An Analytical Model for Capillary Pressure–Saturation Relation for Gas–Liquid System in a Packed-Bed of Spherical Particles |
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Authors: | Katja Lappalainen Mikko Manninen Ville Alopaeus Juhani Aittamaa John Dodds |
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Institution: | (1) Chemical Engineering and Plant Design, Helsinki University of Technology, P.O. Box 6100, 02015 Espoo, Finland;(2) VTT Technical Research Centre of Finland, P.O. Box 1000, 02044 Espoo, Finland;(3) Neste Jacobs Oy, P.O. Box 310, 06101 Porvoo, Finland;(4) RAPSODEE UMR 2392, Ecole des Mines d’Albi, 810013 Albi, France |
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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 (Sáez 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. |
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Keywords: | Analytical model Capillary pressure Liquid dispersion Packed-beds Porous media |
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