DiffusionF

Chemical Reactor Design Toolbox Reference Manual

ChemReactorDesign.Basic.Gas.Transport.DiffusionF

Description

The component generates the diffusional fluxes for generalized Fickian diffusion (Ross Taylor and R. Krishna, 1993) due to partial pressure fraction gradients.

$\begin{equation*} J_{i} = - \frac{1}{R \, T} \, \sum_{i}^{N-1} D_{ij} \, \frac{d p_{j}}{dz} \quad \text{for} \quad i=1,\dots,N-1 \end{equation*}$

$\begin{equation*} J_{N} = - \sum_{i}^{N-1} J_{i} \end{equation*}$

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.

Assumptions and Limitations

Actually, the equations presented above are sufficient to determine the molar flow rates for the case of an equimolar counterdiffusion, i.e. $\sum_{i}^{N} F_{i} = 0$ . If this condition cannot be fulfilled, an additional convection component must be added in parallel to account for the emerging difference in total pressure (Stefan flux).

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

Generalized Fickian diffusion coefficients
```
D = {1.0e-06*ones(1,1),'m^2/s'};
```
Note Initially only two species are considered, i.e. $N-1 = 1$ . As the number of species can be changed via the properties dialogue, the size of the array must be adjusted accordingly.

Nomenclature

$D_{ij}}$	generalized Fickian diffusion coefficient
$F_{i}$	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

Bibliography

Ross Taylor and R. Krishna (1993). Multicomponent Mass Transfer, Wiley.