Porous Medium

Understanding the role of thin films in porous media is vital to elucidate wettability at the pore level. The type and thickness of films coating pore walls determine reservoir wettability and whether or not reservoir rock can be altered from its initial state of wettability. Pore shape, especial& pore wall curvature, is important in determining wetting-film thicknesses. Yet, pore shape and physics of thin wetting films are generally neglected in flow models in porous rocks. Thin-film forces incorporated into a collection of star-shaped capillary tubes model describe the geological development of mixed wettability in reservoir rock. Here, mixed wettability refers to continuous and distinct oil and water-wetting surfaces coexisting in the porous medium. This model emphasizes the remarkable role of thin films.

The porosityofyoung limestonesexperiencing meteoricdiagenesisin the vicinityof theirdeposition(eagenetic karst) is mainly a doubleporosityconsistingoftouching-vug channelsandpreferredpassagewayslacingthrougha matrixof interparticleporosity. Incontrast,the porosityoflimestonesexperiencingsubaerialerosionfollowingburialdiagenesisandupliftitelogenetic karst) ismainlya doubleporosityconsisting ofconduits within a network offractures. The stark contrast between these two kinds of karst is illustratedby their position on a graph showing thehydraulic characteristics ofanequivalentporousmediumconsistingofstraight,cylindricaltubes(II-Dspace,wheren isporosity,D isthediameter ofthe tubes, and log n is plotted against log D).

The St. Lawrence Lowlands platform, Quebec, Canada, is a densely-populated area, heavily dependent on groundwater resources. In 1999, the Geological Survey of Canada initiated a large-scale hydrogeological assessment study over a 1,500 km2 region northwest of Montreal. The objectives were to define the regional groundwater flow, and to give quantitative estimates of the groundwater dynamic parameters and of the available groundwater resources. The applied approach consisted of defining the hydrogeologic framework, hydraulic properties of the aquifer units, and groundwater dynamic components. Lower Paleozoic sedimentary rocks represent regional aquifer units. Coarse Quaternary fluvio-glacial sediments locally overlay the rock sequence and constitute an interface aquifer unit. Fine marine sediments confine most of the regional aquifers. Collected GIS based information was synthesized in a finite element numerical model. The regional saturated steady-state flow was calibrated under current stress conditions assuming an equivalent porous medium approach. Water budget calculations show that the total groundwater flow in regional aquifers amounts to 97.7 Mm3/y. Infiltration from precipitation provides 86.6% of the groundwater supply, while 9.6% comes from subsurface inflow and the remaining 3.8% is induced recharge from surface waters. Discharge from regional aquifers occurs through flow to streams (76.9%), groundwater withdrawal (18.4%), and underground outflow (4.7%). La plateforme Lowllands du Saint-Laurent, Québec, Canada, est une aire densément peuplée, dépendant grandement des ressources en eau souterraine. En 1999, le Service Géologique du Canada a initié une étude hydrogéologique à grande-échelle sur 1500 km2 au Nord-Ouest de Montréal. Le sobjectifs ont été de définir la dynamique de l’écoulement régional, et de donner des estimations quantitatives des paramètres dynamiques des ressources disponibles en eau souterraine. L’approche utilisée consista à définir le cadre hydrogéologique de travail, les propriétés hydrauliques des unités aquifères, et les composantes dynamiques des eaux souterraines. Les roches sédimentaires du Paléozoïque Inférieur représentent les unités aquifères régionales. Les sédiments marins fins confinent la plus grande partie des aquifères régionaux. Les informations de base, collectées dans un SIG, ont été synthétisées dans un modèle numérique aux éléments finis. L’écoulement permanent régional, en zone saturée, a été calibré en conditions de stress en assumant une approche de milieu poreu équivalent. Les calculs du bilan hydrologique montrent que l’écoulement total des eaux souterraines dans les aquifères régionaux atteind 97,7 Mm3/an. L’infiltration à partir des précipitations apporte 86.6% de l’eau souterraine exploitée; sachant que 9,6% proviennent d’écoulement de subsurfaces, et que les 3,8% restants proviennent de la recharge via les eaux de surface. Le débit pompé des aquifères régionaux apparaît à travers l’écoulement des cours d’eau, le rabattement des eaux souterraines (18.4%), et l’écoulement ascendant (4.7%). La plataforma de Tierras Bajas San Lorenzo, Quebec, Canadá, es un área densamente poblada que depende fuertemente de recursos de agua subterránea. En 1999 el Servicio Geológico de Canadá inició un estudio de evaluación hidrogeológica a gran escala sobre un área de 1,500 km2 en la región noroeste de Montreal. Los objetivos fueron definir el flujo regional de agua subterránea y aportar estimados cuantitativos de los parámetros dinámicos de agua subterráne y de los recursos disponibles de agua subterránea. El enfoque aplicado consistió en definir el marco hidrogeológico, propiedades hidráulicas de las unidades acuíferas, y los componentes dinámicos de agua subterránea. Rocas sedimentarias del Paleozoico Inferior representan unidades regionales de acuíferos. Sedimentos fluvio-glaciares Cuaternarios gruesos sobreyacen localmente la secuencia rocosa y constituyen una unidad acuífera interfacial. Sedimentos marinos finos confinan la mayoría de acuíferos regionales. Información colectada basada en SIG se sintetizó en un modelo numérico de elemento finito. El flujo regional saturado en régimen permanente se calibró bajo condiciones de stress asumiendo un enfoque de medio poroso equivalente. Los cálculos de balance hídrico muestran que el flujo total de agua subterránea en acuíferos regional alcanza 97.7 Mm3/año. Infiltración a partir de lluvia aporta el 86.6% del abastecimiento al agua subterránea, mientras que el 9.6% proviene de entradas subsuperficiales y el restante 3.8% consiste de recarga inducida a partir de aguas superficiales. La descarga proveniente de acuíferos regionales ocurre a través de flujo a ríos (76.9%), utilización de agua subterránea (18.4%), y salida subterránea (4.7%).

RIASSUNTO L'eccessivo sfruttamento degli acquiferi carsici del Salento ha prodotto, da tempo, l'insorgere del fenomeno della salsificazione delle acque di falda. L'uso di acque salmastre per l'irriga-zione delle colture può determinare, nel lungo termine, la perdita del ...

We investigate the critical speeding up of heat equilibration by the piston effect (PE) in a nearly supercritical van der Waals (vdW) fluid confined in a homogeneous porous medium. We perform an asymptotic analysis of the averaged linearized mass, momentum and energy equations to describe the response of the medium to a boundary heat flux. While nearing the critical point (CP), we find two universal crossovers depending on porosity, intrinsic permeability and viscosity. Closer to the CP than the first crossover, a pressure gradient appears in the bulk due to viscous effects, the PE characteristic time scale stops decreasing and tends to a constant. In infinitly long samples the temperature penetration depth is larger than the diffusion one indicating that the PE in porous media is not a finite size effect as it is in pure fluids. Closer to the CP, a second cross over appears which is characterized by a pressure gradient in the thermal boundary layer (BL). Beyond this second crossover, the PE time remains constant, the expansion of the fluid in the BL drops down and the PE ultimately fades away.

The question of whether effective diffusivities in porous materials under reactive and nonreactive conditions are equal is addressed. Previous studies had considered the problem with first-order reactions. We study the issue with two nonlinear reactions-a second-order reaction and one governed by the Michaelis-Menten kinetics. Pore network and continuum models of porous media are utilized to estimate the effective diffusivities under reactive and nonreactive conditions. We show that the two effective diffusivities are significantly different. The difference is due to the heterogeneities of the porous material, and the fluctuations that they cause in the spatially varying local concentrations and diffusivities, and can be as large as a few orders of magnitude. Theoretical analysis of diffusion and reactions in porous media is also presented that supports the results of the simulations. In particular, it is shown that the results of pore network simulations cannot be fitted to the classical continuum equation of diffusion and reaction, and that a more complex continuum equation should be used for this purpose. ᭧

A problem of reflection and transmission of obliquely incident plane transverse wave at a plane interface between two porous elastic half-spaces in welded contact is investigated. The theory developed by Cowin and Nunziato [S.C. Cowin, J.W. Nunziato, Linear elastic materials with voids, Journal of Elasticity 13 (1983) 125-147] has been used to write down the equations of motion and constitutive relations for the elastic medium with voids. Potential method is used to obtain the reflection and transmission coefficients. It is found that these coefficients are functions of angle of incident, elastic constants, void parameters and that of the frequency of the incident wave. Numerical computations have been performed for a particular model and the results obtained are depicted graphically. The results of Ciarletta and Sumbatyan [M. Ciarletta, M.A. Sumbatyan, Reflection of plane waves by the free boundary of a porous elastic half-space, Journal of Sound and Vibration 259 (2) (2003) 253-264] have been reduced as a special case of the present formulation. The expression for the partition of energy at the interface during transmission and reflection of waves have also been presented.

Analytical investigation was conducted on the transient natural convection flow past an oscillating infinite vertical plate in present of magnetic field and radiative heat transfer. The classical solution of this problem for impulsively moving plate is given by Seth in [2] and is found to be a special case of the solution to be presented. The governing model equations are solved analytically with the help of Laplace transform technique. The results are expressed in terms of the velocity and temperature profiles as well as the skin-friction and Nusselt number.

This study concerns the storage of thermal energy in a porous bed mainly formed by a vertical channel, filled with glass beads, heated on one of the vertical walls by a constant heat flux. The use of glass beads is motivated by the possible use of such a system for storage of solar energy by sensitive heat and its optimization. The medium is characterized by a large thermal inertia which favors a slow return of the heat stored during the heating phase. After model reduction, the system can be dynamically modeled as a simple first order which allows us to evaluate the heat transfer coefficient and to predict its response to real values of the solar flux. The system efficiency defined as the ratio of the stored energy to the energy provided increases with the storage volume and decreases with the return time for fixed width and storage time.

The paper analytically investigated the double-diffusive natural convective boundarylayer flow of a nanofluid past a vertical plate with heat flux condition. The diffusive model used for nanofluid included the effects of Brownian motion and Thermophoresis. A similarity solution was presented and numerical calculations were performed by Maple software. The reduced Nusselt number as a function of a buoyancy-ratio number Nr, a Brownian motion number Nb, and a Thermophoresis number Nt was found with a various values of Prandtl number Pr and Lewis number Le.

Summary Simplified 2 D finite element fracture models have been presented in this paper. The model handles matrix-fracture, fracture- fracture, and matrix-matrix connections. Finite element method is used for 2 D single-phase flow in fractured porous medium. We have modeled horizontal and vertical fractures through porous and less permeable medium. We have also modeled fractures intersected at a right angle.

The flow in a rigid porous medium with a crack is usually modeled by Darcy equations coupled with the Stokes problem. We first propose a new variational formulation of the Stokes system, where the unknowns are the vorticity, the velocity and the pressure, and describe the corresponding finite element discretization. We extend this discretization to the case where Darcy and Stokes equations are coupled and prove optimal a priori and a posteriori error estimates. We conclude with some numerical experiments. Résumé: Un modèle usuel pour l'écoulement dans un milieu poreux rigide avec une fracture consisteà coupler leséquations de Darcy et de Stokes. Nous proposons tout d'abord une nouvelle formulation variationnelle deséquations de Stokes où les inconnues sont le tourbillon, la vitesse et la pression et décrivons la discrétisation paréléments finis correspondante. Nousétendons cette discrétisation au cas où les systèmes de Darcy et de Stokes sont couplés et prouvons des estimations d'erreur a priori et a posteriori optimales. Nous présentons quelques expériences numériques.

We describe here a new experimental device developed for the study of a combustion front propagation in a reactive medium: crushed oil shale (500 to 1000 µm). We are interested in the propagation of a front supplied by air in co-current. The cell is a vertical cylinder of 90mm internal diameter and 300mm height, made up of an insulating material. To start the combustion and to obtain a plane flame front, it was set up a sophisticated device of ignition, namely the cone calorimeter. The reactor is finely instrumented. A whole of thermocouples makes it possible to measure the temperature along the axis for the cell and over a horizontal cross section (at middle height) of the packed bed. The pressure drop and the total mass of the particle bed are continuously recording. A new device was developed and set up to improve the physicochemical investigation of the structure of the flame front: micro-sampling. Its originality lies in the possibility of micro sampling gas at a fined point in...

Industrial processes where the heating of large surfaces is required lead to the possibility of using large surface porous radiant burners. This causes additional temperature uniformity problems, since it is increasingly difficult to evenly distribute the reactant mixture over a large burner surface while retaining its stability and keeping low pollutant emissions. In order to allow for larger surface area burners, a nonuniform velocity profile mechanism for flame stabilization in a porous radiant burner using a single large injection hole is proposed and analyzed for a double-layered burner operating in open and closed hot (laboratory-scale furnace, with temperature-controlled, isothermal walls) environments. In both environments, local mean temperatures within the porous medium have been measured. For lower reactant flow rate and ambient temperature the flame shape is conical and anchored at the rim of the injection hole. As the volumetric flow rate or furnace temperature is raised, the flame undergoes a transition to a plane flame stabilized near the external burner surface. However, the stability range envelope remains the same in both regimes.

Effluent organic matter Managed aquifer recharge Riverbank filtration Biotransformation Co-metabolism Primary substrate a b s t r a c t This study explored the effect of different bulk organic carbon matrices on the fate of trace organic chemicals (TOrC) during managed aquifer recharge (MAR). Infiltration through porous media was simulated in biologically active column experiments under aerobic and anoxic recharge conditions. Wastewater effluent derived organic carbon types, differing in hydrophobicity and biodegradability (i. e., hydrophobic acids, hydrophilic carbon, organic colloids), were used as feed substrates in the column experiments. These carbon substrates while fed at the same concentration differed in their ability to support soil biomass growth during porous media infiltration. Removal of degradable TOrC (with the exception of diclofenac and propyphenazone) was equal or better under aerobic versus anoxic porous media infiltration conditions. During the initial phase of infiltration, the presence of biodegradable organic carbon (BDOC) enhanced the decay of degradable TOrC by promoting soil biomass growth, suggesting that BDOC served as a co-substrate in a cometabolic transformation of these contaminants. However, unexpected high removal efficiencies were observed for all degradable TOrC in the presence of low BDOC concentrations under well adopted oligotrophic conditions. It is hypothesized that removal under these conditions is caused by a specialized microbial community growing on refractory carbon substrates such as hydrophobic acids. Findings of this study reveal that the concentration and character of bulk organic carbon present in effluents affect the degradation efficiency for TOrC during recharge operation. Specifically aerobic, oligotrophic microbiological soil environments present favorable conditions for the transformation of TOrC, including rather recalcitrant compounds such as chlorinated flame retardants. (J.E. Drewes). A v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / w a t r e s 0043-1354/$ -see front matter ª w a t e r r e s e a r c h 4 4 ( 2 0 1 0 ) 4 4 9 -4 6 0

The extended Darcy's law is a commonly used equation for the description of immiscible two-phase flow in porous media. It dates back to the 1940s and is essentially an empirical relationship. According to the extended Darcy's law, pressure gradient and gravity are the only driving forces for the flow of each fluid. Within the last two decades, more advanced and physically based descriptions for multiphase flow in porous media have been developed. In this work, the extended Darcy's law is compared to a thermodynamically consistent approach which explicitly takes the important role of phase interfaces into account, both as entities and as parameters. In this theoretically derived approach, forces related to capillarity and interfaces appear as driving/resisting forces, in addition to the traditional terms. It turns out that the extended Darcy's law and the thermodynamically based approach are compatible if either (i) relative permeabilities are a function of saturation only, but capillary pressure is a function of saturation and specific interfacial area or (ii) relative permeabilities are a function of saturation and saturation gradients. Theoretical considerations suggest that the former alternative is only valid in case of reversible displacement while in the general case (irreversible displacement), the latter alternative is relevant.

In this presentation we analyzed and compared the software packages Eclipse 2004A, NGT BOS v.2.1 and ANSYS CFX v11.0 for the task of the oil and gas flows simulation in a porous medium. We identified the common features, examined the differences and explored recommended fields of application.

A one-dimensional model to determine the laminar ow of a uid in a porous channel with wall suction or injection is proposed. The approach is based on the integration of the Navier-Stokes equations using the analytical solutions for the two-dimensional local velocity and pressure ÿelds obtained from the asymptotic developments at low ÿltration Reynolds number proposed by Berman (J. Appl. Phys. 24 (1953) 1232) and Yuan and Finkelstein (Trans. ASME 74 . It is noticeable that the resulting one-dimensional model preserves the whole ow properties, in particular the inertial terms which can a ect the wall suction conditions and the spatial distribution of the growing particle cake layer at the wall encountered in ÿltration processes. The model is validated in the case of a single porous channel of rectangular or circular cross-section with uniform or variable wall suction. Then the model is applied to a two-dimensional multi-channel system which consists of a great number of adjacent entrance and exit channels connected by a ÿlter porous medium. It is shown that the e ect of non-uniform boundary conditions and the in uence of heterogeneous geometrical characteristics on the heterogeneity of the uid ow structure can be studied using such a model. ?

This paper presents a theoretical analysis of the problem of cuttings transport for a two-region system composed of a fluid bed (ω-region) and a stationary bed of drill cuttings, which is considered as a porous medium (η-region) in the two-phase system. The ω-region is made up of a solid phase (σ-phase) dispersed in a continuos fluid phase (β-phase), while the η-region consists of a stationary solid phase (σ-phase) and a fluid phase (β-phase). The volume averaging method was applied in this study. Volumeaveraged transport equations were derived for both the fluid bed and the porous medium regions. These equations are based on the non-local form of the volume-averaged momentum transport equation that is valid within the bounded region. Outside this region, the non-local form reduces to the classic volume-averaged transport equation. From these equations, a one-equation model was obtained, and the constraints that the one-equation model must satisfy were applied. For estimating the averaged pressure drop and the averaged velocity, the one-equation model was solved numerically by using the finite-difference technique in the implicit scheme. Numerical results are in agreement with experimental data and theoretical results reported in the literature.

In the absence of capillarity the single-component two-phase porous medium equations have the structure of a nonlinear parabolic pressure (equivalently, temperature) diffusion equation, with derivative coupling to a nonlinear hyperbolic saturation wave equation. The mixed parabolic-hyperbolic system is capable of substaining saturation shock waves. The Rankine-Hugoniot equations show that the volume flux is continuous across such a shock.

This work presents a specific application of a new powder rheometer prototype, for the characterization of liquid-impregnated particles which are used in chemical engineering for gas treatment on fixed beds. This new type of rheological characterization can provide useful information about the surface state of the particles and could contribute to the optimization of the impregnation process. The rheometer, consisting of a stress-imposed rheometer coupled with a vibrating cell, generates a Brownian-like motion at a macroscopic scale which makes the sample behave as a non-Newtonian condensed fluid, and allows rheological property measurements of powders which are very sensitive to changes on their surface. Their rheological behavior and its relationship with the impregnation ratio have been analyzed for several samples having different impregnation ratios, thanks to a free volume structural model taking into account the shear rate, the frictional stress, the granular pressure, the vibration frequency, the vibration energy, the free volume distribution and the mass of the samples. The resulting interpretation suggests a stepped kinetic of impregnation: first the liquid adsorbs on the surface of the silica matrix, then it fills progressively the pores, and finally it coats the outer surface of the particles.

Experiments investigating the mass transfer of several dissolved volatile organic compounds (VOCs) across the air-water interface were conducted using a single-airchannel air-sparging system. Three different porous media were used in the study. Air velocities ranged from 0.2 cm s-• to 2.5 cm s-•. The tortuosity factor for each porous medium and the air-water mass transfer coefficients were estimated by fitting experimental data to a one-dimensional diffusion model. The estimated mass transfer coefficients K G ranged from 1.79 x 10 -3 cm min -• to 3.85 x 10 -2 cm min -•. The estimated lumped gas phase mass transfer coefficients KGa were found to be directly related to the air diffusivity of the VOC, air velocity, and particle size, and inversely related to the Henry's law constant of the VOCs. Of the four parameters investigated, the parameter that controlled or had a dominant effect on the lumped gas phase mass transfer coefficient was the air diffusivity of the VOC. Two empirical models were developed by correlating the Damkohler and the modified air phase Sherwood numbers with the air phase Peclet number, Henry's law constant, and the reduced mean particle size of porous media. The correlation developed in this study may be used to obtain better predictions of mass transfer fluxes for field conditions.

Analytical solutions for the water flow and solute transport equations in the unsaturated zone are presented. We use the Broadbridge & White non-linear model to solve the Richards' equation for vertical flow under a constant infiltration rate. Then we extend the water flow solution and develop an exact parametric solution for the advectiondispersion equation. The location of a solute front is determined with the method of characteristics. The dispersion component is incorporated into the final solution using a singular perturbation method. The analytical solutions are simple and can be generated without resorting to computationally demanding numerical schemes. Indeed, the analytical solutions provide tools to verify the accuracy of numerical models. Comparison with a finite element numerical solution indicates that a good match for the predicted water content is achieved when the mesh grid is one fourth the capillary length scale of the porous medium. However, numerical dispersion and spatial oscillations were significant in solving the solute transport equation at this level of discretization.

Capillary rise experiments were performed in columns filled with glass beads and Berea sandstones, using visual methods to register the advance of the water front. For the glass bead filled columns, early time data are well fitted by the Washburn equation. However, in the experiments, the advancing front exceeded the predicted equilibrium height. For large times, an algebraic behavior of the velocity of the front is observed (T. Delker et al., Phys. Rev. Lett. 76, 2902 (1996)). A model for studying the capillary pressure evolution in a regular assembly of spheres is proposed and developed. It is based on a quasi-static advance of the meniscus with a piston-like motion and allows us to estimate the hydraulic equilibrium height, with values very close to those obtained by fitting early time data to a Washburn equation. The change of regime is explained as a transition in the mechanism of advance of the meniscus. On the other hand, only the Washburn regime was observed for the sandstones. The front velocity was fitted to an algebraical form with an exponent close to 0.5, a value expected from the asymptotic limit of the Washburn equation. C 2001 Academic Press

When the latent heat of a phase change material (PCM) with a lower melting point than ambient temperature was assessed according to the standard T-history method using a vertically oriented test tube, a temperature gradient occurred in the longitudinal direction of the tube due to natural convection. This led to a decrease in the accuracy of the latent heat of fusion measurement. In this study, the accuracy of the measurement with the original T-history method was improved without decreasing the test's simplicity and convenience by setting the test tube horizontally. The heat transfer to the vapor-layer of the tube under volume change during melting was assumed to be negligible and the results were calculated using the two inflection points of temperature as the start and end of latent heat period. Under these assumptions, the results agree closely with other reference data. And, the new method proposed in this study showed a remarkable reduction in data scattering.

A new mathematical model is proposed for time-independent laminar flow through a rigid isotropic and consolidated porous medium of spatially varying porosity. The model is based upon volumetric averaging concepts. Explicit assumptions regarding the mean-geometric properties of the porous microstructure lead to a relationship between tortuosity and porosity. Microscopic inertial effects are introduced through consideration of flow development within the pores. A momentum transport equation is derived in terms of the fluid properties, the porous medium porosity and a characteristic length of the microstructure. In the limiting cases of porosity unity and zero, the model yields the required Navier-Stokes equation for free flow and no flow in a solid, respectively.

Based on the generalized van der Waals theory, a cubic equation of state (the van der Waals equation) was extended to describe the behavior of pure fluids and mixtures confined in porous solids. Each pore was assumed to be a cylinder with a continuous and homogeneous surface. Fluid molecules were assumed spherical, interacting with each other and with the wall of the pore through square-well potentials. Pairwise additivity was assumed for the attractive parts of all interaction potentials. The repulsive part of the equation of state for confined fluids was modeled based on literature data for the packing of hard spheres in cylinders. The effect of pore size on fluid properties was explicitly represented in the model, allowing its application to both confined and bulk fluids thus providing a consistent description of adsorption systems for all pore sizes. The resulting equation of state has two fitting parameters for each component of the fluid, which are related to the interaction between the fluid molecules and the pore walls. Calculations of pure fluid adsorption were carried out in order to analyze the sensitivity of the model to its fitting parameters and to pore size. It was found that the model is able to describe different types of adsorption isotherms. The model correlated experimental data of pure fluid adsorption quite well and was then used to predict the adsorption of several binary mixtures and one ternary mixture with no additional fitting, with good results. The methodological framework presented here can be extended to other widely used equations of state for modeling confined fluids.

The past decade has seen considerable progress in the development of models simulating pesticide transport in structured soils subject to preferential flow (PF). Most PF pesticide transport models are based on the two-region concept and usually assume one (vertical) dimensional flow and transport. Stochastic parameter sets are sometimes used to account for the effects of spatial variability at the field scale. In the past decade, PF pesticide models were also coupled with Geographical Information Systems (GIS) and groundwater flow models for application at the catchment and larger regional scales. A review of PF pesticide model applications reveals that the principal difficulty of their application is still the appropriate parameterization of PF and pesticide processes. Experimental solution strategies involve improving measurement techniques and experimental designs. Model strategies aim at enhancing process descriptions, studying parameter sensitivity, uncertainty, inverse parameter identification, model calibration, and effects of spatial variability, as well as generating model emulators and databases. Model comparison studies demonstrated that, after calibration, PF pesticide models clearly outperform chromatographic models for structured soils. Considering nonlinear and kinetic sorption reactions further enhanced the pesticide transport description. However, inverse techniques combined with typically available experimental data are often limited in their ability to simultaneously identify parameters for describing PF, sorption, degradation and other processes. On the other hand, the predictive capacity of uncalibrated PF pesticide models currently allows at best an approximate (order-of-magnitude) estimation of concentrations. Moreover, models should target the entire soil-plant-atmosphere system, including often neglected above-ground processes such as pesticide volatilization, interception, sorption to plant residues, root uptake, and losses by runoff. The conclusions compile progress, problems, and future research choices for modelling pesticide displacement in structured soils.

The use of porous structures with high external surface area represents an important breakthrough in industrial applications. Foam structures receive more and more scientific and industrial interest as catalyst support. Knowledge of pressure drop induced by these foam matrices is essential for successful design and operation of high performance industrial systems. In this context, the aim of this paper is to critically review the relation between permeability and structural parameters of the different foam structures. This work is willing to examine the effect of a large number of structural parameters (struts diameter, porosity, size of pores, specific surface area . . .) in the prediction of bed permeability based on principals of experimental and theoretical works on the single-phase flow model found in the literature. The stateof-the-art of modeling pressure drop in foams is summarized in . The goal was to assess and to critically evaluate all available design tools, whether empirical or theoretical.

Fluid flow behavior in a porous medium is a function of the geometry and topology of its pore space. The construction of a three dimensional pore space model of a porous medium is therefore an important first step in characterizing the medium and predicting its flow properties. A stochastic technique for reconstruction of the 3D pore structure of unstructured random porous media from a 2D thin section training image is presented. The proposed technique relies on successive 2D multiple point statistics simulations coupled to a multi-scale conditioning data extraction procedure. The Single Normal Equation Simulation Algorithm (SNESIM), originally developed as a tool for reproduction of long-range, curvilinear features of geological structures, serves as the simulation engine. Various validating criteria such as marginal distributions of pore and grain, directional variograms, multiple-point connectivity curves, single phase effective permeability and two phase relative permeability calculations are used to analyze the results. The method is tested on a sample of Berea sandstone for which a 3D micro-CT scanning image is available. The results confirm that the equi-probable 3D realizations obtained preserve the typical patterns of the pore space that exist in thin sections, reproduce the long-range connectivities, capture the characteristics of anisotropy in both horizontal and vertical directions and have single and two phase flow characteristics consistent with those of the measured 3D micro-CT image.

-Étude théorique et expérimentale de la précipitation de sulfate de calcium en milieu poreux sur micromodèle de verre-Le mélange de deux eaux incompatibles lors d'injection d'eau donne habituellement lieu à précipitation et formation de dépôts minéraux dans les milieux poreux. Ces dépôts qui réduisent la porosité et surtout la perméabilité de la roche ont une influence considérable sur les performances des scénarios d'injection d'eau. Dans cette étude, une série d'expériences a permis d'étudier l'effet de différents paramètres sur la précipitation progressive de sulfate de calcium. Il s'agit notamment de la température, de la concentration des saumures mélangées, de la pression et du débit. En raison de sa transparence, un micromodèle de réseau représentatif d'un grès mouillable à l'eau a été utilisé comme support poreux et a permis d'observer facilement la formation et la distribution des dépôts minéraux. De plus, le suivi du déplacement des particules solides est largement facilité par le nouveau dispositif expérimental proposé. Les photos de coupes obtenues en microscopie montrent que le dépôt est initié sur les parois et les seuils des pores, qu'il se propage vers l'intérieur de ces pores, et que les cristaux solides ont une forme en crête de coq. Pour une meilleure compréhension de l'effet de chacun des paramètres mentionnés ci-dessus, il a été tracé une courbe de la réduction de perméabilité en fonction du volume de solution de saumure injectée dans les pores. Les résultats ont indiqué que l'augmentation de la température, de la concentration de saumure et du débit conduisent à une augmentation de la tendance au dépôt de minéraux. La pression n'a qu'un rôle mineur sur le développement du processus. Le dépôt de CaSO 4 se modélise comme une fonction de réduction de la perméabilité dépendante des différents paramètres. C'est pourquoi il a été proposé une fonction exponentielle (de corrélation) qui intègre sous une forme adimensionnelle tous les paramètres physiques ayant une influence sur le comportement du système. Le nombre de Reynolds, l'index de précipitation et l'écart par rapport aux conditions d'équilibre constituent le fondement de cette corrélation. Les exposants ajustables de l'équation ont été déterminés et optimisés au moyen d'un algorithme génétique. Cette corrélation significative peut également prédire, avec une précision raisonnable, les résultats issus d'expériences sur carottes.

In this work a simple mathematical model for diffusion and dissolution in reactive porous medium is presented. The case of lime and lead in solid phase enclosed in cement matrices is considered more specifically. A numerical method based on finite difference and on a marching technique is proposed and some numerical results are provided. In a simple case, the results obtained are compared with numerical results available in literature.

In this paper, we are considering viscous incompressible fluid flow through a porous medium between two coaxial cylinders. The governing equations have been solved by using Finite element Galekin's approach. The velocity and temperature profiles of the flow are computed numerically and their behaviours are discussed by graphs for different values of the parameters.

A two-dimensional mathematical model has been developed to study fluid flow inside ceramic foam filters, used for molten metal filtration, as a function of their structural characteristics. The model is based on the selection of a unit cell, geometric model, formed by two interconnected half-pores. The good agreement between experimental and computed permeabilities showed that the unit cell model approximates very well the effect of filter structure on the flow conditions inside the filter. The validity of the model is supported by the fact that permeabilities are calculated from directly measured structural parameters, i.e., without the introduction of any fitting variable, such as tortuosity. The laminar flow solutions for the Navier-Stokes equation, in steady state, were obtained numerically using the control-volume method. The boundary of the unit cell was represented through axisymmetrical, body-fitted coordinates to obtain a better representation of the complex pore shape. The generality of the model, to study fluid flow in reticulated media, was tested by comparing the computed specific permeabilities with values measured for ceramic foam filters and for the new ceramic filter of lost packed bed (CEFILPB). Such a comparison shows good agreement and discloses a fundamental property of the last kind of porous medium: the critical porosity. The model indicates how porosity and pore dimensions of reticulated filters may be tailored to meet specific fluid flow requirements.

The present work analyzes the effects of a solid boundary and the inertial forces on flow and heat transfer in porous media. Specific attention is given to flow through a porous medium in the vicinity of an impermeable boundary. The local volume-averaging technique has been utilized to establish the governing equations, along with an indication of physical limitations and assumptions made in the course of this development. A numerical scheme for the governing equations has been developed to investigate the velocity and temperature fields inside a porous medium near an impermeable boundary, and a new concept of the momentum boundary layer central to the numerical routine is presented. The boundary and inertial effects are characterized in terms of three dimensionless groups, and these effects are shown to be more pronounced in highly permeable media, high Prandtl-number fluids, large pressure gradients, and in the region close to the leading edge of the flow boundary layer.On analyse les effets d'une frontière solide et des forces d'inertie sur l'écoulement et le transfert thermique dans les milieux poreux. Une attention particulière est portée à l'écoulement à travers un milieu poreux au voisinage d'une frontière imperméable. La technique de la moyenne locale en volume a été utilisée pour établir les équations avec une indication sur les limitations physiques et sur les hypothèses. Un schéma numérique a été développé pour déterminer les champs de vitesse et de température dans un milieu poreux près d'une frontière imperméable et un nouveau concept de couche limite placé au centre de la routine numérique est présenté. Les effets de limite et d'inertie sont caractérisés par trois groupements sans dimension et ces effets sont montrés plus prononcés dans les milieux fortement imperméables, pour des fluides à grand nombre de Prandtl, pour des forts gradients de pression et dans la région proche du bord d'attaque de la couche limite de l'écoulement.Die vorliegende Arbeit untersucht die Einflüsse einer festen Begrenzung und der Trägheitskräfte auf die Strömung und den Wärmeübergang in porösen Medien.Besondere Aufmerksamkeit wird der Strömung durch ein poröses Medium in der Nähe einer undurchlässigen Begrenzung gewidmet. Das Verfahren der örtlichen Volumen-Mittelbildung wurde bei der Aufstellung der beschreibenden Gleichungen und der Angabe der physikalischen Vereinfachungen und Näherungen verwendet, die im Verlauf der Herleitung getroffen wurden. Für die beschreibenden Gleichungen wurde ein numerisches Lösungsverfahren entwickelt, um die Geschwindigkeits- und Temperaturfelder innerhalb des porösen Mediums nahe einer undurchlässigen Begrenzung zu untersuchen. Für die Impulsgrenzschicht wird ein neues Konzept innerhalb des numerischen Verfahrens vorgestellt. Die Rand- und Trägheitseinflüsse werden durch drei dimensionslose Gruppen ausgedrückt. Diese Einflüsse erweisen sich als stärker ausgeprägt in gut durchlässigen Medien, in Fluiden mit groβer Prandtl-Zahl, bei groβen Druckgradienten und im Bereich nahe der Vorderkante der Strömungsgrenzschicht.AнAлизиpyeтcя Bлияниe тBepдoй гpAницы и cил инepции нA тeчeниe и тeплoпepeнoc B пopиcтыч cpeдAч. ocoбoe BнимAниe yдeляeтcя тeчeнию чepeз пopиcтyю cpeдy Bблизи нeпpoницAeмoй гpAницы. Для BыBoдA ocнoBныч ypABнeний иcпoльзyeтcя мeтoд лoкAльнoгo ycpeднeния пo oбъeмy. yкAзыBAeтcя нA физичecкиe oгpAничeния и пpинятыe дoпyщeния. c цeлью иccлeдoBAния пoлeй cкopocти и тeмпepAтypы Bнyтpи пopиcтoй cpeды y нeпpoницAeмoй гpAницы pAзpAбoтAнA чиcлeннAя cчeмA для peшeния ocнoBныч ypABнeний и BBeдeнo нoBoe пoнятиe пoгpAничнoгo cлoя кoличecтBA дBизeния, яBляющeгocя ocнoBным B чиcлeннoй cчeмe peшeния. Bлияниe гpAницы и cил инepции BыpAзAeтcя c пoмoщью тpeч бeзpAзмepныч кoмплeкcoB. ПoкAзAнo, чтo Bлияниe бoлee зAмeтнo B cpeдAч c Bыcoкoй пpoницAeмocтью, зидкocтяч c бoльшим чиcлoм ПpAндтля, бoльшими гpAдиeнтAми дABлeния и B oблAcти пoгpAничнoгo cлoя y пepeднeй кpoмки.

Thermoacoustic energy conversion is based on the Stirling cycle. In their most basic forms, thermoacoustic devices are comprised of two heat exchangers, a porous medium, both placed inside a resonator. Work is created through the interaction of strong sound waves with the porous medium that is subject to external heating. This work explores the effect of resonator curvature on the thermoacoustic effect. A CFD analysis of a whole thermoacoustic engine was developed and the influence of a curved resonator on the thermoacoustic effect is discussed. The variation of pressure amplitude and operating frequency serves as metrics in this investigation. It was found that the introduction of curvature affects the pressure amplitude achieved. Severely curved resonators also exhibited a variation in operating frequency.

Reçu le 18 février 2002 ; accepté après révision le 8 avril 2002 Note présentée par Charles-Michel Marle. Résumé On s'intéresse au transfert de quantité de mouvement dans un milieu poreux. Les équations du milieu continu équivalent sont écrites par la méthode de prise de moyenne mais la fermeture est obtenue en utilisant une thermodynamique étendue. Le modèle résultant correspond à l'équation de Navier-Stokes, dans laquelle la force exercée par la matrice sur le fluide satisfait une équation différentielle du premier ordre. Ce modèle d'équation de Navier-Stokes avec mémoire généralise le modèle de Darcy avec terme intégro-différentiel. Pour citer cet article : O. Séro-Guillaume, D. Calogine, C. R. Mecanique 330 (2002) 383-389.  2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS mécanique des fluides / milieux poreux / Navier-Stokes avec mémoire / E.I.T.