Heat exchanger network synthesis using a stagewise superstructure with non-isothermal mixing Ke Feng Huang a , Eid M. Al-mutairi b , I.A. Karimi a,b,n a Department of Chemical & Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore b Chemical Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia article info Article history: Received 14 July 2011 Received in revised form 4 November 2011 Accepted 17 January 2012 Available online 28 January 2012 Keywords: Heat exchanger network synthesis (HENS) Non-isothermal mixing Design Optimization System engineering Mathematical modeling abstract Much work on heat exchanger network synthesis (HENS) via mathematical programming has employed a stagewise superstructure with the assumption of isothermal mixing. It is well known that the superstructure may miss potentially better networks. In this article, we propose a mixed-integer nonlinear programming formulation and a solution strategy to incorporate non-isothermal mixing in HENS. We use an existing modification of the stagewise superstructure, propose novel and improved temperature bounds, and propose logical constraints to obtain superior HENs. Using several examples, we show that our approach finds superior networks compared to those known in the literature, especially for larger and more difficult problems. Furthermore, we propose exact approaches for handling log-mean temperature difference (LMTD) without numerical difficulty, and compare the effectiveness of the known LMTD approximations. We also show that including the stage bypass variables and constraints improves solution quality and efficiency. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction Energy is a global concern. Depleting fossil energy resources, soaring energy demands, stringent environmental regulations, alarming climate changes, growing international competition and market globalization, etc. highlight the importance of energy conservation. Heat exchanger network synthesis (HENS) is a holistic approach to utilize energy efficiently and economically in a chemical process. It tries to exchange heat optimally between the hot and cold process streams and utilities within a process to reduce energy consumption. Because of its extensive energy usage, the chemical process industry has given serious and significant attention to HENS in both research and practice for several decades now. Masso and Rudd (1969) were the first to define and formulate the problem of HENS. The basic idea is to derive a network of 2-stream heat exchangers with minimum total annualized cost (TAC), which integrates given sets of hot and cold process streams and utilities with known flow rates, heat contents, and inlet and outlet temperatures. Gundersen and Naess (1988), Linnhoff (1993), Jezowski (1994a, 1994b), and Furman and Sahinidis (2002) have reviewed the literature extensively. The early models or approaches (Linnhoff and Hindmarsh, 1983; Papoulias and Grossmann, 1983; Floudas et al., 1986; Re ´ v and Fonyo ´ , 1986; Wood et al., 1991; Suaysompol and Wood, 1991) for HENS were sequential. They viewed HENS as a sequence of three problems (Linnhoff and Ahmad, 1990) and relied on the concept of pinch (Linnhoff and Hindmarsh, 1983). Such approaches first compute minimum utility usage, then determine the minimum number of heat exchangers (HEs) for that usage, and finally minimize the total investment cost with the fewest HEs. While the sequential approach solves smaller subproblems, it may give suboptimal solutions, as it does not holistically trade-off the various factors (utility usage, number and areas of HEs, heat transfer across pinch) that impact TAC. Therefore, advances in optimization methodologies and tools have made the simultaneous approach more attractive in recent years, as it does not rely on the pinch concept and makes all decisions in a simultaneous and integrated manner to increase the possibility of obtaining better networks. Since this work focuses on the simultaneous approach based on mathematical programming, we limit our review of the work on the sequential approach. Most optimization models for the simultaneous synthesis of HENs employ a superstructure of possible 2-stream matches of HEs and result in a mixed-integer nonlinear programming (MINLP) model. Floudas et al. (1986) presented a hyperstructure of single-stage stream superstructures with the possibility of crossflow among them. The crossflow and mixing before each stage resulted in a nonlinear energy balance for each stream. Ciric Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ces Chemical Engineering Science 0009-2509/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2012.01.032 n Corresponding author at: Department of Chemical & Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore. Tel.: þ65 6516 6359; fax: þ65 6779 1936. E-mail address: cheiak@nus.edu.sg (I.A. Karimi). Chemical Engineering Science 73 (2012) 30–43