ON FLOW IN POROUS MEDIA

渗流是流体在多孔介质中的流动，渗流现象广泛地存在于自然界、工程材料、动物、植物中。多孔介质种类繁多，包括岩石(含各类矿藏)、土壤、生物材料和人工多孔介质材料等。渗流理论已经成为人类开发地下水、地热、石油、天然气、煤炭与煤层气等诸多地下资源的重要理论基础。本文从渗流的基本概念、渗流的分类、渗流的影响因素、渗流的特征以及渗流的研究意义等方面进行了阐述。     

低渗透多孔介质中的非线性渗流理论简

文中论述了低渗透性多孔介质中非线性渗流理论的几个问题,阐明了渗流流体的性质,指出了多孔介质对流体通过的选择性,提出了新的非线性渗流方程,用实验资料对其进行了验证,分析了该方程演变功能,表明它可以描述各种渗流规律.该方程的各项参数都可从实验中直接得到,应用方便,并且参数的物理意义明确.     

Vibration-isolation and damping properties of fluid-saturated porous solids

This paper aims at analyzing the vibration-isolation and damping properties of fluid-saturated porous media. Considerations are based on examining an elastic porous cylinder with viscous fluid. Free and forced vibrations of the cylinder with a concentrated mass representing the mass of a technical device resting on it are studied. Graphs illustrating the dependence of the amplitude multiplication factor and the force transmission coefficient are presented.     

An overview on nonlinear porous flow in low permeability porous media

This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy's linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir, is established. This model can describe various patterns of porous flow, as Darcy's linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.     

渗流力学研究的现状和发展趋势

渗流力学在能源、环境、水利、岩土、交通、生物等工程领域有广泛的应用，渗流力学经过约一个半世纪的发展，已经积累了相当多的成果。随着现代科学的发展以及生产实践需求的不断提高，渗流力学仍然有进一步完善和发展的广阔空间。本文简述了水利、环境、能源工程和生物学中的渗流力学问题，扼要概括了渗流力学理论研究的现状，并指出渗流力学在多孔介质描述、裂缝型介质渗流、多相多组分渗流、物理化学渗流、非线性渗流、非饱和渗流、微观渗流、渗流模拟等理论及相关方法和测试技术等方面的发展趋势。     

Phase Transitions in Gas- and Liquid-Saturated Porous Solids

Phase transitions in porous media consisting of a porous solid filled with liquid and gas constituents can occur, for example, due to freezing and drying processes. Although these phenomena are of certain relevance in soil mechanics and material sciences, a general thermo-dynamical theory is still awaited. Based on recent findings in the porous media theory, this paper is concerned with the development of thermodynamic restrictions for the constitutive relations of an elastic, incompressible porous solid, filled with an incompressible liquid and a compressible gas. The investigations show that mass conversions are related to the differences of the chemical potentials and energy transitions to the differences of temperatures. Thus, they confirm well-known results in classical thermodynamics of gases.     

基于CFD模拟的翅片管束多孔介质模型建立方法及流场模拟

为了利用多孔介质模型对翅片管束外流场进行计算,首先利用实体模型计算了局部管束的流场特性以获得多孔介质参数,在验证了多孔介质模型的准确性后,使用该模型对大尺度管束的流场特性进行了计算。结果表明:可以采用多孔介质模型对翅片管束进行简化计算,局部计算得到的多孔介质参数可以应用到增大长度、高度和宽度后的大尺度同型管束区域计算上,多孔介质模型与实体模型的误差基本在10%以内。     

多孔介质输运性质的分形分析研究进展

首先对多孔介质输运性质的传统实验测量、解析分析和数值模拟计算研究进展作了扼要的评述.然后,着重综述采用分形理论和方法研究多孔介质输运性质分析解的理论、方法和所取得的进展.最后,指出采用分形理论和方法有可能解决其它尚未解决的有关多孔介质输运性质的若干课题和方向.      

Nonlinear fluid flow laws for orthotropic porous media

Nonlinear fluid flow laws for orthotropic porous media are written in invariant tensor form. As usual in the theory of fluid flow through porous media [1, 2], the equations contain the flow velocity up to the second power. Expressions that determine the nonlinear resistances to fluid flow are presented and it is shown that, on going over from linear to nonlinear flow laws, the asymmetry effect may manifest itself, that is, the fluid flow characteristics may differ along the same straight line in the positive and negative directions. It is shown that, as compared with the linear fluid flow law for orthotropic media when for three symmetry groups a single flow law is sufficient, in nonlinear laws the anisotropy manifestations are much more variable and each symmetry group must be described by specific equations. A system of laboratory measurements for finding the nonlinear flow characteristics for orthotropic porous media is considered.     

多孔介质的流变模型研究

多孔介质在应力作用下具有弹性变形和黏性变形两种完全不同的变形机制，多孔介质的弹性变形是由介质的本体有效力所致，而黏性变表则是由介质的结构有效应力所致。多孔介质的总变形为弹性变形和黏性变形的叠加，计算多孔介质总应变量的流变模型必须同时采用本体有效应力和结构有效应力（双重有效应力），而传统的流变模型仅采用Terzaghi有效应力是不妥当的，它无法正确描述多孔的应变行为，采用了双重有效应力之后的流变模型，通过调节介质特性参数，可以拟合介质的实际应变行为，并且把多孔介质与普通固体联系了起来。     

Thermodynamic Automaton Simulations of Fluid Flow and Diffusion in Porous Media

A thermodynamic automaton model of fluid flow in porous media is presented. The model is a nonrelativistic version of a Lorentz invariant lattice gas model constructed by Udey et al. (1998). In the previous model it was shown that the energy momentum tensor and the relativistic Boltzman equation can be rigorously derived from the collision and propagation rules. In the present paper we demonstrate that this nonrelativistic model can be used to accurately simulate well known results involving single phase flow and diffusion in porous media. The simulation results show that (1) one-phase flow simulations in porous media are consistent with Darcy's law; (2) the apparent diffusion coefficient decreases with a decrease in permeability; (3) small scale heterogeneity does not affect diffusion significantly in the cases considered.     

关于渗流中流线不封闭的特性和条件

本文对于流体在多孔介质中流动的特性进行理论研究和数值计算，提出两个关于渗流中流线不封闭的特性和条件，得到了在一般工程实际情况中的多孔介质区域内部不存在封闭流线的结论。本文以突变截面圆管中不可压缩渗流为算例，利用半人工瞬变方法进行数值计算，得到流体在充满多孔介质的突扩截面圆管和突缩截面圆管中流动时关于速度分布和压力分布的结果。由此表明，在突变截面附近的渗流区域中不存在回流和分离流，也不存在封闭的流线。渗流的这些流动特性不同于在无多孔介质的空间区域中的流动特性。     

裂缝角度对含气多孔介质热流耦合特性影响研究

为研究含裂缝多孔介质内部流体的流动和传热特性,通过热-流耦合传热实验测试对5种裂缝倾角(0°,15°,30°,150°,165°)多孔介质进行了研究。结果表明:裂缝角度γ=0°的多孔介质达到稳态需要时间最长,约为720min,传热速率最慢,适用于削弱传热应用;裂缝角度旋转方向对多孔介质内高低温流体的混合能力影响较大,裂缝逆时针旋转时,其传热速率大于裂缝顺时针旋转时传热速率,适用于强化传热应用。     

不可压饱和粘弹性多孔介质固结问题的Gurtin型变分原理

基于多孔介质理论,在固相骨架和孔隙流体微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,利用卷积积分的性质,本文首先建立了以固相骨架位移、孔隙流体相对速度和孔隙流体压力为宗量的流体饱和粘弹性多孔介质固结问题的一个Gurtin型变分原理.其次,利用Lagrange乘子法解除相关的变分约束条件,建立了流体饱和粘弹性多孔介质固结问题的若干广义Gurtin型变分原理,包括第三类的Hu-Washizu型变分原理.最后,简单讨论了等价初边值问题的相应变分原理.这些Gurtin型变分原理的建立不仅丰富了饱和粘弹性多孔介质的相关理论,而且为相关数值模拟方法,如有限元法、无网格法等的建立奠定了理论基础.     

多孔介质自发渗吸研究进展

自发渗吸是发生在多孔介质里的一种常见自然现象, 存在于众多工程应用和自然科学领域, 多孔介质 中自发渗吸的基本静力学和动力学问题已成为当前国际研究的热点课题之一. 本文综述了传统理论研究中的 Lucas{Washburn(LW) 模型, Terzaghi 模型, Handy 模型, Mattax 和Kyte 无因次时间标度模型, Aronofsky 归 一化采收率标度模型以及近十年最新研究进展, 分析了渗吸机理判别参数研究, 简述了数值模拟研究及渗吸率 影响机理的实验研究现状, 总结了基于分形理论研究多孔介质自发渗吸的最新进展, 并展望了多孔介质以及裂 缝性双重多孔介质中牛顿流体和非牛顿流体自发渗吸研究的方向和课题.      

Upscaling Forchheimer law

We investigate the high velocity flow in heterogeneous porous media. The model is obtained by upscaling the flow at the heterogeneity scale where the Forchheimer law is assumed to be valid. We use the method of multiple scale expansions, which gives rigorously the macroscopic behaviour without any prerequisite on the form of the macroscopic equations. We show that Forchheimer law does not generally survive upscaling. The macroscopic flow law is strongly non-linear and anisotropic. A 2-point Padé approximation of the flow law in the form of a Forchheimer law is given. However, this approximation is generally poor. These results are illustrated in two particular cases: a layered composite porous media and a composite constituted by a square array of circular porous inclusions embedded in a porous matrix. We show that non-linearities are sources of anisotropy.     

Review on Scale Dependent Characterization of the Microstructure of Porous Media

The paper discusses local porosity theory and its relation with other geometric characterization methods for porous media such as correlation functions and contact distributions. Special emphasis is placed on the charcterization of geometric observables through Hadwigers theorem in stochastic geometry. The four basic Minkowski functionals are introduced into local porosity theory, and for the first time a relationship is established between the Euler characteristic and the local percolation probabilities. Local porosity distributions and local percolation probabilities provide a scale dependent characterization of the microstructure of porous media that can be used in an effective medium approach to predict transport.     

On Determining the Percolation Reynolds Number and the Characteristic Linear Dimension for Ideal and Fictitious Porous Media

Various versions of representations of the percolation Reynolds number for porous media with isotropic and anisotropic flow properties are considered. The formulas are derived and the variants are analyzed with reference to model porous media with a periodic microstructure formed by systems of capillaries and packings consisting of spheres of constant diameter (ideal and fictitious porous media, respectively). A generalization of the Kozeny formula is given for determining the capillary diameter in an ideal porous medium equivalent to a fictitious medium with respect to permeability and porosity and it is shown that the capillary diameter is nonuniquely determined. Relations for recalculating values of the Reynolds number determined by means of formulas proposed earlier are given and it is shown that taking the microstructure of porous media into account, as proposed in [1, 2], makes it possible to explain the large scatter of the numerical values of the Reynolds number in processing the experimental data.     

基于蒙特卡罗随机有限元方法的随机多孔介质内流体自然对流不确定性研究

为分析孔隙率不确定性对多孔介质方腔内自然对流换热的影响,发展了一种基于KL（Karhunen-Loeve展开）-蒙特卡罗随机有限元算法的随机多孔介质内自然对流不确定性分析数理模型及有限元数值模拟程序框架。通过K-L展开及基于拉丁抽样法生成多孔介质孔隙率随机实现,并耦合多孔介质自然对流有限元程序,进行随机多孔介质内自然对流传热数值模拟,得出了多孔介质内流场与温度场平均值与标准偏差,并分析了孔隙率不确定性条件下Da数对Nu数的影响。结果表明,孔隙率不确定性对多孔介质方腔内自然对流有重要影响。随机多孔介质内流场及温度场与确定性条件下的流场及温度场存在一定偏差,Nu数标准偏差随着Da的增大先增大后减小。     

Macroscale Thermodynamics and the Chemical Potential for Swelling Porous Media

The thermodynamical relations for a two-phase, N-constituent, swelling porous medium are derived using a hybridization of averaging and the mixture-theoretic approach of Bowen. Examples of such media include 2-1 lattice clays and lyophilic polymers. A novel, scalar definition for the macroscale chemical potential for porous media is introduced, and it is shown how the properties of this chemical potential can be derived by slightly expanding the usual Coleman and Noll approach for exploiting the entropy inequality to obtain near-equilibrium results. The relationship between this novel scalar chemical potential and the tensorial chemical potential of Bowen is discussed. The tensorial chemical potential may be discontinuous between the solid and fluid phases at equilibrium; a result in clear contrast to Gibbsian theories. It is shown that the macroscopic scalar chemical potential is completely analogous with the Gibbsian chemical potential. The relation between the two potentials is illustrated in three examples.