Exact solutions to steady radial flow in a porous medium with variable permeability

A wide class of exact solutions to equations of steady flow of ideal gas in a porous medium is obtained in a planar annular domain comprising sectors of distinct permeabilities. The formulation involves an unconventional Sturm–Liouville problem. The class also admits solutions to configurations with respective distinct generation rates. The solutions are expected to be applicable to landfill gas or natural gas extraction. The breaking of axial symmetry enables realistic modeling of the radius of influence for both horizontal and vertical wells. The analysis proves that the well’s reach would have an azimuthal dependence in any problem with a heterogeneous medium. Therefore, it is suggested that the concept of radius of influence as perceived today be revised.