Mathematical methods for heat exchanger network synthesis

This paper gives an overview of the evolution of mathematical methods for heat exchanger network synthesis over the last 25 years. Two major developments have been methods for targeting and methods for automated synthesis through simultaneous optimization. The former have helped to expand the scope and increase the accuracy of pinch based methods; the latter have provided a framework to automate the synthesis of networks while explicitly accounting for trade-offs between energy consumption, number of units and area. Basic ideas behind these methods are discussed, as well as their capabilities and implementation in computer software. Several application examples are also presented. The paper concludes with the major lessons that have been learned in developing these methods, as well as future directions and prospects for automated synthesis capabilities which can greatly enhance the productivity of design engineers and the quality of their designs. Introduction Given that industrial applications for heat exchanger network (HEN) synthesis have proved to be very successful (e.g. see Linnhoff and Vredeveld, 1984; Gundersen and Naess, 1987) one may wonder as to why there is a need to investigate and develop synthesis techniques that are based on mathematical methods. Is this just an interesting academic exercise, or are there in fact capabilities in these methods that cannot be accomplished with the largely graphical and manual techniques of pinch based methods? Furthermore, to what extent do mathematical methods replace or complement the decision making process of engineers in the synthesis of these networks? The above questions, which were prevalent in the early 80s, have to a large extent been resolved with the research work that has been done and over the last 10 years. Mathematical methods for the synthesis of HEN's have shown that they can play an important role in terms of automating the search among many design alternatives, while explicitly accounting for economic trade-offs between investment and operating costs. Furthermore, it has been shown that these methods can be used effectively by engineers without having to be experts in optimization, and in a way where their productivity can be enhanced, while allowing them to retain control of the synthesis process. Mathematical methods in fact are complementary in nature to the ones based on physical insights. It has also been shown that aside from the fact that mathematical methods can produce innovative solutions, they can also be extended beyond HEN synthesis so as to perform process flowsheet optimization simultaneously with heat integration which can produce substantial economic savings. Despite these advances it is clear that not all the issues have been solved with mathematical techniques; for instance, problem size and nonconvexities are still problems that await for improved solutions. It is the main purpose of this paper to provide a general overview of mathematical methods giving a brief account on how they have evolved, emphasizing the most recent developments. Due to space limitations in this paper, we will not dwell into the detailed mathematical formulations of the various models that have been proposed. Instead, we will University Libraries Carnegie Mellon University 1 Pittsburgh PA 15213-3890 highlight the main ideas and show the application of the techniques with several example problems. Finally, current limitations and future directions will be discussed. Assumptions and basic equations Mathematical optimization models have commonly relied on the following assumptions for synthesizing HENHs: a) Constant heat capacity flowrates b) Fixed inlet and outlet temperatures c) Constant heat transfer coefficients d) Single-pass countercurrent heat exchangers e) Layout and pressure drop costs are neglected f) Operating cost is given in terms of the heat duties of utilities g) Investment cost is given in terms of the areas of the exchangers. A number of the above assumptions can in fact be relaxed with some of the methods, although often at the expense of significant computational expenseAlso, it should be noted that while initially fixed minimum temperature approaches had to be assumed, (HRAT heat recovery approach temperature, EMAT individual exchanger approach) this is no longer required in the most recent methods as will be discussed later in the paper. Based on the above assumptions, the three basic modules or units for HEN's are modelled as follows (see Fig. 1): a) Splitter mass balance F i F } + I f (1) which gives rise to linear equations. b) Mixer heat balance FT= F* TJ + F? T? f>\ which gives rise to nonlinear (bilinear) equations. c) Heat exchanger heat balance, design equation Q = Fi(Tj-T?) Q = i«H> (3) Q=UA(T;-tf)-q?-tj)