The design of heat exchangers, especially shell and tube heat exchangers was originally proposed as a trial and error procedure where guesses of the heat transfer coefficient were made and then verified after the design was finished. This traditional approach is highly dependent of the experience of a skilled engineer and it usually results in oversizing. Later, optimization techniques were proposed for the automatic generation of the best design alternative. Among these methods, there are heuristic and stochastic approaches as well as mathematical programming. In all cases, the models are mixed integer non‐linear and non‐convex. In the case of mathematical programming solution procedures, all the solution approaches were likely to be trapped in a local optimum solution, unless global optimization is used. In addition, it is very well‐known that local solvers need good initial values or sometimes they do not even find a feasible solution. In this article, we propose to use a robust mixed integer global optimization procedure to obtain the optimal design. Our model is linear thanks to the use of standardized and discrete geometric values of the heat exchanger main mechanical components and a reformulation of integer nonlinear expressions without losing any rigor. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1907–1922, 2017

In a recent article (Gonçalves et al., AIChE J. 2017. DOI: 10.1002/aic.15556), we presented a mixed-integer linear programming formulation for the detailed design of shell and tube heat exchangers based on the Kern approach (Kern, D. Q. Process Heat Transfer; McGraw Hill, 1950). The formulation relies on the use of standardized values for several mechanical parts, which we express in terms of discrete choices. Because we aim at having this model used as part of more complex models (i.e., heat exchanger networks synthesis), we identified a need to improve its computational efficiency. In this article, we explore several different modeling options to speed up solutions. These options are based on different alternatives of aggregation of the discrete values in relation to the set of binary variables. Numerical results show that these procedures allow large computational effort reductions.

In this article, we present a rigorous reformulation of the Bell–Delaware model for the design optimization of shell and tube heat exchanger to obtain a linear model. We extend a previously presented methodology1,2 of rigorously reformulate the mixed‐integer nonlinear programing Kern model and we add disjunctions to automatically choose the different correlations to calculate heat transfer coefficients and pressure drop under different flow regimes. The linear character of the formulation allows the identification of the global optimum, even using conventional optimization algorithms. The proposed mixed‐integer linear programming formulation with the Bell–Delaware method is able to identify feasible solutions for the design of heat exchangers at a lower cost than those obtained through conventional design formulations in the literature. Comparisons with the Kern method also indicate an average 22% difference (usually lower) in area.

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