Analytical model and experimental investigation of the adsorption thermodynamics of coalbed methane

The study on adsorption thermodynamics is conducive to a deep understanding of the heat and mass transfer mechanism of coalbed methane in a coal seam. In this work, the analytical expressions of the isosteric heat for six adsorption models taking into account the temperature variations are directly derived according to Clausius-Clapeyron equation. Meanwhile, the adsorption content and adsorption heat at different pressures and temperatures are measured by the volumetric method of adsorption with a microcalorimetry system. It is found that the the adsorption heats obtained by different adsorption models exhibit different trends. The fitting quality of the experimental isotherms for different adsorption models affects the adsorption heat result. However, even if the models well fit the experimental isotherms, the theoretical adsorption heat values may be inconsistent. Furthermore, the calorimetric heats for all coal samples decreases with the increase in adsorption content in relation to the micropore distribution of coal. For all coal samples, the modified Dubinin-Astakhov (D-A) model can well fit the experimental isotherms and agree well with the results of calorimetric heats. By comparing the theoretical heat for different k values and the measured heat, the pseudo-saturation vapor pressure of the modified D-A model can be determined. Finally, by virtue of the isosteric heat of adsorption in a small temperature range, the adsorption isotherms at other adjacent temperatures are predicted successfully.