A superstructure optimization approach for water network synthesis with membrane separation-based regenerators

This work addresses the problem of water network synthesis. We propose a superstructure with fixed topology for a water network that consists of three layers, similar to a pooling problem: sources for reuse/recycle; regenerators for contaminants removal; and sinks for acceptance of water for reuse/recycle. The superstructure encompasses multiple freshwater sources, membrane separation-based partitioning regenerators of the industrially favored ultrafiltration and reverse osmosis, and sinks for incineration and deep ocean discharge. A mixed-integer nonlinear program is formulated based on this superstructure to determine the optimal interconnections in terms of total flowrates and contaminant concentrations. The main decisions include determining the split fractions of the source flowrates, extents of regeneration, and mixing ratios of the sources and regenerated streams subject to compliance with the maximum allowable inlet contaminant concentration limits of the sinks and discharge regulations. We also develop linear models for the membrane regenerators that admit a more general expression for the retentate stream concentration based on liquid-phase recovery factors and removal ratios. Computational studies are performed using GAMS/BARON on an industrially significant case study of a petroleum refinery water system. We incorporate linear logical constraints using 0-1 variables that enforce certain design and structural specifications to tighten the model formulation and enhance solution convergence. A globally optimal water network topology is attained that promotes a 27% savings equivalent to about $218,000/year reduction in freshwater use.