Steady State Flow Passing Through a Cylinder of Permeability Different From the Surrounding Medium

Abstract

The problem of steady state porous media flow around and through an infinitely permeable cylinder and the problem of steady state flow around an impermeable cylinder have well‐known hydrodynamic solutions. Until recently, the problem of flow to a sink around and through a cylinder of finite (but different) permeability than the surrounding medium has not been treated. A generalized method is presented by which a cylinder of permeability K2 is embedded in the surrounding porous medium (K1). The method is valid for any complex potential flow field that obeys the Laplace equation. Two types of flow fields are considered as examples: first, the case of a flow field for a sink; and second, the case of a uniform flow field. From the solutions, equations are obtained for the relative amount of flow passing through the cylinder compared to the surrounding medium. The method and the solutions presented have potential applications in contaminant transport problems and for the direct measurement of groundwater velocity in boreholes.