SAFE DESIGN AND OPERATION OF FLUIDIZED-BED REACTORS : CHOICE BETWEEN REACTOR MODELS
For three different catalytic fluidized bed reactor models, two models presented by Werther and a model: presented by van Deemter, the region of safe and unique operation for a chosen reaction system was investigated. Three reaction systems were used: the oxidation of benzene to maleic anhydride, the oxidation of naphthalene to phthalic anhydride, and the oxidation of ethylene to ethylene oxide. Predictions of the optimal yietd, the operating temperature and the conversion were also subjects ofour study. It appeared that for reactions carried out in a Auidired bed operating under conditions of good fluidization all models predicted the same region of safe and unique operation. For a well-designed fluid&d bed only the constraint of uniqueness is affected by the reactor model chosen. Predictions of the yield, conversion and operating temperature appeared to fit slightly less well. But still a good indication can be obtained from any of the models since the deviation in the results was less then a few percent for all three reaction systems. The strongest deviations between the models occurs in the region of gas loads only slightly higher than the minimum fluidization velocity. As the heat transfer characteristics are bad at low gas loads this region is unsuitable for highly exothermic reactions where large amounts of heat have to be removed by the coolant. In the region of good heat transfer with gas loads at least several times higher than the minimum the three mod& predict the same resulk+. Fur this rtzabon wc finally rccommt-nd tht: use of simple models. INTRODUCTION Over the last two decades many studies have been published dealing with the modeIling of fluidized-bed reactors. The aim of these models is to describe the operation of a fluidized-bed reactor in terms of operating and design parameters. For an extensive discussion of the various models we refer to van Swaaij (1985). Recently studies have been presented that investigate the difference in results obtained from different reactor models. Johnson et al. (1987) studied the production of phthalic anhydride from naphthalene. Three reactor models were investigated; a model presented by Kunii and Levenspiel, a reactor model developed by Kato and Wen, and a model presented by Grace. They verified the models studying a reactor of an industrial scale. For the phthalic anhydride reactor they concluded that all three models predicted the conversion and product distribution equally well. The influences of the grid jets and the freeboard appeared to be negligible. Jaffrtis et al. (1984) studied the agreement between two reactor models-the model of Orcutt, Davidson and Pigford and the model of Kato and Wen-for the oxidation of benzene to maleic anhydride in a small-scale laboratory unit. They concluded that both models predicted the same conversion but only the model of Kato and Wen calculated the correct product distribution. A reactor model should lead to results such as yields, heat production and stability characteristics of the reactor. Reactor models can be used in two ways: either to describe the performance of an existing ‘Author to whom correspondence should be addressed. reactor-so that the operator is able to control his process in a more elaborated sense--or to design a reactor, in which case the model should be able to predict scale up effects as well. Westerink and Westerterp (1990) presented a method to combine both uses into one method to design and operate a fluidized-bed reactor. In their approach a plot is made of the slope of the heat withdrawal rate line-as known from the theory of tank reactors-vs the residence time in the reactor. In this plot all constraints to the design and operation can be shown and result in a region of possible operating parameters for which operation is safe, and an a priori required yield or selectivity can be obtained. In this region we can select a set of design parameters. The other way round is to have a set of design and operating parameters as obtained from an existing plant, that results in a point of operation in the plot. In that case the possible region of operation can be influenced by altering the lines that account for the constraints. To obtain the operating region in a fluidized-bed reactor Westerink and Westerterp used the simple model of van Deemter (1961) for a system of two consecutive or parallel reactions. They used correlations presented by van Swaaij and Zuiderweg (1972) to calculate the mass transfer coefficient, and of Werther (1978) to calculate the bubble hold-up. The use of these correlations is not compulsory: the region of operation derived with their approach can be obtained from any model and works for extensive networks of multiple reactions as well. Of course, the predicted region of safe operation will be affected by the model that is chosen. To study this effect we will investigate the predictions of three models for the region of safe operation, and use three
Mathematische Modellierung von Wirbelschichtreaktoren
Mathematical modelling of fluidized bed reactors. Among the many fluidized bed models to be found in the literature, the two-phase model originally proposed by May has proved most suitable for accommodation of recent advances in flow mechanics: this model resolves the gas/solids fluidized bed into a bubble phase and a suspension phase surrounding the bubbles. Its limitation to slow reactions is a disadvantage. On the basis of the analogy between fluidized beds and gas/liquid systems, a general two-phase model that is valid for fast reactions has therefore been developed and its validity is confirmed by comparison with the experimental results obtained by other authors. The model describes mass transfer across the phase interface with the aid of the film theory known from gas/liquid reactor technology, and the reaction occurring in the suspension phase as a pseudo-homogeneous reaction. Since the dependence of the performance of fluidized bed reactors upon geometry is accounted for, the model can also be used for scale-up calculations. Its use is illustrated with the aid of design diagrams.
Numerical Simulation of Induction Heating Process of Continuous Casting Slab
Compared with traditional blazing furnace, the Continuous Casting-Direct Rolling is an advanced manufacturing steel technology, which can reduce energy waste, decrease pollution and enhance efficiency. The characteristics of steels during induction heating are complex, the change of material properties with temperature makes exact analysis methods very difficult to implement. Therefore, a powerful computer aided numerical tool (i.e., finite difference analysis) is selected to numerically model the induction heating process in this paper. The mathematic model coupling with electromagnetic field and thermal field was established, and it was solved by finite difference method (FDM), thus the slab temperature distribution and its variation with time were obtained, and the characteristics in whole induction heating process were studied. To validate the program feasible, the results were evaluated and compared with experiment results, which showed that the simulation results are reliable and effective. The skin effect in heating process from the two results was studied and demonstrated, the temperature change caused by different parameters such as the induced power intensity and the corner radian were also presented, which indicate that the slab temperature can be heated uniformly through adjusting these parameters, thus the continuous casting slab can meet the rolling requirement.