Heat Transfer

# Fundamentals of Cooling Tower Heat Transfer – Part 1

03 November 2015

Cooling towers are critical heat exchangers at many facilities. Often, however, this equipment may be taken for granted. Scaling, fouling and other issues can impede heat transfer in cooling towers, and the collapse of tower fill because of the weight gain from fouling is not an uncommon phenomenon. This three-part series examines the basics of cooling tower heat transfer and outlines methods to keep towers clean.

Cooling Tower Heat Transfer Fundamentals

The figure illustrates process conditions that could easily exist in a cooling system. We will calculate the mass flow rate of air needed to cool 150,000 gpm of tower inlet water to the desired temperature. We will also calculate the water lost by evaporation.

Illustration of the cycles of concentration vs. blowdown for example cooling tower.

The first step is to determine the energy balance around the tower, where the blowdown is a negligible flow. [Ref. 1]

So, with an inlet cooling water flow rate of 150,000 gpm (1,251,000 lb/min), the calculated air flow rate (a) is 1,248,000 lb/min. By chance in this case, it is close to the cooling water mass flow rate. (Obviously, the air flow requirement would change depending upon ambient temperature, inlet water temperature, flow rate and other factors. That is why cooling towers typically have multiple cells and often include fans that have adjustable speed control.) The volumetric air flow rate can be found using the psychrometric chart, where inlet air at 68o F and 50% RH has a tabulated specific volume of 13.46 ft3/lb. Multiplying the mass flow rate by this conversion factor gives a volumetric air flow rate of nearly 17,000,000 ft3/min. As should be obvious, cooling towers must move a great deal of air to perform properly.

A Simplified Approach to Calculations

The factor of 1,000 is the approximate latent heat of water vaporization (Btu/lb). To check this calculation’s general accuracy, consider the previous problem we solved in detail. Evaporation was 3,159 gpm with a recirculation rate of 150,000 gpm and a range of 27o F. This gives a correction factor of 0.78, which corresponds well with the rule-of-thumb range.

Cycles of Concentration

Evaporation causes dissolved and suspended solids in the cooling water to increase in concentration. This concentration factor is (somewhat logically) termed the “cycles of concentration” (C). C, or perhaps more accurately, allowable C, varies from tower to tower depending upon many factors including makeup water chemistry and quality, heat load, effectiveness of chemical treatment programs and any restrictions on water discharge.

Cycles of concentration may be monitored by comparing the ratio of the concentration of a highly soluble ion, such as chloride or magnesium, in the makeup (MU) and recirculating (R) water. Comparing the specific conductivity of the two streams is common, particularly where automatic control is used to blow down recirculating water when it becomes too concentrated. A typical range for C in systems having a straightforward chemistry control is 4 to 8. As the graph shows, water savings become minimal at high cycles of concentration.

Besides blowdown, some water also escapes as fine moisture droplets in the cooling tower exhaust. This water loss is known as drift (D). When towers are well designed, drift is small and can be as low as 0.0005% of the recirculation rate. Drift particulate minimization is important in the U.S. as regulations for particulate emissions from cooling towers continue to tighten. Leaks in the cooling system are referred to as losses (L). The following equations show the relationships between evaporation, blowdown, makeup, losses and cycles of concentration in a cooling tower.

C = MU/BD

MU = E + BD + D + L

BD = E/(C – 1)

Excellent and extensive information on all aspects of cooling towers is available from the Cooling Technology Institute (CTI). Additional details may be found at www.cti.org.

Part 2 of this article examines issues related to selection of cooling tower fill. Part 3 will examine some current concepts regarding cooling water treatment. Evolution of makeup water sources and wastewater discharge regulations are significantly influencing cooling tower chemistry programs. Simple programs are no longer the norm.

References

1. Potter, M.C., Ph.D., and C.W. Somerton, Ph.D., Thermodynamics for Engineers, Schaum’s Outline Series, McGraw-Hill, 1993.