A general solution and approximation for the diffusion of gas in a spherical coal sample  

作　　者：Wang Yucang Xue Sheng Xie Jun 

机构地区：[1]CSIRO Earth Science and Resource Engineering, Kenmore, QLD 4069, Australia

出　　处：《International Journal of Mining Science and Technology》2014年第3期345-348,共4页矿业科学技术学报（英文版）

摘　　要：The square root relationship of gas release in the early stage of desorption is widely used to provide a simple and fast estimation of the lost gas in coal mines. However, questions arise as to how the relationship was theoretically derived, what are the assumptions and applicable conditions and how large the error will be. In this paper, the analytical solutions of gas concentration and fractional gas loss for the diffusion of gas in a spherical coal sample were given with detailed mathematical derivations based on the diffusion equation. 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 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 spherical coal sample.The square root relationship of gas release in the early stage of desorption is widely used to provide a simple and fast estimation of the lost gas in coal mines. However, questions arise as to how the relation-ship was theoretically derived, what are the assumptions and applicable conditions and how large the error will be. In this paper, the analytical solutions of gas concentration and fractional gas loss for the dif-fusion of gas in a spherical coal sample were given with detailed mathematical derivations based on the diffusion equation. 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 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 spherical coal sample.

关 键 词：Coal content Lost gas Spherical coal sample Gas diffusion APPROXIMATION Error analysis 

分 类 号：TD712[矿业工程—矿井通风与安全]