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| A basic model of unconventional gas microscale flow based on lattice Boltzmann method |
| ZHAO Yulong1, LIU Xiangyu1, ZHANG Liehui1, SHAN Baochao2 |
1. State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China;
2. State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China |
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Abstract A new method for selecting dimensionless relaxation time in the lattice Boltzmann model was proposed based on similarity criterion and true gas physical parameters. At the same time, the dimensionless relaxation time was modified by considering the influence of the boundary Knudsen layer. On this basis, the second-order slip boundary condition of the wall was considered, and the key parameters in the corresponding combined bounce-back/specular-reflection boundary condition were deduced to build a new model of unconventional gas microscale flow simulation based on the lattice Boltzmann method suitable for high temperatures and high pressures. The simulation results of methane gas flow in infinite micro-channel under high temperature and high pressure were compared with the numerical and analytical solutions in the literature to verify the accuracy of the model, and the dimensionless relaxation time modification was formally optimized. The results show that the new model can effectively characterize the slippage effect, compression effect, gas density and the effect of boundary Knudsen layer in the micro-scale flow of unconventional natural gas. The new model can achieve a more comprehensive characterization of the real gas flow conditions and can be used as a basic model for the simulation of unconventional gas flow on the micro-nano scale.
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Received: 17 March 2020
Published: 10 August 2020
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[1] BEEBE D J, MENSING G A, WALKER G M.Physics and applications of microfluidics in biology[J]. Annual Review of Biomedical Engineering, 2002, 4(1): 261-286.
[2] MOHITH S, KARANTH P N, KULKARN S M.Recent trends in mechanical micropumps and their applications: A review[J]. Mechatronics, 2019, 60: 34-55.
[3] ZHANG L, SHAN B, ZHAO Y, et al.Review of micro seepage mechanisms in shale gas reservoirs[J]. International Journal of Heat and Mass Transfer, 2019, 139: 144-179.
[4] ZHAO Y, TANG X, ZHANG L, et al.Numerical solution of fractured horizontal wells in shale gas reservoirs considering multiple transport mechanisms[J]. Journal of Geophysics and Engineering, 2018, 15(3): 739-750.
[5] ZHANG L, CHEN Z, ZHAO Y.Well production performance analysis for shale gas reservoirs[M]. Amsterdam: Elsevier, 2019.
[6] 姜振学, 宋岩, 唐相路, 等. 中国南方海相页岩气差异富集的控制因素[J]. 石油勘探与开发, 2020, 47(3): 617-628.
JIANG Zhenxue, SONG Yan, TANG Xianglu, et al.Controlling factors of marine shale gas differential enrichment in southern China[J]. Petroleum Exploration and Development, 2020, 47(3): 617-628.
[7] REN J, GUO P, GUO Z, et al.A lattice Boltzmann model for simulating gas flow in kerogen pores[J]. Transport in Porous Media, 2015, 106(2): 285-301.
[8] 姚军, 赵建林, 张敏, 等. 基于格子Boltzmann方法的页岩气微观流动模拟[J]. 石油学报, 2015, 36(10): 1280-1289.
YAO Jun, ZHAO Jianlin, ZHANG Min, et al.Microscale shale gas flow simulation based on lattice Boltzmann method[J]. Acta Petrolei Sinica, 2015, 36(10): 1280-1289.
[9] LI Z, MIN T, KANG Q, et al.Investigation of methane adsorption and its effect on gas transport in shale matrix through microscale and mesoscale simulations[J]. International Journal of Heat and Mass Transfer, 2016, 98: 675-686.
[10] ZHANG L, LI J, JIA D, et al.Study on the adsorption phenomenon in shale with the combination of molecular dynamic simulation and fractal analysis[J]. Fractals, 2018, 26(2): 1840004.
[11] 张烈辉, 刘香禺, 赵玉龙, 等. 孔喉结构对致密气微尺度渗流特征的影响[J]. 天然气工业, 2019, 39(8): 50-57.
ZHANG Liehui, LIU Xiangyu, ZHAO Yulong, et al.Effect of pore throat structure on micro-scale seepage characteristics of tight gas reservoirs[J]. Natural Gas Industry, 2019, 39(8): 50-57.
[12] SCHAAF S A, CHAMBRÉ P L.Flow of rarefied gases[M]. Princeton: Princeton University Press, 1961.
[13] CHEN S Y, DOOLEN G D.Lattice Boltzmann method for fluid flows[J]. Annual Review of Fluid Mechanics, 1998, 30(1): 329-364.
[14] NIU X D, SHU C, CHEW Y T.A lattice Boltzmann BGK model for simulation of micro flows[J]. Europhysics Letters, 2004, 67(4): 600-606.
[15] LIM C Y, SHU C, NIU X D, et al.Application of lattice Boltzmann method to simulate microchannel flows[J]. Physics of Fluids, 2002, 14(7): 2299-2308.
[16] 宁正福, 王波, 杨峰, 等. 页岩储集层微观渗流的微尺度效应[J]. 石油勘探与开发, 2014, 41(4): 492-499.
NING Zhengfu, WANG Bo, YANG Feng, et al.Microscale effect of microvadose in shale reservoirs[J]. Petroleum Exploration and Development, 2014, 41(4): 492-499.
[17] NING Y, JIANG Y, LIU H, et al.Numerical modeling of slippage and adsorption effects on gas transport in shale formations using the lattice Boltzmann method[J]. Journal of Natural Gas Science & Engineering, 2015, 26: 345-355.
[18] 赵志刚, 张永波, 赵同彬, 等. 基于格子Boltzmann的煤岩渗透率研究方法[J]. 煤矿安全, 2016, 47(4): 30-34.
ZHAO Zhigang, ZHANG Yongbo, ZHAO Tongbin, et al.A research method for coal and rock permeability based on lattice Boltzmann method[J]. Safety in Coal Mines, 2016, 47(4): 30-34.
[19] 吴子森, 董平川, 袁忠超, 等. 基于格子Boltzmann方法的致密气藏微尺度效应研究[J]. 断块油气田, 2016, 23(6): 793-796.
WU Zisen, DONG Pingchuan, YUAN Zhongchao, et al.Micro-scale effect in tight gas reservoir based on lattice Boltzmann method[J]. Fault-Block Oil & Gas Field, 2016, 23(6): 793-796.
[20] REN J, GUO P, PENG S, et al.Investigation on permeability of shale matrix using the lattice Boltzmann method[J]. Journal of Natural Gas Science & Engineering, 2016, 29: 169-175.
[21] 张烈辉, 贾鸣, 郭晶晶. 基于REV尺度格子Boltzmann方法的页岩气流动数值模拟[J]. 力学与实践, 2017, 39(2): 130-134.
ZHANG Liehui, JIA Ming, GUO Jingjing.Numerical simulation of shale gas flow based on the lattice Boltzmann method at REV scale[J]. Mechanics in Engineering, 2017, 39(2): 130-134.
[22] 任岚, 傅燕鸣, 胡永全, 等. 基于LBM页岩微观尺度气体流动模拟研究[J]. 特种油气藏, 2017, 24(3): 70-75.
REN Lan, FU Yanming, HU Yongquan, et al.Simulation of microscopic gas flowing in shale based on LBM[J]. Special Oil & Gas Reservoirs, 2017, 24(3): 70-75.
[23] WANG J, KANG Q, LI C, et al.Pore-scale lattice Boltzmann simulation of micro-gaseous flow considering surface diffusion effect[J]. International Journal of Coal Geology, 2017, 169(2): 62-73.
[24] 赵金洲, 符东宇, 李勇明, 等. 基于格子Boltzmann方法的页岩气藏气体滑脱效应分析[J]. 油气地质与采收率, 2016, 23(5): 65-70.
ZHAO Jinzhou, FU Dongyu, LI Yongming, et al.Analysis on slippage effect in shale gas reservoir based on lattice Boltzmann method[J]. Petroleum Geology and Recovery Efficiency, 2016, 23(5): 65-70.
[25] ZHAO J, FU D, LI Y, et al.REV-scale simulation of gas transport in shale matrix with lattice Boltzmann method[J]. Journal of Natural Gas Science and Engineering, 2018, 57: 224-237.
[26] ZHAO T, ZHAO H, LI X, et al.Pore scale characteristics of gas flow in shale matrix determined by the regularized lattice Boltzmann method[J]. Chemical Engineering Science, 2018, 187(21): 245-255.
[27] REN J, ZHENG Q, GUO P, et al.Pore-scale lattice Boltzmann simulation of two-component shale gas flow[J]. Journal of Natural Gas Science and Engineering, 2018, 61: 46-70.
[28] 郭照立, 郑楚光. 格子Boltzmann方法的原理及应用[M]. 北京: 科学出版社, 2009.
GUO Zhaoli, ZHENG Chuguang.The principle and application of lattice Boltzmann method[M]. Beijing: Science Press, 2009.
[29] WANG J, CHEN L, KANG Q, et al.The lattice Boltzmann method for isothermal micro-gaseous flow and its application in shale gas flow: A review[J]. International Journal of Heat and Mass Transfer, 2016, 95: 94-108.
[30] NIE X, DOOLEN G D, CHEN S.Lattice-Boltzmann simulations of fluid flows in MEMS[J]. Journal of Statistical Physics, 2002, 107(1/2): 279-289.
[31] LEE T, LIN C.Rarefaction and compressibility effects of the lattice-Boltzmann-equation method in a gas microchannel[J]. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2005, 71(4): 046706.
[32] GUO Z, ZHAO T, SHI Y.Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows[J]. Journal of Applied Physics, 2006, 99(7): 74903.
[33] TANG G, TAO W, HE Y.Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions[J]. Physics of fluids, 2005, 17(5): 058101.
[34] ZHANG Y, QIN R, EMERSON D R.Lattice Boltzmann simulation of rarefied gas flows in microchannels[J]. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2005, 71(4): 047702.
[35] GUO Z, SHI B, ZHAO T, et al.Discrete effects on boundary conditions for the lattice Boltzmann equation in simulating microscale gas flows[J]. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2007, 76(5): 056704.
[36] SHI Y, ZHAO T S, GUO Z L.Lattice Boltzmann simulation of dense gas flows in microchannels[J]. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2007, 76(1): 016707.
[37] STOPS D W.The mean free path of gas molecules in the transition regime[J]. Journal of Physics D: Applied Physics, 1970, 3(5): 685-696.
[38] LI Q, HE Y, TANG G, et al.Lattice Boltzmann modeling of microchannel flows in the transition flow regime[J]. Microfluidics and Nanofluidics, 2011, 10(3): 607-618.
[39] MICHALIS V K, KALARAKIS A N, SKOURAS E D, et al.Rarefaction effects on gas viscosity in the Knudsen transition regime[J]. Microfluidics and Nanofluidics, 2010, 9(4/5): 847-853.
[40] ZHANG Y, GU X, BARBER R W, et al.Capturing Knudsen layer phenomena using a lattice Boltzmann model[J]. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2006, 74(4): 046704.
[41] TANG G, ZHANG Y, GU X, et al.Lattice Boltzmann modelling Knudsen layer effect in non-equilibrium flows[J]. Europhysics Letters, 2008, 83(4): 226-234.
[42] GUO Z, SHI B, ZHENG C.An extended Navier-Stokes formulation for gas flows in the Knudsen layer near a wall[J]. Europhysics Letters, 2007, 80(2): 24001.
[43] QIAN Y, D'HUMIÈRES D, LALLEMAND P. Lattice BGK models for Navier-Stokes equation[J]. Europhysics Letters, 1992, 17(6): 479-484.
[44] BHATNAGAR P L, GROSS E P, KROOK M.A model for collision processes in gases. I. Small amplitude processes in charged and neutral one: Component systems[J]. Physics Reviews, 1954, 94(3): 511-525.
[45] HE X, LUO L S.Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation[J]. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 1997, 56(6): 6811-6817.
[46] 董波. 非混相驱替过程的格子Boltzmann模拟[D]. 大连: 大连理工大学, 2011.
DONG Bo.Lattice Boltzmann simulation of immiscible displacement[D]. Dalian: Dalian University of Technology, 2011.
[47] 何雅玲, 王勇, 李庆. 格子Boltzmann方法的理论及应用[M]. 北京: 科学出版社, 2009.
HE Yaling, WANG Yong, LI Qing.The theory and application of lattice Boltzmann method[M]. Beijing: Science Press, 2009.
[48] ZOU Q, HE X.On pressure and velocity boundary conditions for the lattice Boltzmann BGK model[J]. Physics of Fluids, 1997, 9(6): 1591-1598.
[49] GUO Z, ZHENG C, SHI B.Non-equilibrium extrapolation method for velocity and boundary conditions in the lattice Boltzmann method[J]. Chinese Physics, 2002, 11(4): 366-374.
[50] TANG G, TAO W, HE Y.Lattice Boltzmann method for simulating gas flow in microchannels[J]. International Journal of Modern Physics C, 2004, 15(2): 335-347.
[51] GUO Z, QIN J, ZHENG C.Generalized second-order slip boundary condition for nonequilibrium gas flows[J]. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2014, 89(1): 013021.
[52] OHWADA T, SONE Y, AOKI K.Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard‐sphere molecules[J]. Physics of Fluids A: Fluid Dynamics, 1989, 1(9): 1588-1599.
[53] GUO Z, ZHENG C, SHI B.Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow[J]. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2008, 77(3): 036707.
[54] CERCIGNANI C.Mathematical methods in kinetic theory[M]. 2nd ed. New York: Plenum Press, 1990.
[55] SHEN C, TIAN D, XIE C, et al.Examination of the LBM in simulation of microchannel flow in transitional regime[J]. Microscale Thermophysical Engineering, 2004, 8(4): 423-432.
[56] ARKILIC E B, SCHMIDT M A, BREUER K S.Gaseous slip flow in long microchannels[J]. Journal of Microelectromechanical Systems, 1997, 6(2): 167-178. |
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