Stochastic programming in process synthesis: A two-stage model with MINLP recourse for multiperiod heat-integrated distillation sequences

Abstract

This paper presents a two-stage stochastic programming approach with MINLP recourse for the synthesis problem of heat integrated distillation sequences that can handle prespecified changes in the composition and/or flowrate of the multicomponent feed to the separation system for a finite number of periods of operation. A new synthesis strategy is proposed that combines the aspects of a superstructure approach with a partitioning of the design variables into two classes: structural and periodic. Structural design variables comprise the fixed elements of a design that are common to all operating conditions, while the periodic design variables are adjustable quantities that can be changed for optimal operation in each period. The synthesis strategy identifies the optimal separation sequence and selection of heat exchanger units that can accommodate the different periods of operation. In addition, for each selected unit, the approach provides simultaneous optimization of the column press ure, reflux ratio, number of trays, diameter and heat integration/exchange matches. The column pressure, reflux, number of trays and diameter are treated explicitly as continuous variables in the model. The mathematical formulation that results is a large-scale mixed-integer nonlinear programming (MINLP) problem. The structure of the problem can be exploited by viewing the multiperiod design problem as a two-stage stochastic programming problem with the feed composition and flowrate as the uncertain parameters. The different periods of operation provide the discretization of the uncertainty and the multiple scenarios of operation have (MINLP) recourse. A nested solution procedure is detailed that combines the Generalized Benders Decomposition and the Outer Approximation/Equality Relaxation algorithms. Emphasis is given to the application of this type of approach to the general synthesis problem and its potential for extension to design problems under uncertainty and/or flexibility requirements. Application of the approach is illustrated through an example problem.