Why concentrated tower water either lays down scale or eats metal, how the Langelier and Ryznar indices predict which, and what the controller does about each — with a worked example.
A cooling tower’s water is always heading one of two ways:
Concentrating the water pushes it towards scale. Each cycle of concentration multiplies calcium and alkalinity, and alkalinity raises the pH. Soft, clean make-up water is usually corrosive; the same water at 4 or 5 cycles is usually scale-forming. The treatment program, the cycles target, and the controller’s setpoints are chosen to hold it in between.
The Langelier Saturation Index (LSI) says whether water is over- or under-saturated with calcium carbonate:
LSI = pH − pHs
pHs is the pH at which the water would be exactly saturated. It depends on calcium, alkalinity, dissolved solids, and temperature:
pHs = (9.3 + A + B) − (C + D)
- A = (log₁₀ TDS − 1) ÷ 10 — TDS in mg/L
- B = −13.12 × log₁₀ (°C + 273) + 34.55
- C = log₁₀ (calcium hardness as CaCO₃) − 0.4 — in mg/L
- D = log₁₀ (M-alkalinity as CaCO₃) — in mg/L
| LSI | The water |
|---|---|
| Below 0 | Under-saturated — dissolves calcium carbonate, and tends to be corrosive |
| About 0 | Balanced |
| Above 0 | Over-saturated — tends to form calcium carbonate scale |
An untreated system scales at an LSI much above zero. Scale inhibitors hold the calcium carbonate in solution well past saturation, so a treated tower can run at a positive LSI. How far is set by the inhibitor and the program — commonly up to about +2.0 to +2.5 — and is the water treater’s figure, not the controller’s.
The Ryznar Stability Index (RSI) uses the same pHs and reads the other way round:
RSI = 2 × pHs − pH
Below about 6, the water tends to scale; above about 7, it tends to corrode; in between is roughly stable. It is a useful second opinion, and some treaters prefer it for high-alkalinity water.
A tower’s make-up water, and the same water at 4 cycles:
| Make-up | Tower at 4 cycles | |
|---|---|---|
| Calcium hardness, as CaCO₃ | 60 mg/L | 240 mg/L |
| M-alkalinity, as CaCO₃ | 80 mg/L | 320 mg/L |
| TDS | 150 mg/L | 600 mg/L |
| pH (measured) | 7.8 | 8.5 |
| Temperature | 20 °C (68 °F) | 35 °C (95 °F) |
Calcium, alkalinity, and TDS are four times the make-up — that is what 4 cycles means (see Cycles of Concentration). The pH does not multiply: it rises as carbon dioxide is stripped in the tower, and has to be measured.
The tower water:
The make-up water, the same way at 20 °C: pHs = 8.32, so LSI = 7.8 − 8.32 = −0.52 and RSI = 8.84. Mildly corrosive — typical of soft make-up.
What it tells the operator:
The indices predict a tendency, not a rate. They say which way the water leans, not how fast it will scale or corrode. Confirm with deposits on coupons or heat exchanger inspections, and with a corrosion rate probe.
Calcium carbonate is the usual one, but not the only one. Each has its own limit, and the lowest limit sets the cycles.
| Scale | Watch |
|---|---|
| Calcium phosphate | Phosphate-based inhibitors, or phosphate in the make-up. Limited by calcium × phosphate at the tower’s pH. |
| Silica | Commonly held below about 150–180 mg/L as SiO₂ in the tower; above that it forms a hard glassy scale that is very hard to remove. High-silica make-up often limits cycles more than calcium does. |
| Calcium sulfate | Rare, unless the make-up is high in sulfate or sulfuric acid is fed for pH control. |
| Iron and manganese | Not true scale, but deposits that shelter corrosion underneath. |
Corrosion is measured as a rate: mils per year (mpy), thousandths of an inch of metal lost per year. Commonly used guidelines for cooling water:
| Metal | Excellent | Good | Fair | Poor |
|---|---|---|---|---|
| Mild steel | Below 1 mpy | 1–3 mpy | 3–5 mpy | Above 5 mpy |
| Copper and copper alloys | Below 0.1 mpy | 0.1–0.2 mpy | 0.2–0.5 mpy | Above 0.5 mpy |
The program’s own targets take precedence. What pushes the rate up:
Localized (pitting) corrosion matters more than the general rate: a low general rate with a high pitting rate still perforates tubes.
| Risk | The controller | See |
|---|---|---|
| Scale from over-concentration | Bleeds on conductivity, holding the cycles target | Cycles of Concentration |
| Scale from high pH | A pH Setpoint Control mode feeding acid | pH |
| Loss of inhibitor | Feeds inhibitor in proportion to make-up, or on a PTSA tracer reading, and alarms on a low tank | Chemical Feed Methods, Pyxis ST-500 |
| Corrosion | Reads general and pitting corrosion rates from a corrosion probe, and alarms on a high rate | Corrosion Rate, Pyxis CR-300 |
| Biocide attack on copper | Holds an ORP setpoint rather than feeding blind | Biocide Programs |
The controller does not calculate the LSI. Work it from a water test, as above, whenever the make-up or the cycles target changes.