Gas Flow Through Square Arrays of Circular Cylinders with Klinkenberg Effect: A Lattice Boltzmann Study
Year: 2010
Communications in Computational Physics, Vol. 8 (2010), Iss. 5 : pp. 1052–1073
Abstract
It is well known that, as non-continuum gas flows through microscale porous media, the gas permeability derived from Darcy law is larger than the absolute permeability, which is caused by the so-called Klinkenberg effect or slippage effect. In this paper, an effective definition of Knudsen number for gas flows through square arrays of circular cylinders and a local boundary condition for non-continuum gas flows are first proposed, and then the multi-relaxation-time lattice Boltzmann equation including discrete effects on boundary condition is used to investigate Klinkenberg effect on gas flow through circular cylinders in square arrays. Numerical results show that the celebrated Klinkenberg equation is only correct for low Knudsen number, and second-order correction to Klinkenberg equation is necessary with the increase of Knudsen number. Finally, the present numerical results are also compared to some available results, and in general an agreement between them is observed.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.010809.081209a
Communications in Computational Physics, Vol. 8 (2010), Iss. 5 : pp. 1052–1073
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
-
Filter-matrix lattice Boltzmann model for microchannel gas flows
Zhuo, Congshan | Zhong, ChengwenPhysical Review E, Vol. 88 (2013), Iss. 5
https://doi.org/10.1103/PhysRevE.88.053311 [Citations: 14] -
Consistent lattice Boltzmann modeling of low-speed isothermal flows at finite Knudsen numbers in slip-flow regime: Application to plane boundaries
Silva, Goncalo | Semiao, ViriatoPhysical Review E, Vol. 96 (2017), Iss. 1
https://doi.org/10.1103/PhysRevE.96.013311 [Citations: 26] -
Multiscale modeling of gas flow behaviors in nanoporous shale matrix considering multiple transport mechanisms
Zhou, Wenning | Yang, Xu | Liu, XunliangPhysical Review E, Vol. 105 (2022), Iss. 5
https://doi.org/10.1103/PhysRevE.105.055308 [Citations: 13] -
Insights into scale translation of methane transport in nanopores
Liu, Lingfu | Wang, Yuhang | Aryana, Saman A.Journal of Natural Gas Science and Engineering, Vol. 96 (2021), Iss. P.104220
https://doi.org/10.1016/j.jngse.2021.104220 [Citations: 20] -
The lattice Boltzmann method for isothermal micro-gaseous flow and its application in shale gas flow: A review
Wang, Junjian | Chen, Li | Kang, Qinjun | Rahman, Sheik S.International Journal of Heat and Mass Transfer, Vol. 95 (2016), Iss. P.94
https://doi.org/10.1016/j.ijheatmasstransfer.2015.12.009 [Citations: 130] -
Kinetic boundary schemes of axisymmetric multi-relaxation-time lattice Boltzmann model for microscale gas flows in microtube
Ren, Junjie | Liu, Xiaoxue | Wu, QingxingPhysica Scripta, Vol. 96 (2021), Iss. 10 P.105207
https://doi.org/10.1088/1402-4896/ac0b89 [Citations: 2] -
Impact of fiber diameter polydispersity on the permeability of fibrous media
Tucny, Jean-Michel | Spreutels, Laurent | Drolet, François | Leclaire, Sébastien | Bertrand, François | Vidal, DavidChemical Engineering Science, Vol. 262 (2022), Iss. P.117984
https://doi.org/10.1016/j.ces.2022.117984 [Citations: 5] -
Numerical Simulation of Heat and Momentum Transport at the Coupled Interface between a Rectangular Channel and Porous Media
Wang, Ye | Wu, Jingyi | Yang, GuangJournal of Thermal Science, Vol. 31 (2022), Iss. 2 P.332
https://doi.org/10.1007/s11630-022-1584-y [Citations: 2] -
Gas Flow Models of Shale: A Review
Javadpour, Farzam | Singh, Harpreet | Rabbani, Arash | Babaei, Masoud | Enayati, SamiraEnergy & Fuels, Vol. 35 (2021), Iss. 4 P.2999
https://doi.org/10.1021/acs.energyfuels.0c04381 [Citations: 58] -
Quantitative visualization and characteristics of gas flow in 3D pore-fracture system of tight rock based on Lattice Boltzmann simulation
Hou, Peng | Liang, Xin | Gao, Feng | Dong, Jiabin | He, Jian | Xue, YiJournal of Natural Gas Science and Engineering, Vol. 89 (2021), Iss. P.103867
https://doi.org/10.1016/j.jngse.2021.103867 [Citations: 56] -
Stochastic Effects of 2D Random Arrays of Cylinders on Rarefied Gas Permeability Using the Lattice Boltzmann Method
Ho, Michel | Leclaire, Sébastien | Reggio, Marcelo | Trépanier, Jean-YvesTransport in Porous Media, Vol. 136 (2021), Iss. 2 P.607
https://doi.org/10.1007/s11242-020-01532-8 [Citations: 3] -
Pore-scale simulation of gas flow in microscopic permeable media with complex geometries
Wang, Yuhang | Aryana, Saman A.Journal of Natural Gas Science and Engineering, Vol. 81 (2020), Iss. P.103441
https://doi.org/10.1016/j.jngse.2020.103441 [Citations: 23] -
Comparison of existing and extended boundary conditions for the simulation of rarefied gas flows using the Lattice Boltzmann method
Tucny, Jean-Michel | Vidal, David | Leclaire, Sébastien | Bertrand, FrançoisInternational Journal of Modern Physics C, Vol. 31 (2020), Iss. 05 P.2050070
https://doi.org/10.1142/S0129183120500709 [Citations: 7] -
Rarefaction effect on the aerodynamics of bristled wings in miniature insects
Physics of Fluids, Vol. 35 (2023), Iss. 5
https://doi.org/10.1063/5.0149131 [Citations: 2] -
High-order asymptotic solutions for gas transport in heterogeneous media with multiple spatial scales
Zuo, Hong | Yang, Zhiqiang | Deng, Shouchun | Li, HaiboPhysics of Fluids, Vol. 35 (2023), Iss. 1
https://doi.org/10.1063/5.0130971 [Citations: 9] -
Permeability calculation of rarefied gas flows through 2D porous structures using the lattice Boltzmann method
Ho, Michel | Pérez, Jesús García | Reggio, Marcelo | Trépanier, Jean-YvesPhysics and Chemistry of the Earth, Parts A/B/C, Vol. 113 (2019), Iss. P.43
https://doi.org/10.1016/j.pce.2019.02.014 [Citations: 9] -
Striving to translate shale physics across ten orders of magnitude: What have we learned?
Mehmani, Yashar | Anderson, Timothy | Wang, Yuhang | Aryana, Saman A. | Battiato, Ilenia | Tchelepi, Hamdi A. | Kovscek, Anthony R.Earth-Science Reviews, Vol. 223 (2021), Iss. P.103848
https://doi.org/10.1016/j.earscirev.2021.103848 [Citations: 28] -
Slip boundary condition for lattice Boltzmann modeling of liquid flows
Wang, Kai | Chai, Zhenhua | Hou, Guoxiang | Chen, Wei | Xu, ShengComputers & Fluids, Vol. 161 (2018), Iss. P.60
https://doi.org/10.1016/j.compfluid.2017.11.009 [Citations: 41] -
Mesoscopic method to study water flow in nanochannels with different wettability
Zhang, Tao | Javadpour, Farzam | Li, Xiangfang | Wu, Keliu | Li, Jing | Yin, YingPhysical Review E, Vol. 102 (2020), Iss. 1
https://doi.org/10.1103/PhysRevE.102.013306 [Citations: 31] -
Consistent lattice Boltzmann modeling of low-speed isothermal flows at finite Knudsen numbers in slip-flow regime. II. Application to curved boundaries
Silva, Goncalo
Physical Review E, Vol. 98 (2018), Iss. 2
https://doi.org/10.1103/PhysRevE.98.023302 [Citations: 24] -
Pore scale visualization of thermal-fluid-structural evolution in the ablation of carbon/carbon composites
Wang, Hui | Ji, Ritian | Xiao, Guangming | Qu, ZhiguoAerospace Science and Technology, Vol. 130 (2022), Iss. P.107924
https://doi.org/10.1016/j.ast.2022.107924 [Citations: 3] -
Lattice Boltzmann Methods for Industrial Applications
Sharma, Keerti Vardhan | Straka, Robert | Tavares, Frederico WanderleyIndustrial & Engineering Chemistry Research, Vol. 58 (2019), Iss. 36 P.16205
https://doi.org/10.1021/acs.iecr.9b02008 [Citations: 28] -
Boundary scheme for lattice Boltzmann modeling of micro-scale gas flow in organic-rich pores considering surface diffusion
Zuo, Hong | Deng, Shou-Chun | Li, Hai-BoChinese Physics B, Vol. 28 (2019), Iss. 3 P.030202
https://doi.org/10.1088/1674-1056/28/3/030202 [Citations: 14] -
Thermal lattice Boltzmann method for complex microflows
Yasuoka, Haruka | Kaneda, Masayuki | Suga, KazuhikoPhysical Review E, Vol. 94 (2016), Iss. 1
https://doi.org/10.1103/PhysRevE.94.013102 [Citations: 2] -
Lattice Boltzmann simulation of three-dimensional Rayleigh-Taylor instability
Liang, H. | Li, Q. X. | Shi, B. C. | Chai, Z. H.Physical Review E, Vol. 93 (2016), Iss. 3
https://doi.org/10.1103/PhysRevE.93.033113 [Citations: 51] -
Lattice Boltzmann simulation of water flow through rough nanopores
Cheng, Zhilin | Ning, Zhengfu | Kang, Dong-HunChemical Engineering Science, Vol. 236 (2021), Iss. P.116329
https://doi.org/10.1016/j.ces.2020.116329 [Citations: 10] -
Limitations of Lattice Boltzmann Modeling of Micro‐Flows in Complex Nanopores
ZUO, Hong | DENG, Shouchun | LI, HaiboActa Geologica Sinica - English Edition, Vol. 93 (2019), Iss. 6 P.1808
https://doi.org/10.1111/1755-6724.14289 [Citations: 17] -
Pore scale characteristics of gas flow in shale matrix determined by the regularized lattice Boltzmann method
Zhao, Tianyi | Zhao, Huawei | Li, Xiangfang | Ning, Zhengfu | Wang, Qing | Zhao, Wen | Zhang, JinglunChemical Engineering Science, Vol. 187 (2018), Iss. P.245
https://doi.org/10.1016/j.ces.2018.03.056 [Citations: 22] -
Discrete effect on single-node boundary schemes of lattice Bhatnagar–Gross–Krook model for convection-diffusion equations
Wang, Liang | Meng, Xuhui | Wu, Hao-Chi | Wang, Tian-Hu | Lu, GuiInternational Journal of Modern Physics C, Vol. 31 (2020), Iss. 01 P.2050017
https://doi.org/10.1142/S0129183120500175 [Citations: 1] -
Gas slippage effect on the permeability of circular cylinders in a square array
Chai, Zhenhua | Lu, Jianhua | Shi, Baochang | Guo, ZhaoliInternational Journal of Heat and Mass Transfer, Vol. 54 (2011), Iss. 13-14 P.3009
https://doi.org/10.1016/j.ijheatmasstransfer.2011.02.049 [Citations: 27] -
Numerical efficiency assessment of the lattice Boltzmann model for digital nano-porous rock applications
Pazdniakou, Aliaksei | Tinet, Anne-Julie | Golfier, Fabrice | Kalo, Kassem | Gaboreau, Stephane | Gaire, PatrickAdvances in Water Resources, Vol. 121 (2018), Iss. P.44
https://doi.org/10.1016/j.advwatres.2018.08.001 [Citations: 4] -
Discrete effect on the halfway bounce-back boundary condition of multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations
Cui, Shuqi | Hong, Ning | Shi, Baochang | Chai, ZhenhuaPhysical Review E, Vol. 93 (2016), Iss. 4
https://doi.org/10.1103/PhysRevE.93.043311 [Citations: 40] -
Axisymmetric lattice Boltzmann model for liquid flows with super-hydrophobic cylindrical surfaces
Ren, Junjie | Wang, Shengzhen | Wu, Qingxing | Song, YinanEuropean Journal of Mechanics - B/Fluids, Vol. 98 (2023), Iss. P.120
https://doi.org/10.1016/j.euromechflu.2022.12.001 [Citations: 2] -
Simulation of microscale gas flow in heterogeneous porous media based on the lattice Boltzmann method
Zhao, Jianlin | Yao, Jun | Li, Aifen | Zhang, Min | Zhang, Lei | Yang, Yongfei | Sun, HaiJournal of Applied Physics, Vol. 120 (2016), Iss. 8
https://doi.org/10.1063/1.4961599 [Citations: 48] -
Discrete effects on some boundary schemes of multiple-relaxation-time lattice Boltzmann model for convection–diffusion equations
Wu, Yao | Zhao, Yong | Chai, Zhenhua | Shi, BaochangComputers & Mathematics with Applications, Vol. 80 (2020), Iss. 3 P.531
https://doi.org/10.1016/j.camwa.2020.04.003 [Citations: 3] -
Scalable Simulation of Pressure Gradient-Driven Transport of Rarefied Gases in Complex Permeable Media Using Lattice Boltzmann Method
Rustamov, Nijat | Douglas, Craig C. | Aryana, Saman A.Fluids, Vol. 8 (2022), Iss. 1 P.1
https://doi.org/10.3390/fluids8010001 [Citations: 4] -
Multiple-relaxation-time lattice Boltzmann model-based four-level finite-difference scheme for one-dimensional diffusion equations
Lin, Yuxin | Hong, Ning | Shi, Baochang | Chai, ZhenhuaPhysical Review E, Vol. 104 (2021), Iss. 1
https://doi.org/10.1103/PhysRevE.104.015312 [Citations: 11] -
Using MRT lattice Boltzmann method to simulate gas flow in simplified catalyst layer for different inlet–outlet pressure ratio
Gao, Yuan
International Journal of Heat and Mass Transfer, Vol. 88 (2015), Iss. P.122
https://doi.org/10.1016/j.ijheatmasstransfer.2015.04.031 [Citations: 28] -
Multi-scale modelling of gas flow in nanoscale pore space with fractures
Xiong, Qingrong | Yang, Diansen | Chen, WeizhongJournal of Rock Mechanics and Geotechnical Engineering, Vol. 12 (2020), Iss. 1 P.32
https://doi.org/10.1016/j.jrmge.2019.06.005 [Citations: 8] -
Influence of slip boundary on the hydrofoil with a curved slip boundary condition for the lattice Boltzmann method
Wang, Kai | Yang, Liuming | Yu, Yang | Hou, GuoxiangPhysics of Fluids, Vol. 30 (2018), Iss. 12 P.123601
https://doi.org/10.1063/1.5052323 [Citations: 20] -
Study of Gas Flow Characteristics in Tight Porous Media with a Microscale Lattice Boltzmann Model
Zhao, Jianlin | Yao, Jun | Zhang, Min | Zhang, Lei | Yang, Yongfei | Sun, Hai | An, Senyou | Li, AifenScientific Reports, Vol. 6 (2016), Iss. 1
https://doi.org/10.1038/srep32393 [Citations: 64] -
A modified lattice Boltzmann model for microcylindrical Couette gas flows
Ren, Junjie | Wang, Shengzhen | Liu, XiaoxuePhysica Scripta, Vol. 97 (2022), Iss. 8 P.085201
https://doi.org/10.1088/1402-4896/ac7910 [Citations: 3] -
Immersed boundary lattice Boltzmann model based on multiple relaxation times
Lu, Jianhua | Han, Haifeng | Shi, Baochang | Guo, ZhaoliPhysical Review E, Vol. 85 (2012), Iss. 1
https://doi.org/10.1103/PhysRevE.85.016711 [Citations: 42] -
Modelling in Nanoporous Shale
Water Flow in Nanoporous Shale
Zhang, Liehui | Zhang, Tao | Zhao, Yulong2024
https://doi.org/10.1007/978-3-031-69142-3_6 [Citations: 0] -
Modeling the effects of gas slippage, cleat network topology and scale dependence of gas transport in coal seam gas reservoirs
Yu, Xu | Xu, Lincheng | Regenauer-Lieb, Klaus | Jing, Yu | Tian, Fang-BaoFuel, Vol. 264 (2020), Iss. P.116715
https://doi.org/10.1016/j.fuel.2019.116715 [Citations: 21] -
Pore-scale lattice Boltzmann simulation of two-component shale gas flow
Ren, Junjie | Zheng, Qiao | Guo, Ping | Peng, Song | Wang, Zhouhua | Du, JianfenJournal of Natural Gas Science and Engineering, Vol. 61 (2019), Iss. P.46
https://doi.org/10.1016/j.jngse.2018.11.011 [Citations: 24] -
Comment on Xu et al. 2017
Landry, Christopher J. | Prodanović, Maša | Eichhubl, PeterAIChE Journal, Vol. 63 (2017), Iss. 10 P.4717
https://doi.org/10.1002/aic.15823 [Citations: 0] -
A pseudopotential-based multiple-relaxation-time lattice Boltzmann model for multicomponent/multiphase flows
Chai, Zhen-Hua | Zhao, Tian-ShouActa Mechanica Sinica, Vol. 28 (2012), Iss. 4 P.983
https://doi.org/10.1007/s10409-012-0123-6 [Citations: 40] -
Direct simulation of supercritical gas flow in complex nanoporous media and prediction of apparent permeability
Landry, Christopher J. | Prodanović, Maša | Eichhubl, PeterInternational Journal of Coal Geology, Vol. 159 (2016), Iss. P.120
https://doi.org/10.1016/j.coal.2016.03.015 [Citations: 87] -
Macroscopic modeling of gas permeability in hierarchical micro/nanoporous media: A unified characterization of rarefaction using Klinkenberg theory and equivalent diameter
Sabet, Safa | Barisik, MuratPhysics of Fluids, Vol. 36 (2024), Iss. 9
https://doi.org/10.1063/5.0231134 [Citations: 0] -
Lattice Boltzmann Model for Rarefied Gaseous Mixture Flows in Three-Dimensional Porous Media Including Knudsen Diffusion
Ho, Michel | Tucny, Jean-Michel | Ammar, Sami | Leclaire, Sébastien | Reggio, Marcelo | Trépanier, Jean-YvesFluids, Vol. 9 (2024), Iss. 10 P.237
https://doi.org/10.3390/fluids9100237 [Citations: 0] -
Investigation of the Klinkenberg effect in a micro/nanoporous medium by direct simulation Monte Carlo method
Yang, Guang | Weigand, BernhardPhysical Review Fluids, Vol. 3 (2018), Iss. 4
https://doi.org/10.1103/PhysRevFluids.3.044201 [Citations: 25] -
Effect of the forcing term in the multiple-relaxation-time lattice Boltzmann equation on the shear stress or the strain rate tensor
Chai, Zhenhua | Zhao, T. S.Physical Review E, Vol. 86 (2012), Iss. 1
https://doi.org/10.1103/PhysRevE.86.016705 [Citations: 88] -
Bifurcate migration of neutrally buoyant particles in unilateral slippery channel flows
Tao, Shi | Zhang, Xilin | Wang, Wenhao | Wang, Liang | He, Qing | Lin, YoushengPhysics of Fluids, Vol. 36 (2024), Iss. 10
https://doi.org/10.1063/5.0230847 [Citations: 0] -
A systematic study of hidden errors in the bounce-back scheme and their various effects in the lattice Boltzmann simulation of viscous flows
Dong, Zhi-Qiang | Wang, Lian-Ping | Peng, Cheng | Chen, TaoPhysics of Fluids, Vol. 34 (2022), Iss. 9
https://doi.org/10.1063/5.0106954 [Citations: 12] -
LaBCof: Lattice Boltzmann boundary condition framework
Namvar, Morteza | Leclaire, SébastienComputer Physics Communications, Vol. 285 (2023), Iss. P.108647
https://doi.org/10.1016/j.cpc.2022.108647 [Citations: 4] -
Lattice Boltzmann modeling and simulation of velocity and concentration slip effects on the catalytic reaction rate of strongly nonequimolar reactions in microflows
Khatoonabadi, Meysam | Prasianakis, I. Nikolaos | Mantzaras, JohnPhysical Review E, Vol. 106 (2022), Iss. 6
https://doi.org/10.1103/PhysRevE.106.065305 [Citations: 4] -
Liquid slippage on rough hydrophobic surfaces with and without entrapped bubbles
Zuo, Hong | Javadpour, Farzam | Deng, Shouchun | Li, HaiboPhysics of Fluids, Vol. 32 (2020), Iss. 8
https://doi.org/10.1063/5.0015193 [Citations: 23] -
Boundary condition for lattice Boltzmann modeling of microscale gas flows with curved walls in the slip regime
Tao, Shi | Guo, ZhaoliPhysical Review E, Vol. 91 (2015), Iss. 4
https://doi.org/10.1103/PhysRevE.91.043305 [Citations: 52] -
Identifying the dominant transport mechanism in single nanoscale pores and 3D nanoporous media
Yin, Ying | Qu, Zhiguo | Prodanović, Maša | Landry, Christopher J.Fundamental Research, Vol. 3 (2023), Iss. 3 P.409
https://doi.org/10.1016/j.fmre.2021.12.010 [Citations: 17] -
GSIS: An efficient and accurate numerical method to obtain the apparent gas permeability of porous media
Su, Wei | Ho, Minh Tuan | Zhang, Yonghao | Wu, LeiComputers & Fluids, Vol. 206 (2020), Iss. P.104576
https://doi.org/10.1016/j.compfluid.2020.104576 [Citations: 19] -
Curved boundary condition for lattice Boltzmann modeling of binary gaseous micro-scale flows in the slip regime
Ren, Junjie | Zheng, Qiao | Li, YulongPhysica A: Statistical Mechanics and its Applications, Vol. 550 (2020), Iss. P.124181
https://doi.org/10.1016/j.physa.2020.124181 [Citations: 9] -
Upscaling Water Flow in Composite Nanoporous Shale Matrix Using Lattice Boltzmann Method
Zhang, Tao | Javadpour, Farzam | Yin, Ying | Li, XiangfangWater Resources Research, Vol. 56 (2020), Iss. 4
https://doi.org/10.1029/2019WR026007 [Citations: 82] -
Discrete effects on boundary conditions of the lattice Boltzmann method for convection-diffusion equations with curved geometries
Wang, Liang | Tao, Shi | Hu, Junjie | Zhang, Kai | Lu, GuiInternational Communications in Heat and Mass Transfer, Vol. 122 (2021), Iss. P.105130
https://doi.org/10.1016/j.icheatmasstransfer.2021.105130 [Citations: 4] -
Lattice Boltzmann methods for complex micro-flows: applicability and limitations for practical applications
Suga, K
Fluid Dynamics Research, Vol. 45 (2013), Iss. 3 P.034501
https://doi.org/10.1088/0169-5983/45/3/034501 [Citations: 46] -
Curved boundary conditions of the lattice Boltzmann method for simulating microgaseous flows in the slip flow regime
Wang, Liang | Tao, Shi | Hu, Junjie | Zhang, Kai | Lu, GuiComputers & Fluids, Vol. 230 (2021), Iss. P.105117
https://doi.org/10.1016/j.compfluid.2021.105117 [Citations: 4] -
Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows
Chai, Zhenhua | Shi, Baochang | Guo, Zhaoli | Rong, FumeiJournal of Non-Newtonian Fluid Mechanics, Vol. 166 (2011), Iss. 5-6 P.332
https://doi.org/10.1016/j.jnnfm.2011.01.002 [Citations: 105] -
Axisymmetric lattice Boltzmann model with slip boundary conditions for liquid flows in microtube
Ren, Junjie | Liu, Xiaoxue | Gao, YangyangEuropean Journal of Mechanics - B/Fluids, Vol. 89 (2021), Iss. P.430
https://doi.org/10.1016/j.euromechflu.2021.07.008 [Citations: 4]