(261c) Deeponet-Driven Surrogate Model for Enhanced Rwgs Membrane Reactor Performance

Atmospheric CO₂ concentrations have reached alarming levels – now exceeding 420 ppm – creating urgent demand for technologies that can both reduce emissions and transform CO₂ into valuable chemical feedstocks [1,2]. The reverse water-gas shift (RWGS) reaction, which converts CO₂ and hydrogen into carbon monoxide (CO) and water vapor, plays a central role in this effort. CO is a key precursor for fuels and chemicals and can be produced more efficiently using water-selective membranes in RWGS reactors that remove water continuously. This removal shifts the reaction equilibrium toward higher CO₂ conversion and improved CO yield at lower temperatures. For this purpose, we study a reactor design that employs a packed-bed tubular and concentric membrane configuration where the catalyst bed is housed in the annular chamber, receiving the feed as the retentate, while a co-current sweeping stream flows through the tubular chamber within the membrane. This arrangement promotes effective interaction between flow, reaction kinetics, and membrane transport, with the governing differential equations capturing the spatial evolution of species and overall reactor performance. However, the design and optimization of this system require multiple simulation runs with varied parameters which can be computationally expensive. Hybrid models like traditional physics-informed neural networks (PINNs) can alleviate this computational burden and model the spatial dynamics with high accuracy for fixed design parameters. Yet, from a data-driven optimization perspective, PINNs would require the retraining for each design parameter set, highlighting the need for more flexible physics-informed modeling approaches that can handle varying spatial and initial temporal conditions [3].

To efficiently model this intricate system, we propose a surrogate based on physics-informed deep neural operator networks (DeepONet) [4,5]. The proposed model leverages DeepONet to learn the nonlinear mapping from operating parameters to the flow rates of key species. By embedding the governing physical laws directly into its architecture, the network approximates the solution operator of the underlying differential equations. Unlike PINNs that require retraining when boundary conditions or parameters change, DeepONet learns the operator mapping between function spaces, allowing it to generalize across different conditions without repetitive and time-consuming retraining. Trained offline using data from detailed mechanistic simulations, the model accurately predicts reactor behavior under diverse operating conditions while delivering substantial computational savings. Integrating this surrogate model within an optimization framework enables rapid identification of reactor conditions that maximize reaction yield and overall process efficiency, offering a robust and scalable tool for reactor design and control in advanced carbon capture and utilization applications [6-9].

References

[1] Tans, P., Dlugokencky, E. and Miller, B., 2020. The power of greenhouse gases.

[2] NOAA Global Monitoring Laboratory. “Trends in atmospheric carbon dioxide”, https://gml.noaa.gov/ccgg/trends/gl_trend.html (accessed 04/01/2025).

[3] Raissi, M., Perdikaris, P. and Karniadakis, G.E., 2019. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational physics, 378, pp.686-707.

[4] Goswami, S., Bora, A., Yu, Y. and Karniadakis, G.E., 2023. Physics-informed deep neural operator networks. In Machine learning in modeling and simulation: methods and applications (pp. 219-254). Cham: Springer International Publishing.

[5] Lu, L., Jin, P., Pang, G., Zhang, Z. and Karniadakis, G.E., 2021. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nature machine intelligence, 3(3), pp.218-229.

[6] Beykal, B. and Pistikopoulos, E.N., 2024. Data-driven optimization algorithms. In Artificial Intelligence in Manufacturing (pp. 135-180). Academic Press.

[7] Beykal, B., Aghayev, Z., Onel, O., Onel, M. and Pistikopoulos, E.N., 2022. Data-driven Stochastic Optimization of Numerically Infeasible Differential Algebraic Equations: An Application to the Steam Cracking Process. In Computer Aided Chemical Engineering (Vol. 49, pp. 1579-1584). Elsevier.

[8] Aghayev Z., Voulanas D., Gildin E. and Beykal B., 2025. Surrogate-assisted optimization of highly constrained oil recovery processes using classification-based constraint modeling. Industrial & Engineering Chemistry Research.

[9] Boukouvala, F. and Floudas, C.A., 2017. ARGONAUT: AlgoRithms for Global Optimization of coNstrAined grey-box compUTational problems. Optimization Letters, 11, pp.895-913.