An improved Langmuir model for evaluating methane adsorption capacity in shale under various pressures and temperatures

A large amount of experimental data for methane adsorption capacity in shale are available and the Langmuir model is capable to describe most of these adsorption isotherms. Two parameters used in the Langmuir model are the Langmuir pressure constant PL and the Langmuir volume constant VL. However, experimental data also demonstrate that the gas adsorption capacity of shale is greatly affected by temperature and the classic Langmuir model, with temperature independent VL and temperature dependent PL, could not well interpret the experimental data. This is partly attributed to the isosteric heat of adsorption, which makes VL vary with temperature. The change of VL with temperature for gas adsorption in shale and its dependency on shale properties are still not well understood. In this study, the variation characteristics of VL with temperature for gas shale are investigated through a modeling analysis on the published gas sorption data on the shales from the US, China, Canada, and etc. The classic Langmuir model is improved by considering the temperature dependent VL. The results show that the improved Langmuir model can reasonably describe the shale gas sorption data with less fitting parameters required and it allows a better understanding of gas sorption capacity under the combined effect of temperature and pressure. In addition, the model parameter analysis indicates that the adsorption capacity of shale samples with lower TOC is more likely to be affected by temperature change on the basis of the limited data available. More experiments are required to investigate how the shale properties affect the thermal impact on the gas adsorption capacity on gas shale.