Influence of solid phase thermal conductivity on species separation rate in packed thermogravitational columns: A direct numerical simulation model

n this work, a direct numerical simulation model has been proposed to study the influence of porous matrix thermal properties on the separation rate in a model of packed thermogravitational column saturated by a binary mixture. The coupled flow, heat and mass dimensionless equations and boundary conditions have been derived in pore-scale and then solved over a vertical column containing fluid and solid phases. The results show that the separation rate is changed significantly by the conductivity ratio of the solid/fluid phases. The classical maximum separation at optimal Rayleigh number increases by decreasing the solid thermal conductivity. We obtained that the influence of the solid thermal conductivity for small Rayleigh number is not considerable but for intermediate Rayleigh number the separation rate initially decreases with increasing the thermal conductivity ratio and then reaches an asymptote. As the Rayleigh number increases, convection dominates and the effect of thermal conductivity ratio on separation rate becomes completely inversed

Effect of solid thermal conductivity and particle-particle contact on effective thermodiffusion coefficient in porous media

Transient mass transfer associated to a thermal gradient through a saturated porous medium is studied experimentally and theoretically to determine the effect of solid thermal conductivity and particle-particle contact on thermodiffusion processes. In this study, the theoretical volume averaging model developed in a previous study has been adopted to determine the effective transport coefficients in the case of particle-particle contact configurations. The theoretical results revealed that the effective thermodiffusion coefficient is independent of the thermal conductivity ratio for pure diffusive cases. In all cases, even if the effective thermal conductivity depends on the particle-particle contact, the effective thermodiffusion coefficient remains independent of the solid phase connectivity. We also found that the porosity can change the impact of dispersion effects on the thermodiffusion coefficients. For large values of the thermal conductivity contrast, dispersion effects are negligible and the effective thermal conductivity coefficients are the same as the ones for the pure diffusion case. Experimental results obtained for the purely diffusive case, using a special two-bulb apparatus, confirm the theoretical results. These results also show that, for non-consolidated porous media made of spheres, the thermal conductivity ratio has no significant influence on the thermodiffusion process for pure diffusion. Finally, the particle-particle contact also does not show a considerable influence on the thermodiffusion process

Theoretical and experimental determination of effective diffusion and thermodiffusion coefficients in porous media

A multicomponent system, under nonisothermal condition, shows mass transfer with cross effects described by the thermodynamics of irreversible processes. The flow dynamics and convective patterns in mixtures are more complex than those of one-component fluids due to interplay between advection and mixing, solute diffusion, and thermal diffusion (or Soret effect). This can modify species concentrations of fluids crossing through a porous medium and leads to local accumulations. There are many important processes in nature and industry where thermal diffusion plays a crucial role. Thermal diffusion has various technical applications, such as isotope separation in liquid and gaseous mixtures, identification and separation of crude oil components, coating of metallic parts, etc. In porous media, the direct resolution of the convection-diffusion equations are practically impossible due to the complexity of the geometry; therefore the equations describing average concentrations, temperatures and velocities must be developed. They might be obtained using an up-scaling method, in which the complicated local situation (transport of energy by convection and diffusion at pore scale) is described at the macroscopic scale. At this level, heat and mass transfers can be characterized by effective tensors. The aim of this thesis is to study and understand the influence that can have a temperature gradient on the flow of a mixture. The main objective is to determine the effective coefficients modelling the heat and mass transfer in porous media, in particular the effective coefficient of thermodiffusion. To achieve this objective, we have used the volume averaging method to obtain the modelling equations that describes diffusion and thermodiffusion processes in a homogeneous porous medium. These results allow characterising the modifications induced by the thermodiffusion on mass transfer and the influence of the porous matrix properties on the thermodiffusion process. The obtained results show that the values of these coefficients in porous media are completely different from the one of the fluid mixture, and should be measured in realistic conditions, or evaluated with the theoretical technique developed in this study. Particularly, for low Péclet number (diffusive regime) the ratios of effective diffusion and thermodiffusion to their molecular coefficients are almost constant and equal to the inverse of the tortuosity coefficient of the porous matrix, while the effective thermal conductivity is varying by changing the solid conductivity. In the opposite, for high Péclet numbers (convective regime), the above mentioned ratios increase following a power law trend, and the effective thermodiffusion coefficient decreases. In this case, changing the solid thermal conductivity also changes the value of the effective thermodiffusion and thermal conductivity coefficients. Theoretical results showed also that, for pure diffusion, even if the effective thermal conductivity depends on the particle-particle contact, the effective thermal diffusion coefficient is always constant and independent of the connectivity of the solid phase. In order to validate the theory developed by the up-scaling technique, we have compared the results obtained from the homogenised model with a direct numerical simulation at the microscopic scale. These two problems have been solved using COMSOL Multiphysics, a commercial finite elements code. The results of comparison for different parameters show an excellent agreement between theoretical and numerical models. In all cases, the structure of the porous medium and the dynamics of the fluid have to be taken into account for the characterization of the mass transfer due to thermodiffusion. This is of great importance in the concentration evaluation in the porous medium, like in oil reservoirs, problems of pollution storages and soil pollution transport. Then to consolidate these theoretical results, new experimental results have been obtained with a two-bulb apparatus are presented. The diffusion and thermal diffusion of a helium-nitrogen and helium-carbon dioxide systems through cylindrical samples filled with spheres of different diameters and thermal properties have been measured at the atmospheric pressure. The porosity of each medium has been determined by construction of a 3D image of the sample made with an X-ray tomograph device. Concentrations are determined by a continuous analysing the gas mixture composition in the bulbs with a katharometer device. A transient-state method for coupled evaluation of thermal diffusion and Fick coefficients in two bulbs system has been proposed. The determination of diffusion and thermal diffusion coefficients is done by comparing the temporal experimental results with an analytical solution modelling the mass transfer between two bulbs. The results are in good agreement with theoretical results and emphasize the porosity of the medium influence on both diffusion and thermal diffusion process. The results also showed that the effective thermal diffusion coefficients are independent from thermal conductivity ratio and particle-particle touching

Derivation of the Darcy-scale filtration equation for foam flow using the volume averaging technique

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Modélisation de l'injection des mousses en milieu poreux : application aux traitements des sols pollués

L'injection de mousses représente une alternative innovante et de grand intérêt pour la remédiation in situ des sols pollués. Les avantages potentiels de l'utilisation des mousses par rapport à l'injection classique de tensioactifs comprennent un meilleur contrôle du volume de fluide injecté, une meilleure homogénéité de contact polluants/tensioactifs, et de facto une meilleure capacité à dissoudre et désorber les polluants. Plusieurs mécanismes rendent difficile la compréhension des phénomènes de transport de la mousse en milieu poreux, notamment le nombre de bulles qui gouverne les caractéristiques de l'écoulement telle que la viscosité, la perméabilité relative, la distribution de fluide, et les interactions entre les fluides. Notre étude est axée sur la modélisation des processus de remédiation par injection des mousses en vue de mieux comprendre les différentes interactions mousses/polluants en milieu poreux. Dans cette étude, l'injection de mousse a été également comparée avec l'injection classique d'air (par air sparging). Les résultats de simulations montrent un front de propagation verticale et latérale plus importante pour la mousse. Cette large différence de propagation latérale vient de la différence entre la mobilité de la mousse et de l'air ainsi que de la différence entre la force capillaire qui existe au niveau des interfaces air/eau et mousse/eau. Par ailleurs, la concentration en polluants des gaz en sortie de colonne est beaucoup plus élevée pour l'injection de mousses (vs l'injection d'air). Ce phénomène est dû à l'augmentation de la solubilité des polluants dans la solution de mousses

Experimental and numerical upscaling of foam flow in highly permeable porous media

Foam in porous media has been studied as a tool for various applications. Recently, the technology has become relevant for contaminated-aquifer remediation, where porous media are highly permeable. Therefore, the behavior of foam flow in high permeability porous media still raises numerous questions. In particular, upscaling of the foam flow from pore to Darcy scale is still under debate. Since the behavior of bulk foam has been studied principally in the food and cosmetics industries, and foam flow in porous media has mainly been investigated in the oil industry, the link between bulk-foam behavior and foam flow in porous media is still missing. The upscaling of foam flow from the pore scale to the laboratory scale could give valuable insight for understanding foam flow in aquifers. We studied the behavior of pre-generated foam with different foam qualities through the rheological character- ization of bulk foam using a rheometer and also when flowing in a porous medium composed of 1 mm glass beads. Foam was formed by co-injecting surfactant solution and nitrogen gas through a porous column filled by fine sand. The homogenization method is used to study macroscopic foam flow properties in porous media by solving the non-linear boundary value problem. The rheology of bulk foam is then used as an input in the upscaling procedure for foam flow in different periodic model 2D and 3D unit cells. From our experiments, we found that the bulk foam is a yield-stress fluid and that the yield-stress values increase with foam quality. Moreover, the rheology of bulk foam corresponds well to the yield stress (Herschel-Bulkley-Papanastasiou) model. We found that foam behaves as a continuous yield-stress fluid in highly permeable porous media. It was also shown that the apparent foam viscosity in porous media increases with the foam quality at the same total flow rate. The results obtained from the rheometer successfully match the outcomes of apparent foam viscosity obtained by flow in porous media by a shifting parameter for the same foam quality. The apparent foam viscosity found in 1 mm glass-bead packing was much higher than bulk foam viscosity. Experimental results were compared to numerical results on simple unit cells. Although we observed considerable differences between the experimental and numerical results of upscaling, the general trend was identical. The differences can be explained by the complexity of the foam flow in porous media, especially foam compressibility. We found that foam flow at low capillary numbers is influenced by the trapping effect and at high pressure gradients by the compressibility. Compressibility was estimated for foam flow in 1 mm glass-bead packing. When foam compressibility is insignificant, the upscaling model can predict foam-flow behavior well at the Darcy scale

Experimental study of the temperature effect on two-phase flow properties in highly permeable porous media: Application to the remediation of dense non-aqueous phase liquids (DNAPLs) in polluted soil

The remediation of aquifers contaminated by viscous dense non-aqueous phase liquids (DNAPLs) is a challenging problem. Coal tars are the most abundant persistent DNAPLs due to their high viscosity and complexity. Pump- ing processes leave considerable volume fractions of DNAPLs in the soil and demand high operational costs to reach cleaning objectives. Thermally enhanced recovery focuses on decreasing DNAPL viscosity to reduce resid- ual saturation. The oil industry has previously applied this technique with great success for enhanced oil recovery applications. However, in soil remediation, high porous media permeabilities and product densities may invali- date those techniques. Additionally, the impacts of temperature on coal tar’s physical properties have not been thoroughly discussed in available literature. Here, we investigated how coal tar’s physical properties, the capillary pressure-saturation curve and the relative permeability of two-phase flow in porous media depend on the temper- ature and flow rate experimentally. Drainage and imbibition experiments under quasi-static (steady-state) and dynamic (unsteady-state) conditions have been carried out at 293.15 K and 323.15 K in a 1D small cell filled with 1 mm homogeneous glass beads. Two different pairs of immiscible fluids have been investigated, coal tar-water and canola oil-ethanol. Results demonstrated similar trends for temperature effect and values of fluid properties for both liquid pairs, which backs up the use of canola oil-ethanol to model coal tar-water flow. It was found that there is no temperature effect on drainage-imbibition curves or residual saturation under quasi-static conditions. In dynamic conditions, the DNAPL residual saturation decreased by 16 % when the temperature changed from 293.15 K to 323.15 K. This drop was mainly linked to decreasing viscous fingering, as well as the appearance of wetting phase films around the glass beads. Both phenomena have been observed only in dynamic experiments. A high enough pumping flow rate is needed to generate dynamic effects in the porous medium. Ethanol and oil’s relative permeabilities also increase with temperature under dynamic measurement conditions. Our findings in- dicate that flow rate is an important parameter to consider in thermal enhanced recovery processes. These effects are not taken into account in the classically used generalized Darcy’s law for modeling two-phase flow in porous media with temperature variation

Assessment of CO2 Health Risk in Indoor Air Following a Leakage from a Geological Storage: Results from the First Representative Scale Experiment

If a leakage of CO2 out of a geological reservoir were to happen and to reach the vadose zone below a building, CO2 could migrate through the vadose and the building's slab and accumulate in the building, leading to possible acute risk for the inhabitants. A representative-scale experiment, including a prototype for a building, was developed to better understand and quantify this possible risk. It brought fruitful directions for further modeling work, since unexplained CO2 peaks were observed in the prototype. Numerical simulations were carried out to address the variability of CO2 concentrations considering the influence of soil and building properties as well as meteorological conditions, with promising results for risk analysis

Assessment of CO2 health risk in indoor air following a leakage reaching unsaturated zone: results from the first representative scale experiment

International audienceLeakage of CO2 from geological reservoirs is one of the most fearsome unexpected scenarios for CO2 storage activities. If a leakage reaches the ground level, exposure to high CO2 concentrations is more likely to occur in low ventilated spaces (pit dug in the ground, basement, building) where CO2 could accumulate to high concentrations. Significant literature and models about indoor exposure resulting from intrusion of soils gases in building are available in several domains (e.g., contaminated soils, radon, etc.). However, there is no guarantee that those approaches are appropriate for the assessment of consequences of CO2 leakage due the specificity of CO2 and due to the singularities of the source in case of leakage from anthropic reservoirs. Furthermore, another singularity compared to conventional approaches is that the risk due to CO2 exposure should be evaluated considering acute concentrations rather than long term exposure to low concentrations. Thus, a specific approach is needed to enable a quantitative assessment of the risk for health and living in indoor environment in case of leakage from a reservoir reaching the unsaturated zone below the buildings. We present the results of the IMPACT-CO2 project that aims at understanding the possible migration of CO2 to indoor environment and to develop an approach to evaluate the risks. The approach is based on modelling and experiments at laboratory scale and at field representative scale. The aim of the experiment is to capture the main phenomena that control the migration of CO2 through unsaturated zone, and its intrusion and accumulation in buildings. The experimental results will also enable numerical confrontation with tools used for risk assessment. Experiments at representative scale (Figure 1) are performed on the PISCO2 platform (Ponferrada, Spain) specifically instrumented and designed for understanding the impacts of CO2 migration towards the soil surface. The experiment is composed of a 2.2 m deep basin filled with sand upon which a specifically designed cylindrical device representing the indoor condition of a building (with controlled depressurization and ventilation) is set up. The device includes a calibrated interface that represents a cracked slab of a building. The injection of CO2 is performed at the bottom of the basin with a flow rate in the range of hundreds of g/d/m². The first results show that the presence of a building influences significantly the transport of CO2 in the surrounding soil leading to two competing phenomena: 1) seepage in the atmosphere mainly controlled by diffusion gradient and 2) advective/diffusive flux entering the building due to the depressurization. Models have been established to quantitatively assess the proportion of CO