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

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 N-B(-1) is smaller than 3.57, the relative error of the imbibition height in a single fracture eta(Ls) will be larger than 10%. In core-scale fractured porous media, the relative error of the total imbibition weight eta(M) is larger than 10% when N-BC(-1) is smaller than 8.8. A method of determining the critical time when the gravity effect should be considered is also proposed.