Free Fluid Flow Through a Visco-Deformable Porous Medium with a Moving Boundary

One-dimensional Darcy-law flow through a porous matrix representing a high-viscosity liquid is investigated. The flow develops in a region which depends on time due to sedimentation. The problem considered simulates the geological process of sedimentation in a basin. In accordance with geological data, the permeability and viscosity coefficients of the matrix are assumed to depend nonlinearly on the porosity. The asymptotic properties of the flow are described for large times. The agreement between the results of asymptotic and numerical solutions is satisfactory at intermediate times and good at large times under the realistic sedimentary basin conditions. The simplicity of the asymptotic solution obtained makes it possible to vary the problem parameters and determine the porosity, pressure, and velocities for particular geological conditions by means of simple calculations.