各向异性储层渗流理论研究与应用
|
摘要
岩石在沉积过程中由于岩石颗粒的取向性及天然裂缝的存在,造成储层的各向异性,对于各向异性储层,如果井网部署与各向异性匹配不合理,注入水沿渗透率主轴方向锥进,势必影响油田的开发效果,甚至影响油田的最终采收率,因此研究各向异性储层相关参数的识别理论及对油田开发的影响具有重要的实际意义。本论文从各向异性储层渗流机理出发,系统地研究了平面各向异性和垂向各向异性储层中直井和垂直裂缝井的渗流理论,以及它们在油田开发中的应用。
首先利用坐标转换及镜像反演理论,推导了单一直井直线边界、平行直线边界的定常渗流的压力分布公式,在此基础上研究了五点法井网、九点法井网定常渗流问题,推导了压力分布方程,分析了等势线及流线的特点,为各向异性储层井网优化提供了理论基础。
文中研究了平面各向异性储层不定常渗流问题,建立了平面各向异性储层交叉直线边界中一口直井渗流的数学模型,利用镜像反演、Laplace变换、Fouier变换及其反变换推导了不同边界条件下直井的Laplace空间解析解,考虑井储和表皮的影响,分析了曲线特征及影响因素的敏感性曲线;并运用影响椭圆及Duhamel叠加原理,推导了平面各向异性储层中垂直裂缝井的压力分布方程,考虑了水力裂缝与主渗透率轴成一定角度对压力及产能的影响,为垂直裂缝井的产能评价及试井分析提供依据。
关于垂向各向异性储层,在文献部分射开直井点源(汇)解的基础上,求解了不同边界条件下部分射开直井的有限井径解,并利用Duhamel叠加原理把该理论推广到部分压开垂直裂缝井中,考虑了定压边界、弱补给边界的情况以及井储和表皮的影响,分析了典型曲线特征及其影响因素,此外,为方便试井应用,对各流动期进行渐近分析。
最后,通过实例给出运用不定常渗流理论确定主渗率方向及各向异性参数的理论和方法,并利用流管模型及矢量井网的思想,推导了各向异性储层开发的动态分析理论及井网优化理论,并借助于数值模型研究了更复杂储层各向异性的井网优化问题。
通过本文的研究,不但完善了各向异性储层参数及渗透率主轴方向的识别方法,为油藏描述和数值模拟提供可靠参数,而且深入分析了各向异性储层的动态分析理论及井网优化理论,为各向异性储层的合理、高效开发提供了理论依据。
Anisotropy is generally formed as result of orientation of asymmetric grains making upthe solid matrix of porous media and naturally fracture in porous media,Water injected maycause fingering and impact on recovery if anisotropy is not taken into account when planningwell pattern. Consequently, it is quite important to research on the theory of recognizing therelated anisotropic parameters and analyzing performance of reservoir. For this reason, thispaper completely study on theory of flowing through anisotropic media, as well as applicationduring field development.
First of all, this paper derives pressure expressions of stable state about vertical well inanisotropic media with various boundary. Based on this, Formulae of pressure distributionfor five-spot pattern and nine-spot pattern have been established, the characters of isobariccontours and streamline are analyzed, and this equips optimum of well pattern with theoreticfoundation.
Second, transient flow for vertical well and fractural well in porous media with arealanisotropy has been researched in this paper. The analytic solution for vertical well andsemi-analytic solution for vertical fractural well is developed by using image inversion,superposition principle, Laplace transformation, Fourier transformation, as well as theirinverse transforms, and storage and skin are taken into account. For vertical fractural well,influence of pressure and productivity is studied when the orientation of artificial fractureisn't in accordance with the direction of major permeability, it is fundamental to evaluatepotential and analyze well test data.
For porous media with vertical anisotropy, this paper solves finite well-bore radiussolution based on point source (sink) solution, and this method is expanded to verticalfractural well with various boundary by using superposition principle. The feature of typicalcurves and related factors are investigated, and asymptotic expressions are made to interpretwell test data for various flow period during well test analysis.
At last, this paper illustrates the identification of major permeability direction and relatedparameters of anisotropic medium, and the theory of dynamic analysis and optimization ofwell pattern are investigate by drawing support from stream tube model and spirit of vectorwell pattern. The numerical simulation must be used for complicate anisotropy.
This paper not only improves the method of determining anisotropic parameters anddirection of major permeability, which are necessary for reservoir description and numericalsimulation, but also provides theory of dynamic analysis and optimization of well pattern, andthese are foundation to develop anisotropic reservoir reasonably and economically.
首先利用坐标转换及镜像反演理论,推导了单一直井直线边界、平行直线边界的定常渗流的压力分布公式,在此基础上研究了五点法井网、九点法井网定常渗流问题,推导了压力分布方程,分析了等势线及流线的特点,为各向异性储层井网优化提供了理论基础。
文中研究了平面各向异性储层不定常渗流问题,建立了平面各向异性储层交叉直线边界中一口直井渗流的数学模型,利用镜像反演、Laplace变换、Fouier变换及其反变换推导了不同边界条件下直井的Laplace空间解析解,考虑井储和表皮的影响,分析了曲线特征及影响因素的敏感性曲线;并运用影响椭圆及Duhamel叠加原理,推导了平面各向异性储层中垂直裂缝井的压力分布方程,考虑了水力裂缝与主渗透率轴成一定角度对压力及产能的影响,为垂直裂缝井的产能评价及试井分析提供依据。
关于垂向各向异性储层,在文献部分射开直井点源(汇)解的基础上,求解了不同边界条件下部分射开直井的有限井径解,并利用Duhamel叠加原理把该理论推广到部分压开垂直裂缝井中,考虑了定压边界、弱补给边界的情况以及井储和表皮的影响,分析了典型曲线特征及其影响因素,此外,为方便试井应用,对各流动期进行渐近分析。
最后,通过实例给出运用不定常渗流理论确定主渗率方向及各向异性参数的理论和方法,并利用流管模型及矢量井网的思想,推导了各向异性储层开发的动态分析理论及井网优化理论,并借助于数值模型研究了更复杂储层各向异性的井网优化问题。
通过本文的研究,不但完善了各向异性储层参数及渗透率主轴方向的识别方法,为油藏描述和数值模拟提供可靠参数,而且深入分析了各向异性储层的动态分析理论及井网优化理论,为各向异性储层的合理、高效开发提供了理论依据。
Anisotropy is generally formed as result of orientation of asymmetric grains making upthe solid matrix of porous media and naturally fracture in porous media,Water injected maycause fingering and impact on recovery if anisotropy is not taken into account when planningwell pattern. Consequently, it is quite important to research on the theory of recognizing therelated anisotropic parameters and analyzing performance of reservoir. For this reason, thispaper completely study on theory of flowing through anisotropic media, as well as applicationduring field development.
First of all, this paper derives pressure expressions of stable state about vertical well inanisotropic media with various boundary. Based on this, Formulae of pressure distributionfor five-spot pattern and nine-spot pattern have been established, the characters of isobariccontours and streamline are analyzed, and this equips optimum of well pattern with theoreticfoundation.
Second, transient flow for vertical well and fractural well in porous media with arealanisotropy has been researched in this paper. The analytic solution for vertical well andsemi-analytic solution for vertical fractural well is developed by using image inversion,superposition principle, Laplace transformation, Fourier transformation, as well as theirinverse transforms, and storage and skin are taken into account. For vertical fractural well,influence of pressure and productivity is studied when the orientation of artificial fractureisn't in accordance with the direction of major permeability, it is fundamental to evaluatepotential and analyze well test data.
For porous media with vertical anisotropy, this paper solves finite well-bore radiussolution based on point source (sink) solution, and this method is expanded to verticalfractural well with various boundary by using superposition principle. The feature of typicalcurves and related factors are investigated, and asymptotic expressions are made to interpretwell test data for various flow period during well test analysis.
At last, this paper illustrates the identification of major permeability direction and relatedparameters of anisotropic medium, and the theory of dynamic analysis and optimization ofwell pattern are investigate by drawing support from stream tube model and spirit of vectorwell pattern. The numerical simulation must be used for complicate anisotropy.
This paper not only improves the method of determining anisotropic parameters anddirection of major permeability, which are necessary for reservoir description and numericalsimulation, but also provides theory of dynamic analysis and optimization of well pattern, andthese are foundation to develop anisotropic reservoir reasonably and economically.
引文
[1] M. Muskat, The Flow of Homogeneous Fluids Through Porous Media, McGraw-Hill Book Co., Inc., New York,1937
[2] Van Everdinger,A.F.el al, Application of the Laplace Transformation to Flow Problems in Reservoirs,Trans.,AIME(1949)186:305
[3] Horner D R., Pressure Buildup in Wells, Proc Third World Pet Cong, Leiden,1951
[4] Carslaw H.S. and Jaeger, Conduction of Heat In Solids, Oxford University Press, Oxford, 1959
[5] K.H. Coats and M.R. Tek, etc, Unsteady-state Liquid Flow Through Porous Media Having Elliptic Boundaries, SPE2050,1959
[6] Prats,M. etc, Effect of Vertical Fracture on Reservoir Behavior-Incompressible Fluid Case, Paper Presented as 35th Annual Fall Meeting of SPE,1960
[7] R. E. Collins, Flow of Fluids through Porous Material, Reinhold Publishing Corp. New York, 1961.
[8] M. Mortada and G.W Nabor, an Approximate Method for Determining Areal Sweep Efficiency and Flow Capacity in Formations with Anisotropic Permeability, SPE16, 1961
[9] Warren,J.E. and Root, P.J., The Behavior of Naturally Fractured Reservoirs, SPEJ, Sept. 1963
[10] I.S. Papadopulos,No-steady Flow to A Well in an infinite Anisotropic Aquifer, Symposium international Association Science Hydrology, Dubrovnik Yugoslavia, 1965
[11] M.W. Clegg and M. Mills,A Study of Behavior of Partially Penetrating wells, SPE2054, 1969
[12] A.C. Overpeck and W.R. Holden, Well Imaging and Fault Detection in Anisotropic reservoirs, Spe2731, 1970
[13] Stehfest H, Numerical Inversion of Laplace Transform, Comm.ACM.1970;( 1) :47-48
[14] Abramowitz, M.,and Stegun,I.A., Handbook of Mathematical Function, Dover Publications, New York(1972):1019-1030
[15] A.C. Grigarden and H.J. Ramey, The Use of Source and Green's Functions in Solving Unsteady-Flow Problems in reservoirs, SPE3818, 1973
[16] A.C. Grigarden and H.J. Ramey, Unsteady Pressure Distribution Created by a Single Horizontal Fracture, and Partial Penetration, or Restricted Entry, SPE3819, 1974
[17] R.K. Prasad and H.J. Gruy, Pressure Transient Analysis in the Presence of Two Intersecting Boundaries,SPE4560,1975
[18] K.S. Crump, Numerical Inversion of Laplace Transforms Using a Fourier series Approximation, J. ACM., 23(1),1976
[19] Gringarten, A. C. et al,Unsteady-State Pressure Distributions Created by a Well with a Single Infinite-Conductivity Vertical Fracture, SPEJ (Aug. 1978)347-360.
[20] Fikri Kucuk and William E. Brigham, Transient Flow in Elliptical Systems, SPE 7488, DEC. 1979
[21] I.M. Buhidma and R. Raghavan, Transient Pressure of Partially Penetrating Wells Subject to Bottom-Water Drive,SPE8143,1980
[22] Brent W. Hale and J.F. Evers, Elliptical Flow Equations For Vertically Fractured Gas Wells, SPE 8943, 1980
[23] Walter Rose, Permeability Anisotropy in low Permeability Formations, SPE10810,1982
[24] S.T.J Brockenbrough, A New Analytlc Solutlon for Finite Condutivity Verbical Fractures With Real Time and Laplace Space Parameter Estimation,SPE 12013,1983
[25] J. Gcodrich, Time Intervals for Spherical Flow As a function of Anisotropy and Well Completion Interval, SPE11812, 1983
[26] F. Rodriguez and H. Cinco-Ley, Partially Penetrating Vertical Fracture: Pressure Transient Behavior of a Finite-Conductivity Fracture, SPE13057, 1984
[27] S.T. obub and T. Ertekin, A composite System Solution in Elliptical Flow Geometry, SPE13078,1984
[28] F.J. Kuchuk and P.A. Kirwan, New Skin and Well bore Storage Type Curves for Partially Penetrated Wells, SPE11676, 1987
[29] P.A. Goode and R.K.M. Thambynayagam, Pressure Drawdown and Buildup Analysis of Horizontal Wells in Anisotropic Media, SPE14250, 1987
[30]E. Ozkan, Performance of Horizontal Wells, PHD Dissertation, 1988
[31]Chen,H.Y., Well Behavoir in Naturally Fractures Reservoirs, PhD Dissertation, Texas College Station (Aug, 1990)
[32] Poston S. and Raghavan, An Application of the Product Solution Principle for Instantaneous Source and Green's Function in the Laplace Domain.,SPE Formation Evalution,June(1991), 161-168
[33] G.J. Lee, The Effects of Permeability Anisotropy on The Eveluation and Design of Hydraulic Fracture Treatment and Well performance, SPE21501,1991
[34] Goode P.A. and Wilkinson, Inflow Performance of Partially Open Horizontal Wells, JPT(August 1991)983~987
[35] J.J. Pop, D.J. Wilkinson and J.K. Jonas, Vertical Interference Testing With a Wire line-Conveyed Straddle-Packer Tool, SPE26481, 1993
[36] Raghavan,Well Test Analysis, P T R Prentice Hall Englewood Cliffs,New Jersey,1993
[37] Yizhu Liao and W.J. Lee, Depth of Investigation for Elliptical Flow Problems and Its Applications to Hydraulically Fractured Wells, SPE27908, 1994
[38] F.J. Kuchuk and Y. Dave, Interpretation of Wire-line Formation Tester Packer and Probe Pressures, SPE28404, 1994
[39] Hantush, Non-Steady Green's Functions for an Infinite Strip of Leaky Aquifer, Trans.,Aug.(1995)Vol.36,101
[40] F.J. kuchuk, etc, Multilayer Reservoir Testing with Multi-probe Wire-line Formation Tester, SPE36176, 1996
[41] M.E. Vellegas, R.A. Wattenbarger, etc, Performance of Longitudinally Fractured Horizontal Wells in High-Permeability Anisotropic Formations, SPE36453, 1996
[42] M. J. Economides, C.W. Brand and T.P. Frick, Well Configuration in Anisotropic Reservoirs, SPE27980, 1996
[43] L. Zhang and M.B. Dusseault, Anisotropic Permeability Estimation by Horizontal Well Tests, SPE37071, 1996
[44] T. Yildiz and E. Ozkan, Influence of Areal Anisotropy on Horizontal Well Performance, SPE38671, 1997
[45] F.J. Kuchuk, Interval Pressure Transient Testing with MDT Packer-Probe Module in Horizontal Wells, SPE39523, 1998
[46] B. Guo, D.S. Schechter, etc, Use of Single-Well Test Data for Estimating Permeability Anisotropy of the Naturally Fractured Spraberry Trend Area Reservoirs,SPE39807,1998
[47] F.J. Kuchuk,A New Method for Determination of Reservoir Pressure,SPE56418,1999
[48] J.P. Spivey and W.J. Lee, Estimating the Pressure-Transient Response for a Horizontal or a Hydraulically Fractured Well at an Arbitrary Orientation in an Anisotropic Reservoir, SPE58119, 1999
[49] F.J. Kuchuk, F. Halford, and M. Zeybek, the Use of Vertical Interference Testing to Improve Reservoir Characterization, SPE87236, 2000
[50] C.S. Kabir, etc, Understanding Coning Performance in a High-Anisotropy Reservoir: The Burgan Reservoir Case Study, SPE62993, 2000
[51] D.T. Hidayati and Her-Yuan Chen, The Reliability of Permeability-Anisotropy Estimation From Interference Testing of Naturally Fractured Reservoirs, SPE59011, 2000
[52] S.B. Cline and D. Tiab, Studies in Vertical and Horizontal Well-Flow Behavior in Cases of Permeability Anisotropy, SPE71085, 2001
[53] M. Al-Khamis, E. Ozkan, etc, Interference Testing with Horizontal Observation Wells, SPE71581, 2001
[54] M. Onur and P.S. Hegeman, A New Method for Determination of Reservoir Pressure, SPE77343, 2002
[55] M. Zeybek and F.J. Kuchuk, A New Method for Determination of Reservoir Pressure, SPE78506, 2002
[56] B. Guira and D. Tiab, Pressure Behavior of A Well in Anisotropic Reservoir, SPE76772, 2002
[57] H.Y. Chen and L.W. Teufel, Timing and Distance of Well Interference in Anisotropic Reservoirs, SPE77455, 2002
[58] H.Y. Chen and L.W. Teufel, A Quick Method to Determine Permeability-Anisotropy Orientation From Interference Testing, SPE84090, 2003
[59] 吴望一,流体力学上册,北京: 北京大学出版社,1982
[60] J. 贝尔著,李竞生,陈崇希译,多孔介质流体动力学,北京:中国建筑工业出版社,1983。
[61] 陈忠祥,袁益让,姜礼尚,二相平面渗流问题的不变流管解法及其理论分析,应用数学和力学,7(7),1986
[62] 刘慈群,杨玠,垂直裂缝井的压力动态分析方法,试采技术,1989,11
[63] 刘慈群,杨玠,双重孔隙介质中有限导流垂直裂缝井的试井分析方法,试采技术,1990,11(3)
[64] 刘慈群,在双重介质中有限导流垂直裂缝井的非牛顿流体试井分析方法,石油学报,1990,11(4)
[65] G.鲍尔.威尔海特,刘民中,唐金华,等译. 注水, 北京:石油工业出版社,1992
[66]钱伟长:《应用数学》.上海.安徽科学技术出版社,1993
[67]李义昌,李宾亭,等,地下水动力学,北京:中国矿业大学出版社,1995
[68] 刘慈群,水平井产能及试井分析公式, 油气井测试, 1995,4(1),45～49
[69] 刘慈群,分形油藏非牛顿流体渗流压力动态[J] ,试采技术,1996,17(1),9～12
[70] 刘慈群,单相和两相流体多维渗流问题[A],见周连第编:第十届全国水动力学学术会议论文集[C],北京海洋工业出版社,1996,439～445。
[71] 刘曰武,刘慈群,渗流力学进展.北京:石油工业出版社,1996
[72] 翟云芳,刘义坤,刘振宇,等,渗流力学.北京:石油工业出版社,1996
[73] 聂立新,黄炳家等,各向异性天然裂缝油藏裂缝方位的确定,石油大学学报(自然科学版),21(6),1997,39～41。
[74] 刘曰武,刘慈群,部分压开的垂直裂缝井试井分析新方法,油气井测试,1997,6(2),13～18。
[75] 李凡华、刘慈群,分形油藏无限导流垂直裂缝井的非牛顿渗流规律,石油学报,1997,18(4),65～69。
[76] 刘曰武、刘慈群:“多层油藏有限导流垂直裂缝井试井方法研究”,油气井测试,1997,6(3),18～24
[77] 李凡华,刘慈群,分形油藏有限导流垂直裂缝井的非牛顿渗流规律,天然气工业,1997,17(5),27～31
[78] 宋付权、刘慈群,低渗透油藏中水平井的非牛顿幂律流体不稳定渗流的研究,油气井测试,1997,9(1),1～7
[79] 王晓冬,水平井不定常渗流研究:[博士学位论文].北京:中国科学院渗流流体力学所,1998
[80] 宋付权,刘慈群,低渗透垂直补给油藏中水平井流态分析,石油勘探与开发,1998,25(4),35～40
[81] 李传亮,张茂林,等,双重各向异性介质的驱替特征及注水开发井网部署研究,大庆石油地质与开发,1999,18(6),29～31
[82] 孔祥言,高等渗流力学.安徽:中国科学技术大学出版社,1999
[83] 刘月田,葛家理,各向异性圆形地层渗流的解析解,石油大学学报,2000,24(2),40～43
[84] 邓英尔,刘慈群,考虑吸渗的双重介质中垂直裂缝井两相渗流,重庆大学学报,2000(23)
[85] 邓英尔,各向异性双重介质两相非达西椭圆渗流,力学学报,2000,32(6),698～706
[86] 邓英尔,刘慈群,王允诚,垂直裂缝井两相非达西椭圆渗流特征线解、差分解及开发指标计算方法,石油勘探与开发,2000,27(1),60～66
[87] 计秉玉,战剑飞,等,油井见效时间和见水时间的计算公式,大庆石油地质与开发,2000,19(5),24～26
[88] 郎兆新,油气地下渗流力学.山东东营:石油大学出版社,2001
[89] 宋付权,刘慈群,吴柏志,各向异性油藏椭圆不定常渗流近似解,石油勘探与开发,2001,28(1), 57～59
[90] 刘月田,各向异性油藏水平井渗流和产能分析,石油大学学报,2002,26(4),40～44
[91] 丁云宏,陈作等,渗透率各向异性的低渗透油藏开发井网研究,2002,23(2),65～67
[92] 宋付权、刘慈群,幂律流体在分形介质中不定常椭圆渗流,应用数学和力学,2002,23(8),778～782
[93] 葛家里、刘月田等编.《现代油藏渗流力学原理》,石油工业出版社,2003,7.
[94] 邓英尔,刘慈群,等,各向异性双重介质两相非达西椭圆渗流,西南石油学院学报,2003,25(3),22～27
[95] 邓英尔 ,刘慈群,双重介质两相驱替问题的新解法,新疆石油地质,2003,24(5),455～457
[96] 李传亮,李炼民,各向异性地层的井距设计研究,新疆石油地质,2003,24(6),559～561
[97] 王洪宝,苏振阁,陈忠云,油藏水驱开发三维流线模型,石油勘探与开发,31(2),2004,99~103
[98] 刘德华,李士伦,吴军,矢量化井网的概念及布井方法初探,江汉石油学院学报,2004,26(4),110～111
[99] 李忠兴,韩洪宝,程林松,低渗透各向异性地层合理井排距比研究,西南石油学院学报,26(1),2004,35~38
[100] 刘月田,张吉昌,各向异性油藏水平井网稳定渗流与产能分析,2004,31(1),94～96
[101] 李阳,王瑞平,李传亮,各向异性油藏的矢量井网,2006,33(2),225~227
[2] Van Everdinger,A.F.el al, Application of the Laplace Transformation to Flow Problems in Reservoirs,Trans.,AIME(1949)186:305
[3] Horner D R., Pressure Buildup in Wells, Proc Third World Pet Cong, Leiden,1951
[4] Carslaw H.S. and Jaeger, Conduction of Heat In Solids, Oxford University Press, Oxford, 1959
[5] K.H. Coats and M.R. Tek, etc, Unsteady-state Liquid Flow Through Porous Media Having Elliptic Boundaries, SPE2050,1959
[6] Prats,M. etc, Effect of Vertical Fracture on Reservoir Behavior-Incompressible Fluid Case, Paper Presented as 35th Annual Fall Meeting of SPE,1960
[7] R. E. Collins, Flow of Fluids through Porous Material, Reinhold Publishing Corp. New York, 1961.
[8] M. Mortada and G.W Nabor, an Approximate Method for Determining Areal Sweep Efficiency and Flow Capacity in Formations with Anisotropic Permeability, SPE16, 1961
[9] Warren,J.E. and Root, P.J., The Behavior of Naturally Fractured Reservoirs, SPEJ, Sept. 1963
[10] I.S. Papadopulos,No-steady Flow to A Well in an infinite Anisotropic Aquifer, Symposium international Association Science Hydrology, Dubrovnik Yugoslavia, 1965
[11] M.W. Clegg and M. Mills,A Study of Behavior of Partially Penetrating wells, SPE2054, 1969
[12] A.C. Overpeck and W.R. Holden, Well Imaging and Fault Detection in Anisotropic reservoirs, Spe2731, 1970
[13] Stehfest H, Numerical Inversion of Laplace Transform, Comm.ACM.1970;( 1) :47-48
[14] Abramowitz, M.,and Stegun,I.A., Handbook of Mathematical Function, Dover Publications, New York(1972):1019-1030
[15] A.C. Grigarden and H.J. Ramey, The Use of Source and Green's Functions in Solving Unsteady-Flow Problems in reservoirs, SPE3818, 1973
[16] A.C. Grigarden and H.J. Ramey, Unsteady Pressure Distribution Created by a Single Horizontal Fracture, and Partial Penetration, or Restricted Entry, SPE3819, 1974
[17] R.K. Prasad and H.J. Gruy, Pressure Transient Analysis in the Presence of Two Intersecting Boundaries,SPE4560,1975
[18] K.S. Crump, Numerical Inversion of Laplace Transforms Using a Fourier series Approximation, J. ACM., 23(1),1976
[19] Gringarten, A. C. et al,Unsteady-State Pressure Distributions Created by a Well with a Single Infinite-Conductivity Vertical Fracture, SPEJ (Aug. 1978)347-360.
[20] Fikri Kucuk and William E. Brigham, Transient Flow in Elliptical Systems, SPE 7488, DEC. 1979
[21] I.M. Buhidma and R. Raghavan, Transient Pressure of Partially Penetrating Wells Subject to Bottom-Water Drive,SPE8143,1980
[22] Brent W. Hale and J.F. Evers, Elliptical Flow Equations For Vertically Fractured Gas Wells, SPE 8943, 1980
[23] Walter Rose, Permeability Anisotropy in low Permeability Formations, SPE10810,1982
[24] S.T.J Brockenbrough, A New Analytlc Solutlon for Finite Condutivity Verbical Fractures With Real Time and Laplace Space Parameter Estimation,SPE 12013,1983
[25] J. Gcodrich, Time Intervals for Spherical Flow As a function of Anisotropy and Well Completion Interval, SPE11812, 1983
[26] F. Rodriguez and H. Cinco-Ley, Partially Penetrating Vertical Fracture: Pressure Transient Behavior of a Finite-Conductivity Fracture, SPE13057, 1984
[27] S.T. obub and T. Ertekin, A composite System Solution in Elliptical Flow Geometry, SPE13078,1984
[28] F.J. Kuchuk and P.A. Kirwan, New Skin and Well bore Storage Type Curves for Partially Penetrated Wells, SPE11676, 1987
[29] P.A. Goode and R.K.M. Thambynayagam, Pressure Drawdown and Buildup Analysis of Horizontal Wells in Anisotropic Media, SPE14250, 1987
[30]E. Ozkan, Performance of Horizontal Wells, PHD Dissertation, 1988
[31]Chen,H.Y., Well Behavoir in Naturally Fractures Reservoirs, PhD Dissertation, Texas College Station (Aug, 1990)
[32] Poston S. and Raghavan, An Application of the Product Solution Principle for Instantaneous Source and Green's Function in the Laplace Domain.,SPE Formation Evalution,June(1991), 161-168
[33] G.J. Lee, The Effects of Permeability Anisotropy on The Eveluation and Design of Hydraulic Fracture Treatment and Well performance, SPE21501,1991
[34] Goode P.A. and Wilkinson, Inflow Performance of Partially Open Horizontal Wells, JPT(August 1991)983~987
[35] J.J. Pop, D.J. Wilkinson and J.K. Jonas, Vertical Interference Testing With a Wire line-Conveyed Straddle-Packer Tool, SPE26481, 1993
[36] Raghavan,Well Test Analysis, P T R Prentice Hall Englewood Cliffs,New Jersey,1993
[37] Yizhu Liao and W.J. Lee, Depth of Investigation for Elliptical Flow Problems and Its Applications to Hydraulically Fractured Wells, SPE27908, 1994
[38] F.J. Kuchuk and Y. Dave, Interpretation of Wire-line Formation Tester Packer and Probe Pressures, SPE28404, 1994
[39] Hantush, Non-Steady Green's Functions for an Infinite Strip of Leaky Aquifer, Trans.,Aug.(1995)Vol.36,101
[40] F.J. kuchuk, etc, Multilayer Reservoir Testing with Multi-probe Wire-line Formation Tester, SPE36176, 1996
[41] M.E. Vellegas, R.A. Wattenbarger, etc, Performance of Longitudinally Fractured Horizontal Wells in High-Permeability Anisotropic Formations, SPE36453, 1996
[42] M. J. Economides, C.W. Brand and T.P. Frick, Well Configuration in Anisotropic Reservoirs, SPE27980, 1996
[43] L. Zhang and M.B. Dusseault, Anisotropic Permeability Estimation by Horizontal Well Tests, SPE37071, 1996
[44] T. Yildiz and E. Ozkan, Influence of Areal Anisotropy on Horizontal Well Performance, SPE38671, 1997
[45] F.J. Kuchuk, Interval Pressure Transient Testing with MDT Packer-Probe Module in Horizontal Wells, SPE39523, 1998
[46] B. Guo, D.S. Schechter, etc, Use of Single-Well Test Data for Estimating Permeability Anisotropy of the Naturally Fractured Spraberry Trend Area Reservoirs,SPE39807,1998
[47] F.J. Kuchuk,A New Method for Determination of Reservoir Pressure,SPE56418,1999
[48] J.P. Spivey and W.J. Lee, Estimating the Pressure-Transient Response for a Horizontal or a Hydraulically Fractured Well at an Arbitrary Orientation in an Anisotropic Reservoir, SPE58119, 1999
[49] F.J. Kuchuk, F. Halford, and M. Zeybek, the Use of Vertical Interference Testing to Improve Reservoir Characterization, SPE87236, 2000
[50] C.S. Kabir, etc, Understanding Coning Performance in a High-Anisotropy Reservoir: The Burgan Reservoir Case Study, SPE62993, 2000
[51] D.T. Hidayati and Her-Yuan Chen, The Reliability of Permeability-Anisotropy Estimation From Interference Testing of Naturally Fractured Reservoirs, SPE59011, 2000
[52] S.B. Cline and D. Tiab, Studies in Vertical and Horizontal Well-Flow Behavior in Cases of Permeability Anisotropy, SPE71085, 2001
[53] M. Al-Khamis, E. Ozkan, etc, Interference Testing with Horizontal Observation Wells, SPE71581, 2001
[54] M. Onur and P.S. Hegeman, A New Method for Determination of Reservoir Pressure, SPE77343, 2002
[55] M. Zeybek and F.J. Kuchuk, A New Method for Determination of Reservoir Pressure, SPE78506, 2002
[56] B. Guira and D. Tiab, Pressure Behavior of A Well in Anisotropic Reservoir, SPE76772, 2002
[57] H.Y. Chen and L.W. Teufel, Timing and Distance of Well Interference in Anisotropic Reservoirs, SPE77455, 2002
[58] H.Y. Chen and L.W. Teufel, A Quick Method to Determine Permeability-Anisotropy Orientation From Interference Testing, SPE84090, 2003
[59] 吴望一,流体力学上册,北京: 北京大学出版社,1982
[60] J. 贝尔著,李竞生,陈崇希译,多孔介质流体动力学,北京:中国建筑工业出版社,1983。
[61] 陈忠祥,袁益让,姜礼尚,二相平面渗流问题的不变流管解法及其理论分析,应用数学和力学,7(7),1986
[62] 刘慈群,杨玠,垂直裂缝井的压力动态分析方法,试采技术,1989,11
[63] 刘慈群,杨玠,双重孔隙介质中有限导流垂直裂缝井的试井分析方法,试采技术,1990,11(3)
[64] 刘慈群,在双重介质中有限导流垂直裂缝井的非牛顿流体试井分析方法,石油学报,1990,11(4)
[65] G.鲍尔.威尔海特,刘民中,唐金华,等译. 注水, 北京:石油工业出版社,1992
[66]钱伟长:《应用数学》.上海.安徽科学技术出版社,1993
[67]李义昌,李宾亭,等,地下水动力学,北京:中国矿业大学出版社,1995
[68] 刘慈群,水平井产能及试井分析公式, 油气井测试, 1995,4(1),45～49
[69] 刘慈群,分形油藏非牛顿流体渗流压力动态[J] ,试采技术,1996,17(1),9～12
[70] 刘慈群,单相和两相流体多维渗流问题[A],见周连第编:第十届全国水动力学学术会议论文集[C],北京海洋工业出版社,1996,439～445。
[71] 刘曰武,刘慈群,渗流力学进展.北京:石油工业出版社,1996
[72] 翟云芳,刘义坤,刘振宇,等,渗流力学.北京:石油工业出版社,1996
[73] 聂立新,黄炳家等,各向异性天然裂缝油藏裂缝方位的确定,石油大学学报(自然科学版),21(6),1997,39～41。
[74] 刘曰武,刘慈群,部分压开的垂直裂缝井试井分析新方法,油气井测试,1997,6(2),13～18。
[75] 李凡华、刘慈群,分形油藏无限导流垂直裂缝井的非牛顿渗流规律,石油学报,1997,18(4),65～69。
[76] 刘曰武、刘慈群:“多层油藏有限导流垂直裂缝井试井方法研究”,油气井测试,1997,6(3),18～24
[77] 李凡华,刘慈群,分形油藏有限导流垂直裂缝井的非牛顿渗流规律,天然气工业,1997,17(5),27～31
[78] 宋付权、刘慈群,低渗透油藏中水平井的非牛顿幂律流体不稳定渗流的研究,油气井测试,1997,9(1),1～7
[79] 王晓冬,水平井不定常渗流研究:[博士学位论文].北京:中国科学院渗流流体力学所,1998
[80] 宋付权,刘慈群,低渗透垂直补给油藏中水平井流态分析,石油勘探与开发,1998,25(4),35～40
[81] 李传亮,张茂林,等,双重各向异性介质的驱替特征及注水开发井网部署研究,大庆石油地质与开发,1999,18(6),29～31
[82] 孔祥言,高等渗流力学.安徽:中国科学技术大学出版社,1999
[83] 刘月田,葛家理,各向异性圆形地层渗流的解析解,石油大学学报,2000,24(2),40～43
[84] 邓英尔,刘慈群,考虑吸渗的双重介质中垂直裂缝井两相渗流,重庆大学学报,2000(23)
[85] 邓英尔,各向异性双重介质两相非达西椭圆渗流,力学学报,2000,32(6),698～706
[86] 邓英尔,刘慈群,王允诚,垂直裂缝井两相非达西椭圆渗流特征线解、差分解及开发指标计算方法,石油勘探与开发,2000,27(1),60～66
[87] 计秉玉,战剑飞,等,油井见效时间和见水时间的计算公式,大庆石油地质与开发,2000,19(5),24～26
[88] 郎兆新,油气地下渗流力学.山东东营:石油大学出版社,2001
[89] 宋付权,刘慈群,吴柏志,各向异性油藏椭圆不定常渗流近似解,石油勘探与开发,2001,28(1), 57～59
[90] 刘月田,各向异性油藏水平井渗流和产能分析,石油大学学报,2002,26(4),40～44
[91] 丁云宏,陈作等,渗透率各向异性的低渗透油藏开发井网研究,2002,23(2),65～67
[92] 宋付权、刘慈群,幂律流体在分形介质中不定常椭圆渗流,应用数学和力学,2002,23(8),778～782
[93] 葛家里、刘月田等编.《现代油藏渗流力学原理》,石油工业出版社,2003,7.
[94] 邓英尔,刘慈群,等,各向异性双重介质两相非达西椭圆渗流,西南石油学院学报,2003,25(3),22～27
[95] 邓英尔 ,刘慈群,双重介质两相驱替问题的新解法,新疆石油地质,2003,24(5),455～457
[96] 李传亮,李炼民,各向异性地层的井距设计研究,新疆石油地质,2003,24(6),559～561
[97] 王洪宝,苏振阁,陈忠云,油藏水驱开发三维流线模型,石油勘探与开发,31(2),2004,99~103
[98] 刘德华,李士伦,吴军,矢量化井网的概念及布井方法初探,江汉石油学院学报,2004,26(4),110～111
[99] 李忠兴,韩洪宝,程林松,低渗透各向异性地层合理井排距比研究,西南石油学院学报,26(1),2004,35~38
[100] 刘月田,张吉昌,各向异性油藏水平井网稳定渗流与产能分析,2004,31(1),94～96
[101] 李阳,王瑞平,李传亮,各向异性油藏的矢量井网,2006,33(2),225~227
© 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 |