赵博,胡铭寰,武天海,丛巍,徐立,冯奕
ZHAO Bo,HU Minghuan,WU Tianhai,CONG Wei,XU Li,FENG Yi

• 1:中国石油大学(华东)石油工业训练中心
• 2:中国石油青海油田第一采油厂

摘要(Abstract)：

位移不连续法被广泛地应用于模拟水力压裂裂缝扩展问题。为了提高常位移不连续单元的计算精度,精确捕获裂缝尖端的奇异行为,基于水力裂缝尖端多尺度渐进解,引入了相应的尖端修正单元,并在尽可能减少引入额外自由度的情况下,构建了混合节点配置的二次位移不连续非尖端单元,形成了一种特殊尖端单元+高次单元的混合位移不连续单元法。结果表明,通过4个典型实例对比发现,采用本方法只需少量的单元就能精确计算任意形状裂缝的应力强度因子和能量释放率,更重要的是能精确捕获不同传播机制主导下水力裂缝的几何尺寸和尖端渐进行为,从而验证了本方法的精确性和优越性。
Displacement discontinuity method is widely used to simulate the fracture propagation during hydraulic fracturing. In order to enhance the calculated precision of the constant displacement discontinuity element and precisely capture the singular behaviors of the crack tip, the corresponding tip-revising element was introduced based on the multi-scale asymptotic solution of the hydraulic crack tip. In the case of minimizing the introduction of the number of the additional freedom degrees, the quadratic displacement discontinuity non-tip element of the hybrid node collocation was established, thus the hybrid displacement discontinuity element method was developed by means of using the special tip element and the higher-order element. The results show that according to the comparison of four typical cases, the method proposed in this paper can precisely calculate the stress intensity factor and energy release rate of an arbitrary fracture only by less elements. And it is more important that the method can precisely capture the geometries and tip singular behaviors of the hydraulic fracture dominated by different propagation regimes, so its accuracy and superiority have been well verified.

关键词(KeyWords)： 水力压裂;裂缝扩展;位移不连续法;尖端渐进解;尖端单元;二次单元
hydraulic fracturing;fracture propagation;displacement discontinuity method;tip asymptotic solution;tip element;quadratic element

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目“液氮辅助页岩体积压裂增效机理研究”(51574270);; 中央高校基本科研业务费专项基金项目“高压电脉冲解堵增渗油气储层装置研究”(18CX02072A)

作者(Author): 赵博,胡铭寰,武天海,丛巍,徐立,冯奕
ZHAO Bo,HU Minghuan,WU Tianhai,CONG Wei,XU Li,FENG Yi

DOI: 10.19597/j.issn.1000-3754.201910021

参考文献(References)：

• [1]ADACHI J,SIEBRITS E,PEIRCE A,et al.Computer simulation of hydraulic fractures[J].International Journal of Rock Mechanics & Mining Sciences,2007,44(5):739-757.
• [2] DETOURNAY E,PEIRCE A.On the moving boundary conditions for a hydraulic fracture[J].International Journal of Engineering Science,2014,84(11):147-155.
• [3] 朱合华.边界元法及其在岩土工程中的应用[M].上海:同济大学出版社,1997.ZHU Hehua.Boundary element method and its application in geotechnology engineering[M].Shanghai:Tongji University Press,1997.
• [4] WU K,OLSON J E.Mechanisms of simultaneous hydraulic-fracture propagation from multiple perforation clusters in horizontal wells[J].SPE Journal,2016,21(3):1000-1008.
• [5] 曾青冬,姚军,孙致学.页岩气藏压裂缝网扩展数值模拟[J].力学学报,2015,47(6):994-999.ZENG Qingdong,YAO Jun,SUN Zhixue.Numerical simulation of fracture network propagation in shale reservoirs[J].Chinese Journal of Theoretical and Applied Mechanics,2015,47(6):994-999.
• [6]GORDELIY E,DETOURNAY E.A fixed grid algorithm for simulating the propagation of a shallow hydraulic fracture with a fluid lag[J].International Journal for Numerical and Analytical Methods in Geomechanics,2011,35(5):602-629.
• [7]CRAWFORD A M,CURRAN J H.Higher-order functional variation displacement discontinuity elements[J].International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1982,19(3):143-148.
• [8]YAN X Q.A special crack tip displacement discontinuity element[J].Mechanics Research Communications,2004,31(6):651-659.
• [9]SHOU K J,CROUCH S L.A higher order displacement discontinuity method for analysis of crack problems[J].International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1995,32(1):49-55.
• [10]MARJI M F.Numerical analysis of quasi-static crack branching in brittle solids by a modified displacement discontinuity method[J].International Journal of Solids and Structures,2014,51(9):1716-1736.
• [11]BEHNIA M,GOSHTASBI K,MARJI M F,et al.On the crack propagation modeling of hydraulic fracturing by a hybridized displacement discontinuity/boundary collocation method[J].Journal of Mining & Environment,2011,2(1):1-16.
• [12]ABDOLLAHIPOUR A,MARJI M F,BAFGHI A Y,et al.On the accuracy of higher order displacement discontinuity method(HODDM) in the solution of linear elastic fracture mechanics problems[J].Journal of Central South University,2016,23(11):2941-2950.
• [13]DONG C Y,DEPATER C J.Numerical implementation of displacement discontinuity method and its application in hydraulic fracturing[J].Computer Methods in Applied Mechanics and Engineering,2001,191(8-10):745-760.
• [14]BLANDFORD G E,INGRAFFEA A R,LIGGETT J A.Two-dimensional stress intensity factor computations using the boundary element method[J].International Journal for Numerical Methods in Engineering,1981,17(3):387-404.
• [15]EXADAKTYLOS G,XIROUDAKIS G.A G2 constant displacement discontinuity element for analysis of crack problems[J].Computational Mechanics,2010,45(4):245-261.
• [16]ZHANG X,JEFFREY R G,DETOURNAY E.Propagation of a hydraulic fracture parallel to a free surface[J].International Journal for Numerical and Analytical Methods in Geomechanics,2005,29(13):1317-1340.
• [17]PEIRCE A,DETOURNAY E.An implicit level set method for modeling hydraulically driven fractures[J].Computer Methods in Applied Mechanics and Engineering,2008,197(33-40):2858-2885.
• [18]ADACHI J I.Fluid-driven fracture in permeable rock[D].Minneapolis:University of Minnesota,2001.
• [19]DETOURNAY E.Propagation regimes of fluid-driven fractures in impermeable rocks[J].International Journal of Geomechanics,2004,4(1):35-45.
• [20]LINKOV A M.Universal asymptotic umbrella for hydraulic fracture modeling[J/OL].Physics,2014,[2014-01-10].http://arXiv preprint arXiv:1404.4165.
• [21]LECAMPION B,PEIRCE A,DETOURNAY E,et al.The impact of the near-tip logic on the accuracy and convergence rate of hydraulic fracture simulators compared to reference solutions[C].Rijeka:ISRM International Conference for Effective and Sustainable Hydraulic Fracturing,2013.
• [22]MARJI M F.On the use of power series solution method in the crack analysis of brittle materials by indirect boundary element method[J].Engineering Fracture Mechanics,2013,98(1):365-382.
• [23]张福蕾,姜瑞忠,崔永正,等.考虑物性时变的裂缝性油藏数值模拟方法[J].特种油气藏,2019,26(4):103-108.ZHANG Fulei,JIANG Ruizhong,CUI Yongzheng,et al.Numerical simulation method of fractured oil reservoir with time-varying physical properties[J].Special Oil & Gas Reservoirs,2019,26(4):103-108.
• [24]房娜,张占女,程明佳,等.基于不同裂缝发育程度下周期注水注采参数优化研究[J].特种油气藏,2019,26(1):131-135.FANG Na,ZHANG Zhannü,CHENG Mingjia,et al.Injection-production parameter optimization study of cyclic water injection at different development levels of fractures[J].Special Oil & Gas Reservoirs,2019,26(1):131-135.