Concentrated Hydrochloric Acid Leaching of Greenland Steenstrupine to Obviate Silica Gel Formation

The Ilimaussaq complex in Greenland contains a rare earth bearing mineral called Steenstrupine. This mineral is a complex sodium rare earth phospho-silicate which also contains significant uranium and thorium. The mineral can be beneficiated via froth flotation to produce a mineral concentrate ranging between 15 and 23% rare earth oxide. Leaching of the mineral concentrate is required to dissolve the contained values and recover them using hydrometallurgy. Steenstrupine contains high amounts of acid soluble silica which can result in the formation of silica gel during leaching. Laboratory scale testwork was performed to determine which leaching conditions offer the control of silica and high extraction of values such as rare earth elements and uranium. A range of leach parameters where investigated to determine which are most significant to leach performance. Optimised parameters consisting of acid strength, residence time and nature of the operation were determined as significant. In conclusion the operating range identified produces high rare earth extractions while yielding a leach residue with suitable solid liquid separation performance. This process may be applied to other rare earth bearing minerals which contain high proportions of soluble silica

Modélisation du changement de phase d'une goutte liquide entourée d'un gaz multi-constituant

Les écoulements constitués de gouttelettes liquides dispersées au sein d'un gaz multi-constituant en présence d'évaporation et de condensation apparaissent dans de nombreuses applications liées aux écoulements diphasiques. Cependant, les modèles existants traitent essentiellement le cas de l'évaporation dans le cadre de la combustion de sprays. Cela signifie que l'énergie est transférée du gaz chaud au liquide pour produire son changement de phase. Cette approche est non-symétrique car dans certaines situations, l'énergie est déjà stockée dans la phase liquide et une évaporation explosive (flashing) se produit comme conséquence de la goutte en surpression. Dans notre approche, un modèle de transfert de masse dans le cadre de gouttelettes est présenté et validé dans chacune des situations : évaporation, flashing et condensation. Il tient compte : - du couplage des diffusions de masse et de chaleur dans la phase gazeuse, - de la thermodynamique du gaz multi-constituant. - de la diffusion de chaleur à l'intérieur de la gouttelette liquide, permettant la considération du chauffage et du refroidissement de la goutte. Ces effets sont importants dans des situations telles que l'évaporation et le flashing. Le modèle résultant est un système non-linéaire algébrique constitué de trois équations. Il fournit ainsi la température d'interface, le débit massique de gaz et la fraction massique de vapeur d'eau dans le gaz déterminée à l'interface. Ces variables d'interface permettent le calcul des taux de transfert de masse des espèces, de mouvement et d'énergie apparaissant dans les modèles d'écoulements diphasiques moyennés en volume. Le couplage est réalisé entre le sous-modèle algébrique de transfert de masse et un modèle d'écoulement diphasique moyenné de type Baer et Nunziato (1986). Des résultats numériques sont présentés

Numerical simulation of multiphase flows, interface problems and phase change

Ce travail porte sur la simulation numérique des écoulements multiphasiques compressibles en déséquilibre de vitesses. Un solveur de Riemann diphasique de type HLLC, à la fois robuste, simple et précis est développé et validé à partir de solutions exactes et de données expérimentales. Cette méthode numérique est étendue au cas 3D non-structuré. Par ailleurs, la construction d’une technique numérique pour la répartition de l’énergie d’une onde de choc dans les différentes phases constituant le milieu est établie et permet le respect des conditions de choc multiphasiques. L’extension multiphasique du solveur de Riemann de type HLLC est réalisée, permettant ainsi la simulation d’une plus large gamme d’applications. Enfin, un modèle de transfert de chaleur et de masse dans un brouillard de gouttes ou nuage de bulles, en présence d’effets couplés de diffusion thermique et massiques, est proposé et dévoile des résultats intéressants.This work deals with the numerical simulation of compressible multiphase flows in velocity disequilibrium. A HLLC-type two-phase Riemann solver is developed and validated against exact solutions and experimental data. This solver is robust, simple, accurate and entropy preserving. The numerical method is then implemented in 3D unstructured meshes. Furthermore, a numerical technique consisting in enforcing the correct energy partition at a discrete level in agreement with the multiphase shock relations is built. The multiphase extension of the HLLC-type Riemann solver is realized and allows the simulation of a wide range of applications. Finally, a droplet heat and mass transfer model with large range of validity is derived. It is valid in any situation: evaporation, flashing and condensation. It accounts for coupled heat and mass diffusion in the gas phase, thermodynamics of the multi-component gas mixture and heat diffusion inside the liquid droplet, enabling in this way consideration of both droplets heating and cooling phenomena

Modeling droplet phase change in the presence of a multi-component gas mixture

International audienceDispersed liquid droplet flows with evaporation and condensation in multi-component gas mixture made of vapor and other gas phase chemical species such as air occur in many engineering applications dealing with two-phase flows. However, existing models are essentially derived for vaporization occurring in sprays combustion. It means that the energy is transferred from a hot gas to the liquid to produce its phase change. This is thus a non-symmetric approach as in some situations the energy is already stored in the liquid phase and flashing occurs as a consequence of pressure drop.In the present paper a droplet mass transfer model is derived and is valid in any situation: evaporation, flashing and condensation. It accounts for:- coupled heat and mass diffusion in the gas phase,- thermodynamics of the multi-component gas mixture,- heat diffusion inside the liquid droplet, enabling consideration of both droplet heating and cooling. These effects are important in evaporating and flashing situations respectively.The resulting model consists in an algebraic non-linear system of three equations giving the interface temperature, the mass flow rate and vapor species concentration at the interface. These interfacial variables enable computation of the mass species, momentum and energy transfer rates appearing in volume averaged two-phase flow models.Computational examples are shown with this mass transfer model embedded in a compressible two-phase flow model of Baer and Nunziato (1986) type

A simple HLLC-type Riemann solver for compressible non-equilibrium two-phase flows

International audienceA simple, robust and accurate HLLC-type Riemann solver for two-phase 7-equation type models is built. It involves 4 waves per phase, i.e. the three conventional right- and left-facing and contact waves, augmented by an extra “interfacial” wave. Inspired by the Discrete Equations Method (Abgrall and Saurel, 2003), this wave speed (uIuI) is assumed function only of the piecewise constant initial data. Therefore it is computed easily from these initial states. The same is done for the interfacial pressure PIPI. Interfacial variables uIuI and PIPI are thus local constants in the Riemann problem. Thanks to this property there is no difficulty to express the non-conservative system of partial differential equations in local conservative form. With the conventional HLLC wave speed estimates and the extra interfacial speed uIuI, the four-waves Riemann problem for each phase is solved following the same strategy as in Toro et al. (1994) for the Euler equations. As uIuI and PIPI are functions only of the Riemann problem initial data, the two-phase Riemann problem consists in two independent Riemann problems with 4 waves only. Moreover, it is shown that these solvers are entropy producing. The method is easy to code and very robust. Its accuracy is validated against exact solutions as well as experimental data

Towards sodium combustion modelling with liquid water

International audienceSolid and liquid sodium combustion with liquid water occurs through a thin gas layer where exothermic reactions happen with sodium and water vapors. It thus involves multiple interfaces separating liquid and gas in the presence of surface tension, phase transition and surface reactions. The gas phase reaction involves compressible effects resulting in possible shock wave appearance in both gas and liquid phases. To understand and predict the complexity of sodium combustion with water a diffuse interface flow model is built. This formulation enables flow resolution in multidimension in the presence of complex motion, such as for example Leidenfrost-type thermo-chemical flow. More precisely sodium drop autonomous motion on the liquid surface is computed. Various modelling and numerical issues are present and addressed in the present contribution. In the author's knowledge, the first computed results of such type of combustion phenomenon in multidimensions are presented in this paper thanks to the diffuse interface approach. Explosion phenomenon is addressed as well and is reproduced at least qualitatively thanks to extra ingredients such as turbulent mixing of sodium and water vapors in the gas film and delayed ignition. Shock wave emission from the thermo-chemical Leidenfrost-type flow is observed as reported in related experiments. emails : [email protected] [email protected] [email protected] [email protected] 2 1. Introduction Fast-neutron reactors (FNR) as well as other engineering systems use sodium (a N) as coolant fluid. Sodium presents excellent physical properties regarding heat transfer efficiency as well as its ability to maintain kinetic energy of fast neutrons. However, it has major drawbacks regarding safety issues as it reacts exothermically with both air and water. In the limit, explosion may occur resulting in shock wave propagation in the liquid and surrounding media. When a liquid or solid sodium drop is set on a liquid water surface surprising phenomenon occurs. A reaction appears rapidly resulting in autonomous drop motion on the liquid surface. It seems that the drop is separated from liquid water by a small gas layer where combustion occurs both in the gas phase and at sodium surface. The phenomenon is reminiscent of the Leidenfrost effect except that the heat needed to vaporize sodium and water comes from the combustion of themselves or their vapors. This combustion induces liquid water evaporation and heating of the sodium drop. After some delay, typically a few seconds, explosion occurs. These complex events are qualitatively reported on many videos available on the web, such as [www.youtube.com/watch?v=ODf_sPexS2Q] for example. They clearly illustrate complexity of the physics and chemistry in presence. Quantitative analytic experiments have been carried out at CEA Cadarache, France, in the facilities SOCRATE, DINAMO, VIPERE and LAVINO (Carnevali 2012, Carnevali et al. 2013, Daudin 2015, Daudin et al. 2018, David et al. 2019). These experiments confirm an important fact: liquid sodium and liquid water are always separated by a gas layer or bubbly zone, resulting in significant lowering of the energy release efficiency compared to the theoretical one. To be more precise, typical reactions of sodium with water assume (ideal) molecular mixing, resulting in energy release of the order of 100 kJ/mol, which is considerable. However, in the experiments and engineering situations of interest, sodium is never mixed with water at molecular scale. Materials are separated by interfaces and the gas layer repels the reactive material (Na) from the oxidizer (water). It results in low energy release rate, with mechanical consequences and blast effects much lower than if the reaction was occurring with molecularly mixed materials. In the limit, reactive materials never mix because of projections, resulting in incomplete reaction, with moderate energy release. The present work attempts to model these effects to understand and predict the physics occurring in this complex two-phase combustion system. To determine the effective energy release and its kinetics in situations relevant to FNR safety, the mixing process between combustible sodium and oxidizer (water) must be modelled. Mixing of reactants controls the energy release rate. This mixing seems to occur through the gas layer separating the two liquids, resulting in temperature and pressure rise through exothermic reactions occurring in the gas phase and at the sodium surface, resulting in turn to autonomous drop motion and possibly explosion. In the author's knowledge, the present paper is the first attempt to model sodium combustion with liquid water in multidimensional configuration. Former contributions considered multidimensional water vapor flow interacting with a liquid sodium surface at rest through a diffusion flame (Deguchi et al., 2015). Marfaing (2014) and Marfaing et al. (2014) considered both liquid and vapor water in the presence of a diffusion flame in 1D spherical configuration. The assumption of 1D flow seemed restrictive, as in reality gas escapes from the film to the atmosphere, as illustrated in the Figure 1

Multiscale multiphase modeling of detonations in condensed energetic materials

International audienceHot spots ignition and shock to detonation transition modeling in pressed explosives is addressed in the frame of multiphase flow theory. Shock propagation results in mechanical disequilibrium effects between the condensed phase and the gas trapped in pores. Resulting subscale motion creates hot spots at pore scales. Pore collapse is modeled as a pressure relaxation process, during which dissipated power by the ‘configuration’ pressure produces local heating. Such an approach reduces 3D micromechanics and subscale contacts effects to a ‘granular’ equation of state. Hot spots criticity then results of the competition between heat deposition and conductive losses. Heat losses between the hot solid-gas interface at pore's scale and the colder solid core grains are determined through a subgrid model using two energy equations for the solid phase. The conventional energy balance equation provides the volume average solid temperature and a non-conventional energy equation provides the solid core temperature that accounts for shock heating. With the help of these two temperatures and subscale reconstruction, the interface temperature is determined as well as interfacial heat loss.The overall flow model thus combines a full disequilibrium two-phase model for the mean solid-gas flow variables with a subgrid model, aimed to compute local solid-gas interface temperature. Its evolution results of both subscale motion dissipation and conductive heat loss. The interface temperature serves as ignition criterion for the solid material deflagration. There is no subscale mesh, no system of partial differential equations solved at grain scale.The resulting model contains less parameter than existing ones and associates physical meaning to each of them. It is validated against experiments in two very different regimes: Shock to detonation transition, that typically happens in pressure ranges of 50 kbar and shock propagation that involves pressure ranges 10 times higher