Langelier equation

A convenient method of interpreting water analysis for the purpose of determining the calcium carbonate solubility equilibrium conditions is embodied in the Langelier equation. The Langelier equation can be used to... 

S Stability Index (Stiff-Dayis Modification OF Langelier Equation)... 

The solubility product of salt changes with temperature and the concentration of the ions present in solution. In oilfield brines, if the surface solubility produced is smaller than their solubility product under down-hole formation, scale formation would occur. Under such conditions, the water is called unstable water. The StabiUty Index (S/) is used to predict the tendency of ions to form scales from oilfield brines which are highly corrosive and encountered during drilling process. The Stiff-Davis Modification of the Langelier equation is used to predict calcium carbonate precipitation from the brines and is given by... 

The mathematical relationship between carbon dioxide, calcium bicarbonate and calcium carbonate has been studied by several workers, including Langelier . The simpler form of his equation is... 

LANGELIER AND RYZNAR EQUATIONS SATURATION AND STABILITY INDEX... 

When the number of concentrations of the circulating water is in the order of 3-7, some of the salts dissolved can exceed their solubility limits and precipitate, causing scale formation in pipes and coolers. The purpose of the treatment of the cooling water is to avoid scale formation. This is achieved by the injection of sulfuric acid to convert Ca and Mg carbonates (carbonate hardness) into more soluble sulfates. The amount of acid used must be limited to maintain some residual alkalinity in the system. If the system pH is reduced to far below 7.0, it would result in an accelerated corrosion within the system. As stated earlier, scale formation and/or corrosion tendency is defined by the Saturation Index (Langelier Index) and Stability Index (Ryznar equation). 

Langelier Saturation Index is calculated using equation 3.10 ... 

Langelier Saturation Index is valid up to about 4,000 ppm TDS. At higher TDS concentrations, the Stiff-Davis Saturation Index (SDSI) is used, Equation 3.12 ... 

List (but do not calculate) the equations required to determine the amount of Ca(OH)2 required to produce a saturated water from one that has a negative Langelier Index. 

For calculating pHj in order to solve the equation, there are tables for values of pK - pK ) at various dissolved solids contents and various temperatures. The calcium content and alkalinity can be easily determined by the plant chemist. If the Langelier index (pH-pH,) is zero, the water is just saturated with CaCOj. If the index is positive, the water is supersaturated with and will tend to deposit CaC03 as well as be more or less scale forming and noncorrosive. If the index is negative, the water tends to be corrosive. 

Equation (29.29) was derived by Langelier [3] on the assumption that K and K2 are based on concentrations (moles/liter) rather than on activities. For example, referring to (29.24), if K, is the true activity product, then Ks = Ksjl, where y refers to the mean ion activity coefficient for CaCOs. The activity coefficient was approximated by Langelier using the Debye-Htickel theory, -logy = where p is the ionic strength and z is the valence. Hence,... 

The primary factor affecting long-term corrosion is whether a water does or does not form scales, which in turn depends on hardness and pH. This property is determined by calculating the Langelier index or the Ryzner stability index. The simpler form of Langelier s equation is ... 

Equilibrium curves can be determined and, on the basis of a given water composition, used to establish whether a water is scaling (not corrosive) or non-scaling (corrosive). Many different methods have been proposed for prediction of the formation of CaCOa. Commonly used equations or indices are the Langelier Saturation Index, LSI (Langelier, 1936) and the Stability Index, RSI, a modification of the LSI proposed by Ryznar (1944). In the German literature the LSI is known simply as the Saturation Index, Is (Morbe et al., 1987). These indices describe the algebraic difference between the actual pH of the water and the calculated pH at which it would be saturated with calcium carbonate ... 

Langelier developed an equation setting forth the conditions of the carbonate equilibrium. By the use of this equation, the pH of water at equilibrium can be calculated. If the pH is higher than the calculated pH, the water has a tendency to form scale if it is lower, the water has a tendency to be corrosive. Langeher s equation can be expressed in a single form as follows ... 

---