Porous rocks encountered in hydrocarbon reservoirs are often saturated with a mixture of two or more fluids. Generation of synthetic seismograms as well as interpretation of in-situ attenuation measurements require a theoretical understanding of the relation between the heterogeneous distribution of fluid patches and the acoustic properties of rocks. Thus, the problem of calculating acoustic properties of rocks saturated with a mixture of two fluids has attracted considerable interest (White, 1975; Murphy, 1982; Gist, 1994; Mavko and Mukerji, 1998; Pride et al., 2004). At the same time, this problem is also interesting from the theoretical point of view because partially saturated rocks represent a particularly interesting situation when the effects of dynamic poroelasticity may be significant at seismic or sonic frequencies. Indeed, it is a radical departure from the situation with a porous material fully saturated with a single fluid. Such a fully saturated material exhibits frequency-dependent effects only at frequencies comparable with Biot's characteristic frequency (Bourbié et al., 1987) ωc = ηϕ/κρf, where ρf is the fluid density, η is fluid viscosity, κ is permeability, and ϕ is porosity. For frequencies much lower than ωc, the dynamic effects can be ignored and Gassmann theory applies.
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Müller et al. (2004) studied this question.