摘要
煤层气的吸附极大值客观存在,对其研究大多是定性或半定量的结果,目前无精确计算吸附极大值的方法。根据多元函数方程出现极值的必要且充分条件是该方程的一阶全微分必须为零的规则,建立1个包括镜质体在内的可用于计算极值条件的齐次方程,即设计地温梯度与压力梯度比、温度与压力的函数关系并使得计算吸附临界深度的齐次方程成为仅剩压力为变量的一元二次方程。基于镜质组最大反射率(Romax)与参数(Δ和β)的关系,先解一元二次方程的特征判别式,然后从中选定1个合理的解为临界压力(Pc),再求临界深度(Hc)和临界吸附量(Vc)。该方法需同时满足的条件为:地温梯度范围为2.5℃/hm~3.5℃/hm,压力梯度范围为0.70 MPa/hm~1.30 MPa/hm,镜质体最大反射率(Romax)为0.65%~2.50%。通过图形可直观判断在等临界深度、等临界压力和等临界吸附量下镜质体最大反射率与温压梯度比之间的变化关系。建议直接采用基于煤岩分析和温压梯度比计算煤层气吸附极大值时深度和压力及吸附量的软件进行数值模拟计算,以快速、精准地计算在不同镜质组最大反射率、地温梯度和地压梯度时煤层气吸附气量达到极值的情况下的临界深度、临界压力和临界吸附量,并显示其镜质组最大反射率和温压梯度比之间的变化关系。
The maximum adsorption value of coalbed methane is the objective existence.At present,most of the research results are qualitative or semi quantitative,there is no accurate method to calculate the adsorption maximum.According to the rule which regulated that the necessary and sufficient condition for the extremum of multivariate function equation is that the first order total differential of the equation must be zero,a homogeneous equation including vitrinite was established,it could be used to calculate the extremum condition.In other words,the ratio of temperature gradient to pressure gradient and the functional relationship between temperature and pressure were designed,and the homogeneous equation for calculating the critical depth of adsorption became a quadratic equation with only pressure as a variable.Based on the relation between maximum reflectivity of vitrinite Romaxand parameters(Δandβ),the feature discriminant of quadratic equation was used to calculate the critical pressure Pc.Furthermore,the critical pressure Pc was used to calculate the critical depth Hc and the critical adsorption capacity Vc.The conditions of this method are as follows:the temperature gradient range is 2.5℃/hm~3.5℃/hm,the pressure gradient range is 0.70 MPa/hm~1.30 MPa/hm,and the maximum reflectance of vitrinite is Romax=0.65%~2.50%.The relationship between the maximum reflectance of vitrinite and the gradient ratio of temperature and pressure can also be seen directly from the graph under the condition of equal critical depth,equal critical pressure and equal critical adsorption capacity in the paper.It is suggested that the“software for calculating the critical depth,critical pressure,critical adsorption capacity of coalbed methane adsorption based on coal petrology analysis and the ratio of temperature gradient to pressure gradient”should be used directly.It can quickly and accurately calculate the critical depth,critical pressure and critical adsorption capacity of coalbed methane when the maximum reflectance,geoth
作者
张学梅
马青华
郝静远
李东
ZHANG Xuemei;MA Qinghua;HAO Jingyuan;LI Dong(Energy & Chemical Engineering Research Center,Xian Siyuan University,Xi’an 710038,China;College of Chemical Engineering,Xi’an Jiaotong University,Xi’an 710038,China)
出处
《煤质技术》
2021年第3期54-59,共6页
Coal Quality Technology
基金
陕西省教育厅2020年度一般专项科学研究计划资助项目(20JK0858)。
关键词
甲烷吸附
临界深度
数值模拟
中煤阶煤
镜质体最大反射率
齐次方程
温压梯度比
methane adsorption
critical depth
numerical simulation
medium-rank coal
maximum reflectivity of vitrinite
homogeneous equation
temperature-pressure gradient ratio
