Langelier Saturation Index (LSI)

The Langelier Saturation index (LSI) is an equilibrium model derived from the theoretical concept of saturation and provides an indicator of the degree of saturation of water with respect to calcium carbonate. It can be shown that the Langelier saturation index (LSI) approximates the base 10 logarithm of the calcite saturation level. The Langelier saturation level approaches the concept of saturation using pH as a main variable. The LSI can be interpreted as the pH change required to bring water to equilibrium.

Water with a Langelier saturation index of 1.0 is one pH unit above saturation. Reducing the pH by 1 unit will bring the water into equilibrium. This occurs because the portion of total alkalinity present as CO₃^2- decreases as the pH decreases, according to the equilibria describing the dissociation of carbonic acid:

If LSI is negative: No potential to scale, the water will dissolve CaCO₃
If LSI is positive: Scale can form and CaCO₃ precipitation may occur
If LSI is close to zero: Borderline scale potential. Water quality or changes in temperature, or evaporation could change the index.

The LSI is probably the most widely used indicator of cooling water scale potential. It is purely an equilibrium index and deals only with the thermodynamic driving force for calcium carbonate scale formation and growth. It provides no indication of how much scale or calcium carbonate will actually precipitate to bring water to equilibrium.

It simply indicates the driving force for scale formation and growth in terms of pH as a master variable. In order to calculate the LSI, it is necessary to know the alkalinity (mg/l as CaCO₃), the calcium hardness (mg/l Ca²⁺ as CaCO₃), the total dissolved solids (mg/l TDS), the actual pH, and the temperature of the water (^oC). If TDS is unknown, but conductivity is, one can estimate mg/L TDS using a conversion table such as the one presented here. LSI is defined as:

LSI = pH - pH_s

Where:
- pH is the measured water pH
- pH_s is the pH at saturation in calcite or calcium carbonate and is defined as:

pH_s = (9.3 + A + B) - (C + D)

Where:
- A = (Log₁₀ [TDS] - 1) / 10
- B = -13.12 x Log₁₀ (^oC + 273) + 34.55
- C = Log₁₀ [Ca²⁺ as CaCO₃] - 0.4
- D = Log₁₀ [alkalinity as CaCO₃]

Click here to see an example of a Langelier Index calculation.

However, there is some controversy concerning the correlation of these indices, and particularly the LSI, with the corrosivity of waters. While some sectors of the water management industry squarely use the indices as a measure of the corrosivity of their waters, more alert specialists, including our dear friends Paul Dillon and Bert Krisher, are very cautious as to how far one can extrapolate the indices to such usage. The Corrosion Doctors have recorded some bits of discussion held on this very topic on the NACE Corrosion Network discussion group. This discussion was held between 24 July and 27 July 2000. Click here to read more on this topic.

Langelier Saturation Index (LSI)

Consult the Water Glossary, Water Cooling Towers