A Multistage MINLP Superstructure Framework for Optimizing Concentration-Dependent Water Treatment Networks in Chemical Plants

Abstract Chemical plants, including petroleum refineries, generate and treat large volumes of wastewater, comprising complex mixtures of organic and inorganic contaminants. Managing treatment costs and freshwater use remains critical, particularly in water-scarce regions where industrial demand continues to strain freshwater supplies. Many existing water treatment network models employ simplified representations of treatment systems based on fixed removal efficiencies, single-stage treatment units, and uniform operating costs, while neglecting the influence of contaminant concentration on treatment performance and treatment economics. Such simplifications may limit the realism of the network designs and economic evaluations. To address these limitations, this work proposes a superstructure-based multistage water treatment network framework formulated as a mixed-integer nonlinear programming model. The framework incorporates concentration-range-dependent treatment-stage operation, stage-specific contaminant removal efficiencies, stage-specific treatment costs, and binary decision variables for the treatment-stage activation. The model minimizes total operating cost while determining freshwater consumption, internal water reuse, regeneration, discharge, and stream-blending decisions, all of which are subject to environmental and operational constraints. The effectiveness of the proposed framework is demonstrated through two case studies: a small-scale illustrative network and a petroleum refinery water-treatment network. The results reveal a trade-off between discharge stringency and operational expenditure, where stricter discharge limits require greater treatment intensity and higher treatment costs, whereas relaxed standards permit selective-stage deactivation and reduced regeneration requirements. By explicitly accounting for concentration-dependent treatment behavior and heterogeneous treatment costs, the proposed framework provides a flexible decision-support tool for industrial water network design and sustainable water management.