Anisotropic Characteristics of Relative Permeability in Sedimentary Reservoirs
Authors: Pei Xuehao , Liu Yuetian , Lin Ziyu , Mao Yuxin , Xue Liang 
Published: September 2023

ABSTRACT
Sedimentary and diagenetic processes are known to cause anisotropy in the physical properties of rocks. However, most existing studies primarily focus on the anisotropy of the absolute permeability of reservoirs. To investigate the effect of the anisotropic structure on oil–water two-phase flow, a three-dimensional staggered coring method is developed to prevent or reduce the influence of the end effect in core experiments. Subsequently, the proposed method was used to perform the anisotropy experiment on two-phase relative permeability of natural sandstone, with oil and water, which verifies the existence of relative permeability anisotropy in sandstone reservoirs. Furthermore, we analyzed the tensor representation of anisotropic relative permeability and established a mathematical model of flow considering the anisotropic relative permeability. Numerical simulation calculations of different types of reservoirs were performed considering anisotropic relative permeability. The results indicate that anisotropic relative permeability impacts reservoir development significantly. Particularly, the direction of oil–water flow gradually exhibits apparent differences with the development process. Moreover, one-way and plane dead oil areas appear successively, resulting in a more complex distribution of remaining oil. In the case of reservoirs with relative permeability anisotropy, the downward flow of the oil phase should be avoided to the highest possible extent. Additionally, the advantages of low residual oil saturation and high oil displacement efficiency in the vertical flow should be exploited to promote the upward flow of crude oil into the wellbore to improve recovery.

INTRODUCTION
Geological effects, such as sedimentation, diagenesis, and tectonics, are known to influence formations. These processes are often characterized by anisotropy, wherein the physical parameters, such as the permeability of a reservoir, are directional. Various mathematical models and simulation methods have been proposed for performing absolute permeability anisotropy (da Cunha Teixeira et al. 2021; Fanchi 2008; Hassanpour et al. 2010; Leung 1986; Mortada and Nabor 1961; Park et al. 2002; Peaceman 1983; Shiralkar 1990). However, significant problems continue to exist in the description methods associated with multiphase flow in anisotropic reservoirs. Several studies have reported that relative permeability is characterized by anisotropy based on different scales, including the representative elementary volume scale (Corey et al. 1956a, 1956b; Keilegavlen et al. 2011, 2012), laboratory scale (Bakhshian et al. 2020; Eichel et al. 2005; Honarpour and Saad 1994), and reservoir scale (Blonsky et al. 2017; Rustad et al. 2008; Yeh et al. 1985a, 1985b). Although these studies report significant differences between the relative permeability scalar models and the actual situation, relative permeability is nearly always modeled as a scalar. This is because anisotropic relative permeability measurements are difficult to obtain, and the saturation-related anisotropic characteristics can significantly increase the complexity of numerical methods. From the perspective of crystal physics, Dmitriev et al. (1998, 2003) mathematically investigated two-phase percolation in anisotropic porous media. Although they provided an expression for relative permeability that applies to all media types, this complete expression is extremely complex for practical determination and application. Additionally, they used the concept of symmetry in crystal physics and mathematically proved that the direction of the effective permeability principal axis of the fluid phase in media with orthogonal symmetry is always in line with the absolute permeability principal axis. By contrast, the direction of the effective permeability principal axis of the fluid phase varies with saturation in the case of media with monoclinic or triclinic symmetry. Subsequently, microscopic two-phase percolation in anisotropic media of different types of symmetry was investigated by several researchers using group theory methods (Dmitriev et al. 2005, 2007, 2010; Kalam et al. 2020) and numerical methods (Bear et al. 1987; Ezeuko et al. 2008; Lei et al. 2016; Pergament et al. 2012; Ringrose et al. 1996; Sedaghat et al. 2019). All these studies verified that anisotropy exists in relative permeability, similar to absolute permeability. Pei et al. (2022) demonstrated the existence of relative permeability anisotropy in sandstone reservoirs using cubic core experiments; however, the limitation of the length-to-diameter ratio of the cubic core itself influences the result. Wenkuan et al. (2019) experimentally verified that micro-fractures significantly influence the shape of the relative permeability curve, which leads to anisotropic relative permeability of the matrix. The aforementioned studies indicate that the research on two-phase flow in anisotropic reservoirs is primarily based on numerical methods, lacking reliable physical experimental methods and computational models with high practicality. However, the oil–water relative permeability curve is essential and forms the basis for development planning and dynamic prediction. Moreover, considering only the absolute permeability anisotropy does not reflect the oil–water flow pattern sufficiently in the reservoir.