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Heat and Mass Transfer

, Volume 41, Issue 9, pp 843–854 | Cite as

A lattice Boltzmann model for adsorption breakthrough

  • Saurabh Agarwal
  • Nishith VermaEmail author
  • Dieter Mewes
Original

Abstract

A lattice Boltzmann model is developed to simulate the one-dimensional (1D) unsteady state concentration profiles, including breakthrough curves, in a fixed tubular bed of non-porous adsorbent particles. The lattice model solves the 1D time dependent convection–diffusion–reaction equation for an ideal binary gaseous mixture, with solute concentrations at parts per million levels. The model developed in this study is also able to explain the experimental adsortption/desorption data of organic vapours (toluene) on silica gel under varying conditions of temperature, concentrations and flowrates. Additionally, the programming code written for simulating the adsorption breakthrough is modified with minimum changes to successfully simulate a few flow problems, such as Poiseuille flow, Couette flow, and axial dispersion in a tube. The present study provides an alternative numerical approach to solving such types of mass transfer related problems.

Keywords

Breakthrough Curve Dispersion Coefficient Couette Flow Axial Dispersion Pure Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

a

external surface area per unit volume of the fiber (m−1)

C

concentration (mol/m3)

Cg

gas phase concentration in the bed (mol/m3)

CS

surface concentration of adsorbed species inside the pores (mol/m2)

d

inside diameter of tube (m), particle density-difference distribution function

dp

particle diameter (m)

e

particle speed (m/s)

D

dispersion or diffusion coefficient (m2/s)

f

particles density distribution function, Fanning friction factor

g

particles density distribution function due to body force

ka

adsorption rate constant (m/s)

kd

desorption rate constant (1/s)

L

bed length (m)

l

lattice size

m

no. of nodes in x direction, slope of the adsorption isotherm (m2/m3)

n

no of nodes in y direction

P

pressure (Pa)

Q

volumetric flow rate of the gas (slpm)

q

direction of lattice particle speed

r

particle location

u

fluid velocity (m/s)

x

x-direction

y

y-direction

t

time (s)

Greek letters

α, β

directions

b

bed porosity

ρ

fluid density (kg/m3)

μ

fluid viscosity (Pa.s)

ν

fluid kinematic viscosity (m2/s)

τ

relaxation time for momentum transport

τd

relaxation time for diffusion

θ

dimensionless coefficient

Subscripts

i

lattice index (0–9)

Superscripts

0

equilibrium

effective

average

Notes

Acknowledgements

N. Verma acknowledges the Humboldt research fellowship (IV0INI/1114920) to conduct the present study at the University of Hannover (Germany).

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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of Chemical EngineeringIndian Institute of Technology KanpurKanpurIndia
  2. 2.Institut fur VerfahrenstechnikUniversitat HannoverHannoverGermany

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