Multi-Objective Optimization of Dividing Wall Columns and Visualization of the High-Dimensional Results

https://doi.org/10.1016/j.compchemeng.2020.107059Get rights and content

Highlights

  • Multi-objective optimization of dividing wall columns.

  • High-dimensional solution space.

  • Visualization in self-organizing patch plots.

  • Filtration of results to determine operating point.

  • Pareto set reusable for same feed stream composition.

  • Optimization-based design.

Abstract

Multi-objective optimization of distillation configurations is a difficult problem that can lead to significantly improved process designs. The identification of improvements depends on a reliable and precise calculation of Pareto points, and the ability to visualize them in potentially high-dimensional spaces.

This paper presents a methodology for comparing optimal solutions for different distillation configurations. Representative Pareto points are calculated and visualized in self-organizing patch plots. A subsequent filtration of the solutions is possible showing only those that satisfy specific requirements. The procedure is illustrated with a ternary feed stream (benzene, toluene and p-xylene), that is purified in a dividing wall column. The data filtration is explained with a case study.

The methodology is applicable to any distillation configuration. This means that the operating ranges for different distillation options can be compared as well as the optimal configuration and its operating point chosen, without performing additional optimization computations.

Introduction

Distillation is an important separation technique in the chemical industry (Humphrey, 1995), that is highly energy intensive. In 2001, distillation accounted for ~2.5% of the total energy demand of the USA (BCS Incorporated and Oak Ridge National Laboratory, 2005; Energy Information Administration, National Energy Information Center, 2002; Humphrey and Keller, 1997), in 2016 already ~10% was reported (Sholl and Lively, 2016). Opportunities to reduce this energy usage are extremely desirable, especially due to environmental factors. In this respect, the dividing wall columns (DWC, see Fig. 1d) can save ~30% of energy consumption compared to a conventional column sequence splitting a ternary feed (Schultz et al., 2002), and have been the subject of much research in the past decades (Yildirim et al., 2011). A disadvantage of this approach is that it involves a higher number of degrees of freedom and thus an increased complexity. Accordingly, a decisive aspect in the search for the most suitable distillation configuration and the corresponding operating point is the implementation of an optimization procedure.

The optimization of a distillation column configuration is a multi-objective problem involving several competing objective functions, such as the total number of theoretical stages ΣN, reboiler duty Q, and product purities. Accordingly, a large number of optimal solutions exist in the Pareto optimal set. The problem combines continuous variables such as the boilup stream and discrete variables such as the stage number. The problem is thus of type mixed-integer non-linear programming (MINLP), its solution and choice of algorithm depend heavily on the specifics of the problem definition. An extensive set of methods is available (Marler and Arora, 2004). To select a solution, or in this context an operating point, from the optimal set, the solution space has to be constrained either before (a priori) or after (a posteriori) the optimization. A common a priori method involves the Total Annualized Costs (TAC) objective function (Luyben, 2013). An optimal configuration for a specific column can be quickly found using this objective. Unfortunately, such results relate to a specific configuration, and are not easily reusable. Since an optimizer is rarely available in the chemical industry, the reusability would be an important aspect.

A drawback of a priori methods is that the weighting factors, representing the preferences of different objectives in the target function, are, to some extent, arbitrary. An alternative a posteriori method for complex distillation configurations seeks to resolve the complete Pareto optimal set by identifying representative Pareto optimal points (Marler and Arora, 2004). Adaptive scalarization methods have been developed, which facilitate the representation of the entire Pareto optimal set by a minimal number of Pareto optimal points (Bortz et al., 2014). The objective space can then be explored using an interactive navigation tool. Several configuration options can thus be compared, for different scenarios, to find the best configuration after the optimization (Asprion et al., 2019; Burger et al., 2014). One main advantage of this methodology is that users without access to an optimizer can use the results and perform problem specific data filtering a posteriori. Therefore, the aim of this article is to present an a posteriori optimization method for distillation configurations.

This paper is organized as follows: Section 2 discusses the theoretical background and the state of the art of distillation, optimization and data visualization. Visualization is an issue in high-dimensional objective spaces. This is resolved with self-organizing patch plots (Stöbener et al., 2016). Section 3 discusses the applied a posteriori methods needed for the systematic exploration of the Pareto set. In Section 4, optimization results for a ternary split in a dividing wall column are presented and a case study is performed to explain the principle of the filtration of the results. With the presented methodology the best suited operating point can be chosen for different scenarios.

Section snippets

Theoretical background and state-of-the-art

This section is organized as follows: The basics of ternary distillations and their shortcut designs are presented in Section 2.1. In Section 2.2, a brief introduction to multi-objective optimization is given, and common definitions of the optimization problem in distillation are presented. Section 2.3 explains self-organizing patch plots, guidelines for reading and interpreting such diagrams are also given.

Materials and methods

The overall calculation steps are simulation (Section 3.1), optimization (Section 3.2), visualization (Section 3.3) and results filtration (Section 3.4). First, the commercial Flowsheet simulator Aspen Plus ® (v.11) is used for the (converging) simulation. Second, the multi-objective optimization is run automatically with an external optimizer. The visualization and result filtration steps are then performed in MATLAB®.

Results and discussion of an example

In this section, the methodology will be explained with a ternary system split in a dividing wall column. First, the choice of the system and the shortcut design of the column are discussed briefly. Afterwards the optimization results are presented in a SOPP followed by a case study for filtrations on the results. In particular, this section shows that the results can be reused depending on the requirements of the user.

Conclusion and outlook

This paper presents an a posteriori method for the multi-objective optimization of complex distillation columns. Optimizing the total stage number, the reboiler duty and the product purities simultaneously results in a high-dimensional solution space. The resulting visualization problem can be solved with self-organizing patch plots. In those, a filtration of the results can be performed several times for different scenarios to determine the best suited operating point. This means that

Abbreviations and symbols

Tables 1 and 2.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

We gratefully acknowledge the funding by Deutsche Forschungsgemeinschaft (DFG), project number 440334941.

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