Knudsen’s Permeability Correction for Tight Porous Media

Abstract

Various flow regimes including Knudsen, transition, slip and viscous flows (Darcy's law), as applied to flow of natural gas through porous conventional rocks, tight formations and shale systems, are investigated. Data from the Mesaverde formation in the United States are used to demonstrate that the permeability correction factors range generally between 1 and 10. However, there are instances where the corrections can be between 10 and 100 for gas flow with high Knudsen number in the transition flow regime, and especially in the Knudsen's flow regime. The results are of practical interest as gas permeability in porous media can be more complex than that of liquid. The gas permeability is influenced by slippage of gas, which is a pressure-dependent parameter, commonly referred to as Klinkenberg's effect. This phenomenon plays a substantial role in gas flow through porous media, especially in unconventional reservoirs with low permeability, such as tight sands, coal seams, and shale formations. A higher-order permeability correlation for gas flow called Knudsen's permeability is studied. As opposed to Klinkenberg's correlation, which is a first-order equation, Knudsen's correlation is a second-order approximation. Even higher-order equations can be derived based on the concept used in developing this model. A plot of permeability correction factor versus Knudsen number gives a typecurve. This typecurve can be used to generalize the permeability correction in tight porous media. We conclude that Knudsen's permeability correlation is more accurate than Klinkenberg's model especially for extremely tight porous media with transition and free molecular flow regimes. The results from this study indicate that Klinkenberg's model and various extensions developed throughout the past years underestimate the permeability correction especially for the case of fluid flow with the high Knudsen number.

Correction of source-rock permeability measurements owing to slip flow and Knudsen diffusion: a method and its evaluation

“…The latter two parameters are given by (Civan 2010;Ziarani and Aguilera 2012;Singh et al 2014;Liu and Cai 2014) k…”

“…As discussed in Ziarani and Aguilera (2012) and references cited therein, gas flow in a capillary tube can be classified into four regimes based on the dimensionless number (Knudsen number) defined by…”

“…The slip-flow regime corresponds to 0.01 \ Kn \ 0.1 (Ziarani and Aguilera 2012). Slip flow occurs when the gas molecules experience slipping at the solid surface.…”

“…On the other hand, the relationships between measured permeability and intrinsic permeability have been well developed for micro/nano-tubes partially as a result of the simplicity of their flow-path geometries (Beskok and Karniadakis 1999). Then efforts have been made in using the relationships for micro/nano-tubes to approximate those for porous media (Civan 2010;Ziarani and Aguilera 2012;Singh et al 2014). However, the usefulness of these approximations is not totally clear because comparisons between results calculated with these approximations and laboratory measurements are very rare in the literature.…”

A kinetic Monte Carlo approach to study fluid transport in pore networks

“…22 Darcy's law can be applied in the case of viscous flows, as it inherently assumes laminar flow (Reynolds number = 1). 27 The transport mechanism also depends on the confinement, as confinement can promote capillary condensation. When the pore pressure exceeds the critical pressure required to fill the pores, the adsorbed molecules condense.…”