Theoretical model for roughness induced opening of cracks subjected to compression and shear loading

Abstract

The phenomenon of roughness induced opening or slip opening is well known in rock mechanics and relates to a crack (or rock joint) behaviour under compression and shear. It has been widely utilised in tight gas and coal bed methane industries to increase the permeability of geological reservoirs during hydraulic stimulations and has recently been extended to geothermal energy technologies for successful harnessing the thermal energy from hot rocks. However, this phenomenon is still poorly understood; and only several semi-empirical equations are currently available in the literature to predict values of the slip openings. In this paper new mechanical and mathematical models of the roughness induced opening are suggested. A computational approach based on the distributed dislocation technique was implemented to analyse various coupled effects. The focus of this paper is on stress analysis of a straight crack with rough faces located in an infinite impermeable body. The crack is subjected to remote normal and shear loading and a uniform fluid pressure applied inside the crack. The developed model A. Kotousov · L. can further be extended to investigate many other interesting and practically important problems such as analysis of fracture initiation in natural faults subjected to fluid pressure, residual opening after releasing the fluid pressure or permeability changes associated with hydraulic stimulations.

A Study of Permeability Changes Due to Cold Fluid Circulation in Fractured Geothermal Reservoirs

“…The second assumption uses a step function (as shown in Figure ) to express the coupling between the shear displacement and the changes in fracture aperture. The normal displacement of the fracture surfaces with respect to each other is described by virtual elastic springs spread along the fracture face (Kotousov et al ). The spring constant for a unit fracture width is calculated based on the “bed of nails” model proposed by Gangi () as , where E is the Young Modulus, L is the fracture length, and b is a constant less than unity.…”

Interface crack embedded in a bi-material plane under shear and compression

“…In addition, Salganik et al (2004) tackled an interface crack-like shear propagating in a material under compression from a mesoscopic viewpoint. Kotousov et al (2011) proposed a theoretical model to describe crack surface roughness induced by opening of a crack under mixed shear-compression loading and the stress intensity factors are found to depend on remote shear loading and roughness. Makaryan et al (2011) also analyzed a cracked elastic layer under compressive loads and found that the crack-tip field is only dominated by mode-II singularity.…”

On the residual opening of hydraulic fractures

“…The problem under consideration has many important applications in gas/oil recovery technologies associated with hydraulic stimulation of underground reservoirs (Kotousov et al 2011). These technologies can provide a significant enhancement of the permeability of geological reservoirs and often result in a considerable increase in the well productivity (Economides and Nolte 2000).…”

“…For example, Papanastasiou (2000) and Dam et al (2000) utilised oversimplified models to assess the residual fracture profiles but merely neglected the proppant compressibility and its distribution inside the fracture. A recent study by Kotousov (2011) deals with the final opening of two semi-infinite planes compressing a rigid circular inclusion of elastic-linear behaviour. Kotousov's work is of great practical interest in situations where the hydraulic fracture length is not known a priori and it is supported by individual particles.…”