OPTIMAL OPERATION OF MULTICOMPONENT BATCH DISTILLATION MULTIPERIOD FORMULATION AND SOLUTION

A method is proposed to deter-mine optimal multiperiod operation polic ies for binary and general multicomponent batch distillation of a give n feed mixture, with several main products and intermediate off-specif ication 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 determi nes 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 pr ofit function by manipulating carefully selected decision variables. T hese are chosen in such a manner that the need of specifying the mole fractions of all the components in the products, as required by previo us methods is avoided. For values of the decision variables fixed by t he 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 st ep to generate the optimal reflux ratio values, reflux switching times and duration of the step. The procedure permits the use of very gener al distillation models described by differential and algebraic equatio ns, including rigorous thermodynamics if desired. The model equations are integrated by using an efficient Gear's type method, the inner loo p optimal control problems are solved using a variational method, and all optimisations are solved using a robust and efficient successive q uadratic programming code (Chen, Ph.D. Thesis, Imperial College, 1988) . Several example problems (involving binary and multicomponent mixtur es) are used to demonstrate the idea and to show the effect of the cos t functions used (in particular the value of the main products) on the optimal solutions.