Conductivity, thermal, data packed beds

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Extensive experimental determinations of overall heat transfer coefficients over packed reactor tubes suitable for selective oxidation are presented. The scope of the experiments covers the effects of tube diameter, coolant temperature, air mass velocity, packing size, shape and thermal conductivity. Various predictive models of heat transfer in packed beds are tested with the data. The best results (to within 10%) are obtained from a recently developed two-phase continuum model, incorporating combined conduction, convection and radiation, the latter being found to be significant under commercial operating conditions. 

TABLE 17.15. Data for the Effective Thermal Conductivity, K, (kcal/mh°C), and the Tube Wall Film Coefficient, (kcal/m h C), in Packed Beds ... 

Figure 9.2 shows existing data for the effective thermal conductivity of packed beds. These data include both ceramic and metallic packings. More accurate results can be obtained from the semitheoretical predictions of Dixon and Cresswell (1979). Once Kr is known, the wall heat transfer coefficient can be calculated from... 

Specific heats of metals and hydrides are easily determined and typically fall in the range of 0.1-0.2 cal/g°C. Thermal conductivity is a little more difficult to determine. The conductivity of the metal or hydride phase is not sufficient the effective conductivity of the bed must be determined. This depends on alloy, particle size, packing, void space, etc. Relatively little data of an engineering nature is now available and must be generated for container optimization. Techniques to improve thermal conductivity of hydride beds are needed. As pointed out earlier, good heat exchange is the most important factor in rapid cycling. 

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