基于模拟有限差分的嵌入式离散裂缝数学模型
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摘要
嵌入式离散裂缝模型划分网格时不需要考虑油藏内的裂缝形态,只需对基岩系统进行简单的网格剖分,可以大大降低网格划分的复杂度,从而能够提高计算效率.并且该模型可以将现有成熟的油藏数值模拟技术和离散裂缝网络模型有机地结合起来,能精细地模拟流体在裂缝性油藏中的流动.本文模型求解采用模拟有限差分方法,该方法基于单个网格的节点和面信息构造数值计算格式,理论上适用于任何复杂网格系统,且具有良好的局部守恒性,将其推广到嵌入式离散裂缝模型后,克服了该模型基于有限差分方法求解时不能有效处理全张量形式的渗透率以及不适用于复杂边界形状裂缝性油藏的局限性.最后通过实际算例验证了本文方法的正确性和优越性.
The meshing of embeded discrete fracture model(EDFM) dose not need to conside the distribution pattern of fractures. It only needs to partition grid for matrix, so it can reduce the complexity of meshing and improve the computational efficiency. The embeded discrete fracture model can combine the mature reservoir simulation technology and the discrete fracture network model. It can simulate the flow of fluid in fractured reservoir accurately. We use mimetic finite difference(MFD) method to solve the model because of its local conservativeness and applicability of complex grids. The embeded discrete fracture model can deal with permeability tensor and be used to simulate fractured reservoir with complex boundary shape. Lastly, we have proven the validity and superiority of this method with some actual examples.
The meshing of embeded discrete fracture model(EDFM) dose not need to conside the distribution pattern of fractures. It only needs to partition grid for matrix, so it can reduce the complexity of meshing and improve the computational efficiency. The embeded discrete fracture model can combine the mature reservoir simulation technology and the discrete fracture network model. It can simulate the flow of fluid in fractured reservoir accurately. We use mimetic finite difference(MFD) method to solve the model because of its local conservativeness and applicability of complex grids. The embeded discrete fracture model can deal with permeability tensor and be used to simulate fractured reservoir with complex boundary shape. Lastly, we have proven the validity and superiority of this method with some actual examples.
引文
1 袁士义,宋新民,冉启全.裂缝性油藏开发技术.北京:石油工业出版社,2004.1–3
2 Snow D.Anisotropic permeability of fractured media.Water Resour Res,1969,5:1273–1289
3 Oda M.Permeability tensor for discontinuous rock masses.Geotechnique,1985,35:483–495
4 Barenblatt G I,Zheltov I P,Kochina I N.Basic concept in the theory of homogeneous liquids in fissured rocks.J Appl Math Mech,1960,24:1286–1303
5 Kazemi H,Porterfield K,Zeman P.Numerical simulation of water-oil flow in naturally fractured reservoirs.Old SPE J,1976,16:317–326
6 Lemonnier P,Bourbiaux B.Simulation of naturally fractured reservoirs.State of the art.Part 1 physical mechanisms and simulator formulation.Oil Gas Sci Technol,2010,65:239–262
7 Lemonnier P,Bourbiaux B.Simulation of naturally fractured reservoirs.State of the art.Part 2 matrix-fracture transfers and typical features of numerical studies.Oil Gas Sci Technol,2010,65:263–286
8 Noorishad J,Mehran M.An upstream finite element method for solution of transient transport equation in fractured porous media.Water Resour Res,1982,18:588–596
9 Kim J G,Deo M D.Finite element,discrete-fracture model for multiphase flow in porous media.AICh E J,2000,46:1120–1130
10 Karimi-Fard M,Firoozabadi A.Numerical simulation of water injection in fractured media using the discrete-fracture model and the Galerkin method.SPE Reserv Eval Eng,2003,6:117–126
11 黄朝琴,姚军,王月英,等.基于离散裂缝模型的裂缝性油藏注水开发数值模拟.计算物理,2011,28:41–49
12 姚军,王子胜,张允,等.天然裂缝性油藏的离散裂缝网络数值模拟方法.石油学报,2010,31:284–288
13 Huang Z Q,Yao J,Wang Y Y,et al.Numerical study on two-phase flow through fractured porous media.Sci China Technol Sc,2011,54:2412–2420
14 Lee S H,Lough M F,Jensen C L.Hierarchical modeling of flow in naturally fractured formations with multiple length scales.Water Resour Res,2001,37:443–455
15 Li L,Lee S H.Efficient field-scale simulation of black oil in a naturally fractured reservoir through discrete fracture networks and homogenized media.SPE Reserv Eval Eng,2008,11:750–758
16 Moinfar A.Development of an efficient embedded discrete fracture model for 3D compositional reservoir simulation in fractured reservoirs.SPE J,2014,19,doi:http://dx.doi.org/10.2118/154246-PA
17 Moinfar A,Varavei A,Sepehrnoori K,et al.Development of a novel and computationally-efficient discrete-fracture model to study IOR processes in naturally fractured reservoirs.In:SPE Improved Oil Recovery Symposium.Tulsa,Oklahoma,2012
18 Brezzi F,Lipnikov K,Simoncini V.A family of mimetic finite difference methods on polygonal and polyhedral meshes.Math Mod Meth Appl S,2005,15:1533–1551
19 Lie K A,Krogstad S,Ligaarden I S,et al.Open-source MATLAB implementation of consistent discretisations on complex grids.Computat Geosci,2012,16:297–322
20 Lipnikov K,Manzini G,Shashkov M.Mimetic finite difference method.J Computat Phys,2014,257:1163–1227
21 Karimi-Fard M,Durlofsky L J,Aziz K.An efficient discrete-fracture model applicable for general-purpose reservoir simulators.SPE J,2004,9:227–236
22 Brezzi F,Lipnikov K,Simoncini V.A family of mimetic finite difference methods on polygonal and polyhedral meshes.Math Mod Meth Appl S,2005,15:1533–1551
2 Snow D.Anisotropic permeability of fractured media.Water Resour Res,1969,5:1273–1289
3 Oda M.Permeability tensor for discontinuous rock masses.Geotechnique,1985,35:483–495
4 Barenblatt G I,Zheltov I P,Kochina I N.Basic concept in the theory of homogeneous liquids in fissured rocks.J Appl Math Mech,1960,24:1286–1303
5 Kazemi H,Porterfield K,Zeman P.Numerical simulation of water-oil flow in naturally fractured reservoirs.Old SPE J,1976,16:317–326
6 Lemonnier P,Bourbiaux B.Simulation of naturally fractured reservoirs.State of the art.Part 1 physical mechanisms and simulator formulation.Oil Gas Sci Technol,2010,65:239–262
7 Lemonnier P,Bourbiaux B.Simulation of naturally fractured reservoirs.State of the art.Part 2 matrix-fracture transfers and typical features of numerical studies.Oil Gas Sci Technol,2010,65:263–286
8 Noorishad J,Mehran M.An upstream finite element method for solution of transient transport equation in fractured porous media.Water Resour Res,1982,18:588–596
9 Kim J G,Deo M D.Finite element,discrete-fracture model for multiphase flow in porous media.AICh E J,2000,46:1120–1130
10 Karimi-Fard M,Firoozabadi A.Numerical simulation of water injection in fractured media using the discrete-fracture model and the Galerkin method.SPE Reserv Eval Eng,2003,6:117–126
11 黄朝琴,姚军,王月英,等.基于离散裂缝模型的裂缝性油藏注水开发数值模拟.计算物理,2011,28:41–49
12 姚军,王子胜,张允,等.天然裂缝性油藏的离散裂缝网络数值模拟方法.石油学报,2010,31:284–288
13 Huang Z Q,Yao J,Wang Y Y,et al.Numerical study on two-phase flow through fractured porous media.Sci China Technol Sc,2011,54:2412–2420
14 Lee S H,Lough M F,Jensen C L.Hierarchical modeling of flow in naturally fractured formations with multiple length scales.Water Resour Res,2001,37:443–455
15 Li L,Lee S H.Efficient field-scale simulation of black oil in a naturally fractured reservoir through discrete fracture networks and homogenized media.SPE Reserv Eval Eng,2008,11:750–758
16 Moinfar A.Development of an efficient embedded discrete fracture model for 3D compositional reservoir simulation in fractured reservoirs.SPE J,2014,19,doi:http://dx.doi.org/10.2118/154246-PA
17 Moinfar A,Varavei A,Sepehrnoori K,et al.Development of a novel and computationally-efficient discrete-fracture model to study IOR processes in naturally fractured reservoirs.In:SPE Improved Oil Recovery Symposium.Tulsa,Oklahoma,2012
18 Brezzi F,Lipnikov K,Simoncini V.A family of mimetic finite difference methods on polygonal and polyhedral meshes.Math Mod Meth Appl S,2005,15:1533–1551
19 Lie K A,Krogstad S,Ligaarden I S,et al.Open-source MATLAB implementation of consistent discretisations on complex grids.Computat Geosci,2012,16:297–322
20 Lipnikov K,Manzini G,Shashkov M.Mimetic finite difference method.J Computat Phys,2014,257:1163–1227
21 Karimi-Fard M,Durlofsky L J,Aziz K.An efficient discrete-fracture model applicable for general-purpose reservoir simulators.SPE J,2004,9:227–236
22 Brezzi F,Lipnikov K,Simoncini V.A family of mimetic finite difference methods on polygonal and polyhedral meshes.Math Mod Meth Appl S,2005,15:1533–1551