Packed Bed Thermal Conductivity

Packed Bed Thermal Conductivity 587 Heat Transfer Coefficient at Walls, to Particles, and Overall 587 Fluidized Beds 589... 

The heat-transfer properties of the suspended-bed operations appear superior to those of the packed-bed operations. In particular, the former have a high effective thermal conductivity, and the development of uneven temperature distributions is therefore less likely. 

Ogura, H., et al., 1991. Thermal conductivity analysis of packed bed reactor with heat transfer fin for Ca(OH)2/CaO chemical heat pump, Kagaku-kogaku Ronbunsyu, 17 (5), 916-923. 

Heat transfer in packed beds. Effective thermal conductivity as a function of Reynolds number. Curve 1 Coberly and Marshall. Curve 2 Campbell and Huntington. Curve 3 Calderbank and Pogorski. Curve 4 Kwong and Smith. Curve 5 Kunii and Smith. (From G. F. Froment, Chemical Reaction Engineering, Adv. Chem. Ser., 109, 1970.)... 

Argo and Smith (106, 107) have presented a detailed discussion of heat transfer in packed beds and have proposed the following relation for the effective thermal conductivity in packed beds ... 

Illustration 12.7 indicates how to estimate an effective thermal conductivity for use with two-dimensional, pseudo homogeneous packed bed models. 

ILLUSTRATION 12.7 DETERMINATION OF THE EFFECTIVE THERMAL CONDUCTIVITY OF A PACKED BED OF CATALYST PELLETS... 

Yagi, S., and Kunii, K., Studies on Effective Thermal Conductivities in Packed Beds, AIChE J., 3 373 (1957)... 

The relatively poor conductivity of a packed bed makes it difficult to get the heat of regeneration into the bed, either from a jacket or from coils embedded in the packing. This is more easily achieved by preheating the purge stream. Even in the best conditions, it takes time for the temperature of the bed to rise to the required level. Thermal regeneration is normally associated with long cycle times, measured in hours. Such cycles require large beds and, since the adsorption wave occupies only a small part of the bed on-line, the utilisation of the total adsorbent in the unit is low. 

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)]... 

Another potential solution technique appropriate for the packed bed reactor model is the method of characteristics. This procedure is suitable for hyperbolic partial differential equations of the form obtained from the energy balance for the gas and catalyst and the mass balances if axial dispersion is neglected and if the radial dimension is first discretized by a technique such as orthogonal collocation. The thermal well energy balance would still require a numerical technique that is not limited to hyperbolic systems since axial conduction in the well is expected to be significant. 

Effective thermal conductivities and heat transfer coefficients are given by De Wasch and Froment (1971) for the solid and gas phases in a heterogeneous packed bed model. Representative values for Peclet numbers in a packed bed reactor are given by Carberry (1976) and Mears (1976). Values for Peclet numbers from 0.5 to 200 were used throughout the simulations. 

De Wasch and Froment (1971) and Hoiberg et. al. (1971) published the first two-dimensional packed bed reactor models that distinguished between conditions in the fluid and on the solid. The basic emphasis of the work by De Wasch and Froment (1971) was the comparison of simple homogeneous and heterogeneous models and the relationships between lumped heat transfer parameters (wall heat transfer coefficient and thermal conductivity) and the effective parameters in the gas and solid phases. Hoiberg et al. (1971)... 

Figure 1736. Effective thermal conductivity and wall heat transfer coefficient of packed beds. Re = dpG/fi, dp = 6Vp/Ap, s -porosity, (a) Effective thermal conductivity in terms of particle Reynolds number. Most of the investigations were with air of approx. kf = 0.026, so that in general k elk f = 38.5k [Froment, Adv. Chem. Ser. 109, (1970)]. (b) Heat transfer coefficient at the wall. Recommendations for L/dp above 50 by Doraiswamy and Sharma are line H for cylinders, line J for spheres, (c) Correlation of Gnielinski (cited by Schlilnder, 1978) of coefficient of heat transfer between particle and fluid. The wall coefficient may be taken as hw = 0.8hp.

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