Modeling of counter-current spontaneous imbibition in independent capillaries with unequal diameters

Kangli Chen, Huaxin Xu, Zhenjie Zhang, Qingbang Meng, Tao Zhang

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Spontaneous imbibition is a crucial process for oil recovery from fractured and unconventional reservoirs. Herein, with the assumption of capillaries being independent, a new mathematical model for spontaneous imbibition is proposed and solved using a numerical method. The simulated results show that the wetting phase preferentially enters smaller capillaries where the advancement velocity is higher than that in larger ones, while the non-wetting phase can be displaced out in the larger capillaries. In addition, the effect of fluid viscosity ratio on counter-current imbibition is analyzed. The results show that imbibition velocity becomes higher with the increase in the viscosity ratio. When the viscosity of the non-wetting phase is larger than that of the wetting phase, the end pressure gradually increases as the imbibition front advances. In contrast, when the viscosity of the non-wetting phase is less than that of the wetting phase, the end pressure decreases with the infiltration. With a higher viscosity ratio of non-wetting and wetting phase, the heterogeneity of the interface advancement among different capillaries increases.

Cited as: Chen, K., Xu, H., Zhang, Z., Meng, Q., Zhang, T. Modeling of counter-current spontaneous imbibition in independent capillaries with unequal diameters. Capillarity, 2022, 5(6): 115-122.


Independent capillary model, counter-current imbibition, fluid viscosity, heterogeneity

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