Fully coupled hydraulic fracture simulation using the improved element partition method

The improved element partition method (IEPM) is a newly developed fracture simulation approach. IEPM allows a fracture to run across an element without introducing extra degrees of freedom. It can also simulate any number of fractures in a prescribed mesh without remeshing. In this study, the IEPM is extended to hydraulic fracture simulation. First, the seepage and volumetric storage matrix of a cracked element are derived using virtual nodes (the intersection points of a crack with element edges). Subsequently, the fully coupled hydromechanical equation is derived for this cracked element. To eliminate the extra degrees of freedom (virtual nodal quantities), the water pressure and displacement of the virtual nodes are associated with their adjacent nodes through least squares interpolation. Finally, the fully coupled equation in terms of nodal quantities is obtained. The verification cases validate the method. By using this method, the field-scale hydraulic fracturing process is well simulated. The proposed approach is simple and efficient for field-scale hydraulic fracture simulation.     

基于单元劈裂法的岩体黏结型结构面数值模拟

节理岩体中富含结构面等不连续体,其中很多结构面之间具有一定黏结强度,在冲击荷载作用下会发生脱结（debond）行为,从而消耗岩体应变能。在该结构面之间的黏结性质在很大程度上决定着岩体的破坏行为,发生脱结后,结构面之间不再具有黏结强度,岩体的力学性能发生弱化。为了对该类结构面进行模拟,在改进的Xu-Needleman势函数基础上推导出结构面单元,并将其嵌入到单元劈裂法中,模拟结构面的开裂过程,当结构面完全脱结后结构面单元就转化为一般节理单元。相应地,在数值实现过程中只是将结构面单元替换为一般节理单元即可。该结构面单元与单元劈裂法相结合,能够有效地模拟节理岩体的破坏过程。     

基于ABAQUS平台的水力裂缝扩展有限元模拟研究

随着扩展有限元理论的深入研究,利用扩展有限元方法模拟水力压裂具有了一定的可操作性。相比于常规有限元方法,XFEM方法具有计算结果精度高和计算量小的优点。但是,如何模拟射孔孔眼、如何模拟流体与岩石相互作用以及分析水力裂缝的扩展规律仍然是难题。以研究水力压裂裂缝扩展规律为目的,建立了岩石多孔介质应力平衡方程、流体渗流连续性方程和边界条件。通过有限元离散化方法对耦合方程矩阵进行处理。通过富集函数定义初始裂缝（射孔孔眼）,选择最大主应力及损伤变量D分别作为裂缝起裂和扩展判定准则,利用水平集方法模拟水力裂缝扩展过程。数值模拟结果显示：增加射孔方位角、压裂液排量和减小水平地应力差,起裂压力上升;黏度对起裂压力无明显影响。增加射孔方位角、压裂液排量、黏度和减小水平地应力差值有助于裂缝宽度的增加。增加水平地应力差值、压裂液排量和减小射孔方位角以及压裂液黏度有助于裂缝长度增加,反之亦然。基于ABAQUS的水力裂缝扩展有限元法可对不同井型和诸多储层物性参数及压裂施工参数进行分析,且裂缝形态逼真,裂缝面凹凸程度清晰,结果准确。此研究可作为一种简便有效研究水力压裂裂缝扩展规律的方法为油田水力压裂设计与施工提供参考与依据。     

基于零厚度内聚力单元的水力裂缝随机扩展方法研究

为有效模拟裂缝性页岩储层中水力裂缝随机扩展过程,基于单元节点的拓扑数据结构,利用网格节点分裂方式,建立了一种基于有限元网格嵌入零厚度内聚力单元的水力裂缝随机扩展新方法。利用KGD模型解析解和2种室内试验,验证了新方法的准确性和有效性。同时,通过数值算例研究了水平地应力差和储层非均质性对水力裂缝随机扩展过程的影响。研究表明:(1)该方法弥补了ABAQUS平台内置的内聚力单元无法有效模拟水力裂缝随机扩展的不足;(2)在较高水平地应力差下页岩储层非均质性越强,与水力裂缝相交的高角度天然裂缝越容易开启。所建方法能准确地描述复杂水力裂缝的随机扩展行为,可为裂缝性页岩储层的数值模拟提供新手段。     

基于DDEM的自然崩落采矿法崩落规律的数值模拟

利用DDEM（可变形离散单元法）原理和方法,研究了自然崩落法矿体崩落规律。针对具体地质条件和赋存情况及矿岩物理力学性质,采用计算机数值模拟分析了自然崩落法的崩落规律,得出了DDEM在用于模拟矿块自然崩落法中崩落规律和分析其崩落机理时是较适合的结论,不仅可以从力学角度对崩落的力学机理进行研究,而且能直观地用图形给出矿体在崩落过程中的具体形态变化,有效地指导放矿,现场试验验证效果良好。     

危岩水力劈裂分析的扩展有限元法

危岩是三峡库区典型的地质灾害类型之一,而主控结构面受荷断裂扩展是危岩发育成灾的关键核心。将危岩主控结构面类比为宏观裂纹,利用扩展有限元法在模拟裂纹扩展方面的优势,基于考虑裂纹面水压力作用的虚功原理推导出了采用扩展有限元法分析水力劈裂问题的控制方程,给出了危岩主控结构面水力劈裂问题的扩展有限元实现方法,对重庆万州太白岩危岩主控结构面的水力劈裂进行了数值模拟分析。计算结果表明：暴雨是威胁危岩稳定性的最敏感因素,随着裂隙水压力上升,裂端拉应力会急剧升高,危岩的稳定性降低;I型裂纹扩展是危岩主要的结构面扩展形式,结构面一旦发生开裂,将处于非稳定扩展状态。     

砂砾岩水力压裂裂缝扩展规律的数值模拟分析

砂砾岩储层一般具有岩性和渗透性变化大、孔隙度低、连通性差、孔隙结构复杂和非均匀性严重等特点,因此,在水力压裂过程中,裂缝扩展形态难以控制,大规模改造难度大。针对国内某典型砂砾岩油藏特征,采用数值计算方法对砂砾岩压裂裂缝的扩展规律进行了研究,包括地应力场、砾石含量和粒径等对裂缝扩展形态及压裂压力的影响。研究表明,砾石的存在增加了压裂裂纹扩展的复杂性,裂纹主要有止裂、偏转、穿透和吸附4种表现模式,但主应力差严格控制着裂纹的走向,随着主应力差的增大,裂纹由总体绕砾扩展转变为总体穿砾扩展,失稳压力随着主应力差的增大而明显减小;砾石含量的多少体现了砂砾岩试样宏观的非均匀性,含量越高均匀性越差,随着砾石含量的提高,裂纹与砾石的相互作用占据主导地位,失稳压力随砾石含量的增加而增大;当砾石体积含量一定时,砾石粒径对压裂压力的影响主要取决于砾石排列的随机性,失稳压力随砾石粒径的增大而略有增大。     

基于逐元算法的地震勘探高精度谱元法数值模拟

针对复杂构造地震勘探,常规正演模拟算法存在精度和计算效率低的问题,笔者研究并提出了基于逐元算法的高精度谱元法数值模拟方法。基于波动方程强、弱形式,推导二维波动方程的谱元解法,进而利用逐元算法,无需形成全局矩阵,仅对于独立的小规模单元结构进行计算,提高计算效率,减少存储空间消耗。应用基于逐元算法的高精度谱元法对复杂金属矿模型进行数值模拟,得出本方法计算精度高、数值频散小,计算效率高。     

水力裂缝在煤岩界面处穿层扩展规律的数值模拟

为研究水力压裂裂缝在煤层与顶板界面处的穿层扩展规律,在分析煤岩界面性质的基础上,应用有限元法研究煤岩界面处裂缝从顶板起裂后的延伸情况,探讨了相关地质参数和施工参数对裂缝跨界面穿层扩展的影响。结果表明：地质因素中的地应力、煤岩界面强度为煤岩界面处裂缝能否穿层扩展的主要影响因素,垂向应力差异系数越大、界面抗剪切强度越大,越有利于裂缝穿层扩展沟通煤层;煤层与顶板间的弹性模量差异、抗拉强度差异是裂缝从顶板穿层进入煤层的有利因素;现场压裂施工应根据地层情况选择合适的施工参数（排量、注入点与界面的距离）以促进裂缝穿层扩展。研究成果能够为煤层顶板分段压裂水平井地面煤层气高效抽采技术的应用提供参考。     

改进的数值流形法在水力劈裂中的应用

数值流形法在非连续变形分析领域具有独特优势。结合裂纹尖端场函数的基本概念,分析了水力劈裂破坏问题,模拟了水力劈裂破坏过程,避免了扩展有限元中的阶跃函数和水平集概念。为了避免裂纹尖端在单元内部不同位置而产生误差,对裂纹尖端附近一定范围内的每一个物理覆盖附加奇异覆盖函数。选取一个算例比较分析了内水压力对应力强度因子的影响,当考虑裂纹面内压时,定量分析比较了各因素对应力强度因子的影响大小,并应用于分支裂纹水力劈裂破坏。计算结果表明,改进后的计算结果与解析解相吻合。未考虑裂纹面内压,误差往往较大。考虑裂纹面内压后,随着裂纹长度的增加,误差逐渐减小;随着网格密度的增加,误差也逐渐减小。分支裂纹的渐进破坏结果表明该改进方法的可行性,具有较大的实际应用价值。     

断裂问题的扩展有限元法研究

扩展有限元（extended finite element method,XFEM）是近年来发展起来的、在常规有限元框架内求解不连续问题的有效数值计算方法,其基于单位分解的思想,在常规有限元位移模式中加入能够反映裂纹面不连续性的跳跃函数及裂尖渐进位移场函数,避免了采用常规有限元计算断裂问题时需要对裂纹尖端重新加密网格造成的不便。在推导扩展有限元算法的基础上,分析了应力强度因子的J积分计算方法及积分区域的选取。采用XFEM对I型裂纹进行了计算,有限元网格独立于裂纹面,无需在裂纹尖端加密网格;分析了积分区域、网格密度对应力强度因子计算精度的影响,指出了计算应力强度因子的合适参数,验证了此方法的可靠性和准确性。     

危岩主控结构面变形破坏的扩展有限元法模拟分析

危岩是三峡库区典型的地质灾害类型之一,主要分为坠落式危岩和倾倒式危岩两种失稳形式,危岩主控结构面受荷断裂扩展是其发育成灾的关键核心。将危岩主控结构面类比为宏观裂纹,运用扩展有限元方法（XFEM）,求解结构面扩展过程的移动非连续问题,探索在荷载作用下危岩主控结构面的断裂扩展行为,以重庆万州太白岩危岩为例,考虑岩石的抗拉强度、主控结构面的几何位置与倾角对危岩的变形破坏模式与稳定性的影响。结果表明,随着岩石抗拉强度的降低,危岩的稳定性程度降低;随着主控结构面倾角的减小,危岩的稳定性程度提高,同时结构面开裂路径也明显改变;危岩体两种失稳模式的破坏机制都为拉剪机制,相对于倾倒式危岩,同等条件下坠落式危岩的稳定性更差。     

大冶铁矿露天转地下开采的离散元数值模拟研究

离散单元方法特别适合于节理比较发育的岩体。对于模拟和分析矿山中因采矿引起的围岩松动和冒落等力学行为是比较有效的。用离散单元法研究了大冶铁矿狮子山采区露天转地下开采，采用充填法、崩落法采掘对露天边坡和围岩的影响及围岩变形规律，并得出了相应的结论，为设计和方案的选用提供了一些有益的根据。     

基于离散元模拟的二元颗粒柱坍塌特性研究

常见的地质灾害如滑坡、泥石流、岩崩等通常都涉及不同形状的颗粒物质运动,这些形状不同的颗粒又多具有不同的尺寸和含量。基于典型的颗粒柱坍塌试验,首先根据试验方法确定了离散元模拟所需的各项参数,然后采用随机多面体方法生成了可控制长细比的大颗粒,利用离散元法就不同大颗粒含量下形态变化对二元颗粒柱坍塌特性的影响开展研究,研究结果表明:(1)利用离散元法可以较好地重现室内试验中小球和多面体组成的二元颗粒系统的颗粒柱坍塌过程;(2)在不同长细比的不规则大颗粒和小球组成的二元颗粒柱系统中,当大颗粒含量高于临界含量值20%时,二元颗粒柱坍塌持续的时间随非球形大颗粒长细比的增加而增加;(3)在不同长细比的不规则大颗粒和小球组成的二元颗粒柱中,当大颗粒含量高于临界含量值20%时,在相同百分比的大颗粒含量下,大颗粒长细比的增加会提高大颗粒平均配位数以及降低颗粒的运动能力,大颗粒间形成更强的互锁作用,降低了颗粒柱的整体流动性,使其最终堆积高度更高、最大跑出距离更短以及更小的归一化动能峰值。(4)在不同长细比的不规则大颗粒和小球组成的二元颗粒柱中,小颗粒可以较为明显降低大颗粒间摩擦及互锁作用,增加流动性,降低大骨料形态对坍塌过程的影响。     

A finite element approach to the simulation of hydraulic fractures with lag

We presented a finite‐element‐based algorithm to simulate plane‐strain, straight hydraulic fractures in an impermeable elastic medium. The algorithm accounts for the nonlinear coupling between the fluid pressure and the crack opening and separately tracks the evolution of the crack tip and the fluid front. It therefore allows the existence of a fluid lag. The fluid front is advanced explicitly in time, but an implicit strategy is needed for the crack tip to guarantee the satisfaction of Griffith's criterion at each time step. We enforced the coupling between the fluid and the rock by simultaneously solving for the pressure field in the fluid and the crack opening at each time step. We provided verification of our algorithm by performing sample simulations and comparing them with two known similarity solutions. Copyright © 2012 John Wiley & Sons, Ltd.     

天然裂缝影响下的花岗岩水力裂缝扩展数值模拟

水力压裂技术是成功实现干热岩资源开发利用的重要手段之一,数值模拟技术能够精准预测水力裂缝扩展。针对典型花岗岩,借助黏性单元法,分别模拟了致密花岗岩和天然裂缝存在情况下的水力裂缝扩展特征,得出以下结论:致密花岗岩的水力裂缝形态单一,天然裂缝的存在增加了压裂后裂缝的复杂性;致密花岗岩水力裂缝拓展主要分为憋压和拓展两个交替往复的阶段,当存在天然裂隙时,水力压裂过程会变得复杂;天然裂缝存在时,水力裂缝的缝长和缝宽分别为致密花岗岩的5.7倍和1.7倍;缝网的形成需要借助复杂的压裂工艺实现。研究结果可以为增强型地热系统(EGS)储层水力刺激工作提供理论支持。     

水压致裂起裂压力的细观离散元模拟及试验研究

水压致裂起裂压力的预测对于油气开采、地应力测量、水工结构物抗裂设计等具有重要的意义。采用颗粒离散元结合域-管道渗流模型的流固耦合非连续数值模拟方法,基于扩展前端法生成的含规则形状钻孔的颗粒体模型,对水压致裂的细观起裂过程和起裂压力大小进行了定量模拟。结果表明,在消除了颗粒体中钻孔形状不规则性的基础上,钻孔壁的接触力链分布与理论解较为一致,拟合的离散元起裂压力公式也与理论解较为接近。进一步地,从颗粒材料受挤压时产生局部张拉力的角度解释了起裂压力拟合公式与理论解之间的差别。最后,设计了含预制钻孔的抗渗砂浆试块制备方法,对不同主应力组合下的起裂压力大小进行了真三轴室内试验,验证了离散元模拟结果的可靠性。     

Simulation of drilling‐induced compaction bands using discrete element method

Rock failure is observed around boreholes often with certain types of failure zones, which are called breakouts. Laboratory‐scale drilling tests in some high‐porosity quartz‐rich sandstone have shown breakouts in the form of narrow localized compacted zones in the minimum horizontal stress direction. They are called fracture‐like breakouts. Such compaction bands may affect hydrocarbon extraction by forming barriers that inhibit fluid flow and may also be a source of sand production. This paper presents the results of numerical simulations of borehole breakouts using 3D discrete element method to investigate the mechanism of the fracture‐like breakouts and to identify the role of far‐field stresses on the breakout dimensions. The numerical tool was first verified against analytical solutions. It was then utilized to investigate the failure mechanism and breakout geometry for drilled cubic rock samples of Castlegate sandstone subjected to different pre‐existing far‐field stresses. Results show that failure occurs in the zones of the highest concentration of tangential stress around the borehole. It is concluded that fracture‐like breakout develops as a result of a nondilatant failure mechanism consisting of localized grain debonding and repacking and grain crushing that lead to the formation of a compaction band in the minimum horizontal stress direction. In addition, it is found that the length of fracture‐like breakouts depends on both the mean stress and stress anisotropy. However, the width of the breakout is not significantly changed by the far‐field stresses. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical study of inter‐particle bond failure by 3D discrete element method

The cohesive‐frictional nature of cementitious geomaterials raises great interest in the discrete element method (DEM) simulation of their mechanical behavior, where a proper bond failure criterion is usually required. In this paper, the failure of bond material between two spheres was investigated numerically using DEM that can easily reproduce the failure process of brittle material. In the DEM simulations, a bonded‐grain system (composed of two particles and bond material in between) was discretized as a cylindrical assembly of very fine particles connecting two large end spheres. Then, the bonded‐grain system was subjected to compression/tension, shear, rolling and torsion loadings and their combinations until overall failure (peak state) was reached. Bonded‐grain systems with various sizes were employed to investigate bond geometry effects. The numerical results show that the compression strength is highly affected by bond geometry, with the tensile strength being dependent to a lesser degree. The shear, rolling and torsion strengths are all normal force dependent; i.e., with an increase in the normal force, these strengths first increase at a declining rate and then start to decrease upon the normal force exceeding a critical value. The combined actions of shear force, rolling moment and torque lead to a spherical failure envelope in a normalized loading space. The fitted bond geometry factors and bond failure envelopes obtained numerically in this three‐dimensional study are qualitatively consistent with those in previous two‐dimensional experiments. The obtained bond failure criterion can be incorporated into a future bond contact model. Copyright © 2015 John Wiley & Sons, Ltd.