Optimal operation of multicomponent batch distillation—multiperiod formulation and solution

Abstract

A method is proposed to determine optimal multiperiod operation policies for binary and general multicomponent batch distillation of a given feed mixture, with several main products and intermediate off-specification cuts. A two-level optimal control formulation is presented so as to maximize a general profit function for the multiperiod operation, subject to general constraints. The solution of this problem determines the optimal amount of each main and off cut, the optimal duration of each distillation step and the optimal reflux ratio profiles during each production period. The outer level optimization maximizes the profit function by manipulating carefully selected decision variables. These are chosen in such a manner that the need of specifying the mole fractions of all the components in the products, as required by previous methods is avoided. For values of the decision variables fixed by the outer loop, the multiperiod operation is decomposed into a sequence of independent optimal control problems, one for each production step. In the inner loop, a minimum time problem is then solved for each step to generate the optimal reflux ratio values, reflux switching times and duration of the step. The procedure permits the use of very general distillation models described by differential and algebraic equations, including rigorous thermodynamics if desired. The model equations are integrated by using an efficient Gear's type method, the inner loop optimal control problems are solved using a variational method, and all optimisations are solved using a robust and efficient successive quadratic programming code (Chen, Ph.D. Thesis, Imperial College, 1988). Several example problems (involving binary and multicomponent mixtures) are used to demonstrate the idea and to show the effect of the cost functions used (in particular the value of the main products) on the optimal solutions.