Effect of compressible parameters on vertical vibration of an elastic pile in multilayered poroelastic media

This paper mainly investigates the influences of compressible parameters on the vertical vibration of a pile embedded in layered poroelastic soil media. The pile is treated as a 1D elastic bar by the finite element method, and fundamental solutions for the layered poroelastic soils due to a vertical dynamic load are obtained by the analytical layer element method. Based on the compatibility conditions, the pile-soil dynamic interaction problem is solved. The numerical scheme has been compiled into a Fortran program for numerical calculation. Influences of the pile-soil stiffness ratio, compressible parameters, vibration frequency and the soil stratification are discussed.     

Macroscopic Electroosmotic Coupling Coefficient in Random Porous Media

A general analysis of electroosmotic phenomena is given for random porous media through which an electrolyte flows. A dimensional analysis demonstrates the crucial importance of the dimensionless coupling parameter a, which is usually very small when compared to 1; this suggests an expansion in terms of a and a numerical scheme that avoids the instabilities occurring in the direct solution. For media whose properties such as permeability are lognormally distributed, an analytical expression of the macroscopic coupling coefficients can be obtained when the fluctuations are small. Various results are provided for laminated media, correlated media, and stratified or fractured media. The influence of some macroscopic geometrical parameters is illustrated.     

裂隙岩石介质中核素迁移的模型及其算子分裂、迎风、均衡格式

建立了放射性核素在裂隙岩石介质中迁移的双重介质模型,对模型的求解提出了一种新的数值方法—Galerkin有限元法与算子分裂、迎风、均衡格式相结合的新方法,给出了水质模型算子分裂、迎风、均衡格式的稳定性条件,且所得到的计算格式是非负的。最后通过对核素90Sr 100年、99Tc 1000年的预测计算,验证了本文所提方法的有效性和稳定性,并得出了一些有重要意义的结论。     

双相介质中纵波方程的高阶有限差分解法

从双相介质中的纵波方程出发,导出了求解双相各向同性介质中纵波方程的高阶差分格式,给出了吸收边界条件和稳定性条件,在此基础上实现了双相各向同性介质中纵波方程的高阶有限差分法正演模拟,数值模拟结果表明,这种算法能在少量增加计算量的前提下大大提高精度,算法可同时应用于叠前和叠后的数值模拟。     

电偶源频率电磁测深三维地电模型有限元正演

在有源变频测深(包括可控源音频大地电磁测深CSAMT)的三维有限元正演中,应用了吸收边界条件和边元有限元算法,计算精度为3%左右,基本上可满足电偶极源三维地电模型情况下频率电磁测深响应特征的分析。同时由于广义变分概念的引入,可使泛函的变分原理应用于有耗媒质电磁场问题。      

二维矢量地震波场的叠前逆时深度偏移

从矢量波动理论出发，导出了二维弹性波逆时传播的高阶差分格式，实现了弹性波在数值空间中的逆时延拓，采用逆时格式差分求解程函方程，得到网格空间中各点的直达波旅行时，以此作为弹性波逆时偏移的成像条件。实现了二维多波多波多分量资料的叠前逆时深度偏移，数值试验得到了满意结果。     

Mortar coupling and upscaling of pore-scale models

Pore-scale models are becoming increasingly useful as predictive tools for modeling flow and transport in porous media. These models can accurately represent the 3D pore-structure of real media. Currently first-principles modeling methods are being employed for obtaining qualitative and quantitative behavior. Generally, artificial, simple boundary conditions are imposed on a model that is used as a stand-alone tool for extracting macroscopic parameters. However, realistic boundary conditions, reflecting flow and transport in surrounding media, may be necessary for behavior that occurs over larger length scales or including pore-scale models in a multiscale setting. Here, pore-scale network models are coupled to adjacent media (additional pore-scale or continuum-scale models) using mortars. Mortars are 2D finite-element spaces employed to couple independent subdomains by enforcing continuity of pressure and flux at shared boundary interfaces. While mortars have been used in the past to couple subdomains of different models, physics, and meshes, they are extended here for the first time to pore-scale models. The approach is demonstrated by modeling single-phase flow in coupled pore-scale models, but the methodology can be utilized to model dynamic processes and perform multiscale modeling in 3D continuum simulators for flow and transport.     

Numerical modeling of the flow and transport of radionuclides in heterogeneous porous media

This paper is concerned with numerical methods for the modeling of flow and transport of contaminant in porous media. The numerical methods feature the mixed finite element method over triangles as a solver to the Darcy flow equation and a conservative finite volume scheme for the concentration equation. The convective term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion–dispersion term is discretized by piecewise linear conforming triangular finite elements. It is shown that the scheme satisfies a discrete maximum principle. Numerical examples demonstrate the effectiveness of the methodology for a coupled system that includes an elliptic equation and a diffusion–convection–reaction equation arising when modeling flow and transport in heterogeneous porous media. The proposed scheme is robust, conservative, efficient, and stable, as confirmed by numerical simulations.      

Errors in the upstream mobility scheme for countercurrent two-phase flow in heterogeneous porous media

In reservoir simulation, the upstream mobility scheme is widely used for calculating fluid flow in porous media and has been shown feasible for flow when the porous medium is homogeneous. In the case of flow in heterogeneous porous media, the scheme has earlier been shown to give erroneous solutions in approximating pure gravity segregation. Here, we show that the scheme may exhibit larger errors when approximating flow in heterogeneous media for flux functions involving both advection and gravity segregation components. Errors have only been found in the case of countercurrent flow. The physically correct solution is approximated by an extension of the Godunov and Engquist–Osher flux. We also present a new finite volume scheme based on the local Lax–Friedrichs flux and test the performance of this scheme in the numerical experiments.     

裂隙各向异性介质2.5维弹性波场数值模拟

研究地震波在各向异性介质中的传播规律是勘探地震学领域的一个重要内容。本文首先讨论了２．５维波动方程，其次，在２．５维空间，用有限元数值模拟方法模拟了裂隙各向异性介质波场，结果用波场切片做了显示。最后对模拟结果做了基本分析，这里讨论的模拟方法也适用于其它类型的得各向异性介。     

Three dimensional simulation of fluid flow in X‐ray CT images of porous media

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.     

非均匀层状介质一维波动方程精确解的有限差分算法

平面波的传播问题通常可以归结为一维波动方程的定解问题。在非均匀介质中,即使简单的一维波动方程也需要借助于数值方法获得近似解。3层5点古典差分格式是计算偏微分方程一种常用算法,作为一种显式迭代格式,需要满足稳定性条件 ,其中 为波速, 为空间采样间隔, 为时间采样间隔。当 时, ,古典差分格式达到临界稳定状态。在这种情况下,平面波在 时间内的传播距离恰好等于空间采样间隔,差分格式真实地反映了平面波的传播原理,因而可以得到一维波动方程的精确解。但是,由于在非均匀介质中存在不连续的波阻抗界面,此方法不适于计算非均匀介质的波场。为了将临界稳定情况下的古典差分格式推广应用至非均匀层状介质,提出了一种能够处理波阻抗界面的有限差分格式,并应用傅里叶分析法得到其稳定性条件。模型算例验证了此算法的正确性。     

Discontinuous Galerkin method for two-component liquid–gas porous media flows

We consider two-component (typically, water and hydrogen) compressible liquid–gas porous media flows including mass exchange between phases possibly leading to gas-phase (dis)appearance, as motivated by hydrogen production in underground repositories of radioactive waste. Following recent work by Bourgeat, Jurak, and Smaï, we formulate the governing equations in terms of liquid pressure and dissolved hydrogen density as main unknowns, leading mathematically to a nonlinear elliptic–parabolic system of partial differential equations, in which the equations degenerate when the gas phase disappears. We develop a discontinuous Galerkin method for space discretization, combined with a backward Euler scheme for time discretization and an incomplete Newton method for linearization. Numerical examples deal with gas-phase (dis)appearance, ill-prepared initial conditions, and heterogeneous problem with different rock types.     

An extended finite volume method and fixed-stress approach for modeling fluid injection–induced tensile opening in fractured reservoirs

Fluid injection–induced tensile opening is modeled using an extended finite volume method (XFVM). An embedded fracture strategy is used for the flow problem, that is, the fractures are discretized using finite volume segments without resolving the grid around them. Further, the discontinuities across fractures are modeled using special basis functions. The fracture openings due to enhanced fluid pressure and the associated shear slip due to traction free boundary condition on the fracture segments are both modeled using these special discontinuity basis functions. Mass transfer between fractures and matrix is modeled using the pressure difference. The enhancement of fracture storativity due to tensile opening leads to stronger coupling between flow and mechanics. An iterative scheme relying on the fixed-stress approach for fractures, which conserves the stress dependent terms over each iteration of the flow problem, has been introduced. Tensile opening has been simulated for single fractures embedded in two- and three-dimensional matrices. The convergence criterion for sequentially implicit fixed-stress scheme for fractures embedded in elastic media is established and has been validated numerically. Further, for 2D simulations, the effect of the matrix permeability for fracture propagation due to tensile opening has been studied.     

FDwave3D: a MATLAB solver for the 3D anisotropic wave equation using the finite-difference method

Seismic modeling plays an important role in geophysics and seismology for estimating the response of seismic sources in a given medium. In this work, we present a MATLAB-based package, FDwave3D, for synthetic wavefield and seismogram modeling in 3D anisotropic media. The seismic simulation is carried out using the finite-difference method over the staggered grid, and it is applicable to both active and passive surveys. The code package allows the incorporation of arbitrary source mechanisms and offers spatial derivative operators of accuracy up to tenth-order along with different types of boundary conditions. First, the methodological aspects of finite-difference method are briefly introduced. Then, the code has been tested and verified against the analytical solutions obtained for the homogeneous model. Further, the numerical examples of layered and overthrust models are presented to demonstrate its reliability.

     

Hydro-micromechanical modeling of wave propagation in saturated granular crystals

Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro-micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two-way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore-scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one-dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face-centered-cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.     

On the use of enriched finite element method to model subsurface features in porous media flow problems

In this paper, a new enrichment scheme is proposed to model fractures and other conduits in porous media flow problems. Inserting this scheme into a partition of unity based method results in a new numerical method that does not require the mesh to honor the specific geometry of these subsurface features. The new scheme involves a specially designed integration procedure and enrichment functions, which can capture effects of local heterogeneity introduced by subsurface features on the pressure solution. The new method is also capable of modeling fractures with low as well as high conductivity. Another feature of the proposed scheme is that, even though two enrichment functions are used to model the permeability change at the two rock/fracture interfaces of a fracture, only one element partition is made for numerical integration. To demonstrate the accuracy and effectiveness of the proposed approach, production problems for wells that were stimulated or completed by longitudinal fracture, transverse fractures, and perforations are studied.     

长江中下游河湖洪水演进的数值模拟

以长江中下游(宜昌-大通)防洪系统为对象,在水文、河道及湖盆地形现状条件下,建立了一个能适应各种复杂条件的一二维非恒定流模型,来进行长江干流、河网、湖泊、分蓄洪区垸及水库的洪水演进和调度仿真.所建模型的洞庭湖部分采用无结构网格二维非恒定有限体积格式,以适应湖区复杂的边界形状和保持水量平衡.河网区部分采用一维非恒定流显隐结合的分块三级算法,以准确实现河网汊点流量的自动分配和往复流动.为了提高模拟精度和扩展模拟功能,在水流数值模拟的范围内侧重讨论了内外动边界处理、分蓄洪运用及阻力项计算等环节,提出了合理可行的数值处理方法.采用20世纪80年代至90年代共6年汛期洪水资料对所建模型进行了严格的率定和检验,高精度的模拟结果证实了模型的合理性和有效性.     

FFT‐based bounds on the permeability of complex microstructures

A numerical scheme for the computation of the permeability of complex microstructures is presented. As a darcean counterpart of the FFT‐based scheme in elasticity, the method is designed to be directly coupled with 3D imaging techniques of porous samples, without meshing or definition of an equivalent pore network. The method relies on the variational principle of Hashin and Shtrikman, which ensures a rigorous upper bound status to the estimated permeabilities and provides an energetically consistent rule for heterogeneous voxels comprising both the solid and fluid phases. Copyright © 2014 John Wiley & Sons, Ltd.     

大口径三维曲线顶管顶力估算及实测分析

顶管顶进阻力由顶管机的迎面阻力和管节与土体间的摩阻力两部分组成,现有的顶力估算公式都具有一定的适用条件,虽然物理意义明确,但参数取值范围较大,往往估算顶力与实际工程顶力的匹配程度较低,尤其是在三维曲线顶管工程中受曲线段的影响,准确估算顶力的难度更大。以长413.0 m,外径为3.8 m,最小曲率半径为313.7 m的三维曲线顶管工程为研究对象,基于现有的顶力公式估算所需顶力大小并布设中继间,在该工程实测数据的基础上分析顶力组成及其与顶程、顶进曲率半径等影响因素之间的关系和顶管在平面曲线和垂直剖面曲线以不同曲率半径顶进的摩阻力变化规律。分析结果显示,曲线顶管摩阻力附加系数是真实存在的,且工程实测值与经验值有所偏差,但顶管在淤泥或黏土层中顶进时的摩阻力按规程推荐取值能够满足工程实践需求。最后提出了顶力估算及中继间的布置建议,为类似工程提供依据。