Predicting calcium carbonate scale in water systems has been done for more than 20 years — often with questionable or even inaccurate results rather than actual field observations.

Perhaps the oldest method is the marble test[1], a crude, qualitative test used primarily for potable water rather than cooling water. The marble test method led to the development of a more quantitative method by Dr. E.F. Langelier in 1936 known as the Langelier saturation index (LSI).[2] Again, this predictive method was developed for potable waters — not cooling water. However, it is being used for cooling water — with questionable results. It is often inaccurate in its prediction of calcium carbonate scale potential.

Several other predictive methods were later developed. The most popular was developed by Dr. Ryznar of Nalco Chemical Co. in 1944.[3] Known as the Ryznar stability index (RSI), this test was developed primarily for predicting the calcium carbonate scale tendency of potable water. It now is being used mainly for cooling water even though it was not modified in any way that I am aware of for use in this application. Other methods also were developed, mainly for potable water, but they were not used much.

It was not until 1983 that a new method was developed primarily for cooling waters. It was dubbed the modified stability index (MSI) when introduced in a paper published by Brooke and Puckorius.[4] The name was changed to the practical scaling index and later to the Puckorius scaling index (PSI) in a 1983 Power magazine article.[5] Since this index is primarily for cooling waters, both end users and water treatment companies have adopted it.

Numerous articles appeared during the next 12 years to promulgate modifications to the LSI and RSI indices to improve scale predictions versus actual scaling waters.[6] These were not major improvements and thus have not been extensively adopted.

An important contribution in recent years has been the development of both slide rules and computer programs.[7] These provide faster results of the LSI, RSI and PSI data and information of calcium carbonate scale tendencies of cooling waters. Perhaps the greatest contribution for more accurately predicting calcium carbonate scaling tendencies of cooling water is the WaterCycle (WC) computer program[8] developed by French Creek Software Inc. in 1990s. This computer program incorporated the influence of common ions on the solubility of calcium carbonate, often referred to in the WC program as calcite.

This article will not attempt to compare all of these methods for predicting calcium carbonate scaling tendencies of cooling water. However, we will compare the most commonly used indices —the LSI, RSI, PSI and WC methods — with regard to how well they relate and their accuracy to actual field cooling waters.

It is important to be clear on one point: All of these indices were developed only to predict calcium carbonate scaling tendencies. The WC program also calculates other scales, depending upon the water constituents. I will thus only be addressing the accuracy of predicting calcium carbonate scale in cooling water systems.

Table 1 provides an overview of the major indices used to predict calcium carbonate scaling. The pHs is the pH of saturation of calcium carbonate, and it is used by all the indices. It is calculated using:

The total dissolved solids or conductivity value.

  • Calcium hardness (as CaCO3) value.
  • The total alkalinity (as CaCO3) value.
  • The maximum water temperature (as Fahrenheit or Celsius) occurring in the cooling water system.

The WC modifies the pHs value as influenced by the common ion effect.

The best review of the LSI, RSI and PSI methods was made independently by Cavano in an article published in The Analyst magazine in the fall of 1999.[9] He found the PSI method provided the most accurate values of the three methods. He determined that it was most accurate when the cooling water values were in the following ranges:

  • Total dissolved solids were between 500 and 1,000 parts per million (ppm).
  • The calcium hardness (as CaCO3) was between 50 and 700 ppm.
  • The total alkalinity (as CaCO3) was between 10 and 800 ppm.
  • The temperature was between 100 and 150°F (38 and 66°C).

These ranges are typical of many cooling tower waters.

Both the LSI and the RSI differ from the PSI in that they use the actual pH of the cooling water being tested. The PSI utilizes an adjusted pH — known as the pH of equilibrium, or pHe — based on the actual measurement of the total alkalinity. The pHe also is calculated by the formula

pHe=1.465 log10 (total alkalinity)

This formula was developed by Brooke and Puckorius based on several hundred cooling tower waters.[10] To simplify this calculation, table 2 was prepared to show the relationship between total alkalinity and pHe.

The WC computer program was developed by Ferguson in 1990s. It has been upgraded several times, with the newest version released in 2009.[11] It was developed for cooling waters and takes into consideration the common ion effect on the solubility of calcium carbonate that can be substantial with dissolved solids of cooling waters above 2,000 mg/L, mainly from chlorides and sulfates. The solubility of calcium carbonate will be greater when this effect is used; thus, the cooling water usually will have a lower scaling tendency.

The software program provides an accurate predictive method for calcium carbonate formation in cooling tower waters. It is interesting to note the PSI is close to the WC values for cooling tower waters with less than 3,500 ppm of dissolved solids.

Comparisons of Indices

Before comparing indices, it is important to remember that the three indices — LSI, RSI and PSI — only predict calcium carbonate scale. (By contrast, WC calculates all scales.) Therefore, when the cooling tower water contains other ions such as phosphates, fluorides and sulfates — ions that can form other calcium scales before forming calcium carbonate — the LSI, RSI and PSI values may be meaningless. This is a primary reason these indices are misused.

The LSI has the greatest misuse and inaccuracies of all three indices. It often predicts that calcium carbonate scale will form when none occurs versus actual field results. Whenever the LSI calculation is positive, Langelier showed that scale will form. However, cooling tower operators often will show that no scale will form even up to a value of 2.0.

We have studied this inconsistency in numerous cooling tower water systems in a number of different industries and found that the water pH does not relate to the bicarbonate/carbonate levels identified by the total alkalinity of the cooling tower water.

Most often, the water pH is buffered higher than the total alkalinity would suggest. This pH buffering was because of the presence of ammonia, chloramines, high carbonates and, at times, the presence of hydroxides, which showed a higher pH than would be expected from the total alkalinity. Because calcium carbonate can only form with calcium and sufficient bicarbonate or carbonates — and not from ammonia or hydroxides — the LSI does not accurately predict the formation of calcium carbonate scale.

We have discovered that plants sometimes identify a specific positive value for LSI — a point at which scale does not form in their cooling tower waters. These plants use that value as the maximum before scale will form. A typical example would be to maintain an LSI maximum of 1.5. Targeting such a value can be misleading, however. We have found that if the quality of the cooling tower makeup water changes, this value of 1.5 might cause scale. Changes to the cooling tower makeup water quality means the water pH now has a different amount of total alkalinity.

Table 3 lists the values identified by the developers of the three indices: LSI, RSI, and the PSI. Table 4 is a good comparison of the values calculated by these indices. It shows the variations that occur in actual cooling tower waters. They illustrate why there is confusion in the results of some of these indices. Please note that the PSI and the WC both show all these cooling tower waters would not form calcium carbonate scale, which is what actually is occurring.

Table 4: Predicted vs. Real-World Results. Water No. 1 is a good example where the pH is very high versus the total alkalinity. This is common when lime-softened water is used in the cooling tower as makeup water. The lime-softened water has both carbonates and some hydroxides that cause the pH to be quite high versus the total alkalinity.

Thus, when the LSI and RSI are calculated, they use the cooling water’s actual pH.  The results indicate that the cooling water should form calcium carbonate scale, with the LSI predicting a very severe scale formation while the RSI indicates a moderate scaling condition. Already, there is a discrepancy between the LSI and RSI values.

The PSI and WC use the total alkalinity to identify the pHe (equilibrium pH) to use in the calculations, not the actual pH. The results, by both PSI and WC, predict no calcium carbonate scale would form in the cooling tower equipment. In actual field tests, no calcium carbonate scale was forming.

Water No. 2 is similar except the total alkalinity and actual pH is closer together. In this case, the LSI and RSI again predict scale but not quite as severe. The PSI and WC again predict no calcium carbonate scale, which was exactly what was happening.

Water No. 3 shows the impact of much higher calcium hardness with a low total alkalinity and a slightly elevated actual pH versus the pHe. The LSI shows a slight amount of calcium carbonate scaling by the cooling water; the RSI, PSI and WC show no scale would form. Again, no scale was forming.

Water No. 4 shows how double the total alkalinity with the same amount of calcium hardness as in Water No. 3. It also still records a slightly elevated pH versus the total alkalinity, which results in the LSI and RSI predicting scale. The PSI and WC again do not predict scale, and there is none found.

Water No. 5 shows the impact of low calcium hardness and a moderate amount of total alkalinity with a buffered pH above what would be expected and predicted by the pHe. Again, the LSI and RSI predict scale while the PSI and WC predict no scale. None formed.

Water No. 6 shows the impact of higher calcium hardness with a low alkalinity. This time, the LSI predicted severe scale formation while the RSI gave neutral water with no scale. The PSI and WC predicted that no scale would form, and it did not occur.

Scale-Dissolving Index Values

In table 3, the various calculated values indicate the severity of the expected formation of calcium carbonate scale as well as the scale-dissolving quality of the cooling tower waters. It is true that the scale-dissolving values would result in the gradual dissolving of calcium carbonate scale from the cooling water equipment. The water treatment industry also uses the scale-dissolving values to indicate that the cooling water is corrosive — mainly to mild steels.

Aerated cooling tower water always is always corrosive to mild steel. The presence of calcium carbonate or other scales, however, can protect mild steel if it is coated uniformly — even in the absence of a mild steel corrosion inhibitor. Cooling tower water is always corrosive to mild steel, but stable or slightly scaling water will reduce mild steel corrosion somewhat.

Interferences of Index Results

One of the times that the LSI, RSI, PSI and even the WC are used incorrectly is when other calcium scales form before calcium carbonate scale occurs.

The most common example is when phosphate is present in the cooling tower water. Phosphate compounds are common for coolingtower corrosion- and scale-control — but also are often in city makeup water. They are present in cooling towers as a continuously added corrosion and scale control water treatment. They can be present as ortho-phosphate, poly-phosphate or as a phosphonate as well as in other combinations. They all produce ortho-phosphate that reacts with the calcium hardness, forming calcium phosphate, which has a lower solubility than calcium carbonate.

Thus, it is meaningless to use any of the indices to predict calcium carbonate scale. A value can be calculated for any or all of these four indices; however, they have no meaning for calcium carbonate formation when phosphate is present in the cooling tower water.

There is a possibility, however, for both calcium phosphate and calcium carbonate to be present in a scale that has formed on cooling water equipment. This occurs when the phosphate present in the cooling water is totally precipitated as calcium phosphate. Then, the remaining bicarbonates can react with the remaining calcium to form calcium carbonate.

Other calcium compounds that are less soluble than calcium carbonate will show the same information.

Another case where the indices provide incorrect information is when crystal-modifier scale inhibitors are used as the scale-control chemical. The crystal modifiers perform in controlling scale — not by keeping the scale soluble but by conditioning the scale to precipitate as a non-adherent sludge rather than a hard scale. Thus, the cooling tower water is in a precipitating mode, and these indices would indicate a scaling condition. At the same time, good scale control is being obtained by the crystal modifiers. Certainly, the precipitated calcium carbonate must be removed from the cooling tower system by blowdown and filtration.

Optimizing a Scale-Control Cooling Water Program

The PSI and the WC programs appear the most accurate for predicting cooling water relative to calcium carbonate scaling tendencies. They also can be used to optimize a scale-control program for cooling tower water systems. This can be done when the effectiveness of the scale inhibitor is known.

The PSI method has incorporated the effectiveness of several commonly used scale inhibitors for cooling water.

The WC computer program has been expanded to include many of the scale inhibitors being used — not only just for calcium carbonate scale control but also for many other calcium scales such as phosphates and sulfates. The WC program also calculates other scales and the effect of scale inhibitors for those scales.[11]

Illustrating how the PSI method can be used to optimize a scale control program is done by using only acid, a specific scale inhibitor or a combination of both. Determining the amount of acid needed to prevent calcium carbonate scale is simply accomplished by reducing the total alkalinity of the cooling tower water and using the PSI to arrive at a value of 6.0 or, to be sure of no scale, achieve a PSI of 6.5. Table 5 illustrates this method.

When common cooling water scale inhibitors such as polyacrylates or phosphonates are used for keeping the calcium carbonate soluble, the PSI and the WC can be used to establish a value where no scale will form. This can be illustrated when there is sufficient knowledge about which chemical and what dosage is needed to be effective.

The PSI value for stable water, or a nonscaling condition without any scale inhibitors, is 6.0 as shown in table 3. The nonscaling PSI value thus can be as low as 4.0 when an effective scale inhibitor is used.

Table 6 illustrates this with several common calcium carbonate scale inhibitors used in cooling tower waters.

Case Histories of Index Use and Comparison

Two case histories can help illustrate index use. In the first example, consider an HVAC cooling tower system is located in the St. Louis area. The local water utility supplies lime-softened potable water that is used for cooling tower makeup water at many facilities. This cooling tower is running at three cycles of concentration. It uses a cooling tower water treatment plan that includes a polyacrylate scale inhibitor along with corrosion and biological treatments.

A consulting service company was asked to provide an assessment of the cooling tower treatment because costs were quite high even though the cooling water equipment was well protected. Study of the cooling water quality and the controls being carried out showed that the water treatment supplier was basing the scale control of the cooling water treatment using the LSI. The consulting company ran three indices (LSI, RSI and PSI) on the cooling tower water. The results are shown in table 7.

The cooling tower water quality showed that the LSI indicated considerable calcium carbonate scale formation. The PSI showed that no scale would form on cooling water equipment. The HVAC equipment owner decided to discontinue the scale inhibitor. No scale formed, and the cost of the cooling water treatment was reduced by $10,000 per year.

Case History No. 2. A cooling tower water system in the Houston area was studied. It was found to be operating at four cycles of concentration and using both acid and a blend of scale inhibitors, plus corrosion and biological treatments. The water treatment program used the LSI for scale control. The overall results were very good, but the facility desired to eliminate the use of acid for safety reasons.

The cooling water quality showed the following values as seen in table 8. The results showed that acid could be eliminated but still allow use of the scale inhibitors to control scale. This provided the operators greater safety, and they saved 20 percent by eliminating the acid. The total alkalinity without acid would be 250 mg/L and it would produce a PSI of 4.92, which would cause severe calcium carbonate scaling; however, that is easily controlled with polyacrylates or phosphonates. Eliminating acid treatment was a major benefit.


Correct understanding and use of calcium carbonate scale-predictive methods can provide improved cooling tower water treatment results as well as possible water treatment cost reduction. The use of the LSI and RSI for cooling tower water scale prediction often results in erroneous information with much greater calcium carbonate scaling tendencies indicated than actually occur. The PSI and the WC computer program provide more accurate calcium carbonate scale prediction for cooling tower waters as well as a tool for optimizing scale-control treatments.

None of the four indices can be used for calcium carbonate scale prediction when the cooling tower water contains other calcium scales that are more insoluble than calcium carbonate. Phosphate-treated cooling tower water systems are the most likely to misuse of the indices.

The WC computer program can provide a prediction of all types of scales potentially possible with a given cooling tower water quality. It is the most accurate scale-predicting method available because it also incorporates common ion influences. PC


1. von Heyer, A. “Die Untersuchung and Beurteilung des Wassers Abwasser” (“The Investigation and Assessment of Water Effluent”), 4th ed., Verlag von Julius Springer, Berlin, Germany, p. 40 (1921).

2. Langelier, W.F. “The Analytical Control of Anti-Corrosive Water Treatment,” Journal of the American Water Works Association 28(10), 1500 (1936).

3. Ryznar, J.W. “A New Index for Determining Amount of Calcium Carbonate Scale formed by a Water,” Journal of the American Water Works Association 36(3), 472 (1944).

4. Brooke, J.M. “The Calcium Carbonate Story,” Corrosion ’83, Paper No. 284, Anaheim, CA (April 18 22, 1983).

5. Puckorius, P.R. “Get a Better Reading on Scaling Tendency of Cooling Water,” Power (September 1983).

6. Bohnsack, G.; Johnson, D.A.; Buss, E. “Corrosion in Fresh Water and its Relationship to Water Quality as Described by the Stability Index,” Corrosion ‘90, Paper No. 101.

7. Puckorius, P.R.; Brooke, M. “A New Practical Index for Calcium Carbonate Scale Prediction in Cooling Water Systems,” Corrosion 90, Paper No. 99, Las Vegas, NV (April 23-27, 1990).

8. WaterCycle Computer Program, French Creek Software, Inc., Valley Forge, Pa.

9. Cavano, R. “Scaling Indices,” The Analyst, p. 37-44 (Fall 1999).

10. Puckorius, P.R. “Tools to Predict Scale in Cooling Water Systems,” PA086, Puckorius Water Training Services, Arvada, Colo (January 1997).

11. WaterCycle Computer Program, Version 7, French Creek Software, Inc., Valley Forge, Pa.