# Investigation of the Effect of Capillary Barrier on Water-Oil Movement in Water Flooding
## 1 Introduction
[PERSON] [30] identified the critical contact angle \(\theta_{\text{c}}\) in pore network models using direct numerical simulations and found that the capillary barrier zones in which capillary forces along with viscous forces resist spontaneous imbibition were observed when contact angle \(\theta\) exceeds \(\theta_{\text{c}}\). Factors affecting capillary effect in two-phase flow include the effect of porous media properties (pore-throat size, grain size, heterogeneity, fracture), the effect of fluid saturation and properties, and the effect of external factors (domain size, surfactant, temperature), which are reviewed extensively in the literature [31]. Previous investigations indicate that the capillary barrier effect is largely responsible for the trapping of a great deal of residual oil after waterflooding, and studies of the underlying mechanism of the capillary barrier effect are in the open literature. Furthermore, studies of the capillary barrier effect in the fields of oil recovery are limited to phenomenological description and qualitative analysis, and detailed, accurate, and quantitative analysis of the capillary barrier phenomenon as well as its specific occurrence conditions are rare. Therefore, it is of great significance to systematically investigate the underlying mechanism of the capillary barrier effect as well as its effect on the mobilization of the residual oil within pore spaces of  
Figure 1: The oil-water interface morphology at different positions: (**a**) the oil-water interface in the throat channel; (**b**) the oil–water interface at the pore–throat interface. the reservoir rock. The main objective of the paper is to qualitatively and quantitatively characterize the capillary effect in the porous media flow and to investigate the influence of the capillary barrier effect on the microscopic oil-water flow dynamics and the macroscopic oil recovery efficiency of waterflooding reservoirs as well as its underlying displacement mechanisms. In order to provide a detailed, accurate and quantitative analysis of the capillary barrier phenomenon as well as its specific occurrence conditions, a conceptual physical model of capillary barrier with circular cross-section is constructed first. Then, the morphology (the shape of the oil-water interface in the displacement process) of the oil-water interface at different positions and their corresponding equivalent hydraulic radius and capillary forces are systemically analyzed in theory. Subsequently, the effect of different contact angles and opening angles on the capillary force are investigated. Finally, the capillary barrier effect on oil-water two-phase flow and the oil displacement efficiency in the constructed pore-scale network with opening angle of 45\({}^{\circ}\) are systematically investigated using the volume of fluid method. This work is of great significance in understanding the underlying mechanism of the oil recovery process in reservoir rock and can provide theoretical and technological guidelines for enhancing the oil recovery of current conventional oil reservoirs.