Flow simulations on porous media, reconstructed from Micro-Computerised Tomography (μCT) scans, is becoming a common tool to compute the permeability of rocks. Still, some conditions need to be met to obtain accurate results. Only if the sample size is equal or larger than the Representative Elementary Volume will the computed effective permeability be representative of the rock at a continuum scale. Moreover, the numerical discretisation of the digital rock needs to be fine enough to reach numerical convergence. In the particular case of using Finite Elements (FE) and cartesian meshes, studies have shown that the meshes should be at least two times finer than the original image resolution in order to reach the simulation's 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 for cartesian meshes, 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 on cartesian meshes. 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.
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- Finite element method
- Flow simulations
- Permeability upscaling
- Unfitted boundary method
- μCT scan