Continuous countercurrent separation processes have been widely used in chemical and related industries for a long time. A well-recognized difficulty in controlling such processes is the nonlinearity of their dynamic behavior. Stemming from nonlinearity, an intriguing phenomenon known as "asymmetric dynamics" was observed by several investigators (Rose et al., 1956;Moczek et al., 1965; Mizuno et al., 1972;De Lorenzo et al., 1972;Fuentes and Luyben, 1983;Stathaki et al., 1985) in their numerical simulation of distillation columns. This term refers to the difference in response times either for a steady state perturbed by a pair of step changes of the same magnitude but in opposite directions, or for the forward and reverse transitions between two steady states. The latter type of asymmetry is of more interest for countercurrent processes. In particular, it was found that the transition departing from the optimal steady state (in the sense of maximum separation) is always faster than the corresponding transition returning to it (De Lorenzo et al., 1972;Stathaki et al., 1985). The difference is usually drastic (Rose et al., 1956; Mizuno et al., 1972). This note aims at providing a cause-and-effect analysis of such behavior by using the concept of wave propagation.Dynamic asymmetry emerges from nonlinearity of a process. Although nonlinearity of countercurrent processes may arise from complex configurations, its major cause is the nonlinearity of equilibrium between the two phases. Only a few studies to date have included the effect of nonlinear equilibrium on countercurrent dynamics. Mohr (1 965) examined the effect of curvature of the equilibrium curve on the response time in binary distillation. Fuentes and Luyben (1 983) showed severe dynamic nonlinearity in long distillation columns producing high-purity products, but did not identify the cause.To exploit nonlinear wave theory, we employ a differential rather than stagewise model because it gives a more readily visualized description of wave propagation. Especially for long columns (large number of transfer units), the differential model can provide a close approximation even to plate columns, and with comparable or less mathematical complexity. Specifically, the differential model developed previously (Hwang, 1987;Hwang andHelfferich, 1988 and1989) is used here to show that asymmetric dynamics in countercurrent operation is a natural consequence of nonlinear wave behavior. In addition, this analysis reveals a monitoring problem and suggests some control strategies for countercurrent processes.
ModelConsidered here is a stripping column, which resembles either section of a fractionating column, but without reflux and reboil. For mathematical demonstration, this stripper is described by a simple differential model which assumes a single-solute system (equivalent to binary distillation), negligible axial dispersion, constant flow rates and holdups, and a constant mass-transfer coefficient based on overall resistance across both phases. However, the effect of axial...