Transport Model for Gas and Water in Nanopores of Shale Gas Reservoirs
Publication: Journal of Energy Engineering
Volume 147, Issue 4
Abstract
Because of the many nanoscale pores in shale gas reservoirs (SGRs), the fluid transport mechanisms in shale are complex. Also, previous research has shown that there exists water in the shale plays. Hence, two-phase gas-water transport model construction becomes very important so as to increase accuracy in numerical simulation work. However, most of the current study is still focused on single-phase gas transport. In this paper, based on the second slip model coupled with the fluid single-pipe flow equation, the Knudsen and surface diffusions, and combined with the fractal theory, the relative permeability model for gas-water in shale was constructed. The model reliability was proven by using the available two-phase gas-water relative permeability data. A sensitivity analysis has been carried out based on the proposed model. The results show that with the pressure decreasing, the relative permeability of gas increases. The increase of the pore size distribution fractal dimensions () and fractal dimension () caused the gas relative permeability () to increase. The increases with the increase of and . The influence of the viscous slip flow, Knudsen diffusion, and surface diffusion are trade-offs, which are mainly controlled by water saturation () and pressure (). The is extremely sensitive when . Under low pressure and low water saturation, the effect of viscous slip flow is secondary. And its contribution increases gradually and becomes the main role with the increase of water saturation or pressure. The effect of the Knudsen diffusion is negligible when and the water saturation . However, it cannot be ignored under other conditions. The influence of surface diffusion reached 21.64%–72.78% when and . A surface diffusion contribution of less than 4.25% was obtained when and .
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Data Availability Statement
All data that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work is funded by the National Natural Science Foundation of China (No. 51704265, PI: Dr. Chaohua Guo), the Outstanding Talent Development Project of China University of Geosciences (CUG20170614, PI: Dr. Chaohua Guo), and the Fundamental Research Funds for National University, China University of Geosciences (Wuhan) (1810491A07).
References
Alnoaimi, K., and A. Kovscek. 2013. “Experimental and numerical analysis of gas transport in shale including the role of sorption.” In Proc., SPE Annual Technical Conf. and Exhibition. Richardson, TX: Society of Petroleum Engineers. https://doi.org/10.2118/166375-MS.
Behie, G., and J. Trangenstein. 1981. Multiphase flow in porous media. Houston: Gulf Publication.
Beskok, A., and G. Karniadakis. 1999. “Report: 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.
Bonnet, E., O. Bour, N. E. Odling, P. Davy, I. Main, P. Cowie, and B. Berkowitz. 2001. “Scaling of fracture systems in geological media.” Rev. Geophys. 39 (3): 347–383. https://doi.org/10.1029/1999RG000074.
Cao, B.-Y., J. Sun, M. Chen, and Z.-Y Guo. 2009. “Molecular momentum transport at fluid-solid interfaces in MEMS/NEMS: A review.” Int. J. Mol. Sci. 10 (11): 4638–4706. https://doi.org/10.3390/ijms10114638.
Chen, Y., and R. Yang. 1991. “Concentration dependence of surface diffusion and zeolitic diffusion.” AIChE J. 37 (10): 1579–1582. https://doi.org/10.1002/aic.690371015.
Choi, J., D. Do, and H. Do. 2001. “Surface diffusion of adsorbed molecules in porous media: Monolayer, multilayer, and capillary condensation regimes.” Ind. Eng. Chem. Res. 40 (19): 4005–4031. https://doi.org/10.1021/ie010195z.
Civan, F. 2010. “Effective correlation of apparent gas permeability in tight porous media.” Transp. Porous Media 82 (2): 375–384. https://doi.org/10.1007/s11242-009-9432-z.
Civan, F., C. Rai, and C. Sondergeld. 2011. “Shale-gas permeability and diffusivity inferred by improved formulation of relevant retention and transport mechanisms.” Transp. Porous Media 86 (3): 925–944. https://doi.org/10.1007/s11242-010-9665-x.
Coppens, M., and A. Dammers. 2006. “Effects of heterogeneity on diffusion in nanopores: From inorganic materials to protein crystals and ion channels.” Fluid Phase Equilib. 241 (1–2): 308–316. https://doi.org/10.1016/j.fluid.2005.12.039.
Cui, X., A. Bustin, and R. Bustin. 2009. “Measurements of gas permeability and diffusivity of tight reservoir rocks: Different approaches and their applications.” Geofluids 9 (3): 208–223. https://doi.org/10.1111/j.1468-8123.2009.00244.x.
Cui, Y., Q. Zhang, and X. Yang. 2003. “Adsorption capacity and isosteric heat of methane adsorption for various types of coal.” [In Chinese.] Nat. Gas Ind. 23 (4): 130–137.
Dang, W., J. Zhang, H. Nie, F. Wang, X. Tang, N Wu, Q. Chen, X. Wei, and R. Wang. 2020. “Isotherms, thermodynamics and kinetics of ethane-shale adsorption pair under supercritical condition: Implications for understanding the nature of shale gas adsorption process.” Chem. Eng. J. 383 (Mar): 123191. https://doi.org/10.1016/j.cej.2019.123191.
Darabi, H., A. Ettehad, F. Javadpour, and K. Sepehrnoori. 2012. “Gas flow in ultra-tight shale strata.” J. Fluid Mech. 710 (Nov): 641–658. https://doi.org/10.1017/jfm.2012.424.
Deng, J., W. Zhu, and Q. Ma. 2014. “A new seepage model for shale gas reservoir and productivity analysis of fractured well.” Fuel 124 (May): 232–240. https://doi.org/10.1016/j.fuel.2014.02.001.
Dongari, N., A. Sharma, and F. Durst. 2009. “Pressure-driven diffusive gas flows in micro-channels: From the Knudsen to the continuum regimes.” Microfluid. Nanofluid. 6 (5): 679–692. https://doi.org/10.1007/s10404-008-0344-y.
Feng, D., X. Li, X. Wang, J. Li, F. Sun, Z. Sun, T. Zhang, P. Li, Yu. Chen, and X. Zhang. 2018. “Water adsorption and its impact on the pore structure characteristics of shale clay.” Appl. Clay Sci. 155 (Apr): 126–138. https://doi.org/10.1016/j.clay.2018.01.017.
Guo, L., X. Peng, and Z. Wu. 2008. “Dynamical characteristics of methane adsorption on monolith nanometer activated carbon.” [In Chinese.] J. Chem. Ind. Eng. 59 (11): 2726–2732.
Hu, Y., D. Devegowda, A. Striolo, A. T. Van Phan, T. A. Ho, F. Civan, and R. Sigal. 2015. “Microscopic dynamics of water and hydrocarbon in shale-kerogen pores of potentially mixed-wettability.” SPE J. 20 (1): 112–124. https://doi.org/10.2118/167234-PA.
Hwang, S., and K. Kammermeyer. 1966. “Surface diffusion in microporous media.” Can. J. Chem. Eng. 44 (2): 82–89. https://doi.org/10.1002/cjce.5450440206.
Inyang, H. I. 2010. “Promotion of sustainable oil and gas operations in Africa.” J. Energy Eng. 136 (3): 67. https://doi.org/10.1061/(ASCE)EY.1943-7897.0000029.
Javadpour, F. 2009. “Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone).” J. Can. Pet. Technol. 48 (8): 16–21. https://doi.org/10.2118/09-08-16-DA.
Javadpour, F., D. Fisher, and M. Unsworth. 2007. “Nanoscale gas flow in shale gas sediments.” J. Can. Pet. Technol. 46 (10): 55–61. https://doi.org/10.2118/07-10-06.
Karniadakis, G., A. Beskok, and N. Aluru. 2005. Microflows and nanoflows. New York: Springer.
Katz, A., and A. Thompson. 1985. “Fractal sandstone pores: Implications for conductivity and pore formation.” Phys. Rev. Lett. 54 (12): 1325–1328. https://doi.org/10.1103/PhysRevLett.54.1325.
Klinkenberg, L. 1941. “The permeability of porous media to liquids and gases.” In Drilling and production practice, 200–213. Washington, DC: American Petroleum Institute.
Krishna, R., and J. Wesselingh. 1997. “The Maxwel Stefan approach to mass transfer.” Chem. Eng. Sci. 52 (6): 861–911. https://doi.org/10.1016/S0009-2509(96)00458-7.
Li, J., S. Wang, S. Lu, P. Zhang, J. Cai, J. Zhao, and W. Li. 2019. “Microdistribution and mobility of water in gas shale: A theoretical and experimental study.” Mar. Pet. Geol. 102 (Apr): 496–507. https://doi.org/10.1016/j.marpetgeo.2019.01.012.
Li, T., H. Song, J. Wang, Y. Wang, and J. Killough. 2016. “An analytical method for modeling and analysis gas-water relative permeability in nanoscale pores with interfacial effects.” Int. J. Coal Geol. 159 (Apr): 71–81. https://doi.org/10.1016/j.coal.2016.03.018.
Majumdar, A., and B. Bhushan. 1990. “Role of fractal geometry in roughness characterization and contact mechanics of surfaces.” J. Tribol 112 (2): 205–216. https://doi.org/10.1115/1.2920243.
Mi, L., H. Jiang, J. Li, and T. Ye. 2014. “Mathematical characterization of permeability in shale reservoirs.” [In Chinese.] Acta Pet. Sin. 35 (5): 928–934. https://doi.org/10.7623/syxb201405013.
Myers, T. 2011. “Why are slip lengths so large in carbon nanotubes?” Microfluid. Nanofluid. 10 (5): 1141–1145. https://doi.org/10.1007/s10404-010-0752-7.
Naraghi, M., and F. Javadpour. 2015. “A stochastic permeability model for the shale-gas systems.” Int. J. Coal Geol. 140 (Feb): 111–124. https://doi.org/10.1016/j.coal.2015.02.004.
Piquemal, J. 1994. “Saturated steam relative permeabilities of unconsolidated porous media.” Transp. Porous Media 17 (2): 105–120. https://doi.org/10.1007/BF00624727.
Qing, W., and L. Zhi. 2019. “A fractal model of water transport in shale reservoirs.” Chem. Eng. Sci. 198 (Apr): 62–73. https://doi.org/10.1016/j.ces.2018.12.042.
Reif, R. 1965. Fundamentals of statistical and thermal physics. Boston: McGraw-Hill.
Roy, S., R. Raju, H. F. Chuang, B. A. Cruden, and M. Meyyappan. 2003. “Modeling gas flow through microchannels and nanopores.” J. Appl. Phys. 93 (8): 4870. https://doi.org/10.1063/1.1559936.
Sang, G., S. Liu, D. Elsworth, Y. Yang, and L. Fan. 2020. “Evaluation and modeling of water vapor sorption and transport in nanoporous shale.” Int. J. Coal Geol. 228 (Aug): 103553. https://doi.org/10.1016/j.coal.2020.103553.
Shen, W., Y. Xu, X. Li, W. Huang, and J. Gu. 2016. “Numerical simulation of gas and water flow mechanism in hydraulically fractured shale gas reservoirs.” J. Nat. Gas Sci. Eng. 35 (Sep): 726–735. https://doi.org/10.1016/j.jngse.2016.08.078.
Sheng, M., G. Li, Z. Huang, and S. Tian. 2014. “Shale gas transient flow model with effects of surface diffusion.” [In Chinese.] Acta Pet. Sin. 35 (2): 347–352. https://doi.org/10.7623/syxb201402016.
Singh, H., F. Javadpour, A. Ettehadtavakkol, and H. Darabi. 2014. “Nonempirical apparent permeability of shale.” SPE Reservoir Eval. Eng. 17 (3): 414–424. https://doi.org/10.2118/170243-PA.
Song, W., J. Yao, D. Wang, Y. Li, H. Sun, Y. Yang, and L. Zhang. 2019. “Nanoscale confined gas and water multiphase transport in nanoporous shale with dual surface wettability.” Adv. Water Resour. 130 (Aug): 300–313. https://doi.org/10.1016/j.advwatres.2019.06.012.
Sun, Z., X. Li, and J. Shi. 2017. “Apparent permeability model for real gas transport through shale gas reservoirs considering water distribution characteristic.” Int. J. Heat Mass Transfer 115 (Dec): 1008–1019. https://doi.org/10.1016/j.ijheatmasstransfer.2017.07.123.
Veltzke, T., and J. Thöming. 2012. “An analytically predictive model for moderately rarefied gas flow.” J. Fluid Mech. 698 (May): 406–422. https://doi.org/10.1017/jfm.2012.98.
Wang, J., H. Liu, L. Wang, H. Zhang, H. Luo, and Y. Gao. 2015. “Apparent permeability for gas transport in nanopores of organic shale reservoirs including multiple effects.” Int. J. Coal Geol. 152 (Dec): 50–62. https://doi.org/10.1016/j.coal.2015.10.004.
Wang, S., D. Elsworth, and J. Liu. 2012. “A mechanistic model for permeability evolution in fractured sorbing media.” J. Geophys. Res. 117 (6): B06205. https://doi.org/10.1029/2011JB008855.
Wu, K., X. Li, C. Guo, and Z. Chen. 2015a. “Adsorbed gas surface diffusion and bulk gas transport in nanopores of shale reservoirs with real gas effect adsorption mechanical coupling.” In Proc., SPE Reservoir Simulation Symp. Richardson, TX: Society of Petroleum Engineers.
Wu, K., X. Li, C. Wang, W. Yu, and Z. Chen. 2015b. “Model for surface diffusion of adsorbed gas in nanopores of shale gas reservoirs.” Ind. Eng. Chem. Res. 54 (12): 3225–3236. https://doi.org/10.1021/ie504030v.
Wu, K., X. Li, C. Wang, W. Yu, C. Guo, D. Ji, G. Ren, and Z. Chen. 2014. “Apparent permeability for gas flow in shale reservoirs coupling effects of gas diffusion and desorption.” In Proc., SPE/AAPG/SEG Unconventional Resources Technology Conf. Richardson, TX: Society of Petroleum Engineers.
Wu, L. 2008. “A slip model for rarefied gas flows at arbitrary Knudsen number.” Appl. Phys. Lett. 93 (25): 253103. https://doi.org/10.1063/1.3052923.
Xiong, X., D. Devegowda, G. G. Michel, R. F. Sigal, and F. Civan. 2012. “A fully-coupled free and adsorptive phase transport model for shale gas reservoirs including non-Darcy flow effects.” In Proc., SPE Annual Technical Conf. and Exhibition. Richardson, TX: Society of Petroleum Engineers.
Xu, P., S. Qiu, B. Yu, and Z. Jiang. 2013. “Prediction of relative permeability in unsaturated porous media with a fractal approach.” Int. J. Heat Mass Transfer 64 (Sep): 829–837. https://doi.org/10.1016/j.ijheatmasstransfer.2013.05.003.
Xu, P., and B. Yu. 2008. “Developing a new form of permeability and Kozeny-Carman constant for homogeneous porous media by means of fractal geometry.” Adv. Water Resour. 31 (1): 74–81. https://doi.org/10.1016/j.advwatres.2007.06.003.
Yan, B., Y. Wang, and J. Killough. 2016. “Beyond dual-porosity modeling for the simulation of complex flow mechanisms in shale reservoirs.” Comput. Geosci. 20 (1): 69–91. https://doi.org/10.1007/s10596-015-9548-x.
Yu, B., and P. Cheng. 2002. “A fractal permeability model for bi-dispersed porous media.” Int. J. Heat Mass Transfer 45 (14): 2983–2993. https://doi.org/10.1016/S0017-9310(02)00014-5.
Yu, B., and J. Li. 2001. “Some fractal characters of porous media.” Fractals 9 (3): 365–372. https://doi.org/10.1142/S0218348X01000804.
Yu, B., and W. Liu. 2004. “Fractal analysis of permeabilities for porous media.” AIChE J. 50 (1): 46–57. https://doi.org/10.1002/aic.10004.
Yue, X., H. Wei, and L. Zhang. 2010. “Low pressure gas percolation characteristic in ultra-low permeability porous media.” Transp. Porous Media 85 (1): 333–345. https://doi.org/10.1007/s11242-010-9565-0.
Zhang, D., and T. Yang. 2013. “An overview of shale-gas production.” [In Chinese.] Acta Pet. Sin. 34 (4): 792–801. https://doi.org/10.7623/syxb201304023.
Zhang, T., X. Li, J. Li, D. Feng, K. Wu, J. Shi, Z. Sun, and S. Han. 2018a. “A fractal model for gas–water relative permeability in inorganic shale with nanoscale pores.” Transp. Porous Media 122: 305–331. https://doi.org/10.1007/s11242-018-1006-5.
Zhang, T., X. Li, X. Wang, J. Li, W. Li, W. Zhao, and T. Yao. 2018b. “Modelling the water transport behavior in organic-rich nanoporous shale with generalized lattice Boltzmann method.” Int. J. Heat Mass Transfer 127: 123–134. https://doi.org/10.1016/j.ijheatmasstransfer.2018.07.070.
Zhu, G. Y., L. Liu, Z. M. Yang, X. G. Liu, Y. G. Guo, and Y. T. Cui. 2007. “Experiment and mathematical model of gas flow in low permeability porous media.” In New trends in fluid mechanics research. Berlin: Springer.
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Published In
Journal of Energy Engineering
Volume 147 • Issue 4 • August 2021
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© 2021 American Society of Civil Engineers.
History
Received: Nov 18, 2020
Accepted: Mar 9, 2021
Published online: May 26, 2021
Published in print: Aug 1, 2021
Discussion open until: Oct 26, 2021
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