Determining the intrinsic permeability of tight porous media based on bivelocity hydrodynetics

Abstract

For tight porous media, the permeability measured from the Darcy test is only an apparent permeability because the Klinkenberg effect occurs when the Knudsen number is high. To determine the intrinsic permeability, we need a simple and rigorous permeability correction that is valid in the entire flow regime. Thus, introducing a non-Maxwellian slip boundary condition, we develop the bivelocity hydrodynetics in this paper. The bivelocity hydrodynetics is defined by combining bivelocity hydrodynamics with kinetic theories. In the framework of the bivelocity hydrodynetics, we derive a simple and rigorous permeability correction based on the analytical solutions of rarefied gas flows in micro- and nano-tubes. After compared with conventional solutions and experiments, the present solutions are validated in the entire flow regime. Moreover, the validation is also a clear proof for the bivelocity theories.