# 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
#### 4.3.2 Oil-Wet Condition  
Figure 20 shows the change of pressure difference between the inlet and outlet and the change of saturation of oil phase in the porous media model under oil-wet conditions. As can be seen from Figure 20a, there is a large fluctuation amplitude of pressure difference before and after the breakthrough of the water phase at the large capillary number of 1.8 \(\times\) 10\({}^{-2}\), which is more obvious than the fluctuation amplitude of the pressure difference at the capillary number of 1.8 \(\times\) 10\({}^{-4}\) and 1.8 \(\times\) 10\({}^{-3}\). With the advancing of the water phase, small fluctuations of the pressure difference are observed. It can be seen from Figure 20b that the highest oil displacement efficiency is obtained at the large capillary number of 1.8 \(\times\) 10\({}^{-2}\), which indicates that the larger the capillary number, the higher the oil displacement efficiency. The higher capillary number indicates that the viscous force dominates the displacement process, which will result in the viscous fingering, and the high capillary pressure in the pore space can be overwhelmed, which will enhance the oil recovery rate [19]. Under oil-wet conditions, the occurrence of the capillary barrier effect facilitates the mobilization of the fluid phase, and the increase of the sweep area when \(\theta-\beta\leq 90^{\circ}\) thus improves the oil displacement efficiency. Figure 19: The distribution of oil and water in the porous media model under different capillary numbers and water-wet conditions with the contact angle of 60\({}^{\circ}\): (**a**) Ca = 1.8 \(\times\) 10\({}^{-4}\); (**b**) Ca = 1.8 \(\times\) 10\({}^{-3}\); (**c**) Ca = 1.8 \(\times\) 10\({}^{-2}\). Figure 21 shows the change of oil and water distribution with time at the capillary number of \(1.8\times 10^{-4}\) under oil-wet conditions. As shown in Figure 21, a couple of capillary barriers are formed in the throat section (as shown in Figure 21d at position \(a\), \(b\), \(c\), \(d\), \(e\), \(f\), \(g\), \(h\), \(i\), \(j\)) and some of the residual oil is trapped in the dead end of the pore space and cannot be displaced from the outlet. Considering \(\theta-\beta<90^{\circ}\) in this case, the capillary force is positive and there is a maximum positive value of the capillary force when the fluid flows into the throat channel and is a type of driving force. Then, the capillary force decreases to a stable negative maximum value in the throat channel and presents resistance characteristics. The capillary force will gradually increase and is still negative when the fluid flows out of the throat channel. That's why part of the residual oil stays stagnant or stays trapped in the throat channel or pore space. At the end of the displacement (0.0736 s), a water-bearing channel is formed in Region I and the residual oil trapped in the lateral direction cannot be extracted thereafter. Likewise, the dramatic fluctuations of pressure difference between the inlet and outlet are due to the formation and breakthrough of the capillary barrier alternatively at low capillary numbers, and the capillary inhibiting effect in parallel channels is also observed in this case. Figure 22 shows the distribution of oil and water in the porous media model with different capillary numbers under oil-wet conditions. As can be seen from Figure 22, the water flows along both sides of the diagonal line of the porous media model at the initial stage and only part of the water can flow into the intermediate region along the diagonal line. Then, the interface of both sides of the diagonal line of the model becomes stagnant at the increase of the displacement force. At the final stage, the water flows out of the model along the diagonal line of the model. The high injection rate leads to the increase of the pressure along with the main displacement direction and viscous force dominating the displacement process, while too high an injection rate can inhibit the spontaneous imbibition perpendicular to the injection direction [38].