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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 oilewater imbibition behavior within the 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 a porous medium under different conditions, including gaseliquid spontaneous imbibition and oilewater imbibition. When the pore size distribution of a tight rock is known, this new model can predict the changes of water saturation during the displacement process in the tight rock, 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 the CMG, while the imbibition rates calculated by the model are validated against the experimental observations of gaseliquid spontaneous imbibition. The good match above indicates the newly proposed model can show the water saturation profile at a macroscopic scale while capture the underlying physics of the multiphase flow in a porous medium 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. [ABSTRACT FROM AUTHOR]

Countercurrent imbibition is an important mechanism for tight oil recovery, that is, water imbibes spontaneously from the fracture into the porous matrix while oil flows reversely into the fracture. Its significance over cocurrent imbibition and forced imbibition is highlighted when permeability reduces. We used the computed tomography (CT) scanning to measure the one-dimensional evolution of water saturation profile and countercurrent imbibition distance (CID) at different fluid pressures, initial water saturations, and permeability. Surprisingly, experiments show that CID evolution for tight reservoir cores dramatically deviates from the classical diffusive rule (i.e., evolutes proportional to square root of time, t0.5). At early stage, CID extends faster than t0.5 (super-diffusive); while at late stage, CID extends much slower than t0.5 (sub-diffusive). After tens of hours, the CID change becomes too slow to be practically efficient for tight oil recovery. This research demonstrates that this deviation from classic theory is a result of (1) a much longer characteristic capillary length than effective invasion depth, which eliminates full development of a classical displacement front; and (2) non-zero flow at low water saturation, which was always neglected for conventional reservoir and is amplified in sub-mili-Darcy rocks. To well depict the details of the imbibition front in this situation, we introduce non-zero wetting phase fluidity at low saturation into classical countercurrent imbibition model and conduct numerical simulations, which successfully rationalizes the non-diffusive behavior and fits experimental data. Our data and theory imply an optimum soaking time in tight oil recovery by countercurrent imbibition, beyond which increasing exposed fracture surface area becomes a more efficient enhanced oil recovery (EOR) strategy than soaking for longer time. [ABSTRACT FROM AUTHOR]