Valve

Chemical Reactor Design Toolbox Reference Manual

ChemReactorDesign.Basic.Gas.Transport.Valve

Description

The component generates a volumetric flow rate due to a pressure difference between the ports for a control valve (Sigurd Skogestad, 2009). To allow for a change in sign upon reversal of flow direction and to eliminate singularities due to flow reversal a modified relation is used

$\begin{equation*} \Delta p = \frac{\rho}{\left(C_{d} \, A\right)^{2}} \, q \, \sqrt{q^{2} + q_{small}^{2}} \end{equation*}$

with $C_{d}$ as the relative capacity coefficient with is related to the value oflost velocity heights

$\begin{equation*} C_{d} = \sqrt{\frac{n}{2}} \end{equation*}$

Then the molar flow rates become

$\begin{equation*} F_{i} = y \, q \, \left(\frac{x_{i} \, p}{z \, R \ T} \right)_{upstream} \end{equation*}$

with $y_{min} \leq y \leq 1$ as control signal to externally adjust the calculated volumetric flow rate.

The energy flow rate is determined as

$\begin{equation*} \Phi = \sum_{i}^{N} F_{i} \, \left({\overline H}_{i}(T)\right)_{upstream} + F_{tot} \, \Big(H_{res}(T,p)\Big)_{upstream} \end{equation*}$

with

$\begin{equation*} F_{tot} = \sum_{i}^{N} F_{i} \end{equation*}$

The positive flow direction is from port A to port B.

Assumptions and Limitations

The parameter $q_{small}$ is internally set to a value of $1.0 \times 10^-6 \, \frac{l}{s}$ .

Ports

Conserving

Gas conserving port
```
Port_A = Gas;  %
```
Gas conserving port
```
Port_B = Gas;  %
```

Input

Physical control signal
```
yin = {0,'1'}; 
```
The signal $y_{min} \leq y \leq 1$ is used to control the calculated volumetric flow rate.
Physical signal that represents the cross sectional area
```
Ain = {0,'m^2'};
```
Dependencies: The port is only visible when areaInput is set to On.

Output

Physical signal that represents the volumetric flow rate at upstream conditions
```
qout = {1,'l/s'};
```
Dependencies: The port is only visible when flowOutput is set to On.

Parameters

Options

Option to select area input
```
areaInput = OnOff.Off; 
```
On | Off
Option to select flow output
```
flowOutput = OnOff.Off; 
```
On | Off
Option to set check valve
```
checkValve = OnOff.Off; 
```
On | Off

Geometry

Cross sectional area
```
A0 = {0,'m^2'};
```
Dependencies: The parameter is only visible when areaInput is set to Off.

Mass Transport

Number of lost velocity heights
```
n = {1,'1'}; 
```

Minimum Control Signal

ymin = {1.0e-06,'1'}; % Minimum Control Signal

Nomenclature

$F_{i}$	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
$N$	total number of species
$p$	pressure
$q$	volumetric flow rate
$t$	time
$T$	temperature
$x_{i}$	mole fraction of species A_i
$z$	compressibility
$y$	control signal
$\beta$	control signal
$\Phi$	energy flow rate

Bibliography

Sigurd Skogestad (2009). Chemical and Energy Process Engineering, CRC Press.