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Chemical process engineering FAQ

Cooling towers

How to calculate cycles, blowdown, evaporation, makeup
Posted: 9 Sep 05 (Edited 22 Nov 06)

.
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:



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)
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) (ΔT) (cp) / HV

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

In SI metric units:

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) (ΔT) (cp) / HV

where:
HV = latent heat of vaporization of water = ca. 2260 kJ / kg
ΔT = water temperature difference from tower top to tower bottom, in °C
cp = specific heat of water = 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 or less 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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