Effects of fracture intersections on seismic dispersion: theoretical predictions versus numerical simulations

Abstract

The detection and characterisation of domains of intersecting fractures are important goals in several disciplines of current interest, including exploration and production of unconventional reservoirs, nuclear waste storage, CO2 sequestration, and groundwater hydrology, among others. The objective of this study is to propose a theoretical framework for quantifying the effects of fracture intersections on the frequency‐dependent elastic properties of fluid‐saturated porous and fractured rocks. Three characteristic frequency regimes for fluid pressure communication are identified. In the low‐frequency limit, fractures are in full pressure communication with the embedding porous matrix and with other fractures. Conversely, in the high‐frequency limit, fractures are hydraulically isolated from the matrix and from other fractures. At intermediate frequencies, fractures are hydraulically isolated from the matrix porosity but can be in hydraulic communication with each other, depending on whether fracture sets are intersecting. For each frequency regime, the effective stiffness coefficients are derived using the linear‐slip theory and anisotropic Gassmann equations. Explicit mathematical expressions for the two characteristic frequencies that separate the three frequency regimes are also determined. Theoretical predictions are then applied to two synthetic 2D samples, each containing two orthogonal fracture sets: one with and another without intersections. The resulting stiffness coefficients, Thomsen‐style anisotropy parameters, and the transition frequencies show good agreement with corresponding numerical simulations. The theoretical results are applicable not only to 2D but also to 3D fracture systems and are amenable to being employed in inversion schemes designed to characterise fracture systems.

Sensitivity of Seismic Attenuation and Phase Velocity to Intrinsic Background Anisotropy in Fractured Porous Rocks: A Numerical Study

“…As far as we know, there are no expressions for the FB-WIFF characteristic frequency for the case of an elastically anisotropic background. For an isotropic background, Guo et al (2016) found that this characteristic frequency can be computed as where a f is the fracture length and D b is the diffusivity of the background that is computed as…”

Effective Elastic Properties of Rocks With Transversely Isotropic Background Permeated by Aligned Penny‐Shaped Cracks

“…When subjected to stresses, fractures can more easily close, which results in the increase of rock elastic moduli (e.g., Glubokovskikh et al, ; Mavko et al, ; Shapiro, ). Due to these important effects of fractures on rock hydraulic and elastic properties, it is of great interest to detect and characterize fractures in many disciplines, such as earth and environmental sciences, and underground engineering, among many others (e.g., Guo et al, ; Guo, Rubino, Barbosa, et al, ; Guo, Rubino, Glubokovskikh, et al, ; Guo, Shuai, et al, ; Huo & Gong, ; Lisjak et al, ; Liu et al, ; Nelson, ; Neuzil, ).…”

Gassmann Consistency for Different Inclusion‐Based Effective Medium Theories: Implications for Elastic Interactions and Poroelasticity

“…For example, Gassmann consistency is not applicable for the case of the coexistence of unconnected compliant cracks and background porosity, because it inherently violates the pore pressure equilibration conditions. For porous sedimentary rocks containing pore heterogeneities (i.e., coexistence of stiff background porosity and cracks), approach (a), based on the Gassmann equation, is commonly considered as the relaxed status of low-frequency limit (Guo et al, 2017), whereas approach (b), ignoring fluid communication, is commonly considered as the unrelaxed status of high-frequency limit. In this case, the elastic properties computed using approach (a) are never consistent with those computed using approach (b).…”