Calculation method of equivalent permeability of dual-porosity media considering fractal characteristics and fracture stress sensitivity

Abstract In the petroleum industry, the accurate calculation of equivalent permeability of dual medium is very important for the estimation of reserves and the design of oil and gas production. At present, there are many methods to calculate the equivalent permeability of dual medium. These methods have their own advantages and disadvantages, and are suitable for different medium characteristics and physical problems, but they cannot calculate the equivalent permeability of dual medium under reservoir conditions. Thus, the emergence of fractal theory provides a theoretical basis for us to study the law of fluid transport in randomly distributed pores and fractures. Many scholars have deduced the analytical solution of the fractal model of double-porosity media, and the fractal dimension of the rock matrix and fracture network has been widely used in the permeability model of dual-porosity media. It has been proven that fracture permeability and pore matrix permeability considering fractal properties can be realistically applied. In this work, the fractal dimension of the rock matrix and fracture network aperture surface tortuosity are introduced to establish a dual-permeability calculation model considering the fracture closure effect. Taking the Yanchi Chang 8 area of the Ordos Basin as an example, comparing the results of the numerical simulation model and fractal model, the proposed two-porosity medium model considering the stress closure effect is more accurate. The sensitivity analysis of each parameter in the equivalent permeability model shows that considering the effect of stress closure reduced the fracture and pore aperture. The equivalent permeability is significantly influenced by the fracture inclination, the fractal dimension of the fracture aperture, and the fractal dimension of the matrix pore diameter. The rougher fracture surface and more tortuous capillary path forces particles to move longer distances, thereby reducing the permeability of the fracture network.