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Case Study: Calcium Carbonate Scaling in Water Mains
A small layer of calcium carbonate scale on water mains protects them from corrosion, but heavy scale
reduces the hydraulic capacity. Finding the middle ground (protection without damage to pipes) is a
matter of controlling the pH of the water. Two measures of the tendency to scale or corrode are the
Langlier saturation index (LSI) and the Ryznar stability index (RSI). These are:

LSI = pH pH s
–
RSI = 2pH s – pH

where pH is the measured value and pH s the saturation value. pH is a calculated value that is a function of
temperature (T), total dissolved solids concentration (TDS), alkalinity [Alk], and calcium concentration [Ca].
[Alk] and [Ca] are expressed as mg/L equivalent CaCO 3 . The saturation pH is pH s = A − log 10 [Ca] − log 10 [Alk],
2.5 µ
where A = 9.3 + log 10 (K s /K 2 ) + ----------------- , in which µ is the ionic strength. K s , a solubility product, and K 2 , an
µ +
5.5
ionization constant, depend on temperature and TDS.
As a rule of thumb, it is desirable to have LSI = 0.25 ± 0.25 and RSI = 6.5 ± 0.3. If LSI > 0, CaCO 3
scale tends to deposit on pipes, if LSI < 0, pipes may corrode (Spencer, 1983). RSI < 6 indicates a tendency
to form scale; at RSI > 7.0, there is a possibility of corrosion.
This is a fairly narrow range of ideal conditions and one might like to know how errors in the measured
pH, alkalinity, calcium, TDS, and temperature affect the calculated values of the LSI and RSI. The
variances of the index numbers are:

Var(LSI) = Var(pH s ) + Var(pH)
2
Var(RSI) = 2 Var(pH s ) + Var(pH)

Given equal errors in pH and pH s , the RSI value is more uncertain than the LSI value. Also, errors in
estimating pH s are four times more critical in estimating RSI than in estimating LSI.
Suppose that pH can be measured with a standard deviation σ = 0.1 units and pH s can be estimated
with a standard deviation of 0.15 unit. This gives:

2
2
Var(LSI) = (0.15) + (0.1) = 0.0325 σ LSI = 0.18 pH units
2 2
Var(RSI) = 4(0.15) + (0.1) = 0.1000 σ RSI = 0.32 pH units
Suppose further that the true index values for the water are RSI = 6.5 and LSI = 0.25. Repeated measure-
ments of pH, [Ca], [Alk], and repeated calculation of RSI and LSI will generate values that we can expect,
with 95% confidence, to fall in the ranges of:

LSI = 0.25 ± 2(0.18) −0.11 < LSI < 0.61

RSI = 6.5 ± 2(0.32) 5.86 < RSI < 7.14

These ranges may seem surprisingly large given the reasonably accurate pH measurements and pH s
estimates. Both indices will falsely indicate scaling or corrosive tendencies in roughly one out of ten
calculations even when the water quality is exactly on target. A water utility that had this much variation
in calculated values would find it difficult to tell whether water is scaling, stable, or corrosive until after
many measurements have been made. Of course, in practice, real variations in water chemistry add to the
“analytical uncertainty” we have just estimated.
© 2002 By CRC Press LLC