流体饱和两相多孔介质动力反应计算分析

基于流体饱和两相多孔介质的弹性波动方程组,运用显式逐步积分格式与局部透射人工边界相结合的时域显式有限元方法对该波动方程组进行求解,对两相介质在输入地震波作用下的弹性动力反应进行计算和分析;对在是否考虑孔隙流体渗流的两种情况下计算得到的两相介质弹性动力反应结果的差异进行对比研究,从而揭示孔隙流体渗流对两相介质动力反应性质的影响。计算结果表明：两相介质弹性动力反应时程的波形与入射地震波的波形相同,且弹性动力反应的峰值出现的时刻对应于入射地震波的峰值出现的时刻;孔隙流体的渗流将对两相介质的弹性动力反应性质产生显著的影响。数值计算同时表明,时域显式有限元方法是进行流体饱和两相多孔介质弹性动力反应计算分析的一种有效的方法。     

Finite element evaluation of diffusion and dispersion tensors in periodic porous media with advection

This paper presents three-dimensional finite element simulations to evaluate diffusion and dispersion tensors in periodic porous media in the presence of an advective velocity field. These tensors are evaluated in the framework of the double-scale expansion technique. Two problems, a Newtonian flow and a vector-valued advection–diffusion equation, have to be sequentially solved at the pore scale. Finite element techniques to approximate these problems are proposed and analyzed. Numerical results in three-dimensional networks of spheres are presented to quantitatively assess the impact of the pore morphology and of the advection velocity on the diffusion and dispersion tensors.     

Transient bifurcation condition of partially saturated porous media at finite strain

Bifurcation of unsaturated soils into a localized shear band is a ubiquitous failure mode of partially saturated soils. The density and degree of saturation have major impacts on the inception of localized deformations in unsaturated soils. Unsaturated fluid flow may dramatically change the density and degree of fluid saturation of unsaturated soils. Therefore, the unsaturated fluid flow is a potential trigger for shear banding in such materials. In this paper, we derive a simplified bifurcation condition of localized deformation in unsaturated soils under the local transient condition at finite strain. This transient bifurcation condition is implemented into a nonlinear finite element code to study the inception of localized deformation in unsaturated soil specimens. Numerical simulations are conducted to study the impact of soil fabrics of density, a ‘bonding’ variable, and intrinsic permeability on the inception of localized failures via the transient bifurcation criterion. Mesh sensitivity analysis is performed to demonstrate the viscosity effect of unsaturated fluid flow on the localized deformation. Numerical simulations demonstrate that the transient bifurcation condition can detect the localized deformation triggered by the internal unsaturated fluid flow process in unsaturated soils. Copyright © 2016 John Wiley & Sons, Ltd.     

单层不可压缩饱和多孔介质一维瞬态响应精确解

基于Biot理论,考虑惯性、黏滞和机械耦合作用,假定固体颗粒和流体均不可压缩,得到了表面任意竖向荷载作用下单层饱和多孔介质一维瞬态响应的精确解。导出了以固体骨架位移表示的无量纲控制方程,并将边界条件齐次化。求解对应无黏滞耦合作用的特征值问题,得到一组满足齐次边界条件、关于空间坐标的正交函数基。利用变异系数法和基函数的正交性,得到一系列相互解耦的、关于时间的二阶常微分方程及相应的初始条件,并采用状态空间法求解常微分方程,得到位移分量。对整体平衡方程关于空间坐标积分,根据边界条件可确定总应力,并进而求得孔隙压力。通过算例验证所得解法的正确性     

Numerical analysis of frost effects in porous media. Benefits and limits of the finite element poroelasticity formulation

The aim of this paper is to analyse the performance of a finite element formulation usable for predicting the mechanical consequences of frost effects on porous media. It considers the characteristics of porous media and how the frost action can be assessed. The problem is then separated into two parts: thermal and poromechanical calculations. The constitutive equations developed in the framework of poromechanics are presented and the implementation in a usual finite element poroelasticity formulation based on Zuber's method is adopted. An analysis of the time‐step influence on the convergence rate is given and leads us to propose a simple method in order to obtain objectivity of the finite element response and avoid over‐long calculations. Frost effect simulations are carried out on real porous media (two fired clays) as a case study. Although the experimental behaviour of the porous media subjected to frost action is in accordance with some observations, the calculated strains appear to be overestimated compared with measurements. The problem could be largely attributable to the difficulty of assessing permeability evolution during frost development. Copyright © 2011 John Wiley & Sons, Ltd.     

采用复合单元法模拟裂隙多孔介质变饱和流动

采用复合单元法建立了模拟裂隙多孔介质变饱和流动的数值模型。该模型具有以下特点:裂隙不需要离散成特定单元,而是根据几何位置插入到孔隙基质单元中形成复合单元;在复合单元中,分别建立裂隙流和孔隙基质流的计算方程,二者通过裂隙-基质界面产生联系并整合成复合单元方程;复合单元方程具有和常规有限单元方程相同的格式,因此,可以使用常规有限单元方程的求解技术。采用欠松弛迭代、集中质量矩阵以及自适应时步调节等技术,开发了裂隙多孔介质变饱和流动计算程序。通过模拟一维干土入渗和复杂裂隙含水层内的流动问题,验证了该模型的合理性和适用性。模拟结果为进一步认识非饱和裂隙含水层地下水流动特性提供了理论依据。     

Natural convection of compressible and incompressible gases in undeformable porous media under cold climate conditions

A numerical model for convective heat and mass transport of compressible or incompressible gas flows with soil-water phase change is presented. In general, the gaseous phase is considered as compressible and the model accounts for adiabatic processes of compression heating and expansion cooling. The inherently compressible gaseous phase may nevertheless be considered as incompressible by adopting the Oberbeck–Boussinesq approximations. The numerical method used to solve the equations that describe natural convection is based on a Galerkin finite element formulation with adaptive mesh refinement and dynamic time step control. As most existing numerical studies have focused on the behavior of incompressible fluids, model substantiation examines the influence of fluid compressibility on two-widely used benchmarks of steady-state convective heat and mass transport. The relative importance of the effect of pressure-compressibility cooling is shown to increase as the thermal gradient approaches the magnitude of the adiabatic gradient. From these results, it may be concluded that pore-air compressibility cannot be neglected in medium to large-sized enclosures at small temperature differentials. After demonstrating its ability to solve fairly complex transient problems, the model is used to further our understanding of the thermal behavior of the toe drain at the LA2-BSU dam in the province of Quebec, Canada.     

Three‐dimensional nonlinear finite element analysis of pile groups in saturated porous media using a new transmitting boundary

The dynamic behaviour of pile groups subjected to an earthquake base shaking is analysed. An analysis is formulated in the time domain and the effects of material nonlinearity of soil, pile–soil–pile kinematic interaction and the superstructure–foundation inertial interaction on seismic response are investigated. Prediction of response of pile group–soil system during a large earthquake requires consideration of various aspects such as the nonlinear and elasto‐plastic behaviour of soil, pore water pressure generation in soil, radiation of energy away from the pile, etc. A fully explicit dynamic finite element scheme is developed for saturated porous media, based on the extension of the original formulation by Biot having solid displacement (u) and relative fluid displacement (w) as primary variables (u–w formulation). All linear relative fluid acceleration terms are included in this formulation. A new three‐dimensional transmitting boundary that was developed in cartesian co‐ordinate system for dynamic response analysis of fluid‐saturated porous media is implemented to avoid wave reflections towards the structure. In contrast to traditional methods, this boundary is able to absorb surface waves as well as body waves. The pile–soil interaction problem is analysed and it is shown that the results from the fully coupled procedure, using the advanced transmitting boundary, compare reasonably well with centrifuge data. Copyright © 2007 John Wiley & Sons, Ltd.     

含液各向异性多孔介质应变局部化分析

工程中的含液多孔介质如饱和或非饱和岩土材料往往具有各向异性特性。采用Rudnicki建立的针对岩土材料的各向异性本构模型,对轴对称压缩试验中的含液多孔介质骨架的各向异性力学行为进行了分析;基于不连续分叉理论,导出了静态非渗流条件下处于轴对称应力状态的含液多孔介质应变局部化发生的临界模量、剪切带方向以及不连续速度矢量的显式表达式,在此基础上计算并讨论了材料参数变化和孔隙液体存在对各向异性多孔介质应变局部化的影响。     

频域内饱和多孔介质的参数反演分析

基于Biot理论,假定固体颗粒和孔隙内流体均不可压缩,建立了以固体骨架位移表示的的控制方程.考虑单层饱和多孔介质在竖向简谐荷载作用下一维动力响应,通过理论推导获得了骨架位移、应力以及孔隙流体压力等物理量的解析表达式.基于饱和土的简谐动力模型试验数据,与所得到的理论解答相结合,将饱和多孔介质材料参数反演问题归结为非线性多峰函数的最优化问题.全局最优解的求解采用了遗传算法和模拟退火算法,并通过试验和数值算例验证了所得材料参数的正确性.     

Numerical manifold method for dynamic nonlinear analysis of saturated porous media

It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd.     

Towards a thermodynamics of immiscible two-phase steady-state flow in porous media

We propose that steady-state two-phase flow in porous media may be described through a formalism closely resembling equilibrium thermodynamics. This leads to a Monte Carlo method that will be highly efficient in studying two-phase flow under steady-state conditions numerically. This work was partially supported by the Norwegian Research Council through grants nos. 154535/432 and 180296/S30.     

A finite element method for localized erosion in porous media with applications to backward piping in levees

This paper presents a computational method able to effectively model both the simultaneous processes typically observed in backward erosion piping, ie, the pipe tip propagation and the conduit cross-section enlargement. The numerical method is based on the novel formulation of a problem of localized erosion along a line propagating in a multidimensional porous medium. In this line, a conduit with evolving transverse size is embedded, which conveys a multiphase flow. The two systems, porous medium and pipe, are bridged by exchange terms of multiphase fluid mass and by a shared fluid pressure field. On the contrary, different fields are considered to describe flows, which are assumed as Darcian in the porous medium and turbulent in the conduit. These two flows drive pipe propagation and enlargement, respectively, as modeled by means of proper erosion kinetic laws. The corresponding numerical formulation is based on the combination between one- and multidimensional finite elements, to model the erosion conduit and the porous medium, respectively. Several simulations are proposed to demonstrate the ability of the proposed approach in reproducing available experimental data of real-scale tests on levees. Our results point out the crucial role played by the combined influence of pipe propagation and enlargement, as well as of three-dimensional (3D) effects. We also assess the mesh independence of the proposed numerical solution, particularly as concerns the calculated pipe propagation history.     

A fracture mapping and extended finite element scheme for coupled deformation and fluid flow in fractured porous media

This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM‐XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum‐based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley & Sons, Ltd.     

井内嵌入同轴多孔与固体圆柱地下水渗流流型分析

对二维无限大多孔介质内单向均匀水平流垂直绕过“固体小圆柱-多孔介质环-水环-多孔介质”复杂四层结构下的流场进行了解析求解。内、外多孔介质区域均采用Brinkman模型,纯流体水环采用Stokes模型,通过耦合界面间的质量、动量守恒关系得到了各区域流函数的通用表达式。在此基础上分析了不同几何参数,不同内、外多孔介质渗透系数情况下,圆柱外绕流的流型变化;着重研究了水环间隙以及内、外多孔介质渗透系数的变化对流型及横向、纵向速度分布的影响。结果表明：外部多孔区流型主要受控于外部渗透系数;水环间隙宽度对水环内速度峰值影响较大;内部渗透系数增加到某一临界值情况下,横截面速度分布从阶梯形变为抛物形,即“穿透”现象。研究结果对有类似结构的地埋管换热器、地下水污染物吸收装置、地下水测速装置等的设计研发有理论指导意义。     

A finite element method for modeling coupled flow and deformation in porous fractured media

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.     

基于图像法的多孔介质双分子反应溶质运移模拟

采用图像分析法确定溶质浓度,以硫酸铜和EDTA二钠作为双分子反应物,在多孔介质模型中开展了不同粒径(1.52.0,2.53.0,3.54.0 mm)和流量(1.0,1.5,2.0 mL/s)下反应性溶质运移实验,探讨了应用不完全混合的对流弥散模型(IM-ADRE)对双分子反应溶质运移的模拟和预测,并进行了参数敏感性分析。结果表明:图像分析法可准确获取多孔介质中显色反应性溶质的浓度,灰度值与浓度的决定系数R²大于0.96;用IM-ADRE模型能够准确预测双分子反应性溶质硫酸铜和EDTA二钠在3种不同多孔介质中的运移过程,误差低于3.71%;实验条件的改变对IM-ADRE模型参数D、m和β₀的影响显著,说明模型参数依赖于环境条件,其变化规律需要根据实际环境条件进一步率定,便于IM-ADRE模型的进一步推广应用。     

多孔介质油水两相k~s~p关系数学模型的实验研究

数学模型是研究相对渗透率与饱和度关系曲线的重要方法。采用自行开发设计的人工平面多孔介质模型,测定了相对渗透率与饱和度的关系曲线。多孔介质选择粒径为0.5~1mm、1~2mm的标准砂,纯净的水为湿润相,用3号苏丹红染色的93#汽油为非湿润相,组成多孔介质油水两相流动系统。采用Van Genuchten and Mualeum(VGM)和Brooks-Corey-Burdine(BCB)两种数学模型计算相对渗透率与饱和度的关系曲线,通过比较两种数学模型计算结果之间和模型计算结果与实测结果的差异以及模型的应用、多相渗流系统自身特征,得出VGM、BCB两种数学模型计算结果符合实际情况,VGM模型应用过程更为简便,但VGM模型具有一定适用条件;在砂性多孔介质中,BCB模型计算相对渗透率与饱和度关系曲线更准确。     

近饱和条件下非饱和多孔介质渗流过程的数值分析

在非饱和多孔介质渗流分析中,近饱和条件下物理模型与数值模型之间的差异会导致数值不稳定问题。为解决这一问题,并保证模拟结果的可靠性,提出了3种方法,并在有限元分析程序U-DYSAC2中分别进行了程序代码的实施。通过数值试验与试验数据的比较,证实了在近饱和条件下土-水特征曲线和水力传导函数的高非线性可引起数值收敛性、稳定性和精度问题,而且在不同条件下含水率和基质吸力的预测结果差异明显。在3种方法中,修正的Van Genuchten模型（MVGM）方法对含水率的预测较为准确,而Line方法对基质吸力的预测较为合理。因此,解决在分析近饱和条件下非饱和多孔介质渗流问题时,为获得接近真实的模拟结果,采用合适的数值方法进行预测是非常关键的。     

三维油藏中应力与渗流的摄动-有限元分析

提出了一个较为实际的石油油藏的三维力学模型。以已有的三维介质中应力与渗流耦合问题的变分原理为基础,用摄动法证明了光油藏厚度变化为小量时,三维问题或简化为平面应变问题,并可采用不同厚度的平面应变单元进行有限元分析,所得到的解即是该三维问题的零阶摄动解。给出了摄动法的推导和有限元格式,计算了一个水驱法进行油田二次开发的算例并给出了计算结果。