ViscousFlow

Chemical Reactor Design Toolbox Reference Manual

ChemReactorDesign.Basic.Gas.Transport.ViscousFlow

Description

The component generates the molar fluxes for viscous flow in porous media due to a pressure gradient.

$\begin{equation*} J_{i} = -\frac{x_{i} \, \frac{\varepsilon_{p}}{\tau} \, B_{0} \, p}{{\overline \mu} \, R \, T} \, \frac{dp}{dz} \end{equation*}$

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

Option to select porosity input

porosityInput = OnOff.Off;   % Porosity Input

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

Permeability
```
B0 = {1.0e-06,'m^2'}; 
```
Void Fraction
```
epsp = {1,'1'};  
```
The parameter is only visible when the option porosityInput is set of Off.
Tortuosity Factor
```
tau  = {1,'1'};
```

Nomenclature

$B_{0}$	permeability
$F_{i}$	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
$\mu$	viscosity
$\Phi$	energy flow rate