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Axial dispersion in packed bed reactors involving viscoinelastic and viscoelastic non-Newtonian fluids

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Abstract

Axial dispersion is an important parameter in the performance of packed bed reactors. A lot of fluids exhibit non-Newtonian behaviour but the effect of rheological parameters on axial dispersion is not available in literature. The effect of rheology on axial dispersion has been analysed for viscoinelastic and viscoelastic non-Newtonian fluids. Aqueous solutions of carboxymethyl cellulose and polyacrylamide have been chosen to represent viscoinelastic and viscoelastic liquid-phases. Axial dispersion has been measured in terms of BoL number. The single parameter axial dispersion model has been applied to analyse RTD response curve. The BoL numbers were observed to increase with increase in liquid flow rate and consistency index ‘K’ for viscoinelastic as well as viscoelastic fluids. Bodenstein correlation for Newtonian fluids proposed has been modified to account for the effect of fluid rheology. Further, Weissenberg number is introduced to quantify the effect of viscoelasticity.

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Abbreviations

BoL :

\( \frac{{{\text{Pe}}_{\text{L}} \;d_{\text{S}} }}{Z} \), Bodenstein number

C(t):

Concentration at time t, g/l

C θ :

\( \frac{C}{{C_{O} }} \), Normalized concentration

D :

Axial dispersion coefficient, m2/s

d C :

Column diameter, m

d S :

Spherical volume equivalent diameter of the particle, m

de :

\( \frac{{d_{\text{S}} \varepsilon }}{{1.5\left( {1 - \varepsilon } \right) + {\raise0.7ex\hbox{${d_{\text{S}} }$} \!\mathord{\left/ {\vphantom {{d_{\text{S}} } {D_{\text{c}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${D_{\text{c}} }$}}}} \)

K :

Flow consistency index, Pa sn

k i :

Blake-Kozeny equation constant

L :

Liquid mass velocity, kg m2−s−1

n :

Flow behaviour index

N 1 :

\( K_{1} \dot{\gamma }^{\text{m}} \), Pa

PeL :

\( \frac{{u_{\text{L}} Z}}{D} \), Peclet number

ReLM :

\( \frac{{d_{\text{S}} L}}{{(\mu_{\text{L}} \;{\text{or}}\;\mu_{\text{a}} )(1 - \varepsilon ).\alpha_{\text{w}} }} \)

v L :

Superficial velocity, m/s

Wi:

\( \lambda_{\text{eff}} .\dot{\gamma }_{\text{w}} \), Weissenberg number

Z :

Packed bed length, m

αw :

\( 1 + \frac{{2d_{\text{S}} }}{{3d_{\text{C}} (1 - \varepsilon )}} \), wall effect

\( \dot{\gamma } \) :

Shear rate (s−1)

\( \dot{\gamma }_{w} \) :

\( \frac{3n + 1}{4n}\frac{{8\;v_{\text{L}} }}{{\varepsilon \,D_{\text{e}} }}\frac{{k_{i} }}{2} \), shear rate at capillary wall, s−1

ε:

Porosity

ϕ:

Sphericity

θ:

\( \frac{t}{{t_{\text{m}} }} \), dimensionless time

λ eff :

\( \frac{{N_{1} }}{{2\dot{\gamma }\tau }} \), effective fluid characteristic time, s

λt :

Time constant of material, s

μl :

Viscosity of liquid, Pa s

μa :

\( K\dot{\gamma }^{n - 1} \), apparent viscosity of liquid phase

τ:

Shear stress, Pa

σl :

Surface tension of the liquid, mNm−1

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Acknowledgments

Personal discussions and the suggestions of Dr R K Wanchoo, Professor, University Institute of Chemical Engineering and Technology, Punjab University, Chandigarh are gratefully acknowledged.

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  1. Department of Chemical Engineering, National Institute of Technology, Jalandhar, 144 011, India

    Renu Gupta & Ajay Bansal

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  1. Renu Gupta
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  2. Ajay Bansal
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Correspondence to Ajay Bansal.

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Gupta, R., Bansal, A. Axial dispersion in packed bed reactors involving viscoinelastic and viscoelastic non-Newtonian fluids. Bioprocess Biosyst Eng 36, 1011–1018 (2013). https://doi.org/10.1007/s00449-012-0853-7

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