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Transport in Porous Media

, Volume 75, Issue 2, pp 133–149 | Cite as

A Semi-empirical Correlation for Pressure Drop in Packed Beds of Spherical Particles

  • Yong Seok Choi
  • Sung Jin KimEmail author
  • Duckjong Kim
Article

Abstract

The effect of a confining wall on the pressure drop of fluid flow through packed beds of spherical particles with small bed-to-particle diameter ratios was investigated to develop an improved pressure drop correlation. The dependency of pressure loss on both wall friction and increased porosity near the wall was accounted for by using a theoretical approach. A semi-empirical model was created based upon the capillary-orifice model, which included a wall correction factor for the inertial pressure loss. In this model, packed beds were treated as a bundle of capillary tubes whose orifice diameter in the core region was different from that of the wall region. Using this model, a new pressure drop correlation was obtained, based on the Ergun equation and applicable for a wide range of Reynolds numbers (10−2–103). The proposed correlation was compared with previous correlations, as well as with experimental data. This correlation showed close agreement with the experimental data for both low- and high-Reynolds number regimes and for a wide range of bed-to-particle diameter ratios. The ratio of the pressure drop in finite packing to that in homogeneous packing was then calculated. This ratio clearly shows how the wall effect depends on the Reynolds number and the bed-to-particle diameter ratio.

Keywords

Packed beds Porous media Pressure drop Wall effect Particle 

Notation

Cd

Discharge coefficient of an orifice

CD

Drag coefficient of an orifice plate

Cw

Wall correction factor for inertial pressure loss term

CCP

Cubic close packing

CLP

Cubic lattice packing

dh

Hydraulic diameter or mean pore diameter, m

do

Orifice diameter, m

dp

Spherical particle diameter, m

D

Bed diameter, m

F1F2

Correlation factors used in the curve-fit of discharge coefficient

L

Bed height, m

M

Wall correction factor proposed by Mehta and Hawley (1969)

n

Number of experimental data

nT

Total number of capillary tubes over the cross-section of the bed

nW

Number of capillary tubes in the wall region

Δp

Pressure drop, Pa

Δphom

Pressure drop for homogenous packing, Pa

r

Correlation coefficient

Re

Reynolds number based on the particle diameter

\({Re_{{d}_{\rm h}}}\)

Reynolds number based on the hydraulic diameter

Reobserved

Experimentally observed Reynolds number

u

Mean pore velocity, m/s

U

Superficial cross-sectional average axial velocity, m/s

Greek letters

β

Ratio between orifice and hydraulic diameter

\({\varepsilon}\)

Mean porosity or mean void fraction

μf

Fluid dynamic viscosity, kg/(ms)

ρf

Fluid density, kg/m3

σ

Relative root mean square deviation

τ

Tortuosity

ψcorr

Dimensionless pressure drop computed by the correlation

ψexp

Experimentally determined dimensionless pressure drop

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.School of Mechanical, Aerospace and Systems EngineeringKorea Advanced Institute of Science and TechnologyDaejeonKorea
  2. 2.Micro/Bio Fluidics TeamKorea Institute of Machinery and MaterialsDaejeonKorea

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