Application of the stretched exponential equation to sorption of mine gases and sorption induced swelling of bituminous coal

An evaluation of the ability of the stretched exponential (SE) equation to describe the sorption kinetics and the rate of expansion/contraction of hard coal in coal-carbon dioxide, coal-methane and coal-CO2/CH4 mixture systems was performed. In order to address this issue the adequate sorption experiments were carried out at high pressure by means of the volumetric method on a cubicoid solid samples. Simultaneously the kinetics of coal sorption-induced swelling were monitored. For two coals under investigation a linear and a non-linear relation between coal expansion and the amount of sorbed gas was observed. The SE equation shows a very good agreement with the sorption experimental data obtained for both coals, it is also able to accurately describe the sorption-induced-swelling of lower rank coal and the CH4-induced swelling of higher rank coal however it does not give a reasonable fit to swelling kinetics induced by sorption of CO2 and CO2\CH4 mixtures on higher rank coal. The highest characteristic rate parameter k was found for CO2 sorption on lower rank coal, the lowest was calculated for CH4 sorption on the same coal and the values of k for higher rank coal are in between. The values of stretching parameter b for higher rank coal are greater than for lower rank coal, i.e. between 0.55 and 0.75 and < 0.5, indicating a relatively narrow and a relatively broad distribution of characteristic relaxation times of sorption processes, respectively. Generally, the values of parameters k and b calculated for CO2, CH4 and CO2\CH4 mixture sorption-induced swelling are lower for lower rank coal. The values of parameter b for swelling phenomena are not compatible with these of sorption processes.