Pore scale numerical investigation of counter-current spontaneous imbibition in multi-scaled pore networks

The multi-scaled pore networks of shale or tight reservoirs are considerably different from the conventional sandstone reservoirs. After hydraulic fracturing treatment, the spontaneous imbibition process plays an important role in the productivity of the horizontal wells. Applying the color-gradient model of Lattice Boltzmann Method (LBM) accelerated with parallel computing, we studied the countercurrent spontaneous imbibition process in two kinds of pore structures with different interlacing distributions of large and small pores. The effect of geometry configuration of pore arrays with different pore-scale and the capillary number $Ca$ on the mechanism of counter-current spontaneous imbibition as well as the corresponding oil recovery factor are studied. We found that the wetting phase tends to invade the small pore array under small $Ca$ in both types of geometry configurations of different pore arrays of four pore arrays zones. The wetting phase also tends to invade the pore array near the inlet for injecting the wetting phase no matter if it is a large pore array or small pore array except for the situation when the $Ca$ is large to a certain value. In this situation, the small pore arrays show resistance to the wetting phase, so the wetting phase doesn't invade the small pore near the inlet, but invades the large pore preferentially. Both the geometry configurations of different pore arrays and $Ca$ have a significant effect on the oil recovery factor. This work will help to solve the doubt about the selectivity of the multi-scaled pores of the wetting phase and the role of pores with different sizes in imbibition and oil draining in countercurrent spontaneous imbibition processes.