Extension of the classical linear slip model for fluid‐saturated fractures: Accounting for fluid pressure diffusion effects

Abstract

We develop extended boundary conditions based on the linear slip model that account for the impact of wave‐induced fluid pressure diffusion between a fracture and its embedding background on the stiffening effect of the fluid saturating the fracture. We include these poroelastic effects into the linear slip model through complex‐valued and frequency‐dependent parameters characterizing the mechanical and hydraulic coupling between the two regions. This new set of effective fracture parameters contains generalized normal and tangential compliances, analogous to those defined in the classical formulation of the linear slip model, and an additional parameter related to the coupling between horizontal and vertical deformation of the fracture. Comparisons of the extended and classical linear slip models with a poroelastic thin layer model show that the extended formulation always performs better when modeling the displacement fields induced by an incident P wave as well as the scattering coefficients. We find that the contribution of the additional effective parameter involved in the proposed boundary conditions is significant at low frequencies with respect to the undrained frequency regime of the fracture and large angles of incidence. These extended boundary conditions can be readily incorporated into viscoelastic modeling algorithms simulating the response of a large‐scale fluid‐saturated fracture or multiple noninteracting fractures of this kind. The proposed model is expected not only to improve the estimation of mechanical characteristics of fractures in corresponding inversion schemes but can also be used for extracting information with regard to other practically important parameters, such as the background permeability.

Estimation of Fracture Compliance From Attenuation and Velocity Analysis of Full‐Waveform Sonic Log Data

“…Moreover, using the thin-layer model, it is straightforward to compute the normal compliance using its classical definition (Schoenberg, 1980), that is, Z N = Δu n n , where Δu n and n are the jump in normal displacement and the average normal stress across the layer, respectively (blue dashed line). Due to the low permeability of the background rock, this compliance estimate is, in turn, similar to that computed as the ratio between the fracture thickness h and its undrained P wave modulus C f as suggested by Barbosa et al (2017;green symbols). Notice that by using the classical definition of the normal compliance and the thin-layer model, we can account for the effects associated to the finite size of the layer, which a linear slip model ignores.…”

“…The imaginary and real components of the compliance can be used not only to determine the weakening effect of the fracture on the rock but also to get information about possible mechanisms of energy dissipation occurring in the fracture or at its immediate vicinity. An example of a dissipation mechanism that can produce a complex‐valued fracture compliance in fluid‐saturated rocks is WIFF between the fracture and the embedding background (Barbosa et al, ). As a result, the stiffening effect of the fluid saturating the fractures can exhibit a frequency‐dependent behavior.…”

Seismically Induced Unclogging in Fluid‐Saturated Faults

“…We compute the seismically induced v eff at the edge of the fault located at y = 0 m in Figure 2. Finally, only the y component of the Darcy velocity ( ) is used to compute v eff as the diffusion process associated with the slow P waves is mainly normal to the fault's plane (Barbosa et al., 2017) and thus 0. Figure 8a shows that, for P wave incidence, v eff decreases as the incidence angle gets closer to the horizontal direction (parallel to the fault).…”

Seismic and Microseismic Signatures of Fluids in Rocks: Bridging the Scale Gap

“…Monitoring MS (field scale) or AE (laboratory scale) activity has been successfully used to remotely characterize rock fracturing and slip events (e.g., hydraulic fracturing, shear fracturing/faulting, and reactivation), as well as fluid migration through porous and/or fractured rocks when local pore pressure perturbations impact the in situ stress field. Most recently, numerous studies focused on the interplay between fluids, fractures, and seismicity have been published (e.g., Barbosa et al, ; Brown & Ge, ; Cueto‐Felgueroso et al, ; De Barros et al, ; Dempsey et al, ; Dempsey & Suckale, ; Diehl et al, ; Fazio et al, ; Goodfellow et al, ; Improta et al, ; Jeanne et al, ; Levandowski et al, ; Noël et al, ; Rivet et al, ; Segall & Lu, ; Zhang et al, ). This highlights the growing interest for such issues in the geoscience community, which is clearly driven by an increased need to better address actual problems encountered during fluid injection/withdrawal operations.…”