饱和多孔介质中动力渗流耦合分析的Biot-Cosserat连续体模型与应变局部化有限元模拟

提出了适用于饱和多孔介质中应变局部化分析及动力渗流耦合分析的Biot-Cosserat连续体模型。基于饱和多孔介质动力渗流耦合分析的Biot理论,将固体骨架看作Cosserat连续体,并考虑旋转惯性,建立了饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型。基于Galerkin加权余量法,对所发展的模型推导了以固体骨架广义位移(包含旋转)及孔隙水压力为基本未知量的有限元公式。利用所发展的数值模型,对包含压力相关弹塑性固体骨架材料的饱和多孔介质进行了动力渗流耦合分析与应变局部化有限元模拟,结果表明,所发展的两相饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型能保持饱和两相介质应变局部化问题的适定性及模拟饱和多孔介质中由应变软化引起的应变局部化现象的有效性。     

不可压渗流驱动问题混合有限元/间断有限元耦合格式的误差分析

多孔介质中渗流驱动问题与环境污染和油藏开采等问题密切相关,是当今的研究热点.对具有分子扩散和弥散效应的不可压渗流驱动问题,本文用混合有限元/间断有限元耦合格式来求解,即用混合有限元方法求解压力方程,用对称内罚间断有限元方法逼近浓度方程.运用比剪切算子更为便捷的归纳假设和插值投影,导出了先验hp误差估计.     

低渗透水平井流入动态研究

针对低渗透油田储层的基本特征及开发现状,结合国内外水平井实践,对水平井开发低渗透油藏做深入研究。利用流入动态曲线反映油藏向井的供油(液)能力,通过对低渗透水平井流入动态研究预测油气井产量。对低渗透水平油井的流入动态进行了研究。介绍了常用的溶解气驱IPR方程,并以刘想平方程为基础建立了油、气、水三相IPR模型;同时针对低渗透多孔介质中,渗流不再符合线性达西定律,而具有启动压力梯度的特点分析了水平井的流入动态。     

各向异性双重孔隙介质的应力与油水两相渗流耦合理论模型

针对天然裂缝性油藏的特性,建立了描述双重孔隙介质中油水两相流体流动特性的流固耦合理论模型。该模型不仅考虑了渗透率的各向异性,而且考虑了岩石固体骨架变形的各向异性。渗流方程是依据双重孔隙的概念建立起来的,而固体骨架变形控制方程则是根据Biot 的等温、线性孔隙弹性理论建立起来的。同时,给出了横向各向同性及结构各向异性、固体材料各向同性时的双重孔隙介质的应力与油水两相渗流耦合理论模型。对该模型进行了简化,并将其简化后模型与单相流的各项同性和各向异性双重孔隙介质流固耦合理论模型进行了比较。     

基于ANSYS软件对SiCp/A1(ZL102)复合材料铸造渗流过程多孔介质结构的有限元处理

采用统计平均的方法描述多孔介质微观结构的影响,根据多孔介质的连续介质模型及有限元方法对多孔介质内的铝液的渗流行为进行数值模拟,给出了可视化的瞬态温度场分布,并且初步预测了不同时刻的渗流有效高度.     

一类具有非线性边界流的双重退化抛物型方程的临界指标

本文研究了一类具有非线性边界流的双重退化抛物型方程,该方程可用来描述多孔介质中的非牛顿渗流现象,可以描述气体或液体在多孔介质中的流动,具有广泛的实际背景.通过构造不同的自相似上、下解得到了方程的临界指标,即整体存在指标po和临界Fujita指标pc.主要结果为:当0＜p≤po时,方程存在整体解;当po＜p＜pc时,方程...     

离心渗铸工艺中铝熔体在SiC多孔介质内的渗流传热过程特征及最弱环损伤模型

针对离心力场中铝熔体在SiC多孔介质内的渗流传热现象,考虑离心力对渗流传热过程的影响,根据局部非热平衡假设建立了多孔介质渗流传热模型。采用全隐格式TDMA算法和第一类迎风差分方法对渗流过程的温度场进行了数值计算。研究分析了不同复合层厚度下离心渗透过程中的流场和温度场瞬态变化规律。计算结果表明,在渗透区域,熔体与SiC颗粒存在着一定温差,而在渗透前沿,这种温差相对较大。渗流速度变化存在两个十分明显的阶段,渗流速度较高且急剧下降的初始渗透阶段以及渗流速度相当平稳的后续阶段。渗流速度的这种瞬态变化规律主要是多孔介质内流体流动与离心压力相互作用的结果。渗透初期形成的紊流状态,是导致熔体卷吸空气、使复合材料内部形成气孔的主要原因之一。选择合适的工艺参数对于确保铸件质量是十分关键的。     

饱和多孔介质不同动力耦合形式数值分析EI北大核心CSCD

Biot饱和多孔介质波动行为的数值模拟在众多工程领域中具有重要的意义和作用,由于固相与液相耦合方程难以解耦,使该问题的数值模拟难度较大。针对饱和多孔介质中部分耦合u-p及全耦合u-p-U方程形式的特征,推导了相应动力耦合控制方程的有限元弱形式,并引入不同耦合形式的饱和多孔介质时域黏性边界,综合利用Comsol Multiphysics提供的偏微分方程应用模式进行二次开发求解,通过一维饱和多孔介质动力响应的解析解和数值解验证了模型求解技术的合理性和可行性,基于u-p-U耦合形式探讨了冲击荷载作用下干砂饱和砂地基动力固结中应力波传播特性。计算结果表明慢纵波对动力固结的影响比较显著,合理的冲击荷载持续时间有利于固结效果的改善。     

饱和多孔介质不同动力耦合形式数值分析

Biot饱和多孔介质波动行为的数值模拟在众多工程领域中具有重要的意义和作用,由于固相与液相耦合方程难以解耦,使该问题的数值模拟难度较大。针对饱和多孔介质中部分耦合u-p及全耦合u-p-U方程形式的特征,推导了相应动力耦合控制方程的有限元弱形式,并引入不同耦合形式的饱和多孔介质时域黏性边界,综合利用Comsol Multiphysics提供的偏微分方程应用模式进行二次开发求解,通过一维饱和多孔介质动力响应的解析解和数值解验证了模型求解技术的合理性和可行性,基于u-p-U耦合形式探讨了冲击荷载作用下干砂饱和砂地基动力固结中应力波传播特性。计算结果表明慢纵波对动力固结的影响比较显著,合理的冲击荷载持续时间有利于固结效果的改善。     

高温熟料非稳态非热平衡渗流换热模型

回转窑卸入篦冷机的高温水泥熟料为红热半透明的多孔介质,其复杂的气固换热机理给篦冷机的工艺改进带来较大难度。针对这一问题,将高温红热颗粒等效为光学厚介质,推导了一种高温熟料颗粒间传导与辐射综合换热系数,基于渗流力学与传热学理论,建立了考虑高温熟料颗粒间热辐射效应的水泥熟料非稳态非热平衡渗流换热模型。通过对所建模型进行求解,得到了料层内熟料温度与气体温度的分布规律,比较了不同区域冷却速率的差异,获得了辐射传热因素对料层温度分布的影响。     

Hydrodynamic permeability of membranes built up by spherical particles covered by porous shells: effect of stress jump condition

This paper concerns the flow of an incompressible, viscous fluid past a porous spherical particle enclosing a solid core, using particle-in-cell method. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid are used. At the fluid–porous interface, the stress jump boundary condition for the tangential stresses along with continuity of normal stress and velocity components are employed. No-slip and impenetrability boundary conditions on the solid spherical core have been used. The hydrodynamic drag force experienced by a porous spherical particle enclosing a solid core and permeability of membrane built up by solid particles with a porous shell are evaluated. It is found that the hydrodynamic drag force and dimensionless hydrodynamic permeability depends not only on the porous shell thickness, particle volume fraction γ and viscosities of porous and fluid medium, but also on the stress jump coefficient. Four known boundary conditions on the hypothetical surface are considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta–Morse’s condition). Some previous results for the hydrodynamic drag force and dimensionless hydrodynamic permeability have been verified.     

Effects of hydrodynamic dispersion on the stability of buoyancy-driven porous media convection in the presence of first order chemical reaction

Carbon dioxide (\(\text {CO}_2\)) sequestration is one of several long-term solutions suggested to decrease the amount of greenhouse gases in the atmosphere. Among different methods of carbon dioxide sequestration, the dissolution of \(\text {CO}_2\) in deep saline aquifers is considered one of the most effective. A significant number of studies are currently being carried out to provide a good understanding of the physical mechanisms involved in this type of storage. The present work focuses on the hydrodynamic part of the problem: setting a model for carbon dioxide-loaded flows in an idealised two-dimensional geometry. It considers the impact of hydrodynamic dispersion in porous media on the development of convective instabilities. Particular attention is paid to the mathematical form of the dispersion tensor widely used in porous media studies, and a new type of bifurcation is investigated. We show that the analysis of bifurcations from the no-flow steady-state solution is a continuous but non-smooth problem, which is a key feature of the analysis. Although the problem is non-smooth, it is also shown that the basic behaviours of linear stability analysis are observed in its solution.     

饱和多孔介质一维瞬态波动问题的解析分析

采用基于混合物理论的多孔介质模型,提出了饱和多孔介质一维动力响应的初边值问题。利用拉氏变换和卷积定理,分别得到了边界自由排水时在任意应力边界条件和任意位移边界条件下瞬态波动过程的解析表达。几种典型的数值算例同时给出了两类边界条件下瞬态波动过程中多孔固体的位移场、应力场和孔隙流体的速度场、压力场。结果表明,饱和多孔介质的波动过程是多孔固体和孔隙流体中以同一速度传播的两种波动的耦合过程,时效特性分析也揭示了饱和多孔介质固有的表观粘弹性性质。     

Gravity wave interaction with porous structures in two-layer fluid

Oblique wave interaction with rectangular porous structures of various configurations in two-layer fluid are analyzed in finite water depth. Wave characteristics within the porous structure are analyzed based on plane wave approximation. Oblique wave scattering by a porous structure of finite width and wave trapping by a porous structure near a wall are studied under small amplitude wave theory. The effectiveness of three types of porous structures—a semi-infinite porous structure, a finite porous structure backed by a rigid wall, and a porous structure with perforated front and rigid back walls—in reflecting and dissipating wave energy are analyzed. The reflection and transmission coefficients for waves in surface and internal modes and the hydrodynamic forces on porous structures of the aforementioned configurations are computed for various physical parameters in two-layer fluid. The eigenfunction expansion method is used to deal with waves past the porous structure in two-layer fluid assuming the associated eigenvalues are distinct. An alternate procedure based on the Green’s function technique is highlighted to deal with cases where the roots of the dispersion relation in the porous medium coalesce. Long wave equations are derived and the dispersion relation is compared with that derived based on small amplitude wave theory. The present study will be of significant importance in the design of various types of coastal structures used in the marine environment for the reflection and dissipation of wave energy.     

Thermal convection and nonlinear effects of a superfluid3He-4He mixture in a porous medium

The convective instability of superfluid³He-⁴He mixtures in porous media is investigated. The general hydrodynamic equations are derived and reduced to a single nonlinear equation for a scalar field. The superfluid mixtures in a porous medium have a constant⁴He chemical potential and behave essentially like a classical fluid in a porous medium. Two-fluid effects are calculated both at the onset of steady convection and the subsequent boundary of instability. The shift of critical Rayleigh number is about 1% or less at the onset of convection, but can be as large as 20% or more at the instability boundary for some regions aroundT 1 K. This two-fluid shift is quite large compared to the corresponding 0.001% shift at the onset of convection for bulk superfluid³He-⁴He mixtures.     

Calculating transport of water from a conduit to the porous matrix by boundary distributed source method

This study presents the development of a suitable numerical method for porous media flow with free and moving boundary (Stefan) problems arising in systems with wetted and unwetted regions of porous media. A non-singular version of the method of fundamental solutions (MFS), termed the boundary distributed source method (BDS), is applied. Darcy flow and homogenous isotropic porous media is assumed. The solution is represented in terms of the fundamental solution of the Laplace equation in two-dimensional Cartesian coordinates. The desingularisation is achieved through boundary distributed sources of the fundamental solution and indirect calculation of the derivatives of the fundamental solution. Respectively, the artificial boundary, characteristic for the classical, singular MFS is not present. The novel BDS is compared with the MFS and the analytical solutions for several numerical examples with excellent agreement. A sensitivity study of the solution, regarding the discretization and the free parameters is performed. The main contributions of the study are the application of the BDS to free and moving boundary problems and the comparison of BDS with MFS for these types of problems. The developed model can be applied to various geohydrological problems.     

Fully coupled hydromechanical multiscale model with microdynamic effects

In this paper, a multiscale finite element framework is developed based on the first‐order homogenization method for fully coupled saturated porous media using an extension of the Hill‐Mandel theory in the presence of microdynamic effects. The multiscale method is employed for the consolidation problem of a 2‐dimensional saturated soil medium generated from the periodic arrangement of circular particles embedded in a square matrix, which is compared with the direct numerical simulation method. The effects of various issues, including the boundary conditions, size effects, particle arrangements, and the integral domain constraints for the microscale boundary value problem, are numerically investigated to illustrate the performance of a representative volume element in the proposed computational homogenization method of fully coupled saturated porous media. This study is aimed to clarify the effect of scale separation and size dependence, and to introduce characteristics of a proper representative volume element in multiscale modeling of saturated porous media.     

Slip condition on the surface of a model fibrous porous medium

We have solved the problem of a creeping two-dimensional shear flow of a viscous incompressible fluid in a flat channel partially filled with a fibrous porous medium, which is modeled by a regular lattice of square cylinders arranged across the flow. The hydrodynamic microscopic velocity fields are determined by numerical methods. The slip coefficient at an effective boundary of the model porous medium is evaluated by macroscopic averaging.     

Linear viscoelastic behavior of porous media with non-uniform saturation

Heterogeneous moisture distribution is usually observed in partially saturated porous media in the form of saturation patches. Such local heterogeneity can significantly influence the macroscopic hydro-mechanical and acoustic behavior of porous media. In this paper, a linear viscoporoelastic model is presented that can be used to address the effects of local fluid flow in the heterogeneously saturated porous media subjected to a small perturbation. The effects of local flow are characterized using the notion of capillary relaxation. The complex, frequency-dependent material properties characterizing the viscoporoelastic behavior are derived. A rigorous procedure is presented to evaluate the material parameters. The proposed model describes well the effects of patchy saturation on the dispersion and attenuation of the compressional wave in partially saturated rocks. It is found that at high saturation the effects of local gas-pressure redistribution are not negligible. A procedure is proposed to determine the capillary relaxation times using acoustic data. The proposed model provides an alternative methodology to characterize the effects of patchy saturation on the acoustic behavior of partially saturated porous media.