Anisotropic permeability: influence on seismic velocity and attenuation*
The permeability is an important parameter for the description of hydrocarbon reservoirs. In isotropic reservoirs the average permeability controls the rate of hydrocarbon production; if reservoirs are heterogeneous, the spatial variation of permeability is essential for the ultimate recovery. Due to fractures or layering the permeability may show strong anisotropy, which defines the main direction of fluid flow during the production process. Such a transversely isotropic (TI) permeability has influence on both velocity and attenuation of seismic waves. To model the wave propagation in TI reservoirs, Biot-theory for homogeneous, liquid saturated porous media is used. This means that only effects of the global fluid flow are considered.
For the frequency range up to approximately 10 kHz it is possible to derive analytical formulae for qP-, qSV- and SH- wave phase velocities and attenuation coefficients. At higher frequencies the assumption of Poiseuille flow is no longer valid. For these higher frequencies, up to 2 MHz, the velocities and attenuation coefficients are analyzed numerically. Whereas at seismic frequencies there is no significant velocity anisotropy due to the anisotropic permeability, the attenuation is strongly affected.
Its anisotropy is equal to the permeability anisotropy, the absolute value of this attenuation, however, is very small. At frequencies of more than approximately 10 kHz, a permeability anisotropy of one order of magnitude leads to a velocity anisotropy of a few percent; the corresponding attenuation anisotropy is reduced. In this frequency range the attenuation due to global flow is larger.