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Cooling Tower LSI at Cycles of Concentration

Also known as cooling tower Langelier index · tower water LSI · LSI at cycles · skin temperature LSI · recirculating water scaling index

LSI=pH−pHs(Ts, N Cam, N Alkm, N TDSm)\mathrm{LSI} = \mathrm{pH} - \mathrm{pH_s}\left(T_s,\ N\,\mathrm{Ca_m},\ N\,\mathrm{Alk_m},\ N\,\mathrm{TDS_m}\right)
sig figs

Worked example: Makeup 90/60/300 at 5 cycles, pH 8.80, 45 C skin → LSI = +2.19. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Cooling Tower LSI at Cycles of Concentration fits

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See also

Predicted Cooling Tower LSI and Maximum Cycles, from the Makeup Analysis: No tower pH to measure yet? This estimates it from the cycled alkalinity and solves for the cycles that reach your limit.Langelier Saturation Index from a Full Water Analysis: Have a lab analysis of the recirculating water itself? Enter it directly and skip the cycling-up.Cycles of Concentration (COC = M/B): Where the cycles figure comes from: makeup over blowdown.Puckorius (Practical) Scaling Index: The index built for poorly buffered tower water, using an equilibrium pH in place of the measured one.Saturation pH (pHs) for Langelier's Index: Both use makeup calcium hardness as CaCO₃ and makeup total alkalinity as CaCO₃.Langelier Saturation Index (LSI): Both use langelier Saturation Index and tower water pH.
19 more relatedSaturation pH (pHs), Rigorous: from the Carbonate Equilibria: Both use makeup calcium hardness as CaCO₃ and makeup total dissolved solids.TDS Estimated from Conductivity (TDS = k × EC): Both use makeup total dissolved solids.Blowdown Rate from Cycles: Both use cycles of concentration.Boiler Blowdown Rate from Steam Rate: Both use cycles of concentration.Boiler Cycles of Concentration: Both use cycles of concentration.Cycles of Concentration from Chloride: Both use cycles of concentration.Cycles of Concentration from Conductivity: Both use cycles of concentration.Surface Temperature Depression Under a Clear Sky: Both use hottest surface temperature.Ryznar Stability Index (RSI): Both use tower water pH.Henderson–Hasselbalch Equation (Weak Acid Buffer): Both use tower water pH.pH and pOH Relation: Both use tower water pH.pH from Hydrogen Ion Concentration: Both use tower water pH.pH of a Weak Acid from Ka: Both use tower water pH.pH of a Weak Base from Kb: Both use tower water pH.Larson–Skold Index: Both use makeup total alkalinity as CaCO₃.Lime Dose for Softening (as CaCO₃): Both use makeup total alkalinity as CaCO₃.Soda Ash Dose for Softening (as CaCO₃): Both use makeup total alkalinity as CaCO₃.Total Alkalinity as CaCO₃ from Species: Both use makeup total alkalinity as CaCO₃.Alkalinity Remaining After Alum: Both use makeup total alkalinity as CaCO₃.
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Cooling Tower LSI at Cycles of Concentration explained

CamAlkmTDSmNpHTsLSI

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.

Solving for cycles here comes with a warning. 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 page says so beside the answer, and 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.

Cooling Tower LSI at Cycles of Concentration formula

LSI=pH−pHs(Ts, N Cam, N Alkm, N TDSm)\mathrm{LSI} = \mathrm{pH} - \mathrm{pH_s}\left(T_s,\ N\,\mathrm{Ca_m},\ N\,\mathrm{Alk_m},\ N\,\mathrm{TDS_m}\right)
Where
  • LSI\mathrm{LSI}= Langelier Saturation Index
  • pH\mathrm{pH}= Tower water pH
  • TsT_s= Hottest surface temperature (°C)
  • NN= Cycles of concentration
  • Cam\mathrm{Ca_m}= Makeup calcium hardness as CaCO₃ (mg/L)
  • Alkm\mathrm{Alk_m}= Makeup total alkalinity as CaCO₃ (mg/L)
  • TDSm\mathrm{TDS_m}= Makeup total dissolved solids (mg/L)
Where this comes from
  • Langelier, W. F. (1936). The analytical control of anti-corrosion water treatment. Journal AWWA, 28(10). Read it
  • Plummer, L. N., & Busenberg, E. (1982). The solubilities of calcite, aragonite and vaterite in CO2-H2O solutions between 0 and 90 °C. Geochimica et Cosmochimica Acta, 46. Read it
  • Davies, C. W. (1962). Ion Association. Butterworths.
Revised 1 November 2026
Cite this page

formula.expert. (2026, November 1). Cooling Tower LSI at Cycles of Concentration Calculator. https://formula.expert/solvers/cooling-tower-lsi-at-cycles

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