Mathematical model for gas diffusion from non-homogeneous coal particles
Abstract
By establishing model and experimental verification, this paper aims at improving the accuracy and applicability of gas diffusion mathematical model from coal particles in engineering applications. Firstly, based on Fick's second law and the continuity theory of gas diffusion in porous media, a new constitutive model for gas diffusion from non-homogeneous coal particles with three-layer pore structure is constructed by considering the difference of characteristics in pore structure between soft coal and hard coal. Then, the analytical solution is derived from the new model, that is, the quantitative relationship between gas diffusion rate (Qt/Q∞) and diffusion time (t). The pore structure parameters of soft coal and hard coal from Juji coal mine were determined by using the mercury injection method. Gas desorption and diffusion rules of coal samples are numerically calculated and investigated by using physical simulation methods. Lastly, the applicability of the constitutive model was verified. The research results show that the homogeneous model widely used only applies to describe gas diffusion process of the hard coal within the initial 10minutes, while the new model can describe the gas diffusion law of different pore structure characteristics. The calculation results from the new model and the physical experimental results are nearly identical within the initial 30 minutes. The difference of gas diffusion process between soft coal and hard coal can be effectively reflected by the parameters of pore structure in the new model.References
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