Sensitivity of S-wave attenuation to the connectivity of fractures in fluid-saturated rocks

Abstract

Biot’s equations of poroelasticity were solved to study the effects of fracture connectivity on S-wave attenuation caused by wave-induced fluid flow at the mesoscopic scale. The methodology was based on numerical quasistatic pure-shear experiments performed on models of water-saturated rocks containing pairs of either connected or unconnected fractures of variable inclination. Each model corresponded to a representative elementary volume of a periodic medium. Inertial terms were neglected, and hence, the observed attenuation was entirely due to wave-induced fluid flow at the mesoscopic scale. We found that when fractures are not connected, fluid flow in the embedding matrix governs S-wave attenuation, whereas fluid flow through highly permeable fractures, from one fracture into the other one, may dominate when fractures are connected. Each of these energy-dissipation phenomena has a distinct characteristic frequency, with the S-wave attenuation peak associated with flow through connected fractures occurring at higher frequencies than that associated with flow in the embedding matrix. Exploring a range of geometric arrangements of either connected or unconnected fractures at different inclinations, we also observed that the magnitude of S-wave attenuation at both characteristic frequencies shows a strong dependence on fracture inclination. For comparison, we performed quasistatic uniaxial compressibility tests to compute P-wave attenuation in the same models. We found that the attenuation patterns of S-waves tend to differ fundamentally from those of P-waves with respect to fracture inclination. The attenuation characteristics of P- and S-waves in fractured media are thus, largely complementary. With respect to fracture connectivity, we observed that S-wave attenuation tends to follow a specific pattern, indeed, more consistently than that of the P-waves. Our results point to the promising perspective of combining estimates of attenuation of P- and S-waves to infer information on fracture connectivity as well as on the effective permeability of fractured media.

Identification of viscoelastic properties from numerical model reduction of pressure diffusion in fluid-saturated porous rock with fractures

“…Hereby, we employ the periodic boundary conditions in the form of (20), (21) and (22). On the right-hand side of the macro-homogeneity condition (51) we can see that, under the chosen periodic boundary conditions, the macroscopic substitute medium is represented by a monophasic Cauchy continuum model.…”

“…The resulting dissipation is frequency dependent and associated with dispersion of the elastic moduli. These effects of fracture interconnectivity on seismic waves represent a great potential A few numerical upscaling approaches have been used in the recent years to compute, at the level of a Representative Volume Element (RVE), frequency-dependent attenuation and the corresponding dispersion of the elastic moduli caused by squirt-type flow in interconnected fractures [22,23,26,30]. They describe the squirt-type flow within the fractures either by using Biot's quasi-static equations of poroelasticity or quasi-static, linearized Navier-Stokes equations, whilst the embedding rock matrix is described either as a poroelastic medium or as a monophasic linear-elastic medium based on Hooke's law.…”

“…Hereby, the matrix representation is based on the full 3D strain vectorε = [ε 11 ,ε 22 ,ε 33 , 2ε 12 , 2ε 13 , 2ε 23 ] T . We observe that the viscoelastic variables are mainly stimulated by the axial strains, but also shear deformations may cause a small viscoelastic reaction, see in particular mode a = 5.…”

Squirt flow due to interfacial water films in hydrate bearing sediments

“…heterogeneities having large aspect ratios, such as the thin interfacial water films, by strongly 22 varying the sizes of the triangular elements (e.g., Quintal et al, 2014). A few elements across 23 the thin interfacial water film are necessary to accurately capture the viscous dissipation in this 24 region, while much larger elements are sufficient in the solid elastic domains.…”

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

“…Furthermore, Rubino [Rubino et al 2009] and Quintal [Quintal et al 2011] have put forward two different quasi-static numerical strategies, in which they used the finite element method in frequency and time domain, for the computation of seismic attenuation due to wave-induced fluid flow. Exploiting the quasi-static finite element method in frequency domain, Carcione [Carcione et al 2012] and Rubino [Quintal et al 2014] have discussed the effects of fracture connectivity and anisotropy on the seismic attenuation and dispersion. Lately, the effects on seismic characteristics of fractured magmatic geothermal reservoirs were numerically modeled [Grab et al 2017] in a simple and efficient way.…”