Mathematical Model of Two-Phase Spontaneous Imbibition with Dynamic Contact Angle

The phenomenon of spontaneous imbibition in porous media is of great importance in many scientific and technical fields, such as oil reservoirs and environmental engineering. In this paper, a combination of theoretical studies and numerical simulations has been used to investigate the two-phase spontaneous imbibition law in a single capillary tube. A mathematical model taking into account the dynamic contact angle was used to characterize two-phase spontaneous imbibition within a single capillary tube. The accuracy of the model was verified against the Lucas–Washburn model and relevant experimental data. The imbibition distance calculated by the mathematical model considering the dynamic contact angle correlates well with the experimental data. The results show that during the spontaneous imbibition process, the dynamic contact angle increases as the imbibition velocity increases. Moreover, a simulation of spontaneous imbibition in a single capillary tube based on the Navier–Stokes equation has been performed in order to investigate the effect of different two-phase viscosity ratios on the accuracy of the model. It was found that the larger the viscosity ratio of the two phases, the smaller the difference in the imbibition distance between the mathematical model considering the dynamic contact angle and the simulation results. Overall, our model reveals the effect of dynamic changes in contact angle on the spontaneous imbibition process and can accurately characterize the two-phase spontaneous imbibition process in porous media.