Temperature-Dependent Langmuir’s Model in the Coal and Methane Sorption Process: Statistics Relationship

"The Langmuir model has been widely used for the coal-methane sorption process via an isothermal test. However, even though the temperature-dependent Langmuir model were recognized theoretically and experimentally, the quantitative relationship between the Langmuir’s constants (a & b) and temperature have not been clarified and confirmed by lab test data. This paper collects 158 methane-coal sorption data under different temperatures, which apply the Langmuir model to consider the relationship between Langmuir’s constants (a & b) and temperature (see APPENDIX I). Even though the Langmuir model cannot be used to show the physical state of methane adsorption on coal, it is widely used because of its simplicity and the reasonable explanation of its parameters (a & b). The results from these published isothermal tests confirm that 1) there is no consistent relationship between Langmuir’s constant-a and temperature; 2) the Langmuir model is a temperature-dependent model, and the temperature-dependent feature is mainly shown by the relationship between Langmuir’s constant-b and temperature; 3) The relationship between Langmuir’s constant-b and temperature can be described by both the exponential and linear relationship with dried coal. This paper provides a database for temperature-dependent Langmuir’s model, which can be used for reservoir simulation of coalbed methane reservoir, coal seam degasification modeling for underground coal mines considering the heating effect induced by geotherm and heat injection (via hot water, hot steam, ultrasonic, etc.). INTRODUCTION The isothermal test for gas sorption on coal is one of the fundamental tests in Coalbed Methane (CBM) recovery fields, such as underground coal mine methane degasification, CBM gas-in-place estimation, and carbon dioxide sequestration in un-minable coal seams. Generally, two methods, volumetric and gravimetric, are employed to obtain isothermal data (Bush, A. & Gensterblum, Y., 2012). Based on these two approaches, a series of commercial and self-assembled instruments are built and several calculation methods are used to obtain isothermal data (Bush, A. & Gensterblum, Y., 2012, Gasparik, K., 2014; Goodman, A. L., et al, 2004; Zhang, L., et al, 2013). In the post-processing stage, many models are provided to analyze isothermal data in order to understand the storage mechanism of gas in coal. Common models include the Langmuir model (and its extended forms), the pore-filling model, multilayer adsorption model (BET), and the Gibbs’ model. Among these models, the Langmuir model is the most widely used for its simplicity and functionality. The Langmuir model is expressed as follows:"