Scaling and corrosion indices

LSILangelierRyznarRSIPuckoriusPSILarson-Skoldsaturation index

Langelier, Ryznar, Puckorius, Larson–Skold and coupon corrosion rate — the indices that say whether water will scale or eat the pipe.

Langelier Saturation Index (LSI)

\mathrm{LSI} = \mathrm{pH} - \mathrm{pH_s}

The classic calcium-carbonate scaling index: measured pH minus the saturation pH, positive for scaling and negative for corrosive water.

Saturation pH (pHs) for Langelier's Index

\mathrm{pH_s} = (9.3 + A + B) - (C + D)

Computes the pH at which water is saturated with calcium carbonate from its TDS, temperature, calcium hardness and total alkalinity as CaCO₃.

Ryznar Stability Index (RSI)

\mathrm{RSI} = 2\,\mathrm{pH_s} - \mathrm{pH}

An empirical scaling index scaled so that values below about 6 predict scale and values above about 7 predict corrosion in the same water.

Puckorius (Practical) Scaling Index

\mathrm{PSI} = 2\,\mathrm{pH_s} - \mathrm{pH_{eq}}, \quad \mathrm{pH_{eq}} = 1.465\,\log_{10}\mathrm{Alk} + 4.54

A Ryznar variant that replaces measured pH with an equilibrium pH derived from alkalinity, giving a truer scaling call in poorly buffered cooling water.

Larson–Skold Index

\mathrm{LS} = \dfrac{\frac{\mathrm{Cl}}{35.45} + \frac{\mathrm{SO_4}}{48.03}}{\frac{\mathrm{Alk}}{50.04}}

Ratio of aggressive chloride and sulphate equivalents to protective bicarbonate alkalinity, predicting pitting of mild steel in distribution water.

Corrosion Rate from Coupon Weight Loss

P = \frac{m \, Y}{\rho \, A \, t}

Uniform corrosion rate as metal thickness lost per year, from a coupon's weight loss, density, exposed area and exposure time.

How they fit together

All of these ask one question — is this water saturated with calcium carbonate? — and answer it by comparing the measured pH against the saturation pH computed from calcium, alkalinity, total dissolved solids and temperature. LSI is the difference and is signed: positive scales, negative dissolves scale and exposes metal. Ryznar rescales the same inputs onto an empirical 4-to-10 band. Puckorius substitutes an equilibrium pH calculated from alkalinity for the measured pH, which stops a shot of acid or a slug of caustic from flattering the result. Larson–Skold is a different question entirely: the ratio of chloride and sulphate to bicarbonate, which is about pitting of steel rather than carbonate scale.

Run LSI first because everything is calibrated to it, and read it as a direction, not a rate — LSI +0.5 tells you calcium carbonate wants to come out of solution, not how fast or where. Use Ryznar or Puckorius when the system is poorly buffered or the pH swings, and Puckorius specifically on cooling towers, where it consistently predicts real behaviour better. Use Larson–Skold when the water is high in chloride or sulphate and the steel is pitting despite a comfortable LSI. The universal mistake is calculating LSI at the bulk water temperature: scale forms on the hottest surface in the system, so a tower at 85 °F with LSI −0.1 can be well positive on a chiller tube skin at 110 °F. Run the index at skin temperature, and confirm what it predicts with coupons, which measure what actually happened in mils per year.