DustyGas

Chemical Reactor Design Toolbox Reference Manual

ChemReactorDesign.Basic.Gas.Transport.DustyGas

Description

The component generates the diffusional fluxes according to the dusty-gas model (Frerich Keil, 1999) due to partial pressure gradients.

$\begin{equation*} \frac{1}{R \, T} \, \frac{d p_{i}}{dz} = \sum_{\stackrel{j}{j \neq i}}^{N} \frac{{\overline x}_{i} \, J_{j} - {\overline x}_{j} \, J_{i}} {\frac{\varepsilon_{p}}{\tau} \, {\cal D}_{ij}} - \frac{J_{i}}{\frac{\varepsilon_{p}}{\tau} \, D_{k_{i}}} \qquad \text{for} \quad i=1,\cdots,N \end{equation*}$

using averaged mole fractions ${\overline x}_{i}$ .

The energy flow rate is determined as

$\begin{equation*} \Phi = \sum_{i}^{N} F_{i} \, \left({\overline H}_{i}(T)\right)_{averaged} + F_{tot} \, \Big(H_{res}(T,p)\Big)_{averaged} \end{equation*}$

with

$\begin{equation*} F_{tot} = \sum_{i}^{N} F_{i} \end{equation*}$

The positive direction for the fluxes is from port A to port B.

Ports

Conserving

Gas conserving port
```
Port_A = Gas;  %
```
Gas conserving port
```
Port_B = Gas;  %
```

Input

Physical signal that controls the cross sectional area
```
Ain = {0,'m^2'}; 
```
Dependencies: The port is only visible when the option areaInput is set to On.

Parameters

Options

Option to select area input
```
areaInput = OnOff.Off;
```
Off | On
Option to select porosity input
```
porosityInput = OnOff.Off;
```
Off | On

Geometry

Cross sectional area
```
A0 = {1,'m^2'};
```
Dependencies: The parameter is only visible when the option areaInput is set to Off.
Transport distance
```
delta  = {1.0e-03,'m'};
```

Mass Transport

Stefan-Maxwell diffusion coefficients
```
Dbin = {ones(2,2),'m^2/s'}; 
```
Note Initially only two species are considered. As the number of species can be changed via the properties dialogue, the size of the array must be adjusted accordingly.
Knudsen diffusion coefficients
```
Dk = {1.0e-06*ones(2,1),'m^2/s'};
```
Note Initially only two species are considered. As the number of species can be changed via the properties dialogue, the size of the array must be adjusted accordingly.
Void Fraction
```
epsp = {1,'1'};
```
Tortuosity Factor
```
tau  = {1,'1'};
```

Nomenclature

${\cal D}_{ij}$	binary Stefan-Maxwell diffusion coefficient
$D_{k_{i}}$	Knudsen diffusion coefficient of species A_i
$F_{i}$	molar flow rate of species A_i
${\overline H}_{i}(T)$	molar enthalpy of species A_i
$\Delta H_{res}$	departure enthalpy of the mixture
$J_{i}$	diffusional flux of species A_i
$N$	total number of species
$p$	pressure
$R$	universal gas constant
$t$	time
$T$	temperature
$x_{i}$	mole fraction of species A_i
$\Phi$	energy flow rate
$\varepsilon_p$	void fraction
$\tau$	tortuosity factor

Bibliography

Frerich Keil (1999). Diffusion und Chemische Reaktionen in der Gas-Feststoff-Katalyse, Springer Berlin.