SLE

Chemical Reactor Design Toolbox Reference Manual

ChemReactorDesign.Basic.Liquid.Transfer.SLE

Description

The component determines the molar flow rates of all species in the respective phases (solid and liquid) due to $M$ individual solid-liquid equilibria (SLE).

The $j^{th}$ dissolution is modelled as reversible reaction be

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

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

$\begin{equation*} r_{j} = k_{j} \, \left( \lambda_{j}^{S} - \frac{\gamma_{j}^{L} \, c_{i}^{L}}{K} \right) \end{equation*}$

with

$\begin{equation*} \lambda^{S}_{j} = \left\{ \begin{array}{ccc} 1 & \text{if} & c_{j}^{S} \geq 0 \\ 0 & \text{else} & \end{array} \right. \end{equation*}$

Variables

The molar rates for both domains are given as

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

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

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

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

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

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 solid domain
```
nu_S = {[-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
```
nu_L = {[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 constant
```
K0 = {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