Mathematical programming synthesis of non-isothermal water networks by using a compact/reduced superstructure and an MINLP model

The synthesis problems of non-isothermal water networks, combining heat exchanger network and water network (WN), usually consist of a significant number of constraints and variables, namely, flow rates, contaminant concentrations, temperatures and a large number of non-linear terms. In most cases, solving medium and large-scale synthesis problems is computationally too expensive and challenging. In order to circumvent that problem, we propose a compact superstructure and mixed-integer non-linear programming model for the simultaneous synthesis of non-isothermal WNs. The proposed superstructure includes heat integration stages enabling direct and indirect heat exchanges with a manageable number of hot and cold streams. This reduces the models size enabling easier solutions of the synthesis problems using local solvers. In addition, a superstructure reduction strategy is proposed making the superstructure flexible and adaptable for different types of problems, namely, pinched and threshold, and providing additional reduction of connections within the proposed superstructure. The proposed model is solved using a two-step solution strategy including initialisation and design steps. The model is applied to the examples of different complexities including single and multiple contaminant problems, and water-using and wastewater treatment units. Using the proposed iterative strategy, the improved locally optimal solutions are identified for most examples, minimising the total annual cost of the overall network.