Fractal theory and dynamic contact angle-based imbibition model for two-phase flow in porous media

During the development of tight oil reservoirs, there are significant occurrences of spontaneous imbibition. Understanding the spontaneous imbibition behavior at the core scale of tight sandstone holds significant importance in improving the recovery rate. This study presents a novel mathematical model for characterizing the spontaneous imbibition phenomenon in tight porous media, drawing upon the fractal theory and the dynamic contact angle in capillary bundles. The proposed model has been verified by the results of core imbibition experiments in the literature. Furthermore, we conducted spontaneous imbibition simulation studies using core structures of different pore types extracted from real tight reservoirs to validate the applicability of the new mathematical model. Comparative analysis shows that the derived mathematical approach fits well with the simulation results, but the heterogeneity of the pore space can lead to certain errors between the model and the simulation results. The influencing factors analysis suggests that the higher the porosity, the higher the final recovery rate, whereas an increase in pore fractal dimension has little effect on the final recovery rate.