Analytical Solutions for Pore-Fluid Flow Focusing Within Inclined Elliptic Inclusions in Pore-Fluid-Saturated Porous Rocks: Solutions Derived in an Elliptical Coordinate System

Exact analytical solutions have been derived rigorously for the pore-fluid velocity, pore-fluid-flow focusing factor, stream function and excess pore-fluid pressure around and within a buried inclined elliptic inclusion in pore-fluid-saturated porous rocks. The geometric characteristics of the buried inclined elliptic inclusion are represented by the aspect ratio and dip angle of the inclusion, while the hydrodynamic characteristic is represented by the permeability ratio of the elliptic inclusion to its surrounding rock. Since an elliptic inclusion of any aspect ratio can be used to approximately represent geological faults and cracks, the present analytical solutions can be used to investigate the pore-fluid-flow patterns around buried faults and cracks within the crust of the Earth. Therefore, the present analytical solution not only provides a better understanding of the physics behind the pore-fluid-flow focusing problem around and within buried faults and cracks, but also provides a valuable benchmark solution for validating any numerical method in dealing with this kind of pore-fluid-flow focusing problem. The pore-fluid-flow focusing factor of a buried elliptic inclusion is demonstrated to be dependent on the aspect ratio, the permeability ratio and the dip angle.