Heat transfer through reactor wall

There may be radial temperature gradients in the reactor that arise from the interaction between the energy released by reaction, heat transfer through the walls of the tube, and convective transport of energy. This factor is the greatest potential source of disparities between the predictions of the model and what is observed for real systems. The deviations are most significant in nonisothermal packed bed reactors. 

The last term is not present in the mass balance (unless the reactor leaks), but heat can be carried in and out not only with flow but also by heat transfer through the walls. An enthalpy balance on the contents of this CSTR gives... 

A radial temperature gradient with a maximum at the wall is observed at the reactor entrance. Further away from the reactor entrance, the radial profile is flat. The mole fraction profiles also contain marked radial gradients within the first 1.5 meters of the reactor. The radial gradients observed in the species concentration profiles are caused by the limited heat flux added to the reactor through the wall. The reactions are endothermic and the heat transferred through the wall and/or from the wall into the bed is not sufficient to smooth out the temperature profile, thus the chemical conversion becomes non-uniform. 

Although the use of a relatively large amount of solvent is effective for a small scale laboratory experiment, it should be noted that the final removal of heat is, in principle, ascribed to heat transfer through the wall of the reactor. Therefore, heat transfer is especially important for a large-scale production in industry. 

At steady state the rate of transformation of energy by reaction mnst be equal to the sum of the energy losses by convective transport and heat transfer through the walls of the reactor. This statement implies that the intersection(s) of... 

Thus, a diffuser-confusor reactor has a higher pressure drop than a cylindrical one (Ap is up to 25 times higher), which is caused by a higher energy loss from the flow of a reaction mixture through local hydrodynamic resistance. As the mass and heat transfer processes are similar, the increase of hydraulic resistance (turbulisation of flows) should be accompanied by an intensification of the heat transfer through a wall. 

If the extruder is used as a polymerization reactor, the heat of reaction plays a more important role than in modification extrusion processes. When this heat of reaction is large compared to the heat transferred through the wall (DalV 1), the throughput can be proportional to D. For DalV 1 no consistent scale rules can be found. 

The method may also be applied on the laboratory scale. In this case pressure is released at the end of the reaction from the reaction vessel — e. g. an autoclave — and the gas vented while heating is continued, resulting in decomposition of the carbonyls and precipitation of the corresponding metals. The big disadvantage of this type of catalyst removal is the fact that the metal not only decomposes on the carrier but also on the wall of the reactor, thus reducing heat transfer through the wall and clogging the reactor. 

Fig. 5.4-23 shows a sketch drawing of a BSC (Brogli et al., 1981). The stirred-tank reactor made of glass (a metal version is also available) is surrounded by a jacket through which a heat-transfer fluid flows at a very high rate the jacket is not insulated. The temperature of the circulation loop is regulated by a cascaded controller so that the heat evolution in the reactor is equilibrated by heat transfer through the reactor wall. The temperature in the loop is adjusted by injection of thermostatted hot or cold fluid. 

The amount of heat transferred through the reactor wall is proportional to the temperamre difference ... 

However, the most complex analysis is that in which heat transfer through the reactor walls is taken into account. This type of operation must be employed when it is necessary to supply or remove energy from the system so as to moderate the temperature excursions that would otherwise follow. It is frequently employed in industrial reactors and, to model such systems, one must often resort to two-dimensional models of the reactor that allow the concentration and temperature to vary in both the radial and axial directions. In the analysis of such systems, we make incremental calculations across the diameter of a given longitudinal segment of the packed bed reactor, and then proceed to repeat the process for successive longitudinal increments. 

When we want to look at the connection between the flow behavior and the amount of heat that is transferred into the fixed bed, the 3D temperature field is not the ideal tool. We can look at a contour map of the heat flux through the wall of the reactor tube. Fig. 19 actually displays a contour map of the global wall heat transfer coefficient, h0, which is defined by qw — h0(Tw-T0) where T0 is a global reference temperature. So, for constant wall temperature, qw and h0 are proportional, and their contour maps are similar. The map in Fig. 19 shows the local heat transfer coefficient at the tube wall and displays a level of detail that would be hard to obtain from experiment. The features found in the map are the result of the flow features in the bed and the packing structure of the particles. 

The mass- and ener -balance equations must be solved numerically in the general situation where heat is transferred to or from walls. There are three terms on the right side of the energy equation, heat flow with reactants and products, reaction heat, and heat transfer through walls. Flowever, the adiabatic reactor is a special case where we need to solve only one equation for a single reaction. 

The first three types (pellets, extrudates and granules) are primarily used in packed bed operations. Usually two factors (the diffusion resistance within the porous structure and the pressure drop over the bed) determine the size and shape of the particles. In packed bed reactors, cooled or heated through the tube wall, radial heat transfer and heat transfer from the wall to the bed becomes important too. For rapid, highly exothermic and endothermic reactions (oxidation and hydrogenation reactions, such as the ox-... 

It should be noted in these two reactor examples that where the cross-flow structure functioned as both a reactor and a heat exchanger, the channel walls separating the flows were not permeable to mass transfer through the walls. 

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