co capture and conversion to syngas: rigorous …
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CO2 CAPTURE AND CONVERSION TO SYNGAS: RIGOROUS MODELING,
OPTIMIZATION AND SUPERSTRUCTURE-BASED PROCESS SYNTHESIS
A Thesis
by
PRIYADARSHINI BALASUBRAMANIAN
Submitted to the Office of Graduate and Professional Studies of
Texas A&M University
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
Chair of Committee, M.M. Faruque Hasan
Committee Members, Mahmoud M. El-Halwagi
Perla B. Balbuena
Head of Department, M. Nazmul Karim
August 2017
Major Subject: Chemical Engineering
Copyright 2017 Priyadarshini Balasubramanian
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ABSTRACT
CO2 emissions from electricity generation have increased by 50% between 2000
and 2013. Large-scale carbon capture and storage is still not deployed for reasons
including high cost, technological barriers and uncertainty in geological storage. A
promising alternative is to convert CO2 to value-added chemicals via syngas (a mixture
of H2 and CO) which is an intermediate for many hydrocarbon-based fuels and
chemicals. In this work, we first perform thermodynamic analysis to benchmark
different CO2 utilization systems based on energy requirement and syngas selectivity for
a range of H2 to CO ratios. Our study reveals that significant energy is required to
achieve reasonable levels of CO2 utilization via thermochemical routes. Furthermore, not
a single reforming technology is optimal for the entire range of syngas ratios of practical
interest. We then perform extensive simulation of various CO2-to-syngas alternatives
using equilibrium, pseudo-homogenous and heterogeneous reactor models to
characterize the gaps between the best-possible and realistically achievable process
performances in terms of energy consumption and CO2 utilization. Lastly, using a
superstructure of process flowsheets with all plausible alternatives, we systematically
design optimal process networks for CO2 utilization considering various raw materials,
such as CO2 from flue gas, methane from stranded sources, oxygen from air and water
and hydrogen. Based on our process synthesis results, we conclude that even the best
possible configurations would have 15-52% gaps between realistic CO2 utilization and
theoretically maximum possible utilization, depending on the target syngas ratio.
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ACKNOWLEDGEMENTS
I would like to heartily thank my committee chair and advisor, Dr. M.M. Faruque
Hasan for being a mentor and a pillar of support throughout the course of my study and
research at Texas A&M University, and without whom this thesis would have not been
possible. I would like to thank my committee members, Dr. Mahmoud M. El-Halwagi
and Dr. Perla B. Balbuena, for their guidance and support throughout the course of this
research.
I would also like to acknowledge my group members and colleagues for all their
constructive feedback, suggestions and collaborations in research and for making the
time at the workplace memorable. I am also grateful to the department faculty and staff,
especially, Ashley and Vickie, for all the help. Big thanks go to my dearest friends for
making my time at Texas A&M University a great experience. Finally, thanks to my
family for their continued support, encouragement and love, without whom this journey
would not have been possible.
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CONTRIBUTORS AND FUNDING SOURCES
Contributors
This work was supervised by a thesis committee consisting of Professor M.M.
Faruque Hasan and Professor Mahmoud M. El-Halwagi of the Department of Chemical
Engineering and Professor Perla B. Balbuena of the Department of Material Science and
Engineering.
All work for the thesis was completed by the student, under the advisement of
Professor M.M. Faruque Hasan of the Department of Chemical Engineering.
Funding Sources
There are no outside funding contributions to acknowledge related to the research
and compilation of this document.
v
TABLE OF CONTENTS
Page
ABSTRACT .............................................................................................................. ii
ACKNOWLEDGEMENTS ...................................................................................... iii
CONTRIBUTORS AND FUNDING SOURCES ..................................................... iv
TABLE OF CONTENTS .......................................................................................... v
LIST OF FIGURES ................................................................................................... vii
LIST OF TABLES .................................................................................................... ix
CHAPTER I INTRODUCTION .......................................................................... 1
1.1 CO2 Utilization Alternatives ...................................................................... 1
1.2 Key Utilization Challenges ........................................................................ 4
1.3 Research Objectives ................................................................................... 7
1.4 Outline of the Thesis .................................................................................. 7
CHAPTER II LITERATURE REVIEW ............................................................... 9
2.1 Thermodynamic Analysis .......................................................................... 10
2.2 Process-scale Analysis ............................................................................... 12
2.3 Reactor Modeling and Simulation ............................................................. 17
CHAPTER III ENERGETIC ANALYSIS OF CO2 UTILIZATION ..................... 32
3.1 Minimum Energy Calculation .................................................................... 32
3.2 Nonlinear (NLP) Optimization Model for Theoretical Minimum
Calculations ............................................................................................... 35
3.3 Results for Minimum Energy, Maximum CO2 Utilization and Maximum
Syngas Selectivity at Equilibrium Conditions .......................................... 40
CHAPTER IV MODELING AND SIMULATION OF REACTORS FOR CO2
UTILIZATION VIA SYNGAS ................................................................................ 46
4.1 Equilibrium-based Reactor Model ............................................................. 46
4.2 Stoichiometry-based Reactor Model .......................................................... 48
4.3 Reaction Rate-based 1-D Reactor Models ................................................. 49
vi
4.4 Simulation Results and Comparison .......................................................... 58
4.5 Surrogate-based Reactor Models ............................................................... 71
CHAPTER V SUPERSTRUCTURE-BASED OPTIMAL SYNTHESIS OF CO2
UTILIZATION PROCESSES .................................................................................. 75
5.1 Process Superstructure ............................................................................... 76
5.2 Superstructure-based Process Synthesis Model ......................................... 78
5.3 Process Synthesis Results ........................................................................... 89
CHAPTER VI CONCLUSIONS AND RECOMMENDATIONS ........................ 94
6.1 Conclusions ................................................................................................ 94
6.2 Recommendations ...................................................................................... 95
REFERENCES .......................................................................................................... 96
APPENDIX A ........................................................................................................... . 111
APPENDIX B ........................................................................................................... 117
APPENDIX C ........................................................................................................... 126
vii
LIST OF FIGURES
FIGURE Page
1.1 Pathways beyond syngas, depicting various conversion routes of syngas,
based on its syngas ratio (SR) .................................................................... 2
1.2 Alternatives for syngas production and/or CO2 utilization ........................ 4
1.3 Classification of technological alternatives based on syngas production
and CO2 utilization ..................................................................................... 4
2.1 The comparison and advantages of combining individual reactors ........... 24
3.1 Results from the energetic analysis for syngas production ........................ 41
3.2 Results from the energetic analysis for syngas production via dry
reforming (DR) ........................................................................................... 42
3.3 Trade-offs between energy and CO2 utilization potentials for combined
dry and steam reforming (CDSMR) ........................................................... 44
4.1 Solution strategy to solve the 1-D heterogeneous reactor model ............... 55
4.2 Validation of the SMR pseudo-homogeneous model ................................ 58
4.3 Dry reforming of methane .......................................................................... 60
4.4 Steam reforming of methane ...................................................................... 61
4.5 Partial oxidation of methane - adiabatic ..................................................... 62
4.6 Partial oxidation of methane - isothermal .................................................. 63
4.7 DR and SMR kinetics comparison ............................................................. 64
4.8 Combined dry and steam reforming of methane ........................................ 65
4.9 Dominating reactions in different temperature regions explaining the
trend in CO2 conversion for combined dry and steam methane reforming 65
4.10 Combined dry reforming and partial oxidation of methane ....................... 66
4.11 Combined steam reforming and partial oxidation of methane ................... 67
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4.12 Tri-reforming of methane ........................................................................... 68
4.13 Reverse water gas shift reaction ................................................................. 69
4.14 Comparison between equilibrium and pseudo-homogeneous reactor for
SMR for higher flowrates ........................................................................... 70
4.15 ALAMO workflow for obtaining surrogate models .................................. 72
4.16 Predicted vs. simulated values for the output variables modeled using
ALAMO for DR ......................................................................................... 74
5.1 Superstructure for the synthesis of CO2 utilization process network ......... 76
5.2 Optimal CO2 utilization process configuration obtained using
equilibrium-based models .......................................................................... 89
5.3 Optimal CO2 utilization process configuration obtained using
stoichiometry-based models ....................................................................... 90
5.4 Optimal CO2 utilization process configuration with maximum CO2
utilization. ................................................................................................... 91
5.5 Optimal CO2 utilization process configuration with minimum cost .......... 92
5.6 Maximum CO2 utilization .......................................................................... 93
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LIST OF TABLES
TABLE Page
2.1 Indicative recent literature in the thermodynamic analysis of CO2
utilization. ................................................................................................... 14
2.2 Indicative recent literature in the areas of modeling, simulation and
optimization of reforming-based CO2 utilization processes ...................... 15
2.3 Rate expressions and parameters for different reactors.............................. 30
4.1 Bounds on input variables for DR for equilibrium model ......................... 48
4.2 Scaled 1-D pseudo-homogeneous and 1-D heterogeneous models ........... 56
4.3 Parameters for reactor models .................................................................... 57
4.4 Reactor simulation conditions .................................................................... 59
5.1 Optimal CO2 utilization results for different methane sources .................. 91
1
CHAPTER I
INTRODUCTION
Carbon dioxide is one of the key greenhouse gases emitted by human activities at
the global scale and its primary source is the burning of fossil fuels to produce energy.
Global CO2 emissions in 2013 increased by 2.2% over 2012 levels to 32.2 GtCO2 and
electricity and heat generation sectors contributed to nearly two-thirds of the emissions.
Emissions from electricity generation specifically increased by 50% between 2000 and
2013 1. According to IPCC AR5, direct CO2 emissions of the energy supply sector will
increase from 14.4 GtCO2/year in 2010 to 24–33 GtCO2/year in 2050 2.
CO2 capture and storage (CCS) of power plant flue gases has gained worldwide
interest as a potential climate change mitigation measure 3, but their wide deployment in
industrial and power sectors is dependent upon substantial cost reductions and the
identification of better storage opportunities 1, 4. In 2010, the National Energy
Technology Laboratory of the U.S. Department of Energy estimated that CCS
technologies would add around 80 percent to the cost of electricity for a new pulverized
coal plant, and around 35 percent to the cost of electricity for a new advanced
gasification-based plant 5. This high cost can be offset by the utilization of carbon
dioxide to produce value added products.
1.1. CO2 Utilization Alternatives
Since CO2 is a source of both carbon and oxygen, it has enormous potential to be
converted to hydrocarbons, if provided with a source of hydrogen. The best routes of
conversion would be to transform CO2 into liquid transportation fuels, aromatics,
2
olefins, and their derivatives 6-8. A promising route is to produce synthesis gas (also
known as syngas) that is a mixture of H2 and CO. It is a universal intermediate that can
be converted to numerous value-added products like jet fuel, diesel, gasoline, acetic acid,
formaldehyde, dimethyl ether, aromatics and olefins via methanol synthesis and Fischer-
Tropsch synthesis 9-10. Syngas can play an important role as an intermediate for the
utilization of unconventional resources, such as shale gas and stranded natural gas to
produce fuels and chemicals 11-14. Furthermore, syngas can be the critical intermediate in
a potential CO2-to-olefins route for storing renewable energy such as solar energy in the
form of high-energy chemicals 15.
Figure 1.1. Pathways beyond syngas, depicting various conversion routes of syngas,
based on its syngas ratio (SR). The syngas upgrading processes through water gas shift
and reverse water gas shift based on SR, their intermediate products and the final
products are shown. FT stand for Fischer-Tropsch synthesis and HTFT, LTFT stand for
the High Temperature and Low Temperature FT syntheses, respectively.
Syn
gas
0.6 < SR <1.7
H2/(2CO+3CO2) = 1.05
HTFTWax, Gasoline, diesel, jet
fuel, olefins, waxes, alcohols
WGSLiquid hydrocarbon, fuels,
methane via FT
SR = 1.7 LTFTWaxes, alcohols, organic
acids
1.8 ≤ SR ≤ 2.1
Methanol
Acetic acid, formaldehyde, methyl methacrylate, MTBE,
olefins
Gasoline via ExxonMobil methanol-to-gasoline (MTG)
Dimethyl ether (DME)
Methanol
FT-synthesisGasoline, diesel, jet fuel, olefins, waxes, alcohols
SR > 2.1
Hydrogen Hydrogen
RWGS
3
It is important to identify the reactions and processes that utilize CO2 via syngas.
Figure 1.1 shows the different pathways with syngas as the starting point with the
corresponding syngas ratios (SR), that is, H2:CO as feed conditions 16-18. Since syngas
has different applications and there are several paths that we can take to produce value-
added products, the quality and quantity of syngas becomes a major criterion. It is
imperative to identify the reactions that produce the syngas of desired SR while
consuming CO2 to decide on the best conversion routes for CO2.
There are several ways to produce syngas. Figures 1.2 and 1.3 show different
reforming options that can be used to produce syngas, utilize CO2, or both. These
alternatives can be distinguished based on the raw materials used. Some of these utilize
CO2, while others produce CO2. Three primary reactions that produce syngas are dry
reforming of methane (DR), steam methane reforming (SMR), and partial oxidation of
methane (POX). These reformers can be also combined in various ways to create
variants such as combined dry and steam methane reforming (CDSMR), combined
partial oxidation and dry reforming (PODR), combined partial oxidation and steam
methane reforming (POSMR), and tri-reforming (TR). DR produces syngas with SR
lesser than 1, whereas SMR produces syngas of SR more than 3. Auto-thermal reforming
of methane and POX produce syngas of SR close to 2. Depending upon the SR, different
routes can be taken to produce the chemicals of interest. The ratio of H2/(2CO+3CO2)
also plays an important role in deciding the selectivity of products when High
Temperature Fischer-Tropsch (HTFT) synthesis is carried out 17. Thus, CO2 can be
indirectly, via syngas or directly with syngas, be converted into useful chemicals.
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Figure 1.2. Alternatives for syngas production and/or CO2 utilization.
Figure 1.3. Classification of technological alternatives based on syngas production
and CO2 utilization.
1.2. Key Utilization Challenges
The overarching goal of this research is to understand the carbon dioxide conversion
systems and to study if converting the carbon dioxide emitted by power plants, rather
than sequestering it, is a viable option. To this end, we seek to answer the following
research questions:
Dry Reforming (DR)
CH4 + CO2 2CO + 2H2
Tri-Reforming (TR)
CH4 + CO2 2CO + 2H2
CH4 + H2O CO + 3H2
CH4 + O2 CO + 2H2
Reverse Water Gas
Shift (RWGS)
CO2 + H2 CO + H2O
Steam Methane
Reforming (SMR)
CH4 + CO2 CO + 3H2
Partial Oxidation (POX)
CH4 + ½ O2 CO + 2H2
Combined Dry and
Steam Reforming
(CDSMR)
CH4 + CO2 2CO + 2H2
CH4 + H2O CO + 3H2
Combined Dry and
Partial Oxidation
(PODR)
CH4 + CO2 2CO + 2H2
CH4 + O2 CO + 2H2
Combined Steam and
Partial Oxidation
(POSMR)
CH4 + H2O CO + 3H2
CH4 + O2 CO + 2H2
DR
CDSMR
PODR
TR
SMR
POX
POSMR
RWGS
Syngas
productionCO2
utilization
5
1. How much CO2 can be converted and if so, how do we determine the maximum
possible utilization of carbon dioxide?
2. What is the realistic utilization of CO2 possible with the current technologies and
reasonable operating conditions?
3. How do we solve complex process models that represent these utilization
alternatives without losing the accuracy?
Several works in the past addressed the first question through theoretical
thermodynamic analysis. Swapnesh et al. (2014) compared the thermodynamic behavior
of CO2 utilization systems and studied the effects of temperature, pressure and feed
ratios. The reactions considered were CO2 hydrogenation to synthesize dimethyl ether
(DME), synthesis of methane and dry reforming [23]. Noureldin et al. (2014) used an
equilibrium model to describe different reforming reactors and optimized the process for
different process and economic objectives [24].
Substantial research has been aimed at answering the second question through
experimental studies [20-22]. Most of these reactions are heterogeneous catalytic
reactions and involve extensive catalyst preparation, pretreatment and regeneration.
Experimentation is tedious and expensive and it may not be possible to study the effects
of various factors like pressure, temperature and feed composition on product yield and
CO2 utilization, as there are physical limitations to the number of experiments that can
be performed. One of the ways to overcome this challenge is to computationally study
the reactor systems by identifying the different phenomena that goes on within the
systems and analyze these models to help answer the above questions.
6
There has been substantial work done on reactor modeling in the past and many
predictive models are being developed. Since all the reactions that we have considered
are catalytic reactions, we will limit our discussion to catalytic reactor/packed bed
reactor models only. In packed bed reactor modeling, there are two types of models,
namely, process-side models and furnace-side models. Process-side models are of more
relevance to us than furnace-side models since we want to study the utilization of carbon
dioxide and production of syngas. Process-side models differ from one other in
considering one or two dimensions, and in the assumptions regarding mass and heat
transfer limitations. The chemical reactions taking place in reactors are usually complex
and this leads to complications and uncertainties in describing them through
mathematical models.
Apart from developing the appropriate equations for representing the mass and
energy balances in the reactors, there are numerical challenges and difficulties in solving
these models as they could be highly nonlinear or non-algebraic depending on the level
of detailing. The more detailed the model gets, the more accurate it becomes and the
more complex it becomes to solve. Thus, we need to use a simple model that best
captures the most salient features of the reaction system.
Section 2 of the thesis discusses in detail, the various models that have been
developed in the past, for the reactor systems that we have considered, enlisting the
advantages, drawbacks and important assumptions. Apart from individual reactor
models, there has been considerable work on the comparison of different reactor systems
that utilize CO2.
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1.3. Research Objectives
The objectives of this research are as follows:
• Identify various reactor alternatives that utilize CO2 and produce syngas.
• Benchmark the maximum CO2 utilization possible via these alternatives through
a theoretical analysis.
• Obtain the realistic values of conversion and syngas yield with the catalysts
available by using rigorous mathematical models describing reactor performance.
• Analyze all plausible alternatives in a single framework to obtain the optimal
route and conditions for the maximum utilization of CO2.
To achieve these, we explore and identify the different processes for CO2 utilization.
The benchmarking of process performance is done using a minimum energy and
equilibrium-based-thermodynamic analysis and the realistic values are obtained using
rigorous kinetics-based models that vary in detail and complexity. Finally, all the
alternatives are embedded in a superstructure framework and optimized to find the
optimal CO2 utilization.
1.4. Outline of the Thesis
In Chapter II, an elaborate literature review has been performed. This review has
been classified into three parts: (1) thermodynamic analysis of the CO2 utilization
systems; (2) modeling, simulation and optimization of the various alternatives for the
utilization of CO2; and (3) superstructure-based process synthesis models and analysis
on CO2 utilization has been performed.
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In Chapter III, a theoretical analysis based on thermodynamics of CO2 utilization
systems, has been done. A nonlinear (NLP) model has been proposed to study the
maximum utilization of CO2, minimum energy and maximum syngas selectivity at
equilibrium while achieving different syngas ratios. The results for three different
objectives for different reaction systems have been reported.
Chapter IV discusses the different reactor models varying in complexity and
accuracy, such as equilibrium reactor model and reaction-rate based reactor models (e.g.,
pseudo-homogeneous and heterogeneous reactor models). Simulation results are
discussed and compared for different reactors. The chapter also describes the surrogate
model development using ALAMO 19 and reports the models and their performance
metrics.
A process synthesis model based on a superstructure framework is described in
Chapter V. The model formulation and the optimization results are also reported.
Chapter VI concludes the thesis with discussions on the research and
recommendations for future work.
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CHAPTER II
LITERATURE REVIEW
An elaborate literature review on the thermodynamic analysis of the CO2
utilization systems, modeling, simulation and optimization of the various alternatives for
the utilization of CO2 and superstructure-based process synthesis has been performed in
this chapter. The conversion of CO2 has been broadly classified into two classes,
depending on its incorporation into chemicals (inorganic and organic carbonates,
carbamates, etc.) or the conversion into one of its reduced forms as fuels (CO, syngas,
methanol, methane and higher hydrocarbons) 20. However, current CO2-based chemicals
production is limited to mainly urea, salicylic acid and polycarbonates 21. The
conversion to fuels is particularly important since the fuels market is 12-14 times larger
than that of chemicals. Furthermore, compared to the currently small utilization of 207
Mt/y in 2016 22 over more than 35 Gt/yr emission for chemicals production suggest that
only conversion to fuels could contribute to a considerable reduction in CO2 emission.
However, the conversion of CO2 to fuels requires energy for the conversion and
hydrogen for the production of chemicals (in fact, maximum utilization of CO2 would
largely depend on the availability of renewable hydrogen 23).
Many reaction routes exist for CO2 utilization. For example, hydrogenation of
CO2 produces methanol, CO2 based cycloaddition produces epoxides, and carbonylation
of amines or alcohols using CO2 produces carbonates. Significant efforts have been
made toward the conversion of CO2 into oxygen containing fuels such as methanol and
dimethyl ether (DME) 24. Heterogeneous catalysts (e.g., metal oxides and zeolites) can
10
be used for the direct transformation of CO2 to organic carbonates such as ethylene
carbonate (EC), propylene carbonate (PC) and dimethyl carbonate (DMC) 25. For
example, Kongpanna et al. 26 synthesized and generated process networks for DMC
production with CO2 utilization, based on a systematic computer-aided framework for
combined process synthesis-design-intensification.
2.1. Thermodynamic Analysis
CO2 is a highly stable molecule with a very low Gibbs energy of formation (–
393.37 kJ/mol gas). The low energetic level of CO2 poses several thermodynamic
limitations of its conversion to other molecules. As summarized by Müller et al. 27, the
low driving force for CO2 conversion due to the high stability has to be compensated by
(i) a highly energy-rich reactant, (ii) subsequent hydrogenation of a double bond, or (iii)
formation of at least two water molecules per CO2 molecule. To this end,
thermodynamic equilibrium analysis such as the minimization of Gibbs free energy can
provide useful information on the potentially minimum and maximum conversion limits,
potential effects of operating conditions (temperature, pressure, feed ratio) on
conversion, and constraints on the design of suitable catalysts and process networks, and
potential carbon formation 28-37. Thermodynamic analysis can be also used to indicate
and/or validate whether complete conversion with very high selectivity is
thermodynamically feasible or not in the presence of multiple conflicting reactions. This
information is particularly useful in designing robust processes for potential application
of upgrading CO2-rich natural gas with variable compositions and impurity levels in the
feed. Furthermore, it also indicates how far the current technologies are from the best
11
possible performance, and how much further improvements can be practically achieved.
Table 2.1 summarizes the recent contributions in the area of Gibbs energy minimization-
based thermodynamic analysis.
While equilibrium analysis provides useful indication on the extent of reforming,
it may not capture the accurate process performance due to the lack of kinetic
information. Recently, Challiwala et al. 38 performed both thermodynamic and thermo-
kinetic analysis of various reforming technologies. Interestingly, their kinetic evaluation
indicated an agreement between combined kinetic model with the thermodynamic
equilibrium results. Wehinger et al. 39 performed detailed numerical simulations of
catalytic fixed-bed reactors for heterogeneous dry reforming using computational fluid
dynamics (CFD) method.
Approximate models have been also successfully applied in the past to describe
reforming schemes. For instance, Larentis et al. 40 developed both empirical and
phenomenological models for PODR. The empirical polynomial models were fitted
based on experimental data to correlate methane conversion, CO selectivity, and H2/CO
ratio as functions of temperature, oxygen/methane ratio, and gas hourly space velocity
(GHSV). The phenomenological model was based on a set of algebraic and differential
equations with parameters fitted with experimental data. While these approximate
models greatly simplify the optimization of PODR reactors when kinetic mechanisms
are not well known, as noted by Larentis et al. 40, they cannot be a routine procedure for
process optimization, as they may suffer from low prediction accuracy due to the lack of
kinetic information. Furthermore, models with large number of parameters require
12
significant experimental/computation efforts. The collection of different reforming
processes is intended to enhance the overall performance by combining the advantages
and overcoming the limitations of individual processes.
2.2. Process-scale Analysis
Table 2.2 summarizes the recent works in the areas of modeling, simulation,
optimization and/control of CO2 utilization processes, mainly focusing on syngas
production. Zhang et al. 41 proposed an efficient process that utilizes recycled CO2 from
a steam methane reformer (SMR) in a combined dry reforming and partial oxidation
(DR+POX). Although CO2 is separated using an additional amine-based absorption unit,
the combination of multiple reformers is found to be more efficient due to reutilization
of CO2 and lower requirement of raw materials. Baltrusaitis and Luyben 42 explored
process flowsheet alternatives based on methane reforming (SMR), dry methane
reforming (DR), auto thermal reforming (ATR), reverse water gas shift (RWGS),
SMR/ATR, SMR/DR or SMR/RWGS in the context of producing syngas with H2:CO
ratio of 2, which is appropriate for FT synthesis. They concluded that lowest total annual
cost (TAC) would feature a system composed of both SMR and DR reactors (SMR/DR).
Parallel reforming using both SMR and DR is also attractive because it is capable of
generating syngas with any H2/CO ratio between 1 and 3, which can be used to adjust for
a large H2/CO feedstocks or processes, such as from a stand-alone SMR. To this end,
Luyben 43 recently studied the plantwide control of a process with DR and SMR units
operating in parallel to produce FT syngas, where the total methane fresh feed is split
between the two parallel processes so as to produce the desired H2/CO ratio. Noureldin
13
et al. 44-45 analyzed, integrated and optimized several individual, parallel and combined
reforming alternatives and highlighted a strong inverse relationship between CO2
chemical fixation and the required syngas H2: CO. Their findings also suggest that
combined reforming involving DR and SMR may benefit from the presence of waste
heat sources.
2.2.1. Reactor Optimization
Though there is rigorous work done on the modeling and simulation of reforming
reactors and study of effects of individual decision variables on the conversion of
methane, the work on optimization of these reactors is limited. Rajesh et al. (2000)
modeled a steam reformer using a 1-D pseudo-homogeneous model with effectiveness
factors and optimized it using genetic algorithm for minimum inlet flowrate of CH4 and
maximum output flowrate of CO [25]. Rahimpour et al. (2012) used differential
evolution (DE) method to optimize a 1-D pseudo homogeneous model of a steam
reformer [26]. Aboosadi et al. optimized a tri-reformer 1-D heterogeneous model using
differential evolution method [27]. Luyben (2014) simulated a dry reformer in Aspen
using RGibbs and RPlug models and performed flowsheet optimization for the optimal
design parameters for minimum total annualized cost [28]. An excellent review on
current technologies and future opportunities in design and optimization of CO2
conversion processes can be found in Roh et al. (2016) [29].
14
Table 2.1. Indicative recent literature in the thermodynamic analysis of CO2 utilization.
Key Methodology Reference
CO2 conversion
systems considered Raw materials
Target
Products
Gibbs free energy minimization Amin and Yaw (2007) 28 PODR Methane,
oxygen, CO2
Syngas
Gibbs free energy minimization Özkara-Aydınoğlu (2010) 29 CDSMR Methane, steam,
CO2
Syngas
Gibbs free energy minimization Nikoo and Amin (2011) 33 DR Methane, CO2 Syngas
Gibbs free energy minimization Nematollahi et al. (2012) 32 CDSMR Methane, steam,
CO2
Syngas
Gibbs free energy minimization Sahebdelfar and Ravanchi
(2015) 30
Hydrogenation of CO2
to methane
Hydrogen, CO2 Methane
Gibbs free energy minimization Chein et al. (2015) 31 DR, PODR Methane, CO2 Syngas
Gibbs free energy minimization Swapnesh et al. (2014) 34 DR, CO2
hydrogenation to
DME or methane
Methane,
hydrogen, CO2
Syngas,
DME,
methane
Gibbs free energy minimization,
Economic evaluation
Cañete et al. (2014) 35 DR, TR, and CR Methane, CO2,
steam, oxygen
Methanol
Gibbs free energy minimization Demidov et al. (2011) 36 DR, CDSMR Methane, steam,
CO2
Syngas
Gibbs free energy minimization Freitas and Guirardello (2014) 37
DR, CDSMR, DAR Methane, steam,
oxygen, CO2
Syngas
Gibbs free energy minimization,
kinetic evaluation
Challiwala et al. (2017) 38 Combined reforming
(CR), CDSMR
Methane, steam,
oxygen, CO2
Syngas
15
Table 2.2. Indicative recent literature in the areas of modeling, simulation and optimization of reforming-based CO2
utilization processes.
Key Methodology Reference
CO2 conversion systems
considered Raw materials
Target
Products
Process design
flowsheet evaluation
Baltrusaitis and Luyben (2015) 42 SMR, DR, ATR, RWGS,
SMR/ATR, SMR/DR,
SMR/RWGS
Methane, steam,
oxygen, CO2
Syngas
Dynamic modeling
and plantwide control
Luyben (2014, 2016) 43, 46 DR, SMR, DR/SMR Methane, steam,
CO2
Syngas
Process design
flowsheet evaluation
Zhang et al. (2014) 41 SMR, PODR Methane, steam,
oxygen, CO2
Hydrogen,
syngas
Gibbs free energy
minimization, process
design
Noureldin et al. (2014, 2015) 44-45 SMR, POX, DR, CDSMR,
PODR.
Methane, steam,
oxygen, CO2
Syngas
Both empirical and
phenomenological
modeling
Larentis et al. (2001) 40 PODR
Methane,
oxygen, CO2
Syngas
Process simulation
using RGibbs
Ayodele and Cheng (2015) 47 DR, PO, and auto-thermal
methane reforming
Methane,
oxygen, CO2
Hydrogen,
syngas
Techno-economic
analysis
Julian-Duran et al. (2014) 48 PO, SMR, ATR, CR Shale gas,
oxygen, steam,
Methanol
Process design and
optimization
Hernández and Martin (2016) 49 DR Biogas, steam Methanol
Process simulation
using RGibbs
Gopaul and Dutta (2015) 50 DR, PODR Biogas, oxygen,
hydrogen
16
Table 2.2. Continued.
Key Methodology Reference
CO2 conversion systems
considered Raw materials
Target
Products
Numerical simulation
and optimization
Aboosadi et al. (2011) 51 TR Methane, CO2,
steam, oxygen
Syngas
Simulation and
exergoeconomic
analysis
Li et al. (2011) 52 PODR, DME synthesis,
MeOH synthesis, DMC
synthesis
Coal gasification
gas, coke oven
gas, tail gas,
oxygen,
Methanol,
DME,
DMC,
power
Modeling and
optimization
Cho et al. (2009) 53 TR, DME synthesis Natural gas,
steam, oxygen
DME
Integrated system
development
Minutillo and Perna (2009) 54 TR, MeOH synthesis Flue gas,
Methane, Air
Methanol
Plug flow reactor
based process
simulation
Kiss et al. (2016) 55 Hydrogenation of CO2 to
methanol
CO2, hydrogen Methanol
Simulation and heat
integration
Pérez-Fortes et al. (2016) 56 Hydrogenation of CO2 to
methanol
CO2, hydrogen Methanol
Process simulation Van-Dal and
Bouallou (2013) 57
Hydrogenation of CO2 to
methanol
CO2, hydrogen Methanol
Multi-objective
optimization
Taghdisian et al. (2015) 58 SMR, MeOH synthesis Natural gas, flue
gas, steam
Syngas,
Methanol
Sustainable design
methodology
Roh et al. (2016) 59 BR, TR, DR, POX, MeOH
synthesis
CO2, hydrogen,
methane, oxygen,
water
Methanol
17
2.3. Reactor Modeling and Simulation
In this section, the different reactors, the reactions involved and the
corresponding rate expressions are first discussed. The rate expressions from literature
are used for modeling the kinetics-based reactors. One major class of syngas production
is through methane reforming. This section has been classified into description and
literature review of (1) primary reformers, (2) combinations/variants of primary
reformers, and (3) reverse water gas shift reactor.
2.3.1. Primary Reformers
This section enlists and describes the three primary methane reforming reactions,
namely, dry reforming, steam reforming and partial oxidation of methane.
2.3.1.1. Dry Reforming of Methane (DR)
Dry reforming of methane is the process in which carbon dioxide is reacted with
methane to produce carbon monoxide and hydrogen. It is an endothermic reaction and
thus, favored by high temperatures. This reaction is represented by Eq. 2.1. This reaction
is accompanied by the reverse water gas shift reaction given by Eq. 2.2. The
corresponding rate expressions for the reactions are given by Richardson and
Paripatyadar (1989) and the parameters are reported in the Dry Reforming section of
Table 2.3. 60
Carbon dioxide reforming of methane has gained attention owing to the
utilization of two greenhouses gases, methane and carbon dioxide. Nikoo et al. (2011)
CH4 + CO2 ↔ 2CO + 2H2 ∆H298° = 247.0 kJ/mol (2.1)
CO2 + H2 ↔ CO + H2O ∆H298° = 41.1 kJ/mol (2.2)
18
studied the equilibrium behavior of the dry reforming reaction and performed direct
minimization of Gibbs free energy 33. The effects of the CH4-CO2 ratio, reaction
temperature and pressure on CH4 equilibrium conversion, CO2 equilibrium conversion,
syngas production and syngas ratios (H2/CO) were studied. The results were compared
with the experimental results reported by Khalesi et al. 61 in which a syngas ratio close to
unity at all temperatures was reported. A syngas ratio of unity is required for producing
liquid fuels such as DME, acetic acid and alcohols via oxo alcohol synthesis. More
detailed models based on kinetics have been developed for characterizing the dry
reforming process. A fixed-bed catalytic reactor was modeled using a 1-D pseudo-
homogeneous model by Benguerba (2014) and the effect of reactor temperature was
studied. The results from the model were compared with experimental results 62. Akpan
et al. (2007) simulated a 2-D packed bed reactor considering the axial dispersion term
and solved it using finite elements method 63. Wehinger et al. (2015) performed detailed
numerical simulations using 3-D computational fluid dynamics (CFD) modeling to study
the dry reforming reaction 39.
While the advantage of DR is that it directly converts CO2 to syngas using
methane, DR has not been used in commercial processes yet. The reasons include (i)
high energy requirement due to intensive endothermic reaction, (ii) catalyst deactivation
due to coke formation, and (iii) low selectivity and low ratio of syngas due to undesired
water formation.
19
2.3.1.2. Steam Reforming of Methane (SMR)
The most common route for producing hydrogen is through steam methane
reforming (SMR). This reaction is represented by Eq. 2.3. The steam reforming reaction
is followed by the water gas shift reaction represented by Eq. 2.4, where more hydrogen
is produced. The complete set of reactions involved in steam methane reforming is given
below. The corresponding rate expressions and parameters given by Xu and Froment
(1989) 64 are given in the Steam Reforming section of Table 2.3.
There has been substantial work done on steam methane reforming, both on the
experimental and modeling fronts. Lutz et al (2003) performed a thermodynamic
analysis of steam methane reforming and compared it with experimental results. From
the comparison, they concluded that the experiment does not reach equilibrium and the
conversion of methane is considerably lower than equilibrium conversion 65. Latham
(2008), performed an extensive literature review on the steam reformer models
developed so far, classified into furnace-side models and process-side models 66. Among
the many furnace-side models, Murty and Murthy (1988) simulated a 1-D pseudo-
homogeneous plug flow reactor and studied the impact of modifying individual reactor
conditions on the conversion and shell side temperatures 67. Alhabdan et al. (1992)
developed a reactor model for an industrial steam reformer based on the kinetics
developed by Xu and Froment. The model uses effectiveness factors in a pseudo-
CH4 + H2O ↔ CO + 3H2 ∆H298° = 206.3 kJ/mol (2.3)
CO + H2O ↔ CO2 + H2 ∆H298° = −41.1 kJ/mol (2.4)
CH4 + 2H2O ↔ CO2 + 4H2 ∆H298° = 164.9 kJ/mol (2.5)
20
homogeneous reactor model to account for the heterogeneity of the reactor 68. Pedernera
et al. (2003) and Wesenberg and Svendsen (2007) developed kinetics-based 2-D
heterogeneous models that included a set of partial differential equations and non-linear
algebraic equations 69-70. Pedernera et al. modeled a single isothermal reformer tube at
steady-state and simulated the concentration and temperature profiles along the radial
and axial coordinates. The partial differential equations in the mathematical model were
discretized by means of central second order finite differences 69. Wesenberg and
Svendsen compared heterogeneous models with pseudo-homogeneous models and
highlighted the importance of including mass and heat transfer coefficients and
interphase transport limitations in studying reaction rates 70. Mokheimer et al. (2014)
focused on studying the effects of varying inlet flowrate, temperature and pressure
individually on methane conversion and hydrogen production using a kinetics-based,
steady state, isothermal CFD model that was solved using Ansys Fluent 71. Onel et al.
(2017) modeled a microchannel steam methane reformer using CFD model using the
commercial software COMSOL. Since this model is computationally expensive to
simulate for use in process synthesis models, grey-box models were proposed 72.
At the industrial scale, steam reforming of methane is mainly used for large-scale
hydrogen production. It is favored by high steam to methane ratio, low pressure and
elevated temperatures to achieve maximum conversion. The outlet temperature of the
reformer should be around 800 to 950 °C for a reasonable conversion of methane and
production of hydrogen 73. Since steam reforming is an endothermic reaction, heat must
be supplied to achieve this outlet temperature. There are several ways to do this:
21
Preheating the gases to higher temperatures, designing the tubular reformers with a
variety of tube and burner arrangements such as side-fired furnaces, top-fired furnaces
and terrace wall furnaces. In fired reformers, typical gas inlet temperatures are 450-650
°C and product gases leave at 800 to 950 °C.
While SMR produces syngas with high H2:CO ratio, the reaction is very
endothermic and requires substantial amounts of heat. About 134 MJ energy is
consumed for every kg of H2 production 41. Furthermore, it produces significant amount
of CO2 (9-12 kg CO2/kg H2). While the conversion in SMR favors low pressure, the
produced syngas requires compression if it is used in FT synthesis, which operates at
high pressure (around 30 bar).
2.3.1.3. Partial Oxidation of Methane (POX)
Partial oxidation of methane is the addition of oxygen to methane in amounts
insufficient for complete combustion. This is represented by Eq. 2.6. The syngas ratio
obtained through partial oxidation is typically around 2 and is suitable for methanol
synthesis and Fischer-Tropsch synthesis. Since this is an exothermic reaction, the
conversion of methane can be expected to reach equilibrium values sooner than for other
reformers.
The partial oxidation reaction is indirectly represented by the following reactions
for which the kinetics and rate expressions are well established.
CH4 +1
2O2 ↔ CO + 2H2 ∆H298
° = −35.6 kJ/mol (2.6)
CH4 + 2O2 ↔ CO2 + 2H2O ∆H298° = −802.7 kJ/mol (2.7)
22
The corresponding rate expressions and their parameters are given in the Partial
Oxidation section of Table 2.3.
One of the pioneering studies on the kinetics of the total combustion of methane
on Pt-Alumina catalysts were performed by Trimm and Lam 74. The kinetics of catalytic
oxidation was also studied by Ma et al. (1996) on a Pt/ δ-Al2O3 75. Groote and Froment
(1996) modeled the catalytic partial oxidation of methane to synthesis gas 76. They used
detailed kinetics on a Ni catalyst and simulated a 1-D adiabatic fixed bed reactor. Zhu et
al. (2001) performed a feasibility study of partial oxidation of methane by
thermodynamic analysis 77. The thermodynamic analysis was performed through Gibbs
free energy minimization method. Smet et al. (2001) simulated a 1-D steady state
heterogeneous reactor model on a Ni catalyst for the catalytic partial oxidation of
methane 78. Donazzi et al. (2008) also simulated a 1-D heterogeneous model for POX of
methane on a Rh-based catalyst 79. Deutschmann et al. (1998) simulated a two-
dimensional model of partial oxidation of methane on Rhodium in a short contact time
reactor 80.
2.3.2. Combined Reformers/ Variants of Primary Reformers
The previous section discussed the three primary reforming reactors, the
operating conditions, the carbon footprint and the syngas ratio achievable. In this
section, we describe the variants of the three reactors by combining two or more of the
CH4 + H2O ↔ CO + 3H2 ∆H298° = 206.3 kJ/mol (2.8)
CO + H2O ↔ CO2 + H2 ∆H298° = −41.1 kJ/mol (2.9)
CH4 + 2H2O ↔ CO2 + 4H2 ∆H298° = 164.9 kJ/mol (2.10)
23
primary reactors, that is, bi-reformers and tri-reformers, such as, combined dry and
steam reformer (CDSMR), combined steam reforming and partial oxidation (POSMR),
combined dry reforming and partial oxidation (PODR) and tri-reformer (TR).
2.3.2.1. Combined Dry Reforming and Steam Reforming of Methane (CDSMR)
As discussed before, dry reforming of methane produces syngas of ratio less than
1, while utilizing CO2. Steam reforming produces syngas in the ratio close to 3. Thus,
combining these two reactors, the syngas ratio can be adjusted to be around 2, while
utilizing CO2, whereas other reactors such as POX that produce similar SR do not utilize
CO2. This syngas ratio is suitable for methanol synthesis. Methanol is a chemical of
commercial importance and can offset the cost of CO2 utilization.
The reactions that constitute the CDSMR are given by Eq. 2.11-13. It is a
combination of dry reforming and steam reforming reactions, but can be represented by
the three reactions that represent SMR. This is because the dry reforming reaction is
indirectly represented by these reactions. Dry reforming reaction (Eq. 2.1) can be
derived by subtracting reaction Eq. 2.13 from reaction Eq. 2.12. This is also shown by
simulating the dry reforming reactor using the steam reforming equations in the later
section.
CH4 + H2O ↔ CO + 3H2 ∆H298° = 206.3 kJ/mol (2.11)
CO + H2O ↔ CO2 + H2 ∆H298° = −41.1 kJ/mol (2.12)
CH4 + 2H2O ↔ CO2 + 4H2 ∆H298° = 164.9 kJ/mol (2.13)
24
The rate expressions and their parameters can be taken from the Steam
Reforming section of Table 2.3 corresponding to the above-mentioned equations since
the catalyst for both dry reforming and steam reforming is Ni-based.
Soria et al. (2011) analyzed and compared the thermodynamic behavior of
combined steam and dry reforming of methane and the experimental results on a
ruthenium catalyst. The equilibrium calculations were done by minimizing the Gibbs
free energy 81. Lim et al. (2012) optimized a combined steam and dry reformer
equilibrium model using ASPEN plus 82. Shahkarami and Fatemi (2015) modeled the
combined dry and steam reforming of methane in a catalytic fluidized bed reactor.
Coking reactions were also considered in the reactor and a genetic algorithm was used to
obtain the optimal operating conditions 83.
Figure 2.1. The comparison and advantages of combining individual reactors. (a)
represents the syngas ratio (SR) of individual Dry Reformer (DR) and Steam Methane
Reformer (SMR) and the outcome if the two outlet streams were to be combined. (b)
represents the Combined Dry and Steam Reforming of Methane (CDSMR) in an
intensified manner and the SR that could be expected of it.
25
The combination of the two individual reforming reactors, at reasonable
operating conditions, could mean an ideal SR with a potential reduction in reactor space,
capital cost and catalyst cost. This is a potential process that could have high impact on
environment, economy and energy. The advantages of this process are also shown in
Figure 2.1.
2.3.2.2. Combined Partial Oxidation and Dry Reforming of Methane (PODR)
It has been observed that the coupling of the endothermic dry reforming with the
exothermic partial oxidation can significantly reduce hot spots in the catalyst bed as well
as reduce the loss of catalyst activity with time. O’Connor et al. 84 studied the effect of
O2 addition on the dry reforming of methane with CO2 to produce synthesis gas over
Pt/ZrO2 catalysts. The dry reforming reaction is highly endothermic and requires
temperatures between 700 K and 1000 K for substantial reaction to occur. It is important
to consider the energy that is spent in raising the temperature of the reactant gases
because it would lead to indirect emissions of carbon dioxide which would contradict the
primary aim of our research. The partial oxidation of methane is an exothermic reaction
and can be combined with dry reforming of methane to raise the reaction temperature to
facilitate dry reforming. This PODR can be indirectly represented by the following set of
reactions. These four reactions can represent the independent reactions of dry reforming
and partial oxidation. Dry reforming can be obtained by subtracting Eq. 2.17 from Eq.
2.16. These are the same reactions used in partial oxidation as well, but the feed
conditions for the two reactors would be different.
CH4 + 2O2 ↔ CO2 + 2H2O ∆H298° = −802.7 kJ/mol (2.14)
26
The corresponding rate expressions and their parameters could be found in the
Partial Oxidation section of Table 2.3.
Amin and Yaw 28 performed thermodynamic analysis of the combined carbon dioxide
and reforming with partial oxidation of methane to syngas. This was done by total Gibbs
energy minimization using Lagrange's undetermined multiplier method. The results
showed that the addition of oxygen to dry reforming improved the methane conversion,
H2 and H2O yields, and syngas ratio, but decreased the CO2 conversion and CO yield 28.
Larentis et al. (2001) modeled a reforming reactor that combines CO2 and partial
oxidation using two mathematical models: an empirical model and a pseudo-
homogeneous model. Detailed heat and mass transfer mechanisms were not considered
in this model 85.
In PODR, two oxidants, namely CO2 and O2, compete to oxidize methane.
However, partial oxidation dominates over dry reforming. An increment in CO2/CH4
feed ratio results in the loss of CO2 conversion while producing more H2O 28. Since the
CO2 conversion is of primary interest, PODR operations need to be optimized to
increase the CO2 utilization. Equilibrium CO2 conversion increases with temperature but
decreases with CO2/CH4 ratio. Higher temperatures are favorable to achieve H2/CO ratio
of syngas close to one and high conversion.
CH4 + H2O ↔ CO + 3H2 ∆H298° = 206.3 kJ/mol (2.15)
CO + H2O ↔ CO2 + H2 ∆H298° = −41.1 kJ/mol (2.16)
CH4 + 2H2O ↔ CO2 + 4H2 ∆H298° = 164.9 kJ/mol (2.17)
27
2.3.2.3. Combined Partial Oxidation and Steam Reforming of Methane
(POSMR)/Auto-thermal Reforming of Methane (ATR)
Since steam methane reforming is highly endothermic, combining it with
exothermic partial oxidation of methane can raise the temperature of the reactor up to
1000 °C and promote SMR which requires high temperatures. This is commonly known
as auto-thermal reforming. There has been considerable work on modeling the auto-
thermal reactors. In fact, this is a common practice in the production of hydrogen. ATR
also provides us an opportunity to adjust the syngas ratio for different applications. Once
again, this combination can be represented by the reactions in Eq. 2.7-10. The
corresponding rate expressions and parameters can be found in Partial Oxidation section
of Table 2.3.
Chan et al. (2000) conducted a detailed thermodynamic analysis of the
simultaneous steam reforming and partial oxidation of methane by minimizing the Gibbs
free energy of the mixture. The effects of varying the steam-methane ratio and air-
methane ratio were studied and the range of conditions for maximum H2 production was
obtained 86. Avci et al. (2001) modeled the combined catalytic oxidation and steam
reforming of methane as a 1-D heterogeneous model and validated the predictions with
experimental results 87. Hoang et al. (2004) presented a 2-D heterogenous model of the
auto-thermal methane reformer to simulate the conversion behavior of the reformer.
They studied the effects of varying individual operating conditions like temperature
while fixing the other conditions. Based on the trends in these effects, they predicted an
optimum condition for the auto-thermal reformer 88. Halabi et al. (2008) simulated a 1-D
28
heterogeneous model that accounted for axial thermal and mass dispersion pressure
distribution, and interfacial and intraparticle transport. Both dynamic and steady state
behavior was analyzed by studying effects of temperature of feed gas and catalyst, O-C
ratio, S-C ratio, gas hourly space velocity and feed contaminations 89.
2.3.2.4. Tri-Reforming of Methane (TR)
Tri-reforming is the combination of dry reforming, steam reforming and the
partial oxidation of methane. This reactor has the combined advantages of multiple bi-
reforming reactors such as achieving desirable syngas ratios and reduction of coke
deposition 90. Though tri-reforming consists of the three independent reactions shown in
Eqs. 2.1, 2.3 and 2.6, it can also be represented by Eqs. 2.7-10, for the same reasons
mentioned in the previous section. The rate expressions and parameters can be found in
Partial Oxidation section of Table 2.3.
Song et al. (2004) proposed this novel concept of tri-reforming and the
advantages mentioned were demonstrated in a laboratory-scale fixed-bed flow reactor 91.
Cho et al. (2009) developed a first principle model for the tri-reforming of natural gas to
produce DME. The model consisted of two regions, one homogeneous and one
heterogeneous. The two sections were one-dimensional steady state plug-flow reactor
models. The models were built on Jacobian dynamic modeling and optimization
software and is compared with an equilibrium model. The reactor optimal length for
maximum hydrogen and maximum carbon monoxide production are found by fixing the
other operational variables 53.
29
As the name suggests, RWGS is the reverse of the water gas shift reaction (Eq.
2.4) that we have discussed previously. This reaction does not require very high
operational temperatures and is favored by Ni catalysts. This reaction utilizes CO2. We
use the kinetic rate expression of the RWGS equation (Eq. 2.2) to represent the RWGS
reactor. The rate expression and the corresponding parameters can be taken from Dry
Reforming section of Table 2.3.
Compared to the other reforming reactors, there is considerably lesser research
done on reverse water gas shift. This is possibly because water gas shift or reverse water
gas shift reactions follow other reforming reactions or are used to upgrade the quality of
the hydrocarbon product rather than being used as an individual reactor. Joo et al. (1999)
compared the direct hydrogenation of carbon dioxide to methanol and the case where
reverse water gas of shift precedes the methanol synthesis on a Cu-based catalyst and
found that the production of methanol was higher by 29% for the latter case and the
recycle volume for the methanol synthesis reactor was considerably lower when the feed
composed of CO, unreacted CO2 and H2 92.
2.3.3. Reverse Water Gas Shift Reactor (RWGS)
30
Table 2.3. Rate expressions and parameters for different reactors. # Reaction Rate Expressions Parameters (units)
Dry Reforming CH4 + CO2 ↔ 2CO + 2H2 𝑟1 =
𝑘1𝐾𝐶𝑂2,1𝐾𝐶𝐻4,1𝑝𝐶𝐻4𝑝𝐶𝑂2
(1 + 𝐾𝐶𝑂2,1𝑝𝐶𝑂2+ 𝐾𝐶𝐻4,1𝑝𝐶𝐻4
)2 (1 −
(𝑝𝐶𝑂𝑝𝐻2)
2
𝐾𝑃1(𝑝𝐶𝐻4
𝑝𝐶𝑂2)
)
…(DR1)
𝑘1 (𝑚𝑜𝑙 𝑘𝑔−1𝑠−1) = 1.29×106𝑒𝑥𝑝 (−102,065
𝑅𝑇)
𝐾𝐶𝑂2,1(𝑏𝑎𝑟−1) = 2.61×10−2𝑒𝑥𝑝 (37,641
𝑅𝑇)
𝐾𝐶𝐻4,1(𝑏𝑎𝑟−1) = 2.60×10−2𝑒𝑥𝑝 (40,684
𝑅𝑇)
𝐾𝑃1= 6.78×1014𝑒𝑥𝑝 (−
259,660
𝑅𝑇)
CO2 + H2 ↔ CO + H2O 𝑟2 =
𝑘2𝐾𝐶𝑂2,2𝐾𝐻2,2𝑝𝐶𝑂2𝑝𝐻2
(1 + 𝐾𝐶𝑂2,2𝑝𝐶𝑂2+ 𝐾𝐻2,2𝑝2)
2 (1 −(𝑝𝐶𝑂𝑝𝐻2
)2
𝐾𝑃2(𝑝𝐶𝑂2
𝑝𝐻2)
)
…(DR2)
𝑘2(𝑚𝑜𝑙 𝑘𝑔−1𝑠−1) = 5.43×105exp (−81,030
𝑅𝑇)
𝐾𝐶𝑂2,2(𝑏𝑎𝑟−1) = 0.5771𝑒𝑥𝑝 (9,262
𝑅𝑇)
𝐾𝐻2,2(𝑏𝑎𝑟−1) = 1.494𝑒𝑥𝑝 (6,025
𝑅𝑇)
𝐾𝑃2= 56.4971𝑒𝑥𝑝 (−
36,580
𝑅𝑇)
Steam Reforming
CH4 + H2O ↔ CO + 3H2
𝑟1 =𝑘1
𝜑2 (𝑝𝐶𝐻4
𝑝𝐻2𝑂
(𝑝𝐻2)2.5 −
(𝑝𝐻2)
0.5𝑝𝐶𝑂
𝐾1)
…(SMR1)
𝑘1 (𝑚𝑜𝑙 𝑘𝑔−1𝑠−1) = 1.17×1015exp (−240100
𝑅𝑇)
𝐾1(𝑏𝑎𝑟2) = 𝑒𝑥𝑝 (−26830
𝑇+ 30.114)
CO + H2O ↔ CO2 + H2 𝑟2 =
𝑘2
𝜑2(
𝑝𝐶𝑂𝑝𝐻2𝑂
𝑝𝐻2
−𝑝𝐶𝑂2
𝐾2)
…(SMR2)
𝑘2(𝑚𝑜𝑙 𝑘𝑔−1𝑠−1) = 5.43×105exp (−81,030
𝑅𝑇)
𝐾2 = 𝑒𝑥𝑝 (4400
𝑇− 4.036)
CH4 + 2H2O ↔ CO2 + 4H2 𝑟3 =
𝑘3
𝜑2 (𝑝𝐶𝐻4
(𝑝𝐻2𝑂)2
(𝑝𝐻2)3.5 −
(𝑝𝐻2)0.5𝑝𝐶𝑂2
𝐾3)
…(SMR3)
𝑘3(𝑚𝑜𝑙 𝑘𝑔−1𝑠−1) = 2.83×1014exp (−243,900
𝑅𝑇)
𝐾3(𝑏𝑎𝑟2) = 𝐾1𝐾2
Where 𝜑 = 1 + 𝐾𝐶𝑂𝑝𝐶𝑂 + 𝐾𝐻2𝑝𝐻2
+ 𝐾𝐶𝐻4𝑝𝐶𝐻4
+ 𝐾𝐻2𝑂𝑝𝐻2𝑂/𝑝𝐻2
…(SMR4) 𝐾𝐶𝑂(𝑏𝑎𝑟−1) = 2.61×10−5𝑒𝑥𝑝 (
70,650
𝑅𝑇)
𝐾𝐻2(𝑏𝑎𝑟−1) = 6.12×10−9𝑒𝑥𝑝 (
82,900
𝑅𝑇)
𝐾𝐶𝐻4(𝑏𝑎𝑟−1) = 6.65×10−4𝑒𝑥𝑝 (
38,280
𝑅𝑇)
𝐾𝐻2𝑂(𝑏𝑎𝑟−1) = 1.77×105𝑒𝑥𝑝 (−88,680
𝑅𝑇)
31
Table 2.3. Continued
# Reaction Rate Expressions Parameters (units)
Partial Oxidation CH4 + H2O ↔ CO + 3H2 𝑟1 =
𝑘1
𝜑2(
𝑝𝐶𝐻4𝑝𝐻2𝑂
(𝑝𝐻2)2.5
−(𝑝𝐻2
)0.5
𝑝𝐶𝑂
𝐾1)
…(POX1)
𝑘1 (𝑚𝑜𝑙 𝑘𝑔−1𝑠−1) = 1.17×1015exp (−240100
𝑅𝑇)
𝐾1(𝑏𝑎𝑟2) = 𝑒𝑥𝑝 (−26830
𝑇+ 30.114)
CO + H2O ↔ CO2 + H2 𝑟2 =
𝑘2
𝜑2 (𝑝𝐶𝑂𝑝𝐻2𝑂
𝑝𝐻2
−𝑝𝐶𝑂2
𝐾2)
… (POX2)
𝑘2(𝑚𝑜𝑙 𝑘𝑔−1𝑠−1) = 5.43×105exp (−81,030
𝑅𝑇)
𝐾2 = 𝑒𝑥𝑝 (4400
𝑇− 4.036)
CH4 + 2H2O ↔ CO2 + 4H2 𝑟3 =
𝑘3
𝜑2 (𝑝𝐶𝐻4
(𝑝𝐻2𝑂)2
(𝑝𝐻2)3.5 −
(𝑝𝐻2)0.5𝑝𝐶𝑂2
𝐾3)
… (POX3)
𝑘3(𝑚𝑜𝑙 𝑘𝑔−1𝑠−1) = 2.83×1014exp (−243,900
𝑅𝑇)
𝐾3(𝑏𝑎𝑟2) = 𝐾1𝐾2
𝜑 = 1 + 𝐾𝐶𝑂𝑝𝐶𝑂 + 𝐾𝐻2𝑝𝐻2
+ 𝐾𝐶𝐻4𝑝𝐶𝐻4
+ 𝐾𝐻2𝑂𝑝𝐻2𝑂/𝑝𝐻2
… (POX4)
𝐾𝐶𝑂(𝑏𝑎𝑟−1) = 2.61×10−5𝑒𝑥𝑝 (70,650
𝑅𝑇)
𝐾𝐻2(𝑏𝑎𝑟−1) = 6.12×10−9𝑒𝑥𝑝 (
82,900
𝑅𝑇)
𝐾𝐶𝐻4(𝑏𝑎𝑟−1) = 6.65×10−4𝑒𝑥𝑝 (
38,280
𝑅𝑇)
𝐾𝐻2𝑂(𝑏𝑎𝑟−1) = 1.77×105𝑒𝑥𝑝 (−88,680
𝑅𝑇)
CH4 + 2O2 → CO2 + 2H2O 𝑟4 =
𝑘4𝑎𝑝𝐶𝐻4𝑝𝑂2
(1 + 𝐾𝐶𝐻4
𝐶 𝑝𝐶𝐻4+ 𝐾𝑂2
𝐶 𝑝𝑂2)
2 +𝑘4𝑏𝑝𝐶𝐻4
𝑝𝑂2
(1 + 𝐾𝐶𝐻4
𝐶 𝑝𝐶𝐻4+ 𝐾𝑂2
𝐶 𝑝𝑂2)
… (POX5)
𝑘4𝑎(𝑚𝑜𝑙 𝑘𝑔−1𝑠−1) = 8.11×105exp (−86,000
𝑅𝑇)
𝑘4𝑏(𝑚𝑜𝑙 𝑘𝑔−1𝑠−1) = 6.82×105exp (−86,000
𝑅𝑇)
𝐾𝐶𝐻4
𝐶 (𝑏𝑎𝑟−1) = 1.26×10−1𝑒𝑥𝑝 (27,300
𝑅𝑇)
𝐾𝑂2
𝐶 (𝑏𝑎𝑟−1) = 7.78×10−7𝑒𝑥𝑝 (92,800
𝑅𝑇)
32
CHAPTER III
ENERGETIC ANALYSIS OF CO2 UTILIZATION
In this section, we address the following questions
• For a target syngas specification (e.g., H2 to CO ratio), what is the theoretically
minimum energy required to convert CO2 into syngas using different reforming
alternatives that use methane, steam, oxygen and/or hydrogen?
• For a given syngas (H2 to CO) ratio, what is the maximum CO2 utilization
possible?
• For a given syngas H2 to CO ratio, what is the maximum achievable syngas
selectivity (combined composition of H2 and CO) over other species in the
product?
We address these questions based on the following thermodynamic analysis.
3.1. Minimum Energy Calculation
The premise of our thermodynamics-based energy calculation is that the
minimum energy required to convert a set of chemical species to another set of chemical
species is the total change in enthalpy (∆𝐻) of a fully reversible system from its initial
state of T1 and P1 to the final state of T2 and P2. The change in enthalpy is given by
𝐸min = ∆𝐻 = ∑ 𝑛𝑖𝐻𝑖(𝑇2, 𝑃2) −𝑖∈𝐼 ∑ 𝑛𝑖𝐹𝐻𝑖(𝑇1, 𝑃1)𝑖∈𝐼 (3.1)
where, 𝑛𝑖𝐹 and ni are the number of moles of species i in the feed and product,
respectively. Furthermore, Hi(T1, P1) and Hi(T2, P2) are the specific enthalpies of species
i in the feed and product, respectively. Since the change in energy is considered for a
fully reversible process, it is the minimum energy required to drive the process if the
33
process is thermodynamically unfavorable (∆𝐺 > 0), and it is the maximum energy that
can be harnessed from the process if the process is thermodynamically favorable (∆𝐺 ≤
0). We further assume ideal gas conditions.
The enthalpy of a species i can be calculated as follows:
𝐻𝑖(𝑇, 𝑃) = ∆𝐻𝑓,𝑖𝑜 + ∫ 𝐶𝑝
𝑖𝑔𝑑𝑇 + 𝐻𝑖
𝑅(𝑇, 𝑃)𝑇
𝑇𝑜(3.2)
where ∆𝐻𝑓,𝑖𝑜 is the standard enthalpy of formation at a reference temperature To, 𝐶𝑝
𝑖𝑔 is
the temperature dependent specific heat capacity in the ideal-gas state, and 𝐻𝑖𝑅 is the
residual enthalpy at the current state of species i at T and P. Since we consider ideal-gas
conditions, we assume 𝐻𝑖𝑅 to be zero. Furthermore, in this work we consider To = T1.
Therefore, the enthalpies in Eq. 3.1 can be expressed as
𝐻𝑖(𝑇1, 𝑃1) = ∆𝐻𝑓,𝑖𝑜 (3.3)
𝐻𝑖(𝑇2, 𝑃2) = ∆𝐻𝑓,𝑖𝑜 + ∫ 𝐶𝑝
𝑖𝑔𝑑𝑇
𝑇2
𝑇1= 𝑅Φ (3.4)
where Φ𝑖 represents the integral ∫𝐶𝑝
𝑖𝑔
𝑅𝑑𝑇
𝑇2
𝑇1.
A key challenge which we still need to address is the estimation of ni which is the
molar flow rate of each species i in the product. To this end, we consider the product
mixture to be at the equilibrium at T2 and P2. Therefore, we can apply the Gibbs energy-
based equilibrium criterion to calculate ni. This criterion is based on the fact that at
equilibrium the total Gibbs energy of the system has its minimum value. Since this is the
most stable condition for given temperature, pressure and initial mixture compositions,
our assignment of ni to be the equilibrium compositions is justified. Also note that the
maximum conversion of feed that can be realistically attained occurs as the system
34
approaches towards the equilibrium. Let 𝐺𝑖(𝑇, 𝑃) denote the Gibbs energy of species i at
the temperature T and pressure P. Therefore, the Gibbs energy of a mixture with i
species is given by ∑ 𝑛𝑖𝐺𝑖(𝑇, 𝑃)𝑖∈𝐼 , where ni represents the number of moles of species i
present in the mixture. The problem is to obtain the values of ni’s which minimize the
total Gibbs energy of the system for specified T and P. One solution to this problem is
based on the method of Lagrange’s undetermined multipliers. Based on this method, the
following two equations define the conditions for minimum total Gibbs energy that can
be used to calculate the values of ni at the equilibrium:
𝐺𝑖(𝑇2, 𝑃2) + 𝑅𝑇2 𝑙𝑛𝑛𝑖
∑ 𝑛𝑖𝑖∈𝐼+ ∑ 𝜆𝑘𝑎𝑖𝑘𝑘 = 0 𝑖 ∈ 𝐼 (3.5)
∑ 𝑛𝑖𝑎𝑖𝑘𝑖∈𝐼 = ∑ 𝑛𝑖𝐹𝑎𝑖𝑘𝑖∈𝐼 𝑘 ∈ 𝐾 (3.6)
where, Ak is the total number of atomic masses of the kth element in the system, aik is the
number of atoms of the kth element present in each molecule of chemical species i, and
𝜆𝑘 is the Lagrange multiplier corresponding to material balance for kth element. Since
we assume ideal gas conditions, from now on, we will consider P1 = P2 = 1 bar.
𝐺𝑖(𝑇2, 𝑃2) can be further expanded as follows:
𝐺𝑖(𝑇2, 𝑃2) = ∆𝐻𝑖𝑜 −
𝑇2
𝑇2(∆𝐻𝑖
𝑜 − ∆𝐺𝑖𝑜) + 𝑅𝛷 − 𝑅𝑇2Ψ𝑖 𝑖 ∈ 𝐼 (3.7)
where Ψ𝑖 represents the integral ∫𝐶𝑝,𝑖
𝑖𝑔
𝑅
𝑑𝑇
𝑇
𝑇2
𝑇1.
We consider the following equation for 𝐶𝑝,𝑖𝑖𝑔
as a function of temperature:
𝐶𝑝,𝑖𝑖𝑔
= 𝐴𝑖 + 𝐵𝑖𝑇 + 𝐶𝑖𝑇2 + 𝐷𝑖𝑇−2 𝑖 ∈ 𝐼 (3.8)
This leads to the following expressions for Φ𝑖 and Ψ𝑖.
35
2 2 3 3
1 1 1
1
11 1 1
2 3
i i ii i
B C DAT T T
T
𝑖 ∈ 𝐼 (3.9)
2
1 1 2 2
1
1ln 1
2
ii i i i
DA BT C T
T
𝑖 ∈ 𝐼 (3.10)
2
1
T
T (3.11)
3.2. Nonlinear (NLP) Optimization Model for Theoretical Minimum Calculations
Base on the above discussion, a nonlinear (NLP) optimization model has been
developed to calculate the thermodynamically minimum energy to produce syngas with
a specified H2:CO ratio. The NLP model is then extended to include other objectives to
find maximum achievable CO2 utilization and maximum achievable syngas selectivity
for a given reforming system. The complete formulation of the NLP model is provided
below.
Sets and Indices
i chemical species (i I, I is the set of total species in the system)
k chemical element (k K, where K is the set of total elements)
Parameters:
T1, P1 initial feed temperature and pressure
∆𝐺𝑖𝑜 standard Gibbs energy of formation of chemical species i
∆𝐻𝑖𝑜 constant molar enthalpy of species i at standard condition
R gas constant
aik number of atoms of the kth element in each molecule of chemical species i
rSG ratio of H2 and CO moles in the product syngas
36
𝑆𝑆𝐺𝑚𝑖𝑛 minimum combined H2 and CO selectivity over other species in syngas
𝑈𝐶𝑂2
𝑚𝑖𝑛 fraction of CO2 from the feed that must be converted
𝑇2𝐿 , 𝑃2
𝐿 , 𝑛𝑖𝐹,𝐿
lower bounds on the final temperature, pressure and molar feed variables
𝑇2𝑈, 𝑃2
𝑈 , 𝑛𝑖𝐹,𝑈
upper bounds on the final temperature, pressure and molar feed variables
Variables:
T2, P2 product temperature and pressure
ni number of moles of chemical species i in the equilibrium product at T2 and P2
𝑛𝑖𝐹 number of moles of chemical species i in the feed
𝑛𝐶𝑂2
𝑎𝑢𝑥 auxiliary emission (moles of CO2) to supply energy for the system
𝜆𝑘 Lagrange multiplier corresponding to material balance for kth element
NLP Model Formulation:
min𝑇2,𝑛𝑖
𝐹 𝐸 = ∑ 𝑛𝑖𝐻𝑖(𝑇2, 𝑃2) −𝑖∈𝐼 ∑ 𝑛𝑖
𝐹𝐻𝑖(𝑇1, 𝑃1)𝑖∈𝐼 (O1)
s.t.
𝐻𝑖(𝑇1, 𝑃1) = ∆𝐻𝑓,𝑖𝑜 (C1)
𝐻𝑖(𝑇2, 𝑃2) = ∆𝐻𝑓,𝑖𝑜 + ∫ 𝐶𝑝
𝑖𝑔𝑑𝑇
𝑇2
𝑇1= 𝑅Φ (C2)
𝐺𝑖(𝑇2, 𝑃2) + 𝑅𝑇2 𝑙𝑛𝑛𝑖
∑ 𝑛𝑖𝑖∈𝐼+ ∑ 𝜆𝑘𝑎𝑖𝑘𝑘 = 0 𝑖 ∈ 𝐼 (C3)
∑ 𝑛𝑖𝑎𝑖𝑘𝑖∈𝐼 = ∑ 𝑛𝑖𝐹𝑎𝑖𝑘𝑖∈𝐼 𝑘 ∈ 𝐾 (C4)
𝐺𝑖(𝑇2, 𝑃2) = ∆𝐻𝑖𝑜 −
𝑇2
𝑇2(∆𝐻𝑖
𝑜 − ∆𝐺𝑖𝑜) + 𝑅𝛷 − 𝑅𝑇2𝛹 𝑖 ∈ 𝐼 (C5)
2 2 3 3
1 1 1
1
11 1 1
2 3
i i ii i
B C DAT T T
T
𝑖 ∈ 𝐼 (C6)
37
2
1 1 2 2
1
1ln 1
2
ii i i i
DA BT C T
T
𝑖 ∈ 𝐼 (C7)
2
1
T
T (C8)
𝑛H2= 𝑟SG𝑛CO (C9)
𝑛𝐻2+ 𝑛CO = 𝑆SG ∑ 𝑛𝑖i∈I (C10)
𝑛𝐶𝑂2
𝐹 − 𝑛𝐶𝑂2− 𝑛𝐶𝑂2
𝑎𝑢𝑥 = 𝑈𝐶𝑂2𝑛𝐶𝑂2
𝐹 (C11)
𝑛𝐶𝑂2
𝐹 = 1; 𝑛𝑖𝐹 = 0 ∀𝑖 ∈ {𝐼\𝐼𝐹} (C12)
𝑛𝐶𝑂2
𝑎𝑢𝑥 = 𝐸 (C13)
𝑇2𝐿 ≤ 𝑇2 ≤ 𝑇2
𝑈, 𝑃2𝐿 ≤ 𝑃2 ≤ 𝑃2
𝑈, 𝑛𝑖𝐹,𝐿 ≤ 𝑛𝑖
𝐹 ≤ 𝑛𝑖𝐹,𝑈 (C14)
Here, the objective function (Eq. O1) is defined such that it minimizes the total
energy required for a thermodynamically reversible process. The key decision variables
are T2, P2 and 𝑛𝑖𝐹. While ni, 𝑛𝐶𝑂2
𝑎𝑢𝑥 and k are also variables, their values depend on the
decision variables and can be readily calculated. Eq. C9 ensures that the product syngas
has a H2:CO ratio of exactly rSG. Depending on specific syngas ratio requirement, rSG
can be fixed. Eq. C10 is used to calculate the selectivity, 𝑆𝑆𝐺. For instance, a value of
𝑆𝑆𝐺 of 0.90 would mean that 90% of the syngas product be composed of only H2 and CO
molecules while the rest be comprised of other chemical species. Since the ultimate
purpose of the process is to utilize CO2 to produce syngas, it is important that we
calculate the net CO2 conversion which is calculated by subtracting the unreacted CO2
(𝑛𝐶𝑂2) and the auxiliary CO2 emission (𝑛𝐶𝑂2
aux) from the total CO2 fed to the system
(𝑛𝐶𝑂2
𝐹 ). Eq. C11 calculates the net CO2 conversion of 𝑈𝐶𝑂2 achieved by the process. To
38
normalize the calculation, we fix 𝑛𝐶𝑂2
𝐹 to be one (Eq. C12), which means that the
minimum energy is calculated as kJ per mol basis. Furthermore, in specific cases, we
might want to consider only a subset, IF, of chemical species to be present in the feed.
Therefore, we fix the number of moles to be zero for those species which are not present
in the feed, as shown in Eq. C12. The auxiliary CO2 emission is calculated using Eq.
C13, which is a function of the energy required by the system (E). In this work, we
assume that the auxiliary emission is a linear function of the energy utilized in a system.
Therefore, a constant emission factor () is used to calculate the auxiliary emission
amount from the total energy consumption amount. Finally, the user-defined bounds on
the decision variables are imposed by Eq. C14. Note that the decision variables can be
also fixed. In that case, the NLP optimization model reduces to a simulation model.
3.2.1. Minimum Energy for Syngas Production without Purification
Eqs. O1 and C1-14 define the complete NLP model. It should be noted that Eqs.
C9-13 are constraints which are specifically written for a system that would utilize CO2
to produce syngas. However, Eqs. O1, C1-8 and C14 are general constraints that will be
always present irrespective of the process goals. In general, the NLP model can be
extended to any chemical process, where Eqs. C9-13 would be replaced by problem
specific constraints.
3.2.2. Minimum Energy for Syngas Production with Purification
The equilibrium product mixture at various conditions will not only include
syngas (H2 and CO), but it will also have other gases, such as CO2, CH4, H2O and O2. So
far, we have only considered the energy required production of syngas, but have not
39
considered the additional energy required for downstream purification. The theoretical
minimum work required to completely separate H2 and CO from the product mixture can
be obtained by considering the separation process to be undergoing a reversible
isothermal, isobaric change. Therefore, in the simple case of syngas separation from one
product stream, considering all streams to be consisting of ideal mixtures, the minimum
energy equals to the minimum work that must be done to separate a mixture into its pure
components which is equal to the changes in Gibbs free energy of a reversible process.
𝐸𝑆𝑒𝑝𝑚𝑖𝑛 = ∆𝐺𝑚𝑖𝑥 = −𝑇∆𝑆𝑚𝑖𝑥 = −𝑅𝑇 ∑ 𝑥𝑖 𝑙𝑛 𝑥𝑖𝑖∈𝐼 (O2)
where
𝑥𝑖 =𝑛𝐻2+𝑛𝐶𝑂
∑ 𝑛𝑖𝑖∈𝐼 (3.13)
Therefore, the same NLP model can be used to calculate the minimum energy for
combined production and separation of H2 and CO as pure syngas. The only
modification that is needed is the revision of the objective function as follows:
min𝑇2,𝑛𝑖
𝐹 𝐸 = ∑ 𝑛𝑖𝐻𝑖(𝑇2, 𝑃2) −𝑖∈𝐼 ∑ 𝑛𝑖
𝐹𝐻𝑖(𝑇1, 𝑃1)𝑖∈𝐼 − 𝑅𝑇 ∑ 𝑥𝑖 𝑙𝑛 𝑥𝑖𝑖∈𝐼 (O2)
The NLP model, which consists of Eqs. O2, C1-14 and Eq. 3.13 will be used to
obtain the minimum energy required to convert CO2 and other gases into syngas and
separate syngas from the product mixture.
3.2.3. Maximum Net CO2 Utilization and Maximum Syngas Selectivity
Again, we can use the same NLP model to obtain the maximum net percentage of
the feed CO2 that can be utilized for a given reformer type. The calculation of net CO2
utilization (feed – conversion + emission) is already embedded in the model (Eq. C11).
40
Only modification we need to do to the model is the change of the objective function
from Eq. O1 to Eq. O3:
max𝑇2,𝑛𝑖
𝐹 𝑈𝐶𝑂2
(O3)
Similarly, to obtain the maximum possible syngas (H2+CO) selectivity in the
product mixture, we just replace the original objective function by the new objective
function given by Eq. O4, which is defined as
max𝑇2,𝑛𝑖
𝐹 𝑆𝑆𝐺 (O4)
3.3. Results for Minimum Energy, Maximum CO2 Utilization and Maximum
Syngas Selectivity at Equilibrium Conditions
Using the proposed NLP model, we have performed the calculation for the
theoretically minimum energy (Emin), maximum CO2 utilization (Umax) and maximum
syngas selectivity (Smax) for different reforming and CO2 conversion alternatives (DR,
CDSMR, PODR, CR, TR and RWGS) for a range of syngas H2 to CO ratio (0 ≤ 𝑟𝑆𝐺 ≤
3). The results are shown in Figure 3.1. It can be noted that different alternatives require
different energy for the same CO2 utilization (Figure 3.1a). The results highlight the fact
that not a single technology may be the best for all syngas ratios. For 0 ≤ 𝑟𝑆𝐺 ≤ 1, all
alternatives can achieve the same CO2 utilization and selectivity, but DR and CDSMR
are not competitive with other alternatives in terms of minimum energy. Combined
reforming technologies show greater promise for syngas production in terms of
energetics for the range of syngas ratio between 0 and 2. While PODR is a promising
alternative up to a syngas ratio of 2, beyond that only TR, CR and RWGS are promising.
41
Figure 3.1. Results from the energetic analysis for syngas production. (a)
Thermodynamically minimum energy requirement, (b) maximum possible CO2
utilization, and (c) maximum attainable syngas selectivity plots for different CO2
conversion alternatives (DR: dry reforming, CDSMR: combined dry and steam methane
reforming, RWGS: reverse water gas, CR: combined reforming with CO2, methane,
oxygen and water as the feed mixture), TR: tri-reforming).
42
Therefore, the syngas ratio plays a critical role determining the energy
requirement and CO2 utilization of a process. This is further amplified by the fact that
the maximum syngas selectivity may not be achieved at the syngas ratio that achieves
minimum energy or maximum CO2 utilization (Figure 3.1c). For instance, the maximum
syngas selectivity obtained is 68.6% at a syngas ratio of 0.58 by a dry-reforming process
operating at equilibrium.
Figure 3.2. Results from the energetic analysis for syngas production via dry
reforming (DR). Thermodynamically minimum energy, maximum possible CO2
utilization, maximum attainable syngas selectivity and the optimal feed CH4/CO2 ratio
for CO2 utilization via dry-reforming route.
43
DR and CDSMR both need more energy compared to the energy needed by other
alternatives. DR can only generate a syngas ratio between 0 and 1. The combined
reformers such as PODR, CR and TR use oxygen, which performs exothermic partial
oxidation. This suggests that theoretically it is possible to extract energy from these
reforming alternatives.
The optimization-based computational framework developed in this work can be
used to benchmark the performance of a CO2 utilization technology based on
thermodynamics and energetics analysis. For instance, we have performed the
thermodynamic analysis for DR. The theoretically minimum energy for DR is equal to
+139 kJ per mol of CO2 utilized via DR. This means that, irrespective of the design, a
DR process operating at equilibrium conditions will always consume more than 139
kJ/mol of energy, even if the process operates at the highest efficiency. The minimum
energy is achieved when the syngas ratio is 0.44. However, this syngas ratio cannot
achieve an overall CO2 utilization more than 72% (see Figure 3.1b). DR can achieve the
maximum CO2 utilization of 100% only when the syngas ratio is set to 1. The results for
DR are summarized in Figure 3.2. Similar analysis can be performed for other
technologies using the proposed NLP-based optimization framework.
Furthermore, the method can be used to analyze the trade-offs between different
objectives such as energy consumption versus CO2 utilization for a given technological
route. For instance, Figure 3.3 shows the difference in energy consumption between two
cases for CDSMR. The green lines correspond to the case when CDSMR is assumed to
be operated at equilibrium with minimum enthalpy change. This provides the lower
44
bound on the energy consumption. As we can see from the Figure 3.3(top), there is a
significant energy penalty if the objective of the CDSMR process deviates from the
minimum energy to the maximum CO2 utilization. At higher syngas ratios, the energy
penalty becomes significant. We also note from the Figure 3.3(bottom) that a change in
the objective from the maximum CO2 utilization (dotted line) to the minimum energy
consumption (solid line) significantly reduces the CO2 utilization potential, especially in
the region around the syngas ratio of two.
Figure 3.3. Trade-offs between energy and CO2 utilization potentials for combined
dry and steam reforming (CDSMR).
0
1000
2000
3000
4000
5000
6000
0 1 2 3
En
erg
y [
kJ
/mo
l]
Syngas H2 to CO ratio
Min. Energy for CDSR
Energy for Max. CO2 Utilizationby CDSR
0
20
40
60
80
100
0 1 2 3
[%]
Syngas H2 to CO ratio
CO2 utilization at Min. Energyby CDSR
Max. CO2 Utilization by CDSR
45
To summarize, a novel nonlinear (NLP) optimization-based framework is
developed for the energetic analysis of different CO2 utilization alternatives via the
production of syngas. The thermodynamics-based analysis of minimum energy,
maximum CO2 utilization potential and maximum attainable syngas selectivity reveal
that not a single reforming technology is optimal for the entire range of syngas of
practical interest. A systematic method needs to be employed to select the technologies.
The energy consumption (hence the cost) of syngas production is affected by the syngas
specifications such as syngas ratio, target CO2 utilization, and target syngas selectivity.
46
CHAPTER IV
MODELING AND SIMULATION OF REACTORS FOR CO2 UTILIZATION
VIA SYNGAS
In this work, four types of reactor models have been considered. The equilibrium
reactor model, the stoichiometry-based reactor model and two 1-D reaction rate-based
models, namely, pseudo-homogeneous and heterogeneous reactor models have been
considered.
4.1. Equilibrium-based Reactor Model
The equilibrium model provides us with a benchmark on the conversion and
yield for any operating condition, based on the thermodynamics limitations. Though, in
practice, reactors may not operate at equilibrium at all times, it is a simple and robust
model to study the nature of the reaction and gain knowledge about the maximum
achievable compositions. By varying the process variables such as reactor temperature
and pressure, we can see the trends and behavior of the output compositions from the
reactor. Let us define the indices used in our models.
𝑖 Represents any component/species like CH4, CO2
𝑗 Represents any reaction like combustion of methane
For the equilibrium reactor model, the Gibbs energy of the system is minimized
to get the equilibrium composition. The total Gibbs energy of a system is given by the
following formula.
𝐺𝑇 = ∑ 𝑛𝑖𝐺𝑖 = ∑ 𝑛𝑖𝜇𝑖 = ∑ 𝑛𝑖𝐺𝑖𝜊
𝑁
𝑖=1
𝑁
𝑖=1
+ 𝑅𝑇 ∑ 𝑛𝑖ln𝑓𝑖
𝑓𝑖0 (4.1)
47
The total Gibbs energy 𝐺𝑇is a function of the system composition, 𝑛𝑖 and the
chemical potential, 𝜇𝑖(𝑇) of all the species present. All the species that can be stable
under the given conditions are to be considered while evaluating the total Gibbs energy.
The total Gibbs energy can then be minimized using numerical or computational
techniques such as Lagrangian-multiplier technique.
For simplicity, we use the Aspen RGIBBS reactor model to perform our
simulations and analyses. We simulate both adiabatic and isothermal conditions based
on our need to study the reactor performance. The reactor inlet feed flowrate,
temperature and pressure are specified for each simulation.
Since the Aspen RGIBBS model has been used to simulate the equilibrium
reactor model, we do not have the functional form for the output compositions for
further analyses. So, surrogate modeling approach has been adopted for building
algebraic functional forms of the equilibrium compositions based on the reactor feed
conditions. For this purpose, we have used the Cubic Radial Basis function, which is an
interpolating function as our basis surrogate model. This is presented by Eq. 4.2.
Latin Hypercube sampling was done for the input variables such as inlet molar
flowrates of reactants, inlet reactor temperature and inlet reactor pressure within the
bounds on each variable and simulations were performed at these points. The bounds for
input variables in DR are given in Table 4.1. The bounds for the input variables of other
𝑦�� = 𝑎𝑘 + ∑ 𝑏𝑖,𝑘𝑥𝑖,𝑘
𝑁𝑣𝑎𝑟
𝑖=1
+ ∑ 𝜆𝑗,𝑘 ( ∑ (𝑥𝑖,𝑘 − 𝑥𝑗,𝑖,𝑘)2
𝑁𝑣𝑎𝑟
𝑖=1
)
3/2|𝑆𝐼|
𝑗=1
∀ 𝑘 ∈ 𝑁𝑜𝑢𝑡 (4.2)
48
reactors can be found in Appendix C, in section C.1. This parameters in the cubic radial
basis function were obtained by solving a linear (LP) optimization problem.
Linear optimization problem to obtain 𝑎𝑘, 𝑏𝑖,𝑘, 𝜆𝑗,𝑘:
min ∑(𝑆𝑃𝑗 + 𝑆𝑁𝑗)
|𝑆𝑉|
𝑗=1
𝑦𝑗 + 𝑆𝑃𝑗 + 𝑆𝑁𝑗 = 𝑦��, 𝑗 = 1, . . , |𝑆𝑉|
𝑦𝑗 = 𝑦��, 𝑗 = 1, . . , |𝑆𝐼|
𝑆𝑃𝑗 , 𝑆𝑁𝑗 ≥ 0, 𝑗 = 1, . . , |𝑆𝑉|
Where |SI| represents the interpolating set and |SV| represents the validation set. In this
problem, the sum of slack variables SPj, SNj is minimized to find a feasible set of
parameters for model fitting.
Table 4.1. Bounds on input variables for DR for equilibrium model.
Input
Variables
Description Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of CH4 to DR 0.1 10 Mol/s
X2 Molar flowrate of CO2 to DR 0.1 10 Mol/s
X3 Inlet pressure of gases to DR 1e5 10e5 Pa
X4 Inlet temperature of gases to DR 600 1200 K
4.2. Stoichiometry-based Reactor Model
Stoichiometry-based reactor model is a simple model where the output of a
product is based upon the conversion of one of the reactants, which is the limiting
49
reactant of the system. In this work, a fixed conversion model is used where the
conversion of a reactant species is taken from literature based on experimental results.
These conversion values are reported in Appendix B, Table B.3.
The model can be described as follows
𝐹𝑜𝑢𝑡𝑛 = 𝐹𝑖𝑛
𝑛 + 𝜂𝑎𝑛𝐹𝑖𝑛𝐿𝑅
where
𝐹𝑜𝑢𝑡𝑛 Output Molar flowrate of a species n
𝐹𝑖𝑛𝑛 Inlet Molar flowrate of a species n
𝐹𝑖𝑛𝐿𝑅 Inlet Molar flowrate of the limiting reactant
𝑎𝑛 Stoichiometric coefficient of the species n
𝜂 Conversion of the limiting reactant
4.3. Reaction Rate-based 1-D Reactor Models
Catalytic reactions are usually carried out in packed bed reactors. A packed bed
reactor is a tubular reactor that is packed with catalyst particles that are usually
uniformly sized. To simulate a packed bed, appropriate rate expressions are required and
the transport phenomena occurring in the bulk fluid and catalyst pellet need to be
modeled. Due to the complex phenomena that takes place in the reactor, the exact
description of the reactor in most cases is impossible. We have used two rate-based
models, namely, the pseudo-homogeneous reactor model and the heterogeneous reactor
model to describe our reactor systems. The following sections describe in detail the key
assumptions, model equations and solution strategy of each model used.
50
4.3.1. Pseudo-Homogeneous Reactor Model
In this section, we describe a 1-D steady state pseudo-homogeneous packed bed
reactor. This is also known as a plug-flow model as convection of the gases is the only
transport mechanism considered. The key assumptions of this model are:
• The catalyst surface is fully exposed to the bulk fluid, that is, there are no fluid-
particle heat and mass transfer resistances.
• Operates at steady state.
• Only axial profiles of concentration, temperature and pressure are considered.
• Radially averaged properties are considered.
• Non-ideality of gas phase is neglected.
The mass balance of each component entering the reactor are given by the following
continuity equations. The change in molar flow rate of each component with respect to
reactor length is given by the following set of differential equations.
The rate of production (consumption), −𝑅𝑖(𝐶, 𝑇), of each component i is given by
The rate expressions 𝑟𝑗 and their corresponding parameters are given in the Table 2.3.
The energy balance in the reactor is given by the following equation. The reactor is
assumed to operate adiabatically. The temperature profile along the axial direction thus
only depends upon the heat of reaction.
𝑑𝐹𝑖
𝑑𝑧= 𝜌𝑏 . 𝐴(−𝑅𝑖(𝐶, 𝑇) ) (4.3)
−𝑅𝑖(𝐶, 𝑇) = ∑ 𝜂𝑗𝛾𝑖,𝑗𝑟𝑗
𝑗
(4.4)
51
The pressure drop across the bed is given by the following equation.
The correlation for the friction factor, f, is given by the Ergun equation:
Where 𝛼 = 150 and 𝛽 = 1.75 93-94.
Hydraulic diameter dh=6×Vp/Ap
The model could be made to represent an isothermal reactor by modifying the energy
balance equation Eq. 4.5 to the following equation.
Boundary conditions: The boundary conditions for the packed bed are given by the inlet
feed conditions.
This model is to be used only when there is a negligible difference between the
solid and the fluid phase conditions. If there are considerable fluid-particle mass and
heat transfer resistances, we need to use a heterogeneous model to describe the reactor.
To simulate the pseudo-homogeneous model for DR reactor, we use the
differential Eqs. 4.3-4.7 for an adiabatic reactor model and 4.3-4.4, and 4.6-4.8 for an
isothermal reactor with expressions DR1, DR2 from Table 2.3 in MATLAB.
∑ 𝐹𝑖𝑐𝑝𝑖𝑖
𝑑𝑇
𝑑𝑧= 𝜌𝑏 . 𝐴 ∑ 𝜂𝑗(−
𝑗
∆𝐻𝑗). 𝑟𝑗 (4.5)
𝑑𝑃
𝑑𝑧= −2𝜌𝑓𝑢𝑠
2𝑓/𝑑ℎ (4.6)
𝑓 =(1 − 휀)
2휀3[𝛼(1 − 휀)
𝑅𝑒ℎ+ 𝛽] (4.7)
𝑑𝑇
𝑑𝑧= 0 (4.8)
At z = 0, 𝐹𝑖 = 𝐹𝑖∘, 𝑇 = 𝑇∘, 𝑃 = 𝑃∘ (4.9)
52
Solving the pseudo-homogeneous model: The pseudo-homogeneous model
consists of a set of ordinary differential equations. To counter any numerical issues, we
scale the equations. The scaled equations can be found in Table 4.2. The ODEs were
solved numerically on MATLABTM using solver ode23s with the boundary conditions
given as per Eq. 4.9 as the initial conditions for the ode solver for a given length, L. The
other parameters are given in Table 4.3.
4.3.2. Heterogeneous Reactor Model
In this section, we describe a 1-D steady state heterogeneous reactor model. This
model takes into account the mass and energy conservation equations separately for the
solid and the fluid phase. As mentioned before, if there are considerable fluid-particle
mass and heat transfer resistances, we need to use a heterogeneous model to describe the
reactor. The fixed bed reactor is assumed to operate at steady state under adiabatic
conditions. The key assumptions of this model are:
• Operates at steady state.
• Only axial profiles of concentration, temperature and pressure are considered.
• Axial dispersion is negligible.
• Non-ideality of gas phase is neglected.
The mass balance of each component in the bulk fluid phase are now revised and are
given by the following continuity equations. The change in molar flow rate of each
component with respect to reactor length is given by the following set of differential
equations.
𝑑𝐹𝑖
𝑑𝑧= 𝑘𝑠𝑖𝑎𝑚𝐴𝜌𝑏 (
𝑦𝑠𝑖𝑃
𝑅𝑇𝑠−
𝑦𝑖𝑃
𝑅𝑇)
(4.10)
53
The energy balance in the bulk fluid phase is given by the following equation. The
reactor is assumed to operate adiabatically.
The pressure drop across the bed is given by the following equation.
The solid phase equations are a set of nonlinear algebraic equations as can be seen in Eq.
13-14.
Mass balance in the solid phase is given by the following equation.
The energy balance in the solid phase is given by the following equation.
The rate expressions for each reaction j, (−𝑟𝑗) has been given in Table 2.3. To get
(−𝑟𝑗)𝑠from (−𝑟𝑗), substitute 𝑦𝑖 , 𝑇 with 𝑦𝑖𝑠, 𝑇𝑠 in the rate expressions, respectively.
For example, the rate expression for dry reforming of methane would become given by
(−𝑟1)𝑠 =𝑘1𝐾𝐶𝑂2,1𝐾𝐶𝐻4,1𝑝𝐶𝐻4
𝑝𝐶𝑂2
(1 + 𝐾𝐶𝑂2,1𝑝𝐶𝑂2+ 𝐾𝐶𝐻4,1𝑝𝐶𝐻4
)2(1 −
(𝑝𝐶𝑂𝑝𝐻2)
2
𝐾𝑃1(𝑝𝐶𝐻4
𝑝𝐶𝑂2)
)
Where 𝑝𝑖 = 𝑦𝑖𝑠𝑃 and 𝑘1 = 1.29×106𝑒𝑥𝑝 (−102,065
𝑅𝑇𝑠)
The model could be made to represent an isothermal reactor by modifying the energy
balance equation Eq. 4.11 to the following equation.
𝑑𝑇
𝑑𝑧=
ℎ𝑠𝑎𝑚𝐴𝜌𝑏(𝑇𝑠 − 𝑇)
∑ 𝐹𝑖𝑐𝑝𝑖𝑖 (4.11)
𝑑𝑃
𝑑𝑧= −2𝜌𝑓𝑢𝑠
2𝑓/𝑑ℎ (4.12)
𝑘𝑠𝑖𝑎𝑚 (𝑦𝑠𝑖𝑃
𝑅𝑇𝑠−
𝑦𝑖𝑃
𝑅𝑇) = ∑ 𝜂𝑗𝜈𝑖𝑗(−𝑟𝑗)
𝑠𝑗
(4.13)
ℎ𝑠𝑎𝑚(𝑇𝑠 − 𝑇) = ∑ 𝜂𝑗(∆𝐻𝑗)(−𝑟𝑗)𝑠
𝑗
(4.14)
54
Boundary conditions:
The initial conditions for solving the ordinary differential equations are given by the
inlet feed conditions of the packed bed reactor.
The bulk to solid mass and heat transfer coefficients 𝑘𝑠𝑖 , ℎ𝑠 in the above equations are
given by the correlations 95.
The model equations used in this work have been reported by Avci et al (2001). 87
For instance, to simulate the heterogeneous reactor model for the DR reactor, we solve
the differential Eqs. 4.10-4.12 in MATLAB and the algebraic Eqs. 4.13-4.14 with
expressions DR1 and DR2 from Table 2.3 on GAMS (General Algebraic Modeling
System). The solution procedure to solve the heterogeneous model is given in the next
section.
Solving the heterogeneous model: The 1-D heterogeneous reactor model
consists of a set of ordinary differential equations and a set of nonlinear algebraic
equations. We solve this system of equations in an iterative manner, that is, represented
by Figure 4.1. The procedure begins on the MATLAB interface where the boundary
conditions (Eq. 4.16) are fed in. The variables are passed on to GAMS, where the set of
𝑑𝑇
𝑑𝑧= 0 (4.15)
At z = 0, 𝐹𝑖 = 𝐹𝑖∘, 𝑇 = 𝑇∘, 𝑃 = 𝑃∘ (4.16)
ℎ𝑠𝐷𝑝
𝜆𝑓= 2 + 1.1𝑃𝑟1/3𝑅𝑒0.6 (4.17)
𝑘𝑠𝑗𝐷𝑝
𝜆𝑓= 2 + 1.1𝑆𝑐1/3𝑅𝑒0.6 (4.18)
55
nonlinear algebraic equations (Eq. 4.13-14) are solved using the global solver
ANTIGONE 96, solving the NLP minimization problem given. The variables of the solid
phase that are solved for, are passed back to MATLAB, where the ODE solver, ode23
integrates the set of ordinary differential equations, equations 4.10-13 for the next step
𝑧𝑘+1 = 𝑧𝑘 + ∆z. The variables in the bulk fluid phase for the new step are then passed
on to GAMS and the steps are repeated over until the end of the bed length L is reached.
This is explained through the flowchart in the Figure 4.1.
Figure 4.1. Solution strategy to solve the 1-D heterogeneous reactor model. The
figure provides the variable interaction between the two platforms – GAMS and
MATLAB.
56
The NLP optimization problem to solve the set of algebraic nonlinear equations is given
below. The objective is to minimize the sum of slack variables, SP, SK, and the
constraints are the set of nonlinear equations.
min(𝑆𝑃𝑘 + 𝑆𝑁𝑘) , k: number of nonlinear equations
s.t.
𝑘𝑠𝑎𝑚 (𝑦𝑠𝑖𝑃
𝑅𝑇𝑠−
𝑦𝑖𝑃
𝑅𝑇) − ∑ (−𝑅𝑗(𝑦𝑠𝑖, 𝑇𝑠) )𝑗 + 𝑆𝑃𝑘 − 𝑆𝑁𝑘 = 0
ℎ𝑠𝑎𝑚(𝑇𝑠 − 𝑇) − ∑ (−𝑗 ∆𝐻𝑗)𝑅𝑗(𝑦𝑠𝑖, 𝑇𝑠) + 𝑆𝑃𝑘 − 𝑆𝑁𝑘 = 0
𝑆𝑃𝑘, 𝑆𝑁𝑘 ≥ 0
To avoid numerical issues due to scaling, we scale the system of equations. The scaled
model with the scaled variables and equations are given in Table 4.1.
Table 4.2. Scaled 1-D pseudo-homogeneous and 1-D heterogeneous models.
1-D Pseudo-Homogeneous Reactor 1-D Heterogeneous Reactor Model
Scaled Process Variables
��𝑖 =𝐹𝑖
𝐹𝑖0, �� =
𝑇
𝑇0, �� =𝑃
𝑃0, 𝑧 =𝑧
𝐿, 𝑦�� = 𝑦𝑖
Scaled Process Variables
��𝑖 =𝐹𝑖
𝐹𝑖0, �� =
𝑇
𝑇0, �� =𝑃
𝑃0, 𝑧 =𝑧
𝐿, 𝑦�� = 𝑦𝑖
��𝑠 =𝑇𝑠
𝑇𝑠0, 𝑦𝑖𝑠 = 𝑦𝑖𝑠
Scaled Equations for Bulk Fluid Scaled Equations for Bulk Fluid
𝑑��𝑖
𝑑𝑧= (
𝐿
𝐹𝑖0)𝜌𝑏. 𝐴(−𝑅𝑖(𝑦��, ��, ��) )
∑ ��𝑖𝑐𝑝𝑖𝑖
𝑑��
𝑑𝑧
= (𝐿
𝑇0)𝜌𝑏. 𝐴 ∑(−
𝑖
∆𝐻𝑖)𝑅𝑖(𝑦��, ��, ��)
𝑑��
𝑑𝑧= (
𝐿
𝑃0)−2𝜌𝑓𝑢𝑠
2𝑓/𝑑ℎ
𝑑��𝑖
𝑑𝑧= (
𝑃0𝐿
𝑇0𝐹𝑖0)𝑘𝑠𝑖𝑎𝑚𝐴𝜌𝑏 (
𝑦𝑠𝑖𝑃
𝑅𝑇𝑠−
𝑦𝑖𝑃
𝑅𝑇)
𝑑��
𝑑𝑧= 𝐿(
ℎ𝑠𝑎𝑚𝐴𝜌𝑏(𝑇𝑠 − 𝑇)
∑ 𝐹𝑖𝑐𝑝𝑖𝑖)
𝑑��
𝑑𝑧= (
𝐿
𝑃0)(−2𝜌𝑓𝑢𝑠
2𝑓/𝑑ℎ)
Scaled Equations for Solid Phase
The nonlinear equations remain the same and
are not scaled.
𝑘𝑠𝑖𝑎𝑚 (𝑦𝑠𝑖𝑃
𝑅𝑇𝑠−
𝑦𝑖𝑃
𝑅𝑇) = ∑ 𝜂𝑗𝜈𝑖𝑗(−𝑟𝑖𝑗)
𝑠𝑗
ℎ𝑠𝑎𝑚(𝑇𝑠 − 𝑇) = ∑ 𝜂𝑗(∆𝐻𝑗)(−𝑟𝑗)𝑠
𝑗
57
Table 4.3. Parameters for reactor models.
Parameter Description Value Unit
dp Particle outer diameter 32e-4 m
hp Particle height 32e-4 m
dt Tube diameter 0.5 m
휀 Porosity 0.4 -
𝜌𝑏 Bed density 1050 kg/m3
am Specific surface area of catalyst pellet 90000 m2/kg
The catalyst particles are assumed to be cylindrical particles.
4.3.3. Reactor Performance Metrics
In this section, we define the metrics that would be used to measure the
performance of the reactor. The first metric is the percentage CH4 converted, which is
defined by the following equation.
The second metric is the percentage CO2 converted which is defined, for all the reactors
where CO2 is a feed, as follows.
For other reactors where CO2 is not present in the feed, such as SMR, POX and POSMR,
it is defined by the following equation.
𝐶𝐻4 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 (%) =(𝐹𝐶𝐻4
𝑓𝑒𝑒𝑑− 𝐹𝐶𝐻4
𝑜𝑢𝑡)
𝐹𝐶𝐻4
𝑓𝑒𝑒𝑑×100 (4.19)
𝐶𝑂2 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 (%) =(𝐹𝐶𝑂2
𝑓𝑒𝑒𝑑− 𝐹𝐶𝐻4
𝑜𝑢𝑡)
𝐹𝐶𝑂2
𝑓𝑒𝑒𝑑×100 (4.20)
58
These are the two metrics studied by performing reactor simulations for different cases,
using different models.
4.4. Simulation Results and Comparison
4.4.1. Model Validation
The pseudo-homogeneous model of the steam reforming reactor is compared
with the experimental results reported in 97. An isothermal reactor is simulated with inlet
pressure as 1.1 bar, and the feed composition and flowrate selected such that CH4: H2O
is 1:3 mol/s. The bed length is 1 m. The pseudo-homogeneous model seems to be in
good agreement with the experimental results as can be seen in Figure 4.2.
Figure 4.2. Validation of the SMR pseudo-homogeneous model. The experimental
values are taken from 97.
In the next section, we shall present the results of the reactor simulations and
comparison between predictions of different models. Since the pseudo-homogeneous
model has been validated with experimental results, we shall study and compare the
640 660 680 700 720 740 760 780 800
0
10
20
30
40
50
60
Isothermal Reactor Temperature (K)
CH
4C
on
vers
ion
(%
)
SMR Pseudo-homogeneous Model Validation Plot
Model Plot
ExperimentalValues
𝐶𝑂2 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 (%) =(𝐹𝐶𝑂2
𝑓𝑒𝑒𝑑− 𝐹𝐶𝐻4
𝑜𝑢𝑡)
𝐹𝐶𝐻4
𝑓𝑒𝑒𝑑×100 (18)
59
model with equilibrium and heterogeneous models for each reactor system discussed in
Section 2.3.
4.4.2. Individual Reactor Simulation
In this section, we present the simulation results of each reactor. The reactor
performance metrics such as CH4 conversion and CO2 conversion are measured and
compared between the different models described before. The CH4 and CO2 conversion
are measured and compared for different reactor inlet temperatures. For all the
endothermic reactors, such as dry reforming (DR), steam methane reforming (SMR) and
combined dry and steam methane reforming (CDSMR), the simulations for both
adiabatic reactor and isothermal reactor has been shown for all the models. For the
exothermic reactors, such as partial oxidation of methane, we have simulated both
adiabatic and isothermal reactors, but the results of the isothermal reactors have been
presented for all the reactors. The reason for this has been explained in the section
below. The simulation conditions are given in Table 4.4.
Table 4.4. Reactor simulation conditions.
Variable Units DR SMR POX CDSMR PODR POSMR TR RWGS
𝐹𝑖𝑛𝑡𝑜𝑡𝑎𝑙 mol/s 2 2 2 3 3 3 4 2
𝑦𝐶𝐻4 - 0.5 0.5 0.5 0.33 0.33 0.33 0.25 0
𝑦𝐶𝑂2 - 0.5 0 0 0.33 0.33 0 0.25 0.5
𝑦𝐻2𝑂 - 0 0.5 0 0.33 0 0.33 0.25 0
𝑦𝑂2 - 0 0 0.5 0 0.33 0.25 0
𝑦𝐻2 - 0 0 0 0 0 0 0 0.5
𝑃𝑖𝑛 bar 1 1 1 1 1 1 1 1
𝐿𝑏𝑒𝑑 m 1 1 1 1 1 1 1 1
60
4.4.2.1. Dry Reforming of Methane (DR)
All three models described previously, namely, equilibrium, 1-D pseudo-
homogeneous and 1-D heterogeneous models, are compared and the results are
presented for CH4 conversion and CO2 conversion in Figure 4.3. Here, the process
variable varied is the inlet temperature, while the inlet flowrate, reactant composition
and inlet pressure are fixed for all the cases for both adiabatic and isothermal reactors as
given by Table 4.4. We see that as the temperature increases, the conversion of both CH4
and CO2 go up and this can be attributed to the endothermic nature of the reaction. Also,
the system reaches equilibrium within the length of reactor bed for the simulated inlet
conditions. We also see that both the pseudo-homogeneous and the heterogeneous
models predict the same conversion at all temperatures.
Figure 4.3. Dry reforming of methane. The CH4 and CO2 conversion vs reactor inlet
temperature is reported here.
4.4.2.2. Steam Methane Reforming (SMR)
The results for CH4 conversion and CO2 conversion are presented in the Figure
4.4. Once again, we see that the system reaches equilibrium for the given inlet conditions
350 550 750 950 1150
0
20
40
60
80
100
120
Reactor Inlet Temperature (K)
Co
nve
rsio
n (
%)
DREquilibrim - Adia - CH4
Pseudo - Adia - CH4
Hetero - Adia - CH4
Equilibrium - Adia - CO2
Pseudo - Adia - CO2
Hetero - Adia - CO2
Pseudo - Iso - CH4
Pseudo - Iso - CO2
61
and that there is no difference between the pseudo-homogeneous and heterogeneous
models. Since the system is endothermic, we can see that the methane conversion
increases with temperature. CO2, along with syngas of high ratios are produced at all
temperatures.
Figure 4.4. Steam reforming of methane. CH4 and CO2 Conversions vs Reactor Inlet
Temperature is reported here.
4.4.2.3. Partial Oxidation of Methane (POX)
We have simulated an isothermal reactor model apart from the adiabatic reactor
model for this reactor since the effect of inlet temperature can be studied better in an
isothermal reactor than in an adiabatic reactor. This is because, in an adiabatic reactor,
the temperature of the gases rises to very high values and CH4 conversion reaches 100%
350 550 750 950 1150
-25
-5
15
35
55
75
95
115
Reactor Inlet Temperature (K)
Co
nve
rsio
n (
%)
SMREquilibrium - Adia - CH4Pseudo - Adia - CH4Heterogeneous - Adia - CH4Equilibrium - Adia - CO2Pseudo - Adia - CO2Heterogeneous - Adia - CO2Pseudo - Iso - CH4Pseudo - Iso - CO2
62
for all inlet temperatures between 700 and 1200 K. The equilibrium conversion for
methane for the range of temperature for the adiabatic reactor is presented in Figure 4.5.
Figure 4.5. Partial oxidation of methane – adiabatic. CH4 Conversion vs Adiabatic
Reactor Inlet Temperature is reported here.
The results for CH4 conversion and CO2 conversion for the isothermal reactor
model are presented in the Figure 4.6. The temperature range of the partial oxidation is
limited between 700K and 1200K since the kinetics for the total combustion of methane
are not valid at lower temperatures 78. We notice once again that the system reaches
equilibrium at all temperatures and that the predictions of pseudo-homogeneous and
heterogeneous models are very similar.
0
20
40
60
80
100
120
250 750 1250 1750
CH
4C
on
vers
ion
(%
)
Adiabatic Reactor Inlet Temperature (K)
POX
63
Figure 4.6. Partial oxidation of methane - isothermal. CH4 and CO2 Conversion vs
Isothermal Reactor Temperature.
4.4.2.4. Combined Dry Reforming and Steam Reforming of Methane (CDSMR)
For simulating the combined dry and steam methane reforming, we use the same
reactions and rate expressions that represent the steam methane reforming reactor. As
mentioned earlier, dry reforming is also indirectly represented by the steam reforming
reactions. This can be validated by simulating the dry reforming reaction using the SMR
equations. The resulting plot for CH4 conversion with reactor outlet temperature is
compared with the results using the DR equations in Figure 4.7.
-70
-50
-30
-10
10
30
50
70
90
110
600 700 800 900 1000 1100 1200 1300
Co
nve
rsio
n (
%)
Isothermal Reactor Temperature (K)
POX
Equilibrium - CH4 Pseudo-homogeneous -CH4 Pseudo-homogeneous -CO2
Equilibrium -CO2 Hetero - CH4 Hetero - CO2
64
Figure 4.7. DR and SMR kinetics comparison. The dry reforming reactor has been
simulated using DR equations and SMR equations and the percentage CH4 and CO2
conversions have been reported here with varying reactor inlet temperature. The exact
match of the two set of equations are seen.
The results for CH4 conversion and CO2 conversion for CDSMR are presented in the
Figure 4.8. We see that the CO2 conversion is positive for a certain range of temperature
and negative for others. This behavior can be explained by studying the individual
reactions and the corresponding rates of reactions in the system which is represented in
Figure 4.9. Thus, from the three primary reforming reactor simulations and one
combined reformer simulation, we see that most systems reach equilibrium and that the
pseudo-homogeneous and heterogeneous models show the same behavior. Thus, for the
other combined reactors and further analysis, we compare the equilibrium reactor with
the simpler rate-based model, the pseudo-homogeneous reactor model.
0
10
20
30
40
50
60
70
80
300 800 1300 1800 2300
Co
nve
rsio
n (
%)
Adiabatic Reactor Inlet Temperature (K)
using SMR eqs - CH4
Using SMR eqs - CO2
Using DR eqs - CH4
Using DR eqs - CO2
65
Figure 4.8. Combined dry and steam reforming of methane. CH4 and CO2
conversions vs reactor inlet temperature is presented here.
Figure 4.9. Dominating reactions in different temperature regions explaining the
trend in CO2 conversion for combined dry and steam methane reforming.
-20
0
20
40
60
80
100
120
350 550 750 950 1150 1350
Co
nve
rsio
n (
%)
Reactor Inlet Temperature (K)
CDSMR
Pseudo - Adia - CH4 Equilibrium - Adia - CH4 Pseudo- Adia - CO2
Equilibrium - Adia - CO2 Hetero - Adia - CH4 Hetero - Adia - CO2
Pseudo - Iso - CH4 Pseudo - Iso - CO2
-8
-6
-4
-2
0
2
4
6
8
10
350 550 750 950 1150 1350
CO
2C
on
vers
ion
(%
)
Adiabatic Reactor Inlet Temperature (K)
Pseudo-homogeneous Equilibrium Heterogeneous
No reaction SMR 2 dominates Reverse WGS dominates
𝐒𝐌𝐑 𝟏 ∶ 𝐂𝐇𝟒 + 𝐇𝟐𝐎 → 𝐂𝐎 + 𝟑𝐇𝟐
𝐒𝐌𝐑 𝟐 ∶ 𝐂𝐇𝟒 + 𝟐𝐇𝟐𝐎 → 𝐂𝐎𝟐 + 𝟒𝐇𝟐
𝐖𝐆𝐒 ∶ 𝐂𝐎 + 𝐇𝟐𝐎 → 𝐂𝐎𝟐 + 𝐇𝟐
66
4.4.2.5. Combined Dry Reforming and Partial Oxidation of Methane (PODR)
The results for CH4 conversion and CO2 conversion in PODR are presented in
the Figure 4.10. The isothermal reactor models of the equilibrium and pseudo-
homogeneous models are compared and it is seen the system reaches equilibrium for
most cases. Though CO2 is present in the feed, it is seen that CO2 is produced at lower
inlet temperature. This is because steam reforming of methane dominates at lower
temperatures producing CO2, owing to the lower enthalpy of reaction than dry reforming
of methane. At higher inlet temperatures, dry reforming of methane takes place thus
utilizing CO2.
Figure 4.10. Combined dry reforming and partial oxidation of methane. CH4 and
CO2 conversions vs isothermal reactor temperature is presented here.
-100
-50
0
50
100
150
650 750 850 950 1050 1150 1250
Co
nve
rsio
n (
%)
Isothermal Reactor Temperature (K)
PODR
Equilibrium - CH4 Pseudo-homogeneous - CH4
Pseudo-homogeneous - CO2 Equilibrium - CO2
67
4.4.2.6. Combined Steam Reforming and Partial Oxidation of Methane
(POSMR)/Auto-thermal Reforming of Methane (ATR)
The results for CH4 conversion and CO2 conversion are presented in the Figure
4.11. The isothermal reactor models of the equilibrium and pseudo-homogeneous
models are compared and it is seen the system reaches equilibrium for most cases. Since
both steam methane reforming and partial oxidation produce CO2, the utilization of CO2
in POSMR is always negative. This could be a viable option in producing syngas of
syngas ratio between 2 and 3.
Figure 4.11. Combined steam reforming and partial oxidation of methane. CH4 and
CO2 conversions vs isothermal reactor temperature is presented here.
4.4.2.7. Tri-Reforming of Methane (TR)
The results for CH4 conversion and CO2 conversion are presented in the Figure
4.12. The isothermal reactor models of the equilibrium and pseudo-homogeneous
models are compared and it is seen the system reaches equilibrium for most cases. For
-100
-50
0
50
100
150
650 750 850 950 1050 1150 1250
Co
nve
rsio
n (
%)
Isothermal Reactor Temperature (K)
POSMR
Equilibrium - CH4 Pseudo-homogeneous - CH4
Pseudo-homogeneous - CO2 Equilibrium - CO2
68
the simulation conditions plotted, we see that the inlet temperature needs to be very high
for CO2 to be utilized. This could be attributed to the precedence of reactions: partial
oxidation followed by steam methane reforming, followed by dry reforming of methane.
This is based upon the enthalpy of reaction. By changing the ratios of the inlet reactant
species, CO2 utilization could be increased.
Figure 4.12. Tri-reforming of methane. CH4 and CO2 Conversions vs isothermal
reactor temperature is presented here.
4.4.2.8. Reverse Water Gas Shift Reactor (RWGS)
The results for CH4 conversion and CO2 conversion are presented in Figure 4.13.
The adiabatic reactor models of the equilibrium and pseudo-homogeneous models are
compared and it is seen the system reaches equilibrium for the simulations performed.
As the reverse water gas shift reaction is endothermic, the CO2 conversion increases
with increasing inlet temperature.
-100
-50
0
50
100
150
650 750 850 950 1050 1150 1250
Co
nve
rsio
n (
%)
Isothermal Reactor Temperature (K)
TR
Equilibrium - CH4 Pseudo-homogeneous - CH4
Pseudo-homogeneous - CO2 Equilibrium - CO2
69
Figure 4.13. Reverse water gas shift reaction. CO2 Conversion vs adiabatic reactor
inlet temperature is presented here.
We see that the rate-based models do not differ much from each other and that
they achieve equilibrium in most cases for the given flowrates and the chosen length of
the reactor bed. The need for a rate-based model over an equilibrium model can be
explained by increasing the flowrate, varying the composition and studying the
conversions against the equilibrium conversion for the same conditions. The ratio of
total flowrate (TF) to reactor bed length (L) plays a key role in deciding the output
composition of the components for a given inlet temperature, pressure and composition.
The outcome of this for a steam methane reformer is represented in Figure 4.14. In the
figure, both the total flowrate (TF) and the reactor bed length (L) has been varied, but
the ratio has been kept constant. A steam to methane ratio of 3:1 has been used and it is
seen that for the same ratio of TF and L, the conversion is the same but varies
significantly from equilibrium conversion.
0
10
20
30
40
50
60
350 550 750 950 1150 1350
CO
2C
on
vers
ion
(%
)
Adiabatic Reactor Inlet Temperature (K)
RWGS
Equilibrium
Pseudo-homogeneous
70
Figure 4.14. Comparison between equilibrium and pseudo-homogeneous reactor
for SMR for higher flowrates. SMR reactor with varying inlet total flowrate (TF) in
mol/s and reactor bed length (L) in m. The system shows significant difference from
equilibrium, but remains the same for the same TF/L ratios.
So far, we have simulated the different reactors by varying inlet temperature,
flowrate and the length of the reactor bed. We studied the methane and carbon dioxide
conversion of each system using three models. The equilibrium model can be used to
benchmark the maximum possible rates of reactions, and thus, conversions of reactants.
For understanding the design parameters, we need a more realistic reactor model such as
a rate-based model. Among the two rate-based models studied, we find that the
heterogeneous and pseudo-homogeneous models deviate from each other by a very small
extent for most cases studied. Keeping in mind the complexity of the model and the
computational time required to perform simulations, we use the pseudo-homogeneous
model amongst the two rate-based models for further analysis.
0
10
20
30
40
50
0 500 1000 1500
CH
4C
on
vers
ion
(%
)
Reactor Inlet Temperature (K)
SMR
TF = 1 ; L = 0.1
TF = 10 ; L = 1
TF = 8 ; L = 0.8
Equilibrium
71
4.5. Surrogate-based Reactor Models
4.5.1. Model Development
As was discussed in the previous section, we have accurate models that can
represent the reactors in question. We shall use the 1-D pseudo-homogeneous model to
represent the reactors for further analysis. To extensively study the effect of all the
variables such as temperature, pressure, flowrate, composition on conversion
simultaneously, an algebraic functional form that relates the reactor performance metrics
to the input variables is necessary. The 1-D pseudo-homogeneous model is a set of
ordinary differential equations and we need an equivalent algebraic form that would be
tractable to use in an algebraic optimization framework. This problem could thus be
looked at as a black-box model with the inputs and outputs given by the pseudo-
homogeneous reactor model.
In this work, the modeling platform ALAMO 98 is used for generating surrogate
models for the reactor models. ALAMO is a software that is used to generate algebraic
models for simulations, experiments or black-box models. The ALAMO workflow is
given in Figure 4.15.
72
Figure 4.15. ALAMO workflow for obtaining surrogate models.
The output variables of all the reactors have been modeled using the following basis
functions:
• Monomial terms with powers (𝑒. 𝑔. , 𝑥12, 𝑥3
3)
• Multivariable terms with powers (𝑒. 𝑔. , (𝑥1𝑥2)2)
START
Model building using initial sampling set
#inputs, #outputs, bounds on inputs
Basis functions
Is Simulator provided?
No
Adaptive Sampling using simulator
Yes
Build model
Convergence criteria met?
Best model possible - STOP
No
Yes
73
• Ratios
• Exponential functions
• Logarithmic functions
A simulator with the model for the pseudo-homogeneous model written on
MATLAB is provided. The simulator is an executable written in the language, Fortran.
A validation set based on Latin Hypercube design is provided along with the ALAMO
code for cross-validation of the model built and the R2 values for the complete set of
points, that is, both validation and training set, is reported.
4.5.2. Results for Model Performance
The algebraic surrogate models have been built for all the 8 reactors. Each
reactor has a certain set of input variables with corresponding bounds and certain set of
output variables. The comparison between the predicted and simulated values for the
output variables modeled using ALAMO for DR is shown in Figure 4.16. The set of
input and output variables along with the bounds is provided for each reactor in
Appendix C. The R2 values for these set of data along with the number of evaluations
taken for each reactor are reported in the Table C17 in Appendix C.
74
Figure 4.16. Predicted vs. simulated values for the output variables modeled using ALAMO for DR.
75
CHAPTER V
SUPERSTRUCTURE-BASED OPTIMAL SYNTHESIS OF CO2 UTILIZATION
PROCESSES
So far, different alternatives for CO2 utilization have been explored and analyzed.
Different reactor types for the utilization of CO2 and production of syngas were studied
through different reactor models. The most appropriate reactor models were chosen to
represent the reactors and surrogate models have been built upon them. Individual
reactor analysis based upon thermodynamic as well as kinetics has been performed and
knowledge of individual reactor performance is present.
There is still no clear understanding as to which is the best alternative for different
objectives and there remain unanswered questions such as
1. Which is the best route for maximum CO2 utilization for a specific syngas ratio?
2. What is the minimum cost of producing syngas of a specific syngas ratio?
3. What are the best operating and design conditions for achieving these objectives?
4. Are there any auxiliary emissions associated with operating at these conditions?
These are important questions to answer to get a big picture view of the CO2
utilization systems. To be able to answer these questions, a process synthesis
superstructure is proposed embedding all the possibilities discussed so far. The raw
materials in these processes along with their original sources are considered for a holistic
analysis.
76
In this chapter, the description of the superstructure framework and the elements
constituting the superstructure is first provided. The mathematical equations that entail
the process synthesis model is presented next along with the optimization problem
statement. Different alternatives for modeling the reactors have been incorporated in the
superstructure and solved to optimality. The optimization results are discussed in the last
section.
Figure 5.1. Superstructure for the synthesis of CO2 utilization process network.
5.1. Process Superstructure
This section describes the proposed process superstructure and the components
and blocks embedded in it. The entire superstructure is presented in the Figure 5.1. The
superstructure consists of several layers such as raw materials, separators, pure
Natural gas (NG)
Flue Gas (FG)
Biogas (BG)
Air
Water
FGS
BGS
AS
ES
NGS
B_H2
B_CO2
B_CH4
B_O2
B_H2O
B_N2
Reverse Water Gas Shift (RWGS)
Steam reforming (SR)
Combined DR & SR (CDSR)
Tri-reforming (TR)
Combined PO & DR (PODR)
Combined PO & SR (POSR)
Dry reforming (DR)
Nitrogen
Vent
Syngas
Partial oxidation (PO)
77
component blocks, reactors and products. Each layer has blocks representing the
different alternatives in that classification. The connectivity through arrows depicts that
mass and energy can flow between the blocks connected.
The layer of reactors includes all the alternatives of reactors for CO2 utilization and
syngas production, discussed before. The sources of the reactant species for these
reactors are chosen from various sources, which encompass the first layer of the
superstructure. The main source of carbon dioxide is flue gas (FG) from power plant and
the main sources of methane are natural gas (NG) and biogas (BG). Other raw materials
such as air and water are also considered. The second layer of the superstructure consists
of the separator blocks where flue gas separation (FGS), which is further divided into
blocks for water separation (WS), CO2 separation (CCS) and oxygen separation (OXS),
separation of methane from natural gas and biogas through natural gas separation (NGS)
and biogas separation (BGS) respectively, air separation (AS) and electrolysis (ES) of
water to produce pure hydrogen are plausible alternatives. The third layer consists of the
pure components blocks, which just act as mixers and splitters in the superstructure,
collecting and distributing the components as dictated by the model. The fourth layer
consists of the reactor blocks, which have been described sufficiently in the previous
chapters. The models of the reactors can be varied and this is described in detailed in the
next section. The last layer is that of the products, syngas (ST) being the most important
one here. There is also a block for venting nitrogen where the nitrogen from stranded
sources are collected and vented.
78
This depiction allows systematic approach and flexibility to add more elements
in the superstructure. It also enables simple modeling approaches which is discussed in
the next section.
5.2. Superstructure-based Process Synthesis Model
This section describes the process synthesis model based on the superstructure
framework described before.
In this section, we will discuss the indices, sets, parameters, variables,
assumptions, mathematical constraints along with the objective function that describe the
mathematical model of the superstructure.
5.2.1. Indices
The following indices are used throughout the mathematical model.
𝑖 Block index (Raw materials, separators, components, reactors, products)
𝑛 Component index
𝑗, 𝑘, 𝑖𝑖 Aliases of i
𝑛𝑛 Alias of n
𝑙 Sample number for surrogate model
𝑖𝑣 Index for input variables for surrogate model
𝑖𝑣 ∈ {𝐵_𝐶𝐻4, 𝐵_𝐶𝑂2, 𝐵_𝐻2, 𝐵_𝐻2𝑂, 𝐵_𝑂2, 𝑃, 𝑇, 𝐿}
5.2.2. Sets
We define two Master Sets, I and N, and the other sets are subsets of these two sets.
Set of all blocks, I, is given as follows:
79
𝑖 ∈ 𝐼 = {
𝐹𝐺, 𝑁𝐺, 𝐵𝐺, 𝐴𝑖𝑟, 𝑊𝑎𝑡𝑒𝑟, 𝑊𝑆, 𝐶𝐶𝑆, 𝑂𝑋𝑆, 𝑁𝐺𝑆, 𝐵𝐺𝑆, 𝐴𝑆, 𝐸𝑆,𝐵_𝐶𝐻4, 𝐵_𝐶𝑂2, 𝐵_𝐶𝑂, 𝐵_𝐻2𝑂, 𝐵_𝐻2, 𝐵_𝑂2, 𝐵_𝑁2,
𝐷𝑅, 𝑆𝑀𝑅, 𝑃𝑂𝑋, 𝐶𝐷𝑆𝑀𝑅, 𝑃𝑂𝐷𝑅, 𝑃𝑂𝑆𝑀𝑅, 𝑇𝑅, 𝑅𝑊𝐺𝑆,𝑆𝑇, 𝑉𝑒𝑛𝑡
}
Set of all components, N, is given as follows:
𝑛 ∈ 𝑁 = {𝐶𝐻4, 𝐶𝑂2, 𝐶𝑂, 𝐻2𝑂, 𝐻2, 𝑂2, 𝑁2 }
where, each species is present in the gas phase.
To establish relationships between blocks with material and energy transfer, we define
subsets as follows:
𝐼𝒊 Set of blocks from which there is input to block i
𝐽𝒊 Set of blocks to which there is output from block i
𝑀𝒊 Set of components in inlet to block I
𝑁𝒊 Set of components in outlet from block i
𝐼𝒊,𝒏 Set of component (n) blocks from which there is input to block i
𝑅𝑆𝒊 Set of first layer raw material blocks from which there is input to separator i
The complete list of subsets can be found in Appendix A.
5.2.3. Parameters
The parameters are defined as follows:
𝑓𝐹𝐺𝑓𝑒𝑒𝑑
: Inlet flowrate of flue gas
𝑦𝑖,𝑛𝑓𝑒𝑒𝑑
: Inlet composition of component n in raw material block i
𝜂𝑖 : Conversion of the limiting reactant in reactor i
𝐹𝑆𝑈 : Upper bound on stoichiometric flow rate
𝑅𝐿 , 𝑅𝑈 : Bounds on syngas ratio at outlet (H2 to CO flow rates)
80
𝛼𝑖,𝑛 : Stoichiometric coefficient of component n for reactor i
𝛿𝑖,𝑛 : Splitting factor for component 𝑛 in separator 𝑖
𝜑𝑖 : Amount of CO2 emitted per inlet flowrate to block i
𝑎𝑖,𝑛 : Reactor surrogate model parameter for reactor 𝑖 for component 𝑛
𝑏𝑖,𝑛,𝑖𝑣 : Reactor surrogate model parameter for reactor 𝑖 for component 𝑛 for input
variables 𝑖𝑣
𝜆𝑖,𝑛,𝑙 : Reactor surrogate model parameter for reactor 𝑖 for component 𝑛 for sample 𝑙
𝑆𝑆𝑖,𝑛,𝑖𝑣,𝑙: Reactor surrogate model parameter for reactor 𝑖 for component 𝑛 for sample 𝑙
for input variable 𝑖𝑣
𝑇𝑟𝑒𝑓 : Reference temperature
𝐴𝑖 , 𝐵𝑖, 𝐶𝑖, 𝐷𝑖 , 𝐸𝑖 : Shomate parameters for component block 𝑖
𝑇𝑝𝑖 : Operating temperature of reactor 𝑖
𝑃𝑝𝑖 : Operating pressure of reactor 𝑖
The complete list of parameters can be found in Appendix B.
5.2.4. Variables
The following variables are used to model the superstructure.
The continuous variables are listed below:
𝐹𝑖𝑓𝑒𝑒𝑑
Feed molar flow rate to raw material block i
𝐹𝑖,𝑗 Total molar flow rate of stream from block i to block j
𝑦𝑖,𝑗,𝑛 Composition of component n in stream from block i to block j
𝐹𝑆𝑖,𝑛 Stoichiometric flow rate of component n to reactor block I
81
𝐹𝑆𝑅𝑖,𝑛 Relaxed stoichiometric flow rate of component n to reactor block i
𝑓𝑛𝑜𝑢𝑡 Flow rate of component n at outlet of Syngas (ST) block
𝑇𝑖 Temperature of reactor 𝑖
𝑃𝑖 Pressure of reactor 𝑖
𝐿𝑖 Bed length of reactor 𝑖
𝑄𝑖 Heat duty of reactor 𝑖
𝑊𝑖 Compressor duty of reactor 𝑖
The binary variable for choosing the limiting reactant for the stoichiometric unit model
is defined as follows:
𝑧𝑖,𝑛 = {1, if 𝑛 is the limiting reactant in reactor 𝑖
0, otherwise
5.2.5. Objective Function
Two objective functions are considered in this work. In one, we maximize the
percent net utilization of carbon dioxide by considering the difference between the input
and output molar flowrates of carbon dioxide. Additionally, we also account for the
carbon dioxide that is emitted during any of the processes in the superstructure.
Max Percent Net CO2 utilization
The second objective function is to minimize the total annual cost (TAC) of syngas
production.
min 𝑇𝐴𝐶 = ∅𝐶𝑖𝑛𝑣𝑡𝑜𝑡𝑎𝑙 + 𝐶𝑜𝑝
𝑎𝑛𝑛𝑢𝑎𝑙
These are described in detail in the constraints section. The objective functions are
subject to constraints as follows.
82
5.2.6. Constraints
The mass balance around raw material blocks is given by the equation,
𝐹𝑖𝑓𝑒𝑒𝑑
= ∑ 𝐹𝑖,𝑗
𝑗∈𝐽𝑖
, 𝑖 ∈ 𝑅𝑀
We fix the input molar flowrate of flue gas.
𝐹𝐹𝐺𝑓𝑒𝑒𝑑
= 𝑓𝐹𝐺𝑓𝑒𝑒𝑑
The mass balance around separator blocks is given by the equation,
𝐹𝑖,𝑗 = ∑ 𝐹𝑗,𝑘
𝑘∈𝐽𝑗
, 𝑗 ∈ 𝑆, 𝑗 ≠ 𝐸𝑆, 𝑖 ∈ 𝐼𝑗
𝐹𝑗,𝑘 = 𝛿𝑖,𝑛𝐹𝑖,𝑗𝑗 , 𝑗 ∈ 𝑆, 𝑘 ∈ 𝐽𝑗 ∩ 𝐶𝐵, 𝑖 ∈ 𝑅𝑆𝑗, 𝑛 ∈ 𝑀𝑘, 𝑗𝑗 ∈ 𝐽𝑖 ∩ 𝑆
The separators are assumed to be sharp splitters and the components are split based on
the split fractions defined below.
𝛿𝑖,𝑛 = 𝑦𝑖,𝑛𝑓𝑒𝑒𝑑
, 𝑖 ∈ 𝑅𝑀, 𝑛 ∈ 𝑀𝑖
𝛿𝑊𝑎𝑡𝑒𝑟,𝐻2= 𝛼𝐸𝑆,𝐻2
𝛿𝑊𝑎𝑡𝑒𝑟,𝑂2= 𝛼𝐸𝑆,𝑂2
The mass balance around component blocks is given by the equation,
∑ 𝐹𝑖,𝑗
𝑖∈𝐼𝑗
= ∑ 𝐹𝑗,𝑘
𝑘∈𝐽𝑗
, 𝑗 ∈ 𝐶𝐵
The equations pertaining to the reactor block are described in the next section. The other
general equations are given here. For all reactors, the output component mole fractions
sum up to 1.
∑ 𝑦𝑗,𝑛,𝑘
𝑛∈𝑁𝑗
= 1, 𝑗 ∈ 𝑅, 𝑘 ∈ 𝐽𝑗
83
We calculate the output molar flowrate of every component by the following equation.
𝑓𝑛𝑜𝑢𝑡 = ∑ 𝑦𝑖,𝑆𝑇,𝑛𝐹𝑖,𝑆𝑇
𝑖∈𝑅
, 𝑛 ∈ 𝑁𝑖
The following constraint gives bounds on the syngas ratio at the outlet.
𝑅𝐿 ≤𝑓𝐻2
𝑜𝑢𝑡
𝑓𝐶𝑂𝑜𝑢𝑡 ≤ 𝑅𝑈
To calculate the auxiliary carbon dioxide emission, we need to calculate the heat duty
and compressor duty required to attain the operating conditions of the reactor.
The heat duty is calculated by the following expression:
𝑄𝑗 = (∑ 𝐹𝑖,𝑗
𝑖∈𝐼𝑗
) ∑ (𝐹𝑖,𝑗
∑ 𝐹𝑖𝑖,𝑗𝑖𝑖∈𝐼𝑗
) (𝐴𝑖
1000(𝑇𝑗 − 𝑇𝑟𝑒𝑓) +
𝐵𝑖
2×10002(𝑇𝑗
2 − 𝑇𝑟𝑒𝑓2 ) +
𝐶𝑖
3×10003(𝑇𝑗
3 − 𝑇𝑟𝑒𝑓3 )
𝑖∈𝐼𝑗
+𝐷𝑖
4×10004(𝑇𝑗
4 − 𝑇𝑟𝑒𝑓4 ) + (𝐸𝑖×1000) (
1
𝑇𝑗
−1
𝑇𝑟𝑒𝑓
)) , 𝑗 ∈ 𝑅
The compressor duty is calculated by
𝑊𝑗 = (∑ 𝐹𝑖,𝑗
𝑖∈𝐼𝑗
)𝛾
𝛾 − 1𝑅𝑇𝑗 [(
𝑃𝑗
𝑃𝑟𝑒𝑓)
𝛾−1𝛾
− 1]
For optimization, we consider two performance metrics, namely, percentage net CO2
utilization and the total annualized cost (TAC).
The first metric is the percentage CO2 utilized which is defined by the following
equation.
𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝑁𝑒𝑡 𝐶𝑂2 𝑢𝑡𝑖𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 = 𝑁𝑒𝑡 𝐶𝑂2 𝑢𝑡𝑖𝑙𝑖𝑧𝑒𝑑
𝑇𝑜𝑡𝑎𝑙 𝐶𝑂2 𝑓𝑒𝑑 ×100
84
The net utilization considers the auxiliary carbon dioxide emissions from the
utility requirements for the reactor and separators. Broadly, the factors contributing to
auxiliary emissions can be divided into electricity and heat requirements.
𝑁𝑒𝑡 𝐶𝑂2 𝑢𝑡𝑖𝑙𝑖𝑧𝑒𝑑 = ∑ 𝑦𝑖,𝐶𝑂2
𝑓𝑒𝑒𝑑
𝑖∈𝑅𝑀
𝐹𝑖𝑓𝑒𝑒𝑑
− ∑ 𝑦𝑖,𝑆𝑇,𝐶𝑂2
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝐹𝑖,𝑆𝑇
𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝑖∈𝑅
− ∑ ∑ 𝐹𝑖,𝑗𝜑𝑗
𝑖∈𝐼𝑗𝑗∈𝑆
− 𝜑ℎ ∑ 𝑄𝑖
𝑖∈𝐻
− 𝜑𝑒 ∑ 𝑊𝑖
𝑖∈𝐸
The first term is the total CO2 fed in, the second term stands for the CO2 exiting
the reactor. The third term stands for the auxiliary emissions due to separation. The
fourth and fifth terms represent the auxiliary emissions due to the heat and compressor
duty involved prior to the reaction. The total CO2 fed is given by the following equation.
𝑇𝑜𝑡𝑎𝑙 𝐶𝑂2 𝑓𝑒𝑑 = ∑ 𝑦𝑖,𝐶𝑂2
𝑓𝑒𝑒𝑑
𝑖∈𝑅𝑀
𝐹𝑖𝑓𝑒𝑒𝑑
For a basis of x units of flue gas from a coal fired power plant, that is to be
captured and converted, the amount of associated electricity produced is X units. This X
units of electricity is the available clean electricity with no associated auxiliary
emissions. The capture and conversion processes utilizes a total electricity amount of Y
units. Let the difference between the total electricity requirement Y and the available
clean electricity X be Z. This amount of electricity Z is obtained from a coal-fired
facility with no carbon capture, thus producing auxiliary emissions.
Two scenarios could occur with respect to the amount of electricity Y required in the
superstructure.
If Z > 0, that is, more electricity than the available clean electricity X is required
by the process, the objective function is formulated in the following manner.
85
𝑁𝑒𝑡 𝐶𝑂2𝑢𝑡𝑖𝑙𝑖𝑧𝑒𝑑 = ( ∑ 𝑦𝑖,𝐶𝑂2
𝑓𝑒𝑒𝑑
𝑖∈𝑅𝑀
𝐹𝑖𝑓𝑒𝑒𝑑
− ∑ 𝑦𝑖,𝑆𝑇,𝐶𝑂2
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝐹𝑖,𝑆𝑇
𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝑖∈𝑅
− ∑ ∑ 𝐹𝑖,𝑗𝜑𝑗
𝑖∈𝐼𝑗𝑗∈𝑆
− 𝜑ℎ ∑ 𝑄𝑖
𝑖∈𝐻
− 𝜑𝑒𝑍)
If Z < 0, that is, electricity required by the process is less than the available clean
electricity X, then there are no additional emissions associated with electricity, and 𝜑𝑒
becomes 0. The objective function then becomes
𝑁𝑒𝑡 𝐶𝑂2𝑢𝑡𝑖𝑙𝑖𝑧𝑒𝑑 = ( ∑ 𝑦𝑖,𝐶𝑂2
𝑓𝑒𝑒𝑑
𝑖∈𝑅𝑀
𝐹𝑖𝑓𝑒𝑒𝑑
− ∑ 𝑦𝑖,𝑆𝑇,𝐶𝑂2
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝐹𝑖,𝑆𝑇
𝑝𝑟𝑜𝑑𝑢𝑐𝑡
𝑖∈𝑅
− ∑ ∑ 𝐹𝑖,𝑗𝜑𝑗
𝑖∈𝐼𝑗𝑗∈𝑆
− 𝜑ℎ ∑ 𝑄𝑖
𝑖∈𝐻
)
The second performance metric is the total annualized cost (TAC). The TAC is
given by the sum of annualized investment cost and the annual operating cost.
𝑇𝐴𝐶 = ∅𝐶𝑖𝑛𝑣𝑡𝑜𝑡𝑎𝑙 + 𝐶𝑜𝑝
𝑎𝑛𝑛𝑢𝑎𝑙
The model equations for the set of reactors, that are based on the stoichiometric
unit model are described first.
5.2.7. Stoichiometry-based Reactor Model
We define the stoichiometric flowrate, ,j nFS of each component 𝑛 entering the reactor 𝑗.
,
, , ,
,
,
, ,j n
i j n i j
i I
j n j
j n
y F
FS j R n M
The limiting reactant is chosen using a binary variable, 𝑧𝑗,𝑛.
𝐹𝑆𝑗,𝑛 ≤ 𝐹𝑆𝑗,𝑛𝑛 + 𝐹𝑆𝑈(1 − 𝑧𝑗,𝑛), 𝑗 ∈ 𝑅1, 𝑛 ∈ 𝑀𝑗 , 𝑛𝑛 ∈ 𝑀𝑗 , 𝑛 ≠ 𝑛𝑛
∑ 𝑧𝑗,𝑛
𝑛∈𝑀𝑗
= 1, 𝑗 ∈ 𝑅
Relaxation of the bilinear term using McCormick’s,
𝐹𝑆𝑅𝑖,𝑛 ≤ 𝐹𝑆𝑈𝑧𝑖,𝑛, 𝑖 ∈ 𝑅, 𝑗 ∈ 𝐽𝑖, 𝑛 ∈ 𝑁𝑖
86
𝐹𝑆𝑅𝑖,𝑛 ≤ 𝐹𝑆𝑖,𝑛, 𝑖 ∈ 𝑅, 𝑗 ∈ 𝐽𝑖 , 𝑛 ∈ 𝑁𝑖
𝐹𝑆𝑅𝑖,𝑛 ≥ 𝐹𝑆𝑖,𝑛 − 𝐹𝑆𝑈(1 − 𝑧𝑖,𝑛), 𝑖 ∈ 𝑅, 𝑗 ∈ 𝐽𝑖 , 𝑛 ∈ 𝑁𝑖
The outlet component flowrate (LHS) from the reactor is given by the stoichiometric
unit model.
𝑦𝑗,𝑘,𝑛𝐹𝑗,𝑘 = ∑ 𝑦𝑖,𝑗,𝑛𝐹𝑖,𝑗
𝑖∈𝐼𝑗,𝑛
+ 𝜂𝑗𝛼𝑗,𝑛 ∑ 𝐹𝑆𝑅𝑗,𝑛𝑛
𝑛𝑛∈𝑀𝑗
, 𝑗 ∈ 𝑅, 𝑘 ∈ 𝐽𝑗 , 𝑛 ∈ 𝑁𝑗
The temperature variables, 𝑇𝑖 and the pressure variables, 𝑃𝑖 for the stoichiometric reactor
set, are fixed according to literature and the values can be found in Appendix B.
𝑇𝑖 = 𝑇𝑝𝑖, 𝑖 ∈ 𝑅
𝑃𝑖 = 𝑃𝑝𝑖, 𝑖 ∈ 𝑅
5.2.8. Equilibrium-based Reactor Model
The model equations for the set of reactors that are based upon equilibrium,
surrogate models are developed and the model equations for the output component
flowrate are as follows.
The surrogate model is a cubic radial basis equation where the output component
flowrates are expressed as a function of the input component flowrates, input stream
temperature, input stream pressure and length of the catalyst bed.
87
𝑦𝑗,𝑘,𝑛𝐹𝑗,𝑘 = 𝑎𝑗,𝑛 + ∑(𝑏𝑗,𝑛,𝑖 𝐹𝑖,𝑗)
𝑖∈𝐼𝑗
+ 𝑏𝑗,𝑛,𝑇 𝑇𝑗 + 𝑏𝑗,𝑛,𝑃 𝑃𝑗 + 𝑏𝑗,𝑛,𝐿 𝐿𝑗
+ ∑ 𝜆𝑗,𝑛,𝑙
𝑁𝑠𝑎𝑚
𝑙=1
[∑(𝐹𝑖,𝑗 − 𝑆𝑆𝑗,𝑛,𝑙,𝑖)2
𝑖∈𝐼𝑗
+ (𝑃𝑗 − 𝑆𝑆𝑗,𝑛,𝑙,𝑃)2
+ (𝑇𝑗 − 𝑆𝑆𝑗,𝑛,𝑙,𝑇)2
+ (𝐿𝑗 − 𝑆𝑆𝑗,𝑛,𝑙,𝐿)2
]
3/2
, 𝑗 ∈ 𝑅2, 𝑘 ∈ 𝐽𝑗 , 𝑛 ∈ 𝑁𝑗
5.2.9. Reaction Rate-based Reactor Models
As mentioned in the previous chapter, detailed models based on kinetics were
used for the reactors for CO2 utilization. Surrogate models based on the pseudo-
homogeneous models were developed using ALAMO 19. The models for the output
variables of each reactor can be found in the Appendix C.
The bounds for temperature, pressure, length of reactor and reactant molar
flowrates are fixed based upon the models developed. All the bounds can be found in
Appendix C.
To illustrate the use of these models in the superstructure, we have provided the
model equation for the dry reforming reactor.
X1 = FB_CH4, DR; X2 = FB_CH4, DR; X3 = TDR; X4 = PDR; X5 = LDR
The dry reforming models for the output flowrates are presented here as an example.
FrDR,ST,CH4 = 1.0490E+00 X1 + 2.5764E-02 X2 - 6.2201E-09 X3 + 2.4723E-03 X4 + 1.1185E-02 X5 +
8.0520E-03 log(X3) - 1.4803E-01 log(X4) + 9.8622E-04 exp(X2) + 1.6480E-02 X22 - 2.1020E-06 X4
2 -
3.4779E-03 X23 + 5.2785E-10 X4
3 - 6.5574E-03 X1 X2 - 7.2718E-05 X1 X4 + 4.9092E-09 X2 X3 - 7.4625E-
05 X2 X4 - 5.3070E-03 X2 X5 + 8.7604E-04 (X1 X2)2 - 1.9956E-05 (X1 X2)3 - 9.6930E-06 X1 X2 X4
88
FrDR,ST,CO2 = 4.0070E-02 X1 + 1.0693E+00 X2 - 1.2195E-08 X3 + 4.8926E-03 X4 - 1.8840E-02 X5 +
9.2583E-03 log(X3) - 2.6077E-01 log(X4) - 1.1505E-03 exp(X1) + 1.2092E-03 exp(X2) + 1.4564E-02 X12
+ 3.5285E-02 X22 - 4.5155E-06 X4
2 - 5.4709E-03 X23 + 1.3389E-09 X4
3 - 5.7239E-03 X1 X2 - 1.3460E-04
X1 X4 + 6.6720E-09 X2 X3 - 2.2731E-04 X2 X4 - 1.0026E-02 X2 X5 + 5.2867E-05 X4 X5
FrDR,ST,CO = - 3.9942E-01 X1 - 5.9635E-01 X2 - 5.3102E-08 X3 - 2.1884E-02 X4 + 9.3347E-02 X5 -
6.3318E-02 log(X3) + 5.9444E+00 log(X4) - 8.1827E-02 log(X5) + 9.9592E-03 exp(X1) + 4.3697E-03
exp(X2) - 8.8431E-02 X12 - 7.2982E-02 X2
2 + 1.3214E-05 X42 + 3.4708E-02 X1
3 + 2.6167E-02 X23 -
3.3924E-09 X43 - 6.1216E-03 X1
4 - 3.6811E-03 X24 - 2.2691E-03 X5
5 - 1.2606E-02 X1 X2 + 3.8818E-04
X1 X4 + 3.1237E-02 X1 X5 - 3.0179E-09 X2 X3 + 5.6069E-04 X2 X4 - 6.5953E-03 X2 X5 - 3.7195E-03 (X1
X2)2 - 7.5233E-09 (X2 X4)2 + 2.2378E-04 (X1 X2)3 - 4.2270E-06 (X1 X2)4 - 1.3328E-09 X1 X2 X3 +
7.7640E-05 X1 X2 X4 - 4.1174E-05 X1 X4 X5 + 1.8754E-05 X2 X4 X5 - 1.0646E-09 (X1 X2 X4)2 +
1.2240E+02 X1/X4 + 1.8426E+02 X2/X4 + 1.0492E-04 X3/X4 - 7.8824E-09 (X3/X4)2 - 2.8261E+01
FrDR,ST,H2O = - 1.2102E-02 X1 - 2.8829E-01 X2 + 1.0982E-08 X3 - 4.6425E-03 X4 + 4.6729E-03 X5 -
1.8497E-02 log(X3) + 1.1424E+00 log(X4) - 3.8853E-05 exp(X1) + 1.9476E-03 exp(X2) - 3.3591E-05 X12
+ 1.2342E-03 X22 + 3.1409E-06 X4
2 - 9.1548E-10 X43 - 7.5475E-05 X2
5 + 8.9438E-03 X1 X2 + 1.0434E-
06 X1 X4 - 1.2830E-09 X2 X3 + 2.4643E-04 X2 X4 + 1.0724E-03 X2 X5 - 8.4114E-06 X4 X5 - 4.9298E-03
(X1 X2)2 + 2.7360E-10 (X1 X4)2 - 3.5696E-09 (X2 X4)2 + 5.0713E-04 (X1 X2)3 - 2.3102E-05 (X1 X2)4 +
3.8463E-07 (X1 X2)5 + 2.5845E-05 X1 X2 X4 + 3.7094E-10 X1 X3 X5 - 2.7815E-10 (X1 X2 X4)2 +
7.4696E+01 X2/X4 - 5.6392E-07 X3/X4 - 8.5347E+00 X4/X3 + 4.0667E+02 (X1/X4)2 - 5.1979E+00
FrDR,ST,H2 = - 3.8839E-01 X1 - 1.4226E-01 X2 + 2.3885E-07 X3 - 2.0271E-02 X4 + 7.1026E-02 X5 +
8.2973E-03 log(X3) + 5.1684E+00 log(X4) - 4.7005E-03 exp(X2) + 1.2441E-05 X42 - 3.1192E-09 X4
3 +
2.1017E-04 X25 - 6.1922E-09 X1 X3 + 3.5515E-04 X1 X4 - 2.8508E-09 X2 X3 + 6.2290E-05 X2 X4 -
1.8831E-02 X2 X5 - 1.9660E-10 X3 X4 - 5.0218E-04 (X2 X5)2 - 4.7712E-08 (X4 X5)2 + 7.9675E-05 X2 X4
89
X5 - 2.1370E-09 (X2 X4 X5)2 + 1.0868E+02 X1/X4 + 4.4728E+01 X2/X4 + 1.8274E-02 X2/X5 - 5.6176E-05
X3/X4 + 1.9529E+01 X4/X3 - 2.2319E+01 X5/X4 - 2.4872E+01
Bounds on the input variables are given as per the bounds for model development. These
can be found in Appendix C.
5.3. Process Synthesis Results
5.3.1. Case Studies based on Equilibrium Reactor Model
Apart from the thermodynamic analysis, two case studies based upon the set of
equilibrium reactors embedded in the process synthesis models have been performed
with fixed syngas ratios. The optimal configurations are presented in Figure 5.2. While
the configuration remains the same, the CO2 utilization varies with syngas ratio. When
the syngas ratio is fixed to be 2.5, with auxiliary emissions accounted for, the maximum
utilization is found to be 63.85%. However, when the syngas ratio is fixed to be 3, the
maximum utilization reduces to 41.5%.
Figure 5.2. Optimal CO2 utilization process configuration obtained using
equilibrium-based models.
B_H2
FG
BG
Water
CDSR
TR
PODR B_CO2
B_CH4
B_O2
B_H2O
B_N2
FGS
BGS
ES
90
5.3.2. Case Studies with Stoichiometry-based Process Synthesis Model
The first case study was based upon the simple stoichiometric reactor model. In
this model, the ratios were fixed according to literature and the auxiliary emissions were
not taken into account. The inlet flowrate of flowrate was fixed to be 1 mole per second.
The syngas ratio had a lower bound of 1.5 and an upper bound of 2.5. The resulting
optimal configuration of the superstructure is given in figure 5.3. The syngas ratio
obtained was 2.5 and the maximum utilization of CO2 was found to be 41.24%.
Figure 5.3. Optimal CO2 utilization process configuration obtained using
stoichiometry-based models.
More case studies were performed with the stoichiometry-based synthesis model
by fixing the source and feed flowrates of the methane sources to study the utilization
with a limited amount of raw materials. The results are reported in Table 5.1.
B_H2
FG
BG
Water
CDSR
TR
B_CO2
B_CH4
B_O2
B_H2O
B_N2
FGS
BGS
ES
91
Table 5.1. Optimal CO2 utilization results for different methane sources.
5.3.3. Cost Analysis for the Process Synthesis Model
As given in the model, a cost function has been added to the process synthesis
model, accounting for the total, that is, the sum of the investment and operating cost of
utilizing CO2. We have considered two objective functions here, one, maximizing the net
CO2 utilization and two, minimizing the total cost of utilization. The optimal
configuration for maximum CO2 utilization is presented in figure 5.4. The maximum
utilization is 57.8% for a syngas ratio of 2 at a total cost of 81.09 million $/year. The
optimal configuration for minimum cost is presented in figure 5.5. The minimum cost is
32.54 million $/year for a syngas ratio of 2 for a utilization of -18.34% (negative, that
means that CO2 is produced in the process).
Figure 5.4. Optimal CO2 utilization process configuration with maximum CO2
utilization.
B_H2
FG
BG
Water
CDSR
TR
B_CO2
B_CH4
B_O2
B_H2O
B_N2
FGS
BGS
ES
92
5.3.4. Synthesis Results with Detailed Models
The process synthesis model with the surrogate models for the detailed reactor
models were solved for maximum CO2 utilization. The syngas ratios were varied for
each case from 0.1 to 3 by an increment of 0.1. The output optimal CO2 utilization is
plotted against the syngas ratio.
Figure 5.5. Optimal CO2 utilization process configuration with minimum cost.
Finally, we compare our process synthesis results with the previously obtained
theoretical limit on the maximum CO2 utilization (Figure 5.6). It is evident that even the
best possible configurations based on our superstructure cannot achieve a CO2 utilization
value within 15% of the theoretically maximum possible utilization. The smallest gap
between these two cases is found for a syngas ratio of 1.7, which suggests that a syngas
ratio of 1.7 is energetically most desirable for CO2 utilization.
B_H2
FG
BG
Water
TR
B_CO2
B_CH4
B_O2
B_H2O
B_N2
FGS
BGS
ES
93
Figure 5.6. Maximum CO2 utilization: (a) based on thermodynamic analysis, (b) based
on optimal process synthesis with rigorous process considerations.
0
20
40
60
80
100
0 1 2 3
CO
2 u
tili
za
tio
n [
%]
syngas H2 to CO ratio
Theoretical maximum
Max. CO2 utilzation based on rigorousprocess synthesis
94
CHAPTER VI
CONCLUSIONS AND RECOMMENDATIONS
6.1. Conclusions
The research entails the different pathways that CO2 can take without being
considered as a pollutant. Various alternatives have been explored and discussed with
special focus on synthesis gas as an intermediate. The challenges in the utilization of
carbon dioxide with respect to benchmarking and computational complexity has been
established and addressed in this thesis. Benchmarking based upon thermodynamic
analysis has led to theoretical bounds on possible utilization of carbon dioxide given
equilibrium conditions. It has come to light that there are thermodynamic constraints on
the reactor performance with respect to specific syngas ratios. The need for detailed
process models has been reiterated based on comparison between different models and
accurate models based on kinetics have been simulated and the effects of process
variables for different processes have been studied. The pseudo-homogeneous is found
to be sufficiently accurate based upon validation with experimental data to represent the
catalytic reactors. Algebraic surrogate models have been developed based on the pseudo-
homogeneous models and the models are validated with data and statistical measures. A
process synthesis superstructure embedding the different alternatives has been proposed
with different reactor models that either deems the complete process synthesis model a
nonlinear (NLP) optimization problem or a mixed integer nonlinear (MINLP)
optimization problem based on the reactor model of choice. The models are solved to
95
optimality using the global solver ANTIGONE for two different objectives,
maximization of CO2 utilization and minimization of total cost of syngas production.
Throughout the analysis, auxiliary emissions are considered as well and this gives the
net overall CO2 utilization possible.
6.2. Recommendations
This research has an enormous scope and potential in identifying possible ways
of reducing carbon dioxide emissions and utilizing it to produce commercially value-
added products. Though extensive research and analysis has been done in this thesis with
respect to alternatives to produce syngas from carbon dioxide, there is vast scope for
future work and the following recommendations are made in that front.
1. The thermodynamic analysis based on the minimization of energy can be extended to
identify the products that could formed from a set of reactants, such that minimum
energy is used by the process.
2. The superstructure could be extended beyond syngas to chemicals and fuels to
identify the best products that could be produced from flue gas and other sources.
3. The problem could be dealt with at a multiscale level where material selection could
be done based upon choosing the optimal material properties for achieving maximum
conversion.
96
REFERENCES
1. (IEA), I. E. A. CO2 Emissions From Fuel Combustion - Highlights - 2015
Edition; 2015.
2. Bruckner T., I. A. B., Y. Mulugetta, H. Chum, A. de la Vega Navarro, J.
Edmonds, A. Faaij, B. Fungtammasan, A. Garg, E. Hertwich, D. Honnery, D. Infield, M.
Kainuma, S. Khennas, S. Kim, H.B. Nimir, K. Riahi, N. Strachan, R. Wiser, and X.
Zhang, Energy Systems. In: Climate Change 2014: Mitigation of Climate Change.
Contribution of Working Group III to the Fifth Assessment Report of the
Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge,
United Kingdom and New York, NY, USA, 2014.
3. IPCC IPCC Special Report on Carbon Dioxide Capture and Storage; Cambridge
University Press, Cambridge, United Kingdom and New York, NY, USA, 2005; p 442.
4. Hasan, M. M. F.; Boukouvala, F.; First, E. L.; Floudas, C. A., Nationwide,
Regional, and Statewide CO2 Capture, Utilization, and Sequestration Supply Chain
Network Optimization. Industrial & Engineering Chemistry Research 2014, 53 (18),
7489-7506.
5. DOE/NETL Carbon Dioxide Capture and Storage RD&D Roadmap; 2010.
6. Yuan, Z.; Eden, M. R.; Gani, R., Toward the Development and Deployment of
Large-Scale Carbon Dioxide Capture and Conversion Processes. Industrial &
Engineering Chemistry Research 2016, 55 (12), 3383-3419.
7. Kondratenko, E. V.; Mul, G.; Baltrusaitis, J.; Larrazabal, G. O.; Perez-Ramirez,
J., Status and perspectives of CO2 conversion into fuels and chemicals by catalytic,
97
photocatalytic and electrocatalytic processes. Energy & Environmental Science 2013, 6
(11), 3112-3135.
8. Xiaoding, X.; Moulijn, J., Mitigation of CO2 by chemical conversion: Plausible
chemical reactions and promising products. Energy & Fuels 1996, 10 (2), 305-325.
9. Rostrup-Nielsen, J. R., Syngas in perspective. Catalysis Today 2002, 71 (3–4),
243-247.
10. Schulz, H., Short history and present trends of Fischer–Tropsch synthesis.
Applied Catalysis A: General 1999, 186 (1), 3-12.
11. Siirola, J. J., The impact of shale gas in the chemical industry. AIChE Journal
2014, 60 (3), 810-819.
12. Ehlinger, V. M.; Gabriel, K. J.; Noureldin, M. M.; El-Halwagi, M. M., Process
design and integration of shale gas to methanol. ACS Sustainable Chemistry &
Engineering 2013, 2 (1), 30-37.
13. Niziolek, A. M.; Onel, O.; Floudas, C. A., Production of benzene, toluene, and
xylenes from natural gas via methanol: Process synthesis and global optimization.
AIChE Journal 2016, 62 (5), 1531-1556.
14. Martinez-Gomez, J.; Nápoles-Rivera, F.; Ponce-Ortega, J. M.; El-Halwagi, M.
M., Optimization of the production of syngas from shale gas with economic and safety
considerations. Applied Thermal Engineering 2017, 110, 678-685.
15. Centi, G.; Iaquaniello, G.; Perathoner, S., Can we afford to waste carbon
dioxide? Carbon dioxide as a valuable source of carbon for the production of light
olefins. ChemSusChem 2011, 4 (9), 1265-1273.
98
16. DOE/NETL Liquid Fuels. https://www.netl.doe.gov/research/coal/energy-
systems/gasification/gasifipedia/methanol.
17. Dry, M. E., The Fischer–Tropsch process: 1950–2000. Catalysis Today 2002, 71
(3–4), 227-241.
18. Steynberg, A.; Dry, M., Fischer-Tropsch Technology. Elsevier Science: 2004.
19. Cozad, A.; Sahinidis, N. V.; Miller, D. C., Learning surrogate models for
simulation‐based optimization. AIChE Journal 2014, 60 (6), 2211-2227.
20. Aresta, M.; Dibenedetto, A.; Quaranta, E., State of the art and perspectives in
catalytic processes for CO2 conversion into chemicals and fuels: The distinctive
contribution of chemical catalysis and biotechnology. Journal of Catalysis 2016, 343, 2-
45.
21. Centi, G.; Perathoner, S., Opportunities and prospects in the chemical recycling
of carbon dioxide to fuels. Catalysis Today 2009, 148 (3), 191-205.
22. Aresta, M.; Dibenedetto, A.; Quaranta, E., State of the art and perspectives in
catalytic processes for CO2 conversion into chemicals and fuels: The distinctive
contribution of chemical catalysis and biotechnology. Journal of Catalysis 2016, 343, 2-
45.
23. Dutta, A.; Farooq, S.; Karimi, I. A.; Khan, S. A., Assessing the potential of CO2
utilization with an integrated framework for producing power and chemicals. Journal of
CO2 Utilization 2017, 19, 49-57.
99
24. Aresta, M.; Dibenedetto, A.; Angelini, A., Catalysis for the valorization of
exhaust carbon: from CO2 to chemicals, materials, and fuels. Technological use of CO2.
Chemical reviews 2013, 114 (3), 1709-1742.
25. Dai, W.-L.; Luo, S.-L.; Yin, S.-F.; Au, C.-T., The direct transformation of carbon
dioxide to organic carbonates over heterogeneous catalysts. Applied Catalysis A:
General 2009, 366 (1), 2-12.
26. Kongpanna, P.; Babi, D. K.; Pavarajarn, V.; Assabumrungrat, S.; Gani, R.,
Systematic methods and tools for design of sustainable chemical processes for CO2
utilization. Computers & Chemical Engineering 2016, 87, 125-144.
27. Müller, K.; Mokrushina, L.; Arlt, W., Thermodynamic constraints for the
utilization of CO2. Chemie Ingenieur Technik 2014, 86 (4), 497-503.
28. Amin, N. A. S.; Yaw, T. C., Thermodynamic equilibrium analysis of combined
carbon dioxide reforming with partial oxidation of methane to syngas. International
Journal of Hydrogen Energy 2007, 32 (12), 1789-1798.
29. Özkara-Aydınoğlu, Ş., Thermodynamic equilibrium analysis of combined carbon
dioxide reforming with steam reforming of methane to synthesis gas. international
journal of hydrogen energy 2010, 35 (23), 12821-12828.
30. Sahebdelfar, S.; Ravanchi, M. T., Carbon dioxide utilization for methane
production: A thermodynamic analysis. Journal of Petroleum Science and Engineering
2015, 134, 14-22.
100
31. Chein, R.; Chen, Y.; Yu, C.; Chung, J., Thermodynamic analysis of dry
reforming of CH4 with CO2 at high pressures. Journal of Natural Gas Science and
Engineering 2015, 26, 617-629.
32. Nematollahi, B.; Rezaei, M.; Lay, E. N.; Khajenoori, M., Thermodynamic
analysis of combined reforming process using Gibbs energy minimization method: In
view of solid carbon formation. Journal of Natural Gas Chemistry 2012, 21 (6), 694-
702.
33. Nikoo, M. K.; Amin, N. A. S., Thermodynamic analysis of carbon dioxide
reforming of methane in view of solid carbon formation. Fuel Processing Technology
2011, 92 (3), 678-691.
34. Swapnesh, A.; Srivastava, V. C.; Mall, I. D., Comparative Study on
Thermodynamic Analysis of CO2 Utilization Reactions. Chemical Engineering &
Technology 2014, 37 (10), 1765-1777.
35. Cañete, B.; Gigola, C. E.; Brignole, N. l. B., Synthesis gas processes for
methanol production via CH4 reforming with CO2, H2O, and O2. Industrial &
Engineering Chemistry Research 2014, 53 (17), 7103-7112.
36. Demidov, D.; Mishin, I.; Mikhailov, M., Gibbs free energy minimization as a
way to optimize the combined steam and carbon dioxide reforming of methane.
international journal of hydrogen energy 2011, 36 (10), 5941-5950.
37. Freitas, A. C.; Guirardello, R., Thermodynamic analysis of methane reforming
with CO2, CO2+H2O, CO2+O2 and CO2+air for hydrogen and synthesis gas production.
Journal of CO2 Utilization 2014, 7, 30-38.
101
38. Challiwala, M.; Ghouri, M.; Linke, P.; El-Halwagi, M.; Elbashir, N., A combined
thermo-kinetic analysis of various methane reforming technologies: Comparison with
dry reforming. Journal of CO2 Utilization 2017, 17, 99-111.
39. Wehinger, G. D.; Eppinger, T.; Kraume, M., Detailed numerical simulations of
catalytic fixed-bed reactors: Heterogeneous dry reforming of methane. Chemical
Engineering Science 2015, 122, 197-209.
40. Larentis, A. L.; De Resende, N. S.; Salim, V. M. M.; Pinto, J. C., Modeling and
optimization of the combined carbon dioxide reforming and partial oxidation of natural
gas. Applied Catalysis A: General 2001, 215 (1), 211-224.
41. Zhang, Y.; Zhang, S.; Lou, H. H.; Gossage, J. L.; Benson, T. J., Steam and dry
reforming processes coupled with partial oxidation of methane for CO2 emission
reduction. Chemical Engineering & Technology 2014, 37 (9), 1493-1499.
42. Baltrusaitis, J.; Luyben, W. L., Methane conversion to syngas for gas-to-liquids
(GTL): is sustainable CO2 reuse via dry methane reforming (DMR) cost competitive
with SMR and ATR processes? ACS Sustainable Chemistry & Engineering 2015, 3 (9),
2100-2111.
43. Luyben, W. L., Control of parallel dry methane and steam methane reforming
processes for Fischer–Tropsch syngas. Journal of Process Control 2016, 39, 77-87.
44. Noureldin, M. M.; Elbashir, N. O.; Gabriel, K. J.; El-Halwagi, M. M., A process
integration approach to the assessment of CO2 fixation through dry reforming. ACS
Sustainable Chemistry & Engineering 2015, 3 (4), 625-636.
102
45. Noureldin, M. M. B.; Elbashir, N. O.; El-Halwagi, M. M., Optimization and
Selection of Reforming Approaches for Syngas Generation from Natural/Shale Gas.
Industrial & Engineering Chemistry Research 2014, 53 (5), 1841-1855.
46. Luyben, W. L., Design and Control of the Dry Methane Reforming Process.
Industrial & Engineering Chemistry Research 2014, 53 (37), 14423-14439.
47. Ayodele, B. V.; Cheng, C. K., Process modelling, thermodynamic analysis and
optimization of dry reforming, partial oxidation and auto-thermal methane reforming for
hydrogen and syngas production. Chemical Product and Process Modeling 2015, 10 (4),
211-220.
48. Julian-Duran, L. M.; Ortiz-Espinoza, A. P.; El-Halwagi, M. M.; Jimenez-
Gutierrez, A., Techno-economic assessment and environmental impact of shale gas
alternatives to methanol. ACS Sustainable Chemistry & Engineering 2014, 2 (10), 2338-
2344.
49. Hernández, B.; Martín, M., Optimal process operation for biogas reforming to
methanol: Effects of dry reforming and biogas composition. Industrial & Engineering
Chemistry Research 2016, 55 (23), 6677-6685.
50. Gopaul, S. G.; Dutta, A., Dry reforming of multiple biogas types for syngas
production simulated using Aspen Plus: The use of partial oxidation and hydrogen
combustion to achieve thermo-neutrality. International Journal of Hydrogen Energy
2015, 40 (19), 6307-6318.
103
51. Arab Aboosadi, Z.; Jahanmiri, A. H.; Rahimpour, M. R., Optimization of tri-
reformer reactor to produce synthesis gas for methanol production using differential
evolution (DE) method. Applied Energy 2011, 88 (8), 2691-2701.
52. Li, Z.; Liu, P.; He, F.; Wang, M.; Pistikopoulos, E. N., Simulation and
exergoeconomic analysis of a dual-gas sourced polygeneration process with integrated
methanol/DME/DMC catalytic synthesis. Computers & Chemical Engineering 2011, 35
(9), 1857-1862.
53. Cho, W.; Song, T.; Mitsos, A.; McKinnon, J. T.; Ko, G. H.; Tolsma, J. E.;
Denholm, D.; Park, T., Optimal design and operation of a natural gas tri-reforming
reactor for DME synthesis. Catalysis Today 2009, 139 (4), 261-267.
54. Minutillo, M.; Perna, A., A novel approach for treatment of CO2 from fossil fired
power plants. Part B: The energy suitability of integrated tri-reforming power plants
(ITRPPs) for methanol production. international journal of hydrogen energy 2010, 35
(13), 7012-7020.
55. Kiss, A. A.; Pragt, J.; Vos, H.; Bargeman, G.; de Groot, M., Novel efficient
process for methanol synthesis by CO2 hydrogenation. Chemical Engineering Journal
2016, 284, 260-269.
56. Pérez-Fortes, M.; Schöneberger, J. C.; Boulamanti, A.; Tzimas, E., Methanol
synthesis using captured CO2 as raw material: techno-economic and environmental
assessment. Applied Energy 2016, 161, 718-732.
57. Van-Dal, É. S.; Bouallou, C., Design and simulation of a methanol production
plant from CO2 hydrogenation. Journal of Cleaner Production 2013, 57, 38-45.
104
58. Taghdisian, H.; Pishvaie, M. R.; Farhadi, F., Multi-objective optimization
approach for green design of methanol plant based on CO2-efficeincy indicator. Journal
of Cleaner Production 2015, 103, 640-650.
59. Roh, K.; Frauzem, R.; Nguyen, T. B.; Gani, R.; Lee, J. H., A methodology for
the sustainable design and implementation strategy of CO2 utilization processes.
Computers & Chemical Engineering 2016, 91, 407-421.
60. Richardson, J. T.; Paripatyadar, S. A., Carbon dioxide reforming of methane with
supported rhodium. Applied Catalysis 1990, 61 (1), 293-309.
61. Khalesi, A.; Arandiyan, H. R.; Parvari, M., Effects of Lanthanum Substitution by
Strontium and Calcium in La-Ni-Al Perovskite Oxides in Dry Reforming of Methane.
Chinese Journal of Catalysis 2008, 29 (10), 960-968.
62. Benguerba, Y.; Dehimi, L.; Virginie, M.; Dumas, C.; Ernst, B., Modelling of
methane dry reforming over Ni/Al2O3 catalyst in a fixed-bed catalytic reactor. Reaction
Kinetics, Mechanisms and Catalysis 2015, 114 (1), 109-119.
63. Akpan, E.; Sun, Y.; Kumar, P.; Ibrahim, H.; Aboudheir, A.; Idem, R., Kinetics,
experimental and reactor modeling studies of the carbon dioxide reforming of methane
(CDRM) over a new – catalyst in a packed bed tubular reactor. Chemical Engineering
Science 2007, 62 (15), 4012-4024.
64. Xu, J.; Froment, G. F., Methane steam reforming, methanation and water-gas
shift: I. Intrinsic kinetics. AIChE Journal 1989, 35 (1), 88-96.
105
65. Lutz, A. E.; Bradshaw, R. W.; Keller, J. O.; Witmer, D. E., Thermodynamic
analysis of hydrogen production by steam reforming. International Journal of Hydrogen
Energy 2003, 28 (2), 159-167.
66. Latham, D. A.; McAuley, K. B.; Peppley, B. A.; Raybold, T. M., Mathematical
modeling of an industrial steam-methane reformer for on-line deployment. Fuel
Processing Technology 2011, 92 (8), 1574-1586.
67. Murty, C. V. S.; Murthy, M. V. K., Modeling and simulation of a top-fired
reformer. Industrial & Engineering Chemistry Research 1988, 27 (10), 1832-1840.
68. Alhabdan, F. M.; Abashar, M. A.; Elnashaie, S. S. E., A flexible computer
software package for industrial steam reformers and methanators based on rigorous
heterogeneous mathematical models. Mathematical and Computer Modelling 1992, 16
(11), 77-86.
69. Pedernera, M. N.; Piña, J.; Borio, D. O.; Bucalá, V., Use of a heterogeneous two-
dimensional model to improve the primary steam reformer performance. Chemical
Engineering Journal 2003, 94 (1), 29-40.
70. Wesenberg, M. H.; Svendsen, H. F., Mass and Heat Transfer Limitations in a
Heterogeneous Model of a Gas-Heated Steam Reformer. Industrial & Engineering
Chemistry Research 2007, 46 (3), 667-676.
71. Mokheimer, E. M. A.; Ibrar Hussain, M.; Ahmed, S.; Habib, M. A.; Al-Qutub, A.
A., On the Modeling of Steam Methane Reforming. Journal of Energy Resources
Technology 2014, 137 (1), 012001-012001.
106
72. Onel, O.; Niziolek, A. M.; Butcher, H.; Wilhite, B. A.; Floudas, C. A., Multi-
scale Approaches for Gas-to-Liquids Process Intensification: CFD Modeling, Process
Synthesis, and Global Optimization. Computers & Chemical Engineering.
73. Rostrup-Nielsen, J. R.; Rostrup-Nielsen, T., Large-Scale Hydrogen Production.
CATTECH 2002, 6 (4), 150-159.
74. Trimm, D. L.; Lam, C.-W., The combustion of methane on platinum—alumina
fibre catalysts—I. Chemical Engineering Science 1980, 35 (6), 1405-1413.
75. Ma, L.; Trimm, D. L.; Jiang, C., The design and testing of an autothermal reactor
for the conversion of light hydrocarbons to hydrogen I. The kinetics of the catalytic
oxidation of light hydrocarbons. Applied Catalysis A: General 1996, 138 (2), 275-283.
76. De Groote, A. M.; Froment, G. F., Simulation of the catalytic partial oxidation of
methane to synthesis gas. Applied Catalysis A: General 1996, 138 (2), 245-264.
77. Zhu, J.; Zhang, D.; King, K. D., Reforming of CH4 by partial oxidation:
thermodynamic and kinetic analyses. Fuel 2001, 80 (7), 899-905.
78. de Smet, C. R. H.; de Croon, M. H. J. M.; Berger, R. J.; Marin, G. B.; Schouten,
J. C., Design of adiabatic fixed-bed reactors for the partial oxidation of methane to
synthesis gas. Application to production of methanol and hydrogen-for-fuel-cells.
Chemical Engineering Science 2001, 56 (16), 4849-4861.
79. Donazzi, A.; Beretta, A.; Groppi, G.; Forzatti, P., Catalytic partial oxidation of
methane over a 4% Rh/α-Al2O3 catalyst: Part I: Kinetic study in annular reactor. Journal
of Catalysis 2008, 255 (2), 241-258.
107
80. Deutschmann, O.; Schmidt, L. D., Two-dimensional modeling of partial
oxidation of methane on rhodium in a short contact time reactor. Symposium
(International) on Combustion 1998, 27 (2), 2283-2291.
81. Soria, M. A.; Mateos-Pedrero, C.; Guerrero-Ruiz, A.; Rodríguez-Ramos, I.,
Thermodynamic and experimental study of combined dry and steam reforming of
methane on Ru/ZrO2-La2O3 catalyst at low temperature. International Journal of
Hydrogen Energy 2011, 36 (23), 15212-15220.
82. Lim, Y.; Lee, C.-J.; Jeong, Y. S.; Song, I. H.; Lee, C. J.; Han, C., Optimal Design
and Decision for Combined Steam Reforming Process with Dry Methane Reforming to
Reuse CO2 as a Raw Material. Industrial & Engineering Chemistry Research 2012, 51
(13), 4982-4989.
83. Shahkarami, P.; Fatemi, S., Mathematical Modeling and Optimization of
Combined Steam and Dry Reforming of Methane Process in Catalytic Fluidized Bed
Membrane Reactor. Chemical Engineering Communications 2015, 202 (6), 774-786.
84. O'Connor, A. M.; Ross, J. R., The effect of O2 addition on the carbon dioxide
reforming of methane over Pt/ZrO2 catalysts. Catalysis Today 1998, 46 (2), 203-210.
85. Larentis, A. L.; de Resende, N. S.; Salim, V. M. M.; Pinto, J. C., Modeling and
optimization of the combined carbon dioxide reforming and partial oxidation of natural
gas. Applied Catalysis A: General 2001, 215 (1–2), 211-224.
86. Chan, S.; Wang, H., Thermodynamic analysis of natural-gas fuel processing for
fuel cell applications. International Journal of Hydrogen Energy 2000, 25 (5), 441-449.
108
87. Avci, A. K.; Trimm, D. L.; İlsen Önsan, Z., Heterogeneous reactor modeling for
simulation of catalytic oxidation and steam reforming of methane. Chemical
Engineering Science 2001, 56 (2), 641-649.
88. Hoang, D. L.; Chan, S. H., Modeling of a catalytic autothermal methane reformer
for fuel cell applications. Applied Catalysis A: General 2004, 268 (1–2), 207-216.
89. Halabi, M. H.; de Croon, M. H. J. M.; van der Schaaf, J.; Cobden, P. D.;
Schouten, J. C., Modeling and analysis of autothermal reforming of methane to
hydrogen in a fixed bed reformer. Chemical Engineering Journal 2008, 137 (3), 568-
578.
90. Lee, S.-H.; Cho, W.; Ju, W.-S.; Cho, B.-H.; Lee, Y.-C.; Baek, Y.-S., Tri-
reforming of CH4 using CO2 for production of synthesis gas to dimethyl ether. Catalysis
Today 2003, 87 (1–4), 133-137.
91. Song, C.; Pan, W., Tri-reforming of methane: a novel concept for catalytic
production of industrially useful synthesis gas with desired H2/CO ratios. Catalysis
Today 2004, 98 (4), 463-484.
92. Joo, O.-S.; Jung, K.-D.; Moon, I.; Rozovskii, A. Y.; Lin, G. I.; Han, S.-H.; Uhm,
S.-J., Carbon Dioxide Hydrogenation To Form Methanol via a Reverse-Water-Gas-Shift
Reaction (the CAMERE Process). Industrial & Engineering Chemistry Research 1999,
38 (5), 1808-1812.
93. Ergun, S.; Orning, A. A., Fluid flow through randomly packed columns and
fluidized beds. Industrial & Engineering Chemistry 1949, 41 (6), 1179-1184.
109
94. Ergun, S., Mass-transfer rate in packed columns-its analogy to pressure loss.
Chemical Engineering Progress 1952, 48 (5), 227-236.
95. Smith, J. M., Heat and mass transfer in packed beds, N. Wakao and S. Kaguei,
Gordon and Breach Science Publishers, 1983,364 pages. AIChE Journal 1983, 29 (6),
1055-1055.
96. Misener, R.; Floudas, C. A., ANTIGONE: Algorithms for coNTinuous / Integer
Global Optimization of Nonlinear Equations. Journal of Global Optimization 2014, 59
(2), 503-526.
97. Gallucci, F.; Paturzo, L.; Basile, A., A simulation study of the steam reforming
of methane in a dense tubular membrane reactor. International Journal of Hydrogen
Energy 2004, 29 (6), 611-617.
98. Cozad, A.; Sahinidis, N. V.; Miller, D. C., Learning surrogate models for
simulation-based optimization. AIChE Journal 2014, 60 (6), 2211-2227.
99. Hasan, M. M. F.; Baliban, R. C.; Elia, J. A.; Floudas, C. A., Modeling,
Simulation, and Optimization of Postcombustion CO2 Capture for Variable Feed
Concentration and Flow Rate. 1. Chemical Absorption and Membrane Processes.
Industrial & Engineering Chemistry Research 2012, 51 (48), 15642-15664.
100. Administration, U. S. E. I. Frequently Asked Questions About Environment.
https://www.eia.gov/tools/faqs/faq.cfm?id=74&t=11.
101. Hasan, M. M. F.; First, E. L.; Floudas, C. A., Cost-effective CO2 capture based
on in silico screening of zeolites and process optimization. Physical Chemistry Chemical
Physics 2013, 15 (40), 17601-17618.
110
102. EIA, U. S. Natural Gas.
https://www.eia.gov/dnav/ng/ng_pri_sum_dcu_nus_m.htm.
103. Barker, J. C. Methane Fuel Gas from Livestock Wastes A Summary North
Carolina Cooperative Extension Service [Online], 2001.
https://www.bae.ncsu.edu/extension/ext-publications/waste/animal/ebae-071-80-
methane-gas-barker.pdf.
104. Baliban, R. C.; Elia, J. A.; Floudas, C. A., Toward Novel Hybrid Biomass, Coal,
and Natural Gas Processes for Satisfying Current Transportation Fuel Demands, 1:
Process Alternatives, Gasification Modeling, Process Simulation, and Economic
Analysis. Industrial & Engineering Chemistry Research 2010, 49 (16), 7343-7370.
105. First, E. L.; Hasan, M.; Floudas, C. A., Discovery of novel zeolites for natural
gas purification through combined material screening and process optimization. AIChE
Journal 2014, 60 (5), 1767-1785.
106. NETL, L. T., Inc DOE/NETL ADVANCED CARBON DIOXIDE CAPTURE
R&D PROGRAM:TECHNOLOGY UPDATE; 2013.
107. Hong, J.; Chaudhry, G.; Brisson, J. G.; Field, R.; Gazzino, M.; Ghoniem, A. F.,
Analysis of oxy-fuel combustion power cycle utilizing a pressurized coal combustor.
Energy 2009, 34 (9), 1332-1340.
111
APPENDIX A
LIST OF SUBSETS FOR THE PROCESS SYNTHESIS MODEL
Set of raw material blocks , 𝑅𝑀 = {𝐹𝐺, 𝑁𝐺, 𝐵𝐺, 𝐴𝑖𝑟, 𝑊𝑎𝑡𝑒𝑟}
Set of Separators, 𝑆 = {𝑊𝑆, 𝐶𝐶𝑆, 𝑂𝑋𝑆, 𝑁𝐺𝑆, 𝐵𝐺𝑆, 𝐴𝑆, 𝐸𝑆}
Set of component blocks, 𝐶𝐵 = {𝐵_𝐶𝑂2, 𝐵_𝐻2𝑂, 𝐵_𝑂2, 𝐵_𝑁2, 𝐵_𝐶𝐻4, 𝐵_𝐻2}
Set of Reactors, 𝑅 = {𝐸𝑆, 𝐷𝑅, 𝑃𝑂𝑋, 𝑆𝑀𝑅, 𝐶𝐷𝑆𝑀𝑅, 𝑃𝑂𝐷𝑅, 𝑃𝑂𝑆𝑀𝑅, 𝑇𝑅, 𝑅𝑊𝐺𝑆}
Set of blocks from which there is input to Separator Blocks
𝐼𝑊𝑆 = {𝐹𝐺}
𝐼𝐶𝐶𝑆 = {𝑊𝑆}
𝐼𝑂𝑋𝑆 = {𝐶𝐶𝑆}
𝐼𝑁𝐺𝑆 = {𝑁𝐺}
𝐼𝐵𝐺𝑆 = {𝐵𝐺}
𝐼𝐴𝑆 = {𝐴𝑖𝑟}
𝐼𝐸𝑆 = {𝑊𝑎𝑡𝑒𝑟}
Set of blocks from which there is input to Component Blocks
𝐼𝐵_𝐶𝑂2= {𝐶𝐶𝑆, 𝑁𝐺𝑆, 𝐵𝐺𝑆}
𝐼𝐵_𝐶𝐻4= {𝑁𝐺𝑆, 𝐵𝐺𝑆}
𝐼𝐵_𝑂2= {𝑂𝑋𝑆, 𝐴𝑆, 𝐸𝑆}
𝐼𝐵_𝐻2𝑂 = {𝑊𝑆, 𝑊𝑎𝑡𝑒𝑟}
𝐼𝐵_𝐻2= {𝐸𝑆}
𝐼𝐵_𝑁2= {𝑂𝑋𝑆, 𝐴𝑆}
112
Set of input blocks to Reactors
𝐼𝐷𝑅 = {𝐵_𝐶𝑂2, 𝐵_𝐶𝐻4}
𝐼𝑆𝑀𝑅 = {𝐵_𝐻2𝑂, 𝐵_𝐶𝐻4}
𝐼𝑃𝑂𝑋 = {𝐵_𝑂2, 𝐵_𝐶𝐻4}
𝐼𝐶𝐷𝑆𝑀𝑅 = {𝐵_𝐶𝑂2, 𝐵_𝐻2𝑂, 𝐵_𝐶𝐻4}
𝐼𝑃𝑂𝐷𝑅 = {𝐵_𝐶𝑂2, 𝐵_𝑂2, 𝐵_𝐶𝐻4}
𝐼𝑃𝑂𝑆𝑀𝑅 = {𝐵_𝐻2𝑂, 𝐵_𝑂2, 𝐵_𝐶𝐻4}
𝐼𝑇𝑅 = {𝐵_𝐶𝑂2, 𝐵_𝐻2𝑂, 𝐵_𝑂2, 𝐵_𝐶𝐻4}
𝐼𝑅𝑊𝐺𝑆 = {𝐵_𝐶𝑂2, 𝐵_𝐻2}
Set of blocks receiving streams from Raw material blocks
𝐽𝐹𝐺 = {𝑊𝑆}
𝐽𝑁𝐺 = {𝑁𝐺𝑆}
𝐽𝐵𝐺 = {𝐵𝐺𝑆}
𝐽𝐴𝑖𝑟 = {𝐴𝑆}
𝐽𝑊𝑎𝑡𝑒𝑟 = {𝐸𝑆, 𝐵_𝐻2𝑂}
Set of blocks receiving streams from Separator blocks
𝐽𝑊𝑆 = {𝐵_𝐻2𝑂, 𝐶𝐶𝑆}
𝐽𝐶𝐶𝑆 = {𝑂𝑋𝑆, 𝐵_𝐶𝑂2}
𝐽𝑂𝑋𝑆 = {𝐵_𝑁2, 𝐵_𝑂2}
𝐽𝑁𝐺𝑆 = {𝐵_𝐶𝑂2, 𝐵_𝐶𝐻4}
𝐽𝐵𝐺𝑆 = {𝐵_𝐶𝑂2, 𝐵_𝐶𝐻4}
𝐽𝐴𝑆 = {𝐵_𝑂2, 𝐵_𝑁2}
113
𝐽𝐸𝑆 = {𝐵_𝑂2, 𝐵_𝐻2}
Set of blocks receiving streams from Component Blocks
𝐽𝐵_𝐶𝑂2= {𝐷𝑅, 𝐶𝐷𝑆𝑀𝑅, 𝑃𝑂𝐷𝑅, 𝑇𝑅, 𝑅𝑊𝐺𝑆}
𝐽𝐵_𝐶𝐻4= {𝐷𝑅, 𝑃𝑂𝑋, 𝑆𝑀𝑅, 𝐶𝐷𝑆𝑀𝑅, 𝑃𝑂𝐷𝑅, 𝑃𝑂𝑆𝑀𝑅, 𝑇𝑅}
𝐽𝐵_𝑂2= {𝑃𝑂𝑋, 𝑃𝑂𝐷𝑅, 𝑃𝑂𝑆𝑀𝑅, 𝑇𝑅}
𝐽𝐵_𝐻2𝑂 = {𝑆𝑀𝑅, 𝐶𝐷𝑆𝑀𝑅, 𝑃𝑂𝑆𝑀𝑅, 𝑇𝑅}
𝐽𝐵_𝐻2= {𝑅𝑊𝐺𝑆, 𝑆𝑇}
𝐽𝐵_𝑁2= {𝑣𝑒𝑛𝑡}
Set of blocks receiving streams from Reactor Blocks
𝐽𝐷𝑅 = {𝑆𝑇}
𝐽𝑆𝑀𝑅 = {𝑆𝑇}
𝐽𝑃𝑂𝑋 = {𝑆𝑇}
𝐽𝐶𝐷𝑆𝑀𝑅 = {𝑆𝑇}
𝐽𝑃𝑂𝐷𝑅 = {𝑆𝑇}
𝐽𝑃𝑂𝑆𝑀𝑅 = {𝑆𝑇}
𝐽𝑇𝑅 = {𝑆𝑇}
𝐽𝑅𝑊𝐺𝑆 = {𝑆𝑇}
Set of component blocks from which there is input to reactor block
𝐼𝐷𝑅,𝐶𝑂2= {𝐵_𝐶𝑂2}
𝐼𝐷𝑅,𝐶𝐻4= {𝐵_𝐶𝐻4}
𝐼𝑆𝑀𝑅,𝐻2𝑂 = {𝐵_𝐻2𝑂}
114
𝐼𝑆𝑀𝑅,𝐶𝐻4= {𝐵_𝐶𝐻4}
𝐼𝑃𝑂𝑋,𝑂2= {𝐵_𝑂2}
𝐼𝑃𝑂𝑋,𝐶𝐻4= {𝐵_𝐶𝐻4}
𝐼𝐶𝐷𝑆𝑀𝑅,𝐶𝑂2= {𝐵_𝐶𝑂2}
𝐼𝐶𝐷𝑆𝑀𝑅,𝐻2𝑂 = {𝐵_𝐻2𝑂}
𝐼𝐶𝐷𝑆𝑀𝑅,𝐶𝐻4= {𝐵_𝐶𝐻4}
𝐼𝑃𝑂𝐷𝑅,𝐶𝑂2= {𝐵_𝐶𝑂2}
𝐼𝑃𝑂𝐷𝑅,𝑂2= {𝐵_𝑂2}
𝐼𝑃𝑂𝐷𝑅,𝐶𝐻4= {𝐵_𝐶𝐻4}
𝐼𝑃𝑂𝑆𝑀𝑅,𝐻2𝑂 = {𝐵_𝐻2𝑂}
𝐼𝑃𝑂𝑆𝑀𝑅,𝑂2= {𝐵_𝑂2}
𝐼𝑃𝑂𝑆𝑀𝑅,𝐶𝐻4= {𝐵_𝐶𝐻4}
𝐼𝑇𝑅,𝐶𝑂2= {𝐵_𝐶𝑂2}
𝐼𝑇𝑅,𝐻2𝑂 = {𝐵_𝐻2𝑂}
𝐼𝑇𝑅,𝑂2= {𝐵_𝑂2}
𝐼𝑇𝑅,𝐶𝐻4= {𝐵_𝐶𝐻4}
𝐼𝑅𝑊𝐺𝑆,𝐻2= {𝐵_𝐻2}
𝐼𝑅𝑊𝐺𝑆,𝐶𝑂2= {𝐵_𝐶𝑂2}
Set of first layer raw material blocks from which there is input to separator i
𝑅𝑆𝑊𝑆 = {𝐹𝐺}
𝑅𝑆𝐶𝐶𝑆 = {𝐹𝐺}
115
𝑅𝑆𝑂𝑋𝑆 = {𝐹𝐺}
𝑅𝑆𝑁𝐺𝑆 = {𝑁𝐺}
𝑅𝑆𝐵𝐺𝑆 = {𝐵𝐺}
𝑅𝑆𝐴𝑆 = {𝐴𝑖𝑟}
𝑅𝑆𝐸𝑆 = {𝑊𝑎𝑡𝑒𝑟}
Set of Components in inlet stream to Raw material blocks
𝑀𝐹𝐺 = {𝐶𝑂2, 𝐻2𝑂, 𝑂2, 𝑁2}
𝑀𝐵𝐺 = {𝐶𝑂2, 𝐶𝐻4}
𝑀𝑁𝐺 = {𝐶𝑂2, 𝐶𝐻4}
𝑀𝐴𝑖𝑟 = {𝑂2, 𝑁2}
𝑀𝑊𝑎𝑡𝑒𝑟 = {𝐻2𝑂}
Set of Components in inlet stream to Component block
𝑀𝐵_𝐶𝑂2= {𝐶𝑂2}
𝑀𝐵_𝑂2= {𝑂2}
𝑀𝐵_𝐶𝐻4= {𝐶𝐻4}
𝑀𝐵_𝐻2𝑂 = {𝐻2𝑂}
𝑀𝐵_𝐻2= {𝐻2}
𝑀𝐵_𝑁2= {𝑁2}
Set of components in inlet stream to Reactors
𝑀𝐷𝑅 = {𝐶𝑂2, 𝐶𝐻4}
𝑀𝑆𝑀𝑅 = {𝐻2𝑂, 𝐶𝐻4}
116
𝑀𝑃𝑂𝑋 = {𝑂2, 𝐶𝐻4}
𝑀𝐶𝐷𝑆𝑀𝑅 = {𝐶𝑂2, 𝐻2𝑂, 𝐶𝐻4}
𝑀𝑃𝑂𝐷𝑅 = {𝐶𝑂2, 𝑂2, 𝐶𝐻4}
𝑀𝑃𝑂𝑆𝑀𝑅 = {𝐻2𝑂, 𝑂2, 𝐶𝐻4}
𝑀𝑇𝑅 = {𝐶𝑂2, 𝐻2𝑂, 𝑂2, 𝐶𝐻4}
𝑀𝑅𝑊𝐺𝑆 = {𝐶𝑂2, 𝐻2}
Set of components in outlet streams from Reactors
𝑁𝐷𝑅 ∈ {𝐶𝑂2, 𝐶𝐻4, 𝐻2, 𝐶𝑂, 𝐻2𝑂}
𝑁𝑆𝑀𝑅 ∈ {𝐻2𝑂, 𝐶𝐻4, 𝐻2, 𝐶𝑂}
𝑁𝑃𝑂𝑋 ∈ {𝑂2, 𝐶𝐻4, 𝐻2, 𝐶𝑂}
𝑁𝐶𝐷𝑆𝑀𝑅 ∈ {𝐶𝑂2, 𝐻2𝑂, 𝐶𝐻4, 𝐻2, 𝐶𝑂}
𝑁𝑃𝑂𝐷𝑅 ∈ {𝐶𝑂2, 𝑂2, 𝐶𝐻4, 𝐻2, 𝐶𝑂}
𝑁𝑃𝑂𝑆𝑀𝑅 ∈ {𝐻2𝑂, 𝑂2, 𝐶𝐻4, 𝐻2, 𝐶𝑂}
𝑁𝑇𝑅 ∈ {𝐶𝑂2, 𝐻2𝑂, 𝑂2, 𝐶𝐻4, 𝐻2, 𝐶𝑂}
𝑁𝑅𝑊𝐺𝑆 = {𝐶𝑂2, 𝐻2, 𝐻2𝑂, 𝐶𝑂}
Components in product outlet
𝑀𝑠𝑦𝑛 = {𝐶𝑂, 𝐻2}
117
APPENDIX B
LIST OF PARAMETERS
Table B1. Fixed parameters.
Parameter Value Units
𝑓𝐹𝐺𝑓𝑒𝑒𝑑
1 mol/s
𝐹𝑆𝑈 100 mol/s
𝑅𝐿 1 -
𝑅𝑈 3 -
𝑇𝑟𝑒𝑓 298 K
Table B2. Inlet composition of component n in raw material block i (𝒚𝒊,𝒏𝒇𝒆𝒆𝒅
).
i n 𝑦𝑖,𝑛𝑓𝑒𝑒𝑑
FG CO2 0.075
FG H2O 0.145
FG O2 0.045
FG N2 0.735
NG CH4 1
NG CO2 0
BG CH4 0.6
BG CO2 0.4
Air O2 0.21
Air N2 0.79
Water H2O 1
118
Table B3. Conversion of the limiting reactant in reactor i (𝜼𝒊).
i Operating
conditions
𝜂𝑖
𝑇𝑝𝑖(°C) 𝑃𝑝𝑖(bar)
DR 550 1 0.8
POX 700 1 0.9
SMR 850 20 0.9
CDSMR 800 1 0.85
PODR 600 1 0.85
POSMR 600 1 0.9
TR 800 1 0.875
RWGS 400 1 0.55
Table B4. 𝜶𝒊,𝒏- Stoichiometric coefficient of component n at the inlet of block i.
n i ES DR SMR POX CDSMR PODR POSMR TR RWGS
CH4 0 -1 -1 -1 -2 -2 -2 -3 0
CO2 0 -1 0 0 -1 -1 0 -1 -1
H2O -1 0 -1 0 -1 0 -1 -1 1
O2 0.5 0 0 -0.5 0 -0.5 -0.5 -0.5 0
CO 0 2 1 1 3 3 2 4 1
H2 1 2 3 2 5 4 5 7 -1
N2 0 0 0 0 0 0 0 0 0
119
Table B5. Operating conditions and catalysts for reactors.
Reactor Temperature Range(°C) Pressure(bar) Catalyst
DR 400-1200 1-25 Ni/Al2O3
SMR 400-1200 1-25 Ni/Al2O3
POX 700-1200 1-25 Ni/Al2O3
CDSMR 400-1200 1-25 Ni-Ce-ZrO2
PODR 700-1200 1-25 Ru/Mg-Al2O3
POSMR 700-1200 1-25 Ni-based
TR 700-1200 1-25 Ni/MgO
RWGS 400-1200 1-25 CuO/ZnO/Al2O3
Table B6. Shomate equation constants.
𝑖 𝐴𝑖 𝐵𝑖 𝐶𝑖 𝐷𝑖 𝐸𝑖
B_CH4 -0.703029 108.4773 -42.52157 5.862788 0.6785
B_CO2 24.99735 55.18696 -33.69137 7.948387 -0.136638
B_H2O 30.09200 6.832514 6.793435 -2.534480 0.082139
B_O2 31.32234 -20.23531 57.86644 -36.50624 -0.007374
B_H2 33.066178 -11.36342 11.432816 -2.772874 -0.158558
B_CO 25.56759 6.096130 4.054656 -2.671301 0.131021
B_N2 19.50583 19.88705 -8.598535 1.369784 0.527601
120
B7. Volumetric composition (in %) of flue gas and CO2 emissions 99.
CO2 N2 O2 H2O
CO2 emissions (tons CO2
per MWh electricity)100
Coal-fired
power plant
14 72 4.3 9.7 0.939
NG-fired
power plant
8.6 71 12.6 7.8 0.55
For 1 mole/s FG,
FG
(mol/s)
CO2
(mol/s)
CO2
(kg/s)
CO2
emissions
(kg
CO2/kWhe)
Available
electricity (X)
(kWhe/mol FG)
Available
electricity (X)
(kWhe/mol CO2)
Coal-
fired 1 0.14 6.16e-3 0.939 6.56e-3 0.0468
NG-
fired 1 0.086 3.78e-3 0.55 6.87e-3 0.0799
Energy penalty for CO2 capture is 124 kwh per ton CO2 captured. 101
For 1 mol CO2, the energy penalty is 5.456e-3 kWhe.
The electricity required for separation of NG is 200 kW per mole NG, that is, 0.055
kWhe per mol NG.
Annualizing factor ∅ = 0.154
Compressor Equations
The compressor is assumed to be an adiabatic compressor.
The compressor duty is calculated by the following equation
121
𝑊𝑗 = ( ∑ 𝐹𝑖
𝑖∈𝑅𝑀
)𝛾
𝛾 − 1𝑅𝑇𝑟𝑒𝑓 [(
𝑃𝑟𝑒𝑎𝑐
𝑃𝑟𝑒𝑓)
𝛾−1𝛾
− 1]
The temperature change of the gases at the outlet of the compressor is given by
𝑇𝑐𝑜𝑚𝑝𝑜𝑢𝑡 = 𝑇𝑟𝑒𝑓 (
𝑃𝑟𝑒𝑎𝑐
𝑃𝑟𝑒𝑓)
(𝛾−1
𝛾)
Heater equations
𝑄𝑖 = ( ∑ 𝑐𝑝𝑖𝐹𝑖
𝑖∈𝑅𝑀
) (𝑇𝑟𝑒𝑎𝑐 − 𝑇𝑐𝑜𝑚𝑝𝑜𝑢𝑡 )
Cost functions
Cost of NG = 2.98 $/MMBTU
Hours/year = 8000
Seconds/hour = 3600
𝐶𝑜𝑝𝑎𝑛𝑛𝑢𝑎𝑙 = 𝐶𝑅𝑀 + 𝐶𝑆𝑒𝑝 + 𝐶𝑜𝑝
ℎ + 𝐶𝑜𝑝𝑐 + 𝐶𝑜𝑝
𝑟𝑒𝑎𝑐
𝐶𝑅𝑀 = ∑ 𝐶𝑖
𝑖∈𝑅𝑀
𝐹𝑖𝑓𝑒𝑒𝑑
×3600×8000
Table B8. Cost of raw materials.
Feed Reported Cost Ci - Cost ($/mol) Reference
FG - 0 -
NG $7/MMBTU 2.65e-3 EIA 102
BG $2.61/MMBtu 4.083e-3 Barker (2001) 103
Air - 0 -
Water $1.003/1000 kg 1.807e-5 Baliban et al. 104
𝐶𝑠𝑒𝑝 = 8000×3600[(𝐶𝑊𝑆 + 𝐶𝐶𝐶𝑆)𝑦𝐹𝐺,𝐶𝑂2
𝑓𝑒𝑒𝑑𝐹𝐹𝐺
𝑓𝑒𝑒𝑑+ 𝐶𝑁𝐺𝑆𝐹𝑁𝐺
𝑓𝑒𝑒𝑑+ 𝐶𝐵𝐺𝑆𝐹𝐵𝐺
𝑓𝑒𝑒𝑑
+ 𝐶𝐴𝑆𝑦𝐴𝑖𝑟,𝑂2
𝑓𝑒𝑒𝑑𝐹𝐴𝑖𝑟
𝑓𝑒𝑒𝑑+ 𝐶𝑊𝑎𝑡𝑒𝑟𝐹𝑊𝑎𝑡𝑒𝑟
𝑓𝑒𝑒𝑑]
𝑇𝐴𝐶 = ∅𝐶𝑖𝑛𝑣𝑡𝑜𝑡𝑎𝑙 + 𝐶𝑜𝑝
𝑡𝑜𝑡𝑎𝑙
𝐶𝑜𝑝𝑎𝑛𝑛𝑢𝑎𝑙 = ∑ 𝐶𝑖
𝑖∈𝑅𝑀
𝐹𝑖𝑓𝑒𝑒𝑑
+ 𝐶𝑒𝑌 + 𝐶ℎ ∑ 𝑄𝑖
𝑖∈𝐻
122
Table B9. Cost of separation.
Separator Reported Cost Parameter Calculated Cost Reference
WS 10.22 $/ton CO2 𝐶𝑊𝑆 4.496×10-4
$/mol CO2
Hasan et al. 101
CCS 16.07 $/ton CO2 𝐶𝐶𝐶𝑆 7.0699×10-
4$/mol CO2
Hasan et al. 101
NGS 0.15 $/MMBTU 𝐶𝑁𝐺𝑆 1.525×10-4
$/mol NG
First et al. 105
BGS $1.04/MMBTU 𝐶𝐵𝐺𝑆 5.76×10-4 $/mol
BG
First et al. 105
AS 31 $/ton O2 𝐶𝐴𝑆 9.92×10-4 $/mol
O2
NETL 106
ES 4.46 $/kg H2 𝐶𝑊𝑎𝑡𝑒𝑟 8.923×10-3
$/mol H2O
NREL
𝐶𝑜𝑝𝑐𝑜𝑚𝑝 = ∑ 𝑊𝑗
𝑗∈𝑅
𝐶𝑒𝑙𝑒𝑐×8000/1000
𝐶𝑜𝑝ℎ = 𝐶𝑁𝐺
ℎ ×3600×8000
𝐶𝑁𝐺ℎ = 𝐶𝑁𝐺
𝑀𝑀𝐵𝑇𝑈×𝐽_𝑀𝑀𝐵𝑇𝑈× ∑ 𝑄𝑖
𝑖∈𝑅
𝐶𝑁𝐺𝑀𝑀𝐵𝑇𝑈 = 7 $/MMBTU
𝐽_𝑀𝑀𝐵𝑇𝑈 = 9.471𝑒 − 10 MMBTU/J
𝐶𝑜𝑝𝑟𝑒𝑎𝑐 = 𝑤𝑡𝑐𝑎𝑡𝐶𝑐𝑎𝑡×8000×3600
Cost of catalyst 𝐶𝑐𝑎𝑡 is assumed to be $2/kg.
𝑤𝑡𝑐𝑎𝑡 = 𝜌𝑏𝑒𝑑 ∑ 𝑉𝑗
𝑗∈𝑅
𝑉𝑗 = 𝐴𝑗𝐿𝑗
𝐴𝑗 = 3×10−5 ∑ 𝐹𝑖,𝑗
𝑖∈𝐼𝑗
123
Capital cost functions
𝐶𝑖𝑛𝑣𝑡𝑜𝑡𝑎𝑙 = 𝐶𝐵𝑀𝐶 + 𝐶𝐵𝑀𝑓 + 𝐶𝐵𝑀𝑟
Bare module cost for compressor:
𝐶𝐵𝑀𝐶 = 𝐶𝑝𝐶𝑜 𝐹𝐵𝑀𝐶
𝑙𝑜𝑔10𝐶𝑝𝐶𝑜 = 𝐾1𝑐 + 𝐾2𝑐𝑙𝑜𝑔10(
𝑊
1000) + 𝐾3[𝑙𝑜𝑔10(𝑊/1000)]2
For centrifugal compressor, 𝐾1𝑐 = 2.2897, 𝐾2𝑐 = 1.3604, 𝐾3𝑐 = −0.1027
(𝑊
1000) 𝜖 [450𝑘𝑊, 3000𝑘𝑊]
𝐹𝐵𝑀𝑐 = 2.8 for centrifugal compressor, which is made of CS.
Bare module cost for furnace:
𝐶𝐵𝑀𝑓 = 𝐶𝑝𝑓𝑜 𝐹𝐵𝑀𝑓
𝑙𝑜𝑔10𝐶𝑝𝑓𝑜 = 𝐾1𝑓 + 𝐾2𝑓𝑙𝑜𝑔10(
𝑄
1000) + 𝐾3𝑓[𝑙𝑜𝑔10(𝑄/1000)]2
For nonreactive fired heater: 𝐾1𝑓 = 7.3488, 𝐾2𝑓 = −1.1666, 𝐾3𝑓 = 0.2028
𝑄 means duty, (𝑄/1000) 𝜖 [1000𝑘𝑊, 100000𝑘𝑊]
𝐹𝐵𝑀𝑓 = 2.2 for nonreactive fired heater, which is made of CS.
Bare module cost for reactor:
𝐶𝐵𝑀𝑟 = 𝐶𝑝𝑟𝑜 𝐹𝐵𝑀𝑟
𝑙𝑜𝑔10𝐶𝑝𝑟𝑜 = 𝐾1𝑟 + 𝐾2𝑟𝑙𝑜𝑔10𝑉 + 𝐾3𝑟[𝑙𝑜𝑔10(𝑉)]2
For mixer/settler reactor: 𝐾1𝑟 = 4.7166, 𝐾2𝑟 = 0.4479, 𝐾3𝑟 = 0.0004
𝑉 means volume, 𝑉 𝜖 [0.04𝑚3, 60𝑚3]
𝐹𝐵𝑀𝑟 = 4.0 for mixer/settler reactor.
124
Auxiliary Emissions
𝐸𝑚𝑖𝑠𝑠𝑖𝑜𝑛𝐴𝑢𝑥 = ∑ ∑ 𝐹𝑖,𝑗𝜑𝑗
𝑖∈𝐼𝑗𝑗∈𝑆
+ 𝜑ℎ ∑ 𝑄𝑖𝑖∈𝑅
− 𝜑𝑒 ∑ 𝑊𝑖
𝑖∈𝐸
Table B9. Auxiliary Emissions due to separation
j Calculated CO2 emitted (mol/s CO2 per mol/s feed) 𝜑𝑗
Reference
Flue gas
Separation (CCS)
0.55 100
Natural Gas
Separation
0.7 105
Biogas Separation 8.4 105
Air Separation 0.02058[5] 107
Water Electrolysis 1.2939
𝜑ℎ = 44.01×10−3×0.453592×117×9.471×10−10 = 1.89×10−11 mol/W
𝜑𝑒 = 0.55/(44.01×10−3) mol/s CO2/W
Table B10. Viscosity Parameters of the Species
𝜇𝑖0 (cP) 𝑇𝑖
0 (Rankine) 𝐶𝑖𝜇
CH4 0.012 491.67 197.8
CO2 0.01480 527.67 240
CO 0.01720 518.67 118
H2 0.00876 528.93 72
O2 0.02018 526.05 127
N2 0.01781 540.99 111
125
Nomenclature
𝑇𝐴𝐶 Total annual cost $/year
𝐶𝑖𝑛𝑣𝑡𝑜𝑡𝑎𝑙 Total investment cost $
∅ Annualizing Factor /year
𝐶𝑜𝑝𝑡𝑜𝑡𝑎𝑙 Total operating cost $/year
𝐶𝑅𝑀 Total cost of raw material $/year
𝐶𝑆𝑒𝑝 Cost of separation $/year
𝐶𝑜𝑝ℎ Operating cost of heater $/year
𝐶𝑜𝑝𝑐𝑜𝑚𝑝
Operating cost of compressor $/year
𝐶𝑜𝑝𝑟𝑒𝑎𝑐 Operating cost of reactor $/year
𝐶𝑖 Unit cost of raw material $/mol
𝑊𝑗 Compressor duty W
𝐶𝑒𝑙𝑒𝑐 Cost of electricity $/kWh
𝑄𝑖 Heat duty W
𝐽_𝑀𝑀𝐵𝑇𝑈 Joule to MMBTU MMBTU/J
𝐶𝑐𝑎𝑡 Cost of catalyst $/kg
𝑤𝑡𝑐𝑎𝑡 Weight of catalyst kg
𝜌𝑏𝑒𝑑 Density of catalyst bed kg/m3
𝑉𝑗 Volume of reactor j m3
𝐴𝑗 Area of reactor j m2
𝐿𝑗 Length of reactor j m
𝐶𝐵𝑀𝐶 Bare module cost for compressor $
𝐶𝐵𝑀𝑓 Bare module cost for furnace $
𝐶𝐵𝑀𝑟 Bare module cost for reactor $
𝜑𝑒 Emission per W electricity mol/s CO2/W
𝜑ℎ Emission per W heat mol/s CO2/W
𝜑𝑗 Emission for separator j mol/s CO2/(mol/s feed)
126
APPENDIX C
REACTOR MODELS, VARIABLE BOUNDS, MODEL STATISTICS
C.1. Equilibrium Reactor Modeling – Surrogate Model
Steam Reforming (SMR)
Input
Variables
Description Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of CH4 to SMR 0.1 10 Mol/s
X2 Molar flowrate of H2O to SMR 0.1 10 Mol/s
X3 Inlet pressure of gases to SMR 1e5 25e5 Pa
X4 Inlet temperature of gases to SMR 600 1200 K
Partial Oxidation (POX)
Input
Variables
Description Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of CH4 to POX 0.1 5 Mol/s
X2 Molar flowrate of O2 to POX 0.1 5 Mol/s
X3 Inlet pressure of gases to POX 1e5 25e5 Pa
X4 Inlet temperature of gases to POX 600 1200 K
Combined Dry Reforming and Steam Methane Reforming (CDSMR)
Input
Variables
Description Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of CH4 to CDSMR 0.1 5 Mol/s
X2 Molar flowrate of CO2 to CDSMR 0.1 5 Mol/s
X3 Molar flowrate of H2O to CDSMR 0.1 5 Mol/s
X4 Inlet pressure of gases to CDSMR 1e5 25e5 Pa
X5 Inlet temperature of gases to CDSMR 600 1200 K
127
Combined Partial Oxidation and Dry Reforming (PODR)
Input
Variables
Description Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of CH4 to PODR 0.1 5 Mol/s
X2 Molar flowrate of CO2 to PODR 0.1 5 Mol/s
X3 Molar flowrate of O2 to PODR 0.1 5 Mol/s
X3 Inlet pressure of gases to PODR 1e5 25e5 Pa
X5 Inlet temperature of gases to PODR 600 1200 K
Combined Partial Oxidation and Steam Methane Reforming (POSMR)
Input
Variables
Description Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of CH4 to POSMR 0.1 5 Mol/s
X2 Molar flowrate of CO2 to POSMR 0.1 5 Mol/s
X3 Molar flowrate of O2 to POSMR 0.1 5 Mol/s
X3 Inlet pressure of gases to POSMR 1e5 25e5 Pa
X5 Inlet temperature of gases to POSMR 600 1200 K
Tri-reforming (TR)
Input
Variables
Description Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of CH4 to TR 0.1 5 Mol/s
X2 Molar flowrate of CO2 to TR 0.1 5 Mol/s
X3 Molar flowrate of H2O to TR 0.1 5 Mol/s
X4 Molar flowrate of O2 to TR 0.1 5 Mol/s
X5 Inlet pressure of gases to TR 1e5 25e5 Pa
X6 Inlet temperature of gases to TR 600 1200 K
128
C.2. ALAMO Reactor Models
Dry Reforming (DR)
Table C1. Input Variables and Bounds for DR
Input
Variables
Description Superstructure
model
variable
Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of
CH4 to DR 𝐹𝐵𝐶𝐻4 ,𝐷𝑅 0 5 Mol/s
X2 Molar flowrate of
CO2 to DR 𝐹𝐵𝐶𝑂2 ,𝐷𝑅 0 5 Mol/s
X3 Inlet pressure of
gases to DR 𝑃𝐷𝑅 1e5 25e5 Pa
X4 Inlet temperature
of gases to DR 𝑇𝐷𝑅 400 1200 K
X5 Length of DR 𝐿𝐷𝑅 0.5 2 M
Table C2. Output Variables for DR
Output
Variables
Description Superstructure
model variable
Unit
Z1 Molar flowrate of CH4 from
DR to Syngas block
𝐹𝑟𝐷𝑅,𝑆𝑇,𝐶𝐻4 Mol/s
Z2 Molar flowrate of CO2 from
DR to Syngas block 𝐹𝑟𝐷𝑅,𝑆𝑇,𝐶𝑂2
Mol/s
Z3 Molar flowrate of CO from
DR to Syngas block 𝐹𝑟𝐷𝑅,𝑆𝑇,𝐶𝑂 Mol/s
Z4 Molar flowrate of H2O from
DR to Syngas block 𝐹𝑟𝐷𝑅,𝑆𝑇,𝐻2𝑂 Mol/s
Z5 Molar flowrate of H2 from
DR to Syngas block 𝐹𝑟𝐷𝑅,𝑆𝑇,𝐻2
Mol/s
Output Variable Models for DR
Z1 = 1.0490E+00 X1 + 2.5764E-02 X2 - 6.2201E-09 X3 + 2.4723E-03 X4 + 1.1185E-02
X5 + 8.0520E-03 log(X3) - 1.4803E-01 log(X4) + 9.8622E-04 exp(X2) + 1.6480E-02 X22
- 2.1020E-06 X42 - 3.4779E-03 X2
3 + 5.2785E-10 X43 - 6.5574E-03 X1 X2 - 7.2718E-05
X1 X4 + 4.9092E-09 X2 X3 - 7.4625E-05 X2 X4 - 5.3070E-03 X2 X5 + 8.7604E-04 (X1
X2)2 - 1.9956E-05 (X1 X2)
3 - 9.6930E-06 X1 X2 X4
129
Z2 = 4.0070E-02 X1 + 1.0693E+00 X2 - 1.2195E-08 X3 + 4.8926E-03 X4 - 1.8840E-02
X5 + 9.2583E-03 log(X3) - 2.6077E-01 log(X4) - 1.1505E-03 exp(X1) + 1.2092E-03
exp(X2) + 1.4564E-02 X12 + 3.5285E-02 X2
2 - 4.5155E-06 X42 - 5.4709E-03 X2
3 +
1.3389E-09 X43 - 5.7239E-03 X1 X2 - 1.3460E-04 X1 X4 + 6.6720E-09 X2 X3 - 2.2731E-
04 X2 X4 - 1.0026E-02 X2 X5 + 5.2867E-05 X4 X5
Z3 = - 3.9942E-01 X1 - 5.9635E-01 X2 - 5.3102E-08 X3 - 2.1884E-02 X4 + 9.3347E-02
X5 - 6.3318E-02 log(X3) + 5.9444E+00 log(X4) - 8.1827E-02 log(X5) + 9.9592E-03
exp(X1) + 4.3697E-03 exp(X2) - 8.8431E-02 X12 - 7.2982E-02 X2
2 + 1.3214E-05 X42 +
3.4708E-02 X13 + 2.6167E-02 X2
3 - 3.3924E-09 X43 - 6.1216E-03 X1
4 - 3.6811E-03 X24
- 2.2691E-03 X55 - 1.2606E-02 X1 X2 + 3.8818E-04 X1 X4 + 3.1237E-02 X1 X5 -
3.0179E-09 X2 X3 + 5.6069E-04 X2 X4 - 6.5953E-03 X2 X5 - 3.7195E-03 (X1 X2)2 -
7.5233E-09 (X2 X4)2 + 2.2378E-04 (X1 X2)
3 - 4.2270E-06 (X1 X2)4 - 1.3328E-09 X1 X2
X3 + 7.7640E-05 X1 X2 X4 - 4.1174E-05 X1 X4 X5 + 1.8754E-05 X2 X4 X5 - 1.0646E-09
(X1 X2 X4)2 + 1.2240E+02 X1/X4 + 1.8426E+02 X2/X4 + 1.0492E-04 X3/X4 - 7.8824E-
09 (X3/X4)2 - 2.8261E+01
Z4 = - 1.2102E-02 X1 - 2.8829E-01 X2 + 1.0982E-08 X3 - 4.6425E-03 X4 + 4.6729E-03
X5 - 1.8497E-02 log(X3) + 1.1424E+00 log(X4) - 3.8853E-05 exp(X1) + 1.9476E-03
exp(X2) - 3.3591E-05 X12 + 1.2342E-03 X2
2 + 3.1409E-06 X42 - 9.1548E-10 X4
3 -
7.5475E-05 X25 + 8.9438E-03 X1 X2 + 1.0434E-06 X1 X4 - 1.2830E-09 X2 X3 +
2.4643E-04 X2 X4 + 1.0724E-03 X2 X5 - 8.4114E-06 X4 X5 - 4.9298E-03 (X1 X2)2 +
2.7360E-10 (X1 X4)2 - 3.5696E-09 (X2 X4)
2 + 5.0713E-04 (X1 X2)3 - 2.3102E-05 (X1
X2)4 + 3.8463E-07 (X1 X2)
5 + 2.5845E-05 X1 X2 X4 + 3.7094E-10 X1 X3 X5 - 2.7815E-
10 (X1 X2 X4)2 + 7.4696E+01 X2/X4 - 5.6392E-07 X3/X4 - 8.5347E+00 X4/X3 +
4.0667E+02 (X1/X4)2 - 5.1979E+00
Z5 = - 3.8839E-01 X1 - 1.4226E-01 X2 + 2.3885E-07 X3 - 2.0271E-02 X4 + 7.1026E-02
X5 + 8.2973E-03 log(X3) + 5.1684E+00 log(X4) - 4.7005E-03 exp(X2) + 1.2441E-05 X42
- 3.1192E-09 X43 + 2.1017E-04 X2
5 - 6.1922E-09 X1 X3 + 3.5515E-04 X1 X4 - 2.8508E-
09 X2 X3 + 6.2290E-05 X2 X4 - 1.8831E-02 X2 X5 - 1.9660E-10 X3 X4 - 5.0218E-04 (X2
X5)2 - 4.7712E-08 (X4 X5)
2 + 7.9675E-05 X2 X4 X5 - 2.1370E-09 (X2 X4 X5)2 +
1.0868E+02 X1/X4 + 4.4728E+01 X2/X4 + 1.8274E-02 X2/X5 - 5.6176E-05 X3/X4 +
1.9529E+01 X4/X3 - 2.2319E+01 X5/X4 - 2.4872E+01
Z6 = - 3.7342E+02 X1 + 4.8773E+02 X2 + 9.9597E-01 X3 + 1.2402E+01 X4 +
1.4535E+03 X5 + 1.8399E+03 log(X3) - 4.5243E+03 log(X4) - 9.5142E+02 log(X5) +
3.8371E+01 X12 - 3.7566E+01 X2
2 - 4.0192E-03 X42 - 4.7442E+01 X1 X2 + 1.9627E-04
X1 X3 - 1.0624E+02 X1 X5 + 2.9565E-04 X2 X3 - 6.0604E-01 X2 X4 - 2.9732E+02 X2 X5
+ 1.4515E-06 X3 X4 + 5.0279E-04 X3 X5 - 1.1942E+00 X4 X5
130
Steam Methane Reforming (SMR)
Table C3. Input Variables and Bounds for SMR
Input
Variables
Description Superstructure
model
variable
Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of
CH4 to SMR 𝐹𝐵𝐶𝐻4 ,𝑆𝑀𝑅 0 5 Mol/s
X2 Molar flowrate of
H2O to SMR 𝐹𝐵𝐻2𝑂,𝑆𝑀𝑅 0 5 Mol/s
X3 Inlet pressure of
gases to SMR 𝑃𝑆𝑀𝑅 1e5 25e5 Pa
X4 Inlet temperature
of gases to SMR 𝑇𝑆𝑀𝑅 400 1200 K
X5 Length of SMR 𝐿𝑆𝑀𝑅 0.5 2 m
Table C4. Output Variables for SMR
Output
Variables
Description Superstructure
model variable
Unit
Z1 Molar flowrate of CH4 from
SMR to Syngas block 𝐹𝑟𝑆𝑀𝑅,𝑆𝑇,𝐶𝐻4
Mol/s
Z2 Molar flowrate of CO2 from
SMR to Syngas block 𝐹𝑟𝑆𝑀𝑅,𝑆𝑇,𝐶𝑂2
Mol/s
Z3 Molar flowrate of CO from
SMR to Syngas block 𝐹𝑟𝑆𝑀𝑅,𝑆𝑇,𝐶𝑂 Mol/s
Z4 Molar flowrate of H2O from
SMR to Syngas block 𝐹𝑟𝑆𝑀𝑅,𝑆𝑇,𝐻2𝑂 Mol/s
Z5 Molar flowrate of H2 from
SMR to Syngas block 𝐹𝑟𝑆𝑀𝑅,𝑆𝑇,𝐻2
Mol/s
Output Variable Models for SMR
Z1 = 1.0440E+00 X1 + 3.2409E-02 X2 - 3.5047E-08 X3 + 2.6214E-03 X4 + 8.0257E-03
X5 + 2.5544E-02 log(X3) - 1.8548E-01 log(X4) - 7.1720E-04 exp(X1) + 7.0433E-03 X12
+ 1.5565E-02 X22 - 2.2862E-06 X4
2 - 1.8639E-03 X23 + 6.5794E-10 X4
3 - 8.2541E-03
X1 X2 + 4.7151E-09 X1 X3 - 1.0835E-04 X1 X4 + 6.8827E-09 X2 X3 - 1.1047E-04 X2 X4
- 5.0603E-03 X2 X5 + 1.7938E-04 (X1 X2)2
Z2 = 1.6095E-02 X1 - 2.0878E-01 X2 - 3.5518E-08 X3 - 4.1109E-04 X4 + 9.6135E-02 X5
- 3.4044E-02 log(X3) + 6.5952E-02 log(X4) - 5.1282E-02 log(X5) - 1.5373E-02 exp(X1)
131
+ 7.0374E-03 exp(X2) - 1.1490E-02 exp(X5) - 1.0256E-01 X12 - 3.9406E-02 X2
2 +
6.8311E-07 X42 + 7.0800E-02 X1
3 + 6.5418E-03 X23 - 3.3477E-10 X4
3 - 1.8565E-02 X14
+ 8.9712E-04 X24 + 2.3008E-03 X1
5 - 4.9323E-04 X25 + 6.3547E-03 X1 X2 + 2.4290E-
09 X1 X3 + 8.0180E-05 X1 X4 + 1.3979E-09 X2 X3 + 2.2287E-04 X2 X4 - 3.2113E-03 X2
X5 + 1.1236E-09 X3 X5 - 1.3476E-03 (X1 X2)2 - 6.1127E-09 (X1 X4)
2 + 3.0916E-04 (X1
X5)2 - 7.1741E-09 (X2 X4)
2 - 1.2804E-08 (X4 X5)2 + 5.9552E-05 (X1 X2)
3 - 1.0096E-06
(X1 X2)4 - 2.0325E-09 X1 X2 X3 + 2.2366E-05 X1 X2 X4 - 1.6661E-03 X1 X2 X5 +
1.1132E-05 X2 X4 X5 + 2.3571E-10 (X1 X4 X5)2 + 5.8151E+02 X1/X3 + 1.0849E+01
X1/X4 + 6.1817E+01 X2/X4 + 5.7402E-05 X3/X4 + 1.6133E+00 X4/X3 - 4.5180E-09
(X3/X4)2
Z3 = - 1.2360E-01 X1 + 1.3643E-01 X2 - 9.5264E-09 X3 - 1.8303E-03 X4 - 9.6869E-02
X5 + 4.0529E-02 log(X3) + 5.6557E-01 log(X4) + 6.8077E-02 log(X5) + 8.6263E-05
exp(X1) - 5.9331E-03 exp(X2) + 1.0674E-03 X12 - 1.3235E-02 X2
2 + 4.2297E-07 X42 -
4.7299E-04 X13 + 1.4619E-02 X2
3 + 1.2260E-10 X43 - 4.8109E-03 X2
4 + 7.2120E-04 X25
+ 6.9610E-04 X55 + 4.4728E-03 X1 X2 + 2.7280E-09 X1 X3 + 9.0363E-05 X1 X4 +
9.3958E-10 X2 X3 - 1.0243E-04 X2 X4 + 3.8036E-09 X3 X5 + 1.1061E-04 X4 X5 +
5.2551E-09 (X1 X4)2 - 7.0122E-05 (X1 X5)
2 + 5.7465E-09 (X2 X4)2 - 1.7598E-04 (X2
X5)2 - 1.8891E-08 (X4 X5)
2 + 1.4605E-07 (X1 X5)5 - 8.3323E-06 X1 X2 X4 - 2.5010E-09
X1 X3 X5 + 6.4156E-06 X1 X4 X5 + 3.5729E-06 X2 X4 X5 - 7.6538E-10 (X1 X4 X5)2 +
3.7767E+01 X1/X4 - 3.2468E-03 X1/X5 + 1.0889E+03 X2/X3 - 4.4003E+01 X2/X4 -
2.5604E-05 X3/X4 + 1.6613E+01 X4/X3 + 5.5358E-05 X4/X5 - 3.8310E+00 X5/X4 +
8.6694E+02 (X2/X4)2 + 2.7135E-09 (X3/X4)
2 - 1.3835E+03 (X4/X3)2 - 3.2032E+00
Z4 = 3.6560E-02 X1 + 9.3935E-01 X2 - 7.9248E-08 X3 + 5.5372E-03 X4 - 9.1634E-03
X5 + 6.3571E-02 log(X3) - 3.8627E-01 log(X4) - 1.6111E-03 exp(X1) - 8.3393E-03
exp(X2) + 1.9820E-02 X12 + 1.5550E-01 X2
2 - 5.2162E-06 X42 - 4.8691E-02 X2
3 +
1.7023E-09 X43 + 6.8786E-03 X2
4 - 9.5129E-03 X1 X2 + 8.5419E-09 X1 X3 - 1.7523E-
04 X1 X4 + 1.2950E-08 X2 X3 - 2.3083E-04 X2 X4
Z5 = - 6.7918E-01 X1 - 2.3154E-01 X2 + 6.5550E-08 X3 - 2.3706E-03 X4 + 4.4595E-01
X5 + 1.0148E-02 log(X3) + 6.8690E-03 log(X4) - 5.6042E-01 log(X5) - 1.5499E-03
exp(X1) - 2.4311E-02 exp(X2) - 3.9183E-03 X12 - 1.9332E-01 X2
2 + 2.7109E-06 X42 +
1.5142E-01 X23 - 7.6417E-10 X4
3 - 3.9282E-02 X24 + 1.3016E-04 X1
5 + 4.4272E-03 X25
- 4.9791E-03 X55 + 1.0235E-01 X1 X2 + 3.1920E-09 X1 X3 + 6.8800E-04 X1 X4 -
1.1863E-01 X1 X5 + 2.4659E-08 X2 X3 + 2.3027E-04 X2 X4 + 1.8634E-01 X2 X5 -
2.0335E-10 X3 X4 + 3.9267E-08 X3 X5 + 1.3300E-04 X4 X5 - 2.1112E-02 (X1 X2)2 -
1.2011E-08 (X1 X4)2 + 3.9963E-02 (X1 X5)
2 - 4.7578E-02 (X2 X5)2 - 7.7135E-08 (X4
X5)2 + 1.8152E-03 (X1 X2)
3 - 5.9186E-03 (X1 X5)3 + 5.7483E-03 (X2 X5)
3 - 7.4763E-05
(X1 X2)4 + 3.0235E-04 (X1 X5)
4 - 2.5476E-04 (X2 X5)4 + 1.1551E-06 (X1 X2)
5 -
5.7526E-09 X1 X2 X3 + 6.0053E-05 X1 X2 X4 - 1.8404E-05 X1 X4 X5 - 1.0375E-08 X2
X3 X5 + 4.0273E-05 X2 X4 X5 + 4.6669E+03 X1/X3 + 1.7382E+02 X1/X4 - 2.3837E-02
X1/X5 + 9.4978E+03 X2/X3
132
Partial Oxidation (POX)
Table C5. Input Variables and Bounds for POX
Input
Variables
Description Superstructure
model
variable
Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of
CH4 to POX 𝐹𝐵𝐶𝐻4 ,𝑃𝑂𝑋 0 5 Mol/s
X2 Molar flowrate of
O2 to POX 𝐹𝐵𝑂2 ,𝑃𝑂𝑋 0 5 Mol/s
X3 Inlet pressure of
gases to POX 𝑃𝑃𝑂𝑋 1e5 25e5 Pa
X4 Inlet temperature
of gases to POX 𝑇𝑃𝑂𝑋 700 1200 K
X5 Length of POX 𝐿𝑃𝑂𝑋 0.5 2 m
Table C6. Output Variables for POX
Output
Variables
Description Superstructure
model variable
Unit
Z1 Molar flowrate of CH4 from
POX to Syngas block
𝐹𝑟𝑃𝑂𝑋,𝑆𝑇,𝐶𝐻4 Mol/s
Z2 Molar flowrate of CO2 from
POX to Syngas block 𝐹𝑟𝑃𝑂𝑋,𝑆𝑇,𝐶𝑂2
Mol/s
Z3 Molar flowrate of CO from
POX to Syngas block 𝐹𝑟𝑃𝑂𝑋,𝑆𝑇,𝐶𝑂 Mol/s
Z4 Molar flowrate of H2O from
POX to Syngas block 𝐹𝑟𝑃𝑂𝑋,𝑆𝑇,𝐻2𝑂 Mol/s
Z5 Molar flowrate of H2 from
POX to Syngas block 𝐹𝑟𝑃𝑂𝑋,𝑆𝑇,𝐻2
Mol/s
Z6 Molar flowrate of O2 from
POX to Syngas block 𝐹𝑟𝑃𝑂𝑋,𝑆𝑇,𝑂2
Mol/s
Output Variable Models for POX
Z1 = 2.2534E-01 X1 - 6.7476E-02 X2 - 9.3246E-08 X3 + 2.8309E-04 X4 + 2.9059E-02
X5 - 3.8493E-02 log(X3) - 2.3835E-02 log(X4) + 3.3349E-02 log(X5) + 2.5346E-02
exp(X1) - 3.4297E-02 exp(X2) + 9.9169E-02 exp(X5) + 4.2939E-01 X12 - 5.7728E-02
X22 - 8.7856E-02 X1
3 + 6.7172E-02 X23 - 3.7672E-01 X1 X2 - 7.9188E-02 X2 X5 -
1.8649E-07 X3 X5 + 5.8689E-03 (X1 X2)2 + 3.4967E-04 X3/X4
133
Z2 = 5.9729E-02 X1 + 7.2917E-03 X2 - 6.9564E-08 X3 + 1.3232E-04 X4 + 1.8382E-03
X5 + 5.4097E-03 log(X3) + 1.7795E-03 log(X4) + 2.0774E-03 log(X5) + 1.9283E-02
exp(X1) - 1.2676E-03 exp(X2) + 3.4565E-03 exp(X5) + 9.4036E-02 X12 + 3.8579E-02
X22 - 2.3242E-07 X4
2 + 2.3096E-03 X52 - 4.3377E-02 X1
3 + 1.0238E-07 X2 X3 -
1.9346E-04 X2 X4 + 2.8865E-03 (X2/X5)3 - 3.7867E-04 (X2/X5)
4
Z3 = - 1.7951E-02 X1 - 2.0793E-02 X2 + 2.8826E-07 X3 - 1.7984E-03 X4 - 7.5183E-04
X5 + 1.1468E-01 log(X3) + 2.634775230179621E-002 log(X4) - 9.1967E-03 log(X5) -
1.8293E-02 exp(X1) + 2.1785E-02 exp(X2) + 1.8752E-04 exp(X5) -6.5945E-02 X12 -
7.8965E-02 X22 + 6.0479E-07 X4
2 + 3.8121E-02 X13 - 3.6106E-02 X2
3 + 3.5645E-01 X1
X2 + 3.7370E-04 X2 X4 - 5.7159E-03 (X1 X2)2 - 5.5673E-04 X3/X4
Z4 = 1.0495E-02 X1 + 2.0381E-03 X2 - 1.4788E-07 X3 + 4.0351E-04 X4 + 4.5096E-03
X5 - 3.0835E-04 log(X3) - 4.5107E-04 log(X4) + 3.8324E-03 log(X5) +
1.259300325907861E-002 exp(X1) + 8.5656E-04 exp(X2) + 1.6668E-02 exp(X5) +
9.5149E-03 X12 + 2.3854E-02 X2
2 - 1.8238E-07 X42 + 1.1530E-02 X5
2 - 3.1957E-02 X13
+ 1.9591E-01 X1 X2 + 2.0869E-07 X2 X3 + 7.0592E-06 X2 X4 - 7.0354E-08 (X2 X4)2
Z5 = 2.9404E-02 X1 + 9.8335E-03 X2 - 8.5569E-09 X3 + 6.4926E-04 X4 - 4.5219E-03
X5 + 5.7174E-04 log(X3) + 1.5981E-03 log(X4) - 4.1438E-03 log(X5) - 1.4629E-03
exp(X1) + 7.4254E-02 exp(X2) - 2.1131E-02 exp(X5) + 1.2130E-01 X12 - 1.1110E-02
X22 - 3.1856E-07 X4
2 - 1.2347E-01 X23 + 4.3430E-01 X1 X2 - 1.4891E-04 X1 X4 -
1.4816E-07 X2 X3 + 7.3432E-04 X2 X4 - 1.5811E-05 (X1 X2)4
Z6 = - 5.0276E-02 X1 + 1.8908E-01 X2 - 2.4865E-07 X3 + 9.1538E-04 X4 - 6.1503E-02
X5 - 8.1683E-03 log(X3) - 6.6483E-04 log(X4) - 5.6905E-02 log(X5) + 1.8778E-02
exp(X1) + 1.7132E-03 exp(X2) + 3.0618E-01 X22 + 9.1545E-02 X1
3 - 3.3515E-02 X23 -
1.7693E-02 X14 - 4.7311E-01 X1 X2 - 5.0464E-04 X1 X4 + 1.5205E-07 (X1 X2)
5 +
2.1979E-04 X1 X2 X4 + 6.9800E-04 (X1 X2 X5)2 + 9.5536E-04 (X2/X5)
3
134
Combined Dry Reforming and Steam Methane Reforming (CDSMR)
Table C7. Input Variables and Bounds for CDSMR
Input
Variables
Description Superstructure
model variable
Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of
CH4 to CDSMR 𝐹𝐵𝐶𝐻4 ,𝐶𝐷𝑆𝑀𝑅 0 5 Mol/s
X2 Molar flowrate of
CO2 to CDSMR 𝐹𝐵𝐶𝑂2 ,𝐶𝐷𝑆𝑀𝑅 0 5 Mol/s
X3 Molar flowrate of
H2O to CDSMR 𝐹𝐵𝐻2𝑂,𝐶𝐷𝑆𝑀𝑅 0 5 Mol/s
X4 Inlet pressure of
gases to CDSMR 𝑃𝐶𝐷𝑆𝑀𝑅 1e5 25e5 Pa
X5 Inlet temperature
of gases to
CDSMR
𝑇𝐶𝐷𝑆𝑀𝑅 400 1200 K
X6 Length of
CDSMR 𝐿𝐶𝐷𝑆𝑀𝑅 0.5 2 m
Table C8. Output Variables for CDSMR
Output
Variables
Description Superstructure
model variable
Unit
Z1 Molar flowrate of CH4 from
SMR to Syngas block 𝐹𝑟𝑆𝑀𝑅,𝑆𝑇,𝐶𝐻4
Mol/s
Z2 Molar flowrate of CO2 from
SMR to Syngas block
𝐹𝑟𝑆𝑀𝑅,𝑆𝑇,𝐶𝑂2 Mol/s
Z3 Molar flowrate of CO from
SMR to Syngas block 𝐹𝑟𝑆𝑀𝑅,𝑆𝑇,𝐶𝑂 Mol/s
Z4 Molar flowrate of H2O from
SMR to Syngas block 𝐹𝑟𝑆𝑀𝑅,𝑆𝑇,𝐻2𝑂 Mol/s
Z5 Molar flowrate of H2 from
SMR to Syngas block 𝐹𝑟𝑆𝑀𝑅,𝑆𝑇,𝐻2
Mol/s
Output Variable Models for CDSMR
Z1 = 1.0282E+00 X1 + 3.5363E-02 X2 + 2.8818E-02 X3 - 1.2255E-08 X4 + 3.4023E-03
X5 - 6.5893E-02 X6 + 1.6033E-02 log(X4) - 1.9426E-01 log(X5) + 4.8419E-02 log(X6) -
5.0706E-04 exp(X1) + 4.3221E-03 exp(X6) + 8.6219E-03 X12 - 2.7848E-06 X5
2 +
135
6.3971E-10 X53 + 5.5788E-09 X1 X4 - 1.2424E-04 X1 X5 + 3.3234E-03 X2 X3 +
4.9173E-09 X2 X4 - 9.4604E-05 X2 X5 - 7.2738E-05
Z2 = - 1.2484E-02 X1 + 9.9394E-01 X2 - 8.1453E-02 X3 + 6.8116E-08 X4 - 2.2670E-03
X5 - 4.5473E-02 log(X4) + 1.9097E-01 log(X5) + 4.8236E-04 exp(X3) + 1.1413E-02 X22
- 1.5297E-02 X32 + 2.8989E-06 X5
2 - 1.4721E-09 X53 + 8.5060E-03 X1 X3 + 8.1863E-03
X2 X3 - 6.1021E-05 X2 X5 - 9.5581E-09 X3 X4 + 2.2143E-04 X3 X5 - 5.4895E-05 (X1
X2)2 - 1.8736E-08 (X2 X5)
2 - 2.0412E-09 X1 X2 X4
Z3 = - 5.4387E-01 X1 - 9.0350E-01 X2 + 4.6802E-01 X3 - 8.2067E-09 X4 + 6.4431E-03
X5 + 5.3489E-02 X6 + 3.5743E-03 log(X4) - 2.8207E-01 log(X5) + 2.5582E-03 log(X6) -
3.1752E-04 exp(X1) - 2.3548E-03 exp(X2) + 2.0056E-03 exp(X3) + 8.9093E-03 X12 -
6.4033E-03 X22 + 2.3160E-02 X3
2 - 7.7833E-06 X52 - 7.5499E-03 X3
3 + 3.2050E-09 X53
+ 5.4255E-04 X24 + 2.3320E-02 X1 X2 - 7.5358E-03 X1 X3 - 6.4534E-09 X1 X4 +
4.6586E-04 X1 X5 + 1.1886E-02 X2 X3 + 8.0036E-04 X2 X5 - 5.5665E-02 X2 X6 +
7.5732E-09 X3 X4 - 4.3953E-04 X3 X5 - 5.8573E-03 X3 X6 - 4.3125E-06 X5 X6 -
2.8526E-03 (X1 X2)2 + 1.3620E-03 (X1 X3)
2 - 6.3492E-09 (X1 X5)2 + 4.0096E-04 (X2
X3)2 + 8.0411E-09 (X2 X5)
2 + 7.7026E-03 (X2 X6)2 + 2.7484E-08 (X3 X5)
2 + 8.0122E-05
(X1 X2)3 - 2.8793E-05 (X1 X3)
3 - 4.0216E-04 (X2 X6)3 + 1.3315E-09 X1 X2 X4 +
2.2932E-05 X1 X2 X5 - 2.7660E-05 X1 X3 X5 - 1.5308E-09 X2 X3 X4 - 4.1411E-05 X2 X3
X5 + 9.1976E-04 X2 X3 X6 + 5.4455E+02 X1/X4 + 1.3813E+02 X1/X5 + 2.6164E+02
X2/X5 - 1.2058E+02 X3/X5
Z4 = 6.4461E-02 X1 - 5.3590E-02 X2 + 1.1107E+00 X3 - 7.1426E-08 X4 + 1.8893E-04
X5 - 9.5955E-01 X6 + 5.2903E-02 log(X4) + 2.6183E-03 log(X5) + 5.6064E-01 log(X6) -
3.5399E-04 exp(X3) + 1.3307E-02 X32 + 1.8725E-01 X6
2 + 6.2995E-04 X13 - 8.3481E-
03 X1 X3 + 8.3708E-09 X1 X4 - 1.2518E-04 X1 X5 - 5.5126E-03 X2 X3 + 1.1639E-04 X2
X5 + 1.4567E-08 X3 X4 - 2.8962E-04 X3 X5
Z5 = - 3.7270E-01 X1 + 4.0515E-01 X2 - 9.7846E-02 X3 + 3.8808E-07 X4 - 5.5827E-02
X5 + 7.4308E+01 X6 - 9.8402E-02 log(X4) + 1.3513E+01 log(X5) - 1.9241E+00 log(X6)
- 1.0873E-01 exp(X1) - 2.5894E-02 exp(X2) + 1.0680E-04 exp(X3) - 6.6898E+01
exp(X6) - 7.9483E-01 X12 - 3.0863E-01 X2
2 - 9.8819E-03 X32 + 3.7148E-05 X5
2 +
2.7174E+01 X62 + 5.2600E-01 X1
3 + 1.7972E-01 X23 - 1.0382E-08 X5
3 + 1.5833E+01
X63 - 1.3588E-01 X1
4 - 4.4733E-02 X24 + 1.6559E-02 X1
5 + 4.9580E-03 X25 +
1.5174E+00 X65 - 5.2676E-02 X1 X2 - 4.9562E-03 X1 X3 - 1.6087E-08 X1 X4 +
9.9858E-04 X1 X5 + 1.3533E-02 X1 X6 - 2.0751E-03 X2 X3 - 9.8359E-09 X2 X4 -
1.2005E-04 X2 X5 - 6.7109E-03 X2 X6 - 2.0301E-08 X3 X4 + 2.4435E-04 X3 X5 +
1.0092E-02 X3 X6 - 3.3861E-10 X4 X5 + 1.3852E-03 (X1 X2)2 - 7.3390E-04 (X1 X3)
2 -
2.4323E-08 (X1 X5)2 + 2.1280E-08 (X2 X5)
2 + 9.4458E-09 (X3 X5)2 - 9.4169E-10 X1 X2
X4 + 5.4589E-05 X1 X2 X5 + 4.7324E-05 X1 X3 X5 - 1.6199E-09 (X1 X2 X5)2 +
3.0396E+02 X1/X5
136
Combined Partial Oxidation and Dry Reforming (PODR)
Table C9. Input Variables and Bounds for PODR
Input
Variables
Description Superstructure
model variable
Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of
CH4 to PODR 𝐹𝐵𝐶𝐻4 ,𝑃𝑂𝐷𝑅 0 5 Mol/s
X2 Molar flowrate of
CO2 to PODR 𝐹𝐵𝐶𝑂2 ,𝑃𝑂𝐷𝑅 0 5 Mol/s
X3 Molar flowrate of
O2 to PODR 𝐹𝐵𝑂2 ,𝑃𝑂𝐷𝑅 0 5 Mol/s
X3 Inlet pressure of
gases to PODR 𝑃𝑃𝑂𝐷𝑅 1e5 25e5 Pa
X5 Inlet temperature
of gases to PODR 𝑇𝑃𝑂𝐷𝑅 700 1200 K
X6 Length of PODR 𝐿𝑃𝑂𝐷𝑅 0.5 2 m
Table C10. Output Variables for PODR
Output
Variables
Description Superstructure
model variable
Unit
Z1 Molar flowrate of CH4 from
PODR to Syngas block 𝐹𝑟𝑃𝑂𝐷𝑅,𝑆𝑇,𝐶𝐻4
Mol/s
Z2 Molar flowrate of CO2 from
PODR to Syngas block 𝐹𝑟𝑃𝑂𝐷𝑅,𝑆𝑇,𝐶𝑂2
Mol/s
Z3 Molar flowrate of CO from
PODR to Syngas block 𝐹𝑟𝑃𝑂𝐷𝑅,𝑆𝑇,𝐶𝑂 Mol/s
Z4 Molar flowrate of H2O from
PODR to Syngas block 𝐹𝑟𝑃𝑂𝐷𝑅,𝑆𝑇,𝐻2𝑂 Mol/s
Z5 Molar flowrate of H2 from
PODR to Syngas block 𝐹𝑟𝑃𝑂𝐷𝑅,𝑆𝑇,𝐻2
Mol/s
Z6 Molar flowrate of O2 from
PODR to Syngas block 𝐹𝑟𝑃𝑂𝐷𝑅,𝑆𝑇,𝑂2
Mol/s
Output Variable Models for PODR
Z1 = 7.3000E-01 X1 - 4.9729E-02 X2 - 4.3555E-01 X3 3.0045E-08 X4 - 5.2091E-04 X5 -
7.5949E-03 X6 + 5.1704E-02 log(X4) + 3.6448E-02 log(X5) - 2.251665241485524E-002
log(X6) - 9.8513E-03 exp(X1) + 6.1901E-04 exp(X2) - 3.3782E-02 exp(X3) - 9.9389E-04
137
exp(X6) + 1.3480E-02 X13 + 6.3581E-02 X3
3 - 3.3396E-01 X1 X3 - 6.7392E-02 X2 X3 +
4.6593E-03 (X1 X3)2 + 8.9121E-03 X1 X2 X3 + 5.2720E-05 X2 X3 X5
Z2 = 4.8259E-03 X1 + 9.8279E-01 X2 - 1.2122E-01 X3 + 2.1836E-07 X4 - 9.4544E-04
X5 - 4.0603E-03 X6 + 4.2677E-02 log(X4) + 1.8298E-02 log(X5) + 2.8175E-03 log(X6)
+ 2.3507E-03 exp(X2) - 8.4432E-03 exp(X3) - 3.0093E-02 exp(X6) + 2.8425E-02 X33 -
8.3711E-02 X1 X2 - 3.6860E-03 X1 X3 - 4.6711E-02 X2 X3 - 1.3347E-04 (X1 X3)3 +
1.6848E-08 (X1 X2 X3)4 - 7.2065E-04 (X2/X6)
4 + 9.0749E-05 (X2/X6)5
Z3 = 1.0823E-01 X1 + 4.1853E-02 X2 + 8.4513E-01 X3 + 1.6249E-08 X4 + 1.1749E-03
X5 - 5.2475E-03 X6 - 8.4378E-02 log(X4) - 2.9472E-02 log(X5) + 3.8236E-03 log(X6) +
2.0459E-02 exp(X1) - 5.8689E-03 exp(X2) + 4.8989E-02 exp(X3) - 3.5128E-02 exp(X6)
+ 1.7698E-01 X12 + 4.5113E-02 X2
2 - 5.1551E-02 X13 - 1.0101E-01 X3
3 + 6.5675E-02
X1 X2 + 2.3711E-01 X1 X3 - 2.2489E-07 X4/X6
Z4 = 3.7628E-02 X1 + 2.6787E-02 X2 + 2.8056E-01 X3 + 2.1693E-08 X4 - 8.9913E-03
X5 + 3.1076E-01 log(X4) + 1.2682E-02 exp(X1) + 1.9502E-02 exp(X2) - 5.0367E-03
exp(X3) + 4.0462E-06 X52 - 5.0989E-02 X1
3 - 2.8521E-02 X23 - 2.6661E-02 X1 X2 +
2.9029E-01 X1 X3 + 5.7081E-04 X1 X5 + 3.3598E-04 X2 X5 -3.5182E-03 (X2 X3)2 +
1.5026E-04 (X1 X3)3 + 5.1480E-02 X1 X2 X3 - 1.8051E-04 X1 X3 X5
Z5 = 9.8390E-02 X1 - 2.6712E-01 X2 + 1.0785E-01 X3 - 5.6680E-08 X4 + 1.0517E-02
X5 - 3.2745E-01 log(X4) + 2.9689E-02 exp(X1) - 5.7024E-02 exp(X3) - 7.3339E-02 X12 -
5.3894E-06 X52 - 2.0527E-01 X3
3 + 4.3618E-02 X34 - 1.6312E-01 X1 X2 + 9.4433E-01
X1 X3 + 2.8710E-01 X2 X3 + 3.3135E-02 (X1 X2)2 - 2.2158E-02 (X1 X3)
2 - 1.0398E-03
(X1 X2)3 - 1.7322E-01 X1 X2 X3 + 6.1118E-04 (X1 X2 X3)
2
Z6 = - 3.5696E-01 X1 + 1.1534E-01 X2 + 5.5073E-01 X3 - 1.1680E-07 X4 + 6.4749E-03
X5 - 1.7705E-01 X6 - 1.6381E-01 log(X4) - 4.0223E-02 log(X5) - 1.3691E-01 log(X6) -
1.2569E-02 exp(X1) + 4.8526E-02 X32 - 3.5423E-06 X5
2 + 3.5732E-02 X13 - 1.5403E-02
X1 X2 - 2.6853E-01 X1 X3 + 1.6505E-03 (X2 X3)2 + 3.8971E-05 X1 X3 X5 - 3.9505E-02
X2 X3 X6 + 1.9629E-04 X3 X5 X6 - 7.3827E-06 (X2/X6)5
138
Combined Partial Oxidation and Steam Methane Reforming (POSMR)
Table C11. Input Variables and Bounds for POSMR
Input
Variables
Description Superstructure
model variable
Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of
CH4 to POSMR 𝐹𝐵𝐶𝐻4 ,𝑃𝑂𝐷𝑅 0 5 Mol/s
X2 Molar flowrate of
CO2 to POSMR 𝐹𝐵𝐶𝑂2 ,𝑃𝑂𝐷𝑅 0 5 Mol/s
X3 Molar flowrate of
O2 to POSMR 𝐹𝐵𝑂2 ,𝑃𝑂𝐷𝑅 0 5 Mol/s
X3 Inlet pressure of
gases to POSMR 𝑃𝑃𝑂𝐷𝑅 1e5 25e5 Pa
X5 Inlet temperature
of gases to
POSMR
𝑇𝑃𝑂𝐷𝑅 700 1200 K
X6 Length of
POSMR 𝐿𝑃𝑂𝐷𝑅 0.5 2 m
Table C12. Output Variables for POSMR
Output
Variables
Description Superstructure
model variable
Unit
Z1 Molar flowrate of CH4 from
POSMR to Syngas block 𝐹𝑟𝑃𝑂𝑆𝑀𝑅,𝑆𝑇,𝐶𝐻4
Mol/s
Z2 Molar flowrate of CO2 from
POSMR to Syngas block
𝐹𝑟𝑃𝑂𝑆𝑀𝑅,𝑆𝑇,𝐶𝑂2 Mol/s
Z3 Molar flowrate of CO from
POSMR to Syngas block 𝐹𝑟𝑃𝑂𝑆𝑀𝑅,𝑆𝑇,𝐶𝑂 Mol/s
Z4 Molar flowrate of H2O from
POSMR to Syngas block 𝐹𝑟𝑃𝑂𝑆𝑀𝑅,𝑆𝑇,𝐻2𝑂 Mol/s
Z5 Molar flowrate of H2 from
POSMR to Syngas block 𝐹𝑟𝑃𝑂𝑆𝑀𝑅,𝑆𝑇,𝐻2
Mol/s
Z6 Molar flowrate of O2 from
POSMR to Syngas block 𝐹𝑟𝑃𝑂𝑆𝑀𝑅,𝑆𝑇,𝑂2
Mol/s
Output Variable Models for POSMR
Z1 = 2.0672E-01 X1 - 1.1787E-01 X2 - 2.1703E-01 X3 - 8.3541E-09 X4 - 1.5895E-04 X5
- 1.5276E-02 X6 + 2.9001E-02 log(X4) + 1.6462E-02 log(X5) - 1.8069E-02 log(X6) +
139
1.3845E-02 exp(X1) + 6.9131E-04 exp(X2) - 2.4304E-02 exp(X3) + 3.6331E-01 X12 -
6.7441E-02 X13 + 4.5765E-02 X3
3 + 1.4758E-02 X1 X2 - 3.7162E-01 X1 X3 + 7.0748E-
03 (X1 X3)2 + 8.9384E-06 X2 X3 X5 - 2.5526E-08 (X1 X3 X6)
4
Z2 = 1.5925E-02 X1 + 9.9429E-03 X2 - 8.4894E-02 X3 - 7.8150E-08 X4 - 4.3326E-03 X5
- 1.3441E-02 X6 + 1.5951E-01 log(X4) + 3.8139E-02 log(X5) + 1.0779E-02 exp(X1) -
1.4217E-02 exp(X3) - 4.3772E-03 X12 - 1.5033E-01 X3
2 + 2.2298E-06 X52 - 1.9140E-02
X13 + 5.3376E-02 X3
3 + 4.2822E-02 X1 X2 + 1.5575E-01 X1 X3 - 6.5305E-03 (X1 X3)2 -
3.4509E-05 (X2 X3)3 + 3.8214E-02 X3/X6
Z3 = -6.1570E-03 X1 + 8.7516E-02 X2 + 5.6925E-01 X3 + 1.1568E-07 X4 + 5.3840E-03
X5 + 8.9789E-03 X6 - 2.2191E-01 log(X4) - 4.5341E-02 log(X5) + 2.1179E-02 log(X6) +
5.6033E-02 exp(X1) - 3.2610E-03 exp(X2) + 2.6973E-02 exp(X3) + 1.2203E-02 exp(X6)
- 2.7364E-06 X52 - 6.9337E-02 X3
3 - 2.0983E-03 X15 + 1.0387E-02 X1 X2 + 2.4775E-01
X1 X3 + 2.1149E-07 (X2 X3)5 - 2.3388E-02 X1 X2 X3
Z4 = 4.0466E-02 X1 + 6.3113E-02 X2 - 8.1352E-04 X3 + 1.9088E-07 X4 - 1.5415E-03
X5 + 1.7120E-02 X6 + 1.4125E-01 log(X4) + 6.1122E-02 log(X5) + 5.5250E-03 log(X6)
+ 1.2763E-02 exp(X1) - 1.5589E-02 exp(X2) + 3.0396E-03 exp(X3) + 1.9137E-01 X22 -
4.8928E-02 X32 - 4.5204E-02 X1
3 + 2.7808E-01 X1 X3 - 4.5628E-02 X2 X3 + 1.3966E-
07 X3 X4 + 1.1871E-04 X2 X3 X5 - 8.8622E-08 (X4/X5)2
Z5 = - 1.3931E-01 X1 + 4.2359E-01 X2 + 1.3052E+00 X3 + 2.2083E-07 X4 + 1.5586E-
02 X5 + 1.7621E-02 X6 - 6.0810E-01 log(X4) - 1.5102E-01 log(X5) + 7.0537E-02
log(X6) - 5.6997E-04 exp(X1) + 1.0935E-03 exp(X2) + 9.6687E-02 exp(X3) - 2.9037E-
02 exp(X6) + 2.6910E-01 X12 - 7.3857E-06 X5
2 - 1.6422E-01 X33 + 1.9030E-01 X1 X3 +
4.6148E-02 X2 X3 - 5.1575E-07 (X1 X3)5 - 1.4813E-04 X2 X3 X5
Z6 = -2.5412E-01 X1 + 7.1965E-02 X2 + 2.5641E-01 X3 + 7.2882E-08 X4 + 9.4540E-03
X5 - 6.5419E-03 X6 - 2.9622E-01 log(X4) - 7.4995E-02 log(X5) + 1.6154E-02 log(X6) -
1.8587E-02 exp(X1) + 1.1440E-03 exp(X2) + 2.3049E-02 exp(X3) + 4.2292E-01 X32 -
4.8775E-06 X52 + 4.3335E-02 X1
3 - 8.0731E-02 X33 - 1.3248E-02 X1 X2 - 3.4603E-01
X1 X3 - 2.2390E-02 X2 X3 + 4.2174E-03 (X1 X3)2
140
Tri-reforming (TR)
Table C13. Input Variables and Bounds for POSMR
Input
Variables
Description Superstructure
model variable
Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of
CH4 to TR 𝐹𝐵𝐶𝐻4 ,𝑇𝑅 0 5 Mol/s
X2 Molar flowrate of
CO2 to TR 𝐹𝐵𝐶𝑂2 ,𝑇𝑅 0 5 Mol/s
X3 Molar flowrate of
H2O to TR 𝐹𝐵𝐻2𝑂,𝑇𝑅 0 5 Mol/s
X4 Molar flowrate of
O2 to TR 𝐹𝐵𝑂2 ,𝑇𝑅 0 5 Mol/s
X5 Inlet pressure of
gases to TR 𝑃𝑇𝑅 1e5 25e5 Pa
X6 Inlet temperature
of gases to TR 𝑇𝑇𝑅 700 1200 K
X7 Length of TR 𝐿𝑇𝑅 0.5 2 m
Table C14. Output Variables for TR
Output
Variables
Description Superstructure
model variable
Unit
Z1 Molar flowrate of CH4 from
TR to Syngas block 𝐹𝑟𝑇𝑅,𝑆𝑇,𝐶𝐻4
Mol/s
Z2 Molar flowrate of CO2 from
TR to Syngas block 𝐹𝑟𝑇𝑅,𝑆𝑇,𝐶𝑂2
Mol/s
Z3 Molar flowrate of CO from
TR to Syngas block 𝐹𝑟𝑇𝑅,𝑆𝑇,𝐶𝑂 Mol/s
Z4 Molar flowrate of H2O from
TR to Syngas block 𝐹𝑟𝑇𝑅,𝑆𝑇,𝐻2𝑂 Mol/s
Z5 Molar flowrate of H2 from
TR to Syngas block 𝐹𝑟𝑇𝑅,𝑆𝑇,𝐻2
Mol/s
Z6 Molar flowrate of O2 from
TR to Syngas block
𝐹𝑟𝑇𝑅,𝑆𝑇,𝑂2 Mol/s
Output Variable Models for TR
Z1 = 4.9319E-02 X1 - 7.1367E-03 X2 - 1.6351E-02 X3 - 1.2483E-01 X4 - 3.4393E-08 X5
- 4.0796E-04 X6 + 2.7174E-03 X7 + 6.1876E-02 log(X5) + 2.6930E-02 log(X6) -
141
2.3636E-03 log(X7) - 1.2391E-02 exp(X1) - 3.8858E-04 exp(X2) + 2.8969E-05 exp(X3) -
3.8202E-02 exp(X4) + 8.6343E-03 exp(X7) + 1.9337E-01 X12 - 1.9744E-01 X4
2 +
9.2889E-02 X43 - 2.4001E-01 X1 X4 + 2.1306E-03 (X1 X4)
2
Z2 = 7.0856E-02 X1 + 9.2428E-01 X2 + 4.8808E-02 X3 - 1.2537E-01 X4 + 1.8139E-07
X5 - 4.7764E-04 X6 - 2.9430E-02 X7 + 6.8267E-03 log(X5) + 2.6021E-02 log(X6) -
2.2505E-02 log(X7) + 3.1446E-02 exp(X1) + 2.7214E-04 exp(X2) - 5.8004E-03 exp(X4)
+ 1.3907E-01 X12 - 6.4662E-02 X1
3 + 2.1032E-02 X43 - 5.6671E-02 X1 X2 + 4.5201E-02
X1 X3 - 1.8417E-02 X1 X4 - 3.2022E-02 X1 X4 X7
Z3 = - 4.2384E-02 X1 + 7.2490E-02 X2 - 1.8373E-01 X3 + 7.2290E-01 X4 - 1.3523E-07
X5 + 8.6088E-04 X6 + 1.0429E-01 X7 - 8.4699E-02 log(X5) - 1.5087E-02 log(X6) +
1.3372E-01 log(X7) - 2.7249E-02 exp(X1) - 1.2126E-03 exp(X2) + 1.9495E-03 exp(X3)
+ 3.4424E-02 exp(X4) + 1.8862E-01 exp(X7) + 3.4118E-02 X13 - 7.9844E-02 X4
3 -
7.6096E-02 X74 + 6.9551E-02 X1 X2 + 2.5061E-01 X1 X4
Z4 = 2.7279E-01 X1 - 1.7546E-01 X2 + 1.0190E+00 X3 - 1.7841E-02 X4 - 1.8456E-08
X5 - 1.1412E-02 X6 - 3.6263E-02 X7 + 3.8268E-01 log(X5) + 7.3735E-02 log(X6) +
4.3142E-02 exp(X1) - 5.1012E-03 exp(X4) + 5.9202E-06 X62 - 8.3583E-02 X1
3 +
9.3761E-02 X1 X2 - 6.5909E-02 X1 X3 + 3.0586E-01 X1 X4 + 1.0114E-01 X1 X7 +
4.5199E-02 X2 X4
Z5 = - 1.7177E-02 X1 + 2.1945E-01 X2 - 3.0883E-02 X3 + 1.1985E+00 X4 + 4.6847E-08
X5 + 1.1239E-02 X6 - 1.1293E-02 X7 - 4.4189E-01 log(X5) - 6.5028E-02 log(X6) -
2.2339E-02 exp(X1) + 5.6607E-02 exp(X4) + 3.3631E-01 X12 - 5.7569E-06 X6
2 -
1.0962E-01 X43 - 7.8377E-02 X1 X2 - 3.3091E-04 X1 X3 + 8.2437E-02 X1 X4 - 1.4021E-
01 X1 X7 - 6.6236E-02 X2 X4 + 8.8069E-05 X1 X3 X6
Z6 = - 2.2893E-01 X1 - 1.7333E-02 X2 - 1.3748E-03 X3 + 2.4204E-01 X4 + 8.9714E-09
X5 + 8.8196E-03 X6 + 5.7684E-03 X7 - 2.6648E-01 log(X5) - 5.2145E-02 log(X6) +
1.6261E-02 log(X7) - 2.3880E-02 exp(X1) + 1.7144E-03 exp(X2) - 3.9312E-04 exp(X3)
+ 1.5226E-02 exp(X4) + 4.1615E-01 X42 - 4.6282E-06 X6
2 + 4.4112E-02 X13 - 7.0894E-
02 X43 - 3.5536E-01 X1 X4 + 5.2162E-03 (X1 X4)
2
142
Reverse Water Gas Shift (RWGS)
Table C15. Input Variables and Bounds for RWGS
Input
Variables
Description Superstructure
model
variable
Lower
Bound
Upper
Bound
Unit
X1 Molar flowrate of
CO2 to RWGS 𝐹𝐵𝐶𝑂2 ,𝑅𝑊𝐺𝑆 0 5 Mol/s
X2 Molar flowrate of
H2 to RWGS 𝐹𝐵𝐻2 ,𝑅𝑊𝐺𝑆 0 5 Mol/s
X3 Inlet pressure of
gases to RWGS 𝑃𝑅𝑊𝐺𝑆 1e5 25e5 Pa
X4 Inlet temperature
of gases to RWGS 𝑇𝑅𝑊𝐺𝑆 400 1200 K
X5 Length of RWGS 𝐿𝑅𝑊𝐺𝑆 0.5 2 M
Table C16. Output Variables for RWGS
Output
Variables
Description Superstructure
model variable
Unit
Z1 Molar flowrate of CO2 from
RWGS to Syngas block
𝐹𝑟𝑅𝑊𝐺𝑆,𝑆𝑇,𝐶𝑂2 Mol/s
Z2 Molar flowrate of CO from
RWGS to Syngas block 𝐹𝑟𝑅𝑊𝐺𝑆,𝑆𝑇,𝐶𝑂 Mol/s
Z3 Molar flowrate of H2O from
RWGS to Syngas block 𝐹𝑟𝑅𝑊𝐺𝑆,𝑆𝑇,𝐻2𝑂 Mol/s
Z4 Molar flowrate of H2 from
RWGS to Syngas block 𝐹𝑟𝑅𝑊𝐺𝑆,𝑆𝑇,𝐻2
Mol/s
Output Variable Models for RWGS
Z1 = 1.1973E+00 X1 + 7.6034E-02 X2 + 3.9936E-08 X3 + 8.9535E-04 X4 - 1.5839E-03
X5 - 3.7632E-02 log(X3) + 3.4336E-03 exp(X1) - 9.7404E-03 exp(X2) + 1.0008E-01 X12
+ 2.7180E-01 X22 - 8.4975E-08 X4
2 - 1.8936E-02 X13 - 8.7942E-02 X2
3 + 1.0977E-02
X24 - 6.3285E-02 X1 X2 - 6.0257E-04 X1 X4 - 5.9405E-04 X2 X4 + 1.1983E-03 (X1 X2)
2
+ 3.4372E-08 (X1 X4)2 + 3.5779E-08 (X2 X4)
2
Z2 = 1.0382E-01 X1 + 5.3013E-01 X2 + 2.8861E-08 X3 + 7.4223E-04 X4 + 1.8174E-02
X5 - 4.1224E-02 log(X3) + 2.5315E-03 exp(X1) - 2.9030E-02 exp(X2) - 4.1754E-02 X12 -
5.4210E-01 X22 - 3.2290E-07 X4
2 + 2.7715E-01 X23 - 6.4113E-02 X2
4 + 6.5477E-03 X25
+ 3.7280E-05 X55 - 4.2948E-02 X1 X2 + 8.9911E-05 X1 X4 + 4.2689E-09 X2 X3 +
9.1305E-05 X2 X4 + 1.0716E-04 X1 X2 X4
143
Z3 = 1.0382E-01 X1 + 5.3013E-01 X2 + 2.8861E-08 X3 + 7.4223E-04 X4 + 1.8174E-02
X5 - 4.1224E-02 log(X3) + 2.5315E-03 exp(X1) - 2.9030E-02 exp(X2) - 4.1754E-02 X12 -
5.4210E-01 X22 - 3.2290E-07 X4
2 + 2.7715E-01 X23 - 6.4113E-02 X2
4 + 6.5477E-03 X25
+ 3.7280E-05 X55 - 4.2948E-02 X1 X2 + 8.9911E-05 X1 X4 + 4.2689E-09 X2 X3 +
9.1305E-05 X2 X4 + 1.0716E-04 X1 X2 X4
Z4 = 1.9729E-01 X1 + 1.0760E+00 X2 + 3.9936E-08 X3 + 8.9535E-04 X4 - 1.5840E-03
X5 - 3.7632E-02 log(X3) + 3.4336E-03 exp(X1) - 9.7404E-03 exp(X2) + 1.0008E-01 X12
+ 2.7180E-01 X22 - 8.4975E-08 X4
2 - 1.8936E-02 X13 - 8.7942E-02 X2
3 + 1.0977E-02
X24 - 6.3285E-02 X1 X2 - 6.0257E-04 X1 X4 - 5.9405E-04 X2 X4 + 1.1983E-03 (X1 X2)
2
+ 3.4372E-08 (X1 X4)2 + 3.5779E-08 (X2 X4)
2
144
Table C17. Model Statistics and Other Data for all the reactors
Reactor Type N-X N-Z N-USER N-INIT N-SAMP N-VAL Time(s) OUTVAR MODSIZE Average R2
DR 5 7 0 200 255 50 1000 Z1 20 1
Z2 20 0.999
Z3 39 0.995
Z4 34 0.996
Z5 28 0.968
SMR 5 7 0 250 899 50 1000 Z1 20 1
Z2 46 0.989
Z3 49 0.9035
Z4 20 0.999
Z5 50 0.9895
POX 5 8 0 200 750 50 1000 Z1 20 0.925
Z2 20 0.5405
Z3 20 0.8615
Z4 20 0.787
Z5 20 0.838
Z6 20 0.882
CDSMR 6 7 0 240 768 60 10000 Z1 20 0.9995
Z2 20 0.998
Z3 50 0.981
Z4 20 0.998
Z5 50 0.9865
PODR 6 8 0 240 984 60 10000 Z1 20 0.9055
Z2 20 0.8455
145
Table C17. Continued. Reactor Type N-X N-Z N-USER N-INIT N-SAMP N-VAL Time(s) OUTVAR MODSIZE Average R2
PODR Z3 20 0.884
Z4 20 0.8915
Z5 20 0.7855
Z6 20 0.8785
POSMR 6 8 0 240 840 60 10000 Z1 20 0.893
Z2 20 0.645
Z3 20 0.846
Z4 20 0.8955
Z5 20 0.8175
Z6 20 0.8635
TR 7 8 0 280 956 70 10000 Z1 20 0.844
Z2 20 0.8505
Z3 20 0.8645
Z4 20 0.9195
Z5 20 0.818
Z6 20 0.8725
RWGS 4 8 200 640 50 10000 Z1 20 0.998
Z2 20 0.9835
Z3 20 0.9835
Z4 20 0.998