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Methanol synthesis in the membrane reactor

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Methanol synthesis in the membrane reactor

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Methanol Synthesis in the Membrane Reactor

by

Fatemeh Sadat Zebarjad

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CHEMICAL ENGINEERING)

August 2021

Copyright 2021 Fatemeh Sadat Zebarjad

ii

DEDICATION

Whole-heartedly, and gratefully so, I dedicate this work to my husband, Dr. Mohammad Sadegh
Riazi, my caring parents, Roza and Mohammad, and my sister, Marzieh, who have all offered me
unconditional love and support and made it possible for me to complete this work.

In Loving Memory of my dear friend, Hadis Hayatdavoudi,
A Chemistry PhD Candidate at Western University,
who we sorrowfully lost in flight PS752 crash.

iii

ACKNOWLEDGEMENTS

I would like to express my deepest gratitude to Professor Theodore T. Tsotsis. He gave me
the opportunity to work on a variety of interesting projects and provided immense insights on how
to perform a well-organized research project. Professor Kassner provided me with knowledge
necessary to conclude my PhD studies and to grow in my future career.
I would also like to express my appreciation to Professor Kristian Jessen, who has been
generously advising me in his immense modeling knowledge. Without his guidance the membrane
reactor modeling would have not been possible.
I would also like to thank my PhD. committee members, Professor G. K. Surya Prakrash,
Professor Shaama Sharada, for their insightful comments on my research. I am truly grateful for
the time they set aside to hear my defense.

iv

TABLE OF CONTENTS
DEDICATION ................................................................................................................................ ii
ACKNOWLEDGEMENTS ........................................................................................................... iii
LIST OF TABLES ......................................................................................................................... vi
LIST OF FIGURES ...................................................................................................................... vii
ABSTRACT .................................................................................................................................... x
CHAPTER 1: EXPERIMENTAL INVESTIGATION OF THE APPLICATION OF IONIC
LIQUIDS TO METHANOL SYNTHESIS IN MEMBRANE REACTORS ................................. 1
1.1 MOTIVATION ............................................................................................................................ 1
1.2 INTRODUCTION ....................................................................................................................... 2
1.3 EXPERIMENTAL SECTION ..................................................................................................... 7
1.3.1 Materials ................................................................................................................................................ 7
1.4 EXPERIMENTAL SET-UP ........................................................................................................ 9
1.4.1 Experimental Procedure ....................................................................................................................... 12
1.4.2 Membrane Modification ...................................................................................................................... 13
1.5 RESULTS AND DISCUSSION ................................................................................................ 18
1.5.1 PBR Experimental Results ................................................................................................................... 18
1.5.2 Membrane Reactor Experiments .......................................................................................................... 19
1.6 CONCLUSIONS ....................................................................................................................... 26
CHAPTER 2: INVESTIGATION OF CO2 AND METHANOL SOLUBILITY AT HIGH
PRESSURE AND TEMPERATURE IN THE IONIC LIQUID [EMIM][BF4] EMPLOYED
DURING METHANOL SYNTHESIS IN A MEMBRANE-CONTACTOR REACTOR .......... 28
2.1 MOTIVATION .......................................................................................................................... 28
2.2 INTRODUCTION ..................................................................................................................... 29
2.3 EXPERIMENTAL SECTION ................................................................................................... 31
2.3.1 Materials .............................................................................................................................................. 31
2.3.2 Experimental Set-Up............................................................................................................................ 32
2.3.3 Experimental Procedure ....................................................................................................................... 33
2.3.4 Measurement of CO 2 Solubility ........................................................................................................... 34
2.3.5 Measurement of Methanol Solubility .................................................................................................. 37
2.3.6 Stability of the [EMIM][BF 4] IL During the MR-MeS Experiments .................................................. 39
2.4 RESULTS AND DISCUSSION ................................................................................................ 40
2.4.1 CO 2 Solubility ...................................................................................................................................... 40

v

2.4.2 Methanol Solubility ............................................................................................................................. 44
2.5 CONCLUSIONS ....................................................................................................................... 48
CHAPTER 3: SIMULATION OF METHANOL SYNTHESIS IN A MEMBRANE-
CONTACTOR REACTOR .......................................................................................................... 50
3.1 MOTIVATION .......................................................................................................................... 50
3.2 INTRODUCTION ..................................................................................................................... 50
3.3 MATHEMATICAL MODEL .................................................................................................... 54
3.3.1 Rate Equations ..................................................................................................................................... 54
3.3.2 MR Model ............................................................................................................................................ 55
3.3.3 Dimensionless Equations ..................................................................................................................... 65
3.4 RESULTS AND DISCUSSION ................................................................................................ 67
3.5 CONCLUSIONS ....................................................................................................................... 82
CHAPTER 4: EXPERIMENTAL INVESTIGATION OF THE APPLICATION OF IONIC
LIQUIDS TO METHANOL SYNTHESIS IN MEMBRANE REACTORS WITH PURE CO2
FEEDS .......................................................................................................................................... 86
4.1 MOTIVATION .......................................................................................................................... 86
4.2 INTRODUCTION ..................................................................................................................... 88
4.3 EXPERIMENTAL SECTION ................................................................................................... 93
4.4 RESULTS AND DISCUSSION ................................................................................................ 93
4.4.1 PBR Experimental Results ................................................................................................................... 96
4.4.2 Membrane Reactor Experiments .......................................................................................................... 99
4.5 CONCLUSIONS ..................................................................................................................... 104
References ................................................................................................................................... 106
Appendices .................................................................................................................................. 114
Appendix A: Dimensionless equations from Chapter 3: ...................................................................... 114
Appendix B: EMSoft codes: ................................................................................................................. 121

vi

LIST OF TABLES
Table 1- 1. Properties of the ceramic membrane ............................................................................ 8
Table 1- 2. MK-121 catalyst properties (catalyst cylinders with domed ends, 6*4 mm) ............... 8

Table 3- 1. Dimensionless variables, parameters and groups ....................................................... 66
Table 3- 2. Parameter values, including the 95% confidence limits, for the global rate
expressions resulting from the fit of the experimental data .......................................................... 67

vii

LIST OF FIGURES
Figure 1- 1. Schematic of the experimental set-up ....................................................................... 10
Figure 1- 2. Schematic of the membrane reactor .......................................................................... 11
Figure 1- 3. Gas-liquid interface in a hydrophobic membrane ..................................................... 14
Figure 1- 4. FAS attachment mechanism during membrane modification (Wei and Li 2009) .... 15
Figure 1- 5. DI water droplets on the surface of the modified membrane .................................... 17
Figure 1- 6. Comparison of experimental vs. calculated carbon conversions .............................. 19
Figure 1- 7. Comparison of measured contact angles on modified and unmodified membranes . 20
Figure 1- 8. Effect of W/F on MR and PBR conversion. P = 32 bar, T = 220 °C ........................ 21
Figure 1- 9. Effect of flow rate (liquid sweep) on MR conversion. P = 32 bar, T = 220
o
C, W/F =
47.2 g*h/mol ................................................................................................................................. 22
Figure 1- 10. Effect of temperature on PBR, MR and equilibrium conversion. P = 32 bar, liquid
sweep rate = 1 cc/min, W/F =47.2 g*h/mol. ................................................................................. 23
Figure 1- 11. Effect of pressure on PBR, MR and equilibrium conversion. T = 220
o
C, liquid
sweep rate = 1 cc/min, W/F = 42.7 g*h/mol ................................................................................. 24

Figure 2- 1. Schematic diagram of the experimental apparatus for measurements of the solubility
of carbon dioxide/methanol in ionic liquids: (1) gas cylinder; (2) reference cell; (3) metal heating
jacket; (4) vacuum pump; (5) sample cell..................................................................................... 33
Figure 2- 2. CO2 solubility, Sc(%), in [EMIM][BF4] at 25 ⁰C. .................................................... 41
Figure 2- 3. CO2 solubility, Sc(%), of different imidazolium-based ILs. at 25 ⁰C (Koel 2008) ... 42
Figure 2- 4. CO2 solubility, Sc(%), in [EMIM][BF4] at high temperatures .................................. 43
Figure 2- 5. Methanol solubility, SM (%), in [EMIM][BF4] and TGDE at high temperatures
(TGDE data are extracted from reference (Kuczynski and Westerterp 1986)). ........................... 44
Figure 2- 6. Methanol solubility, SM (%), in [EMIM][BF4] and TGDE vs. temperature at 1.0 Mpa
of pressure (all the TGDE data were extracted from reference (Kuczynski and Westerterp 1986)).
....................................................................................................................................................... 46
Figure 2- 7. 400 MHz
1
H NMR results of the [EMIM][BF4] IL before and after it was used in the
MR-MeS experiments. .................................................................................................................. 48

viii

Figure 3- 1. Iso-conversion plot that including additional PBR data ........................................... 68
Figure 3- 2. Effect of W/F on PBR and MR (calculated and experimental) conversion for two
different sweep liquid flow rates; T = 220 °C, P = 32 bar ............................................................ 69
Figure 3- 3. Effect of sweep liquid flow rate on MR (calculated and experimental) conversions. T
= 220 °C, P = 32 bar, W/F = 47.2 g*h/mol. .................................................................................. 70
Figure 3- 4. Effect of temperature on MR (calculated and experimental MR) and PBR
conversion. P = 32 bar, W/F = 47.2g*h/mol, and liquid sweep rate = 1 cc/min .......................... 71
Figure 3- 5. Effect of pressure on MR (calculated and experimental MR) and PBR conversion T
= 220 °C, W/F = 47.2 g*h/mol, and liquid sweep rate = 1 cc/min ............................................... 72
Figure 3- 6. Conversion vs. W/F for different temperatures. P = 30 bar, CF = 0.625, SN = 2,
𝑎𝑚𝐹𝜌𝑏 = 0.53 cm
2
/g, and sweep flow rate = 6 cc/min. ............................................................... 73
Figure 3- 7. Conversion vs. W/F for different pressures. T = 220 °C, CF = 0.625, SN = 2,
𝑎𝑚𝐹𝜌𝑏 = 0.53 cm
2
/g, and sweep flow rate = 6 cc/min. ............................................................... 75
Figure 3- 8. Conversion vs. W/F for different liquid flow rates. T = 220 °C, P = 30 bar, CF =
0.625, SN = 2, 𝑎𝑚𝐹𝜌𝑏 = 0.53 cm
2
/g. ........................................................................................... 76
Figure 3- 9. Conversion vs. W/F for different liquid thicknesses as indicated in the . T = 220°C,
P = 30bar, CF = 0.625, SN = 2, 𝑎𝑚𝐹𝜌𝑏 = 0.53cm
2
/g, sweep flow rate = 6 cc/min. .................... 77
Figure 3- 10. Conversion vs. W/F for different membrane surface areas. T = 220°C, P = 30bar,
CF = 0.625, SN = 2, and sweep flow rate = 6 cc/min. .................................................................. 78
Figure 3- 11. Conversion vs. W/F for different feed compositions, as indicted in the insert. T =
220 °C, P = 30 bar, 𝑎𝑚𝐹𝜌𝑏 = =0.53 cm
2
/g, sweep flow rate = 6 cc/min. .................................... 79
Figure 3- 12. Conversion vs. liquid flow rate for different solvents. T = 220 °C, P = 30 bar,
𝑎𝑚𝐹𝜌𝑏 = =0.53cm
2
/g, .................................................................................................................. 80
Figure 3- 13. Conversion vs. Da2/Da20 for different Da1/Da10. T = 220 °C, P = 30 bar, 𝑎𝑚𝐹𝜌𝑏 =
=0.53cm
2
/g, W/F = 47.2 g*h/mol, sweep flow rate = 6 cc/min. ................................................... 82

Figure 4- 1. 2-D P&ID of the combined RWGSR and MCR-MeS system .................................. 93
Figure 4- 2. CO2 equilibrium conversion of the reverse water gas shift reaction versus the feed
H2:CO2 molar ratio at different temperatures. .............................................................................. 95
Figure 4- 3. Carbon factor of the reverse water gas shift reaction outlet versus the feed H2:CO2
ratio at different temperatures and equilibrium pressure. ............................................................. 96

ix

Figure 4- 4. PBR carbon conversion versus temperature and CF at different pressures a) P=20
bar, b) P=25 bar, c) P=30 bar. Other conditions SN=2 and W/F= 20 kg*s/mol (red dots represent
the experimental data and the surfaces are calculated using the kinetics model presented in
chapter 3). ..................................................................................................................................... 98
Figure 4- 5. PBR carbon conversion versus pressure and CF at different temperatures a) T=200
℃, b) T=220 ℃, c) T=240 ℃. Other conditions SN=2 and W/F= 20 kg*s/mol (red dots
represent the experimental data and the surfaces are calculated using the kinetics model
presented in chapter 3). ................................................................................................................. 99
Figure 4- 6. MCR and PBR and calculated equilibrium carbon conversion versus pressure at
different temperatures a) T=200 ℃, top plots b) T=220 ℃, middle plots c) T=240 ℃, bottom
plots. Other conditions SN=2 and W/F= 30 kg*s/mol CF=0.37 (left-side plots) and CF=0.502
(right side plots). ......................................................................................................................... 100
Figure 4- 7. MCR and PBR and calculated equilibrium carbon conversion versus weight of the
catalyst/gas flow rate (W/F) at different temperatures. Equilibrium conversion does not vary with
W/F and is, therefore, shown as a horizontal line. Other conditions SN=2 and P=30 bar.
CF=0.37 (left-side plots) and CF=0.502 (right side plots). ........................................................ 101
Figure 4- 8. MCR and PBR and calculated equilibrium carbon conversion versus weight of the
catalyst/gas flow rate (W/F) at different pressures. Equilibrium conversion does not vary with
W/F and is, therefore, shown as a horizontal line. Other conditions SN=2 and T= 220
o
C.
CF=0.37 (left-side plots) and CF=0.502 (right side plots). ........................................................ 102
Figure 4- 9. MCR and PBR and calculated equilibrium carbon conversion versus liquid flow rate
at various temperatures. PBR and equilibrium conversions do not vary with liquid flow rates.
Other conditions CF=0.37, W/F=20 kg*s/mol, SN=2, P=30bar . .............................................. 103
Figure 4- 10. MCR and PBR and calculated equilibrium carbon conversion versus liquid flow
rate at various temperatures. PBR and equilibrium conversions do not vary with liquid flow rates.
Other conditions CF=0.37, W/F=20 kg*s/mol, SN=2, T=220 ⁰C. ............................................. 104

x

ABSTRACT
In the first chapter a high-pressure membrane reactor (MR) was employed to carry-out the
methanol synthesis (MeS) reaction. Syngas was fed into the MR shell-side where a commercial
MeS catalyst was used, while the tube-side is swept with a high boiling point liquid with good
solubility towards methanol. A mesoporous alumina ceramic membrane was utilized, after its
surface had been modified to be rendered more hydrophobic. The efficiency of the MR was
investigated under a variety of experimental conditions (different pressures, temperatures, sweep
liquid flow rates, and types of sweep liquids). The results reveal improved per single-pass carbon
conversions when compared to the conventional packed-bed reactor. An ionic liquid (IL), 1-ethyl-
3-methylimidazolium tetrafluoroborate ([EMIM][BF4]) was utilized in the MR as the sweep liquid.
The experimental results are compared to those previously reported by our Group (Li and Tsotsis,
J. Membrane Sci., 2019) while using a conventional petroleum-derived solvent as sweep liquid,
tetraethylene glycol dimethyl ether (TGDE). Enhanced carbon conversion (over the petroleum-
derived solvent) was obtained using the IL.
In the second chapter, the solubility properties of the ionic liquid (IL), 1-ethyl-3-
methylimidazolium tetrafluoroborate ([EMIM][BF4]) were studied using a high-pressure, high-
temperature set-up employing the pressure-drop technique. [EMIM][BF4] was selected because it
is used as sweep liquid in a membrane reactor (MR)-based methanol synthesis (MR-MeS) process
described in chapter 1. The MR-MeS studies indicated high methanol (MeOH) solubilities in the
IL under typical MeS reaction conditions, which then motivated this study to measure such
solubilities directly under non-reactive conditions to validate the MR study findings in the first
chapter. In addition, during the MR-MeS studies concerns existed about the CO2 solubility in the

xi

[EMIM][BF4], since it is a reactant and its dissolution in the IL would be detrimental for
performance. Studies, therefore, were also carried out to investigate CO2, in addition to MeOH
solubility. Our investigation indicates that though CO2 solubility is high at room temperature, it
becomes negligible at the typical MeS conditions.
In the third chapter, a steady-state model is developed to simulate the MR behavior during
MeS, and is validated by the experimental data presented in chapter 1. The model is then used to
study the reactor behavior for a broader range of operating conditions beyond those that can be
accessed and studied experimentally in the laboratory-scale reactor. Converting the model
equations into their dimensionless form helps to identify the key dimensionless groups determining
reactor performance and enables one to better evaluate the efficacy of the MR system and guides
further process design and scale-up.
In the last chapter, we study the direct conversion of CO2 into MeOH by coupling the MCR-
MeS Lab-scale set-up with a reverse water gas shift (RWGS) reactor (RWGSR). The idea here is
that CO2 is first fed into the RWGSR to be converted into syngas, which is then processed in the
MeS-MCR and converted into MeOH. Efforts are currently under way in our Group to construct
the combined RWGSR/MeS-MCR system to experimentally validate the concept, but they have
yet to reach completion. In this chapter, we model the behavior of the RWGSR, instead, and use
the simulated exit compositions from the reactor as feeds for the MeS-MCR. Employing such
compositions, the MCR subsystem is then experimentally investigated for a broad range of
pressures and temperatures, sweep liquid flow rates, reactor space times to validate its ability to
effeicienctly convert the off-gas from the RWGSR into MeOH.
In the future once the RWGSR/MeS-MCR set-up is completed, as part of the ongoing efforts
in the Group in the area of CO2 capture and utilization (CCU), we plan to further extend the

xii

preliminary work in chapter 3 to experimentally validate the CO2 to MeOH direct conversion
concept. Further, since constraints with the size of the Lab-scale RWGSR/MeS-MCR set-up may
limit access to regions of the parameter space where a commercial system may be operating, we
will also use an in-house, experimentally-validated model for the MeS-MCR, see chapter 3) and a
mathematical model for the RWGSR, to be developed and experimentally validated in our
research, to assess the full range of attainable conversions, aiming to obtain >90% carbon
separation/capture. Based on the results of the planned laboratory studies, and in collaboration
with National Energy Technology Laboratory (NETL) researchers, we will carry out a techno-
economic analysis (TEA) of the proposed novel CCU process to compare its economics with those
of the conventional, absorption-based technologies. We expect the economics of the new process
to be superior to those of the existing processes.

1

CHAPTER 1: EXPERIMENTAL INVESTIGATION OF THE
APPLICATION OF IONIC LIQUIDS TO METHANOL
SYNTHESIS IN MEMBRANE REACTORS
*

1.1 MOTIVATION
In this chapter a high-pressure membrane reactor (MR) was employed to carry-out the
methanol synthesis (MeS) reaction. Syngas was fed into the MR shell-side where a commercial
MeS catalyst was used, while the tube-side is swept with a high boiling point liquid with good
solubility towards methanol. A mesoporous alumina ceramic membrane was utilized, after its
surface had been modified to be rendered more hydrophobic. The efficiency of the MR was
investigated under a variety of experimental conditions (different pressures, temperatures, sweep
liquid flow rates, and types of sweep liquids). The results reveal improved per single-pass carbon
conversions when compared to the conventional packed-bed reactor. An ionic liquid (IL), 1-ethyl-
3-methylimidazolium tetrafluoroborate ([EMIM][BF4]) was utilized in the MR as the sweep liquid.
The experimental results are compared to those previously reported by our Group (Li and Tsotsis
2019) while using a conventional petroleum-derived solvent as sweep liquid, tetraethylene glycol
dimethyl ether (TGDE). Enhanced carbon conversion (over the petroleum-derived solvent) was
obtained using the IL.

*
The material presented in this chapter has previously appeared in: Zebarjad, F., Hu, S., Li, Z., and Tsotsis,
T.T., “Experimental Investigation of the Application of Ionic Liquids to Methanol Synthesis in Membrane
Reactors,” Ind. Eng. Chem. Res., 58. 11911, 2019.

2

1.2 INTRODUCTION
Since the industrial revolution human activities like fossil-fuel combustion have produced
CO2, thought to contribute to global warming, thus leading to an increase in its atmospheric
concentration of ~40% (Stocker 2014). During the same period, the world’s rising demand for
energy increased the use of fossil fuels, such as oil, gas, and coal; combined with the limited
availability of these resources, this has intensified the need for finding new technologies to meet
the world’s energy needs. CO2 capture and utilization (CCU) to produce fuels and chemicals, and
the use of renewable energy resources (e.g., biomass) in the place of fossil fuels are two approaches
intensively studied today for reducing the CO2 environmental impact and for diminishing the
world’s reliance on fossil fuels.
Recently, CO2 conversion into methanol (MeOH), as a CCU process, and MeOH production
from biomass have attracted increased attention. MeOH is one of the most commonly used
industrial chemicals; its widespread applications includes utilizing it as a feedstock for producing
chemicals (e.g., C2-C4 olefins and aromatics (Unneberg and Kolboe 1988, Zeng, Yang et al. 2007,
Conte, Lopez-Sanchez et al. 2012)), fuels and fuel additives (e.g., DME, MTBE and DMC (Elvers
2008)), and as a H2 carrier in energy storage. The most common method to produce MeOH is from
a mixture of CO, CO2 and H2 known as syngas; it is generated from the catalytic reforming of
natural gas or the gasification of coal and biomass. The following three global reactions are thought
to take place during MeOH synthesis (MeS) (though there are differing opinions among
researchers on the carbon source for MeOH during MeS, and all three reactions are noted in the
literature, only two out of three are linearly independent. It is noted that only the first and third
reactions are considered in the kinetics part of this study, to be discussed later).

3

CO2 + 3H2 → CH3OH + H2O ΔH
o
= -49.5 (kJ/mol) (R1)
CO + 2H2 → CH3OH ΔH
o
= -90.6 (kJ/mol) (R2)
CO + H2O → CO2 + H2 ΔH
o
= -41.2 (kJ/mol) (R3)
Today’s commercial MeS processes (Aasberg-Petersen, Nielsen et al. 2008, Behr 2014)
utilize the so-called low-pressure (pressures range from 50-80 bar) Cu-ZnO-Al2O3 MeS catalyst
(also employed in this study) which is highly selective (selectivity, typically, >99 %), with DME
being the main by-product (Kirk and Othmer 1953). They have different technical features, but are
all designed to overcome two key challenges: first, low per-pass conversions dictating recycle of
unreacted syngas (Behr 2014), and second, the need to remove the reaction heat efficiently. Newer
MeS processes have also been developed (Merkx, Kopp et al. 2001, Zhang, He et al. 2003,
Muradov and Veziroǧlu 2005, Choudhary and Goodman 2006, Abbas and Daud 2010), but none
has, as yet, to reach commercial maturity. The first, and foremost, challenge (low per-pass
conversion) is particularly problematic for MeOH production from small-scale, distributed-type
renewable biomass sources, for which the use of oxygen-blown gasifiers is not economically
justified, with the resulting syngas thus containing large concentration of N2. For such applications,
increasing the per-pass conversion (to ~85%) is essential for commercial adaptation. Such
requirement motivates the consideration of reactive separations for such an application, including
membrane reactors (MR), since they are capable to overcome the aforementioned thermodynamic
limitations of MeS.
Several prior studies report the use of MR for MeS to increase the conversion rate and
thermal efficiency (Espinoza, Du Toit et al. 2000, Struis and Stucki 2001, Barbieri, Marigliano et
al. 2002, Rahimpour and Ghader 2003, Chen and Yuan 2004, Gallucci, Paturzo et al. 2004, Rohde,

4

Unruh et al. 2005, S. Soltani 2013). Galucci et al. (Gallucci, Paturzo et al. 2004), for example,
investigated a packed-bed membrane reactor (PBMR) for MeS using a commercial Cu-Zn catalyst
and a zeolite-A membrane. For similar reactor conversions, the PBMR showed higher selectivity
than the conventional PBR, which was attributed to the selective removal of H2O and CH3OH by
the membrane. Earlier, Barbieri et al. (Barbieri, Marigliano et al. 2002) had predicted such
behavior via simulation. Struis et al. (Struis, Stucki et al. 1996) used a Nafion® membrane for
selective separation of MeOH in a MR; syngas was fed in the membrane tube-side, while sweep
gas was directed to the shell-side in a counter-current direction of flow. Their experiments were
performed using membranes with different counter-ions for temperatures up to 200
o
C. Their
studies showed that the higher the pressure is, the better is the reactor performance; it was also
found that optimizing the membrane structure and the module configuration can lead to a
significant improvement in reactor performance. The experimental results were also validated in a
modeling study (Struis and Stucki 2001). In another study that was conducted employing a silicone
rubber composite membrane, a higher conversion rate was reported for thr PBMR compared to the
conventional reactors (Chen and Yuan 2004). The experiments showed conversions of less than
10%, and the stability of these membranes is doubtful long-term under the high pressure/high
temperature MeS conditions. A modeling study of the use of a MR for MeS employing a water-
permselective silica membrane (Farsi and Jahanmiri 2012) revealed a slight improvement (~4 %)
in conversion over equilibrium; removing the water was reported, however, as a key factor to
improve catalyst lifetime, since its presence was claimed to intensify catalyst deactivation via
sintering.
Studies also exist on the use of distributor-type MR’s (in these reactors, reactants flow on
either side of the membrane, that provides a means through which one reactant is dosed into

5

another) for the Fischer-Tropsch (FT) process and for alcohol synthesis (Leonard, Miachon et al.
2003, Rahimpour and Ghader 2003, Vanhove 2003, Marvast, Sohrabi et al. 2005, Rohde, Unruh
et al. 2005, Rohde, Unruh et al. 2005, Rahimpour, Mirvakili et al. 2011, Vakili, Rahimpour et al.
2012), including MeS. A Pd-membrane based distributor-type MR for MeS was simulated by
Rahimpour and coworkers (Rahimpour and Ghader 2003); they also modeled dual-reactor systems
(Bayat and Rahimpour 2011, Rahimpour and Bayat 2011, Bayat and Rahimpour 2012, Bayat and
Rahimpour 2012, Bayat, Rahimpour et al. 2012) including a distributor-type MR (Khademi,
Setoodeh et al. 2009, Khademi, Rahimpour et al. 2010, Khademi, Rahimpour et al. 2012) that
coupled MeS with cyclohexane dehydrogenation via a Pd/Ag membrane, but to date none of these
systems have been validated experimentally. Bradford et al. (Bradford, Te et al. 2005) studied the
FT reaction in a contactor-type MR using a catalytic porous alumina membrane running in a “flow-
through” mode (FTCMR). The results showed a higher C2+ hydrocarbon yield and a lower
olefin/paraffin ratio attained in the MR than in the conventional reactor, which they explained to
be due to a higher H2/CO-ratio prevailing within the catalytic membrane. Khassin et al. (Khassin,
Sipatrov et al. 2005) also investigated the FT reaction in a similar MR and obtained high selectivity
toward C5+ hydrocarbons, a higher space-time yield of liquid hydrocarbons, and up to three times
higher catalyst activity with the FTCMR when compared with a slurry reactor.
Our Group previously investigated (Li and Tsotsis 2019) a different MR methanol
synthesis process; a high-temperature inorganic membrane was utilized in MeS as a porous
selective barrier in between the reaction side and a liquid solvent flowing in its tube-side
(permeate-side). Tetraethylene glycol dimethyl ether (TGDE) was used as the sweep liquid, in
which MeOH has good solubility, while other components of syngas (like H2 and CO) do not.
Removing the MeOH in situ from the reaction side, allows achieving conversion for MeOH

6

beyond its equilibrium value. An advantage of this over other MR processes for alcohol synthesis,
is that the selective separation is done by the sweep liquid; thus commercial, off-the-self inorganic
membranes can be used (as in this study), which require no further development effort beyond
needing to modify the hydrophobicity of their surface. Thus, one is no longer constrained by the
limited commercial availability (or lack of robustness) of appropriate membranes, and can, instead,
rely on the greater range of available solvents to attain desired selective properties.
Though employing a petroleum-derived solvent like TGDE in a MR system (but even in a
conventional trickle-bed reactor) shows good benefit, there are still disadvantages relating to its
application to the MeS reaction. Its relatively low boiling point (275
o
C) dictates that the reaction
temperature is kept rather low. In addition, though its vapor pressure is quite low (<0.001kPa at
20
o
C) it is still finite. For these reasons, here we investigate, instead, a different sweep liquid,
specifically an ionic liquid (IL) 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF4]). It
has been demonstrated to date that certain ILs are highly polar compounds; as a result, MeOH has
considerably higher solubility than CO and H2 in them (Domańska and Marciniak 2004).
Dissolution of the MeOH produced during MeS into the ILs enables its in situ removal from the
reactor, and this (similarly to using the TGDE) enhances the conversion. The IL solvent’s
advantages over the competing organic solvents (e.g., TGDE) for the specific MeS reactive
separation process under study are: (1) their extremely low vapor pressures (<10
-9
bar), which
prevents significant loss of the sweep solvent into the gas phase, and simplifies downstream
separations of the MeOH in the IL sweep stream; (2) the thermal properties of the IL solvents,
including their broad operating range, and their high decomposition temperatures, which permit
their use for a broader region of conditions in MeS that, typically, takes place commercially in the
temperature range of (220~300
o
C). Specifically, the high MeOH solubility (Domańska and

7

Marciniak 2004) and decomposition temperature (447
o
C) (Nishida, Tashiro et al. 2003) of the
[EMIM][BF4] compared to other ILs have made it a good choice of sweep liquid for our MR
design.
In summary, in this chapter the conversion of the MeS reaction in a MR using IL as the
sweep liquid was measured at different conditions and the results were compared with the MR
system employing TGDE as the sweep liquid. In what follows, we first describe the experimental
system utilized, and the method to modify the commercial inorganic membrane used to make it
more appropriate for the proposed application. Experimental results are then presented and
discussed.
1.3 EXPERIMENTAL SECTION
1.3.1 Materials
Gases. Ultra high purity (UHP) Nitrogen (N2, 99.999% pure), and UHP Hydrogen (H2, 99.999%
pure) were purchased from Praxair. The CO/CO2 (37.5% CO2) mixture was purchased pre-mixed
from Praxair with the purity of 99.999%.
Ionic Liquid. 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF4]) with a reported
purity of ≥98% was purchased from Zhejiang Arts & Crafts Imp. & Exp. Company, China. Upon
being received at USC, the purity of the IL was confirmed via 400 MHz
1
H and the 375
19
F NMR
analysis (the analysis results can be found in the Supplementary materials section).
Membrane. A multilayer ceramic membrane from Media and Process Technology, Inc. (M&PT)
of Pittsburgh, PA, whose properties, as reported by the manufacturer, are shown in Table 1- 1 has
been utilized. The porosity of the membrane was measured to be 22.8% with the helium expansion

8

method, employing a helium porosimeter apparatus and measurement procedures which are
described elsewhere (Yu 2013).
Table 1- 1. Properties of the ceramic membrane
Layer Material Thickness (µm) Average pore size (Å)
Support α- Alumina 1100 2000-4000
First layer α- Alumina 10-20 500
Second layer γ- Alumina 2-3 100
Outer diameter: 5.7 mm, Inner diameter: 4.7 mm

Catalyst. A commercial Cu-based MeS catalyst (MK-121, purchased from Haldor-Topsoe) was
utilized (properties, as provided by the manufacturer, are presented in Table 1- 2). The as received
catalyst was in a pellet form. Prior to being loaded into the reactor, 30 g of the catalyst were ground
into powder with particle sizes in the range from 650 µm to 850 µm, which were then diluted with
quartz particles of the same size. Further details about how the catalyst is loaded into the reactor
are provided below.
Table 1- 2. MK-121 catalyst properties (catalyst cylinders with domed ends, 6*4 mm)
Property Value
Chemical composition
Cu >43 %

9

Zn 20±3 %
Al 5±1 %
Axial crush strength >220 kg/cm
2
Expected filling density 1 kg/l

1.4 EXPERIMENTAL SET-UP
Figure 1- 1 shows the schematic of experimental set-up. The gas delivery system, the reactor
module, and the gas analysis section are the three main components of the set-up. The inlet syngas
feed-stream is prepared by mixing pre-determined flows of H2 and the aforementioned CO/CO2
gas mixture, with their flow rates being controlled by individual Mass Flow Controllers (MFC,
Brooks 5400). After pre-heating, the resulting syngas mixture is fed into the high-pressure/high-
temperature lab-scale MeS reactor. The MeS experiments were carried-out over a pressure range
of 20-30 bar and a temperature range of 200-240 °C. The reactor’s temperature was controlled by
temperature controllers and monitored by a three-point thermocouple (from OMEGA). Further
details about the experimental apparatus can be found elsewhere (Li and Tsotsis 2019).

10

Figure 1- 1. Schematic of the experimental set-up
Figure 1- 2 shows a schematic of the MR itself, showing that the reactor is divided into two
zones by a tubular ceramic membrane: the shell-side (reject-side) and the tube-side (permeate-
side). The shell-side contains a packed-bed of catalysts and the MeS reaction occurs in this zone.
The methanol produced is then transported through the membrane and is dissolved into a sweep
liquid that flows in the tube-side. A back-pressure regulator (BPR) is used to control the pressure
of the MR shell-side. A condenser is installed at the outlet of the shell-side to ensure that complete
condensation takes place of the methanol, H2O, and other potential by-products in the gas phase
exiting the reactor. Glass beads are used in the condenser for improving cooling of the gas stream;
a cooling bath containing dry-ice and acetone with the fixed temperature of -78 °C is also used in
which the condenser is immersed.

11

Figure 1- 2. Schematic of the membrane reactor
No methanol and other organic compounds were detected (using a Gas Chromatograph
equipped with a Thermal Conductivity Detector (GC-TCD)) in the gas stream exiting the
condenser, which verifies that complete condensation of such compounds takes place in the
condenser. CO, CO2 and H2 were the only compounds detected in the gas stream by GC-TCD. A
Gas Chromatograph equipped with a Flame Ionization Detector (GC-FID) was used to analyze the
composition of the liquid phase collected in the condenser.
The sweep liquid is injected into the membrane permeate-side using a HPLC pump, with a
BPR (installed in the exit line) being employed for controlling the pressure. Due to the potential
of gases being dissolved in the sweep liquid, it is directed after the BPR into a condenser/separator
operating at atmospheric pressure and room temperature, to separate any such gas components
from the sweep liquid. For the purpose of properly closing mass balances, the gas stream from the
liquid condenser is recombined with the gas stream exiting the BPR in the MR shell-side, the

12

resulting total gas stream then being fed into the shell-side condenser. The same experimental set-
up, as described above (and also described in greater detail elsewhere (Li and Tsotsis 2019)), is
used for performing the packed-bed reactor (PBR) experiments; this is accomplished by closing
both the inlet and outlet lines in the tube-side of the membrane.
1.4.1 Experimental Procedure
As shown in Figure 1- 2, the ceramic membrane is installed in the center of the reactor,
which is an autoclave made of stainless steel. It is attached to the top of the autoclave with flexible
stainless steel tubing that accommodates potential thermal expansion; it is connected to that tubing
via Swagelok fittings and Teflon O-rings. The bottom of the reactor is first loaded with quartz
particles (150 µm to 650 µm in diameter, see Figure 1- 2) up to a level reaching the bottom of the
membrane. The reactor is then packed along the length of the membrane with a mixture of catalyst
and quartz (650 µm to 850 µm in diameter, as described above). A bed of quartz particles (850 µm
to 1000 µm in diameter, see Figure 1- 2) is then packed from the top of the membrane all the way
to the top of the autoclave The syngas is fed into the reactor by means of a tube that traverses the
length of the reactor from the top of the autoclave into the middle of the fine quartz particle bed at
the bottom of the reactor. The liquid sweep flows through the flexible tubing connected, on either
side to the membrane (in the PBR mode of operation, the inlet and outlet of the membrane tube-
side are closed). The reactor (in both the PBR and the MR experiments) operates isothermally
(temperature difference across the reactor length: less than 2
o
C), and isobarically (pressure drop:
less than 0.1 bar).
After calibration of the MFC’s and GC’s, the set-up is tested to ensure that it is leak-free (for
that, the system is pressurized at 30 bar with N2, and the target for leak-free operation is a pressure

13

drop of <0.2 bar over a 24 h period). Then, the catalyst is activated in situ, following a
hydrogenation treatment protocol recommended by its manufacturer (for further details, see Li
and Tsotsis (Li and Tsotsis 2019)). After the catalyst activation step and before starting the
experiments, the reactor is purged with N2 at a flow rate of 600 cc/min for about 1 h; after that, the
operating conditions are adjusted according to the design of experiments. The IL chosen
([EMIM][BF4]) has a relatively high viscosity at room temperature (~45 cP), therefore, to reduce
its viscosity to facilitate pumping, it is preheated to 50
o
C (via a water bath) prior to pumping via
the HPLC pump. In order to achieve a steady-state condition, the outlet composition and flow rate
should have negligible variations (the acceptable range: less than 5% for the concentration and less
than 2% for the outlet flow rate); therefore, beside the pressure and temperature of the reactor, the
composition and flow rate of the outlet gas are monitored accurately via GC-TCD and bubble-flow
meters, respectively.
1.4.2 Membrane Modification
The membrane’s key role during the reaction is to provide a well-defined interface between
the sweep liquid (permeate-side) and the gas phase in the reactor side (shell-side) for the reaction
products to dissolve into and be carried away by the sweep liquid. Complete wetting of the
membrane by the liquid is not desirable, however, since that creates a large transport resistance.
The ideal configuration, instead, is shown schematically in Figure 1- 3 whereby the liquid is
confined only in the top membrane layer creating an impermeable layer preventing the gas from
simply bubbling through.

14

Figure 1- 3. Gas-liquid interface in a hydrophobic membrane
The M&PT mesoporous ceramic membrane is intrinsically relatively hydrophilic and the
sweep liquids are polar compounds capable to remove the MeOH from the reaction zone; they,
thus, have affinity towards hydrophilic surfaces and are non-wetting toward hydrophobic ones. In
order to prevent the solvent from completely penetrating through, prior to its use in the MR
experiments the membrane surface must be modified to become more hydrophobic. For that, a
surface modification method (Lu, Yu et al. 2009) has been developed, which uses a
fluoroalkylsilane (FAS) compound as a surface modifier that has both hydrolysable groups and
hydrophobic ends (Wei and Li 2009) (the structure of the FAS compound employed in this study
is shown in Figure 1- 4). The mechanism for the surface modification, reportedly, involves the
FAS compound being attached to the metal oxide surface through a reaction between its
hydrolysable groups with the surface hydroxyl groups, as shown in Figure 1- 4.

15

Figure 1- 4. FAS attachment mechanism during membrane modification (Wei and Li 2009)
Prior to the modification of its surface, the membrane tube is cleaned by ultra-sonification
with ethanol for 30 min and then with de-ionized (DI) water for an additional 30 min (the
membrane is glazed on both ends, ~1 cm, before any modification takes place, to ensure complete
sealing when installed inside the reactor, with the glazing procedure being explained in greater
detail in (Li 2017)). Then, the membrane is soaked in an ethanol/DI water solution (2:1 volume
ratio) for 24 h, and is then dried in air at 60 °C for 24 h. The dry membrane is then immersed into
a FAS/hexane (0.1 mol/l) solution, which is prepared by dissolving FAS into hexane at room
temperature under vigorous stirring for 12 h, ultra-sonicated for 30 min and then left in the FAS
solution for an additional 24 h to allow the surface coupling reaction to complete. The unreacted
FAS on the surface of the membrane is removed by rinsing with hexane solution for several times
and then placed in an oven for 12 h at 100 °C to dry. The aforementioned steps (soaking the
membrane in the FAS/hexane solution, washing and drying) are then repeated four times. As the
final step, the modified membrane gets heated at 200 °C in a furnace for 6 h in flowing Argon.
As it can be seen in Figure 1- 5, which shows DI water droplets on the membrane, the
surface becomes hydrophobic after the modification procedure. In order to quantify the ability of
the FAS modification method to alter the wettability of the membrane surface toward a more

16

hydrophobic one, a number of characterization tests were performed during the initial development
of method. They included break-through pressure tests, contact angle tests, membrane morphology
testing via electron microscopy (SEM), FTIR-DRIFTS characterization, and thermogravimetric
analysis (TGA), the latter to assess whether the surface modification is robust at the temperatures
employed in MeS. Further details regarding the results of the studies can be found elsewhere
(Soltani 2014).
We report here contact angle tests with both the modified and unmodified membranes with
DI water, TGDE and IL at room temperature and pressure using a Rame-Hart (Model #290)
automated goniometer, to validate the ability of the method to modify the hydrophilicity
characteristics of the membrane surface. For such testing, the membrane to be studied was cut into
numerous small pieces, each used in a single contact angle measurement. For the unmodified
membranes, liquid droplets placed on their surface (due to the relatively low hydrophobicity of the
surface) vanish quickly, typically after 10 min. Therefore, the contact angle measurements reported
here are taken within the first few seconds after the droplet’s placement on the surface. On the
other hand, the droplets placed on the modified membranes’ surface remain stable for over an hour.
For each droplet, an average of 6 contact angle measurements on different membrane pieces is
reported in the following section.

17

Figure 1- 5. DI water droplets on the surface of the modified membrane
During the MR experiments, the pressure in the tube-side is kept a bit higher (typically, 0.5-
1 bar) than that of the shell-side, to assure that the liquid will penetrate into the membrane to block
gas transport. Complete infiltration of the membrane by the solvent is not desirable, however,
because it creates a large resistance for the MeOH molecules to permeate through. To assure than
no solvent penetration and leak-through occurs during the MR experiments, after the membrane is
installed in the reactor and prior to loading the catalyst, the reactor shell-side is pressurized with
N2 at a temperature of 210 °C and a pressure 25 and 7 bar, while the sweep liquid is flowing
through the tube-side (at a flow rate of 0.5 ml/min) at a sufficiently high overpressure to prevent
the gas from bubbling through, but not exceedingly high so that the liquid itself breaks through
(typically <1 bar). After passing through the membrane, the solvent is redirected into a reservoir,
and it is then recycled to the membrane tube-side. The recycling of the sovent enables us to
estimate its loss (leak-through) rate by monitoring the change in the solvent mass in the reservoir.
If less than 1 ml of the IL liquid is lost over a-12 hour period, it is considered that the membrane
surface modification and the membrane sealing are satisfactory, and the membrane overpressure
is sufficiently high.

18

1.5 RESULTS AND DISCUSSION
1.5.1 PBR Experimental Results
In addition to the MR experiments reported here, we have also carried-out PBR
experiments to provide a basis for comparison for the MR experiments, i.e., whether the MR is
less or more efficient than the PBR under the same experimental conditions. These experiments
were performed in the same lab-scale reactor (Error! Reference source not found.) with the m
embrane in place but with the permeate-side inlet and outlet being closed. In the PBR experiments,
the effect of five parameters on the performance of the reactor were investigated, including the
temperature (T), pressure (P), catalyst weight to inlet molar flow-rate ratio (W/F), the carbon factor
in the feed (CF = mol CO/( mol CO + mol CO2)), and the feed stoichiometric number (SN = (mol
H2- mol CO2)/(mol CO + mol CO2) ). The exact experimental conditions investigated and the
obtained carbon conversions (defined by Eq. 1-1 below) are shown in Table S1 in the
Supplementary Materials section.
𝑋 𝑐𝑎𝑟𝑏𝑜𝑛 =
(𝐹 𝑖𝑛𝑙𝑒𝑡 𝐶𝑂
+𝐹 𝑖𝑛𝑙𝑒𝑡 𝐶 𝑂 2
)−(𝐹 𝑜𝑢𝑡𝑙𝑒𝑡 𝐶𝑂
+𝐹 𝑜𝑢𝑡𝑙𝑒𝑡 𝐶 𝑂 2
)
(𝐹 𝑖𝑛𝑙𝑒𝑡 𝐶𝑂
+𝐹 𝑖𝑛𝑙𝑒𝑡 𝐶 𝑂 2
)
∗ 100 (Eq. 1- 1)
where Fi is the molar flow rate (mol/s) of species i at the designated location.
In these studies, after the reactor reaches steady-state (based on the gas phase
measurements), the experiment was run for an additional time period during which time a liquid
sample was collected in the condenser (its volume measured and its composition determined via
GC-FID analysis). This is done in order to close mass balances (by determining the quantity of
liquid products and comparing with the carbon reacted determined via the gas-phase
measurements), and to measure reactor selectivity toward MeOH. For the experiments reported
here, both the selectivity and carbon balance are always higher than 98%.

19

The experimental results were also fitted to global rate expressions for reactions R1 and
R3 from the technical literature (Chinchen, Denny et al. 1987, Bussche and Froment 1996,
Rozovskii and Lin 2003), and to available data for the thermodynamic parameters (Graaf,
Stamhuis et al. 1988). Figure 1- 6 shows comparison of experimental and calculated carbon
conversions (Eq. 1), indicating a reasonable agreement between the experimental and modeling
data.

Figure 1- 6. Comparison of experimental vs. calculated carbon conversions
1.5.2 Membrane Reactor Experiments
Prior to being installed in the reactor for the MR experiments, the surface of the membrane
must be rendered sufficiently hydrophobic to prevent complete wetting of the membrane structure
by the solvent and break-through into the shell-side. A routine means to assess the hydrophobicity
of the surface is via contact-angle measurements. Such data with one of the membranes for TGDE,
the IL, and DI water are shown in Figure 1- 7. It is clear from Error! Reference source not
0
10
20
30
40
50
60
0 10 20 30 40 50 60
Experimental Conversion, %
Calculated Conversion, %

20

found., that the wettability of the surface has been altered towards being more hydrophobic, since
the contact angles measured for all three liquids have increased after the modification. For instance,
for the IL the contact angle has changed from 78 degrees (relatively hydrophilic) to 122 degrees
(strongly hydrophobic). The lowest values of contact angle among the three fluids were obtained
with the TGDE (TGDE also has the lowest viscosity and density at room temperature and
pressure). IL has the highest contact angle among the three liquids, but also the highest viscosity,
which further diminishes the chance of breaking through the membrane and leaking into the shell-
side.

Figure 1- 7. Comparison of measured contact angles on modified and unmodified membranes
During the MR experiments, the liquid sweep flowing in the tube-side removes in situ the
methanol generated in the reactor (shell-side), leading to equilibrium shift and enhanced methanol
production. Another important role of the sweep liquid is carrying away the exothermic heat of
reaction. The membrane acts as an interphase contactor in between the reactor side and the product-
0
20
40
60
80
100
120
140
Modified Membrane Unmodified Membrane
Contact Angle (degree)
DI Water
TGDE
IL

21

removing solvent, without requiring the solvent to come directly in contact with the catalyst, as in
the case of employing a trickle-bed reactor for the same purpose. This, then, helps to reduce the
potential impact of the catalyst on solvent stability, or of the solvent on catalyst activity, thus
extending both their life-times.
In this part of the study, the performance of the membrane reactor was investigated at
different experimental conditions (variables: T, P, sweep liquid flow rates, and W/F) and the results
were compared with the PBR under the same conditions (for all such experiments, we kept the
stoichiometric number and the carbon factor constant, i.e., SN = 1.96 and CF=0.625).

Figure 1- 8. Effect of W/F on MR and PBR conversion. P = 32 bar, T = 220 °C
We have previously reported (Li and Tsotsis 2019) experiments with the same catalyst bed
and membrane employing TGDE as the sweep solvent. For this study, prior to carrying-out the
experiments with the IL we repeated several of these experiments with the TGDE as the solvent
35
40
45
50
55
60
65
70
75
80
25 30 35 40 45 50
Conversion (%)
Weight of catalyst/Flow rate (g*h/mol))
MR-IL (LF=6cc/min)
MR-TGDE (LF=6cc/min)
MR-IL (LF=1cc/min)
MR-TGDE (LF=1cc/min)
Equilibrium
PBR

22

to verify the state of the membrane and catalyst. Excellent repeatability in carbon conversion with
the previous tests (Li and Tsotsis 2019) was observed (error ≤2%).
Figure 1- 8 shows the carbon conversion for both the MR and PBR as a function of W/F
under a pressure of 32 bar, a temperature of 220
o
C, and for two different sweep liquid flow rates
(LF), namely 1 cc/min and 6 cc/min. In this study, the catalyst weight and syngas composition are
both constant, therefore, increasing the W/F means reducing the syngas flow rate. Predictably, the
increase of W/F leads to enhancement in conversions for both the MR and PBR. As it can be seen
from the figure, for larger W/F the PBR conversion approaches the equilibrium value.

Figure 1- 9. Effect of flow rate (liquid sweep) on MR conversion. P = 32 bar, T = 220
o
C, W/F = 47.2 g*h/mol
The membrane reactor conversions, on the other hand, with both sweep liquids manage to
exceed the equilibrium values. When the IL is used as the sweep liquid, the observed conversions
consistently exceed those measured with the TGDE being employed as the solvent, and are on a
relative basis 22.2 - 51.3% higher than the PBR conversions. In addition, the IL offers the
30
40
50
60
70
80
90
0 1 2 3 4 5 6 7
Conversion (%)
Flow Rate (cc/min)
Ionic Liquid
TGDE
Equilibrium

23

advantage of a significantly lower vapor pressure, which simplifies downstream separation
requirements when compared to TGDE, and also means diminished solvent losses due to
vaporization.
To further investigate the effect of varying the sweep liquid flow rate, a series of
experiments were performed at different sweep liquid flow rates and constant pressure (32 bar),
temperature (220
o
C), and W/F (47.2 g*h/mol). The results are presented in Figure 1- 9.

Figure 1- 10. Effect of temperature on PBR, MR and equilibrium conversion. P = 32 bar, liquid sweep rate = 1
cc/min, W/F =47.2 g*h/mol.
For both sweep liquids, the MR conversion increases with increasing sweep liquid flow
rates, attributed to the fact that a greater amount of methanol is extracted from the shell-side as a
result of increasing liquid sweep flow rate, thereby, pushing further the equilibrium conversion to
the right toward methanol generation. The sweep liquid flow rate plays a crucial role in process
30
35
40
45
50
55
60
190 195 200 205 210 215 220 225
Conversion (%)
Temperature ( °C)
MR-IL
MR-TGDE
PBR
Equilibrium

24

design optimization: a higher flow rate results in higher conversions, as Figure 1- 9 amply
manifests but, on the other hand, the resulting solutions have a lower MeOH concentration, and
thus are more challenging to separate the alcohol from.

Figure 1- 11. Effect of pressure on PBR, MR and equilibrium conversion. T = 220
o
C, liquid sweep rate = 1 cc/min,
W/F = 42.7 g*h/mol
Figure 1- 10 shows the carbon conversion for the MR and PBR as a function of temperature
for a constant pressure (32 bar), W/F (47.2 g*h/mol), and sweep liquid flow rate (1 cc/min). The
rather narrow range of temperatures studied was due to the fact that the FAS coating gets damaged
at higher temperatures; and because temperatures lower than 200
o
C may lead to catalyst
deactivation. In Figure 1- 10, the PBR conversion first increases, passes through a maximum at a
certain temperature, and then decreases at the higher temperatures (e.g., reaching a lower
conversion at T= 220
o
C compared to that of T=214
o
C). This can be explained by the fact that at
30
35
40
45
50
55
15 20 25 30 35
Conversion (%)
Pressure (bar)
MR-IL
MR-TGDE
PBR
Equilibrium

25

the higher temperatures the reactor conversion starts “tracking” the thermodynamic equilibrium
conversion (shown also on the Figure) of this exothermic reaction.

The conversion of MR, on the other hand, increases steadily with increasing temperature
for either sweep solvent employed, which can be attributed to the increased reaction rate as well
as enhanced methanol transport across the membrane, as the temperature rises. For all temperatures
studied in Figure 1- 10, the MR conversions (for both the TGDE and IL) are higher than the
corresponding PBR values. From a certain temperature and beyond, in fact, the MR conversion
exceeds the thermodynamic equilibrium conversion value as well. Moreover, the IL results in
higher conversion due to its higher solubility towards methanol at the reaction conditions, likely,
due to its more polar nature.
Figure 1- 11 shows the effect of changing the reactor pressure on the MR (for both types of
sweep solvent, IL and TGDE) and PBR conversion as well as the thermodynamic equilibrium
conversion while keeping constant the reactor temperature (220
o
C), the sweep liquid flow rate (1
cc/min), and W/F (47.2 g*h/mol). Predictably, both the thermodynamic equilibrium and PBR
conversions (which at this relatively high temperature closely track the equilibrium values)
increase with increasing pressure, due to the fact that the total number of moles reduces as a result
of MeS reaction which is thermodynamically favored at higher pressures. The MR conversion also
increases with increasing pressure, the added reason for that being that a greater pressure means
that a higher amount of methanol will also transport through the membrane to be removed by the
sweep liquid, thereby the equilibrium condition is further shifted towards the methanol generation.
Comparing the MR performance when employing the two different sweep liquids, higher

26

conversions are obtained for the IL over the whole range of pressures studied, thus manifesting the
advantage in terms of MeS reactor efficiency of using the IL when compared to TGDE. As noted
previously, using the IL portends additional advantages related to diminished solvent loss, lower
potential for damage to the catalyst, and simplified downstream separation requirements.
1.6 CONCLUSIONS
This chapter presents experimental data in support of a novel concept of carrying-out MeS
in a MR. In this reactor, the membrane divides its volume into two sections, the membrane shell-
side and tube-side. A Cu-based commercial MeS catalyst is packed in the shell-side where the
reaction takes place, while a sweep liquid flows in the membrane tube-side; its role is to remove
the produced MeOH from the reaction zone in-situ, thus allowing the reactants to produce more
MeOH (“breaking the equilibrium”). A commercial alumina membrane is employed, whose
surface is rendered hydrophobic via modification with a FAS agent, in order to prevent any liquid
leakage, thus avoiding solvent loss and potential catalyst deactivation. In our previous work (Li
and Tsotsis 2019), we used a petroleum-derived solvent (TGDE) as the sweep liquid to conduct
the MR experiments. Though employing the TGDE allowed the MR to attain higher conversion
and yield compared to the PBR, there are disadvantages relating to its use. They include its
relatively low boiling point (275
o
C) that dictates the reaction temperature to be kept rather low.
Moreover, though its vapor pressure is quite low it is still finite, and this creates a concern for
potential solvent loss due to vaporization. Therefore, in this chapter we have investigated, instead,
a new sweep liquid, specifically the ionic liquid [EMIM][BF4], that demonstrated during MeS in
the MR high solubility towards MeOH, whose in situ removal from the reactor, similarly to when
using the TGDE, resulted in enhanced MR conversion. The IL solvent’s advantages over TGDE
for our MR design include: (1) its extremely low vapor pressures, which eliminates potential loss

27

of solvent and substantially simplifies downstream separations; (2) its broad operating temperature
range, and high decomposition temperature, which permit the operation of the MR for a broader
region of MeS conditions. In addition, when using the IL, the observed conversions consistently
exceeded those measured with the TGDE.
One of the key goals of the proposed MeS-MR technology is to attain a sufficiently high per-
pass syngas conversion and yield into MeOH (>85%) to avoid the need for syngas recycle. This is
particularly important, when the aim is to produce alcohols from renewable biomass. Though
limitations with the lab-scale system did not allow in this study to meet the target per-pass yield
(>85%), preliminary process scale-up simulations employing a data-validated model indicate the
potential of the proposed concept to meet such a target. We presently continue to investigate the
MeS-MR technology by focusing on optimization and on technical and economic analysis (TEA)
for process scale-up. There are several important optimization conditions one must consider, such
as syngas composition, gas and liquid flow rates, temperature, pressure, catalyst weight and
activity, membrane area, the concentration of MeOH in the solvent, and the fraction of the MeOH
product recovered in the product stream. In our studies, we employ a MR model validated by our
MR experimental data that allows us to investigate process performance under operating
conditions that are not readily accessible by the lab-scale experimental system. Results of these
studies will be presented in an upcoming publication.

28

CHAPTER 2: INVESTIGATION OF CO2 AND METHANOL
SOLUBILITY AT HIGH PRESSURE AND TEMPERATURE
IN THE IONIC LIQUID [EMIM][BF4] EMPLOYED DURING
METHANOL SYNTHESIS IN A MEMBRANE-CONTACTOR
REACTOR
†

2.1 MOTIVATION
In this chapter, the solubility properties of the ionic liquid (IL), 1-ethyl-3-
methylimidazolium tetrafluoroborate ([EMIM][BF4]) were studied using a high-pressure, high-
temperature set-up employing the pressure-drop technique. [EMIM][BF4] was selected because it
is used as sweep liquid in a membrane reactor (MR)-based methanol synthesis (MR-MeS) process
explained in chapter 1. The MR-MeS studies indicated high methanol (MeOH) solubilities in the
IL under typical MeS reaction conditions, which then motivated this study to measure such
solubilities directly under non-reactive conditions to validate the MR study findings. In addition,
during the MR-MeS studies concerns existed about the CO2 solubility in [EMIM][BF4], since it is
a reactant and its dissolution in the IL would be detrimental for performance. Studies, therefore,
were also carried out to investigate CO2, in addition to MeOH solubility. Our investigation
indicates that though CO2 solubilities are high at room temperature, they become negligible at the
typical MeS conditions.

†
The material presented in this chapter has previously appeared in: Zebarjad FS, Wang Z, Li H,
Hu S, Tang Y, Tsotsis TT. Investigation of CO2 and methanol solubility at high pressure and
temperature in the ionic liquid [EMIM][BF4] employed during methanol synthesis in a membrane-
contactor reactor. Chemical Engineering Science. 2021.

29

2.2 INTRODUCTION
Ionic liquids (ILs) have been studied extensively during the last decade or so due to their
unique characteristics such as high thermal stability, high electrical conductivity, very low vapor
pressure, and good solvation properties (Blanchard, Hancu et al. 1999, Fredlake, Crosthwaite et
al. 2004, Hayes, Warr et al. 2015, Qin, Wang et al. 2016). These favorable properties make ILs
good potential ‘green’ alternatives to conventional organic solvents. One of the promising
applications of the ILs in the chemical industry is to use them as absorption media for gas
separations. This has, then, spurred significant interest in studying the solubility of various gases
into ILs in order to optimally design such absorption processes.
In chapter 1, we used an IL, specifically, 1-ethyl-3-methylimidazolium tetrafluoroborate
([EMIM][BF4]), in our studies of methanol synthesis (MeS) in a high pressure and temperature
membrane reactor (MR) system (Zebarjad, Hu et al. 2019). In our research, we employed a packed-
bed MR set-up that operates in a pressure range of 20-30 bar and a temperature range of 200-240
⁰C. The reactor contains a high-temperature ceramic membrane (further details about the
experimental set-up and conditions utilized can be found elsewhere (Li and Tsotsis 2019, Zebarjad,
Hu et al. 2019)). A commercial MeS catalyst is placed in between the membrane and the reactor
wall (the membrane shell-side) while the IL flows inside the membrane tube. During reactor
operation, syngas (CO2, CO, H2) is continuously injected into the MR shell-side and in the presence
of the catalyst reacts to produce methanol (MeOH).
The role of the flowing IL is as an absorption-medium to remove the MeOH from the
reactor and, thus, help overcome equilibrium limitations and to increase the MeOH production
rate. Using this reactor concept, carbon conversions significantly higher than equilibrium are
attained. In our studies we have also employed a petroleum-derived solvent, namely tetraethylene

30

glycol dimethyl ether (TGDE), as a sweep liquid. In addition to offering greater improvements in
conversion over the TGDE, the IL offers other advantages over the petroleum-based solvent
relevant to the proposed MR-MeS process that include: (1) its extremely low vapor pressure, which
eliminates potential loss of solvent and substantially simplifies downstream separations; (2) its
broad operating temperature range, and high decomposition temperature, which permit the
operation of the MR for a broader region of MeS conditions.
In choosing [EMIM][BF4] as the sweep solvent, the initial expectation was that MeOH
would have a good solubility in it while other permanent gases like H2 and CO would not (Liu,
Dai et al. 2014). The main concern with the choice was that CO2 may also have a high solubility
in the IL, and since it serves as a reactant for MeS this would not be a good thing. In fact, the
[EMIM][BF4] was specifically selected among other ILs because of its (1) relative high
decomposition temperature (447 ⁰C) (Nishida, Tashiro et al. 2003), and (2) its reported relatively
lower CO2 solubility when compared to other imidazolium-based ILs (Liu, Dai et al. 2014).
While CO2 is a reactant for MeS and high solubility in the IL is not desirable for our reactor,
CO2 is also a key greenhouse gas and ILs have been studied in recent years as absorption media
for its capture to reduce its emissions. Extensive research efforts have, therefore, been undertaken
in recent years and a good volume of data on CO2 solubility in ILs at or near ambient temperature
and pressure conditions are presently available (Lei, Yuan et al. 2010, Lei, Han et al. 2012, Liu,
Dai et al. 2014, Qin, Wang et al. 2015). For the specific IL of interest in this study, [EMIM][BF4],
several studies have appeared on its CO2 solubility (Lei, Han et al. 2012, Qin, Wang et al. 2015,
Akbari and Rahimpour 2018, Jalili, Shokouhi et al. 2019). All have, however, been carried out at
low temperature (298.15-353.15 K) and pressure conditions, and the only experimental study, we
are aware of, performed at high pressure (~15 MPa) was carried out at room temperature (Lei,

31

Yuan et al. 2010). Therefore, past technical literature data are of no direct relevance for the use of
[EMIM][BF4] in the high pressure and temperature MeS reactive application. Such data are
presented for the first time in this chapter.
In the remainder of the chapter, we first describe the experimental set-up and procedures
that were followed. We then present the solubility data of CO2 and MeOH in [EMIM][BF4] at
conditions relevant to the MeS reaction. For the CO2, we compare our experimental data with the
available data from the literature at room temperature. For the IL, we compare MeOH solubility
in the [EMIM][BF4] with solubility data under similar conditions with the petroleum-based TGDE
solvent. We also present, here for the first time, experimental data using the Nuclear Magnetic
Resonance (NMR) technique that validate the thermochemical stability of the [EMIM][BF4]
during experiments with the MR- MeS set-up.
2.3 EXPERIMENTAL SECTION
2.3.1 Materials
Ultra-high purity (UHP) CO2 (99.999% pure) was purchased from Praxair. UHP 5.0 Grade
Nitrogen (N2) was purchased from the Airgas Company. The [EMIM][BF4], with a reported purity
of ≥98% was purchased from Zhejiang Arts & Crafts Imp. & Exp. Company, China. Upon being
received at our Lab, the purity of the IL was confirmed via 400 MHz
1
H and 375 MHz
19
F NMR
analysis (the results can be found in the Supplementary materials section). HPLC-grade MeOH
with purity of ≥99.9% was purchased from Sigma Aldrich (a summary of all the chemicals utilized
in this study, their supplier, purity, etc. is presented in the Supplementary Materials section).

32

2.3.2 Experimental Set-Up
A schematic of the experimental apparatus used in the equilibrium solubility measurements
is shown in Figure 2- 1. The main part of the set-up consists of two cells, namely a reference cell
and a sample cell. The reference cell, with an inner volume of 250 mL, was purchased from the
Anhui Kemi Machinery Technology Co., Ltd., China. Its maximum working temperature and
pressure are 300 °C and 200 bar, respectively. A micro-stirred reactor (Series 4590) from the Parr
Instrument Company serves as the sample cell (with an inner volume of 50 mL) connected to the
reference cell. Its maximum operating temperature and pressure are 275 °C and 345 bar,
respectively. Both cells are made of stainless steel, to avoid any potential reaction with corrosive
substances. The cells are heated by individual matching metal heating jackets to accurately control
the inner temperature for each cell. The pressure in each cell was measured by high accuracy digital
pressure gauges (Omega Engineering, DPG4000-1k USA) with data-logging capability. The
pressure range of the gauges is 0-1000 psi, with a resolution of 0.1 psi and accuracy of 0.05% full
scale. The sample cell is equipped with a stirrer connected to an overhead agitator controlled by a
Parr 4843 controller for the purpose of accelerating the attainment of vapor-liquid phase
equilibrium during the measurement of the solubilities.

33

Figure 2- 1. Schematic diagram of the experimental apparatus for measurements of the solubility of carbon
dioxide/methanol in ionic liquids: (1) gas cylinder; (2) reference cell; (3) metal heating jacket; (4) vacuum pump; (5)
sample cell.
2.3.3 Experimental Procedure
There are a number of methods that are currently being used to measure the solubility of
pure gases in ILs (Koel 2008). The methods include: (i) the stoichiometric technique (Aki, Mellein
et al. 2004, Kumełan, Kamps et al. 2006, Muldoon, Aki et al. 2007, Mittenthal, Flowers et al.
2017), which involves metering known amounts of gas and liquid into a cell equipped with a
viewing window, stirring vigorously for equilibrium to be established at constant temperature,
letting the mixture stand and then measuring the level of the liquid with a cathetometer; (ii) the
pressure-drop technique (Husson-Borg, Majer et al. 2003, Jacquemin, Gomes et al. 2006,
Jacquemin, Husson et al. 2006) during which two separate, known-volume cells are used, one
referred to as the reference cell, in which a certain mass of gas is pressurized, and another as the
sample cell, in which the IL is placed and which is operating at the start of the tests under vacuum.
The cells are connected through a valve which is opened at the beginning of the experiment to

34

allow the gas from the reference cell to fill the sample cell and to dissolve in the IL. When
equilibrium is reached, the pressures of the cells are recorded to calculate the solubility of the gas
in the IL; (iii) gravimetric methods (Barghi, Tsotsis et al. 2015, Turnaoglu, Minnick et al. 2019),
which use a high-pressure gravimetric microbalance in which a specified mass of IL is loaded and
then exposed to the gas while the weight of the IL is being continuously measured until equilibrium
is established. In-situ spectroscopic methods such as Fourier Transform Infrared Spectroscopy
(FTIR), are also finding use, e.g., to study the chemical interactions of CO 2 molecules with
expanded ILs (Sakellarios and Kazarian 2005, Seki, Grunwaldt et al. 2009). In our experiments,
we employ the pressure-drop technique, which is the simplest among all methods utilized, needing
no specialized hardware. A challenge with the pressure-drop technique, but to a certain degree
with all other solubility measurement methods, as well, are the long times needed to reach
solvation equilibrium, particularly for the less soluble gases. To overcome such a difficulty, in the
experiments reported here, we employ a vigorously stirred sample cell.
2.3.4 Measurement of CO2 Solubility
The CO2 solubility in the IL was measured using the experimental set-up shown in Figure
2- 1. Prior to initiating the experiments, the system was leak-tested using N2. For that, the sample
and reference cells were pressurized with N2 at a pressure of 30 bar. Valves V3 and V7 were then
closed and the change in the system pressure was monitored over a 24 h period. For the
experiments reported here, the pressure drop was less than 0.1 psi during the 24 h period
corresponding to a leak rate of less than 0.046 mmol N2/h. Since the total quantity of CO2 that
dissolves in the IL during each experiment is at least 0.0014 moles of gas, this leak rate is
considered negligible. Though the volumes of both the reference and the sample cells are known
accurately, that is not the case for the volumes of the tubing, valves, etc. associated with each cell.

35

The Helium (He) expansion method was, therefore, used to measure the actual volume of the cell
(the details of this experimental procedure are explained elsewhere (API 1998)).
After leak-testing the whole set-up, the top of the sample cell was opened and a pre-
determined mass of the IL (10 mL) was loaded into the cell. The cell was then closed, and the
whole system was leak-tested once more overnight to ensure that it is leak-free. A mechanical
vacuum pump was then connected to the system via Valve 7 for two hours to remove any gases
present in the cell (including moisture) and/or dissolved in the IL. The temperature controllers
were then turned on to control the temperature of both the reference and sample cell at the present
value. To carry-out the CO2 solubility experiments valves V4, V7 are closed. Then, valve V2
connecting the CO2 cylinder to the reference cell is opened to let the gas flow into the reference
cell until a certain pre-determined pressure is reached. When the temperature and pressure in the
cell stabilize at their desired values, then valve V3 is closed and valve V4 is opened to let the CO2
flow into the sample cell and be dissolved into the IL. The overhead agitator in the sample cell
was turned on during this time to vigorously mix the IL with the CO2 to facilitate equilibration.
Once the pressure change became negligible, typically, within the first 2 hours, meaning that the
dissolution process had been completed, the equilibrium pressure was recorded from the pressure
gauges
After the equilibrium pressure was reached, valve V4 was closed again and V3 was opened
to allow gas into the reference cell at a higher initial pressure and the above experiment was
repeated once more. By repeating the above procedure a number of times, the equilibrium
solubilities corresponding to various pressures were obtained. The experiment was then repeated
for another temperature. For each temperature, three different experiments were carried out and
the absolute relative percent deviation was calculated to be lower than 2%.

36

The number of moles present in the reference cell at the beginning of the experiment, and
the number of moles in both cells at equilibrium were calculated based on the known volumes of
the cells and the measured temperature and pressure by employing the NIST Chemistry WebBook
(Databases 2016). The number of moles ni injected into the set-up during each CO2 charge into the
reference cell during the ith pressure increment, i.e., starting from equilibration pressure Pi-1,eq (i=1,
2. 3, …n – P0,eq = 0 bar) during the (i-1)th step and ending with initial pressure Pi,in for the ith step
can be calculated from the following equation:
𝑛 𝑖 = 𝑉 1
∗ (𝑣 𝑖 − 𝑣 𝑖 −1,𝑒𝑞
) (Eq. 2- 1)
where 𝑉 1
(cm
3
) is the measured volume of the reference cell (including the volume of associated
tubing, valve dead volume, etc.), 𝑣 𝑖 −1,𝑒𝑞
(mol/cm
3
)

is the specific volume corresponding to the
equilibration pressure Pi-1,eq, and 𝑣 𝑖 (mol/cm
3
)

is the specific volumes corresponding to the initial
pressure Pi,in for the ith step.
The moles of CO2, nil, dissolved at equilibrium in the [EMIM][BF4] at a given temperature
T and pressure Pi,eq are determined by the following equations:
𝑛 𝑖𝑙
= 𝛴 𝑛 𝑖 − 𝑉 𝑔 ∗ 𝑣 𝑖 ,𝑒𝑞
(Eq. 2- 2)
𝑉 𝑔 + 𝑉 𝑙 = 𝑉 1
+ 𝑉 2
(Eq. 2- 3)
where 𝑉 𝑔 (cm
3
) is the total gas volume (reference + sample cell) and 𝑉 𝑙 is the IL volume in the
sample cell at equilibrium. 𝑉 2
is the volume of the sample cell, with 𝑉 1
+ 𝑉 2
being the total set-up
volume. In his study of the same IL for a similar region of pressures (<4 MPa), Kang et al. (Qin,
Wang et al. 2015) concluded that the volume expansion of the IL due to dissolution of CO 2 was
negligible (< 2 % at 25 ℃). We have also measured in independent experiments the thermal
expansion of IL in the temperature range from 25 ℃ to 220 ℃ and found it to be negligible (<1

37

%). These experiments were carried out using a stainless steel cell equipped with a viewing
window and a CMOS camera (C, 1080P, Microsoft, USA) to monitor the change in the liquid level
in the cell as the temperature is raised from 25 ℃ to 220 ℃. For the analysis of the CO2 solubility
data, we have, therefore, assumed that the liquid phase volume can be assumed equal to the initial
volume of the pure IL.
Finally, the solubility 𝑆 𝐶 (%) of CO2 in [EMIM][BF4] at each pressure is then given by:
𝑆 𝐶 (%)=
𝑛 𝑖𝑙
𝑛 𝐼𝐿
× 100% (Eq. 2- 4)
where 𝑛 𝐼𝐿
is the number of moles of the IL.
2.3.5 Measurement of Methanol Solubility
For the MeOH experiments, we only used the sample cell. To start the experiment, a
solution of MeOH in the IL of a pre-determined concentration was loaded into the sample cell.
After leak-testing the cell (see above), the temperature of the cell was raised to a pre-set value
employing the temperature controller while stirring vigorously the liquid phase to accelerate the
equilibration process between the vapor and liquid phases. After a certain period, the pressure in
the cell stops from rising, indicative that vapor/liquid phase equilibrium has been reached. The
pressure P would then be recorded and the experiment stopped. A new experiment would then be
carried out employing a fresh MeOH in IL solution of different initial composition.
At equilibrium, the liquid-phase volume Vl is described by the following equation:
𝑉 𝑙 = 𝑛 𝑀𝐿
∗ 𝑣 𝑀𝐿
𝑜 + 𝑛 𝐼𝐿
∗ 𝑣 𝐼𝐿
𝑜 (Eq. 2- 5)
where 𝑛 𝑀𝐿
,𝑛 𝐼𝐿
are the number of moles of methanol and [EMIM][BF4] in the liquid phase,
respectively, and 𝑣 𝑀𝐿
𝑜 ,𝑣 𝐼𝐿
𝑜 are their pure state specific volumes. The basic assumption in Eqn. 5 is

38

that volume changes due to mixing can be neglected (Valderrama and Rojas 2009). In Eqn. 5, 𝑣 𝑀𝐿
𝑜
is obtained from the NIST Chemistry WebBook, while 𝑣 𝐼𝐿
𝑜 was determined by the Rackett equation
(Valderrama and Rojas 2009).
𝑣 𝐼𝐿
𝑜 =
𝑅 𝑇 𝑐 𝑝 𝑐 𝑍 𝑐 [1+(1−
𝑇 𝑇 𝑐 )
2/7
]
(Eq. 2- 6)
where 𝑇 𝑐 , 𝑝 𝑐 ,𝑍 𝑐 are the critical temperature and pressure and the compressibility factor,
respectively. The volume of gas phase 𝑉 𝑔 is given by:
𝑉 𝑔 = 𝑛 𝑀𝐺
∗ 𝑣 (𝑇 ,𝑝 ) (Eq. 2- 7)
where 𝑛 𝑀𝐺
is the number of moles of methanol in the gas phase, and 𝑣 (𝑇 ,𝑝 ) is the molar volume
of the methanol gas phase, which is obtained from the NIST Chemistry WebBook [17]. 𝑉 𝑔 and 𝑉 𝑙
add together to the known volume of the sample cell 𝑉 .
𝑉 𝑔 + 𝑉 𝑙 = 𝑉 (Eq. 2- 8)
The sum of the number of moles of MeOH in the gas phase 𝑛 𝑀𝐺
and in the liquid phase 𝑛 𝑀𝐿
is
equal to the initial number of moles of methanol 𝑛 𝑀𝐿 0
dissolved in the IL (equal to the mass of
methanol divided by its molecular weight).
Solving Eqns. (5)-(8) for 𝑛 𝑀 𝐿 and 𝑛 𝑀𝐺
, we can finally obtain the solubility (molar basis)
𝑆 𝑀 (%) of methanol in [EMIM][BF4] by:
𝑆 𝑀 (%)=
𝑛 𝑀𝑙
𝑛 𝐼𝐿
× 100% (Eq. 2- 9)

39

2.3.6 Stability of the [EMIM][BF4] IL During the MR-MeS Experiments
Due to the high temperature and pressure conditions employed during the MR-MeS
experiments, a key requirement for the sweep liquids chosen is that they remain stable under such
conditions. To ensure that this is, indeed, the case for the [EMIM][BF4], the IL utilized during the
MR-MeS experiments is collected, the dissolved products and reactants are removed, and the IL
is analyzed via NMR for its structure, which is then compared with that of a pristine IL not used
in such experiments. The MR-MeS experimental set-up is shown in Figure 1- 1, and described in
greater detail elsewhere (Li and Tsotsis 2019, Zebarjad, Hu et al. 2019). It consists of the syngas
delivery system, the MR, the sweep liquid delivery system, and the analysis section using a GC.
A mesoporous alumina membrane, whose surface is rendered hydrophobic via grafting of an
appropriate modifying agent, is installed in the MR. During operation, the syngas is fed into the
shell-side, where it contacts under high pressure and temperature the Cu-ZnO-Al2O3 MeS catalyst
to convert into MeOH. The sweep liquid (the [EMIM][BF4] in this case) is pumped through the
membrane tube-side to remove the produced MeOH (and the co-product water) to help increase
the MeS conversion/yield.
The IL collected is placed in a closed, magnetically-stirred glass vessel and is heated at 110
⁰C in the presence of flowing inert Ar gas to remove any of the MeS components dissolved in it.
The IL remaining, free of methanol and water, was then used to prepare samples for NMR analysis
and to be compared with those from a pure IL that has not been used in any reactor experiments.
1
H and
19
F NMR spectra were obtained at room temperature with a Varian 400-MR spectrometer
using 5 mm thin-walled NMR sample tubes (provided by Wilmad-LabGlass). All chemical shifts
(δ) are reported in parts per million (ppm) relative to residual HDO in D2O (δ - 4.80,
1
H NMR)
and C6F6 (δ -164.9,
19
F NMR). NMR spectra processing was performed with MestReNova 11.0.2.

40

2.4 RESULTS AND DISCUSSION
2.4.1 CO2 Solubility
When choosing the [EMIM][BF4] IL as the sweep solvent, the expectation was that MeOH
would have a good solubility in it while other permanent gases involved in MeS like H2 and CO
would not (Jacquemin, Gomes et al. 2006, Jacquemin, Husson et al. 2006, Liu, Dai et al. 2014).
So, by helping to extract the MeOH from the reactor environment, while leaving the reactants like
H2 and CO unaffected, the IL sweep would help enhance the yield and selectivity. CO 2 solubility
was, however, a concern since it serves as a reactant for MeS, and ILs including the [EMIM][BF4]
are known to exhibit high CO2 solubilities (Qin, Wang et al. 2015). In fact, ILs have been studied
in recent years as absorption media for CO2 capture to reduce its emissions, since CO2 is
considered a key greenhouse gas. Such high CO2 solubility, if it was to be sustained at the high
temperatures and pressure conditions of the MeS reaction would, of course, be detrimental to
reactor performance.
Due to the potential use of ILs in CO2 separation, capture and storage efforts, numerous
research efforts were undertaken in recent years and a good volume of data exist on the CO2
solubility in ILs at or near ambient temperature and pressure conditions (Nishida, Tashiro et al.
2003, Lei, Yuan et al. 2010, Lei, Han et al. 2012, Qin, Wang et al. 2015). For the [EMIM][BF4],
the IL of interest in this study, several studies exist reporting its CO2 solubility (Lei, Yuan et al.
2010, Lei, Han et al. 2012, Qin, Wang et al. 2015, Akbari and Rahimpour 2018, Jalili, Shokouhi
et al. 2019) at low pressure and /or temperature conditions. In fact, as noted previously, the reason
we selected the [EMIM][BF4] IL for our MR-MeS study was due to its lower solubility toward
CO2 as compared to other better-known Imidazolium-based ILs (Akbari and Rahimpour 2018).

41

Though past low temperature data may have guided the initial selection of the IL, they offer,
however, no insight on the potential performance of [EMIM][BF4] under the high pressure and
temperature MeS reactive conditions. Generating such data is, therefore, a key objective of this
chapter.

Figure 2- 2. CO 2 solubility, S c(%), in [EMIM][BF 4] at 25 ⁰C.
Prior to measuring CO2 solubility in [EMIM][BF4] under MeS-relevant temperature and
pressure conditions, we first generated such data at 25
o
C. These are shown in Figure 2- 2.
Shown on the same figure are experimental solubility data of CO2 in the [EMIM][BF4] at
25 ⁰C from the technical literature (Lei, Yuan et al. 2010, Akbari and Rahimpour 2018, Jalili,
Shokouhi et al. 2019). Our CO2 solubility data are in good agreement with the prior literature data
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
[Lei et al., 2010]
[Jalili et al., 2019]
[Akbari and Rahimpour, 2018]
This work
S
c
(%), ×10
2
Equilibrium Pressure(MPa)

42

showing an average of absolute relative percent deviation (𝐴𝑅𝐷 % =
100
𝑁 ∑ |
𝑋 𝑖 −𝑋 𝑖 𝑟𝑒𝑓 𝑋 𝑖 𝑟𝑒𝑓 |
𝑁 𝑖 =1
) of 5.1%
from the data in (Jalili, Shokouhi et al. 2019), 1.8% from the data in (Jalili, Shokouhi et al. 2019)
and 2.3% from the data in (Lei, Yuan et al. 2010). The good agreement with the experimental
literature data clearly confirms the ability of our experimental technique to accurately measure the
CO2 solubility in the IL.

Figure 2- 3. CO 2 solubility, S c(%), of different imidazolium-based ILs. at 25 ⁰C (Koel 2008)
Figure 2- 3 compares our experimental data at 25
o
C with solubility data from the technical
literature with other well-known Imidazolium-based ILs (Akbari and Rahimpour 2018), such as
[EMIM][Tf2N], [BMIM][Tf2N], [BMIM][BF4], and [BMIM][PF6].

0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Equilibrium Pressure (MPa)
[EMIM][BF4]
[EMIM][TF2N]
[BMIM][BF4]
[BMIM][PF6]
[BMIM][TF2N]
This Work
S
c
(%), ×10
2

43

As the data in Figure 2- 3 indicate, the [EMIM][BF4] has the lowest room temperature CO2
solubility value among all other ILs. However, its solubility is still high enough, that if it was to
be sustained at the MeS reaction temperature conditions, it would render the IL inappropriate for
use as a sweep liquid in the MeS-MR system, since it would result in substantial loss of reactant
CO2. This, however, is not the case as Figure 2- 4 shows where we plot our experimental CO2
solubility measurements in the [EMIM][BF4] for various temperatures.

Figure 2- 4. CO 2 solubility, S c(%), in [EMIM][BF 4] at high temperatures
As one can see from Error! Reference source not found., as the temperature increases t
he CO2 solubility decreases, and at temperatures relevant to the MeS reaction (~220 ⁰C) it is
negligible, i.e., Sc(%)= 1% at 3 MPa, compared with a corresponding solubility Sc(%)= 36% at 25
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
S
c
(%), ×10
2
Equilibrium Pressure (MPa)
25°C
40°C
60°C
70°C
220°C

44

o
C. This is a very positive finding concerning the ability of this particular IL to function as a sweep
liquid in the MR-MeS system.
2.4.2 Methanol Solubility
Our experiments indicate that at room temperature (25 ⁰C) liquid MeOH is completely
soluble in the [EMIM][BF4]. The interest in this study, however, is to determine the MeOH
solubility for temperatures of relevance to the MeS reaction, i.e., temperatures in excess of 200 ⁰C.
Figure 2- 5 shows the MeOH solubility in [EMIM][BF4] vs. its equilibrium pressure.

Figure 2- 5. Methanol solubility, S M (%), in [EMIM][BF4] and TGDE at high temperatures (TGDE data are
extracted from reference (Kuczynski and Westerterp 1986)).
Shown on the same Figure are the solubility data taken from the technical literature
(Kuczynski and Westerterp 1986) for a petroleum-based organic solvent TGDE that we have also
used in our MR-MeS studies (and other Groups have also employed in reactive separation studies
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.5 1 1.5 2 2.5 3 3.5
S
M
(%), ×10
2
Equilibrium Pressure (Mpa)
TGDE-170°C
TGDE-190°C
TGDE-210°C
IL-170°C
IL-190°C
IL-210°C

45

of MeS (Kuczynski and Westerterp 1986)). TGDE is more readily available and affordable than
[EMIM][BF4], but its relatively high vapor pressure (compared to the IL) results in solvent loss
during the MR-MeS operation and a more complicated downstream process to separate the MeOH
from the TGDE.
In addition, as detailed in our previous paper (Zebarjad, Hu et al. 2019), the use of the IL
as a sweep liquid compared to TGDE results in higher MeOH production rates in the MR-MeS
system under otherwise similar experimental conditions. The reason for the higher conversions
becomes obvious from Figure 2- 5, which shows that the MeOH solubility in [EMIM][BF4] is
higher than that in TGDE. In the context of the operation of the MR-MeS system, this means that
more MeOH is swept away by the IL rather than by the TGDE, which enhances the MeOH
production rates. Figure 2- 6 shows the MeOH solubility at a pressure of 1.0 MPa as a function of
temperature for both the [EMIM][BF4] and TGDE. As the temperature increases the solubility of
MeOH in both solvents decreases, but the solubility in the [EMIM][BF4] remains always higher
than that in the TGDE, confirming once more that the increased MeOH productivities in the MR-
MeS lab-scale system, when using the IL vs. the TGDE as a sweep solvent, are due to the higher
MeOH solubilities in the [EMIM][BF4]. The high selectivity of MeOH adsorption in the
[EMIM][BF4] as compared to CO2, presented in this work, is consistent with the experimental
findings of our prior MR-MeS studies (Zebarjad, Hu et al. 2019) in which we observed 22.2-51.3%
higher methanol conversions than the conventional packed-bed reactor conversions. The solubility
measurements and the MR studies validate, in our opinion, the ability of the IL solvent to favorably
impact the MeS reaction kinetics.

46

Figure 2- 6. Methanol solubility, S M (%), in [EMIM][BF4] and TGDE vs. temperature at 1.0 Mpa of pressure (all the
TGDE data were extracted from reference (Kuczynski and Westerterp 1986)).
Water vapor is one of the by-products of the MeS reaction. The concern about water is not
with the effect that its dissolution in the IL may have on the reactor conversion (our studies indicate
that at room temperature water is completely soluble in the IL), which will in this case be beneficial
in terms of enhancing conversion, but on the impact that such dissolution may have on the IL’s
structural properties. There are a number of past investigations that were done on mixing of water
with the imidazolium-based ILs at room temperature showing that the physical and chemical
properties (including electrical conductivity, reactivity, viscosity, polarity and solvation
characteristics) of the IL may be affected by the presence of water (Brown, Pollet et al. 2001,
Najdanovic-Visak, Esperanca et al. 2003, Wang, Tian et al. 2003, Domańska and Marciniak 2005).
The impact seems to correlate well with the quantity of water present in the IL. Zhang et al. (Zhang,
Xu et al. 2008), for example, studied solutions of water with 1-ethyl-3-methylimidazolium [(EMI
+
)
BF4
-
] in the range of water molar fractions of 0.02 ≤ 𝑥 𝑤 ≤0.90. By monitoring the stretching
vibrations, C2-H, C4-H, C5-H, B-F, as water is being added to [(EMI
+
) BF4
-
] they reported no
0.2
0.3
0.4
0.5
0.6
0.7
0.8
140 160 180 200 220 240
S
M
(%), ×10
2
T (°C)
TGDE
IL

47

major changes for low water contents of 0.02 ≤ 𝑥 𝑤 ≤0.30 which begin to appear, however, at
higher water molar fractions (>0.3). Takamuku et al. (Takamuku, Kyoshoin et al. 2009)
investigated the effect of water on the structure of the [EMIM][BF4]. The absorption enthalpy in
the low molar fraction range of 𝑥 𝑤 ≤∼0.30 is lower than the enthalpy of vaporization for bulk
water; however, the absorption enthalpy overtakes the bulk water enthalpy for 𝑥 𝑤 ≥∼0.5. This
finding suggests that the water molecules in this lower molar fraction range (<0.5) are weakly
interacting with the IL, while they are more strongly interacting with the IL for 𝑥 𝑤 ≥∼0.50. During
opration of our MR-MeS system the molar fraction water dissolved in the [EMIM][BF4] will never
exceed 0.3,
The aforementioned studies on the impact of water on the stability of the [EMIM][BF4] IL
indicate that if any effect was to be present it would be minimal. These investigations, however,
were not conducted under the MR-MeS experimental temperature conditions of our study. A
systematic study was, therefore, initiated (following the experimental procedure described in
section 2.3.3 above) designed to validate the stability of the [EMIM][BF4] IL during the MR-MeS
system operation. Figure 8 compares the 400 MHz
1
H NMR characterization results of the IL, after
it had been utilized in such experiments, to that of the pristine IL as received by the manufacturer.
The six groups shown on the Figure correspond to the different hydrogen bonding environments
that exist in the [EMIM][BF4] structure. If any decomposition or irreversible bonding with water
(and/or MeOH) had happened, the intensity and/or the locations of the peaks for any of these
groups in the NMR spectra in the used IL would differ from those of the pristine one. However,
as Figure 2- 7 shows, this is clearly not the case here. Therefore, we are confident that the IL
solubility properties remain unchanged during the MR-MeS experiments.

48

Figure 2- 7. 400 MHz
1
H NMR results of the [EMIM][BF 4] IL before and after it was used in the MR-MeS
experiments.
2.5 CONCLUSIONS
In this Chapter we investigated the CO2 and MeOH solubilities in [EMIM][BF4], to
validate its applicability as a sweep solvent in the MR-MeS process currently under study by our
Group (Li and Tsotsis 2019, Zebarjad, Hu et al. 2019). The role of the sweep liquid in the MR-
MeS process, occurring at high temperatures (200 ⁰C - 240 ⁰C) and high pressures (20 MPa - 40
MPa) is to strip in situ the methanol produced in the reactor from the syngas. The sweep liquid is,
thus, required to have, under the MR-MeS conditions, a low solubility toward the syngas
components and high solubility toward the MeOH. With respect to the syngas components, the IL
is known to have very low room temperature solubilities toward CO, and H2, and these were no
further investigated under the MR-MeS conditions. [EMIM][BF4] has a relatively high room

49

temperature solubility toward CO2, and its solubility in the IL under the MR-MeS conditions was
further investigated in this research. CO2 was shown to have negligible solubility in the IL under
such conditions, which is a positive finding with respect to the applicability of the selected IL for
the MR-MeS process. We also studied the solubility of MeOH in the [EMIM][BF4] under the MR-
MeS conditions and compared it with its solubility in a petroleum-based organic solvent (TGDE)
that we and others have previously used in reactive separation processes for MeS. Methanol was
shown to have a higher solubility in the IL than in the petroleum solvent, which explains the higher
MeOH production rates observed in the MR-MeS system when using the IL solvent.

50

CHAPTER 3: SIMULATION OF METHANOL SYNTHESIS IN
A MEMBRANE-CONTACTOR REACTOR
3.1 MOTIVATION
In chapter 1, we investigated experimentally in the laboratory (Zebarjad, Hu et al. 2019)
the MeS reaction in a novel high-pressure membrane reactor (MR) using TGDE and an IL as the
sweep liquids. We reported significantly higher carbon conversion (per single-pass) compared to
a traditional packed-bed reactor (PBR), as a result of the in situ removal of methanol by the sweep
liquid. In this chapter, a steady-state model is developed to simulate the MR behavior during MeS,
and is validated by the experimental data. The model is then used to study the reactor behavior for
a broader range of operating conditions beyond those that can be accessed and studied
experimentally in the laboratory-scale reactor. Converting the model equations into their
dimensionless form helps to identify the key dimensionless groups determining reactor
performance and enables one to better evaluate the efficacy of the MR system and guides further
process design and scale-up.
3.2 INTRODUCTION
Methanol (MeOH) is a key industrial raw material utilized today in the production of a
number of important chemicals including, among others, formaldehyde, dimethyl ether, and acetic
acid (Methanol-Institute 2010). Methanol, in addition, shows good potential for use as an
alternative fuel which further highlights its importance as a chemical (Rasmussen, Janssens et al.
2012). Methanol is manufactured from syngas (a mixture of CO/CO2/H2) produced primarily today
from natural gas via steam or autothermal reforming. A Cu/ZnO/Al2O3 catalyst is, typically,
utilized operating at temperatures in the range from 220
o
C - 300
o
C and pressures up to 50 bar

51

(Kapran and Orlyk 2017). The following three global reactions have been discussed in the
scientific literature as taking place during MeOH synthesis (MeS).
CO2 + 3H2 → CH3OH + H2O ΔH
o
= -49.5 (kJ/mol) (R1)
CO + 2H2 → CH3OH ΔH
o
= -90.6 (kJ/mol) (R2)
CO + H2O → CO2 + H2 ΔH
o
= -41.2 (kJ/mol) (R3)
Only two out of these three reactions are linearly independent for their rates to be taken into
account for reactor modeling purposes (Zebarjad, Hu et al. 2019). In this chapter, following the
recommendation of Van den Bussche et al. (Welty, Rorrer et al. 2020), we consider reactions R1
and R3. This choice of reactions is consistent with isotopic studies that report that the source of
carbon in methanol is the CO2 (Liu, Willcox et al. 1985, Chinchen, Waugh et al. 1986).
The MeS reaction is exothermic and equilibrium-limited, and at the experimental
conditions typically utilized single-pass conversions are, generally, low around 25 - 30%, which
then dictates the recycle of the unreacted syngas. The recent focus on using renewable energy
resources to substitute for conventional fossil fuels, has generated the impetus to produce MeOH
from raw resources, such as waste biomass, rather than from natural gas. The required syngas in
such case, will be produced from biomass gasification, and will contain a large concentration of
nitrogen, since such facilities will, typically, be distributed and small- to medium-scale, and
employing an air separation unit (ASU) and an oxygen-blown gasifier is unlikely to be economic.
Recycling a syngas with high nitrogen content will be energy-intensive and will adversely impact
the process economics.

52

A number of studies, particularly in recent years have been done to improve the efficiency
of the MeS process. The focus of most of these studies is the development of new reactor designs
to help overcome reaction equilibrium limitations via the in-situ removal of the reaction products
(water or MeOH) and, thus, to improve the per single-pass carbon conversion. Though some
studies have done that via in situ product condensation (Reubroycharoen, Vitidsant et al. 2003,
Van Bennekom, Venderbosch et al. 2013), most investigations to date have utilized reactive
separation systems, such as adsorptive reactors (e.g., the study by Kuczynski et al. (1989)
employing a gas-solid-solid trickle-bed flow reactor using fine alumina powder for in situ MeOH
removal), absorptive reactors (Westerterp, Kuczynski et al. 1989) employing liquid solvents for
methanol (e.g., TGDE and n-butanol), and membrane reactors (MR).
Most of the efforts, particularly in recent years, employ membrane reactors (Sunarso,
Hashim et al. 2017, Abuabdou, Ahmad et al. 2020, Chen and Chen 2020). Struis et al. (Struis,
Stucki et al. 1996), for example, in one of the earliest invetsigations studied experimentally a MR
for MeS employing a water permeable Nafion® membrane. The reactor showed increased
methanol yield. Struis and Stucki (2001) in a follow-up study presented a mathematical model for
their reactor that was validated by their experiments and used it to show that such a MR shows
promising results. The downside of the Nafion® membranes for such an application is their
relatively low temperature tolerance (200 ⁰C). Gallucci et al. (Gallucci, Paturzo et al. 2004) used
a MR for MeS employing a hydrophilic zeolite membrane and compared its behavior with that of
a conventional packed-bed reactor; higher methanol conversion was attained in the MR, and the
experimental results were later validated by a mathematical model (Barbieri, Marigliano et al.
2002). Hydrophilic zeolite membranes are finding commercial application today for
pervaporation-type, dehydration applications (Van der Bruggen and Luis 2015), but their ability

53

to selectively (over the reactants H2 and CO2) remove in situ the water product under typical MeS
conditions diminishes greatly with temperature. Rahimpour and coworkers in a series of modeling
investigations have proposed the use of silica (Farsi and Jahanmiri 2012) or Pd and Pd-alloy
membranes in a variety of novel MR designs (Rahimpour and Ghader 2003, Parvasi, Mostafazadeh
et al. 2009, Rahimpour, Rahmani et al. 2011, Bayat and Rahimpour 2012, Bayat and Rahimpour
2012, Dehghani, Rahimpour et al. 2021), but these systems still remain to be investigated
experimentally.
In our previous studies (Li and Tsotsis 2019, Zebarjad, Hu et al. 2019) we introduced a
membrane contactor reactor (MCR) design that employs a MeOH solvent as a sweep and a
mesoporous alumina membrane that serves as the contactor interface between the catalytic zone
and the sweep liquid that removes the methanol in-situ; so doing, helps to overcome the
equilibrium limitations and to increase methanol production. We have shown experimentally (Li
and Tsotsis 2019, Zebarjad, Hu et al. 2019) that this novel design, indeed, overcomes equilibrium
limitations and increases syngas conversion into MeOH to near 80%, a value that substantially
surpasses the per-pass conversions of ~25% - 30% attained, typically, today by the commercial
MeS processes. In this chapter, we formulate and analyze a mathematical model of the MCR
system which we validate by the experimental data. The model is then used to study the reactor
behavior for a broader range of operating conditions beyond those that can be studied
experimentally in the laboratory-scale reactor. Converting the model equations into their
dimensionless form helps to identify the key dimensionless groups determining reactor
performance and enables one to better evaluate the efficacy of the MR system and guides further
process design and scale-up.

54

The lab-scale MCR setup has been described in detail in chapter 1. In what follows, we
first describe the model equations. The numerical integration method for the model and its
validation by the experimental data are then described. Finally, the model is utilized to describe
the MCR behavior for a broad range of operating conditions.
3.3 MATHEMATICAL MODEL
In this section we describe the development of the mathematical model. We first present
the global catalytic rate equations that we employ in the reactor models. Then, the membrane MR
model equations are presented, including the approach we take to describe transport through the
partially liquid-filled multilayer membrane. We conclude this section by rendering the model
equations dimensionless which helps us identify the key dimensionless groups determining reactor
performance.
3.3.1 Rate Equations
The global catalytic rate expressions for reactions R1 and R3 are presented below (Eqns.
3-1 and 3-2). They were originally proposed by Van den Bussche et al. (Bussche and Froment
1996) and were experimentally validated by us for the catalyst employed in this study using the
experimental set-up in Figure 1- 1 and Figure 1- 2. The thermodynamic parameters are from the
study by Graaf et al. (Graaf, Stamhuis et al. 1988), Eqns. 3–3 to 3-5, below.
𝑟 1
= 𝑟 𝑅𝑊𝐺𝑆 =
𝐾 1𝑤 𝑃 𝐶 𝑂 2
[1−𝐾 𝑒𝑞𝑤
∗(
𝑃 𝐶𝑂
𝑃 𝐻 2
𝑂 𝑃 𝐻 2
𝑃 𝐶 𝑂 2
)]
[1+𝐾 2
𝑃 𝐻 2
𝑂 𝑃 𝐻 2
+ (𝐾 3
𝑃 𝐻 2
)
1
2
+𝐾 4
𝑃 𝐻 2
𝑂 ]
(Eq. 3- 1)
𝑟 2
= 𝑟 𝑀𝑒𝑂𝐻 =
𝐾 1𝑚 𝑃 𝐶 𝑂 2
𝑃 𝐻 2
[1−(
1
𝐾 𝑒𝑞𝑚
)∗(
𝑃 𝑀𝑒𝑂𝐻 𝑃 𝐻 2
𝑂 𝑃 𝐻 2
3
𝑃 𝐶 𝑂 2
)]
[1+𝐾 2
𝑃 𝐻 2
𝑂 𝑃 𝐻 2
+ (𝐾 3
𝑃 𝐻 2
)
1
2
+𝐾 4
𝑃 𝐻 2
𝑂 ]
3
(Eq. 3- 2)

55

𝑙𝑜𝑔 10
𝐾 1
∗
=
3066
𝑇 − 10.592 (Eq. 3- 3)
𝑙𝑜𝑔 10
1/𝐾 3
∗
=
−2073
𝑇 + 2.029 (Eq. 3- 4)
𝐾 (𝑖 )
= 𝐴 (𝑖 )∗ (exp −
𝐵 (𝑖 )
𝑅 (
1
𝑇 𝐴𝑉
−
1
𝑇 )) (Eq. 3- 5)

3.3.2 MR Model
For the model, we assume that the reactor operates isothermally, under plug-flow
conditions, and there are no pressure drops in either the feed-side (shell-side) or the permeate-side
(tube-side), all these assumptions being true for the lab-scale system. Then, the mass balance
equations for the reactor feed-side and permeate-side are as follows:

𝑑 𝐹 𝑖 𝐹 𝑑𝑉
= 𝜌 𝑏 𝑅 𝑖 − (𝑎 𝑚 𝐹 )𝑁 𝑖 𝑚𝑔
(Eq. 3- 6)
𝑑 𝐹 𝑖 𝑃 𝑑𝑉
= (𝑎 𝑚 𝑃 )𝑁 𝑖 𝑚𝑙
(Eq. 3- 7)

In the above Equations, 𝐹 𝑖 𝐹 (mol/s), (i = CO, CO2, H2, H2O, CH3OH, TGDE) is the molar
flow rate of each component in the feed-side and 𝐹 𝑖 𝑃 (mol/s), (i = CO, CO2, H2, H2O, CH3OH,
TGDE) is the molar flow rate of each component in the permeate-side. 𝜌 𝑏 (kg/m
3
) is the bulk
catalyst density, 𝑅 𝑖 (mol/kg.s) the total reaction rate for species i, 𝑉 (m
3
) the reactor volume
variable, 𝑁 𝑖 𝑚𝑔
(mol/m
2
.s) the molar flux of species i through the membrane on the feed-side, 𝑁 𝑖 𝑚𝑙

(mol/m
2
.s) the molar flux of species i through the membrane on the permeate-side, 𝑎 𝑚 𝐹 (m
2
/m
3
) the
membrane geometric area per unit of reactor volume on the feed-side, and 𝑎 𝑚 𝑃 (m
2
/m
3
) the
membrane geometric area per unit of reactor volume on the permeate-side. We use here the TGDE

56

as sweep solvent. This is because for this solvent we have a more complete data base of
thermodynamic and transport properties. Current efforts are ongoing in the Group to generate a
similar set of data for other applicable solvents, including ionic liquids (Zebarjad, Hu et al. 2019)
to further extend the range of applications for the model.
For the lab-scale reactor, shown in Figure 1- 2, employing a single membrane in an
expanded form and in terms of the membrane length as the independent variable the above
equations become:
𝑑 𝐹 𝐶𝑂
𝐹 𝑑𝑧
=
𝜌 𝑏 𝐴 𝑟 𝑅𝑊𝐺𝑆 −
𝑎 𝑚 𝐹 𝐴 𝑁 𝐶𝑂 ,𝑚 𝑒 𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡 𝑚𝑔
(Eq. 3- 8)
𝑑 𝐹 𝐶𝑂
2
𝐹 𝑑𝑧
= (−
𝜌 𝑏 𝐴 𝑟 𝑀𝑒𝑡 ℎ𝑎𝑛𝑜𝑙 −
𝜌 𝑏 𝐴 𝑟 𝑅𝑊𝐺𝑆 )−
𝑎 𝑚 𝐹 𝐴 𝑁 𝐶𝑂
2
,𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡 𝑚𝑔
(Eq. 3- 9)
𝑑 𝐹 𝐻 2
𝐹 𝑑𝑧
= (−
𝜌 𝑏 𝐴 𝑟 𝑀𝑒𝑡 ℎ𝑎𝑛𝑜𝑙 −
𝜌 𝑏 𝐴 𝑟 𝑅𝑊𝐺𝑆 )−
𝑎 𝑚 𝐹 𝐴 𝑁 𝐻 2
,𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡 𝑚𝑔
(Eq. 3- 10)
𝑑 𝐹 𝐻 2𝑂 𝐹 𝑑𝑧
= (
𝜌 𝑏 𝐴 𝑟 𝑀𝑒𝑡 ℎ𝑎𝑛𝑜𝑙 +
𝜌 𝑏 𝐴 𝑟 𝑅𝑊𝐺𝑆 )−
𝑎 𝑚 𝐹 𝐴 𝑁 𝐻 2𝑂 ,𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡 𝑚𝑔
(Eq. 3- 11)
𝑑 𝐹 𝐶𝐻
3
𝑂𝐻
𝐹 𝑑𝑧
=
𝜌 𝑏 𝐴 𝑟 𝑀𝑒𝑡 ℎ𝑎𝑛𝑜𝑙 −
𝑎 𝑚 𝐹 𝐴 𝑁 𝐶𝐻
3
𝑂𝐻 ,𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡 𝑚𝑔
(Eq. 3- 12)
𝑑 𝐹 𝑇𝐺𝐷𝐸 𝐹 𝑑𝑧
= −
𝑎 𝑚 𝐹 𝐴 𝑁 𝑇𝐺𝐷𝐸 ,𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡 𝑚𝑔
(Eq. 3- 13)

𝑑 𝐹 𝑖 𝑃 𝑑𝑧
=
𝑎 𝑚 𝐹 𝐵 𝑁 𝑖 ,𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑚𝑙
，i = CO, CO2, H2, H2O, CH3OH, TGDE (Eq. 3- 14)
𝐴 =
1
(𝜋 𝑟 𝑅𝑒𝑎𝑐𝑡𝑜𝑟 2
−𝜋 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡 2
)
, 𝐵 =
1
𝜋 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 2

Equations 8-14 are coupled together with the following initial conditions at z=0:

57

𝐹 𝐶𝑂
0,𝐹 = 𝐹 𝐶𝑂
𝑓𝑒𝑒𝑑 ,𝐹 (Eq. 3- 15) 𝐹 𝐶𝑂
0,𝑃 = 0 (Eq. 3- 16)
𝐹 𝐶𝑂
2
0,𝐹 = 𝐹 𝐶𝑂
2
𝑓𝑒𝑒𝑑 ,𝐹 (Eq. 3- 17) 𝐹 𝐶𝑂
2
0,𝑃 = 0 (Eq. 3- 18)
𝐹 𝐻 2
0,𝐹 = 𝐹 𝐻 2
𝑓𝑒𝑒𝑑 ,𝐹 (Eq. 3- 19) 𝐹 𝐻 2
0,𝑃 = 0 (Eq. 3- 20)
𝐹 𝐻 2
𝑂 0,𝐹 = 𝐹 𝐻 2
𝑂 𝑓𝑒𝑒𝑑 ,𝐹 = 0 (Eq. 3- 21) 𝐹 𝐻 2
𝑂 0,𝑃 = 0 (Eq. 3- 22)
𝐹 𝐶𝐻
3
𝑂𝐻
0,𝐹 = 𝐹 𝐶𝐻
3
𝑂𝐻
𝑓𝑒𝑒𝑑 ,𝐹 = 0 (Eq. 3- 23) 𝐹 𝐶𝐻
3
𝑂𝐻
0,𝑃 = 0 (Eq. 3- 24)
𝐹 𝑇𝐺𝐷𝐸 0,𝐹 = 0 (Eq. 3- 25) 𝐹 𝑇𝐺𝐷𝐸 0,𝑃 = 𝐹 𝑇𝐺𝐷𝐸 𝑓𝑒𝑒𝑑 ,𝑃 (Eq. 3- 26)

In the above Equations, 𝑟 𝑀𝑒𝑡 ℎ𝑎𝑛𝑜𝑙 is the rate of reaction R1, 𝑟 𝑅𝑊𝐺𝑆 the rate of the reverse water gas
shift reaction, rmembrane out is the outside membrane radius, rmembrane the inside membrane radius,
rReactor the reactor tube inside radius, and z the membrane length variable. The initial conditions
describe the case where pure solvent (TGDE) is fed in the membrane permeate side.
As Figure 1- 2 shows, the liquid solvent during operation partially invades the membrane
structure, so one distinguishes two regions inside the membrane: One that is occupied by gas and
another that is occupied by the liquid. To describe the transport of each component inside the
section of the membrane that is occupied by the gas phase, the Dusty Gas Model (DGM) is used.
The diffusion process is due to two different mechanisms, namely (i) molecule–pore wall
interactions (Knudsen diffusion), which are more prevalent in small pores, and (ii) molecule-
molecule interactions (molecular diffusion), In the presence of an overall pressure gradient,
convective, non-separatory flow may also takes place. The DGM, is described by the following
Eq. 3-27

58

∑
𝑥 𝑗 𝑁 𝑖 −𝑥 𝑖 𝑁 𝑗 𝐷 𝑖𝑗
𝑒 +
𝑁 𝑖 𝐷 𝑖 ,𝑘 𝑒 = −
1
𝑅𝑇
∇𝑃 𝑖 𝑛 𝑗 =1
𝑗 ≠𝑖 −
𝑃 𝑖 𝑅𝑇
(
𝐵 0
µ
)
∇𝑃 𝐷 𝑖 ,𝑘 𝑒 , (Eq. 3- 27)
in which xi is the mole fraction of component i, 𝑃 (atm) is the total pressure, 𝑃 𝑖 (atm) is the
component partial pressure, T (K) the temperature, and R (J/mol.K) the gas constant. 𝐷 𝑖𝑗
𝑒 (m
2
/s),
and 𝐷 𝑖 ,𝑘 𝑒 (m
2
/s), are the effective Knudsen and molecular diffusion coefficients, B0 (m
3
/m
2
.s.atm)
is the permeability coefficient, and µ (µP) the mixture viscosity, which in this work is calculated
using the Corresponding States Method (Teja and Rice 1981). For the 3-layer membrane employed
in this chapter, Eqn. 3-27 is solved separately in each individual regions (as long as it is either
partially or fully occupied with gas), with continuity of fluxes and partial pressures applying at the
interface in between regions.
The effective Knudsen diffusivity of species i, 𝐷 𝑖 ,𝑘 𝑒 (m
2
/s), is calculated using the following
equation
𝐷 𝑖 ,𝑘 𝑒 =
𝘀 𝜏 𝑑 𝑝 3
√
8𝑅𝑇
𝜋 𝑀 𝑖 , (Eq. 3- 28)
where Mi (kg/kmol) the molecular weight of species i, 𝘀 the porosity, 𝜏 the tortuosity and dp (m)
the average pore size of the porous layer. The effective binary diffusivity is calculated by Eqn. 3-
29
𝐷 𝑖𝑗
𝑒 =
𝘀 𝜏 𝐷 𝑖𝑗
, (Eq. 3- 29)
where Dij (m
2
/s) is the binary gas phase diffusivity of i and j calculated by Eqn. 3-30

59

𝐷 𝑖𝑗
=
(10
−7
)𝑇 1.75
(
1
𝑀 𝑖 +
1
𝑀 𝑗 )
0.5
𝑃 [(𝑣 𝑖 )
1
3+(𝑣 𝑗 )
1
3
]
2
, (Eq. 3- 30)
where Mi, Mj are the molecular weight of i and j in kg/kmol, and 𝑣 𝑖 , 𝑣 𝑗 (m
3
/g-mol) are the molar
volumes.
In the model, we assume there is no overall pressure gradient in the part of the membrane
that is occupied by the gas, i.e., that there is no convective flow. We also assume that the gas phase
is ideal, which is a relatively good approximation given the high temperatures of the MeS reaction
(this is, typically, done in the application of DGM to gas phase systems. Relaxing such an
assumption and using, instead, an Equation of State to relate the chemical potential gradient to
concentration gradient is rather straightforward but entails substantial additional efforts, which go
beyond the scope of this initial model development effort). which means that Eq. 3-27 simplifies
into Eq. 3-31 below:
∑
𝑥 𝑖 𝑁 𝑗 −𝑥 𝑗 𝑁 𝑖 𝐷 𝑖𝑗
𝑒 −
𝑁 𝑖 𝐷 𝑖 ,𝑘 𝑒 =
1
𝑅𝑇
𝑑 𝑃 𝑖 𝑑𝑟
𝑛 𝑗 =1
𝑗 ≠𝑖 =
𝑑 𝐶 𝑖 𝑑𝑟
(Eq. 3- 31)
The concentration profiles for different components in the gas-filled membrane section are then
described by the following DGM equations
∑
𝑥 𝑖 𝑁 𝑗 𝑚𝑔
−𝑥 𝑗 𝑁 𝑖 𝑚𝑔
𝐷 𝑖𝑗
𝑒 −
𝑁 𝑖 𝑚𝑔
𝐷 𝑖 ,𝑘 𝑒 =
1
𝑅𝑇
𝑑 𝑃 𝑖 𝑚𝑔
𝑑𝑟
𝑛 𝑗 =1
𝑗 ≠𝑖 =
𝑑 𝑐 𝑖 𝑚𝑔
𝑑𝑟
,
(Eq. 3- 32)
which can be re-written in a matrix form:
𝐷 𝐷𝐺𝑀 ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑
∗ 𝑁 𝑚𝑔
⃑⃑⃑⃑⃑⃑⃑⃑⃑
=
𝑑 𝑐 𝑚𝑔
𝑑𝑟
⃑⃑⃑⃑⃑⃑⃑⃑
(Eq. 3- 33)

60

𝐷 𝐷𝐺𝑀 ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑
=
{

−
∑
𝑐 𝑗 𝑚𝑔
𝐷 𝑖𝑗
𝑒
6
𝑗 =1
𝑗 ≠𝑖 ∑ 𝑐 𝑘 𝑚𝑔
6
𝑘 =1
+
1
𝐷 𝑖 ,𝑘 𝑒 𝑓𝑜𝑟 𝑖 = 𝑗 , 𝑖 = 𝐶𝑂 ,𝐶 𝑂 2
,𝐻 2
,𝐻 2
𝑂 ,𝐶𝐻
3
,𝑇 𝐺 𝐷𝐸
𝑐 𝑖 𝐷 𝑖𝑗
𝑒 ∑ 𝑐 𝑘 𝑚𝑔
6
𝑘 =1
𝑓𝑜𝑟 𝑖 ≠ 𝑗 , 𝑖 ,𝑗 = 𝐶𝑂 ,𝐶 𝑂 2
,𝐻 2
,𝐻 2
𝑂 ,𝐶𝐻
3
,𝑇𝐺𝐷𝐸
(Eq. 3- 34)

𝑑𝑐
𝑑𝑟
⃑⃑⃑
has the following form:
𝑑𝑐 𝑑𝑟 ⃑⃑⃑⃑
= [
𝑑 𝑐 1
𝑑𝑟 𝑑 𝑐 2
𝑑𝑟
𝑑 𝑐 3
𝑑𝑟
𝑑 𝑐 4
𝑑𝑟 𝑑 𝑐 5
𝑑𝑟 𝑑 𝑐 6
𝑑𝑟 ]
𝑇
(Eq. 3- 35)
The continuity equation in cylindrical coordinates is
𝑑 (𝑟 𝑁 𝑖 𝑚𝑔
)
𝑑𝑟
= 0 𝑖 = 𝐶𝑂 ,𝐶 𝑂 2
,𝐻 2
,𝐻 2
𝑂 ,𝐶𝐻
3
,𝑇𝐺𝐷𝐸
(Eq. 3- 36)
Eqns. 3-32 and 3-36 in their expanded form constitute twelve independent ordinary differential
equations. The feed concentrations for all species in the entrance of the reactor on the shell-side of
the membrane (see Eqns. (3-15) to (3-25)) are known; if the fluxes for all the species (𝑁 𝑖 𝑚𝑔
, i=CO,
CO2, H2O, H2, CH3OH, TGDE) were known there as well, one would then be able to integrate the
equations as an initial value problem and calculate the transport of all the components in the
membrane. This then points out the feasibility of using a shooting method to calculate the values
of these fluxes, which will be described later in this section.
The equations describing the transport of each component in the liquid-filled section of the
membrane are as follows:

61

𝑁 𝑖 𝑚𝑙
= −𝐷 𝑖 𝑒 .𝑝 𝑑 𝑐 𝑖 𝑙 𝑑𝑟
(Eq. 3- 37)
𝑖 = (𝐶𝑂 ,𝐶𝑂
2
,𝐻 2
𝑂 ,𝐻 2
,𝐶 𝐻 3
𝑂𝐻 )
where 𝑁 𝑖 𝑚𝑙
(mol/m
2
.s) is the flux and 𝐷 𝑖 𝑒 .𝑝 (m
2
/s) the effective diffusivity of species in the solvent
given by
𝐷 𝑖 𝑒 .𝑝 =
𝘀 𝜏 𝐷 𝑖
(Eq. 3- 38)
𝐷 𝑖 = 7.4 ∗ 10
−8
√𝜑 𝐵 𝑀 𝑆 𝑇 𝜇 𝜗 𝐴 0.6

(Eq. 3- 39)
where 𝐷 𝑖 , the bulk diffusivity of species i in the solvent, is described by the Wilke-Chang Eq. 3-
39, in which 𝜗 𝐴 (cm
3
/mol) is the molar volume of solute A at its normal boiling temperature, 𝜇
(cP) is the viscosity of the solvent (TGDE), 𝜑 𝐵 is an associative parameter (taken to be equal to
2.6 for water, 1.9 for methanol, and 1 for other components), 𝑀 𝑆 the molecular weight of solvent.
The continuity equation in cylindrical coordinates in the liquid-filled part of the membrane is
described by the following set of equations
where 𝛿 (cm) is the thickness of the liquid-filled part of, and 𝑐 𝑖 𝑙 (mol/m
3
) is the concentration of
species i in the liquid-filled part of the membrane, 𝑐 𝑖 𝑠 (mol/m
3
) is the concentration of species i at
𝑑 (𝑟 𝑁 𝑖 𝑚𝑙
)
𝑑𝑟
= 0 𝑖 = 𝐶𝑂 ,𝐶 𝑂 2
,𝐻 2
,𝐻 2
𝑂 ,𝐶𝐻
3
𝑂𝐻
(Eq. 3- 40)
@ 𝑟 = 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 , 𝑐 𝑖 𝑙 = 𝑐 𝑖 𝑠
(Eq. 3- 41)
@ 𝑟 = 𝑟 𝑚𝑒𝑚𝑒𝑏𝑟𝑎𝑛𝑒 + 𝛿 , 𝑐 𝑖 𝑙 = 𝑐 𝑖 𝑒𝑞
,
(Eq. 3- 42)

62

the inside surface of the membrane tube, and 𝑐 𝑖 𝑒𝑞
(mol/m
3
) the concentration on the liquid side at
the gas-liquid interface within the membrane in equilibrium with the gas phase on the other side.
By solving the continuity Eq. 3-40 and the corresponding BCs, Eqns. 3-41 and 3-42 the
flux of species i in the liquid-filled part of the membrane at the membrane inside surface is
described by Eq. 3-43
𝑁 𝑖 𝑚𝑙
=
𝐷 𝑖 𝑒 .𝑝 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 ∗ln(
𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒
𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 +𝛿
)
(𝑐 𝑖 𝑒𝑞
− 𝑐 𝑖 𝑠 ) .
(Eq. 3- 43)
The flux 𝑁 𝑖 𝑚𝑙
(mol/m
2
.s) of the species i in the membrane tube-side in the presence of mass
transfer limitations is described by the following Eqn.
𝑁 𝑖 𝑚𝑙
= −𝑘 𝑖 (𝑐 𝑖 𝑠 − 𝑐 𝑖 𝑝 )
(Eq. 3- 44)
where 𝑘 𝑖 (m/s) is the mass transfer coefficient describing transport in the boundary layer in the
membrane inner surface and 𝑐 𝑖 𝑝 (mol/m
3
) is the bulk phase concentration of species i. 𝑘 𝑖 (m/s) is
described by the following equation
𝑘 𝑖 = 𝐾 0
𝜈 𝐿 1/3
𝐷 𝑖 −2/3

(Eq. 3- 45)
In the above Eqns, 𝐷 𝑖 (m
2
/s) is the diffusion coefficient of species i in the solvent (TGDE)
described by Eqn. 3-39, and 𝜈 𝐿 (m/s) is the average velocity of the liquid in the membrane tube-
side. K0 is an empirical coefficient which depends on the membrane geometry and size
characteristics (e.g., internal diameter and length for a tubular membrane – for a number of
correlations describing K0 , see [Eq. 3-45]).

63

By setting the two fluxes at the membrane internal surface described by Eqns. 3-43 and 3-
44 equal to each other and eliminating the unknown concentration 𝑐 𝑖 𝑠 one derives the following
Eqn.
𝑁 𝑖 𝑚𝑙
= 𝐾 𝑖 𝑜𝑣
(𝑐 𝑖 𝑒𝑞
− 𝑐 𝑖 𝑃 )
(Eq. 3- 46)
𝐾 𝑖 𝑜𝑣
=
𝐷 𝑖 𝑒 .𝑝 ∗ 𝑘 𝑖 −𝐷 𝑖 𝑒 .𝑝 + 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 ln(
𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒
𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 + 𝛿
)∗ 𝑘 𝑖
(Eq. 3- 47)
In describing the transport of the solvent (TGDE) through the membrane, we assume that
it is limited by transport through the gas-filled part of the membrane, so one needs not to be
concerned with describing transport through the liquid-filled part of the membrane. Further,
because of its very low volatility, we assume that solvent concentration in the gas phase at the gas-
liquid interface is equal to the vapor pressure of pure TGDE. It should be noted, that TGDE
transport does not significantly affect the gas-phase transport of the other species because of its
low concentration. So, the main reason for calculating the TGDE transport is to determine its
potential loss due to evaporation. Further, the assumption that the gas phase concentration of
TGDE at the gas-liquid interface is equal to the pure TGDE vapor pressure (i.e., that it is not
affected by the presence of the other species dissolved in the TGDE at the liquid-side of the gas-
liquid interface) probably provides a conservative estimate of TGDE loss, as the true TGDE
concentration at the interface is likely to be less than the pure TGDE vapor pressure.
For solving the above boundary value problem, one must be able to calculate 𝑐 𝑖 𝑒𝑞
, the
concentration of species i in the liquid phase at the gas-liquid interface (r=rliq-gas =𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 + 𝛿 ) ,
as a function of 𝐶 𝑖 𝑚𝑔
the concentration of the same species in the gas phase inside the membrane
at the same interface. For that, we assume that liquid-gas equilibrium is reached at the interface,

64

thus the fugacity of a given component i in the gas phase, 𝑓 𝑖 𝑔 , must be equal to the fugacity of the
same component in the liquid phase,𝑓 𝑖 𝑙 .
𝑓 𝑖 𝑔 = 𝑓 𝑖 𝑙 (𝑖 = 𝐶𝑂 ,𝐶𝑂
2
,𝐻 2
𝑂 ,𝐻 2
,𝐶𝐻
3
𝑂𝐻 ,𝑇𝐺𝐷𝐸 )
(Eq. 3- 48)
The Soave-Redlich-Kwong (SRK) EOS, Eqn. 3-49 below, is used to calculate the fugacity of each
component at the liquid-gas interface. The SRK equation has been validated previously with
experimental data from the literature, but also in direct comparison in HYSYS calculations (Li and
Tsotsis 2019).
ln
𝑓 𝑖 𝑝 𝑥 𝑖 =
𝑏 𝑖 𝑏 (𝑍 − 1)− ln(𝑍 − 𝐵 )−
𝐴 𝐵 (2
𝑎 𝑖 0.5
𝑎 0.5
−
𝑏 𝑖 𝑏 )ln(1 +
𝐵 𝑍 ) (Eq. 3- 49)
where,
𝐴 =
0.42747𝑃 𝑇 2
(∑𝑥 𝑖 𝑇 𝑐𝑖
𝛼 𝑖 0.5
𝑃 𝑐𝑖
0.5
)
2
(Eq. 3- 50)
𝐵 =
0.08664𝑃 𝑇 ∑𝑥 𝑖 𝑇 𝑐𝑖
𝑃 𝑐𝑖
(Eq. 3- 51)
𝛼 𝑖 is calculated by 𝛼 𝑖 0.5
= 1 + 𝑚 𝑖 (1− 𝑇 𝑅𝑖
0.5
) , where 𝑚 𝑖 = 0.480+ 1.57𝜔 𝑖 − 0.176 𝜔 𝑖 2

𝑎 𝑖 0.5
𝑎 0.5
=
𝛼 𝑖 0.5
𝑇 𝑐𝑖
𝑃 𝑐𝑖
0.5
∑
𝑥 𝑖 𝛼 𝑖 0.5
𝑇 𝑐𝑖
𝑃 𝑐𝑖
0.5
(Eq. 3- 52)
𝑏 𝑖 𝑏 =
𝑇 𝑐𝑖
𝑃 𝑐𝑖
∑
𝑥 𝑖 𝑇 𝑐𝑖
𝑃 𝑐𝑖
(Eq. 3- 53)
Z is obtained by solving the following cubic equation
𝑍 3
− 𝑍 2
+ 𝑍 (𝐴 − 𝐵 − 𝐵 2
)− 𝐴𝐵 = 0 (Eq. 3- 54)

65

The smallest root is chosen for the liquid phase and the largest one for the vapor phase. The value
of Z is then substituted into Eq. 3-49 to calculate the fugacity of each component.
A shooting technique is used to solve the above system of equations. The technique
requires a reasonable initial guess for the flux of each species through the membrane. We begin
integration at the entrance of the reactor where the values of 𝐶 𝑖 𝑚𝑔
and 𝐶 𝑖 𝑝 are known. We then
assume that the gas phase concentration at the gas-liquid interface in the membrane is equal to the
feed concentration, which means that transport is dominated by liquid-phase mass transport (which
is, typically, the case for large membrane thicknesses). Then from the gas-liquid equilibrium
relationship Eq. 3-48 one can calculate 𝐶 𝑖 𝑒𝑞
. From Eq. 3-46 and 3-47 one can then calculate the
flux at the gas-liquid interface, which then constitutes a good initial guess for getting started with
the shooting calculation. Once the shooting simulation converges at the entrance of the reactor
(grid point 1), one can then propagate to the next grid point 2 in solving the equations. For the
initial guess for the flux at the interface one uses the value of the flux calculated at the grid point
#1. The process is then repeated for grid step 3, etc., till one propagates to the end of the reactor.
3.3.3 Dimensionless Equations
In order to gain further insight into the model behavior and the impact of the various
experimental parameters and conditions, the model equations above were rendered dimensionless.
Table 3- 1 lists the various dimensionless variables and groups, and the dimensionless equations
themselves are shown in the Appendix. A separate version of the code was developed to solve the
dimensionless equations and the results were compared and matched with those from simulating
the original equations.

66

Table 3- 1. Dimensionless variables, parameters and groups
Dimensionless
variable, group or
parameter
Mathematical
expression
Physical definition
𝛿 𝑖
𝐷 𝑖 ,𝑘 𝑒 𝐷 𝐻 2,
𝑘 𝑒
Dimensionless effective Knudsen diffusivity
𝛾 𝑖𝑗

𝐷 𝑖𝑗
𝑒 𝐷 𝐻 2
,𝐶𝑂
𝑒 Dimensionless effective binary diffusivity
𝜔 𝐷 𝐻 2
,𝐶𝑂
𝑒 𝐷 𝐻 2
𝑘 𝑒 -
𝑥 𝑖 𝑃 𝑖 𝑚𝑔
𝑃 𝑡
Mole fraction of component I in the gas phase within the
membrane
𝜉
𝑟 − 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡 − 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒
Dimensionless radius
𝘁
𝑉 𝑉 𝑅 Dimensionless volume variable
𝐾 3
′

𝐾 3
𝑃 𝑡 1
2

Dimensionless reaction constant
𝐾 4
′
𝐾 4
𝑃 𝑡 Dimensionless reaction constant
𝑦 𝑖 𝐹 𝑖 𝐹 𝐹 𝑡 𝐹 Mole fraction of component i at feed side
𝑁 𝑔 ′ ̅̅̅̅

(Ω
𝑔 )
−1
∗ 𝑁 𝑔 ̅̅̅̅
Dimensionless molar flux vector in the gas phase within the
membrane
𝜔 𝑖 𝐷𝑒
𝑖 𝑒 .𝑝 𝐷𝑒
𝑀𝑒𝑂𝐻 𝑒 .𝑝 -
𝑧 𝑖 𝑐 𝑖 𝑙 𝑐 𝑡 𝑒𝑞

Dimensionless concentration in liquid phase within the
membrane
𝐷 𝛼 1

(
𝑤 𝑐 𝐹 𝑡 𝐹 )𝐾 1𝑤 𝑃 𝑡
Damköhler number of the RWGS reaction
𝐷 𝛼 2

(
𝑤 𝑐 𝐹 𝑡 𝐹 )𝐾 1𝑀 𝑃 𝑡 2

Damköhler number of the MeS reaction
𝑃𝑒
𝑔 𝐹 𝑡 𝐹 𝛼 𝑚 𝐹 𝑉 𝑅 Ω
𝑔 Péclet number of the membrane shell-side
𝑃𝑒
𝑙
𝐹 𝑠 0
𝛼 𝑚 𝑃 𝑉 𝑅 Ω
𝑙 Péclet number of of the membrane tube-side
𝑆 ℎ
𝑖 𝐾 𝑖 𝑐 𝑡 𝑒𝑞
Ω
𝑙
Sherwood number of component i

67

3.4 RESULTS AND DISCUSSION
Prior to performing the MeS-MCR experiments, the laboratory set-up in Fig. 1-1 and Fig.
1-2 was used to carry out kinetic studies to determine the parameters of the global reaction rate
expressions (Eqns. 3-1 and 3-2). For that to happen, the liquid inlet and outlet in the reactor are
closed and the reactor is allowed to operate as a conventional PBR. In addition to generating the
experimental data to fit the kinetic rate constants, such experiments also allow one to directly
compare the MR conversions with the corresponding conversions for the PBR system. Table 3- 2
shows the parameter values, including the 95% confidence limits, for the global rate expressions
(Eqns. 3-1 and 3-2) resulting from the fit of the experimental data. Figure 3- 1 shows the iso-
conversion plot that includes the data in Fig. 3-1 and additional PBR data presented in chapter 1.
The global rate expressions appear to do a good job in fitting the experimental data, as one judges
from the iso-conversion plot and the magnitude of the confidence limits in Table 3- 2.
Table 3- 2. Parameter values, including the 95% confidence limits, for the global rate expressions resulting from the
fit of the experimental data
Kinetic constant labeling
This work
Vanden Bussche
A B A B
KA 1m 1.459928 1.07 1.07 36696
KA2 2 18766.2 3453.38 3453.38 --
Kh2 3 7.79461E-7 0.249 0.249 34394
Kh2o 4 4.64815E-11 6.62E-11 6.62E-11 124119
ka1 1w 153463133.88 1.22E10 1.22E10 -94765

68

Figure 3- 1. Iso-conversion plot that including additional PBR data
The MeS-MCR experiments are presented in this Thesis (chapter 1 and chapter 4) and also
in the previous publications by our Group (Li and Tsotsis 2019, Zebarjad, Hu et al. 2019). To fit
the MR model to the experimental data we employ two adjustable parameters: The liquid layer
thickness (𝛿 ) and the mass transfer parameter K0 in Eqn. 3-45. To determine the values of these
parameters, we minimize the value of the objective function 𝐸 = ∑ [𝑋 𝑒𝑥𝑝 − 𝑋 𝑐𝑎𝑙𝑐 ]
2 𝑛 𝑖 =1
where X is
the carbon conversion defined by Eqn. 1- 1, and the subscripts “exp” and “calc” refers to the
experimentally measured and calculated conversions, respectively.
Figure 3-2 presents the MR experimental conversions as reported in (Li and Tsotsis 2019)
as function of catalyst weight/gas molar flow rate (W/F) for two different liquid flow rates. Shown
on the same Figure are the corresponding PBR, the calculated MR conversions and the equilibrium
conversion. The conversions for both the BPR and MR increase with W/F as expected. For the

69

PBR the conversions (for both the model and the experiments) approach the equilibrium
conversion while for the MR the conversions exceed the equilibrium values. Conversions in the
MR are higher for the larger sweep liquid flow rate, indicating the positive impact of the liquid
sweep. For the higher sweep flow rate, the model underpredicts the experimental data by an
average of 7.2 %. The opposite is true for the lower flow rate for which the model overpredicts the
experimental by an average of 5.2%.

Figure 3- 2. Effect of W/F on PBR and MR (calculated and experimental) conversion for two different sweep liquid
flow rates; T = 220 °C, P = 32 bar

Figure 3- 3 shows the calculated and experimental MR conversions as a function of the
sweep liquid flow rate (shown on the Figure is also the corresponding PBR conversion). As
expected, increasing the sweep liquid flow rate increases the MR conversion. The model slightly
overpredicts the experiments for the lower flow rates and underpredicts them for the higher ones.
25 30 35 40 45 50
W/F - g*h/mol
35
40
45
50
55
60
65
70
75
80
Conversion - %
MR(LF=6cc/min)
MR(experimental, LF=6cc/min)
MR(LF=1cc/min)
MR(experimental, LF=1cc/min)
PBR
PBR(experimental)
Equilibrium

70

Figure 3- 3. Effect of sweep liquid flow rate on MR (calculated and experimental) conversions. T = 220 °C, P = 32
bar, W/F = 47.2 g*h/mol.

Figure 3- 4 shows the calculated and experimental MR conversions and the corresponding
BPR conversions as a function of reactor temperature. Shown on the same Figure are the calculated
equilibrium conversions. Since the MeS reaction is exothermic, the equilibrium conversion
decreases with temperature, as expected. The PBR conversion, as is typically the case with
exothermic reactions, first increases with temperature, and then at higher temperatures decreases
as the reactor conversion begins “tracking” the equilibrium conversion. The experimental MR
conversions on the other hand keep increasing with temperature finally crossing the equilibrium
line. The calculated MR convesions are in satisfactory agreement with ethe experimental data.
0 1 2 3 4 5 6 7
LF - cc/min
30
35
40
45
50
55
60
65
70
75
80
Conversion - %
MR
MR(experimental)
PBR

71

Figure 3- 4. Effect of temperature on MR (calculated and experimental MR) and PBR conversion. P = 32 bar, W/F =
47.2g*h/mol, and liquid sweep rate = 1 cc/min

Figure 3- 5 shows the calculated and experimental MR conversions and the corresponding
BPR conversions as a function of reactor pressure. Shown on the same Figure are the calculated
equilibrium conversions. Since the MeS reaction results in a decrease in the total number of moles,
the equilibrium conversion increase with pressure as expected, and so do the experimental PBR
and MR conversions. The calculated MR conversions also increase with pressure and are again in
satisfactory agreement with the experimental data.
190 195 200 205 210 215 220 225 230
T -
°
C
20
25
30
35
40
45
50
55
60
65
70
Conversion - %
MR
MR(experimental)
PBR
PBR(experimental)
Equilibrium

72

Figure 3- 5. Effect of pressure on MR (calculated and experimental MR) and PBR conversion T = 220 °C, W/F =
47.2 g*h/mol, and liquid sweep rate = 1 cc/min

One benefit of having a data-validated model is that one can study the reactor behavior for
a broader region of experimental conditions that can br readily attained in the laboratory with a
small size, one-membrane experimental set-up. Further, such a model can also be used for reactor
scale-up and process design and technical and economic analysis (TEA). In the remainder of this
chapter, the focus will be on gaining a better understanding of the behavior of the MeS-MCR
system. In a separate manuscript, we will address process scale-up and TEA aspects.
Figure 3- 6 shows MR and PBR conversions vs. W/F for four different temperatures. An
interesting aspect of these simulations are the crossovers in the conversion lines observed for both
15 20 25 30 35
P - bar
30
35
40
45
50
55
Conversion - %
MR
MR(experimental)
PBR
PBR(experimental)
Equilibrium

73

the PBR and MR systems. Such behavior was previously reported experimentally for the PBR in
Figure 3- 4, but due to the limited number of experiments carried out, it was not observed
previously for the MeS-MCR.

Figure 3- 6. Conversion vs. W/F for different temperatures. P = 30 bar, CF = 0.625, SN = 2,
𝑎 𝑚 𝐹 𝜌 𝑏 = 0.53 cm
2
/g, and
sweep flow rate = 6 cc/min.
For intermediate values of W/F one observes non-monotonic behavior, with the conversion
becoming maximum at an intermediate temperature value.
Figure 3- 7Error! Reference source not found. shows the conversion vs. W/F for
different pressures. As also observed experimentally (see Figure 3- 5), for a fixed W/F the
conversion for both the PBR and the MCR increases with pressure. For a fixed pressure, as the
W/F increases for the PBR the conversion reaches the equilibrium value, while for the MCR the
conversion continues to increase reaching ultimately (for the higher pressures) single-pass
0 50 100 150 200 250 300 350
W/F - kg*s/mol
0
10
20
30
40
50
60
70
80
Conversion - %
MR, T=215
°
C
MR, T=220
°
C
MR, T=230
°
C
MR, T=240
°
C
PBR, T=215
°
C
PBR, T=220
°
C
PBR, T=230
°
C
PBR, T=240
°
C

74

conversions in excess of 85%, which preliminary TEA calculation inicatate will be sufficient to
avoid the need for unreacted syngas recycle. As the W/F increases, the relative gain in conversion
in the MCR over the PBR (MCR conversion minus PBR conversion divided by PBR conversion),
increases, with the maximum such gains in Figure 3- 7 ranging from 82% for P=20 bar to 76% for
P=50 bar.

Figure 3- 8 shows the conversion vs. W/F for different sweep liquid flow rates. As also observed
experimentally (see Figure 3- 2), MR conversion increases with increasing sweep liquid flow rate,
but the favorable impact diminishes at the higher liquid flow rates. The positive impact of
increasing the sweep liquid flow rate derives from two causes: (i) It enhances the “sweeping
action” by lowering the concentration of products in the permeate side, thus increasing the
concentration gradient driving transport; (ii) it increases the mass transfer coefficient (see Eqn. 3-
45). Though increasing sweep flow rate has a significantly positive effect on conversion, it has
also a downside in that it makes it more challenging to separate the products from the sweep fluid.
So, it is a key operating parameter to be considered in process optimization and scale-up.

75

Figure 3- 7. Conversion vs. W/F for different pressures. T = 220 °C, CF = 0.625, SN = 2,
𝑎 𝑚 𝐹 𝜌 𝑏 = 0.53 cm
2
/g, and
sweep flow rate = 6 cc/min.

The liquid penetration thickness in the membrane structure, 𝛿 , is a key determinant of MCR
performance. Some degree of imbibition in the membrane is desirable to avoid the gas from
bubbling through. Uncontrolled spontaneous imbibition is highly undesirable, however, as it
increases the transport resistance through the membrane, and may also result in unwanted spillage
of the sweep solvent into the reactor side. As outlined in chapter 1, significant efforts are
undertaken to appropriately modify the membrane surface to “discourage” spontaneous solvent
imbibition into the membrane structure. The negative impact of deep solvent penetration on MR
performance is shown in Figure 3- 9. In this case, we allow for three different scenarios: (i) The
0 50 100 150 200 250 300 350
W/F - kg*s/mol
0
10
20
30
40
50
60
70
80
90
Conversion - %
MR, P=20bar
MR, P=30bar
MR, P=40bar
MR, P=50bar
PBR, P=20bar
PBR, P=30bar
PBR, P=40bar
PBR, P=50bar

76

sweep liquid completely penetrates the top membrane layer; (ii) the sweep liquid invades
completely the top two layers; and (iii) the sweep fluid also partially invades the membrane support
layer. Clearly, case 3 is highly undesirable and must be avoided. As shown in Table 3- 2, during
the experiments there is only minimal penetration of the solvent, which only partially fills the top
layer.

Figure 3- 8. Conversion vs. W/F for different liquid flow rates. T = 220 °C, P = 30 bar, CF = 0.625, SN = 2,
𝑎 𝑚 𝐹 𝜌 𝑏 =
0.53 cm
2
/g.
0 50 100 150 200 250 300 350
W/F - kg*s/mol
0
10
20
30
40
50
60
70
80
Conversion - %
MR, LF=2cc/min
MR, LF=3cc/min
MR, LF=4cc/min
MR, LF=5cc/min
MR, LF=6cc/min
PBR

77

Figure 3- 9. Conversion vs. W/F for different liquid thicknesses as indicated in the . T = 220°C, P = 30bar, CF =
0.625, SN = 2,
𝑎 𝑚 𝐹 𝜌 𝑏 = 0.53cm
2
/g, sweep flow rate = 6 cc/min.
The lab-scale MeS-MCR accommodates only one membrane which limits the membrane
area available for transport. Having a data-validated model allows one to investigate the impact of
increasing the available membrane area. Figure 3- 10 shows these simulations. Here we plot the
MR conversion vs. W/F for various values of
𝑎 𝑚 𝐹 𝜌 𝑏 , which represent the ratio of membrane area to
catalyst weight.
𝑎 𝑚 𝐹 𝜌 𝑏 = 0.53 cm
2
/g for the laboratory experiments. Clearly, increasing this ratio has
a significant positive impact on MR performance. However, one cannot increase that ratio with
“impunity” as beyond a certain value the negative impact of reactant loss, albeit small, begins to
have an adverse effect. This clear in Figure 3- 10 where the conversion line for the case for which
0 50 100 150 200 250 300 350
W/F - kg*s/mol
0
10
20
30
40
50
60
70
80
Conversion - %
MR, 1st layer filled (3 m)
MR, 2nd layer filled (23 m)
MR, 3nd layer partically filled (500 m)
PBR

78

𝑎 𝑚 𝐹 𝜌 𝑏 = 2.0 cm
2
/g for a certain value ofW/F and above crosses over the corresponding line for
𝑎 𝑚 𝐹 𝜌 𝑏 =
3.0 cm
2
/g.

Figure 3- 10. Conversion vs. W/F for different membrane surface areas. T = 220°C, P = 30bar, CF = 0.625, SN = 2,
and sweep flow rate = 6 cc/min.
The MCR experiments employing the TGDE solvent were for a fixed syngas composition,
specifically for SN~2 and CF=0.625 (MCR experiments with the IL solvent for a broader range of
compositions are reported in chapter 4). To investigate the impact the feed composition has on MR
performance we utilized the model to calculate conversion for four different compositions: (SN=2,
CF=0.714), (SN=3, CF=0.714), (SN=2, CF=0.625), (SN=2, CF=0.0.625) with the results shown

79

if Figure 3- 10. Looking at Figure 3- 11, one observes for feeds with a fixed SN increased CF (i.e.,
more CO-rich syngas) results in a higher conversion for both the PBR and the MCR. Similar trends
are observed for feeds with a constant CF when one increases the SN, i.e., when employing syngas
with higher than stoichiometric hydrogen content.

Figure 3- 11. Conversion vs. W/F for different feed compositions, as indicted in the insert. T = 220 °C, P = 30 bar,
𝑎 𝑚 𝐹 𝜌 𝑏 = =0.53 cm
2
/g, sweep flow rate = 6 cc/min.

In Figure 3- 12 we plot MCR conversion vs. the solvent flow rate for the TGDE solvent.
On the same Figure we also plot the conversions for two hypothetical solvents. For the first solvent
(A) the SRK parameters for water and methanol are taken as 0.0088, 0.004 (as opposed to the
0 50 100 150 200 250 300 350
W/F - kg*s/mol
10
20
30
40
50
60
70
80
Conversion - %
SN=2, CF=0.625
SN=3, CF=0.625
SN=2, CF=0.714
SN=3, CF=0.714
SN=2, CF=0.625 PBR
SN=3, CF=0.625 PBR
SN=2, CF=0.714 PBR
SN=3, CF=0.714 PBR

80

experimental values of 0.044, 0.002 for the TGDE employed in this paper). For the 2
nd
solvent (B).
the SRK parameters for water and methanol are taken as -0.0088, -0.004. The advantage that
solvents with higher solubility (e.g., IL’s) offer is clear from this Figure.

Figure 3- 12. Conversion vs. liquid flow rate for different solvents. T = 220 °C, P = 30 bar,
𝑎 𝑚 𝐹 𝜌 𝑏 = =0.53cm
2
/g,

The advantage of making the reactor equations dimensionless is that such equations offer
one the ability to gain a deeper insight into the system behavior, and to identify groupings of
experimental parameters (dimensionless groups) on which reactor performance is uniquely
0 50 100 150 200 250 300 350
W/F - kg*s/mol
0
10
20
30
40
50
60
70
80
Conversion - %
MR, low solubility
MR, TGDE
MR, high solubility
PBR

81

dependent upon. Two such key dimensionless groups that strongly influence reactor behavior are
the two Damköhler numbers, 𝐷 𝛼 1
for the RWGS reaction and 𝐷 𝛼 2
for the MeS. In Figure 3- 13, we
keep all dimensionless groups and parameters in Table 3- 1 constant (other than the two Damköhler
numbers), their values calculated from the values of the operating reactor parameters shown on the
Figure caption. We then analyze and plot the MR and PBR conversion as a function of (Da2/Da20),
where Da10 is the value of the Damköhler number (for the MeS reaction) for the experimental
catalyst studied in this work, and Da2 is the corresponding Damköhler number of a hypothetical
catalyst with different MeS activity. We do this for three different values of (Da1/Da10), where
Da10 is the value of the Damköhler number (for the RWGS reaction) for the experimental catalyst
studied in this work and Da1 is the corresponding RWGS Damköhler number of the same
hypothetical catalyst. From Figure 3- 13 we observes that increased MeS activity of the catalyst
(for a fixed RWGS activity) results in increased PBR conversions, however, the benefit eventually
diminishing as the reactor approaches equilibrium. For the MCR, however, increased Da2 continue
to have a beneficial impact on reactor performance. When keeping Da2 constant while increasing
Da1 the conversion increases first for both the PBR and the MCR, but then the favorable impact
diminishes for larger values of Da1 for both the PBR and the MCR.

82

Figure 3- 13. Conversion vs. Da 2/Da 20 for different Da 1/Da 10. T = 220 °C, P = 30 bar,
𝑎 𝑚 𝐹 𝜌 𝑏 = =0.53cm
2
/g, W/F = 47.2
g*h/mol, sweep flow rate = 6 cc/min.

3.5 CONCLUSIONS
In this chapter, simulation of a novel membrane reactor has been investigated through a
dimensional and dimensionless model. The reactor uses a sweep liquid (high solubility toward
methanol) inside the membrane for MeOH in-situ removal. The MeS reaction occurs in the shell
side of the reactor. The advantages of this design compared to the absorptive reactor system are
the decreased interaction between the solvent and the catalyst and loss of the solvent. The both
models were indicating matching conversion results and predicted up to 85% conversion per single
10
-1
10
0
10
1
Da
2
/Da
20
20
30
40
50
60
70
80
Conversion - %
MR, Da
1
/Da
10
=0.1
MR Da
1
/Da
10
=0.2
MR Da
1
/Da
10
=0.5
MR, Da
1
/Da
10
=1
MR, Da
1
/Da
10
=10
PBR, Da
1
/Da
10
=0.1
PBR Da
1
/Da
10
=0.2
PBR Da
1
/Da
10
=0.5
PBR, Da
1
/Da
10
=1
PBR, Da
1
/Da
10
=10

83

pass of syngas in all of the simulations MR results showed higher conversion compared to the
traditional packed bed reactor. MATLAB used to optimize the liquid thickness inside the
membrane with the previous experimental work we have done with the same system (Zebarjad,
Hu et al. 2019). An extra dimensionless steady state heterogenous model was created to validate
the dimensional model which the results were successfully the same. The validated model in this
work will make the next step scale up from the laboratory setup to a plant version feasible and the
parameters studied in this work will significantly affect the design of the future plant version setup.
A key future task in our ongoing studies will be larger TEA studies on the scale up version of the
design.

84

Nomenclature
𝑎 𝑚
Membrane geometric area per unit of reactor
volume (m
2
/m
3
)
𝑋 𝑐
Conversion (%)
𝐵 0

Permeability coefficient
𝑥 𝑖
Mole fraction of component i at
gas side within membrane
𝑐 𝑖
Concentration of component i (mol/ m
3
)
𝑦 𝑖
Dimensionless molar flow rate at
feed side
𝑑 𝑚
Membrane diameter (m)
𝑧
Membrane length variable (m)
𝑑 𝑝
Average pore size (m)
𝑧 𝑖
Dimensionless concentration at
membrane liquid phase
𝐷 𝑖
Wilke-Chang equation of component i (m
2
/s)
Z
Compressibility factor
𝐷 𝑖𝑗

Binary gas phase diffusivity of component i and
j (m
2
/s)
Greek letters

𝐷 𝑖 ,𝑘
Knudsen diffusivity of component I (m
2
/s)
𝛼 𝑖𝑖

First dusty gas model diffusivity
matrix element
𝐷 𝑖 𝑒 .𝑝
Effective diffusivity of Wilke-Chang equation
of component i (m
2
/s)
𝛼 𝑖𝑗

Second dusty gas model diffusivity
matrix element
𝐷 𝐷𝐺𝑀 ⃑⃑⃑⃑⃑⃑⃑⃑⃑

Duty gas model diffusivity matrix
𝛼 ′
𝑖𝑖

First dimensionless dusty gas
model diffusivity matrix element
𝐷 𝐷𝐺𝑀 ′
⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑

Dimensionless duty gas model diffusivity matrix
𝛼 ′
𝑖𝑗

Second dimensionless dusty gas
model diffusivity matrix elements
𝐷𝛼
Damköhler number
𝛾 𝑖𝑗

Dimensionless binary diffusivity
𝐹 𝑖
Molar flow rate of component i (mol/s)
𝛿
Liquid thickness
𝐹 𝑠 0

Total initial solvent feed flow rate (mol/s)
𝛿 𝑖
Dimensionless Knudsen diffusivity
𝐹 𝑡
Total molar flow rate (mol/s)
𝘀
Porosity
𝑓 𝑖
Fugacity of component i
𝘁
Dimensionless volume variable
𝑘 𝑖
External mass transfer coefficient in membrane
liquid phase of component I (m/s)
𝜇
Viscosity (centipoises)
𝐾 𝑖 𝑜𝑣

Overall external mass transfer coefficient in
membrane liquid phase of component i (m/s)
𝜌 𝑏
Bulk density (kg/m
3
)
𝐾 𝑒𝑞𝑚
Equilibrium constant for 𝑟 𝑀𝑒𝑂𝐻
𝜗 𝐴
Molar volume of solute A
(cm
2
/mol)
𝐾 𝑒𝑞𝑚 ′

Factor contains 𝐾 𝑒𝑞𝑚
for dimensionless
equations
𝜈 𝐿
Average velocity of liquid in
membrane (m/s)
𝐾 𝑒𝑞𝑤
Equilibrium constant for 𝑟 𝑅𝑊𝐺𝑆
𝑣 𝑖
Molecular volume (cm
3
/g-mol)
𝐿
Reactor length (m)
𝑣 𝑖 𝑚
Molar volume (m
3
/mol)
𝑀 𝑖
Molecular weight of component i (kg/kmol)
𝜉
Dimensionless radius
𝑀 𝐵
Molecular weight of solvent B (kg/kmol)
𝜌 𝑏
Bulk density (kg/m
3
)
𝑁 𝑖
Molar flux of component i (mol/ m
2
s)
𝜏
Tortuosity
𝑁 𝑔 ⃑⃑⃑⃑

Molar flux vector of gas phase within membrane
𝜐 𝑖𝑗

Stoichiometric coefficients
𝑁 𝑔 ′ ⃑⃑⃑⃑⃑

Dimensionless molar flux vector of gas phase
within membrane
𝜑 𝐵
Associative parameter for solvents
𝑁 𝑖 𝑚𝑔

Molar flux of component i at membrane gas
phase (mol/ m
2
s)
𝜔 𝑖
Dimensionless diffusivity at
membrane liquid phase
𝑁 𝑖 𝑚𝑔
′

Dimensionless molar flux of component i in
membrane gas phase
𝜔
Dimensionless parameter
𝑁 𝑖 𝑚𝑙

Molar flux of component i at membrane liquid
phase
(mol/m
2
s)
Ω
𝑔
Factor of dimensionless molar flux
at membrane gas phase (m
2
s/mol)
𝑁 𝑖 𝑚𝑙
′

Dimensionless molar flux of component i in
membrane liquid phase
Ω
𝑙
Factor of dimensionless molar flux
at membrane liquid phase (m
2
s/mol)
𝑃 𝑖
Pressure of component i (bar)
Superscripts

𝑃 𝑖 𝑚𝑔

Pressure vector of gas phase within membrane
0
Inlet conditions

85

𝑃 𝑡
Total pressure (bar)
e
Effective
𝑃𝑒
Péclet number
eq
The gas-liquid interface within in
the membrane
𝑟 𝑖
Rate of reaction of component i
F
Feed side
𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒
Inside membrane radius (m)
g
Gas phase
𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡
Outside membrane radius (m)
l
Liquid phase
𝑅
Gas constant (J/mol
-1
K
-1
)
mg
Gas phase within membrane
S
Sweep ration defined in equation
ml
Liquid phase within membrane
𝑆 ℎ
𝑖
Sherwood number of component i
z
Permeate side
𝑇 𝑖
Temperature of component i (K)
s
Tube side
𝑇 𝑐𝑖

Critical temperature of component i (K)
Subscripts

𝑃 𝑐𝑖

Critical pressure of component I (bar)
i
0

Initial condition of component i
𝑉
Reactor Volume variable (m
3
)
i
Component i
𝑉 𝑅
Reactor Volume (m
3
)
j
Component j
𝑤 𝑖
Dimensionless molar flow rate at permeate side
t
Total

86

CHAPTER 4: EXPERIMENTAL INVESTIGATION OF THE
APPLICATION OF IONIC LIQUIDS TO METHANOL
SYNTHESIS IN MEMBRANE REACTORS WITH PURE CO2
FEEDS
4.1 MOTIVATION
The goal of this project is to investigate a transformational, low-cost reactive post-
combustion CO2 separation technology that will allow the continued competitive operation of
existing and planned fossil fuel-based power generation infrastructure in a low-carbon future
energy landscape. The proposed novel CO2 reactive separation system is appropriate for use in
both new and existing power plants, requires no media regeneration, and produces the separated
carbon in the form of MeOH, a valuable liquid product that is more convenient to sequester, if so
desired, than gaseous CO2 or which can be sold as fuel (to replace the use of other fossil fuels, still
offering zero net emissions), thus providing a way to monetize the carbon captured to offset
process costs. Thus, the new process offers promise to deliver economics that go beyond present
2
nd
generation CO2 separation system performance.
Waste CO2 separation via MeS has been discussed in recent years (Zare, Khanipour et al.
2019). The severe thermodynamic limitations facing MeS makes it not possible, however, to
convert (separate) in a single pass a large fraction of the CO2, thus requiring recycling of the
unconverted gas. This, of course, is not a realistic prospect for dilute CO2 streams like flue gas.
One option here is to first process the flue gas via a conventional route, e.g., absorption (Chen, Dai
et al. 2021) or adsorption (Hefti and Mazzotti 2018) to separate the CO2, and then employ it to
produce methanol (or other alcohols), the goal here being to monetize at least part of the CO2

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produced to defray some of the operationg costs. Such an approach is hampered by the substantial
energy penalty associated with the initial step of CO2 separation out of the flue gas, but it is also
negatively impacted by the thermodynamics and slow kinetics of CO2-based MeS.
In the past, as described in the first three chapters of the Thesis, our Group developed a novel
MeS process, employing a membrane contactor reactor (MCR) system that attains carbon
conversions significantly higher than equilibrium from syngas, approaching under some
conditions 90% or higher. The driver for the development of the MeS-MCR technology is its
application as a distributed process for waste biomass utilization, as a companion technology to
thermochemical biomass conversion employing an air-blown gasifier. The syngas produced from
such a gasifier contains a large fraction of N2, and high single-pass conversions are again required,
since recycle of large volumes of such dilute unconverted syngas is also not economically feasible.
In this chapter, we study the feasibility of using the MeS-MCR system to convert the CO2 in the
flue gas from power plants into MeOH at high enough efficiencies to satisfy current carbon capture
and storage (CCS) targets of 80 - 90% or higher. In contrast with the distributed biomass
application, where one deals with a CO-rich syngas, the CCS case involves a CO2/N2 feed (or pure
CO2 in the case for which one separates the CO2 from the flue gas first for further conversion at a
later stage). Conventional MeS catalysts show notoriously slow kinetics for direct CO2 conversion
into MeOH. The presence of large CO2 fraction in syngas, in addition, implies the added
consumption of H2 and the production of large quantities of H2O that is known to inhibit the
catalytic kinetics (Keshavarz, Mirvakili et al. 2020).
Our focus in this chapter is on validating the application of the MeS-MCR system for
processing pure CO2 feeds. For that, we combine the MeS-MCR system with a separate reactor
that precedes it which converts the CO2 stream into a syngas mixture via the reverse water gas

88

shift (RWGS) reaction. In this preliminary effort the composition of the exit stream from the
RWGS reactor (RWGSR) is simulated, on the assumption that the reactor reaches equilibrium.
The key focus is instead on validating experimentally the ability of the MeS-MCR to process as a
feed the RWGSR exit stream. We investigate the performance of the individual RWGSR and MCR
subsystems and of the overall RWGSR/MCR device for a broad range of pressures and
temperatures, sweep liquid flow rates, reactor space times and flue gas feed compositions. The
preliminary findings have been encouraging, and research is currently ongoing in the Group to
experimentally validate the performance of the integrated (RWGSR+MeS-MCR) system.

4.2 INTRODUCTION
The continued reliance on fossil fuels like coal, oil and natural gas, has resulted in increased
CO2 emissions to the point where they have become today a global concern (von der Assen, Müller
et al. 2016). Long-term, the solution to this technical challenge is to replace the fossil fuels with
alternative renewable energy sources (e.g., solar, geothermal, wind-power, etc.). In the interim
period though, it is important that we separate, capture, and sequester the CO2 generated so that it
does not end up as emissions to the atmosphere. Current CCS processes are both capital- and
energy-intensive, however. So, a focus in recent years has been on developing technologies (known
as CCU processes) that utilize the CO2 captured to convert it into fuels and chemicals, the
motivation here being through the sale of such products to be able to defray at least some of the
significant costs associated with CCS (Rafiee, Khalilpour et al. 2018). For such technologies to
have an impact in addressing the CO2 emissions challenge, the chemical(s) produced must have
widespread use and significant market potential. One such chemical is MeOH whose potential
production from waste CO2 has been studied in recent years (Samimi, Hamedi et al. 2019).

89

Direct catalytic conversion of CO2 into MeOH has been receiving increased attention
(Doss, Ramos et al. 2009, Pontzen, /Liebner et al. 2011) with a number of catalysts being prepared
and studied. The conventional Cu/ZnO/Al2O3 catalyst, which was used in Chapter 1 of this Thesis
continues to be the most widely utilized catalyst formulation for converting CO2 into MeOH
because of its good activity and low cost. However, this catalyst was originally developed for the
conversion of CO-rich syngas mixtures into MeOH and is, therefore, not optimized for the
conversion of pure CO2 or CO2-rich mixtures; current challenges include improving its low
temperatures activity, overcoming time-on-stream deactivation, and minimizing by-product
formation of by-products (Dang, Yang et al. 2019, Guil-López, Mota et al. 2019).
A number of Groups have modified the conventional Cu-Zn-based catalyst by substituting
in its formulation the Al2O3 using with other trivalent or tetravalent metal oxides. One of the most
commonly studied such oxides is ZrO2 (Tisseraud, Comminges et al. 2015, Dang, Yang et al.
2019), which has a weaker hydrophilic character compared to alumina. This is reported to enhance
Cu dispersion and stability and to impede the absorption of water (Tisseraud, Comminges et al.
2015). It has also been reported, the substitution of Al2O3 by ZrO2 increases the basicity of the
catalyst (Tisseraud, Comminges et al. 2015) which in turn favors the selectivity to methanol during
MeS from CO2-rich syngas mixtures.
Non-Cu type catalysts have also been studied employing noble metals, primarily Pd
(Bahruji, Bowker et al. 2016, García-Trenco, Regoutz et al. 2018, Din, Shaharun et al. 2019) and
to a lesser extent Au (Li, Na et al. 2017, Wu, Zhang et al. 2017). Pd is very active for the
hydrogenation of CO2, with its selectivity to methanol depends on the type of support and
promoters utilized (Bahruji, Bowker et al. 2016). Pd when supported on ZnO forms s bimetallic
PdZn alloy which acts as active phase for the selective production of methanol (Bahruji, Bowker

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et al. 2016). The use non-noble metals and (Cu, Co, and Fe) supported on Mo2C as active catalysts
for the selective hydrogenation of CO2 into methanol under mild conditions (135–200 ºC in a liquid
solvent of 1,4-dioxane) was reported by Chen, Choi et al. (2016). The Mo2C served as a support
and co-catalyst for the reaction. Using pure Mo2C, methanol was the main product at 135 ºC, while
hydrocarbons, methanol, ethanol, and C2+ compounds were produced at 200 ºC. The addition of
Cu to the Mo2C improved the production of methanol, while the addition of Co and Fe only
increased the production of C2+ hydrocarbons (Chen, Choi et al. 2016).
There have also been a number of industrial efforts for the direct conversion of CO2 into
methanol, One of the earlier industrial-scale CO2 to methanol processes was developed by Lurgi
AG in 1990’s (Konig and Gohna 1995, Goeppert, Olah et al. 2018). A two-stage process was
developed. A make-up gas consisting of ~20% of carbon oxides (CO+CO2) in H2 is pre-converted
in an adiabatic fixed bed reactor in a once- through operation before entering a methanol synthesis
loop incorporating a steam producing non-isothermal reactor. Methanol formation and WGSR
proceed simultaneously, and methanol and water are separated to increase the methanol conversion
in the second reactor.
A single-stage CO2 to methanol pilot-plant investigation was carried out by (Pontzen,
Liebner et al. 2011). They reported a single-pass conversion of 30-40% over the commercial
Cu/ZnO catalyst with a feed H2/CO2 ratio equal to 3 at a temperature of 250 ºC and a pressure of
70-80 bar. The process was done in the via Lurgi's MTP® process. Specht and coworkers (Specht,
Bandi et al. 1998, Specht 2012) studied the conversion of atmospheric CO2 and hydrogen into
methanol in a bench-scale packed bed reactor over a Cu/ZnO catalyst and reported a 23%
conversion per pass. A lab-scale CO2 into MeOH conversion set-up was developed by Morgan and
Acker (2015). The hydrogen for the reaction is produced on-site via electrolysis and the CO2 is

91

from decentralized sources. The overall efficiency of methanol production and electricity
combined are very low (~16%).
A two-stage process for CO2 hydrogenation into methanol (named CAMERE) was
developed by the Korean Institute of Science and Technology (Joo, Jung et al. 1999, Park, Chang
et al. 2004). The first stage is a RWGSR that operates at high temperatures, 600-700 °C, with the
goal of converting CO2 into CO (conversion efficiency of ~60%). The exit stream from the
RWGSR, after removal of the water produced, is then fed into the second stage MeS reactor.
Although the methanol conversion was increased due to the increase in CO content of the feed and
water removal before the methanol synthesis reactor the reported overall space time yields (kg lcat
-
1
h
-1
), excluding the catalyst volume in the RWGSR, are almost the same with the values reported
for the direct CO2 hydrogenation pilot plants (Specht, Bandi et al. 1998, Matsushita, Haganuma et
al. 2011, Pontzen, Liebner et al. 2011, Matsushita, Haganuma et al. 2013).
In 2014, Carbon Recycling International (CRI) reported (Stefansson 2015) the operation of
a commercial scale CO2 to methanol plant in Svartsengi, Iceland. The plant uses a conventional
Cu/ZnO-catalyst and operates at 250
o
C and 100 atm. It utilizes 5600 tons/per year of CO2 released
by a nearby geothermal power plant to produce 4000 tons/year of methanol. The hydrogen used
in the process is produced by an alkaline electrolysis unit (Sigurbjornsson 2013). We do not know
of any other commercial plant presently producing MeOH from pure CO2 feeds.
In summary, there is a lot of interest today in ways to beneficially utilize waste CO2 and its
conversion to MeOH appears to be a promising route. Direct conversion of CO2 into MeOH faces
technical hurdles, however, that include slow kinetics and sensitivity to water of conventional MeS
catalysts, and severe thermodynamic limitations. Most of the efforts to date have focused on the
development of novel catalysts with improved kinetics over the conventional Cu-Zn MeS catalyst.

92

However, such developments do not address the thermodynamic limitations associated with MeS
and the correspondingly low single-pass conversions. In this work we study a novel direct CO2
into MeOH conversion process that overcomes the limitations faced by current CO2-based MeS
processes. The process is inspired by the two-step CAMERE design (Joo, Jung et al. 1999, Park,
Chang et al. 2004). However, for the second stage instead of a conventional PBR our process
employs the MeS-MCR system discussed in chapters 1 and 2 of this Thesis and in (Li and Tsotsis
2019, Zebarjad, Hu et al. 2019) that helps overcome the thermodynamic limitations associated
with the MeS reaction by removing MeOH and water in situ during the reaction and which attains
conversions nearing 90% or higher. The MeS-MCR concept also helps to overcome the other key
challenge that MeS faces, which is accommodating the exothermicity of the reaction via the
recirculating sweep solvent. Its modular character, furthermore, makes it ideal for distributed type
of applications, which is not always the case for the large scale commercial MeS processes which
benefit from economy of scale (Dieterich, Buttler et al. 2020) and do not always down-scale
properly.
Though work is ongoing in the Group to experimentally validate the novel two-stage
RWGSR/MeS-MCR process, the focus in this chapter is on the study of its MeS-MCR component,
since the operation of the RWGSR is presently well understood (Chen, Chen et al. 2020, González-
Castaño, Dorneanu et al. 2021). So, the assumption here is that the RWGSR has been optimally
designed to attain thermodynamic equilibrium for all condition studied, and the focus is instead on
validating the ability of the MeS-MCR to beneficially process the gas mixtures exiting the
RWGSR

93

4.3 EXPERIMENTAL SECTION
Technical details regarding the experimental MeS-MCR set-up, the catalyst and membrane
used, membrane modification, gas and liquid measurement methods system and data analysis are
described in chapter 1 of the Thesis and also in (Li and Tsotsis 2019). The experimental set-up for
the combined RWGSR/MeS-MCR system is currently under construction in our Group (see Figure
4- 1 for a schematic) but at the moment of the writing of this Thesis there are no experimental data
available on its performance.

Figure 4- 1. 2-D P&ID of the combined RWGSR and MCR-MeS system

4.4 RESULTS AND DISCUSSION
As noted previously, in this chapter the focus is on experimentally investigating the
performance of the MeS-MCR subsystem. We have assumed, therefore, to that the RWGS catalyst
we use is sufficiently active so that equilibrium conditions are attained at the RWGSR exit for all

94

conditions studied. We proceeded then to calculate these exit compositions which were
subsequently utilized as feeds in the MeS-MCR experiments. In the simulations, we utilize the
equilibrium constant reported by Choi and coworkers (Choi and Stenger 2003). We also assume ,
in this preliminary project phase, that the feed to the RWGSR consists of a CO2/H2 gas mixture
(later in this research, once our studies with pure CO2 feeds are completed, we plan to also
investigate the direct utilization of flue gas). In Figure 4- 2 we plot the equilibrium conversion
versus the H2:CO2 molar ratio in the RWGSR feed. Since the RWGS reaction is endothermic, as
expected, the CO2 conversion increases with temperature. The CO2 conversion also increases as
the H2:CO2 ratio increases.
In the experiments with the MeS-MCR (but also for its MeS-PBR counterpart), in addition
to the reactor temperature (T), pressure (P), and inlet molar flow-rate (specifically, the catalyst
weight to molar flow rate ratio (W/F)), the feed composition is a key consideration. Traditionally,
in MeS reactor design the syngas feed composition is characterized by two measures: The carbon
factor (CF = mol CO/(mol CO + mol CO2)), and the feed stoichiometric number (SN = (mol H2-
mol CO2)/ (mol CO + mol CO2)). In the proposed process, the outlet flow from the RWGS reactor
constitutes the feed to the MeS reactor, so the SN remains invariant among the two reactors (SN=2
corresponds to the stoichiometric ratio of H2/CO2=3). The CF depends on the conversion of the
RWGSR and it is plotted for different temperatures as a function of the the H2/CO2 molar ratio in
the feed of the RWGSR in Figure 4- 3. The CF increases with increasing temperature and H2/CO2
molar ratio. Typically, conventional MeS reactors operate with a CF in the range of 0.6 - 0.7, which
is also the range of CF values in which we operated previously the MeS-MCR (Li and Tsotsis
2019, Zebarjad, Hu et al. 2019). For a feed SN=2 (corresponding to a stoichiometric H2/CO2 feed
molar ratio equal to 3) to attain such CF values the operating RWGSR temperatures should be in

95

the range of 873 K - 973 K, which is in line with the operating temperatures of the original
CAMERE process. Operating the RWGSR at such high CO2 conversion levels is costly (the
RWGS reaction is strongly endothermic) so a key objective of this research was to investigate the
performance of the MeS-MCR system when operating with feeds with significantly lower CF
values.

Figure 4- 2. CO 2 equilibrium conversion of the reverse water gas shift reaction versus the feed H 2:CO 2 molar ratio at
different temperatures.

0
10
20
30
40
50
60
70
80
0 1 2 3 4 5
CO
2
EQUILIBRIUM CONVERSION %
RWGSR Feed H
2
:CO
2
RATIO
T=673K
T=773K
T=873K
T=973K

96

Figure 4- 3. Carbon factor of the reverse water gas shift reaction outlet versus the feed H 2:CO 2 ratio at different
temperatures and equilibrium pressure.

4.4.1 PBR Experimental Results
Figure 4- 2Figure 4- 4 shows the experimental carbon (CO+CO2) conversions measured in
the MeS-MCR set-up, in its operational mode as a PBR (with the inlet and outlet of the membrane
being kept closed and no liquid sweep flowing). In these experiments, since the lab-scale RWGSR
is not presently operational, we used a simulated RWGSR exit stream, which, in line with the
original CAMERE process, contains only CO/CO2/H2, on the assumption that the heat exchanger
downstream of the RWGSR (see Figure 4- 1) will remove all the H2O from the RWGSR exit
stream (during the operation of the combined RWGSR/MeS-MCR experimental system, we expect
some minor concentration of H2O to remain in the MCR feed stream since we use tap water as the
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 1 2 3 4 5
Carbon Factor of the RWGSR Outlet
RWGSR Feed, H
2
:CO
2
Ratio
T=673K
T=773K
T=873K
T=973K

97

cooling fluid – if that turns out to have a significant impact on performance, we may consider using
a different coolant). The reason for doing so, is because mathematical simulations show that
removing the water from the feed stream has a very positive impact on MeS-PBR conversion, and
on the MeS-MCR performance as well, though less so since a key characteristic of the latter reactor
is to remove in situ the water that is produced. Removing the water from the exit stream confers
additional process complexity, since one has to cool the stream first and then reheat to the
temperature of the MeS step. In future efforts, we will investigate therefore whether only partial
removal of the water content of the RWGSR exit stream is a more optimal condition for the
operation of the combined system.
In the experiments presented here, SN=2, corresponding to a H2:CO2 feed molar ratio for
the RWGSR equal to 3, as noted above (using H2:CO2 ratios higher than 3 will increase the feed
CF as Figure 4- 2 shows, but it also requires a higher quantity of H2 to be used, which for CCS
processes implies a higher energetic penalty per ton of CO2 avoided). One observes from Figure
4- 4 that the CF has a significant impact on conversion, with the conversion (at constant reactor
temperature) increasing substantially as CF increases. The impact of temperature is typical of that
of exothermic reactions, with conversion first increasing as the temperature increases and then
decreasing again, as the exit conditions begin tracking the equilibrium conversion line, since for
exothermic reactions the equilibrium conversion decreases with temperature. Figure 4- 5 shows
the carbon conversions in the MeS-PBR as a function of CF and pressure. Pressure, as expected,
has a positive impact on reactor conversion.
The surfaces shown in Figure 4- 4 and Figure 4- 5 represent the results of simulations of
the PBR utilizing the MeS kinetics previously presented in chapter 3. There is good agreement
between the experimental data and the model results for a broad range of temperatures, pressures,

98

and feed compositions, which validates these global rate expressions. The same kinetics were
utilized in chapter 3 to simulate the behavior of the MeS-MCR component, and will also be used
in the future to study the performance of the combined RWGSR/MeS-MCR system.

Figure 4- 4. PBR carbon conversion versus temperature and CF at different pressures a) P=20 bar, b) P=25 bar, c)
P=30 bar. Other conditions SN=2 and W/F= 20 kg*s/mol (red dots represent the experimental data and the surfaces
are calculated using the kinetics model presented in chapter 3).

99

Figure 4- 5. PBR carbon conversion versus pressure and CF at different temperatures a) T=200 ℃, b) T=220 ℃, c)
T=240 ℃. Other conditions SN=2 and W/F= 20 kg*s/mol (red dots represent the experimental data and the surfaces
are calculated using the kinetics model presented in chapter 3).

4.4.2 Membrane Reactor Experiments
In chapter 1 we carried out experiments with the MeS-MCR for two CF values equal to
0.625 and 0.714. Here, we carry out MeS-MCR experiments with two lower CF values equal to
0.37 and 0.502. These experiments together with the previous tests cover the whole range of feed
conditions one would encounter during the operation of the combined RWGSR/MeS-MCR
system, see Figure 4- 4 and Figure 4- 5. In Figure 4- 6 we plot the carbon conversions for the MeS-
MCR and the PBR as a function of reactor pressure for three different temperatures. On the same
a)
b)
c)

100

Figure we also plot the calculated equilibrium conversions under the same conditions. The left-
side plots in Figure 4- 6 are for CF=0.37 while the right-side plots are for CF=0.502.

Figure 4- 6. MCR and PBR and calculated equilibrium carbon conversion versus pressure at different temperatures
a) T=200 ℃, top plots b) T=220 ℃, middle plots c) T=240 ℃, bottom plots. Other conditions SN=2 and W/F= 30
kg*s/mol CF=0.37 (left-side plots) and CF=0.502 (right side plots).

For all cases studied the MCR conversions exceed the corresponding PBR conversions, the
differences in relative terms (conversion of MCR minus conversion of PBR divided by conversion
of PBR) terms being in the range of 11-35%. For the higher temperatures the MCR conversions
even exceed the calculated equilibrium conversions. The positive impact of working with feeds
with higher CF values is clear from comparing the plots on the left side of the Figure with those
on the right side. Note, furthermore, that the conversion of the MCR operating with the low CF
feeds (left-side plots) exceeds the corresponding conversion of the PBR operating with the higher
CF feed.

101

In Figure 4- 7 we plot the carbon conversions for the MeS-MCR and the PBR as a function
of W/F for three different temperatures. The plots on the left side of the Figure are for feeds with
CF=0.37 while those on the right side are for feeds with CF=0.502. Again, as the data in Figure 4-
7 indicate the MCR attains conversions which are significantly higher than those attained by the
PBR and for the higher temperatures also significantly exceed the calculated equilibrium values
as well. The PBR behavior shown in the two Figures is complex, in line with the behavior observed
previously (see Figure 3- 5 in chapter 3) with the CF=0.625 feeds.

Figure 4- 7. MCR and PBR and calculated equilibrium carbon conversion versus weight of the catalyst/gas flow rate
(W/F) at different temperatures. Equilibrium conversion does not vary with W/F and is, therefore, shown as a
horizontal line. Other conditions SN=2 and P=30 bar. CF=0.37 (left-side plots) and CF=0.502 (right side plots).

In Figure 4- 8 we plot the carbon conversions for the MeS-MCR and the PBR as a function
of W/F for three different pressures. The plots on the left side of the Figure are again for feeds
with CF=0.37 while those on the right side are for feeds with CF=0.502. Once more, as the data in
Figure 4- 8 indicate the MCR attains conversions which are significantly higher than those attained

102

by the PBR and for the conditions in Figure 4- 8 also significantly exceed the calculated
equilibrium values as well. As pressure increases both the PBR and the MCR conversions increase
as one expects form a reaction like MeS that results in a reduction in the number of moles. This is
true for both feeds, in line with the observations made with the feed with CF=0.625 in chapter 1.

Figure 4- 8. MCR and PBR and calculated equilibrium carbon conversion versus weight of the catalyst/gas flow rate
(W/F) at different pressures. Equilibrium conversion does not vary with W/F and is, therefore, shown as a horizontal
line. Other conditions SN=2 and T= 220
o
C. CF=0.37 (left-side plots) and CF=0.502 (right side plots).

103

Figure 4- 9. MCR and PBR and calculated equilibrium carbon conversion versus liquid flow rate at various
temperatures. PBR and equilibrium conversions do not vary with liquid flow rates. Other conditions CF=0.37,
W/F=20 kg*s/mol, SN=2, P=30bar .

10
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7
Conversion%
Liquid Flow rare (cc/min)
Equilibrium=200℃
PBR=200℃
MR=200℃
Equilibrium=220℃
PBR=220℃
MR=220℃
Equilibrium=240℃
PBR=240℃
MR=240℃
15
20
25
30
35
40
45
50
0 1 2 3 4 5 6 7
Conversion%
Liquid Flow rare (cc/min)
Equilibrium=20bar
PBR=20bar
MR=20bar
Equilibrium=25bar
PBR=25bar
MR=25bar
Equilibrium=30bar
PBR=30bar
MR=30bar
Equilibrium=35bar
PBR=35bar
MR=35bar

104

Figure 4- 10. MCR and PBR and calculated equilibrium carbon conversion versus liquid flow rate at various
temperatures. PBR and equilibrium conversions do not vary with liquid flow rates. Other conditions CF=0.37,
W/F=20 kg*s/mol, SN=2, T=220 ⁰C.

Figure 4- 9 and Figure 4- 10 illustrate the liquid flow rate effect on the conversion. The liquid
flow rate has no effect on the PBR or equilibrium conversions but the MCR conversion increases
as the liquid flow rate increases, as expected. In all cases, the MR conversion values are higher
than PBR conversion values and under some conditions even higher than the equilibrium
conversions as well.

4.5 CONCLUSIONS
In this chapter our efforts focused on validating the application of the MeS-MCR system for
processing pure CO2 feeds. For that, we combined the MeS-MCR system with a separate RWGS
reactor that precedes it which converts the CO2 stream into a syngas mixture. In this preliminary
effort, due to experimental limitations, the composition of the exit stream from the RWGSR is
simulated, on the assumption that the reactor reaches equilibrium. The key focus is instead on
validating experimentally the ability of the MeS-MCR to process as a feed the RWGSR exit stream
after the water it contains is removed. We investigated the performance of the individual RWGSR,
(via computations) and MCR (via experimentation) subsystems and of the overall RWGSR/MCR
device for a broad range of pressures and temperatures, sweep liquid flow rates, reactor space
times and flue gas feed compositions. The preliminary findings have been encouraging, indicating
the advantage offered by the combined RWGSR/MCR system over the conventional PBR as well
as the standalone MeS-MCR systems. Research is currently ongoing in the Group to
experimentally validate the performance of the integrated (RWGSR+MeS-MCR) system.

105

..

106

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114

APPENDICES
APPENDIX A: DIMENSIONLESS EQUATIONS FROM CHAPTER 3:
DGM:
1
𝑅𝑇
∇𝑃 𝑖 𝑚𝑔
= ∑
𝑥 𝑖 𝑁 𝑗 𝑚𝑔
−𝑥 𝑗 𝑁 𝑖 𝑚𝑔
𝐷 𝑖𝑗
𝑒 −
𝑁 𝑖 𝑚𝑔
𝐷 𝑖 ,𝑘 𝑒 𝑛 𝑗 =1
𝑗 ≠𝑖 = −𝑁 𝑖 𝑚𝑔
(∑
𝑥 𝑗 𝐷 𝑖𝑗
𝑒 𝑖 ≠𝑗 +
1
𝐷 𝑖 ,𝑘 𝑒 )+ 𝑥 𝑖 ∑
𝑁 𝑖 𝑚𝑔
𝐷 𝑖𝑗
𝑒
(A.1)
1
𝑅𝑇
𝑑𝑃
𝑖 𝑚𝑔
𝑑𝑟
=𝐷 𝐷𝐺𝑀 ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑
∗ 𝑁 𝑔 ⃑⃑⃑⃑⃑

(A.2)
𝑃 𝑖 𝑚𝑔
= (
𝑃 1
𝑚𝑔
𝑃 2
𝑚𝑔
⋯
𝑃 𝑛 𝑚𝑔
)
(A.3)
𝑁 𝑔 ⃑⃑⃑⃑⃑
= (
𝑁 1
𝑚𝑔
𝑁 2
𝑚𝑔
⋯
𝑁 𝑛 𝑚𝑔
)
(A.4)
and 𝐷 𝐷𝐺𝑀 ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑
is a matrix whose elements are
𝛼 𝑖𝑖
= −(∑
𝑥 𝑗 𝐷 𝑖𝑗
𝑒 𝑖 ≠𝑗 +
1
𝐷 𝑖 ,𝑘 𝑒 )
(A.5)
𝛼 𝑖𝑗
𝑖 ≠𝑗 = 𝑥 𝑖 ∑
1
𝐷 𝑖𝑗
𝑒 𝑛 𝑗 =1
𝑗 ≠𝑖
(A.6)
𝐷 𝑖 ,𝑘 𝑒 𝐷 𝑗 ,𝑘 𝑒 = √
𝑀 𝑗 𝑀 𝑖
(A.7)
Make 𝐷 𝑖 ,𝑘 𝑒 dimensionless with respect to 𝐷 𝐻 2
𝑘 𝑒

𝛿 𝑖 =
𝐷 𝑖 ,𝑘 𝑒 𝐷 𝐻 2,
𝑘 𝑒 = √
𝑀 𝐻 2
𝑀 𝑖
(A.8)
𝐷 𝑖 ,𝑘 𝑒 = 𝐷 𝐻 2
,𝑘 𝑒 √
𝑀 𝐻 2
𝑀 𝑖 = 𝐷 𝐻 2
,𝑘 𝑒 ∗ 𝛿 𝑖
(A.9)

Dimensionalize the 𝐷 𝑖𝑗
𝑒 with respect to 𝐷 𝐻 2
,𝐶𝑂
𝑒

115

𝛾 𝑖𝑗
=
𝐷 𝑖𝑗
𝑒 𝐷 𝐻 2
,𝐶𝑂
𝑒 ⇒ 𝐷 𝑖𝑗
𝑒 = 𝐷 𝐻 2
,𝐶𝑂
𝑒 ∗ 𝛾 𝑖𝑗

(A.10)
𝛼 𝑖𝑖
= −(∑
𝑥 𝑗 𝐷 𝐻 2
,𝐶𝑂
𝑒 ∗𝛾 𝑖𝑗
𝑗 =1
𝑗 ≠𝑖 +
1
𝐷 𝐻 2,
𝑘 𝑒 ∗𝛿 𝑖 )
(A.11)
= −
1
𝐷 𝐻 2
,𝐶𝑂
𝑒 (∑
𝑥 𝑗 𝛾 𝑖𝑗
𝑛 𝑗 =1
𝑗 ≠𝑖 +
𝐷 𝐻 2
,𝐶𝑂
𝑒 𝐷 𝐻 2
,𝑘 𝑒 ∗𝛿 𝑖 )
𝛼 𝑖𝑗
=
𝑥 𝑖 𝐷 𝐻 2
,𝐶𝑂
𝑒 ∑
1
𝛾 𝑖𝑗

(A.12)
Define
𝜔 =
𝐷 𝐻 2
,𝐶𝑂
𝑒 𝐷 𝐻 2,
𝑘 𝑒
(A.13)
𝑥 𝑖 =
𝑃 𝑖 𝑚𝑔
𝑃 𝑡
(A.14)
𝜉 =
𝑟 −𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡 −𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒
(A.15)
𝑑𝜉 =
𝑑𝑟
𝑑
(A.16)
𝑑 = 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡 − 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒
(A.17)
where 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 is the inside membrane diameter, 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡
is the outside
membrane diameter and d is the membrane thickness. Then Eqn. (A.2) becomes:

𝑃 𝑡 𝑅𝑇𝑑
∗
𝑑 𝑥 ̅
𝑑𝜉
=
1
𝐷 𝐻 2
,𝐶𝑂
𝑒 ∗𝐷 𝐷𝐺𝑀 ′
⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑
∗ 𝑁 𝑔 ⃑⃑⃑⃑⃑

(A.18)
and 𝐷 𝐷𝐺𝑀 ′
⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑
is a matrix whose elements are
𝛼 ′
𝑖𝑖
= −(∑
𝑥 𝑗 𝛾 𝑖𝑗
𝑗 =1
𝑗 ≠𝑖 +
𝜔 𝛿 𝑖 ) (A.19)
𝛼 ′
𝑖𝑗
= 𝑥 𝑖 ∑
1
𝛾 𝑖𝑗

(A.20)
Define
Ω
𝑔 = (
𝑅𝑇𝑑
𝐷 𝐻 2
,𝐶𝑂
𝑒 𝑃 𝑡 )
−1

(A.21)

116

𝑁 𝑔 ′
⃑⃑⃑⃑⃑⃑⃑
=
𝑅𝑇𝑑
𝐷 𝐻 2
,𝐶𝑂
𝑒 𝑃 𝑡 ∗ 𝑁 𝑔 ⃑⃑⃑⃑⃑
= (Ω
𝑔 )
−1
∗ 𝑁 𝑔 ⃑⃑⃑⃑⃑

(A.22)
Then Eqn. (A.18) becomes
𝑑𝑥
𝑖 ̅̅̅̅̅
𝑑𝜉
=𝐷 𝐷𝐺𝑀 ′
⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑
∗ 𝑁 𝑔 ′
⃑⃑⃑⃑⃑⃑⃑

(A.23)

Dimensionless Equations for the MR Feed-side
𝑑 𝐹 𝑖 𝐹 𝑑 𝑉 = 𝜌 𝑏 ∑ 𝜐 𝑖𝑗
𝑟 𝑗 2
𝑗 =1
− 𝛼 𝑚 𝐹 𝑁 𝑖 𝑚𝑔
|
𝑟 =𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡
(A.24)

𝑟 𝑖 = ∑ 𝜐 𝑖𝑗
𝑟 𝑗 2
𝑗 =1

(A.25)
𝑟 1
= 𝑟 𝑅𝑊𝐺𝑆 =
𝐾 1𝑤 𝑃 𝐶 𝑂 2
[1−𝐾 𝑒𝑞𝑤 ∗(
𝑃 𝐶𝑂
𝑃 𝐻 2
𝑂 𝑃 𝐻 2
𝑃 𝐶 𝑂 2
)]
[1+𝐾 2
𝑃 𝐻 2
𝑂 𝑃 𝐻 2
+(𝐾 3
𝑃 𝐻 2
)
1
2
+𝐾 4
𝑃 𝐻 2
𝑂 ]

(A.26)
=
𝐾 1𝑤 𝑃 𝑡 𝑥 𝐶 𝑂 2
[1−𝐾 𝑒𝑞𝑤 𝑥 𝐶𝑂
𝑥 𝐻 2
𝑂 𝑥 𝐻 2
𝑥 𝐶 𝑂 2
]
[1+𝐾 2
𝑥 𝐻 2
𝑂 𝑥 𝐻 2
+(𝐾 3
𝑃 𝑡 𝑥 𝐻 2
)
1
2
+𝐾 4
𝑃 𝑡 𝑥 𝐻 2
𝑂 ]
=
𝐾 1𝑤 ′
𝑥 𝐶 𝑂 2
[1−𝐾 𝑒𝑞𝑤 𝑥 𝐶𝑂
𝑥 𝐻 2
𝑂 𝑥 𝐻 2
𝑥 𝐶 𝑂 2
]
[1+𝐾 2
𝑥 𝐻 2
𝑂 𝑥 𝐻 2
+𝐾 3
′
𝑥 𝐻 2
1
2
+𝐾 4
′
𝑥 𝐻 2
𝑂 ]
= 𝐾 1𝑤 ′
𝐹 1
(𝑥 𝑖 )

𝑟 2
= 𝑟 𝑀𝑒𝑂𝐻 =
𝐾 1𝑚 𝑃 𝐶 𝑂 2
𝑃 𝐻 2
[1−(
1
𝐾 𝑒𝑞𝑚 )∗(
𝑃 𝑀𝑒𝑂𝐻 𝑃 𝐻 2
𝑂 𝑃 𝐻 2
3
𝑃 𝐶 𝑂 2
)]
[1+𝐾 2
𝑃 𝐻 2
𝑂 𝑃 𝐻 2
+(𝐾 3
𝑃 𝐻 2
)
1
2
+𝐾 4
𝑃 𝐻 2
𝑂 ]
3

(A.27)
=
𝐾 1𝑚 𝑃 𝑡 2
𝑥 𝑐𝑜
2
𝑥 𝐻 2
[1−(
1
𝐾 𝑒𝑞𝑚 )∗(
𝑥 𝑀𝑒𝑂𝐻 𝑥 𝐻 2
𝑂 𝑥 𝐻 2
3
𝑥 𝐶 𝑂 2
𝑃 𝑡 2
)]
[1+𝐾 2
𝑥 𝐻 2
𝑂 𝑥 𝐻 2
+𝐾 3
′
𝑥 𝐻 2
1
2
+𝐾 4
′
𝑥 𝐻 2
𝑂 ]
3
=
𝐾 1𝑚 ′
𝑥 𝑐𝑜
2
𝑥 𝐻 2
[1−(
1
𝐾 𝑒𝑞𝑚 ′
)∗(
𝑥 𝑀𝑒𝑂𝐻 𝑥 𝐻 2
𝑂 𝑥 𝐻 2
3
𝑥 𝐶 𝑂 2
)]
[1+𝐾 2
𝑥 𝐻 2
𝑂 𝑥 𝐻 2
+𝐾 3
′
𝑥 𝐻 2
1
2
+𝐾 4
′
𝑥 𝐻 2
𝑂 ]
3
=
𝐾 1𝑚 ′
𝐹 2
(𝑥 𝑖 ) (A.28)
𝐾 1𝑤 ′
= 𝐾 1𝑤 𝑃 𝑡 ; 𝐾 3
′
= (𝐾 3
𝑃 𝑡 )
1
2
; 𝐾 4
′
= 𝐾 4
𝑃 𝑡 ; 𝐾 1𝑚 ′
= 𝐾 1𝑚 𝑃 𝑡 2
; 𝐾 𝑒𝑞𝑚 ′
= 𝐾 𝑒𝑞𝑚 𝑃 𝑡 2

(A.29)

Define
𝑦 𝑖 =
𝐹 𝑖 𝐹 𝐹 𝑡 𝐹 (A.30)
𝘁 =
𝑉 𝑉 𝑅
(A.31)

117

where 𝐹 𝑡 𝐹 is total molar flow rate in the reaction side. Then Eqn. (A.24) becomes

𝑑 𝑦 𝑖 𝑑𝘁
=
𝜌 𝑏 𝐾 1𝑤 ′
𝑉 𝑅 𝐹 𝑡 𝐹 𝜐 𝑖 1
𝐹 1
(𝑥 𝑖 )+
𝜌 𝑏 𝐾 1𝑀 ′
𝑉 𝑅 𝐹 𝑡 𝐹 𝜐 𝑖 2
𝐹 2
(𝑥 𝑖 )− Ω
𝑔 𝛼 𝑚 𝐹 𝑉 𝑅 𝐹 𝑡 𝐹 𝑁 𝑖 𝑚𝑔
′
|
𝜉 =1

(A.32)

Define
𝐷 𝛼 1
=
𝜌 𝑏 𝐾 1𝑤 ′
𝑉 𝑅 𝐹 𝑡 𝐹 ; 𝐷 𝛼 2
=
𝜌 𝑏 𝐾 1𝑀 ′
𝑉 𝑅 𝐹 𝑡 𝐹
(A.33)
𝑃𝑒 𝑔 =
𝐹 𝑡 𝐹 𝛼 𝑚 𝐹 𝑉 𝑅 Ω
𝑔
(A.34)
Then Eqn. (A.32) becomes,

𝑑 𝑦 𝑖 𝑑𝘁
= 𝐷 𝛼 1
𝜐 𝑖 1
𝐹 1
(𝑥 𝑖 )+ 𝐷 𝛼 2
𝜐 𝑖 2
𝐹 2
(𝑥 𝑖 )−
𝑁 𝑖 𝑚𝑔
′
|
𝜉 =1
𝑃 𝑒 𝑔

(A.35)
= ∑ 𝐷 𝛼 𝑖 𝜐 𝑖𝑗
2
𝑗 =1
𝐹 𝑗 (𝑥 𝑖 )−
𝑁 𝑖 𝑚𝑔
′
|
𝜉 =1
𝑃 𝑒 𝑔

Mass Conservation in the Gas Phase Inside the Membrane
𝑑 (𝑟 𝑁 𝑖 𝑚𝑔
)
𝑑𝑟
= 0 ⇒
𝑑 ((𝜉 +𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 /𝑑 )∗𝑁 𝑖 𝑚𝑔
′
)
𝑑𝜉
= 0
(A.36)

Mass Conservation in the Liquid Phase Inside the Membrane
𝑁 𝑖 𝑚𝑙
= −𝐷 𝑖 𝑒 .𝑝 𝑑𝑐
𝑖 𝑙 𝑑𝑟

(A.37)

𝑐 𝑡 𝑒𝑞
= ∑𝑐 𝑖 0
𝑒𝑞

(A.38)

Define,
𝜔 𝑖 =
𝐷 𝑖 𝑒 .𝑝 𝐷 𝑀𝑒𝑂𝐻 𝑒 .𝑝
(A.39)
𝑧 𝑖 =
𝑐 𝑖 𝑙 𝑐 𝑡 𝑒𝑞

(A.40)
Where 𝑐 𝑖 0
𝑒𝑞
is concentration of species dissolved in the solvent in equilibrium with 𝑐 𝑖 0
𝑔 , i.e, the
feed concentration of species i.

118

Then
𝑁 𝑖 𝑚𝑙
= −
𝐷 𝑀𝑒𝑂𝐻 𝑒 .𝑝 𝑐 𝑡 𝑒𝑞
𝑑 𝜔 𝑖 𝑑 𝑧 𝑖 𝑑𝜉

(A.41)

Define
𝑁 𝑖 𝑚𝑙
′
= −
𝑑 𝐷 𝑀𝑒𝑂𝐻 𝑒 .𝑝 𝑐 𝑡 𝑒𝑞
𝑁 𝑖 𝑚𝑙
= Ω
𝑙 −1
𝑁 𝑖 𝑚𝑙

(A.42)
where
Ω
𝑙 =
𝐷 𝑀𝑒𝑂𝐻 𝑒 .𝑝 𝑐 𝑡 𝑒𝑞
𝑑
(A.43)

Then Eqn. (A.37) becomes
𝑁 𝑖 𝑚𝑙
′
= −𝜔 𝑖 𝑑 𝑧 𝑖 𝑑𝜉

(A.44)
𝑑 (𝑟 𝑁 𝑖 𝑚𝑙
)
𝑑𝑟
= 0 ⇒
𝑑 ((𝜉 +𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 /𝑑 )∗𝑁 𝑖 𝑚𝑙
′
)
𝑑𝜉
= 0
(A.45)

Dimensionless Equations for the MR Permeate-side
𝑑 𝐹 𝑖 𝑃 𝑑𝑉
= (𝛼 𝑚 𝑃 )𝑁 𝑖 𝑚𝑙
|
𝑟 =𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒
(A.46)
Define
𝑤 𝑖 =
𝐹 𝑖 𝑃 𝐹 𝑠 0

(A.47)
where 𝐹 𝑠 0
is the total solvent feed flow rate,

Then Eqn. (A.46) becomes,
𝑑 𝑤 𝑖 𝑑𝘁
=
𝛼 𝑚 𝑃 𝐷 𝑀𝑒𝑂𝐻 𝑒 .𝑝 𝑐 𝑡 𝑒𝑞
𝑑 𝑉 𝑅 𝐹 𝑠 0
𝑁 𝑖 𝑚𝑙
′
|
𝜉 =0
=
𝑁 𝑖 𝑚𝑙
′
|
𝜉 =0
𝑃𝑒
𝑙
(A.48)
1
𝑃𝑒
𝑙 =
𝛼 𝑚 𝑃 𝐷 𝑀𝑒𝑂𝐻 𝑒 .𝑝 𝑐 𝑡 𝑒𝑞
𝑑 𝑉 𝑅 𝐹 𝑠 0
= 𝛼 𝑚 𝑃
Ω
𝑙
𝑉 𝑅 𝐹 𝑠 0

(A.49)

Conversion Equation
𝑋 𝑐 =
(𝐹 𝑐𝑜
𝐹 +𝐹 𝑐𝑜
2
𝐹 )
𝑖𝑛
−(𝐹 𝑐𝑜
𝐹 +𝐹 𝑐𝑜
2
𝐹 )
𝑜𝑢𝑡 −(𝐹 𝑐𝑜
𝑃 +𝐹 𝑐𝑜
2
𝑃 )
𝑜𝑢𝑡 (𝐹 𝑐𝑜
𝐹 +𝐹 𝑐𝑜
2
𝐹 )
𝑖𝑛

=
(𝑦 𝑐𝑜
+𝑦 𝑐𝑜
2
)
𝑖𝑛
−(𝑦 𝑐𝑜
+𝑦 𝑐𝑜
2
)
𝑜𝑢𝑡 −𝑆 (𝑤 𝑐𝑜
+𝑤 𝑐𝑜
2
)
𝑜𝑢𝑡 (𝑦 𝑐𝑜
+𝑦 𝑐𝑜
2
)
𝑖𝑛

(A.50)

119

where S=sweep ratio=
𝐹 𝑠 0
𝐹 𝑡 𝐹

Initial Conditions, Reactor
At 𝘁 =0 𝑦 𝑖 = 𝑦 𝑖 0
; 𝑤 𝑖 = 𝑤 𝑖 0

(A.51)

Boundary Condition, Membrane
At 𝑟 = 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡

where 𝜉 = 1
𝑃 𝑖 𝐹 = 𝑃 𝑖 𝑚𝑔
⇒ (
𝐹 𝑖 𝐹 ∑𝐹 𝑖 𝐹 )𝑃 𝑡 = 𝑃 𝑖 𝑚𝑔
⇒
(A.52)
(
𝑦 𝑖 ∑𝑦 𝑖 ) = 𝑥 𝑖 (A.53)
At 𝑟 = 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 + 𝛿
where 𝜉 =
𝛿 𝑑
𝑁 𝑖 𝑚𝑔
= 𝑁 𝑖 𝑚𝑙
; 𝑓 𝑖 𝑔 (𝑃 𝑖 𝑚𝑔
)= 𝑓 𝑖 𝑙 (𝑐 𝑖 𝑙 )
(A.54)
Ω
𝑔 𝑁 𝑖 ′𝑚𝑔
= Ω
𝑙 𝑁 𝑖 ′𝑚𝑙
; (A.55)
𝑁 𝑖 𝑚𝑔
′
= (
Ω
𝑙 Ω
𝑔 )𝑁 𝑖 𝑚𝑙
′
;
(A.56)
𝑓 𝑖 𝑔 (𝑥 𝑖 )= 𝑓 𝑖 𝑙 (𝑧 𝑖 )
(A.57)
At 𝑟 = 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒
where 𝜉 = 0
-𝑁 𝑖 𝑙 = 𝐾 𝑖 (𝑐 𝑖 𝑙 − 𝑐 𝑖 𝑃 )
(A.58)

where 𝑐 𝑖 𝑃 is the concentration of the permeate side, given as:
𝑐 𝑖 𝑃 =
𝐹 𝑖 𝑃 ∑𝐹 𝑖 𝑃 𝑐 𝑡 𝑃
(A.59)
where 𝑐 𝑡 𝑃 is the total mixture concentration given as
𝑐 𝑡 𝑃 =
∑𝐹 𝑖 𝑃 ∑𝐹 𝑖 𝑃 𝑖 𝜐 𝑖 𝑚 =
∑𝑤 𝑖 ∑𝑤 𝑖 𝑣 𝑖 𝑚
(A.60)
where 𝜐 𝑖 𝑚 is molar volume
-Ω
𝑙 𝑁 𝑖 𝑚𝑙
′
= 𝐾 𝑖 𝑐 𝑡 𝑒𝑞
(
𝑐 𝑖 𝑙 𝑐 𝑡 𝑒 𝑞 −
𝑐 𝑖 𝑃 𝑐 𝑡 𝑒𝑞
) = 𝐾 𝑖 𝑐 𝑡 𝑒𝑞
(𝑧 𝑖 −
𝑤 𝑖 ∑𝑤 𝑖 𝑐 𝑡 𝑃 𝑐 𝑡 𝑒𝑞
)
(A.61)
−𝑁 𝑖 𝑚𝑙
′
=
𝐾 𝑖 𝑐 𝑡 𝑒𝑞
Ω
𝑙 (𝑧 𝑖 −
𝑤 𝑖 ∑𝑤 𝑖 𝑐 𝑡 𝑃 𝑐 𝑡 𝑒𝑞
) = 𝑆 ℎ(𝑧 𝑖 −
𝑤 𝑖 ∑𝑤 𝑖 𝑐 𝑡 𝑃 𝑐 𝑡 𝑒𝑞
)
(A.62)
where

120

𝑆 ℎ
𝑖 =
𝐾 𝑖 𝑐 𝑡 𝑒𝑞
Ω
𝑙
(A.63)

Dimensionless Parameters
𝛿 𝑖 =
𝐷 𝑖 ,𝑘 𝑒 𝐷 𝐻 2,
𝑘 𝑒 = √
𝑀 𝐻 2
𝑀 𝑖
(A.8)
𝐾 3
′
= 𝐾 3
𝑃 𝑡 1
2

(A.29)
𝛾 𝑖𝑗
=
𝐷 𝑖 𝑗 𝑒 𝐷 𝐻 2
,𝐶𝑂
𝑒
(A.10)
𝐾 4
′
= 𝐾 4
𝑃 𝑡
(A.29)
𝜔 =
𝐷 𝐻 2
,𝐶𝑂
𝑒 𝐷 𝐻 2
𝑘 𝑒
(A.13)
𝜔 𝑖 =
𝐷𝑒
𝑖 𝑒 .𝑝 𝐷𝑒
𝑀𝑒𝑂𝐻 𝑒 .𝑝
(A.39)

Dimensionless Variables
𝑥 𝑖 =
𝑃 𝑖 𝑚𝑔
𝑃 𝑡
(A.14)
𝑦 𝑖 =
𝐹 𝑖 𝐹 𝐹 𝑡 𝐹
(A.30)
𝜉 =
𝑟 −𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑜𝑢𝑡 −𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 =
𝑟 −𝑟 𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 𝑑
(A.15)
𝘁 =
𝑉 𝑉 𝑅
(A.31)
𝑁 𝑔 ′
̅̅̅̅̅
= (Ω
𝑔 )
−1
∗ 𝑁 𝑔 ̅̅̅̅

(A.22)
𝑧 𝑖 =
𝑐 𝑖 𝑙 𝑐 𝑡 𝑒𝑞

(A.40)

Dimensionless Groups
𝐷 𝛼 1
= 𝐷𝑎𝑚𝑘𝑜 ℎ𝑙𝑒𝑟 𝑛𝑢𝑚𝑏𝑒𝑟 =
𝜌 𝑏 𝑉 𝑅 𝐾 1𝑤 𝑃 𝑡 𝐹 𝑡 𝐹 = (
𝑤 𝑐 𝐹 𝑡 𝐹 )𝐾 1𝑤 𝑃 𝑡
(A.33)
𝐷 𝛼 2
=
𝜌 𝑏 𝐾 1𝑀 𝑉 𝑅 𝑃 𝑡 2
𝐹 𝑡 𝐹 = (
𝑤 𝑐 𝐹 𝑡 𝐹 )𝐾 1𝑀 𝑃 𝑡 2

(A.33)
where 𝑤 𝑐 is the weight of catalyst.
𝑃𝑒 𝑔 = 𝑃𝑒𝑐𝑙𝑒𝑡 𝑁𝑢𝑚𝑏𝑒𝑟 =
𝐹 𝑡 𝐹 𝛼 𝑚 𝐹 𝑉 𝑅 Ω
𝑔
(A.34)
𝑃𝑒 𝑙 =
𝐹 𝑠 0
𝛼 𝑚 𝑃 𝑉 𝑅 Ω
𝑙
(A.49)
𝑆 ℎ
𝑖 = 𝑆 ℎ𝑒𝑟𝑤𝑜𝑜𝑑 𝑁𝑢𝑚𝑏𝑒𝑟 =
𝐾 𝑖 𝑐 𝑡 𝑒𝑞
Ω
𝑙
(A.63)

121

In our lab-scale reactor the variables we can vary are: (1) reactor temperature, T; (2)
reactor total pressure, 𝑃 𝑡 ; (3) total molar feed flow rate on reactor side, 𝐹 𝑡 𝐹 ; (4) feed
composition, 𝐹 𝑖 0
𝐹 ; (5) total solvent flow rate, 𝐹 𝑠 0
; (6) liquid film thickness, 𝛿 . We
assume here that the membrane properties including the surface areas
(𝛼 𝑚 𝐹 𝑉 𝑅 ,𝛼 𝑚 𝑃 𝑉 𝑅 ) and the total quantity of catalyst 𝑤 𝑐 are fixed.
For T constant Ω
𝑙 ~𝑐 𝑡 𝑒𝑞
; Ω
𝑔 ~𝑃 𝑡 ; 𝐷 𝛼 1
~(
𝑤 𝑐 𝐹 𝑡 𝐹 )𝑃 𝑡 ; 𝐷 𝛼 2
~(
𝑤 𝑐 𝐹 𝑡 𝐹 )𝑃 𝑡 2
; 𝑃 𝑒 𝑔 ~
𝐹 𝑡 𝐹 𝛼 𝑚 𝐹 𝑉 𝑅 Ω
𝑔
~
𝐹 𝑡 𝐹 𝑃 𝑡 ;
𝑃 𝑒 𝑙 ~
𝐹 𝑡 𝑃 Ω
𝑙 ~
𝐹 𝑡 𝑃 𝑐 𝑡 𝑒𝑞
; 𝑆 ℎ
𝑖 ~
𝐾 𝑖 𝑐 𝑡 𝑒𝑞
Ω
𝑙 ~ 𝐾 𝑖 .

APPENDIX B: EMSOFT CODES:

Abstract (if available)

Abstract In the first chapter a high-pressure membrane reactor (MR) was employed to carry-out the methanol synthesis (MeS) reaction. Syngas was fed into the MR shell-side where a commercial MeS catalyst was used, while the tube-side is swept with a high boiling point liquid with good solubility towards methanol. A mesoporous alumina ceramic membrane was utilized, after its surface had been modified to be rendered more hydrophobic. The efficiency of the MR was investigated under a variety of experimental conditions (different pressures, temperatures, sweep liquid flow rates, and types of sweep liquids). The results reveal improved per single-pass carbon conversions when compared to the conventional packed-bed reactor. An ionic liquid (IL), 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF₄]) was utilized in the MR as the sweep liquid. The experimental results are compared to those previously reported by our Group (Li and Tsotsis, J. Membrane Sci., 2019) while using a conventional petroleum-derived solvent as sweep liquid, tetraethylene glycol dimethyl ether (TGDE). Enhanced carbon conversion (over the petroleum-derived solvent) was obtained using the IL. ❧ In the second chapter, the solubility properties of the ionic liquid (IL), 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF₄]) were studied using a high-pressure, high-temperature set-up employing the pressure-drop technique. [EMIM][BF₄] was selected because it is used as sweep liquid in a membrane reactor (MR)-based methanol synthesis (MR-MeS) process described in chapter 1. The MR-MeS studies indicated high methanol (MeOH) solubilities in the IL under typical MeS reaction conditions, which then motivated this study to measure such solubilities directly under non-reactive conditions to validate the MR study findings in the first chapter. In addition, during the MR-MeS studies concerns existed about the CO₂ solubility in the [EMIM][BF₄], since it is a reactant and its dissolution in the IL would be detrimental for performance. Studies, therefore, were also carried out to investigate CO₂, in addition to MeOH solubility. Our investigation indicates that though CO₂ solubility is high at room temperature, it becomes negligible at the typical MeS conditions. ❧ In the third chapter, a steady-state model is developed to simulate the MR behavior during MeS, and is validated by the experimental data presented in chapter 1. The model is then used to study the reactor behavior for a broader range of operating conditions beyond those that can be accessed and studied experimentally in the laboratory-scale reactor. Converting the model equations into their dimensionless form helps to identify the key dimensionless groups determining reactor performance and enables one to better evaluate the efficacy of the MR system and guides further process design and scale-up. ❧ In the last chapter, we study the direct conversion of CO₂ into MeOH by coupling the MCR-MeS Lab-scale set-up with a reverse water gas shift (RWGS) reactor (RWGSR). The idea here is that CO₂ is first fed into the RWGSR to be converted into syngas, which is then processed in the MeS-MCR and converted into MeOH. Efforts are currently under way in our Group to construct the combined RWGSR/MeS-MCR system to experimentally validate the concept, but they have yet to reach completion. In this chapter, we model the behavior of the RWGSR, instead, and use the simulated exit compositions from the reactor as feeds for the MeS-MCR. Employing such compositions, the MCR subsystem is then experimentally investigated for a broad range of pressures and temperatures, sweep liquid flow rates, reactor space times to validate its ability to efficiently convert the off-gas from the RWGSR into MeOH. ❧ In the future once the RWGSR/MeS-MCR set-up is completed, as part of the ongoing efforts in the Group in the area of CO₂ capture and utilization (CCU), we plan to further extend the preliminary work in chapter 3 to experimentally validate the CO₂ to MeOH direct conversion concept. Further, since constraints with the size of the Lab-scale RWGSR/MeS-MCR set-up may limit access to regions of the parameter space where a commercial system may be operating, we will also use an in-house, experimentally-validated model for the MeS-MCR, see chapter 3) and a mathematical model for the RWGSR, to be developed and experimentally validated in our research, to assess the full range of attainable conversions, aiming to obtain >90% carbon separation/capture. Based on the results of the planned laboratory studies, and in collaboration with National Energy Technology Laboratory (NETL) researchers, we will carry out a techno-economic analysis (TEA) of the proposed novel CCU process to compare its economics with those of the conventional, absorption-based technologies. We expect the economics of the new process to be superior to those of the existing processes.

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Asset Metadata

Creator Zebarjad, Fatemeh Sadat (author)

Core Title Methanol synthesis in the membrane reactor

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Chemical Engineering

Degree Conferral Date 2021-08

Publication Date 08/06/2023

Defense Date 06/11/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag ionic liquid,membrane reactor,membrane reactor modeling,methanol synthesis,OAI-PMH Harvest

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Tsotsis, Theodore T. (committee chair), Jessen, Kristian (committee member), Prakrash, G. K. Surya (committee member), Sharada, Shaama (committee member)

Creator Email fatemehzebarjad@gmail.com,Zebarjad@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC15719913

Unique identifier UC15719913

Legacy Identifier etd-ZebarjadFa-10020

Document Type Dissertation

Format application/pdf (imt)

Rights Zebarjad, Fatemeh Sadat

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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