A model for wave propagation in a composite solid matrix saturated by a single-phase fluid

Abstract

This paper presents a theory to describe wave propagation in a porous medium composed of twosolids saturated by a single-phase fluid for spatially variable porosity. This problem has beenpreviously solved for constant porosity when one of the solids is ice or clay, but that model is notuseful for most realistic situations. The equations for variable porosity are derived from the virtualwork principle, where the generalized coordinates are identified as the displacements of the twosolid phases and a new variable associated with the relative fluid flow, whose divergence is thechange in fluid content. The generalized forces are the fluid pressure and combinations of the stresstensor of each solid phase and the fluid pressure. The Lagrangian equations of motion are derivedfor the isotropic case and a theorem on the existence and uniqueness of their solution is given. Theplane wave analysis reveals the existence of three compressional and two shear waves. The theoryis applied to wave propagation in shaley sandstones showing that phase velocities of the faster P andS waves agree very well with experimental data for varying porosity and clay content. A simulationthrough a plane interface separating two frozen sandstones of different ice contents is presented.