Dissolution of Cavities and Porous Media: a Multi-Scale View

Dissolution of underground cavities or porous media involves many different scales that must be taken into account in modeling attempts. This paper presents a review of some of these problems. The paper starts with an introduction to non-equilibrium models, which play an important role in understanding dissolution physics for such media. In particular, their fundamental importance in catching dissolution instability diagrams is emphasized. A second multi-scale aspect is the introduction of the concept of effective surface for dealing with heterogeneous and/or rough surfaces. All these concepts may be used to develop efficient large-scale simulations. Examples are given for simple situations which emphasize the strong coupling between dissolution and buoyancy plumes generated within the dissolution boundary laye

Sûreté Nucléaire : mythes et réalités

La prise en compte des risques dans les choix technologiques, notamment ceux liés à l'utilisation des ressources naturelles, est un enjeu majeur depuis plusieurs décennies dans de nombreux domaines, et particulièrement en ce qui concerne l'utilisation de l'énergie nucléaire. Plusieurs accidents graves d'importances différentes sont venus rappeler que les enjeux associés à la sûreté des installations nucléaires sont considérables. La conférence a pour objectif de donner, d'un point de vue scientifique, les clefs essentielles à la compréhension des principaux scénarios d'accidents graves de réacteur nucléaire et de leurs conséquences, permettant ainsi de mieux saisir les éléments des débats citoyens autour de l'utilisation de cette source d'énergie

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

Equivalence between volume averaging and moments matching techniques for mass transport models in porous media.

This paper deals with local non-equilibrium models for mass transport in dual-phase and dual-region porous media. The first contribution of this study is to formally prove that the time-asymptotic moments matching method applied to two-equation models is equivalent to a fundamental deterministic perturbation decomposition proposed in Quintard et al. (2001) [1] for mass transport and in Moyne et al. (2000) [2] for heat transfer. Both theories lead to the same one-equation local non-equilibrium model. It has very broad practical and theoretical implications because (1) these models are widely employed in hydrology and chemical engineering and (2) it indicates that the concepts of volume averaging with closure and of matching spatial moments are equivalent in the one-equation non-equilibrium case. This work also aims to clarify the approximations that are made during the upscaling process by establishing the domains of validity of each model, for the mobile–immobile situation, using both a fundamental analysis and numerical simulations. In particular, it is demonstrated, once again, that the local mass equilibrium assumptions must be used very carefully

Upscaling multi-component two-phase flow in porous media with partitioning coefficient

This paper deals with the upscaling of multicomponents two-phase flow in porous media. In this paper, chemical potential equilibrium at the interface between both phases is assumed to be described by a linear partitioning relationship such as Raoult or Henry’s law. The resulting macro-scale dispersion model is a set of two equations related by a mass transfer coefficient and which involves several effective coefficients. These coefficients can be evaluated by solving closure problems over a representative unit-cell. The proposed model is successfully validated through direct analytical and numerical calculations

Dissolution of underground cavities: a multiple-scale view

The generation of underground cavities through dissolution processes is used favorably in many industrial applications (mining, gas storage, ...) but is also the source of hazardous phenomena due to cavity collapse. Dissolution is also fundamental in understanding karstic formations. Because of the intrinsic heterogeneous nature of geological formations, modeling dissolution processes must take into account the different multiple-scale features. Several questions are discussed in this paper to emphasize these multi-scale aspects. First, the mathematical nature of dissolution models for porous formations is analyzed based on the upscaling of a simple, generic, dissolution problem. It is shown that several models may arise from the upscaling process depending on the relative importance of local and non-local effects. It is also pointed out that non traditional terms may play an important quantitative role, a problem which has been often underestimated in the literature. Then, the question of determining effective surface conditions for describing in a smooth manner the dissolution of chemically and physically heterogeneous surfaces is discussed based on a domain decomposition technique. Such approaches are crucial if one wants to develop large-scale dissolution numerical simulations. It is then shown how dissolution processes may be affected by dissolution instabilities (wormholing for instance) and how the size of the domain under investigation affects the stability conditions. Another interesting problem is the dissolution patterns induced by the coupling with hydrodynamic instabilities (natural convection for example) generated in the boundary layer near the dissolving surface. Finally, some questions related to the numerical modeling of the dissolution of large-scale cavities are discussed: use of explicit interface tracking (such as ALE) versus diffuse interface models, the use of simplified momentum balance equations, etc..

Transfers in Porous Media

Modelling heat transfer in porous media requires to take into account multiple-scale aspects inherent to porous media structures. Several methodologies have been developed to upscale the equations at a lower-scale and to obtain upper-scale models as it is outlined in a brief review based on a simple heat conduction example proposed in the first part of this paper. The more general and classical problem of heat transfer in porous media is reviewed in this paper with the emphasis on the fact that different behaviours and hence different models emerge at a given macro-scale, depending on the interplay of the various characteristic times and lengths characterizing the problem. Various classes of models are discussed and their relation ships outlined. Extensions to more complicated problems of heat transfer in porous media are discussed: coupling with mass diffusion, effect of heat sources, radiation, boiling, et

Effective Surface and Boundary Condition for Heterogeneous Salt Media with Insoluble Material

Effective Surface and Boundary Condition for Heterogeneous Salt Media with Insoluble Materia

Biofilms in porous media: development of macroscopic transport equations via volume averaging with closure for local mass equilibrium conditions

In this work, we upscale a pore-scale description of mass transport in a porous medium containing biofilm to develop the relevant Darcy-scale equations. We begin with the pore-scale descriptions of mass transport, interphase mass transfer, and biologically-mediated reactions; these processes are then upscaled using the method of volume averaging to obtain the macroscale mass balance equations. We focus on the case of local mass equilibrium conditions where the averaged concentrations in the fluid and biological phases can be assumed to be proportional and for which a one-equation macroscopic model may be developed. We predict the effective dispersion tensor by a closure scheme that is solved for the cases of both simple and complex unit cells. The domain of validity of the approach is clearly identified, both theoretically and numerically, and unitless groupings indicating the domain of validity are reported

A suitable parametrization to simulate slug flows with the Volume-Of-Fluid method

Diffuse–interface methods, such as the Volume-Of-Fluid method, are often used to simulate complex multiphase flows even if they require significant computation time. Moreover, it can be difficult to simulate some particular two-phase flows such as slug flows with thin liquid films. Suitable parametrization is necessary to provide accuracy and computation speed. Based on a numerical study of slug flows in capillary tubes, we show that it is not trivial to optimize the parametrization of these methods. Some simulation problems described in the literature are directly related to a poor model parametrization, such as an unsuitable discretization scheme or too large time steps. The weak influence of the mesh irregularity is also highlighted. It is shown how to capture accurately thin liquid films with reasonably low computation times