Cooling Tower LSI at Cycles of Concentration

A cooling tower is a machine for concentrating its own makeup water. Evaporation leaves as pure vapour and the minerals stay behind, so at five cycles the recirculating water carries five times the calcium, five times the alkalinity and five times the dissolved solids of what came in through the fill valve. This page does that multiplication and then asks the rigorous Langelier question of the result: given the tower's measured pH, how far above calcite saturation is this water at the hottest surface it touches? A makeup of 90 mg/L calcium hardness, 60 alkalinity and 300 TDS, run at five cycles with the tower at pH 8.80, reads +2.19 at a 45 °C exchanger skin.

The temperature is the input people get wrong most often, and it is the one that matters most. Calcite is less soluble hot. The same water that reads +2.08 at a 35 °C basin reads +2.19 at the 45 °C skin, and scale forms where the index is highest, which is on the heat-transfer surface you are paying to keep clean. Use the skin temperature of the hottest exchanger: for a condenser that is closer to the refrigerant condensing temperature than to the water leaving it. The page will also run backwards and tell you the surface temperature at which the water reaches a limit you choose, so you can check every exchanger against one number.

The multiplication assumes calcium and alkalinity cycle up in full, and that is worth testing, because it turns the page into a diagnostic. Cycles are best measured on something that cannot precipitate, chloride or conductivity. If chloride says six cycles and calcium says four and a half, the missing calcium has not gone to drain. It is on your tubes. A tower water analysis that shows less calcium or less alkalinity than cycles times makeup is the earliest warning of scaling you will get, well before approach temperatures creep up. Acid feed breaks the assumption deliberately by destroying alkalinity; for an acid-fed tower, put the measured analysis of the tower water into the full-analysis page and skip the cycling-up.

There is no solve-for-cycles here, on purpose. Holding the pH at today's reading and asking how many cycles reach a limit gives an optimistic answer, because a tower's pH climbs as it cycles up and the alkalinity rises. The companion page estimates that climb and answers the cycles question honestly. And like every saturation index this is a tendency, not a rate: it does not know what inhibitor is in the water, it has no ion pairing, and it looks only at calcium carbonate. Silica, calcium sulphate and calcium phosphate each set a ceiling of their own.