Page 33 - Gas Purification 5E

Introduction 23

A = solute
yA = mole fraction of A in the gas phase
fA = fractional saturation of the reactive component of the solution with A

With this coordinate system the operating line is straight. The equilibrium curve may be
based on actual data for the specific system at column operating conditions or may be
approximated on the basis of related data. Rousseau and Staton outline steps for estimating
equilibrium curves based on the Henry’s law constant for unreacted component A in the liq-
uid and the equilibrium constant for the chemical reaction of A with the reactive component.
The graphical procedure is very useful for preliminary studies to establish the minimum
flow rates for absorption and stripping options, and for estimating the number of ideal
stages (theoretical trays) required once design flow rates have been set. The number of ideal
stages can be converted to actual trays by applying an appropriate tray efficiency.
Analytical procedures that closely resemble those employed for calculating the number of
transfer units have also been developed for tray columns. A particularly useful equation sug-
gested by Colbum (1939) for the case of low solute concentration and a straight equilibrium
line is

(1-18)

where Np = number of theoretical plates and the other symbols have the same meaning as in
equation 1-17
As noted in the preceding section, the parameter mGM/LM represents the ratio of the slope
of the equilibrium curve to the slope of the operating line and is called the stripping factor, S.
This factor and its reciprocal, the absorption factor, A, normally vary somewhat over the
length of the column due to changes in all three variables. Kremser (1930) proposed defining
A in terms of the lean solution and feed gas flow rates as follows:

The fractional absorption of any component, C, by an absorber of N theoretical plates is
given by the following equation, often referred to as the Kremser (or Kremser-Brown)
equation:

(1-20)

Where: yN + = mole fraction C in the inlet gas
y1 = mole fraction C in outlet gas
yo = mole fraction C in equilibrium with lean solution
LMO = lean solution flow rate, moles/hr
GM(N + = feed gas rate, moles/hr
N = number of theoretical plates in the absorber
m = K = y/x at equilibrium (assumed constant over the length of the
column)