Langelier Saturation Index (LSI)
The Langelier Saturation Index is a means of evaluating water quality data to determine if the water has a tendency to form a chemical scale. In order to use this index, the following laboratory analysis is needed: pH, conductivity, total dissolved solids, alkalinity, and total hardness. The Saturation Index is typically either negative or positive and rarely 0. A Saturation Index of zero indicates that the water is "balanced" and is less likely not to cause scale formation. A negative Saturation Index suggests that the water is undersaturated with respect to carbonate equilibrium and the water may be more likely to have a greater corrosive potential.
The Langelier Index is a gauge of whether a water will precipitate or dissolve calcium carbonate. It is calculated using the pH, alkalinity, calcium concentration, total dissolved solids, and water temperature of a water sample collected at the tap using the followig formula:
LSI = pH - pHs
pHs takes into account the pH of Saturation, temperature (°C), Total Dissolved Solids (TDS in mg/L), Alkalinity (mg/L as CaCO3 ), Calcium Hardness (mg/L as CaCO3 ).
pHs = (9.3 + A + B) - (C + D)
Where:
9.3 is a constant
Constant A is a correction for the ionic strength of the sample. This constant is based on TDS.
Constant B takes into account the effect of temperature.
Value C is obtained from hardness correspondig to calcium hardness.
Value D is obtained from hardness corresponding to total alkalinity.
The LSI is the difference between the actual pH of the solution and pHs calculated from the values determined above.
. If:
It is important to remember that the LSI value isn ot a quantitative measure of calcium carbonate saturation or corrosion.
A perfect score on the Langelier Saturation Index (LSI) is zero (0.00). Zero is perfectly balanced water; saturated with the perfect amount of calcium carbonate, and has a stable pH. Being the universal solvent, if water is out of balance, it will naturally try to find its own balance and equilibrium, because it wants to be at 0.00 LSI. The LSI is basically a way to determine if water is corrosive (negative LSI) or scale-forming (positive LSI). LSI between -0.30 and +0.30 is the widely accepted range, while 0.00 is perfect equilibrium. Water can only hold so much calcium in solution. Water will stop at nothing to find equilibrium...so when it's hungry for calcium, it will aggressively look for it. When the water does not have a readily available source of calcium, corrosion and degradation can occur anywhere in the equipment. Another important thing to remember: water cannot over-saturate itself. It will take only what it can hold, and nothing more.
Analogy:
When you add sugar to your drink and stir it, it will dissolve. Add more sugar, and it will dissolve too. But at some point, when you add too much sugar, what happens to that sugar? It just swirls around at the bottom of the glass, unable to dissolve. That's because you have exceeded the drink's saturation limit; it can no longer hold any more sugar. If you insist upon dissolving more sugar, there are a couple of things you can do. First, you can make it a much larger drink, which changes the volume, and reduces the saturation. You can also increase the temperature, say, to a boil. If you have ever made desserts, you know that boiling water can hold a LOT more sugar than cold water, because its saturation properties have changed. Now, replace the word "sugar" with "calcium". The LSI tells us how saturated the water is with calcium. The properties can change with six factors, not just water temperature. And it's worth noting that unlike sugar, cold water can hold more calcium in solution, and that's why cold water is more aggressive than warm.
Sometimes an operator is already given the calculated values of A, B, C and D in the pHs formula. However, sometimes you need to be able to determine it yourself. Here's the breakdown on how to determine the values of the constants:
Constant A refers to the TDS value in the equation:
A = (log10 x (TDS) - 1) / 10
Constant B refers to the temperature value in the equation:
B = (-13.12 x log10(Temp. + 273)) + 34.55
Constant C refers to the calcium hardness value in the equation:
C = log(Ca) - 0.4
Constant D refers to the alkalinity value in the equation:
D = log10(Alk)
Once all these values are determined you can plug them into the LSI formula:
LSI = pH - pHs
So, let's work an examples in which you have determine all the constant values.
Example:
A sample of water from the tap has the following parameters: temperature = 25°C; pH = 8.0, TDS = 500 mg/L; Calcium as CaCO3 = 250 mg/L; Alkalinity as CaCO3 = 100 mg/L. Determine the LSI of the water.
First we need to determine the values of all the constants:
A = (log10 x (TDS) - 1) / 10
A = (log10 x (500) - 1) / 10
A = 0.17
See how to enter it into the calculator.
B = (-13.12 x log10(Temp. + 273)) + 34.55
B = (-13.12 x log10(25 + 273)) + 34.55
B = 2.08
See how to enter it into the calculator.
C = log(Ca) - 0.4
C = log(250) - 0.4
C = 2.0
See how to enter it into the calculator.
D = log10(Alk)
D = log10(100)
D = 2.0
See how to enter it into the calculator.
Now that we know the values of all the constants, we can determine pHs. Sometimes you are already given the constants, so you can skip straight to this step.
pHs = (9.3 + A + B) - (C + D)
pHs = (9.3 + 0.17 + 2.08) - (2.0+ 2.0)
pHs = 7.6
Finally we can determine the LSI of the water:
LSI = pH - pHs
LSI = 8.0 - 7.6
LSI = 0.4
By this value (0.4) we know that the water is slightly scale forming. It meets the guidelines because the value is positive and the value of pHs (pH solution) is less than the actual pH of 8.0.