Chemical Engineering February 2012 - 27

Saturated air film
enthalpy, hw
Water
droplet
FIGURE 1. The Merkel equation is derived
by considering a falling water droplet
surrounded by saturated air
100
120
140
160
180
200
220
240
260
280
300
320
40
60
80
20
(1)
FIGURE 2. This plot, known as the driving force diagram, shows the enthalpy versus
temperature for water and air
Liquid-to-gas ratio (L/G). The L/G
ratio of a cooling tower is the ratio of
the liquid (water) mass flowrate (L)
to gas (air) mass flowrate (G). Cooling
towers have certain design values,
but seasonal variations require
adjustment and tuning of water and
air flowrates to get the best cooling
tower effectiveness.
Number of transfer units (NTU).
Also called the tower coefficient,
the NTU is a numerical value that
results from theoretical calculations
based on a set of performance
characteristics. The value of NTU
is also representative of the degree
of difficulty for the cooling process.
The NTU corresponding to a set of
hypothetical conditions is called the
required coefficient and is an evaluation
of the problem. The same calculations
applied to a set of test
conditions is called the available
coefficient of the tower involved. The
available coefficient is not a constant
but varies with operating conditions.
The operating characteristic
of a cooling tower is developed from
an empirical correlation that shows
how the available coefficient varies
with operating conditions.
Cooling capacity. The cooling capacity
of a tower is the heat rejected
[kcal/h or TR (refrigeration tons; 1
TR = 12,000 Btu/h = 3,025.9 kcal/h)],
and is determined by the product of
mass flowrate of water, times the
specific heat times the temperature
difference.
Theory - the Merkel equation
In a cooling tower operating in counter
current flow, there are two basic
principles involved for removing heat
by the cooling water:
1. sensible heat transfer due to a difference
in temperature levels
2. latent heat equivalent of the mass
transfer resulting from the evaporation
of a portion of the circulating
water
Merkel developed the basic equation
based on the above principles. The
Merkel model is universally accepted
for designing and rating of counterflow
cooling towers. The model is based
on a drop of water falling through an
upstream flow of unsaturated air at
a wet-bulb temperature of twb with
enthalpy hA (Figure 1), in a counterflow
cooling tower. The drop of water
is assumed to be surrounded by a film
of saturated air at the water temperature
WT with saturation enthalpy hW.
As the drop travels downward, heat
and mass transfer takes place from
the interface air film to the upstream
air, thereby cooling the water from hot
temperature to a cold temperature.
The main assumptions of Merkel
theory are the following:
1. The saturated air film is at the temperature
of the bulk water.
2. The saturated air film offers no resistance
to heat transfer.
3. The vapor content of the air is proportional
to the partial pressure of
the water vapor.
4. The heat transferred from the air to
the film by convection is proportional
to the heat transferred from the film
to the ambient air by evaporation.
5. The specific heat of the air-water
vapor mixture and the heat of vaporization
are constant.
6. The loss of water by evaporation is
neglected.
7. The force driving heat transfer is
the differential enthalpy between
the saturated and bulk air.
This cooling process can best be explained
on a psychometric chart,
which plots enthalpy versus temperature.
The process is illustrated
in the so-called driving-force diagram
shown in Figure 2. The air film is represented
by the water operating line
on the saturation curve. The main air
is represented by the air operating
line, the slope of which is the ratio of
liquid (water) to air (L/G). The cooling
characteristic, a degree of difficulty
to cooling is represented by the
Merkel equation:
(2)
Where:
K = overall enthalpy transfer coefficient,
lb/h-ft2
a = Surface area per unit tower volume,
ft2/ft3
V = Effective tower volume, ft3
L = Water mass flowrate, lb/h
Equation 2 basically says that at any
point in the tower, heat and water
vapor are transferred into the air due
(approximately) to the difference in
CHEMICAL ENGINEERING WWW.CHE.COM FEBRUARY 2012 25
25
Enthalpy
B
Saturation
curve
A
WBT 30
CWT 35
Water operating
line, hw
driving force,
(hw - hA)
Air
operating
line, hA
tan = L/G
40
Temperature, °C
HWT 45
50
55
C
D
Air enthalpy, hA
Air enthalpy, hA
Enthalpy, kJ/kg
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Chemical Engineering February 2012

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