Cooling in a Cooling Tower

General Description

A cooling tower is used as a specialized heat exchanger; the two fluids involved are water and air. During this operation water is sprayed into the tower from the top and air enters through the side-wall (crossflow configuration). A percentage of the water is vaporized which results in heat transfer from the liquid to the gas stream. The modeling of the cooling in tower operation is very specific to this process, and calculations will not be performed (or if performed will not be accurate) for large deviations from the typical cooling tower operation conditions.

The inlet water stream, may contain some contaminants. If these are volatile, emission calculations can be performed. If the composition of water stream is specified so that water is less than 95%, calculations will not be accurate, even though they are still performed. If the inlet gas stream contains other components in concentrations > 5% calculations will not be accurate, even though they are still performed.

Unit Procedure Availability

● Cooling in a Cooling Tower Procedure

Cooling in a Cooling Tower: Modeling Calculations

The model is based on a classical treatment of cooling tower design (with the basic assumptions), as described in references 1-3. The Cooling Tower Range is calculated as:

eq. (A.318)

where T_wI and T_wO are the input (hot) and output (cold) water temperatures. The Approach Temperature (T_appr) is calculated as:

eq. (A.319)

where T_wb is the air wet bulb temperature.

The flowrate of the input water (L) is the flowrate of the water input stream. The flowrate of the input air (G) is calculated from the water-to-air flow ratio (r = L/G) which is either set by user (design mode) or calculated by the model (rating mode). The required flow of the air stream, is propagated backwards, through the network of connectivity.

The maximum water-to-air ratio (r_max) for feasible cooling tower operation is calculated based on the above variables, following a graphical method as described in references 1-3. In design mode the user specifies the ratio r, and if this is greater than r_max a warning message will come up prompting for reducing its value.

Energy Balance:

The energy balance is represented by the following equation:

eq. (A.320)

where Q is the cooling duty, H_ai and H_aoare the enthalpies of the input and output air, respectively, and c_pw is the specific heat capacity of water. Note that the psychotropic equations (see reference 5) are used to relate the enthalpy of air to its humidity and temperature or the wet bulb temperature (T_wb).

In design mode, the enthalpy of output air (H_ao) is obtained from the energy balance. The theoretical number of stages (n), or tower characteristic integral, is then calculated by the Merkel equation:

eq. (A.321)

where T_w is the temperature of water (obtained from energy balance for given the air enthalpy) and H_a,sat is the Saturation Enthalpy of air at that temperature (the temperature of the water-air interface). Since this integral applies to a counter-current configuration, a correction factor for a crossflow configuration is used (see reference 4). This theoretical number of stages is used for sizing calculations.

In rating mode, the L/G ratio is first calculated solving simultaneously the Merkel equation and the sizing correlations. The enthalpy of the output air (H_ao) is then calculated from the energy balance. The Water Loading is calculated based on the input water flow rate and the area of the tower.

The temperature of output air (T_ao) is calculated from numerical integration the following equation:

eq. (A.322)

where H_a and T_a represent the enthalpy and temperature of air, respectively, and T_sat and H_a,sat represent the “interface” temperature and air enthalpy, that is, the water temperature and air saturation enthalpy, respectively. In order to obtain T_sat and H_a,sat for every given air temperature the energy balance and the phychotropic equations are used. The equation above is derived from a combination of the heat and a mass transfer balances and the Lewis relations. Therefore, it is only valid for water-air systems (see reference 1-2).

Knowing the temperature and enthalpy of the input and output air, the psychotropic equations are used to calculate the humidity of the input and output air (Y_wi and Y_wo). The water uptake of the air stream represents the water evaporation rate.

Equipment Sizing

In design mode, the packing height is calculated based on the Tower Characteristic Integral (theoretical number of stages), using correlations for wood-splash bar packed towers (see reference 4). The tower area is calculated based on the water flow rate and water loading specified by the user.