Universität Stuttgart
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Item Open Access Kinetic instabilities in heterogeneously catalyzed reactions. Pt. 1, Rate multiplicity with Langmuir-type kinetics(1978) Eigenberger, GerhartThis paper is concerned with the occurrence of rate multiplicities (ignition-extinction phenomena). It is shown that rate multiplicity can be caused by the competing chemisorption of A and B upon the same active sites of the catalyst. Rate multiplicity can occur if at least one of the chemisorption or reaction steps is of second order. No rate multiplicity can be expected, if either A or B reacts via an Eley-Rideal type mechanism.Item Open Access On the dynamic behavior of the catalytic fixed-bed reactor in the region of multiple steady states. Pt. 1, The influence of heat conduction in two phase models(1972) Eigenberger, GerhartDie Benutzung des Zweiphasenmodells für den katalytischen Festbettreaktor führte im Bereich mehrfacher stationärer Zustände bisher stets zu Schwierigkeiten, da sich ein Kontinuum von mehrfachen stationären Lösungen ergab. Dabei war es gleichgültig, ob die von Liu und Amundson aufgestellten kontinuierlichen Zweiphasenmodelle oder die von Amundson und Mitarbeitern entwickelten Zellenmodelle zugrunde gelegt wurden. In der vorliegenden Arbeit wird gezeigt, daß sich die unendliche Mannigfaltigkeit stationärer Lösungen auf wenige Lösungen reduziert, wenn man annimmt, daß Wärmeleitung in der Katalysatorphase stattfindet. Unterschiede zwischen den bisher benutzten Modellen und dem vorgeschlagenen Modell werden am Beispiel der Zündung und des Verlöschens der Reaktion dargelegt.Item Open Access Mechanismen und Auswirkungen kinetischer Instabilitäten bei heterogen-katalytischen Reaktionen(1976) Eigenberger, GerhartDie gewonnenen Ergebnisse lassen den Schluß zu, daß kinetische Instabilitäten bei heterogen-katalytischen Reaktionen mit formalkinetischen Ansätzen vom Langmuir-Typ sinnvoll beschrieben werden können. Die gelegentlich geäußerte Hoffnung, daß aus einer solchen modellmäßigen Beschreibung der Reaktion im Instabilitätsbereich Schlüsse auf die tatsächlich wirksamen Mechanismen (Mikrokinetik) der Reaktion gezogen werden können, wird allerdings selten erfüllt sein. Wie bei der Aufstellung von Langmuir-Hinshelwood-Ansätzen für eine Oberflächenreaktion ergibt sich auch hier eine beinahe unbeschränkte Mannigfaltigkeit bei der Postulation möglicher Mechanismen. Hier wie dort wird es das Ziel der reaktionstechnischen Betrachtung sein, einen möglichst einfachen Mechanismus mit einem möglichst großen Gültigkeitsbereich zu finden. Für den Fall der CO-Oxydation an Platin sollte diese Arbeit einige Hinweise dazu liefern.Item Open Access Influence of the wall on the dynamic behavior of homogeneous tubular reactors with a highly exothermic reaction(1974) Eigenberger, GerhartThe influence of the tube wall on the behavior of tubular reactors with a highly exothermic reaction was studied. The effect of heat accumulation in the wall has a considerable influence upon the transient behavior of the reactor. Because of this influence excess temperatures can occur if the feed temperature is lowered or the flow velocity is raised. For a gas phase reaction the transient behavior is determined almost completely by the heat capacity of the wall. An example of multiple steady states caused by axial heat conduction in the wall is given, and the influence of heat conduction in the wall is compared with that in the reaction mixture.Item Open Access Kinetic instabilities in heterogeneously catalyzed reactions. Pt. 2, Oscillatory instabilities with Langmuir type reactions(1978) Eigenberger, GerhartAn analysis of the kinetic model studied in Part I of this contribution gave no indication for the occurrance of periodic solutions. However if an additional slow chemisorption ("buffer") step is added to the model, relaxation oscillations can develop in regions where the original model exhibited multiple solutions. The behaviour of the extended model is analysed via the singular perturbation approach and by simulation. It is shown that a broad variety of slow chemisorption steps can serve as buffer with the restriction that the buffer step should not, or at least only slightly, contribute to the surface reaction.Item Open Access A modified Crank-Nicolson technique with non-equidistant space steps(1976) Eigenberger, Gerhart; Butt, John B.A finite difference method with non-equidistant space steps, based upon the Crank-Nicolson technique is presented. Its prime feature is the automatic positioning of axial grid points at required positions. Thus reducing considerably the total number of grid points and hence the amount of computer time. The method is demonstrated for a number of examples of tubular reactor calculations. It proves to be well suited for the solution of all kinds of diffusion type models, especially if steep gradients or moving profiles occur, and can be used even on moderate size process computers.Item Open Access Kinetic instabilities in catalytic reactions : a modelling approach(1976) Eigenberger, GerhartIt is the purpose of this contribution to show under which conditions relatively simple Langmuir-type rate mechanisms exhibit steady state multiplicity as well as periodic instabilities and may serve as models for experimentally observed phenomena.Item Open Access On the dynamic behavior of the catalytic fixed-bed reactor in the region of multiple steady states. Pt. 2, The influence of the boundary conditions in the catalyst phase(1972) Eigenberger, GerhartIt has been shown in a preceding paper that a reasonable two-phase model for the catalytic fixed-bed reactor in the region of multiple steady states should take into account heat conduction in the catalyst phase. In this paper the study of the proposed model will be continued using the example of the adiabatic fixed-bed reactor. It turns out that the behavior in the region of multiple steady states is essentially affected by the boundary conditions of the catalyst phase. If one assumes that the catalyst phase is isolated adiabatically at the front of the reactor, threefold stable steady states in a wide range of hysteresis can be obtained. If heat exchange by radiation takes place in the frontal surface of the catalyst phase threefold stable steady states can also occur but the range of hysteresis is much narrower. Twofold stable steady states exist only if the fixed-bed is composed of three parts; the first and third parts consist of inert material and the second contains the active catalyst. The results of the computation of this example will be compared qualitatively with the experiments of Padberg and Wicke.Item Open Access Practical problems in the modeling of chemical reactions in fixed bed reactors(1984) Eigenberger, GerhartEstablishing a reaction rate model consists of the following steps: experimental design, evaluation of experimental results, choice of main components and main reaction steps, choice of a mathematical model for the test reactor and the rate equations and parameter identification. It will be shown that each of the above steps requires a number of decisions and assumptions which limit the general validity and extrapo!ability of the resulting model. In particular there is a strong interrelation of the rate equation and the underlying model of the reactor in which the kinetic experiments are performed. The restricted extrapolability requires discrimination between two different ways of using mathematical models. For design purposes, models are required which have the character of interpolations between experiments rather than that of extrapolations. In the second category models are used for speculative extrapolations to gain a better qualitative understanding of the complex interactions of transport and reaction. This in tum provides a base for decisions among rival options in chemical reaction engineering research and development.