Fluid injection-induced cavity expansion in dry porous medium

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.