Experimental investigation and mathematical modelling of shale gas adsorption and desorption hysteresis

To quantify shale gas contents and hysteresis behaviour of the Ordovician Goldwyer shales as functions of temperature and rock properties, methane adsorption and desorption isotherms were measured at four temperatures. Early pore saturation was observed for all eight samples tested and consequently, the measured sorption isotherms could not be directly modelled by Langmuir isotherm or its modified version. Thus, a hybrid-modelling approach comprising the use of Dubinin–Radushkevich (D-R) model to obtain the adsorbed phase density (ρ_ads) needed to convert excess amounts to absolute followed by Langmuir model to describe the resultant absolute isotherms. Significant hysteresis observed resulted in lower Langmuir parameters for the desorption isotherms compared to the adsorption isotherms. For both processes, Langmuir volumes positively correlated with TOC contents but showed no significant correlations with total clay contents. To capture the effect of clay contents, the ratio of total clay to TOC (subsequently referred to as clay-to-organic-carbon, COC) was applied as a single predictor instead. The results showed that Langmuir volumes, and the size of the hysteresis showed significant correlations with TOC contents and COC. Lastly, analytical models were developed for the temperature-dependence of Langmuir volume as functions of each of TOC contents and COC for both adsorption and for the first time, desorption isotherms. The models showed significant match with experimental results and as such, can be adopted for conditions beyond those investigated in this study.