On the propagation of a disturbance in a heterogeneous, deformable, porous medium saturated with two fluid phases

The coupled modeling of the flow of two immiscible fluid phases in a heterogeneous, elastic, porous material is formulated in a manner analogous to that for a single fluid phase. An asymptotic technique, valid when the heterogeneity is smoothly varying, is used to derive equations for the phase velocities of the various modes of propagation. A cubic equation is associated with the phase velocities of the longitudinal modes. The coefficients of the cubic equation are expressed in terms of sums of the determinants of 3 × 3 matrices whose elements are the parameters found in the governing equations. In addition to the three longitudinal modes, there is a transverse mode of propagation, a generalization of the elastic shear wave. Estimates of the phase velocities for a homogeneous medium, based upon the formulas in this paper, agree with previous studies. Furthermore, predictions of longitudinal and transverse phase velocities, made for the Massilon sandstone containing varying amounts of air and water, are compatible with laboratory observations.