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Article(id=1149741820827054476, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149741815273800564, articleNumber=1003-3033(2024)01-0125-08, orderNo=null, doi=10.16265/j.cnki.issn1003-3033.2024.01.0774, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1692028800000, receivedDateStr=2023-08-15, revisedDate=1700409600000, revisedDateStr=2023-11-20, acceptedDate=null, acceptedDateStr=null, onlineDate=1752049411255, onlineDateStr=2025-07-09, pubDate=1706371200000, pubDateStr=2024-01-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752049411255, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1752049411255, creator=13701087609, updateTime=1752049411255, updator=13701087609, issue=Issue{id=1149741815273800564, tenantId=1146029695717560320, journalId=1146031787341344770, year='2024', volume='34', issue='1', pageStart='1', pageEnd='252', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1752049409931, creator=13701087609, updateTime=1756468937446, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1168278657316430156, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149741815273800564, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1168278657316430157, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149741815273800564, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=125, endPage=132, ext={EN=ArticleExt(id=1149741821011603853, articleId=1149741820827054476, tenantId=1146029695717560320, journalId=1146031787341344770, language=EN, title=Correlation analysis and prediction of coal spontaneous combustion risk based on correlation coefficient method, columnId=1149733269173878863, journalTitle=China Safety Science Journal, columnName=Safety engineering technology, runingTitle=null, highlight=null, articleAbstract=

In order to shorten the identification time of coal spontaneous combustion tendency，firstly，industrial analyzer and temperature programmed test device were used to measure the coal quality index value and the content of coal spontaneous combustion indicator gas at different temperatures. The critical temperature point of low-temperature oxidation was determined by CO volume fraction. Then，the equation between temperature and oxygen consumption rate was fitted through the Arrhenius formula，and the apparent activation energy of each coal sample at different stages before and after the critical temperature was solved. The correlation between the coal quality index value and the apparent activation energy before and after the critical temperature was analyzed by Pearson correlation coefficient method，and the correlation coefficient was calculated. Finally，the coal quality index value with the largest correlation coefficient was selected，and a multiple linear regression model for calculating the apparent activation energy of coal samples was established to analyze and predict the spontaneous combustion risk of coal. The results show that the correlation coefficients between different components of coal quality and the apparent activation energy before and after the critical temperature are significantly different. The negative correlation coefficients between volatile matter and the apparent activation energy before and after the critical temperature are the largest，which are -0.893 and -0.977 respectively. The positive correlation coefficients between fuel ratio and the apparent activation energy before and after the critical temperature are the largest，which are 0.956 and 0.968 respectively. The fitting degree of the established multiple linear regression model can reach 0.912 5 and 0.933 0.

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为缩短煤自燃倾向性的鉴定时间，首先利用工业分析仪及程序升温试验装置，测得各煤样煤质指标值及不同温度下煤自燃指标气体含量，并通过CO体积分数确定各煤样低温氧化临界温度点；然后再通过Arrhenius公式拟合得出温度与耗氧速率间的方程，并求解出各煤样临界温度前后不同阶段的表观活化能，通过Pearson相关系数法进行煤质指标值与煤样临界温度前后表观活化能之间的关联分析，并计算其相关系数；最后选取相关系数最大的煤质指标值，建立用于计算煤样表观活化能的多元线性回归模型，分析并预测煤自燃危险性。结果表明：煤质指标中不同成分与临界温度前后表观活化能间的相关系数有较大差异，其中挥发分与临界温度前后表观活化能的负相关系数最大，分别为-0.893和-0.977，燃料比与临界温度前后表观活化能的正相关系数最大，分别为0.956和0.968。所建立的多元线性回归模型，其拟合度可达0.912 5和0.933 0。

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张玉涛 (1982—)，男，山东烟台人，博士，教授，主要从事煤炭自燃和建筑火灾防控方面的研究。E-mail：。

李亚清，副教授

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张玉涛 (1982—)，男，山东烟台人，博士，教授，主要从事煤炭自燃和建筑火灾防控方面的研究。E-mail：。

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张玉涛 (1982—)，男，山东烟台人，博士，教授，主要从事煤炭自燃和建筑火灾防控方面的研究。E-mail：。

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李亚清，副教授

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李亚清，副教授

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figureFileBig=6MDLpmuZg07AhcODcjvE4g==, tableContent=null), ArticleFig(id=1168122946594811979, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149741820827054476, language=EN, label=Tab.1, caption=

Industrial analysis of test coal samples%

, figureFileSmall=null, figureFileBig=null, tableContent=
煤级 煤样 水分 灰分 挥发分 固定碳 自燃倾向性
长焰煤 CY1 11.93 12.76 26.58 48.73 自燃
长焰煤 CY2 7.49 18.93 24.25 49.33 易自燃
不黏煤 BN 5.41 15.32 23.34 55.93 易自燃
气煤 QM1 1.80 18.52 22.58 57.10 自燃
气煤 QM2 4.43 15.26 21.70 58.61 自燃
肥煤 FM 0.79 14.24 20.91 64.06 自燃
焦煤 JM1 0.82 11.19 21.20 66.79 自燃
焦煤 JM2 0.82 11.25 20.60 67.33 自燃
焦煤 JM3 0.98 10.95 20.16 67.91 自燃
贫煤 PM 1.56 11.77 18.54 68.13 自燃
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试验煤样工业分析

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煤级 煤样 水分 灰分 挥发分 固定碳 自燃倾向性
长焰煤 CY1 11.93 12.76 26.58 48.73 自燃
长焰煤 CY2 7.49 18.93 24.25 49.33 易自燃
不黏煤 BN 5.41 15.32 23.34 55.93 易自燃
气煤 QM1 1.80 18.52 22.58 57.10 自燃
气煤 QM2 4.43 15.26 21.70 58.61 自燃
肥煤 FM 0.79 14.24 20.91 64.06 自燃
焦煤 JM1 0.82 11.19 21.20 66.79 自燃
焦煤 JM2 0.82 11.25 20.60 67.33 自燃
焦煤 JM3 0.98 10.95 20.16 67.91 自燃
贫煤 PM 1.56 11.77 18.54 68.13 自燃
), ArticleFig(id=1168122946766778445, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149741820827054476, language=EN, label=Tab.2, caption=

Activation energy and function curve fitting degree of coal samples with different degrees of metamorphism

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煤样 临界温度前 临界温度后
R2 A E1/(J·mol-1) R2 A E2/(J·mol-1)
CY1 0.988 0 -3.739 4 13.855 3 0.971 7 6.405 0 41.533 4
CY2 0.983 2 -4.451 0 14.458 0 0.974 3 6.829 8 42.997 5
BN 0.987 6 -3.587 1 16.110 9 0.977 2 6.501 0 43.445 6
QM1 0.990 1 -3.331 1 16.578 1 0.977 4 6.209 5 45.164 1
QM2 0.987 1 -3.975 4 17.342 2 0.992 6 6.515 4 46.522 7
FM 0.986 8 -3.237 2 18.414 7 0.978 1 6.089 8 47.024 8
JM1 0.996 3 -1.702 7 23.038 1 0.978 3 6.239 1 47.062 2
JM2 0.964 4 -1.520 3 23.132 9 0.981 4 6.113 9 47.172 0
JM3 0.972 1 -2.228 0 23.963 4 0.980 4 5.563 7 47.356 5
PM 0.990 2 -0.855 3 26.422 7 0.986 4 6.158 1 48.646 9
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不同变质程度煤样活化能及函数曲线拟合度

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煤样 临界温度前 临界温度后
R2 A E1/(J·mol-1) R2 A E2/(J·mol-1)
CY1 0.988 0 -3.739 4 13.855 3 0.971 7 6.405 0 41.533 4
CY2 0.983 2 -4.451 0 14.458 0 0.974 3 6.829 8 42.997 5
BN 0.987 6 -3.587 1 16.110 9 0.977 2 6.501 0 43.445 6
QM1 0.990 1 -3.331 1 16.578 1 0.977 4 6.209 5 45.164 1
QM2 0.987 1 -3.975 4 17.342 2 0.992 6 6.515 4 46.522 7
FM 0.986 8 -3.237 2 18.414 7 0.978 1 6.089 8 47.024 8
JM1 0.996 3 -1.702 7 23.038 1 0.978 3 6.239 1 47.062 2
JM2 0.964 4 -1.520 3 23.132 9 0.981 4 6.113 9 47.172 0
JM3 0.972 1 -2.228 0 23.963 4 0.980 4 5.563 7 47.356 5
PM 0.990 2 -0.855 3 26.422 7 0.986 4 6.158 1 48.646 9
), ArticleFig(id=1168122946913579088, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149741820827054476, language=EN, label=Tab.3, caption=

Fitting curve between activation energy and coal quality index

, figureFileSmall=null, figureFileBig=null, tableContent=
参数 临界温度前 临界温度后
拟合曲线 R 1 2 拟合曲线 R 1 2
水分 y=-0.634 8x+15.875 0.563 8 y=-1.452 7x+69.981 0.801 9
灰分 y=-0.495 8x+23.604 0.546 2 y=-0.661 6x+44.247 0.264 1
挥发分 y=-0.463 1x+30.939 0.958 3 y=-0.972 2x+23.604 0.955 3
固定碳 y=1.593 8x+29.582 0.876 6 y=3.086 4x-80.635 0.892 9
可燃组分 y=1.130 6x+60.521 0.840 1 y=2.114 3x-14.228 0.797 9
燃料比 y=0.130 1x+0.288 0.933 3 y=0.252 7x-8.744 0.936 3
), ArticleFig(id=1168122946989076562, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149741820827054476, language=CN, label=表3, caption=

活化能与煤质指标拟合曲线

, figureFileSmall=null, figureFileBig=null, tableContent=
参数 临界温度前 临界温度后
拟合曲线 R 1 2 拟合曲线 R 1 2
水分 y=-0.634 8x+15.875 0.563 8 y=-1.452 7x+69.981 0.801 9
灰分 y=-0.495 8x+23.604 0.546 2 y=-0.661 6x+44.247 0.264 1
挥发分 y=-0.463 1x+30.939 0.958 3 y=-0.972 2x+23.604 0.955 3
固定碳 y=1.593 8x+29.582 0.876 6 y=3.086 4x-80.635 0.892 9
可燃组分 y=1.130 6x+60.521 0.840 1 y=2.114 3x-14.228 0.797 9
燃料比 y=0.130 1x+0.288 0.933 3 y=0.252 7x-8.744 0.936 3
), ArticleFig(id=1168122947077156947, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149741820827054476, language=EN, label=Tab.4, caption=

Multiple linear regression model before and after critical temperature

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所属阶段 拟合结果 R R 2 2 标准误差
临界温度前 Z1=-43.842 0+1.351 8I1+11.954 2I2 0.955 2 0.912 5 1.631 0
临界温度后 Z2=63.191 2-0.880 0I1+0.628 2I2 0.965 9 0.933 0 0.668 4
), ArticleFig(id=1168122947140071509, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149741820827054476, language=CN, label=表4, caption=

临界温度前后多元线性回归模型

, figureFileSmall=null, figureFileBig=null, tableContent=
所属阶段 拟合结果 R R 2 2 标准误差
临界温度前 Z1=-43.842 0+1.351 8I1+11.954 2I2 0.955 2 0.912 5 1.631 0
临界温度后 Z2=63.191 2-0.880 0I1+0.628 2I2 0.965 9 0.933 0 0.668 4
), ArticleFig(id=1168122947207180375, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149741820827054476, language=EN, label=Tab.5, caption=

Comparison between detected value and actual value

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煤样 检测值 实际值 误差值
临界温度前 临界温度后 临界温度前 临界温度后 临界温度前 临界温度后
CY1 14.005 6 40.952 1 13.855 3 41.533 4 0.150 3 -0.581 3
QM1 16.912 3 44.909 0 16.578 1 45.164 1 0.334 2 -0.255 1
JM2 23.077 7 47.116 1 23.132 9 47.172 0 -0.055 2 -0.055 9
), ArticleFig(id=1168122947282677849, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149741820827054476, language=CN, label=表5, caption=

检测值与实际值对比

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煤样 检测值 实际值 误差值
临界温度前 临界温度后 临界温度前 临界温度后 临界温度前 临界温度后
CY1 14.005 6 40.952 1 13.855 3 41.533 4 0.150 3 -0.581 3
QM1 16.912 3 44.909 0 16.578 1 45.164 1 0.334 2 -0.255 1
JM2 23.077 7 47.116 1 23.132 9 47.172 0 -0.055 2 -0.055 9
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基于相关系数法的煤自燃危险性关联分析及预测
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张玉涛 1, 2 , 郭强 1, 2 , 张园勃 1, 2 , 李亚清 1 , 孙亚利 1
中国安全科学学报 | 安全工程技术 2024,34(1): 125-132
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中国安全科学学报 | 安全工程技术 2024, 34(1): 125-132
基于相关系数法的煤自燃危险性关联分析及预测
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张玉涛1, 2 , 郭强1, 2, 张园勃1, 2, 李亚清1, 孙亚利1
作者信息
  • 1 西安科技大学 安全科学与工程学院，陕西 西安 710054
  • 2 陕西省煤火灾害防治重点实验室，陕西 西安 710054

    • 张玉涛 (1982—)，男，山东烟台人，博士，教授，主要从事煤炭自燃和建筑火灾防控方面的研究。E-mail：。

    李亚清，副教授

Correlation analysis and prediction of coal spontaneous combustion risk based on correlation coefficient method
Yutao ZHANG1, 2 , Qiang GUO1, 2, Yuanbo ZHANG1, 2, Yaqing LI1, Yali SUN1
Affiliations
  • 1 School of Safety Science and Engineering，Xi'an University of Science and Technology，Xi'an Shaanxi 710054，China
  • 2 Shaanxi Key Laboratory of Prevention and Control of Coal Fire，Xi'an Shaanxi 710054，China
出版时间: 2024-01-28 doi: 10.16265/j.cnki.issn1003-3033.2024.01.0774
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摘要
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为缩短煤自燃倾向性的鉴定时间，首先利用工业分析仪及程序升温试验装置，测得各煤样煤质指标值及不同温度下煤自燃指标气体含量，并通过CO体积分数确定各煤样低温氧化临界温度点；然后再通过Arrhenius公式拟合得出温度与耗氧速率间的方程，并求解出各煤样临界温度前后不同阶段的表观活化能，通过Pearson相关系数法进行煤质指标值与煤样临界温度前后表观活化能之间的关联分析，并计算其相关系数；最后选取相关系数最大的煤质指标值，建立用于计算煤样表观活化能的多元线性回归模型，分析并预测煤自燃危险性。结果表明：煤质指标中不同成分与临界温度前后表观活化能间的相关系数有较大差异，其中挥发分与临界温度前后表观活化能的负相关系数最大，分别为-0.893和-0.977，燃料比与临界温度前后表观活化能的正相关系数最大，分别为0.956和0.968。所建立的多元线性回归模型，其拟合度可达0.912 5和0.933 0。

相关系数法  /  煤自燃危险性  /  表观活化能  /  低温氧化  /  指标气体  /  临界温度

In order to shorten the identification time of coal spontaneous combustion tendency，firstly，industrial analyzer and temperature programmed test device were used to measure the coal quality index value and the content of coal spontaneous combustion indicator gas at different temperatures. The critical temperature point of low-temperature oxidation was determined by CO volume fraction. Then，the equation between temperature and oxygen consumption rate was fitted through the Arrhenius formula，and the apparent activation energy of each coal sample at different stages before and after the critical temperature was solved. The correlation between the coal quality index value and the apparent activation energy before and after the critical temperature was analyzed by Pearson correlation coefficient method，and the correlation coefficient was calculated. Finally，the coal quality index value with the largest correlation coefficient was selected，and a multiple linear regression model for calculating the apparent activation energy of coal samples was established to analyze and predict the spontaneous combustion risk of coal. The results show that the correlation coefficients between different components of coal quality and the apparent activation energy before and after the critical temperature are significantly different. The negative correlation coefficients between volatile matter and the apparent activation energy before and after the critical temperature are the largest，which are -0.893 and -0.977 respectively. The positive correlation coefficients between fuel ratio and the apparent activation energy before and after the critical temperature are the largest，which are 0.956 and 0.968 respectively. The fitting degree of the established multiple linear regression model can reach 0.912 5 and 0.933 0.

correlation coefficient method  /  coal spontaneous combustion risk  /  apparent activation energy  /  low temperature oxidation  /  indicator gas  /  critical temperature
张玉涛, 郭强, 张园勃, 李亚清, 孙亚利. 基于相关系数法的煤自燃危险性关联分析及预测. 中国安全科学学报, 2024 , 34 (1) : 125 -132 . DOI: 10.16265/j.cnki.issn1003-3033.2024.01.0774
Yutao ZHANG, Qiang GUO, Yuanbo ZHANG, Yaqing LI, Yali SUN. Correlation analysis and prediction of coal spontaneous combustion risk based on correlation coefficient method[J]. China Safety Science Journal, 2024 , 34 (1) : 125 -132 . DOI: 10.16265/j.cnki.issn1003-3033.2024.01.0774
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0 引言
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煤自燃是威胁煤矿安全生产的热动力灾害之一，在煤矿重特大事故中占比最高、致灾最重、损失最大[1-2]。随着煤矿开采深度及开采规模的不断扩大，煤层自燃的风险日益严重[3]。因此，开展煤自身属性以及煤自燃前期特征变量的综合性分析对于预测煤自燃危险性，保障煤矿安全生产具有极其重要的意义。
针对煤自燃问题，国内外学者从试验测试、数学模型等角度进行了大量研究，为煤自燃防治提供了重要的研究基础。ZHAO Jingyu等[4]研究了升温速率和氧浓度对煤自燃特征温度的影响，同时分析了不同氧浓度下表观活化能的变化特征；ONIFADE等[5]研究结果表明：煤的自燃倾向性随着碳、氢、氮含量的增加而增加；YAN Hongwei等[6]研究结果表明：表观活化能随着煤自燃的进行而增大，且与煤的粒径成正相关；贾廷贵[7]等研究表明：煤自燃过程中所需的活化能与煤样的变质程度成正相关，煤阶越高的煤样，发生自燃时所需的能量越多；翟小伟等[8]对比分析了不同粒径煤样在不同氧化阶段的表观活化能及指前因子之间的关系；WANG Kai等[9]利用Pearson相关系数法分析了不同预氧化时间下煤样表观活化能与官能团之间的相关性，确定了-OH是影响煤低温吸热阶段的关键结构；张玉涛等[10]利用Pearson相关系数法分析了不同官能团与煤自燃特征温度之间的相关性，并利用C-H和COO- 官能团建立了煤自燃倾向性多元线性回归模型。
以上研究主要分析了单一煤样在低温氧化过程中外界环境因素、煤样元素组成、煤样粒径大小、煤样官能团含量与其自燃倾向性之间的关系，暂未分析不同变质程度煤样间煤质指标与表观活化能之间的相关性，以及通过煤质指标关键参数来预测煤自燃危险性。因此，笔者将通过计算不同变质程度煤样间的表观活化能，分析其与煤质指标之间的相关性，同时寻找煤质指标参数中对煤自燃影响较大的关键参数，并建立多元线性回归模型，进而预测煤自燃危险性，以期缩短煤自燃倾向性的鉴定时间。
1 煤质指标及低温氧化气体测定
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1.1 煤样制备及试验装置
试验选取来自陕西及河南部分矿区的煤样，煤级涵盖长焰煤、不黏煤、气煤、肥煤、焦煤、贫煤。将以上10组煤样分别在氮气气氛中破碎，用标准样品筛筛分粒径为[0，0.9)，[0.9，3)，[3，5)，[5，7)，[7，10) mm煤粒，各粒径范围内取200g制成混合粒径煤样，依次命名为CY1、CY2、BN、QM1、QM2、FM、JM1、JM2、JM3、PM，并对以上10组煤样进行煤自燃指标气体测试，煤样工业分析结果见表1。
程序升温试验装置主要包括气路、程序升温、气体检测、气体成分及含量分析等部分。在程序升温箱中放入2个煤样罐，入口处流量为120mL/min，初始温度为30℃，在出口处设置气体采集及分析装置(气相色谱仪)，温度每升高10℃进行一次定量分析并保存相应数据，试验结束温度为170℃，共采集15组数据后停止加热，关闭气源及程序升温箱电源，打开程序升温箱箱门自然降温，结束试验，如图1所示。
1.2 煤自燃临界温度确定
CO气体属于煤氧化早期产物，因其具有产生时间早，灵敏性高，贯穿煤低温氧化整个阶段，随温度变化趋势明显等优点，常作为一种指标气体来表征煤自燃的进程。依据试验结果绘制的CO体积分数随温度的变化曲线如图2所示。
图2表明：随煤体温度上升，CO体积分数均呈现出指数增长的趋势[11]，不同变质程度煤样间CO气体体积突变温度点不同，CY1和CY2煤样在60℃，BN、QM1和QM2煤样在70℃，FM、JM1、JM2和JM3煤样在80℃，PM煤样在90℃时出现第一次显著增加，该温度点为各煤样的临界温度点。通过对比观察可知：煤样变质程度越高，其临界温度点越滞后，主要原因为高变质程度的煤样较为稳定，发生反应所需温度较高。临界温度前煤样主要以物理吸附及化学吸附为主，煤体表面部分活性结构发生煤氧复合反应并释放出一定量的热量，整体反应较为缓慢，随着试验温度的不断升高，煤样中更多的活性物质被激活，煤氧复合速率加快，呈现出第一次突变。
2 临界温度前后活化能变化特征
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2.1 表观活化能计算
程序升温试验装置由空气发生器提供气源，入口处氧气体积分数约为21%，出口处的氧气体积分数可由气相色谱仪测出，通过进出口氧气体积分数的变化求出煤样耗氧速率，并绘制耗氧速率随试验温度的变化趋势图。
v O 2 0 = Q C O 2 0 S L · l n C O 2 0 C O 2 = Q C O 2 0 V m l n C O 2 0 C O 2
式中： v O 2 0为煤样实际耗氧速率，mol/(cm3·s);Q为供风量，2mL/s; C O 2 0为新鲜风流中氧气含量，9.375×10-6;S为煤样罐断面积，cm2;L为煤样罐内煤柱高度，cm; C O 2为煤样出口处氧气体积分数，%;Vm为试验煤样体积，cm3。
根据式(1)，得到不同变质程度煤样的耗氧速率与温度的变化曲线，如图3所示。
煤自燃过程中，煤体内部的活性基团与氧气发生反应，释放出大量气体并产生一定热量，氧化反应
示意式如下：
C o a l + O 2 → φ 1 ( C O ) + φ 2 ( C O 2 ) + B
式中： φ 1 ( C O ) 、 φ 2 ( C O 2 )分别为CO、CO2的体积分数，%;B为煤自燃过程中的其他气体产物的体积分数，%。煤自燃氧化过程中的耗氧速率服从一级Arrhenius公式：
v O 2 = A C O 2 0 e x p - E D T
式中： v O 2为实际耗氧速率，mol/(cm3·s);A为指前因子；E为无量纲表观活化能；D为无量纲摩尔气体常数，8.314;T为无量纲热力学温度。
将式(1)代入式(3)，得耗氧速率与活化能的计算公式为：
v O 2 0 = A C O 2 0 e x p - E D T
将式(4)取对数后整理得：
l n v O 2 0 C O 2 0 = - E D T + l n A
在直角坐标系中以1/T为横坐标， l n ( v O 2 0 / C O 2 0 )为纵坐标，即可建立一条直线方程，该方程的斜率即为所求的表观活化能。
2.2 表观活化能对比分析
将煤样的临界温度作为划分煤氧化进程的依据，根据式(5)分别拟合临界温度前后1/T与 l n ( v O 2 0 / C O 2 0 )的函数曲线，其中，x表示拟合表达式中的1/T，y表示拟合表达式中的 l n ( v O 2 0 / C O 2 0 )，R2为拟合度；拟合相关参数见表2，结果如图4所示。
由表2可知：临界温度前表观活化能与变质程度呈正相关，E1(CY1)为13.855 3 J/mol，E1(PM)为26.422 7 J/mol，差值为12.567 4 J/mol。变质程度越高，内部化学键越稳定，稳定基团变为活跃状态所需活化能越多；临界温度后呈现的特征与临界温度前一致， E 2 ( C Y 1 )为41.533 4 J/mol，E2(PM)为48.646 9 J/mol，差值为7.113 5 J/mol。该阶段煤体放热量增加，煤温急剧上升，较为稳定的化学键开始断裂，产生大量的活性基团促进煤氧化进程发展。 E 2 ( C Y 1 )与E2(PM)差值较E1(CY1)与E1(PM)更小，主要因为临界温度后煤氧复合反应所消耗的物质相近或类似，均为煤样中稳定大分子物质化学键断裂所主导的反应。
同一煤样临界温度前后表观活化能差值较大，主要因为临界温度前氧气与煤体表面的活性物质发生反应，此阶段反应较为容易进行，临界温度后活性物质消耗殆尽，氧气需与更稳定的化学键发生反应，化学键断裂需更高能量；JM1、JM2与JM3煤样属于变质程度相同的煤样，内部化学键及结构类似，导致煤氧复合过程中所需活化能接近。
3 煤自燃危险性关联分析及预测
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3.1 Pearson相关系数法分析
煤低温氧化过程中所需的活化能与煤质指标存在一定关联性。以上试验研究表明：临界温度前后所需的表观活化能与煤样的变质程度相关，煤质指标为煤样变质程度的具体参数。
为研究煤低温氧化过程中所需的活化能与煤质指标中水分、灰分、挥发分、固定碳、可燃组分(固定碳与挥发分之和)、燃料比(固定碳与挥发分之比)间的关系，采用Pearson相关系数法计算表观活化能与煤质指标之间的相关系数。统计学中常用Pearson相关系数法来确定因变量与自变量之间的线性相关程度，其输出值介于-1~1，计算公式为：
r = n ∑ X i Y i - ( ∑ X i ) ( ∑ Y i ) [ n ∑ X i 2 - ( ∑ X i 2 ) ] [ n ∑ Y i 2 - ( ∑ Y i 2 ) ]
式中：n为参与统计的样本总量；X和Y为2个变量的观测值；输出r值越接近“1”说明表观活化能与煤质指标某一参数正相关性越强；r值越接近“-1”，说明两者间负相关性越强。计算结果如图5所示。
由图5可知：临界温度前后表观活化能与水分、灰分、挥发分之间呈负相关，负相关系数最大的为挥发分，临界温度前后分别为-0.893和-0.977;临界温度前后表观活化能与固定碳、可燃组分、燃料比之间呈正相关，正相关系数最大的为燃料比，临界温度前后分别为0.956和0.968，据此初步确定煤质指标中，影响煤低温氧化进程的主要变量为挥发分及燃料比。
3.2 煤自燃危险性预测
线性拟合可用于预测和解释变量间的变化关联性，也可用于控制变量达到预期结果；多元线性回归分析用来评价某因变量与多个自变量间的线性关系。
为进一步量化煤质指标与表观活化能间的关系，拟合了表观活化能与水分、灰分、挥发分、固定碳、可燃组分和燃料比之间的关系，并选取线性拟合度最大的2个变量，建立多元线性回归模型，用来预测煤样表观活化能，活化能与煤质指标间的线性拟合结果见表3。
由表3可知：表观活化能与挥发分之间呈线性负相关且最大，与燃料比之间呈线性正相关且最大，进一步选取挥发分与燃料比作为反应煤样临界温度前后所求表观活化能的特征变量，建立多元线性回归模型预测煤样在临界温度前后的表观活化能值，所建立的多元线性回归模型为：
Z = β 0 + β 1 I 1 + β 2 I 2 + ε
式中：因变量Z为被解释变量，即为临界温度前后表观活化能； β 0为回归常数， β 1和 β 2为回归系数； I 1和 I 2为解释变量，即为挥发分值和燃料比值； ε为随机误差。
将CY1、QM1、JM2煤样作为检测变量，剩余7组煤样的挥发分和燃料比数值导入在线数据分析软件SPASSPRO，进行多元线性回归，得到的临界温度前后的回归模型及其参数见表4。临界温度前后回归方程的 R 2 2为0.912 5和0.933 0，拟合效果较好，具有较高的可信度；将CY1、QM1、JM2挥发分和燃料比煤样数值作为检验数据，对多元线性回归模型进行检验，检测值与实际值见表5。
由以上分析可知：煤质指标中挥发分、燃料比与临界温度前后表观活化能的相关系数最大，主要原因为煤氧反应中煤体缓慢蓄热，随温度升高，煤体内部挥发性气体析出，析出气体可较早的参与煤氧复合进程，并进一步推动煤氧复合进程加速发展，因此，挥发分值较高的煤样自燃倾向性较高，易自燃；燃料比则代表煤样的煤化程度，煤化程度越高燃料比值越大，燃料比较高的煤样本身结构较为稳定，煤氧反应中需要较高的能量打开稳定的化学键，其自燃倾向性越低，不易自燃。
通过上述检验结果可知：所建立的多元线性回归模型误差值在±0.581 3内，因此，可通过该模型来计算煤样表观活化能，预测煤自燃倾向性。
4 结论
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1) 煤样低温氧化阶段，10组不同变质程度煤样间CO气体含量均呈现指数型增长趋势；通过温度与耗氧速率间拟合方程所计算的表观活化能，可表征煤低温氧化过程中所需的能量及反应进行的难易程度。
2) 通过Pearson相关系数法分析可得，煤质指标中挥发分及燃料比与临界温度前后表观活化能之间的相关系数最大，分别为-0.893、-0.977及0.956、0.968。
3) 通过挥发分及燃料比建立的多元线性回归模型，可用于计算不同变质程度煤样临界温度前后的表观活化能，并据此快速预测煤自燃倾向性。
基金
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  • 国家自然科学基金资助(51974235)
  • 国家资助博士后研究人员计划(GZC20232138)
  • 中国博士后科学基金资助(2023M742817)
  • 陕西省博士后科研项目(2023BSHEDZZ299)
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2024年第34卷第1期
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文章信息
doi: 10.16265/j.cnki.issn1003-3033.2024.01.0774
  • 接收时间：2023-08-15
  • 首发时间：2025-07-09
  • 出版时间：2024-01-28
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出版历史
  • 收稿日期：2023-08-15
  • 修回日期：2023-11-20
基金
国家自然科学基金资助(51974235)
国家资助博士后研究人员计划(GZC20232138)
中国博士后科学基金资助(2023M742817)
陕西省博士后科研项目(2023BSHEDZZ299)
作者信息
    1 西安科技大学 安全科学与工程学院，陕西 西安 710054
    2 陕西省煤火灾害防治重点实验室，陕西 西安 710054
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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