#### Saturation Calculation

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Whether the job involves starting up a brand-new plaster pool or maintaining chemistry in an old fiberglass vessel, pool professionals know that a proper understanding of water balance is essential.

Balanced water is especially crucial during a plaster pool’s 28-day start-up period. In fact, it often makes all the difference between a smooth, durable surface and a scarred disaster zone.

Though some problems resulting from improper water balance, such as calcium scaling, usually can be corrected if caught in time, others, such as etching, can permanently ruin weeks of plaster work in less than a single day. Once a pool project goes south, millions of dollars may suddenly be at stake in court, as the customer, and judge, demand answers about what wrecked the job — sloppy plastering practices or inaccurate water-balance calculations.

On the other hand, a strong grasp of the physical principles underlying water balance can help prevent these sorts of disasters altogether — or at least correct them, and identify their causes, before they get out of hand. Careful calculation and diligent record-keeping typically go a long way toward keeping the pool service technician out of legal hot water.

One popular method for calculating water balance is the Langelier Saturation Index — often abbreviated as “LSI” or simply “SI” — which uses five basic factors to calculate the water’s overall tendency to scale or corrode the pool’s surface. Though it might seem complex at first glance, calculating the LSI of a pool’s water essentially comes down to simple arithmetic.

Here, we’ll walk through the calculation process step by step, clearing up a few tricky spots and debates along the way.

### A Repurposed Index

The LSI was first developed in 1936 by Professor W.F. Langelier, a chemist working at the University of California, Berkeley. Professor Langelier’s original goal was to create a formula that would indicate whether water stored in large boilers would tend to create etching on the one hand, or calcium scale on the other.

Below is his original formula:

### AF: ALKALINITY FACTOR, CONSTANT: TDS CONSTANT)

Throughout the 1930s, calcium scale was causing major clogging problems in municipal water storage, while etching was considered less of a danger to the surfaces of metal boilers. However, the situation in swimming pools today is precisely the opposite: Calcium scaling usually can be treated, but etching often causes permanent damage to surfaces. Thus, today’s service professionals and scientists generally recommend that water be balanced toward the higher (potentially scaling) side of the LSI, rather than the lower (potentially etching) end.

The LSI is particularly helpful for plaster pools, because those surfaces tend to be especially vulnerable to aggressive or scaling water. In chemical terminology, the LSI is used to determine the degree of calcium carbonate saturation in a pool’s water — in other words, whether the water is more aggressive (undersaturated with calcium), and will tend to dissolve calcium carbonate out of the plaster; or whether it’s more scaling (oversaturated with calcium), and will tend to form calcium deposits on the pool’s surfaces.

Speaking in more general terms, balanced water creates a carbonate alkalinity buffer, which prevents the water’s pH from drifting too high or too low when alkaline or acidic substances are added to a pool.

In view of this background, the actual factors used in calculating LSI will make more sense. Now it’s time to delve into each factor in detail.

### 1 pH

#### Ideal range: 7.2 to 7.6

As many pool technicians know, pH is a measurement of a substance’s acidity or basicity — values below 7 are more acidic, while values above 7 are more basic. Not as well known is the fact that the pH scale is base-ten logarithmic: A pH of 5, for example, is ten times more acidic than a pH of 6, which, in turn, is ten times more acidic than a pH of 7 — making a pH of 5 one hundred times more acidic than a pH of 7.

This means even small changes in pH can create major changes in water chemistry — a shift from 7.8 to 7.5 doubles the concentration of calcium and carbonates needed to balance the water. Thus, many techs and scientists say that pH should be the first factor measured for LSI calculations, and it’s the one most important to measure with precision.

While not everyone agrees on the exact pH range that’s non-damaging to plaster surfaces, it has been widely agreed that a range of 7.2 to 7.6 is ideal. Some extend that range to 7.8 — and others as high as 8.2.

As can be seen in Graph A, when pH rises to 8 and above, more and more of the water’s carbonate alkalinity exists in the form of carbonate ions (CO32-), which tend to bond with calcium ions (Ca2+) to form calcium carbonate (CaCO3), the chemical compound that often causes cloudiness, precipitate and scale in plaster pools. In water with a pH around 7.4, however, the vast majority of carbonate alkalinity will be in the form of bicarbonate ions (HCO3-), which don’t provide any free carbonate ions for this reaction.

In short, pH should be tested — and, if possible, balanced into the ideal range — before any other LSI factors are adjusted.

### 2 Temperature (TF)

#### Ideal range: 0.6 to 0.9 (76° to 104° Fahrenheit)

Water temperature is perhaps the simplest of all the LSI factors to measure. For several reasons, it’s a significant influence on water’s tendency to etch or scale. Most importantly, hotter water accelerates the loss of carbon dioxide (CO2) from the pool, which causes pH to drift upward. More generally, the higher the water’s temperature, the faster chemical reactions will occur.

Another important aspect of temperature is related to a unique property of calcium: It’s more soluble at lower temperatures than at warmer ones. This means colder water is more corrosive to the surfaces of plaster pools.

Unlike pH, the actual temperature measurement is not the factor used when calculating LSI. Instead, the LSI uses a temperature factor (TF), which is a number corresponding to a particular temperature. Table B shows the TFs for a wide range of water temperatures.

It’s important not to try to estimate a decimal number between two TF values — instead, find the temperature on the chart that’s closest to the actual temperature measured in the water, and choose the TF that lines up with that temperature. Then, simply plug that TF value into the LSI equation.

### 3 Carbonate Alkalinity (AF)

#### Ideal range: 1.9 to 2.0(80 to 120 ppm carbonate alkalinity)

This measurement indicates the water’s ability to resist shifts in pH — higher total alkalinity readings indicate a greater resistance to pH shifts. Though Langelier’s original formula only called for a measurement of the water’s overall alkalinity, the complexity of modern pool chemistry requires that two different types of alkalinity be taken into account when performing total alkalinity calculations.

Most test kits measure total alkalinity, which indicates the overall alkalinity of the water. Much of this is carbonate alkalinity, which is contributed by bicarbonate (HCO3-) or carbonate ions (CO32-), depending on the water’s pH (see “pH” above). However, many pools today use cyanuric acid as a stabilizer — both in pure form, and as a component of dichlor or trichlor tablets — and this chemical contributes another type of alkalinity: Cyanurate alkalinity.

However, the LSI is focused on alkalinity’s ability to keep calcium carbonate in solution — and thus, only carbonate alkalinity should be taken into account for the calculation.

“Since the alkalinity factor used in the LSI calculation is based on bicarbonate alkalinity only, the titratable cyanurate alkalinity requires correction,” says Tom Metzbower, vice president of sales at Taylor Technologies in Sparks, Md. “Generally, this correction equates to one third of the cyanuric acid concentration.”

The percentage of alkalinity as carbonate can be separated from percentage as cyanurate through a simple process of multiplication and subtraction. In fact, cyanuric acid percentage varies quite predictably as a function of pH. Table C lists conversion factors for cyanurate alkalinity at a range of common pH values.

After finding the appropriate conversion factor on the table above, multiply this factor by the test kit’s actual cyanuric acid reading (in ppm). Then, subtract this product from the test kit’s total alkalinity reading (in ppm) to reach the correct carbonate alkalinity reading:

#### Carbonate Alkalinity = Total Alkalinity – (Cyanuric Acid x F)

Now comes the final step in applying alkalinity to LSI calculations. On Table D, simply find the alkalinity ppm value that most closely matches the carbonate (not total) alkalinity value calculated.

As with the temperature factor, don’t try to estimate an alkalinity factor between two AF values on the chart — just find the ppm value closest to the calculated carbonate alkalinity, then apply the alkalinity factor that matches it.

### 4 Calcium hardness (CF)

#### Ideal range: 1.9 to 2.2 (200 to 400 ppm calcium hardness)

This measurement simply reflects the amount of calcium dissolved in the water. However, some kits test for total hardness, which measures other chemicals in the water as well. Thus, it’s important to check that the test is measuring calcium hardness only.

Though the level of calcium is an important contributor to water balance, a calcium hardness reading alone does not predict how likely calcium is to precipitate (fall) out of solution — pH is actually the main factor in determining this likelihood, with alkalinity also playing a major role. Thus, these three factors are all closely intertwined.

Converting calcium hardness for use in the LSI is straightforward. Find the ppm reading on Table E to the right that most closely matches the test kit’s calcium hardness reading, and apply that calcium hardness factor (CF) to the equation.

As with the temperature and alkalinity conversions, just choose the number on the chart that falls closest to the test kit’s calcium hardness ppm value, and plug in the matching CF value.

### 5 Total dissolved solids (TDS)

#### Constant Ideal range: Non-salt pools, 12.1 to 12.19 (300 to 1,800 ppm); salt pools, 12.29 to 12.35 (2,500 to 3,500 ppm)

The final factor in an LSI calculation depends on the water’s dissolved solids. The TDS value is not plugged directly into the equation at all; rather, it’s used to determine whether Langelier’s original constant of 12.1 is suitable, or if a slightly higher constant should be used. This is because some modern pool systems — especially those that generate chlorine from salt — carry much higher levels of TDS than the boilers Langelier was studying back in the 1930s.

As Table F shows, most non-salt pools will still use Langelier’s original constant of 12.1. However, saline pools, or others with unusually high TDS, may need to apply a slight adjustment factor.

“If the TDS falls on the low side, you don’t need to change the constant,” says Kim Skinner, co-owner of Pool Chlor in Livermore, Calif. “But in reality, the TDS in some pools is going to be higher than 1,000 — and in those cases, I think service techs are wise to adjust it a little higher.”

#### Putting it all together

Once all the values have been converted into usable factors, the LSI equation itself is an easy arithmetic problem:

### Point of Debate

Acceptable Ranges vs. Ideal Ranges

A common cause of debate in LSI calculations is whether acceptable ranges or ideal ranges should be emphasized. For example, some have found that a pH as high as 8.2 fails to cause scaling in certain pools, and should thus be considered part of the acceptable (i.e., non-damaging) range. Others, however, say that students of the LSI should be taught a narrower ideal range, which is highly unlikely to lead to scaling or etching in the majority of plaster pools. The debate continues — and not just for pH, but for all LSI factors. When a document specifies a range for any factor, it’s helpful to check whether that range is ideal, or merely acceptable.

### Point of Debate

Ranges and Overall Balance

Many service professionals say that keeping all individual SI values within their ideal ranges — or at least the acceptable ranges — is just as crucial as having a balanced LSI overall. However, others claim the purpose of the LSI is to determine what chemical adjustments are necessary to balance others. This, they say, means if, for example, the calcium hardness out of the tap is 75 ppm, a total alkalinity of 1,100 ppm would be necessary to balance the LSI — and therefore, this would balance the water as well. However, the Association of Pool & Spa Professionals’ Basic Pool & Spa Technology manual states, “Although [such] water is technically balanced, the low pH and calcium hardness plus the high TA would cause the water to act corrosive. It will also be difficult to lower the pH because of the buffering effect of the high TA.” In short, emphasizing overall LSI balance over the ranges of individual factors can be a dangerous game to play.