DiffusionK

Chemical Reactor Design Toolbox Reference Manual

ChemReactorDesign.Basic.Gas.Transport.DiffusionK

Description

The component generates the diffusional fluxes for Knudsen diffusion (Frerich Keil, 1999) due to partial pressure gradients.

$\begin{equation*} J_{i} = - \frac{D_{k_{i}}}{R \, T} \, \frac{dp_{i}}{dz} \quad \text{for} \quad i=1,\dots,N \end{equation*}$

Then the molar flow rates become

$\begin{equation*} F_{i} = A \, J_{i} \end{equation*}$

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

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

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.

Nomenclature

$D_{k_{i}}$	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
$\Phi$	energy flow rate

Bibliography

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