Knowledgebase

# Wet cooling tower material balance

Solution

Quantitatively, the material balance around a wet, evaporative cooling tower system is governed by the operational variables of make-up flow rateevaporation and windage losses, draw-off rate, and the concentration cycles.[12][13]

In the adjacent diagram, water pumped from the tower basin is the cooling water routed through the process coolers and condensers in an industrial facility. The cool water absorbs heat from the hot process streams which need to be cooled or condensed, and the absorbed heat warms the circulating water (C). The warm water returns to the top of the cooling tower and trickles downward over the fill material inside the tower. As it trickles down, it contacts ambient air rising up through the tower either by natural draft or by forced draft using large fans in the tower. That contact causes a small amount of the water to be lost as windage/drift (W) and some of the water (E) to evaporate. The heat required to evaporate the water is derived from the water itself, which cools the water back to the original basin water temperature and the water is then ready to recirculate. The evaporated water leaves its dissolved salts behind in the bulk of the water which has not been evaporated, thus raising the salt concentration in the circulating cooling water. To prevent the salt concentration of the water from becoming too high, a portion of the water is drawn off/blown down (D) for disposal. Fresh water make-up (M) is supplied to the tower basin to compensate for the loss of evaporated water, the windage loss water and the draw-off water.

Fan-induced draft, counter-flow cooling tower

Using these flow rates and concentration dimensional units:

 M = Make-up water in m³/h C = Circulating water in m³/h D = Draw-off water in m³/h E = Evaporated water in m³/h W = Windage loss of water in m³/h 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 (dimensionless) ppmw = parts per million by weight

A water balance around the entire system is then:[13]

M = E + D + W

Since the evaporated water (E) has no salts, a chloride balance around the system is:[13]

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

and, therefore:[13]

${X_C \over X_M} = \text{Cycles of concentration} ={ M \over (D + W)} = {M \over (M - E)} = 1 + {E \over (D + W)}$

From a simplified heat balance around the cooling tower:

$E = {C \Delta T c_p \over H_V}$
 where: HV = latent heat of vaporization of water = 2260 kJ / kg ΔT = water temperature difference from tower top to tower bottom, in °C cp = specific heat of water = 4.184 kJ / (kg$\cdot$°C)

Windage (or drift) losses (W) is the amount of total tower water flow that is evaporated into the atmosphere. From large-scale industrial cooling towers, in the absence of manufacturer's data, it may be assumed to be:

W = 0.3 to 1.0 percent of C for a natural draft cooling tower without windage drift eliminators
W = 0.1 to 0.3 percent of C for an induced draft cooling tower without windage drift eliminators
W = about 0.005 percent of C (or less) if the cooling tower has windage drift eliminators
W = about 0.0005 percent of C (or less) if the cooling tower has windage drift eliminators and uses sea water as make-up water.