Evolution of fluid pressure and fracture propagation during contact metamorphism

Abstract Rock fracture enhances permeability and provides pathways through which fluids migrate. During contact metamorphism, fluids contained in isolated pores and fractures expand in response to temperature increases caused by the dissipation of heat from magmas. Heat transport calculations and thermomechanical properties of water-rich fluids demonstrate (1) that thermal energy is a viable mechanism to produce and maintain pore fluid pressure (P_f) in a contact metamorphic aureole; (2) that the magnitude of P_f generated is sufficient to propagate fractures during the prograde thermal history (cause hydrofracture) and enhance permeability; and (3) that P_f-driven fracture propagation is episodic with time-scales ranging from years to thousands of years. Because P_f dissipation is orders of magnitude faster than P, _f buildup, P_f oscillations and cyclical behaviour are generated as thermal heating continues. The P_f cycle amplitude depends on the initial fracture length, geometry and the rock's resistance to failure whereas the frequency of fracture depends on the rate of heating. Consequently, oscillation frequency also varies spatially with distance from the heat source. Time series of fluid pressures caused by this process suggest that cyclical fracture events are restricted to an early time period of the prograde thermal event near the intrusive contact. In the far field, however, individual fracture events have a lower frequency but continue to occur over a longer time interval. Numerous fracture cycles are possible within a single thermal event. This provides a provisional explanation for multiple generations of veins observed in outcrop. P _f cycling and oscillations may explain several petrological features. If pore fluids are trapped at various positions along a pressure cycle, the large amplitude of P_f variations for small fractures may account for different pressures recorded by fluid inclusions analysed from a single sample. P_f oscillations, during a single thermal episode, also drive chemical reactions which can produce complex mineral textures and assemblages for discontinuous reactions and/or zoning patterns for continuous reactions. These can mimic polymetamorphic or disequilibrium features. Temporal aspects of fracture propagation and permeability enhancement also constrain the likely timing of fluid flow and fluid-mineral interactions. These data suggest that fluid flow and fluid-mineral reactions are likely to be restricted to an early period in the prograde thermal history, characterized by high P_f coincident with relatively high temperatures, fracture propagation and consequent increases in permeability. This early prograde hydration event is followed by diffusional peak metamorphic reactions. This relationship is evident in the complex mineralogical textures common in some metamorphosed rocks.     

Crack propagation trajectories for rocks under mixed mode I-II fracture

Propagation of a crack in engineering materials including rocks can cause failure. Knowledge of the stress state under which a crack can propagate, and the trajectory it may follow during its growth are thus very important for the stability of rock masses/materials and for the safe design of structures in/on rocks. In this paper, the crack initiation angle and subsequent crack propagation path are experimentally investigated for limestone rock specimens. This investigation was conducted under various mixed mode I-II loading conditions, including pure mode-I and pure mode-II.This study includes conducting diametrical compression tests on notched Brazilian disk specimens. Moreover, the effect of confining pressure and temperature on crack initiation and propagation were also studied. The experimental results were compared with theoretical predictions of crack initiation angle. The results showed that limestone behaves in brittle fashion, and the effects of confining pressure and temperature on failure trajectories were not significant. Generally, the crack initiation angle can be predicted by the maximum tangential stress criterion. However, for notched Brazilian disk with high value of crack orientation with respect to loading direction, crack does not propagate from the tip of the crack. This important observation indicated that the tensile-strength failure can become more critical than the fracture-toughness failure.     

Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.     

Analysis of fracture propagation in a rock mass surrounding a tunnel under high internal pressure by the element-free Galerkin method

Fractures developed around high pressurized gas or air storage tunnels can progressively extend to the ground surface, eventually leading to an uplift failure. A tool reasonably reproducing the failure patterns is necessary for stability assessment. In this study, a numerical method based on the element-free Galerkin (EFG) method with a cohesive crack model is developed to simulate fracture propagation patterns in the rock mass around a tunnel under high internal pressure. A series of physical model tests was also conducted to validate the reliability of the developed method. A qualitative agreement between physical model tests and numerical results can be obtained. The in situ stress ratio, k, has a strong influence on both the position of crack initiation and the propagation direction. The numerical analyses were extended to full-scale problems. Numerical tests were performed to investigate the prime influencing factors on the failure patterns of a high pressurized gas circular tunnel with varying parameters. The results suggest that initial in situ stress conditions with a high k (larger than 1) is favorable for construction of pressurized gas or air storage tunnels.     

考虑裂隙水压力的岩体压剪裂纹扩展规律研究

在库水位大幅度升、降变化时,容易导致岩体内增量裂隙压力的集中,使断裂面上有效应力降低,裂纹面尖端的应力强度因子增加。当达到临界强度因子时,可能使岩体内裂纹、裂隙贯通、扩展,形成连续的复式破坏面,从而使边坡稳定性降低,造成边坡的失稳。基于此,从断裂力学角度分析了裂隙水压力对裂纹强度因子的影响,对考虑裂隙水压力作用的Ⅰ、Ⅱ型复合裂纹扩展规律进行了研究,结果表明：Ⅰ、Ⅱ型复合裂纹的裂纹扩展角的变化,不仅与裂纹的闭合程度、斜裂纹倾角、双向应力大小有关,还与裂隙水压力的大小、裂纹面的摩擦系数有关;并且在相同情况下,未闭合裂纹的扩展角要大于闭合裂纹的扩展角;对于闭合裂纹,裂纹面摩擦系数越小,扩展角越大;最后,推导了基于摩尔-库仑准则考虑裂隙水压力的岩体断裂韧度KIc、KIIc和压剪状态下Ⅰ、Ⅱ型复合断裂判据。研究成果为分析水岩作用下裂隙岩体的失稳破坏提供了重要的参考。     

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。     

预制横缝条件下水力裂缝的起裂和扩展

针对高角度天然裂缝发育地层中的水平井水力压裂问题,开展了水力裂缝自天然裂缝处起裂扩展的理论和试验研究。尝试将天然裂缝简化为与井筒轴线垂直的横向裂缝,基于线弹性断裂力学理论和最大拉应力准则,给出了水力裂缝起裂压力和扩展过程中应力强度因子的计算方法。利用预制横缝模拟高角度天然裂缝,开展了室内水力压裂试验,对水力裂缝的扩展形态和起裂压力进行了研究。理论计算表明,（1）水力裂缝自预制横缝端部起裂后,扩展距离超过1倍的预制横缝端部半径时可将预制横缝和水力裂缝合并起来,整体视作一条横向裂缝来计算应力强度因子;（2）水力裂缝尖端距井壁处的距离大于4倍的井筒半径时,应力强度因子的计算可忽略井筒的影响,近似采用硬币形裂缝的计算公式。试验研究发现,（1）水力裂缝在预制横缝端部起裂并扩展,形成与井筒轴线垂直的横向裂缝,裂缝的扩展呈现出Ⅰ型断裂的特点,形态近似呈圆形,未发现与井筒轴线平行的纵向裂缝的起裂和扩展;（2）排量对破裂净压力和起裂净压力有重要影响,大排量会导致较高的破裂净压力和起裂净压力,在大、小两种排量下起裂净压力的离散性均较小,计算得到的KⅠ临界断裂值的离散性也较小。研究结果可为改善裂缝发育储层的近井裂缝形态提供指导,也可为煤矿开采中预制横向切槽的水力压裂设计提供参考。     

孔隙水压力对岩石裂纹扩展影响的数值模拟

应用岩石破坏过程渗流-应力-损伤(FSD)耦合分析软件F-RFPA2D,通过对孔隙水压作用下岩石试件加载破坏过程的数值模拟,对孔隙水压力大小和梯度对岩石试样中裂纹的萌生和扩展进行了数值模拟研究。模拟结果再现了孔隙水压力作用下裂纹萌生扩展的全过程,表明孔隙水压力大小和梯度对岩石中裂纹的萌生和扩展模式都有很大的影响。     

大尺寸真三轴煤岩水力压裂模拟试验与裂缝扩展分析

水力压裂是一项广泛应用于低渗煤层的卸压增透技术。为了深入研究煤岩受力、天然裂缝、泵注排量对水力裂缝扩展规律及空间结构的影响,采用大尺寸真三轴水力压裂试验系统、压裂液中添加示踪剂等方式,在真三轴条件下对大尺寸煤岩进行了水力压裂试验。通过剖切压裂试样描述了水力裂缝扩展和空间展布规律,分析了裂缝宽度与应力之间的关系,并初步探讨了煤岩水力裂缝网络的形成机制。结果表明:(1)水力裂缝自割理处起裂并沿割理扩展、连接割理,进而形成复杂的裂缝网络结构;(2)水力裂缝受应力条件作用明显,当最大水平主应力和垂向应力相近,且远大于最小水平主应力时,易形成复杂的裂缝形态;(3)煤岩天然裂隙的存在是形成裂缝网络结构的前提,泵注排量对裂缝网络的形成也有重要影响;(4)煤岩裂隙在局部区域影响水力裂缝转向、分叉,但最终水力裂缝在扩展过程中逐渐转向至最大主应力方向;(5)水力压裂过程中,裂缝宽度的变化不仅与煤岩所受应力有关,还受到压裂液排量、天然裂缝等因素的影响。研究结果可以为煤岩裂缝网络的形成机制、现场施工参数的选取提供技术支持。     

煤岩水力压裂起裂压力和裂缝扩展机制实验研究

为了研究煤岩水力压裂的起裂压力和水力压裂裂缝扩展规律,采用型煤试样,利用自主研发的水力压裂实验系统,参照现场压裂施工制定了“施加三向应力-顶部注水”的煤岩水力压裂物理模拟实验方案并开展了水力压裂实验,分析了不同条件下泵注压力和水力压裂裂缝。实验结果表明：压裂液泵注排量越大,起裂压力越大。三向应力满足最大水平主应力σ_H > 垂向应力σ_v > 最小水平主应力σ_h,水力压裂裂缝沿着垂直于σ_h的方向扩展。σ_v和σ_h一定,随着σ_H的增大,煤岩起裂压力先增大后减小,水力压裂裂缝扩展路径越平直。当σ_H远大于σ_v和σ_h时,水力压裂裂缝扩展路径越复杂,分叉缝角度越大。研究结果可为煤岩水力压裂理论的完善提供一定的参考和借鉴。     

高水压下岩体裂纹扩展的渗流-断裂耦合机制与数值实现

采用渗流力学、断裂力学理论结合Monte Carlo方法描述岩体裂纹的随机分布,研究高水压作用下岩体原生裂纹的变形和翼形裂纹的萌生、扩展、贯通的渗流-断裂耦合作用机制,建立高水压作用下岩体裂纹的渗流-断裂耦合数学模型,给出该数学模型的求解策略与方法,在Fortran95平台下开发高水压下岩体裂纹扩展的渗流-断裂耦合分析程序HWFSC.for。高水压下岩体裂纹扩展的渗流-断裂耦合体现在岩体裂纹网络和渗流初始条件都随渗流时步变化。对高压注水岩体裂纹扩展过程进行渗流-断裂耦合分析。结果表明,高压注水条件下,岩体裂纹扩展存在起动水压力,当水压力大于起动水压力时,裂纹尖端开始萌生翼形裂纹,随着裂纹水压力的增加,翼形裂纹扩展,进而与其他裂纹搭接贯通,停止扩展。渗流-断裂耦合分析考虑了裂纹动、静水压力对裂纹产生的法向扩张效应及翼形裂纹的扩展而形成新的渗流通道两方面的影响,连通裂纹数随渗流的发展而增加。岩体裂纹的渗流-断裂耦合分析,能较真实地再现岩体裂纹的水力劈裂现象,描述岩体裂纹的扩展、贯通过程及与之相耦合的渗流响应。     

一种新的断裂计算方法

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。     

高渗压条件下压剪岩石裂纹断裂损伤演化机制研究

探讨了高渗透压作用下压剪岩石裂纹的起裂规律及分支裂纹尖端应力强度因子的演变规律,建立了高渗压下裂隙岩体发生拉剪破坏的临界水压力值和初裂强度判据,分析了不同渗压作用下裂纹的扩展情况表明,渗透压的存在加剧了分支裂纹的扩展,高渗透压作用下分支裂纹扩展由稳定扩展变成不稳定扩展,并导致分支裂纹尖端岩桥剪切破坏,同时考虑分支裂纹的相互作用,建立了高渗透压作用下压剪岩石裂纹体岩桥剪切贯通的断裂破坏力学模型,最后依据裂隙岩体的损伤力学效应研究了岩体的初始损伤及损伤演化柔度张量,提出了高渗压下压剪岩石裂纹渐进破坏的损伤演化方程。该理论为定量研究高渗压下裂隙岩体的失稳破坏提供了理论依据。     

Simulating damage evolution and fracture propagation in sandstone containing a preexisting 3-D surface flaw under uniaxial compression

Preexisting flaws and rock heterogeneity have important ramifications on the process of rock fracturing and on rock stability in many applications. Therefore, there is great interest in numerical modelling of rock fracture and the underlying mechanisms. We simulated damage evolution and fracture propagation in sandstone specimens containing a preexisting 3-D surface flaw under uniaxial compression. We applied the linear elastic damage model based on the unified strength theory following the rock failure process analysis code. However, in contrast to the rock failure process analysis code, we used the finite element method with tetrahedron elements on unstructured meshes. It provided higher geometrical flexibility and allowed for a more accurate representation of the disk-shaped flaw with various flaw depths, angles, and lengths through locally adapted meshes. The rock heterogeneity was modelled by sampling the initial local Young's modulus from a Weibull distribution over a cubic grid. The values were then interpolated to the computational finite element method mesh. This method introduced an additional length scale for the rock heterogeneity represented by the cell size in the sampling grid. The generation of three typical surface cracking patterns, called wing cracks, anti-wing cracks, and far-field cracks, were identified in the simulation results. These depend on the geometry of the preexisting surface flaw. The simulated fracture propagation, coalescence types, and failure modes for the specimens with preexisting surface flaw show good agreement with recent experimental studies.     

Geometric nature of hydraulic fracture propagation in naturally-fractured reservoirs

The geometry of hydraulic fracture propagation in the absence and presence of natural fractures in reservoirs was studied. The results revealed a marked influence of natural fractures on the symmetry of fracture propagation observed for rock free of natural fractures. Natural fracture properties such as stiffness and approaching angle, and the distance from wellbore to the natural fracture were found to influence the hydraulic fracture geometry. Furthermore, the location of the wellbore with respect to the natural fractures in a reservoir having a system of natural fractures displayed a significant influence on the resulting geometry of hydraulic fracture propagation.     

Investigation of thermal-hydro-mechanical coupled fracture propagation considering rock damage

Thermal-hydro-mechanical (THM) coupled fracture propagation is common in underground engineering. Rock damage, as an inherent property of rock, significantly affects fracture propagation, but how it influences the THM coupled fracturing remains stubbornly unclear. A pore-scale THM coupling model is developed to study this problem, which combines the lattice Boltzmann method (LBM), the discrete element method (DEM), and rock damage development theory together for the first time. This model can more accurately calculate the exchanged THM information at the fluid-solid boundary and fluid conductivity dependent on fracture and rock damage. Based on the developed model, the synergistic effect of injected temperature difference (fluid temperature below rock temperature) and rock damage (characterized by the parameter “critical fracture energy”, abbreviated as “CFE”) on fracture propagation of shale are investigated particularly. It is found that: (1) the generation of branched cracks is closely related to the temperature response frontier, and the fracture process zone of single bond failure increases in higher CFE. (2) through the analysis of micro failure events, hydraulic fracturing is more pronounced in the low CFE, while thermal fracturing displays the opposite trend. The fluid conductivity of fractured rock increases with a higher injected temperature difference due to the more penetrated cracks and wider fracture aperture. However, this enhancement weakens when rock damage is significant. (3) in the multiple-layered rock with various CFEs, branched cracks propagating to adjacent layers are more difficult to form when the injection hole stays in the layer with significant rock damage than without rock damage.

     

页岩储层体积压裂裂缝扩展机制研究

页岩储层天然裂缝、水平层理发育,水力压裂过程中可能形成复杂的体积裂缝。针对页岩储层体积裂缝扩展问题,基于流-固耦合基本方程和损伤力学原理,建立了页岩储层水力压裂体积裂缝扩展的三维有限元模型。将数值模型的模拟结果与页岩储层裂缝扩展室内试验结果进行对比,二者吻合较好,从而证明了数值模型的可靠性。通过一系列数值模拟发现：（1）水力压裂过程中水平层理可能张开,形成水平缝,水平与垂直缝相互交错,形成复杂的体积裂缝网络;（2）水平主应力差增大,体积裂缝的分布长度（水平最大主应力方向压裂裂缝的展布距离）增加、分布宽度（水平最小主应力方向压裂裂缝的展布距离）减小,体积裂缝的长宽比增加;（3）压裂施工排量增大,体积裂缝的分布长度减小、宽度增加,压裂裂缝的长宽比降低;（4）天然裂缝的残余抗张强度增大,体积裂缝分布宽度减小、分布长度增加,体积裂缝的长宽比增加。研究成果可以为国内的页岩气的压裂设计和施工提供一定的参考和借鉴。     

Simulation of hydraulic fracture propagation near a natural fracture using virtual multidimensional internal bonds

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.