Multi-Objective Optimization of Dividing Wall Columns and Visualization of the High-Dimensional Results
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.
References (58)
- et al.
Pareto-Navigation in Chemical Engineering
- et al.
From Single Process Simulation and Optimization to Decision Making Based on a Multitude of Solutions
29th European Symposium on Computer Aided Process Engineering
(2019) - et al.
Multi-criteria optimization in chemical process design and decision support by navigation on Pareto sets
Comput Chem Eng
(2014) - et al.
Simulation based approach to optimal design of dividing wall column using random search method
Comput Chem Eng
(2014) - et al.
Energy consumption maps for quaternary distillation sequences
26th European Symposium on Computer Aided Process Engineering
(2016) - et al.
Pareto front of ideal Petlyuk sequences using a multiobjective genetic algorithm with constraints
Comp. Chem Eng
(2009) - et al.
Energy efficient distillation
J Nat Gas Sci Eng
(2011) - et al.
Optimal design for dividing wall column using support vector machine and particle swarm optimization
Chem. Engg. Research and Design
(2017) Essentials of the self-organizing map
Neural Networks
(2013)- et al.
Parametrization of two-center Lennard-Jones plus point-quadrupole force field models by multicriteria optimization
Fluid Phase Equilib
(2016)
SOM-based data visualization methods
IDA
Optimization-based design of dividing wall columns with extended and multiple dividing walls for three- and four-product separations
Chem. Engg. and Processing: Process Intensification
Dividing wall columns in chemical process industry: a review on current activities
Sep Purif Technol
Navigation in multiobjective optimization methods
J. Multi-Crit. Decis. Anal.
Topology-oriented self-organizing maps: a survey
Pattern Anal Applic
Nonlinear Programming: Analysis and Methods
Multi-Objective Optimization and Decision Support in Process Engineering - Implementation and Application
Chemie Ingenieur Technik
Annual Energy Review 2001
A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization
Math. Prog. Comp.
Fractionation of Straight-Run Pennsylvania Gasoline
Ind. Eng. Chem.
Multicomponent Rectification Estimation of the Number of Theoretical Plates as a Function of the Reflux Ratio
Ind. Eng. Chem.
Multiobjective Stochastic Optimization of Dividing-wall Distillation Columns Using a Surrogate Model Based on Neural Networks
Chem. Biochem. Eng. Q.
Minimum Energy Requirements Minimum Energy Requirements in Complex Distillation Arrangements
Minimum Energy Consumption in Multicomponent Distillation. 1. Vmin Diagram for a Two-Product Column
Ind. Eng. Chem. Res.
Minimum Energy Consumption in Multicomponent Distillation. 2. Three-Product Petlyuk Arrangements
Ind. Eng. Chem. Res.
Minimum Energy Consumption in Multicomponent Distillation. 3. More Than Three Products and Generalized Petlyuk Arrangements
Ind. Eng. Chem. Res.
Vapor-Liquid Equilibrium Data for Toluene-p-Xylene System
Shiyou-huagong
Cited by (11)
First multiple dividing wall column: Design and operation
2023, Chemical Engineering Research and DesignInitial design and multi-objective optimization of four-product dividing wall column
2023, Separation and Purification TechnologyCitation Excerpt :The prevailing practice is using single objective optimization algorithms, such as the sequential iterative optimization method [15,20], genetic algorithm [11,21], differential evolution algorithm [22,23], and particle swarm optimization algorithm [24,25], to minimize the total annual cost (TAC). Although a solution with maximal profitability can be quickly found using these methods, such a biased solution usually has poor reusability [26,27]. In this respect, a more flexible and reliable practice is using multi-objective optimization algorithms, which could handle trade-offs between different objectives and allow decision-makers more choices.
Towards sustainability assessment through a flexibility index as the condition number
2022, Chemical Engineering and Processing - Process IntensificationTransforming conventional distillation sequence to dividing wall column: Minimizing cost, energy usage and environmental impact through genetic algorithm
2022, Separation and Purification TechnologyCitation Excerpt :However, very few works have reported the multi-objective optimization (MOO) of dividing wall columns. Ränger and co-authors [52] have proposed a posteriori method of constraining the optimal solutions obtained from MOO of dividing wall columns. Based on our knowledge, no optimization study has been reported so far that optimizes the cost, energy usage and environmental impact along with production-related objectives through MOO for a conventional distillation sequence and its dividing wall counterpart using the rigorous method of simulation to find the optimal design and operating condition.
Enhanced extractive distillation processes for separating n-hexane and 1,2-dichloroethane via bottom flash heat pump
2022, Chemical Engineering and Processing - Process IntensificationSimultaneous simulation and optimization of multiple dividing wall columns
2022, Computers and Chemical EngineeringCitation Excerpt :Depending on their values the specifications are modified until a satisfying result is found. The procedure is explained in more detail in the works by von Kurnatowski et al. (2017) and Ränger et al. (2020). In this section we apply the developed methods to two examples.