Reaktormodelle für heterogen katalysierte Gasphasenreaktionen

Emig, G.

doi:10.1002/bbpc.19860901109

Mathematical Modeling

Bockhorn

¹

2000

Ullmann's Encyclopedia of Industrial Chemistry

0

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The article contains sections titled: 1. Introduction 1.1. Terminology 1.2. Application Areas of Mathematical Modeling in Industrial Chemistry and Chemical Engineering 1.3. Limitations of Mathematical Models 2. Construction and Classification of Mathematical Models 2.1. Construction of Mathematical Models 2.2. Classification of Mathematical Models 3. Empirical Models 3.1. Linear Empirical Models 3.1.1. Linear Empirical Models with One Variable 3.1.1.1. Parameter Estimation (Linear Regression) 3.1.1.2. Assessment of Estimated Parameter Values 3.1.1.3. Sensitivity Analysis 3.1.1.4. Example of a Linear Model 3.1.1.5. Concluding Remarks 3.1.2. Linear Empirical Models with Several Variables 3.1.2.1. Parameter Estimation 3.1.2.2. Assessment of Estimated Parameter Values 3.1.2.3. Concluding Remarks 3.2. Nonlinear Empirical Models 3.2.1. Parameter Estimation (Nonlinear Regression) 3.2.1.1. Transformation of the Model into Linear Form 3.2.1.2. Direct Search Methods 3.2.1.3. Gradient Methods 3.2.2. Assessment of Estimated Parameter Values 3.2.3. Example of a Nonlinear Model 3.2.4. Concluding Remarks 3.3. Further Calculation Methods and Model Types 3.3.1. Further Methods of Parameter Estimation 3.3.2. Other Types of Models 3.3.2.1. Models with Constraints on the Parameters 3.3.2.2. Models Based on Differential Equations 4. Models Based on Transport Equations for Probability Density Functions 4.1. Terminology 4.1.1. One‐Dimensional Distribution and Probability Density Functions 4.1.2. Multidimensional Distribution and Probability Density Functions 4.1.3. Conditional Probability Density Functions 4.2. Transport Equations for Single‐Point Probability Density Functions 4.2.1. General form of the Transport Equations for Probability Density Functions 4.2.2. Limitations of Single‐Point Probability Density Functions 4.3. Examples of Calculating Probability Density Functions 4.3.1. Solutions for Deterministic Systems 4.3.1.1. Age (Residence Time) Distributions in Chemical Reactors 4.3.1.2. Size Distribution in Continuously Operating Crystallizers 4.3.2. Solutions for Statistical Systems 4.3.2.1. Closure of the Transport Equation for Probability Density Functions 4.3.2.2. Solution Methods of the Transport Equation for Probability Density Functions 4.3.2.3. Example: Combustion of Propane in a Turbulent Diffusion Flame 5. Models Based on Physicochemical Principles (Transport Phenomena) 5.1. Application of the Principle of Conservation of Momentum 5.1.1. Laminar Tube Flow 5.1.2. Turbulent, Nonreactive Free Jets 5.1.2.1. Models for Reynolds Stresses 5.1.2.2. Solution Method of the Resulting System of Partial Differential Equations 5.1.2.3. Example: Turbulent Flow of Nitrogen in Air 5.2. Applications of the Principle of Conservation of Enthalpy 5.2.1. Heat Conduction 5.2.2. Heat Transfer 5.2.2.1. Exact Solution for a Boundary Layer Problem 5.2.2.2. General Principles of Modeling Heat Transfer 5.3. Applications of the Law of Conservation of Mass 5.3.1. Mass Transfer without Chemical Reaction 5.3.1.1. Exact Solution for a Boundary Layer Problem 5.3.1.2. General Principles for Modeling Mass Transfer 5.3.1.3. Examples of Simultaneous Mass and Heat Transfer: Dynamic Models 5.3.1.4. Examples of Simultaneous Mass and Heat Transfer: Static Models 5.3.2. Mass Transfer with Chemical Reactions 5.3.3. Chemical Reactions in the Homogeneous Phase 5.3.3.1. Isothermal Reactors with Frictionless Flow, Constant Density, and Reactions Without Volume Changes 5.3.3.1.1. Stability of Isothermal Reactors 5.3.3.1.2. Sensitivity Analysis 5.3.3.2. Nonisothermal Reactors 5.3.3.2.1. Heterogeneous Catalytic Reactions 5.3.3.2.2. Stability Analysis of Nonisothermal Reactors 5.3.3.2.3. Use on Statistical Processes

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Entwicklung eines Simulationsprogramms zum Scale‐up von Hydrierreaktoren

Greger

¹

,

Gutsche

²

,

Jeromin

³

1992

Chemie Ingenieur Technik

3

0

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Die Ubertragung von in kleinen Rieselbettreaktoren durchgefuhrten Versuchen auf Technikums-und Produktionsanlagen ist bislang schlecht moglich, so daB beim Scale-up rnit z .T. erheblichen ,,Sicherheitszuschlagen" gearbeitet werden muB. Auf der Basis eines Zellenmodells wurde ein Simulationsprogramm fur Rieselbettreaktoren entwickelt. Bei der Wahl des Modells spielte die Uberlegung eine Rolle, dai3 dabei die GroBe einer Zelle mit den geometrischen Abmessungen der venvendeten Katalysatorteilchen verknupft ist. In dem Reaktionsgeschwindigkeitsansatz wird rnit einem effektiven Geschwindigkeitskoeffizienten gearbeitet, der die wesentliche Anpassungsgrol3e darstellt. In ihm finden neben dem intrinsischen Geschwindigkeitskoeffizienten, der Stofftransport und die unvollstandige Flussigkeitsbenetzung der Katalysatorteilchen Berucksichtigung. Das Model1 wurde fur die Hartung von Fettsauren und die Hydrierung von Fettsauremethylestern zu Fettalkoholen an Versuchsdaten aus Laborreaktoren angepaBt und liefert fur Pilot-und Produktionsanlagen gute Ergebnisse, so daB es zum Scale-up von Rieselbettreaktoren fur die Hydrierung verwendet werden kann.Development of a simulation program for the scale-up of hydrogenation reactors. The scale-up of trickle-bed reactors to pilot and production scale has been difficult and necessitated considerable over-dimensioning. Therefore a simulation program based on a cell model has been developed in which the dimensions of a cell are directly related to the dimensions of the catalyst particles used.The kinetic equation is formulated with an effective rate coefficient as the only key parameter to be adjusted. With this coefficient the intrinsic rate coefficient, the mass transfer, and the incomplete catalyst particle wetting are considered.The model was applied to the hardening of fatty acids and the hydrogenation of fatty acid methyl esters in laboratory reactors. Comparison with experimental results of pilot and industrial scale is favourable. Thus the model can be used for the scale-up of trickle-bed reactors.

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