Capillary imbibition of confined water in nanopores

Fanhui Zeng, Qiang Zhang, Jianchun Guo, Yong Meng, Xianzhen Shao, Yingjie Zheng

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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 water 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.

Cited as: Zeng, F., Zhang, Q., Guo, J., Meng, Y., Shao, X., Zheng, Y. Capillary imbibition of confined water in nanopores. Capillarity, 2020, 3(1): 8-15, doi: 10.26804/capi.2020.01.02


Keywords


Shale gas formation; nanopore confined flow; slippage; wettability; viscosity; spontaneous imbibition

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Abgrall, P., Nguyen, N.T. Nanofluidic devices and their applications. Anal. Chem. 2008, 80(7): 2326-2341.

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.

Alkouh, A. New advances in shale gas reservoir analysis using water flowback data. Texas A&M University, Texas, American, 2014.

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.

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.

Bocquet, L., Tabeling, P. Physics and technological aspects of nanofluidics. Lab. Chip 2014, 14(17): 3143-3158.

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.

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.

Chan, D., Horn, R.G. The drainage of thin liquid films between solid surfaces. J. Chem. Phys. 1985, 83(10): 5311-5324.

Cipolla, C.L. Modeling production and evaluating fracture performance in unconventional gas reservoirs. J. Petrol. Technol. 2009, 61(9): 84-90.

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.

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.

Din, X., Michaelides, E.E. Kinetic theory and molecular dynamics simulations of microscopic flows. Phys. Fluids 1997, 9(12): 3915-3925.

Falk, K., Coasne, B., Pellenq, R., et al. Subcontinuum mass transport of condensed hydrocarbons in nanoporous media. Nat. Commun. 2015, 6: 6949.

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.

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.

Ghanbari, E., Dehghanpour, H. The fate of fracturing water: A field and simulation study. Fuel 2016, 163: 282-294.

Granick, S. Motions and relaxations of confined liquids. Science 1991, 253(5026): 1374-1379.

Granick, S., Zhu, Y., Lee, H. Slippery questions about complex fluids flowing past solids. Nat. Mater. 2003, 2: 221-227.

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.

Heinbuch, U., Fischer, J. Liquid flow in pores: Slip, no-slip, or multilayer sticking. Phys. Rev. A 1989, 40(2): 1144.

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.

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.

Kalyon, D.M. Apparent slip and viscoplasticity of concentrated suspensions. J. Rheol. 2005, 49(3): 621-640. Kannam, S.K. Todd, B.D., Hansen, J.S., et al. Slip flow in graphene nanochannels. J. Chem. Phys. 2011, 135(14): 144701.

Klein, J., Kumacheva, E. Confinement-induced phase transitions in simple liquids. Science 1995, 269(5225): 816-819.

Lalibert´e, M. Model for calculating the viscosity of aqueous solutions. J. Chem. Eng. Data 2007, 52(2): 321-335.

Li, T., Gao, J., Szoszkiewicz, R., et al. Structured and viscous water in subnanometer gaps. Phys. Rev. B 2007, 75(11): 115415.

Liu, H., Cao, G. Effectiveness of the Young-Laplace equation at nanoscale. Sci. Rep. 2016, 6: 23936.

Lucas, R. Rate of capillary ascension of liquids. Kolloid-Zeitschrift 1918, 23(1): 15-22.

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.

Lorenz, U.J., Zewail, A.H. Observing liquid flow in nanotubes by 4D electron microscopy. Science 2014, 344(6191): 1496-1500.

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.

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.

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.

M¨uller, M., Pastorino, C., Servantie, J. Flow, slippage and a hydrodynamic boundary condition of polymers at surfaces. J. Phys.: Condens. Matter 2008, 20(49): 494225.

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.

Ortiz-Young, D., Chiu, H.C., Kim, S., et al. The interplay be-tween apparent viscosity and wettability in nanoconfined water. Nat. Commun. 2013, 4: 2482.

Petravic, J., Harrowell, P. Spatial dependence of viscosity and thermal conductivity through a planar interface. J. Phys. Chem. B 2009, 113(7): 2059-2065.

Raviv, U., Laurat, P., Klein, J. Fluidity of water confined to subnanometre films. Nature 2001, 413(6851): 51-54.

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.

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.

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.

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.

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.

Shaat, M. Viscosity of water interfaces with hydrophobic nanopores: application to water flow in carbon nanotubes. Langmuir 2017, 33(44): 12814-12819.

Shah, D.O. Thin liquid films and boundary layers: special discussion of the faraday society. AIChE J. 1973, 19(6): 1283-1283.

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.

Sofos, F., Karakasidis, T.E., Liakopoulos, A. Surface wet-tability effects on flow in rough wall nanochannels. Microfluid. Nanofluid. 2012, 12(1): 25-31.

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.

Thomas, J.A., McGaughey, A.J.H. Reassessing fast water transport through carbon nanotubes. Nano Lett. 2008b, 8(9): 2788-2793.

Thomas, J.A., McGaughey, A.J.H. Water flow in carbon nanotubes: transition to subcontinuum transport. Phys. Rev. Lett. 2009, 102(18): 184502.

Thompson, P.A., Robbins, M.O. Origin of stick-slip motion in boundary lubrication. Science 1990, 250(4982): 792-794.

Thompson, P.A., Troian, S.M. A general boundary condition for liquid flow at solid surfaces. Nature 1997, 389(6649): 360-362.

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.

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.

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.

Washburn, E.W. The dynamics of capillary flow. Phys. Rev. 1921, 17(9): 273-283.

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.

Wu, K., Chen, Z., Li, J., et al. Wettability effect on nanoconfined water flow. Proc. Natl. Acad. Sci. USA 2017, 114(13): 3358-3363.

Xiao, J., Cai, J., Xu, J. Saturated imbibition under the influence of gravity and geometry. J. Colloid Interf. Sci. 2018, 521: 226-231.

Yang, L., Yao, T., Tai, Y. The marching velocity of the capillary meniscus in a microchannel. J. Micromech. Microeng. 2004, 14(2): 220-225.

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.

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.

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.

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.


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