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| A NUMERICAL METHOD FOR DISCRETE FRACTURE NETWORK MODEL FOR FLOW AND HEAT TRANSFER IN TWO-DIMENSIONAL FRACTURED ROCKS |
| CHEN Biguang1,2,SONG Erxiang1,2,CHENG Xiaohui1,2 |
| (1. Department of Civil Engineering,Tsinghua University,Beijing 100084,China;2. Key Laboratory of Civil Engineering Safety and Durability of Ministry of Education,Tsinghua University,Beijing 100084,China) |
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Abstract For the problem of flow and heat transfer in fractured rocks,two hypotheses of heat exchange between rock matrix and fluid in the fracture are compared analytically. It is found that the same result will be obtained for that the fracture aperture is small in general. A discrete fracture network model is realized in commercial finite element software COMSOL for the computation of flow and heat transfer in fractured rock. Both fluid flow and heat transfer in rock matrix and fracture can be calculated in this model,as well as fluid and heat exchange between them. The results are validated by comparing with analytical solutions. Finally,the model is used to simulate a randomly generated fracture network to study the characteristics of flow and heat transfer in fractured rock;and reasonable results are obtained.
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Received: 20 February 2013
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| [1] TESTER J W,ANDERSON B,BATCHELOR A,et al. The future of geothermal energy:impact of enhanced geothermal systems(EGS) on the United States in the 21st century[R]. Massachusetts:Massachusetts Institute of Technology,2006.
[2] ZHENG K Y,HAN Z S,ZHANG Z G. Steady industrialized development of geothermal energy in China-country update report 2005–2009[C]// Proceedings of World Geothermal Congress 2010. Bali,Indonesia:[s. n.],2010. http://www.geothermal-energy.org/ publications_and_services/conference_paper_database.html.
[3] STEFANSSON V. Geothermal reinjection experience[J]. Geothermics,1997,26(1):99–139
[4] BANKS D. Thermogeological assessment of open-loop well-doublet schemes:a review and synthesis of analytical approaches[J]. Hydrogeology Journal,2009,17(5):1 149–1 155.
[5] National Research Council(US) Committee on Fracture Characterization and Fluid Flow. Rock fractures and fluid flow:contemporary understanding and applications[M]. [S. l.]:National Academy Press,1996:316.
[6] WARREN J E,ROOT P J. The behavior of naturally fractured reservoirs[J]. Old SPE Journal,1963,3(3):245–255.
[7] PRUESS K. A practical method for modeling fluid and heat flow in fractured porous media[J]. Old SPE Journal,1985,25(1):14–26.
[8] CACAS M C,LEDOUX E,DE MARSILY G,et al. Modeling fracture flow with a stochastic discrete fracture network:calibration and validation:the flow model[J]. Water Resources Research,1990,26(3):479–489.
[9] KODLITZ O. Modelling flow and heat transfer in fractured rocks:Conceptual model of a 3D deterministic fracture network[J]. Geothermics,1995,24(3):451–470.
[10] WITHERSPOON P A,WANG J S Y,IWAI K,et al. Validity of cubic law for fluid flow in a deformable rock fracture[J]. Water Resources Research,1980,16(6):1 016–1 024.
[11] JUANES R,SAMPER J,MOLINERO J. A general and efficient formulation of fractures and boundary conditions in the finite element method[J]. International Journal for Numerical Methods in Engineering,2002,54(12):1 751–1 774.
[12] 赵延林,王卫军,曹 平,等. 不连续面在双重介质热–水–力三维耦合分析中的有限元数值实现[J]. 岩土力学,2010,31(2):638–644.(ZHAO Yanlin,WANG Weijun,CAO Ping,et al. Numerical implementation of discontinuities in dual media 3D model for thermo-hydro-mechanical coupling[J]. Rock and Soil Mechanics,2010,31(2):638–644.(in Chinese))
[13] 杨强生,浦保荣. 高等传热学[M]. 上海:上海交通大学出版社,2001:144–146.(YANG Qiangsheng,PU Baorong. Advanced heat transfer[M]. Shanghai:Shanghai Jiao Tong University Press,2001:144–146.(in Chinese))
[14] ZHANG K,WOODBURY A D. A Krylov finite element approach for multi-species contaminant transport in discretely fractured porous media[J]. Advances in Water Resources,2002,25(7):705–721.
[15] MARTIN V,JAFFRE J,ROBERTS J E. Modeling fractures and barriers as interfaces for flow in porous media[J]. SIAM Journal on Scientific Computing,2005,26(5):1 667–1 691.
[16] CHENG A H D,GHASSEMI A,DETOURMAY E. Integral equation solution of heat extraction from a fracture in hot dry rock[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2001,25(13):1 327–1 338.
[17] LAUWERIE H A. The transport of heat in an oil layer caused by the injection of hot fluid[J]. Applied Scientific Research:Section A,1955,5(2/3):145–150.
[18] NELSON R,Geologic analysis of naturally fractured reservoirs[M]. [S. l.]:Gulf Professional Publishing,2001:78.
[19] DIETRICH P,HELMIG R,SAUTER M,et al. Flow and Transport in Fractured Porous Media[M]. Berlin:Springer-Verlag,2005:18.
[20] SHOOK G M. Predicting thermal breakthrough in heterogeneous media from tracer tests[J]. Geothermics,2001,30(6):573–589.
[21] BARENDS F B J. Complete solution for transient heat transport in porous media,following Lauwerier?s concept[C]// SPE Annual Technical Conference and Exhibition. Florence:[s. n.],2010,DOI:10.2118/134670–MS.
[22] BERKOWITZ B. Characterizing flow and transport in fractured geological media:a review[J]. Advances in Water Resources,2002,25(8/12):861–884.
[23] DERSHOWITZ W S,EINSTEIN H H. Characterizing rock joint geometry with joint system models[J]. Rock Mechanics and Rock Engineering,1988,21(1):21–51.
[24] LEUNG C T O,ZIMMERMAN R W. Estimating the hydraulic conductivity of two-dimensional fracture networks using network geometric properties[J]. Transport in Porous Media,2012,93(3):777–797.
[25] MATTHAI S K,BELAYNEH M. Fluid flow partitioning between fractures and a permeable rock matrix[J]. Geophysical Research Letters,2004,31(7):DOI:10. 1029/2003GL019027.
[26] OGATA A,BANDS R B. A solution of the differential equation of longitudinal dispersion in porous media[M]. Washington,DC:US Government Printing Office,1961:4. |
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