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The Practical Application of Ion Association Model Saturation Level Indices to Commercial Water Treatment Problem Solving

R.J. Ferguson, French Creek Software, Kimberton, PA 19442 USA
A.J. Freedman, Arthur Freedman Associates, East Stroudsburg, PA 18301-9045 USA
G. Fowler, Nederlandse Aardolie Maatschappij, Schoonebeek, Netherlands
A.J. Kulik, LEPO Custom Manufacturing, Midland, TX 79702 USA
J. Robson, Chemco, Vancouver, WA 98682 USA
D.J. Weintritt, Weintritt Consulting Services, Lafayette, LA 70503-5603 USA

American Chemical Society 1994

The availability of fast personal computers has allowed ion association models to be developed for the relatively inexpensive and widely available "PC" platforms.

Ion association models predict the equilibrium distribution of species for a cooling water, oil field brine, waste water, or other aqueous solution of commercial interest. Scale potential indices based upon the free ion concentrations estimated by ion association models have been used extensively in the past decade to predict scale problems in industrial cooling water systems.

Indices calculated by the models have been found to be transportable between waters of diverse composition and ionic strength. They have overcome many of the problems encountered with simple indices which do not account for ion pairing. This paper discusses the application of ion association model saturation level indices to predicting and resolving scale formation problems in cooling water systems, oil field brines, and for optimizing storage conditions for low level nuclear wastes.

Examples are presented in case history format which demonstrate the use of the models in field applications.


Simple indices are widely used by water treatment personnel to predict the formation of scale. In many cases, simple indices are used as the basis for adjusting controllable operating conditions such as pH to prevent scale formation.

Simple indices include the Langelier Saturation Index,1 Ryznar Stability Index,2 Stiff-Davis Saturation Index,3 and Oddo-Tomson index4 for calcium carbonate. Indices have also been developed for other common scales such as calcium sulfate and calcium phosphate.

The simple indices provide an indicator of scale potential, but lack accuracy due to their use of total analytical values for reactants. They ignore the reduced availability of ions such as calcium which occurs due to association with sulfate and other ions.5 The simple indices assume that all ions in a water analysis are free and available as a reactant for scale forming equilibria.

For example, the simple indices assume that all calcium is free. Even in low ionic strength waters, a portion of the analytical value for calcium will be associated with ions such as sulfate, bicarbonate, and carbonate (if present). This leads to over-prediction of the scaling tendency of a water in high ionic strength waters. The impact of these "common ion" effects can be negligible in low ionic strength waters. They can lead to errors an order of magnitude high in high ionic strength brines. Table 1 outlines some of the ion associations which might be encountered in natural waters.


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)(CO3) = Ksp


(Ca) is the calcium activity
(CO3) is the carbonate activity
Ksp is the solubility product for calcium carbonate at the temperature under study.

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:

IAP = Ksp

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):

Saturation Level= IAP/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 2 defines the saturation level for common scale forming species encountered in industrial applications. These formulas provide the basis for discussion of these scales in this paper.


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 analytical 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 prohibitive without the use of a computer for the number crunching required. The process is iterative and involves:

  1. 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).
  2. Estimating ionic strength, calculating and correcting activity coefficients and dissociation constants for temperature, correcting alkalinity for non-carbonate alkalinity.
  3. Iteratively calculating the distribution of species in the water from dissociation constants (a partial listing is outlined in Table 1).
  4. Checking the water for balance and adjusting ion concentrations to agree with analytical values.
  5. Repeating the process until corrections are insignificant.
  6. Calculating 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.

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.

Pitzer Coefficient Estimation Of Ion Pairing Impact
The ion association model provides a rigorous calculation of the free ion concentrations based upon the solution of the simultaneous non-linear equations generated by the relevant equilibria.5,6,7,8 A simplified method for estimating the effect of ion interaction and ion pairing is sometimes used instead of the more rigorous and direct solution of the equilibria.9

Pitzer coefficients estimate the impact of ion association upon free ion concentrations using an empirical force fit of laboratory data. This method has the advantage of providing a much less calculation intensive direct solution. It has the disadvantage of being based upon typical water compositions and ion ratios, and of unpredictability when extrapolated beyond the range of the original data.

The use of Pitzer coefficients is not recommended when a full ion association model is available.


Storage costs for low level nuclear wastes are based upon volume. Storage is therefore most cost effective when the aqueous based wastes are concentrated to occupy the minimum volume. Precipitation is not desirable because it can turn a low level waste into a much more costly to store high level waste. Precipitation can also foul heat transfer equipment used in the concentration process.

The ion association model approach has been used at the Oak Ridge National Laboratory to predict the optimum conditions for long term storage.10 Optimum conditions involve the parameters of maximum concentration, pH, and temperature. Figure 1 and Figure 2 depict a profile of the degree of super saturation for silica and magnesium hydroxide as a function of pH and temperature. It can be seen that amorphous silica deposition may present a problem when the pH falls below approximately 10, and that magnesium hydroxide deposition is predicted when the pH rises above approximately 11. A pH range of 10 to 11 is recommended based upon this preliminary run for storage, and concentration.

Other potential precipitants are screened using the ion association model to provide an overall evaluation of a waste water prior to concentration.


There are several fields in the Netherlands that produce hydrocarbon gas associated with very high total dissolved solids connate waters. Classical oilfield scales problems are minimal in these fields (e.g. calcium carbonate, barium sulfate, and calcium sulfate). Halite (NaCl), however, is precipitated to such an extent that production can be lost in hours. As a result, a bottom hole fluid sample is retrieved from all new wells. Unstable components are "fixed" immediately after sampling and pH is determined under pressure. A full ionic and physical analysis is carried out in the group central laboratory.

The analyses are run through an ion association model computer program with the objective of determining susceptibility of the brine to halite (and other scale) precipitation, If a halite precipitation problem is predicted, the ion association model is run in a "mixing" mode to determine if mixing the connate water with boiler feed water will prevent the problem. The computer program used estimates the chemical and physical properties of mixtures over the range of ratios specified, and then calculates the degree of supersaturation for common, and not so common scale forming species.

This approach has been used successfully to control salt deposition in the well with the composition outlined in Table 3. Originally, production on this well was on a test basis. This allowed fluid chemistry and scale data to be studied. Ion association model evaluation of the bottom hole chemistry indicated that the water was slightly supersaturated with sodium chloride under the bottom hole conditions of pressure and temperature. As the fluids cooled in the well bore, the production of copious amounts of halite was predicted.

The ion association model predicted that the connate water would require a minimum dilution of 15% with boiler feed water to prevent halite precipitation (figure 3). The computer model also predicted that over-injection of dilution water would promote barite (barium sulfate) formation (figure 4). Although the well produces H2S at a concentration of 50 mg/l, the program did not predict the formation of iron sulfide due to the combination of low pH and high temperature (figure 5).

Boiler feed water was injected into the bottom of the well using the downhole injection valve that was normally used for corrosion inhibitor injection. Injection of dilution water at a rate of 25 to 30% has allowed the well to produce successfully since start-up. Barite and iron sulfide precipitation has not been observed, and plugging with salt has not occurred.


It has been well established that ozone is an microbiological control agent in open recirculating cooling water systems (cooling towers). It has also been reported that commonly encountered scales were not observed in ozonated cooling systems under conditions where scale would be expected. The water chemistry of 13 ozonated cooling systems was evaluated using an ion association model.11 Each system was treated solely with ozone on a continuous basis at the rate of 0.05 to 0.2 mfg/l based upon recirculating water flow rates.

The saturation levels for common cooling water scales were calculated, including calcium carbonate, calcium sulfate, amorphous silica, and magnesium hydroxide. Magnesium hydroxide saturation levels were included due to the potential for magnesium silicate formation from the adsorbtion of silica upon precipitating magnesium hydroxide.

Each system was evaluated by:

    1. Estimating the concentration ratio of the systems by comparing recirculating water chemistry to makeup water chemistry;
    2. Calculating the theoretical concentration of recirculating water chemistry based upon makeup water analysis and the apparent, calculated concentration ratio from step 1;
    3. Comparing the theoretical and observed ion concentrations to determine precipitation of major species;
    4. Calculating the saturation level for major species based upon both the theoretical and observed recirculating water chemistry;
    5. Comparing differences between the theoretical and actual chemistry to the observed cleanliness of the cooling systems and heat exchangers with respect to heat transfer surface scale buildup, scale formation in valves and on non-heat transfer surfaces, and precipitate buildup in the tower fill and basin.

Three categories of systems were encountered:

  • Category 1: Those where the theoretical chemistry of the concentrated water is not scale forming (is under-saturated) for the scale forming species evaluated.
  • Category 2: Those systems where the concentrated recirculating water would have a moderate to high calcium carbonate scale forming tendency. Water chemistry observed in these systems is similar to those run successfully using traditional scale inhibitors such as phosphonates.
  • Category 3: These systems demonstrated an extraordinarily high scale potential for at least calcium carbonate and magnesium hydroxide. These systems operated with a theoretical recirculating water chemistry more like that of a softener than of a cooling system. The Category 3 water chemistry is above the maximum saturation level for calcium carbonate where traditional inhibitors such as phosphonates are able to inhibit scale formation.

Ozonated Systems Study Results

Table 4 outlines the theoretical versus actual water chemistry for the thirteen (13) systems evaluated. Saturation levels for the theoretical and actual recirculating water chemistries are presented in table 5.

A comparison of the predicted chemistries to observed system cleanliness revealed the following:

  • Category 1 - (Recirculating Water Chemistry under-saturated):
    Category 1 systems showed no scale formation.
  • Category 2 - (Conventional Alkaline Cooling System Control Range):
    Scale formation was observed in eight (8) of the nine (9) category 2 systems evaluated.
  • Category 3 - (The Cooling Tower As A Softener):
    Deposit formation on heat transfer surface was not observed in most of these systems.

Rationale For Results

Category 2 systems fall into the general operating range for alkaline cooling systems. typical calcite saturation levels for such systems fall into the range of 10 to 150 ( [Ca][CO3]/Ksp). In the absence of chemical treatment, scale would be expected, and was observed, in these systems. In this saturation level range, only a small quantity of the total reactive calcium and carbonate in the system is precipitated.

By comparison, the saturation levels predicted for the concentrated water (before precipitation) range well above 1,000. These levels of super-saturation are typical of softening processes. Under these conditions calcite tends to precipitate as finely divided seed crystals in the bulk solution, rather than by growth on existing active sites. Once such bulk precipitation begins, calcite formation on metal surfaces is greatly reduced because of the overwhelming surface area of suspended calcite crystals. The high flow velocities through heat exchangers in these systems tends to keep the crystals in suspension.

This is the rationale proposed for the unexpectedly low level of scale observed on heat transfer surfaces in the extremely saturated category 3 systems in comparison to the category 2 systems, where scale formation on heat transfer surfaces occurred. It must be noted that precipitation was observed in low flow areas of the Category 3 systems.

Conclusions From The Ozonated Systems Study Analysis of the water chemistry and system cleanliness data from a number of recirculating cooling systems treated solely with ozone show that calcium carbonate (calcite) scale forms most readily on heat transfer surfaces in systems operating in a calcite saturation level range of 20 to 150 - the typical range for chemically treated cooling water.

At much higher saturation levels, in excess of 1,000, calcite precipitated in the bulk water. Because of the overwhelming high surface area of the precipitating crystals relative to the metal surface in the system, continuing precipitation leads to growth on crystals in the bulk water, rather than on heat transfer surfaces.

The presence of ozone in cooling systems does not appear to influence calcite precipitation and/or scale formation.


A major manufacturer of polymers for calcium phosphate scale control in cooling systems has developed laboratory data on the minimum effective scale inhibitor (copolymer) dosage required to prevent calcium phosphate deposition over a broad range of calcium and phosphate concentrations, and a range of pH and temperatures, The data was developed using static tests, but has been observed to correlate well with the dosage requirements for the copolymer in operating cooling systems. The data was developed using relatively low dissolved solids test waters. Recommendations from the data were typically made as a function of calcium concentration, phosphate concentration, and pH. This data base was used to project the treatment requirements for a utility cooling system which used a geothermal brine for make-up water. An extremely high dosage (30 to 35 mg/l) was recommended based upon the laboratory data.

It was believed that much lower dosages would be required in the actual cooling system due to the reduced availability of calcium anticipated in the high TDS recirculating water. As a result, it was believed that a model based upon dosage as a function of the ion association model saturation level for tricalcium phosphate would be more appropriate, and accurate, to use than a simple look-up table of dosage versus pH and analytical values for calcium and phosphate. The ion association model was projected to be more accurate due to its use of free values for calcium and phosphate concentrations rather than the analytical values used by the look-up tables. Tricalcium phosphate saturation levels were calculated for each of the laboratory data points. Regression analysis was used to develop a model for dosage as a function of saturation level and temperature. Predicted versus observed dosages for the model are depicted in Figure 6.

The model was used to predict the minimum effective dosage for the system with the make-up and recirculating water chemistry found in Table 6. A dosage in the range of 10 to 11 mg/l was predicted rather than the 30 ppm derived from the look-up tables.

A dosage minimization study was conducted to determine the minimum effective dosage. The system was treated with the copolymer initially at a dosage of 30 mg/l in the recirculating water. The dosage was decreased until deposition was observed. Failure was noted when the recirculating water concentration dropped below 10 mg/l, validating the ion association based dosage model.


It has been well established that phosphonate scale inhibitors function by extending the induction time prior to crystal formation and growth occurrence.12,13,14,15 The induction time extension achieved has been reported to be a function of calcite saturation level, temperature as it affects rate, and phopshonate dosage.

The formula for the models to which data has been successfully fit is a modification of the classical induction time relationship which adds dosage as a parameter:


Dosage models developed from laboratory and field data have been used successfully to model the minimum effective scale inhibitor dosage in cooling water systems. These models were applied to the problem of calcite scale control in a separator.

Carbon dioxide flashes as oil field brines pass through a separator, and go from a high partial pressure of CO2 to atmospheric.

Figure 7 depicts the impact of CO2 flashing upon pH, and calcite saturation levels. Dosage were predicted from the models for the phosphonate HEDP (1,1-hydroxyethylidene diphosphonic acid). Figure 8 depicts the dosage requirement increase as CO2 flashes, and pH rises, across the separator. The dosages predicted by the model for this application are within 30% of those determined through field evaluations.


Ion association model saturation levels provide an effective tool for predicting and resolving scale problems in a wide variety of commercial applications. The use of personal computer versions of the models make their use in the field as an engineering tool practical, and removes the restriction of their use solely as a research tool in a laboratory environment.

1 Langelier, W.F., The Analytical Control Of Anti-Corrosion Water Treatment, JAWWA, Vol. 28, No. 10, p. 1500-1521, 1936.

2 Ryznar, J.W., A New Index For Determining The Amount Of Calcium Carbonate Scale Formed By Water, JAWWA, Vol. 36, p. 472, 1944.

3 Stiff, Jr., H.A., Davis, L.E., A Method For Predicting The Tendency of Oil Field Water to Deposit Calcium Carbonate, Pet. Trans. AIME 195;213 (1952).

4 Oddo,J.E., Tomson, M.B.,Scale Control, Prediction and Treatment Or How Companies Evaluate A Scaling Problem and What They Do Wrong, CORROSION/92, Paper No. 34, (Houston, TX:NACE INTERNATIONAL 1992).

5 Ferguson, R.J., Computerized Ion Association Model Profiles Complete Range of Cooling System Parameters, International Water Conference, 52nd Annual Meeting, Pittsburgh, PA, IWC-91-47.

6 W. Chow, J.T. Aronson, W.C. Micheletti, Calculations Of Cooling Water Systems: Computer Modeling Of Recirculating Cooling Water Chemistry, International Water Conference, 41rst Annual Meeting, Pittsburgh, PA, IWC-80-41.

7 Johnson, D.A., Fulks, K.E.,Computerized Water Modeling In The Design And Operation of Industrial Cooling Systems, International Water Conference, 41rst Annual Meeting, Pittsburgh, PA, IWC-80-42.

8 Truesdell, A.H., Jones, B.F., 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.

9 Musil, R.R., Nielsen, H.J., Computer Modeling Of Cooling Water Chemistry, International Water Conference, 45th Annual Meeting, Pittsburgh, PA, IWC-84-104.

10 Fowler, V.L., Perona, J.J., Evaporation Studies On Oak Ridge National Laboratory Liquid Low Level Waste,ORNL/TM-12243.

11 Ferguson, R.J., Freedman, A.J., A Comparison Of Scale Potential Indices With Treatment Program Results In Ozonated Systems, CORROSION/93,Paper No. 279,(Houston, TX:NACE INTERNATIONAL 1993).

12 Gill, J.S., Anderson, C.D., Varsanik, R.G., Mechanism Of Scale Inhibition By Phosphonates, International Water Conference, 44th Annual Meeting, Pittsburgh, PA, IWC-83-4.

13 Amjad, Z., Masler,III, W.F., The Inhibition Of Calcium Sulfate Dihydrate Crystal Growth By Polyacrylates And The Influence Of Molecular Weight, CORROSION/85, Paper No. 357, Houston, TX: NACE INTERNATIONAL, 1985).

14 Ferguson, R.J., Developing Scale Inhibitor Models, WATERTECH, Houston, TX, 1992.

15 Ferguson, R.J., Codina, O., Rule, W., Baebel, R., Real Time Control Of Scale Inhibitor Feed Rate, International Water Conference, 49th Annual Meeting, Pittsburgh, PA, IWC-88-57.

16 Ferguson, R.J., Weintritt, D.J., Modeling Scale Inhibitor Dosages For Oil Field Operations, CORROSION/94, Paper No. 46, (Houston, TX:NACE INTERNATIONAL, 1994).

Table 1: Example Ion Pairs Used To Estimate Free Ion Concentrations

[Calcium] = [Ca+II] + [CaSO4] + [CaHCO3+I] + [CaCO3] + [Ca(OH)+I]
  + [CaHPO4] + [CaPO4-I] + [CaH2PO4+I]
[Magnesium] = [Mg+II] + [MgSO4] + [MgHCO3+I] + [MgCO3] + [Mg(OH)+I]
  + [MgHPO4] + [MgPO4-I]+[MgH2PO4+I]+[MgF+I]
 [Barium] = [Ba+II] + [BaSO4] + [BaHCO3+I] + [BaCO3] + [Ba(OH)+I]
 [Strontium] = [Sr+II] + [SrSO4] + [SrHCO3+I] + [SrCO3] + [Sr(OH)+I]
[Sodium] = [Sr+II] + [SrSO4] + [SrHCO3+I] + [SrCO3] + [Sr(OH)+I]
[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)3]
  + [Fe(OH)4-I] + [Fe(OH)2] + [FeH2PO4+II]
[Aluminum] = [Al+III] + [Al(OH)+II] + [Al(OH)2+I] + [Al(OH)4-I] + [AlF+II] + [AlF2+I]


        • Saturation level is the ratio of the Ion Activity
          Product to the Solubility Product for the scale
          forming specie.

        For calcium carbonate:
        SL = (Ca)(CO3)/Ksp'

        For barium sulfate:
        SL = (Ba)(SO4)/Ksp'

        For calcium sulfate:
        SL = (Ca)(SO4)/Ksp'

        Saturation Levels should be calculated based upon free ion activities using the solubility product for the form typical of the conditions studied (e.g. calcite for low temperature calcium carbonate, aragonite at higher temperatures.)

        Saturation levels can be interpreted as follows:

        • A water will tend to dissolve scale of
          the compound if the saturation level is less than 1.0
        • A water is at equilibrium when the Saturation Level
          is 1.0 . It will not tend to form or dissolve scale.
        • A water will tend to form scale as the Saturation
          Level increases above 1.0 .

Table 3: Hot Gas Well Water Analysis


Analytical Values Expressed as the Ion Units Bottom Hole Connate Boiler Feed Water
Temperature oC 121 70
Pressure bars 350 1
pH (site) 4.26 9.10
Density kg/m3 1.300 1.000
TDS mg/L 369,960 <20
Dissolved CO2 mg/L 223 < 1
H2S (gas phase) mg/Nm3 50 0
H2S (aqueous phase) mg/L <0.5 0
Bicarbonate mg/L 16 5.0
Chloride mg/L 228,485 0
Sulfate mg/L 320 0
Phosphate mg/L < 1 0
Borate mg/L 175 0
Organic Acids <C6 mg/L 12 < 5
Sodium mg/L 104,780 < 1
Potassium mg/L 1,600 < 1
Calcium mg/L 30,853 < 1
Magnesium mg/L 2,910 < 1
Barium mg/L 120 < 1
Strontium 1,164 < 1
Total Iron 38.0 < 0.01
Lead 5.1 < 0.01
Zinc 3.6

Table 4: Theoretical Versus Actual Recirculating Chemistry Values

Table 4: Theoretical Versus Actual Recirculating Water Chemistry

System (Category) Theoretical Recirculating Calcium Actual Recirculating Calcium Difference in ppm Theoretical Recirculating Magnesium Actual Recirculating Magnesium Difference in ppm Theoretical Recirculating Silica Actual Recirculating Silica Difference in ppm System Cleanliness
1 (1) 56 43 13 28 36 -8 40 52 -12 No scale observed
2 (2) 80 60 20 88 38 50 24 20 4 Basin buildup
3 (2) 238 288 -50 483 168 315 38 31 7 Heavy scale
4 (2) 288 180 108 216 223 -7 66 48 18 Valve scale
5 (3) 392 245 147 238 320 -82 112 101 11 Condenser tube scale
6 (3) 803 163 640 495 607 -112 162 143 19 No scale observed
7 (3) 1,464 200 1,264 549 135 414 112 101 11 No scale observed
8 (3) 800 168 632 480 78 402 280 78 202 No scale observed
9 (3) 775 95 680 496 78 418 186 60 126 No scale observed
10 (3) 3,904 270 3,634 3,172 508 2,664 3,050 95 2,995 Slight valve scale
11 (3) 4,170 188 3,982 308 303 5 126 126 0 No scale observed
12 (3) 3,660 800 2,860 2,623 2,972 -349 6,100 138 5,962 No scale observed
13 (3) 7,930 68 7,862 610 20 590 1,952 85 1,867 No scale observed

Table 5: Theoretical Versus Actual Recirculating Water Saturation Level

Table 5: Theoretical Versus Actual Recirculating Water Saturation Level

System (Category) Theoretical Calcite Saturation Actual Calcite Saturation Theoretical Brucite Saturation Actual Brucite Saturation Theoretical Silica Saturation Actual Silica Saturation
1 (1) 0.03 0.02 <0.001 <0.001 0.20 0.25 No scale observed
2 (2) 49 5.4 0.82 0.02 0.06 0.09 Basin buildup
3 (2) 89 611 2.4 0.12 0.10 0.12 Heavy scale
4 (2) 106 50 1.3 0.55 0.13 0.16 Valve scale
5 (3) 240 72 3.0 0.46 0.21 0.35 Condenser tube scale
6 (3) 540 51 5.3 0.73 0.35 0.49 No scale observed
7 (3) 598 28 10 0.17 0.40 0.52 No scale observed
8 (3) 794 26 53 0.06 0.10 0.33 No scale observed
9 (3) 809 6.5 10 <0.01 0.22 0.27 No scale observed
10 (3) 1,198 62 7.4 0.36 0.31 0.35 Slight valve scale
11 (3) 1,670 74 4.6 0.36 0.22 0.44 No scale observed
12 (3) 3,420 37 254 0.59 1.31 0.55 No scale observed
13 (3) 7,634 65 7.6 0.14 1.74 0.10 No scale observed


Table 6: Calcium Phosphate Inhibitor Dosage Optimization Example

Water Analysis at 6.2 Cycles Deposition Potential Indicators
Calcium (as CaCO3) 1,339 Calcite 38.8
Magnesium (as CaCO3) 496 Aragonite 32.9
Sodium (as Na) 1,240 Silica 0.4
ANIONS Tricalcium phosphate 1,074
Chloride (as Cl) 620 Anhydrite 1.3
Sulfate (as SO4) 3,384 Gypsum 1.7
Bicarbonate (as HCO3) 294 Fluorite 0.0
Carbonate (as CO3) 36 Brucite < 0.1
Silica (as SiO2) 62 SIMPLE INDICES
PARAMETERS Langelier 1.99
pH 8.40 Ryznar 4.41
Temperature (oC) 36.7 Practical 4.20
1/2 Life (hours) 72 Larson-Skold 0.39
100% Active Copolymer (mg/L) 10.53


Amorphous Silica scale potential increases as pH decreases and Temperature decreases.

Brucite (magnesium hydroxide) saturation level increases as temperature and pH increase.

Sodium chloride precipitation should not occur when boiler feed water injection exceeds 15% of the brine flow.

Excessive injection of boiler feed water can result in barium sulfate precipitation.

Iron sulfide precipitation is not predicted despite the presence of iron and sulfide in the brine.

The calcium phosphate model developed shows a marginal scatter.  Errors are highest at lowest saturation.

Brine pH rises as CO2 flashes across the separator, resulting in an increased scale potential for calcium carbonate.

Scale inhibitor requirements increase as pH and calcite saturation level rise when the brine passes through the separator.