Zugl.: Magdeburg, Univ., Diss., 2008

Th. doct.--Sci.--Paris--Ec. natl. supér. mines, 1994. / 1995 d'après la déclaration de dépôt légal. Thèse soutenue à la fois devant l'École nationale supérieure des mines de Paris et l'École nationale supérieure du pétrole et des moteurs de Rueil-Malmaison. Bibliogr. p. 371-385.

Die grundlegenden Aspekte chemischer Reaktionen auf Oberflächen können anhand von geeigneten Modelsystemen unter Vakuumbedingungen untersucht werden. Siliciumdioxid (SiO2) als wichtiges Material für hochmoderne Technologieanwendungen in der Mikroelektronik, Photonik und Katalyse, war Gegenstand zahlreicher Studien, um die Beziehungen zwischen der atomaren Struktur und funktionalen Eigenschaften von Silizium-basierten Materialien zu erklären. Diese Arbeit untersucht die Wechselwirkung von Gasen mit epitaktisch gewachsenen Silikat-Dünnschichten auf einem Ru(0001) Einkristall. Unter Verwendung von Infrarot-Reflexions-Absorptions-Spektroskopie (IRAS) und temperaturprogrammierter Desorptionspektroskopie (TPD) konnten die Hydroxy-Spezies auf reinen Silikatfilmen als isolierte Silanole (Si-OH) identifiziert werden. Isotopenexperimente haben gezeigt, dass sich thermisch stabile Oberflächenhydroxylate hauptsächlich aus der Adsorption von Wassermolekülen bilden. Ein Austausch der Silanole mit Sauerstoffatomen im Kristallgitter während des Dehydroxylierungsprozesses wurde nicht beobachtet. Durch die Adsorption von Gasen wie CO, H2 und O2 bei erhöhtem Druck, lässt sich auf komplexere Prozesse schließen. Dies beinhaltet Gastransport durch Poren im Film, was mit strukturellen Defekten in dem Silikatfilm verbunden ist, sowie nachfolgende Adsorption und Diffusion auf dem unterliegenden Ru(0001)-Substrat. Während der Einlagerung der Moleküle in die Silikatschicht bleibt der Oxidfilm auch unter hohem Druck (~ 10 mbar) sowie hoher Temperatur (~900 K) intakt. Solch ein Hybridsystem, welches eine robuste Siliciumdioxidmembran mit einem sich darunter befindlichen, chemisch aktiven Metall kombiniert, könnte ein interessantes Materialsystem für technische Anwendungen darstellen, insbesondere zur Herstellung von Katalysatoren und Sensoren sowie für Korrosionsanwendungen. / The fundamental aspects of the chemical reactions at surfaces can be elucidated by using well-defined model systems under the controlled conditions provided by vacuum-based techniques. Silicon dioxide (SiO2) as one of the crucial materials in modern technological applications, including microelectronics, photonics, and catalysis, has been subjected to numerous studies in order to rationalize relationships between the atomic structure and functional properties of silica-based materials. This work marks the attempt to understand interaction of ambient gases with a well-ordered, ultrathin silicate film grown on a Ru(0001) substrate. Using infrared reflection absorption spectroscopy (IRAS) and temperature programmed desorption (TPD), hydroxo species, primarily in the form of isolated silanols (Si-OH), were identified on pristine silicate films. Isotopic experiments demonstrated that surface hydroxyls form primarily from the water molecules. Silanols do not undergo scrambling with the lattice oxygen atoms upon dehydroxylation. Steps on a silicate sheet and/or “holes” in these ultrathin films are proposed as active sites for hydroxylation. Adsorption of gases such as CO, H2 and O2 at elevated pressures revealed a more complex behavior. It involves gas transport through the pores, associated with structural defects in the silicate film, subsequent adsorption, and diffusion across the Ru(0001) surface underneath. During this intercalation, the silicate film stays intact even under high pressure (~10 mbar) and high temperature conditions (~900 K). The silicate layer does however strongly passivate the Ru surface towards RuO2(110) formation that readily occurs on bare Ru(0001) under the same conditions. Such a hybrid system, which combines a robust silica “membrane” and a chemically active metal underneath, could become an interesting material for technological applications, in particular in catalysis, sensors and anti-corrosion applications.

Diese Arbeit liefert, in den ersten beiden Kapiteln einen allgemeinen Überblick über die klassischen Ansätze zur Optimierung unter Unsicherheit mit einem Schwerpunkt auf probabilistischen Randbedingung. Anschließend wird im dritten Kapitel eine neue Klasse von sogenannten Probust Randbedingungen beim Auftreten von Modellen mit unsicheren Parametern mit teilweise stochastischem und teilweise nicht-stochastischem Charakter eingeführt. Wir zeigen dabei die Relevanz dieser Aufgabentypen für zwei Problemstellungen in einem stationären Gasnetz auf. Erstens liegen beim Gastransport probabilistische Randbedingungen bezüglich der Gasnachfrage vor sowie auch robuste Randbedin- gungen bezüglich der Rauheitskoeffizienten in den Rohren, welche in der Regel unbekannt sind, da es keine zuverlässigen Messmöglichkeiten gibt. Zweitens lösen wir ein Problem für einen Netzbetreiber, der zum Ziel hat, die angebotene Kapazität für alte und neue Kunden zu maximieren. In diesem Fall ist man mit einer ungewis- sen Gesamtnachfrage konfrontiert, die sich aus der probabilistischen Nachfrage für Altkunden und der robusten Nachfrage für Neukunden zusammensetzt. Für beide Fälle zeigen wir, wie mit probusten Randbedingungen im Rahmen der sogenannten sphärisch-radialen Zerlegung multivariater Gauß-Verteilungen umgegangen werden kann. Starke und schwache Halbstetigkeitsergebnisse werden für den allgemeinen Fall, in Abhängigkeit davon ob Strategien in Lebesgue oder Sobolev Räumen angenommen werden, erstellt. Für ein ein- faches zweistufiges Modell werden überprüfbare Bedingungen für die Lipschitz- Stetigkeit und die Differenzierbarkeit dieser Wahrscheinlichkeitsfunktion abgeleitet und mit expliziten Ableitungsformeln unterstützt. Diese Werkzeuge werden dann verwendet, um das Problem des Bäckers und zwei Probleme des Wasserkraftmanagements zu lösen. / This thesis offers, in the first and second chapter, a general overview of the classical approaches to solving optimization under uncertainty, with a focus on probabilistic constraints. Then, in the third chapter, a new class of so-called Probust constraints is introduced in the presence of models with uncertain parameters having partially stochastic and partially non-stochastic character. We show the relevance of this class of approach and solve two problems in a stationary gas network. First, in the context of gas transportation, one ends up with a constraint, which is probabilistic with respect to the load of gas and robust with respect to the roughness coefficients of the pipes (which are uncertain due to a lack of attainable measurements). Secondly, we solve a problem for a network operator, who would like to maximize the offered capacity for old and new customers. In this case, one is faced with an uncertain total demand which is probabilistic for old clients and robust for new clients. In both problems, we demonstrate how probust constraints can be dealt within the framework of the so-called spheric-radial decomposition of multivariate Gaussian distributions. Furthermore, in chapter four, we present novel structural and numerical results for optimization problems under a dynamic joint probabilistic constraint. Strong and weak semicontinuity results are obtained for the general case depending on whether policies are supposed to be in Lebesgue or Sobolev spaces. For a simple two-stage model, verifiable conditions for Lipschitz continuity and differentiability of this probability function are derived and endowed with explicit derivative formulae. These tools are then used to solve the Baker's problem and two hydro-power management problems.

Gas injection into saturated porous media has a high practical relevance. It is applied in groundwater remediation (air sparging), in CO2 sequestration into saline aquifers, and in enhanced oil recovery of petroleum reservoirs. This wide range of application necessitates a comprehensive understanding of gas flow patterns that may develop within the porous media and required modeling of multi-phase flow. There is an ongoing controversy in literature, if continuum models are able to describe the complex flow pattern observed in heterogeneous porous media, especially the channelized stochastic flow pattern. Based on Selker’s stochastic hypothesis, a gas channel is caused by a Brownian-motion process during gas injection. Therefore, the pore-scale heterogeneity will determine the shape of the single stochastic gas channels. On the other hand there are many studies on air sparging, which are based on continuum modeling. Up to date it is not clear under which conditions a continuum model can describe the essential features of the complex gas flow pattern. The aim of this study is to investigate the gas flow pattern on bench-scale and field scale using the continuum model TOUGH2. Based on a comprehensive data set of bench-scale experiments and field-scale experiments, we conduct for the first time a systematic study and evaluate the prediction ability of the continuum model. A second focus of this study is the development of a “real world”-continuum model, since on all scales – pore-scale, bench scale, field scale – heterogeneity is a key driver for the stochastic gas flow pattern. Therefore, we use different geostatistical programs to include stochastic conditioned and unconditioned parameter fields. Our main conclusion from bench-scale experiments is that a continuum model, which is calibrated by different independent measurements, has excellent prediction ability for the average flow behavior (e.g. the gas volume-injection rate relation). Moreover, we investigate the impact of both weak and strong heterogeneous parameter fields (permeability and capillary pressure) on gas flow pattern. The results show that a continuum model with weak stochastic heterogeneity cannot represent the essential features of the experimental gas flow pattern (e.g., the single stochastic gas channels). Contrary, applying a strong heterogeneity the continuum model can represent the channelized flow. This observation supports Stauffer’s statement that a so-called subscale continuum model with strong heterogeneity is able to describe the channelized flow behavior. On the other hand, we compare the theoretical integral gas volumes with our experiments and found that strong heterogeneity always yields too large gas volumes. At field-scale the 3D continuum model is used to design and optimize the direct gas injection technology. The field-scale study is based on the working hypotheses that the key parameters are the same as at bench-scale. Therefore, we assume that grain size and injection rate will determine whether coherent channelized flow or incoherent bubbly flow will develop at field-scale. The results of four different injection regimes were compared with the data of the corresponding field experiments. The main conclusion is that because of the buoyancy driven gas flow the vertical permeability has a crucial impact. Hence, the vertical and horizontal permeability should be implemented independently in numerical modeling by conditioned parameter fields.

Gas injection into saturated porous media has a high practical relevance. It is applied in groundwater remediation (air sparging), in CO2 sequestration into saline aquifers, and in enhanced oil recovery of petroleum reservoirs. This wide range of application necessitates a comprehensive understanding of gas flow patterns that may develop within the porous media and required modeling of multi-phase flow. There is an ongoing controversy in literature, if continuum models are able to describe the complex flow pattern observed in heterogeneous porous media, especially the channelized stochastic flow pattern. Based on Selker’s stochastic hypothesis, a gas channel is caused by a Brownian-motion process during gas injection. Therefore, the pore-scale heterogeneity will determine the shape of the single stochastic gas channels. On the other hand there are many studies on air sparging, which are based on continuum modeling. Up to date it is not clear under which conditions a continuum model can describe the essential features of the complex gas flow pattern. The aim of this study is to investigate the gas flow pattern on bench-scale and field scale using the continuum model TOUGH2. Based on a comprehensive data set of bench-scale experiments and field-scale experiments, we conduct for the first time a systematic study and evaluate the prediction ability of the continuum model. A second focus of this study is the development of a “real world”-continuum model, since on all scales – pore-scale, bench scale, field scale – heterogeneity is a key driver for the stochastic gas flow pattern. Therefore, we use different geostatistical programs to include stochastic conditioned and unconditioned parameter fields. Our main conclusion from bench-scale experiments is that a continuum model, which is calibrated by different independent measurements, has excellent prediction ability for the average flow behavior (e.g. the gas volume-injection rate relation). Moreover, we investigate the impact of both weak and strong heterogeneous parameter fields (permeability and capillary pressure) on gas flow pattern. The results show that a continuum model with weak stochastic heterogeneity cannot represent the essential features of the experimental gas flow pattern (e.g., the single stochastic gas channels). Contrary, applying a strong heterogeneity the continuum model can represent the channelized flow. This observation supports Stauffer’s statement that a so-called subscale continuum model with strong heterogeneity is able to describe the channelized flow behavior. On the other hand, we compare the theoretical integral gas volumes with our experiments and found that strong heterogeneity always yields too large gas volumes. At field-scale the 3D continuum model is used to design and optimize the direct gas injection technology. The field-scale study is based on the working hypotheses that the key parameters are the same as at bench-scale. Therefore, we assume that grain size and injection rate will determine whether coherent channelized flow or incoherent bubbly flow will develop at field-scale. The results of four different injection regimes were compared with the data of the corresponding field experiments. The main conclusion is that because of the buoyancy driven gas flow the vertical permeability has a crucial impact. Hence, the vertical and horizontal permeability should be implemented independently in numerical modeling by conditioned parameter fields.