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1.
This paper analyses the problem of a fluid‐driven fracture propagating in an impermeable, linear elastic rock with finite toughness. The fracture is driven by injection of an incompressible viscous fluid with power‐law rheology. The relation between the fracture opening and the internal fluid pressure and the fracture propagation in mobile equilibrium are described by equations of linear elastic fracture mechanics (LEFM), and the flow of fluid inside the fracture is governed by the lubrication theory. It is shown that for shear‐thinning fracturing fluids, the fracture propagation regime evolves in time from the toughness‐ to the viscosity‐dominated regime. In the former, dissipation in the viscous fluid flow is negligible compared to the dissipation in extending the fracture in the rock, and in the later, the opposite holds. Corresponding self‐similar asymptotic solutions are given by the zero‐viscosity and zero‐toughness (J. Numer. Anal. Meth. Geomech. 2002; 26 :579–604) solutions, respectively. A transient solution in terms of the crack length, the fracture opening, and the net fluid pressure, which describes the fracture evolution from the early‐time (toughness‐dominated) to the large‐time (viscosity‐dominated) asymptote is presented and some of the implications for the practical range of parameters are discussed. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

2.
This paper analyses the problem of a hydraulically driven fracture, propagating in an impermeable, linear elastic medium. The fracture is driven by injection of an incompressible, viscous fluid with power‐law rheology and behaviour index n?0. The opening of the fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self‐similar form. A solution that describes the crack length evolution, the fracture opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self‐similar solution is obtained by expanding the fracture opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

3.
The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.  相似文献   

4.
In this paper, a fully coupled model is developed for numerical modeling of hydraulic fracturing in partially saturated weak porous formations using the extended finite element method, which provides an effective means to simulate the coupled hydro‐mechanical processes occurring during hydraulic fracturing. The developed model is for short fractures where plane strain assumptions are valid. The propagation of the hydraulic fracture is governed by the cohesive crack model, which accounts for crack closure and reopening. The developed model allows for fluid flow within the open part of the crack and crack face contact resulting from fracture closure. To prevent the unphysical crack face interpenetration during the closing mode, the crack face contact or self‐contact condition is enforced using the penalty method. Along the open part of the crack, the leakage flux through the crack faces is obtained directly as a part of the solution without introducing any simplifying assumption. If the crack undergoes the closing mode, zero leakage flux condition is imposed along the contact zone. An application of the developed model is shown in numerical modeling of pump‐in/shut‐in test. It is illustrated that the developed model is able to capture the salient features bottomhole pressure/time records exhibit and can extract the confining stress perpendicular to the direction of the hydraulic fracture propagation from the fracture closure pressure. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

5.
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   

6.
A computational procedure is developed for solving the problem of a circular hydraulic fracture propagating under the action of frac-0fluid being pumped in at a central wellbore. The crack is modelled as continuous distributions of ring dislocations and the resulting elasticity singular integral equation is solved numerically. The fluid flow equations are approximated by local and global interpolation finite difference schemes. The coupling between elasticity and fluid flow is handled numerically, by, two different algorithms: one iterates on crack tip velocity whereas the other varies the time step size until it agrees with the chosen increment in crack length. Sample results are given; it is found that the velocity algorithm is computationally more, efficient and more stable. The model allows detailed tracing of pressure distribution and fluid flow in the fracture, even under complex conditions of cyclic injection and fluid rheology. It may serve as a stand-alone model of (horizontal) hydrafracs–especially at shallow depths–or it may be used as a reference frame to test the various numerical formulation/algorithms required for the ongoing development of a fully 3-D hydrafrac simulator.  相似文献   

7.
We present an algorithm to simulate curvilinear hydraulic fractures in plane strain and axisymmetry. We restrict our attention to sharp fractures propagating in an isotropic, linear elastic medium and driven by the injection of a laminar, Newtonian fluid governed by lubrication theory, and we require the existence of a finite lag region between the fluid front and the crack tip. The key novelty of our approach is in how we discretize the evolving crack and fluid domains: we utilize universal meshes (UMs), a technique to create conforming triangulations of a problem domain by only perturbing nodes of a universal background mesh in the vicinity of the boundary. In this way, we construct meshes, which conform to the crack and to the fluid front. This allows us to build standard piecewise linear finite element spaces and to monolithically solve the quasistatic hydraulic fracture problem for the displacement field in the rock and the pressure in the fluid. We demonstrate the performance of our algorithms through three examples: a convergence study in plane strain, a comparison with experiments in axisymmetry, and a novel case of a fracture in a narrow pay zone.  相似文献   

8.
This paper presents a coupled hydro‐mechanical formulation for the simulation of non‐planar three‐dimensional hydraulic fractures. Deformation in the rock is modeled using linear elasticity, and the lubrication theory is adopted for the fluid flow in the fracture. The governing equations of the fluid flow and elasticity and the subsequent discretization are fully coupled. A Generalized/eXtended Finite Element Method (G/XFEM) is adopted for the discretization of the coupled system of equations. A Newton–Raphson method is used to solve the resulting system of nonlinear equations. A discretization strategy for the fluid flow problem on non‐planar three‐dimensional surfaces and a computationally efficient strategy for handling time integration combined with mesh adaptivity are also presented. Several three‐dimensional numerical verification examples are solved. The examples illustrate the generality and accuracy of the proposed coupled formulation and discretization strategies. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

9.
Research investigations on three-dimensional (3-D) rectangular hydraulic fracture configurations with varying degrees of fluid lag are reported. This paper demonstrates that a 3-D fracture model coupled with fluid lag (a small region of reduced pressure) at the fracture tip can predict very large excess pressure measurements for hydraulic fracture processes. Predictions of fracture propagation based on critical stress intensity factors are extremely sensitive to the pressure profile at the tip of a propagating fracture. This strong sensitivity to the pressure profile at the tip of a hydraulic fracture is more strongly pronounced in 3-D models versus 2-D models because 3-D fractures are clamped at the top and bottom, and pressures in the 3-D fractures that are far removed from the fracture tip have little effect on the stress intensity factor at the fracture tip. This rationale for the excess pressure mechanism is in marked contrast to the crack tip process damage zone assumptions and attendant high rock fracture toughness value hypotheses advanced in the literature. A comparison with field data is presented to illustrate the proposed fracture fluid pressure sensitivity phenomenon. This paper does not attempt to calculate the length of the fluid lag region in a propagating fracture but instead attempts to show that the pressure profile at the tip of the propagating fracture plays a major role in fracture propagation, and this role is magnified in 3-D models. © 1997 by John Wiley & Sons, Ltd. Int. J. Numer. Anal. Meth. Geomech., vol. 21, 229–240 (1997).  相似文献   

10.
The hydraulic fracturing propagation regimes in the plane strain model are uniformly investigated using a numerical method based on the finite element method. The regimes range from toughness‐dominated cases to viscosity‐dominated cases, covering zero leak‐off situations and small leak‐off situations. Unlike the asymptotic solutions, the numerical method is independent of the energy dissipation regimes and fluid storage regimes. The numerical method pays no special attention to the fracture tip, and it simulates fracture tip behaviors by increasing the number of functions in a natural and uniform manner. The numerical method is verified by comparing its results with the asymptotic solutions. The effect of the model sizes on the numerical method is discussed along with the robustness of the numerical method. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

11.
刘跃东  林健  冯彦军  司林坡 《岩土力学》2018,39(5):1781-1788
为了揭示水压致裂法和巴西劈裂法测量岩石抗拉强度的关系,开展了理论和现场试验研究。基于经典的水压致裂法理论,推导了不同围压下钻孔破裂压力和抗拉强度。利用断裂力学理论建立了水压致裂法和巴西劈裂法测得抗拉强度的关系。利用预制切槽方法模拟天然裂纹,对水力裂缝的起裂压力进行了研究。结果表明：围压为最大主应力等于3倍最小主应力测得的抗拉强度大于围压为0测得的抗拉强度;水压致裂法和巴西劈裂法测量抗拉强度关系与应力场、裂纹长度、断裂韧度3个变量有关;通过在晋城矿区王台铺矿的预制切槽试验,运用断裂力学建立的抗拉强度计算式更为符合现场实际。研究结果可为坚硬难垮落顶板预制切槽的水力压裂设计提供参考。  相似文献   

12.
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.  相似文献   

13.
Thermal recovery from a hot dry rock (HDR) reservoir viewed as a deformable fractured medium is investigated with a focus on the assumption of local thermal non‐equilibrium (LTNE). Hydraulic diffusion, thermal diffusion, forced convection and deformation are considered in a two‐phase framework, the solid phase being made by impermeable solid blocks separated by saturated fractures. The finite element approximation of the constitutive and field equations is formulated and applied to obtain the response of a generic HDR reservoir to circulation tests. A change of time profile of the outlet fluid temperature is observed as the fracture spacing increases, switching from a single‐step pattern to a double‐step pattern, a feature which is viewed as characteristic of established LTNE. A dimensionless number is proposed to delineate between local thermal equilibrium (LTE) and non‐equilibrium. This number embodies local physical properties of the mixture, elements of the geometry of the reservoir and the production flow rate. All the above properties being fixed, the resulting fracture spacing threshold between LTNE and LTE is found to decrease with increasing porosity or fluid velocity. The thermally induced effective stress is tensile near the injection well, illustrating the thermal contraction of the rock, while the pressure contribution of the fracture fluid is negligible during the late period. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

14.
水力压裂扩展的流固耦合数值模拟研究   总被引：5，自引：2，他引：3  
连志龙  张劲  吴恒安  王秀喜  薛炳 《岩土力学》2008,29(11):3021-3026
以临界应力作为裂纹扩展准则并采用流固耦合模型模拟了水力压裂扩展问题,推导出裂缝面内的压降方程表达式,并编写出用户子程序嵌入到ABAQUS中。建立的计算模型能够模拟地应力、岩石力学特性、压裂液流体特性等各种复杂因素对水力压裂扩展的影响。通过计算分析得到一些有益结论,采用有限元软件ABAQUS求解可渗透油藏水力压裂扩展过程问题是可行的;提出了临界宽度的概念,它可以作为判断裂缝是作为起渗透作用的孔隙通道还是作为起导流作用的裂缝的依据;其结论对于压裂作业优化具有参考价值。  相似文献   

15.
黄达  金华辉  黄润秋 《岩土力学》2011,32(4):997-1002
开挖卸荷岩体裂隙面通常处于拉剪应力状态。在裂隙应力和变形状态分析的基础上,采用线弹性断裂力学理论和物理模型试验研究了拉剪应力状态下裂隙扩展的力学机制。岩体裂隙在拉剪应力状态下沿裂隙面间的滑动抗剪摩擦力消失,裂隙起裂沿Ⅰ型张拉裂隙断裂韧度KⅠ最小的方向起裂,并最终发展与卸荷拉应力方向垂直;拉剪应力状态下岩体的总位移方向平行于拉应力方向,通过合理的位移假设,基于能量及线弹性断裂力学理论,求解了拉剪应力状态下分支裂隙扩展过程中尖端的动态应力强度因子和扩展长度判据;通过拉剪应力状态下单裂隙扩展物理模型试验验证了理论推导的正确性。  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.
李晓照  邵珠山  戚承志 《岩土力学》2019,40(11):4249-4258
岩石内部细观裂纹的存在,对压缩作用下岩石剪切断裂的宏观现象有着重要的影响。然而,能够通过解析解阐释细观裂纹几何特性、围压等影响因素对压缩作用下剪切断裂面角度变化趋势的研究很少。基于Ashby模型中提出的裂纹尖端应力强度因子,提出了一种改进的考虑裂纹角度影响的应力强度因子表达式。利用该改进的应力强度因子表达式,推出了一个可以预测岩石峰值强度的裂纹扩展、应变与应力之间的本构关系。结合本构关系的峰值强度与摩尔-库仑失效准则,得到了岩石损伤与内摩擦角、黏聚力、剪切强度及失效断裂面角度之间的理论关系;讨论了围压、裂纹尺寸、角度及摩擦系数对岩石宏观剪切断裂面角度的影响,通过试验结果验证了模型合理性。结果表明：随着损伤增大,内摩擦角、黏聚力及剪切强度不断减小;随着围压增大、摩擦系数增大和初始裂纹尺寸减小,剪切断裂面角度不断增大;随着裂纹角度增大,剪切断裂纹面角度先减小后增大。  相似文献   

18.
This study investigates parametric space of solutions for a planar hydraulic fracture propagating in a homogeneous anisotropic rock. It is assumed that the fracture has an elliptical shape and is driven by a power-law fluid. The purpose of this study is to investigate the influence of anisotropy and power-law fluid rheology on the parametric space of solutions. Rock anisotropy is represented by having two values of fracture toughness, one in the vertical direction and another one in the horizontal direction. Similarly, the effect of elastic anisotropy is approximated by using two different effective elastic moduli in the vertical and horizontal directions. In contrast to the isotropic case, for which there are four limiting solutions, the problem for anisotropic rocks features six different limiting cases. These cases represent competition between toughness and viscosity in the vertical and horizontal directions and competition between fluid storage inside the fracture and fluid leak-off into formation. Approximate expressions for the limiting solutions are obtained using global volume balance and tip asymptotic solutions. Despite the developed solutions rely on a series of approximations, they precisely capture all the scaling laws associated with the problem. Zones of applicability of these limiting solutions are calculated, and their dependence on the problem parameters is investigated.  相似文献   

19.
This paper presents an algorithm and a fully coupled hydromechanical‐fracture formulation for the simulation of three‐dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3‐D fracture front at every fracture propagation step. A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time‐dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3‐D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented.  相似文献   

20.
Hydraulic fracturing (HF) of underground formations has widely been used in different fields of engineering. Despite the technological advances in techniques of in situ HF, the industry uses semi‐analytical tools to design HF treatment. This is due to the complex interaction among various mechanisms involved in this process, so that for thorough simulations of HF operations a fully coupled numerical model is required. In this study, using element‐free Galerkin (EFG) mesh‐less method, a new formulation for numerical modeling of hydraulic fracture propagation in porous media is developed. This numerical approach, which is based on the simultaneous solution of equilibrium and continuity equations, considers the hydro‐mechanical coupling between the crack and its surrounding porous medium. Therefore, the developed EFG model is capable of simulating fluid leak‐off and fluid lag phenomena. To create the discrete equation system, the Galerkin technique is applied, and the essential boundary conditions are imposed via penalty method. Then, the resultant constrained integral equations are discretized in space using EFG shape functions. For temporal discretization, a fully implicit scheme is employed. The final set of algebraic equations that forms a non‐linear equation system is solved using the direct iterative procedure. Modeling of cracks is performed on the basis of linear elastic fracture mechanics, and for this purpose, the so‐called diffraction method is employed. For verification of the model, a number of problems are solved. According to the obtained results, the developed EFG computer program can successfully be applied for simulating the complex process of hydraulic fracture propagation in porous media. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

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