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Fractured karstic carbonate reservoirs have obvious multi-scale characteristics and severe heterogeneity due to the development of abundant karst caves and fractures with different scales. Darcy and non-Darcy flows coexist due to this property. Therefore, selecting the appropriate flow equations for different regions in the numerical simulation of fluid flows, particularly two-phase and multiphase flows, is a critical topic. This paper compares and analyses the displacement distance differences of waterfront travel using the Darcy, Forchheimer and Barree–Conway equations, as well as analyzes the influence of the Forchheimer constant, fluid viscosity, flow rate and absolute permeability on inertia action based on the Buckley–Leverett theory. The results show that the Forchheimer number/Reynolds number of water/oil two-phase flow is not a constant value and varies with water saturation, making it difficult to determine whether the inertial action should be considered solely based on these values; the influence of inertial action can be measured well by comparing the difference between the displacement distances of the waterflood front, and the quantitative standard is given for the selection of the flow equation of different regions by calculating the allowable error of the displacement distance of the waterflood front. The magnitude of the inertial effect is affected by the physical properties of the fluid and reservoir medium and the fluid velocity. The smaller the difference in the viscosity of the oil/water fluid, the smaller the inertial effect is. This technique was used a preliminary attempt to analyze the fractured karstic carbonate reservoirs at Tarim, and the results confirmed the validity of the method described in this article. [ABSTRACT FROM AUTHOR]

Two-phase flow in fractured and karstified porous media subject to coupled hydro-mechanical conditions is an important issue for oil recovery in carbonate reservoirs. However, due to the co-existence of porous media flow, fracture flow and free flow, as well as their couplings with geomechanical deformation, modeling the behavior of fractured karst systems remains challenging. In this work, a novel coupled hydro-mechanical model for simulating the complex behavior of fractured and karstified porous media is developed. Two-phase Darcy's equation is used to describe fluid flow in both matrix and fractures, while the free flow in cavities is considered based on an assumption of phase instantaneous gravity segregation. A modified Barton-Bandis's constitutive model is used to mimic the nonlinear fracture deformation. The cavity deformation is solved based on the fluid pressure on the cavity boundaries. A mixed finite volume-finite element method and a fixed-stress iterative splitting method are adopted to numerically solve the coupled system of equations. The model is then applied to a series of 2D and 3D problems to unravel the impacts of fractures and cavities on two-phase flow and geomechanical deformation in fractured karst systems. The results indicate that cavities hinder water breakthrough due to storage effects, while water may quickly migrate through highly conductive fractures. Cavities tend to dominate the flow and mechanical processes even though fractures are present as well. Significant stress concentration is observed around cavities. Furthermore, the results of 3D cases imply that phase gravity segregation in cavities leads to lower water saturation in the area above cavities and delays water breakthrough. [ABSTRACT FROM AUTHOR]

• Coupled porous media and free flow model of fluid flow in fractured karst reservoirs. • Analytical expression of connectivity for discrete fracture-cave networks. • Flow channeling dominated by network connectivity. • Permeability scaling with connectivity in a power law for connected systems. Fractured karst reservoirs play a significant role in hydrocarbon reserves and groundwater storage. They often exhibit complex multiscale heterogeneities involving pores, fractures and caves, whose length scales range from microns to tens or hundreds of meters. Thus, the study of fractured karst reservoirs is faced with a significant unresolved challenge in quantitatively characterizing the geometrical connectivity and hydraulic conductivity as well as their interrelationships in such strongly heterogeneous, multicomponent systems. In this paper, we propose an analytical formulation to characterize the connectivity of discrete fracture-cave networks building upon the excluded area concept of the percolation theory. By implementing a state-of-the-art computational model solving coupled Navier-Stokes (free flow) and Darcy (porous media flow) equations, we numerically derive the permeability of a fractured and karstified porous media, such that the relationship between the connectivity and permeability is further explored. The high-fidelity numerical model also permits us to elucidate the process of flow channelization within the fracture-cave network. The results show that the fracture-cave network connectivity correlates to the permeability via a power law scaling for connected systems. Significant flow channeling occurs around the percolation threshold where the flow is dominated by a limited number of preferential pathways. Caves play a crucial role in the flow due to the fact that caves could globally enhance the network connectivity and locally serve as hotspots for high fluid velocity. Finally, a semi-analytical permeability model for fractured karst reservoirs is developed. The results of our research and insights obtained have important implications for understanding the subsurface fluid flow in fractured karst reservoirs. [ABSTRACT FROM AUTHOR]