低渗透储层开发压裂的油藏数值模拟研究
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摘要
开发压裂的油藏数值模拟主要用于压裂前后油藏动态的拟合和预测，为进行不同压裂方案的对比提供依据，是开发压裂优化设计中的核心内容。研究和开发能更好地模拟压裂前后低渗油气藏生产动态的模拟技术，对于经济有效地动用及开发好低渗储量，具有重要的理论和实际意义。
在开发压裂的油藏数值模拟研究中，综合考虑双重介质、储层基质低速非达西流、裂缝中高速非达西流、渗透率随孔隙压力变化、任意压裂裂缝方位(方向、倾角)、压裂缝导流能力随位置及时间变化等是开发生产提出、亟待解决的实际问题，尚未见公开报道。
本文在继承传统双重介质模型的处理思想基础之上，通过引入任意分布的大裂缝(用以表征压裂改造后的人工裂缝)和非达西渗流规律，综合考虑上述因素建立了一新型的非线性渗流模型。并在模型建立、离散、求解、编程调试成功的基础上，进行了模拟器稳定性检验、与前人研究对比及生产实际的应用研究，结果表明整个模拟器计算方法稳定、结果可靠，实例应用符合生产实际。
本文建立的模型主要具有如下特点：
1．可用于双重介质或单重介质地层压裂前后生产动态的模拟；
2．既能描述线性的达西渗流现象，又能描述低渗和高渗两种情况下的非线性渗流问题；
3．考虑了渗透率随孔隙压力指数变化的时变效应；
4．考虑了实际中可能的任意压裂裂缝方位(方向、倾角)；
5．考虑了压裂裂缝导流能力随时间指数或半对数规律下降的情况；
6．可用于多缝及非对称压裂缝条件下生产动态的模拟；
7．可用于单井压裂、单井重复压裂、整体压裂、开发压裂及整体重复压裂的油藏生产动态模拟。
This study of numerical simulation for reservoir developed by fracturing is mainly used on reservoir performance prediction of pre-frac and post-frac . It can provide the basis for the comparison of different fracturing projects. It is the kernel parts of optimizing fracturing projects for developing.To simulate the pre-frac and post-frac performance of low permeable reservoir , the technology studying and developing is needed,and this will do good for improving economically developing low permeable reservoir,it is significant in theory and practice.On the study of numerical simulation for reservoir developed by fracturing,the simulator of consider dual-porosity reservoir, non-Darcy-flow in reservoir and fracture , permeability changed with the effective porosity pressure, arbitrary fracture azimuth , fracture conductivity change in the fracture with the time is a really problem urge to solve. There is not any paper published on this so far.Based on the conventional dual-porosity simulation model, a new non-linear combined-flow-rule model for fluid flow, has been used in this paper by introducing the large-opening fractures with arbitrary azimuths and non-Darcy-flow rule. This model can describe not only the linear Darcy's flow phenomena but also the nonlinear flow cases including low-velocity-flow in low permeability media and high-velocity-flow in high permeability media.In the model of this paper, the fluids flow in large-opening fractures are described by the high-velocity non- Darcy -flow rule, and the influences of start-up pressure to fluids flow in low permeability media are represented by low-velocity non-Darcy-flow rule, while the linear-flow phenomena are characterized by the Darcy rule.Considering the variation of rock permeability with time is one of the important works of this paper. The practice and experiments show that the changes of the reservoir pressure could result in the variation of the permeability in the reservoir. In addition, the pressure of reservoir would vary with the different development time, thus the permeability of the reservoir would change with the development time. This phenomenon is called time-difference-effect in this paper.A detailed discussion is given in this paper about the variation of conductivity of large-opening fracture with time, and a measure is raised to settle this problem.The function of characterizing large-opening fractures with arbitrary orientation is another feature of this simulator. By this function, the simulator could simulate
conveniently the influences, exerted by the man-made fractures with arbitrary azimuth, to the dynamics of fractured wells or reservoirs.This simulator can be used in simulating the multi-fracture or symmetry fracture cases, it can be used in post-frac performance prediction of single well fracture , refracture and systematic fracture.Tests and applications of the research achievements are important contents of this paper. Examples given in the paper have verified respectively the effects of all the methods and functions which have been presented.
在开发压裂的油藏数值模拟研究中，综合考虑双重介质、储层基质低速非达西流、裂缝中高速非达西流、渗透率随孔隙压力变化、任意压裂裂缝方位(方向、倾角)、压裂缝导流能力随位置及时间变化等是开发生产提出、亟待解决的实际问题，尚未见公开报道。
本文在继承传统双重介质模型的处理思想基础之上，通过引入任意分布的大裂缝(用以表征压裂改造后的人工裂缝)和非达西渗流规律，综合考虑上述因素建立了一新型的非线性渗流模型。并在模型建立、离散、求解、编程调试成功的基础上，进行了模拟器稳定性检验、与前人研究对比及生产实际的应用研究，结果表明整个模拟器计算方法稳定、结果可靠，实例应用符合生产实际。
本文建立的模型主要具有如下特点：
1．可用于双重介质或单重介质地层压裂前后生产动态的模拟；
2．既能描述线性的达西渗流现象，又能描述低渗和高渗两种情况下的非线性渗流问题；
3．考虑了渗透率随孔隙压力指数变化的时变效应；
4．考虑了实际中可能的任意压裂裂缝方位(方向、倾角)；
5．考虑了压裂裂缝导流能力随时间指数或半对数规律下降的情况；
6．可用于多缝及非对称压裂缝条件下生产动态的模拟；
7．可用于单井压裂、单井重复压裂、整体压裂、开发压裂及整体重复压裂的油藏生产动态模拟。
This study of numerical simulation for reservoir developed by fracturing is mainly used on reservoir performance prediction of pre-frac and post-frac . It can provide the basis for the comparison of different fracturing projects. It is the kernel parts of optimizing fracturing projects for developing.To simulate the pre-frac and post-frac performance of low permeable reservoir , the technology studying and developing is needed,and this will do good for improving economically developing low permeable reservoir,it is significant in theory and practice.On the study of numerical simulation for reservoir developed by fracturing,the simulator of consider dual-porosity reservoir, non-Darcy-flow in reservoir and fracture , permeability changed with the effective porosity pressure, arbitrary fracture azimuth , fracture conductivity change in the fracture with the time is a really problem urge to solve. There is not any paper published on this so far.Based on the conventional dual-porosity simulation model, a new non-linear combined-flow-rule model for fluid flow, has been used in this paper by introducing the large-opening fractures with arbitrary azimuths and non-Darcy-flow rule. This model can describe not only the linear Darcy's flow phenomena but also the nonlinear flow cases including low-velocity-flow in low permeability media and high-velocity-flow in high permeability media.In the model of this paper, the fluids flow in large-opening fractures are described by the high-velocity non- Darcy -flow rule, and the influences of start-up pressure to fluids flow in low permeability media are represented by low-velocity non-Darcy-flow rule, while the linear-flow phenomena are characterized by the Darcy rule.Considering the variation of rock permeability with time is one of the important works of this paper. The practice and experiments show that the changes of the reservoir pressure could result in the variation of the permeability in the reservoir. In addition, the pressure of reservoir would vary with the different development time, thus the permeability of the reservoir would change with the development time. This phenomenon is called time-difference-effect in this paper.A detailed discussion is given in this paper about the variation of conductivity of large-opening fracture with time, and a measure is raised to settle this problem.The function of characterizing large-opening fractures with arbitrary orientation is another feature of this simulator. By this function, the simulator could simulate
conveniently the influences, exerted by the man-made fractures with arbitrary azimuth, to the dynamics of fractured wells or reservoirs.This simulator can be used in simulating the multi-fracture or symmetry fracture cases, it can be used in post-frac performance prediction of single well fracture , refracture and systematic fracture.Tests and applications of the research achievements are important contents of this paper. Examples given in the paper have verified respectively the effects of all the methods and functions which have been presented.
引文
1．低渗未动用储量会议材料冲国石油勘探开发研究院廊坊分院，2002．3
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7．任晓娟，阎庆来等．低渗气层气体的渗流特征实验研究．西安石油学院学报，1997．5．
8．宋付权，刘慈群．含启动压力梯度油藏的两相渗流分析．石油大学学报，1999．3．
9．宋付权，刘慈群．低渗透油藏启动压力梯度的简单测量．特种油气藏，2000．1．
10. K.H.Guppy.Non-Darcy in Wells With Finite-Conductivity Vertical Fractures. SPE8281.1982
11．非常规油气藏的开发
12．俞绍诚．陶粒支撑剂和兰州压裂砂长期裂缝导流能力的评价．石油钻采工艺，1987．5
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25. Gringarten A. C..The Use of Soure and Green's Function in solving UnsteadyFlow Problems in reservoirs .SPEJ, 1973: 285-296
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32. J.Lelbel.Designing Hydraulic Fractures for Efficient Reserve Recovery.
33. Yizhu Liao, W.J. Lee .New Solutions for wells With Finite-conductivity Fractures Including Wellbore Storage and Fracture-Face Skin.SPE26912, 1993.
34．刘慈群．垂直裂缝地层中流体的渗流．石油勘探与开发，1987
35．张义堂，刘慈群．垂直裂缝井椭圆流模型近似解的进一步研究．石油学报，1996年，73-77
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2．J. L. Gidley, etc．水力压裂技术新发展．第一版．北京：石油工业出版社，1995．1～90
3．2000年中国石油天然气集团公司压裂酸化情况统计．中国石油股份有限公司采油工艺处，2001．4．
4. Collins, R.E..Flow of Fluids Through Porous Materials.Van Nostrand Reinhold , New York, 1961.
5. Bear, J. Dynamics of Fluids in Porous Media. American Elsevier, New York, 1972.
6．冯文光．非达西低速渗流的研究现状与展望．石油勘探与开发，1986．4．
7．任晓娟，阎庆来等．低渗气层气体的渗流特征实验研究．西安石油学院学报，1997．5．
8．宋付权，刘慈群．含启动压力梯度油藏的两相渗流分析．石油大学学报，1999．3．
9．宋付权，刘慈群．低渗透油藏启动压力梯度的简单测量．特种油气藏，2000．1．
10. K.H.Guppy.Non-Darcy in Wells With Finite-Conductivity Vertical Fractures. SPE8281.1982
11．非常规油气藏的开发
12．俞绍诚．陶粒支撑剂和兰州压裂砂长期裂缝导流能力的评价．石油钻采工艺，1987．5
13. Dyes , etc. Effect of Fractures on Sweep-Out Pattern " Trans.AIME(1958) Vol-213, 245-249.
14. Craw ford , P. B. Estimated Effects of Vertical Fractures on Secondary Recovery. Trans , AIME(1954) Vol.201, 192-196.
15. Jack Simmons.Swept Areas After Breakthrough in Vertically Fractured Five-Spot atterns. P1959.T.P.8058.
16. Harsock, J.H..The Effect of Mobility Ratio and Vertical Fractures on the Sweep Effiency of a Five-spot.Producers monthly(1961.9)2-7.
17. Hansford, J.T., etc..The Relation of Multi-Well Vertical Frac-tures to Five-Spot Sweep Efficiency at Breakthrough n prod. Monthly (1967)Vol-31, 2.
18. D.A.T. Donohue.The Effect of Induced Vertically-Oriented Fractures on Five-Spot Sweep Efficiency. FF SPE1948.
19. W.J.McGuire, V.J. Sikora.The Effect of Vertical Fractures on Well Productivity.Trans , AIME 1960, 401-403.
20. Prats, M..Effect of Vertical Fractures on Reservoir Behavior-Compressible Fluid Case.SPE(Oct., 1961), 105-118.
21. Tinsley, J.M. et al.Vertical Fracture Height-Its Effect on Steady State Production Increase.J.Pet.Tech.(May 1969)633-38.
22. Mao, M.-L..Performance of Vertically Fractured Wells with Finite Conductivity Fractures.PhD dissertation, Stanford U, 1977.
23. M.Y. Soliman.Modifications to Production Increase Calculations for a Hydraulically Fractured Well.JPT 1983.1.
24. L.R.Raymond, G.G.Binder.Productiviwof Wells in Vertically Fractured, Damaged Formations, "JPR, Jan. 1967, 120-130.
25. Gringarten A. C..The Use of Soure and Green's Function in solving UnsteadyFlow Problems in reservoirs .SPEJ, 1973: 285-296
26. Heber Cinco-Ley .Transient Pressure Analysis for Fractured Wells."SPE 7490, 1978
27. H.Z. Meng . Production Systems Analysis of Vertically Fractured Wells. SPE10842, 1982.
28. Ram G.Agarwal, .R.D Carter .Evaluation and Prediction of Low Permeability Gas WellsStimulated by Massive Hydralllic Fracturing.SPE6838, 1979
29. Stephen A.Holditch etc..The Optimization of Well Spacing and Fracture Length in Low Permeability Gas Reservoirs.SPE7496, Oct., 1978
30. Curtis.Bennett, Albert C-Reynolds etc. Conductivity Vertically Fractured Wells in Single-Layer Reservoirs .SPE11029, 1982.
31. C.O.Bennett, N.D.Rosato, A.C.Reynolds and R.Raghavan.Influence of Fracture Heterogeneity and Wing Length on the Response of Vertically Fractured Wells. SPE9886, 1981.
32. J.Lelbel.Designing Hydraulic Fractures for Efficient Reserve Recovery.
33. Yizhu Liao, W.J. Lee .New Solutions for wells With Finite-conductivity Fractures Including Wellbore Storage and Fracture-Face Skin.SPE26912, 1993.
34．刘慈群．垂直裂缝地层中流体的渗流．石油勘探与开发，1987
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