**By Brad Buecker**

The continued planning, construction, and operation of combined cycle power plants (and other energy and industrial facilities) is introducing many new personnel to numerous water-related issues, including those related to cooling. A critical unit operation at many of these facilities is energy transfer in one or more cooling towers.

This article examines important cooling tower heat transfer fundamentals, and modern methods for maintaining proper chemistry control in cooling systems.

A critical element of operation at many combined cycle power plants is energy transfer in one or more cooling towers. There are important cooling tower heat transfer fundamentals and modern methods for maintaining proper chemistry control in cooling systems. |

## Cooling Tower Heat Transfer

The basic cooling tower process is outlined in Figure 1.

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.” This statement highlights a fundamental aspect of cooling towers that those new to the industry may not fully recognize; the majority of heat transfer in a cooling tower (typically 65 to 85 percent depending upon atmospheric conditions) is due to evaporation of a small amount of the circulating water. This aspect will be outlined in a subsequent example.

Outline of Cooling Tower Process |

A very important concept for understanding cooling tower heat transfer is that of “wet bulb” temperature. Consider a warm summer day with 90°F shade temperature at 40 percent relative humidity. A standard thermometer would naturally read 90o, which is the “dry bulb” temperature. Now, attach another thermometer alongside the dry bulb thermometer but with a soaked piece of cloth around the bulb of the second thermometer, and put both on a swivel such that the thermometers can be swirled very rapidly through the air. This 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. 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. The data below show the relative size of a cooling tower for a range of approach temperatures.

The table indicates that a “standard” sized cooling tower should approach the wet bulb temperature within about 15°F. The curve becomes asymptotic as approach temperatures narrow. Thus, for any cooling tower application at some point the law of diminishing returns takes over. This data is only for general consideration, as the approach temperature may be significantly influence by several factors including the type of cooling tower fill, which will be explored later in greater detail.

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, but a psychrometric chart provides data for the following parameters.

- Dew point temperature
- Dry bulb temperature
- Enthalpy (Btu/lbm)
- Humidity ratio (absolute value of moisture in air on a lb/lb basis)
- Relative humidity
- Specific volume (ft
^{3}/lbm) - Wet bulb temperature

If any two properties of air are known, all of the other properties can be determined. Programs are available on-line that will calculate psychrometric parameters with a few simple user inputs.

At this point, we will populate Figure 1 with some real-world data and calculate the mass flow rate of air needed to cool 150,000 gpm of tower inlet water to the desired temperature, and also calculate the water lost by evaporation.

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

(m_{a1}*h_{a1}) + (m_{w3}*h_{w3}) = (m_{a2}*h_{a2}) + (m_{w4}*h_{w4}), where Eq. 1

ma = mass flow rate of dry air ha = enthalpy of dry air streams hw = enthalpy of water streams

Utilizing algebra, the fact that ma1 = ma2, and that a mass balance on the water flow is m4 = m3 – (w2 -w1)*ma, where w = humidity ratio; the energy balance equation can be rewritten in the following form.

m_{a} = (m_{3}*(h_{4} – h_{3}))/((h_{1} – h_{2}) + (w_{2} – w_{1})*h4 Eq. 2

From a psychrometric chart and the steam tables, we find

the following. h1 = 24.6 Btu/lbm

h_{2} = 52.5 Btu/lbm

h_{3} = 72.0 Btu/lbm h4 = 45.1 Btu/lbm

w_{1} = 0.0075 lbs moisture per lb of dry air

w_{2} = 0.0286 lbs moisture per lb of dry air

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 very 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.)

Cooling Tower Example Conditions |

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,

m_{4} = m_{3}– (w_{2} – w_{1})*ma Eq. 3

Utilizing the data above, m_{4} = 146,841 gpm. Thus, the water lost to evaporation is, m_{3} – m_{4} = 3,159 gpm

Note that only about 2 percent evaporation is sufficient to provide so much cooling.

This is due to the fact that the latent heat of evaporation at common atmospheric conditions is close to 1,000 Btu/lbm. Thus, as water evaporates it carries away a great deal of heat.

Example of Cooling Tower Film Fill |

A simpler method is available to more quickly calculate the typical evaporation from a cooling tower. The standard formula is,

E = (f * R * DT)/1000, where

Eq. 4 E = Evaporation in gpm

R = Recirculation rate in gpm

DT = Temperature difference (range) between the warm and cooled circulating water (°F)

f = A correction factor that helps to account for sensible heat transfer, where

f (average) is often considered to be 0.65 to 0.85, but will rise in summer and decline in winter.

The factor of 1,000 is, of course, the approximate latent heat of vaporization (Btu/lb) of water. 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, which is quite in line with where ƒ should be for the conditions shown.

This example was taken at sea-level conditions. Conditions can be significantly different at higher elevations.

The Cooling Technology Institute (www.cti.org) offers more sophisticated programs (and much other extremely useful information) to perform cooling tower calculations.

*Liquid-to-Gas Ratio*

A very important factor with regard to cooling towers or other processes of this type, including wet flue gas scrubbers, is the liquid-to-gas ratio (L/G). This parameter can also be evaluated from Equation 1, where the enthalpy of the water streams is simply the heat capacity of the water multiplied by the temperature. Designating ma = G and mw = L from Equation 1 transforms it to: C_{p}*L_{3}*t_{3} + G*h_{a1} = C_{p}*L_{4}*t_{4} + G*h_{a2} Eq. 5

We know that L_{4} = L_{3}*G(w_{2} – w_{1}), and using some simplifying algebra, elimination of a negligible flow term, and that tw_{2} – tw_{1} is the “Range” between inlet and outlet cooling water temperature, Equation 5 reduces to:

h_{a2} = h_{a1} + L/G*Range

Thus, it can be seen that the heat transfer is significantly influenced by the liquid-to-gas ratio. So, the more that liquid/gas interaction can be enhanced, the better the heat transfer properties.

This explains the intensive past and continuing research into cooling tower fill design. Most towers now are equipped with some variety of film fill.

As the name film fill implies, the material induces the incoming return water to form a film that greatly increases its surface area. Critical to proper performance of film fill are correct design and maintenance of the water distribution system above the fill.

Also critical, and a subject that will be covered in a future article, is cooling water chemical treatment to prevent fill fouling, especially from microbiological colonies and silt. Not only will fouling inhibit heat transfer,

## Author

Brad Buecker is a senior process specialist in the Water Technologies group of Kiewit Engineering Group Inc.