Gas Emission Control - Mathematics and Statistics for the Environment - page 461

where
Z = Height of packing (m).
N OG = Number of transfer units based on overall gas film coefficient.
H OG = Height of a transfer unit based on overall gas film coefficient (m).
N OL = Number of transfer units based on overall liquid film coefficient.
H OL = Height of a transfer unit based on overall liquid film coefficient (m).

Values for the height of a transfer unit used in designing absorption systems are usually obtained
from experimental data. To ensure the greatest accuracy, vendors of absorption equipment normally
perform pilot plant studies to determine the height of a transfer unit. When no experimental data are
available, or if only a preliminary estimate of absorber efficiency is needed, there are generalized
correlations available to predict the height of a transfer unit. The correlations for predicting the H OG
or the H OL are empirical in nature and are a function of

• Type of packing
• Liquid and gas low rates
• Concentration and solubility of the contaminant
• Liquid properties
• System temperature

These correlations can be found in engineering texts. For most applications, the height of a transfer
unit ranges between 0.305 and 1.22 m (1 and 4 ft). As a rough estimate, 0.6 m (2.0 ft) can be used.
The number of transfer units (NTUs) can be obtained experimentally or calculated from a variety
of methods. When the solute concentration is very low and the equilibrium line is straight, Equation
16.11 can be used to determine the number of transfer units ( N OG ) based on the gas phase resistance:

YmX
YmX

−
−

mG
L +

mG
L

1 2 m

m

m
m

ln 1 −

2 2

N = (16.11)

OG

mG
L

m

1 −

m

where
N OG = Transfer units.
Y 1 = Mole fraction of solute in entering gas.
m = Slope of the equilibrium line.
X 2 = Mole fraction of solute entering the absorber in the liquid.
Y 2 = Mole fraction of solute in exiting gas.
G m = Molar flow rate of gas (kg-mol/hr).
L m = Molar flow rate of liquid (kg-mol/hr).

Equation 16.9 may be solved directly or graphically by using the Colburn diagram presented in
Figure 16.9. The Colburn diagram is a plot of N OG vs. ln[ Y 1 - mX 2 )/( Y 2 - mX 2 )], reading up the graph
to the line corresponding to ( mG m / L m ), and then reading across to obtain the value for N OG .
Equation 16.11 can be further simplified for situations where a chemical reaction occurs or if the
solute is extremely soluble. In these cases, the solute exhibits almost no partial pressure, and, there-
fore, the slope of the equilibrium line approaches zero ( m = 0). For either of these cases, Equation
16.11 reduces to Equation 16.12:

N OG = ln( Y 1 / Y 2 ) (16.12)