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1.
Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation 
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下载免费PDF全文 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
2.
三维流形单元的生成是进行三维数值流形分析的首要问题之一。详细研究了三维流形单元的生成过程,并采用C++语言编写了相应的程序。借鉴二维流形单元的形成技术,基于拓扑学的“有向性”原理,将点、有向边、有向环、有向面和有向壳等作为三维块体的基本数据结构。将材料体和数学网格进行布尔交运算,并对形成的流形块体进行有效性检测,满足要求后即形成新的三维流形单元。每个数学网格的顶点作为新流形单元的数学覆盖,再对数学覆盖进行细分,形成流形单元的物理覆盖。分别选取凹形体、空心体和包含有限结构面的材料体与数学网格进行布尔交运算,并选取一个典型工程来检查该方法和程序的可行性。计算结果表明,该方法可以对复杂块体（凹形体、空心体和包含有限结构面的体）进行处理,为今后进行复杂结构计算和分析奠定基础,具有较强的适应性和可靠性。 相似文献
3.
Hydraulic fracturing is the method of choice to enhance reservoir permeability and well efficiency for extraction of shale gas. Multi‐stranded non‐planar hydraulic fractures are often observed in stimulation sites. Non‐planar fractures propagating from wellbores inclined from the direction of maximum horizontal stress have also been reported. The pressure required to propagate non‐planar fractures is in general higher than in the case of planar fractures. Current computational methods for the simulation of hydraulic fractures generally assume single, symmetric, and planar crack geometries. In order to better understand hydraulic fracturing in complex‐layered naturally fractured reservoirs, fully 3D models need to be developed. In this paper, we present simulations of 3D non‐planar fracture propagation using an adaptive generalized FEM. This method greatly facilitates the discretization of complex 3D fractures, as finite element faces are not required to fit the crack surfaces. A solution strategy for fully automatic propagation of arbitrary 3D cracks is presented. The fracture surface on which pressure is applied is also automatically updated at each step. An efficient technique to numerically integrate boundary conditions on crack surfaces is also proposed and implemented. Strongly graded localized refinement and analytical asymptotic expansions are used as enrichment functions in the neighborhood of fracture fronts to increase the computational accuracy and efficiency of the method. Stress intensity factors with pressure on crack faces are extracted using the contour integral method. Various non‐planar crack geometries are investigated to demonstrate the robustness and flexibility of the proposed simulation methodology. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
4.
Boris Jeremi&#x; Gerik Scheuermann Jan Frey Zhaohui Yang Bernd Hamann Kenneth I. Joy Hans Hagen 《国际地质力学数值与分析法杂志》2002,26(10):925-944
We present a novel technique for visualizing tensors in three dimensional (3D) space. Of particular interest is the visualization of stress tensors resulting from 3D numerical simulations in computational geomechanics. To this end we present three different approaches to visualizing tensors in 3D space, namely hedgehogs, hyperstreamlines and hyperstreamsurfaces. We also present a number of examples related to stress distributions in 3D solids subjected to single and load couples. In addition, we present stress visualizations resulting from single‐pile and pile‐group computations. The main objective of this work is to investigate various techniques for visualizing general Cartesian tensors of rank 2 and it's application to geomechanics problems. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
5.
C. Fidelibus 《国际地质力学数值与分析法杂志》2007,31(11):1329-1348
This paper describes the essential features of a numerical technique for the simulation of the coupled fluid flow and deformation in a 2D assembly of poroelastic blocks and transmissive fractures. The boundary element method (BEM) is applied to each block to reduce Navier and diffusion equations to a set of integral equations involving block boundary terms, whereas a Galerkin weighted‐residuals finite element method (FEM) is applied to the fracture diffusion equations. In addition, fracture local equilibrium is rendered through spring‐like equations relating the stresses to the relative displacements of the fracture walls. A time‐marching process is implemented leading to an algebraic system where the right‐hand side vector is built based on the collected solutions of the previous time steps. The technique requires the meshing of the fracture network only. The accuracy of the results is adequate even with relatively coarse meshes without the resort to small time steps at the beginning of the simulation. It furnishes outputs that focus only on the salient features of the response. The efficiency of the technique is demonstrated through the illustration of the results of three examples. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
6.
A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
7.
Behnam V. Damirchi Marcelo R. Carvalho Luís A. G. Bitencourt Osvaldo L. Manzoli Daniel Dias‐da‐Costa 《国际地质力学数值与分析法杂志》2021,45(1):83-107
A new discrete fracture model is introduced to simulate the steady‐state fluid flow in discontinuous porous media. The formulation uses a multi‐layered approach to capture the effect of both longitudinal and transverse permeability of the discontinuities in the pressure distribution. The formulation allows the independent discretisation of mesh and discontinuities, which do not need to conform. Given that the formulation is developed at the element level, no additional degrees of freedom or special integration procedures are required for coupling the non‐conforming meshes. The proposed model is shown to be reliable regardless of the permeability of the discontinuity being higher or lower than the surrounding domain. Four numerical examples of increasing complexity are solved to demonstrate the efficiency and accuracy of the new technique when compared with results available in the literature. Results show that the proposed method can simulate the fluid pressure distribution in fractured porous media. Furthermore, a sensitivity analysis demonstrated the stability regarding the condition number for wide range values of the coupling parameter. 相似文献
8.
针对高放射性核废物地下处置库近场饱和裂隙岩体环境,提出一种由分布热源、饱和单裂隙和两侧无限大岩石构成的三维水流-传热简化模型,建立了控制微分方程和基于拉氏变换域格林函数的积分方程;采用矩形单元把裂隙面域离散化,利用极坐标下的解析方法计算包含奇点的单元积分,利用数值方法计算分布热源和不包含奇点的单元积分,建立拉氏变换域的线性代数方程组,求解后,利用拉氏数值逆变换,计算任意时刻裂隙水和岩石的温度分布。对两个无内热源、流场确定的计算模型进行了计算,与仅考虑岩石沿裂隙面法向一维热传导的解析解进行了对比。计算分析了分布热源作用下饱和单裂隙岩体的三维水流-传热特征及其对裂隙水流速、岩石热传导系数和热源热流集度的敏感度。计算结果表明：与直接采用高斯数值积分相比,提出的解析法奇异积分精度较高;就裂隙水温度而言,单裂隙岩体三维水流-传热半解析计算方法与解析法得到的结果基本一致,但由于半解析计算方法考虑了岩石的三维热传导,使得裂隙水的上游温度较低,而下游温度较高;无分布热源作用时,岩石热传导系数越大,裂隙水温度越低;裂隙水流速越大,裂隙进水温度对裂隙水和岩石温度分布的影响越明显;由于受到裂隙水流动传热的作用,分布热源对裂隙水温度和岩石温度的影响在裂隙水流的下游区域比较显著。 相似文献
9.
In a previous publication we developed a new mixed least‐squares method for poro‐elasticity. The approximate solution was obtained via a minimization of a least‐squares functional, based upon the equations of equilibrium, the equations of continuity and weak forms of the constitutive relationships for elasticity and Darcy flow. The formulation involved four independent types of variables: displacements, stresses, pore pressures and velocities. All of them were approximated by linear continuous triangles. Encouraged by the computational results, obtained from the two‐dimensional implementation of the method, we extended our formulation to three dimensions. In this paper we present numerical examples for the performance of continuous linear tetrahedra within the context of the mixed least‐squares method. The initial results suggest that the method works well in the nearly and entirely incompressible limits for elasticity. For poro‐elasticity, the obtained pore pressures are stable without exhibiting the oscillations, which are observed when the standard Galerkin formulation is used. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
10.
Ha H. Bui Jayantha K. Kodikara Abdelmalek Bouazza Asadul Haque Pathegama G. Ranjith 《国际地质力学数值与分析法杂志》2014,38(13):1321-1340
Segmental retaining wall (SRW) systems are commonly used in geotechnical practice to stabilize cut and fill slopes. Because of their flexibility, these systems can tolerate minor movements and settlements without incurring damage or crack. Despite these advantages, very few numerical studies of large deformations and post‐failure behavior of SRW systems are found in the current literature. Traditional numerical methods, such as the finite element method, suffer from mesh entanglement, thus are unable to simulate large deformations and flexible behavior of retaining wall blocks in SRW systems. To overcome the above limitations, a novel computational framework based on the smoothed particle hydrodynamics (SPH) method was developed to simulate large deformations and post‐failure behavior of soils and retaining wall blocks in SRW systems. The proposed numerical framework is a hybrid continuum/discontinuum approach that can model soil as an elasto‐plastic material and retaining wall blocks as independent rigid bodies associated with both translational and rotational degrees of freedom. A new contact model is proposed within the SPH framework to simulate the interaction between the soil and the blocks and between the blocks. As an application of the proposed numerical method, a two‐dimensional simulation of an SRW collapse was simulated and compared to experimental results conducted under the same conditions. The results showed that the proposed computational approach provided satisfactory agreement with the experiment. This suggests that the new framework is a promising numerical approach to model SRW systems. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
11.
为了改进计算区域离散化问题,本文利用自适应非结构化网格有限单元法求解二维地电结构下大地电磁场满足的加权余量表达式。在有限元求解电磁场的过程中,网格剖分越精细、计算精度越高,计算量也会越大。此外,结构化网格难以适应任意地形以及复杂地质构造。而自适应非结构化网格在电性变化剧烈的区域会自动加密,在电性缓变的区域则生成粗疏的网格,从而优化网格质量与数量。因此,文中引入COMSOL Multiphysics软件,以实现若干地电模型的构建及非结构化自由四边形单元网格化。将网格数据信息导入本文算法,计算大地电磁场响应,并与解析解及数值解对比。结果表明,基于非结构化网格的正演模拟精度高、适应性强,为计算区域网格化提供了新的方法。 相似文献
12.
A mixed finite element–boundary element solution for the analysis of two-dimensional flow in porous media composed of rock blocks and discrete fractures is described. The rock blocks are modelled implicitly by using boundary elements whereas finite elements are adopted to model the discrete fractures. The computational procedure has been implemented in a hybrid code which has been validated first by comparing the numerical results with the closed-form solution for flow in a porous aquifer intercepted by a vertical fracture only. Then, a more complex problem has been solved where a pervious, homogeneous and isotropic matrix containing a net of fractures is considered. The results obtained are shown to describe satisfactorily the main features of the flow problem under study. © 1997 by John Wiley & Sons, Ltd. 相似文献
13.
Fast multipole displacement discontinuity method (FM‐DDM) for geomechanics reservoir simulations 下载免费PDF全文
下载免费PDF全文 The displacement discontinuity method (DDM) is frequently used in geothermal and petroleum applications for modeling the behavior of fractures in linear‐elastic rocks. The DDM requires O(N2) memory and O(N3) floating point operations (where N is the number of unknowns) to construct the coefficient matrix and solve the linear system of equations by direct methods. Therefore, the conventional implementation of the DDM is not computationally efficient for very large systems of cracks, often limiting its application to small‐scale problems. This work presents an approach for solving large‐scale fracture problems using the fast multipole method (FMM). The approach uses both the DDM and a kernel‐independent version of the FMM along with a preconditioned generalized minimal residual algorithm to accelerate the solution of linear systems of equations using desktop computers. Using the fundamental solutions for constant displacement discontinuity in a two‐dimensional elastic medium, several numerical examples involving fracture networks representing fractured reservoirs are treated. Numerical results show good agreement with analytical solutions and demonstrate the efficiency of the FMM implementation of the DDM for large‐scale simulations. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
14.
S. Berrone C. Fidelibus S. Pieraccini S. Scialò 《Rock Mechanics and Rock Engineering》2014,47(6):2171-2182
In this paper a numerical method for the simulation of the steady-state fluid flow in discrete fracture networks is described. It is based on the use of non-conforming meshes, enrichment functions and an optimization procedure. The meshing process is performed on each fracture independently of the other fractures, i.e. without geometrical conformity at the intersections (traces). The slope discontinuities due to the flux exchange at the traces are then captured with the enrichment functions of the extended finite elements, and finally a functional is minimized by resorting to an optimization procedure. The method can be easily implemented for parallel computers being based on many small independent problems. In order to show the effectiveness of the method and the quality of the results, simulations of fluid flow in simple networks are illustrated. 相似文献
15.
Coupled formulation and algorithms for the simulation of non‐planar three‐dimensional hydraulic fractures using the generalized finite element method 下载免费PDF全文
下载免费PDF全文 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.
W. Zhou 《Environmental Geology》2001,40(7):797-808
Two-phase flow in fractured rock is an important phenomenon related to a range of practical problems, including non-aqueous phase liquid contamination of groundwater. Although fractured rocks consist of fracture networks, the study of two-phase flow in a single fracture is a pre-requisite. This paper presents a conceptual and numerical model of two-phase flow in a variable fracture. The void space of the fracture is conceptualized as a system of independent channels with position-dependent apertures. Fundamental equations, governing two-phase displacement in each channel, are derived to represent the interface positions and fractional flows in the fracture. For lognormal aperture distributions, simple approximations to fractional flows are obtained in analytical form by assuming void occupancy based on a local capillary allowability criterion. The model is verified by analytical solutions including two-phase flow in a parallel-plate fracture, and used to study the impacts of aperture variation, mobility ratio and fracture orientation on properties of two-phase flow. Illustrative examples indicate that aperture variation may control the distribution of wetting and non-wetting fluids within the fracture plane and hence the ability of the fracture to transmit these fluids. The presence of wetting fluid does little to hinder non-wetting fluid flow in fractures with large aperture variations, whereas a small volume of non-wetting fluid present in the fracture can significantly reduce wetting fluid flow. Large mobility ratios and high fracture slope angles facilitates the migration of non-wetting fluid through fractures. 相似文献
17.
In this paper, 3D steady‐state fluid flow in a porous medium with a large number of intersecting fractures is derived numerically by using collocation method. Fluid flow in the matrix and fractures is described by Darcy's law and Poiseuille's law, respectively. The recent theoretical development presented a general potential solution to model the steady‐state flow in fractured porous media under a far‐field condition. This solution is a hypersingular integral equation with pressure field in the fracture surfaces as the main unknown. The numerical procedure can resolve the problem for any form of fractures and also takes into account the interactions and the intersection between fractures. Once the pressure field and then the flux field in fractures have been determined, the pressure field in the porous matrix is computed completely. The basic problem of a single fracture is investigated, and a semi‐analytical solution is presented. Using the solution obtained for a single fracture, Mori‐Tanaka and self‐consistent schemes are employed for upscaling the effective permeability of 3D fractured porous media. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
18.
M. Felix 《Sedimentology》2002,49(3):397-419
A two‐dimensional numerical model is used to describe the flow structure of turbidity currents in a vertical plane. To test the accuracy of the model, it is applied to historical flows in Bute Inlet and the Grand Banks flow. The two‐dimensional spatial and temporal distributions of velocity and sediment concentration and non‐dimensionalized vertical profiles of velocity, turbulent kinetic energy and sediment concentration are discussed for several simple computational currents. The flows show a clear interaction between velocity, turbulence and sediment distribution. The results of the numerical tests show that flows with fine‐grained sediment have low vertical and high horizontal gradients of velocity and sediment concentration, show little increase in flow thickness and decelerate slowly. Steadiness and uniformity in these flows are comparable for velocity and concentration. In contrast, flows with coarse‐grained sediment have high vertical and low horizontal velocity gradients and high horizontal concentration gradients. These flows grow considerably in thickness and decelerate rapidly. Steadiness and uniformity in flows with coarse‐grained sediment are different for velocity and concentration. The results show the influence of spatial and temporal flow structure on flow duration and sediment transport. 相似文献
19.
To investigate the movement mechanism of debris flow, a two‐dimensional, two‐phase, depth‐integrated model is introduced. The model uses Mohr‐Coulomb plasticity for the solid rheology, and the fluid stress is modeled as a Newtonian fluid. The interaction between solid and liquid phases, which plays a major role in debris flow movement, is assumed to consist of drag and buoyancy forces. The applicability of drag force formulas is discussed. Considering the complex interaction between debris flow and the bed surface, a combined friction boundary condition is imposed on the bottom, and this is also discussed. To solve the complex model equations, a numerical method with second‐order accuracy based on the finite volume method is proposed. Several numerical experiments are performed to verify the feasibilities of model and numerical schemes. Numerical results demonstrate that different solid volume fractions substantially affect debris flow movement. 相似文献
20.
分布热源作用下裂隙岩体渗流-传热的拉氏变换-格林函数半解析计算方法 总被引：1，自引：0，他引：1
以裂隙岩体高放射性核废物地下处置库性能评估为目标,提出了分布热源作用下单裂隙岩体渗流-传热的简化概念模型、控制微分方程和拉氏变换-格林函数半解析法,为进一步采用半解析法计算分布热源作用下多裂隙岩体的渗流-传热问题奠定了基础。针对单裂隙岩体的渗流-传热问题,建立考虑岩石内热源和二维热传导的控制微分方程,利用拉氏变换域微分方程的基本解建立格林函数积分方程,采用解析法处理其中的奇点,通过数值积分和拉氏数值逆变换求解,计算任意时刻裂隙水和岩石的温度分布。通过算例,与基于岩石一维热传导假定的解析解进行了对比,并计算分析了分布热源作用下单裂隙岩体的渗流-传热特征及其对裂隙开度、岩石热传导系数和热流集度的敏感度。算例表明,（1）就裂隙水温度而言,由于考虑了岩石的二维热传导,拉氏变换-格林函数半解析解小于基于岩石一维热传导假定的解析解;（2）裂隙水温度和岩石温度对裂隙开度和热流集度的敏感度较大,对岩石热传导系数的敏感度较小。 相似文献