低渗透应力敏感油藏实验及数值模拟研究
|
摘要
低渗透油藏普遍存在应力敏感现象，当前储层应力敏感性实验一般参照行业标准进行，这种实验过程与地下真实储层应力变化过程不一致。本文改进实验方法，研究了储层岩石在流体压力变化的情况下的应力敏感性。大量的研究证实Terzaghi有效应力应用在低渗透储层时可能存在误差，本次研究引入双重有效应力理论进行储层应力敏感及流固耦合数值模拟研究。
本文首先对多孔介质变形机理进行了分析，回顾了有效应力的发展历程，引入了双重有效应力理论。针对多孔介质特殊的孔隙结构特征，建立了一个新的简化孔隙力学模型，并由该模型导出了渗透率与有效应力的二次多项式关系。
对大量岩心进行了应力敏感性实验研究，一部分实验参照行业标准进行，一部分实验则采用变流体压力的方式进行。与常规应力敏感实验相比，变流体压力条件下的实验更能反映地下储层真实应力变化情况，并且可以消除有效应力系数的不同所造成的评价指标的差异，该实验还为数值模拟中的动态参数模型提供了可靠的基本数据。从油藏实际应力条件出发，提出了储层应力敏感性的油气藏评价方法。通过对实验数据的拟合分析，认为用二次多项关系式来描述有效应力与渗透率之间的关系是合适的。储层应力敏感存在滞后效应，这是储层岩石塑性变形对孔渗造成了永久性损害的原因，文中提出储层渗透率永久性伤害的概念，并给出其计算公式。
低渗透储层存在较为显著的流固耦合现象，本文在前人研究的基础上，利用有效应力方程，推导了岩石骨架的变形场方程和流体的渗流微分方程，不同的有效应力方程在数学模型中体现在有效应力系数的不同。对岩石骨架变形场方程采用有限元方法进行数值求解，对渗流微分方程采用有限差分方法求数值解，并用显式耦合的方法对整体流固耦合方程进行求解。
耦合模型中的动态参数模型一般采用理论推导的方程，但是影响地下储层岩石变形的因素较多，理论参数模型不能完全考虑到所有的因素。因此本次数值模拟以实验数据为基础，利用回归方程作为模拟的动态参数模型，不仅能体现该特定地区储层孔渗的变化规律，更节约了计算时间。
对应力敏感油藏的压实模拟方法忽略了地层应力在孔隙流体压力变化过程的变化，因此夸大了地层的应力敏感性。本文对此做出改进，考虑地层附加应力，对流体压力与孔隙度渗透率的关系进行修正，从而使得模拟更加符合实际情况。
最后，分别采用不同的流固耦合模型和常规应力敏感模型进行了实例计算。结果表明，不同耦合模型的计算结果差别不大，而采用修正后的流体压力～孔渗关系的常规应力敏感模型的模拟结果与耦合模型的结果也只有很少的差别。总的
The stress sensitivity phenomenon is notable in low permeability reservoir. The experiment research on the stress sensitivity is performed referring to the trade standard in present, but this experiment procedure is not consistent with the true course of stress changing. This paper improves the experiment method and equipment to research the stress sensitivity on the changing fluid pressure condition. It will induce errors to use the Terzaghi effective stress principle in the low permeability reservoir, so the double effective stress principle is introduced to research the stress sensitivity and fluid-solid coupling.
This paper discusses the deformation mechanism of porous media, and reviews the development history of effective stress theory, and introduces the double effective stress theory. A new simple pore mechanics model is established based the pore structure of low permeability reservoir rock, from which the quadratic equation of effective stress and permeability can be educed.
This paper carries sufficient experimental researches to learn the stress sensitivity of low permeability rock, and some experiments do referring to the trade standard and other do on the changing fluid pressure condition. The changing fluid pressure experiment method can reflects the actual changing path of reservoir stress, and eliminates the difference of the calculational results with different effective coefficient, and it provides the basic data of dynamic parameter model of fluid-solid coupled model. The stress sensitivity estimate is performed based the experimental results, and the new method is bring forward to estimate the actual reservoir rock. It also shows that the quadratic equation of effective stress and permeability is appropriate to the experimental data. The hysteresis effect of stress sensitivity is the appearance of the plastic deformation of rock, which is the reason of irreversible damage to the rock. This paper introduces the concept of permanent damage of reservoir physical properties such as permeability and porosity, and presents the calculational formula.
The fluid-solid coupled phenomenon is evident in low permeability reservoir. On the bases of a great number of theoretical studies of former researchers and the effective stress theory, this paper set up the mathematical model of reservoir rock and the seepage flow equation. The effective stress coefficient distinguishes the different effective stress equation. The reservoir rock deformation equation is resolved with the
本文首先对多孔介质变形机理进行了分析，回顾了有效应力的发展历程，引入了双重有效应力理论。针对多孔介质特殊的孔隙结构特征，建立了一个新的简化孔隙力学模型，并由该模型导出了渗透率与有效应力的二次多项式关系。
对大量岩心进行了应力敏感性实验研究，一部分实验参照行业标准进行，一部分实验则采用变流体压力的方式进行。与常规应力敏感实验相比，变流体压力条件下的实验更能反映地下储层真实应力变化情况，并且可以消除有效应力系数的不同所造成的评价指标的差异，该实验还为数值模拟中的动态参数模型提供了可靠的基本数据。从油藏实际应力条件出发，提出了储层应力敏感性的油气藏评价方法。通过对实验数据的拟合分析，认为用二次多项关系式来描述有效应力与渗透率之间的关系是合适的。储层应力敏感存在滞后效应，这是储层岩石塑性变形对孔渗造成了永久性损害的原因，文中提出储层渗透率永久性伤害的概念，并给出其计算公式。
低渗透储层存在较为显著的流固耦合现象，本文在前人研究的基础上，利用有效应力方程，推导了岩石骨架的变形场方程和流体的渗流微分方程，不同的有效应力方程在数学模型中体现在有效应力系数的不同。对岩石骨架变形场方程采用有限元方法进行数值求解，对渗流微分方程采用有限差分方法求数值解，并用显式耦合的方法对整体流固耦合方程进行求解。
耦合模型中的动态参数模型一般采用理论推导的方程，但是影响地下储层岩石变形的因素较多，理论参数模型不能完全考虑到所有的因素。因此本次数值模拟以实验数据为基础，利用回归方程作为模拟的动态参数模型，不仅能体现该特定地区储层孔渗的变化规律，更节约了计算时间。
对应力敏感油藏的压实模拟方法忽略了地层应力在孔隙流体压力变化过程的变化，因此夸大了地层的应力敏感性。本文对此做出改进，考虑地层附加应力，对流体压力与孔隙度渗透率的关系进行修正，从而使得模拟更加符合实际情况。
最后，分别采用不同的流固耦合模型和常规应力敏感模型进行了实例计算。结果表明，不同耦合模型的计算结果差别不大，而采用修正后的流体压力～孔渗关系的常规应力敏感模型的模拟结果与耦合模型的结果也只有很少的差别。总的
The stress sensitivity phenomenon is notable in low permeability reservoir. The experiment research on the stress sensitivity is performed referring to the trade standard in present, but this experiment procedure is not consistent with the true course of stress changing. This paper improves the experiment method and equipment to research the stress sensitivity on the changing fluid pressure condition. It will induce errors to use the Terzaghi effective stress principle in the low permeability reservoir, so the double effective stress principle is introduced to research the stress sensitivity and fluid-solid coupling.
This paper discusses the deformation mechanism of porous media, and reviews the development history of effective stress theory, and introduces the double effective stress theory. A new simple pore mechanics model is established based the pore structure of low permeability reservoir rock, from which the quadratic equation of effective stress and permeability can be educed.
This paper carries sufficient experimental researches to learn the stress sensitivity of low permeability rock, and some experiments do referring to the trade standard and other do on the changing fluid pressure condition. The changing fluid pressure experiment method can reflects the actual changing path of reservoir stress, and eliminates the difference of the calculational results with different effective coefficient, and it provides the basic data of dynamic parameter model of fluid-solid coupled model. The stress sensitivity estimate is performed based the experimental results, and the new method is bring forward to estimate the actual reservoir rock. It also shows that the quadratic equation of effective stress and permeability is appropriate to the experimental data. The hysteresis effect of stress sensitivity is the appearance of the plastic deformation of rock, which is the reason of irreversible damage to the rock. This paper introduces the concept of permanent damage of reservoir physical properties such as permeability and porosity, and presents the calculational formula.
The fluid-solid coupled phenomenon is evident in low permeability reservoir. On the bases of a great number of theoretical studies of former researchers and the effective stress theory, this paper set up the mathematical model of reservoir rock and the seepage flow equation. The effective stress coefficient distinguishes the different effective stress equation. The reservoir rock deformation equation is resolved with the
引文
[1] 李允，陈军，张烈辉．一个新的低渗气藏开发数值模拟模型．天然气工业，2004，24(8)
[2] 贾文瑞，李福垲，肖敬修．低渗透油田开发部署中几个问题的研究．石油勘探与开发，1995，22(4)
[3] 石玉江，孙小平．长庆致密碎屑岩储集层应力敏感性分析．石油勘探与开发，2001年10月
[4] 阮敏，王连刚．低渗透油田开发与压敏效应．石油学报，2002年5月
[5] H. Ruistuen and L.W. Teufel. Influence of Reservoir Stress Path on Deformation and Permeability of Weakly Cemented Sandstone Reservoirs. SPE 56989
[6] Terzaghi K. Theoretical soil mechanics[M]. Wiley, NewYork, 1943
[7] J. Geertsma. The effect of fluid pressure decline on volumetric changes of porous rocks. Trans. AIME, 1957, 210:331-340
[8] Geertsma. J. The effective stress laws for fluid-saturated porous rocks. J. Geophys. Res., 78. 5911～5921
[9] P.V. Lade and R., De Boer. The concept of effective stress for soil, concrete and rock. Geotechnique, 1997, 47(1): 61～78
[10] Warpinski, N.R., Teufel, L.W. Determination of the effective stress law for permeability and deformation in low permeability rocks. SPE 20572
[11] 李传亮，孔祥言，徐献芝，李培超．多孔介质的双重有效应力．自然杂志，1999，Vol．5
[12] (苏)戈尔布诺夫(著)，李树宝(译)：异常油田开发，北京：石油工业出版社，1987
[13] Fatt, I., and Davis, D. H. Reduction in Permeability with Overburden Pressure. Trans., AIME (1952), 195
[14] Fatt, I. The Effect of Overburden Pressure on Relative Permeability. Trans., AIME (1953), 198, 325～326
[15] McLatchie, A. S., Hemstock, R. A., and Young, J. W. The Effective Compressibility of Reservoir Rock and Its Effects on Permeability. Trans., AIME (1958), 213,386～388
[16] Dobrynin, V. M. Effect of Overburden Pressure on Some Properties of Sandstone. SPEJ., (Dec., 1962), 360～366
[17] Brace, W. F., Walch, J. B, and Francos, W. T. Permeabilities of Granite under High Pressure. J. Geoph. Res., (1968), 73, No. 6:2225～2236
[18] Vairogs, J., Heam, C. N., Dareing, D. W., and Rhoades, V. W. Effect of Rock Stress on Gas Production from Low-Permeability Reservoirs. JPT., Sept., 1971, 1161～1167
[19] Wilhelmi, R., and Somerton, W. H. Simultaneous Measurement of Pore and Elastic Properties of Rocks under Triaxial Stress Conditions. SPEJ., (Sept., 1967), 283～294
[20] Wyble, D.O. Effect of Applied Pressure on the Conductivity, Porosity, and Permeability of Sandstones. JPT (Nov. 1958), 57
[21] Thomas, R. D. and Ward, D. C. Effect of Overburden Pressure and Water on Gas Permeability of Tight Sandstone Cores. JPT., February, 1972, 120～124
[22] Jones, F. O. and Owens, W. W. A Laboratory Study of Low Permeability Gas Sands. SPE 7551
[23] 范学平，等．用流固耦合方法研究油藏压裂后应力应变和孔渗特性变化．岩土力学，2001，22(1)
[24] 许季军．可变形多孔介质渗透率的实验研究．沈阳：东北大学硕士论文，1997
[25] 陈祖安，伍向阳，孙德明，杨伟．砂岩渗透率随静压力变化的关系研究．岩石力学与工程学报，1995，14(2)：155～159
[26] 张新红等．低渗岩心物性参数与应力关系的试验研究．石油大学学报(自然科学版)，2001，25(4)
[27] 范学平，徐向荣．地应力对岩心渗透率伤害实验及机理分析．石油勘探与开发，2002年4月
[28] 石玉江，孙小平．长庆致密碎屑岩储集层应力敏感性分析．石油勘探与开发，2001年10月
[29] 赵明跃，王新海，等．储层参数压力敏感性研究．油气井测试，2001年8月
[30] Casse, F. J., and Ramey, H. J. Jr. The Effect of Temperature and Confining Pressure on Single-Phase Flow in Consolidated Rocks. JPT., (Aug., 1979), 1051～1059
[31] Aruna, M. The Effect of Temperature and Pressure on Absolute Permeability of Sandstones. Ph.D. Dissertation, Stanford University, 1976
[32] Aruna, M. Arihara, N., and Ramey, H. J. Jr. The Effect of Temperature and Stress on the Absolute Permeability of Sandstones and Limestones. Presented at the American Nuclear Society Topical Meeting, April, 1977
[33] Aktan, T. and Farouq Ali, S. M. Effect of Cyclic and In-situ Heating on the Absolute Permeabilities, Elastic Constants, and Electrical Resistivities of Rocks. SPE 5633
[34] Somerton, W. H., and Gupta, V. S. Role of Fluxing Agents in Thermal Alteration of Sandstones. JPT., (May, 1965), 585～588
[35] Somerton, W. H., Mehta, M. M., and Dean, G. W. Thermal Alteration of Sandstones. JPT., (May, 1965), 589～593
[36] Weinbrandt, R. M., Ramey, H. J., Jr., and Casse, F. J. The Effect of Temperature on Relative and Absolute Permeability of Sandstones. SPEJ., (Oct., 1975), 376～384
[37] Brian David Gobran, William E. Brigham, and Henry J. Ramey Jr. Absolute Permeability as a Function of Confining Pressure, Pore Pressure and Temperature. SPE 10156
[38] 蒋海军，等．裂缝性储层应力敏感性实验研究．石油钻探技术，2000年12月
[39] Dobrynin, V. M. Effect of Overburden Pressure on Some Properties of Sandstone. SPEJ., (Dec., 1962), 360～366
[40] Soedder, D.J., and Randolf, P.L. Porosity, Permeability and Pore Structure of the Tight Mesaverde Sandstone, Pieeanee Basin, Colorado. SPEFE, (June 1987), 129～137
[41] J.P. Davies, and D.K. Davies. Stress-Dependent Permeability: Characterization and Modeling. SPE 56813
[42] 尹昕，应文敏．鄂尔多斯盆地大牛地气田上古生界低孔渗砂岩储层评价．矿物岩石，2005，25(2)
[43] 范学平，徐向荣．地应力对岩心渗透率伤害实验及机理分析．石油勘探与开发，2002年4月
[44] J.P. Davies, and D.K. Davies. Stress-Dependent Permeability: Characterization and Modeling. SPE 56813
[45] Bernabe, Y. An effective pressure law for permeability in Chelmsford granite and Barre granite. Int. J. Rock Mech. Min. Sci. Geomech. Abastr. 1986(23), 267～275
[46] Teufel, L.W., Rhett, D.W., and Farrell, H.E. Effect of Reservoir Depletion and Pore Pressure Drawdown on In Situ Stress and Deformation in the Ekofisk Field, North Sea. Proc. 32nd U.S. Symposium on Rock Mechanics, Norman, Oklahoma, 10-12 July 1991
[47] Teufel, L.W. Influence of Pore Pressure and Production-Induced Changes in Pore Pressure on In Situ Stress. Sandia National Laboratories Report No. SAND96-0534, 1996
[48] Rhett, D.W. and Teufel, L.W. Stress Path Dependence of Matrix Permeability of North Sea Sandstone Reservoir Rock. Proc 33rd U.S. Symposium on Rock Mechanics. Santa Fe, New Mexico, 3-5 June 1992, 345-355, J.R. Tillerson et al. (ed.)
[49] H. Ruistuen and L.W. Teufel. Influence of Reservoir Stress Path on Deformation. and Permeability of Weakly Cemented Sandstone Reservoirs. SPE 56989
[50] M. Khan, Lawrence W. Teufel. Determining the Effect of Geological and Geomechanical Parameters on Reservoir Stress path through Numerical Simulation. SPE 63261
[51] 王秀娟，赵永胜，等．低渗透储层应力敏感性与产能物性下限．石油与天然气地质，2003年6月
[52] Wissler, T.H., and G. Simmons. The physical properties of a set of sandstones, 2, Permanent and elastic strains in hydrostatic compression to 200MPa, Int. J. Rock Meck. Min. Sci. Geomech. Abstr. 22, 393～406, 1985
[53] Bernabe, Y. The effective pressure law for permeability during pore pressure and confining pressure cycling of several crystalline rocks. J. Geoph. Res. 92. No. B1,649～657
[54] Geertsma. J. The effective stress laws for fluid-saturated porous rocks. J. Geophys. Res., 78. 5911～5921
[55] P.V. Lade and R. De Boer. The concept of effective stress for soil, concrete and rock. Geotechnique, 1997, 47(1): 61～78
[56] 李传亮．多孔介质的有效应力及其应用研究[D]．合肥：中国科学技术大学， 2000
[57] Biot, M.A. General solution of the equation of elasticity and consolidation for a porous material. J.Appl.Mech. 1956,78:91～96
[58] Biot, M.A. Theory of deformation of a porous viscoelasic anisotropic solid. J. Appl. Phys. 1956, 27:452-469
[59] Finol A, Farouq Ali S M. Numerical simulation of oil production with simultaneous ground subsidence [J]. SPEJ, October, 1975:411～424
[60] Noorishad J, Ayatollahi M S, Witherspoon P A. A finite element method for coupled stress and fluid flow analysis in fractured rock masses[J].Int J Rock Mech Min Sci & Geomech Abstr.1982,(19):185～193
[61] Settari A, Kry P R, Yee C T. Coupling of fluid flow and soil behavior to model injection into uncemented oil sands[J]. JCPT, 1989, (1):81～92
[62] Bruno, M.S. and Nakagawa, F. M. pore pressure influence on tensile fracture propagation in sedimentary rock. Int. J. Rock Mech. Min. Sci. & Geomech.. Abstr. 1991, 28(4): 261～273
[63] Vandamme, M. and Roegiers, J. C. Poroelasticity in hydraulic fracturing simulators. JPT, 1990:1199～1203
[64] Chen, H.Y, Coupled Fluid Flow and Geomechanics in Reservoir Study.1. Theory and Governing Equations, SPE 30752
[65] Susan E. Minkoff, Charlesm. Stone, J. Staggered In Time Coupling of Reservoir Flow Simulation and Geomechanicl Deformation: Step one. way Coupling, SPE 51920
[66] Fung L S K. Reservoir simulation with a control-volume finite-element method [C]. SPE 21224
[67] Fung L S K. Coupled geomechanical-thermal simulation for deforming heavy oil reservoirs [J]. JCPT, 1994,(4):22～28
[68] Tortike W S, Farouq Ali S M. Prediction of oil sands failure due to steam-induced stresses [J]. JCPT, 1991,(1):87～96
[69] Mokhtar Kirane, Said Kouachi. Global solutions to a system of strongly coupled reaction diffusion equations[J]. Nonlinear Analysis, Theory, Methods and Applications, 1996, 26(8): 1387～1396
[70] Didier Lasseux,Michel Quintard.Determination of permeability tensorfor two plase flow in homogeneous porous media Ⅰ: Theory[J].Transport in Porous Media, 1996,24:107～137
[71] 吴林高，贺章安．考虑含水层参数随应力变化的地下水渗流．同济大学学报，1995，23(3)：281～287
[72] 李世平，李玉寿，吴振业．岩石全应力应变过程的渗透率．应变方程[J]．岩石工程学报，1995，17(2)：13～19
[73] 李锡夔，朴光虎，邓子辰．考虑固结效应的结构土壤相互作用分析及其有限元解．计算结构力学及其应用，1990，7(3)：1～11
[74] 陈平，张有天．裂隙岩体渗流与应力耦合分析[J]．岩石力学与工程学报，1994，13(4)：299～308
[75] 黎水泉，徐秉业．双重介质裂缝型油气藏油水两相流动与固体变形耦合数学模型[J]．天然气工业，1999，19(4)：43～45
[76] 件彦卿，柴军瑞．裂隙网络岩体三维渗流场与应力场耦合分析[J]．西安理工大学学报，2000，16(1)：1～5
[77] 冉启全，李仕伦等．用综合数值模拟方法预测油藏开发过程中的应力分布．钻采工艺，1995，18(4)：41～43
[78] 冉启全，顾小芸．弹塑性变形油藏中多相渗流的数值模拟[J]．计算力学学报，1999，16(1)：24～31
[79] 董平川．油气储层流固耦合理论、数值模拟及应用[D]．沈阳：东北大学．1998
[80] 范学平，李秀生等．低渗透气藏整体压裂流．固耦合渗流数学模拟．石油勘探与开发，2000，27(1)：76～83
[81] 范学平，李秀生，张士诚，徐向荣．低渗透变形介质油气藏渗流流固耦研究．新疆石油地质，2001，22(1)：76～78
[82] 刘建军，耿万东．地下水渗流的固液耦合理论及数值方法[J]．勘察科学技术，2000年第4期：7～9
[83] 刘建军．天然气流固耦合渗流计算的有限元方法[J]．新疆石油地质，2000，21(6)：487～490
[84] 刘建军，梁冰，章梦涛．非等温条件下煤层瓦斯运移规律研究．西安矿业学院学报，1999，19(4)
[85] 孙广忠．岩石结构力学．北京：科学出版社，1994
[86] I. Fatt. Pore volume compressibilities of sandstone reservoir rocks. Trans. AIME, 1958, 213～362
[87] W. Van der Knaap. Nonlinear behavior of elastic porous media. Trans. AIME, 1959,216:179～187
[88] M. K. Hubbert, W.W.Rubey. Role of fluid pressure in mechanics of ovderthrust faulting. Bull. Geol. Soc. Am., 1960, 70:115～205
[89] R.W. Zimmerman, W. H. Somerton, M. S. King. Compressibility of porous rocks. J. Geoph. Res., 1986, 91:765～777
[90] Wyllie, M. R. J. and Gardner, G. G. F. The generalized Kozeny-Carman equation. World Oil, April, 1958:210～228
[91] Darryl H. Fenwick, Martin J. Blunt. Network Modeling of Three-Phase Flow in Porous Media. 1998, SPE 38881
[92] Stig Bakke. 3-D Pore-Scale Modelling of Sandstones and Flow Simulations in the Pore Networks. 1997, SPE 35479
[93] 蒲秀刚，吴永平，周建生，廖前进，肖敦清，柳飒．低渗油气储层孔喉的分形结构与物性评价新参数．天然气工业，2005，25(12)
[94] 李留仁，赵艳艳，李忠兴，焦李成，薛中天．多孔介质微观孔隙结构分形特征及分形系数的意义．石油大学学报(自然科学版)，2004，28(3)
[95] Jennings, James B., Carroll, Herbert B., Raible, Clarence J. The relationship of permeability to confining pressure in low permeability rock.. SPE 9870
[96] Obert, L. and Duval, W. I. Rock mechanics and the design of structures in rock. John Wiley, New York, 1967:148-149
[97] 兰林，康毅力，等．储层应力敏感性评价实验方法与评价指标探讨．钻井液与完井液，2005，22(3)
[98] 蔡勇胜，范荣菊．渤南油田储层压力敏感性分析．油气地质与采收率，2003年8月
[99] Marcela Z. Formation Damage Evaluation by Means of FRT Test. SPE 81080
[100] 李传亮．储层岩石的应力敏感性评价方法．大庆石油地质与开发，2006，25(1)
[101] J．C耶格，N．G．W．库克著．中国科学院工程力学研究所译．岩石力学基础．北京：科学出版社，1981
[102] 谢康和，周健编著．岩石工程有限元分析理论与应用．北京：科学出版社，2002
[103] 刘先贵，刘建军．降压开采对低渗储层渗透性的影响．重庆大学学报(自然科学版)，2000，23(增刊)
[104] 冉启全，李士伦．流固耦合油藏数值模拟中物性参数动态模型研究．石油勘探与开发，1997，(24)3
[105] 陈祖安，伍向阳，孙德明，杨伟．砂岩渗透率随静压力变化的关系研究．岩石力学与工程学报，1995，14(2)
[106] 吴林高，缪俊发．渗流力学[M]．上海：上海科学技术文献出版社，1992
[107] 吴凡，孙黎娟，何江．孔隙度、渗透率与净覆压的规律研究和应用．西南石油学院学报，1999，21(4)
[108] 王正茂．油藏含砂流体渗流机理及流固耦合单井数值模拟研究[D]．成都：西南石油学院，2004
[109] 蒋维城．固体力学有限元分析．北京：北京理工大学出版社，1989
[110] 周志军，等．低渗透储层流固耦合渗流理论模型．大庆石油学院学报，2002，26(3)
[2] 贾文瑞，李福垲，肖敬修．低渗透油田开发部署中几个问题的研究．石油勘探与开发，1995，22(4)
[3] 石玉江，孙小平．长庆致密碎屑岩储集层应力敏感性分析．石油勘探与开发，2001年10月
[4] 阮敏，王连刚．低渗透油田开发与压敏效应．石油学报，2002年5月
[5] H. Ruistuen and L.W. Teufel. Influence of Reservoir Stress Path on Deformation and Permeability of Weakly Cemented Sandstone Reservoirs. SPE 56989
[6] Terzaghi K. Theoretical soil mechanics[M]. Wiley, NewYork, 1943
[7] J. Geertsma. The effect of fluid pressure decline on volumetric changes of porous rocks. Trans. AIME, 1957, 210:331-340
[8] Geertsma. J. The effective stress laws for fluid-saturated porous rocks. J. Geophys. Res., 78. 5911～5921
[9] P.V. Lade and R., De Boer. The concept of effective stress for soil, concrete and rock. Geotechnique, 1997, 47(1): 61～78
[10] Warpinski, N.R., Teufel, L.W. Determination of the effective stress law for permeability and deformation in low permeability rocks. SPE 20572
[11] 李传亮，孔祥言，徐献芝，李培超．多孔介质的双重有效应力．自然杂志，1999，Vol．5
[12] (苏)戈尔布诺夫(著)，李树宝(译)：异常油田开发，北京：石油工业出版社，1987
[13] Fatt, I., and Davis, D. H. Reduction in Permeability with Overburden Pressure. Trans., AIME (1952), 195
[14] Fatt, I. The Effect of Overburden Pressure on Relative Permeability. Trans., AIME (1953), 198, 325～326
[15] McLatchie, A. S., Hemstock, R. A., and Young, J. W. The Effective Compressibility of Reservoir Rock and Its Effects on Permeability. Trans., AIME (1958), 213,386～388
[16] Dobrynin, V. M. Effect of Overburden Pressure on Some Properties of Sandstone. SPEJ., (Dec., 1962), 360～366
[17] Brace, W. F., Walch, J. B, and Francos, W. T. Permeabilities of Granite under High Pressure. J. Geoph. Res., (1968), 73, No. 6:2225～2236
[18] Vairogs, J., Heam, C. N., Dareing, D. W., and Rhoades, V. W. Effect of Rock Stress on Gas Production from Low-Permeability Reservoirs. JPT., Sept., 1971, 1161～1167
[19] Wilhelmi, R., and Somerton, W. H. Simultaneous Measurement of Pore and Elastic Properties of Rocks under Triaxial Stress Conditions. SPEJ., (Sept., 1967), 283～294
[20] Wyble, D.O. Effect of Applied Pressure on the Conductivity, Porosity, and Permeability of Sandstones. JPT (Nov. 1958), 57
[21] Thomas, R. D. and Ward, D. C. Effect of Overburden Pressure and Water on Gas Permeability of Tight Sandstone Cores. JPT., February, 1972, 120～124
[22] Jones, F. O. and Owens, W. W. A Laboratory Study of Low Permeability Gas Sands. SPE 7551
[23] 范学平，等．用流固耦合方法研究油藏压裂后应力应变和孔渗特性变化．岩土力学，2001，22(1)
[24] 许季军．可变形多孔介质渗透率的实验研究．沈阳：东北大学硕士论文，1997
[25] 陈祖安，伍向阳，孙德明，杨伟．砂岩渗透率随静压力变化的关系研究．岩石力学与工程学报，1995，14(2)：155～159
[26] 张新红等．低渗岩心物性参数与应力关系的试验研究．石油大学学报(自然科学版)，2001，25(4)
[27] 范学平，徐向荣．地应力对岩心渗透率伤害实验及机理分析．石油勘探与开发，2002年4月
[28] 石玉江，孙小平．长庆致密碎屑岩储集层应力敏感性分析．石油勘探与开发，2001年10月
[29] 赵明跃，王新海，等．储层参数压力敏感性研究．油气井测试，2001年8月
[30] Casse, F. J., and Ramey, H. J. Jr. The Effect of Temperature and Confining Pressure on Single-Phase Flow in Consolidated Rocks. JPT., (Aug., 1979), 1051～1059
[31] Aruna, M. The Effect of Temperature and Pressure on Absolute Permeability of Sandstones. Ph.D. Dissertation, Stanford University, 1976
[32] Aruna, M. Arihara, N., and Ramey, H. J. Jr. The Effect of Temperature and Stress on the Absolute Permeability of Sandstones and Limestones. Presented at the American Nuclear Society Topical Meeting, April, 1977
[33] Aktan, T. and Farouq Ali, S. M. Effect of Cyclic and In-situ Heating on the Absolute Permeabilities, Elastic Constants, and Electrical Resistivities of Rocks. SPE 5633
[34] Somerton, W. H., and Gupta, V. S. Role of Fluxing Agents in Thermal Alteration of Sandstones. JPT., (May, 1965), 585～588
[35] Somerton, W. H., Mehta, M. M., and Dean, G. W. Thermal Alteration of Sandstones. JPT., (May, 1965), 589～593
[36] Weinbrandt, R. M., Ramey, H. J., Jr., and Casse, F. J. The Effect of Temperature on Relative and Absolute Permeability of Sandstones. SPEJ., (Oct., 1975), 376～384
[37] Brian David Gobran, William E. Brigham, and Henry J. Ramey Jr. Absolute Permeability as a Function of Confining Pressure, Pore Pressure and Temperature. SPE 10156
[38] 蒋海军，等．裂缝性储层应力敏感性实验研究．石油钻探技术，2000年12月
[39] Dobrynin, V. M. Effect of Overburden Pressure on Some Properties of Sandstone. SPEJ., (Dec., 1962), 360～366
[40] Soedder, D.J., and Randolf, P.L. Porosity, Permeability and Pore Structure of the Tight Mesaverde Sandstone, Pieeanee Basin, Colorado. SPEFE, (June 1987), 129～137
[41] J.P. Davies, and D.K. Davies. Stress-Dependent Permeability: Characterization and Modeling. SPE 56813
[42] 尹昕，应文敏．鄂尔多斯盆地大牛地气田上古生界低孔渗砂岩储层评价．矿物岩石，2005，25(2)
[43] 范学平，徐向荣．地应力对岩心渗透率伤害实验及机理分析．石油勘探与开发，2002年4月
[44] J.P. Davies, and D.K. Davies. Stress-Dependent Permeability: Characterization and Modeling. SPE 56813
[45] Bernabe, Y. An effective pressure law for permeability in Chelmsford granite and Barre granite. Int. J. Rock Mech. Min. Sci. Geomech. Abastr. 1986(23), 267～275
[46] Teufel, L.W., Rhett, D.W., and Farrell, H.E. Effect of Reservoir Depletion and Pore Pressure Drawdown on In Situ Stress and Deformation in the Ekofisk Field, North Sea. Proc. 32nd U.S. Symposium on Rock Mechanics, Norman, Oklahoma, 10-12 July 1991
[47] Teufel, L.W. Influence of Pore Pressure and Production-Induced Changes in Pore Pressure on In Situ Stress. Sandia National Laboratories Report No. SAND96-0534, 1996
[48] Rhett, D.W. and Teufel, L.W. Stress Path Dependence of Matrix Permeability of North Sea Sandstone Reservoir Rock. Proc 33rd U.S. Symposium on Rock Mechanics. Santa Fe, New Mexico, 3-5 June 1992, 345-355, J.R. Tillerson et al. (ed.)
[49] H. Ruistuen and L.W. Teufel. Influence of Reservoir Stress Path on Deformation. and Permeability of Weakly Cemented Sandstone Reservoirs. SPE 56989
[50] M. Khan, Lawrence W. Teufel. Determining the Effect of Geological and Geomechanical Parameters on Reservoir Stress path through Numerical Simulation. SPE 63261
[51] 王秀娟，赵永胜，等．低渗透储层应力敏感性与产能物性下限．石油与天然气地质，2003年6月
[52] Wissler, T.H., and G. Simmons. The physical properties of a set of sandstones, 2, Permanent and elastic strains in hydrostatic compression to 200MPa, Int. J. Rock Meck. Min. Sci. Geomech. Abstr. 22, 393～406, 1985
[53] Bernabe, Y. The effective pressure law for permeability during pore pressure and confining pressure cycling of several crystalline rocks. J. Geoph. Res. 92. No. B1,649～657
[54] Geertsma. J. The effective stress laws for fluid-saturated porous rocks. J. Geophys. Res., 78. 5911～5921
[55] P.V. Lade and R. De Boer. The concept of effective stress for soil, concrete and rock. Geotechnique, 1997, 47(1): 61～78
[56] 李传亮．多孔介质的有效应力及其应用研究[D]．合肥：中国科学技术大学， 2000
[57] Biot, M.A. General solution of the equation of elasticity and consolidation for a porous material. J.Appl.Mech. 1956,78:91～96
[58] Biot, M.A. Theory of deformation of a porous viscoelasic anisotropic solid. J. Appl. Phys. 1956, 27:452-469
[59] Finol A, Farouq Ali S M. Numerical simulation of oil production with simultaneous ground subsidence [J]. SPEJ, October, 1975:411～424
[60] Noorishad J, Ayatollahi M S, Witherspoon P A. A finite element method for coupled stress and fluid flow analysis in fractured rock masses[J].Int J Rock Mech Min Sci & Geomech Abstr.1982,(19):185～193
[61] Settari A, Kry P R, Yee C T. Coupling of fluid flow and soil behavior to model injection into uncemented oil sands[J]. JCPT, 1989, (1):81～92
[62] Bruno, M.S. and Nakagawa, F. M. pore pressure influence on tensile fracture propagation in sedimentary rock. Int. J. Rock Mech. Min. Sci. & Geomech.. Abstr. 1991, 28(4): 261～273
[63] Vandamme, M. and Roegiers, J. C. Poroelasticity in hydraulic fracturing simulators. JPT, 1990:1199～1203
[64] Chen, H.Y, Coupled Fluid Flow and Geomechanics in Reservoir Study.1. Theory and Governing Equations, SPE 30752
[65] Susan E. Minkoff, Charlesm. Stone, J. Staggered In Time Coupling of Reservoir Flow Simulation and Geomechanicl Deformation: Step one. way Coupling, SPE 51920
[66] Fung L S K. Reservoir simulation with a control-volume finite-element method [C]. SPE 21224
[67] Fung L S K. Coupled geomechanical-thermal simulation for deforming heavy oil reservoirs [J]. JCPT, 1994,(4):22～28
[68] Tortike W S, Farouq Ali S M. Prediction of oil sands failure due to steam-induced stresses [J]. JCPT, 1991,(1):87～96
[69] Mokhtar Kirane, Said Kouachi. Global solutions to a system of strongly coupled reaction diffusion equations[J]. Nonlinear Analysis, Theory, Methods and Applications, 1996, 26(8): 1387～1396
[70] Didier Lasseux,Michel Quintard.Determination of permeability tensorfor two plase flow in homogeneous porous media Ⅰ: Theory[J].Transport in Porous Media, 1996,24:107～137
[71] 吴林高，贺章安．考虑含水层参数随应力变化的地下水渗流．同济大学学报，1995，23(3)：281～287
[72] 李世平，李玉寿，吴振业．岩石全应力应变过程的渗透率．应变方程[J]．岩石工程学报，1995，17(2)：13～19
[73] 李锡夔，朴光虎，邓子辰．考虑固结效应的结构土壤相互作用分析及其有限元解．计算结构力学及其应用，1990，7(3)：1～11
[74] 陈平，张有天．裂隙岩体渗流与应力耦合分析[J]．岩石力学与工程学报，1994，13(4)：299～308
[75] 黎水泉，徐秉业．双重介质裂缝型油气藏油水两相流动与固体变形耦合数学模型[J]．天然气工业，1999，19(4)：43～45
[76] 件彦卿，柴军瑞．裂隙网络岩体三维渗流场与应力场耦合分析[J]．西安理工大学学报，2000，16(1)：1～5
[77] 冉启全，李仕伦等．用综合数值模拟方法预测油藏开发过程中的应力分布．钻采工艺，1995，18(4)：41～43
[78] 冉启全，顾小芸．弹塑性变形油藏中多相渗流的数值模拟[J]．计算力学学报，1999，16(1)：24～31
[79] 董平川．油气储层流固耦合理论、数值模拟及应用[D]．沈阳：东北大学．1998
[80] 范学平，李秀生等．低渗透气藏整体压裂流．固耦合渗流数学模拟．石油勘探与开发，2000，27(1)：76～83
[81] 范学平，李秀生，张士诚，徐向荣．低渗透变形介质油气藏渗流流固耦研究．新疆石油地质，2001，22(1)：76～78
[82] 刘建军，耿万东．地下水渗流的固液耦合理论及数值方法[J]．勘察科学技术，2000年第4期：7～9
[83] 刘建军．天然气流固耦合渗流计算的有限元方法[J]．新疆石油地质，2000，21(6)：487～490
[84] 刘建军，梁冰，章梦涛．非等温条件下煤层瓦斯运移规律研究．西安矿业学院学报，1999，19(4)
[85] 孙广忠．岩石结构力学．北京：科学出版社，1994
[86] I. Fatt. Pore volume compressibilities of sandstone reservoir rocks. Trans. AIME, 1958, 213～362
[87] W. Van der Knaap. Nonlinear behavior of elastic porous media. Trans. AIME, 1959,216:179～187
[88] M. K. Hubbert, W.W.Rubey. Role of fluid pressure in mechanics of ovderthrust faulting. Bull. Geol. Soc. Am., 1960, 70:115～205
[89] R.W. Zimmerman, W. H. Somerton, M. S. King. Compressibility of porous rocks. J. Geoph. Res., 1986, 91:765～777
[90] Wyllie, M. R. J. and Gardner, G. G. F. The generalized Kozeny-Carman equation. World Oil, April, 1958:210～228
[91] Darryl H. Fenwick, Martin J. Blunt. Network Modeling of Three-Phase Flow in Porous Media. 1998, SPE 38881
[92] Stig Bakke. 3-D Pore-Scale Modelling of Sandstones and Flow Simulations in the Pore Networks. 1997, SPE 35479
[93] 蒲秀刚，吴永平，周建生，廖前进，肖敦清，柳飒．低渗油气储层孔喉的分形结构与物性评价新参数．天然气工业，2005，25(12)
[94] 李留仁，赵艳艳，李忠兴，焦李成，薛中天．多孔介质微观孔隙结构分形特征及分形系数的意义．石油大学学报(自然科学版)，2004，28(3)
[95] Jennings, James B., Carroll, Herbert B., Raible, Clarence J. The relationship of permeability to confining pressure in low permeability rock.. SPE 9870
[96] Obert, L. and Duval, W. I. Rock mechanics and the design of structures in rock. John Wiley, New York, 1967:148-149
[97] 兰林，康毅力，等．储层应力敏感性评价实验方法与评价指标探讨．钻井液与完井液，2005，22(3)
[98] 蔡勇胜，范荣菊．渤南油田储层压力敏感性分析．油气地质与采收率，2003年8月
[99] Marcela Z. Formation Damage Evaluation by Means of FRT Test. SPE 81080
[100] 李传亮．储层岩石的应力敏感性评价方法．大庆石油地质与开发，2006，25(1)
[101] J．C耶格，N．G．W．库克著．中国科学院工程力学研究所译．岩石力学基础．北京：科学出版社，1981
[102] 谢康和，周健编著．岩石工程有限元分析理论与应用．北京：科学出版社，2002
[103] 刘先贵，刘建军．降压开采对低渗储层渗透性的影响．重庆大学学报(自然科学版)，2000，23(增刊)
[104] 冉启全，李士伦．流固耦合油藏数值模拟中物性参数动态模型研究．石油勘探与开发，1997，(24)3
[105] 陈祖安，伍向阳，孙德明，杨伟．砂岩渗透率随静压力变化的关系研究．岩石力学与工程学报，1995，14(2)
[106] 吴林高，缪俊发．渗流力学[M]．上海：上海科学技术文献出版社，1992
[107] 吴凡，孙黎娟，何江．孔隙度、渗透率与净覆压的规律研究和应用．西南石油学院学报，1999，21(4)
[108] 王正茂．油藏含砂流体渗流机理及流固耦合单井数值模拟研究[D]．成都：西南石油学院，2004
[109] 蒋维城．固体力学有限元分析．北京：北京理工大学出版社，1989
[110] 周志军，等．低渗透储层流固耦合渗流理论模型．大庆石油学院学报，2002，26(3)