Interface In Porous Medium Research Articles

细观渗流的研究与进展

随着渗流力学在各个领域的发展，很多问题需求描述细观的渗流过程例如多孔介质中气液界面的运动。本文基于多孔介质，阐述了经典渗流力学、CT扫描建模技术、逾渗理论、微观渗流仿真模拟技术和拓扑网络模型等若干方法对细观单相渗流与多相渗流的描述与解决方法，并对每种方法的特点进行总结分析，展望了发展前景。 With the development of seepage mechanics in various fields, many problems demand the flow process of micro seepage such as the movement of gas-liquid interface in porous medium. In this paper, the problems and solutions of the single phase and multi phase micro seepage based on the classical seepage mechanics, CT scanning technique, percolation theory, micro seepage simulation technique and topology network model in porous medium are expounded. Also the characteristics of each method were analyzed, and the future development was prospected.

Computational modeling of moving interfaces between fluid and porous medium domains

This paper presents a numerical procedure for computational modeling of moving interfaces between fluid and porous medium domains. To avoid the direct description of the interface boundary conditions at the interface between the fluid and porous medium domains, Darcy’s law is used to simulate fluid flows in both the fluid and porous medium domains. For the purpose of effectively simulating the fluid flow using Darcy’s law, the artificial permeability of the fluid domain is used to establish a permeability ratio between the artificial permeability in the fluid domain and the real permeability in the porous medium domain. Using the proposed permeability ratio, the ratio of fluid pressure gradient in the porous medium domain to that in the fluid domain can be appropriately simulated. To verify the proposed numerical procedure, analytical solutions have been derived for a benchmark problem, which can be simulated using the proposed numerical procedure. Comparison of the numerical solutions with the derived analytical solutions has demonstrated the correctness and accuracy of the proposed numerical procedure. Through applying the proposed numerical procedure to several examples associated with the fluid–porous medium interface propagation problems, the related numerical solutions have demonstrated that: (1) the proposed numerical procedure is capable of simulating the morphological instability of the fluid–porous medium interface in a coupled fluid flow–chemical dissolution system when the system is in a supercritical state; and (2) the permeability ratio can have a considerable effect on the evolved morphologies of the fluid–porous medium interface in the coupled fluid flow–chemical dissolution system.

The Effective Permeability of Cracks and Interfaces in Porous Media

The presence of interfaces in fluid/solid biphasic media is known to strongly influence their behavior both in terms of solid deformation and fluids flow. Mathematical models have traditionally represented these interfaces as lines of no-thickness and whose behavior is given in terms of effective permeabilities whose physical meaning is often disconnected to the microscopic nature of the interface. This article aims to reconcile macroscopic and microscopic interface representations by investigating how the nature of microscopic flows and pressures in the interface can be used to explain its macroscopic behavior. By invoking a proper thickness average operation, we derive an closed form expression that relates the effective interfaces permeabilities to its microscopic properties. In particular, we find that the effective interface permeabilities are strongly influenced by three factors: the ratio of bulk and interface permeabilities, the fluid viscosity, and the physical thickness of the interface.

Three-dimensional evolution of the boundary of a polluted area in a bounded piecewise homogeneous porous material

A mathematical model describing the three-dimensional evolution of a liquid-liquid interface in a piecewise homogeneous porous medium containing impermeable rock and a basin with a free liquid is constructed using the Leibenzon-Muskat model. As an example, the dispersion of pollutants from a point source is numerically simulated.

The Simulation Study on 3D Gas Flow Field and Structure Improvement with Tower Continuous Vacuum Dryer

The 3D gas flow field, including the gas pressure and gas velocity was studied by computer fluid dynamics simulation (CFD). The tower continuous vacuum dryer’s structure was improved and the pumping gas sketch was also optimized. The model was resoled by standard turbulence model. The porous medium zone was adopted to the material zone. The Darcy law, Ergun equation and porous medium interface jump boundary condition was applied. The effect of the drying intensity, vacuum pumping pipes setting and vacuum degree of gas outlet was analyzed. The result shows that the pressure of gas outlet should be maintained lower at 8000 Pa, and the pressure of grain inlet and outlet should be maintained at 9000 Pa. The vacuum pumping pipes should be set at the bottom of last drying stage of the drying room in order to improve the gas flowing direction, and to improve vacuum performance. The pressure and velocity of gas along height of dryer is not the main effect factor of drying quality. On the top of each drying stage of the vacuum dryer, two horny pumping pipelines were set. It has good velocity uniformity, but more simple compared with three horny pumping pipelines.

Steady and Unsteady Heat Transfer in a Channel Partially Filled with Porous Media Under Thermal Non-Equilibrium Condition

Steady and pulsatile flow and heat transfer in a channel lined with two porous layers subject to constant wall heat flux under local thermal non-equilibrium (LTNE) condition is numerically investigated. To do this, a physical boundary condition in the interface of porous media and clear region of the channel is derived. The objective of this work is, first, to assess the effects of local solid-to-fluid heat transfer (a criterion indicating on departure from local thermal equilibrium (LTE) condition), solid-to-fluid thermal conductivity ratio and porous layer thickness on convective heat transfer in steady condition inside a channel partially filled with porous media; second, to examine the impact of pulsatile flow on heat transfer in the same channel. The effects of LTNE condition and thermal conductivity ratio in pulsatile flow are also briefly discussed. It is observed that Nusselt number inside the channel increases when the problem is tending to LTE condition. Therefore, careless consideration of LTE may lead to overestimation of heat transfer. Solid-to-fluid thermal conductivity ratio is also shown to enhance heat transfer in constant porous media thickness. It is also revealed that an increase in the amplitude of pulsation may result in enhancement of Nusselt number, while Nusselt number has a minimum in a certain frequency for each value of amplitude.

Reply to the Comments on “About the Beavers and Joseph Boundary Condition”

1. The respective domains of validity of the investigations in Jager and Mikelic (2009) and in Beavers and Joseph (1967) are different. The claim “We suppose the conditions of the experiment by Beavers and Joseph” in Jager and Mikelic (2009) is not exact, nor was exact “We assume the situation of the experiment by Beavers and Joseph” in Jager and Mikelic (2000). In Beavers and Joseph (1967), the experiments which support the BJBC are conducted for heights h of the “free” fluid channel of the order of magnitude of the pore size √ k, see Figure 4, where σ = h/√k < 10 (σ = b/ < 10 in Jager and Mikelic notations). Beavers and Joseph call our attention to this important point: “...for values of σ near √ 2 the average size of the individual pores within the material is at least equal to the height of the channel....” Therefore, there is no separation of scales between the pores and the channel height, b = O( ), in the experiments of Beavers and Joseph. Whereas the analysis by W. Jager and A. Mikelic is conducted thanks to a separation of scales, b/ 1, a necessary assumption for the validity of their analysis. It results that presenting their results so as to support the BJBC is misleading. 2. What are the consequences of the absence of separation of scales, b = O( ), in the Beavers and Joseph experiments? These consequences are analyzed in Auriault (2010). Equivalent macroscopic models do not exist. A macroscopic boundary condition like the BJBC is not possible. Fluid–porous medium interface averages are meaningless. W. Jager and A. Mikelic demonstrate that the shear stress on the interface in the free fluid is equal to the surface average of the shear stress in the pore fluid when b/ 1; this relation is not physically admissible when b = O( ). 3. What are W. Jager and A. Mikelic demonstrating in their work (2009)? They rigorously show that in the presence of a separation of scales, b/ 1, the boundary condition

Instability in gravity-driven flow over uneven permeable surfaces

Abstract We develop a theoretical model for inclined free-surface flow over a porous surface exhibiting periodic undulations. The effect of bottom permeability is incorporated by imposing a slip condition that accounts for the nonplanar geometry of the fluid–porous medium interface. Under the assumption of shallow flow, equations of motion accounting for inertial effects are obtained by retaining in the Navier-Stokes equations terms that are up to second-order with respect to a small shallowness parameter. The explicit dependence on the cross-stream coordinate is eliminated from these equations by means of a weighted residual procedure. A linear stability analysis of the steady flow is performed in connection with Floquet–Bloch theory. The results predict that bottom permeability has a destabilizing influence on the flow. A physical explanation has been proposed which involves examining how permeability affects the steady-state flow. Conclusions are drawn regarding the combined effect of the surface tension of the fluid and the parameters describing the bottom surface including permeability, inclination and the amplitude and wavelength of the undulations that generate the bottom topography. A numerical scheme for solving the fully nonlinear governing equations is also outlined. The instability of particular steady flows is determined by conducting nonlinear simulations of the temporal evolution of the flow and comparisons are made with the predictions from the linear analysis. Comparisons with existing experimental data are also included.

Modeling Acoustic Properties of the Fluid-Fluid Interface in Porous Medium

The purpose of this study is to present mathematical modeling of the acoustic properties of fluid-fluid interface in porous medium in order to to identify fluid-fluid interfaces according to their different acoustic properties. Biot's theory of acoustic wave’s propagation inhomogenous porous medium is used to calculate reflection and transmission coefficients of an interface in the porous medium. It is found that these coefficients are sensitive to the frequency and the angle of the incident wave, which is regarded as the significant acoustic property of fluid-fluid interfaces an d of discontinuities of the porous medium. Acoustic properties of general fluid-fluid interfaces or porous medium discontinuities are presented as series of plots of coefficient magnitude versus incident frequency or angle. It is shown that there is significant acoustic difference between a fluid-fluid interface and a discontinuity of the porous medium, which can be used to identify a fluid-fluid interface. Here, methods are designed to locate, identify a fluid-fluid interface, and measure its shape, using reflection and/or transmission of waves.

PIV measurements of flow through a model porous medium with varying boundary conditions

This paper reports an experimental investigation of pressure-driven flow through models of porous media. Each model porous medium is a square array of circular acrylic rods oriented across the flow in a rectangular channel. The solid volume fraction φ of the arrays ranged from 0.01 to 0.49. Three boundary conditions were studied. In the first boundary condition, the model porous medium was installed on the lower wall of the channel only and was bounded by a free zone. In the second and third boundary conditions, porous media of equal and unequal φ were arranged on the lower and upper channel walls so that the two media touched (second boundary condition), and did not touch (third boundary condition). Using water as the working fluid, the Reynolds number was kept low so that inertia was not a factor. Particle image velocimetry was used to obtain detailed velocity measurements in the streamwise-transverse plane of the test section. The velocity data were used to study the effects of φ and the different boundary conditions on the flow through and over the porous medium, and at the interface. For the first boundary condition, it was observed that at φ = 0.22, flow inside the porous medium was essentially zero, and the slip velocity at the porous medium and free zone interface decayed with permeability. In the second and third boundary conditions, flow communication between the porous media was observed to be dependent on the combinations of φ used, and the trends of the slip velocities at the interface between the two porous media obtained for that boundary condition were indicative of complicated interfacial flow.

Infiltration time and imprint shape of a sessile droplet imbibing porous medium

The infiltration of a sessile droplet into a homogeneous porous medium for a constant droplet base radius case is solved numerically, where the porous medium is represented as a capillary network consisting of pores and throats. For a homogeneous medium, the network is built of the spherical pores of constant radius, and the cylindrical throats of constant radius and height. Having such defined network, the droplet imbibes porous medium in a single-phase flow for which the free interface in porous medium is smooth, and the liquid phase permeability and the capillary pressure are constant. Using the numerical solution we carry out the parametric study in which: (i) liquid viscosity and surface tension, (ii) droplet volume and base radius, and (iii) porous medium porosity and permeability are varied. The droplet infiltration time, and the imprint shape that is given with two spheroid half-axes are calculated. The dimensionless analysis is utilized to correlate the droplet infiltration parameters from which master curves for the droplet infiltration time and the droplet imprint shape are obtained. Using the infiltration time correlation, both numerical and experimental results show a linear behavior.

A gray lattice Boltzmann model for power-law fluid and its application in the study of slip velocity at porous interface

A gray lattice Boltzmann model (LBM) for the simulation of power-law fluid through porous media is proposed in this paper. The constitutive equation of power-law fluid is introduced into the model by relating the relaxation time of the original gray LBM to the local shear rate, which is calculated using a new scheme to avoid dealing with the derivative of the velocity. The model is validated by simulating the Poiseuille flow of power-law fluid between two infinite parallel plates filled with homogeneous porous media. When the solid volume fraction n s ( x ) = 0, i.e. the flow degenerates into free flow of power-law fluid (no solid matrix), and when the solid volume fraction n s ( x ) > 0, the numerical results agree well with the theoretical predictions. Darcy's law of power-law fluid through the homogeneous porous media is confirmed by our numerical results. A power-relation between the drag force induced by the porous matrix and the particle distribution functions is found. Using this model, the slip velocity of power-law fluid at the interface of porous media is studied. The results indicate that the slip velocity of power-law fluid at the porous interface increases as the power index increases for a given porous medium, and increases as the porosity of the porous media increases for a given power-law fluid.

Fluid flow simulation at open–porous medium interface using the lattice Boltzmann method

AbstractThe present study investigates, using the lattice Boltzmann method, the influence on the flow of the boundary condition at the open and porous medium interface for a two‐dimensional channel with half of the channel filled with a random porous medium. By simulating the fluid flow at pore level, the proposed macroscopic hydrodynamic boundary conditions are evaluated; correlations for the empirical constant in one of the most widely used models are also presented. The predicted values for the flow rate are in overall agreement with the previously published values. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Some Fundamental Observations on the Diesel Jet Destruction and Spatial Distribution in Highly Porous Structures

The article presents results of experimental investigations of common-rail Diesel jet impingement on highly porous, open cell structures. A model describing characteristic phases of Diesel jet interaction with a porous structure is presented in the article. Phase A represents outlet from the nozzle and free jet formation; phase B contains jet interaction with the porous medium interface; phase C relates to liquid distribution throughout the porous medium volume; and phase D describes liquid leaving the porous medium volume. Phases B and D can significantly be reduced or eliminated owing to the pore density, impingement velocity, and porous medium thickness. Special attention is focused on the spatial distribution of the jet throughout the porous medium volume, giving rise to a very effective homogenization effect, and under hot conditions, also for vaporization of liquid. A multijet splitting has been defined to explain destruction and spatial distribution of a free jet momentum inside the porous medium structure. The effect of injection parameters (especially injection pressure) and pore density (pore size) is also investigated in this article.

Rayleigh-Taylor instability of an interface in a nonwettable porous medium

Rayleigh-Taylor instability of an interface in a nonwettable porous medium

Fluid–fluid interface and equivalent impedance plane

In the domain of outdoors sound propagation, the prediction of the monopole field is generally performed by replacing the porous ground by an impedance plane, i.e. a plane boundary with an impedance independent on the angle of incidence. An air–porous medium interface can be replaced by a fluid–fluid interface if the porous frame is motionless. In the present work, comparisons are performed around grazing incidence between the monopole fields above semi-infinite fluid–fluid interfaces, and above impedance planes. It is shown that the monopole field above an impedance plane satisfies an impedance condition which is the same as for a plane field, the ratio of the pressure to the normal velocity on the plane is equal to the constant impedance. It is shown that a similar impedance condition can be satisfied with a good approximation above a semi-infinite fluid–fluid interface. In this case, the impedance is the impedance at the angle of incidence where the pole is located. Some results have been obtained by transposing to acoustics a previous study by Baños of the electromagnetic Zenneck wave. An illustration is given with a semi-infinite porous layer having a small porosity.

Flow through a Tube with an Annual Porous Medium Layer

In this study, the boundary conditions necessary for continuum numerical modeling of flow involving a porous-medium-free-fluid interface are examined. In a region within the free flow adjacent to a porous medium interface, the momentum dispersion persists due to the extension of the spatial velocity fluctuation into the free flow. Consequently, at elevated flow rates, the viscous response to flow of the fluid in the region adjacent to a porous medium has to be modified due to the presence of such spatial velocity fluctuations caused by the porous medium. This influence decays exponentially and extends several pore sizes into the free fluid. Experimental and numerical studies have shown that, at moderately high flow rates, the pressure drop through a porous bed is a quadratic function of the flow discharge rate. For flow through a straight tube containing no porous structures, the pressure drop is linearly related to the flow discharge rate in the laminar regime. However, experimental observation shows that when fluid flows through a tube with an annular porous medium ring, the qualitative trend of the pressure drop is similar to flow through a porous medium. This behavior confirms our expectations on the existence of momentum dispersion. An exponential decay model is proposed to account for the momentum dispersion variation.

Laser-induced surface modes at an air–porous medium interface

A description of the laser-induced wave excitation of surface modes at a fluid–porous medium interface using the Biot model is presented. For the case of a material much heavier than the fluid, the porous frame behaves like an elastic medium in vacuum with a small frequency-dependent structural damping due to the viscous losses. Predictions concerning the shape of the Rayleigh-like wave are given. Measurements show the effect of scattering for ceramics of different pore sizes on this wave.

Dynamics of water and oil at the solid–liquid interface in macroporous media and reservoir rocks

Nuclear magnetic relaxation dispersion experiments at different temperatures, using the magnetic field-cycling method, are reported. These experiments allow the obtaining of original information about water or oil molecular dynamics at solid–liquid interface in porous media, such as grain packing or reservoir rocks. These results on molecular dynamics at the pore surface are of real interest for oil-recovery. The water surface diffusion coefficients are compared to the volume self-diffusion coefficients of water in pores, measured by PGSE method, the latter values being more than an order of magnitude higher than the surface ones. Nous avons obtenu des informations originales sur la dynamique de l’eau et de l’huile aux interfaces solide–liquide de milieux poreux plus ou moins complexes, comme les empilements granulaires et les roches réservoirs. Ces informations proviennent d’expériences de relaxation magnétique nucléaire du proton en champ magnétique cyclé à différentes températures. Ces résultats sur la dynamique des molécules à la surface des pores présentent un réel intérêt dans le domaine de la récupération du pétrole. Des mesures de diffusion par la méthode des gradients de champ pulsés permettent une comparaison entre les coefficients de diffusion en surface et en volume, ces derniers étant de plus d’un ordre de grandeur supérieurs à ceux en surface.

Gravity-elastic deformation and stability of fluid–fluid interface in porous media

A new generalized model is proposed to describe deformations of the mobile interface separating two immiscible weakly compressible fluids in a weakly deformable porous medium. It describes gravity non-equilibrium processes, including evolution of the gravitational instability, and represents a system of parabolic or anti-parabolic equations.