Nanoscale flow model modelling and analysis of tight reservoir based on viscosity change and interfacial slip characteristics in confined space

Abstract

Understanding the flow mechanisms between hydrocarbons and interfaces in nanopores is critical for fluid supply in tight reservoirs with huge reserves. In this paper, the nanoscale liquid-solid interface interaction potential is analyzed based on the molecular interface theory, and a new nanoscale fluid viscosity model is constructed through the Eyring model, and the fluid velocity and flow flux models in nanopores are derived based on the liquid-solid interface slip condition. In addition, n-pentane flow characteristics in quartz nanopores were investigated with key parameters including: the Hamaker constant, the decay length, the wetting angle, the boundary slip and the flux coefficient. The proposed model is validated in a comparison of theory, simulation and laboratory results. The study results show: (1) influenced by the liquid-solid interfacial effect, there is a viscosity gap between the fluid in the bulk and at the boundary, resulting in a non-linear variation of the flow velocity. Of the multiple microscopic forces considered by the model, Ligshitz-Van der Waals force has the strongest effect in confined pores below 40 nm, and electrostatic force has the weakest effect. When the pore diameter less than 10 nm, the constrained fluid viscosity was improved above 4 times. (2) based on the microscopic liquid-solid interface slip condition, a constrained space velocity model is derived, which indicates that the flow is directly dependent on the effective shear stresses on the fluid and the strength of the liquid-solid interface effect. Under the low shear stress in a tight reservoir, the slip at the liquid-solid interface has obvious linear characteristics, and the slip velocity depends on the effective shear stress. The liquid-solid interfacial effect parameter is increased from 1 to 30, and the slip velocity is reduced to 3.2 Å/ps, which is a 55% reduction. (3) in this paper, the hamaker constant of n-pentane-quartz interface based on the molecular spacing variation and the decay constant for different water types and solute concentrations are obtained, and the effect of the decay length on the flow coefficient of the nano confined flow model is explored for different pore radiuses. The flux coefficient increases with pore radius, and the effect of the decay length is greater for pores < 100 nm.

Keywords

Nanopore flow modelling / Confined space / Viscosity change / Liquid-solid interaction slip / Flow characterization analysis

CRediT authorship contribution statement

Yang Hongnan: Writing-review & editing, Writing-original draft, Methodology, Data curation. Yue Ping: Visualization, Software, Methodology, Funding acquisition. Wang Zhouhua: Validation, Software, Methodology, Investigation. Xiong Yuewen: Writing-original draft, Software, Investigation. Fan Wei: Visualization, Investigation, Data curation. Zhang Shaoshuai: Visualization, Software, Data curation. Shi Wenxiang: Writing-review & editing, Methodology, Data curation.

Declaration of competing interest

No potential conflict of interest is reported by the authors.

Acknowledgements

This work was supported by the Key Program of the National Natural Science Foundation of China [No. U24B200683], Natural Science Foundation of Sichuan Provincial, China [No. 2024NSFSC2012].

References

[1] B. Ning, D. Ren, H. Wang, H. Zhang, J. Guo, N. Fu, J. Lii, Q. Li, Multi-scale combination characterization of micropore structure of tight sandstone gas reservoirs, Fault-Block Oil Gas Field 31 (2024) 34-41, https://doi.org/10.6056/dkyqt202401005.

[2] J. Qian, Y. Jiang, T. Luo, Y. Yang, Y. Fu, W. Chen, C. Sun, Z. Wang, Micro-scopic pore and fracture evolution characteristics and influencing factors during imbibition process of shale reservoirs: a case study of the first section of the first member of Longmaxi Formation, western Chongqing area, Sichuan Basin, Pet. Geol. Exp. 46 (2024) 1336-1348, https://doi.org/10.11781/sysydz2024061336.

[3] Y. Ma, J. Zhao, L. Sun, Y. Bao, Q. Cao, X. Gong, Z. Chen, H. Wang, Microscopic occurrence characteristics and seepage law of water bodies in gas reservoir under stress: a case study of tight reservoirs in the eighth member of Permian Shihezi Formation, Shenmu Gas Field, Ordos Basin, Pet. Geol. Exp. 45 (2023) 466-473, https://doi.org/10.11781/sysydz202303466.

[4] L. Huang, X. Feng, Q. Yang, J. Wu, X. Yang, S. Huang, Microscopic occurrence characteristics of methane in kerogen nanopores of deep shale reservoirs, Pet. Drilling Tech. 51 (2023) 112-120, https://doi.org/10.11911/syztjs.2023086.

[5] X. Han, Z. Song, P. Li, S. Deng, Y. Song, Y. Zhang, C. Cao, Z. Yang, Simulation of pore-scale microscopic spontaneous imbibition of shale based on level-set method, Pet. Geol. Recovery Eff. 31 (2024) 63-71, https://doi.org/10.13673/j.pgre.202307028.

[6] L. Chen, C. Jia, R. Zhang, P. Yue, X. Jiang, J. Wang, Z. Su, Y. Xiao, Y. Lv, High-pressure capacity expansion and water injection mechanism and indicator curve model for fractured-vuggy carbonate reservoirs, Petroleum 10 (2024) 511-519, https://doi.org/10.1016/j.petlm.2024.01.001.

[7] X. Wang, J. Huan, X. Peng, C. Zhang, W. Yuan, Y. Wang, Flow mechanism and pore structures of tight sandstone based on digital core analysis, Pet. Geol. Recovery Eff. 29 (2022) 22-30, https://doi.org/10.13673/j.cnki.cn37-1359/te.202109036.

[8] C. Huang, P.Y. K Choi, K. Nandakumar, W.K. Larry, Comparative study between continuum and atomistic approaches of liquid flow through a finite length cylindrical nanopore, J. Chem. Phys. 126 (2007) 224702, https://doi.org/10.1063/1.2739541.

[9] R. Cui, S.M. Hassanizadeh, S. Sun, Pore-network modeling of flow in shale nanopores: network structure, flow principles, and computational algorithms, Earth Sci. Rev. 234 (2022) 104203, https://doi.org/10.1016/j.earscirev.2022.104203.

[10] C. Sun, R. Zhou, Z. Zhao, B. Bai, Extending the classical continuum theory to describe water flow through two-dimensional nanopores, Langmuir 37 (2021) 6158-6167, https://doi.org/10.1021/acs.langmuir.1c00298.

[11] S. Roy, R. Raju, H. Chuang, J. Appl. Modeling gas flow through microchannels and nanopores, Phys. 93 (2003) 4870-4879, https://doi.org/10.1063/1.1559936.

[12] M.M. Kratzer, S.K. Bhatia, A.Y. Klimenko, J. Chem. Stochastic models of free-molecular nanopore flows, Phys. 158 (2023), https://doi.org/10.1063/5.0148289.

[13] W. Ren, G. Li, S. Tian, M. Sheng, X. Fan, An analytical model for real gas flow in shale nanopores with non-circular cross-section, AIChE J. 62 (2016) 2893-2901, https://doi.org/10.1002/aic.15254.

[14] W. Song, J. Yao, D. Wang, Y. Li, H. Sun, Y. Yang, Dynamic pore network modelling of real gas transport in shale nanopore structure, J. Petrol. Sci. Eng. 184 (2020) 106506, https://doi.org/10.1016/j.petrol.2019.106506.

[15] F. Sun, Y. Yao, G. Li, S. Zhang, Z. Xu, Y. Shi, X. Li, A slip-flow model for oil transport in organic nanopores, J. Petrol. Sci. Eng. 172 (2019) 139-148, https://doi.org/10.1016/j.petrol.2018.09.045.

[16] J. Cai, X. Qin, X. Xia, X. Jiao, H. Chen, H. Wang, Y. Xia, Numerical modeling of multiphase flow in porous media considering micro-and nanoscale effects: a comprehensive review, Gas Sci. Eng. 131 (2024) 205441, https://doi.org/10.1016/j.jgsce.2024.205441.

[17] C. Sun, K. Tang, R. Zhou, B. Bai, Two-phase imbibition of water-oil displacement in silica nanochannels, Int. J. Multiphas. Flow 172 (2024) 104710, https://doi.org/10.1016/j.ijmultiphaseflow.2023.104710.

[18] Y.H. Tsao, Y.C. Liao, H.K. Tsao, Channel width-dependent viscosity and slip length in nanoslits and effect of surface wettability, Phys. Fluids 36 (2024) 053608, https://doi.org/10.1063/5.0208948.

[19] H. Wang, W. Wang, Y. Su, Z. Jin, Lattice Boltzmann model for oil/water two-phase flow in nanoporous media considering heterogeneous viscosity, liquid/solid, and liquid/liquid slip, SPE J. 27 (2022) 3508-3524, https://doi.org/10.2118/210564-PA.

[20] A. Alizadeh Pahlavan, J.B. Freund, Effect of solid properties on slip at a fluid-solid interface, Phys. Rev. E 83 (2011) 021602, https://doi.org/10.1103/PhysRevE.83.021602.

[21] K. Wu, Z. Chen, J. Xu, Y. Hu, J. Li, X. Dong, Y. Liu, M. Chen, A Universal Model of Water Flow through Nanopores in Unconventional Reservoirs: Relationships between Slip, Wettability and Viscosity, SPE Annual Technical Conference and Exhibition, UAE, Dubai, September 2016, https://doi.org/10.2118/181543-MS.

[22] J. Zhang, H. Song, W. Zhu, J. Wang, Liquid transport through nanoscale porous media with strong wettability, Transport Porous Media MED 140 (2021) 697-711, https://doi.org/10.1007/s11242-020-01519-5.

[23] D. Fan, W. Wang, A. Ettehadtavakkol, Y. Su, Confinement Facilitates Wetting Liquid Slippage through Mixed-Wet and Heterogeneous Nanoporous Shale Rocks, SPE/AAPG/SEG Unconventional Resources Technology Conference, Denver, Colorado, USA, July 2019, https://doi.org/10.15530/urtec-2019-520.

[24] S. Peng, Does Liquid Slip Flow Occur in Unconventional Reservoir Rocks? A Laboratory Study of Liquid Permeability, SPE/AAPG/SEG Unconventional Resources Technology Conference, Denver, Colorado, USA, June 2023, https://doi.org/10.15530/urtec-2023-3859466.

[25] A. Martini, A. Roxin, R.Q. Snurr, Q. Wang, S. Lichter, Molecular mechanisms of liquid slip, J. Fluid Mech. 600 (2008) 257-269, https://doi.org/10.1017/S0022112008000475.

[26] M. Sahraoui, M. Kaviany, Slip and no-slip velocity boundary conditions at interface of porous, plain media, Int. J. Heat Mass Tran. 35 (1992) 927-943, https://doi.org/10.1016/0017-9310(92)90258-T.

[27] V. Sofonea, R.F. Sekerka, Boundary conditions for the upwind finite difference Lattice Boltzmann model: evidence of slip velocity in micro-channel flow, J. Comput. Phys. 207 (2005) 639-659, https://doi.org/10.1016/j.jcp.2005.02.003.

[28] J.J. Thalakkottor, K. Mohseni, Unified slip boundary condition for fluid flows, Phys. Rev. E 94 (2016) 023113, https://doi.org/10.1103/PhysRevE.94.023113.

[29] F. Wang, Y. Zhao, Slip boundary conditions based on molecular kinetic theory: the critical shear stress and the energy dissipation at the liquid-solid interface, Soft Matter 7 (2011) 8628-8634, https://doi.org/10.1039/C1SM05543G.

[30] S.T. Bose, P. Moin, A dynamic slip boundary condition for wall-modeled large-eddy simulation, Phys. Fluids 26 (2014) 015104, https://doi.org/10.1063/1.4849535.

[31] L. Szalmás, Slip-flow boundary condition for straight walls in the lattice Boltzmann model, Phys. Rev. E 73 (2006) 066710, https://doi.org/10.1103/PhysRevE.73.066710.

[32] I.J. Rao, K.R. Rajagopal, The effect of the slip boundary condition on the flow of fluids in a channel, Acta Mech. 135 (1999) 113-126, https://doi.org/10.1007/BF01305747.

[33] C. Neto, D.R. Evans, E. Bonaccurso, H.J. Butt, V.S.J. Craig, Boundary slip in Newtonian liquids: a review of experimental studies, Rep. Prog. Phys. 68 (2005) 2859, https://doi.org/10.1088/0034-4885/68/12/R05.

[34] J.N. Israelachvili, Intermolecular and Surface Forces[M]. 3ed. America, Academic Press, 2015.

[35] W. Sparreboom, A.vanden Berg, J.C.T. Eijkel, Principles and applications of nanofluidic transport, Nat. Nanotechnol. 4 (2009) 713-720, https://doi.org/10.1038/nnano.2009.332.

[36] H.C. Hamaker, The London — van der Waals attraction between spherical particles, Physica 4 (1937) 1058-1072, https://doi.org/10.1016/S0031-8914(37)80203-7.

[37] W.C. Tian, Research on MEMS and Nanocontacts[D], University of Electronic Science and Technology, Xi'an, 2004.

[38] N.R. Tas, J. Haneveld, H.V. Jansen, M. Elwenspoek, A. vanden Berg, Capillary filling speed of water in nanochannels, Appl. Phys. Lett. 85 (2004) 3274-3276, https://doi.org/10.1063/1.1804602.

[39] D. Erickson, D. Li, C. Werner, An improved method of determining the ζ-potential and surface conductance, J. Colloid Interf. Sci. 232 (2000) 186-197, https://doi.org/10.1006/jcis.2000.7153.

[40] F. Wang, Y. Zhu, H. Wu, Structure and transport of confined liquids in nanochannels, Science China: Physics, mechanics, Astronomy 48 (2018) 117-133, https://doi.org/10.1360/SSPMA2018-00161.

[41] D. Feng, X. Li, X. Wang, J. Li, T. Zhang, Z. Sun, M. He, Q. Liu, J. Qin, S. Han, Capillary filling of confined water in nanopores: coupling the increased viscosity and slippage, Chem. Eng. Sci. 186 (2018) 228-239, https://doi.org/10.1016/j.ces.2018.04.055.

[42] H. Eyring, Viscosity, plasticity, and diffusion as examples of absolute reaction rates, J. Chem. Phys. 4 (1936) 283-291, https://doi.org/10.1063/1.1749836.

[43] J. Baudry, E. Charlaix, A. Tonck, D. Mazuyer, Experimental evidence for a large slip effect at a nonwetting fluid-solid interface, Langmuir 17 (2001) 5232-5236, https://doi.org/10.1021/la0009994.

[44] E. Bonaccurso, M. Kappl, H.J. Butt, Hydrodynamic force measurements: boundary slip of water on hydrophilic surfaces and electrokinetic effects, Phys. Rev. Lett. 88 (2002) 076103, https://doi.org/10.1103/PhysRevLett.88.076103.

[45] O.I. Vinogradova, K. Koynov, A. Best, F. Feuillebois, Direct measurements of hydrophobic slippage using double-focus fluorescence cross-correlation, Phys. Rev. Lett. 102 (2009) 118302, https://doi.org/10.1103/PhysRevLett.102.118302.

[46] S. Lichter, A. Roxin, S. Mandre, Mechanisms for liquid slip at solid surfaces, Phys. Rev. Lett. 93 (2004) 086001, https://doi.org/10.1103/PhysRevLett.93.086001.

[47] A. Martini, H.Y. Hsu, N.A. Patankar, S. Lichter, Slip at high shear rates, Phys. Rev. Lett. 100 (2008) 206001, https://doi.org/10.1103/PhysRevLett.100.206001.

[48] K. Falk, F. Sedlmeier, L. Joly, R.R. Netz, L. Bocquet, Molecular origin of fast water transport in carbon nanotube membranes: superlubricity versus curvature dependent friction, Nano Lett. 10 (2010) 4067-4073, https://doi.org/10.1021/nl1021046.

[49] S. Sinha, Molecular Dynamics Simulation of Interfacial Tension and Contact Angle of Lennard-Jones fluid[M], University of California, Los Angeles, 2004.

[50] R.S. Voronov, D.V. Papavassiliou, L.L. Lee, Review of fluid slip over superhydrophobic surfaces and its dependence on the contact angle, Ind. Eng. Chem. Res. 47 (2008) 2455-2477, https://doi.org/10.1021/ie0712941.

[51] D. Feng, X. Li, K. Wu, J. Li, W. Zhao, Capillary dynamic under nanoconfinement: coupling the energy dissipation of contact line and confined water, Int. J. Heat Mass Tran. 127 (2018) 329-338, https://doi.org/10.1016/j.ijheatmasstransfer.2018.07.114.

[52] A.D. Sen, V.G. Anicich, T. Arakelian, Dielectric constant of liquid alkanes and hydrocarbon mixtures, J. Phys. D Appl. Phys. 25 (1992) 516, https://doi.org/10.1088/0022-3727/25/3/027.

[53] D. Savio, N. Fillot, P. Vergne, M. Zaccheddu, A model for wall slip prediction of confined n-alkanes: effect of wall-fluid interaction versus fluid resistance, Tribol. Lett. 46 (2012) 11-22, https://doi.org/10.1007/s11249-011-9911-6.

[54] D. Feng, Study on the Seepage Mechanism of Shale Matrix Fracturing Fluid and its Influence on Gas production[D], China University of Petroleum, Beijing, 2021, https://doi.org/10.27643/d.cnki.gsybu.2021.000137.

[55] M. Shaat, Viscosity of water interfaces with hydrophobic nanopores: application to water flow in carbon nanotubes, Langmuir 33 (2017) 12814-12819, https://doi.org/10.1021/acs.langmuir.7b02752.

[56] B.V. Derjaguin, N.V. Churaev, V.M. Muller, Surface Forces, Consultants Bureau, New York, 1987.

[57] J. Haneveld, N.R. Tas, N.54Brunets, H.V. Jansen, M. Elwenspoek, Capillary filling of sub-10nm nanochannels, J. Appl. Phys. 104 (2008), https://doi.org/10.1063/1.2952053.

[58] F. Persson, L.H. Thamdrup, M. Mikkelsen, S.E. Jaarlgard, P. Skafte-Pedersen, H. Bruus, A. Kristensen, Double thermal oxidation scheme for the fabrication of SiO2 nanochannels, Nanotechnology 18 (2007) 245301, https://doi.org/10.1088/0957-4484/18/24/245301.

[59] S. Gruener, Z. Sadjadi, H.E. Hermes, A.V. Kityk, K. Knorr, S.U. Egelhaaf, H. Rieger, P. Huber, Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores, Proc. Natl. Acad. Sci. 109 (2012) 10245-10250, https://doi.org/10.1073/pnas.1119352109.

[60] V.V. Pisarev, A.G. Kalinichev, Couette flow of pentane in clay nanopores: molecular dynamics simulation, J. Mol. Liq. 366 (2022) 120290. https://doi.org/10.1016/j.molliq.2022.120290.

[61] L. Wang, K.B. Neeves, X. Yin, E. Ozkan, Experimental Study and Modeling of the Effect of Pore Size Distribution on Hydrocarbon Phase Behavior in Nanopores. SPE Annual Technical Conference and Exhibition, October 2014. Amsterdam, The Netherlands, https://doi.org/10.2118/170894-MS.

[62] S. Wu, Z. Li, C. Zhang, G. Lv, P. Zhou, Nanohydrodynamic model and transport mechanisms of tight oil confined in nanopores considering liquid-solid molecular interaction effect, Ind. Eng. Chem. Res. 60 (2021) 18154-18165, https://doi.org/10.1021/acs.iecr.1c03615.

[63] H. Ye, H. Zhang, Z. Zhang, Y. Zheng, Size and temperature effects on the viscosity of water inside carbon nanotubes, Nanoscale Res. Lett. 6 (2011) 87, https://doi.org/10.1186/1556-276x-6-87.

[64] Z. Wang, C. Yu, J. Zhao, P. Guo, H. Liu, Molecular dynamics simulation for quantitative characterization of wettability transition on silica surface, J. Mater. Res. Technol. 19 (2022) 4371-4380, https://doi.org/10.1016/j.jmrt.2022.06.161.

[65] C. Yu, J. Zhao, Z. Wang, P. Guo, H. Liu, Z. Su, H. Liao, Vapor-liquid phase equilibrium of n-pentane in quartz nanopores by grand canonical Monte Carlo calculation, J. Mol. Liq. 365 (2022) 120075, https://doi.org/10.1016/j.molliq.2022.120075.

[66] W. Tian, J. Jia, G. Chen, Numerical density and Hamaker constant analysis of Hamaker's theory of microscopic continuous media, Computational Physics (2006) 366-370, https://doi.org/10.19596/j.cnki.1001-246x.2006.03.016.