Experimental verification of the anisotropic Gassmann model for fluid substitution in fractured reservoirs

Abstract

Porous reservoirs with aligned fractures exhibit frequency dependent seismic anisotropy due to wave induced fluid flow between pores and fractures. We model this frequency dependent anisotropy by combining the low-frequency anisotropic Gassmann model with the Hudson et al. model for frequency dependent properties of a porous material with penny-shaped cracks. The predictions of the anisotropic Gassmann model are compared with experimental measurements of elastic wave velocities as function of angle for a synthetic sample with aligned disc-like cracks. The properties of the host rock and fracture compliances are obtained from P, SV, and SH velocities measured on the dry sample. The dry fractured porous rock properties serve as input to anisotropic Gassmann fluid substitution model, which is used to compute the saturated rock properties. The stiffnesses of the saturated fractured porous rock are used to calculate the angular dependent compressional and shear wave velocities. The predicted velocities are then compared to the measured velocities. The agreement is reasonably good for both S-wave velocities, but P-wave anisotropy is overestimated by about 25%. This discrepancy can be explained by the fact that the low frequency assumption of the anisotropic Gassmann model does not account for the fluid diffusion effects occurring at relatively high frequencies used in the experiment (100 KHz). A combination of the low frequency anisotropic Gassmann model with the Hudson et al. frequency dependency accounts for fluid diffusion effects and results in an excellent agreement for P- as well as S- waves.