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A unified model for non-Newtonian flow in packed beds and porous media

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Abstract

A generalized equation describing the flow of any time-independent purely viscous non-Newtonian fluid in packed beds and porous media is proposed. The equation, which is expressed in terms of the Kozeny constantk i and the bed tortuosityT, unifies the three well-known packed bed models due to Blake, Blake-Kozeny and Kozeny-Carman within a general framework which also brings out their differences. The accuracy of each of the three bed models is assessed by comparing the predictions with existing experimental results, and is found to depend on the rheological properties of the fluid. The Kozeny-Carman model appears to give the best overall description of the flow of pseudoplastic (shear-thinning) fluids in packed beds and porous media although the Blake-Kozeny model gives a better representation for the high shear-thinning fluids.

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Abbreviations

a, b :

geometric parameters for an arbitrary flow channel

a 0,b 0 :

geometric parameters in Blake-Kozeny and Kozeny-Carman bed models

D c :

column diameter

D p :

particle or packing diameter

f :

friction factor defined by eq. (32)

k i :

2 (a + b), Kozeny constant

k 0 :

2 (a 0 +b 0), shape factor in Blake-Kozeny and Kozeny-Carman bed models

K :

fluid consistency coefficient in power law model

K * :

consistency index defined by eq. (36)

K′ :

consistency index defined for circular pipe flow

L :

length of packed bed; subscripte denotes equivalent length

n :

flow behaviour index in power-law model

n * :

index defined by eq. (25)

n′ :

index defined for circular pipe flow

P :

p + ϱ g h, hydrostatic potential

q :

ε〈u〉, superficial average velocity

q w :

εū w , superficial effective velocity at the wall

R h :

hydraulic radius

Re *p :

Reynolds number for packed bed defined by eq. (34) or (35)

Re′ :

Reynolds number for circular pipe flow

S 0 :

surface area per unit volume of solids

T :

tortuosity

〈u〉:

average velocity

ū w :

effective average velocity at the surface

α :

flow behaviour index in Ellis model

γ w :

shear rate at the wall

ε :

porosity

η :

non-Newtonian viscosity

η D :

Darcy viscosity defined by eq. (22)

η 0 :

lower limiting viscosity in Ellis model

µ :

Newtonian viscosity

ξ :

b/a, aspect factor; subscripto refers to channels in Blake-Kozeny and Kozeny-Carman models

ϱ :

density

\(\bar \tau _w \) :

average shear stress at the wall, shear stress parameter for packed bed

τ 1/2 :

parameter in Ellis model

B :

Blake bed model

BK :

Blake-Kozeny bed model

KC :

Kozeny-Carman bed model

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Authors and Affiliations

  1. Department of Chemical Engineering, University of Ottawa, K1N 9B4, Ottawa, Ontario, Canada

    W. Kozicki

  2. Department of Chemical Engineering, Monash University, 3168, Clayton, Victoria, Australia

    C. Tiu

Authors
  1. W. Kozicki
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  2. C. Tiu
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Kozicki, W., Tiu, C. A unified model for non-Newtonian flow in packed beds and porous media. Rheol Acta 27, 31–38 (1988). https://doi.org/10.1007/BF01372447

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  • DOI: https://doi.org/10.1007/BF01372447

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