Velocity variations in carbonate rocks due to dual porosity and wave-induced fluid flow

Stiffness variations in carbonates may be described as resulting from different concentrations of flat compliant pores or cracks, which can have a significant effect on the effective stiffness and acoustic properties (e.g., velocities and attenuations) of dry as well as saturated carbonates, although they carry extremely little porosity. As shown in this paper, the effects of dual porosity and wave-induced fluid flow or pore pressure communication may also play a significant role. On the basis of a previously published T-matrix approach to model the effective viscoelastic properties of cracked porous media, we illustrate the (frequency-dependent) effects of wave-induced fluid flow (mainly squirt flow) or pore pressure communication for a model structure consisting of a mixture of fluid-saturated porous grains and fluid-saturated cavities (vugs, etc.) that are embedded in a solid matrix associated with carbonates. We assume that the pores within the porous grains are decoupled from the pores in the solid matrix (and possibly saturated with different fluids) but that each pore system at the micro and/or mesoscale may or may not be connected. For each of four different connectivity models, we present numerical results for four different cases of microstructure (that emphasize the importance of cracks and flat compliant pores). Our numerical results indicate that the velocity and attenuation spectra of carbonates vary significantly, even when the crack density and all other volume concentrations are constant.