Numerical Simulation Approach for a Dynamically Operated Sorption-Enhanced Water-Gas Shift Reactor
Abstract
:1. Introduction
- 1.
- Providing synthesis gas (syngas) with a H2/CO ratio of approximately two for the subsequent Fischer–Tropsch synthesis.
- 2.
- Removing the by-product CO2 and refeeding it to the plasma reactor.
- pressurization (feed: reactants);
- reactive adsorption (feed: reactants);
- depressurization (no feed, often purged);
- regeneration (feed: purge gas).
2. SEWGS Model
2.1. Model Development
- Homogeneous distribution of uniformly sized catalyst and sorbent particles according to their weight fraction assumed as one phase
- Uniform gas distribution in the reaction chambers
- Isothermal conditions in the slits
- Negligible pressure drop in the slits
- Constant superficial velocity (which is only the case for sufficient dilution, [27])
- No gradients rectangular to flow direction
- Axial dispersion considered with axial dispersion coefficient
- External mass transfer limitations neglected (Maers criterion)
- Internal mass transfer limitations considered (Weisz–Prater criterion) and implemented with linear driving force (LDF) model (Glueckauf criterion)
- Equilibrium-based desorption of H2O and CO2.
2.2. Model Equations
2.3. Model Parameters
3. Numerical Simulation Approaches
3.1. Built-In Solver
3.2. Method-of-Lines (MoL)
3.3. Simulink
3.3.1. Model Implementation and Data Structure
3.3.2. Solver Selection
3.3.3. Cyclic Process Design
4. Results and Discussion
4.1. Reactive Adsorption
4.2. Process Design
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
The following abbreviations are used in this manuscript: | ||
BFDM | Backward finite difference method of first order | |
CFDM | Centered finite difference method of second order | |
Ch. | Chamber | |
CSTR | Continuously stirred tank reactor | |
DAE | Differential algebraic equation | |
DASOLV | Implicit backward differentiation formula solver in gPROMS | |
DMES | Dimethyl ether synthesis | |
FD | Finite Difference | |
FEM | Finite elements method | |
K-HTC | K2CO3-promoted hydrotalcite | |
LDF | Linear driving force model | |
M1-M4 | Mode 1-4 | |
MoL | Method-of-lines | |
ODE | Ordinary differential equation | |
ode15s | Solver for stiff ODEs in MATLAB | |
PDE | partial differential equation | |
pdepe | Solver for systems of parabolic and elliptic PDEs in MATLAB | |
PLC | Programmable logic controller | |
PSA | Pressure swing adsorption | |
PTSA | Pressure temperature swing adsorption | |
SEWGS | Sorption-enhanced water–gas shift | |
SMR | Steam-methane reforming | |
TSA | Temperature swing adsorption | |
WGS | Water–gas shift | |
The following symbols are used in this manuscript: | ||
activation energy change | () | |
bed void fraction | (–) | |
particle void fraction | (–) | |
stoichiometric reaction coefficient | (–) | |
bulk density | () | |
adsorption rate | () | |
pdepe diagonal matric | (–) | |
bulk phase concentration | () | |
particle void phase concentration | () | |
axial dispersion coefficient | ( ) | |
effective diffusion coefficient | ( ) | |
gas mixture diffusion coefficient | ( ) | |
activation energy | () | |
equilibrium | (–) | |
pdepe flux term coefficient | (–) | |
volumetric flow rate at STP | () | |
h | slit height | (mm) |
standard reaction enthalpy | () | |
i | species CO, H2O, CO2, H2, N2 | (–) |
j | sorption site A, B, C | (–) |
exchange rate coefficient 1 | () | |
exchange rate coefficient 2 | () | |
equilibrium constant | (–) | |
Freundlich adsorption coefficient | () | |
adsorption coefficient | () | |
desorption coefficient | () | |
desorption coefficient | () | |
linear driving force coefficient | () | |
frequency factor | () | |
l | slit length | (mm) |
tiny value exponent | (–) | |
pdepe symmetry constant | (–) | |
n | index variable | (–) |
N | number of cells | (–) |
Freundlich adsorption intensity | (–) | |
O | approximation error | (–) |
pdepe boundary coefficient | (–) | |
(partial) pressure | (bar) | |
pdepe boundary coefficient | (–) | |
sorbent loading of species i on site j | () | |
particle radius | (m) | |
WGS reaction rate | ( ) | |
R | gas constant | ( ) |
pdepe source term coefficient | (–) | |
t | time | () |
T | temperature | () |
u | gas velocity | () |
v | dependent variable | (–) |
w | slit width | (mm) |
catalyst weight fraction | (–) | |
volume fraction | (–) | |
z | axial coordinate | () |
Appendix A
Adsorption / Desorption | |
---|---|
WGS Reaction | |
MoL | pdepe | ||||||
---|---|---|---|---|---|---|---|
Number of Cells | 10 | 30 | 50 | 100 | 200 | 250 | 3000 |
(-) | |||||||
Computation Time | 0.04 | 0.22 | 0.27 | 4.96 | 46.81 | 90.93 | 12.19 |
(min) |
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Reaction | Adsorption | Numerical Solution | Reference |
---|---|---|---|
- | CO2 on K-HTC | MATLAB: MoL (N = 500) / ode15s solver | [13] |
SMR | CO2 on K-HTC | MATLAB: MoL / ode15s solver | [14] |
WGS | CO2 on K-HTC | gPROMS: CFDM (N = 600) / DASOLV solver | [15] |
WGS | CO2 | COMSOL Multiphysics: FEM | [16] |
SMR | CO2 on CaO-mayenite | MATLAB: pdepe solver | [17] |
DMES | H2O on LTA zeolite | MATLAB: MoL (N = 30) / ode15s solver | [18] |
DMES | H2O on LTA zeolite 3A | gPROMS: BFDM (N = 60) / DASOLV solver | [19,20] |
WGS | CO2 on K-HTC | MATLAB: MoL (N = 250) / ode15s solver | [21] |
SMR | CO2 on CaO | MATLAB: pdepe solver | [22] |
- | CO2 on K-HTC | gPROMS | [23] |
General Parameters | |
---|---|
1096 | |
100 | |
Adsorption Parameters | |
p | 8 bar |
T | 250 |
2000 mL / | |
Desorption Parameters | |
p | 1 bar |
T | 250 |
1000 mL / | |
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Stadler, T.J.; Knoop, J.-H.; Decker, S.; Pfeifer, P. Numerical Simulation Approach for a Dynamically Operated Sorption-Enhanced Water-Gas Shift Reactor. Processes 2022, 10, 1160. https://doi.org/10.3390/pr10061160
Stadler TJ, Knoop J-H, Decker S, Pfeifer P. Numerical Simulation Approach for a Dynamically Operated Sorption-Enhanced Water-Gas Shift Reactor. Processes. 2022; 10(6):1160. https://doi.org/10.3390/pr10061160
Chicago/Turabian StyleStadler, Tabea J., Jan-Hendrik Knoop, Simon Decker, and Peter Pfeifer. 2022. "Numerical Simulation Approach for a Dynamically Operated Sorption-Enhanced Water-Gas Shift Reactor" Processes 10, no. 6: 1160. https://doi.org/10.3390/pr10061160
APA StyleStadler, T. J., Knoop, J. -H., Decker, S., & Pfeifer, P. (2022). Numerical Simulation Approach for a Dynamically Operated Sorption-Enhanced Water-Gas Shift Reactor. Processes, 10(6), 1160. https://doi.org/10.3390/pr10061160