Modeling of diffusion kinetics during gas adsorption in a coal seam with a dimensionless inversion method

Abstract

• A free gas density gradient (FGDG)-driven model of gas adsorption and diffusion in coal matrix was proposed. • A novel inversion method of diffusion coefficient combining dimensionless variables and empirical correlation was developed. • A gas adsorption experiment with constant pressure boundary was conducted to validate simulation results. • Evaluation and discussion were made to differentiate the previous FGDGMs and the newly proposed one. Modeling gas diffusion kinetics in a coal seam plays an essential role in predicting performance of both coalbed methane production and its enhanced recovery. Throughout the diffusion period, not only does there exist a large deviation between the analytical solution of the classical Fickian unipore diffusion model (UDM) and experimental measurements, but also constant diffusion coefficients calculated with the inversion of the simplified empirical/semi-empirical correlations are still not accurate enough. In this paper, we proposed a free gas density gradient model (FGDGM) to characterize the gas adsorption and transport properties in a coal seam. Experimentally, isothermal experiments were performed using a high-temperature and high-pressure gas adsorption analyzer with methane gas. Theoretically, a Langmuir gas concentration was derived and improved as a function of free gas density, and then we correlated a numerical inversion model to determine the effective diffusion coefficients by combining dimensionless variables and empirical correlations. Finally, the developed models were validated with the measured gas adsorption isotherms. The numerical solution curves based on the FGDGM are found to be basically consistent with the measured data in the entire time scale, while the developed inversion method is accurate as well as efficient in computational expenses. On the basis of the ideal gas assumption, the actual density gradient and diffusion coefficient will be underestimated and overestimated, respectively. By incorporating real gas behaviour into the improved FGDGM, both gas mass flux and effective diffusion coefficient can be determined more accurately to model gas diffusion kinetics and gas flow patterns in a coal seam.