Computational Study of the Use of Set Trimming for the Globally Optimal Design of Gasketed-Plate Heat Exchangers

Abstract

In this article, we present for the first time, a globally optimal design procedure of gasketed-plate heat exchangers using a new proposed technique: Set Trimming. Set Trimming is a recently developed optimization technique based on the sequential application of inequality constraints to gradually reduce the search space. This method eliminates several drawbacks that affect other optimization techniques: (i) it guarantees global optimality; (ii) it does not depend on good initial estimates; (iii) it guarantees convergence; and (iv) it does not require any tuning of algorithm parameters. The formulation of the optimization problem corresponds to the minimization of the heat exchanger area or the total annualized cost subjected to pressure drop bounds, flow velocity bounds, and required area constraint. Another contribution of this work is a new analysis of the Set Trimming method by finding the fastest algorithmic alternative through methodical application of each constraint. To validate the conjecture that our Set Trimming method is computationally faster for the design of plate heat exchangers, we compare its performance with results obtained using mixed-integer nonlinear programming (MINLP), mixed-integer linear programming (MILP), particle swarm optimization (PSO), genetic algorithms (GA), and simulated annealing (SA), which showed increased performance by orders of magnitude. These results suggest that Set Trimming can be a useful resource for the solution of design problems when the degrees of freedom are represented by integer variables.

Set Trimming approach for the globally optimal design of sieve trays in separation columns

“…Costa and Bagajewicz 13 generalized it conceptually to apply to any optimization problem with discrete independent variables. The same technique was successfully applied by Lemos et al 19 and Nahes et al 20 to the design optimization of shell and tube heat exchangers and plate heat exchangers, respectively.…”

“…Costa and Bagajewicz 13 generalized it conceptually to apply to any optimization problem with discrete independent variables. The same technique was successfully applied by Lemos et al 19 and Nahes et al 20 13 The steps of each trim of Set Trimming method, using the model of the sieve tray design are shown below, according to the representation depicted in Figure 5. In these steps, each set is defined as a subset of the previous one, thus eliminating the infeasible candidates from each step.…”

Design of shell and tube heat exchangers considering the interaction of fouling and hydraulics

“…Figure 4 shows the sequence of trimmings to identify the feasible heat exchangers in a given set of candidates. Examples of successful application of Set Trimming for optimization of thermal equipment design can be found in Lemos et al 32 and Nahes et al 45 The search space corresponds to the set of heat exchanger candidates composed of all possible combinations of the available discrete values of the design variables. This set is partitioned into five subsets according to the corresponding fouling behavior described in the previous section.…”

“…Figure 4 shows the sequence of trimmings to identify the feasible heat exchangers in a given set of candidates. Examples of successful application of Set Trimming for optimization of thermal equipment design can be found in Lemos et al 32 and Nahes et al 45 …”