Fractal-Time-Dependent Fick Diffusion Model of Coal Particles Based on Desorption–Diffusion Experiments

Abstract

The diffusion coefficient is a crucial parameter to manifest the diffusivity of methane in coal, which is obtained by solving mathematical and physical equations that characterize the diffusion process. The diffusion model established by combining the pore structure parameters and time-dependent characteristics in Euclidean space cannot reflect the natural heterogeneity of coal. There is a fundamental difference between the fractal structure and time-dependent diffusion characteristics in Euclidean space. Based on the classic homogeneous spherical Fick diffusion model of coal particles, the full-aperture comprehensive fractal dimension and time-dependent diffusion decay coefficient are introduced, forming the fractal-time-dependent Fick diffusion (FTFD) model of coal particles. To verify the new model, we obtained model parameters by mercury injection, low-temperature liquid nitrogen adsorption, and desorption−diffusion experiments, and the model fitting curve was drawn, which was compared with the desorption−diffusion rate experimental points. In addition, the calculation method of lost-gas content based on the √t approach was also corrected. The results indicated that the new model could describe the whole process of gas diffusion in the heterogeneous coal with good accuracy and stability. The new model also covered the traditional classical homogeneous spherical Fick diffusion and dynamic diffusion-coefficient models with more general theoretical significance. The lost-gas content calculated by the new model was consistent with the actual lost-gas content, improving the accuracy of the lost-gas calculation. The investigation results have important theoretical significance for a comprehensive understanding of the diffusion and transport of pore gas in coal seams.

Experimental Study on Methane Diffusion Characteristics of Different Metamorphic Deformed Coals Based on the Counter Diffusion Method

“…Coals with similar degrees of deformation had D that showed an increasing trend with increasing metamorphism degree; under the same degree of deformation, D of anthracite was larger than that of fat coal. D measured via the granular method [13,60] continuously increased with an increase in the degree of coal deformation, which differs from the finding obtained from counter diffusion experiments with different degrees of columnar coal sample metamorphism and deformation. The solidity coefficient of coal (f) indicates its solidity.…”

“…The pores and fractures in coal are storage spaces for coalbed methane and channels for methane migration [10,11]. Due to the differences in the causes, forms, and scales of pores and fractures in coal, the different migration mechanisms of methane in the pore and fracture channels can be divided into pore diffusion and fracture seepage [12,13]. Seepage can occur through the cleavage and fracture system in the coal body, which is driven by pressure differences, following Darcy's law [14,15]; diffusion can occur within the coal matrix pores and micro-fractures, which is driven by concentration differences, following Fick's law [16,17].…”

Study on the Solution and Variation Law of Diffusion Coefficient Based on the Numerical Simulation Optimization Method

“…Meanwhile, due to the assumption of a constant diffusion coefficient, the single-pore diffusion model has a large deviation in describing desorption curve over a long period of time. For this reason, the time-dependent diffusion coefficient model and the fractal diffusion coefficient model have been proposed, − yet the principle and physical implication of diffusion coefficient variation have not been explained scientifically. Therefore, the diffusion coefficient solution and the diffusion law need to be further studied.…”

Effect of Desorption Damage on the Kinetic Characteristics of Coal Particle Gas Desorption

“…The fractal dimension can also be used to quantitatively analyze the gas adsorption capacity of coal samples and to reflect the diffusion coefficient of coal, which indicates that there is a certain relationship between the diffusion coefficient D i of coal and the fractal dimensions D 1 and D 2 . − By analysis of the relationship between the diffusion coefficient and fractal dimension of each coal sample (Figure ), it was found that the diffusion coefficient and fractal dimension exhibit a positive linear correlation. The fractal dimension increases as the diffusion coefficient increases, and the correlation coefficient R 2 reaches more than 0.9, indicating that the diffusion coefficient is also related to the roughness of the coal pore surface and the complexity of the pore volume, and that of the coal sample with desorption damage is more obvious.…”