Mathematical model for heat integrated water network systems

Water is crucial for process industries to carry out its operations. Water used in the process industries, may require heating and/or cooling to meet its operating temperature requirements. This requires synthesis of a heat integrated water network (HIWN) to manage water and energy of a process industry in an economic and sustainable manner. HIWN is obtained by combining water network design model (having freshwater sources, water using process units and wastewater treatment units etc.) with the heat exchanger network (HEN) design model. Several sequential (water network and HEN are solved separately and sequentially) and simultaneous (water network and HEN are combined and solved as a single system) methodologies have been developed for the synthesis of HIWNs in the literature, with the simultaneous models seemingly providing HIWN with better costs because of simultaneously considering appropriate trade-offs in the elements of water network and HEN. This paper presents a new superstructure and step-wise solution strategy for the synthesis of HIWN. The step-wise solution strategy involves the solution of two mathematical models. The first model aims to minimize water and energy costs of the entire network. The goal of this model is to find minimum freshwater and optimal water flowrates within the network. Using these optimal flowrates, different topological configurations of the entire network are enumerated and evaluated for the purpose of heat integration. The second model is the stage-wise HEN model which is solved for each of the evaluated network topological configuration in a sequential manner. Using this proposed sequential methodology, a set of locally optimal HIWN are produced from which the best one is chosen based on a particular objective. The objective, in this study, is to synthesize HIWN with minimum total annualized cost (TAC). A case study from the literature is used to test the proposed mathematical model and solution strategy. The result from the tested example show that the TAC of HIWN obtained using the proposed mathematical model and solution strategy, despite being sequential in nature, provided solutions that are close to those obtained using simultaneous approaches.