Poroelastic model to relate seismic wave attenuation and dispersion to permeability anisotropy

Abstract

A transversely isotropic model with a horizontal axis of symmetry, based on the Biot and squirt-flow mechanisms, predicts seismic waves in poroelastic media. The model estimates velocity dispersion and attenuation of waves propagating in the frequency range of crosswell and high-resolution reverse vertical seismic profiling (VSP) (250-1250 Hz) for vertical permeability values much greater than horizontal permeability parameters. The model assumes the principal axes of the stiffness constant tensor are aligned with the axes of the permeability and squirt-flow tensors. In addition, the unified Biot and squirt-flow mechanism (BISQ) model is adapted to simulate cracks in permeable media. Under these conditions, the model simulations demonstrate that the preferential direction of fluid flow in a reservoir containing fluidfilled cracks can be determined by analyzing the phase velocity and attenuation of seismic waves propagating at different azimuth and incident angles. As a result, the fast compressional wave can be related to permeability anisotropy in a reservoir. The model results demonstrate that for a fast quasi-P-wave propagating perpendicular to fluid-filled cracks, the attenuation is greater than when the wave propagates parallel to the plane of the crack. Theoretical predictions and velocity dispersion of interwell seismic waves in the Kankakee Limestone Formation at the Buckhorn test site (Illinois) demonstrate that the permeable rock matrix surrounding a low-velocity heterogeneity contains vertical cracks.

Poroelastic wave equation including the Biot/squirt mechanism and the solid/fluid coupling anisotropy

“…In the previous studies, Dvorkin and coworkers [1,2] and Parra [9,10] have confirmed the BISQ theory by comparing the BISQ-predicted phase velocity and the attenuation values with the experimental data from Klimentos and McCann [19] and crosswell seismic data. Comparing the present poroelastic wave equation with that of Parra [9] in the space-frequency domain, we can find that both results are essentially identical when assuming ρ ax = ρ ay = ρ az in a 2D PTL porous medium (see Fig.…”

“…The BISQ model relates the dynamic poroelastic behavior of a saturated rock to traditional poroelastic constants such as porosity, permeability, fluid compressibility and viscosity, and the characteristic squirt-flow length. Parra [9,10] extends this BISQ theory to include the transversely isotropic poroelastic medium. Parra's derivations are based on both the constitutive relations in the frequency domain [assuming exp(−jωt) variation] given by Kazi-Aoual et al [11] and the isotropic description of the solid/fluid coupling effect which is measured by mass coupling density ρ a originally introduced by Biot [4].…”

Karakteristik Gelombang Stoneley dalam Menentukan Permeabilitas Reservoir Sumur Pemboran

“…Dalam menenentukan permeabilitas dari sumur pemboran suatu reservoir adalah mungkin dengan menggunakan multi array sonic sonde [1] telah menentukan permeabilitas yang berhubungan dengan atenuasi gelombang akustik P. Berbagai model permeabilitas yang bersifat teori telah dikemukakan oleh [2] dan [3] dalam squit-flow mechanics. Model medium poroelastik dari Para 4) juga telah berusaha meyakinkan untuk menentukan permeabilitas melalui data gelombang akustik.…”

Application of oil–water discrimination technology in fractured reservoirs using the differences between fast and slow shear-waves

“…However, real seismic data from fractured reservoir show that seismic attenuation and dispersion, as well as anisotropic information are frequency-dependent (Parra, 2000;Van der Kolk et al, 2001;Maultzsch et al, 2007). Some extracted information from multicomponent data such as fast and slow shear-wave time delay varies with frequency .…”

“…Hudson et al (1996) improved and proposed a new equant pore model with considering the wave-induced fluid substitution between cracks and equant pores, but this model is not effective in the whole frequency band. Parra (2000) combined BISQ (Biot/Squirt flow theory) with Thomsen theory to establish rock model allowing fluid flow from cracks to pores, however, due to micro-cracks assumption, the dispersion and attenuation estimates of this model are much lower than that in seismic frequency band. The effective-medium theory based on the work by O'Connell and Budiansky (1977) and by Sayer and Kachanov (1991) refers to as BOSK theory (Hudson and Crampin, 2003).…”