Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

Isobutane Alkylation Process Synthesis by means of Hybrid Simulation-Multiobjective Optimization

Multiobjective Generalized Disjunctive Programming (MO-GDP) optimization has been used for the synthesis of an important industrial process, isobutane alkylation. The two objective functions to be simultaneously optimized are the environmental impact, determined by means of LCA (Life Cycle Assessment), and the economic potential of the process. The main reason for including the minimization of the environmental impact in the optimization process is the widespread environmental concern by the general public. For the resolution of the problem we employed a hybrid simulation- optimization methodology, i.e., the superstructure of the process was developed directly in a chemical process simulator connected to a state of the art optimizer. The model was formulated as a GDP and solved using a logic algorithm that avoids the reformulation as MINLP -Mixed Integer Non Linear Programming-. Our research gave us Pareto curves compounded by three different configurations where the LCA has been assessed by two different parameters: global warming potential and ecoindicator-99.