ZHANG Xiao-dong，ZHANG Shuo，YANG Yan-lei，ZHANG Peng，WEI Gao-yang . Numerical Simulation of Fracture Extending in Coal Seam under Hydraulic Fracturing Engineering Based on Fractal Theory[J]. Natural Gas Geoscience, 2015 , 26(10) : 1992 -1998 . DOI: 10.11764/j.issn.1672-1926.2015.10.1992

[1]Jeffrey R G,Vlahovic W,Doyle R P,et al.Propped Fracture Geometry of Three Hydraulic Fractures in Sydney Basin Coal[HJ2.2mm]Seams[R].SPE Asia Pacific Oil and Gas Conference and Exhibition,12-14 October,Perth,Australia.SPE 50061,1998.
[2]Tao Shu,Tang Dazhen,Xu Hao,et al.Analysis on influence factors of coalbed methane wells productivity and  development proposals in southern Qinshui Basin[J].Journal of China Coal Society,2011,36(2):194-198.[陶树,汤达祯,许浩,等.沁南煤层气井产能影响因素分析及开发建议[J].煤炭学报,2011,36(2):194-198.]
[3]Zhang Xiaodong,Zhang Peng,Liu Hao,et al.Fracture extended model under hydraulic fracturing engineering for high rank coal reservoirs[J].Journal of China University of Mining & Technology,2013,42(4):573-579.[张小东,张鹏,刘浩,等.高煤级储层水力压裂裂缝扩展模型研究[J].中国矿业大学学报,2013,42(4):573-579.]
[4]Xu Lulu,Cui Jinbang,Huang Saipeng,et al.Analysis and application of fracture propagated model by hydraulic fracturing in coal-bed methane reservoir[J].Journal of China Coal Society,2014,39(10):2068-2074.[许露露,崔金榜,黄赛鹏,等.煤层气储层水力压裂裂缝扩展模型分析及应用[J].煤炭学报,2014,39(10):2068-2074.]
[5]Wu Xiaodong,Xi Changfeng,Wang Guoqiang.The mathematic model research of complicated fractures system in coalbed methane wells[J].Natural Gas Industry,2006,26(3):124-126.[吴晓东,席长丰,王国强.煤层气井复杂水力压裂裂缝模型研究[J].天然气工业,2006,26(3):124-126.]
[6]Li Anqi,Jiang Hai,Chen Caihong.Hydraulic fracturing practice and coalbed fracture model selecting for coalbed gas wells in China[J].Natural Gas Industry,2004,24(5):91-93.[李安启,姜海,陈彩虹.我国煤层气井水力压裂的实践及煤层裂缝模型选择分析[J].天然气工业,2004,24(5):91-93.]
[7]Xie Xiaoyong,Guo Xinjiang,Jiang Zujun,et al.Study on formation damage and fractal feature of pore structure[J].Natural Gas Geoscience,2011,22(6):1128-1132.[谢晓永,郭新江,蒋祖军,等.储层的孔隙结构分形特征与损害研究[J].天然气地球科学,2011,22(6):1128-1132.]
[8]Thompson A H,Katz A J,Krohn C E.The microgeometry and transport properties of sedimentary rock[J].Advances in Physics,1987,36(5):625-649.
[9]Cai Jianchao,Yu Boming.Prediction of maximum pore size of porous media based on fractal geometry[J].Fractals,2010,18(4):417-423.
[10]He Wei,Zhong Fuxun,He Chengzu,et al.Fractal texture research on the pores in reservoir rocks and its application[J].Natural Gas Industry,2000,20(2):67-70.[贺伟,钟孚勋,贺承祖,等.储层岩石孔隙的分形结构研究和应用[J].天然气工业,2000,20(2):67-70.]
[11]Zheng Bin,Li Juhua.A new fractal permeability model for porous media based on Kozeny-Carman equation[J].Natural Gas Geoscience,2015,26(1):193-198.[郑斌,李菊花.基于Kozeny-Carman方程的渗透率分形模型[J].天然气地球科学,2015,26(1):193-198.]
[12]Wang Wenfeng,Xu Lei,Fu Xuehai.Correlation on preservation and movement features between coal bed gas and ground water[J].Coal Geology of China,2002,14(2):26-27.[王文峰,徐磊,傅雪海.应用分形理论研究煤孔隙结构[J].中国煤田地质,2002,14(2):26-27.]
[13]Hu Zunguo,Su Jun,Li Zidan.The fractal chayacteys of porosity in porous media and its fractal dimension calculation[J].Hydrogeology & Engineering Geology,1992,19(1):10-11.[胡尊国,苏军,李子丹.多孔介质孔隙的分形特征与分维数计算[J].水文地质工程地质,1992,19(1):10-11.]
[14]Li Liuren,Yuan Shiyi,Hu Yongle.A new model for describing the relationship between the permeability and the porosity of fractal porousmedia[J].Journal of Xi′an Shiyou University,2010,25(3):49-51,74.[李留仁,袁士义,胡永乐.分形多孔介质渗透率与孔隙度理论关系模型[J].西安石油大学学报,2010,25(3):49-51,74.]
[15]Zhou Hongwei,Xie Heping.Estimation of permeability of porous media by using renormalization group[J].Journal of China University of Mining & Technology,2000,29(3):244-248.[周宏伟,谢和平.孔隙介质渗透率的重正化群预计[J].中国矿业大学学报,2000,29(3):244-248.]
[16]Wu Fan,Sun Lijuan,He Jiang.The research and application of permeability,porosity and net overburden pressure laws[J].Journal of Southwest Petroleum Institute,1996,21(4):23-26.[吴凡,孙黎娟,何江.孔隙度、渗透率与净覆压的规律研究和应用[J].西南石油学院学报,1996,21(4):23-26.]
[17]Gidley J L,Nplte K G.New Progress in Hydraulic Fracture Technique[M].Jiang Tian translation.Beijing:Petroleum Industry Press,1995.[Gidley J L,Nplte K G.水力压裂技术新进展[M].蒋阗译.北京:石油工业出版社,1995.]
[18][JP2]Li Ting,Yang Qi,Chen Wangang,et al.Evaluation on influence factors of comprehensive filtration lost coefficient in coal bed methane fracturing[J].Coal Science and Technology,2013,41(3):81-83.[李亭,杨琦,陈万钢,等.煤层气压裂综合滤失系数的影响因素评价[J].煤炭科学技术,2013,41(3):81-83.]
[19]Liu Hong,Fu Zhaorong,Huang Zhen,et al.Study on hydraulic fracturing mechanics[J].Drilling & Production Technology,2006,5(36):36-37.[刘洪,符兆荣,黄桢,等.水力压裂力学机理新探索[J].钻采工艺,2006,5(36):36-37.]
[20]Xie H P,Sanderson D J.Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities[J].International Journal of Fracture,1995,74(1):29-42.
[21]Xie Heping,Gao Feng,Zhou Hongwei,et al.Fractal fracture and fragmentation in rocks[J].Journal of Disaster Prevention and Mitigation Engineering,2003,23(4):3-4.[谢和平,高峰,周宏伟,等.岩石断裂和破碎的分形研究[J].防灾减灾工程学报,2003,23(4):3-4.]
[22][JP2]Zhang Peng.The Numerical Simulation of Hydraulical Fracture of Coal Reservoirs in Southern Qinshui Basin[D].Jiaozuo:Henan Polytechnic University,2014.[张鹏.沁水盆地南部煤储层水力压裂裂缝模拟研究[D].焦作:河南理工大学,2014.]
[23]England A H,Green A E.Some two dimensional punch and crack problems in classical elasticity[J].Mathematical Proceeding of the Cambridge Philosophical Society,1963,59:489-500.
[24]Luo Taotao.Coal Rock Characteristics and Fracturing Methods for Qinshui Reservoir[D].Chengdu:Chengdu University of Technology,2010.[罗陶涛.沁水盆地煤岩储层特征及压裂增产措施研究[D].成都:成都理工大学,2010.]