Kinetic Characteristics of CH4 Adsorption on Coals under Variable Temperature–Pressure Coupling Interaction

The accurate determination of coalbed methane (CBM) content is of great significance for its development and utilization as well as for the prevention and control of coal mine gas disaster. In the process of determining CBM content, the coal–gas adsorption system existing in the natural environment is affected by variable temperature–pressure interactions. In this study, methane (CH4) adsorption tests were carried out on coals at different initial equilibrium pressures (IEPs) and in different cooling processes (CPs). The test results indicate that dominant and retrograde adsorption processes existed in the cooling and adsorption processes of the coal sample reaction chamber. During the adsorption process, the temperature variation broke the original adsorption equilibrium, which in turn induced the pressure change in the coal sample reaction chamber, thus resulting in the retrograde adsorption. The intensity of the dominant adsorption increased and then decreased, causing an increase and then a decrease in the retrograde adsorption rate. The commonly used adsorption kinetic models were modified, including the modified pseudo-first-order kinetic model, modified pseudo-second-order kinetic model, modified Bangham kinetic model (MBKM), modified intra-particle diffusion model and modified double exponential model (MDEM). These modified models were used to describe the kinetic characteristics of the dominant process of CH4 adsorption on coals in a variable temperature and pressure environment. The results show that among the modified kinetic models, the MDEM can describe better the kinetic process of the dominant adsorption, followed by the MBKM. The IEP showed positive correlation with the dominant adsorption rate at the initial stage of cooling. For the two CPs (i.e., 293.15–283.15 K and 273.15–263.15 K), the initial adsorption rates at the IEP of 3.83 MPa were, respectively, about 4 and 3 times higher than those at the IEP of 0.72 MPa. The retrograde adsorption process can be described better by a linear model. A peak retrograde adsorption rate existed throughout the adsorption process and increased with increasing IEP. The study of the kinetic process of CH4 adsorption on the coal matrix under the effect of low temperatures and variable pressures will improve understanding of the CH4 adsorption mechanism in a low temperature and variable pressure environment, and provide theoretical support for the development and application of new techniques for CBM content determination.