Compressional-wave propagation in porous media saturated with two fluids

Abstract

A theory of porous media with voids filled by two immiscible fluids should comply with Laplace’s law of capillary pressure at the pore level. For the convenience of practical use, it ideally should also involve only the generic elastic coefficients of the mineral grains and pore-filling fluids and avoid the use of “bulk” coefficients of the dry solid frame, whose measurement involves idealized experiments, or poorly understood “phase-coupling” coefficients. It should be reconcilable with the body of empirical data as well. Such a theory and the resulting propagation of the conventional compressional wave can be deduced from principles of linear elasticity. Although the interfacial tension between the fluids is rigorously included, it turns out to have no effect on the velocity of seismic waves. To be reconcilable with observational data, the theory needs to be modified to (1) postulate a power-law effect of the volume fraction of the solid and fluid phases on the reduction of their elastic moduli contributing to the aggregate value and (2) honor the additivity of fluid compressibilities versus bulk moduli to form the effective bulk modulus of the fluids. Empirical calibration of the constants of the power law is necessary to make the theory applicable to a specific class of rock. Constructed this way for well-cemented rocks such as sandstones or limestones, the theory agrees well with the empirical data describing (1) the bulk modulus of the dry solid frame, (2) the bulk modulus of the solid frame filled with one fluid, both as functions of porosity; (3) the data on wave velocity in such rocks filled with one fluid, as a function of porosity, and (4) the measurements of wave velocity in such rocks filled with air and water, as a function of water saturation.