This article introduces the concept of minimal structure (MSTR) and presents an enumeration algorithm for the synthesis of heat exchanger networks based on MSTR. Minimal Structures refer to a class of heat exchanger networks featuring acyclic heat transfer networks without energy loops. The enumerations used are either exhaustive or smart with a stopping criterion. Without loss of generality we use the isothermal mixing Synheat model, that is, the method applies identically to other superstructures, with likely variations in the optimization models associated to each step. A conjecture is used to state that the algorithm renders solutions that are globally optimal. Literature examples are used to demonstrate the capabilities of the enumeration algorithm. Most of our solutions compare favorably with the best reported ones in literature, with exceptions where the reported solution is not minimal.

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This paper investigates the design optimization of double pipe heat exchanger using mathematical programming. The heat exchanger area is minimized and the thermo-fluid dynamic conditions are considered for the use of the right transport correlations, together with design specifications, such as, maximum pressure drops and minimum excess area. The modular nature of this kind of heat exchanger and the allocation of the streams (inside the inner tube or in the annulus) are also contemplated. Two mixed-integer nonlinear programming (MINLP) approaches are proposed. One approach relates the binary variables to the nonlinear constraints directly. In the second, the resulting nonlinearities involving binary variables are formally linearized, without loss of rigor (e.g., no use of truncated Taylor series). The proposed methodology can get better solutions than traditional trial and error procedures. The flexibility of the model is illustrated, together with a comparison between the performances of both MINLP formulations. Additionally, computational time and local optimality issues are discussed.

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