Study on size effect and model optimization of methane desorption-diffusion in high rank coal

Methane diffusion models are numerous, but their application, pros, and cons need to be summarized urgently, the link between particle size and methane desorption-diffusion is uncertain. Therefore, this paper carries out the methane desorption-diffusion experiments under multi-scale pressure and particle size conditions to study the effect of coal sample particle size on methane desorption-diffusion. Based on MATLAB, different diffusion models were fitted and comparatively analyzed, and the models were improved in view of their deficiencies. The results showed that the cumulative methane desorption amount and rate are inversely related to the particle size of coal. Comparative analysis of the models revealed that diffusion model under the third type of boundary conditions has a low fitting accuracy for full process of methane desorption, whereas it has a high fitting accuracy of 0.9831 for the first 1000 s of desorption data. Unipore diffusion model, bidisperse diffusion model and new model of dynamic diffusion coefficient have high fitting accuracy for the desorption data of high homogeneous coal, reaching above 0.97, but unipore diffusion model has only 0.5434 fitting accuracy for non-homogeneous coal samples. The fitting accuracy of improved classical unipore diffusion model for both homogeneous and non-homogeneous coals reaches 0.99, which is more extensive than that of unipore diffusion model, only take the first term can satisfy the accuracy requirement, so it is more convenient in the practical engineering application, and has certain reference significance for engineering calculations of gas content and prediction of gas protrusion.