COOLING TOWER MATERIAL BALANCE

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

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 steams 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.

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:

M = E + D + W

Since the evaporated water (E) has no salts, a chloride balance around the system is{\displaystyle MX_{M}=DX_{C}+WX_{C}=X_{C}(D+W)}

MX_M = DX_C + WX_C = X_C (D+W)

and, therefore

X_C / X_M = Cycle of concentration = M / (D+W) = M / (M-E)

X_C / X_M = 1 + E / (D+W)

{\displaystyle {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 ΔT c_p / H_V

{\displaystyle E={C\Delta Tc_{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{\displaystyle \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.

CYCLES OF CONCENTRATION:

Cycle of concentration represents the accumulation of dissolved minerals in the recirculating cooling water. Discharge of draw-off (or blow-down) is used principally to control the build-up of these minerals.

The chemistry of the make-up water, including the amount of dissolved minerals, can vary widely. Make-up waters low in dissolved minerals such as those from surface water supplies (lakes, rivers etc.) tend to be aggressive to metals (corrosive). Make-up waters from ground water supplies (such as wells) are usually higher in minerals, and tend to bescaling (deposit minerals). Increasing the amount of minerals present in the water by cycling can make water less aggressive to piping; however, excessive levels of minerals can cause scaling problems.

As the cycles of concentration increase, the water may not be able to hold the minerals in solution. When the solubility of these minerals have been exceeded they can precipitate out as mineral solids and cause fouling and heat exchange problems in the cooling tower or the heat exchangers. The temperatures of the recirculating water, piping and heat exchange surfaces determine if and where minerals will precipitate from the recirculating water. Often a professional water treatment consultant will evaluate the make-up water and the operating conditions of the cooling tower and recommend an appropriate range for the cycles of concentration. The use of water treatment chemicals, pre-treatment such as water softening, pH adjustment, and other techniques can affect the acceptable range of cycles of concentration.

Concentration cycles in the majority of cooling towers usually range from 3 to 7. In the United States, many water supplies use well water which has significant levels of dissolved solids. On the other hand, one of the largest water supplies, for New York City, has a surface rainwater source quite low in minerals; thus cooling towers in that city are often allowed to concentrate to 7 or more cycles of concentration.

Since higher cycles of concentration represent less make-up water, water conservation efforts may focus on increasing cycles of concentration Highly treated recycled water may be an effective means of reducing cooling tower consumption of potable water, in regions where potable water is scarce.