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# 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 CO32- 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 - pHs

• Where:

• pH is the measured water pH

• pHs is the pH at saturation in calcite or calcium carbonate and is defined as:

pHs = (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]