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1.
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   

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.
程万  蒋国盛  周治东  魏子俊  张宇  王炳红  赵林 《岩土力学》2018,39(12):4448-4456
水平井中多条水力裂缝间的应力干扰行为,造成了压裂液排量的非均匀分配,影响了水力裂缝的几何形态。采用边界元法研究岩体在压裂液作用下的变形程度,以幂律流体泊肃叶平板流动方程来研究水力裂缝内部的压裂液流场,考虑了多条裂缝间应力干扰和压裂液流量分配,建立了流-固耦合的水平井多条水力裂缝同步扩展模型。模型可模拟水平井多条水力裂缝几何形态、应力干扰情况和压裂液排量的分配情况,可解释水力裂缝之间的竞争机制。多条裂缝同步扩展时,压裂液排量并非均等地分配到各个裂缝之中,进入到内部裂缝的压裂液流量最小,内部裂缝宽度最小;内部的水力裂缝增长一定长度后,停止增长,并且在应力干扰下逐渐闭合。  相似文献   

4.
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   

5.
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   

6.
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   

7.
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   

8.
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   

9.
The paper presents an embedded strong discontinuity approach to simulate single hydraulic fracture propagation in the poroelastic medium under plane-strain conditions. The method enriches the strain field with the discontinuous deformation mode and allows the fracture to be modeled inside elements. The Mode-I fracture initiation and propagation are described by the trilinear cohesive law, which is implemented by the penalty method. The enhanced permeability inside the fractured elements is dependent on the fracture aperture. Hydraulic fracture propagation is driven by the high pressure gradient near the fracture. Fluid transfer between the fracture and bulk rock is automatically captured within the poroelastic framework. The numerical framework is verified by the comparisons with the asymptotic analytical solutions for single hydraulic fracture propagation.  相似文献   

10.
We present an extended finite element framework to numerically study competing hydraulic fracture propagation. The framework is capable of modeling fully coupled hydraulic fracturing processes including fracture propagation, elastoplastic bulk deformation and fluid flow inside both fractures and the wellbore. In particular, the framework incorporates the classical orifice equation to capture fluid pressure loss across perforation clusters linking the wellbore with fractures. Dynamic fluid partitioning among fractures during propagation is solved together with other coupled factors, such as wellbore pressure loss (\(\Delta p_w\)), perforation pressure loss (\(\Delta p\)), interaction stress (\(\sigma _\mathrm{int}\)) and fracture propagation. By numerical examples, we study the effects of perforation pressure loss and wellbore pressure loss on competing fracture propagation under plane-strain conditions. Two dimensionless parameters \(\Gamma = \sigma _\mathrm{int}/\Delta p\) and \(\Lambda = \Delta p_w/\Delta p\) are used to describe the transition from uniform fracture propagation to preferential fracture propagation. The numerical examples demonstrate the dimensionless parameter \(\Gamma \) also works in the elastoplastic media.  相似文献   

11.
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   

12.
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   

13.
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   

14.
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   

15.
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   

16.
A procedure based on the finite element method is suggested for modeling of 3D hydraulic fracturing in the subsurface. The proposed formulation partitions the stress field into the initial stress state and an additional stress state caused by pressure buildup. The additional stress is obtained as a solution of the Biot equations for coupled fluid flow and deformations in the rock. The fluid flow in the fracture is represented on a regular finite element grid by means of “fracture” porosity, which is the volume fraction of the fracture. The use of the fracture porosity allows for a uniform finite element formulation for the fracture and the rock, both with respect to fluid pressure and displacement. It is demonstrated how the fracture aperture is obtained from the displacement field. The model has a fracture criterion by means of a strain limit in each element. It is shown how this criterion scales with the element size. Fracturing becomes an intermittent process, and each event is followed by a pressure drop. A procedure is suggested for the computation of the pressure drop. Two examples of hydraulic fracturing are given, when the pressure buildup is from fluid injection by a well. One case is of a homogeneous rock, and the other case is an inhomogeneous rock. The fracture geometry, well pressure, new fracture area, and elastic energy released in each event are computed. The fracture geometry is three orthogonal fracture planes in the homogeneous case, and it is a branched fracture in the inhomogeneous case.  相似文献   

17.
基于人工裂隙网络模型,展开一系列不同边界荷载作用下含不同交叉点个数的裂隙网络渗流试验。针对所有试验工况,模型进水口水压力范围均为0～0.6 MPa,侧压力系数均由1.0增加至5.0。试验结果表明：裂隙网络体积流速和水力梯度之间的相关性可以通过Forchheimer函数进行拟合,拟合方程中线性和非线性项系数均随着侧压力系数的增加逐渐增大,而随着裂隙网络交叉点个数的增加逐渐减小;渗流试验过程中,非线性效应系数E和水力梯度J之间的相关性可采用一个幂指数函数进行描述,随着水力梯度的增加,非线性效应系数逐渐增大;随着侧压力系数的增加,裂隙网络临界水力梯度呈现逐渐增大的趋势,对于所有裂隙网络交叉点个数（1～12）,当侧压力系数由1.0增加至5.0,临界水力梯度由0.63～12.13增加至6.01～81.55;提出数学模型 对归一化导水系数 随水力梯度的增大而减小的特征进行分析,随着侧压力系数的增加,两者之间的拟合曲线逐渐上移,拟合系数 整体呈现逐渐增大的趋势。裂隙网络的等效渗透系数随侧压力系数的增加逐渐降低。  相似文献   

18.
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   

19.
Rock is a heterogeneous geological material. When rock is subjected to internal hydraulic pressure and external mechanical loading, the fluid flow properties will be altered by closing, opening, or other interaction of pre-existing weaknesses or by induced new fractures. Meanwhile, the pore pressure can influence the fracture behavior on both a local and global scale. A finite element model that can consider the coupled effects of seepage, damage and stress field in heterogeneous rock is described. First, two series of numerical tests in relatively homogeneous and heterogeneous rocks were performed to investigate the influence of pore pressure magnitude and gradient on initiation and propagation of tensile fractures. Second, to examine the initiation of hydraulic fractures and their subsequent propagation, a series of numerical simulations of the behavior of two injection holes inside a saturated rock mass are carried out. The rock is subjected to different initial in situ stress ratios and to an internal injection (pore) pressure at the two injection holes. Numerically, simulated results indicate that tensile fracture is strongly influenced by both pore pressure magnitude and pore pressure gradient. In addition, the heterogeneity of rock, the initial in situ stress ratio (K), the distance between two injection holes, and the difference of the pore pressure in the two injection holes all play important roles in the initiation and propagation of hydraulic fractures. At relatively close spacing and when the two principal stresses are of similar magnitude, the proximity of adjacent injection holes can cause fracturing to occur in a direction perpendicular to the maximum principal stress.  相似文献   

20.
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   

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