Establishing a New Piecewise Method for Understanding and Rectifying Mass Balance Miscalculation of Gas Adsorption on Coal and Shale

Sorption isotherms provide fundamental information for investigating the mechanism and phenomenon of gas adsorption on carboniferous rocks. However, adsorption isotherms of physical adsorbents, such as coal and shale, give rise to an unexpected and often negative adsorption phenomenon, which is decreased gas uptake under high pressure. Here, we demonstrate that a Gibbs discarded amount should be responsible for the negative adsorption phenomenon. The Gibbs discarded amount, a product of the free gas density and the adsorbed phase volume, increases continuously with the increased pressure during sorption isotherm measurement, but the Gibbs discarded amount has been subtracted from the absolute adsorption amount in the mass balance calculation. This leads to not only a linear decline in the sorption isotherm after adsorption saturation, but also underestimation of the absolute adsorption capacity on the whole adsorption isotherm. Hence, a piecewise method is developed to correct the error caused by the Gibbs discarded amount and is examined by experimental data of CH4-coal sorption, CH4-shale sorption, and CO2-coal sorption. Results indicate that the piecewise method is valid in rectifying the underestimation of Gibbs sorption isotherm and that the Gibbs discarded amount cannot be neglected any longer in the porous rock adsorption; various densities of the adsorbed phase estimated by the piecewise method are more practicable than a constant density as normal. This method may reduce both the experimental and computational effort required for the determination of absolute sorption isotherms.

Automated summary

The Gibbs discarded amount is responsible for the negative adsorption phenomenon in physical adsorbents, and a piecewise method has been developed to correct errors caused by the Gibbs discarded amount, resulting in more practical estimates of adsorbed phase density. This method may reduce both the experimental and computational effort required for the determination of absolute sorption isotherms.