Darcy flow around a two-dimensional permeable lens

The flow in and around a fracture modelled as a two-dimensional permeable lens immersed in an infinite porous medium of different permeability is analytically solved by means of conformal mapping and Fourier transform. When the lens is more permeable than the surrounding medium, singularities occur at angular points for flow parallel to the lens, while velocities vanish at these points for flow perpendicular to the lens. In the opposite case, when the lens is less permeable than the surrounding medium, singularities are exchanged and flows parallel and perpendicular to the lens are regular and singular, respectively. Predictions are successfully compared with data obtained by a numerical code.