水平井渗流理论及产能评价方法研究
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摘要
近些年,水平井技术己经在石油工业得到了迅速发展,日益普及整个石油工业。水平井技术在薄层油藏、天然裂缝油藏、断块油藏、存在气锥和水锥问题的油藏、存在底水锥进的气藏中得到了广泛的应用。另外,水平井在开采重油、水驱以及其它提高采收率措施中也正在发挥越来越重要的作用。目前在水平井渗流理论及产能计算方面,还有许多复杂的问题需要进行深入研究。本文以水平井和对称多分支水平井为研究对象,从油气藏的储层特征和水平井的渗流过程出发,综合运用油气藏地质、油气藏渗流理论、点源函数、Green函数、保角变换、偏微分方程及计算数学等多学科知识,研究出适合于描述水平井渗流与产能计算的理论与方法,主要取得了以下成果:
(1)在源函数基本理论研究的基础上,对水平井不稳定渗流理论以及压力响应特征进行了研究,对比研究了水平井线源模型以及杆源模型之间的差异,分析了各种因素对水平井压力动态曲线的影响;针对存在断层情况下的水平井,通过模型求解及绘制样板曲线,研究了水平井与断层之间的距离及夹角对压力动态的影响;针对对称多分支水平井,研究了分支数、无因次总井筒长度以及分支干扰对水平井压力动态的影响。
(2)对无限导流以及有限导流条件下水平井的流量分布特征进行了研究。在无限导流条件下,当水平平面内不存在断层时,流量分布趋于稳定后呈对称“U”型分布;当水平井与断层之间存在夹角时,流量趋于稳定后呈不对称“U”型分布;对于对称多分支水平井,由于发生了分支间的干扰,流量趋于稳定后呈不对称“U”型分布乃至单调分布,分支越多,干扰越严重;在有限导流条件下,水平井流量分布出现不对称“U”型分布特征,且跟端的井筒流入大于趾端的井筒流入,这是由于跟端的井筒压力最低,生产压差最大,因而井筒流入流量最多。
(3)综合分析了Borisov,Joshi,Giger,Renard-Dupuy水平井产能方程之间的异同。推导出了上下封闭边界中无限大油藏水平井的三维稳态产能解析公式,针对Joshi公式中垂直方向渗流阻力分母上少π的问题,偏心距的处理问题以及简化的二维渗流场与三维渗流场之间的差异问题进行了研究,并提出相应的改进方法。
(4)建立和求解了包含水平气井井身结构参数、近井区高速非达西渗流条件下气体紊流因素以及启动压力梯度效应的水平气井渗流模型,推导出了描述水平气井产能的二项式产能方程。对水平气井和直井的产能进行了对比,定量研究了启动压力梯度以及非达西渗流对水平气井产能的影响。研究结果对于水平气井产能分析的现场应用具有重要的指导意义。
(5)在前人研究的基础上,研究了水平井通用的拟稳态产能方程并对各种影响因素进行了分析。该方程不但以统一的形式描述了均一流量以及均一压力条件下水平井的产能,而且也以统一的形式描述了裂缝以及水平井的产能,同时也统一并扩展了经典的水平井拟稳态产能Babu-Odeh公式以及Kuchuk公式。以此为基础,从复杂的机理出发,推导出了不同于Genliang Guo的裂缝油藏水平井的产能计算公式。结合油藏地质特征,可以研究裂缝长度、裂缝密度以及裂缝方位对裂缝性油藏水平井产能的影响规律。
(6)在对水平井产能理论研究的基础之上,结合伊朗Mis油田实例进行了研究。现场应用结果表明,本文所改进和完善的的公式具有较高的准确性,可以加以推广应用。
Horizontal well technology has got rapid development in recent years and it was popular in whole petroleum industry increasingly. Horizontal well was widely used in thin layer reservoir, naturally fractured reservoir, fault-block reservoir as well as those oil reservoir with gas or water coning and those gas reservoir with bottom water coning. Moreover, horizontal well has played an more and more important role in the exploitation of heavy oil reservoir, water flooding reservoir and those reservoir with other EOR measures. Nowadays, there are many complicated problems need to be researched in the aspects of seepage theory and productivity calculation of horizontal well. This dissertation makes horizontal well and symmetric multibranch horizontal wells as research object, according to reservoir characteristics and the seepage process of horizontal well, using multidisciplinary knowledges comprehensively including reservoir geology, reservoir seepage theory, point source function, Green function, conformal transformation, partial differential equation and computational mathematics et al, then researches theory and method suitable for describing seepage process and productivity calculation of horizontal well. Main research achievements are as follows:
(1) On the basis of source function theory researches, transient seepage theory and pressure response characteristics of horizontal well was researched. The differences between line source model and bar model of horizontal well were compared and the influences of diversified issues on the dynamic pressure curves were researched. For the horizontal well in the reservoir with fault, the distance and angle between horizontal well and fault were researched through model solving and type-curve plotting. For symmetric multibranch horizontal wells, the influences of branch numbers, dimensionless total well-bore length and branch interferences on the pressure response were researched.
(2)Flow distribution characteristics of horizontal well under infinite-conductivity and finite-conductivity conditions were calculated. Under infinite-conductivity conditions, when there is no fault in the reservoir, the flow distribution displays symmetric U-type distribution characteristics when flow is stable. When there is an angle between horizontal well and the fault, the flow distribution displays asymmetric U-type distribution characteristics when flow is stable. For symmetric multibranch horizontal wells, because of branch interferences, the flow distribution displays asymmetric U-type distribution and even monotonic distribution characteristics. Branch interferences increased with branch numbers. Under finite-conductivity conditions, the flow distribution also displays asymmetric U-type distribution characteristics with bigger inflow in the heel end than in the toe end when flow is stable. This is because the wellbore pressure in the heel end is the lowest and it has the biggest pressure drop and wellbore inflow.
(3)Horizontal well productivity equation of Borisov's , Joshi's , Giger's and Renard-Dupuy's formulae were analyzed comprehensively, and then their differences and similarities were compared. 3-D analytical productivity equation of horizontal well in infinite-acting reservoir with sealed boundary was derived. For the problem of Joshi's formula withoutπin the denominator of vertical seepage resistance term and the treatment of eccentricity as well as the differences between 2-D and 3-D seepage flow field, corresponding improvement method was proposed.
(4) Horizontal gas well model considering well-bore structure parameters, turbulent flow under high-speed non-Darcy flow and start-up pressure gradient was established and solved. Binomial deliverability equation describing horizontal gas well was derived. Deliverability of horizontal and vertical well was compared. The influences of start-up pressure gradient and non-Darcy flow on the deliverability of horizontal gas well was researched. The research results had important guiding significance for field application of horizontal gas well productivity analysis.
(5)On the basis of previous researches, universal pseudo-steady state productivity equation of horizontal well was researched and the influences of diversified issues on the productivity were analysed. The universal pseudo-steady state productivity equation not only describes horizontal well productivity under both uniform-flux and uniform-pressure wellbore conditions with unified form, but also describes fracture and horizontal well productivity with unified form. It also included and enlarged classical pseudo-steady state productivity equation of Babu-Odeh's and Kuchuk's. On the basis of universal pseudo-steady state productivity equation, naturally fractured horizontal well productivity equation with complex seepage mechanisms different from Genliang Guo's was deduced. Combined with reservoir geological characteristics, the new formula can be used to research the influences of fracture length, fracture density and fracture azimuth on naturally fractured horizontal well productivity.
(6) On the basis of theory researches for the productivity of horizontal well, corresponding formulae were applied in Mis Oilfield in Iran actually. Field application results indicated that modified and improved horizontal well productivity formulae in the dissertation had good accuracy and they could be popularly applied.
(1)在源函数基本理论研究的基础上,对水平井不稳定渗流理论以及压力响应特征进行了研究,对比研究了水平井线源模型以及杆源模型之间的差异,分析了各种因素对水平井压力动态曲线的影响;针对存在断层情况下的水平井,通过模型求解及绘制样板曲线,研究了水平井与断层之间的距离及夹角对压力动态的影响;针对对称多分支水平井,研究了分支数、无因次总井筒长度以及分支干扰对水平井压力动态的影响。
(2)对无限导流以及有限导流条件下水平井的流量分布特征进行了研究。在无限导流条件下,当水平平面内不存在断层时,流量分布趋于稳定后呈对称“U”型分布;当水平井与断层之间存在夹角时,流量趋于稳定后呈不对称“U”型分布;对于对称多分支水平井,由于发生了分支间的干扰,流量趋于稳定后呈不对称“U”型分布乃至单调分布,分支越多,干扰越严重;在有限导流条件下,水平井流量分布出现不对称“U”型分布特征,且跟端的井筒流入大于趾端的井筒流入,这是由于跟端的井筒压力最低,生产压差最大,因而井筒流入流量最多。
(3)综合分析了Borisov,Joshi,Giger,Renard-Dupuy水平井产能方程之间的异同。推导出了上下封闭边界中无限大油藏水平井的三维稳态产能解析公式,针对Joshi公式中垂直方向渗流阻力分母上少π的问题,偏心距的处理问题以及简化的二维渗流场与三维渗流场之间的差异问题进行了研究,并提出相应的改进方法。
(4)建立和求解了包含水平气井井身结构参数、近井区高速非达西渗流条件下气体紊流因素以及启动压力梯度效应的水平气井渗流模型,推导出了描述水平气井产能的二项式产能方程。对水平气井和直井的产能进行了对比,定量研究了启动压力梯度以及非达西渗流对水平气井产能的影响。研究结果对于水平气井产能分析的现场应用具有重要的指导意义。
(5)在前人研究的基础上,研究了水平井通用的拟稳态产能方程并对各种影响因素进行了分析。该方程不但以统一的形式描述了均一流量以及均一压力条件下水平井的产能,而且也以统一的形式描述了裂缝以及水平井的产能,同时也统一并扩展了经典的水平井拟稳态产能Babu-Odeh公式以及Kuchuk公式。以此为基础,从复杂的机理出发,推导出了不同于Genliang Guo的裂缝油藏水平井的产能计算公式。结合油藏地质特征,可以研究裂缝长度、裂缝密度以及裂缝方位对裂缝性油藏水平井产能的影响规律。
(6)在对水平井产能理论研究的基础之上,结合伊朗Mis油田实例进行了研究。现场应用结果表明,本文所改进和完善的的公式具有较高的准确性,可以加以推广应用。
Horizontal well technology has got rapid development in recent years and it was popular in whole petroleum industry increasingly. Horizontal well was widely used in thin layer reservoir, naturally fractured reservoir, fault-block reservoir as well as those oil reservoir with gas or water coning and those gas reservoir with bottom water coning. Moreover, horizontal well has played an more and more important role in the exploitation of heavy oil reservoir, water flooding reservoir and those reservoir with other EOR measures. Nowadays, there are many complicated problems need to be researched in the aspects of seepage theory and productivity calculation of horizontal well. This dissertation makes horizontal well and symmetric multibranch horizontal wells as research object, according to reservoir characteristics and the seepage process of horizontal well, using multidisciplinary knowledges comprehensively including reservoir geology, reservoir seepage theory, point source function, Green function, conformal transformation, partial differential equation and computational mathematics et al, then researches theory and method suitable for describing seepage process and productivity calculation of horizontal well. Main research achievements are as follows:
(1) On the basis of source function theory researches, transient seepage theory and pressure response characteristics of horizontal well was researched. The differences between line source model and bar model of horizontal well were compared and the influences of diversified issues on the dynamic pressure curves were researched. For the horizontal well in the reservoir with fault, the distance and angle between horizontal well and fault were researched through model solving and type-curve plotting. For symmetric multibranch horizontal wells, the influences of branch numbers, dimensionless total well-bore length and branch interferences on the pressure response were researched.
(2)Flow distribution characteristics of horizontal well under infinite-conductivity and finite-conductivity conditions were calculated. Under infinite-conductivity conditions, when there is no fault in the reservoir, the flow distribution displays symmetric U-type distribution characteristics when flow is stable. When there is an angle between horizontal well and the fault, the flow distribution displays asymmetric U-type distribution characteristics when flow is stable. For symmetric multibranch horizontal wells, because of branch interferences, the flow distribution displays asymmetric U-type distribution and even monotonic distribution characteristics. Branch interferences increased with branch numbers. Under finite-conductivity conditions, the flow distribution also displays asymmetric U-type distribution characteristics with bigger inflow in the heel end than in the toe end when flow is stable. This is because the wellbore pressure in the heel end is the lowest and it has the biggest pressure drop and wellbore inflow.
(3)Horizontal well productivity equation of Borisov's , Joshi's , Giger's and Renard-Dupuy's formulae were analyzed comprehensively, and then their differences and similarities were compared. 3-D analytical productivity equation of horizontal well in infinite-acting reservoir with sealed boundary was derived. For the problem of Joshi's formula withoutπin the denominator of vertical seepage resistance term and the treatment of eccentricity as well as the differences between 2-D and 3-D seepage flow field, corresponding improvement method was proposed.
(4) Horizontal gas well model considering well-bore structure parameters, turbulent flow under high-speed non-Darcy flow and start-up pressure gradient was established and solved. Binomial deliverability equation describing horizontal gas well was derived. Deliverability of horizontal and vertical well was compared. The influences of start-up pressure gradient and non-Darcy flow on the deliverability of horizontal gas well was researched. The research results had important guiding significance for field application of horizontal gas well productivity analysis.
(5)On the basis of previous researches, universal pseudo-steady state productivity equation of horizontal well was researched and the influences of diversified issues on the productivity were analysed. The universal pseudo-steady state productivity equation not only describes horizontal well productivity under both uniform-flux and uniform-pressure wellbore conditions with unified form, but also describes fracture and horizontal well productivity with unified form. It also included and enlarged classical pseudo-steady state productivity equation of Babu-Odeh's and Kuchuk's. On the basis of universal pseudo-steady state productivity equation, naturally fractured horizontal well productivity equation with complex seepage mechanisms different from Genliang Guo's was deduced. Combined with reservoir geological characteristics, the new formula can be used to research the influences of fracture length, fracture density and fracture azimuth on naturally fractured horizontal well productivity.
(6) On the basis of theory researches for the productivity of horizontal well, corresponding formulae were applied in Mis Oilfield in Iran actually. Field application results indicated that modified and improved horizontal well productivity formulae in the dissertation had good accuracy and they could be popularly applied.
引文
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[59]陈伟,杨宇,李允等.无限导流水平井不稳态压力计算模型.油气井测试,2006,15(4):8-10
[60]V.R.Penmatcha,and Khalid Aziz.Comprehensive Reservoir/Wellbore Model for Horizontal Wells.SPE 57194,1999
[61]V.R.Penmatcha,and Khalid Aziz.Effects of Pressure Drop in Horizontal Wells and Optimum Well Length.SPE 57193,1999
[62]周生田,张琪.水平井水平段压降的一个分析模型.石油勘探与开发,1997,24(3):49-52
[63]曾祥林.水平井及分支井产能预测理论研究.西南石油大学博士学位论文,2002:68-76
[64]W.Chen,D.Zhu,A.D.Hill.A Comprehensive Model of Multilateral Well Deliverability.SPE 64751,2000
[65]Liang-biao Ouyang,Khalid Aziz.Steady-state gas flow in pipes.Journal of Petroleum Science and Engineering 14(1996) 137-158
[66]Borisov J P.Oil production using horizontal and multiple devaiation wells,Nedra, Moscow[M].Translated into English by Strauss J,Edited by Joshi S D.Philips Petroleum CO.The R&D Library Translation,Bartlesville,Okahoma,1984
[67]Joshi S D.Augmentation of well productivity using slant and horizontal wells.SPE 15375,1988
[68]Giger F M,Resis L H,Jourdan A P.The reservoir engineering aspects of horizontal drilling.SPE 13024,1984
[69]Renand G,Dupuy J M.Formation damage effects on horizontal well flow efficiency.SPE19414,1991
[70]Elgaghah S A,Osisanya S O,and Tiab D.A Simple Productivity Equation for Horizontal Wells Based on Drainage Area Concept.SPE 35713,1996
[71]陈元千.水平井产量公式的推导与对比.新疆石油地质,2008,29(1):68-71
[72]窦宏恩.水平井与分支水平井产能计算的几个问题.石油钻采工艺,1999,21(6):56-59
[73]Joshi,S.D.A Review of Horizontal Well and Drainhole Technology.SPE 16868,1987
[74]郭肖,伍勇.启动压力梯度和应力敏感效应对低渗透气藏水平井产能的影响.石油与天然气地质,2007,28(4):539-543
[75]李晓平,刘启国,赵必荣.水平气井产能影响因素分析.天然气工业,1998,18(2):53-56
[76]范子菲.裂缝性气藏水平井稳态解公式研究.石油勘探与开发,1997,24(5):67-71
[77]张黔川,吕涛,吕劲.气藏水平井非达西流动二项式产能试井公式.天然气工业,2004,24(10):83-85
[78]高海红,程林松,冯儒勇.考虑启动压力梯度的低渗气藏水平井产能计算.天然气工业,2008,28(7):75-77
[79]吴晓东,安永生,李凡华.考虑储层伤害影响的水平气井产能.天然气工业,2008,28(7):78-80
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[81]刘想平,气藏水平井稳态产能计算新模型.天然气工业,1998,18(1):37-40
[82]Travis Billiter,John Lee and Robert Chase.Dimensionless Inflow-Performance-Relationship Curve for Unfractured Horizontal Gas Wells.SPE 72361,2001
[83]Robert W.Chase,Cassandra R.Steffy.Predicting Horizontal Gas Well Deliverability Using Dimensionless IPR Curves.SPE 91101,2004
[84]范子菲.底水驱动油藏水平井产能公式研究.石油勘探与开发,1993,20(1):71-75
[85]范子菲,林志芳.底水驱动油藏水平井临界产量公式及其变化规律研究.石油勘探与开发,1994,21(1):65-70
[86]陈志海.底水油藏的水平井开发.石油与天然气地质,2000,21(3):214-219
[87]吕爱民,姚军,武兵厂.底水油藏水平井最优垂向位置研究.石油钻探技术,2007,35(1):66-68
[88]程林松,李春兰,郎兆新等.分支水平井产能的研究.石油学报,1995,16(2):49-55
[89]程林松,李春兰,马志远.气藏多分支水平井产能的计算方法.石油学报,1998,19(4):69-72
[90]王晓冬,于国栋,李治平.复杂分支水平井产能研究.石油勘探与开发,2006,33(6):729-733
[91]周生田,张琪,李明忠等.水平井变质量流研究进展.力学进展,2002,32(1):119-126
[92]Babu D K and Odeh A S.Productivity of a Horizontal Well Appendices A and B.SPE18334,1988
[93]Goode P A,Kuehuk F J.Inflow Performance of Horizontal Wells.SPE21460,1991
[94]Economides M J,Brand C W,Frick T P.Well Configurations in Anisotropic Reservoirs.SPE 27980,1996
[95]Dikken,Ben J.,Pressure Drop in Horizontal Wells and Its Effect on Production Performance.SPE 19824,1990
[96]万仁溥等编译.水平井开采技术.北京:石油工业出版社,1995:594-625
[97]关德.海上油田水平井开采油藏工程优化研究.西南石油大学博士学位论文,2002
[98]蒋廷学,单文文,杨艳丽.垂直裂缝井稳态产能的计算.石油勘探与开发,2001,28(2):61-63
[99]范子菲,方宏长.裂缝性油藏水平井稳态解产能公式研究.石油勘探与开发,1996,23(3):52-63
[100]James R.Gilman,Hosssein Kazemi.Improvements in Simulation of Naturally Fractured Reservoirs.SPE 10511,1983
[101]Mutalik,P.N.,Godbole,S.P.,and Joshi,S.D.,Effect Of Drainage Area Shapes On The Productivity Of Horizontal Wells.SPE 18301,1988
[102]Genliang Guo and R.D.Evans.Inflow performance of a horizontal well intersecting natural fractures.SPE 25501,1993
[103]张继芬,王再山,高文君.(拟)稳定流斜直井产能预测方法.大庆石油地质与开发,1995,14(4):69-74
[104]郭世慧,王晓冬.大斜度井两种计算产能和表皮系数方法的对比与讨论.油气井测试,2008,17(4):21-23
[105]Cinco-Ley Heber,Ramey Jr,Miller H J.Pseudo-skin Factors for Partially-Penetrating Directionally-Drilled Wells.SPE 5589,1975
[106]Besson J.Performance of Slanted and Horizontal Wells on an Anisotropic Medium.SPE 20965,1990
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[12]Kuchuk F J,Goode P A,and Wilkinson D J.Pressure-transient Bahavior of Horizontal Wells with and Without Gas Gap or Aquifer.SPE17413,1991
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[15]Leif Larsen.Pressure-Transient Behavior of Multibranched Wells in Layered Reservoirs.SPE 60911,2000
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[18]Ogunsanya B O,Oetama T P,and Lea J F et al.A Coupled Model for Analyzing Transient Pressure Behavior of Horizontal Drainholes.SPE 94331,2005
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[24]V.R.Penmatcha,and Khalid Aziz.Effects of Pressure Drop in Horizontal Wells and Optimum Well Length.SPE 57193,1999
[25]W.Chen,D.Zhu,A.D.Hill.A Comprehensive Model of Multilateral Well Deliverability.SPE 64751,2000
[26]Travis Billiter,John Lee,and Robert Chase.Dimensionless Inflow-Performance-Relationship Curve for Unfractured Horizontal Gas Wells.SPE 72361,2001
[27]D.Zhu,A.D.Hill,W.R.Landrum.Evaluation of Crossflow Effects in Multilateral Wells.SPE 75250,2002
[28]Turhan Yildiz.Multilateral Pressure-Transient Response.SPE 83631,2003
[29]R.Kamkom and D.Zhu.Evaluation of two-phase IPR correlations for horizontal wells,SPE 93986,2005
[30]H.-Y.Chen,N.Asaad,SPE.Horizontal-Well Productivity Equations With Both Uniform-Flux and Uniform-Pressure Wellbore Modes.SPE 97190,2005
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[43]王晓冬,于国栋,李治平.复杂分支水平井产能研究.石油勘探与开发,2006,33(6):729-733
[44]王明,朱维耀,宋考平.非牛顿流体多分支水平井产能模型及数值模拟.大庆石油学院学报,2006,30(5):38-41
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[47]Ozken Z,Raghavan R.New Solution for Well Test Analysis Problems:part Ⅰ-Analytical Considerration.SPE 18615,1991:359-368
[48]Erdal Ozkan.Supplement to SPE 18615,NewSolutions for Well-Test-Analysis Problems:Part 1-Analytical Considerations.SPE 23593,1991
[49]Ozken Z,Raghavan R.New Solution for Well Test Analysis Problems:Part Ⅱ-Computation Considerration and Applications.SPE 18616,1991:369-377
[50]Ozken Z,Raghavan R.New Solution for Well Test Analysis Problems:Part Ⅲ-Additional Algorithms.SPE28424,1994
[51]吴小庆,黎薰,白东华.各向异性油藏水平井渗流模型的体源精确解.四川大学学报(自然科学版),1995,32(2):109-116
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[53]X.Y.Kong,X.Z.Xu.Pressure Transient Analysis for Horizontal Well and Multi-Branched Horizontal Wells.SPE 37069,1996
[54]孔祥言,徐献芝,卢德唐.分支水平井的样板曲线和试井分析.石油学报,1997,18(3):98-103
[55]黄世军,程林松,李秀生等.多分支水平井压力系统分析模型.石油学报,2003,24(6):81-85
[56]于国栋,王晓冬,魏奎生.分支水平井不稳定压力和产量的计算.大庆石油学院学报,2004,28(1):21-24
[57]段永刚,陈伟,黄天虎等.多分支井渗流和不稳定压力特征分析.西安石油大学学报(自然科学版),2007,22(2):136-138
[58]王德山,李兆敏,聂立新.水平分支井试井解释方法研究.西南石油大学学报,2007,29(1):70-74
[59]陈伟,杨宇,李允等.无限导流水平井不稳态压力计算模型.油气井测试,2006,15(4):8-10
[60]V.R.Penmatcha,and Khalid Aziz.Comprehensive Reservoir/Wellbore Model for Horizontal Wells.SPE 57194,1999
[61]V.R.Penmatcha,and Khalid Aziz.Effects of Pressure Drop in Horizontal Wells and Optimum Well Length.SPE 57193,1999
[62]周生田,张琪.水平井水平段压降的一个分析模型.石油勘探与开发,1997,24(3):49-52
[63]曾祥林.水平井及分支井产能预测理论研究.西南石油大学博士学位论文,2002:68-76
[64]W.Chen,D.Zhu,A.D.Hill.A Comprehensive Model of Multilateral Well Deliverability.SPE 64751,2000
[65]Liang-biao Ouyang,Khalid Aziz.Steady-state gas flow in pipes.Journal of Petroleum Science and Engineering 14(1996) 137-158
[66]Borisov J P.Oil production using horizontal and multiple devaiation wells,Nedra, Moscow[M].Translated into English by Strauss J,Edited by Joshi S D.Philips Petroleum CO.The R&D Library Translation,Bartlesville,Okahoma,1984
[67]Joshi S D.Augmentation of well productivity using slant and horizontal wells.SPE 15375,1988
[68]Giger F M,Resis L H,Jourdan A P.The reservoir engineering aspects of horizontal drilling.SPE 13024,1984
[69]Renand G,Dupuy J M.Formation damage effects on horizontal well flow efficiency.SPE19414,1991
[70]Elgaghah S A,Osisanya S O,and Tiab D.A Simple Productivity Equation for Horizontal Wells Based on Drainage Area Concept.SPE 35713,1996
[71]陈元千.水平井产量公式的推导与对比.新疆石油地质,2008,29(1):68-71
[72]窦宏恩.水平井与分支水平井产能计算的几个问题.石油钻采工艺,1999,21(6):56-59
[73]Joshi,S.D.A Review of Horizontal Well and Drainhole Technology.SPE 16868,1987
[74]郭肖,伍勇.启动压力梯度和应力敏感效应对低渗透气藏水平井产能的影响.石油与天然气地质,2007,28(4):539-543
[75]李晓平,刘启国,赵必荣.水平气井产能影响因素分析.天然气工业,1998,18(2):53-56
[76]范子菲.裂缝性气藏水平井稳态解公式研究.石油勘探与开发,1997,24(5):67-71
[77]张黔川,吕涛,吕劲.气藏水平井非达西流动二项式产能试井公式.天然气工业,2004,24(10):83-85
[78]高海红,程林松,冯儒勇.考虑启动压力梯度的低渗气藏水平井产能计算.天然气工业,2008,28(7):75-77
[79]吴晓东,安永生,李凡华.考虑储层伤害影响的水平气井产能.天然气工业,2008,28(7):78-80
[80]杨小松,刘传喜,严谨等.鱼骨型多分支水平气井产能规律研究.石油学报,2008,29(5):727-733
[81]刘想平,气藏水平井稳态产能计算新模型.天然气工业,1998,18(1):37-40
[82]Travis Billiter,John Lee and Robert Chase.Dimensionless Inflow-Performance-Relationship Curve for Unfractured Horizontal Gas Wells.SPE 72361,2001
[83]Robert W.Chase,Cassandra R.Steffy.Predicting Horizontal Gas Well Deliverability Using Dimensionless IPR Curves.SPE 91101,2004
[84]范子菲.底水驱动油藏水平井产能公式研究.石油勘探与开发,1993,20(1):71-75
[85]范子菲,林志芳.底水驱动油藏水平井临界产量公式及其变化规律研究.石油勘探与开发,1994,21(1):65-70
[86]陈志海.底水油藏的水平井开发.石油与天然气地质,2000,21(3):214-219
[87]吕爱民,姚军,武兵厂.底水油藏水平井最优垂向位置研究.石油钻探技术,2007,35(1):66-68
[88]程林松,李春兰,郎兆新等.分支水平井产能的研究.石油学报,1995,16(2):49-55
[89]程林松,李春兰,马志远.气藏多分支水平井产能的计算方法.石油学报,1998,19(4):69-72
[90]王晓冬,于国栋,李治平.复杂分支水平井产能研究.石油勘探与开发,2006,33(6):729-733
[91]周生田,张琪,李明忠等.水平井变质量流研究进展.力学进展,2002,32(1):119-126
[92]Babu D K and Odeh A S.Productivity of a Horizontal Well Appendices A and B.SPE18334,1988
[93]Goode P A,Kuehuk F J.Inflow Performance of Horizontal Wells.SPE21460,1991
[94]Economides M J,Brand C W,Frick T P.Well Configurations in Anisotropic Reservoirs.SPE 27980,1996
[95]Dikken,Ben J.,Pressure Drop in Horizontal Wells and Its Effect on Production Performance.SPE 19824,1990
[96]万仁溥等编译.水平井开采技术.北京:石油工业出版社,1995:594-625
[97]关德.海上油田水平井开采油藏工程优化研究.西南石油大学博士学位论文,2002
[98]蒋廷学,单文文,杨艳丽.垂直裂缝井稳态产能的计算.石油勘探与开发,2001,28(2):61-63
[99]范子菲,方宏长.裂缝性油藏水平井稳态解产能公式研究.石油勘探与开发,1996,23(3):52-63
[100]James R.Gilman,Hosssein Kazemi.Improvements in Simulation of Naturally Fractured Reservoirs.SPE 10511,1983
[101]Mutalik,P.N.,Godbole,S.P.,and Joshi,S.D.,Effect Of Drainage Area Shapes On The Productivity Of Horizontal Wells.SPE 18301,1988
[102]Genliang Guo and R.D.Evans.Inflow performance of a horizontal well intersecting natural fractures.SPE 25501,1993
[103]张继芬,王再山,高文君.(拟)稳定流斜直井产能预测方法.大庆石油地质与开发,1995,14(4):69-74
[104]郭世慧,王晓冬.大斜度井两种计算产能和表皮系数方法的对比与讨论.油气井测试,2008,17(4):21-23
[105]Cinco-Ley Heber,Ramey Jr,Miller H J.Pseudo-skin Factors for Partially-Penetrating Directionally-Drilled Wells.SPE 5589,1975
[106]Besson J.Performance of Slanted and Horizontal Wells on an Anisotropic Medium.SPE 20965,1990