**3.2 Langelier saturation index (LSI)**

The most commonly used index that provides a measure of the stability of a water with respect to its degree of calcium carbonate saturation is the Langelier Saturation Index (LSI). This is due to the fact that it provides both qualitative representation of the corrosivity of water, and is relatively easy to calculate. First proposed by Prof. WF Langelier in 1936 [14], the Langelier Saturation Index can be calculated as follows:

$$\mathbf{L}\mathbf{S}\mathbf{I} = \mathbf{p}\mathbf{H} - \mathbf{p}\mathbf{H}\_{\mathrm{s}}$$

where pHs represents the saturation pH of the water, in which condition the water is in the equilibrium state and neither dissolves, nor precipitates calcium carbonate.

The saturation pH is a complex iterative calculation, similar to the calculation for CCPP, requiring a program to accurately determine it. A simplification of this can be performed by using the ABCD method, which is calculated as follows:

$$\mathbf{pH\_s} = (\mathbf{9.3} + \mathbf{A} + \mathbf{B}) - (\mathbf{C} + \mathbf{D})\mathbf{j\_s}$$

and the parameters defined as:

A = (log [TDS] � 1)/10. B = �13.12 � log (°C + 273) + 34.55. C = log [Ca+2]. D = log [Alk].

with TDS expressed in mg/l, Ca2+ expressed as mg/l as CaCO3, and Alk expressed as equivalent CaCO3 in mg/l. The plots of **Figure 1** show the slight discrepancy between these two calculation methods.

Waters with positive LSI are oversaturated and tend to form a protective layer of calcium carbonate (scaling effect) on the pipe walls. Highly positive LSI are

**Figure 1.** *Relationship between calcium hardness and saturation pH for water with 80 ppm of alkalinity (as CaCO3).*

corresponding to high precipitation effect resulting in incrustation. On the other hand, a water with negative LSI value is typically under-saturated with respect to calcium carbonate and so it will potentially dissolve the protective calcium carbonate scale and so be potentially corrosive. LSI alone however, cannot provide an indication of the true indication of the corrosivity of water, as the pH also needs to be considered. A water with LSI of �0.5 at pH 6.0 is much more corrosive than a water with LSI -0.5 at pH 8.0 for example.

LSI is not a reliable indicator of the corrosive tendencies of potable water and that the use of this index together with other models such as empirical determination of chloride, sulfate, alkalinity, dissolved oxygen, buffer capacity, calcium and length of time of exposure would provide information that is more reliable [15].

#### **3.3 Ryznar stability index (RI)**

Another parameter similar to the LSI is the Ryznar Stability Index [16], which is looks at the relationship between the saturation pH of the water (with respect to calcium carbonate) and the actual pH of the water. It is given by:

$$\text{RSI} = \text{2pH}\_{\ast} - \text{pH}$$

Based on the value assumed by the RSI index, waters are classified as:


This index provides a reasonably good estimate of expected scale formation even in the presence of phosphate-based inhibitors.

#### **3.4 Puckorius scaling index (PSI)**

Similar to both the Langelier Saturation Index and the Ryznar Stability Index, also the Puckorius Scaling Index (PSI) also considers the corrosion potential of the water based on the calcium carbonate saturation of the water [17]. Instead of considering the actual pH of the water however, it defines a new parameter – the equilibrium pH and is defined as:

$$\text{PSI} = \mathcal{2}\left(\text{pH}\_{\text{EQ}}\right) - \text{pH}\_{\text{s}}$$

where, pHs is the saturation pH as calculated for the previous indices, and pHEQ is the equilibrium pH as calculated by:

$$\text{pH}\_{\text{EQ}} = \text{1.465} \times \log \text{ [Alk]} + \text{4.54}$$

*Remineralization and Stabilization of Desalinated Water DOI: http://dx.doi.org/10.5772/intechopen.99458*

Thus the water will be:

