Cooling tower material balances (Chemical Engineering)

Here are the governing relationships for the makeup flow rate, the evaporation and windage losses, the draw-off rate, and the concentration cycles in an evaporative cooling tower system:


M = Make-up water in m³/hr
C = Circulating water in m³/hr
D = Draw-off water in m³/hr
E = Evaporated water in m³/hr
W = Windage loss of water in m³/hr
X = Concentration in ppmw (of any completely soluble salts … usually chlorides)
Xm = Concentration of chlorides in make-up water (M), in ppmw
Xc = Concentration of chlorides in circulating water (C), in ppmw
Cycles = Cycles of concentration = Xc / Xm
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 (Xm) = D (Xc) + W (Xc) = Xc (D + W)

and, therefore:

Xc / Xm = Cycles = M / (D + W) = M / (M – E) = 1 + {E / (D + W)}

From a simplified heat balance around the cooling tower:

(E) = (C) (∆T) (cp)/ Hv

Hv = latent heat of vaporization of water = ca. 2260 kJ / kg
∆T = water temperature difference from tower top to tower bottom, in °C
cp = specific heat of water = ca. 4.184 kJ / kg / °C

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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