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A critical review of dispersion in packed beds

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Abstract

The phenomenon of dispersion (transverse and longitudinal) in packed beds is summarized and reviewed for a great deal of information from the literature. Dispersion plays an important part, for example, in contaminant transport in ground water flows, in miscible displacement of oil and gas and in reactant and product transport in packed bed reactors. There are several variables that must be considered, in the analysis of dispersion in packed beds, like the length of the packed column, viscosity and density of the fluid, ratio of column diameter to particle diameter, ratio of column length to particle diameter, particle size distribution, particle shape, effect of fluid velocity and effect of temperature (or Schmidt number). Empirical correlations are presented for the prediction of the dispersion coefficients (D T and D L) over the entire range of practical values of Sc and Pem, and works on transverse and longitudinal dispersion of non-Newtonian fluids in packed beds are also considered.

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Abbreviations

a :

Radius of soluble cylinder

b :

Width of slab

C :

Concentration of solute

\(\bar{C}\) :

Concentration of the outflowing central solution

C 0 :

Bulk concentration of solute

C * :

Equilibrium concentration of solute (i.e. solubility)

C S :

Concentration of solute in outlet

d :

Average diameter of inert particles

D :

Diameter of packed bed

D L :

Longitudinal dispersion coefficient

D m :

Molecular diffusion coefficient

D′m:

Apparent molecular diffusion coefficient (=D m/τ)

D T :

Transverse dispersion coefficient

E(θ):

Distribution function for residence times

F(θ):

(C − C 0)/(C S − C 0)

k :

Average mass transfer coefficient over soluble surface

L :

Length

n :

Total mass transfer rate

N :

Local flux of solute

p :

Variable of Eq. 13 or Eq. 18

Pef :

Peclet number defined by Eq. 42

PeL(0):

Asymptotic value of PeL when Re → 0

PeL (∞):

Asymptotic value of PeL when Re → ∞

PeT (0):

Asymptotic value of PeT when Re → 0

PeT (∞):

Asymptotic value of PeT when Re → ∞

Q :

Volumetric flow rate

r :

Radial co-ordinate

R :

Column radius

R i :

Injector tube radius

t :

Time

\(\bar{t}\) :

Mean residence time

T :

Absolute temperature

t c :

Time of contact (=L/u)

U :

Superficial fluid velocity

u :

Average interstitial fluid velocity

x, y, z :

Cartesian coordinates

α i :

Roots of different equations

β n :

Positive root of Bessel function of first kind, of order 1

ɛ:

Bed voidage

ϕr :

Accumulation of solute

μ:

Dynamic viscosity

θ:

Dimensionless time

θc :

Dimensionless time of contact (=D T t c/R 2)

ρ:

Density

τ:

Tortuosity

ξc :

Variable defined by Eqs. 17d–e

Pea :

Peclet number based on longitudinal dispersion coefficient (=uL/D L)

Pem :

Peclet number of inert particle (=ud/D m)

Pe′m :

Effective Peclet number of inert particle (=ud/D′m)

PeL :

Peclet number based on longitudinal dispersion coefficient (=ud/D L)

PeT :

Peclet number based on transversal dispersion coefficient (=ud/D T)

Re:

Reynolds number (=ρ Ud/μ)

Sc:

Schmidt number (=μ/ρ D m)

J0(x):

Bessel function of first kind of zero order

J1(x):

Bessel function of first kind of first order

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  1. Departamento de Engenharia Química, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    J. M. P. Q. Delgado

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  1. J. M. P. Q. Delgado
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Appendix

Appendix

Table 1 Summary of the previous work with experimental data on axial dispersion of liquids in packed beds
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Table 2 Summary of the previous work with experimental data on axial dispersion of gases in packed beds
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Table 3 Summary of the previous work with experimental data on axial dispersion of non-Newtonian fluids in packed beds
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Table 4 Summary of the previous work with experimental data on transverse dispersion of liquids in packed beds
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Table 5 Summary of the previous work with experimental data on transverse dispersion of gases in packed beds
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Table 6 Summary of the previous work with experimental data on transverse dispersion of non-Newtonian fluids in packed beds
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Delgado, J.M.P.Q. A critical review of dispersion in packed beds. Heat Mass Transfer 42, 279–310 (2006). https://doi.org/10.1007/s00231-005-0019-0

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