A modified rock physics model for analysis of seismic signatures of low gas-saturated rocks

In seismic applications, the bulk modulus of porous media saturated with liquid and gas phases is often estimated using Gassmann's fluid substitution formula, in which the effective bulk modulus of the two-phase fluid is the Reuss average of the gas and liquid bulk moduli. This averaging procedure, referred to as Wood's approximation, holds if the liquid and gas phases are homogeneously distributed within the pore space down to sizes well below the seismic wavelength and if the phase transfer processes between liquid and gas domains induced by the pressure variations of the seismic wave are negligible over the timescale of the wave period. Using existing theoretical results and low-frequency acoustic measurements in bubbly liquids, we argue that the latter assumption of “frozen” phases, valid for large enough frequencies, is likely to fail in the seismic frequency range where lower effective bulk modulus and velocity, together with dispersion and attenuation effects, are expected. We provide a simple method, which extends to reservoir fluids a classical result by Landau and Lifshitz valid for pure fluids, to compute the effective bulk modulus of thermodynamically equilibrated liquid and gas phases. For low gas saturation, this modulus is significantly lower than its Wood's counterpart, especially at the crossing of bubble point conditions. A seismic reflector associated to a phase transition between a monophasic and a two-phase fluid thus will appear. We discuss the consequences of these results for various seismic applications including fizz water discrimination and hydrocarbon reservoir depletion and CO₂ geological storage monitoring.