Cooling Tower

In the customary USA units:

M = Make-up water in gal/min
C = Circulating water in gal/min
D = Draw-off water in gal/min
E = Evaporated water in gal/min
W = Windage loss of water in gal/min
X = Concentration in ppmw (of any completely soluble salts … usually chlorides)
X_M = Concentration of chlorides in make-up water (M), in ppmw
X_C = Concentration of chlorides in circulating water (C), in ppmw
Cycles = Cycles of concentration = X_C / X_M
ppmw = parts per million by weight

A water balance around the entire system is:

M = E + D + W

Since the evaporated water (E) has no salts, a chloride balance around the system is:

M (X_M) = D (X_C) + W (X_C) = X_C (D + W)

and, therefore:

X_C / X_M = Cycles = M / (D + W) = M / (M - E) = 1 + {E / (D + W)}

From a simplified heat balance around the cooling tower:

(E) = (C) (ΔT) (c_p) / H_V

where:
H_V = latent heat of vaporization of water = ca. 1,000 Btu/pound
ΔT = water temperature difference from tower top to tower bottom, in °F
c_p = specific heat of water = 1 Btu/pound/°F

Windage losses (W), in the absence of manufacturer's data, may be assumed to be:

W = 0.3 to 1.0 percent of C for a natural draft cooling tower
W = 0.1 to 0.3 percent of C for an induced draft cooling tower
W = about 0.01 percent of C if the cooling tower has windage drift eliminators

Concentration cycles in petroleum refinery cooling towers usually range from 3 to 7. In some large power plants, the cooling tower concentration cycles may be much higher.

(Note: Draw-off and blowdown are synonymous. Windage and drift are also synonymous.)
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