煤粒孔隙的分形模型与分形特性研究
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摘要
为了定量表征煤粒孔隙结构特性,选取褐煤、烟煤和无烟煤3个不同煤阶煤样分别破碎成3个不同粒度的煤粒进行压汞试验,基于Menger海绵模型和热力学模型对试验数据进行处理,研究了煤粒孔隙的分形特性。研究表明:基于Menger海绵模型得到的试验曲线不符合线性关系,曲线分为2段,前段分形维数DM大于3,后段线性拟合度太低;采用热力学模型分析孔隙分形特性时,曲线呈现显著的线性关系,拟合度均在0.98以上,且分形维数DT均在2~3。表明热力学模型较Menger海绵模型更适合研究煤粒孔隙的分形特性。DT随着煤粒度的减小而减小,且煤粒度对其影响较小;DT随着煤阶的升高而减小,并从煤变质作用的角度分析了其原因。
In order to indicate the structure properties of the coal porosity quantitatively,three different coal rank samples,including lignite,bituminous coal and anthracite,were selected to break into three different granularity,and the mercury porosimetry test was then performed. Based on the Menger sponge model and the thermodynamic model,the experimental data were processed to study the fractal characteristics of coal porosity. The results showed that the curves obtained from the Menger sponge model did not fit the linear relationship.The curve was divided into two segments. The fractal dimension value DMof the front segment was greater than 3,and the linear fitting degree of the back segment was too low. When the thermodynamic model was used to analyze the fractal characteristics of the pore,the curves showed a significant linear relationship,and the fitting degree was more than 0.98. Meanwhile,the fractal dimension DTwas between 2 and 3.It was shown that the thermodynamic model was more suitable for studying the fractal characteristics of the coal porosity than Menger sponge model. DTdecreased with the decrease of the coal particle size,and the coal particle size had little effect on it. DTdecreased with the increase of coal rank,and the reason was analyzed from the viewpoint of the coal metamorphism.
In order to indicate the structure properties of the coal porosity quantitatively,three different coal rank samples,including lignite,bituminous coal and anthracite,were selected to break into three different granularity,and the mercury porosimetry test was then performed. Based on the Menger sponge model and the thermodynamic model,the experimental data were processed to study the fractal characteristics of coal porosity. The results showed that the curves obtained from the Menger sponge model did not fit the linear relationship.The curve was divided into two segments. The fractal dimension value DMof the front segment was greater than 3,and the linear fitting degree of the back segment was too low. When the thermodynamic model was used to analyze the fractal characteristics of the pore,the curves showed a significant linear relationship,and the fitting degree was more than 0.98. Meanwhile,the fractal dimension DTwas between 2 and 3.It was shown that the thermodynamic model was more suitable for studying the fractal characteristics of the coal porosity than Menger sponge model. DTdecreased with the decrease of the coal particle size,and the coal particle size had little effect on it. DTdecreased with the increase of coal rank,and the reason was analyzed from the viewpoint of the coal metamorphism.
引文
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[15]王秀娟,要惠芳,李伟,等.基于热力学模型的煤孔隙结构分形表征[J].煤田地质与勘探,2014,42(6):20-23.Wang Xiujuan,Yao Huifang,Li Wei,et al.Fractal characterization of pore structure in coals based on thermodynamics model[J].Coal Geology&Exploration,2014,42(6):20-23.
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[19]陈义林,秦勇,田华,等.基于压汞法无烟煤孔隙结构的粒度效应[J].天然气地球科学,2015,26(9):1629-1639.Chen Yilin,Qin Yong,Tian Hua,et al.Particle size effect of pore structure ofanthracite by mercury porosimetry[J].Natural Gas Geoscience,2015,26(9):1629-1639.
[20]陈振宏,贾承造,宋岩,等.高煤阶与低煤阶煤层气藏物性差异及其成因[J].石油学报,2008,29(2):179-184.Chen Zhenhong,Jia Chengzao,Song Yan,et al.Differences and origin of physical properties of low-rank and high-rank coal-bed methanes[J].Acta Petrolei Sinica,2008,29(2):179-184.
[2]程庆迎.煤的孔隙和裂隙研究现状[J].煤炭工程,2011(12):91-93.Cheng Qingying,Research status of pore and crack in coal[J].Coal Engineering,2011(12):91-93.
[3]李伟,要惠芳,刘鸿福,等.基于显微CT的不同煤体结构煤三维孔隙精细表征[J].煤炭学报,2014,39(6):1127-1132.Li Wei,Yao Huifang,Liu Hongfu,et al.Advanced characterization of three-dimensional pores in coals with different coal-body structure by Micro-CT[J].Journal of China Coal Society,2014,39(6):1127-1132.
[4]降文萍,宋孝忠,钟玲文.基于低温液氮试验的不同煤体结构煤的孔隙特征及其对瓦斯突出影响[J].煤炭学报,2011,36(4):609-614.Jiang Wenping,Song Xiaozhong,Zhong Lingwen.Research on the pore properties of different coal body structure coals and the effects on gas outburst based on the low-temperature nitrogen adsorption method[J].Journal of China Coal Society,2011,36(4):609-614.
[5]何学秋,王恩元.孔隙气体对煤体变形及蚀损作用机理[J].中国矿业大学学报,1996,25(1):6-11.He Xueqiu,Wang Enyuan.Coal deformation and fracture mechanism under pore gas action[J].Journal of China University of Mining&Technology,1996,25(1):6-11.
[6]谢和平.分形-岩石力学导论[M].北京:科学出版社,1996.
[7]李留仁,赵艳艳,李忠兴,等.多孔介质微观孔隙结构分形特征及分形系数的意义[J].石油大学学报:自然科学版,2004,28(3):105-107.Li Liuren,Zhao Yanyan,Li Zhongxing,et al.Fractal characteristics of micropore structure of porous media and the meaning of fractal coefficient[J].Journal of the University of Petroleum:Natural Science Edition,2004,28(3):105-107.
[8]Zhu J F,Liu J Z,Yang Y M,et al.Fractal characteristics of pore structures in 13 coal specimens:relationship among fractal dimension,pore structure parameter,and slurry ability of coal[J].Fuel Processing Technology,2016,149:256-267.
[9]郗兆栋,唐书恒,张松航,等.腐泥煤的孔隙结构及分形特征[J].煤炭科学技术,2016,44(11):103-109.Xi Zhaodong,Tang Shuheng,Zhang Songhang,et al.Pore structure and fractal features of sapropelite[J].Coal Science and Technology,2016,44(11):103-109.
[10]张来娣,王婷婷,赵万春,等.基于多重分形理论页岩孔裂隙结构特征的研究[J].中州煤炭,2016(8):122-126.Zhang Laidi,Wang Tingting,Zhao Wanchun,et al.Study on the structural characteristics of shale pore structure based on multifractal theory[J].Zhongzhou Coal,2016(8):122-126.
[11]李子文,林柏泉,郝志勇,等.煤体多孔介质孔隙度的分形特征研究[J].采矿与安全工程学报,2013,30(3):125-130,136.Li Ziwen,Lin Boquan,Hao Zhiyong,et al.Fractal characteristics of porosity for porous media in coal mass[J].Journal of Mining&Safety Engineering,2013,30(3):125-130,136.
[12]Friesen W I,Mikula R J.Fractal dimensions of coal particles[J].Journal of Colloid and Interface Science,1987,120(1):263-271.
[13]Zhang B,Li S.Determination of the surface fractal dimension for porous media by mercury porosimetry[J].Industrial&Engineering Chemistry Research,1995,34(4):1383-1386.
[14]刘永忠,陈三强,孙皓.冻干物料孔隙特性表征的分形模型与分形维数[J].农业工程学报,2004,20(6):41-45.Liu Yongzhong,Chen Sanqiang,Sun Hao.Characterizing pores in freeze-dried materials by fractal models and fractal dimensions[J].Transactions of the Chinese Society of Agricultural Engineering,2004,20(6):41-45.
[15]王秀娟,要惠芳,李伟,等.基于热力学模型的煤孔隙结构分形表征[J].煤田地质与勘探,2014,42(6):20-23.Wang Xiujuan,Yao Huifang,Li Wei,et al.Fractal characterization of pore structure in coals based on thermodynamics model[J].Coal Geology&Exploration,2014,42(6):20-23.
[16]Mandelbrot B B,PignoniR.The fractal geometry of nature[M].New York:WH Freeman,1983.
[17]Rootare H M,Prenzlow C F.Surface areas from mercury porosimetry measurements[J].Journal of Physical Chemistry,1967,71(8):2733-2736.
[18]霍多特B B.煤与瓦斯突出[M].宋士钊,王佑安,译.北京:中国工业出版社,1966.
[19]陈义林,秦勇,田华,等.基于压汞法无烟煤孔隙结构的粒度效应[J].天然气地球科学,2015,26(9):1629-1639.Chen Yilin,Qin Yong,Tian Hua,et al.Particle size effect of pore structure ofanthracite by mercury porosimetry[J].Natural Gas Geoscience,2015,26(9):1629-1639.
[20]陈振宏,贾承造,宋岩,等.高煤阶与低煤阶煤层气藏物性差异及其成因[J].石油学报,2008,29(2):179-184.Chen Zhenhong,Jia Chengzao,Song Yan,et al.Differences and origin of physical properties of low-rank and high-rank coal-bed methanes[J].Acta Petrolei Sinica,2008,29(2):179-184.