Martin Lesueur, Hadrien Rattez, Oriol Colomés

Flow simulations on porous media, reconstructed from Micro-Computerised Tomography (μCT)-scans, is becoming a common tool to compute the permeability of rocks. In order for the value of this homogenised hydraulic property to be representative of the rock at a continuum scale, the sample considered needs to be at least as large as the Representative Elementary Volume. More- over, the numerical discretisation of the digital rock needs to be fine enough to reach numerical convergence. In the particular case of Finite Elements (FE), studies have shown that simulations should use structured meshes at least two times finer than the original image resolution in order to reach the mesh convergence. These two conditions and the increased resolution of μCT-scans to observe finer details of the microstructure, can lead to extremely computationally expensive numerical simulations. In order to reduce this cost, we couple a FE numerical model for Stokes flow in porous media with an unfitted boundary method, which allows to improve results precision for coarse meshes. Indeed, this method enables to obtain a definition of the pore-grain interface as precise as for a conformal mesh, without a computationally expensive and complex mesh generation for μCT-scans of rocks. From the benchmark of three different rock samples, we observe a clear improvement of the mesh convergence for the permeability value using the unfitted boundary method. An accurate permeability value is obtained for a mesh coarser than the initial image resolution. The method is then applied to a large sample of a high resolution μCT-scan to showcase its advantage.