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Porous monolith reactors are attractive supports for heterogeneous catalysis due to their high surface-to-volume ratios and intricate pore networks, which promote efficient contact between reactants and catalyst. However, performance indicators such as productivity, pressure drop, selectivity, and operational safety depend strongly on the underlying pore geometry and are often tightly coupled. These competing objectives, together with the complex mechanisms by which geometry influences transport and reaction phenomena, make the physics-based design of porous monolithic reactors challenging.
One major barrier to the broader adoption of engineered porous structures for heterogeneous catalysis is the efficient identification of reaction-dependent optimal geometries. On the one hand, a wide range of geometry generation methods enable exploration of a high-dimensional design space, including triply periodic minimal surface (TPMS) formulations, stochastic methods, and data-driven generators. On the other hand, advances in fabrication techniques such as additive manufacturing and high-precision etching increasingly enable the fabrication of complex monolith geometries, making performance evaluation prior to manufacture a critical bottleneck. High-fidelity approaches such as pore-resolved computational fluid dynamics (PRCFD) provide detailed access to flow, transport, and reaction mechanisms at the pore scale, but remain prohibitively expensive for use in iterative geometry optimisation or large-scale design space exploration.
In this work, we leverage machine learning (ML) models, specifically convolutional neural networks (CNNs) and multiscale extensions inspired by the MSNet architecture [1,2], to construct surrogate models capable of predicting pressure, velocity, and concentration fields in porous monoliths. By predicting physically meaningful fields rather than only scalar performance values, the surrogate models retain sensitivity to geometry-induced transport mechanisms that are known to play a central role in porous media. The models are trained on PRCFD-generated datasets and used to rapidly evaluate candidate geometries. We investigate trends associated with dataset size and geometric variability, and their influence on surrogate accuracy. We further examine how these factors affect the Pareto-optimal solutions obtained when the models are embedded within a surrogate-assisted geometry optimisation framework.
To generate the high-fidelity datasets required for surrogate training, we rely on PRCFD simulations performed using Lethe [3]. Lethe is an open-source multiphysics PRCFD software based on the finite-element library deal.II [4], which solves the Navier–Stokes, mass conservation, and advection-diffusion-reaction equations in complex porous geometries using a sharp immersed-boundary method [5]. This approach eliminates the need for body-fitted meshing and enables efficient simulation of digitally generated structures across a range of geometries and operating conditions.
Rather than focusing on finalized optimal designs, we provide a proof of concept and a modular, extensible framework for ML-assisted, multi-objective geometry optimisation of monolithic reactors. The proposed approach explicitly targets trade-offs between conflicting objectives such as pressure drop and conversion, and illustrates how PRCFD-trained ML surrogates can shift pore-scale simulation from a purely diagnostic role toward a design-oriented tool in porous media. While additive manufacturing is not addressed directly, the workflow is compatible with AM-ready geometry generators and provides a pathway for translating pore-scale physics into application-specific reactor design strategies.
| References | [1] J. E. Santos et al., “Computationally Efficient Multiscale Neural Networks Applied to Fluid Flow in Complex 3D Porous Media,” Transport in Porous Media, vol. 140, no. 1, pp. 241–272, May 2021, doi: https://doi.org/10.1007/s11242-021-01617-y. [2] Agnese Marcato, J. E. Santos, G. Boccardo, H. Viswanathan, D. Marchisio, and Maša Prodanović, “Prediction of local concentration fields in porous media with chemical reaction using a multi scale convolutional neural network,” Chemical Engineering Journal, vol. 455, pp. 140367–140367, Nov. 2022, doi: https://doi.org/10.1016/j.cej.2022.140367. [3] A. Alphonius et al., “Lethe 1.0: An open-source parallel high-order computational fluid dynamics software framework for single and multiphase flows,” Computer Physics Communications, vol. 318, p. 109880, Jan. 2026, doi: https://doi.org/10.1016/j.cpc.2025.109880. [4] D. Arndt et al., “The deal.II Library, Version 9.5,” Journal of Numerical Mathematics, vol. 31, no. 3, pp. 231–246, Aug. 2023, doi: https://doi.org/10.1515/jnma-2023-0089. [5] Olivier Guévremont, L. Barbeau, V. Moreau, F. Galli, N. Virgilio, and B. Blais, “Robust pore-resolved CFD through porous monoliths reconstructed by micro-computed tomography: From digitization to flow prediction,” Chemical Engineering Journal, pp. 158577–158577, Dec. 2024, doi: https://doi.org/10.1016/j.cej.2024.158577. |
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| Country | Canada |
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