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1.
Alastair Beach 《Journal of Structural Geology》1980,2(4):425-438
The hydraulic fracture is modelled as an ellipse in an infinite elastic medium with an internal fluid pressure and loaded under biaxial stresses at infinity. The available stress function for this model has been evaluated numerically, and the magnitudes of the stresses generated around the crack calculated for a variety of loading conditions and crack orientations. Fracture initiation is predicted from the Griffith maximum tensile stress criterion. The location of the maximum tensile stress around the crack is recorded and it is found that for many conditions of applied stresses and crack fluid pressure, the hydraulic shear fracture has a symmetrically developed maximum tensile stress and fracture initiation will occur by growth along the direction of the crack. It is also predicted that fracture initiation will occur when the ratio of fluid pressure to applied least principal stress is considerably less than one. The elastic strain energy fields around elliptical hydraulic flaws have been calculated, and in particular, the change in strain energy upon introduction of a small flaw, and the change in strain energy upon growth of this flaw, have been investigated. The results allow an evaluation of the second part of the Griffith criterion-that fracture growth is accompanied by a decrease in strain energy-for hydraulic fractures. Changes in strain energy with small increases in fluid pressure provide a physical basis for dilatancy hardening and fracture instability. Quasi-static growth from a flaw is modelled by calculating changes in strain energy for unit increases in half length. The distinction between fractures which show an increasing and a decreasing rate of change in strain energy with increasing length, and between fractures which may only extend spontaneously for short distances and those which may show extensive spontaneous growth on the basis of the rate of change of strain energy with length, is made. A gradual drop in crack fluid pressure once the threshold for fracture initiation has been passed may promote the extent to which spontaneous crack growth occurs.The formation of syntectonic veins, particularly in rocks being deformed under low grade metamorphic conditions, is often the most abundant evidence of natural hydraulic fracturing in rocks. Commonly observed geometric features of syntectonic veins-length, simple tapering, symmetric and asymmetric forking, branching, irregular zig-zag traces, en échelon patterns—are discussed primarily with reference to the strain energy model for growth established, and the geometric variation is interpreted in terms of variation in applied stress and fluid pressure conditions and the rate of change of stored strain energy with crack growth. In particular, terminal branching arises when the minimum stress changes from a symmetric to an asymmetric location at the tip of a growing shear fracture, and terminal forking results when there is an increase in the energy release rate during crack growth, and may be symmetric or asymmetric depending on the location of the minimum stress at the crack tip at the time of forking. 相似文献
2.
In this work, we investigate the main pumping parameters that influence a fluid‐driven fracture in cohesive poroelastic and poroelastoplastic weak formations. These parameters include the fluid viscosity and the injection rate. The first parameter dominates in the mapping of the propagation regimes from toughness to viscosity, whereas the second parameter controls the storage to leak‐off dominated regime through diffusion. The fracture is driven in weak permeable porous formation by injecting an incompressible viscous fluid at the fracture inlet assuming that the fracture propagates under plane strain conditions. Fluid flow in the fracture is modeled by lubrication theory. Pore fluid movement in the porous formation is based on the Darcy law. The coupling follows the Biot theory, whereas the irreversible rock deformation is modeled with the Mohr–Coulomb yield criterion with associative flow rule. Fracture propagation criterion is based on the cohesive zone approach. Leak‐off is also considered. The investigation is performed numerically with the FEM to obtain the fracture opening, length, and propagation pressure versus time. We demonstrate that pumping parameters influence the fracture geometry and fluid pressures in weak formations through the viscous fluid flow and the diffusion process that create back stresses and large plastic zones as the fracture propagates. It is also shown that the product of the propagation velocity and fluid viscosity, µv that appears in the scaling controls the magnitude of the plastic zones and influences the net pressure and fracture geometry. These findings may explain partially the discrepancies in net pressures between field measurements and conventional model predictions for the case of weak porous formation. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
3.
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4.
This paper analyses the plane strain problem of a fracture, driven by injection of an incompressible viscous Newtonian fluid, which propagates parallel to the free surface of an elastic half‐plane. The problem is governed by a hyper‐singular integral equation, which relates crack opening to net pressure according to elasticity, and by the lubrication equations which describe the laminar fluid flow inside the fracture. The challenge in solving this problem results from the changing nature of the elasticity operator with growth of the fracture, and from the existence of a lag zone of a priori unknown length between the crack tip and the fluid front. Scaling of the governing equations indicates that the evolution problem depends in general on two numbers, one which can be interpreted as a dimensionless toughness and the other as a dimensionless confining stress. The numerical method adopted to solve this non‐linear evolution problem combines the displacement discontinuity method and a finite difference scheme on a fixed grid, together with a technique to track both crack and fluid fronts. It is shown that the solution evolves in time between two asymptotic similarity solutions. The small time asymptotic solution corresponding to the solution of a hydraulic fracture in an infinite medium under zero confining stress, and the large time to a solution where the aperture of the fracture is similar to the transverse deflection of a beam clamped at both ends and subjected to a uniformly distributed load. It is shown that the size of the lag decreases (to eventually vanish) with increasing toughness and compressive confining stress. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
5.
《Journal of Structural Geology》2002,24(6-7):1029-1043
In-situ observations of transmitted-light experiments of syntaxial vein growth during lateral fluid flow in a simulated fracture show a decrease in growth rate towards the downstream end. As a consequence, the fracture is sealed at the inlet. Our observations show the rapid, non-linear growth competition of grains, which is a result of anisotropic growth kinetics and the complex fluid flow around the individual crystals.We compared our results with simulations based on a simplified numerical model, which builds on existing simulation techniques of this system. The model incorporates plug flow and a fluid-flow velocity dependent crystal growth rate law based on literature data. Simulations are in reasonable agreement with experimental results. A sensitivity analysis shows that a high fluid flow velocity and a low supersaturation increase the potential to seal a vein homogeneously, in agreement with previous work. Additionally, the effect of the initial crack shape is explored. 相似文献
6.
In this article, we investigate the main parameters that influence the propagation of a fluid‐driven fracture in a poroelastoplastic continuum. These parameters include the cohesive zone, the stress anisotropy, and the pore pressure field. The fracture is driven in a permeable porous domain that corresponds to weak formation by pumping of an incompressible viscous fluid at the fracture inlet under plane strain conditions. Rock deformation is modeled with the Mohr–Coulomb yield criterion with associative flow rule. Fluid flow in the fracture is modeled by the lubrication theory. The movement of the pore fluid in the surrounding medium is assumed to obey the Darcy law and is of the same nature as the fracturing fluid. The cohesive zone approach is used as the fracture propagation criterion. The problem is modeled numerically with the finite element method to obtain the solution for the fracture length, the fracture opening, and the propagation pressure as a function of the time and distance from the pumping inlet. It is demonstrated that the plastic yielding that is associated with the rock dilation in an elastoplastic saturated porous continuum is significantly affected by the cohesive zone characteristics, the stress anisotropy, and the pore pressure field. These influences result in larger fracture profiles and propagation pressures due to the larger plastic zones that are developing during the fracture propagation. Furthermore, it is also found that the diffusion process that is a major mechanism in hydraulic fracture operations influences further the obtained results on the fracture dimensions, plastic yielding, and fluid pressures. These findings may explain partially the discrepancies in net pressures between field measurements and conventional model predictions. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
7.
当岩石中含有裂缝时,岩石的弹性模量(主要指体模量、剪切模量、泊松比以及地震波的速度)会发生变化,而且这种弹性模量的变化又随裂缝中是否含有流体而不同。如果我们用地震的方法探测出地下目的层弹性模量的变化情况,无疑对我们了解目的层的裂缝发育情况将会有很大的帮助。在以往的研究中,人们常常把裂缝的产状定义成垂直裂缝和水平裂缝来研究。但是,实际中存在的裂缝多表现为几种体系的裂缝分布。本文在假设裂缝是随机分布的情况下,研究了含流体裂缝体和不含流体裂缝体的弹性模量与裂缝密度的关系。 相似文献
8.
A three-phase hydro-mechanical model for hydraulic fracturing is proposed. Three phases include: porous solid, fracturing fluid and host fluid. Discontinuity is handled using extended finite element method (XFEM) while cohesive crack model is used as fracturing criterion. Flow through fracture is defined as one-dimensional laminar flow, and flow through porous medium (host reservoir) is defined as two-dimensional Darcy flow. Coupling between two fluids in each space, fracture and pore, is captured through capillary pressure–saturation relationship, while the identical fluids in fracture and pore are coupled through a so-called leak-off mass transfer term. Coupling between fluids and deformation is captured through compatibility of volumetric strain of fluids within fracture and pore, and volumetric strain of the matrix. Spatial and temporal discretisation is achieved using the standard Galerkin method and the finite difference technique, respectively. The model is verified against analytical solutions available from literature. The leaking of fracturing fluid into the medium and suction of porous fluid into the fracture around the tip, are investigated. Sensitivity analyses are carried out for cases with slow and fast injection rates. It is shown that the results by single-phase flow may underestimate the leak-off. 相似文献
9.
煤层中瓦斯和水的赋存及运移与裂隙的密度、走向、填充物类型等因素密切相关,为了预防和控制矿井突水、瓦斯突出等灾害性事故,进行煤层裂隙的识别和预测研究,对煤矿开采的安全性评价有重要指示作用。基于裂隙等效模型理论,将Schoenberg线性滑动模型与煤层干裂隙（气充填）和饱水裂隙相结合,分析煤层缝隙中流体因子随不同充填物与裂隙弱度参数（裂隙密度、纵横比、体积模量、剪切模量、拉梅系数）的变化特征,并通过对含垂向裂隙的煤储层进行地震波各向异性速度的响应计算。从HTI型煤层理论模型的正演模拟结果可知,模型中裂隙流体因子与裂隙密度和几何形态呈正相关函数关系,而与充填流体体积模量呈负相关。HTI型煤层P波群、相速度对裂隙中的气、水都比较灵敏,SV波群、相速度对干裂隙（气充填）不敏感,SV波群速度对裂隙中的水很灵敏。通过HTI型煤层裂隙流体因子与各向异性速度等参数的响应分析实现煤层裂隙流体预测的可行性,为分析裂隙型煤层地震波传播特征打下基础,为煤层裂隙流体预测提供理论支持。 相似文献
10.
A hydro-mechanical coupled model that can simultaneously consider the pore seepage of a rock matrix and the fracture seepage is proposed to simulate three-dimensional hydraulic fracturing. This model appropriately takes into account the fluid leak-off into the surrounding rock matrix from the fracture. Several examples are given to validate the seepage algorithms and the coupled model. The results suggest that this model can solve problems involving pore seepage and fracture seepage through simple pure fracture seepage. Moreover, it can reproduce the fluid pressure distribution and the crack initiation and propagation and consider the fluid loss during hydraulic fracturing. 相似文献
11.
Flowback analysis recently has been considered as a potential tool for assessing induced fractures through corresponding pressure analyses and rate transient analysis. In this paper, we study fracture closure mechanisms during the flowback of fracturing fluid after hydraulic fracturing treatments. Although it is known that flowback can be significantly affected by the geometry of the fractures and closure stress, there has not been any effort to understand the problem from the geomechanical point of view; rather, available studies assume that a fracture closes uniformly with constant fracture compressibility. The coupled geomechanics and fluid flow model presented in this paper help to elucidate how geostresses may affect fracturing fluid recovery under different conditions. We perform a scaling analysis to formulate the occurrence of different fracture closure modes and then use numerical analyses to verify our scaling parameters. The factors governing the flowback process include the mechanical and petrophysical properties of the rock as well as preexisting discontinuities such as natural fractures. Three different closure modes for fracture networks are described and numerically verified. The occurrence of each mode can dramatically affect fracturing fluid recovery. The role of fluid leakoff into the formation, fractures conductivity, and drawdown strategy are examined for each fracture closure scenario. 相似文献
12.
Contact mechanism of a rock fracture subjected to normal loading and its impact on fast closure behavior during initial stage of fluid flow experiment 
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下载免费PDF全文 Fast closure of rock fractures has been commonly observed in the initial stage of fluid flow experiments at environmental temperatures under low or moderate normal stresses. To fully understand the mechanisms that drive this fast closure, the evolution of local stresses acting on contacting asperities on the fracture surfaces prior to fluid flow tests needs to be evaluated. In this study, we modeled numerically the asperity deformation and failure processes during initial normal loading, by adopting both elastic and elastic–plastic deformation models for the asperities on a real rock fracture with measured surface topography data, and estimated their impact on initial conditions for fluid flow test performed under laboratory conditions. Compared with the previous models that simulate the normal contact of a fracture as the approach of two rigid surfaces without deformations, our models of deformable asperities yielded smaller contact areas and higher stresses on contacting asperities at a given normal stress or normal displacement. The results show that the calculated local stresses were concentrated on the contacts of a few major asperities, resulting in crushing of asperity tips. With these higher contact stresses, however, the predicted closure rates by pressure solution are still several orders of magnitude lower than that of the experimental measurements at the initial stage of fluid flow test. This indicates that single pressure solution may not likely to be the principal compaction mechanism for this fast closure, and that the damages on contacting asperities that occur during the initial normal loading stage may play an important role. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
13.
We develop a new analytical model, called OpenT, that solves the elasticity problem of a hydraulic fracture (HF) contact with a pre-existing discontinuity natural fracture (NF) and the condition for HF re-initiation at the NF. The model also accounts for fluid penetration into the permeable NFs. For any angle of fracture intersection, the elastic problem of a blunted dislocation discontinuity is solved for the opening and sliding generated at the discontinuity. The sites and orientations of a new tensile crack nucleation are determined based on a mixed stress- and energy-criterion. In the case of tilted fracture intersection, the finite offset of the new crack initiation point along the discontinuity is computed. We show that aside from known controlling parameters such stress contrast, cohesional and frictional properties of the NFs and angle of intersection, the fluid injection parameters such as the injection rate and the fluid viscosity are of first-order in the crossing behavior. The model is compared to three independent laboratory experiments, analytical criteria of Blanton, extended Renshaw?Pollard, as well as fully coupled numerical simulations. The relative computational efficiency of OpenT model (compared to the numerical models) makes the model attractive for implementation in modern engineering tools simulating hydraulic fracture propagation in naturally fractured environments. 相似文献
14.
In this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second‐order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro–macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
15.
渗流-化学溶解耦合作用下岩石单裂隙渗透特性研究 总被引：3，自引：0，他引：3
为揭示在渗流-化学溶解耦合作用下单裂隙渗透特性的变化规律,建立了描述二维渗流-化学溶解耦合作用的偏微分方程组,并利用COMSOL Multiphysics软件成功地求解该方程组。首先,模拟了文献[1]中的盐岩渗流-溶解耦合渗流试验结果,数值模拟结果与试验结果较为吻合,验证了数学模型的正确性和有效性。然后,利用分形理论生成了一个粗糙的裂隙面数字模型,着重分析了二维石灰岩粗糙裂隙面在水流、矿物溶解和输运过程中其渗透特性的变化规律。数值分析显示,（1）溶质浓度对裂隙面的溶解具有非常重要的作用,从而水流进口端的溶解厚度比出口端大得多。（2）裂隙的整体渗透性在初始时刻增加较慢,随着裂隙开度的增大和贯通,溶解速度会逐渐增大,是一个加速的过程。 相似文献
16.
Y. NAKASHIMA 《Journal of Metamorphic Geology》1995,13(6):727-736
Abstract Aqueous fluid released in metamorphism is transported upwards from depth to the Earth's surface. I propose a hydrofracturing model for the fluid transport. In the model, fluid is transported by the upward propagation of a two-dimensional vertical fluid-filled crack from a fluid reservoir (e.g. overpressured compartment under a seal) at depth to the Earth's surface; fluid is injected consecutively from the reservoir into the crack at a given (but not necessarily constant) injection rate; some of the injected fluid is lost by infiltration from the crack walls into the surrounding permeable rock. An approximate solution of the crack propagation is obtained using fluid dynamics for turbulent film flow and linear elastic fracture mechanics. The solution shows the transition from a regime in which the excess pressure of the fluid in the reservoir drives the propagation to a regime in which the buoyancy of the fluid in the crack drives the propagation. For example, if the net injection rate of H2O is 1 m2/s, the regime transition occurs when the vertical crack length becomes 280 m; after the transition, the propagation velocity and average aperture are constant: 21 m/s and 4.8 cm. If the injection rate is lower than a critical value, hydrofracturing cannot be an effective mode for the fluid transport because of the significant fluid loss by infiltration from the crack walls into the surrounding permeable rock. Assuming a fluid-saturated crust with hydrostatic pore fluid pressure, a lower limit can be estimated for the injection rate required to transport H2O by hydrofracturing without significant fluid loss. For example, the lower limit for transport from a depth of 15 km to the Earth's surface is estimated at 0.2 m2/s if the crustal permeability is 10-17 m2. The lower limit decreases with decreasing crustal permeability. 相似文献
17.
为了研究含缺陷胶结充填体的断裂特性,分别设置了裂纹偏置比为0、0.25、0.50、0.75,缝高比为0.10、0.25、0.50的胶结充填体试件进行三点弯曲试验,利用高速摄像机进行裂纹扩展模式全程捕捉,借助二维颗粒流软件PFC2D对充填体裂纹扩展全程、破断方式及断裂机制进行分析。试验结果表明：相同缝高比下,随着裂纹偏置比的增加,断裂峰值荷载越大;当偏置比一定时,随着缝高比的增加,断裂峰值荷载越小;裂纹偏置比在0、0.25和0.50时,裂纹从偏置处扩展,且随着偏置比的增加,偏折角增大;裂纹偏置比在0.75时,裂纹从中心处扩展;断裂裂纹可分为3个阶段,且呈锯齿状扩展并在发育的过程中不断有碎裂状颗粒产生和脱落。利用二维颗粒流模拟充填体试件的力链网络、速度场及破断方式,结合其宏观力学的试验结果进行对比分析,探讨了细观断裂机制,其断裂时的峰值荷载与试验值相差不超过3.8%。 相似文献
18.
Buoyancy-driven propagation of an isolated fluid-filled crack in rock: implication for fluid transport in metamorphism 总被引：1，自引：0，他引：1
Yoshito Nakashima 《Contributions to Mineralogy and Petrology》1993,114(3):289-295
A new model for upward transport of buoyant fluid released during metamorphism is proposed. The model is fluid transport by buoyancy-driven propagation of isolated fluid-filled cracks. The mechanical behavior of a two-dimensional, isolated, vertical, and fluid-filled crack in impermeable rock is investigated using linear fractire mechanics and fluid dynamics. The results show that steady-state crack propagation which causes long-distance transport of the fluid occurs when the vertical cross-sectional area of the crack exceeds a critical value. Propagation velocity and average thickness of the crack under the steady-state propagation regime are expressed explicitly by the following seven parameters: vertical crack length; rigidity, Poisson's ratio, and fracture toughness of the rock; fluid viscosity; density difference between the rock and the fluid; gravitational acceleration. An isolated H2O-filled crack of vertical length 100 m, for example, propagates upwards in the crust at 0.3 m/s with the average thickness 0.2 mm when the following likely values are assumed: 0.1 mPa s for the H2O viscosity; 3 MPa m1/2 for the fracture toughness of the crustal rock. The application of the obtained results to the transport of H2O released during metamorphism suggests that the number density of isolated cracks propagating in the crust is very low. Since the propagation velocity is high, our model is suitable particularly for fluid transport through hot quartz-rich rock where fluid-filled cracks have geologically short lifetimes. 相似文献
19.
热液流体泵吸上侵管流动力学模拟及其预测意义 总被引：1，自引：0，他引：1
地球流体相在各种地质过程中的行为和作用 ,是地球物质科学的核心课题。通过对山西义兴寨脉状金矿热液流体上侵动力学的模拟计算证明 ,构造泵吸驱动的矿液流动具有有压管流的性质 ,并探索引入柏努利方程对其流动状态进行描述。论证了地质流体因其性质和所处地质环境的不同 ,可划分为多孔介质中的渗流和较宽阔裂隙中的管流 (流动 )两种。赋存于地壳中深部或由岩浆冷却分异形成的成矿流体 ,在张剪性断裂活动中 ,主要由构造泵吸机制驱使其上侵成矿。热液在相对封闭 (未喷出地表 )的较宽阔的断裂系统中受应力驱动上侵流动 ,其性质接近于流体力学中的有压管流 ,可以用柏努利方程进行描述。推导出了描述热液管流上侵动力学特征的柏努利方程关系式 ,表明热液的流速与所处构造压力差、流体的性质 (温度和密度等 ) ,以及流动通道的结构特征有关。对义兴寨脉状金矿进行的计算结果证明 ,热液上侵流速场的空间变化与金矿化分布格局相吻合 ,流体的高流速地段指示含矿石英脉密集区 ,因此具有成矿预测意义。针对热液管流上侵过程建立的动力学总方程中 ,每一个变量都有明确的地质意义 ,并可以在矿区实际测量 ;绘制的几组理论关系曲线有助于具体分析各种地质和地球化学条件对成矿的控制作用。 相似文献
20.
基于完全流-固耦合的弹塑性理论给出了水力压裂数值计算的弥散裂缝模型,其中材料的弹性部分采用线弹性本构关系,塑性部分采用摩尔-库仑破坏准则及强化准则。依据当前的有效应力状态修正渗透系数来模拟压裂液在裂缝中的流动。渗透系数的修改使用双曲正切函数,并采用平均有效应力作为水力裂缝的起裂判据。在ABAQUS软件中通过用户自定义程序添加了该模型。根据岩石的切面照片建立了含有硬包裹体分布的非均质岩石的有限元计算模型,模拟了中心点注水条件下的水力压裂传播过程,讨论了在常应力状态下非均质岩石中开裂区域、典型位置的应力路径变化和裂缝传播范围随时间变化的特点。进行了多种条件下含有硬包裹体分布的岩石材料的数值试验,得出了基岩材料的弹性模量、凝聚力和渗透系数以及注水速率对峰值注水压力、平均注水压力和裂缝开度的影响规律。 相似文献