The Supercritical Adsorption Potential Equation for Shale Gas and Its Application: A Case Study of Methane Adsorption in Danish Bornholm Shale

Since shale gas adsorption belongs to supercritical gas adsorption, the ideal gas adsorption potential equation is not suitable for calculating the adsorption potential of shale gas. In this study, the supercritical gas adsorption potential equation is proposed based on the assumption that the adsorbed phase is a real gas. The adsorbed phase pressure, as the parameter in the adsorption potential equation, was calculated using the Amankwah equation. For the unknown parameter K in the Amankwah equation, a method for determining the optimal value of K based on the consistency of the adsorption characteristic curve and the accuracy of the predicted isothermal adsorption curve is proposed, thus obtaining the adsorbed phase pressure. Simultaneously, based on a comparison of the ideal gas and supercritical gas adsorption potential, a simplified equation for the supercritical gas adsorption potential is proposed. In this paper, the isothermal adsorption curve of CH4 adsorbed by Holm shale is used to carry out practical calculations. This study revealed that the optimal value of K for the CH4 adsorption system in Holm shale is 2.9, with the adsorbed phase pressure ranging from 17.11 to 32.19 MPa within the temperature range of 300–373 K. The supercritical gas adsorption characteristic curves exhibited excellent consistency, and the average relative error of the predicted ascending segment of the excess adsorption isotherm at 373 K was merely 1.77%, thereby substantiating the rationality of the supercritical gas adsorption potential equation. The simplified equation for supercritical gas adsorption potential is straightforward in form, facilitating its widespread application and promotion.