The analytical mathematical solutions of gas concentration and fractional gas loss for the diffusion of gas in a cylindrical coal sample were given with detailed mathematical derivations by assuming that the diffusion...The analytical mathematical solutions of gas concentration and fractional gas loss for the diffusion of gas in a cylindrical coal sample were given with detailed mathematical derivations by assuming that the diffusion of gas through the coal matrix is concentration gradient-driven and obeys the Fick’s Second Law of Diffusion.The analytical solutions were approximated in case of small values of time and the error analyses associated with the approximation were also undertaken.The results indicate that the square root relationship of gas release in the early stage of desorption,which is widely used to provide a simple and fast estimation of the lost gas,is the first term of the approximation,and care must be taken in using the square root relationship as a significant error might be introduced with increase in the lost time and decrease in effective diameter of a cylindrical coal sample.展开更多
The diffusion,viscosity and thermal conductivity coefficients of gases between two parallel solid walls have been obtained analytically based on the Green-Kubo relation under a hard-sphere model.They decrease nonlinea...The diffusion,viscosity and thermal conductivity coefficients of gases between two parallel solid walls have been obtained analytically based on the Green-Kubo relation under a hard-sphere model.They decrease nonlinearly as the Knudsen number defined as the ratio of the mean free path to the wall distance increases.This theoretical prediction was in good agreement by the DSMC results.展开更多
基金provided by the Science and Technology Grant of Huainan City of China (No.2013A4001)the Key Research Grant of Shanxi Province of China (No.201303027-1)
文摘The analytical mathematical solutions of gas concentration and fractional gas loss for the diffusion of gas in a cylindrical coal sample were given with detailed mathematical derivations by assuming that the diffusion of gas through the coal matrix is concentration gradient-driven and obeys the Fick’s Second Law of Diffusion.The analytical solutions were approximated in case of small values of time and the error analyses associated with the approximation were also undertaken.The results indicate that the square root relationship of gas release in the early stage of desorption,which is widely used to provide a simple and fast estimation of the lost gas,is the first term of the approximation,and care must be taken in using the square root relationship as a significant error might be introduced with increase in the lost time and decrease in effective diameter of a cylindrical coal sample.
基金supported by the National Natural Science Foundation of China (Grant No.10921062)
文摘The diffusion,viscosity and thermal conductivity coefficients of gases between two parallel solid walls have been obtained analytically based on the Green-Kubo relation under a hard-sphere model.They decrease nonlinearly as the Knudsen number defined as the ratio of the mean free path to the wall distance increases.This theoretical prediction was in good agreement by the DSMC results.
