Theoretical Derivation of a Prediction Model for CO₂ Adsorption by Coal

Adsorption characteristics of CO₂ by coal are an important reservoir parameter to determine the CO₂ storage capacity of the coal seam. The Langmuir isotherm adsorption model is commonly used to describe the isothermal adsorption line of coal. However, we cannot predict the CO₂ adsorption capacity at other temperatures by using the Langmuir model based on the experimental data at a fixed temperature. This paper analyzes the ε-V _ad adsorption characteristic curves of three coal samples over a range of temperatures and pressures. The study demonstrates that the adsorption characteristic curves of CO₂ gas are independent of temperature and depend mainly on the dispersion force between coal and the CO₂ molecules. In addition, the adsorption potential of CO₂ gas has a negative correlation with the volume of the adsorbed phase. Hence, the CO₂ adsorption characteristic curve of coal conforms to the logarithmic function. Based on the adsorption potential theory, the prediction model of CO₂ adsorption by coal is derived. The deviation analysis from measured data shows that the average relative deviation of the three coal samples is ∼5%, and the prediction results are accurate and reliable. Under different temperature and pressure conditions of the three coal samples, the results from the prediction model of CO₂ adsorption by coal and the Langmuir model have a strong correlation with the experimental results. In comparison with the Langmuir model, the prediction model of CO₂ adsorption by coal can predict the adsorption capacity under different temperature and pressure conditions. Hence, it has a wide range of applications when compared to that of the Langmuir model. In practical applications, better results are achieved with a significant reduction in experimental time and labor.