Page 24 - Gas Purification 5E

14 Gas purification

Where: GM’= solute-free gas flow rate, lb-mol& ft
LM’= solute-free liquid flow rate, lb-mole/ h ft
X = mole ratio solute in the liquid phase
= x/(l - x), where x =mole fraction
Y = mole ratio solute in the gas phase
= y/(l - y), where y = mole fraction

Rearranging equation (1-1) gives

which is the equation of the operating line. The line is straight on rectangular coordinate
paper and has a slope of LM’/GM’. The coordinates of the ends of the operating line represent
conditions at the ends of the column, i.e., X2, Yz (top) and XI, Y, (bottom).
Absorber design correlations are not always based on solutefree flow rates and mole
ratios. The original JSremser (1930) and Souders and Brown (1932) design equations, for
example, are based on the lean solvent rate and the rich gas. When the solute concentrations
in gas and liquid are low, x is approximately equal to X, and y is approximately equal to Y.
In addition, the total molar flow mtes are approximately equal to the solute-free flow rates.
In these cases equation 1-2 simplifies to

which is easier to use because equilibrium data are usually given in terms of mole fractions
rather than mole ratios.
Although absorber designs can be effectively accomplished using analytical correlations
and computer programs, the performance of countercurrent absorbers can best be visualized
by the use of a simple diagram such as Figure 1-6. In this figure both the operating lines and
equilibrium curve are plotted on X,Y coordinates.
Typically the known parameters are the feed gas flow rate, GM’, the mole ratio of solute in
the feed gas, Y1, the mole ratio of solute (if any) in the lean solvent, X2, and the required
mole ratio of solute in the product gas, Y2. The goal is to estimate the required liquid
flowrate and, ultimately, the dimensions of the column.
Two possible operating lines have been drawn on Figure 1-6; line A represents a typical
design, and line B represents the theoretical minium liquid flow rate. The distance between
the operating line and the equilibrium curve represents the driving force for mass transfer at
any point in the column. Since line B actually touches the equilibrium curve at the bottom of
the column, it would require an infinitely tall column, and therefore represents the limiting
condition with regard to liquid flow rate. Typically liquid flow rates (or UG ratiosF20 to
100% higher than the minimum-are specified.
Frequently absorption is accompanied by the release of heat, causing an increase in tem-
perature within the column. When this occurs it is necessary to modify the equilibrium curve
so that it corresponds to the actual conditions at each point in the column. For tray columns
this can best be accomplished by a rigorous tray-by-tray heat and material balance such as
one proposed by Sujata (1961). For packed columns, a computer program approach was