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Article(id=1149741766271746573, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149741761771258326, articleNumber=1003-3033(2024)02-0176-09, orderNo=null, doi=10.16265/j.cnki.issn1003-3033.2024.02.1453, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1691769600000, receivedDateStr=2023-08-12, revisedDate=1699977600000, revisedDateStr=2023-11-15, acceptedDate=null, acceptedDateStr=null, onlineDate=1752049398247, onlineDateStr=2025-07-09, pubDate=1709049600000, pubDateStr=2024-02-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752049398247, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1752049398247, creator=13701087609, updateTime=1752049398247, updator=13701087609, issue=Issue{id=1149741761771258326, tenantId=1146029695717560320, journalId=1146031787341344770, year='2024', volume='34', issue='2', 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=1752049397175, creator=13701087609, updateTime=1756468934610, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1168278645379440971, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149741761771258326, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1168278645379440972, tenantId=1146029695717560320, journalId=1146031787341344770, issueId=1149741761771258326, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=176, endPage=184, ext={EN=ArticleExt(id=1149741766464684558, articleId=1149741766271746573, tenantId=1146029695717560320, journalId=1146031787341344770, language=EN, title=Study on gas adsorption characteristics of coal under high temperature and high pressure atmosphere, columnId=1149733269173878863, journalTitle=China Safety Science Journal, columnName=Safety engineering technology, runingTitle=null, highlight=null, articleAbstract=

Deep mining faces high temperature and pressure environments. In order to understand the adsorption gas characteristics of deep coal bodies，an isothermal adsorption experiment was conducted to study the coal's adsorption characteristics under different temperature and pressure conditions. The experiment examined both macro and micro perspectives of the coal's adsorption behavior，molecular dynamics isothermal adsorption simulation and theoretical analysis. The research results are as follows. When the gas pressure is low，the difference between the absolute adsorption capacity and the excess adsorption capacity is not significant at different temperatures. When the gas pressure is high，the difference between the absolute adsorption capacity and the excess adsorption capacity increases with the increase in temperature. In the process of gas pressure increasing from 0 to 20 MPa，the amount of gas adsorbed by coal is divided into three stages. The growth pattern consists of a rapid increase during the initial stage，followed by short-term stability in the middle stage，and a gradual decline in the later stage. The equal adsorption heat and adsorption capacity of coal meet the exponential function relationship. The temperature-pressure adsorption model based on the equivalent adsorption heat deduction can predict the quantity of isothermal adsorption gas under any temperature and pressure conditions，and the relative error between the measured and predicted values is 10%.

, correspAuthors=Jiwei YUE, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Xiaojing SHEN, Jiwei YUE, Yuehui LIANG, Chen WANG, Jinlin XU, Qijun HAN), CN=ArticleExt(id=1149741790716150357, articleId=1149741766271746573, tenantId=1146029695717560320, journalId=1146031787341344770, language=CN, title=高温高压氛围下煤体吸附瓦斯特性研究, columnId=1149733269727526997, journalTitle=中国安全科学学报, columnName=安全工程技术, runingTitle=null, highlight=null, articleAbstract=

深部开采面临着高温高压环境，为厘清深部煤体的吸附瓦斯特性，采用等温吸附试验、分子动力学等温吸附模型及理论分析相结合的方法，从宏观角度和微观角度，探究高温高压氛围下煤体吸附瓦斯特性。结果表明：瓦斯压力较低时，不同温度下，绝对吸附量与过剩吸附量的差值差别不大；瓦斯压力较高时，绝对吸附量与过剩吸附量的差值随着温度的升高而增大；瓦斯压力从0 MPa逐渐增加到20 MPa的过程中，煤体吸附瓦斯量分为前期快速增加、中期短暂稳定、后期逐渐减小3个阶段；煤的等量吸附热与吸附量满足指数函数关系；基于等量吸附热推演的温度-压力吸附模型可以预测任意温度和压力条件下的等温吸附瓦斯量，预测值与实测值相对误差小于12%。

, correspAuthors=岳基伟, authorNote=null, correspAuthorsNote=
** 岳基伟(1990—)，男，河南临颍人，博士，副教授，主要从事瓦斯灾害防治理论与技术研究。E-mail：。
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申晓静 (1991—)，女，河南郑州人，硕士，助教，主要从事吸附理论、水基型灭火剂、有机化学等方面的研究。E-mail：。

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申晓静 (1991—)，女，河南郑州人，硕士，助教，主要从事吸附理论、水基型灭火剂、有机化学等方面的研究。E-mail：。

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申晓静 (1991—)，女，河南郑州人，硕士，助教，主要从事吸附理论、水基型灭火剂、有机化学等方面的研究。E-mail：。

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Basic parameters of coal samples

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真密度/
(g·cm-3)		 视密度/
(g·cm-3)		 孔隙率/% 坚固性
系数		 煤的工业分析
水分% 灰分/% 挥发分/%
1.42 1.39 5.67 0.94 1.03 8.09 16.98
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煤样的基本参数

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真密度/
(g·cm-3)		 视密度/
(g·cm-3)		 孔隙率/% 坚固性
系数		 煤的工业分析
水分% 灰分/% 挥发分/%
1.42 1.39 5.67 0.94 1.03 8.09 16.98
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Fitting parameters of adsorption capacity and lnp

, figureFileSmall=null, figureFileBig=null, tableContent=
温度/K h i R2
303.15 0.123 67 13.036 78 0.974 72
323.15 0.125 01 13.183 58 0.975 81
343.15 0.126 73 13.316 5 0.977 17
363.15 0.128 17 13.452 48 0.978 28
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吸附量与lnp的拟合参数

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温度/K h i R2
303.15 0.123 67 13.036 78 0.974 72
323.15 0.125 01 13.183 58 0.975 81
343.15 0.126 73 13.316 5 0.977 17
363.15 0.128 17 13.452 48 0.978 28
), ArticleFig(id=1168128969225281807, tenantId=1146029695717560320, journalId=1146031787341344770, articleId=1149741766271746573, language=EN, label=Tab.3, caption=

Equation of isometric adsorption line and isometric adsorption heat

, figureFileSmall=null, figureFileBig=null, tableContent=
V/
(mL·g-1)		 d C 相关
系数		 Qst/
(kJ·mol-1)
5 -807.25 16.215 5 0.997 73 6.711 3
10 -836.11 17.140 84 0.997 66 6.951 3
15 -875.64 17.835 47 0.997 54 7.280
20 -933.15 18.501 57 0.997 29 7.758
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等量吸附线方程及等量吸附热

, figureFileSmall=null, figureFileBig=null, tableContent=
V/
(mL·g-1)		 d C 相关
系数		 Qst/
(kJ·mol-1)
5 -807.25 16.215 5 0.997 73 6.711 3
10 -836.11 17.140 84 0.997 66 6.951 3
15 -875.64 17.835 47 0.997 54 7.280
20 -933.15 18.501 57 0.997 29 7.758
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高温高压氛围下煤体吸附瓦斯特性研究
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申晓静 1 , 岳基伟 1, 2, 3, ** , 梁跃辉 1 , 王辰 1 , 徐金林 1 , 韩奇峻 1
中国安全科学学报 | 安全工程技术 2024,34(2): 176-184
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中国安全科学学报 | 安全工程技术 2024, 34(2): 176-184
高温高压氛围下煤体吸附瓦斯特性研究
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申晓静1 , 岳基伟1, 2, 3, ** , 梁跃辉1, 王辰1, 徐金林1, 韩奇峻1
作者信息
  • 1 安徽理工大学 安全科学与工程学院，安徽 淮南 232001
  • 2 煤矿深井开采灾害防治技术科技研发平台，安徽理工大学，安徽 淮南 232001
  • 3 河南理工大学 河南省瓦斯地质与瓦斯治理重点实验室-省部共建国家重点实验室培育基地，河南 焦作 454000

    • 申晓静 (1991—)，女，河南郑州人，硕士，助教，主要从事吸附理论、水基型灭火剂、有机化学等方面的研究。E-mail：。

通讯作者:

** 岳基伟(1990—)，男，河南临颍人，博士，副教授，主要从事瓦斯灾害防治理论与技术研究。E-mail：。
Study on gas adsorption characteristics of coal under high temperature and high pressure atmosphere
Xiaojing SHEN1 , Jiwei YUE1, 2, 3, ** , Yuehui LIANG1, Chen WANG1, Jinlin XU1, Qijun HAN1
Affiliations
  • 1 School of Safety Science and Engineering，Anhui University of Science & Technology，Huainan Anhui 232001，China
  • 2 Scientific and Technological Research Platform for Disaster Prevention and Control of Deep Coal Mining，Anhui University of Science and Technology，Huainan Anhui 232001，China
  • 3 State Key Laboratory Cultivation Base for Gas Geology and Gas Control (Henan Polytechnic University)，Henan Polytechnic University，Jiaozuo Henan 454000，China
出版时间: 2024-02-28 doi: 10.16265/j.cnki.issn1003-3033.2024.02.1453
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摘要
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深部开采面临着高温高压环境，为厘清深部煤体的吸附瓦斯特性，采用等温吸附试验、分子动力学等温吸附模型及理论分析相结合的方法，从宏观角度和微观角度，探究高温高压氛围下煤体吸附瓦斯特性。结果表明：瓦斯压力较低时，不同温度下，绝对吸附量与过剩吸附量的差值差别不大；瓦斯压力较高时，绝对吸附量与过剩吸附量的差值随着温度的升高而增大；瓦斯压力从0 MPa逐渐增加到20 MPa的过程中，煤体吸附瓦斯量分为前期快速增加、中期短暂稳定、后期逐渐减小3个阶段；煤的等量吸附热与吸附量满足指数函数关系；基于等量吸附热推演的温度-压力吸附模型可以预测任意温度和压力条件下的等温吸附瓦斯量，预测值与实测值相对误差小于12%。

高温高压  /  煤体吸附瓦斯  /  吸附特性  /  绝对吸附量  /  过剩吸附  /  等量吸附热

Deep mining faces high temperature and pressure environments. In order to understand the adsorption gas characteristics of deep coal bodies，an isothermal adsorption experiment was conducted to study the coal's adsorption characteristics under different temperature and pressure conditions. The experiment examined both macro and micro perspectives of the coal's adsorption behavior，molecular dynamics isothermal adsorption simulation and theoretical analysis. The research results are as follows. When the gas pressure is low，the difference between the absolute adsorption capacity and the excess adsorption capacity is not significant at different temperatures. When the gas pressure is high，the difference between the absolute adsorption capacity and the excess adsorption capacity increases with the increase in temperature. In the process of gas pressure increasing from 0 to 20 MPa，the amount of gas adsorbed by coal is divided into three stages. The growth pattern consists of a rapid increase during the initial stage，followed by short-term stability in the middle stage，and a gradual decline in the later stage. The equal adsorption heat and adsorption capacity of coal meet the exponential function relationship. The temperature-pressure adsorption model based on the equivalent adsorption heat deduction can predict the quantity of isothermal adsorption gas under any temperature and pressure conditions，and the relative error between the measured and predicted values is 10%.

high temperature and high pressure  /  adsorption gas of coal  /  adsorption characteristics  /  absolute adsorption capacity  /  excess adsorption  /  equal adsorption heat
申晓静, 岳基伟, 梁跃辉, 王辰, 徐金林, 韩奇峻. 高温高压氛围下煤体吸附瓦斯特性研究. 中国安全科学学报, 2024 , 34 (2) : 176 -184 . DOI: 10.16265/j.cnki.issn1003-3033.2024.02.1453
Xiaojing SHEN, Jiwei YUE, Yuehui LIANG, Chen WANG, Jinlin XU, Qijun HAN. Study on gas adsorption characteristics of coal under high temperature and high pressure atmosphere[J]. China Safety Science Journal, 2024 , 34 (2) : 176 -184 . DOI: 10.16265/j.cnki.issn1003-3033.2024.02.1453
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0 引言
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煤炭是中国能源安全的稳定器和压舱石，其稳定供应关系着我国国民经济的发展[1]。目前，我国浅部煤炭资源的开采已接近枯竭，深部煤炭开采势在必行。然而，深部煤炭开采面临着高地温、高瓦斯、低透气性的环境条件，瓦斯灾害逐渐凸显，严重威胁深部煤炭资源的安全开采[2]。
煤对瓦斯的吸附特性与煤层瓦斯治理难易程度紧密相关，影响煤体吸附瓦斯特性的主要因素有温度[3]、压力[4]、变质程度[5]、水分[6]、粒径[7]等。然而，温度与压力是影响深部煤层瓦斯赋存的主要因素。王思琪[8]、SAKUROVS [9]、李祥春[10]等研究认为，煤对瓦斯的吸附量与吸附平衡压力呈正相关关系，与试验温度呈负相关关系。TANG Xu等[11]探究了低温及常温条件下(243.15~303.15 K)煤对瓦斯的吸附特性，发现温度越低、压力越大，煤对瓦斯的吸附量越大。QI Lingling等[12]研究了焦煤在吸附平衡压力(11 MPa)下的吸附瓦斯特性，发现煤对瓦斯的吸附量与温度呈负相关关系。研究煤对瓦斯吸附特性的方法，除试验法外，分子动力学模拟也是较常用的方法之一，例如：陈向军等[13]采用分子动力学模拟法研究了单组分气体在不同吸附平衡压力条件下的吸附瓦斯量，发现单组分的吸附平衡压力小于15 MPa时，煤对瓦斯的吸附量随吸附平衡压力的增加而逐渐增加，当瓦斯压力高于15 MPa后，煤对瓦斯的平均吸附量达到饱和状态。YANG Yanhui[14] 、YAN Jingxue[15]等基于分子动力学模拟法，研究了吸附平衡压力为0~15 MPa时煤对甲烷分子吸附特性的影响，发现随着吸附平衡压力的增加而增加。岳基伟等[16]采用分子动力学模拟的方法，探究了不同温度(353.15~413.15 K)、不同压力(0~8 MPa)条件下煤对甲烷及氘代甲烷的吸附差异性，指出煤对甲烷及氘代甲烷的吸附性能差别不大。MOSHER 等[17]采用分子动力学模型研究了煤、页岩系统中微孔和中孔对甲烷吸附特性的影响。SONG Yu等 [18]通过比较煤分子、石墨烯分子对瓦斯分子吸附的差异性发现，吸附位置、吸附位点和吸附取向对吸附性能至关重要。
由前述可知：煤体吸附瓦斯特性的试验研究主要聚焦于低温-常温(243.15~303.15 K)及低压(0~11 MPa)条件，尤其是单因素作用下，煤对瓦斯吸附特性的影响，然而深部煤层瓦斯的赋存温度、压力均高于浅部煤层，高温高压对于瓦斯的赋存而言是一对矛盾体，二者协同作用会对煤层瓦斯的赋存产生影响。鉴于此，为获得高温高压氛围下煤体吸附瓦斯的特性，笔者拟采用分子动力学及试验的方法，获得低压条件下煤对瓦斯的吸附量；并基于等量吸附热及煤对瓦斯的吸附量，建立高温高压氛围下等温吸附模型，定量分析高温高压氛围下煤体吸附瓦斯的特性，以期为深部煤炭的安全开采、瓦斯资源的开发及瓦斯灾害防治奠定理论基础。
1 等温吸附试验
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1.1 煤样的采集与制备
选取位于山西省沁源县西南部的新源煤矿山西组中段2号煤层的煤作为等温吸附试验的煤样，该矿最大原始瓦斯压力为1.2 MPa，平均瓦斯含量为14.98 mL/g，煤质为焦煤，煤样的基本参数测定结果见表1。
1.2 煤样的等温吸附试验方案
采用高温高压气体吸附仪进行试验测试，进而从宏观角度分析煤样吸附瓦斯的特性。新源矿的平均地温梯度为3.9 ℃/100 m(277.05 K/100 m)，压力梯度为0.76 MPa/100 m。为了研究800m以下煤体对瓦斯的吸附特性，基于压力梯度和地温梯度确定试验研究的最高瓦斯压力为20 MPa，最高温度为363.15 K。高温高压气体吸附仪最高测试压力为10 MPa，试验温度分别为303.15、323.15、343.15及363.15 K。试验步骤如下：
1) 选取粒径为3~6 mm的煤样作为试验煤样，将煤样烘干装入样品管中，将样品管安装到仪器样品处理区域。
2) 将煤样进行真空干燥，真空干燥时间设置为4 h，温度设置为105 ℃。
3) 真空干燥结束后，将控制程序中的最大吸附平衡压力设置为10 MPa，试验温度设置为303.15 K。 仪器达到吸附平衡自动记录吸附量，由此得到不同吸附平衡压力点的吸附数据，试验结束。
4) 重复以上试验步骤，分别开展303.15、323.15、343.15及363.15 K温度下的煤吸附瓦斯试验。
由于试验设备存在达不到高压的缺陷，文中采用分子模拟和试验相结合的方法，从微观角度研究高温高压氛围下煤样吸附瓦斯的特性。通过Materials Studio分子模拟软件，构建煤的大分子模型，进而对其进行几何优化和退火，并选取能量最低的煤大分子模型模拟周期性边界条件，并模拟不同温度(303.15、323.15、343.15及363.15 K)、最高压力20 MPa条件下的等温吸附过程。
2 煤分子结构模型的构建
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焦煤的二维结构大分子模型如图1所示[19]，采用Materials Studio中的Geometry Optimization项和Anneal项对初始模型进行几何优化和退火优化，精度为Fine，力场选择COMPASS，电荷选择USE Current[20]。几何优化处理通常进行5~10次，退火循环次数设为10次。每次循环结束以后，输出一个分子构型，再优化该分子结构，从而得到几何最稳定能量构型和退火最稳定能量构型。煤分子经过几何优化和退火后，最低能量结构如图2所示。最后采用Materials Studio中的Forcite模块，建立优化后的煤分子的周期性边界条件，密度选择为1.3 g/cm3，结果如图3所示。优化后的结构模型达到能量最低最稳定的状态，出现了扭转与变形，具有良好的三维结构，所有芳香层状结构以平行与重叠的形式存在。
3 煤吸附瓦斯试验及模拟结果
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3.1 等温吸附试验结果
等温吸附试验中直接测得的过剩吸附量如图4所示；过剩吸附量指实际吸附相内的密度减去气相密度后剩余的吸附量。由图4可知：吸附平衡压力为0~10 MPa时，煤样吸附瓦斯量随着压力的升高而增加，增加阶段分为快速增加和缓慢增加2个阶段。
3.2 等温吸附模拟结果
3.2.1 过剩吸附量校正
分子模拟得到的等温吸附量是绝对吸附量，为进一步将模拟数据与试验数据相比，应将绝对吸附量转化为过剩吸附量，根据绝对吸附量的定义，过剩吸附量与绝对吸附量的关系如下[21]:
V a d = V e x / 1 - ρ g ρ f
式中：Vad为过剩吸附量，mL/g;Vex为绝对吸附量，mL/g; ρg为气相密度，g/cm3；ρf为吸附相密度，g/cm3。
由式(1)可知：实现过剩吸附量向绝对吸附量的转换，须确定ρg与ρf。气相密度通过公式pM=ρg RT 获得(p为瓦斯压力，MPa;M为摩尔质量，g/mol; R为气体常数，8.314J/(mol·K)；T为温度，K)。采用Ozawa经验公式可计算吸附相密度，将模拟得到的Vex转化为Vad，如图5所示。
由图5可知：当瓦斯压力较低时，绝对吸附量与过剩吸附量差别不大，其由于大部分瓦斯吸附到煤分子孔隙表面，游离相密度较小，因此，绝对吸附量和过剩吸附量随着压力的增加而线性增加。当煤分子对瓦斯的吸附量趋于饱和时，吸附相密度不再随着吸附平衡压力的增加而显著增大，但是游离相密度仍然随着压力的增加而增大，导致过剩吸附量随着压力的增加而减小。瓦斯压力较低时，不同温度下，绝对吸附量与过剩吸附量的差值差别不大。瓦斯压力较高时，绝对吸附量与过剩吸附量的差值随着温度的增加而增加。0~10 MPa范围内的模拟结果与试验结果对比，如图6所示。
由图6可知：在0~10 MPa范围内，分子模拟获得的吸附量与试验测试结果相差不大，且二者的差值随着温度的升高、压力的增加而减小。在低压1 MPa 的条件下，模拟值与试验值的误差率较大，其他压力点的误差率最大值为16.24%，最小误差率为0.525%。其说明采用分子模拟和试验相结合的方法，能够阐释高温高压氛围下煤体吸附瓦斯的特性。
3.2.2 分子动力学模拟结果
由上述分析可知：建立的煤分子结构在设定参数下的模拟结果具有可信度，弥补了气体吸附仪不能进行高温高压测试的局限性，文中模拟了吸附平衡压力为0~20 MPa、温度分别为303.15、323.15、343.15及363.15 K条件下煤样吸附瓦斯的特性，模拟结果如图7所示。
由图7可知：吸附曲线具有明显升高段、平缓段及下降段。吸附前期(吸附曲线明显升高段)，随着吸附平衡压力的增加，吸附瓦斯量快速增加。因为随着吸附平衡压力的增加，游离相及吸附相密度增大过剩吸附量就不断增大；吸附中期(吸附曲线平缓段)，吸附瓦斯量出现短暂稳定，其原因是吸附平衡压力逐渐增大，煤对瓦斯的吸附逐渐至饱和，当吸附相密度达到最大值时，过剩吸附量也最大，即等温线的顶点。
在吸附后期(吸附曲线下降段)，游离相密度继续增加，但吸附相密度趋于稳定，因此吸附量逐渐减小。即使压力继续增加，吸附相密度也不再变化，过剩吸附量呈现下降趋势。当吸附平衡压力相同时，随着温度升高，煤对瓦斯的过剩吸附量逐渐减少，在高压段范围内，减小幅度不明显。其原因是煤分子内部的吸附位点几乎已吸附饱和，提高温度会增加瓦斯分子的动能，瓦斯分子从较弱的吸附位点逃逸。在低压区域中，具有较丰富的空吸附位点，吸附的瓦斯分子受壁层吸引力更大，所以逃逸难度会增加。
3.3 等量吸附热
吸附热是对吸附过程中热量变化的综合反应，其影响主要反映在吸附剂与吸附质之间的作用强度。通过计算吸附热，人们可以判断吸附作用的形式和分析吸附作用表面的热均匀性和特性。目前，有关吸附热的计量主要方式有直接计量热法、Clapeyron-Clausius方程法、气相色谱法等[22-23]。采用直接法计算吸附热时需借助吸附装置上所附送的直接测量热仪；而气相色谱法通过计算气体在煤中的停留时间和保留体积计算吸附热，该方法会对气体体积计算造成较大误差。一般计算吸附热的方法是采用Clapeyron-Clausius方程(式(2))，通过测量在相同吸附量下的压力和温度，绘制以对数值即为lnp/MPa和1/T为纵横坐标的图形，并计算吸附热(对p取对数时不考虑单位，下同)。
∂ l n p ∂ T = Q s t R T 2
分别对式(2)左右两边进行不定积分：
l n p = - Q s t R T + C
式中：Qst为等量吸附热，kJ/mol；C为常数。
由于不同温度的吸附量V在0~21 mL/g之间，因此，选取0~21 mL/g之间的吸附量，可以推算出某一温度下的压力值p。取lnp作为纵坐标，V作为横坐标，绘制图形(图8)。lnp与V满足lnp=hV+i的关系，其中，h，i为拟合参数，见表2。
由表2可获得参数h、i与T的散点图，如图9所示。参数h与T满足h=7.61×10-5T +0.100 54 的关系；参数i与T满足i=0.006 9T+10.948 7的关系。因此，lnp与V满足lnp=(7.61×10-5T +0.100 54)V+(0.006 9T+10.948 7)的关系。
根据图7可计算获得吸附量分别为5、10、15及20 mL/g时所对应的温度，分别以lnp和1/T为纵坐标横坐标作图，即可获得lnp和1/T的散点曲线，如图10所示。lnp和1/T满足线性关系lnp=d/T+C。由式(3)可知：直线斜率为Qst与R的比值，斜率与气体常数的乘积为等量吸附热，拟合参数d、C及计算的等量吸附热见表3，lnp和1/T的关系如图10所示。
由表4可知：煤样的吸附热区间为6.7~8 kJ/mol整个吸附过程吸附热均小于物理吸附热的上限值40 kJ/mol，所以煤对瓦斯的吸附属于物理吸附，是自发放热的过程。
由图11可知：煤对瓦斯的吸附热随着吸附量的增加而增加，这是由于吸附剂表面的不均匀性以及吸附质之间的相互作用力引起的。由于吸附剂表面不均匀，吸附质先在活性较高的位置吸附，接着逐渐向活性较低的位置吸附。随着吸附瓦斯分子数量的增加，分子间的相互排斥作用逐渐加强，进而导致释放的能量逐步提升，吸附热和吸附量满足Qst=0.395 47exp(0.070 09V)+6.150 84的函数关系。
4 高温高压氛围下煤体吸附瓦斯模型
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目前，我国煤层瓦斯含量的测试方法有2种：一是通过直接法测试瓦斯含量，二是间接法测试瓦斯含量。随着浅部资源的枯竭，大部分矿井逐渐转为深部开采，而大多数矿井的深部区域无法现场获取瓦斯的解吸数据，只能采用间接法获得煤层瓦斯含量。在以往的研究中，吸附模型的研究仅仅考虑了温度、压力单因素的影响，且吸附模型仅对浅部煤层具有适用性。温度和压力作为一对矛盾体，二者共同作用对煤的吸附瓦斯特性影响较大。科学合理地获得深部煤样的煤层瓦斯含量，必须同时考虑压力和温度对煤体吸附瓦斯特性的影响。
由式(3)可知：已知T1温度下瓦斯的等温吸附曲线、吸附过程中瓦斯的等量吸附热，可计算温度T2不同压力条件下吸附瓦斯量。利用等量吸附热推导的温度压力吸附模型(式(7))，以山西新源煤矿煤样303.15 K时的等温吸附曲线模拟值为基础，可以预测323.15、343.15及363.15 K，瓦斯压力为0~19MPa条件下的等温吸附瓦斯量；303.15、323.15、343.15及363.15 K，瓦斯压力为0~19MPa条件下等温吸附量的模拟值及预测值如图12所示。303.15、323.15、343.15及363.15 K，瓦斯压力为0~19MPa条件下等温吸瓦斯量的预测值及实测值如图13所示。
l n p 1 = - Q s t R T 1 + C = - 0.395   47 e x p ( 0.070   09 V ) + 6.150   84 R T 1 + C
l n p 2 = - Q s t R T 2 + C = - 0.395   47 e x p ( 0.070   09 V ) + 6.150   84 R T 2 + C
式(5)与式(4)相减可得下式：
l n p 2 = l n p 1 + 0.395   47 e x p ( 0.070   09 V ) + 6.150   84 R T 1 - 0.395   47 e x p ( 0.070   09 V ) + 6.150   84 R T 2
将式lnp2=(7.61×10-5 T2+0.100 54)V+(0.006 9 T2+10.948 7)代入式(6)可得下式：
( 7.61 × 10 - 5 T 2 + 0.100   54 ) V + ( 0.006   9 T 2 + 10.948   7 ) = l n p 1 + 0.395   47 e x p ( 0.070   09 V ) + 6.150   84 R T 1 - 0.395   47 e x p ( 0.070   09 V ) + 6.150   84 R T 2
由图12可知：采用等量吸附热推导的温度-压力吸附模型所预测的吸附瓦斯量与模拟值差别不大，相对误差小于12%。采用等量吸附热推导的温度—压力吸附模型所预测的吸附瓦斯量与实测值(0~11 MPa)差别也不大，相对误差小于14%。其中低压环境下煤的吸附瓦斯量较小，预测值与模拟值、预测值与实测值的相对误差率稍大，而压力较高时，预测值与模拟值、预测值与实测值的相对误差率较小。
5 结论
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1) 瓦斯压力较低时，不同温度下，绝对吸附量与过剩吸附量的差值差别不大；瓦斯压力较高时，绝对吸附量与过剩吸附量的差值随着温度的增加而增加。
2) 随着温度的升高，瓦斯吸附量逐渐下降；随着瓦斯压力的升高，瓦斯吸附量变化主要分为前期快速增加、中期短暂稳定及后期减小3个阶段。
3) 煤对瓦斯气体的吸附热随吸附量的增加而增加，二者呈指数的函数关系。
4) 基于等量吸附热推导的温度-压力吸附瓦斯模型预测煤的吸附瓦斯量精度较高，尤其是当压力较高时；该可以预测任意温度和压力条件下煤对瓦斯的吸附量，预测值与模拟值相对误差率小于12%。该研究为深部煤炭资源的安全开采、瓦斯资源的开发及瓦斯灾害防治奠定理论基础。
基金
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  • 国家自然科学基金资助(52304200)
  • 国家自然科学基金资助(U23A20601)
  • 安徽省自然科学基金资助(2308085QE152)
  • 河南省瓦斯地质与瓦斯治理重点实验室-省部共建国家重点实验室培育基地开放基金资助(WS2022B03)
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2024年第34卷第2期
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doi: 10.16265/j.cnki.issn1003-3033.2024.02.1453
  • 接收时间：2023-08-12
  • 首发时间：2025-07-09
  • 出版时间：2024-02-28
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  • 收稿日期：2023-08-12
  • 修回日期：2023-11-15
基金
国家自然科学基金资助(52304200)
国家自然科学基金资助(U23A20601)
安徽省自然科学基金资助(2308085QE152)
河南省瓦斯地质与瓦斯治理重点实验室-省部共建国家重点实验室培育基地开放基金资助(WS2022B03)
作者信息
    1 安徽理工大学 安全科学与工程学院，安徽 淮南 232001
    2 煤矿深井开采灾害防治技术科技研发平台，安徽理工大学，安徽 淮南 232001
    3 河南理工大学 河南省瓦斯地质与瓦斯治理重点实验室-省部共建国家重点实验室培育基地，河南 焦作 454000

通讯作者:

** 岳基伟(1990—)，男，河南临颍人，博士，副教授，主要从事瓦斯灾害防治理论与技术研究。E-mail：。
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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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