Infiltration of a Two-State Compressible Fluid Through a Linearly Deformed, Porous, Elastic, Fissured Rock

A theory is formulated for a double porosity medium with two-component vector porosity field. In particular, the performance of a fissured rock medium subjected to a variable load in the space and time domain is considered. The deformation-flow interaction phenomenon is described by five, linear, partial differential equations which contain nine unknown coefficients. The evaluation of coefficients is achieved through the design of an experimental measurement to yield their numerical values. Next, the mixed initial-boundary value problem is formulated by combining the five field equations with sufficient initial and boundary conditions. The finite element weighted residual method employing the Galerkin approach is selected for the solution of the time-dependent problem. A finite element computer program is developed to calculate solid displacements and stresses, fluid pressures and flows. The numerical examples include a one-dimensional column, a two-dimensional layer, and a two-dimensional halfspace of fissured rock. The selected examples indicate that the double porosity model predicts larger displacements and smaller pressure values than those corresponding to a single porosity model for a particular behavior of the pores. Suggestions for future prospects of research are given; inclusion of mechanical and hydraulic anisotropy, viscous flow, and plastic deformations are suggested.