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。     

一种孔隙介质力学模型及在水泥基材料的应用

基于细观力学和断裂力学的基本理论提出一个新的分析模型, 对孔隙介质的力学性能进行了分析. 依据孔隙介质内部孔隙的几何描述和状态参数,如孔隙率、形状、尺度及分布等,通过等效夹杂理论获得孔隙介质的等效本构方程,其最终变量为应力、应变和孔隙的形态参数. 根据断裂理论中材料承受载荷作用下破坏增长过程中的能量守恒,对孔隙介质变形过程中机械能、弹性应变能和载荷提供的势能进行分析, 根据能量守恒定律建立能量守恒方程,其最终变量也为应力、应变和孔隙的形态参数. 根据等效本构方程和能量守恒方程,获得孔隙介质承受载荷作用下的应力应变关系. 最后将该力学模型应用于水泥基材料,计算水泥基材料的力学性能并与文献中的结果进行对比分析,结果显示模型的计算结果准确有效.      

ONSET CONDITION OF STRAIN LOCALIZATION IN MATRIX OF SATURATED POROUS MEDIA

Introduction Strainlocalizationofgeomaterialsisoneofmostpopularfailuretypesinnature,which canbeshowedaslandslidesandmudflowsinmountainousareasunderincessantorheavy raining,especiallythevegetationisseverelydamagedbywoodsharvest;pipingeffect,a typeoflocalfa…     

一维流体饱和粘弹性多孔介质层的动力响应

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论，在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下，建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型，利用Laplace变换，求得了原初边值问题在变换空间中的解析解，并利用Laplace逆变换的Crump数值反演方法，得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应，分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明，与不可压流体饱和弹性多孔介质相同，不可压流体饱和粘弹性多孔介质中亦只存在一个纵波，并且固相骨架的粘性对动力行为有显著的影响。     

Saturated Compressible and Incompressible Porous Solids: Macro- and Micromechanical Approaches

In this paper two complementary approaches are used to describe the mechanical behavior of saturated compressible and incompressible porous solids. The macroscopic investigation is based on the mixture theory, restricted by the volume fraction concept. In the micromechanical approach, a hierarchy of conditionally ensemble averaged fluid and solid phase momentum balance equations are derived for a simple model of quasi-static liquid saturated porous media. The ensemble averaged equations for both the phases agree remarkably well with the macroscopic results. A micromechanical basis for Terzhagi's effective stress concept is presented. In addition, an expression for additional partial solid stress modifying the effective stress principle, to account for deformability of solid materials, is also derived.     

Influence of Nonlinear Local Properties on Effective Transport

The assumption of constant local coefficients is one of the first restrictions in most of the smoothing theories for transport in porous media. In this paper we present a formal analysis of the effects produced by nonconstant local transport coefficients on the nonlinear behavior of the effective transport properties. In particular, we use the volume averaging method to study heat transport in a two-component system considering the local thermal conductivities as analytical functions of the temperature. Within this approach we obtain a general expression for the effective nonlinear thermal conductivity dependence on the averaged temperature gradient. The important result is that the effective conductivity is obtained by a linearly bounded problem (the closure problem), just as if the conductivities were constants, by replacing the constant conductivities by the actual temperature dependent ones. As an example, we model the porous medium as cylindrical inclusions in a periodic array and solve the closure problem for the case of the one-equation model. We analyze the values of the second derivative of the thermal conductivity with respect to the temperature to establish the range where the nonlinear corrections must be considered to correctly describe the effective transport.     

Investigation of Generalized Relative Permeability Coefficients for Electrically Assisted Oil Recovery in Oil Formations

Evaluation of relative permeability coefficients is one of the key steps in reliable simulation of two-phase flow in porous media. An extensive body of work exists on evaluation of these coefficients for two-phase flow under pressure gradient. Oil transport under an applied electrical gradient in porous media is also governed by the principles of two-phase flow, but is less understood. In this paper, relative permeability coefficients under applied electric field are evaluated for a specific case of two- phase fluid flow in water-wet porous media, where the second fluid phase is oil. It is postulated that the viscous drag on the oil phase, exerted by the electro-osmotic flow of the water phase, is responsible for the transport of oil in the absence of a pressure gradient. Reliable prediction of the flow patterns necessitates accurate representation and determination of the relative permeability coefficients under the electrical gradient. The contribution of each phase to the flow is represented mathematically, and the relative permeability coefficients are evaluated through electro-osmotic flow measurements conducted on oil bearing rock cores.     

Stress equivalence principle for saturated porous mediaPrincipe d'équivalence en contrainte pour milieux poreux saturés

The stress equivalence principle for saturated porous media is studied in the plastic domain using a homogenization approach. The skeleton is composed of a micro-isotropic and micro-homogeneous material. The stress localization law in saturated porous media is first obtained. This makes it possible to define an appropriate effective stress tensor in the sense of the stress equivalence principle. The form of the effective stress tensor is examined for two particular yield functions of skeleton material. To cite this article: D. Lydzba, J.-F. Shao, C. R. Mecanique 330 (2002) 297–303.     

Smoothed Particle Hydrodynamics Model for Diffusion through Porous Media

A smoothed particle hydrodynamics (SPH) model is presented for the study of diffusion in spatially periodic porous media. The method of SPH is formulated to solve the convection–diffusion equation for tracer diffusion under steady state and transient conditions. Solutions obtained using SPH are compared with other available solutions and the model is used to calculate diffusion coefficients of spatially periodic porous media for the steady state diffusion problem. Diffusion coefficients are then used to calculate nondimensional diffusivities of the media. The effects of media properties on the values of nondimensional diffusivity are also presented.     

Global behavior of compressible three-phase flow in heterogeneous porous media

The homogenization method is used to analyze the equivalent behavior of a compressible three-phase flow model in heterogeneous porous media with periodic microstructure, including capillary effects. Asymptotic expansions lead to the definition of a global or effective model of an equivalent homogeneous reservoir. The resulting equations are of the same type as the points equations, with effective coefficients. The method allows the determination of these effective coefficients from a knowledge of the geometrical structure of the basic cell and its heterogeneities. Numerical computations to obtain the homogenized coefficients of the entire reservoir have been carried out via a finite element method.     

Macroscopic modelling of transport phenomena in porous media. 2: Applications to mass,momentum and energy transport

In this second paper, the averaging rules presented in Part 1 are employed in order to develop a general macroscopic balance equation and particular equations for mass, mass of a component, momentum and energy, all of a phase in a porous medium domain. These balance equations involve averaged fluxes. Then macroscopic equations are developed for advective, dispersive and diffusive fluxes, all in terms of averaged state variables of the system. These are combined with the macroscopic balance equations to yield field equations that serve as the core of the mathematical models that describe the transport of extensive quantities in a porous medium domain. It is shown that the methodology of averaging leads to a better understanding of the effective stress concept employed in dealing with transport phenomena in deformable porous media.     

裂缝性油藏流固耦合渗流

本文给出了考虑介质变形的双重孔隙介质流固耦合渗流模型,并考虑渗流参数随有效应力而变化的非线性双重孔隙介质流固耦合渗流,在此基础上,本文还推导了双重孔隙介质非线性系数非线性等流固耦合流流计算,并给出了算例。     

Anisotropic porochemoelectroelastic Mandel's problem solutions for applications in reservoir modeling and laboratory characterization

The porochemoelectroelastic analytical models have been used to describe the response of chemically active and electrically charged saturated porous media such as clay soils, shales, and biological tissues. In this work, the porochemoelectroelastic theory is applied to derive the solution for stress, pore pressure, strain, and displacement of the Mandel's problem for orthotropic charged saturated porous media. Numerical examples are given to demonstrate applications of the present solutions to laboratory characterization and hydraulic fracturing analysis of shale formation. The analysis shows that ignoring either the porochemoelectroelastic effects or the material anisotropy can leads to inaccurate prediction of the pore pressure and effective stress distributions in the shale sample or formations during these processes.     

A study on interstitial heat transfer in consolidated and unconsolidated porous media

The Nusselt number expressions are presented for the interstitial heat transfer coefficients for both consolidated and unconsolidated porous media. A boundary layer consideration is made for unconsolidated porous media to derive a general Nusselt number correlation, which shows its square root dependence of the Reynolds number, and matches fairly well with existing experimental data and correlations. As for low density consolidated porous media, rigorous mathematical arguments based on the volume averaging theory are provided, so as to explain the reason why the Reynolds number exponent of the Nusselt number expression for the case of low density consolidated porous media is much greater than that of unconsolidated porous media. The resulting expressions are compared against available experimental data and empirical correlations, and found to be in good accord with them.     

On the use of conventional cocurrent and countercurrent effective permeabilities to estimate the four generalized permeability coefficients which arise in coupled,two-phase flow

In the case of coupled, two-phase flow of fluids in porous media, the governing equations show that there are four independent generalized permeability coefficients which have to be measured separately. In order to specify these four coefficients at a specific saturation, it is necessary to conduct two types of flow experiments. The two types of flow experiments used in this study are cocurrent and countercurrent, steady-state permeability experiments. It is shown that, by taking this approach, it is possible to define the four generalized permeability coefficients in terms of the conventional cocurrent and countercurrent effective permeabilities for each phase. It is demonstrated that a given generalized phase permeability falls about midway between the conventional, cocurrent effective permeability for that phase, and that for the countercurrent flow of the same phase. Moreover, it is suggested that the conventional effective permeability for a given phase can be interpreted as arising out of the effects of two types of viscous drag: that due to the flow of a given phase over the solid surfaces in the porous medium and that due to momentum transfer across the phase 1-phase 2 interfaces in the porous medium. The magnitude of the viscous coupling is significant, contributing at least 15% to the total conventional cocurrent effective permeability for both phases. Finally, it is shown that the nontraditional generalized permeabilities which arise out of viscous coupling effects cannot equal one another, even when the viscosity ratio is unity and the surface tension is zero.     

Renormalization Group Model of Large-Scale Turbulence in Porous Media

Renormalization group methods are used to develop a macroscopic (large-scale) turbulence model for incompressible flow in porous media. The model accounts for the large-distance and large-time behavior of velocity correlations generated by the momentum equation for a randomly stirred, incompressible flow. Utilizing the renormalization procedure, the transport equations for the large-scale modes and expressions for effective transport coefficients are obtained. Expressions for renormalized turbulent viscosity, which accounts for the ultraviolet subrange of the turbulent kinetic energy spectrum, are also obtained.     

非饱和土力学理论的研究进展

回顾了非饱和土有效应力的发展,目前普遍认同采用两个应力变量来建立本构模型,且对基质吸力中毛细和粘吸两部分作用进行了阐述。分析了非饱和土强度问题,包括抗剪强度和抗拉强度。讨论了非饱和土的本构模型问题,包括基于净应力和基质吸力的弹塑性模型,基于Bishop有效应力和基质吸力的水力力学耦合弹塑性模型,以及双孔隙结构的模型。最后探讨了热力学方法和多孔介质理论在非饱和土中的应用,基于多孔介质理论在多场耦合条件下土体复杂的行为是当前值得研究的问题。     

Origin and quantification of coupling between relative permeabilities for two-phase flows in porous media

An extended formulation of Darcy's two-phase law is developed on the basis of Stokes' equations. It leads, through results borrowed from the thermodynamics of irreversible processes, to a matrix of relative permeabilities. Nondiagonal coefficients of this matrix are due to the viscous coupling exerted between fluid phases, while diagonal coefficients represent the contribution of both fluid phases to the total flow, as if they were alone. The coefficients of this matrix, contrary to standard relative permeabilities, do not depend on the boundary conditions imposed on two-phase flow in porous media, such as the flow rate. This formalism is validated by comparison with experimental results from tests of two-phase flow in a square cross-section capillary tube and in porous media. Coupling terms of the matrix are found to be nonnegligible compared to diagonal terms. Relationships between standard relative permeabilities and matrix coefficients are studied and lead to an experimental way to determine the new terms for two-phase flow in porous media.     

Effective stresses — a clarification

Summary Although the phenomenon of effective stresses was known for a long time, the theoretical foundation has remained unsatisfactory until now. Due to new experimental and theoretical findings in the porous media theory, the concept of effective stresses will be reexamined. This is necessary for porous media such as concrete and rock which show at high pressure a significant deviation of the real effective stresses from those calculated with von Terzaghi's concept due to the compressibility of the true material. A second feature of the present paper is the investigation of the effective stress principle in unsaturated porous media.Financial support provided by the Deutsche Forschungsgemeinschaft (DFG) and the Volkswagen-Stiftung is greatly appreciated.     

Monte Carlo Simulations of Observation Time-Dependent Self-Diffusion in Porous Media Models

Observation time-dependent self-diffusion coefficients can be used to obtain microstructural information of porous media. This paper presents two different kinds of Monte Carlo simulations of the self diffusion process of fluids like water in porous systems, a lattice-free method and a lattice-based method. The results for simple porous media model geometries agree well with each other and with published analytical as well as semi-analytical equations. The use of these equations, which are important for the interpretation of Pulsed Field Gradient-Nuclear Magnetic Resonance (PFG-NMR) time-dependent diffusion data with respect to properties of porous media, is discussed.