The mechanical properties of materials with interconnected cracks and pores

Abstract

This paper studies the effect on the overall properties of a cracked solid of the existence of connections between otherwise isolated cracks and of small-scale porosity within the 'solid' material. The intention is to provide effective medium models for the calculation of elastic wave propagation with wavelengths greater than the dimensions of the cracks. The method follows that of earlier papers in which the overall elastic properties are directly related to parameters governing the microstructure, such as crack number density and the mean radius and spacing distance of the cracks. Expressions derived by the method of smoothing are evaluated to second order in the number density of cracks, thereby incorporating crack-crack interactions through both the strain field in the solid and the flow field of fluids in the pores.Flow of interstitial liquids tends to weaken the material; the limit of zero flow is equivalent to isolating the cracks and the limit of free flow is equivalent to dry (gasfilled) cracks. It also introduces additional attenuation. The inclusion of small-scale porosity gives a model of 'equant porosity' which is more closely constrained by the details of crack dynamics than earlier models.

Linking microseismic event observations with geomechanical models to minimise the risks of storing CO2 in geological formations

“…The measurements 183 are inverted for the strikes and fracture densities of two vertical fracture 184 sets -this approximates the observations made on core samples regarding 185 aligned fractures in the reservoir (Brown, 2002). Fracture density refers to 186 the nondimensional term given by Hudson et al (1996) …”

Critical analysis of theoretical basics of displacement discontinuity model for media with oriented fractures.

“…От модели Linear Slip Шонберга [Schoenberg, 1980[Schoenberg, , 1983 можно перейти к более сложным, в первую оче-редь к модели Хадсона для монетообразных трещин [Hudson, 1980[Hudson, , 1981[Hudson, , 1988Hudson et al, 1996]. Как показано в статье [Bakulin et al, 2000а], общим в мо-делях Шонберга и Хадсона является одинаковая струк-тура матрицы упругих модулей в том смысле, что в обеих имеются только четыре независимых компонен-ты матрицы, тогда как пятая (с 13 ), становится зависи-мой, связанной с остальными определенным соотно-шением [Hsu, Schoenberg, 1993].…”

“…Одним из воз-можных механизмов поглощения будет возникающий при распространении волны переток флюида между ориентированными трещинами и изометричными по-рами [Hudson et al, 1996;Pointer et al, 2000;Chapman, 2003Chapman, , 2009.…”

Seismic Characterization of Reservoirs with Multiple Fracture Sets Using Velocity and Attenuation Anisotropy Data

“…However, following Hudson et al, 1996, Tod, 2001, Jakobsen et al, 2003band Jakobsen and Chapman (2009, we eliminate the dependency of * C on the effective wave vector * k by using the approximation…”