Computerized Ion Association Model
Profiles Complete Range of Cooling System Parameters
Robert J. Ferguson, French Creek Software, Inc., Kimberton,
PA 19442 U.S.A.
Paper Number IWC-91-47
52ND ANNUAL MEETING
INTERNATIONAL WATER CONFERENCE
OCTOBER 21 - 23, 1991
Keywords: cooling water, indices, scale, water chemistry, computer models,
This paper describes the application of a microcomputer (PC) based software
system to establishing operating parameter limits for open recirculating
cooling systems. The software used evaluates recirculating water chemistry
over the typical, user defined, operating range of concentration ratio,
temperature, and pH to provide an in-depth, panoramic estimation of deposition
potentials. The deposition potentials calculated for a cooling water are
based upon the free concentration of reactants and account for common ion
effects. The approach of profiling the entire operating range using an
ion association model overcomes two criticisms of water chemistry evaluations
and their applicability towards predicting scale problems in a system and
comparing indices versus results between cooling systems.
Many cooling water chemistry evaluations are based upon a single water
analysis. Even sophisticated computerized programs in use rely upon a single
recirculating water analysis and a single set of operating parameters for
an evaluation of scale potential and corrosivity. Their evaluations and
predicted deposition potentials are based, in most cases, upon a single
pH and single temperature. Even small changes in water chemistry or operating
parameters can invalidate the results of single point evaluations. In the
worst case, evaluation at one set of conditions (e.g. highest temperature,
highest pH) can effectively portray scale potential for a foulant such
as calcium carbonate under the harshest conditions for it, but result in
the evaluation of a foulant such as amorphous silica under the conditions
where it is most soluble.
Commonly used indices for scale potential base their calculations upon
the analytical values for scale forming species. Common ion effects are
not included in the calculations.1 This can result in
decisions, such as the maximum concentration ratio for operation, based
upon inflated scale potentials.
The program discussed uses an ion association model to estimate the
saturation level (ion activity product over solubility product) for common
foulants including calcium carbonate, calcium sulfate, amorphous silica,
calcium fluoride, magnesium silicates, and tricalcium phosphate. Saturation
level calculations include ion pairing to account for common ion effects
and provide a more reproducible, and representative driving force. Traditional
saturation derived indices (Langelier2, Ryznar3
and Puckorius4) are also profiled by the system based
upon the analytical values input.
Examples are presented which compare the indices calculated by traditional
methods to those done using an in-depth, panoramic profile over the typical
operating range for a cooling system.
THE CONCEPT OF SATURATION - A majority of the indices used routinely
by water treatment chemists are derived from the basic concept of saturation.
A water is said to be saturated with a compound (e.g. calcium carbonate)
if it will not precipitate the compound and it will not dissolve any of
the solid phase of the compound when left undisturbed, under the same conditions,
for an infinite period of time. A water which will not precipitate or dissolve
a compound is at equilibrium for the particular compound.
By definition, the amount of a chemical compound which can be dissolved
in a water and remain in solution for this infinite period of time is described
by the solubility product (Ksp). In the case of calcium carbonate, solubility
is defined by the relationship:
- (Ca) is the activity of calcium (CO3) is the carbonate activity
- Ksp is the solubility product for calcium carbonate at the temperature
In a more generalized sense, the term (Ca)(CO3) can be called
the Ion Activity Product (IAP) and the equilibrium condition described
by the relationship:
It can be shown that the Langelier Saturation Index is the base ten
logarithm of calcite saturation level based upon total calcium in the water,
an estimate of carbonate calculated from total alkalinity, and the solubility
product for the calcite polymorph of calcium carbonate.2,5
The degree of saturation of a water is described by the relationship
of the ion activity product (IAP) to the solubility product (Ksp) for the
compound as follows:
- If a water is undersaturated with a compound: IAP< Ksp
(It will tend to dissolve the compound).
- If a water is at equilibrium with a compound: IAP= Ksp
(It will not tend to dissolve or precipitate the compound).
- If a water is supersaturated with a compound: IAP>Ksp
(It will tend to precipitate the compound).
The index called Saturation Level, Degree of Supersaturation, or Saturation
Index, describes the relative degree of saturation as a ratio of the ion
activity product (IAP) to the solubility product (Ksp):
In actual practice, the saturation levels calculated by the various
computer programs available differ in the method they use for estimating
the activity coefficients used in the IAP; they differ in the choice of
solubility products and their variation with temperature; and they differ
in the dissociation constants used to estimate the concentration of reactants
(e.g. CO3 from analytical values for alkalinity, PO4
from analytical orthophosphate).
Table 1 defines the saturation
level for common cooling water foulants and provides the basis for discussion
of these foulants in this paper.
ION PAIRING - The Saturation Index discussed can be calculated
based upon total analytical values for the reactants. Ions in water, however,
do not tend to exist totally as free ions.6,7,8 Calcium,
for example, may be paired with sulfate, bicarbonate, carbonate, phosphate
and other species. Bound ions are not readily available for scale formation.
The computer program calculates saturation levels based upon the free concentrations
of ions in a water rather than the total anaytical value which includes
those which are bound.
Early indices such as the Langelier Saturation Index (LSI) for calcium
carbonate scale, are based upon total analytical values rather than free
species primarily due to the intense calculation requirements for determining
the distribution of species in a water. Speciation of a water is time prohibited
without the use of a computer for the iterative number crunching required.
The process is iterative and involves:
- Checking the water for a electroneutrality via a cation-anion balance,
and balancing with an appropriate ion (e.g sodium or potassium for cation
deficient waters, sulfate, chloride, or nitrate for anion deficient waters).
- Estimating ionic strength, calculating and correcting activity coefficients
and dissociation constants for temperature, correcting alkalinity for non-carbonate
- Iteratively calculating the distribution of species in the water from
(a partial listing is outlined in figure
- Checking the water for balance and adjusting ion concentrations to
agree with analytical values.
- Repeating the process until corrections are insignificant.
- Calclulating saturation levels based upon the free concentrations of
ions estimated using the ion association model (ion pairing).
The use of ion pairing to estimate the free concentrations of reactants
overcomes several of the major shortcomings of traditional indices. Indices
such as the LSI correct activity coefficients for ionic strength based
upon the total dissolved solids. They do not account for "common ion"
effects.1 Common ion effects increase the apparent solubility
of a compound by reducing the concentration of reactants available. A common
example is sulfate reducing the available calcium in a water and increasing
the apparent solubility of calcium carbonate. The use of indices which
do not account for ion pairing can be misleading when comparing waters
where the TDS is composed of ions which pair with the reactants versus
ions which have less interaction with them.
When indices are used to establish operating limits such as maximum
concentration ratio or maximum pH, the differences between the use of indices
calculated using ion pairing can be of extreme economic significance. In
the best case, a system is not operated at as high a concentration ratio
as possible, because the use of indices based upon total analytical values
resulted in high estimates of the driving force for a scalant. In the worst
case, the use of indices based upon total ions present can result in the
establishment of operating limits too high. This can occur when experience
on a system with high TDS water is translated to a system operating with
a lower TDS water. The high indices which were found acceptable in the
high TDS water may be unrealistic when translated to a water where ion
pairing is less significant in reducing the apparent driving force for
Table 2 summarizes the
impact of TDS upon Langelier Saturation Index when calculated using total
analytical values for calcium and alkalinity, and when calculated using
the free calcium and carbonate concentrations calculated using an ion association
model. The same data is presented graphically in Figure
ECONOMIC IMPACT OF ION PAIRING - Indices based upon ion association
models provide a common denominator for comparing results between systems.
For example, calcite saturation level calculated using free calcium and
carbonate concentrations, has been used successfully as the basis for developing
models which describe the minimum effective scale inhibitor dosage which
will maintain clean heat transfer surfaces.9,10,11,12
The calcite saturation level driving force provided a common denominator
for applying the models to cooling systems across the country with varying
water quality, and varying degrees of common ion effects mediating the
apparent driving force for scale formation. Previous models, based upon
total analytical values, did not provide results as reproducible between
Indices based upon ion pairing provide an excellent basis for optimising
operating parameters for the high alkalinity, high pH all organic treatment
programs in use today. Many of these programs rely upon phosphonates for
calcium carbonate scale control. It has been reported, (and is the author's
experience), that most inhibitor programs lose scale control when the Langelier
Saturation Index exceeds 2.5 .13 A magic index value
is used by most water treatment companies in establishing an upper limit
for concentration ratio and pH to prevent loss of control. This value is
based upon laboratory and field experience with the scale inhibitors. The
use of total analytical concentrations for calcium and alkalinity can result
in the establishment of limits significantly lower than possible, if the
limits are based upon a lower TDS water than that of the cooling system,
or higher than appropropriate, if established with data from a higher TDS
water. Indices calculated using ion pairing and free species provide a
common denominator for comparing results between systems. Limits based
upon indices calculated using total analytical concentrations are best
applied to similar waters.
Calcite saturation level has also been used to establish the upper limit
for all organic programs. A typical "magic" number of 150 is
reasonable for free ion calcite saturation level.14
This is comparable to a Langelier Saturation Index of 2.50 in waters
with makeup compositions similar to the Great Lakes. Figure 3 and Figure
4 compare the "magic number" concentration ratio for a low
and high sulfate water based upon an LSI of 2.5 and a free ion calcite
saturation level of 150.
In the case of the low sulfate, lower TDS water, the LSI limit of 2.50
and the calcite saturation level limit of 150 both occur near a concentration
ratio of 5.6 to 5.7. The difference between the two limits is negligible.
In the case of the high sulfate water, the use of the ion association
model to determine the maximum concentration ratio would increase the maximum
from 6.5 to7.8 in comparison to the concentration ratio limit which would
be imposed based upon the use of the traditional Langelier Saturation Index
for the calculations.
The differences in limits between the two waters result from the impact
of sulfate upon the free calcium ion concentration. Table 3 compares the concentration ratio limit which
would be calculated based upon the LSI with limits based upon ion association
model calcite saturation level for four (4) waters.
It should be noted that these waters represent a computer simulation
and were chosen to demonstrate a trend. The addition of other anions and
cations to the analysis will further impact the trends, and have varying
impacts upon the concentration ratios where the LSI or calcite saturation
level limits are reached.
The use of ion association model indices can provide a common denominator
for the water treater. When faced with a variety of water sources and operating
parameters, ion pairing provides a more reproducible driving force for
the development of operational limits for inhibitor programs than indices
calculated using total anaytical values. The use of free ions for index
calculations eliminates or minimizes the impact of total dissolved solids
and their composition upon the calculated index to allow for better reproducibility
between waters and cooling systems.
OPERATING RANGE SOLUBILITIES - Many cooling water evaluations
assume that the cooling system is static. Indices for scale potential are
calculated at the "harshest" conditions for the foulant under
study. In the case of calcium carbonate scale, indices are typically calculated
at the highest expected temperature and highest expected pH: the conditions
where calcium carbonate is least soluble. In the case of silica, the opposite
conditions are used. Amorphous silica has its lowest solubility at the
lowest temperature, and lowest pH encountered. Indices calculated under
these conditions would be acceptable in many cases. Unfortunately, cooling
systems are not static. This section describes the use of operating range
profiles to answer questions such as:
- What happens if the pH rises a tenth or two above the control range
- What happens with acid overfeed and a pH well below the minimum desired?
- What happens if the system cycles above the maximum target concentration
The foulants silica and tricalcium phosphate are used as examples to
demonstrate the use of operating range profiles in developing an in-depth
evaluation of scale potential, and the impact of loss of control.
Silica - Guidelines for the upper silica operating limits have
been well defined in water treatment practice, and have evolved with the
treatment programs. In the days of acid chromate cooling system treatment,
an upper limit of 150 ppm silica as SiO2 was common. The limit
increased to 180 ppm with the advent of alkaline treatments and pH control
limits up to 9.0 . Silica control levels approaching or exceeding 200 ppm
as SiO2 have been reported for the current high pH, high alkalinity
all organic treatment programs where pH is allowed to equilibrate at 9.0
The evolution of silica control limits can be readily understood by
reviewing the a silica solubility profile. As depicted in Figure 5, amorphous silica solubility increases with
increasing pH. Silica solubility also increases with increasing temperature.
In the pH range of 6.0 to 8.0 and temperature range of 70 to 90 °F,
cooling water will be saturated with amorphous silica when the concentration
reaches 106 ppm as SiO2 (70 °F), or 140 ppm (90 °F).
These concentrations correspond to a saturation level of 1.0. The traditional
silica limit for this pH range has been 150 ppm as SiO2. As
outlined in Table 4, a limit
of 150 ppm would correspond roughly to a saturation level of 1.4 at 70
F and 1.1 at 90 °F.
At the upper end of the cooling water pH range (9.0), silica solubility
increases to 117 ppm (70 °F) and 140 ppm (90 °F). A control limit
of 180 ppm would correspond to a saturation levels of 1.5 and 1.3, respectively.
The author's experience is that a slight degree of saturation is acceptable
in most systems, and that a silica saturation level of 1.1 to 1.2 at the
cold well temperature is a conservative limit. In systems where concentration
ratio is limited by silica solubility, it is recommended that the concentration
ratio limit be re-established seasonally based amorphous silica saturation
level or whenever significant temperature changes occur. Figure 6 profiles silica saturation level versus concentration
ratio at 70 and 90 °F for a well water. An increase of concentration
ratio from 4.3 to 6.1 is indicated based upon a target saturation level
Operating range profiles of silica saturation quickly provide a picture
of pH and temperature limits within a system where silica is the limiting
factor for operational concentration ratio. An overview such as the profile
in figure 7 provide a point of
reference for the degree of temperature, pH, or concentration change which
indicates athat a review of the recirculating water chemistry is in order.
Such profiles are also useful tools in establishing concentration ratio
targets, and in determining if silica solubility is a limiting factor.
Cooling systems vary in the degree of supersaturation they can carry
before measurable fouling occurs. As a result, it is recommended that saturation
levels be used to establish limits based upon conditions where no silica
deposition has been encountered. Once limits have been established, silica
solubility profiles provide a useful tool in maximizing concentration ratio
in silica limited systems.
Calcium Phosphate - Neutral phosphate programs can benefit from
saturation level profiles for tricalcium phosphate. Treatment programs
using orthophosphate as a corrosion inhibitor must operate in a narrow
range of pH if satisfactory corrosion inhibition is to be achieved without
catastrophic calcium phosphate deposition occurring. Operating range profiles
for tricalcium phosphate can assist the water treatment chemist in establishing
limits for pH, concentration ratio, and orthophosphate in the recirculating
water. Such profiles are also useful in showing operators the impact of
loss of pH control, chemical overfeed, or over concentration. Figure
8 is a typical profile for a neutral pH phosphate treatment program.
It can be observed that tricalcium phosphate scale potential is negligible
below a pH of 7.3 in this operating scheme. Minor alkaline pH excursions
would quickly result in deposition if a copolymer or other calcium phosphate
scale inhibitor were not present. The rapidity with which saturation level
increases with pH is due to the fifth order nature of tricalcium phosphate
(Figure 1). The saturation level is very sensitive to pH, which affects
the orthophosphate concentration of the water, and calcium.
Frequent operating range profiles should be run for cooling systems
which use pH control as the primary means for calcium phosphate fouling
SUMMARY - This paper presented an overview of the application
of computerized modeling of cooling water scale potential. Prior to the
advent of the AT and 386 based personal computers, ion association calculations
were restricted to mainframe computers. As a result, few cooling water
chemists were equipped to routinely profile the scale potential of a cooling
system over the entire operating range. Indices were calculated based upon
total analytical values for reactants such as calcium, and did not account
for common ion effects. The use of ion association models allows the water
treatment chemist the freedom to explore the operating range of a particular
cooling system and optimize its operation. Indices calculated using ion
association models also improve the portability of knowledge between waters
and systems. The ion association saturation level indices provide a common
denominator for comparing results, inhibitor limitations, and failure points
where control was lost. They also have served as the driving force for
dosage modulation models. And finally, the graphic presentation of complex
profiles allows them to be assimilated quickly by water treatment chemists
and operational personnel.
1 G. Caplan, Cooling Water Computer Calculations: Do They
Compare?, Corrosion '90, Paper 100, National Association of Corrosion Engineers,
Houston, Texas, 1990.
2 W.F. Langelier, The Analytical Control of Anti-Corrosion Water
Treatment, JAWWA, Vol. 28, No 10, p. 1500-1521, 1936.
3 J.W. Ryznar, A New Index For Determining Amount of Calcium
Carbonate Scale Formed By Water, JAWWA, Vol. 36, p. 472, April 1944.
4 P. Puckorius, Get A Better Reading on Scaling Tendency of
Cooling Water, Power, p. 79-81, September, 1983.
5 W. Stumm and J.J. Morgan, Aquatic Chemistry, 2nd edition,
John Wiley and Sons, New York, New York, pp. ,1981.
6 A.H. Truesdell and B.F. Jones, Wateq - A Computer Program
for Calculating Chemical Equilibria of Natural Waters, J. Research, U.S.
Geological Survey Volume 2, No. 2, p. 233-248, 1974.
7 W. Chow, J.T. Arson, W.C. Micheletti, Calculations of Cooling
Water Systems: Computer Modeling of Recirculating Cooling Water Chemistry,
International Water Conference 41rst Annual Meeting, Pittsburgh, Pennsylvania,
8 D.A. Johnson, K.E. Fulks, Computerized Water Modeling in the
Design and Operation of Industrial Cooling Systems, International Water
Conference, 41rst Annual Meeting, Pittsburgh, Pennsylvania, IWC-80-42.
9 R.J. Ferguson, A Kinetic Model for Calcium Carbonate Deposition,
Corrosion '84, Paper 120, National Association of Corrosion Engineers,
Houston, Texas, 1984.
10 R.J. Ferguson, O. Codina, W. Rule, R. Baebel, Real Time Control
of Scale Inhibitor Feed Rate, International Water Conference, 49th Annual
Meeting, Pittsburgh, Pennsylvania, IWC-88-57.
11 S. Costa, M.H. Hwang, C.J. McCloskey, The Impact of Computer
Models on New Plant Utility Systems, International Water Conference, 51rst
Annual Meeting, Pittsburgh, Pennsylvania, IWC-90-46.
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TABLE 1 - SATURATION LEVEL FORMULAS
Calcium carbonate__ ___
S.L. = ___________
____________ _____________ __Ksp
____________ ____ __________(Ca)(SO4)
Calcium sulfate________ S.L. = ____________
Tricalcium phosphate___S.L. =
Amorphous silica ______S.L.
* Ksp SiO2
Calcium fluoride_______S.L. =
Magnesium hydroxide_ S.L. = ____________
Table 2: Impact of Ion Pairing on
Impact on LSI
Table 3: Concentration Ratio Limit
for Langelier Saturation
Index of 2.5
For Calcite Saturation
Level of 150
|Sulfate, Chloride Mix
Common Makeup Water Constituents
Table 4: Silica Limits For Three
(3) Treatment Schemes
|Lowest Temperature oF
|Saturation Level Limit
Figure 1: Example Ion Pairs Used To
Estimate Free Ion Concentrations
[Magnesium] = __ [Mg+II] +
[MgSO4] + [MgHCO3+I] + [MgCO3]
_____________+ [MgHPO4] + [MgPO4-I]+[MgH2PO4+I]+[MgF+I]
[Sodium] = _____[Na+I] + [NaSO4-I]
+ [Na2SO4] + [NaHCO3] + [NaCO3-I]
____________ + [Na2CO3]
[Potassium] = __ [K+I]+[KSO4-I]
+ [KHPO4-I] + [KCl]
[Iron] = _______[Fe+II] + [Fe+III]
+ [Fe(OH)+I] + [Fe(OH)+II] + [Fe(OH)3-I]
__________ _+ [FeHPO4+I] + [FeHPO4]
+ [FeCl+II] + [FeCl2+I] + [FeCl3]
__________ _+ [FeSO4] + [FeSO4+I]
+ [FeH2PO4+I] + [Fe(OH)2+I]
+ [Fe(OH)2] + [FeH2PO4+II]
[Aluminum] = _[Al+III] + [Al(OH)+II]
+ [Al(OH)2+I] + [Al(OH)4-I]
+ [AlF+II] + [AlF2+I]
__________+ [AlF3] + [AlF4-I]
+ [AlSO4+I] + [Al(SO4)2-I]