Modeling and stage-to-stage computation of multicomponent distillation processes as a multistage optimization problem

This paper presents a general formulation and a simulation method for multicomponent distillation processes. The design of distillation columns is formulated as a multistage optimization problem. A new iterative method is developed for generating feasible solutions and solving the necessary conditions for an extremum. The independent variables are the bottom liquid compositions. Analytical equations are used for the partial derivatives of vapor compositions with respect to liquid compositions by use of the implicit function theorem. This method can avoid the numerical difficulties that other stage-to-stage methods often present and exhibits good convergence characteristics for ten typical distillation problems in complex columns.