低渗气藏超正压射孔投产理论研究
摘要
超高压正压射孔工艺(EOP)是国外九十年代提出的射孔新工艺技术，应用前景广阔。国内由于缺乏相应的理论研究，实践应用不多。虽然提高射孔井产能的砂岩油田负压射孔优化设计技术已在全国普遍使用，然而针对低渗低产气藏，负压射孔技术并不能充分体现气井产能，而超正压射孔技术作为一种补充能充分适应这一情况。为了大量使用该项新工艺为油田低渗气藏增储上产做贡献，必须针对工艺机理、影响工艺效果的因素进行研究，获得工艺参数设计方法，并通过气井产能分析进行相应的技术经济评价，以便正确合理指导施工，获得最佳的经济效益。
本研究从低渗低产气藏压裂适应性分析、EOP射孔投产适应性分析出发，阐述了EOP工艺的特点。从裂缝起裂的机理分析、射孔参数对裂缝起裂的影响分析出发，研究了EOP工艺的实质与机理、EOP工艺井筒流体动态模拟、裂缝扩展动态模拟方法，提出了EOP工艺射孔参数设计原则，为EOP工艺在油田实施打下了坚实的理论基础。
The novel technique of extreme overbalance perforating(EOP) was evolved in 1990's,field application has been broadened greatly abroad because of its dramatic and cost-effective improvement in initial well productivity, but less applications in China because of lacking of theoretical foundations. Although underbalance perforating is widely used and accepted as an industrial standard, it applicability decreases, however, with a decline in reservoir pressure, permeability or rock strength, where exetreme overbalance perforating can sidestep these problems as a complemental technique. In order to put this new technique (EOP job) into practice more effectively in China and benefit from it, It is very necessary to launch a program to study the characteristics, influencing factors and mechanism of extreme overbalance perforating, accordingly, get the way of designing of EOP job. Incorporating with productivity analysis and economic evaluation, the EOP field operations will be guided reasonably and effectively and the maximum benefit could be expected.Based on its suitability analysis for low permeable gas formations and fracture initiation study, the characteristics and mechanism of extreme overbalance perforating have been addressed in this paper. The design method for operational parameters of EOP has also been proposed after numerical modeling of wellbore flowing and fracture propagation during EOP process. The oilfield application shows good results according to well test interpretation and it is very helpful in oil productivity enhancement.
本研究从低渗低产气藏压裂适应性分析、EOP射孔投产适应性分析出发，阐述了EOP工艺的特点。从裂缝起裂的机理分析、射孔参数对裂缝起裂的影响分析出发，研究了EOP工艺的实质与机理、EOP工艺井筒流体动态模拟、裂缝扩展动态模拟方法，提出了EOP工艺射孔参数设计原则，为EOP工艺在油田实施打下了坚实的理论基础。
The novel technique of extreme overbalance perforating(EOP) was evolved in 1990's,field application has been broadened greatly abroad because of its dramatic and cost-effective improvement in initial well productivity, but less applications in China because of lacking of theoretical foundations. Although underbalance perforating is widely used and accepted as an industrial standard, it applicability decreases, however, with a decline in reservoir pressure, permeability or rock strength, where exetreme overbalance perforating can sidestep these problems as a complemental technique. In order to put this new technique (EOP job) into practice more effectively in China and benefit from it, It is very necessary to launch a program to study the characteristics, influencing factors and mechanism of extreme overbalance perforating, accordingly, get the way of designing of EOP job. Incorporating with productivity analysis and economic evaluation, the EOP field operations will be guided reasonably and effectively and the maximum benefit could be expected.Based on its suitability analysis for low permeable gas formations and fracture initiation study, the characteristics and mechanism of extreme overbalance perforating have been addressed in this paper. The design method for operational parameters of EOP has also been proposed after numerical modeling of wellbore flowing and fracture propagation during EOP process. The oilfield application shows good results according to well test interpretation and it is very helpful in oil productivity enhancement.
引文
[1] Tariq S M, Ichara M J. Performance of Perforated Comepletions in the Presence of Common Heterogeneities: Anisotropy, Laminations, or Natural Fractures[C]. SPE 14320, 1985: 317～329.
[2] T.D．范 高尔夫-拉特著．裂缝油藏工程基础[M]．秦同洛等译．北京：石油工业出版社，1989：231～268．
[3] 潘迎德等．使油井产能最高的射孔参数优选[J]．西南石油学院学报，1990，12(2)：27～36．
[4] 李开泰，黄艾香，黄庆怀．有限元方法及其应用[M]．西安：西安交通大学出版社，1984：107～218．
[5] 李海涛，王永清．预测气井射孔最大无砂负压的方法研究[J]．天然气工业，1999．5
[6] 李海涛，王永清．确定油井射孔最大付压的新方法研究[J]．石油钻采工艺，1997．8
[7] 李海涛，王永清．压裂施工井的射孔优化设计方法[J]．天然气工业，1999．5
[8] Klotz, J. A., Krueger, R. F., Pye, D. S.: "Effect of Perforation Damage on Well Productivity, " J. Pet. Tech.. (Nov. 1974), 1303-1314.
[9] Tariq, S.M.: "Evaluation of Flow Characteristics of Perforation Including Nonlinear Effects Using Finite-Element Method, " Paper SPE 12781 presented at the 1984 California Regional Meeting, Long Beach, CA, April 11-13.
[10] Tariq, S.M., Ichara, M.J. and Ayestaran, L.:" Performance of Perforated Completions in the Presence of Common Heterogeneities: Anisotropy, Laminations, or Natural Fractures, " paper SPE 14320 presented at the 1985 SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, Sept. 22-25.
[11] 唐愉拉，潘迎德：“有限元方法在射孔完井中的应用”，石油学报，1989年，10(3)，48-57。
[12] 唐愉拉，潘迎德，祝渝培：“气井非达西流射孔完井的有限元数值模拟研究”，石油学报，1992年，13(4)，85-96。
[13] L.A.Behrman, B. McDondd:"Underbalance or Extreme overbalance."SPE57390
[14] "modeling of fracture propagation during overbalance perforating" SPE28560
[15] "extreme overbalance perforating extends perforations without vertical growth" SPE37325
[16] "performance Evaluation of Extreme overbalance perforating" A. Ghalambor.etc SPE39459
[17] 杨春盛．“超高压射孔技术的应用”．世界石油工业．vol 4．No．9
[18] 方方编译．“超高压射孔法---对负压射孔法的挑战”．试采技术．Vol16．No．1
[19] Haimson, Fairhurst. "Hydraulic Fracturing in Porous Permeable Materials". J. P. T, July 1969
[20] Bradley. "Failure Of Inclined Boreholes". J. Energy Res. Tech., 1979
[21] C.H.Yew, Y.Li."Fracturing Of a Deviated Wells". SPE16930
[22] C.H.Yew, Y.Li."On Fraemfing Design Of a Deviated Wells". SPE19722
[23] M.M.Hossain, M.K.Rahman, S.S.Rahman."A Comprehensive Monograph for Hydrnulic Fracture Initiation fromD eviated Wellbores under Arbitrary Stress Regimes". SPE54360
[24] 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
[25] 余雄鹰等．“斜井的破裂压力和裂缝方位”．江汉石油学院学报．1994，16(3)：57-60
[26] 黄荣樽．”水力压裂裂缝的起裂和扩展”．石油勘探与开发，1981(5)
[27] 陈勉，陈治喜，黄荣樽．“大斜度井水压裂缝起裂研究”．石油大学学报．1995，19(2)：30-35
[28] 金衍，陈勉等．“大位移井的井壁稳定力学分析”．地质力学学报．1999，5(1)：4-11
[29] 楼一珊等．“大斜度井泥页岩井壁稳定的力学分析”．江汉石油学院学报．1997，19(1)：61-64
[30] 柳贡慧等．“考虑地应力影响下的射孔初始方位角的确定”．石油学报．2001．22(1)：105-108
[31] 张士诚，王世贵等．“限流法压裂射孔方案优化设计”．石油钻采工艺．2000，22(2)：60-63
[32] L.A.Behrmann, K.G..Nolte. "Perforating Requirements foe Fracture Stimulations". SPE 59480, 1999, 228-234
[33] A.A.Daneshy. "Experimental Investigation of Hydraulic Fracturing Through Perforations': Trans AIME. Oct.1973 1201-1206
[34] L.A.Behrmann, J.L.Elbel. "Effect of Perforations On Fracture Initiation". SPE 20661
[35] L.Petitjean, B.Couet. "Modeling of Gas-driven Fracture Propagation for Oil and Gas Well Stimulation". SPE 28084
[36] A.Ghalambor, M.Asadi, M.Azari. "Performance Evaluation of Extreme Overbalanced Perforating." SPE 39459
[37] J.C.Guoynes, W.M.Palmer. J.Grantham. "Extreme-Overbalance Perforating Extends Perforations without Vertical Growth". SPE 37325
[38] L.Petitjean, J.C.Abel, J.H.Schmidt. "Well Productivity Improvement Using Extreme Overbalanced Perforating and Surging - Case Study". SPE 30527
[39] B.Grieser, C.C.Smith, B.Bertrand. "Overbalanced Perforating Field Study in the Tubb Sand, Bravo Dome Field". SPE 37478
[40] J.M.Dees, P.J.Handren. "A New Method of Overbalanced Perforating and Surging of Resin for Sand Control". SPE 26545
[41] P.J.Handran, T.B.Jupp, J.M.Dees. "Overbalance Perforating and Stimulation Method for Wells". SPE 26515
[42] J.B.Crump, M.W.Conway. "Effects of Perforation Entry Friction on Bottomhole Treating Analysis". SPE 15474
[43] D.D.Cramer, B.J.Titan. "The Application of Limited-Entry Techniques in Massive Hydauli Fracturing Treatments", SPE 16189
[44] C.M.Peason, A.J.Bond, M.E.Eck. "Result of Stress-Oriented and Aligned Perforating in Fracturing Deviated Wells". SPE 22836
[45] C.M.Peason, A.J.Bond, M.E.Eck."Optimal Fracture Stimulation of a Moderate Permeability Reservoir, Kuparuk River Unit". SPE 20707
[46] C.Guresbeck, R.E.Collins. "Particle Transport Through Perforations". AIME, Dec. 1982, 857-865
[47] D.L.Lord, S.N.Shah. "Study of Perforation Friction Pressure Empolying a Large-Scale Fracturing Flow Simulator". SPE 28508
[48] C.A.M.Veeken, D.R.Davies. "Limited Communication Between Hydraulic Fracture and (Deviated) Wellbore". SPE 18982
[49] J.D.Willingham, H.C.Tan, L.R.Norman. "Perforation Friction Pressure of Fracturing Fluid Slurries". SPE 25891
[50] C.M.Pearson, E.W.Reinbold. "An Investigation Into the Use of High Pressure Nitrogen Breakdown Treatments Prior to Hydraulic Fracturing". SPE35741
[51] L.L.Lacy. "Comparison of Hydraulic-Fracture Orientation Techniques". SPEFE, March, 1987, 66-76'
[52]J.L.吉德利等：“水力压裂技术新发展”，北京，石油工业出版社，1995。
[53] 蒋建勋，“油气井酸化模型及专家系统”，西南石油学院博士论文，1997．5．
[54] Morgenthaler, L.H.: " Application of a Three-Dimensional Hydranlic Fracturing Simulators for Design of Acid Fracturing Treatment, "SPE25413
[55] 胥耘、黄志强：“拟三维酸压设计软件研究与应用，“石油钻采工艺，1996年(第18卷)第1期．
[56] Perkins, T.K., and Kern, L.R. : "Widths of Hydraulic Fractures, "J.Petroleum Technology, Vol. 13, sept. 1961, 937-949.
[5
[57] Nordgren, R.P.: "Propngation of a vertical Hydraulic Fractures, " Society of Petroleum Engineers Journal, Vol. 12, Aug. 1972, 306-314.
[58] Christianovich, S.A., and Zheltov, Y.R: "Formation of Vertical Fractures by Means of Highly Viscons Liquid, "Proceeding of the fourth World Petroleum Congress, Section Ⅱ , Paper3.
[59] Christianovich, S.A., and Zheltov, Y.P.: "Theoretical Principles of Hydraulic Fracturing of Oil Strate, "Fifth World Petroleum Congress, Section Ⅱ, Paper23.
[60] Geertsma, J., and Deklerk, F.: "A Rapid Method of Pridicting Width and Extent of Hydraulically Induced Fractures, "JPT., Vol. 21, Dec.1969, 1571-1582.
[61] Le-Tirant, P., and Dupuy, M.: "Dimensions of the Fractures Obtained by Hydraulic Fracturing of Oil-Bearing Formations, "evue de linstitut Francais du Petuole, Jan, 1967, 44-98.
[62] Mcleod, H.O., Jr.: "A Simplified Approach to Design of Fracturing Treatments Using High-Viscosity Cross-linked Fluids, "SPE11614
[63] Van Eekelen: "Hydraulic Fracture Geometry: fracture Contain-ment in Layered Formation, "SPEJ., Vol.22, 1982, 341-349.
[64] Advani, S.H., GanggeRao, H.V.S., Chang, H.Y., Komar, C.A., and Khan, S.: "Hydraulic Fracture Modeling for the Eastern Gas Shales Prcject, "Proceeding, DOE Second Eastern Gas Shales symposium, Morgantown, 1978, 84-93.
[65] Advani, S.H., Chang, H.Y., Komar, C.A., and Stonesifer, R.: "Rock Mechanics Aspects of Hydraulic Fracturing in the Devonian Shale, "Presented at the 21th Rock Mechancis Symposium, 1980.
[66] Advani, S.H., and Lee, J.K... "Finite Element Model Simulations Associated with Hydranlic Fracturing, "SPEJ., Vol.22, 1982.
[67] 中国航空研究院主编，应力强度因子手册，科学出版社，1981．
[68] Palmer, I.D., and Craig, H.R. : Modeling Asymmefric Vertical Growth in Elongated Hydraulic Fractures and Application to first MWX Stimulation, SPE/DIE/GRI, 12879, 1984.
[69] 李宾元，裂缝中垂直裂缝高度的讨论，石油钻采工艺，1984年第五期．
[70] Palmer, I.D., and CarrolI, Jr.H.B.: "Numerical Solution for Reight and Elongated Hydraulic Fractures, "SPE/DOE 11627, 1983.
[71] Gdanski, R.D., and Lee, W.S.: "On the Design of Fracture Acidizing Treatments, "SPE 18895, 1989.
[7
[72] Michael J. Economides and Kenneth G. Nolte：油藏增产技术，石油工业出版社，1990．
[73] 王鸿勋，李平．“水力压裂过程中井筒温度的数值计算方法，”石油学报，1987．4
[74] 王鸿勋，张琪，“采油工艺原理”，石油工业出版社，1989．
[75] Cleary, M.P.: "Comprehensive Design Formulae for Hydraulic Fracturing, "Spe 9259, Sept.1980.
[76] Settari, A., and Cleary, M.P.: "Three-Dimensional Simulation of Hydraulic Fuacturing, "JPT., Vol.36 July 1984, 1177-1190.
[77] Settari, A., and Cleary, M.P.: "Development and Testing of a Pseudo-Three Dimensional Model of Hydraulic Fracture Geometry (P3DH), "SPE 10505, 1982.
[78] Cleary, M.P., KecK, R.G., and Mear, M.E., : "Micro computer Models for the Design of Hydraulic Fractures, " SPE/DOE 11628, 1983.
[79] Palmer, I.D., and Carrol, H.B., Jr.: "Numerical Solution for Height and Elongated Hydraulic Fracture Propagation in the Presence of Stress Variations, " SPE/DOE 10849, 1982.
[80] Palmer, I.D., and Carrol, H.B., Jr.: "Numerical Solution for Height of Elongated Hydraulic Fracture, "SPEJ., Vol. 23, Dec. 1983.
[81] Handren, P.J., Dee.J.M. :"Overbalance Perforating and Stimulation Methods for Wells." SPE 26515, 1993 Annual SPE Meeting, Houston. October 3-6, 1993
[82] J.M.Dees et al: "A New Method of Overbalance Perforating and Surging of Resin for Sand Control." SPE 26545
[83] L.Petitjean et al :"Modeling of Fracture Propagation During Overbalanced perforating, " SPE 28560
[84] L.A.Behrmann et al: "Underbalance or Extreme Overbalance, " SPE 31083
[85] M.Dees et al: "Extreme Overbalance Perforating Improves Well Performance, " World Oil, January 1994
[2] T.D．范 高尔夫-拉特著．裂缝油藏工程基础[M]．秦同洛等译．北京：石油工业出版社，1989：231～268．
[3] 潘迎德等．使油井产能最高的射孔参数优选[J]．西南石油学院学报，1990，12(2)：27～36．
[4] 李开泰，黄艾香，黄庆怀．有限元方法及其应用[M]．西安：西安交通大学出版社，1984：107～218．
[5] 李海涛，王永清．预测气井射孔最大无砂负压的方法研究[J]．天然气工业，1999．5
[6] 李海涛，王永清．确定油井射孔最大付压的新方法研究[J]．石油钻采工艺，1997．8
[7] 李海涛，王永清．压裂施工井的射孔优化设计方法[J]．天然气工业，1999．5
[8] Klotz, J. A., Krueger, R. F., Pye, D. S.: "Effect of Perforation Damage on Well Productivity, " J. Pet. Tech.. (Nov. 1974), 1303-1314.
[9] Tariq, S.M.: "Evaluation of Flow Characteristics of Perforation Including Nonlinear Effects Using Finite-Element Method, " Paper SPE 12781 presented at the 1984 California Regional Meeting, Long Beach, CA, April 11-13.
[10] Tariq, S.M., Ichara, M.J. and Ayestaran, L.:" Performance of Perforated Completions in the Presence of Common Heterogeneities: Anisotropy, Laminations, or Natural Fractures, " paper SPE 14320 presented at the 1985 SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, Sept. 22-25.
[11] 唐愉拉，潘迎德：“有限元方法在射孔完井中的应用”，石油学报，1989年，10(3)，48-57。
[12] 唐愉拉，潘迎德，祝渝培：“气井非达西流射孔完井的有限元数值模拟研究”，石油学报，1992年，13(4)，85-96。
[13] L.A.Behrman, B. McDondd:"Underbalance or Extreme overbalance."SPE57390
[14] "modeling of fracture propagation during overbalance perforating" SPE28560
[15] "extreme overbalance perforating extends perforations without vertical growth" SPE37325
[16] "performance Evaluation of Extreme overbalance perforating" A. Ghalambor.etc SPE39459
[17] 杨春盛．“超高压射孔技术的应用”．世界石油工业．vol 4．No．9
[18] 方方编译．“超高压射孔法---对负压射孔法的挑战”．试采技术．Vol16．No．1
[19] Haimson, Fairhurst. "Hydraulic Fracturing in Porous Permeable Materials". J. P. T, July 1969
[20] Bradley. "Failure Of Inclined Boreholes". J. Energy Res. Tech., 1979
[21] C.H.Yew, Y.Li."Fracturing Of a Deviated Wells". SPE16930
[22] C.H.Yew, Y.Li."On Fraemfing Design Of a Deviated Wells". SPE19722
[23] M.M.Hossain, M.K.Rahman, S.S.Rahman."A Comprehensive Monograph for Hydrnulic Fracture Initiation fromD eviated Wellbores under Arbitrary Stress Regimes". SPE54360
[24] 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
[25] 余雄鹰等．“斜井的破裂压力和裂缝方位”．江汉石油学院学报．1994，16(3)：57-60
[26] 黄荣樽．”水力压裂裂缝的起裂和扩展”．石油勘探与开发，1981(5)
[27] 陈勉，陈治喜，黄荣樽．“大斜度井水压裂缝起裂研究”．石油大学学报．1995，19(2)：30-35
[28] 金衍，陈勉等．“大位移井的井壁稳定力学分析”．地质力学学报．1999，5(1)：4-11
[29] 楼一珊等．“大斜度井泥页岩井壁稳定的力学分析”．江汉石油学院学报．1997，19(1)：61-64
[30] 柳贡慧等．“考虑地应力影响下的射孔初始方位角的确定”．石油学报．2001．22(1)：105-108
[31] 张士诚，王世贵等．“限流法压裂射孔方案优化设计”．石油钻采工艺．2000，22(2)：60-63
[32] L.A.Behrmann, K.G..Nolte. "Perforating Requirements foe Fracture Stimulations". SPE 59480, 1999, 228-234
[33] A.A.Daneshy. "Experimental Investigation of Hydraulic Fracturing Through Perforations': Trans AIME. Oct.1973 1201-1206
[34] L.A.Behrmann, J.L.Elbel. "Effect of Perforations On Fracture Initiation". SPE 20661
[35] L.Petitjean, B.Couet. "Modeling of Gas-driven Fracture Propagation for Oil and Gas Well Stimulation". SPE 28084
[36] A.Ghalambor, M.Asadi, M.Azari. "Performance Evaluation of Extreme Overbalanced Perforating." SPE 39459
[37] J.C.Guoynes, W.M.Palmer. J.Grantham. "Extreme-Overbalance Perforating Extends Perforations without Vertical Growth". SPE 37325
[38] L.Petitjean, J.C.Abel, J.H.Schmidt. "Well Productivity Improvement Using Extreme Overbalanced Perforating and Surging - Case Study". SPE 30527
[39] B.Grieser, C.C.Smith, B.Bertrand. "Overbalanced Perforating Field Study in the Tubb Sand, Bravo Dome Field". SPE 37478
[40] J.M.Dees, P.J.Handren. "A New Method of Overbalanced Perforating and Surging of Resin for Sand Control". SPE 26545
[41] P.J.Handran, T.B.Jupp, J.M.Dees. "Overbalance Perforating and Stimulation Method for Wells". SPE 26515
[42] J.B.Crump, M.W.Conway. "Effects of Perforation Entry Friction on Bottomhole Treating Analysis". SPE 15474
[43] D.D.Cramer, B.J.Titan. "The Application of Limited-Entry Techniques in Massive Hydauli Fracturing Treatments", SPE 16189
[44] C.M.Peason, A.J.Bond, M.E.Eck. "Result of Stress-Oriented and Aligned Perforating in Fracturing Deviated Wells". SPE 22836
[45] C.M.Peason, A.J.Bond, M.E.Eck."Optimal Fracture Stimulation of a Moderate Permeability Reservoir, Kuparuk River Unit". SPE 20707
[46] C.Guresbeck, R.E.Collins. "Particle Transport Through Perforations". AIME, Dec. 1982, 857-865
[47] D.L.Lord, S.N.Shah. "Study of Perforation Friction Pressure Empolying a Large-Scale Fracturing Flow Simulator". SPE 28508
[48] C.A.M.Veeken, D.R.Davies. "Limited Communication Between Hydraulic Fracture and (Deviated) Wellbore". SPE 18982
[49] J.D.Willingham, H.C.Tan, L.R.Norman. "Perforation Friction Pressure of Fracturing Fluid Slurries". SPE 25891
[50] C.M.Pearson, E.W.Reinbold. "An Investigation Into the Use of High Pressure Nitrogen Breakdown Treatments Prior to Hydraulic Fracturing". SPE35741
[51] L.L.Lacy. "Comparison of Hydraulic-Fracture Orientation Techniques". SPEFE, March, 1987, 66-76'
[52]J.L.吉德利等：“水力压裂技术新发展”，北京，石油工业出版社，1995。
[53] 蒋建勋，“油气井酸化模型及专家系统”，西南石油学院博士论文，1997．5．
[54] Morgenthaler, L.H.: " Application of a Three-Dimensional Hydranlic Fracturing Simulators for Design of Acid Fracturing Treatment, "SPE25413
[55] 胥耘、黄志强：“拟三维酸压设计软件研究与应用，“石油钻采工艺，1996年(第18卷)第1期．
[56] Perkins, T.K., and Kern, L.R. : "Widths of Hydraulic Fractures, "J.Petroleum Technology, Vol. 13, sept. 1961, 937-949.
[5
[57] Nordgren, R.P.: "Propngation of a vertical Hydraulic Fractures, " Society of Petroleum Engineers Journal, Vol. 12, Aug. 1972, 306-314.
[58] Christianovich, S.A., and Zheltov, Y.R: "Formation of Vertical Fractures by Means of Highly Viscons Liquid, "Proceeding of the fourth World Petroleum Congress, Section Ⅱ , Paper3.
[59] Christianovich, S.A., and Zheltov, Y.P.: "Theoretical Principles of Hydraulic Fracturing of Oil Strate, "Fifth World Petroleum Congress, Section Ⅱ, Paper23.
[60] Geertsma, J., and Deklerk, F.: "A Rapid Method of Pridicting Width and Extent of Hydraulically Induced Fractures, "JPT., Vol. 21, Dec.1969, 1571-1582.
[61] Le-Tirant, P., and Dupuy, M.: "Dimensions of the Fractures Obtained by Hydraulic Fracturing of Oil-Bearing Formations, "evue de linstitut Francais du Petuole, Jan, 1967, 44-98.
[62] Mcleod, H.O., Jr.: "A Simplified Approach to Design of Fracturing Treatments Using High-Viscosity Cross-linked Fluids, "SPE11614
[63] Van Eekelen: "Hydraulic Fracture Geometry: fracture Contain-ment in Layered Formation, "SPEJ., Vol.22, 1982, 341-349.
[64] Advani, S.H., GanggeRao, H.V.S., Chang, H.Y., Komar, C.A., and Khan, S.: "Hydraulic Fracture Modeling for the Eastern Gas Shales Prcject, "Proceeding, DOE Second Eastern Gas Shales symposium, Morgantown, 1978, 84-93.
[65] Advani, S.H., Chang, H.Y., Komar, C.A., and Stonesifer, R.: "Rock Mechanics Aspects of Hydraulic Fracturing in the Devonian Shale, "Presented at the 21th Rock Mechancis Symposium, 1980.
[66] Advani, S.H., and Lee, J.K... "Finite Element Model Simulations Associated with Hydranlic Fracturing, "SPEJ., Vol.22, 1982.
[67] 中国航空研究院主编，应力强度因子手册，科学出版社，1981．
[68] Palmer, I.D., and Craig, H.R. : Modeling Asymmefric Vertical Growth in Elongated Hydraulic Fractures and Application to first MWX Stimulation, SPE/DIE/GRI, 12879, 1984.
[69] 李宾元，裂缝中垂直裂缝高度的讨论，石油钻采工艺，1984年第五期．
[70] Palmer, I.D., and CarrolI, Jr.H.B.: "Numerical Solution for Reight and Elongated Hydraulic Fractures, "SPE/DOE 11627, 1983.
[71] Gdanski, R.D., and Lee, W.S.: "On the Design of Fracture Acidizing Treatments, "SPE 18895, 1989.
[7
[72] Michael J. Economides and Kenneth G. Nolte：油藏增产技术，石油工业出版社，1990．
[73] 王鸿勋，李平．“水力压裂过程中井筒温度的数值计算方法，”石油学报，1987．4
[74] 王鸿勋，张琪，“采油工艺原理”，石油工业出版社，1989．
[75] Cleary, M.P.: "Comprehensive Design Formulae for Hydraulic Fracturing, "Spe 9259, Sept.1980.
[76] Settari, A., and Cleary, M.P.: "Three-Dimensional Simulation of Hydraulic Fuacturing, "JPT., Vol.36 July 1984, 1177-1190.
[77] Settari, A., and Cleary, M.P.: "Development and Testing of a Pseudo-Three Dimensional Model of Hydraulic Fracture Geometry (P3DH), "SPE 10505, 1982.
[78] Cleary, M.P., KecK, R.G., and Mear, M.E., : "Micro computer Models for the Design of Hydraulic Fractures, " SPE/DOE 11628, 1983.
[79] Palmer, I.D., and Carrol, H.B., Jr.: "Numerical Solution for Height and Elongated Hydraulic Fracture Propagation in the Presence of Stress Variations, " SPE/DOE 10849, 1982.
[80] Palmer, I.D., and Carrol, H.B., Jr.: "Numerical Solution for Height of Elongated Hydraulic Fracture, "SPEJ., Vol. 23, Dec. 1983.
[81] Handren, P.J., Dee.J.M. :"Overbalance Perforating and Stimulation Methods for Wells." SPE 26515, 1993 Annual SPE Meeting, Houston. October 3-6, 1993
[82] J.M.Dees et al: "A New Method of Overbalance Perforating and Surging of Resin for Sand Control." SPE 26545
[83] L.Petitjean et al :"Modeling of Fracture Propagation During Overbalanced perforating, " SPE 28560
[84] L.A.Behrmann et al: "Underbalance or Extreme Overbalance, " SPE 31083
[85] M.Dees et al: "Extreme Overbalance Perforating Improves Well Performance, " World Oil, January 1994