The mathematical models presented earlier for rigorous calculations of multistage, multicomponent distillation-type separations assume that equilibrium with respect to both heat and mass transfer is attained at each stage. Unless temperature changes significantly from stage to stage, the assumption that vapor and liquid phases exiting from a stage are at the same temperature is generally valid. However, in most cases, equilibrium with respect to mass transfer is not a valid assumption. If all feed components have the same mass-transfer efficiency, the number of actual stages or trays is simply related to the number of equilibrium stages used in the modeling calculations by an overall stage efficiency. For distillation, as discussed in Sec. 14, this efficiency for well-designed trays typically varies from 40 to 120 percent; the higher value being achieved in some large-diameter towers because of a cross-flow effect. Efficiencies for absorption and extractive distillation can be lower than 40 percent.
When it is desired to compute, with rigorous methods, actual rather than equilibrium stages, Eqs. (13-69) and (13-94) can be modified to include the Murphree vapor-phase efficiency n y, defined by Eq. (13-29). This is particularly desirable for multistage operations involving feeds containing components of a wide range of volatility and/or concentration, in which only a rectification (absorption) or stripping action is provided and all components are not sharply separated. In those cases, the use of a different Murphree efficiency for each component and each tray may be necessary to compute recovery accurately.
Departures from the equilibrium-stage model may also occur when entrainment of liquid droplets in the rising vapor or occlusion of vapor in the liquid flow in the downcomer is significant. The former condition may occur at high vapor loading when flooding is approached. The latter condition is possible at high operating pressures when vapor and liquid densities are not drastically different. Entrainment and occlusion effects are not strictly due to mass-transfer inefficiency and are best taken into account by including entrainment terms in the modeling equations, as shown by Loud and Waggoner [Ind. Eng. Chem. Process Des. Dev., 17, 149 (1978)].
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