水平井井筒—油藏耦合问题的理论与试验研究
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摘要
水平井技术是一项高效的油田开发、挖潜、提高采收率技术，近年来在油气勘探与开发中得到了广泛的应用。水平井注采过程中，井筒与油藏互为边界条件，相互影响，相互制约，构成了一个复杂的井筒-油藏耦合动力学系统。开展水平井井筒-油藏耦合问题的理论及试验研究，对于认清井筒、油藏耦合机制，预测注采动态，优化注采方案，提高水平井开发效果具有十分重要的意义。本文重点开展了以下几方面工作：
1、从井筒、油藏流动特征及耦合机理出发，基于固体力学、流体力学、渗流力学、传热学等相关理论，采用连续介质力学方法建立了一个综合的水平井井筒-油藏耦合数学模型。其中，井筒自由流采用Navier-Stokes（NS）方程描述，油藏多孔介质渗流采用Darcy定律（DL）描述。该模型在考虑井筒管流与油藏渗流耦合的同时，还考虑了流场与温度场以及岩体变形场之间的耦合，为水平井井筒-油藏系统动态特性研究提供了理论依据。
2、利用Brinkman（BR）方程描述井筒自由流与油藏多孔介质渗流之间的近井过渡流，建立了基于NS-BR-DL耦合的井筒管流与油藏渗流耦合方法，为井筒管流与油藏渗流耦合过程的准确描述以及耦合机制的深入研究提供了新的途径。其中，NS方程和BR方程采用稳定化Galerkin最小二乘有限元离散，DL方程采用标准Galerkin有限元离散，三类方程同时联立求解。在前人研究的基础上，考虑井筒在不同流动形态下径向流入/流出对其沿程压力损失的影响，提出了改进的等效渗流模型及方法，为油田级大尺度井筒管流与油藏渗流耦合数值模拟提供了有效途径。
3、在改进等效渗流法基础上，针对热-流-变形耦合条件下的水平井井筒-油藏双重耦合问题，提出了基于Galerkin有限元空间离散技术和二阶向后差分时间离散技术的迭代求解方案。热对流扩散方程采用稳定化人工粘性方法求解，避免了对流占优条件下标准Galerkin有限元法的伪数值震荡问题。定量分析了水平井注汽和采油过程中井筒-油藏系统的温度、压力、应力、孔渗特性时空变化规律和动态耦合关系。
4、基于源函数思想和势的叠加原理，建立了渗流-变形弱耦合条件下均质各向同性油藏水平井井筒-油藏耦合问题的半解析方法，并通过坐标变换和非均质性定量表征等一系列手段将该方法推广到大斜度井和非均质、各向异性油藏，为水平井注采动态的快速预测提供了有效的途径。定量分析了井斜角、渗透率非均质性和各向异性对水平井流入动态及流量/压力剖面的影响。
5、基于势的叠加原理，将定量表征孔眼汇聚流及近井地层损害的经验表皮系数法与源函数法相结合，实现了射孔水平井井筒-油藏耦合问题的半解析求解。在此基础上，提出了通过变孔深、变孔密射孔调整非均质油藏水平井产液剖面的新方法，为水平井射孔方案设计提供了理论依据。定量分析了套管尺寸和近井非均质性对水平井变参数射孔的影响。
6、基于流动相似理论，开展了射孔水平井井筒-油藏耦合的地面小比例模型试验。通过不同射孔方案下射孔井段的流量数据对比，验证了水平井变参数射孔方法的调剖效果，并提出了相关应用建议。在此基础上，采用Visual Basic编程语言开发了配套的水平井射孔优化设计软件，对油田现场10口水平井的射孔方案进行优化设计，通过优化前后生产数据测试结果对比，进一步检验了变参数射孔调剖方法的应用效果。
Horizontal well technology is an efficient oilfield developing and potential tapping technology,which enhances oil recovery and has been widely used in oil and gas exploration and development inrecent years. During injection and production processes, wellbore and reservoir influence and restricteach other, constituting a complex wellbore-reservoir coupling dynamical system. Theoretical andexperimental studies on wellbore-reservoir coupling for horizontal wells are significant for therecognition of coupling mechanism and the prediction of injection/production performances. Theresults can also guide the optimization of injection/production programs and improve the developmenteffect of horizontal wells.
In this paper, the main works are as follows:
1. Considering the flow characteristics and coupling mechanism of wellbore and reservoir, acomprehensive wellbore-reservoir coupling model is developed by using continuum mechanicsapproach, based on the theories of solid mechanics, fluid mechanics, seepage mechanics and heattransfer. In this model, the free flow in wellbore is described by Navier-Stokes equation (NS), and theporous media flow in reservoir is described by Darcy Law (DL). Not only the coupling of wellboreflow and reservoir flow, but also the coupling of fluid flow, heat transfer and rock deformation, aretaken into account in this model, which provides a theoretical basis for the dynamic characteristicstudy of wellbore-reservoir system.
2. By using Brinkman equation (BR) to describe the near-well transitional flow between the freeflow in wellbore and the porous media flow in reservoir, a NS-BR-DL-based approach to couplewellbore flow and reservoir flow is established, which provides a new way for more accuratedescription of the coupling process and further study of the coupling mechanism. In addition, theNavies-Stokes and Brinkman equations discretized by Galerkin/least-squares finite element method,along with the Darcy Equation discretized by standard Galerkin finite element method are solvedsimultaneously. On the basis of previous research, an improved equivalent permeability model andmethod is developed, considering the influence of radial inflow/outflow on the pressure loss along thewellbore under different flow patterns. The results can provide an effective way for the oilfield-level,large-scale numerical simulation of coupled wellbore flow and reservoir flow.
3. Based on the improved equivalent permeability method, an iterative solution method isestablished for double coupled wellbore-reservoir problems under the thermal-hydro-mechanicalcoupling conditions. This method uses standard Galerkin finite element method for spatial discretization and second order backward difference method for temporal discretization. The thermalconvection diffusion equation is solved by using stabilized artificial viscosity method, which avoidsspurious oscillations of standard Galerkin finite element method under convection dominatedconditions. Considering the wellbore-reservoir system in both steam injection and oil productionprocesses, temporal/spatial variations and dynamic coupling relationships of temperature, pressure,stress, porosity and permeability characteristics are analyzed quantitatively.
4. Based on the idea of source function and the principle of potential superposition, asemi-analytical method for wellbore-reservoir coupling problems is developed for horizontal wells inhomogeneous isotropic reservoirs under weak hydro-mechanical coupling conditions. Extended by aseries of measures, such as coordinate transformation and heterogeneity quantitative characterization,this method can also apply to highly deviated wells and heterogeneous, anisotropic reservoirs,providing an effective way for quick prediction of injection/production performances of horizontalwells.. The effects of deviation angle, heterogeneity and anisotropy on the inflow performance andflow/pressure profiles of horizontal wells are studied quantitatively.
5. Based on the principle of potential superposition, empirical skin factor method for quantitativecharacterization of perforation convergence and near-well formation damage is combined with sourcefunction method for the semi-analytical solution of wellbore-reservoir coupling problems ofperforated horizontal wells. On this basis, a new method for adjusting production profiles ofhorizontal wells in heterogeneous reservoirs through variable-depth and variable-density perforatingis proposed, which provides a theoretical basis for the design of perforating program of horizontalwells. The effects of casing size and near-well heterogeneity on variable-parameter perforating areanalyzed quantitatively.
6. Based on the theory of flow similarity, ground small-scale model tests of perforatedhorizontal-well wellbore-reservoir coupling are carried out. Comparing flow data of perforatedsegments under different perforating programs, the effect of adjusting production profiles of thevariable-parameter perforating method is verified and some related recommendations for applicationare given. On this basis, a perforation optimization software for horizontal wells is developed inVisual Basic, by which the perforation programs of10horizontal wells in oil field are optimized.Through comparison of production data before and after optimization, the effects of thevariable-parameter perforating method are further examined.
1、从井筒、油藏流动特征及耦合机理出发，基于固体力学、流体力学、渗流力学、传热学等相关理论，采用连续介质力学方法建立了一个综合的水平井井筒-油藏耦合数学模型。其中，井筒自由流采用Navier-Stokes（NS）方程描述，油藏多孔介质渗流采用Darcy定律（DL）描述。该模型在考虑井筒管流与油藏渗流耦合的同时，还考虑了流场与温度场以及岩体变形场之间的耦合，为水平井井筒-油藏系统动态特性研究提供了理论依据。
2、利用Brinkman（BR）方程描述井筒自由流与油藏多孔介质渗流之间的近井过渡流，建立了基于NS-BR-DL耦合的井筒管流与油藏渗流耦合方法，为井筒管流与油藏渗流耦合过程的准确描述以及耦合机制的深入研究提供了新的途径。其中，NS方程和BR方程采用稳定化Galerkin最小二乘有限元离散，DL方程采用标准Galerkin有限元离散，三类方程同时联立求解。在前人研究的基础上，考虑井筒在不同流动形态下径向流入/流出对其沿程压力损失的影响，提出了改进的等效渗流模型及方法，为油田级大尺度井筒管流与油藏渗流耦合数值模拟提供了有效途径。
3、在改进等效渗流法基础上，针对热-流-变形耦合条件下的水平井井筒-油藏双重耦合问题，提出了基于Galerkin有限元空间离散技术和二阶向后差分时间离散技术的迭代求解方案。热对流扩散方程采用稳定化人工粘性方法求解，避免了对流占优条件下标准Galerkin有限元法的伪数值震荡问题。定量分析了水平井注汽和采油过程中井筒-油藏系统的温度、压力、应力、孔渗特性时空变化规律和动态耦合关系。
4、基于源函数思想和势的叠加原理，建立了渗流-变形弱耦合条件下均质各向同性油藏水平井井筒-油藏耦合问题的半解析方法，并通过坐标变换和非均质性定量表征等一系列手段将该方法推广到大斜度井和非均质、各向异性油藏，为水平井注采动态的快速预测提供了有效的途径。定量分析了井斜角、渗透率非均质性和各向异性对水平井流入动态及流量/压力剖面的影响。
5、基于势的叠加原理，将定量表征孔眼汇聚流及近井地层损害的经验表皮系数法与源函数法相结合，实现了射孔水平井井筒-油藏耦合问题的半解析求解。在此基础上，提出了通过变孔深、变孔密射孔调整非均质油藏水平井产液剖面的新方法，为水平井射孔方案设计提供了理论依据。定量分析了套管尺寸和近井非均质性对水平井变参数射孔的影响。
6、基于流动相似理论，开展了射孔水平井井筒-油藏耦合的地面小比例模型试验。通过不同射孔方案下射孔井段的流量数据对比，验证了水平井变参数射孔方法的调剖效果，并提出了相关应用建议。在此基础上，采用Visual Basic编程语言开发了配套的水平井射孔优化设计软件，对油田现场10口水平井的射孔方案进行优化设计，通过优化前后生产数据测试结果对比，进一步检验了变参数射孔调剖方法的应用效果。
Horizontal well technology is an efficient oilfield developing and potential tapping technology,which enhances oil recovery and has been widely used in oil and gas exploration and development inrecent years. During injection and production processes, wellbore and reservoir influence and restricteach other, constituting a complex wellbore-reservoir coupling dynamical system. Theoretical andexperimental studies on wellbore-reservoir coupling for horizontal wells are significant for therecognition of coupling mechanism and the prediction of injection/production performances. Theresults can also guide the optimization of injection/production programs and improve the developmenteffect of horizontal wells.
In this paper, the main works are as follows:
1. Considering the flow characteristics and coupling mechanism of wellbore and reservoir, acomprehensive wellbore-reservoir coupling model is developed by using continuum mechanicsapproach, based on the theories of solid mechanics, fluid mechanics, seepage mechanics and heattransfer. In this model, the free flow in wellbore is described by Navier-Stokes equation (NS), and theporous media flow in reservoir is described by Darcy Law (DL). Not only the coupling of wellboreflow and reservoir flow, but also the coupling of fluid flow, heat transfer and rock deformation, aretaken into account in this model, which provides a theoretical basis for the dynamic characteristicstudy of wellbore-reservoir system.
2. By using Brinkman equation (BR) to describe the near-well transitional flow between the freeflow in wellbore and the porous media flow in reservoir, a NS-BR-DL-based approach to couplewellbore flow and reservoir flow is established, which provides a new way for more accuratedescription of the coupling process and further study of the coupling mechanism. In addition, theNavies-Stokes and Brinkman equations discretized by Galerkin/least-squares finite element method,along with the Darcy Equation discretized by standard Galerkin finite element method are solvedsimultaneously. On the basis of previous research, an improved equivalent permeability model andmethod is developed, considering the influence of radial inflow/outflow on the pressure loss along thewellbore under different flow patterns. The results can provide an effective way for the oilfield-level,large-scale numerical simulation of coupled wellbore flow and reservoir flow.
3. Based on the improved equivalent permeability method, an iterative solution method isestablished for double coupled wellbore-reservoir problems under the thermal-hydro-mechanicalcoupling conditions. This method uses standard Galerkin finite element method for spatial discretization and second order backward difference method for temporal discretization. The thermalconvection diffusion equation is solved by using stabilized artificial viscosity method, which avoidsspurious oscillations of standard Galerkin finite element method under convection dominatedconditions. Considering the wellbore-reservoir system in both steam injection and oil productionprocesses, temporal/spatial variations and dynamic coupling relationships of temperature, pressure,stress, porosity and permeability characteristics are analyzed quantitatively.
4. Based on the idea of source function and the principle of potential superposition, asemi-analytical method for wellbore-reservoir coupling problems is developed for horizontal wells inhomogeneous isotropic reservoirs under weak hydro-mechanical coupling conditions. Extended by aseries of measures, such as coordinate transformation and heterogeneity quantitative characterization,this method can also apply to highly deviated wells and heterogeneous, anisotropic reservoirs,providing an effective way for quick prediction of injection/production performances of horizontalwells.. The effects of deviation angle, heterogeneity and anisotropy on the inflow performance andflow/pressure profiles of horizontal wells are studied quantitatively.
5. Based on the principle of potential superposition, empirical skin factor method for quantitativecharacterization of perforation convergence and near-well formation damage is combined with sourcefunction method for the semi-analytical solution of wellbore-reservoir coupling problems ofperforated horizontal wells. On this basis, a new method for adjusting production profiles ofhorizontal wells in heterogeneous reservoirs through variable-depth and variable-density perforatingis proposed, which provides a theoretical basis for the design of perforating program of horizontalwells. The effects of casing size and near-well heterogeneity on variable-parameter perforating areanalyzed quantitatively.
6. Based on the theory of flow similarity, ground small-scale model tests of perforatedhorizontal-well wellbore-reservoir coupling are carried out. Comparing flow data of perforatedsegments under different perforating programs, the effect of adjusting production profiles of thevariable-parameter perforating method is verified and some related recommendations for applicationare given. On this basis, a perforation optimization software for horizontal wells is developed inVisual Basic, by which the perforation programs of10horizontal wells in oil field are optimized.Through comparison of production data before and after optimization, the effects of thevariable-parameter perforating method are further examined.
引文
[1] Joshi, S.D.,班景昌.水平井工艺技术.北京:石油工业出版社,1998.
[2]陈红伟,郝振宪,何汉坤,等.水平井设计应用与展望.钻采工艺,2004,27(6):8-11.
[3]郑俊德,杨长祜.水平井,分支井采油工艺现状分析与展望.石油钻采工艺,2006,27(6):93-96.
[4]沈忠厚.现代钻井技术发展趋势.石油勘探与开发,2005,32(1):89-91.
[5] Douglas Jr J, Peaceman D W, Rachford Jr H H. A method for calculating multi-dimensionalimmiscible displacement. Trans., AIME,1959,216:297-308.
[6] Shutler N D. Numerical three-phase model of the two-dimensional steamflood process. Old SPEJournal,1970,10(4):405-417.
[7] Settari A, Aziz K. A computer model for two-phase coning simulation.1974(3):221-236.
[8] Williamson A S, Chappelear J E. Representing wells in numerical reservoir simulation: part1-theory.1981(06):323-338.
[9] Siu A, Li Y, Nghlem L, et al. Numerical modelling of a thermal horizontal well. Annual TechnicalMeeting, Calgary, Alberta,1990.
[10] Winterfeld P H. Simulation of pressure buildup in a multiphase wellbore/reservoir system. SPEFormation Evaluation,1989(2):247-252.
[11] Almehaideb R A, Aziz K, Pedrosa Jr O A. A reservoir/wellbore model for multiphase injection andpressure transient analysis. Middle East Oil Show, Bahrain,1989.
[12] Xiao J J, Fuentes-N F A, Alhanati F, et al. Modeling and analyzing pressure buildup data affected byphase redistribution in the wellbore. SPE Advanced Technology Series,1996,4(1):28-37.
[13] Livescu S, Durlofsky L J, Aziz K, et al. A new model for simulating nonisothermal multiphase flowin wellbores and pipes.2008.
[14] Stone T W, Edmunds N R, Kristoff B J. A comprehensive wellbore/reservoir simulator. SPESymposium on Reservoir Simulation, Houston, Texas,1989.
[15] Coats K H. A highly implicit steamflood model.1978(10):369-383.
[16] Su H, Lee S H. Modeling transient wellbore behavior in horizontal wells. International Meeting onPetroleum Engineering, Beijing, China,1995.
[17] Nolen J, Berry D W. Tests of the stability and time-step sensitivity of semi-implicit reservoirstimulation techniques. Old SPE Journal,1972,12(3):253-266.
[18] Collins D, Nghiem L, Sharma R, et al. Field-scale simulation of horizontal wells. Journal of CanadianPetroleum Technology,1992,31(1):14-21.
[19]陈崇希.岩溶管道—裂隙—孔隙三重空隙介质地下水流模型及模拟方法.地球科学：中国地质大学学报,1995,20(4):361-366.
[20]吴淑红,刘翔鹗,郭尚平.水平段井筒管流的简化模型.石油勘探与开发,1999,26(4):64-65.
[21] Peaceman D W. Interpretation of well-block pressures in numerical reservoir simulation(includesassociated paper6988).1978,18(3):183-194.
[22] Peaceman D W. Interpretation of well-block pressures in numerical reservoir simulation withnonsquare grid blocks and anisotropic permeability.1983,23(3):531-543.
[23] Morita N, Singh S P, Chen H S, et al. Three-dimensional well model pre-processors for reservoirsimulation with horizontal and curved inclined wells. SPE Annual Technical Conference andExhibition, New Orleans, Louisiana,1990.
[24] Babu D K, Odeh A S, Al-Khalifa A J, et al. The relation between wellblock and wellbore pressures innumerical simulation of horizontal wells. SPE Reservoir Engineering,1991,6(3):324-328.
[25] Ewing R E, Lazarov R D, Lyons S L, et al. Numerical well model for non-darcy flow throughisotropic porous media. Computational Geosciences,1999,3(3):185-204.
[26] Ding Y U, Renard G. A new representation of wells in numerical reservoir simulation. SPE ReservoirEngineering,1994,9(2):140-144.
[27] Ding Y, Renard G, Weill L. Representation of wells in numerical reservoir simulation. SPE ReservoirEvaluation&Engineering,1998,1(1):18-23.
[28] Chen Z, Zhang Y. Well flow models for various numerical methods. International Journal ofNumerical Analysis&Modeling,2009,6(3):375-388.
[29] Krogstad S, Durlofsky L J. Multiscale mixed-finite-element modeling of coupled wellbore/near-wellflow. SPE Journal,2009(1):78-87.
[30] Collins D, Nghiem L, Sharma R, et al. Field-scale simulation of horizontal wells with hybrid grids.11th SPE Symposium on Reservoir Simulation, Anaheim, California,1991.
[31] Ewing R E, Boyett B A, Babu D K, et al. Efficient use of locally refined grids for multiphasereservoir simulation. SPE Symposium on Reservoir Simulation, Houston, TX,1989.
[32] Pedrosa Jr O, Aziz K. Use of a hybrid grid in reservoir simulation. SPE Reservoir Engineering,1986,1(6):611-621.
[33] Oliveira R. Study of the horizontal wellbore and reservoir coupling. SPE Annual TechnicalConference and Exhibition, Denver, Colorado, USA,2011.
[34] Bahonar M, Azaiez J, Chen Z. A semi-unsteady-state wellbore steam/water flow model for predictionof sandface conditions in steam injection wells. Journal of Canadian Petroleum Technology,2010,49(09):13-21.
[35] Dikken B J. Pressure drop in horizontal wells and its effect on production performance. SPE Journalof Petroleum Technology,1990,42(11):1426-1433.
[36] Ozkan E, Sarica C, Haciislamoglu M, et al. The influence of pressure drop along the wellbore onhorizontal well productivity. Production Operations Symposium, Oklahoma,1993.
[37] Sarica C, Haciislamoglu M, Raghavan R, et al. influence of wellbore hydraulics on pressure behaviorand productivity of horizontal gas wells. SPE Annual Technical Conference and Exhibition, NewOrleans, Louisiana,1994.
[38] Suzuki K. Influence of wellbore hydraulics on horizontal well pressure transient behavior. SPEFormation Evaluation,1997(3):175-181.
[39] Ouyang L, Aziz K. A simplified approach to couple wellbore flow and reservoir inflow for arbitrarywell configurations. SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana,1998.
[40] Penmatcha V R, Aziz K. A comprehensive reservoir/wellbore model for horizontal wells. SPE IndiaOil and Gas Conference and Exhibition, New Delhi, India,1998.
[41]刘想平,蒋志祥.射孔完井的水平井向井流动态关系.石油勘探与开发,1999,26(2):71-78.
[42]刘想平,郭呈柱,蒋志祥,等.油层中渗流与水平井筒内流动的耦合模型.石油学报,1999,20(3):82-86.
[43]苏玉亮,张东,李明忠.油藏中渗流与水平井筒内流动的耦合数学模型.中国矿业大学学报,2007,36(06):752-758.
[44] Terzaghi K. Principles of soil mechanics. Engineering News Record,1925,95(8).
[45] Biot M A. General theory of three‐dimensional consolidation. Journal of Applied Physics,1941,12(2):155-164.
[46] Biot M A. Theory of elasticity and consolidation for a porous anisotropic solid.1955,26(2):182-185.
[47] Geertsma J. Problems of rock mechanics in petroleum production engineering.1st ISRM Congress,Lisbon, Portugal,1966.
[48] Geertsma J. Land subsidence above compacting oil and gas reservoirs. SPE Journal of PetroleumTechnology,1973(6):734-744.
[49] Finol A, Farouq Ali S M. Numerical simulation of oil production with simultaneous groundsubsidence.1975(5):411-424.
[50] Merle H A, Kentie C J P, van Opstal G H C, et al. The bachaquero study-a composite analysis of thebehavior of a compaction drive/solution gas drive reservoir. SPE Journal of Petroleum Technology,1976(9):1107-1115.
[51] Rattia A J, Farouq Ali S M. Effect of formation compaction on steam injection response. SPE AnnualTechnical Conference and Exhibition, San Antonio, Texas,1981.
[52] Chase Jr C A, Dietrich J K. compaction within the south belridge diatomite. SPE ReservoirEngineering,1989(4):422-428.
[53] Boade R, Chin L, Siemers W. Forecasting of ekofisk reservoir compaction and subsidence bynumerical simulation,1988.
[54] Fredrich J T, Arguello J G, Deitrick G L, et al. Geomechanical modeling of reservoir compaction,surface subsidence, and casing damage at the belridge diatomite field. SPE Reservoir Evaluation&Engineering,2000,3(4):348-359.
[55] Fung L, Wan R, Rodriguez H, et al. An advanced elasto-plastic model for borehole stability analysisof horizontal wells in unconsolidated formation. Journal of Canadian Petroleum Technology,1999,38(12):41-49.
[56] Ali S M F, Blunschi J. Cyclic steam stimulation with formation parting. Annual Technical Meeting,Banff,1983.
[57] Settari A, Kry P R, Yee C T. Coupling of fluid flow and soil behaviour to model injection intouncemented oil sands. Journal of Canadian Petroleum Technology,1989,28(1):81-92.
[58] Tortike W S, Ali S M F. Prediction of oil sand failure due to steam-induced stresses. Journal ofCanadian Petroleum Technology,1991,30(01):87-95.
[59] Tortike W S, Ali S M F. Reservoir simulation integrated with geomechanics. Journal of CanadianPetroleum Technology,1993,32(05):28-37.
[60] Fung L S K. A coupled geomechanic-multiphase flow model for analysis of in situ recovery incohesionless oil sands. Journal of Canadian Petroleum Technology,1992,31(06):56-67.
[61] Chin L Y, Raghavan R, Thomas L K. fully coupled geomechanics and fluid-flow analysis of wellswith stress-dependent permeability. SPE Journal,2000(1):32-45.
[62] Pinzon C L, Chen H, Teufel L W. numerical well test analysis of stress-sensitive reservoirs. SPERocky Mountain Petroleum Technology Conference, Keystone, Colorado,2001.
[63] Chen H, Teufel L W. Coupling fluid-flow and geomechanics in dual-porosity modeling of naturallyfractured reservoirs. SPE Annual Technical Conference and Exhibition, San Antonio, Texas,1997.
[64] Lewis R W, Ghafouri H R. A novel finite element double porosity model for multiphase flow throughdeformable fractured porous media.1997,21(11):789-816.
[65] Bagheri M A, Settari A. Modeling of geomechanics in naturally fractured reservoirs. SPE ReservoirEvaluation&Engineering,2008(02):108-118.
[66] Jabbari H, Zeng Z. A three-parameter dual porosity model for naturally fractured reservoirs. SPEWestern North American Region Meeting, Anchorage, Alaska, USA,2011.
[67]董平川,徐小荷.储层流固耦合的数学模型及其有限元方程.石油学报,1998,19(1):64-70.
[68]薛世峰.非混溶饱和两相渗流与变形孔隙介质耦合作用的理论研究及其在石油开发中的应用,
[博士学位论文].北京:中国地震局地质研究所,2000.
[69]徐向荣,范学平.油藏多相流体渗流流-固耦合数学模拟研究.岩石力学与工程学报,2002,21(01):93-97.
[70]黎水泉,徐秉业,段永刚.裂缝性油藏流固耦合渗流.计算力学学报,2001,18(02):133-137.
[71]刘建军,裴桂红.裂缝性低渗透油藏流固耦合渗流分析.应用力学学报,2004,21(01):37-39.
[72]王自明,杜志敏.变温条件下弹塑性油藏中多相渗流的流固耦合数学模型与数值模拟.石油勘探与开发,2001,28(06):68-72.
[73]薛世峰,马利成.热采过程中地层超孔隙压力与井眼应力的定量评价.中国石油大学学报(自然科学版),2006,30(04):78-81.
[74] Gutierrex M, Lewis R W. The role of geomechanics in reservoir simulation. SPE/ISRM RockMechanics in Petroleum Engineering, Trondheim, Norway,1998.
[75] Schrefler B A, Simoni L, Turska E. Standard staggered and staggered newton schemes inthermo-hydro-mechanical problems. Comput. Methods Appl. Mech. Engrg.,1997,144(01):93-109.
[76] Lewis R W, Sukirman Y. Finite element modelling of three-phase flow in deforming saturated oilreservoirs. International Journal for Numerical and Analytical Methods in Meomechanics,1993,17(8):577-598.
[77] Yin S, Dusseault M B, Rothenburg L. Thermal reservoir modeling in petroleum geomechanics.International Journal for Numerical and Analytical Methods in Geomechanics,2009,33(4):449-485.
[78] Du Du J, Wong R C K. Development of a coupled geomechanics-thermal reservoir simulator usingfinite element method. Canadian International Petroleum Conference, Calgary, Alberta,2005.
[79] Chin L Y, Raghavan R, Thomas L K. Fully coupled analysis of well responses in stress-sensitivereservoirs. SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana,1998.
[80] Lewis R W, Sukirman Y. Finite element modelling for simulating the surface subsidence above acompacting hydrocarbon reservoir. International Journal for Numerical and Analytical Methods inGeomechanics,1994,18(9):619-639.
[81] Tran D, Nghiem L, Buchanan L. Improved iterative coupling of geomechanics with reservoirsimulation. SPE Reservoir Simulation Symposium, The Woodlands, Texas,2005.
[82] Tran D, Settari A, Nghiem L. New iterative coupling between a reservoir simulator and ageomechanics module. SPE Journal,2004(3):362-369.
[83] Thomas L K, Chin L Y, Pierson R G, et al. Coupled geomechanics and reservoir simulation. SPEAnnual Technical Conference and Exhibition, San Antonio, Texas,2002.
[84] Settari A, Mourits F M. a coupled reservoir and geomechanical simulation system. SPE Journal,1998(3):219-226.
[85] Huang M, Zienkiewicz O C. New unconditionally stable staggered solution procedures for coupledsoil‐pore fluid dynamic problems. International journal for numerical methods in engineering,1998,43(6):1029-1052.
[86] Zienkiewicz O C, Paul D K, Chan A. Unconditionally stable staggered solution procedure forsoil‐pore fluid interaction problems. International Journal for Numerical Methods in Engineering,1988,26(5):1039-1055.
[87] Minkoff S E, Stone C M, Bryant S, et al. Coupled fluid flow and geomechanical deformationmodeling. Journal of Petroleum Science and Engineering,2003,38(1-2):37-56.
[88] Settari A, Walters D A. advances in coupled geomechanical and reservoir modeling with applicationsto reservoir compaction. SPE Journal,2001(09):334-342.
[89] Fung L S K, Buchanan L, Wan R G. Coupled geomechanical-thermal simulation for deformingheavy-oil reservoirs. Journal of Canadian Petroleum Technology,1994,33(4):22-28.
[90] Settari A, Mourits F M. Coupling of geomechanics and reservoir simulation models. ComputerMethods and Advances in Geomechanics,1994,3:2151-2158.
[91] Minkoff S, Stone C, Arguello J, et al. Staggered in time coupling of reservoir flow simulation andgeomechanical deformation: step1-one-way coupling. SPE Symposium on Reservoir Simulation,Houston, Texas,1999.
[92] Fredrich J T, Arguello J G, Thorne B J, et al. Three-dimensional geomechanical simulation ofreservoir compaction and implications for well failures in the belridge diatomite. SPE AnnualTechnical Conference and Exhibition, Denver, Colorado, U.S.A,1996.
[93]万仁溥.现代完井工程.北京:石油工业出版社,2000.
[94] Landman M J, Goldthorpe W H. Optimization of perforation distribution for horizontal wells. SPEAsia-Pacific Conference, Perth. Australia,1991.
[95] Marett B P, Landman M J. Optimal perforation design for horizontal wells in reservoirs withboundaries. SPE Asia Pacific Oil and Gas Conference, Singapore,1993.
[96] Asheim H, Oudeman P. Determination of perforation schemes to control production and injectionprofiles along horizontal wells. SPE Drilling&Completion,1997,12(1):13-18.
[97]周生田,马德泉,等.射孔水平井孔眼分布优化研究.石油大学学报：自然科学版,2002,26(3):52-54.
[98]刘冰,徐兴平,李继志,等.基于序列二次规划算法的射孔水平井孔眼分布优化.中国石油大学学报(自然科学版),2010,34(04):79-83.
[99]刘冰,徐兴平,李继志.水平井射孔优化设计的增广拉格朗日乘子法.钻采工艺,2010(03):67-71.
[100]吴望一.流体力学.北京:北京大学出版社,1983.
[101]杜庆华,郑百哲.连续介质力学.北京:清华大学出版社,1986.
[102]杨世铭,陶文栓.传热学.北京:高等教育出版社,1998.
[103]薛守义.论连续介质概念与岩体的连续介质模型.岩石力学与工程学报,1999,18(2):230-232.
[104]Zienkiewicz O C, Shiomi T. Dynamic behaviour of saturated porous media; The generalized biotformulation and its numerical solution. International Journal for Numerical and Analytical Methods inGeomechanics,2005,8(1):71-96.
[105]王晓冬.渗流力学基础.北京:石油工业出版社,2006.
[106]Carman P C. Flow of gases through porous media. London: Butterworths Scientific Publications,1956.
[107]严宗达,王洪礼.热应力.北京:高等教育出版社,1993.
[108]Salinger A G, Aris R, Derby J J. Finite element formulations for large‐scale, coupled flows inadjacent porous and open fluid domains. International Journal for Numerical Methods in Fluids,1994,18(12):1185-1209.
[109]金朝明.液压流体力学.北京:国防工业出版社,1994.
[110]Ouyang L, Arbabi S, Aziz K. General wellbore flow model for horizontal, vertical, and slanted wellcompletions. SPE Journal,1998,3(2):124-133.
[111]White F M. Fluid mechanics. New York: McGraw-Hill Book Company,1986.
[112]Sir William Thomson L K. Mathematical and physical papers. Cambridge: University Press,1884.
[113]Carslaw H S, Jaeger J C. Conduction of heat in solids. Oxford: Clarendon Press,1959.
[114]Nisle R G. The effect of partial penetration on pressure build-up in oil wells. Trans., AIME,1958,213:85-90.
[115]Gringarten A C, Ramey Jr H J. The use of source and green's functions in solving unsteady-flowproblems in reservoirs. Society of Petroleum Engineers Journal,1973,13(5):285-296.
[116]Besson J. Performance of slanted and horizontal wells on an anisotropic medium. EuropeanPetroleum Conference, The Hague, Netherlands,1990.
[117]Ozkan E, Raghavan R. A computationally efficient, transient-pressure solution for inclined wells.SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana,1998.
[118]Cinco H, Miller F G, Ramey Jr H J. Unsteady-state pressure distribution created by a directionallydrilled well. SPE Journal of Petroleum Technology,1975,27(11):1392-1400.
[119]Karakas M, Tariq S M. Semianalytical productivity models for perforated completions. SPEProduction Engineering,1991,6(1):73-82.
[120]Furui K, Zhu D, Hill A D. A new skin-factor model for perforated horizontal wells. SPE Drilling&Completion,2008,23(3):205-215.
[121]卢祥国,王凤兰,徐典平,等.完井与试井.哈尔滨:哈尔滨工业大学出版社,2000.
[122]Yildiz T. Assessment of total skin factor in perforated wells. SPE European Formation DamageConference, The Hague, Netherlands,2003.
[123]Duilofsky L J. An approximate model for well productivity in heterogeneous porous media.mathematical geology,2000,32(4):421-438.
[124]闫文文.水平井射孔密度优化研究,[硕士学位论文].东营:中国石油大学,2010.
[2]陈红伟,郝振宪,何汉坤,等.水平井设计应用与展望.钻采工艺,2004,27(6):8-11.
[3]郑俊德,杨长祜.水平井,分支井采油工艺现状分析与展望.石油钻采工艺,2006,27(6):93-96.
[4]沈忠厚.现代钻井技术发展趋势.石油勘探与开发,2005,32(1):89-91.
[5] Douglas Jr J, Peaceman D W, Rachford Jr H H. A method for calculating multi-dimensionalimmiscible displacement. Trans., AIME,1959,216:297-308.
[6] Shutler N D. Numerical three-phase model of the two-dimensional steamflood process. Old SPEJournal,1970,10(4):405-417.
[7] Settari A, Aziz K. A computer model for two-phase coning simulation.1974(3):221-236.
[8] Williamson A S, Chappelear J E. Representing wells in numerical reservoir simulation: part1-theory.1981(06):323-338.
[9] Siu A, Li Y, Nghlem L, et al. Numerical modelling of a thermal horizontal well. Annual TechnicalMeeting, Calgary, Alberta,1990.
[10] Winterfeld P H. Simulation of pressure buildup in a multiphase wellbore/reservoir system. SPEFormation Evaluation,1989(2):247-252.
[11] Almehaideb R A, Aziz K, Pedrosa Jr O A. A reservoir/wellbore model for multiphase injection andpressure transient analysis. Middle East Oil Show, Bahrain,1989.
[12] Xiao J J, Fuentes-N F A, Alhanati F, et al. Modeling and analyzing pressure buildup data affected byphase redistribution in the wellbore. SPE Advanced Technology Series,1996,4(1):28-37.
[13] Livescu S, Durlofsky L J, Aziz K, et al. A new model for simulating nonisothermal multiphase flowin wellbores and pipes.2008.
[14] Stone T W, Edmunds N R, Kristoff B J. A comprehensive wellbore/reservoir simulator. SPESymposium on Reservoir Simulation, Houston, Texas,1989.
[15] Coats K H. A highly implicit steamflood model.1978(10):369-383.
[16] Su H, Lee S H. Modeling transient wellbore behavior in horizontal wells. International Meeting onPetroleum Engineering, Beijing, China,1995.
[17] Nolen J, Berry D W. Tests of the stability and time-step sensitivity of semi-implicit reservoirstimulation techniques. Old SPE Journal,1972,12(3):253-266.
[18] Collins D, Nghiem L, Sharma R, et al. Field-scale simulation of horizontal wells. Journal of CanadianPetroleum Technology,1992,31(1):14-21.
[19]陈崇希.岩溶管道—裂隙—孔隙三重空隙介质地下水流模型及模拟方法.地球科学：中国地质大学学报,1995,20(4):361-366.
[20]吴淑红,刘翔鹗,郭尚平.水平段井筒管流的简化模型.石油勘探与开发,1999,26(4):64-65.
[21] Peaceman D W. Interpretation of well-block pressures in numerical reservoir simulation(includesassociated paper6988).1978,18(3):183-194.
[22] Peaceman D W. Interpretation of well-block pressures in numerical reservoir simulation withnonsquare grid blocks and anisotropic permeability.1983,23(3):531-543.
[23] Morita N, Singh S P, Chen H S, et al. Three-dimensional well model pre-processors for reservoirsimulation with horizontal and curved inclined wells. SPE Annual Technical Conference andExhibition, New Orleans, Louisiana,1990.
[24] Babu D K, Odeh A S, Al-Khalifa A J, et al. The relation between wellblock and wellbore pressures innumerical simulation of horizontal wells. SPE Reservoir Engineering,1991,6(3):324-328.
[25] Ewing R E, Lazarov R D, Lyons S L, et al. Numerical well model for non-darcy flow throughisotropic porous media. Computational Geosciences,1999,3(3):185-204.
[26] Ding Y U, Renard G. A new representation of wells in numerical reservoir simulation. SPE ReservoirEngineering,1994,9(2):140-144.
[27] Ding Y, Renard G, Weill L. Representation of wells in numerical reservoir simulation. SPE ReservoirEvaluation&Engineering,1998,1(1):18-23.
[28] Chen Z, Zhang Y. Well flow models for various numerical methods. International Journal ofNumerical Analysis&Modeling,2009,6(3):375-388.
[29] Krogstad S, Durlofsky L J. Multiscale mixed-finite-element modeling of coupled wellbore/near-wellflow. SPE Journal,2009(1):78-87.
[30] Collins D, Nghiem L, Sharma R, et al. Field-scale simulation of horizontal wells with hybrid grids.11th SPE Symposium on Reservoir Simulation, Anaheim, California,1991.
[31] Ewing R E, Boyett B A, Babu D K, et al. Efficient use of locally refined grids for multiphasereservoir simulation. SPE Symposium on Reservoir Simulation, Houston, TX,1989.
[32] Pedrosa Jr O, Aziz K. Use of a hybrid grid in reservoir simulation. SPE Reservoir Engineering,1986,1(6):611-621.
[33] Oliveira R. Study of the horizontal wellbore and reservoir coupling. SPE Annual TechnicalConference and Exhibition, Denver, Colorado, USA,2011.
[34] Bahonar M, Azaiez J, Chen Z. A semi-unsteady-state wellbore steam/water flow model for predictionof sandface conditions in steam injection wells. Journal of Canadian Petroleum Technology,2010,49(09):13-21.
[35] Dikken B J. Pressure drop in horizontal wells and its effect on production performance. SPE Journalof Petroleum Technology,1990,42(11):1426-1433.
[36] Ozkan E, Sarica C, Haciislamoglu M, et al. The influence of pressure drop along the wellbore onhorizontal well productivity. Production Operations Symposium, Oklahoma,1993.
[37] Sarica C, Haciislamoglu M, Raghavan R, et al. influence of wellbore hydraulics on pressure behaviorand productivity of horizontal gas wells. SPE Annual Technical Conference and Exhibition, NewOrleans, Louisiana,1994.
[38] Suzuki K. Influence of wellbore hydraulics on horizontal well pressure transient behavior. SPEFormation Evaluation,1997(3):175-181.
[39] Ouyang L, Aziz K. A simplified approach to couple wellbore flow and reservoir inflow for arbitrarywell configurations. SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana,1998.
[40] Penmatcha V R, Aziz K. A comprehensive reservoir/wellbore model for horizontal wells. SPE IndiaOil and Gas Conference and Exhibition, New Delhi, India,1998.
[41]刘想平,蒋志祥.射孔完井的水平井向井流动态关系.石油勘探与开发,1999,26(2):71-78.
[42]刘想平,郭呈柱,蒋志祥,等.油层中渗流与水平井筒内流动的耦合模型.石油学报,1999,20(3):82-86.
[43]苏玉亮,张东,李明忠.油藏中渗流与水平井筒内流动的耦合数学模型.中国矿业大学学报,2007,36(06):752-758.
[44] Terzaghi K. Principles of soil mechanics. Engineering News Record,1925,95(8).
[45] Biot M A. General theory of three‐dimensional consolidation. Journal of Applied Physics,1941,12(2):155-164.
[46] Biot M A. Theory of elasticity and consolidation for a porous anisotropic solid.1955,26(2):182-185.
[47] Geertsma J. Problems of rock mechanics in petroleum production engineering.1st ISRM Congress,Lisbon, Portugal,1966.
[48] Geertsma J. Land subsidence above compacting oil and gas reservoirs. SPE Journal of PetroleumTechnology,1973(6):734-744.
[49] Finol A, Farouq Ali S M. Numerical simulation of oil production with simultaneous groundsubsidence.1975(5):411-424.
[50] Merle H A, Kentie C J P, van Opstal G H C, et al. The bachaquero study-a composite analysis of thebehavior of a compaction drive/solution gas drive reservoir. SPE Journal of Petroleum Technology,1976(9):1107-1115.
[51] Rattia A J, Farouq Ali S M. Effect of formation compaction on steam injection response. SPE AnnualTechnical Conference and Exhibition, San Antonio, Texas,1981.
[52] Chase Jr C A, Dietrich J K. compaction within the south belridge diatomite. SPE ReservoirEngineering,1989(4):422-428.
[53] Boade R, Chin L, Siemers W. Forecasting of ekofisk reservoir compaction and subsidence bynumerical simulation,1988.
[54] Fredrich J T, Arguello J G, Deitrick G L, et al. Geomechanical modeling of reservoir compaction,surface subsidence, and casing damage at the belridge diatomite field. SPE Reservoir Evaluation&Engineering,2000,3(4):348-359.
[55] Fung L, Wan R, Rodriguez H, et al. An advanced elasto-plastic model for borehole stability analysisof horizontal wells in unconsolidated formation. Journal of Canadian Petroleum Technology,1999,38(12):41-49.
[56] Ali S M F, Blunschi J. Cyclic steam stimulation with formation parting. Annual Technical Meeting,Banff,1983.
[57] Settari A, Kry P R, Yee C T. Coupling of fluid flow and soil behaviour to model injection intouncemented oil sands. Journal of Canadian Petroleum Technology,1989,28(1):81-92.
[58] Tortike W S, Ali S M F. Prediction of oil sand failure due to steam-induced stresses. Journal ofCanadian Petroleum Technology,1991,30(01):87-95.
[59] Tortike W S, Ali S M F. Reservoir simulation integrated with geomechanics. Journal of CanadianPetroleum Technology,1993,32(05):28-37.
[60] Fung L S K. A coupled geomechanic-multiphase flow model for analysis of in situ recovery incohesionless oil sands. Journal of Canadian Petroleum Technology,1992,31(06):56-67.
[61] Chin L Y, Raghavan R, Thomas L K. fully coupled geomechanics and fluid-flow analysis of wellswith stress-dependent permeability. SPE Journal,2000(1):32-45.
[62] Pinzon C L, Chen H, Teufel L W. numerical well test analysis of stress-sensitive reservoirs. SPERocky Mountain Petroleum Technology Conference, Keystone, Colorado,2001.
[63] Chen H, Teufel L W. Coupling fluid-flow and geomechanics in dual-porosity modeling of naturallyfractured reservoirs. SPE Annual Technical Conference and Exhibition, San Antonio, Texas,1997.
[64] Lewis R W, Ghafouri H R. A novel finite element double porosity model for multiphase flow throughdeformable fractured porous media.1997,21(11):789-816.
[65] Bagheri M A, Settari A. Modeling of geomechanics in naturally fractured reservoirs. SPE ReservoirEvaluation&Engineering,2008(02):108-118.
[66] Jabbari H, Zeng Z. A three-parameter dual porosity model for naturally fractured reservoirs. SPEWestern North American Region Meeting, Anchorage, Alaska, USA,2011.
[67]董平川,徐小荷.储层流固耦合的数学模型及其有限元方程.石油学报,1998,19(1):64-70.
[68]薛世峰.非混溶饱和两相渗流与变形孔隙介质耦合作用的理论研究及其在石油开发中的应用,
[博士学位论文].北京:中国地震局地质研究所,2000.
[69]徐向荣,范学平.油藏多相流体渗流流-固耦合数学模拟研究.岩石力学与工程学报,2002,21(01):93-97.
[70]黎水泉,徐秉业,段永刚.裂缝性油藏流固耦合渗流.计算力学学报,2001,18(02):133-137.
[71]刘建军,裴桂红.裂缝性低渗透油藏流固耦合渗流分析.应用力学学报,2004,21(01):37-39.
[72]王自明,杜志敏.变温条件下弹塑性油藏中多相渗流的流固耦合数学模型与数值模拟.石油勘探与开发,2001,28(06):68-72.
[73]薛世峰,马利成.热采过程中地层超孔隙压力与井眼应力的定量评价.中国石油大学学报(自然科学版),2006,30(04):78-81.
[74] Gutierrex M, Lewis R W. The role of geomechanics in reservoir simulation. SPE/ISRM RockMechanics in Petroleum Engineering, Trondheim, Norway,1998.
[75] Schrefler B A, Simoni L, Turska E. Standard staggered and staggered newton schemes inthermo-hydro-mechanical problems. Comput. Methods Appl. Mech. Engrg.,1997,144(01):93-109.
[76] Lewis R W, Sukirman Y. Finite element modelling of three-phase flow in deforming saturated oilreservoirs. International Journal for Numerical and Analytical Methods in Meomechanics,1993,17(8):577-598.
[77] Yin S, Dusseault M B, Rothenburg L. Thermal reservoir modeling in petroleum geomechanics.International Journal for Numerical and Analytical Methods in Geomechanics,2009,33(4):449-485.
[78] Du Du J, Wong R C K. Development of a coupled geomechanics-thermal reservoir simulator usingfinite element method. Canadian International Petroleum Conference, Calgary, Alberta,2005.
[79] Chin L Y, Raghavan R, Thomas L K. Fully coupled analysis of well responses in stress-sensitivereservoirs. SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana,1998.
[80] Lewis R W, Sukirman Y. Finite element modelling for simulating the surface subsidence above acompacting hydrocarbon reservoir. International Journal for Numerical and Analytical Methods inGeomechanics,1994,18(9):619-639.
[81] Tran D, Nghiem L, Buchanan L. Improved iterative coupling of geomechanics with reservoirsimulation. SPE Reservoir Simulation Symposium, The Woodlands, Texas,2005.
[82] Tran D, Settari A, Nghiem L. New iterative coupling between a reservoir simulator and ageomechanics module. SPE Journal,2004(3):362-369.
[83] Thomas L K, Chin L Y, Pierson R G, et al. Coupled geomechanics and reservoir simulation. SPEAnnual Technical Conference and Exhibition, San Antonio, Texas,2002.
[84] Settari A, Mourits F M. a coupled reservoir and geomechanical simulation system. SPE Journal,1998(3):219-226.
[85] Huang M, Zienkiewicz O C. New unconditionally stable staggered solution procedures for coupledsoil‐pore fluid dynamic problems. International journal for numerical methods in engineering,1998,43(6):1029-1052.
[86] Zienkiewicz O C, Paul D K, Chan A. Unconditionally stable staggered solution procedure forsoil‐pore fluid interaction problems. International Journal for Numerical Methods in Engineering,1988,26(5):1039-1055.
[87] Minkoff S E, Stone C M, Bryant S, et al. Coupled fluid flow and geomechanical deformationmodeling. Journal of Petroleum Science and Engineering,2003,38(1-2):37-56.
[88] Settari A, Walters D A. advances in coupled geomechanical and reservoir modeling with applicationsto reservoir compaction. SPE Journal,2001(09):334-342.
[89] Fung L S K, Buchanan L, Wan R G. Coupled geomechanical-thermal simulation for deformingheavy-oil reservoirs. Journal of Canadian Petroleum Technology,1994,33(4):22-28.
[90] Settari A, Mourits F M. Coupling of geomechanics and reservoir simulation models. ComputerMethods and Advances in Geomechanics,1994,3:2151-2158.
[91] Minkoff S, Stone C, Arguello J, et al. Staggered in time coupling of reservoir flow simulation andgeomechanical deformation: step1-one-way coupling. SPE Symposium on Reservoir Simulation,Houston, Texas,1999.
[92] Fredrich J T, Arguello J G, Thorne B J, et al. Three-dimensional geomechanical simulation ofreservoir compaction and implications for well failures in the belridge diatomite. SPE AnnualTechnical Conference and Exhibition, Denver, Colorado, U.S.A,1996.
[93]万仁溥.现代完井工程.北京:石油工业出版社,2000.
[94] Landman M J, Goldthorpe W H. Optimization of perforation distribution for horizontal wells. SPEAsia-Pacific Conference, Perth. Australia,1991.
[95] Marett B P, Landman M J. Optimal perforation design for horizontal wells in reservoirs withboundaries. SPE Asia Pacific Oil and Gas Conference, Singapore,1993.
[96] Asheim H, Oudeman P. Determination of perforation schemes to control production and injectionprofiles along horizontal wells. SPE Drilling&Completion,1997,12(1):13-18.
[97]周生田,马德泉,等.射孔水平井孔眼分布优化研究.石油大学学报：自然科学版,2002,26(3):52-54.
[98]刘冰,徐兴平,李继志,等.基于序列二次规划算法的射孔水平井孔眼分布优化.中国石油大学学报(自然科学版),2010,34(04):79-83.
[99]刘冰,徐兴平,李继志.水平井射孔优化设计的增广拉格朗日乘子法.钻采工艺,2010(03):67-71.
[100]吴望一.流体力学.北京:北京大学出版社,1983.
[101]杜庆华,郑百哲.连续介质力学.北京:清华大学出版社,1986.
[102]杨世铭,陶文栓.传热学.北京:高等教育出版社,1998.
[103]薛守义.论连续介质概念与岩体的连续介质模型.岩石力学与工程学报,1999,18(2):230-232.
[104]Zienkiewicz O C, Shiomi T. Dynamic behaviour of saturated porous media; The generalized biotformulation and its numerical solution. International Journal for Numerical and Analytical Methods inGeomechanics,2005,8(1):71-96.
[105]王晓冬.渗流力学基础.北京:石油工业出版社,2006.
[106]Carman P C. Flow of gases through porous media. London: Butterworths Scientific Publications,1956.
[107]严宗达,王洪礼.热应力.北京:高等教育出版社,1993.
[108]Salinger A G, Aris R, Derby J J. Finite element formulations for large‐scale, coupled flows inadjacent porous and open fluid domains. International Journal for Numerical Methods in Fluids,1994,18(12):1185-1209.
[109]金朝明.液压流体力学.北京:国防工业出版社,1994.
[110]Ouyang L, Arbabi S, Aziz K. General wellbore flow model for horizontal, vertical, and slanted wellcompletions. SPE Journal,1998,3(2):124-133.
[111]White F M. Fluid mechanics. New York: McGraw-Hill Book Company,1986.
[112]Sir William Thomson L K. Mathematical and physical papers. Cambridge: University Press,1884.
[113]Carslaw H S, Jaeger J C. Conduction of heat in solids. Oxford: Clarendon Press,1959.
[114]Nisle R G. The effect of partial penetration on pressure build-up in oil wells. Trans., AIME,1958,213:85-90.
[115]Gringarten A C, Ramey Jr H J. The use of source and green's functions in solving unsteady-flowproblems in reservoirs. Society of Petroleum Engineers Journal,1973,13(5):285-296.
[116]Besson J. Performance of slanted and horizontal wells on an anisotropic medium. EuropeanPetroleum Conference, The Hague, Netherlands,1990.
[117]Ozkan E, Raghavan R. A computationally efficient, transient-pressure solution for inclined wells.SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana,1998.
[118]Cinco H, Miller F G, Ramey Jr H J. Unsteady-state pressure distribution created by a directionallydrilled well. SPE Journal of Petroleum Technology,1975,27(11):1392-1400.
[119]Karakas M, Tariq S M. Semianalytical productivity models for perforated completions. SPEProduction Engineering,1991,6(1):73-82.
[120]Furui K, Zhu D, Hill A D. A new skin-factor model for perforated horizontal wells. SPE Drilling&Completion,2008,23(3):205-215.
[121]卢祥国,王凤兰,徐典平,等.完井与试井.哈尔滨:哈尔滨工业大学出版社,2000.
[122]Yildiz T. Assessment of total skin factor in perforated wells. SPE European Formation DamageConference, The Hague, Netherlands,2003.
[123]Duilofsky L J. An approximate model for well productivity in heterogeneous porous media.mathematical geology,2000,32(4):421-438.
[124]闫文文.水平井射孔密度优化研究,[硕士学位论文].东营:中国石油大学,2010.
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