Paul-Michael Weinspach

Modeling and simulation of bubble column reactors

Abstract The mathematical equations and a comprehensive computer program for modeling and simulating bubble column reactors with internal heat exchange installations are presented. Detailed reactor model equation systems on the basis of the axial dispersion model and the cell model with backflow are developed by linking together the mathematical description o the multiphase flow properties with the momentum, mass and energy balances of the reactor. A highly modular constructed computer program is presented summarizing a lot of theoretical and empirical knowledge about multiphase flow and heat and mass transfer processes in bubble columns. The enhanced possibilities of this new software system are demonstrated by simulating two industrial processes. The methanol synthesis in the slurry phase is chosen in oder to test the model accuracy for a multicomponent reaction system including a hermodynamically balanced chemical reaction. Secondly, the wet air oxidation of municipal sewage sludge in a large-scale slurry bubble column reactor is simulated as an example of a highly exothermic oxidation carried out at extreme pressure and temperature conditions. This chemical process requires special attention for reaction heat removal. The numerical treatment of the algebraic equation system based on the cell model with backflow is easier and leads to average computing times up to 100 times lower than for the reactor model based on the axial dispersion model. The iteration process for solving the boundary value problem runs into numerical convergence difficulties for the case of highly exothermic process conditions with considerable temperature gradients in the reactor. So the finite-difference technique cannot be recommended from a numerical point of view, whereas the cell model formulation allows computations on an IBM-compatible PC (386, 25 MHz) with tolerable computing times of the order of minutes.

Heat transfer in two- and three-phase bubble column reactors with internals

Abstract Indirect and direct heat transfer is an important aspect in the design of bubble column reactors used for many industrial organic and inorganic processes. Longitudinal flow or cross-flow tube-bundle heat-exchangers, jacket cooling, direct evaporative cooling or circulation cooling are possible methods for this purpose. The existing physical and empirical models describing heat transfer in bubble columns are reviewed. The results of experimental investigations of longitudinal-flow and cross-flow tube-bundle heat-exchangers in bubble columns are presented and compared with empirical and semi-theoretical correlations. In the second part of the article the governing equations describing heat transfer in gas/liquid bubble column reactors are derived under the assumptions of the axial dispersion model and the cell model with backflow. For steady-state conditions, the axial dispersion model leads to a boundary value problem consisting of non-linear ordinary differential equations, whereas the cell model with backflow can be represented by a system of non-linear algebraic equations. Both equation systems include strong non-linearities and can be solved only by special numerical methods. As an example of the use of heat-transfer correlations in modelling bubble columns, the wet air oxidation of municipal sewage sludge carried out in a three-phase bubble column reactor (18 m in height, 2 m in diameter) is simulated considering different heat-removal methods. The simulation runs were carried out with the BCR program, which was developed at the University of Dortmund and the UMSICHT institute for the simulation of bubble column reactors operated under industrial conditions.

Modeling of Gasification of Wood in a Circulating Fluidized Bed

An one-dimensional mathematical model for describing the fluidization and the gasification reactions of wood in a circulating fluidized bed combustor (CFBC) has been developed. The mathematical model consists of modules to calculate the fluid-dynamic parameters, the kinetics of the gasification reactions and the temperature in the CFBC. It is shown that in the pilot plant measured pressure drop and the temperatures correspond very well with the calculation. The calculation of the product gas composition shows qualitatively correct tendencies. Further comparison with measurements has to be done in the future.

Heat transfer and flow of bulk solids in a moving bed

Abstract The indirect heat transfer of steam-heated tube bundles in a moving bed has been examined in an experimental apparatus. Heat transfer in single tubes is typified by a characteristic flow of the bulk solids along the outer tube wall surface. A cuneiform rest zone is created at the upper tube wall (stagnation point), in which the particles remain for a long time. An ‘insulating’ effect is exhibited by the dammed bulk zone and is responsible for the poor heat transfer in this area. Near the sides of the lateral tubes heat transfer is good and icreases with increasing mass flux and bulk solids velocity. Bubbling occurs at the lower tube wall and the heat transfer again decreases due to the small number of wall-particle contacts. The experimentally confirmed ‘trace theory’ describes the temperature profile at the outlet of a moving bed heat exchanger, being characterized by very good cross-mixing of the bulk solids which allows the intergral heat transition to be calculated. A modelling approach to the heat transfer and bulk solids movement in the moving bed provides a physical model which describes the dependence of the heat transfer at a single tube on the flow profile between two neighbouring tubes. In order to determine the flow profile, the continuity equation is solved vectorially, allowing an analytical relationship of the velocity profile between two tubes to be obtained via the coaxiality of stress and deformation. To allow such a calculation, the heat-transfer model makes use of the residence and contact time behaviour resulting from the velocity profile, with the different components of heat transfer at a tube being determined from the friction properties of the specific bulk material. Calculation of the integral heat transfer in the moving bed may be achieved via heat transfer at a single tube. By using the theory of ‘extended contact time’, the total residence time of the bulk at the first tubes may be considered as a case history for the other tubes. The integral overall heat-transfer coefficients of moving bed heat exchangers thereby determined have been verified experimentally.

Wärmeübergang und Druckverlust wässeriger Tensidlösungen in Rohren

ZusammenfassungEine Zugabe geringer Mengen kationischer Tenside in Wasser bewirkt eine Dämpfung der axialen und vornehmlich radialen Turbulenzschwankungen und daraus resultierend eine Verminderung der Rohrreibungsverluste und des Wärmeübergangs gegenüber relnem Wasser. Neu entwickelte mizellare Tensidsysteme erfüllen die von der Fernwärmewirtschaft gestellten Anforderungen an eine hohe thermische und mechanische Langzeitstabilität und können als Reibungsminderer zur Reduzierung der Pumpleistung in den Transport- und Verteilungsleitungen eingesetzt werden. Um die Kosten beim Einsatz reibungsmindernder Tenside in Fernwärmesystemen beurteilen zu können, sind zunächst genauere Daten zum Wärmeübergang und Druckverlust in den für die Wärmeein- und- auskopplung benötigten Wärmetauschern zu ermitteln. In dieser Arbeit werden der Wärmeübergang und der Druckverlust wässeriger Tensidlösungen in geraden Rohren experimentell untersucht und unter Einbeziehung der in der Literatur vorliegenden Informationen zum Strömungsverhalten dieser Lösungen beschrieben. Den Abschluß der Arbeit bildet die Aufstellung einer Berechnungsgleichung für den Wärmeübergang wässeriger Tensidlösungen.

Heat transfer to trickling granular materials

Abstract Heat transfer to trickling granular materials, falling on single horizontal tubes, was investigated. The tubes could be heated by steam or by electricity. Local or total heat transfer coefficients were determined. The experimental results show that the maximum of the local heat transfer coefficients at low solids mass fluxes occurs at the stagnation point. With an increasing solids mass flux two maxima occur, each at an angle of about 30°–45° to the vertical. The total heat transfer coefficient increases with increasing solids mass flux or temperature and with decreasing tube or particle size. A model of heat exchange to trickling solids falling on single tubes was developed. It is based on a serial connection of the particle-to-surface heat transfer and the heat conduction in bulk solids packets. The heat transfer coefficient depends on the contact time of a packet with the wall. This contact time can be determined considering the forces affecting a packet. An energy balance is developed taking the influence of these forces into consideration in order to derive a set of dimensionless groups. A suitable simplification of this set of groups leads to an easy equation which allows contact times to be calculated as a function of all important properties.

Hydrodynamische Einlauflänge und Widerstandsgesetz von reibungsmindernden kationschen Tensidlösungen

ZusammenfassungDurch Zugabe geeigneter Tensidsysteme in Wasser kann der Strömungsdruckverlust in geraden Rohren erheblich gesenkt werden. Die diesem Effekt zugrunde liegenden Mechanismen wurden in früheren Arbeiten eingehend diskutiert. In dieser Arbeit werden neue Ergebnisse vorgestellt, die sowohl die Bestimmung der hydrodynamischen Einlauflänge als auch die Ermittlung der Widerstandsbeiwerte im ausgebildeten Strömungszustand ermöglichen. Für den Bereich der ausgebildeten Rohrströmung wird eine neue Berechnungsgleichung vorgeschlagen. Durch Erweiterung der bisherigen Modellvorstellungen ergibt sich ein Widerstandsgesetz für den gesamten Wirkungsbereich des Tensids. Die Ergebnisse stützen sich auf Untersuchungen mit zwei verschiedenen Additivsystemen, bei denen die Parameter Strömungsgeschwindigkeit, Temperatur und Einsatzkonzentration variiert wurden.

Quasi‐One‐Dimensional Modelling of Pressure Relief with Systems of Varying Viscosity

A theoretical background for the dynamic multiphase flow during the pressure relief process is developed on the basis of the balance equations for quasi-one-dimensional vapour/liquid flow. The vapour in the reactor is assumed to consist of two phases with small and large bubbles. The differential mass and momentum conservation equations in the axial direction of the reactor are formulated in Eulerian approach for all three phases with particular regard to the consideration of the interfacial exchange between the phases. Experimental investigations of the pressure relief with systems of varying viscosity in different reactor scales are used for the validation of the developed physical model.

Wärmeübergang und Druckverlust wässeriger Tensidlösungen an einer querangeströmten berippten Rohrwendel

ZusammenfassungDurch Zugabe geeigneter Reibungsminderer in das Wasser von Fernwärmenetzen kann der auftretende Druckverlust beträchtlich gesenkt und somit die benötigte elektrische Antriebsenergie der Förderpumpen reduziert werden. Neu entwickelte Tensidsysteme erfüllen die Anforderungen der Fernwärmepraxis an die thermische und mechanische Belastbarkeit. Ein wichtiger Aspekt ist dabei die Beeinflussung des Wärmeüberganges in den für Fernwärmenetze gebräuchlichen Wärmeübertragern. In früheren Arbeiten wurden der Wärmeübergang und der Druckverlust wässeriger Tensidlösungen in geraden Rohren und in Rohrwendeln untersucht. Aufbauend auf diesen Erkenntnissen werden in dieser Arbeit der Wärmeübergang und der Druckverlust wässeriger Tensidlösungen bei umströmten Rippenrohren, wie sie bei Brauchwassererwärmern auftreten, untersucht. Das Ziel ist die Darstellung und Beschreibung der auftretenden Effekte beim Einsatz solcher Lösungen, wobei aufgrund der komplexen Strömungszustände bisher keine Berechnungsgleichungen entwickelt werden konnten.

Zur Berechnung der effektiven Wärmeleitfähigkeit von evakuierten Dämmaterialien

Presentation de modeles pour le calcul de la conductivite thermique effective de materiaux isolants dans lesquels on a fait le vide