A new interacting capillary bundle model on the multiphase flow in micropores of tight rocks

Surfactants are widely used in the fracturing fluid to enhance the imbibition and thus the oil recovery rate. However, current numerical models cannot capture the physics behind capillary imbibition during the wettability alteration by surfactants. Although the interacting capillary bundle (ICB) model shows potential in characterizing imbibition rates in different pores during wettability alteration, the existing ICB models neglect the influence of wettability and viscosity ratio on the imbibition behavior, making it difficult to accurately describe the oil–water imbibition behavior within porous media. In this work, a new ICB mathematical model is established by introducing pressure balance without assuming the position of the leading front to comprehensively describe the imbibition behavior in porous media under different conditions, including gas–liquid spontaneous imbibition and oil–water imbibition. When the pore size distribution of tight rocks is known, this new model can predict the changes of water saturation during the displacement process in tight rocks, and also determine the imbibition rate in pores of different sizes. The water saturation profiles obtained from the new model are validated against the waterflooding simulation results from CMG, while the imbibition rates calculated by the model are validated against the experimental observations of gas–liquid spontaneous imbibition. The good match above indicates the new proposed model can show the water saturation profile at a macroscopic scale while capture the underlying physics of the multiphase flow in porous media at a microscopic scale. Simulation results obtained from this model indicate that both wettability and viscosity ratio can affect the sequence of fluid imbibition into pores of different sizes during the multiphase flow, where less-viscous wetting fluid is preferentially imbibed into larger pores while more-viscous wetting fluid tends to be imbibed into smaller pores. Furthermore, this model provides an avenue to calculate the imbibition rate in pores of different sizes during wettability alteration and capture the non-Darcy effect in micro- and nano-scale pores.