裂隙单元修正等效渗透率模型及其验证
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摘要
采用裂隙单元表征裂隙网络,引入裂隙单元等效渗透率的概念,按照流量等效的原则计算其大小,然而阶梯状裂隙单元造成渗流流程的增加,同时压差不变导致流量的减少,为解决这一问题,用裂隙在网格中的实际流程长度与裂隙迹长之比来修正裂隙单元等效渗透率,并且针对复杂裂隙网络,对其进行预处理——删除孤立裂隙、死端裂隙、孤立裂隙簇等非连通裂隙。用此修正模型对单裂隙、相交裂隙、复杂裂隙网络进行渗流数值模拟,并与理论解及离散裂隙网络模型方法渗流结果进行比较,结果显示:研究区域下游出口总流量及出口处流量分布均取得较好一致性;同时,此裂隙单元修正等效渗透率模型也能反映出裂隙岩体渗流的非均质和各向异性。
A conceptual model of fracture element is presented that characterizes the discrete fracture network with fracture elements.We calculate the equivalent permeability of fracture element based on the principle of equivalence of flux between a single fracture and a square element.But the"stair-case"fracture elements increase the length of flow path,and result in a decrease of flux with an unaltered hydraulic pressure difference.To solve this problem,we modify the fracture elementary permeability through considering the ratio of length of flow path to fracture length;and for the complex fracture network,the isolated fractures,dead-end parts of fractures and the isolated fracture clusters are deleted to build up a connected fracture configuration.To verify the modified equivalent permeability model we perform fluid flow simulations on a series of single fracture,intersecting fractures and complex fracture network.The calculated total flow rate and flux distribution along the downstream outlet are consistent with the analytical results and discrete fracture network model results.The modified equivalent permeability model can also characterize the heterogeneity and anisotropy of fluid flow in fractured rock mass.
A conceptual model of fracture element is presented that characterizes the discrete fracture network with fracture elements.We calculate the equivalent permeability of fracture element based on the principle of equivalence of flux between a single fracture and a square element.But the"stair-case"fracture elements increase the length of flow path,and result in a decrease of flux with an unaltered hydraulic pressure difference.To solve this problem,we modify the fracture elementary permeability through considering the ratio of length of flow path to fracture length;and for the complex fracture network,the isolated fractures,dead-end parts of fractures and the isolated fracture clusters are deleted to build up a connected fracture configuration.To verify the modified equivalent permeability model we perform fluid flow simulations on a series of single fracture,intersecting fractures and complex fracture network.The calculated total flow rate and flux distribution along the downstream outlet are consistent with the analytical results and discrete fracture network model results.The modified equivalent permeability model can also characterize the heterogeneity and anisotropy of fluid flow in fractured rock mass.
引文
[1]宋晓晨,徐卫亚.裂隙岩体渗流概念模型研究[J].岩土力学,2004,25(2):226–232.(SONG Xiaochen,XU Weiya.A study on conceptualmodels of fluid flow in fractured rock[J].Rock and Soil Mechanics,2004,25(2):226–232.(in Chinese))
[2]王恩志,王洪涛.三维裂隙网络渗流数值模型研究[J].工程力学,1997,(增2):520–525.(WANG Enzhi,WANG Hongtao.Study onnumerical model of three-dimensional fluid flow in fracture network[J].Engineerign Mechanics,1997,(Supp.2):520–525.(in Chinese))
[3]宋晓晨,徐卫亚.裂隙岩体渗流模拟的三维离散裂隙网络数值模型(I):裂隙网络的随机生成[J].岩石力学与工程学报,2004,23(12):2 015–2 020.(SONG Xiaochen,XU Weiya.Numerical model ofthree-dimensional discrete fracture network for seepage in fracturedrocks(I):generation of fracture network[J].Chinese Journal of RockMechanics and Engineering,2004,23(12):2 015–2 020.(in Chinese))
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[6]PAN P Z,FENG X T,HUANG X H,et al.Coupled THM processes inEDZ of crystalline rocks using an elastoplastic cellular automaton[J].Environmental Geology,2009,57(6):1 299–1 311.
[7]SVENSSON U.A continuum representation of fracture networks.PartI:Method and basic test cases[J].Journal of Hydrology,2001,250(1/4):170–186.
[8]DOUGHTY C,SALVE R,WANG J S Y.Liquid-release tests inunsaturated fractured welded tuffs:II.Numerical modeling[J].Journalof Hydrology,2002,256(1/2):80–105.
[9]ITO K,SEOL Y A.Three-dimensional discrete fracture networkgenerator to examine fracture-matrix interaction using TOUGH2[C]//Proceedings of the TOUGH2 symposium 2003 Lawrence BerkeleyNational Laboratory.Berkeley:[s.n.],2003:12–14.
[10]MCKENNA S A,REEVES P C.Fractured continuum approach tostochastic permeability modeling[C]//COBURN T C,YARUS J M,CHAMBERS R L,ed.Stochastic Modeling and Geostatistics:Principles,Methods,and Case Studies.[S.l.]:[s.n.],2006:173–186.
[11]赵红亮,陈剑平.裂隙岩体三维网络流的渗透路径搜索[J].岩石力学与工程学报,2005,24(4):622–627.(ZHAO Hongliang,CHENJianping.Searching for seepage path of 3D network in fractured rockmasses[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(4):622–627.(in Chinese))
[12]LI J H,ZHANG L M,WANG Y,et al.Permeability tensor andrepresentative elementary volume of saturated cracked soil[J].CanadianGeotechnical Journal,2009,46(8):928–942.
[13]PRUESS K,OLDENBURG C M,MORIDIS G J.TOUGH2 User sguide version 2[R].[S.l.]:Lawrence Berkeley National Laboratory,1999.
[14]ZHAO Z,RUTQVIST J,LEUNG C,et al.Impact of stress on solutetransport in a fracture network:A comparison study[J].Journal ofRock Mechanics and Geotechnical Engineering,2013,to be pressed.
[15]RUTQVIST J,LEUNG C,HOCH A,et al.Linked multicontinuumand crack tensor approach for modeling of coupled geomechanics,fluid flow and transport in fractured rock[J].Journal of Rock Mechanicsand Geotechnical Engineering,2013,5(1):18–31.
[2]王恩志,王洪涛.三维裂隙网络渗流数值模型研究[J].工程力学,1997,(增2):520–525.(WANG Enzhi,WANG Hongtao.Study onnumerical model of three-dimensional fluid flow in fracture network[J].Engineerign Mechanics,1997,(Supp.2):520–525.(in Chinese))
[3]宋晓晨,徐卫亚.裂隙岩体渗流模拟的三维离散裂隙网络数值模型(I):裂隙网络的随机生成[J].岩石力学与工程学报,2004,23(12):2 015–2 020.(SONG Xiaochen,XU Weiya.Numerical model ofthree-dimensional discrete fracture network for seepage in fracturedrocks(I):generation of fracture network[J].Chinese Journal of RockMechanics and Engineering,2004,23(12):2 015–2 020.(in Chinese))
[4]LONG J C S,REMER J S,WILSON C R,et al.Porous mediaequivalents for networks of discontinuous fractures[J].Water ResourcesResearch,1982,18(3):645–658.
[5]MIN K B,JING L,STEPHANSSON O.Determining the equivalentpermeability tensor for fractured rock masses using a stochastic REVapproach:method and application to the field data from Sellafield,UK[J].Hydrogeology Journal,2004,12(5):497–510.
[6]PAN P Z,FENG X T,HUANG X H,et al.Coupled THM processes inEDZ of crystalline rocks using an elastoplastic cellular automaton[J].Environmental Geology,2009,57(6):1 299–1 311.
[7]SVENSSON U.A continuum representation of fracture networks.PartI:Method and basic test cases[J].Journal of Hydrology,2001,250(1/4):170–186.
[8]DOUGHTY C,SALVE R,WANG J S Y.Liquid-release tests inunsaturated fractured welded tuffs:II.Numerical modeling[J].Journalof Hydrology,2002,256(1/2):80–105.
[9]ITO K,SEOL Y A.Three-dimensional discrete fracture networkgenerator to examine fracture-matrix interaction using TOUGH2[C]//Proceedings of the TOUGH2 symposium 2003 Lawrence BerkeleyNational Laboratory.Berkeley:[s.n.],2003:12–14.
[10]MCKENNA S A,REEVES P C.Fractured continuum approach tostochastic permeability modeling[C]//COBURN T C,YARUS J M,CHAMBERS R L,ed.Stochastic Modeling and Geostatistics:Principles,Methods,and Case Studies.[S.l.]:[s.n.],2006:173–186.
[11]赵红亮,陈剑平.裂隙岩体三维网络流的渗透路径搜索[J].岩石力学与工程学报,2005,24(4):622–627.(ZHAO Hongliang,CHENJianping.Searching for seepage path of 3D network in fractured rockmasses[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(4):622–627.(in Chinese))
[12]LI J H,ZHANG L M,WANG Y,et al.Permeability tensor andrepresentative elementary volume of saturated cracked soil[J].CanadianGeotechnical Journal,2009,46(8):928–942.
[13]PRUESS K,OLDENBURG C M,MORIDIS G J.TOUGH2 User sguide version 2[R].[S.l.]:Lawrence Berkeley National Laboratory,1999.
[14]ZHAO Z,RUTQVIST J,LEUNG C,et al.Impact of stress on solutetransport in a fracture network:A comparison study[J].Journal ofRock Mechanics and Geotechnical Engineering,2013,to be pressed.
[15]RUTQVIST J,LEUNG C,HOCH A,et al.Linked multicontinuumand crack tensor approach for modeling of coupled geomechanics,fluid flow and transport in fractured rock[J].Journal of Rock Mechanicsand Geotechnical Engineering,2013,5(1):18–31.