基于离散缝洞网络模型的缝洞型油藏混合模型
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摘要
针对存在大尺度导流裂缝的复杂缝洞型油藏,为了克服目前常用数学模型不能准确高效对其进行流动模拟的缺陷,提出一种新的混合模型。首先根据缝洞的结构特征划分合适的正交网格,在每个网格单元内建立离散缝洞网络模型(DFVN),基于超样本技术和体积平均方法求得网格单元的等效渗透率张量,对小尺度的缝洞结构进行等效处理;以形成的正交网格为基础建立嵌入式离散裂缝模型,对大尺度导流裂缝进行显示处理,并基于模拟有限差分方法建立能准确处理全张量形式渗透率的数值计算格式;最后通过单相稳定渗流数值算例验证本文方法的正确性和优越性。研究结果表明:对于缝洞结构易发生变化的油藏,只需根据变化后的缝洞结构进行局部的参数修正,避免了类似于离散缝洞网络模型的整体网格重构,有效提高了计算效率。
The existing numerical simulation methods are inaccurate or inefficient when modeling the flow and transport processes in fractured-vuggy reservoir with long fractures. A numerically efficient hybrid model was proposed to solve this problem, in which small fractures and vugs were modeled by equivalent permeability tensor, and long fractures were modeled by embedded discrete fracture model. Firstly, the orthogonal grid system was made according to the structure characteristics of fractures and vugs. Then, the discrete fracture-vug model(DFVN) was implemented in each orthogonal grid to calculate equivalent permeability tensor based on volume average method and oversampling technology, and the long fractures were embedded in equivalent media system. After that, an efficient numerical simulator was devised to solve the coupled system of long fracture and equivalent media based on mimetic finite difference method. At last, several single-phase steady numerical examples were shown to verify the validity and accuracy of the hybrid model. The results show that the proposed model is suitable for the fractured-vuggy reservoirs with dynamically changing fractures and vugs, because they can be simulated with an element effectively adapting itself to changes. Therefore the challenges associated with the remeshing for whole reservoirs, which has to be done in the DFVN, are bypassed entirely, and the computational costs can be reduced greatly.
The existing numerical simulation methods are inaccurate or inefficient when modeling the flow and transport processes in fractured-vuggy reservoir with long fractures. A numerically efficient hybrid model was proposed to solve this problem, in which small fractures and vugs were modeled by equivalent permeability tensor, and long fractures were modeled by embedded discrete fracture model. Firstly, the orthogonal grid system was made according to the structure characteristics of fractures and vugs. Then, the discrete fracture-vug model(DFVN) was implemented in each orthogonal grid to calculate equivalent permeability tensor based on volume average method and oversampling technology, and the long fractures were embedded in equivalent media system. After that, an efficient numerical simulator was devised to solve the coupled system of long fracture and equivalent media based on mimetic finite difference method. At last, several single-phase steady numerical examples were shown to verify the validity and accuracy of the hybrid model. The results show that the proposed model is suitable for the fractured-vuggy reservoirs with dynamically changing fractures and vugs, because they can be simulated with an element effectively adapting itself to changes. Therefore the challenges associated with the remeshing for whole reservoirs, which has to be done in the DFVN, are bypassed entirely, and the computational costs can be reduced greatly.
引文
[1]李阳.塔河油田碳酸盐岩缝洞型油藏开发理论及方法[J].石油学报,2013,34(1):115-121.LI Yang.The theory and method for development of carbonate fractured-cavity reservoirs in Tahe oilfield[J].Acta Petrolei Sinica,2013,34(1):115-121.
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[12]张世明,严侠,孙红霞,等.基于离散裂缝模型的裂缝性介质等效渗透率求解新方法[J].科学技术与工程,2014,14(16):36-40.ZHANG Shiming,YAN Xia,SUN Hongxia,et al.An efficient calculation of equivalent permeability of fractured porous media based on discrete fracture model[J].Science Technology and Engineering,2014,14(16):36-40.
[13]HUANG Zhaoqin,YAO Jun,LI Yajun,et al.Permeability analysis of fractured vuggy porous media based on homogenization theory[J].Science China Technological Sciences,2010,53(3):839-847.
[14]HUANG Zhaoqin,YAO Jun,LI Yajun,et al.Numerical calculation of equivalent permeability tensor for fractured vuggy porous media based on homogenization theory[J].Communications in Computational Physics,2011,9(1):180-204.
[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[J].SPE Reservoir Evaluation&Engineering,2008,11(04):750-758.
[16]严侠,黄朝琴,姚军,等.基于模拟有限差分的嵌入式离散裂缝数学模型[J].中国科学:技术科学,2014,44(12):1333-1342.YAN Xia,HUANG Zhaoqin,YAO Jun,et al.The embeded discrete fracture model based on mimetic finite difference method[J].Science China:Technological Sciences,2014,44(12):1333-1342.
[17]ZHOU Fangqi,SHI Anfeng,WANG Xiaohong.An efficient finite difference model for multiphase flow in fractured reservoirs[J].Petroleum Exploration and Development,2014,41(2):262-266.
[18]DURLOFSKY L J.Upscaling and gridding of fine scale geological models for flow simulation[C]//8th International Forum on Reservoir Simulation Iles Borromees,Stresa,Italy.2005:20-24.
[19]KARIMI F M,DURLOFSKY L J,AZIZ K.An efficient discrete-fracture model applicable for general-purpose reservoir simulators[J].SPE Journal,2004,9(2):227-236.
[20]LIPNIKOV K,MANZINI G,SHASHKOV M.Mimetic finite difference method[J].Journal of Computational Physics,2014,257:1163-1227.
[21]BREZZI F,LIPNIKOV K,SIMONCINI V.A family of mimetic finite difference methods on polygonal and polyhedral meshes[J].Mathematical Models and Methods in Applied Sciences,2005,15(10):1533-1551.
[22]黄朝琴,高博,王月英,等.基于模拟有限差分法的离散裂缝模型两相流动模拟[J].中国石油大学学报(自然科学版),2014,38(6):97-105.HUANG Zhaoqin,GAO Bo,WANG Yueying,et al.Two-phase flow simulation of discrete fracture model using a novel mimetic finite difference method[J].Journal of China University of Petroleum(Edition of Natural Science),2014,38(6):97-105.
[23]YAN Xia,HUANG Zhaoqin,YAO Jun,et al.An efficient embedded discrete fracture model based on mimetic finite difference method[J].Journal of Petroleum Science and Engineering,2016,145:11-21.
[2]李亚军.缝洞型介质等效连续模型油水两相流动模拟理论研究[D].青岛:中国石油大学石油工程学院,2011:17-64.LI Yajun.Theoretical study of the equivalent continuum model for simulating oil-water two-phase flow in fractured-vuggy porous media[D].Qingdao:China University of Petroleum.School of Petroleum Engineering,2011:17-64.
[3]HUANG Zhaoqin,YAO Jun,WANG Yueying.An efficient numerical model for immiscible two-phase flow in fractured Karst reservoirs[J].Communications in Computational Physics,2013,13(2):540-558.
[4]吴玉树,葛家理.三重介质裂-隙油藏中的渗流问题[J].力学学报,1983,19(1):81-85.WU Yushu,GE Jiali.The transient flow in naturally fractured reservoirs with three-porosity systems[J].Chinese Journal of Theoretical and Applied Mechanics,1983,19(1):81-85.
[5]ABDASSAH D,ERSHAGHI I.Triple-porosity systems for representing naturally fractured reservoirs[J].SPE Formation Evaluation,1986,1(2):113-127.
[6]杨坚,姚军,王子胜.三重介质复合油藏压力动态特征研究[J].水动力学研究与进展(A辑),2005,20(4):418-425.YANG Jian,YAO Jun,WANG Zisheng.Study of pressure-transient characteristic for triple-medium composite reservoirs[J].Journal of Hydrodynamics(Series A),2005,20(4):418-425.
[7]WU Yushu,QIN Guan,EWING R,et al.A multiple-continuum approach for modeling multiphase flow in naturally fractured vuggy petroleum reservoirs[C]//SPE International oil&Gas Conference and Exhibition.Beijing:SPE,2006:1-12.
[8]姚军,黄朝琴,王子胜,等.缝洞型油藏的离散缝洞网络流动数学模型[J].石油学报,2010,31(5):15-20.YAO Jun,HUANG Zhaoqin,WANG Zisheng,et al.Mathematical model of fluid flow in fractured vuggy reservoirs based on discrete fracture-vug network[J].Acta Petrolei Sinica,2010,31(5):815-819.
[9]YAO Jun,HUANG Zhaoqin,LI Yajun,et al.Discrete fracture-vug network model for modeling fluid flow in fractured vuggy porous media[C]//The CPS/SPE International Oil&Gas Conference and Exhibition.Beijing,China:SPE 2010:1-14.
[10]李亚军,姚军,黄朝琴,等.基于Darcy-Stokes耦合模型的缝洞型介质等效渗透率分析[J].中国石油大学学报(自然科学版),2011,35(2):91-95.LI Yajun,YAO Jun,HUANG Zhaoqin,et al.Estimating equivalent permeability of fractured-vuggy media based on coupled Darcy-Stokes model[J].Journal of China University of Petroleum(Edition of Natural Science),2011,35(2):91-95.
[11]李亚军,姚军,黄朝琴,等.裂缝性油藏等效渗透率张量计算及表征单元体积研究[J].水动力学研究与进展(A辑),2010,25(1):1-7.LI Yajun,YAO Jun,HUANG Zhaoqin,et al.Calculation of equivalent permeability tensor and study on representative element volume for modeling fractured reservoirs[J].Journal of Hydrodynamics(Series A),2010,25(1):1-7.
[12]张世明,严侠,孙红霞,等.基于离散裂缝模型的裂缝性介质等效渗透率求解新方法[J].科学技术与工程,2014,14(16):36-40.ZHANG Shiming,YAN Xia,SUN Hongxia,et al.An efficient calculation of equivalent permeability of fractured porous media based on discrete fracture model[J].Science Technology and Engineering,2014,14(16):36-40.
[13]HUANG Zhaoqin,YAO Jun,LI Yajun,et al.Permeability analysis of fractured vuggy porous media based on homogenization theory[J].Science China Technological Sciences,2010,53(3):839-847.
[14]HUANG Zhaoqin,YAO Jun,LI Yajun,et al.Numerical calculation of equivalent permeability tensor for fractured vuggy porous media based on homogenization theory[J].Communications in Computational Physics,2011,9(1):180-204.
[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[J].SPE Reservoir Evaluation&Engineering,2008,11(04):750-758.
[16]严侠,黄朝琴,姚军,等.基于模拟有限差分的嵌入式离散裂缝数学模型[J].中国科学:技术科学,2014,44(12):1333-1342.YAN Xia,HUANG Zhaoqin,YAO Jun,et al.The embeded discrete fracture model based on mimetic finite difference method[J].Science China:Technological Sciences,2014,44(12):1333-1342.
[17]ZHOU Fangqi,SHI Anfeng,WANG Xiaohong.An efficient finite difference model for multiphase flow in fractured reservoirs[J].Petroleum Exploration and Development,2014,41(2):262-266.
[18]DURLOFSKY L J.Upscaling and gridding of fine scale geological models for flow simulation[C]//8th International Forum on Reservoir Simulation Iles Borromees,Stresa,Italy.2005:20-24.
[19]KARIMI F M,DURLOFSKY L J,AZIZ K.An efficient discrete-fracture model applicable for general-purpose reservoir simulators[J].SPE Journal,2004,9(2):227-236.
[20]LIPNIKOV K,MANZINI G,SHASHKOV M.Mimetic finite difference method[J].Journal of Computational Physics,2014,257:1163-1227.
[21]BREZZI F,LIPNIKOV K,SIMONCINI V.A family of mimetic finite difference methods on polygonal and polyhedral meshes[J].Mathematical Models and Methods in Applied Sciences,2005,15(10):1533-1551.
[22]黄朝琴,高博,王月英,等.基于模拟有限差分法的离散裂缝模型两相流动模拟[J].中国石油大学学报(自然科学版),2014,38(6):97-105.HUANG Zhaoqin,GAO Bo,WANG Yueying,et al.Two-phase flow simulation of discrete fracture model using a novel mimetic finite difference method[J].Journal of China University of Petroleum(Edition of Natural Science),2014,38(6):97-105.
[23]YAN Xia,HUANG Zhaoqin,YAO Jun,et al.An efficient embedded discrete fracture model based on mimetic finite difference method[J].Journal of Petroleum Science and Engineering,2016,145:11-21.