Two-step mathematical programming synthesis of pinched and threshold heat-integrated water networks

• Synthesis of heat-integrated water networks without treatment units is studied.
• A novel model is proposed for the synthesis of pinched and threshold problems.
• A two-step strategy is presented to efficiently solve related non-convex problems.
• Three examples are solved in order to illustrate the proposed solution strategy.

This contribution describes a novel simultaneous mathematical programming model for the synthesis of pinched and threshold heat-integrated water networks (HIWNs). A two-step solution strategy is proposed consisting of a subsequent solution using two models. Firstly, the nonlinear programming (NLP) targeting model is solved by assuming a given value for the heat recovery approach temperature (HRAT), with the objective of minimising the operating cost of the network. This model provides a good initialisation point and rigorous bounds (freshwater and utilities consumption) for the mixed integer nonlinear programming (MINLP) model solved during the second synthesis step. The solution procedure is repeated for a range of HRAT values providing different initialisations and constraints identifying a set of good locally-optimal solutions. In this study we considered and presented solutions for three types of HIWN problems, namely, pinched in which both utilities are required, threshold in which a hot utility is required, and threshold requiring a cold utility. The obtained results indicate that the proposed mathematical programming model and the solution strategy can be successfully applied to the synthesis of pinched and threshold HIWNs.