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Dynamic Operation of Power-to-X Processes
Demonstrated by Methanol Synthesis
zur Erlangung des akademischen Grades eines
DOKTORS DER INGENIEURWISSENSCHAFTEN
von der KIT-Fakultät für Chemieingenieurwesen und Verfahrenstechnik des
Karlsruher Instituts für Technologie (KIT)
genehmigte
DISSERTATION
von
Florian Nestler
Tag der mündlichen Prüfung: 20.05.2022
Erstgutachter: Prof. Dr.-Ing. Thomas Kolb
Zweitgutachter: Prof. Dr.-Ing. Jürgen Karl
Beharrlichkeit
– Perseverance
ii
Abstract
Chemical energy storage in the context of so-called Power-to-X (PtX) processes will play a
key-role in the future energy system due to the increasing power production from renewable
energy and the urging defossilization of industry and transport sector. Among possible PtX
products, methanol produced from carbon dioxide (CO
2
) and sustainably produced hydrogen
(H
2
) is going to play a key-role due to its high relevance in the global fuel and chemical market.
Compared to conventional methanol synthesis based on fossil feedstocks, methanol synthesis based
on CO
2
-rich gas streams captured from industrial processes, biomass processing or ultimately
captured from air is subjected to decreased equilibrium conversions, inhibited reaction kinetics
and an accelerated catalyst aging. Moreover, the production of H
2
from water electrolysis
operated with renewable power and the coupled CO
2
-supplying industrial process can impose
dynamic fluctuations to syngas supply unknown to the current-state-of-the-art. For these new
boundary conditions, design of the synthesis reactor and operation of the process become more
challenging and do demand for detailed models for each unit operation in the synthesis process.
However, for the kinetic simulation of the synthesis reactor under these conditions only scarce
knowledge exists in the scientific community. Thus, a detailed kinetic description of the reaction
network in industrial reactors is required to enable methanol synthesis from sustainable resources
in the future.
To tackle that deficit, this work used a scale-flexible simulation platform to design a miniplant
facility with the reactor reproducing the thermochemical behavior of an industrial steam cooled
tube bundle reactor with a high agreement. An innovative analytical concept using the highly
resolved fiber optic temperature measurement to analyze the axial temperature profile in the
reactor combined with an FTIR product composition measurement was implemented to derive a
kinetic model for reactor- and process design validated over the complete range of relevant load
conditions for Power-to-Methanol (PtM) processes. Comparison to kinetic models obtained from
literature highlighted both the scientific value of methodical approach implemented in this work
and the high relevance of the herein proposed kinetic model for the practical implementation of
PtM processes. Furthermore, the validation of the dynamic reactor model implemented in this
work by a exemplary load change performed with the miniplant showed a high level of agreement
between the experimental data and the simulation results. Thus, the scientific potential of the
herein proposed miniplant validation approach for the investigation of stationary and dynamically
operated PtX processes could be demonstrated.
iv
Kurzfassung
Chemische Energiespeicher hergestellt im Rahmen von sogenannten Power-to-X (PtX) Prozessen
werden in Zukunft aufgrund des fortschreitenden Ausbaus der Strompoduktion aus regenerativen
Energiequellen und der notwendigen Defossilisierung von Industrie- und Verkehrssektor eine zu-
nehmend wichtige Rolle spielen. Hierbei wird der Methanolsynthese aus Kohlendioxid (CO
2
) und
nachhaltig produziertem Wasserstoff (H
2
) im Energiesystem eine Schlüsselposition zugeschrieben,
da Methanol bereits heute ein wichtiger Baustein im globalen Treibstoff- und Chemiemarkt ist.
Im Vergleich zur konventionellen Methanolsynthese basierend auf fossilen Energieträgern birgt
die Methanolsynthese aus CO
2
-reichen Gasen, welche aus industriellen Prozessen, der Biomasse-
verwertung oder der Luft gewonnen werden, die Problematik schlechterer Gleichgewichtsumsätze,
einer veränderten Reaktionskinetik und der beschleunigten Katalysatordesaktivierung. Zudem
unterliegen die Herstellung von H
2
aus der Wasserelektrolyse mit erneuerbarem Strom und
ggf. die CO
2
-Versorgung aus dem gekoppelten Industrieprozess einer Dynamik, die für die Me-
thanolsynthese eine große Abweichung vom aktuellen Stand der Technik darstellt. Für diese
geänderten Rahmenbedingungen existieren in der wissenschaftlichen Gemeinschaft insbesondere
zur Simulation des Synthesereaktors keine validierten Modelle. Eine detaillierte reaktionskineti-
sche Beschreibung des Reaktionsnetzwerkes in technischen Reaktoren ist daher notwendig, um
die Methanolsynthese aus nachhaltigen Rohstoffen in Zukunft zu ermöglichen.
Um dieses Defizit zu adressieren, wurde in dieser Arbeit mithilfe einer skalenübertragbaren Simula-
tionsplattform eine Miniplantanlage dimensioniert, deren Reaktor das thermochemische Verhalten
eines industriellen dampfgekühlten Rohrbündelreaktors mit hoher Übereinstimmung abbildet. Ein
neuartiges Messkonzept bestehend aus einer hochaufgelösten faseroptischen Temperaturmessung
zur Erfassung des axialen Temperaturprofils im Reaktor sowie einer FTIR-Produktanalyse wurde
implementiert, um ein Kinetikmodell für das Reaktor- und Prozessdesign abzuleiten, welches
über den gesamten für Power-to-Methanol (PtM) Prozesse relevanten Parameterbereich validiert
wurde. Der Vergleich zu Kinetikmodellen aus der Literatur demonstrierte deren Limitierungen
und zeigte den Mehrwert des in dieser Arbeit implementierten methodischen Ansatzes sowie die
Relevanz des neuen Kinetikmodells zur praktischen Umsetzung von PtM Verfahren. Darüber
hinaus zeigte die Validierung des im Rahmen dieser Arbeit aufgestellten dynamischen Modells
anhand eines exemplarischen Lastwechsels an der Miniplant eine hohe Übereinstimmung zwischen
experimentellen Daten und Simulationsergebnissen. Somit konnte die hohe wissenschaftliche
Relevanz des vorgestellten Miniplant-Validierungsansatzes für die Untersuchung des stationären
und dynamischen Reaktorverhaltens von PtX Synthesen gezeigt werden.
v
Contents
Abstract ............................................. iv
Kurzfassung ........................................... v
Notation ............................................. ix
List of Figures .......................................... xv
List of Tables ........................................... xix
1 Introduction ......................................... 1
2 Literature Review and Scientific Approach ........................ 4
2.1 Significance of methanol as a commodity chemical . . . . . . . . . . . . . . . . . 4
2.2 Properties of the synthesis gas for methanol synthesis . . . . . . . . . . . . . . . 5
2.2.1 Carbonoxideratio............................... 6
2.2.2 Stoichiometricnumber............................. 6
2.2.3 Inertgasfraction................................ 7
2.2.4 Impurities.................................... 7
2.3 Feedstocks used for methanol synthesis . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Coal, biomass and refinery residues . . . . . . . . . . . . . . . . . . . . . . 7
2.3.2 Naturalgas................................... 8
2.3.3 Alternative feedstocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.4 Classification of make-up-gases . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Technological overview on methanol synthesis . . . . . . . . . . . . . . . . . . . . 12
2.4.1 Reaction conditions and equilibrium . . . . . . . . . . . . . . . . . . . . . 12
2.4.2 Synthesisprocess................................ 15
2.4.3 Reactorconcepts................................ 18
2.4.4 Dynamicoperation............................... 20
2.4.5 Capability of reactor types for dynamic operation . . . . . . . . . . . . . . 22
2.5 Kinetic validation in methanol synthesis . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 Problem definition and scientific approach . . . . . . . . . . . . . . . . . . . . . . 26
3 Materials and Methods ................................... 29
3.1 Simulationplatform .................................. 29
3.1.1 Heattransfermodel .............................. 30
3.1.2 Kineticmodels ................................. 37
3.1.3 Diffusionmodel................................. 41
3.1.4 Steady state reactor model . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1.5 Dynamic reactor model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1.6 Process simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
vi
Contents
3.2 Numericalmethods................................... 44
3.2.1 Optimization methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Scale-down of the industrial reactor . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4 Miniplantsetup..................................... 49
3.4.1 Fiber optic temperature measurement . . . . . . . . . . . . . . . . . . . . 51
3.5 Experimentalvalidation ................................ 54
3.5.1 Integral literature data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.5.2 Differential miniplant data . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4 Results and Discussion ................................... 60
4.1 Kinetic model derived from integral literature data . . . . . . . . . . . . . . . . . 60
4.1.1 Analysis of the reaction rates . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1.2 Comparison of reactor simulations . . . . . . . . . . . . . . . . . . . . . . 65
4.1.3 Concluding remarks on the integral kinetic model . . . . . . . . . . . . . . 69
4.2 Kinetic model derived from differential miniplant data . . . . . . . . . . . . . . . 70
4.2.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2.2 Validation of literature kinetics . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2.3 Fittedkineticmodel .............................. 76
4.2.4 Impact on industrial scale . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2.5 Co-verification of the kinetic model Nestlerdiff ................ 80
4.2.6 Optimal design for the miniplant setup . . . . . . . . . . . . . . . . . . . 81
4.2.7 Concluding remarks on the differential kinetic model . . . . . . . . . . . . 82
4.3 Validation of the dynamic reactor model . . . . . . . . . . . . . . . . . . . . . . . 84
4.4 Application on process scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5 Conclusion and Outlook .................................. 94
Bibliography ........................................... 98
Acknowledgements .......................................120
Verification of the contribution of co-authors ........................121
Publication list .......................................... 125
Appendix ............................................. A
A.1 Derivation of the equilibrium constant . . . . . . . . . . . . . . . . . . . . . . . . A
A.2 Literature use of kinetic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . C
A.3 Industrial reactor data available in scientific literature . . . . . . . . . . . . . . . C
A.4 Cell model for heat transfer inside the packed bed . . . . . . . . . . . . . . . . . D
A.5 Sensitivity of Thiele modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E
A.6 Experimental data used for integral kinetic model . . . . . . . . . . . . . . . . . . G
A.7 CAD drawing of the miniplant setup . . . . . . . . . . . . . . . . . . . . . . . . . L
A.8 Measurement of thermal oil flow rate . . . . . . . . . . . . . . . . . . . . . . . . . M
vii
Table of contents
A.9 Thermophysical properties of the thermal oil . . . . . . . . . . . . . . . . . . . . N
A.10 Analysis of the catalyst particle size distribution . . . . . . . . . . . . . . . . . . O
A.11 Purity of the gases used within the miniplant experiments . . . . . . . . . . . . . O
A.12 Overview on the experimental campaign executed on the scale down miniplant . P
A.13 Experimental data obtained from the miniplant experiments . . . . . . . . . . . . S
A.14 Mass balances of the miniplant experiments . . . . . . . . . . . . . . . . . . . . . AB
A.15Axialdeactivation ................................... AC
A.16 NMR liquid phase measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . AD
A.17KineticmodelbyGraaf ................................ AE
A.18 Kinetic model by Bussche . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AH
A.19KineticmodelbyPark................................. AJ
A.20KineticmodelbyHenkel................................ AL
A.21 Alternative kinetic approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . AN
A.22 Single versus global data fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . AP
A.23 Comparison of experimental and simulated gas phase composition data . . . . . AR
A.24 Dynamic simulation study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AS
viii
Notation
Abbreviations
ATR Autothermal reforming
BFG Blast furnace gas
BOFG Basic oxygen furnace gas
CAGR Compound annual growth rate
COG Coke oven gas
CCU Carbon cature and utilization
CRI Carbon Recycling International
DAC Direct air capture
DIPPR Design Institute for Physical Properties
DME Dimethyl ether
EoS Equation of state
FTIR Fourier-transform infrared spectrometer
GHG Greenhouse gas
ICI Imperial Chemical Industries
LCA Life cycle assessment
LPG Liquefied petroleum gas
MTBE Methyl tert-butyl ether
MTO Methanol-to-olefin
MTP Methanol-to-propylene
MUG Make-up gas
NIST National Institute of Standards and Technology
NMR Nuclear magnetic resonance spectroscopy
NG Natural gas
ODE Ordinary differential equation
PDE Partial differential equation
POx Partial oxidation
PtM Power-to-Methanol
PtX Power-to-X
RDS Rate determining step
RMSE Root mean square error
rWGS Reverse water-gas-shift
SMR Steam methane reforming
SRK Soave-Redlich-Kwong
ToS Time on stream
VDI Verein Deutscher Ingenieure
WGS Water-gas-shift
ix
Notation
Symbols (Latin)
Symbol Designation Unit
aiParameter variable unit
ARCross sectional area m2
BDeformation parameter -
Bo Bodenstein number -
CfShape factor -
COR Carbon oxide ratio -
cpSpecific heat capacity J kg-1 K-1
˜cpSpecific molar heat capacity J mol-1 K-1
dDiameter m
Dax Axial diffusion coefficient m2s-1
Dj,k Binary diffusion coefficient between component j and k m2s-1
DK,j Knudsen diffusion coefficient of component j m2s-1
De
m,j Effective diffusion coefficient of component j m2s-1
EQiEquilibrium term of reaction i -
fjFugacity of component j Pa
f(x)Objective function variable unit
GGibbs free energy J mol-1
GHSV Gas hourly space velocity h-1
hHeight m
∆H0
REnthalpy of formation under standard conditions kJ mol-1
kbed Reduced thermal conductivity of the catalyst bed -
kc
Reduced thermal conductivity of the core of the unit cell (see Ap-
pendix A.4)
-
Keq Equilibrium constant variable unit
K′
eq Pseudo equilibrium constant -
kiReaction rate constant of reaction i variable unit
k′
iPseudo-first-order rate constant of reaction i
mol s
-1
m
-3
Pa
-1
KjAdsorption constant of component j variable unit
kpReduced thermal conductivity of the catalyst particle -
KrReciprocal of the slope parameter -
LCE Loop carbon efficiency %
LCEext External hydrogen efficiency %
LCEint Internal hydrogen efficiency %
MjMolar mass of component j kg mol-1
NNumber -
x
Notation
Symbol Designation Unit
˙njMolar flow of component or stream j mol s-1
Nu Nusselt number -
pPressure Pa
prRelative pressure -
P e0Molecular Péclet number -
P r Prandtl number -
˙qHeat flow density W m-2
RUniversal gas constant J mol-1 K-1
Re Reynolds number -
RepReynolds particle number -
riReaction velocity of reaction i mols-1 kgcat -1
RMSE Root mean square error variable unit
RR Recycle ratio -
siActive site number i -
SMeOH Selectivity towards methanol -
SN Stoichiometric number -
ST Y Space time yield
kg
MeOH
l
cat-1
s
-1
tTime s
TTemperature K
UOverall heat transfer coefficient W m-2 K-1
uVelocity m s-1
u0Empty tube velocity m s-1
VVolume m3
˙
VjVolumetric flow rate of component j m3s-1
xjMass fraction of component j -
XCCarbon conversion -
YCCarbon yield -
yjMolar fraction of component j -
zAxial length m
Symbols (Greek)
Symbol Designation Unit
αConvective heat transfer coefficient W m-2 K-1
∆Difference -
xi
Notation
Symbol Designation Unit
εPorosity -
ζiReaction progress coefficient of reaction i mol s-1
ηeff,j Efficiency factor of component j -
λbed Radial heat conductivity of catalyst bed without fluid flow W m-1 K-1
λc
Radial heat conductivity of the core of the unit cell (see Ap-
pendix A.4)
W m-1 K-1
λrad Radial heat conductivity of flowed-through catalyst bed W m-1 K-1
λwall Heat conductivity of reactor wall W m-1 K-1
νfKinematic viscosity of fluid m2s-1
νjStoichiometric factor of component j -
ρDensity kg m-3
τTortuosity -
φReactor-particle diameter ratio -
ϕM,j Thiele modulus of component j -
Indices
Symbol Designation
∞Infinite
ann Annular
bBoiling
bulk Bulk
cat Catalyst
calib Calibrated
CO Carbon monoxide (-hydrogenation)
CO2Carbon dioxide (-hydrogenation)
CO2, eq CO2-equivalent
comp Components
cool Coolant
crit Critical
data pt Experimental data points
diff Differential
eff Efficient
eq Equilibrium
exp Experimental
xii
Notation
Symbol Designation
ext External
fFluid phase
feed Reactor feed
flash At flash separator
gGas phase
H2Hydrogen
H2OWater
hs Hot spot
hydr Hydraulic
iCounting index (reaction, data point)
in At inlet
inc Increment
ind Industrial scale
inert Inert gas
int Internal
integ Integral
jCounting index (component, axial increment)
kCounting index (component)
lLiquid phase
min Minimal
miniplant Miniplant scale
max Maximal
MeOH Methanol
MUG Make-up gas
norm Norm conditions
oil Thermal oil
original Original
out At outlet
pParticle
prof il Profile
purge Purge gas
RReactor
recycle Recycle gas
ref Reference condition
rW GS Reverse water-gas-shift-reaction
shell Shell
sim Simulated
TTemperature
tubes Reactor tubes
xiii
Notation
Symbol Designation
wall Reactor wall
yMolar composition
xiv
List of Figures
1.1 Schematic flow diagram of the Power-to-Methanol process chain. . . . . . . . . . 1
2.1
Worldwide consumption of methanol divided by the sectors fuel, methanol-to-
olefin/methanol-to-propylene and traditional derivatives. . . . . . . . . . . . . . . 5
2.2 Gas composition of steel mill gas streams. . . . . . . . . . . . . . . . . . . . . . . 10
2.3
Comparison of the estimated inert gas content and COR of syngas obtained from
conventional and alternative feedstocks conditioned for methanol synthesis. . . . 11
2.4 Carbon yield of methanol at equilibrium over temperature. . . . . . . . . . . . . 14
2.5 Basic scheme of a methanol synthesis process. . . . . . . . . . . . . . . . . . . . . 16
2.6
Comparison of LCE, LHE
ext
, and LHE
int
computed with varied COR in the MUG
at constant loop conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.7 Main types of industrially applied methanol synthesis reactors. . . . . . . . . . . 19
2.8
Number of publications in the literature data base generated in this work over
decades for experimental work as well as simulation work. . . . . . . . . . . . . . 21
2.9 Exemplary simulation of a multi-bed adiabatic quench bed reactor. . . . . . . . . 23
2.10
Range of experimental validation conditions applied by Graaf, Bussche, Henkel
andPark. ........................................ 25
3.1 Simulation platform applied in this work. . . . . . . . . . . . . . . . . . . . . . . 29
3.2
External heat transfer coefficient calculated using the correlations by Fritz, Holman
and VDI Heat Atlas over the temperature difference between wall and cooling fluid.
35
3.3
Sensitivity of the parameters of the heat transfer model towards the overall heat
transfercoefficient.................................... 37
3.4 Speed-up of the simulation platform exemplified by a sensitivity analysis. . . . . 44
3.5 Simplified flow sheet of the experimental miniplant setup. . . . . . . . . . . . . . 50
3.6
Calibration offset over the calibrated temperature between 50
◦
C and 265
◦
C
together with the fitted 3rd-order polynomial extrapolated to 25 ◦C and 300 ◦C. . 52
3.7
Calibrated and Savitky-Golay smoothed temperature profile measured by the fiber
opticprocessingunit................................... 53
3.8 Illustration of the parameter fitting methodology applied in this work. . . . . . . 58
4.1
Parity plot of the kinetic model fitted to the measured data published by Park et
al.[203]. ......................................... 60
4.2
Arrhenius plot of the kinetic constants k
1
, k
2
, K
1
, K
2
, and K
3
for the Nestler
integ
model in comparison to those calculated with the model by Henkel. . . . . . . . . 62
4.3 Reaction rates of the kinetic models considered within this study. . . . . . . . . . 63
4.4
Carbon conversion over COR in the reactor feed for the kinetic models by Graaf,
Bussche, Henkel and the Nestlerinteg model at a reaction pressure of 50 bar. . . . 64
xv
List of Figures
4.5
Comparison of the one-dimensional temperature and product molar fraction profiles
obtained by a reactor simulation at COR= 0.75, SN = 3.0, GHSV = 10,000 h-1 at
a pressure of 65 bar utilizing the kinetic model by Bussche and the Nestler
integ
kineticmodel....................................... 66
4.6
Sensitivity study discussing the hot spot temperatures and positions obtained
from the simulation of an industrial scale tubular reactor with the kinetic models
by Graaf, Bussche and Henkel (Berty) as well as with the Nestler
integ
kinetic model.
67
4.7 Trend of the space time yield over time-on-stream at benchmark conditions. . . . 71
4.8
Equilibrium and measured molar fraction of methanol and water at COR= 0.7
andCOR=0.95. .................................... 72
4.9
Hot spot temperature measured at COR = 0.7 and COR= 0.95 and GHSV = 12,000 h
-1
.
73
4.10
Parity plots for the outlet molar fractions of methanol and water as well as hot
spot temperature and axial hot spot position; Experiments were carried out with
the miniplant setup; Simulation was performed using the kinetic models by Graaf
and Bussche as published as well as the Nestlerinteg kinetic model. . . . . . . . . 74
4.11
Parity plots of the refitted kinetic model Nestler
diff
for outlet molar fractions of
methanol and water as well as hot spot temperature and axial hot spot position;
Experiments were carried out with the miniplant setup. . . . . . . . . . . . . . . 78
4.12
Sensitivity study discussing the behavior of the kinetic models Nestler
integ
and
Nestler
diff
by means of hot spot temperature and position as well as product molar
fraction of methanol and water at a synthesis pressure of 50bar and 80 bar in the
range 0.7 ≤COR ≤0.98, 2.0 ≤SN ≤8.0 at GHSV = 6,000 h-1 ............. 79
4.13
Parity plot comparing the kinetic model Nestler
diff
fitted to the miniplant experi-
mental data to the integral experimental data published by Park et al.[203]. . . . 81
4.14
Optimized inner reactor diameter of the miniplant over COR and SN at GHSV =9,000 h
-1
and T
cool
= 240
◦
C for maximized comparability towards the industrial reactor at
50barand80bar..................................... 82
4.15
Smoothened temperature profiles obtained from the miniplant experiments and
simulated temperature profiles using the kinetic models by Graaf [192], Buss-
che[145] as well as the kinetic model Nestlerinteg and Nestlerdiff ........... 83
4.16
Shift of the temperature profile during a load change from COR = 0.8; SN = 2.0;
GHSV = 6,000 h
-1
to COR = 0.9; SN = 4.0; GHSV = 12,000 h
-1
at 80 bar and a
cooling temperature of 240 ◦C. ............................ 85
4.17
Comparison of experimental and simulation data obtained during a load change
using different heat capacities for the catalyst particle. . . . . . . . . . . . . . . . 88
4.18 Sensitivity of SNMUG and RR on the operating condition of the process. . . . . . 90
4.19 Sensitivity of SNMUG and RR on the operating condition of the process. . . . . . 92
A.1
Literature use of the kinetic models by Bussche [145] and Graaf [192] over decades
since1980......................................... C
A.2 Schematic of the unit cell model as defined by Zehner and Schlünder[213]. . . . . D
xvi
List of Figures
A.3
Intrinsic reaction rate of CO
2
-hydrogenation (r
CO2
) and rWGs (r
rWGS
) simulated
with the kinetic model Nester
diff
as well as the efficiency factor calculated by
Thiele modulus for an ideal isothermal reactor. . . . . . . . . . . . . . . . . . . . E
A.4 Sensitivity analysis of efficiency factor calculated using Thiele modulus . . . . . . F
A.5
Experimental data published by Park et al.[203] classified with regard to synthesis
pressure, reactor temperature, GHSV CORfeed and SNfeed.............. K
A.6 CAD drawing of the miniplant setup with its most important components[250]. . L
A.7
Measurement and simulation of the system characteristic curve of the miniplant
setup at 130 ◦C, 200 ◦C and 250 ◦C........................... M
A.8
Temperature-compensated volumetric flow rate obtained in the thermal oil cycle
at constant rotational speed of the thermostat pump shaft between 130
◦
C and
250 ◦C thermal oil temperature [260]. . . . . . . . . . . . . . . . . . . . . . . . . . M
A.9 Thermophysical properties of the thermal oil used in the miniplant setup. . . . . N
A.10
Particle size distribution of the catalyst obtained by a flotation measurement using
the Laser Diffraction Particle Size Analyzer LS 13 320 by Beckman Coulter. . . . O
A.11 C-/H-/O- balance of the miniplant experimental points used within this study. . AB
A.12
Temperature profile at benchmark point at beginning of the experimental cam-
paign, after 25 h, 50 h, 75h as well as 100 h. . . . . . . . . . . . . . . . . . . . . . AC
A.13 NMR measurement of a liquid product sample. . . . . . . . . . . . . . . . . . . . AD
A.14
Parity plots of the refitted model "Graaf
fit
" for outlet molar fractions of methanol
and water as well as hot spot temperature and axial hot spot position; Experiments
were carried out with the miniplant setup. . . . . . . . . . . . . . . . . . . . . . . AG
A.15
Parity plots of the refitted model "Bussche
fit
" for outlet molar fractions of methanol
and water as well as hot spot temperature and axial hot spot position; Experiments
were carried out with the miniplant setup. . . . . . . . . . . . . . . . . . . . . . . AI
A.16
Remaining objective function with respect to Eq. 3.79 obtained for the kinetic
models Bussche
fit
, Graaf
fit
and Nestler
diff
as well as for all possible combinations
ofEq.A.89untilEq.A.96................................ AO
A.17
Sensitivity analysis of the objective function defined in Eq.3.79 on the kinetic
parameters
Ak1
and
Bk1
as well as
Ak2
and
Bk2
simulated for all experimental
data points with the kinetic model Nestlerfit. .................... AP
A.18
Sensitivity analysis of the objective function defined in Eq. 3.79 on the adsorption
parameters
AK1
and
BK1
,
AK2
and
BK2
as well as
AK3
and
BK3
simulated for
all experimental data points with the kinetic model Nestlerfit............ AQ
A.19 Gas phase compositions obtained from the miniplant experiments and simulated
using the kinetic models by Graaf [192], Bussche [145] as well as the kinetic model
Nestlerinteg and Nestlerdiff ............................... AR
A.20
Development of the reactor’s space time yield and hot spot temperature during a
load reduction from GHSV = 10,000 h-1 to GHSV = 4,000 h-1 . ........... AT
A.21
Development of the reactor’s temperature profile during a load reduction from
GHSV = 10,000 h-1 to GHSV = 4,000 h-1 . ....................... AU
xvii
List of Tables
3.1 Kinetic parameters proposed by Graaf et al. [193]. . . . . . . . . . . . . . . . . . . 39
3.2 Kinetic parameters proposed by Bussche et al.[145]. . . . . . . . . . . . . . . . . 40
3.3
Kinetic parameters fitted by Henkel for the Berty reactor and the micro fixed bed
reactor[202]. ...................................... 40
3.4
Characteristic catalyst properties for the calculation of Thiele modulus determined
byHenkel[202]...................................... 41
3.5
Design parameters of the Shiraz methanol synthesis reactor based on scientific
literature[74]....................................... 47
3.6
Design parameters determined for the miniplant setup determined by the simulation-
based scale-down and experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.7 Dimensionless index numbers for the industrial and the miniplant reactor. . . . . 48
3.8 Parameters applied for the experimental campaign at the miniplant setup. . . . . 55
4.1 Parameters for the Nestlerinteg kinetic model proposed within this work. . . . . . 61
4.2
Comparison of the RMSE for the molar fractions measured by Park and simulated
using the kinetic models by Graaf, Bussche and Henkel as well as the kinetic model
Nestlerinteg. ....................................... 61
4.3 Parameter set varied within the sensitivity study in this section. . . . . . . . . . 65
4.4
Objective function and RMSEs calculated between the experimental data and the
reactor simulations using the original kinetic models by Graaf and Bussche as well
as the Nestlerinteg kineticmodel. ........................... 75
4.5
Objective function and RMSEs calculated between the experimental data and the
reactor simulations using the fitted kinetic models. . . . . . . . . . . . . . . . . . 76
4.6 Parameters for the kinetic model Nestlerdiff...................... 77
4.7
Comparison of the RMSE for the measured molar fractions published by Park[203]
and the simulated molar fractions utilizing the kinetic models Nestler
integ
and
Nestlerdiff......................................... 80
A.1
Design parameters for steam cooled tube bundle reactors available in scientific
literature. ........................................ C
A.2
Experimental data taken from Park et al.[203] that was used for the integral
kinetic model Nestlerinteg. ............................... G
A.3 Supplier and purity of the technical gases used for the miniplant experiments. . . O
A.4 Chronological progress of the experimental campaign. . . . . . . . . . . . . . . . P
A.5
Experimental data obtained during the steady state experiments at the miniplant
setup. .......................................... S
A.6 Original kinetic parameters proposed by Graaf et al. [193]. . . . . . . . . . . . . . AF
A.7 Kinetic parameters for the Graaffit model obtained with the miniplant setup. . . AF
A.8 Original kinetic parameters proposed by Bussche et al. [145]. . . . . . . . . . . . . AH
xix
List of tables
A.9 Kinetic parameters for the Busschefit model obtained with the miniplant setup. . AI
A.10 Kinetic parameters proposed by Park et al. [203, 261]. . . . . . . . . . . . . . . . AK
A.11
Kinetic parameters fitted by Henkel for the Berty reactor and the micro fixed bed
reactor[202]. ...................................... AL
A.12
Fitted parameters for the Nestler
integ
kinetic model obtained from the measured
databyParketal.[203].................................AM
A.13
Fitted parameters for the Nestler
diff
kinetic model obtained from the miniplant data.
AM
xx
1 Introduction
The international commitment to mitigate greenhouse gas emissions with the aim of limiting
anthropogenic global warming to less than 2K has triggered political efforts to implement zero
CO
2
emission technologies in many countries [1, 2]. As the share of renewable power production in
the electric grid increases, the need for a so-called defossilization of other sectors as transportation
as well as heavy industries, e.g. steel production, and chemical industry arises to further reduce
carbon dioxide (CO
2
) emissions. The avoidance of fossil fuels in these sectors will inevitably lead
to their substitution by electric energy produced with a low greenhouse gas (GHG) footprint.
Nuclear accidents as the disaster of Fukushima in 2011 have forced many governments to
reconsider their view on nuclear power production, creating new perspectives for renewable
energy sources as solar-, wind-, biomass-, or hydropower [3]. However, as renewable energy
power plants rely on natural resources with fluctuations determined by weather, daytime, seasons
and location, strategies for their storage and distribution need to be examined. Hydrogen (H
2
)
produced by water electrolysis operated with renewable energies was recently politically identified
as a promising molecular platform for large-scale energy storage [4, 5].
Figure 1.1: Schematic flow diagram of the Power-to-Methanol process chain.
Chemical conversion of H
2
to molecules with enhanced properties for handling and transportation,
e.g. increased energy densities, opens manifold possibilities for H
2
-derived energy carriers and
base chemicals. As these H
2
carriers vary in molecular nature, aggregate phase and physical prop-
erties, their synthesis processes are collectively referred to as "Power-to-X" (PtX) technologies[6].
Among the currently most discussed H
2
carrier molecules range ammonia (NH
3
) [7], methane
(CH
4
) [8], light hydrocarbons, dimethyl ether (DME) as well as methanol (MeOH)[9]. Many
of the chemical processes to produce these chemicals are among the oldest known to chemical
industry, e.g. Sabatier (CH
4
), Haber-Bosch (NH
3
), methanol synthesis and Fischer-Tropsch
(hydrocarbons) [10]. However, the transition of these processes currently operated with fossil
energy carriers towards sustainable feedstocks supplied by renewable energy and off-gases from
1
1 Introduction
industrial processes demands for manifold research activities.
Among possible PtX products, methanol is one of the most promising candidates for a techno-
logical application as the synthesis is operated at moderate process conditions, it is a liquid at
ambient conditions and provides access to a worldwide trade infrastructure related to the fuel and
chemical market[10, 11]. Besides economical barriers due to the comparably high production costs
for electrolytic H
2
[12, 13] and the low prices for fossil feedstocks, some technological challenges
prevent so-called "Power-to-Methanol" (PtM) processes from their industrial implementation[14].
Today methanol is commercially produced from carbon monoxide (CO)-rich synthesis gas (syngas)
derived from gasification of coal or heavy oil residues as well as reforming of natural gas. Opposed
to that, sustainable methanol synthesis is based on electrolytic H
2
and CO
2
captured from indus-
trial processes, biomass fermentation or from the air. High CO
2
contents are known to negatively
affect the reaction kinetics, the chemical equilibrium as well as catalyst lifetime in methanol
synthesis. Moreover, fluctuations in syngas quality and/or quantity caused by intermittent avail-
ability of renewable power or load changes in the coupled CO
2
supplying process are unknown to
state-of-the-art methanol processes, conventionally operated at steady state (compare Fig.1.1).
The usage of gas buffer tanks would be an option to prevent dynamic load changes in the syngas
generation from breaking through to the stationary operated methanol synthesis process. However,
the extensive application of buffer tanks was shown to be economically detrimental [15]. Dynamic
operation of the methanol synthesis process could be feasible, though, for this option a better
understanding of the behavior of the synthesis reactor under transient load conditions is necessary.
This work aims to contribute to the technological implementation of PtM processes from
CO
2
-rich gas streams under steady state and dynamic load conditions. To obtain in-depth
insights into the kinetic behavior of a dynamically operated synthesis reactor, an experimental
miniplant setup featuring a highly resolved axial temperature measurement was designed, built
and operated within this work with the aim to reflect the thermochemical conditions in an
industrial scale reactor. Based on the comprehensive set of steady state experimental data
obtained from this setup an enhanced differential kinetic model was derived. Comparison of this
model to an integral kinetic model derived from an isothermal fixed bed reactor for a similar
catalyst as well as towards important scientific literature standard kinetic models was executed
to demonstrate the significance of this work. Finally, the differential kinetic model derived under
steady state conditions was integrated into a dynamic simulation model and validated against
data from a representative load change experiment on the miniplant setup.
2
2 Literature Review and Scientific Approach
Patented in 1923, methanol synthesis is one of the oldest thermochemical high pressure pro-
cesses [14]. In order to maximize catalyst selectivity and productivity, methanol synthesis was
subject of numerous scientific studies in the past century[10, 11, 16]. The long scientific and
industrial history of the process shows the necessity of a comprehensive literature survey to
identify the scientific potential and ensure the novelty of the herein conducted work.
The composition of the make-up gas (MUG) fed into the process emerges as one main difference
between conventional and renewable methanol synthesis. Therefore, a technological overview
presenting key indicators for the gas composition will be provided in Sec. 2.2. These key indicators
are then applied to the most important feedstocks from conventional and renewable sources in
Sec. 2.3.
As a strong feedback between research in methanol synthesis and the technological application
exists, Sec. 2.4 will deal with the current state-of-the-art in methanol synthesis technology –
practical limitations caused by chemical equilibrium and the narrow thermal operational window
of methanol synthesis are related to process and reactor scale. This discussion finally leads to a
discrimination of different reactor types for dynamic operation of methanol synthesis.
As the kinetic modeling was identified one key-challenge for the simulative description of methanol
synthesis, state-of-science in reaction kinetics and the validation of kinetic models in methanol
syntheses will be presented in Sec.2.5. The overall scientific approach of this work is then
summarized in Sec. 2.6.
2.1 Significance of methanol as a commodity chemical
With an annual consumption of 105Mt estimated for 2019 [17], methanol is after ammonia
(182 Mt a
-1
[18]) and ethylene (160 Mt a
-1
[19]) one of the most important base chemicals on the
world market.
In Fig. 2.1 the development of world-wide methanol production is given divided by sectors
according to a study published by IHS Markit[20]. In this graph, traditional derivatives are
mainly considered formaldehyde and acetic acid, while fuels are regarded as dimethyl ether
(DME), methyl tert-butyl ether (MTBE) as well as direct blend in gasoline [20]. The trends of
both fuel market and traditional derivatives show a steady increase over time. From 2012 the
application of so-called methanol-to-olefin (MTO) and methanol-to-propylene (MTP) processes
started developing a significant share in methanol consumption[17]. These processes are operated
with the goal of producing ethylene and propylene from coal-based methanol instead of mineral
oil and natural gas. Similar to the application of methanol in the fuel sector, this development
was mainly driven by China with the aim of substituting mineral oil by local coal and lignite
reserves.
Independently of the utilization chain, methanol production was responsible for 7.2 % of the green
house gas (GHG) emission of the chemical industry in 2010, with an average cradle-to-gate GHG
4
2 Literature Review and Scientific Approach
Figure 2.1:
Worldwide consumption of methanol divided by the sectors fuel, methanol-to-olefin
(MTO)/methanol-to-propylene (MTP) and traditional derivatives[17, 20].
footprint of 1.55 t
CO2,eq
t
MeOH-1
[21]. Transfer of this footprint to the CO
2
emissions and methanol
production in 2019, makes methanol production responsible for approximately 0.4 % of the global
GHG emissions [22]. These numbers emphasize the necessity for carbon-neutral technologies for
methanol production in the future. The use of CO
2
captured from industry off-gases, e.g. the
cement or steel industry as well as biomass processing or direct air capture (DAC) could deliver
CO
2
-neutral or even negative possibilities for methanol production. H
2
production by water
electrolysis operated with renewable energy or by methane pyrolysis were identified as sustainable
pathways for H
2
production [15, 23, 24]. The main differences in gas composition and supply of
these sustainable feedstocks compared to their conventional counterpart will be elaborated in the
following sections.
2.2 Properties of the synthesis gas for methanol synthesis
Methanol synthesis on commercial Cu/ZnO/Al
2
O
3
catalysts is macroscopically observed via
the following equilibrium-limited exothermal reactions including CO
2
-hydrogenation (Eq. 2.1),
water-gas-shift (WGS) (Eq. 2.2) and CO-hydrogenation (Eq. 2.3) [25]:
CO2(g)+ 3H2(g)⇄CH3OH(g)+H2O(g)∆H0
R=−50 kJ mol−1(2.1)
CO(g)+H2O(g)⇄CO2(g)+H2(g)∆H0
R=−41 kJ mol−1(2.2)
CO(g)+ 2H2(g)⇄CH3OH(g)∆H0
R=−91 kJ mol−1(2.3)
5
2 Literature Review and Scientific Approach
Radiolabeling studies by several research groups proved that methanol mainly originates from
CO
2
-hydrogenation, whereas the direct hydrogenation of CO does scarcely proceed [26, 27].
Hence, CO conversion towards methanol can be considered as WGS with subsequent CO
2
-
hydrogenation[28, 29]. However, the interplay between CO and CO
2
in methanol synthesis is
even today a controversial topic in the scientific community[14].
The quality of the synthesis gas (syngas) plays an important role in the design of both, methanol
synthesis processes and reactors. The following four main factors can be considered concerning
syngas composition.
2.2.1 Carbon oxide ratio
The methanol synthesis process can be designed for different ratios of the molar fractions of CO
2
(y
CO2
) and CO (y
CO
) in the syngas. The carbon oxide ratio (COR) is defined as follows [30–33]:
COR =yCO2
yCO2+yCO
(2.4)
Based on the reaction enthalpies of Eq. (1) and (3), the overall temperature rise in the reactor
decreases with increasing COR. As an equimolar amount of H
2
O is produced during the conversion
of CO
2
, H
2
-consumption of methanol synthesis increases with COR. Several research groups
observed that an increased H
2
O content in the reactor enhances deactivation of the catalyst
and decreases catalyst activity[32, 34–37]. For these reasons COR is kept as low as possible in
conventional applications.
However, as the direct hydrogenation of CO does scarcely occur on commercial catalysts, a
certain amount of CO
2
(or water) needs to be present in the reactor feed to enable the WGS
reaction and, thus, CO conversion to methanol on Cu/ZnO/Al
2
O
3
catalysts [30, 31, 34, 38–41]. A
maximum methanol formation rate was experimentally observed by various researchers at a CO
2
mole fraction of approximately 2mol.-% in the reactor feed [28, 30, 31, 38, 42–48]. With a further
increase in CO
2
content, the reaction rate of the methanol synthesis is known to decelerate and
the equilibrium yield decreases [49, 50]. The distribution and amount of side-products is also
known to depend on the COR - typically more carbonaceous side-products are formed with
decreasing COR [35, 51, 52].
2.2.2 Stoichiometric number
As the conversion of CO and CO
2
to methanol demand for different molar ratios of H
2
, a measure
of the stoichiometry, the stoichiometric number (SN), is defined by the molar fractions of H
2
(yH2), CO and CO2in the syngas [53]:
SN =yH2−yC O2
yCO +yC O2
(2.5)
For a stoichiometric conversion SN = 2 is necessary. Most methanol synthesis processes are known
to operate at slightly increased H
2
content[11, 54]. Nevertheless some processes employ an excess
of H
2
with SN
≤
3 (see Sec. 2.3.2). A high stoichiometric number can be lowered via the addition
6
2 Literature Review and Scientific Approach
of CO or CO
2
, providing room for a capacity revamp. SN < 2 should be avoided, as a H
2
shortage
in the syngas is known to promote the formation of undesired byproducts[10, 55].
2.2.3 Inert gas fraction
Inert gases are components that do not contribute to the synthesis reactions. Thus, their effect
on process design is limited to a dilution, in turn lowering the partial pressures of the reactants.
On the other hand, the presence of inert gases can be useful to lower the temperature rise in the
reactor. A high inert gas fraction in the syngas leads to an accumulation of inert components in
the recycle loop of a methanol synthesis process (see Sec. 2.4.2), which has to be compensated by
either increasing the recycle ratio or the purge fraction, in turn negatively influencing overall
process economics [56, 57]. Therefore, the inert gas content in the syngas should be kept as low
as possible in order to minimize methanol production costs [58]. Common inert gases in the
methanol process are nitrogen (N2) and methane (CH4), but also argon (Ar) or helium (He).
2.2.4 Impurities
In contrast to inert components, impurities in this work are referred to as all species originating
from the feedstock and influencing the synthesis reaction, i.e. without being a main reactant.
Most impurities have an inhibiting or deactivating effect on the catalyst, e.g. sulfur or chlorine [34,
59–61]. Other than that, unwanted side-product formation can occur, for example the presence
of NH
3
is known to result in the formation of trimethylamine, decreasing the product value due
to its characteristic odor [62]. Specific countermeasures can be taken to cope with impurities,
such as an enhanced upstream gas cleaning, a more complex downstream distillation unit or a
higher catalyst volume in the reactor.
2.3 Feedstocks used for methanol synthesis
Methanol synthesis is today almost exclusively based on fossil feedstocks such as coal, crude oil
and natural gas (NG). Despite growing coal-to-methanol capacities in China, 55% of the total
installed production capacity is based on NG [63]. Independently of source, fossil feedstocks must
firstly be converted into syngas via a gas generation process. Carbon-containing compounds,
such as elemental carbon, CH
4
and higher hydrocarbons, need to be converted to CO, CO
2
and
H
2
. The two main technologies used for syngas generation are gasification and reforming, see
references [11, 57, 58, 64–66] for further details. This section continues with an overview on
feedstocks used for methanol synthesis, highlighting the respective properties of the generated
syngas.
2.3.1 Coal, biomass and refinery residues
There are numerous solid and liquid feedstocks that are commonly used to prepare an appropriate
syngas for the methanol synthesis[11, 66]. Among them are fossil products of natural coalification
processes, including peat, lignite, bituminous coal through to anthracite - these are all typically
gasified. Most residues from crude oil, like heavy oils, naphtha or liquefied petroleum gas (LPG)
7
2 Literature Review and Scientific Approach
can either be gasified or reformed. Due to limited local availability and chemical heterogeneity,
gasification of (municipal) waste and biomass can only been seen as a minor source for the
production of methanol. However, benefits of their utilization are the potential mitigation of
greenhouse gases and, in the case of waste, reduction of hazards associated with emittance to
the natural environment [67].
All feedstocks differ in their chemical composition and impurity content. Accordingly, numerous
technologies for syngas generation are existing on current-state-of-the-art, also with respect to
gasification schemes[52, 68, 69]. Through natural carbonization, the amount of fixed carbon
increases, whereas volatile compounds, especially bound H
2
and oxygen (O
2
), are decreased [52].
As a result, the produced syngas is sub-stoichiometric for methanol synthesis [66]. Hence, in order
to adjust SN to the correct level, H
2
can either be added or the carbon oxide content can be
decreased by shifting CO (Eq.2.2) and subsequently removing surplus CO
2
[52]. Typical syngas
from coal gasifiers has an inert gas fraction between 0.5% and 6 %, predominantly of CH
4
[52,
66, 69].
Most syngases originating from biomass or fossil carbonization products typically contain many
organic and inorganic impurities, making a comprehensive gas cleaning necessary[11, 52]. The
main advantage of coal gasification processes is the inexpensive feedstock price compared to
NG. As it is well distributed in the world, it is also geopolitically more independent, but entails
drawbacks like significantly higher CO
2
emissions arising from gas conditioning and elevated
investment costs compared to a NG-based synthesis process [10, 57, 70].
2.3.2 Natural gas
NG contains light hydrocarbons, mainly CH
4
, inert components (e.g. N
2
) and impurities, such as
sulfur-containing compounds or He. Besides ongoing efforts to develop methods for direct selective
oxidation of CH
4
to methanol [71, 72], in commercial processes hydrocarbons are (catalytically)
reformed into syngas. Steam methane reforming (SMR) is the most established route for NG-
based feedstocks [14]. However, there are also routes utilizing CO
2
such as dry reforming and
bi-reforming [73]. Syngas produced by SMR usually contains excess H
2
(2.5
≤
SN
≤
3.0) [57, 64,
74]. External CO
2
can therefore be added to increase methanol capacity [58]. Steam reforming of
higher hydrocarbons, however, can result in a H2-shortage.
The inert gas content of the syngas is determined by the N
2
content of NG and the CH
4
slip
of the SMR reaction, with a value of 3% to 5 % considered typically. As NG contains fewer
impurities and is easier to handle than solid feedstocks, the gas cleaning is simplified compared
to gasification processes. With the development of new reforming technologies, such as partial
oxidation (POx)[58], autothermal reforming (ATR) [75, 76] and combined reforming[64], the
reaction conditions have been increasingly optimized for the reforming reaction, resulting in
a significant decrease of the CH
4
content in the syngas. These technologies also provide the
possibility to adjust stoichiometry to the perfect level for methanol synthesis[58].
8
2 Literature Review and Scientific Approach
2.3.3 Alternative feedstocks
Qin et al. have calculated a CO
2
-equivalent of 2.97 t
CO2,eq
t
MeOH-1
based on a cradle-to-gate life
cycle assessment (LCA) of a coal-based methanol production plant in China[77]. For a NG-based
process the according CO
2
-equivalent accounts to 0.85t
CO2,eq
t
MeOH-1
[6]. In comparison, the
direct hydrogenation of captured CO
2
to produce methanol, i.e. based on renewable electricity
driven H
2
O electrolysis - commonly referred to as "Power-to-Methanol" (PtM), has been reported
to have a CO
2
-equivalent of -0.67 t
CO2,eq
t
MeOH-1
[6]. This implicates possible carbon emission
savings of 1.52t
CO2,eq
t
MeOH-1
of PtM-based methanol in comparison to NG-based methanol
showing the sensitivity of methanol pricing towards political regulations such as CO
2
taxation
and trading systems [6, 15, 78].
The debate regarding the use and implementation of sustainable feedstocks and CO
2
-neutral
processes for methanol synthesis arrived in the scientific community in the early 90s via con-
tributions from both academic and industrial research groups [79–84]. As a consequence, new
feedstocks are under discussion in order to find methanol synthesis concepts with increasingly
lower carbon footprints. The following two sections introduce two types of alternative feedstocks:
CO
2
point sources as e.g. cement production, biogas plants or DAC, and carbon oxide (CO
x
)-rich
industrial off-gases that may arise from existing industrial processes, e.g. steel industry.
2.3.3.1 CO2-based feedstocks
CO
2
-rich gas streams can be captured from industrial processes such as the chemical, steel
or cement industry as well as combustion-based power plants[6]. Demonstration facilities at
the small and industrial scale have led to enhanced knowledge concerning the advantages and
drawbacks of CO2-based methanol synthesis [81, 84–92].
A benefit of a CO
2
-rich syngas for methanol synthesis is the lower heat duty emerging from
CO
2
-hydrogenation enabling less complex cooling concepts for the reactor. Another advantage
compared to conventional processes is the lower catalyst selectivity towards hydrocarbon side-
products, e.g. ketones, leading to lower costs in product purification [81, 84, 91, 93–95]. The
main drawbacks of the CO
2
-based methanol synthesis arise from an increased H
2
consumption
due to the formation of H
2
O leading to an increased catalyst deactivation and efficiency losses of
the process chain [37, 81, 91, 96].
Besides catalyst research, industrial process solutions were developed allowing handling of CO
2
-
rich syngas[28, 79, 84, 97, 98]. While some processes directly hydrogenate CO
2
to methanol [91],
most of CO
2
-based process concepts condition the CO
2
-rich syngas by shifting CO
2
to CO via
reverse WGS chemistry, e.g. the so-called CAMERE process [12, 83, 86, 99]. A process concept
proposed and indeed realized at a near industrial scale by Carbon Recycling International (CRI),
also considers the option of a reverse WGS reactor to increase the CO content in the syngas[100].
The inert gas fraction for CO
2
-based processes is almost zero if an appropriate CO
2
removal is
used in CO
2
capture. However, even with optimized process solutions the disadvantage of an
elevated H
2
consumption persists [11]. This reinforces concerns linked to a sustainable H
2
supply
which is known to be one of the core issues regarding future methanol synthesis[10, 87, 101].
9
2 Literature Review and Scientific Approach
2.3.3.2 Steel Mill Gases
Compared to carbon capture and utilization (CCU) schemes based on CO
2
-rich syngases, gas
sources with an elevated CO content decrease water content in the reaction product and therefore
increase the overall process efficiency. Promising options in this context are gases emerging
from steel mill processes [6]. The steelmaking industry has the potential to provide large volume
gas streams containing H2, CO and CO2over the blast furnace route schematically depicted in
Fig. 2.2. As such, a number of research initiatives aim to utilize steel mill gases for synthesis
processes in order to decrease overall GHG emissions[102–105]. Other routes for steel production
with H
2
as reducing agent and electric arc furnaces are proposed by industry, but will not be
further discussed within this work[106–108]. As the steel industry accounts for approximately
6.7 % of all global CO
2
emissions [109] (1.9 t
CO2,eq
t
Steel-1
are emitted on average through steel
production [110]), it is reasonable to utilize "waste" process gases.
Figure 2.2:
Gas composition of steel mill gas streams according to [111, 112]; Values in brackets
show fraction of the total volumetric gas stream emitted from the steel mill.
The compositions of three main types of steel mill gases, i.e. blast furnace gas (BFG), coke oven
gas (COG) and basic oxygen furnace gas (BOFG), are provided in Fig. 2.2 [111]. With a fraction
of approximately 87% of the total volume of all gases, BFG is the predominant gas stream [112].
However, this gas stream has an inert gas fraction of approx. 50 %, in this case N
2
[105, 113,
114]. BOFG and COG have smaller inert gas contents, but cover only a small percentage of
the total volume of all gas streams. Due to a high H
2
content, COG can be considered as a H
2
source [115–117] that can also be transferred to commercial syngas by conventional reforming
technologies[116, 118–122]. BOFG and BFG are both poor in H
2
(BFG: SN
≈
-0.40 and BOFG:
SN
≈
-0.15) and therefore require additional H
2
to establish the correct SN. Another possibility
of BFG utilization is the removal of CO
2
. In this case pure CO
2
is obtained and can therefore be
processed with respect to Sec. 2.3.3.1.
10
2 Literature Review and Scientific Approach
Research projects concerning the utilization of steel mill gases are currently being funded in
Europe, where reduction and recycling of CO
2
are major political goals, e.g. as supported by
national initiatives[123], creating new challenges for energy-intensive industries. One project
initiated in this context by the European Union through the FP8/Horizon2020 "SPIRE" program
is FReSMe, which is the follow-on of the previously funded MefCO2 and STEPWISE projects [102,
124, 125]. It focuses on CO
2
capture and methanol synthesis at a Swedish steel mill. A comparable
project funded by the German ministry of research and education (BMBF) is Carbon2Chem
®
[105].
This initiative aims to utilize steel mill gases in order to produce methanol, but also higher
hydrocarbons, ammonia, urea and polymers in a cross industrial or "sector coupling" network.
The project collaborations Carbon2Value and Steelanol set a focus on Fisher-Tropsch synthesis
and fermentation processes from steel mill gases [103, 104].
2.3.4 Classification of make-up-gases
Fig. 2.3 categorizes the estimated composition of conventional and alternative syngases conitioned
for methanol synthesis by means of COR and inert gas fraction[66, 126, 127]. For the conventional
Figure 2.3:
Comparison of the estimated inert gas content and COR of syngas obtained from
conventional and alternative feedstocks conditioned for methanol synthesis[52, 66,
111, 112, 126, 127]; Arrows indicate fluctuations in gas composition.
syngas generation processes like gasification or reforming, wide ranges were defined in the diagram,
as the inert gas fraction as well as COR strongly depend on the composition of the feedstock
used. In case of the steel mill gases, SN was adapted to SN = 2.1. As the design of methanol
synthesis process mainly depends on syngas composition, even different feedstocks can lead to
the same design, if comparable syngas compositions are available. Therefore Fig. 2.3 is capable
of showing whether new feedstocks either result in the elaboration of completely new synthesis
processes or only in the slight adaptation of existing processes. This simplifies the selection of
11
2 Literature Review and Scientific Approach
synthesis loop parameters and helps to categorize different syngas compositions.
As mentioned in Sec.2.3.3.2, the steel mill gases can be processed by a WGS unit with subsequent
N
2
-removal in order to decrease the inert gas content. This option is especially promising for
the blast furnace gas representing the biggest share of steel mill gases (87%). In this case, the
processed synthesis gases from the steel mill would be assigned CO
2
-based in Fig. 2.3. However,
with regard to CO
2
-rich synthesis gases in methanol synthesis many open questions arise at
current-state-of-science with regard to reaction kinetics, catalyst deactivation and dynamic
operation [14]. Therefore, this work will focus on gas compositions at high COR without inert
gas.
2.4 Technological overview on methanol synthesis
As a measure to assess the quality of methanol synthesis in a technical process or reactor, some
basic key indicators must be defined:
1.
The carbon conversion
XC
can be used as a measure of the molar quantity of CO
x
reacted
towards methanol related to the molar quantity of CO
x
in the feed. In a continuous reactor
it is defined via the molar flow entering
˙nj,in
and the molar flow leaving the reactor
˙nj,out
as follows:
XC=( ˙nC O,in + ˙nCO2,in)−( ˙nCO,out + ˙nCO2,out)
˙nC O,in + ˙nCO2,in
(2.6)
2.
The carbon yield
YC
relates the amount of the desired product towards the maximum
possible amount of product with regard to the stoichiometry of the educts. Related to CO
and CO2present in the feed gas, the carbon yield can be defined as follows:
YC=˙nM eOH,out
˙nC O,in + ˙nCO2,in
(2.7)
3.
Methanol selectivity
SMeOH
represents the degree of the formation of the desired product
among all products formed. In case of methanol synthesis, selectivity with regard to carbon
is defined as follows:
SMeOH =˙nMeOH,out
( ˙nC O,in + ˙nCO2,in)−( ˙nCO,out + ˙nCO2,out)(2.8)
4.
The space-time-yield
ST Y
is defined as the mass flow of product formed over time related
to the volume of the catalyst bed inside the reactor
Vcat
. Therefore it can be used as
a measure of productivity influenced by reaction kinetics and operating conditions. For
methanol synthesis is defined as follows[11]:
ST Y =˙nM eOH,out ·MM eOH
Vcat
(2.9)
2.4.1 Reaction conditions and equilibrium
Due to the exothermic and mole-decreasing nature of methanol synthesis from CO and CO
2
,
the equilibrium of these reactions is positively affected by low temperatures and high pressures
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2 Literature Review and Scientific Approach
(compare Eq. 2.1 and Eq. 2.3). Equilibrium constant
Keq
at a temperature T can be calculated
using the following equation including the change of Gibbs free energy ∆
G0
caused by the
reaction at the respective temperature [128]:
lnKeq (T)=−∆G0(T)
R·T(2.10)
To obtain an accurate description of the equilibrium of methanol synthesis, many studies were
conducted by the scientific community providing a set of equilibrium constants [128–132].
In Eq. 2.10, ∆
G0
(
T
)is calculated based on the change of Gibbs free energy at reference conditions
∆
G0
(
Tref
). Given the exact value for ∆
G0
(
Tref
)and the temperature dependent change in heat
capacity, ∆
G0
(
T
)can be calculated by the change in enthalpy ∆
H0
(
T
)applying the Kirchhoff
equation [133, 134]:
−∆G0(T)
T=−∆G0(Tref )
Tref
+ZT
Tref
∆H0(T)
T2dT (2.11)
∆H0(T)=∆H0(Tr ef ) + ZT
Tref
∆˜c0
p(T)dT (2.12)
However, by a sensitivity analysis comparing different literature values of ∆
G0
(
Tref
)for methanol,
Graaf and Winkelmann found that already small changes in this parameter largely influence the
equilibrium constant of methanol synthesis[129]. Based on this analysis, the authors determined
a semi-empirical set of parameters to calculate the equilibrium constant based on experimental
equilibrium data published in scientific literature. The experimental data the authors considered
cover the temperature range between 200
◦
C and 1000
◦
C as well as pressures between 0bar
and 294 bar. The parameters
a1
to
a7
were provided for CO-hydrogenation (
Keq,CO
) and rWGS
(Keq,rW GS ) for the following equation:
lnKeq (T)=1
R·T·a1+a2·T+a3·T2+a4·T3+a5·T4+a6·T5+a7·T·ln(T)(2.13)
The equilibrium constant of CO
2
-hydrogenation (
Keq,CO2
) can be calculated by the following
correlation [129]:
Keq,CO2=Keq,C O ·Keq,r W GS (2.14)
Details on the derivation of Eq.2.13 are provided in Appendix A.1 of this work [129, 133]. The
work published by Graaf and Winkelman in 2016 contains the most recent and comprehensive
parameter set for the calculation of the equilibrium constants
Keq,CO2
and
Keq,rW GS
[129].
Therefore, the values published within their study will be used throughout this work. From these
equilibrium constants chemical equilibrium composition can be calculated iteratively varying the
fugacities fjof the reactants to fulfill the following criteria[128]:
0!
=Keq,CO2− fM eOH ·fH2O
fCO2·f3
H2!eq
(2.15)
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2 Literature Review and Scientific Approach
0!
=Keq,rW GS − fCO ·fH2O
fCO2·fH2!eq
(2.16)
In these equations the fugacities
fj
at equilibrium conditions are calculated using the equation of
state (EoS) by Soave, Redlich and Kwong (SRK) [128, 129, 135, 136]. Equilibrium composition
can be obtained by varying the reaction progress coefficient of CO
2
-hydrogenation
ζ1
and rWGS
ζ2applying a molar balance for the reactants H2, CO, CO2, MeOH and H2O:
˙nC O,eq = ˙nCO,in +ζ2(2.17)
˙nC O2,eq = ˙nCO2,in −ζ1−ζ2(2.18)
˙nH2,eq = ˙nH2,in −3·ζ1−ζ2(2.19)
˙nM eOH,eq = ˙nMeOH,in +ζ1(2.20)
˙nH2O,eq = ˙nH2O,in +ζ1+ζ2(2.21)
In Fig. 2.4 the carbon yield of methanol at chemical equilibrium was calculated for gas compositions
in the range of 0.0
≤
COR
≤
1.0 at SN = 2.0 (A, D) and SN = 4.0 (B, E). To show the influence
of inert gas on chemical equilibrium of methanol synthesis, a N
2
content of 40% was applied in
Fig. 2.4 (C) and (F) at SN = 4.0. Temperature was varied between 180
◦
C
≤
T
≤
340
◦
C at the two
Figure 2.4:
Carbon yield of methanol at equilibrium over temperature calculated utilizing the
equilibrium constants as published by Graaf and Winkelman [129]; Simulation param-
eters: 0.0 < COR < 1.0; SN = 2.0 (A, D), SN = 4.0 (B, E) and SN = 4.0 at y
inert
= 0.4
(C, F); p = 50 bar (A, B, C) and 80 bar (D, E, F).
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2 Literature Review and Scientific Approach
pressure levels of 50bar (A, B, C) and 80 bar (D, E, F). The graphs indicate a strong correlation
between synthesis pressure and temperature towards the formation of methanol. Overall, the
simulation results are in line with Le Chatelier’s principle. While an increase in temperature
decreases equilibrium conversion towards methanol, an increase of pressure shifts equilibrium
further to the side of the products.
Moreover, a strong correlation between COR and the equilibrium methanol yield can be identified
from Fig. 2.4. While at COR = 0.0 the yield approaches a value of 1.0 at low temperature,
significantly lower yields are obtained when COR is increased to 1.0. Due to the stoichiometric
factor of H
2
, an increase of SN leads to growing methanol yields. In case of an increased inert
gases content, the fugacity of the reactants decreases. Therefore, lower equilibrium yields are
obtained for syngas with high inert gas content. Overall, some boundary conditions can be
defined for methanol synthesis from the analysis of the chemical equilibrium[96]:
1.
High pressures and low temperatures are beneficial for the equilibrium conversion towards
methanol.
2.
Low CO
2
contents shift chemical equilibrium to the side of methanol. Consequently high
CO contents in the syngas are desirable.
3. As inert gas decreases equilibrium yield, low inert gas contents are preferable.
2.4.2 Synthesis process
Due to continuous improvements in syngas cleaning technology, Imperial Chemical Industries
(ICI, today Nouryon) in 1966 patented a process for the so-called "low pressure" methanol
synthesis as it is known today[137]. Higher purities with sulfur contents below 1 ppmw in the
synthesis gas enabled the application of Cu/Zn/Al
2
O
3
catalysts instead of the formerly applied
ZnO/Cr2O3catalyst, which was known to be more robust against sulfur poisoning [16]. Due to
its enhanced activity, the more active Cu-catalyst could be industrially applied at temperatures
below 300
◦
C. As shown in Sec.2.4.1, lower temperatures are beneficial for the equilibrium conver-
sion of methanol. Consequently, synthesis pressure of methanol synthesis could be lowered from
pressures exceeding 250 bar to below 100 bar when the Cu/Zn/Al
2
O
3
catalyst was applied[10,
137]. Even though, the catalyst was modified by numerous companies[138] and researchers,
modern commercial catalysts are still based on the catalytic system proposed by ICI in 1966 [14].
Due to the equilibrium limitation shown in Fig.2.4, today’s industrial methanol synthesis is
carried out at elevated pressures between 50 bar and 80 bar [14]. Due to the fact that low temper-
atures do positively affect the equilibrium conversion towards methanol, low temperatures would
be beneficial for the synthesis from a thermodynamic point of view. However, state-of-the-art
catalysts need to be operated within a temperature range between 200
◦
C and 280
◦
C. On the
one hand, temperatures below this operating window lead to inapplicable reaction kinetics for
industrial processes. On the other hand, the catalyst is known to be rapidly deactivated at
temperatures over 280
◦
C due to thermal sintering[37]. Consequently, an accurate reactor model
is obligatory when a methanol synthesis reactor is operated within an industrial process with
high requirements towards catalyst stability and productivity.
Optimized methanol plants can show a high level of complexity depending on the plant man-
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2 Literature Review and Scientific Approach
Figure 2.5:
Basic scheme of a methanol synthesis process with the main components and the
reference points for the calculation of LCE, LHEint, and LHEext.
ufacturer’s intellectual property and technological frame conditions as e.g. the connection to
other chemical processes [139]. Focusing on the main process equipment, a basic flow scheme of
a methanol synthesis loop is provided in Fig.2.5 as a simplified, demonstrating example. The
conditioned syngas enters the process as so-called make-up gas (MUG). After being compressed
to synthesis pressure it is mixed with recycled gas from the process loop. This gas stream
designated as reactor feed hereafter enters the methanol reactor, where the catalytic conversion
according to Eq. 2.1, 2.2 and 2.3 occurs. Downstream the reactor, the product stream is cooled
to temperatures between 30
◦
C and 40
◦
C to separate unreacted syngas from the liquid product.
Condensed liquid raw methanol, i.e. a mixture of methanol, H
2
O, dissolved gases and side
products, is removed from the loop in a flash separator. Non-converted gas is returned to the
reactor by the recycle loop. The recycle ratio RR is defined as the ratio between recycle molar
flow and MUG molar flow[140]:
RR =˙nrecycle
˙nM U G
(2.22)
In order to avoid the accumulation of inert components, a small portion of the recycle gas is
purged from the loop. The higher the chosen recycle ratio, the lower the amount of purge gas.
The raw methanol product is sent to methanol storage and purification, typically implemented
by distillation.
The properties of the syngas described in Sec. 2.2 need to be considered for the technical im-
plementation of methanol production as a direct consequence of the feedstock used (compare
Fig. 2.3). Inert components and unreacted syngas leave the process loop via the raw methanol
and purge gas stream [57, 91]. Hence, an economical balance between recycle ratio and amount
of purge gas has to be found for every individual scenario.
The Loop Carbon Efficiency (LCE) indicates the ratio between carbon chemically bound in the
raw methanol (
˙nC H3OH,flash,l
), to the overall amount of carbon oxides in the MUG, i.e. CO
(
˙nC O,M U G
) and CO
2
(
˙nC O2,M U G
) [129, 141–144]. Carbon losses are mainly caused by the purge
gas stream, side-product formation and dissolved gases in the raw methanol. The LCE is
16
2 Literature Review and Scientific Approach
expressed by the following definition:
LCE [%] = ˙nC H3OH,flash,l
˙nC O,M U G + ˙nC O2,M U G ·100 % (2.23)
The LCE as defined in Eq. 2.23 is capable of comparing different loop designs and/or feedstocks.
However, carbon efficiency can be defined accordingly at other reference points, e.g. by considering
the total amount of carbon bound in the feedstock.
For processes where H
2
is externally generated, another parameter describing the utilization of
H
2
concurrent to the LCE is deemed reasonable[118, 141]. However, the definition of a Loop
Hydrogen Efficiency (LHE) is more complex. In addition to the above mentioned losses for LCE,
it needs to be considered that H
2
O is formed as inevitable byproduct from CO
2
-hydrogenation
and rWGS. There are two ways to evaluate the hydrogen efficiency:
a)
An external Loop Hydrogen Efficiency (LHE
ext
) balancing the amount of H
2
solely bound
in the methanol produced relative to the amount of H2in the MUG (˙nH2,M U G ):
LHEext [%] = 2·˙nCH3OH,f lash,l
˙nH2,M U G ·100 % (2.24)
This definition is capable of comparing processes utilizing MUG with different COR. As in
case of pure CO
2
-feed one third of the H
2
introduced into the process is converted into
H
2
O, the theoretical maximum of
LHEext
decreases from 100 % towards 66%, when COR
is increased from 0.0 towards 1.0. Consequently, gases with a high amount of CO
2
are
less-favored with regard to this key indicator.
b)
An internal Loop Hydrogen Efficiency (LHE
int
) considering water in the raw methanol
(˙nH2O,flash,l) as a product:
LHEint [%] = 2·˙nCH3OH,f lash,l + ˙nH2O,f lash,l
˙nH2,M U G ·100 % (2.25)
This definition is capable of comparing the efficiency of loop design independently of COR,
equivalent to LCE.
In order to illustrate the above described key indicators, gas mixtures with varied COR are
introduced into the basic process depicted in Fig. 2.5 and compared by LCE, LHE
ext
and LHE
int
in Fig. 2.6. For this simulation, loop conditions were held constant at RR= 6, T
in
= 230
◦
C
and SNMUG = 2.05 at a synthesis pressure of 80bar. As reactor type, the tubular steam raising
reactor was selected with the kinetic model provided by Bussche and Froment[145]. Details on
this reactor type as well as the kinetic model will be given later in this chapter, see Sec.2.4.3
and Sec. 2.5, respectively. The process model was implemented in MATLAB
®
and Simulink
®
.
Development of this model was based on prior and parallel academic studies executed within the
working group [146–149].
In the process simulation LHE
int
and LCE show a similar, decreasing trend when COR content is
increased. This can be explained by the decreased equilibrium yield as well as the slower reaction
kinetics at high CO
2
contents. Due to the slight over-stoichiometry in the MUG, more H
2
is
purged in comparison to CO
x
, leading to a lower LHE
int
in comparison to LCE. As the process
was not optimized by means of an increase in RR for higher CO
2
contents in the MUG, the key
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2 Literature Review and Scientific Approach
Figure 2.6:
Comparison of LCE (x), LHE
ext
(
•
), and LHE
int
(∆) computed with varied
COR in the MUG at constant loop conditions; Simulation parameters: RR = 6;
Tin = Tcool = 230 ◦C; p = 80 bar; SN = 2.05.
indicators decrease due to the smaller conversion of the educts in the reactor. Moreover, the
increased H
2
demand for CO
2
-rich gas becomes visible considering LHE
ext
. This key indicator
decreases faster than LHEint over COR due to the byproduct-formation of water.
2.4.3 Reactor concepts
Among other equipment as compressors and heat exchangers, the reactor is one key-component
in the methanol synthesis process. The combination of geometry, cooling concept as well as gas
composition and flow rate largely influences the behavior of the reaction network. One character-
istic number quantifying the reactor exploitation independently of pressure and temperature is
the gas-hourly-space-velocity GHSV. This key indicator correlates the volumetric flow rate of
reactor feed at norm conditions to the catalyst bulk volume inside the reactor[140]:
GHSV =˙
Vnorm
Vcat
(2.26)
At a high GHSV, residence time in the reactor decreases, leading to reduced contact times
between the reactants and the catalyst. As a consequence the gas composition at the reactor exit
does not reach thermodynamic equilibrium. Contrary to that, a reduction of GHSV prolongs
residence time in the reactor and enables an approach to thermodynamic equilibrium. GHSV as
a measure for the reactor load can be optimized depending on the reaction conditions with regard
to STY, X
C
or Y
C
. This optimization is, however, besides the reaction kinetics and operation
conditions largely depending on the thermal operation of the reactor, i.e. the heat removal from
the reaction zone.
Multiple concepts for temperature control and process layout are currently patented or under
investigation[14]. As the exothermic heat of the reactions occurring in the methanol synthesis
reactor results in a temperature rise, chemical equilibrium would be affected negatively (compare
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2 Literature Review and Scientific Approach
Figure 2.7:
Main types of industrially applied methanol synthesis reactors: Adiabatic intercooled
reactor (A), adiabatic quench bed reactor (B), steam cooled tubular reactor (C) and
the counter-current gas cooled tubular reactor (D); Own illustration based on[9, 53,
159].
Sec. 2.4.1). Therefore, measures need to be taken in order to keep the reaction temperature
under control. This can be done either by dividing the catalyst bed into intercooled zones or by
heat removal along the catalyst bed. The former type of reactor can be described as adiabatic
intercooled reactor, while the latter type is of a polytropic nature.
In Fig. 2.7, the most commonly applied reactor types in methanol synthesis are depicted with
their characteristic temperature-yield profiles. Fig. 2.7 shows the adiabatic intercooled reactor
as typically applied by Haldor Topsoe (A) [150–152] as well as the adiabatic quench bed reactor
as proposed by ICI (B) [141, 142]. In these two reactor types, methanol yield at the adiabatic
temperature limit is approached along each fixed bed. By intercooling or quenching of fresh
syngas temperature is decreased to enable higher methanol yields. The number and height of
catalyst beds as well as the size of the intercooler or the amount of quench gas introduced,
respectively, are defined by reactor design in dependence of the gas composition and operating
conditions [153–158].
Adiabatic multi-bed reactors have the advantage of a simple design and an easy catalyst replace-
ment[53]. However, these types of reactors have the disadvantages of a more complex startup
behavior [153], a possible mal-distribution of the syngas flow and the residence time as well as
increased side product formation due to higher synthesis temperatures [159]. Moreover, the high
temperatures reached at the exit of each reactor stage lead to faster thermal catalyst degradation
in these zones.
The steam raising polytroptic tubular reactor depicted in Fig. 2.7 (C) was patented in 1971 by
Metallgesellschaft AG (later Lurgi, today GEA Group AG)[160]. This reactor type has the
advantage of an easier start-up behavior, an improved temperature control and higher possible
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2 Literature Review and Scientific Approach
yields per pass in comparison to the adiabatic reactor types [153]. Moreover, a decrease in
catalyst activity due to catalyst aging can be compensated by an increase of the pressure (and
consequently boiling temperature) in the steam drum [161–163]. Today the steam raising reactor
is the most commonly applied reactor type in methanol synthesis industry[9, 159]. For this
reactor type detailed knowledge of the reaction kinetics is mandatory to optimize the gas load
and the coolant temperature. As it is applied in most scientific studies with regard to simulation
of industrial methanol synthesis, manifold literature on the geometric dimensions and possible
simulation approaches exists in scientific literature [90, 127, 136, 152, 164–171].
Another reactor design commonly applied in methanol synthesis is the counter-current gas cooled
tubular reactor schematically depicted in Fig.2.7 (D). In this type of reactor the incoming reactor
feed is introduced into the shell side and directly preheated by the heat of reaction released from
the catalyst-filled tubes [172]. In the upper section of the reactor the gas is reversed in direction
and enters the reaction zone. Due to the high temperature gradient along the reactor, this reactor
type implies an optimal combination of fast reaction kinetics at elevated temperatures (top) and
a high equilibrium conversion at low temperatures (bottom). However, the main disadvantages
of this reactor emerge from the complex design, the low load flexibility and a difficult start up
behavior. Due to the comparably low heat transfer coefficient between tube and shell side, this
converter is rather suitable for mild gas conditions.
2.4.4 Dynamic operation
In the synthesis reactor a load point can be defined as a combination of gas composition, i.e. COR,
SN and inert gas content, and the quantity of gas passing through the reactor, i.e.
˙n
or GHSV,
at a certain pressure and temperature. During a load change, one or multiple parameters are
varied within a certain time span.
Dynamic load changes in conventional methanol synthesis plants usually appear due to scheduled
events as ramp-up at beginning of plant operation, shut-down at the end of the catalyst life
time [153] or temperature increase in the steam drum to account for catalyst aging [161–163].
As conventional methanol plants are individually designed for the composition of the exploited
resource, i.e. the natural gas field or coal deposit, strong fluctuations in the gas supply are not
accounted for in the design of these plants.
However, in case of methanol synthesis from sustainably produced H
2
and captured CO
x
,
fluctuation in the gas supply are likely to occur [173]. In case of a decreased production of
renewable energy, H
2
supply could decrease drastically. If no appropriate buffer storage for H
2
is
available, the shortage in H
2
production would be handed through to the methanol synthesis
process. Depending on the control scheme of the plant, the H
2
shortage could be handled
by decreasing SN in the MUG (SN
MUG
) or by a reduction of the overall flow rate of MUG.
In the latter case, SN would be held constant, however, the process would go into part load
with the consequence of a decreased GHSV in the reactor. In case of a decrease in SN
MUG
,
sub-stoichiometric gas compositions could be reached at the reactor inlet (compare Sec. 2.2.2).
When the CO
x
stream is captured from an industrial batch process, e.g. biomass fermentation or
steel production, fluctuations in this stream could be another possible source for dynamics in the
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2 Literature Review and Scientific Approach
gas supply [61] disturbing SN
MUG
or, especially in case of steel mill gases, COR in the MUG
(CORMUG) [174].
To review the development regarding the consideration of dynamics in the scientific community
over the past decades, the number of publications explicitly dealing with reactor simulation or
experimental campaigns was extracted from the literature data base build during this work. In
Fig. 2.8 the number of simulative (turquoise, hatched) and experimental studies (gray, solid)
are plotted over the decades from 1970 until today. Both groups are separated by steady state
and dynamic studies. The graph indicates, that the majority of scientific studies considers
steady state methanol synthesis only. In case of the dynamic simulation studies in the 1990s
and 2000s, catalyst deactivation[161, 162, 175–177] and reversed flow reactor configurations, i.e.
process concepts where the direction of gas flow in the reactor is periodically reversed to control
temperature [178, 179] were in focus of research. From 2005 on, also the topic of process control
was addressed by various researchers [169, 180, 181]. Dynamic simulation of a synthesis reactor
in the context of PtM was not addressed by any of the simulation studies available in literature.
Figure 2.8:
Number of publications in the literature data base generated in this work over decades
for experimental work (gray) divided by lab scale and miniplant scale work for steady
state and dynamic as well as simulation work (turquoise, hatched) for steady state
and dynamic consideration.
With regard to experimental investigations, numerous steady state studies describing the reaction
kinetics of methanol synthesis were published in the last decades[14, 38, 45, 139, 182]. Contrary
to that, only few studies were conducted dealing with its dynamic behavior. While the dynamic
experimental studies carried out in the 1980s until the 2000s focus on periodic operation of the
synthesis reactor[29, 39, 183–185], some studies considering dynamics in the context of PtM
emerged during in the last years[186–189]. Ash-Kulander et al. [186] investigated the influence of
a daily startup and shutdown in a CO
2
-rich syngas in a lab scale reactor. In their study they
found that the interruption of operation enhanced aging of the catalyst. Besides, their results
indicated that flushing of the reactor with N
2
over night enhanced deactivation. However, these
findings are in contrast to Ruhland et al.[187] who investigated the effect of load changes on
catalyst stability by a variation of SN. In their study no enhancement of deactivation was found
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2 Literature Review and Scientific Approach
compared to a steady state reference experimental campaign. Seidel and Vollbrecht derived a
kinetic model from experimental data obtained from a Micro-Berty type reactor [188, 189]. In
their study the authors concluded that a dynamic kinetic model would be beneficial for the
description of a methanol synthesis reactor under transient conditions. The dynamic kinetic
model derived by the group was characterized by a dynamically changing catalyst morphology,
i.e. the fraction of oxidized and reduced active sites, depending on the composition of the syngas.
The time-dependent change in the catalyst morphology was included by a differential equation
into their kinetic model. However, the authors claimed a lack of experimental data in order
to uniquely determine the parameters of their dynamic kinetic model [188]. Due to the high
number of model parameters and the computational complexity, the model derived by Seidel and
Vollbrecht will not be considered further in this work.
Numerous studies treating the experimental behavior of methanol synthesis on the miniplant
or pilot scale are available in literature [81, 84–91]. However, as these studies were exclusively
executed under steady state conditions, the behavior of technologically relevant methanol synthesis
reactors or processes operated under transient load conditions is one open question in the scientific
community.
Overall, it can be concluded from this section, that methanol synthesis is likely to be confronted
with fluctuating syngas conditions in the future if PtM technologies are to be implemented on an
industrial scale. However, no validated steady state or dynamic reactor model of an industrial
sized experimental setup does exist in scientific literature. This research gap must be tackled to
enable a stable and economically feasible operation of methanol synthesis process under PtM
conditions as described in Sec. 2.3.3.
2.4.5 Capability of reactor types for dynamic operation
Among the reactor types described in Sec. 2.4.3 an assessment regarding their capability for
dynamic operation was performed. As already mentioned, the fixed beds of the two adiabatic
reactor types (see Fig. 2.7 (A) and (B)) are designed for one load point [158, 190].
In Fig. 2.9, an exemplary simulation of an adiabatic quench bed reactor with three catalyst
bed stages was performed for four different load cases. Fig. 2.9 (A) represents the base case at
p = 80 bar, SN = 2.0, COR = 0.8 and a GHSV of 8,500 h
-1
. The volumetric flow rates and inlet
temperatures of the quenched gas streams were adapted to ensure that the critical temperature
level of 280
◦
C was not exceeded. Fig. 2.9 (B) shows the behavior of the reactor at 50% load
with the distribution of the quench steams and inlet temperatures held constant. In this scenario
the critical temperature level of 280
◦
C would be exceeded at the end of each catalyst bed stage
due to the longer residence times and consequently a higher conversion towards equilibrium.
Fig. 2.9 (C) and (D) show an decrease and increase of COR, respectively. At COR = 0.7 (C)
temperature in the first reactor stage would exceed 300
◦
C and therefore lead to serious damage
of the catalyst and increased formation of byproducts. However, at COR = 0.9 (D) the reaction
would terminate as the cold quench streams would decrease the inlet temperatures of the reaction
mixture below 200
◦
C. Overall, the discussion of the scenarios considered in Fig.2.9 indicates the
requirement of control strategies for the distribution of the feed gas and/or the inlet temperatures
22
2 Literature Review and Scientific Approach
Figure 2.9:
Exemplary simulation of a multi-bed adiabatic quench bed reactor at a base case
of p = 80 bar, SN = 2.0, COR = 0.8 and a GHSV of 8,500 h
-1
(A), reduced GHSV to
4,250 h
-1
(B) as well as COR= 0.7 (C) and COR = 0.9 (D); The distribution of the
gas streams and the inlet temperatures for the base case were adjusted so that the
critical temperature range starting from 280 ◦C (blue area) was not reached.
to enable the dynamic operation of this reactor type. Therefore, the adiabatic quench bed reactor
can be assessed as not viable for rapid load changes if these strategies are not available. Similar
conclusions were drawn by Nassirpour et al., who investigated control strategies for different
reactor types [190]. In their study the authors found, that both, adiabatic quench bed reactor
and adiabatic intercooled reactor are difficult to control on a plant level. Therefore, the adiabatic
reactor types will not be considered further within this work.
Similar to the adiabatic multi-bed reactors a strong relation between the cooling strategy and
the reaction in the catalyst bed exists for the counter current gas cooled tubular reactor (see
Fig. 2.7 (D)). Fluctuations in reactor load or gas composition would influence both, heat transfer
coefficients and temperature differences. As the heat transfer coefficient is limited due to the
gas-wall-gas heat exchange characteristics and inlet temperature into the catalyst bed is directly
affected by the heat produced during the reaction, this reactor type was also assessed not
preferable for dynamic operation.
In comparison to the other three reactor types presented in Sec.2.4.3, the steam cooled tubular
reactor was found to be less sensitive towards fluctuations in load. On the one hand this is due
to the adjustable heat removal provided by the steam cooling. On the other hand, the high heat
transfer coefficient of the boiling steam on the shell side enables high heat fluxes to be removed
from the reaction volume. As it is well documented in scientific literature and comparably robust
23
2 Literature Review and Scientific Approach
against dynamic load changes, the steam cooled tubular reactor was selected to be in focus of
this work.
2.5 Kinetic validation in methanol synthesis
For a proper design of the methanol synthesis reactor and the process, detailed knowledge on the
reaction kinetics of methanol synthesis is necessary. Multiple kinetic models based on different
mechanism and rate determining steps were published in scientific literature, a detailed overview
is provided elsewhere[14]. Most of these models are based on Langmuir-Hinshelwood-Hougen-
Watson mechanisms, where the reactants adsorb on an active site before the step-wise reaction
towards the product occurs [14, 191]. As the nature of the methanol synthesis mechanism was not
yet resolved by the scientific community, all proposed rate equations are based on assumptions
and semi-empirical parameters fitted to experimental data. As these parameters are related
to various different catalysts, a cross-correlation of different experimental data is usually not
possible. In order to evaluate kinetic rate expressions capable of describing industrial methanol
synthesis reactors, kinetic models based on commercial catalysts are in focus of this work.
The kinetic model proposed by Graaf in 1988 is mechanistically based on the stepwise hydration
of adsorbed CO and CO
2
on two active sites [192]. The parameter set for the model was updated
by the authors in 1990[193]. In their experimental studies the authors utilized a spinning basket
reactor filled with a commercial MK-101 catalyst produced by Haldor Topsoe. Even though
their kinetic model was published over 30 years ago, it is still applied within recent simulation
studies [136, 194–196]. The mechanism, kinetic rate equations and parameter set are provided in
Sec. 3.1.2.
In 1996, Bussche and Froment [145] published a kinetic model which became another important
literature standard through the last decades [136, 197–200]. The authors proposed a mechanism
via the carbonate species on one active site. In their kinetic measurements a fixed bed reactor
filled with the ICI 51-2 catalyst was used. Other than in the model of Graaf, no direct CO-
hydrogenation reaction was considered. By doing so, the authors accounted for current research
results stating that methanol is mainly produced by CO
2
-hydrogenation [201]. Further details on
the kinetic model by Bussche et al. are given in Sec.3.1.2 and Appendix A.18.
In 2011, Graaf’s kinetic model was updated by Henkel during his PhD studies performing a
comprehensive kinetic study utilizing a commercial catalyst by Südchemie (today Clariant)[202].
Henkel used two different experimental setups, i.e. a Berty reactor and a micro fixed bed reactor.
Due to results published by the scientific community and the quality of his parameter fitting,
CO-hydrogenation was not considered within his final kinetic model. The mechanism for rWGS
and CO
2
-hydrogenation was overtaken from Graaf’s kinetic model. Details on this model are
provided in Sec. 3.1.2.
Park et al. used a commercial Clariant state-of-the-art catalyst within their kinetic fixed bed
studies in 2014 [203]. The kinetic model they proposed was based on the original reaction
mechanism provided by Graaf [192] coupled with an additional DME kinetic model published by
Chadwick et al. [204].
The kinetic models considered within this work are displayed with their respective validated
24
2 Literature Review and Scientific Approach
data range in Fig. 2.10 with regard to temperature (A), pressure (B), SN (C) and COR (D). All
kinetic models cover the temperature ranges relevant for industrial methanol synthesis. In terms
of synthesis pressure, Graaf and Bussche only validated their kinetic model for pressures up to
50 bar, whereas Henkel and Park considered higher synthesis pressures up to 75 bar and 90 bar,
respectively. As industrial methanol synthesis is usually carried out at pressures exceeding
50 bar, this is a major drawback of the two literature standard models proposed by Bussche and
Graaf [157].
Figure 2.10:
Range of experimental validation conditions applied by Graaf [192], Bussche[145],
Henkel[202] and Park [203] with regard to temperature (A), synthesis pressure (B),
stoichiometric number (C) and carbon oxide ratio (D).
Another important factor for the kinetic performance emerges from SN applied in the kinetic
studies. Unfortunately, for this key parameter no data were provided by Bussche et al.[145].
Therefore it is left unclear, for which SN-range their kinetic model was derived. While Graaf and
Henkel measured both, sub- and over-stoichiometric conditions, Park et al. did not investigate
the reaction kinetics at H2shortage for their model (i.e. SN < 2.0).
Besides stoichiometry, COR largely influences the kinetics of methanol synthesis as water produced
by CO
2
-hydrogenation considerably limits the reaction kinetics[38]. This effect is enhanced with
increasing COR [205]. In the context of PtM technologies, it therefore needs to be mentioned
that Henkel’s kinetic model probably does not account for these limitations as he performed
measurements only until COR= 0.57 (Berty reactor) and COR = 0.93 (fixed bed reactor).
Among all kinetic models published in scientific literature, the kinetic models by Graaf [192]
25
2 Literature Review and Scientific Approach
and Bussche[145] are the most important literature standards, as these two models are used
throughout numerous publications with regard of methanol synthesis simulation (compare
Appendix A.2). However, both models show deficits for the application in the simulation of PtM
reactors due to the usage of probably outdated catalysts [170, 206] and the insufficient validation
range (compare Fig. 2.10). As it seemed most promising among the kinetic models considered in
this work, an attempt was made to implement the kinetic model proposed by Park et al. [203].
However, an implementation of this model was found impossible due to the lack of some kinetic
parameters in their original publication.
Thus, for the modeling of reactors in PtM processes with CO
2
-rich syngas no kinetic model
covering the relevant range of reaction conditions exists in scientific literature. However, for
the design of an economical and technologically feasible methanol synthesis process detailed
knowledge on optimized reactor working conditions and technological limitations is obligatory.
Therefore, a new kinetic model using a state-of-the-art commercial catalyst in the PtM-relevant
parameter range needs to be derived.
2.6 Problem definition and scientific approach
Design and operation of PtM-based methanol synthesis processes will be impacted by the shift in
syngas supply from fossil-based towards sustainable feedstocks. Higher CO
2
contents in the MUG
will decrease both, equilibrium yield (compare Fig. 2.4) and reaction kinetics due to increased
water contents in the product as a consequence of CO
2
-hydrogenation (compare Eq. 2.1). As
discussed in Sec. 2.5 a new kinetic model covering the relevant parameter range of PtM processes
will be necessary for reactor design under these new boundary conditions.
Moreover, fluctuations in the supply of syngas obtained from alternative feedstocks are likely
to occur in future PtM processes (compare Sec. 2.4.4). Therefore, detailed knowledge on the
dynamic behavior of a methanol synthesis reactor will necessary for the implementation of this
technology.
For this purpose, a new kinetic model will be experimentally derived and discussed for its
suitability regarding steady state and dynamic reactor design. In order to maximize the practical
relevance of this work, the kinetic model will be derived and validated with experimental data
obtained from a miniplant setup. This miniplant was designed using a simulation platform
including state-of-the-art kinetic models (extrapolated from there original validation range) as
well as a detailed heat transfer and diffusion model to obtain a high level of agreement to the
kinetic and thermal behavior of an industrial methanol synthesis reactor.
A well documented steam cooled tubular methanol synthesis reactor was selected as industrial
reference for the scale-down as this reactor type was found suitable for dynamic operation (see
Sec. 2.4.3). To obtain detailed validation data on the axial thermal behavior of this reactor
under both steady state and dynamic load conditions, the miniplant reactor was equipped with
a sensor for highly resolved fiber optic temperature measurement [207] in addition to a FTIR
online product analysis.
To demonstrate the significance of the herein introduced methodology, the kinetic model adjusted
to the miniplant experimental data will be compared against a kinetic model obtained from
26
2 Literature Review and Scientific Approach
a "classic" integral kinetic setup. Furthermore, the kinetic model obtained under steady state
conditions will be held against the dynamic experimental data obtained from the miniplant
setup to investigate the necessity for dynamic reaction kinetics for the description of methanol
synthesis reactor as proposed by other research groups[188] (compare Sec. 2.4.4). Finally, the
differential kinetic model will be discussed on industrial scale to demonstrate the impact of this
work towards technical reactor and process design.
27
3 Materials and Methods
In this chapter, the reactor model as the basis of the here presented methodology including the
simulation-based scale-down, the validation of the kinetic models and the transfer of the results
to industrial scale will be explained. Subsequently, details on the design and characteristics of
the miniplant setup will be provided. Finally, the methodology for the model validation will be
presented.
3.1 Simulation platform
Both, steady state and dynamic reactor model were built on a common modeling basis, wrapped
by a simulation platform (see Fig.3.1). This platform includes the sub-models for heat transfer,
powder kinetics and diffusion. Thermodynamic properties for the gas phase are calculated by a
sub-module based on NIST- and DIPPR-database [208, 209] with the mixing rules referenced by
VDI Heat Atlas[210] as well as the Soave Redlich Kwong equation of state (SRK EoS) for the
calculation of gas phase density and fugacity[135]. The thermodynamic models were validated
against the data obtained by commercial process simulation software in previous work[211]. To
keep the simulation platform flexible for different sizes and reactor types, geometrical parameters
are selected from a parameter data-base.
Figure 3.1: Simulation platform applied in this work.
As both, the steady-state and the dynamic reactor model rely on common sub-models, adaptions
and enhancements in the sub-models are automatically updated in the whole simulation platform.
This has the advantage, that improved models, e.g. for a kinetic expression, can directly be
discussed on various design scales and simulation cases. The reactor model was built applying
the following assumptions:
1.
Radial gradients in concentration and temperature along the catalyst bed are neglected
(one-dimensional simulation).
29
3 Materials and Methods
2. Bulk phase and gas phase are considered as one pseudo-homogeneous mixed phase.
3. Ideal plug flow behavior is assumed; Axial dispersion is neglected (see 3.3).
4.
No external diffusion limitation is present at the catalyst surface; Only internal diffusion is
accounted for by the efficiency factor ηeff,j (see Sec. ??).
3.1.1 Heat transfer model
The sub-model accounting for the heat transfer between reaction zone and cooling medium was
referenced from VDI Heat Atlas providing established state-of-the-art approaches for engineering
heat transfer problems [210]. This sub-model provides semi-empirical approaches for heat transfer
in packed beds with gas flow (
λrad
,
αint
) and the heat transfer outside the reactor tube (
αext
).
In case of the miniplant
αext
was expressed by convective thermal oil heat transfer, while for the
industrial scale a correlation for a steam cooling was applied, respectively. Overall heat transfer
coefficient Uwas calculated as follows[212]:
1
U=1
αint
+dint
8·λrad
+dint ·ln dext
dint
2·λwall
+dint
αext ·dext
(3.1)
The calculation of the effective thermal conductivity of the fixed bed as well as the convective
heat transfer coefficients inside and outside the reactor wall will be discussed in the following
sections.
3.1.1.1 Heat transfer in the catalyst bed
Heat transfer in the catalyst bed was calculated in accordance to VDI Heat Atlas sections D6.3
and M7 [210]. Properties of the activated methanol catalyst were extracted from the PhD thesis
by Henkel[202], where the efficient thermal conductivity (
λcat
) and the heat capacity (
cp,cat
) of
the catalyst were measured.
The calculation of the effective heat conductivity of the catalyst bed was based on the work by
Zehner and Schlünder[213] who investigated thermal conductivity in packed beds without fluid
flow. In their work the shape of the particles and the porosity of the fixed bed are transformed to
a model cell representing fluid phase and solid phase in cylindrical coordinates (see Appendix A.4).
The deformation parameter Bin the heat transfer model is defined as follows:
B=Cf·"1−ε
ε#10/9
(3.2)
The semi-empirical shape factor
Cf
in this equation must be determined by experiments. Based
on literature data Zehner and Schlünder determined values for Cfas follows [213]:
a) Spherical particles: Cf= 1.25
b) Crushed particles: Cf= 1.4
c) Cylinders and Raschig rings: Cf= 2.5
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3 Materials and Methods
Due to wall effects, the mean porosity (
ε
) of a fixed bed in a containment with a low diameter-
to-particle-ratio can be higher than in an infinite containment (
ε∞
). In the reactor tube
ε
can
be calculated by applying the following semi-empirical correlation for cylindrical particles[210]:
ε=ε∞+ (1 −ε∞)·0.480
din/dcat
(3.3)
The reduced thermal conductivity of the core of the unit cell
kc
, i.e. the ratio of the heat
conductivity of the core of the model unit cell
λc
in relation to the heat conductivity in the fluid
phase λfis calculated as follows[213]:
kc=λc
λf
=2
N·"B
N2·(kp−1)
kp·ln kp
B!−(B+ 1)
2−B−1
N#(3.4)
In Eq. 3.4, the parameters kpand Nare defined by:
kp=λcat
λf
(3.5)
N= 1 −B
kp
(3.6)
Finally, the reduced thermal conductivity of the catalyst bed without gas flow
kbed
, i.e. the ratio
of the effective heat conductivity of the catalyst bed
λbed
to the heat conductivity of the fluid
phase is calculated as follows:
kbed =λbed
λf
= 1 −√1−ε+√1−ε·kc(3.7)
This equation can then be rearranged to calculate the effective heat conductivity of the fixed
bed without gas flow. In a subsequent study, Schlünder, Bauer and Zehner adapted the model
presented above by inclusion of secondary parameters like the heat radiation between the particles
and the influence of pressure [214, 215]. This model is also provided by VDI Heat Atlas, however,
the effect towards the overall heat transfer coefficient was found to be negligible by a simulative
comparison for the conditions applied within this work. Consequently the secondary parameters of
the model were neglected, in order to decrease the number of semi-empirical influence parameters.
For the influence of fluid flow on the effective radial heat transfer the following correlation is
proposed by VDI Heat Atlas[210]:
λrad =λf· kbed +P e0
Kr!(3.8)
31
3 Materials and Methods
In this equation, the reciprocal of the slope parameter
Kr
together with the molecular Péclet
number
P e0
represent the diffusion of the gas with regard to the particle shape as well as gas
properties and velocity. Calculation of Kris formulated as follows:
Kr=Kr,∞· 2−2
din/dp2!(3.9)
The reciprocal slope parameter in an infinitely expanded containment is defined for different
particle shapes [210]:
a) Spherical particles: Kr,∞= 7
b) Crushed particles: Kr,∞= 5.7
c) Cylindrical particles: Kr,∞= 4.6
The molecular Péclet number in Eq. 3.8 is calculated as:
P e0=u0·ρf·cp,f ·dp
λf
(3.10)
Nusselt number at the inner reactor wall
Nuint
can be calculated according to Martin and Nilles
by the following semi-empirical equation[216]:
Nuint = 1.3 + 5
din/dp!·λbed
λf
+ 0.19 ·Re0.75
p·P r1/3(3.11)
In Eq. 3.11, Reynolds particle number Repand Prandtl P r number are calculated as follows:
Rep=u0·dp
νf
(3.12)
P r =νf·ρf·˜cp,f
λf·Mf
(3.13)
The empty tube fluid velocity u0in the reactor was calculated by continuity equation applying
the empty tube cross sectional area
AR
and the volumetric flow rate
˙
V
at rated pressure and
temperature:
u0=˙
V
AR
(3.14)
Thermophysical properties of the gas phase as the molar heat capacity
˜cp,f
, density
ρf
, kinematic
viscosity
νf
and molar mass
Mf
were calculated according to DIPPR equations, SRK EoS[135]
and VDI Heat Atlas[210]. The heat transfer coefficient at the inner reactor wall
αint
can then
be calculated by:
αint =Nuint ·λf
dp
(3.15)
Sensitivity of the model input parameters on the overall heat transfer coefficient will be discussed
in Sec. 3.1.1.4.
32
3 Materials and Methods
3.1.1.2 External heat transfer coefficient of the industrial reactor
In the steam cooled industrial tubular reactor nucleate boiling can be assumed to appear on
the shell side of the reactor [136]. Numerous calculation methods exist in scientific literature to
calculate the heat transfer in a boiling liquid based on semi-empirical correlations derived from
lab scale measurements[210, 217, 218]. Three different calculation methods were considered in
this work:
1. Method by Fritz [217]:
The calculation method for the boiling heat transfer coefficient proposed by Fritz is based
on heat transfer measurements on horizontal and vertical tubes. The vapor pressure
of the boiling liquid
pb,H2O
at cooling temperature
Tcool
was calculated based on NIST
Webbook [208].
αext = 77.8·Twall,ext −Tcool
K2.57
·pb,H2O
Pa ·10−60.857 W m−2K−1(3.16)
2. Method by Holman [218]:
The calculation by Holman is structurally similar to the approach proposed by Fritz.
However, it discriminates between two semi-empirical equations depending on the range
of
αext
and accounts for the orientation of the heat transfer area. For a vertical geome-
try as it is found in an industrial tube bundle reactor the calculation is performed as follows:
- For 0 W m-2 K-1 <αext < 670 W m-2 K-1 :
αext = 537 ·Twall,ext −Tcool
K1/7
·pb,H2O
Pa ·10−50.4W m−2K−1(3.17)
- For 680 W m-2 K-1 <αext < 6680 W m-2 K-1 :
αext = 7.96 ·Twall,ext −Tcool
K3
·pb,H2O
Pa ·10−50.4W m−2K−1(3.18)
3. Method proposed by VDI Heat Atlas Sec. H2 [210]:
This calculation method for
αext
is more complex compared to those by Fritz and Holman.
With regard to VDI Heat Atlas,
αext
is determined from a fluid-specific normalized state
(for water αext,ref = 5,6 kW m-2 K-1) as follows:
αext =αext,ref ·Fq·Fp·Fwall (3.19)
In this equation, correction factors are provided for the heat flow density
˙q
(
Fq
), for pressure
of the boiling heat exchange fluid (Fp) and characteristics of the wall (Fwall) as follows:
Fq= ˙q
˙qref !0.9−0.3·p0.15
r
(3.20)
33
3 Materials and Methods
Fp= 1.73 ·p0.27
r+ 6.1 + 0.68
1−pr!·p2
r(3.21)
According to VDI Heat Atlas calculation of
Fwall
is objected to significant inaccuracies, as
it is weakly validated by experiments[210]. Therefore, this correction factor was set to 1.0,
however, better knowledge of the material factor could be gathered by a comparison with
measured data from an industrial reactor.
In Eq. 3.20 the normalized heat flow density is defined as
˙qref
= 20 kW m
-2
. The heat flow
density at the working point ˙qcan be calculated as follows:
˙q=Uwall,ext ·(TR−Twall,ext)(3.22)
Uwall,ext
as the overall heat transfer between the catalyst bed and the outer reactor wall
outside can be calculated removing αext from Eq. 3.1:
1
Uwall,ext
=1
αint
+dint
8·λrad
+dint ·ln dext
dint
2·λwall
(3.23)
Relative pressure
pr
in Eq. 3.20 and 3.21 is calculated by relating the critical pressure of
water of pcrit,H2O=220.64 bar to the vapor pressure at Tcool as follows:
pr=pb,H2O
pcrit,H2O
(3.24)
Fig. 3.2 shows
αext
calculated by applying the three calculation methods by Fritz [217], Hol-
man [218] and VDI Heat Atlas[210] over the temperature difference between reactor wall and
cooling medium for
Tcool
= 200
◦
C and
Tcool
= 280
◦
C. The two temperature levels of the steam
cooling correlate to vapor pressures of 14.6 bar and 64.5 bar, respectively [208]. The graph shows
that for all three models an increase of ∆
T
and
Tcool
leads to a rise of
αext
. However, while the
correlation by Holman does only show a low sensitivity towards
Tcool
, the calculations by VDI
Heat Atlas and Fritz are influenced by the temperature of the cooling medium more strongly.
Overall, the correlation by Holman shows a different trend compared to Fritz and VDI Heat
Atlas. At low temperature differences between reactor wall and cooling medium higher heat
transfer coefficients are calculated with a offset of approx. 1,000W m
-2
K
-1
or 2,000 W m
-2
K
-1
at 200
◦
C and 280
◦
C, respectively, while at higher ∆
T
this correlation calculated the lowest
heat transfer coefficients. At
Tcool
= 200
◦
C the correlations by VDI Heat Atlas and Fritz show a
similar behavior, however, at
Tcool
= 280
◦
C VDI Heat Atlas predicts significantly higher heat
transfer coefficients than the formula by Fritz. Measured data from an industrial steam cooled
reactor would be necessary to select the best correlation for
αext
. For the reactor simulation in
this work, the correlation by VDI Heat Atlas was selected, as it provides the most adjustable
and up-to-date model for the heat transfer coefficient in boiling medium.
As shown in Fig.3.2,
αext
depends on the temperature difference between
Twall,ext
and
Tcool
.
Vice versa
Twall,ext
is dependent on
αext
, as the external heat transfer influences the radial
temperature profile along the reactor. Therefore, an iterative determination of
Twall,ext
needs to
34
3 Materials and Methods
Figure 3.2:
External heat transfer coefficient calculated using the correlations by Fritz [217],
Holman [218] and VDI Heat Atlas [210] over the temperature difference between outer
reactor wall and cooling fluid for Tcool = 200 ◦C and Tcool = 280 ◦C.
be applied. This iteration can be performed by equating the calculation for the heat flux density
from inside the reactor to the outer wall with the heat flux density from the outer wall towards
the cooling medium as follows:
Uwall,ext ·(TR−Twall,ext)!
=αext ·(Twall,ext −Tcool )(3.25)
In case of a correct value for
Twall,ext
, both heat flux densities are equal. Therefore, a minimization
of the difference between the two heat flux densities can be performed varying
Twall,ext
in the
boundary TR> Twall,ext > Tcool .
3.1.1.3 External heat transfer coefficient of the miniplant reactor
As the experimental miniplant setup described in Sec. 3.4 is cooled by forced convection of
thermal oil flowing through an annular gap around the catalyst-filled reactor tube, calculation of
αext
for the miniplant differs significantly from the previously described methodology for the
industrial reactor. The calculation method was taken from the Nusselt correlations of VDI Heat
Atlas in Sec.G2 for laminar flow, transition region and turbulent flow [210]. Calculation of the
Reynolds number of the thermal oil Reoil in the annular is performed as follows:
Reoil =uoil ·dhydr
νoil
(3.26)
35
3 Materials and Methods
In case of the annular gap, the hydraulic diameter
dhydr
is defined as the difference between the
inner diameter of the annular tube
dann
and the external diameter of the reactor tube
dext
[210]:
dhydr =dann −dext (3.27)
Velocity of the thermal oil uoil is calculated using the continuity equation as follows:
uoil =4·˙
Voil
π·(d2
ann −d2
ext)(3.28)
Insertion of Eq. 3.27 and Eq. 3.28 into Eq. 3.26 leads to the following expression for the
Reoil
[210]:
Reoil =4·˙
Voil
π·(dann +dext)·νoil
(3.29)
Besides the width of the annular gap, Reoil depends on the volumetric flow rate of the thermal
oil
˙
Voil
and the kinematic viscosity of the thermal oil
νoil
. For the determination of
˙
Voil
, an
experimental campaign was performed measuring the volumetric flow rate of the thermal oil
rotameter in dependence of oil temperature and rotational speed of the shaft of the thermostat
pump. Moreover, the pressure in the thermal oil cycle was measured and compared to a pressure
loss simulation of the thermal oil cycle performed with the software "Druckverlust"[219] to verify
plausibility of the measurement. Details regarding the measurement of
˙
Voil
are provided in
Appendix A.8. The volumetric flow rate of the thermostat in dependence of temperature was im-
plemented into the simulation platform by a 3rd order polynomial (see Eq. A.21 in Appendix A.8).
Thermophysical data of the thermal oil provided by manufacturer[220] were transformed into
a temperature dependent polynomial and integrated into the simulation platform (see Ap-
pendix A.9).
3.1.1.4 Sensitivity of the heat transfer model parameters
In Fig. 3.3 a sensitivity analysis for the overall heat transfer coefficient calculated with regard
to Eq. 3.1 was carried out for both, industrial reactor (A) and the miniplant reactor (B) at
a base case of
TR
= 260
◦
C,
Tcool
= 240
◦
C and GHSV = 10,000 h
-1
at a pressure of 65 bar. A
gas composition of SN = 4.0 and COR = 0.9 was selected for the sensitivity analysis. Details
on the dimensions of the industrial and miniplant reactor will be provided in Sec.3.3 and 3.4,
respectively. For the sensitivity analysis, the input parameters influencing the heat transfer
through the catalyst bed and the reactor wall were varied in a range of
±
50 %. As the heat
transfer in the annular gap of the miniplant reactor was found to be largely influenced by
˙
Voil
(compare Sec. 3.1.1.3) this parameter was included into the analysis for the miniplant reactor.
The graphs indicate the importance of the correct determination of particle size for the simulation
of heat transfer for both, industrial and miniplant reactor. The larger sensitivity of this parameter
for the industrial heat transfer model is due to the larger particle size and therefore larger range
varied for this reactor type. A flotation particle size measurement was executed for the particles
used in the miniplant experiments in order to accurately determine this parameter (see App.A.10).
Besides particle diameter, the semi-empirical inverse slope parameter
Kr,∞
applied in Eq. 3.9
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3 Materials and Methods
does affect the overall heat transfer coefficient. By decreasing the value of
Kr,∞
, higher heat
transfer coefficients are obtained. Moreover, thermal conductivities of both, the reactor wall
λwall
and the catalyst
λcat
do influence the heat transfer coefficient for industrial and miniplant
reactor. While
λwall
was obtained from VDI Heat Atlas of stainless steel[210],
λcat
needs to be
determined by experiments. As Henkel determined this parameter during his PhD thesis for the
activated catalyst, this parameter was overtaken from his work[202].
Figure 3.3:
Sensitivity of the parameters of the heat transfer model towards the overall heat
transfer coefficient U
overall
for the industrial reactor (A) and the miniplant reactor (B);
Simulation parameters: T
cool
= 240
◦
C; T
R
= 260
◦
C; GHSV = 10,000 h
-1
; p = 65 bar;
SN = 4.0; COR = 0.9; For reactor design parameters see Tab. 3.5 and Tab. 3.6
The parameter influencing the heat transfer coefficient of the miniplant most strongly was found
to be
˙
Voil
. Therefore, this parameter was determined by experiments as described in Sec. 3.1.1.3.
3.1.2 Kinetic models
Some of the most commonly used kinetic models for methanol synthesis are the models provided
by Graaf[192, 195, 196, 221, 222] and Bussche-Froment [145, 199, 200, 223, 224] (compare Ap-
pendix A.2). Graaf’s kinetic model is based on dual-site Langmuir-Hinshelwood-Hougen-Watson
mechanism. In this mechanism, CO and CO
2
adsorb competitively on site one (s1), while H
2
and H2O adsorb on site two (s2) competitively as follows:
37
3 Materials and Methods
CO + s1 ⇌CO*s1 (3.30)
CO2+ s1 ⇌CO2*s1 (3.31)
H2+ 2s2 ⇌2H*s2 (3.32)
H2O + s2 ⇌H2O*s2 (3.33)
For H
2
, a dissociative adsorption is assumed for the mechanism. The adsorption of methanol as
the reaction product is assumed to be negligible in comparison to the other reactants. Adsorbed
on s1, CO and CO
2
are stepwisely hydrated. The elementary steps of the reaction network can
be expressed as follows [192].
CO2-hydrogenation
A1 CO2*s1 + H*s2 ⇌HCO2*s1 + s2 (3.34)
A2 HCO2*s1 + H*s2 ⇌H2CO2*s1 + s2 (3.35)
A3 H2CO2*s1 + H*s2 ⇌H3CO2*s1 + s2 RDS (3.36)
A4 H3CO2*s1 + H*s2 ⇌H2CO*s1 + H2O*s2 (3.37)
A5 H2CO*s1 + H*s2 ⇌H3CO*s1 + s2 (3.38)
A6 H3CO*s1 + H*s2 ⇌CH3OH + s1 + s2 (3.39)
rWGS
B1 CO2*s1 + H*s2 ⇌HCO2*s1 + s2 (3.40)
B2 HCO2*s1 + H*s2 ⇌CO*s1 + H2O*s2 RDS (3.41)
CO-hydrogenation
C1 CO*s1 + H*s2 ⇌HCO*s1 + s2 (3.42)
C2 HCO*s1 + H*s2 ⇌H2CO*s1 + s2 (3.43)
C3 H2CO*s1 + H*s2 ⇌H3CO*s1 + s2 RDS (3.44)
C4 H3CO*s1 + H*s2 ⇌CH3OH + s1 + s2 (3.45)
The rate determining steps (RDS) A3B2C3 were determined by Graaf by means of an er-
ror discussion of the 48 possible combinations of RDS for CO-hydrogenation, CO
2
-hydrogenation
and rWGS[191, 192, 225]. The kinetic model by Graaf is formulated by the following rate
equations [192]:
rCO2=k1·K2·EQ1
(1 + K1·fCO +K2·fC O2)f0.5
H2+K3·fH2O(3.46)
rrW GS =k2·K2·EQ2
(1 + K1·fCO +K2·fC O2)f0,5
H2+K3·fH2O(3.47)
rCO =k3·K1·EQ3
(1 + K1·fCO +K2·fC O2)f0,5
H2+K3·fH2O(3.48)
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3 Materials and Methods
The equilibrium terms for CO
2
-hydrogenation (
EQ1
), rWGS (
EQ2
) and CO-hydrogenation
(EQ3) can be expressed as follows according to Graaf et al. [129]:
EQ1= 1 −fCH3OH ·fH2O
fCO2·f3
H2·Keq,1
(3.49)
EQ2= 1 −fCO ·fH2O
fCO2·fH2·Keq,2
(3.50)
EQ3= 1 −fCH3OH
fCO ·f2
H2·Keq,3
(3.51)
The fugacities were calculated using the Soave-Redlich-Kwong equation of state (SRK EoS) [135].
The model parameters of the above mentioned kinetic models are expressed by an Arrhenius
correlation as follows for the kinetic rate constants kiand adsorption constants Kj[226]:
ki=Aki ·exp −Bki
R·T(3.52)
Kj=AKj ·exp −BK j
R·T(3.53)
The semi-empirical constants
Aki
and
Bki
as well as
AKj
and
BKj
in Eq. 3.52 and 3.53, respectively,
can be tuned in order to obtain agreement between experimental data and reactor simulation[226].
The parameters determined by Graaf are listed in Tab. 3.1 [193].
Table 3.1: Kinetic parameters proposed by Graaf et al. [193].
Unit Parameters
k1mol ·kg−1·s−1·bar−11.09 ·105·exp −87,500
R·T
k2mol ·kg−1·s−1·bar−0.59.64 ·1011 ·exp −152,900
R·T
k3mol ·kg−1·s−1·bar−14.89 ·107·exp −113,000
R·T
K1bar−12.16 ·10−5·exp 46,800
R·T
K2bar−17.05 ·10−7·exp 61,700
R·T
K3bar−0.56.37 ·10−9·exp 84,000
R·T
In contrast to the mechanism applied by Graaf, Bussche and Froment considered a different
reaction mechanism based only on CO
2
-hydrogenation coupled with rWGS via the formyl species
on a single active site[145]. From the mechanism in combination with the RDS (details see
Appendix A.18) the authors derived the following rate equations:
rCO2=k1·fC O2·fH2·EQ1
1 + K1·fH2O
fH2+K2·f0,5
H2+K3·fH2O3(3.54)
rrW GS =k2·fCO2·EQ2
1 + K1·fH2O
fH2+K2·f0,5
H2+K3·fH2O(3.55)
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3 Materials and Methods
The parameters Bussche et al. fitted towards their measured data are provided in Tab. 3.2.
Further details on this kinetic model are given in Appendix A.18.
Table 3.2: Kinetic parameters proposed by Bussche et al.[145].
Unit Parameters
k1mol ·kg−1·s−1·bar−21.07 ·exp 36,696
R·T
k2mol ·kg−1·s−1·bar−11.22 ·1010 ·exp −94,765
R·T
K1−3,453.38
K2bar−0.50.499 ·exp 17,197
R·T
K3bar−16.62 ·10−11 ·exp 124,119
R·T
In 2011, Henkel proposed a kinetic model based on the mechanism by Graaf, however, with
direct CO-hydrogenation neglected[202]. In agreement to Graaf’s finding, the steps A3 and B2
were considered rate determining by Henkel. The following set of rate equations was derived by
Henkel:
rCO2=k1·K2·fC O2·f1,5
H2·EQ1
(1 + K1·fCO +K2·fC O2)f0,5
H2+K3·fH2O(3.56)
rrW GS =k2·K2·fCO2·fH2·EQ2
(1 + K1·fCO +K2·fC O2)f0,5
H2+K3·fH2O(3.57)
As Henkel could not obtain one kinetic parameter set for the two experimental setups used within
his studies (compare Sec. 2.5) he proposed the two parameter sets listed in Tab. 3.3.
Table 3.3:
Kinetic parameters fitted by Henkel for the Berty reactor and the micro fixed bed
reactor [202].
Unit Berty Micro fixed bed
k1mol ·kg−1·s−1·P a−14.629 ·10−4·exp −47,472
R·T3.172 ·10−4·exp −45,893
R·T
k2mol ·kg−1·s−1·P a−0.512.975 ·exp −60,609
R·T2.021 ·106·exp −112,322
R·T
K1P a−12.743 ·10−17 ·exp 108,082
R·T2.420 ·10−14 ·exp 81,976
R·T
K2P a−11.935 ·10−41.000 ·10−4
K3P a−0.55.797 ·10−14 ·exp 112,322
R·T1.040 ·10−8·exp 61,856
R·T
In 2014, Park et al. published a kinetic model based on the rate equations as provided by
Graaf [203, 227]. As the authors used a catalyst similar to the one applied in this study and
covered a wide parameter range by their experiments their kinetic model was considered highly
relevant for this work. However, the kinetic model proposed by the authors entailed some
weaknesses:
40
3 Materials and Methods
a)
In contrast to the models proposed by Bussche and Henkel, their kinetic rate equations still
did account for CO-hydrogenation. This topic is discussed controversially in the scientific
community [49].
b)
The authors included the DME kinetics originally measured over a different catalyst [204]
in order to close their mass balances.
c)
The parameter set derived from their parameter fitting was not provided completely within
their original publication (see parameters in Appendix A.19).
Therefore, the kinetic model published by Park et al. is not explicitly treated within this study.
Nonetheless, as the authors published a complete set of integral experimental data, this data can
be used for validation and parameter regression (for details see Sec.3.5.1).
3.1.3 Diffusion model
Methanol synthesis is known to be subjected to mass transfer limitations depending on particle
size and reaction conditions applied [139, 228]. The Thiele modulus [229]
ϕM
is frequently
applied in scientific literature to describe the diffusion limitation caused by the reactants passing
through the porous structure of the catalyst towards the active sites[14, 168, 230]. Calculation
methodology was adopted from Lommerts et al. [230] who discussed the applicability of Thiele
modulus against the Dusty Gas Model: In their study the authors stated Thiele modulus as
an appropriate compromise between computational time and accuracy. Thiele modulus was
calculated via the pseudo-first order reaction rate with
K′
eq,H2O
and
K′
eq,M eOH
representing
the pseudo equilibrium constant[230] as well as
k′
H2O
and
k′
MeOH
as pseudo-first-order rate
constant [231]:
ϕM,j =dp
6v
u
u
t
k′
j·(K′
eq,j + 1 )
De
m,j ·K′
eq,j
(3.58)
The effective diffusion coefficients for water and methanol in the mixture were obtained as
follows [230, 231]:
1
De
m,j
=τ
εp·
N
X
j=1
j=k
1
Dj,k
+1
DK,j
(3.59)
The diffusion coefficients for the single components in the reaction mixture
Dj,k
were calculated
according to Fuller et al. [232] while calculation of the Knudsen diffusion coefficients
DK,j
was
performed with regard to Westerterp et al.[231]. Tortuosity
τ
and porosity of the catalyst
εp
overtaken from Henkel[202] are listed in Tab. 3.4.
Table 3.4:
Characteristic catalyst properties for the calculation of Thiele modulus determined by
Henkel [202].
Parameter Unit Value
τ- 2.99
εp- 0.58
41
3 Materials and Methods
The efficiency factor
ηeff
of the reactions
i
is calculated for the components
j
water and methanol
as follows [230, 231]:
ηeff,j =ref f,i
ri
=3ϕM,j ·coth (3 ϕM,j )−1
3ϕ2
M,j
(3.60)
Amongst the two efficiency factors obtained for water and methanol, the smaller value was
considered for the effective reaction rate in order to describe the maximum overall diffusion
limitation in the reaction network. Sensitivity of the efficiency factor towards
τ
,
εp
and
dp
was
discussed by a singular variation of these influence parameters within a one-dimensional reactor
simulation for one representative working point (see Appendix A.5).
3.1.4 Steady state reactor model
Based on the sub-models for heat transfer, powder kinetics and diffusion, a steady state reactor
model can be built utilizing the following ordinary differential equations (ODE) for mass, energy,
and momentum balance[210]:
a) Material balance:
d˙nj
dz =ρbulk ·AR·Xυj·ri(3.61)
b) Energy balance:
dT
dz =P∆HR,i ·ri·AR·ρbulk
˜cp,f ·˙ntot
+π·dint ·U·(Tcool −T)
˜cp,f ·˙ntot
(3.62)
c) Momentum balance [210]:
dp
dz =− 1.75 + 150 ·1−εbulk
Rep!·1−εbulk
ε3
bulk ·dp·ρf·u2
0(3.63)
Reynolds particle number
Rep
applied in Ergun’s equation (Eq. 3.63) was calculated by Eq.3.12.
The reactor model was verified by a comparison with other publications performing similar
simulations with the proposed kinetic models [136, 145, 211, 233].
Due to the nature of the one-dimensional model, radial gradients inside the reactor were neglected
in the simulation. However, the effect of this assumption towards the parameter fitting and
scale-up may be investigated in future studies, utilizing more powerful computational resources.
3.1.5 Dynamic reactor model
Compared to the steady state reactor model, for the dynamic reactor model the storage term
dx/dt
is calculated in order to account for the transition of heat and mass from one load point
to another. Consequently, the differential equations cannot be handled as ordinary differential
42
3 Materials and Methods
equations, but must be treated as partial differential equations (PDE). The following system of
PDEs was applied for the dynamic reactor model:
dxj
dt =−˙min
AR·dxj
dz +Mj·Pυj·ri·ρbulk
εbulk ·ρf
(3.64)
dT
dt =−˙min ·cp,f
AR·dT
dz +4·U
din ·(Tcool −T) + P∆HR,i ·ri·ρbulk
ρbulk ·cp,cat +εbulk ·ρf·cp,f
(3.65)
In comparison to the steady state model, for the dynamic reactor model mass fractions
xj
were
used to account for the mole reduction of the reaction more easily[180, 234]. The first-order
derivative in the z-coordinate is solved using the two-point upwind finite difference method,
where the axial grid is stepped through as follows [169, 235]:
dxj
dz ≈xj,n −xj,n−1
∆z(3.66)
dT
dz ≈Tn−Tn−1
∆z(3.67)
For the first element of the grid the boundary conditions
x1
=
xin
and
T1
=
Tin
were applied [235].
Due to the discretization of axial dimension of the PDE, the problem is transferred into the
structure of an ODE and can be handled by the solvers implemented in MATLAB
®
. In order to
define both, temperature and concentration of the reactants in every grid point, the grid is filled
with starting values obtained from a steady state simulation at t= 0.
In Eq. 3.65 the heat capacity of the catalyst
cp,cat
significantly influences the speed of adaption
of the reactor towards a new load point. A comprehensive analysis of
cp,cat
was performed by
Henkel[202] who measured the heat capacity of the activated catalyst by temperature modulated
differential scanning calorimetry. As a result Henkel provided a temperature dependent trend of
cp,cat which can be expressed by the following linear correlation:
cp,cat = 428.584 J
kg ·K−0.264 J
kg ·K2·T(3.68)
Comparison between the steady state reactor model and the dynamic reactor model under
steady state conditions showed similar simulation outputs. Small deviations in the reaction and
temperature profile can be explained by the error of the two-point upwind difference method.
However, this deviation was mitigated by a decrease of the step size of the axial grid. The
behavior of the dynamic reactor model is discussed by means of a dynamic simulation campaign
in App. A.24.
3.1.6 Process simulation model
To evaluate the impact of the kinetic model used in the reactor model introduced in Sec. 3.1.4
towards the operation of the methanol synthesis loop process, it was included into a process
simulation performed in MATLAB
®
Simulink. The synthesis loop was implemented as depicted
in Fig. 2.5. In the flow diagram, the loop balance was closed by calculation of the purge gas molar
43
3 Materials and Methods
flow
˙npurge
from the difference of the molar flow of non-condensed gas after the flash separator
˙nf lash,g
and the desired molar flow for the recycle loop
˙nrecycle
expressed via the molar flow of
the MUG ˙nM U G multiplied by the recycle ratio RR as follows:
˙npurge = ˙nf lash,g −˙nrecycle = ˙nf lash,g −RR ·˙nM U G (3.69)
The calculation of fluid phase equilibrium in the flash separator was performed using SRK
EoS [135].
3.2 Numerical methods
The differential equations of the pseudo-homogeneous reactor model for both steady state and
dynamic simulation were calculated by the solvers for ordinary differential equations implemented
into MATLAB
®
. A selection of the solvers was performed with regard to MATLAB
®
documen-
tation [236]. Since non-stiff solvers as "ode45" and "ode23" took long calculation times to solve
the differential equations, "ode15s" as a non-stiff equation solver was selected instead. All three
solvers led to the same profiles for molar fractions, temperature and pressure along the reactor,
however, with ode15s being the most efficient solver.
Performance of the reactor model was found to be a key-element for the simulation platform, as
complex analyses as e.g. the parameter fitting of a kinetic model on a large experimental data
set requires numerous reactor simulations and consequently simulation time. Therefore, once
implemented and tested, the reactor model was analyzed for issues in computational time. These
issues were addressed during the development progress of the simulation platform as shown in
Fig. 3.4 depicting the simulation time for four model revisions. For the comparison, a sensitivity
analysis covering 480 steady state reactor simulations was carried out for the industrial reactor
model.
Figure 3.4:
Speed-up of the simulation platform exemplified by a sensitivity analysis covering
480 reactor simulations.
The bottle-neck of the simulation with regard to computational time was identified as the
sub-module for calculation of the thermodynamic data due to the high number of function calls
in the integrator. Among the most important measures taken in order to speed-up the simulation
code were:
1.
Identification of slow program passages and MATLAB
®
commands, e.g. "roots()", nested
for-loops or "xlsread()" (Tool: MATLAB®Profiler).
44
3 Materials and Methods
2.
Replacement by faster calculation methods, e.g. Cardano’s formula for determination of
the zero points of a 3rd-order polynomial for SRK EoS instead of "roots()".
3. Vectorization of (nested) for-loops wherever possible.
4.
Reduction of function calls by pre-definition of vectors and matrices in the main program
and hand-through, e.g. for thermodynamic parameters.
5. Parallelization of "for"-loops (Tool: Parallel Computing Toolbox).
6. Translation of MATLAB®-code into c-code (Tool: MATLAB®Coder Toolbox).
All of these measures were applied to the source code of the simulation platform as the sub-models
were developed further over time and complexity of the simulations increased. It is to be denoted,
that the simulation time displayed in Fig. 3.4 was obtained for a sensitivity analysis using the
industrial reactor model. As approximately 35 % of the calculation time of the industrial reactor
model was consumed by the iterative approximation of the outer wall temperature of the steam
cooled reactor (compare Sec. 3.1.1.2) the miniplant reactor model was less time consuming as
this iteration is not necessary for convective thermal oil cooling. Due to the speed-up measures
described in this section, the accuracy and convergence of the reactor model was not influenced.
As a consequence, a parameter fitting requiring approximately 1Mio. reactor simulations was
possible in less than one day overall simulation time on a regular desktop computer.
3.2.1 Optimization methodology
Within this work, several optimization issues arose during the reactor simulation and design of the
miniplant setup, e.g. for determination of the outer wall temperature in case of the steam cooled
industrial reactor (see Sec. 3.1.1.2) or the simulation-based scale-down of the industrial reactor to
miniplant size (see Sec.3.3). While these problems did only feature one-dimensional optimization
problems, i.e. optimization problems with one variable, the parameter fitting of kinetic models
was a more complex issue. As the kinetic models considered within this study feature ten to
twelve variables (compare Sec.3.1.2), the optimization becomes a multi-dimensional problem.
The selection of the optimization algorithm is of high importance for an efficient treatment
of the problem in hand. As the simulation platform builds a reactor model resulting in a
non-smooth behavior of simulation outputs for example due to numerical noise caused by
tolerance of the ode-solvers, gradient-based optimization methods as the "fmincon"-algorithm
implemented into MATLAB
®
Optimization Toolbox were unsuitable for the estimation of the
kinetic parameters [237].
The "fminsearch"-algorithm as a direct search method was selected for the parameter fitting of
the kinetic models instead [237, 238]. This algorithm suggests new variables around the initial
starting values defined for the optimization problem. This so-called "simplex" is then moved
by the operations "reflect", "expand", "contract inside", "contract outside" and "shrink" until
the objective function is constant within a certain threshold or the minimum step size for the
variation of the optimization problem is reached [237].
One main drawback of the "fminsearch"-algorithm in connection to the parameter fitting of the
kinetic models was identified as the tendency of the solver to settle inside local minima. In order
to mitigate this problem, the global "State Transition Algorithm" (STA) published by Zhou et
45
3 Materials and Methods
al. [239] was implemented into MATLAB
®
and tested for the purpose of the kinetic parameter
fitting. This algorithm is based on random numbers spread around the local optimum by a
Gaussian normal distribution. On the one hand this method led towards lower objective functions
than the "fminsearch"-algorithm. On the other hand, the STA was found very inefficient resulting
in impractical computational effort. Therefore, the STA was not applied further during this
work.
Instead, it was found that a restart of the "fminsearch"-algorithm led to lower values for the
objective function. This finding is based on to the fact that the simplex was expanded by the
restart of the algorithm and thus able to overcome local minima. Therefore, it was concluded
that "fminsearch" could be applied as a quasi-global optimizer within this work. Further research
applying evolutionary optimization algorithms in combination with "fminsearch" are planned for
future work.
3.3 Scale-down of the industrial reactor
Design of reactors for kinetic measurements is a complex topic subjected by numerous scientific
studies [240–242]. In general, dimensions of kinetic setups are determined by dimensionless index
number as e.g.:
a)
The Bodenstein number
Bo
with the axial dispersion coefficient calculated according to
Kraume [243]
Bo =u0·hcat
Dax
(3.70)
b) The Reynolds particle number (see Eq. 3.12)
c) The reactor-particle diameter ratio [244].
φ=dint
dp
(3.71)
However, already in 1938 Damköhler et al. found that the scale-down of heterogeneous fixed bed
reactors is not possible without violation of the terms of similarity [245]. Therefore, in classical
kinetic setups ideal conditions by means of fluid dynamics, thermal operation and diffusion are
acquired which, however, significantly differ from the industrial scale [241]. Hence, multiple
experimental campaigns need to be executed to accurately transfer the results of small-scale
measurements towards industrial scale.
The reactor of Shiraz methanol synthesis plant in Iran was used as a reference for the industrial
scale in this study, as it is well documented in scientific literature[74, 164, 171, 246]. The steam
cooled reactor is part of a conventional methanol synthesis facility producing methanol from a
syngas obtained by NG reforming[74]. Design parameters for the industrial synthesis reactor are
given in Tab. 3.5 [74, 169, 246, 247].
With regard to methanol synthesis as one of the oldest high pressure reactions, versatile research
has been performed and rich knowledge on the modelling of heat transfer, kinetics and diffusion
was published in the past decades[14, 44]. Therefore, a simulation-based approach was realized
in this work in order to design an experimental miniplant setup with a high transferability of the
46
3 Materials and Methods
Table 3.5:
Design parameters of the Shiraz methanol synthesis reactor based on scientific litera-
ture [74, 169, 246, 247].
Parameter Unit Value
dint m 0.038
dext m 0.042
hcat m 7.022
dpm 0.0054
εbulk - 0.39
ρbulk kg m-3 1132
experimental results towards industrial scale. As a key parameter, the GHSV was held equal
for both industrial and miniplant reactor simulation to obtain similar residence times inside the
reactor on both scales.
Based on this approach and infrastructural boundary conditions, the miniplant setup used within
this work was designed and built. The following procedure was applied to design the reactor
dimensions:
1. Definition of the miniplant scale considering the lab infrastructure
2.
Design of a cooling system for a comparable heat transfer in the miniplant related to the
industrial scale
3.
Optimization of the reactor dimensions by minimizing the difference between the simulated
temperature profiles of the industrial reactor and the miniplant using the simulation
platform
In contrast to the industrial reactor implemented as multi tubular steam cooled reactor, the
miniplant reactor consists of a double pipe arrangement with thermal oil circulated through the
annular gap while the catalyst is placed inside the inner tube. The idea behind the thermal
oil cooling of the miniplant was to counter-balance the higher cooling-area-to-catalyst-volume
ratio of the miniplant in comparison to the industrial reactor by the lower external heat transfer
coefficient
αext
of the miniplant. The overall objective of this advanced cooling concept was to
achieve a temperature profile inside the miniplant reactor comparable to that of the industrial
reactor. Further details on the design of the miniplant are provided in Sec.3.4.
In order to determine the reactor dimensions for a maximized comparability of the miniplant
setup to the industrial scale, the diameter of the miniplant setup was varied with the catalyst
bed length adjusted to the catalyst volume
Vcat
defined in the conceptual design of the miniplant
correspondingly:
hcat =4·Vcat
π·d2
int
(3.72)
47
3 Materials and Methods
The temperature profile inside the reactor was identified one key indicator for the similarities
between industrial and miniplant reactor. Therefore, the RMSE between the temperature profiles
was considered as objective function for the optimization of the miniplant geometry:
RMSET=v
u
u
tPNT,inc
i=1 (Tx,i,ind −Tx,i,miniplant)2
NT,inc
(3.73)
RMSET
was minimized by the Nelder Mead algorithm implemented as a "fminsearch"-algorithm
in MATLAB
®
[238]. By performing simulations for both, industrial and miniplant setup, the
dimensions listed in Tab. 3.6 were iteratively defined.
Table 3.6:
Design parameters determined for the miniplant setup determined by the simulation-
based scale-down and experiments.
Parameter Unit Value
dint m 1.3·10-2 *
dext m 1.6·10-2 *
hcat m 1.14 *
dpm 1.0·10-3 (see App. A.10)
εbulk - 0.395 [248]
ρbulk kg m-3 1134 [248]
dshell m 2.1·10-2 *
˙
Voil l min-1 17.1 (see App.A.8)
*determined by simulation-based scale-down
The dimensionless index numbers defined previously are provided for both, industrial and
miniplant setup in Tab. 3.7.
Table 3.7:
Dimensionless index numbers for the industrial and the miniplant reactor; Bodenstein
number
Bo
and Reynolds particle number
Rep
were calculated at the following working
point: Tin = 240 ◦C; p = 80 bar; COR = 0.9; SN = 4.0; GHSV = 6,000 h-1 .
Parameter Unit Industrial Miniplant
reactor[74] reactor
Bo - 1014 900
φ- 7.04 13
Rep- 1185 36
Comparison of the dimensionless indices shows that both reactor scales satisfy the criteria for
ideal plug flow [212], i.e.
Bo
> 80, and non-laminar particle flow, i.e.
Rep
> 10. The difference
of the
Rep
numbers between industrial and miniplant reactor due to the adjusted reactor and
catalyst geometries was considered in the simulation of pressure loss as well as convective heat
transfer inside the reactor. As the reactor-particle-ratio satisfies the criterion
φ
> 10, wall effects
in the miniplant were neglected[212, 241]. However, in case of the industrial reactor
φ
was below
this critical threshold. Measured data obtained from this reactor would be helpful to quantify
48
3 Materials and Methods
possible deviations from the herein assumed ideal plug flow behavior for the industrial reactor.
The inner diameter of 13 mm for the miniplant reactor was obtained by the simulation-based
scale-down utilizing the kinetic model by Bussche-Froment [145] at high CO
2
contents. As the
choice of the kinetic model was found to influence the optimal reactor dimensions significantly,
optimized miniplant dimensions applying the kinetic model derived within this work will be
presented in Sec.4.2.6. These were determined for a wide range of synthesis conditions covering
two different pressure levels of 50bar and 80 bar at GHSV= 9,000h
-1
. Feed gas composition was
varied in the range 2.0≤SN ≤8.0 and 0.5 ≤COR ≤1.0.
3.4 Miniplant setup
Concept design of the miniplant setup was performed before the final reactor diameter and length
were defined by the simulation-based scale-down described in Sec. 3.3. In order to be able to
directly measure the reaction product from both, steady state and dynamic experiments, the
recycle loop of the industrial process was not included into the miniplant setup. On the one
hand this simplification moves the behavior of the miniplant setup away from the industrial
precursor as non-condensed recycled products like water and methanol are not present in the
reactor feed and the diluting effect of the recycle loop is not accounted for. On the other
hand, the once-through operation enables a scale-independent consideration of load changes and
simplifies gas phase measurement as well as mass balancing of the miniplant. Moreover, the
control strategy and the miniplant behavior are easier to handle compared to a setup including
the recycle loop [249]. Emulation of the recycle loop, however, was possible by the flexible gas
dosing capable of accounting for the complex interplay between CO
2
-hydrogenation and rWGS
in the industrial loop process.
A simplified flow sheet of the miniplant setup utilized within this work is given in Fig.3.5. The
reaction educts CO, CO
2
, H
2
as well as the inert gas nitrogen (N
2
) can be flexibly and precisely
dosed into the system. Due to the high synthesis pressures up to 80 bar applied to the system, a
liquid dosing of CO2utilizing an HPLC-pump coupled with a Coriolis flow meter was designed
for the system [250]. The liquid CO
2
was mixed with the other educts and evaporated along a
heated line towards the reactor. The correct calibration of the gas dosing unit was verified by
gas phase measurements through the bypass line at the beginning of each experimental day.
The heat released by the reaction inside the inner tube was removed by thermal oil circulating
along the annular gap in counter current flow. Volumetric flow rate of the oil was measured by a
rotameter calibrated for the thermal oil used inside the cooling system (Fragoltherm X-400-A).
Temperature of the thermal oil was controlled by a closed-cycle thermostat.
The reactor was filled with a commercial Cu-based catalyst provided by Clariant AG. The
pelletized catalyst particles were ground and sieved to a particle size of d
p
= 1 mm to avoid wall
effects inside the reactor. The analysis of the particle size distribution of the catalyst is provided
in Appendix A.10. An inert bed of
α
-alumina supplied by Merck KGaA was placed above and
below the catalyst bed. The fixed bed was held inside the reactor with a porous stainless steel
support disc. Blind tests introducing syngas into the heated reactor only filled with the inert
material confirmed the inert behavior of this material, as no trace compounds were detected by
49
3 Materials and Methods
Figure 3.5: Simplified flow sheet of the experimental miniplant setup.
the gas phase measurement.
In order to gather axial information about the reaction kinetics, the reactor was equipped with a
system for fiber optical temperature measurement described in detail in Sec. 3.4.1. The glass
fiber was placed inside a 0.8 mm steel capillary; the optical signal was generated and processed by
a Luna ODiSI 6102 unit. An axial resolution of ∆z = 2.6 mm was selected for the measurement
campaign leading to 438 measurement increments for temperature measurement (
NT,inc
) inside
the catalyst bed with a length of 1.14 m. Calibration of the fiber was carried out by heating the
thermal oil cycle to constant temperature levels between 50
◦
C and 265
◦
C. The oil inlet and
outlet temperatures were measured by two Pt-100 temperature sensors at the oil inlet (TI02) and
outlet (TI01); a heat loss resulting in a temperature decrease of approximately 1.5 K between
thermal oil inlet and outlet was regarded by a linear temperature decrease along the reactor.
The cooling temperature T
cool
was adjusted to the reading of TI01. As a result of the calibration
a polynomial of 3rd degree was determined for each increment along the fiber. Extrapolation of
these polynomials was performed for temperatures exceeding 265
◦
C as the thermal oil did not
allow for higher calibration temperatures due to reasons related to plant safety.
For analysis of the reaction products a MKS MultiGas
TM
2030 on-line Fourier-transform infrared
50
3 Materials and Methods
spectrometer (FTIR) with an optical path length of 35 cm was used for quantitative product
analysis. Since H
2
as a homonuclear gas cannot be detected by FTIR, the molar fraction of this
gas was determined by the component balance as follows:
yH2= 1 −
Ncomp
X
j=1
yj(3.74)
Besides the main reactants CO, CO
2
, H
2
O and MeOH, side products such as methyl formate,
methane, ethanol, acetone and acetic acid were calibrated and analyzed by the FTIR. However,
their concentrations below 100ppm in the product gas made an exact quantification in the gas
phase impossible with the FTIR applied in this work. Therefore, the side products mentioned
above were excluded from the mass balance over the reactor.
Besides the gas phase analysis, the main product stream was led through a cooler-condenser
unit at an operating temperature of 10
◦
C to separate the liquid products from the gas phase for
qualitative analysis of condensable trace compounds. Analysis of the liquid phase was carried
out using Nuclear magnetic resonance spectroscopy (NMR).
All real time information on sensor properties such as volumetric flow rates, inlet and outlet
pressures, temperature profile as well as gas phase composition were logged with a sample rate
of 1 Hz.
3.4.1 Fiber optic temperature measurement
One key-element of the miniplant setup is the fiber optic temperature measurement. The
measurement principle of this technology is based on axial variation of the refractive index along
a glass fiber due to impurities or local defects [207]. Application of Fourier transformation to a
back-scattered light signal leads to continuous information about the (thermal) expansion of the
fiber and thereby delivers a highly resolved temperature information.
Measured data obtained from the fiber was acquired with a frequency of 1 Hz. However, in order
to remove time-resolved noise from the signal, the maximum measurement frequency of 128Hz
was applied for five values in a sequence. The median value was used to remove outliers from the
temporally resolved signal.
To account for the non-linearity and possible mechanical tension of the fiber optic temperature
sensor, calibration of the measurement system was executed[248]. Due to axial irregularities in
the displayed output values, the calibration had to be performed separately for each increment
along the fiber. The thermal oil cycle was adjusted to fixed temperature levels to set a constant
temperature along the axial reactor length. During calibration the reactor was filled with N
2
,
however, without gas flow to prevent convective heat transfer phenomena at the gas inlet zone.
In order to transform the uncalibrated temperature reading into an accurate output signal, the
following temperature dependent 3rd-order polynomial was fitted for each increment along the
fiber:
Tcalib =A·T3+B·T2+C·T+D(3.75)
51
3 Materials and Methods
The inlet and outlet temperature of the thermal oil were measured by Pt-100 temperature sensors.
Depending on the temperature level, the oil outlet temperature was 1.0 K to 2.0 K below the
oil inlet temperature. As the temperature difference increased by rising temperature level, this
phenomena was ascribed to heat losses through the axial insulation of the reactor. These losses
were accounted by a linear interpolation of the temperature profile of thermal oil between the
Pt-100 temperature sensors.
Calibration was executed between temperatures of 50
◦
C and 265
◦
C. Higher temperatures were
not possible as the flame point of the thermal oil was specified by the manufacturer to 275
◦
C [220].
With regard to the safety concept, temperature was kept 10
◦
C below the flame point to have a
buffer for a possible emergency turn-off or a control overshoot of the thermostat. Calibration
temperature was increased by steps of 25K from 50
◦
C until 200
◦
C and by increments of 5K
for temperatures exceeding 200
◦
C to achieve a maximum accuracy in the relevant temperature
range. As a consequence of the conversion error of the analogue-digital converters of the Pt-100
temperature sensors, the measurement error accounted to
±
0.4 K. In Fig. 3.6 the temperature
offset between calibrated and displayed temperature is plotted over the calibrated temperature
for one measurement increment of the fiber. The calibration polynomial is displayed as dashed
line.
Figure 3.6:
Calibration offset over the calibrated temperature between 50
◦
C and 265
◦
C together
with the fitted 3rd-order polynomial extrapolated to 25
◦
C and 300
◦
C at one mea-
surement increment along the fiber.
As temperatures exceeding 265
◦
C occurred in the reactor during the kinetic experiments, the
polynomial had to be extrapolated. Extrapolation could result in an error, however, this procedure
was inevitable due to the reasons of plant safety mentioned above. Overall, the calibration set
resulted in 580 polynomials in the heated zone of the reactor covering the height of the catalyst
bed and the inert bed approximately 20 cm above and below the catalyst bed. In order to obtain
information on the temperature profile along the inert bed outside the heating zone, the mean
values of the polynomial parameters fitted inside the heated zone were applied as calibration
parameters. However, these zones were not relevant for the validation of the kinetic reactor
model.
52
3 Materials and Methods
Issues for the calibration of the measurement system arose from H
2
diffusing through the shell of
the stainless-steel capillary into the glass fiber. This phenomenon led to a long-term drift of the
calibration. Repetition of the calibration procedure showed, that this drift could be addressed
by adjustment of the offset
D
in Eq. 3.75. Moreover, a leakage was detected during the kinetic
measurements at the bottom soldering point at the end of the fiber. This issue, however, could
be fixed by an in situ repair applying tungsten inert gas welding inside the bottom flange of the
reactor. The problem probably arose, as the bottom of the fiber was sealed by copper instead of
stainless-steel by the manufacturer.
The temperature profiles measured by the fiber optic processing unit were subjected to fluctuations
caused by slight heterogeneity of the distribution of the catalyst particles along the fiber. Among
other possible smoothing filters as e.g. the moving median or a Gaussian weighted moving
average[236], the Savitzky-Golay filter [251] was identified as the most robust and least distorting
algorithm.
Figure 3.7:
Calibrated temperature profile measured by the fiber optic processing unit and
Savitky-Golay smoothed temperature profile obtained with a moving window of 40
elements at p = 80 bar; T
cool
= 240
◦
C; SN = 5.0 and GHSV = 9,000 h
-1
for COR = 0.7,
0.8, 0.9, 0.95 and 0.98.
In Fig. 3.7 the calibrated original data as obtained by the fiber optic processing unit is displayed
together with the Savitzky-Golay smoothened data. The working points were obtained at a
working pressure of 80bar and a cooling temperature of 240
◦
C at GHSV = 9,000 h
-1
. SN was
held constant at 5.0, while COR was varied between 0.7 and 0.98. The graph indicates that the
smoothing filter is capable of removing noise from the signal without loosing the core information
obtained from the measurements. During the parameter fitting of the kinetic models described
in Sec. 3.5.2.2, better results with less conflicts due to local minima were obtained with the
smoothened data instead of the original data. For the algorithm a moving window of 40 elements
53
3 Materials and Methods
was applied. Smaller moving windows increased the noise on the signal, while higher values led
to loss of information on the hot spot position and temperature.
3.5 Experimental validation
To evaluate the impact of the herein proposed methodology, a steady state kinetic model was
derived from both, integral measured data taken from literature[203] and differential temperature
data in combination with the integral FTIR product measurement from the miniplant. The
methodology for both approaches will be explained in Sec. 3.5.1 and 3.5.2, respectively.
3.5.1 Integral literature data
In order to obtain a kinetic model applicable towards a wide working range of conventional and
renewable feedstock-based methanol synthesis, a kinetic model was derived from the experimental
data published by Park et al.[203]. Application of the kinetic rate equations published by Henkel
(i.e. Eq. 3.56 and Eq. 3.57) refitted to the experimental data was presumed to lead to a highly
relevant kinetic model based on a commercial state-of-the-art catalyst. The model parameters
will be compared to those elaborated by Henkel in Sec. 4.1. The macroscopic effect of the integral
kinetic model derived within this work in comparison to state-of-the-art models will be discussed
within a comprehensive sensitivity study utilizing the one-dimensional model of an industrial
methanol synthesis reactor in Sec.4.1.2. Details on the experimental setup used by Park et al. are
provided elsewhere [203].
For the re-fitting of the kinetic model to the measured data provided in the publication by
Park et al.[203], a parameter screening and pre-selection of the data was performed. As the
mechanism proposed by Henkel does not consider direct CO-hydrogenation, measured values
with COR = 0.00 were not considered within this study. Four experimental points were therefore
excluded from the data set. The remaining quantity of 114 experimental points (Ndata pt) were
used for the parameter fitting within this study (see App. A.6). Based on C, H, O balances,
the mole fractions at the reactor exit were determined from the CO and CO
2
conversion given
in the original publication. This calculation procedure was performed in order to decrease the
sensitivity of the parameter fitting towards measurement errors at low concentrations. Before
this procedure was applied, high conversion rates at low total concentrations did largely affect
the resulting model parameters especially when measurements at low COR were included to
the fitting. Therefore, it is concluded that the measurement campaign by Park et al. could be
affected by measurement errors especially at low concentrations of CO
2
. This statement, however,
needs to be validated by additional experimental data.
For the fitting procedure, the data were imported into a MATLAB
®
reactor model of the kinetic
reactor as documented by Park et al.[203]. The simulated output values (
yj,sim
) were then
compared against the measured data (
yj,exp
) by means of the root mean square error (RMSE).
RMSE was calculated for the molar fractions of CO and CO2as follows:
f(x) = RMSECO2+RM SECO (3.76)
54
3 Materials and Methods
RMSECO2=v
u
u
tPNdata pt
i=1 (yCO2,sim,i −yCO2,exp,i)2
Ndata pt
(3.77)
RMSECO =v
u
u
tPNdata pt
i=1 (yCO,sim,i −yCO,exp,i)2
Ndata pt
(3.78)
The objective function
f
(
x
)defined as the sum of RMSE
CO
and RMSE
CO2
was minimized by
adaption of the ten model parameters with the starting values taken from Henkel’s original
parameter set (see Tab. 3.3). For minimization, the multidimensional unconstrained non-linear
Nelder-Mead algorithm implemented within the "fminsearch"-method by MATLAB
®
was ap-
plied [238].
3.5.2 Differential miniplant data
For deeper insights into the kinetic performance of methanol synthesis on industrial scale, a
novel approach for the validation of reaction kinetics using the miniplant described in Sec. 3.4
was investigated within this work. In comparison to classic kinetic setups as e.g. the one applied
by Park et al.[203], this setup was intentionally held under polytropic operating conditions by a
thermal oil cooling system. Application of fiber optical temperature measurement delivered highly
resolved axial information on the differential catalytic activity which was used in connection
with FTIR product measurement for the validation and adjustment of kinetic models. The
experimental campaign executed with the miniplant setup as well as the validation procedure
will be presented in the following sections.
3.5.2.1 Experimental plan
In order to determine the reaction kinetics over a wide parameter range relevant for application
with CO
2
-rich syngas, a comprehensive experimental plan was executed. Besides pressure, the
parameters GHSV, COR and SN were varied in the experimental campaign due to their relevance
for reaction kinetics [206]. The variation ranges of the experimental parameters are provided in
Tab. 3.8. All combinations of the parameters listed were applied to the experimental setup at a
cooling temperature of 240 ◦C.
Table 3.8: Parameters applied for the experimental campaign at the miniplant setup.
Parameter Varied range
p 50 bar; 65 bar; 80 bar
GHSV 6,000 h-1; 9,000 h-1; 12,000 h-1
COR 0.7; 0.8; 0.9; 0.95; 0.98
SN 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0
To consider the effect of lower cooling temperatures the parameter variation at 50bar was also
executed at Tcool = 220 ◦C in a COR range between 0.7 and 0.95 and SN between 2.0 and 8.0.
55
3 Materials and Methods
When the experimental campaign was executed, 24/7 operation of the miniplant facility was
not implemented yet. Therefore, the campaign was interrupted, when no operation was possible,
e.g. over night, weekend or during maintenance intervals. While the miniplant setup was held
at 160
◦
C and flushed with N
2
over night (hot standby), it was blocked with N
2
at ambient
temperature (cold standby) for longer downtime periods. However, the activity of the catalyst
was benchmarked at the beginning and end of each experimental day – no effects due to hot or
cold standby could be observed. The chronological progress of the overall experimental campaign
is provided in App.A.12.
Due to instability of some experimental points as a result of oscillations in CO
2
dosing or hot spot
temperatures expected to exceed the critical threshold of 280
◦
C, some of the data points could not
be included into the validation resulting in an overall set of 324 data points (
Ndata pt
). To account
for activity changes during the experimental campaign a benchmark measurement was repeatedly
executed. The benchmark condition was defined at COR = 0.9, SN = 4.0, GHSV = 12,000 h
-1
and
Tcool = 240 ◦C in coordination with project partners [252].
The experimental plan was executed in seven phases as follows:
1. Ramp-up at benchmark conditions at 50 bar:
p = 50 bar; Tcool = 240 ◦C; SN = 4.0; COR = 0.9; GHSV = 12,000 h-1;
2. Parameter variation at 50 bar and 240 ◦C:
p = 50 bar; T
cool
= 240
◦
C; 2.0
≤
SN
≤
8.0; 0.7
≤
COR
≤
0.95; 6,000 h
-1 ≤
GHSV
≤
12,000 h
-1
3. Parameter variation at 65 bar and 240 ◦C:
p = 65 bar; T
cool
= 240
◦
C; 2.0
≤
SN
≤
8.0; 0.7
≤
COR
≤
0.95; 6,000 h
-1 ≤
GHSV
≤
12,000 h
-1
4. Parameter variation at 80 bar and 240 ◦C:
p = 80 bar; T
cool
= 240
◦
C; 2.0
≤
SN
≤
8.0; 0.7
≤
COR
≤
0.95; 6,000 h
-1 ≤
GHSV
≤
12,000 h
-1
5. Parameter variation at COR = 0.98 and 240 ◦C:
50 bar
≤
p
≤
80 bar; T
cool
= 240
◦
C; 2.0
≤
SN
≤
8.0; COR = 0.98; 6,000 h
-1 ≤
GHSV
≤
12,000 h
-1
6. Parameter variation at 50 bar and 220 ◦C:
p = 50 bar; T
cool
= 220
◦
C; 2.0
≤
SN
≤
8.0; 0.7
≤
COR
≤
0.95; 6,000 h
-1 ≤
GHSV
≤
12,000 h
-1
7. Benchmark at conditions of phase 1.)
During phase 1.) the benchmark conditions were held constant for 56h time-on-stream (ToS).
In phase 5.) COR was held constant at 0.98 at the three pressure levels considered. This
variation was not included into phases 2.) to 4.) as catalyst deactivation was expected during
these experiments due to the high CO2content. After the parameter variation was terminated,
the benchmark point of phase 1.) was held constant for another 12h.
3.5.2.2 Validation and parameter fitting
To validate the performance of the kinetic models proposed by Bussche and Graaf (see Sec.3.1.2)
as well as the integral kinetic model derived in Sec.4.1, reactor simulations utilizing these models
were executed for all working points gathered during the experimental campaign. In order to
quantify the deviations between the these models and the experimental data, RMSE values
considering both, information on the thermal behavior and the composition of the gas phase
were calculated. The objective function
f
(
x
)for the parameter fitting was formulated as the
56
3 Materials and Methods
sum of the weighted root mean square errors for temperature profile (
RMSET,prof ile
), hot spot
temperature (RM SET ,hs) and gas phase composition at reactor outlet (RM SEy):
f(x) = α·RMSET,prof ile +β·RM SET ,hs +γ·RM SEy(3.79)
RMSET,prof ile
in Eq. 3.79 was calculated considering all working points
i
along the axial tem-
perature measurement increments jfrom the start to end of the catalyst bed as follows:
RMSET,prof ile =
v
u
u
u
u
u
tPNdata pt
i=1 PNT,inc
j=1 |Texp,i,j −Tsim,i,j |
NT,inc !2
Ndata pt
(3.80)
RMSET,hs
was calculated for the maximum temperature measured and simulated for the working
points using the following equation:
RMSET,hs =v
u
u
tPNdata pt
i=1 (Ths, exp,i −Ths, sim,i )2
Ndata pt
(3.81)
To account for the gas phase composition,
RMSEy
was calculated for all working points
considering the molar fractions of the components jin the product gas mixture:
RMSEy=
v
u
u
u
u
u
tPNdata pt
i=1 PNcomp
j=1 |yexp,i,j −ysim,i,j |·100%
Ncomp !2
Ndata pt
(3.82)
The weighting factors
α
,
β
and
γ
were fixed to constant values of
α
=2K
-1
,
β
=3K
-1
and
γ
= 25
by an empirical approach in order to balance the RMSE of temperature and composition to
comparable numerical values [253].
Fig. 3.8 right shows a comparison between the experimental data obtained at the benchmark
gas composition at 50 bar and the reactor simulation using the kinetic model as proposed by
Bussche[145]. As the model by Bussche was derived from a different catalyst using integral
experimental data, strong deviations between the experimental data and the simulation are
present in temperature profile, hot spot temperature and product composition. A detailed
discussion on the deviation between the experimental data and the simulation results obtained
using the original kinetic models proposed by Bussche and Graaf as well as the integral kinetic
model fitted to Park’s experimental data is given in Sec.4.2.2.
To minimize the deviation between the reactor simulation and the experimental data, the kinetic
constants and adsorption constants of the kinetic models were adjusted by a parameter fitting
minimizing the objective function f(x)defined in Eq. 3.79.
A flow diagram indicating the procedure of the parameter fitting is provided in Fig.3.8 on
the left. The initial parameter set for the rate equations considered was overtaken from the
original publications by Graaf and Bussche as well as from the integral kinetic model derived in
Sec. 4.1. The objective function, i.e. the deviation between the experimental data and the reactor
57
3 Materials and Methods
Figure 3.8:
Illustration of the parameter fitting methodology applied in this work (left) and an
exemplary working point a benchmark conditions at 50bar showing the temperature
profile (right, top) and gas phase molar fractions (right bottom) obtained from the
experiment (solid, red) and the miniplant reactor simulation (dotted, blue) using
the kinetic model as proposed by Bussche [145]; Red arrows and areas indicate
the deviations between the simulation and the experimental data addressed by the
parameter fitting; The measured temperature profile is smoothed by the Savitzky-
Golay filter [251].
simulation results, was then minimized during the primary optimization by the "fminsearch"
algorithm (see Sec. 3.2.1). Starting from the improved parameter set, the optimization algorithm
was repeated (secondary optimization) until the objective function was not improved further to
mitigate local minima. Once a set of kinetic parameters was found fulfilling the stopping criteria,
this set was subjected to a further analysis.
3.5.2.3 Impact on industrial reactor design
For the demonstration of the impact of the differential kinetic model on the industrial scale
reactor in comparison to the integral kinetic model [206], a simulation study was performed
analyzing hot spot position and temperature as well as product composition, in an industrial
reactor simulation at the pressure levels 50bar and 80 bar at GHSV = 6,000 h
-1
. For the gas
composition the range applied in the experimental campaign was considered (see Tab. 3.8). Inlet
and cooling temperatures were set to 240 ◦C.
58
4 Results and Discussion
In this chapter the main results of the kinetic parameter fitting performed for integral and
differential experimental data will be discussed Sec. 4.1 and Sec. 4.2, respectively. As both sets
of measured data are based on a similar catalyst, a comparison between the derived kinetic
models will be performed in order to demonstrate their deviations originating from the different
methodical approaches. The integral model based on Henkel’s kinetic model and fitted to
the measured data published by Park et al. will be designated as "Nestler
integ
" from hereon.
The differential kinetic model based on Nestler
integ
fitted to the miniplant data will be labeled
"Nestlerdiff".
In Sec. 4.3, the performance of the dynamic reactor simulation including the Nestler
diff
kinetic
model will be validated against one representative load change experiment measured at the
miniplant setup. Finally, in Sec.4.4, the differential kinetic model derived within this work will
be held against one important literature standard on the process scale.
4.1 Kinetic model derived from integral literature data
In Fig. 4.1 the final fitting result is presented for the Nestler
integ
kinetic model in a parity plot
comparing the measured and simulated molar fractions of CO and CO
2
at the exit of the reactor.
The plot illustrates that most values lie within the 20% error region. RMSE values of 0.042 for
the CO molar fractions and 0.084 for CO
2
molar fractions were obtained applying the kinetic
model after the parameter estimation. These deviations could be based on analytical inaccuracies
Figure 4.1:
Parity plot of the kinetic model fitted to the measured data published by Park et
al. [203] including the error lines for 0 % (solid, black), 10 % (dashed, black) and 20%
(dashed, gray).
60
4 Results and Discussion
or systematic errors as e.g. the deactivation of the catalyst or temperature gradients along the
fixed bed. However, these possible issues were not discussed by Park et al. [203]. Moreover, the
remaining error could be due to insufficient mechanistic assumption within the proposed model
equation.
Generally, the model describes the whole range of the measured data set in acceptable range.
Importantly, the kinetic model Nestler
integ
proposed within this section does not constitute a
final kinetic expression, but rather a working base which can will compared to the kinetic model
derived from the differential miniplant experimental data in Sec. 4.2.
The kinetic parameters obtained from the fitting procedure are given in Tab. 4.1.
Table 4.1: Parameters for the Nestlerinteg kinetic model proposed within this work.
Unit Nestlerinteg kinetic parameters
k1mol ·kg−1·s−1·P a−15.411 ·10−4·exp −45,458
R·T
k2mol ·kg−1·s−1·P a−0.54.701 ·exp −54,970
R·T
K1P a−13.321 ·10−18 ·exp 109,959
R·T
K2P a−18.262 ·10−6
K3P a−0.56.430 ·10−14 ·exp 119,570
R·T
In agreement with literature findings the reaction rate constants for CO
2
-hydrogenation (k
1
) and
rWGS (k2) increase with increasing temperature [145, 192, 254].
While the adsorptions constants for CO (K
1
) as well as H
2
O and H
2
(K
3
) decrease with increasing
temperature, the adsorption constant for CO
2
(K
2
) does not show any temperature dependence.
This finding is in line with the parameter estimation by Henkel who also did not determine a
temperature dependence of this constant [202].
In Tab. 4.2 the RMSE values for the measured data published by Park and the kinetic models by
Graaf, Bussche and Henkel as well as Nestler
integ
are listed. It can be concluded that the model
by Graaf shows the highest deviation from the measured data and is therefore not appropriate
for the description of the kinetic data considered in this study. A better fitting result could
be achieved with the models by Bussche and Henkel. However, by application of the fitting
Table 4.2:
Comparison of the RMSE for the molar fractions measured by Park[203] and simulated
using the kinetic models by Graaf [192], Bussche[145] and Henkel [202] as well as the
kinetic model Nestlerinteg.
Kinetic model RMSECO in % RMSECO2 in %
Graaf 2.453 0.917
Bussche 1.085 0.528
Henkel, Berty 0.833 0.529
Henkel, fixed bed 0.877 0.522
Nestlerinteg 0.605 0.441
61
4 Results and Discussion
Figure 4.2:
Arrhenius plot of the kinetic constants k
1
(A), k
2
(B), K
1
(C), K
2
(D), and K
3
(E) for the Nestler
integ
model in comparison to those calculated with the model by
Henkel [202] between 203 ◦C and 315 ◦C.
procedure to the kinetic parameters of the model proposed by Henkel it was possible to decrease
the RMSE by 27.4% for CO and 16.6 % for CO
2
with regard to the closest literature model,
i.e. Henkel Berty.
The kinetic parameters determined by Henkel (see Tab. 3.3) are compared to the parameter set
listed in Tab. 4.1 in Fig. 4.2 by means of Arrhenius diagrams between 203
◦
C and 315
◦
C. The
graphs show differences in the temperature dependence of both, reaction (A, B) and adsorption
constants (C, D, E) between the Nestler
integ
kinetic model and Henkel’s kinetic models obtained
for Berty and fixed bed reactor. For the Nestler
integ
model k
1
(CO
2
-hydrogenation) and k
2
(rWGS) are higher in comparison to those by Henkel over the whole temperature range considered.
K
1
, i.e. the adsorption constant for CO, of the Nestler
integ
kinetic model is below the parameter
range determined by Henkel for both, Berty and fixed bed reactor. K
2
representing the adsorption
constant of CO
2
was computed at a lower value in comparison to Henkel. K
3
representing the
adsorption constant of water and H
2
has due to the structure of Eq. 3.56 and 3.57 the highest
sensitivity on the reaction rate for CO
2
-rich syngas. At temperatures exceeding 300
◦
C the values
for K
3
are in a comparable range to those obtained by Henkel with the fixed bed reactor. At lower
temperatures, however, increased values for K
3
were determined leading to decreased reaction
kinetics at high partial pressures of water in the reacting gas mixture in comparison to the model
by Henkel. As high partial pressures of water are known to occur with increasing COR, this
finding may be explained by the experimental range covered by Henkel and Park. While Park et
62
4 Results and Discussion
al. considered COR up 1.0 in their experimental campaign, Henkel did not perform experiments
at COR exceeding 0.9 within his study (see Fig. 2.10). As the kinetic model proposed by Henkel
does not account for the kinetic inhibition caused by water adsorption on the active sites of the
catalyst, it can be concluded, that experimental data with COR > 0.9 is necessary in order to
accurately describe this effect. Therefore, kinetic models applied for the design of PtM processes
should be validated at high CO2in the synthesis gas.
4.1.1 Analysis of the reaction rates
In order to show the influence of product formation on the reaction rates, the Nestler
integ
kinetic
model is discussed in comparison to the kinetic models by Graaf, Bussche and Henkel for different
levels of reaction products formed (see Fig. 4.3). Temperature dependent reaction rates were
calculated for CO
2
-hydrogenation at 50bar with a feed composition of COR = 1.0 and SN = 2.0.
Three cases were considered, (A) without product, (B) with 0.5 mol-% of methanol and 1.7 mol-%
of water and (C) 1.6mol-% of methanol and 4.5 mol-% of water. The increased product contents
in (B) and (C) correspond to typical gas compositions formed along an industrial reactor at this
composition of the feed gas. Fig. 4.3 (A) shows that the reaction rate of CO
2
-hydrogenation
without products in the gas mixture calculated by Bussche’s kinetic model is more than one order
of magnitude higher than those calculated with the other kinetic models. The reaction rates
calculated with Henkel’s parameter set show a similar trend as the Nestlerinteg model, however,
at a lower level. The lowest reaction rates were calculated using Graaf’s kinetic model.
Figure 4.3:
Reaction rates of the kinetic models considered within this study at SN = 2.0,
COR = 1.0, p = 50 bar without product (A), with approx. 0.5 mol-% methanol and
1.7 mol-% water (B), and 1.6mol-% methanol and 4.5 mol-% water (C).
63
4 Results and Discussion
At increased product formation (i.e. 1.7 mol-% water and 0.5mol-% methanol, (Fig. 4.3 (B)) the
reaction rates calculated by Bussche drop significantly. While Bussche’s kinetic model shows a
maximum reaction rate at approx. 300
◦
C the reaction rate of the Nestler
integ
model increases
with rising temperature comparable to the models by Henkel and Graaf. At temperatures below
270 ◦C the reaction rate of the Nestlerinteg model falls below that of Henkel’s models.
The limiting effect of the products formed towards the reaction rates for the model by Bussche
and the Nestler
integ
model is enhanced when more water and methanol are formed within the
reactor (Fig. 4.3 (C)). Below 300
◦
C the reaction rates calculated with the models by Henkel and
Graaf are moderately decreasing while temperature is reduced, however, the limiting effect of
water is not as strongly developed as in the model published by Bussche and the model proposed
within this section. At 1.6 mol-% of methanol and 4.5 mol % of H
2
O the equilibrium limitation of
the reaction can be determined at approx. 325 ◦C.
Concerning the influence of COR on the reaction rates, in scientific literature a maximum reaction
rate of methanol formation was reported for a educt gas with approx. 2mol-% of CO
2
[28, 30, 31,
38, 42–44, 46–48, 185]. In Fig. 4.4 the carbon conversion (
XC
) of an ideally cooled isothermal
reactor was calculated at a pressure of 50bar and a constant temperature of 250
◦
C for the kinetic
models considered. COR was varied from 0.001 to 1.0 with SN fixed at 2.0. In order to compare
the XCwithin the kinetic regime, a GHSV of 20,000 h-1 was selected.
Figure 4.4:
Carbon conversion over COR in the reactor feed for the kinetic models by Graaf [192],
Bussche[145], Henkel [202] and the Nestler
integ
model at a reaction pressure of 50 bar;
SN adjusted to 2.0; reaction temperature of 250
◦
C; GHSV of 20,000 h
-1
; ideal
isothermal reactor.
The simulation results show a maximum X
C
at low COR for all kinetic models, however, with
Graaf’s model indicating the lowest sensitivity towards COR, i.e. X
C
= 12.3 % and X
C
= 7.5 % for
COR = 0.001 and COR = 1.0, respectively. In comparison to the other kinetic models the activity
of Graaf’s kinetic model is at the lowest level. This finding is in good agreement with those by
other researchers stating a low activity of Graaf’s kinetic model [170]. Bussche’s model indicates
the highest influence of COR towards X
C
with a maximum of X
C
= 47.4 % achieved at COR = 0.16
(i.e. 5.1 mol-% of CO
2
). This maximum is, however, not based on kinetic measurements as Bussche
et al. did not consider gas compositions with COR < 0.2. At COR = 1.0 (i.e. 25.0 mol-% of CO
2
)
XCcalculated with Bussche’s model decreases towards the values obtained by Graaf.
64
4 Results and Discussion
While the simulations with Henkel’s kinetic models show lower activities than the kinetic model
by Bussche for low COR, higher conversions are obtained at COR exceeding 0.80 and 0.84 for the
Berty and the fixed bed parameters, respectively. These high conversions predicted by Henkel’s
kinetic model again show the necessity to provide an appropriate data basis especially for the
rate limiting effect of water at high COR.
The kinetic model Nestler
integ
shows a maximum X
C
of 30.5 % at COR = 0.18 (i.e. 5.5 mol-% of
CO
2
) in the reactor feed and is therefore within the range of the models proposed by Henkel
(fixed bed) and Bussche with regard to the gas composition. The considerably higher X
C
of
Bussche’s kinetic model in comparison to that of Henkel and the Nestler
integ
model could be due
to weak validation data of the kinetic data set by Bussche at low COR and SN = 2.0. Slightly
increased X
C
is obtained at COR = 1.0 by the Nestler
integ
model in comparison to Bussche and
Graaf. With 8.4 % this value is, however, well below the prediction made by the Henkel’s kinetic
models at 12.7 % and 11.7 % for Berty and fixed bed parameters, respectively.
Overall, it can be concluded from the discussion of the kinetic performance of the kinetic models
considered in this section, that the validation at high CO
2
contents in the educt gas is of high
importance to account for the rate limitation of water in the derived kinetic model. Therefore,
the kinetic models proposed by Henkel should not be applied for PtM-simulations with a high
COR in the syngas. Moreover, the discussion showed, that the kinetic model by Graaf calculated
significantly lower reaction rates in comparison to the other rate equations and is therefore very
likely based on an outdated catalyst. Analysis of the kinetic performance with regard to COR
showed that all kinetic models with the exception of Graaf show a maximum in catalytic activity
at low COR and, thus, behave plausible with respect to literature findings [48].
4.1.2 Comparison of reactor simulations
To demonstrate the consequences of the Nestler
integ
kinetic model on reactor design, a simulative
sensitivity study varying the reaction conditions was conducted. The Nestler
integ
kinetic model is
directly compared with the kinetic models by Graaf, Bussche as well as Henkel. The parameter
range of the sensitivity analysis is provided in Tab. 4.3; A wide range of COR and SN was
considered for three pressure levels. Data analysis was performed with focus on the hot spot
temperature and position, as the temperature profile is one key feature for industrial reactor
design and largely affected by the reaction kinetics[136, 167, 169, 170, 234]. Dimensions of the
reactor were applied with regard to Tab. 3.5.
All combinations of COR and SN were varied with the result of 20 simulation runs for each
kinetic model and pressure level. The diffusion model presented in Sec.
??
was not applied for
Table 4.3: Parameter set varied within the sensitivity study in this section.
Parameter Unit Values
p bar 50; 65; 80
COR - 0.25; 0.5; 0.75; 1.0
SN - 1.5; 2.0; 2.5; 3.0; 3.5
65
4 Results and Discussion
this analysis to simplify the interpretation of the simulation results. With regard to Kordabadi
et al. [74] the temperatures of the reactor feed T
in
and the cooling steam T
cool
were set to
Tin = 230 ◦C and Tcool = 252 ◦C, respectively.
1D-temperature and product concentration profiles simulated for a steam cooled tubular reactor
utilizing the Nestlerinteg kinetic model and Bussche’s kinetic model are provided in Fig. 4.5. As
inlet parameters for the syngas COR = 0.75 and SN = 3.0 at a pressure of 65 bar were selected.
Figure 4.5:
Comparison of the one-dimensional temperature profiles (left) and product molar
fraction profiles (right) obtained by a reactor simulation at COR = 0.75, SN = 3.0,
GHSV = 10,000 h
-1
at a pressure of 65 bar utilizing the kinetic model by Bussche and
the Nestler
integ
kinetic model; Inlet temperature of the feed T
in
was set to 230
◦
C,
temperature of the cooling medium (steam) was set to T
cool
= 252
◦
C with respect to
Kordabadi et al.[74]; Design parameters were applied according to Tab.3.5.
The concentration profiles of the products are closely linked to the temperature profiles in the
reactor. The kinetic model by Bussche shows a higher rate of methanol and water formation at
the reactor entry in comparison to the Nestler
integ
model. Nonetheless, both simulations approach
equilibrium at cooling temperature at the reactor exit, however, with an overall lower conversion
and therefore slower reaction kinetics of the Bussche model in comparison to Nestlerinteg.
Based on the previously shown results, hot spot position and magnitude were used for an advanced
analysis of the model behavior depending on COR, SN and synthesis pressure for the parameter
range listed in Tab. 4.3. The data on position and temperature of the hot spot are presented in
Fig. 4.6. As the kinetic model Henkel determined from the Berty reactor experiments is validated
over a wider temperature range and higher pressures than the fixed bed model, the latter was not
considered within the sensitivity study. Pressures exceeding the valid range of the kinetic models
were applied in the simulation as the extrapolation of the pressure range is commonly done in
scientific publications performing reactor simulations[136, 194, 195, 255, 256]. To indicate the
extrapolation of the kinetic models in the simulation study regarding temperature, pressure, SN
and COR, the data points exceeding the validated data ranges of the kinetic models with respect
to Fig. 2.10 were bleached out in the diagram.
66
4 Results and Discussion
Figure 4.6:
Sensitivity study discussing the hot spot temperatures (top) and positions (bot-
tom) obtained from the simulation of an industrial scale tubular reactor with the
kinetic models by Graaf [192], Bussche [145] and Henkel (Berty)[202] as well as
with the Nestler
integ
kinetic model for the parameter range between 0.25
≤
COR
≤
1,
1.5
≤
SN
≤
3.5 at GHSV = 10,000 h
-1
at the pressure levels of 50bar, 65 bar and 80 bar;
SN was varied in steps of 0.5; Inlet temperature of the feed T
in
was set to 230
◦
C,
temperature of the cooling medium (steam) was set to T
cool
= 252
◦
C with respect to
Kordabadi et al.[74]; Data points exceeding the validated data range of the kinetic
models with regard to Fig. 2.10 were bleached out; Design parameters were applied
according to Tab. 3.5.
67
4 Results and Discussion
Overall results from the sensitivity study show that hot spot temperature rises with increasing
pressure and decreasing COR for all kinetic models. This behavior is in line with literature
findings regarding the maximum methanol reaction rates and the increased exothermic heat
at high CO contents in the reactor feed gas. The increase of reaction kinetics with increasing
pressure is in agreement with Le Chatelier’s principle. However, big differences in position and
temperature of the hot spot were determined between the different kinetic models proving the
necessity of an appropriate description of reaction kinetics for reactor design purposes. Among
all considered kinetic models the lowest sensitivity of hot spot temperature and position towards
COR is predicted by Graaf. In addition, this model delivers the lowest hot spot temperatures
for the COR range between 0.25 and 0.75. The poor activity of Graaf’s model was already
documented within the scientific community [170] and could be due to the fact that the catalyst
for Graaf’s kinetic model was less active than those applied by other researchers. Therefore, this
model should be used with caution for the description of state-of-the-art methanol synthesis.
The kinetic model by Bussche provides a higher sensitivity towards changes in COR in comparison
to Graaf. The highest temperatures are achieved at low SN-values for COR between 0.25 and
0.75. A strong decrease of the hot spot temperature can be denoted with increasing SN. This
behavior is in contrast to the other kinetic models depicted in Fig. 4.6 as these show a slight
increase of the catalytic activity, i.e. higher hot spot temperatures and further upstream positions,
with rising SN. An increase of the reaction rates with rising SN was also found by Chanchlani
et al. who performed an experimental study on the influence of H
2
on the rate of methanol
formation [31]. As the SN-range of the kinetic study was not documented within the publication
by Bussche et al., the diverging behavior of this model could be explained by a missing variation
of SN in their experimental campaign. Therefore, it can be stated, that the model by Bussche
should be carefully applied with regard to variations in SN.
The hot spot temperatures and positions simulated with the model proposed by Henkel ranges
between those predicted by Bussche and Graaf at COR between 0.25 and 0.75. The Nestler
integ
model shows a comparable sensitivity towards COR as the model by Bussche, however, with the
hot spot formed further downstream for COR ranging between 0.25 and 0.75 (also see Fig.4.5).
Synthesis pressure is predicted with a higher effect towards hot spot temperature as compared to
Bussche. This is most likely due to the higher pressures applied in the experimental campaign
by Park et al. setting the validation basis for the Nestler
integ
kinetic model (compare Fig. 2.10).
The insufficient description of the reaction kinetics by Bussche at pressures exceeding 50 bar
was already claimed by Mignard et al. proposing a pressure extension for this model [38, 157].
However this extension was based on the measured data by Klier from 1982 and therefore most
likely based on a different catalyst than the one applied within Bussche’s study.
Due to the low reaction enthalpy of CO
2
-hydrogenation coupled with the low equilibrium
conversion, all kinetic models show low hot spot temperatures for the case of COR = 1.0. However,
the maximum temperature rise slightly increases with rising SN. For the cases with COR = 1.0
the positions of the hot spots for the kinetic models by Bussche and the Nestler
integ
kinetic model
are almost similar, while Graaf and Henkel show the hot spot further upstream. The kinetic
model by Henkel is most active for high CO
2
contents by means of hot spot temperature and
position. This is most probably due to the fact that Henkel did not perform measurements at
68
4 Results and Discussion
high COR. Therefore, this model cannot account for the inhibiting effect of water at high COR
appropriately [31, 38, 205].
Generally, the Nestler
integ
kinetic model was proven to behave plausibly in comparison to the
other kinetic models considered in this study. As this model covers the technical relevant pressure
and COR range for methanol synthesis, it is likely that the trends shown by the sensitivity
analysis are more realistic than those given by the other models.
4.1.3 Concluding remarks on the integral kinetic model
For the application of kinetic models for methanol synthesis it is of significant importance that
the relevant parameter range is considered in the experimental data used for derivation of the
kinetic model. The extrapolation of the catalytic activity is not necessarily valid as long as the
mechanism of methanol synthesis is not understood completely. In this section, a kinetic model
based on recent experimental data published by Park et al. [203] was presented. The performance
of this kinetic model was systematically compared against the kinetic models proposed by Graaf,
Bussche and Henkel to identify the potential of the model for the application at operation
conditions relevant for both conventional and PtM-based methanol synthesis.
Furthermore, a sensitivity analysis on the industrial reactor scale was conducted to compare the
performance of the kinetic models with regard to pressure, COR and SN. The results demonstrated
that Bussche’s kinetic model shows an inverse sensitivity towards SN compared to the other
kinetic models indicating an important inconsistency within this model. The kinetic model by
Graaf was proven to be less active and sensitive towards COR than the other models considered
in this section. Therefore, special caution should be taken applying this model for the description
of modern methanol synthesis reactors. As water is known to have a strong rate-inhibiting effect
on the kinetics of methanol synthesis, measurements with high CO
2
contents should be included
into kinetic measurement campaigns, especially with regard to PtM applications. Exclusion of
high CO
2
contents from the kinetic measurement could lead to an overestimated model activity
as shown with the kinetic models proposed by Henkel.
Consequently, the Nestler
integ
kinetic model based on Park’s experimental data and the rate
equations proposed by Henkel covers the widest parameter range of kinetic models available in
scientific literature for methanol synthesis on a commercial catalyst. Therefore, this model can
be applied for reactor and process design covering the complete range of pressure, temperature,
SN and COR with a high level of confidence.
However, the experimental data set published by Park et al. is mainly based on gas phase
measurements at GHSVs between 9,000h
−1
and 23,000 h
−1
. This leads to possible model
weaknesses with regard to the axial catalytic performance and, thus, inaccuracies in the calculation
of the temperature profile in industrial reactors. Therefore, measurements at higher GHSVs
would be necessary on order to accurately describe the reaction kinetics at low conversion.
Moreover, only a small quantity of experimental points was measured by Park et al. at elevated
CO
2
contents in the feed gas (compare Fig.A.5 in App. A.6). To obtain a more reliable kinetic
model for the design of methanol synthesis reactors in PtM applications, an improved methodical
69
4 Results and Discussion
approach delivering differential experimental data along the reactor of a polytropic miniplant
will be presented in the next section.
4.2 Kinetic model derived from differential miniplant data
In order to gain experimental data for the adjustment of the kinetic model Nestler
integ
, the
miniplant described in Sec. 3.4 was operated with the experimental plan presented in Sec. 3.5.2.
Besides an analysis of the reaction product, the experimental data obtained from the miniplant
setup provide axially resolved information on the temperature profile inside the reactor – a direct
output of the interplay between the reaction kinetics and the heat flux into the thermal oil. Due
to the high resolution of the temperature data, a detailed picture of the kinetic performance along
the catalyst fixed bed is provided (compare Fig. 3.7). This data set will be used to derive an
axially validated kinetic model (Nestler
diff
) for CO
2
-rich syngas as further evolution of Nestler
integ
.
4.2.1 Experimental results
The experimental data obtained from the miniplant setup indicated strong sensitivities of hot spot
temperature, product composition and space time yield (STY) towards pressure, stoichiometry
and COR. However, the measurement campaign was overlaid by a continuous deactivation of
the catalyst. In Fig. 4.7 STY is plotted over experimental ToS for the benchmark composition
of SN = 4.0 and COR = 0.9 at the three pressure levels as well as the two cooling temperatures
applied in this study. The graph indicates that STY stabilized during ramp up after approx. 50 h
ToS. However, stronger deactivation of the catalyst was observed during the experimental plan
at 80 bar (phase 4.)) and COR = 0.98 (phase 5.)). As both, the highest temperatures and the
highest water contents were measured during these phases, based on these observations it can
be concluded that the deactivation of the catalyst was mainly correlated to these two factors.
This is in good agreement to the work of Fichtl et al. who considered hydrothermal degradation
of the active sites as the main reason for catalyst deactivation in cleaned syngas [37]. However,
their group showed the necessity for longer experimental campaigns exceeding 1,600 h ToS to
obtain satisfactory information about deactivation kinetics. As this, though, was not in the scope
of this study, the influence of catalyst deactivation was not yet included consequently leading
to inaccuracies for the kinetic fitting. However, the strong decrease of the catalyst’s activity
during the formation phase (phase 1. in Fig. 4.7) was excluded from the kinetic parameter fitting.
Future research is planned to derive advanced axially resolved deactivation kinetics using the
miniplant setup.
In Fig. 4.8 the molar fractions of water and methanol obtained from the experiments at
GHSV = 12,000 h
-1
and a cooling temperature of 240
◦
C at the three pressure levels for COR= 0.7
(left) and COR = 0.95 (right) are depicted over SN. Thermodynamic equilibrium for the data
points was calculated at reactor outlet temperature applying the equilibrium constants published
by Graaf et al. as described in Sec. 2.4.1 [129]. As shown by the difference between equilibrium
and measured molar fraction of methanol, all experiments at this GHSV were carried out within
the kinetic regime of the methanol reaction. However, water production did reach the thermody-
70
4 Results and Discussion
Figure 4.7:
Trend of the space time yield over time-on-stream at benchmark conditions COR= 0.9;
SN = 4.0; GHSV = 12,000 h
-1
at 50 bar, 65 bar and 80 bar; Sectors marked: 1.)
ramp up, benchmark at 50 bar, T
cool
= 240
◦
C; 2.) experimental plan at 50bar,
T
cool
= 240
◦
C; 3.) experimental plan at 65 bar, T
cool
= 240
◦
C; 4.) experimental plan
at 80 bar, T
cool
= 240
◦
C; 5.) variation of SN at COR= 0.98, T
cool
= 240
◦
C and 50 bar
to 80 bar; 6.) experimental plan at 50 bar, T
cool
= 220
◦
C; 7.) benchmark at 50 bar,
Tcool = 240 ◦C.
namic equilibrium, probably due to faster reaction kinetics of rWGS. As expected considering Le
Chatelier’s principle, increased synthesis pressures led to increased equilibrium molar fractions
of methanol and water and consequently to faster reaction kinetics due to an enhanced driving
force. The highest methanol molar fraction was obtained at COR = 0.7 and SN = 2.0. While at
COR = 0.7 an increase of SN led to a decrease of methanol molar fraction, the molar fraction of
methanol was not sensitive to SN at COR= 0.95. This finding can be explained with the rate
inhibiting effect of high water partial pressures that was already recorded in literature[32, 49,
51].
Besides product concentration, another indicator for the catalytic activity can be gathered from
the temperature profile inside the reactor. In Fig. 4.9 the hot spot temperatures for the three
pressure levels at GHSV = 12,000 h
-1
and COR = 0.7 and COR = 0.95 are plotted over SN. The
graph indicates a strong correlation between COR and the achieved temperatures inside the
reactor. While at COR = 0.7 a maximum hot spot temperature of 278
◦
C was reached (SN= 2.0;
p = 80 bar), temperatures were on a significantly lower level at COR = 0.95 with a maximum hot
spot temperature of 257
◦
C at SN = 5.0 and p = 80 bar. This can be explained as an increase of
CO molar fraction in the feed gas decreases the amount of water produced and consequently
increases the reaction rates for methanol synthesis. Due to the higher exothermic heat released
inside the reactor (Eq. 2.3), heat removal requires a higher temperature difference between cooling
fluid and catalyst, leading to an increase of hot spot temperature. The hot spot position was
71
4 Results and Discussion
Figure 4.8:
Equilibrium and measured molar fraction of methanol (black) and water (grey)
at COR = 0.7 (left) and COR = 0.95 (right); Equilibrium molar fractions at 50bar
(dotted), 65 bar (dashed) and 80 bar (solid); measured molar fractions of methanol
and water at GHSV = 12,000 h
-1
at 50 bar (triangle), 65 bar (diamond) and 80 bar
(circle).
measured between 0.1m and 0.2 m downstream the inlet of the catalyst bed at COR= 0.7 and at
0.06 m at COR = 0.95, respectively. Due to the heterogeneities of the particle distribution along
the temperature sensor, a clear sensitivity of hot spot position towards SN could not be derived
(compare raw data in Fig.3.7).
At COR= 0.7 an increase of SN led to a decrease of hot spot temperature at 65 bar and 80 bar,
whereas it was almost constant at 50bar. This can be explained by chemical equilibrium of
methanol synthesis decreasing by rising SN and temperature as well as the acceleration of reaction
kinetics at increased temperature and pressure. Most probably hot spot temperature was limited
by chemical equilibrium at 65bar and 80 bar when SN exceeded a value of 3.0. Downstream the
hot spot, temperature in the reactor approaches the temperature of the cooling fluid. As shown
in Sec. 2.4.1, lower temperatures enable higher equilibrium conversions. However, due to the
decrease in reaction kinetics at decreasing temperature, equilibrium at the cooling temperature
is not reached inside the reactor (compare Fig.4.8).
While at COR = 0.7 an increase of synthesis pressure from 50 bar to 65 bar as well as from 65bar
to 80 bar increased the hot spot temperature by at least 7 K, at COR = 0.95 only a small rise of
hot spot temperature of less than 3.5 K was measured. Moreover, sensitivity towards SN was
weaker at COR= 0.95 with the highest hot spot temperature obtained at SN = 5.0 for all three
pressure levels. Overall, the sensitivities of hot spot temperatures towards COR and SN are in
72
4 Results and Discussion
Figure 4.9:
Hot spot temperature measured at COR = 0.7 (black) and COR = 0.95 (gray) and
GHSV = 12,000 h
-1
; pressure levels: 50 bar (triangle), 65 bar (diamond) and 80 bar
(circle).
good agreement with the results previously shown in Fig. 4.6 using the kinetic model Nestler
integ
.
NMR side-product analysis of the liquid product showed the presence of low concentrations
of ethanol, propanol and formic acid (see Appendix A.16), which is in good agreement with
Göhna et al. who analyzed the side-products of CO
2
-based methanol synthesis[84]. However, as
non-condensable side-products as methane and DME could not be trapped in the liquid phase, no
comprehensive analysis could be drawn from the liquid phase measurements executed. Further
side-product gas phase measurements utilizing a FTIR with a longer optical path length to
identify possible traces of these components could be applied in future studies.
Overall, the experimental results obtained from the miniplant setup were plausible regarding the
trends in hot spot temperature and product composition. Therefore, the measured data provide
a reliable data basis for the validation and adjustment of kinetic models.
4.2.2 Validation of literature kinetics
In order to discuss the ability of the kinetic models available in literature for the description
of the measured data obtained from the miniplant setup, reactor simulations using the kinetic
models as proposed by Graaf [193] and Bussche [145] as well as the Nestler
integ
kinetic model,
were performed for all experimental working points. For the sake of clarity, the kinetic models
with the parameter set applied as published Graaf and Bussche are hereon labeled with the index
"original".
In Fig. 4.10 parity plots for the three models are provided for the product molar fractions of
73
4 Results and Discussion
methanol (A) and water (B) as well as hot spot temperature (C) and position (D), with a
confidence interval of 10 %. The graphs for the outlet molar fraction of water and methanol
show a high level of agreement between experiment and simulation in terms of the kinetic model
Nestler
integ
. The models Bussche
original
and Graaf
original
, however, show strong deviations from
the experiments with the tendency of underestimated reaction kinetics.
Figure 4.10:
Parity plots for the outlet molar fractions of methanol (A) and water (B) as well as
hot spot temperature (C) and axial hot spot position (D) including error lines for
0 % (solid line) and for 10 % (dashed line); Experiments were carried out with the
miniplant setup; Simulation was performed using the kinetic models by Graaf (+)
and Bussche (o) as published as well as the Nestlerinteg kinetic model (x) .
Interestingly, none of the models considered in Fig. 4.10 was able to precisely describe the thermal
behavior of the reactor. Even though the hot spot temperatures of all kinetic models lie within the
10 % confidence interval, position of the hot spot was estimated further downstream in the catalyst
bed for all kinetic models considered here. The strong disagreement between the experimentally
obtained temperature profiles and the simulations performed with the Nestler
integ
kinetic model
74
4 Results and Discussion
underlines the requirement of kinetic measurements either at high GHSV (>40,000 h
-1
) or with
a high axial resolution.
In Tab. 4.4 the objective function obtained from Eq. 3.79 is shown for the three original models
considered in this study together with the respective RMSE-values (compare Eq.3.79 to Eq. 3.82).
Table 4.4:
Objective function and RMSEs calculated between the experimental data and the
reactor simulations using the original kinetic models by Graaf and Bussche as well as
the Nestlerinteg kinetic model.
Parameter Unit Graaforiginal Busscheoriginal Nestlerinteg
f(x) - 52.06 59.54 24.25
RMSET,prof ile K 2.3 2.5 2.6
RMSET,hs K 9.2 8.4 4.0
RMSEy% 0.79 1.18 0.27
The value obtained for RMSE
y
proves the high accuracy of the Nestler
integ
model for calculation of
the product composition in comparison to the literature standards Graaf
original
and Bussche
original
.
While these models predict product composition with a mean error of 0.79 % and 1.18 %,
respectively, a smaller mean error of 0.22 % is obtained when the Nestler
integ
model is applied.
Besides composition, the Nestler
integ
kinetic model delivers a better description of the temperature
profile and hot spot position in comparison to Graaf
original
and Bussche
original
. However, hot spot
temperature of this model is still predicted with a mean error of 4 K. As the temperature profile
is coupled with the conversion of synthesis gas towards methanol, wrong outlet concentrations
could be calculated when the original kinetic models considered here are transferred towards
different reactor geometries, working conditions or even other reactor types, e.g. an adiabatic
quench bed reactor. Even though, the Nestler
integ
kinetic model delivers a satisfactory description
of the outlet concentration for the experimental conditions applied, high deviations could be the
case, especially when the kinetic model is used for high COR and higher GHSV.
Summarizing the behavior of the kinetic models discussed in this section it can be stated, that
the kinetic models Graaf
original
and Bussche
original
show a higher disagreement towards the kinetic
performance measured with the miniplant setup compared to Nestler
integ
. This finding can be led
back on different catalysts considered in the studies by Graaf and Bussche and missing validation
data at pressures exceeding 50 bar. The simulations carried out with the Nestler
integ
kinetic
model shows lower deviations with regard to product composition and hot spot temperature.
However, a more accurate prediction of the temperature profile is necessary if this kinetic model
should be applied for reactor design.
The three kinetic models considered in this section are based on different assumptions regarding
the mechanism, RDS and presence of CO-hydrogenation. As these assumptions are controversially
discussed within the scientific community, a parameter fitting of these models to the experimental
data of the miniplant is reasonable to analyze their validity.
75
4 Results and Discussion
4.2.3 Fitted kinetic model
In order to enhance the applicability of the kinetic models described previously, their semi-
empirical parameters (see Eq. 3.52 and Eq. 3.53) were fitted to the experimental results measured
with the miniplant. The parameter fitting was subjected to the weighting factors in Eq. 3.79.
Other weighting factors could influence the fitting result along the Pareto front of the optimization
problem [257]. The kinetic models by Bussche and Graaf refitted to the experimental data will
be denoted with the index "fit" hereafter; The kinetic model adapted from Nestler
integ
will be
labeled Nestlerdiff from hereon.
In Tab. 4.5 the results of the parameter fitting are listed by means of the objective function and
the respective RMSE values.
Table 4.5:
Objective function and RMSEs calculated between the experimental data and the
reactor simulations using the fitted kinetic models.
Parameter Unit Graaffit Busschefit Nestlerdiff
f(x)- 17.50 24.97 17.93
RMSET,prof ile K 1.4 1.8 1.5
RMSET,hs K 1.7 3.4 1.8
RMSEy% 0.38 0.45 0.38
Comparison of the fitted kinetic models shows similar remaining errors for the models Graaf
fit
and Nestler
diff
, while for the model Bussche
fit
larger deviations remain for temperature profile
and product concentration. This can be explained by the reaction mechanisms and RDS of the
kinetic models. Graaf
fit
and Nestler
diff
rely on a common mechanism and similar RDS, however
with Nestler
diff
not considering CO-hydrogenation. In contrast, Bussche’s rate equation is based
on a different mechanism. Due to the high remaining errors after the parameter fitting (compare
Tab. 4.5) the rate equations of the Bussche-model were found not applicable for the description
of methanol synthesis kinetics on the catalyst considered in this study.
The remaining RMSE values show that the fitted models Graaf
fit
and Nestler
diff
predict the
temperature profile with a mean error of 1.4 K or 1.5 K, respectively, and therefore with a higher
accuracy than the original literature models. A deeper look into the reaction rate of the fitted
kinetic models at T
cool
= 240
◦
C over the whole considered parameter range showed, that the
direct CO-hydrogenation in the Graaf
fit
kinetic model can be neglected due to a very small
reaction rate (
|¯rCO|<
6
.
0
·10−8
mol s
-1
kg
cat-1
) obtained in comparison to CO
2
-hydrogenation
(
|¯rCO2|>
3
.
2
·10−3
mol s
-1
kg
cat-1
) and rWGS (
|¯rrW GS |>
1
.
5
·10−3
mol s
-1
kg
cat-1
). Due to this
finding, it can be stated, that CO-hydrogenation can be neglected for the description of the
kinetic behavior inside the reactor, which is in good agreement to the findings of the scientific
community[49, 258]. Consequently, the kinetic model Nestler
diff
will be used throughout the
following discussion of this work.
The set of fitted kinetic parameters for the proposed kinetic model based on the rate equations
of Eq. 3.56 and Eq. 3.57 is given in Tab. 4.6. The parameter sets of the fitted kinetic models
Graaffit and Busschefit are listed in Appendix A.17 and A.18, respectively.
76
4 Results and Discussion
Table 4.6: Parameters for the kinetic model Nestlerdiff.
Unit Proposed kinetic parameters
k1mol kg-1 s-1 Pa-1 2.385 ·10−5·exp −14,709
R·T
k2mol kg-1 s-1 Pa-0.5 244.433 ·exp −53,741
R·T
K1Pa-1 1.440 ·10−17 ·exp −570
R·T
K2Pa-1 4.223 ·10−6
K3Pa-0.5 6.407 ·10−13 ·exp 126,843
R·T
In Fig. 4.11 the parity plots for the outlet concentrations of methanol (A), water (B) as well as
the hot spot temperature (C) and position (D) simulated with the Nestler
diff
kinetic model are
provided. The graphs indicate that the description of both, hot spot position and temperature
were improved significantly in comparison to the original model (compare Fig. 4.10). However,
while the description of the temperature profile was enhanced with the proposed model, a slightly
higher error can be observed regarding the composition of the products methanol and water. This
is most likely due to inaccuracies in the measurements of axial temperature profile and product
composition. Besides, the remaining error could be a consequence of inaccuracies in the reactor
model, e.g. the diffusion or heat transfer sub-models. Application of the validation methodology
presented within this study to other reactor geometries could help identifying possible simulation
issues and improve the simulation platform.
A comparison between the experimental data and the simulation results applying the kinetic
models Graaf
original
, Bussche
original
, Nestler
integ
and Nestler
diff
is provided in App.A.23 for data
points at SN = 5.0 at a pressure of 80 bar over the whole COR range considered in this study.
Despite the slightly lower accuracy of the proposed model in comparison to Nestler
integ
for the
calculation of product composition, it is worth pointing out, that the correct description of
reaction kinetics along the reactor is vital to enable a reliable transfer of the kinetic model
towards industrial scale. To the best of the authors’ knowledge, the herein proposed kinetic model
delivers such a description and is therefore of a high value for reactor design problems. However,
the validity of the herein proposed kinetic model was only confirmed within the parameter range
applied for the experimental campaign (compare Tab. 3.8). Expansion of the validated parameter
range should only be applied with caution [206]; More experimental data will be obtained from
the miniplant for a wider COR range in future work to obtain a kinetic model applicable also for
conventional gas compositions.
4.2.4 Impact on industrial scale
To quantify the behavior of the herein proposed kinetic model on the industrial scale, a compre-
hensive simulation study was executed. As the Nestler
integ
kinetic model is based on a similar
catalyst, though exclusively based on the measurement of the outlet concentration of a kinetic
reactor [206], a comparison to this model is capable of showing the impact of the herein proposed
77
4 Results and Discussion
Figure 4.11:
Parity plots of the refitted kinetic model Nestler
diff
for outlet molar fractions of
methanol (A) and water (B) as well as hot spot temperature (C) and axial hot
spot position (D) including error lines for 0% (solid line) and for 10% (dashed line);
Experiments were carried out with the miniplant setup.
validation approach. In Fig. 4.12 industrial reactor simulations applying both, the kinetic model
Nestler
integ
and the proposed adapted kinetic model Nestler
diff
are compared by means of hot
spot temperature (A, B) and position (C, D) as well as methanol (E, F) and water outlet molar
fraction (G, H) at synthesis pressures of 50bar (left side) and 80 bar (right side). The graphs
A and B indicate a lower sensitivity of the Nestler
diff
model with regard to the dependency of
hot spot position and temperature towards COR in comparison to Nestler
integ
. While hot spot
temperatures of both models are comparable at COR = 0.8 the Nestler
diff
kinetic model shows
lower hot spot temperatures at COR = 0.7 and increased temperatures at higher COR.
As expected from the comparison of the parity plots of Nestler
integ
model and Nestler
diff
model in
Fig. 4.10 and Fig. 4.11, respectively, high deviations between the kinetic models are observed with
regard to hot spot position. This shows that large inaccuracies on the industrial reactor scale
78
4 Results and Discussion
Figure 4.12:
Sensitivity study discussing the behavior of the kinetic models Nestler
integ
(o) and
Nestler
diff
(x) by means of hot spot temperature (A, B) and position (C, D) as
well as product molar fraction of methanol (E, F) and water (G, H) at a synthesis
pressure of 50 bar (A, C, E, G) and 80 bar (B, D, F, H) in the range 0.7
≤
COR
≤
0.98,
2.0 ≤SN ≤8.0 at GHSV = 6,000 h-1.
79
4 Results and Discussion
can be obtained with kinetic models derived from experimental data measured in traditional
integral reactors. Differential measurement of concentration or, as presented here, highly resolved
temperature measurements add information to the data set which are advantageous when a
transfer from lab to industrial scale is performed. The more accurate and reliable description of
the thermal behavior inside the reactor provides increased security for reactor and process design
on the industrial scale. Looking at the product molar fraction of methanol (E, F) and water (G,
H) increasing deviations between the two models are present with decreasing SN. This is probably
due to larger deviations in hot spot position predicted with decreasing SN. On the one hand this
finding again shows the importance of the interlink between a correct kinetic axial description
and accurate calculation of product formation. On the other hand, detailed knowledge of the
product composition at the reactor exit is of high importance, when the synthesis reactor is
embedded in a loop process.
4.2.5 Co-verification of the kinetic model Nestlerdiff
In order to verify the new methodology proposed in this work, the kinetic model fitted to the
differential miniplant data was compared to the integral experimental data measured by Park
et al. [203]. In Fig. 4.13 a parity plot is shown comparing this set of experimental data to the
simulation using the kinetic model Nestlerdiff.
Comparison of Fig. 4.1 to Fig. 4.13 shows that both integral and differential kinetic model are
capable of describing the experimental data published by Park et al.[203]. This finding is
remarkable as the validity range of the differential kinetic model obtained from the miniplant
data is largely exceeded in terms of COR – while Park et al. covered the whole COR-range from
0.0 until 1.0, the miniplant-data only covers the range 0.7
≤
COR
≤
1.0. However, in terms of
product composition the Nestler
diff
kinetic model is still capable of describing the experimental
data by Park.
Compared to the Nestler
integ
kinetic model, a slightly higher scatter can be observed in Fig. 4.13.
A look at the remaining errors for both kinetic models in Tab. 4.7, shows higher deviations for
the Nestler
diff
kinetic model in comparison to Nestler
integ
. However, still the errors are below
those by the literature kinetic models listed in Tab. 4.2.
Table 4.7:
Comparison of the RMSE for the measured molar fractions published by Park[203]
and the simulated molar fractions utilizing the kinetic models derived in Sec.4.1
(Nestlerinteg) and in this section (Nestlerdiff).
Kinetic model RMSECO in % RMSECO2 in %
Nestlerinteg 0.605 0.441
Nestlerdiff 0.784 0.437
Therefore, it can be concluded that the Nestler
diff
kinetic model can be extrapolated towards
higher COR to describe the reactor outlet composition. However, as no validation using the
temperature profile was performed for COR
<
0.7 with this model, it should be applied with
caution for reactor design purposes at these gas compositions.
80
4 Results and Discussion
Figure 4.13:
Parity plot comparing the kinetic model Nestler
diff
fitted to the miniplant experi-
mental data to the integral experimental data published by Park et al.[203]; Error
lines for 0 % (solid, black), 10% (dashed, black) and 20 % (dashed, gray).
Finally, the high degree of agreement between the integral experimental data and the two kinetic
models shows that multiple combinations of parameter sets can be found to deliver an appropriate
kinetic description when only the reactor outlet concentration is measured (integral measurement).
However, the fact that the axial performance of the two models Nestler
integ
and Nestler
diff
differs
significantly (compare Fig.4.12) emphasizes the necessity of kinetic data gathered at high GHSVs
(GHSV > 40,000 h
-1
) or at differential axial positions along the reactor in methanol synthesis.
From this finding it can be concluded, that differential measurement of the temperature profile
along the reactor is one valid methodology to tackle this requirement. Moreover, this finding
shows the potential of the here proposed miniplant-based validation approach for the transfer
towards the kinetic validation of other fixed bed syntheses as e.g. Fischer Tropsch synthesis,
methanation or NH3synthesis.
4.2.6 Optimal design for the miniplant setup
In order to optimize the miniplant geometry for an improved agreement between industrial
and miniplant scale, scale-down from industrial scale to the miniplant dimensions was repeated
applying the Nestler
diff
kinetic model. In Fig. 4.14 the optimized reactor diameters determined
at GHSV = 9,000 h
-1
and the pressure levels of 50bar (A) and 80 bar (B) are shown in a 2D
contour plot. The graphs indicate that scale-down of the industrial reactor to miniplant scale
is correlated to the working range applied. While pressure and COR reveal higher sensitivities
towards optimal reactor dimensions, SN does affect the diameter less significantly. With regard to
the methodology applied, an inner reactor diameter of 9 mm
≤din ≤
12 mm would be beneficial for
the miniplant setup to improve the similarity towards the industrial reactor scale. Moreover, the
smaller reactor diameter would lead to a better heat removal from the reactor and consequently
81
4 Results and Discussion
enable the setup to be used for syngas with lower COR. However, wall effects (Eq.3.71) as well
as other relevant design criteria [241] must be considered when the geometry of the miniplant
reactor is changed to the dimensions proposed here.
Figure 4.14:
Optimized inner reactor diameter of the miniplant over COR and SN at
GHSV = 9,000 h
-1
and T
cool
= 240
◦
C for maximized comparability towards the
industrial reactor (see Tab. 3.5) at 50 bar (A) and 80 bar (B); Color code indicates
the optimized reactor diameter.
As the implementation of Thiele modulus for the description of the diffusion limitation showed
to significantly influence the results of the scale-down, further research will be necessary in order
to validate the diffusion model against experimental data. This could be done by introduction of
larger catalyst particles into the miniplant reactor in future work or by comparing the reactor
simulation to measured data obtained from a pilot/commercial scale facility.
4.2.7 Concluding remarks on the differential kinetic model
In this section, a novel approach for kinetic model validation and parameter estimation using
experimental data from a miniplant setup featuring a highly resolved fiber optic temperature
measurement in a polytropic miniplant combined with FTIR product analysis was presented.
In Fig. 4.15, the smoothened temperature profiles obtained from the miniplant setup at
GHSV = 9,000 h
-1
and SN = 5.0 at a pressure level of 80bar over the whole COR range con-
sidered in the miniplant experiments (for raw data see Fig.3.7) are compared against the
reactor simulation using the kinetic models Graaf
original
(A), Bussche
original
(B), Nestler
integ
(C)
and Nestler
diff
(D). The graphs indicate strong deviations between the temperature profiles
obtained from the miniplant experiments and the simulations performed with kinetic models
Graaf
original
and Bussche
original
known to be the most frequently used kinetic models on the
current-state-of-science in methanol synthesis (compare Sec.2.5). A better description of hot
spot temperature and gas phase composition (see also Fig. A.19) is achieved by the Nestler
integ
kinetic model based on the experimental data published by Park et. al. [203]. However, as this
model was not validated against data at a high GHSV (compare Fig.A.5 (C)), the position of
82
4 Results and Discussion
Figure 4.15:
Smoothened temperature profiles obtained from the miniplant experiments and simu-
lated temperature profiles using the kinetic models by Graaf [192] (A), Bussche [145]
(B) as well as the kinetic model Nestler
integ
(compare Sec. 4.1, C) and Nestler
diff
(compare Sec. 4.2, D) at p = 80 bar; T
cool
= 240
◦
C, SN = 5.0 and GHSV = 9,000 h
-1
for COR = 0.7, 0.8, 0.9, 0.95 and 0.98.
83
4 Results and Discussion
the hot spot is estimated too far downstream in the reactor. This could consequently lead to
large inaccuracies in the design of industrial methanol synthesis reactors for PtM applications.
The kinetic model Nestler
diff
fitted to the differential temperature data along the miniplant
reactor and the product composition provides the highest accuracy with regard to the axial
kinetic performance of all kinetic models considered in this work. This result emphasizes the high
practical relevance of the Nestler
diff
kinetic model for the implementation of methanol synthesis
from CO
2
-rich gases and H
2
on industrial scale. To the best of the author’s knowledge the
herein proposed novel approach for the validation of reaction kinetics of fixed bed reactions is
a significant improvement over state-of-the-art kinetic measurements as it offers an enhanced
methodology for bridging between experimental and industrial reactors.
4.3 Validation of the dynamic reactor model
In this section, the behavior of the dynamic reactor model presented in Sec. 3.1.5 will be validated
using experimental data from the miniplant setup and comparing the temperature profiles of
both, experiment and simulated data. A detailed analysis regarding the behavior of the dynamic
reactor model during sharp load transitions was executed prior to the validation in order to
verify the plausible behavior of the model. The results of this analysis are provided in App. A.24.
Dynamic load changes were experimentally observed at the miniplant setup during every transition
from one steady state working point to another. During these load changes no temperature
over-swing could be observed at any of the load changes performed. However, as Seidel et
al. [188] observed a dynamic kinetic behavior of the catalyst in their Berty reactor (compare
Sec. 2.4.4), the research question arises, whether a steady state kinetic model as the one proposed
in Sec. 4.2 is sufficient for the description of a dynamically operated fixed bed reactor in methanol
synthesis. Therefore, the simulation using this kinetic model will be held against one load change
simultaneously altering COR, SN and GHSV measured with the miniplant setup. In this section,
only the temperature profile measured inside the reactor will be used for the analysis. The
FTIR measurement as implemented at the miniplant was found inappropriate for the analysis of
dynamic experiments, as dynamic adsorption/desorption processes would lead to a change in the
total flow rate of the reactor product. Moreover, the gas flow through the FTIR was objected to
backmixing behavior due to the volume of the measurement cell. A continuous measurement
of the flow rate of the reaction product would be necessary in order to accurately obtain the
dead-time behavior of the analyzed gas stream.
The load change analyzed in this section was performed at a synthesis pressure of 80bar and
a cooling temperature of 240
◦
C. COR was varied from 0.8 to 0.9, SN from 2.0 to 4.0 and
GHSV from 6,000 h
-1
to 12,000 h
-1
. In Fig. 4.16 a) left, the measured axial temperature profile is
displayed directly before the load change(0s) as well as 10 s, 20 s, 30 s and 40 s after the load
change. The graph indicates that the hot spot temperature decreases by 17 K in the first 20 s
after the load change. After this period, the hot spot temperature decreases by only 3 K in the
following 20s. However, during this period the position of the hot spot is shifted to the reactor
inlet. Besides the decrease of the maximum temperature in the reactor, it can be observed, that
the temperature at the reactor outlet is increased by approx. 3K. This behavior can be explained
84
4 Results and Discussion
a)
Temperature profiles in the reactor over the axial reactor length for the time steps t= 0s, 10 s,
20 s, 30 s and 40 s; thin black lines in the experimental data (left) mark the non-smoothened,
originally measured temperature profiles.
b)
Heat map representing the temperature shift over the axial reactor length; color code
represents the temperature along the relative axial length of the reactor (x-axis) over time
(y-axis); the green line marks the hot spot position.
Figure 4.16:
Shift of the temperature profile during a load change from COR = 0.8; SN = 2.0;
GHSV = 6,000 h
-1
to COR = 0.9; SN = 4.0; GHSV = 12,000 h
-1
at 80 bar and a cool-
ing temperature of 240
◦
C obtained by experiment (left) and simulation (right);
experimental values were smoothened by the Savitzky-Golay filter[251].
85
4 Results and Discussion
by the higher GHSV as well as the increased COR. While the reaction was approaching chemical
equilibrium at the reactor outlet before the load change, the higher load of synthesis gas as well
as the slower reaction kinetics extend the kinetic zone to the outlet of the reactor.
In the steady state after the load change, the temperature directly downstream the hot spot
drops from 257
◦
C to 253
◦
C. This decrease was caused by a strong reduction of the reaction rate
at this point in the reactor. After this temperature reduction, reaction kinetics are obtained
at a low, slightly decreasing level from z/h
cat
= 0.12. The fact that activity of the catalyst
is obtained at a low level leading to higher outlet temperatures than the steady state before
the load change shows that the rapid axial temperature decrease is rather of a kinetic nature
than due to an equilibrium limitation. A similar behavior was observed during all experimental
points with COR
≥
0.9 and SN
≤
5.0 (compare Fig. 4.15). Therefore, this rapid axial decrease of
reaction kinetics could very likely be linked to a mechanistic switch in reaction kinetics due to
the increased partial pressure of water. Advanced analyses measuring the axial concentration
profile could confirm this hypothesis in future work.
On the right side of Fig.4.16 a), the transition of the temperature profile obtained with the
dynamic reactor model is displayed during the same dynamic load change. Compared to the
measured data, the shift of the temperature profile over time follows a similar trend. Within 20 s
after the load change the temperature of the hot spot decreases significantly and its position
moves downstream in the catalyst bed. Then, between 20s and 40 s after the load change,
the primary hot spot vanishes and a new hot spot forms near the reactor inlet. Due to the
remaining inaccuracy of the kinetic model obtained from the steady state measurements in
Sec. 4.2, deviations remain in both steady states before and after the load change. However, the
overall dynamic behavior of the reactor is well described with the dynamic model explained in
Sec 3.1.5.
In Fig. 4.16 b), the temperature profiles are displayed over time for both, experimental data (left)
and simulation (right) as a heat map. In these graphs, the color code represents the reactor
temperature. This kind of graphical illustration was found to be advantageous in displaying
deviations of the temperature profiles over time. The two graphs show slight deviations in the
steady states of the simulations (t= 0 s and t = 40 s). While the measured temperature in the
hot spot is higher before the load change compared to the simulation, lower temperatures are
predicted downstream the hot spot by the simulation model after the load change. A closer
look at the position of the hot spot (solid green line) shows a comparable dynamic behavior of
simulation and experiment. Within the first 22 s after the load change, the hot spot moves to the
back of the reactor. Simultaneously, the new hot spot is formed further upstream the reactor.
23 s after the load change, the temperature of the newly formed, secondary hot spot exceeds the
temperature of the vanishing primary hot spot. This time is marked in Fig.4.16b) by the shift
of the hot spot position to the reactor inlet. Interestingly, this shift appears at the same time for
both experiment and dynamic simulation. Overall it can be concluded that the characteristic of
the load change considered here is well described by the dynamic reactor model.
With regard to Eq. 3.65, the speed of the temperature shift inside the reactor is determined by
density and heat capacity of both catalyst and gas phase. While the density of the gas phase
was determined by SRK EoS (see Sec.3.1), the solid density of the catalyst and porosity of the
86
4 Results and Discussion
fixed bed were measured during the filling of the reactor [248]. Therefore, the heat capacity of
the activated catalyst inside the reactor can be considered as the determinant parameter for the
speed of the load change inside the reactor. In Fig. 4.17 a) three dynamic reactor simulations
were carried out varying the heat capacity of the catalyst. For the base case (middle), the heat
capacity was overtaken as measured by Henkel[202]. In Fig. 4.17 a) left, the heat capacity was
reduced by 30%, while it was increased by 30 % on the right. The graphs show the temperature
profiles before the load change (0 s) as well as 10s, 20 s and 30 s after it was performed.
With regard to the steady state working point before the load change, the graphs show, that the
heat capacity of the catalyst does not influence the dynamic simulation model in agreement to
Eq. 3.62. This finding also confirms that the stability of the ODE-solver was not influenced by
the variation of this parameter.
In terms of the dynamic behavior of the simulations, only small deviations in hot spot temperature
at 10 s and 20 s are shown between the base case simulation and the experimental data. Between
20 s and 30 s the hot spot obtained by the simulation moves to the reactor inlet in a comparable
manner as the experimental data.
Compared to the base case, the reduction of the catalyst’s heat capacity decreased the time
for the adaption to the new load point significantly. In this case, the temperature and position
of the hot spot approach the steady state already after 20 s, i.e. 10 s ahead of the base case
simulation and the experimental data. On the other hand, the increase of the catalyst’s heat
capacity extends the time for adaption to the new load point compared to the base case. Hot
spot temperature for this case exceeds the temperature of the experiment already 10 s after
the load change. The fact that this difference increases over time shows that heat capacity is
overestimated when heat capacity is increased from the base case.
In Fig. 4.17 b), a heat map symbolizing the relative deviations between the experiment and
simulation is shown for the three heat capacities considered. In the graphs, the color code
represents the relative temperature deviation between simulation and experiment. Blue color
represents a underestimation of the temperature obtained by the simulation, while the red color
marks overestimated temperatures. In the areas of white color, a relative deviation of 0 % between
simulation and experiment was obtained. All three graphs show that the temperature of the
steady state before the load change is underestimated by the reactor simulation. Besides, the
graphs indicate a weakness of the model for the steady state working point at COR= 0.9 after
the load change. Here, the kinetic model is not capable of following the sharp decrease of the
experimentally obtained temperature at 0.06 m reactor length downstream the hot spot. Further
research will be necessary to include this kinetic shift probably caused by the increased water in
the gas mixture into a kinetic model for methanol synthesis.
With regard to the deviation between simulation and experimental data, the graphs clearly
indicate the sensitivity of the heat capacity of the catalyst on the reactor performance. In case
of the base case, the lowest deviations are obtained after the load change, especially at the
hot spot position (dotted line: simulation; dashed line: experimental data). Remarkably, the
positions as well as the previously mentioned shift of the hot spot only show minor deviations.
Contrary to that, in the simulation case with decreased heat capacity, Fig. 4.17 b) (left) indicates
an underestimation of the temperature around the hot spot. This can be interpreted as a too
87
4 Results and Discussion
a)
Temperature profiles obtained by experiments (solid lines) and dynamic simulation (dashed
lines) before the load change (0 s) as well as 10s, 20 s and 30 s after the load change.
b)
Heat map on the relative temperature difference along the axial reactor length (x-axis) between
simulation and experiment over time (y-axis); the color code represents the relative temperature
difference: blue – temperature obtained by simulation is lower than the measured temperature;
white – temperature of simulation and experiment are equal; red – temperature obtained by
simulation exceeds the experimental data; Lines mark the measured (solid) and simulated
(dashed) hot spot position.
Figure 4.17:
Comparison of experimental and simulation data obtained during a load change from
COR = 0.8; SN = 2.0; GHSV = 6,000 h
-1
to COR = 0.9; SN = 4.0; GHSV = 12,000 h
-1
at 80 bar and T
cool
= 240
◦
C using different heat capacities for the catalyst particle;
Heat capacity of the simulation was reduced by 30% (left) and increased by 30 %
(right) from the base case (middle) representing the heat capacity as published by
Henkel [202].
88
4 Results and Discussion
fast load change when the catalyst heat capacity is reduced in the simulation. This statement is
supported by the development of hot spot position obtained by experiment (dashed line) and
simulation (dotted line). In this case, the shift of the hot spot to the reactor inlet obtained from
the simulation is observed 6s ahead of the experiment.
On the other hand, an increase of the heat capacity leads to an overestimation of the temperature
of the hot spot after the load change. This behavior shows that the temperature profile obtained
by the simulation with increased c
p,cat
decreases slower compared to the experimental data.
Besides, the shift of the hot spot temperature in the simulation appears 6 s after the simulation.
Overall, it can be concluded from the analysis of the load change performed here that the
heat capacity measured by Henkel is well applicable to the catalyst used within this work.
Moreover, the dynamic model presented in Sec.3.1.5 was validated by the detailed comparison
with experimental data. The herein proposed differential steady state kinetic model seems suitable
to describe the experimental data with an appropriate accuracy. This finding is in contradiction
to the work published by Seidel et al. proposing the necessity of a dynamic kinetic model to
accurately describe the dynamic behavior of methanol synthesis. These differences, however, are
very likely due to the differences in the experimental setups. While in this work, the load change is
largely determined by temperature change depending on the heat capacity of the catalyst, Seidel
et al. used an ideal isothermal Berty-type reactor. Probably, the researchers were able to observe
dynamic effects caused by the change of catalyst morphology as the influence of temperature
was eliminated in their measurement. The results of this work, however, propose that a dynamic
kinetic model is not necessary for the description of an industrial reactor under transient load
conditions. Further research including a dynamic quantitative gas phase measurement would be
necessary in order to further support this statement.
4.4 Application on process scale
To demonstrate the effect of the differential kinetic model derived in this work on design of the
synthesis process schematically depicted in Fig. 2.5, a simulation study was performed integrating
the adapted reactor model into the process model implemented in MATLAB
®
Simulink with
regard to Sec. 3.1.6. In order to account for a load case using a CO
2
-based synthesis gas (compare
Sec. 2.3.4), COR = 1.0 was applied for the MUG. For this simulation study, the stoichiometry
of the MUG was varied in the range 0.5
≤
SN
MUG ≤
4.0 to demonstrate the influence of syngas
stoichiometry on process design (see also Sec. 2.4.4). As another important parameter for process
design, the recycle ratio (see Eq. 2.22) was varied as second parameter in the range 1.0
≤
RR
≤
14.0.
The cooling temperature was held constant at
Tcool
= 240
◦
C as this temperature was applied
within the validation experiments presented in Sec. 4.2. GHSV in the reactor was fixed to
10,000 h-1.
In Fig. 4.18 the sensitivity of SN
MUG
and the RR on the operating conditions of the synthesis
process are discussed. By an increase of RR, conversion of the syngas is increased as the gas
mixture is led through the reactor more often. However, increased values for RR entail the
drawback of larger process equipment, as the amount of gas in the loop process strongly increases.
Moreover, RR strongly influences the composition of the gases in the loop. At high RR, inert
89
4 Results and Discussion
Figure 4.18:
Sensitivity of SN
MUG
and RR on the operating condition of the process; Color repre-
sents the simulated values for SN
feed
(A) and COR
feed
(B) balancing in the synthesis
loop as well as LCE (C) and LHE
int
(D); Hatched area marks sub-stoichiometric
gas mixtures at reactor inlet; gray area indicates unstable working points where the
recycle ratio could not be adjusted due full loop conversion; Simulation parameters:
GHSV = 10,000 h
-1
; p = 65 bar; T
cool
= 240
◦
C; COR
MUG
= 1.0; T
flash
= 40
◦
C; kinetic
model: Nestlerdiff.
.
gases and the excessive reactant species, i.e. H
2
for over-stoichiometric gas mixtures and CO
x
for
sub-stoichiometric gas mixtures, are accumulated in the loop.
In Fig. 4.18 (A) the influence of SN
MUG
and RR to SN of the reactor feed (SN
feed
) is discussed.
The hatched area marks the values with SN
feed
< 2.0, which was not experimentally investigated
within this work, as this gas composition was expected to lead to an increased formation of
reaction byproducts [10, 55]. The border line of the marked area for SN < 2.0 slightly decreases
from RR = 1.0 to RR = 3.8 due to the solubility of CO
2
in the liquid raw methanol at the flash
separator of the process. At RR > 3.8 and SN < 2.0 a blank area is displayed in the graph
indicating unstable process parameters, where the set recycle ratio cannot be adjusted due to
full conversion of the reactants towards raw methanol. In a real process the full conversion of
the educts towards methanol and water achieved at these process conditions would lead to a
decrease in process pressure. At SN
MUG
> 2.0, H
2
is accumulated in the synthesis loop, while it
is depleted for SN
MUG
< 2.0. Accumulation of excess H
2
in the loop is strongly enhanced by an
90
4 Results and Discussion
increase of RR, ending up at gas compositions, where exclusively H
2
is present in the reactor
feed.
Fig. 4.18 (B) shows the development of COR
feed
in dependence of SN
MUG
and RR. The graph
indicates a decrease of COR when RR is increased from 1.0 to 3.8. This change can be led
back to the equilibrium of the rWGS reaction which is shifted towards CO and H
2
O by the
removal of water in the flash separator. A minimal value of COR
feed
of 0.87 is reached in the sub-
stoichiometric (hatched) area at RR= 5.1 and SN
MUG
= 1.6. However, validation measurements
would be necessary in order to determine the kinetic activity of the rWGS for sub-stoichiometric
gas mixtures. Overall, the simulation shows, that the COR-range investigated within the
experimental campaign at the miniplant (see Tab. 3.8) does represent the gas composition on
process scale.
With regard to the educt utilization, LCE (compare Eq. 2.23) and LHE
int
(compare Eq. 2.25)
were considered as key indicators for conversion of the educt gases into raw methanol obtained
at the flash separator. LCE and LHE
int
are depicted in Fig. 4.18 (C) and (D), respectively.
Comparison of the two efficiencies shows opposing trends in dependence of SN
MUG
. While both
key indicators increase with increasing RR, LCE approaches 100% at SN
MUG
> 2.0, while LHE
int
reaches a maximum at the border of the unstable (gray) area and at SN
MUG
< 2.0. As the price
of methanol produced from electrolytic H
2
is mainly determined by the operating cost of H
2
production [13, 15, 259], LHE
int
is of higher importance for PtM processes than LCE. Therefore,
in future experimental studies special attention should be drawn on the gas compositions in the
hashed area of Fig. 4.18.
In order to demonstrate the influence of the kinetic model on process design, the kinetic model
by Bussche was integrated into the process and subjected to the same sensitivity analysis. In
Fig. 4.19 the results of the analysis are displayed applying the same color code as in Fig.4.18.
With regard to SN
feed
(A), the graph indicates that less H
2
is enriched within the loop at
SN
MUG
> 2.0 in comparison to Fig. 4.18 (A). Considering COR
feed
(Fig. 4.19 (B)) the lower values
for SN
feed
can be explained by an increased activity of the rWGS in the kinetic model by Bussche
for over-stoichiometric gas compositions. The lower activity of the kinetic model by Bussche in
comparison to the here proposed model Nestler
diff
(compare Fig. 4.10) is reflected by the unstable
(gray) area shifting to higher RR. As a consequence, process design based on Bussche’s kinetic
model would lead to an unnecessarily large dimensioned synthesis loop.
Consideration of two different kinetic models on process scale showed, that selection of the
kinetic model does largely influence gas composition and process design. This results emphasized
the significance of kinetic validation and the herein proposed approach for the technological
implementation of PtM-processes.
Application of the differential kinetic model derived within this work (Nestler
diff
) on the process
scale showed that the parameters of the validation campaign presented in Tab.3.8 represent
the synthesis conditions in a CO
2
-based process. With regard to SN
feed
, values exceeding the
validated range of the kinetic model could be reached in case of high RR and SN
MUG
> 2.
However, from an economical point of view, increased RR would lead to growing equipment
cost. As shown in Fig. 4.18 (D), the optimum LHEint would be reached along the unstable area
already at RR = 3.8. Consequently higher RR would not lead to an increase of H
2
utilization
91
4 Results and Discussion
Figure 4.19:
Sensitivity of SN
MUG
and RR on the operating condition of the process; Color
represents the simulated values for SN
feed
(A) and COR
feed
(B) balancing in the
synthesis loop; Hatched area marks sub-stoichiometric gas mixtures at reactor
inlet; gray area indicates unstable working points where the recycle ratio could not
be obtained due full loop conversion; Simulation parameters: GHSV = 10,000 h
-1
;
Tcool = 240 ◦C; CORMUG = 1.0; TFlash = 40 ◦C; kinetic model: Busscheorig [145].
and therefore probably negatively affect the overall plant economics. SN > 8.0 would therefore
be unlikely to occur in a CO2-based methanol synthesis process.
SN < 2.0 seems a promising option for CO
2
-based PtM processes with regard to LHE
int
(compare
Fig. 4.18 (D)). However, sub-stoichiometric gas compositions remain one open research question
for an experimental validation and an extension of the validated data range of the differential
kinetic model derived in this work. Advanced gas phase analysis as e.g. an FTIR with a longer
optical path length would be necessary for sub-stoichiometric experimental campaigns in order to
accurately determine the formation of side-products in dependence of SN. If these experiments
could verify a stable catalytic activity and a lower formation of side-products than expected,
PtM process could be operated within a wider range of economic operating conditions.
Finally, control and design strategies could be enhanced to dynamically operated PtM-process in
future work. In order to verify the behavior of the catalyst and the reactor under fluctuating
MUG-conditions on process scale, the miniplant setup could be connected with a dynamic process
model.
92
5 Conclusion and Outlook
For the implementation of dynamically operated PtX processes, a deep understanding of the
behavior of the process equipment under varying load conditions is necessary. With regard
to Power-to-Methanol (PtM) processes using CO
2
-rich syngas and electrolytically produced
H
2
supplied by fluctuating renewable energy, the simulative description of the stationary and
dynamically operated synthesis reactor was identified one core-challenge. The complex interplay
between the thermodynamically and kinetically limited CO
2
-hydrogenation and reverse water-
gas-shift reaction at non-conventional gas compositions required for a detailed kinetic study.
Four kinetic models were investigated closer within this work due to their role as literature
standard, i.e. Graaf [192] and Bussche [145], or due to their validation on a modern commercial
catalyst, i.e. Henkel [202] and Park[203]. However, the experimental data used by Graaf, Bussche
and Henkel to derive their kinetic models were found not representative for the parameter ranges
relevant for PtM processes, either by pressure, COR and/or SN (compare Fig. 2.10). The kinetic
model published by Park et al. is based on experimental data captured over a wide parameter
range for both conventional and PtM-based methanol synthesis – however, this model was found
not usable due to missing kinetic model parameters and inconsistencies in the kinetic description
(for details see Sec. 3.1.2). Therefore, the experimental data measured by Park et al. with an
integral kinetic reactor was used to derive the kinetic model "Nestler
integ
" based on the rate
equation proposed by Henkel. Due to the wide validation range, this model was shown to be a
significant improvement in comparison to the kinetic models available in scientific literature for
methanol synthesis.
However, the Nestler
integ
kinetic model was scarcely validated at high GHSVs and elevated COR
with the possible consequence of an inappropriate description of the axial kinetic performance
of the catalyst and consequently improper sizing of the reactor. In order to further validate
and improve the kinetic model, a novel experimental approach including a highly resolved axial
temperature measurement in a polytropic miniplant-scale reactor coupled with a FTIR gas
phase analysis was implemented. To ensure a high relevance of this work for the application on
industrial scale, the miniplant reactor was designed for a maximized thermochemical agreement
to a steam cooled tube bundle reactor by a simulation-based scale-down (see Sec.3.3). By
means of a comprehensive experimental campaign covering 324 experimental points for pressures
between 50bar and 80 bar over the complete PtM-relevant COR-, SN- and GHSV-range, a
data set for the validation of kinetic models was gathered. During the experimental campaign,
temperature gradients up to 50 K between cooling medium and catalyst bed as well as methanol
molar fractions in the product of up to 11 % were observed depending on the load conditions
applied underlining the high transferability of the miniplant data to industrial scale.
A comparison of the experimental miniplant data to simulations using the kinetic models by
Graaf and Bussche showed strong deviations with regard to temperature profile and product
composition. Compared to those, the kinetic model Nestler
integ
showed a better agreement
to the data obtained from the miniplant setup in terms of hot spot temperature and product
94
5 Conclusion and Outlook
composition, though, with significant deviations in the calculation of hot spot position.
As none of the three kinetic models considered for the validation of the miniplant experimental
data was capable of sufficiently describing the axial kinetic performance with their original kinetic
parameters, these models were subjected to a parameter fitting. As a result, the fitted kinetic
models Graaf
fit
and Nestler
diff
were able to describe the experimental data by a high level of
agreement. In comparison to these models, the kinetic model Bussche
fit
showed strong deviations
from the experimental data after the parameter estimation, underlining the capability of the
herein proposed miniplant validation approach to verify mechanistic assumptions of complex
reaction networks. Therefore, the rate equation proposed by Bussche was identified unsuitable
for the kinetic description methanol synthesis.
Since the reaction velocity of CO-hydrogenation calculated with the adjusted kinetic model
Graaf
fit
was found to be negligible, it was concluded that the Nestler
diff
model based on the
same mechanism, however, neglecting CO-hydrogenation was appropriate to describe methanol
synthesis from CO
2
-rich gases. Consequently, the kinetic model Nestler
diff
was identified the
most adequate description for the reaction kinetics of methanol synthesis with an average root
mean square error (RMSE) of 0.4 % with regard to product composition and 1.5 K in the axial
temperature profile.
Application of the final kinetic model in the dynamic reactor simulation delivered a highly
accurate description of an exemplary load change performed with the miniplant setup. Thus, it
was concluded, that a steady state kinetic model can be appropriate for the kinetic description
of an industrial fixed bed reactor under fluctuating load conditions.
In a final step, consideration of the Nestler
diff
kinetic model on process scale showed that the
applied ranges for SN and COR in the experimental campaign represent the gas composition
balancing in an industrial CO
2
-based PtM process underlining the high reliability of the kinetic
model. Implementation of a detailed economic model into the process model is currently in
progress to optimize the process layout and operation conditions for improved competitiveness of
PtM processes operated under fluctuating load. Moreover, this result proved the capability of
the miniplant setup for the analysis of dynamic load changes in polytropically operated fixed
bed reactors.
Besides possible enhancements of the reactor simulation platform, e.g. by upgrading from the
one-dimensional towards a two-dimensional model, the deactivation of the catalyst was identified
as an important field for further research (see also Fig.A.12). As the experimental campaign
executed with the miniplant setup was subjected to catalyst degradation, especially at high
pressures and CO
2
contents in the feed gas, a better accuracy for the kinetic model could be
obtained when this influence was described by a deactivation model. Furthermore, a better
understanding of the catalyst deactivation mechanisms using the axially resolved experimental
data from the miniplant setup could contribute to prolong the catalyst lifetime by enhanced
operating conditions and improved catalyst formulation. Consequently, a detailed study on
the catalyst deactivation is likely to increase the competitiveness of PtM-based methanol in
comparison to the conventionally produced counterpart.
Even though a high level of agreement was obtained between the reactor simulation using the
Nestler
diff
kinetic model and the experimental data from the miniplant setup, further research
95
5 Conclusion and Outlook
on the influence of water on the reaction kinetics will be necessary to improve the accuracy of
the kinetic model at high COR and catalyst formulation. Moreover, a better understanding of
the rate inhibiting effect of water would enable the adaption of the process operating conditions
to accelerate reaction kinetics on the industrial scale.
To reinforce the herein presented methodology for the simulation-based scale-down, experimental
data obtained from a large scale methanol reactor would be helpful to enhance the model of the
industrial reactor with regard to diffusion and heat transfer in future work. This could contribute
to enhance the comparability of the performance of the miniplant reactor and the industrial scale
by a higher level of confidence.
Finally, this work proved that a miniplant experimental setup featuring a highly resolved
temperature measurement can be used to derive detailed kinetic models for exothermic equilibrium
limited reactions which can be applied under steady state and dynamic load conditions. Moreover,
it was shown that this measurement method can be superior over "classic" kinetic measurements in
isothermal integral reactors if appropriate models for heat transfer, diffusion and reaction kinetics
are available. Transfer of this new methodology towards other syntheses as e.g. methanation,
Fischer-Tropsch synthesis or NH
3
synthesis in future studies could make an important contribution
to evaluate the potential of a flexible operation of these processes in the context of Power-to-X
technology.
96
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Acknowledgements
This thesis was developed during my period as doctoral researcher at Engler-Bunte Insitute
at KIT in Karlsruhe, my employment as scientific assistant at Fraunhofer Institute for Solar
Energy Systems ISE in Freiburg and my time as Deutsche Bundesstiftung Umwelt PhD scholar
(20017/517). Many people in these three institutions supported this work during the past years –
I would hereby like to express my appreciation and thankfulness to everyone of them.
Special thanks go to my supervisors Prof. Dr. Thomas Kolb and Dr. Siegfried Bajohr at
Engler-Bunte Institute for their strong scientific and personal support as well as their time and
feedback during this interesting and intense time. I am looking forward to staying in connection
with them and their research group for the next joint research projects to come.
Prof. Dr. Jürgen Karl from FAU Nürnberg-Erlangen is sincerely thanked for his agreement
to evaluate this thesis as second reviewer.
This work would not have been possible without the strong support of my colleagues at Fraunhofer
ISE who invested plenty of their energy and dedication into making this work a success. Special
thanks go to Prof. Dr. Christopher Hebling, Dr. Achim Schaadt, Dr. Ouda Salem and Max
Hadrich for their supervision, trust, encouragement and organizational support during the past
years. Turning scientific ideas into reality demands for a strong and dedicated team. I am grateful
for my dear colleagues, students and friends in the whole division Hydrogen Technologies for their
support in the construction and automation of the miniplant facility, their great generousness
with regard to the sharing of their scientific equipment and knowledge, their assistance in topics
related to analytical problems and software bugfixing issues as well as their passion for endless
scientific discussions at any daytime.
Acceptance for my scholarship provided by Deutsche Bundesstiftung Umwelt was one of the most
motivating and encouraging moments during my professional career so far. Thus, I am grateful
to DBU for their financial support and for providing access to the DBU network.
Last but not least, I would like to thank my partner Charlotte as well as my family and
friends for their patience, support and care during the past years.
120
Verification of the contribution of co-authors
121
Verification of the contribution from the co-authors
Title: Methanol Synthesis – Industrial Challenges within a Changing Raw Material Landscape
Journal: Chemie Ingenieur Technik (Wiley)
Authors: Florian Nestler, Matthias Krüger, Johannes Full, Max J. Hadrich, Robin J. White, Achim
Schaadt
Position in the dissertation:
The content of this paper has been included in Chapter 2.
Contribution of Florian Nestler:
- Literature review on methanol synthesis and syngas generation
- Composition of the manuscript (70%)
Contribution of Matthias Krüger:
- Input of industrial experience
- Composition of the manuscript (30%)
Contribution of Johannes Full:
- Simulation on process scale
- Proofreading and scientific reviewing of the manuscript
Contribution of Max J. Hadrich:
- Proofreading and scientific reviewing of the manuscript
Contribution of Robin J. White:
- Proofreading and scientific/methodical reviewing of the manuscript
Contribution of Achim Schaadt:
- Proofreading and scientific/methodical reviewing of the manuscript
Verification of the contribution from the co-authors
Title: Kinetic modelling of methanol synthesis over commercial catalysts: A critical assessment
Journal: Chemical Engineering Journal (Elsevier)
Authors: Florian Nestler, Arif R. Schütze, Mohamed Ouda, Max J. Hadrich, Achim Schaadt, Siegfried
Bajohr, Thomas Kolb
Position in the dissertation:
The content of this paper has been included in Chapters 2, 3 and 4.
Contribution of Florian Nestler:
- Elaboration of the validation methodology
- Implementation of the simulation platform (90%)
- Structuring and implementation of the methodological approach
- Analysis and discussion of experimental data and simulation results
- Composition of the manuscript
Contribution of Arif R. Schütze:
- Implementation of the simulation platform (10%)
- Transfer of the experimental data into the validation toolbox
- Execution of the fitting procedure
- Structuring and composition of the appendix
Contribution of Mohamed Ouda:
- Support in structuring of the manuscript
- Supervision of the research
- Proofreading of the manuscript
Contribution of Max J. Hadrich:
- Proofreading of the manuscript
Contribution of Achim Schaadt:
- Supervision of the research
- Proofreading of the manuscript
Contribution of Siegfried Bajohr:
- Supervision of the research
- Proofreading of the manuscript
Contribution of Thomas Kolb:
- Supervision of the research
- Proofreading of the manuscript
Verification of the contribution from the co-authors
Title: A Novel Approach for Kinetic Measurements in Exothermic Fixed Bed Reactors: Advancements
in Non-Isothermal Bed Conditions Demonstrated for Methanol Synthesis
Journal: Reaction Chemistry & Engineering (RSC)
Authors: Florian Nestler, Viktor P. Müller, Mohamed Ouda, Max J. Hadrich, Achim Schaadt, Siegfried
Bajohr, Thomas Kolb
Position in the dissertation:
The content of this paper has been included in Chapters 3 and 4.
Contribution of Florian Nestler:
- Elaboration of the miniplant design and analytical concept
- Built up and structuring of the simulation platform
- Data extraction, processing and selection
- Implementation of the validation library and parameter fitting scripts (90%)
- Conduction of the miniplant experiments (70%)
- Analysis and discussion of the experimental data and simulation results
- Composition of the manuscript
Contribution of Viktor P. Müller:
- Elaboration of weighting factors for the multi objective parameter fitting
- Implementation of the validation library and parameter fitting scripts (10%)
- Conduction of the miniplant experiments (30%)
Contribution of Mohamed Ouda:
- Support in structuring of the manuscript
- Critical discussion of the results
- Supervision of the research
- Proofreading of the manuscript
Contribution of Max J. Hadrich:
- Support in the design of the miniplant facility
- Proofreading of the manuscript
Contribution of Achim Schaadt:
- Supervision of the research
- Proofreading of the manuscript
Contribution of Siegfried Bajohr:
- Supervision of the research
- Proofreading of the manuscript
Contribution of Thomas Kolb:
- Supervision of the research
- Proofreading of the manuscript
Publication list
Journal publications sorted by year
•
F. Nestler, V. P. Müller, M. Ouda, M. J. Hadrich, A.Schaadt, S. Bajohr, T. Kolb. "A Novel
Approach for Kinetic Measurements in Exothermic Fixed Bed Reactors: Advancements in
Non-Isothermal Bed Conditions Demonstrated for Methanol Synthesis". In RSC Reaction
Chemistry & Engineering 6 (2021), pp. 1092–1107. DOI: 10.5445/IR/1000131790.
•
M. Martens, M. J. Hadrich, F. Nestler, M. Ouda, A. Schaadt. "Combination of Refractom-
etry and Densimetry – A Promising Option for Fast Raw Methanol Analysis". In Chemie
Ingenieur Technik 92.10 (2020), pp. 1474–1481. DOI: 10.1002/cite.202000058.
•
F. Nestler, A. R. Schütze, M. Ouda, M. J. Hadrich, A. Schaadt, S. Bajohr, T. Kolb. "Kinetic
modelling of methanol synthesis over commercial catalysts: A critical assessment". In
Chemical Engineering Journal 394 (2020), pp. 124881. DOI: 10.1016/j.cej.2020.124881.
•
M. Ouda, C. Hank, F. Nestler, M. J. Hadrich, J. Full, A. Schaadt, C. Hebling. "Power-to-
Methanol: Techno-Economical and Ecological Insights". In Zukünftige Kraftstoffe. Ed. by
Wolfgang Maus. Vol. 55. Berlin, Heidelberg: Springer Berlin Heidelberg, 2019, pp. 380–409.
ISBN : 978-3-662-58005-9. DOI: 10.1007/978-3-662-58006-6_17.
•
F. Nestler, M. Krüger, J. Full, M. J. Hadrich, R. J. White, A. Schaadt. "Methanol Synthesis
– Industrial Challenges within a Changing Raw Material Landscape". In Chemie Ingenieur
Technik 90.10 (2018), pp. 1409–1418. DOI: 10.1002/cite.201800026.
•
F. Nestler, L. Burhenne, M. J. Amtenbrink, T. Aicher. "Catalytic decomposition of
biomass tars. The impact of wood char surface characteristics on the catalytic perfor-
mance for naphthalene removal". In Fuel Processing Technology 145 (2016), pp. 31–41.
DOI: 10.1016/j.fuproc.2016.01.020.
Conference contributions sorted by year
•
F. Nestler, M. J. Hadrich, M. Ouda, A. Schaadt, S. Bajohr, T. Kolb "Dynamic behavior of
a methanol synthesis reactor under flexible load conditions – Validation of a reactor model
using a miniplant setup". 13th European Congress of Chemical Engineering (2021), Poster
contribution.
•
F. Nestler, J. Full, M. J. Hadrich, M. Ouda, A. Schaadt, S. Bajohr, C. Hebling, T. Kolb
"Experimentelle Validierung eines Kinetikmodells für die Methanolsynthese anhand einer
Miniplant-Anlage". 10. ProcessNet Jahrestagung (2020), Poster contribution.
125
Publication list
•
F. Nestler, M. Ouda, M. J. Hadrich, A. Schaadt, S. Bajohr, T. Kolb. "Experimentelle
Validierung eines dynamischen Modells für die Methanolsynthese". ProcessNet Energiever-
fahrenstechnik (2020), Oral presentation, DOI : 10.1002/cite.202055427.
•
F. Nestler, R. Mayorga-Gonzalez, J. Full, A. Schaadt, S. Bajohr, T. Kolb. "Dynamische
1D/2D-Analyse kritischer Reaktor-Lastzustände". ProcessNet Energieverfahrenstechnik
(2019), Oral presentation
•
R. Becka, F. Nestler, S. Bajohr, M. Ouda, A. Schaadt, T. Kolb "Methanol synthesis in
fixed-bed and slurry bubble column reactors". ProcessNet Reaktionstechnik (2019), Poster
contribution.
126
Appendix
A.1 Derivation of the equilibrium constant
The derivation of Eq.2.13 from Eq. 2.10 is based on the work provided by Graaf and Winkel-
mann [129] and Thomas et al. [133].
Basic expression:
lnKeq (T)=−∆G0(T)
R·T(A.1)
Calculation of ∆G0(T)by the change in enthalpy from a reference temperature:
−∆G0(T)
T=−∆G0(Tref )
Tref
+ZT
Tref
∆H0(T)
T2dT (A.2)
Application of the Kirchhoff equation for ∆H0(T):
∆H0(T)=∆H0(Tr ef ) + ZT
Tref
∆˜c0
p(T)dT (A.3)
Temperature dependence of heat capacity can be calculated by 4
th
order polynomial as follows:
∆˜c0
p(T) = ∆˜cp·A+ ∆˜cp·B·T+ ∆˜cp·C·T2+ ∆˜cp·D·T3+ ∆˜cp·E·T4(A.4)
Insertion of Eq. A.4 and Eq. A.3 into A.2 with subsequent integration delivers:
∆H0(T) = IH+ ∆˜cp·A·T+1
2∆˜cp·B·T2+1
3∆˜cp·C·T3+1
4∆˜cp·D·T4+1
5∆˜cp·E·T5(A.5)
with IHas the integration constant for the lower boundary:
IH= ∆H0(Tref )−∆˜cp·A·Tref −1
2∆˜cp·B·T2
ref
−1
3∆˜cp·C·T3
ref −1
4∆˜cp·D·T4
ref −1
5∆˜cp·E·T5
ref
(A.6)
Insertion of Eq. A.5 into Eq.A.2 leads to:
−∆G0(T)
T=−∆G0(Tref )
Tref
+ZT
Tref
IH+ ∆˜cp·A·T+1
2∆˜cp·B·T2+1
3∆˜cp·C·T3+1
4∆˜cp·D·T4+1
5∆˜cp·E·T5
T2dT
(A.7)
A
Appendix
Simplification leads towards:
−∆G0(T)
T=−∆G0(Tref )
Tref
+ZT
Tref
IH/T 2+ ∆˜cp·A/T +1
2∆˜cp·B
+1
3∆˜cp·C·T+1
4∆˜cp·D·T2+1
5∆˜cp·E·T3dT
(A.8)
Integration of Eq.A.8 delivers:
−∆G0(T)
T=IG−IH
T+∆˜cp·A·ln(T) + 1
2∆˜cp·B·T
+1
6∆˜cp·C·T2+1
12∆˜cp·D·T3+1
20∆˜cp·E·T4
(A.9)
with IGas the integration constant for the lower boundary:
IG=−∆G0(Tref )
Tref
+IH
Tref −∆˜cp·A·ln(Tref )−1
2∆˜cp·B·Tref
−1
6∆˜cp·C·T2
ref −1
12∆˜cp·D·T3
ref −1
20∆˜cp·E·T4
ref
(A.10)
Substitution in Eq. A.10 with the parameters a1bis a7:
a1=−IH(A.11)
a2=IG(A.12)
a3=1
2∆˜cp·B(A.13)
a4=1
6∆˜cp·C(A.14)
a5=1
12∆˜cp·D(A.15)
a6=1
20∆˜cp·E(A.16)
a7= ∆˜cp·A(A.17)
Leads towards:
−∆G0(T)
T=a1
T+a2+a3·T+a4·T2+a5·T3+a6·T4+a7·ln(T)(A.18)
Rearrangement towards ∆G0(T):
−∆G0(T) = a1+a2·T+a3·T2+a4·T3+a5·T4+a6·T5+a7·T·ln(T)(A.19)
Finally insertion into Eq.A.1 leads towards the final expression for Keq(T):
lnKeq (T)=1
R·T·a1+a2·T+a3·T2+a4·T3+a5·T4+a6·T5+a7·T·ln(T)(A.20)
B
Appendix
A.2 Literature use of kinetic models
Figure A.1:
Literature use of the kinetic models by Bussche [145] and Graaf [192] over decades
since 1980.
A.3 Industrial reactor data available in scientific literature
Table A.1:
Design parameters for steam cooled tube bundle reactors available in scientific litera-
ture.
Parameter Unit Kordabadi al et. Hartig et al. Yusup et al. Chen et al.
2005 1993 2010 2011
References - [74, 169, 246, 247] [127] [163, 166] [167]
dint m 0.038 0.05 0.0445 0.04
dext m - - 0.0485 -
hcat m 7.022 5 7.26 7
Ntubes - 2962 9100 4801 1620
dpm 0.0054 0.0042 0.006 0.0054
εbulk - 0.39 0.4 0.4 0.285
ρbulk kg m-3 1132 1062 1100 1190
Tin ◦C 230 238 225 225
p bar 76.98 81.95 82.3 69.7
Tcool ◦C 252 260 250 220
C
Appendix
A.5 Sensitivity of Thiele modulus
Figure A.3:
Intrinsic reaction rate (primary axis) of CO
2
-hydrogenation (r
CO2
) and rWGs (r
rWGS
)
simulated with the kinetic model Nester
diff
as well as the efficiency factor calculated
by Thiele modulus (secondary axis) for an ideal isothermal reactor at T = 240
◦
C
with the kinetic model Nestler
diff
at SN = 4.0; COR = 0.9; GHSV = 10,000 h
−1
and a
pressure of 80 bar.
E
Appendix
Figure A.4:
Sensitivity analysis of efficiency factor calculated using Thiele modulus (compare
Sec.
??
) towards the catalyst parameters
dp
(A),
εp
(B) and
τ
(C); Simulation was
performed within an ideal isothermal reactor at T = 240
◦
C with the kinetic model
Nestler
diff
at SN = 4.0; COR = 0.9; GHSV = 10,000 h
−1
and a pressure of 80 bar;
Parameters were varied from the base case (red, solid) towards -45% (dashed, gray),
-90% (dotted, gray) as well as +45% (dashed, black), +90% (dotted, black); In case
of
εp
and
τ
the upper or lower boundary were limited by these parameters physical
meaning, respectively.
F
Appendix
A.6 Experimental data used for integral kinetic model
Table A.2:
Experimental data taken from Park et al.[203] that was used for the integral kinetic
model Nestlerinteg.
Feed composition Reactor conditions Conversion
Ndata pt yCO yCO2 yH2 yAr p T GHSV XCO XCO2
[-] [-] [-] [-] [-] [bar] [◦C] [h-1] [-] [-]
1 0.19 0.11 0.70 0.00 50 249.85 22,640 0.4105 0.0784
2 0.19 0.11 0.70 0.00 50 269.85 22,640 0.3378 0.0605
3 0.19 0.11 0.70 0.00 50 299.85 22,640 0.1806 0.0618
4 0.19 0.11 0.70 0.00 50 319.85 22,640 0.0914 0.068
5 0.19 0.11 0.70 0.00 50 339.85 22,640 0.0327 0.0838
6 0.19 0.11 0.70 0.00 50 249.85 9,056 0.5428 0.0946
7 0.19 0.11 0.70 0.00 50 249.85 22,640 0.4121 0.061
8 0.19 0.11 0.70 0.00 50 249.85 33,960 0.3413 0.0482
9 0.19 0.11 0.70 0.00 50 249.85 45,280 0.2893 0.0462
10 0.19 0.11 0.70 0.00 50 249.85 9,056 0.5229 0.1068
11 0.19 0.11 0.70 0.00 70 249.85 9,056 0.6678 0.1005
12 0.19 0.11 0.70 0.00 90 249.85 9,056 0.7478 0.1098
13 0.00 0.24 0.72 0.04 50 249.85 9,056 -0.0936 0.2332
14 0.11 0.16 0.68 0.05 50 249.85 9,056 0.5254 0.1073
15 0.17 0.11 0.67 0.05 50 249.85 9,056 0.526 0.0809
16 0.22 0.07 0.66 0.05 50 249.85 9,056 0.499 0.0037
17 0.26 0.05 0.64 0.05 50 249.85 9,056 0.4562 0.0005
18 0.27 0.03 0.65 0.05 50 249.85 9,056 0.446 0
19 0.28 0.02 0.65 0.05 50 249.85 9,056 0.4221 0
20 0.29 0.02 0.64 0.05 50 249.85 9,056 0.365 0
21 0.18 0.10 0.67 0.05 50 249.85 9,056 0.5755 0.0782
22 0.16 0.09 0.70 0.05 50 249.85 9,056 0.5796 0.08
23 0.13 0.07 0.76 0.04 50 249.85 9,056 0.6231 0.0938
24 0.09 0.05 0.83 0.03 50 249.85 9,056 0.6977 0.1511
25 0.19 0.11 0.70 0.00 50 249.85 9,056 0.5716 0.058
26 0.14 0.08 0.50 0.29 50 249.85 9,056 0.409 0.0432
27 0.14 0.08 0.50 0.29 70 249.85 9,056 0.574 0.0532
28 0.19 0.11 0.70 0.00 70 249.85 9,056 0.7303 0.1101
29 0.00 0.24 0.72 0.04 70 249.85 9,056 -0.074 0.287
30 0.17 0.11 0.67 0.05 70 249.85 9,056 0.6446 0.1002
31 0.22 0.07 0.66 0.05 70 249.85 9,056 0.6085 0.0421
32 0.27 0.03 0.65 0.05 70 249.85 9,056 0.5741 -0.0643
33 0.29 0.02 0.64 0.05 70 249.85 9,056 0.5419 -0.2302
G
Appendix
Feed composition Reactor conditions Conversion
Ndata pt yCO yCO2 yH2 yAr p T GHSV XCO XCO2
[-] [-] [-] [-] [-] [bar] [◦C] [h-1] [-] [-]
34 0.00 0.24 0.72 0.04 70 269.85 9,056 -0.1022 0.2646
35 0.17 0.11 0.67 0.05 70 269.85 9,056 0.4993 0.0478
36 0.22 0.07 0.66 0.05 70 269.85 9,056 0.4844 -0.0127
37 0.27 0.03 0.65 0.05 70 269.85 9,056 0.4638 -0.3565
38 0.29 0.02 0.64 0.05 70 269.85 9,056 0.4566 -0.4762
39 0.00 0.24 0.72 0.04 50 249.85 9,056 -0.0844 0.2461
40 0.00 0.22 0.74 0.04 50 249.85 9,056 -0.0913 0.2539
41 0.00 0.17 0.80 0.03 50 249.85 9,056 -0.0988 0.3147
42 0.00 0.12 0.86 0.02 50 249.85 9,056 -0.1051 0.4094
43 0.00 0.24 0.72 0.04 60 249.85 9,056 -0.0789 0.2621
44 0.00 0.22 0.74 0.04 60 249.85 9,056 -0.0835 0.28
45 0.00 0.17 0.80 0.03 60 249.85 9,056 -0.0896 0.3423
46 0.00 0.12 0.86 0.02 60 249.85 9,056 -0.0858 0.4515
47 0.00 0.24 0.72 0.04 70 249.85 9,056 -0.073 0.2836
48 0.00 0.22 0.74 0.04 70 249.85 9,056 -0.078 0.3037
49 0.00 0.17 0.80 0.03 70 249.85 9,056 -0.0833 0.3595
50 0.00 0.12 0.86 0.02 70 249.85 9,056 -0.0802 0.4844
51 0.07 0.05 0.62 0.26 80 249.85 9,056 0.7593 0.1675
52 0.07 0.05 0.62 0.26 80 259.85 9,056 0.6736 0.1894
53 0.07 0.05 0.62 0.26 80 269.85 9,056 0.5905 0.2096
54 0.07 0.05 0.62 0.26 80 269.85 11,320 0.5791 0.1701
55 0.19 0.11 0.70 0.00 50 229.85 22,640 0.3712 0.0829
56 0.19 0.11 0.70 0.00 50 239.85 22,640 0.4379 0.0834
57 0.19 0.11 0.70 0.00 50 249.85 22,640 0.4266 0.0832
58 0.19 0.11 0.70 0.00 50 259.85 22,640 0.3842 0.0786
59 0.19 0.11 0.70 0.00 50 269.85 22,640 0.3221 0.0714
60 0.19 0.11 0.70 0.00 50 279.85 22,640 0.2794 0.0685
61 0.19 0.11 0.70 0.00 50 289.85 22,640 0.2375 0.0694
62 0.19 0.11 0.70 0.00 50 299.85 22,640 0.1756 0.0588
63 0.19 0.11 0.70 0.00 50 309.85 22,640 0.1161 0.0577
64 0.19 0.11 0.70 0.00 50 319.85 22,640 0.0842 0.0463
65 0.19 0.11 0.70 0.00 50 339.85 22,640 0.0631 0.0575
66 0.11 0.06 0.83 0.00 50 229.85 22,640 0.5543 0.1562
67 0.11 0.06 0.83 0.00 50 239.85 22,640 0.5282 0.3012
68 0.11 0.06 0.83 0.00 50 249.85 22,640 0.558 0.1529
69 0.11 0.06 0.83 0.00 50 259.85 22,640 0.518 0.1404
70 0.11 0.06 0.83 0.00 50 269.85 22,640 0.4595 0.1212
71 0.11 0.06 0.83 0.00 50 279.85 22,640 0.3914 0.0929
H
Appendix
Feed composition Reactor conditions Conversion
Ndata pt yCO yCO2 yH2 yAr p T GHSV XCO XCO2
[-] [-] [-] [-] [-] [bar] [◦C] [h-1] [-] [-]
72 0.11 0.06 0.83 0.00 50 289.85 22,640 0.327 0.0742
73 0.11 0.06 0.83 0.00 50 299.85 22,640 0.2675 0.0388
74 0.19 0.11 0.70 0.00 50 229.85 9,056 0.5642 0.1215
75 0.19 0.11 0.70 0.00 50 239.85 9,056 0.5565 0.1128
76 0.19 0.11 0.70 0.00 50 249.85 9,056 0.5137 0.1009
77 0.19 0.11 0.70 0.00 50 269.85 9,056 0.3657 0.0922
78 0.11 0.06 0.83 0.00 50 229.85 9,056 0.7618 0.1888
79 0.11 0.06 0.83 0.00 50 239.85 9,056 0.7228 0.1786
80 0.11 0.06 0.83 0.00 50 249.85 9,056 0.6593 0.1707
81 0.11 0.06 0.83 0.00 50 259.85 9,056 0.5927 0.159
82 0.11 0.06 0.83 0.00 50 269.85 9,056 0.5032 0.1159
83 0.11 0.06 0.83 0.00 50 279.85 9,056 0.4414 0.1024
84 0.11 0.06 0.83 0.00 50 289.85 9,056 0.3976 0.0694
85 0.11 0.06 0.83 0.00 50 299.85 9,056 0.3669 0.0251
86 0.18 0.10 0.67 0.05 70 249.85 22,640 0.5423 0.0545
87 0.18 0.10 0.67 0.05 70 219.85 22,640 0.3172 0.0409
88 0.18 0.10 0.67 0.05 70 229.85 22,640 0.5562 0.0561
89 0.18 0.10 0.67 0.05 70 239.85 22,640 0.5792 0.0561
90 0.18 0.10 0.67 0.05 70 249.85 22,640 0.5321 0.0398
91 0.18 0.10 0.67 0.05 70 259.85 22,640 0.4976 0.0372
92 0.18 0.10 0.67 0.05 70 269.85 22,640 0.443 0.0335
93 0.18 0.10 0.67 0.05 70 279.85 22,640 0.3745 0.0158
94 0.18 0.10 0.67 0.05 70 299.85 22,640 0.2795 0.0031
95 0.18 0.10 0.67 0.05 70 249.85 22,640 0.5318 0.0423
96 0.18 0.10 0.67 0.05 70 299.85 22,640 0.2622 0.0289
97 0.18 0.10 0.67 0.05 70 249.85 22,640 0.5373 0.0518
98 0.18 0.10 0.67 0.05 50 249.85 22,640 0.4126 0.0637
99 0.18 0.10 0.67 0.05 70 249.85 22,640 0.4859 0.0428
100 0.18 0.10 0.67 0.05 90 249.85 22,640 0.5321 0.0398
101 0.00 0.24 0.72 0.04 50 249.85 22,640 -0.1513 0.2564
102 0.11 0.16 0.68 0.05 50 249.85 22,640 0.3355 0.0864
103 0.17 0.11 0.67 0.05 50 249.85 22,640 0.3557 0.0423
104 0.22 0.07 0.66 0.05 50 249.85 22,640 0.3876 0.0629
105 0.27 0.03 0.65 0.05 50 249.85 22,640 0.3045 -0.1195
106 0.29 0.02 0.64 0.05 50 249.85 22,640 0.2893 -0.1501
107 0.18 0.10 0.67 0.05 50 249.85 9,056 0.5392 0.0747
108 0.13 0.07 0.76 0.04 50 249.85 9,056 0.6484 0.1721
109 0.09 0.05 0.83 0.03 50 249.85 9,056 0.7193 0.2426
I
Appendix
Feed composition Reactor conditions Conversion
Ndata pt yCO yCO2 yH2 yAr p T GHSV XCO XCO2
[-] [-] [-] [-] [-] [bar] [◦C] [h-1] [-] [-]
110 0.18 0.10 0.67 0.05 50 249.85 22,640 0.3036 0.0716
111 0.16 0.09 0.70 0.05 50 249.85 22,640 0.3159 0.0885
112 0.13 0.07 0.76 0.04 50 249.85 22,640 0.3683 0.1402
113 0.11 0.06 0.80 0.03 50 249.85 22,640 0.3871 0.1764
114 0.09 0.05 0.83 0.03 50 249.85 22,640 0.401 0.2091
J
Appendix
A.8 Measurement of thermal oil flow rate
Figure A.7:
Measurement (symbols) and simulation of the system characteristic curve of the
miniplant setup at 130
◦
C (triangle / dotted), 200
◦
C (diamond / dashed) and 250
◦
C
(rectangle / solid); Variation of the volumetric flow rate was performed by variation
of the rotating speed of the pump; Pressure was obtained from the pressure sensor of
the oil thermostat; Simulation was carried out using the software "druckverlust" [219].
Figure A.8:
Temperature-compensated volumetric flow rate obtained in the thermal oil cycle at
constant rotational speed of the thermostat pump shaft between 130
◦
C and 250
◦
C
thermal oil temperature [260].
Obtained temperature-flow correlation:
˙
Voil =−2.73 ·10−9·T2
cool ·m3
s K2+ 3.03 ·10−6·Tcool ·m3
s K −5.50 ·10−4·m3
s(A.21)
M
Appendix
A.10 Analysis of the catalyst particle size distribution
Figure A.10:
Particle size distribution of the catalyst obtained by a flotation measurement using
the Laser Diffraction Particle Size Analyzer LS 13 320 by Beckman Coulter.
A.11 Purity of the gases used within the miniplant experiments
Table A.3: Supplier and purity of the technical gases used for the miniplant experiments.
Gas Supplier Purity
N2Linde GmbH 5.0 (99.999 %)
CO2Linde GmbH 4.5 (99.995 %)
CO Linde GmbH 3.7 (99.97 %)
H2Linde GmbH 5.0 (99.999 %)
O
Appendix
A.12 Overview on the experimental campaign executed on the scale down
miniplant
Table A.4: Chronological progress of the experimental campaign.
Date Activity Comment
02.04.2020 Catalyst preparation and reactor
filling
171 g of catalyst filled
03.04.2020 Leakage testing of the miniplant Pressure tested at 85 bar
06.04.2020 Activation of the catalyst (day 1) N2-blocking over night
07.04.2020 Activation of the catalyst (day 2) N2-blocking over night
09.04.2020 Calibration of the fiber optic
temperature sensor
Calibration between 50 °C and 265 °C
under N2atmosphere
14.04.2020 Formation of the catalyst (day 1) Benchmark conditions at 50bar;
Time on stream added: 5:45 h;
N2-blocking over night at hot standby
(Tcool = 160 °C)
15.04.2020 Formation of the catalyst (day 2) Benchmark conditions at 50bar;
Time on stream added: 5:20 h;
N2-blocking over night at hot standby
(Tcool = 160 °C)
16.04.2020 Formation of the catalyst (day 3) Benchmark conditions at 50bar;
Time on stream added: 6:05 h;
N2-blocking of the miniplant;
Ramp-down to cold standby
17.04.2020 -
05.05.2020
Replacement of the process control
valve; infrastructure measures in
laboratory
N2-blocking of the miniplant
06.05.2020 Formation of the catalyst (day 4) Benchmark conditions at 50bar;
Time on stream added: 7:15 h;
N2-blocking over night at hot standby
(Tcool = 160 °C)
07.05.2020 Formation of the catalyst (day 5) Benchmark conditions at 50bar;
Time on stream added: 6:00 h;
N2-blocking over night at hot standby
(Tcool = 160 °C)
P
Appendix
Date Activity Comment
08.05.2020 Formation of the catalyst (day 6) Benchmark conditions at 50bar;
Time on stream added: 6:20 h;
N2-blocking of the miniplant;
Ramp-down to cold standby
12.05.2020 Formation of the catalyst (day 7) Benchmark conditions at 50bar;
Time on stream added: 4:48 h;
N2-blocking over night at hot standby
(Tcool = 160 °C)
13.05.2020 Formation of the catalyst (day 8) Benchmark conditions at 50bar;
Time on stream added: 5:10 h;
N2-blocking over night at hot standby
(Tcool = 160 °C)
14.05.2020 Formation of the catalyst (day 9) Benchmark conditions at 50bar;
Time on stream added: 4:40 h;
N2-blocking of the miniplant;
Ramp-down to cold standby
19.05.2020 Formation of the catalyst (day 10) Benchmark conditions at 50 bar;
Time on stream added: 5:10 h;
Leakage of the fiber optic temperature
sensor detected at the end of the
experiment;
N2-blocking of the miniplant;
Ramp-down to cold standby
20.05.2020 -
17.06.2020
Repair of a leakage in the thermo
sensor
Reactor flushed with N2permanently;
Sensor was fixed by tungsten inert gas
welding without removal of the catalyst
bed
18.06.2020 Leakage testing of the miniplant Pressure tested at 85 bar
19.06.2020 Parameter variation at 50bar;
Tcool = 240 °C
N2-blocking over night at hot standby
(Tcool = 160 °C)
22.06.2020 Parameter variation at 65bar;
Tcool = 240 °C
N2-blocking over night at hot standby
(Tcool = 160 °C)
23.06.2020 Parameter variation at 80bar;
Tcool = 240 °C
Experiment was canceled due to a
leakage in H2gas dosing MFC;
Emergency stop;
N2-blocking of the miniplant;
Ramp down to cold standby
Q
Appendix
Date Activity Comment
24.06.2020 -
20.08.2020
Repair of the broken MFC by the
manufacturer;
replacement of the sealings of the
other MFCs
N2-blocking of the miniplant
21.08.2020 -
25.08.2020
Leakage testing of the miniplant and
commissioning
Pressure tested at 85 bar
26.08.2020 Parameter variation at 80bar;
Tcool = 240 °C
N2-blocking over night at hot standby
(Tcool = 160 °C)
27.08.2020 Parameter variation at COR= 0.98 at
the pressure levels 50bar, 65 bar,
80 bar and Tcool = 240 °C
N2-blocking of the miniplant
Ramp-down to cold standby
02.09.2020 Parameter variation at 50bar;
Tcool = 220 °C
N2-blocking over night at hot standby
(Tcool = 160 °C)
03.09.2020 Benchmark conditions at 50 bar Time on stream added: 5:40 h
N2-blocking of the miniplant;
Ramp-down to cold standby
07.09.2020 Benchmark conditions Time on stream added: 5:40 h;
N2-blocking of the miniplant;
Ramp-down to cold standby
R
Appendix
A.13 Experimental data obtained from the miniplant experiments
Table A.5:
Experimental data obtained during the steady state experiments at the miniplant
setup.
Feed composition Reactor conditions Product composition Hot spot
Ndata pt COR SN GHSV TI01 TI02 p yCO yCO2 yMeOH yH2O Ths zhs
[-] [-] [-] [h-1 ] [◦C] [◦C] [bar] [mol-%] [mol-%] [mol-%] [mol-%] [◦C] [m]
1 0.9 8 12,105 240.8 242.3 50 1.27% 5.73% 3.90% 4.36% 251.8 0.057
2 0.9 7 12,105 240.9 242.3 50 1.43% 6.74% 3.96% 4.44% 251.9 0.060
3 0.9 7 9,079 241.0 242.3 50 1.22% 6.54% 4.50% 4.78% 252.6 0.060
4 0.9 6 12,105 240.8 242.2 50 1.63% 7.98% 4.01% 4.59% 251.9 0.057
5 0.9 6 9,079 240.9 242.2 50 1.41% 7.86% 4.60% 4.94% 252.7 0.057
6 0.9 5 12,105 240.8 242.2 50 1.89% 9.69% 4.06% 4.68% 252.0 0.060
7 0.9 5 9,079 241.0 242.2 50 1.64% 9.52% 4.69% 5.03% 252.7 0.057
8 0.9 5 6,053 241.1 242.2 50 1.38% 9.32% 5.47% 5.53% 254.2 0.055
9 0.9 4 12,105 240.9 242.2 50 2.22% 11.94% 4.07% 4.76% 252.1 0.060
10 0.9 4 9,079 241.0 242.2 50 1.95% 11.98% 4.75% 5.14% 252.8 0.057
11 0.9 4 6,053 241.0 242.2 50 1.64% 11.81% 5.61% 5.65% 254.0 0.055
12 0.9 3 12,105 240.9 242.2 50 2.71% 15.42% 4.04% 4.81% 252.0 0.060
13 0.9 3 9,079 240.9 242.2 50 2.38% 15.38% 4.73% 5.15% 252.5 0.057
14 0.9 3 6,053 241.0 242.2 50 2.00% 15.25% 5.68% 5.71% 253.6 0.055
15 0.9 2 12,105 240.9 242.2 50 3.39% 20.35% 3.90% 4.75% 251.7 0.060
16 0.9 2 9,079 241.0 242.2 50 3.04% 20.58% 4.61% 5.08% 252.4 0.060
17 0.8 8 12,105 241.1 242.2 50 1.40% 5.39% 4.33% 3.79% 252.5 0.094
18 0.8 8 6,053 241.1 242.2 50 1.00% 5.00% 5.45% 4.47% 256.9 0.088
19 0.8 7 12,105 241.0 242.2 50 1.61% 6.33% 4.46% 3.87% 252.6 0.088
20 0.8 7 9,079 241.1 242.2 50 1.34% 6.23% 5.08% 4.22% 254.5 0.060
21 0.8 7 6,053 241.2 242.2 50 1.12% 5.86% 5.71% 4.57% 257.4 0.091
22 0.8 6 12,105 241.0 242.2 50 1.87% 7.51% 4.57% 3.92% 252.7 0.094
23 0.8 6 9,079 241.1 242.2 50 1.57% 7.41% 5.27% 4.29% 254.7 0.060
24 0.8 5 12,105 241.1 242.2 50 2.20% 9.02% 4.68% 3.96% 252.9 0.088
25 0.8 5 9,079 241.1 242.2 50 1.85% 9.00% 5.45% 4.36% 254.9 0.088
26 0.8 5 6,053 241.2 242.2 50 1.52% 8.77% 6.29% 4.82% 257.9 0.094
27 0.8 4 12,105 240.8 242.2 50 2.71% 11.39% 4.75% 3.98% 252.7 0.088
28 0.8 4 9,079 241.1 242.2 50 2.27% 11.35% 5.61% 4.35% 254.9 0.088
29 0.8 4 6,053 241.2 242.2 50 1.85% 11.19% 6.60% 4.87% 258.1 0.101
30 0.8 3 12,105 240.9 242.2 50 3.44% 14.58% 4.79% 3.93% 252.8 0.088
31 0.8 3 6,053 241.1 242.2 50 2.33% 14.49% 6.86% 4.83% 258.2 0.101
32 0.8 2 12,105 241.0 242.2 50 4.60% 19.59% 4.72% 3.72% 252.7 0.101
33 0.8 2 9,079 241.1 242.2 50 3.92% 19.87% 5.73% 4.07% 254.6 0.101
S
Appendix
Feed composition Reactor conditions Product composition Hot spot
Pt. No. COR SN GHSV TI01 TI02 p yCO yCO2 yMeOH yH2O Ths zhs
[-] [-] [-] [h-1 ] [◦C] [◦C] [bar] [mol-%] [mol-%] [mol-%] [mol-%] [◦C] [m]
34 0.8 2 6,053 241.2 242.2 50 3.15% 20.01% 7.03% 4.53% 258.1 0.101
35 0.7 8 12,105 240.9 242.2 50 1.52% 4.94% 4.90% 3.30% 254.9 0.187
36 0.7 8 6,053 241.0 242.2 50 1.14% 3.98% 5.59% 3.35% 260.1 0.125
37 0.7 7 12,105 241.2 242.2 50 1.07% 4.65% 6.04% 3.91% 263.4 0.101
38 0.7 7 6,053 241.1 242.2 50 1.21% 5.46% 6.40% 4.00% 255.5 0.190
39 0.7 6 12,105 241.2 242.2 50 2.07% 6.90% 5.33% 3.42% 255.6 0.190
40 0.7 6 9,079 240.9 242.2 50 1.70% 6.80% 6.11% 3.73% 259.6 0.125
41 0.7 6 6,053 241.2 242.2 50 1.41% 6.59% 6.80% 4.12% 264.8 0.101
42 0.7 5 12,105 241.2 242.2 50 2.52% 8.39% 5.54% 3.41% 255.8 0.187
43 0.7 5 9,079 240.9 242.2 50 2.06% 8.35% 6.41% 3.75% 260.0 0.125
44 0.7 4 9,079 241.0 242.2 50 2.57% 10.52% 6.76% 3.71% 260.9 0.190
45 0.7 3 12,105 241.2 242.2 50 4.20% 13.63% 5.94% 3.23% 256.1 0.190
46 0.7 3 9,079 241.0 242.2 50 3.05% 12.22% 7.16% 3.56% 262.5 0.187
47 0.7 3 6,053 241.1 242.2 50 2.68% 13.80% 8.36% 3.94% 268.3 0.122
48 0.7 2 12,105 241.2 242.2 50 5.91% 18.52% 6.03% 2.95% 255.7 0.190
49 0.7 2 9,079 240.8 242.2 50 4.85% 18.93% 7.47% 3.25% 261.5 0.190
50 0.7 2 6,053 241.1 242.2 50 3.82% 19.24% 8.89% 3.53% 269.0 0.122
51 0.95 8 12,105 241.2 242.2 50 1.21% 5.99% 3.70% 4.63% 251.6 0.057
52 0.95 8 9,079 240.8 242.2 50 1.06% 5.78% 4.16% 4.93% 252.0 0.052
53 0.95 8 6,053 240.9 242.2 50 0.91% 5.52% 4.69% 5.33% 252.3 0.052
54 0.95 7 12,105 240.8 242.2 50 1.34% 6.91% 3.71% 4.77% 251.5 0.057
55 0.95 7 9,079 241.0 242.2 50 1.16% 6.69% 4.22% 5.08% 252.2 0.052
56 0.95 6 12,105 240.8 242.2 50 1.52% 8.20% 3.76% 4.92% 251.5 0.057
57 0.95 6 9,079 241.0 242.2 50 1.33% 8.06% 4.30% 5.27% 252.1 0.052
58 0.95 5 12,105 240.7 242.2 50 1.76% 9.96% 3.78% 5.07% 251.7 0.060
59 0.95 5 9,079 240.9 242.2 50 1.54% 9.89% 4.35% 5.43% 252.2 0.052
60 0.95 5 6,053 240.7 242.2 50 1.32% 9.60% 5.09% 5.90% 252.3 0.052
61 0.95 4 12,105 240.9 242.2 50 2.03% 12.25% 3.76% 5.17% 251.7 0.057
62 0.95 4 9,079 240.9 242.2 50 1.81% 12.15% 4.37% 5.56% 252.0 0.052
63 0.95 4 6,053 240.8 242.2 50 1.55% 12.03% 5.17% 6.08% 252.2 0.052
64 0.95 3 12,105 240.8 242.2 50 2.39% 15.73% 3.70% 5.29% 251.5 0.057
65 0.95 3 9,079 240.9 242.2 50 2.16% 15.60% 4.30% 5.64% 252.0 0.052
66 0.95 3 6,053 240.7 242.2 50 1.85% 15.54% 5.16% 6.17% 252.1 0.052
67 0.95 2 12,105 240.9 242.2 50 2.89% 20.70% 3.56% 5.34% 251.2 0.057
68 0.95 2 9,079 240.9 242.2 50 2.66% 20.84% 4.15% 5.71% 251.6 0.052
69 0.9 8 12,105 241.6 242.2 65 0.81% 4.99% 5.58% 5.55% 257.7 0.052
70 0.9 8 9,079 241.7 242.4 65 0.80% 4.93% 5.55% 5.58% 257.8 0.052
71 0.9 7 12,105 241.5 242.3 65 1.10% 6.25% 5.06% 5.28% 255.9 0.055
T
Appendix
Feed composition Reactor conditions Product composition Hot spot
Pt. No. COR SN GHSV TI01 TI02 p yCO yCO2 yMeOH yH2O Ths zhs
[-] [-] [-] [h-1 ] [◦C] [◦C] [bar] [mol-%] [mol-%] [mol-%] [mol-%] [◦C] [m]
72 0.9 7 9,079 241.4 242.3 65 0.91% 5.91% 5.72% 5.74% 257.7 0.052
73 0.9 7 6,053 241.7 242.2 65 0.77% 5.67% 6.33% 5.85% 259.6 0.052
74 0.9 6 12,105 241.3 242.3 65 1.27% 7.42% 5.14% 5.42% 255.8 0.055
75 0.9 6 9,079 241.5 242.2 65 1.06% 7.19% 5.89% 5.91% 257.8 0.052
76 0.9 6 6,053 241.7 242.3 65 0.88% 6.92% 6.60% 6.09% 259.7 0.052
77 0.9 5 12,105 241.3 242.2 65 1.50% 9.11% 5.21% 5.53% 256.0 0.052
78 0.9 5 9,079 241.5 242.2 65 1.26% 8.91% 6.04% 6.10% 257.9 0.055
79 0.9 5 6,053 241.6 242.2 65 1.03% 8.62% 6.91% 6.38% 259.7 0.052
80 0.9 4 12,105 241.3 242.2 65 1.79% 11.49% 5.24% 5.60% 256.0 0.052
81 0.9 4 6,053 241.5 242.2 65 1.25% 11.14% 7.10% 6.35% 259.6 0.052
82 0.9 3 12,105 241.4 242.2 65 2.24% 15.12% 5.21% 5.62% 256.0 0.055
83 0.9 3 9,079 241.4 242.2 65 1.90% 15.02% 6.16% 6.17% 257.6 0.055
84 0.9 3 6,053 241.6 242.2 65 1.53% 14.49% 7.43% 6.92% 259.2 0.052
85 0.9 2 12,105 241.2 242.2 65 2.87% 20.22% 5.06% 5.50% 255.4 0.055
86 0.9 2 9,079 241.4 242.2 65 2.46% 20.35% 6.03% 6.00% 257.2 0.052
87 0.8 8 12,105 241.3 242.2 65 1.01% 4.82% 5.50% 4.65% 257.1 0.055
88 0.8 8 6,053 241.6 242.2 65 0.71% 4.30% 6.64% 5.41% 264.7 0.099
89 0.8 7 12,105 241.3 242.2 65 1.16% 5.73% 5.71% 4.73% 257.3 0.125
90 0.8 7 9,079 241.5 242.2 65 0.95% 5.47% 6.40% 5.19% 260.9 0.125
91 0.8 7 6,053 241.6 242.2 65 0.80% 5.20% 6.96% 5.40% 265.9 0.099
92 0.8 6 12,105 241.2 242.2 65 1.38% 6.97% 5.92% 4.80% 257.5 0.127
93 0.8 6 9,079 241.5 242.2 65 1.12% 6.71% 6.68% 5.31% 261.1 0.125
94 0.8 5 9,079 241.4 242.2 65 1.34% 8.32% 6.97% 5.37% 261.2 0.125
95 0.8 4 12,105 241.3 242.2 65 2.04% 10.99% 6.23% 4.90% 257.7 0.091
96 0.8 4 9,079 241.4 242.2 65 1.66% 10.79% 7.26% 5.45% 261.3 0.125
97 0.8 4 6,053 241.8 242.2 65 1.34% 10.54% 8.24% 5.67% 267.3 0.122
98 0.8 3 12,105 241.2 242.2 65 2.65% 14.19% 6.35% 4.78% 257.7 0.091
99 0.8 3 6,053 241.7 242.2 65 1.70% 14.02% 8.63% 5.57% 268.4 0.122
100 0.8 2 12,105 241.1 242.2 65 3.62% 19.59% 6.37% 4.56% 257.3 0.091
101 0.8 2 9,079 241.3 242.2 65 2.92% 19.73% 7.68% 4.97% 260.8 0.125
102 0.8 2 6,053 241.6 242.2 65 2.30% 19.78% 9.03% 5.48% 268.4 0.125
103 0.7 8 12,105 241.2 242.2 65 1.02% 4.34% 6.22% 4.22% 262.1 0.125
104 0.7 8 9,079 241.4 242.2 65 0.84% 4.12% 6.78% 4.50% 268.6 0.125
105 0.7 8 6,053 241.7 242.2 65 0.73% 3.95% 7.21% 4.80% 272.8 0.099
106 0.7 7 12,105 241.0 242.2 65 1.19% 5.21% 6.54% 4.25% 262.9 0.127
107 0.7 7 6,053 241.5 242.2 65 0.84% 4.78% 7.74% 4.85% 274.4 0.099
108 0.7 6 12,105 241.1 242.2 65 1.41% 6.38% 6.87% 4.33% 263.5 0.187
109 0.7 6 9,079 241.4 242.2 65 1.16% 6.11% 7.65% 4.67% 270.9 0.125
U
Appendix
Feed composition Reactor conditions Product composition Hot spot
Pt. No. COR SN GHSV TI01 TI02 p yCO yCO2 yMeOH yH2O Ths zhs
[-] [-] [-] [h-1 ] [◦C] [◦C] [bar] [mol-%] [mol-%] [mol-%] [mol-%] [◦C] [m]
110 0.7 6 6,053 241.7 242.2 65 0.98% 5.88% 8.25% 5.00% 276.0 0.099
111 0.7 5 12,105 241.2 242.2 65 1.71% 7.85% 7.27% 4.30% 264.0 0.195
112 0.7 5 9,079 241.4 242.2 65 1.41% 7.71% 8.14% 4.69% 271.6 0.125
113 0.7 5 6,053 241.7 242.2 65 1.16% 7.49% 8.86% 5.15% 277.4 0.099
114 0.7 4 9,079 241.4 242.2 65 1.75% 10.00% 8.70% 4.79% 272.4 0.125
115 0.7 3 12,105 241.3 242.2 65 2.89% 13.46% 8.14% 4.10% 266.2 0.195
116 0.7 3 9,079 241.6 242.2 65 2.31% 13.35% 9.31% 4.60% 273.9 0.125
117 0.7 3 6,053 241.9 242.2 65 1.87% 13.21% 10.29% 4.97% 281.0 0.101
118 0.7 2 12,105 241.3 242.2 65 4.18% 18.74% 8.57% 3.78% 266.3 0.195
119 0.7 2 9,079 241.8 242.2 65 3.32% 18.95% 9.93% 4.18% 274.2 0.127
120 0.7 2 6,053 241.9 242.2 65 2.68% 19.12% 11.07% 4.54% 282.6 0.125
121 0.95 8 12,105 240.7 242.2 65 0.94% 5.44% 4.66% 5.36% 254.5 0.052
122 0.95 8 9,079 240.9 242.2 65 0.80% 5.17% 5.23% 5.79% 255.8 0.052
123 0.95 8 6,053 241.0 242.2 65 0.68% 4.91% 5.81% 5.98% 256.6 0.049
124 0.95 7 12,105 240.6 242.2 65 1.08% 6.43% 4.69% 5.54% 254.3 0.055
125 0.95 7 9,079 240.9 242.2 65 0.91% 6.19% 5.34% 5.96% 255.8 0.052
126 0.95 7 6,053 241.0 242.2 65 0.77% 5.90% 6.00% 6.13% 256.5 0.049
127 0.95 6 9,079 240.8 242.2 65 1.08% 7.58% 5.48% 6.17% 255.7 0.052
128 0.95 5 12,105 240.7 242.2 65 1.45% 9.56% 4.78% 5.82% 254.8 0.052
129 0.95 5 9,079 240.9 242.2 65 1.23% 9.20% 5.54% 6.37% 256.0 0.052
130 0.95 5 6,053 241.0 242.2 65 1.02% 8.85% 6.43% 6.68% 256.5 0.049
131 0.95 4 12,105 240.7 242.2 65 1.71% 11.86% 4.76% 5.93% 254.7 0.052
132 0.95 4 6,053 241.0 242.2 65 1.22% 11.43% 6.57% 6.91% 256.4 0.049
133 0.95 3 12,105 240.6 242.2 65 2.07% 15.35% 4.69% 6.01% 254.4 0.055
134 0.95 3 9,079 240.7 242.2 65 1.80% 15.20% 5.50% 6.46% 255.6 0.052
135 0.95 3 6,053 241.0 242.2 65 1.49% 15.12% 6.58% 6.89% 256.0 0.049
136 0.95 2 12,105 240.6 242.2 65 2.57% 20.52% 4.49% 6.03% 254.1 0.055
137 0.95 2 9,079 240.9 242.2 65 2.25% 20.46% 5.30% 6.53% 255.0 0.052
138 0.9 8 12,105 240.8 242.2 80 0.75% 4.76% 5.91% 5.90% 258.9 0.055
139 0.9 8 9,079 240.9 242.2 80 0.63% 4.41% 6.55% 6.32% 261.1 0.094
140 0.9 8 6,053 240.8 242.2 80 0.53% 4.12% 7.00% 6.25% 264.8 0.094
141 0.9 7 12,105 240.8 242.2 80 0.87% 5.65% 6.05% 6.09% 258.8 0.055
142 0.9 7 9,079 240.9 242.2 80 0.72% 5.33% 6.83% 6.72% 261.0 0.055
143 0.9 7 6,053 240.7 242.2 80 0.61% 4.94% 7.54% 6.94% 264.7 0.094
144 0.9 6 12,105 240.9 242.2 80 1.02% 7.01% 6.18% 6.25% 259.0 0.055
145 0.9 6 9,079 240.9 242.2 80 0.85% 6.62% 6.93% 6.49% 261.1 0.055
146 0.9 6 6,053 240.8 242.2 80 0.70% 6.23% 7.56% 6.48% 264.2 0.094
147 0.9 5 12,105 241.0 242.2 80 1.23% 8.66% 6.23% 6.44% 259.1 0.055
V
Appendix
Feed composition Reactor conditions Product composition Hot spot
Pt. No. COR SN GHSV TI01 TI02 p yCO yCO2 yMeOH yH2O Ths zhs
[-] [-] [-] [h-1 ] [◦C] [◦C] [bar] [mol-%] [mol-%] [mol-%] [mol-%] [◦C] [m]
148 0.9 5 9,079 241.0 242.2 80 1.01% 8.22% 7.17% 7.06% 261.1 0.055
149 0.9 5 6,053 240.9 242.2 80 0.84% 7.99% 7.93% 6.58% 264.0 0.094
150 0.9 4 12,105 240.8 242.3 80 1.50% 11.07% 6.27% 6.44% 259.1 0.055
151 0.9 4 9,079 241.1 242.3 80 1.23% 10.80% 7.30% 7.03% 261.2 0.055
152 0.9 4 6,053 240.9 242.3 80 1.01% 10.30% 8.53% 7.77% 263.8 0.055
153 0.9 3 12,105 240.8 242.3 80 1.91% 14.50% 6.26% 6.37% 259.1 0.055
154 0.9 3 9,079 241.0 242.3 80 1.56% 14.24% 7.37% 6.84% 261.1 0.055
155 0.9 3 6,053 240.9 242.2 80 1.26% 14.01% 8.53% 7.32% 263.3 0.055
156 0.9 2 12,105 240.7 242.2 80 2.49% 19.97% 6.04% 6.21% 258.6 0.055
157 0.9 2 9,079 240.9 242.2 80 2.08% 19.96% 7.21% 6.82% 260.5 0.055
158 0.9 2 6,053 241.0 242.2 80 1.67% 19.93% 8.56% 7.14% 262.0 0.055
159 0.8 8 12,105 241.3 242.2 80 0.77% 4.30% 6.46% 5.38% 262.5 0.099
160 0.8 8 6,053 241.2 242.2 80 0.54% 3.74% 7.52% 5.77% 273.7 0.094
161 0.8 7 12,105 241.4 242.2 80 0.89% 5.18% 6.73% 5.50% 263.3 0.094
162 0.8 7 9,079 241.3 242.2 80 0.74% 4.87% 7.48% 5.85% 268.5 0.099
163 0.8 7 6,053 241.2 242.2 80 0.62% 4.60% 7.99% 5.99% 275.1 0.094
164 0.8 6 12,105 241.5 242.2 80 1.06% 6.46% 7.02% 5.66% 263.7 0.094
165 0.8 6 9,079 241.5 242.2 80 0.86% 6.06% 7.85% 6.05% 269.3 0.127
166 0.8 6 6,053 241.3 242.2 80 0.71% 5.68% 8.51% 6.46% 276.0 0.094
167 0.8 5 9,079 241.5 242.2 80 1.05% 7.74% 8.22% 6.18% 269.6 0.127
168 0.8 5 6,053 241.5 242.2 80 0.87% 7.41% 8.95% 6.26% 277.5 0.094
169 0.8 4 12,105 241.4 242.2 80 1.60% 10.44% 7.55% 5.76% 263.8 0.094
170 0.8 4 9,079 241.5 242.2 80 1.29% 10.10% 8.66% 6.33% 269.7 0.127
171 0.8 4 6,053 241.5 242.2 80 1.07% 9.77% 9.54% 6.77% 278.3 0.094
172 0.8 3 12,105 241.4 242.2 80 2.09% 13.68% 7.73% 5.61% 263.8 0.094
173 0.8 3 6,053 241.5 242.2 80 1.35% 13.31% 10.42% 7.13% 278.8 0.094
174 0.8 2 12,105 241.4 242.2 80 2.94% 19.30% 7.76% 5.19% 263.3 0.094
175 0.8 2 9,079 241.5 242.2 80 2.32% 19.34% 9.18% 5.85% 268.9 0.127
176 0.8 2 6,053 241.5 242.2 80 1.83% 19.06% 10.92% 7.19% 278.6 0.099
177 0.7 8 12,105 241.6 242.2 80 0.74% 3.81% 7.21% 4.93% 270.9 0.153
178 0.7 7 12,105 241.6 242.2 80 0.87% 4.65% 7.64% 4.98% 272.8 0.153
179 0.7 7 6,053 241.4 242.2 80 0.64% 4.12% 8.72% 5.52% 285.3 0.094
180 0.7 6 12,105 241.8 242.2 80 1.04% 5.77% 8.12% 5.08% 274.4 0.153
181 0.7 6 9,079 241.7 242.2 80 0.87% 5.52% 8.83% 5.49% 281.7 0.127
182 0.7 6 6,053 241.5 242.2 80 0.74% 5.19% 9.27% 5.58% 287.1 0.094
183 0.7 5 12,105 241.7 242.2 80 1.29% 7.31% 8.63% 5.20% 275.7 0.153
184 0.7 5 9,079 241.8 242.2 80 1.06% 7.07% 9.44% 5.65% 283.6 0.127
185 0.7 5 6,053 241.7 242.2 80 0.90% 6.72% 10.27% 6.17% 289.7 0.094
W
Appendix
Feed composition Reactor conditions Product composition Hot spot
Pt. No. COR SN GHSV TI01 TI02 p yCO yCO2 yMeOH yH2O Ths zhs
[-] [-] [-] [h-1 ] [◦C] [◦C] [bar] [mol-%] [mol-%] [mol-%] [mol-%] [◦C] [m]
186 0.7 4 9,079 241.8 242.2 80 1.33% 9.23% 10.08% 5.67% 285.7 0.127
187 0.7 3 12,105 241.7 242.2 80 2.18% 12.95% 9.81% 5.04% 278.1 0.153
188 0.7 3 9,079 242.0 242.2 80 1.77% 12.84% 10.87% 5.58% 287.4 0.127
189 0.7 2 12,105 241.5 242.2 80 3.15% 18.55% 10.41% 4.57% 278.2 0.198
190 0.95 8 12,105 241.0 242.2 80 0.79% 5.01% 5.39% 5.97% 257.3 0.055
191 0.95 8 9,079 240.6 242.2 80 0.65% 4.68% 6.09% 6.51% 258.1 0.052
192 0.95 8 6,053 241.0 242.2 80 0.55% 4.31% 6.77% 6.84% 259.5 0.055
193 0.95 7 12,105 240.9 242.2 80 0.91% 6.07% 5.46% 6.20% 257.1 0.055
194 0.95 7 9,079 240.6 242.2 80 0.75% 5.64% 6.21% 6.51% 258.0 0.052
195 0.95 7 6,053 240.8 242.2 80 0.62% 5.24% 6.87% 6.48% 259.3 0.055
196 0.95 6 9,079 240.8 242.2 80 0.88% 6.95% 6.38% 6.98% 258.0 0.052
197 0.95 5 12,105 240.7 242.2 80 1.25% 9.01% 5.56% 6.49% 257.4 0.055
198 0.95 5 9,079 240.6 242.2 80 1.05% 8.72% 6.45% 6.95% 258.2 0.052
199 0.95 5 6,053 240.8 242.2 80 0.84% 8.23% 7.49% 7.45% 259.1 0.052
200 0.95 4 12,105 240.7 242.2 80 1.51% 11.51% 5.54% 6.61% 257.3 0.055
201 0.95 4 6,053 240.5 242.2 80 1.01% 10.72% 7.83% 8.01% 258.8 0.036
202 0.95 3 12,105 240.6 242.2 80 1.85% 15.10% 5.45% 6.72% 257.1 0.055
203 0.95 3 9,079 240.5 242.2 80 1.57% 14.71% 6.42% 7.07% 257.8 0.052
204 0.95 3 6,053 240.6 242.2 80 1.27% 14.40% 7.71% 7.62% 258.3 0.036
205 0.95 2 12,105 240.5 242.2 80 2.34% 20.18% 5.19% 6.55% 256.6 0.055
206 0.95 2 9,079 240.3 242.2 80 2.00% 20.20% 6.18% 7.12% 257.3 0.055
207 0.98 8 12,105 240.3 242.2 50 1.24% 6.21% 3.27% 4.63% 250.7 0.055
208 0.98 8 9,079 240.2 242.2 50 1.10% 6.08% 3.75% 4.92% 250.9 0.052
209 0.98 8 6,053 240.2 242.2 50 0.92% 5.70% 4.33% 5.36% 251.5 0.036
210 0.98 7 12,105 240.1 242.2 50 1.40% 7.20% 3.28% 4.77% 250.5 0.055
211 0.98 7 9,079 240.2 242.2 50 1.23% 7.02% 3.77% 5.10% 250.9 0.052
212 0.98 7 6,053 240.3 242.2 50 1.03% 6.71% 4.42% 5.55% 251.7 0.036
213 0.98 6 9,079 240.2 242.2 50 1.39% 8.32% 3.80% 5.24% 250.8 0.052
214 0.98 5 12,105 240.1 242.2 50 1.76% 10.19% 3.30% 5.08% 250.5 0.055
215 0.98 5 9,079 240.2 242.2 50 1.58% 10.10% 3.83% 5.40% 251.0 0.052
216 0.98 5 6,053 240.2 242.2 50 1.34% 9.88% 4.58% 5.95% 251.8 0.034
217 0.98 4 12,105 240.0 242.2 50 2.01% 12.59% 3.28% 5.25% 250.5 0.052
218 0.98 4 6,053 240.2 242.2 50 1.56% 12.14% 4.61% 6.12% 251.8 0.034
219 0.98 3 12,105 240.0 242.2 50 2.32% 15.97% 3.21% 5.42% 250.4 0.055
220 0.98 3 9,079 240.2 242.2 50 2.13% 15.90% 3.74% 5.74% 250.8 0.052
221 0.98 3 6,053 240.1 242.2 50 1.86% 15.80% 4.55% 6.29% 251.4 0.034
222 0.98 2 12,105 240.0 242.2 50 2.70% 21.04% 3.09% 5.53% 250.1 0.055
223 0.98 2 9,079 240.1 242.2 50 2.56% 20.97% 3.57% 5.88% 250.3 0.052
X
Appendix
Feed composition Reactor conditions Product composition Hot spot
Pt. No. COR SN GHSV TI01 TI02 p yCO yCO2 yMeOH yH2O Ths zhs
[-] [-] [-] [h-1 ] [◦C] [◦C] [bar] [mol-%] [mol-%] [mol-%] [mol-%] [◦C] [m]
224 0.98 8 12,105 240.3 242.2 65 1.03% 5.75% 4.14% 5.26% 253.3 0.052
225 0.98 8 9,079 240.3 242.2 65 0.87% 5.51% 4.76% 5.73% 253.9 0.052
226 0.98 8 6,053 240.4 242.3 65 0.71% 5.12% 5.50% 6.33% 254.8 0.036
227 0.98 7 12,105 240.3 242.3 65 1.15% 6.83% 4.17% 5.41% 253.3 0.052
228 0.98 7 9,079 240.3 242.3 65 0.98% 6.53% 4.83% 5.90% 253.9 0.052
229 0.98 7 6,053 240.3 242.2 65 0.80% 6.15% 5.66% 6.54% 254.9 0.036
230 0.98 6 9,079 240.4 242.3 65 1.11% 7.77% 4.89% 6.07% 253.9 0.052
231 0.98 5 12,105 240.3 242.2 65 1.50% 9.89% 4.21% 5.75% 253.5 0.052
232 0.98 5 9,079 240.4 242.2 65 1.28% 9.46% 4.94% 6.26% 254.3 0.052
233 0.98 5 6,053 240.4 242.2 65 1.06% 9.09% 5.93% 7.01% 255.0 0.036
234 0.98 4 12,105 240.3 242.2 65 1.74% 12.10% 4.18% 5.90% 253.4 0.052
235 0.98 4 6,053 240.3 242.2 65 1.24% 11.62% 6.00% 7.19% 254.9 0.034
236 0.98 3 12,105 240.2 242.2 65 2.05% 15.62% 4.10% 6.07% 253.3 0.052
237 0.98 3 9,079 240.5 242.2 65 1.81% 15.45% 4.85% 6.57% 254.1 0.052
238 0.98 3 6,053 240.4 242.2 65 1.53% 15.23% 5.95% 7.32% 254.8 0.034
239 0.98 2 12,105 240.2 242.2 65 2.45% 20.42% 3.92% 6.16% 253.0 0.052
240 0.98 2 9,079 240.4 242.2 65 2.23% 20.73% 4.62% 6.65% 253.3 0.052
241 0.98 8 12,105 240.5 242.2 80 0.80% 5.18% 4.95% 6.05% 255.8 0.055
242 0.98 8 9,079 240.7 242.2 80 0.67% 4.86% 5.78% 6.57% 257.2 0.055
243 0.98 8 6,053 240.6 242.2 80 0.55% 4.44% 6.53% 6.86% 257.9 0.036
244 0.98 7 12,105 240.6 242.2 80 0.93% 6.25% 5.10% 6.15% 256.1 0.055
245 0.98 7 9,079 240.7 242.2 80 0.77% 5.86% 5.91% 6.76% 257.2 0.055
246 0.98 7 6,053 240.7 242.2 80 0.62% 5.41% 6.72% 6.84% 258.0 0.036
247 0.98 6 9,079 240.7 242.2 80 0.89% 7.11% 6.01% 6.99% 257.1 0.055
248 0.98 5 12,105 240.6 242.2 80 1.26% 9.29% 5.18% 6.52% 256.6 0.055
249 0.98 5 9,079 240.7 242.2 80 1.05% 8.96% 6.08% 7.07% 257.4 0.055
250 0.98 5 6,053 240.6 242.2 80 0.85% 8.44% 7.19% 7.63% 258.0 0.036
251 0.98 4 12,105 240.5 242.2 80 1.49% 11.67% 5.15% 6.66% 256.5 0.055
252 0.98 4 6,053 240.7 242.2 80 1.01% 10.96% 7.31% 7.82% 258.0 0.036
253 0.98 3 12,105 240.5 242.2 80 1.80% 15.20% 5.03% 6.79% 256.3 0.055
254 0.98 3 9,079 240.5 242.2 80 1.55% 14.85% 5.98% 7.40% 256.9 0.052
255 0.98 2 12,105 240.3 242.2 80 2.23% 20.59% 4.78% 6.82% 255.6 0.052
256 0.98 2 9,079 240.6 242.2 80 1.93% 20.40% 5.69% 7.46% 256.1 0.052
257 0.9 8 12,105 220.2 222.2 50 1.53% 6.75% 2.24% 2.99% 228.6 0.057
258 0.9 8 9,079 220.3 222.2 50 1.42% 6.53% 2.68% 3.31% 229.8 0.055
259 0.9 8 6,053 220.2 222.2 50 1.15% 6.19% 3.44% 3.82% 230.4 0.052
260 0.9 7 12,105 220.2 222.2 50 1.69% 7.81% 2.25% 3.06% 228.6 0.057
261 0.9 7 9,079 220.1 222.2 50 1.57% 7.49% 2.68% 3.39% 229.6 0.055
Y
Appendix
Feed composition Reactor conditions Product composition Hot spot
Pt. No. COR SN GHSV TI01 TI02 p yCO yCO2 yMeOH yH2O Ths zhs
[-] [-] [-] [h-1 ] [◦C] [◦C] [bar] [mol-%] [mol-%] [mol-%] [mol-%] [◦C] [m]
262 0.9 7 6,053 220.3 222.2 50 1.30% 7.31% 3.49% 3.90% 230.8 0.052
263 0.9 6 12,105 220.3 222.2 50 1.87% 9.07% 2.26% 3.10% 229.1 0.057
264 0.9 6 9,079 220.2 222.2 50 1.79% 8.86% 2.72% 3.47% 229.9 0.057
265 0.9 6 6,053 220.1 222.2 50 1.47% 8.47% 3.52% 3.96% 231.0 0.057
266 0.9 5 12,105 220.1 222.2 50 2.09% 10.78% 2.28% 3.15% 229.1 0.057
267 0.9 5 9,079 220.3 222.2 50 2.02% 10.54% 2.73% 3.52% 230.1 0.055
268 0.9 5 6,053 220.3 222.2 50 1.71% 10.35% 3.55% 4.04% 231.7 0.057
269 0.9 4 12,105 220.2 222.2 50 2.39% 13.00% 2.28% 3.19% 229.3 0.073
270 0.9 4 9,079 220.3 222.2 50 2.31% 12.74% 2.74% 3.56% 230.2 0.057
271 0.9 4 6,053 220.2 222.2 50 2.01% 12.55% 3.57% 4.09% 231.8 0.057
272 0.9 3 12,105 220.2 222.2 50 2.81% 16.44% 2.26% 3.22% 229.5 0.075
273 0.9 3 9,079 220.1 222.1 50 2.73% 16.32% 2.72% 3.60% 230.1 0.060
274 0.9 3 6,053 220.1 222.2 50 2.43% 16.13% 3.54% 4.09% 232.0 0.057
275 0.9 2 12,105 220.0 222.2 50 3.41% 21.28% 2.20% 3.20% 229.3 0.075
276 0.9 2 9,079 220.2 222.1 50 3.33% 21.36% 2.65% 3.56% 230.2 0.057
277 0.9 2 6,053 220.3 222.2 50 3.06% 21.47% 3.47% 4.06% 232.1 0.057
278 0.8 8 12,105 220.1 222.1 50 2.14% 6.29% 2.29% 2.54% 228.3 0.057
279 0.8 8 6,053 220.3 222.2 50 1.38% 5.81% 3.80% 3.26% 230.8 0.057
280 0.8 7 12,105 220.1 222.1 50 2.39% 7.19% 2.32% 2.59% 228.4 0.057
281 0.8 7 9,079 220.2 222.1 50 2.10% 7.03% 2.86% 2.84% 229.6 0.055
282 0.8 7 6,053 220.3 222.1 50 1.58% 6.79% 3.87% 3.30% 231.2 0.057
283 0.8 6 12,105 220.1 222.1 50 2.75% 8.44% 2.34% 2.59% 228.5 0.057
284 0.8 6 9,079 220.3 222.1 50 2.42% 8.17% 2.90% 2.86% 229.7 0.060
285 0.8 6 6,053 220.3 222.2 50 1.85% 8.00% 3.93% 3.32% 231.7 0.057
286 0.8 5 9,079 220.3 222.2 50 2.82% 9.85% 2.92% 2.89% 229.9 0.055
287 0.8 4 12,105 220.2 222.1 50 3.69% 12.12% 2.34% 2.63% 229.0 0.075
288 0.8 4 9,079 220.2 222.1 50 3.38% 11.94% 2.92% 2.88% 230.0 0.060
289 0.8 4 6,053 220.3 222.2 50 2.73% 11.95% 4.03% 3.31% 232.1 0.055
290 0.8 3 12,105 220.0 222.1 50 4.51% 15.30% 2.31% 2.60% 229.0 0.075
291 0.8 3 6,053 220.3 222.2 50 3.43% 15.25% 4.04% 3.23% 232.3 0.055
292 0.8 2 12,105 220.1 222.2 50 5.74% 19.79% 2.24% 2.47% 229.0 0.075
293 0.8 2 9,079 220.1 222.2 50 5.41% 20.05% 2.81% 2.73% 229.8 0.060
294 0.8 2 6,053 220.3 222.1 50 4.59% 20.18% 3.96% 3.08% 232.2 0.055
295 0.7 8 12,105 220.2 222.1 50 2.78% 5.74% 2.39% 2.14% 227.8 0.057
296 0.7 8 9,079 220.2 222.1 50 2.33% 5.47% 3.06% 2.37% 229.2 0.055
297 0.7 7 12,105 220.2 222.1 50 3.17% 6.57% 2.42% 2.16% 228.0 0.057
298 0.7 7 6,053 220.3 222.1 50 1.87% 6.23% 4.39% 2.83% 231.4 0.057
299 0.7 6 12,105 220.1 222.2 50 3.64% 7.51% 2.43% 2.16% 228.1 0.057
Z
Appendix
Feed composition Reactor conditions Product composition Hot spot
Pt. No. COR SN GHSV TI01 TI02 p yCO yCO2 yMeOH yH2O Ths zhs
[-] [-] [-] [h-1 ] [◦C] [◦C] [bar] [mol-%] [mol-%] [mol-%] [mol-%] [◦C] [m]
300 0.7 6 9,079 220.4 222.1 50 3.19% 7.48% 3.13% 2.35% 229.5 0.055
301 0.7 6 6,053 220.3 222.1 50 2.27% 7.41% 4.51% 2.80% 231.6 0.057
302 0.7 5 12,105 220.1 222.1 50 4.32% 8.97% 2.43% 2.17% 228.2 0.057
303 0.7 5 9,079 220.3 222.1 50 3.77% 8.94% 3.14% 2.33% 229.6 0.060
304 0.7 5 6,053 220.4 222.1 50 2.77% 8.92% 4.60% 2.76% 231.9 0.057
305 0.7 4 9,079 220.3 222.2 50 4.68% 11.00% 3.13% 2.33% 229.6 0.060
306 0.7 3 12,105 220.1 222.1 50 6.56% 13.70% 2.37% 2.09% 228.5 0.075
307 0.7 2 12,105 220.2 222.1 50 8.66% 18.26% 2.27% 1.98% 228.6 0.078
308 0.95 8 12,105 220.1 222.1 50 1.29% 7.01% 2.22% 3.28% 228.9 0.060
309 0.95 8 9,079 220.3 222.1 50 1.24% 6.81% 2.62% 3.64% 229.7 0.055
310 0.95 8 6,053 220.2 222.2 50 1.07% 6.48% 3.32% 4.15% 230.5 0.055
311 0.95 7 12,105 220.2 222.2 50 1.40% 8.05% 2.22% 3.33% 229.0 0.057
312 0.95 7 9,079 220.2 222.1 50 1.36% 7.77% 2.62% 3.72% 229.7 0.055
313 0.95 7 6,053 220.1 222.1 50 1.18% 7.41% 3.33% 4.24% 230.8 0.057
314 0.95 6 9,079 220.2 222.2 50 1.50% 9.09% 2.63% 3.80% 229.8 0.055
315 0.95 5 12,105 220.1 222.1 50 1.65% 11.14% 2.25% 3.47% 229.1 0.057
316 0.95 5 9,079 220.2 222.1 50 1.66% 10.86% 2.66% 3.89% 230.0 0.057
317 0.95 5 6,053 220.1 222.1 50 1.50% 10.57% 3.38% 4.45% 231.5 0.055
318 0.95 4 12,105 220.1 222.1 50 1.84% 13.43% 2.25% 3.53% 229.2 0.055
319 0.95 4 6,053 220.3 222.1 50 1.73% 12.95% 3.38% 4.56% 231.8 0.055
320 0.95 3 12,105 220.2 222.1 50 2.05% 16.88% 2.23% 3.58% 229.3 0.055
321 0.95 3 9,079 220.2 222.1 50 2.14% 16.56% 2.63% 4.04% 230.4 0.057
322 0.95 3 6,053 220.1 222.1 50 2.01% 16.46% 3.34% 4.63% 231.8 0.055
323 0.95 2 12,105 220.0 222.1 50 2.41% 22.07% 2.18% 3.57% 229.2 0.055
324 0.95 2 9,079 220.2 222.1 50 2.50% 21.77% 2.57% 4.04% 230.2 0.057
AA
Appendix
A.14 Mass balances of the miniplant experiments
Figure A.11: C-/H-/O- balance of the miniplant experimental points used within this study.
AB
Appendix
A.15 Axial deactivation
Figure A.12:
Temperature profile at benchmark point (COR = 0.9; SN = 4.0; GHSV = 12,000 h
-1
;
p = 50 bar; T
cool
= 240
◦
C) at beginning of the experimental campaign, after 25 h,
50 h, 75 h as well as 100h.
AC
Appendix
A.16 NMR liquid phase measurement
Figure A.13:
NMR measurement of a liquid product sample;
1
H NMR (400 mHz, D
2
O):
δ
/ppm = 8,139 (s,
H
COOH, traces), 4,8 (s,
H2
O), 3,362 (s, C
H3
OH; CH
3
C
H2
OH
and CH
3
CH
2
C
H2
OH is covered by CH
3
OH), 1,552 (m, CH
3
C
H2
CH
2
OH), 1,181 (t,
CH3CH2OH), 0,893 (t, CH3CH2CH2OH).
AD
Appendix
A.17 Kinetic model by Graaf
Reaction mechanism proposed by Graaf[192]:
Adsorption of educts
CO + s1 ⇌CO*s1 (A.22)
CO2+ s1 ⇌CO2*s1 (A.23)
H2+ 2s2 ⇌2H*s2 (A.24)
H2O + s2 ⇌H2O*s2 (A.25)
CO2-hydrogenation
A1 CO2*s1 + H*s2 ⇌HCO2*s1 + s2 (A.26)
A2 HCO2*s1 + H*s2 ⇌H2CO2*s1 + s2 (A.27)
A3 H2CO2*s1 + H*s2 ⇌H3CO2*s1 + s2 RDS (A.28)
A4 H3CO2*s1 + H*s2 ⇌H2CO*s1 + H2O*s2 (A.29)
A5 H2CO*s1 + H*s2 ⇌H3CO*s1 + s2 (A.30)
A6 H3CO*s1 + H*s2 ⇌CH3OH + s1 + s2 (A.31)
rWGS
B1 CO2*s1 + H*s2 ⇌HCO2*s1 + s2 (A.32)
B2 HCO2*s1 + H*s2 ⇌CO*s1 + H2O*s2 RDS (A.33)
CO-hydrogenation
C1 CO*s1 + H*s2 ⇌HCO*s1 + s2 (A.34)
C2 HCO*s1 + H*s2 ⇌H2CO*s1 + s2 (A.35)
C3 H2CO*s1 + H*s2 ⇌H3CO*s1 + s2 RDS (A.36)
C4 H3CO*s1 + H*s2 ⇌CH3OH + s1 + s2 (A.37)
Rate equations proposed by Graaf [192]:
rCO2=k1·K2·EQ1
(1 + K1·fCO +K2·fC O2)f0.5
H2+K3·fH2O(A.38)
rrW GS =k2·K2·EQ2
(1 + K1·fCO +K2·fC O2)f0,5
H2+K3·fH2O(A.39)
rCO =k3·K1·EQ3
(1 + K1·fCO +K2·fC O2)f0,5
H2+K3·fH2O(A.40)
AE
Appendix
Table A.6: Original kinetic parameters proposed by Graaf et al. [193].
Unit Parameters
k1mol ·kg−1·s−1·bar−11.09 ·105·exp −87,500
R·T
k2mol ·kg−1·s−1·bar−0.59.64 ·1011 ·exp −152,900
R·T
k3mol ·kg−1·s−1·bar−14.89 ·107·exp −113,000
R·T
K1bar−12.16 ·10−5·exp 46,800
R·T
K2bar−17.05 ·10−7·exp 61,700
R·T
K3bar−0.56.37 ·10−9·exp 84,000
R·T
Table A.7: Kinetic parameters for the Graaffit model obtained with the miniplant setup.
Unit Parameters
k1mol ·kg−1·s−1·bar−15.861 ·104·exp −62,403
R·T
k2mol ·kg−1·s−1·bar−0.53.027 ·1011 ·exp −123,083
R·T
k3mol ·kg−1·s−1·bar−1−1.459 ·108·exp −159,919
R·T
K1bar−16.830 ·10−5·exp 37,420
R·T
K2bar−18.014 ·10−8·exp 68,624
R·T
K3bar−0.51.181 ·10−8·exp 105,009
R·T
AF
Appendix
Figure A.14:
Parity plots of the refitted model "Graaf
fit
" for outlet molar fractions of methanol
(A) and water (B) as well as hot spot temperature (C) and axial hot spot position
(D) including error lines for 0% (solid line) and for 10% (dashed line); Experiments
were carried out with the miniplant setup.
AG
Appendix
A.18 Kinetic model by Bussche
Reaction mechanism proposed by Bussche and Froment [145]:
Adsorption of educts
H2+ 2s ⇌2H*s (A.41)
CO2+ s ⇌O*s + CO RDS (A.42)
CO2+ O*s + s ⇌CO3*s (A.43)
H2O + s ⇌H2O*s (A.44)
CO2-hydrogenation
A1 CO3*2s + H*s ⇌HCO3*2s + s (A.45)
A2 HCO3*2s + s ⇌HCO2*2s + O*s (A.46)
A3 HCO2*2s + H*s ⇌H2CO2*2s + s RDS (A.47)
A4 H2CO2*2s ⇌H2CO*s + O*s (A.48)
A5 H2CO*s + H*s ⇌H3CO*s + s (A.49)
A6 H3CO*s + H*s ⇌CH3OH + 2s (A.50)
rWGS
B1 O*s + H*s ⇌OH*s + s (A.51)
B2 OH*s + H*s ⇌H2O*s + s (A.52)
Rate equations proposed by Bussche[145]:
rCO2=k1·fC O2·fH2·EQ1
1 + K1·fH2O
fH2+K2·f0,5
H2+K3·fH2O3(A.53)
rrW GS =k2·fCO2·EQ2
1 + K1·fH2O
fH2+K2·f0,5
H2+K3·fH2O(A.54)
Table A.8: Original kinetic parameters proposed by Bussche et al.[145].
Unit Parameters
k1mol ·kg−1·s−1·bar−21.07 ·exp 36,696
R·T
k2mol ·kg−1·s−1·bar−11.22 ·1010 ·exp −94,765
R·T
K1−3,453.38
K2bar−0.50.499 ·exp 17,197
R·T
K3bar−16.62 ·10−11 ·exp 124,119
R·T
AH
Appendix
Table A.9: Kinetic parameters for the Busschefit model obtained with the miniplant setup.
Unit Parameters
k1mol ·kg−1·s−1·bar−20.020 ·exp −29,122
R·T
k2mol ·kg−1·s−1·bar−11.989 ·109·exp −119,461
R·T
K1−0.337 ·exp −2
R·T
K2bar−0.5−1.438 ·10−3·exp 17,263
R·T
K3bar−11.972 ·10−10 ·exp 90,516
R·T
Figure A.15:
Parity plots of the refitted model "Bussche
fit
" for outlet molar fractions of methanol
(A) and water (B) as well as hot spot temperature (C) and axial hot spot position
(D) including error lines for 0% (solid line) and for 10% (dashed line); Experiments
were carried out with the miniplant setup.
AI
Appendix
A.19 Kinetic model by Park
Reaction mechanism proposed by Park et al.[203]:
Adsorption of educts
CO + s1 ⇌CO*s1 (A.55)
CO2+ s3 ⇌CO2*s3 (A.56)
H2+ 2s2 ⇌2H*s2 (A.57)
H2O + s2 ⇌H2O*s2 (A.58)
CO2-hydrogenation
A1 CO2*s3 + H*s2 ⇌HCO2*s3 + s2 (A.59)
A2 HCO2*s3 + H*s2 ⇌H2CO2*s3+ s2 (A.60)
A3 H2CO2*s3 + H*s2 ⇌H3CO2*s3 + s2 RDS (A.61)
A4 H3CO2*s3 + H*s2 ⇌H2CO*s3 + H2O*s2 (A.62)
A5 H2CO*s3 + H*s2 ⇌H3CO*s3 + s2 (A.63)
A6 H3CO*s3 + H*s2 ⇌CH3OH + s3 + s2 (A.64)
rWGS
B1 CO2*s3 + H*s2 ⇌HCO2*s3 + s2 (A.65)
B2 HCO2*s3 + H*s2 ⇌CO*s3 + H2O*s2 RDS (A.66)
CO-hydrogenation
C1 CO*s1 + H*s2 ⇌HCO*s1 + s2 (A.67)
C2 HCO*s1 + H*s2 ⇌H2CO*s1 + s2 (A.68)
C3 H2CO*s1 + H*s2 ⇌H3CO*s1 + s2 RDS (A.69)
C4 H3CO*s1 + H*s2 ⇌CH3OH + s1 + s2 (A.70)
Rate equations proposed by Park et al.[203]:
rCO2=
k′
C·KCO2·fCO2·f1,5
H2−fH2O·fM eOH /Keq,1·f1,5
H2
1 + KCO 2·fC O2·1 + K0,5
H2·f0,5
H2+KH2O·fH2O(A.71)
rW GS =−
k′
B·KCO2·fCO2·fH2−fCO ·fH2O/Keq,2
1 + KCO 2·fC O2·1 + K0,5
H2·f0,5
H2+KH2O·fH2O(A.72)
rCO =
k′
A·KCO ·fC O ·f1,5
H2−fM eOH /Keq,3·f0,5
H2
1 + KCO ·fC O ·1 + K0,5
H2·f0,5
H2+KH2O·fH2O(A.73)
rDM E =
k′
DM E ·K2
MeOH ·c2
MeOH −cH2O·cDM E /Kp,DME
1+2√KMeOH ·cM eOH +KH2O,DM E ·cH2O4(A.74)
AJ
Appendix
Table A.10: Kinetic parameters proposed by Park et al.[203, 261].
Unit Parameters
k′
Amol ·kg−1·s−1·bar−1.51.88 ·108·exp−133,711
R·T
k′
Bmol ·kg−1·s−1·bar−11.16 ·1010 ·exp−126,573
R·T
k′
Cmol ·kg−1·s−1·bar−1.57.08 ·104·exp−68,252
R·T
KCO *bar−18.00 ·10−7·exp58,015
R·T
KCO2*bar−11.02 ·10−7·exp67,439
R·T
KH2*bar−127.08 ·exp−6,291
R·T
KH2Obar−13.80 ·10−10 ·exp 80,876
R·T
k′
DM E mol ·kg−1·s−18.54 ·109·exp−123,779
R·T
KMeOH m3·mol−17.9·10−4·exp70,500
R·T
KH2O,DM E m3·mol−10.84 ·10−1·exp41,100
R·T
Kp,DM E −0.106 ·exp2.1858·104
R·T
*
these parameters were published by the group subsequently to their
original publication [262]
AK
Appendix
A.20 Kinetic model by Henkel
Reaction mechanism proposed by Henkel[202]:
Adsorption
CO + s1 ⇌CO*s1 (A.75)
CO2+ s1 ⇌CO2*s1 (A.76)
H2+ 2s2 ⇌2H*s2 (A.77)
H2O + s2 ⇌H2O*s2 (A.78)
CO2-hydrogenation
A1 CO2*s1 + H*s2 ⇌HCO2*s1 + s2 (A.79)
A2 HCO2*s1 + H*s2 ⇌H2CO2*s1 + s2 (A.80)
A3 H2CO2*s1 + H*s2 ⇌H3CO2*s1 + s2 RDS (A.81)
A4 H3CO2*s1 + H*s2 ⇌H2CO*s1 + H2O*s2 (A.82)
A5 H2CO*s1 + H*s2 ⇌H3CO*s1 + s2 (A.83)
A6 H3CO*s1 + H*s2 ⇌CH3OH + s1 + s2 (A.84)
rWGS
B1 CO2*s1 + H*s2 ⇌HCO2*s1 + s2 (A.85)
B2 HCO2*s1 + H*s2 ⇌CO*s1 + H2O*s2 RDS (A.86)
Rate equations proposed by Henkel[202]:
rCO2=k1·K2·fC O2·f1,5
H2·EQ1
(1 + K1·fCO +K2·fC O2)f0,5
H2+K3·fH2O(A.87)
rrW GS =k2·K2·fCO2·fH2·EQ2
(1 + K1·fCO +K2·fC O2)f0,5
H2+K3·fH2O(A.88)
Table A.11:
Kinetic parameters fitted by Henkel for the Berty reactor and the micro fixed bed
reactor [202].
Unit Berty Micro fixed bed
k1mol ·kg−1·s−1·P a−14.629 ·10−4·exp −47,472
R·T3.172 ·10−4·exp −45,893
R·T
k2mol ·kg−1·s−1·P a−0.512.975 ·exp −60,609
R·T2.021 ·106·exp −112,322
R·T
K1P a−12.743 ·10−17 ·exp 108,082
R·T2.420 ·10−14 ·exp 81,976
R·T
K2P a−11.935 ·10−41.000 ·10−4
K3P a−0.55.797 ·10−14 ·exp 112,322
R·T1.040 ·10−8·exp 61,856
R·T
AL
Appendix
Table A.12:
Fitted parameters for the Nestler
integ
kinetic model obtained from the measured
data by Park et al.[203] in Sec. 4.1.
Unit Nestlerinteg kinetic parameters
k1mol ·kg−1·s−1·P a−15.411 ·10−4·exp −45,458
R·T
k2mol ·kg−1·s−1·P a−0.54.701 ·exp −54,970
R·T
K1P a−13.321 ·10−18 ·exp 109,959
R·T
K2P a−18.262 ·10−6
K3P a−0.56.430 ·10−14 ·exp 119,570
R·T
Table A.13:
Fitted parameters for the Nestler
diff
kinetic model obtained from the miniplant data
in Sec. 4.2.3.
Unit Proposed kinetic parameters
k1mol kg-1 s-1 Pa-1 2.385 ·10−5·exp −14,709
R·T
k2mol kg-1 s-1 Pa-0.5 244.433 ·exp −53,741
R·T
K1Pa-1 1.440 ·10−17 ·exp −570
R·T
K2Pa-1 4.223 ·10−6
K3Pa-0.5 6.407 ·10−13 ·exp 126,843
R·T
AM
Appendix
A.21 Alternative kinetic approaches
As the set of rate equations proposed by Henkel[202] is based a assumption regarding the
rate determining step in the suggested mechanism (see Eq.A.75 until Eq. A.86), the question
arises whether this combination led to the lowest possible deviation between experimental and
simulation data. In order to clarify this question, rate equations were derived for all possible
combinations of RDS in rWGS and CO2-hydrogenation:
A1
rA1=kA1·KCO2·pKH2·fCO2 ·pfH2·EQ1
(1 + KCO ·fCO +KCO2·fCO2)·(1 + KH2O·fH2O+qKH2·fH2)(A.89)
A2
rA2=kA2·KCO2·KH2·fCO2·fH2·EQ1
(1 + KCO ·fCO +KCO2·fCO2)·(1 + KH2O·fH2O+qKH2·fH2)(A.90)
A3
rA3=kA3·KCO2·K1.5
H2·f1.5
H2·fCO2 ·EQ1
(1 + KCO ·fCO +KCO2·fCO2)·(1 + KH2O·fH2O+qKH2·fH2)(A.91)
A4
rA4=kA4·KCO2·K2
H2·fCO2·f2
H2·EQ1
(1 + KCO ·fCO +KCO2·fCO2)·(1 + KH2O·fH2O+qKH2·fH2)(A.92)
A5
rA5=kA5·KCO2·K2.5
H2·K−1
H2O·fCO2·f2.5
H2
fH2O·EQ1
(1 + KCO ·fCO +KCO2·fCO2)·1 + KH2O·fH2O+qKH2·fH2(A.93)
A6
rA6=
kA6·K3
H2·KCO2
KH2O·f3
H2·fCO2
fH2O·EQ1
(1 + KCO ·fCO +KCO2·fCO2)·(1 + KH2O·fH2O+qKH2·fH2)(A.94)
B1
rB1=kB1·KCO2·pKH2·fCO2 ·pfH2·EQ2
(1 + KCO ·fCO +KCO2·fCO2)·(1 + KH2O·fH2O+pKH2·fH2)(A.95)
B2
rB2=kB2·KCO2·KH2·fCO2·fH2·EQ2
(1 + KCO ·fCO +KCO2·fCO2)·(1 + KH2O·fH2O+qKH2·fH2)(A.96)
AN
Appendix
All possible combinations of rate equations were then subjected to the parameter fitting described
in Sec. 3.5.2.2. The remaining errors depicted in Fig. A.16 show that the best parameter estimation
was obtained with the combinations of RDS proposed by Henkel (A3B2). The fact that other
combinations led to higher deviations underlines the ability of the miniplant setup to discriminate
between different mechanistic assumptions.
Figure A.16:
Remaining objective function with respect to Eq. 3.79 obtained for the kinetic
models Bussche
fit
, Graaf
fit
and Nestler
diff
as well as for all possible combinations of
Eq. A.89 until Eq. A.96; Arrows indicate the same combination of RDS, however in
case of A3B2 without the simplification 1
≪KH2O·fH2O
+
qKH2·fH2
proposed by
Graaf [192].
AO
Appendix
A.22 Single versus global data fitting
Figure A.17:
Sensitivity analysis of the objective function defined in Eq.3.79 on the kinetic pa-
rameters
Ak1
and
Bk1
(A) as well as
Ak2
and
Bk2
(B) simulated for all experimental
data points with the kinetic model Nestler
fit
; Color of the heat map symbolizes
the value of the objective function; The gray area could not be calculated due to
divergence of the kinetic model; The final data set fitted for all experimental data
points in Sec.4.2.3 is marked by (x); The values fitted for each individual data point
are marked by (+).
AP
Appendix
Figure A.18: Sensitivity analysis of the objective function defined in Eq.3.79 on the adsorption
parameters
AK1
and
BK1
(A),
AK2
and
BK2
(B) as well as
AK3
and
BK3
(C)
simulated for all experimental data points with the kinetic model Nestlerfit; Color
of the heat map symbolizes the value of the objective function; The final data set
fitted for all experimental data points in Sec.4.2.3 is marked by (x); The values
fitted for each individual data point are marked by (+).
AQ
Appendix
A.23 Comparison of experimental and simulated gas phase composition data
Figure A.19:
Gas phase compositions obtained from the miniplant experiments and simulated
using the kinetic models by Graaf [192] (A), Bussche[145] (B) as well as the kinetic
model Nestler
integ
(compare Sec. 4.1, C) and Nestler
diff
(compare Sec. 4.2, D) at
p = 80 bar; T
cool
= 240
◦
C; SN = 5.0 and GHSV = 9,000 h
-1
for COR = 0.7, 0.8, 0.9,
0.95 and 0.98.
AR
Appendix
A.24 Dynamic simulation study
In order to discuss the behavior of a steam cooled tubular reactor under transient conditions
and account for possible issues arising for reactor design, a dynamic simulation campaign was
performed applying the Nestler
diff
kinetic model and the dynamic reactor model presented in
Sec. 3.1.5. The reactor dimensions were considered with regard to Tab.3.5. To keep the simulation
parameters in the validated data range of the kinetic model, a base case of COR= 0.85, SN= 3.0
and GHSV = 10,000 h
-1
was defined for the three pressure levels of 50bar, 65 bar and 80 bar at
a cooling temperature of 240
◦
C. The load changes in the simulation campaign were applied
separately for COR, SN and GHSV from the base case and executed as step (transition time 0 s)
and ramps of 1 s, 2 s as well as 5 s. COR was varied to 0.7 and 1.0, SN to 2.0 and 4.0 and GHSV
to 4,000 h
-1
and 16,000 h
-1
. THe diffusion limitation (compare Sec. 3.5.2) was neglected in this
simulation campaign to decrease computation time.
The goal of this simulation campaign was the determination of possible critical load gradients,
e.g. due to a temperature overshoot during the load change. However, it is to be denoted that
the load changes applied in the simulation campaign would be very unlikely to proceed in a
state-of-the-art methanol synthesis process as the dead volume of the process equipment in the
recycle loop would decrease the gradient. In case of an uncritical behavior of the reactor during
the load changes considered here, it can therefore be assumed that the reactor can be operated
dynamically when it is integrated into the methanol synthesis loop process.
In Fig. A.20, the development of the reactor’s STY (a) (compare Eq.2.9) and hot spot temperature
is shown during the reduction of the GHSV from 10,000h
-1
to 4,000 h
-1
for the four load gradients.
Fig. A.20 (a) indicated a sharp decrease in STY during the time of the load transition with a
subsequent slight increase and a stabilization at the new steady state. The initial decrease in
STY can be explained by the reduced reactor output due to the lower flow rate, however, with
an output composition related to the shorter residence time in the reactor before the load change
(GHSV = 10,000 h-1). The slight increase of STY after the load change can be explained by the
longer residence time of the gas in the reactor after the load change and the consequently higher
conversion. Except of the change in transition time, no fundamental differences in the STY
calculated for the four load gradients considered can be observed.
In Fig. A.20 (b) the increase in hot spot temperature over time as a consequence of the decreased
GHSV can be observed. For the load transition performed as step, within 1 s as well as within
2 s, a change in the slope of the temperature increase after the load change can be observed.
As shown in FigA.21 (a) this effect is the consequence of a new hot spot forming upstream the
original hot spot position. This effect is not observed at the load change performed within 5 s, as
the new hot spot is in this case superimposed by the load hot spot moving upstream (compare
Fig. A.21 (b)).
AS
Appendix
a) Space time yield.
b) Hot spot temperature.
Figure A.20:
Development of the reactor’s space time yield (a) and hot spot temperature (b)
during a load reduction from GHSV = 10,000 h
-1
to GHSV = 4,000 h
-1
at COR = 0.85,
SN = 3.0, T
cool
= 240
◦
C and p = 80 bar; Load change performed as a step as well as
ramp of 1 s, 2 s and 5 s (from left to right).
AT
Appendix
a) Load transition performed as step.
b) Load transition performed as ramp of 5 s.
Figure A.21:
Development of the reactor’s temperature profile during a load reduction from
GHSV = 10,000 h
-1
to GHSV = 4,000 h
-1
at COR = 0.85, SN = 3.0, T
cool
= 240
◦
C
and p = 80 bar; Load change performed as a step (a) as well as ramp of 5 s (b).
AU
Appendix
In Fig. A.22 the dynamic load changes described in Sec. 3.1.5 are discussed with regard to their
impact on hot spot temperature. Marked were the hot spot temperatures before the load
transition (green triangle), after the load transition was performed (red triangle) as well as the
maximum temperature inside the reactor during the total time of the load change (blank circle).
In order to discuss the influence of transition time, the load changes were performed as step as
well as ramps of 1s, 2 s and 5 s (per section from left to right).
Figure A.22:
Dynamic simulation campaign applying load changes from the base case COR= 0.85,
SN = 3.0, GHSV = 10,000 h
-1
, T
cool
= 240
◦
C at 50 bar, 65 bar and 80 bar towards
COR = 0.7 (
↓
), COR = 1.0 (
↑
), SN = 2.0 (
↓
), SN = 4.0 (
↑
), GHSV = 4,000 h
-1
(
↓
) and
GHSV = 16,000 h
-1
(
↑
) as a step as well as a ramp within 1s, 2 s and 5 s (symbols
per section from left to right).
Fig. A.22 shows that both, a decrease of COR as well as a reduction of GHSV lead to higher
hot spot temperatures. In case of COR this can be explained by the higher exothermic heat of
CO-hydrogenation in comparison to CO
2
-hydrogenation. In case of GHSV the lower gas velocity
inside the reactor leads to a higher heat production per reactor volume. As this heat cannot
instantly be removed, temperature rises until the ∆T between reactor inside and steam cooling
is sufficient for the removal of the exothermic heat. Vice versa, lower hot spot temperatures
are obtained when COR and GHSV are increased. Smaller effects on hot spot temperature are
obtained by a variation of SN. While a decline to SN = 2.0 decreases hot spot temperature, an
increase to SN = 4.0 leads towards slightly higher temperatures. This effect is obtained, as excess
of H
2
moves equilibrium to the side of the products and consequently increases the reactions
driving force (compare Fig. 2.4). Moreover, higher H
2
contents in the syngas decrease the partial
pressure of water and therefore increase reaction kinetics.
Overall, load changes towards higher CO contents and lower GHSVs could be problematic from
AV
Appendix
a thermal point of view. However, even though hot spot temperature decreases in case of an
increase of the CO
2
, this load point could be problematic regarding to catalyst stability as a
result of the higher water contents in the reaction product. An appropriate deactivation model
would be necessary to determine the critical water content with regard to catalyst stability.
In terms of the dynamic behavior of the hot spot temperature, none of the cases considered here
resulted in the formation of an intermediate hot spot exceeding that of the steady states before
or after the load change, respectively. Similar results were obtained in a comparable analysis
with higher CO contents, i.e. working points with a higher exothermic heat and consequently
increased hot spot temperatures. Therefore, according to the simulation results obtained for
the load changes considered here the steady state model could be applied to identify critical
hot spot temperatures in the reactor instead of the dynamic model for the benefit of a reduced
model complexity and faster computation time. This finding stresses the necessity of an accurate
steady-state reactor model for dynamically operated PtM processes.
AW
