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Application of Computational Mass Transfer (IV): Fixed-Bed Catalytic Reaction

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Introduction to Computational Mass Transfer

Part of the book series: Heat and Mass Transfer ((HMT))

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Abstract

In this chapter, an exothermic catalytic reaction process is simulated by using computational mass transfer (CMT) models as presented in Chap. 3. The difference between the simulation in this chapter from those in Chaps. 4, 5, and 6 is that chemical reaction is involved. The source term S n in the species conservation equation represents not only the mass transferred from one phase to the other, but also the mass created or depleted by a chemical reaction. Thus, the application of the CMT model is extended to simulating the chemical reactor. The simulation is carried out on a wall-cooled catalytic reactor for the synthesis of vinyl acetate from acetic acid and acetylene by using both \( \overline{{c^{\prime 2} }} - \varepsilon_{{{\text{c}}^{\prime } }} \) model and Reynolds mass flux model. The simulated axial concentration and temperature distributions are in agreement with the experimental measurement. As the distribution of \( \mu_{\text{t}} \) shows dissimilarity with D t and \( \alpha_{\text{t}} \), the Sc t or Pr t are thus varying throughout the reactor. The anisotropic axial and radial turbulent mass transfer diffusivities are predicted where the wavy shape of axial diffusivity D t,x along the radial direction indicates the important influence of catalysis porosity distribution on the performance of a reactor.

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Abbreviations

a :

Surface area, m

C :

Mass concentration, kg m−3

\( \overline{{c^{2} }} \) :

Concentration variance, kg2 m−6

\( C_{\mu } ,\;c_{1} ,\;c_{2} \) :

Model parameters in \( k - \varepsilon \) model equations

C c0, C c1, C c2, C c3 :

Model parameters in \( \overline{{c^{2} }} - \varepsilon_{c} \) model equations

C D0, C D1, C D2, C D3, C D4 :

Model parameters in \( \overline{{t^{2} }} - \varepsilon_{\text{t}} \) model equations

C p :

Specific heat, J kg−1 K−1

\( C_{\text{si}}^{\text{s}} \) :

Mass concentration of reactive species at the surface of catalyst

d e :

Effective diameter of catalyst particle, m

D e :

Effective turbulent mass diffusivity, m2 s−1

D s :

Intra-diffusivity of the catalyst, m2 s−1

D t :

Turbulent mass diffusivity, m2 s−1

G :

Gas-phase flow rate per unit cross-sectional area, kg m−2 s−1

h :

Film coefficient of mass transfer, m s−1

H :

Axial distance measured from column bottom (H = 0 at column bottom), m

\( \Delta H_{\text{r}} \) :

Heat of reaction, kJ mol−1

k :

Turbulent kinetic energy, m2 s−2

M :

Molar mass, kg mol−1

Pe t :

Turbulent Peclet number

r :

Position in radial direction, m

R :

Radius of the column

m :

Molar reaction rate mol/kg catalyst

s :

Apparent reaction rate

R 0 :

The resistant coefficient of porous media

R s :

Apparent reaction rate, kmol kg−1 (cat) s−1

Sc :

Turbulent Schmidt number

t 0 :

Fluid inlet temperature, °C

\( \overline{{t^{2} }} \) :

Temperature variance, K2

T :

Temperature, K

U :

Fluid superficial velocity, m s−1

x :

Axial position, m

z :

Dimensionless distance, z = (R−r)/d e

\( \alpha ,\;\alpha_{\text{t}} \) :

Molecular and turbulent thermal diffusivities, respectively, m2 s−1

\( \varepsilon \) :

Turbulent dissipation rate, m2 s−3

\( \varepsilon_{\text{c}} \) :

Turbulent dissipation rate of concentration fluctuation, kg2 m−6 s−1

ε t :

Turbulent dissipation rate of temperature fluctuation, K2 s−1

\( \varPhi \) :

Variable

\( \gamma \) :

Porosity distribution of the random packing bed

\( \gamma_{\infty } \) :

Porosity in an unbounded packing

\( \lambda \) :

Thermal conductivity, KJ m−1 K−1 s−1

\( \mu_{\text{t}} \) :

Turbulent viscosity, kg m−1 s−1

\( \rho \) :

Density, kg m−3

\( \rho_{\text{b}} \) :

Bulk density of catalyst, kg/m3

\( \nu_{\text{t}} \) :

Turbulent kinetic viscosity, m2 s−1

\( \sigma_{c} ,\sigma_{{\varepsilon_{\text{c}} }} \) :

Model parameters in \( \overline{{c^{2} }} - \varepsilon_{\text{c}} \) model equations

\( \sigma_{\text{t}} \) :

Model parameter in \( \overline{{t^{2} }} - \varepsilon_{\text{t}} \) model equations

\( \sigma_{\text{k}} ,\;\sigma_{\varepsilon } \) :

Model parameters in \( k - \varepsilon \) model equations

c:

Coolant

G:

Gas phase

i:

Interface

s:

Catalyst; reactive species

w:

Reactor wall

1:

Inner

2:

Outer

s:

Surface

References

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Authors and Affiliations

  1. School of Chemical Engineering and Technology, Tianjin University, Tianjin, People’s Republic of China

    Kuo-Tsong Yu & Xigang Yuan

Authors
  1. Kuo-Tsong Yu
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  2. Xigang Yuan
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Correspondence to Kuo-Tsong Yu .

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Yu, KT., Yuan, X. (2014). Application of Computational Mass Transfer (IV): Fixed-Bed Catalytic Reaction. In: Introduction to Computational Mass Transfer. Heat and Mass Transfer. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53911-4_7

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  • DOI: https://doi.org/10.1007/978-3-642-53911-4_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53910-7

  • Online ISBN: 978-3-642-53911-4

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