Christopher Petrovitch

Combined Scaling of Fluid Flow and Seismic Stiffness in Single Fractures

The connection between fluid flow and seismic stiffness in single fractures is governed by the geometry of the fracture through the size and spatial distributions of the void and contact areas. Flow and stiffness each exhibit scaling behavior as the scale of observation shifts from local to global sample sizes. The purpose of this study was to explore the joint scaling of both properties using numerical models. Finite-size scaling methods are used to extract critical thresholds and power laws for fluid flow through weakly correlated fractures under increasing load. An important element in the numerical fracture deformation is the use of extended boundary conditions that simulate differences between laboratory cores relative to in situ field studies. The simulated field conditions enable joint scaling of flow and stiffness to emerge with the potential to extrapolate from small laboratory samples to behavior on the field scale.

A discontinuous Galerkin method with a modified penalty flux for the propagation and scattering of acousto-elastic waves

We develop an approach for simulating acousto-elastic wave phenomena, including scattering from fluid-solid boundaries, where the solid is allowed to be anisotropic, with the Discontinuous Galerkin method. We use a coupled first-order elastic strain-velocity, acoustic velocity-pressure formulation, and append penalty terms based on interior boundary continuity conditions to the numerical (central) flux so that the consistency condition holds for the discretized Discontinuous Galerkin weak formulation. We incorporate the fluid-solid boundaries through these penalty terms and obtain a stable algorithm. Our approach avoids the diagonalization into polarized wave constituents such as in the approach based on solving elementwise Riemann problems.

Wave guiding in fractured layered media

Abstract Many carbonate rocks are composed of layers and contain fracture sets that cause the hydraulic, mechanical and seismic properties to be anisotropic. Co-located fractures and layers in carbonate rock lead to competing wave-scattering mechanisms: both layers and parallel fractures generate compressional-wave (P-wave) guided modes. The guided modes generated by the fractures may obscure the presence of the layers. In this study, we examine compressional-wave guided modes for two cases: wave guiding by fractures in a layered medium with sub-wavelength layer thickness; and wave guiding in media with competing scattering mechanisms, namely layering (where the thickness is greater than a wavelength) and parallel sets of fractures. In both cases, the fracture spacing is greater than a wavelength. When the layer thickness is smaller than a wavelength, P-wave guiding is controlled by the spacing of the fractures, fracture specific stiffness, the frequency of the signal and the orientation of the layering relative to the fracture set. The orientation of the layering determines the directionally dependent P-wave velocity in the anisotropic matrix. When the layer thickness is greater than a wavelength and an explosive point source of a signal is located in the layer containing a fracture, the fracture either enhanced or suppressed compressional-mode wave guiding caused by the layering in the matrix.

The Effect of Fabric-Controlled Layering On Compressional And Shear Wave Propagation In Carbonate Rock

Mixed chemical and clastic sedimentary processes form carbonate rock with fine bedding that results in a weakly directed fabric. Laboratory experiments were performed to determine the effect of fabric-controlled layering on compressional and shear wave propagation. X-ray tomographic scans of the sample found a density variation among the layers that ranged from 1700 kg/m 3 to 2300 kg/m 3 in a cubic sample 100 mm on edge. Wavefront imaging results show that the density contrasts among the layers produced energy confinement. The amplitude and arrival time of the compressional and shear waves are affected by saturation of the sample with water, i.e., by changing the impedance contrast among the layers. Seismic monitoring of the fluid-front during saturation indicates that the fine bedding also affects the hydraulic properties of the sample.

Interpreting Fracture Specific Stiffness for Fractures in Anisotropic Rock

Laboratory experiments were performed on cubic samples of aluminum and Austin Chalk to investigate the effect of fabric-induced anisotropy on the interpretation of fracture specific stiffness. Seismic data were analyzed using the displacement discontinuity theory for wave propagation across a single fracture. For the aluminum standard, the theory successfully simulated the effect of a synthetic fracture seismic wave transmission and normal and shear fracture specific stiffness were estimated. However, fractures specific stiffness could not be interpreted for the Austin Chalk samples because of the layering in the sample. Wavelet analysis of the Austin Chalk data showed that multiple reflections between layers caused constructive-destructive interference which attenuated the high frequency components of the signals from the intact sample. The presence of the fracture interrupted the interference and enabled high frequency components to be transmitted through the fractured sample.