Influence of roughness on spontaneous air-water imbibition in fractures: Insights from mathematical model analysis

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