Cooling Tower Makeup Water and Cycles of Concentration

For a steady basin inventory, makeup $M=E+D+B$. A conservative dissolved-solids balance gives $M c_m=(D+B)c_c$, so cycles $N=c_c/c_m=M/(D+B)$. Combining these balances gives

Drift is concentrated liquid, not pure evaporated water. The implemented balance follows SPX Evaporation and Water Usage (2019), PDF p. 3.

Cooling range is $T_h-T_c$ and approach is $T_c-T_{wb}$. These describe boundary conditions used in Merkel's evaporative cooling framework; this tool does not evaluate the Merkel integral. Estimated evaporation uses $E=0.00144 R\Delta T$ with $R$ and $E$ in the same volume/time units and range in K. This is SPX Cooling Tower Fundamentals, 2nd ed. (2009), printed p. 31 / PDF p. 32: 0.0008 per °F of range. Select a known evaporation rate when better operating data are available.

The simplified Langelier screen follows WRC TT 874/2/21 (2022), PDF pp. 81 and 97:

Here $A=(\log_{10}(TDS)-1)/10$, $B_T=34.55-13.12\log_{10}(T_K)$, $C=\log_{10}(Ca_H)-0.4$, and $D_A=\log_{10}(Alk)$. Concentrations are numerical mg/L; calcium hardness and alkalinity are as CaCO₃. The steps normalize dimensional values by 1 mg/L or 1 K before taking logarithms. This implementation uses the SI offset 273.15 K; WRC's worked example uses the rounded 273.2, changing its LSI by less than 0.001.

Holding circulating pH and temperature fixed while all three concentrations multiply by $N$ gives $LSI(N)=LSI(1)+1.9\log_{10}(N)$. Therefore $N_{LSI}=10^{(LSI_{limit}-LSI(1))/1.9}$. Used cycles are the minimum of the request, that ceiling, the entered site ceiling and $10000/TDS_m$. No usable solution is shown if the combined chemistry ceiling is at or below 1.01 or required blowdown is negative. Baseline cycles remain unchanged for the comparison. Volumes equal rate times operating hours.

For positive drift, setting blowdown to zero gives the drift-only cycles ceiling $N_D=1+E/D$. Both water-demand curves are omitted where their implied blowdown is negative. A vertical line marks $N_D$ when it falls within the plotted cycles range; the result card also gives this ceiling. It is a hydraulic feasibility boundary, separate from the chemistry screen. With zero drift there is no finite drift-only ceiling.

• Steady operation, a well-mixed basin and approximately equal liquid densities. The circulation rate and thermal duty represent one operating condition.
• Evaporated water contains no dissolved solids; drift and blowdown have the circulating-water concentration. Leaks, overflow, rain, airborne salt loading and other withdrawals are excluded.
• TDS, calcium hardness and alkalinity concentrate conservatively. No precipitation, acid feed, softening or inhibitor chemistry is simulated. Circulating pH is entered independently and stays fixed across the sweep; it is not multiplied by cycles.
• The hottest relevant wetted temperature is supplied by the user. Heat-exchanger surface temperatures can exceed bulk hot-water temperature.
• The default +0.5 LSI allowance permits supersaturation. It and the default site limit of 6 cycles are illustrative, not safety recommendations.
• Savings compare identical evaporation, drift and operating hours. Negative savings mean increased water use.
• Flow-rate cards are provided in both m³/h and US gal/min. Flow inputs accept typed compatible units. The SI/US viewer switch changes absolute temperatures and operating volumes; temperature differences remain in K.

A planning balance for evaporative freshwater circuits, with an approximate calcium carbonate screen restricted here to pH 6.5–9.5, screening temperatures 1–90°C and projected TDS no greater than 10,000 mg/L. These are calculator scope limits, not a guarantee of accuracy or acceptable water quality. Strongly saline water, unusual buffers, treatment-altered alkalinity and chemically reactive species require a fuller chemistry model.

LSI describes thermodynamic calcium carbonate saturation, not scale quantity, deposition rate, overall corrosivity, silica scaling or microbial risk. A separate site ceiling must address other constituents, materials and treatment capability. Positive approach only checks the entered temperatures; it does not prove a tower can meet them. Range and approach are reported without fill sizing, air-flow calculation, fan selection or a Merkel-number calculation.

The SPX evaporation coefficient is an approximate operating estimate; ambient humidity and sensible heat transfer change actual evaporation. Prefer measured or manufacturer-calculated evaporation for operational decisions. Hours at one duty do not predict a seasonal load profile. Charts beyond the chemistry screening ceiling are hypothetical. Both water-demand curves omit negative-blowdown operating points; the vertical drift-limit marker denotes zero blowdown. No point to its right is a feasible steady balance at the entered evaporation and drift.

DOE BMP #10 quotes 20% less makeup and 50% less blowdown for 3 to 6 cycles. The makeup claim agrees with the fixed-evaporation balance; with negligible drift the blowdown reduction is 60%, since $1/(3-1)$ becomes $1/(6-1)$. The calculator retains this balance.