Hybrid Modeling in Chemical Process Intensification: Architectures, Applications, and Critical Challenges

Authors

  • Pakiza Iman School of Water and Environment, Chang'an University, China
  • Noor Fatima School of Biochemistry, Bahauddin Zakariya University, Pakistan

DOI:

https://doi.org/10.70112/ajeat-2026.15.2.4383

Keywords:

Hybrid Modeling, Process Intensification, Physics-Informed Machine Learning, Gray-Box Models, Reaction Engineering, Digital Twins

Abstract

The hybrid models that use both first principles knowledge and machine learning: the first represents what is known about a process, while the second represents what is not. This review is based on the four domains of chemical process intensification (PI): structure, energy, synergy and time and discusses hybrid modelling for PI. Data demand, interpretability, extrapolation and training cost are used to define and compare serial, parallel and physics-constrained architectures. Soft sensing and control, CO2 capture and power to X, design of intensified equipment and integrated reaction-separation units are considered in the applications. The four reaction-engineering case studies are then revisited using their original sources: methanol synthesis, coupled syngas and methanol synthesis and water–gas shift network, catalyzed polymerization, and oxidation of iso-octanol. The hybrid methanol model with the optimally designed experiments was found to have a test error of 8.49%, which is just slightly higher than the 9.06% of the recalibrated mechanistic model, and the mechanistic model with the experiments deleted had a test error of 13.20%. A thermodynamically consistent power-law backbone was found to have a lower test error (6.7%) than a Langmuir–Hinshelwood backbone (9.5%). The errors in polymerization predictions were decreased by 84%, 86% for the two dominant reagents for the two main cases, and for the surrogate-based hybrids the errors were reduced by more than 400 times when compared with simulation-based optimization and were run approximately 45 times faster than CFD. The key open challenges are the lack of data, particularly scarce and unbenchmarked data, coupled models trained together, guaranteed physical consistency, multiscale coupling, and uncertainty quantification. Type of synergy units have been the least researched. Priorities for future work include hybrid DT, closed-loop experimental design, and multiscale modelling.

References

[1] A. I. Stankiewicz and J. A. Moulijn, “Process intensification: Transforming chemical engineering,” Chem. Eng. Prog., vol. 96, no. 1, pp. 22–34, 2000.

[2] T. Van Gerven and A. Stankiewicz, “Structure, energy, synergy, time the fundamentals of process intensification,” Ind. Eng. Chem. Res., vol. 48, no. 5, pp. 2465–2474, 2009, doi: 10.1021/ie801501y.

[3] Y. Tian, S. E. Demirel, M. M. F. Hasan, and E. N. Pistikopoulos, “An overview of process systems engineering approaches for process intensification: State of the art,” Chem. Eng. Process. –Process Intensif., vol. 133, pp. 160–210, 2018, doi: 10.1016/j.cep.2018.07.014.

[4] D. S. Sholl and R. P. Lively, “Seven chemical separations to change the world,” Nature, vol. 532, no. 7600, pp. 435–437, 2016, doi: 10.1038/532435a.

[5] G. J. Harmsen, “Reactive distillation: The front-runner of industrial process intensification. A full review of commercial applications, research, scale-up, design and operation,” Chem. Eng. Process. –Process Intensif., vol. 46, no. 9, pp. 774–780, 2007, doi: 10.1016/j.cep.2007.06.005.

[6] F. Esposito, U. Di Caprio, S. Buzzi, F. Vermeire, and M. E. Leblebici, “Hybrid modelling approaches in process intensification: A thorough review,” Chem. Eng. Process. –Process Intensif., vol. 217, Art. no. 110496, 2025, doi: 10.1016/j.cep.2025.110496.

[7] M. von Stosch, R. Oliveira, J. Peres, and S. Feyo de Azevedo, “Hybrid semi-parametric modeling in process systems engineering: Past, present and future,” Comput. Chem. Eng., vol. 60, pp. 86–101, 2014, doi: 10.1016/j.compchemeng.2013.08.008.

[8] A. Beck, M. A. Newton, L. G. A. van de Water, and J. A. van Bokhoven, “The enigma of methanol synthesis by Cu/ZnO/Al2O3-based catalysts,” Chem. Rev., vol. 124, no. 8, pp. 4543–4678, 2024, doi: 10.1021/acs.chemrev.3c00148.

[9] M. B. Fichtl et al., “Kinetics of deactivation on Cu/ZnO/Al2O3 methanol synthesis catalysts,” Appl. Catal. A: Gen., vol. 502, pp. 262–270, 2015, doi: 10.1016/j.apcata.2015.06.014.

[10] M. R. Dobbelaere, P. P. Plehiers, R. Van de Vijver, C. V. Stevens, and K. M. Van Geem, “Machine learning in chemical engineering: Strengths, weaknesses, opportunities, and threats,” Engineering, vol. 7, no. 9, pp. 1201–1211, 2021, doi: 10.1016/j.eng.2021.03.019.

[11] P. Shah, S. Pahari, R. Bhavsar, and J. S.-I. Kwon, “Hybrid modelling of first principles and machine learning: A step-by-step tutorial review for practical implementation,” Comput. Chem. Eng., vol. 194, Art. no. 108926, 2025, doi: 10.1016/j.compchemeng.2024.108926.

[12] A. Mukherjee and V. M. Zavala, “Physics-constrained machine learning for chemical engineering,” Curr. Opin. Chem. Eng., vol. 51, Art. no. 101228, Mar. 2026; preprint: arXiv:2508.20649.

[13] A. M. Schweidtmann, D. Zhang, and M. von Stosch, “A review and perspective on hybrid modeling methodologies,” Digit. Chem. Eng., vol. 10, Art. no. 100136, 2024, doi: 10.1016/j.dche.2023.100136.

[14] D. C. Psichogios and L. H. Ungar, “A hybrid neural network-first principles approach to process modeling,” AIChE J., vol. 38, no. 10, pp. 1499–1511, 1992, doi: 10.1002/aic.690381003.

[15] M. L. Thompson and M. A. Kramer, “Modeling chemical processes using prior knowledge and neural networks,” AIChE J., vol. 40, no. 8, pp. 1328–1340, 1994, doi: 10.1002/aic.690400806.

[16] J. Sansana, M. N. Joswiak, I. Castillo, Z. Wang, R. Rendall, L. H. Chiang, and M. S. Reis, “Recent trends on hybrid modeling for Industry 4.0,” Comput. Chem. Eng., vol. 151, Art. no. 107365, 2021, doi: 10.1016/j.compchemeng.2021.107365.

[17] C. L. Gargalo et al., “Navigating Industry 4.0 and 5.0: The role of hybrid modelling in (bio)chemical engineering’s digital transition,” Front. Chem. Eng., vol. 6, Art. no. 1494244, 2024, doi: 10.3389/fceng.2024.1494244.

[18] L. Kaps et al., “Optimal experiments for hybrid modeling of methanol synthesis kinetics,” Comput. Chem. Eng., vol. 204, Art. no. 109387, 2026, doi: 10.1016/j.compchemeng.2025.109387.

[19] E. Oguta and I. E. Ihua-Maduenyi, “Modelling and performance analyses of annular equivalent circulation density in extended reach wells using response surface methodology,” Asian J. Eng. Appl. Technol., vol. 14, no. 2, pp. 1–17, 2025, doi: 10.70112/ajeat-2025.14.2.4298.

[20] N. Sharma and Y. A. Liu, “A hybrid science-guided machine learning approach for modeling chemical processes: A review,” AIChE J., vol. 68, no. 5, Art. no. e17609, 2022, doi: 10.1002/aic.17609.

[21] W. Bradley et al., “Perspectives on the integration between first principles and data-driven modelling,” Comput. Chem. Eng., vol. 166, Art. no. 107898, 2022, doi: 10.1016/j.compchemeng.2022.107898.

[22] M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” J. Comput. Phys., vol. 378, pp. 686–707, 2019, doi: 10.1016/j.jcp.2018.10.045.

[23] G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang, “Physics-informed machine learning,” Nat. Rev. Phys., vol. 3, no. 6, pp. 422–440, 2021, doi: 10.1038/s42254-021-00314-5.

[24] C. Rackauckas et al., “Universal differential equations for scientific machine learning,” arXiv:2001.04385, 2020, doi: 10.48550/arXiv.2001.04385.

[25] R. Oliveira, “Combining first principles modelling and artificial neural networks: A general framework,” Comput. Chem. Eng., vol. 28, no. 5, pp. 755–766, 2004.

[26] M. Brendel and W. Marquardt, “Experimental design for the identification of hybrid reaction models from transient data,” Chem. Eng. J., vol. 141, no. 1–3, pp. 264–277, 2008, doi: 10.1016/j.cej.2007.12.027.

[27] K. Merkelbach et al., “HybridML: Open source platform for hybrid modelling,” Comput. Chem. Eng., vol. 160, Art. no. 107736, 2022, doi: 10.1016/j.compchemeng.2022.107736.

[28] F. Sorourifar, Y. Peng, I. Castillo, L. Bui, J. Venegas, and J. A. Paulson, “Physics-enhanced neural ordinary differential equations: Application to industrial chemical reaction systems,” Ind. Eng. Chem. Res., vol. 62, no. 38, pp. 15563–15577, 2023, doi: 10.1021/acs.iecr.3c01471.

[29] D. Ghosh, E. Hermonat, P. Mhaskar, S. Snowling, and R. Goel, “Hybrid modeling approach integrating first-principles models with subspace identification,” Ind. Eng. Chem. Res., vol. 58, no. 30, pp. 13533–13543, 2019, doi: 10.1021/acs.iecr.9b00900.

[30] N. A. Nasruddin, N. Islam, S. Vernuccio, and J. Oyekan, “Hybridised mechanistic and machine learning digital twins for modelling and optimising chemical processes in flow: A comparative analysis of parallel and series-based hybridisation,” Chem. Eng. J. Adv., vol. 23, Art. no. 100775, 2025, doi: 10.1016/j.ceja.2025.100775.

[31] M. Velioglu, S. Zhai, S. Rupprecht, A. Mitsos, A. Jupke, and M. Dahmen, “Physics-informed neural networks for dynamic process operations with limited physical knowledge and data,” Comput. Chem. Eng., vol. 192, Art. no. 108899, 2025, doi: 10.1016/j.compchemeng.2024.108899.

[32] Z. Wu, H. Wang, C. He, B. Zhang, T. Xu, and Q. Chen, “The application of physics-informed machine learning in multiphysics modeling in chemical engineering,” Ind. Eng. Chem. Res., vol. 62, no. 44, pp. 18178–18204, 2023, doi: 10.1021/acs.iecr.3c02383.

[33] H. Kay, F. Vega-Ramon, R. Gallen, E. H. Stitt, and D. Zhang, “Developing a hybrid modeling framework for enhanced prediction in chemical reaction kinetics,” Ind. Eng. Chem. Res., vol. 64, no. 33, pp. 16027–16038, 2025, doi: 10.1021/acs.iecr.5c01597.

[34] P. Kadlec, B. Gabrys, and S. Strandt, “Data-driven soft sensors in the process industry,” Comput. Chem. Eng., vol. 33, no. 4, pp. 795–814, 2009, doi: 10.1016/j.compchemeng.2008.12.012.

[35] H. Jin, X. Chen, L. Wang, K. Yang, and L. Wu, “Adaptive soft sensor development based on online ensemble Gaussian process regression for nonlinear time-varying batch processes,” Ind. Eng. Chem. Res., vol. 54, no. 30, pp. 7320–7345, 2015.

[36] N. P. Lawrence et al., “Machine learning for industrial sensing and control: A survey and practical perspective,” Control Eng. Pract., vol. 145, Art. no. 105841, 2024, doi: 10.1016/j.conengprac.2024.105841.

[37] Z. Wu, A. Tran, D. Rincon, and P. D. Christofides, “Machine-learning-based predictive control of nonlinear processes. Part I: Theory,” AIChE J., vol. 65, no. 11, Art. no. e16729, 2019, doi: 10.1002/aic.16729.

[38] T. Keßler et al., “Two degrees of freedom control of a multistage power to methanol reactor,” Comput. Chem. Eng., vol. 192, Art. no. 108893, 2024, doi: 10.1016/j.compchemeng.2024.108893.

[39] G. T. Rochelle, “Amine scrubbing for CO2 capture,” Science, vol. 325, no. 5948, pp. 1652–1654, 2009, doi: 10.1126/science.1176731.

[40] U. Di Caprio, F. Vermeire, T. Van Gerven, and M. E. Leblebici, “Physics-informed machine learning predicting CO2 capture performances of organic mixtures,” Chem. Eng. Process.–Process Intensif., vol. 216, Art. no. 110410, 2025, doi: 10.1016/j.cep.2025.110410.

[41] U. Di Caprio et al., “Hybrid modelling of a batch separation process,” Comput. Chem. Eng., vol. 177, Art. no. 108319, 2023, doi: 10.1016/j.compchemeng.2023.108319.

[42] C. Seidel, A. Jörke, B. Vollbrecht, A. Seidel-Morgenstern, and A. Kienle, “Kinetic modeling of methanol synthesis from renewable resources,” Chem. Eng. Sci., vol. 175, pp. 130–138, 2018.

[43] X. Zhou, Z. Zhang, M. Zhu, H. Zhao, H. Yan, and C. Yang, “A hybrid modeling strategy based on deep learning surrogate models for accurate process multi-objective optimization of iso-octanol oxidation,” ENG. Chem. Eng., vol. 20, Art. no. 10, 2026, doi: 10.1007/s11705-026-2630-1.

[44] X. Zhou et al., “Hybrid modelling incorporating reaction and mechanistic data for accelerating the development of isooctanol oxidation,” Chin. J. Chem. Eng., vol. 80, pp. 166–183, 2025, doi: 10.1016/j.cjche.2025.02.003.

[45] O. C. Boy, I. B. R. Nogueira, U. Di Caprio, and M. E. Leblebici, “AI-aided process intensification of structures,” Chem. Eng. Process.–Process Intensif., vol. 216, Art. no. 110406, 2025, doi: 10.1016/j.cep.2025.110406.

[46] H. Kay, F. Vega-Ramon, and D. Zhang, “Hybrid modelling for reaction network simulation in syngas methanol production,” Syst. Control Trans., vol. 4, pp. 111–116, 2025, doi: 10.69997/sct.172680.

[47] S. K. Wilkinson, L. G. A. van de Water, B. Miller, M. J. H. Simmons, E. H. Stitt, and M. J. Watson, “Understanding the generation of methanol synthesis and water gas shift activity over copper-based catalysts – A spatially resolved experimental kinetic study using steady and non-steady state operation under CO/CO2/H2 feeds,” J. Catal., vol. 337, pp. 208–220, 2016, doi: 10.1016/j.jcat.2016.01.025.

[48] Y. Tian, J. Zhang, and J. Morris, “Modeling and optimal control of a batch polymerization reactor using a hybrid stacked recurrent neural network model,” Ind. Eng. Chem. Res., vol. 40, no. 21, pp. 4525–4535, 2001, doi: 10.1021/ie0010565.

[49] O. Sobhani et al., “A hybrid predictive modeling approach for catalyzed polymerization reactors,” Chem. Eng. J. Adv., vol. 20, Art. no. 100662, 2024, doi: 10.1016/j.ceja.2024.100662.

[50] C. Plate, C. J. Martensen, and S. Sager, “Optimal experimental design for universal differential equations,” IEEE Trans. Autom. Control, 2025 (early access), doi: 10.1109/TAC.2025.3609533.

[51] J. Pinto, M. Mestre, J. Ramos, R. S. Costa, G. Striedner, and R. Oliveira, “A general deep hybrid model for bioreactor systems: Combining first principles with deep neural networks,” Comput. Chem. Eng., vol. 165, Art. no. 107952, 2022, doi: 10.1016/j.compchemeng.2022.107952.

[52] M. S. F. Bangi, K. Kao, and J. S.-I. Kwon, “Physics-informed neural networks for hybrid modeling of lab-scale batch fermentation for β-carotene production using Saccharomyces cerevisiae,” Chem. Eng. Res. Des., vol. 179, pp. 415–423, 2022, doi: 10.1016/j.cherd.2022.01.041.

[53] T. Zhou, R. Gani, and K. Sundmacher, “Hybrid data-driven and mechanistic modeling approaches for multiscale material and process design,” Engineering, vol. 7, no. 9, pp. 1231–1238, 2021.

[54] D. C. Boffito, “Scaling process intensification technologies: What does it take to deploy?,” Chem. Eng. Process.–Process Intensif., vol. 212, Art. no. 110275, 2025, doi: 10.1016/j.cep.2025.110275.

[55] Y. Ureel et al., “Active machine learning for chemical engineers: A bright future lies ahead,” Engineering, vol. 27, pp. 23–30, 2023, doi: 10.1016/j.eng.2023.02.019.

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Published

20-09-2026

How to Cite

Iman, P., & Fatima, N. (2026). Hybrid Modeling in Chemical Process Intensification: Architectures, Applications, and Critical Challenges. Asian Journal of Engineering and Applied Technology, 15(2), 15–26. https://doi.org/10.70112/ajeat-2026.15.2.4383

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Review Article

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