An analytical model for capillary pressure-saturation relation for gas-liquid system in a packed-bed of spherical particles

Katja Lappalainen (Corresponding Author), Mikko Manninen, Ville Alopaeus, Juhani Aittamaa, J. Dodds

Research output: Contribution to journalArticleScientificpeer-review

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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.
Original languageEnglish
Pages (from-to)17-40
Number of pages24
JournalTransport in Porous Media
Volume77
Issue number1
DOIs
Publication statusPublished - 2009
MoE publication typeA1 Journal article-refereed

Fingerprint

Capillarity
Packed beds
Analytical models
Gases
Liquids
Pressure gradient
Hydrodynamics
Cellular automata
Liquid films
Colloids
Computational fluid dynamics
Porosity
Particle size

Keywords

  • analytical model
  • capillary pressure
  • liquid dispersion
  • packed-beds
  • porous media

Cite this

Lappalainen, Katja ; Manninen, Mikko ; Alopaeus, Ville ; Aittamaa, Juhani ; Dodds, J. / An analytical model for capillary pressure-saturation relation for gas-liquid system in a packed-bed of spherical particles. In: Transport in Porous Media. 2009 ; Vol. 77, No. 1. pp. 17-40.
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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 (S{\'a}ez 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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An analytical model for capillary pressure-saturation relation for gas-liquid system in a packed-bed of spherical particles. / Lappalainen, Katja (Corresponding Author); Manninen, Mikko; Alopaeus, Ville; Aittamaa, Juhani; Dodds, J.

In: Transport in Porous Media, Vol. 77, No. 1, 2009, p. 17-40.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - An analytical model for capillary pressure-saturation relation for gas-liquid system in a packed-bed of spherical particles

AU - Lappalainen, Katja

AU - Manninen, Mikko

AU - Alopaeus, Ville

AU - Aittamaa, Juhani

AU - Dodds, J.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - analytical model

KW - capillary pressure

KW - liquid dispersion

KW - packed-beds

KW - porous media

U2 - 10.1007/s11242-008-9259-z

DO - 10.1007/s11242-008-9259-z

M3 - Article

VL - 77

SP - 17

EP - 40

JO - Transport in Porous Media

JF - Transport in Porous Media

SN - 0169-3913

IS - 1

ER -