Intrinsic relationship between Langmuir sorption volume and pressure for coal: Experimental and thermodynamic modeling study

Abstract

Abstract Gas adsorption volume has long been recognized as an important parameter for coalbed methane (CBM) resource assessment as it determines the overall gas capacity of coal. As the industrial standard practice, Langmuir volume (VL) is used to describe the gas adsorption volume. Another important parameter, Langmuir pressure (PL), is typically overlooked because it does not directly relate to the resource estimation. However, PL defines the slope of the adsorption isotherm and the ability of a well to attain the critical desorption pressure in a significant reservoir volume, which is critical to plan the initial water depletion rate for a CBM well. Qualitatively, both VL and PL are related to the fractal pore structure of coal, but the intrinsic relationships among fractal pore structure, VL, and PL are not well studied and quantified due to the complex pore structure of coal. In this study, a series of experiments were conducted to measure the fractal dimensions of coal and their relationship to methane adsorption capacity. The thermodynamic model of the gas adsorption on heterogonous surfaces was revisited, and the theoretical models that correlate the fractal dimensions with the Langmuir constants were proposed. Applying the fractal theory, adsorption capacity ( V L ) is proportional to a power function of specific surface area and fractal dimension, and the slope of the regression line contains information on the molecular size of the adsorbed gas. We also found that P L is linearly correlated with sorption capacity, which is defined as a power function of total adsorption capacity ( V L ) and a heterogeneity factor (ν). This implies that PL is not independent of VL, instead, a positive correlation between V L and P L has been noted elsewhere (e.g., Pashin [1]). In the Black Warrior Basin, Langmuir volume is positively related to coal rank (Pashin, 2010; Kim, 1977) [1,2], and Langmuir pressure is inversely related to coal rank. It was also found that P L is negatively correlated with adsorption capacity and fractal dimension. A complex surface corresponds to a more energetic system, which results in an increase in the number of available adsorption sites and adsorption potential, which raises the value of V L and reduces the value of P L .