A fractal theory based fractional diffusion model used for the fast desorption process of methane in coal

Based on the realistic property of the pore structure in coal, we established a fractal theory based Fractional diffusion model (FFDModel) by introducing the fractal dimension df to the Fick's classical model and changing the first-order partial differential equation about time into a υ fractional-order partial differential equation. Then, the solution of the FFDModel was obtained with separation variables technique. In order to verify the correctness of the solution, three coal samples with different rank from China were collected to do the methane desorption experiment of the fast desorption stage. The results indicate that the fractal dimension (df) of the coking coal is the lowest of the three coal ranks. By comparing the FFDModel with Fick's classical model, we can see that the FFDModel fits better with the three measured samples.