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

Abstract

Absence of subcritical instabilities and global nonlinear stability for porous ternary diffusive-convective fluid mixtures Phys. Fluids 24, 104101 (2012) Capillary filling dynamics of water in nanopores Appl. Phys. Lett. 101, 153112 (2012) Division by fluid incision: Biofilm patch development in porous media Phys. Fluids 24, 091107 (2012) Core-flood experiment for transport of reactive fluids in rocks Rev. Sci. Instrum. 83, 084501 (2012) On a singular incompressible porous media equationTraditional 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 ͑1941͔͒ 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.

Investigation of the Klinkenberg effect in a micro/nanoporous medium by direct simulation Monte Carlo method

“…(c) Knudsen diffusivity coefficient from Bravo [40], and the present D p , the predicted results by Kalarakis et al [41] are also presented in Fig. 7 and compared with the present DSMC data at ε = 0.75.…”

“…Jones [39] experimentally found b ∝ K ∞ −0.36 ; Bravo [40] considered b as a function of K ∞ and the Knudsen diffusivity coefficient, and the latter could also be correlated as a function of K ∞ . However, the effect of pore-scale geometry features was not included in these correlations.…”

“…Therefore, these correlations are accurate only for porous media of specific microstructures. Kalarakis et al [41] improved the expression of b on the basis of Bravo [40] by including a numerical factor a for the length-to-width ratio of the pore. However, that study only gave empirical values of a = 3.4 and 4 for the porous structures used in their study with ε = 0.7 and 0.8, the expressions to fully describe the geometry features were unavailable.…”

A study on pressure-driven gas transport in porous media: from nanoscale to microscale

“…For low permeability porous media, Jones (1972) found that the Klinkenberg coefficient b and the liquid permeability K 0 have the relation, b ∝ K −0.36 0 . Bravo (2007) developed the generalized model of the Klinkenberg coefficient b for the whole range of the Knudsen number. In his model, the Klinkenberg coefficient b is a function of the Knudsen number.…”

Exploring the Klinkenberg effect at different scales

“…Circumstances are not necessarily identical for a network of channels. We require at least a second order model, which leads to κ varying inversely with the pressure (1/p) 2 [8][9][10][11].…”