Effect of Water Distribution on Spontaneous Imbibition of Tight Rocks: A Fractal Approach

The original water distribution characteristic plays an important role in the fracturing liquid retention in actual tight reservoirs. In this paper, an analytical model was proposed to characterize the water distribution and its effect on the spontaneous imbibition, based on the capillary tube model and fractal theory. Furthermore, the effect of the water film and the non-piston-like front related to the pore size are included in our model. The proposed model was successfully validated with the experimental results of core imbibition tests. Our work demonstrates that water distribution is influenced by displacement pressure and pore structure. For a small differential pressure, the porous media with richer large pores usually possesses a lower water saturation, and this difference will decrease with the increase of differential pressure. Moreover, compared with previous studies, the proposed imbibition model can not only distinguish the valid pores and invalid pores for imbibition but it can also predict the initial imbibition rate and equilibrium time of tight porous media with different water saturation. The results show that the equilibrium time is controlled by the minimum effective pore radius while the initial imbibition rate is mainly controlled by the large pores. Both of these two parameters will decrease with an increase of water saturation; the former is more sensitive to a low water saturation, while the latter decreases more quickly for a middle-high water saturation.