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.@en

Digital Rock Physics has reached a level of maturity on the characterisation of primary properties that depend on the microstructure - such as porosity, permeability or elastic moduli - by numerically solving field equations on μCT scan images of rock. After small deformations or at depth though, most rocks eventually reach their limit of elasticity and the complementary plastic properties are needed to describe the full mechanical behaviour. Currently, determination of a rock's yield surface from its microstructure is often restricted to semi-analytical criteria derived by limit analysis or numerical simulations performed on idealised geometries. Such simplification lacks representativeness, particularly for processes that affect directly the pore-grain interface such as the cementation phenomenon, happening during diagenesis. Eventually, only direct numerical simulation of elasto-plasticity performed on digitalised microstructures can be used to assess the strength of different cemented materials and its evolution with the alteration of the microstructure. In this study, we provide a comprehensive parametric study on the impact of cementation on rock strength for real microstructures of cemented granular materials. Compared to most previous studies, the whole yield surface is determined numerically (using Finite Element Method) in order to assess the influence of cementation for different stress-paths. The previously known tendency of rock to strengthen with increasing cementation volume is verified. New results on the influence of cement property namely Young's modulus, friction and cohesion on the rock's yield surface are explored. The envelopes obtained are compared to the ones obtained by experimental data and existing models. The framework presented in this study showcases the wider possibility of determining any rock's or porous material's yield surface from its microstructure. @en