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Multiscale Analysis of Transport in Porous Media

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Multiscale Analysis of Transport in Porous Media AIX-MARSEILLE UNIVERSITY THESIS Submitted with the view of obtaining the degree of DOCTOR OF AIX-MARSEILLE UNIVERSITY Discipline: Material Science Doctoral school: Physics and Material Science by Khac-Long NGUYEN Thesis defense: May 22th 2019 MULTISCALE ANALYSIS OF TRANSPORT IN POROUS MEDIA Supervisors: Dr. Renaud DENOYEL Dr. Véronique WERNERT JURY Dr. Anne Galarneau, ICGM, Montpellier Reviewer Dr. Benoit Coasne, LIPHY, Grenoble Reviewer Prof. Pascaline Pré, IMT Atlantique Examiner Prof. Frédéric Dallemer, Aix-Marseille University Examiner Dr. Renaud Denoyel, Aix-Marseille University Thesis Director Dr. Véronique Wernert, Aix-Marseille University Thesis Co-Director To my parents To my wife, Lien NGUYEN and my son Anh-Vu NGUYEN ACKNOWLEDGEMENT First and foremost, I would like to express my sincere gratitude to my supervisors Dr. Renaud Denoyel and Dr. Véronique Wernert for their support and the valuable discussion during my PhD work. Special thanks to Dr. Renaud Denoyel for giving me this opportunity to pursue a doctoral degree at Aix-Marseille University. Great thanks should be given to Dr. Véronique Wernert who devoted a great time for my calculation and experiments. I will forever be indebted to them for the patience, inspiration, encouragement and motivating comments effective and crucial in my academic life. I would like to thank the Ministry of Education and Training of Vietnam for the financial support and the opportunity to study in France. I would like to express my deep gratitude to ANR TAMTAM for the support with my conference travel and the experimental apparatus. I wish to express my acknowledge to Dr. Isabelle Beurroies for supporting me in all the discussions and the training course in adsorption that helped me to be an independent user of the experimental instrument for vapor adsorption. I would also like to express my thanks to the reviewers, Dr. Anne Galarneau and Dr. Benoit Coasne and all the members of the committee, Prof. Pascaline Pré and Prof. Frédéric Dallemer, for taking the time to review this dissertation. My special thanks would give to all the lab mates in MADIREL: Wei, Tracy, Lobna, André, Hailong, Ritu, Pingping, Weiliang, Paul, Vinsensia, Pierre-Henry, Rifan, Ephrem, Girish and Damien for the instructions with mercury porosimetry and my friends: Tung, Hai, Tan, Hung, Thinh, Nam for spending a lot of time together, for their friendship letting me feel happy in the foreign country. Most importantly, I would like to sincerely thank my family, especially my beloved wife, Lien Nguyen, and son, Anh-Vu Nguyen, also to my parents and brother, sister for their love and patience. They give me encouragement, support, strength all these years. I would like to express my wholehearted regards to my family. i ABSTRACT The correlation of the structural parameters with the transfer properties of a fluid through a porous media is a significant subject in physics, chemistry, geology, and engineering. The architectural parameters such as porosity and pore size distribution do not describe the complexity of most porous organizations consisting of labyrinths of interconnected pores with random shapes and cross-sections. This complexity is described by a parameter called tortuosity. Classical methods such as measurements of nitrogen adsorption isotherms, Hg porosimetry and determination of the tortuosity by electrical measurements are used together to better model transport properties. The materials are also characterized by inverse size exclusion chromatography. The apparent total and particle tortuosities are determined by the analysis of the peak shape of chromatographic probes. In the latter case, the particle tortuosity of silica is calculated from effective intraparticle diffusion coefficient determined by modelling the chromatographic peak broadening of polystyrenes obtained either in dynamic or in static conditions under non-adsorbing conditions by using the solvent tetrahydrofuran (THF). In dynamic conditions, the constant term in the van Deemter equation is a combined contribution of eddy diffusion and polydispersity of the polystyrenes and depends on the size of the molecule. The broad pore size distribution of totally porous silica contributes also to the spreading of the peak. The transport of polystyrenes through silica columns has also been studied in adsorbing conditions by changing the solvent. With the mixture of n-heptane and THF, one obtains many peaks for a polystyrene sample due to the polydispersity of the polystyrene. In fact, the adsorption increases with the molecular weight of the polystyrenes. The surface diffusion of polystyrene decreases with an increase in the retention factor or molecular size. Keywords: porous media; porosity; tortuosity; morphology; transport; liquid chromatography; diffusion; adsorption ii RÉSUMÉ La corrélation entre les propriétés structurales des matériaux et les propriétés de transport d’un fluide à travers les matériaux poreux intervient dans de nombreux procédés en physique, chimie, géologie et ingénierie. Les propriétés telles que la porosité et la distribution de taille de pore ne reflètent pas la complexité du réseau poreux qui consiste en un réseau de pores interconnectés irrégulier et de différentes sections. La complexité peut être décrite par un paramètre appelé la tortuosité. Les matériaux sont caractérisés avec les méthodes classiques de caractérisation comme les isothermes d’adsorption de l’azote, la porosimétrie au mercure et la détermination de la tortuosité par des mesures électriques afin de modéliser les propriétés de transport. Les tortuosités de silices ayant différentes morphologies (particules poreuses, particules de type cœur-coquille et monolithe) ont également été déterminées par chromatographie liquide. En chromatographie liquide la tortuosité intraparticulaire est calculée à partir du coefficient de diffusion intraparticulaire de polystyrènes déterminés à partir de l’élargissement des pics obtenus en mode dynamique et en mode statique en conditions non-adsorbantes avec le solvant tétrahydrofurane (THF). En mode dynamique, dans l’équation de van Deemter, le terme constant dépend de la diffusion d’eddy et de la polydispersité des polystyrènes. La silice poreuse Si100 présente une distribution de taille des pores assez large ce qui entraîne l’élargissement des pics chromatographiques. Le transport de polystyrènes à travers les silices en conditions adsorbantes a également été étudié en modifiant le solvant. En conditions adsorbantes, avec un mélange de THF et d’heptane, pour un polymère de taille donné, plusieurs pics sont obtenus en raison de la polydispersité du polystyrène. L’adsorption augmente avec la masse molaire du polystyrène. La diffusion de surface diminue lorsque le facteur de rétention ou la masse molaire augmentent. Mots clés: milieu poreux; porosité; tortuosité; morphologie; transport; chromatographie en phase liquide ; diffusion; adsorption iii TABLE OF CONTENTS ACKNOWLEDGEMENT ................................................................................................................. i ABSTRACT ...................................................................................................................................... ii RÉSUMÉ .......................................................................................................................................... iii TABLE OF CONTENTS ................................................................................................................. iv LIST OF FIGURES ......................................................................................................................... vii LIST OF TABLES ........................................................................................................................... xi NOMENCLATURE ........................................................................................................................ xii 1 INTRODUCTION .......................................................................................................................... 1 1.1. Research objectives ................................................................................................................ 1 1.2. Structure of this thesis ............................................................................................................ 2 1.3. Transport properties in porous media ..................................................................................... 3 1.3.1. The relationship between tortuosity and porosity in porous media ................................. 3 1.3.2. Determination of diffusion coefficients by liquid chromatography ................................ 8 1.3.2.1. Fundamental theory of dynamic method. ................................................................ 10 1.3.2.2. Peak parking method ............................................................................................... 16 1.3.3. Eddy diffusion ................................................................................................................ 19 1.3.4. Adsorption and surface diffusion ................................................................................... 22 1.4. Literature survey ................................................................................................................... 24 1.4.1. Silica topology analysis ................................................................................................. 24 1.4.2. Eddy diffusion in liquid chromatography .....................................................................
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