留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于扩展有限元的页岩水力压裂数值模拟

曾青冬 姚军

曾青冬, 姚军. 基于扩展有限元的页岩水力压裂数值模拟[J]. 应用数学和力学, 2014, 35(11): 1239-1248. doi: 10.3879/j.issn.1000-0887.2014.11.007
引用本文: 曾青冬, 姚军. 基于扩展有限元的页岩水力压裂数值模拟[J]. 应用数学和力学, 2014, 35(11): 1239-1248. doi: 10.3879/j.issn.1000-0887.2014.11.007
ZENG Qing-dong, YAO Jun. Numerical Simulation of Shale Hydraulic Fracturing Based on the Extended Finite Element Method[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1239-1248. doi: 10.3879/j.issn.1000-0887.2014.11.007
Citation: ZENG Qing-dong, YAO Jun. Numerical Simulation of Shale Hydraulic Fracturing Based on the Extended Finite Element Method[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1239-1248. doi: 10.3879/j.issn.1000-0887.2014.11.007

基于扩展有限元的页岩水力压裂数值模拟

doi: 10.3879/j.issn.1000-0887.2014.11.007
基金项目: 国家自然科学基金(51234007);长江学者和创新团队发展计划(IRT1294);中央高校基本科研业务费专项资金(11CX05005A)
详细信息
    作者简介:

    曾青冬(1987—),男,江西赣州人,博士生(E-mail: upc.zengqd@163.com);姚军(1964—),男,山东平邑人,教授,博士生导师(通讯作者. E-mail: rcogfr_upc@126.com).

  • 中图分类号: O346.1;O242.21

Numerical Simulation of Shale Hydraulic Fracturing Based on the Extended Finite Element Method

Funds: The National Natural Science Foundation of China(51234007)
  • 摘要: 考虑裂缝内流体流动和周围岩石应力变形,建立了页岩人工裂缝扩展的数学模型,分别采用有限元和扩展有限元求解裂缝流场和岩石应力场,并通过Picard迭代方法耦合求解,计算结果与经典模型结果吻合,验证了模型正确性.在此基础上,分析了岩石弹性模量、Poisson(泊松)比和注入速度对裂缝几何形态的影响以及水力裂缝任意角度逼近天然裂缝扩展动态.结果表明:弹性模量和注入速度对裂缝形态具有重要影响,而Poisson比对裂缝形态影响较小;随着页岩脆性增高,压裂裂缝趋于“长窄型”扩展;地应力差和逼近角越大,水力裂缝越易贯穿天然裂缝;水力裂缝与天然裂缝相交处裂缝宽度存在相对较大的降低;扩展有限元方法避免了计算过程中的网格重构与网格加密,减少了计算量,该模型可以为页岩压裂设计提供理论指导.
  • [1] Fisher M K, Wright C A, Davidson B M, Goodwin A K, Fielder E O, Buckler W S, Steinsberger N P. Integrating fracture mapping technologies to optimize stimulations in the barnett shale[C]//Proceedings of the SPE Annual Technical Conference and Exhibition.San Antonio, Texas. Society of Petroleum Engineers, 2002: 1-7.
    [2] Gu H, Weng X. Criterion for fractures crossing frictional interfaces at non-orthogonal angles[C]//Proceedings of 44th U S Rock Mechanics Symposium and 5th U S-Canada Rock Mechanics Symposium.Salt Lake City, UT. American Rock Mechanics Association, 2010:1-6.
    [3] Warpinski N R, Teufel L W. Influence of geologic discontinuities on hydraulic fracture propagation[J]. Journal of Petroleum Technology,1987,39(2): 209-220.
    [4] Blanton T L. An experimental study of interaction between hydraulically induced and pre-existing fractures[C]//Proceedings of the SPE Unconventional Gas Recovery Symposium.Pittsburgh, Pennsylvania. Society of Petroleum Engineers, 1986: 559-561.
    [5] 周健, 陈勉, 金衍. 裂缝性储层水力裂缝扩展机理试验研究[J]. 石油学报, 2007,28(5): 109-113.(ZHOU Jian, CHEN Mian, JIN Yan. Experimental study on propagation mechanism of hydraulic fracture in naturally fractured reservoir[J]. Acta Petrolei Sinica,2007,28(5): 109-113.(in Chinese))
    [6] Perkins T K, Kern L R. Widths of hydraulic fractures[J]. Journal of Petroleum Technology,1961,13(9): 937-949.
    [7] Geersma J, Klerk F D. A rapid method of predicting width and extent of hydraulically induced fractures[J]. Journal of Petroleum Technology,1969,21(12): 1571-1581.
    [8] XU Wen-yue, Thiercelin M J, Ganguly U, WENG Xiao-wei, GU Hong-ren, Onda H, SUN Jian-chun, Calvez J L. Wiremesh: a novel shale fracturing simulator[C]//Proceedings of International Oil and Gas Conference and Exhibition.Beijing, China. Society of Petroleum Engineers, 2010: 1-6.
    [9] WENG Xiao-wei, Kresse O, Cohen C-E, WU Rui-ting, GU Hong-ren. Modeling of hydraulic-fracture-network propagation in a naturally fractured formation[J]. SPE Production & Operation,2011,26(4): 368-380.
    [10] Lecampion B. An extended finite element method for hydraulic fracture problems[J]. Communications in Numerical Methods in Engineering,2009,25(2): 121-133.
    [11] Keshavarzi R, Mohammadi S. A new approach for numerical modeling of hydraulic fracture propagation in naturally fractured reservoirs[C]//Proceedings of SPE/EAGE European Unconventional Resources Conference & Exhibition-From Potential to Production.Vienna, Austria, 2012: 1-12.
    [12] REN Qing-wen, DONG Yu-wen, YU Tian-tang. Numerical modeling of concrete hydraulic fracturing with extended finite element method[J]. Science in China Series E: Technological Sciences,2009,52(3): 559-565.
    [13] Taleghani A D. Analysis of hydraulic fracture propagation in fractured reservoirs: an improved model for the interaction between induced and natural fractures[D]. PhD Thesis. Austin: The University of Texas, 2009.
    [14] Renshaw C E, Pollard D D. An experimentally verified criterion for propagation across unbounded frictional interfaces in brittle, linear elastic materials[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1995,32(3): 237-249.
    [15] Lawn B, 龚江宏. 脆性固体断裂力学[M]. 北京: 高等教育出版社, 2010.(Lawn B, GONG Jiang-hong. Fracture of Brittle Solid [M]. Beijing: Higher Education Press, 2010.(in Chinese))
    [16] Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing[J]. International Journal for Numerical Methods in Engineering,1999,45(5): 601-620.
    [17] Mohammadi S. Extended Finite Element Method for Fracture Analysis of Structures [M]. John Wiley & Sons, 2008.
    [18] Adachi J, Siebrits E, Peirce A. Computer simulation of hydraulic fractures[J]. International Journal of Rock Mechanics & Mining Sciences,2007,44(5): 739-757.
    [19] Rickman R, Mullen M, Petre E. A practical use of shale petrophysics for stimulation design optimization: all shale plays are not clones of the Barnett shale[C]//Proceedings of SPE Annual Technical Conference and Exhibition.Denver, Colorado, USA, 2008: 1-11.
    [20] 李庆辉, 陈勉, 金衍. 页岩气储层岩石力学特性及脆性评价[J]. 石油钻探技术, 2012,40(4): 17-22.(LI Qing-hui, CHEN Mian, JIN Yan. Rock mechanical properties and brittleness evaluation of shale gas reservoir[J]. Petroleum Drilling Techniques,2012,40(4): 17-22.(in Chinese))
    [21] Arogundade O, Sohrabi M. A review of recent developments and challenges in shale gas recovery[C]//Proceedings of SPE Saudi Arabia Section Technical Symposium and Exhibition.Al-Khobar, Saudi Arabia, 2012: 1-31.
    [22] LI Ya-wei, Ahmad G. Creep behavior of Barnett, Haynesville, and Marcellus shale[C]//Proceedings of the 46th US Rock Mechanics/Geomechanics Symposium.Chicago, USA, 2012: 1-7.
    [23] HAN De-hua, Batzlez M L. Gassmann’s equation and fluid-saturation effects on seismic velocities[J]. Geophysics,2004,69(2): 398-405.
    [24] Barree R D, Gilbert J V, Conway M W. Stress and rock property profiling for unconventional reservoir stimulation[C]//Proceedings of SPE Hydraulic Fracturing Technology Conference.Woodlands, Texas, USA, 2009: 1-18.
    [25] Rijken P, Cooke M L. Role of shale thickness on vertical connectivity of fractures: application of crack-bridging theory to the Austin Chalk, Texas[J]. Tectonophysics,2001,337(1/2): 117-133.
  • 加载中
计量
  • 文章访问数:  1530
  • HTML全文浏览量:  69
  • PDF下载量:  1591
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-01-06
  • 修回日期:  2014-09-30
  • 刊出日期:  2014-11-18

目录

    /

    返回文章
    返回