Page 27 - Gas Purification 5E

Introduction 17

the absorption coefficient and driving forces and then integrating this equation over the
length of the column. For the individual film coefficients, this results in the following
expression for column height (Sherwood and Pigford, 1952):
L
h=Ghjp' PBM dP =-Ic1 dc
p2 kba(P - -pel pL c2 kLa(ce - c) (1-8)

Where: h = height of packed wne, ft
G'M = superficial molar mass velocity of inert gas, lb moles/(hr)(sq ft)
p, = partial pressure of solute in entering gas, atm
p2 = partial pressure of solute in leaving gas, atm
P = total pressure of system, atm
p = partial pressure of solute in main gas stream, atm
pe = partial pressure of solute in equilibrium with main body of solution, atm
PBM = log mean of inert gas pressures
VG = (peM/p) = special mass-transfer coefficient which is independent of gas
composition, lb moles/(br)(sq ft)(atm)
L = liquid flow rate, lb/(hr)(sq ft)
pL = liquid density, lb/cu ft (assumed constant)
c1 = solute concentration in liquid leaving bottom of column, lb moleslcu ft
c2 = solute concentration in liquid fed to top of column, lb moledcu ft
c = solute concentration in main body of liquid, lb moleslcu ft
c, = concentration of solute in liquid phase in equilibrium with main body of
gas, lb molesku ft

The equations may be integrated graphically by a method developed by Walker et. a1
(1937) that is also described by Sherwood and Pigford (1952). Simplified forms of these
equations have been developed which are much more readily used and which are sufficiently
accurate for most engineering-design calculations. Two of these forms are particularly adapt-
ed to the low gas and liquid concentrations that are frequently encountered in gas purifica-
tion. These equations assume that the following conditions hold

1. The equilibrium curve is linear over the range of concentrations encountered (and there-
fore overall coefficients can be used).
2. The partial pressure of the inert gas is essentially constant over the length of the column.
3. The solute contents of gaseous and liquid phases are sufficiently low that the partial pres-
sure and liquid concentration values may be assumed proportional to the corresponding
values when expressed in terms of moles of solute per mole of inert gas (or of solvent).

In terms of the overall gas coefficient and gas-phase compositions, the tower height can be
estimated by equation 1-9:

or, where the overall liquid absorption coefficient is available, the column height may be cal-
culated in tenns of liquid-phase compositions: