Influence of roughness on spontaneous air-water imbibition in fractures: Insights from mathematical model analysis
Abstract view|21|times PDF download|5|times
Abstract
With the aim to explore the effects of fracture surface roughness on spontaneous imbibition behavior, this study investigates spontaneous air-water imbibition in rough fractures. For this purpose, a mathematical model that comprehensively accounts for fracture surface roughness and gravitational influence is developed. Using the Lambert function, a fully analytical solution for the imbibition height during the spontaneous air-water imbibition process is derived. The results indicate that neglecting fracture surface roughness leads to the overestimation of imbibition rate in model predictions. Moreover, the equilibrium imbibition height is significantly greater than the actual values, which aligns with the experimental observations. As the fractal dimension increases, the rate of imbibition height change decreases, and the imbibition height attained within the same time period is correspondingly reduced. A decrease in contact angle and an increase in interfacial tension both amplify the effect of roughness on imbibition behavior. Additionally, both the equilibrium height and the time required to reach equilibrium decrease with increasing fractal dimension. This research not only deepens the understanding of fluid flow mechanisms in complex fracture networks but also provides essential theoretical support and scientific guidance for engineering applications such as oil and gas extraction.
Document Type: Original article
Cited as: Cheng, H., Lai, R., Liu, J., Zhao, X., Yuan, Y., Wang, F. Influence of roughness on spontaneous air-water imbibition in fractures: Insights from mathematical model analysis. Capillarity, 2025, 16(3): 87-94. https://doi.org/10.46690/capi.2025.09.03
Keywords
Full Text:
PDFReferences
Abd, A. S., Elhafyan, E., Siddiqui, A. R., et al. A review of the phenomenon of counter-current spontaneous imbibition: Analysis and data interpretation. Journal of Petroleum Science and Engineering, 2019, 180: 456-470.
Andersen, P. O. Early- and late-time prediction of countercurrent spontaneous imbibition, scaling analysis and estimation of the capillary diffusion coefficient. Transport in Porous Media, 2023, 147(3): 573-604.
Brabazon, J. W., Perfect, E., Gates, C. H., et al. Rock fracture sorptivity as related to aperture width and surface roughness. Vadose Zone Journal, 2019a, 18: 180156.
Brabazon, J. W., Perfect, E., Gates, C. H., et al. Spontaneous imbibition of a wetting fluid into a fracture with opposing fractal surfaces: Theory and experimental validation. Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 2019b, 27(1): 1940001.
Cai, J., Chen, Y., Liu, Y., et al. Capillary imbibition and flow of wetting liquid in irregular capillaries: A 100-year review. Advances in Colloid and Interface Science, 2022, 304: 102654.
Cai, J., Hu, X., Standnes, D., et al. An analytical model for spontaneous imbibition in fractal porous media including gravity. Colloids and Surfaces a-Physicochemical and Engineering Aspects, 2012, 414: 228-233.
Cai, J., Qin, X., Wang, H., et al. Pore-scale investigation of forced imbibition in porous rocks through interface curvature and pore topology analysis. Journal of Rock Mechanics and Geotechnical Engineering, 2025, 17(1): 245-257.
Cheng, H., Wang, F. Effects of gravity and buoyancy on spontaneous liquid-liquid imbibition in fractured porous media. Capillarity, 2024, 10(1): 1-11.
Family, F., Vicsek, T. Dynamics of fractal surfaces. Fractal Concepts in Surface Growth, 1991.
Fries, N., Dreyer, M. An analytic solution of capillary rise restrained by gravity. Journal of Colloid and Interface Science, 2008, 320(1): 259-263.
Guo, J., Zhao, Y., He, L., et al. Spontaneous imbibition of unsaturated sandstone under different vertical temperature gradients: Neutron radiography experiments and dynamic models. Advances in Water Resources, 2024, 193: 104832.
Hu, Y., Xu, W., Zou, L., et al. Evaluating the long-term barrier performance of fractured granite for nuclear waste disposal: Impact of fast water-conducting path. Engineering Geology, 2024, 337: 107583.
Janetti, M. B., Janssen, H. Effect of dynamic contact angle variation on spontaneous imbibition in porous materials. Transport in Porous Media, 2022, 142(3): 493-508.
Khan, J., Padmanabhan, E., Ul Haq, I., et al. Hydraulic fracturing with low and high viscous injection mediums to investigate net fracture pressure and fracture network in shale of different brittleness index. Geomechanics for Energy and the Environment, 2023, 33: 100416.
Ma, G., Ma, C., Chen, Y., et al. An equivalent model for fluid flow along a rough-walled fracture considering the effect of the multi-scale roughness and internal contacts. Geoenergy Science and Engineering, 2025, 247: 213677.
Meng, Q., Liu, H., Wang, J., et al. Effect of gravity on spontaneous imbibition from cores with two ends open in the frontal flow period. Journal of Petroleum Science and Engineering, 2016, 141: 16-23.
Minakov, A., Pryazhnikov, M., Neverov, A., et al. Wettability, interfacial tension, and capillary imbibition of nanomaterial-modified cross-linked gels for hydraulic fracturing. Capillarity, 2024, 12(2): 27-40.
Munoz, L., Mejia, C., Rueda, J., et al. Iterative coupling of DDM and FEM for planar hydraulic fracturing under non-uniform confining stresses. Computers and Geotechnics, 2025, 186: 107432.
Nazridoust, K., Ahmadi, G., Smith, D. A new friction factor correlation for laminar, single-phase flows through rock fractures. Journal of Hydrology, 2006, 329(1-2): 315-328.
Perfect, E., Brabazon, J. W., Gates, C. H. Forward prediction of early-time spontaneous imbibition of water in unsaturated rock fractures. Vadose Zone Journal, 2020, 19(1): e20056.
Rezaei, A., Mousavi, Z. Characterization of land deformation, hydraulic head, and aquifer properties of the gorgan confined aquifer, iran, from insar observations. Journal of Hydrology, 2019, 579: 124196.
Salam, A., Wang, X. An analytical solution on spontaneous imbibition coupled with fractal roughness, slippage and gravity effects in low permeability reservoir. Journal of Petroleum Science and Engineering, 2022, 208: 109501.
Shi, Y., Yassin, M., Dehghanpour, H. A modified model for spontaneous imbibition of wetting phase into fractal porous media. Colloids and Surfaces a-Physicochemical and Engineering Aspects, 2018, 543: 64-75.
Srivastava, M. K., Kishor, K., Singh, A. K., et al. Tectonically deformed coal: Focus on microstructures & implications for basin evolution. Marine and Petroleum Geology, 2025, 172: 107223.
Standnes, D. C. Analysis of oil recovery rates for spontaneous imbibition of aqueous surfactant solutions into preferential oil-wet carbonates by estimation of capillary diffusivity coefficients. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2004, 251(1-3): 93101.
Torkan, M., Uotinen, L., Baghbanan, A., et al. Experimental and numerical characterization of hydro-mechanical properties of rock fractures: The effect of the sample size on roughness and hydraulic aperture. International Journal of Rock Mechanics and Mining Sciences, 2025, 186: 106009.
Wang, F., Cheng, H. Effect of gravity on spontaneous imbibition of the wetting phase into gas-saturated tortuous fractured porous media: Analytical solution and diagnostic plot. Advances in Water Resources, 2020, 142: 103657.
Wang, F., Cheng, H., Song, K. A mathematical model of surfactant spontaneous imbibition in a tight oil matrix with diffusion and adsorption. Langmuir, 2021, 37(29): 8789-8800.
Washburn, E. W. The dynamics of capillary flow. Physical Review Journal, 1921, 17(3): 273-283.
Wenzel, R. N. Resistance of solid surfaces to wetting by water. Transactions of the Faraday Society, 1936, 28(8): 988994.
Wolansky, G., Marmur, A. Apparent contact angles on rough surfaces: The wenzel equation revisited. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 1999, 156(1-3): 381-388.
Wu, M., Jiang, C., Song, R., et al. Comparative study on hydraulic fracturing using different discrete fracture network modeling: Insight from homogeneous to heterogeneity reservoirs. Engineering Fracture Mechanics, 2023, 284: 109274.
Xia, Y., Tian, Z., Xu, S., et al. Effects of microstructural and petrophysical properties on spontaneous imbibition in tight sandstone reservoirs. Journal of Natural Gas Science and Engineering, 2021, 96: 104225.
Yaghoubi, A. Hydraulic fracturing modeling using a discrete fracture network in the barnett shale. International Journal of Rock Mechanics and Mining Sciences, 2019, 119: 98-108.
Yoon, W. W., Han, W. S., Hwang, J., et al. Effect of fracture characteristics on groundwater flow adjacent to high-level radioactive waste repository. Journal of Hydrology, 2024, 629: 130593.
Zhang, J., Chen, J., Zhao, Z., et al. Numerical modeling on nuclide transport around a nuclear waste repository under coupled thermo-hydro-mechanical condition. Computers and Geotechnics, 2023a, 164: 105776.
Zhang, S., Liu, X. A semi-analytical solution for the equivalent permeability coefficient of the multilayered porous medium with continuous fracture. Water Resources Research, 2024, 60(2): e2023WR036203.
Zhang, S., Liu, X., Wang, E. Quantitative evaluation of the onset and evolution for the non-darcy behavior of the partially filled rough fracture. Water Resources Research, 2024a, 60(3): e2023WR036494.
Zhang, S., Liu, X., Wang, E., et al. A novel model of hydraulic aperture for rough single fracture: Insights from fluid inertial and fracture geometry effects. Journal of Geophysical Research-Solid Earth, 2024b, 129(7): e2024JB029018.
Zhang, X., Ye, Q., Deng, J., et al. Experimental study and mechanism analysis of spontaneous imbibition of surfactants in tight oil sandstone. Capillarity, 2023b, 7(1): 1-12.
Zhou, W., Kulenkampff, J., Heredia, D. J., et al. Variability of fracture surface roughness in crystalline host rocks: Implications for transport model simplifications. Applied Geochemistry, 2025, 186: 106401.
Refbacks
- There are currently no refbacks.
Copyright (c) 2025 The Author(s)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.