Effects of fracture aperture and roughness on hydraulic and mechanical properties of rocks : implication of seismic characterization of fractured reservoirs

Roughness and aperture are two important characteristic parameters controlling fluid flow in natural joints and fractures. It has been demonstrated by many authors that knowledge of roughness does not directly lead to that of aperture, and aperture should be handled as a separate geometrical descriptor. To determine the normal deformability and flow response of a fracture, the aperture distribution and the mechanical properties of the rock matrix are required. When shearing of joints and fractures is considered, roughness comes into play and affects the evolution of the aperture distribution. The aperture distribution can be evaluated by knowing the correlation between the asperity profiles of the rock walls of a rock fracture. Thus, the distributions of contact area and void space determine the fracture dilation and hydraulic properties during shearing. In the seismic characterization of fractured reservoirs, various equivalent medium theories describing the effective elastic properties of fractured media have been proposed. One relatively simple theory is based on the assumption of the linear slip interface or displacement discontinuity model of fractures. Two parameters are usually used in the linear slip interface model: the normal and shear fracture compliances defined as the ratio of normal (shear) displacement discontinuity and normal (shear) stress. Fracture compliances are by definition functions of mechanical aperture and are also influenced by the roughness (surface asperity distribution) of fracture surfaces. In this study, I investigate the effects of fracture roughness and apertures on the hydraulic and mechanical properties of fractured rock. Specifically, I focus on two kinds of fracture models which are commonly used in describing the effective hydraulic and mechanical (elastic) response of natural fractures. The first is the rough-walled fracture model and the second is an interface with distributions of contacts and voids (called the asperity fracture model)

Boundary integral modelling of elastic wave propagation in multi-layered 2D media with irregular interfaces

We present a semi-analytic method based on the propagation matrix formulation of indirect boundary element method to compute response of elastic (and acoustic) waves in multi-layered media with irregular interfaces. The method works recursively starting from the top-most free surface at which a stress-free boundary condition is applied, and the displacement-stress boundary conditions are then subsequently applied at each interface. The basic idea behind this method is the matrix formulation of the propagation matrix (PM) or more recently the reflectivity method as wide used in the geophysics community for the computation of synthetic seismograms in stratified media. The reflected and transmitted wave-fields between arbitrary shapes of layers can be computed using the indirect boundary element method (BEM, sometimes called IBEM). Like any standard BEM, the primary task of the BEM-based propagation matrix method (thereafter called PM-BEM) is the evaluation of element boundary integral of the Green's function, for which there are standard method that can be adapted. In addition, effective absorbing boundary conditions as used in the finite difference numerical method is adapted in our implementation to suppress the spurious arrivals from the artificial boundaries due to limited model space. To our knowledge, such implementation has not appeared in the literature. We present several examples in this paper to demonstrate the effectiveness of this proposed PM-BEM for modelling elastic waves in media with complex structure