A Novel Trilinear Flow Model for Capturing Dynamic Behavior of Water Flooding in Core Plug with Different Fracture Inclinations in Carbonate Reservoirs
Authors: Sun Meng , Guo Hongxin , Zhao Wenqi , Wang Peng , Zhao Lun , Fan Zifei , Wang Shuqin 
Published: January 2022

Abstract
The purpose of this study is to introduce a new three-linear flow model for capturing the dynamic behavior of water flooding with different fracture occurrences in carbonate reservoirs. Low-angle and high-angle fractures with different occurrences are usually developed in carbonate reservoirs. It is difficult to simulate the water injection development process and the law of water flooding is unclear, due to the large variation of the fracture dip. Based on the characteristics of water flooding displacement streamlines in fractured cores with different occurrences, the matrix is discretized into a number of one-dimensional linear subregions, and the channeling effect between each subregion is considered in this paper. The fractures are divided into the same number of fracture cells along with the matrix subregion, and the conduction effect between the fracture cells is considered. The fractured core injection-production system is divided into three areas of linear flow: The injected fluid flows horizontally and linearly from the matrix area at the inlet end of the core to the fracture and then linearly diverts from the fracture area. Finally, the matrix area at the outlet end of the core also presents a horizontal linear flow pattern. Thus, a trilinear flow model for water flooding oil in fractured cores with different occurrences is established. The modified BL equation is used to construct the matrix water-flooding analytical solution, and the fracture system establishes a finite-volume numerical solution, forming a high-efficiency semianalytical solution method for water-flooding BL-CVF. Compared with traditional numerical simulation methods, the accuracy is over 86%, the model is easy to construct, and the calculation efficiency is high. In addition, it can flexibly portray cracks at any dip angle, calculate various indicators of water flooding, and simulate the pressure field and saturation field, with great application effect. The research results show that the greater the fracture dip angle, the higher the oil displacement efficiency. When the fracture dip angle is above 45°, the fracture occurrence has almost no effect on the oil displacement efficiency. The water breakthrough time of through fractures is earlier than that of nonthrough fractures, and the oil displacement efficiency and injection pressure are more significantly affected by the fracture permeability. With the increase of fracture permeability, the oil displacement efficiency and the injection pressure of perforated fractured cores dropped drastically. The findings of this study can help for better understanding of the water drive law and optimizing its parameters in cores with different fracture occurrences. The three-linear flow model has strong adaptability and can accurately solve low-permeability reservoirs and high-angle fractures, but there are some errors for high-permeability reservoirs with long fractures.