https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Wed, 16 Sep 2026 19:15:42 GMT 2026-09-16T19:15:42Z http://hdl.handle.net/10985/26026 Clarifications about upscaling diffusion with heterogeneous reaction in porous media VALDÉS-PARADA, Francisco J.; LASSEUX, Didier The upscaling process of coupled (single- and two-species) diffusion with heterogeneous chemical reaction in homogeneous porous media is revisited in this work with several important clarifications following the article from Bourbatache et al. (Acta Mech 234: 2293-2314, 2023. https://doi.org/10.1007/s00707-023-03501-w). It is shown that the upscaled model obtained from the volume averaging method (VAM) or, equivalently, following an adjoint and Green’s formulation technique provides a closed model without any a priori assumption on the form of the solution for the pore-scale concentration involved in the spectral approach used in the periodic homogenization method (PHM) reported in the above reference. Through comparison with direct pore-scale simulations, the VAM model is shown to outperform the predictions of the average concentration and average flux profiles for the simple two-dimensional configuration considered in Bourbatache et al. (Acta Mech 234: 2293-2314, 2023. https://doi.org/10.1007/s00707-023-03501-w) in comparison with the model obtained from PHM in this reference. Finally, identification of the apparent effective diffusion coefficient from these pore-scale simulations, which serve as in silico experiments, proves that the correct dependence upon the Damkhöler number is the one predicted by the model obtained with VAM, in contradiction with the conclusion put forth in Bourbatache et al. (Acta Mech 234: 2293-2314, 2023. https://doi.org/10.1007/s00707-023-03501-w). The physical explanation lies in the corrective contribution of the reactive part to the apparent effective diffusion coefficient, which is positive and adds up to the pure intrinsic diffusive part. The discrepancy between PHM and VAM approaches is proved to originate from the choice of changes of variables in the pore-scale concentration used in the spectral approach while employing PHM. © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2025. Wed, 01 Jan 2025 00:00:00 GMT http://hdl.handle.net/10985/26026 2025-01-01T00:00:00Z VALDÉS-PARADA, Francisco J. LASSEUX, Didier The upscaling process of coupled (single- and two-species) diffusion with heterogeneous chemical reaction in homogeneous porous media is revisited in this work with several important clarifications following the article from Bourbatache et al. (Acta Mech 234: 2293-2314, 2023. https://doi.org/10.1007/s00707-023-03501-w). It is shown that the upscaled model obtained from the volume averaging method (VAM) or, equivalently, following an adjoint and Green’s formulation technique provides a closed model without any a priori assumption on the form of the solution for the pore-scale concentration involved in the spectral approach used in the periodic homogenization method (PHM) reported in the above reference. Through comparison with direct pore-scale simulations, the VAM model is shown to outperform the predictions of the average concentration and average flux profiles for the simple two-dimensional configuration considered in Bourbatache et al. (Acta Mech 234: 2293-2314, 2023. https://doi.org/10.1007/s00707-023-03501-w) in comparison with the model obtained from PHM in this reference. Finally, identification of the apparent effective diffusion coefficient from these pore-scale simulations, which serve as in silico experiments, proves that the correct dependence upon the Damkhöler number is the one predicted by the model obtained with VAM, in contradiction with the conclusion put forth in Bourbatache et al. (Acta Mech 234: 2293-2314, 2023. https://doi.org/10.1007/s00707-023-03501-w). The physical explanation lies in the corrective contribution of the reactive part to the apparent effective diffusion coefficient, which is positive and adds up to the pure intrinsic diffusive part. The discrepancy between PHM and VAM approaches is proved to originate from the choice of changes of variables in the pore-scale concentration used in the spectral approach while employing PHM. © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2025. http://hdl.handle.net/10985/24588 Effective transmissivity for slip flow in a fracture ZAOUTER, Tony; VALDÉS-PARADA, Francisco J.; PRAT, Marc; LASSEUX, Didier A simple efficient method is presented for the determination of the intrinsic transmissivity tensor, as well as the intrinsic correction tensors at successive orders in the dimensionless slip parameter, that predicts the effective transmissivity tensorial coefficient for steady, one-phase, isothermal, creeping flow of a Newtonian fluid with slip boundary condition in a rough fracture. It is demonstrated that the solution of the first $N$ ancillary closure problems provides the slip correction tensors up to the $2N-1$ order, hence reducing the computational requirements by a factor of ${\sim }2$ compared with the conventional approach. In particular, the first-order correction tensor (i.e. a Klinkenberg-like tensor) can be obtained by solving the closure problem required for the computation of the intrinsic transmissivity tensor. In addition, symmetry and definiteness (positiveness or negativeness) properties of the individual tensors are analysed. It is shown that a Padé approximant, built on the correction tensors at the first three orders, outperforms the predictions for the effective transmissivity tensor. The new approach is illustrated and validated with numerical examples on model rough fractures. Fri, 11 Aug 2023 00:00:00 GMT http://hdl.handle.net/10985/24588 2023-08-11T00:00:00Z ZAOUTER, Tony VALDÉS-PARADA, Francisco J. PRAT, Marc LASSEUX, Didier A simple efficient method is presented for the determination of the intrinsic transmissivity tensor, as well as the intrinsic correction tensors at successive orders in the dimensionless slip parameter, that predicts the effective transmissivity tensorial coefficient for steady, one-phase, isothermal, creeping flow of a Newtonian fluid with slip boundary condition in a rough fracture. It is demonstrated that the solution of the first $N$ ancillary closure problems provides the slip correction tensors up to the $2N-1$ order, hence reducing the computational requirements by a factor of ${\sim }2$ compared with the conventional approach. In particular, the first-order correction tensor (i.e. a Klinkenberg-like tensor) can be obtained by solving the closure problem required for the computation of the intrinsic transmissivity tensor. In addition, symmetry and definiteness (positiveness or negativeness) properties of the individual tensors are analysed. It is shown that a Padé approximant, built on the correction tensors at the first three orders, outperforms the predictions for the effective transmissivity tensor. The new approach is illustrated and validated with numerical examples on model rough fractures. http://hdl.handle.net/10985/25632 Effective Reynolds Model Coefficients for Flow Between Rough Surfaces in Sliding Motion LASSEUX, Didier; VALDÉS-PARADA, Francisco J.; PRAT, Marc In this Letter, it is shown how the determination of the effective coefficients involved in the macroscopic model for pressure driven and/or Couette flow in a rough fracture can be simplified by solving only one closure problem instead of two as originally reported in Prat et al. (Transp Porous Media 48(3):291–313, 2002 Wed, 13 Dec 2023 00:00:00 GMT http://hdl.handle.net/10985/25632 2023-12-13T00:00:00Z LASSEUX, Didier VALDÉS-PARADA, Francisco J. PRAT, Marc In this Letter, it is shown how the determination of the effective coefficients involved in the macroscopic model for pressure driven and/or Couette flow in a rough fracture can be simplified by solving only one closure problem instead of two as originally reported in Prat et al. (Transp Porous Media 48(3):291–313, 2002