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Capillarity 2020, 3(1): 8-15 https://doi.org/10.26804/capi.2020.01.02
Original Artical | Open Access | Issue | Published: 09 March 2020

Capillary imbibition of confined fluid in nanopores

Show Author's Information Fanhui Zeng1( ),  Qiang Zhang1,  Jianchun Guo1,  Yong Meng2,  Xianzhen Shao2,  Yingjie Zheng2
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, P. R. China
Hekou Oil Production Plant, Shengli Oil Field, Dongying 257200, P. R. China
Keywords:
viscosity, wettability, slippage, spontaneous imbibition, Shale gas formation, nanopore confined flow
Cite this article:
Zeng F, Zhang Q, Guo J, et al. Capillary imbibition of confined fluid in nanopores. Capillarity, 2020, 3(1): 8-15. https://doi.org/10.26804/capi.2020.01.02
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Abstract Full text About this article

The spontaneous capillary imbibition of confined nanopores is investigated using an analytical model that includes the slip effect, wettability and effective viscosity at the water surface interface. The results show that the effective viscosity of confined fluid is larger than that of bulk water and decreases with diameter and wettability. The effective slip length is negative for a contact angle of 0 ∘, and the effective slip length is positive and increases with diameter. The results of the presented model show that the capillary imbibition length for nanoconfined water can vary up to 0.389 - 1.033 times that determined by the Lucas-Washburn equation with no-slip boundary conditions for nanopores due to the effective viscosity and slippage with various dimensions and contact angles. The enhancement increases with diameter and contact angle. These results elucidate the confined movement through nanopores, which can be used to understand fracturing-fluid flow in the nanopores of shale reservoir formations.


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About this article

Capillary imbibition of confined fluid in nanopores

Show Author's information Fanhui Zeng1( ), Qiang Zhang1, Jianchun Guo1, Yong Meng2, Xianzhen Shao2, Yingjie Zheng2
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, P. R. China
Hekou Oil Production Plant, Shengli Oil Field, Dongying 257200, P. R. China

Abstract

The spontaneous capillary imbibition of confined nanopores is investigated using an analytical model that includes the slip effect, wettability and effective viscosity at the water surface interface. The results show that the effective viscosity of confined fluid is larger than that of bulk water and decreases with diameter and wettability. The effective slip length is negative for a contact angle of 0 ∘, and the effective slip length is positive and increases with diameter. The results of the presented model show that the capillary imbibition length for nanoconfined water can vary up to 0.389 - 1.033 times that determined by the Lucas-Washburn equation with no-slip boundary conditions for nanopores due to the effective viscosity and slippage with various dimensions and contact angles. The enhancement increases with diameter and contact angle. These results elucidate the confined movement through nanopores, which can be used to understand fracturing-fluid flow in the nanopores of shale reservoir formations.

Keywords: viscosity, wettability, slippage, spontaneous imbibition, Shale gas formation, nanopore confined flow

References(68)

Abgrall, P., Nguyen, N.T. Nanofluidic devices and their applications. Anal. Chem. 2008, 80(7): 2326-2341.
DOI Google Scholar
Akbarabadi, M., Saraji, S., Piri, M., et al. Nano-scale experimental investigation of in-situ wettability and spontaneous imbibition in ultra-tight reservoir rocks. Adv. Water Resour. 2017, 107: 160-179.
DOI Google Scholar
Alkouh, A. New advances in shale gas reservoir analysis using water flowback data. Texas A&M University, Texas, American, 2014.
DOI
Benavente, D., Lock, P., Cura, M.A.G.D., et al. Predicting the capillary imbibition of porous rocks from microstructure. Trans. Porous Media 2002, 49(1): 59-76.
DOI Google Scholar
Birdsell, D.T., Rajaram, H., Dempsey, D., et al. Hydraulic fracturing fluid migration in the subsurface: A review and expanded modeling results. Water Resour. Res. 2015, 51(9): 7159-7188.
DOI Google Scholar
Bocquet, L., Tabeling, P. Physics and technological aspects of nanofluidics. Lab. Chip 2014, 14(17): 3143-3158.
DOI Google Scholar
Cai, J., Hu, X., Standnes, D.C., et al. An analytical model for spontaneous imbibition in fractal porous media including gravity. Colloids Surf. A: Physicochem. Eng. Asp. 2012, 414: 228-233.
DOI Google Scholar
Cai, J., Perfect, E., Cheng, C., et al. Generalized modeling of spontaneous imbibition based on Hagen-Poiseuille flow in tortuous capillaries with variably shaped apertures. Langmuir 2014, 30(18): 5142-5151.
DOI Google Scholar
Chan, D., Horn, R.G. The drainage of thin liquid films between solid surfaces. J. Chem. Phys. 1985, 83(10): 5311-5324.
DOI Google Scholar
Cipolla, C.L. Modeling production and evaluating fracture performance in unconventional gas reservoirs. J. Petrol. Technol. 2009, 61(9): 84-90.
DOI Google Scholar
Cottin-Bizonne, C., Barrat, J.L., Bocquet, L., et al. Low-friction flows of liquid at nanopatterned interfaces. Nat. Mater. 2003, 2(4): 237-240.
DOI Google Scholar
Dimitrov, D.I., Milchev, A., Binder, K. Capillary rise in nanopores: molecular dynamics evidence for the Lucas-Washburn equation. Phys. Rev. Lett. 2007, 99(5): 054501.
DOI Google Scholar
Din, X., Michaelides, E.E. Kinetic theory and molecular dynamics simulations of microscopic flows. Phys. Fluids 1997, 9(12): 3915-3925.
DOI Google Scholar
Falk, K., Coasne, B., Pellenq, R., et al. Subcontinuum mass transport of condensed hydrocarbons in nanoporous media. Nat. Commun. 2015, 6: 6949.
DOI Google Scholar
Feibelman, P.J. Viscosity of ultrathin water films confined between aluminol surfaces of kaolinite: ab initio simulations. J. Chem. Phys. 2013, 117(12): 6088-6095.
DOI Google Scholar
Fradin, C., Braslau, A., Luzet, D., et al. Reduction in the surface energy of liquid interfaces at short length scales. Nature 2000, 403(6772): 871-874.
DOI Google Scholar
Ghanbari, E., Dehghanpour, H. The fate of fracturing water: A field and simulation study. Fuel 2016, 163: 282-294.
DOI Google Scholar
Granick, S. Motions and relaxations of confined liquids. Science 1991, 253(5026): 1374-1379.
DOI Google Scholar
Granick, S., Zhu, Y., Lee, H. Slippery questions about complex fluids flowing past solids. Nat. Mater. 2003, 2: 221-227.
DOI Google Scholar
Haria, N.R., Grest, G.S., Lorenz, C.D. Viscosity of nanoconfined water between hydroxyl basal surfaces of kaolinite: classical simulation results. J. Chem. Phys. C 2012, 17(12): 6096-“6104.
DOI Google Scholar
Heinbuch, U., Fischer, J. Liquid flow in pores: Slip, no-slip, or multilayer sticking. Phys. Rev. A 1989, 40(2): 1144.
DOI Google Scholar
Herington, E.F.G. Recommended reference materials for realization of physicochemical properties. Oxford, UK, Pergamon Press, 1977.
Holt, J.K., Park, H.G., Wang, Y., et al. Fast mass transport through sub-2-nanometer carbon nanotubes. Science 2006, 312(5776): 1034-1037.
DOI Google Scholar
Hsu, S.Y., Tsai, J.P., Chang, L.C. Pore-scale study of the effect of the saturation history on fluid saturation and relative permeability of three-fluid flow in porous media. Paper Presented at the AGU Fall Meeting Abstracts, San Francisco, American, December, 2014.
Huang, D.M., Sendner, C., Horinek, D., et al. Water slippage versus contact angle: A quasiuniversal relationship. Phys. Rev. Lett. 2008, 101(22): 226101.
DOI Google Scholar
Kalyon, D.M. Apparent slip and viscoplasticity of concentrated suspensions. J. Rheol. 2005, 49(3): 621-640.
DOI Google Scholar
Kannam, S.K. Todd, B.D., Hansen, J.S., et al. Slip flow in graphene nanochannels. J. Chem. Phys. 2011, 135(14): 144701.
DOI Google Scholar
Klein, J., Kumacheva, E. Confinement-induced phase transitions in simple liquids. Science 1995, 269(5225): 816-819.
DOI Google Scholar
Laliberté, M. Model for calculating the viscosity of aqueous solutions. J. Chem. Eng. Data 2007, 52(2): 321-335.
DOI Google Scholar
Li, T., Gao, J., Szoszkiewicz, R., et al. Structured and viscous water in subnanometer gaps. Phys. Rev. B 2007, 75(11): 115415.
DOI Google Scholar
Liu, H., Cao, G. Effectiveness of the Young-Laplace equation at nanoscale. Sci. Rep. 2016, 6: 23936.
DOI Google Scholar
Lucas, R. Rate of capillary ascension of liquids. Kolloid-Zeitschrift 1918, 23(1): 15-22.
DOI Google Scholar
Loucks, R.G., Reed, R.M., Ruppel, S.C., et al. Spectrum of pore types and networks in mudrocks and a descriptive classification for matrix-related mudrock pores. AAPG Bull. 2012, 96(6): 1071-1098.
DOI Google Scholar
Lorenz, U.J., Zewail, A.H. Observing liquid flow in nanotubes by 4D electron microscopy. Science 2014, 344(6191): 1496-1500.
DOI Google Scholar
Maali, A., Cohen-Bouhacina, T., Kellay, H. Measurement of the slip length of water flow on graphite surface. Appl. Phys. Lett. 2008, 92(5): 053101.
DOI Google Scholar
Mashl, R.J., Joseph, S., Aluru, N.R., et al. Anomalously immobilized water: A new water phase induced by confinement in nanotubes. Nano Lett. 2003, 3(5): 589-592.
DOI Google Scholar
Mortensen, N.A., Okkels, F., Bruus, H. Reexamination of Hagen-Poiseuille flow: Shape dependence of the hydraulic resistance in microchannels. Phys. Rev. E 2005, 71(5): 057301.
DOI Google Scholar
Müller, M., Pastorino, C., Servantie, J. Flow, slippage and a hydrodynamic boundary condition of polymers at surfaces. J. Phys.: Condens. Matter 2008, 20(49): 494225.
DOI Google Scholar
Nair, R.R., Wu, H., Jayaram, P.N., et al. Unimpeded permeation of water through helium-leak-tight graphene-based membranes. Science 2012, 335(6067): 442-444.
DOI Google Scholar
Ortiz-Young, D., Chiu, H.C., Kim, S., et al. The interplay between apparent viscosity and wettability in nanoconfined water. Nat. Commun. 2013, 4: 2482.
DOI Google Scholar
Petravic, J., Harrowell, P. Spatial dependence of viscosity and thermal conductivity through a planar interface. J. Phys. Chem. B 2009, 113(7): 2059-2065.
DOI Google Scholar
Raviv, U., Laurat, P., Klein, J. Fluidity of water confined to subnanometre films. Nature 2001, 413(6851): 51-54.
DOI Google Scholar
Ruppert, L.F., Sakurovs, R., Blach, T.P., et al. A usans/sans study of the accessibility of pores in the barnett shale to methane and water. Energ. Fuels 2013, 27(2): 772-779.
DOI Google Scholar
Salwen, H., Cotton, F.W., Grosch, C.E. Linear stability of Poiseuille flow in a circular pipe. J. Fluid Mech. 1980, 98(2): 273-284.
DOI Google Scholar
Scatena, L.F., Brown, M.G., Richmond, G.L. Water at hydrophobic surfaces: weak hydrogen bonding and strong orientation effects. Science 2001, 292(5118): 908-912.
DOI Google Scholar
Schmid, K.S., Alyafei, N., Geiger, S., et al. Analytical solutions for spontaneous imbibition: Fractional-flow theory and experimental analysis. SPE J. 2016, 21(6): 2308-2316.
DOI Google Scholar
Sedghi, M., Piri, M., Goual, L. Molecular dynamics of wetting layer formation and forced water invasion in angular nanopores with mixed wettability. J. Chem. Phys. 2014, 141(19): 194703.
DOI Google Scholar
Shaat, M. Viscosity of water interfaces with hydrophobic nanopores: application to water flow in carbon nanotubes. Langmuir 2017, 33(44): 12814-12819.
DOI Google Scholar
Shah, D.O. Thin liquid films and boundary layers: special discussion of the faraday society. AIChE J. 1973, 19(6): 1283-1283.
DOI Google Scholar
Shannon, M.A., Bohn, P.W., Elimelech, M., et al. Science and technology for water purification in the coming decades. Nature 2008, 452(7185): 301-310.
DOI Google Scholar
Sofos, F., Karakasidis, T.E., Liakopoulos, A. Surface wettability effects on flow in rough wall nanochannels. Microfluid. Nanofluid. 2012, 12(1): 25-31.
DOI Google Scholar
Thomas, J.A., McGaughey, A.J.H. Density, distribution, and orientation of water molecules inside and outside carbon nanotubes. J. Chem. Phys. 2008a, 128(8): 084715.
DOI Google Scholar
Thomas, J.A., McGaughey, A.J.H. Reassessing fast water transport through carbon nanotubes. Nano Lett. 2008b, 8(9): 2788-2793.
DOI Google Scholar
Thomas, J.A., McGaughey, A.J.H. Water flow in carbon nanotubes: transition to subcontinuum transport. Phys. Rev. Lett. 2009, 102(18): 184502.
DOI Google Scholar
Thompson, P.A., Robbins, M.O. Origin of stick-slip motion in boundary lubrication. Science 1990, 250(4982): 792-794.
DOI Google Scholar
Thompson, P.A., Troian, S.M. A general boundary condition for liquid flow at solid surfaces. Nature 1997, 389(6649): 360-362.
DOI Google Scholar
Vinogradova, O.I., Koynov, K., Best, A., et al. Direct measurements of hydrophobic slippage using double-focus fluorescence cross-correlation. Phys. Rev. Lett. 2009, 102(11): 118302.
DOI Google Scholar
Voronov, R.S., Papavassiliou, D.V., Lee, L.L. Boundary slip and wetting properties of interfaces: Correlation of the contact angle with the slip length. J. Chem. Phys. 2006, 124(20): 204701.
DOI Google Scholar
Wang, J., Rahman, S.S. Investigation of water leakoff considering the component variation and gas entrapment in shale during hydraulic-fracturing stimulation. SPE Reserv. Eval. Eng. 2016, 19(3): 511-519.
DOI Google Scholar
Washburn, E.W. The dynamics of capillary flow. Phys. Rev. 1921, 17(9): 273-283.
DOI Google Scholar
Werder, T., Walther, J.H., Jaffe, R.L., et al. Molecular dynamics simulation of contact angles of water droplets in carbon nanotubes. Nano Lett. 2001, 1(12): 697-702.
DOI Google Scholar
Wu, K., Chen, Z., Li, J., et al. Wettability effect on nanoconfined water flow. Proc. Natl. Acad. Sci. USA 2017, 114(13): 3358-3363.
DOI Google Scholar
Xiao, J., Cai, J., Xu, J. Saturated imbibition under the influence of gravity and geometry. J. Colloid Interf. Sci. 2018, 521: 226-231.
DOI Google Scholar
Yang, L., Yao, T., Tai, Y. The marching velocity of the capillary meniscus in a microchannel. J. Micromech. Microeng. 2004, 14(2): 220-225.
DOI Google Scholar
Zeng, F., Guo, J. Optimized design and use of induced complex fractures in horizontal wellbores of tight gas reservoirs. Rock Mech. Rock Eng. 2016, 49(4): 1411-1423.
DOI Google Scholar
Zeng, F., Guo, J., Ma, S., et al. 3D observations of the hydraulic fracturing process for a model non-cemented horizontal well under true triaxial conditions using an X-ray CT imaging technique. J. Nat. Gas Sci. Eng. 2018, 52: 128-140.
DOI Google Scholar
Zhang, S., Sheng, J. Study of the propagation of hydration-induced fractures in mancos shale using computerized tomography. Int. J. Rock Mech. Min. Sci. 2017, 95: 1-7.
DOI Google Scholar
Zhang, X., Morrow, N.R., Ma, S. Experimental verification of a modified scaling group for spontaneous imbibition. SPE Reserv. Eng. 1996, 11(4): 280-285.
DOI Google Scholar
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Publication history

Received: 21 February 2020
Revised: 03 March 2020
Accepted: 04 March 2020
Published: 09 March 2020
Issue date: March 2020

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© The Author(s) 2020

Acknowledgements

This work was supported by the Natural Science Foundation of China (Grant No. 51504203, 51525404, and 51874250), the National Key and Development Program of China (Grant No. 2017ZX05037-004) and the National Students’ Platform for Innovation and Entrepreneurship Training Program of China (Grant No. 201810615007).

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