Effect of gravity on spontaneous imbibition of the wetting phase into gas-saturated tortuous fractured porous media: Analytical solution and diagnostic plot

• Published in: Advances in water resources 2020-08, Vol.142, p.103657, Article 103657
• Main Authors: Wang, Fuyong, Cheng, Hui
• Format: Article
• Language: English
• Subjects: Capillary pressure; Fractal theory; Fracture; Gravity; Spontaneous imbibition
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2020.103657

•Analytical solutions for spontaneous imbibition in a fracture with and without gravity.•Effect of gravity on spontaneous imbibition in a fracture and fractured porous media.•The dimensionless plot of NB−1 versus ηLs as a diagnostic plot for gravity effect evaluation.•Determination of the critical time when the gravity effect should be considered. Quantitatively evaluating the gravity effect on spontaneous imbibition in fractured porous media is challenging due to the lack of a suitable model and the complex fracture distribution. In this paper, new analytical solutions for spontaneous imbibition in a single fracture with and without gravity are first derived. Then, assuming a fractal distribution of fractures and with the tortuous plate fracture model, a semianalytical model for spontaneous imbibition of the wetting phase into gas-saturated fractured porous media is derived. Expressions of the wetting phase weight imbibed into fractured porous media with and without gravity are derived. Finally, the effects of gravity on spontaneous imbibition in a single fracture and core-scale fractured porous media are quantitatively evaluated with the inverse Bond number. The research results show that our newly derived analytical solutions attain a better performance in predicting the imbibition height over time in a fracture compared with the Lucas-Washburn model or the Fries and Dreyer model, which has been verified with experimental data from the literature. When NB−1 is smaller than 3.57, the relative error of the imbibition height in a single fracture ηLs will be larger than 10%. In core-scale fractured porous media, the relative error of the total imbibition weight ηM is larger than 10% when NBC−1 is smaller than 8.8. A method of determining the critical time when the gravity effect should be considered is also proposed.