A theoretical study on the critical adsorption depth of high-rank coal

This paper presents the theoretical significance of the temperature-pressure-adsorption equation (TPAE) over the limitations of the Langmuir isothermal adsorption equation. The series isothermal adsorption data of low-rank coal from Xiangshan coal mine in Shaanxi Province, China were used to verify the practicality of the TPAE, and four parameters were obtained. According to the TPAE sought, the adsorption value of any tests between 30°C-100°C and pressure between 0-30 MPa can be arbitrarily calculated, with an average relative error of less than 10.54 %, and expressed by a three-dimensional adsorption surface. According to the total differential of the multivariate function is the sum of the differentials of each independent variable, assuming that the ground temperature gradient of Xiangshan coal mine is 3°C/100 m and the ground pressure gradient is 1.0 MPa/100 m, it can be precisely calculated that both partial deviations of temperature and pressure. It can be approximately calculated that the critical adsorption depth of the low-rank coal is about 600~700 m underground, the critical adsorption pressure is about 6 MPa, the critical adsorption temperature is about 30°C, and the critical adsorption capacity is 20.0 cm3/g.