Analytical Exact Solution for Co-Current Spontaneous Imbibition in Porous Media Considering Early- and Late-Time Effects

Spontaneous imbibition (SI) of the wetting phase through the porous medium to displace the nonwetting phase is determined by capillary diffusion and injection fluid advection. This system is described using a transport equation of involved mechanisms and a pressure equation. The Buckley-Leverett solution is a particular case when capillary pressure is negligible. There are also analytical solutions available for cases with capillary diffusion as the dominant involved mechanism. In this study, a new mathematical model is developed to consider how both effects are significant. The model proposes an exact valid solution for both early-time (until the saturation front reaches effluent) and late-time imbibition. The accuracy of the model has been validated by comparing the suggested analytical model with numerical and experimental data. One of the advantages of the developed model is that despite the previous models, the injection rate does not need to be proportional to the square root of time, and other functional forms can be applied. Furthermore, the suggested analytical scheme is valid for strongly water-wet (SWW), weakly water-wet (WWW), and mixed-wet (MW) rock surfaces.