Influence of inter-grain cementation stiffness on the effective elastic properties of porous Bentheim sandstone

Effective elastic properties of porous media are known to be significantly influenced by porosity. In this paper, we investigated the influence of another critical factor, the inter-grain cementation stiffness, on the effective elastic properties of a granular porous rock (Bentheim sandstone) using an advanced numerical workflow with realistic rock microstructure and a theoretical model. First, the disparity between the experimentally tested elastic properties of Bentheim sandstone and the effective elastic properties predicted by empirical equations was analysed. Then, a micro-computed tomography (CT)-scan based approach was implemented with digital imaging software AVIZO to construct the 3D (three-dimensional) realistic microstructure of Bentheim sandstone. The microstructural model was imported to a mechanics solver based on the 3D finite element model with inter-grain boundaries modelled by cohesive elements. Loading simulations were run to test the effective elastic properties for different shear and normal inter-grain cementation stiffness. Finally, a relation between the macroscale Young's modulus and inter-grain cementation stiffness was derived with a theoretical model which can also account for porosity explicitly. Both the numerical and theoretical results indicate the influence of the inter-grain cementation stiffness, on the effective elastic properties is significant for porous sandstone. The calibrated normal and shear stiffnesses at the inter-grain boundaries are 1.2 × 105 and 4 × 104 GPa/m, respectively.