Modeling high-frequency acoustics velocities in patchy and partially saturated porous rock using differential effective medium theory

Differential effective medium (DEM) theory is applied here to the problem of modeling physical properties of poroelastic media that are partially saturated with liquid. Typical fluid saturants are air and water, or gas and oil. If the liquid and gas saturants are homogeneously mixed, then we say the medium is partially saturated. If the liquid and gas saturants are poorly mixed, so each constituent occupies separate, but contiguous, regions of the porous medium, we say the medium has patchy saturation. Some examples are presented to show that a reasonable approach to modeling the effects of patchy saturation at high frequencies (200 kHz and above) is produced by treating the medium as if it is a composite of gas-saturated and liquid-saturated porous inclusions that are homogeneously mixed together. Estimates of the properties are obtained using differential effective medium theory. The results differ dramatically from those predicted by Gassmann’s equations for homogeneous mixing of the fluids in individual pores. In particular, the shear modulus depends on the elastic properties of the fluid constituents, unlike the quasistatic behavior predicted by Gassmann.