(540b) Global Optimization for the Synthesis of Integrated Water Systems in Chemical Processes

Karuppiah, R., Carnegie Mellon University
Grossmann, I. E., Carnegie Mellon University

The efficient and responsible utilization of water in the process industry is becoming a very important problem, given the increasing concerns about the environmental impact of effluent discharge and shortages of water that are predicted in the next few decades. The conventional approach that has been used is to import freshwater for process use (e.g. reaction, extraction), and then perform treatment of the wastewater generated, in a central common facility to remove contaminants to meet regulatory specifications for water disposal. In order to reduce the intake of freshwater in the water using processes, water reuse schemes can be used. Furthermore, to reduce the cost of wastewater treatment, decentralized configurations of the treatment networks have been proposed, in which effluent streams from different sources are treated separately instead of combining them into a single stream prior to treatment. This reduces the capital and operating costs since these are directly proportional to the water flowrate through a treatment unit.

Synthesizing an optimal network that integrates both water reuse and wastewater treatment, is a major challenge as there are many possible design alternatives, and also because the mathematical models of the integrated networks involve non-convexities. Most of the studies in the past have addressed the problem of optimizing water using process networks separately from that of optimizing wastewater treatment networks (see Bagajewicz (2000) for a review). Furthermore, most of these methods do not guarantee global optimality. In this work, 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 in such a way that the total cost of obtaining freshwater for use in the water using operations, and treating wastewater is globally minimized. A general superstructure, which incorporates all feasible design alternatives for water treatment, reuse and recycle, is proposed. We formulate the optimization of this superstructure 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 globally optimizing such systems, in which piecewise under- and over-estimators are used to approximate the non-convex (bilinear and concave) 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 optimum within a branch and bound procedure. We also propose a special cut and some computational strategies to expedite the search for the global optimum within the branch and bound framework. The proposed method has been applied to the optimization of several integrated water networks, involving up to 5 process units, 3 treatment units and 3 contaminants. The computational expense of the proposed algorithm was compared with that of using GAMS/BARON 7.2 (Sahinidis, 1996), a general purpose software for global optimization. It was observed that while BARON works well for small problems, it fails to verify global optimality of the solution for large problems, while the proposed global optimization technique was found to take a reasonable amount of computational time for finding the global optimum, even for medium and large scale systems.


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