A mixed-integer nonlinear programming formulation for the synthesis of heat-integrated distillation sequences

Abstract

Sequences of distillation columns are widely employed in chemical plants as the main system for the separation of various multicomponent mixtures into their components. Considerable savings in plant operating costs can often be obtained by adjusting the operating pressures of the columns in a separation sequence so as to allow for heat transfer between the condenser of one column and the reboiler of another. Because of the importance of distillation sequences in the operation of the entire chemical process and the large investment and operating costs represented by them, the synthesis of optimal heat-integrated distillation sequences becomes an important synthesis problem. In this paper, a systematic framework is presented for the synthesis problem of heat-integrated distillation sequences with the column pressures treated as continuous variables for a single multi-component feed of fixed composition. This framework consists of the mathematical formulation of the distillation sequence superstructure as a mixed-integer nonlinear programming MINLP problem. The mathematical formulation features as an objective function, the minimum total annual cost comprised of investment costs for the distillation columns and heat exchangers plus the operating costs based on utility consumption. The heat integration options are incorporated in the proposed formulation through the assignment of integer variables representing the potential condenser-reboiler matches. Solution of this mathematical formulation, which can be obtained automatically using the computer programming procedure APROS provides the optimal distillation sequence and heat integration matches as well as the operating pressures required for each column. The effectiveness of this systematic framework is illustrated with three example problems.