Capturing Carbon Dioxide
directly from the air
A theoretical modeling approach
Master of Science Thesis
Stijn de Flart
© Walt van der Veen
Process & Energy
Capturing Carbon Dioxide
directly from the air
A theoretical modeling approach
Master of Science Thesis
For the degree of Master of Science in Mechanical Engineering at Delft
University of Technology
Stijn de Flart
May 11, 2016
Faculty of Mechanical, Maritime and Materials Engineering (3mE) · Delft University of
Technology
The work in this thesis was supported by EBN. Their co-operation is hereby gratefully acknowledged.
c Process & Energy (P&E)
Copyright All rights reserved.
Delft University of Technology
Department of
Process & Energy (P&E)
The undersigned hereby certify that they have read and recommend to the Faculty of
Mechanical, Maritime and Materials Engineering (3mE) for acceptance a thesis
entitled
Capturing Carbon Dioxide
directly from the air
by
Stijn de Flart
in partial fulfillment of the requirements for the degree of
Master of Science Mechanical Engineering
Dated: May 11, 2016
Supervisor(s):
Prof.dr. W. Buijs
Dr.ir. H.J.M. Kramer
Reader(s):
Prof. dr. F.M. Mulder
Abstract
The transition towards a more sustainable society, one where less greenhouse gases are emitted
and where industrial processes become more efficient and renewable. It is an important
topic that drives lots of research. One of the biggest challenges is to reduce the greenhouse
gas emissions, especially carbon dioxide. Carbon dioxide emissions generally arise during
the combustion of fossil fuels and its sources can be classified as either large point sources
(industrial facilities, electricity generation) and small point sources (transport, residential).
Small point sources are very distributed (such as cars) and emit a lot less CO2 compared
to large point sources, however, added up they still account for more than 41% of the total
CO2 emissions. Conventional technologies are unable to address the CO2 emissions that arise
from these small point sources, which has been driving innovations in new technologies such
as Direct Air Capture (DAC).
DAC technologies capture carbon dioxide from ambient air and aim to utilize the captured
carbon dioxide; this would allow CO2 capture independent of source and location and can
therefore address all CO2 emissions. Since CO2 is also an important feedstock for many
processes, DAC technologies can additionally be used to regenerate the CO2 on site, avoiding
unnecessary transport of CO2 . There are already a large number of processes and materials
that are capable of this, however, it is still not yet widely applied in industry. The aim of
this thesis is to first select a suitable material and then provide the tools to start designing
such a process.
This research discusses several direct air capture technologies and materials, and identifies the
solid amine-based sorbents as an interesting candidate for further research. A specific solid
amine-based sorbent, VP OC 1065, has been selected as being the most suitable material for
this process. The VP OC 1065 contains primary amine groups (NH2 ) which interact with the
CO2 molecules and are responsible for the CO2 capture, which in general can be classified
as a chemisorption process. When designing an adsorption process both the CO2 capacity
of the VP OC 1065 as well as the speed of adsorption should be known. In order to extract
the speed of adsorption a mathematical model of a packed bed has been created which uses
a linear driving force model to describe the rate of adsorption. The model can be matched
with so-called breakthrough experiments in order to extract the speed of adsorption, using
the CO2 capacity of the VP OC 1065 as an input for the model.
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The CO2 capacity of the VP OC 1065 is expected to be directly linked to the chemical
interaction between the functional amine groups and CO2 molecules, as is often the case in
chemisorption processes. When conducting this research it became clear that various studies
report different kinds of interaction with CO2 for these kind of sorbents. The quantum
chemical calculations in the present work show that in order for this specific sorbent to
capture CO2 the reaction needs a catalyst. It was found that functional amine groups are
close enough to each other to catalyze CO2 capture. Besides that it was found that H2 O
can also catalyze the CO2 capture. The CO2 reacts with these molecules to either form a
carbamic acid complex or a bicarbonate complex with the other (protonated) amine. The H2 O
catalyzed CO2 capture, where it reacts to form carbamic acid, was somewhat unexpected; no
reports of this mechanism were encountered in literature during the study.
Due to the two different reaction pathways (H2 O catalyzed or amine catalyzed), a dualsite Langmuir isotherm model was proposed to describe the CO2 capacity for the VP OC
1065. Thermodynamic properties such as heat of adsorption from the quantum chemical
calculations were successfully implemented to describe the temperature dependence of the
CO2 capacity and the model was validated. The dual-site model was able to describe the
sorbent’s equilibrium capacity for CO2 as a function of the CO2 concentration and serves as
an input for the mathematical model. The mathematical packed bed model was solved and
validated, which together with the isotherm description can be used to start designing an
actual CO2 capture process.
Processes using solid sorbents seem to be highly scalable. It can be applied everywhere and
can be designed as a modular system. Once a single DAC unit has been designed that captures
1 kg of CO2 a day it can used in a modular system of several units, eventually scaling up to
tonnes of CO2 per day. The sorbent in this study regenerates the CO2 at a temperature of
approximately 80 ◦ C which could be supplied in the form of waste heat. Using this technology,
CO2 becomes available everywhere, makes further use of waste heat and is able to address
CO2 emissions from every source (vehicles, industry, residential).
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Table of Contents
Preface
xiii
Acknowledgements
xv
1 Introduction
1-1 Climate Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1
1-2 Increasing carbon dioxide concentrations in the atmosphere . . . . . . . . . . . .
2
1-3 Sources of CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-4 Carbon Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
3
1-4-1
Carbon Capture and Storage . . . . . . . . . . . . . . . . . . . . . . . .
3
1-4-2
Carbon Capture and Utilization . . . . . . . . . . . . . . . . . . . . . . .
4
1-4-3
Limitations conventional technology . . . . . . . . . . . . . . . . . . . .
5
1-5 Recycling CO2 from the air . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1-6 Energy Transition Scholarship . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1-7 Aim of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2 Direct Air Capture
7
2-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-2 Thermodynamics of air capture . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
8
2-3 Technologies and processes for CO2 capture from air . . . . . . . . . . . . . . .
8
2-3-1
Inorganic Chemisorbents (solid) . . . . . . . . . . . . . . . . . . . . . . .
9
2-3-2
Inorganic Chemisorbents (in solution) . . . . . . . . . . . . . . . . . . .
10
2-3-3
2-3-4
Solid sorbents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Physisorbents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
11
2-3-5 Solid amine-based adsorbents . . . . . . . . . . . . . . . . . . . . . . . .
2-4 Sorbent selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
15
16
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Table of Contents
3 Sorbent characterization and modeling approach
17
3-1 Model introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-1-1 Equilibrium considerations . . . . . . . . . . . . . . . . . . . . . . . . .
3-1-2
17
18
Rate of adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
3-2 Sorbent characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-3 Modeling Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
23
3-3-1
Modeling Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3-3-2
System description . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3-3-3
Hypotheses and assumptions . . . . . . . . . . . . . . . . . . . . . . . .
23
3-3-4
Governing equations and boundary conditions . . . . . . . . . . . . . . .
25
3-4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
4 Molecular modeling
29
4-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-2 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-3 Modeling approach and development . . . . . . . . . . . . . . . . . . . . . . . .
29
30
31
4-3-1
4-3-2
Carbamic acid route . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Amine catalyzed route . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
37
4-3-3
Carbamic acid catalyzed route . . . . . . . . . . . . . . . . . . . . . . .
42
4-3-4 Effect of water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-4 Conluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
50
5 Model development and results
53
5-1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-2 Isotherm model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-2-1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
54
58
5-2-2
Low pressure regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
5-2-3
Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
5-3 Numerical solution method . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-3-1 Discretization of equations . . . . . . . . . . . . . . . . . . . . . . . . .
60
60
5-3-2
Operator splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
5-4 Packed bed model validation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-4-1 Static validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-4-2 Dynamic validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
65
65
5-5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
5-6 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
6 Conclusion and recommendations
6-1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6-3 Future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
71
72
72
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A Energy Transition Scholarship
73
B Experimental breakthrough set up
81
B-1 Experimental procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
B-2 Required equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
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List of Figures
1-1 Atmospheric CO2 concentration from Mauna Loa (Source: Earth System Research
Laboratory) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1-2 U.S. carbon dioxide emissions by source [2] . . . . . . . . . . . . . . . . . . . .
3
1-3 Carbon Dioxide management. (Courtesy of CO2 CRC) . . . . . . . . . . . . . . .
4
2-1 Carbon Dioxide capture process using sodium hydroxide. Reproduced with permission from [63]. Copyright (2007) American Chemical Society. . . . . . . . . . . .
10
2-2 From left to right, primary to quaternary amine functional groups. . . . . . . . .
13
2-3 Different reaction pathways for primary to tertiary amines. Reprinted from [18]
with permission from John Wiley and Sons . . . . . . . . . . . . . . . . . . . . .
13
2-4 Chemical structure PEI(L) Sorbent sample (R) . . . . . . . . . . . . . . . . . . .
14
2-5 Chemical composition sorbent (L) and the actual sample (R) . . . . . . . . . . .
15
3-1 Schematic representation of a packed bed adsorption process . . . . . . . . . . .
18
3-2 Typical type 1 isotherm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
3-3 Experimental and theoretical breakthrough curves for CO2 adsorption on aminefunctionalized mesoporous silica. Reprinted from [50] with permission from Elsevier. 20
3-4 Adsorption isotherms of the sorbent. Reprinted from [56] with permission
Elsevier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-5 Alternative reaction mechanism . . . . . . . . . . . . . . . . . . . . . . . .
3-6 Schematic representation of a packed bed separation process . . . . . . . .
from
. . .
. . .
. . .
21
22
24
4-1 Typical reaction profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
4-2 Molecular modeling approach . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
4-3 L: Molecular model benzylamine. R: Van der Waals complex between benzylamine
and CO2 (b3lyp 31-G*). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
4-4 Energy profile calculation for the transition state starting structure (CO2 approaching the nitrogen atom, pm3). . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
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List of Figures
4-5 Transition state geometry between CO2 and benzylamine (i1723, b3lyp 31-G*). .
34
4-6 Product geometry of the reaction between CO2 and benzylamine (b3lyp 31-G*).
35
4-7 Reaction profile for the Zwitterion route with Methylamine and CO2 . . . . . . .
36
4-8 Initial geometry of the simplified VP OC 1065 model (MMFF). . . . . . . . . . .
38
4-9 L: Close up of the simplified VP OC 1065 model. Amine groups are encircled. R:
Conformer distribution, of the 100 best conformers (MMFF). . . . . . . . . . . .
38
4-10 Van der Waals complex between CO2 and 2 methylamine molecules (b3lyp 31-G*). 39
4-11 Proton transfer to the second methylamine (pm3). . . . . . . . . . . . . . . . .
39
4-12 Transition State between CO2 and two methylamine groups (i570, b3lyp 31-G*).
40
4-13 Product geometry for the reaction between CO2 and two methylamine groups
(b3lyp 31-G*). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
4-14 Reaction profile for the amine catalyzed carbamate formation. . . . . . . . . . .
41
4-15 Van der Waals complex between carbamic acid, methylamine and CO2 (b3lyp
31-G∗ ).
4-16 Starting structure transition state calculation (pm3). . . . . . . . . . . . . . . .
4-17 Transition state geometry (i861 b3lyp
31-G∗ ).
42
42
. . . . . . . . . . . . . . . . . . .
43
4-18 Product geometry for the carbamic acid catalyzed CO2 capture (b3lyp 31-G∗ ). .
43
4-19 Reaction profile carbamic acid catalyzed CO2 capture. . . . . . . . . . . . . . . .
44
4-20 Van der Waals complex between methylamine, CO2 and H2 O (b3lyp 31-G*). . .
45
4-21 Carbon atom of CO2 approaching the oxygen atom H2 O (pm3). . . . . . . . . .
46
4-22 Transition state geometry for the H2 O CO2 methylamine complex (i685, b3lyp
31-G*). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
4-23 Product geometry for the bicarbonate route (b3lyp 31-G*). . . . . . . . . . . . .
47
4-24 Reaction profile for the bicarbonate route. . . . . . . . . . . . . . . . . . . . . .
48
4-25 L: Starting geometry for the transition state calculation (pm3). R: Transition state
showing the water molecule acting as a catalyst (i1499, b3lyp 31-G*). . . . . . .
49
4-26 Product geometry for water catalyzed carbamic acid formation (b3lyp 31-G*). . .
49
4-27 Reaction profile water catalyzed carbamic acid formation. . . . . . . . . . . . . .
50
5-1 Original data from Veneman et al. Reprinted from [55] with permission from Elsevier. 54
5-2 Curve fitting session to isotherm data at 303 K. . . . . . . . . . . . . . . . . . .
55
5-3 Calculated isotherm according to dual site model for ∆H1 = -66.14 kJ/mol, corresponding to the bicarbonate route. Experimental data from Veneman et al. . .
57
5-4 Calculated isotherm according to dual site model for ∆H1 = -75.23 kJ/mol, corresponding to the carbamic acid route. Experimental data from Veneman et al. .
57
5-5 Adsorption capacity for ∆H1 = -71 kJ/mol. . . . . . . . . . . . . . . . . . . . .
58
5-6 Sensitivity upon changing reaction energies. . . . . . . . . . . . . . . . . . . . .
59
5-7 CO2 adsorption capacity of VP OC 1065 as a function of the relative humidity at
a CO2 partial pressure of 40 Pa. Reprinted from [55] with permission from Elsevier. 59
5-8 Sorbent capacity conditions relevant for air capture. . . . . . . . . . . . . . . . .
60
5-9 Numerical grid representation of the packed bed. . . . . . . . . . . . . . . . . .
62
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5-10 Comparison of the calculated breakthrough curve with the one reported by Barry
et al. (2000). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
5-11 Breakthrough curve for DL = 6 cm2 d−1 . . . . . . . . . . . . . . . . . . . . . .
67
5-12 Breakthrough curve for u = 12 cm d− 1. . . . . . . . . . . . . . . . . . . . . . .
68
5-13 Breakthrough curve for k = 1
(d−1 ).
. . . . . . . . . . . . . . . . . . . . . . . .
68
B-1 Possible breakthrough experiment set-up. . . . . . . . . . . . . . . . . . . . . .
81
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List of Tables
2-1 Compositions of ambient air and flue gas . . . . . . . . . . . . . . . . . . . . . .
8
2-2 Chemical reactions in the NaOH process . . . . . . . . . . . . . . . . . . . . . .
11
2-3 Characteristics Physical and Chemical adsorption . . . . . . . . . . . . . . . . .
11
2-4 Solid amine-based sorbent selection . . . . . . . . . . . . . . . . . . . . . . . . .
16
3-1 Sorbent properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
3-2 Model assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
4-1 Calculated total energies of the zwitterion route for Benzylamine and CO2 . . . .
35
4-2 Comparison of zwitterion route for methylamine and benzylamine. . . . . . . . .
36
4-3 Calculated total energies of the amine route for 2 Methylamine and CO2 . . . . .
41
4-4 Calculated total energies of the amine route for 2 Methylamine and CO2 . . . . .
44
4-5 Calculated total energies of the bicarbonate route for H2 O, Methylamine and CO2 . 47
4-6 Calculated total energies of the carbamic acid route for H2 O, Methylamine and CO2 . 49
4-7 Reaction pathways for CO2 adsorption in VP OC 1065. . . . . . . . . . . . . . .
51
5-1 Isotherm data points at reference temperature of 303K (bold faced values were
additionally added, rounded values are shown). . . . . . . . . . . . . . . . . . .
55
5-2 Isotherm parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
5-3 Simulation parameters from Barry et al. (2000). . . . . . . . . . . . . . . . . . .
65
5-4 Parameters for the dynamic validation of the packed bed model (breakthrough
curves are computed at 5 cm in the bed). . . . . . . . . . . . . . . . . . . . . .
66
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Master of Science Thesis
Preface
Direct Air Capture is quite an unusual subject for a mechanical engineering master thesis and
the reader might be wondering how this became the specific topic that I’ve chosen. Somewhat
more than a year ago, a friend of mine told me that he was planning on publishing a magazine
and asked me if I could write a science related article about basically any kind of subject. The
topic that I picked: write an energy scenario for 2050. In 2050 we are starting to get close to
running out of fossil fuels. Not only are fossil fuels used for energy generation but they are
also a source for many other products that we use in daily life. It did not seem obvious to me
that we simply could replace this with renewable energy sources, since we somehow need a
source of carbon as well. This made me wondering how we could somehow create this source
ourselves in the future, which is where I encountered Direct Air Capture for the first time.
Direct Air Capture could serve as a renewable source of carbon in the future and it made me
so interested in the subject that I wanted to learn more about it.
Besides my interest for Direct Air Capture I found my lacking knowledge in chemistry related
subjects somewhat annoying. The molecular modeling part of this research allowed me to
tackle this and greatly improved my chemical knowledge. During my research I spend a lot of
time taking online courses in chemistry at for instance Khan Academy and read a lot about it
from which I currently enjoy the benefits. It provides my mechanical engineering background,
with a specialization in process technology, the right amount of chemical knowledge to get a
better understanding of the overall process.
The concept of using low-grade heat to recycle CO2 from the air and utilize it on site proved
to be a well received concept as a tool for climate change mitigation. It made me win the
Energy Transition Scholarship which made this research a lot easier. Due to the money price
I was able to finance a big part of my time spent and besides that I met a lot of great people
who share my vision. We have to switch to a more sustainable society, and in my vision
Direct Air Capture will greatly help to achieve this!
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Preface
Master of Science Thesis
Acknowledgements
This thesis would not exist if it was not for my supervisors Prof. dr. Wim Buijs and Dr. ir.
Herman Kramer for allowing me to formulate my own thesis research. Besides that I would
like to thank Wim for all the in-depth support he has given me and for the good conversations
that we’ve had. In addition I would like to thank Herman for supporting me in this research.
I would like to thank Dr. ir. Mathieu Pourquie for advising me with the numerical solution
routines and I would like Prof. dr. Fokko Mulder for introducing me to the subject as well as
being part of my committee. I would like to thank ir. Max Beaumont for his in-depth support
in this project. Furthermore of course a big thanks to ir. Birgit de Bruin (Universiteitsfonds
Delft) and Prof. dr. ir. Jacob Fokkema for supporting me during my research. I would
also like to express my gratitude to ir. Erwin Niessen and dr. Berend Scheffers from EBN,
who together with Universiteitsfonds Delft made the Energy Transition Scholarship possible.
Some people who I do not want to leave unmentioned are of course Alexander Gunkel and
Bardia Alaee. This research was exceptionally challenging, not only due to the complexity of
the subject but also due to the focus on computational chemistry as a mechanical engineer
and I could not have done it without the help of many other people.
Finally I would like to thank my family and friends for encouraging me and taking my mind
off studying now and then.
Delft, University of Technology
April 2016
Master of Science Thesis
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Acknowledgements
Master of Science Thesis
Chapter 1
Introduction
Lately, a lot of scientific research has been aimed at Direct Air Capture (DAC) technologies.
DAC is a term that is often used to describe the process of capturing CO2 from the ambient
air. However, before diving into this specific field of research, the more general topic of CO2
capture is introduced and the underlying reasons why it is done.
1-1
Climate Change
At the moment of writing this thesis it is stated in the news that 2015 will likely be the
warmest year ever measured. And, as the Intergovernmental Panel on Climate Change stated
in Climate Change 2013 (IPCC 2013, p. 4 [52]): ‘Warming of the climate system is unequivocal, and since the 1950s, many of the observed changes are unprecedented over decades
to millennia.’ Some of the effects of the change in climate are observed as warming of the
ocean and atmosphere, diminishing of the amounts of snow and ice, rising sea levels and the
increased concentration of greenhouse gases (GHG). It is evident that the change in climate
is causing an impact on both natural as well as human systems and a solution is required
(IPCC 2014, p. 3 [43]). More reason to underline the fact that we have to switch towards a
more sustainable society.
Since the industrialization, the concentration of greenhouse gases in the atmosphere have
been increasing rapidly. It is clear that the increase in atmospheric GHG’s are due to human
activities such as fossil fuel burning for energy generation. These GHG’s influence the earth’s
energy balance which is known as the so-called greenhouse effect. It is common practice to
describe the change in the earth’s energy balance in terms of radiative forcing (RF), which
is a quantity that accounts for the change in energy fluxes. A positive RF value leads to
surface warming whereas a negative RF value leads to surface cooling (IPCC 2013, p. 11
[52]). Four principal greenhouse gases that are emitted into the atmosphere during these
processes have been identified: carbon dioxide (CO2 ), methane (CH4 ), nitrous oxide (N2 O)
and the halocarbons (a group of gases containing bromine, chlorine and fluorine [42]). As
IPCC states, the total radiative forcing is positive and the largest contributor to this is the
increase in the atmospheric concentration of carbon dioxide.
Master of Science Thesis
Stijn de Flart
2
Introduction
1-2
Increasing carbon dioxide concentrations in the atmosphere
As became clear in the previous paragraph, the increase in atmospheric CO2 concentration is
the main contributor to the warming of the climate system. Figure 1-1 shows the atmospheric
CO2 concentration over the last decades (IPCC 2013, p. 15 [52]). The increase in atmospheric
Figure 1-1: Atmospheric CO2 concentration from Mauna Loa (Source: Earth System Research
Laboratory)
CO2 levels is considered to be the cause of human activities such as burning of fossil fuels
for energy generation and using fossil fuels for transportation. In order to limit the climate
change, the emission of greenhouse gases has to be substantially reduced. A good starting
point is to see where most of the CO2 emissions arise and how they are currently being
managed.
1-3
Sources of CO2
One of the main human activities that increases the CO2 concentration in the atmosphere is
the combustion of fossil fuels. Therefore it is no surprise to learn that the power and industry
sector, where a lot of fossil fuels are combusted, are responsible for a big part of the CO2
emissions. Figure 1-2 shows the CO2 emissions of the U.S. by source and from this graph it
becomes clear that industry and power generation account for more than 50% of the total
CO2 emissions. Besides the emissions that arise in industry, where fossil fuels are generally
combusted in large boilers and furnaces, there are numerous of distributed smaller sources
of CO2 such as cars for transportation. A good way to distinguish between these different
type of sources of CO2 emissions is by classifying them either as large point sources or as
small point sources. The large point sources are found in industry where often emissions are
being emit to the atmosphere through large flue gas stacks. The small point sources are more
Stijn de Flart
Master of Science Thesis
1-4 Carbon Management
3
Figure 1-2: U.S. carbon dioxide emissions by source [2]
distributed and consist of for instance cars for transportation or boilers in residential areas.
Each of the smaller sources emit a very small amount of CO2 , but when they are added up
they still account for more than 41% of the total CO2 emissions. As became clear in the
previous paragraph, in order to limit the climate change the emissions of CO2 have to be
reduced drastically. Some of these CO2 emissions are currently being captured, which will
become more clear in the next paragraph.
1-4
Carbon Management
Concerns over climate change and general awareness of the limited availability of earth’s
natural resources drive innovations in technologies for stabilizing the CO2 concentration in the
atmosphere as well as to make our current processes more efficient. To reduce CO2 emissions
Goeppert et al. (2012) [26] identified three approaches: emitting less CO2 , sequestering CO2
and utilizing CO2 . Emitting less CO2 can for instance be achieved by making our technologies
more energy-efficient, by switching to different fuels (substitution of coal with oil or gas) or
by switching towards renewable energy sources (Aresta 2010, p. 5 [4]). Besides making our
current processes more efficient it is also possible to capture CO2 and store it, or utilize
it. Figure 1-3 shows some CO2 streams during these recycling processes. CO2 is generally
captured from large point sources from where it is transported, utilized or stored.
1-4-1
Carbon Capture and Storage
As described in the above section, one of the promising approaches is Carbon Capture and
Storage (CCS). CCS is a term used for the process of capturing and storing CO2 , arising from
large point sources such as fossil fuel burning power plants. The process can be divided into
Master of Science Thesis
Stijn de Flart
4
Introduction
Figure 1-3: Carbon Dioxide management. (Courtesy of CO2 CRC)
three basic steps: separation of CO2 from gas streams, transportation of CO2 , and finally
storage where CO2 will be stored away permanently. CCS is generally applied at large point
sources due to its economical feasibility and the high amounts of CO2 emitted. For the
separation of CO2 from a flue gas stream four main approaches have been identified, namely,
cryogenic distillation, membrane purification, absorption with liquids and adsorption using
solids [1]. After the separation step the CO2 is transported ideally through pipelines to the
storage site. Eventually, the captured and transported CO2 is injected in geological storage
sites for long term storage. (IPCC 2005, summary for policy makers [40]).
1-4-2
Carbon Capture and Utilization
Although CO2 is often placed in a negative context, being responsible for global climate
change, it is also a gas that is vital to life on Earth and it is a viable resource for many kinds
of industrial processes such as [4]:
1. Biofuel production;
2. Greenhouses;
3. Fuel synthesis;
4. Water treatment.
Stijn de Flart
Master of Science Thesis
1-5 Recycling CO2 from the air
5
Instead of storing the captured CO2 , it can also be utilized as a resource. To give an indication
for the CO2 requirement for biofuel production from microalgae; 1.72 g of CO2 is required
to obtain 1 g of biomass, so producing tonnes of biomass would require almost the double
amount of mass in CO2 (González-Fernández et al., 2011 [28]).
1-4-3
Limitations conventional technology
One of the most suitable technologies that is widely employed at large point sources is absorption in aqueous amine solutions, which is common practice in industry [26]. However,
this technology is applied at concentrated sources (e.g. power plants) and cannot address the
CO2 emissions originating from all the smaller, distributed point sources. As became clear, in
total the smaller point sources still produce more than 40% of the total CO2 emissions and in
order to limit the climate change also these emissions need to be addressed. Furthermore, the
regeneration of CO2 introduces a high energy penalty to the process (MacDowell et al. 2010
[39]). To give an example, in case of chemical absorption it is expected that implementation of
the technology will reduce the thermal efficiency of a modern power plant from approximately
45% to roughly 35%.
The final remark is not necessarily a limitation of the conventional technology regarding CO2
capture but it is an inconvenient characteristic of the technology in case of utilization of CO2 .
As became clear there are quite some processes that use CO2 as a feedstock and it makes
sense to utilize the captured CO2 for this. Since the technology of separation is often applied
at large point sources, the facilities that require CO2 should be close to these, something
that is illustrated by Figure 1-3. However, these processes are not always located near the
fossil fuel burning power plants where CO2 can be captured. This puts a constraint on the
location of such facilities and often CO2 is supplied in the form of pressurized cylinders. This
causes additional transport and energy costs. Although Figure 1-3 is just an impression and
does not reflect any geological scales, it does provide some insight in the limitations of the
conventional CO2 capture and recycling technologies.
1-5
Recycling CO2 from the air
Basically, two challenges have to be overcome. With current technology only the large point
sources can be equipped with a carbon capture system, where the smaller distributed point
sources will keep on emitting CO2 to the atmosphere. The other challenge is the fact that
often the CO2 has to be transported to the utilization sites, introducing transport costs. A
possible solution to overcome these challenges is to separate CO2 from the air, which has
already been proposed as a solution for stabilizing the CO2 concentration in the atmosphere
in literature many times ([32][53][36]). These studies indicate that capturing carbon dioxide
from the air is a feasible process that is able to address the emission of the smaller distributed
point sources. When carbon dioxide is captured from the air it becomes decoupled from
industry. Every type of source (small or large) can be addressed and it becomes possible to
start generating CO2 directly at the utilization sites. Direct Air Capture could provide a
solution to the above mentioned challenges. Possible future prospects for the technology, as
stated by Klaus Lackner et al. (2011) [29], recycle the captured CO2 from the atmosphere into
Master of Science Thesis
Stijn de Flart
6
Introduction
hydrocarbons, using renewable energy as an input which completely would close the carbon
loop.
1-6
Energy Transition Scholarship
The transition to a future that is less dependent on fossil fuels and more energy efficient is
one of humanities big challenges and innovative solutions are definitely needed. To encourage
students to come up with innovative solutions, Universiteitsfonds Delft and EBN organized
the Energy Transition Scholarships. Students who are doing their master thesis research in
the field of for instance CO2 capture can submit their solution to apply for this scholarship.
A proposal was written for the concept described above of utilizing CO2 on-site while making
use of waste heat, and has been awarded the Energy Transition Scholarship of 2015 [21]. The
winning proposal can be found in Appendix A.
1-7
Aim of this thesis
Capturing CO2 from air seems a very promising technology, and although it is a novel technology, already quite some sorbent materials have been reported to be able to capture carbon
dioxide under atmospheric conditions. The aim of this thesis is to tune down to a specific
sorbent material that can capture carbon dioxide and to characterize this material in order
to improve the understanding of how it captures CO2 . As will become clear, a sorbent material has two important parameters that have to be determined which are basically the total
capacity of the material for CO2 as well as the capture rate of the material. Both a molecular
model as well as a mathematical model have been developed that can be used as tools in order
to learn more about this material and to eventually help turn it into a commercial process.
Stijn de Flart
Master of Science Thesis
Chapter 2
Direct Air Capture
In the previous chapter both the background and the motivation for the technology of Direct
Air Capture became clear. DAC could provide an additional tool in the mitigation of climate
change and seems very promising to be used as a stand alone CO2 generator. The air will
do the transport of CO2 and just as windmills or solar panels create energy on-site, this
technology allows to create CO2 on site. This chapter gives a broad overview of all the
different DAC technologies that have been reported in literature and aims to select one specific
technology which will be modeled in the further chapters.
2-1
Introduction
How is air capture of CO2 different from conventional post combustion CO2 capture and why
are the current state of the art technologies not convenient for capturing CO2 directly from
the air? One of the main differences of capturing CO2 directly from the air compared to
capturing CO2 from the larger point sources is its concentration. Although the concentration
of carbon dioxide in the atmosphere has been rising rapidly, it is still only 0.04%, whereas in
a conventional flue gas stack the concentration of carbon dioxide is often between 5-15% [14].
A good indication of the challenge of direct air capture is obtained by looking at how much
volume of air has to be processed in order to capture 1 kg of CO2 for both processes. The
compositions of the respective gases as well as their molar masses are presented in Table 21. The CO2 concentration in kg/m3 for both gases can be calculated by multiplying the
respective CO2 concentration with the density of CO2 . The CO2 density can be calculated
according to the ideal gas law and for the sake of simplicity it is assumed that the flue gas
is at the same temperature and pressure as ambient air since this figure only serves as an
illustration.
P MCO2
ρCO2 =
≈ 1.829kg/m3
(2-1)
RT
In equation (2-1), P represents the total pressure of the gas mixture (101.325 kPa), MCO2 is
the molar mass of CO2 (44.009 g/mol) and R is the universal gas constant (8.314 J/mol K).
For the calculations a temperature of 293.15 K was used which is considered as a reference
Master of Science Thesis
Stijn de Flart
8
Direct Air Capture
Table 2-1: Compositions of ambient air and flue gas
CO2
N2
O2
Ar
Air [%]
Flue gas [%]
Molar mass
0.04
78
21
0.996
14
81
5
-
44.009
28.014
31.998
39.948
g mol
ambient temperature. Using the calculated CO2 density, the effective concentrations for both
the flue gas and the ambient air can be calculated:
g
fg
≈ 256.06 g/m3
ρfCO
= yCO
ρ
2
2 CO2
(2-2)
ρair
CO2
(2-3)
=
air
yCO
ρ
2 CO2
3
≈ 0.73 g/m
Capturing a kg of CO2 in the flue gas would require at least 4 m3 of gas to be processed
whereas in the case of capturing a kg of CO2 from the air this number becomes roughly 1370
m3 , which is an enormous amount of air that has to be processed. Applying the conventional
technology based on absorption in liquid amines therefore will have to deal with large amounts
of solvent evaporation, making the process much more complex [26]. It is evident that if it
is desired to separate CO2 from the air new processes have to be designed and although it
seems to be a challenging task, a lot of highly selective sorbents capable of fulfilling this task
have already been identified [34].
2-2
Thermodynamics of air capture
Another way of looking at the difference in the processes is by calculating the free energy required to separate one mole of CO2 under ambient conditions. The thermodynamic minimum
free energy required to separate one mol of CO2 from a gas mixture is given by [63]:
∆G = RT ln
P
P0
(2-4)
In this equation, P resembles the CO2 partial pressure after the separator, and P0 is the total
pressure. As Lackner describes in Thermodynamics of direct air capture [35], the goal of air
capture is not to completely reduce the output partial pressure of CO2 to 0 Pa but rather to
harvest the CO2 as efficient as possible which is referred to as skimming. Taking T at 300
K, and P0 at 100,000 Pa and P at 40 Pa, the free energy of adsorption must at least be 20
kJ/mol. Material candidates for direct air capture should therefore have a strong interaction
energy with CO2 in order to be able to effectively capture it at ambient conditions.
2-3
Technologies and processes for CO2 capture from air
Before going into specific materials and processes that have been identified to be capable of
capturing CO2 from the air it is important to first get a good understanding of the characteristics of the process. A good starting point for this are the operating conditions of the process.
Stijn de Flart
Master of Science Thesis
2-3 Technologies and processes for CO2 capture from air
9
Since the sorbent has to be capable of capturing CO2 under very dilute conditions, in the
presence of moisture (due to the humidity) and close to room temperature the sorbent has
to have a high selectivity towards CO2 , an acceptable adsorption rate under these conditions
and it has to be highly stable. Furthermore since the aim of the process is to generate and
utilize CO2 on-site it has to be easy to regenerate and it has to be stable over many cycles.
Since many processes have a different CO2 demand it is also important that the technology
is easy to scale. Summing up all these characteristics:
1. High selectivity towards CO2 (compared to other gases present in air)
2. Sufficient binding energy (higher than the 20 kJ/mol from the thermodynamic minimum)
3. Stable under moisture
4. Fast kinetics at ambient conditions
5. Easy to regenerate (not too strongly bound)
6. Scalable
7. Low energy requirement for regeneration
Many sorbent materials are known to be able to capture carbon dioxide ([26], [18], [59]), of
which some of these are also capable of doing so from the air. In Air as the renewable carbon
source of the future Goeppert et al. give an overview of the many different technologies
capable of capturing CO2 directly from the air. Generally, they can be divided in three
groups, namely: inorganic chemisorbents (either in solid form or in solution), physical (solid)
sorbents and solid amine based sorbents. Wang et al. (2014) discusses a great variety of solid
sorbents capable of CO2 capture, however not all of them are suitable for air capture due to
a low selectivity of CO2 , nonetheless the interested reader is referred to the work of Wang et
al. [59]. Some of the above mentioned sorbents will be briefly discussed below.
2-3-1
Inorganic Chemisorbents (solid)
This group of materials mainly include alkaline metal oxides (Na2 O, K2 O) and alkaline earth
metal oxides (CaO, MgO). These sorbents typically react with CO2 in a 1:1 stoichiometry
which can be described by the following reaction:
M O(s) + CO2 (g) M CO3 (s)
(2-5)
Where M can be for example Mg, Ca, Sr, Ba. One of the big advantages is that Calcium
minerals are one of the most abundant minerals on earth and therefore could be an interesting
candidate for CO2 capture at a large scale. The downside however is that these kind of
sorbents require temperatures in excess of 573 K in order to capture CO2 at a reasonable
rate, which introduces a high energy penalty as an unwanted feature. This would imply that
the air first has to be heated up before the CO2 will be captured making this process less
feasible [18].
Master of Science Thesis
Stijn de Flart
10
Direct Air Capture
2-3-2
Inorganic Chemisorbents (in solution)
More interesting for the application of direct air capture are the inorganic chemisorbents in
solution. Strong bases such as sodium hydroxide (NaOH) and potassium hydroxide (KOH)
are capable of reacting with CO2 under atmospheric conditions, forming carbonates. The
general chemical reaction that takes place can be described as follows:
CO2 + 2M OH → M2 CO3 (s) + H2 O
(2-6)
Where again, M represents metals such as Na or K. In this case, the CO2 will react with the
hydroxide group in order to form carbonates. Zeman and Lackner proposed a process that uses
sodium hydroxide to capture CO2 from ambient air [64]. Figure 2-1 shows an overview of this
process. A brief description is given below. In the first step of the process, air is contacted
Figure 2-1: Carbon Dioxide capture process using sodium hydroxide. Reproduced with permission
from [63]. Copyright (2007) American Chemical Society.
with a sodium hydroxide solution which produces dissolved sodium carbonate. After this
initial step, the carbonate ion is removed from the solution in the so-called ’Causticization’
process, where it is reacted with calcium hydroxide, producing calcite (CaCO3 ) and sodium
hydroxide. The sodium hydroxide is recycled back to the air contactor and the calcite is
filtered from the solution. As a final step in the process the calcium carbonate is thermally
decomposed in the Lime Kiln where gaseous CO2 is produced which can be utilized or stored.
In order to prevent an additional gas separation step the thermal decomposition of calcite is
performed in a lime kiln fired with oxygen. Finally, hydration of the lime (CaO) completes
the cycle and produces calcium hydroxide which is used in the causticization process. Table 22 presents the cycle of chemical reactions that are involved in this process. The estimated
energy costs of this process range between 442 and 679 kJ/mol CO2 captured [63], where the
most energy intensive step is the regeneration of the CO2 which requires high temperatures.
As Goeppert et al point out, Calcium hydroxide and other inorganic hydroxides strongly bind
CO2 in general, often far more than needed to capture CO2 from air which introduces high
energy costs in the regeneration process. Combined with their corrosive nature and other
factors it has shifted the focus towards the use of solid sorbents.
Stijn de Flart
Master of Science Thesis
2-3 Technologies and processes for CO2 capture from air
11
Table 2-2: Chemical reactions in the NaOH process
Process
Reaction
Enthalpy of reaction
Air scrubbing
Causticization
Calcination
Hydration
2N aOH + CO2 → N a2 CO3 + H2 O
N a2 CO3 + Ca(OH)2 → 2N aOH + CaCO3
CaCO3 → CaO + CO2
CaO + H2 O → Ca(OH)2
-109.4
-5.3
179.2
-64.5
2-3-3
kJ
molCO2
Solid sorbents
Many solid sorbents have been reported in literature for their capability of capturing and
storing CO2 from air. Sorbents that have been reported range from physical sorbents such
as zeolites or carbon based materials to selective chemisorbents such as solid amine-based
adsorbents. As mentioned in the preceding paragraph, the solid sorbents can basically be
classified as either physical sorbents or chemisorbents. In Principles of adsorption and adsorption processes Ruthven gives the characteristics of both classes and also for this work it
is important to be able to distinguish them (Ruthven 1984, p. 29 [48])
Table 2-3: Characteristics Physical and Chemical adsorption
Physical Adsorption
Chemisorption
Low heat of adsorption (<2 or 3 times latent
heat of evaporation.)
Non specific
Monolayer or multilayer
No dissociation of adsorbed species
Only significant at relatively low temperatures
Rapid, non-activated, reversible
No electron transfer although polarization of
sorbate may occur
High heat of adsorption (> 2 or 3 times latent
heat of evaporation.)
Highly specific
Monolayer only
May involve dissociation
Possible over a wide range of temperature
Activated, may be slow and irreversible
Electron transfer leading to bond formation between sorbate and surface
2-3-4
Physisorbents
Physical solid sorbents capable of capturing CO2 that have been reported in literature mainly
consist of zeolites and activated carbons ([26], [18], [59]). These kind of sorbents are promising
candidates due to their low costs and high surface area as well as the ease of regeneration.
During physical adsorption, both van der Waals forces and electrostatic interactions can play
a role in order to capture a certain molecule. As Ruthven mentions, the van der Waals contribution will always be present whereas the electrostatic contributions will only be significant if
the sorbent has an ionic structure. Zeolites, which are very porous crystalline aluminosilicates,
have been investigated for their CO2 adsorption. As Wang et al. mention, the framework of a
zeolite consist of interlocking tetrahedrons of SiO4 and AlO4 joined together in arrangements
through shared oxygen atoms. The negative charge that is created by the substitution of
a SiO4 tetrahedron for an AlO4 tetrahedron is balanced by exchangeable cations. Wang et
Master of Science Thesis
Stijn de Flart
12
Direct Air Capture
al. [60] report that various studies have already revealed that zeolites in this case have a
physical interaction with the CO2 molecules in the form of an ion-dipole interaction (shown
in equation (2-7)).
(metalion)x+ .....δ− O = C = Oδ+
(2-7)
Although these materials have several excellent characteristics, the adsorption of CO2 on
these kind of materials is physical and relatively weak and they have a reduced capacity in
the presence of moisture. As became clear in the thermodynamics section, the minimum
change in free energy of adsorption is in the range of 20 kJ/mol and the physical interaction
will often be too weak to effectively harvest CO2 . Furthermore physical adsorption is non
specific making it rather competitive with for instance H2 O molecules. A required high
selectivity for CO2 , easily regeneration, scalability, these are all characteristics that point
in the direction of a different type of solid sorbent that has been studied extensively: solid
amine-based adsorbents.
2-3-5
Solid amine-based adsorbents
Having said that absorption in liquid amine solutions is considered to be the state of the art
technology for CO2 capture it makes sense to see how this kind of technology can be applied
by making use of solid sorbents. These kind of sorbents consist of two main ingredients,
namely, a solid and highly porous support such as fumed silica, and a functional amine such
as polyethylenimine (PEI) which is supported on the porous support [16]. Compared to
amine solutions these solid sorbents often have a lower capital cost and require less energy for
regeneration [64] due to their lower heat capacity. Many different kind of solid amine-based
adsorbents have been reported in literature for their capability of capturing CO2 directly from
the air ([16], [9], [37], [13], [61], [33]), which are classified by Goeppert et al based on the
interaction between the support and the active sorbent. They divide the supported amine
sorbents in three classes: class 1 sorbents, class 2 sorbents and class 3 sorbents. Before diving
into the different sorbent classes it is important to understand the role of the amines in the
sorbents.
Type of amine
Choi et al. [18] give a very extensive overview of all different kind of amines that can be used
for impregnation on solid supports, which are mainly silica. The amine group is the part of
the sorbent responsible for the actual capture of the CO2 molecules, where it is expected that
a chemical reaction takes place in order to fixate the CO2 molecules. The interaction between
the amine and the CO2 molecules can be described by several mechanisms, depending on the
nature of the functional group. To clarify this, a little bit of extra background on amines
is required. As can be seen in Figure 2-2, amines are distinguished by their amount of
hydrogen atoms and are classified as Primary Amines, Secondary Amines, Tertiary Amines
and even Quaternary Amines ([61], [33]). As Choi et al. already discussed, primary and
secondary amines can react directly with CO2 molecules to produce carbamates, whereas
tertiary amines catalyze the formation of bicarbonate which is then fixated due to electrostatic
forces. Figure 2-3 shows some of the possible reaction pathways as discussed by Choi et al.
Stijn de Flart
Master of Science Thesis
2-3 Technologies and processes for CO2 capture from air
13
Figure 2-2: From left to right, primary to quaternary amine functional groups.
Figure 2-3: Different reaction pathways for primary to tertiary amines. Reprinted from [18] with
permission from John Wiley and Sons
On top of this there are quaternary amines, such as those proposed by Lackner et al [61]
which are capable of capturing CO2 molecules from ambient air. Very briefly, this sorbent
captures CO2 while it is dry and releases it when wet. This has led to their so-called moisture
swing cycle, which regenerates the CO2 from the material by wetting it. This is somewhat
similar to the capture mechanism of tertiary amines, which also need H2 O in order to be able
to capture CO2 molecules [19]. As each different amine (primary to quaternary) interacts
with CO2 in a different way, it influences the capture speed and regenerability. As Ko et al.
[33] discussed, primary amines exhibit the highest adsorption rate, however the desorption
rate constants of primary amines were almost 4 times lower compared to those of tertiary
amines. Nevertheless, chowdhury et al. mentioned that the low rates of CO2 adsorption make
Master of Science Thesis
Stijn de Flart
14
Direct Air Capture
tertiary amines difficult to use for gas removal. Furthermore, Didas et al. ([22]) evaluated
that primary amines exhibit higher adsorption capacities as well as amine efficiencies under air
capture conditions. Summarizing, desorption is more easily achieved in the order of tertiary
to primary amines, whereas adsorption is better in the order of primary to tertiary amines.
Class 1 supported amine sorbents
This class of sorbents consists of monomeric or polymeric amines that have been physically
adsorbed on support materials such as silica, mesoporous materials or other porous supports.
Goeppert et al for instance prepared a sorbent where fumed silica was impregnated with different weight percentages of branched PEIs (Figure 2-4). They reported high CO2 adsorption
capacities under atmospheric conditions (107 mg CO2 /g), fast kinetics and almost complete
desorption at 85 ◦ C. Exactly the kind of characteristics that are interesting for this thesis.
According to Choi et al, PEI is the most commonly used amine. It is basically build up out
of primary amines, secondary amines and tertiary amines, combining the characteristics of
all 3 different amines.
Figure 2-4: Chemical structure PEI(L) Sorbent sample (R)
A sample of the material was supplied by the Loker Hydrocarbon Research Institute and
Department of Chemistry from the University of Southern California. The sample contains
51.8% PEI and is supported by fumed silica with a particle size of approximately between
500-1700 micrometer, sieved. These kind of sorbents are easy to prepare but due to the
weak interaction between the amines and the support they sometimes have the tendency to
decrease in performance due to leaching of amines.
Class 2 supported amine sorbents
To overcome the degradation issues for the class 1 sorbents the functional amine groups in
the class 2 sorbents are being held in place by covalent bonds. Alesi et al. [3] for instance
investigated a polystyrene supported primary amine resin, VP OC 1065, for which the chemical structure can be seen in Figure 2-5. As is discussed in their article, the primary amines
are covalently attached to the polymer backbone which can solve the leaching problem of the
class 1 supported amine sorbents.
Stijn de Flart
Master of Science Thesis
2-4 Sorbent selection
15
Figure 2-5: Chemical composition sorbent (L) and the actual sample (R)
During their study on the CO2 adsorption characteristics it was shown that the adsorption
capacities were stable over 18 cycles, CO2 is adsorbed under ambient conditions and the VP
OC 1065 is fully regenerated at temperatures of 100 ◦ C (when it’s adsorbed under ambient
conditions). This indicates that this indeed is a material that could be a candidate for a DAC
process. A sample of the material was supplied by Aqua-com.
Class 3 supported amine sorbents
The final class of supported amine sorbents that is discussed by Goeppert et al. are the
sorbents that consist of an inorganic support and a chemically grafted polyamine component. These sorbent materials combine the advantages of the covalently attached amine to
the support together with the high nitrogen loading of polymeric amines, enhancing CO2
adsorption. Choi et al. [17] reports class 3 sorbents referred to as hyperbranched aminosilica
(HAS) materials. Unfortunately no sorbent sample was acquired.
2-4
Sorbent selection
Several different materials and processes have been discussed in the preceding paragraphs
that seem to be suitable candidates for a process that captures CO2 from ambient air. As
became clear in the first two paragraphs of this chapter, a good candidate should be able to
selectively extract CO2 under conditions that are common for air capture (low concentration,
moisture). Other important characteristics are the ease of regeneration (in terms of speed as
well as energy requirement) and the stability over many cycles. Based on these characteristics
most physical sorbents are not being considered any further, since they often bind too weakly
to CO2 and their capacity is sensitive to the presence of moisture. The inorganic chemisorbents such as NaOH or KOH seem to be promising materials however, they require high
temperatures for regeneration and during for instance the production of Sodium Hydroxide a
lot of chlorine is produced which is a toxic gas. This has shifted the focus towards the solid
amine-based sorbents as a candidate for direct air capture.
Master of Science Thesis
Stijn de Flart
16
Direct Air Capture
Table 2-4: Solid amine-based sorbent selection
Sorbent
Class
Amine type
Capacity mg/g 1
reference
FS-PEI-50
VP OC 1065
HAS-6
Class 1
Class 2
Class 3
PEI
Primary Amine
Aminopolymer
62
62
75.7
[25]
[55]
[17]
It was found that most of the solid amine-based sorbents could be regenerated at temperatures around 100 ◦ C, which could be supplied by renewable energy sources or waste heat.
Furthermore do solid sorbents not suffer from solvent evaporation which makes them an ideal
candidate as a sorbent that is exposed to big amounts of air. The use of solid sorbents allows
for a very modular design and once a single unit is able to deliver 1 kg of CO2 per day it can
be easily scaled up. The solid amine-based sorbents seem to meet the process criteria that
were defined earlier in this chapter and therefore has been chosen for this research.
It would be beyond the scope of this thesis to identify every single amine sorbent that has
been reported (although it would be very interesting) and therefore only 1 sorbent per sorbent
class is considered here, outlined in Table 2-4. Based on their differences it is possible to judge
them according to the DAC criteria that have been outlined in the beginning of paragraph
2.3.
From the overview it seems that the HAS-6 sorbent definitely has the best characteristics,
however they do report that the 75.7 mg/g of CO2 adsorption was achieved for an amineloading of 9.9 mmol/g. As they state in their study, the high amine loading increases the
capacity of the sorbent but is accompanied by a decrease in adsorption speed. A suitable
sorbent should not only have a high capacity for CO2 under ambient conditions, it should
also have a good adsorption and desorption rate as well as a high stability under many cycles.
The FS-PEI-50 has good characteristics however as Goeppert et al. pointed out, class 1
sorbents are less stable compared to class 2 sorbents. Based on these arguments and on the
fact that no sample of the HAS-6 sorbent was available it was decided to continue the research
on the VP OC 1065.
2-5
Concluding remarks
Having identified a suitable sorbent for CO2 capture under ambient conditions the following
chapters will shift the focus towards modeling the actual process where it is to be applied.
Stijn de Flart
Master of Science Thesis
Chapter 3
Sorbent characterization and modeling
approach
In the previous two chapters it was explained what direct air capture is, how it could serve
as a tool in the battle against climate change, what kind of materials can be used in this
technology and which material will be focused on in this thesis. As was mentioned earlier,
this thesis aims to identify and model a CO2 capturing process. Having a model that is
capable to predict the sorbents behavior can eventually used as an input for the design of
direct air capture equipment. Having such a device would allow industrial facilities to start
harvesting their own CO2 by recycling it from the air, whereas the only input is heat which
could be supplied in the form of waste heat. This chapter discusses the chosen sorbent in
more detail and gives an overview of the modeling approach that was used in order to model
the CO2 capturing process.
3-1
Model introduction
Although it was referred to as direct air capture in chapter 2, generally speaking it is an
adsorption process. Chapter 2 narrowed down to a single sorbent material which is a solid
polystyrene material, functionalized with primary amines and the actual physics behind this
capture mechanism can be described as those of an adsorption process. In an adsorption process, certain components of a fluid phase (in this case ambient air) are selectively transferred
to solid particles which are often packed in a bed. During adsorption, molecules in a gas (or
liquid) diffuse to the surface of the solid (or a highly viscous resin), where they either undergo
a chemical reaction (chemisorption) which fixates them or where they are being held by weak
intermolecular forces, in case of physical adsorption (Seader and Henley, 2006 p. 548 [20]).
In describing an adsorption process, two parameters are of main concern which have to be
determined both experimentally as well as through modeling. A sorbent has a limited capacity to store a specific gas which is highly dependent on the partial pressure of this gas
as well as the temperature, and one would also need to obtain knowledge about the speed
Master of Science Thesis
Stijn de Flart
18
Sorbent characterization and modeling approach
of adsorption. As Ruthven mentions, obtaining knowledge about the capacity of the sorbent
is done experimentally by measuring isotherms of the material. To obtain an actual speed
of adsorption however is often done by packing the sorbent in a fixed bed and study the response of an initially sorbate free bed to a step change in sorbate concentration at the column
inlet, a so called breakthrough measurement. To extract the adsorption speed however, the
experimental breakthrough curve has to be matched to a mathematical model and therefore
it is important to have one.
In chapter two it became clear that the aim of air capture is rather to skim the air, capturing
the CO2 as efficient as possible. This somehow contradicts the packed bed configuration
where the aim is to completely purify the air stream of CO2 , something that is illustrated
by Figure 3-1. Nevertheless, it is common practice when characterizing a sorbent material
to measure the breakthrough curves ([27], [25], [9]) and therefore it seems a logical step to
create a model of a packed bed reactor.
Figure 3-1: Schematic representation of a packed bed adsorption process
3-1-1
Equilibrium considerations
In an adsorption process, a dynamic phase equilibrium is established between the adsorbate in
the fluid phase and the solid surface of the sorbent. It is common to describe this equilibrium,
or capacity, as a function of the adsorbate fluid concentration which for gaseous adsorption is
the partial pressure of this species. In order to obtain the equilibrium capacity it is necessary
to do experiments. During such experiments the amount of solute loading on the sorbent is
measured as a function of the partial pressure of the solute in the fluid phase which is better
Stijn de Flart
Master of Science Thesis
3-1 Model introduction
19
Figure 3-2: Typical type 1 isotherm
known as an adsorption isotherm (Seader and Henley, 2006 p. 559). Isotherms often have
a characteristic shape and they have been classified into five common types by Brunauer et
al [11]. Discussing all these five different types is not within the scope of this thesis and
only the simplest Type I isotherm will be discussed here. The type I isotherm corresponds to
unimolecular adsorption, where the sorbate covers a single layer on the sorbents surface. Once
a single layer of sorbate molecules cover the sorbent surface it is saturated, which is often
the case for chemisorption processes since there is a limited amount of functional sites. The
isotherm shown in Figure 3-2 is calculated from the Langmuir equation (3-1) and is restricted
to a Type I isotherm. The Langmuir isotherm assumes chemisorption and is named after
Irving Langmuir (1881-1957). It is widely used to describe the reversible chemisorption of
reactants on a solid surface and since it is expected that the CO2 molecules interact in
a chemical way with the sorbent (chapter 2), the Langmuir isotherm seems to be a good
starting point. The general form of the equation is shown below:
θ=
Ki P
1 + Ki P
(3-1)
Where θ is the surface coverage (the fraction of the actual loading divided by the maximum
loading), Ki is the adsorption equilibrium constant and P is the partial pressure of the gas to
be adsorbed. For i is larger than 1 the equation is often referred to as a Dual-site Langmuir
isotherm (i = 2) or even triple sites, which can give a better representation of the experimental
data. In theory any isotherm can be modeled by an n-site Langmuir model, however the link
to reality will be lost since it will obtain a ’curve-fitting’ character.
3-1-2
Rate of adsorption
As discussed in the previous paragraph, the rate of adsorption is a parameter that is of great
importance for the actual design and sizing of an adsorption system. This parameter can
be obtained by doing breakthrough experiments and by matching the breakthrough curve to
Master of Science Thesis
Stijn de Flart
20
Sorbent characterization and modeling approach
Figure 3-3: Experimental and theoretical breakthrough curves for CO2 adsorption on aminefunctionalized mesoporous silica. Reprinted from [50] with permission from Elsevier.
a theoretical model. During a breakthrough experiment, an initially sorbate free column is
exposed to a step concentration of the adsorbable gas and the concentrations at the inlet and
outlet are being monitored. As soon as these concentrations are the same, breakthrough has
occurred and the column can be considered as saturated. By matching this curve with the
mathematical model one can use the kinetic parameters to fit the theoretical model to the
experimental data and will obtain information about the kinetics of the sorbent at certain
process conditions (partial pressure and temperature). A good example of such an experiment
where the theoretical breakthrough curve is matched with the experimental one is shown in
Figure 3-3. The dashed lines indicate the experimental results and the solid lines represent
the matched theoretical model.
3-2
Sorbent characterization
As already became clear in chapter 2, the sorbent chosen for this thesis consists of primary
amine functionalized polystyrene porous beads. According to Alesi et al. 8-10% of the
polymeric structure is cross-linked with divinylbenzene in order to increase the structural
stability of the resin [3]. During their study they exposed the sorbent to a 10 vol % CO2
in N2 mixture at adsorption temperatures ranging from 30 to 70 ◦ C. The capture capacity
remained stable over 18 cycles and the capacities ranged from 1.85 to 1.15 mol CO2 /kg
sorbent. Although they did not expose the resin to atmospheric CO2 levels they do report that
the resin already takes up 1 mol CO2 /kg sorbent upon exposure to air, which is comparable
to other air capturing sorbents. Some other characteristics of the resin are summarized in
Table 3-1. Veneman et al. [56] did a similar study of the adsorption behavior of CO2 on this
resin where they looked at the effect of H2 O on the CO2 adsorption capacity. They measured
adsorption isotherms for both CO2 and H2 O at different temperatures and concluded that the
Stijn de Flart
Master of Science Thesis
3-2 Sorbent characterization
21
Table 3-1: Sorbent properties
reference
BET Surface area (m2 /g)
BJH pore volume (cm3 /g)
Amine loading (mol N/kg)
CO2 capture capacity in air (mol CO2 /kg resin)
Bulk density (cm3 /g)
Median particle size (mm)
26.2
0.26
5.9
1
0.45
0.7
[3]
[3]
[30]
[3]
[3]
[3]
Figure 3-4: Adsorption isotherms of the sorbent. Reprinted from [56] with permission from
Elsevier.
resin adsorbs 4-5 times more H2 O than CO2 under conditions relevant for post-combustion
CO2 capture. Furthermore they concluded that H2 O has a rather positive effect on the CO2
adsorption; the resin adsorbs more CO2 in the presence of water in the gas phase. From
Figure 3-4 it can be seen that the isotherm indeed has the characteristic Type I shape.
Unfortunately, the isotherm was computed for partial pressures of CO2 that are relevant for
post combustion capture (80 kPa) whereas for direct air capture the range between 0 to 100
Pa partial pressure is more of an interest.
When describing an isotherm for chemisorption it is often important to be aware of the
chemical interaction between the solute and the sorbent’s functional groups. The primary
amines are responsible for the chemisorption of CO2 and different kind of reaction mechanisms
have been reported in literature. Alesi et al. used infrared spectroscopy while exposing it
to CO2 to identify what kind of mechanisms could explain the CO2 capture. They found
evidence that carbamic acid/carbamate species are formed and possibly bicarbonate species.
A mechanism that is also reported by Satyapal et al. [49] where they propose the following
Master of Science Thesis
Stijn de Flart
22
Sorbent characterization and modeling approach
reactions:
CO2 + 2R2 N H R2 N H2+ + R2 N COO− (carbamatef ormation)
(3-2)
When moisture is present the carbamate ion can react with water to form bicarbonate:
R2 N COO− + 2H2 O + CO2 R2 N H2+ + 2HCO3− (bicarbonatef ormation)
(3-3)
Which may also form directly from the amine, CO2 water reaction.
CO2 + R2 N H + H2 O R2 N H2+ + HCO3−
(3-4)
Furthermore they concluded that the resin also captures CO2 by solubility in the polymer,
however this was under 10% CO2 and it is not expected that any CO2 will dissolve in the
resin under ambient conditions. Having that said the main CO2 capture mechanism is based
upon a chemical reaction. Choi et al. propose a somewhat different chemical mechanism for
primary amines where the CO2 molecules interact directly with the primary amine, through
a zwitterion mechanism as shown below [18]:
Figure 3-5: Alternative reaction mechanism
The lone pair of electrons on the amine starts to attack the carbon atom from the CO2 in
order to form the zwitterion. From there, the zwitterion is deprotonated by a free base which
could be a second amine group or perhaps a water molecule. This would suggest that under
dry conditions the theoretical maximum CO2 capacity would be 0.5 mol per mol of N and
under humid conditions the theoretical maximum capacity would be 1 mol CO2 per mol N.
As Lu et al. (2013) already mentioned, it is very important to keep the chemical characteristics
of the sorbent in mind when fitting the isotherm model to the experimental data. In their
study they investigated several Amine-grafted porous polymer networks where they used a
three-site Langmuir model in order to represent the isotherm of the sorbent for CO2 adsorption
[37]. Since it is unclear which of the above mentioned reactions play a role in the CO2 capture
under gaseous conditions for the VP OC 1065, molecular modeling with Spartan software has
been used which will be discussed in chapter 4. By applying molecular modeling insight into,
different reaction pathways is obtained. Not only will this give input for an isotherm model,
but as will become more clear later, it will also provide thermodynamic quantities that can
be used to describe the temperature dependence of the CO2 capacity. Having characterized
the sorbent the next paragraph focuses on the modeling approach that is used for the packed
bed model.
Stijn de Flart
Master of Science Thesis
3-3 Modeling Approach
3-3
23
Modeling Approach
Modeling an adsorption process can be a rather complex and challenging task and a good
and structured approach is necessary in order to simplify the model as much as possible and
to get a good understanding of the actual physics describing the process. A common method
that has been proposed during the course ’Modeling of Processes and Energy Systems’ (P.
Colonna, 2014) is the 9 step method [44], which provides a structured approach to tackle
complex modeling problems. For this model, some of those steps were applied in order to get
a complete understanding of the modeling goal and system to be modeled.
3-3-1
Modeling Goal
As already became clear, a common way to characterize the rate of adsorption is by doing
breakthrough experiments, however to extract this information it has to be matched to theoretical models. The model should therefore be capable to describe the adsorptive behavior
of a solid sorbent in a packed configuration when it is exposed to a step change in sorbate
concentration. The desired output of the model are breakthrough curves such as shown in
Figure 3-3.
3-3-2
System description
A schematic representation of the process is shown in Figure 3-6. As is indicated in the
sketch, the packed bed is exposed to an air stream with a certain velocity u. The dimensions
of the packed bed are indicated as well as the packing density, which takes the void area into
account. When the air travels through the bed it selectively adsorbs the CO2 , where it travels
from the fluid phase into the solid (or adsorbed) phase. The system boundary is indicated
by the dashed line. In order to actually predict the breakthrough curve the model should be
able to describe the CO2 concentration in both the fluid phase (cf (z, t)) as well as the solid
phase (cs (z, t)) at every moment in time as well as every position in the bed.
3-3-3
Hypotheses and assumptions
As with most engineering problems, the starting point for a mathematical description of
a physical system is often provided by the conservation equations (mass, momentum and
energy). However, these equations can often be simplified drastically by applying the correct
assumptions. Ruthven provides a very useful classification scheme which allows a detailed
analysis of the system which will be used as well for this work. As Ruthven mentions (1984,
p. 224): ’the dynamic behavior of an adsorption system may be classified according to the
nature of the mass transfer front and the complexity of the mathematical model required to
describe the system.’ The nature of the mass transfer front is determined by the isotherm
whereas the complexity of the mathematical model depends on sorbate concentration in the
fluid phase, the choice of the mass transfer rate equation and the choice of the flow model.
The starting point for the model is the differential mass balance equations for a small control
volume in the adsorption column:
− DL
Master of Science Thesis
∂2c
∂
∂c
+
(uc) +
+
∂z 2 ∂z
∂t
1−
∂ q̄
ρp
=0
∂t
(3-5)
Stijn de Flart
24
Sorbent characterization and modeling approach
Figure 3-6: Schematic representation of a packed bed separation process
∂ q̄
= f (q, c)
(3-6)
∂t
Where c represents the adsorbate concentration in the fluid phase, DL is the axial dispersion
coefficient, u is the velocity through the bed and is the void area in the bed. Equation (3-6)
is the mass transfer rate expression for the adsorbable component into the solid phase. This
term is commonly a set of equations containing diffusion equations with respective boundaries
which incorporates the equilibrium constraints (given by the isotherm) to which the mass
transfer term must eventually reduce to. The solution to the mass balance equation will give
the distribution of the gas composition throughout the bed. Equation (3-5) is the very general
mass balance equation for a fixed bed system which is commonly used to describe packed bed
adsorption ([24], [51]) and can often be simplified according to Ruthvens classification scheme
which is outlined below (Ruthven, 1984 p. 224).
Nature of Equilibrium Relationship
Langmuir isotherms are classified as Favorable Isotherms. In this case the mass transfer front
that is created when the bed is exposed to a sorbate concentration approaches a constant
pattern form. For some special cases analytical solutions are available.
Isothermal or Near Isothermal
Since adsorption is an exothermic process and temperature changes may have an effect on
both the equilibrium relation as well as the adsorption rate the internal heat generation has
to be considered. However, in systems where the adsorbable component is present only at
very low concentration (which is the case for DAC) the system can be classified as isothermal.
Concentration level of adsorbable components
Stijn de Flart
Master of Science Thesis
3-3 Modeling Approach
25
If the adsorbable component is present at low concentration the system can be classified as a
trace system. Since both the concentrations of water as well as carbon dioxide are very low
the DAC system can be described as a trace system. Changes in the fluid velocity across the
mass transfer zone are therefore negligible.
Flow Model
The flow model can be either classified as plug flow or as dispersed plug flow. In a plug
flow system, the axial dispersion term that is present in the mass transfer equation can be
neglected however since it is unclear if this can be neglected without doing experiments the
system is classified as a dispersed plug flow system.
Complexity of the Kinetic Model
As was pointed out, the ∂∂tq̄ term in equation (3-5) is often a set of complex diffusion equations and a very common simplification is the linear driving force (LFD) model ([20], [50]).
Shafeeyan et al. [51] give a review of mathematical modeling of fixed-bed columns for carbon
dioxide adsorption where they give an overview of 34 modeling studies of which 28 made use
of the LDF model showing its wide applicability. The LDF model assumes that the uptake
rate of the adsorbable component is proportional to the linear difference between the adsorbate loading in equilibrium with the solute concentration in the bulk fluid, and its average
concentration within the particle (denoted as q̄). The equilibrium loading can be computed
from the isotherm of the material and finally the linear rate expression is given by:
∂ q̄
= k(q ∗ − q̄)
∂t
(3-7)
Table 3-2 summarizes all the assumptions that have been done for this model.
Table 3-2: Model assumptions
Equilibrium
relationship
Flow pattern
Mass transfer rate
model
Heat effects
Others
Langmuir
isotherm
Axial dispersed plug
flow
LDF
Isothermal
Trace system, negligible
pressure drop
3-3-4
Governing equations and boundary conditions
Implementing the above mentioned assumptions, the fluid mass balance becomes:
−DL
Master of Science Thesis
∂c
∂2c
∂
+ u (c) +
+
∂z 2
∂z
∂t
1−
∂ q̄
ρp
=0
∂t
∂ q̄
= k(q ∗ − q̄)
∂t
qm Ki P
q∗ =
1 + Ki P
(3-8)
(3-9)
(3-10)
Stijn de Flart
26
Sorbent characterization and modeling approach
As Serna-Guerrero et al. (2010) [50] already pointed out, since the system behaves as an
isothermal system the mass balance equation can be solved without solving the energy balance.
Initially, the column is sorbate free:
c(z, 0) = 0
(3-11)
q̄(z, 0) = 0
(3-12)
At the inlet a third-type boundary condition is considered and at the outlet the no-flux
boundary condition was applied.
DL
∂c
|z=0 = −u|z=0 (cf − c|z=0 )
∂z
∂c
|z=L = 0
∂z
(3-13)
(3-14)
When a fluid is flowing through a packed bed axial mixing can occur. This is an unwanted
effect since it reduces the efficiency of the separation (Ruthven 1984, p. 208). In the fluid
mass balance equation all the effects that contribute to axial mixing are lumped in a single
parameter DL . The axial dispersion coefficient can be determined experimentally or can be
estimated from correlations. For gaseous systems a good first approximation is often given
by:
DL = γ1 Dm + γ2 Dp u
(3-15)
Where γ1 and γ2 are constants which normally have values of 0.7 and 0.5 respectively, Dp is
the particle diameter and Dm denotes the molecular diffusivity of the adsorbable component.
The value for k in equation (3-9) denotes the overall mass transfer coefficient which can be
pressure and temperature dependent and is fitted to experimental results which is common
to do [15]. Finally, the equilibrium capacity for the sorbent is determined by the isotherm.
As was mentioned, equation (3-10) can represent an x-site Langmuir isotherm where Ki is
the equilibrium constant. The equilibrium constant is temperature dependent and can be
correlated to the heat of adsorption according to the Van ’t Hoff equation.
−∆Hads
Ki = K0i exp
RT
(3-16)
The heat of adsorption can be determined experimentally, however, often it takes a lot of time
to set up these experiments. Since it is a chemical reaction that fixates the CO2 molecules, a
very promising alternative is to apply molecular modeling. As was already mentioned earlier,
not only can molecular modeling provide insight in how many site’s the isotherm model would
need (e.g. dual site for 2 reaction pathways involved in CO2 capture), it can also provide
thermodynamic quantities such as heats of adsorption which can be used to describe the
equilibrium constant given in (3-16). Since the possibilities with molecular modeling software
are huge and this will be discussed seperately in chapter 4.
3-4
Concluding remarks
A mathematical description of the packed bed system was discussed and a hypothetical x-site
langmuir isotherm was proposed as a description for the CO2 capacity. Additional information about the chemical interaction of the sorbent with CO2 is required to further specify
Stijn de Flart
Master of Science Thesis
3-4 Concluding remarks
27
the isotherm model whereas values such as heat of adsorption are needed to describe the
temperature dependence of the model. Since literature reports different kinds of reaction
mechanisms, of which some are based upon the interaction of CO2 with amines in an aqueous
environment, it was decided to use quantum chemical calculations to justify how the CO2
interacts with the VP OC 1065. Chapter 4 will focus on the quantum chemical calculations
that have been performed in this study. The results of these calculations will serve as an input
for the mathematical model described in this chapter. Solving the system of equations is quite
a challenging task. Due to the Langmuir isotherm it is a non-linear system and no general
analytical solution exists. Generally, a numerical solution has to be obtained. Chapter 5 will
describe the applied numerical routine in order to solve the system of equations.
Master of Science Thesis
Stijn de Flart
28
Stijn de Flart
Sorbent characterization and modeling approach
Master of Science Thesis
Chapter 4
Molecular modeling
In the previous chapters it became clear that different reaction mechanisms have been reported
in literature for the reaction between CO2 and functional amine groups in solid sorbents. On
top of this, the mathematical model for the packed bed requires a description of the isotherm
of the sorbent. When creating a model for the sorbent’s capacity it is important to have
a good understanding about the chemical interaction of the material. Molecular modeling
can be used to support or justify the proposed reaction mechanisms from literature and can
be used to estimate thermodynamic data such as activation barriers or reaction energies.
As became clear in the previous chapter, thermodynamic data can be used to describe the
temperature dependence of the sorbent’s CO2 capacity. This data often compares very well
to experimental data [46], [45].
4-1
Introduction
As Young mentions: ’Computational chemistry is used in a number of different ways. One
particularly important way is to model a molecular system prior to synthesizing that molecule
in the laboratory’. Although molecular models should not be considered as the perfect or exact
solution (very few aspects of chemistry can be computed exact), they are often good enough
to rule out 90% of the possible compounds being unsuitable for their intended use (Young,
2001 p. 3 [62]), avoiding experimental work without the desired results. More applicable to
this study is the second use of computational chemistry. Computational chemistry can be
used to understand a problem more completely. Thermodynamic properties such as heat of
reaction and heat of adsorption can be determined theoretically as a starting estimate before
conducting experiments and transition states can be calculated and visualized to provide
information about the reaction mechanism.
The software of choice for this study is Wavefunction’s Spartan’14 which has become a big
favorite of both experimental chemists and educational institutions. Spartan offers ab initio,
density functional (DFT), semi-empirical and molecular mechanics methods which are integrated in an easy to use graphical interface. One of the strengths of the software is the ease
Master of Science Thesis
Stijn de Flart
30
Molecular modeling
of use and the robustness (Young, 2001 p. 330 [62]). Discussing all fundamental principles
on which computational chemistry is based would lie outside of the scope of this thesis. It is
considered more important to know how to apply the software on a practical level by using
rules of thumb and guidelines provided by Young, Wavefunction and experts, rather than
knowing in detail how the properties and geometries are calculated.
In chapter 3 it became clear that different mechanisms are being reported for the interaction
of CO2 with amine functionalized solids. Instead of setting up different kind of experiments
in order to conclude the reaction mechanism, Spartan will be used to model these mechanisms
and see which ones seem to be the most plausible. Furthermore the heats of reaction can be
used as an input for the mathematical model. It is important to use simplifications wherever
possible in order to reduce computational time and increase accuracy.
4-2
Research Questions
A reaction mechanism between primary amines and CO2 that is often encountered is the
zwitterion-carbamate route. The carbon atom is attacked by the free electrons on the nitrogen
atom in order to form the zwitterion.
CO2 + RN H2 RN H2+ COO−
RN H2+ COO−
−
+ B RN HCOO + BH
+
(Zwitterion f ormation)
(4-1)
(P roton transf er to f ree base B)
(4-2)
The zwitterion is then deprotonated by a free base, which can be another amine group or
a water molecule to form a carbamate (or carbamic acid). This mechanism is reported
in different studies and is based upon the reaction of amines with CO2 in an aqueous
environment.[18][12][19][22] An interesting question that arises is that if in the case of a solid
sorbent, in a gas-solid interface compared to an aqueous environment, the zwitterion route
still holds. Besides the zwitterion route, a somewhat similar reaction mechanism is reported
involving the direct formation of carbamate where CO2 reacts with two amine groups (4-3)
which was described earlier in 3.2.
CO2 + 2RN H2 RN H3+ + R2 N COO−
(Direct carbamate f ormation)
(4-3)
An important consideration is that in a solid sorbent the amine functional groups have a
fixed position. Will the functional amine groups be close enough to each other in order for
the proton transfer to occur? Alesi et al. also identified the formation of bicarbonate species
in their study. The bicarbonate formation can be explained by the reaction mechanisms that
has been reported by Satyapal et al. (2001 [49]).
CO2 + RN H2 + H2 O RN H3+ + HCO3−
R2 N COO− + 2H2 O + CO2 R2 N H2+ + 2HCO3−
(Direct bicarbonate f ormation)
(4-4)
(Carbamate to bicarbonate reaction)
(4-5)
Interesting thus is to model and see what kind of effect water will have during the interaction
of the primary amine functional groups and the CO2 molecules. Summarizing, three basic
questions can be formulated which can be modeled within the Spartan environment in order
to come to a conclusion.
Stijn de Flart
Master of Science Thesis
4-3 Modeling approach and development
31
1. Is the zwitterion route also valid in a ’dry’ and gaseous environment?
2. Will the functional amine groups be close enough to each other to play a role in the
proton transfer and carbamate formation?
3. What effect does water have on the CO2 adsorption of functional amines?
In order to answer these questions several molecular models have been made within spartan
which will be discussed below.
4-3
Modeling approach and development
The aim of the molecular modeling is to justify the proposed reaction mechanisms. In determining an entire reaction coordinate, a number of molecular structures and their energies are
important in order to define a reaction mechanism (Young, 2001 p. 147 [62]). For the most
simple single-step reaction, 5 of those structures should be included:
1. Reactants, separated by large distances
2. The van der Waals complex between the reactants
3. The transition structure
4. The van der Waals complex between the products
5. The products separated by large distances
Using these 5 steps as a so-called reaction coordinate and plotting them against the total
energy of the compounds it can be visualized as a reaction profile such as seen in Figure 4-1
The reaction profile is a useful visualization for grasping quantities such as activation energy
Figure 4-1: Typical reaction profile
(Ea) or the heat of reaction. For activated complexes, the activation energy can give the
dependence of the rate of reaction on temperature in the form of the Arrhenius equation.
k = k0 exp−Ea /RT
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Molecular modeling
Where k is the rate constant and k0 is the pre-exponential factor. The rate constant is directly
proportional to the rate of reaction and depends on the reactant concentration. For a first
order reaction the rate of reaction is given according to equation (4-7).
r = k[A]
(4-7)
Where [A] is the reactant concentration. As can be seen in the reaction profile, a maximum
exists which corresponds to a transition structure. The geometry of such a transition structure
is an important piece of information since it provides insight in the transition from reactants
to products. In order to model the compounds in each of the 5 steps a general approach is
needed. As was mentioned before, the aim of this thesis is not necessarily to discuss all the
different quantum mechanical methods but rather to apply routines that are commonly used
to model each system. According to Buijs [58], a good approach is to use molecular mechanics
to identify the most stable conformers. The most stable conformer is further optimized using
the semi-emperical pm3 method, which is then used as an input for the density functional
calculations (b3lyp, 31-G*) . This general approach, explained in Figure 4-2, is used in various
molecular modeling studies and seems like a suitable approach in order to tackle each of the
research questions [10] [45].
Figure 4-2: Molecular modeling approach
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Transition states can be obtained by creating an energy profile by varying the Van der Waals
complex (for instance by increasing a bond length) at pm3 level. The energy profile is then
used as an input for the transition state geometry calculation, which is further optimized at
b3lyp (31-G*) level. All the following models use the approach shown in Figure 4-2. Every
geometry is first calculated at pm3 level and then further optimized at b3lyp (31-G*) level.
4-3-1
Carbamic acid route
As became clear in section 2.4 the VP OC 1065 is build up out of repeated benzylamine
units that are cross-linked with divinylbenzene in order to improve its mechanical properties.
Modeling a complete part of this polymeric resin would lead to enormous computational times.
Since it is expected that the functional amine groups on the benzylamine will be responsible
for the reaction, rather than the complete resin, it seems to be a good starting point to model
a single benzylamine unit. After having modeled the separate reactants, the second step is the
Van der Waals complex, where physical forces keep the CO2 molecule fixated to the functional
amine group. Figure 4-3 shows the Van der Waals complex between a CO2 molecule and the
benzylamine unit. The electrostatic potential map shows that the partially positive carbon
atom gets attracted by the negative nitrogen atom, forming a complex.
Figure 4-3: L: Molecular model benzylamine. R: Van der Waals complex between benzylamine
and CO2 (b3lyp 31-G*).
The next step would be to find a transition state for which a good starting ’guess’ is required.
A good starting structure could be provided by decreasing the distance between the carbon
atom and the nitrogen atom in small steps and calculating the equilibrium geometry at each
step. A so-called energy profile is obtained, which visualizes what happens when the carbon
atom starts to get closer to the nitrogen atom. From this energy profile calculation, a starting
structure for the transition state calculation was obtained, shown in Figure 4-4.
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Molecular modeling
Figure 4-4: Energy profile calculation for the transition state starting structure (CO2 approaching
the nitrogen atom, pm3).
Using the complex from the energy profile as a starting geometry, while removing all the
constraints, the following transition state was obtained. Characteristic to a valid transition
state is a single imaginary frequency, which when animated represents the reaction itself. A
good way to validate a transition state is thus to animate this frequency and see if it shows
the expected behavior. For the transition state between benzylamine and CO2 the imaginary
frequency was found to be i1723, and when animated it shows proton transfer from the amine
functional group towards the oxygen atom of the CO2 , indicating the formation of carbamic
acid.
Figure 4-5: Transition state geometry between CO2 and benzylamine (i1723, b3lyp 31-G*).
Following the transition state geometry, the product to be modeled consists of the functional
amine group, where one proton has transfered to the oxygen atom and the carbon atom has
bonded with the nitrogen atom shown in Figure 4-6.
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Table 4-1: Calculated total energies of the zwitterion route for Benzylamine and CO2 .
Compound
Reactants
Van der Waals Complex
Transition State
Carbamic acid anti
Carbamic acid normal
E (kJ/mol)
Hcorr (kJ/mol)
∆H
-1353412.6
-1353427.5
-1353254.4
-1353396.8
-1353430.7
444.72
444.23
437.11
447.92
449.07
0
-15.44
150.62
18.98
-13.72
Figure 4-6: Product geometry of the reaction between CO2 and benzylamine (b3lyp 31-G*).
Besides providing equilibrium geometries spartan also calculates the total energy’s of each
compound. For instance, the heat of reaction can be calculated according to equation (4-8)
[46]. Having identified all the different compounds for each step a reaction profile can be
computed.
∆Ereaction = Eproducts − Ereactants
(4-8)
As is mentioned in the Quantum Mechanics Energy FAQ from Wavefunction: ’The quantum
chemical calculations in Spartan assume that molecules are isolated, with a temperature of
zero Kelvin, and with stationary nuclei. Real experiments are carried out with vibrating
molecules at finite temperature (often 298.15 K). In order to correct for these differences
Spartan can use calculated frequency data to determine a set of normal-mode vibrational
frequencies (νi ).’[54]. In practice this translates itself into an enthalpy correction, split into
four terms. The ’Zero point energy’ (Zp), the temperature correction (Hv), enthalpy due to
translation (Ht), and enthalpy due to rotation (Hr). Using equation (4-8) together with the
enthalpy correction, the energies for each complex can be calculated and are shown in Table 41. Where ∆H in this case is the change in enthalpy relative to the reactants (Benzylamine
and CO2 together).
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Molecular modeling
Model simplification
Since benzylamine is a relatively large molecule it is worth the effort to see whether it can
be simplified even further in order to reduce computational times. The most simple approximation would be to model the benzylamine as methylamine, since it would still contain the
C-N bond at the methyl nitrogen interface and it still contains the functional amine group.
Doing the exact same calculations as described above, the following energies were calculated
which are shown in Table 4-2.
Table 4-2: Comparison of zwitterion route for methylamine and benzylamine.
Compound
Reactants
Van der Waals Complex
Transition State
Carbamic acid anti
Carbamic acid normal
E (kJ/mol)
Hcorr (kJ/mol)
∆HM ethylamine
∆HBenzylamine
-746782.3
-746798.2
-746628.2
-746768.9
-746803.2
220.33
221.37
214.43
225.22
225.77
0
-14.87
148.25
18.32
-15.45
0
-15.44
150.62
18.98
-13.72
When comparing the change in enthalpy from each of the reaction steps between Methylamine
and Benzylamine it can be seen that the difference is almost negligible, indicating that the
functional amine group plays a much bigger role in the reaction than the polymer backbone.
For this reason, Methylamine is chosen as the model to represent the functional groups in the
resin since this will greatly reduce the computational time. Using the values in Table 4-2, a
reaction profile can be computed, which is shown in Figure 4-7.
Figure 4-7: Reaction profile for the Zwitterion route with Methylamine and CO2
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Concluding remarks
Looking at the reaction profile in Figure 4-7 it can be seen that it is a slightly exothermic,
activated reaction. The barrier for reaction is in the order of 160 kJ/mol. Jamróz et al.
[31] performed a similar theoretical study where they investigated the hypothetical zwitterion
structure. They report experimental activation barriers ranging from 38-55 kJ/mol for this
reaction whereas their quantum-chemical results were found to be in the order of 188 kJ/mol.
A general rule of thumb is that reactions with an activation barrier below 88 kJ/mol will
proceed readily at room temperature. Since CO2 does get adsorbed by the resin at room
temperature the reaction barrier of 160+ kJ/mol seems to be much too high to be a realistic
model for the reaction; catalysis is needed. Since several other reaction pathways have been
proposed it is expected that perhaps those play a more dominant role in the capture of CO2 .
4-3-2
Amine catalyzed route
The reaction between a CO2 molecule and two functional amine groups has been reported as
a possible reaction pathway in solid amine-based sorbents (4-9).
2RN H2 + CO2 RN H3+ + R2 N COO−
(4-9)
For this reaction to be possible the two functional amine groups should be close enough
to each other for the proton transfer to occur. Since no data is available on this matter,
the Spartan software can be used to provide additional insight. Alesi et al. (2012) used
Energy-dispersive X-ray spectroscopy in order to estimate the mass and molar concentration
of nitrogen within the resin. This measurement calculated the composition as 10.7 wt % of
N with the balance C. Based on stoichiometry this equals to 8.3:10.7:81.0 H:N:C on a weight
basis. Furthermore 8-10 % wt of the resin is cross-linked with divinylbenzene to increase
its mechanical properties. Based on this data, a simplified model for the polystyrene with
primary amine groups and cross-linked with divinylbenzene was made with Spartan. The
model is build up out of benzylamine units and contains one divinylbenzene group acting as
a cross-linker. The model has a composition of 8.4:9.6:82 H:N:C based on mass and a total
weight of 1318.941 amu.
In order to justify if the amine groups will be close enough to each other a conformer distribution was made with Spartan. During the conformation searching, Spartan starts to change
the initial geometry to find a lower-energy geometry. Figure 4-8 shows the initial geometry
that was used as an input for the conformation searching in Spartan. From the calculated
conformations the 100 lowest-energy conformations were selected and studied in more detail.
Figure 4-9 shows a close-up of the lowest energy conformers where it immediately becomes
clear that the 3 primary amine groups are close to each other.
The distances N9-N2 and N2-N5 were measured to be 3.138 Å and 3.051 Å respectively
which is considered as close enough for proton transfer to occur. When studying the first 10
conformations (which are already 98.3 % of the most likely geometries) it became clear that
roughly 50 % of the primary amines were positioned close to each other, implying that indeed
two functional amine groups could be involved in capturing a single CO2 molecule.
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Molecular modeling
Figure 4-8: Initial geometry of the simplified VP OC 1065 model (MMFF).
Figure 4-9: L: Close up of the simplified VP OC 1065 model. Amine groups are encircled. R:
Conformer distribution, of the 100 best conformers (MMFF).
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4-3 Modeling approach and development
39
Reaction mechanism
Based on the conformer distribution generated by Spartan it is likely that 40-50% of the
primary amine groups will be near each other in order to play a role in the reaction with
CO2 . A similar calculation as with the zwitterion mechanism can be performed, where the
starting geometry in this case consists of 2 methylamine molecules, interacting with CO2 .
Figure 4-10 shows the Van der Waals complex for this system.
Figure 4-10: Van der Waals complex between CO2 and 2 methylamine molecules (b3lyp 31-G*).
It can be seen that a hydrogen bond exists between one of the oxygen atoms from CO2 and
a hydrogen atom from the primary amine. Furthermore the slightly negative nitrogen atom
interacts with the slightly positive carbon atom, fixating the CO2 . It was found that proton
transfer triggered the reaction, which can be seen from the snapshot of the energy profile in
Figure 4-11.
Figure 4-11: Proton transfer to the second methylamine (pm3).
Letting the H-N bond length increase in steps, the CO2 molecule starts approaching the
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Molecular modeling
nitrogen atom whereas the other proton starts approaching the oxygen atom. The calculated
transition state is shown in Figure 4-12.
Figure 4-12: Transition State between CO2 and two methylamine groups (i570, b3lyp 31-G*).
Upon animation of the unique frequency of i570 it shows clear carbamate formation, where
the product of the reaction is the salt between carbamate and methylammonium which is
the input for the product geometry calculation. The optimized product geometry on b3lyp
(31-G*) level is shown in Figure 4-13.
Figure 4-13: Product geometry for the reaction between CO2 and two methylamine groups
(b3lyp 31-G*).
From the product geometry it becomes clear that the system leans towards a carbamic acid
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- methylamine configuration. Table 4-3 shows the total energies together with the enthalpy
corrections for this route.
Table 4-3: Calculated total energies of the amine route for 2 Methylamine and CO2 .
Compound
Reactants
Van der Waals Complex
Transition State
Product
E (kJ/mol)
Hcorr (kJ/mol)
∆H
-998445.11
-998487.99
-998417.85
-998529.34
400.78
403.95
400.73
409.75
0
-39.71
27.22
-75.26
Again, the ∆H represents the change in enthalpy relative to the reactants. It can be seen
that the reaction has become much more exothermic, with an enthalpy of reaction of -75.26
kJ/mol, which compares rather well with the heat of adsorption of 84 kJ/mol for primary
amines reported by Satyapal et al. (2001). Compared to the zwitterion route, the activation
barrier of 66.93 kJ/mol for this reaction is more than 2 times lower. Figure 4-14 shows the
reaction profile for this route. The values for the heat of reaction and activation barrier are
calculated from Table 4-3 and displayed in the profile. In addition, the activation barrier
for the reverse reaction equals 102.48 kJ/mol, shifting the equilibrium to the right at low
temperatures. An activation barrier of 66.93 kJ/mol fits rather well in the image of CO2
adsorption under ambient temperature. Based on the results of this simulation the direct
reaction of 2 amine groups and a CO2 molecule therefore seems to be a possible reaction
pathway.
Figure 4-14: Reaction profile for the amine catalyzed carbamate formation.
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Molecular modeling
4-3-3
Carbamic acid catalyzed route
Planas et al. (2013) performed a quantum chemical study on the adsorption of CO2 in
amine functionalized metal organic frameworks (mof) [46]. During their study they performed
quantum chemical calculations on a similar system, where 2 amine groups are positioned
close to each other. They indeed found the amine catalyzed reaction between CO2 and the
two functional amine groups, however, they found that when the carbamic acid - amine
complex exists, a second CO2 molecule can be captured through carbamic acid catalysis. In
order to investigate this route for the VP OC 1065 some quantum chemical calculations were
performed. The starting complex is the VdW complex between the product geometry from
Figure 4-13 and a CO2 molecule (Figure 4-15).
Figure 4-15: Van der Waals complex between carbamic acid, methylamine and CO2 (b3lyp
31-G∗ ).
Letting the CO2 approach the unoccupied amine site, the following starting structure for the
transition state calculations was obtained, shown in Figure 4-16.
Figure 4-16: Starting structure transition state calculation (pm3).
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The hydrogen atom from the carbamic acid starts to orient itself in the direction of the oxygen
atom from the CO2 molecule, whereas the hydrogen atom from the functional amine group
orients itself towards the oxygen atom from the carbamic acid group. Using this starting
structure, the following transition state was obtained (Figure 4-17).
Figure 4-17: Transition state geometry (i861 b3lyp 31-G∗ ).
The transition state shows the formation of a second carbamic acid complex, which is catalyzed by the already present carbamic acid. The product is completely in-line with the work
of Planas et al. where they also found formation of a second carbamic acid group. The final
product geometry is shown in Figure 4-18.
Figure 4-18: Product geometry for the carbamic acid catalyzed CO2 capture (b3lyp 31-G∗ ).
In a similar matter as before, the total energies for this route can be calculated and visualized
which will provide some thermodynamic quantities (Table 4-4).
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Molecular modeling
Table 4-4: Calculated total energies of the amine route for 2 Methylamine and CO2 .
Compound
E (kJ/mol)
Hcorr (kJ/mol)
∆H
Reactants
Van der Waals Complex
Transition State
Product
-1493648.97
-1493656.61
-1493605.14
-1493696.02
449.63
448.00
439.36
452.61
0
-9.27
33.56
-44.07
Having values for the total energies the complete route can be visualized by adding the first
amine catalyzed CO2 capture which was discussed in the previous paragraph. The resulting
reaction profile is shown in Figure 4-19.
Figure 4-19: Reaction profile carbamic acid catalyzed CO2 capture.
The reaction profile provides a lot of information about this route. What can be seen is
that the barrier for reaction is much lower for the second CO2 molecule compared to the
first one. In addition, also the heat of adsorption has dropped, which equals -44 kJ/mol
(−119.3 − −75.3). Adsorption through carbamic acid catalysis is possible, however with the
results from these calculations it seems much less favorable from a thermodynamic point of
view.
Stijn de Flart
Master of Science Thesis
4-3 Modeling approach and development
4-3-4
45
Effect of water
As Alesi et al. reported, the resin contained around 50 wt % water as received from the
supplier and also adsorbs quite some water upon exposure to the atmosphere. Interesting
thus to see how this can affect the CO2 adsorption of the resin. Literature reports the
formation of bicarbonate as a possible mechanism for CO2 capture in solid sorbents. On top
of this, the quantum chemical calculations showed that a second mechanism involving water
could play a role in CO2 capture as will become clear in the sections below.
Bicarbonate route
The first route of interest is the direct bicarbonate formation.
CO2 + RN H2 + H2 O RN H3+ + HCO3−
(4-10)
Carbon dioxide directly reacts with a water molecule to form carbonic acid, which then
transfers a proton to the functional amine group. Figure 4-20 shows the Van der Waals
complex for a system composed of H2 O, CO2 and methylamine.
Figure 4-20: Van der Waals complex between methylamine, CO2 and H2 O (b3lyp 31-G*).
As can be seen, two hydrogen bonds stabilize the complex. The stabilization energy for the
complex of -53.4 kJ/mol is somewhat higher than the 2 methylamine - CO2 complex of -39.7
kJ/mol (energy of the complex relative to the energy of the reactants). A good starting guess
for the transition state geometry can by found by letting the carbon atom from CO2 approach
the oxygen atom from H2 O, which is shown in Figure 4-21
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Molecular modeling
Figure 4-21: Carbon atom of CO2 approaching the oxygen atom H2 O (pm3).
As can be seen, the carbon dioxide molecule starts to bend slightly whereas the partially
positive proton from the water molecule already starts to point towards the partially negative
nitrogen atom. Using this geometry as a starting geometry for the transition state calculation
the following transition state was obtained.
Figure 4-22: Transition state geometry for the H2 O CO2 methylamine complex (i685, b3lyp
31-G*).
Upon animation of the characteristic imaginary frequency of i685 proton transfer from the
water molecule to the nitrogen atom was shown, together with the formation of bicarbonate
from which the product geometry can be determined. Figure 4-23 shows the product geometry
for this route, where it becomes clear that it is a rather reversible system between the salt
methylammonium-bicarbonate and methylamine carbonic acid. The total energies for this
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Figure 4-23: Product geometry for the bicarbonate route (b3lyp 31-G*).
Table 4-5: Calculated total energies of the bicarbonate route for H2 O, Methylamine and CO2 .
Compound
Reactants
Van der Waals Complex
Transition State
Product
E (kJ/mol)
Hcorr (kJ/mol)
∆H
-947394.2
-947454.61
-947387.19
-947474.44
285.82
292.80
289.08
299.92
0
-53.43
10.26
-66.14
route as well as the relative change in enthalpy are shown in Table 4-5. The heat of reaction
is a bit lower compared to the amine route. As was mentioned in section 2-3-5, tertiary amines
capture CO2 by catalyzing bicarbonate formation, which is similar to this route. Satyapal
et al. report a heat of reaction of 48 kJ/mol for tertiary amines which is already closer to
the -66.14 kJ/mol obtained from the quantum-chemical calculations. Interesting to see is
that the activation barrier for the reverse reaction is only 76.37 kJ/mol, making it a rather
reversible route. Compared to the amine catalyzed route it has a slightly lower activation
barrier, however due to its lower heat of reaction it is expected that the amine catalyzed
route will be dominant when two groups are available for reaction. On the other hand, when
only one amine group is available for reaction, the bicarbonate route seems like a feasible
option. Finally, the energy profile is shown in Figure 4-24. In addition, the carbamate to
bicarbonate reaction has also been investigated in order to justify it (equation (4-5)). None of
these calculations came close to a similar reaction mechanism and in order to conclude if this
route is a possible CO2 capture mechanism additional research would be required. However,
it was found that water can catalyze the carbamate formation in a system consisting of 1
amine group, a CO2 molecule and an H2 O molecule which will be discussed below.
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Molecular modeling
Figure 4-24: Reaction profile for the bicarbonate route.
Water catalyzed CO2 capture
Besides that water plays a role in the bicarbonate route, it was also found that it significantly
lowers the activation barrier in the carbamic acid route, acting as a catalyst. The Van der
Waals complex for this route in this case is the same as the one shown in Figure 4-20. When
an energy profile is computed where the carbon dioxide starts to approach the nitrogen atom
instead of the water molecule a different starting guess for a transition state was obtained.
Running a transition state calculation on b3lyp level with the geometry shown in Figure 4-25
as a starting geometry, a transition state was obtained which showed that the water molecule
acts as a catalyst for the carbamic acid formation. The carbon dioxide molecule starts to
approach the nitrogen atom, which loses a proton to the water molecule. The water molecule
transfers a proton to the carbamate ion, forming carbamic acid. Looking at the calculated
total energies in Table 4-6 it can be seen that the barrier for this reaction has dropped
tremendously, indicating that water acts as a catalyst in the direct formation of carbamic
acid. Since the zwitterion mechanism is based upon reaction of CO2 in an aqueous solution
of amines this is expected. The product geometry shown in Figure 4-26 shows a complex
between carbamic acid and a water molecule, leading to a heat of reaction of -75.23 kJ/mol
which is almost exactly the same as the amine catalyzed route.
The barrier for reaction for this route equals 84.64 kJ/mol. In comparison with the amine
catalyzed route and the bicarbonate route this is around 20 kJ/mol more. The barrier for
reaction for the bicarbonate route was only 63.69 kJ/mol which points in the direction of
competitive adsorption between these two mechanisms. On top of that, Alesi et al. measured
formation of bicarbonate species which makes the bicarbonate route a likely mechanism for
the CO2 capture. Figure 4-27 shows the reaction profile for this route.
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Table 4-6: Calculated total energies of the carbamic acid route for H2 O, Methylamine and CO2 .
Compound
Reactants
Van der Waals Complex
Transition State
Product
E (kJ/mol)
Hcorr (kJ/mol)
∆H
-947394.2
-947454.61
-947359.39
-947482.34
285.82
292.80
282.23
298.73
0
-53.43
31.22
-75.23
Figure 4-25: L: Starting geometry for the transition state calculation (pm3). R: Transition state
showing the water molecule acting as a catalyst (i1499, b3lyp 31-G*).
Figure 4-26: Product geometry for water catalyzed carbamic acid formation (b3lyp 31-G*).
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Figure 4-27: Reaction profile water catalyzed carbamic acid formation.
4-4
Conluding remarks
Based on the results of the molecular modeling it seems that there are 4 routes through which
CO2 molecules are captured by the functional amine groups. First of all, the simplified resin
representation showed that around 50 % of the functional amine groups will be close enough
to justify the reaction mechanism where two amine groups capture a single CO2 molecule.
CO2 + 2RN H2 RN H2 + R2 N COOH
(4-11)
In addition it was found that a second CO2 molecule could be captured through carbamic
acid catalysis, which is in-line with the results from Planas et al.
RN HCOOH + RN H2 + CO2 2RN HCOOH
(4-12)
Besides the amine catalyzed carbamic acid formation it was found that when water is present
two reactions can play a role in CO2 capture. The formation of bicarbonate, which forms a
salt with methyl ammonium, and formation of carbamic acid where water acts as a catalyst.
Especially the latter reaction is interesting since no reports in literature on this mechanism
were found during this study. Unlike the general zwitterion route proposed by Choi et al.
(shown in equation 4-1) water does not act as a base to form carbamate, but rather acts as
a catalyst to form carbamic acid. The different reaction routes are summarized in Table 4-7
combined with some thermodynamic quantities.
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Table 4-7: Reaction pathways for CO2 adsorption in VP OC 1065.
Reaction path
Eaf (kJ/mol)
Ear (kJ/mol)
∆H (kJ/mol)
66.9
42.8
63.7
84.6
102.48
77.63
76.4
106.45
-75.3
-44.1
-66.1
-75.2
2RN H2 + CO2 RN HCOOH + RN H2
RN HCOOH + RN H2 + CO2 2RN HCOOH
RN H2 + H2 O + CO2 RN H3+ + HCO3−
RN H2 + H2 O + CO2 RN HCOOH + H2 O
Table 4-7 starts with the 2 amine catalyzed reaction pathways. Looking at the thermodynamic quantities, the first reaction is in good agreement with experimental data for heat of
adsorption reported in literature. The carbamic acid catalyzed CO2 capture however seems
to be rather reversible with a very low heat of adsorption. Although it has a low barrier for
reaction, it seems that the reactions with H2 O molecules are more favorable and therefore it
will be left out for this study.
Looking at the H2 O catalyzed reactions and by comparing the energy barriers for both reactions it seems that bicarbonate formation is more likely to occur due to its 20 kJ/mol lower
reaction barrier at low temperatures, whereas the carbamic acid formation is thermodynamically more favorable at higher temperatures due to its higher heat of adsorption. Finally it
was found that in a gaseous and dry environment the proposed zwitterion route seems to be
unlikely due to its high activation barrier of 163.1 kJ/mol. When water is present however,
this mechanism does seem possible since it almost halves the barrier for reaction.
From the conformational study it became clear that 3 amine groups are positioned close
to each other, from which 2 can be involved in capturing a CO2 molecule, leaving 5 single
amine groups. The other CO2 molecules are expected to be captured in the presence of water
through one of the two routes. The results of this modeling study are in good agreement with
the results from Alesi et al. (2012) who measured both carbamate and bicarbonate species
when the resin is exposed to CO2 .
Having identified two different reaction pathways for the CO2 capture (one with water and one
with amines) the proposed x-site Langmuir isotherm model reduces to a dual-site Langmuir
model describing the temperature dependency according to the heat of reactions.
q=
Where Ki is given by:
qs1 K1 P
qs2 K2 P
+
1 + K1 P
1 + K2 P
−∆Hads
Ki = K0i exp
RT
(4-13)
(4-14)
The values for ∆Hads that are required in equation (4-13) can directly be taken from the
quantum chemical calculations for the different reaction mechanisms. The hypothetical model
for the adsorption isotherm can now be implemented in the dynamic adsorption model that
was discussed in chapter 3. Due to its non-linearity no analytical solution exists and numerical
approximations have to be used, which will be discussed in the next chapter.
Master of Science Thesis
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Stijn de Flart
Molecular modeling
Master of Science Thesis
Chapter 5
Model development and results
Chapter 3 outlined the mathematical representation of an adsorption column, whereas chapter
4 proposed a hypothetical model for the adsorption isotherm, with the thermodynamic data
from the quantum chemical calculations as an input. Having this data the total system can
be solved using numerical techniques which provides knowledge about the rate of adsorption.
No analytical solutions exist in order to solve this non-linear, time dependent model and
numerical routines have to be applied. This chapter will describe the numerical solution
method that has been used in order to solve the model equations that were described in
chapter 3.
5-1
Introduction
Just for clarity the model equations are shown below, combined with the hypothetical isotherm
model that was proposed at the end of chapter 4.
∂2c
∂
∂c
−DL 2 + u (c) +
+
∂z
∂z
∂t
1−
∂ q̄
ρp
=0
∂t
∂ q̄
= k(q ∗ − q̄)
∂t
qs1 K1 P
qs2 K2 P
q∗ =
+
1 + K1 P
1 + K2 P
(5-1)
(5-2)
(5-3)
Equation (5-3) contains 4 unknowns, qsi and Ki , that have to be obtained by curve fitting. qsi
relates to the maximum capacity for the relative reaction mechanism and Ki is an equilibrium
constant that describes the temperature dependence of the CO2 capacity of the sorbent. Normally, Ki should be estimated at different temperatures, however, due to the thermodynamic
data for ∆Hads from the quantum chemical calculations a single fit at a reference temperature
is sufficient. Recalling that Ki can be rewritten as a function of temperature, the following
equation is obtained:
−∆Hads
Ki = K0i exp
(5-4)
RT
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Model development and results
K0i in equation (5-4) is a constant that can be obtained by fitting (5-3) to experimental
data at a reference temperature. Since K0i is independent of temperature it can be used to
describe the sorbents isotherm at different temperatures so only a single curve fit is required.
In order to model the packed bed system a validated isotherm model is required. Therefore,
before diving into the numerical solution of the general mass balance the first aim is to obtain
values for K0i and qsi which are an input for the dynamic model.
5-2
Isotherm model validation
Equation (5-3) contains several constants that are obtained by fitting the isotherm model
to experimental data (qsi , Ki ). ∆Hads from the quantum chemical calculations can be used
as an input for equation (5-4) and a single fit is sufficient at a reference temperature of 303
K. Experimental data on the isotherm can be obtained from the study from Veneman et al.
(2015), shown in Figure 5-1. In order to extract the experimental data from this graph a
webplotdigitizer tool was used [47]. This tool allows its user to upload a graph and quite
accurately extract the data points. The webplotdigitizer tool provides the data in a matrix
form which can be directly used as an input for Matlab’s curve fitting tool. The data points
that were extracted at 303 K are shown in Table 5-1.
Figure 5-1: Original data from Veneman et al. Reprinted from [55] with permission from Elsevier.
Stijn de Flart
Master of Science Thesis
5-2 Isotherm model validation
55
Table 5-1: Isotherm data points at reference temperature of 303K (bold faced values were
additionally added, rounded values are shown).
P (Pa)
0
329
988
1537
3073
4280
8671
14159
45549
71012
q (mol/kg)
0
1.59
1.94
2.05
2.16
2.34
2.52
2.65
2.81
2.94
In order to obtain a good fit for the model it was necessary to add two additional data points
in the low pressure regime, denoted by the bold faced values in Table 5-1. The data points
can be implemented in matlab’s curve fitting tool, which uses equation (5-3) to fit a curve
to the data points by changing values of qsi and Ki . The curve fitting session is shown in
Figure 5-2.
Figure 5-2: Curve fitting session to isotherm data at 303 K.
The fit has an excellent R-square value of 0.9988 and provides values for qs1 , qs2 , K1 and
K2 , denoted in Table 5-2. Table 5-2 also contains values for ∆H1 and ∆H2 which are results
from the quantum chemical calculations obtained in the previous chapter. It however is still
Master of Science Thesis
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Model development and results
Table 5-2: Isotherm parameters
Parameter
Value
Description
Source
qs1 (mol/kg)
K1 (Pa−1 )
qs2 (mol/kg)
K2 (Pa−1 )
∆H1 (kJ/mol)
∆H2 (kJ/mol)
1.942
0.01201
1.061
0.0001444
-66.14, -75.23
-75.26
CO2 capacity
Equilibrium constant
CO2 capacity
Equilibrium constant
H2 O catalyzed heat of ads.
Amine catalyzed heat of ads.
Curve fitting
Curve fitting
Curve fitting
Curve fitting
Quantum Chemical calculations
Quantum Chemical calculations
unclear which heat of adsorption ∆Hi belongs to which qsi . In Table 5-2, the two values of
∆H1 are related to water catalyzed CO2 capture and ∆H2 is related to amine catalyzed CO2
capture. It is thus needed to link these values to the correct qs1 and qs2 .
What can be seen is that qs1 is much larger than qs2 , indicating that qs1 is linked to the
reaction mechanism that is most likely dominant in the CO2 capture. Recalling the conformer
distribution from chapter 4, it became clear that less or more 2 groups of 3 primary amines
were close to each other and 3 amine groups were more isolated. Since only two groups can
participate in the amine catalyzed route the other 5 are expected to capture CO2 by using
H2 O as a catalyst. It is thus expected that the contribution of H2 O to the CO2 adsorption
will be larger (4 groups for the amine catalysis and 5 groups for the water catalysis). Since
qs1 is larger than qs2 , qs1 is attributed to the water catalyzed part of the CO2 adsorption and
thus uses the values of ∆H1 to describe the temperature dependence.
Using the thermodynamic data, values for K01 and K02 can be calculated and the isotherm
model can be used to describe the CO2 capacity of the VP OC 1065 at different temperatures.
K1
exp(−∆H1 /RT )
K2
=
exp(−∆H2 /RT )
K01 =
(5-5)
K02
(5-6)
Having calculated K01 and K02 equation (5-3) and (5-4) can now be used to describe the
CO2 capacity at different temperatures. Table 5-2 shows 2 different values for ∆H1 which
is due to the two different routes where H2 O plays a role. As was mentioned in chapter
4, the bicarbonate route has a lower energy barrier, however also a lower heat of reaction
making it a rather reversible route. The H2 O catalyzed carbamic acid route has a similar
heat of reaction to the amine catalyzed route, making it a more stable reaction product. It
is expected that kinetics will prefer the bicarbonate route at lower temperatures whereas at
higher temperatures the H2 O catalyzed carbamic acid route may have the preference. Upon
calculation and implementation of the different K0i ’s in the isotherm model the following
results were obtained, shown in Figure 5-3 and Figure 5-4.
Stijn de Flart
Master of Science Thesis
5-2 Isotherm model validation
57
Dual site isotherm model. ∆ H1 = -66.14 kJ/mol)
3
Loading in mol/kg
2.5
2
1.5
1
Veneman et al. reference model (T = 303 K)
Veneman et al. reference model (T = 313 K)
Veneman et al. reference model (T = 343 K)
Veneman et al. reference model (T = 353 K)
Veneman et al. reference model (T = 373 K)
0.5
0
0
1
2
3
4
5
6
7
8
9
10
×10 4
Partial CO2 pressure in Pa
Figure 5-3: Calculated isotherm according to dual site model for ∆H1 = -66.14 kJ/mol, corresponding to the bicarbonate route. Experimental data from Veneman et al.
Dual site isotherm model. ∆ H1 = -75.23 kJ/mol)
3
Loading in mol/kg
2.5
2
1.5
1
Veneman et al. reference model (T = 303 K)
Veneman et al. reference model (T = 313 K)
Veneman et al. reference model (T = 343 K)
Veneman et al. reference model (T = 353 K)
Veneman et al. reference model (T = 373 K)
0.5
0
0
1
2
3
4
5
6
7
Partial CO2 pressure in Pa
8
9
10
×10 4
Figure 5-4: Calculated isotherm according to dual site model for ∆H1 = -75.23 kJ/mol, corresponding to the carbamic acid route. Experimental data from Veneman et al.
Master of Science Thesis
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Model development and results
It can be seen that the dual site model fits the experimental data quite well for both values
of ∆H1 . Using the reaction energy for the bicarbonate route the model has a better fit at
the lower temperatures whereas the H2 O catalyzed reaction energy has a better fit at higher
temperatures. The best fit to the experimental data was obtained when ∆H1 was set to -71
kJ/mol, shown in Figure 5-5 which is somewhat in the middle of the two reaction energies.
Dual site isotherm model. ∆ H1 = -71 kJ/mol)
3
Loading in mol/kg
2.5
2
1.5
1
Veneman et al. reference model (T = 303 K)
Veneman et al. reference model (T = 313 K)
Veneman et al. reference model (T = 343 K)
Veneman et al. reference model (T = 353 K)
Veneman et al. reference model (T = 373 K)
0.5
0
0
1
2
3
4
5
6
7
8
9
10
×10 4
Partial CO2 pressure in Pa
Figure 5-5: Adsorption capacity for ∆H1 = -71 kJ/mol.
5-2-1
Sensitivity
The sensitivity of the model was tested in order to see how well the isotherms match the
experimental data upon a small change of the heat of reaction. Figure 5-6 shows the results
for two different heat of reactions. It can be seen that especially at higher temperatures the
isotherms did not match with the experimental data at all anymore, showing that the model
is not simply a model that fits for any heat of reaction and describes the chemical behavior
of the material rather well.
Stijn de Flart
Master of Science Thesis
5-2 Isotherm model validation
Dual site isotherm model. ∆ H1,2 = -60 kJ/mol
3
2.5
2.5
2
2
1.5
1
Veneman et al. reference model (T = 303 K)
Veneman et al. reference model (T = 313 K)
Veneman et al. reference model (T = 343 K)
Veneman et al. reference model (T = 353 K)
Veneman et al. reference model (T = 373 K)
0.5
0
0
1
2
3
4
5
6
7
Partial CO2 pressure in Pa
8
Dual site isotherm model. ∆ H1,2 = -85 kJ/mol
3
Loading in mol/kg
Loading in mol/kg
59
9
10
×10
4
1.5
1
Veneman et al. reference model (T = 303 K)
Veneman et al. reference model (T = 313 K)
Veneman et al. reference model (T = 343 K)
Veneman et al. reference model (T = 353 K)
Veneman et al. reference model (T = 373 K)
0.5
0
0
1
2
3
4
5
6
7
8
Partial CO2 pressure in Pa
9
10
×10 4
Figure 5-6: Sensitivity upon changing reaction energies.
5-2-2
Low pressure regime
More interesting for direct air capture applications is the low partial pressure regime, ranging
from 0 to 100 pascal. Figure 5-7 shows experimental data from the VP OC 1065’s CO2
capacity at 40 Pa partial pressure and different relative humidities. Under ambient conditions
it can be seen that the capacity will be around 1.4 mol/kg. The theoretical model predicts
capacities of 1 mol/kg for both ∆H1 values which is lower than the measurements from
Veneman et al. but still an acceptable approximation of the CO2 capacity under atmospheric
conditions for initial design calculations (Figure 5-8).
Figure 5-7: CO2 adsorption capacity of VP OC 1065 as a function of the relative humidity at a
CO2 partial pressure of 40 Pa. Reprinted from [55] with permission from Elsevier.
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60
Model development and results
Dual site isotherm model. ∆ H1 = -66.14 kJ/mol
2.5
2.5
2
2
1.5
1
0.5
Dual site isotherm model. ∆ H1 = -75.23 kJ/mol
3
Theoretical sorbent capacity. T = 298 K
Loading in mol/kg
Loading in mol/kg
3
Theoretical sorbent capacity. T = 298 K
1.5
1
0.5
0
0
0
10
20
30
40
50
60
70
80
90
100
Partial CO2 pressure in Pa
0
10
20
30
40
50
60
70
80
90
100
Partial CO2 pressure in Pa
Figure 5-8: Sorbent capacity conditions relevant for air capture.
5-2-3
Concluding remarks
The results from the quantum chemical calculations were successfully implemented in an
isotherm model. Not only did the quantum chemical calculations provide information about
the amount of necessary sites in the Langmuir model, they also provided the thermodynamic
data that was used to describe the temperature dependence of the model while keeping a link
to reality. After implementation the isotherm model was able to describe the CO2 capacity
of the VP OC 1065 at different temperatures. Additionally at conditions relevant for direct
air capture the model was capable of predicting the equilibrium capacities rather well.
5-3
Numerical solution method
Having an isotherm model for the VP OC 1065’s CO2 capacity the focus can shift towards the
actual solution of the system of equations shown in 5-1 to 5-3. Shafeeyan et al. give a very
broad overview of different modeling studies done on the adsorption of CO2 in a fixed-bed
column. Many of the studies use finite difference methods in order to solve the system of
equations which have been reported in other studies as well ([51], [41] [38]). Finite Difference
Methods are relatively easy to implement and can be used to solve various types of differential
equations.
5-3-1
Discretization of equations
Upon applying a finite difference discretization for the spatial operators, the system of equations in 5-1 to 5-3 (for a single species) can be expressed as follows, which will also become
Stijn de Flart
Master of Science Thesis
5-3 Numerical solution method
61
more clear later in this chapter:
dq
dc
1−
ρp
+
= Ac + b
dt
dt
dq
= k [q∗ (c) − q]
dt
qs2 K2 RT c
qs1 K1 RT c
+
q∗ =
1 + K1 RT c 1 + K2 RT c
(5-7)
(5-8)
(5-9)
Where in this case c is multiplied with RT in order to convert it to a partial pressure. It
should be noted though that in (5-9) not necessarily two vectors will be divided by each other;
the equations are solved element wise using matlab’s build in root finding algorithm. In (5-7),
∂2c
∂c
the A matrix contains the central difference approximations of both the terms ∂z
2 and ∂z
from the general mass balance equation given in (5-1). The vector b contains the boundary
conditions in its discretized form. The differential equations can be made discrete by giving
∂z a finite value of ∆z. The total length of the adsorption column is then made discrete by
creating a grid of n nodes with a spacing of ∆z in between. To get a good understanding of
the grid and how it represents the theoretical model the following section discusses it in some
more detail.
Grid generation
Figure 5-9 displays again the physical model of the packed bed, where below it shows the
actual grid that in this case represents the packed bed. In the one dimensional grid, the
length of the bed is split up in n+1 nodes where the length between two nodes equals ∆z.
By making ∆z finite one can start formulating the differential equations in its numerical and
finite form, which can then be formulated as a system of algebraic equations which can be
∂2c
∂c
solved. By applying central differences in order to approximate the terms ∂z
2 and ∂z the
following equations are obtained [57]:
∂2c
ci−1 − 2ci + ci+1
≈
∂z 2
∆z 2
∂c
ci+1 − ci+1
≈
∂z
2∆z
(5-10)
(5-11)
In equations 5-10 and 5-11, ci represents the CO2 concentration in a node which is directly
linked to a specific coordinate in the grid. It can be seen that when i = 1, there is the robin
boundary condition whereas at i = n there is the no flux boundary condition. Having the
discretized form of the spatial operators, the mass balance can be rewritten in the following
form.
dc
1−
dq
DL
u
+
ρp
=
(ci+1 − 2ci + ci−1 ) −
(ci+1 − ci−1 )
(5-12)
dt
dt
∆z 2
2∆z
Similarly, the boundary conditions can be approximated as well by central differences.
∂c
c2 − c0
|z=0 = −u (cf − c|z=0 ) ≈ DL
= −u [cf − c1 ]
∂z
2∆z
∂c
cn+1 − cn−1
|z=0 = 0 ≈
∂z
2∆z
DL
Master of Science Thesis
(5-13)
(5-14)
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62
Model development and results
Figure 5-9: Numerical grid representation of the packed bed.
From Figure 5-9 it becomes clear that i is in the range of 1 to n. When i = 1 is entered however
in equation (5-12) it is seen that a value of c0 is required (similar to cn+1 ). The discretized
boundary conditions can be written in the form to calculate c0 and cn+1 to provide this value.
c0 =
cn+1
2∆zu
(cf − c1 ) + c2
DL
= cn−1
(5-15)
(5-16)
System of equations
Equation (5-12) can be solved for i = 1,2,...,n by using the boundary conditions at i = 1 and i
= n. To make the system of equations a bit more manageable the following substitution was
done:
DL
∆z 2
u
σ=
2∆z
ρ=
Stijn de Flart
(5-17)
(5-18)
Master of Science Thesis
5-3 Numerical solution method
63
Inserting i = 1 to n in equation (5-12) the following equation is obtained (after simplifying it
with some algebra):
∂q
∂c
1−
ρp
+
= (ρ + σ)c0 + (−2ρ)c1 + (ρ − σ)c2
∂t
∂t
∂q
∂c
1−
ρp
+
= (ρ + σ)ci−1 + (−2ρ)ci + (ρ − σ)ci+1
∂t
∂t
∂q
1−
∂c
ρp
+
= (ρ + σ)cn−1 + (−2ρ)cn + (ρ − σ)cn+1
∂t
∂t
(i = 1)
(5-19)
(i = 2, 3, ..., n − 1)
(5-20)
(i = n)
(5-21)
It becomes clear that indeed values for c0 and cn+1 are needed since they do not exist in the
grid. These are provided by the boundary conditions and upon implementation of those the
following system is obtained:
∂c
+
∂t
∂c
+
∂t
∂c
+
∂t
∂q
2∆zu
1−
2∆zu
ρp
c1 + (2ρ)c2 + (ρ + σ)
cf
= −2ρ − (ρ + σ)
∂t
DL
DL
(i = 1)
(5-22)
1−
∂q
ρp
= (ρ + σ)ci−1 + (−2ρ)ci + (ρ − σ)ci+1
∂t
(i = 2, 3, ..., n − 1)
(5-23)
1−
∂q
ρp
= (2ρ)cn−1 + (−2ρ)cn
∂t
(i = n)
(5-24)
Comparing this system with equation (5-7) it becomes clear what the A matrix and the b
vector become.
−2ρ − (ρ + σ) 2∆zu
DL


ρ+σ


0


A=
0

0



0
0
(ρ + σ) 2∆zu
0
0
0
0
c1
DL cf






0
0
0
0   c2 
0




 c3 


.
0
0
0 
0









.
.
0
0  . b = 
.

 c



.
.
.
0   n−2 
.






c


0 ρ + σ −2ρ ρ − σ   n−1 
.
cn
0
0
2ρ
−2ρ
0
(5-25)
Using the A matrix and the b vector, the mass balance equation can indeed be written as:


2ρ
0
−2ρ ρ − σ
.
.
0
.
0
0
0
0
0
0
dc
+
dt
1−
dq
ρp
= Ac + b
dt



(5-26)
Equation (5-26) can be solved by using a split-operator method, which decouples the transport
term (which is the right side of the equation) and the reaction term (which is the ∂q
∂t ).
5-3-2
Operator splitting
Solving the Diffusion-Advection-Reaction equation is quite a challenging task, especially in the
case of adsorption systems where the reaction term is often non-linear due to the adsorption
isotherm. A way to simplify this is by separating the adsorption part from the transport part
Master of Science Thesis
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64
Model development and results
which is better known as the operator splitting method. This method calculates a solution to
the system of equations without the adsorption part during the first step. In the second step,
the adsorption part is added and corrects the concentrations that were calculated during the
first step. The operator splitting method is well-known and often applied in modeling chemical
transport equations ([7] [5] [6]). Barry et al. (2000) compare several split-operator methods
for solving the discretized system of equations. The operator splitting method separates the
∂q
∂c
∂t term from the ∂t term.
∂q
First, a suitable finite difference method to discretize the ∂c
∂t and ∂t terms is required in
order to solve the system of equations. The Crank-Nicolson method is an implicit method
that is second order in time O(∆t2 ) and is unconditionally stable. Central differences have a
second-order accuracy as well O(∆z 2 ). The Crank-Nicolson method itself will not be discussed
in detail in this thesis and can be found in most of the numerical methods for differential
equations literature. Using the Crank-Nicolson method for the system of equations given in
5-7, 5-8 and 5-9 the following O(∆t2 ) scheme:
AL cn+1 +
1−
1−
∆t
ρp qn+1 =
ρp qn + AR cn + (bn+1 + bn )
2
(5-27)
where cn is the numerical solution for the CO2 concentration throughout the bed at the nth
∆t
time step. AL = I − A ∆t
2 and AR = I + A 2 . Similarly the linear driving force equation
becomes (5-8):
(∆t/2)[q∗ (cn+1 ) + q∗ (cn )] + (1 − k(∆t/2))qn
qn+1 =
(5-28)
1 + k(∆t/2)
Where q∗ gives the equilibrium capacity according to the dual-site langmuir isotherm. Substituting equation (5-28) in (5-27) would yield a system that can be solved iteratively for
cn+1 which is O(∆t2 , ∆z 2 ) accurate. Solving this system however is a difficult task and very
computational intense which can be avoided by using a two-step method. Barry et al. (2000)
propose the following two-step method in order to solve equations (5-26) and (5-27):
n
n+1
c∗,n+1 = A−
+ bn )
L 1 AR c + (b
∆t
2
(5-29)
1−
1−
ρp qn+1 = c∗,n+1 +
ρp qn
(5-30)
Where first the transport step is calculated in equation (5-29) and is followed by the reaction
step in (5-30). In equation (5-30), cn+1 can be solved iteratively using root finding techniques,
where it is input for cn in the next time step. This two-step method makes it lots easier to
solve the equations however it goes at the cost of accuracy since this scheme is O(∆t) accurate
instead of O(∆t2 ) for the Crank-Nicolson method.
cn+1 +
5-4
Packed bed model validation
A matlab code was written in order to solve equations (5-29) and (5-30). To conclude if the
mathematical model delivers the correct results two validation studies have been performed.
In the static validation, the breakthrough curve is compared with known results from literature
for the same parameters and isotherm. During the dynamic validation, the isotherm remains
the same and parameters such as velocity, axial dispersion and mass transfer rate are changed.
The behavior of the model is analyzed, resulting in a conclusion.
Stijn de Flart
Master of Science Thesis
5-4 Packed bed model validation
65
Table 5-3: Simulation parameters from Barry et al. (2000).
Curve type
u (cmd− 1)
DL (cm2 d− 1)
k(d− 1)
ν
Ks
A1
A2
A3
L(cm)
BTC at 5 cm
6
3
100
0.1
2
0
1
0
40
5-4-1
Static validation
Barry et al. (2000) provide an example for the breakthrough calculation and in order to
validate this model the same calculation was performed. The system they solve is slightly
different and is shown below:
∂c
∂c ∂q
∂2c
+
= DL 2 − u
∂t
∂t
∂z
∂x
∂q
= k [q ∗ (c) − q]
∂t
P2
j
j=0 aj c
∗
q =
Ks A2 (ν − 1) − A2 A3 ν − a2 c
(5-31)
(5-32)
(5-33)
Where, u (which they call V) is the velocity and
a0 = Ks A1 A2 (ν − 1) − A2 A3 (A2 + νA1 )
a1 = Ks A2 (1 − ν) + ν(A2 A3 − uA1 )A2 u − A2 u
a2 = uν
It should be noted that a1 is different than the one shown in [6], however it is expected that
it contains a typo since they refer to their previous study for this isotherm which contains
the A2 u term [8]. To validate the code, the same parameters (Table 5-3) were used and the
breakthrough curve was computed at a distance of 5 cm for a total column length of 40 cm.
The total simulation time was 5 days with a ∆t of 0.01 days and a ∆z of 0.1 cm. Figure 5-10
shows the breakthrough curve that has been computed at a distance of 5 cm in the column
and compares the computed breakthrough curve with the one given by Barry et al. (using
the webplot digitizer tool). It can be seen that the breakthrough curve that was calculated
with the matlab code has an excellent match with their breakthrough curve.
5-4-2
Dynamic validation
Besides having the correct breakthrough curve it is also important to see how the model
responds to changes in for instance the mass transfer coefficient (k), the axial dispersion term
(DL ) and the bed velocity (u). A couple of simulations have been done in order to compare
the results with the base case. The simulation parameters are shown in Table 5-4.
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Model development and results
Breakthrough curve at 5 cm
1
0.9
Relative concentration
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Breakthrough curve from Barry et al. (2000)
Calculated breakthrough curve
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (days)
Figure 5-10: Comparison of the calculated breakthrough curve with the one reported by Barry
et al. (2000).
Table 5-4: Parameters for the dynamic validation of the packed bed model (breakthrough curves
are computed at 5 cm in the bed).
Case
u (cmd− 1)
DL (cm2 d− 1)
k(d− 1)
ν
Ks
A1
A2
A3
L(cm)
1:
2:
3:
4:
6
6
12
6
3
6
3
3
100
100
100
1
0.1
0.1
0.1
0.1
2
2
2
2
0
0
0
0
1
1
1
1
0
0
0
0
40
40
40
40
Base case
Axial dispersion change
Bed velocity change
Mass transfer change
Case 2: change in axial dispersion
The axial dispersion is increased and the effect on the breakthrough curve is studied. Having
a higher axial dispersion coefficient the expected behavior would be that the mass transfer
front is less ’sharp’ and the breakthrough curve is less steep. Due to the higher dispersion,
introducing more axial mixing, breakthrough should occur sooner and saturation of the bed
should take longer. Figure 5-11 shows the result of the simulation which indeed show the
expected results. Breakthrough already occurs after half a day whereas saturation did not
occur at all after 5 days.
Case 3: change in bed velocity
When increasing the velocity through the bed (with a note that the mass transfer coefficient is
still very high) the expected behavior is basically a much steeper breakthrough and a shorter
Stijn de Flart
Master of Science Thesis
5-4 Packed bed model validation
67
Breakthrough curve after 5 days, D L = 6 (cm 2 d -1)
1
0.9
Relative concentration
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (days)
Figure 5-11: Breakthrough curve for DL = 6 cm2 d−1 .
saturation time. Figure 5-12 shows the result of a simulation where the bed velocity has been
doubled. The saturation time has indeed less or more halved and the breakthrough curve is
steeper, however the breakthrough time remains the same. In a normal system this would
be very unexpected behavior since a quicker breakthrough is also expected but it should be
pointed out that in this case the equilibrium isotherm contains a velocity term in the a1 and
a2 coefficient.
In the base case, the equilibrium capacity of the model is 1.5 mol/kg whereas in the case 3,
the equilibrium capacity has doubled. Therefore it makes sense that the breakthrough time
remains the same. It could be argued that if the capacity doubles and the velocity doubles the
saturation time should remain the same. However, velocity plays a bigger role now making
the system is less dispersed. This results in a steeper breakthrough curve resulting in a much
shorter saturation time.
Case 4: change in the mass transfer coefficient
The mass transfer coefficient basically describes the adsorption rate of the adsorbate. Having a
very high mass transfer coefficient means that the overall kinetics of the system are determined
by parameters such as velocity and dispersion whereas having a low mass transfer coefficient
the saturation time rather depends on the mass transfer coefficient. When decreasing the mass
transfer coefficient to 1 (d−1 ) the following breakthrough curve was obtained. From Figure 513 it becomes clear that the breakthrough curve has become much more broad, indicating
that for k = 1 (d− 1) the mass transfer becomes a limiting factor. Breakthrough occurs rather
quickly since the adsorbate in the fluid phase starts to travel through the column without
being adsorbed into the solid phase. The residence time is too low for complete adsorption
Master of Science Thesis
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Model development and results
Breakthrough curve after 5 days, u = 12 (cm d -1)
1
0.9
Relative concentration
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (days)
Figure 5-12: Breakthrough curve for u = 12 cm d− 1.
Breakthrough curve after 5 days, k = 1 (d -1)
1
0.9
Relative concentration
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (days)
Figure 5-13: Breakthrough curve for k = 1 (d−1 ).
Stijn de Flart
Master of Science Thesis
5-5 Implementation
69
and that is something that is illustrated by the breakthrough curve.
5-5
Implementation
Based on the dynamic and static validation it was shown that the packed bed adsorption
model shows the correct behavior for the validation case. The model works correctly and
can be used to start modeling the breakthrough curves for the VP OC 1065 sorbent which
can be matched to experimental breakthrough curves. A description of such an experiment
is found in Appendix B which should be performed. Other parameters such as the packing
density () and the axial dispersion coefficient DL can be estimated using correlations given
in chapter 3. To determine them more accurately however experiments should be performed
as well. Nevertheless upon implementation of the isotherm model for the VP OC 1065 a good
starting guess for adsorption rate can still be made by using correlations and matching the
experimental breakthrough curve by varying the mass transfer coefficient.
5-6
Concluding remarks
Simulation times for all the cases were in the order of a couple of minutes however it was
noticed that they are highly dependent on the complexity of the isotherm model. The model
can definitely be improved by using a more efficient root-finding algorithm or by using other
numerical routines. The alternative would be to start using software like gPROMS which
have standard adsorption models included [23].
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Stijn de Flart
Model development and results
Master of Science Thesis
Chapter 6
Conclusion and recommendations
6-1
Conclusion
This work has identified solid amine-based sorbents as a suitable candidate for a Direct Air
Capture process. A process where CO2 can be captured from air and recycled using low grade
heat of around 80◦ C. Especially the class 2 solid sorbents containing primary amine groups
proved to be very promising due to their stability over many cycles which is an important
criteria for a air capture process. This work selected the class 2 VP OC 1065 sorbent,
functionalized with primary amine groups to focus on.
In designing an air capture adsorption process, two parameters are essential to know which
are the rate of adsorption, and the capacity of the material. The rate of the process can
be extracted by matching experimental results of breakthrough curves with a mathematical
model. The capacity of the material is a function of the partial pressure and is dependent on
the chemical behavior of the material.
It became clear that the reaction mechanisms of such materials are not yet completely understood, as literature reports different reaction mechanisms, and in order to justify them
molecular modeling using the Spartan software was applied. The quantum chemical calculations showed that the reaction between CO2 and a functional amine will only proceed if
there is a catalyst. This catalyst was found to be either a water molecule, or a nearby second
amine group. When CO2 is captured, it is either stored as an carbamic acid (where the
reaction is catalyzed by a nearby second amine group or a H2 O molecule) or as a bicarbonate
complex. Especially the H2 O catalyzed carbamic acid formation was interesting, since during
this study no reports of it were found in literature. The results of the modeling study are in
good agreement with mechanisms reported in literature and were successfully implemented
in an isotherm model to describe the sorbent’s CO2 capacity.
The system of equations describing an adsorption process were successfully solved using an
operator splitting method with a Crank-Nicolson scheme. The molecular modeling results
served as an input for the model from where it can be matched to experimental results. The
model was validated for a similar case and the dynamic behavior is considered to be correct.
Master of Science Thesis
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72
Conclusion and recommendations
The molecular modeling revealed good insight in the VP OC 1065 and the mathematical
model can be used as a tool to extract an adsorption rate. These are the tools needed to start
designing an direct air capture process.
6-2
Recommendations
To get one step closer to designing this process lots of experimental work has to be performed.
Breakthrough experiments should be performed for different column lengths and the model
needs to be used to estimate the adsorption speed. In addition low partial pressure isotherm
measurements can be used to get a better description of the low pressure regime of the CO2
capacity.
Computational time can be reduced by improving the mathematical model. A different root
finding algorithm can be implemented, a different method can be applied (finite volume) or a
software package could be used (gPROMS). Finally, the numerical routine can be implemented
in Fortran instead of matlab to improve the computational time.
Besides that there are still technological as well as commercial challenges before this technology is ready to be applied in industry. To create a completely autonomous system, either
waste-heat or renewable energy sources should be used to regenerate the CO2 from the sorbent. The further use of waste heat could additionally improve the overall plant efficiency.
Even though CO2 is a resource, the price of CO2 is currently low and the technology has to
be able to compete with such low prices.
6-3
Future prospects
The benefits of the technology are clear, all CO2 emissions can be captured whereas at the
same time CO2 can be made available everywhere. Just as currently energy generation is
decentralized (in the form of solar panels) this technology could decentralize CO2 capture.
Everywhere where waste-heat is available the technology can be applied and the CO2 can be
regenerated locally.
In a future where fossil fuels become a rarity, the recycling of CO2 and H2 O could serve as
a way to synthesize hydrocarbons using well known processes such as the Fischer-Tropsch
process. CO2 capture is decentralized and transported to a facility that converts the CO2 in
fuels again, closing the carbon loop and creating an artificial ’unlimited’ source of fuels.
Stijn de Flart
Master of Science Thesis
Appendix A
Energy Transition Scholarship
Master of Science Thesis
Stijn de Flart
Carbon Dioxide as a resource Recycling it directly from the air
Stijn de Flart
October 16, 2015
I NTRODUCTION
During my studies I became specifically interested in the world of renewable energy sources
and the transition towards a more sustainable society. The world energy demand continues to
grow whereas the conventional energy sources are getting depleted. We are currently facing an
enormous technological and societal challenge where we have to become more sustainable
and I actively want to contribute to help and face this challenge.
To introduce myself, I’m Stijn de Flart and am enrolled in the Sustainable Processes & Energy
Technologies master track at the TU Delft (part of the Mechanical Engineering master tracks).
I’ve already started my master thesis where I had a very clear view of what I wanted to research,
namely, capturing and recycling carbon dioxide directly from the air.
Figure 1: Illustrative figure made by a friend of mine, Walt van der Veen.
1
S OCIETAL AND INDUSTRIAL CHALLENGE
Since the beginning of the industrialization the CO 2 concentration in the atmosphere has
been rapidly increasing. The increase in atmospheric CO 2 levels is considered to be the cause
of human activities such as burning of fossil fuels for energy generation and using fossil
fuels for transportation. It is generally acknowledged that the increase in atmospheric CO 2
concentration, along with other greenhouse gases, cause global climate change (IPCC 2007).
Concerns over climate change and general awareness of the limited availability of earths
natural resources drive innovations in technologies for stabilizing the CO 2 concentration in
the atmosphere as well as to make our current processes more efficient.
C ARBON D IOXIDE AS A RESOURCE
Although CO 2 is often placed in a negative context, being responsible for global climate change,
it is also a gas that is vital to life on Earth and it is a viable resource for many kinds of industrial
processes (Aresta 2010) such as :
1. Biofuel production;
2. Greenhouses;
3. Fuel synthesis;
4. Water treatment.
To give an indication for the CO 2 requirement for biofuel production from microalgae; 1.72 g
of CO 2 is required to obtain 1 g of biomass, so producing tonnes of biomass would require
almost the double amount of mass in CO 2 . (González-Fernández, C. et al., 2011).
C ONVENTIONAL T ECHNOLOGY AND LIMITATIONS
Among the technologies to control the CO 2 emissions are carbon capture and sequestration
(CCS) and carbon capture and utilization (CCU). With CCU, CO 2 is turned into a resource instead of a waste, creating an artificial carbon loop. One of the most suitable ways of separating
CO 2 from a gas stream is based on absorption in liquid amines, which is common practice in
industry (Goeppert et al., 2012). However, this technology is applied at concentrated sources
(e.g. power plants) and regenerating the CO 2 introduces a high energy penalty to the process
(IPCC 2005). This puts a constraint on the location of processes that require CO 2 since they
should be close to power plants.
Not all industrial processes that require CO 2 are located near power plants and often it is
supplied in the form of pressurized cylinders. This causes additional transport costs and
additional energy costs. Generally speaking, two solutions are needed. One to control the CO 2
emissions and one to supply CO 2 , both in a sustainable way.
2
G ET IT FROM THE AIR !
A possible solution to overcome these challenges is to separate CO 2 from the air by making
use of solid sorbents. Solid sorbents require less heat for regeneration due to their lower heat
capacity and capturing CO 2 from the air has several advantages (Alesi et al., 2012). The biggest
is that it can be decoupled from the fossil fuel power generation, making use of renewable
energy sources as an input. In this way, the carbon loop can be closed. Direct air capture
proves promising for processes such as biofuel production since the CO 2 can be produced
on-site in a sustainable way. Low grade heat is required for regeneration (around 100 degrees
Celsius) which is often available at industrial processes in the form of waste heat or can be
supplied by renewable energy sources. (Goeppert et al., 2014) By making further use of this
waste heat the overall plant efficiency can be increased.
F UTURE PROSPECTS
In essence, CO 2 is half of the reagents needed to synthesize hydrocarbons. The other half is of
course H2O and together they can be converted by having energy as an input to hydrocarbons.
(Lackner et al., 2011). Imagine that the hydrocarbons we burn can be recycled back into their
original form! Whereas this is still something for the future, the technology can already be
applied at a much smaller (kg/day) scale, where the CO 2 can be used for one of the processes
described above. The great advantage of capturing CO 2 from the air is that it can be decoupled
from fossil fuel based power plants. It is available everywhere, and with this technology it can
be made available everywhere. Low grade heat (around 100 degrees Celsius) is needed for the
regeneration process, which can be either supplied by renewable energy sources or in the form
of waste heat from an other industrial process. Industrial processes that are best carried out at
remote locations requiring CO 2 can now directly generate it themselves, with the possibility to
make use of waste heat which otherwise would have not been used anymore.
P ROPOSED S OLUTION
Several solid sorbents have been identified to be able to capture CO 2 from the atmosphere.
These adsorbents can operate via physisorption or chemisorption. Zeolites, activated carbons,
calcium oxides, hydrotalcites, metal-organic frame (MOF) materials, aminopolymers and
organic-inorganic hybrid materials make up the main classes of adsorbents (Ko Y. G. et al.
2011) able of accomplishing this. A solid sorbent for atmospheric CO 2 capture should have two
important characteristics. The sorbent must have a high selectivity towards CO 2 at ambient
operating conditions and the captured CO 2 has to be easily regenerated so it can be used as a
feedstock. Another important characteristic is the stability of the sorbents and the kinetics of
the process. The sorbents are generally employed in a cyclic process, making use of pressure
swings or temperature swings to desorb the material after adsorptions.
3
S OLID A MINES
Ko, Y G. et al (2011) demonstrated the interaction between CO2 and various amines. Solid
Amine sorbents can be divided into several classes:
1. Primary Amines, containing the N H2 functional group;
2. Secondary Amines, containing the N H functional group;
3. Tertiary Amines, containing the N functional group.
P RIMARY A MINES
Ko, Y. G. et al (2011) identified that primary amines possessed the highest bonding-affinity to
CO 2 . Didas, S. A. et al (2012) also identified that primary amines exhibit significantly higher
adsorption capacities of CO 2 in ultra-dilute gas streams, making them suitable for atmospheric
CO 2 capture. Goeppert A. et al. (2014) exposed polyethylenimine (PEI) supported on fumed
silica to a gas stream containing 400 ppm CO 2 which was effectively adsorbed by this sorbent.
P RIMARY B ENZYLAMINE
Alesi, W. R. et al. (2012) proposed a primary benzylamine for applications in CO2 capture. The
material exhibited high CO 2 capacities and showed low moisture adsorption which is desired
for a process in which CO 2 will be cyclically captured and released. Moreover the CO 2 capture
capacity remained stable over multiple cycles which is another desired characteristic for this
process.
R ESEARCH GOAL
In order to come up with a process that can be used in industry it is important to get a good
understanding of the CO 2 capture process. The aim of this study is to model the CO 2 capture
process and determine if it can be turned into a viable process in industry. The material chosen
is the primary benzylamine described by Alesi, W. R. et al. (2012) due to its high stability and
CO 2 capture capacity.
4
R ESEARCH PLAN AND CURRENT PROGRESS
In order to achieve the described goal which is to model the adsorption process of CO 2
under atmospheric conditions the research project has been divided in several milestones of
which some have been reached. The research is supervised by TU Delft professor W. Buijs,
Engineering Thermodynamics group, Process & Energy Department, 3mE.
M ATHEMATICAL MODEL
The aim of the first milestone is to describe the process mathematically. Based on the outcome
of a literature study a mathematical model has been proposed, which is able to describe fixed
bed adsorption. The fixed bed configuration is chosen because this is the most common way
for adsorption processes (Cussler, 1997, p. 312). Currently the model has been validated for
several cases and now has to be adapted towards the application of benzylamine.
M OLECULAR MODELING
In order to get insight in how the CO 2 molecules interact with the material, molecular modeling
with Spartan software has been used. As an addition, the molecular modeling will be able to
provide heats of reactions which will serve as an input to describe how the sorbent behaves at
different temperatures.
E XPERIMENTS
Whereas the molecular modeling provides an input for the reaction mechanism as well as
the heats of reaction, still some experiments have to be conducted in order to measure the
equilibrium capacity of the sorbent for different CO 2 concentrations which are commonly
encountered in atmospheric or near atmospheric environments (e.g. office spaces). In parallel
breakthrough curve experiments have to be performed.
P ROGRESS SO FAR
Most of the mathematical modeling has been done whereas the model is currently being
validated. The focus is currently on the molecular modeling and the experiments. The
mathematical model will eventually be compared and fitted to the experimental data making
it able to describe the adsorption process.
5
B IBLIOGRAPHY
Intergovernmental Panel on Climate Change. (2005): Special Report on Carbon Dioxide Capture and Storage. Prepared by Working Group III of the Intergovernmental Panel on Climate
Change [Metz, B., O. Davidson, H. C. de Coninck, M. Loos, and L. A. Meyer (eds.)]. Cambridge
University Press, Cambridge, United Kingdom and New York, NY, USA, 442 pp.
Intergovernmental Panel on Climate Change. (2007): Climate Change 2007: Mitigation. Contribution of Working Group III to the Fourth Assessment Report of the Intergovernmental Panel
on Climate Change [B. Metz, O.R. Davidson, P.R. Bosch, R. Dave, L.A. Meyer (eds)], Cambridge
University Press, Cambridge, United Kingdom and New York, NY, USA., XXX pp.
Aresta M. (2010) Carbon Dioxide as Chemical Feedstock [online]. Available from https://
books.google.nl/books?id=Ng5qzi52etMC&dq=carbon+dioxide+as+a+chemical+feedstock&
lr=&hl=nl&source=gbs_navlinks_s assessed on 15-10-2015.
González-Fernández, C., Sialve B., Bernet N., Steyer J. P. (2011). Impact of microalgae characteristics on their conversion to biofuel. Part 1: Focus on cultivation and biofuel production.
Biofuels, Bioprod. Bioref. 6: 105-113 (2012).
Ko Y. G., Shin S. S., Choi U, S. (2011) Primary, secondary, and tertiary amines for CO 2 capture:
Designing for mesoporous CO 2 adsorbents. Journal of Colloid and Interface Science, 361 (2011)
594-602.
Cussler E. L. (2nd) (1997) Diffusion: Mass Transfer in Fluid Systems. Cambridge: Press Syndicate of the University of Cambridge.
Alesi, WR. & Kitchin, JR. (2012) Evaluation of a Primary Amine Functionalized Ion-Exchange
Resin for CO 2 Capture. Industrial & Engineering Chemistry Research, 51 (2012) 6907-6915.
Didas, S. A., Kulkarni A. R., Sholl D. S., Jones C. W. (2012) Role of Amine Structure on Carbon Dioxide Adsorption from Ultradilute Gas Streams such as Ambient Air. ChemSusChem
2012, 5, 2058-2064.
Goeppert A, Zhang H, Czaun M, May R. B., Surya Prakash G. K., Olah G. A., Narayanan S.
R. (2014) Easily Regenerable Solid Adsorbents Based on Polyamines for Carbon Dioxide Capture from the Air. ChemSusChem 7 (2014) 1386-1397.
Graves C, Ebbesen S. D., Mogensen M, Lackner K. S. (2011) Sustainable hydrocarbon fuels by recycling CO 2 and H2O with renewable or nuclear energy. Renewable and Sustainable
Energy Reviews 15 (2011) 1-23.
Goeppert A., Czaun M., Surya G. K., Olah G. A. (2012) Air as the renewable carbon source of the
future: an overview of CO 2 capture from the atmosphere. Energy Environ. Sci., 2012, 5, 7833.
6
80
Stijn de Flart
Energy Transition Scholarship
Master of Science Thesis
Appendix B
Experimental breakthrough set up
When conducting a breakthrough experiment, a known amount of solute free sorbent is packed
in a column. In line with this thesis, the gas of interest is CO2 under atmospheric conditions
(400 ppm, 20 ◦ C and a relative humidity varying from 40 to 80%). The sorbent is exposed
to a known flow rate and at the inlet and outlet the relative humidity as well as the CO2
concentration is measured. As soon as the inlet and outlet CO2 concentration are identical,
the sorbent is saturated and the breakthrough curve can be computed.
Figure B-1: Possible breakthrough experiment set-up.
Master of Science Thesis
Stijn de Flart
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Experimental breakthrough set up
The experimental set-up is shown in Figure B-1. During the experiment, the sorbent temperature should remain constant should be controllable. In order to achieve this the, sorbent
will be packed in a glass u-tube and will be suspended in a temperature controllable bath.
Two pieces of glass wool can be used to hold the sorbent in place. The sorbent adsorbs a
big amount of CO2 when it is exposed to the air and should be pre-evacuated before every
experiment starts. This is achieved by heating up the sorbent to a temperature of around 90
◦ C with nitrogen.
B-1
Experimental procedure
The experiment can be performed using the following procedure:
1. Heat sorbent and evacuate all the CO2 and water from the sorbent;
2. Weigh the sorbent and load it in the column;
3. Heat up the sorbent;
4. Flush the heated sorbent with nitrogen or air to desorb all CO2 ;
5. Cool down the sorbent;
6. Data logging of CO2 concentration and relative humidity;
7. Start breakthrough experiment, supply air at a fixed flowrate and control the temperature;
8. When the in- and outlet concentrations match the experiment is completed.
B-2
Required equipment
The following equipment would be needed in order to perform this experiment:
1. Vacuum oven / Thermogravimetic analyzer to heat up the sorbent under 90 degrees
nitrogen until the mass stabilizes;
2. Mass balance (to weigh the sorbent);
3. Glass u-tube (small diameter, 8 mm for instance);
4. Glass wool;
5. Fixed flowrate of air at a specific relative humidity (controlled by massflow controllers);
6. CO2 sensors and relative humidity sensors;
7. Nitrogen line to flush the sorbent;
8. Temperature control bath;
9. Data logging software.
Stijn de Flart
Master of Science Thesis
Bibliography
[1] Separation of CO2 from Flue Gas: A Review. Separation Science and Technology,
40(1):321–348, 2005.
[2] EPA United States Environmental Protection Agency. U.S. Carbon Dioxide emissions,
by source. viewed on 2016-01-04.
[3] W Richard Alesi Jr and John R Kitchin. Evaluation of a primary amine-functionalized
ion-exchange resin for co2 capture. Industrial & Engineering Chemistry Research,
51(19):6907–6915, 2012.
[4] Michele Aresta. Carbon dioxide as chemical feedstock. John Wiley & Sons, 2010.
[5] D. A. Barry, K. Bajracharya, and C. T. Miller. Alternative split-operator approach for
solving chemical reaction/groundwater transport models. 19:261–275, 1996.
[6] D.a. Barry, K. Bajracharya, M. Crapper, H. Prommer, and C.J. Cunningham. Comparison of split-operator methods for solving coupled chemical non-equilibrium reaction/groundwater transport models. 53:113–127, 2000.
[7] DA Barry, CT Miller, PJ Culligan, and K Bajracharya. Split operator methods for
reactive chemical transport in groundwater. 1995.
[8] DA Barry and GC Sander. Exact solutions for water infiltration with an arbitrary surface
flux or nonlinear solute adsorption. Water resources research, 27(10):2667–2680, 1991.
[9] Youssef Belmabkhout, Rodrigo Serna-Guerrero, and Abdelhamid Sayari. Adsorption of
co2-containing gas mixtures over amine-bearing pore-expanded mcm-41 silica: application for gas purification. Industrial & Engineering Chemistry Research, 49(1):359–365,
2009.
[10] Christophe Bouvier, Wim Buijs, Jorge Gascon, Freek Kapteijn, Bogdan C. Gagea,
Pierre A. Jacobs, and Johan A. Martens. Shape-selective diisopropylation of naphthalene
in H-Mordenite: Myth or reality? Journal of Catalysis, 270:60–66, 2010.
Master of Science Thesis
Stijn de Flart
84
Bibliography
[11] Stephen Brunauer, Lola S Deming, W Edwards Deming, and Edward Teller. On a
theory of the van der waals adsorption of gases. Journal of the American Chemical
society, 62(7):1723–1732, 1940.
[12] M. Caplow. Carbamate formation and breakdown - Kinetics and mechanism. Journal of
American Chemical Society, 90(8):6795–6803, 1968.
[13] Watcharop Chaikittisilp, Ratayakorn Khunsupat, Thomas T Chen, and Christopher W
Jones. Poly (allylamine)–mesoporous silica composite materials for co2 capture from
simulated flue gas or ambient air. Industrial & Engineering Chemistry Research,
50(24):14203–14210, 2011.
[14] Shrikar Chakravarti, Amitabh Gupta, and Balazs Hunek. Advanced technology for the
capture of carbon dioxide from flue gases. 2001.
[15] Romain Chauveau, Georges Grévillot, Stéphanie Marsteau, and Cécile Vallières. Values
of the mass transfer coefficient of the linear driving force model for voc adsorption on
activated carbons. Chemical Engineering Research and Design, 91(5):955–962, 2013.
[16] Zhenhe Chen, Shubo Deng, Haoran Wei, Bin Wang, Jun Huang, and Gang Yu.
Polyethylenimine-impregnated resin for high co2 adsorption: an efficient adsorbent for
co2 capture from simulated flue gas and ambient air. ACS applied materials & interfaces,
5(15):6937–6945, 2013.
[17] Sunho Choi, Jeffrey H Drese, Peter M Eisenberger, and Christopher W Jones. Application of amine-tethered solid sorbents for direct co2 capture from the ambient air.
Environmental science & technology, 45(6):2420–2427, 2011.
[18] Sunho Choi, Jeffrey H Drese, and Christopher W Jones. Adsorbent materials for carbon
dioxide capture from large anthropogenic point sources. ChemSusChem, 2(9):796–854,
2009.
[19] Firoz Alam Chowdhury, Hidetaka Yamada, Takayuki Higashii, Kazuya Goto, and
Masami Onoda. Co2 capture by tertiary amine absorbents: a performance comparison study. Industrial & Engineering Chemistry Research, 52(24):8323–8331, 2013.
[20] Seader J D and Henley Ernest J. Separation Process Principles. 2nd edition, 2006.
[21] Universiteitsfonds Delft. Eerste energy transition scholarship uitgereikt door ebn.
[22] Stephanie A Didas, Ambarish R Kulkarni, David S Sholl, and Christopher W Jones.
Role of amine structure on carbon dioxide adsorption from ultradilute gas streams such
as ambient air. ChemSusChem, 5(10):2058–2064, 2012.
[23] Process Systems Enterprise. gPROMS ProcessBuilder viewed on 2016-04-04. http:
//www.psenterprise.com/processbuilder/libraries.html.
[24] M Gholami, MR Talaie, and S Roodpeyma. Mathematical modeling of gas dehydration
using adsorption process. Chemical Engineering Science, 65(22):5942–5949, 2010.
[25] Alain Goeppert, Miklos Czaun, Robert B May, GK Surya Prakash, George A Olah, and
SR Narayanan. Carbon dioxide capture from the air using a polyamine based regenerable
solid adsorbent. Journal of the American Chemical Society, 133(50):20164–20167, 2011.
Stijn de Flart
Master of Science Thesis
85
[26] Alain Goeppert, Miklos Czaun, GK Surya Prakash, and George A Olah. Air as the
renewable carbon source of the future: an overview of co 2 capture from the atmosphere.
Energy & Environmental Science, 5(7):7833–7853, 2012.
[27] Alain Goeppert, Hang Zhang, Miklos Czaun, Robert B May, GK Prakash, George A
Olah, and SR Narayanan. Easily regenerable solid adsorbents based on polyamines for
carbon dioxide capture from the air. ChemSusChem, 7(5):1386–1397, 2014.
[28] Cristina González-Fernández, Bruno Sialve, Nicolas Bernet, and Jean-Philippe Steyer.
Impact of microalgae characteristics on their conversion to biofuel. part i: Focus on
cultivation and biofuel production. Biofuels, Bioproducts and Biorefining, 6(1):105–113,
2012.
[29] Christopher Graves, Sune D Ebbesen, Mogens Mogensen, and Klaus S Lackner. Sustainable hydrocarbon fuels by recycling co 2 and h 2 o with renewable or nuclear energy.
Renewable and Sustainable Energy Reviews, 15(1):1–23, 2011.
[30] Alexander P Hallenbeck and John R Kitchin. Effects of o2 and so2 on the capture
capacity of a primary-amine based polymeric co2 sorbent. Industrial & Engineering
Chemistry Research, 52(31):10788–10794, 2013.
[31] Michat H Jamrz, Jan Cz Dobrowolski, and Marek A Borowiak. Ab initio study on the 1
âĂć 2 reaction of CO2 with dimethylamine. 404:105–111, 1997.
[32] David W Keith, Minh Ha-Duong, and Joshuah K Stolaroff. Climate strategy with co2
capture from the air. Climatic Change, 74(1-3):17–45, 2006.
[33] Young Gun Ko, Seung Su Shin, and Ung Su Choi. Primary, secondary, and tertiary
amines for co 2 capture: designing for mesoporous co 2 adsorbents. Journal of colloid
and interface science, 361(2):594–602, 2011.
[34] Klaus S Lackner. Capture of carbon dioxide from ambient air. The European Physical
Journal Special Topics, 176(1):93–106, 2009.
[35] Klaus S Lackner. The thermodynamics of direct air capture of carbon dioxide. Energy,
50:38–46, 2013.
[36] Klaus S Lackner, Patrick Grimes, and Hans-Joachim Ziock. Carbon dioxide extraction
from air: is it an option? 24th Annual Technical Conference on Coal Utilization & Fuel
Systems, 1999.
[37] Weigang Lu, Julian P Sculley, Daqiang Yuan, Rajamani Krishna, and Hong-Cai Zhou.
Carbon dioxide capture from air using amine-grafted porous polymer networks. The
Journal of Physical Chemistry C, 117(8):4057–4061, 2013.
[38] Pourquie M. Computational fluid dynamics Lecture notes., 2015.
[39] Niall MacDowell, Nick Florin, Antoine Buchard, Jason Hallett, Amparo Galindo, George
Jackson, Claire S Adjiman, Charlotte K Williams, Nilay Shah, and Paul Fennell. An
overview of co 2 capture technologies. Energy & Environmental Science, 3(11):1645–1669,
2010.
Master of Science Thesis
Stijn de Flart
86
Bibliography
[40] Bert Metz, Ogunlade Davidson, Heleen De Coninck, Manuela Loos, Leo Meyer, et al.
Carbon dioxide capture and storage. 2005.
[41] Miguel Monsanto, Adithya Thota Radhakrishnan, David Sevillano, Nasim Hooshyar,
J. Meuldijk, and E. Zondervan. Modeling and Optimization of an Adsorption Process
for the Recovery of Catechins from Green Tea. 33:1441–1446, 2014.
[42] Inter Governmental Panel on Climate Change. FAQ 2.1 How do human activities contribute to climate change and how do they compare with natural influences? viewed on
2016-01-04. http://www.ipcc.ch/publications_and_data/ar4/wg1/en/faq21.html.
[43] Intergovernmental Panel on Climate Change. Climate Change 2014–Impacts, Adaptation
and Vulnerability: Regional Aspects. Cambridge University Press, 2014.
[44] Colonna P. Modeling of processes and energy systems. part 1 - introduction. Lecture
notes., 2014.
[45] Helene Perrotin-Brunel, Wim Buijs, Jaap Van Spronsen, Maaike J E Van Roosmalen,
Cor J. Peters, Rob Verpoorte, and Geert Jan Witkamp. Decarboxylation of ∆9 tetrahydrocannabinol: Kinetics and molecular modeling. Journal of Molecular Structure,
987(1-3):67–73, 2011.
[46] Nora Planas, Allison L Dzubak, Roberta Poloni, Li-Chiang Lin, Alison McManus,
Thomas M McDonald, Jeffrey B Neaton, Jeffrey R Long, Berend Smit, and Laura
Gagliardi. The mechanism of carbon dioxide adsorption in an alkylamine-functionalized
metal–organic framework. Journal of the American Chemical Society, 135(20):7402–7405,
2013.
[47] Ankit Rohatgi. WebPlotDigitizer viewed on 2016-02-25.
WebPlotDigitizer/.
http://arohatgi.info/
[48] Douglas M Ruthven. Principles of adsorption and adsorption processes. John Wiley &
Sons, 1984.
[49] Sunita Satyapal, Tom Filburn, John Trela, and Jeremy Strange. Performance and properties of a solid amine sorbent for carbon dioxide removal in space life support applications.
Energy & Fuels, 15(2):250–255, 2001.
[50] Rodrigo Serna-Guerrero and Abdelhamid Sayari. Modeling adsorption of co 2 on aminefunctionalized mesoporous silica. 2: Kinetics and breakthrough curves. Chemical Engineering Journal, 161(1):182–190, 2010.
[51] Mohammad Saleh Shafeeyan, Wan Mohd Ashri Wan Daud, and Ahmad Shamiri. A
review of mathematical modeling of fixed-bed columns for carbon dioxide adsorption.
Chemical engineering research and design, 92(5):961–988, 2014.
[52] Thomas F Stocker. Climate change 2013: the physical science basis: Working Group I
contribution to the Fifth assessment report of the Intergovernmental Panel on Climate
Change. Cambridge University Press, 2014.
[53] Joshuah K Stolaroff. Capturing CO2 from ambient air: a feasibility assessment. PhD
thesis, Carnegie Mellon University Pittsburgh, PA, 2006.
Stijn de Flart
Master of Science Thesis
87
[54] Phil Klunzinger Wavefunction Support. Quantum Mechanics Energy FAQ viewed on
2016-03-11. https://www.wavefun.com/support/sp_compfaq/Energies_FAQ.html.
[55] Rens Veneman, Natalia Frigka, Wenying Zhao, Zhenshan Li, Sascha Kersten, and Wim
Brilman. Adsorption of h 2 o and co 2 on supported amine sorbents. International
journal of greenhouse gas control, 41:268–275, 2015.
[56] Rens Veneman, Wenying Zhao, Zhenshan Li, Ningsheng Cai, and Derk WF Brilman.
Adsorption of co 2 and h 2 o on supported amine sorbents. Energy procedia, 63:2336–
2345, 2014.
[57] C Vuik, P van Beek, F Vermolen, and J van Kan. Numerieke methoden voor differentiaalvergelijkingen. VSSD, 2006.
[58] Buijs W. Spijsvertering en thermodynamica Lecture notes., 2015.
[59] Junya Wang, Liang Huang, Ruoyan Yang, Zhang Zhang, Jingwen Wu, Yanshan Gao,
Qiang Wang, Dermot O’Hare, and Ziyi Zhong. Recent advances in solid sorbents for co
2 capture and new development trends. Energy & Environmental Science, 7(11):3478–
3518, 2014.
[60] Qiang Wang, Jizhong Luo, Ziyi Zhong, and Armando Borgna. Co2 capture by solid adsorbents and their applications: current status and new trends. Energy & Environmental
Science, 4(1):42–55, 2011.
[61] Tao Wang, Klaus S Lackner, and Allen Wright. Moisture swing sorbent for carbon dioxide
capture from ambient air. Environmental science & technology, 45(15):6670–6675, 2011.
[62] David Young. Computational chemistry: a practical guide for applying techniques to real
world problems. John Wiley & Sons, 2001.
[63] Frank Zeman. Energy and material balance of co2 capture from ambient air. Environmental science & technology, 41(21):7558–7563, 2007.
[64] Frank S Zeman and Klaus S Lackner. Capturing carbon dioxide directly from the atmosphere. World Resource Review, 16(2):157–172, 2004.
Master of Science Thesis
Stijn de Flart