Langelier Saturation Index from a Full Water Analysis

Hand this page the five numbers off a water analysis and it returns the Langelier index in one step: $\mathrm{LSI} = \mathrm{pH} - \mathrm{pH_s}$, with the saturation pH built from temperature-dependent equilibrium constants and an activity correction, the way Standard Methods writes it, and not from the four-term handbook shortcut. Positive means the water is supersaturated with calcium carbonate and will tend to lay it down. Negative means undersaturated: it will dissolve calcite, and it offers bare steel no protective film. Within about half a unit of zero, the sign is inside the uncertainty of a field pH reading and a routine lab analysis, so do not read a direction into it.

The refinement that matters most at high pH is what happens to the alkalinity. A titration counts everything that takes up acid: $\mathrm{Alk} = [\mathrm{HCO_3^-}] + 2[\mathrm{CO_3^{2-}}] + [\mathrm{OH^-}] - [\mathrm{H^+}]$. The index wants bicarbonate alone. At pH 7.5 the two are the same number to within a percent. At pH 8.8 and 35 °C, a water titrating 300 mg/L carries only about 267 as bicarbonate; the other tenth is carbonate and hydroxide. Feed the whole 300 into the saturation pH and the index comes out too high by the log of that ratio. This page separates them using the measured pH, and prints the split beside the answer so you can see what it did.

Where people get it wrong. First, total hardness is not calcium hardness, and entering it inflates the index. Second, an index quoted without a temperature is not a number anyone can use: the same analysis is a different index at the basin, at the heat-exchanger skin and in the sample bottle on the bench an hour later. Third, the pH has to be measured on site. A sample that has sat open loses or gains carbon dioxide and its pH drifts by tenths, and the index moves one for one with it. Fourth, LSI is a tendency, a statement about which way the water will move toward equilibrium. It says nothing about how fast, which is why a tower can run for years at +2 with a good inhibitor and foul in a week at +1 without one.

It is also blind to everything that is not calcium carbonate. Silica, calcium sulphate, calcium phosphate and zinc all have their own limits, and chloride and sulphate will pit steel and stainless whatever the LSI says, which is what the Larson–Skold index is for. There is no ion pairing here either: calcium tied up in ion pairs is not subtracted, so high-sulphate and high-TDS waters read a little more scale-forming than they do in speciation software. Take it as the conservative side of the same answer.