Analysis of attenuation and dispersion of propagating wave due to the coexistence of three fluid phases in the pore volume

Abstract

In exploration geophysics, the efforts to extract subsurface information from wave characteristics exceedingly depend on the construction of suitable rock physics model. Analysis of different rock physics models reveals that the strength and magnitude of attenuation and dispersion of propagating wave exceedingly depend on wave‐induced fluid flow at multiple scales. In current work, a comprehensive analysis of wave attenuation and velocity dispersion is carried out at broad frequency range. Our methodology is based on Biot's poroelastic relations, by which variations in wave characteristics associated with wave‐induced fluid flow due to the coexistence of three fluid phases in the pore volume is estimated. In contrast to the results of previous research, our results indicate the occurrence of two‐time pore pressure relaxation phenomenon at the interface between fluids of disparate nature, that is, different bulk modulus, viscosity and density. Also, the obtained results are compatible with numerical results for the same 1D model which are accounted using Biot's poroelastic and quasi‐static equation in frequency domain. Moreover, the effects of change in saturation of three‐phase fluids were also computed which is the key task for geophysicist. The outcomes of our research reveal that pore pressure relaxation phenomenon significantly depends on the saturation of distinct fluids and the order of saturating fluids. It is also concluded that the change in the saturation of three‐phase fluid significantly influences the characteristics of the seismic wave. The analysis of obtained results indicates that our proposed approach is a useful tool for quantification, identification and discrimination of different fluid phases. Moreover, our proposed approach improves the accuracy to predict dispersive behaviour of propagating wave at sub‐seismic and seismic frequencies.

An Exact Expression for the Effective Bulk Modulus for Acoustic Wave Propagation in Cylindrical Patchy-Saturation Rocks

“…Concentric Cylinder Geometry. Since being first proposed by White [15] and White et al [16], the patchysaturated rock theory has undergone considerable development [16][17][18][19][20][21][22][23][24][28][29][30][31][32][33]. Periodic slabs and concentric spheres are two well-known patch distributions.…”

“…Subsequently, the decoupling method proposed by Dutta and Odé has been extended to a full frequency range [20][21][22] and an exact solution [22]. The patch distribution demonstrates important progress of the patchy-saturation model [23][24][25][26]. It should be noted that the solutions derived by White [15] and Johnson [19] are approximate expressions for patchysaturation rocks, and the exact solutions derived by Dutta and Odé [17,18] and Vogelaar et al [22] do not estimate P-wave propagation at high frequencies.…”