Presented herein is the formulation of a more general model for the unsteady state operation of a distillation column than has been available previously. Suitable numerical methods for solving the equations required to describe the model are also presented. The reliability of the proposed numerical methods was established by solving a wide variety of problems ( 1 8 ) . To demonstrate some of the characteristics of the model as well as possible uses, such as the analysis of various control schemes, selected numerical results are presented in a subsequent section.In general, the models proposed for distillation columns in unsteady state operation may be divided into two groups: one group consists of those models used to obtain analytical and analog computer solutions; and the other group consists of those models used to obtain numerical solutions by use of digital computers. Analytical and analog models generally require many simplifying assumptions, such as linear equilibrium relationships, the lumping together of plates, and the treatment of multicomponent mixtures as binary mixtures. In the past these models have proved to be useful for the broad understanding of the operation of distillation columns ( 6 ) and are presently being used successfully as a basis for column control (9).Models of the second group used to obtain numerical solutions on digital computers need not contain many of the simplifying assumptions generally used for the simpler analytical and analog models. Models of the second group, which give an accurate description of column operation, Previous models have neglected the combination of mixing effects on the plates and in the downcomers, and in most models the mixing effects in the holdups of the reflux drum and transfer lines have been neglected also.The present model includes the effect of mixing in all of these holdups. Liquid passing through a column exhibits some degree of mixing in the direction of bulk flow. The mixing effects of a liquid in bulk flow, without dead volume, on a plate and its downcomer are bounded by those for the three limiting cases: perfect mixing, plug flow, and channeling. The third limiting case was introduced to acreasons for t K eir superiority over the approximate models
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