# Investigation of the Effect of Capillary Barrier on Water-Oil Movement in Water Flooding
## 3 Capillary Barrier Phenomenon
### Variation of the Capillary Force along the Central Axis
#### 3.3.2 The Maximal Value and Minimal Value of the Capillary Force and Its Corresponding Conditions  
From the abovementioned theoretical analysis of the position of the interface and the equivalent capillary tube radius at stage I presented in Section 3.3.1, the capillary force increases with \(x\) if \(R>0\), and the maximum capillary force is obtained when the rightmost value is assigned to \(R\), which leads to the maximum driving force; while the capillary force decreases with the increase of \(x\) when \(R<0\), and the minimum capillary force is obtained when the rightmost value is assigned to \(R\), which leads to the maximum resistance in this case. Therefore, the capillary force is a type of driving force when the interface enters the throat section if the following condition is satisfied:  
\[|\beta-\theta|<90^{\circ} \tag{30}\]  
The opening angle \(\beta\) of pore space in oil reservoirs is generally less than \(90^{\circ}\), and the capillary force is always a type of driving force under water-wet conditions, only when Equation (28) holds true; while the capillary force at stage I presents characteristics of driving force under oil-wet conditions if the opening angle \(\beta\) is large enough. The capillary force presents resistance characteristics if the following condition is satisfied:  
\[\theta-\beta>90^{\circ} \tag{31}\]  
Based on the specific values of the contact angle \(\theta\) and the opening angle \(\beta\), the extrema of the capillary force under water-wet and oil-wet conditions when the interface entering the throat section and leaving the throat section are derived, as listed in Tables 1-3.  
There are various types of pores and throats in realistic sandstone, and the radii of the pores and throats vary considerably with different positions. Generally, the radius at the junction of the pore space and the throat channel changes abruptly. From the abovementioned theoretical analysis presented in Section 3.3.1, it is noted that the capillary force under water-wet conditions is positive and is a type of driving force when the oil-wet interface advances in the throat section. The direction of the force (pointing to the concaved side of the interface) is consistent with the direction of the oil-water two-phase flow. The  
Figure 11: Interface morphology in the fifth stage.  
static contact angle formed by the interface and the wall of the pore space is \(\theta\) when the liquid flows out of the throat section. When \(\theta+\beta>90^{\circ}\), the oil-water interface will reverse, and the direction of the capillary force will point to the side of the water phase. There exists a negative maximum value of the capillary force. In this case, the capillary force impedes the forward movement of the two-phase flow, that is, the capillary force under water-wet conditions can be changed to a type of resistance under certain conditions. The interface will stay immobile if the displacement force is insufficient to overcome the maximum resistance and the morphology of the interface continues to change, either increasing or decreasing the displacement force. The resistance dwindles when the displacement force is sufficient to overcome the maximum resistance and the interface can still move forward slowly under the low displacement pressure. Therefore, the displacement pressure must exceed a specific threshold value of the capillary force to displace the fluid. Once the displacement pressure exceeds the threshold value, the pressure needed to displace the fluid will gradually decrease.