This chapter focuses on heat exchanger network synthesis approaches based on optimization methods. Sections 8.1 and 8.2 provide the motivation and problem definition of the HEN synthesis problem. Section 8.3 discusses the targets of minimum utility cost and minimum number of matches. Section 8.4 presents synthesis approaches based on decomposition, while section 8.5 discusses simultaneous approaches. Heat exchanger network HEN synthesis is one of the most studied synthesis/design problems in chemical engineering. This is attributed to the importance of determining energy costs and improving the energy recovery in chemical processes. The comprehensive review of Gundersen and Naess (1988) cited over 200 publications while a substantial annual volume of studies has been performed in the last few years. The HEN synthesis problem, in addition to its great economic importance features a number of key difficulties that are associated with handling: (i) The potentially explosive combinatorial problem for identifying the best pairs of hot and cold streams (i.e., matches) so as to enhance energy recovery; (ii) Forbidden, required, and restricted matches; (iii) The optimal selection of the HEN structure; (iv) Fixed and variable target temperatures; (v) Temperature dependent physical and transport properties; (vi) Different types of streams (e.g., liquid, vapor, and liquid-vapor); and (vii) Different types of heat exchangers (e.g., counter-current, noncounter-current, multistream), mixed materials of construction, and different pressure ratings. It is interesting to note that the extensive research efforts during the last three decades toward addressing these aforementioned difficulties/issues exhibit variations in their objectives and types of approaches which are apparently cyclical. The first approaches during the 1960s and early 1970s treated the HEN synthesis problem as a single task (i.e., no decomposition into sub-tasks). The work of Hwa (1965) who proposed a simplified superstructure which he denoted as composite configuration that was subsequently optimized via separable programming was a key contribution in the early studies, as well as the tree searching algorithms of Pho and Lapidus (1973). Limitations on the theoretical and algorithmic aspects of optimization techniques were, however, the bottleneck in expanding the applicability of the mathematical approaches at that time.
On the Number of Shortest Weighted Paths in a Triangular Grid