Optimal design of double pipe heat exchanger modular units - Melo, Alice Peccini de (2017)
Although shell-and-tube heat exchangers are the most common heat transfer equipment in the chemical industry, other types may be more suitable in various situations. This work investigates the design optimization of double pipe heat exchangers using mathematical programming. The objective function is the minimization of the heat exchanger area and the constraints encompass the thermo-fluid dynamic model and design specifications, such as, maximum pressure drops and minimum excess area. The set of design variables explores the modular nature of this kind of heat exchanger, encompassing the allocation of the streams (inside the inner tube or in the annulus), the inner and outer tube diameters, the tube length, the number of parallel branches, and the number of units in series or in parallel in each branch. Three different mathematical formulations are proposed, the first corresponds to a mixed-integer nonlinear programming (MINLP), the second is a modified MINLP formulation, where mathematical transformations allow the reorganization of the problem to eliminate the nonlinearities associated to the binary variables. Finally, the third formulation corresponds to a mixed-integer linear programming (MILP), which allows the identification of the global optimum. The application of the proposed optimization to a design task from the literature was able to identify a heat exchanger with smaller area, when compared to a solution obtained through a traditional trial and error procedure. A comparison between both MINLP approaches point out the importance of the identification of the global optimum, which is obtained with the third approach for a set of design problems. Additional examples illustrate the flexibility of the model to describe different flow regimes, adapt to modifications in process throughput and explores the trade-off between available pressure drop and heat transfer area.