# Investigation of the Effect of Capillary Barrier on Water-Oil Movement in Water Flooding
## 4 Effect of the Capillary Barrier on Oil-Water Two-Phase Flow in Porous Media Model
### Results and Discussion
#### 4.3.1 Water-Wet Condition

Table 5: Numerical boundary conditions. value of the contact angle (60\({}^{\circ}\)) and opening angle (45\({}^{\circ}\)) in this case, the capillary force is positive and continues to increase until a maximum positive value is reached before the water phase flows into the throat channel. Then, the capillary force decreases suddenly to a stable value as the fluid fully flows into the throat channel. The capillary force here is a type of driving force; while when the fluid flows out of the throat channel, \(\theta+\beta>90^{\circ}\), the value of the capillary force becomes negative and decreases dramatically to a maximum negative value, which presents resistance characteristics. Therefore, the capillary blocking effect is generally observed when the fluid flows out of the throat channel. As shown in Figure 18, a large amount of residual oil keeps a stagnant state and is trapped in the pore space when the fluid leaves the throat channel. The displacement pressure is not sufficient to overcome the capillary barrier resistance formed at these sections, thus resulting in the trapping of the oil in the pore space. As shown in Figure 18d, the capillary barriers formed at position \(a\), \(b\), \(c\), \(d\), \(e\),\(f\), \(g\), \(h\), \(i\), and \(j\) cannot be overcome even at the end of the displacement (0.0687 s). Furthermore, a backflow phenomenon is observed at position \(c\) shown in Figures 18a and 18b, which can be explained by the capillary inhibiting effect in parallel channels. The capillary imbibition will accelerate the fluid in the channel and has an inhibiting effect on the fluid in parallel channels. The continuous formation and breakthrough of the capillary barrier in the displacement process is the main reason for the fluctuations of pressure difference before time 0.0687 s. Therefore, the capillary pressure barrier plays a crucial role in determining the oil-water two-phase flow under low capillary numbers. Figure 19 shows the distribution of oil and water in the porous media model with different capillary numbers under water-wet conditions. As shown in Figure 19, the oil-water interface stays immobile at the sudden expansion section of the pore-throat connection with the increase of the capillary number. Under a larger capillary number, the influence of the capillary force is relatively small, and the viscous force plays a leading role. The effect of the capillary front is not significant, and the water phase displaces the oil phase along the shortest path (main path); while the liquid following along other paths flows at relatively low speed and the residual oil is displaced rapidly from the pore space when the liquid flows along the main path. The effect of the capillary barrier on the fluid mobilization in other paths weakens as with the decrease of the resistance along the main path. Under lower capillary numbers, the capillary force is dominant, and the effect of the capillary front is significant, thus resulting in the detour flow. When the water flows out of the outlet, the decreased pressure difference is insufficient to overcome the capillary  
Figure 17: Under water-wet conditions and the contact angle as 60\({}^{\circ}\): (**a**) The change of pressure difference between the inlet and outlet with time under different capillary numbers; (**b**) The change of saturation of oil with time under different capillary numbers. force and the residual oil is trapped in the pore space. From the authors' perspective, the pressure drop along the channel is mainly due to the viscous dissipation of the fluid.