科研之友
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摘要
The gas-liquid flow in the porous medium of coal is the foundation for understanding the theoretical expression of permeability, and it is also play a vital role in revealing the mechanism of low-permeability. Based on the fractal structure of capillary in micro and nano scales, a fractal tortuosity model established in the longitudinal direction and a fractal cross-section model established in the transverse direction were employed to quantitatively analyze the pore structure of low permeability coal. The differences in the definition of the tortuosity based on the Hagen-Poiseuille equation and the capillary pressure formula are analyzed. The latter one combined with the mercury intrusion experiments is more suitable for the seepage of coal pores below the micro scale. Based on the relationship of fractal scales, the effects of the aspect ratio and the fractal dimension of tortuosity on the fractal coefficient were theoretically analyzed. The mercury intrusion tests in coal were also carried out, and the average tortuosity and fractal dimensions were calculated;the product of the two was defined as the fractal coefficient. Based on the Carman-Kozeny equation, the fractal equation of cross-section can be deduced, including the theoretical expressions on the fractal dimension of perimeter and area. A gas-liquid displacement model was established based on Washburn dynamic equations;the fractal equations of the interface position and velocity were obtained. The nano-micro pore structure of low-permeability coal was reconstructed based on Nano-CT and the pore size and volume distribution were obtained. The fractal dimension of the perimeter and area was calculated based on the experimental data. Finally, a two-phase of N2-H2O displacement experiment was carried out based on NMR. Moreover, the distance and velocity distribution of the interface were obtained. The results show that the fractal structure of capillary model can be used as a geometric bridge to explain the mechanism of low permeability. The defined fractal coefficient can effectively reflect the influence of tortuosity and fractal dimension, as well as the linear relationship with permeability. The reliability of the fractal cross-section model was verified, and the low-permeability mechanism of coal should still consider the influence of fractal cross-section roughness. The validity of the fractal dynamic equation was confirmed by the distribution of water flooding signals by NMR.
