Page 26 - Gas Purification 5E

16 Gas Puriijication

face must equal the quantity transferred from the interface to the body of the liquid, the fol-
lowing relationship holds:

Where: NA = quantity of component A transferred per unit time, per unit area
p = partial pressure of A in main body of gas
pi = partial pressure of A in gas at interface
c = concentration of A in main body of liquid
q = concentration of A in liquid at interface

Any consistent set of units may be used, however, it is convenient to express p in atmos-
pheres and c in pound moles per cubic foot, in which case k~ is expressed as lb moles/(br)(sq
ft)(atm) and kL as lb moles/(hr)(sq ft)(lb moledcu ft).
The use of equation 1-4 for design requires a knowledge of both and kL as well as the
equilibrium relationship and the interfacial area per unit volume of absorber. Although these
factors can be estimated for special design cases, it is more practical to use overall coeffi-
cients which are based on the total driving force from the main body of the gas to the main
body of the liquid and which relate directly to the contactor volume rather than to the interfa-
cial area. These overall coefficients, & and KLa, are defined as follows:

NAa dV = &a@ - p,) dV = KLa(ce - c) dV

Where: a = interfacial area per unit volume of absorber
pe = partial pressure of A in equilibrium with a solution having the composition of
main body of liquid
c, = concentration of A in a solution in equilibrium with main body of gas
V = volume of packing

The overall coefficients are related to the individual film coefficients as follows:
1
-=- 1 +- H
KGa kGa kLa
1
-- -- 1 +- 1
KLa kLa HkGa

where H is Henry’s law constant, pi/ci, or, in cases where Henry’s law does not hold, @, - pd/
(Ci - Ce).
The use of overall coefficients is strictly valid only where the equilibrium line is straight
over the operating region. However, because of their convenience, they are widely used for
reporting test data, particularly on commercial equipment, and are therefore very useful for
design.
In order to apply absorption coefficient data to the design of commercial columns, it is
necessary to consider the changes in liquid and gas compositions that occur over the length
of the column. This involves equating the quantity of material transferred (as indicated by
gas- or liquid-composition change) to the quantity indicated to be transferred on the basis of