Flow in deformable porous media I: Simple Analysis

Many processes in the earth, such as magma migration, can be described by the flow of a low viscosity fluid in a viscously deformable, permeable matrix. The purpose of this and a companion paper is to develop a better physical understanding of the equations governing these two-phase flows. This paper presents a series of analytic approximate solutions to the governing equations to show that the equations describe two different modes of matrix deformation. Shear deformation of the matrix is governed by Stokes equation and can lead to porosity driven convection. Volume changes of the matrix are governed by a non-linear dispersive wave equation for porosity. Porosity waves exist because the fluid flux is an increasing function of porosity and the matrix can expand or compact in response to variations in the fluid flux. The speed and behaviour of the waves depend on the functional relationship between permeability and porosity. If the partial derivative of the permeability with respect to ..