Modeling Hysteretic Adsorption and Desorption of Methane on Shale

To model the hysteretic adsorption and desorption of methane on shale, a modified Langmuir model has been proposed by combining the adsorption-induced volumetric strain and Langmuir models. The modified Langmuir model introduces a hysteresis parameter, β, to quantify the degree of hysteresis during desorption. Unlike previous studies where β was considered a constant, this model treats β as a linear function of the adsorbed amount. This modification allows the model to capture the dependence of desorption hysteresis on temperature and pressure. The modified Langmuir model was successfully validated against published adsorption and desorption measurements on shale. The model accurately represents the experimental data, achieving an average relative error of 3.67%. The degree of hysteresis is influenced by the mineralogical composition of shale, particularly the contents of organic matter and quartz. This is because kerogen─a relatively soft organic material─acts as the main host for adsorbed gas. Quartz, being a rigid mineral, resists adsorption-induced deformation, thereby limiting the degree of hysteresis.