Local voidage variation in a randomly packed bed of equal-sized spheres

Haughey, D. P.; Beveridge, G.S.G.

doi:10.1016/0009-2509(66)85084-4

Cited by 67 publications

(16 citation statements)

References 17 publications

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“…For low D/d p ratios, the flow behaviour is determined by the anisotropic structure of the porous matrix, which leads to a rather discontinuous variation of the velocity field. This is confirmed by Benenati and Brosilow [40], Haughey and Beveridge [41], Zotin [42], Govindarao and Froment [43], Dixon [44], Mueller [39], and Zou and Yu [45], who investigated the void distribution in packed beds.…”

Section: One-phase (Homogeneous) Modelsmentioning

confidence: 54%

Simulation of thermal conversion of solid fuel by the discrete particle method

Peters¹,

Džiugys²,

Navakas³

2011

Lith. J. Phys.

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We introduce the discrete particle method (DPM) that derives from the discrete element method (DEM). This is an advanced numerical simulation tool that takes into account both motion and chemical conversion of granular material, such as coal or biomass, in furnaces in conjunction with computational fluid dynamics (CFD). However, predictions of solely motion or conversion in a decoupled mode are also applicable. The DPM uses object oriented computational techniques that support objects representing three-dimensional particles of various shapes, size, and physical properties of particle material. This makes DPM a highly versatile tool in dealing with a variety of problems related to different industrial applications of granular matter. A review of literature concerning different approaches to mass and heat transfer in packed beds is presented.

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Section: One-phase (Homogeneous) Modelsmentioning

confidence: 54%

Simulation of thermal conversion of solid fuel by the discrete particle method

Peters¹,

Džiugys²,

Navakas³

2011

Lith. J. Phys.

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“…(15). It must be noted that the conclusion concerning the lack of interaction of atrazine and linuron with the catalytic surface is not dependent on the particular values of R h ct or R c .…”

Section: Resultsmentioning

confidence: 95%

“…In this work and for the most unfavourable case the aforementioned ratios were 44 and 480 respectively. Bed porosity was estimated in line with Haughey and Beveridge [15].…”

Section: Resultsmentioning

confidence: 99%

Catalytic ozonation of atrazine and linuron on MnO /Al2O3 and MnO /SBA-15 in a fixed bed reactor

Rosal

Gonzalo

Rodrı́guez

et al. 2010

Chemical Engineering Journal

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“…Empirical correlations to express N c as a function of the bed porosity have been proposed, for example, by Haughey and Beveridge (1966), German (1989), and van der Merwe et al (2004). They Fig.…”

Section: Pendular Regionmentioning

confidence: 98%

An Analytical Model for Capillary Pressure–Saturation Relation for Gas–Liquid System in a Packed-Bed of Spherical Particles

Lappalainen¹,

Manninen

Alopaeus³

et al. 2008

Transp Porous Med

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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(AIChE J., 34: -1860(AIChE J., 34: , 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; K. Lappalainen (B) · V. Alopaeus Chemical Engineering and Plant Design, Nomenclatures A c Cross-sectional area (m 2 ) d Half spacing between neighboring microcylinders (m) d p Particle diameter (m) d min As defined in Eq. 5 (m) D H Hydraulic diameter (m) f Wetting efficiency J (S L ) Leverett's J -function k Permeability (m 2 ) N c Number of particle contact points per particle p c Capillary pressure (Pa) p i Pressure of phase i (Pa) r 1,2 Scaled radii of curvature R 1,2 Radii of curvature (m) R Particle radius (m) R * Mean curvature of the meniscus (m) s Perimeter (m) S L Liquid saturation V f Volume of fluid in a pendular ring (m 3 )Greek letters ε Void fraction of the packed-bed ϕ Filling angle (see Fig. 3) (rad) (x) Gamma function θ Liquid-solid contact angle (rad) θ i Holdup of phase i ρ i Density of phase i (kg · m −3 ) σ Surface tension between the wetting and the non-wetting phases (N · m −1 ) X(1 − cos ϕ)

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Local voidage variation in a randomly packed bed of equal-sized spheres

Cited by 67 publications

References 17 publications

Simulation of thermal conversion of solid fuel by the discrete particle method

Simulation of thermal conversion of solid fuel by the discrete particle method

Catalytic ozonation of atrazine and linuron on MnO /Al2O3 and MnO /SBA-15 in a fixed bed reactor

An Analytical Model for Capillary Pressure–Saturation Relation for Gas–Liquid System in a Packed-Bed of Spherical Particles

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