Determining diffusion coefficients of coal particles by solving the inverse problem based on the data of methane desorption measurements

Abstract

The diffusion coefficient is the key parameter been used to evaluate the methane diffusion behavior. Generally, the diffusion coefficient is determined by analytical solutions, including the unipore diffusion model and the bidisperse diffusion model. However, the essential assumptions limit the applicability and accuracy of analytical solutions. Inverse modeling has been proved to be useful in a variety of disparate fields. In this work, the detailed process and principles of using inverse modeling in gas diffusion are introduced. The effectiveness and accuracy of MMA, SNOPT and LM algorithms in determining the diffusion coefficient are analyzed. Results show that the inverse problem is a feasible method and the LM algorithm takes the shortest time and is recommended. The analytical solution (diffusion coefficient) of particles whose sizes are 0.074–0.2 mm, 0.25–0.5 mm and 0.5–1 mm are 13.8% times, 5.0% times and 1.6% times larger than that of the numerical solution, respectively. The numerical method has higher computing accuracy of small coal particles. As the current work is the first to present efficient techniques for the solution of diffusion coefficient-related inverse problems in COMSOL, the applicability of inverse modeling in complicated gas diffusion problems has also been prospected.