Multirate Mass Transfer Approach for Double‐Porosity Poroelasticity in Fractured Media

Abstract

AbstractNatural and anthropogenic fractured aquifers and reservoirs are dual porosity matrix‐fracture systems, where the fracture network provides highly–conductive flow pathways and the low–permeability matrix stores most of the fluid. The coupling between flow and mechanical deformation in fractured media is often modeled using the classical theory of dual‐porosity poroelasticity (DPP), based on Barenblatt's hypothesis of pressure equilibrium inside the rock matrix blocks. Equilibrium can be expected if the matrix blocks are small and the matrix diffusion time is comparable to the flow time scales along the fractures. In practice, matrix blocks may be large enough so that diffusion time scales are long, and the equilibrium hypothesis breaks down. Here, we study nonequilibrium effects in coupled flow and deformation in fractured media. We compare analytical predictions and modeling results of coupled flow and deformation in heterogeneous fractured porous media. The theoretical analysis is a nonequilibrium, dual‐porosity model. We use this theory to (a) Reveal the limitations of classical DPP formulations. (b) Obtain the scalings for drainage and displacement to be expected for coupled flow and deformation in highly heterogeneous, fractured media. (c) Identify what behavior to expect in fractured aquifers and reservoirs regarding flow and deformation. We observe strong tailing in fluid fluxes and land subsidence that cannot be captured by the classical DPP approach or a single porosity effective medium approach. We show that theoretical predictions from the multirate DPP model and high‐fidelity models agree, even for highly heterogeneous matrix‐fracture systems, and reproduce the observed nonequilibrium effects.