Diameter ratio, heat transfer packed beds

A. Grab, U. Nowak, M. Schreier, R. Adler, Radial heat transfer in fixed-bed packing with small tube/particle diameter ratios. Heat Mass Transfer, 45, 417-425 (2009). 

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)]... 

Flow through the porous bed enhances the radial effective or apparent thermal conductivity of packed beds [10, 26]. Winterberg andTsotsas [26] developed models and heat transfer coefficients for packed spherical particle reactors that are invariant with the bed-to-particle diameter ratio. The radial effective thermal conductivity is defined as the summation of the thermal transport of the packed bed and the thermal dispersion caused by fluid flow, or ... 

Normally, such heat transfer coefficients for packed beds are significantly greater than those for empty tubes at the same gas flow rate. Early reports of such data were usually reported as ratios of the coefficient in the packed bed to that in the empty tube. Typical ratios range from 5 to 7.8, depending on the ratio of the pellet diameter to the tube diameter. Jakob (101) has proposed the following correlation for wall heat transfer coefficients as a generalization of an earlier correlation by Colburn (102) ... 

Dixon A, Di Costanzo M, Soucy B (1984) Fluid-phase radial transport in packed beds of low tube-to-particle diameter ratio. Int J Heat Mass Transfer 27(10) 1701-1713... 

However, in the region of Reynolds numbers of interest, heat transfer through the solid packing is significant, as already shown, and therefore we prefer a continuum description, in spite of reservations on its suitability to beds of low tube to particle diameter ratio. 

Several workers have inferred the existence of a radial velocity profile in a packed bed of low tube-to-particle diameter ratio from measurements of the fluid velocity at the bed exit [30]. However, their results are in considerable disagreement. A semi-theoretical study, using a modified Brinkmann model [31], indicates the existence of a steep maximum in the velocity next to the wall, but this remains unsubstantiated. Non-intrusive measurements of gas velocity within the packed bed are needed before a proper evaluation of the interactions of radial velocity, radial heat transfer, conversion and reaction selectivity are forthcoming. 

Dixon A G., Cresswell D L, Paterson W R., "Heat transfer in packed beds of low tube/particle diameter ratio", ACS Symp. Series 65, 238 (1978). 

Heat Transfer in Packed Beds of Low Tube/Particle Diameter Ratio... 

In spite of much research (1-7), identification of the relevant heat transfer parameters in packed beds and their subsequent estimation continue to provide challenging problems,especially so for beds having a small tube to particle diameter ratio, where so few experimental data are reported. 

An experimental evaluation of homogeneous continum models of steady state heat transfer in packed beds of low tube/particle diameter ratio has been carried out. It was found that both axial and radial conduction effects were important in such beds for N j 500, which covers the flow range in many industrial reactors. Heat transfer resistance at the wall was significant, but of secondary importance. 

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