Variations of the in‐situ stress within nonhomogeneous layers of the subsurface rock induced by changes in pore fluid pressure

Abstract

AbstractThis paper presents a three‐dimensional analytical solution for deformation and stress change inside and outside a porous layer of rock subjected to prescribed axisymmetric disturbance in the pore fluid pressure. The porous layer is confined between two impermeable layers of rock. Different mechanical moduli are considered for the porous and confining strata. The solution is derived from Navier's equations of static equilibrium while considering the continuity of stress and deformation across the rock layers which are assumed to follow linearly poroelastic constitutive behavior. Results for the case of uniform pore fluid pressure change within the porous layer are demonstrated in terms of rock deformation, as well as changes in the magnitude and orientation of principal stresses, inside and outside the porous layer. Variations of these results with key problem parameters including the stiffness ratio of rock layers and the aspect ratio of disturbed pore pressure volume are presented. Findings indicate the large effect of layers heterogeneity on redistribution and reorientation of the in‐situ stress, yet, less significantly on deformation of the porous layer. Results further reveal the substantial error rates that uniaxial strain models may produce in estimating the stress path of depleted or injected reservoirs.