工程力学 ›› 2018, Vol. 35 ›› Issue (9): 17-25,36.doi: 10.6052/j.issn.1000-4750.2017.06.0421

• 基本方法 • 上一篇    下一篇

自适应有限元-离散元算法、ELFEN软件及页岩体积压裂应用

王永亮1,2, 鞠杨1,3, 陈佳亮1,2, 杨永明1,2, Li C F4   

  1. 1. 中国矿业大学煤炭资源与安全开采国家重点实验室, 北京 100083;
    2. 中国矿业大学力学与建筑工程学院, 北京 100083;
    3. 中国矿业大学深部岩土力学与地下工程国家重点实验室, 徐州 221116;
    4. Swansea 大学 Zienkiewicz 工程计算中心, 英国 Swansea SA2 8PP
  • 收稿日期:2017-06-04 修回日期:2017-08-30 出版日期:2018-09-29 发布日期:2018-09-15
  • 通讯作者: 鞠杨(1967-),男,山东人,教授,博士,博导,主要从事矿山岩体力学研究(E-mail:juy@cumtb.edu.cn). E-mail:juy@cumtb.edu.cn
  • 作者简介:王永亮(1985-),男,河北人,助理研究员,博士,主要从事矿山岩体力学和计算固体力学的研究((E-mail:wangyl@tsinghua.org.cn);陈佳亮(1989-),男,河北人,博士生,主要从事矿山岩体力学和计算固体力学的研究(E-mail:chenjl@student.cumtb.edu.cn);杨永明(1979-),男,山西人,副教授,博士,硕导,主要从事矿山岩体力学研究(E-mail:yangym@cumtb.edu.cn);Li C F (1976-),男,黑龙江人,英国Swansea大学教授,博士,博导,主要从事计算固体力学研究(E-mail:c.f.li@swansea.ac.uk).
  • 基金资助:
    国家杰出青年科学基金项目(51125017);国家自然科学基金项目(41877275,51608301,51374213);国家自然科学创新研究群体科学基金项目(51421003);国家重点研究发展计划项目(2016YFC0600705);中国博士后科学基金项目(2018T110158,2016M601170)

ADAPTIVE FINITE ELEMENT-DISCRETE ELEMENT ALGORITHM, SOFTWARE ELFEN AND APPLICATION IN STIMULATED RESERVOIR VOLUME OF SHALE

WANG Yong-liang1,2, JU Yang1,3, CHEN Jia-liang1,2, YANG Yong-ming1,2, Li C F4   

  1. 1. State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing 100083, China;
    2. School of Mechanical & Civil Engineering, China University of Mining and Technology, Beijing 100083, China;
    3. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China;
    4. Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Swansea SA2 8PP, UK
  • Received:2017-06-04 Revised:2017-08-30 Online:2018-09-29 Published:2018-09-15

摘要: 该文介绍流体-固体-断裂耦合分析的自适应有限元(FE)-离散元(DE)算法,引进一款新近基于该方法研发的数值计算软件ELFEN,并将其应用于页岩分段体积压裂的三维数值计算和机理分析。该方法引入有限元应力恢复的超收敛拼片恢复(SPR)法,获得应力的超收敛SPR解,利用SPR解估计常规有限元解的误差,通过裂纹尖端局部区域的自适应网格重划分获得高精度应力解答并得以有效描述裂纹动态扩展,形成分析策略和求解方案。数值算例表明该算法和软件分析流体-固体-断裂耦合作用下单一、多水平井分段体积压裂的可靠性、有效性和实用性。

关键词: 自适应分析, 有限元-离散元耦合, 流体-固体-断裂耦合, 体积压裂, ELFEN

Abstract: The adaptive algorithm of finite element (FE)-discrete element (DE) for fluidic-mechanical-fracture coupling analysis was introduced in this study. The novel computational software ELFEN based on this method was introduced and applied in a three-dimensional mechanism analysis of a staged stimulated reservoir volume of shale. The superconvergent patch recovery (SPR) method was used to obtain the superconvergent FE stress solutions, by which the error of conventional FE stress solutions was estimated. The adaptive local remesh for domains of crack tips was expected to be characterized by efficient analysis strategy and application for more accurate stress solutions and reliable crack propagation path. Numerical examples were given to show the effectivity, reliability and practicability of the numerical algorithm and the software for staged stimulated reservoir volume of single-and multi-horizontal wells with fluidic-mechanical-fracture coupling.

Key words: adaptive analysis, FE-DE coupling, fluidic-mechanical-fracture coupling, stimulated reservoir volume, ELFEN

中图分类号: 

  • O34
[1] 谢和平, 高峰, 鞠杨, 等. 页岩气储层改造的体破裂理论与技术构想[J]. 科学通报, 2016(1):36-46. Xie Heping, Gao Feng, Ju Yang, et al. Novel idea of the theory and application of 3D volume fracturing for stimulation of shale gas reservoirs[J]. Chinese Science Bulletin, 2016(1):36-46. (in Chinese)
[2] Ooi E T, Song C, Tin-Loi F, et al. Polygon scaled boundary finite elements for crack propagation modelling[J]. International Journal for Numerical Methods in Engineering, 2012, 91(3):319-342.
[3] Shi G H. Discontinuous deformation analysis:a new numerical model for the statics and dynamics of deformable block structures[J]. Engineering Computations, 1992, 9(2):157-168.
[4] Dverstorp B, Andersson J. Application of the discrete fracture network concept with field data:Possibilities of model calibratin and validation[J]. Water Resources Research, 1989, 25(3):540-550.
[5] Dolbow J, Belytschko T. A finite element method for crack growth without remeshing[J]. International Journal for Numerical Methods in Engineering, 1999, 46(1):131-150.
[6] Mohammadnejad T, Khoei A R. An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model[J]. Finite Elements in Analysis and Design, 2013, 73:77-95.
[7] Qing D Z, Yao J. Numerical simulation of shale hydraulic fracturing based on the extended finite element method[J]. Applied Mathematics & Mechanics, 2014, 35(11):887-1000.
[8] Zeng Q, Liu Z, Wang T, et al. Fully coupled simulation of multiple hydraulic fractures to propagate simultaneously from a perforated horizontal wellbore[J]. Computational Mechanics, 2017:1-19.
[9] Wang L X, Li S H, Zhang G X, et al. A GPU-based parallel procedure for nonlinear analysis of complex structures using a coupled FEM/DEM approach[J]. Mathematical Problems in Engineering, 2013, 15(2):1-15.
[10] Liu P, Ju Y, Ranjith P G, et al. Experimental investigation of the effects of heterogeneity and geostress difference on the 3D growth and distribution of hydrofracturing cracks in unconventional reservoir rocks[J]. Journal of Natural Gas Science & Engineering, 2016, 35:541-554.
[11] Ju Y, Liu P, Chen J, et al. CDEM-based analysis of the 3D initiation and propagation of hydrofracturing cracks in heterogeneous glutenites[J]. Journal of Natural Gas Science & Engineering, 2016, 35:614-623.
[12] Peng P H, Ju Y, Wang Y L, et al. Numerical analysis of the effect of natural micro-cracks on the supercritical CO2 fracturing crack network of shale rock based on bonded particle models[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2017, 41(18):1992-2013.
[13] 袁驷, 王永亮, 徐俊杰. 二维自由振动的有限元线法自适应分析新进展[J]. 工程力学, 2014, 31(1):15-22. Yuan Si, Wang Yongliang, Xu Junjie. New progress in self-adaptive FEMOL analysis of 2D free vibration problems[J]. Engineering Mechanics, 2014, 31(1):15-22. (in Chinese)
[14] Yuan S, Wang Y L, Ye K S. An adaptive FEM for buckling analysis of non-uniform Bernoulli-Euler members via the element energy projection technique[J]. Mathematical Problems in Engineering, 2013, 40(7):221-239.
[15] Wang Y L, Ju Y, Zhuang Z, et al. Adaptive finite element analysis for damage detection of non-uniform Euler-Bernoulli beams with multiple cracks based on natural frequencies[J]. Engineering Computations, 2017, 35(3):1203-1229.
[16] Zienkiewicz O C, Zhu J Z. The superconvergent patch recovery (SPR) and adaptive finite element refinement[J]. Computer Methods in Applied Mechanics and Engineering, 1992, 101(1):207-224.
[17] Azadi H, Khoei A R. Numerical simulation of multiple crack growth in brittle materials with adaptive remeshing[J]. International Journal for Numerical Methods in Engineering, 2011, 85(8):1017-1048.
[18] ELFEN TGR user and theory manual[R]. Swansea United Kingdom:Rockfield Software Lted. 2016.
[19] Profit M, Dutko M, Yu J, et al. Complementary hydro-mechanical coupled finite/discrete element and microseismic modelling to predict hydraulic fracture propagation in tight shale reservoirs[J]. Computational Particle Mechanics, 2016, 3(2):229-248.
[20] Lewis R W, Schrefler J Z. The finite element method in the static and dynamic deformation and consolidation of porous media[J]. Meccanica, 1999, 34(3):231-232.
[21] Zienkiewicz O C, Taylor R L, Nithiarasu P. The finite element method (volume Ⅲ):The finite element method for fluid dynamics[M]. Seventh ed. Singapore:Elsevier Private Limited, 2015:423-449.
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[3] 梁力;林韵梅. 有限元网格修正的自适应分析及其应用[J]. 工程力学, 1995, 12(2): 109-118.
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