压裂直井试井解释理论与方法
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摘要
压裂是开发低渗油藏的有效措施,已在油田现场广泛应用。低渗油藏压裂后形成垂直裂缝和水平裂缝,因此需要充分认识压裂后裂缝对油藏渗流的影响,再结合试井资料正确了解地层性质。本文应用Green函数方法和Newman乘积方法,建立了垂直裂缝压裂井垂直裂缝在无限大油藏、封闭边界油藏、定压边界油藏三种情形下的试井解释理论模型,每种情形下又分为不考虑裂缝开度和考虑裂缝开度两种情形,并求得了井底压力的解析解,绘制了压力和压力导数的双对数曲线,分析了裂缝开度、对称性、油藏和裂缝尺度等的影响;其次本文还应用上述方法建立了垂直井水平裂缝试井解释理论模型,同样分为不考虑裂缝开度和考虑裂缝开度两种情形,得到井底压力解析解,绘制了压力和压力导数的双对数曲线,研究发现由于水平裂缝开度很小,对井底压力影响可以忽略不计,但水平裂缝在垂向上的位置对井底压力影响较大,必须予以考虑。最后建立了考虑启动压力梯度的低渗油藏数学模型,通过Laplace变换得到拉氏空间下井底压力的解,通过数值反演得到了井底压力的数值解,发现启动压力梯度的存在使渗流偏离达西渗流,且启动压力梯度越大,偏离线性渗流的时间越早,偏离幅度越大;另外还分析了裂缝导流能力、水力扩散系数、井筒存储和表皮系数等参数的影响。
Fracturing is the effective measures for development of low permeability which have been widely used in the oil field. After fracturing in low permeability reservoir vertical fractures and horizontal fractures formed,it is necessary to fully understand the impact of fractures on reservoir flow,and then combined with well testing data we can fully understand the nature of the reservior. In this paper,the Green function method and Newman product method are used to build the vertical fracture welltesting models in the infinite reservoir,closed boundary reservoir,constant pressure outer boundary reservoir,each case is divided into two cases,considering fracture aperture and without considering fracture aperture,the analytic solutions of bottom pressure is obtained and drawing the pressure and pressure derivative log-log type curves,analyse the influences of the fracture aperture,fracture symmetry and reservoir and fracture scale; Using the same method the horizontal fracture model in vertical well is built and obtain the analytic solution,drawing its pressure and pressure derivative log-log type curves,generally the horizontal fracture aperture is very small and its influence can be ignored,but the vertical position of horizontal fracture in the reservoir should be taken into consideration. Finally considering the actuating pressure gradient,the flow model for low permeability reservoir are built,the numerical solution of bottom-hole pressure is derived,it is found that the flow deviates from the Darcy flow because of the presence of actuating pressure gradient ,and the greater the actuating pressure gradient is ,the earlier the flow deviates from the linear flow and the greater deviation; analyse the influemces of fracture conductivity,hydraulic diffusivity,wellbore storage and wellbore storage for bottom hole pressure.
Fracturing is the effective measures for development of low permeability which have been widely used in the oil field. After fracturing in low permeability reservoir vertical fractures and horizontal fractures formed,it is necessary to fully understand the impact of fractures on reservoir flow,and then combined with well testing data we can fully understand the nature of the reservior. In this paper,the Green function method and Newman product method are used to build the vertical fracture welltesting models in the infinite reservoir,closed boundary reservoir,constant pressure outer boundary reservoir,each case is divided into two cases,considering fracture aperture and without considering fracture aperture,the analytic solutions of bottom pressure is obtained and drawing the pressure and pressure derivative log-log type curves,analyse the influences of the fracture aperture,fracture symmetry and reservoir and fracture scale; Using the same method the horizontal fracture model in vertical well is built and obtain the analytic solution,drawing its pressure and pressure derivative log-log type curves,generally the horizontal fracture aperture is very small and its influence can be ignored,but the vertical position of horizontal fracture in the reservoir should be taken into consideration. Finally considering the actuating pressure gradient,the flow model for low permeability reservoir are built,the numerical solution of bottom-hole pressure is derived,it is found that the flow deviates from the Darcy flow because of the presence of actuating pressure gradient ,and the greater the actuating pressure gradient is ,the earlier the flow deviates from the linear flow and the greater deviation; analyse the influemces of fracture conductivity,hydraulic diffusivity,wellbore storage and wellbore storage for bottom hole pressure.
引文
[1]程时清,李跃刚.低速非达西渗流试井模型的数值解及其应用.天然气工业,1995;16(3):27-30.
[2]程时清,张占峰.低速非达西渗流条件下段塞流试井分析方法.油气井测试,1996;5(3):4-8.
[3]程时清,李功权.双重介质油气藏低速非达西渗流试井有效井径数学模型及典型曲线.天然气工业,1997;17(2):35-37.
[4]程时清,张宗盛等.低速非达西渗流动边界问题的积分解.力学与实践,2001;24(3):15-17.
[5]程时清,张宗盛等.低渗透非均质油藏油单相渗流敏感系数.应用数学和力学,2002,23(6):635-642.
[6]程时清,李相方,张宗盛等.低渗透非均质油藏油水两相渗流敏感系数理论模型.应用数学,2002,15(4):123-127.
[7]同登科,葛家理.分形油藏非达西低速渗流模型及其解.大庆石油地质与开发,1996;15(3):18-23.
[8]同登科,葛家理.分形油气藏不稳定渗流时关于续流和表皮效应的影响.天然气工业,1997;17(1):55-57.
[9]同登科,葛家理.分形裂缝气藏不稳定渗流问题.天然气工业,1996;15(2):45-48
[10]姚约东,葛家理.低渗透油藏非达西渗流机理的研究.新疆石油地质,2000;21(3):213-215.
[11]姚约东,葛家理.低渗透油藏不稳定渗流规律的研究.石油大学学报(自然科学版),2003;27(2):55-62.
[12]姚约东,葛家理.低渗透油藏油水两相渗流研究.石油大学学报(自然科学版),2005;29(2):52-56.
[13]尚建林和杨学等.低速非线性渗流试井分析理论研究.新疆石油地质,2002;23(4):321-325.
[14]李中锋,何顺利等.低渗透油田非达西渗流规律研究.油气井测试,2005;14(3):14-17.
[15]王志伟,张宁生,何秋轩等.低渗透油藏非达西渗流视渗透率及其对开发的影响.钻采工艺,2006;29(3):48-52.
[16] Dyes A.B,Kemp C.E et al. Effect of Fractures on Sweep Out Pattern Trans. AIME(1958) 1958;213:245-259.
[17] Prats M.Hazebroek. Effect of Vertical Fractures on Reservior Behavior-Compressible–Fluid Case,SPE98,1962 SPEJ,1962;2(2):87-94.
[18] Scott J.O. The Effect of Vertical Fractures on Transient Pressure Behavior of Wells,JPT(Dec.1963).
[19] Russell D.G. and Truitt,N.E. Transient Pressure Behavior in Vertically Fractured Reservoirs .JPT(Oct1964) 97-110.
[20] Lee W.J.Jr. Analysis of Hydraulical Fractured Wells With Pressure Buildup Tests .SPE1820.
[21]R.Raghavan,G.V.Cady and H.J.Ramey. Well Test Analysis For Vertically Fractured Wells. SPE3013.
[22] Gringarten A.C. and Ramey H.J.Jr. Unsteady State Pressure Distributions Created by a well with a Single-Infinite Conductivity Vertical Fracture .SPE4051:347-360.
[23]Gringarten A.C and Ramey H.J.Jr. Unsteady State Pressure Distributions Created By A Well With A Single Horizontal Fracture,Partial Penetration,Or Restricted Entry Conductivity Vertical Fracture. SPE3819.
[24] Gringarten A.C,Ramey,H. J. Jr,and Raghavan.R. Applied Pressure Analysis for Fractured Wells .SPE5496. J.P.T (July,1975):887-892.
[25] Cinco-Ley,H.Samaniego V.F. and Dominguez N. Transient Pressure Behavior for a Well with a Finite Conductivity Vertical Fracture .SPEJ,1978.
[26] Kern H,Guppy Heber. Transient Flow Behavior Of A Vertically Fractured Well Producing At Constant Pressure ,SPE9963.
[27] M.J Bouteca. 3D Analytical Model for Hydraulic Fracturing Theory and Field Test,SPE13276(1984):2-8.
[28] M.Y Soliman and J.J Venditto. Evaluation Fractured Well Performance Using Type Curves .SPE12598.
[29] Sheng-Tai Lee and John R.Brockenbrough. A New Approximate Analytic Solution for Finite-Conductivity Vertical Fractures . SPE12013.
[30] R.Aguilera. Effect of Wellbore Storage ,Skin,and Outer Reservior Boundaries on The Transient Behavior of Naturally Fractured Reserviors With Hydraulic Vertical Fractures,SPE17023(1987):4-19.
[31] R.Aguilera. Well Test Analysis of Dual-Porosity Systems Intercepted by Hydraulic Vertical Fractures of Finite Conductivity,SPE18948(1989):193-212.
[32] A.N.Duong. Applying the Line-Source Solution Type Curves for Vertically Fractured Wells,SPE18401(1988).
[33] Azari,W.O Wooden and L.E Coble. A Complete Set of Laplace Transforms for Finite-Conductivity Vertical Fractures Under Billnear and Trillinear Flows. SPE20556.
[34] M.Azari,W.O.Wooden and L.E.Coble. Further Investigation On The Analytic Solutions for Finite-Conductivity Vertical Fractures.SPE21402.
[35] Djebbar Tiab. Analysis of Pressure and Pressure Derivative Without Type-Curve Matching-Vertically Fractured Wells in Closed Systems.SPE26138(1993).
[36] Freddy H. Escobar,Djebbar Tiab and Sergio Berumen Campos. Well Pressure Behavior Of A Finite-Conductivity Fracture Intersecting A Finite Sealing-Fault. SPE80547,2003,643-658
[37] G.Chavez and M.Alejandro . Effect of Pressure in a Well with a Vertical Fracture with Variable Conductivity and Skin Fracture,SPE104004(2008):2-10.
[38]刘慈群.在双重孔隙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):61-67.
[39]刘曰武,刘慈群.无限导流垂直裂缝井的快速试井分析方法.大庆石油地质与开发,1993;12(4):55-60.
[40]刘曰武,刘慈群.考虑井筒存储和表皮效应的有限导流垂直裂缝井的试井分析方法.油气井测试,1993;12(2):2-21.
[41]刘曰武,刘慈群.垂直裂缝井试井分析中应考虑的诸多因素.1995年第五次国际石油工程会议论文集,SPE30005.
[42]刘慈群.垂直裂缝井的各类试井方法综述.石油勘探与开发,1995;22(1):59-60.
[43]宋付权,刘慈群.低渗透油藏中垂直裂缝井的不定常渗流.试采技术,2000;21(3):5-8.
[44]刘香山.复杂低渗透砂岩油藏试井分析方法.中国石油大学(华东)硕士论文,2006.
[45]付春权,尹洪军等.低速非达西渗流垂直裂缝井试井分析.大庆石油地质与开发,2007;26(5):53-56.
[2]程时清,张占峰.低速非达西渗流条件下段塞流试井分析方法.油气井测试,1996;5(3):4-8.
[3]程时清,李功权.双重介质油气藏低速非达西渗流试井有效井径数学模型及典型曲线.天然气工业,1997;17(2):35-37.
[4]程时清,张宗盛等.低速非达西渗流动边界问题的积分解.力学与实践,2001;24(3):15-17.
[5]程时清,张宗盛等.低渗透非均质油藏油单相渗流敏感系数.应用数学和力学,2002,23(6):635-642.
[6]程时清,李相方,张宗盛等.低渗透非均质油藏油水两相渗流敏感系数理论模型.应用数学,2002,15(4):123-127.
[7]同登科,葛家理.分形油藏非达西低速渗流模型及其解.大庆石油地质与开发,1996;15(3):18-23.
[8]同登科,葛家理.分形油气藏不稳定渗流时关于续流和表皮效应的影响.天然气工业,1997;17(1):55-57.
[9]同登科,葛家理.分形裂缝气藏不稳定渗流问题.天然气工业,1996;15(2):45-48
[10]姚约东,葛家理.低渗透油藏非达西渗流机理的研究.新疆石油地质,2000;21(3):213-215.
[11]姚约东,葛家理.低渗透油藏不稳定渗流规律的研究.石油大学学报(自然科学版),2003;27(2):55-62.
[12]姚约东,葛家理.低渗透油藏油水两相渗流研究.石油大学学报(自然科学版),2005;29(2):52-56.
[13]尚建林和杨学等.低速非线性渗流试井分析理论研究.新疆石油地质,2002;23(4):321-325.
[14]李中锋,何顺利等.低渗透油田非达西渗流规律研究.油气井测试,2005;14(3):14-17.
[15]王志伟,张宁生,何秋轩等.低渗透油藏非达西渗流视渗透率及其对开发的影响.钻采工艺,2006;29(3):48-52.
[16] Dyes A.B,Kemp C.E et al. Effect of Fractures on Sweep Out Pattern Trans. AIME(1958) 1958;213:245-259.
[17] Prats M.Hazebroek. Effect of Vertical Fractures on Reservior Behavior-Compressible–Fluid Case,SPE98,1962 SPEJ,1962;2(2):87-94.
[18] Scott J.O. The Effect of Vertical Fractures on Transient Pressure Behavior of Wells,JPT(Dec.1963).
[19] Russell D.G. and Truitt,N.E. Transient Pressure Behavior in Vertically Fractured Reservoirs .JPT(Oct1964) 97-110.
[20] Lee W.J.Jr. Analysis of Hydraulical Fractured Wells With Pressure Buildup Tests .SPE1820.
[21]R.Raghavan,G.V.Cady and H.J.Ramey. Well Test Analysis For Vertically Fractured Wells. SPE3013.
[22] Gringarten A.C. and Ramey H.J.Jr. Unsteady State Pressure Distributions Created by a well with a Single-Infinite Conductivity Vertical Fracture .SPE4051:347-360.
[23]Gringarten A.C and Ramey H.J.Jr. Unsteady State Pressure Distributions Created By A Well With A Single Horizontal Fracture,Partial Penetration,Or Restricted Entry Conductivity Vertical Fracture. SPE3819.
[24] Gringarten A.C,Ramey,H. J. Jr,and Raghavan.R. Applied Pressure Analysis for Fractured Wells .SPE5496. J.P.T (July,1975):887-892.
[25] Cinco-Ley,H.Samaniego V.F. and Dominguez N. Transient Pressure Behavior for a Well with a Finite Conductivity Vertical Fracture .SPEJ,1978.
[26] Kern H,Guppy Heber. Transient Flow Behavior Of A Vertically Fractured Well Producing At Constant Pressure ,SPE9963.
[27] M.J Bouteca. 3D Analytical Model for Hydraulic Fracturing Theory and Field Test,SPE13276(1984):2-8.
[28] M.Y Soliman and J.J Venditto. Evaluation Fractured Well Performance Using Type Curves .SPE12598.
[29] Sheng-Tai Lee and John R.Brockenbrough. A New Approximate Analytic Solution for Finite-Conductivity Vertical Fractures . SPE12013.
[30] R.Aguilera. Effect of Wellbore Storage ,Skin,and Outer Reservior Boundaries on The Transient Behavior of Naturally Fractured Reserviors With Hydraulic Vertical Fractures,SPE17023(1987):4-19.
[31] R.Aguilera. Well Test Analysis of Dual-Porosity Systems Intercepted by Hydraulic Vertical Fractures of Finite Conductivity,SPE18948(1989):193-212.
[32] A.N.Duong. Applying the Line-Source Solution Type Curves for Vertically Fractured Wells,SPE18401(1988).
[33] Azari,W.O Wooden and L.E Coble. A Complete Set of Laplace Transforms for Finite-Conductivity Vertical Fractures Under Billnear and Trillinear Flows. SPE20556.
[34] M.Azari,W.O.Wooden and L.E.Coble. Further Investigation On The Analytic Solutions for Finite-Conductivity Vertical Fractures.SPE21402.
[35] Djebbar Tiab. Analysis of Pressure and Pressure Derivative Without Type-Curve Matching-Vertically Fractured Wells in Closed Systems.SPE26138(1993).
[36] Freddy H. Escobar,Djebbar Tiab and Sergio Berumen Campos. Well Pressure Behavior Of A Finite-Conductivity Fracture Intersecting A Finite Sealing-Fault. SPE80547,2003,643-658
[37] G.Chavez and M.Alejandro . Effect of Pressure in a Well with a Vertical Fracture with Variable Conductivity and Skin Fracture,SPE104004(2008):2-10.
[38]刘慈群.在双重孔隙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):61-67.
[39]刘曰武,刘慈群.无限导流垂直裂缝井的快速试井分析方法.大庆石油地质与开发,1993;12(4):55-60.
[40]刘曰武,刘慈群.考虑井筒存储和表皮效应的有限导流垂直裂缝井的试井分析方法.油气井测试,1993;12(2):2-21.
[41]刘曰武,刘慈群.垂直裂缝井试井分析中应考虑的诸多因素.1995年第五次国际石油工程会议论文集,SPE30005.
[42]刘慈群.垂直裂缝井的各类试井方法综述.石油勘探与开发,1995;22(1):59-60.
[43]宋付权,刘慈群.低渗透油藏中垂直裂缝井的不定常渗流.试采技术,2000;21(3):5-8.
[44]刘香山.复杂低渗透砂岩油藏试井分析方法.中国石油大学(华东)硕士论文,2006.
[45]付春权,尹洪军等.低速非达西渗流垂直裂缝井试井分析.大庆石油地质与开发,2007;26(5):53-56.