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Coupling of high Knudsen number and non-ideal gas effects in microporous media

Published online by Cambridge University Press:  06 February 2018

Ziyan Wang ,
Moran Wang Open the ORCID record for Moran Wang [Opens in a new window]  and
Shiyi Chen
Ziyan Wang
Affiliation:
Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084, China
Moran Wang*
Affiliation:
Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084, China
Shiyi Chen
Affiliation:
State Laboratory of Turbulence and Complex Systems, Peking University, Beijing 100871, China Southern University Science and Technology, Shenzhen 518055, Guangdong, China
*
†Email address for correspondence: mrwang@tsinghua.edu.cn
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Abstract

High Knudsen number non-ideal gas flows in porous media are important and fundamental in various applications including shale gas exploitation and carbon dioxide sequestration. Because of the small pore size in tight rocks, the Knudsen number (Kn) may be high (i.e. much higher than 0.01) even though the gas is really dense. In fact, due to the high pressure and temperature underground, the gas usually manifests a strong non-ideal gas effect. Understanding the coupling mechanism of the high Kn effect and non-ideal gas effect is a premise to accurately model deep-seated underground gas exploitation or carbon dioxide sequestration. In this work, we theoretically analyse the high Kn non-ideal gas flows in microporous media. Based on the relative importance of the non-ideal gas effect and high Kn effect, the coupling is divided into four types. The analysis is subsequently validated by multiscale numerical simulations, in which the four types of coupling are clearly demonstrated. After applying the analysis to laboratory measurements, we propose a characteristic pressure model to calculate the gas permeability of tight rocks with better precision. The new model incorporates the non-ideal gas effect with the high Kn effect accurately and better bridges the laboratory measurements with the reservoir engineering.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 840 , 10 April 2018 , pp. 56 - 73
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Copyright
© 2018 Cambridge University Press 

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References

Ahmed, T. & McKinney, P. 2005 Advanced Reservoir Engineering. Gulf Professional Publishing.Google Scholar
Al-Hussainy, R., Ramey, H. J. & Crawford, P. B. 1966 The flow of real gases through porous media. J. Petrol. Tech. 18, 624–636.CrossRefGoogle Scholar
Ansumali, S. & Karlin, I. V. 2002 Kinetic boundary conditions in the lattice Boltzmann method. Phys. Rev. E 66, 026311.Google ScholarPubMed
Beskok, A. & Karniadakis, G. E. 1999 A model for flows in channels, pipes, and ducts at micro and nano scales. Microscale Therm. Engng 3, 43–77.Google Scholar
Bird, G. A. 1983 Definition of mean free path for real gases. Phys. Fluids 26, 3222–3223.CrossRefGoogle Scholar
Chen, S. & Doolen, G. D. 1998 Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364.CrossRefGoogle Scholar
Civan, F. 2010 Effective correlation of apparent gas permeability in tight porous media. Trans. Porous Med. 82, 375–384.CrossRefGoogle Scholar
Darabi, H., Ettehad, A., Javadpour, F. & Sepehrnoori, K. 2012 Gas flow in ultra-tight shale strata. J. Fluid Mech. 710, 641–658.CrossRefGoogle Scholar
Gensterblum, Y., Ghanizadeh, A. & Krooss, B. M. 2014 Gas permeability measurements on Australian subbituminous coals: fluid dynamic and poroelastic aspects. J. Nat. Gas Sci. Engng 19, 202–214.CrossRefGoogle Scholar
Guo, J., Wang, H. & Zhang, L. 2016 Transient pressure and production dynamics of multi-stage fractured horizontal wells in shale gas reservoirs with stimulated reservoir volume. J. Nat. Gas Sci. Engng 35, 425–443.CrossRefGoogle Scholar
Guo, Z., Zheng, C. & Shi, B. 2008 Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow. Phys. Rev. E 77, 036707.Google ScholarPubMed
Guo, Z. L., Zheng, C. G. & Shi, B. C. 2002 Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chin. Phys. 11, 366–374.Google Scholar
He, X. Y. & Luo, L. S. 1997 Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E 56, 6811–6817.Google Scholar
Higuera, F. J., Succi, S. & Benzi, R. 1989 Lattice gas-dynamics with enhanced collisions. Europhys. Lett. 9, 345–349.CrossRefGoogle Scholar
d’Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P. & Luo, L. S. 2002 Multiple-relaxation-time lattice Boltzmann models in three dimensions. Phil. Trans. R. Soc. Lond. A 360, 437–451.CrossRefGoogle ScholarPubMed
Klinkenberg, L. J. 1941 The permeability of porous media to liquids and gases. In Drilling and Production Practice, pp. 200–213. American Petroleum Institute.Google Scholar
Knudsen, M. H. C. 1933 The Kinetic Theory of Gases; Some Modern Aspects. Methuen.Google Scholar
Lallemand, P. & Luo, L. S. 2000 Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61, 6546–6562.Google ScholarPubMed
Lasseux, D., Valdes Parada, F. J., Ochoa Tapia, J. A. & Goyeau, B. 2014 A macroscopic model for slightly compressible gas slip-flow in homogeneous porous media. Phys. Fluids 26, 053102.CrossRefGoogle Scholar
Li, Q., He, Y. L., Tang, G. H. & Tao, W. Q. 2011 Lattice Boltzmann modeling of microchannel flows in the transition flow regime. Microfluid Nanofluid 10, 607–618.CrossRefGoogle Scholar
Lunati, I. & Lee, S. H. 2014 A dual-tube model for gas dynamics in fractured nanoporous shale formations. J. Fluid Mech. 757, 943–971.CrossRefGoogle Scholar
Ma, J. S., Sanchez, J. P., Wu, K. J., Couples, G. D. & Jiang, Z. Y. 2014 A pore network model for simulating non-ideal gas flow in micro-and nano-porous materials. Fuel 116, 498–508.CrossRefGoogle Scholar
MoradiDowlatabad, M. & Jamiolahmady, M. 2017 The lifetime performance prediction of fractured horizontal wells in tight reservoirs. J. Nat. Gas Sci. Engng 42, 142–156.CrossRefGoogle Scholar
Pan, C., Luo, L.-S. & Miller, C. T. 2006 An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comput. Fluids 35, 898–909.CrossRefGoogle Scholar
Ren, J., Guo, P., Guo, Z. & Wang, Z. 2015 A lattice Boltzmann model for simulating gas flow in kerogen pores. Trans. Porous Med. 106, 285–301.CrossRefGoogle Scholar
Rushing, J. A., Newsham, K. E., Lasswell, P. M., Cox, J. C. & Blasingame, T. A. 2004 Klinkenberg-corrected permeability measurements in tight gas sands: steady-state versus unsteady-state techniques. In SPE Annual Technical Conference and Exhibition, p. 89867. Society of Petroleum Engineers.Google Scholar
Setzmann, U. & Wagner, W. 1991 A new equation of state and tables of thermodynamic properties for methane covering the range from the melting line to 625 K at pressures up to 1000 MPa. J. Phys. Chem. Ref. Data 20, 1061–1155.CrossRefGoogle Scholar
Smits, A. J. & Dussauge, J. P. 2006 Turbulent Shear Layers in Supersonic Flow. Springer.Google Scholar
de Socio, L. M. & Marino, L. 2006 Gas flow in a permeable medium. J. Fluid Mech. 557, 119–133.CrossRefGoogle Scholar
Villazon, M., German, G., Sigal, R. F., Civan, F. & Devegowda, D. 2011 Parametric investigation of shale gas production considering nano-scale pore size distribution formation factor and non-Darcy flow mechanisms. In SPE Annual Technical Conference and Exhibition, p. 147438. Society of Petroleum Engineers.Google Scholar
Vishal, V., Ranjith, P. G., Pradhan, S. P. & Singh, T. N. 2013 Permeability of sub-critical carbon dioxide in naturally fractured Indian bituminous coal at a range of down-hole stress conditions. Engng Geol. 167, 148–156.CrossRefGoogle Scholar
Wang, M. & Chen, S. 2007 Electroosmosis in homogeneously charged micro- and nanoscale random porous media. J. Colloid Interface Sci. 314, 264–273.CrossRefGoogle ScholarPubMed
Wang, M., Lan, X. D. & Li, Z. X. 2008 Analyses of gas flows in micro- and nanochannels. Intl J. Heat Mass Transfer 51, 3630–3641.CrossRefGoogle Scholar
Wang, M. & Li, Z. X. 2003 Nonideal gas flow and heat transfer in micro- and nanochannels using the direct simulation Monte Carlo method. Phys. Rev. E 68, 046704.Google ScholarPubMed
Wang, M. & Pan, N. 2008 Predictions of effective physical properties of complex multiphase materials. Mater. Sci. Engng 63, 1–30.CrossRefGoogle Scholar
Wang, M., Pan, N., Wang, J. K. & Chen, S. Y. 2007a Lattice Poisson–Boltzmann simulations of electroosmotic flows in charged anisotropic porous media. Commun. Comput. Phys. 2, 1055–1070.Google Scholar
Wang, M., Wang, J., Pan, N. & Chen, S. 2007b Mesoscopic predictions of the effective thermal conductivity for microscale random porous media. Phys. Rev. E 75, 036702.Google ScholarPubMed
Wang, M. R. & Kang, Q. J. 2009 Electrokinetic transport in microchannels with random roughness. Anal. Chem. 81, 2953–2961.CrossRefGoogle ScholarPubMed
Wang, X. & Economides, M. 2009 Advanced Natural Gas Engineering. Elsevier.Google Scholar
Wang, Z., Guo, Y. & Wang, M. 2016 Permeability of high-Kn real gas flow in shale and production prediction by pore-scale modeling. J. Nat. Gas Sci. Engng 28, 328–337.CrossRefGoogle Scholar
Wei, M., Duan, Y., Dong, M. & Fang, Q. 2016 Blasingame decline type curves with material balance pseudo-time modified for multi-fractured horizontal wells in shale gas reservoirs. J. Nat. Gas Sci. Engng 31, 340–350.CrossRefGoogle Scholar
White, C. M. et al. 2005 Sequestration of carbon dioxide in coal with enhanced coalbed methane recovery – a review. Energy & Fuels 19, 659–724.CrossRefGoogle Scholar
Wu, K. L., Chen, Z. X. & Li, X. F. 2015 Real gas transport through nanopores of varying cross-section type and shape in shale gas reservoirs. Chem. Engng J. 281, 813–825.CrossRefGoogle Scholar
Wu, L., Ho, M. T., Germanou, L., Gu, X.-J., Liu, C., Xu, K. & Zhang, Y. 2017 On the apparent permeability of porous media in rarefied gas flows. J. Fluid Mech. 822, 398–417.CrossRefGoogle Scholar
Wu, L., Liu, H. H., Reese, J. M. & Zhang, Y. H. 2016 Non-equilibrium dynamics of dense gas under tight confinement. J. Fluid Mech. 794, 252–266.CrossRefGoogle Scholar
Xu, K. & Li, Z. H. 2004 Microchannel flow in the slip regime: gas-kinetic BGK-Burnett solutions. J. Fluid Mech. 513, 87–110.CrossRefGoogle Scholar
Younglove, B. A. & Ely, J. F. 1987 Thermophysical properties of fluids. 2. Methane, ethane, propane, isobutane, and normal butane. J. Phys. Chem. Ref. Data 16, 577–798.CrossRefGoogle Scholar