Effect of fluid leakage at the crack tip on dynamics of two-dimensional fluid-filled crack

Dynamic response of a reservoir crack with fluid leakage at the crack tip is studied by using a two-dimensional fluid-filled crack in an elastic medium, i.e. a rock mass. We use Darcy's law for describing fluid leakage at the crack tip. It is revealed that the eigen angular frequencies become smaller with increasing fluid leakage at the crack tip. It is also revealed that attenuation becomes stronger with increasing fluid leakage. However, for fluid leakage exceeding a certain level, the situation is opposite, i.e., attenuation becomes weaker with increasing fluid leakage. These effects of fluid leakage on the eigen angular frequencies are stronger for the larger interfacial stiffness due to contact between the asperities on the upper and lower crack surfaces. They are also weaker for larger ratio of the crack length to the initial aperture of the crack.