Optimal design of multiple dividing wall columns based on genetic programming

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Abstract

In this work, two schemes are analyzed for the reduction on energy consumptions for ternary distillation: a Petlyuk column, PC, and a Petlyuk with postfractionator system, PCP. To perform the optimal design of the analyzed systems, the use of multiobjective genetic algorithms has been considered. Moreover, a strategy for diameter calculation is proposed for the dividing wall column, DWC, and double dividing wall column, DDWC, which is based on their distribution of internal flows. Results show that genetic algorithm tool allows obtaining optimal designs for the PC and PCP systems, with low energy consumptions. Furthermore, the design strategy for the DWC and DDWC shows that the physical structure required for one or two dividing walls is quite similar; thereby, it appears to be an adequate method for the sizing of the dividing wall systems.

Introduction

Thermally coupled distillation sequences are a good option to reduce energy consumption in the separation of fluid mixtures. One of the more important thermally coupled schemes is the Petlyuk column, which may reduce energy requirements up to 30% in comparison to conventional sequences [1]. An alternative system, recently analyzed, consists on a Petlyuk system with an additional column attached, known as postfractionator; in some cases, this system can achieve even lower heat duties than the Petlyuk column [2]. Because of mechanical issues, a thermodynamically equivalent system known as the dividing wall column is used instead of the Petlyuk column; for the Petlyuk column with postfractionator it has been proposed that its equivalent could be a double dividing wall column [3]. A dividing wall column consists in a shell, in which a metallic wall is inserted; thus an appropriate diameter must be used to support the maximum vapor flow rate, allowing a proper pressure drop along the column and avoiding flooding. A strategy to calculate the diameter of the DWC has been recently proposed [4], based on the vapor flow rate distribution on the column; nevertheless, there is no such methodology for DDWC. Therefore, in this work an extension of the methodology for the DWC is proposed to obtain proper diameter calculations for the DDWC. To obtain low-energy designs for the dividing wall systems, a multiobjective genetic algorithm has been used to find the Pareto front of optimal designs for the DWC and DDWC. The optimal designs obtained offer a good distribution of the vapor flows, which allows requiring trays with a lower diameter.

Section snippets

Design and optimization tool: multi objective genetic algorithm

The design and optimization of the analyzed systems have been performed by using a multi objective genetic algorithm with constraints, coupled to the process simulator Aspen Plus. Due to the characteristics of the search space, conventional derivativebased optimization methodologies may present considerable difficulties finding a solution near to global optimum, while stochastic optimization algorithms are robust and efficient tools for solving such optimization problems. When a multiobjective

Calculation of the diameter of the dividing wall columns

For the determination of the diameters of these systems, the strategy presented by Premkumar and Rangaiah [4] for the DWC has been extended for the DDWC. For a single tray: D=(4G/0.8πρvVmax)1/2

In Eq. 2, D is the diameter of the tray (m), G is the total vapor flow rate (kg/s), DQG ρV is the vapor density (kg/m3). It has been considered that the actual vapor velocity corresponds to the 80% of the maximum vapor velocity, Vmax . The equivalencies for the vapor flows for the DDWC are shown in Figure

Case of study

The analyzed mixtures are shown in Table 1. It can be seen that the mixture M1 has a low molar feed composition of the middle-boiling component, n-hexane, while mixture M2 has a high composition of the middle-boiling component, methanol, in the feed stream. Pareto fronts of both Petlyuk-like schemes have been generated with the multiobjective genetic algorithm; the parameters of this optimization were 50 generations of 1000 individuals each one. From the Pareto front, 10 optimal designs

were

Results

Since this work has been developed to observe the performance of the DDWC, In Figure 2 the Pareto fronts for the DDWC are shown.

For the mixture M1 the energy consumption for the DDWC has been observed to be lower or similar than for the DWC. For mixture M2, in most cases the DWC shows lower energy consumption, and even small changes in the structure of the DDWC may have a great impact on the heat duty of the system, as can be seen in Table 2, where the distribution of stages on the columns in

Conclusions

In this work a design and optimization strategy based on evolutionary techniques has been presented. The multiobjective genetic algorithm allows obtaining a number of optimal solutions to the design and optimization problem. It has been found that a good design of the DDWC presents lower energy requirements than the DWC for mixtures, where the middle-boiling component appears in a low concentration on the feed stream. On the other hand, when the composition of the middle-boiling component on

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