A Novel Model of Counter-Current Imbibition in Interacting Capillaries with Different Size Distribution

The imbibition phenomenon widely exists in nature and industrial applications. It is of great significance to study the mechanism of imbibition and the influence laws of related factors. In this paper, based on the assumption of interacting capillaries, a capillary bundle model of counter-current imbibition is established. In addition, the characteristics of imbibition and the influences of capillary size and fluid viscosity are analyzed. The results show that water is imbibed into the smaller capillaries and expelled from the larger capillaries. The rate of the meniscus in water-imbibition capillaries is proportional to the square root of time. In the interacting capillaries, oil production by counter-current imbibition decreases and then increases gradually with the increase of the capillary diameter difference. When the total cross-sectional area of the capillary remains unchanged, the cross-sectional area of the total water-imbibition capillaries is affected by the size distribution of the capillaries. The larger the viscosity of the non-wetting phase, the more uneven the imbibition front, the lower the imbibition efficiency. The higher the viscosity of the wetting phase, the more uniform the imbibition front, and the higher the imbibition efficiency.