On the flow in piecewise-homogeneous porous media containing fractures and barriers located along a straight line

Abstract

The plane linear flow generated by an arbitrary array of singular points (sources, sinks) in piecewise-homogeneous porous media in the presence of a rectilinear system of series-connected highly permeable fractures and low-permeability barriers is considered. The cases when the system consists of a fracture and a barrier along the rays departing from a common point and of two ray-like barriers separated by a fracture along a segment are investigated. Integral representations of the flow potentials in terms of harmonic functions are derived. Concrete examples of flows are presented.