Open-cell Foams as Catalyst Support: A Description of Morphology, Fluid Dynamics and Catalytic Performance
Offenzellige Schäume als Katalysatorträger: Beschreibung von Morphologie, Fluiddynamik und katalytischer Performance
Der Technischen Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg zur Erlangung des Doktorgrades Dr.-Ing.
vorgelegt von
Amer Inayat
aus Lahore
Als Dissertation genehmigt von der Technische Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg Tag der mündlichen Prüfung: 31.10.2013
Vorsitzende des Promotionsorgans: Prof. Dr.-Ing. Marion Merklein
Gutachter/in: Prof. Dr. rer. nat. Wilhelm Schwieger Prof. Dr.-Ing. Carolin Körner
Parts of this work were already published or submitted to Chemical Engineering Science, Advanced Materials, Advanced Engineering Materials and Chemie Ingenieur Technik:
A. Inayat, H. Freund, T. Zeiser, W. Schwieger, Determining the specific surface area of ceramic foams: The tetrakaidecahedra model revisited, Chemical Engineering Science, 66 (2011) 1179–1188
A. Inayat, J. Schwerdtfeger, H. Freund, C. Körner, R.F. Singer, W. Schwieger, Periodic open-cell foams: Pressure drop measurements and modeling of an ideal tetrakaidecahedra packing, Chemical Engineering Science, 66 (2011) 2758–2763
A. Inayat, H. Freund, A. Schwab, T. Zeiser, W. Schwieger, Predicting the Specific Surface Area and Pressure Drop of Reticulated Ceramic Foams Used as Catalyst Support, Advanced Engineering Materials, 13 (2011) 990–995.
S. Lopez-Orozco, A. Inayat, A. Schwab, T. Selvam, W. Schwieger, Zeolitic Materials with Hierarchical Porous Structures, Advanced Materials, 23 (2011) 2602–2615
W. Schwieger, S. Lopez, A. Inayat, H. Freund, T. Selvam, Zeolite-Containing Materials with Hierarchical Porous Structures, Chemie Ingenieur Technik, 84 (2012) 1427-1427
Additional journal publications:
G.E. Schröder-Turk, W. Mickel, S.C. Kapfer, M.A. Klatt, F.M. Schaller, M.J.F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, K. Mecke, Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures, Advanced Materials, 23 (2011) 2535-2553
I. Paramasivam, A. Avhale, A. Inayat, A. Bosmann, P. Schmuki, W. Schwieger: MFI-type (ZSM-5) zeolite-filled TiO2 nanotubes for enhanced photocatalytic activity. Nanotechnology 20 (2009) 225607 (5pp)
A. Avhale, G.T.P. Mabande, A. Inayat, W. Schwieger, T. Stief, R. Dittmeyer, Defect-free zeolite membranes of the type BEA for membrane reactor applications, Chemie Ingenieur Technik, 81 (2009) 1090-1090
Für meine Eltern und Alexandra
Acknowledgements
The present work was carried out between February 2007 and February 2012 in the Institute of Chemical Reaction Engineering at the Friedrich-Alexander-University Erlangen- Nuremberg, Germany. At this point, I would like to express my gratitude and thanks to all who contributed to this work.
• My first and foremost gratitude goes to my supervisor Prof. Dr. Wilhelm Schwieger (head of the research group “Heterogeneous Catalysis and Porous Materials”) for accepting me as a researcher and giving me the chance of conducting my PhD work in his group. I am grateful for his continuous guidance and keen interest in my work. Under his supervision not only I learned to carry out research independently, but also to perform collaborative research in an effective manner. I am truly thankful for all his help, support and encouragement in both professional and personal matters.
• My special thanks go to Prof. Dr. Hannsjörg Freund (head of the research group “Catalytic Reactors and Process Technology”) for his help, useful advice and insightful discussions during this work.
• I would like to thank Prof. Dr. Peter Wasserscheid (head of the institute), Prof. Dr. Bastian Etzold (head of the research group “Chemical Vapor Processes and Catalytic Materials”), Prof. Dr. Nadejda Popovska-Leipertz and Prof. Dr. Martin Hartmann (director of ECRC, Erlangen) for their acceptance, encouragement and facilitation.
• Collaborative work with the other departments and institutes as well technical assistance from their personnel was an important element towards the successful completion of the present work. In this regard, I would like to thank Prof. Dr. Carolin Körner and Prof. Dr. Robert F. Singer (WTM Erlangen) for accepting the idea of a collaborative work on the EBM structures and I would like to express my gratitude to Dr. Jan Schwerdtfeger (ZMP, Fürth) and Peter Heinl (WTM, Erlangen) for manufacturing the SEBM structures (periodic cellular structures) for this work. I further take the opportunity to thank Dr. Herald Wiehler and Johannes Hartmann (WTM, Erlangen) for performing the computed tomography measurements. I am grateful to Tobias Heidig and Dr. Enrico Bianchi (Prof. Dr. Hannsjörg Freund’s group) for their useful inputs also during the time when they were at MPI, Magdeburg, Germany. I would also like to thank Prof. Dr. Peter Greil and Dr. Tobias Fey (Institute of Glass and Ceramics, Erlangen), Prof. Dr. Delgado and Tobias Horneber (LSTM, Erlangen), Prof. Dr. Cornelia Rauh (TU Berlin) and Dr. Thomas Zeiser (RRZE, Erlangen) for their cooperation.
Acknowledgements
• A valuable contribution to this work was made by the students who wrote their bachelor/master thesis for the topic as well as who worked as student research assistant. In this respect, I would like to express my thanks and appreciation to Stephanie Reuss, Markus Probst and Matthias Kick for their worthwhile roles.
• My sincere gratitude is rendered to all members of Schwieger research group for providing a friendly and enjoyable working atmosphere. I am especially thankful to Dr. Abhijeet Avhale, Dr. Saiprasath Gopalakrishna and Dr. Jürgen Bauer for their help and support during the very initial phase of my PhD work. I owe thanks to Alexandra Inayat, Sofia Lopez-Orozco, Stephanie Reuss, Marcelle Fankam, Elena Pleissner, Yingxue Zhang, Michael Klumpp, Jimmi Ofili, Andreas Schwab, Dr. Thangaraj Selvam, Hasan Baser, Dr. Ayyappan Ramakrishnan, Hendryk Partsch and Regine Mueller for being friendly and supportive colleagues. I am also thankful to the colleagues in other research groups at CRT as well as at ECRC.
• I would like to acknowledge the vital contribution of friendly, capable and competent CRT staff. Sincere thanks go to Mr. Michael Schmacks, Mr. Achim Mannke and Mr. Julian Karl (mechanical workshop), Mr. Gerhard Dommer and Mr. Karl-Heinz Ksoll (electrical workshop and IT), Mr. Walter Fischer and Mr. Hendryk Partsch (IT) and Mr. Helmut Gerhard. I am truly thankful to Mrs. Michelle Menuet, Mrs. Petra Singer, Mrs. Petra Weber and Mrs. Monika Bittan for the enduring support in administrative issues.
• To all my family members and friends goes my deepest gratitude without whose unwavering support, continuous encouragement and unconditional love I would never have made it this far. Here, I am especially grateful to my wife Alexandra and daughter Karla for their patience, perseverance and understanding during this busy time of my life.
• Finally, I gratefully acknowledge the funding of the German Research Council (DFG), which, within the framework of its `Excellence Initiative´ supports the Cluster of Excellence `Engineering of Advanced Materials´ at the University of Erlangen-Nuremberg.
Erlangen, October 2013 Amer Inayat
ii
Kurzbeschreibung
In der chemischen Prozessindustrie kann die Verwendung von strukturierten Reaktoren (z.B. Wabenkörper und Schäume) verschiedene Nachteile, wie z.B. hohen Druckverlust und Hotspots herkömmlicher gepackter Festbettreaktoren vermeiden. Deswegen wurden strukturierte Reaktoren (oder strukturierte Katalysatoren) in den vergangenen Jahrzehnten intensiv als Alternative zur Festbettreaktor-Technologie untersucht. Die bekanntesten und erfolgreichsten Beispiele für den technischen Einsatz strukturierter Reaktoren sind wabenförmige monolithische Katalysatoren, die aufgrund ihrer hervorragenden Eigenschaften (wie z.B. besonders geringes Verhältnis zwischen Druckverlust und geometrischer spezifischer Oberfläche) in den meisten Anwendungen im Umweltbereich die Standard- Katalysatorform geworden sind. Allerdings fehlen den Wabenkörpern aufgrund ihrer geraden Kanäle ohne Vernetzung einige andere reaktionstechnisch wichtige Eigenschaften, wie z.B. Strömungstortuosität und radiale Vermischung.
Offenzellige Schäume hingegen vereinen aufgrund ihrer hohen Porosität und dreidimensionalen zellulären Struktur die Vorteile von Festbetten (z.B. radiale Vermischung und Strömungstortuosität) und Wabenkörpern (hohe geometrische spezifische Oberfläche und geringer Druckverlust). Allerdings sind Schäume trotz ihrer hervorragenden Eigenschaften noch nicht in großen kommerziellen Operationen als Ersatz für konventionelle Festbetten angewendet worden. Dies kann mit ihren hohen Herstellungskosten, dem Mangel an ausreichenden Kenntnissen über Transportprozesse in derartigen Strukturen, sowie mit mangelnden Erfahrungen im Umgang mit Schäumen begründet werden.
Das Hauptziel dieser Arbeit war es, die Probleme im Zusammenhang mit der Bestimmung der Transporteigenschaften von offenzelligen Schäumen anzugehen. In dieser Hinsicht wurde zunächst eine umfassende Charakterisierung der offenzelligen Schäume hinsichtlich ihrer morphologischen Kenngrößen durchgeführt. Zudem wurde für offenzellige Schäume eine Gleichung zur theoretischen Vorhersage ihrer geometrischen spezifischen Oberfläche, die relevant für Wärme und Stofftransport ist entwickelt. Zu diesem Zweck wurde die Tetrakaidecahedron-Geometrie verwendet, bei der es sich um eine effizient raumfüllende und weithin akzeptierte repräsentative Geometrie für Schäume handelt. Die Gleichung berücksichtigt verschiedene Formen von Stegquerschnitten bei Schaumstrukturen. Darüber hinaus wurden periodisch offenzellige Schäume mit idealer Tetrakaidecahedron-Geometrie als Modellsysteme verwendet, um den Druckverlust in Schäumen (nicht-ideale Geometrie) zu beschreiben. In dieser Hinsicht wurde zuerst eine Gleichung für die Druckverlustabschätzung
Kurzbeschreibung in periodischen offenzelligen Schäumen entwickelt, welche dann für nicht-ideale offenzellige Schäume angepasst wurde. Die Anwendbarkeit der vorgeschlagenen Gleichungen für die Vorhersage von geometrischer spezifischer Oberfläche und Druckverlust wurde an nicht- idealen offenzelligen Schäumen aus unterschiedlichem Material (Keramik und Metall) für ein großes Spektrum an Porengrößen und offenen Porositäten validiert. Zu diesem Zweck wurden experimentelle Daten für spezifische Oberfläche und Druckverlust aus der vorliegenden Arbeit sowie aus der offenen Literatur verwendet. Es wurde gezeigt, dass die Gleichungen, die in der vorliegenden Arbeit vorgeschlagen wurden, die geometrische spezifische Oberfläche und Druckverlust in Schäumen mit mehr Präzision vorhersagen können als bereits bekannten Gleichungen.
Ein weiteres Ziel der vorliegenden Arbeit war es, die katalytische Leistung von Schaum/Katalysator-Kompositen mit der einer Katalysatorschüttung im Festbett zu vergleichen. Zu diesem Zweck wurden in einem ersten Schritt offenzellige Schäume aus gesintertem Siliziumcarbid (SSiC) mit Zeolith vom Typ ZSM-5 beschichtet. SSiC-Schäume mit unterschiedlicher Porengröße und H-ZSM-5-Zeolith mit verschiedener Azidität wurden eingesetzt. Außerdem wurde H-ZSM-5 in verschiedener Pellet größe hergestellt. Alle Katalysatorsysteme wurden in der Methanol-zu-Olefine Umwandlung in einer Versuchsanlage im Labormaßstab getestet. Methanol-Umsatz sowie Selektivität zu leichten
Olefinen (C2-C4) wurden bei verschiedenen Reaktionstemperaturen für beide Reaktor- Konfigurationen bestimmt. Dabei zeigten SSiC-Schaum/Zeolith-Komposite eine höhere Selektivität zu leichten Olefinen und eine bessere Stabilität gegenüber Deaktivierung. Die überlegene Leistung der Schaum/Zeolith-Komposite wurde darauf zurückgeführt, dass die Makroporosität von Schäumen und die dünne Zeolithschicht an Stelle von Pellets die Diffusion von Edukten und Produkten verbessern können. Außerdem kann die gute Wärmeleitfähigkeit von Siliciumcarbid den Abtransport von Reaktionswärme in der exothermen Methanol-zu-Olefin-Reaktion verbessern.
iv
Abstract
In the chemical process industry, the use of structured reactors (e.g. monolithic honeycombs and foams) may eliminate the drawbacks (e.g. high pressure drop and hotspots) exhibited by the conventional randomly packed fixed-bed reactors. Therefore, in the last few decades, structured reactors (or structured catalysts) have been extensively investigated as alternative to the fixed-bed reactor technology. The most prominent and successful examples of structured reactors are the honeycomb-shaped monolithic catalysts, which due to their excellent properties (e.g. exceptionally low ratio of pressure drop to geometric specific surface area) have become the standard catalyst shape in most environmental applications. However, the monolithic honeycombs lack some other important properties, e.g. tortuosity of the flow and radial mixing which can be attributed to their straight channels with no interconnectivity.
Open-cell foams on the other hand, due to their high porosities and three dimensional cellular structure, can combine the advantages of packed beds (radial mixing and tortuosity of the flow) and honeycombs (high geometric specific surface area and low pressure drop) on one platform. However, despite their attractive properties which can be exploited in the chemical process industry, foams have still not been applied in large-scale commercial operations to replace the conventional packed bed reactors. This can be ascribed to their high manufacturing cost, lack of sufficient knowledge of transport processes in foam like structures as well as lack of handling experience.
The main aim of the present work was to address the problems related to the determination of transport properties of open-cell foams. In this regard, as a first step, a comprehensive characterization of open-cell foams with respect to their morphological parameters was performed. In addition, in order to theoretically determine the geometric specific surface area (which is relevant for heat and mass transport) of open-cell foams, a mathematical correlation was developed. For this purpose the tetrakaidecahedron geometry (an efficiently space-filling and widely accepted representative geometry of foams) was used and different shapes of strut cross-sections of foam structures were taken explicitly into account. Furthermore, periodic cellular materials of ideal tetrakaidecahedron geometry were used as model systems to describe the pressure drop in open-cell foams (replicated foams with non-ideal geometry). In this regard, as a first step, a correlation for pressure drop estimation in periodic cellular materials of ideal tetrakaidecahedron geometry was developed which was then adapted for the open-cell foams that exhibit non-ideal geometry. The applicability of the proposed
Abstract correlations for geometric specific surface area and pressure drop was validated for open-cell foams of different material (ceramic and metal) with a large range of pore size and open porosity. For this purpose experimental data of specific surface area and pressure drop from the present work as well as from the open literature was used. It was demonstrated that the correlations proposed in the present work can predict the geometric specific surface area and pressure drop in foams with more precision than any other state-of-the-art correlation either theoretical or empirical.
A further aim of the present work was to directly compare the catalytic performance of foam/catalyst composites (used as reactor internal) with the packed bed of catalyst pellets in a test reaction. For this purpose, open-cell foams made of sintered silicon carbide (SSiC) were coated with zeolite of the type ZSM-5. SSiC foam samples of different pore size and H-ZSM- 5 zeolite of different acidity were used. In addition H-ZSM-5 was pelletized in different pellet sizes. Methanol-to-olefin conversion was performed on SSiC-foam/zeolite composite and on zeolite pellets in a lab-scale reactor setup. Methanol conversion and selectivity towards light olefins were determined at different reaction temperatures for both monolithic (foam/zeolite composite) and packed bed (zeolite pellets) reactor configurations. The SSiC-foam/zeolite composites showed higher selectivity towards light olefins and better stability towards deactivation. The superior performance of foam/zeolite composites was ascribed primarily to the macro porosity of foams and a thin layer of zeolite (instead of pellets), which can enhance the diffusion of reactant and products. Another important factor was the high thermal conductivity of silicon carbide material which can facilitate the rapid evacuation of heat in methanol-to-olefin conversion (an exothermic reaction) and accelerate the mass transfer.
vi
Table of Contents
1 Introduction ...... 1
1.1 Motivation and aims ...... 1 1.2 Scope and outline of this work ...... 3
2 Morphological characterization of open-cell foams ...... 5
2.1 Background...... 5 2.1.1 Foam matrix ...... 6 2.1.2 Manufacturing of open-cell foams ...... 7 2.1.3 Periodic cellular materials ...... 10 2.2 Experimental...... 12 2.2.1 The foam samples ...... 12 2.2.2 Characterization of the porosity ...... 14 2.2.3 Characterization of the pore size, strut thickness, strut cross-section and strut morphology ...... 15 2.2.4 Characterization of the specific surface area ...... 16 2.3 Results and discussion ...... 17
2.3.1 Porosity ...... 17 2.3.2 Pore size ...... 19 2.3.3 Strut thickness, cross-section and morphology ...... 21 2.3.4 Specific surface area ...... 23 2.4 Summary and conclusion ...... 24
3 Geometric modeling of open-cell foams ...... 27
3.1 Background...... 27 3.2 State-of-the-art geometric models ...... 28
3.3 State-of the-art correlations for predicting the geometric specific surface area (Sv-geo) ...... 31
3.4 Performance of state-of-the-art correlations for predicting the Sv-geo...... 38 3.4.1 Selection of the geometric model ...... 41 3.4.2 Variation of the strut cross-section with porosity ...... 41
3.5 New correlation for predicting the Sv-geo ...... 43 3.5.1 Triangular struts ...... 44 3.5.2 Cylindrical struts ...... 46 3.5.3 Concave triangular struts ...... 47 3.6 Validating the new correlation ...... 50 3.7 Summary and conclusion ...... 53
Table of Contents
4 Pressure drop measurement and modeling on open-cell foams ...... 55
4.1 Background...... 55 4.2 State-of-the-art correlations for the pressure drop prediction in open-cell foams ...... 57 4.3 Pressure drop measurement over open-cell foams ...... 62 4.3.1 Experimental ...... 62 4.3.2 Results ...... 62 4.4 Periodic cellular structures as model systems for the description of the pressure drop in open- cell foams...... 68
4.4.1 Pressure drop modeling on periodic cellular structures: the Ergun equation revisited ...... 68 4.4.2 Correlation for the pressure drop in periodic cellular structures: extension for low porosity porous media ...... 72 4.4.3 Adapting the correlation for replicated open-cell foams ...... 76 4.4.4 Validating the correlation for foams with different strut cross-sections ...... 80 4.5 Summary and conclusion ...... 86
5 SSiC-foam/zeolite composites for methanol-to-olefin conversion ...... 89
5.1 Background...... 89
5.1.1 Zeolites ...... 89 5.1.2 Structured reactors ...... 93 5.1.3 Structured zeolitic composites ...... 97 5.1.4 Methanol conversion to hydrocarbons ...... 101 5.2 Experimental...... 105
5.2.1 Preparation of SSiC-foam/zeolite composites by dip-coating ...... 105 5.2.2 Characterization ...... 107 5.2.3 Methanol conversion ...... 109 5.3 Results and discussion ...... 113
5.3.1 Dip-coating ...... 113 5.3.2 SSiC-foam/zeolite composites ...... 116 5.3.3 Characterization of zeolite catalysts ...... 119 5.3.4 Methanol conversion ...... 122 5.4 Summary and conclusion ...... 130
6 Summary and general conclusion ...... 133
7 References ...... 139
Appendix ...... 151
viii
1 Introduction
1.1 Motivation and aims
Owing to their remarkable properties such as large external surface area, high mechanical strength, high porosity and a low resulting pressure drop open-cell foams (ceramic or metal) are excellent candidates for a variety of industrial applications.
Open-cell foams are highly porous reticulated cellular materials with a sponge like structure that consists of three dimensionally interconnected struts. The struts (solid phase) are surrounded by void spaces that constitute the cells. The foam matrix is usually described by its morphological parameters, namely cell size, window size, strut thickness and porosity. The most commonly used characteristic of open-cell foams is the PPI (pores per inch) or so called pore count value, which can be obtained by counting the pores in a linear inch [1-3]. The manufacturing routes of open-cell foams can be mainly classified into three methods , namely replication method, sacrificial template method and direct foaming [4, 5]. Most commercially available open-cell foams are produced by the replication method which was invented and patented by Schwartzwalder and Sommer [4]. The replication technique uses polymer foam, usually polyurethane foam, as a template. Though, foam templates of other polymer materials can be equally effective [5, 6].
The first commercial application of open-cell foams reported in the literature was the use of ceramic foams as filters for molten metals [7, 8]. Over the last two decades, they have been extensively investigated for a number of other applications including gas filters, heat exchangers, porous burners and catalyst supports [3, 6, 9-16].
In chemical engineering, for the application as reactor internals, open-cell foams offer clear advantages over conventional randomly packed (irregular arrangement of individual particles) fixed-bed reactors e.g. remarkably low ratio of pressure drop to geometric specific surface area and enhanced heat and mass transfer. Thus, for the chemical process industry, where the majority of heterogeneously catalyzed gas-phase reactions is carried out in fixed-bed reactors which have some obvious disadvantages, open-cell foams as reactor internals represent themselves as a promising alternative [14, 16-19]. In this regard, open-cell foams may combine the advantages of aforementioned geometry related properties of foams with the superior thermal and mechanical properties of foam materials (e.g. metal foams, SiC foams) [20-22]. The unique combination of superior properties of foam geometry and material can thus be of a great advantage in applications involving high flow rates and/or strongly
1 Introduction endothermic or exothermic reactions. However, in spite of their outstanding properties which can be exploited in the chemical process industry, open-cell foams have still not been applied in large-scale commercial operations. A study of recent literature reveals that this is partly due to the complex and expensive manufacturing process of foam catalyst beds and partly due to the fact that despite a large amount of research conducted on open-cell foam their chemical engineering parameters are still not completely clear. Furthermore, the handling of foam catalyst beds e.g. loading and unloading of a foam beds into and from the reactor respectively and avoiding a bypass flow can also be challenging [6, 23, 24].
From chemical engineering point of view, in order to successfully design and apply monolithic foam reactors in the chemical process industry, a comprehensive knowledge of the geometric, morphological and fluid transport properties of foam structures is the primary prerequisite. In recent years several authors have reported their work on open-cell foams as potential catalyst support investigating the aforementioned properties [13, 14, 19, 25, 26]. These authors have introduced different experimental methods and proposed various geometric models and mathematical correlations in order to determine the foam properties e.g. geometric specific surface area (relevant for heat and mass transfer) and pressure drop, which are essential parameters for a successful reactor design. However, as mentioned before, despite a considerable amount of research that has been performed in this area over the past few decades, no generally applicable correlations for determining the foam properties have been proposed so far. According to the recent literature, for a realistic modeling of foams and to develop appropriate correlations for estimating the foam properties, it is extremely important to select a suitable representative geometry and consider the variations in the strut cross-section with the porosity. In this regard, in the first part of the present work, the problem of determining/estimating the morphological, geometric and fluid dynamic properties of open-cell foams is addressed. The aims include:
• An experimental characterization of open-cell foams with respect to their pore size, strut size, porosity, and geometric specific surface area • Development of a mathematical correlation in order to theoretically determine the geometric specific surface area of open-cell foams by taking into account the different strut morphologies (hollow or dense) and different shapes of the strut cross-section • Pressure drop measurement in open-cell foams as well as development of a generally applicable correlation in order to predict the pressure drop over foams of different material with a wide range of pore size and porosity
2 1.2 Scope and outline of this work
As described above, the use of foam structures as catalyst support can be beneficial in case of strongly exothermic or endothermic reactions. For these cases the thermal conductivity of the foam material is very important as it can allow for a rapid heat exchange which may accelerate the mass transfer. In addition, a thin layer of catalyst coated on foam (instead of catalyst pellet as in the case of packed bed configuration) and the macro porosity of the foam structure can improve the diffusion of reactants and products which may lead to a better performance of the catalyst. In the literature the methods reported for coating structured supports can be mainly divided in two categories, in-situ (direct crystallization of a catalyst on the support surface) and ex-situ (dip coating, slurry coating) [6, 14, 16, 21, 22]. In-situ coating results in a good adherence between support and the coated layer but has disadvantages of high cost and longer preparation time. In case of ex-situ coating (low cost and faster preparation), the support/layer bond is not as strong as in in-situ coating, however the layer offers the advantage of intra-particle porosity (enhances diffusion).
The second part of the present work deals with the coating of a thin layer of zeolite catalyst on sintered silicon carbide (SSiC) foams and the use of coated foams in the catalytic methanol- to-olefin conversion (an exothermic reaction). The aims of this part include:
• Development of SSiC-foam/zeolite composite by dip coating method • Performing catalytic methanol-to-olefin conversion over SSiC-foam/zeolite composites (monoliths) as well as over packed beds of zeolite pellets • Investigating the effect of reactor configuration (packed bed and foam monolith), pore size of the foam structure and acidity of the zeolite catalyst on the selectivity towards light olefins and stability towards deactivation in catalytic methanol-to-olefin conversion
1.2 Scope and outline of this work
The following paragraphs present the goals set for each chapter as well as a brief overview of the experimental and theoretical approaches used.
An experimental characterization of the morphological parameters of open-cell foams is presented in the second chapter. The aim is to highlight the important morphological properties (necessary for geometric description/modeling) of open-cell foams and to give their clear definitions in order to avoid any ambiguity between the unclear definitions. The measured parameters of foams are used in the following chapters for developing and validating the correlations in order to estimate the properties of open-cell foams which are important for their applications in chemical engineering. 3 1 Introduction
The state-of-the-art geometric models of open-cell foams as well as correlations for predicting the geometric specific surface area are discussed in the third chapter. The goal of this chapter is to evaluate the validity and applicability of state-of-the-art correlation for predicting the geometric properties of reticulated open-cell foams, mainly the geometric specific surface area. Another goal is to develop a correlation for the theoretical determination of geometric specific surface area of open-cell foams by taking into consideration the different strut morphologies (hollow or dense) as well as different shapes of the strut-cross-section. For this purpose geometric constants of tetrakaidecahedron geometry (an efficiently space filling and widely accepted representative geometry for reticulated open-cell foams) are used.
In the fourth chapter the problem of predicting the pressure drop in open-cell foams is addressed. The goal is to develop a generalized correlation which allows the theoretical determination of the pressure drop to a satisfactory level for open-cell foams of different materials with a wide range of pore size and porosity. For this purpose, as a first step, pressure drop in periodic cellular (foam-like) materials with ideal tetrakaidecahedron geometry is studied to develop a correlation for the theoretical determination of the pressure drop in periodic structures. The correlation developed for periodic cellular structures of ideal tetrakaidecahedron geometry is then adapted for open-cell foams with non-ideal/random geometries. The validity of the adapted correlation (for foams of different materials, porosities and pore sizes) is examined by comparing the predictions with the experimental pressure drop data of open-cell foams from present work as well as from the open literature.
The fifth chapter is devoted to the catalytic methanol-to-olefin conversion over SSiC- foam/zeolite composites and packed beds of zeolite pellets. The main aim is to compare the performance of both systems for the catalytic methanol conversion, selectivity towards light olefins (C2-C4) and stability towards deactivation for long term applications. A further aim is to study the influence of acidity of the zeolite and the pore size of foam supports on both methanol conversion and selectivity for light olefins. For this purpose as a first step, a dip- coating method is developed and optimized by varying different coating parameters in order to obtain the SSiC-foam/zeolite composites. For the composites, zeolite of the type H-ZSM-5 with different acidity and SSiC foam support with different pore sizes are used. The catalytic testing of SSiC-foam/zeolite composites and zeolite pellets (packed bed) is carried out in a lab-scale reactor setup.
A summary of the entire present work is given in chapter six, in which major findings and the concluding remarks from each of the previous chapters are presented.
4
2 Morphological characterization of open-cell foams
2.1 Background
Open-cell foams are highly porous cellular materials with pore densities of usually 10-100 PPI (pores per inch) and typical porosity ranges of 75% to 90% for ceramic foams and 60 to 97 % for metal foams [3, 6, 13]. They have a complex three dimensional internal architecture with widely distributed properties [1-3].
Open-cell foams may exhibit considerable variations in their structure which can be caused by different factors, namely manufacturing rout, polymer foam templates and the slurry (ceramic or metallic) used. This may hold true even for foams of similar PPI [2, 23]. Also, the manufacturing route and the porosity range influence the foam properties to a large extent e.g. manufacturing route determines the strut morphology (dense or hollow) and porosity range determines the shape of the strut cross-section (circular, triangular or concave triangular) [27- 29].
In this chapter a brief overview of different manufacturing routes for the production of reticulated open-cell foams along with the influence of the manufacturing methods on foam properties is given. In addition, manufacturing techniques of producing periodic cellular structures/foams is briefly described. The goal of this chapter is to perform a comprehensive experimental characterization of the morphological properties of open-cell foams. A second goal is to highlight and define the properties of open-cell foams which are necessary for their geometric description and modeling.
A thorough description of the complex three dimensional architecture of the reticulated open- cell foams requires several structural or morphological properties such as, e.g., porosity, cell and strut size, strut morphology and specific surface area [2, 14, 24].
For the present work the following properties of the open-cell foams are studied:
- Porosity : εο (open), εs (strut) : [-]
- Cell size : dc : [m]
- Window size : dw : [m]
- Strut thickness : ds : [m] - Strut morphology : dense or hollow : [-] - Strut cross-section : circular, triangular, concave triangular : [-] -1 - Surface to volume ratio : Sv-geo (geometric specific surface area) : [m ]
2 Morphological characterization of open-cell foams
2.1.1 Foam matrix
Engineered foams have cellular structures and are categorized as either open-cell or closed- cell foams. The structure of both open and closed-cell foams consists of an assembly of irregularly shaped polyhedral cells enclosed by the three dimensional strut network. In case of open-cell foams the cells are connected to each other with solid edges (struts) and cell to cell connectivity takes place via open faces (windows) whereas, in closed-cell foams, the cells are connected to each other with solid faces with no interconnectivity between them [2, 30].
A comparison between the cell unit of open and closed-cell foams is given in the Figure 2.1. Since closed-cell foams are not in the scope of this work, from here onwards only open-cell foams will be discussed.
(a) (b)
Figure 2.1: Components of the structure of a cell unit in a) open and b) closed cell foams [2]
The basic building blocks in open-cell foams are the struts, which are connected to each other three dimensionally constituting polyhedral cells (void volumes) and generate its sponge-like structure. A typical foam matrix of reticulated open-cell foams is shown in Figure 2.2.
Figure 2.2: An open-cell (silicon carbide) foam matrix [31]
The strut morphology and the shape of the strut cross-section (resulting from the manufacturing route and the porosity range respectively) can affect the geometric properties of the foam to a great extent [2, 5, 29]. The details of different strut morphologies and shapes of the strut cross-section are discussed in the next sections in detail.
6 2.1 Background
Open-cell-foams exhibit high porosities. Their porosity is mainly due to the void volume (cells) enclosed by the struts. However, an additional porosity (so called internal or strut porosity) may be present in an open-cell foam structure which originates from the manufacturing process in which polymer foam is used as a template or replica. Porosity is an important property of a foam structure. It has a great influence on the permeability and fluid dynamic behavior of foams [13, 14].
Open-cell foams are usually available in a wide range of cell/pore sizes. The cell size is one of the key parameters in the designing and manufacturing of open-cell foams, as for many engineering applications the foam performance can be directly influenced by its cell size. The conventional way of representing the cell or pore size of a foam structure is as PPI (pores per inch), which is obtained by counting pores in a linear inch. It is also termed as pore count or pore density [6, 23, 27]. The term PPI, pore-count or pore density can be confusing due to the unclear definition of a pore, because it could be a window or a cell.
The pore density or pore count used by the foam manufacturers does not give a precise measure but merely reflects a range of cell or pore sizes. Usually, each foam manufacturer has his own reference scale e.g. a foam considered as 40 PPI by one manufacturer could be defined as 60 PPI by another. Also in practice, there can be a wide variation between the measured pore size and the pore diameter calculated from the PPI value which is provided by the manufacturer [2, 3].
Most replicated open-cell foams are anisotropic in nature. They may have ellipsoidal cells shape (caused by elongation) and deformed strut network. The anisotropy in foam structures may be ascribed to the manufacturing process [14, 25].
Open-cell foams usually have high geometric specific surface area (surface to volume ratio). In a foam structures the geometric surface area is relevant for momentum, heat and mass transfer and hence is of fundamental importance for designing industrial systems based on foam matrices such as, e.g. catalyst carriers, gas filters, heat exchangers packing in columns etc. [9, 14, 19, 32, 33]. Therefore, an accurate determination of the specific surface area of foams is extremely important for their successful industrial application.
2.1.2 Manufacturing of open-cell foams
The fact that no one manufacturing route of foams is flexible enough to yield all the necessary structures and properties has led to the development of different manufacturing and processing methods [5, 34].
7 2 Morphological characterization of open-cell foams
Today, a variety of manufacturing routes for open-cell foams is available. However, they can be mainly divided in three categories i.e. replication technique, direct foaming and sacrificial template method, with a series of variations in the basic recipe [4, 5, 35, 36]. In this chapter, the most commonly used methods (replication technique and direct foaming) for producing open-cell foams are discussed.
2.1.2.1 Replication technique
The replication of polymer foams was one of the first manufacturing techniques developed to produce ceramics with controlled macro porosity. Most commercial ceramic foams of open- cell type are produced by applying the replication technique [4, 37, 38] in which they are obtained as positive image of the polymeric foam template. For the replication technique, usually polyurethane foam is used as a template, although foams of other polymer materials can be equally effective [5, 6]. The replication technique involves infiltration of ceramic slurry into the polymer foam, removal of excess slurry, drying and burning of the polymer phase. As a result, the ceramic particles are sintered together to give a foam structure consisting of hollow struts (with internal void volume) [3, 4]. Figure 2.4 shows some examples of open-cell foams produced by the replication technique.
Figure 2.3: Manufacturing of reticulated open-cell foams by replication, adapted from [3]
Figure 2.4: Reticulated ceramic foams of different pore sizes and materials [31]
8 2.1 Background
2.1.2.2 Direct foaming
In direct foaming technique a gas is dispersed in the form of bubbles into a ceramic slurry or suspension. This can be achieved by two means: • introducing an external gas by mechanical mixing, injecting a gas stream, or applying an aerosol propellant • evolution of gas in situ
For the manufacturing of ceramic foams by the introduction of an external gas, certain additives and surfactants are generally required in order to reduce the surface tension between the gas-liquid interfaces. These materials stabilize the gas bubbles and give the structure a certain shape before it is subject to drying and a subsequent calcination [5, 35].
(a) (b) Figure 2.5: Strut morphology of foam struts a) hollow struts from replication of reticulated polyurethane foam and b) dense strut from direct foaming of a ceramic suspension, adapted from [2]
Since there is no precursor foam involved in the direct foaming technique, the foams produced using this technique feature dense struts (Figure 2.5b). Also, foams resulting from direct foaming are generally less open compared to the ones produced by the replication method [2, 27, 39].
Direct foaming can also be achieved by in-situ evolution of a gas. This usually involves the addition of a foaming agent that generates gas bubbles during its decomposition due to heat or a chemical reaction [40].
9 2 Morphological characterization of open-cell foams
2.1.3 Periodic cellular materials
In contrast to replicated open-cell foams that exhibit irregular cellular structures, periodic cellular materials (foam-like structures) represent a class of cellular materials with defined cell/pore size, cell geometry and cell orientation. They can be produced by rapid prototyping using different techniques, e.g. selective electron beam melting (SEBM), selective laser sintering, 3D printing etc. [41, 42]. With these techniques it is possible to control the morphological and geometrical parameters of foam structures with a high degree of reproducibility and vary these properties in a controlled manner.
Owing to a fine control (through manufacturing techniques) on the geometrical and morphological properties of periodic cellular structures, they can be considered as ideal systems to study the effect of morphological parameters on the mechanical, thermal and fluid transport properties of foams and foam-like structures. The knowledge obtained from such a systematic study can thus be applied in mathematical modeling as to develop appropriate correlations for the prediction of important data needed for designing a column or a reactor which uses a foam matrix as internal. The mathematical and geometrical models as well as correlations developed for ideal foam/cellular geometries can then be adapted for the non- ideal geometries as encountered in replicated open-cell foams.
Figure 2.6: An example of periodic cellular lattice [43] (a), periodic cellular structure produced by using selective laser sintering [41] (b)
Selective electron beam melting (SEBM)
Selective electron beam melting is an additive manufacturing technique which allows the free form generation of three dimensional metallic components from metal powder. In contrast to conventional machining, in additive manufacturing technique parts are produced by successive melting of layers of materials rather than removing the material [44, 45].
The basic requirement for applying SEBM technique is the generation of three dimensional computer aided design (CAD) of the component which is to be produced. In order to generate
10 2.1 Background the layer information, the CAD model is sliced into layers of constant thickness. Each layer is then melted to an exact geometry as defined by the 3D CAD model. The SEBM process is carried out in vacuum in order to avoid the exposure of the materials to atmosphere. The complete description of the procedure and the process parameters of the SEBM manufacturing technique can be found elsewhere [42, 44, 45].
Figure 2.7: Component generation using the SEBM technique [44]
Figure 2.8: (a) cellular materials produced by selective electron beam melting, (b) CAD design (left) and CT scan of produced sample (right) [46]
11 2 Morphological characterization of open-cell foams
2.2 Experimental
2.2.1 The foam samples
2.2.1.1 Ceramic foams
The ceramic foams investigated in this thesis work were made of sintered silicon carbide (SSiC). These foams were manufactured on request by Fraunhofer IKTS, Dresden, via the replication technique [37, 38].
The foam samples were supplied in cylindrical shape with 30 mm diameter and 90 mm length with pore densities of 10, 20 and 30 PPI and nominal porosities of ca. 90%. Figure 2.9 a and b show top and lateral view of the samples respectively. For characterization purposes, all foam samples were cut into pieces of length 30 mm.
(a)
(b)
Figure 2.9: (a) Top and (b) lateral view of investigated SSiC foams of different PPI
12 2.2 Experimental
2.2.1.2 Metal foams
The metal foams used were made of aluminum. The foam samples were manufactured by m.pore GmbH, Dresden, and were supplied in cylindrical shape with pore densities of 10 and 20 PPI. For the morphological characterization the foam samples of 20 and 30 mm length were used. Figure 2.10 a and b show the top and lateral view of the investigated aluminum foams respectively.
(a)
(b)
Figure 2.10: (a) Top and (b) lateral view of investigated aluminum foams of different PPI
2.2.1.3 Periodic cellular structures
In addition to reticulated ceramic and metal foams, periodic cellular structures with ideal kelvin and cubic cell geometries (Figure 2.11) were also studied. The samples were manufactured and provided by WTM (Lehrstuhl Werkstoffkunde und Technologieder Metalle), Universität Erlangen-Nürnberg). For the production of the periodic cellular structures SEBM (selective electron beam melting) process was used. For this work, samples of different pore size and porosities were used.
(a) (b)
Figure 2.11: Periodic cellular structures with ideal (a) cubic and (b) tetrakaidecahedron packing
13 2 Morphological characterization of open-cell foams
2.2.2 Characterization of the porosity
The total porosity of the foam samples was determined by using the definition of relative density (equation 2.1), where ρg is the apparent density and ρs is the solid density.
ρ ε 1−= g t ρ (2.1) s
The apparent density was obtained from the apparent volume (calculated using the dimensions of the foam sample) and mass of the foam sample, whereas the solid density was obtained by He-pycnometry, which measures the solid volume of the sample material by helium displacement. He-pynometric measurements were done by using a Thermoelectron pycnometer of the type Pycnomatic ATC.
The open porosity, which is relevant for the fluid dynamics inside foam, was calculated using equation 2.2, where ρb is the strut bulk density.
ρ ε 1−= g o ρ (2.2) b
The strut bulk density, given in equation 2.3 is the density of the solid struts, assuming they were nonporous with a smooth surface. This assumption was established to account for the hollow strut volume. Since ceramic foams investigated in present work have hollow struts, the additional hollow strut volume must be determined to get the strut bulk density. Therefore, in order to obtain the value of ρb, the hollow strut volume was added to the solid volume (see equation 2.3). For equation 2.3, Vsolid was obtained by He-pycnometry and the hollow strut volume (Vhollow-strut) was obtained by mercury intrusion porosimetry.
mass ρ = foam b + (2.3) solid VV hollow−strut
The porosimetry measurements were done on a Thermoelectron porosimeter of the type Pascal 140 and 440. The strut porosity was finally calculated by subtracting open porosity from total porosity of the foams.
14 2.2 Experimental
2.2.3 Characterization of the pore size, strut thickness, strut cross-section and strut morphology
Image analysis was performed for the characterization of pore (window) diameter and strut thickness of reticulated open-cell foams investigated for the present work.
For this purpose magnified digital images of the foam samples from the top, bottom and sides (similar to Figure 2.12) were analyzed by the software DatInf® measure (Version 2.1d).
Due to the anisotropy, foam structure may have elongated cells and consequently elongated or deformed window, which leads to different window size in different direction. In order to account for this phenomenon, instead of measuring the window diameter, the area of each window was determined with the help of the above mentioned software. The window area was then converted into diameter of an equivalent circle (with corresponding area) which was taken as characteristic window size (Figure 2.12). In this way more than 100 windows were analyzed and the average window size was calculated as an arithmetic mean.
Figure 2.12: Determining the window and the strut size of foams by image analysis
The strut thickness was measured at the middle of the strut and more than 100 struts were analyzed to get an average value. Strut and pore size distribution were obtained from CT data for which the mean pore and strut size of the foam samples were determined by using the peak fitting module of the software Origin 8. The strut shape and morphology was determined by visual examination and with the help of SEM images of the foam struts.
For periodic cellular structures (with ideal tetrakaidecahedron and ideal cubic packing), both window and strut size was determined with the help of a Veriner caliper. Average values of the window as well as strut thickness were obtained for one hundred measurements.
15 2 Morphological characterization of open-cell foams
2.2.4 Characterization of the specific surface area
Open-cell foams usually exhibit high geometric specific surface area which makes them interesting candidates for many chemical engineering applications. The geometric specific surface area of foams is usually defined as the total external surface of the struts bed (as if they had smooth surface) per unit volume of the foam [14]. For porous materials, the specific surface area is usually determined by conventional physisorption measurements of gases e.g. applying the BET method [47]. This method, however, cannot be applied for reticulated open- cell foams because of the nature of the struts, as they feature a rough surface and may possess internal void volumes, which would lead to an overestimation of the specific surface area values. Recently, Grosse et al. [48] and Incera Garrido et al. [14] have used magnetic resonance imaging (MRI) to measure the specific surface area of ceramic foams. These authors investigated alumina foams. X-ray computed tomography (CT) has also been applied by different authors to characterize the morphological parameters of foam structures [49-52]. More recently Grosse et al. [25] have reported their work on determining the morphological characteristics of ceramic foams. These authors applied X-Ray computed tomography to silicon infiltrated silicon carbide foams in order to determine their specific surface area.
For the present work X-ray micro computed tomography was used to determine the specific surface area of SSiC and aluminum foams. The measurements were carried out on a Scanco Medical tomograh of the type µ-CT 40. The detailed description of the principle, the measurement method and the algorithm used can be found elsewhere [53].
Figure 2.13: Reconstruction of foam geometry from data obtained by µ-CT
For the evaluation of CT data and the reconstruction of foam geometry (Figure 2.13), a threshold value of 60 was used. With this threshold value the internal strut pores were filled and the mean pore and strut sizes obtained were comparable (see section 2.3.2) to the ones obtained from image analysis.
16 2.3 Results and discussion
2.3 Results and discussion
2.3.1 Porosity
Figure 2.14 shows the structure and a strut cross-section of a 10 PPI open-cell foam investigated in the present work. From the figure, two types of porosities are visible i.e. the external or so-called open porosity (εo), which is due to the void volume enclosed by the foam strut network, and internal strut porosity (εs), which originates from the manufacturing process.
As described in section 2.1.2, replicated open-cell foams are manufactured as positive image of a polymeric foam structure therefore a void volume in the solid strut network appears after the polymer phase is burnt away during calcination. This additional void volume, which stems from the burnt precursor strut network, is responsible for the strut porosity in a foam matrix.
Hence, the total porosity (εt) of a replicated open-cell foam can be expressed as the sum of its open (εo) and the strut porosity (εs.) i.e.: εt = εo + εs.
Figure 2.14: Foam matrix showing open and strut porosity
The results of determined properties of open-cell foams investigated in the present work are shown in Table 2.1-2.3. From the values of total and open porosities, it can be observed that all SSiC-foam samples show strut porosity which seems to be in a similar range and is less than 5%. The strut porosity is hardly accessible for the fluids flowing through foam structures. Therefore, in order to determine the fluid dynamic or pressure drop properties of foams open porosity instead of total porosity must be used. Aluminum foams as well as periodic cellular structures used in the present work feature dense struts i.e. the struts show no internal void volume. Therefore the strut porosity in their case is essentially zero and total porosity can be taken as equal to the open porosity.
17 2 Morphological characterization of open-cell foams
Table 2.1: Properties of SSiC and Al foams investigated in the present work
d d w, image s, image ε ε ε ρ S Material PPI n t o solid v, µ-CT analysis analysis (-) (-) (-) ( -3) (m-1) (mm) (mm) g.cm SSiC
10 1.798 0.701 0.883 0.878 0.853 3.115 732 20 1.297 0.480 0.901 0.896 0.873 3.108 858 30 1.030 0.399 0.894 0.885 0.862 3.043 1136
Aluminum 10 2.550 0.544 - 0.932 0.932 2.674 429
20 1.895 0.343 - 0.931 0.931 2.717 582
Table 2.2: Properties of the periodic cellular structures with Kelvin’s cell geometry
d d ε ρ CPI w s-cylindrical o solid (mm) (mm) (-) (g.cm-3) 3.5 3.085 1.104 0.871 4.453
4.5 2.397 1.016 0.846 4.453
5 2.166 0.733 0.861 4.453
6 1.689 0.999 0.799 4.453
Table 2.3: Properties of the periodic cellular structures with cubic cell geometry
a d ε ρ CPI s-cylindrical o solid (mm) (mm) (-) (g.cm-3) 5.5 4.624 1.351 0.870 4.453
8.5 2.938 1.029 0.835 4.453
10 2.271 0.782 0.855 4.453
11 2.294 1.025 0.725 4.453
18 2.3 Results and discussion
2.3.2 Pore size
As described in section 2.1.1, the conventional method of determining the pore size i.e. by counting the pores per linear inch, can be confusing due to the ambiguous definition of a pore, as a pore can be a window or a cell. Therefore, in order to avoid any confusion between different terms e.g. pore, cell, and a window, clear definition of cell and window size are given in the Figure 2.15. Where, the cell size is constituted by the void volume enclosed by the three dimensionally interconnected foam struts and the window is defined as an opening into the cell which serves as a medium for cell to cell connectivity.
For the present work, the term pore (which can be a window or a cell) will only be used in a general sense. For the geometric modeling of foam or any analytical calculations, pore size will be explicitly specified as a window or a cell.
Figure 2.15: Cell unit of an open-cell foam showing components of a cell
In order to account for the cell (consequently strut and window) anisotropy caused by the elongation of cells during manufacturing [14, 25], window and strut size were determined in both axial and perpendicular planes. In addition instead of measuring the window diameter which has different length in different directions, the area of the window was determined and converted into a diameter of an equivalent circle which was then taken as the characteristic window size.
Table 2.1 shows the results of the morphological characterization of reticulated open-cell foams (SSiC and aluminium) which have been investigated in the present work. It can be observed that for all foam samples the window diameter decreases with increasing PPI. This is because with increasing number of pores in a linear inch the cell size decreases which consequently results in a smaller diameter of the windows in a cell.
19 2 Morphological characterization of open-cell foams
It can also be observed that both 10 and 20 PPI Al foams have larger window diameters compared to the respective 10 and 20 PPI SSiC foams. This can be attributed to the high porosity of Al foams, due to which they have larger window diameters and thinner struts for a certain PPI in comparison with SSiC. In addition, this can also be due to the fact that SSiC and aluminium foams were supplied by different manufacturer and a PPI value from different manufacturers can be different.
From the reconstructed geometry resulting from µ-CT measurements, pore size distributions can be obtained. As an example, pore size distribution plot of the 20 PPI SSiC foam is shown in Figure 2.16. The plot was deconvoluted by using a Gaussian distribution with the help of Origin 8.
Figure 2.16: Pore size distribution of the 20 PPI SSiC foam obtained from µ-CT
In the deconvoluted plot shown in Figure 2.16, two distinct peaks can be seen which represent window and cell size distribution respectively. The average window size obtained from the Gaussian distribution was comparable to the one determined by image analysis.
The characterization results of the periodic cellular structures of both Kelvin and cubic cell geometry studied for the present work are given in Table 2.2 and Table 2.3 respectively. For both cell geometries CPI (cells per inch) analogues to PPI (pore per inch) along with window size were determined.
As observed in the case of SSiC and aluminum foams, the window size decreases as CPI (analogue to PPI) increases for both Kelvin and cubic cell geometries. A similar explanation as given in the case of SSiC and aluminum foams applies here as well.
20 2.3 Results and discussion
2.3.3 Strut thickness, cross-section and morphology
Figure 2.17 shows a single strut of SSiC foam studied in the present work. From the figure it can be seen that the strut thickness of reticulated foam varies along the length; it has maximum value at the intersections (nodes) and minimum at the center.
Figure 2.17: Strut thickness along the length (left), measurement of the strut thickness “ds” (right)
The variation in strut thickness along the length is due to the fact that during the manufacturing process the precursor slurry deposits more at the nodes instead of distributing homogeneously along the length. Therefore, the struts have minimum thickness at their centers.[14, 26].
Figure 2.18: Strut size distribution of the 20 PPI SSiC foam obtained from µ-CT
Figure 2.18 shows the strut size distribution of the 20 PPI SSiC foam obtained from the reconstructed geometry resulted from µ-CT measurements. The plot was deconvoluted into three peaks corresponding to three different strut thicknesses along the length. As for the morphological characterization the strut thickness is measured at the center where it has a minimum thickness. Therefore, from the deconvolution plot the first peak (corresponding to the thinner most part of the strut) was taken as characteristic strut thickness. The mean values of strut size obtained from the deconvolution of strut size distribution plot was comparable to the one obtained from image analysis. 21 2 Morphological characterization of open-cell foams
Variation of strut thickness along the length was also observed for the Al foams but to a less extent as compared to the SSiC foams. This can be explained on the basis of high porosity of Al foams compared to the SSiC foams used in the present work. During the manufacturing process the distribution of the slurry along the length of a precursor strut is more homogeneous for high porosity foams than for the foams produced with low porosity. Therefore, strut size in the case of high porosity foams has a narrower distribution compared to the ones with low porosity.
Figure 2.19 shows SEM micrographs of strut cross-sections of SSiC and aluminum foams. It can be observed that SSiC foam has hollow-circular whereas Al foams have dense triangular strut cross-section.
Figure 2.19 Strut cross-section of SSiC (left) and Al (right) foams studied in the present work
As described in section 2.2, the hollow cavity in struts originates from burring out the precursor foam during the calcination. The hollow strut volume in foams is responsible for the strut porosity.
The shape of the strut cross-section (circular, triangular and concave triangular) in foam structure depends upon the porosity. Bhattacharya et al. [28] reported this phenomenon for metal foams and gave porosity ranges for different shapes of the strut cross-section. They concluded that the strut cross-section changes from circular to triangular as the porosity reaches to 93.5%. For the porosities higher than 93.5 % the cross-section becomes concave triangular. For the present work in case of aluminum foam samples with porosities in the range of 93.5% triangular struts were observed which validates the findings of Bhattacharya et al. [28]. In their work on modeling of foam structures Truong et al. [29] discussed only two strut shapes i.e. cylindrical and triangular. They concluded that when porosity value crosses 90% the strut cross-section changes from circular to triangular shape. They established this phenomenon for all solid foams e.g. ceramic and metal.
From the present results as well as from the open literature [54] it can be concluded that ceramic foams with porosity lower than 90% exhibit circular strut cross-section.
22 2.3 Results and discussion
In 2007 Lacroix et al. [26] investigated β-SiC foams including foam samples with open porosities above 90%. A SEM micrograph from their work (Figure 2.20c) shows that ceramic foams with open porosities greater than 90% can also have a concave triangular shape. This confirms that ceramic foams with porosities greater than 90% exhibit not only triangular but concave triangular strut cross-section. However, the porosity border where triangular strut shape gets concave triangular is still not confirmed.
Figure 2.20: Different strut shapes of reticulated open-cell ceramic foams (figures adapted from respective references); (a) triangular [39], (b) cylindrical [54], and (c) concave triangular [26]
From the above discussion it can be concluded that the reticulated open-cell foams (ceramic or metal) show mainly three types of strut cross-section i.e. circular, triangular and concave triangular. However, the porosity ranges for ceramic and metal foams for different strut shapes are different.
2.3.4 Specific surface area
Table 2.1 and 2.2 show the results of specific surface area of SSiC and aluminium foams respectively, obtained from the micro computed tomography. From the results, a strong dependency of the specific surface area on the PPI value can be observed i.e. the specific surface area increases as the PPI value increases. This is due to the fact that with increasing pore density (pores per inch), the number of cells and hence the number of struts (the solid phase in the foam structure that accounts for the external surface) per unit volume increases, resulting in an increase of the specific surface area of the foam per unit bulk volume.
The specific surface area of foam structures can also be predicted by applying mathematical correlations using measured parameters such as pore size, strut size and porosity.
23 2 Morphological characterization of open-cell foams
In open literature there have been several correlations presented for the estimation of the specific surface area of the foam structures. The evaluation of these correlations by comparing their results with the experimental data of specific surface area from present work as well as from the open literature will be presented in the next chapter. In addition, a new approach for developing a correlation for the specific surface area of foams will be presented.
2.4 Summary and conclusion
Open-cell foams (ceramic or metal) offer interesting properties such as large specific surface area, high mechanical strength, high porosity and a low resulting pressure drop. Due to these properties they are excellent candidates for many industrial applications such as gas filters, heat exchangers, porous burners and catalyst supports etc. Open-cell foams have a complex three dimensional internal architecture with widely distributed properties. Therefore a thorough description of their geometry requires a comprehensive characterization of their structural/morphological parameters.
In this chapter morphological characterization of replicated (ceramic and metal) and periodic (metal) open-cell foams of different cell geometries, cell sizes and porosities has been presented. For ceramic foams, sintered silicon carbide foams with pore densities of 10, 20 and 30 PPI and for metal foams aluminum foams of pore densities 10 and 20 PPI were used. In case of periodic cellular structures, samples with Kelvin and cubic cell geometries were studied. The foam samples were characterized with respect to their morphological parameters by using different methods including image analysis, mercury intrusion porosimetry, He- pycnometry, and X-ray micro-computed tomography.
Reticulated open-cell foams are mostly manufactured via the replication technique and can be produced in a large range of porosity and pore size. During the manufacturing process the slurry material accumulates more at the nodes than at the center of the strut. Therefore strut has minimum thickness at its center which is measured as the characteristic strut thickness. The manufacturing technique determines the strut morphology of the open-cell foams e.g. open-cell foams produced by the replication technique usually have hollow struts whereas those produced by direct foaming feature dense struts. Hence, foams produced by the replication technique feature additional porosity i.e. internal strut porosity.
The strut porosity is hardly accessible to the fluid that flows through the foam structures therefore it must be subtracted from the total porosity in order to obtain hydrodynamic related porosity or so called open porosity of the foam.
24 2.4 Summary and conclusion
Due to the unclear definition of a pore, the conventional way of representing cell size or pore size by PPI (pores per inch) does not give reliable information because a pore can be a cell or an opening into the cell i.e. window. Therefore PPI should be considered as merely a nominal value and is not recommended to be used in any modeling work or analytical calculations. Hence, when giving a pore size of a foam sample it is recommended to specify it as either cell or window size.
Depending upon porosity, reticulated open-cell foams (ceramic or metal) show different strut cross-sections, namely circular, triangular and concave triangular. However (according to open literature data as well as from the results of the present work) it can be concluded that the porosity ranges for different strut cross-sections are different for metal and ceramic foams. In case of ceramic foams, for open porosities less than 90 %, the struts exhibit a circular cross-section, and for values greater than 90 % the struts tend to have a triangular or a concave triangular shape. In case of metal foams, the strut cross-section changes from circular to triangular as the porosity value reaches ca. 93.5%, and for porosities higher than 93.5 % it tends to become concave triangular.
Due to the roughness and internal porosity of the foam struts, the specific surface area (Sv) of ceramic foams cannot be measured by conventional physisorption methods. µ-CT and MRI can be used to determine Sv of the foams experimentally. The specific surface area has a strong dependency on PPI i.e. it increases with increasing PPI value and vice versa.
In contrast to reticulated open-cell foams, periodic cellular (foam-like) structures have a defined cell/pore size, geometry and orientation. The manufacturing techniques like selective electron beam melting, selective laser sintering and 3D printing allow the production of periodic cellular structures with a precise control over their geometrical and morphological properties.
Periodic cellular structures with ideal tetrakaidecahedron geometry manufactured by selective electron beam melting (SEBM) were investigated. The samples were produced at the Lehrstuhl für Werkstoffkunde und Technologie der Metalle, Universität Erlangen-Nürnberg. The foam samples were produced in different cell sizes and porosities. A characterization of the foam samples with respect to the morphological parameters was performed.
25
26
3 Geometric modeling of open-cell foams
3.1 Background
As described in the previous chapters, for chemical engineering applications, open-cell foams offer clear advantages such as, e.g., high porosity, low pressure drop, high tortuosity, enhanced radial heat and mass flow, over known and established packing/structures (e.g. beads, honeycombs) used for the column and reactor configurations [6, 27, 55]. However, in contrast to the already known configurations where geometry is extensively studied and well- defined, the properties of foam structures are difficult to determine due to the irregular nature of their structure and geometry [1, 14, 17, 56]. A comprehensive experimental characterization of open-cell foams in terms of their structural, morphological and mechanical as well as fluid dynamic properties can be time-consuming and expensive. Therefore it is essential to develop geometric models and correlations that allow the prediction of the foam properties which are important for the reactor and column design with foams as internals. In this chapter the validity and applicability of state of the arte geometric models and correlations for specific surface area is examined. In addition a new correlation for geometric specific surface area of open-cell foams is developed by taking into account the different shapes of strut cross-section.
Reticulated open-cell foams have complex three-dimensional internal architecture with widely distributed properties. Therefore, geometrical modeling of these structures is considerably more difficult compared to the known packings e.g. beads, cylinders, honeycombs etc.
In literature there has been a considerable number of studies on modeling of foams [13, 24, 25, 28, 29, 57, 58] where several researchers have proposed different models of foam structure. The proposed geometrical models, which are based on a certain cell unit, have been further applied to develop mathematical correlations in order to estimate the morphological, geometrical and transport properties of the foams. From chemical engineering point of view the important models of foam structure which have been presented in the open literature are listed below and will be further discussed in the next section. • the cubic cell model [1, 59] • Weaire-Phelan model [25, 27] • tetrakaidecahedra model [1, 60] • pentagonal dodecahedra model [1, 29] • representative unit cell (RUC) model [58, 61]
3 Geometric modeling of open-cell foams
3.2 State-of-the-art geometric models
In this section a brief overview of stat-of-the-art geometric models of foam structure is given. The mathematical correlations/expressions derived using these models in order to determine the important properties of foams are summarized in section 3.3.
The first model discussed here was presented by Du Plessis et al. [58] and fourie and Du Plessis [61]. These authors considered a cell unit which is based on three rectangular struts which are connected to each other perpendicularly (Figure 3.1). They named it as representative unit cell (RUC) model. Using this model the authors derived mathematical correlations for the estimation of foams properties e.g. specific surface area, tortuosity, and pressure drop.
Figure 3.1: Cubic representative unit cell (RUC) for foams [58]
The second reported model is the cubic cell model which was proposed by Lu et al. [59] who investigated the heat transfer in metal foams. In this model, foam structure is represented by a regular packing of cubes. The foam struts are represented as cylindrical ligaments which are connected to each other three dimensionally (Figure 3.2) in order to give a regular cubic lattice. The cubic cell model was also used by Giani et al. [13] who studied the mass transfer characteristics of metal foams and Lacroix et al. [26] who studied pressure drop in ceramic foams.
Figure 3.2: Cubic cell model by Lu, Stone and Ashby [13, 59]
28 3.2 State-of-the-art geometric models
The third model presented here is the tetrakaidecahedron model. The geometry of tetrakaidecahedra is based on a cell unit first described by Lord Kelvin [60] and therefore is named as Kelvin’s cell. The cell unit of tetrakaidecahedra or Kelvin’s cell (Figure 3.3 a) consists of 14 faces or windows (6 squares and 8 hexagons) and 24 ligaments (struts). In a regular packing of tetrakaidecahedra these struts are connected with each other to generate a dense packing (Figure 3.3 c).
(a) (b)
(c)
Figure 3.3 Kelvin’s tetrakaidecahedron (a), with slightly curved faces (b), adapted from [62] and dense packing of tetrakaidecahedra (c) [2]
According to Zhang and Ashby [2] the cell geometry best representing isotropic foams and capable of efficient filling of space is a tetrakaidecahedron. In more precise term, it is truncated octahedron (Figure 3.3 b) which they considered as the best unit cell for portioning space into cavities of equal volume while minimizing the interfacial area.
Gibson and Ashby [1] in their review on cellular solids discussed different models of foam structure in which foams are considered as regular packing of various polyhedra including triangular prisms, rectangular prisms, hexagonal prisms, rhombic dodecahedra and tetrakaidecahedra. They also preferred the tetrakaidecahedra model since it gave most consistent agreement with observed properties. Tetrakaidecahedron model was used by Richardson et al. [3] and Buciuman and Kraushaar-Czarnetzki [57] who derived mathematical correlations in order to estimate the geometric properties of foams.
29 3 Geometric modeling of open-cell foams
For over a century it was considered that the space filling cell which minimizes the surface per unit volume was Kelvin’s tetrakaidecahedron with slightly curved faces [1, 60]. However, in 1995 Weaire and Phelan [63], using computer software for minimization of surface area, discovered a unit cell with even lower (about 0.3%) surface area per unit volume The unit cell is made up of 8 polyhera (two pentagonal dodecahedra and six 14-hedra) [27]. In 2009, Grosse et al. [25] used Weaire-Phelan structure to model the ceramic foams. They proposed theoretical and empirical correlations (based on Weaire-Phelan structure) for the estimation of foam properties.
Figure 3.4: Weaire –Phelan unit cell consisting of eight polyhedra[2]
The fifth model of foam structure which has been reported in literature is the pentagonal dodecahedra. Gibson and Ashby [1] also reviewed pentagonal dodecahedra model. They reported that the pentagonal dodecahedron do not perfectly fill the space, therefore they preferred tetrakaidecahedron packing.
Figure 3.5: Packing of regular pentagonal dodecahedra [29]
However, Anderson et al. [64] and Bourret et al. [65] showed that it is possible to obtain a packing of regular dodecahedra through the modification of regular pentagonal dodecahedra.
Truong Huu et al. [29] used the pentagonal dodecahedra model for modeling of solid foams. They considered four different cases of the unit cell of pentagonal dodecahedron which are illustrated in the next subsection.
30 3.3 State-of-the-art correlations for predicting the geometric specific surface area (Sv-geo)
3.3 State-of the-art correlations for predicting the geometric specific
surface area (Sv-geo)
Geometric specific surface area is one of the most important properties of foam structures. It is relevant for the momentum, heat and mass transfer [23, 32]. Therefore, from chemical engineering perspective (e.g. using foams as reactor or column internals) the accurate determination of geometric specific surface area of foams (either theoretically or experimentally) is extremely important.
As described in the second chapter, for reticulated open-cell foams due to the nature of their struts, as they feature rough surface and may possess internal strut porosity, conventional physisorption methods e.g. BET method cannot be applied to determine the geometric specific surface area. X-ray computed tomography or magnetic resonance imaging can be used instead [14, 48]. Besides these expensive and lengthy experimental approaches, the specific surface area of foams can also be determined theoretically by applying mathematical correlations. In literature several correlations have been proposed in order to estimate the geometric specific surface area of foams theoretically. These correlations are based on certain geometrical models of foam structure and use two or three measured parameters usually porosity, pore and strut size for the prediction of the specific surface area.
In this section an overview and comparison of state-of -the-art correlations for specific surface area of foams is presented. The most frequently used correlations in recent literature have been discussed and a summary of other correlations along with the structure-property relationship is given in the Table 3.1. These correlations will be examined to evaluate their validity and applicability for different foam materials, porosities and pore densities. For this purpose the predicted specific surface area using these correlations will be compared with the experimental data from open literature as well as from the present work.
Du Plessis et al. [58] and fourie and Du Plessis [61] investigated high porosity metal foams in their work and used RUC model to derive their correlation (Equation 3.1) for the geometric specific surface area of foam structures. They introduced the notion of tortuosity (χ) to derive their correlation. In order to predict the geometric specific surface area (Sv-geo), their correlation uses window (dw) and strut diameter (ds) along with tortuosity (χ) of the foam.
3 S = ( )(χχ −− 13 ) −geov + (3.1) dd sw
31 3 Geometric modeling of open-cell foams
The tortuosity for equation 3.1 can be calculated by applying another correlation (Equation
3.2) from Du Plessis et al. [58, 61] which uses the value of open porosity (εo).
4π 1 − χ += cos22 + 1 ()ε − 12cos (3.2) 3 3 o
Lu et al. [59] studied heat transfer properties of open-cell metal foams. They used the cubic cell model for the development of their correlation for Sv-geo (Equation 3.3). The correlation uses characteristic pore size “a” (see Figure 3.2), and open porosity as measured quantities for predicting the Sv-geo of foams.
π = 32 ()− ε 5.0 S −geov 1 o (3.3) a
Richardson et al. [3] discussed three different models of foam geometries including; tetrakaidecahedron and parallel cylinders. They however preferred the model of parallel cylinders to derive their correlation for Sv-geo of ceramic foams and came up with an expression given in equation 3.4.
ε = 4 o S − geov (3.4) dw
Using the geometric constants of tetrakaidecahedron derived by Gibson and Ashby [1], Buciuman and Kraushaar-Czarnetzki [57] developed the following equation (Equation 3.5) for predicting the Sv-geo of ceramic foams. They investigated alumina mullite and china porcelain foams.
1 S = 82.4 1− ε −geov + o (3.5) dd sw
In 2005 Giani at el. [13] also applied cubic cell model for their study on mass transfer properties of metal foams. They came up with the following correlation:
2 S = []()13 − επ 5.0 −geov + o (3.6) dd sw )(
32 3.3 State-of-the-art correlations for predicting the geometric specific surface area (Sv-geo)
Lacroix et al [26] investigated silicon carbide foams in their work on pressure drop modeling in open-cell ceramic foams. They also used cubic cell model for their work and preferred the following form of the correlation for Sv-geo.
4 ()−= ε S −geov 1 o (3.7) ds
Grosse et al. [25] used the Weaire-Phelan structure to model their foams and to derive their correlation for the geometric specific surface area. They followed the same procedure to derive the correlation as used by Buciuman and Kraushaar-Czarnetzki [57] for Kelvin’s cell structure. The correlation is given in equation 3.8, where εn is the nominal porosity which is provided by the manufacturer.
ε (155.1121.8 −−− ε ) S = n n (3.8) − geov ()+ dd sw
The correlation derived by Grosse et al. [25] given in equation 3.8 was unable to reproduce their experimental results of specific surface area. Therefore, they used an empirical fitting procedure to redefine the coefficient and obtained a semi-empirical correlation given in equation 3.9. The results obtained from the semi empirical form (Equation 3.9) of the correlation (Equation 3.8) gave close agreement to their experimental data.
ε ( −−− ε ) o 164.2184.4 o S − = (3.9) geov ()+ dd sw
Recently, Truong Huu et al. [29] have presented a detailed work on modeling of foam structures using pentagonal dodecahedron model. They discussed the notion of different strut cross-section for different porosity ranges. According to them, for the porosity value less 90% the struts exhibit cylindrical and for porosity values 90 % they tend to have triangular shape. They established these porosity ranges for different strut shapes for both ceramic and metal foams. This however is contrary to the conclusion of Bhattacharya et al. [28] as they gave different porosity range for triangular cross-section for the metal foams (also confirmed by present work , see previous chapter). According to Bhattacharya et al [28], the strut cross- section of metal foams tends to get triangular at the porosity value of ca. 93.5% or greater. Moreover, they discussed a third type of strut cross-section i.e. concave triangular, which has not been considered in the work of Truong Huu et al. [29].
33 3 Geometric modeling of open-cell foams
Truong Huu et al [29] considered four different cases of foam geometry and two different strut shapes (cylindrical and triangular) of the strut cross-section for the development of the correlation for Sv-geo. Accordingly they proposed four different correlations based on the pentagonal dodecahedron geometry for the estimation of the geometric specific surface of foams. These correlations are for different strut shapes namely; fat cylindrical, fat triangular, slim cylindrical, slim triangular. Equation 3.10 gives geometric specific surface area of fat pentagonal dodecahedron geometry. Where ϕ is the golden ratio and k and F can be obtained using equation 3.11 and 3.12 respectively. The other three correlations from Truong Huu et al. [29] are given in Table 3.1.
2 k 2 k 2 π πk112 − 115 − sin2 2 3 2 3 5 = 1 + (3.10) S −geov F d 35 −ϕϕ ()32 −ϕ w
2 5π k 2 102 π 12k 5ϕ ϕπ 2 k 2 k 2 1− + k 3 + − 1− 4 4 4 ϕ 2 3 12ϕ 5ϕ 34 −ϕ ()34 −ϕ 2 3 π 3 2 2 k 2 π ϕ − 2 2 sin 1 sin ϕ 5 2 3 1 5 40 − ()3332 −ϕ 4 − 39 ϕ + () ε =−− 01 (3.11) 5ϕ 4 o
− k 2 1 2 3 F = (3.12) 3 −ϕϕ
Note that Truong Huu et al. [29] considered non porous dense struts (struts with no internal voids) in their modeling, which implies that in their case the total porosity of the foam matrix is the same as the open porosity (which is the void fraction accessible for the fluid flow). Therefore, for calculating the specific surface area using the correlation derived by Huu et al., the open porosity (which is actually the void fraction accessible for the fluid flow and is relevant for the outer specific surface area) should be used instead of using the total porosity.
34 3.3 State-of-the-art correlations for predicting the geometric specific surface area (Sv-geo)
Table 3.1: State-of-the-art correlation for determining the specific surface area of foams
Reference Geometric specific surface area [m-1] Relation between morphological parameter Geometric model and strut morphology
Lu et al. [59] π Cubic cell model = 32 []− ε 5.0 = 2 []− ε 5.0 S −geov o )1( dd ws o )1( a )( 3π Cylindrical struts
− ε o )1(4 Innocentini et al. [66] S − = ------geov εd w
5.0 5.0 − ε Tetrakaidecahedra model [ −− ε ] d ow )1(5338.0 o )1(971.01 = = − ε ds 5.0 Richardson et al. [3] S −geov 979.12 5.0 )1( −− ε Triangular struts − ε o )1(971.01 d ow )1(
4ε Hydraulic diameter model S = o −geov --- Cylindrical struts d w
ε = o ------S −geov d w
Du Plessis and 3 2 RUC model S = (χχ )(−− 13 ) = dd −1 Fourie & Du Plessis [58, 61] −geov + ws − χ Rectangular struts dd sw 3
π χ += 4 + 1 −1 ()ε − cos22 o 12cos 3 3
35 3 Geometric modeling of open-cell foams
Reference Geometric specific surface area [m-1] Relation between morphological parameter Geometric model and strut morphology
− ε 5.0 Tetrakaidecahedra model 1 = o )1( Buciuman et al. [57] S = 82.4 1− ε dd ws Triangular struts v + dd o 59.2 sw
5.0 Cubic cell model 4 += 4 − ε S ()1−= ε ddd sws )( o )1( Giani et al. [13] − geov o π Cylindrical struts ds 3
Cubic cell model [ − επ] 5.0 4 dw o )1(34 Lacroix et al. [26] S − ()1−= ε d = Cylindrical struts geov d o s []−− επ 5.0 s o )1(341
Grosse et al. [25] ε −−− ε )1(55.1121.8 --- Weaire-Phelan model S = o o −geov ()+ dd sw Cylindrical strut
Empirical, based on ε −−− ε )1(64.2184.4 S = o --- Weaire-Phelan structure −geov ()+ dd sw Cylindrical struts
36 3.3 State-of-the-art correlations for predicting the geometric specific surface area (Sv-geo)
Reference Geometric specific surface area [m-1] Relation between morphological parameter Geometric model and strut morphology
Troung Huu et al. [29] Slim pentagonal dodecahedra 1 F 1 2 2 3 1015 S = 160 − kk With kk () ε =−−− 01 Triangular struts − geov 2 4 ϕϕ4 o dw 5ϕ 2 3 3
2 2 2 1015 12k 5ϕ ϕπ k 2 π 2 kk 3 +− − 1− π − k 2 − k 2 2 4 4 4 k112 115 sin 3 5ϕϕϕ 34 −ϕ ()34 −ϕ 2 3 F 2 3 2 3 5 S − = + geov − ()− ϕ With 3 Fat pentagonal dodecahedra dw 35 ϕϕ 32 π ϕ 22 − k 2 π 22 sin 1 sin ϕ Triangular struts 5 2 3 1 5 40 − ()3332 −ϕ 4 − 39 ϕ + ()ε =−− o 01 5ϕ 4
1 F 1 2 With 5π k 2 102 π Slim pentagonal dodecahedra S = 120 − kk k 21− + k 3 ()ε =−− 01 −geov 2 4 4 o dw 5ϕ 2 3 ϕ 2 3 12ϕ Cylindrical struts
2 2 5π k 2 102 π 12k 5ϕ ϕπ2 k 2 k 2 k 2 π k 2 1 − − k 3 + − 1 − 2 4 4 πk 112 − 115 − sin ϕ 2 3 12ϕ ϕ 4 − ϕ ()34 − ϕ 2 3 2 3 2 3 5 With 5 34 = F + S − 3 geov −ϕϕ ()−ϕ dw 35 32 π k 2 π 2 ϕ 2 − 2 2 sin 1 sin ϕ 5 2 3 1 5 Fat pentagonal dodecahedra 40 − ()3332 − ϕ 4 − 39 ϕ Cylindrical struts − k 2 1 + ()ε =−− 01 2 3 4 o Where: F = 5ϕ 3 −ϕϕ
37 3 Geometric modeling of open-cell foams
3.4 Performance of state-of-the-art correlations for predicting the Sv-geo
In this section validity and suitability of state-of-the-art correlations (hence the geometric models behind them) for foams of different materials, pore size and porosity is examined. For this purpose theoretical (predictions from the correlations) and experimental (from open literature; Table 3.2 and present work) dimensionless surface area of open-cell foams is plotted versus porosity and is shown in Figure 3.6.
The plot in Figure 3.6, which shows a comparison between theoretical and experimental dimensionless specific surface area for ceramic as well as metal foams is divided into low and high porosity regimes. In case of ceramic foams, the low porosity regime covers the foams which have porosity less than 90% and consequently exhibit cylindrical struts (see section 2.33). The high porosity regime includes ceramic foams which have porosity greater than 90% and hence tend to show triangular and concave triangular struts.
In case of metal foams, it can be noted that the border line between low and high porosity regimes corresponding to cylindrical and triangular (including concave triangular) struts respectively is drawn at the porosity value of 93.5% (Figure 3.6.) which is different than in the case of ceramic foams. The border value of the porosity for metal foams is based on the observations of Bhattacharya et al. [28] as well as on the results obtained from the present work (see section 2.3.3).
From the comparison (shown in Figure 3.6) between different correlations resulting from different geometric models, it can be noted that although theses correlations are based on different geometric models yet some of them have shown similar results for certain ranges of porosities. This phenomenon is more pronounced at high porosities.
However, when the theoretical results are compared to the experimental data, a large deviation can be observed. For ceramic foams nearly all correlations seem to overestimate the measured specific surface area. For metal foams, except for the correlations of Truong Huu et al. [29] and, Buciuman and Kraushaar-Czarnetzki [57], all the other correlations have overestimated the experimental specific surface area.
The deviation of theoretical results (estimated by state-of-the-art correlations) from experimental data may be attributed to two main factors i.e. selection of the geometric model for deriving the correlation and the variation of strut cross-section with porosity. The influence of these factors on determining the specific surface area of foams is discussed in detail in the following subsections.
38 3.4 Performance of state-of-the-art correlations for predicting the Sv-geo
Table 3.2: Properties of open-cell foams used for the comparison of measured and predicted specific surface area
εεε PPI εεε d d S References n o w s v (measured) (-) (-) (-) (mm) (mm) (m-1)
Große et al. [25]
0.75 10 0.688 1.974 0.101 639
20 0.719 1.070 0.561 1260
80 10 0.773 1.796 0.944 664
20 0.745 0.955 0.509 1204
30 0.754 0.847 0.391 1474
45 0.763 0.781 0.138 1884
0.85 10 0.812 1.952 0.809 629
20 0.813 1.137 0.544 1109
30 0.793 0.860 0.273 1520
45 0.783 0.651 0.217 1816
Incera Garrido et al. [14]
0.80 10 0.772 1.933 0.835 675.4
20 0.751 1.192 0.418 1187.0
30 0.766 0.871 0.319 1437.8
45 0.761 0.666 0.201 1884.3
0.85 10 0.812 1.131 0.451 1109.1
20 0.814 0.861 0.330 1422.4
30 0.807 0.687 0.206 1816.3
45 0.801 1.069 0.460 1290.3
Dietrich et al. [67]
80 10 0.765 2.253 0.967 664
20 0.748 1.091 476 1204
30 0.752 0.884 391 1402
45 0.757 0.625 195 1884
39 3 Geometric modeling of open-cell foams
Figure 3.6: Dimensionless geometric specific surface area versus open porosity of foams: theoretical and experimental values (no empirical or semi empirical model is included)
40 3.4 Performance of state-of-the-art correlations for predicting the Sv-geo
3.4.1 Selection of the geometric model
From the results shown in Figure 3.6, it can be concluded that the selection of geometric model is very important as most correlations, derived using different geometric models, have produce widely differing results. This phenomenon is more prominent in low porosity regime i.e. for porosities less than 90%.
In Figure 3.6, for low porosity regime, the maximum deviation is shown by Weaire-Phelan model and cubic cell model which indicates the unsuitability of these models to represent the open-cell foam geometries. The RUC model and slim model for pentagonal dodecahedron geometry also show large deviation and hence are not recommended to be used as representative geometric model for open-cell foams. Among all models the minimum deviation in low porosity regime is shown by pentagonal dodecahedron model (fat geometry [29]), though predicted values by this model are still significantly higher than the measured ones. The second closest predictions in low porosity region in Figure 3.6 have been shown by tetrakaidecahedron model from Buciuman and Kraushaar-Czarnetzki [57]. However, it is to be noted that this correlation was developed for triangular struts, but the foams with porosities less than 90 % usually exhibit cylindrical struts [29]. This may be a possible explanation for the deviation of predicted values by this correlation from the experimental data. Hence, it does not seem appropriate to apply the correlation from Buciuman and Kraushaar-Czarnetzki [57] (originally developed for triangular struts) for foams having porosities less than 90%, as in this porosity range they exhibit cylindrical struts. A correlation for cylindrical struts based on tetrakaidecahedron model has not been reported in the open literature so far.
In Figure 3.6, for high porosity regime i.e. porosities greater than 90%, from the trends it can be observed that weaire and Phelan model continue to show higher values compared to all other models. The RUC model, cubic cell model and pentagonal dodecahedron (slim model) show a similar behavior. The pentagonal dodecahedron (fat model) and tetrakaidecahedron model (triangular struts) have produced very similar results. Their predictions show minimum deviation from the two experimental data point (obtained for Al foam: present work).
3.4.2 Variation of the strut cross-section with porosity
Until recently most authors for their correlation for specific surface area considered just one type of strut cross-section, e.g. Du Plessis et al. [58] and fourie and Du Plessis [61] considered rectangular strut-cross-section, Lu et al. [59] and Grosse et al. [25] discussed cylindrical struts, Buciuman and Kraushaar-Czarnetzki [57] and Richardson et al. [3] considered triangular strut cross-section. As discussed in the previous chapter, depending upon the 41 3 Geometric modeling of open-cell foams porosity, open-cell foams (ceramic or metal) exhibit different shapes of their strut cross- section namely; circular, triangular and concave triangular. The range of porosity for different strut cross-section however can be different for ceramic and metal foams. The strut shape and morphology can have a significant impact on the geometrical properties of foams including geometric specific surface area. Due to the fact that foams exhibit different strut shapes at different porosities, one correlation cannot account for the whole range of porosity and hence the shapes of the strut cross-section. Therefore when applying one correlation for all strut shapes, a large deviation compared to the experimental data can be expected, which can be observed from the comparison shown in the Figure 3.6.
More recently, Truong Huu et al. [29] presented their work on solid foams in which different correlations for different strut shapes as well as foam geometry (so called fat and slim geometry) were proposed. These authors chose pentagonal dodecahedron model for the foam geometry. Although Truong Huu et al. [29] came up with different correlations for different strut shapes (cylindrical and triangular) still a large deviation from literature experimental data can be observed (Figure 3.6.) The deviation in this case may be attributed to the geometrical model selected for the modeling.
From Figure 3.6, in high porosity regime it can also be observed that predictions according to the correlation of Buciuman and Kraushaar-Czarnetzki [57] and Truong Huu et al. [29] are quite close to the two experimental data point of metal foams used in in the present work.
The correlation of Buciuman and Kraushaar-Czarnetzki [57] uses tetrakaidecahedron model and considers triangular strut cross-section. It seems that their correlation is applicable to the foams of high porosity which exhibit triangular struts. However, it cannot be applied for foams with porosity less than 90% where they show cylindrical struts.
For triangular strut cross-section, Truong Huu et al. [29] proposed two correlations corresponding to slim and fat geometry. In Figure 3.6, the predictions according to fat model are quite close to the experimental data, whereas slim model predicts much too high values of specific surface area compared to the experimental data. It is important to note that the shape of the struts of Al foams (whose experimental specific surface area is shown in Figure 3.6) resemble more the slim triangular than the fat triangular. In that case correlation of Truong Huu et al. [29] for slim triangular struts should be applied which show larger deviation from the experimental data points.
42 3.5 New correlation for predicting the Sv-geo
3.5 New correlation for predicting the Sv-geo
In this section a new approach is applied to derive correlation for specific surface area of open-cell foams. For this purpose tetrakaidecahedron model is used and different shapes of strut cross-section namely; circular, triangular and concave triangular have been explicitly taken into account. As described in previous chapter many authors [1, 2, 14, 57] preferred tetrakaidecahedron model for the geometric modeling of foams, as it gives closer agreement with the observed properties. The tetrakaidecahedron model is based on Kelvin’s cell whose details are given in section 3.1. Gibson and Ashby [1] derived geometric relationships (given in Table 3.3) for the cell unit of tetrakaidecahedron.
For the present work in order to derive the correlation for specific surface area of foams of different strut cross-sections, the geometric constants of tetrakaidecahedron given in Table 3.3 are used.
Table 3.3: Geometric constants of the tetrakaidecahedron (adapted from [1, 3])
Property Symbol Formula
0.5 Strut length ltriangular 0.5498dw / [1-0.971(1-εο) ]
0.5 Strut thickness ds-triangular 0.971(1-ε ο) ltriangular
3 Cell volume Vc-triangular 11.31l triangular
Surface area of the struts Ss-triangular 36ds-triangularltriangular
Surface area per unit solid volume Sv-solid-triangular Ss-triangular/Vc-triangular (1-εο)
Figure 3.7: Tetrakaidecahedron geometry (b) representative cell unit model for foam structure with triangular struts (c) cross-section of the triangular strut with an internal cavity (adapted from [3]) 43 3 Geometric modeling of open-cell foams
3.5.1 Triangular struts
From Table 3.3, taking the definition of specific surface area per unit solid volume for triangular struts (Equation 3.13)
S − S = s triangular solidv −− triangular − ε (3.13) Vc−triangular o )1(
for which Ss-triangular is given by equation 3.14 and Vc-triangular is given by equation 3.15 (where 36 and 11.31 are geometric constants from the tetrakaidecahedra model).
= S s−triangular (36 ds−triangular ) ltriangular (3.14)
3 V − = 31.11 l c triangular triangular (3.15)
By substituting the values of Ss-triangular and Vc-triangular in equation 3.13, equations 3.16 and 3.17 can be obtained.
(36 ds−triangular )ltriangular S −− = solidv triangular 3 − ε l triangular o )1(31.11 (3.16)
ds−triangular 1 S −− = 183.3 (3.17) solidv triangular − ε )1( 2 o ltriangular
Here, ltriangular (from Table 3.3) is given by equation 3.18
−− .50 = (. 197101 εo ) 1/ltriangular (3.18) 54980 d. w
The definition of strut thickness ds-triangular and the strut length ltriangular from Table 3.3 can be applied and an expression for ds-triangular independent of ltriangular can be obtained.
44 3.5 New correlation for predicting the Sv-geo
Equation 3.19 gives the thickness of a triangular strut which is independent of ltriangular, here dw and εο are measured quantities.
− ε 5.0 d ow )1(5338.0 d − = (3.19) s triangular −− ε 5.0 o )1(971.01
Now by substituting ds-triangular (from equation 3.19) and ltriangular (from equation 3.18) in equation 3.17, equation 3.20 and 3.21 are obtained.
− ε 5.0 ( −− ε 5.0 )2 1 d ow )1(5338.0 o )1(971.01 S −− = 183.3 (3.20) solidv triangular − ε )1( ( −− ε 5.0 ) ()2 o o )1(971.01 5498.0 dw
( −− ε 5.0 )2 1 dw o )1(971.01 (3.21) S −− = 62.5 solidv triangular − ε 5.0 ( −− ε 5.0 ) ()2 o o )1(971.01)1( dw
Simplifying equation 3.21 gives the expression for the specific surface area per unit solid volume for triangular struts:
[ −− ε 5.0 ] o )1(971.01 S −− = 62.5 (3.22) solidv triangular − ε 5.0 d ow )1(
Equation 3.22 is multiplied by the factor (1-εo) to give the equation 3.23 which is the expression for the specific surface area per unit bulk volume (geometric specific surface area) for the foams with triangular struts.
[ −− ε 5.0 ] o )1(971.01 S −− = 62.5 − ε )1( (3.23) geov triangular − ε 5.0 o d ow )1(
45 3 Geometric modeling of open-cell foams
3.5.2 Cylindrical struts
In order to derive the expression for the specific surface area of foams with cylindrical struts, the definitions of Ss-cylindrical (Equation 3.24), Vc-cylindrical (Equation 3.25), lcylindrical (equation
3.26) and ds-cylindrical (equation 3.28) are required. Note that equations 3.24, 3.25 and 3.26 are adopted from Table 3.3 for the cylindrical strut system (the coefficients in these equations are constants from the tetrakaidecahedra model.
= S s− lcylindrica s− lcylindrica )(36 ld lcylindrica (3.24)
3 V − = 31.11 l c lcylindrica lcylindrica (3.25)
d − l = s lcylindrica lcylindrica − ε 5.0 (3.26) o )1(971.0
In order to derive the expression for ds-cylindrical (given in Equation 3.28) from ds-triangular, (given in Equation 3.19), following steps were taken:
By simple geometric consideration it can be shown that the diameter of a circumscribed circle is 2/√3 times greater than the side length of an enclosed equilateral triangle (Figure 3.8). Considering this fact the following correlation, given in equation 3.27, between the thicknesses of cylindrical and triangular struts can be obtained.
Figure 3.8: Geometrical considerations for the derivation of the new correlation for cylindrical struts
46 3.5 New correlation for predicting the Sv-geo
= 2 d − d − (3.27) s lcylindrica 3 s triangular
− ε 5.0 = d ow )1(6164.0 d s− lcylindrica (3.28) −− ε )1(971.01 5.0 o
By substituting the value of ds-cylindrical from equation 3.28 in equation 3.26, the following equation is obtained which gives the lcylindrical in terms of dw.
−− .50 = . εo )1(97101 1 /l lcylindrica (3.29) 6340 8d. w
Using the equations 3.24, 3.25, 3.28 and 3.29 and following the same procedure as used for the triangular struts, equation 3.30 is obtained which gives the specific surface area per unit solid volume of cylindrical struts.
[ −− ε 5.0 ] o )1(971.01 S −− = 867.4 solidv lcylindrica − ε 5.0 (3.30) d ow )1(
The above equation is multiplied by the factor (1-εo) to obtain equation 3.30, which gives the specific surface area per unit bulk volume of the foam structure with cylindrical struts.
[ −− ε 5.0 ] o )1(971.01 S −− = 867.4 − ε )1( (3.31) geov lcylindrica − ε 5.0 o d ow )1(
3.5.3 Concave triangular struts
For concave triangular strut cross-section, the outer surface of the struts is bent inwards (Figure 2.20 c). For the derivation of the expression for the specific surface area of concave triangular struts two ideal struts of the same length; one with triangular and the other with concave triangular morphology are considered. As shown in Figure 3.9, the equilateral triangle (representing the cross-section of triangular strut) has an equal distance (ds-triangular) between its corners. The concave triangular strut (with each side bent inwards according to an angle of approximately 120°) has the same distance (i.e. apparent dsconcave-triangular) between its corners as in the case of triangular strut.
47 3 Geometric modeling of open-cell foams
Therefore, the apparent thickness of the concave triangular strut remains the same as for the triangular strut. Hence, equation 3.19 can be applied to define the so-called apparent strut thickness of a concave triangular strut (Equation 3.32).
− ε 5.0 d ow )1(5338.0 (d −− ) = (3.32) concaves triangular apparant −− ε 5.0 o )1(971.01
But the concave triangular strut will have a higher surface to volume ratio compared to triangular struts because the outer surface of concave triangular strut is now increased (bent inwards) and the volume (material volume) is decreased.
Through geometrical consideration shown in Figure 3.9, it can be seen that the “effective strut thickness” (i.e. c + c) of the concave triangular strut, which is relevant for the outer surface, is
2/√3 times greater than that of the triangular strut (ds-triangular). This implies that the definition for the effective ds-triangular-concave is required (given in equation 3.33) for the derivation of the specific surface area of concave triangular struts.
− ε 5.0 d ow )1(6164.0 (d −− ) = (3.33) concaves triangular effective −− ε 5.0 o )1(971.01
To sum up, for deriving an expression for the specific surface area of the foams with concave triangular struts, the definition of Ss-concave-triangular (Equation 3.34), Vc- concave-triangular (Equation
3.35), l concave-triangular (Equation 3.36) and (ds- concave-triangular)effective which is given in equation 3.33, are established.
Note that in equation 3.34, for the surface area of the concave triangular struts, (ds-concave- triangular)effective is used, as the effective thickness is related to the outer surface area of the strut (see Figure 3.9). = Ss − concave-triangular (36 ds− concave-triangular )effectice l concave-triangular (3.34)
3 V − = 31.11 l c concave-triangular concave-triangular (3.35)
−− 5.0 = εo )1(971.01 (3.36) 1 l/ concave-triangular 5498.0 dw
48 3.5 New correlation for predicting the Sv-geo
Figure 3.9: Geometrical considerations for the derivation of the new correlation for concave triangular struts
Now, following the same procedure as for the triangular and cylindrical struts, an expression for Sv-triangular-concave (Equation 3.37) for the considered concave triangular shape can be derived.
Using the equations 3.33-3.36 and following the same procedure as in the case of cylindrical and triangular struts, equation 3.37 is obtained which gives the specific surface area per unit solid volume of concave triangular struts.
[ −− ε 5.0 ] o )1(971.01 S −−− = 49.6 (3.37) solidv concave triangular − ε 5.0 d ow )1(
[ −− ε 5.0 ] o )1(971.01 S −−− = 49.6 − ε )1( (3.38) geov concave triangular −ε 5.0 o d ow )1(
The equation 3.37 is multiplied by the factor (1-εo) to obtain equation 3.38 which gives the specific surface area per unit bulk volume of the foam structure with concave triangular struts.
49 3 Geometric modeling of open-cell foams
3.6 Validating the new correlation
In this section experimental data of specific surface area of foams from the present study as well as from the open literature is used in order to evaluate the validity and suitability of various correlations and hence geometrical models of foam structures.
In open literature only few authors have compared the theoretical specific surface area with their experimental values. Moreira and Coury [68] measured the specific surface area by image analysis. Since the results of these authors have a large uncertainty range [29] they will not be discussed here. Recently, Incera Garrido et al. [14] and Grosse et al. [25, 48] have applied MRI and CT to measure the specific surface area of ceramic foams of different materials, pore size and porosity. The experimental data from these authors will be used here for comparison purpose.
Nearly all the correlations which have been shown in Table 3.1 overestimated the experimental specific surface area. In case of ceramic foams the closest predictions of specific surface area were obtained by the empirical correlations developed by Grosse et al. [25] and in case of metal foams by correlation from Truong Huu et al. [29] and Buciuman and Kraushaar-Czarnetzki [57]. The predictions according to theses correlations along with the results obtained by using the correlation proposed in the present work will be discussed in the following paragraphs.
Figure 3.10 shows a comparison of experimentally determined specific surface area of ceramic foams of different materials with the theoretical values predicted by three different correlations. These correlations include, a correlation based on pentagonal dodecahedra geometry( from Truong Huu et al. [29]), a semi-empirical correlation based on Weaire and Phelan structure (from Grosse et al. [25]) and a correlation based on tetrakaidecahedron geometry (from present work). The cumulative deviation of the predicted specific surface area values from the experimental values was calculated for all foam samples of each set of nominal porosity and is also shown in Figure 3.10.
For the correlation developed by Huu et al. [29], which is based on pentagonal dodecahedron geometry with cylindrical struts a general trend of overestimating the experimental data can be seen The lowest deviation was observed for the case of a nominal porosity of 90%. The correlation is based on the pentagonal dodecahedron geometry, which seems not to be the best representative geometry of ceramic foam structures.
50 3.6 Validating the new correlation
a a´
b b´
c c´
d d´
Figure 3.10: Comparison of correlations for determining the geometric specific surface area of the foams having nominal porosities of (a & a´) 90 %, (b & b´) 85 %, (c & c´) 80 % and (d & d´) 75 %
51 3 Geometric modeling of open-cell foams
Grosse et al. [25] developed two correlations for the specific surface area of foams namely; a theoretical correlation which is based on Weaire-Phelan structure and an empirical correlation which they obtained by redefining the coefficients in the theoretical correlation by an empirical fitting procedure. Both of these correlations were tested. The theoretical correlation predicted much too high values which are not shown in in the Figure 3.10. However, the semi-empirical form of this correlation seems to give a better agreement to the experimentally determined values of the specific surface area. The deviation in this case can be attributed to the fact that the coefficients for this correlation were adapted to the experimental data of a limited number of foam samples; hence the correlation may not be appropriate for different kinds of foams. Since the theoretical correlation based on Weaire-Phelan structure could not predict the experimental specific surface area and the coefficient had to be substituted by empirical values, it can be concluded that Weaire-Phelan model also does not give the best representation of the geometry of open-cell foams.
Figure 3.11: Comparison of correlations for determining the geometric specific surface area of metal foams
Figure 3.11 shows the comparison measured and estimated specific surface area of aluminum foams. From the cumulative deviation plot, it can be observe the correlation from Truong Huu et al. (fat model [29]) and correlation developed in the present work have shown the minimum deviation compared to all other correlations. It is to be noted that the geometry of Al foam samples used in present work is more similar to “slim model” than to “fat model” from Truong Huu et al. [29]. Therefore, in this case slim model is applicable which over estimates the measured value.
From Figure 3.10 and Figure 3.11, it is clear that the new correlation proposed in the present study, based on the tetrakaidecahedron geometry, predicts the specific surface area of ceramic foams with higher precision compared to other – either theoretical or empirical – correlations
52 3.7 Summary and conclusion available from literature. In this correlation, no empirical fitting of coefficients is required. The model is based on geometrical aspects of tetrakaidecahedron and takes into account the different shapes (circular, triangular, concave triangular) of strut cross-section. This indicates that the tetrakaidecahedron geometry represents the foam structure better than the cubic, Weaire-Phelan or pentagonal dodecahedron geometry.
3.7 Summary and conclusion
Open-cell foams offer many advantages over known and established materials and geometries used for chemical engineering applications. However, due to the complex nature of their structure and geometry, properties of open-cell foams are very difficult to determine compared to the known and well-studied materials and configurations, such as, e.g., packed bed of particles and honeycombs. Experimental characterization of open-cell foams can be time-consuming and sometimes very expensive (e.g. application of MRI, µ-CT etc.). Alternatively, properties of foams can be predicted by using mathematical correlations (which can be derived using certain geometric model) that require some measured parameters for the calculation.
In open literature several geometric models and correlations for predicting/estimating the foam properties have been proposed. In this chapter an overview of important geometric models and resulting correlations for geometric specific surface area of open-cell foams has been presented. The validity of the correlations for the specific surface area and hence the geometric models has been evaluated by comparing the theoretical and experimental data of specific surface area of foams from open literature as well as from the present work.
An important conclusion from the evaluation and comparison of theoretical and experimental data of foams from the state-of-the-art literature is that, despite a number of publications on this subject during the last two decades, no generally applicable correlation for the predicting of geometric specific surface area has been proposed so far.
It is interesting to note that in open literature only a few authors have compared their predicted geometric specific surface area with the experimental data. The comparative study presented in this chapter shows that nearly all state-of-the-art correlations for specific surface area tend to overestimate the experimental data.
The deviation of theoretical results from the experimental data can be ascribed to two main factors i.e. selection of geometric model and variation of strut cross-section with porosity.
53 3 Geometric modeling of open-cell foams
The selection of geometric model to represent the geometry of open-cell foams is very important as different geometric models may result in widely differing geometric properties and consequently a large deviation from the measured data. Another important fact which must be considered for the modeling of foams is that, open-cell foams exhibit different shapes (circular, triangular, concave triangular) of their strut cross-section with different porosities. This phenomenon can influence the geometric properties of foams to a great extent including their geometric specific surface area. Therefore, a single correlation developed for a certain strut shape cannot account for all the other shapes of the strut cross-section.
In open literature most authors have considered only one type of strut cross-section for the development of their correlations and have established it for wide range of porosity and hence different strut shapes. This has led to a large deviation of predicted specific surface area from the experimental data.
Among all the correlations compared and discussed in this chapter, the new correlation derived in the present work has produced results with minimum deviation from the experimental data of the foams of different materials with a wide range of porosities and pore densities. It is to be noted that this correlation is based on the space filling tetrakaidecahedron geometry and is based on the theoretical aspects only as no empirical fitting of coefficients is involved. It is therefore concluded that the tetrakaidecahedron model is the most suitable model to describe the geometrical configuration of the open-cell foams.
54
4 Pressure drop measurement and modeling on open-cell foams
4.1 Background
In the literature, pressure drop upon fluid flow in cellular materials or any kind of porous media has been extensively investigated as it plays an important economic role in most engineering processes that involve fluid flow through porous medium, such as, e.g., filtration, heat exchange and chemical reaction. As the efficiency of these processes depends to a great extent on the permeability of the porous medium employed therefor, it is very important to understand its fluid dynamics as well as the methods to evaluate its permeability or the pressure drop properties [23, 27, 69-73].
The concept of permeability was first reported by Henry Darcy in 1856. He conducted his experiments on a local fountain through beds of sand of various thicknesses [74]. He showed that the velocity over the sand bed was directly proportional to the driving pressure and inversely proportional to the thickness of the bed. Darcy’s law (equation 4.1) takes into account the viscous effects on the fluid pressure drop and establishes a linear relationship between pressure gradient and the fluid velocity through the porous media [24, 73, 75].
dP µ =− V (4.1) kdx 1 Where:
dP/dx : pressure gradient along the flow direction : [Pa m-1] µ : viscosity of the fluid : [Pa-s] V : velocity of the fluid : [m s-1] 2 k1 : Darcyan permeability : [m ]
Forchheimer extended Darcy’s equation by introducing the inertial effects in addition to the viscous effects on the fluid pressure drop in a porous medium. This gave a parabolic dependence of pressure gradient on the fluid velocity. Forchheimer equation can be expressed as follows: µ ρ dP 2 V +=− V (4.2) kdx 1 k2 Where:
k2 : Non-Darcyan permeability : [m] ρ : density of the fluid : [kg m-3]
4 Pressure drop measurement and modeling on open-cell foams
2 It is to be noted that in equation 4.2, k1 and k2 have different dimensions (k1: L and k2: L ), though both of them are referred to as permeability.
In literature, Forchheimer equation has been often used to evaluate the permeability of the porous media [73, 76-78]. The most widely accepted interpretation of Forchheimer equation was presented by Ergun and Orning [79, 80]. They proposed the following equation to estimate the pressure drop in packed beds:
∆P −ε )(1 2 µV −ε )(1 ρV 2 = A o + B o (4.3) ε 3 2 ε 3 L o d p o d p Where:
∆P : pressure drop : [Pa] L : bed length of the porous medium : [m] Α : coefficient of viscous term : [-] Β : coefficient of inertial term : [-]
εο : open porosity of the porous media : [-]
Note that coefficient of viscous and inertial terms (A: 150 and B: 1.75) were determined by Ergun empirically by fitting a large amount of experimental pressure drop data from the open literature.
In literature, many authors have further used Ergun equation to propose Ergun-type correlations for the pressure drop estimation/prediction in open-cell foams [3, 26, 66, 68]. Some authors (e.g. Lacrioix et al. [26] and Truong Huu et al. [29]) have even used the same coefficients which were originally determined for the packed bed system. The permeabilities reported in all cases follow the Forchheimer equation.
In summary, a multitude of correlation for pressure drop prediction in open-cell foams can be found in the literature, though none of them bears a general applicability. An overview of the stat-of-the-art correlations for pressure drop prediction in open-cell foams is presented in the following section.
56 4.2 State-of-the-art correlations for the pressure drop prediction in open-cell foams
4.2 State-of-the-art correlations for the pressure drop prediction in open- cell foams
For chemical engineering applications open-cell foams, due to their high porosities, offer much lower pressure drop (for similar geometric specific surface area) compared to the packed-bed reactor and columns. This property of foams can specially be exploited in situations where high space velocities are involved. Therefore, for such applications, in order to design a reactor or column with open-cell foams as internals, a precise determination of the pressure drop is extremely important [3, 24, 81-83].
In open literature several authors have presented their work on pressure drop in foam structures proposing correlation for the pressure drop prediction [3, 13, 14, 26, 58, 61, 66-68, 84-91]. Edouard et al. [24] in their study on pressure drop modeling on solid foams presented a review on the state-of-the-art correlations for the pressure drop in foams. They concluded:
“It appears from this study that no model is perfect and that the standard deviation between experimental and theoretical values can be as high as 100 %”[24].
Nevertheless, Edouard et al. [24] recommended using the correlation developed by Lacroix et al. [26] and Du Plessis et al. [58]. Recently, Incera Garrido et al. [14] evaluated the state-of- the-art correlations for pressure drop predictions in foams by comparing the predictions with their own experimental data. They reported that the prediction of all of the correlations from literature was not satisfactory.
In this section most often used correlations for the prediction of the pressure drop in open-cell foams included the ones recommended by Edouard et al. [24] are discussed. An overview of the other correlations is given in the Table 4.1.
The first correlation discussed here is from Du Plessis et al. [58] and Fourie and Du Plessis [61]. The correlation is based on representative unit cell (RUC). The details of the RUC model are given in the previous chapter. Using this model the authors developed the following correlation (Equation 4.4) for the pressure drop predictions in metallic foams.
P −− χχχ∆ )3)(1(36 2 χ − )1(05.2 = µV + ρV 2 (4.4) ε 22 ε 2 L 4d wo 4dwo Where:
χ : tortuosity of the of the foam : [-]
dw : window diameter of the foam : [m]
57 4 Pressure drop measurement and modeling on open-cell foams
The tortuosity for equation 4.4 can be determined by applying equation 4.5 which uses open porosity as a measured value to calculate the tortuosity.
4π 1 − χ += cos22 + 1 ()ε − 12cos (4.5) 3 3 o
Lacroix et al. [26] modified the Ergun equation (equation 4.3, originally developed for packed bed of particles) for the prediction of the pressure drop in open-cell foams. They replaced the particle diameter (dp) with strut size (ds) to give an Ergun-Lacroix equation (Equation 4.6).
∆P 4 2 − ε )(1 2 µV 4 − ε )(1 ρV 2 = A o + B o (4.6) ε 3 2 ε 3 L 6 o d s 6 o d s
In order to obtain a relationship between dp and ds, Lacroix et al. [26] used a direct analogy between packed bed of spherical particles and open-cell foams (assuming the same porosity) and came up with a correlation which is given in Equation 4.7. For the definition of ds to be used in equation 4.7, they derived another correlation (equation 4.8) for which they adopted the cubic cell model. The dw in equation 4.8 is the window diameter in open-cell foams.
6 = dd (4.7) p 4 s
d [ − επ )1(34 ] 5.0 d = w o (4.8) s []−− επ 5.0 0 )1(341
Lacroix et al. [26] measured cell diameter (dc) of the foam samples they investigated. In order to obtain the window diameter they used the following expression (equation 4.9) which is often used by foam manufacturers [29] for an approximation. d d = c (4.9) w 2.3
It is to be noted that Lacroix et al. [26] used the same coefficient (A: 150 and B: 1.75; for viscous and inertial terms respectively) for open-cell foams as in the Ergun equation (equation 4,3). These coefficients were determined by Ergun empirically for packed bed of particles.
58 4.2 State-of-the-art correlations for the pressure drop prediction in open-cell foams
More recently, Dietrich et al. [67, 92] have presented another correlation for pressure drop prediction in ceramic and metal foams which is given in equation 4.10. This Ergun-type correlation is based on the definition of friction factor (ƒ) and uses the hydraulic diameter (dh) and the open porosity of foams to predict the pressure drop. The coefficients 110 and 1.45 in equation 4.10 were determined by fitting the experimental data.
∆P µ ρ =110 V +1.45 V 2 (4.10) ε 2 ε 2 dL ho o dh Where:
dh : hydraulic diameter : [m]
The definition of hydraulic diameter is given in equation 4.11, which uses geometric specific surface area and open porosity of open-cell foams.
ε = 4 o dh (4.11) S − geov
In order to determine the geometric specific surface area (Sv-geo), Dietrich et al. [67] recommended an empirical form (equation 4.12.) of a correlation which was originally developed by Buciuman and Kraushaar-Czarnetzki [57].
1 .250 − = .S 872 ()1 − ε (4.12) geov + o dd sw
Dietrich et al. [92] showed that their correlation could predict the experimental pressure drop from open literature with most of the data points lying between ±40%.
From the above paragraphs, it is very clear that no generally applicable correlation for the pressure drop prediction in open-cell foams has yet been proposed. Therefore, further work is definitely needed in this area. In the following section a new approach for developing a correlation for pressure drop prediction in open-cell foams is presented. As a starting point, pressure drop in periodic cellular structures of tetrakaidecahedron geometry (a widely accepted representative geometry for open-cell foams) is studied.
59 4 Pressure drop measurement and modeling on open-cell foams
Table 4.1: State of the art correlation for predicting the pressure drop in foams (partly adapted from [24])
Reference Geometric specific surface area [m-1] Relation between morphological parameter Correlation for pressure drop prediction
Lu et al.[59] π 2 5.0 0080 ( d/d. ) − ρ ( 1− d/d/vd ) 32 5.0 = []−ε += sw .150 = s ws S − = []− ε )1( dd ws o )1( .f 0440 + Re;Re geov o π () 131430 d/d(.. )ws µ a 3 d/d sw
∆P − ε )(1 2 µV − ε )(1 ρV 2 = 150 o + .751 o ε 3 2 ε 3 Innocentini et al. [66] − ε )1(4 L d d p S = o o p o − geov ε dw ( − ε ) ρ −ε )(1 1 pvd = o + =1 5 o Re;d.d = f 150 .751 p w ε µ Rep
5.0 2 2 2 Richardson et al. [3] 4ε − ε ∆P α S − − ε µV)(1 βS − − ρεV)(1 = o d ow )1(5338.0 = solidv o + solidv o S − d = geov d s −− ε 5.0 L ε 3 ε 3 w o )1(971.01 o o − .75230 .071580 − β = ( −ε ) α = .7430 ( − ε ) .09820 03680 d. w 1 o dw 1973 o
Du Plessis and P ( )(3136 −− χχχ∆)2 . (χ −1052 ) = µV + ρV 2 Fourie and Du Plessis [58, 61] ε 22 ε 2 L 4dwo 4dwo 3 2 = (χχ )(−− ) = − ρχ 2 S −geov 13 dd ws 1 3 BA + dd 3 − χ f (χχ )(−−= 13 ) + v sw ε 2 ()+ 4 ddv swo 42
− .6670 4π 1 − 24 µε ρ (ddv χ )(−+ 1 ) χ += 22 cos + cos 1 ()ε −12 A = o B; += 101 sw o (χρχ )(+− ) µε 3 3 3 sw vdd 2 o
60 4.2 State-of-the-art correlations for the pressure drop prediction in open-cell foams
Reference Geometric specific surface area [m-1] Relation between morphological parameter Correlation for pressure drop prediction
Moreira et al. [68] ------∆P −ε )(1 2 −ε )(1 =1.275x109 o µV + x.. 10891 4 o ρV 2 ε − .0503 ε − .2503 L d wo d wo
2 2 ∆P − ε )(1 µV − ε )(1 ρV =150 o + .751 o ε 3 2 ε 3 Lacroix et al.[26] 4 [ ( −επ )] .50 L o dp o dp ()−= ε dw 134 o S −geov 1 o = ds .50 ds []()−− επ 1341 o ρ − ε )(1 pvd = o + = 51 Re;d.d = f 150 .751 p ps µ Rep
∆P d 3 d 3 =13.56 w µV + .870 w ρv 2 Giani et al. [13] 4 4 .50 L − d )2(d 4 − d )2(d 4 S ()1−= ε += ()− ε sw sw −geov o sws )dd(d 1 o d s 3π 56.13 ρ vd 87.0f += Re; = s Re µ
∆P µ ρ ∆P d 3 = + V1.45V110 2 Hg = h Dietrich et. [67] ε ε 2 ε 2 ∆ ρυ 2 1 25.0 4 o L d ho d ho L S − = 87.2 ()1−ε d = geov + dd o h S sw −geov . µd += 2 Re = h 110ReHg 1.45Re υε o
61 4 Pressure drop measurement and modeling on open-cell foams
4.3 Pressure drop measurement over open-cell foams
4.3.1 Experimental
The pressure drop over SSiC and aluminum foams as well as over periodic cellular structures (characterized in 2nd chapter) was measured using an apparatus schematized in Figure 4.1. Air at room temperature was used as working fluid. The glass tube used for the pressure drop measurement was equipped with a flow distributor in front of the sample. During the pressure drop measurements, in order to avoid a bypass flow, the foam samples were wrapped in a thin ceramic mat.
The velocity of the air was measured with the help of Testo hot wire anemometer of the type Testo 425 (0-20 m/s) and the pressure drop was measured by a Furnace control micro mano- meter of the type FCO 14 (0-10 mbar).
For comparison purposes the pressure drop over a random packing of glass beads (packing length: ca. 45 mm, packing porosity of 0.39) with average diameter of 1.9 mm was also measured.
Figure 4.1: Pressure drop measurement
4.3.2 Results
The pressure drop results for SSiC foams, aluminum foams and periodic cellular structures of Kelvin’s cell geometry are shown in Figure 4.2 a, b, and c respectively. From these results it can be observed that pressure drop, as expected, follows the Forchheimer equation. A significant dependency of the pressure drop on PPI and CPI (analogous to PPI) values can be observed. At about similar porosities pressure drop is directly proportional to PPI or CPI values. This can be explained by the fact that with increasing PPI or CPI, the cell size decrease and the effective pore size (window size) available for the fluid flow also decreases, which in turns increases the flow resistance for a fluid thereby increasing the pressure drop.
62 4.3 Pressure drop measurement over open-cell foams
Figure 4.2: Measured pressure drop over SSiC foams, aluminum foams and periodic cellular structures of Kelvin’s cell geometry
63 4 Pressure drop measurement and modeling on open-cell foams
4.3.2.1 Comparison with literature data
In order to compare the measured pressure drop over reticulated open-cell foams investigated in present work with the literature data, pseudo experimental pressure drop values from open literature and measured data from the present work were plotted versus velocity (Figure 4.3). For this comparison, literature pressure drop data of only similar foams was taken. The similarity was established on the bases of PPI, porosity and/or pore size.
In Figure 4.3, in case of ceramic foams of 10 PPI, the foam sample from Dietrich et al. [67] shows the highest pressure drop. This may be because of the lowest porosity of their sample compared to other 10 PPI foams presented in the Figure 4.3. The samples from Incera Garrido et al. [14] show results in a similar range as compared to the ones from Richardson et al. [3] and from present work, though the foams sample from Incera Garrido et al. [14] has lower porosity than the other two. This may be attributed to the larger window diameter of 10 PPI sample from Incera Garrido et al. [14], which lowers the pressure drop of their sample (which was originally expected to be higher) with the given pore size and porosity. For 20 PPI ceramic foams, although sample from Moreira et al. [68] has highest porosity yet it shows the maximum pressure drop compared to others. This may be ascribed to a large number of closed window in their sample (which can be observed from the figures show by Moreira et al. [68] in the publication) as well as to a comparatively smaller window diameter.
A lower pressure drop shown by ceramic foams of 20 and 30 PPI from present work compared to the literature data is due to their comparatively higher porosities. A high pressure drop of 30 PPI sample from Richardson et al. [3] despite the highest porosity among the shown 30 PPI samples can be explained on the basis of the smallest windows size.
For metal foams, the pressure drop values obtained from the present work are mostly in close agreement with the literature data. A higher pressure drop for the 10 PPI metal foam from Phanikumar and Mahajan [88], despite similar porosity compared to other two 10 PPI samples, is may be due to its comparatively smaller window size.
A comparison of pressure drop of periodic cellular structures of Kelvin’s cell geometry with literature data was not possible, as no data of pressure drop in foams of ideal Kelvin’s cell geometry has been reported in the literature so far.
64 4.3 Pressure drop measurement over open-cell foams
Figure 4.3: Comparison of measured pressure drop over reticulated foams with the literature data
65 4 Pressure drop measurement and modeling on open-cell foams
4.3.2.2 Performance of state-of-the-art correlations for pressure drop prediction
None of the correlation from open literature could reproduce the experimental pressure drop values from the present work to a satisfactory level. A comparison between experimental pressure drop data from present work with the predictions of the correlations as suggested by Edouard et al. [24] (i.e. correlations from Lacroix et al. [26] and Fourie and Du Plessis [61]) along with the predictions of a recently presented correlation from Dietrich et al. [67] are shown the Figure 4.3.
Ceramic foams In case of ceramic foams, the largest deviation was shown by the correlation from Du Plessis et al. [58] and Fourie and Du Plessis [61]. It is to be noted that this correlation is based on RUC model (see section 3.2 and 4.2) considering rectangular strut cross-section and does not involve any fitting of experimental data. The correlation shows an overestimation of the experimental pressure drop data exceeding 70%. These results are not surprising as it has already been shown in section 4 of the present work that RUC model overestimates the specific surface area of open-cell foams. Since specific surface area of the porous medium is directly related to the pressure drop, overestimation of specific surface area would result in an over estimation of the pressure drop. A similar explanation can be invoked for the deviation shown by the correlation from Lacroix et al. [26]. In addition, the empirical coefficient (A: 150 and B: 1.75, so called Ergun’s constants, originally proposed for the packed-beds) in the correlation proposed by Lacroix et al. [26] may also enhance the deviation of predicted pressure drop from the experimental data for open-cell foams. Dietrich et al. [67, 92] reported that their correlation could predict the experimental pressure drop data from open literature with most data points within the range of ±40. For the present work, a deviation of +40% from experimental pressure drop was observed for their correlation. This may be ascribed to the coefficient in their correlation which they determined by fitting of experimental data.
Metal foams In case of metal foams (open porosity ~ 0.935), it is interesting to observe that all three correlations (Dietrich et al. [67], Lacroix et al. [26] and Fourie and Du Plessis [61]) have shown a deviation of ca. +40%. The correlation from Dietrich et al. [92] has produced similar results as in the case of ceramic foams. The similar behavior of over estimating the pressure drop shown by the correlations from Lacroix et al. [26] and Du Plessis et al. [58] can be explained on the basis of their comparable trend of over estimating the geometric specific surface area (see Figure 3.6) of foams with porosities greater than 90%.
66 4.3 Pressure drop measurement over open-cell foams
Figure 4.4: Performance of state-of-the-art correlations (measured data: from present work)
67 4 Pressure drop measurement and modeling on open-cell foams
4.4 Periodic cellular structures as model systems for the description of the pressure drop in open-cell foams
4.4.1 Pressure drop modeling on periodic cellular structures: the Ergun equation revisited
In this section pressure drop modeling on periodic cellular structures of tetrakaidecahedron geometry is presented. In order to model the pressure drop and to develop a correlation for pressure drop prediction, the original form of Ergun equation is used. Note that the original form of Ergun equation [79] does not contain any empirical factors and represents the most widely accepted interpretation of Forchheimer equation which is generally used to evaluate the pressure drop properties of the porous media.
The correlation obtained for periodic cellular structures (porous media with high porosities) will be examined for its extension towards porous media with low porosities as encountered in packed bed systems. Finally, the correlation will be tested/adapted for the non-ideal foam geometries as encountered in replicated open-cell foams.
4.4.1.1 The Ergun equation
Pressure drop in porous media follows the Forchheimer equation which was adopted by Ergun and Orning [79] to develop the following equation (equation 4.13) for the prediction of pressure drop over packed beds of particles (porous media with low porosities).
P α∆ S 2 − )(1 2 µε βS − )(1 ρε = −solidv o V + −solidv o V 2 (4.13) ε 3 ε 3 L o o Here:
α : coefficient of viscous term : [-]
β : coefficient of inertial term : [-]
-1 Sv-solid : specific surface area per unit solid volume : [m ]
Note that equation 4.13 is the original form of the Ergun with no empirical coefficients in it. The empirical form of the Ergun equation given as equation 4.14 (with Ergun’s constants A: 150 and B: 1.75) can be derived by introducing the coefficient values of α=4.17 and β=0.292 and substituting the value of Sv-solid for spheres from equation 4.15 in equation 4.13 (where dp is the particle diameter). The values of α and β were determined by Ergun empirically for packed bed configurations. 68 4.4 Periodic cellular structures as model systems for the description of the pressure drop in open-cell foams
∆P − ε )(1 2 µV −ε )(1 ρV 2 = 150 o +1.75 o (4.14) ε 23 ε 3 L d po o d p
= 6 S −solidv (4.15) d p
Also, using the relation for the specific surface area of spheres (equation 4.15), the original form of Ergun equation (equation 4.13) can be written as given in equation 4.16. The dimensionless friction factor (ƒ) can be derived from equation 4.16 and is then expressed as given in equation 4.17. Here, the particle Reynolds number Rep is introduced as given in equation 4.18. ∆ − 2 µεα − ρεβ 2 P = o V + o )(16)(136 V (4.16) ε 32 ε 3 L d op d op
3 ∆P d ε − ε )(1 f = op = 36α o + 6β (4.17) − ρε 2 L o )(1 V Rep
ρVd Re = p (4.18) p µ
The friction factor derived from equation 4.14 (empirical form of Ergun equation) is then given in equation 4.19.
3 ∆P d ε − ε )(1 f = op = 150 o + 75.1 (4.19) − ρε 2 L o )(1 V Rep
In the next subsection a new approach will be presented in order to obtain the coefficient α and β for the periodic structures.
69 4 Pressure drop measurement and modeling on open-cell foams
4.4.1.2 Correlation for pressure drop prediction in periodic cellular structures
For the development of a new correlation for the pressure drop in periodic cellular materials, the original form of the Ergun equation given in equation 4.13 is used. In order to apply the original form of Ergun equation the following parameters of periodic cellular structures are required:
εο : open-porosity : [-]
α : coefficient of viscous term : [-]
β : coefficient of inertial term : [-]
-1 Sv-solid : specific surface area per unit solid volume : [m ]
The specific surface area (per unit solid volume) of the periodic foam structures of tetrakaidecahedron geometry to be used in equation 4.13 can be calculated using the equation 3.30 (which gives the specific surface area of foams with tetrakaidecahedron geometry with cylindrical struts). The open porosity of periodic foams can be measured experimentally. For the coefficients α and β mathematical expressions are derived.
In literature, most author agree that α and β are not constant but rather parameters that depend upon the properties of the medium [3, 6]. This was also observed in the present work that α and β depend upon the window diameter, strut thickness, and the open porosity of the foams. Therefore geometric properties of ideal tetrakaidecahedron were used to develop the dimensionless expression for α and β. For this purpose several combinations of geometric properties of ideal tetrakaidecahedron were tested. The best results were obtained by using the expressions given in equation 4.20 and 4.21 respectively. In both equations, the first term is the ratio of window diameter to strut thickness (see chapter 3.5.1) for the tetrakaidecahedron geometry with cylindrical struts. The second term is the open porosity, i.e. εο for α
(coefficient of viscous term), and the solid volume fraction, i.e. (1-εο) for β (coefficient of inertial term), respectively. Note that in equations 4.20 and 4.21 the numerical values are geometric constants of ideal tetrakaidecahedron geometry, the value of α and β depend upon the open porosity only.
−1 −− ε )1(971.01 5.0 α = o ε )( (4.20) −ε 5.0 o o )1(6164.0
−− ε )1(971.01 5.0 β = o −ε )1( (4.21) −ε 5.0 o o )1(6164.0
70 4.4 Periodic cellular structures as model systems for the description of the pressure drop in open-cell foams
Using equation 4.13 with the definition of the specific surface area from equation 3.30 and the definition of α and β from equation 4.20 and 4.21 respectively, the pressure drop for periodic cellular structures with ideal tetrakaidecahedron geometry can be predicted. Figure 4.5 shows a comparison between measured and predicted/calculated pressure drop data for the three samples of periodic cellular structures of ideal tetrakaidecahedron geometry. It can be seen that the new correlation proposed in this contribution successfully predicts the pressure drop, with the majority of the data featuring a deviation of less than ±10%.
Figure 4.5: Prediction of pressure drop according to the proposed correlation developed in present work compared with the measured pressure drop over periodic cellular structures of tetrakaidecahedron geometry
71 4 Pressure drop measurement and modeling on open-cell foams
4.4.2 Correlation for the pressure drop in periodic cellular structures: extension for low porosity porous media
In order to examine the applicability of the new correlation for a large range of porosities the experimental and calculated friction factors for porous media with high porosity (foam structures) and with low porosity (packed beds) were compared for a large range of modified
Reynolds numbers i.e. Re/(1-εo). The results of these comparisons are shown in Figure 4.6 and Figure 4.7.
In Figure 4.6 the friction factor for high porosity porous media obtained from the new correlation (i.e. equation 4.17 with α and β from equation 4.20 and 4.21, respectively), from the empirical Ergun equation (equation 4.19 which is obtained by substituting α=4.17 and β=0.292), and from the measured data are plotted versus the modified Reynolds number. For the plot average porosity of periodic foams was used. It can be seen that the new correlation is successfully validated by the experimental results obtained for the periodic cellular structures, whereas the Ergun equation with fixed values of α and β for sphere packing is not extendable to porous media with high porosities. This is not surprising because the values of α and β in the Ergun equation were empirically determined for randomly packed fixed beds of spherical particles which usually have porosities in the range between 0.35 and 0.5 (most often around 0.4). Hence it can be concluded that the Ergun equation with its coefficients, determined for packed beds, which have low porosities, is not appropriate for foam structures which usually have high porosities (0.7 to 0.95).
Figure 4.7 shows the comparison of experimental and calculated friction factors obtained for porous media of both, high (i.e. foam) and low (packed bed) porosities. It is to be noted that for Reynolds numbers of 0-1000 a porosity of 0.425 is assumed, while for Reynolds numbers > 1000 a porosity of 0.844 (average porosity of periodic structures of tetrakaidecahedron geometry used in the present work) has been used for computing both solid curve (present correlation) as well as the dashed curve (empirical Ergun equation). The solid curve shows a discontinuous jump as the open porosity changes from 0.425 to 0.844. This is due to the change in the value of α and β as they are both functions of the open porosity. The dashed curve, however, shows no discontinuity as the open porosity changes which is due to the fixed values of α and β for the empirical Ergun equation.
It can be observed that for porous media of low porosity, the new correlation proposed in the present work produces similar results compared to that of the empirical form of the Ergun equation (which is widely used for packed beds). In addition, in the high porosity region the
72 4.4 Periodic cellular structures as model systems for the description of the pressure drop in open-cell foams new correlation successfully predicts the experimental results obtained for the periodic cellular materials, whereas the empirical form of the Ergun equation fails in this porosity region.
73 4 Pressure drop measurement and modeling on open-cell foams
Figure 4.6: Friction factor versus modified Reynolds number for porous media of high porosities
74 4.4 Periodic cellular structures as model systems for the description of the pressure drop in open-cell foams
Figure 4.7: Friction factor versus modified Reynolds number for porous media of low (spheres: [84], [93] and present work) and high porosities (periodic cellular structures: present work)
75 4 Pressure drop measurement and modeling on open-cell foams
4.4.3 Adapting the correlation for replicated open-cell foams
In order to examine the extension of the new correlation for the irregular geometries as encountered in replicated foams, the equation 4.13 along with the equations 3.30, 4.20 and 4.21 were applied to predict the measured pressure drop of reticulated foams investigated in the present work.
This, however, resulted in an over estimation of the experimental values of the pressure drop (Figure 4.8). Therefore, in order to reconcile the experimental and theoretical results of replicated foams, the relations for α and β (given in equation 4.20 and 4.21) to be used in equation 4.13 were modified (Figure 4.9). Equation 4.22 and 4.23 (modified for reticulated foams) are essentially based on the same assumptions as used for the periodic cellular structures of tetrakaidecahedron geometry only the exponents 1.3 were determined empirically.
Figure 4.8: Prediction of the experimental pressure drop of replicated foams with unchanged exponents in equation 4.20 and 4.21
76 4.4 Periodic cellular structures as model systems for the description of the pressure drop in open-cell foams
Figure 4.9: Adapting the correlation for reticulated open-cell foams
77 4 Pressure drop measurement and modeling on open-cell foams
By using equation 4.13 together with equation 3.30, 4.22, and 4.23, the pressure drop in replicated open-cell foams of irregular geometry (with cylindrical struts i.e. for porosities less than 90%) can be predicted. In Table 4.2 the expressions for α and β as well as correlations for specific surface area (to be used in equation 4.13) for cylindrical, triangular and concave triangular struts are summarized. Figure 4.10 shows the comparison of predicted (using modified exponents) and measured pressure drop data. It can be observed that most predicted values are within the range of ±10%.
3.1 −− ε 5.0 o )1(971.01 α − = ε )( (4.22) strutslcylindrica − ε 5.0 o o )1(6164.0
3.1 −− ε 5.0 o )1(971.01 β − = − ε )1( (4.23) strutslcylindrica − ε 5.0 o o )1(6164.0
Figure 4.10: Prediction of the experimental pressure drop of reticulated foams with modified exponents in equation 4.22 and 4.33 78 4.4 Periodic cellular structures as model systems for the description of the pressure drop in open-cell foams
Table 4.2: Expressions for α and b, and the correlations for specific surface area (to be used in equation 4.12) for cylindrical, triangular and concave triangular strut
Strut Specific surface area Coefficient for viscous term Coefficient for inertial term 2 3 α cross-section (per unit solid volume) [m /m ] ( ) [-] (βββ) [-]
3.1 3.1 −− ε 5.0 5.0 5.0 o )1(971.01 −− ε )1(971.01 Circular [ −− ε )1(971.01 ] α − = ε )( β = o − ε = o strutslcylindrica 5.0 o −strutslcylindrica o )1( S solidv −− lcylindrica 867.4 − ε )1(6164.0 −ε 5.0 −ε 5.0 o o )1(6164.0 d ow )1(
3.1 3.1 −− ε 5.0 −− ε )1(971.01 5.0 Triangular [ −− ε 5.0 ] α = o )1(971.01 ε β = o −ε o )1(971.01 Triangular−struts o )( Triangular −struts o )1( S −− = 62.5 − ε 5.0 − ε )1(5338.0 5.0 solidv triangular −ε 5.0 o )1(5338.0 o d ow )1(
3.1 3.1 5.0 −− ε 5.0 −− ε 5.0 [ −− ε )1(971.01 ] o )1(971.01 o )1(971.01 Concave = o α − − = ε )( β − − = − ε )1( S solidv concave−−− triangular 49.6 Concave triangular struts − ε 5.0 o concave triangular struts − ε 5.0 o − ε 5.0 o )1(5338.0 o )1(5338.0 triangular d ow )1(
79 4 Pressure drop measurement and modeling on open-cell foams
4.4.4 Validating the correlation for foams with different strut cross-sections
For the validation, all three variations of the proposed correlation (corresponding to three different strut cross-sections) were applied to predict the measured pressure drop data of foams from the open literature. The results are shown in the following subsections. The properties of foams used are given in the Table 4.3.
4.4.4.1 Circular strut cross-section
Figure 4.11: Prediction of the pressure drop according to the proposed correlation for ceramic foams of different PPI with circular strut cross-section (*open porosity is obtained by subtracting strut porosity, according to the authors: 5%, from the total porosity)
80 4.4 Periodic cellular structures as model systems for the description of the pressure drop in open-cell foams
Figure 4.12: Prediction of pressure drop according to the proposed correlation for metal foams of different PPI with circular strut cross-section
Figure 4.11 and Figure 4.12 show the prediction of the pressure drop according to the proposed correlation for ceramic and metal foams respectively. It can be seen that for both ceramic and metal foams of different pore size and porosity and with circular strut cross- section, most predicted values are within the range of ± 15%.
81 4 Pressure drop measurement and modeling on open-cell foams
4.4.4.2 Triangular strut cross-section
Figure 4.13: Prediction of pressure drop according to the proposed correlation for metal foams of different PPI with triangular strut cross-section
Figure 4.13 shows the prediction of the pressure drop according to the proposed correlation for metal foams with triangular struts. Again, it can be observed as in the case of cylindrical struts that the most predicted data for metal foams of different pore size and porosity area within the range of ± 15%.
For ceramic foams with triangular strut cross-sections, no experimental data of pressure drop was available in the open literature. Therefore, no comparison was possible.
82 4.4 Periodic cellular structures as model systems for the description of the pressure drop in open-cell foams
4.4.4.3 Concave triangular strut cross-section
Figure 4.14: Prediction of pressure drop according to the proposed correlation for ceramic foams of different average cell size with concave triangular strut cross-section
Figure 4.15: Prediction of pressure drop according to the proposed correlation for metal foams with concave triangular strut cross-section
Prediction of pressure drop according to the proposed correlation for ceramic and metal foams with concave triangular struts is presented in the Figure 4.14 and Figure 4.15 respectively. Similar results obtained as in the case of cylindrical and triangular struts can be observed for the concave triangular strut cross-section.
83 4 Pressure drop measurement and modeling on open-cell foams
Table 4.3: Properties of solid foams used for the pressure drop predictions
Open Window Geometric PPI Material Reference porosity Diametera specific surface [-] [-] [mm] areab [m-1]
Incera Garrido et al. [14]
10 Alumina 0.772 1.93 645
20 Alumina 0.719 1.06 1171
20 Alumina 0.751 1.192 1050
20 Alumina 0.814 1.13 1077
Lacroix et al. [26]
- β-SiC 0.914 1.598 852
- β-SiC 0.910 1.163 1186
- β-SiC 0.915 0.772 1757
Bhattacharya et al. [28]
5 Aluminum 0.905 1.652 636
5 Aluminum 0.946 1.70 689
10 Aluminum 0.909 1.287 807
10 Aluminum 0.914 1.423 716
10 Aluminum 0.949 1.348 849
20 Aluminum 0.906 1.130 927
20 Aluminum 0.925 1.261 898
20 Aluminum 0.949 1.174 975
40 Aluminum 0.937 0.870 1227
40 Aluminum 0.952 0.861 1300
40 Aluminum 0.959 0.751 1411
Dietrich et al. [67]
10 Mullite 0.735c 2.111 594
20 Alumina 0.748 1.09. 1148
20 Alumina 0.811 1.46 835
20 Mullite 0.784c 1.522 816
30 Mullite 0.748 1.127 1111
84 4.4 Periodic cellular structures as model systems for the description of the pressure drop in open-cell foams
Open Window Geometric PPI Material Reference porosity Diametera specific surface [-] [-] [mm] areab [m-1]
30 Alumina 0.752 0.884 1416
45 Alumina 0.757 0.625 2001
45 Mullite 0.744 0.685 1829
Dukhan [86]
10 Aluminum 0.915 - 810
10 Aluminum 0.919 - 790
20 Aluminum 0.924 - 1200
Phanikumar and Mahajan [88]
5 Aluminum 0.899 1.835 583
5 Aluminum 0.930 1.890 585
10 Aluminum 0.909 1.488 699
10 Aluminum 0.939 1.484 713
20 Aluminum 0.920 1.210 825
20 Aluminum 0.935 1.184 909
40 Aluminum 0.909 0.841 1234
Calmidi and Mahajan [91]
5 Aluminum 0.912 1.652 623
5 Aluminum 0.973 1.748 516
10 Aluminum 0.949 1.361 843
20 Aluminum 0.901 1.212 949
20 Aluminum 0.955 1.174 934
40 Aluminum 0.913 0.783 1308
40 Aluminum 0.927 0.878 1274
40 Aluminum 0.937 0.870 1227 a window diameter given directly by the authors or calculated from the given cell size using equation 4.9 b Geometric specific surface area calculated by using correlations from the present work c Open porosity is obtained by subtracting strut porosity (according to the authors: 5%) from the total porosity
85 4 Pressure drop measurement and modeling on open-cell foams
4.5 Summary and conclusion
Fluid flow and pressure drop in porous media is one of the key topics in chemical engineering, especially for designing columns and reactors that employ a certain porous medium (cellular materials or packed beds). For a similar geometric specific surface area, open-cell foams offer a considerably lower pressure drop compared to the conventional randomly packed fixed-bed reactor or column configuration and thus present themselves as promising alternatives for reactor or column internals.
In this chapter the problem of pressure drop prediction in open-cell foams has been addressed. For this purpose as a first step, pressure drop in periodic cellular structures of ideal tetrakaidecahedron geometry (preferred representative geometry for reticulated open-cell foams) was studied. Using the original form of the Ergun equation, a correlation for the pressure drop prediction in periodic cellular structures with ideal tetrakaidecahedron geometry was developed. The correlation was validated by the experimental results of the pressure drop obtained for the periodic structures investigated in the present work. With the new correlation it is possible to predict the pressure drop in periodic structures of ideal tetrakaidecahedron geometry by using only two measured parameters, namely the open porosity and the window diameter. The extended applicability of the new correlation for a large range of porosities was examined by comparing the friction factors for porous media with both, high (foam structure) and low porosities (packed beds) for a large range of Reynolds numbers. The new correlation presented in this work proved to be applicable for both, low and high porosity porous media.
As a second step, the correlation was tested for the non-ideal geometries as encountered in replicated open-cell foams. This, however, overestimated the experimental data of pressure drop. Therefore, in order to reconcile the predicted value of pressure drop with experimental data, the exponents in the expressions for α and β (coefficient for viscous and inertial terms respectively) were modified (see equations 4.20 and 4.21).
As in the case of specific surface area, three variations of the proposed correlation, corresponding to three different strut cross sections (i.e. cylindrical, triangular and concave triangular) were presented. In order to apply the appropriate form of the proposed correlation, it is important to identify the shape of the strut cross-section of the foam sample. This can be easily determined with the help of light microscopy or SEM. Once the shape of the strut cross-section is known, one out of three forms of the correlation (corresponding to the observed strut cross-section) can be used to predict the pressure drop. The correlation uses open porosity and the window diameter as the measured parameters.
86 4.5 Summary and conclusion
In order to validate the correlation for different foam materials and a large range of pore size and porosity (and hence different strut cross-sections), it was applied to predict the pressure drop data from open literature. It has been shown that the new correlation can predict a large amount of literature data of pressure drop (of different foam material, porosities, and strut cross-sections) with most data points within the range of ±15%.
87
88
5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
5.1 Background
5.1.1 Zeolites
Zeolites are defined as micro-porous crystalline aliminosilicates characterized by an extensive three dimensional pore network in the range of 0.2 to 1.3 nm [94, 95]. The name “zeolite” has its origin in two Greek words zeo (to boil) and lithos (a stone) and was first used by a Swedish mineralogist A. F. Cronstedt in 1756, after observing that certain mineral (Stilbite) began to bubble upon strong heating [96, 97].
Due to the regular nature and size of their pores (in the same order of magnitude of molecule diameters), zeolites are also termed as molecular sieves. This is a huge class of materials, not necessarily limited to crystalline frameworks, capable of separating components of a mixture on the basis of molecular size and shape (McBain, 1932) [94, 95, 97].
Zeolite structure consists of tetrahedral building units of [SiO4]4- and [AlO4]5-, which are arranged into various framework structures by sharing the oxygen atoms. The general formula can be described as follow [98]:
m+ - m/y )[(SiOA x2 . 2 )(AlO y .] 2OzH
With:
A : Cation m : Charge of the cation x + y : Number of tetrahedra per unit crystallographic unit cell x / y : Silicon to aluminum ratio z : Number of water molecules
Zeolites are mainly classified into small pore zeolites (free diameter 0.30 – 0.45 nm), medium pore (0.45 – 0.60 nm) and large pore zeolites (0.60 – 0.80 nm). The free pore diameter is determined by the ring size of the pore opening. Rings can contain up to 20 members. Zeolites with the same general structure are grouped and marked with a 3 letter code. Apart from these groups there is no standard nomenclature for specific zeolites [94].
5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
In Figure 5.1 the structures of three different zeolite types can be seen. The FAU belongs to the group of large pore, MFI to the middle pore and CHA (chabazite group) to the group of small pore zeolite.
Figure 5.1: FAU left, MFI (ZSM-5) middle, CHA (SAPO-34) right [99]
Zeolites are minerals available in nature, though most types of different zeolites were discovered in the laboratory. In the laboratory they are synthesized by hydrothermal synthesis under alkaline or acidic conditions. The synthesis gel consisting of a silica source (e.g. silica gel, sodium silicate), an aluminum source (e.g. sodium aluminate, Al-salts) and if necessary, a template (e.g. amine, alcohols) is mixed and aged. Afterwards, the mixture is heated between 70 °C to 200 °C in an autoclave. The different types of zeolite are produced through different synthesis routes and a wide range of post synthesis treatment methods. Variations are possible in the composition of the synthesis mixture or the template. Also, the length and the temperature of the hydrothermal treatment influence the resulting zeolite. Ion exchange can be carried out afterwards for changing the pore opening or inserting metal ions for creating different active sites.
The first zeolites were synthesized in the 1930s. The first commercialization was realized by Union Carbide around 1954, with the zeolites A, X and Y for catalytic processes [100]. Up till now, 206 structures of different zeolites are known and catalogued by the International Zeolite Association (IZA) [99]. Even more structures are expected to be discovered in future.
It is also possible to create mesoporosity in zeolites for enhancing the mass transport [101- 104]. Mei et al. [105] tested mesoporous high silica ZSM-5 (structure type: MFI) for methanol conversion. They reported that a shorter diffusion path increases the propylene yield in methanol conversion. Furthermore, the propylene selectivity using mesoporous ZSM- 5could be increased about three times compared to that obtained with ZSM-5 having microspores only.
90 5.1 Background
The industrial applications of zeolites are mainly in the field of adsorption, catalysis, molecular sieving and ion-exchange. In heterogeneous catalysis, Zeolites can be used as an active catalyst itself or as support for other active materials. Another versatility of zeolite is that they can be used as acid, base, or redox catalyst. Examples for acid catalysis are the use of acidic FAU in Fluid Catalytic Cracking (FCC) or the use of MFI in the conversion of methanol to olefins. The protonic sites are responsible in most cases for the catalytic activity of zeolites. The number of protonic sites which give rise to the acidity is limited by the number of framework aluminum atoms and can be influenced and adjusted during the synthesis or with post treatment. The acidity of zeolites is characterized by the type of the acidic site, acid site density and strength [100].
For the present work, as catalytic material (for coating the monolithic foam structures) zeolite of the type ZSM-5 with different modules i.e. different SiO2/Al2O3 ratio was used.
As mentioned before ZSM-5 is a medium-pore size zeolite. The 3D pore structure consists of straight (5.6 x 5.3 Å) and sinusoidal channels (5.5 x 5.1 Å). The structure of ZSM-5 consists of the Pentasil units as depicted in Figure 5.2 . These cage-building units form chains and with this a planar sheet. Parallel sheets are then linked by oxygen bridges for building a 3D structure [106]. Each layer contains 10-ring holes, which form the straight channels in the framework.
Figure 5.2: Framework type MFI: Pentasil unit (left), Pentasil chain (middle), framework (right) [99, 107]
ZSM-5 was discovered in 1972 by Landolt and Argauer (Mobile Oil Company) [97]. It can be synthesized in a wide range of Si/Al ratios, even an aluminum free (silicalite) version is possible [106]. For acid catalysis, the H-form of ZSM-5 (H-ZSM-5) is necessary. This form is obtained easily by the calcination of the synthesized ammonium form (NH4-ZSM-5). It is suitable for high temperature applications as it is stable up to around 700 C.
91 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
The synthesis mixture of ZSM-5 usually contains [97]: • a Si and Al source • a base as mineralizing agent (e.g. NaOH) • a template or an organic structure-directing agent (SDA) • water as medium
The acidic catalytic activity of ZSM-5 (due to the Brønsted acid sites) depends upon the Al- content in the framework and therefore on the module of the zeolite. A higher Si/Al ratio causes a decrease in acidity [108, 109]. Brønsted acidity of the ZSM-5 is caused by the OH- bridging of framework Al and Si. Also, two Brønsted acid sites upon dehydration form one Lewis acid site (Figure 5.3). The strength of the Lewis acid sites is usually weaker than Brønsted acid sites.
Figure 5.3: Brønsted acid sites (top) and Lewis acid sites (bottom) scheme, adapted from [97, 110]
The quantification of zeolite acidic sites can be done by NH3-TPD assuming that one ammonia molecule is adsorbed per acid site. In desorption spectrum of ammonia for H-ZSM- 5, the Lewis acid sites constitute a low temperature peak and the Brønsted and double Lewis sites form a high temperature peak. Under certain circumstances, Lewis sites can enhance the nearby Brønsted sites thus taking an indirect part in the catalytic activity [98]. Lewis acid sites can also have direct influence on the catalytic activity e.g. for methanol to olefins conversion, weak lewis acidity favors the production of propylene and lower olefins [108].
In summary, zeolites offer excellent properties including high surface area, high adsorption capacity, small pores, ion-exchange capability, tunable acidity and the high thermal and hydrothermal stability. Furthermore, the variable properties for example the acidity or basicity or the variation of hydrophylicity and hydrophobicity is also interesting for many industrial applications [97].
92 5.1 Background
5.1.2 Structured reactors
In the last decades structured and multifunctional reactors have drawn much attention for the process intensification in the chemical industry. The development and application of structured reactors have been triggered by the requirements of low pressure-drop and high surface area for reactions with very low residence times and high space velocities. Unlike conventional fixed-bed reactors (which contain random packing i.e. irregular arrangement of individual particle), in structured reactors or structured catalyst (which amounts the same) the entire geometry is fixed by design and not by chance. The predetermined geometry can thus be further optimized to have a better control over heat and mass transfer which results in a high precision, thereby boosting the reactor performance [18, 97, 111, 112].
5.1.2.1 Monolithic honeycombs
Monolithic honeycomb reactor is the best known example of structured reactors. Developed and introduced in 70s; they have become standard catalyst shapes for most environmental applications such as, e.g. the use of honeycomb structures in exhaust gas treatment systems for both stationary and mobile applications [97, 113-117].
The term monolith has its origin in Greek language; mono means single and lithos means stone. A monolithic structure is sometimes referred to as a honeycomb structure; although in technical context the term monolith has broader meaning [118, 119].
Figure 5.4 shows an example of monolithic honeycomb reactor showing its different components and Figure 5.5 shows an over view of heat and mass transfer phenomenon in a monolithic reactor channel.
Figure 5.4: Structural hierarchy in a monolithic honeycomb reactor [97, 119]
93 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
Figure 5.5: Schematic diagram showing an over view of heat and mass transfer phenomenon in a monolithic reactor channel, adapted from [119]
In heterogeneous catalysis a monolithic structure is applied as a support for an active catalyst (coated catalyst) or directly as a catalyst if the active component is integral part of the monolith (e.g. extruded honeycomb catalyst) (Figure 5.7). The composites (support + active material) thus obtained, either by coating or extrusion, offer many advantages over packed bed reactors including low pressure drop, better access of reactants to the catalyst surface and elimination of hotspots [17, 117-120].
Figure 5.6: Automotive catalyst structural design including honeycomb support and mounting can [114]
Figure 5.7: Different preparation paths for extruded catalysts, adapted from [120]
94 5.1 Background
5.1.2.2 Monolithic foams
For heterogeneous catalysis, monolithic foam structures as catalyst support can combine the advantages of honeycombs and the packed-bed configurations. Honeycomb structures although offer much lower pressure drop compared to the packed-bed systems yet lack other important properties (e.g. radial mass flow and tortuosity of the flow), which are present to a fair extent in packed-bed configurations. Foam structures on the other hand, due to their high porosity and three dimensional pore-network offer not only lower pressure drop but also radial mixing and tortuosity of the flow. Due to this excellent combination of properties, among many different structures which have been reported in the literature as support for catalysts, monolithic foams are gaining more and more importance [6, 27, 121]. Monolithic foams are usually available in a wide range of porosity, pore size and the material. The details about their structure, morphology, and flow properties have been presented in the previous chapters. In Table 5.1 properties of monolithic foams (important for reactor design) are compared with the honeycombs and packed-beds and in Table 5.2 examples of monolithic foams as catalyst support from open literature are presented.
Table 5.1: Comparison of properties: packed beds, honeycombs and foams, adapted from [16]
Properties Packed bed Honeycomb Foam
Radial mass flow fair no very good
Radial heat exchange fair no very good
Tortuosity of the gas flow yes no yes
Resulting pressure drop high medium-low low
Geometrical macro porosity 35-40% 70-90 % 60 – 95 %
95 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
Table 5.2: Monolithic foam structures as catalyst support Reference Foam Application/test reaction Coating Remarks
wash-coating withLA2O3/ determination of mass and heat Richardson et al. [3, 19] α-Al2O3 mass and heat transfer γ-Al2O3 transfer properties and pressure drop
Ivanova et al. [22, 122] β-SiC with SiO2 surface MTO in-situ coating with ZSM-5 test of different zeolites
Patcas et al. [93] Alumina foam CO oxidation Pt/SnO2 comparative study
monolith out of zeolite without a Lee et al. [108] zeolite foam MTO --- different support
potential applications: adsorption, Zampieri et al. [123] SiC/Si-O-C foam --- In-situ coating of MFI catalysis
Patcas [124] α-alumina bound with mullite MTO wash-coating with ZSM-5 comparison foam and fixed be
alumina, mullite, china, wash-coating with zeolite Buciuman et al. [125] --- optimization of coating procedure cordierite, nanocrystals
wet impregnation with
Ding et al.[126] α-Al2O3 Partial oxidation of CH4 test of catalyst deactivation Rh-α-Al2O3
potential applications: adsorption, Scheffler et al. [127] Al foam --- In-situ coating of MFI catalysis
potential applications: adsorption, Barg et al. [128] Al/ceramic foam --- In-situ coating FAU catalysis
96 5.1 Background
5.1.3 Structured zeolitic composites
In general, a structured reactor can be considered as a composite comprised of a macro porous support and an active catalyst i.e. the macro porous support materiel is used as a catalyst (active material) carrier. Such an active material can also be porous itself such as, e.g. zeolites. Thus, a surface modification or a surface functionalization of the macro porous monolithic structure with zeolite would result in a “structured zeolitic composite”. In this regard the use of appropriate materials like micro-porous zeolites or micro-mesoporous zeolites permits the development of a hierarchical organization of the porosity on two (micro- macro) or three different (micro-meso-macro) levels (Figure 5.8). Thus, hierarchically organized structured zeolitic composites can benefit from both, the zeolitic function (e.g. separation or catalytic performance) and the properties of the support (e.g. high mechanical stability, low pressure drop, enhanced heat and mass transport) [22, 111, 122, 129].
Figure 5.8: Hierarchy concept: combing different porosity levels, adapted from [130]
Zeolitic composites can be prepared either by direct hydrothermal synthesis of zeolite in the form of a layer on the support surface (‘in-situ coating’, sometimes also referred to as ‘direct coating’) or by depositing a layer of pre-synthesized zeolite crystals on the substrate (ex-situ coating, e.g. dip-coating, slurry-coating).
97 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
5.1.3.1 Zeolitic composites by in-situ coating
With in-situ coating technique, zeolite can be directly synthesized on the support surface. This is usually carried out in closed autoclaves under hydrothermal conditions in the presence of support material and the synthesis mixture for a desired zeolite formulation. The preparation of zeolitic composites by in-situ coating can be further classified into two types: • in-situ coating on a reactive support • in-situ coating on an inter support
In-situ coating on a reactive support
The reactive support usually contains either free silicon or aluminum which is dissolved and consumed (by taking part in zeolite crystallization) during the hydrothermal synthesis of the zeolite [128, 131]. In this process the zeolite crystallization takes place into and onto the support surface thus making the zeolite/support bond very strong as zeolite layer and support material are interlocked and behave essentially as a single body (Figure 5.9 a).
(a)
(b)
Figure 5.9: (a) zeolite crystallization on an reactive support ,adapted from [127], (b) zeolite crystallization on an inert support ,adapted from [123]
In-situ coating on an inert support
In case of inert support, the zeolite crystallization takes place onto the support surface only (Figure 5.9 b) [123]. Although the zeolite layer is bonded directly to the support surface, the support/zeolite bond may not be as strong as in the case of reactive support as no support/zeolite interlocking is present. In Table 5.3 typical examples for the in-situ techniques applied on structured supports are summarized.
98 5.1 Background
Table 5.3: Zeolite coatings on structured supports by in-situ techniques.
Support type Type of Zeolite Support type Potential application/ Literature
test reaction
Reactive support MFI Al foam Adsorption/Catalysis Scheffler et al. [127]
CHA/AEI/AFI Al-foil Water adsorption Bauer et al. [132]
MFI SiSiC ceramic n-Hexane cracking Zampieri [97]
MFI Porous glass n-Hexane cracking Rauscher et al. [133]
FAU Al/ceramic foam Gas separation Barg et al. [128]
FAU Kaolin Heavy crude oil cracking Tan et al. [134]
BEA Mesoporous TUD-1 n-Hexane cracking Waller et. al. [135]
FAU Al foam n-Hexane cracking Wagner [136]
MFI/Silicalite-1 Silicalite-1 nanocrystals N. N. Rhodes et al. [137]
MFI/ZSM-5 Silica Isobutene cracking Landau [138]
MFI/ZSM-5 Porous glass monolith n-Hexane cracking Louis et al. [139]
Inert-Support MFI SiC/Si-O-C foam Catalysis/Adsorption. Zampieri et al. [123]
MFI/BEA α-Al2O3 Isomerization/cracking Puil et al. [140]
MFI β-SiC foams MTO Ivanova et al. [22]
99 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
5.1.3.2 Zeolitic composites by ex-situ coating
Ex-situ coating involves the immersion of the structured support in a suspension of zeolite in a solvent (mostly containing a binder) followed by evaporation of the solvent by drying and calcination. The use of binder in ex-situ coating might influence the performance of the zeolite during the catalytic application. However, in contrast to in-situ hydrothermal coating, ex-situ coating simplifies the process of making structured zeolitic composites by decoupling the synthesis and the coating step. Furthermore, applying zeolite crystals on structured supports by ex-situ coating techniques yields a layer consisting of randomly oriented zeolite crystals which is typically characterized by a certain voidage, thus allowing for intercrystalline diffusion [101, 102, 111, 141, 142] and facilitating the mass transfer thereby. In Table 5.4 typical examples for the ex-situ techniques applied on structured supports are summarized.
Table 5.4: Zeolite coatings on structured supports by ex-situ coating techniques
Coating technique Zeolite type Support type Reference
wash-coating MFI alumina-mullite foam Patcas [124]
Buciuman,Kraushaar- wash-coating MFI alumina-mullite foam Czarnetzki [125]
dip-coating BEA silica and cordierite monoliths Beers et al. [129]
slurry coating Fe-MFI stainless-steel plate Heimer et al. [142]
wash-coating MOR, MFI, BEA, FAU cordierite honeycomb Mitra et al.[143]
wash-coating Cu-MFI cordierite monolith Lisi et al. [144]
slurry wash-coating NH4-MFI cordierite honeycombs Zamaro et al. [145]
100 5.1 Background
5.1.4 Methanol conversion to hydrocarbons
Conversion of methanol to hydrocarbons (MTG: methanol to gasoline, MTO: methanol to olefin, and MTP: methanol to propylene) over zeolite catalyst is an alternative technology for the production of gasoline, olefins and petrochemicals in order to meet their increasing demand in the market [22, 146].
The basic research on catalytic methanol conversion was done during the 70s, where the first catalysts were developed and the first patents were granted [147]. In 1999, Stöcker [146] presented a review on the methanol to hydrocarbons technologies (MTHC) over the last 20 years. According to him, in beginning, the process methanol-to-gasoline (MTG) was based on ZSM-5.
In the 1980s, SAPOs with small pore sizes were used. Through the smaller pore size of this catalyst, the selectivity was higher towards smaller carbon chains (Figure 5.10) which are the major target products due to their increasing demand in the international market [148].
Figure 5.10 MTO product composition SAPO-34 and ZSM-5 [149]
UOP of Norway developed the first commercially available pilot plant for converting methanol into olefins. Starting from natural gas, it is a two-step process. Methane is converted into methanol by a well-established process (via syngas). The actual process scheme is depicted in Figure 5.11. Crude methanol, produced in the first step is used as feed. The catalyst is called MTO-100, which is based on Ni-SAPO-34 [150]. It is placed in a fluidized bed (reactor); therefore a continuous exchange of the deactivated catalyst pellets is possible. For reactivation, the coke is burned off with air in a separate regenerator, the flue gas is wasted and the reactivated pellets are recycled into the reactor. From the product stream water and CO2 are removed. In several separation columns (dryer, deethanizer, acetylene saturator), the smaller olefins are separated from each other. Ethylene is separated from methane and
101 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion ethane in the column demethanizer and propylene from the higher olefins in depropanizer. UOP/HYDRO proved a long time stability of a methanol conversion of 99.8% and a rate of 0.75 MT per day.
Figure 5.11: UOP/HYDRO MTO process, adapted from [151]
The ratio of propylene to ethylene can be varied in the range of 0.77 to 1.33 [151], so a flexible response for the market demands is possible. The advantages of the process are that there is only a limited amount of byproducts, and the ethylene and propylene are produced in high purities, so there is no need for a complicated separation of alkenes and alkanes. Without using any splitter columns, UOP/Hydro MTO process reaches a purity of the light olefins of about 97%. Other advantages of the fluidized bed, in comparison of a fixed bed, is the easy adjustment of the operating conditions and the better heat recovery, due to the fact, that MTO is an exothermic. Soundararajan et al. [152] reported a reaction enthalpy of around 50 kJ/mol for the MTO process.
Also, the partial pressure of methanol can play an important role in the selectivity of olefins. If the partial pressure of methanol is lower, a higher selectivity towards ethylene is reached. For the temperature, a compromise must to be found. If it is higher, the production of light olefins especially ethylene is favored, but the coke formation increases as well [149].
102 5.1 Background
In recent years, several research groups focused on the development of new catalyst and reactor types for improving the efficiency and for reaching a higher productivity and purity of ethylene or propylene [149, 152]. The MTO plant for example can be integrated with an olefin cracking process (OCP), where the higher olefins produced can be cracked into ethylene and propylene. UOP/Hydro and Total Petrochemicals researched together on the integration of the OCP and a polymerization set up on one site [153].
Besides the MTO conversion, processes are developed for the production of gasoline (MTG) and propylene (MTP). One promising process, also available for commercialization, is designed by Lurgi GmbH. They offer a methanol to propylene (MTP) process for producing cheap propylene with a quality higher than 97 % (Figure 5.12).
Figure 5.12: MTP Process, Lurgi GmbH, adapted from [153]
In this process 3 fixed bed reactors are used, one can be regenerated, whereas the other 2 used for conversion. The process uses a pre-reactor where methanol is already converted into DME, which is then converted further to olefins. The reactors have a run time of 500 h - 600 h. The products are fractionated into gasoline, propylene, and byproducts and if required they are recycled. Table 5.5 compares the Lurgi’s MTP with UOP/HYDRO process. Both processes are available for licensing and commercialization, projects are planned but up till now, none is fully realized. A big disadvantage of both processes is the high investment costs for the production of synthesis gas, methanol and olefins if they are compared to the established technologies, for example cracking or steam reforming [148].
103 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
Table 5.5: Comparison of the two possible routes for conversion of methanol, adapted from [148] MTO MTP®
License UOP/HYDRO LURGI
Reactor fluidized bed fixed bed
Temperature; pressure 350 °C; 2 bar 450 °C; 1.5 bar
Yield [wt%]
Flue gas 2 1
Ethylene 39 -
Propylene 42 72
Butylene 12 -
C5 + gasoline 5 27
Another approach was reported by Gujar et al.[154]. They studied the conversion of higher alcohols over ZSM-5 in a MTO batch experiment. They showed that the yield of gasoline phase increases with higher alcohols, so for the future it is also an interesting research topic to try out this variation of MTO.
For the present work SSiC foams are used as support for zeolite catalyst to obtain SSiC- foam/zeolite composites for methanol conversion. For this purpose, SSiC foams of different pore sizes and zeolite of the type ZSM-5 with different Si/Al ratio are used The aim is to compare the performance of SSiC-foam/zeolite composite with the packed bed of zeolite pellets for methanol conversion as well as selectivity towards light olefins.
104 5.2 Experimental
5.2 Experimental
5.2.1 Preparation of SSiC-foam/zeolite composites by dip-coating
In this section, the development of a dip-coating method in order to obtain SSiC-foam/ zeolite composite is described. The aim is to deposit a thin and homogeneous layer of zeolite catalyst on SSiC foams, active for catalytic methanol-to-olefin conversion.
As described in the previous section, the slurry or suspension used for dip-coating in order to obtain a catalytically active composite usually consists of a peptizing agent (e.g. ethanol, water, and acetic acid), a binder (e.g. aluminum oxide) and a catalyst. The dip-coating method/procedure can be optimized by adjusting the amount and type of binder, viscosity of the suspension and the number of dipping steps [125, 142].
For the present work the dip-coating method developed to obtain the structured zeolitic composites is optimized by tuning the following parameters: • Viscosity of the suspension • Peptizing agent • Amount and type of the binder used • Number of dipping steps
5.2.1.1 The foam sample
The SSiC foam samples of 10, 20 and 30 PPI having cylindrical shape with 3 cm diameter and 3 cm length (also used for the characterization of the morphological properties, see chapter 3) were used to coat the zeolite in order to obtain the SSiC-foam/zeolite composite. The morphological properties of the samples are given in Table 2.1.
5.2.1.2 Zeolite catalyst and additives
Zeolite of the type ZSM-5 with different silicon to aluminum ratios, purchased from Süd- Chemie AG, was used as catalytic material. For the initial experiments, performed to optimize the dip-coating method for SSiC foams, ZSM-5 of module 55 (SM55) i.e. nominal value of silica to alumina ratio of 55 was used. After an optimal procedure was established, the foams samples were coated with zeolites of different modules i.e. SM 80 and SM 200 in addition to the SM 55. Prior to the coating, all zeolite samples (powder) were calcined in a muffle oven at
550 °C and characterized using XRD, ICP and NH3-TPD. As a binder material colloidal boehmite (Disperal®, Condea, RWE-DEA Aktiengesellschaft, Brunsbüttel) and colloidal silica (LUDOX AS-40, 40 wt% suspension in water, Sigma-Aldrich) were tested. Acetic acid (100 %, AppliChem GmbH) and distilled water were tested as peptizing agents.
105 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
5.2.1.3 Experimental Setup and procedure
In order to prepare the suspension for the dip-coating as a first step the binder and the zeolite were mixed and grinded in a mortar. The peptizing agent was then added slowly in the mortar to obtain a suspension of desired dilution. The suspension was then transferred to a glass beaker of size 100 ml (Ø: 50 mm). To prevent the sedimentation of the zeolite or binder particles, the beaker containing the suspension was kept on a magnetic stirring plate. For stirring, a magnetic stirring bar of length 2 cm at an rpm of 600 was used. During the dip- coating however the stirring speed was reduced to 160 rpm.
The dip-coating was carried out with an apparatus schematized in Figure 5.13. The apparatus was built at the Chair of Chemical Reaction Engineering at the University of Erlangen- Nürnberg.
Figure 5.13: Schematic representation of the dip-coating apparatus used for the present work
Before the dip-coating the SSiC foam samples were washed with acetone and dried overnight in a drying oven at 100 °C. To carry out the dip-coating the foam samples were mounted on the holder of the apparatus with the help of a rigid wire. The up and downwards movement of the holder was adjusted by choosing the velocity between 1-3 cm/min. In order to air dry the foam samples between the successive dips and to remove the excess slurry, a fan running at a constant speed was used. To avoid the possible inhomogeneity in the coated layer caused by the unidirectional air flow, the foam was turned around after half of the drying time about its vertical axis. Also, between the two consecutive dips, the foam was turned around on the horizontal axis for a uniform loading. At the end of each coating session the foam samples were removed from the holder and air dried at the atmospheric condition for 6 min. After the air drying the samples were oven dried at 100 °C for 5 min. Finally the SiSiC foam/zeolite composite obtained was calcined in a muffeloven at 550 °C for 6 h (heating ramp: 1.5 K/min). 106 5.2 Experimental
After the calcination, the SSiC-foam/zeolite composites were characterized for determining the active sites, micropore volume, and the pressure drop. The mechanical stability of the coated layer was tested by exposing the composites to a high air flux.
5.2.2 Characterization
5.2.2.1 Structural analysis via X-ray diffraction
X-ray diffraction is used to determine the crystalline structure of compounds. It can be applied for identifying the materials and determining the crystallinity. The diffraction of X- ray beams can be calculated with the Bragg equation and hence the position of atoms in a crystal can be determined [155]. It is also possible to determine the relative crystallinity of the samples by using some standard e.g. for zeolites α-Al2O3 can be used as standard [156].
For the present work, X-ray diffraction analysis was carried out with a Philips Analytical instrument of the type X-Pert Pro diffractometer, using CuKα radiation. For the measurements, the powder samples (original and the ones obtained by drying the excess suspension used for dip coating) were pressed in stainless steel sample holders. The scanning range of 2 to 50° on a 2 Theta scale was used and measurement point was recorded every second. The resulting peak positions and heights were analyzed using the software X’Pert High Score. Identification of diffraction patterns was carried out by comparing with the spectrum of standard sample Figure 5.14.
Figure 5.14: XRD-pattern for ZSM-5, adapted from [157]
5.2.2.2 Elemental analysis
Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) was used for the elemental analysis of the zeolite samples. The advantage of ICP-OES lies in the large number of elements measurable, and the large range of possible concentrations. For the present work, the silicon and aluminium content was determined for the different zeolite samples by using a Spectro ICP-OES device of the type Spectro Ciros CCD. 107 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
5.2.2.3 Acidic properties
In literature different techniques have been applied to characterize the acidic properties of zeolites. These techniques include nuclear magnetic resonance (NMR), Fourier transform infrared spectroscopy (FTIR), pyridine adsorption and temperature programmed desorption of ammonia (NH3- TPD) [98, 110, 158, 159]. For the present work in order to determine the acidic properties of the zeolite samples temperature programmed desorption (TPD) of Ammonia was performed. The aim was to quantify the Brønsted acid sites. The experiments were carried out using a TPD instrument from Thermo Electron Corporation of the type TPDRO 1100 equipped with a TCD detector. Figure 5.15 shows the schematic diagram of the
NH3-TPD set-up used. For the measurements, powder sample of zeolite of ca. 100 mg was packed in the reactor between the quartz wool layers. Helium was used as inert gas for flushing the lines and the sample. The adsorption and desorption of ammonia was performed at 30 °C (under constant ammonia flow of 10 ml/min) and at 550 °C (heating ramp 10 K/min, under constant helium flow of 20 ml/min) respectively.
Figure 5.15: Schematic diagram of the NH3-TPD setup
Figure 5.16: A scheme of typical NH3-TPD spectrum of the H-form of ZSM-5, adapted from [97]
Figure 5.16 shows a typical NH3-TPD spectrum of acidic form of ZSM 5 where two distinct peaks i.e. low and high temperature peaks corresponding to weak and strong acidic sites respectively can be observed.
108 5.2 Experimental
With the assumption that one ammonia molecule adsorbs per acidic site, the density of the acidic site was determined. For the calculation, the amount of binder and the water content obtained from TGA were subtracted from the sample weight.
5.2.2.4 Measurement of viscosity
The viscosity measurements of the suspensions (consisting of peptizing agent, binder and zeolite) were carried out on a Rheometer Physica MCR 100 (Anton Paar) that uses the Software Rheoplus. For each run, around 2 ml of the suspension sample was taken and the temperature was kept constant at 20 °C. The shear rate was first increased from 10 to 1000 s-1 in 20 intervals and then decreased back to 10 s-1. In this way 40 measurements points were recorded for which shear stress and rpm were obtained.
5.2.2.5 Adherence test for the zeolite layer
The adherence of the coated layer can be tested by exposing the composites to a high air flux for a certain period of time [125]. For the present work, the samples were exposed to an air stream with a volumetric flow rate of 95 L/min for up to 24 h. The weight of the samples before and after the test was recorded.
5.2.3 Methanol conversion
5.2.3.1 Test-rig
Dosing system
For methanol delivery a HPLC pump of the type K-120 from Knauer was used. The gas flows were regulated by Bronkhorst mass flow controllers. Stainless steel pipes of diameter 6 mm were used as reactor setup lines. In order to avoid any condensation of reactants or products, all the lines in the reactor setup were heated up to 180 °C (with the help of electrical heating coils) and were well insulated. The temperature of the lines was monitored and controlled by several thermocouples (inserted in the insulation bands around the lines) and the electrical heaters respectively.
Evaporator
The evaporator consisted of a stainless steel tube (length: 450 mm, diameter: 45 mm) filled with glass beads. At the inner bottom of the evaporator a glass frit was installed. For the methanol delivery a stainless steel capillary (size: 1/16”) was used which was installed underneath the glass frit. The evaporator was equipped with a heating jacket and a temperature controller.
109 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
Reactor tube
A flanged DIN 4571 stainless-steel tube, 275 mm in length with an inner diameter of 39.3 mm and wall thickness of 5.45 was used as reactor. At the inlet and outlet, the reactor was sealed with DIN 4571flanges (tighten with 4 screws: M 50 x 12) using graphite sealing. The reactor tube was heated externally with the help of a tailor made heating jacket (Horst, Germany) equipped with three heating zones and temperature controllers. The temperature inside the reactor tube was monitored with the help of two thermocouples integrated from top and bottom of the reactor. The SSiC/zeolite composites (wrapped in an inert ceramic mat for avoiding a bypass flow) were placed in a metal holder which was kept in the isothermal zone of the reactor.
Thermocouple Capillary tube CH OH/N 3 2 Flanges and Graphite ring sealing
Heating Reactor wall
Quartz wool
ceramic paper sealing Catalyst case foam or fixed bed catalyts Steel grid
Steel packing
Products
Capillary tube Thermocouple
Figure 5.17: reactor tube (left) and evaporator unit (right)
5.2.3.2 Analytics
For the analysis a gas chromatograph of the type 7890A GC System from Agilent Technologies, equipped with HP-Plot-Q column connected to a flame ionization detector
110 5.2 Experimental
(FID) was used. The Plot-Q column is suitable for separating small hydrocarbons even at low temperatures; the maximal temperature limit for the column is 300 °C. Retention times were determined especially for methane, ethylene, ethane, propylene, propane, DME, methanol, butenes and butanes. A calibration for evaluating the amount of reactant and products was carried out with methane, methanol, DME and alkenes. During the analysis, the oven temperature program shown in Figure 5.18 was used. The length of a measurement run was adjusted to 34 min. In between two runs, it took 2 min to cool down the oven back to 60 °C.
Figure 5.18: Oven temperature program used for the GC
5.2.3.3 Procedure
Methanol was delivered with the HPLC pump to the evaporator, where it was evaporated at 180 °C and mixed with a nitrogen flow of 150 ml/min. The gas mixture was led into the preheating zone of the reactor tube and then to the SSiC-foam/zeolite composite where catalytic methanol-to-olefin reaction took place. The product stream was split into two parts. The smaller part was sent to the gas chromatograph (GC) for online analysis. The other part was sent through a gas washing device to the exhaust. For in-situ reactivation of the SSiC- foam/zeolite composites, the nitrogen flow was bypassed the evaporator and mixed with an air flow of 40 mL/min. The reactivation of the composites was carried out at 550 °C.
5.2.3.4 Data Evaluation
The data obtained for methanol to olefin conversion was evaluated by using the following Parameters:
%
%
111 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
Figure 5.19: Flow sheet of the Lab-scale reactor setup used for methanol to olefin
112 5.3 Results and discussion
5.3 Results and discussion
5.3.1 Dip-coating
5.3.1.1 Amount of suspension
After testing different compositions (see section 5.2.1.2) for preparing the suspension used for the dip-coating of SSiC foams, the preferred composition (peptizing agent: acetic acid, binder: Disperal) was found to be similar to the one used by Hiemer et al. [142] (previously developed in the same research group). However, it is to be noted that Hiemer et al. [142] used slurry coating method and coated different geometrical structure (stainless steel plates: 2D). For the present work in order to coat the three dimensional foam samples the amount of suspension and the degree of dilution was optimized for achieving a complete dipping of foam samples and reaching the desired loading without blocking the pores.
During the optimization experiments performed, it was observed that due to the evaporation the rate of loss of acetic acid was much faster than the material loss (material loading on the foams) hence, the viscosity of suspension increased over times. Therefore, in order to keep the viscosity constant during the whole dip-coating session, a certain amount of acetic acid was added after each dip. The amount of acetic acid to be added after each dip was determined with the help of the curve (Figure 5.20) obtained from the experiment performed to evaluate the rate of evaporation (under similar conditions as used for the dip coating) of acetic acid from a beaker of size 100 ml (as used for the dip coating).
Figure 5.20: Evaporation curve of acetic acid
The amount of zeolite and binder loaded on the foam sample was also determined by weighing the dried simple after each dip. The binder/zeolite mixture amount equal to the loading on foam sample was added in the suspension in order to keep the solid fraction constant in the suspension.
113 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
5.3.1.2 Influence of viscosity
For the dip-coating experiments suspensions with different solid fractions i.e. of different viscosities were tested. The values of dynamic viscosity (µ) for different weight fractions used are plotted in Figure 5.21 which shows an increase in viscosity of the suspension with increase of the solid amount.
Figure 5.21: dynamic viscosity vs. solid amount in the suspension
During the dip-coating the experiments were stopped after 20 dips or when the pores started to block i.e. the air stream was not able to blow off the excess suspension from the pores of the foam samples.
Figure 5.22: Thicker bars: dynamic viscosity vs. loading on the foam, thinner bars: dynamic viscosity vs. number of dips till pore blocking started
Figure 5.22 illustrates that with increasing viscosity the number of dips (thinner bars) i.e. the preparation time could be reduced in order to reach a certain loading (thicker basrs). Higher viscosities however caused a faster blockage of the outer pores, because the excess liquid
114 5.3 Results and discussion could not be removed by the forced convection applied through the fan. With lower viscosities, it was not possible to obtain a homogenous layer or a high loading even after 20 dips. Based on these observations, all further experiments were started with a viscosity of 3.44 mPa-s and during the course of the dip-coating after a homogenous layer was reached; the viscosity was increased in small steps to 4.43 mPa-s in order to accelerate the loading.
5.3.1.3 Influence of type and amount of binder
For the present work, LUDOX (SiO2) and Disperal (Al2O3) were tested as binders for the development of dip-coating method. During the optimization experiments it was observed that with 10 wt% LUDOX-40 after 20 dips a loading of 7 wt% was reached (Figure 5.23a), whereas with 10 wt% Disperal a loading of ca. 30 wt% was already reached after 13 dips. Based on these observations, 10% Disperal was used as binder for coating the zeolite on all SSiC foam samples to obtain SSiC-foam/zeolite composites to be tested for methanol conversion.
(a) (b)
Figure 5.23: (a) Type and amount of binder vs. loading (zeolite + binder) for 20 dips, (b) Variation of Al2O3 (Disperal) amount vs. loading (zeolite + binder) on the foam (thicker bars) and vs. number of dips (thinner bars)
As described earlier, the presence of binder may influence the catalytic properties of zeolites by blocking access to the active site. Therefore dip-coating of foams was also tested without the binder. However, in this case the coated layer had a poor adherence and was peeled off during the handling. Based on the facts presented above, 10 wt% Disperal was preferred for the coating of SSiC foam samples.
115 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
5.3.2 SSiC-foam/zeolite composites
The dip-coating method described in the previous section allowed for the coating of SSiC foam supports with an essentially homogeneous zeolite layer. Figure 5.24 shows SSiC foam composites obtained through dip coating of SSiC foams with zeolite of the type ZSM-5.
(a) (b)
(c) SSiC foam strut Zeolite
Figure 5.24: SSiC foams coated with zeolite of the type ZSM-5 (a) 10 PPI (b) 20 PPI (c) strut cross section
Table 5.6 shows SSiC-foam/zeolite composites (with nomenclature) obtained via dip-coating method which was developed in the present work. The composite were tested for methanol conversion in order to study the effect of different PPI and different silicon to aluminum ratio of the zeolite used.
Table 5.6: SSiC-foam/zeolite composites obtained for the present work
Si/Al Composite Foam Zeolite module Si/Al Loading(zeolite + binder) PPI SiO2/Al2O3 /liter(foam) [g/L] 19 10PPI-55 19 10 55 19 15
42 10PPI-80-42 10 80 42 20
92 10PPI-200-92 10 200 92 15
42 20PPI-80-42 20 80 42 17
92 20PPI-200-92 20 200 92 17
92 30PPI-200-92 30 200 92 12
92 30PPI R*-200-92 30 200 92 16
* 30 PPI foam samples with increased surface roughness
116 5.3 Results and discussion
5.3.2.1 Layer thickness and stability
It was possible to obtain a zeolite layer of different thickness by changing the dip-coating time. Figure 5.25 shows SEM images of two 10 PPI SSiC/zeolite composites loaded with different (zeolite + binder) amounts. The layer thickness of the sample b (for which the number of dips was almost double as compared to the sample a) is almost 2 times the layer thickness of the left hand side sample.
a b
23 µm SSiC foam SSiC foam strut 53 µm strut
Figure 5.25: SEM micrographs of 10 PPI SSiC-foam (diameter: 30 mm, length: 30mm) loaded with different amounts (zeolite + binder); (a) 0.66 g (b) 1.26 g
The mechanical stability (adherence) of the coated layer was examined by exposing the components to a high air flux for over 24 hours and samples were weighed before and after the exposure. It was observed that the mass loss after the exposure was less than 1% which may be caused by the handling of the samples.
Also, in order to study the effect of surface roughness on the adherence of coated layer, a 30PPI foam with increased surface roughness (application of an extra coating of SiC particle layer: performed by the manufacturer, Figure 5.26a) was also tested. Essentially no difference in stability of the layer coated on both regular and on treated surface was observed.
a b
Figure 5.26: 30 PPI foam samples with different surface roughness: (a) treated surface, (b) regular/untreated
117 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
5.3.2.2 Pressure drop over SSiC-foam/zeolite composites
In Figure 5.27, a comparison of pressure drop over 10 PPI SSiC foam, SSiC-foam/zeolite composites and packed beds of similar geometric specific surface area is presented.
As expected, the pressure drop over foam/zeolite composites is higher than over uncoated foams. The increase in pressure for foam/zeolite composite is due to the loading (~17wt %) during the dip-coating which resulted in a reduction of window size of the foam as well as of open porosity. Despite the reduction in the open porosity and pore size of foam structure, the pressure drop over foam composite is still an order of magnitude lower compared to the packed bed of similar geometric specific surface area.
Figure 5.27: Pressure drop over 10 PPI SSiC foams, 10 PPI SSiC-foam/zeolite composites and packed beds of similar geometric specific surface area
It is to be noted that the comparison of pressure drop for three different systems is based on the similar geometric specific surface area. For similar geometric specific surface area, which is relevant for the heat and mass transfer, the foam composite offer much lower pressure drop compared to the packed bed configuration.
118 5.3 Results and discussion
5.3.3 Characterization of zeolite catalysts
5.3.3.1 XRD analysis
In Figure 5.28, a comparison of XRD patterns obtained for original zeolite samples (SM 55, SM 80 and SM 200) and for the corresponding excess powder (obtained by drying the excess suspension) with the standard XRD pattern of MFI [157] zeolite is shown.
Figure 5.28: Comparison of XRD patterns obtained for original zeolite sample and for the excess powder (obtained by drying the excess suspension) with the standard XRD pattern of MFI zeolite
It can be observed that for all zeolite samples used in the dip coating preserved their crystal structure. The dip-coating conditions i.e. the use of binder and 100% acetic acid had no significant influence on the zeolite crystal structure.
119 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
5.3.3.2 Acidity analysis
The acidity of zeolite is responsible for the catalytic activity in methanol conversion. Hence, it was important to evaluate accurately the acidity of zeolite. For the present work ammonium form (SM) of zeolite of the type ZSM-5 with three different modules were used i.e.:
• SM 55 (SiO2/Al2O3: 55)
• SM 80 (SiO2/Al2O3: 80)
• SM 200 (SiO2/Al2O3: 200)
The module number in the above nomenclature represents the silica to alumina ratio which also determines the silicon to aluminum ratio in a zeolite. Ammonia-TPD was performed for all the above mentioned samples using the apparatus discussed in the section 5.2.2.3.
For the SSiC-foam/zeolite composites obtained it was not possible to perform ammonia-TPD directly due to the oversized dimensions of the composite for the TPD reactor. Therefore, as in the case of XRD analysis, TPD analysis was performed on the excess powder which was obtained by drying the excess suspension used for the dip-coating.
(a) (b)
Figure 5.29: (a) Ammonia-TPD spectrum for original and excess powder sample, (b) acidity evaluation: shaded area represents the Brønsted acid sites
Figure 5.29a shows ammonia-TPD profiles for both original and excess powder sample of H- ZSM-5 of module 55. Both samples show TPD curve with two distinct peaks i.e. low and high temperature peaks. Woolery et al. [110] stated that the low temperature is due to the Lewis acid centers caused by the extra or non-framework aluminum. According to Lónyi and + Valyon [158], at high coverage, ammonia may form NH4 (NH3)n complexes, this may also contribute to the low temperature peak in the ammonia TPD spectrum of H-ZSM-5. In Figure 5.29, the high temperature peak indicates the presence of Brønsted acidity in H-ZSM-5. As described earlier in section 5.1.1, the Brønsted acidity of H-ZSM-5 is due to the presence of
120 5.3 Results and discussion frame work aluminum. Therefore, zeolites with low silicon to aluminum ratio (assuming Al at framework positions) show higher Brønsted acidity (see Table 5.7). For the quantification of Brønsted acidity, the high temperature peak is evaluated with the assumption that one ammonia molecule is adsorbed per Brønsted acid site (Figure 5.29b).
Table 5.7: Acidity analysis of the sample used for methanol conversion
Zeolite SiO2/Al2O3 Si/Al* Brønsted acidity samples [-] [-] [µ mol/g]
SM 55-original 55 19 652 SM-55-excess 55 ** 634 SM 80-original 80 42 245 SM 80- excess 80 ** 251 SM 200-original 200 92 158 SM 200-excess 200 ** 163 *the values were obtained by ICP-OES analysis **it was not possible to apply ICP-OEC as external Al2O3 is present as binder, which would overestimate the Al amount
The results obtained for the acidity analysis of the zeolite samples (original and excess powders) used in the present work are summarized in Table 5.7.
From the results, it can be observed that in case of high aluminum sample i.e. SM 55 the acidity of excess powder sample is slightly decreased compared to the original sample. This is can be due to the acetic acid treatment during the dip-coating, which might have resulted in some delamination that led to a decrease in the acidity.
The acetic acid treatment seems to have no effect on other two modules (lower aluminum content) for which acidity in the excess powder sample is slightly increased compared to the original samples. This slight increase in acidity may be attributed to the presence of alumina, which was used as binder for the suspension used for the dip-coating of foams.
121 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
5.3.4 Methanol conversion
5.3.4.1 Influence of zeolite acidity
Conversion and selectivity at different temperatures
Figure 5.30 shows methanol conversion and selectivity for light olefins for 3 samples of 10 PPI SSiC foams coated with different zeolite modules (SM 55, SM 80 and SM 200) having different Si/Al ratios (19, 42 and 92 respectively) and hence different acid site density. The conversion and selectivity were obtained at different temperatures after steady state had reached.
Figure 5.30: Methanol conversion and selectivity for C2 – C4 over 10 PPI foam samples coated with different zeolite modules: (a) SM 55 with Si/Al of 19, (b) SM80 with Si/Al of 42 and (c) SM 200 with Si/Al of 92
From the figure it can be observed that for all zeolite modules, at weight hourly space velocity (WHSV i.e. mass flow rate of methanol/mass of loaded catalyst) of ca. 2 the methanol conversion reached ~ 100% at 350 °C. The composite 10 PPI-55-19 which had lowest zeolite module i.e. 55 (hence highest aluminum content and highest acid site density) showed less selectivity for light olefins. Instead, it showed higher selectivity for paraffin and DME (not shown here). The highest selectivity for light olefins was shown by the composite 10PPI-200- 92 which had lowest Al content among the three composites shown in Figure 5.30 a, b and c.
A high Al content (high acid site density) favors the formation of paraffin and aromatics [108,
160] which may result in a lower selectivity for light olefins (C2-C4) and increase in the coke 122 5.3 Results and discussion formation respectively. A proper control of acidity is therefore required to allow for the highly selective conversion of methanol [146]
Long term stability
The effect of zeolite acidity on long term stability (towards deactivation) and selectivity for light olefins for methanol conversion over SSiC-foam/zeolite composites was also studied. For this purpose, methanol conversion was performed over three samples of 10 PPI SSiC foams/zeolite composites (at 450 °C and 500 °C) having different silicon to aluminum ratios (i.e. different acid site density). The results obtained are shown in Figure 5.31 and Figure 5.32. From the results shown in Figure 5.31, it can be observed that at 450 °C for the composite 10PPI-55-19 which had the highest Al content and hence highest acid site density showed methanol conversion of nearly ~ 100% in the beginning which dropped to about 85% after 20 hours. The selectivity towards light olefins reached 30% at about10 hours but dropped to zero after 18 hours of time on stream where 90% of DME instead of light olefin was produced.
Figure 5.31: Methanol conversion and selectivity for light olefins (C2 to C4) vs. time on stream at 450 °C for SSiC-foam/zeolite composites having different acidity
The conversion and selectivity for 10PPI-80-42 showed similar trends in the beginning as compared to the 10PPI-55-19, but in this case the composite even after 15 hours of time on stream showed a conversion of over 90 %. The deactivation rate as well as loss of activity was much slower compared to 10PPI-55-19. The composite 10PPI-200-92 showed a quite stable selectivity of around 55 % and only a slight decrease in conversion and selectivity was observed after 30 hours of time on stream. The behavior towards deactivation of can be explained on the basis of Si/Al ratio and consequently the coke formation during the reaction. 123 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
According to the carbon balance, the coke formation (assuming missing carbon mole in the product stream responsible for the coke formation) during most runs was found to be: • 17 % to 23 % for10PPI-55-19 • around 16% for 10PPI-80-42 • 5 to 8 % for 10PPI-200-92
In 1999, Stöcker [40] stated that the coke formation depends upon on the acidity of the zeolites. A lower Si/Al ratio (high acid site density) favors the coke formation due to the higher amount of aromatics produced. This explains the faster deactivation and lower selectivity towards the light olefins for the composites with high Al content i.e. lower Al/Si ratio.
Figure 5.32: Methanol conversion and selectivity for light olefins (C2 to C4) vs. time on stream at 500 °C for SSiC-foam/zeolite composites having different acidity
Similar trend were obtained for the composite based on 10 PPI SSiC foam and zeolites of different Si/Al ratios for methanol conversion performed at 500 °C as in the case of 450 °C (Figure 5.32). However the composites 10PPI-80-42 and 10PPI-200-92 not only showed better stability towards deactivation but also a higher selectivity for light olefins. This may be caused by the catalytic cracking of higher hydrocarbons (produced during the reaction) at temperature as high as 500 °C. The higher hydrocarbons (which may contribute to coke formation can cause the catalyst to deactivate faster) upon cracking increase the ethylene production [108] which can be observed in Figure 5.30 c. Ethylene as cracking product can increase the overall light olefin C2-C4 selectivity. This can be observed by comparing the C2-
C4 selectivity at 450 and 500 °C.
124 5.3 Results and discussion
5.3.4.2 Influence of PPI
In Figure 5.33, methanol conversion and selectivity towards light olefins over 3 different SSiC-foam/zeolite composites (with different PPI but same Si/Al ratio) at 450 °C is presented.
The methanol conversion for both 20 and 30 PPI foam composites show very similar trend and remains nearly 100 % for over 40 h. For the selectivity towards light olefins (C2 - C4), 30 PPI foam composite show very stable profile by keeping the value slightly above 50%, whereas 20 PPI foam composite showed a selectivity of about 60% in beginning which decreased slightly after 10 hours but remained higher than that shown by 30 PPI.
In case of 10 PPI, the methanol conversion was nearly 100 % for first 15 hours but then it started to drop and went below 90% after 40 hours. For selectivity, the 10 PPI composite have shown similar behavior as 20 PPI for first 25 hours but then it started to drop reaching a value of 40% after 40 hours of time on stream.
Figure 5.33: MeOH conversion and C2-C4 selectivity vs. time on stream for SM200 coated on PPI
The reason for comparatively faster deactivation of 10 PPI sample may be its comparatively lower geometric surface area which may lead to a slightly thicker zeolite layer for similar loading compared to the other two samples. The thicker zeolite layer may cause higher diffusion resistance which can result in increased rate of coke formation leading to faster deactivation of the active site.
125 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
A similar deactivation behavior of 10 PPI sample was observed for a lower zeolite module (higher acidity) which can be seen in Figure 5.34 a. in comparison with 20 PPI foam coated with the same zeolite.
(a)
(b)
Figure 5.34: Methanol conversion conversion and C2-C4 selectivity with time on stream: 10PPI-80-42 vs. 20PPI- 80-42
In Figure 5.34 b, it is to be noted that at 500 °C, 10 PPI sample has kept its stability for methanol conversion and selectivity towards light olefins for long period of time compared to at 450 °C. This behavior is already explained in section 5.3.4.1 by taking into account the possibility of catalytic cracking of higher hydrocarbon at 500 °C which may favor the production of light olefins and decrease the deactivation behavior caused by the higher hydrocarbons (or coke precursors).
126 5.3 Results and discussion
5.3.4.3 SSiC-foam/zeolite composites vs. packed bed of zeolite pellets
Conversion and selectivity at different temperatures
In order to compare the performance of packed bed of zeolite pellets and the SSiC- foam/zeolite composites for methanol conversion and selectivity towards light olefins, the data obtained for both systems at different temperatures is plotted in Figure 5.35.
Figure 5.35: Methanol conversion and selectivity for light olefins: SSiC-foam/zeolite composites vs. packed bed
From the results it can be observed that for methanol conversion, at temperatures lower than 400 °C, the composites have shown better performance compared to the packed bed of zeolite pellets. Whereas, for temperature 400 °C and above both systems have shown essentially the same behavior.
Similar trends as observed for the methanol conversion were also observed for the selectivity towards light olefins. At lower temperatures, the foam-/zeolite composites have shown comparatively higher selectivity whereas; at higher temperature their performance is comparable with the packed of zeolite pellets.
For both systems, in order to investigate the long term stability towards deactivation as well as selectivity towards light olefins, long term experiments at temperature 450 and 500 °C were performed, where data for over 40 hour time on stream was obtained.
127 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
Long term stability
For long term stability, in order to compare the performance of SSiC-foam/zeolite composites and packed bed of zeolite pellets, methanol conversion and selectivity for light olefins, over foam/zeolite composites (having different pore size) and packed zeolite particles (with different particle size), is plotted versus time on stream in Figure 5.36 a and b respectively.
(a)
(b)
Figure 5.36: Methanol conversion and selectivity for light olefins with time on stream: SSiC-foam/zeolite composites vs. packed bed
From the figure, it can be observed that in case of zeolite pellets the methanol conversion started to drop already after 10 hours. Whereas, for zeolite/foam composites, in case of 20 and
128 5.3 Results and discussion
30 PPI the methanol conversion stays nearly 100 % even after 40 hours of time on stream. The similar behavior is observed for the selectivity towards light olefins.
It can also be observed that for packed bed configurations; smaller zeolite pellets showed faster deactivation than the bigger ones. However, despite faster activity loss the selectivity for light olefins was higher in the case of smaller particle for first 15 hours. After that, both pellets size showed selectivity for light olefins in a similar range and exhibited a similar rate of decrease in selectivity.
The possible explanation for the superior performance of SSiC-foam/zeolite composites in comparison with packed bed of zeolite pellets may be explained on the basis of the following facts: • macro porosity of foams • thin layer of zeolite instead of pellets • thermal properties of SSiC foam support
The macro porosity of foam, a thin layer (in micrometer range) of zeolite on foam support as well as inter crystalline/inter particle voidage (present in the coated layer of zeolite), all improve the diffusion of reactants, intermediates and products as well as coke precursors during the methanol conversion.
The enhanced molecular diffusion of reactants intermediates and the products favors the production of light olefin [108]. This also reduces the rate of coke formation leading to improved stability towards deactivation. On the other hand, bulk zeolite (larger crystals, particles) have the tendency to retain the intermediate products and coke precursors which increase the rate of coke formation leading to loss of activity and the poor selectivity of the catalyst.
Also, the excellent thermal conductivity of SSiC material can allow for a rapid heat evacuation and mass transfer thereby enhancing the performance of the composites. It is to be noted that in case of packed bed configuration, in order to have the same reactor volume as that of the zeolite/foam composites, zeolite pellets were mixed with quartz granulates. In comparison with quartz glass, the SSiC foams (used as support for zeolite catalyst) have higher thermal conductivity, which might have contributed to the better performance of SSiC- foam/zeolite composites.
129 5 SSiC-foam/zeolite composites for methanol-to-olefin conversion
5.4 Summary and conclusion
In chemical process industry, the use of structured reactors (e.g. monolithic honeycombs and foams) may eliminate the obvious disadvantages (e.g. high pressure drop, hot spots and non- uniform access of reactants to the active sites of the catalyst) of the conventional randomly packed fixed-bed reactors.
Structured reactors based on structured zeolitic composites allow for a hierarchical organization of the porosity on two or three levels. This can be achieved either by creating mesoporosity in zeolites which results in micro-meso system, or by coating of micro or micro-meso porous zeolites on a macro porous support (honeycombs or foams) which results in a micro-macro or micro-meso-macro system respectively. For the hierarchical organization of the porosity, the coating of zeolites can be carried out either by using in-situ or ex-situ coating techniques. The properties of macro porous support e.g. material, geometry and macro porosity can be tuned independently according to the target application. Thus, the resulting hierarchically organized, structured zeolitic composites combine the advantages of zeolite functionality (e.g. separation, catalysis) with the optimized properties of the support materials (e.g. macro porosity, thermal properties).
In this chapter catalytic performance of SSiC-foam/composites in comparison with packed bed of zeolite pellets for catalytic methanol-to-olefin conversion is investigated. In order to obtain foam/zeolite composites a dip-coating method was developed. The method allowed for the coating of SSiC foam with a zeolite layer of controllable thickness. The dip-coating or slurry coating of a zeolite on a support material usually involves the addition of a binder in order to improve the adherence of the coated zeolite to the support surface. However, the binder material may enhance the diffusion resistance for reactants and/or products by blocking the zeolite micro pores by surrounding zeolite crystals. Therefore, it is important to analyze the active sites in the coated zeolite. The characterization of the zeolite (excess powder from the dip-coating) coated on the foams support revealed no significant change in the acidic properties (active sites). Also, despite the harsh condition e.g. the use of 100% acetic acid, the crystal structure of zeolite was preserved.
The zeolite layer coated on the SSiC foams showed an essentially homogeneous distribution of the zeolite layer and exhibited a good adherence to the foam supports. The pressure drop over foam composites was slightly higher compare to the uncoated foams. However, it was still an order of magnitude lower compared to the packed bed of particles with similar geometric specific surface area.
130 5. 4 Summary and conclusion
The methanol-to-olefin conversion was performed on SSiC-foam/ zeolite composites and a packed bed of zeolite pellets in a lab scale reactor setup. The reaction was carried out at different temperatures in the range of 300 to 500 °C. For the analysis an online gas chromatograph was used.
In a comparison with packed bed of zeolite pellets, the foam/zeolite composites showed better performance for methanol-to-olefin conversion by showing longer stability towards deactivation and higher selectivity for light olefins (C2-C4). This was attributed to macro porosity of foams as well as thin layer of zeolite with inter-crystalline voidage (instaed of zeolite pellets) both of which facilitated the diffusion processes during the reaction. The superior performance of SSiC-foam/zeolite composite was also ascribed to the excellent thermal conductivity of silicon carbide material which can allow for a rapid heat evacuation and improved mass transfer.
According to the results obtained for foam/zeolite composites used for methanol conversion, it was observed that the foam/zeolite composite with lower PPI value showed faster deactivation compared to the ones with higher PPI. The PPI of foams is strongly related to the pore size/cell size of the foam samples as well as to the geometric specific surface area. A lower PPI value means less number of cells per inch and hence a lower geometric specific surface area. After coating a similar amount of catalyst, the sample with lower PPI value will have thicker layer of the catalyst due to the lower geometric specific surface area compared to the one with higher PPI value and hence higher geometric specific surface area. The thicker layer tends to retain the intermediates and coke precursors thus, causing higher diffusion resistance and leading to the coke formation and loss in activity.
It was observed that the acidity of zeolites had a strong impact on selectivity of the light olefins. The composites with higher acidity showed faster deactivation and lower selectivity towards light olefins (C2-C4). The highly acidic zeolite catalyst can favor the formation of paraffin as well as the aromatics which may lead to the loss of selectivity for light olefins and loss of activity due to the coke formation. The highest selectivity was shown by the sample with comparatively lower acidity. The sample also showed the better stability towards deactivation compared to the other samples.
131
132
6 Summary and general conclusion
The present work was devoted to the investigation of morphological and fluid dynamic properties of open-cell foams and to the study of the catalytic performance of foam/catalyst composites. The aim was to develop generally applicable correlations for estimating the geometric specific surface area (relevant for heat and mass transfer) and pressure drop, which are key parameters for designing columns and reactors with foams as internals. A further aim was to directly compare the catalytic performance of foam/zeolite composites with packed beds of zeolite pellets for methanol-to-olefin conversion. In the following paragraphs a complete summary of the present work along with the concluding remarks is given.
• In the second chapter, the morphological characterization of open-cell foams of non- ideal geometry and periodic cellular structures of tetrakaidecahedron geometry (an efficiently space filling and widely accepted representative geometry of reticulated foams) and cubic cell geometry has been given. The characterization was carried out by using different experimental methods. Image analysis was used to determine the window and strut size as well as shape of the strut cross-section. Helium pycnometry and mercury intrusion prosimetery were applied to determine the total, open, and strut porosity. X-ray µ-CT was used to determine the geometric specific surface area. The conventional way of representing the cell size i.e. PPI does not give reliable information about the cell size. This is because of the unclear definition of a pore as it can be a window or a cell. Therefore it is important to specify the pore size explicitly as window or cell. The PPI value should be treated merely as a nominal value. Its use as a modeling parameter or in developing correlations is not recommended. Depending upon the porosity, open-cell foams exhibit different shapes of their strut cross-section, namely circular, triangular and concave triangular. The shape of the strut cross-section can affect the geometric as well as flow properties of foams. Therefore, it is recommended to consider the shape of the strut cross-section for geometric or pressure drop modeling on open-cell foams. The replicated open-cell foams have hollow struts and hence exhibit a certain strut porosity. The strut porosity is hardly accessible by the fluid that flows through a foam structure. Therefore, in order to determine the open or so-called hydrodynamic related porosity, the strut porosity must be subtracted from the total porosity of the foam.
6 Summary and general conclusion
Due to the nature of the struts, as they feature a rough surface and may possess internal strut porosity, geometric specific surface area cannot be determined by conventional physisorption methods. Volume image analysis e.g. X-ray µ-CT or MRI can be applied to determine the geometric specific surface area of open-cell foams. • A comprehensive experimental characterization of open-cell foams can be time consuming and expensive. Therefore, it is important to derive mathematical correlations that allow the prediction of the important properties of foams by using some easily measureable parameters. In this regard, in the third chapter, geometric modeling of open-cell foams was presented where an overview of the state-of the-art geometric models as well as correlations for predicting the geometric specific surface area has been given. The validity of state-of-the-art correlations was examined by comparing the experimental data (from present work as well as from open literature) with the predictions of the correlations. It was observed that the state-of-the-art correlations for specific surface area are not predictive and there could be a large deviation between the predicted and the measured values. The deviation from experimental data can be attributed to the selection of geometric model used to derive the correlation and to the variation in the strut cross- section (if not considered when developing a correlation) with porosity. A new correlation for the theoretical estimation of the geometric specific surface area of open-cell foams was proposed. The correlation was derived by using tetrakaidecahedron as representative geometry and taking into account the different strut cross-sections of foam structure. The correlation therefore has three different forms with slight variation in the coefficients which correspond to the three different shapes of the strut-cross-sections. The correlation was validated by the experimental values of the specific surface area from the present work as well as form open literature for foams of different materials with a wide range of pore size and porosity. It has been demonstrated that the proposed correlation can predict the geometric specific surface area of foams with more precision than any other state-of-the-art correlation either empirical or theoretical. • Pressure drop along with the specific surface area is among the key parameters for designing a chemical reactor or column. It plays an important economic role in an industrial operation as it is directly related to the energy consumption. For similar
134 6 Summary and general conclusion
exchange surface area (geometric specific surface area) open-cell foams offer much lower pressure drop compared to conventional randomly packed fixed-bed reactors. Pressure drop measurement and modeling on open-cell foams along with state of the art correlation for pressure drop estimation has been given in the fourth chapter of the present work. As in the case of geometric specific surface area, it has been shown that the current models and correlations for the prediction of the pressure drop in open-cell foams are not predictive. A new approach for developing a correlation for the theoretical estimation of pressure drop in foams was proposed. For this purpose, periodic cellular structures with ideal tetrakaidecahedron geometry were used as model systems in order to describe the pressure drop in non-ideal geometries of reticulated open-cell foams. As a first step a correlation for pressure drop in periodic foams was developed. The validity was tested for porous media of high and low porosity. For high porosity porous media the correlation predicted the experimental pressure drop of periodic foams investigated in the present work. For porous media with low porosity, the correlation produced similar results as the Ergun equation for fixed-bed of sphere packing (low porosity porous media). The correlation developed for periodic cellular structures was then adapted for replicated open-cell foams (non-ideal geometry). The validity of the adopted correlation was demonstrated by predicting the experimental data of pressure drop from the present work and from open literature for foams of different materials having a wide range of pore size and porosity. • In the chemical process industry, the use of structured reactors offers many advantages over randomly packed fixed-bed reactors. Structured reactors based on structured zeolitic composites allow the hierarchical organization of the porosity on two or three levels. Thus, hierarchically organized structured zeolitic composites can benefit from both, the zeolitic function (e.g. separation or catalytic performance) and the properties of the support (e.g. high mechanical stability, low pressure drop, enhanced heat and mass transport). In the sixth chapter, the preparation of SSiC-foam/zeolite composites and their catalytic behavior in the methanol-to-olefin conversion has been described. The aim was to compare the catalytic performance of foam/zeolite composite with packed beds of zeolite pellets. A further aim was to study the influence of PPI of the support and
zeolite acidity on the methanol conversion and selectivity for light olefins (C2-C4).
135 6 Summary and general conclusion
The SSiC-foam/zeolite composites were obtained via dip-coating of SSiC foams with a zeolite-binder system in the presence of a peptizing agent. The dip-coating method developed allowed for coating an essentially homogeneous layer of zeolite with controllable thickness. The foam/zeolite composites showed higher selectivity for light olefins and improved resistance towards deactivation compared to the packed bed of zeolite pellets. The superior performance of SSiC-foam/zeolite composite was explained on the basis of macro porosity of foams, thin layer of zeolite instead of pellets and high thermal conductivity of the SSiC foam support. The product selectivity as well as stability of the catalyst towards deactivation can be optimized by tuning the catalyst properties (e.g. pore size, layer thickness in case of coated catalyst) and/or the reactor configuration (packed bed, fluidized bed, monolithic). For example, by shortening the diffusion path of the reactants (which may be achieved by optimizing the pore regime/porosity of the catalyst system and adjusting the thickness of the coated layer) can improve the yield of light olefins, whose production is limited by the contact time of reactants with the catalyst during methanol conversion. Also, as methanol conversion is an exothermic reaction, the faster evacuation of reaction enthalpy can improve the heat and mass transfer. The SSiC-foam/zeolite composites with lower PPI value showed faster deactivation as well as loss in selectivity compared to the ones with higher PPI. This was ascribed to the lower specific surface area in case of lower PPI foams that led to a comparatively thicker zeolite layer for similar loading compared to the higher PPI foams. The thicker layer of zeolite can cause higher diffusion resistance and increased rate of coke formation which leads to faster deactivation of the catalyst.
In the chemical process industry, open-cell foams as catalyst support offer many advantages over their traditional counter parts. Their unique structure combines the advantages of honeycomb monoliths (i.e. a low ratio of pressure drop to geometric specific surface area) and of packed beds (e.g. radial mixing and tortuosity of the flow). These properties can be beneficial in situations that involve high flow rates (offering low pressure drop), or where a highly open porous structure helps to control selectivity. Furthermore, in case of strongly exothermic or endothermic operations, the superior thermal properties of foam materials (silicon carbide or metal) can improve the heat transfer.
In the past two decades, there has been a considerable amount of research performed on the use of open-cell foams as catalyst carrier investigating their morphological, thermal and fluid
136 6 Summary and general conclusion transport properties. This has given a better understanding of structure-property relationships in foams and of the parameters which are essential for designing monolithic foams reactors.
However, according to recent research reports, in order to take full advantage of the outstanding properties of foams (by replacing the conventional reactor configuration with the monolithic foam reactor) there are some other facts that must be taken into consideration. One of the most important points in this regard is that the production of foam monoliths as reactor internal is quite expensive compared to the cost of conventional catalyst pellets. In order to produce the foam monoliths in large quantities, their manufacturing cost must be brought down in the range of the conventional catalysts which may be realized by introducing a fully automated manufacturing process. Furthermore, the manufacturing process should be optimized to improve the quality of the foam pieces by minimizing the amount of closed cells or windows as well as the anisotropy in open-cell foam structures.
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Appendix
A1 Pressure drop in periodic cellular structures with ideal cubic cell geometry
A2 Pressure drop in periodic cellular structures: comparison between ideal cubic and TTKD cell geometries
A3 A chromatogram of methanol to olefin conversion
A4 Symbols abbreviations and dimensionless numbers
A5 Publications and presentations
Appendix
A1 Pressure drop in periodic cellular structures with ideal cubic cell geometry
Figure 0.1 shows measured pressure drop over periodic cellular structures with ideal cubic cell geometry. As observed in the case of periodic cellular structures of ideal tetrakaidecahedron geometry, pressure drop has strong dependency on CPI (hence on Sv). However, 10 CPI sample despite its higher CPI value as well as higher specific surface area shows similar pressure drop compared to 8.5 CPI sample. This can be attributed to the comparatively higher open porosity of 10 CPI sample which is responsible for the reduction in expected higher pressure drop. Hence the difference between the pressure drop values of both samples is lower than expected.
Figure 0.1: Pressure drop measurement over periodic cellular structures with ideal cubic cell geometry
152 A2 Pressure drop in periodic cellular structures: comparison between ideal cubic and TTKD cell geometries
A2 Pressure drop in periodic cellular structures: comparison between ideal cubic and TTKD cell geometries
In Figure 0.2 pressure drop over periodic cellular materials of ideal cubic and TTKD cell geometries is plotted vs. the specific surface area.
It can be seen that at similar specific surface area and open porosity, the samples with ideal TTKD cell geometry show higher pressure drop compared to the ones with ideal cubic cell geometry. This may be attributed to the expected higher flow tortuosity of TTKD cell geometry (which may increase the pressure drop) compared to the cubic cell geometry.
Figure 0.2: Pressure drop vs. geometric specific surface area: comparison between ideal cubic and tetrakaidecahedron (TTKD) cell geometry
153 Appendix
A3 A chromatogram of methanol-to-olefin conversion
Component Retension time 16.725 Methan 1.954
17.187 Ethylen 2.749 Ethan 3.176 Propylene 9.066 16.782 Propan 10.337 17.344 DME 13.814 Methanol 15.542
Iso-Butane 16.45 16.450 Iso-Butene 16.725 1 Butene 17.187 n-Butane 17.344
Figure 0.3: A typical chromatogram of methanol-to-olefin conversion obtained for present work
154 A4 Symbols, abbreviations and dimensionless numbers
A4 Symbols, abbreviations and dimensionless numbers
Greek symbols α : Coefficient for viscous term : [-] β : Coefficient for inertial term : [-]
εn : Nominal porosity of the foam (provided by the manufacturer) : [-]
εo : Open porosity : [-]
εs : Strut porosity : [-]
εt : Total porosity (εo + εs) of the foam : [-] 3 ρg : Apparent density : [g/cm ] 3 ρs : Solid density : [g/cm ] 3 ρb : Bulk density : [g/cm ] ν : Kinematic viscosity : [m2/s] µ : Dynamic viscosity : [Pa-s] χ : Tortuosity : [-] φ : Golden ratio (~ 1.6180) : [-]
Latin symbols dc : Cell diameter : [m] dp : Particle diameter : [m] ds : Strut thickness : [m] dw : Window diameter : [m] ds-triangular : Strut thickness of triangular struts : [m] ds-cylindrical : Strut thickness of cylindrical struts : [m] ds-triangular-concave : Strut thickness of triangular concave struts : [m] l triangular : Strut length of triangular struts : [m] l cylindrical : Strut length of cylindrical struts : [m] l triangular-concave : Strut length of triangular concave struts : [m] -1 Sv-geo : Geometric specific surface area of the foam : [m ]
Sv-geo-triangular : Geometric specific surface area of the foam with triangular struts : [m-1]
155 Appendix
Sv-geo-cylindrical : Geometric specific surface area of the foam with Cylindrical struts : [m-1]
Sv-geo- concave triangular : Geometric specific surface area of the foam with concave triangular struts : [m-1] -1 Sv-solid : Specific Surface area per unit solid volume : [m ] 3 Vc : Cell volume : [m ] dh : Hydraulic diameter : [m] ∆P : Pressure drop : [Pa] L : Characteristic length : [m] T : Temperature : [°C] p : Pressure : [Pa]
Abbreviations CPI : Cells per inch PPI : Pores per inch SSiC : Sintered silicon carbide µ-CT : Micro computed tomography MRI : Magnetic resonance imaging SEBM : Selective electron beam melting CHA : Chabazite group of zeolites DME : Dimethyl ether MFI : Mordenite framework inverted ZSM-5 : Zeolite Socony Mobil - 5 FAU : Faujasite group of zeolites MTO : Methanol to olefin MTG : Methanol to gasoline MTP : Methanol to propylene OCP : Olefin cracking process TPD : Temperature programmed desorption XRD : X-ray diffraction TGA : Thermo gravimetric analysis SEM : Scanning electron microscopy TEM : Transmission electron microscopy ICP-OES : Inductively coupled plasma-optical emission spectroscopy
156 A4 Symbols, abbreviations and dimensionless numbers
WHSV : Weight hour space velocity FCC : Fluid catalytic cracking
Dimensionless Numbers dvρ Re = Reynolds number : µ
∆P d 3 Hagen number : Hg = h L ρυ∆ 2
157 Appendix
A5 Publications and presentations
Journals
I. A. Inayat, H. Freund, T. Zeiser, W. Schwieger, Determining the specific surface area of ceramic foams: The tetrakaidecahedra model revisited, Chemical Engineering Science, 66 (2011) 1179–1188
II. A. Inayat, J. Schwerdtfeger, H. Freund, C. Körner, R.F. Singer, W. Schwieger, Periodic open-cell foams: Pressure drop measurements and modeling of an ideal tetrakaidecahedra packing, Chemical Engineering Science, 66 (2011) 2758–2763
III. A. Inayat, H. Freund, A. Schwab, T. Zeiser, W. Schwieger, Predicting the Specific Surface Area and Pressure Drop of Reticulated Ceramic Foams Used as Catalyst Support, Advanced Engineering Materials, 13 (2011) 990–995.
IV. S. Lopez-Orozco, A. Inayat, A. Schwab, T. Selvam, W. Schwieger, Zeolitic Materials with Hierarchical Porous Structures, Advanced Materials, 23 (2011) 2602–2615
V. W. Schwieger, S. Lopez, A. Inayat, H. Freund, T. Selvam, Zeolite-Containing Materials with Hierarchical Porous Structures, Chemie Ingenieur Technik, 84 (2012) 1427-1427
VI. G.E. Schröder-Turk, W. Mickel, S.C. Kapfer, M.A. Klatt, F.M. Schaller, M.J.F. Hoffmann, N. Kleppmann, P. Armstrong, A. Inayat, D. Hug, M. Reichelsdorfer, W. Peukert, W. Schwieger, K. Mecke, Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures, Advanced Materials, 23 (2011) 2535-2553
VII. I. Paramasivam, A. Avhale, A. Inayat, A. Bosmann, P. Schmuki, W. Schwieger: MFI-type (ZSM-5) zeolite-filled TiO2 nanotubes for enhanced photocatalytic activity. Nanotechnology 20 (2009) 225607 (5pp)
VIII. A. Avhale, G.T.P. Mabande, A. Inayat, W. Schwieger, T. Stief, R. Dittmeyer, Defect- free zeolite membranes of the type BEA for membrane reactor applications, Chemie Ingenieur Technik, 81 (2009) 1090-1090
Oral Presentations
I. A. Inayat, H. Freund, W. Schwieger, Periodic open-cell foams as model systems for the description of the pressure drop in reticulated foams, 8th European Congress of Chemical Engineering, Berlin (Germany), 25-29 September. 2011
158 A5 Publications and presentations
II. A. Inayat, S. Feldmeier, A. Schwab, W. Schwieger, Ceramic foam monoliths as support for zeolite catalyst systems, NANO-HOST Workshop for Design of Hierarchically Ordered Materials for Catalysis, ICGM Montpellier (France), 4-6 October 2010
III. A. Inayat, H. Freund, T. Zeiser, W. Schwieger, Predicting the specific surface area and pressure drop of ceramic foam catalyst supports, CELLMAT 2010, Dresden (Germany), 27-29 October 2010
Poster Presentations
I. A. Inayat, S. Feldmeier, H. Freund, T. Zeiser, W. Schwieger, SiC-Foams as support for zeolite catalyst systems, International Zeolite Conference, Sorrento-Naples (Italy), 4-9 July 2010
II. A. Inayat, S. Feldmeier, H. Freund, T. Zeiser, W. Schwieger, Dip-Coated SiC foams for catalytic applications, Jahrestreffen Reaktionstechnik, Würzburg (Germany), 10- 12 May 2010
III. A. Avhale, G.T.P. Mabande, A. Inayat, W. Schwieger, Th. Stief, R. Dittmeyer Defect- free BEA and MFI membranes with high Al content and their potential use in membrane reactors, 9th International Conference on Catalysis in Membrane Reactors, Lyon, June 28th – July 2nd 2009
IV. A. Inayat, H. Freund, J. Bauer, T. Zeiser, W. Schwieger, On the characterization of ceramic foam catalyst supports, Jahrestreffen Reaktionstechnik, Würzburg (Germany), 8-10 June 2009
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