Global optimization for the synthesis of integrated water systems in chemical processes

In this paper, we address the problem of optimal synthesis of an integrated water system, where water using processes and water treatment operations are combined into a single network such that the total cost of obtaining freshwater for use in the water using operations, and treating wastewater is globally minimized. A superstructure that incorporates all feasible design alternatives for water treatment, reuse and recycle, is proposed. We formulate the optimization of this structure as a non-convex Non-Linear Programming (NLP) problem, which is solved to global optimality. The problem takes the form of a non-convex Generalized Disjunctive Program (GDP) if there is a flexibility of choosing different treatment technologies for the removal of the various contaminants in the wastewater streams. A new deterministic spatial branch and contract algorithm is proposed for optimizing such systems, in which piecewise under- and over-estimators are used to approximate the non-convex terms in the original model to obtain a convex relaxation whose solution gives a lower bound on the global optimum. These lower bounds are made to converge to the solution within a branch and bound procedure. Several examples are presented to illustrate the optimization of the integrated networks using the proposed algorithm.