Poroelasticity During Fluid Injection in Confined Geological Reservoirs: Incorporating Effects of Seal-Rock Stiffness

Abstract

Summary This paper presents a new poroelastic solution to describe the time-dependent response of a confined geological reservoir to fluid injection through a fully penetrating vertical well treated as a point source. Unlike previous studies, vertical-confinement effects of seal rocks are incorporated in the solution. To facilitate analytical description of a fully coupled poroelastic behavior within the reservoir, the stiffness of surrounding rocks is described by the Winkler model, simplifying the response of seal rocks in the direction perpendicular to the reservoir plane. Analytical expressions are obtained for axisymmetric stress and strain components in the reservoir and for the vertical reaction stress. The latter is essential for evaluation of integrity of seal rocks during injection. Solutions are also obtained for the magnitude and location of the maximum-induced radial displacement as a function of time during injection. The effects of poroelastic coupling are articulated through the equivalent diffusion constant of the reservoir-seal rocks system. The latter is expressed through traditional poroelastic parameters as well as the relative stiffness of reservoir and seal rocks. The Winkler modulus of seal rocks, which is involved in all analytical relationships presented in this paper, is empirically linked to elastic characteristics of surrounding strata by comparing their response with the same pressure change in the reservoir according to the ideally elastic and Winkler models. The derived solutions are compared with previous studies, and verified against fully coupled numerical simulations. A comprehensive sensitivity analysis is conducted to assess the effects of the stiffness of the confining strata on the response of a uniform reservoir to injection. The vertical component of stress and the radial and vertical displacements are found to be substantially sensitive to the magnitude of the vertical restraint. The findings note the significance of incorporating seal-rock characteristics to attain a realistic assessment of the geomechanics of injection, specifically in formations with lower elastic moduli.