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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 mathematical theorem 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 analyzes 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.