Radial heat transport

In catalyst packings transverse flow components arc automatically established as a result of the nonuniform arrangement and the twisted flow around the pellets. Hollow and full cylinders with a length-to-diameter ratio of 1 3 are particularly effective in this respect. Despite the fact that radial heat transport takes place... 

Monolith forms can have very high specific surfaces combined with a very low pressure loss. Monoliths with straight, parallel channels, such as used for automobile exhaust control have only very poor radial heat transport properties. Crossed corrugated structures are considerably more favorable for isothermal reaction control. They have a very high radial thermal conductivity which is almost independent of the specific surface area the latter can be varied over a wide range by means of the channel dimensions. 

It must be remembered that with crossed corrugated structures, convective radial heat transport occurs only in one plane perpendicular to the main flow direction. In addition, the flow behavior in tubes of circular cross section is rather nonuniform over the circumference, which is why it is advantageous to arrange short packing sections in series, each section being displaced by 90 The heat transport parameters in Figure 7 were determined for structures arranged in this way. 

Radial heat transport very fast slow... 

Note that criterion 7.186 requires a knowledge of the apparent activation energy for the reaction. Criterion 7.186 holds whether internal diffusion limitations exist or not. When the criterion concerning external heat transfer is compared to criterion 7.167 concerning radial heat transport limitations through the bed, it can been seen that the latter are more critical unless ... 

T must be accurate enough to allow a formal description of the radial heat transport to the wall by conduction with the help of a heat transfer model. 

Mears [97] found that the reaction rates in fixed-bed catalytic reactors are highly affected by two heat transfer resistances resistance to radial heat transfer and resistance to particle-to-fluid heat transfer. Considerable effort has therefore been directed toward finding the effective radial conductivity and the fluid-to-wall heat transfer coefficient (which represents the radial heat transport) and particle-liquid heat transfer coefficient (which represents particle-to-fluid heat transport). 

As a rule of thumb, axial dispersion of heat and mass (factors 2 and 3) only influence the reactor behavior for strong variations in temperature and concentration over a length of a few particles. Thus, axial dispersion is negligible if the bed depth exceeds about ten particle diameters. Such a situation is unlikely to be encountered in industrial fixed bed reactors and mostly also in laboratory-scale systems. Radial mass transport effects (factor 1) are also usually negligible as the reactor behavior is rather insensitive to the value of the radial dispersion coefficient. Conversely, radial heat transport (factor 4) is really important for wall-cooled or heated reactors, as such reactors are sensitive to the radial heat transfer parameters. 

The model equations of the fixed bed reactor given by Eqs. (4.10.125) and (4.10.126) are still rather complicated. Thus, criteria would be helpful to decide whether and which of the different dispersion effects can be neglected. In Section 4.10.7.2, these criteria are examined. In Section 4.10.7.3, we will give deeper insight into the modeling of wall-cooled fixed bed reactors and the problems related to the modeling of radial heat transport. 

Two-Dimensional Model of a Wall-Cooled Fixed Bed Reactor Radial heat transport is an important factor in wall-cooled (or heated) reactors, particularly if we have a strong exothermic reaction with the danger of a temperature runaway. Figure 4.10.67 shows a typical radial temperature profile in a cooled tubular fixed... 

The mechanism for radial heat transport is complicated. It consists of a combination of heat conduction through the solid particles, solid/gas heat transfer, and radial mixing. The combined process is usually describ by an effective heat conductivity, that is a function of solid and gas properties, and of flow conditions. The radid heat flux q is expressed as... 

We can compare this with the rate of radial heat transport in the bed, by dividing the effective conductivity by the radius of the bed, which gives 208 W/m K. Apparently, the heat transfer coefficient at the wall is rate determining. Still, the influence of the limited rate of radial heat transport on the reaction rate can be considerable. 

Radial. heat transport may be a problem in trickle flow but is never a problem in slurry reactors. Also the heat remoyal/addition in slurry reactors is much more easy because high heat transfer rates to cooling surfaces are possible. In trickle flow reactors interstage cooling, cold shot techniques and cooling with an evaporating solvent are possible and the latter technique can also be applied with slurry reactors. 

Heat released by the reaction must be carried from the reactor by the flow of both the fluids, thermal conduction through the solid particles axially and radially and exchange through the vessel walls. Models for axial and radial heat transport to ensure... 

Radial heat transport may usually be represented by a pseudo-homogeneous model with two parameters (Specchia and Baldi [81], Specchia et al. [82], Specchia and Sicardi [83]). The catalytic bed is assumed to be a pseudo-homogeneous system characterized by an effective thermal conductivity k - and by a heat transfer resistance located at the wall of the reactor. The corresponding coefficient is h. In any point in the reactor the three phases (gas, liquid, solid) are supposed to be at the same temperature. 

The radial heat transport is complex, involving conduction, convection, and radiation between voids and solid and between solid particles. Possible modes of heat transfer in the radial direction are shown in Figure 14.3. Different physical models result depending on whether various resistances to the heat transport are in series, parallel, or a combination of both. Here an additive model is considered, which assumes that the radial effective thermal conductivity consists of static (conduction and radiation) and dynamic contributions, the latter caused by fluid motion. These two contributions are considered to be additive ... 

The advantages of trickle flow reactors are low pressure drop, good contacting properties emd simple construction in comparison with tray columns. These properties are combined with general advantages of counter current operation extraction of reactants or products out of the reaction zone possible (e.g. for equilibrium reactions), efficient heat exchange between solids and gas phase, etc. The radial heat transport, wall heat transfer coefficients and scaling-up factors are not yet known. 

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