DiffusionS

Chemical Reactor Design Toolbox Reference Manual

ChemReactorDesign.Basic.Gas.Transport.DiffusionS

Description

The component generates the diffusional fluxes for Stefan-Maxwell diffusion (Ross Taylor and R. Krishna, 1993) due to partial pressure gradients.

$\begin{equation*} \frac{1}{R \, T} \, \frac{dp_{i}}{dz} = \sum_{\stackrel{j}{j \neq i}}^{N} \frac{{\overline x}_{i} \, J_{j} - {\overline x}_{j} \, J_{i}} {\dcal_{ij}} \qquad \text{for} \quad i=1,\cdots,N-1 \end{equation*}$

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

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

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

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.

Nomenclature

$\dcal_{ij}$	binary Stefan-Maxwell 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.