Numerical modeling of frequency-dependent velocity and attenuation in a fractured-porous rock saturated with two immiscible fluids

The dispersion and attenuation of seismic-wave propagation induced by ‘squirt flow’ effects in hydrocarbon-saturated reservoirs are significantly affected by their rock properties and fluid content. In this study, we analyse the frequency-dependent velocity, attenuation, and seismic responses when fractured porous rock is saturated with two immiscible fluids. First, when considering reservoir wettability, we calculate the effective fluid viscosity using a stable parameter, the capillary pressure, and a lattice Boltzmann model (LBM)-based relative permeability equation, which is a function of the saturation and viscosity ratio of the immiscible two-phase fluid. Then, we explore the frequency-dependent effects of fractured porous rocks saturated with two immiscible fluids under different cases of viscosity ratios and capillary pressure parameters by employing the Chapman model from the dynamic equivalent-medium theory. Then, we use a four-layer model to analyse the frequency-dependent seismic responses. The results show that the characteristics of frequency-dependent velocity and attenuation are both affected by the wettability, capillary pressure parameter, saturation, and viscosity ratio. The frequency-dependent features are greatly influenced by the capillary pressure parameter and viscosity ratio. For a larger viscosity ratio and lower capillary parameter, a dispersive effect can occur in the seismic frequency band. This indicates that the velocity dispersion anomalies are sensitive to wettability, capillary pressure parameter and viscosity ratio and should not be neglected. Synthetic seismic records demonstrate that the seismic reflection signatures, such as the waveform, amplitude, and reflective travel time, at the interfaces for saturated reservoirs are significantly affected by wettability and saturation. The numerical modeling helps to improve the wave propagation in rocks saturated by two immiscible fluids.