From Block-Oriented Models to the Koopman Operator: A Comprehensive Review on Data-Driven Chemical Reactor Modeling

Mustapha Kamel Khaldi, Mujahed Al-Dhaifallah (), Ibrahim Aljamaan, Fouad Mohammad Al-Sunni, Othman Taha and Abdullah Alharbi
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Mustapha Kamel Khaldi: Control and Instrumentation Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Mujahed Al-Dhaifallah: Control and Instrumentation Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Ibrahim Aljamaan: Biomedical Engineering Department, Imam Abdulrahman Bin Faisal University, Dammam 31451, Saudi Arabia
Fouad Mohammad Al-Sunni: Control and Instrumentation Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Othman Taha: Process & Control Systems Department, Saudi Aramco, Dhahran 31261, Saudi Arabia
Abdullah Alharbi: Department of Accounting & Finance, KFUPM Business School, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Mathematics, 2025, vol. 13, issue 15, 1-30

Abstract: Some chemical reactors exhibit coupled dynamics with multiple equilibrium points and strong nonlinearities. The accurate modeling of these dynamics is crucial to optimal control and increasing the reactor’s economic performance. While neural networks can effectively handle complex nonlinearities, they sacrifice interpretability. Alternatively, block-oriented Hammerstein–Wiener models and Koopman operator-based linear predictors combine nonlinear representation with linear dynamics, offering a gray-box identification approach. This paper comprehensively reviews recent advancements in both the Hammerstein–Wiener and Koopman operator methods and benchmarks their accuracy against neural network-based approaches to modeling a large-scale industrial Fluid Catalytic Cracking fractionator. Furthermore, Monte Carlo simulations are employed to validate performance under varying signal-to-noise ratios. The results demonstrate that the Koopman bilinear model significantly outperforms the other methods in terms of accuracy and robustness.

Keywords: Deep Neural Network; Fluid Catalytic Cracking; Hammerstein–Wiener; Koopman operator; Long Short-Term Memory networks; modeling; review (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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