s- Fixed costs
FIG. 13-39 Location of the optimum reflux for a given feed and specified separation.
A system with constant relative volatility can be handled conveniently by the equation of Smoker [Trans. Am. Inst. Chem. Eng., 34, 165 (1938)]. The derivation of the equation is shown, and its use is illustrated by Smith (op. cit.).
Stage Efficiency The use of the Murphree plate efficiency is particularly convenient on y-x diagrams. The Murphree efficiency is defined for the vapor phase as n = (yn - yn - i)/(y* - yn -1) (13-29)
where y*n is the composition of the vapor that would be in equilibrium with the liquid leaving stage n and is the value read from the equilibrium curve. The yn - 1 and yn are the actual (nonequilibrium) values for vapor streams leaving the n - 1 and n stages respectively. Note that the yn-1 and yn values assume that vapor streams are completely mixed and uniform in composition. An analogous efficiency can be defined for the liquid phase.
The application of a 50 percent Murphree vapor-phase efficiency on a y-x diagram is illustrated in Fig. 13-40. A "pseudo-equilibrium" curve is drawn halfway (on a vertical line) between the operating lines and the true-equilibrium curve. The true-equilibrium curve is used for the first stage (the partial reboiler is assumed to be an equilibrium stage), but for all other stages the vapor leaving each stage is assumed to approach the equilibrium value y * only 50 percent of the way. Consequently, the steps in Fig. 13-40 represent actual trays.
Application of a constant efficiency to each stage as in Fig. 13-40 will not give, in general, the same answer as obtained when the number of equilibrium stages (obtained by using the true-equilibrium curve) is divided by the same efficiency factor.
The prediction and use of stage efficiencies are described in detail in Sec. 14.
Miscellaneous Operations The y-x diagrams for several other column configurations have not been presented here. The omitted items are partial condensers, rectifying columns (feed introduced to the bottom stage), stripping columns (feed introduced to the top stage), total reflux in the top section but not in the bottom section, multiple feeds, and introduction of open steam to the bottom stage to eliminate the reboiler. These configurations are discussed in Smith (op. cit.) and Henley and Seader (op. cit.), who also describe the more rigorous Ponchon-Savarit method, which is not included here.
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