(104e) Efficient Optimization and Accurate Approximation Using Surrogate Models – Tools and Case Studies from RAPID Synopsis Project

Surrogate models, also known as response surfaces, black-box models, metamodels, or emulators, are simplified approximations of more complex, higher-order models. These models are used to map input data to output data when the actual relationship between the two is unknown or computationally expensive to evaluate (Han & Zhang, 2012). Surrogate models can also be constructed for surrogate-based optimization when a closed analytical form of the relationship between input data and output data does not exist or is not conducive for use in traditional gradient-based optimization methods. Surrogate modeling techniques are of particular interest where high-fidelity, thus expensive, simulations are needed (Han & Zhang, 2012) or when the fundamental relationship between the design variables and output variables is not well understood, such as in the design of cell or tissue manufacturing processes (Du et al., 2016).

This presentation showcases and compares a suite of tools developed for accurate output approximation and efficient optimization using surrogate models applied to the synthesis and design of three case studies. The case studies include process synthesis of reactive distillation column for 2-pentene metathesis to 2-butene and 3-hexene (Demirel et al., 2020), and process synthesis of a membrane reactor for methanol production from syngas (Monjur et al., 2021), and design and operating conditions optimization of an industrial cumene production process (Luyben, 2012).

A recommendation tool is utilized to select the best surrogate modeling technique for the datasets in the case studies. The tool uses the input-output dataset characteristics and random forest modeling (Breiman, 2001) to identify the best modeling technique for the end-use application, output approximation or surrogate-based optimization (Williams & Cremaschi, 2019, 2021a, 2021b). The dataset characteristics are defined using (1) common statistical measures such as mean and standard deviation of each input and output, (2) gradient-based attributes (Garud et al., 2018) such as the mean of gradient estimates, (3) extrema-based attributes such as percentage of data points within the top 5% of the output values, (4) input domain-related attributes such as the maximum Mahalanobis distance between input data, and (5) other attributes percentage of data points with a gradient estimates within a narrow band of zero. The accuracy of the tool’s recommendations is tested by training surrogate models using all approaches considered by the tool and comparing the recommended model to the best one for each dataset.

An adaptive sampling surrogate-based optimization tool is employed to identify optimal operating and design decisions of the chemical processes (Kim and Boukouvala, 2020). The Mixed-Integer Nonlinear Optimization using Approximations (MINOAn) toolbox utilizes a variety of different surrogate models, that are adaptively re-trained and re-optimized until convergence. The accuracy, sampling cost and computational efficiency of different approximation models recommended by our collective suite of tools towards identifying globally optimal solutions are presented. Moreover, best practices with respect to the use of surrogate-based optimization for case studies with multiple process units (i.e., integrated flowsheet models) are proposed. Specifically, a comparative analysis will be presented between representing each process unit as a separate surrogate model, as opposed to treating the entire flowsheet as a black-box simulation. All of the presented optimization results using approximations are benchmarked against globally optimal solutions identified using equation-based optimization techniques.

The reactive distillation and membrane reactors combine reaction and separation phenomena in single intensified units to offer energy efficient, cost effective, compact, modular and sustainable designs. The Synthesis and Process Intensification of Chemical Enterprises (SPICE) and SPICE_MARS tools (Demirel et al., 2017; Monjur et al., 2021) use equation-oriented predictive models for the optimal design and synthesis of these complex intensified process systems. However, the presence of complex interactions and the highly nonlinear equilibrium and kinetic behavior of simultaneous reaction and separation often make rigorous process synthesis computationally expensive. To that end, we will develop surrogate models for representing/optimizing membrane reactors for two industrially important applications: (i) partial oxidation of methane to produce syngas, and (ii) methanol synthesis from syngas. For given feed flow rate and composition, reactor length, and the pressures and temperatures of both the permeate and retentate sides, these models will be used to predict and/or optimize the overall conversion, yield, product purity, and the total cost. The production of cumene (isopropylbenzene) occurs through an irreversible exothermic reaction of gaseous reactants over solid catalysts. The process requires careful plant operation to minimize undesirable side reaction (which is favored by high reaction temperatures) and separations costs. To demonstrate how surrogate models can be used within the framework of commercial simulation tools, the most complex units (reactor and distillation columns) of a cumene process flowsheet model, implemented in gPROMS Process, are replaced by surrogates generated based on insights from the recommendation tool. The resulting hybrid flowsheet is utilized to optimize the plant energy consumption by varying the column reflux ratios and the reactants’ preheat temperature. Results from the optimization of the hybrid flowsheet are evaluated against those from the first-principle model.

References

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Demirel, S. E.; Li, J.; Hasan, M. M. F. (2017). Systematic Process Intensification using Building Blocks. Computers & Chemical Engineering, 150, 2–38.

Demirel, S. E.; Li, J.; El-Halwagi, M. M.; Hasan, M. M. F. (2020). Sustainable Process Intensification using Building Blocks. ACS Sustainable Chemistry & Engineering, 8, 48, 17664–17679.

Du, D.; Yang, H.; Ednie, A. R.; Bennett, E. S. (2016). Statistical Metamodeling and Sequential Design of Computer Experiments to Model Glyco-Altered Gating of Sodium Channels in Cardiac Myocytes. IEEE J Biomed Health Inform, 20, 1439-1452.

Garud, S. S.; Karimi, I. A.; Kraft, M. (2018). LEAPS2: Learning based Evolutionary Assistive Paradigm for Surrogate Selection. Computers & Chemical Engineering, 119, 352-370.

Han, Z.; Zhang, K. (2012). Surrogate-Based Optimization. In O. Roeva (Ed.), Real-World Applications of Genetic Algorithms (pp. 343-362). Rijeka, Croatia: InTech Open.

Kim, S. H.; Boukouvala, F. (2020). Surrogate-based optimization for mixed-integer nonlinear problems, Computers & Chemical Engineering, 140, 106847.

Luyben, W.L. (2012). Principles and Case Studies of Simultaneous Design, Wiley, New Jersey.

Monjur, M. S.; Demirel, S. E.; Li, J.; Hasan, M. M. F. (2021). SPICE_MARS: A Process Synthesis Framework for Membrane-Assisted Reactive Separations. Under Review.

Williams, B.; Cremaschi, S. (2019). Surrogate Model Selection for Design-Space Approximation and Surrogate-Based Optimization. Computer-Aided Chemical Engineering, 47, 353-358.

Williams, B.; Cremaschi, S. (2021a). Selection of Surrogate Modeling Techniques for Surface Approximation and Surrogate-Based Optimization. Chemical Engineering Research and Design. Accepted.

Williams, B.; Cremaschi, S. (2021b). Novel Tool for Selecting Surrogate Modeling Techniques for Surface Approximation. Computer-Aided Chemical Engineering. Accepted.