## Multicomponent Systems

When no chemical reactions are involved in the absorption of more than one soluble component from an insoluble gas, the design conditions (temperature, pressure, liquid-to-gas ratio) are normally determined by the volatility or physical solubility of the least soluble component for which the recovery is specified.

The more volatile (i.e., less soluble) components will only be partially absorbed even for an infinite number of trays or transfer units. This can be seen in Fig. 14-9, in which the asymptotes become vertical for values of mGM/LM greater than unity. If the amount of volatile component in the fresh solvent is negligible, then the limiting value of y1/y2 for each of the highly volatile components is y1/y2 = S/(S — 1) (14-50)

where S = mGM/LM and the subscripts 1 and 2 refer to the bottom and top of the tower, respectively.

When the gas stream is dilute, absorption of each constituent can be considered separately as if the other components were absent. The following example illustrates the use of this principle.

Example 7: Multicomponent Absorption, Dilute Case Air entering a tower contains 1 percent acetaldehyde and 2 percent acetone. The liquid-to-gas ratio for optimum acetone recovery is LM/GM = 3.1 mol/mol when the fresh-solvent temperature is 31.5°C. The value of yo/x for acetaldehyde has been measured as 50 at the boiling point of a dilute solution, 93.5°C. What will the percentage recovery of acetaldehyde be under conditions of optimal acetone recovery?

Solution. If the heat of solution is neglected, yo/x at 31.5°C is equal to 50(1200/7300) = 8.2, where the factor in parentheses is the ratio of pure-acetaldehyde vapor pressures at 31.5 and 93.5°C respectively. Since LM/GM is equal to 3.1, the value of S for the aldehyde is S = mGM/LM = 8.2/3.1 = 2.64, and y1/y2 = S/(S — 1) = 2.64/1.64 = 1.61. The acetaldehyde recovery is therefore equal to 100 x 0.61/1.61 = 38 percent recovery.

In concentrated systems the change in gas and liquid flow rates within the tower and the heat effects accompanying the absorption of all the components must be considered. A trial-and-error calculation from one theoretical stage to the next usually is required if accurate results are to be obtained, and in such cases calculation procedures similar to those described in Sec. 13 normally are employed. A computer procedure for multicomponent adiabatic absorber design has been described by Feintuch and Treybal [Ind. Eng. Chem. Process Des. Dev., 17, 505 (1978)]. Also see Holland, Fundamentals and Modeling of Separation Processes, Prentice Hall, Englewood Cliffs, N.J., 1975.

In concentrated systems, the changes in the gas and liquid flow rates within the tower and the heat effects accompanying the absorption of all components must be considered. A trial-and-error calculation from one theoretical stage to the next is usually required if accurate and reliable results are to be obtained, and in such cases calculation procedures similar to those described in Sec. 13 need to be employed.

When two or more gases are absorbed in systems involving chemical reactions, the system is much more complex. This topic is discussed later in the subsection "Absorption with Chemical Reaction."

Graphical Design Method for Dilute Systems The following notation for multicomponent absorption systems has been adapted from Sherwood, Pigford, and Wilke (Mass Transfer, McGraw-Hill, New York, 1975, p. 415):

LSM = moles of solvent per unit time

G0M = moles of rich feed gas to be treated per unit time

X = moles of one solute per mole of solute-free solvent fed to top of tower

Y = moles of one solute in gas phase per mole of rich feed gas

Subscripts 1 and 2 refer to the bottom and the top of the tower, respectively, and the material balance for any one component may be written as or else as

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