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Pore structure in coal is fundamental to determining the flowability properties and mechanical functions. Various insights into pore structure, including pore size distribution, specific area, and pore volume, have been obtained in experiments with many methods. Systematic research is lacking on how to characterize pore structure with more detailed information using fractal theory. Here, using the small-angle X-ray scattering (SAXS) method, we studied the fractal characters of four coal samples and showed how the deviation corrected, coal rank, and gas adsorption affected the fractal dimension of the pore structure. The average pore diameters of four samples obtained by the gyration radius using Guinier curves were 50.25–52.95 nm. The surface fractal of coal samples was the dominant feature, and the fractal features altered with the q value. Scattering information of simple bodies, such as pores and fractures, could superimpose the non-integer nature of the fractal dimension. The Porod and Debye laws guided the deviation correction process in the high q region. Pore fractals might be changed into surface fractals through the fractal dimension after the deviation correction, and the SAXS data obtained by Debye law correction maintained the originality and validity better than Porod law correction. The irregular shape of M was observed on the curve of fractal dimension as the maximum reflectance of vitrinite increases, resulting in three stages. More adsorption sites per unit projection area could be found in a larger fractal dimension of the pore surface, which results in an increase in Langmuir adsorption volume. The increase in the adsorption pressure reduced the fractal dimension. Our findings enhance the experimental support for comprehending the structure of coal nanopores. [Display omitted] • Surface fractals dominated the coal nanopores with the sizes of 2.21–70.24 nm. • The deviation correctness may be changed surface fractal into pore fractal by Porod law and Debye law. • Surface fractal dimensions show an irregular M-curve trend with an increase in maximum vitrinite reflectance. • Gas adsorption increase the smoothness of coal pore surface and decrease the fractal dimension. [ABSTRACT FROM AUTHOR]

An accurate model of gas desorption and diffusion is the necessary prerequisite to accurately predict gas transfer and evaluation of gas content in the coal. A new modified shrinking core model was proposed and modified based on the shrinking core model and taking into account the time-depend diffusivity. It was to predict the kinetic process of gas desorption and diffusion including three processes: (1) desorption on the undesorbed core surface, (2) diffusion through the desorbed layer, and (3) diffusion through the gas film. The kinetic data of gas desorption and diffusion was obtained from a series of experimental tests conducted under isothermal conditions. The model showed the best agreement with the experimental data, comparison with the shrinking core model, the simplified unipore diffusion model, and the simplified bidisperse diffusion model. Comparison and validation of simulated curves and experimental data indicated the diffusion through the desorbed layer had a dominant role in the whole process of gas transfer in coal particle. The effect of adsorption equilibrium pressure, temperature, and particle size on the initial diffusivity was discussed by using the modified shrinking core model to model the experimental data. The initial diffusivity was affected slightly by the adsorption pressure and increased with the increase in temperature and the particle size. This research provides a new modified shrinking core model to describe the gas transfer process in coal particles better. • Gas transfer in coal particles consisted of three steps: desorption, internal diffusion, and external diffusion. • Shrinking core model was modified based on time-dependent diffusivity. • The modified Shrinking core model showed good applicability in describing gas desorption and diffusion behavior. • The effect of pressure, temperature, and particle size on initial diffusivity was discussed by the modified Shrinking core model. [ABSTRACT FROM AUTHOR]