT FAIL

DS

pH

TIME (days) TIME (days) 0.5

1.0

TIME (days) TIME (days) 1.5


2.0

Index

Index terms

Links

A alloys

xiv

B boilers

xiii

buffer capacity

xi

ix

65

73

calcium

xi 25 60

xii 27 62

ix 37 64

xiv 41 88

1 42 92

16 44 93

18 53

19 57

21 59

calcium carbonate

xi

xii

ix

xiv

1

16

18

19

21

25

27

41

45

48

50

51

53

60

calcium phosphate

xi

ix

xiv

37

41

42

44

45

48

calcium sulphate

xi

ix

xiv

10

27

35

37

C

carbonate

xi

xii

ix

xiv

1

16

18

19

21

25

27

41

45

48

50

51

53

60

chlorine

xi

94

chlorine residual

xi

94

96

97

cold systems

78

80

copper

xi

ix

xiv

77

78

87

97

corrosion

xi 71

ix 73

xiv 77

53 78

55 90

56

58

63

69

corrosion of mild steel

ix

53

xiv

2

11

14

28

D deposition


193

194

Index terms

Links

E Edwards

10

11

9

16

21

22

39

87

field

13

19

31

44

56

57

62

73

fouling

ix 31

xiv 32

1 35

14 37

16 41

21 44

23 51

27 53

38

39

41

40

41

60

61

error

F 28 60

G Green & Holmes

H heat exchangers

98

L Langelier

xi

1

3

17

22

Langelier index

xi

5

17

22

60

Lucey

xi

77

89

90

96

Lucey index

xi

78

81

89

90

margin of

16

21

65

87

Mattsson

90

97

Mattsson parameters

92

93

97

mild steel

ix 65

xiv 74

53

organic

xiv

95

98

organic slimes

xiv

7

10

M

55

56

58

60

21

65

90

97

O

P parameters

4


63

195

Index terms

Links

phosphate

xi

ix

xiv

37

41

42

44

93

97

pitting

xi

ix

78

79

83

84

90

propensity index

xi

ix

78

79

23

27

32

48

59

64

75

81

82

91

98

recirculating systems

23

32

33

48

81

98

Ryznar

xi 59

1 60

6 65

14 73

17

22

53

55

57

Ryznar index

xi

1

3

6

12

14

22

53

55

57

59

60

65

73

saturation

xi 41

ix 42

4 48

9

27

29

33

35

37

saturation index

xi 42

4 48

9

27

29

33

35

37

41

slimes

xiv

R recirculating

S

steel

ix

xiv

53

55

58

60

63

65

74

sulphate

xi 82

xii 88

ix 92

xiv

10

27

28

37

80

systems

ix

xiii

xiv

1

2

7

23

32

33

37 87

48 95

56

59

70

77

78

80

81

84

95

13

19

31

44

57

62

73

78

80

82

84

86

T time scales

U Use in

V Van Slyke concept

66

vectors

xii


Quantitative Forecasting of Problems in Industrial Water Systems (Chemical Engineering)

Quantitative Forecasting of Problems in Industrial Water Systems

Uncertainty Forecasting In Engineering

Chemical Biophysics. Quantitative Analysis of Cellular Systems

Uncertainty Forecasting in Engineering

Parametric Sensitivity in Chemical Systems (Cambridge Series in Chemical Engineering)

Water Demand Forecasting

Geographic Information Systems in Water Resources Engineering

Geographic Information Systems in Water Resources Engineering

Handbook of Industrial and Systems Engineering (Industrial Innovation)

Chemical Engineering in Medicine

Frontiers In Chemical Engineering

Vogel's Quantitative chemical analysis

Quantitative Chemical Analysis

Quantitative Methods in Reservoir Engineering

Vibration Problems in Engineering

History of Chemical Engineering

Matrices in Engineering Problems

Chemical Engineering

Solutions To The Problems In Coulson & Richardson's Chemical Engineering

Industrial Water Quality

Chemical Engineering

Chemical engineering plant design (Chemical engineering series)

Operational and Environmental Consequences of Large Industrial Cooling Water Systems

Handbook of Military Industrial Engineering (Industrial Innovation)

Thermodynamics of Chemical Systems

Thermodynamics of chemical systems

industrial water pollution control

Industrial engineering in apparel production

Industrial Chemical Process Design

Quantitative Forecasting of Problems in Industrial Water Systems (Chemical Engineering)