# Investigation of the Effect of Capillary Barrier on Water-Oil Movement in Water Flooding
## 1 Introduction
Wettability is the most important factor that directly determines the magnitude and direction of the capillary force. In a straight capillary tube, the capillary force is the driving force to promote the movement of oil and water under hydrophilic condition. However, the capillary force is resistant under hydrophobic condition, which hinders the movement of oil and water. In complex porous media, the pore geometry will affect the apparent wettability [15]. The reservoir rock is characterized mainly via X-ray tomography and scanning electron microscopy methods to obtain characteristics of the void space such as the facies, the pore throat size, and the structure heterogeneity, which has a significant impact on the multiphase flow within porous media [16; 17; 18; 19]. To mobilize the residual oil in the void space, it is necessary to study the capillary effect based on the structure of the void space. In a certain pore structure, the oil-water interface may still show resistance under hydrophilic condition, as shown in Figure 1. Figure 1a shows the oil-water interface in the throat channel; (b) the oil-water interface at the pore-throat interface. Among them, \(\theta\) is the wetting angle and \(\beta\) is the opening angle from pore to throat. Under hydrophilic condition (\(\theta<90^{\rm o}\)), when the oil-water interface is in the throat, the capillary force is the driving force for the oil in the water flooding process; When the oil-water interface moves to the throat outlet and enters the pore, the oil-water interface will gradually deform and show a contact angle \(\theta\) with the pore wall. As a result, the oil-water interface may reverse and show resistance (Figure 1b). Subsequently, it moves forward along the pore wall, the radius increases, and the capillary force decreases. During the movement of the oil-water interface from throat to pore, the capillary effect will have peak resistance. When the displacement force is not enough to break through the peak resistance, the oil-water interface will stop, hinder the spread of water, and cause the remaining oil. This peak resistance is the capillary barrier discussed in this paper. The capillary barrier is specific capillary behavior when the oil-water interface meets the pore-throat interface. The capillary barrier phenomenon in porous media was initially observed that the water cannot flow from the fine layers upwards to the coarse layers in the subsurface; the phenomenon was termed 'capillary barrier', which was later employed in the fields of soil remediation, landfill cover design, unclear waste management, microfluidics, chemical engineering, and multiphase flow in porous media [20; 21; 22; 23; 24; 25]. In the fields of microscale immiscible two-phase flow within porous media, a variety of studies have been conducted on the capillary barrier effect. [PERSON] [26] investigated the interplay between viscous and capillary forces as a function of oil viscosity and injection velocity via water flooding experiments. Interaction between capillary and viscous effects plays a significant role in the flow instability and immiscible displacement and is verified by macroscopic capillary number with a critical value of N\({}_{\text{ca}}\)\(\sim\)1 [27]. [PERSON] [28] pointed out that the displacement pattern can be transitioned between capillary-dominated and viscous-dominated modes via the adjustment in pore geometry, capillary fingering in porous media with hierarchical structures can be suppressed by adjusting the pore geometry, and the weak capillary effects can enhance the displacement stability. The complex capillary pressure distribution and configuration of fluid during displacement in highly heterogeneous porous media were measured via image processing methods and the results can facilitate better understanding of fluid displacement process [29].