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A fully coupled element‐free Galerkin model for hydro‐mechanical analysis of advancement of fluid‐driven fractures in porous media 
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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
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This paper introduces a new generator algorithm and computer program for 3-D numerical simulation of packing configuration in a granular assemblies composed of ellipsoidal particles of different a/b aspect ratios. Each ellipsoidal particle is approximated by the revolution of an ellipse, formed by four connected arcs, about the major axis passing through its centroid. The centroid co-ordinates, major axis direction and lengths of the major and minor axes are the essential data for the packing generation and associated contact detection. The domain to be filled with particles can be a polyhedron of any shape. The packing program was coded based on a newly proposed scheme which obeys the no interpenetration kinematics of solid bodies. New contact detection algorithms for any two ellipsoids in the packing space were developed. Though simple, these algorithms effectively determine the contact condition and contact point without solving the simultaneous equations of the two ellipsoidal surfaces. Each particle's packing location, contact-point co-ordinates, and three-dimensional graphs can be created using the packing domain given boundaries, along with numbers, and geometrical information of particles to be generated. Simulation results show that this new algorithm provides an effective packing model as a required initial input for analysing the mechanics of granular material. This generation scheme potentially can explore the complex 3-D behaviours of material composed of discrete particles. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
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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
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Explicit dynamic relaxation is an efficient tool that has been used to solve problems involving highly non-linear differential equations. The key feature of this method is the ability to use explicit dynamic algorithms in solving static problems. Few attempts have been made to date to apply this technique in conventional geotechnical engineering. In this study, an algorithm that incorporates the application of a stiffness dependent time step scheme is proposed. The algorithm has been successfully used to solve 2D and 3D non-linear geotechnical engineering problems. To calibrate the developed algorithm, numerical simulations have been conducted for a strip and square footings supported by Mohr–Coulomb material. Performance of four different types of brick elements used in collapse load calculation is examined in terms of convergence speed and accuracy. In addition, the role of employing adaptive time steps in reducing the number of iterations needed for convergence is also evaluated. 相似文献
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The cable shovel is widely used in surface mining. High operating and ownership costs necessitate efficient use of the cable
shovel. Operator practices have long been suspected to contribute towards the inefficient use of the shovel. Crowd arm and
hoist rope speeds are key measures of operator practices. The objective of this work is to find the crowd arm and hoist rope
speeds for optimal shovel performance for given initial conditions and material properties. Shovel kinematics and dynamic modeling, using shovel
geometry and the simultaneous constraint method, respectively, have been employed to build models of the excavation process.
Dynamic models of the shovel payload and the material cutting resistance have also been developed using geometric simulation
and passive soil pressures techniques, respectively. These models are solved numerically by combining Runge–Kutta and Gaussian
elimination algorithms to compute the work done and the resistive forces during shovel excavation. The algorithms have been
combined into a shovel simulator. The simulator has been used to simulate the P&H 2100BL shovel. The simulation results indicate
that input energy and digging time increase with increasing crowd arm and decreasing hoist rope speeds. The input energy per
unit loading rate is proposed as an appropriate measure of shovel performance. High energy per unit loading rate occurs for
high crowd speeds and low hoist rope speeds. For the simulated conditions and crowd arm and hoist rope speeds ranging from
0.25 to 0.5 ms−1 and 0.5 to 0.7 ms−1, respectively, the optimal crowd arm and hoist rope speeds were found to be 0.25 ms−1 and 0.7 ms−1, respectively, and the objective function value was 0.21 KJs/kg. This work establishes, theoretically, the fact that operator
practices have an effect on shovel performance and is useful in establishing optimum practices. The results are the initial
steps towards full automation of the excavation process. 相似文献
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Daniel T. C. Yao Waldyr Lopes de Oliveira‐Filho Xiao‐Chuan Cai Dobroslav Znidarcic 《国际地质力学数值与分析法杂志》2002,26(2):139-161
The consolidation and desiccation behaviour of soft soils can be described by two time‐dependent non‐linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi‐implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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一个计算机模拟水-岩反应过程的数学模型 总被引：1，自引：0，他引：1
本文对计算机模拟水-岩反应过程的地球化学背景作了详细的讨论,指出偏平衡假设对于水-岩反应过程是合理的,因而可用一准平衡过程逼近于一真实的地球化学过程。根据热力学原理和地质概念模型,作者建立了一个完整的数学模型,它可以模拟不同的地球化学过程。该模型由一组非线性方程构成,其中包括质量守恒方程和化学平衡方程。为了求解,作者将非线性方程组化为最小平方和形式,然后采用改进的牛顿迭代法进行数值求解。作者还采取了初始值初步改善和变量替换等措施,避免了求解水-岩反应方程组常遇到的两个问题,即初始值选取和负浓度的出现。本文所给出的算法具有很好的数值稳定性。作者模拟了黄铁矿型矿床的形成过程,计算结果与矿床的实际典型分带相一致。 相似文献
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An-Bin Huang 《国际地质力学数值与分析法杂志》1989,13(5):551-564
A numerical technique has been implemented to perform strain path analyses for arbitrary three-dimensional (3D) penetrometers. The technique is based on that developed in aeronautical engineering for the calculation of incompressible potential flows about arbitrary 3D, non-lifting bodies. It uses a source-density distribution on the surface of the body and solves for the distribution necessary to make the normal component of fluid velocity zero on the boundary. The surface of a 3D body is approximated by a series of plane quadrilaterals, and the integral equation for the source density is replaced by a set of linear algebraic equations which are then solved for the source densities on the quadrilaterals. The displacements and strains are eventually derived based on these source densities. A series of strain-path analyses have been performed for cone and flat dilatometer penetrations. Results show that the soil responses to these two types of penetrometers are fundamentally different. 相似文献
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T. T. Garipov P. Tomin R. Rin D. V. Voskov H. A. Tchelepi 《Computational Geosciences》2018,22(4):1039-1057
We present a reservoir simulation framework for coupled thermal-compositional-mechanics processes. We use finite-volume methods to discretize the mass and energy conservation equations and finite-element methods for the mechanics problem. We use the first-order backward Euler for time. We solve the resulting set of nonlinear algebraic equations using fully implicit (FI) and sequential-implicit (SI) solution schemes. The FI approach is attractive for general-purpose simulation due to its unconditional stability. However, the FI method requires the development of a complex thermo-compositional-mechanics framework for the nonlinear problems of interest, and that includes the construction of the full Jacobian matrix for the coupled multi-physics discrete system of equations. On the other hand, SI-based solution schemes allow for relatively fast development because different simulation modules can be coupled more easily. The challenge with SI schemes is that the nonlinear convergence rate depends strongly on the coupling strength across the physical mechanisms and on the details of the sequential updating strategy across the different physics modules. The flexible automatic differentiation-based framework described here allows for detailed assessment of the robustness and computational efficiency of different coupling schemes for a wide range of multi-physics subsurface problems. 相似文献
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In this paper a finite element formulation for a linear viscoelastic ageing material is developed. It is shown that these equations can be solved in the from of an eigenvalue expansion thus reducing the problem to the solution of a set of Volterra Integral equations. An alternative method of solution based on expansion in terms of an operator related to Poisson's ratio is also developed and this solution method is found to significantly reduce the computational effort necessary in the solution of aproblem. 相似文献
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井眼轨道的软着陆设计模型的求解可以归结为一个七元非线性方程组的求解问题。前人给出了数值迭代求解算法,然而并没有证明该迭代算法的收敛性,并且该算法是否收敛严重依赖于用户给出的迭代初始值。通过一系列的消元、化简的数学技巧,将七元非线性方程组化简为一元多项式方程,并在此基础上给出了软着陆设计模型的一个新算法。理论分析和实际算例表明,新算法的主要计算工作量是求多项式方程的非负实数根,其他未知数与实数根是简单的函数关系,计算量很小。新算法克服了迭代算法的初值依赖性以及迭代过程可能发散等缺陷,并且在设计模型有多个解的情况下,可以同时求出这些解。 相似文献
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建立了基于高阶Boussinesq水波方程的一维波浪破碎数值模型。基于一组具有二阶完全非线性特征的Boussinesq水波方程,建立了交错网格下的高精度差分格式,推导了适用于该组方程的永形波解析解,其和松弛造波技术相结合实现了数值波浪水槽中(强)非线性波浪的无反射入射。通过模拟封闭容器内水体晃动问题对数值格式进行了验证,通过模拟孤立波在斜坡海岸上的浅化过程说明了将方程从弱非线性发展到完全非线性的必要性。采用涡粘方法处理波浪破碎,利用物理模型实验数据,分析了模型中各波浪破碎参数对数值结果的影响并对参数进行了率定。应用该模型对规则波在斜坡海岸上的传播、变浅以及破碎过程进行了数值模拟研究,数值结果同实验数据吻合良好,验证了模型的有效性。 相似文献
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Clint N. Dawson Héctor Klíe Mary F. Wheeler Carol S. Woodward 《Computational Geosciences》1997,1(3-4):215-249
A new parallel solution technique is developed for the fully implicit three‐dimensional two‐phase flow model. An expandedcell‐centered finite difference scheme which allows for a full permeability tensor is employed for the spatial discretization, and backwardEuler is used for the time discretization. The discrete systems are solved using a novel inexact Newton method that reuses the Krylov information generated by the GMRES linear iterative solver. Fast nonlinear convergence can be achieved by composing inexact Newton steps with quasi‐Newton steps restricted to the underlying Krylov subspace. Furthermore, robustness and efficiency are achieved with a line‐search backtracking globalization strategy for the nonlinear systems and a preconditioner for each coupled linear system to be solved. This inexact Newton method also makes use of forcing terms suggested by Eisenstat and Walker which prevent oversolving of the Jacobian systems. The preconditioner is a new two‐stage method which involves a decoupling strategy plus the separate solutions of both nonwetting‐phase pressure and saturation equations. Numerical results show that these nonlinear and linear solvers are very effective. 相似文献
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This paper presents an exact analytical solution to fully coupled axisymmetric consolidation of a semi‐infinite, transversely isotropic saturated soil subjected to a uniform circular loading at the ground surface. The analysis is under the framework of Biot's general theory of consolidation. First, the governing equations of consolidation are transformed into a set of equivalent partial differential equations with the introduction of two auxiliary variables. These partial differential equations are then solved using Hankel–Laplace integral transforms. Once solutions in the transformed domain have been obtained, the actual solutions in the physical domain for displacements and stress components of the solid matrix, pore‐water pressure and fluid discharge can be finally obtained by direct numerical inversion. The accuracy of the numerical solutions developed is confirmed by comparison with an existing exact solution for an isotropic and saturated soil that is a special case of the more general problem addressed. Numerical analyses are also presented to investigate the influence of the degree of material anisotropy on the consolidation settlement. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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二维圆柱坐标下FDTD法对多频电磁波测井的数值模拟 总被引：5，自引：2，他引：3
刘四新 《吉林大学学报(地球科学版)》2004,34(2):283-286
在介质围绕Z轴旋转对称的情况下,三维直角坐标下的麦克斯韦方程可变成两组分别对应TM波和TE波的二维柱坐标下的偏微分方程.采用线圈作为电磁波测井的发射器和接收器的时候,可采用TE波对应的方程,这时相当于磁极子的情况.而采用电偶极子作为发射和接收器的时候,则对应TM波的方程.采用时间和空间均为二阶精确的有限差分方法,将偏微分方程进行差分化.这样,空间的电磁场可由时间域有限差分法(FDTD)来求解. 相似文献
18.
J. Wang J. Sui P. Chen 《International Journal of Environmental Science and Technology》2009,6(1):1-12
In this paper, the k-? two-equation turbulence model has been used to simulate ice accumulation under ice cover along a river bend. A 2D depth-averaged numerical model has been developed in a nonorthogonal coordinate system with nonstaggered curvilinear grids. In this model, the contravariant velocity has been treated as an independent variable. To avoid the pressure oscillation in the nonstaggered grids, the momentum interpolation has been introduced to interpolate variables at the interface. The discretization equations have been solved by using pressure correction algorithms. An equation has been developed for describing the deformation of ice jam bottom. The thickness distribution of ice accumulation (ice jam) along the bend has been simulated. The developed model has been applied to the experimental studies under different conditions carried out at the Hefei University of Technology. Results indicate that all simulated thickness of ice accumulation agrees reasonably well with the measured thickness of ice accumulation in laboratory. 相似文献
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A general approach for obtaining the consistent tangent operator for constitutive rate equations is presented. The rate equations can be solved numerically by the user's favourite time integrator. In order to obtain reliable results, the substepping in integration should be based on a control of the local error. The main ingredient of the consistent tangent operator, namely the derivative of the stress with respect to the strain increment must be computed simultaneously with the same integrator, applied to a numerical approximation of the variational equations. This information enables finite‐element packages to assemble a consistent tangent operator and thus guarantees quadratic convergence of the equilibrium iterations. Several numerical examples with a hypoplastic constitutive law are given. As numerical integrator we used a second‐order extrapolated Euler method. Quadratic convergence of the equilibrium iteration is shown. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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基于Zienkiewicz提出的非饱和多孔介质波动理论,考虑两相流体和固体颗粒的压缩性以及惯性、黏滞和机械耦合作用,采用半解析的方法获得了一类典型边界条件下单层非饱和多孔介质一维瞬态响应解。首先推导出无量纲化后以位移表示的控制方程,并将其写成矩阵形式;然后,将边界条件齐次化,求解控制方程所对应的特征值问题,得到了满足齐次边界条件的特征值和相对应的特征函数。根据变异系数法并利用特征函数的正交性,得到了一系列仅黏滞耦合的关于时间的二阶常微分方程及相应的初始条件。在此基础上,运用精细时程积分法给出了常微分方程组的数值解。最后,通过若干算例验证了结果的正确性并探讨了单层非饱和多孔介质一维瞬态动力响应的特点。该方法可推广应用于其他典型的边界条件。 相似文献