Effect of transition from slip to free molecular flow on gas transport in porous media

Traditional models, such as the advection-diffusion and the dusty gas models, overlook the contribution of the transition flow regime between the slip and the free molecular flow, on the gas transport in porous media. In this work we demonstrate that, due to the existence of this intermediate regime, the Klinkenberg [Drill. & Prod. Prac. 1941, 200 (1941)] parameter b depends on the pressure. Reported experiments were used to corroborate such an effect and a formulation that extends the Klinkenberg equation—to include the effect of a region at pore scale where both molecule-molecule and molecule-wall interactions are important—was developed. The mathematical form of the extended Klinkenberg equation remains the same, but the slippage Klinkenberg’s parameter b is now a generalized parameter that is a function of Knudsen’s number. It was demonstrated that the widely accepted relation between the parameter b and the Knudsen diffusion coefficient is a good approximation just for Knudsen numbers corresponding to the free molecular flow regime. The model proposed in this paper reproduces the experimental data and predicts practical situations where important errors on total flow rate can be expected if the transition flow regime is neglected in the formalism.