Boundary scheme for lattice Boltzmann modeling of micro-scale gas flow in organic-rich pores considering surface diffusion

doi:10.1088/1674-1056/28/3/030202

摘要/Abstract

摘要： We propose a boundary scheme for addressing multi-mechanism flow in a porous medium in slip and early transition flow regimes, which is frequently encountered in shale gas reservoirs. Micro-gaseous flow in organic-rich shale involves a complex flow mechanism. A self-developed boundary scheme that combines the non-equilibrium extrapolation scheme and the combined diffusive reflection and bounce-back scheme (half-way DBB) to embed the Langmuir slip boundary into the single-relaxation-time lattice Boltzmann method (SRT-LBM) enables us to describe this process, namely, the coupling effect of micro-gaseous flow and surface diffusion in organic-rich nanoscale pores. The present LBM model comes with the careful consideration of the local Knudsen number, local pressure gradient, viscosity correction model, and regularization procedure to account for the rarefied gas flows in irregular pores. Its validity and accuracy are verified by several benchmarking cases, and the calculated results by this boundary scheme accord well with our analytical solutions. This boundary scheme shows a higher accuracy than the existing studies. Additionally, a subiteration strategy is presented to tackle the coupled micro-gaseous flow and surface diffusion, which necessitates the iteration process matching of these two mechanisms. The multi-mechanism flow in the self-developed irregular pores is also numerically investigated and analyzed over a wide range of parameters. The results indicate that the present model can effectively capture the coupling effect of micro-gaseous flow and surface diffusion in a tree-like porous medium.

关键词: lattice Boltzmann method (LBM), surface diffusion, Langmuir slip model, boundary scheme

Abstract: We propose a boundary scheme for addressing multi-mechanism flow in a porous medium in slip and early transition flow regimes, which is frequently encountered in shale gas reservoirs. Micro-gaseous flow in organic-rich shale involves a complex flow mechanism. A self-developed boundary scheme that combines the non-equilibrium extrapolation scheme and the combined diffusive reflection and bounce-back scheme (half-way DBB) to embed the Langmuir slip boundary into the single-relaxation-time lattice Boltzmann method (SRT-LBM) enables us to describe this process, namely, the coupling effect of micro-gaseous flow and surface diffusion in organic-rich nanoscale pores. The present LBM model comes with the careful consideration of the local Knudsen number, local pressure gradient, viscosity correction model, and regularization procedure to account for the rarefied gas flows in irregular pores. Its validity and accuracy are verified by several benchmarking cases, and the calculated results by this boundary scheme accord well with our analytical solutions. This boundary scheme shows a higher accuracy than the existing studies. Additionally, a subiteration strategy is presented to tackle the coupled micro-gaseous flow and surface diffusion, which necessitates the iteration process matching of these two mechanisms. The multi-mechanism flow in the self-developed irregular pores is also numerically investigated and analyzed over a wide range of parameters. The results indicate that the present model can effectively capture the coupling effect of micro-gaseous flow and surface diffusion in a tree-like porous medium.

Key words: lattice Boltzmann method (LBM), surface diffusion, Langmuir slip model, boundary scheme

中图分类号: (Numerical simulation; solution of equations)

02.60.Cb

05.20.Dd (Kinetic theory) 02.60.Cb (Numerical simulation; solution of equations)

左鸿, 邓守春, 李海波. Boundary scheme for lattice Boltzmann modeling of micro-scale gas flow in organic-rich pores considering surface diffusion[J]. 中国物理B, 2019, 28(3): 30202-030202.

Hong Zuo(左鸿), Shou-Chun Deng(邓守春), Hai-Bo Li(李海波). Boundary scheme for lattice Boltzmann modeling of micro-scale gas flow in organic-rich pores considering surface diffusion[J]. Chin. Phys. B, 2019, 28(3): 30202-030202.

参考文献 75

[1]	Landry C J, Prodanović M and Eichhubl P 2016 Int. J. Coal Geology 159 120 doi: 10.1016/j.coal.2016.03.015
[2]	Zuo H, Deng S, Huang Z, Xiao C, Zeng Y and Jiang J 2018 Int. J. Oil, Gas and Coal Technology
[3]	Yin Y, Qu Z G and Zhang J F 2017 Fuel 210 569 doi: 10.1016/j.fuel.2017.09.018
[4]	Wu K, Li X, Guo C, Wang C and Chen Z 2016 Spe Journal. 21 1
[5]	Kazemi M and Takbiri-Borujeni A 2015 Int. J. Coal Geology 146 188 doi: 10.1016/j.coal.2015.05.010
[6]	Cui X, Bustin A M M and Bustin R M 2009 Geofluids 9 208 doi: 10.1111/j.1468-8123.2009.00244.x
[7]	Hannon M J and Finsterle S 2017 Transp. Porous Media. 123 545
[8]	Liu H, Dan G and Chen J 2018 Petroleum Science 15 116 doi: 10.1007/s12182-017-0200-3
[9]	Sander R, Pan Z and Connell L D 2017 J. Nat. Gas Sci. & Eng. 37 248 doi: t. Gas Sci.
[10]	Zhao J, Yao J, Zhang L, Sui H and Zhang M 2016 Int. J. Heat & Mass Transfer 103 1098 doi: J. Heat
[11]	Yu H, Chen J, Zhu Y B, Wang F C and Wu H A 2017 Int. J. Heat & Mass Transfer 111 1172 doi: J. Heat
[12]	Xue Q, Tao Y, Liu Z, Lu S, Li X, Wu T, Jin Y and Liu X 2015 Rsc Adv. 5 25684 doi: 10.1039/C4RA16682E
[13]	Lin K, Yuan Q and Zhao Y P 2017 Comput. Mater. Sci. 133 99 doi: 10.1016/j.commatsci.2017.03.010
[14]	Christou C and Dadzie S K 2016 Spe Journal. 21 938 doi: 10.2118/173314-PA
[15]	Geng L, Li G, Zitha P, Tian S, Sheng M and Fan X 2016 Fuel 181 887 doi: 10.1016/j.fuel.2016.05.036
[16]	Qian Y H, D'Humiéres D and Lallemand P 1992 Epl 17 479 doi: 10.1209/0295-5075/17/6/001
[17]	Shan X, Yuan X and Chen H 2006 J. Fluid Mech. 550 413 doi: 10.1017/S0022112005008153
[18]	Guo Z and Shu C 2013 Lattice Boltzmann Method and its Applications in Engineering (Singapore: World Scientific Publishing Co. Pte. Ltd)
[19]	Succi S 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (New York: Clarendon Press)
[20]	Guo Z and Zheng C 2008 Int. J. Comput. Fluid Dyn. 22 465 doi: 10.1080/10618560802253100
[21]	Guo Z, Zheng C and Shi B 2008 Phys. Rev. E 77 036707 doi: 10.1103/PhysRevE.77.036707
[22]	Guo Z L, Shi B C and Zheng C G 2007 Epl 80 24001 doi: 10.1209/0295-5075/80/24001
[23]	Tang G H, Zhang Y H, Gu X J and Emerson D R 2008 Epl 83 226
[24]	Zhang Y H, Gu X J, Barber R W and Emerson D R 2006 Phys. Rev. E 74 046704 doi: 10.1103/PhysRevE.74.046704
[25]	Chikatamarla S S and Karlin I V 2009 Phys. Rev. E 79 046701 doi: 10.1103/PhysRevE.79.046701
[26]	Chikatamarla S S and Karlin I V 2006 Phys. Rev. Lett. 97 190601 doi: 10.1103/PhysRevLett.97.190601
[27]	De I L, Rouet J L and Izrar B 2011 Phys. Rev. E 84 066705 doi: 10.1103/PhysRevE.84.066705
[28]	Dehdashti E 2016 Chin. Phys. B 25 024702 doi: 10.1088/1674-1056/25/2/024702
[29]	Zuo W, Yan L and Jia-Zhong Z 2016 Acta Phys. Sin. 65 291 (in Chinese)
[30]	Guo Z, Shi B and Zheng C 2011 Computers & Mathematics with Applications 61 3519 doi: ters
[31]	Chai Z, Guo Z, Zheng L and Shi B 2008 J. Appl. Phys. 104 014902 doi: 10.1063/1.2949273
[32]	Chai Z, Shi B, Guo Z and Lu J 2010 Commun. Comput. Phys. 8 1052 doi: 10.4208/cicp.010809.081209a
[33]	Tao S and Z G 2015 Phys. Rev. E 91 043305 doi: 10.1103/PhysRevE.91.043305
[34]	Luo L S 2009 J. Comput. Phys. 228 147 doi: 10.1016/j.jcp.2008.09.004
[35]	Ansumali S and Karlin I V 2002 Phys. Rev. E 66 026311 doi: 10.1103/PhysRevE.66.026311
[36]	Zhao J, Yao J, Li A, Zhang M, Zhang L, Yang Y and Sun H 2016 J. Appl. Phys. 120 579
[37]	Tao S and Guo Z 2017 Chem. Eng. & Technol. 40 1758 doi: Eng.
[38]	Tao S, Zhang H and Guo Z 2017 J. Aerosol Sci. 103 105 doi: 10.1016/j.jaerosci.2016.10.006
[39]	Fathi E and Akkutlu I Y 2012 Spe J. 18 27
[40]	Wang J, Kang Q, Chen L and Rahman S S 2017 Int. J. Coal Geology 169 62 doi: 10.1016/j.coal.2016.11.013
[41]	Wang L, Zeng Z, Zhang L, Qiao L, Zhang Y and Lu Y 2018 Physica A 495 180 doi: 10.1016/j.physa.2017.12.028
[42]	Guo Z, Zheng C and Shi B 2002 Phys. Fluids 14 2007 doi: 10.1063/1.1471914
[43]	Inamuro T, Yoshino M and Ogino F 1995 Phys. Fluids 7 2928 doi: 10.1063/1.868766
[44]	Ning Y, Jiang Y, Liu H and Qin G 2015 J. Nat. Gas Sci. & Eng. 26 345 doi: t. Gas Sci.
[45]	Chen Y Y, Yi H H and Li H B 2008 Chin. Phys. Lett. 25 184 doi: 10.1088/0256-307X/25/1/050
[46]	Chen L, Fang W, Kang Q, De'Haven H J, Viswanathan H S and Tao W Q 2015 Phys. Rev. E 91 033004 doi: 10.1103/PhysRevE.91.033004
[47]	Chen L, Kang Q, Dai Z, Viswanathan H S and Tao W 2015 Fuel 160 346 doi: 10.1016/j.fuel.2015.07.070
[48]	Wang J, Chen L, Kang Q and Rahman S S 2016 Fuel 181 478 doi: 10.1016/j.fuel.2016.05.032
[49]	Tan Y L, Teng G R and Ze Z 2010 Chin. Phys. Lett. 27 174
[50]	Ren J, Guo P, Guo Z and Wang Z 2015 Transp. Porous Media 106 285 doi: 10.1007/s11242-014-0401-9
[51]	Ren J, Guo P, Peng S and Yang C 2016 J. Nat. Gas Sci. & Eng. 29 7 doi: t. Gas Sci.
[52]	Ren J 2015 Study of Microscopic Transport Mechanisms of Shale Gas Using the Lattice Boltzmann method (Chengdu: Southwest Petroleum University)
[53]	Ren J, Guo P, Peng S and Yang C 2016 J. Nat. Gas Sci. & Eng. 29 169 doi: t. Gas Sci.
[54]	Myong R S 2004 J. Comput. Phys. 195 655 doi: 10.1016/j.jcp.2003.10.015
[55]	Bhattacharya D K and Eu B C 1987 Phys. Rev. A 35 821 doi: 10.1103/PhysRevA.35.821
[56]	Wang J, Li C, Kang Q and Rahman S S 2016 Int. J. Heat & Mass Transfer 95 94 doi: J. Heat
[57]	Succi S 2002 Phys. Rev. Lett. 89 064502 doi: 10.1103/PhysRevLett.89.064502
[58]	Guo Z S 2013 Lattice Boltzmann Method and its Applications in Engineering
[59]	Zhang R, Shan X and Chen H 2006 Phys. Rev. E 74 046703 doi: 10.1103/PhysRevE.74.046703
[60]	Suga K 2013 Fluid Dyn. Res. 45 034501 doi: 10.1088/0169-5983/45/3/034501
[61]	Latt J and Chopard B 2006 Math. & Comput. Simul. 72 165
[62]	Zhang T Y and Suen C Y 1984 Communications of the ACM 27 236 doi: 10.1145/357994.358023
[63]	Silin D and Patzek T 2006 Phys. A 371 336 doi: 10.1016/j.physa.2006.04.048
[64]	Ohwada T, Sone Y and Aoki K 1989 Phys. Fluids A Fluid Dyn. 1 1588 doi: 10.1063/1.857304
[65]	Li Q, He Y L and Tao W Q 2011 Microfluid. & Nanofluid. 10 607 doi: fluid.
[66]	Shen C, Tian D B, Xie C and Fan J 2004 Microscale Thermophysical Eng. 8 423 doi: 10.1080/10893950490516983
[67]	Lee T and Lin C L 2005 Phys. Rev. E 71 046706 doi: 10.1103/PhysRevE.71.046706
[68]	M Aminpour S G T, Scheuermann A and Li L 2018 Phys. Rev. E 98 043110 doi: 10.1103/PhysRevE.98.043110
[69]	Pan C, Luo L S and Miller C T 2006 Comput. & Fluids 35 898 doi: t.
[70]	He X, Zou Q, Luo L S and Dembo M 1997 J. Stat. Phys. 87 115 doi: 10.1007/BF02181482
[71]	Mousavi M A 2012 Transp. Porous Media 94 537 doi: 10.1007/s11242-012-0017-x
[72]	Sakhaee-Pour A and Bryant S L 2014 Aapg Bull. 98 663 doi: 10.1306/08011312078
[73]	Zou Q and He X 1997 Phys. Fluids 9 1591 doi: 10.1063/1.869307
[74]	Ambrose R J, Hartman R C, Diaz-Campos M, Akkutlu I Y and Sondergeld C H 2012 Spe J. 17 219 doi: 10.2118/131772-PA
[75]	Hadjiconstantinou N G 2003 Phys. Fluids 15 2352 doi: 10.1063/1.1587155