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Journal Article

The statistical character of bed-scale effective heat transport coefficients for packed beds

01 Jan 1993-Chemical Engineering Research & Design (Institution of Chemical Engineers)-Vol. 70, Iss: 6, pp 610-619
TL;DR: In this article, the influence of the actual bed structure on the values of the overall heat transfer coefficient, as used in the pseudo-homogeneous one-dimensional model, was studied.
Abstract: The influence is studied of the actual bed structure on the values of the overall heat transfer coefficient, as used in the pseudo-homogeneous one-dimensional model. The bed structure is described by a radially averaged and axially varying porosity profile. The influence of the tube to particle diameter ratio on this profile is studied theoretically for a perfectly packed bed. Axial porosity profiles were determined experimentally for spheres, full cylinders and Raschig rings and for each of them the bed was repacked ten times. From these profiles the local and the overall heat transfer coefficients were calculated, using literature relations. Furthermore, experimental values for the overall heat transfer coefficient have been obtained for a wall-cooled packed bed, for six different packing types, at four different gas flow rates and for 10-20 difference bed structures. The changes in the bed structure were made by repacking the bed. Although the local rate of heat transport can possess a statistical character, it can be concluded that the effective heat transport coefficients, as used in the bed scale models, are generally not distributed. Only for a very low number of particles present in the bed the local phenomena may lead to a statistical spread in these coefficients. The statistical character, as observed in temperature measurements in packed beds, is due to the heterogeneous character of the packed bed and the discrete character of the temperature measurements. If the actual structure of a packed bed and, as a result of this, the local rate of heat transport are expected to determine the behaviour of the packed bed as a whole, deterministic bed-scale continuum models become less applicable and models have to be used that take the structure and stochastic character of a packed bed into account
Citations
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Journal ArticleDOI
TL;DR: An analytical model for capillary pressure-saturation relation is developed for the pendular and funicular regions and the factors affecting the capillary region are discussed in this article, where the model is based on the assumption that the particles are covered with a liquid film, which provides hydrodynamic continuity.
Abstract: Capillary pressure is considered in packed-beds of spherical particles. In the case of gas-liquid flows in packed-bed reactors, capillary pressure gradients can have a significant influence on liquid distribution and, consequently, on the overall reactor performance. In particular, capillary pressure is important for non-uniform liquid distribution, causing liquid spreading as it flows down the packing. An analytical model for capillary pressure-saturation relation is developed for the pendular and funicular regions and the factors affecting capillary pressure in the capillary region are discussed. The present model is compared to the capillary pressure models of Grosser et al. (AIChE J., 34:1850-1860, 1988) and Attou and Ferschneider (Chem. Eng. Sci., 55:491-511, 2000) and to the experiments of Dodds and Srivastava (Part Part Syst. Charact., 23:29-39, 2006) and Dullien et al. (J. Colloid Interface Sci., 127:362-372, 1989). The non-homogeneity of real packings is considered through particle size and porosity distributions. The model is based on the assumption that the particles are covered with a liquid film, which provides hydrodynamic continuity. This makes the model more suitable for porous or rough particles than for non-porous smooth particles. The main improvements of the present model are found in the pendular region, where the liquid dispersion due to capillary pressure gradients is most significant. The model can be used to improve the hydrodynamic models (e.g., CFD and cellular automata models) for packed-bed reactors, such as trickle-bed reactors, where gas, liquid, and solid phases are present. Models for such reactors have become quite common lately (Saez and Carbonell, AIChE J., 31:52-62, 1985; Holub et al., Chem. Eng. Sci, 47, 2343-2348, 1992; Attou et al., Chem. Eng. Sci., 54:785-802, 1999; Iliuta and Larachi, Chem. Eng. Sci., 54:5039-5045, 1999, IJCRE 3:R4, 2005; Narasimhan et al., AIChE J., 48:2459-2474, 2002), but they still lack proper terms causing liquid dispersion.

31 citations

Journal ArticleDOI
TL;DR: In this article, the authors applied the limiting current method to characterize the local mass transfer in the axial, radial and angular directions throughout a packed bed of Pall rings, expressing in terms of the particle-to-fluid mass transfer coefficient of ferricyanide ions obtained from the limiting currents measured during its reduction to ferrocyanide at different locations in the bed.

10 citations

Journal ArticleDOI
TL;DR: In this paper, experimental heat transfer studies were carried out in 50.8 mm diameter packed beds of glass beads percolated by water and heated from the wall, and the radial temperature profile at the bed entrance, measured by a ring-shaped sensor, was uniform except very close to the tube wall.
Abstract: Experimental heat transfer studies were carried out in 50.8 mm diameter packed beds of glass beads percolated by water and heated from the wall. The tube-to-particle diameter ratio (D/dp) ranged from 1.72 to 13.7 and the water flow rate from 1.1 to 9.9 l/min. Bed heights ranged from 100 mm to 700 mm. The radial temperature was measured above the bed surface by five aligned sheathed thermocouples. Variations in angular temperature were observed, independent of both radial position and particle diameter. Results of repeated tests with the same packing and with repacking did not differ statistically. The radial temperature profile at the bed entrance, measured by a ring-shaped sensor, was uniform except very close to the tube wall.

9 citations


Cites background from "The statistical character of bed-sc..."

  • ...On the other hand, there are a number of studies on gas flow discussing experimental, statistical and theoretical aspects, and the results are quite conclusive (e.g. see Tsotsas and Schlünder, 1990; Borkink et al., 1992; Freiwald and Paterson, 1992; Thoméo and Freire, 2000)....

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  • ...For gas flow studies, a large variation in To was observed with both radial position and gas flow rate (Dixon, 1985; Borkink et al., 1992; Thoméo and Freire, 2000), and this variation was attributed to the entrance effects rather than to the effective thermal parameters with the increasing axial distance....

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  • ...For gas flow studies, a large variation in To was observed with both radial position and gas flow rate (Dixon, 1985; Borkink et al., 1992; Thoméo and Freire, 2000), and this variation was attributed to the entrance effects rather than to the effective thermal parameters with the increasing axial…...

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Journal ArticleDOI
TL;DR: In this paper, the significance of the statistical character of wall-cooled packed-bed reactors was studied by measuring angular temperature variations, which result from the random nature of the packing.
Abstract: The significance of the statistical character of wall-cooled packed-bed reactors was studied by measuring angular temperature variations, which result from the random nature of the packing. These are neglected in present-day mathematical models designed to describe the reactor behavior. The amplitude of these variations was determined experimentally as a function of the mass flux and the position in the tube, under conditions of heat transfer as well as of reaction. Angular variations are significant whenever radial temperature gradients are large. Different methods used to average observed variations were surveyed. For the system presented, the angular variations have only a limited influence on the reaction rates if the angular averaged temperature is used. Thus, a two-dimensional deterministic continuum model can be used, notwithstanding the statistical character of the packed bed.

7 citations


Cites background from "The statistical character of bed-sc..."

  • ...Therefore, some authors have suggested that the statistical character of a packed bed should be incorporated in the reactor model (see Fedoseev and Shanin, 1986; Wijngaarden and Westerterp, 1992a,b; Borkink et al., 1992)....

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  • ...Another approach to average angular variations is repacking the bed (see Borman and Westerterp, 1992; Borkink et al., 1992; and Wijngaarden and Westerterp, 1992b)....

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  • ...…also argued that over longer bed lengths the gas has undergone an axial averaging by contacts with so many particles, consequently differences caused by variation of streamlines through the packing should average out, unless there is a bypass in some part of the bed (see also Borkink et al., 1992)....

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