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Porométrie Liquide-Liquide, Évaporométrie Et Simulations Sur Réseau De Pores

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Porométrie Liquide-Liquide, Évaporométrie Et Simulations Sur Réseau De Pores En vue de l'obtention du DOCTORAT DE L'UNIVERSITÉ DE TOULOUSE Délivré par : Institut National Polytechnique de Toulouse (Toulouse INP) Discipline ou spécialité : Dynamique des fluides Présentée et soutenue par : M. OTMAN MAALAL le mercredi 7 octobre 2020 Titre : Porométrie liquide-liquide, évaporométrie et simulations sur réseau de pores. Ecole doctorale : Mécanique, Energétique, Génie civil, Procédés (MEGeP) Unité de recherche : Institut de Mécanique des Fluides de Toulouse ( IMFT) Directeur(s) de Thèse : M. MARC PRAT M. DIDIER LASSEUX Rapporteurs : M. DENIS BOUYER, UNIVERSITE MONTPELLIER 2 M. PASCAL ROYER, Laboratoire de Mécanique et Génie Civil Membre(s) du jury : Mme CORINNE CABASSUD, INSA TOULOUSE, Président M. ANTHONY SZYMCZYK, UNIVERSITE RENNES 1, Membre M. DIDIER LASSEUX, CNRS AQUITAINE, Membre M. MARC PRAT, CNRS TOULOUSE, Membre Remerciements Je tiens à remercier chaleureusement toutes les personnes qui ont contribué de prés ou de loin à l’élaboration et la réussite de ce travail de thèse. Je remercie d’emblée mes directeurs de thèse Marc Prat et Didier Lasseux pour leurs conseils ainsi que leur grande disponibilité qui a permis à ce travail de se dérouleur dans les meilleures conditions. Ce travail n’aurait pas pu aboutir sans le soutien de l’Institut de la Filtration et des Techniques Séparatives (IFTS) qui s’est amplement investi dans ce projet. Dans ce sens, je tiens à remercier M. Vincent Edery, directeur général de l’IFTS, pour sa confiance et son engagement dans ce projet. Je remercie également René Peinador, ingénieur de recherche à l’IFTS, pour son encadrement et son implication dans l’aspect expérimental de la thèse. J’en profite aussi pour remercier Pascal Ginisty, Nicolas Petillon, Isabelle Durand, Cecile Mutti ainsi que tout le personnel de l’IFTS. Je tiens aussi à exprimer ma profonde gratitude à Manuel Marcoux, enseignant-chercheur à L’IMFT pour son engagement dans ce travail. Je remercie également mes collègues Malick Niang et Marouane Talbi pour les discussions enrichissantes sur le sujet. Mes derniers remerciements vont à ma famille. En particulier, ma mère Nouzha, ma sœur Dounia et mon frère Mohamed pour leurs encouragements. Finalement, je dédie ce modeste travail à la mémoire de mon père Abdelahad. Résumé Les milieux nanoporeux (milieux dont les tailles de pores sont submicroniques) sont des objets de haute technologie utilisés dans les techniques de séparation ou encore dans les piles à combustible. La distribution de taille de pores (PSD) de ces milieux, en particulier quand ils sont minces, est une information cruciale pour les applications concernées. La porométrie fluide-fluide et l’évapoporométrie sont deux techniques intéressantes de mise en œuvre relativement simple visant à obtenir cette information. Les deux méthodes exploitent les propriétés de capillarité des milieux qui contrôlent la hiérarchie dans les classes de pores selon laquelle se fait l’invasion progressive du milieu lors d’un déplacement fluide-fluide immiscible (cas de la porométrie fluide-fluide) ou le séchage du milieu (cas de l’évapoporométrie). Toutefois, l’exploitation des données obtenues (seuil de pression versus débit ou masse évaporée versus humidité relative) passe par un modèle pour obtenir les données visées. Les modèles actuellement utilisées considèrent le milieu poreux comme un faisceau de tubes parallèles. Ceci convient parfaitement à certains types de membranes poreuses utilisées en filtration par exemple où la nanostructure est similaire à un arrangement de tubes parallèles. En revanche, beaucoup d’autres milieux présentent des nanostructures enchevêtrées considérablement plus complexes, rendant très critiquables ou pour le moins douteuses l’exploitation des données expérimentales selon le modèle de tubes parallèles. Dans ce contexte, l’objectif de la thèse est de développer des modèles et des simulations numériques permettant d’assoir l’exploitation des données des deux techniques de porométrie sur une base plus solide dans le cas des milieux à nanostructures complexes. L’idée est de s’appuyer sur des modélisations de type réseau de pores des processus concernés : évaporation ou déplacement fluide-fluide immiscible en milieu nanoporeux. Les méthodes réseau de pores s’appuient sur des représentations simplifiées de l’espace des pores permettant des calculs rapides (comparé à des méthodes de calcul directes) tout en prenant en compte les propriétés morphologiques de la nanostructure. Ces méthodes sont utilisées pour l’étude des écoulements diphasiques en milieu poreux. Une première étape consistera à réaliser la simulation de drainage pour la porométrie fluide-fluide et la simulation de séchage pour la technique d'évapoporométrie. Cela revient à simuler, à l'aide de la méthode des réseaux poreux, les écoulements diphasiques qui ont lieu lors de l'utilisation de chacune des deux techniques. Nous évaluerons le modèle de tubes parallèles considéré dans l'analyse par le poromètre fluide-fluide ainsi que les résultats obtenus par l'évapoporomètre. Dans un second temps, nous tenterons de proposer un algorithme d'optimisation pour obtenir la PSD en considérant le modèle de réseau de pores adaptable à différentes classes de nanostructures (milieux fibreux, assemblages de particules sphériques, etc.). Enfin, nous exploiterons l'algorithme d'optimisation pour déterminer la fraction de mouillabilité d'un milieu avec une caractéristique de mouillabilité mixte en utilisant les informations qui peuvent être recueillies à partir du poromètre fluide-fluide. 3 Abstract Nanoporous media (media with submicron pore sizes) are high-tech objects used in separation techniques or even in fuel cells. The pore size distribution (PSD) of these media, especially when they are thin, is crucial information for the applications concerned. Fluid-fluid porometry and evapoporometry are two interesting relatively simple techniques to obtain this information. The two methods exploit the properties of capillarity of the media which control the hierarchy in the classes of pores according to which the progressive invasion of the medium takes place during an immiscible fluid-fluid displacement (case of fluid- fluid porometry) or drying (case of evapoporometry). However, the use of the data obtained (pressure threshold versus flow rate or evaporated mass versus relative humidity) requires a model to obtain the targeted data. The models currently in use consider the porous medium as a bundle of parallel tubes. This is perfectly suited to certain types of porous membranes used in filtration, for example where the nanostructure is similar to an arrangement of parallel tubes. On the other hand, many other environments present considerably more complex entangled nanostructures, making it very questionable or at least doubtful the exploitation of experimental data according to the parallel tube model. In this context, the objective of the thesis is to develop models and numerical simulations allowing the exploitation of the data from the two porometry techniques on a more solid basis in the case of media with complex nanostructures. The idea is to rely on pore network type modeling of the processes involved: evaporation or immiscible fluid-fluid displacement in a nanoporous medium. Pore lattice methods are based on simplified representations of pore space allowing fast calculations (compared to direct calculation methods) while taking into account the morphological properties of the nanostructure. These methods are used for the study of two-phase flows in porous media. A first step will consist in performing the simulation of drainage for the fluid-fluid porometry and drying simulation for the evapoporometry technic. This amounts to simulating, using the pore networks method, the two-phase flows that take place during the use of each of the two techniques. We will evaluate the parallel tubes model considered in the analysis by the fluid-fluid porometer as well as the results obtained by the evapoporometer. In a second step, we will try to propose an optimization algorithm to get the PSD by considering the pore network model that can be adapted to different classes of nanostructures (fibrous media, assemblies of spherical particles, etc.). Finally, we will exploit the optimization algorithm to determine the wettability fraction of a medium with a mixed wettability characteristic using the information that can be gathered from the fluid-fluid porometer. 4 Table des matières Introduction ................................................................................................................................................... 6 Determination of the throat size distribution of a porous medium as an inverse optimization problem combining pore network modeling and genetic and hill climbing algorithms. ........................................... 16 Pore network simulations of fluid-fluid displacement porosimetry for evaluation of pore size distribution ..................................................................................................................................................................... 56 Pore network model of drying with kelvin effect........................................................................................ 90 Membrane characterization by evapoporometry and liquid-liquid displacement porosimetry: assessment from pore network simulation .................................................................................................................. 125 Identification of local contact angle distribution
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