含轻质组分稠油油藏蒸汽注采数值模拟自适应网格法研究
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摘要
注蒸汽热采稠油是稠油油藏开采的主要方法之一。在含轻质组分稠油油藏注蒸汽热采过程中,油相中的轻质组分可能会发生相变,蒸汽腔内部或界面附近不仅存在温度和饱和度变化剧烈的锋面,还存在各组分摩尔分数变化剧烈的锋面。由于这些锋面处的物理量梯度非常大,从计算精度考虑,在锋面处需要非常精细的网格计算。若对全场划分均匀的网格,则计算耗时将难以承受。为了提高计算效率,将自适应网格法应用到模拟过程中,在物理量梯度大的区域采用细网格、物理量梯度小的区域采用粗网格计算。本文主要研究在应用自适应网格法时出现的若干问题,以及轻质组分的挥发对不同注采方式下注采效率的影响。
为了减少在计算过程中网格取向效应的影响,控制方程组采用九点离散格式。提出九点离散格式下的不同层次网格之间流量和导热量的计算方法,并给出计算边界处的处理方案。
由于自适应网格法在计算过程中需要对物理量进行插值,这给三相区内中主变量选取带来一系列的问题。为此,本文对主变量的选取进行了详细地分析,得出三相区内以Sw,So,X1,p作为主变量更为合适,并从理论及实例上对它进行了解释和验证。
对于自适应网格法中细化准则问题,文中提出根据轻质组分的平均分子量的大小来判断是否需要增加组分摩尔分数的判据：若油藏中轻质组分的平均分子量较低(碳数小于C9)时,组分摩尔分数的锋面和蒸汽锋面大体重合,则可以不需要组分摩尔分数的判据；若油藏中轻质组分的平均分子量较大(C9+)时,轻质组分会在蒸汽腔内部发生聚集,此时必须要增加组分摩尔分数作为网格划分的判据以确保计算精度。
由于蒸汽腔内部轻质组分不断的挥发出来,使得蒸汽腔内轻质组分含量较低,为避免常用插值方法在网格细化插值过程中可能的出现非物理震荡(例如各相组分含量小于0或大于1)现象,本文提出了采用守恒修正的分片线性插值算法,该算法不仅能够满足插值过程中物理量的守恒性,而且能够保证插值网格物理量都属于内插,从而避免了插值方式可能带来的问题。
在上述工作的基础上,采用结构化程序设计编写数值模拟计算程序,并对自适应网格法的计算精度和计算效率进行了验证。结果表明,AMR方法与精细网格解的计算结果在SAGD和蒸汽驱两种注采方式下都非常吻合,而且计算至注采结束时,AMR方法的计算速度都比精细网格解的计算速度快5倍左右,说明AMR方法的计算效率非常高,可以节省了大量的计算时间,具有很好的工程应用价值。
本文利用自适应网格法模拟程序对稠油油藏中轻质组分的挥发作用进行了详细的研究,研究结果表明：
在蒸汽注采过程中,蒸汽腔内挥发出来的轻质组分和水蒸气一起向锋面聚集,从而提高了锋面附近的油相流动能力,而重力作用将会使得轻质组分更易聚集在蒸汽腔上半部的锋面附近。通过数值算例发现,轻质组分的挥发对采油效率的影响与注采方式有关,对蒸汽驱影响较大,而对SAGD影响较小；
当油藏中可挥发的轻质组分的分子量越小或者含量越高时,则轻质组分的挥发使得在蒸汽锋面附近聚集的油相和气相轻质组分含量越高,蒸汽注采的效率也就更高；在蒸汽突破至生产井后,轻质组分的加速流失将无法充分发挥它的溶剂降粘作用,从而不利于稠油的开采。
若仅对油的产量或蒸汽注采效率感兴趣,对于SAGD开采的数值模拟或对轻质组分总体分子量较大(C1。+)且含量较低稠油油藏蒸汽驱开采的数值模拟,可以不考虑轻质组分挥发的影响,将计算模型简化为三相二组分模型。
Steam injection is an improtant thermal recovery methods in heavy oil reservoirs. Light components in the oil phase may change phase in the heavy oil reservoir during steam injection thermal recovery process, leading to not only the existence of very sharp temperature and saturation fronts but also the existence of a very sharp light components front. Due to the rapid variations of physical quantities, such as temperature, staturation and mole fraction of the components etc., very fine grids are required around the fronts to guarantee the numerical simulation accuracy. A large amount of CPU time is needed if applying uniformly fine grids to the whole domain. In order to improve the efficiency of numerical simulation, 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 while coarser grids are used where the variations of temperature and saturations are slower. This thesis focuses on a number of problems arised when getting the adaptive mesh refinement technique involed in thremal recovery of the heavy oil reservoir with light components and the effects of volatility of light components on heavy oil thermal recovery are evaluated using the AMR technique.
In order to reduce the grid orientation effect during the simulation process, the nine-point discrete method is applied and the flow and conduction rate on different hierarchical grid interfaces are calculated under nine-point discrete method, moreover, the calculation boundary treatments are given in this paper.
Physical quantities'interpolation and calculation based on the grid are needed when AMR is applied to numerical reservoir simulation, which will bring a problem of the selection of main variables in three phase zone. Therefore, in this paper, the selection of main variables are analyzed in details and Sw,S0,X1,p are more suitable for the main variables in three phase zone, which is explained and verified from the theory and examples.
For AMR grid refining, whether to use the component molar fraction as a refining criterion is determined by the average molecular weight of the lighter components. When the average molecular weight of the light components is low ( The light components content inside the steam chamber is low because of light components'volatilisation, which may cause unphysical oscillations to the component mole fractions by the possible extrapolation during the refining operation, resulting in the mole fractions being either negative or bgger than1. A conservative piece-wise linear interpolation algorithm is proposed, which can not only satisfy the physical conservation but also ensure the interpolation of physical quantities of the grids. and problems caused by the extrapolation can be avoided in this way.
In order to improve the efficiency of the realization of the AMR programs, a structured program design is introduced and a program flow chart of the AMR programs is provided. AMR calculation accuracy and computational efficiency are verified through simulating SAGD and Steam flooding process with the AMR programs. The numerical example results show that, The AMR calculation results are in agreement with the fine-grid solution, moreover, the calculation speed of AMR method calculation is about five times faster than fine-grid during the simulation processes. Therefore, with faster speed and almost same accuracy of the fine-grid method, the proposed AMR technique will have a very good value in engineering application.
With the use of adaptive grid method simulation program, the paper carried out a detailed study on the effects of volatilization of the lighter components in the heavy oil reservoirs, study results show that:
The steam and light components volatilized from oil phase inside the steam chamber are moved towards the thermal fronts during steam injection thermal recovery process and the aggregation of the light components increases the local oil mobility. The light components tend to aggregate on the thermal fronts at the upper part of the steam chamber due to gravity. Therefore, the influences of the volatility of the light components on the oil production depend upon the types of the thermal recovery. The influence for the steam drive process is more obvious than that for the SAGD process.
The smaller molecular weight or the higher the content of the volatile light components in the reservoir, the content of gaseous and oil phase light components gathered more in the vicinity of the steam front, resulting in a higher oil recovery efficiency. Steam breakthrough to the producing wells will accelerate the loss of light components, so it will not be able to make full use of the viscosity reduction by the light components, which is not conducive to the exploitation of heavy oil.
If it is only interested in the production or recovery efficiency of oil, the impact of the volatility of light components can be ignored and the calculation model can be simplified to the three-phase two-component model for the numerical simulation of SAGD or the simulation of steam flooding in heavy oil reservoir with light components of large molecular weight (C10+) or low content.
为了减少在计算过程中网格取向效应的影响,控制方程组采用九点离散格式。提出九点离散格式下的不同层次网格之间流量和导热量的计算方法,并给出计算边界处的处理方案。
由于自适应网格法在计算过程中需要对物理量进行插值,这给三相区内中主变量选取带来一系列的问题。为此,本文对主变量的选取进行了详细地分析,得出三相区内以Sw,So,X1,p作为主变量更为合适,并从理论及实例上对它进行了解释和验证。
对于自适应网格法中细化准则问题,文中提出根据轻质组分的平均分子量的大小来判断是否需要增加组分摩尔分数的判据：若油藏中轻质组分的平均分子量较低(碳数小于C9)时,组分摩尔分数的锋面和蒸汽锋面大体重合,则可以不需要组分摩尔分数的判据；若油藏中轻质组分的平均分子量较大(C9+)时,轻质组分会在蒸汽腔内部发生聚集,此时必须要增加组分摩尔分数作为网格划分的判据以确保计算精度。
由于蒸汽腔内部轻质组分不断的挥发出来,使得蒸汽腔内轻质组分含量较低,为避免常用插值方法在网格细化插值过程中可能的出现非物理震荡(例如各相组分含量小于0或大于1)现象,本文提出了采用守恒修正的分片线性插值算法,该算法不仅能够满足插值过程中物理量的守恒性,而且能够保证插值网格物理量都属于内插,从而避免了插值方式可能带来的问题。
在上述工作的基础上,采用结构化程序设计编写数值模拟计算程序,并对自适应网格法的计算精度和计算效率进行了验证。结果表明,AMR方法与精细网格解的计算结果在SAGD和蒸汽驱两种注采方式下都非常吻合,而且计算至注采结束时,AMR方法的计算速度都比精细网格解的计算速度快5倍左右,说明AMR方法的计算效率非常高,可以节省了大量的计算时间,具有很好的工程应用价值。
本文利用自适应网格法模拟程序对稠油油藏中轻质组分的挥发作用进行了详细的研究,研究结果表明：
在蒸汽注采过程中,蒸汽腔内挥发出来的轻质组分和水蒸气一起向锋面聚集,从而提高了锋面附近的油相流动能力,而重力作用将会使得轻质组分更易聚集在蒸汽腔上半部的锋面附近。通过数值算例发现,轻质组分的挥发对采油效率的影响与注采方式有关,对蒸汽驱影响较大,而对SAGD影响较小；
当油藏中可挥发的轻质组分的分子量越小或者含量越高时,则轻质组分的挥发使得在蒸汽锋面附近聚集的油相和气相轻质组分含量越高,蒸汽注采的效率也就更高；在蒸汽突破至生产井后,轻质组分的加速流失将无法充分发挥它的溶剂降粘作用,从而不利于稠油的开采。
若仅对油的产量或蒸汽注采效率感兴趣,对于SAGD开采的数值模拟或对轻质组分总体分子量较大(C1。+)且含量较低稠油油藏蒸汽驱开采的数值模拟,可以不考虑轻质组分挥发的影响,将计算模型简化为三相二组分模型。
Steam injection is an improtant thermal recovery methods in heavy oil reservoirs. Light components in the oil phase may change phase in the heavy oil reservoir during steam injection thermal recovery process, leading to not only the existence of very sharp temperature and saturation fronts but also the existence of a very sharp light components front. Due to the rapid variations of physical quantities, such as temperature, staturation and mole fraction of the components etc., very fine grids are required around the fronts to guarantee the numerical simulation accuracy. A large amount of CPU time is needed if applying uniformly fine grids to the whole domain. In order to improve the efficiency of numerical simulation, 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 while coarser grids are used where the variations of temperature and saturations are slower. This thesis focuses on a number of problems arised when getting the adaptive mesh refinement technique involed in thremal recovery of the heavy oil reservoir with light components and the effects of volatility of light components on heavy oil thermal recovery are evaluated using the AMR technique.
In order to reduce the grid orientation effect during the simulation process, the nine-point discrete method is applied and the flow and conduction rate on different hierarchical grid interfaces are calculated under nine-point discrete method, moreover, the calculation boundary treatments are given in this paper.
Physical quantities'interpolation and calculation based on the grid are needed when AMR is applied to numerical reservoir simulation, which will bring a problem of the selection of main variables in three phase zone. Therefore, in this paper, the selection of main variables are analyzed in details and Sw,S0,X1,p are more suitable for the main variables in three phase zone, which is explained and verified from the theory and examples.
For AMR grid refining, whether to use the component molar fraction as a refining criterion is determined by the average molecular weight of the lighter components. When the average molecular weight of the light components is low (
In order to improve the efficiency of the realization of the AMR programs, a structured program design is introduced and a program flow chart of the AMR programs is provided. AMR calculation accuracy and computational efficiency are verified through simulating SAGD and Steam flooding process with the AMR programs. The numerical example results show that, The AMR calculation results are in agreement with the fine-grid solution, moreover, the calculation speed of AMR method calculation is about five times faster than fine-grid during the simulation processes. Therefore, with faster speed and almost same accuracy of the fine-grid method, the proposed AMR technique will have a very good value in engineering application.
With the use of adaptive grid method simulation program, the paper carried out a detailed study on the effects of volatilization of the lighter components in the heavy oil reservoirs, study results show that:
The steam and light components volatilized from oil phase inside the steam chamber are moved towards the thermal fronts during steam injection thermal recovery process and the aggregation of the light components increases the local oil mobility. The light components tend to aggregate on the thermal fronts at the upper part of the steam chamber due to gravity. Therefore, the influences of the volatility of the light components on the oil production depend upon the types of the thermal recovery. The influence for the steam drive process is more obvious than that for the SAGD process.
The smaller molecular weight or the higher the content of the volatile light components in the reservoir, the content of gaseous and oil phase light components gathered more in the vicinity of the steam front, resulting in a higher oil recovery efficiency. Steam breakthrough to the producing wells will accelerate the loss of light components, so it will not be able to make full use of the viscosity reduction by the light components, which is not conducive to the exploitation of heavy oil.
If it is only interested in the production or recovery efficiency of oil, the impact of the volatility of light components can be ignored and the calculation model can be simplified to the three-phase two-component model for the numerical simulation of SAGD or the simulation of steam flooding in heavy oil reservoir with light components of large molecular weight (C10+) or low content.
引文
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钟立国.2005.水热裂解开采稠油关键技术研究[博士论文].大庆：大庆石油学院.
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Berger MJ, Oliger J.1984. Adaptive mesh refinement for hyperbolic partialdifferential equations[J]. J. Comput. Phys.,53:484-512.
Berger MJ, Colella P.1989. Local adaptive mesh refinement forshockhydrodyn-amiccs[J]. J. Comput. Phys.,82:64-84.
Butler RM, Stephens DJ.1981. The gravity drainage of steam heated to parallel horizontal wells[J]. JCPT, April-June:90-96.
Butler RM, McNab GS, 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.1991. Thermal Recovery of Oil and Bitumem[M]. Prentice Hall, Englew-ood Cliffs, N.J.
Butler RM.1994. Steam-assister gravity drainage:concept, development,performanc-e and future [J]. Journal of Canadian Petroleum Technology,33(2):44-50.
Christensen J R,Darche G,Dechelette B,et al.2004. Application of dynamic gridding to thermal simulations[R].SPE 86969.
Coats KH, Modine AD.1983. A consistent method for calculating transmissibilities in nine-point difference equations [R]. SPE 12248
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.
Farouq Ali S M.1977. A three-phase,two-dimensional compositional thermal simulator for steam injection processes[J]. The Journal of Canadian Petroleum Technology,16(l):78-90.
Ferrer J, Farouq Ali S M.1977. A three-phase,two-dimensional compositional thermal simulator for steam injection processes[J]. The Journal of Canadian Petroleum Technology,16(1):78-90.
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.
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[R], SPE 86962.
Haldenwang P, Pignol D.2002. Dynamically adapted mesh refinement for combustio-n front tracking [J]. Computers and Fluids,31:589-606.
Hornung RD, Trangenstein JA.1997. Adaptive mesh refinement and multilevel iterat-ion for flow in porous media [J]. J. Comput. Phys.,136:522-545.
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.
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.
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Mohammad T, Vafaei R, Eslamloueyan L, et al.2009. Analysis and simulation of steam distillation mechanism during the steam injection process [J].Energy & Fuels,23(1),327-333.
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Nilsson J, Gerritsen M, Younis R.2005. Towards An Adaptive, High-Resolution Simulator for Steam Injection Processes[R], SPE 93881.
Northrop P S,Venkatesan V N.1993. Analytical steam distillation model for thermal enhanced oil recovery processes [J].Ind.Eng.Chem.Res,32(9):2039-2046
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
Peter H.2003. Dynamic grid refinement and amalgamation for compositional simulation[R].SPE 79683.
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.
Redlich O, Kwong, JNS.1949. On the thermodynamics of solutions. V. an equation of state. fugacifies of gaseous solutions[J].Chem.Rev.,44:233-244
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Trangenstein JA.2002. Multi-scale iterative techniques and adaptive mesh refinement for flow in porous media[J]. Adv. in Water Resources,25:1175-1213.
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Venuturumilli R, Chen LD.2004. Numerical Simulation Using Adaptive Mesh Refin-ement for Laminar Jet Diffusion Flames[J]. Numer. Heat Transfer B,46:101-120.
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Azin R, Kharrat R,Ghotbi C,et al.2008. Effect of fracture spacing on VAPEX performance in heavy oil fracture systems[J].Iran.J.Chem.Chem.Eng.,27(1):35-45.
Berger MJ, Oliger J.1984. Adaptive mesh refinement for hyperbolic partialdifferential equations[J]. J. Comput. Phys.,53:484-512.
Berger MJ, Colella P.1989. Local adaptive mesh refinement forshockhydrodyn-amiccs[J]. J. Comput. Phys.,82:64-84.
Butler RM, Stephens DJ.1981. The gravity drainage of steam heated to parallel horizontal wells[J]. JCPT, April-June:90-96.
Butler RM, McNab GS, 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.1991. Thermal Recovery of Oil and Bitumem[M]. Prentice Hall, Englew-ood Cliffs, N.J.
Butler RM.1994. Steam-assister gravity drainage:concept, development,performanc-e and future [J]. Journal of Canadian Petroleum Technology,33(2):44-50.
Christensen J R,Darche G,Dechelette B,et al.2004. Application of dynamic gridding to thermal simulations[R].SPE 86969.
Coats KH, Modine AD.1983. A consistent method for calculating transmissibilities in nine-point difference equations [R]. SPE 12248
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.
Farouq Ali S M.1977. A three-phase,two-dimensional compositional thermal simulator for steam injection processes[J]. The Journal of Canadian Petroleum Technology,16(l):78-90.
Ferrer J, Farouq Ali S M.1977. A three-phase,two-dimensional compositional thermal simulator for steam injection processes[J]. The Journal of Canadian Petroleum Technology,16(1):78-90.
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.
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[R], SPE 86962.
Haldenwang P, Pignol D.2002. Dynamically adapted mesh refinement for combustio-n front tracking [J]. Computers and Fluids,31:589-606.
Hornung RD, Trangenstein JA.1997. Adaptive mesh refinement and multilevel iterat-ion for flow in porous media [J]. J. Comput. Phys.,136:522-545.
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.
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/s11242-008-9325-6.
Luo HS, Wang XH, Shi AF.2009. The AMR Technique For SAGD Process in Highly Heterogenous 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.
Mohammad T, Vafaei R, Eslamloueyan L, et al.2009. Analysis and simulation of steam distillation mechanism during the steam injection process [J].Energy & Fuels,23(1),327-333.
Mohammad M.2010. Solubility and diffusivity of carbon dioxide ethane and propane in heavy oil and its sara fractions [D].Industrial Systems Engine-ering University of Regina
Mukhopadhyay S,Sahimi M.1992. Heat Transfer and Two-Phase Flow in Flow in Fractured Reservoirs[R].SPE 24043.
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[R], SPE 93881.
Northrop P S,Venkatesan V N.1993. Analytical steam distillation model for thermal enhanced oil recovery processes [J].Ind.Eng.Chem.Res,32(9):2039-2046
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
Peter H.2003. Dynamic grid refinement and amalgamation for compositional simulation[R].SPE 79683.
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.
Redlich O, Kwong, JNS.1949. On the thermodynamics of solutions. V. an equation of state. fugacifies of gaseous solutions[J].Chem.Rev.,44:233-244
Reis J C.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 J C.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.
Sarkar AK, Sarathi PS.1993. Thermal processes for heavy oil recovery[R]. DOI. 10.2172/10108843.
Sharper HN, Richardson WC, Lolley TS.1995. Representation of steam distillation and In-situ upgrading processes in a heavy oil simulation [R]. SPE 30301.
Shutler ND.1969.Numerical, Three-Phase Simulation of the Linear Steamflood Process [R]. SPE 2233.
Shutler ND.1970.Numerical Three-Phase Model of the Two-Dimensional Steamflood Process [R]. SPE 2798.
Tamim M, Abou-Kassem J H, Farouq Alic S M.2000. Recent developments in numerical simulation techniques of thermal recovery processes[J].Journal of Petroleum Science and Engineering,26(1-4):283-289.
Trangenstein JA.2002. Multi-scale iterative techniques and adaptive mesh refinement for flow in porous media[J]. Adv. in Water Resources,25:1175-1213.
Venu G R N.2010. Simulation study of sweep improvement in heavy oil CO2 floods[D].B.Tech., Indian School of Mines.
Venuturumilli R, Chen LD.2004. Numerical Simulation Using Adaptive Mesh Refin-ement for Laminar Jet Diffusion Flames[J]. Numer. Heat Transfer B,46:101-120.
Wang XH, Quintard M, Darche G.2006. Adaptive mesh refinement for one-dimensi-onal three-phase flow with phase change in porous media[J]. Numerical Heat Transfer B,50:231-268.
Willman BT,Valleroy VV.1961. Runberg GW.1961, Laboratory studies of oil recovery by steam injection [R]. SPE 1537-G.
Wu CH, Elder RB.1983. Correlation of crude oil steam distillation yields with basic crude oil properties [J]. Society of Petroleum Engineers Journal,23(6),937-945.
Wu B, Luo HS, Wang XH, Shi AF.2009. Renormalization methods for Calculating Three- dimensional Effective Permeability[C]. Proceedings of 4th ICAPM, Aug 10-12, Istanbul, TURKEY.
Yanosik JL, McCraken TA.1976. A nine-point, finite-difference reservoir simulator for realistic prediction of adverse mobility ratio displacements[R]. SPE 5734.
Johnson FS, Walker CJ, Bayazeed AF.1971. Oil vaporization during steamflooding. [J]. Journal of Petroleum Technology,23(6),731-742.
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