POROUS MEDIA AND ITS APPLICATIONS IN SCIENCE, ENGINEERING, AND INDUSTRY: 3rd International Conference
1254(2010); http://dx.doi.org/10.1063/1.3453835View Description Hide Description
An analytical Ergun‐type equation for spongelike media is introduced in which developing flow in the short ducts of high porosity metallic foams are accounted for. Instead of the customary procedure of adjusting the empirical coefficients of the Ergun equation to apply to consolidated spongelike media, a pore scale model is introduced and the physical flow conditions remodelled. The pore‐scale linear dimensions are expressed as a function of porosity and the dependence of the form drag coefficient on porosity is incorporated into the model which leads to satisfactory predictions for the inertial coefficient. The model predictions are compared to experimental data from the literature and the satisfactory correspondence provides confidence in the physical adaptability of the model.
1254(2010); http://dx.doi.org/10.1063/1.3453846View Description Hide Description
The modeling of transport phenomena between homogeneous regions requires the derivation of jump boundary conditions. These conditions account for the rapid spatial variations of the transport properties taking place near the dividing surface of the media. There has been a long debate in the literature about whether the discontinuity should apply to the fields (e.g., velocity, temperature, concentration) or to their fluxes. In this work, a general methodology giving rise to jump conditions for both the fields and the fluxes is proposed. This method, besides using a microscopic closure, introduces macroscopic deviation fields that lead to closure schemes for both jump conditions. The methodology is applied first to the diffusive mass transport of a passive solute between a porous medium and a plain fluid and second to the classical problem of momentum transport in a channel partially filled with a porous medium. In both cases, it is required to account for the spatial variations of effective transport coefficients as well as the width and position where the jump conditions must be satisfied. One attractive feature of this methodology is related to its ability to provide the necessary length‐scale constraints under which the jump conditions can be applied.
Permeability in Fixed Beds of Spheres with Size Distributions and Stochastically Generated Porous Media Analogs1254(2010); http://dx.doi.org/10.1063/1.3453803View Description Hide Description
We present a numerical study on the permeability in fixed beds of spheres with binary size distributions. The two particle species were randomly mixed and pressure gradients were applied to generate fluid flow through the particle assembly. The flow was resolved by a lattice Boltzmann method, and the drag forces on the particles were averaged and analyzed. In this study, the total volume fraction of the fixed bed was varied between 0.1 and 0.4, the volume fraction ratio from 1:1 to 1:6, and the particle size ratio from 1:1.5 to 1:4. A drag law for bidisperse fixed beds was established and extensions to fixed beds with polydisperse or continuous size distributions were proposed. If the size distribution is Gaussian, the permeability can be well approximated by that of a monodisperse fixed bed where the size of spheres equals the Sauter mean of the size distribution. If the size distribution is log‐normal, an additional correction that is a function of the first, second and third order moments of the sphere size distribution may be needed. We constructed stochastic 2D and 3D porous media models using angular grains. While the permeability of 2D geometries is much smaller than the prediction of the drag law, the permeability of 3D geometries agrees very well with the prediction.
1254(2010); http://dx.doi.org/10.1063/1.3453814View Description Hide Description
In the context of temporary near‐surface or reversible deep geological storage of intermediate‐level radioactive waste (ILW), most wastes package concepts comprise an external container made of fiber reinforced concrete, receiving several primary waste packages. Self‐irradiation of encapsulating and/or embedding matrices can lead to continuous production of hydrogen which, for obvious safety reasons, must be removed from the container. Previous studies have demonstrated that gas transport depends on two interdependent factors: the water saturation and the microstructural properties of the material. Most techniques used to investigate cement paste porosity require drying of the cement paste prior to the test, which can modify the material microstructure and does not permit the localization of the aqueous phase in the material with various degrees of saturations. This paper focuses on the characterization of pores in cement paste by thermoporometry. The technique, based on the thermodynamic conditions of the melting‐solidification reactions of a condensate inside a porous body, provides a simple method for determining the pore size distribution in saturated cement pastes. The results obtained on cement pastes of different formulations with different types of cement are discussed in term of material microstructure and compared with those obtained by other techniques.
1254(2010); http://dx.doi.org/10.1063/1.3453825View Description Hide Description
A volume averaging theory was exploited to obtain the set of macroscopic energy equations for turbulent flows in low density consolidated porous media. The resulting energy equations along with mathematical modeling reveal 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 such as packed beds. The present expressions obtained on the basis of the volume averaging theory are compared against available experimental data and empirical correlations, and are found to be valid for a wide range of the porosity and Reynolds number.
1254(2010); http://dx.doi.org/10.1063/1.3453834View Description Hide Description
A novel experimental technique to measure the tensile yield stress of fluidized beds of magnetic powders stabilized by an externally applied cross‐flow magnetic field is shown. Basically, the tensile yield stress of the magnetically stabilized bed (MSB) is measured by means of the pressure drop of a gas flow that puts the bed under tension. A first relevant result is that the yield stress depends strongly on the field operation mode. In the H off/on operation mode, the bed was driven to bubbling by imposing a high gas velocity in the absence of magnetic field. Once the gas velocity was decreased below the bubbling onset and the bed was stabilized by the natural cohesive forces alone, the field was applied. The yield stress of the naturally stabilized bed is not essentially changed by application of the field a posteriori (H off/on), which can be attributed to the inability of the field to alter the arrangement of the particles once they were jammed in the stable fluidization state. In the H on/on mode, the field was kept during the whole process of bubbling and stabilization at reduced gas velocities. In this operation mode, the field was the main stabilizing source. In contrast with the H off/on mode results, the yield stress in the H on/on mode was observed to be appreciably increased, which is a consequence of the formation of particle chains as the gas velocity is decreased in the presence of the magnetic field. The influence of other parameters such as particle size distribution reveals also a correlation between the microstructure of the MSB and its yield stress. In analogy with structured magneto‐and electro‐rheological fluids, it is found that the yield stress increases as the average particle size is increased. Moreover, the microstructure of the MSB is relevantly affected by the natural cohesiveness of the powder due to van der Waals forces, which leads to the formation of large‐scale branched chains when the field is applied, thus enhancing the yield stress. Our work shows therefore that it is the microstructure of the MSB as affected by the presence of the magnetic field what essentially determines its yield stress.
1254(2010); http://dx.doi.org/10.1063/1.3453836View Description Hide Description
We present an overview of different aspects of quasi‐static water invasion and evaporation in hydrophobic and partially hydrophobic thin porous layers in relation with the water management problem in PEM fuel cells. Influence of contact angle and injection boundary condition on the water invasion pattern are studied as well as the droplet breakthrough problem. The examples considered in this paper illustrate the problems posed by thin systems, a class of systems for which continuum models are likely to lead to poor predictions.
LINEAR AND NONLINEAR EVOLUTION OF ISOLATED DISTURBANCES IN A GROWING THERMAL BOUNDARY LAYER IN POROUS MEDIA1254(2010); http://dx.doi.org/10.1063/1.3453837View Description Hide Description
We consider the onset and development of convection in a saturated porous half‐space which is initially cold, but where the lower boundary has its temperature raised suddenly to a new uniform level. The resulting thermal boundary layer diffuses upwards and eventually becomes thermoconvectively unstable. Previous works by the present authors have considered in turn linearised theory, the nonlinear development of cells, and the destabilisation of such cells due to subharmonic disturbances. In all three papers it was assumed that the convection pattern is horizontally periodic. In the present paper we relax this restriction by considering how an isolated disturbance develops in time, and this is compared with the horizontally periodic flows. New cells are generated outboard of existing ones so that the convecting region spreads horizontally with time. The effective wavelengths are also found to increase with time, newer cells having larger wavelengths than older ones. We also consider the nonlinear development of these disturbances.
1254(2010); http://dx.doi.org/10.1063/1.3453838View Description Hide Description
The mechanisms and formulations of gas transfer under different conditions in tight porous media are reviewed. The characteristic features of the fundamental flow mechanisms are examined. The essential parameters of relevant modeling approaches are identified and discussed. The present formulations are modified for real gas conditions.
1254(2010); http://dx.doi.org/10.1063/1.3453839View Description Hide Description
Engineering equipment design and environmental impact analyses can benefit from proper and more accurate modeling of turbulent transport in porous media. Several natural and engineering systems can be seen as porous structures through which a working fluid permeates. Turbulence models proposed for such flows depend on the order of application of time and volume average operators. Two methodologies, following the two orders of integration, lead to different governing equations for the statistical quantities. The concept of double‐decomposition is discussed and models are classified in terms of the order of application of time and volume averaging operators, among other peculiarities. For hybrid media, involving both a finite porous structure and a clear flow region, difficulties arise due to the proper mathematical treatment given at the interface. This paper presents and discusses numerical solutions for such hybrid medium.
Transient Mixed Convection In Channels Partially Heated Filled With A Porous Medium In Non‐Local Thermal Equilibrium1254(2010); http://dx.doi.org/10.1063/1.3453840View Description Hide Description
In this paper, reference is made to transient mixed convection in air in a vertical channel with porous media and the two principal flat plates at uniform temperature with adiabatic extensions downstream. The numerical analysis is carried out in transient laminar, two dimensional and in nonlocal thermal equilibrium. The physical domain consists of two parallel plates which form a channel and the adiabatic extensions downstream to the heated walls. Both plates are heated at uniform temperature. The fluid between the two plates is air. The study is carried out employing Brinkman‐Forchheimer‐extended Darcy model and two energy equations. The flow in the channel is assumed to be two‐dimensional, laminar, incompressible. Results in terms of local Nusselt number profiles as a function of mass flow rate, adiabatic extensions length, wall temperatures and channel spacing are presented. Average Nusselt numbers are presented for different values of characteristic parameters.
Downscaling Method from Macroscopic to Microscopic Scale in a Periodic Two‐Dimensional Porous Medium1254(2010); http://dx.doi.org/10.1063/1.3453841View Description Hide Description
A downscaling procedure applied to the steady laminar convective heat transfer through a two‐dimensional homogeneous porous medium is proposed. Local conservation equations are numerically solved. A filtering procedure applied on the computed local fields gives the macroscopic dynamic and thermal behavior of the fluid. Our interest is to reconstruct the fields at microscopic scale in one or more arbitrary sub‐areas of the medium. To this end, numerical simulations of the chosen sub‐areas are carried out using the Trio_U CFD code. Cell‐averaged quantities deduced from the reference volume averages are used as constraints on the solutions. A periodicity assumption is used for velocity and temperature spatial deviation. Reconstructed fields are compared to reference fields.
A macroscopic turbulence model based on a two‐scale analysis for incompressible flows in porous media1254(2010); http://dx.doi.org/10.1063/1.3453842View Description Hide Description
In this paper, turbulent flows in media laden with solid structures are considered. A complete set of macroscopic transport equations is derived by spatially averaging the Reynolds averaged governing equations. A two‐scale analysis highlights energy transfers between macroscopic and sub‐filter mean kinetic energies and turbulent kinetic energy. Additional terms representing solids / fluid interactions and turbulent contributions are modeled. Closure expressions are determined using physical considerations and spatial averaging of microscopic computations. Results of the present model are successfully compared to volume‐averaged reference results coming from fine scale computations. Furthermore, this model is able to provide accurate boundary conditions for clear flow turbulent simulations.
1254(2010); http://dx.doi.org/10.1063/1.3453843View Description Hide Description
The modeling of transport phenomena in the zone of rapid changes between a fluid and a porous medium (i.e., the inter‐region) can be carried out using two distinctive approaches. The first one, generally called the one‐domain approach, describes transport phenomena in the whole fluid‐porous system using averaged macroscopic conservation equations including spatially dependent effective properties. These coefficients reduce to their respective constant values in the homogeneous fluid and porous regions of the system. As an alternative, the two‐domain approach uses the transport equations with constant coefficients in the entire domain of each region, including the zone of drastic changes. To overcome this approximation, jump conditions are introduced but their derivation requires the knowledge of the corresponding one‐domain approach model.
This work deals with the derivation of the governing macroscale equations for convective heat transfer in the inter‐region using a volume averaging procedure. Under a one‐domain formulation, local thermal equilibrium (TE) and non‐local thermal equilibrium (NTE) models are explored. In both cases, the associated closure problems are derived and solved numerically. This allows the computation of the spatial variations of the associated effective transfer properties in the inter‐region. Comparisons of the temperature fields obtained with direct numerical simulations evidence that the TE model is good enough for describing the abrupt heat transfer variations in the inter‐region under certain conditions.
Combined Radiation And Natural Convection Within An Open ended Porous Channel—Validity Of The Rosseland Approximation1254(2010); http://dx.doi.org/10.1063/1.3453844View Description Hide Description
The present work deals with a numerical study of coupled fluid flow and heat transfer by transient natural convection and thermal radiation in a vertical channel opened at both ends and filled with a fluid‐saturated porous medium. The bounding walls of the channel are isothermal and gray.
In the present study we suppose the validity of the Darcy flow model and the local thermal equilibrium assumption. In order to examine the validity of the Rosseland approximation, the radiative term in the energy conservation equation was expressed via two different approaches. The first is based on the resolution of the radiative transfer equation (RTE) in the most general case while the second is based on assuming the Rosseland approximation to be valid.
Numerical results show that the Rosseland approximation is valid only for optically thick media and far from the bounding walls. A parametric study shows that this approximation can be used with high confidence for large Planck number values, for temperature ratios close to 1 and/or for single scattering albedo near or equal to 1.
1254(2010); http://dx.doi.org/10.1063/1.3453845View Description Hide Description
Quantitative models for fluid flow in long sloping warm‐water aquifers with layered structures are formulated. The steady‐state profiles for the temperature and the fluid volume flux parallel to the boundaries, as well as the associated heat transport, in a sloping system subjected to a perpendicular temperature gradient, are calculated for low Rayleigh numbers. The movement of a pollutant injected into such a system is also modelled, with a view to estimating passage times to, and concentrations at, fluid sampling or withdrawal points. The mathematical models are solved partly by analytic means; this allows more efficient examination of the effects of parameter variation.
1254(2010); http://dx.doi.org/10.1063/1.3453794View Description Hide Description
Two‐phase oil‐gas flow in porous media is often encountered during oil production from oil bearing sedimentary rocks. Traditionally such flow is modeled by extending the Darcy’s law to two‐phase flow by employing the concept of saturation dependent relative permeability. This model is remarkably successful as long as the fluid distribution within the porous medium is controlled by capillary forces. Under this condition, the two fluids appear to flow in their own continuous flow channels. This flow description is applicable to most reservoir flow scenarios encountered in light oil production. However, in primary production of heavy oil under solution‐gas drive, this flow model often fails to provide a satisfactory match of the observed behaviour.
Many heavy oil reservoirs under solution gas drive show much higher rate of oil production and final recovery factor than what would be predicted by the theory based on the conventional two‐phase flow model. Different mechanisms have been postulated to explain the high recovery factors observed in the field. A widely accepted cause of this increase in productivity is the foamy oil flow, which is a non‐Darcy form of two‐phase flow of gas and oil that involves the flow of dispersed gas bubbles. The flow of gas in the form of a gas‐in‐oil dispersion dramatically reduces the fractional flow of gas and helps in diverting more of the drive energy to oil flow.
This paper discusses the current understanding in this area. A brief review of the Canadian field practices and observations related to cold production of heavy oil is presented along with a discussion of the pore‐scale mechanisms involved and the interplay between capillary and viscous forces. Experimental results on the influence of various process parameters are presented and their implications are discussed. The strengths and shortcomings of various modeling approaches are also reviewed.
A Coupled Multiphase Fluid Flow And Heat And Vapor Transport Model For Air‐Gap Membrane Distillation1254(2010); http://dx.doi.org/10.1063/1.3453795View Description Hide Description
Membrane distillation (MD) is emerging as a viable desalination technology because of its low energy requirements that can be provided from low‐grade, waste heat and because it causes less fouling. In MD, desalination is accomplished by transporting water vapour through a porous hydrophobic membrane. The vapour transport process is governed by the vapour pressure difference between the two sides of a membrane. A variety of configurations have been tested to impose this vapour pressure gradient, however, the air‐gap membrane distillation (AGMD) has been found to be the most efficient.
The separation mechanism of AGMD and its overall efficiency is based on vapour‐liquid equilibrium (VLE). At present, little knowledge is available about the optimal design of such a transmembrane VLE‐based evaporation, and subsequent condensation processes. While design parameters for MD have evolved mostly through experimentations, a comprehensive mathematical model is yet to be developed. This is primarily because the coupling and non‐linearity of the equations, the interactions between the flow, heat and mass transport regimes, and the complex geometries involved pose a challenging modelling and simulation problem. Yet a comprehensive mathematical model is needed for systematic evaluation of the processes, design parameterization, and performance prediction. This paper thus presents a coupled fluid flow, heat and mass transfer model to investigate the main processes and parameters affecting the performance of an AGMD.
1254(2010); http://dx.doi.org/10.1063/1.3453796View Description Hide Description
This paper presents the problem of advective transport of a chemical from the pressurized boundary of a three‐dimensional spheroidal cavity region. The results are presented in exact closed form; the solutions to problems dealing with advective transport from a flat crack or an elongated borehole can be obtained as limiting cases of the spheroidal shape. The solution presented also accounts for attenuation of the migration chemical and can be extended to include transient decay of both the pressure in the cavity region and the chemical concentration at the boundary.