Simultaneous Optimization of Heat-Integrated Water Allocation Networks Using the Mathematical Model with Equilibrium Constraints Strategy

Abstract

A general optimization model is proposed for the simultaneous optimization of integrated water allocation and heat exchanger networks (WAHEN). An improved superstructure and mathematical model for the WAHEN problem is presented. Complementary formulations are applied to model the discrete decisions, and a mathematical model with equilibrium constraints (MPEC) is formulated. Both the MINLP model and the MPEC model are developed and solved for the problem. The effectiveness of the proposed model is illustrated with two case studies. A comparison between the results obtained by the proposed model and those obtained from the model in the literature is carried out. Case studies show that the proposed simultaneous methodology performs well and is efficient.

Water and energy integration: A comprehensive literature review of non-isothermal water network synthesis

“…The best reported results (2,652,959 $/y) until now have been obtained by an MP applying MINLP models Ibrić et al, 2013a) or using complementary formulations to model discrete decisions , where an MINLP was reformulated as a mathematical programme with equilibrium constraints (MPEC). The reader is referred to the papers Zhou et al, 2015;Liu et al, 2015b) which provide comparisons of the results for this example obtained by different approaches and methods reported within the literature. Table 10 presents the summarised results for this example.…”

Synthesis of Heat-Integrated Water Allocation Networks: A Meta-Analysis of Solution Strategies and Network Features

“…Nevertheless the original mathematical formulation was not decomposed before solving [110,113,120,143]). Generally, an MINLP model requires good initialization which can be achieved by solving a relaxed instance of the original model either through fixing continuous variables (resulting in an MILP initialization model), fixing binary variables (mainly by excluding the HEN matches, and hence resulting in an NLP model [124,126,[129][130][131]134]), solving an MINLP model of water network with no heat integration [133], or by generating random values [38,135]. Boondarik Leewongwanawit [108] used an MILP model for initialization of MINLP superstructure by fixing the contamination loading at the outlet of water units and linearizing the HEN cost formulation.…”

“…Under this classification, the original MINLP model is transformed/simplified/relaxed by redefining/removing/adding extra constraints. Zhou et al [135] formulated a HIMAN superstructure using MPEC and applied complementarity formulations [155] to model binary variables. They solved the problem by transforming the model into NLP.…”

Design of a water allocation and energy network for multi-contaminant problems using multi-objective optimization

“…Removal ratio Gunaratnam et al (2005)˛based on Bagajewicz and Faria (2009) Inlet temp. Table 3 -Cost and operating parameters for the HEN (Zhou et al, 2015). Overall and partial heat transfer coefficients for hot and cold streams…”

“…Recently, simultaneous approaches have been widely used for non-isothermal streams mixing (Bogataj and Bagajewicz, 2008), in the case of mono-contaminant or multi-contaminant networks (Liao et al, 2011;Leewongtanawit and Kim, 2008;Dong et al, 2008;Bogataj and Bagajewicz, 2008;Ahmetović and Kravanja, 2014;Chen et al, 2014;Hou et al, 2014;Zhou et al, 2015;Yan et al, 2016b). A thorough review of the related works can be found in (Morar and Agachi, 2010;Ahmetović et al, 2015).…”