Quantifying grain contact and grain volume stress-strain fields in simulated sandstone: a high-resolution FEM approach

Fluid extraction from subsurface reservoir sandstones frequently results in surface subsidence and induced seismicity, such as observed in the Groningen Gas field (the Netherlands). The cause lies in reservoir compaction driven by the increase in effective overburden stress. Deformation of sandstone includes instantaneous elastic deformation, inelastic, time-independent processes, such as critical grain breakage and/or compaction of intergranular clay rims, creep due to stress corrosion and pressure solution. However, no physics-based models exist to predict inelastic reservoir compaction under in-situ conditions, limiting the ability to evaluate the impact of reservoir exploitation. Deformation is driven by stresses transmitted across grain-to-grain contacts. Therefore, it is key to relate the grain-scale deformation mechanisms to grain-scale stress distribution, grain strength and deformation rate. We performed 2D FEM simulations on sandstone aggregates, consisting of quartz, feldspar and/or intergranular clay, with porosities in the range 10-25%, up to 2% volumetric strain. Our simulations showed significant stress concentrations at contact edges, which increased in magnitude with increasing porosity. Intergranular clay rims with a thickness of up to 0.5% of the grain diameter significantly reduced the stress concentration between quartz-quartz contacts, while also reducing the macroscopic Young’s modulus by up to 80%. A more extensive zone of tensile stress is observed within feldspar grains, compared to quartz grains. Our results suggest that composition plays an important role in controlling the grain contact and volume stress-strain behavior, which could lead to over/underestimation of the magnitude of local stress, hence the driving force for grain-scale deformation, if not adequately accounted for.