Abstract
As the core function of dual-porosity model in fluids flow simulation of fractured reservoirs, matrix-fracture transfer function is affected by several key parameters, such as shape factor. However, modeling the shape factor based on Euclidean geometry theory is hard to characterize the complexity of pore structures. Microscopic pore structures could be well characterized by fractal geometry theory. In this study, the separation variable method and Bessel function are applied to solve the single-phase fractal pressure diffusion equation, and then the obtained analytical solution is used to deduce one-dimensional, two-dimensional and three-dimensional fractal shape factors. The proposed fractal shape factor can be used to explain the influence of microstructure of matrix on the fluid exchange rate between matrix and fracture, and is verified by numerical simulation. Results of sensitivity analysis indicate that shape factor decreases with tortuosity fractal dimension and characteristic length of matrix, increases with maximum pore diameter of matrix. Furthermore, the proposed fractal shape factor is effective in the condition that tortuosity fractal dimension of matrix is roughly between 1 and 1.25. This study shows that microscopic pore structures have an important effect on fluid transfer between matrix and fracture, which further improves the study on flow characteristics in fractured systems.
Highlights
Fractured reservoirs account for a large proportion of the world’s resources and play an important role in the world’s energy structure
The fractal shape factor model presented in this paper (Eqs. (13), (26) and (39)) is in term of tortuosity fractal dimension, maximum pore diameter and characteristic length of matrix
Six values of tortuosity fractal dimension of matrix are selected as 1.0, 1.1, 1.2, 1.3, 1.4 and 1.5, respectively, which reflect the different curvature of flow channels in porous media
Summary
Fractured reservoirs account for a large proportion of the world’s resources and play an important role in the world’s energy structure. Zimmerman et al (1993) developed a single-phase dual-porosity model in fractured reservoirs and solved the non-linear ordinary differential equation to obtain matrix-fracture transfer function, which was more accurate than the linear Warren and Root (1963) equation to calculate the flux in the early and late stages. Sarma and Aziz (2004) believed that fracture networks were non-orthogonal, and solved the nonorthogonal single-phase pressure diffusion equation to deduce 2D and 3D shape factors Their results were verified by comparing the discrete fracture model with the dualporosity model. Yao et al (2012) believed that fractures have fractal characteristics and established two dual-porosity equations based on circular matrix and cylindrical matrix, respectively They used Laplace method to get the pressure analytical solution, and analyzed the influences of matrix shape and fractal parameters on the transient pressure characteristics of fractured reservoirs. The influences of microstructure and characteristic length of matrix on the shape factor are discussed
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