Anomalous Pressure Diffusion and Deformation in Two‐ and Three‐Dimensional Heterogeneous Fractured Media

In fractured and stress‐sensitive reservoirs and aquifers, hydromechanical coupling is important, in connection with their heat and solute transport properties, and because the fluid production or extraction leads to land subsidence and potentially to induced seismicity. Classical dual‐porosity poroelasticity (DPP) models cannot upscale pressure diffusion and deformation in fractured porous media, which are characterized by anomalous behaviors that manifest in strong tailing in the temporal evolution of flow rate and subsidence. We study these behaviors using detailed numerical simulations of fluid production in naturally fractured formations characterized by multi‐Gaussian distributions of the matrix permeability. We find that the tailing behaviors depend on the permeability contrast between fracture and matrix, on the permeability distribution in the matrix, and on the correlation length. We use a non–equilibrium, multi‐porosity model to quantify the coupled behaviors of anomalous pressure diffusion, fluid flow and deformation. The model is parameterized by medium and fluid properties, which set the characteristic pressure diffusion time scales. It allows to identify the emerging scaling regimes and scaling behaviors of flow rate and subsidence. We propose a model implementation that captures the full anomalous evolution of flow rates and displacements observed in the detailed numerical simulations in terms of the permeability distribution and matrix length scales. The presented results shed new light on the controls of medium heterogeneity and geometry on pressure diffusion, fluid production and subsidence in highly heterogeneous fractured media.