Expansion of the Klinkenberg's slippage equation to low permeability porous media

Moghadam, Al; Chalaturnyk, Rick

doi:10.1016/j.coal.2013.10.008

Cited by 107 publications

(44 citation statements)

References 11 publications

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“…The flow mechanism, in which a single gas molecule passes through the nanochannel by colliding back and forth with the wall of a pore, stems from the fact that the pore size and the mean free path of the gas molecule are both of the same order of magnitude. This flow mechanism, which is independent of the gas pressure gradient can increase K g of the medium and is designated as the slippage effect (Ashrafi Moghadam & Chalaturnyk, 2014; Klinkenberg, 1941).…”

Section: Introductionmentioning

confidence: 99%

Laboratory Research on Gas Transport in Shale Nanopores Considering the Stress Effect and Slippage Effect

Sun

Zhou

et al. 2020

JGR Solid Earth

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The low permeability of shale, in accretionary complexes and passive continental margins, influences pore pressure generation, and thus induces deformation and fault slip behavior. It is also key in hindering the ability to evaluate shale gas production. Gas is commonly used in measuring the permeability of shale and generally yields high values than that of liquids, due to slippage effect. Separation of the slippage effect from gas permeability is a critical task in the study of low‐permeability media. This study measured the gas permeability (Kg) of the Longmaxi shale parallel to bedding (L1P) and perpendicular to bedding (L1V) under different confining pressures (Cp) and pore pressures (Pp), while simultaneously measuring porosity for different values of Cp. Additionally, a new approach is proposed to define the effective stress coefficient and boundary condition for the Klinkenberg correction. The results show that the Kg of L1P is almost unaffected by the slippage effect, while, for L1V, the Klinkenberg correction is required. The Klinkenberg plot of L1V follows the quadratic model from the study by Ashrafi Moghadam and Chalaturnyk (2014, https://doi.org.10/1016/j.coal.2013.10.008), rather than the classic linear Klinkenberg equation. The results also show that, as the Cp increases and/or the Pp decreases, the contribution of the slippage effect to the L1V Kg increased from 20% to 86.5%. Finally, based on the Knudsen number (Kn), the flow regime of L1P changes from Darcy flow (Kn < 0.01) to slip flow (0.01 < Kn < 0.1), and that of L1V is slip flow.

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Section: Introductionmentioning

confidence: 99%

Laboratory Research on Gas Transport in Shale Nanopores Considering the Stress Effect and Slippage Effect

Sun

Zhou

et al. 2020

JGR Solid Earth

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“…As such, the absolute permeability is greatly affected by the pore-throat aperture, especially in tight sandstone reservoirs [15]. Although the quantitative relationship between the pore-throat structure and the absolute permeability is not available, it has been reported that both the slippage effect and the absolute permeability are dramatically affected by the pore-throat structure [16][17][18]. Dong et al demonstrated that the slippage effect is more remarkable in smaller throats by comparing volcanic core samples with similar permeabilities, but different throat size distributions [19].…”

Section: Introductionmentioning

confidence: 99%

Determination of Klinkenberg Permeability Conditioned to Pore-Throat Structures in Tight Formations

et al. 2017

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This paper has developed a pragmatic technique to efficiently and accurately determine the Klinkenberg permeability for tight formations with different pore-throat structures. Firstly, the authors use steady-state experiments to measure the Klinkenberg permeability of 56 tight core samples under different mean pore pressures and confining pressures. Secondly, pressure-controlled mercury injection (PMI) experiments and thin-section analyses are conducted to differentiate pore-throat structures. After considering capillary pressure curve, pore types, throat size, particle composition, and grain size, the pore-throat structure in the target tight formation was classified into three types: a good sorting and micro-fine throat (GSMFT) type, a moderate sorting and micro-fine throat (MSMFT) type, and a bad sorting and micro throat (BSMT) type. This study found that a linear relationship exists between the Klinkenberg permeability and measured gas permeability for all three types of pore-throat structures. Subsequently, three empirical equations are proposed, based on 50 core samples of data, to estimate the Klinkenberg permeability by using the measured gas permeability and mean pore pressure for each type of pore-throat structure. In addition, the proposed empirical equations can generate accurate estimates of the Klinkenberg permeability with a relative error of less than 5% in comparison to its measured value. The application of the proposed empirical equations to the remaining six core samples has demonstrated that it is necessary to use an appropriate equation to determine the Klinkenberg permeability of a specific type of pore-throat structure. Consequently, the newly developed technique is proven to be qualified for accurately determining the Klinkenberg permeability of tight formations in a timely manner.

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“…The value of C 2 varies depending on the author [17,26], and λ is the mean free path. Solving the Stokes equation for the steady state flow subject to a constant pressure gradient with these boundary conditions gives the 053015-2 velocity profile…”

Section: A Wall Velocitymentioning

confidence: 99%

Exploring the Klinkenberg effect at different scales

Izrar

Rouet

2014

Phys. Rev. E

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Simulations of microflows usually require sophisticated numerical tools. Nevertheless in the slip regime, the hydrodynamic equation with slip boundary condition may be sufficient to account for the so-called Klinkenberg effect. We propose to visit this effect using a basic network of microchannels in which the Knudsen number is multiplied by two or four by introducing successive derivations to the channel. We derived an equivalent hydraulic conductivity up to second order. Theoretical results are compared both with the results of the Navier-Stokes equations with slip condition and with those obtained using a Bhatnagar-Gross-Krook-Hermite model developed especially for flows with a large spectrum of Knudsen numbers (typically 10^{-4}

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Expansion of the Klinkenberg's slippage equation to low permeability porous media

Cited by 107 publications

References 11 publications

Laboratory Research on Gas Transport in Shale Nanopores Considering the Stress Effect and Slippage Effect

Laboratory Research on Gas Transport in Shale Nanopores Considering the Stress Effect and Slippage Effect

Determination of Klinkenberg Permeability Conditioned to Pore-Throat Structures in Tight Formations

Exploring the Klinkenberg effect at different scales

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