Cooling tower relationships

[Milton Beychok]

Anyone whose plant includes an evaporative cooling tower and is concerned with the amount of blowdown or control of the concentration cycles will be interested in this.

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 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)
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) (delta T) (cp) / HV

where:
HV = latent heat of vaporization of water = ca. 1,000 Btu/pound
delta T = temperature difference from tower top to tower bottom, in degrees F
cp = specific heat of water = 1 Btu/pound/degree 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.)

Milton Beychok
(Visit me at http://www.air-dispersion.com)

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