我国低透气性煤储层较多，煤层的孔隙结构直接决定了煤层瓦斯的渗流及运移过程，同时也是造成煤层内部瓦斯非线性渗流的主要原因，严重制约煤层气高效开发利用，因此低透气性煤孔隙结构及其分布对瓦斯 非线性渗流的影响规律需进一步研究。本文选取低透气性煤层煤作为实验煤样，通过实验及理论分析，研究了低透气性煤的孔隙结构特征及全孔径段孔隙结构复杂性，探究了实验煤样瓦斯渗流规律及非线性渗流特性，分析了煤样孔隙结构特征对非线性渗流的影响规律。主要结论如下：

通过核磁共振、压汞实验及低温氮吸附实验，获得低透气性煤样的孔隙特征参数及孔隙类型，发现实验煤样微、小孔发育，孔径3～8nm范围内孔隙含量最高，孔隙形态以墨水瓶形孔及楔形孔等半开口型孔为主，低温氮吸附法与压汞法在联合表征煤样孔径分布方面与核磁共振法具有等效性。

应用分形理论，分孔径段对实验煤样孔隙结构进行分形表征，建立孔隙连通率计算模型，分析煤样孔隙结构复杂性，发现煤样分形维数均在2.5以上，孔隙结构总体复杂程度较高，非均质性较强；煤样孔径小于100nm的微小孔结构较为复杂，孔径大于100nm的中大孔结构较为简单，均质性强；孔径小于10nm的孔隙，孔隙连通率较低，大于10nm的孔隙，孔隙连通率较高；煤样内部的渗流孔连通性好，吸附孔连通性较差。

利用自主研发的煤岩芯渗透率自动测试仪进行瓦斯渗流实验，测得不同影响因素对煤样渗透率的影响规律，得出围压、有效应力和温度与渗透率具有负相关关系；煤样渗透率与瓦斯压力呈二次函数关系变化趋势呈“V”字型，在瓦斯压力1MPa附近处出现拐点，煤样渗流规律呈明显的非线性特征。研究表明，启动压力梯度和滑脱效应的存在导致低透气性煤出现瓦斯非线性渗流现象。

实验煤样孔隙结构特征和瓦斯非线性渗流之间的关系显示煤样孔隙率、渗流孔占比、孔隙连通率与克氏渗透率呈正相关关系；迂曲度、吸附孔占比和分形维数与克氏渗透率呈负相关关系；孔隙率与滑脱因子、启动压力梯度呈负相关关系；迂曲度与滑脱因子和启动压力梯度呈正相关关系。渗流孔占比与滑脱因子和启动压力梯度呈负相关关系；吸附孔占比与滑脱因子和启动压力梯度呈正相关关系，微孔在总孔隙中的占比是控制煤样瓦斯渗流滑脱效应的主要因素；孔隙连通率与启动压力梯度和滑脱因子呈负相关关系。分形维数与滑脱因子、启动压力梯度呈正相关性。

最后，利用分形理论，分析分形维数与煤样渗透率的关系以及孔隙结构对渗透率的影响度，推导出低透气性煤样的分形维数及分形维数与渗透率的关系式。研究表明，吸附孔对渗透率的影响度较小，孔径大于100nm的渗流孔对渗透率影响较大，是煤体发生渗流的主要场所。

本文利用多种实验手段及方法探究了低透气性煤孔隙结构及其分布对瓦斯非线性渗流的影响规律，研究结果有助于加深对低透气性煤瓦斯渗流规律的认识，为煤层气的高效安全开发提供理论支撑。

There are many low permeability coal reservoirs in China. The pore structure of coal seam directly determines the seepage and migration process of coal seam gas, and it is also the main cause of gas nonlinear seepage in coal seam, which seriously restricts the efficient development and utilization of coalbed methane. Therefore, the influence of pore structure and distribution of low permeability coal on gas nonlinear seepage needs further research.  In this paper, the low permeability coal seam is selected as the experimental coal sample. Through experimental and theoretical analysis, the pore structure characteristics of low permeability coal and the complexity of pore structure in full aperture section are studied. The gas seepage law and nonlinear seepage characteristics of experimental coal samples are explored. The influence of pore structure characteristics of coal samples on nonlinear seepage is analyzed.  The main conclusions are as follows :

The pore characteristic parameters and pore types of low-permeability coal samples were obtained through NMR, mercury injection experiment and low-temperature nitrogen adsorption experiment. It was found that the micro-pores and small pores of the experimental coal samples were developed. The pore content was the highest in the range of pore size 3～8 nm. The pore morphology was dominated by semi-open pores such as ink bottle-shaped pores and wedge-shaped pores. The low-temperature nitrogen adsorption method and mercury injection method were equivalent to the NMR method in characterizing the pore size distribution of coal samples.

The fractal theory was used to characterize the pore structure of the experimental coal samples by dividing the pore size section, and the calculation model of pore connectivity was established to analyze the complexity of the pore structure of the coal samples. It was found that the fractal dimensions of the coal samples were all above 2.5, and the overall complexity of the pore structure was high and the heterogeneity was strong. The micro-pore structure of coal sample with pore size less than 100 nm is relatively complex, and the medium-large pore structure with pore size greater than 100 nm is relatively simple and has strong homogeneity. For pores with pore size less than 10 nm, the pore connectivity is low, and for pores with pore size greater than 10 nm, the pore connectivity is high ; The connectivity of seepage holes in coal samples is good, while that of adsorption holes is poor.

The gas seepage experiment is carried out by using the self-developed automatic permeability tester of coal core, and the influence law of different influencing factors on the permeability of coal samples is measured. It is concluded that the confining pressure, effective stress and temperature have a negative power function relationship with permeability. The relationship between coal sample permeability and gas pressure is quadratic function, and the change trend is ‘V’ type. The inflection point of gas pressure appears near 1 MPa, and the seepage law of coal sample shows obvious nonlinear characteristics. Research shows that the existence of starting pressure gradient and slippage effect leads to the non-linear seepage of gas in low permeability coal.

The relationship between the pore structure characteristics of the experimental coal samples and the nonlinear seepage of gas shows that the porosity of coal samples, the proportion of seepage pores, and the pore connectivity rate are positively correlated with the permeability. The tortuosity and adsorption pore ratio were negatively correlated with the permeability. porosity is negatively correlated with slippage factor and start-up pressure gradient ; The tortuosity is positively correlated with slippage factor and starting pressure gradient. The proportion of seepage holes is negatively correlated with slippage factor and starting pressure gradient ; The proportion of adsorption pores is positively correlated with slippage factor and starting pressure gradient. The proportion of micropores in total pores is the main factor to control the slippage effect of gas seepage in coal samples. Pore connectivity is negatively correlated with starting pressure gradient and slippage factor. The fractal dimension is negatively correlated with the permeability, and positively correlated with the slippage factor and the starting pressure gradient. Finally, the fractal theory is used to analyze the relationship between fractal dimension and permeability of coal samples and the influence of pore structure on permeability. The fractal dimension of low permeability coal samples and the relationship between fractal dimension and permeability are derived. The research shows that the adsorption hole has a small influence on the permeability, and the seepage hole with pore size greater than 100 nm has a great influence on the permeability, which is the main place for coal seepage.

In this paper, a variety of experimental methods and methods are used to explore the influence of pore structure and distribution of low permeability coal on gas nonlinear seepage. The results are helpful to deepen the understanding of gas seepage law of low permeability coal, and provide theoretical support for the efficient and safe development of coalbed methane.

[1]刘峰, 曹文君, 张建明, 等. 我国煤炭工业科技创新进展及“十四五”发展方向[J]. 煤炭学报, 2021,46(01):1-15.

[2]孙旭东, 张蕾欣, 张博. 碳中和背景下我国煤炭行业的发展与转型研究[J]. 中国矿业, 2021,30(02):1-6.

[3]张福祥, 郑新权, 李志斌, 等. 钻井优化系统在国内非常规油气资源开发中的实践[J]. 中国石油勘探, 2020,25(2):96-109.

[4]Mallick N, Prabu V. Energy analysis on Coalbed Methane (CBM) coupled power systems[J]. Journal of CO2 Utilization, 2017,19:16-27.

[5]Wen S, Zhou K, Lu Q. A discussion on CBM development strategies in China: A case study of PetroChina Coalbed Methane Co., Ltd.[J]. Natural Gas Industry B, 2019,6(6):610-618.

[6]Yun J, Xu F, Liu L, et al. New progress and future prospects of CBM exploration and development in China[J]. International Journal of Mining Science and Technology, 2012,22(3):363-369.

[7]侯风岗, 李玉魁. 我国煤层气井重复压裂综合技术探讨: 2014年中国地球科学联合学术年会——专题57：盆地动力学与非常规能源, 2014[C].

[8]肖晓春, 潘一山. 低渗煤储层气体滑脱效应试验研究[J]. 岩石力学与工程学报, 2008,27(a02):3509.

[9]史今雄, 曾联波, 谭青松, 等. 沁水盆地南部煤岩储层天然裂缝有效性及对煤层气开发的影响[J]. 石油与天然气地质, 2020,v.41(03):173-182.

[10]李滔, 李闽, 荆雪琪, 等. 孔隙尺度各向异性与孔隙分布非均质性对多孔介质渗透率的影响机理[J]. 石油勘探与开发, 2019,46(03):157-167.

[11]周斌, 许江, 彭守建, 等. 突出过程中煤层及巷道多物理场参数动态响应[J]. 煤炭学报, 2020,v.45;No.307(4):181-193.

[12]朱子斌王亮郑思文赵伟陈大鹏. 淮北煤田煤与瓦斯突出灾害差异性和控制因素研究[J]. 煤炭科学技术, 2020,v.48;No.551(10):80-88.

[13]张井, 韩宝平, 唐家祥, 等. 煤及煤层顶底板的孔隙结构特征[J]. 煤田地质与勘探, 1998,000(002):28.

[14]杨宇航, 杨青, 李剑, 等. 海拉尔盆地褐煤全孔径结构特征及影响因素[J]. 天然气地球科学, 2020,v.31;No.216(11):93-104.

[15]霍多特著 B. B., 宋士钊, 王佑安. 煤与瓦斯突出[M]. 1966.

[16]Walker P L, Verma S K, Rivera-Utrilla J, et al. Densities, porosities and surface areas of coal macerals as measured by their interaction with gases, vapours and liquids[J]. Fuel, 1988,67(12):1615-1623.

[17]张小东, 杜志刚, 李朋朋. 不同煤体结构的高阶煤储层物性特征及煤层气产出机理[J]. 中国科学:地球科学, 2017(1):76-85.

[18]侯锦秀, 张玉贵, 张进春. 构造煤原生结构煤微孔特征的多重统计对比及其差异成因机制[J]. 安全与环境学报, 2018.

[19]霍永忠, 张爱云. 煤层气储层的显微孔裂隙成因分类及其应用[J]. 煤田地质与勘探, 1998(06):29-33.

[20]桑树勋, 朱炎铭, 张时音, 等. 煤吸附气体的固气作用机理(Ⅰ)——煤孔隙结构与固气作用[J]. 天然气工业, 2005,25(1):13-15.

[21]赵兴龙, 汤达祯, 许浩, 等. 煤变质作用对煤储层孔隙系统发育的影响[J]. 煤炭学报, 2010(9):96-101.

[22]郝琦. 煤的显微孔隙形态特征及其成因探讨[J]. 煤炭学报, 1987(04):51-56.

[23]张慧. 煤孔隙的成因类型及其研究[J]. 煤炭学报, 2001,26(1):40-44.

[24]Niu Q, Pan J, Cao L, et al. The evolution and formation mechanisms of closed pores in coal[J]. Fuel, 2017,200:555-563.

[25]陈萍,唐修义. 低温氮吸附法与煤中微孔隙特征的研究[J]. 煤炭学报, 2001(05):552-556.

[26]Clarkson C R, Bustin R M. Variation in micropore capacity and size distribution with composition in bituminous coal of the Western Canadian Sedimentary Basin: Implications for coalbed methane potential[J]. 1996,75(13):1483-1498.

[27]孟巧荣, 赵阳升, 胡耀青, 等. 焦煤孔隙结构形态的实验研究[J]. 煤炭学报, 2011,36(03):487-490.

[28]姚晋宝, 郝春生, 杨昌永. 基于压汞法的成庄井田3号煤孔隙特征研究[J]. 能源与环保, 2019(7):134-139.

[29]秦雷. 液氮循环致裂煤体孔隙结构演化特征及增透机制研究[D]. 中国矿业大学, 2018.

[30]赵志根, 唐修义. 低温氮吸附法测试煤中微孔隙及其意义[J]. 煤田地质与勘探, 2001(05):28-30.

[31]刘高峰, 张子戌, 张小东, 等. 气肥煤与焦煤的孔隙分布规律及其吸附–解吸特征[J]. 岩石力学与工程学报, 2009,28(08):1587-1592.

[32]顾熠凡, 王兆丰, 戚灵灵. 基于压汞法的软、硬煤孔隙结构差异性研究[J]. 煤炭科学技术, 2016,44(04):64-67.

[33]Zhou S, Liu D, Cai Y, et al. Fractal characterization of pore–fracture in low-rank coals using a low-field NMR relaxation method[J]. Fuel, 2016,181:218-226.

[34]Li X, Kang Y, Haghighi M. Investigation of pore size distributions of coals with different structures by nuclear magnetic resonance (NMR) and mercury intrusion porosimetry (MIP)[J]. Measurement, 2018,116:122-128.

[35]Liu X, Song D, He X, et al. Nanopore structure of deep-burial coals explored by AFM[J]. Fuel, 2019,246:9-17.

[36]SUN Y, SUN Q, ZHAO Y, et al. Synchrotron radiation facility-based quantitative evaluation of pore structure heterogeneity and anisotropy in coal[J]. Petroleum Exploration and Development Online, 2019,46(6):1195-1205.

[37]Zhao Y, Sun Y, Liu S, et al. Pore structure characterization of coal by synchrotron radiation nano-CT[J]. Fuel, 2018,215:102-110.

[38]林海飞, 卜婧婷, 严敏, 等. 中低阶煤孔隙结构特征的氮吸附法和压汞法联合分析[J]. 西安科技大学学报, 2019,39(01):1-8.

[39]戚灵灵, 王兆丰, 杨宏民, 等. 基于低温氮吸附法和压汞法的煤样孔隙研究[J]. 煤炭科学技术, 2012,40(08):36-39.

[40]张召召, 潘结南, 李猛, 等. 基于压汞和低温氮吸附联合试验的不同变质程度煤全孔隙结构特征研究[J]. 煤矿安全, 2018,49(04):25-29.

[41]Qin L, Li S, Zhai C, et al. Joint analysis of pores in low, intermediate, and high rank coals using mercury intrusion, nitrogen adsorption, and nuclear magnetic resonance[J]. Powder Technology, 2020,362:615-627.

[42]Xie F, Li Z, Wang W, et al. In-situ SAXS study of pore structure during carbonization of non-caking coal briquettes[J]. Fuel, 2020,262:116547.

[43]Kwiecińska B, Pusz S, Valentine B J. Application of electron microscopy TEM and SEM for analysis of coals, organic-rich shales and carbonaceous matter[J]. International Journal of Coal Geology, 2019,211:103203.

[44]王超勇, 鲍园, 琚宜文. 利用FE-SEM、HIP、N_2吸附实验表征生物气化煤系有机岩储层微观孔隙结构演化[J]. 地球科学, 2018:1-14.

[45]Liu S Q, Sang S, Liu H, et al. Growth characteristics and genetic types of pores and fractures in a high-rank coal reservoir of the southern Qinshui basin[J]. Ore Geology Reviews, 2015,64:140-151.

[46]Weishauptová Z, Medek J, Ková L. Bond forms of methane in porous system of coal II[J]. fuel, 2004,83(13):1759-1764.

[47]Moore T A. Coalbed methane: A review[J]. 2012,101(none).

[48]吴财芳, 张晓阳. 煤层气井排采过程中渗透率动态变化研究进展[J]. 煤炭科学技术, 2016,44(06):7-13.

[49]杨延辉, 刘世奇, 桑树勋, 等. 基于三维空间表征的高阶煤连通孔隙发育特征[J]. 煤炭科学技术, 2016,44(10):70-76.

[50]Sun M, Zhang L, Hu Q, et al. Pore connectivity and water accessibility in Upper Permian transitional shales, southern China[J]. Marine and Petroleum Geology, 2019.

[51]范俊佳, 琚宜文, 侯泉林, 等. 不同变质变形煤储层孔隙特征与煤层气可采性[J]. 地学前缘, 2010,17(05):325-335.

[52]薛光武, 刘鸿福, 要惠芳, 等. 韩城地区构造煤类型与孔隙特征[J]. 煤炭学报, 2011,36(11):1845-1851.

[53]Liu S, Sang S, Wang X, et al. FIB-SEM and X-ray CT characterization of interconnected pores in high-rank coal formed from regional metamorphism[J]. Journal of Petroleum Science and Engineering, 2017,148:21-31.

[54]Hall P J, Antxustegi M, Ruiz W. Contrast-matching small-angle neutron scattering evidence for the absence of a connected pore system in Pittsburgh No. 8 coal[J]. Fuel, 1998,77(14):1663-1665.

[55]郭红玉, 罗源, 马俊强, 等. 不同煤阶煤的微生物增透效果和机理分析[J]. 煤炭学报, 2014,39(09):1886-1891.

[56]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(06):1127-1132.

[57]王小垚, 曾联波, 周三栋, 等. 低阶煤储层微观孔隙结构的分形模型评价[J]. 天然气地球科学, 2018,29(02):277-288.

[58]Gao F, Song Y, Li Z, et al. Quantitative characterization of pore connectivity using NMR and MIP: A case study of the Wangyinpu and Guanyintang shales in the Xiuwu basin, Southern China[J]. International Journal of Coal Geology, 2018,197:53-65.

[59]周世宁, 孙辑正. 煤层瓦斯流动理论及其应用[J]. 煤炭学报, 1965(01):26-39.

[60]谭学术, 袁静. 矿井煤层真实瓦斯渗流方程的研究[J]. 土木建筑与环境工程, 1986(1):109-115.

[61]孙培德. 煤层瓦斯动力学的基本模型[J]. 西安科技大学学报, 1989.

[62]孙培德. 瓦斯动力学模型的研究[J]. 煤田地质与勘探, 1993(1).

[63]孙培德. 煤层瓦斯流动方程补正[J]. 煤田地质与勘探, 1993(5).

[64]丁广骧. 煤层瓦斯实用动力学方程及其有限元解法[J]. 中国矿业大学学报, 1997(4):74-77.

[65]李云浩, 杨清岭, 杨鹏. 煤层瓦斯流动的数值模拟及在煤壁的应用[J]. 中国安全生产科学技术, 2007,3(2):74-77.

[66]罗新荣. 煤层瓦斯运移物理与数值模拟分析[J]. 煤炭学报, 1992,17(2):49-56.

[67]骆祖江, 杨锡禄, 赵俊峰, 等. 煤层气井数值模拟研究[J]. 中国矿业大学学报, 2000,29(3):306-309.

[68]彭英明, 邵先杰, 李锋, 等. 煤层气达西、非达西渗流理论和扩散理论的研究进展综述[J]. 煤炭工程, 2019,51(06):28-33.

[69]汪周华, 钟兵, 伊向艺, 等. 低渗气藏考虑非线性渗流特征的稳态产能方程[J]. 天然气工业, 2008(08):81-83.

[70]宋洪庆, 朱维耀, 王一兵, 等. 煤层气低速非达西渗流解析模型及分析[J]. 中国矿业大学学报, 2013,42(01):93-99.

[71]陈超凡, 王睿, 薛东杰, 等. 低渗煤样CH_4非线性压力分布与渗透率演化[J]. 煤矿安全, 2016,47(09):169-172.

[72]李波, 魏建平, 王凯, 等. 煤层瓦斯渗流非线性运动规律实验研究[J]. 岩石力学与工程学报, 2014,33(S1):3219-3224.

[73]Huang G, Song H, Cao Y, et al. Numerical investigation of low-velocity non-Darcy flow of gas and water in coal seams[J]. Journal of Natural Gas Science and Engineering, 2016,34:124-138.

[74]胡耀青, 赵阳升, 杨栋, 等. 煤体的渗透性与裂隙分维的关系[J]. 岩石力学与工程学报, 2002(10):1452-1456.

[75]张天军, 尚宏波, 李树刚, 等. 三轴应力下不同粒径破碎砂岩渗透特性试验[J]. 岩土力学, 2018,39(07):2361-2370.

[76]王刚, 杨鑫祥, 张孝强, 等. 基于CT三维重建的煤层气非达西渗流数值模拟[J]. 煤炭学报, 2016,41(04):931-940.

[77]Chen Y, Lian H, Liang W, et al. The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses[J]. International Journal of Rock Mechanics and Mining Sciences, 2019,113:59-71.

[78]汪周华, 钟兵, 伊向艺, 等. 低渗气藏考虑非线性渗流特征的稳态产能方程[J]. 天然气工业, 2008(08):81-83.

[79]杨其銮, 王佑安. 瓦斯球向流动的数学模拟[J]. 中国矿业学院学报, 1988(03):58-64.

[80]韩颖, 张飞燕. 煤屑瓦斯扩散规律研究[J]. 煤炭学报, 2013,38(9):1589-1596.

[81]聂百胜, 何学秋, 王恩元. 瓦斯气体在煤层中的扩散机理及模式[J]. 中国安全科学学报, 2000(6):24-28.

[82]闫宝珍, 王延斌, 倪小明, 等. 地层条件下基于纳米级孔隙的煤层气扩散特征[J]. 煤炭学报, 2008,33(6):657-660.

[83]陈向军, 程远平, 何涛, 等. 注水对煤的瓦斯扩散特性影响[J]. 采矿与安全工程学报, 2013,30(3):443-448.

[84]周市伟, 张玉贵, 雷东记. 煤粒瓦斯初始扩散系数及其影响因素[J]. 煤矿安全, 2016,47(10):1-4.

[85]安丰华, 贾宏福, 刘军. 基于煤孔隙构成的瓦斯扩散模型研究[J]. 岩石力学与工程学报:1-10.

[86]Zheng S, Yao Y, Liu D, et al. Characterizations of full-scale pore size distribution, porosity and permeability of coals: A novel methodology by nuclear magnetic resonance and fractal analysis theory[J]. International Journal of Coal Geology, 2018,196:148-158.

[87]刘朋志, 郭和坤, 沈瑞, 等. 基于气体吸附法和压汞法对页岩孔隙结构的研究[J]. 力学与实践, 2018,40(05):514-519.

[88]秦雷, 王平, 林海飞, 等. 基于氮气吸附和压汞法液氮冻结煤体孔隙结构精细化表征研究[J]. 西安科技大学学报, 2020,40(06):945-952.

[89]Avnir D, Jaroniec M. An isotherm equation for adsorption on fractal surfaces of heterogeneous porous materials[J]. Langmuir, 1989,5(6):1431-1433.

[90]Xie H, Wang J, Qan P. Fractal characters of micropore evolution in marbles[J]. Physics Letters A, 1996,218(3-6):275-280.

[91]童宏树, 胡宝林. 鄂尔多斯盆地煤储层低温氮吸附孔隙分形特征研究[J]. 煤炭技术, 2004,23(7):1-3.

[92]Friesen W I, Ogunsola O I. Mercury porosimetry of upgraded western Canadian coals[J]. Fuel, 1995,74(4).

[93]张松航, 唐书恒, 汤达祯, 等. 鄂尔多斯盆地东缘煤储层渗流孔隙分形特征[J]. 中国矿业大学学报, 2009,38(05):713-718.

[94]Dullien F A L. Porous media : fluid transport and pore structure[M]. Academic Press, 2013.

[95]彭安兰, 蒋明煊. 用毛管压力资料计算迂曲度的方法探讨[J]. 石油勘探与开发, 1986(01):59-63.

[96]Koponen A, Kataja M, Timonen J. Tortuous flow in porous media[J]. Physical Review E, 1996,54(1):406-410.

[97]A B Y, B J L, A Z L, et al. Permeabilities of unsaturated fractal porous media[J]. International Journal of Multiphase Flow, 2003,29(10):1625-1642.

[98]李波. 受载含瓦斯煤渗流特性及其应用研究[D]. 中国矿业大学（北京）, 2013.

[99]周建辛. 含瓦斯煤固-流-热耦合数学模型及渗透特性研究[D]. 太原理工大学, 2019.

[100]李俊乾, 刘大锰, 姚艳斌, 等. 气体滑脱及有效应力对煤岩气相渗透率的控制作用[J]. 天然气地球科学, 2013,24(05):1074-1078.

[101]程远平, 胡彪. 微孔填充—煤中甲烷的主要赋存形式[J]. 煤炭学报, 2020:1-14.

[102]Ouyang Z, Liu D, Cai Y, et al. Fractal Analysis on Heterogeneity of Pore-Fractures in Middle-High Rank Coals with NMR[J]. Energy & Fuels, 2016,30(JUL.SPEC.):5449-5458.

[103]徐欣, 徐书奇, 邢悦明, 等. 煤岩孔隙结构分形特征表征方法研究[J]. 煤矿安全, 2018,49(03):148-150.

[104]Yu B, Cheng P. A fractal permeability model for bi-dispersed porous media[J]. International Journal of Heat & Mass Transfer, 2002,45(14):2983-2993.

[105]Bo-Ming Y U, Jian-Hua L I. A Geometry Model for Tortuosity of Flow Path in Porous Media[J]. 中国物理快报:英文版, 2004,21(008):1569-1571.

[106]郁伯铭. 多孔介质输运性质的分形分析研究进展[J]. 力学进展, 2003(03):333-346.

[107]Wu J, Yu B, Yun M. A fractal resistance model for flow through porous media[J]. International Journal of Heat & Mass Transfer, 2008,71(3):331-343.