Non-Hertzian Stress Fields in Simulated Porous Sandstone Grains and Implications for Compactive Brittle Failure—A High-Resolution FEM Approach

Fluid extraction from sandstone reservoirs leads to reservoir compaction, potentially inducing surface subsidence and seismicity, as observed in the Groningen Gas Field, Netherlands. Such compaction is partly elastic, but can additionally be caused by instantaneous plastic and rate/time-dependent processes, such as subcritical crack growth, meaning that compaction may continue even if production is stopped. Despite the need to evaluate the impact of post-abandonment reservoir behavior ($>$10–100 years), few mechanism-based, rate/time-dependent compaction laws exist. Compaction due to grain breakage, either via critical or subcritical crack growth, is driven by tensile stresses acting on surface and volume flaws. We performed high-resolution 3D linear elastic finite element method simulations on simplified grain assemblies to investigate the effect of stress–strain boundary conditions, porosity and mineralogical variations on grain-scale stress fields. Our simulations showed tensile stress concentrations at grain contact edges and on pore walls, which increased in magnitude with increasing aggregate porosity and local porosity variation. The fraction of surface area with tensile stresses sufficient to extend flaws with a size up to $30\mathrm{\mu m}$ showed a clear correlation with compactive yield envelopes for the Groningen reservoir sandstone. This suggests that compactive failure is related to the probability of pre-existing surface flaws, falling in a pore surface region where the Griffith criterion is satisfied. A preliminary, time-independent failure probability model, using the observed tensile stress distribution, qualitatively predicts a non-linear increase in grain cracking during deviatoric loading, and suggests a new route to predict sandstone compaction through brittle grain failure.