Fluid injection‐induced cavity expansion in dry porous medium

Abstract

Fluid injection‐induced deformation around a cylindrical cavity is of particular interest in the area of subsurface energy extraction. In this study, a model is proposed to analyze the time‐dependent expansion of a cavity caused by fluid injection in an elastoplastic dry porous medium. This problem is characterized by the existence of two moving boundaries, a permeation front and an elastoplastic interface, which leads to distinct time‐dependent zones governed by different sets of equations. The interplay between these two boundaries leads to three phases of solution. The a priori unknown partitioning of the injection rate into the rate of change of cavity volume and infiltration in the porous medium necessitates the introduction of a time‐dependent permeation coefficient as one of the primary variables. The method of solution takes advantage of the quasi‐static and quasi‐stationary nature of the problem, which makes it possible to treat time as a parameter rather than a variable. It follows that the problem can be solved in two steps. In a first step, closed‐form expressions for the pore pressure, displacement, and stress fields in each zone are derived, with parameters in these expressions depending explicitly on four time‐dependent variables, namely the positions of the two interfaces, the cavity radius, and the permeation coefficient. In a second step, the rate equations governing the evolution of these variables during different phases are derived and solved numerically. The paper concludes with a parametric analysis of the influence of the stiffness and strength of the material on the solution.