Alternative technique for assessing efficacy of industrial evaporative cooling water cooling tower

The traditional equation used for determining thermal efficiency of process cooling tower is:

CT Thermal efficiency,η =Range ?T,oC÷(CW hot return ,oC - WBT,oC)

However, this method considers only the water temperature profiles across the cooling tower. Considering Merket & Braun equation and later Soylemez, Gauss-Newton & Levenberg. Each of the developing thermodynamic models attempt to delve deeper into the functioning of the evaporative cooling tower in terms of the transport phenomena occurring in the cooling inside the structure and outside. After many years of scientific negligence on this aspect recently there is an increasing awareness to improve the cooling tower performance across industrial spectrum.

Merkel & Braun were the first scientists to propose a ?model of heat exchange mechanism in evaporative cooling tower based in enthalpy differential as the driving force for heat transfer from water to air. The foundation for NTU method to determine the cooling tower size was laid. However, the simple thermal approach to cooling tower efficiency is fraught with significant deficiencies in view of the following considerations:

Range is determined by the heat load in MW and the cooling water circulation rate. Range is not dependent on the cooling tower size or number of transfer units (NTU). Heat rejected to the atmosphere with hot saturated air ?from the cooling water equals total heat duty Q on the cooling tower given by equation Q = m*Cp*Range = m* Range.

Approach temperature depends on cooling tower capability . Approach temperature is inversely proportional to the size of the cooling tower or NTUs.

The heat removal from hot cooling water is achieved by a. Evaporation (major phenomenon) and b. sensible heat (minor phenomenon). The wet bulb temperature of air entering the cooling tower affects the thermal performance of the CT but the rate of evaporation is affected by the dry bulb temperature and relative humidity of the air entering the CT.

Given these contrasting scenario while assessing the CT performance it is imperative to consider other techniques based on fundamental laws of energy and mass balances. Drawing from all the models it is practical to consider enthalpy transfer as a basis for assessing the CT efficacy. Enthalpy difference is the driving force for thermal energy exchange in CT.?

The following figures and equations depict the mechanism of energy transfer and heat rejection in evaporative CT:

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The figures and equations are self-explanatory.

Let us examine the 2 thermal efficacy models as discussed in the foregoing statements namely traditional temperature differential method and the enthalpy differential method for an experimental model cooling tower having the following operating data set:

Cooling water recirculating rate, m3/hr ????????????? : 78

Inlet cooling water temperature, oC????????????????????: 39

Outlet cooling water temperature, oC???????????????? : 31

Range, R, oC?????????????????????????????????????????????????????????: 8

Evaporation Rate, E, m3/hr???????????????????????????????????: 1.04

Blowdown rate, BD,m3/hr????????????????????????????????????: 0.15

Make up water rate, mu, m3/hr ?????????????? ????????????: 1.19

Ambient Wet bulb temperature, oC?????????????????????: 27

Ambient Dry buld temperature, oC??????????????????????: 38

Approach temperature, oC???????????????????????????????????: 4

Makeup water temperature, oC???????????????????????????: 32

Method 1 Traditional:

CT efficiency: ?Range / (CW inlet Temperature – wet bulb temperature)

η = 8/(38-27) = 0.72 or 72%

?

Method 2: Enthalpy Method:

Equation 1 previously stated can be stated as below considering Cp of water to be 1.0.

ε???={(mw,i*Tw,i )+ (mm*Tm) –(mw,o-Tw,o)} ÷((mw,o*(Tw.i -Twb))

ε???= {(78*39)+(1.19*32) – (76.97*30)} / (77*(39-27)) = (3042+38.08-2310)/(77*12))

ε???=752.08/924=0.814 or 81.4%

?

The CT efficacy based on enthalpy exchange appears to be more realistic than the traditional thermal efficiency calculation due to the following conditions of the cooling tower:

Range is high at 8 oC

Approach temperature is 3oC reasonably? low when considering the high ambient temperature and wet bulb temperature.???????????

This model applies equally to both counter flow and cross flow cooling towers.

The limitations are:

1.??????? Measurement errors

2.??????? Air flow measurement errors

3.??????? Internal structural defects in cooling towers such as air and water distribution mechanisms etc

The enthalpy model for CT efficacy determination is more reasonable and more rigorous representing a better understanding of cooling tower efficiency.

Another technique the NTU method is also an important technique to establish the cooling tower capacity & capability.