Larson–Skold Index

Also known as larson ratio · chloride sulfate ratio

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

Worked example: Cl 50, SO4 80, Alk 150 mg/L → LS = 1.026 — press Try an example to run it live, then adjust anything.

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Larson–Skold Index explained

Langelier and Ryznar only ever look at calcium carbonate. Larson and Skold, working on Great Lakes water for the Illinois State Water Survey in 1958, went after the other half of the story: chloride and sulphate are penetrating anions that break down the passive film on mild steel, while bicarbonate alkalinity helps repair it. Their index is a straight equivalents ratio — divide each ion by its equivalent weight (35.45 for Cl⁻, 48.03 for SO₄²⁻, 50.04 for alkalinity as CaCO₃) and compare aggressors to protectors. A water with 50 mg/L chloride, 80 mg/L sulphate and 150 mg/L alkalinity gives (1.410 + 1.666)/2.998 = 1.03.

Read it in thirds: below 0.8 chloride and sulphate are unlikely to interfere with film formation, 0.8 to 1.2 means corrosion rates run higher than open-recirculating norms, and above 1.2 you should expect localized pitting rather than general wastage. This is the index that explains why a softened, high-chloride makeup can hold a perfect +0.2 LSI and still perforate a carbon-steel line in eighteen months, and why blowing down a tower on conductivity alone concentrates exactly the ions Larson–Skold cares about. Note that it is silent on stainless and copper — for those, chloride's absolute concentration and temperature matter more than the ratio.

Larson–Skold Index formula

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

Where

$\mathrm{LS}$ = Larson–Skold Index
$\mathrm{Cl}$ = Chloride as Cl⁻ (%)
$\mathrm{SO_4}$ = Sulphate as SO₄²⁻ (%)
$\mathrm{Alk}$ = Total alkalinity as CaCO₃ (%)

Missing one of these? Work it out first, then come back

Chloride as Cl⁻ — Cycles of Concentration from Chloride, Percent Yield
Sulphate as SO₄²⁻ — Percent Yield, Percent Composition of an Element
Total alkalinity as CaCO₃ — Saturation pH (pHs) for Langelier's Index, Langelier Saturation Index from a Full Water Analysis

Part of this formula set

Scaling and corrosion indices

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