Heat-transfer coefficients in packed beds

Other useful correlations of heat transfer coefficients in packed beds have been proposed. Among these is a simple relation of Calderbank and Pogorski (104)... 

Littman, H. and Sliva, D. E. (1971). Gas-Particle Heat Transfer Coefficient in Packed Beds at Low Reynolds Number. In Heat Transfer 1970, Paris-Versailles, CT 1.4. Amsterdam ... 

Table I. Correlations to calculate mass and heat transfer coefficients in packed beds [S, 7, 30, 31] and monoliths [32-34],...

A. Matsuura, Y. Hitake, T. Akehata, and T. Shirai, Apparent Wall Heat Transfer Coefficient in Packed Beds with Downward Co-Current Gas-Liquid Flow, Heat Transfer—Japanese Research, (8) 53-60,1979. 

Investigator Type of correlation Phases involved System Li and Finlayson [37] Wall-to-bed heat transfer coefficient in packed bed Fluid-solid Spherical particle-air system... 

A more detailed review and summary of the correlations for estimati il of heat transfer coefficients in packed beds has been givert by Rodrigues et al. ... 

Wakao N, Kaguei S, Funazkri T. Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds. Correlation of nusselt numbers. Chemical Engineering Science 1979 34(3) 325-336. 

Dixon AG. An improved equation for the overall heat transfer coefficient in packed beds. Chemical Engineering and Processing Process Intensification I996 35 323-331. 

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.

Both criteria for extraparticle gradients contain observables and can be calculated based on experimental observations of reaction rates. For heat and mass transfer coefficients in packed beds various correlations exist in terms of dimensionless numbers. In Table 1 the most appropriate ones for laboratory reactors are given [5, 7, 30, 31]. Values of k( and h for gases in laboratory systems range between O.l-lOms-1 and 100-1000JK-1s-1 m-2, respectively. In the case of monoliths, other correlations should be used because of the different geometry [32-34],... 

The model discussed here uses the effective transport concept, this time to formulate the fiux of heat or mass in the radial direction. This flux is superposed on the transport by overall convection, which is of the plug flow type. Since the effective diffusivity is mainly determined by the flow characteristics, packed beds are not isotropic for effective diffusion, so that the radial component is different from the axial mentioned in Sec. 11.6.b. Experimental results concerning D are shown in Fig. 11.7.a-l [61, 62,63]. For practical purposes Pe may be considered to lie between 8 and 10. When the effective conductivity, X , is determined from heat transfer experiments in packed beds, it is observed that X decreases strongly in the vicinity of the wall. It is as if a supplementary resistance is experienced near the wall, which is probably due to variations in the packing density and flow velocity. Two alternatives are possible either use a mean X or consider X to be constant in the central core and introduce a new coefficient accounting for the heat transfer near the wall, a , defined by ... 

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) ... 

Correlations for heat-transfer coefficients for packed beds are useful in designing fixed-bed systems such as catalytic reactors, dryers for solids, and p>ebble-bed heat exchangers. In Section 3.1C the pressure drop in packed beds was considered and discussions of the geometry factors in these beds were given. For determining the rate of heat transfer in packed beds for a differential length dz in m,... 

Since the flow channels between the particles in packed beds are irregular and intricate, transport rates are generally expressed in terms of average mass and heat transfer coefficients that can be estimated from semiempirical correlations that are developed using mass and heat transfer data in packed beds together with dimensionless groups describing the flow conditions in the bed. 

Wakao, N., Particle-to-fluid heat/mass transfer coefficients in packed bed catalytic reactors, in Recent Advances in the Engineering Analysis of Chemically Reacting Systems (Ed. L.K. Doraiswamy), Wiley Eastern, New Delhi, 1984. 

In contrast to the behavior of single particles (discussed in Chapter 2) for which analytical solutions may be available, the heat transfer coefficients in fixed beds have to be determined from empirical corrrelations. For convective fluid-to-particle heat transfer these relationships are very similar to those described earlier for single particles. Additional problems do arise, however, in the case of packed beds, where we must also consider radiative particle-particle heat transfer and convective heat transfer between the wall and the bed. 

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. 

The only reported-study on heat transfer is by Weekman and Myers.105 They measured wall-to-bed heat-transfer coefficients in a cocurrent air-water downward flow through a packed column. Three types of packings. 0.65-cm alumina spheres, 0.475-cm glass spheres and 0.38-cm TCC beads were examined. The heat-transfer coefficients were much higher than those observed for single-phase liquid flow. The transition from homogeneous to pulsed flow corresponded to an increase of... 

In order to assess transport mechanisms due to convection various correlation for heat and mass transfer coefficients in a packed bed have been derived. For the present application the transfer coefficient in the bed is related to the transfer coefficient of a single particle in a gas flow according to [15]. Due to the outflow of the gases during pyrolysis and char conversion the calculated transfer coefficient is decreased, thus Stefan correction is included to calculate the transfer coefficient at a finite flow over the boundary. 

Gillespie, B.M. Crandall, E.D. Carberry, J.J. Local and average interphase heat transfer coefficients in a randomly packed bed of spheres. Amer. Inst. Chem. Eng. J. 14 (1968) 483-490... 

Knowledge of the heat transfer characteristics and spatial temperature distributions in packed beds is of paramount importance to the design and analysis of the packed-bed catalytic or non-catalytic reactors. Hence, an attempt is made in this section to quantify the heat transfer coefficients in terms of correlations based on a wide variety of experimental data and their associated heat transfer models. The principal modes of heat transfer in packed beds consist of conduction, convection, and radiation. The contribution of each of these modes to the overall heat transfer may not be linearly additive, and mutual interaction effects need to be taken into account [23,24]. Here we limit our discussion to noninteractive modes of heat transfer. 

The methods of experimental measurement of heat and mass transfer coefficients are summarized in Table 4.8, and resulted mainly from heat and mass transfer investigations in packed beds. Heat transfer techniques are either steady or unsteady state. In steady-state methods, the heat flow is... 

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