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1.
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
2.
D. I. Garagash 《国际地质力学数值与分析法杂志》2006,30(14):1439-1475
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
3.
Numerical modeling of hydraulic fracture propagation,closure and reopening using XFEM with application to in‐situ stress estimation 
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下载免费PDF全文 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
4.
In this paper, a mathematical model is presented for the analysis of dynamic fracture propagation in the saturated porous media. The solid behavior incorporates a discrete cohesive fracture model, coupled with the flow in porous media through the fracture network. The double‐nodded zero‐thickness cohesive interface element is employed for the mixed mode fracture behavior in tension and contact behavior in compression. The crack is automatically detected and propagated perpendicular to the maximum effective stress. The spatial discretization is continuously updated during the crack propagation. Numerical examples from the hydraulic fracturing test and the concrete gravity dam show the capability of the model to simulate dynamic fracture propagation. The comparison is performed between the quasi‐static and fully dynamic solutions, and the performance of two analyses is investigated on the values of crack length and crack mouth opening. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
5.
In this paper, a fully coupled thermo-hydro-mechanical model is presented for two-phase fluid flow and heat transfer in fractured/fracturing porous media using the extended finite element method. In the fractured porous medium, the traction, heat, and mass transfer between the fracture space and the surrounding media are coupled. The wetting and nonwetting fluid phases are water and gas, which are assumed to be immiscible, and no phase-change is considered. The system of coupled equations consists of the linear momentum balance of solid phase, wetting and nonwetting fluid continuities, and thermal energy conservation. The main variables used to solve the system of equations are solid phase displacement, wetting fluid pressure, capillary pressure, and temperature. The fracture is assumed to impose the strong discontinuity in the displacement field and weak discontinuities in the fluid pressure, capillary pressure, and temperature fields. The mode I fracture propagation is employed using a cohesive fracture model. Finally, several numerical examples are solved to illustrate the capability of the proposed computational algorithm. It is shown that the effect of thermal expansion on the effective stress can influence the rate of fracture propagation and the injection pressure in hydraulic fracturing process. Moreover, the effect of thermal loading is investigated properly on fracture opening and fluids flow in unsaturated porous media, and the convective heat transfer within the fracture is captured successfully. It is shown how the proposed computational model is capable of modeling the fully coupled thermal fracture propagation in unsaturated porous media. 相似文献
6.
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
7.
In this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
8.
新疆油田某地区油藏的储隔层岩性组合复杂,呈现突出的薄互层产状特征,研究合、分压判断条件有利于提高压裂效率,增强储层动用程度与压后改造效果。水力裂缝在薄互层中的穿层与裂缝扩展行为受薄互层地质特征与压裂施工参数的影响。基于此,开展了薄互层物理模型压裂试验,研究界面胶结、岩层分布、岩层厚度、压裂液黏度与注液排量对薄互层中水力裂缝垂向扩展的影响分析。试验结果表明：薄互层的地层特征界面胶结与岩层分布是水力裂缝垂向扩展的主要控制因素,界面胶结强度对裂缝垂向扩展行为的影响强于岩层分布;由于弱胶结界面的存在,水力裂缝垂向扩展穿层时可发生方向偏转,抑制裂缝垂向扩展;提高压裂液黏度与注液排量有利于薄互层中水力裂缝的穿层垂向扩展。 相似文献
9.
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。 相似文献
10.
We present a stabilized extended finite element formulation to simulate the hydraulic fracturing process in an elasto‐plastic medium. The fracture propagation process is governed by a cohesive fracture model, where a trilinear traction‐separation law is used to describe normal contact, cohesion and strength softening on the fracture face. Fluid flow inside the fracture channel is governed by the lubrication equation, and the flow rate is related to the fluid pressure gradient by the ‘cubic’ law. Fluid leak off happens only in the normal direction and is assumed to be governed by the Carter's leak‐off model. We propose a ‘local’ U‐P (displacement‐pressure) formulation to discretize the fluid‐solid coupled system, where volume shape functions are used to interpolate the fluid pressure field on the fracture face. The ‘local’ U‐P approach is compatible with the extended finite element framework, and a separate mesh is not required to describe the fluid flow. The coupled system of equations is solved iteratively by the standard Newton‐Raphson method. We identify instability issues associated with the fluid flow inside the fracture channel, and use the polynomial pressure projection method to reduce the pressure oscillations resulting from the instability. Numerical examples demonstrate that the proposed framework is effective in modeling 3D hydraulic fracture propagation. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
11.
The Helvetic nappes in Switzerland consist of sediments, which have been sheared off and thrust over the crystalline basement of the European passive continental margin during Alpine orogeny. Their basal shear zones usually root above the external crystalline massifs. However, the mechanisms that initiated the shear zones and the associated nappe formation are still debated. We perform two-dimensional numerical simulations of the shearing of linear viscous fluids above a linear viscous fluid with considerably higher viscosity (quasi-undeformable). The boundary between the fluid, mimicking the sediments, and the quasi-undeformable fluid, mimicking the basement, exhibits geometrical perturbations, mimicking half-grabens. These geometrical perturbations can trigger significant strain localization and the formation of shear zones within the linear viscous fluid although no rheological softening mechanism is active. This kinematic, ductile strain localization is caused by the half-grabens and the viscosity ratio between basement and sediments. The viscosity ratio has a strong control on the kinematics of strain localization, whereas the depth of the half-grabens has a weak control. For sediment viscosities in the order of 1021 Pas and typical half-graben geometries of 5 km depth and 25 km width the localization generates (a) low-angle shear zones at the basement-sediment interface, but also entirely within the sediments, (b) horizontal transport >10 km associated with the shear zones, (c) shear zones with thickness in the order of 100 m, (d) an ordered stacking of model nappes and (e) shear zones that root above the basement. The results suggest that tectonic inheritance in the form of half-grabens and associated kinematic strain localization could have been the triggering mechanism for Helvetic nappe formation, and not rheological softening mechanisms, which might, however, have subsequently further intensified shear localization significantly. 相似文献
12.
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
13.
水力压裂作为一种主要的地热能开采手段,其压裂效果除与岩体基本物理力学性质有关外,还与裂隙分布、地应力状态、压裂工程参数等密切相关.为了探究以上因素对水力压裂过程中裂缝扩展行为的影响,以冀中坳陷碳酸盐岩储层岩体为研究对象,基于扩展有限元法,建立裂缝扩展流固耦合模型,分析了水平应力差、射孔方位角、注入液排量和压裂液黏度等参数对裂缝扩展行为的影响.结果表明:单裂缝扩展时,射孔方位角越小、注入量越大、越有利于裂缝扩展;双裂缝扩展时,水平应力差增大,裂缝偏转程度变小;水力裂缝与天然裂缝相交时,较小水平应力差有利于天然裂缝开启. 相似文献
14.
Field injectivity tests are widely used in the oil and gas industry to obtain key formation characteristics. The prevailing approaches for injectivity test interpretation rely on traditional analytical models. A number of parameters may affect the test results and lead to interpretation difficulties. Understanding their impacts on pressure response and fracture geometry of the test is essential for accurate test interpretation. In this work, a coupled flow and geomechanics model is developed for numerical simulation of field injectivity tests. The coupled model combines a cohesive zone model for simulating fluid-driven fracture and a poro-elastic/plastic model for simulating formation behavior. The model can capture fracture propagation, fluid flow within the fracture and formation, deformation of the formation, and evolution of pore pressure and stress around the wellbore and fracture during the tests. Numerical simulations are carried out to investigate the impacts of a multitude of parameters on test behaviors. The parameters include rock permeability, the leak-off coefficient of the fracture, rock stiffness, rock toughness, rock strength, plasticity deformation, and injection rate. The sensitivity of pressure response and fracture geometry on each parameter is reported and discussed. The coupled flow and geomechanics model provides additional advantages in the understanding of the fundamental mechanisms of field injectivity tests. 相似文献
15.
A finite element method for modeling coupled flow and deformation in porous fractured media 下载免费PDF全文
下载免费PDF全文 Ahmad Pouya 《国际地质力学数值与分析法杂志》2015,39(16):1836-1852
Modeling the flow in highly fractured porous media by finite element method (FEM) has met two difficulties: mesh generation for fractured domains and a rigorous formulation of the flow problem accounting for fracture/matrix, fracture/fracture, and fracture/boundary fluid mass exchanges. Based on the recent theoretical progress for mass balance conditions in multifractured porous bodies, the governing equations for coupled flow and deformation in these bodies are first established in this paper. A weak formulation for this problem is then established allowing to build a FEM. Taking benefit from recent development of mesh‐generating tools for fractured media, this weak formulation has been implemented in a numerical code and applied to some typical problems of hydromechanical coupling in fractured porous media. It is shown that in this way, the FEM that has proved its efficiency to model hydromechanical phenomena in porous media is extended with all its performances (calculation time, couplings, and nonlinearities) to fractured porous media. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
16.
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
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18.
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。 相似文献
19.
A fully coupled element‐free Galerkin model for hydro‐mechanical analysis of advancement of fluid‐driven fractures in porous media 下载免费PDF全文
下载免费PDF全文 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
20.
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