Search

In this paper, a novel porous media permeability model is established by using particle model, capillary bundle model and fractal theory. The three-dimensional irregular spatial characteristics composed of two ideal particles are considered in the model. Compared with previous models, the results of our model are closer to the experimental data. The results show that the tortuosity fractal dimension is negatively correlated with porosity, while the pore area fractal dimension is positively correlated with porosity; The permeability is negatively correlated with the tortuosity fractal dimension and positively correlated with the integral fractal dimension of pore surface and particle radius. When the tortuosity fractal dimension is close to 1 and the pore area fractal dimension is close to 2, the faster the permeability changes, the greater the impact. Different particle arrangement has great influence on porous media permeability. When the porosity is close to 0 and close to 1, the greater the difference coefficient is, the more the permeability of different arrangement is affected. In addition, the larger the particle radius is, the greater the permeability difference coefficient will be, and the greater the permeability difference will be for different particle arrangements. With the increase of fractal dimension, the permeability difference coefficient first decreases and then increases. When the pore area fractal dimension approaches 2, the permeability difference coefficient changes faster and reaches the minimum value, and when the tortuosity fractal dimension approaches 1, the permeability difference coefficient changes faster and reaches the minimum value. Our research is helpful to further understand the connotation of medium transmission in porous media.

Based on fractal geometry theory, the Hagen−Poiseuille law, and the Langmuir adsorption law, this paper established a mathematical model of gas flow in nano-pores of shale, and deduced a new shale apparent permeability model. This model considers such flow mechanisms as pore size distribution, tortuosity, slippage effect, Knudsen diffusion, and surface extension of shale matrix. This model is closely related to the pore structure and size parameters of shale, and can better reflect the distribution characteristics of nano-pores in shale. The correctness of the model is verified by comparison with the classical experimental data. Finally, the influences of pressure, temperature, integral shape dimension of pore surface and tortuous fractal dimension on apparent permeability, slip flow, Knudsen diffusion and surface diffusion of shale gas transport mechanism on shale gas transport capacity are analyzed, and gas transport behaviors and rules in multi-scale shale pores are revealed. The proposed model is conducive to a more profound and clear understanding of the flow mechanism of shale gas nanopores.