1994). Réflexions sur la modélisation de la propagation de polluants dans les hydrosystèmes souterrains

Les modèles de simulation de propagation de polluants dans les eaux souterraines sont de plus en plus utilisés comme outils de gestion de cette ressource. La qualité des simulations dépend étroitement des connaissances que l'on a des processus et des paramètres de transport nécessaires à la mise en application des modèles. La fiabilité des résultats repose sur: - le choix du bon modèle en fonction de l'échelle d'observation - la mesure des paramètres représentatifs du transport liée à l'échelle de discrétisation du site - la spatialisation de mesures locales. Compte tenu des spécificités des hydrosystèmes souterrains (invisibilité, accès coûteux), la connaissance du milieu restera trop fragmentaire pour réaliser des simulations fines. Seules les approches stochastiques permettent alors d'intégrer ces incertitudes dans les simulations.Groundwater quality modelling has become a tool for water management. The accuracy of the simulations closely depends on the available knowledge concerning the transport processes and the parameters used in the model. The accuracy of the results depends on the choice ofa suitable model adapted to the observation scale, the measurement of the effective parameters linked to the discretization of the field and the spatialization of the local measurements.The mathematical model used to describe mass transport in porous media is the dispersion-convection equation. The velocity is calculated by solving the flow equation. For heterogeneous media, numerical schemes which simultaneously solve heads and velocities have to be preferred to classical finite element or finite differences techniques. The dispersion coefficient represents the velocity fluctuations around the average velocity. Therefore, it strongly depends on the dimension and the scale of the discretization.A predictive simulation of the Twin Lake Tracer Test experiment has been done. After a very fine calibration of the flow (differences between measured and calculated heads less than 1 cm), the transport simulation did not succeed. The headgradients were not calculated with enough accuracy and the simulated plume travelled in a wrong direction.Due to the nature of groundwater (invisible, expensive rneasurements), knowledge of the structure of the aquifer will always be too incomplete to perform very detailed simulations. Stochastic computations may be the way to take into account uncertainities in groundwater modening

Influence of the disorder on tracer dispersion in a flow channel

Tracer dispersion is studied experimentally in periodic or disordered arrays of beads in a capillary tube. Dispersion is measured from light absorption variations near the outlet following a steplike injection of dye at the inlet. Visualizations using dye and pure glycerol are also performed in similar geometries. Taylor dispersion is dominant both in an empty tube and for a periodic array of beads: the dispersivity $l\_d$ increases with the P\'eclet number $Pe$ respectively as $Pe$ and $Pe^{0.82}$ and is larger by a factor of 8 in the second case. In a disordered packing of smaller beads (1/3 of the tube diameter) geometrical dispersion associated to the disorder of the flow field is dominant with a constant value of $l\_d$ reached at high P\'eclet numbers. The minimum dispersivity is slightly higher than in homogeneous nonconsolidated packings of small grains, likely due heterogeneities resulting from wall effects. In a disordered packing with the same beads as in the periodic configuration, $l\_d$ is up to 20 times lower than in the latter and varies as $Pe^\alpha$ with $\alpha = 0.5$ or $= 0.69$ (depending on the fluid viscosity). A simple model accounting for this latter result is suggested.Comment: available online at http://www.edpsciences.org/journal/index.cfm?edpsname=epjap&niv1=contents&niv2=archive

Pore-scale numerical investigation of pressure drop behaviour across open-cell metal foams

The development and validation of a grid-based pore-scale numerical modelling methodology applied to five different commercial metal foam samples is described. The 3-D digital representation of the foam geometry was obtained by the use of X-ray microcomputer tomography scans, and macroscopic properties such as porosity, specific surface and pore size distribution are directly calculated from tomographic data. Pressure drop measurements were performed on all the samples under a wide range of flow velocities, with focus on the turbulent flow regime. Airflow pore-scale simulations were carried out solving the continuity and Navier–Stokes equations using a commercial finite volume code. The feasibility of using Reynolds-averaged Navier–Stokes models to account for the turbulence within the pore space was evaluated. Macroscopic transport quantities are calculated from the pore-scale simulations by averaging. Permeability and Forchheimer coefficient values are obtained from the pressure gradient data for both experiments and simulations and used for validation. Results have shown that viscous losses are practically negligible under the conditions investigated and pressure losses are dominated by inertial effects. Simulations performed on samples with varying thickness in the flow direction showed the pressure gradient to be affected by the sample thickness. However, as the thickness increased, the pressure gradient tended towards an asymptotic value

Hydrodynamic and transport properties of packed beds in small tube-to-sphere diameter ratio: pore scale simulation using an Eulerian and a Lagrangian approach

In fixed bed catalytic reactors radial heterogeneities of the granular structure are present owing to topologic constraints imposed by the reactor wall. In order to analyse the influence of this structure on the fluid flow and the radial mass transfer properties, the study of sphere packings in cylindrical container and flow simulations at the pore scale are carried out. A collocated finite volume is used to solve the 3D Navier–Stokes equations. The Reynolds number ranges from 7 to 200 allowing to use the direct numerical simulation method in stationary flow regime combined to the no-slip condition at the interface solid/fluid. Therefore no correlation are used in this study. Furthermore, representative fixed beds, composed of several hundreds of spheres, are used for a diameter ratio of 5.96 and 7.8. Radial profile of the longitudinal velocity and the probability density function of the velocity components agree with the experimental data found in the literature. At low Reynolds number, the computation of current lines reveals the presence, at the reactor wall, of a layer whose width is around one-fourth of the sphere diameter. In this layer, the fluid flow is longitudinal and tangential. Particle tracking reveals also the existence of a second layer all along the spheres in contact with the reactor wall. Mass transfer in these two regions is controlled by the diffusive mechanism at low Reynolds number. The flow structure at high Reynolds number contains lots of eddies distributed homogeneously in the fixed beds. These structures are not recirculating zones (particle traps). On contrary, they accelerate the radial mass transfer so that the layers found at low Reynolds number tend to disappear at high Reynolds

CFD simulations of two stirred tank reactors with stationary catalytic basket

International audienceAmong the different systems used for laboratory kinetic investigation, stationary catalytic basket stirred tank reactors (SCBSTRs) allow one to study triphasic reactions involving shaped catalyst with large size. The hydrodynamics of these complex reactors is not well known and has been studied experimentally in only a few cases. Despite the difference in the design of two commercial SCBSTRs reported in these works, the local measurements of the liquid–solid mass transfer coefficient inside the catalytic basket revealed the same velocity profile. The aim of the present work is therefore to investigate more accurately the hydrodynamics of the two reactors by means of CFD in order to compare the effect of the blade/baffle hydrodynamic interaction on the flow pattern. Owing to the geometrical complexity of the reactors, the hydrodynamic investigation is based on the kk–εε model and the Brinkman–Forsheimer equations. The agreement at the local level with the experimental data (PIV and mass transfer measurements) validates this preliminary work performed with the standard values of the parameters present in the turbulent model and the Brinkman–Forsheimer equations. The simulations reveal in both reactors a ring-shaped vortex around the impeller in the agitation region. The high axial location of its centre induces a reverse flow at the tips of the basket. Owing to the fluid friction in the porous medium, the azimuthal flow in the core region is transformed into a radial flow in the basket where the flow decreases abruptly. Vertical vortices are located at the blade tips and at the downstream face of the baffles or they are located in the basket on both sides of the baffles, depending on the design and the location of the baffles. At the inner radius interface of the basket, the vertical blade impeller induces a rather homogeneous velocity profile, but the pitched blade impeller imposes a high velocity at the plane of symmetry. Therefore the simulations demonstrate that two different local velocity patterns and two different porous media may induce the same mass transfer properties

CFD and kinetic methods for mass transfer determination in a mesh microreactor

The global gas-liquid-solid volumetric mass-transfer coefficient KLa of a catalytic multiphase microstructured film contactor, featuring 5 m dimensions, a 155 m liquid film thickness, and a 15 m thin catalytic layer is determined, using the very fast hydrogenation of -methylstyrene with a Pd/-alumina catalyst. The volumetric mass-transfer coefficients measured experimentally fall in the range 0.8 - 1.6 s-1 above that predicted by the film model and those obtained from a CFD (3-D model) simulation, and from an analytical solution