Slip Velocity of Methane Flow in Nanopores With Kerogen and Quartz Surfaces
- Naoki Okamoto (Kyoto University) | Kazuya Kobayashi (Kyoto University) | Yunfeng Liang (University of Tokyo and Kyoto University) | Sumihiko Murata (Kyoto University) | Toshifumi Matsuoka (Fukada Geological Institute and Kyoto University) | Takashi Akai (Japan Oil, Gas, and Metals National Corporation) | Sunao Takagi (Japan Oil, Gas, and Metals National Corporation)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- February 2018
- Document Type
- Journal Paper
- 102 - 116
- 2018.Society of Petroleum Engineers
- Shale Gas, Permeability Correction, Kerogen Nanopores, Slip Flow
- 5 in the last 30 days
- 320 since 2007
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Slip phenomenon is one of the major characteristics of gas flow through porous media—in particular, in unconventional gas reservoirs with small pore throats, such as tight sands, coal seams, and shale formations. Consequently, a permeability correction needs to be considered to evaluate the gas-flow ability in these reservoirs. Various analytically derived and empirical correction models exist for engineering applications. However, it is not well-understood which one should be implemented in real-shale-reservoir problems. In this paper, slip velocity and permeability for gas flow in nanopores are studied by molecular-dynamics (MD) simulations. For simplicity, the system considered is methane gas flow in a parallel-plate channel of quartz and kerogen. The fluid flow is characterized by the Knudsen number (Kn), which is defined as the ratio between the mean free path and the representative length of the pores. Studies with various Knudsen numbers were conducted by changing (1) the methane density (the mean free path) or (2) the plate-spacing (pore size). Simulation results show that the relationships between slip velocity and Knudsen number and between the permeability-correction factors and Knudsen number agree well with the Beskok and Karniadakis (1994) analytical solution (BK model) for large nanopores (12–34 nm) in both quartz and kerogen cases. This model considered rarefaction and compressibility effects on gas microflows, and was tested experimentally with characteristic dimensions of one-micrometer order. Our simulation results indicate that this model can be extended to nanoflows existing in unconventional reservoirs. Under temperature and pressure conditions that we studied, deviation from the BK model is noted for small nanopores (<12 nm), but for a pore size smaller than 6 nm, it converges to a constant value in the quartz slit pore. In contrast, a radical increase of slip velocity is observed in the kerogen pore. The deviation from the BK model for a pore size smaller than 12 nm is ascribed to the fact that the overall fluid is no longer homogeneous (i.e., the fluid at the interface region plays a crucial role in the overall flow behavior). An adsorption structure is observed in the proximity of the solid walls because of the interaction from the wall molecules. Moreover, it is found that the effect of roughness becomes significant in an extremely small kerogen nanopore.
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Adesida, A. G., Akkutlu, I. Y., Resasco, D. E. et al. 2011. Kerogen Pore Size Distribution of Barnett Shale Using DFT Analysis and Monte Carlo Simulations. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 30 October–2 November. SPE-147397-MS. https://doi.org/10.2118/147397-MS.
Akai, T., Takakura, Y., and Sato, K. 2016. Pressure Dependent Permeability of Tight Rocks. Presented at the SPE Low Perm Symposium, Denver, 5–6 May. SPE-180262-MS. https://doi.org/10.2118/180262-MS.
Akkutlu, I. Y. and Fathi, E. 2012. Multiscale Gas Transport in Shales With Local Kerogen Heterogeneities. SPE J. 17: 1002–1011. SPE-146422-PA. https://doi.org/10.2118/146422-PA.
Al Hinai, A., Rezaee, R., Esteban, L. et al. 2014. Comparisons of Pore Size Distribution: A Case From the Western Australian Gas Shale Formations. Journal of Unconventional Oil and Gas Resources 8: 1–13. https://doi.org/10.1016/j.juogr.2014.06.002.
Ambrose, R., Hartman, R., Diaz-Campos, M. et al. 2012. Shale Gas-in-Place Calculations Part I: New Pore-Scale Considerations. SPE J. 17: 219–229. SPE-131772-PA. https://doi.org/10.2118/131772-PA.
Arya, G., Chang, H.-C., and Maginn, E. J. 2001. A Critical Comparison of Equilibrium, Non-Equilibrium and Boundary-Driven Molecular Dynamics Techniques for Studying Transport in Microporous Materials. Journal of Chemical Physics 115 (17): 8112–8124. https://doi.org/10.1063/1.1407002.
Barrat, J.-L. and Bocquet, L. 1999. Large Slip Effect at a Nonwetting Fluid-Solid Interface. Physical Review Letters 82 (23): 4671–4674. https://doi.org/10.1103/PhysRevLett.82.4671.
Beskok, A. and Karniadakis, G. E. 1994. Simulation of Heat and Momentum Transfer in Complex Microgeometries. Journal of Thermophysics & Heat Transfer 8: 647–655. https://doi.org/10.2514/3.594.
Beskok, A., Karniadakis, G. E., and Trimmer, W. 1996. Rarefaction and Compressibility Effects in Gas Micoflows. Journal Fluids Engineering 118: 448–456. https://doi.org/10.1115/1.2817779.
Bitsanis, I., Somers, S. A., Davis, H. T. et al. 1990. Microscopic Dynamics of Flow in Molecularly Narrow Pores. Journal of Chemical Physics 93: 3427–3431. https://doi.org/10.1063/1.458823.
Botan, A., Rotenberg, B., Marry, V. et al. 2011. Hydrodynamics in Clay Nanopores. Journal of Physical Chemistry C 115: 16109–16115. https://doi.org/10.1021/jp204772c.
Botan, A., Marry, V., Rotenberg, B. et al. 2013. How Electrostatics Influences Hydrodynamic Boundary Conditions: Poiseuille and Electro-Osmostic Flows in Clay Nanopores. Journal of Physical Chemistry C 117: 978–985. https://doi.org/10.1021/jp3092336.
Cercignani, C. 1964. Higher Order Slip According to the Linearized Boltzmann Equation. Institute of Engineering Research Report AS-64-19: University of California, Berkeley.
Cercignani, C. and Lorenzani, S. 2010. Variational Derivation of Second-Order Slip Coefficients on the Basis of the Boltzmann Equation for Hard-Sphere Molecules. Physics of Fluids 22: 062004. https://doi.org/10.1063/1.3435343.
Chen, S. and Tian, Z. 2009. Simulation of Microchannel Flow Using the Lattice Boltzmann Method. Physica A 388: 4803–4810. https://doi.org/10.1016/j.physa.2009.08.015.
Chen, L., Zhang, L., Kang, Q. et al. 2015. Nanoscale Simulation of Shale Transport Method: Permeability and Diffusivity. Scientific Reports 5: 8089. https://doi.org/10.1038/srep08089.
Cieplak, M., Koplik, J., and Banavar, J. R. 2001. Boundary Conditions at a Fluid-Solid Interface. Phys. Rev. Lett. 86 (5): 803. https://doi.org/10.1103/PhysRevLett.86.803.
Collell, J., Galliero, G., Vermorel, R. et al. 2015. Transport of Multicomponent Hydrocarbon Mixtures in Shale Organic Matter by Molecular Simulations. Journal of Physical Chemistry C 119 (39): 22587–22595. https://doi.org/10.1021/acs.jpcc.5b07242.
Cottin-Bizonne, C., Barrat, J.-L., Bocquet, L. et al. 2003. Low-Friction Flows of Liquid at Nanopatterned Interfaces. Nature Materials 2: 237–240. https://doi.org/10.1038/nmat857.
Cottin-Bizonne, C., Barentin, C., Charlaix, E. et al. 2004. Dynamics of Simple Liquids at Heterogeneous Surfaces: Molecular-Dynamics Simulations and Hydrodynamic Description. The European Physical Journal E 15 (4): 427–438. https://doi.org/10.1140/epje/i2004-10061-9.
Cracknell, R. F., Nicholson, D., and Quirke, N. 1995. Direct Molecular Dynamics Simulation of Flow Down a Chemical Potential Gradient in a Slit-Shaped Micropore. Physical Review Letters 74 (13): 2463–2466. https://doi.org/10.1103/PhysRevLett.74.2463.
Cygan, R. T., Liang, J.-J., and Kalinichev, A. G. 2004. Molecular Models of Hydroxide, Oxyhydroxide, and Clay Phases and the Development of a General Force Field. Journal of Physical Chemistry B 108: 1255–1266. https://doi.org/10.1021/jp0363287.
Deissler, R. G. 1964. An Analysis of Second-Order Slip Flow and Temperature-Jump Boundary Conditions for Rarefied Gases. International Journal of Heat and Mass Transfer 7: 681–694. https://doi.org/10.1016/0017-9310(64)90161-9.
Elgmati, M., Zhang, H., Bai, B. et al. 2011. Submicron-Pore Characterization of Shale Gas Plays. Presented at the SPE North American Unconventional Conference and Exhibition, The Woodlands, Texas, USA, 14–16 June. SPE-144050-MS. https://doi.org/10.2118/144050-MS.
Falk, K., Coasne, B., Pellenq, R. et al. 2015. Subcontinuum Mass Transport of Condensed Hydrocarbons in Nanoporous Media. Nature Communications 6: 6949.
Fan, X.-J., Nhan, P.-T., Yong, N.-T. et al. 2002. Molecular Dynamics Simulation of a Liquid in a Complex Nano Channel Flow. Physics of Fluids 14 (3): 1146–1153. https://doi.org/10.1063/1.1447916.
Fathi, E. and Akkutlu, I. Y. 2013. Lattice Boltzmann Method for Simulation of Shale Gas Transport in Kerogen. SPE J. 18: 27–37. SPE-146821-PA. https://doi.org/10.2118/146821-PA.
Feng, F. and Akkutlu, I. Y. 2015. Flow of Hydrocarbons in Nanocapillary: A Non-Equilibrium Molecular Dynamics Study. Presented at the SPE Asia Pacific Unconventional Resources Conference and Exhibition, Brisbane, Australia, 9–11 November. SPE-177005-MS. https://doi.org/10.2118/177005-MS.
Galea, T. M. and Attard, P. 2004. Molecular Dynamics Study of the Effect of Atomic Roughness on the Slip Length at the Fluid-Solid Boundary During Shear Flow. Langmuir 20 (8): 3477–3482. https://doi.org/10.1021/la035880k.
Hadjiconstantinou, N. G. 2003. Comment on Cercignani’s Second-Order Slip Coefficient. Physics of Fluids 15 (8): 2352–2354. https://doi.org/10.1063/1.1587155.
Haghshenas, B., Clarkson, C. R., and Chen, S. 2013. Multi-Porosity Multi-Permeability Models for Shale Gas Reservoirs. Presented at the SPE Unconventional Resources Conference Canada, Calgary, 5–7 November. SPE-167220-MS, https://doi.org/10.2118/167220-MS.
Heinbuch, U. and Fischer, J. 1989. Liquid Flow in Pores: Slip, No-Slip, or Multilayer Sticking. Physical Review A 40 (2): 1144–1146. https://doi.org/10.1103/PhysRevA.40.1144.
Hess, B., Kutzner, C., Van Der Spoel, D. et al. 2008. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. Journal of Chemical Theory and Computation 4: 435–447. https://doi.org/10.1021/ct700301q.
Ho, T. A., Papavassiliou, D. V., Lee, L. L. et al. 2011. Liquid Water Can Sip on a Hydrophilic Surface. Proc., National Academy of Sciences, USA. 108 (39): 16170–16175. https://doi.org/10.1073/pnas.1105189108.
Hoover, W. G. 1985. Canonical Dynamics: Equilibrium Phase-Space Distributions. Physical Review A. 31: 1695–1697. https://doi.org/10.1103/PhysRevA.31.1695.
Hsia, Y. T. and Domoto, G. A. 1983. An Experimental Investigation of Molecular Rarefaction Effects in Gas Lubricated Bearings at Ultra-Low Clearances. ASME Journal of Lubrication Technology 105: 120–129. https://doi.org/10.1115/1.3254526.
Jabbarzadeh, A., Atkinson, J. D., and Tanner, R. I. 2000. Effect of the Wall Roughness on Slip and Rheological Properties of Hexadecane in Molecular Dynamics Simulation of Couette Shear Flow Between Two Sinusoidal Walls. Physical Review E 61 (1): 690–699.
Javadpour, F., Fisher, D., and Unsworth, M. 2007. Nanoscale Gas Flow in Shale Gas Sediments. J Can Pet Technol 46: 55–61. PETSOC-07-10-06. https://doi.org/10.2118/07-10-06.
Jin, Z. and Firoozabadi, A. 2015. Flow of Methane in Shale Nanopores at Low and High Pressure by Molecular Dynamics Simulations. Journal of Chemical Physics 143 (1): 104315. https://doi.org/10.1063/1.4930006.
Jorgensen, W. L., Maxwell, D. S., and Tirado-Rives, J. 1996. Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. Journal of American Chemical Society 118: 11225–11236. https://doi.org/10.1021/ja9621760.
Kannam, S. K., Todd, B. D., Hansen, J. S. et al. 2011. Slip Flow in Graphene Nanochannels. The Journal of Chemical Physics 135 (14): 144701. https://doi.org/10.1063/1.3648049.
Kannam, S. K., Todd, B. D., Hansen, J. S. et al. 2012. Interfacial Slip Friction at a Fluid/Solid Cylindrical Boundary. The Journal of Chemical Physics 136 (24): 244704. https://doi.org/10.1063/1.4730167.
Karniadakis, G., Beskok, A., and Aluru, N. 2005. Microflows and Nanoflows: Fundamentals and Simulation. Interdisciplinary Applied Mathematics Springer.
Katasho, Y., Liang, Y., Murata, S. et al. 2015. Mechanisms for Enhanced Hydrophobicity by Atomic-Scale Roughness. Scientific Reports 5: 13790. https://doi.org/10.1038/srep13790.
Kazemi, K. and Takbiri-Borujeni, A. 2016. Flow of Gases in Organic Nanoscale Channels: A Boundary-Driven Molecular Simulation Study. Energy & Fuels 30 (1): 8156–8163. https://doi.org/10.1021/acs.energyfuels.6b01456.
Klinkenberg, L. J. 1941. The Permeability of Porous Media to Liquid and Gases. API Drilling and Production Practices, pp. 200–213. New York.
Koplik, J., Banavar, J. R., and Willemsen, J. F. 1988. Molecular Dynamics of Poiseuille Flow and Moving Contact Lines. Physical Review Letters 60 (13): 1282–1285. Not available.
Koplik, J., Banavar, J. R., and Willemsen, J. F. 1989. Molecular Dynamics of Fluid Flow at Solid Surfaces. Physics of Fluids A 1 (5): 781–794. https://doi.org/10.1063/1.857376.
Kunert, C. and Harting, J. 2007. Roughness Induced Boundary Slip in Microchannel Flows. Physical Review Letters 99 (17): 176001. https://doi.org/10.1103/PhysRevLett.99.176001.
Kunert, C. and Harting, J. 2008. Simulation of Fluid Flow in Hydrophobic Rough Microchannels. International Journal of Computational Fluid Dynamics 22 (7): 475–480. https://doi.org/10.1080/10618560802238234.
Lauga, E., Brenner, M., and Stone, H. 2007. Microfluidics: The No-slip Boundary Condition. In Springer Handbook of Experimental Fluid Mechanics, 1219–1240. Springer Berlin Heidelberg.
Lee, T., Charrault, E., and Neto, C. 2014. Interfacial Slip on Rough, Patterned and Soft Surfaces: A Review of Experiments and Simulations. Advances in Colloid and Interface Science 210: 21–38. https://doi.org/10.1016/j.cis.2014.02.015.
Ledyastuti, M., Liang, Y., Kunieda, M. et al. 2012. Asymmetric Orientation of Toluene Molecules at Oil-Silica Interfaces. Journal of Chemical Physics 137: 064703. https://doi.org/10.1063/1.4742696.
Lemmon, E. W., McLinden, M. O., and Friend, D. G. 2005. Thermophysical Properties of Fluid Systems, NIST Chemistry WebBook, NIST Standard Reference Database No. 69, ed. P. J. Linstrom and W. G. Mallard. National Institutes of Standards and Technology: Gaithersburg, Maryland.
Li, J., Liao, D., and Yip, S. 1998. Coupling Continuum to Molecular Dynamics Simulation: Reflecting Particle Method and the Field Estimator. Physical Review E 57 (6): 7259–7267.
Loucks, R. G., Reed, R. M., Ruppel, S. C. et al. 2009. Morphology, Genesis, and Distribution of Nanometer-Scale Pores in Siliceous Mudstones of the Mississippian Barnett Shale. Journal of Sedimentary Research 79: 848–861. https://doi.org/10.2110/jsr.2009.092.
Milliken, K. L., Rudnicki, M., Awwiller, D. N. et al. 2013. Organic Matter–Hosted Pore System, Marcellus Formation (Devonian), Pennsylvania. AAPG Bull. 97 (2): 177–200. https://doi.org/10.1306/07231212048.
Mitsuya, Y. 1993. Modified Reynolds Equation for Ultra-Thin Film Gas Lubrication Using 1.5-Order Slip-Flow Model and Considering Surface Accommodation Coefficient. Journal of Tribology 115: 289–294. https://doi.org/10.1115/1.2921004.
Mo, G. and Rosenberger, F. 1990. Molecular Dynamics Simulation of Flow in a Two-Dimensional Channel With Atomically Rough Walls. Physical Review A 42 (8): 4688–4692. https://doi.org/10.1103/PhysRevA.42.4688.
Nagayama, G. and Cheng, P. 2004. Effects of Interface Wettability on Microscale Flow by Molecular Dynamics Simulation. International Journal of Heat and Mass Transfer 47 (3): 501–513. https://doi.org/10.1016/j.ijheatmasstransfer.2003.07.013.
Neto, C., Evans, D. R., Bonaccurso, E. et al. 2005. Boundary Slip in Newtonian Liquids: A Review of Experimental Studies. Reports on Progress in Physics 68 (12): 2859. https://doi.org/10.1088/0034-4885/68/12/R05.
Noorian, H., Toghraie, D., and Azimian, A. R. 2014. Molecular Dynamics Simulation of Poiseuille Flow in a Rough Nano Channel With Checker Surface Roughnesses Geometry. Heat and Mass Transfer 50 (1): 105–113. https://doi.org/10.1007/s00231-013-1232-x.
Nosé, S. A. 1984. Molecular Dynamics Method for Simulations in the Canonical Ensemble. Molecular Physics 52: 255–258. https://doi.org/10.1080/00268978400101201.
Priezjev, N. V. and Troian, S. M. 2006. Influence of Periodic Wall Roughness on the Slip Behavior at Liquid/Solid Interfaces: Molecular-Scale Simulations Versus Continuum Predictions. Journal of Fluid Mechanics 554: 25–46. https://doi.org/10.1017/S0022112006009086.
Riewchotisakul, S. and Akkutlu, I. Y. 2016. Adsorption-Enhanced Transport of Hydrocarbons in Organic Nanopores. SPE J. 21: 1960–1969. SPE-175107-PA. https://doi.org/10.2118/175107-PA.
Roy, S., Raju, R., Chuang, H. F. et al. 2003. Modeling Gas Flow Through Microchannels and Nanopores. Journal of Applied Physics 93: 4870–4879. https://doi.org/10.1063/1.1559936.
Sawa, Y., Liang, Y., Murata, S. et al. 2015. Pore-Filling Nature of CH4 Adsorption Behavior in Kerogen Nanopores: A Molecular View Based on Full-Atom Kerogen Models. Presented at the SPE Asia Pacific Unconventional Resources Conference and Exhibition, Brisbane, Australia, 9–11 November. SPE-176999-MS. https://doi.org/10.2118/176999-MS.
Schamberg, R. 1947. The Fundamental Differential Equations and the Boundary Conditions for High Speed Slip-Flow, and Their Application to Several Specific Problems. PhD dissertation, California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-12272004-161736.
Schwartz, A., Smart, E., Dixon, M. et al. 2013. Use of Digital Imaging for Improved Evaluation of Unconventional Reservoirs. Presented at the SPE Reservoir Characterization and Simulation Conference and Exhibition, Abu Dhabi, 16–18 September. SPE-166065-MS. https://doi.org/10.2118/166065-MS.
Shinn, J. H. 1984. From Coal to Single-Stage and Two-Stage Products: A Reactive Model of Coal Structure. Fuel 63 (9): 1187–1196. https://doi.org/10.1016/0016-2361(84)90422-8.
Sokhan, V. P., Nicholson, D., and Quirke, N. 2001. Fluid Flow in Nanopores: An Examination of Hydrodynamic Boundary Conditions. Journal of Chemical Physics 115 (8): 3878–3887. https://doi.org/10.1063/1.1387976.
Sokhan, V. P., Nicholson, D., and Quirke, N. 2002. Fluid Flow in Nanopores: Accurate Boundary Conditions for Carbon Nanotubes. Journal of Chemical Physics 117 (18): 8531–8539. https://doi.org/10.1063/1.1512643.
Sommerfeld, A. 1908. “Ein Beitrag zur hydrodynamischen Erkläerung der turbulenten Flüssigkeitsbewegüngen (A Contribution to Hydrodynamic Explanation of Turbulent Fluid Motions)”. International Congress of Mathematicians 3: 116–124.
Sondergeld, C. H., Ambrose, R. J., Rai, C. S. et al. 2010. Micro-Structural Studies of Gas Shales. Presented at the SPE Annual Technical Conference and Exhibition, Pittsburgh, Pennsylvania, USA, 23–25 February. SPE-131771-MS. https://doi.org/10.2118/131771-MS.
Sreekanth, A. K. 1969. Slip Flow Through Long Circular Tubes. In Proc., of the 6th International Symposium on Rarefied Gas Dynamics, ed. L. Trilling and H. Y. Wachman, pp. 667–680. New York: Academic Press.
Sun, M. and Ebner, C. 1993. Molecular Dynamics Study of Flow at a Fluid-Wall Interface. Physical Review Letters 69 (24): 3491–3494. https://doi.org/10.1103/PhysRevLett.69.3491.
Swami, V. and Settari, A. 2012. A Pore Scale Gas Flow Model for Shale Gas Reservoir. Presented at the SPE Americas Unconventional Resources Conference, Pittsburgh, Pennsylvania, USA, 5–7 June. SPE-155756-MS. https://doi.org/10.2118/155756-MS.
Tang, G. H., Tao, W. Q., and He, Y. L. 2005. Gas Slippage Effect on Microscale Porous Flow Using the Lattice Boltzmann Method. Physical Review E 72: 056301. https://doi.org/10.1103/PhysRevE.72.056301.
Thompson, P. A. and Robbins, M. O. 1989. Simulations of Contact-Line Motion: Slip and the Dynamic Contact Angle. Physical Review Letters 63 (7): 766–769. https://doi.org/10.1103/PhysRevLett.63.766.
Thompson, P. A. and Robbins, M. O. 1990. Shear Flow Near Solids: Epitaxial Order and Flow Boundary Conditions. Physical Review A 41 (12): 6830–6837. https://doi.org/10.1103/PhysRevA.41.6830.
Thompson, P. A. and Troian, S. M. 1997. A General Boundary Condition for Liquid Flow at Solid Surfaces. Nature 389: 360–362. https://doi.org/10.1038/38686.
Travis, K. P., Todd, B. D., and Evans, D. J. 1997. Departure From Navier-Stokes Hydrodynamics in Confined Liquids. Physical Review E 55 (4): 4288–4295. https://doi.org/10.1103/PhysRevE.55.4288.
Travis, K. P., Gubbins, K. E., and Carolina, N. 2000. Poiseuille Flow of Lennard-Jones Fluids in Narrow Slit Pores. Journal of Chemical Physics 112: 1984–1994. https://doi.org/10.1063/1.480758.
Viswanathan, R. K. K., Minh, C. C., Zielinski, L. et al. 2011. Characterization of Gas Dynamics in Kerogen Nanopores by NMR. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 30 October–2 November. SPE-147198-MS. https://doi.org/10.2118/147198-MS.
Wang, J., Wolf, R. M., Caldwell, J. W. et al. 2004. Development and Testing of a General Amber Force Field. Journal of Computational Chemistry 25 (9): 1157–1174. https://doi.org/10.1002/jcc.20035.
Wang, S., Javadpour, F., and Feng, Q. 2016a. Molecular Dynamics Simulations of Oil Transport Through Inorganic Nanopores in Shale. Fuel 171: 74–86. https://doi.org/10.1016/j.fuel.2015.12.071.
Wang, S., Javadpour, F., and Feng, Q. 2016b. Fast Mass Transport of Oil and Supercritical Carbon Dioxide Through Organic Nanopores in Shale. Fuel 181: 741–758. https://doi.org/10.1016/j.fuel.2016.05.057.
Wang, G. X., Massarotto, P., and Rudolph, V. 2009. An Improved Permeability Model of Coal for Coalbed Methane Recovery and CO2 Geosequestration. International Journal of Coal Geology 77 (1–2): 127–136. https://doi.org/10.1016/j.coal.2008.10.007.
Wu, T. and Zhang, D. 2016. Impact of Adsorption on Gas Transport in Nanopores. Scientific Reports 6: 23629. https://doi.org/10.1038/srep23629.
Xu, J. L. and Zhou, Z. Q. 2004. Molecular Dynamics Simulation of Liquid Argon Flow at Platinum Surfaces. Heat and Mass Transfer 40 (11): 859–869. https://doi.org/10.1007/s00231-003-0483-3.
Zhang, X., Xiao, L., Shan, X. et al. 2014. Lattice Boltzmann Simulation of Shale Gas Transport in Organic Nano-Pores. Scientific Reports 4: 4843. https://doi.org/10.1038/srep04843.
Zhang, C. and Chen, Y. 2014. Slip Behavior of Liquid Flow in Rough Nanochannels. Chemical Engineering and Processing: Process Intensification 85: 203–208. https://doi.org/10.1016/j.cep.2014.09.003.
Ziarani, A. S. and Aguilera, R. 2012. Knudsen’s Permeability Correction for Tight Porous Media. Transport in Porous Media 91: 239–260. https://doi.org/10.1007/s11242-011-9842-6.