Packed beds wall coefficients

As can be seen in the table above, the upper two results for heat transfer coefficients hp between particle and gas are about 10% apart. The lower three results for wall heat transfer coefficients, h in packed beds have a somewhat wider range among themselves. The two groups are not very different if errors internal to the groups are considered. Since the heat transfer area of the particles is many times larger than that at the wall, the critical temperature difference will be at the wall. The significance of this will be shown later in the discussion of thermal sensitivity and stability. 

Reproducible correlations for the heat transfer coefficient between a fluid flowing through a packed bed and the cylindrical wall of the container are very difficult to obtain. The main difficulty is that a wide range of packing conditions can occur in the vicinity of the walls. However, the results quoted by Zenz and Othmer(44) suggest that ... 

Modeling of the packed bed catalytic reactor under adiabatic operation simply involves a slight modification of the boundary conditions for the catalyst and gas energy balances. A zero flux condition is needed at the outer reactor wall and can be obtained by setting the outer wall heat transfer coefficients /iws and /iwg (or corresponding Biot numbers) equal to zero. Simulations under adiabatic operation do not significantly alter any of the conclusions presented throughout this work and are often used for verification... 

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.

Mechanistic equations describing the apparent radial thermal conductivity (kr>eff) and the wall heat transfer coefficient (hw.eff) of packed beds under non-reactive conditions are presented in Table IV. Given the two separate radial heat transfer resistances -that of the "central core" and of the "wall-region"- the overall radial resistance can be obtained for use in one-dimensional continuum reactor models. The equations are based on the two-phase continuum model of heat transfer (3). 

There is even more uncertainty in estimating the heat-transfer coefficient at the wall of the tube than in estimating the effective thermal conductivity in the bed of catalyst. The measurement is essentially a difficult one, depending either on an extrapolation of a temperature profile to the wall or on determining the resistance at the wall as the difference between a measured over-all resistance and a calculated resistance within the packed bed. The proper exponent to use on the flow rate to get the variation of the coefficient has been reported as 0.33 (C4), 0.47 (C2), 0.5 and 0.77 (HI), 0.75 (A2), and 1.00 (Ql). 

The choice of a model to describe heat transfer in packed beds is one which has often been dictated by the requirement that the resulting model equations should be relatively easy to solve for the bed temperature profile. This consideration has led to the widespread use of the pseudo-homogeneous two-dimensional model, in which the tubular bed is modelled as though it consisted of one phase only. This phase is assumed to move in plug-flow, with superimposed axial and radial effective thermal conductivities, which are usually taken to be independent of the axial and radial spatial coordinates. In non-adiabatic beds, heat transfer from the wall is governed by an apparent wall heat transfer coefficient. ... 

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 17.36. Effective thermal conductivity and wall heat transfer coefficient of packed beds. Re = r/ G/jjL, dp = SVpjAp, s = poros-...

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

Under smooth fluidization the motion, heat capacity, and small size of the particles result in a remarkably uniform temperature throughout the bed. Radial gradients, so important in fixed beds, are negligible. The transfer of heat to or from the reactor can be considered by assuming that a finite heat-transfer coefficient exists at the wall, and that the temperature across the bed is uniform. This situation is depicted in Fig. 13-18, where curve c applies to the fluidized bed. For comparison, curve b represents a homogeneous tubular reactor in turbulent flow, where the temperature profile is not so flat as in the fluidized bed but is still more uniform than for the packed bed, case (a). ... 

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... 

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... 

Recently Nasr et al. [38] studied the augmentation of heat transfer by embedding the heat transfer surface in a packed bed. They found that in the presence of particles, the wall-to-bed heat transfer coefficient was up to 7 times greater than that for the case where heat transfer surface was placed in a cross flow. It was shown that the heat transfer coefficient increases with decreasing particle diameter and increasing thermal conductivity of the packing mate-... 

Packed-bed heat transfer can be conveniently expressed by the concept of effective thermal conductivity, which is based on the assumption that on a macroscale the bed can be described by a continuum. In general, the effective thermal conductivity increases with increasing operating pressure. The wall-to-bed heat transfer coefficient increases with decreasing particle diameter. 

M. Pons, P. Dantzer, and J. J. Guilleminot, A Measurement Technique and a New Model for the Wall Heat Transfer Coefficient of a Packed Bed of (Reactive) Powder Without Gas Flow, Int. J. Heat Mass Transfer (36/10) 2635,1993. 

---