Predicted Cooling Tower LSI and Maximum Cycles, from the Makeup Analysis

Before a tower is built, or before its cycles are raised, there is no tower water to measure, only a makeup analysis and a question: how far can this water be concentrated before calcium carbonate becomes the problem? This page projects the answer. It cycles the makeup's calcium, alkalinity and TDS up by N, estimates the pH the tower will settle at from the cycled alkalinity using $\mathrm{pH_{eq}} = 1.465\,\log_{10}(\mathrm{Alk}) + 4.54$, the empirical correlation Puckorius built his index on, and then computes the rigorous Langelier index at the hottest surface. Solved the other way, it returns the cycles at which the index reaches a limit you choose.

Work it through with a makeup of 90 mg/L calcium hardness, 60 alkalinity and 300 TDS, and a 45 °C exchanger skin. At four cycles the alkalinity is 240, the estimated pH is 8.03 and the index is +1.31. At five cycles the alkalinity is 300, the estimated pH is 8.17 and the index is +1.61. Notice that both halves of the index move the same way as the cycles climb: the pH goes up because the alkalinity does, and the saturation pH comes down because calcium and alkalinity both rise. That is why scaling tendency accelerates with cycles, and why the last cycle of water saving is always the expensive one.

The pH estimate is the soft spot, and the page says so beside every answer. The correlation describes an open, well-aerated tower with no acid feed, and real towers scatter around it by a few tenths of a pH unit depending on how hard the fill strips carbon dioxide, on ammonia or process leaks, and on the treatment chemistry itself. The index moves one for one with pH, so a tower that actually sits at 8.8 where the estimate said 8.2 is more than half a unit further into scaling territory. Use this page to plan, then measure the pH once the tower is running and move to the measured-pH page.

The limit you enter is yours, and it belongs to your programme. An untreated system wants to stay near zero; modern phosphonate and polymer programmes are routinely run well above +2; where exactly depends on the chemistry, the skin temperatures and the residence time, and whoever supplies the programme should put their name to the number. Whatever it is, the answer here is the calcium-carbonate ceiling only. Silica, calcium sulphate, calcium phosphate, chloride on stainless steel and a plain conductivity limit each set a ceiling of their own, and the lowest one governs the tower.