Packed beds thermal behavior

Equation (57) applies to material transport in tubes and yields an average deviation of 9.5% from the experimental data. An expression of similar form yielded an average deviation of 14.8% for the thermal transport. The ratio of thermal to material transport was found to be 1.09 with an average deviation of 13.7% (S3). Somewhat better agreement with predicted behavior was encountered for the studies on packed beds (S2). These data serve to illustrate the uncertainties which presently exist in the prediction of simultaneous material and thermal transfer under a variety of conditions. Satterfield s work has made a distinct contribution to understanding the macroscopic influences of combined thermal and material transport. Some of the discrepancy he noted may relate to assumptions concerning the nature of the chemical reaction associated with the decomposition of hydrogen peroxide. 

Pinjala V, Chen YC, Luss D. Wrong-way behavior of packed-bed reactors. II. Impact of thermal dispersion. AIChE J 1988 34 1663-1672. 

Pinjala, V., Chen. Y. C., and Luss, D. Wrong-Way Behavior of Packed-Bed Reactors II. Impact of Thermal Dispersion. AIChE J., 34, 1663-1672 (1988). 

This review on concurrently operated multiphase packed bed reactors shows that much information on the behavior of these reactor types has been accumulated in the past, but we are still far from a complete elucidation. The difficulty still exists that not enough information is available on systems different from air/water nonporous packings to safely scale-up multiphase reactors using a sophisticated mathematical model. The fact that fluid-dynamics and thermal effects may be different in laboratory units from those in technical reactors restricts the usefulness of simplified, i.e. lumped, models in reactor scale-up. On the contrary, the different mechanisms acting in multiphase catalytic reactions have to be kept separated to a certain extent, thus enabling the correct inclusion of their probably changing amount of influence during scale-up. 

One-Dimensional Model of a Wall-Cooled Fixed Bed Reactor In some cases, it may be convenient to use a simple one-dimensional model, for example, to get an initial insight into the reactor behavior by a less complicated model. This model also takes into account A ad and aw,int> but we now introduce a mean (constant) bed temperature Tnean and an overall heat transfer coefficient of the bed, the thermal transmittance [/ted. which collects the interplay of heat conduction in the bed (A d) and the heat transfer at the wall (a i t) (Figure 4.10.68). According to this model, heat transfer from a packed bed to a heat transfer medium that cools the outer surface of the wall of a tubular reactor is given by ... 

ETC is an important parameter describing the thermal behavior of packed beds with a stagnant or dynamic fluid and has been extensively investigated experimentally and theoretically in the past. Various mathematical models, including continumn models and microscopic models, have been proposed to help solve this problem, but they are often limited by the homogeneity assumption in a continuum model (Wakao and Kaguei, 1982 Zehner and Schliinder, 1970) or the simple assumptions in a microscopic model... 

It should be noted that a fluid bed has many particles. A hmited number of hot spheres cannot fuUy represent the averaged thermal behavior of all particles in a bed. Thus, Zhou et al. (2009) further examined the HTCs of all the particles and found that the features are similar to those observed for hot spheres (Fig. 17). The similarity illustrates that the hot sphere approach can, at least partially, represent the general features of particle thermal behavior in a particle—fluid bed. Overall, the particles in a uniformly fluidized bed behave similarly. But a particle may behave differently from another at a given time. The probabiHty density distributions of time-averaged HTCs due to particle—fluid convection and particle conduction are obtained, respectively (Fig. 18). The convective HTC in the packed bed varies in a small range due to the stable particle structure. Then, the distribution curve moves to the r ht as U increases, indicating the increase of convective HTC. The distribution curve also becomes wider. It is explained that, in a fluidized bed, clusters and bubbles can be formed, and the local flow... 

The tubular reactor can be an empty vessel if no catalyst is used. If a solid catalyst is required, the vessel is packed with catalyst, either in a bed or inside tubes. The dynamic behavior of the reactor is significantly affected by the presence of catalyst in the reactor because the thermal capacitance of the catalyst is usually greater than that of the process fluid, particularly if the system is gas-phase. The temperatures of both the process fluid and the catalyst change with time. Of course, under steady-state conditions, the two temperatures are equal at any axial position. 

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