LLE

Chemical Reactor Design Toolbox Reference Manual

ChemReactorDesign.Basic.Liquid.Transfer.LLE

Description

The component determines the molar flow rates of all species in two distince liquid phases (domains) due to $M$ individual liquid-liquid equilibria (LLE).

The $j^{th}$ mass transfer rate is modelled as reversible reaction between the respective species in both domains.

$\begin{equation*} A_{i}^{L_{1}} \rightleftharpoons A_{k}^{L_{2}} \qquad \text{for} \qquad j = 1,\cdots,M \end{equation*}$

Since for every equilibrium under consideration only one species per domain is involved, only one respective stoichiometric coefficient in the $j^{th}$ mass transfer rate is different from zero. Using this criterion the relevant data are extracted and used in calculating the sorption rate.

The mass transfer rate is given as

$\begin{equation*} r_{j} = k_{j} \, \left( \gamma_{i}^{L_{1}} \, x_{i}^{L_{1}} - \frac{\gamma_{k}^{L_{2}} \, x_{k}^{L_{2}}}{K_{j}} \right) \end{equation*}$

The component is composed of two instances of a Coupler components as shown below

Abbildung 1: LLE Subsystem

Variables

The molar rates for both domains are given as

$\begin{equation*} F_{i}^{L_{1}} = A \, \sum_{j}^{M} \nu_{ij}^{L_{1}} \, r_{j} \end{equation*}$

$\begin{equation*} F_{i}^{L_{2}} = A \, \sum_{j}^{M} \nu_{ij}^{L_{2}} \, r_{j} \end{equation*}$

Since the heat transport associated with the mass transport is implicitly accounted for in the model equations of the associated balance component the energy flow rates become

$\begin{equation*} \Phi^{L_{1}} = 0 \end{equation*}$

$\begin{equation*} \Phi^{L_{2}} = 0 \end{equation*}$

Ports

Conserving

Liquid 1 conserving port
```
Port_B1 = Liquid;  %
```
Liquid 2 conserving port
```
Port_B1 = Gas;  %
```

Input

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

Parameters

Options

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

Geometry

Surface Area
```
A0 = {0,'cm^2'}; 
```
Dependencies: The parameter is only visible when the option areaInput is set to Off.

Stoichiometry

Stoichiometric coefficients for liquid domain 1
```
nu1 = {[-1;0],'1'}; 
```
Note Initially only one equilibrium is considered. When the number of individual equilibria is increased, the size of the array must be adjusted accordingly.
Stoichiometric coefficients for liquid domain 2
```
nu2 = {[1;0],'1'};
```
Note Initially only one equilibrium is considered. When the number of individual equilibria is increased, the size of the array must be adjusted accordingly.

Thermodynamics

Equilibrium coefficients
```
Kpart = {1,'1'};
```
Note Initially, only one equilibrium is considered. When the number is increased, the size of the array must be adjusted accordingly.

Kinetics

Rate constants
```
k = {0,'mol/(m^2*s)'}; 
```
Note Initially only one equilibrium is considered. When the number of individual equilibria is increased, the size of the array must be adjusted accordingly.

Nomenclature

$A$	area
$F_{i}$	molar flow rate of species A_i
${\Delta_{f} H}$	molar enthalpy of species A_i
$K$	equilibrium constant
$k$	rate constant
$N$	total number of species
$M$	number of equlibria
$p$	pressure
$r$	mass transfer rate
$R$	universal gas constant
$T$	temperature
$x_{i}$	mole fraction of species A_i
$\Phi$	energy flow rate
$\gamma$	activity coefficient of species A_i