基于分形理论的储层特征及压裂造缝机理研究
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摘要
自上个世纪四十年代末期,水力压裂第一次成功应用以来,就广泛应用于低渗透储层的改造中,并成为一项有效的低渗透油田增产增注措施。为了提高压裂施工的成功率和进一步改善压裂效果,学者们逐渐开展了以岩石断裂力学为基础的水力压裂断裂机理研究,逐渐形成了压裂裂缝沿垂直于最小主应力的单一平面延伸和扩展的结论。该结论成为水力压裂裂缝形态分析的根本,并为水力压裂数值模拟奠定了理论基础。
随着油田开发的深入,需要改造的储层逐渐复杂化,学者们也渐渐认识到用单一平面裂缝无法在理论上圆满解释一些复杂情况下的压裂施工。大量现场实践表明,压裂储层存在多条同时延伸的裂缝,且裂缝形状也未必是平面的。这种情况在裂缝性储层表现的尤为明显。针对这一问题,本文将以研究储层孔隙介质特征为出发点,以分形理论为研究手段,在室内实验及现场施工资料的基础上,对不同储层下水力压裂的造缝机理展开研究,深入分析水力压裂的裂缝形态及其影响因素。
在理论研究方面,首先应用分形方法分析储层存储介质的分形特征,并由孔隙介质特征的分形描述成功建立孔隙介质有效应力分形模型,为重新分析井壁围岩应力状态奠定基础,然后根据新的井壁围岩应力状态方程分析孔隙性储层和裂缝性储层的水力压裂造缝机理。
在实验分析方面,首先通过扫描电镜和压汞法分析和测定砂岩孔隙结构的分形维数和对裂缝性储层取心测定了裂缝结构的分形维数,为用分形方法分析储层存储介质的分形特征奠定数据基础,然后根据水力压裂破裂过程模拟实验来分析孔隙性储层和裂缝性储层中水力压裂的造缝机理,以作为理论研究的实验基础。
论文的主要研究内容及研究成果如下：
1.应用分形几何方法分析了储层孔隙介质的微观特征。根据孔隙结构特征的分形模型建立了基于分形特征参数的孔隙介质有效应力模型,并给出有效应力模型的简化式,使之能够适用不同现场情况。该模型定量地描述了孔隙介质结构特征在骨架颗粒和孔隙流体支撑总应力时起到的协调关系,且将孔隙介质的微观参数和宏观统计参数联系在一起。
2.基于孔隙介质有效应力的分形模型重新推导了井壁围岩应力状态方程,并进而推导了裸眼完井、射孔完井情况下含有分形参数的压裂起裂判别准则。新模型中引入了描述孔隙介质结构特征的分形参数,为应用分形方法分析储层水力压裂的造缝机理奠定了基础。
3.应用分形几何方法分析了储层裂缝介质的分布特征。建立VB.Net & OpenGL三维可视化平台,根据裂缝介质系统的分形分布规律通过确定性离散建模方法,模拟了布达特储层裂缝介质系统三维分布。模拟结果证明,分形方法能很好地描述单一裂缝的随机性和整体裂缝系统的复杂性,是裂缝性储层建模的有效方法。
4.应用分形几何方法分析了岩石断裂面的延伸特性。使用分形方法描述裂纹的曲折扩展形态,将分形特征量引入到岩石断裂韧性中,由此建立了基于分形特征参数的Ⅰ型、Ⅱ型和混合型岩石断裂韧性的计算方法。
5.应用了模拟水力压裂过程的装置,进行孔隙性储层和裂缝性储层水力压裂模拟实验,根据实验结果分析影响水力压裂造缝机理的因素。实验结果表明,储层中的天然裂缝对水力压裂裂缝的起裂压力和裂缝延伸形态有重要影响。天然裂缝的存在降低了岩石的破裂压力,使压裂裂缝的形态变得更加复杂。
6.应用分形方法分析天然裂缝的分布规律,确定孔隙度和渗透率随分形参数的变化关系。由此,根据二维的PKN、KGD模型分析了分形参数对压裂裂缝缝长、缝宽的影响。
水力压裂造缝过程是一个岩石断裂过程。多方面的影响因素使这个断裂过程变得复杂。本文的研究明确了不同因素对岩石断裂过程的影响情况,尤其是天然裂缝存在的情况下各影响因素之间的转变。通过本文的研究加深了对水力压裂造缝机理的认识,为进一步分析水力压裂造缝机理和指导现场压裂施工提供了理论指导和技术支持。
Hydraulic fracturing has been widely used in the reconstruction of low-permeability reservoirs, and becomes an effective method of stimulation for low-permeability oilfield since its first successful application in the late 1940's. In order to increase the success ratio of fracturing operation and further improve the efficiency of hydraulic fracturing, researches on fracture mechanism which based on rock fracture mechanics have been done by scholars. We can draw a conclusion that induced fracture's direction of extending and expanding which is perpendicular to single plane cracks of minimum principal stress. This conclusion has become the basis of shapes analysis and numerical simulation of hydraulic fracturing.
Along with further development of oilfield, reservoirs needing to reform become more complex, and scholars have gradually recognized that single-plane cracks theorem can not give a perfect explanation on fracturing operation under complex situations in theory. The considerable field practices show that fractured reservoir has multi-fracture extending at the same time and the fracture shape may not be flat. And this situation is especially obvious in fractured reservoir. This paper, by means of fractal theory study, analyzes fracture shape of hydraulic fracturing and its influential factors via the study on the fracture initiation mechanism under different reservoirs by laboratory experiments and field data.
To ensure dissertation, this study use the approach of combining theoretical research with experimental analysis. In the aspect of theory, first, analyzing fractal features of reservoir media with the method of fractal theory and setting up the effective stress fractal model.Then, analyzing fracture initiation mechanism of fractured and porosity reservoirs according to new stress condition equations of rock around borehole.
In the aspect of experimental analysis, firstly, fractal dimensions of pore texture are determined by means of scanning electron microscope (SEM), mercury porosimetry method (MPM) and fractal dimensions of fractured texture are measured by coring.That provides data basis of fractal features for analysis of reservoir storage medium in fractal method. Then, it analyze the fracture initiation mechanism of fractured and porosity reservoirs on the basis of large dimension hydraulic fracturing simulation experiments as the experimental base on theoretical investigation.
The main contents and outcomes are as following:
1. Analyzing the microscopic feature of porous media using fractal geometric methods. To meet the filed requirement, effective stress fractal model is built according to fractal model of pore structure characteristics and simplified effective stress model is introduced. Coordinating connections between pore fluid and skeletal grains of pore structure on support total stress are quantitatively described by this model as well as the micro-parameters of porous medium are linked with the macro-parameters.
2.Fractal model based on effective stress of porous medium derives new stress condition equation of rock around borehole and gets fracturing discrimination criteria with fractal parameters in the condition of casingless completion and perforation completion on further derivation.New model introduces fractal parameters describing the structure characteristics of porous medium.It is the basis of analysing fracture initiation mechanism of reservoir by use of fractal model.
3. Analyzing the structural feature of porous media by use of fractal geometric methods. Establishing 3-D visualization platform such as VB.Net & OpenGL.3-D distribution of Budate formation's fracture system is simulated on the base of distribution rules of fracture medium by use of deterministic scattered modeling approach. In terms of simulation results, fractal theory can reflect randomness of single fracture and complexity of fracture system and it is an effective modeling method.
4. Analyzing fracture criterion (rock fracture toughness) according to fractal geometry model. By using fractal method, shape and propagation direction of fracture are given. The fractal character is introduced into the fracture toughness, as a result, the fracture toughness values of type-Ⅰ, type-Ⅱand mixed rocks are obtained.
5. Using large dimension hydraulic fracturing simulant installation, the study analyze factors of fracture initiation mechanism according to the results of hydraulic fracturing simulation experiment. Experiments show that natural fracture has a significant influence on initiation pressure and fracture propagation shapes. The existence of natural fracture reduces the fracture pressure of rock, and makes the fracture geometry more complex.
6. Analyzing the distribution rules of natural fracture by use of fractal methods, and ascertaining the relationship between porosity fractal parameters and permeability fractal parameters.Thus, Analyzing fractal parameters'influence on fracture length and fracture width according to PKN and KGD model which are 2-D.
Fracture creation of hydraulic fracturing is a rock fracture process.Several different factors make the process more complex. This dissertation briefly concerns the effects of various factors on rock fracture, especially when natural fractures exist. This research deepened our understanding of fracture initiation mechanism and can be used for further research as well as direction of field fracturing practice in theory and technology.
随着油田开发的深入,需要改造的储层逐渐复杂化,学者们也渐渐认识到用单一平面裂缝无法在理论上圆满解释一些复杂情况下的压裂施工。大量现场实践表明,压裂储层存在多条同时延伸的裂缝,且裂缝形状也未必是平面的。这种情况在裂缝性储层表现的尤为明显。针对这一问题,本文将以研究储层孔隙介质特征为出发点,以分形理论为研究手段,在室内实验及现场施工资料的基础上,对不同储层下水力压裂的造缝机理展开研究,深入分析水力压裂的裂缝形态及其影响因素。
在理论研究方面,首先应用分形方法分析储层存储介质的分形特征,并由孔隙介质特征的分形描述成功建立孔隙介质有效应力分形模型,为重新分析井壁围岩应力状态奠定基础,然后根据新的井壁围岩应力状态方程分析孔隙性储层和裂缝性储层的水力压裂造缝机理。
在实验分析方面,首先通过扫描电镜和压汞法分析和测定砂岩孔隙结构的分形维数和对裂缝性储层取心测定了裂缝结构的分形维数,为用分形方法分析储层存储介质的分形特征奠定数据基础,然后根据水力压裂破裂过程模拟实验来分析孔隙性储层和裂缝性储层中水力压裂的造缝机理,以作为理论研究的实验基础。
论文的主要研究内容及研究成果如下：
1.应用分形几何方法分析了储层孔隙介质的微观特征。根据孔隙结构特征的分形模型建立了基于分形特征参数的孔隙介质有效应力模型,并给出有效应力模型的简化式,使之能够适用不同现场情况。该模型定量地描述了孔隙介质结构特征在骨架颗粒和孔隙流体支撑总应力时起到的协调关系,且将孔隙介质的微观参数和宏观统计参数联系在一起。
2.基于孔隙介质有效应力的分形模型重新推导了井壁围岩应力状态方程,并进而推导了裸眼完井、射孔完井情况下含有分形参数的压裂起裂判别准则。新模型中引入了描述孔隙介质结构特征的分形参数,为应用分形方法分析储层水力压裂的造缝机理奠定了基础。
3.应用分形几何方法分析了储层裂缝介质的分布特征。建立VB.Net & OpenGL三维可视化平台,根据裂缝介质系统的分形分布规律通过确定性离散建模方法,模拟了布达特储层裂缝介质系统三维分布。模拟结果证明,分形方法能很好地描述单一裂缝的随机性和整体裂缝系统的复杂性,是裂缝性储层建模的有效方法。
4.应用分形几何方法分析了岩石断裂面的延伸特性。使用分形方法描述裂纹的曲折扩展形态,将分形特征量引入到岩石断裂韧性中,由此建立了基于分形特征参数的Ⅰ型、Ⅱ型和混合型岩石断裂韧性的计算方法。
5.应用了模拟水力压裂过程的装置,进行孔隙性储层和裂缝性储层水力压裂模拟实验,根据实验结果分析影响水力压裂造缝机理的因素。实验结果表明,储层中的天然裂缝对水力压裂裂缝的起裂压力和裂缝延伸形态有重要影响。天然裂缝的存在降低了岩石的破裂压力,使压裂裂缝的形态变得更加复杂。
6.应用分形方法分析天然裂缝的分布规律,确定孔隙度和渗透率随分形参数的变化关系。由此,根据二维的PKN、KGD模型分析了分形参数对压裂裂缝缝长、缝宽的影响。
水力压裂造缝过程是一个岩石断裂过程。多方面的影响因素使这个断裂过程变得复杂。本文的研究明确了不同因素对岩石断裂过程的影响情况,尤其是天然裂缝存在的情况下各影响因素之间的转变。通过本文的研究加深了对水力压裂造缝机理的认识,为进一步分析水力压裂造缝机理和指导现场压裂施工提供了理论指导和技术支持。
Hydraulic fracturing has been widely used in the reconstruction of low-permeability reservoirs, and becomes an effective method of stimulation for low-permeability oilfield since its first successful application in the late 1940's. In order to increase the success ratio of fracturing operation and further improve the efficiency of hydraulic fracturing, researches on fracture mechanism which based on rock fracture mechanics have been done by scholars. We can draw a conclusion that induced fracture's direction of extending and expanding which is perpendicular to single plane cracks of minimum principal stress. This conclusion has become the basis of shapes analysis and numerical simulation of hydraulic fracturing.
Along with further development of oilfield, reservoirs needing to reform become more complex, and scholars have gradually recognized that single-plane cracks theorem can not give a perfect explanation on fracturing operation under complex situations in theory. The considerable field practices show that fractured reservoir has multi-fracture extending at the same time and the fracture shape may not be flat. And this situation is especially obvious in fractured reservoir. This paper, by means of fractal theory study, analyzes fracture shape of hydraulic fracturing and its influential factors via the study on the fracture initiation mechanism under different reservoirs by laboratory experiments and field data.
To ensure dissertation, this study use the approach of combining theoretical research with experimental analysis. In the aspect of theory, first, analyzing fractal features of reservoir media with the method of fractal theory and setting up the effective stress fractal model.Then, analyzing fracture initiation mechanism of fractured and porosity reservoirs according to new stress condition equations of rock around borehole.
In the aspect of experimental analysis, firstly, fractal dimensions of pore texture are determined by means of scanning electron microscope (SEM), mercury porosimetry method (MPM) and fractal dimensions of fractured texture are measured by coring.That provides data basis of fractal features for analysis of reservoir storage medium in fractal method. Then, it analyze the fracture initiation mechanism of fractured and porosity reservoirs on the basis of large dimension hydraulic fracturing simulation experiments as the experimental base on theoretical investigation.
The main contents and outcomes are as following:
1. Analyzing the microscopic feature of porous media using fractal geometric methods. To meet the filed requirement, effective stress fractal model is built according to fractal model of pore structure characteristics and simplified effective stress model is introduced. Coordinating connections between pore fluid and skeletal grains of pore structure on support total stress are quantitatively described by this model as well as the micro-parameters of porous medium are linked with the macro-parameters.
2.Fractal model based on effective stress of porous medium derives new stress condition equation of rock around borehole and gets fracturing discrimination criteria with fractal parameters in the condition of casingless completion and perforation completion on further derivation.New model introduces fractal parameters describing the structure characteristics of porous medium.It is the basis of analysing fracture initiation mechanism of reservoir by use of fractal model.
3. Analyzing the structural feature of porous media by use of fractal geometric methods. Establishing 3-D visualization platform such as VB.Net & OpenGL.3-D distribution of Budate formation's fracture system is simulated on the base of distribution rules of fracture medium by use of deterministic scattered modeling approach. In terms of simulation results, fractal theory can reflect randomness of single fracture and complexity of fracture system and it is an effective modeling method.
4. Analyzing fracture criterion (rock fracture toughness) according to fractal geometry model. By using fractal method, shape and propagation direction of fracture are given. The fractal character is introduced into the fracture toughness, as a result, the fracture toughness values of type-Ⅰ, type-Ⅱand mixed rocks are obtained.
5. Using large dimension hydraulic fracturing simulant installation, the study analyze factors of fracture initiation mechanism according to the results of hydraulic fracturing simulation experiment. Experiments show that natural fracture has a significant influence on initiation pressure and fracture propagation shapes. The existence of natural fracture reduces the fracture pressure of rock, and makes the fracture geometry more complex.
6. Analyzing the distribution rules of natural fracture by use of fractal methods, and ascertaining the relationship between porosity fractal parameters and permeability fractal parameters.Thus, Analyzing fractal parameters'influence on fracture length and fracture width according to PKN and KGD model which are 2-D.
Fracture creation of hydraulic fracturing is a rock fracture process.Several different factors make the process more complex. This dissertation briefly concerns the effects of various factors on rock fracture, especially when natural fractures exist. This research deepened our understanding of fracture initiation mechanism and can be used for further research as well as direction of field fracturing practice in theory and technology.
引文
[1]吉德利J L.水力压裂技术新发展[M].第一版.北京：石油工业出版社,1995.
[2]王鸿勋,张士诚.水力压裂设计数值计算方法[M].北京：石油工业出版社,1998.
[3]埃克诺米德斯M J,诺尔特K.G等著,张保平等译.油藏增产措施(第三版)[M].北京：石油工业出版社,2002.
[4]谢和平.分形—岩石力学导论[M].北京：科学出版社,1997.
[5]蔡美峰.岩石力学与工程[M].北京：科学出版社,2002.
[6]Mandelbrot B B. Les Objects Fractal:from hasard et dimension, Paris, Flammarion,1975.
[7]Costin I S. A microcrack model for the deformation and failure of brittle rock[J].Geophys, Res.1983,88:9485-9492.
[8]Botsis J, Kunin B. On self-similarity of crack layer[J]. Int. J. Fracturing, 1987,35,51-56.
[9]谢和平.分形几何及其在岩石力学中的应用[J].岩土工程学报,1992,14(1)：1424.
[10]谢和平,陈至达.分形几何与岩石断裂[J].力学学报,1988,20(3),264-275.
[11]Mandelbrot B B, et al. fractal character of fracturing surfaces of metals[J].Nature,1984,308:721-723.
[12]Mandelbrot B B. How long is the coast of Britaina-statistical self-similarity and fractional dimension,Science,1967,156(3775):636-638.
[13]Mandelbrot B B. The Fractal Geometry of Nature, New York, W. H. Freman,1982.
[14]曼德尔布洛特B.分形—形、机遇与维数[M].世界图书出版公司,1999.
[15]董连科.分形理论及应用[M].辽宁科学技术出版社,1991.
[16]Xie Heping. Fractals in Rock Mechanics[M]. Rotterdam:A. A. Balkema Publishers,1993.
[17]Rieu M, Sposito G. Fractal fragmentation:soil porosity and soil water properties[J].Soil Sci Sco Am J,1991,55:1231-1238.
[18]Wong Po-zen. The statistical physics of sedimentary rock[J].Physics Today 4,1988,24-32.
[19]Thompson A H. Fractal in rock physics [J]. Annual Review of Earth and Planetary Sciences.1991,19:237-262.
[20]Thompson A H, et al.The micro geometry and transport properties of sedimentary rocks, Advance[J].Physics,1987,36(5),625-694.
[21]Garrison J R, Pearn W C, Von Rosenberg D U. The Fraetal Nature of Geologieal Data Sets:Power Law Proeesses Every where[J]. SPE22842,1991.
[22]林鸿溢,李映雪.分形论—奇异性探索[M].北京理工大学出版社,1992.
[23]Krohn C E, Thompson A H. Fractal sandstone pores:Automated measurements using scanning-electron-microscope images[J].1986, Phys. Rev. B33, pp6366-6374.
[24]李克文,沈平平,等.砂岩分形结构研究[M].中国科技大学出版社,1993.
[25]Orford J.O, Whalley. W.B.The use of the fractal dimension to quantify the morphology of irregular-shaped particles. Ssdimentology[J].1988,30, 655-668.
[26]Mandelbrot B. Fractal-a geometry of nature[J]. New Scientists,1990, 1127(1734):38-43.
[27]Katz A J, Thompson A H. Fractal sandstone pores:implications for conductivity and pore formation[J]. Phys. Rev.Lett,1985,54(12):1325-1328
[28]Krohn C E. Sandstonefractal and Euclidean pore volume distributions[J]. Geophys.Res,1988,93(B4),3286-3296.
[29]Pfeifer P, Avnir D. Chemistry in noninteger dimensions between two and three Ⅰ:fractal theory of heterogeneous surfaces[J]. Chem. phys,1983,79,3558-3565.
[30]Avnir D. Chemistry in noninte.gerdimensions between two and threeⅡ:fractal surfaces of adsorbents[J]. Chem. phys,1983,79,3566-3571.
[31]Wong P Z, Howard J, Lin J S. Surface roughening and the fractal nature of rock[J].Phys. Rev. Lett,1986,57(5):637-640.
[32]LI K. Characterization of rock heterogeneity using fractal geometry[J]. SPE86975,2004.
[33]马新仿,张士诚,朗兆新.储层岩石孔隙结构的分形研究[J].中国矿业,2003,12(9)：46～48.
[34]文慧俭,闫林,姜福聪等著.低孔低渗储层孔隙结构分形特征[J].大庆石油学院学报,2007,31(1)：15～19.
[35]徐满才,史作清,何炳林.分形表面及其性能[J].化学通报,1994(3)：10～13.
[36]李云省,邓鸿斌,吕国祥.储层微观非均质性的分形表征研究[J].天然气工业,2002,22(1)：37～40．
[37]何琰,吴念胜.确定孔隙结构分形维数的新方法[J].石油实验地质,1999(4).
[38]Seholz C H, Aviles C A. Fractal dimension of the1906 San Andreas fault and 1915 Pleasant Valley faults(abstraet)[J]. Earth quakes Notes,1985,55: 20.
[39]金章东,卢新卫,张传林.江西德兴斑岩铜矿田断裂分形研究[J].地质论评,1998,44(1)：57～62.
[40]连长云,苏小四,朴寿成,等.中国大陆深断裂系的分形特征[J].世界地质,1995,14(3)：35～39.
[41]Cello G. Fractal analysis of a Quaternary fault array in the central Apennines, Italy[J]. Journal of Structural Geology,1997,1(7):945-953.
[42]陈江峰,胡诚.煤中断裂分布的分形特征[J].煤田地质与勘探,1999,27(1)：7～9.
[43]谢焱石,谭凯旋.断裂构造的分形研究及其地质应用[J].地质地球化学,2002,30(1)：71～77.
[44]Berry M V, Lewis Z V. On the Weierstrass-Mandelbrot fractal function[J]. Proc.R. Soc,1980,70:459-484.
[45]Scholz C H, Aviles C A. Fractal dimension of the 1906 San Andreas fault and 1915 Pleasant valley faults[J]. Earthquakes Notes,1985,55:20.
[46]Barton C C, LaPointe P R. Fractals in petroleum geology and earth science processes[J]. Plenum Press, New York,1995,23-89.
[47]徐景祯,刘明斌,刘晓冬.断层体系的分形维数及其对深源气运移条件的指示作用[J].大庆石油地质与开发,1997,16(3)：14～18.
[48]周新桂,孙宝珊,刘金红.辽河科尔康油田断裂分形特征与油气关系[J].地质力学学报,1997,3(1)：81～87.
[49]沈忠民,马祖钧,周光甲.断裂体系分维与油田分布[J].地球科学(中国地质大学学报),1995,20(1)：73～78.
[50]谢和平,Pariseau W G.岩石节理粗糙系数(JRC)的分形估计[J].中国科学(B辑),1994,38(5)：524～530.
[51]周尽.海原断层系分形研究[J].西北地震学报,1991,13(3)：78～85.
[52]易顺民,唐辉明.活动断裂的分形结构特征[J].地球科学(中国地质大学学报),1995,20(1)：58～62.
[53]Hirata T, SatohT, ItoK. Fraetal strueture of Spatial distribution of mierofraeturing in roek[J]. Geophys.J. Roy. Astron. Soe,1987,90:369-374.
[54]吴大奎,甘其刚.应用分形插值预测裂缝[J].石油地球物理勘探,1995,30(6)：823～827.
[55]付晓飞,苏玉平,吕延防,等.断裂和裂缝的分形特征[J].地球科学(中国地质大学学报),2007,32(2)：227～234.
[56]Korvin G. Fraetal Modeling the Earth Seienee[M]. Amsterdam:EISevier.1992.
[57]张吉昌,田国清,刘建中.储层构造裂缝的分形分析[J].石油勘探与开发,1996,23(4)：65～68.
[58]高如曾,何光明,刘开时等.断层系的分维及储层裂缝发育带的预测技术[J].四川地质学报,1996,16(2),180～185.
[59]徐光黎.岩石结构面几何特征的分形与分维[J].水文地质工程地质,1993：20～22.
[60]Pointe P R. A method to characterize fracturing density and connectivity through. fractal geometry [J]. Int. J. Rock. Mech. Mim. Sci.&. Geomech. Abstri, 1990, V01.27:No.3.
[61]谢和平,Sanderson D J.断层分形分布之间的相关关系[J].煤炭学报,1994,5：445～448.
[62]徐志斌,王继尧,张大顺,等.煤矿断层网络复杂程度的分维描述[J].煤炭学报,1996,21(4)：358～363.
[63]赵阳升,康天合.煤岩体裂隙分形特征的研究[C].全国青年岩土工程学术会议论文集,科学出版社,1994.
[64]赵阳升.全国煤层导水特征分类研究报告[D].原山西矿业学院,1994.
[65]冯增朝,赵阳升,文再明.岩体裂缝面数量三维分形分布规律研究[J].岩石力学与工程学报,2005,24(4)：601～608.
[66]赵阳升,文再明,冯增朝.岩体裂隙面数量的三维分形分布仿真理论与技术.岩石力学与工程学报,2005,24(6)：994～998.
[67]National Research Council. Rock Fracturings and Fluid Flow-Contemporary Understanding and Applications. National Academy Press[R].Washington, D. C, USA.1996.
[68]Carrera J, Heredia J, Vomvoris S, et al. Modeling of Flow on A Small Fracturingd Monzonitic Gneiss Block.In:Neuman, S.P.and Neretnieks, I. (eds), Hydrogeology of Low Permeability Environments [J]. Inernational Association of Hydro-Geologists, Hanover,1990, pp.115-167.
[69]Pruess K. Narasimhan T N. Numerical Modeling of Multiphase and Nonisothermal Flow in Fracturingd Media. Symposium Conference on Fluid Flow in Fracturingd Rocks[D]. Georgia State University,1998, May15-18.
[70]Davision C CURL Drawdown Experiment and Comparision with Models. Atomic Energy of Canada Ltd. TR375[J]. Pinawa, Manitoba,1985.
[71]Ganzer L. J.Simulating Fracturingd Reserviros Using Adaptive Dual Continuum[J].SPE75233.2002.
[72]Neuman S P, Depner J S. Use of Variable Scale Pressure Test Data to Estimate the Log Hydraulic Conductivity Covariance and Dispersivities of Fracturingd Granites Near Oracle[J]. Arizona. Journal of Hydrology,1988, 102(1-4). pp.475-501.
[73]Long J C S, KarasakiK, Davey A, at al. Inverse Approach to the Construction of Fracturing Hydrology Models Conditioned by Geophysical Data. An Example from the Validation Exercises at the Stripa Mine[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1991,28(2-3), pp.121-142.
[74]Jensen O K, Bresling S, Christensen O W, et al. Natural Fracturing Distribution in Reservoirs Modeled by Back-Stripping and FiniteElement Stress Analysis[C].SPE18429,1989.
[75]Bourne S J, Ri jkels L, Stephenson B J, et al. Predictive Modeling of Naturally Fracturingd Reservoirs Using Geomechanics and Flow Simulation [J]. Geoarabia, 2001,6(1), pp.27-42.
[76]Olson J E, Qiu Y,Holder J, et al. Constraining the Spatial Distribution of Fracturing Networks in Naturally Fracturingd Reservoirs Using Fracturing Mechanics and Core Measurements[C].SPE71342,2001.
[77]Cacas M C, Daniel J M, Letouzey J. Nested Geological Modeling of Naturally Fracturingd Reservoirs[J]. Petroleum Geosicence,2001,7, pp. S43-S52.
[78]Swaby P A, Rawnsley K D. An Interactive 3D Fracturing Modeling Environment [J]. Society of Petroleum Engineers Petroleum Computer Conference, Texas, USA, 1996,6 (2-5), SPE36004.
[79]Rawnsley K,wei L. Evaluation of a New Method to Build Geological Models of Fracturingd Reservoirs Calibrated to Production Data[J]. Petroleum geoscience,2001,7, pp.23-33.
[80]Hart Retal. Formulation of a three-dimentional discrete element model-pall Mechanical calculation for motion and interaction of system composed of many polyhedral block. Int[J]. Rock.Mech. Mm.Sci & Geomech. Abstr.1988,25(16): 339-362.
[81]周维垣,杨若琼,尹建民,等.三维岩体构造网络生成的自协调法及工程应用[J].岩石力学与工程学报,1997,16(1)：29～35.
[82]陈征宙,胡伏生,方磊,等.岩体裂隙网络模拟技术研究[J].岩土工程学报,1998,20(1)：22～25.
[83]杨更社,谢定义,张长庆.节理岩体的损伤与分形几何的关系.西安矿业学院学报[J].1995,15(4)：294～296.
[84]刘连峰,王泳嘉.三维节理岩体计算模型的建立[J].岩石力学与工程学报,1997,16(1)：36～42.
[85]朱焕春,陈文理.生成节理随机数的直接法[J].武汉水利水电大学学报,1997,30(2)：10～12.
[86]马宇,赵阳升.岩体的裂隙分布规律及分形仿真研究[D].太原理工大学硕士论文.1999.
[87]文再明.岩体裂缝面数量三维分形分布规律研究与仿真理论.硕士学位论文[D].太原理工大学.2003.
[88]Hubbert M K, Willis D G. Mechanics of hydraulic fracturing[J]. Trans, AIME, 1957,210:153-166.
[89]Haimson B, Fairhurst C. Initiation and Extension of Hydraulic Fracturings in Rocks[C].SPE1710.
[90]Haimson B, Fairhurst C. Initiation and Extension of Hydraulic Fracturings in Rocks[J].SPEJ, Sept.1967:310-318.
[91]Haimson B, Fairhurst C. Hydraulic Fracturing in Porous-Permeable Materials[R].SPE 2354.
[92]Aimson B. Hydraulic Fracturing in Porous and non-porous rock and its potential for determining In-Situ stresses at great depth[D]. PhD thesis, U. of Minnesota, Minneapolis,1968.
[93]Radley.Failure of Inclined Bore holes[J]. EnergyRes. Teeh,1979.
[94]黄荣樽.水力压裂裂缝的起裂与扩展[J].石油勘探与开发,1981,5：62～74.
[95]李传亮,孔祥言.油井压裂过程中岩石破裂压力计算公式的理论研究[J].石油钻采工艺,2000,22(2)：54～56.
[96]Abbas Ali Daneshy. Experimental Investigation of Hydraulic Fracturing Through Perforations[R]. SPE 4333,
[97]Behrmann L A, Elbel J L. Effect of perforations on fracturing initiation [J]. JPT, May 1991:608-615.
[98]Hazim H. Abass, David L.Meadows, et al.Oriented Perforations-A Rock Mechanicals View[R].SPE 28555.
[99]Yang Z, Crosby D G, et al. Investigation of the factors influencing hydraulic fracturing initiation in highly stressed formations[R]. SPE 38043.
[100]Papanastasiou P, Zervos A. Three-dimensional Stress Analysis of a Wellbore with Perforations and a Fracturing[R].Paper SPE/ISRM 47378. July,1998.
[101]Walton I C, Atwood D C, et al. Perforating Unconsolidated Sands:An Experimental and Theoretical Investigation[R]. SPE 79041.
[102]柳贡慧等.考虑地应力影响下的射孔初始方位角的确定[J].石油学报,2001,22(1)：105～108.
[103]李传亮.射孔完井条件下的岩石破裂压力计算公式[J].石油钻采工艺,2002年,24(2)：37～38.
[104]银本才.压裂井射孔设计方法及其软件研制[D].西南石油学院工程硕士论文,2004.
[105]胡永全,赵金洲,曾庆坤,等.计算射孔井水力压裂破裂压力的有限元方法.天然气工业,2003,23(2)：58～59.
[106]张广清,陈勉,殷有泉,孙华纯.射孔对地层破裂压力的影响研究[J].岩石力学与工程学报,2003,22(1)：40～44.
[107]邓金根,蔚宝华,王金凤,等.定向射孔提高低渗透油藏水力压裂效率的模拟试验研究[J].石油钻探技术,2003,31(5)：14～16.
[108]Reugelsdijk L J L, De Pater C J, Sato K.Experimental hydraulic fracturing propagation in multi-fracturingd medium[R]. SPE59419,2000:1-8.
[109]Peacock D C P, Mann A. Controls on fracturing in carbonaterocks[R]. SPE92980,2005:1-6.
[110]Warpinski N R, Teufel L W. Influence of geologic discontinuitieson hydraulic fracturing propagation [J].JPT,1987,28(3):209-220.
[111]金衍,张旭东,陈勉.天然裂缝地层中垂直井水力裂缝起裂压力模型研究[J].石油学报,2005,26(6)：113～118.
[112]金衍,陈勉,张旭东.天然裂缝地层斜井水力裂缝起裂压力模型研究[J].石油学报,2006,27(6)：124～126.
[113]李玉喜,肖淑梅.储层天然裂缝与压裂裂缝关系分析[J].特种油气藏,2000,7(3)：26～30.
[114]范振忠,刘振华,高立峰.低渗透裂缝性油藏封堵裂缝后转向压裂工艺[J].科学技术与工程.2009,9(1)：113～115.
[115]姚飞,王晓泉.水力裂缝起裂延伸和闭合的机理分析[J].钻采工艺,2000,23(2)：21-24.
[116]李民河,聂振荣,廖健德,等.水力压裂缝延伸方向分析及其应用[J].新疆地质,2003,21(4)：486～488.
[117]姚飞,陈勉,吴晓东,张广清.天然裂缝性地层水力裂缝延伸物理模拟研究[J].石油钻采工艺.2008,30(3)：83～86.
[118]Thiercelin M, Naceur K B, Lemanczyk Z R. Simulation of three-dimensional propagation of a vertical hydraulic fracturing[R]. SPE/DOE 13861,1985.
[119]Anderson G D. Effects of friction on hydraulic fracturing growth near unbonded interfaces in Rocks[J]. SPEJ 8347,1981,21(1):21-29.
[120]Teufel L W, Clark J A. Hydraulic fracturing propagation in layeredrock: experimental studies of fracturing containment [J]. SPEJ9878,1984,24(2): 449-456.
[121]Medlin W L, Masse L. Laboratory experiments in fracturingpropagation[J]. SPEJ 10377,1984,22(6):161-188.
[122]Warpinski N R, Clark J. A, Schmidt, et al. Laboratory in vestigation on the effect of in-situ stress on hydraulic fracturing containment [J]. SPEJ 9834, 1982,22(3):55-66.
[123]De Pater C J, Cleary M P, et al. Experimental verification of dimensional analysis [J].1992, SPE 24994.
[124]柳贡慧,庞飞,陈治喜.水力压裂模拟实验中的相似准则[J].石油大学学报(自然科学版)2000,24(5)：45～50.
[125]陈勉,庞飞,金衍.大尺寸真三轴水力压裂模拟与分析[J].岩石力学与工程学报,2000,19(增刊)：868-872.
[126]陈勉,周健,金衍,等.随机裂缝性储层压裂特征实验研究[J].石油学报,2008,29(3)：431～433.
[127]李玮,闫铁,毕雪亮.基于分形方法的水力压裂裂缝起裂扩展机理研究[J].中国石油大学学报(自然科学版),2009,32(5)：87～91.
[128]李玮,闫铁,毕雪亮.水力致裂法测定分形裂纹下岩石的断裂韧性[J].岩石力学工程学报.2009,28(221)：2789～2793.
[129]闫铁,李玮,毕雪亮.清水压裂裂缝闭合形态的力学分析[J].岩石力学工程学报.2009,28(222)：3471～3476.
[2]王鸿勋,张士诚.水力压裂设计数值计算方法[M].北京：石油工业出版社,1998.
[3]埃克诺米德斯M J,诺尔特K.G等著,张保平等译.油藏增产措施(第三版)[M].北京：石油工业出版社,2002.
[4]谢和平.分形—岩石力学导论[M].北京：科学出版社,1997.
[5]蔡美峰.岩石力学与工程[M].北京：科学出版社,2002.
[6]Mandelbrot B B. Les Objects Fractal:from hasard et dimension, Paris, Flammarion,1975.
[7]Costin I S. A microcrack model for the deformation and failure of brittle rock[J].Geophys, Res.1983,88:9485-9492.
[8]Botsis J, Kunin B. On self-similarity of crack layer[J]. Int. J. Fracturing, 1987,35,51-56.
[9]谢和平.分形几何及其在岩石力学中的应用[J].岩土工程学报,1992,14(1)：1424.
[10]谢和平,陈至达.分形几何与岩石断裂[J].力学学报,1988,20(3),264-275.
[11]Mandelbrot B B, et al. fractal character of fracturing surfaces of metals[J].Nature,1984,308:721-723.
[12]Mandelbrot B B. How long is the coast of Britaina-statistical self-similarity and fractional dimension,Science,1967,156(3775):636-638.
[13]Mandelbrot B B. The Fractal Geometry of Nature, New York, W. H. Freman,1982.
[14]曼德尔布洛特B.分形—形、机遇与维数[M].世界图书出版公司,1999.
[15]董连科.分形理论及应用[M].辽宁科学技术出版社,1991.
[16]Xie Heping. Fractals in Rock Mechanics[M]. Rotterdam:A. A. Balkema Publishers,1993.
[17]Rieu M, Sposito G. Fractal fragmentation:soil porosity and soil water properties[J].Soil Sci Sco Am J,1991,55:1231-1238.
[18]Wong Po-zen. The statistical physics of sedimentary rock[J].Physics Today 4,1988,24-32.
[19]Thompson A H. Fractal in rock physics [J]. Annual Review of Earth and Planetary Sciences.1991,19:237-262.
[20]Thompson A H, et al.The micro geometry and transport properties of sedimentary rocks, Advance[J].Physics,1987,36(5),625-694.
[21]Garrison J R, Pearn W C, Von Rosenberg D U. The Fraetal Nature of Geologieal Data Sets:Power Law Proeesses Every where[J]. SPE22842,1991.
[22]林鸿溢,李映雪.分形论—奇异性探索[M].北京理工大学出版社,1992.
[23]Krohn C E, Thompson A H. Fractal sandstone pores:Automated measurements using scanning-electron-microscope images[J].1986, Phys. Rev. B33, pp6366-6374.
[24]李克文,沈平平,等.砂岩分形结构研究[M].中国科技大学出版社,1993.
[25]Orford J.O, Whalley. W.B.The use of the fractal dimension to quantify the morphology of irregular-shaped particles. Ssdimentology[J].1988,30, 655-668.
[26]Mandelbrot B. Fractal-a geometry of nature[J]. New Scientists,1990, 1127(1734):38-43.
[27]Katz A J, Thompson A H. Fractal sandstone pores:implications for conductivity and pore formation[J]. Phys. Rev.Lett,1985,54(12):1325-1328
[28]Krohn C E. Sandstonefractal and Euclidean pore volume distributions[J]. Geophys.Res,1988,93(B4),3286-3296.
[29]Pfeifer P, Avnir D. Chemistry in noninteger dimensions between two and three Ⅰ:fractal theory of heterogeneous surfaces[J]. Chem. phys,1983,79,3558-3565.
[30]Avnir D. Chemistry in noninte.gerdimensions between two and threeⅡ:fractal surfaces of adsorbents[J]. Chem. phys,1983,79,3566-3571.
[31]Wong P Z, Howard J, Lin J S. Surface roughening and the fractal nature of rock[J].Phys. Rev. Lett,1986,57(5):637-640.
[32]LI K. Characterization of rock heterogeneity using fractal geometry[J]. SPE86975,2004.
[33]马新仿,张士诚,朗兆新.储层岩石孔隙结构的分形研究[J].中国矿业,2003,12(9)：46～48.
[34]文慧俭,闫林,姜福聪等著.低孔低渗储层孔隙结构分形特征[J].大庆石油学院学报,2007,31(1)：15～19.
[35]徐满才,史作清,何炳林.分形表面及其性能[J].化学通报,1994(3)：10～13.
[36]李云省,邓鸿斌,吕国祥.储层微观非均质性的分形表征研究[J].天然气工业,2002,22(1)：37～40．
[37]何琰,吴念胜.确定孔隙结构分形维数的新方法[J].石油实验地质,1999(4).
[38]Seholz C H, Aviles C A. Fractal dimension of the1906 San Andreas fault and 1915 Pleasant Valley faults(abstraet)[J]. Earth quakes Notes,1985,55: 20.
[39]金章东,卢新卫,张传林.江西德兴斑岩铜矿田断裂分形研究[J].地质论评,1998,44(1)：57～62.
[40]连长云,苏小四,朴寿成,等.中国大陆深断裂系的分形特征[J].世界地质,1995,14(3)：35～39.
[41]Cello G. Fractal analysis of a Quaternary fault array in the central Apennines, Italy[J]. Journal of Structural Geology,1997,1(7):945-953.
[42]陈江峰,胡诚.煤中断裂分布的分形特征[J].煤田地质与勘探,1999,27(1)：7～9.
[43]谢焱石,谭凯旋.断裂构造的分形研究及其地质应用[J].地质地球化学,2002,30(1)：71～77.
[44]Berry M V, Lewis Z V. On the Weierstrass-Mandelbrot fractal function[J]. Proc.R. Soc,1980,70:459-484.
[45]Scholz C H, Aviles C A. Fractal dimension of the 1906 San Andreas fault and 1915 Pleasant valley faults[J]. Earthquakes Notes,1985,55:20.
[46]Barton C C, LaPointe P R. Fractals in petroleum geology and earth science processes[J]. Plenum Press, New York,1995,23-89.
[47]徐景祯,刘明斌,刘晓冬.断层体系的分形维数及其对深源气运移条件的指示作用[J].大庆石油地质与开发,1997,16(3)：14～18.
[48]周新桂,孙宝珊,刘金红.辽河科尔康油田断裂分形特征与油气关系[J].地质力学学报,1997,3(1)：81～87.
[49]沈忠民,马祖钧,周光甲.断裂体系分维与油田分布[J].地球科学(中国地质大学学报),1995,20(1)：73～78.
[50]谢和平,Pariseau W G.岩石节理粗糙系数(JRC)的分形估计[J].中国科学(B辑),1994,38(5)：524～530.
[51]周尽.海原断层系分形研究[J].西北地震学报,1991,13(3)：78～85.
[52]易顺民,唐辉明.活动断裂的分形结构特征[J].地球科学(中国地质大学学报),1995,20(1)：58～62.
[53]Hirata T, SatohT, ItoK. Fraetal strueture of Spatial distribution of mierofraeturing in roek[J]. Geophys.J. Roy. Astron. Soe,1987,90:369-374.
[54]吴大奎,甘其刚.应用分形插值预测裂缝[J].石油地球物理勘探,1995,30(6)：823～827.
[55]付晓飞,苏玉平,吕延防,等.断裂和裂缝的分形特征[J].地球科学(中国地质大学学报),2007,32(2)：227～234.
[56]Korvin G. Fraetal Modeling the Earth Seienee[M]. Amsterdam:EISevier.1992.
[57]张吉昌,田国清,刘建中.储层构造裂缝的分形分析[J].石油勘探与开发,1996,23(4)：65～68.
[58]高如曾,何光明,刘开时等.断层系的分维及储层裂缝发育带的预测技术[J].四川地质学报,1996,16(2),180～185.
[59]徐光黎.岩石结构面几何特征的分形与分维[J].水文地质工程地质,1993：20～22.
[60]Pointe P R. A method to characterize fracturing density and connectivity through. fractal geometry [J]. Int. J. Rock. Mech. Mim. Sci.&. Geomech. Abstri, 1990, V01.27:No.3.
[61]谢和平,Sanderson D J.断层分形分布之间的相关关系[J].煤炭学报,1994,5：445～448.
[62]徐志斌,王继尧,张大顺,等.煤矿断层网络复杂程度的分维描述[J].煤炭学报,1996,21(4)：358～363.
[63]赵阳升,康天合.煤岩体裂隙分形特征的研究[C].全国青年岩土工程学术会议论文集,科学出版社,1994.
[64]赵阳升.全国煤层导水特征分类研究报告[D].原山西矿业学院,1994.
[65]冯增朝,赵阳升,文再明.岩体裂缝面数量三维分形分布规律研究[J].岩石力学与工程学报,2005,24(4)：601～608.
[66]赵阳升,文再明,冯增朝.岩体裂隙面数量的三维分形分布仿真理论与技术.岩石力学与工程学报,2005,24(6)：994～998.
[67]National Research Council. Rock Fracturings and Fluid Flow-Contemporary Understanding and Applications. National Academy Press[R].Washington, D. C, USA.1996.
[68]Carrera J, Heredia J, Vomvoris S, et al. Modeling of Flow on A Small Fracturingd Monzonitic Gneiss Block.In:Neuman, S.P.and Neretnieks, I. (eds), Hydrogeology of Low Permeability Environments [J]. Inernational Association of Hydro-Geologists, Hanover,1990, pp.115-167.
[69]Pruess K. Narasimhan T N. Numerical Modeling of Multiphase and Nonisothermal Flow in Fracturingd Media. Symposium Conference on Fluid Flow in Fracturingd Rocks[D]. Georgia State University,1998, May15-18.
[70]Davision C CURL Drawdown Experiment and Comparision with Models. Atomic Energy of Canada Ltd. TR375[J]. Pinawa, Manitoba,1985.
[71]Ganzer L. J.Simulating Fracturingd Reserviros Using Adaptive Dual Continuum[J].SPE75233.2002.
[72]Neuman S P, Depner J S. Use of Variable Scale Pressure Test Data to Estimate the Log Hydraulic Conductivity Covariance and Dispersivities of Fracturingd Granites Near Oracle[J]. Arizona. Journal of Hydrology,1988, 102(1-4). pp.475-501.
[73]Long J C S, KarasakiK, Davey A, at al. Inverse Approach to the Construction of Fracturing Hydrology Models Conditioned by Geophysical Data. An Example from the Validation Exercises at the Stripa Mine[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1991,28(2-3), pp.121-142.
[74]Jensen O K, Bresling S, Christensen O W, et al. Natural Fracturing Distribution in Reservoirs Modeled by Back-Stripping and FiniteElement Stress Analysis[C].SPE18429,1989.
[75]Bourne S J, Ri jkels L, Stephenson B J, et al. Predictive Modeling of Naturally Fracturingd Reservoirs Using Geomechanics and Flow Simulation [J]. Geoarabia, 2001,6(1), pp.27-42.
[76]Olson J E, Qiu Y,Holder J, et al. Constraining the Spatial Distribution of Fracturing Networks in Naturally Fracturingd Reservoirs Using Fracturing Mechanics and Core Measurements[C].SPE71342,2001.
[77]Cacas M C, Daniel J M, Letouzey J. Nested Geological Modeling of Naturally Fracturingd Reservoirs[J]. Petroleum Geosicence,2001,7, pp. S43-S52.
[78]Swaby P A, Rawnsley K D. An Interactive 3D Fracturing Modeling Environment [J]. Society of Petroleum Engineers Petroleum Computer Conference, Texas, USA, 1996,6 (2-5), SPE36004.
[79]Rawnsley K,wei L. Evaluation of a New Method to Build Geological Models of Fracturingd Reservoirs Calibrated to Production Data[J]. Petroleum geoscience,2001,7, pp.23-33.
[80]Hart Retal. Formulation of a three-dimentional discrete element model-pall Mechanical calculation for motion and interaction of system composed of many polyhedral block. Int[J]. Rock.Mech. Mm.Sci & Geomech. Abstr.1988,25(16): 339-362.
[81]周维垣,杨若琼,尹建民,等.三维岩体构造网络生成的自协调法及工程应用[J].岩石力学与工程学报,1997,16(1)：29～35.
[82]陈征宙,胡伏生,方磊,等.岩体裂隙网络模拟技术研究[J].岩土工程学报,1998,20(1)：22～25.
[83]杨更社,谢定义,张长庆.节理岩体的损伤与分形几何的关系.西安矿业学院学报[J].1995,15(4)：294～296.
[84]刘连峰,王泳嘉.三维节理岩体计算模型的建立[J].岩石力学与工程学报,1997,16(1)：36～42.
[85]朱焕春,陈文理.生成节理随机数的直接法[J].武汉水利水电大学学报,1997,30(2)：10～12.
[86]马宇,赵阳升.岩体的裂隙分布规律及分形仿真研究[D].太原理工大学硕士论文.1999.
[87]文再明.岩体裂缝面数量三维分形分布规律研究与仿真理论.硕士学位论文[D].太原理工大学.2003.
[88]Hubbert M K, Willis D G. Mechanics of hydraulic fracturing[J]. Trans, AIME, 1957,210:153-166.
[89]Haimson B, Fairhurst C. Initiation and Extension of Hydraulic Fracturings in Rocks[C].SPE1710.
[90]Haimson B, Fairhurst C. Initiation and Extension of Hydraulic Fracturings in Rocks[J].SPEJ, Sept.1967:310-318.
[91]Haimson B, Fairhurst C. Hydraulic Fracturing in Porous-Permeable Materials[R].SPE 2354.
[92]Aimson B. Hydraulic Fracturing in Porous and non-porous rock and its potential for determining In-Situ stresses at great depth[D]. PhD thesis, U. of Minnesota, Minneapolis,1968.
[93]Radley.Failure of Inclined Bore holes[J]. EnergyRes. Teeh,1979.
[94]黄荣樽.水力压裂裂缝的起裂与扩展[J].石油勘探与开发,1981,5：62～74.
[95]李传亮,孔祥言.油井压裂过程中岩石破裂压力计算公式的理论研究[J].石油钻采工艺,2000,22(2)：54～56.
[96]Abbas Ali Daneshy. Experimental Investigation of Hydraulic Fracturing Through Perforations[R]. SPE 4333,
[97]Behrmann L A, Elbel J L. Effect of perforations on fracturing initiation [J]. JPT, May 1991:608-615.
[98]Hazim H. Abass, David L.Meadows, et al.Oriented Perforations-A Rock Mechanicals View[R].SPE 28555.
[99]Yang Z, Crosby D G, et al. Investigation of the factors influencing hydraulic fracturing initiation in highly stressed formations[R]. SPE 38043.
[100]Papanastasiou P, Zervos A. Three-dimensional Stress Analysis of a Wellbore with Perforations and a Fracturing[R].Paper SPE/ISRM 47378. July,1998.
[101]Walton I C, Atwood D C, et al. Perforating Unconsolidated Sands:An Experimental and Theoretical Investigation[R]. SPE 79041.
[102]柳贡慧等.考虑地应力影响下的射孔初始方位角的确定[J].石油学报,2001,22(1)：105～108.
[103]李传亮.射孔完井条件下的岩石破裂压力计算公式[J].石油钻采工艺,2002年,24(2)：37～38.
[104]银本才.压裂井射孔设计方法及其软件研制[D].西南石油学院工程硕士论文,2004.
[105]胡永全,赵金洲,曾庆坤,等.计算射孔井水力压裂破裂压力的有限元方法.天然气工业,2003,23(2)：58～59.
[106]张广清,陈勉,殷有泉,孙华纯.射孔对地层破裂压力的影响研究[J].岩石力学与工程学报,2003,22(1)：40～44.
[107]邓金根,蔚宝华,王金凤,等.定向射孔提高低渗透油藏水力压裂效率的模拟试验研究[J].石油钻探技术,2003,31(5)：14～16.
[108]Reugelsdijk L J L, De Pater C J, Sato K.Experimental hydraulic fracturing propagation in multi-fracturingd medium[R]. SPE59419,2000:1-8.
[109]Peacock D C P, Mann A. Controls on fracturing in carbonaterocks[R]. SPE92980,2005:1-6.
[110]Warpinski N R, Teufel L W. Influence of geologic discontinuitieson hydraulic fracturing propagation [J].JPT,1987,28(3):209-220.
[111]金衍,张旭东,陈勉.天然裂缝地层中垂直井水力裂缝起裂压力模型研究[J].石油学报,2005,26(6)：113～118.
[112]金衍,陈勉,张旭东.天然裂缝地层斜井水力裂缝起裂压力模型研究[J].石油学报,2006,27(6)：124～126.
[113]李玉喜,肖淑梅.储层天然裂缝与压裂裂缝关系分析[J].特种油气藏,2000,7(3)：26～30.
[114]范振忠,刘振华,高立峰.低渗透裂缝性油藏封堵裂缝后转向压裂工艺[J].科学技术与工程.2009,9(1)：113～115.
[115]姚飞,王晓泉.水力裂缝起裂延伸和闭合的机理分析[J].钻采工艺,2000,23(2)：21-24.
[116]李民河,聂振荣,廖健德,等.水力压裂缝延伸方向分析及其应用[J].新疆地质,2003,21(4)：486～488.
[117]姚飞,陈勉,吴晓东,张广清.天然裂缝性地层水力裂缝延伸物理模拟研究[J].石油钻采工艺.2008,30(3)：83～86.
[118]Thiercelin M, Naceur K B, Lemanczyk Z R. Simulation of three-dimensional propagation of a vertical hydraulic fracturing[R]. SPE/DOE 13861,1985.
[119]Anderson G D. Effects of friction on hydraulic fracturing growth near unbonded interfaces in Rocks[J]. SPEJ 8347,1981,21(1):21-29.
[120]Teufel L W, Clark J A. Hydraulic fracturing propagation in layeredrock: experimental studies of fracturing containment [J]. SPEJ9878,1984,24(2): 449-456.
[121]Medlin W L, Masse L. Laboratory experiments in fracturingpropagation[J]. SPEJ 10377,1984,22(6):161-188.
[122]Warpinski N R, Clark J. A, Schmidt, et al. Laboratory in vestigation on the effect of in-situ stress on hydraulic fracturing containment [J]. SPEJ 9834, 1982,22(3):55-66.
[123]De Pater C J, Cleary M P, et al. Experimental verification of dimensional analysis [J].1992, SPE 24994.
[124]柳贡慧,庞飞,陈治喜.水力压裂模拟实验中的相似准则[J].石油大学学报(自然科学版)2000,24(5)：45～50.
[125]陈勉,庞飞,金衍.大尺寸真三轴水力压裂模拟与分析[J].岩石力学与工程学报,2000,19(增刊)：868-872.
[126]陈勉,周健,金衍,等.随机裂缝性储层压裂特征实验研究[J].石油学报,2008,29(3)：431～433.
[127]李玮,闫铁,毕雪亮.基于分形方法的水力压裂裂缝起裂扩展机理研究[J].中国石油大学学报(自然科学版),2009,32(5)：87～91.
[128]李玮,闫铁,毕雪亮.水力致裂法测定分形裂纹下岩石的断裂韧性[J].岩石力学工程学报.2009,28(221)：2789～2793.
[129]闫铁,李玮,毕雪亮.清水压裂裂缝闭合形态的力学分析[J].岩石力学工程学报.2009,28(222)：3471～3476.