P‐wave dispersion and attenuation in fractured and porous reservoirs – poroelasticity approach

Abstract

A B S T R A C TNatural fractures in hydrocarbon reservoirs can cause significant seismic attenuation and dispersion due to wave induced fluid flow between pores and fractures. We present two theoretical models explicitly based on the solution of Biot's equations of poroelasticity. The first model considers fractures as planes of weakness (or highly compliant and very thin layers) of infinite extent. In the second model fractures are modelled as thin penny-shaped voids of finite radius. In both models attenuation is a result of conversion of the incident compressional wave energy into the diffusive Biot slow wave at the fracture surface and exhibits a typical relaxation peak around a normalized frequency of about 1. This corresponds to a frequency where the fluid diffusion length is of the order of crack spacing for the first model and the crack diameter for the second. This is consistent with an intuitive understanding of the nature of attenuation: when fractures are closely and regularly spaced, the Biot's slow waves produced by cracks interfere with each other, with the interference pattern controlled by the fracture spacing. Conversely, if fractures are of finite length, which is smaller than spacing, then fractures act as independent scatterers and the attenuation resembles the pattern of scattering by isolated cracks. An approximate mathematical approach based on the use of a branching function gives a unified analytical framework for both models.

Experimental observation of water saturation effects on shear wave splitting in synthetic rock with fractures aligned at oblique angles

“…An additional mechanism not considered by White's model, but believed to be responsible for the additional dispersion (at partial gas and full water saturation) observed at high frequencies, is squirt or local fluid flow (see Mavko and Nur, 1979, Winkler, 1985, Dvorkin et al, 1994, Carcione et al, 2003. The presence of fractures is also known to cause dispersion in saturated rocks through the squirt flow mechanism (see Chapman, 2003, Gurevich et al, 2009. This squirt flow mechanism as a result of the presence of fractures is incorporated in the model of Chapman (2003).…”

Computation of Wave Attenuation and Dispersion, by Using Quasi-Static Finite Difference Modeling Method in Frequency Domain

“…Several analytical solutions are also put forward to estimate wave attenuation and velocity dispersion due to WIFF at microscopic scale [Mavko et al 1975, Mavko et al 1979, Budiansky et al 1976, Palmer et al 1980, Dvorkin et al 1995, Chapman et al 2002, Pride et al 2003, Gurevich et al 2009. Apart from the ability to precisely predict wave attenuation and velocity dispersion at sonic frequency frequencies, investigations reveal that the microscopic scale theories lack to predict wave attenuation and velocity dispersion within seismic frequency band.…”

Numerical modeling of 2D seismic wave propagation in fluid saturated porous media using graphics processing unit (GPU): Study case of realistic simple structural hydrocarbon trap

“…effects on length scales larger than the pore size but still smaller than the seismic wavelength, produce characteristic attenuation and dispersion behavior in porous rocks. There are various theories of wave propagation in patchy-saturated and cracked porous media [10,11,12] that take into account mesoscopic effects.…”