Heat exchanger network synthesis with non-isothermal mixing using a stagewise superstructure

Abstract

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. As a holistic approach to utilize energy efficiently and economically in a chemical process, heat exchanger network synthesis (HENS) 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. Many optimization models for the simultaneous HENS have employed superstructures (Yee & Grossmann, 1990; Ciric & Floudas, 1991) of possible 2-stream matches of HEs. Yee & Grossmann (1990) proposed a multistage superstructure of HEs for each stream. They assumed that all split substreams of a stream exiting a stage have the same temperature. The literature has called this assumption isothermal mixing, which makes the energy balances for substream mixing at each stage linear. However, as Yee & Grossmann (1990) explained, the stagewise superstructure misses several HEN configurations, and the assumption of isothermal mixing obviously omits configurations involving non-isothermal mixing. Yee & Grossmann (1990) remarked that isothermal mixing may restrict the area trade-offs between the exchangers and overestimate the area cost, when stream splits with non-isothermal mixing may give superior HENs. In spite of these known limitations of isothermal mixing, non-isothermal mixing in stagewise superstructure has attracted limited attention in the HENS literature. Yee & Grossmann (1990) proposed an effective heuristic strategy to improve the suboptimal HENS arising from isothermal mixing. While this strategy overcomes partially the impact of isothermal mixing, the overall approach still cannot guarantee a global solution due to the inherent nonconvex nature of the simultaneous HENS. Bjork & Westerlund (2002) compared HENS with and without isothermal mixing in the stagewise superstructure of Yee and Grossmann (1990) using a global optimization strategy. Recently, Hasan et al. (2009) slightly modified the stagewise superstructure and generalized simultaneous HENS to address non-isothermal phase changes, nonlinear T-H profiles, and non-isothermal mixing. In this work, we modify the Synheat model of Yee and Grossmann (1990) to address HENS with non-isothermal mixing. Specifically, we focus on the limitations of literature models for handling non-isothermal mixing, and propose new and improved bounds and logical constraints to obtain superior HENs. We demonstrate the effectiveness of our modifications and solution algorithms by presenting examples in which our approach yields better HENs compared to the existing literature. We show that even the global optimization algorithm of Bjork & Westerlund (2002) for non-isothermal mixing fails to obtain globally best HENs in case of some large problems. We also study the impact of using LMTD approximations in HENS formulations.