Significance of axial heat dispersion for the description of heat transport in wall‐cooled packed beds

Abstract

A two-dimensional pseudo-homogeneous model with axial dispersion of heat has been solved numerically with different boundary conditions at the inlet and outlet of the packed bed. The model solutions are fitted to experimental temperature profiles, determined in a wall-cooled packed bed in which a hot gas is cooled down, and best fit values of the effective axial and radial thermal conductivities and the wall heat transfer coefficient are obtained. In the range of Reynolds numbers employed, Re; > 50, the axial dispersion of heat is found to be of no significance for the description of heat transport in wall-cooled packed beds without reaction, provided that the inlet boundary conditions are chosen appropriately. If a radially flat inlet temperature profile is assumed, while the actual profile is curved, an apparent improvement in the description of heat transport is observed when axial dispersion is incorporated into the heat balance and high effective axial thermal conductivities are obtained. If a Danckwerts type inlet boundary condition is used, assuming a flat temperature profile immediately in front of the inlet, an apparent improvement is also found on incorporation of axial dispersion of heat. This is caused by the temperature jump at the inlet, compensating for the overestimation of inlet temperature, in the case of cooling. The latter also explains why the inclusion of axial dispersion may eliminate the so-called "length effect", often related to the effective radial thermal conductivity and the wall heat transfer coefficient. It is shown for the outlet boundary condition that deletion of the axial dispersion term from the heat balance at the outlet is a convenient boundary condition for the model being solved numerically.

Oxidation of ethene in a wall-cooled packed-bed reactor

“…Axial dispersion of heat was found to be of no significance provided correct boundary conditions were chosen [see Borkink and Westerterp (1992a)].…”

“…The gas is in plug flow so no radial velocity variation is incorporated in the model; axial dispersion of both mass and heat is neglected. This is allowed according to Borkink and Westerterp (1992a)_ Also, pressure drop over the reactor, local changes in porosity, free convection and heat transport by radiation are neglected. With the criteria of Mears (1971) it was verified that intraparticle resistances for heat and mass transport are not important.…”

Thermal Dispersion in Porous Media—A Review on the Experimental Studies for Packed Beds

“…Table 2 shows that the aim of the most studies was to determine the radial effective thermal conductivity, and the axial thermal conductivity was neglected or calculated from a reported correlation in the literature. Bunnell et al [28], Borkink and Westerterp [34], Metzger et al [51], Testu et al [52,53], Gunn and Khalid [41], Clement and Jorgensen [44], and Levec and Carbonell [45] determined both the axial and transverse effective thermal conductivity ratios, experimentally. Elsari and Hughes [46], Yagi et al [47], Vortuba et al [48], Gunn and de [49] performed the experimental study to determine only the axial effective thermal conductivity.…”

“…Furthermore, the same experimental setup with alumina cylinder packings was used [34]. Reynolds numbers between 70 and 600 were considered.…”

“…Calculated Neglected A reported correlation was used Smirnov et al [23][24][25] X X Thomeo and Freire [26] X X Demirel et al [27] X X Bunnell et al [28] X X Wen and Ding [29] X X Dixon and van Dongeren [30] X X Borkink and Westerterp [32,33] X X Borkink and Westerterp [34] X X Kwong and Smith [35] X X Bey and Eigenberger [36] X X Jorge et al [38] X X Dekhtyar et al [40] X X Gunn and Khalid [41] X X Gunn and De Souza [43] X X Clement and Jorgensen [44] X X Levec and Carbonell [45] X X Elsari and Hughes [46] X X Yagi et al [47] X X Vortuba et al [48] X X Vortmeyer and Adam [49] X X Metzger et al [51] X X Testu et al [52,53] X X Water, 0 < Re < 18…”