EQUILIBRIUM-STAGE OPERATIONS

Your objectives in studying this section are to be able to  

Define the concepts stage, ideal stage, and cascade. 

Calculate the number of ideal stages in a cascade required for a given separation and ratio of flow rates. 

For most cases, because of either a curved operating line or equilibrium curve, the relation between number of stages, compositions, and flow ratio must be determined graphically, as shown. For the special case where both are straight, however, with the equilibrium curve continuing straight to the origin (Yi - mX(), an analytical 

Notice from equation (3-51) that the absorption factor is really the ratio of the slope of the operating line to that of the equilibrium relation. The Kremser equations are as follows  

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The analysis of equilibrium-stage operations is normally performed on the basis of counter-current flow between two phases. Because most separation processes, whether described in terms of equilibrium or mass transfer rates, operate in this flow scheme, it is useM to compare countercurrent to cocurrent flow. Figure 2.2 illustrates cocurrent and counter-current operation. Assuming mass transfer across a barrier between the two fluid phases, generic concentration profiles can be drawn for each case (Figure 2.3). 

Henley, E. J. and J. D. Seader, Equilibrium Stage Operations in Chemical Engineering (New York John Wiley and Sons, 1981). 

B. D. Smith, Design of Equilibrium Stage Operations, McGraw-Hill, New York, 1963. 

Both absorption and stripping can be operated as equilibrium stage operations with contact of liquid and vapor. Since distillation is also an equilibrium stage operation with contact of liquid and vapor, we would expect the equipment to be quite similar. This is indeed the case both absorption and stripping are operated in packed and plate towers. Plate towers can be designed by following an adaptation of the McCabe-Thiele method. Packed towers can be designed by use of HETP or preferably by mass transfer considerations (see Chapter 16T... 

Because of extract cling on the surface of the solid it is difficult to determine the position of the saturation line precisely. The apparent value of (Z/)m tends to decrease as the solid particle size decreases and cling consequently increases. If the amount of cling does not change, it can be treated as part of the solid for equilibrium-stage operations, and equilibrium compositions for the solid can be based on the apparent saturation line. For nonequilibrium processes, however, solid composition should be computed on a cling-free basis. 

Seader J.D. (1985). The B.C. (Before Computers) and A.D. of equilibrium-stage operations. Chemical... 

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