Langelier Saturation Index

\[LSI=pH-pH_s\]

Variables

LSILangelier Saturation Index (-)

pHmeasured water pH (-)

pHssaturation pH (-)

TDStotal dissolved solids (mg/L)

Twater temperature (°C)

CaHcalcium hardness as CaCO3 (mg/L)

Alktotal alkalinity as CaCO3 (mg/L)

ATDS factor (-)

Btemperature factor (-)

Ccalcium hardness factor (-)

Dalkalinity factor (-)

Description

What is this formula?

The Langelier Saturation Index (LSI) predicts whether water tends to precipitate calcium carbonate scale or dissolve existing mineral deposits.

When to use it

Use it when evaluating cooling towers, boilers, drinking water systems, industrial water treatment, swimming pools, desalination plants, and distribution networks.

Example

Data:

pH = 7.8

TDS = 500 mg/L

T = 25 °C

CaH = 150 mg/L

Alk = 120 mg/L

Formula:

LSI = pH − pHs

Intermediate calculations:

A = (log(500)-1)/10 = 0.170

B = -13.12·log(25+273)+34.55 = 2.09

C = log(150)-0.4 = 1.776

D = log(120) = 2.079

pHs = (9.3+A+B)-(C+D)

pHs = 7.705

LSI = 7.8 − 7.705

Result:

LSI = 0.095

Applications

Water treatment, cooling towers, boilers, reverse osmosis systems, swimming pools, municipal water systems, corrosion control, and scaling prevention.

Note

LSI is an empirical index, not a physical law. Positive values generally indicate a tendency to form calcium carbonate scale, while negative values indicate corrosive tendencies. Several modified saturation indices exist and may be preferred for high-salinity waters or specialized industrial applications.