A numerical approach to upgrade the estimation of gas diffusion coefficient in coal matrix

Accurately estimating diffusion coefficient of coal is of great significance for coalbed gas production planning. However, the most commonly used approach (written as infinite series) to inverse D may result in erroneous estimation due to assuming a constant surface concentration in solving the Fick diffusion model. This study first conducted a succession of experiments on coal-gas (CH₄ and CO₂) ad/desorption, and on the basis of Fick diffusion model, both an analytical approach and a numerical approach were proposed to inverse D in coal. The inversion result shows D is not a constant, it increases with pore pressure decreasing. The discrepancy resulted from using distinct inversion approaches varies with the pore pressure changing. It implies using the analytical approach to inverse D will underestimate the gas diffusivity of coal in some extend. Assuming a constant surface concentration will introduce some unpredictable deviation, even some unacceptable error. Finally, a dimensionless processing for Fick diffusion model was proposed to easy the numerical approach to inverse gas diffusion coefficient. This work is expected to make a clear evaluation on the influence of holding a constant surface concentration in solving Fick diffusion model and suggest a high-accuracy and efficient approach to estimate gas diffusion coefficient and model gas transport behaviors in coal matrix.