Gas diffusion in a cylindrical coal sample – A general solution,approximation and error analyses  

作　　者：Li Yaobin Xue Sheng Wang Junfeng Wang Yucang Xie Jun 

机构地区：[1]Key Laboratory of Integrated Coal Exploitation and Gas Extraction,Anhui University of Science and Technology [2]School of Energy and Safety,Anhui University of Science and Technology [3]CSIRO Earth Science and Resource Engineering [4]School of Mining Engineering,Taiyuan University of Science and Technology

出　　处：《International Journal of Mining Science and Technology》2014年第1期69-73,共5页矿业科学技术学报（英文版）

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)

摘　　要：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.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 dif- fusion 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 anal- yses 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.

关 键 词：Gas content Lost gas Gas diffusion Cylindrical coal sample Approximation Error analysis 

分 类 号：TD712[矿业工程—矿井通风与安全]