Evaluation and improvement of high-pressure isothermal adsorption model for methane in shale

This study aims to fit experimental excess adsorbance and calculate absolute adsorbance accurately by determining the reasonable high-pressure isothermal adsorption model for methane in shale. Eight adsorption formulations and three adsorption phase density calculation methods were chosen for setting up the high-pressure isothermal adsorption model. The goodness of fitting (R2) for excess adsorbance,the rationality of absolute adsorbance correction,the rationality of adsorption phase density calculation,and the rationality of the choice of adsorption theories were chosen as evaluation indexes. Thereafter,a total of 18 sets of experimental data at 333 K and 363 K were used to quantitatively evaluate the models,respectively. Moreover,the function of the adsorption phase’s density related to pressure and temperature was derived,and the adsorption formulas of Langmuir-Freundlich and Dubinin-Radushkevich were combined.Then,an improved high-pressure isothermal adsorption model of methane in shale was proposed. The results show that the fitting density method of the adsorption phase is the best method among the three calculation methods of adsorption phase density. Combining this method with Langmuir-Freundlich or Dubinin-Radushkevich adsorption formulas,the currently most accurate high-pressure isothermal adsorption models can be obtained,which the R2 to the excess adsorbance are 0. 998 3 and 0. 997 8,respectively. However,the adsorption model composed by the given adsorption phase density method has a low R2 to the excess adsorbance. The accuracy of the method for calculating the adsorption phase density based on the relation of excess adsorbance and gas density is poor. Furthermore,the average R2 of the 18 groups’excess adsorbance fitted by the improved model in this paper is 0. 996 9. Its calculated deviation of the absolute adsorbance is 0. 087,which is better than the existing model. Thus,the improved model in this paper has a physical basis and is consistent with the adsorption mechanism of methane in shale,which can provide the theoretical basis for the reserve estimation and exploitation plan formulation of shale gas.