# Langelier Saturation Index (LSI)

The Langelier Saturation Index (or Langelier Stability Index) is a calculated parameter to predict the calcium carbonate stability of water. It is defined as the difference between the actual pH of the water and the saturation pH (abbreviated by pHS):

 (1) LSI   =   pH – pHS

Based on the numerical value of LSI aqion uses the following classification:

 LSI ≈ 0 The water is in equilibrium with calcite. LSI < -0.03 The water tends to be corrosive. LSI >  0.03 The water tends to be scale forming.

The results are displayed in a special window as shown here.

In literature several formulas and approximations are available to calculate the saturation pH, i.e. pHS, that enters Eq.(1). aqion does not need to use such formulas because it already rests on strict reaction thermodynamics (provided by PhreeqC and its thermodynamic database).

Note that LSI is not exactly the same as the saturation index of calcite, SI, but it is a good approximation of SI: SI ≈ LSI. This is shown in the ‘Mathematical Derivation’ below.

Just as any other saturation index, LSI only indicates the presence of a driving force; it does not guarantee that calcite will actually precipitate, but informs us that the tendency to scale will actually occur.

Mathematical Derivation of the LSI Equation

 (2) CaCO3(s) = Ca+2 + CO3-2 log KS = -8.48 (3) HCO3- = H+ + CO3-2 log K2 = -10.33

Substracting Eq.(3) from Eq.(2) leads to

 (4) CaCO3(s) + H+   =   Ca+2 + HCO3- log KS2 = log KS – log K2 = 1.85

The equilibrium constant KS2 is related to the equilibrium state, whereas the ion activation product (IAP) refers to the actual state:

 (5) KS2 = {HCO3-}eq ∙ {Ca+2}eq / {H+}eq (6) IAP = {HCO3-}act ∙ {Ca+2}act / {H+}act

The species in curly brackets indicate activities (rather than concentrations). The ratio of the above quantities yields the saturation index of calcite:

 (7) $$SI = \ log \, \dfrac{I\! AP}{K_{S2}} \ = \ log \,\left(\dfrac{\{HCO_3^-\}_{act} \cdot \{Ca^{+2}\}_{act} }{\{HCO_3^-\}_{eq} \cdot \{Ca^{+2}\}_{eq}} \cdot \dfrac{\{H^+\}_{eq}}{\{H^+\}_{act}}\right)$$

Using the common definition of pH and pHS,

 (8) pH   =   – log {H+}act and pHS   =   – log {H+}eq

and the abbreviation

 (9) $$A \ = \ \dfrac{\{HCO_3^-\}_{act} \cdot \{Ca^{+2}\}_{act} }{\{HCO_3^-\}_{eq} \cdot \{Ca^{+2}\}_{eq}}$$

In the approximation, A ≈ 1, it yields the final result:

 (11) SI   ≈   (pH – pHS)   =   LSI

This shows that LSI is not exactly the same as the saturation index SI, but LSI becomes a good approximation for SI when Eq.(9) approaches 1 (which is valid in most cases).

Remarks & Footnotes

1. Here and in the following, the shorter notation ‘log x’ is used for the decadic logarithm: log10 x.