用户名: 密码: 验证码:
水力压裂多裂缝基础理论研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
水力压裂是一种广泛应用的改造低渗储层的工艺技术。自上世纪八十年代以来,随着石油工业的发展、需要改造储层的复杂性增加,人们认识到用单一平面裂缝理论无法在理论上圆满解释一些施工参数、施工情况;多种检测手段证明地下存在多条横向上或纵向上同时延伸的裂缝,而这也是造成早期砂堵与加砂施工失败的原因;目前关于多裂缝的理论模型较少。因此,迫切需要研究多裂缝的形成机理、多裂缝同时延伸的模型等,来研究、理解多裂缝存在的利弊、多裂缝延伸的施工压力异常、多裂缝情况下的裂缝延伸形态、早期砂堵机理等,进而为多裂缝的消除提供理论上的支撑,以指导人们顺利改造低渗透、复杂储层。另一方面,也将提升人们对压裂机理的认识,促进基础理论的发展。
     多裂缝理论是水力压裂理论的前沿理论,研究难度较大,面临问题很多。本文完成了以下探索研究工作,形成了一套研究多裂缝问题的思路与模型:
     1、根据弹性力学、岩石力学、断裂力学、空间几何的基本原理,建立了套管射孔斜井中射孔孔眼周围两孔相交处由于应力的“二次集中”而产生的切应力的计算模型;建立了存在较小微环面情况下、较大微环面情况下套管射孔斜井的破裂压力计算模型。根据类比推理,建立了射孔孔眼内部的破裂压力模型;建立了射孔破裂后形成的裂缝对相邻射孔孔眼破裂压力影响的模型;建立了一般斜井不同方位射孔处起裂裂缝的总的转向角度的计算模型。
     2、利用弹性力学、工程力学、断裂力学、有限元基本理论的相关理论,建立了三种用于计算应力强度因子的理论模型,即端部应力模型、DDM模型、位错密度模型;建立了计算转向角度的几种模型。上述模型可用于研究近井裂缝连接。
     3、在普通二维压裂模型的基础上,考虑近井裂缝转向与沿程闭合应力变化,建立了二维单裂缝转向延伸的新模型,该模型解法的主要特点是以每单元的长度为准去搜索对应的延伸时间。
     4、在考虑井筒流体压缩性形变的基础上,结合裂缝的延伸,建立了考虑井筒内压力升高的多个三维裂缝相继开启的新模型,主要包括井筒憋压模型、三维单裂缝转向延伸模型、井筒憋压模型,同时考虑裂缝连接模型和破裂压力模型,该模型用于压裂初期判断井底压力升高、多个裂缝相继开启的情况,模拟水力压裂过程中初期裂缝条数的变化。
     5、结合井筒内压力协调的模型、多裂缝的连接模型、单个大裂缝的转向延伸模型的模拟结果,阐述了多裂缝的产生机理。
     6、在考虑多裂缝的闭合应力干扰、滤失规律变化、裂缝转向、流量分流的基础上,建立了计算多条二维裂缝同时延伸的模型与多条纵向三维裂缝同时延伸的新模型,模拟了多裂缝闭合应力的干扰、滤失规律的变化对施工压力、裂缝宽度、长度的影响。
     7、建立了分析不同方位起裂的转向多裂缝、同方位起裂的转向多裂缝、同方位起
Hydraulic fracturing is a widely used stimulation technique in petroleum industry for enhanced hydrocarbon recovery from low permeable reservoirs. From 1980' of the last century,along with the development of petroleum industry and the requirement to stimulate reservoirs which is more complicated,more and more people have realized that the theory of single and planar fracture can't give satisfying explain over some complex phenomena and parameter in numerous field setting.Many direct and indirect diagnostic technologies have shown the simultaneous growth of multiple-hydraulic fractures which is the main causation of the emergence premature screen-outs with low proppant concentration and the failure in hydraulic fracturing treatments.So it is urgent to analysis the forming mechanism of multiple-hydraulic fractures and the theory of simultaneous propagation of multiple hydraulic fractures ,to understand the advantages and disadvantages and the extremely high net fracturing pressures,the extend configuration of every fracture ,the mechanism of premature screen-outs,so can we offer theoretic suggestion to minimize the simultaneous propagation of multiple hydraulic fractures to give successful stimulation on low permeable or /and complicated reservoirs. And to promote the development of hydraulic fracturing theory.
    The theory of multiple fractures is very hard to study which is immethoding theory. A set of theoretical models has been established through comprehensive research :
    1 、 According to the basic conception of elasticity mechanics and rock mechanics ,the mathematical model of shear stress root in the stress centralization around the perforations in deviated wellbores with perforations and the prediction model of hydraulic fracture initiation pressure and the location of fractures on the wellbore wall under different size of microannulus are established.Based on the principle of analogism,the estimation method of fracture initiation pressure inside the perforations is sought out. One theoretical model about the influence of a fracture on the initiation pressure of the adjacent perforations has been developed on the foundation of fracture mechanics. A formula is also be studied about the total turning angle from different local and direction in deviated wellbores.
    2、 For the goal to investigate the feasibility of fracture link-up ,integrating elasticity mechanics,engineering mechanics,fracure mechanics and finite element method, using the new method of displacement discontinuity in building engineering ,this paper established three theoretic models including fracture edge stress model,the Displacement Discontinuity Method(DDM) and the Dislocation Parameter Model.Several methods are also presented to calculate the turning angel at the end of fracture. To analyze the fracture geometry paramerers and to estimate the likelihood of the link-up of fractures ,a set of approach is builded up.
    3、 Based on the ordinary 2D mathematical model ,considering the fracture orientation and the changing of the confining stress in the near-wellbore region,the improved 2D mathematical model for fracture propagation and its detailed solution are established ,the main characteristic of which is to search corresponding prolongation time according to the length of every unit.
引文
[1]B. W. McDaniel,D. E. McMechan and N. A. Stegent.Proper Use of Proppant Slugs and Viscous Gel Slugs Can Improve Proppant Placement During Hydraulic Fracturing Applications. SPE 71661,2001.
    [2]W.K.overbuy Jr,BDM;A.B.Yost ll;and DA.Wilkins,Grace,Shursen.Inducing Multiple Hydraulic Fractures From Horizontal Wellbore .SPE 18249,1988.
    [3]H.H.Abass,Saeed Hedayati.and D.L.Meadows.Nonplanar Fracture Propagation From a Horizontal Wellbore; Experimental Study. SPE24823.1996
    [4]J.L.Brumley and H.H.Abass,HalIiburton Energy Services.Hydraulic Fracturing of Deviated Wells: Interpretation of Breakdown of Breakdown and Initial Fracture Opening Pressure .SPE 37363,1996.
    [5]K.D.Mahrer and W.W.Aud, and J.T.Hansen.Far-Field Hydraulic Fracture Geometry: A Changging Paradigm.SPE 36441,1996.
    [6]L.Weijers,C.A.Wright;H.Sugiyama;K.Sato.Simu]taneous Propagation of Multiple Hydraulic Fractures-Evidence,Impact and Modeling Implictions.SPE 64772,2000.
    [7].C.L.Cipolla,SPE,and C.A.Wright. SPE,Pinnacle Technologies Diagnostic Techniques To Understand Hydraulic Fracturing: What?Why?and How? SPE 75359, 2002.
    [8].R.D.Barree Barree and Associates.M.K.Fisher.R.A.Woodroof.A Practical Guide to Hydraulic Fracture Diagnostic Technologies.SPE 77442,2002.
    [9]P.T.Branagan,R.E.Peterson,and T.B.Wright,Characterization of a Remotely Intersected Set of Hydraulic Fractures: Results of Intersection Well No 1-B, GRI/DOE Multi-Site Project.SPE 36452,1996.
    [10]Lyle.V. Lehman,SPE, and John L.Brumley,Halliburton Energy Services.Etiology of Multiple Fractures.SPE 37406,1997.
    [11]N.Arihara,M.Abbaszadeh,C.A.Wright.Integration of Fracturing Dynamics and Pressure Transient Analysis for Hydraulic Fracture Evaluation.SPE 36551,1996
    [12]C.H. Yew and Y.Li.U.of Texas.Fracturing of a Deviated Well.SPE 16930,1987.
    [13]R.G.van de Ketterij .SPE. and CJ.de Pater. SPE. Delft University of Technology. Experimental Study on the Impact of Perforations on Hydraulic Fracture Tortuosity.SPE 38149,1997
    [14]Woltgang F.J. Deeg.SPE , Halliburton Enerices,Inc.Hydraulic Fracture-Initiation in Deviated or Horizontal Openhole Wellbores. SPE 47386,1998.
    [15]M.M.Hossain,M.K.Rahman,S.S.Rahman.A Comprehensive Monograph for hydrnulic fracture initiation from deviated wellbores under arbitrary stress regimes.SPE, 54360,1999.
    [16]M.M.Hossain,M.k.Rahman.Hydraulic fracture initiation and propagation:roles of wellbore trajectory, perforation and stress regmes. J.Pet.Sci.Eng,2000,(27): 129-149.
    [17]Zhengwen Zeng ,SPE,and Jean-Claude Roegiers,SPE,The University of Oklahoma.Experimental Observatoon of Injection Rate Influence on the Hydraulic Fracturing Behavior of a Tight Gas Sandstone. SPE78172,2002.
    [18]K.Q.Nolte.Dlscusslon of Examination of a Cored Hydraulic Fracture in a Deep Gas Well.SPE 26302,1993.
    [19]Jerome m. Stadulis.Development of a Completion Design To Control Screenouts Caused by Multiple Near-Wellbore Fractures, SPE 29549,1995.
    
    [20]L. A. Behrmann,K.G. Nolte.Perforating Requirements for Fracture Stimulations. SPE 39453,1998.
    [21]J.L.Brumley and H.H.Abass,Halliburton Energy Services.Hydraulic Fracturing of Deviated Wells: Interpretation of Breakdown of Breakdown and Initial Fracture Opening Pressure .SPE 37363,1996.
    [22]Jeffrey,R. G.,Vandamme,L.,and Roegiers,J.-C.:"Mechanical Interactions in Branched or Subparallel Hydraulic Fractures," paper SPE 16422,1987.
    [23] D.G.Crosby, Z.Yang and S.S.Rahman.The Successful Use of Transverse Hydraulic Fractures from Horizontal Weilbores.SPE 50423,1998.
    [24] Behrmann, L.A. and Elbel, J.L.: "Effect of Perforations on Fracture Initiation," paper SPE 20661 presented at the 1990 SPE Annual Technical Conference and Exhibition, New Orleans, Sept. 23-26.
    [25] 罗钟鸣.射孔对水力压裂的影响研究.西南石油学院硕士学位论文,2005.
    [26] C.H.Yew, U.of Texas;J.H.Schmidt, and Yi Li.On Fracture Design of Deviated Wells. SPE 19722,1999
    [27] Chien-Ke Lu, Wuhan U. Ching H.Yew, U.of Texas.Bonded Half-Planes Containing Two Arbitarily Oriented Cracks:A Study of Containment of Hydraulically Induced Fractures. SPE 11871, 1985.
    [28] Xiaowei Weng.Fracture Initiation and Propagation From Deviated Wellbores. SPE 26597,1993.
    [29] R.H.Morales and B.H.Brady, A.R.lngraffea.Three-Dimensionl Analysis and Visualization of the Wellbore and the Fracturing Process in Inclined Wells. SPE 25889,1993.
    [30] C.H.Yew, M.E. Mear, C.C.Chang,and X.C.Zhang,U.of Texas.On Perforating and Fracturing of Deviated Cased Wellbores. SPE 26514,1993
    [31] C.y.Dong, and C.J.de pater. Numerical modeling of crack reorientation and link-up.adv.ances in engineering software 33(2002):577-587.
    [32] R.G.van de ketterij,and C.J.de pater.numerical simulations of hydraulic fracture link-up of perforations at deviated wellbores.SPE 54751, 1999.
    [33] R.G.van de Ketterij,SPE, and C.J.de Pater, SPE,Delft Universty of Technology. Impact of Perforations on Hydraulic Fracture Tortuosity.SPE 56193,1999.
    [34] 黄醒春,顾隽超,夏小和.压载条件下裂纹断裂扩展的位移不连续数值分析[J].上海交通大学学报,2001,35(10):1486-1490.
    [35] 黄醒春,周斌,顾隽超.任意多裂纹应力强度因子的位移不连续数值算法[J].上海交通大学建筑工程与力学学院,2001年5月,第23卷第3期.
    [36] 卢海星,路晓波,韩保红.位移不连续法在裂纹扩展仿真中的应用[J].军械工程学院学报,2004年12月,第16卷第6期.
    [37] Z.Chen and M.J.Economides.fracturing pressures and near-well fracture geometry of arbitrarily oriented and horizontal weils,SPE,1995,30531.
    [38] Z.Chen and M. J. Economies.University.Fracturing Pressures And Near-Well Fracture Geometry Of Arbitrarily oriented And Horizontal wells. SPE24823,1996.
    [39] J.Romero, M. G. Mack and J. L.Elbel, SPE,Schlumberger Dowell. Theoretical Model and Numerical Investigation of Near Wellbore Effects in Hydraulic Fracturing. SPE30506,1995.
    [40] Hallan S D, Last N C. Geometry of hydraulic fractures from modestly deviated well bores[R]. SPE 20656,1991.
    [41] C.A.M.Veeken,D.R.Davies,and J.V.Valters.Limited Communication Between Hydraulic Fracture and(Deviated) Welibore.SPE 18982,1989..
    [42] Jean Romero,SPE,M.G.Mack,SPE,and J.L.Elbel Schlumberger.Theoretical Model and Numerical Investigation of Near-Wellbore Effects in Hydraulic Fracturing.SPE 63009, 2000.
    [43] Zhongrning Chen,,and M.J.Economides.U.Effect of Near-WEllbore Fracture Geometry on Fracture Execution and Post-Treatment Well Production of Deviated and Horizontal Wells.SPE 57388,1999
    [44] K. Ben Naceur, and J.C. Roegiers. Design of fracturing treatment in multi.layered formations. SPE 17712, 1988.
    [45] J.L. Elbel, A.R. Piggott, and M.G. Mack. Numerical modeling of multilayer fracture treatment. SPE 23982, 1992.
    [46] K.e.Olson.Mobil E&P U. S.INC.and A.W.M.E1-Rabaa.Mobil E&P Technical Center SPE Members .Hydraulic Fracturing of the Multizone Wells in the Pegasus Field,West Texas.SPE 27718,1994.
    [47]H. Gu.J.Desroches and J.L.Elbel. SPE, Schlumberger.Computer Simlation of Multilayer Hydraulic Fractures. SPE 64789,2000.
    [48]Davidson B M. Analysis of abnormally high fracture treating pressure by complex fracture growth[A]. In.Proc. of Gas Technology Symposium[C]. Calgary, Albert. Canada: [s. n.]. 1993.
    [49] Sato, K., Wright, C.A., and Ichikawa, M.: "Post-Frac Analyses Indicating Multiple Fractures Created in a Volcanic Formation," paper SPE 39513 presented at the 1998 India Oil and Gas Conference, New Delhi, Feb10-12.
    [50].B.W.McDaniel.SPE,D.E.McMechan,SPE,andN.A.Stegent.SPE Halliburton Energy Services, Inc.Proper Use of Proppant Slugs and Viscous Gel Slugs Can Improve Proppant Placement During Hydraulic Fracturing Applications. SPE71661,2001.
    [51]C. Gardner, Amoco Production Co .SPE Member.High Fracturing Practuring Pressures for Shales and Which Tip Effects May Be Responsible.SPE 24852,1992.
    [52]B.M.Davidson,B.F.Saunders,B.M.Robinson,and S.A.Holditch&Assocs. Inc.SPE Members.Analysis of Abnormally High Fracture Treating Pressures Caused by Complex Fracture Growth.SPE 26154,1993.
    [53]L.Weijers,C.A.Wright,Pinnacle Technologies;H.Sugiyama,Teikoku Oil Company; K.Sato, U of Tokyo;L.Zhigang North China Bureau of Petroleum.Simultaneous Propagation of Multiple Hydraulic Fractures-Evidence Impact and Modeling Implictions.SPE 64772,2000.
    [54]S.D.Hallam and N.C.Last,BP Research.Geometry of Hydraulic Fractures From Modestly Deviated Wellbores.SPE 20656,1990.
    [55]W.E1 Rabaa,Halliburton Services,SPE Member.ExperimentalStudy of Hydraulic Fracture Geometry Initiated From Horizontal Wells.SPE 19720.
    [56]Hazim H.Abass,David L.Brumley.Saeed Hedayati, and James J.Venditto Halliburton Energy Services SPE Members.Oriented Perforation-A Rock Mechanics View. SPE 28555,1994.
    
    [57]王鸿勋.水力压裂原理[M].北京,石油工业出版社,1987.
    
    [58]Klaas A.W. van Gijtenbeek.SPE ,and Reinhard Pongratz ,SPE, Halliburton.Perforating and Hydraulic Proppant Fracturing in Western Siberia, Russia. SPE 90238.2004.
    [59]L.Weijers, L.G.Griffin,H.Sugiyama,and S.Takada;K.K.Chong,J.M.Terracina,and C.A. Wright.The First Successful Fracture Treatment Campaign Conducted in Japan: Stimulation Challenges in a Deep ,NaturalIy Fractured Volcanic Rock. SPE 77678,2002.
    [60]J.F.Manrique and A .Venkitaraman.Oriented Fracturing-A Practical Technique for Production Optimization .SPE 71652,2001.
    [61]Hazim H. Aba, PeterHagist, JamesHarry,L.Hunt,MarkShumway,NazGazi Pennzoil.,Ltd.A Case History of Completing and Fracture Stimulating a Horizontal Well. SPE 29443,1995.
    [62]L.A. Behrmann,K.G.NoIte.Perforating Requirements for Fracture Stimulations. SPE 59480,1999.
    [63]L.A.Behrmann,J.L.Elbel.Effect of Perforating on Fracture Stimulations. JPT.May,1999.
    [64]M.P.Cleary,D.E.Johnson,H-H. Kogsboll and K.A. Owens,K.F. Perry.C.J.de Pater.Field Implementation of Proppant Slugs To Avoid Premature Screen-Out of Hydraulic Fractures With Adequate Proppant Concentration. SPE 25892,1993.
    [65]M.A.Emanuele,W,A.Minner and L. Weijers.D.M.Blevens.A Case History:Completion and Stimulation of Horizontal Wells with Multiple Transverse Hydraulic Fractures in the Lost Hills Diatomite.SPE 46193,1998.
    [66]W.W.Aud,T.B.Wright,C.L.Cipolla,J.D.Harkrider,J.T.Hansen.The Effect of Viscosity on Near-Wellbore Tortuosity and Premature Screenouts.SPE 28492.
    [67]J.B.Surjaatmadja,H.H.Abass,.&dJ.L..Brvrnley.Elimination of Near-Wellbore Tortuosities by Means of Hydrojetting. SPE,28761,1994.
    [68] 廖成锐.射孔对水力压裂的影响.西南石油学院工程硕士论文.2003年5月.
    [69] 余雄鹰等.斜井的破裂压力和裂缝方位[J].江汉石油学院学报,1994,16(3):57-60.
    [70] 黄荣樽.水力压裂裂缝的起裂和扩展[J].石油勘探与开发,1981(5).
    [71] 陈勉,陈治喜,黄荣樽.大斜度井水压裂缝起裂研究[J].石油大学学报,1995,19(2):30-35.
    [73] 胡永全等.计算射孔井水力压裂破裂压力的有限元方法[J].天然气工业,2003,23(2):58-59.
    [74] 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,2002,24(2):37-38.
    [75] 徐芝纶.弹性力学简明教程[M].人民教育出版社,1979.
    [76] Phillip M.Halleck,Y.Serdar Dogulu.Show How Perforators Damage Natural Fractures. SPE 37330,1996.
    [77] C,P,Tan and D,R, Willoughby.Critical Mud Weight and Risk Contour Plots for Designing Inclined Wells.SPE 26325,1993
    [78] 贾学明,王启智.三维断裂分析软件FRANC3D[J].计算力学学报,2004,21(6):764-768.
    [79] MUSKHELISHVILI著.数学弹性力学的几个基本问题[M].赵元惠译.北京:科学出版社,1958.
    [80] Shoukeh-jian, Napier JAL.A two-dimensionalinear variation displacement discontinuity method for three-layered delastic media [J].Intemational Journal of Rock Mechanic Sand Mining Sciences, 1999, 36(4):719-729.
    [81] Crouch SL.Solution of plane elasticity problems by the displacement discontinuity method [J]. International Journal Numerical Methods Engineering, 1976, 10:301-343.
    [82] 范天佑.断裂力学基础[M].江苏科学技术出版社,1978.
    [83] 洪起超.工程断裂力学[M].上海:上海交通大学出版社.1987.
    [84] 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.
    [85] 王鸿勋著.水力压裂原理[M].北京:石油工业出版社,1987.
    [86] 袁恩熙著.工程流体力学[M].北京:石油工业出版社,1993.
    [87] J.L. Elbel. A method to estimate multizone injection profiles during hydraulic fracturing. SPE 21869, 1991.
    [88] 米卡尔J.埃克诺米德斯,肯尼斯G诺尔特著,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.
    [89] 宋瑜,万德立等.工程力学[M].石油工业出版社,1997.
    [90] Thailak, S., Rothenburg, L., and Dusseault. M,: "Simulation of Multiple Hydraulic Fractures in a Discrete Element System,"presentedat the 32nd US Symposium on Rock Mechamcs, Norman.OK, july 10-12,1991.
    [91] Cleary,M.P.:"Critical Issues in Hydraulic Fracturing of High-Permeability Reservoirs," paper SPE 27618 presented at the1994 SPE European Production Operations Conference& Exhibition,Aberdeen, Scotland, March 15-17.
    [92] Jeffrey, R.G., et al.: "Propagation of Fractures in Coal: Equivalent Modulus and Parallel Fracture Effects," present at the 1987 Coalbed Methane Symposium, Tuscaloosa, AL,November16-19.
    [93] R.A. Langedijk, SPE, S. A1-Naabi, H. AI-Lawati, Petroleum Development, Oman, R. Pongratz, SPE, M.P. Elia, SPE and T. Abdulrab, SPE, Halliburton Energy Services. Optimization of Hydraulic Fracturing in a Deep, Multilayered, Gas-Condensate Reservoir. SPE 63109,2000.
    [94] A.T. Jones, SPE, M.S. A1 Salhi, SPE, S.M. A1 Shidl, SPE, Petroleum Development Oman, M. England, SPE, R. Pongratz, SPE, Halliburton Worldwide Ltd. Multiple Hydraulic Fracturing of Deep Gas-Condensate Wells in Oman. SPE 49100,1998.
    [95] D.GCrosby.The successful use of transverse hydraulic fractures from horizontal wellbores.SPE50423, 1998.
    [96] Wright, C.A.: "On-Site Step-Down Test Analysis Diagnoses Problems and Improves' Fracture Treatment Success," Hart's Petroleum Engineer International (January 1997).
    [97] Meyer, B.R. and Henry, R.Implementation of Fracture Calibration Equations for Pressure Dependent Leakoff.SPE 62545, 2000.
    [98] Roberts, G.A., Chipperfield, S.T., and Miller, W.K.: "The Evolution of a High Near-Wellbore Pressure Loss Treatment Strategy for the Australian Cooper Basin," paper SPE 63029 presented at the 2000 SPE Annual Technical Conference and Exhibition,Dallas, October 1-4.
    [99] 陈小新、魏英杰,粉砂在压裂施工中的应用效果显著[J],钻采工艺,2002.4.
    [100] J.L.吉德利等.水力压裂技术新发展[M].北京:石油工业出版社,1995
    [101] 中国航空研究院主编.应力强度因子手册[M].科学出版社,1981
    [102] 田根宝.复变函数与积分变换[M].上海交通大学出版社,1997
    [103] 屈本宁.工程力学[M]..科学出版社,2003
    [104] 杨庆生,孙艳丰.裂纹扩展过程的数值模拟[J].铁道学报,1997,19(5):116-120.
    [105] 杨庆生,杨卫.断裂过程的有限元模拟[J].计算力学学报,1997,14(4):407-412.
    [106] 嵇醒,臧跃龙,程玉民著.边界元法进展及通用程序[M].同济大学出版社,1997.
    [107] 朱合华,陈清军等著.边界元法及其在岩土工程中的应用[M].同济大学出版社,1997.
    [108] 张有天,王镭,陈平著.边界元法及其在工程中的应用[M].水利电力出版社,1989.
    [109] 袁懋咏.断裂力学理论及其工程应用[M].重庆大学出版社,1989.
    [110] 徐芝纶.弹性力学简明教程[M].人民教育出版社,1979.
    [111] 郭建春,罗天雨,赵金洲.气井压后稳态产能模型及求取无阻流量的变系数一点法[J].天然气工业,2005年第12期.
    [112] 赵金洲,郭建春,罗天雨等.砾石充填效果评价及优化技术研究成果报告[M].西南石油学院,2004年10月.
    [113] 罗天雨,赵金洲,郭建春.薄层多层压裂的拟三维模型及应用[J].特种油气藏,2005年第6期.
    [114] 罗天雨,郭建春,赵金洲.求取压裂气井无阻流量的新方法[J].新疆石油地质,2005年第5期.
    [115] 罗天雨,郭建春,赵金洲.套管射孔斜井起裂位置与转向角度研究[J].石油学报.
    [116] 罗天雨,郭建春,赵金洲.三种砾石充填方式的油藏条件[J].海洋石油,2005年第4期.
    [117] 赵金洲,任书泉.考虑温度场影响时裂缝几何尺寸的数值计算模型与方法[J].石油学报.1987,8(1):71-82.
    [118] 胡永全,任书泉.压裂裂缝拟三维延伸的数值模拟[J].西南石油学院学报,1992,14(2):54-62
    [119] 张平.水力压裂裂缝延伸三维数值模拟研究[J].石油钻采工艺,1997,9(3),53-59,69.
    [120] 敖西川.多产层水力压裂裂缝延伸数学模型研究[J].西南石油学院硕士学位论文,2004.
    [121] 杜卫平.薄层多层压裂应力剖面与压裂裂缝形态研究[M].西南石油学院博士学位论文,2005.
    [122] 罗天雨.多裂缝防治措施研究[J].断块油气田.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700