裂缝性油藏稠油蒸汽注采数值模拟自适应网格法的研究
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摘要
蒸汽注采是在裂缝性稠油油藏开发中应用非常广泛且驱油效率较高的开采方法。对于裂缝性油藏稠油蒸汽注采的数值模拟,其困难在于在流场相变区域附近存在一个非常陡峭的温度和饱和度锋面。由于物理量在跨越锋面界面时变化非常剧烈,在锋面附近必须采用很小的网格尺寸才能满足精度的要求。如果对全场都采用均匀细网格,计算量将非常巨大。因此,对于这类问题非常有必要采用能够自动追踪物理量变化剧烈的锋面的自适应网格法,在物理量梯度大的位置采用细网格,而在物理量变化缓慢的区域采用较粗的网格。
本文工作的目标是将自适应网格法应用于裂缝性油藏蒸汽注采的数值模拟。对于均匀裂缝性油藏,建议对裂缝和基质采用完全相同的自适应网格结构,这种结构下的自适应网格算法既简便又有效。数值算例的结果表明该自适应网格法相比全精细网格计算能够在保证计算精度的前提下大幅提高计算速度。同时,裂缝性油藏蒸汽辅助重力驱油(SAGD)过程算例的结果显示了在SAGD过程中由于受到裂缝渗透能力强的影响,蒸汽腔容易较早地接触油藏顶部,对蒸汽热能的利用率有着不利的影响。
然而,在非均匀裂缝性情况下实施自适应网格法,需要面临一些复杂的数学物理问题。
首先,本文发现,由于裂缝与基质之间的流体交换受基质渗透率大小的控制,而且相邻基质块之间的联系很微弱,因此基质渗透率在空间的急剧变化会导致相邻基质饱和度的空间不连续,直接对基质粗网格的变量进行插值或平均将带来问题的复杂性。为了解决这一问题,本文对裂缝和基质方程分别使用不同的网格系统——仅对裂缝使用自适应网格结构,而对基质使用全精细网格。由于在DP模型下不考虑基质之间的影响,本文在Newton-Raphson迭代过程中使用一种特殊的裂缝-基质方程解耦方法,将基质方程和变量完全消去,仅剩下自适应网格下的裂缝方程和变量需要参与大型稀疏矩阵的求解。此外,这一解耦方法也同样适合于DK模型,只需将相邻基质网格的变量暂时“显式化”,即在进行Newton-Raphson迭代过程中取上一迭代步的值。数值算例的结果表明,本文提出的针对非均匀裂缝性油藏的自适应网格法相比于全精细网格计算也拥有很大的计算速度优势,并且保持了较高的计算精度。数值计算效率的提高来源于对裂缝采用自适应网格结构及方程求解时采用了这一特殊的裂缝-基质变量解耦方法。
其次,在非均匀情况下对粗网格等效渗透率的计算一直是国际上关注的难题。特别是对于多层网格结构下的等效渗透率求解方法,问题变得更加复杂。这是由于大多数等效渗透率方法蕴含有统计属性(需要粗网格包含有大量的精细网格)或者需要使用周期性边界条件。对于多层网格结构中的较细层次,它们包含的精细网格数量太少,可能不足以使这些等效渗透率算法有效。为了解决这一问题,本文建议在估算一个粗网格的等效渗透率时,不应只关注其自身所携带的有限信息,而应考虑其他区域对他的影响。于是,本文从大尺度平均理论出发,利用大尺度平均理论在全场求得“辅助变量”,它描述了压力和速度的脉动与大尺度平均的压力梯度之间的关系。利用“辅助变量”携带的信息,可以求解任意一个局部区域的等效渗透率。这一方法提供了一个恰当的方式来计算多层网格结构下粗网格的等效渗透率,而且无需对它引入任何边界条件。数值算例的结果表明这种方法相对其他常用的方法对等效渗透率的估算在多层网格下有着更好的近似。
自适应网格法的计算速度很快,可以使人们在不同参数情况下快速进行大量的数值模拟,有利于发现油藏开采中的问题及优化开采策略。在对一维裂缝性油藏蒸汽驱过程进行大量数值实验后,发现毛管力渗吸驱油机制只在某些条件下起作用。当改变油藏参数导致进入油藏的液态水量减少时,裂缝中可能出现过热蒸汽。在这些情况下,裂缝蒸汽压力的降低导致油从基质流向裂缝。
综上,本文的工作对在裂缝性油藏蒸汽注采数值模拟自适应网格算法及实施自适应网格法时遇到的数学物理问题开展研究。相应的数值算例显示了自适应网格算法在计算效率上相当可观的优越性。同时,还观察到了在改变参数时有趣的油藏驱替现象。本文期望自适应网格法能够对生产现场的裂缝性油藏蒸汽注采数值模拟带来实际的帮助。
Steam injection is a widely used efficient recovery technique for fractured reservoirs containing viscous oil.The difficulty for the numerical simulations of this problem is the existence of very sharp temperature and saturation fronts around the phase change regions.Due to the rapid variations of physical quantities across the fronts,very fine grids are required to satisfy the simulation accuracy.If applying uniformly fine grids to the whole domain,very huge CPU time is needed.Therefore, it's quite reasonable to consider the use of adaptive mesh refinement(AMR) technique,which is capable of using fine grids in the area with steep gradients but coarser grids where the variations of temperature and saturations are slower,to track the moving fronts inside the calculation domain.
The object of this paper is to apply the AMR technique to the numerical simulations of steam thermal recovery processes in fractured petroleum reservoirs. For homogeneous fractured reservoirs,we suggest using the same AMR grid structures for fracture and matrix,for it is not only convenient but also effective.The numerical examples indicate the AMR technique results are both accurate and fast compared with the solutions under referenced uniformly fine grids.The numerical example for SAGD process also shows that the steam chamber could easily reach the top of the reservoir,which is harmful to the thermal efficiency of steam energy for the SAGD process in fractured reservoirs.
However,there are several mathematical difficulties to face with under heterogeneous circumstances.
Firstly,it's found that since the matrix-fracture mass exchange is relevant to the matrix permeability and the communications between the adjacent matrix blocks are very tiny,the spatial variations of matrix permeability will cause saturation discontinuities between the neighboring matrix blocks.Directly performing refining (downscaling) operations or coarsening(upscaling) operations upon these matrix quantities may lead to difficulties tied to the upscaling or downscaling of the exchange term.In order to avoid this problem,we suggest using two separated grid systems for the fracture and matrix equations,respectively.The AMR grid structure is applied to the fracture equation,while uniform fine-grids are maintained for the matrix equation.Under the consideration that there is no direct communication between the matrix blocks under DP model,the fracture and matrix equations can be decoupled by a special decomposition approach during the Newton-Raphson procedure for solving the nonlinear resulting equations.After that,only fracture varibles under AMR grid structures are left to participate in the large spare matrix computations.Moreover,this decomposition approach is also validated under DK model,as long as we use the variables of the neighboring matrix blocks at the last Newton-Raphson iteration step.The numerical examples show that the proposed AMR technique is fast and can give good accuracy compared to the reference fine-grid results.The improvement of the computing efficiency obtained with the proposed AMR technique comes from the use of the adaptive fracture grid as well as the special decomposition approach.
Second,how to calculate the effective permeability of coarse grids is a difficult problem that has attracted much attention.For the equivalent permeability under multi-level grid,the situation becomes even more complicated.As most upscaling techniques have their origins in statistical physics or require the use of periodic boundary conditions,these cells in such levels may include insufficient information to satisfy the precondition of the upscaling methods.To deal with the problem,we suggest not treating the coarse cells isolately but considering the influence of the other region of the domain.We start from the large scale averaging theory whose closure variables are able to provide the description of the deviation map of the pressure and velocity of the domain.With the help of the information,we are able to obtain the equivalent of an arbitrary region inside the domain.This technique provides an appropriate way to calculate the equivalent permeability for multi-level grids,without introducing any boundary condition upon them.The numerical examples presented in this paper indicate that the proposed model may provide relatively good approximations for the equivalent permeabilities of the coarse cells of multiple nested grids
AMR simulations are much faster than the uniformly fine-grid simulations. Therefore,it enables us to implement large amount of simulations rapidly with different parameters.It is of help to find out problems and make better decisions for pertroleum recovery.After having implemented large amount of numerical experiments upon the steam drive process for a one-dimensional fractured reservoir, we find that oil displacement in matrix is dominated by oil-water capillary pressure only under certain conditions.When conditions are changed to decrease the amount of water entering into fractured media from the boundary of the flow field,water in fracture may be vaporized to superheated steam.In these cases,the appearance of superheated steam in fracture rather than in matrix will decrease the fracture pressure and generate the pressure difference between matrix and fracture,which results in oil flowing from matrix to fracture.
In summary,several problems relevant to the AMR numerical simulations of steam thermal recovery for fractured petroleum reservoirs are carefully stutied in this work.The numerical results indicate the considerable adavantage of AMR technique in computational efficiency.And we also observe some interesting behaviors for oil displacement in fractured reserviors.We expect the AMR technique to have a practical help to the fractured reservoir simulations in the future.
本文工作的目标是将自适应网格法应用于裂缝性油藏蒸汽注采的数值模拟。对于均匀裂缝性油藏,建议对裂缝和基质采用完全相同的自适应网格结构,这种结构下的自适应网格算法既简便又有效。数值算例的结果表明该自适应网格法相比全精细网格计算能够在保证计算精度的前提下大幅提高计算速度。同时,裂缝性油藏蒸汽辅助重力驱油(SAGD)过程算例的结果显示了在SAGD过程中由于受到裂缝渗透能力强的影响,蒸汽腔容易较早地接触油藏顶部,对蒸汽热能的利用率有着不利的影响。
然而,在非均匀裂缝性情况下实施自适应网格法,需要面临一些复杂的数学物理问题。
首先,本文发现,由于裂缝与基质之间的流体交换受基质渗透率大小的控制,而且相邻基质块之间的联系很微弱,因此基质渗透率在空间的急剧变化会导致相邻基质饱和度的空间不连续,直接对基质粗网格的变量进行插值或平均将带来问题的复杂性。为了解决这一问题,本文对裂缝和基质方程分别使用不同的网格系统——仅对裂缝使用自适应网格结构,而对基质使用全精细网格。由于在DP模型下不考虑基质之间的影响,本文在Newton-Raphson迭代过程中使用一种特殊的裂缝-基质方程解耦方法,将基质方程和变量完全消去,仅剩下自适应网格下的裂缝方程和变量需要参与大型稀疏矩阵的求解。此外,这一解耦方法也同样适合于DK模型,只需将相邻基质网格的变量暂时“显式化”,即在进行Newton-Raphson迭代过程中取上一迭代步的值。数值算例的结果表明,本文提出的针对非均匀裂缝性油藏的自适应网格法相比于全精细网格计算也拥有很大的计算速度优势,并且保持了较高的计算精度。数值计算效率的提高来源于对裂缝采用自适应网格结构及方程求解时采用了这一特殊的裂缝-基质变量解耦方法。
其次,在非均匀情况下对粗网格等效渗透率的计算一直是国际上关注的难题。特别是对于多层网格结构下的等效渗透率求解方法,问题变得更加复杂。这是由于大多数等效渗透率方法蕴含有统计属性(需要粗网格包含有大量的精细网格)或者需要使用周期性边界条件。对于多层网格结构中的较细层次,它们包含的精细网格数量太少,可能不足以使这些等效渗透率算法有效。为了解决这一问题,本文建议在估算一个粗网格的等效渗透率时,不应只关注其自身所携带的有限信息,而应考虑其他区域对他的影响。于是,本文从大尺度平均理论出发,利用大尺度平均理论在全场求得“辅助变量”,它描述了压力和速度的脉动与大尺度平均的压力梯度之间的关系。利用“辅助变量”携带的信息,可以求解任意一个局部区域的等效渗透率。这一方法提供了一个恰当的方式来计算多层网格结构下粗网格的等效渗透率,而且无需对它引入任何边界条件。数值算例的结果表明这种方法相对其他常用的方法对等效渗透率的估算在多层网格下有着更好的近似。
自适应网格法的计算速度很快,可以使人们在不同参数情况下快速进行大量的数值模拟,有利于发现油藏开采中的问题及优化开采策略。在对一维裂缝性油藏蒸汽驱过程进行大量数值实验后,发现毛管力渗吸驱油机制只在某些条件下起作用。当改变油藏参数导致进入油藏的液态水量减少时,裂缝中可能出现过热蒸汽。在这些情况下,裂缝蒸汽压力的降低导致油从基质流向裂缝。
综上,本文的工作对在裂缝性油藏蒸汽注采数值模拟自适应网格算法及实施自适应网格法时遇到的数学物理问题开展研究。相应的数值算例显示了自适应网格算法在计算效率上相当可观的优越性。同时,还观察到了在改变参数时有趣的油藏驱替现象。本文期望自适应网格法能够对生产现场的裂缝性油藏蒸汽注采数值模拟带来实际的帮助。
Steam injection is a widely used efficient recovery technique for fractured reservoirs containing viscous oil.The difficulty for the numerical simulations of this problem is the existence of very sharp temperature and saturation fronts around the phase change regions.Due to the rapid variations of physical quantities across the fronts,very fine grids are required to satisfy the simulation accuracy.If applying uniformly fine grids to the whole domain,very huge CPU time is needed.Therefore, it's quite reasonable to consider the use of adaptive mesh refinement(AMR) technique,which is capable of using fine grids in the area with steep gradients but coarser grids where the variations of temperature and saturations are slower,to track the moving fronts inside the calculation domain.
The object of this paper is to apply the AMR technique to the numerical simulations of steam thermal recovery processes in fractured petroleum reservoirs. For homogeneous fractured reservoirs,we suggest using the same AMR grid structures for fracture and matrix,for it is not only convenient but also effective.The numerical examples indicate the AMR technique results are both accurate and fast compared with the solutions under referenced uniformly fine grids.The numerical example for SAGD process also shows that the steam chamber could easily reach the top of the reservoir,which is harmful to the thermal efficiency of steam energy for the SAGD process in fractured reservoirs.
However,there are several mathematical difficulties to face with under heterogeneous circumstances.
Firstly,it's found that since the matrix-fracture mass exchange is relevant to the matrix permeability and the communications between the adjacent matrix blocks are very tiny,the spatial variations of matrix permeability will cause saturation discontinuities between the neighboring matrix blocks.Directly performing refining (downscaling) operations or coarsening(upscaling) operations upon these matrix quantities may lead to difficulties tied to the upscaling or downscaling of the exchange term.In order to avoid this problem,we suggest using two separated grid systems for the fracture and matrix equations,respectively.The AMR grid structure is applied to the fracture equation,while uniform fine-grids are maintained for the matrix equation.Under the consideration that there is no direct communication between the matrix blocks under DP model,the fracture and matrix equations can be decoupled by a special decomposition approach during the Newton-Raphson procedure for solving the nonlinear resulting equations.After that,only fracture varibles under AMR grid structures are left to participate in the large spare matrix computations.Moreover,this decomposition approach is also validated under DK model,as long as we use the variables of the neighboring matrix blocks at the last Newton-Raphson iteration step.The numerical examples show that the proposed AMR technique is fast and can give good accuracy compared to the reference fine-grid results.The improvement of the computing efficiency obtained with the proposed AMR technique comes from the use of the adaptive fracture grid as well as the special decomposition approach.
Second,how to calculate the effective permeability of coarse grids is a difficult problem that has attracted much attention.For the equivalent permeability under multi-level grid,the situation becomes even more complicated.As most upscaling techniques have their origins in statistical physics or require the use of periodic boundary conditions,these cells in such levels may include insufficient information to satisfy the precondition of the upscaling methods.To deal with the problem,we suggest not treating the coarse cells isolately but considering the influence of the other region of the domain.We start from the large scale averaging theory whose closure variables are able to provide the description of the deviation map of the pressure and velocity of the domain.With the help of the information,we are able to obtain the equivalent of an arbitrary region inside the domain.This technique provides an appropriate way to calculate the equivalent permeability for multi-level grids,without introducing any boundary condition upon them.The numerical examples presented in this paper indicate that the proposed model may provide relatively good approximations for the equivalent permeabilities of the coarse cells of multiple nested grids
AMR simulations are much faster than the uniformly fine-grid simulations. Therefore,it enables us to implement large amount of simulations rapidly with different parameters.It is of help to find out problems and make better decisions for pertroleum recovery.After having implemented large amount of numerical experiments upon the steam drive process for a one-dimensional fractured reservoir, we find that oil displacement in matrix is dominated by oil-water capillary pressure only under certain conditions.When conditions are changed to decrease the amount of water entering into fractured media from the boundary of the flow field,water in fracture may be vaporized to superheated steam.In these cases,the appearance of superheated steam in fracture rather than in matrix will decrease the fracture pressure and generate the pressure difference between matrix and fracture,which results in oil flowing from matrix to fracture.
In summary,several problems relevant to the AMR numerical simulations of steam thermal recovery for fractured petroleum reservoirs are carefully stutied in this work.The numerical results indicate the considerable adavantage of AMR technique in computational efficiency.And we also observe some interesting behaviors for oil displacement in fractured reserviors.We expect the AMR technique to have a practical help to the fractured reservoir simulations in the future.
引文
郭福军,孙岩.1995.稠油油藏蒸汽吞吐年油汽比的变化规律及其预测方法[M].石油勘探与开发,22(5):54-56.
过洪波,刘静,陈珂,王好军.1997.裂缝性油藏注蒸汽热采先导试验的实践与认识——以克拉玛依油田九区石炭系油藏为例[J].新疆石油地质,18(2):176-179.
韩大匡,陈钦雷,闰存章.1993.油藏数值模拟基础[M].北京:石油工业出版社.
侯健,陈月明.1997.综合化的蒸汽吞吐注采参数优化设计[J].石油大学学报:自然科学版,21(3):36-39.
孔祥言.1999.高等渗流力学[M].合肥:中国科学技术大学出版社。
李平科,张侠.1996.蒸汽驱开发采收率预测新方法[J].石油勘探与开发.23(1):51-54.
梁作利,唐清山.2000.稠油油藏蒸汽驱开发技术[J].特种油气藏,7(2):46-49.
刘斌.1994.计算稠油油藏蒸汽吞吐阶段可采储量的方法[J].河南石油,8(1):43-45.
刘学利,杜志敏,韩忠艳,吴林.2003.裂缝性稠油油藏蒸汽吞吐动态预测模型[J].新疆石油地质,24(5):448-450.
刘文章.1991.稠油油田蒸汽吞吐转入蒸汽驱开采的技术策略[J].石油钻采工艺,13(4):45-50.
王威,马德胜,张鹰.1999.杜84块水平井开采数值模拟研究[J].西部探矿工程,11(1):24-27.
王选茹,程林松,刘双全等..2006.蒸汽辅助重力泄油渗流机理研究[J].西南石油学院学报,28(2):44-47.
吴向红,叶继根,马远乐..2002.水平井蒸汽辅助重力驱油藏模拟方法[J].计算物理,19(11):549-552.
徐丕东,韦涛,孙丙和.2000.草古1潜山裂缝性碳酸盐岩稠油油藏开采特征[J].特种油气藏,7(3):21-24.
杨立强,陈月明,王宏远,田利.2007.超稠油直井-水平井组合蒸汽辅助重力泄油物理和数值模拟[J].中国石油大学学报,31(4):64-69.
袁士义,宋新民,冉启全.2004.裂缝性油藏开发技术[M].北京:石油工业出版社.
袁士义,冉启全,胡永乐,任宝生,王毅忠.2005.火成岩裂缝性稠油油藏有效开发方式[J].石油学报,26(4):63-68.
岳清山,赵洪岩.1997.蒸汽驱最优方案设计新方法[J].特种油气藏,4(4):19-23.
张方礼,张丽萍等.2007.蒸汽辅助重力泄油技术在超稠油开发中的应用[J].特种油气藏,14(2):70-72.
张烈辉,李允,杜志敏.1996.裂缝性油藏水平井模型[J].西南石油学院学报,18(2):48-55.
张锐.1999.稠油热采技术[M].北京:石油工业出版社.
张义堂等.2006.热力采油提高采收率技术[M].北京:石油工业出版社.
朱志宏,武俊学,1997.克拉玛依油田九7,九8区超稠油水平井蒸汽辅助重力泄油物理模拟研究[J].新疆石油科技,7(4)17-27.
Abad BP,Hensley CA.1984.The Effect of Stratification,Fractures,and Dip on Steam Sweep Efficiency and Heat Requirements of Steamflood Operations[C].paper SPE 12748 presented at the 1984 California Regional Meeting,Long Beach,CA,April 11-13.
Aziz K,Ramesh AB,Woo PT.1987.Fourth SPE comparative solution project:comparison of steam injection simulators[J].Journal of Petroleum Technology 39(12):1576-1584.
Aziz K,Settari A.1979.Petroleum Reservoir Simulation[M],Applied Science Publishers Ltd.,London.
Bagci AS.2005.Experimental and simulation studies of SAGD process in fractured reservoirs [C].SPE Paper 99920.
Bastian P,Helmig R.1999.Efficient fully-coupled solution techniques for two phase flow in porous media.Parallel multigrid solution and large scale computations[J].Adv.Water Resour.,23:199-216.
Begg SH,King PR.1985.Modelling the effects of shales on reservoir performance:calculation of effective vertical permeability[J].Soc Pet Eng Tech Paper 13529.
Berger MJ,Colella P.1989.Local adaptive mesh refinement for shock hydrodynamics[J].J.Comput.Phys.,82:64-84.
Berger MJ,Oliger J.1984.Adaptive mesh refinement for hyperbolic partial differential equations[J].J.Comput.Phys.,53:484-512.
Brandt A.1977.Multi-level adaptive solution to boundary-value problems[J].Math.Comput.31:333-396.
Briggs PJ,Beck DL,Black CJ,Bissell R.1992.Heavy Oil from Fractured Carbonate Reservoirs[J].SPE Reservoir Engineering,7:173-179.
Britton MW,Martin WL,Leibrecht RJ,Harmon RA.1982.The Street Ranch Pilot Test of Fracture-Assisted Steamflood Technology[C].paper SPE 10707.presented at the 1982 SPE California Regional Meeting,San Francisco,CA,March 24-26.
Brooks RH,Corey AT.1966.Properties of porous media affecting fluid flow[J].Journal of Irrigation and Drainage Division,Proceedings of the American Society of Civil Engineers,92(IR2):61-88.
Butler RM.1991.Thermal Recovery of Oil and Bitumem[M].Prentice Hall,Englewood Cliffs,N.J.
Butler RM.1994.Steam-assister gravity drainage:concept,development,performance and future [J],Journal of Canadian Petroleum Technology,33(2):44-50.
Butler RM,McNab G.S,Lo HY.1981.Theoretical studies on the gravity drainage of heavy oil during in-situ steam heating[J],Canadian J.of Chem.Engineering,59:455-460.
Butler RM,Stephens DJ.1981.The gravity drainage of steam heated to parallel horizontal wells[J].JCPT,April-June:90-96.
Chen WH,Wasserma ML,Fitzmorris RE.1987.A thermal simulator for naturally fractured reservoirs[C].Paper presented at the 9th SPE symposium on reservoir simulation,San Antonio,TX.,1-4 February.
Chierici GL,Delle Canne A,Properzi O.1985.Steam Drive in a Fractured Carbonate:The Vallecupa,Italy,Pilot Plant[C].presented at the 1985 European Meeting on Improved Oil Recovery,Rome,Italy,April.
Chow L,Butler RM.1996.Numerical Simulation of the Steam-assisted Gravity Drainage Process (SAGD)[J].JCPT,35:55-62.
Closmann PJ,Smith RA.1983.Temperature Observations and Steam-ZoneRise in the Vicinity of a Steam-Heated Fracture[J].Soc.of Pet.Eng.J.,35:575-586.
Couderc BM,Verpeaux JF,Monfrin D,Quettier LH.1987.Emeraude Vapeur:A Steam Pilot in an Offshore Environment^].SPE Reservoir Engineering 5:508-516.
Dagan G.1989.Flow and Transport in Porous Formations[M].Springer-Verlag,New York.Dendy JE,McCormick SF,Ruge JW,Russell TF,Schaffer S.1989.Multigrid methods for three-dimensional petroleum reservoir simulation[J],SPE 18409.
Deutsh C,Journel A.1992.GSLIB:Geostatistical Software Library and User's Guide[M].Oxford University Press,New York.
Dillabough JA,Prats M.1974.Recovering Bitumen from Peace River Deposits[J].The Oil and Gas Journal Nov.:186-196.
Dindoruk MDS,Aziz K,Brigham W,Castanier L.1996.A study of steam injection in fractured media[D].Dissertation,Stanford University,California.
Dreher KD,Kenyon DE.1986.Heat Flow During Steam Injection Into a Fractured Carbonate Reservoir[C].paper SPE 14902 presented at the 1986 SPE/DOE Symposium on Enhanced Oil Recovery,Tulsa,OK,April 20-23.
Duerksen JH,Cruikshank GW,Wasserman ML.1984.Performance and Simulation of a Cold Lake Tar Sand Steam-Injection Pilot[J].Journal of Petroleum Technology,36:1781-1790.
Durlofsky LJ.1991.Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media[J].Water Resources Research,27:699-708.
Edwards MG,Rogers CF.1998.Finite volume discretization with imposed flux continuity for the general tensor pressure equation[J].Comput.Geo.,no.2:259-290.
Falta RW,Pruess K,Javandel I,Witherspoon PA.1992.Numerical Modeling of Steam Injection for the Removal of Nonaqueous Phase Liquids From the Subsurface 1.Numerical Formulation[J].Water Resour.Res.,28(2),433-449.
Friedel H,Grauer R,Marliani C.1997.Adaptive mesh refinement for singular current sheets in incompressible magnetohydrodynamic flows[J].J.Comput.Phys.,134:190-198.
Fulton SR.1997.A Comparison of Multilevel Adaptive Methods for Hurricane Track Prediction[J].Electronic Trans,on Numer.Anal.,6:120-132.
Gautier Y,Noetinger B.1997.Preferential Flow-Paths Detection for Heterogeneous Reservoirs Using a New Renormalization Technique[J],Trans.Porous Media,26:1-23.
Gerritsen M,Kovscek A,Castanier L,Nilsson J,Younis R,He B.2004.Experimental Investigation and High Resolution Simulator of in-situ Combustion Processes:1.Simulator Design and Improved Combustion with Metallic Additives[J],SPE 86962.
Geshelin BM,Grabowski JW,Pease EC.1981.Numerical Study of Transport of Injected and Reservoir Water in Fractured Reservoirs During Steam Stimulation[C].paper SPE 10322 presented at the 1981 SPE Annual Fall Technical Conference and Exhibition,San Antonio,TX,October 5-7.
Gilman JR.1986.An efficient finite-difference method for simulating phase segregation in the matrix blocks in double-porosity reservoirs[J].SPE J.1(4):403-413.
Gilman JR,Kazemi H.1987.Improve calculations for viscous and gravity displacement in matrix blocks in dual-porosity simulators [C].Paper presented at the 9th SPE symposium on reservoir simulation,San Antonio,TX.,1-4 February.
Haldenwang P,Pignol D.2002.Dynamically adapted mesh refinement for combustion front tracking [J].Computers and Fluids,31:589-606.
Hartemink M,Escovedo BM,Hoppe JE,Macaulay,R.1995.Quarn Alam:Application of Simulation for Steam Pilot Design in a Fractured Reservoir,presented at the 1995 European IOR Symposium,Vienna,Austria,May.
Hill AC,Thomas GW.1985.A new approach for simulating complex fractured reservoirs[C].Paper presented at the SPE Middle east oil tech.conference and exhibition,Bahrain,11-14 March.
Honarpour MM,Koederitz F,Herbert A.1986.Relative permeability of petroleum reservoirs[M].CRC Press Inc,Boca Raton,FL.
Hornung RD,Trangenstein JA.1997.Adaptive mesh refinement and multilevel iteration for flow in porous media [J].J.Comput.Phys.,136:522-545.
Hou TY,Wu XH.1997.A Multiscaie Finite Element Method for Elliptic Problems in Composite Materials and Porous Media [J],J.Comput Phys.,134:169-189.
Howell LH,Pember RB,Colella P.1999.A Conservative Adaptive-Mesh Algorithm for Unsteady,Combined-Mode Heat Transfer Using the Discrete Ordinates Method[J],Numer.Heat Transfer B,35:407-433.
Howes FA,Whitaker S.1985.The spatial averaging theorem revisited[J],Chemical Engineering Science 40(8):1387-1392.
Jasak H,Gosman AD.2000.Automatic Resolution Control for the Finite-Volume Method,Part 3:Turbulent Flow Applications[J],Numer.Heat Transfer B,38:273-290.
Jensen TB.1991.Steam Flooding of Fractured Reservoirs:Experimental and Numerical Studies,PhD dissertation[D].University of Wyoming,August.
Kazemi K,Merrill LS,Porterfield KP,Zeman PR.1976.Simulation of water-oil flow in naturally fractured reservoirs[J].SPE J.16(6):317-326.
Kazemi H,Merrill LS.1979.Numerical simulation of water imbibition in fractured cores[J].SPE J.16:175-182.
King PR.1989.The Use of Renormalization for Calculating Effective Permeability[J],Trans.Porous Media,4:37-58.
Le Loc'h G.1987.Etude de la composition des permeabilites par des methodes variationnelles[D].PhD Thesis,Paris School of Mines.
Lee BYQ,Tan TBS.1987.Application of a multiple porosity/permeability simulator in fractured reservoir simulation[J].SPE J.27:181-192.
Lim KT,Aziz K.1995.Matrix-fracture transfer shape factors for dual-porosity simulators[J].Journal of Petroleum Science and Engineering 13:169-178.
Luo HS,Wang XH,Quintard M.2008.Adaptive Mesh Refinement for One Dimensional Three-Phase Flows in Heterogeneous Fractured Porous Media[J].Numerical Heat Transfer B,Fundamentals,54(6):476-498.
Luo HS,Wang XH.2009.Oil Displacement for One-Dimensional Three-Phase Flow with Phase Change in Fractured Media[J].Transport in Porous Media,DOI 10.1007/sl 1242-008-9325-6.
Luo HS,Wang XH,Shi AF.2009.The AMR Technique For SAGD Process in HighlyHeterogenous Fractured Reservoirs[C].Proceedings of 6th ICCHMT,May 18-21,Guangzhou,CHINA.
Mandl G,Volek CW.1967.Heat and mass transport in steam-drive processes[C].42.annual SPE of AIME fall meeting,Houston,TX,USA,1 Oct.
Mukhopadhyay S,Sahimi M.1992.Heat Transfer and Two-Phase Flow in Fractured Reservoirs [C].paper SPE 24043 presented at the 1992 SPE Western Regional Meeting,Bakersfield,CA,March 30-April 1.
Myhill NA,Stegemeier GL.1975.Steam drive correlation and prediction[C].SPE-5572,50.annual fall meeting and exhibition,Dallas,TX,USA,28 Sep.
Nilsson J,Gerritsen M,Younis R.2005.Towards An Adaptive,High-Resolution Simulator for Steam Injection Processes[J],SPE 93881.
Noetinger B,Estebenet T,Landereau P.2000.Up-scaling of double porosity fractured media using continuous-time random walks methods[J].Transport Porous Media.39:315-337.
Nolan JB,Ehrlich R,Crookston RB.1980.Applicability of Steamflooding for Carbonate Reservoirs[C].paper SPE 8821 presented at the 1980 SPE/DOE Symposium on Enhanced Oil Recovery,Tulsa,OK,April 20-23.
Oballa V,Coombe DA,Buchanan WL.1993.Factors affecting the thermal response of naturally fractured reservoirs[J].The Journal of Canadian Petroleum Technology 32(8):1-42.
Peaceman DW.1982.Interpretation of Well-Block Pressures in Numerical Reservoir Simulation With Nonsquare Grid Blocks and Anisotropic Permeability[J],SPE 10528.
Pember RB,Bell JB,Colella P.1995.An Adaptive Cartesian Grid Method for Unsteady Compressible Flow in Irregular Regions[J],J.Comput.Phys.,120:278-304.
Pooladi-Darvish M.,Tortike WS,Ali F.1994.Steam Heating of Fractured Formations Containing Heavy Oil:Basic Premises and a Single-Block Analytical Model[C].paper SPE 28642 presented at the 1994 SPE Annual Technical Conference and Exhibition,New Orleans,LA,September 25-28.
Pruess K,Narasimhan TN.1985.A practical method for modelling fluid and heat flow in fractured porous media[J],SPE J.25(1):14-26.
Pruess K,Wu YS.1989.A new semi-analytical method for numerical simulation of fluid and heat flow in fractured reservoirs[C].Paper presented at the SPE symposium on reservoir simulation,Houston,TX.,6-8 February.
Prouvost L,Quintard M.1990.Stability criteria for the design of graded polymer buffers[J].Journal of Petroleum Science and Engineering,3(4):333-343.
Quintard M,Whitaker S.1987.Ecoulements monophasiques en milieu poreux:effet des heterogeneites locales[J],J.Meca.Theo.Appl.,6:691-726.
Quintard M,Whitaker S.1993.One-and two-equation models for transient diffusion processes in two-phase systems[J].Advances Heat Transfer 23:369-464.
Quintard M,Whitaker S.1994.Convection,dispersion,and interfacial transport of contaminants:Homogeneous media[J],Advances in Water Resources 17:221-239.
Quintard M,Whitaker S.1996.Transport in Chemically and Mechanically Heterogeneous Porous Media I:Theoretical Development of Region Averaged Equations for Slightly
Compressible Single-Phase Flow[J],Advances in Water Resources,19(1),:29-47.
Reis JC.1990.Studies of Fractures Induced During Cyclic Steam Injection[C].paper SPE 20033 presented at the 1990 California Regional Meeting,Ventura,CA,April 4-6.
Reis JC.1990.Oil recovery mechanisms in fractured reservoirs during steam injection[C].Paper presented at the SPE/DOE symposium on enhanced oil recovery,Tulsa,OK,22-25 April.
Renard P,de Marsily G.1997.Calculating the Equivalent Permeability:A Review[J].Advances in Water Resources,20:253-278.
Sahuquet BC,Ferrier JJ.1982.Steam-Drive Pilot in a Fractured CarbonateReservoir:Lacq Superieur Field[J].J.Pet.Tech.Apr.:873-880.
Sanchez-Palencia E.1980.Non Homogeneous Media and Vibration Theory.Lecture Notes in Physics,127,Berlin:Springer-Verlap.
Sandler SI.1977.Chemical and Engineering Thermodynamics[M].John Wiley and Sons.
Sarkar AK,Sarathi PS.1993.Thermal processes for heavy oil recovery[R].DOI.10.2172/10108843.
Satman A.1988.Solutions of Heat-and Fluid-Flow Problems in Naturally FracturedReservoirs:Part 1-Heat Flow Problems[J].SPE Production Engineering,Nov.:463-466.
Satter A.1967.A Prediction Method for Conduction Heating of Reservoirs by Steam Injection[C].paper SPE 1950 presented at the 1967 SPE Annual Fall Meeting,Houston,TX,Oct.1-4.
Schmidt E.1982.Properties of sater and steam in S.I.Units[M].Springer,Berlin.
Shi AF,Jia JT,Wang XH,Luo HS.2009.Adaptive mesh refinement for 2D and 3D numerical simulations of steam-assisted gravity drainage process[C].Proceeding of International Conference on Computational Heat and Mass Transfer,Guangzhou,China,May 18-21.
Stang HR,Soni Y.1987.Saner Ranch Pilot Test of Fracture-Assisted Steamflood Technology [J].J.Pet.Tech.39(6):684-696.
Stone HL.1973.Estimation of three-phase relative permeability and residual oil data[J].Journal of Petroleum Technology 12(4):52-61.
Thomas LK,Dixon TN,Pierson RG.1983.Fractured reservoir simulation[J],SPE J.,23:42-54.
Trangenstein JA.2002.Multi-scale iterative techniques and adaptive mesh refinement for flow in porous media[J].Adv.in Water Resources,25:1175-1213.
Trangenstein JA,Bi Z.2002.Multi-scale iterative techniques and adaptive mesh refinement for Miscible Displacement Simulation [J].SPE,75232.
Tregoures N,Fichot F,Duval F,Repetto G,Quintard M.2003.Multi-dimensional Numerical Study of Core Debris Bed Reflooding under Severe Accident Conditions[C],paper C00218,Tenth International Topical Meeting on Nuclear Reactor Thermal Hydraulics,October,Seoul,Korea.
Udell KS.1983.Heat transfer in porous media heated from above with evaporation,condensation,and capillary effects[J],Journal of Heat Transfer 105:485-492.
Van Golf-Racht TD.1982.Fundamentals of fractured reservoir engineering[M].Elsevier Scientific Publishing Company,New York.
Van Wunnik JNM,Wit K.1992.Improvement of Gravity Drainage by Steam Injection into a Fractured Reservoir:An Analytical Evaluation[J].SPE Reservoir Engineering,7:59-66.
Venuturumilli R,Chen LD.2004.Numerical Simulation Using Adaptive Mesh Refinement for Laminar Jet Diffusion Flames[J].Numer.Heat Transfer B,46:101-120.
Vinsome PKW,Westerveld J.1980.A Simple Method for Predicting Cap andBase Rock Heat Losses in Thermal Reservoir Simulators[J].Journal of Canadian Petroleum Technolog,19(3):87-90.
Wagner C,Kinzelbach W,Wittum G.1997.Schur-complement multigrid:A robust method for groundwater flow and transport problems[J].Numer.Math.,75:523-545.
Wang XH,Quintard M,Darche G.2006.Adaptive mesh refinement for one-dimensional threephase flow with phase change in porous media[J].Numerical Heat Transfer B,50:231-268.
Warren JE,Root PJ.1963.The Behavior of Naturally Fractured Reservoirs[J].SPE J.,3(9):245-255.
Wheeler JA.1969.Analytical Calculations for Heat Transfer from Fractures[J].No.SPE 2494.
Wu B,Luo HS,Wang XH,Shi AF.2009.Renormalization methods for Calculating Threedimensional Effective PermeabilityfC].Proceedings of 4th ICAPM,Aug 10-12,Istanbul,TURKEY.
Wu YS,Haukwa C,Bodvarsson GS.1999.A site-scale model for fluid and heat flow in the unsaturated zone of Yucca Mountain,Nevada[J].Journal of Contaminant Hydrology,38:185-21.
Wu YS,Pruess K.1988.A multiple-porosity method for simulation of naturally fractured petroleum reservoirs[J].SPE 3:327-336.
Wu YS,Pruess K.2000.Numerical simulation of non-isothermal multiphase tracer transport in heterogeneous fractured porous media[J].Advances in Water Resources 23:699-723.
Yeo IW.Zimmerman RW.2001.Accuracy of the Renormalization Method for Computing Effective Conductivities of Heterogeneous Media[J].Trans.Porous Media,45:129-138.
过洪波,刘静,陈珂,王好军.1997.裂缝性油藏注蒸汽热采先导试验的实践与认识——以克拉玛依油田九区石炭系油藏为例[J].新疆石油地质,18(2):176-179.
韩大匡,陈钦雷,闰存章.1993.油藏数值模拟基础[M].北京:石油工业出版社.
侯健,陈月明.1997.综合化的蒸汽吞吐注采参数优化设计[J].石油大学学报:自然科学版,21(3):36-39.
孔祥言.1999.高等渗流力学[M].合肥:中国科学技术大学出版社。
李平科,张侠.1996.蒸汽驱开发采收率预测新方法[J].石油勘探与开发.23(1):51-54.
梁作利,唐清山.2000.稠油油藏蒸汽驱开发技术[J].特种油气藏,7(2):46-49.
刘斌.1994.计算稠油油藏蒸汽吞吐阶段可采储量的方法[J].河南石油,8(1):43-45.
刘学利,杜志敏,韩忠艳,吴林.2003.裂缝性稠油油藏蒸汽吞吐动态预测模型[J].新疆石油地质,24(5):448-450.
刘文章.1991.稠油油田蒸汽吞吐转入蒸汽驱开采的技术策略[J].石油钻采工艺,13(4):45-50.
王威,马德胜,张鹰.1999.杜84块水平井开采数值模拟研究[J].西部探矿工程,11(1):24-27.
王选茹,程林松,刘双全等..2006.蒸汽辅助重力泄油渗流机理研究[J].西南石油学院学报,28(2):44-47.
吴向红,叶继根,马远乐..2002.水平井蒸汽辅助重力驱油藏模拟方法[J].计算物理,19(11):549-552.
徐丕东,韦涛,孙丙和.2000.草古1潜山裂缝性碳酸盐岩稠油油藏开采特征[J].特种油气藏,7(3):21-24.
杨立强,陈月明,王宏远,田利.2007.超稠油直井-水平井组合蒸汽辅助重力泄油物理和数值模拟[J].中国石油大学学报,31(4):64-69.
袁士义,宋新民,冉启全.2004.裂缝性油藏开发技术[M].北京:石油工业出版社.
袁士义,冉启全,胡永乐,任宝生,王毅忠.2005.火成岩裂缝性稠油油藏有效开发方式[J].石油学报,26(4):63-68.
岳清山,赵洪岩.1997.蒸汽驱最优方案设计新方法[J].特种油气藏,4(4):19-23.
张方礼,张丽萍等.2007.蒸汽辅助重力泄油技术在超稠油开发中的应用[J].特种油气藏,14(2):70-72.
张烈辉,李允,杜志敏.1996.裂缝性油藏水平井模型[J].西南石油学院学报,18(2):48-55.
张锐.1999.稠油热采技术[M].北京:石油工业出版社.
张义堂等.2006.热力采油提高采收率技术[M].北京:石油工业出版社.
朱志宏,武俊学,1997.克拉玛依油田九7,九8区超稠油水平井蒸汽辅助重力泄油物理模拟研究[J].新疆石油科技,7(4)17-27.
Abad BP,Hensley CA.1984.The Effect of Stratification,Fractures,and Dip on Steam Sweep Efficiency and Heat Requirements of Steamflood Operations[C].paper SPE 12748 presented at the 1984 California Regional Meeting,Long Beach,CA,April 11-13.
Aziz K,Ramesh AB,Woo PT.1987.Fourth SPE comparative solution project:comparison of steam injection simulators[J].Journal of Petroleum Technology 39(12):1576-1584.
Aziz K,Settari A.1979.Petroleum Reservoir Simulation[M],Applied Science Publishers Ltd.,London.
Bagci AS.2005.Experimental and simulation studies of SAGD process in fractured reservoirs [C].SPE Paper 99920.
Bastian P,Helmig R.1999.Efficient fully-coupled solution techniques for two phase flow in porous media.Parallel multigrid solution and large scale computations[J].Adv.Water Resour.,23:199-216.
Begg SH,King PR.1985.Modelling the effects of shales on reservoir performance:calculation of effective vertical permeability[J].Soc Pet Eng Tech Paper 13529.
Berger MJ,Colella P.1989.Local adaptive mesh refinement for shock hydrodynamics[J].J.Comput.Phys.,82:64-84.
Berger MJ,Oliger J.1984.Adaptive mesh refinement for hyperbolic partial differential equations[J].J.Comput.Phys.,53:484-512.
Brandt A.1977.Multi-level adaptive solution to boundary-value problems[J].Math.Comput.31:333-396.
Briggs PJ,Beck DL,Black CJ,Bissell R.1992.Heavy Oil from Fractured Carbonate Reservoirs[J].SPE Reservoir Engineering,7:173-179.
Britton MW,Martin WL,Leibrecht RJ,Harmon RA.1982.The Street Ranch Pilot Test of Fracture-Assisted Steamflood Technology[C].paper SPE 10707.presented at the 1982 SPE California Regional Meeting,San Francisco,CA,March 24-26.
Brooks RH,Corey AT.1966.Properties of porous media affecting fluid flow[J].Journal of Irrigation and Drainage Division,Proceedings of the American Society of Civil Engineers,92(IR2):61-88.
Butler RM.1991.Thermal Recovery of Oil and Bitumem[M].Prentice Hall,Englewood Cliffs,N.J.
Butler RM.1994.Steam-assister gravity drainage:concept,development,performance and future [J],Journal of Canadian Petroleum Technology,33(2):44-50.
Butler RM,McNab G.S,Lo HY.1981.Theoretical studies on the gravity drainage of heavy oil during in-situ steam heating[J],Canadian J.of Chem.Engineering,59:455-460.
Butler RM,Stephens DJ.1981.The gravity drainage of steam heated to parallel horizontal wells[J].JCPT,April-June:90-96.
Chen WH,Wasserma ML,Fitzmorris RE.1987.A thermal simulator for naturally fractured reservoirs[C].Paper presented at the 9th SPE symposium on reservoir simulation,San Antonio,TX.,1-4 February.
Chierici GL,Delle Canne A,Properzi O.1985.Steam Drive in a Fractured Carbonate:The Vallecupa,Italy,Pilot Plant[C].presented at the 1985 European Meeting on Improved Oil Recovery,Rome,Italy,April.
Chow L,Butler RM.1996.Numerical Simulation of the Steam-assisted Gravity Drainage Process (SAGD)[J].JCPT,35:55-62.
Closmann PJ,Smith RA.1983.Temperature Observations and Steam-ZoneRise in the Vicinity of a Steam-Heated Fracture[J].Soc.of Pet.Eng.J.,35:575-586.
Couderc BM,Verpeaux JF,Monfrin D,Quettier LH.1987.Emeraude Vapeur:A Steam Pilot in an Offshore Environment^].SPE Reservoir Engineering 5:508-516.
Dagan G.1989.Flow and Transport in Porous Formations[M].Springer-Verlag,New York.Dendy JE,McCormick SF,Ruge JW,Russell TF,Schaffer S.1989.Multigrid methods for three-dimensional petroleum reservoir simulation[J],SPE 18409.
Deutsh C,Journel A.1992.GSLIB:Geostatistical Software Library and User's Guide[M].Oxford University Press,New York.
Dillabough JA,Prats M.1974.Recovering Bitumen from Peace River Deposits[J].The Oil and Gas Journal Nov.:186-196.
Dindoruk MDS,Aziz K,Brigham W,Castanier L.1996.A study of steam injection in fractured media[D].Dissertation,Stanford University,California.
Dreher KD,Kenyon DE.1986.Heat Flow During Steam Injection Into a Fractured Carbonate Reservoir[C].paper SPE 14902 presented at the 1986 SPE/DOE Symposium on Enhanced Oil Recovery,Tulsa,OK,April 20-23.
Duerksen JH,Cruikshank GW,Wasserman ML.1984.Performance and Simulation of a Cold Lake Tar Sand Steam-Injection Pilot[J].Journal of Petroleum Technology,36:1781-1790.
Durlofsky LJ.1991.Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media[J].Water Resources Research,27:699-708.
Edwards MG,Rogers CF.1998.Finite volume discretization with imposed flux continuity for the general tensor pressure equation[J].Comput.Geo.,no.2:259-290.
Falta RW,Pruess K,Javandel I,Witherspoon PA.1992.Numerical Modeling of Steam Injection for the Removal of Nonaqueous Phase Liquids From the Subsurface 1.Numerical Formulation[J].Water Resour.Res.,28(2),433-449.
Friedel H,Grauer R,Marliani C.1997.Adaptive mesh refinement for singular current sheets in incompressible magnetohydrodynamic flows[J].J.Comput.Phys.,134:190-198.
Fulton SR.1997.A Comparison of Multilevel Adaptive Methods for Hurricane Track Prediction[J].Electronic Trans,on Numer.Anal.,6:120-132.
Gautier Y,Noetinger B.1997.Preferential Flow-Paths Detection for Heterogeneous Reservoirs Using a New Renormalization Technique[J],Trans.Porous Media,26:1-23.
Gerritsen M,Kovscek A,Castanier L,Nilsson J,Younis R,He B.2004.Experimental Investigation and High Resolution Simulator of in-situ Combustion Processes:1.Simulator Design and Improved Combustion with Metallic Additives[J],SPE 86962.
Geshelin BM,Grabowski JW,Pease EC.1981.Numerical Study of Transport of Injected and Reservoir Water in Fractured Reservoirs During Steam Stimulation[C].paper SPE 10322 presented at the 1981 SPE Annual Fall Technical Conference and Exhibition,San Antonio,TX,October 5-7.
Gilman JR.1986.An efficient finite-difference method for simulating phase segregation in the matrix blocks in double-porosity reservoirs[J].SPE J.1(4):403-413.
Gilman JR,Kazemi H.1987.Improve calculations for viscous and gravity displacement in matrix blocks in dual-porosity simulators [C].Paper presented at the 9th SPE symposium on reservoir simulation,San Antonio,TX.,1-4 February.
Haldenwang P,Pignol D.2002.Dynamically adapted mesh refinement for combustion front tracking [J].Computers and Fluids,31:589-606.
Hartemink M,Escovedo BM,Hoppe JE,Macaulay,R.1995.Quarn Alam:Application of Simulation for Steam Pilot Design in a Fractured Reservoir,presented at the 1995 European IOR Symposium,Vienna,Austria,May.
Hill AC,Thomas GW.1985.A new approach for simulating complex fractured reservoirs[C].Paper presented at the SPE Middle east oil tech.conference and exhibition,Bahrain,11-14 March.
Honarpour MM,Koederitz F,Herbert A.1986.Relative permeability of petroleum reservoirs[M].CRC Press Inc,Boca Raton,FL.
Hornung RD,Trangenstein JA.1997.Adaptive mesh refinement and multilevel iteration for flow in porous media [J].J.Comput.Phys.,136:522-545.
Hou TY,Wu XH.1997.A Multiscaie Finite Element Method for Elliptic Problems in Composite Materials and Porous Media [J],J.Comput Phys.,134:169-189.
Howell LH,Pember RB,Colella P.1999.A Conservative Adaptive-Mesh Algorithm for Unsteady,Combined-Mode Heat Transfer Using the Discrete Ordinates Method[J],Numer.Heat Transfer B,35:407-433.
Howes FA,Whitaker S.1985.The spatial averaging theorem revisited[J],Chemical Engineering Science 40(8):1387-1392.
Jasak H,Gosman AD.2000.Automatic Resolution Control for the Finite-Volume Method,Part 3:Turbulent Flow Applications[J],Numer.Heat Transfer B,38:273-290.
Jensen TB.1991.Steam Flooding of Fractured Reservoirs:Experimental and Numerical Studies,PhD dissertation[D].University of Wyoming,August.
Kazemi K,Merrill LS,Porterfield KP,Zeman PR.1976.Simulation of water-oil flow in naturally fractured reservoirs[J].SPE J.16(6):317-326.
Kazemi H,Merrill LS.1979.Numerical simulation of water imbibition in fractured cores[J].SPE J.16:175-182.
King PR.1989.The Use of Renormalization for Calculating Effective Permeability[J],Trans.Porous Media,4:37-58.
Le Loc'h G.1987.Etude de la composition des permeabilites par des methodes variationnelles[D].PhD Thesis,Paris School of Mines.
Lee BYQ,Tan TBS.1987.Application of a multiple porosity/permeability simulator in fractured reservoir simulation[J].SPE J.27:181-192.
Lim KT,Aziz K.1995.Matrix-fracture transfer shape factors for dual-porosity simulators[J].Journal of Petroleum Science and Engineering 13:169-178.
Luo HS,Wang XH,Quintard M.2008.Adaptive Mesh Refinement for One Dimensional Three-Phase Flows in Heterogeneous Fractured Porous Media[J].Numerical Heat Transfer B,Fundamentals,54(6):476-498.
Luo HS,Wang XH.2009.Oil Displacement for One-Dimensional Three-Phase Flow with Phase Change in Fractured Media[J].Transport in Porous Media,DOI 10.1007/sl 1242-008-9325-6.
Luo HS,Wang XH,Shi AF.2009.The AMR Technique For SAGD Process in HighlyHeterogenous Fractured Reservoirs[C].Proceedings of 6th ICCHMT,May 18-21,Guangzhou,CHINA.
Mandl G,Volek CW.1967.Heat and mass transport in steam-drive processes[C].42.annual SPE of AIME fall meeting,Houston,TX,USA,1 Oct.
Mukhopadhyay S,Sahimi M.1992.Heat Transfer and Two-Phase Flow in Fractured Reservoirs [C].paper SPE 24043 presented at the 1992 SPE Western Regional Meeting,Bakersfield,CA,March 30-April 1.
Myhill NA,Stegemeier GL.1975.Steam drive correlation and prediction[C].SPE-5572,50.annual fall meeting and exhibition,Dallas,TX,USA,28 Sep.
Nilsson J,Gerritsen M,Younis R.2005.Towards An Adaptive,High-Resolution Simulator for Steam Injection Processes[J],SPE 93881.
Noetinger B,Estebenet T,Landereau P.2000.Up-scaling of double porosity fractured media using continuous-time random walks methods[J].Transport Porous Media.39:315-337.
Nolan JB,Ehrlich R,Crookston RB.1980.Applicability of Steamflooding for Carbonate Reservoirs[C].paper SPE 8821 presented at the 1980 SPE/DOE Symposium on Enhanced Oil Recovery,Tulsa,OK,April 20-23.
Oballa V,Coombe DA,Buchanan WL.1993.Factors affecting the thermal response of naturally fractured reservoirs[J].The Journal of Canadian Petroleum Technology 32(8):1-42.
Peaceman DW.1982.Interpretation of Well-Block Pressures in Numerical Reservoir Simulation With Nonsquare Grid Blocks and Anisotropic Permeability[J],SPE 10528.
Pember RB,Bell JB,Colella P.1995.An Adaptive Cartesian Grid Method for Unsteady Compressible Flow in Irregular Regions[J],J.Comput.Phys.,120:278-304.
Pooladi-Darvish M.,Tortike WS,Ali F.1994.Steam Heating of Fractured Formations Containing Heavy Oil:Basic Premises and a Single-Block Analytical Model[C].paper SPE 28642 presented at the 1994 SPE Annual Technical Conference and Exhibition,New Orleans,LA,September 25-28.
Pruess K,Narasimhan TN.1985.A practical method for modelling fluid and heat flow in fractured porous media[J],SPE J.25(1):14-26.
Pruess K,Wu YS.1989.A new semi-analytical method for numerical simulation of fluid and heat flow in fractured reservoirs[C].Paper presented at the SPE symposium on reservoir simulation,Houston,TX.,6-8 February.
Prouvost L,Quintard M.1990.Stability criteria for the design of graded polymer buffers[J].Journal of Petroleum Science and Engineering,3(4):333-343.
Quintard M,Whitaker S.1987.Ecoulements monophasiques en milieu poreux:effet des heterogeneites locales[J],J.Meca.Theo.Appl.,6:691-726.
Quintard M,Whitaker S.1993.One-and two-equation models for transient diffusion processes in two-phase systems[J].Advances Heat Transfer 23:369-464.
Quintard M,Whitaker S.1994.Convection,dispersion,and interfacial transport of contaminants:Homogeneous media[J],Advances in Water Resources 17:221-239.
Quintard M,Whitaker S.1996.Transport in Chemically and Mechanically Heterogeneous Porous Media I:Theoretical Development of Region Averaged Equations for Slightly
Compressible Single-Phase Flow[J],Advances in Water Resources,19(1),:29-47.
Reis JC.1990.Studies of Fractures Induced During Cyclic Steam Injection[C].paper SPE 20033 presented at the 1990 California Regional Meeting,Ventura,CA,April 4-6.
Reis JC.1990.Oil recovery mechanisms in fractured reservoirs during steam injection[C].Paper presented at the SPE/DOE symposium on enhanced oil recovery,Tulsa,OK,22-25 April.
Renard P,de Marsily G.1997.Calculating the Equivalent Permeability:A Review[J].Advances in Water Resources,20:253-278.
Sahuquet BC,Ferrier JJ.1982.Steam-Drive Pilot in a Fractured CarbonateReservoir:Lacq Superieur Field[J].J.Pet.Tech.Apr.:873-880.
Sanchez-Palencia E.1980.Non Homogeneous Media and Vibration Theory.Lecture Notes in Physics,127,Berlin:Springer-Verlap.
Sandler SI.1977.Chemical and Engineering Thermodynamics[M].John Wiley and Sons.
Sarkar AK,Sarathi PS.1993.Thermal processes for heavy oil recovery[R].DOI.10.2172/10108843.
Satman A.1988.Solutions of Heat-and Fluid-Flow Problems in Naturally FracturedReservoirs:Part 1-Heat Flow Problems[J].SPE Production Engineering,Nov.:463-466.
Satter A.1967.A Prediction Method for Conduction Heating of Reservoirs by Steam Injection[C].paper SPE 1950 presented at the 1967 SPE Annual Fall Meeting,Houston,TX,Oct.1-4.
Schmidt E.1982.Properties of sater and steam in S.I.Units[M].Springer,Berlin.
Shi AF,Jia JT,Wang XH,Luo HS.2009.Adaptive mesh refinement for 2D and 3D numerical simulations of steam-assisted gravity drainage process[C].Proceeding of International Conference on Computational Heat and Mass Transfer,Guangzhou,China,May 18-21.
Stang HR,Soni Y.1987.Saner Ranch Pilot Test of Fracture-Assisted Steamflood Technology [J].J.Pet.Tech.39(6):684-696.
Stone HL.1973.Estimation of three-phase relative permeability and residual oil data[J].Journal of Petroleum Technology 12(4):52-61.
Thomas LK,Dixon TN,Pierson RG.1983.Fractured reservoir simulation[J],SPE J.,23:42-54.
Trangenstein JA.2002.Multi-scale iterative techniques and adaptive mesh refinement for flow in porous media[J].Adv.in Water Resources,25:1175-1213.
Trangenstein JA,Bi Z.2002.Multi-scale iterative techniques and adaptive mesh refinement for Miscible Displacement Simulation [J].SPE,75232.
Tregoures N,Fichot F,Duval F,Repetto G,Quintard M.2003.Multi-dimensional Numerical Study of Core Debris Bed Reflooding under Severe Accident Conditions[C],paper C00218,Tenth International Topical Meeting on Nuclear Reactor Thermal Hydraulics,October,Seoul,Korea.
Udell KS.1983.Heat transfer in porous media heated from above with evaporation,condensation,and capillary effects[J],Journal of Heat Transfer 105:485-492.
Van Golf-Racht TD.1982.Fundamentals of fractured reservoir engineering[M].Elsevier Scientific Publishing Company,New York.
Van Wunnik JNM,Wit K.1992.Improvement of Gravity Drainage by Steam Injection into a Fractured Reservoir:An Analytical Evaluation[J].SPE Reservoir Engineering,7:59-66.
Venuturumilli R,Chen LD.2004.Numerical Simulation Using Adaptive Mesh Refinement for Laminar Jet Diffusion Flames[J].Numer.Heat Transfer B,46:101-120.
Vinsome PKW,Westerveld J.1980.A Simple Method for Predicting Cap andBase Rock Heat Losses in Thermal Reservoir Simulators[J].Journal of Canadian Petroleum Technolog,19(3):87-90.
Wagner C,Kinzelbach W,Wittum G.1997.Schur-complement multigrid:A robust method for groundwater flow and transport problems[J].Numer.Math.,75:523-545.
Wang XH,Quintard M,Darche G.2006.Adaptive mesh refinement for one-dimensional threephase flow with phase change in porous media[J].Numerical Heat Transfer B,50:231-268.
Warren JE,Root PJ.1963.The Behavior of Naturally Fractured Reservoirs[J].SPE J.,3(9):245-255.
Wheeler JA.1969.Analytical Calculations for Heat Transfer from Fractures[J].No.SPE 2494.
Wu B,Luo HS,Wang XH,Shi AF.2009.Renormalization methods for Calculating Threedimensional Effective PermeabilityfC].Proceedings of 4th ICAPM,Aug 10-12,Istanbul,TURKEY.
Wu YS,Haukwa C,Bodvarsson GS.1999.A site-scale model for fluid and heat flow in the unsaturated zone of Yucca Mountain,Nevada[J].Journal of Contaminant Hydrology,38:185-21.
Wu YS,Pruess K.1988.A multiple-porosity method for simulation of naturally fractured petroleum reservoirs[J].SPE 3:327-336.
Wu YS,Pruess K.2000.Numerical simulation of non-isothermal multiphase tracer transport in heterogeneous fractured porous media[J].Advances in Water Resources 23:699-723.
Yeo IW.Zimmerman RW.2001.Accuracy of the Renormalization Method for Computing Effective Conductivities of Heterogeneous Media[J].Trans.Porous Media,45:129-138.
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