Stochastic Multiscale Analysis of Porous Media Flow through Data-Driven Stochastic Upscaling

  • Nguyen, Phu Thien (Leibniz Universität Hannover)
  • Zheng, Zhibao (Leibniz Universität Hannover)
  • Chamoin, Ludovic (Université Paris-Saclay)
  • Nackenhorst, Udo (Leibniz Universität Hannover)
  • Beer, Micheal (Leibniz Universität Hannover)

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This work presents a data-driven uncertainty analysis framework for stochastic multiscale flow in porous media. In the context of stochastic homogenization, random pore-scale geometries obtained from μ-CT scans [1] are used to define stochastic representative volume elements (SRVEs). For each geometric realization of SRVE, pore-scale flow simulations are performed using the Lattice Boltzmann method (LBM) to compute equivalent permeability tensors [1, 2]. Unlike conventional approaches that rely on predefined or idealized SRVEs, the proposed framework directly extracts the pore microstructure from μ-CT data. Furthermore, in contrast to most mesh-based methods [3], the voxel-based nature of the LBM eliminates the need for costly remeshing when dealing with complex and randomly varying pore geometries, thereby significantly improving the computational efficiency and robustness of stochastic SRVE simulations. The data-driven equivalent permeability is subsequently upscaled to the Darcy scale through stochastic homogenization. By incorporating macroscale spatial correlation and efficient stochastic finite element methods, spatial uncertainty is further modeled and propagated to macroscale flow solutions. Overall, the proposed framework establishes a comprehensive pipeline, from efficient stochastic SRVE analysis, through stochastic homogenization, to macroscale spatial correlation modeling and stochastic solution. This framework enables a more faithful representation of microscale geometric uncertainty and ensures its physically consistent propagation to the Darcy scale. [1] P. T. Nguyen, U. Navrath, Y. Heider, J. Carmai, B. Markert, Investigating the impact of deformation on foam permeability through CT scans and the Lattice-Boltzmann method, Proceedings in Applied Mathematics & Mechanics, 24, e202300154, 2023. [2] M. Chaaban, Y. Heider, B. Markert, Upscaling LBM-TPM simulation approach of Darcy and non-Darcy fluid flow in deformable, heterogeneous porous media, International Journal of Heat and Fluid Flow, 83, 108566, 2020. [3] Z. Zheng, U. Nackenhorst, Efficient uncertainty propagation for stochastic multiscale linear elasticity, Computer Methods in Applied Mechanics and Engineering, 428, 117085, 2024