(380b) General Superstructure and Global Optimization Model for the Design of Integrated Process Water Networks

The process industry consumes a large amount of water. For instance, water is used for washing operations, separation processes, steam and power generation, cooling, etc. These processes in turn generate wastewater which is usually processed in treatment units before discharge to the environment. The shortage of freshwater, its increasing cost and the one of treatment processes, as well as strict environmental regulations on the industrial effluents provide a strong motivation for developing techniques to design more efficient process water networks. The two major approaches to address for the optimal design of water network systems are the water pinch technology and mathematical programming. The water pinch technology relies on graphic representations, while the mathematical programming approach is based on the optimization of a superstructure. A review of these approaches is given by Mann and Liu (1999), Bagajewicz (2000) and Je?owski (2008).

In this paper, we propose a novel superstructure and a general optimization model for the global optimal design of integrated process water networks. The superstructure consists of multiple sources of water, water-using processes, and water treatment operations. The unique features are first that all feasible interconnections are considered between them, including water re-use, water regeneration and re-use, water regeneration recycling and local recycling around process and treatment units. Second, multiple sources of water of different quality that can be used in the various operations are included. Third, the superstructure incorporates both the mass transfer and non-mass transfer operations, including cooling towers. The proposed model of the integrated water network is formulated as a Non-Linear Programming (NLP) and as a Mixed Integer Non-Linear Programming (MINLP) problem for the case when 0-1 variables are included to model the cost of piping and/or selection of technologies for treatment. The objective function of these problems is to minimize the total network costs. The MINLP model can be successfully used to find optimal solution of water network designs with various degrees of complexity of the piping network. In order to obtain the optimal solution for these non-convex models variable bounds are very important. In this work, we propose to express the bounds on the variables as general equations obtained by physical inspection of the superstructure and using logic specifications needed for successfully solving the model. We also incorporate the cut proposed by Karuppiah and Grossmann (2006) to significantly improve the strength of the lower bound for the global optimum. The proposed model is tested on the several illustrative examples, including large-scale problems. The general purpose global optimization solver BARON and LINDO GLOBAL are used to find the optimal design of the process water network. For large scale MINLP problems we propose a two-stage solution method in which we first solve the relaxed MINLP in order to fix a subset of 0-1 variables to zero so as to solve a reduced size MINLP. We also present results to illustrate how the complexity of the water networks can be controlled by restricting the number of piping connections.

Keywords: Integrated water networks; Superstructure optimization; Non-convex NLP and MINLP model;

References

Bagajewicz, M. (2000). A review of recent design procedures for water networks in refineries and process plants. Computers and Chemical Engineering, 24, 2093-2113.

Je?owski, J. (2008). Review and analysis of approaches for designing optimum industrial water networks. Chemical and Process Engineering, 29, 663-681.

Karuppiah, R., & Grossmann, I. E. (2006). Global optimization for the synthesis of integrated water systems in chemical processes. Computers and Chemical Engineering, 30, 650-673.

Mann, J. G., & Liu, Y. A. (1999). Industrial water reuse and wastewater minimization. New York, USA: McGraw-Hill.