By Charles Nicolson

pH is the most widely-used measure of what has been described as the basic technical ‘character’ of water.

pH itself was defined and formalised only in 1923, less than one hundred years ago, which is surprisingly late considering the mass of research work previously concentrated on it. pH is not a measure which has any units like mass, volume, or viscosity for example.

It is a ratio of the amounts of positive and negative ionic charges present and therefore simply a number which varies from 0.00 (zero) up to fourteen (14.00). pH is a fundamental value which occurs wherever water is present, even in tiny trace amounts. pH, therefore, is present in all heating and cooling water circuits used in HVAC installations which are becoming more numerous as more heat pumps are used and various solar developments are increasingly included.

The technical formalisation of pH in 1923 enabled indexes to be developed which predict whether the nature and quality of different types of supply waters can be expected to result in corrosion and/or scale deposition problems in water circuits.

Indexes calculated from water analyses which predict not only whether corrosion and/or scaling can be expected to occur but also the severity of these potential problems are very useful in determining optimum water treatment programmes at lowest practical costs over the projected lifetime of an HVAC plant installation.

Water supplied to closed re-circulating heating and cooling loops in which water flow transfers heat from one or more heat exchangers to other heat exchangers does not, in theory, change in character when it becomes circulating water.

Water fed to open re-circulating loops such as evaporative cooling and adiabatic humidifying plants will almost always change in character, often very markedly, when the feedwater becomes circulating water. However, these water changes can be calculated accurately enabling cost-effective water treatment programmes to be implemented.

In 1936, Dr Langelier introduced the entirely new idea of a ‘theoretical pH’ calculated for when water held as much calcium carbonate in solution as it could. Dr Langelier called this the ‘Saturated pH’ and designated his new concept as pHs. The actual method of calculating pHs shows how Dr Langelier maintained pHs within the same chemical character as pH.

pHs = [9.3 (a constant) + A + B] – [C + D]




(Log10 [TDS] – 1) / 10



-13.12 x Log10 (o C + 273) + 34.55



Log10 [Ca2+ as CaCO3] – 0.4



Log10 [alkalinity as CaCO3]


  • Factor A represents the effect of varying TDS [total dissolved solids].
  • Factor B is the effect of temperature and is a reminder that the character of circulating water varies as it flows through different temperature zones.
  • Factors C and D calculated from theoretical amounts of calcium carbonate needed for saturation and the total alkalinity created by these amounts are the major factors in determining pHs values.

To complete his major advance in deriving a useful predictive index which is still possibly the most widely used one today, as well as being the basis for all the other recognised and generally used indexes, Dr Langelier proposed his Langelier Saturation Index [LSI] as – LSI = pH – pHs – Where pH is the actual ‘as measured’ pH.

LSI values above 0 indicate scaling potential which increases according to the increase of the positive LSI values.

An LSI value of 0 is neutral water which has no scaling or corrosion potential. Negative LSI values mean potential corrosion which increases as LSI values become more negative.

As the LSI became increasingly adopted worldwide by water technicians responsible for treating heating and cooling water circuits, it became a reasonably reliable indicator of how different types of waters would behave in heating and cooling circuits and the severity of scaling or corrosion to be expected. LSI guidelines for HVAC water circuits indicate scaling at +1.5 or greater and corrosion at 0.0 getting more severe as the LSI becomes more negative.

“Scaling indexes give little or no attention to chloride and sulphate content which are among the most widely recognised contributors to corrosion.”

As the LSI expanded in popularity, particularly amongst municipalities who applied it to many thousands of water distribution lines, more inaccuracies in scaling and corrosion predictions began to appear as well as some totally wrong predictions. Further investigations revealed that water containing unusual ratios of dissolved substances along with the ubiquitous calcium carbonate were the main sources of these LSI anomalies as well as water containing small amounts of strong alkalis such as caustic soda [NaOH] which cause higher than normal pH values.

In 1944 John Ryznar had seen that it was, surprisingly, possible for low hardness and high hardness waters to both have the same LSI. To get around this problem he created what is now known as the Ryznar Stability Index

RSI = 2pHs – pH

By reversing the positions of the two variables (pH and pHs), Ryznar obtained values which more accurately predicted the severity of scaling tendencies and, in addition, were always positive, falling within the range of +1 to + 13 which is close enough to be consistent with the 0 to 14 range of pH.

The RSI became generally adopted in place of the LSI as a better indicator of potential corrosion of mild steel.

Practical guidelines for applying the RSI to both closed and evaporative water circuits adopted the following RSI values –

< 5.5

definitely scaling

5.5 to 7.5

very small amounts of scaling or corrosion

> 7.5

definitely corrosive


Through ease of use and improved accuracy, the RSI became the practical successor to the LSI.

40 years went by until any alteration was made to the RSI mainly to give it greater accuracy over a wider range of water types. The change was replacing pH by another calculated pH known as the equilibrium pH or pHeq, an index derived from water alkalinity analyses. This new index became known during the early 1980s as the Puckorius Scaling Index [PSI] where

PSI = 2(pHs) – pHeq.

The PSI has an identical structure to the RSI and the calculated values result in numbers of similar magnitude. While the PSI appears to be an improvement over the LSI and RSI for many applications, it is not completely free of inaccuracies.

LSI, RSI and PSI are still used by water technologists today because of simple quick calculations which are sufficiently accurate to run the majority of heating and cooling water circuits as close to their cost-efficient optimums as is practically possible. A more rigorous assessment of the potential for calcium carbonate scale to form under varying conditions of heat transfer has been developed for improved coverage of water circuit profiles over their complete operating ranges.

This is the Calcium Saturation Index [CSI] which requires a large number of separate calculations therefore software tools such as the popular WaterCycle are used for rapid calculation of CSI values and often of other relevant water parameters at the same time.

One other area in which a more specialised scaling prediction index has been developed is where waters contain very high amounts of sodium chloride, specifically sea water widely used in marine engine cooling and other heat transfer circuits such as those in nuclear power stations.

For high salt [sodium chloride] content the Stiff & Davis Stability Index (S&DSI) is used to express the scaling potential for calcium carbonate. The data needed to calculate the S&DSI is the same as the data needed to calculate the LSI.

RSI and LSI are still the most widely used assessments for anticipated corrosion enabling counter-measures to be specified at an early stage of a project. Calculating possible corrosion rates has never been possible on a scientific basis so it has become generally accepted that proven anti-corrosion treatment should be used in any water circuits where corrosion is a possibility.

Scaling indexes give little or no attention to chloride and sulphate content which are among the most widely recognized contributors to corrosion. Paul Puckorius, co-developer of the PSI has suggested that cooling water – and presumably also heating water in HVAC installations – is always corrosive, mainly because of the presence of dissolved oxygen and dissolved solids. This is true even when the water is scale-forming, and particularly true if it is not scale-forming.