Exact solutions for flow through porous media with the Klinkenberg effect

The effect of gas compressibility during flow through a porous medium modifies the governing equation for pressure, and low pressures, this leads to so-called Klinkenberg effect. Darcy’s law remains unchanged, accounting state parabolic pressure. increased rate at pressure nonlinearity equation. We present two broad approaches constructing exact solutions steady problem. First, geometric reduction is employed construct in Cartesian polar coordinates. Next, interpreted so that stream function exists flow, used demonstrate can only be found when irrotational. A second, rather broad, class thus constructed from potential flows their generalization variable permeability cases. latter non-constant coefficient problem, we provide both an algorithm illustrating how use existing linear numerical solver solve nonlinear problem explicit solution annular domain.