A New Unified Gas-Transport Model for Gas Flow in Nanoscale Porous Media
- Di Chai (University of Kansas) | Zhaoqi Fan (University of Kansas) | Xiaoli Li (University of Kansas)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- April 2019
- Document Type
- Journal Paper
- 698 - 719
- 2019.Society of Petroleum Engineers
- Knudsen diffusion, Viscous flow, Surface diffusion, Gas transport in nanopores
- 0 in the last 30 days
- 265 since 2007
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A new unified gas-transport model has been developed to characterize single-component real-gas flow in nanoscale organic and inorganic porous media by modifying the Bravo (2007) model. More specifically, a straight capillary tube is characterized by a conceptual layered model consisting of a viscous-flow zone, a Knudsen-diffusion zone, and a surface-diffusion zone. To specify the contributions of the viscous flow and the Knudsen diffusion to the gas transport, the virtual boundary between the viscous-flow and Knudsen-diffusion zones is first determined using an analytical molecular-kinetics approach. As such, the new unified gas-transport model is derived by integrating the weighted viscous flow and Knudsen diffusion, and coupling surface diffusion. The model is also comprehensively scaled up to the bundles-of-tubes model considering the roughness, rarefaction, and real-gas effect. Nonlinear programming methods have been used to optimize the empirical parameters in the newly proposed gas-transport model. Consequently, the newly proposed gas-transport model yields the most accurate molar fluxes compared with the Bravo (2007) model and four other analytical models. One of the advantages of the new unified gas-transport model is its great flexibility, because the Knudsen number is included as an independent variable, which also endows the newly proposed model with the capability to cover the full-flow regimes. In addition, the apparent permeability has been mathematically derived from the new unified gas-transport model. A series of simulations has been implemented using methane gas. It is found through sensitivity analysis that apparent permeability is strongly dependent on pore size, porosity, and tortuosity, and weakly dependent on the surface-diffusivity coefficient and pore-surface roughness. The increased viscosity can reduce the total molar flux in the inorganic pores up to 66.0% under the typical shale-gas-reservoir conditions. The viscous-flow mechanism cannot be neglected at any pore sizes under reservoir conditions, whereas the Knudsen diffusion is found to be important when pore size is smaller than 2 nm and pressure is less than 35.0 MPa. The contribution of surface diffusion cannot be ignored when the pore size is smaller than 10 nm and the pressure is less than 15.0 MPa.
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Akkutlu, I. Y. and Fathi, E. 2012. Multiscale Gas Transport in Shales With Local Kerogen Heterogeneities. SPE J. 17 (4): 1002–1011. SPE-146422-PA. https://doi.org/10.2118/146422-PA.
Al-Hussainy, R., Ramey, H. J. Jr., and Crawford, P. B. 1966. The Flow of Real Gases Through Porous Media. J Pet Technol 18 (5): 624–636. SPE-1243-A-PA. https://doi.org/10.2118/1243-A-PA.
Ambrose, R. J., Hartman, R. C., Diaz-Campos, M. et al. 2012. Shale Gas-in-Place Calculations Part I: New Pore-Scale Considerations. SPE J. 17 (1): 219–229. SPE-131772-PA. https://doi.org/10.2118/131772-PA.
Beskok, A. and Karniadakis, G. E. 1999. A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales. Microscale Thermophys. Eng. 3 (1): 43–77. https://doi.org/10.1080/108939599199864.
Binder, K., Horbach, J., Kob, W. et al. 2004. Molecular Dynamics Simulations. J. Phys. Condens. Matter 16 (5): 429–453. https://doi.org/10.1088/0953-8984/16/5/006.
Bird, G. A. 1994. Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford, UK: Oxford University Press.
Bravo, M. C. 2007. Effect of Transition From Slip to Free Molecular Flow on Gas Transport in Porous Media. J. Appl. Phys. 102 (7): 1–10. https://doi.org/10.1063/1.2786613.
Bui, K. and Akkutlu, I. Y. 2017. Hydrocarbons Recovery From Model-Kerogen Nanopores. SPE J. 22 (3): 854–862. SPE-185162-PA. https://doi.org/10.2118/185162-PA.
Carmichael, D. G. 1980. Computation of Pareto Optima in Structural Design. Int. J. Numer. Meth. Eng. 15 (6): 925–952. https://doi.org/10.1002/nme.1620150610.
Chapman, S. and Cowling, T. G. 1970. The Mathematical Theory of Non-Uniform Gases, third edition. Cambridge, UK: Cambridge EngineeringUniversity Press.
Christou, C. and Dadzie, S. K. 2015. Direct Simulation Monte Carlo Method in Porous Media With Varying Knudsen Number. Presented at the SPE Reservoir Simulation Symposium, Houston, 23–25 February. SPE-173314-MS. https://doi.org/10.2118/173314-MS.
Civan, F. 2010. A Review of Approaches for Describing Gas Transfer Through Extremely Tight Porous Media. AIP Conf. Proc. 1254 (1): 53–58. https://doi.org/10.1063/1.3453838.
Coppens, M. O. and Dammers, A. J. 2006. Effects of Heterogeneity on Diffusion in Nanopores—From Inorganic Materials to Protein Crystals and Ion Channels. Fluid Phase Equilibr. 241 (1): 308–316. https://doi.org/10.1016/j.fluid.2005.12.039.
Cunningham, R. E. and Williams, R. J. J. 1980. Diffusion in Gases and Porous Media. New York City: Plenum Press.
Curtis, J. B. 2002. Fractured Shale-Gas Systems. AAPG Bull. 86 (11): 1921–1938. https://doi.org/10.1306/61EEDDBE-173E-11D7-8645000102C1865D.
Darabi, H., Ettehad, A., Javadpour, F. et al. 2012. Gas Flow in Ultra-Tight Shale Strata. J. Fluid Mech. 710 (10 November): 641–658. https://doi.org/10.1017/jfm.2012.424.
Didar, B. R. and Akkutlu, I. Y. 2013. Pore-Size Dependence of Fluid Phase Behavior and Properties in Organic-Rich Shale Reservoirs. Presented at the SPE International Symposium on Oilfield Chemistry, The Woodlands, Texas, 8–10 April. SPE-164099-MS. https://doi.org/10.2118/164099-MS.
Do, D. D. and Wang, K. 1998. Dual Diffusion and Finite Mass Exchange Model for Adsorption Kinetics in Activated Carbon. AIChE J. 44 (1): 68–82. https://doi.org/10.1002/aic.690440109.
Ertekin, T., King, G. A., and Schwerer, F. C. 1986. Dynamic Gas Slippage: A Unique Dual-Mechanism Approach to the Flow of Gas in Tight Formations. SPE Form Eval 1 (1): 43–52. SPE-12045-PA. https://doi.org/10.2118/12045-PA.
Ewart, T., Perrier, P., Graur, I. et al. 2007. Tangential Momentum Accommodation in Microtube. Microfluid Nanofluidics 3 (6): 689–695. https://doi.org/10.1007/s10404-007-0158-3.
Fathi, E. and Akkutlu, I. Y. 2009. Nonlinear Sorption Kinetics and Surface Diffusion Effects on Gas Transport in Low-Permeability Formations. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 4–7 October. SPE-124478-MS. https://doi.org/10.2118/124478-MS.
Firouzi, M., Alnoaimi, K., Kovscek, A. et al. 2014. Klinkenberg Effect on Predicting and Measuring Helium Permeability in Gas Shales. Int. J. Coal Geol. 123 (1 March): 62–68. https://doi.org/10.1016/j.coal.2013.09.006.
Frenkel, D. and Smit, B. 2001. Understanding Molecular Simulation, second edition. Orlando, Florida: Academic Press.
GAMS Development Corporation. 1987. GAMS: General Algebraic Modeling System software, version 25.1. https://www.gams.com.
Gupta, N., Fathi, E., and Belyadi, F. 2018. Effects of Nano-Pore Wall Confinements on Rarefied Gas Dynamics in Organic Rich Shale Reservoirs. Fuel 220 (15 May): 120–129. https://doi.org/10.1016/j.fuel.2018.01.120.
Haimes, Y. Y., Lasdon, L. S., and Wismer, D. A. 1971. On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization. IEEE Trans. Syst. Man. Cybernet. 1 (3): 296–297. https://doi.org/10.1109/TSMC.1971.4308298.
Javadpour, F. 2009. Nanopores and Apparent Permeability of Gas Flow in Mudrocks (Shales and Siltstone). J Can Pet Technol 48 (8): 16–21. PETSOC-09-08-16-DA. https://doi.org/10.2118/09-08-16-DA.
Javadpour, F., Fisher, D., and Unsworth, M. 2007. Nanoscale Gas Flow in Shale Gas Sediments. J Can Pet Technol 46 (10): 55–61. PETSOC-07-10-06. https://doi.org/10.2118/07-10-06.
Jia, B., Tsau, J.-S., and Barati, R. 2018a. A Workflow to Estimate Shale Gas Permeability Variations During the Production Process. Fuel 220 (15 May): 879–889. https://doi.org/10.1016/j.fuel.2017.11.087.
Jia, B., Tsau, J., and Barati, R. 2018b. Different Flow Behaviors of Low-Pressure and High-Pressure Carbon Dioxide in Shales. SPE J. 23 (4): 233–269. SPE-191121-PA. https://doi.org/10.2118/191121-PA.
Kazemi, M. and Takbiri-Borujeni, A. 2016. Flow of Gases in Organic Nanoscale Channels: A Boundary-Driven Molecular Simulation Study. Energy Fuels 30 (10): 8156–8163. https://doi.org/10.1021/acs.energyfuels.6b01456.
Kennard, E. H. 1938. Kinetic Theory of Gasses. New York City: McGraw-Hill.
Klinkenberg, L. J. 1941. The Permeability of Porous Media to Liquids and Gases. Drilling and Production Practice, 1 January, New York, New York, API-41-200.
Knudsen, M. 1909. Die Gesetze der Molekularströmung und der inneren Riebungsströmung der Gase durch Röhnen. Annalen der Physik 333 (1): 75–130. https://doi.org/10.1002/andp.19093330106.
Kou, R., Alafnan, S. F. K., and Akkutlu, I. Y. 2017. Multi-Scale Analysis of Gas Transport Mechanisms in Kerogen. Transport Porous Med. 116 (2): 493–519. https://doi.org/10.1007/s11242-016-0787-7.
Landry, C. J., Prodanovic, M., and Eichhubl, P. 2016. Direct Simulation of Supercritical Gas Flow in Complex Nanoporous Media and Prediction of Apparent Permeability. Int. J. Coal Geol. 159 (1 April): 120–134. https://doi.org/10.1016/j.coal.2016.03.015.
Liu, Q., Shen, P. and Yang, P. 2002. Pore Scale Network Modeling of Gas Slippage in Tight Porous Media. In Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment, eds. Z. Chen and R. E. Ewing, Vol. 295, 367–375. Providence, Rhode Island: American Mathematical Society.
Loebenstein, W. V. 1971. Calculations and Comparisons of Nonideal Gas Corrections for Use in Gas Adsorption. J. Colloid Interf. Sci. 36 (3): 397–400. https://doi.org/10.1016/0021-9797(71)90011-7.
Loyalka, S. K. and Hamoodi, S. A. 1990. Poiseuille Flow of a Rarefied Gas in a Cylindrical Tube, Solution of Linearized Boltzmann Equation. Phys. Fluids A 2 (11): 2061–2065. https://doi.org/10.1063/1.857681.
Mahmoud, M. A. 2013. Development of a New Correlation of Gas Compressibility Factor (Z-Factor) for High Pressure Gas Reservoir. Presented at the North Africa Technical Conference and Exhibition, Cairo, 15–17 April. SPE-164587-MS. https://doi.org/10.2118/164587-MS.
Mason, E. A., Malinauskas, A. P., and Evans, R. B. III. 1967. Flow and Diffusion of Gases in Porous Media. J. Chem. Phys. 46 (8): 3199–3216. https://doi.org/10.1063/1.1841191.
Michalis, V. K., Kalarakis, A. N., Skouras, E. D. et al. 2010. Rarefaction Effects on Gas Viscosity in the Knudsen Transition Regime. Microfluid. Nanofluid. 9 (4–5): 847–853. https://doi.org/10.1007/s10404-010-0606-3.
Riewchotisakul, S. and Akkutlu, I. Y. 2016. Adsorption Enhanced Transport of Hydrocarbons in Organic Nanopores. SPE J. 21 (6): 1960–1969. SPE-175107-MS. https://doi.org/10.2118/175107-MS.
Roohi, E. and Darbandi, M. 2009. Extending the Navier-Stokes Solutions to Transition Regime in Two-Dimensional Micro- and Nanochannel Flows Using Information Preservation Scheme. Phys. Fluids 21 (8): 1–12. https://doi.org/10.1063/1.3177351.
Roth, A. 1982. Vacuum Technology, revised second edition. Amsterdam: Elsevier.
Roy, S., Raju, R., Chuang, H. F. et al. 2003. Modeling Gas Flow Through Microchannels and Nanopores. J. Appl. Phys. 93 (8): 4870–4879. https://doi.org/10.1063/1.1559936.
Ruíz-Canales, P. and Rufián-Lizana, A. 1995. A Characterization of Weakly Efficient Points. Mathemat. Programm. 68 (1–3): 205–212. https://doi.org/10.1007/BF01585765.
Sakhaee-Pour, A. and Bryant, S. 2012. Gas Permeability of Shale. SPE Res Eval & Eng 15 (4): 401–409. SPE-146944-PA. https://doi.org/10.2118/146944-PA.
Santos, J. M. and Akkutlu, I. Y. 2013. Laboratory Measurement of Sorption Isotherm Under Confining Stress With Pore-Volume Effects. SPE J. 18 (5): 924–931. SPE-162595-PA. https://doi.org/10.2118/162595-PA.
Schaaf, S. A. and Chambre, P. L. 1961. Flow of Rarefied Gases. Princeton, New Jersey: Princeton University Press.
Standing, M. B. and Katz, D. L. 1942. Density of Natural Gases. Trans. AIME 146 (1): 140–149. SPE-942140-G. https://doi.org/10.2118/942140-G.
Sutton, R. P. 2007. Fundamental PVT Calculations for Associated and Gas/Condensate Natural-Gas Systems. SPE J. 10 (3): 270–284. SPE-97099-PA. https://doi.org/10.2118/97099-PA.
Swami, V., Clarkson, C. R., and Settari, A. 2012. Non-Darcy Flow in Shale Nanopores: Do We Have a Final Answer? Presented at the SPE Canadian Unconventional Resources Conference, Calgary, 30 October–1 November. SPE-162665-MS. https://doi.org/10.2118/162665-MS.
Tison, S. A. 1993. Experimental Data and Theoretical Modeling of Gas Flows Through Metal Capillary Leaks. Vacuum 44 (11–12): 1171–1175. https://doi.org/10.1016/0042-207X(93)90342-8.
Veltzke, T. and Tho¨ming, J. 2012. An Analytically Predictive Model for Moderately Rarefied Gas Flow. J. Fluid Mech. 698 (10 May): 406–422. https://doi.org/10.1017/jfm.2012.98.
Villazon, G. G. M., Sigal, R. F., Civan, F. et al. 2011. Parametric Investigation of Shale Gas Production Considering Nano-Scale Pore Size Distribution, Formation Factor, and Non-Darcy Flow Mechanisms. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 30 October–2 November. SPE-147438-MS. https://doi.org/10.2118/147438-MS.
Wasaki, A. and Akkutlu, I. Y. 2015. Permeability of Organic-Rich Shale. SPE J. 20 (6): 1384–1396. SPE-170830-PA. https://doi.org/10.2118/170830-PA.
Wu, K., Chen, Z., and Li, X. 2015. Real Gas Transport Through Nanopores of Varying Cross-Section Type and Shape in Shale Gas Reservoirs. Chem. Eng. J. 281 (1 November): 813–825. https://doi.org/10.1016/j.cej.2015.07.012.
Wu, K., Li, X., Guo, C. et al. 2016. A Unified Model for Gas Transfer in Nanopores of Shale Gas Reservoirs: Coupling Pore Diffusion and Surface Diffusion. SPE J. 21 (5): 1583–1611. SPE-2014-1921039-PA. https://doi.org/10.2118/2014-1921039-PA.
Wu, K., Chen, Z., Li, X. et al. 2017. Flow Behavior of Gas Confined in Nanoporous Shale at High Pressure: Real-Gas Effect. Fuel 205 (1 October): 173–183. https://doi.org/10.1016/j.fuel.2017.05.055.
Xiong, X., Devegowda, D., Villazon, G. G. M. et al. 2012. A Fully-Coupled Free and Adsorptive Phase Transport Model for Shale Gas Reservoirs Including Non-Darcy Flow Effects. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8–10 October. SPE-159758-MS. https://doi.org/10.2118/159758-MS.
Yamaguchi, H., Hanawa, T., Yamamoto, O. et al. 2011. Experimental Measurement on Tangential Momentum Accommodation Coefficient in a Single Microtube. Microfluid. Nanofluid. 11 (1): 57–64. https://doi.org/10.1007/s10404-011-0773-x.
Yu, H., Fan, J., Chen, J. et al. 2018. Pressure-Dependent Transport Characteristic of Methane Gas in Slit Nanopores. Int. J. Heat Mass Tran. 123 (August): 657–667. https://doi.org/10.1016/j.ijheatmasstransfer.2018.03.003.