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1.
A virtual multidimensional internal bond (VMIB) model developed to simulate the propagation of hydraulic fractures using the finite‐element method is formulated within the framework of the virtual internal bond theory (VIB) that considers a solid as randomized material particles in the micro scale, and derives the macro constitutive relation from the cohesive law between the material particles with an implicit fracture criterion. Hydraulic pressure is applied using a new scheme that enables simulation of hydraulically driven cracks. When the model is applied to study hydraulic fracture propagation in the presence of a natural fracture, the results show the method to be very effective. It shows that although the in situ stress ratio is the dominant factor governing the propagation direction, a natural fault can also strongly influence the hydraulic fracture behavior. This influence is conditioned by the shear stiffness of the fault and the distance to the original hydraulic fracture. The model results show that when the fault is strong in shear, its impact on hydraulic fracture trajectory is weak and the hydraulic fracture will likely penetrate the fault. For a weak fault, however, the fracture tends to be arrested at the natural fault. The distance between the fault and the hydraulic fracture is also important; the fault influence increases with decreasing distance. The VMIB does not require selection of a fracture criterion and remeshing when the fracture propagates. Therefore, it is advantageous for modeling fracture initiation and propagation in naturally fractured rock. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
2.
VMIB (Virtual Multi-dimensional Internal Bonds)模型是在VIB(Virtual Internal Bond) 模型基础上发展起来的一种多尺度力学模型。VIB认为,固体材料在微观上是由随机分布的质量微粒（Material particle）构成,微粒与微粒之间由一虚内键（virtual internal bond）连结,材料的宏观本构方程则直接由微粒之间的连结法则（Cohesive law）导出。而在VMIB中,微粒之间引入了切向效应,材料的宏观本构方程由虚内键刚度系数导出。由于考虑了微粒之间的切向效应,VMIB能够再现材料不同泊松比。依据VMIB,材料的宏观力学行为决定于微观虚内键的演化。岩石材料在围压条件下强度显著增强,破坏模式一般表现为剪切破坏,其微观机制在于虚内键的演化决定于自身的法向和切向变形,并且演化速度决定于连续层次上材料微元的应力状态。为描述这种微观虚内键的演化机制,提出了一种虚内键演化方程。通过该演化方程,可以宏观再现岩石材料在围压条件下的断裂破坏行为。作为初步应用,没有考虑材料的塑性变形机制,因此,还有待于进一步的理论完善。 相似文献
3.
Modeling 3D thermal fracture propagation by transient cooling using virtual multidimensional internal bonds 
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下载免费PDF全文 Thermal fracturing can play an important role in development of unconventional petroleum and geothermal resources. Thermal fractures can result from the nonlinear deformation of the rock in response to thermal stress related to cold water injection as well as heating. Before the rock reaches the final failure stage, material softening and bulk modulus degradation can cause changes in the thermo‐mechanical properties of the solid. In order to capture this aspect of the rock fracture, a virtual multidimensional internal bond‐based thermo‐mechanical model is derived to track elastic, softening, and the failure stages of the rock in response to the temporal changes of its temperature field. The variations in thermo‐mechanical properties of the rock are derived from a nonlinear constitutive model. To represent the thermo‐mechanical behavior of pre‐existing fractures, the element partition method is employed. Using the model, numerical simulation of 3D thermal fracture propagation in brittle rock is carried out. Results of numerical simulations provide evidence of model verification and illustrate nonlinear thermal response and fracture development in rock under uniform cooling. In addition, fracture coalescence in a cluster of fractures under thermal stress is illustrated, and the process of thermal fracturing from a wellbore is captured. Results underscore the importance of thermal stress in reservoir stimulation and show the effectiveness of the model to predict 3D thermal fracturing. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
4.
岩体中普遍存在着断层﹑节理和裂隙等结构面,这些结构面的存在和发展对岩体的整体强度﹑变形及稳定性有极大的影响。因此,研究岩体中原生结构面的萌生﹑发展以及贯通演化过程对评估岩体工程安全性和可靠性具有非常重要的理论与现实意义。扩展有限元法（XFEM）作为一种求解不连续问题的有效数值方法,模拟裂隙时独立于网格,因此,在模拟岩体裂隙扩展﹑水力劈裂等方面具有独特优势。针对扩展有限元法的基本理论及其在岩体裂隙扩展模拟中的应用展开了研究,建立了扩展有限元法求解岩体裂隙摩擦接触、岩体裂隙破坏等问题的数值模型,并将计算模型应用于岩质边坡稳定性分析和重力坝坝基断裂破坏等工程问题。 相似文献
5.
Discrete fracture model for simulating waterflooding processes under fracturing conditions 下载免费PDF全文
下载免费PDF全文 In our study, we develop a model for simulating fracturing processes in a poroelastic medium. The proposed approach combines the discrete fracture model enriched with contact plane mechanics. The model captures mechanical interactions of fractures and a deformable medium, fluid, and heat transfer in fractures and in a porous medium. Both effects of poroelasticity and thermoelasticity are accounted in our model. Mass and heat conservation equations are approximated by the finite volume method, and mechanical equilibrium equations are discretized by means of the Galerkin finite element approach. Two‐dimensional grid facets between 3‐dimensional finite elements are considered as possible fracture surfaces. Most of these facets are inactive from the beginning and are activated throughout the simulation. A fracture propagation criterion, based on Irwin's approach, is verified on each nonlinear iteration. When the criterion is satisfied, additional contact elements are added into finite element and discrete fracture model formulations respectively. The proposed approach allows modeling of existing natural and artificially created fractures within one framework. The model is tested on single‐ and multiple‐phase fluid flow examples for both isothermal and thermal conditions and verified against existing semianalytical solutions. The applicability of the approach is demonstrated on an example of practical interests where a sector model of an oil reservoir is simulated with different injection and production regimes. 相似文献
6.
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。 相似文献
7.
Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution 下载免费PDF全文
下载免费PDF全文 We propose a numerical method that couples a cohesive zone model (CZM) and a finite element‐based continuum damage mechanics (CDM) model. The CZM represents a mode II macro‐fracture, and CDM finite elements (FE) represent the damage zone of the CZM. The coupled CZM/CDM model can capture the flow of energy that takes place between the bulk material that forms the matrix and the macroscopic fracture surfaces. The CDM model, which does not account for micro‐crack interaction, is calibrated against triaxial compression tests performed on Bakken shale, so as to reproduce the stress/strain curve before the failure peak. Based on a comparison with Kachanov's micro‐mechanical model, we confirm that the critical micro‐crack density value equal to 0.3 reflects the point at which crack interaction cannot be neglected. The CZM is assigned a pure mode II cohesive law that accounts for the dependence of the shear strength and energy release rate on confining pressure. The cohesive shear strength of the CZM is calibrated by calculating the shear stress necessary to reach a CDM damage of 0.3 during a direct shear test. We find that the shear cohesive strength of the CZM depends linearly on the confining pressure. Triaxial compression tests are simulated, in which the shale sample is modeled as an FE CDM continuum that contains a predefined thin cohesive zone representing the idealized shear fracture plane. The shear energy release rate of the CZM is fitted in order to match to the post‐peak stress/strain curves obtained during experimental tests performed on Bakken shale. We find that the energy release rate depends linearly on the shear cohesive strength. We then use the calibrated shale rheology to simulate the propagation of a meter‐scale mode II fracture. Under low confining pressure, the macroscopic crack (CZM) and its damaged zone (CDM) propagate simultaneously (i.e., during the same loading increments). Under high confining pressure, the fracture propagates in slip‐friction, that is, the debonding of the cohesive zone alternates with the propagation of continuum damage. The computational method is applicable to a range of geological injection problems including hydraulic fracturing and fluid storage and should be further enhanced by the addition of mode I and mixed mode (I+II+III) propagation. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
Capturing the two‐way hydromechanical coupling effect on fluid‐driven fracture in a dual‐graph lattice beam model 下载免费PDF全文
下载免费PDF全文 Fluid‐driven fractures of brittle rock is simulated via a dual‐graph lattice model. The new discrete hydromechanical model incorporates a two‐way coupling mechanism between the discrete element model and the flow network. By adopting an operator‐split algorithm, the coupling model is able to replicate the transient poroelasticity coupling mechanism and the resultant Mandel‐Cryer hydromechanical coupling effect in a discrete mechanics framework. As crack propagation, coalescence and branching are all path‐dependent and irreversible processes, capturing this transient coupling effect is important for capturing the essence of the fluid‐driven fracture in simulations. Injection simulations indicate that the onset and propagation of fractures is highly sensitive to the ratio between the injection rate and the effective permeability. Furthermore, we show that in a permeable rock, the borehole breakdown pressure, the pressure at which fractures start to grow from the borehole, depends on both the given ratio between injection rate and permeability and the Biot coefficient. 相似文献
9.
岩石裂纹的扩展是一个经典的不连续问题,常规有限元方法难以实现裂纹扩展过程的仿真模拟。扩展有限元法(XFEM)实现了计算网格与不连续面相互独立,因此模拟移动的不连续面时无需对网格进行重新剖分。本文介绍了XFEM基本原理和岩石断裂力学常用判据,尝试对岩石类材料单缝Ⅰ型三点弯曲、单缝剪切和双缝平板实验进行模拟。分析结果表明:扩展有限元模拟岩石类材料断裂问题不受网格划分限制,裂纹以实际应力场分布随机扩展;直观地给出岩样的微裂纹产生、演化,直至完全破坏的全过程,并与实验结果吻合。该方法能够应用到岩石断裂力学方面的研究,模拟岩石类材料的宏细观破坏过程,为解决复杂问题提供了方便的途径。 相似文献
10.
Hydraulic fracturing (HF) treatment often involves particle migration and is applied for propping or plugging fractures. Particle migration behaviors, e.g., bridging, packing, and plugging, significantly affect the HF process. Hence, it is crucial to effectively simulate particle migration. In this study, a new numerical approach is developed based on a coupled element partition method (EPM). The EPM is used to model natural and hydraulic fractures, in which a fracture is allowed to propagate across an element, thereby avoiding remeshing in fracture simulations. To characterize the water flow process in a fracture, a fully hydromechanical coupled equation is adopted in the EPM. To model particle transportation in fractures with water flow, each particle is treated as a discrete element. The particles move in the fracture as a result of being dragged by fluid. Their movement, contact, and packing behaviors are simulated using the discrete element method. To reflect the plugging effect, an equivalent aperture approach is proposed. Using this method, the particle migration and its effect on water flow are well simulated. The simulation results show that this method can effectively reproduce particle bridging, plugging, and unblocking in a hydraulic fracture. Furthermore, it is demonstrated that particle plugging significantly affects water flow in a fracture and hence the propagation of hydraulic fracture. This method provides a simple and feasible approach for the simulation of particle migration in a hydraulic fracture. 相似文献
11.
Hydraulic fracturing is the method of choice to enhance reservoir permeability and well efficiency for extraction of shale gas. Multi‐stranded non‐planar hydraulic fractures are often observed in stimulation sites. Non‐planar fractures propagating from wellbores inclined from the direction of maximum horizontal stress have also been reported. The pressure required to propagate non‐planar fractures is in general higher than in the case of planar fractures. Current computational methods for the simulation of hydraulic fractures generally assume single, symmetric, and planar crack geometries. In order to better understand hydraulic fracturing in complex‐layered naturally fractured reservoirs, fully 3D models need to be developed. In this paper, we present simulations of 3D non‐planar fracture propagation using an adaptive generalized FEM. This method greatly facilitates the discretization of complex 3D fractures, as finite element faces are not required to fit the crack surfaces. A solution strategy for fully automatic propagation of arbitrary 3D cracks is presented. The fracture surface on which pressure is applied is also automatically updated at each step. An efficient technique to numerically integrate boundary conditions on crack surfaces is also proposed and implemented. Strongly graded localized refinement and analytical asymptotic expansions are used as enrichment functions in the neighborhood of fracture fronts to increase the computational accuracy and efficiency of the method. Stress intensity factors with pressure on crack faces are extracted using the contour integral method. Various non‐planar crack geometries are investigated to demonstrate the robustness and flexibility of the proposed simulation methodology. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
12.
Numerical Simulation of 3D Hydraulic Fracturing Based on an Improved Flow-Stress-Damage Model and a Parallel FEM Technique 总被引：4，自引：4，他引：0
L. C. Li C. A. Tang G. Li S. Y. Wang Z. Z. Liang Y. B. Zhang 《Rock Mechanics and Rock Engineering》2012,45(5):801-818
The failure mechanism of hydraulic fractures in heterogeneous geological materials is an important topic in mining and petroleum engineering. A three-dimensional (3D) finite element model that considers the coupled effects of seepage, damage, and the stress field is introduced. This model is based on a previously developed two-dimensional (2D) version of the model (RFPA2D-Rock Failure Process Analysis). The RFPA3D-Parallel model is developed using a parallel finite element method with a message-passing interface library. The constitutive law of this model considers strength and stiffness degradation, stress-dependent permeability for the pre-peak stage, and deformation-dependent permeability for the post-peak stage. Using this model, 3D modelling of progressive failure and associated fluid flow in rock are conducted and used to investigate the hydro-mechanical response of rock samples at laboratory scale. The responses investigated are the axial stress–axial strain together with permeability evolution and fracture patterns at various stages of loading. Then, the hydraulic fracturing process inside a rock specimen is numerically simulated. Three coupled processes are considered: (1) mechanical deformation of the solid medium induced by the fluid pressure acting on the fracture surfaces and the rock skeleton, (2) fluid flow within the fracture, and (3) propagation of the fracture. The numerically simulated results show that the fractures from a vertical wellbore propagate in the maximum principal stress direction without branching, turning, and twisting in the case of a large difference in the magnitude of the far-field stresses. Otherwise, the fracture initiates in a non-preferred direction and plane then turns and twists during propagation to become aligned with the preferred direction and plane. This pattern of fracturing is common when the rock formation contains multiple layers with different material properties. In addition, local heterogeneity of the rock matrix and macro-scale stress fluctuations due to the variability of material properties can cause the branching, turning, and twisting of fractures. 相似文献
13.
This paper develops a practical approach to simulating fracture propagation in rock and concrete based on an augmented virtual internal bond (VIB) method in which the cohesion of solid is modeled as material particles interconnected by a network of randomized virtual micro bonds described by the Xu–Needleman potential. The micro bond potential is used to derive macroscale constitutive relations via the Cauchy–Born rule. By incorporating different energy contributions due to stretch and shearing, as well as different energy levels under tension and compression of each micro bond, the derived macro constitutive laws are particularly useful for modeling quasi‐brittle materials such as rock and concrete which usually have different Poisson ratios and much higher compressive strength than tensile strength. The mesh‐size sensitivity associated with strain‐softening in the present constitutive model is addressed by adjusting material constants near the crack tip so that the biJ‐integral is kept equal to the intrinsic fracture energy of the material. Numerical examples demonstrate that the proposed VIB method is capable of simulating mixed mode fracture propagation in rock and concrete with results in consistency with relevant experimental observations. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
14.
H. Y. Liu S. Q. Kou P.-A. Lindqvist C. A. Tang 《Rock Mechanics and Rock Engineering》2007,40(2):107-144
Summary A series of numerical tests including both rock mechanics and fracture mechanics tests are conducted by the rock and tool
(R–T2D) interaction code coupled with a heterogeneous masterial model to obtain the physical–mechanical properties and fracture
toughness, as well as to simulate the crack initiation and propagation, and the fracture progressive process. The simulated
results not only predict relatively accurate physical–mechanical parameters and fracture toughness, but also visually reproduce
the fracture progressive process compared with the experimental and theoretical results. The detailed stress distribution
and redistribution, crack nucleation and initiation, stable and unstable crack propagation, interaction and coalescence, and
corresponding load–displacement curves can be proposed as benchmarks for experimental study and theoretical research on crack
propagation. It is concluded that the heterogeneous material model is reasonable and the R–T2D code is stable, repeatable and a valuable numerical tool for research on the rock fracture process. 相似文献
15.
Thierry Reuschié 《地学学报》1992,4(5):591-597
Fracture in a heterogeneous medium is simulated by a network model. Heterogeneity is introduced by randomly distributing an initial population of cracks on a triangular network of bonds. Each ruptured bond represents a crack. External stresses are applied onto the network and the evolution of the crack population is analysed when the stresses are increased. A crack will propagate to an intact bond if the critical crack extension force is reached. This propagation leads to the coalescence of bonds: crack clusters are formed. When their shapes are complex we approximate them by simpler ones to compute a crack extension force. Crack interactions are introduced by adding for a given bond the contributions of all adjacent dusters. By using this kind of approach combining fracture mechanics and network modelling, we are able to simulate the rupture of a rock specimen under compression/ traction or shear stresses and to give some characteristics of the macroscopic fracture. 相似文献
16.
The response of deformable fractures to changes in fluid pressure controls phenomena ranging from the flow of fluids near wells to the propagation of hydraulic fractures. We developed an analysis designed to simulate fluid flows in the vicinity of asperity‐supported fractures at rest, or fully open fractures that might be propagating. Transitions between at‐rest and propagating fractures can also be simulated. This is accomplished by defining contact aperture as the aperture when asperities on a closing fracture first make contact. Locations on a fracture where the aperture is less than the contact aperture are loaded by both fluid pressure and effective stress, whereas locations where the aperture exceeds the contact aperture are loaded only by fluid pressure. Fluid pressure and effective stress on the fracture are determined as functions of time by solving equations of continuity in the fracture and matrix, and by matching the global displacements of the fracture walls to the local deformation of asperities. The resulting analysis is implemented in a numerical code that can simulate well tests or hydraulic fracturing operations. Aperture changes during hydraulic well tests can be measured in the field, and the results predicted using this analysis are similar to field observations. The hydraulic fracturing process can be simulated from the inflation of a pre‐existing crack, to the propagation of a fracture, and the closure of the fracture to rest on asperities or proppant. Two‐dimensional, multi‐phase fluid flow in the matrix is included to provide details that are obscured by simplifications of the leakoff process (Carter‐type assumptions) used in many hydraulic fracture models. Execution times are relatively short, so it is practical to implement this code with parameter estimation algorithms to facilitate interpretation of field data. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
17.
交叉节理普遍存在于实际岩体中,但其对岩体力学破裂特性的影响至今未有全面深入的研究。制作了含3D打印交叉节理试样,采用声发射、CT扫描技术和数字图像相关技术(DIC)分析手段对单轴条件下含交叉节理试样的力学及破裂特性进行了研究。研究结果表明:(1)主节理倾角较小时裂隙的分形维数DB与单轴强度、弹性模量和泊松比之间的变化关系比主节理倾角较大时的一致性更好,前者破裂模式的规律性好于后者。(2)主节理倾角较大时压密和弹性阶段节理和块体之间在张拉作用下会产生聚集性微破裂声发射事件,主节理倾角较小时不会产生这种现象。DIC应变云图中裂隙扩展路径上的微应变先于宏观破裂,可通过计算压缩条件下微应变最大区域预测破裂模式。(3)主节理对起裂角和裂隙扩展模式起主要作用,且声发射和分形特性具有统一性。次节理平行最大主应力时,总损伤主要由主节理扩展造成,累积声发射事件数量AAEE和DB均最大。AAEE和DB越大,破裂模式越复杂。(4)三维破裂模式以节理端部扩展产生的2~3个张拉翼裂隙面为主,内部三维宏观裂隙面上存在由不完全张拉破裂引起的非连续结构。 相似文献
18.
一种新的断裂计算方法 总被引：3，自引：1，他引：2
利用单元中嵌合无厚度不连续面的方法 ,模拟断裂面的形成过程。用虚功原理建立包含断裂面影响的有限元平衡方程 ;利用余虚功原理推导了断裂面的矩阵的具体形式 ; 以第一类断裂问题 -开裂问题为例 ,建立了开裂面粘塑性开裂本构关系,进一步得到了以弹粘塑性形式表示的有限元计算格式。 通过简单算例证明了该方法的正确性。 相似文献
19.
APPLICATION OF A SPLITTING FRACTURE MODEL TO THE SIMULATION OF ROCK INDENTATION SUBSURFACE FRACTURES
A two-dimensional fracture model based on micro-fracture mechanics is applied to the Hertzian indentation stress field to simulate subsurface fractures in an axi-symmetrical plane. The simulation of fracture development reveals quantitatively the effects of loading force, mechanical properties of the rocks, and original micro cracks on the formation of subsurface fractures. The distribution patterns of the subsurface fractures are determined by the magnitudes and trajectories of the indentation stresses. Lateral confinement prohibits the fracture development. Simulations of the subsurface fractures in granite and marble are in good agreement with the indentation experiments. © 1997 by John Wiley & Sons, Ltd. 相似文献
20.
岩体内裂隙等非连续结构面对岩体的强度及变形等力学特性有着显著的影响,研究岩体裂隙起裂、扩展、相互作用和贯通机制,对工程岩体力学行为的表征和工程性能的评价十分重要。本文基于连续介质力学模型的离散元方法,通过考虑裂隙分布、模型加载条件及其与裂隙产状的关系,建立了一系列裂隙力学计算模型,研究了不同模型裂隙扩展演化特征和岩体破裂机制,分析了岩体裂隙扩展规律及其对岩体破坏路径和强度的影响,研究结果表明:（1）裂隙岩体模型加载条件下的破坏起裂点、最终贯通破坏特征及损伤分布受控于裂隙的产状及其与最大主压应力取向角度大小及围压大小。（2）裂隙弱面走向与最大主压应力取向斜交时,裂隙弱面在加载条件下其端部裂隙扩展、贯通破坏表现比较明显,反之,当裂隙弱面走向与最大主压应力取向一致时,裂隙弱面被动影响裂隙模型内新生裂隙的萌生、扩展和贯通模式,自身未出现新的扩展破坏。（3）裂隙数目的增多和围压的增大会显著增加模型内部剪切裂缝的数量和模型破坏后的破碎程度,模型内部的损伤区域主要围绕破裂面呈滑移线型交叉分布,非破裂面区域损伤呈条带状X型分布。（4）裂隙弱面走向与最大主压应力取向斜交时,裂隙对岩体模型强度的弱化程度高于裂隙弱面走向与最大主压应力取向一致的情况,而裂隙模型破坏后的残余强度则正好相反。 相似文献