| Abstract |
Dynamic response of a reservoir crack with fluid leakage along the crack periphery is studied by using a two-dimensional fluid-filled crack in an elastic medium, i.e. a rock mass. In order to understand the source mechanism of microseismic events observed during hydro fracturing, many crack models were constructed and were analyzed. Those crack models were made up of an infinite fluid-filled slit or a single crack. However, in HDR/HWR fields, geothermal reservoirs consist of networks of cracks and permeable layers. This means that fluid leakage from the crack tip likely to be one of the main parameters governing the dynamics of a fluid-filled crack. A simple model is constructed to examine how the fluid leakage at the crack tip affects the dynamics of the crack, where we take account of the effect of fluid viscosity, permeability of rock and interfacial stiffness due to contact between the asperities on the upper and lower surfaces of the crack. We model the fluid leakage from the crack tip to be one-dimensional fluid flow in the direction along the extension line of the crack and express a variety of fluid leakage phenomena by introducing an appropriate boundary condition for fluid motion at the crack tip. We use Darcyís law for describing fluid leakage at the crack tip. We derive a singular integral equation for determining the displacement gap across the crack in the Laplace image and Fourier image spaces, where the motion of fluid in the crack is taken into account, and we solve the integral equation numerically. It is revealed that fluid leakage has strong effect on the higher modes of oscillation. The eigen angular frequencies become smaller with increasing fluid leakage at the crack tip. Nodes of each mode of oscillation approach the crack tip with increasing fluid leakage. It is also revealed that intensity of attenuation becomes stronger with increasing fluid leakage. However, for fluid leakage exceeding a certain value, the situation is opposite, i.e., attenuation becomes weaker with increasing fluid leakage. These effects of fluid leakage at the crack tip are stronger for the larger interfacial stiffness along the crack line and weaker for larger fluid viscosity and for larger aspect ratio, i.e. the ratio of the crack length to the initial aperture of the crack. |