煤层气的温度-压力-吸附方程的数学分析和诠释

Mathematical Analysis and Explanation of Pressure-Temperature-Adsorption Equation of Coalbed Methane

本文建立温度、压力、吸附介质(自变量)与吸附量(应变量)的数学方程TPAE。并通过对鄂尔多斯盆地东部4种煤的系列等温吸附实验的兰格缪尔吸附体积和兰格缪尔吸附压力进行回归,得到TPAE的4个参数。四种煤样的平均相对偏差在8.73%~12.6%之间,和TPAE曲面与吸附量点吻合很好都说明TPAE适用于处理系列等温吸附实验数据。通过例子证实吸附量对温度偏导、吸附量对压力偏导、和吸附量对温度和压力的全微分是可以精确计算的。当煤样表征温度影响Δ和表示压力影响β已定,如满足一定的温度和压力,吸附量会出现极大值;吸附量极大值出现的温度和压力与煤样的变质程度(镜质组最大反射率)有关。

A temperature-pressure-absorbing equation（ TPAE） has been derived in the paper. The 4 parameters of TPAE have been obtained by the regression of the Langmuir adsorption volume and Langmuir adsorption pressure through the experiment of series isothermal adsorption for 4 types of coal in Eastern Ordos Basin. Not only the average relative errors comparing Langmuir value of the coal samples are 8. 73% ~ 12. 6%,but also the TPAE curvature surface and adsorption points match very well. All evidence approved that TPAE is applicable to interpret the series isothermal adsorption data. All necessary pieces information,such as adsorption,partial differential of temperature,partial differential of pressure and complete differential,can be accurately calculated. When the temperature effect Δ and the pressure effect β of the coal samples have been measured and under certain temperature and pressure conditions,maximum adsorption occurs and is inter-related to coal metamorphism（ maximum reflectivity of vitrinite）.