The design of a tray tower for gas absorption and gas-stripping operations involves many of the same principles employed in distillation calculations, such as the determination of the number of theoretical trays needed to achieve a specified composition change (see Sec. 13). Distillation differs from absorption because it involves the separation of components based upon the distribution of the various substances between a vapor phase and a liquid phase when all components are present in both phases. In distillation, the new phase is generated from the original phase by the vaporization or condensation of the volatile components, and the separation is achieved by introducing reflux to the top of the tower.
In gas absorption, the new phase consists of a relatively nonvolatile solvent (absorption) or a relatively insoluble gas (stripping), and normally no reflux is involved. This section discusses some of the considerations peculiar to gas absorption calculations for tray towers and some of the approximate design methods that can be applied (when simplifying assumptions are valid).
Graphical Design Procedure Construction of design diagrams (xy curves showing the equilibrium and operating curves) should be an integral part of any design involving the distribution of a single solute between an inert solvent and an inert gas. The number of theoretical trays can be stepped off rigorously, provided the curvatures of the operating and equilibrium lines are correctly represented in the diagram. The procedure is valid even though an inert solvent is present in the liquid phase and an inert gas is present in the vapor phase.
Figure 14-8 illustrates the graphical method for a three theoretical stage system. Note that in gas absorption the operating line is above the equilibrium curve, whereas in distillation this does not happen. In gas stripping, the operating line will be below the equilibrium curve.
On Fig. 14-8, note that the stepping-off procedure begins on the operating line. The starting point xr, y3 represents the compositions of the entering lean wash liquor and of the gas exiting from the top of the tower, as defined by the design specifications. After three steps one reaches the point Xi, yf representing the compositions of the solute-rich feed gas yf and of the solute-rich liquor leaving the bottom of the tower x1.
Algebraic Method for Dilute Gases By assuming that the operating and equilibrium curves are straight lines and that heat effects are negligible, Souders and Brown [Ind. Eng. Chem., 24, 519 (1932)] developed the following equation:
where N = number of theoretical trays, y1 = mole fraction of solute in the entering gas, y2 = mole fraction of solute in the leaving gas, y2 = mx2 = mole fraction of solute in equilibrium with the incoming solvent
Operating curve (slope =LM/GMK
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