A disjunctive programming model for superstructure optimization of power and desalting plants

In this paper, a new formulation based on disjunctive programming to model the superstructure of alternative configurations for the synthesis, design and analysis of combined cycle power and desalination plant recently developed in Mussati et al. [Desalination, 182 (2005) 123–129] is presented. In this new formulation, boolean variables model discrete decisions while continuous variables represent the operation conditions of the process, e.g., flow rates, energy demand. Optimal unit configuration and operating conditions are computed by solving the proposed model in order to satisfy electricity generation and freshwater productions demands. Rigorous, non-convex and highly non-linear constraints are involved in the formulation, therefore, robust and efficient solution algorithms have to be used. The Logic-Based Outer Approximation (LOA) algorithm developed by Turkay and Grossmann [Comp. Chem. Eng., 20 (8) (1996) 959] with the modifications introduced by Yeomans and Grossmann [Ind. Eng. Chem. Res., 39 (6) (2000) 1637] are used as part of the solution procedure. The model is implemented and solved in the General Algebraic Modeling System (GAMS). Several study cases for different required power to water ratios are presented and analyzed in order to illustrate the robustness and computational performance of the proposed model.

This paper has presented a Generalized Disjunctive Programming model for the optimal synthesis and design of a DPP. The LOA algorithm developed by Turkay and Grossmann [15] with the modifications introduced by Yeomans and Grossmann [14] has been implemented in the solution procedure. This algorithm solves the disjunctive programming problem by iterating between reduced NLP subproblems and MILP master problems. Several examples have been successfully solved by applying the algorithm, from which two examples have been presented in this paper to illustrate the robustness and computational performance of the proposed formulation. Despite that the MINLP formulation presented recently in Mussati et al. [3] has efficiently solved the problem for different demands of freshwater and electricity, the proposed GDP formulation resulted to be more flexible and robust than the MINLP formulation which convergence is strongly dependent on a good initial solution. In fact, the convergence of the NLP subproblems in the GDP solution algorithm is facilitated because the constraints related to selected equipments are only considered in the problem, increasing its robustness and flexibility. In addition, we have observed that the GDP formulation is not as strongly dependent on the initial values as the MINLP formulation.