This paper provides a critical review of the literature on heat-exchanger network synthesis, the most commonly studied problem in process synthesis. After a review of solution methods, we present the chronological milestones in the development of the field and we discuss separately each of 461 related works leading up to the turn of the century. Then, we present several classification schemes of this body of work based on a number of modeling and algorithmic criteria. Finally, we offer a critical assessment of the current status of research in this area and provide suggestions for future research.

In this work we present an Outer-Approximation algorithm to obtain the global test examples, significant savings were realized in the computational effort required to obtain the globally optimal solutions and to verify their global optimality.

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A generalized model is proposed for the continuous time scheduling problem of fluid transfer in tanks. This model generally and more robustly handles the synchronization of time events with material balances than previous proposed models in the literature. A novel method for representing the flow to and from a tank is developed with the potential for significant reduction in the number of necessary time events required for continuous time scheduling formulations. The problem involves the optimal operation of fluid transfer from input sources to tanks, transfer between the tanks, and the transfer from tanks to output destinations. An efficient mixed-integer nonlinear programming formulation is developed based on continuous representation of time domain under the assumption of no simultaneous input and output flow to a tank for fluid streams comprised of multiple components. The new modeling paradigm is applied to examples from the literature for developing refinery crude unit charging schedules.

Although the use of heuristics has been prevalent in the process synthesis literature, their justification has been exclusively based on empirical evidence obtained through computational testing. As a result, heuristics currently in use offer no guarantee of optimality. Optimization algorithms, on the other hand, offer rigor but suffer from the combinatorial explosion of computational requirements necessary to produce an optimal solution. Recognizing this gap between heuristic and optimization approaches in process synthesis, we propose the use of analytical techniques in the development and assessment of heuristics. The primary purpose of this paper is to introduce the analysis of algorithm performance into the field of process synthesis and develop the first approximation algorithms for process synthesis. Approximation algorithms are heuristics with guaranteed performance. In the context of the classical matches problem in heat exchanger network synthesis, we develop approximation algorithms based on primal rounding, dual rounding, Lagrangean relaxation rounding, primal−dual approximation, and greedy approximation. We provide an analytical characterization of the worst-case behavior of these as well as any heuristic that may be devised for the matches problem. In computational experiments with a test set of 29 problems from the literature, we find that the developed suite of algorithms performs much better than its theoretical worst-case bound and provides solutions that average within 25% of optimality. On the other hand, five of these test problems are beyond the capabilities of current state-of-the-art optimization software. Finally, we pose a number of interesting research challenges in this area.