Cooling Tower Heat Transfer 101

By Brad Buecker, Contributing Editor

Many power plants and other industrial facilities utilize open recirculating cooling systems equipped with cooling towers for heat transfer from condensers and other heat exchangers. Cooling towers commonly sit well away from the main plant, and it is often possible to forget about them until something goes awry. This article outlines the fundamentals of heat transfer in a cooling tower and important issues for maximizing heat exchange.

Psychrometry and Heat Transfer

In the words of an excellent reference manual on cooling, “Evaporation is utilized to its fullest extent in cooling towers, which are designed to expose the maximum transient water surface to the maximum flow of air — for the longest period of time.” (1) If cooling was only a result of sensible heat transfer, then cooling towers would be enormously large due to massive air flow requirements. Evaporation is the key to maximizing efficiency. As air passes through a cooling tower, it induces evaporation. For water to evaporate it must consume a large amount of energy to change state from a liquid to a gas. This is known as latent heat of vaporization, which at atmospheric conditions is typically around 1,000 Btu/lb. So, even the small percentage of evaporation that occurs in a cooling tower significantly lowers the temperature of the water returning to the condenser and other heat exchangers. We will examine this process in more detail below.

A very important concept for understanding cooling tower heat transfer is that of “wet bulb” temperature. Consider being outdoors, but in the shade, on a 90 F day at 40 percent relative humidity. A standard thermometer would naturally read 90 F, which is the “dry bulb” temperature. Now, let’s say we had another thermometer attached alongside the dry bulb thermometer, but in this case we have placed a soaked piece of cloth around the bulb of the other thermometer, and have put both on a swivel such that the thermometers can be swirled very rapidly through the air. This instrument, a simple and common device, is known as a sling psychrometer. After a while, the dry bulb thermometer will still read 90 F but the other thermometer will read 71.2 F. (2) This latter reading is the wet bulb temperature, and is the lowest temperature that can be achieved by evaporative cooling.

No matter how efficient, a cooling tower can never chill the recirculating water to the wet bulb temperature, and at some point costs and space requirements limit cooling tower size. The separation in temperature between the chilled water and wet-bulb value is known as the approach.

A well-known cooling tower reference indicates that a “standard” sized cooling tower should approach the wet bulb temperature within about 15 F. (1) The curve becomes asymptotic as approach temperatures narrow. Thus, for any cooling tower application at some point the law of diminishing returns takes over.

The data needed to calculate heat transfer by air cooling and evaporation has been compiled in a graph known as a psychrometric chart.

All versions of psychrometric charts are “very busy” and at times difficult to follow. A critical feature of a psychrometric chart is that if two properties of air are known, all of the other properties can be found. (An easy-to-follow, color-coded chart can be found at www.coolerado.com.) Consider the following practical example, which outlines how heat is transferred in a cooling tower.

Figure 1 shows 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.

The first step is to determine the energy balance around the tower.³

Utilizing algebra, the fact that m_a1 = m_a2, and that a mass balance on the water flow is m₄ = m₃ — (W₂ —W₁)*m_a, where W = humidity ratio; the energy balance equation can be rewritten in the following form.

From a psychrometric chart and steam table, we find the following.

So, with an inlet cooling water flow rate of 150,000 gpm (1,251,000 lb/min), the calculated air flow is 1,248,000 lb/min, which, by chance in this case, is close to the cooling water flow rate. (Obviously, the air flow requirement would change significantly depending upon air temperature, inlet water temperature and flow rate, and other factors, and that is why cooling towers typically have multiple cells, often including fans that have adjustable speed control.) The volumetric air flow rate can be found using the psychrometric chart, where inlet air at 68 F and 50 percent RH has a tabulated specific volume of 13.46 ft³/lb. Plugging this value into the mass flow rate gives a volumetric flow rate of almost 17,000,000 ft³/min.

The amount of water lost to evaporation can be simply calculated by a mass balance of water only. We have already seen that,

Utilizing the data above, m4 = 146,841 gpm. Thus, the water lost to evaporation is,

A very interesting aspect of this calculation is that only about 2 percent evaporation is sufficient to provide so much cooling. For those wishing to more quickly evaluate cooling tower evaporation, a simpler equation is available. The standard formula is,

The factor of 1,000 is the approximate latent heat of vaporization (Btu/lb) that was outlined earlier. To check the general accuracy of this calculation, 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 27 F. This gives a correction factor of 0.78.

Evaporation causes dissolved and suspended solids in the cooling water to increase in concentration. This concentration factor is (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 possible restrictions on water discharge. Cycles of concentration can be monitored by comparing the ratio of the concentration of a very soluble ion, such as chloride or magnesium, in the makeup (MU) and recirculating (R) water. Very common is a comparison of the specific conductivity of the two streams, particularly where automatic control is utilized to bleed off recirculating water when it becomes too concentrated. A common range for C in systems where chemistry control is straightforward is 4 to 6, as water savings via bleed off, also known as blowdown (BD), beyond this range become minimal. In arid locations, C may need to be high, and “some [western] states are mandating 7 [to even] 10 cycles for water conservation. (4) Of course, chemistry control and monitoring become even more important and difficult as cycles increase.

Besides blowdown, some water also escapes the process as fine moisture droplets in the cooling tower fan exhaust. This water loss is known as drift (D). Where towers are well-designed, drift is quite small and can be as low as 0.0005 percent of the recirculation rate. (5) Drift particulate minimization is very important, as regulations on particulate emissions from cooling towers continue to tighten. Leaks in the cooling system are referred to as losses (L). The following equations show relationships between evaporation, blowdown, makeup, losses, and cycles of concentration in a cooling tower as based on flow rates.

An important development regarding these calculations and many others for cooling towers comes from the Cooling Technology Institute (CTI, www.cti.org).

Ensuring Good Tower Efficiency

Critical to maximum efficiency in a cooling tower is intimate contact between the warm inlet water and the air flowing through the tower. Space limitations prevent a detailed discussion of tower internals, but one technological achievement that has greatly improved heat transfer over the decades is development of film fill.

As the name implies, layers of this film fill material placed between the inlet water sprays/distributors and the air rising from below cause the water to form a film on the packing. The filming water exposes much surface area to the air. Film fill is quite efficient, provided water chemistry is properly monitored and maintained. Microbes, and bacteria in particular, just love enclosed, warm and wet spaces to form colonies. Bacteria, as a protective mechanism, secrete a sticky polysaccharide coating that traps silt and other debris in cooling water. Entire sections of fill may become completely plugged, greatly reducing heat transfer. Furthermore, the deposits add so much weight to the packing that structural failures may also result. Collapse of cooling tower internals or even entire sections of the tower is not pretty, to say the least. Much research has gone into film fill design, and low-fouling configurations are available that can be individually specified based on water quality parameters, particularly the suspended solids content. Selection of the proper fill type is an important process ahead of tower installation. However, this does not eliminate the need for proper chemistry to control bacterial colonization, fungal growth within wood towers that can cause rot, and algae blooms on cooling tower decks and wetted components exposed to sunlight. Good chemistry control is also imperative to protect fill, condenser tubes, and other components within the cooling water system from scaling and/or corrosion. (6)

 References:

1. J.C. Hensley, ed., Cooling Tower Fundamentals, 2nd Edition; The Marley Cooling Tower Company (now part of SPX Cooling Technologies, Overland Park, Kan.), 1985.

2. S.D. Swenson, HVAC Heating, Ventilating, and Air Conditioning, Third Edition; American Technical Publishers, Inc., Homewood, Ill., 2004.

3. Potter, M.C. and C.W. Somerton, Schaum’s Outlines Thermodynamics for Engineers; McGraw-Hill, New York, N.Y., 1993.

4. Personal conversation with Ray Post of ChemTreat.

5. Personal conversation with Rich Aull of Brentwood Industries.

6. Buecker, B., Selby, T., and S. Shulder, “Cooling Water Chemistry Seminar”; the 29th Annual Electric Utility Chemistry Workshop, Champaign, Ill., June 2, 2009.

Author: Brad Buecker is a contributing editor for Power Engineering. He has nearly 30 years of experience in or affiliated with the power industry, much of it in chemistry, water treatment, air quality control, and results engineering positions with City Water, Light & Power (Springfield, Ill.) and Kansas City Power & Light Co’s (La Cygne, Kan.) station. He has written many articles and three books for PennWell on steam generation topics.

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