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Copyright and Citation Considerations for This Thesis/ Dissertation

Copyright and Citation Considerations for This Thesis/ Dissertation

COPYRIGHT AND CITATION CONSIDERATIONS FOR THIS THESIS/ DISSERTATION

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How to cite this thesis

Surname, Initial(s). (2012) Title of the thesis or dissertation. PhD. (Chemistry)/ M.Sc. (Physics)/ M.A. (Philosophy)/M.Com. (Finance) etc. [Unpublished]: University of Johannesburg. Retrieved from: https://ujcontent.uj.ac.za/vital/access/manager/Index?site_name=Research%20Output (Accessed: Date). ATTAINABLE REGIONS FOR OPTIMAL REACTION NETWORKS: APPLICATION OF ΔH-ΔG PLOT TO DIRECT SYNTHESIS OF DIMETHYL ETHER FROM SYNGAS

By

THULANE PAEPAE

Submitted In Fulfilment of the Requirements of

MASTERS TECHNOLOGIAE

In

CHEMICAL ENGINEERING

In the

FACULTY OF ENGINEERING AND THE BUILT ENVIRONMENT Of the UNIVERSITY OF JOHANNESBURG

Supervisor: Dr Tumisang Seodigeng

Co-supervisor: Prof Freeman Ntuli

Johannesburg, 2015 DECLARATION

I hereby declare that this dissertation which I submit in fulfilment for the qualification

MAGISTER OF TECHNOLOGIAE IN

to the University of Johannesburg, Department of Chemical Engineering is, apart from the recognized assistance from my supervisors, my own work which has not previously been submitted by me or any other person to any institution to obtain a degree.

On this Day of

i

ABSTRACT

Industrial processes pose a serious threat to the world’s natural resources for they consume them in high proportions as sources of energy for driving chemical processes that provide raw materials for many industrial chemicals. The chemical and petrochemical industries consume about 61% of global industrial energy and emit about 36% of carbon dioxide to the environment. A significant portion of the energy demand is entirely for feedstock, which cannot be reduced through energy efficiency measures. The responsibility therefore for cutting back on the amount of energy needed for chemical processes rests on improving the efficiency of the processes used.

The purpose of this research is to demonstrate the use of a novel method of synthesizing process flowsheets, using a graphical tool called the GH-space and in particular to look at how it can be used to compare the reactions of a combined simultaneous process with regard to their thermodynamics. This allows us to synthesize flow-sheets that are reversible and which meet the process targets by implementing mass and energy integration. It also provides guidance on what design decisions would be best suited to developing new processes that are more effective and make lower demands on raw material and energy usage. The approach also provides useful information for evaluating processes through likely limiting extents with respect to the reaction pathways, and comparison between the research findings and their theoretical targets in order to identify any possible energy savings that can be made.

The GH-space technique uses fundamental thermodynamic principles to allow the mass, energy and work balances locate the attainable region for chemical processes in a reactor. Furthermore, processes and unit operations can be defined as vectors in the GH-space. Using the targets, one can combine the vector processes in such a way as to approach the target. These vector processes, and the way they are combined, can then be interpreted in terms of flowsheets. This is opposite to what is normally done and allows the process balances to determine what the best flowsheet might look like, allowing for great innovation from the very start of a design. In addition to this, probably the greatest advantage of the GH-space technique is that processes of great complexity can all be analysed on a set of two- dimensional axes. After finding the attainable region, its boundaries can be interpreted in

ii terms of the prospective limiting extents through mass balances. By these means we can deduce the process reaction pathways. The technique allows for easy and rapid interpretation of the results, such as the effects of changes in operating conditions. It also provides insight into the likely reactions achievable in the reactor under different process conditions.

This approach was applied to the direct synthesis of dimethyl ether from syngas. The graphical plots show that the introduction of carbon dioxide in the feed changes the shape and size of the attainable region, resulting in multiple reaction pathways. They also demonstrate that the reaction pathways leading to the product and the change in ΔG across the reactor are interlinked. It was shown in this work that with clear understanding of the flows of mass, energy and work within a process, the reaction path analysis could become an important tool in the preliminary stages of since it can identify the most desirable reaction routes.

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DEDICATION

This dissertation is utterly dedicated to the Lord Almighty, for His immeasurable mercy, compassion and guidance throughout this work.

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ACKNOWLEDGMENTS

I owe thanks to many people, whose assistance was fundamental to the accomplishment of this project.

Firstly, I express my sincere gratitude to my supervisor, Dr Tumisang Seodigeng for his technical guidance and constructive advice, continual suggestions, and encouragement to develop me into an independent researcher. Many thanks for his help which extended beyond my research.

I would like to thank Prof Freeman Ntuli for his assistance in the accomplishment of this project.

I am indebted to the National Research Foundation (NRF), and the University of Johannesburg for the financial support.

Above all, I would like to thank my family: my mother, brothers and sisters for their support, encouragement and love throughout my life.

Lastly, I offer my regards and blessings to all of those whose names are not mentioned here but supported me in one way or another towards the success of this research.

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TABLE OF CONTENTS

LIST OF FIGURES ...... viii

LIST OF TABLES ...... xi

LIST OF ACRONYMS ...... xii

CHAPTER 1: INTRODUCTION ...... 1

1.1 Background and Motivation...... 1

1.2 Research Aims and Objectives ...... 5

1.2.1 Aims ...... 5

1.2.2 Objectives...... 5

1.3 Significance and Impact of this Research ...... 6

1.4 Thesis Overview ...... 7

CHAPTER 2: LITERATURE REVIEW ...... 12

2.1 Introduction ...... 12

2.2 Optimal Reactor Networks ...... 12

2.3 Attainable Region Targeting ...... 14

2.3.1 Kinetically attainable region ...... 14

2.3.2 Thermodynamically attainable region ...... 16

2.4 Dimethyl Ether Synthesis ...... 18

2.4.1 Introduction ...... 18

2.4.2 Chemistry ...... 19

2.4.3 Reaction kinetics ...... 22

2.4.4 Essential factors to consider for dimethyl ether production ...... 23

vi

CHAPTER 3: METHODOLOGY ...... 42

3.1 Introduction ...... 42

3.2 Thermodynamic Analysis of the Process ...... 42

3.2.1 Effect of Temperature on the Equilibrium Conversions of Chemical Reactions .. 44

3.2.2 Effect of Pressure on the Equilibrium Conversions of Chemical Reactions ...... 50

3.3.3 Effect of Initial Composition on the Equilibrium Conversions of Chemical Reactions ...... 51

CHAPTER 4: RESULTS, ANALYSIS AND DISCUSSION ...... 56

4.1 Introduction ...... 56

4.2 Thermodynamically Attainable Region ...... 56

4.2.1 Stoichiometric subspace for a single reaction ...... 64

4.2.2 Presenting the stoichiometric subspace in terms of the GH space ...... 67

4.2.3 Energy and work balances in the GH space ...... 69

4.2.4 Effects of changes in temperature and pressure on GH space for a one reaction . 70

4.2.5 Stoichiometric subspace and GH space involving three reactions ...... 75

4.2.6 Feed analysis on the GH space ...... 82

4.2.7 The attainable region for the reactor ...... 94

4.2.8 Effect of changes in operating conditions ...... 95

CHAPTER 5: CONCLUSION AND RECOMMENDATIONS ...... 103

5.1 Summary of Results...... 104

5.2 Recommendations and Future Work ...... 106

APPENDIX A: THERMODYNAMIC DATA ...... 107

vii

LIST OF FIGURES

1.1-1: Financial features and degrees of freedom of the several stages in process design [6]...... 3

2.1-1: Dimethyl ether production diagram [34]...... 19

2.1-2: A scheme of indirect synthesis process [34]...... 19

2.1-3: A schematic of direct synthesis process [34]...... 20

2.1-4: Effects of temperature on equilibrium constant of reactions involved in DME synthesis...... 24

2.1-5a: Temperature effect at 50 bar and H2: CO = 1 on syngas conversion to DME [53]. .. 25

2.1-6b: Temperature effect at 50 bar and H2: CO = 1 on the selectivity and productivity of DME at SV of 15,000 Nml/gcat/h [53]...... 26

0 2.1-7: Pressure effect on the synthesis of DME at 250 C, H2: CO = 2 and SV of 15,000 Nml/gcat/h [53]...... 27

2.1-8: Equilibrium conversion of syngas at 50 bar and 280 0C [64]...... 30

2.1-9: Selectivity and conversion against syngas ratio at 50 bar and 260 0C [64]...... 31

3.2-1: Representation of this typical process showing feed and product streams...... 43

4.1-1: Area under the curve or heat added in raising the temperature from T1 to T2...... 57

4.1-2: Area under the curve or heat added in raising the temperature from 298 to 523 K. . 60

viii

4.1-3: An extent plot for a single reaction...... 66

4.1-4: Depiction of a using the G-H plot for one reaction at standard conditions (1 bar and 25 0C)...... 67

4.1-5: Energy balance analysis by means of the G-H plot...... 69

4.1-6: Work balance analysis by means of the G-H plot...... 70

4.1-7: The effects of temperature variations on methanol dehydration reaction at 1 bar. ... 71

4.1-8: The effects of temperature variations on methanol synthesis reaction...... 72

4.1-9: The effects of pressure variations on methanol synthesis reaction...... 73

4.1-10: Effects of pressure variations on a methanol dehydration reaction...... 74

4.1-11: Extent plot for the summation of three reactions using a stoichiometric feed...... 78

4.1-12: Depiction of the GH plot showing methanol and water gas shift reactions at 25°C and 1 bar using a stoichiometric feed...... 80

4.1-13: Depiction of the GH plot showing MeOH synthesis and DME synthesis reactions, at 25°C and 1 bar, using a stoichiometric feed...... 81

4.1-14: The Gibbs free energy as a function of the extent of the reaction...... 82

4.1-15: Depiction of a chemical process using the G-H plot for DME synthesis reactions

using a four component feed containing CO (2 mols), H2 (3 mols), H2O (0.5 mol),

and CH3OH (2 mols)...... 83

ix

4.1-16: Depiction of a chemical process using the G-H plot for DME synthesis using a five-

feed component of CO (2 mol), CO2 (1 mol), H2 (3 mols), H2O (0.5 mol), and

CH3OH (2 mols)...... 84

4.1-17: Extent plot for MeOH and WGS reactions, with a feed consisting of CO (1 mol), H2

(3 mols), CO2 (1 mol) and 0.5 mols of H2O...... 87

4.1-18: G-H plot for DME synthesis reactions, with a feed of CO (2 mols), CO2 (1 mol), H2

(3 mols), H2O (0.5 mol), and CH3OH (2 mols)...... 89

4.1-19: Attainable region for DME synthesis in GH space at 25 0C and 1 bar, using a feed of

CO (2 mol), CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol)...... 94

4.1-20: Reactor’s AR for DME synthesis in GH space at 200 0C and 50 bar, with a feed of

CO (2 mol), CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol)...... 96

4.1-21: Reactor’s AR for DME synthesis in GH space at 260 0C and 50 bar, with a feed of

CO (2 mol), CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol)...... 97

4.1-22: AR for DME synthesis in GH space at 300 0C and 50 bar, using a feed of CO (2

mol), CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol)...... 98

4.1-23: AR for DME synthesis in GH space at 260 0C and 30 bar, using a feed of CO (2

mol), CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol)...... 99

4.1-24: AR for DME synthesis in GH space at 260 0C and 70 bar, using a feed of CO (2

mol), CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol)...... 100

x

LIST OF TABLES

4.1-1: Heat capacity constants and sample calculations...... 61

4.1-2: Part of enthalpy calculation as a function of temperature...... 61

4.1-3: Part of Gibbs free energy calculation as a function of temperature...... 62

4.1-4: Part of Gibbs free energy calculation as a function of pressure...... 62

4.1-5: Enthalpy and Gibbs free energy at standard conditions...... 63

xi

LIST OF ACRONYMS

Symbol Designation

GTL Gas to Liquid

DME Dimethyl ether

CO Carbon monoxide

CO2 Carbon dioxide

H2 Hydrogen

CH3OH/ MeOH Methanol

ZnO Zinc oxide

Al2O3 Aluminium Oxide

PFR Plug Flow Reactor

CSTR Continuous Stirred Tank Reactor

MINLP Mixed Integer Non Linear Programming

AR Attainable Region

ARC Candidate Attainable Region

DSR Differential Side Reactor

LPG Liquefied Petroleum Gas

WGS Water Gas Shift

SV Space Velocity

xii

LIST OF SYMBOLS

Symbol Designation Unit

H Enthalpy (heat content) J/mol

H0 Enthalpy of formation J/mol

Hp Enthalpy of products J/mol

Hr Enthalpy of reactants J/mol G Gibbs free energy J/mol

G0 Gibbs free energy of formation J/mol

S Entropy J/mol P Pressure Bar

P0 1 Bar pressure Bar P0 Pressure other than 1 Bar Bar T Absolute temperature K

T0 Standard temperature K T0 Temperature other than 298K K

Cp Heat capacity J⁄ mol. K

0 Cp Heat capacity above 298K J⁄ mol. K

R Gas constant J⁄ mol. K 휀 Extent of reaction Mole Δ Change of function of state -

xiii

CHAPTER 1: INTRODUCTION

1.1 Background and Motivation

Energy is a fundamental element of the modern economy hence its management must be sustainable and less dependent on increasingly scarce fossil fuels. The use of energy entails substantial financial, environmental and security costs that cannot be quantified in economic terms alone. But still, customers should be able to count on a reliable supply of energy at viable prices. To achieve this, all forms of safe and reliable energy options are essential. In view of the changing climate and the decreasing availability of fossil fuel, a realistic transition to sustainable energy is required in the longer term. These calls for an international economic approach that ensures businesses and the public are not saddled with unnecessarily high costs. A viable method for reducing the cost of energy while retaining its benefits is to produce it more efficiently [1].

Industrial processes pose a serious threat to the world’s natural resources for they consume them in high proportions as sources of energy for driving chemical processes that provide raw materials for many industrial chemicals. The chemical and petrochemical industries consume about 61% of global industrial energy and emit about 36% of carbon dioxide to the environment [2]. A significant portion of the energy demand is entirely for feedstock, which cannot be reduced through energy efficiency measures.

The responsibility therefore for cutting back on the amount of energy needed for chemical processes rests on improving the efficiency of the processes used. In the context of preventing/avoiding changes in regional climate patterns (climate change), this type of approach becomes significant since it reduces the consumption of fossil fuels hence less carbon dioxide emission to the environment. A decrease in carbon dioxide emission means that the process is efficient (considering the emission standards and legalities attached to acceptable emission limits) which is fundamental to achieving three most important goals of energy policy: environmental protection, security of supply, and economic growth. Carbon dioxide is considered the major course of global warming since it constitutes about 72% of

1 emitted greenhouse gases; hence its reduction is in line with the energy policy. Kyoto Protocol scheme was born of the need for international community to address the greenhouse effect and its detrimental effect on the environment [3]-[4].

There is a growing need among design engineers to develop energy efficient chemical processes that focus on reducing raw material and energy requirements [5]. Entropy, energy, and mass balances are the fundamental concepts utilised to achieve the energy policy and also give insights into processes. These concepts allow the engineer to establish plant performance targets and also improve the overall process performance, leading to savings in capital and operating costs hence a sustainable chemical process [5]-[7]. Sustainability in this context means [8]-[9]:

 Efficient operation  Economic  Correct raw material  Low waste  Low environmental impact

Decisions taken during the conceptual design phase are very important as about 80% of the total process capital and operating costs is fixed at this stage [6] as shown in Figure 1.1-1. As seen in this Figure, cost and degrees of freedom are in inverse relationship, which is expected since there is normally not enough information available during the conceptual design phase. Unfortunately, once the flowsheet and chemistry of the process has been decided, most of the opportunities for improvement and innovation have been lost. This therefore justifies the need for systematic techniques that can be applied with as little information as possible and still provide sufficient and accurate information to aid in making decisions toward more sustainable processes at this phase since the success of a chemical process is essentially realised by the conceptual design.

2

Figure 1.1-1: Financial features and degrees of freedom of the several stages in process design [6].

New liquid fuels synthesis has been the subject of intense study internationally in recent years. Dimethyl ether (DME) as one of the alternatives has attracted some attention due to its probable impact on the society. Due to its high cetane number (about 55-60), it is a potential for high quality diesel fuel [10]-[11]. Its combustion does not emit gases that are harmful to the environment; hence it is known to be a clean fuel. It has physical properties comparable to those of Liquefied Petroleum Gas (LPG) and therefore can be used for heating and home cooking. DME has a higher boiling point compared to LPG hence storage, transportation and usage of, do not pose any serious problems. Dimethyl ether can therefore be considered as an alternate fuel and replace LPG to reduce the reliance on petroleum [12]-[18]. DME can be synthesised from a number of different sources like; biomass, gas, petroleum, and coal. However, the conventional route is via methanol dehydration over an acidic porous catalyst such as γ − Al2O3 [19]-[21].

3

There has been a significant amount of research conducted on experimental and simulation of both DME synthesis routes (direct and indirect) in different reactor configurations. Among others, Nasehi et al. [22] modelled and simulated a two-step dimethyl ether synthesis route by investigating the effects of changing an adiabatic fixed bed reactor inlet conditions. Raoof et al. [23] used the same reactor (adiabatic fixed bed) to perform an experimental and simulation study on methanol dehydration to DME. Their results showed a much slower catalyst deactivation when pure methanol was used as feed to the process.

Thermodynamics has been shown to be a useful tool in studying chemical processes [24]. Its methods can be used to compare different processes [25] and also be used to understand and improve them [26]. Okonye et al. [27] presented a thermodynamic method that can be used to analyse reactions occurring in a reactor. The technique helps the design engineer know which among all the reactions happening in a reactor is/are likely to dominate in that process. It also helps the designer know the conversions and yields achievable in that particular process. This technique further makes it possible to evaluate and compare process efficiencies against their theoretical targets and allows one to identify where inefficiencies could be coming from within the process. The method can be applied to industrial processes aiming to: (1) obtain optimal results, (2) identify probable means of saving energy, and (3) devise procedures for supplying or recovering energy from the processes so as to enhance process reversibility and efficiency. The authors [27] applied this technique to the synthesis of methanol where they identified and defined the thermodynamic Attainable Region (AR).

The AR provides the theoretical basis for design engineers to graphically visualise all possible concentration combinations in the solution space, which can be achieved in any chemical reaction system without restricting choices/options in an attempt to making the problem smaller. This is different from the way that reactor synthesis is often done. For instance, in the absence of theoretical tools like the AR, heuristics or “rules of thumb” are often used to limit the problem space. This approach is more of a trial and error and the trouble is that decisions are not based on science but rather on the way things have always been done [27]-[28]. Not that past experience is not important or should be overlooked, but new combinations will certainly not be realised by relying only on experience and rules of thumb, and there is a potential of accidentally ruling out optimal approaches by limiting combinations of operations.

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1.2 Research Aims and Objectives

1.2.1 Aims

The aim of the study was to use fundamental thermodynamic principles to consider what measures could render the synthesis of Dimethyl ether (DME) more efficiently.

1.2.2 Objectives

The main objective was to evaluate the direct synthesis of dimethyl ether from syngas using a simple graphical approach which could identify the space of all possibilities (or AR), and in particular visualizing what that space looks like so as to gain better insights into the inner workings of this chemical system. This technique provides a systematic way for process designers to not only determine process targets or achieve optimal efficiency but also understand what could be essential to meeting these targets.

Previous work by [27] has shown that thermodynamic analysis is a very influential tool for the setting and evaluation of process targets. The approach used in this dissertation is based on the idea that every process in which certain feed materials are converted into products has a certain amount of heat and work associated with it. Understanding the relationship between this heat and work can provide insight into the process and can also give an indication of what the process structure would be. The analysis involves the use of performance targets for a chemical process that are based on mass, energy and entropy (the second law of thermodynamics). This approach looks at chemical processes holistically, where only the inlet and outlet streams are considered. Processes are represented and classified in different thermodynamic regions in a ΔH-ΔG space (GH-diagram) where their feasibility and reversibility are analysed. Since the approach does not require much information or complex calculations, it is suitable to be used in the early stage of process design since it can proffer a quick insight into the design of new processes as well as ideas for enhancing the performance of older ones if properly used.

The purpose of this research is to extend the approach described above and in particular to look at how it can be used to compare more than two reactions of a combined simultaneous

5 process with regard to their thermodynamics. This allows us to synthesize flow-sheets that are reversible and which meet the process targets by implementing mass and energy integration. It also provides guidance on what design decisions would be best suited to developing new processes that are more effective and make lower demands on raw material and energy usage. The approach also provides useful information for evaluating processes through likely limiting extents with respect to the reaction pathways, and comparison between the research findings and their theoretical targets in order to identify any possible energy savings that can be made.

1.3 Significance and Impact of this Research

The research intends to contribute to the current debate on how to improve the chemical processes efficiency and reduce carbon dioxide emissions. Ideally, the process aims to contribute to:

 The reduction of CO2 emissions, which degrade the environment and accelerate the threat of climate change;  The use of smaller amounts of raw materials and energy, to increase process efficiency and lower costs, thus ensuring industrial sustainability;  The substitution of alternate sources of fuel from biomass, coal, or gases; and  The adoption of DME fuel as an efficient source of energy that is renewable, economically competitive and has a low environmental impact.

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1.4 Thesis Overview

The thesis is outlined as follows:

Chapter 1: Provides a clear understanding of the subject matter of this thesis. It discusses the background and motivation of the study; presents the challenges posed by threats to environmental sustainability; it highlights the objectives of the research; the research problem and the academic/industrial contribution this work is expected to make.

Chapter 2: Encompasses a literature review, which is presented in three parts. The first gives an overview of optimal reactor networks; the second focuses mainly on thermodynamic and kinetic attainable region analysis while the third discusses the dimethyl ether synthesis process which looks at the process chemistry, reaction kinetics, and the effects of changes in process conditions for this synthesis.

Chapter 3: Comprehensively discusses the methodology used, the fundamental principles involved; the application of mass balances, energy balances, work balances, and reaction coordinate calculations to map the extent plot, which is eventually explained in terms of the GH-space.

Chapter 4: Discusses the probable results of the dimethyl ether synthesis process under altered process conditions. The analysis is made via the reactor’s attainable region, the expected reaction pathways, and the reactions occurring within the reactor.

Chapter 5: Summarises the research undertaken, gives the overall conclusions, and makes recommendations for further development of the DME process synthesis.

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References

[1] Ministry of Economic Affairs, Agriculture and Innovation. Energy Report, (2011).

[2] International Energy Agency (IEA, 2007). Tracking Industrial Energy Efficiency and

CO2 Emissions. Organisation for Economic Co-Operation and Development/ International Energy Agency (OECD/ IEA), 23-25.

[3] Enick, R. M., Hill, J., Cugini, A. V., Rothenberger, K. S. & Mcllvried, H.G. (1999). A model of a high temperature, high pressure water gas shift tubular membrane reactor. ACS Division of Fuel Chemistry Preprints, 44 (4), 1999.

[4] McMillen, K. R., Meyer, T. R. & Clark, B. C. (1993). Methanol: A Fuel for Earth and Mars, A presentation at the Case for Mars Conference, American Astronomical Society (AAS-93, 880), 26th – 29th May 1993, 3-17.

[5] International Energy Agency (IEA, 2008). International standards to develop and promote energy efficiency and renewable energy sources. IEA Information paper in support of G8 plan of action. Organisation for Economic Co-Operation and Development/ International Energy Agency (OECD/ IEA), Paris, France.

[6] Moran, M. J. & Shapiro, H. N. (2006). Fundamentals of Engineering Thermodynamics, Kinetics and Reactor Design. 5th edition, John Wiley & Sons, Inc., Chichester, West Sussex, England.

[7] OECD, (1998). Biotechnology for clean industrial products and processes: Towards Industrial Sustainability. Organisation for Economic Co-operation and Development. Paris, France.

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[8] WCED, (1987). Our Common Future (The Brundtland Report). A Report of the World Commission on Environment and Development, Oxford University press, Oxford, 43.

[9] Song, C. (2002). Fuel processing for low-temperature and high-temperature fuel cells: challenges, and opportunities for sustainable development in the 21st century. Catalysis Today, 77, 17-49.

[10] Ng, K. L., Chadwick, D. & Toseland, B. A. (1999). Kinetics and modelling of dimethyl ether synthesis from synthesis gas. Chemical and Engineering Science, 54, 3587-92.

[11] Galvita, V. V., Semin, G. L., Belyaev, V. D., Yuieva, T. M. & Sobyanin, V. A. (2001). Production of hydrogen from dimethyl ether. Applied Catalysis A, 216 (1-2), 85-90.

[12] Tartamella, T. L. & Lee, S. (1997). Development of speciality chemicals from dimethyl ether. Fuel Process Technology, 38 (4), 228.

[13] Alam, M., Fujita, O. & Ito, K. (2004). Performance of NOx reduction catalysts with simulated dimethyl ether diesel engine exhausts gas. Process Instrumentation and Part J Power Energy, 218-89.

[14] Sorenson, S. C. (2001). Dimethyl ether in diesel engines: progress and perspectives. Journal of Engineering Gas Turbines, Power Trans ASME, 123, 652-8.

[15] Rouhi, A. M. & Topsoe, A. H. (1995). Develop dimethyl ether as alternative diesel fuel. Chemical Engineering News, 73-37.

[16] Fleisch, T. H., Basu, A., Gradassi, M. J. & Masin, J. G. (1995). Dimethyl ether: a fuel for the 21st century. Natural Gas Convers IV, Stud Surf Scientific Catalysis, 107-17.

[17] Song, J., Huang, Z., Qiao, X. Q. & Wang, W. L. (2004). Performance of a controllable premixed combustion engine fuelled with dimethyl ether. Energy Convers Manage, 45 (13-14), 2223-32.

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[18] Zannis, T. C. & Hountalas, D. T. (2004). DI diesel engine performance and emissions from the oxygen enrichment of fuels with various aromatic content. Energy Fuels, 18 (3), 659-66.

[19] Lu, W. Z., Teng, L. H. & Xiao, W. D. (2004). Simulation and experiment study of Dimethyl ether synthesis from syngas in a fluidized-bed reactor. Chemical and Engineering Science, 59, 5455-64.

[20] Bercic, G. & Levec, J. (1993). Catalytic dehydration of methanol to dimethyl ether- Kinetic investigation and reactor simulation. Industrial and Engineering Chemistry Research, 32 (11), 2478-84.

[21] Nie, Z. H., Liu, H., Liu, D., Ying, W. & Fang, D. (2005). Intrinsic kinetics of dimethyl ether synthesis from syngas. J Nat Gas Chemistry, 14 (1), 22-8.

[22] Nasehi, S. M., Eslamlueyan, R. & Jahanmiri, A. (2006). Simulation of DME reactor from methanol. In: Proceedings of the 11th chemical engineering conference, Iran, Kish Island.

[23] Raoof, F., Taghizadeh, M., Eliassi A. & Yaripour, F. (2008). Effects of temperature and feed composition on catalytic dehydration of methanol to dimethyl ether over calumina fuel. Industrial and Engineering Chemistry Research, 87, (13-14), 2967-71.

[24] Patel, B., Hildebrandt, D., Glasser, D. & Hausberger, B. (2005). Thermodynamics analysis of processes. 1. Implications of work integration. Industrial & Engineering Chemistry Research, 44, 3529-3537.

[25] Patel, B., Hildebrandt, D. & Glasser, D. (2010). An overall thermodynamic view of processes: Comparison of fuel producing processes. Chemical Engineering Research and Design, 88, 844-860.

[26] Hildebrandt, D., Glasser, D., Hausberger, B., Patel, B. & Glasser, B. (2009). Invited perspectives article. Producing transportation fuels with less work. Science, 323, 1680- 1681.

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[27] Okonye L. U., Hildebrandt, D., Glasser, D., & Patel, B. (2012). Attainable regions for a reactor: Application of ∆H − ∆G plot. Chemical Engineering Research and Design, 90, 1590-1609.

[28] Glasser, D., Hildebrandt, D. & Crow, C. A. (1987). A geometric approach to steady flow reactors: the attainable region and optimization in concentration space. Industrial Engineering Chemical Resource, 26, 1803-1810.

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CHAPTER 2: LITERATURE REVIEW

2.1 Introduction

Many theories have been proposed to explain the optimisation of reactor networks. Although the literature covers a wide variety of theories, this review will focus only on two major themes which emerge repeatedly throughout the literature reviewed. These themes are: the attainable region which has been studied extensively for the past two decades, DME synthesis process technologies where the chemistry, kinetics and process conditions will be discussed. Although the literature presents the AR in a variety of contexts, this project primarily focuses on its application via thermodynamic principles to the synthesis of DME from syngas.

2.2 Optimal Reactor Networks

Chemical processes turn inexpensive chemicals (raw materials) into valuable ones (desired products) in chemical reactors hence the performance of these reactors is very important to chemical engineers. Surprisingly, relatively few systematic procedures for optimal reactor network synthesis have been proposed even though reactor design is of such importance in chemical processes. The reactor network synthesis field has however grown significantly in the last two decades [1].

The goal of reactor network synthesis is to discover optimal reactor types, arrangements and flow configurations as well as key design parameters for given operating conditions and underlying reaction kinetics that will optimize an explicit objective function. Superstructure optimization methods and geometric/targeting methods are major mathematical programming strategies that are used for synthesis of reactor networks. In superstructure optimization, a fixed network of reactors is used to find an optimal sub-network that maximizes/optimizes a given objective function. With this technique, it is difficult to confirm that all possible networks have been selected in the initial superstructure and the solution relies entirely on the initial superstructure chosen therefore this approach may be suboptimal [2].

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Horn and Tsai [3] utilised the adjoint variables of optimization to study the effects of local and global mixing. Jackson [4] postulated an adjoint reactor superstructure made of plug flow reactors (PFR) interconnected with side-streams. As a modification to Jackson’s work, Ravimohan [5] added continuous-stirred tank reactors (CSTR) instead. From the middle point along the length of a reactor, Chitra and Govind [6]-[7] studied superstructures made up of PFR systems with a recycle stream optimizing both the point of recycle and the recycle ratio and finally suggested that this reactor system could possibly model PFR's, CSTR's and recycle reactors with the objective functions based mainly on reaction yield.

Achenie and Biegler [8]-[9] also revised Jackson’s approach by using optimal control philosophy generated by a system of adjoint equations to compute tangents for a nonlinear programming algorithm. Kokossis and Floudas [10]-[12] proposed a global technique for reactor network superstructure optimization where the superstructure was modeled and optimized as a mixed-integer nonlinear programming (MINLP) problem. This superstructure optimization incorporated CSTRs and PFRs with various interconnections. The PFRs were estimated by a sequence of equal-sized sub-CSTRS and integer variables were utilised to show the presence of the reactor units. The resulting formulation was a large-scale, complex, non-convex MINLP free of differential equations.

Kokossis et al. [13]-[14] took this superstructure approach further by using stochastic optimization to handle stability of reactor networks and integration with recycle systems. Although this superstructure method leads to an operative synthesis procedure, the subsequent solution is only guaranteed to be locally ideal and is only as rich as the anticipated superstructure. Increasing the richness comes at the cost of increasing the complexity of the model. This approach also allows arbitrarily general network configurations but leads to large MINLP formulations. It was therefore claimed [2] that by making use of attainable region properties, an easier MINLP formulation results with the generality still maintained.

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2.3 Attainable Region Targeting

Targeting for reactor network synthesis is based on the concept of the attainable region in concentration space. The attainable region is defined as the set of all possible points in concentration space that are attainable through reaction and mixing from a given feed point. In targeting, an attempt is made irrespective of the actual reactor configuration to find an achievable bound on the performance index of the system considering only the set of fundamental processes (e.g. reaction, mixing etc.) that can occur. Subsequently, this region thoroughly enumerates the performance of a reacting system [2].

2.3.1 Kinetically attainable region

To overcome the limitations of superstructure optimization, targeting approaches were developed based on the attainable region concept first introduced by Horn [15] while at the imperial college in London, in which he showed that once the AR is found, the establishment of an optimal reaction network is simplified. The kinetically AR is defined as the set of all possible outcome states for the system under consideration that can be obtained by the use of all permitted fundamental processes operating for a given input, subject to all the constraints placed on the system [15]-[19].

While addressing the issue of finding the optimal reactor structure, Horn [15] noted that with known kinetics and given feeds, it could be possible to identify all likely output (AR) concentrations from all possible reactor systems. Knowing the AR makes it possible to search and find the output conditions over that region that optimises a given objective function which in reactor design could be product yield, selectivity, cost effectiveness and/or environmental concerns, among others.

This approach offered two advances in reactor design [20]. Firstly, it simplified the optimization problem by making it possible to search for the maximum of an objective function over defined limits, which is a fairly simple and standard procedure. Secondly, the objective function results could then be used as design measures/targets upon which to evaluate/measure the process performance. However, because of the probable inability to explicitly state any general technique for finding the AR, this concept languished in relative

14 obscurity for about 20 years until ground-breaking work at the University of the Witwatersrand in Johannesburg, South Africa became known [20]-[22].

More than two decades after Horn proposed the AR concepts, Glasser and Hildebrandt [16] approached the problem of finding the AR from a different angle by not following the initial procedure of looking at the equipment, but rather looked at fundamental processes (reaction and mixing) occurring in a reactor. Reaction and mixing were described in terms of vectors in the concentration space. They [16] determined conditions for the AR by using a growing algorithm in conjunction with some necessary conditions. This allowed them to search the AR so as to find and specify the targets for the objective function. This approach eventually ended the 20 year search for the answer to solving the problem of finding an optimum solution for an objective function. Not only was the optimal value for the objective function found, but also the reactor type (optimal equipment) required to achieving this output. It must however be noted that the reactions considered by the authors were the Van de Vusse and the Trambouze reactions [20]-[22].

Hildebrandt and Glasser [17] further examined the geometry of the attainable region. Candidate attainable regions (ARC) under adiabatic (process in which no heat is lost or gained by the system) and isothermal (a change of a system, in which the temperature change remains constant) conditions were identified in this paper by studying several reaction systems, including the Trambouze with assigned kinetics. CSTRs and PFRs with suitable by- pass arrangements were considered in order to analyse the effects of direct and indirect cooling upon the relevant ARC. The authors firstly confirmed the applicability of geometric ideas to solve reactor problems, and secondly conceded that they could not as yet conclude that ARC was the ultimate AR for the specified conditions.

Clear suppositions about optimum process combinations were only affirmed after Glasser et al. [23] made a more refined input on the geometric techniques by proposing geometric principles governing the occurrence of the optimal trajectories for fundamental processes (reaction and mixing) on the attainable region boundary. Differential Side-stream Reactor (DSR) was the term given to this optimal structure. DSR as defined by [23] represents a reaction in which both reaction and mixing happen at the same time in a controlled ratio. DSR can be simply thought of as a Plug Flow Reactor (PFR) with fresh feed introduced along the length of a reactor.

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The mathematical ideologies governing the properties of AR boundary in three dimensions were formalised by Love [24]. Application examples utilising the attainable regions method for optimising network problems were presented by Godorr [25]. Nisoli et al. [26] considered the applicability of the attainable region theory to more complicated processes combining reaction, mixing and separation occurring all at the same time. Two different processes of producing ethers: (1) DME synthesis by methanol dehydration and (2) methyl tertiary butyl ether (MTBE) synthesised from butane and methanol were examined in a two-phase CSTR with a flash separator and a PFR consisting of two-phase CSTRs in series. Vapour and liquid phases were separated in both reactors and the relevant candidate attainable regions identified by removing the vapour and sending it to either the section (MTBE) or to a condenser (DME). The results obtained validated the procedures by Glasser et al. [16] since the geometric properties in concentration space were the same as those of simple reactor models.

2.3.2 Thermodynamically attainable region

The transformation of raw materials into valuable products by means of chemical reactions is an essential step since a vast array of commercial commodities is obtained by chemical synthesis. There are often numerous reactions employed to form desired products. The performance of chemical reactors is of paramount interest; hence the must be accustomed with chemical reactor design and operation. The analysis of these chemical reactors is achieved by studying reacting chemical species behaviours, so as to know the effects of changes in temperature, pressure, and composition of reactants [27]-[28].

A chemical process is subjected to multiple constraints, some of which are: safety considerations, environmental considerations, and economic viability which is subjected to the costs of raw materials, separation and disposal of by-products, and overall process operations. Any increase in product demand necessitates substantial product generation, which in turn sets limits on the acceptable reaction yield. Thermodynamics is central in this sense for it provides an upper bound on the reaction’s attainable yield. The process is said to be thermodynamically feasible if the yield specified by thermodynamics is equal to or greater than the yield warranting economic viability [29].

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Thermodynamics is a remarkable intellectual structure, for it deals with the scientific relationships amongst observations and is independent of the hypothetical models of the infinitesimal nature of matter; because of this independence and immediacy, it is remarkably useful. From diverse experiments (and so now from tabulated data), one can predict properties such as the direction of spontaneous chemical and physical change and the composition of reaction mixtures at equilibrium, and the response of these properties to changes in the conditions. Hence, thermodynamic analysis if properly utilized can predict what happens in a chemical reactor. Taking into account the dependence of equilibrium conversions of chemical reactions on temperature, pressure and initial compositions, one can develop a methodology to analyse and consequently understand the performance of chemical systems [30]. However, the equilibrium positions predicted by thermodynamics may not always be attainable in practice since thermodynamics does not consider the kinetics of a chemical reaction [31].

A chemical reaction always brings about changes in Gibbs free energy and enthalpy of the system as a result of the destruction, rearrangement, or formation of new chemical bonds during the formation of products. The enthalpy change of a reaction (ΔH) is essential for the analysis of engineering systems for it provides information necessary for the first law of thermodynamics. It also helps establish the relationship between temperature and equilibrium constant of the reaction which affects the reaction yield. The Gibbs free energy is on the other hand useful in ascertaining whether or not chemical equilibrium exists, and how changes in process conditions could influence the reaction yield. When chemical equilibrium exists (ΔG = 0), the subsequent amounts of products and reactants in the reactor can be found via the equilibrium constant K (T), which depends on the Gibbs free energy of formation (ΔGo). Knowing the relationship between K and (ΔGo) as well as their dependence on Temperature (T), a procedure aiming to overcome the thermodynamic feasibility barrier for any reaction under consideration can be developed [29]-[31].

Looking at a system with identified reactants and products, there could be a number of different reactions capable of producing the desired products but only a few of them are physically feasible. Knowing the stoichiometric coefficients of all reacting species in a balanced overall reaction makes it possible to calculate the changes in ΔH and changes in ΔG of the system. The two reaction variables (enthalpy and Gibbs free energy) are significant in

17 thermodynamic analysis for they allow for the interpretation of the process in terms of how much heat and work can be added or removed from the process. The ideal situation would be having both ΔG and ΔH negative as that would mean having a spontaneous exothermic reaction which implies that we can harness the chemical energy of that system if need be. Drawing ΔH against ΔG for the chemical species involved create lines that define the thermodynamic attainable region [32]. ΔG and ΔH are both extensive properties that are calculated independently of one another. This is different from, for instance, pinch diagrams where an extensive property is plotted against intensive property. ΔS could be used instead of ΔG but the latter is used in this dissertation due to its easier relation to work.

2.4 Dimethyl Ether Synthesis

2.4.1 Introduction

Dimethyl ether, also known as wood ether, methyl ether, or methyl oxide is a colourless liquid or compressed gas which has traditionally been used as a propellant in aerosols industry. Its common use is also in organic synthesis where it works as a reaction solvent for systems requiring volatile polar solvents. A novel and possibly large volume application of dimethyl ether is as a fuel where promising fuel applications include [33]:

 Power generation  Diesel blending and substitute  Acetylene substitute  Liquid petroleum gas (LPG) blending and substitute

Egypt has recently been blending DME with LPG in substantial amounts with the aim of reducing the dependence on LPG imports.

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2.4.2 Chemistry

DME is produced in a minimum of two steps. Firstly, hydrocarbons predominantly from natural gas are converted into synthesis gas (also known as syngas), a combination of carbon monoxide (CO) and hydrogen (H2). Secondly, the synthesis gas is then transformed into dimethyl ether in two different techniques as shown in Figure 2.1-1. The first technique is a conventional two-step process which consists of methanol synthesis and dehydration; the second is a one-step process which directly produces DME from syngas [33]-[35].

Figure 2.1-1: Dimethyl ether production diagram [34].

The two-step (indirect) process as illustrated in Figure 2.1-2 is currently the most proven/commercialised technology to produce DME. The technology produces DME via two different reactors where one is required for methanol synthesis and the other for methanol dehydration. This result in the technology being economically infeasible since the process also needs a number of recycles to improve the overall CO conversion in the methanol synthesis step [33].

Figure 2.1-2: A scheme of indirect synthesis process [34].

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The single step (direct) process synthesizes DME directly from syngas by combining methanol synthesis and dehydration in the same reactor with the aid of hybrid catalysts made by pressing the powders of both methanol synthesis and methanol dehydration catalysts. Compared to the indirect process via methanol synthesis, the direct method is more economical because of the following reasons [33]-[36]:

 The limitations associated with thermodynamic equilibrium of CO conversion to methanol could be surpassed since the consumption of methanol in a consequent reaction to form DME will shift the methanol synthesis equilibrium towards higher methanol conversion according to Le Chatelier's principle.

 Because methanol and dimethyl ether are produced simultaneously in one reactor, the cost of methanol separation and its preparation as a feed to the DME synthesis reactor could be eradicated.

Yuanyuan et al. [37] proposed a direct synthesis process as shown in Figure 2.1-3. This process was inspired by the realisation that separation of DME and CO2 in the presence of methanol is more difficult. The proposed process offered an alternative in a sense that water was used to absorb the condensed methanol and water that resulted from one-step reaction. The liquid stream that contained DME was finally distilled to produce DME with high purity.

Figure 2.1-3: A schematic of direct synthesis process [34].

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The direct synthesis of dimethyl ether from synthesis gas can be presumed to consist of the following reactions [38]:

Methanol synthesis from CO:

o CO + 2H2 ↔ CH3OH ΔH 298 K = −90.41 kJ/mol (2.1)

Methanol synthesis from CO2:

o CO2 + 3H2 ↔ CH3OH + H2O ΔH 298 K = −49.24 kJ/mol (2.2)

Water gas shift (WGS):

o CO + H2O ↔ CO2 + H2 ΔH 298 K = −41.17 kJ/mol (2.3)

Methanol dehydration:

o 2CH3OH ↔ CH3OCH3 + H2O ΔH 298 K = −24.03 kJ/mol (2.4)

Reactions (2.1), (2.2), and (2.3) are catalysed by a methanol synthesis catalyst (either Cu or

ZnO or Al2O3) and reaction (2.4) by an acidic catalyst (e.g. γ − Al2O3). Compared to the syngas-to-methanol process, these reactions form a synergistic system yielding higher syngas conversion hence greater productivity [39]. The synergy works as follows: methanol, which would otherwise be near its equilibrium value, is consumed by Reaction (2.4), and water formed by Reactions (2.2) and (2.4) is consumed by Reaction (2.3), while Reaction (2.3) generates hydrogen which improves Reaction (2.1). All these reactions are reversible and exothermic.

We then made the following assumption concerning these equations when performing the analysis:

 Since equation (2.2) is merely the summation of equations ((2.1), (2.3)), we would only consider the three independent reactions ((2.1), (2.3), and (2.4)) for analysis in this dissertation.

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CO + 2H2 ↔ CH3OH (2.1)

CO2 + H2 ↔ CO + H2O (2.3)

CO2 + 3H2 ↔ CH3OH + H2O (2.2)

2.4.3 Reaction kinetics

Chemical engineers are normally distinguished from other types of engineers by their ability to analyse systems in which chemical reactions are occurring and to apply the results of their study in a way that benefits the society [40]. Kinetic data frequently play a significant role in designing chemical reactors and DME synthesis is no different. There has been a significant amount of work done on the kinetics of DME synthesis from syngas. Bercic et al. [41] studied the dehydration of methanol on γ − Al2O3 in a differential fixed bed reactor operated at a pressure of 146 kPa and a temperature range of 290 – 360 ℃. A kinetic equation describing a Langmuir-Hinshelwood was found to perfectly fit the experimental results.

Lu et al. [42] rather performed their experiments for this synthesis in a laboratory fluidized bed reactor. Their experimental results showed a higher CO conversion and productivity than that obtained in a differential fixed bed. The authors [42] then proposed a new kinetic model and a reaction mechanism which was later modified by Mollavali et al. [43] to develop their rate equation where they assumed a different rate determining step which resulted in them developing a kinetic model different from that of [42].

Cheng et al. [44] argued that there is a temperature runaway in traditional tubular fixed bed reactors due high exothermic nature of this process synthesis which irreversibly deactivates the catalyst, hence the growing interest in the use of a three phase slurry reactor which they utilised in their analysis. The researchers [44] investigated the Langmuir-Hinshelwood kinetic model based on methanol synthesis and dehydration models by fitting their experimental data. Apart from kinetic models of exponential form, the combination of methanol synthesis model proposed by Graaf [45] and methanol dehydration model proposed by Bercic et al. [41] is very common [46].

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2.4.4 Essential factors to consider for dimethyl ether production

It has well been illustrated [47]-[52] that the reaction conditions (reaction temperature, operating pressure, H2/CO ratio, CO2 content of the feed, water removal, and space velocity) considerably affect the performance of the hybrid catalyst, the conversion of CO and CO2, and selectivity and yield of DME. Both the rate and the equilibrium conversion depend on the temperature, pressure, and composition of reactants, hence they must be considered in the exploitation of chemical reactions for commercial purposes. Although reaction rates are not susceptible to thermodynamic treatment, equilibrium conversions are.

Many industrial reactions are not carried to equilibrium; reactor design is then based primarily on reaction rate. However, the choice of operating conditions may still be influenced by equilibrium considerations. Moreover, the equilibrium conversion of a reaction provides a goal by which to measure improvements in a process. Similarly, it may determine whether or not an experimental investigation of a new process is worthwhile. For example, if thermodynamic analysis indicates that a yield of only 25% is possible at equilibrium and if a 60% yield is necessary for the process to be economically attractive, there is no purpose to an experimental study. On the other hand, if the equilibrium yield is 85%, an experimental program to determine the reaction rate for various conditions of operation (catalyst, temperature, pressure, etc.) may be warranted.

Equilibrium constant (Keq)

The CO conversion depends on the equilibrium constant (Keq), which in its turn depends on operating temperature in the reactor. Before describing how the CO conversion changes with temperature, the relationship between the equilibrium constants for the reactions involved in dimethyl ether synthesis and temperatures need to be analysed.

The equilibrium constants as a function of temperature were considered within the temperature range of 400K-850K. Within this temperature range, calculations were done and whose results are represented by curves of Figure 2.1-4, which show how the equilibrium constants (ΔHrxn is assumed constant) depend on temperature.

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Figure 2.1-4: Effects of temperature on equilibrium constant of reactions involved in DME synthesis.

From Figure 2.1-4, it can be seen that the equilibrium constant of reactions involved in methanol and dimethyl ether synthesis decreases with temperature. In a comparative way, the water gas shift reaction (reaction (2.3)) has the largest equilibrium constant over this temperature range and this is followed by the equilibrium constant of reaction (2.4), which is the transformation of methanol into dimethyl ether and then reaction (2.1) with the lowest equilibrium constant. When the three reactions are in competition in the same reactive environment, the water gas shift reaction is likely to take place more easily than reactions (2.1) and (2.4). Knowing the equilibrium constant values for each reaction at a particular temperature, it is possible to evaluate the theoretical equilibrium conversion of reactants with respect to temperature.

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2.4.4.1 Operational temperature

Dimethyl ether synthesis is usually/industrially carried out at a temperature of 200 − 300 ℃ [53]-[54]. Temperature has a direct effect on CO conversion, selectivity to DME, and yield of

DME as seen in Figure 2.1-5a [53]. CO and CO2 hydrogenation reactions are exothermic; and a rise in temperature will thermodynamically result in an increase in their rates but only up to a certain temperature [55]. Lower temperatures lead to the reaction being controlled by kinetics and the reaction rate is a function of temperature. CO conversion at low temperature is seen to be low and this is believed to be due to CO and CO2 competitively adsorbing on the catalyst. At higher temperatures, however, the thermodynamics of the exothermal reaction are unfavourable, and the conversion is thermodynamically limited as shown in this Figure.

Figure 2.1-5a: Temperature effect at 50 bar and H2: CO = 1 on synthesis conversion to DME [53].

The conversion decreases as temperature is increased and this can be attributed firstly to the restrictions imposed by thermodynamics on the exothermic reactions and secondly, to copper (Cu) sintering, which aggravates fractional loss of catalyst activity [52]. For two deferent

25 space velocities (SV) showed in this Figure, CO conversion increases linearly with temperature while approaching DME equilibrium; with the conversion of CO evidently exceeding the methanol synthesis equilibrium constraint. As seen in Figure 2.1-6b, DME selectivity increases just a little and this is due to higher temperatures favouring methanol dehydration catalyst activity than methanol synthesis catalyst activity [53]-[54].

Figure 2.1-6b: Temperature effect at 50 bar and H2: CO = 1 on the selectivity and productivity of DME at SV of 15,000 Nml/gcat/h [53].

2.4.4.2 Pressure

Pressure directly affects DME synthesis as predicted by thermodynamics [50]. An increase in pressure significantly increases both the DME productivity and conversion of CO as shown in Figure 2.1-7. This confirms the synergy that producing DME directly from syngas shifts the equilibrium conversion of CO by dehydrating the methanol product to DME. This therefore implies that synthesising DME directly from syngas may be operated at lower pressure than that used in the MeOH synthesis, leading to a more economical process with equal or higher CO conversion [54]. Due to water being one product in methanol dehydration

26 reaction, increased pressure is believed to have a negative effect on this reaction [53] by suppressing the CO conversion as a result of water adsorption and blocking of MeOH adsorption sites [55]. The syngas gas ratio of 2 shown in this Figure indicates that part of the water formed will be stoichiometrically consumed by the water gas shift. The effect of water may possibly be more evident at higher conversion, which could be recognized by either utilizing an optimum catalyst or addition of steam to the feed mixture [48]-[49]. Depending on the syngas composition, direct DME synthesis choice of operating pressure may be compromised by a hindrance by water effect. Despite compromised equilibrium conversion, reduced pressure could also be suggested by compression costs [56].

0 Figure 2.1-7: Pressure effect on the synthesis of DME at 250 C, H2: CO = 2 and SV of 15,000 Nml/gcat/h [53].

As shown in Figure 2.1-7, an increase in pressure favours both the conversion of CO and the productivity of DME. This happens because pressure increase accelerates mainly methanol synthesis reaction (according to mole-number reducing stoichiometry theory), hence the whole reaction network [57]-[58]. This implies that the WGS and methanol dehydration

27 reactions will not be affected by pressure increase and therefore methanol synthesis by the hydrogenation of both CO and CO2 would be the only limiting steps [59]-[60].

It is further observed [59] that the bi-functional catalyst (CZA/γ − Al2O3) deactivates slightly due to coke deposition during the transformation of syngas into DME. This increase in coke content as a result of an increase in pressure is attributed to the enrichment of condensation reactions that bring about coke formation. Increasing the pressure in slurry reactors has an extra consequence of decreasing the bubble size, which then increases the volumetric coefficient that leads to a decrease in mass transfer resistance in the slurry phase [61].

2.4.4.3 Space velocity (SV)

Space velocity (SV) is very crucial since it influences the performance of a catalyst [62]. The conversion of CO in the direct synthesis of DME in fixed bed reactors dramatically decreases with increasing SV, with a similar behaviour expected in slurry reactors [62]-[64]. Mass transfer coefficient and mean residence time both decrease with an increase in superficial gas velocity. At higher gas velocities, the influence of mean residence time on the conversion of CO is greater than that of the mass transfer coefficient, leading to a reduction in the conversion of CO due to insufficient time for synthesis gas to diffuse into the slurry phase and get to the surface of the catalyst. DME productivity is in such systems under the effect of two dissimilar behaviours. Firstly, an increase in the superficial velocity at higher catalyst concentration and also in syngas flow rate into the column increases DME production. Secondly, DME productivity decreases at higher velocity due to a decrease in CO conversion at low catalyst concentration [65].

Although there is still no general relation between SV and DME selectivity, Wang et al. [62] observed that when increasing the SV, the DME/CO2 ratio decreased significantly, which suggests that CO2 selectivity is being favoured than DME selectivity. Erena et al. [63] observed a linear relationship between both the selectivity and yield of DME at low values of space time. These results support the theory that low space time values favour the WGS while high values favour the methanol dehydration reaction.

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2.4.4.4 Syngas ratio and CO2 content of the feed

Syngas is manufactured industrially from hydrocarbon fuels [66], typically natural gas, either by steam reforming (SR), CO2 reforming (CDR), or catalytic partial oxidation (CPO). The desired syngas (H2/CO) ratio is application specific with SR producing syngas very rich in H2 compared that of CDR which is too lean. CPO produces syngas close to the preferred output ratio for dimethyl ether production. Principally, the hydrogen to carbon monoxide combination can be adjusted by the WGS.

The direction of the WGS reaction can be changed by varying the H2/CO ratio. Low ratios of

H2/CO causes the reaction to produce CO2 that aids in the improvement of both the dimethyl ether and methanol synthesis while increased H2/CO ratio results in a decrease in CO2 production which consequently results in DME reduction. This therefore suggests that there is an optimal value for H2/CO ratio, which is inversely proportional to temperature leading to a decrease in this optimum ratio. With an increase in temperature, WGS reaction attains equilibrium conditions quickly, which ultimately results in the reduction of carbon dioxide production [67].

Kabir et al. [68] reported that removing CO2 prior to dimethyl ether reactor greatly improves the yield. High purity CO2 would at this stage be provided by separation which would also be beneficial for sequestration [68]. This means that CO2 content of the feed must always be controlled since it partakes in both the methanol synthesis and the WGS reactions, which makes it a bridge relating the two reactions [69]. CO2 molecules adsorb and occupy the active sites quicker than the syngas molecules on the methanol synthesis catalyst, and this result in a reduction in methanol production [65]. Consequently, CO2 concentration should not be increased in the feed stream since it would be unfavourable to both reactions [62] and would lead to a decrease in syngas conversion along with DME selectivity [70]-[71], [64].

Due to the effect the H2/CO ratio has on both the conversion and selectivity in direct synthesis of dimethyl ether, it is essential to find the optimum value of this ratio. Thermodynamically, the optimal syngas conversion can be obtained at the ratio of 1.0 [64]. As seen in Figure 2.1-8 and Figure 2.1-9, DME selectivity decreases slightly with an increase in this ratio while that of methanol increases.

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Figure 2.1-8: Equilibrium conversion of syngas at 50 bar and 280 0C [64].

30

Figure 2.1-9: Selectivity and conversion against syngas ratio at 50 bar and 260 0C [64].

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2.4.4.5 Water removal

CO/CO2 feed composition ratio is an important parameter in direct synthesis of DME. A robust synergy is attained with carbon monoxide-rich feed as a result of the active methanol removal by the dehydration reaction and removal of produced H2O by the water gas shift reaction [72]. On the contrary, CO2-rich feeds adversely affect methanol production owing to the large quantities of water produced in both methanol synthesis and dehydration steps, thus constraining methanol dehydration and therefore lowering dimethyl ether selectivity. It is for this reason expected that water removal during dimethyl ether synthesis may bring some favourable effects.

Water is the side product in the methanol dehydration reaction. So, its presence in excess shifts the equilibrium backward (according to Le Chatelier’s principle) and consequently reducing the initial methanol dehydration activity and selectivity of dimethyl ether. At equilibrium, H2O and methanol compete for the same sites on the catalyst surface and this necessitates an increase in temperature for achieving the same degree of conversion [73],

[65]. At high CO2 content, water removal shifts the equilibrium towards WGS reaction, favouring the formation of CO [74] which helps produce more MeOH resulting in improved DME production [75]-[76]. In the case of hydrogen-rich syngas, water removal would again favour the selectivity of dimethyl ether [77]. The sorption-enhanced reaction process may offer an attractive possibility of H2O removal by adsorption as shown by Carvill et al. [78] and Iliuta et al. [79].

By applying the adsorption-enhanced theory, CO2 could be used as a constituent in syngas as in removal of water that speeds the reverse water gas shift reaction. The reason for water removal in this process displaced the water gas shift equilibrium to improve CO2 conversion to methanol and to enhance the productivity of the reactor. The simulated results showed that under the conditions of water removal, dimethyl ether selectivity and yield were preferred and the productivity of methanol improved. A probable shortcoming of water removal is the deactivation of the catalyst (CuO-ZnO-Al2O3) metallic function by coke deposition [80].

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dimethyl ether from the gas mixture containing CO2 with high space velocity. Applied Energy, 98, 92-101.

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[48] Hu, J., Wang, Y., Cao, C., Elliott, D. C., Stevens, D. J., & White, J. F. (2005). Conversion of biomass syngas to DME using a microchannel reactor. Industrial & engineering chemistry research, 44(6), 1722-1727.

[49] Sofianos, A. C., & Scurrell, M. S. (1991). Conversion of synthesis gas to dimethyl ether over bi-functional catalytic systems. Industrial & engineering chemistry research, 30(11), 2372-2378.

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[51] Hengyong, X. U., Qingjie, G. E., Wenzhao, L. I., Shoufu, H. O. U., Chunying, Y. U., & Meilin, J. I. A. (2001). The synthesis of dimethyl ether from syngas obtained by catalytic partial oxidation of methane and air. Studies in Surface Science and Catalysis, 136, 33-38.

[52] Erena, J., Garoña, R., Arandes, J. M., Aguayo, A. T., & Bilbao, J. (2005). Effect of operating conditions on the synthesis of dimethyl ether over a CuO-ZnO-Al 2 O 3/NaHZSM-5 bi-functional catalyst. Catalysis today, 107, 467-473.

[53] Hayer, F., Bakhtiary-Davijany, H., Myrstad, R., Holmen, A., Pfeifer, P., & Venvik, H. J. (2011). Synthesis of dimethyl ether from syngas in a microchannel reactor-simulation and experimental study. Chemical Engineering Journal, 167(2), 610-615.

[54] Chen, H. J., Fan, C. W., & Yu, C. S. (2013). Analysis, synthesis, and design of a one- step dimethyl ether production via a thermodynamic approach. Applied Energy, 101, 449-456.

[55] Chen, Z., Zhang, H., Ying, W., & Fang, D. (2010). Global kinetics of direct dimethyl ether synthesis process from syngas in slurry reactor over a novel Cu-Zn-Al-Zr slurry catalyst. World Academy of Science, Engineering and Technology, 68, 1426-1432.

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[56] Nie, Z., Liu, H., Liu, D., Ying, W., & Fang, D. (2005). Intrinsic kinetics of dimethyl ether synthesis from syngas. Journal of Natural Gas Chemistry, 14, 22-28.

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[58] Peng, X. D., Toseland, B. A., & Tijm, P. J. A. (1999). Kinetic understanding of the chemical synergy under LPDMETM conditions-once-through applications. Chemical Engineering Science, 54 (13), 2787-2792.

[59] Ereña, J., Sierra, I., Aguayo, A. T., Ateka, A., Olazar, M., & Bilbao, J. (2011). Kinetic

modelling of dimethyl ether synthesis from (H2 + CO2) by considering catalyst deactivation. Chemical Engineering Journal, 174(2), 660-667.

[60] Moradi, G. R., Yaripour, F., & Vale-Sheyda, P. (2010). Catalytic dehydration of methanol to dimethyl ether over mordenite catalysts. Fuel Processing Technology, 91(5), 461-468.

[61] Bakopoulos, A. (2006). Multiphase fluidization in large-scale slurry jet loop bubble columns for methanol and or dimethyl ether production. Chemical engineering science, 61(2), 538-557.

[62] Wang, L., Fang, D., Huang, X., Zhang, S., Qi, Y., & Liu, Z. (2006). Influence of reaction conditions on methanol synthesis and WGS reaction in the syngas-to-DME process. Journal of Natural Gas Chemistry, 15(1), 38-44.

[63] Erena, J., Garoña, R., Arandes, J. M., Aguayo, A. T., & Bilbao, J. (2005). Effect of

operating conditions on the synthesis of dimethyl ether over a CuO-ZnO-Al2O

3/NaHZSM-5 bi-functional catalyst. Catalysis today, 107, 467-473.

[64] Stiefel, M., Ahmad, R., Arnold, U., & Döring, M. (2011). Direct synthesis of dimethyl ether from carbon-monoxide-rich synthesis gas: influence of dehydration catalysts and operating conditions. Fuel Processing Technology, 92(8), 1466-1474.

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[65] Moradi, G. R., Yaripour, F., & Vale-Sheyda, P. (2010). Catalytic dehydration of methanol to dimethyl ether over mordenite catalysts. Fuel Processing Technology, 91(5), 461-468.

[66] Cho, W., Song, T., Mitsos, A., McKinnon, J. T., Ko, G. H., Tolsma, J. E., & Park, T. (2009). Optimal design and operation of a natural gas tri-reforming reactor for DME synthesis. Catalysis Today, 139(4), 261-267.

[67] Mardanpour, M. M., Sadeghi, R., Ehsani, M. R., & Esfahany, M. N. (2012). Enhancement of dimethyl ether production with application of hydrogen-perm selective Pd-based membrane in fluidized bed reactor. Journal of Industrial and Engineering Chemistry, 18(3), 1157-1165.

[68] Kabir, K. B., Hein, K., & Bhattacharya, S. (2013). Process modelling of dimethyl ether production from Victorian brown coal-Integrating coal drying, gasification and synthesis processes. Computers & Chemical Engineering, 48, 96-104.

[69] Ereña, J., Sierra, I., Aguayo, A. T., Ateka, A., Olazar, M., & Bilbao, J. (2011). Kinetic

modelling of dimethyl ether synthesis from (H2 + CO2) by considering catalyst deactivation. Chemical Engineering Journal, 174(2), 660-667.

[70] Chen, W. H., Lin, B. J., Lee, H. M., & Huang, M. H. (2012). One-step synthesis of

dimethyl ether from the gas mixture containing CO2 with high space velocity. Applied Energy, 98, 92-101.

[71] Diban, N., Urtiaga, A. M., Ortiz, I., Ereña, J., Bilbao, J., & Aguayo, A. T. (2013). Influence of the membrane properties on the catalytic production of dimethyl ether with

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[72] Ng, K. L., Chadwick, D., & Toseland, B. A. (1999). Kinetics and modelling of dimethyl ether synthesis from synthesis gas. Chemical Engineering Science, 54(15), 3587-3592.

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[73] Vishwanathan, V., Roh, H. S., Kim, J. W., & Jun, K. W. (2004). Surface properties and

catalytic activity of TiO2-ZrO2 mixed oxides in dehydration of methanol to dimethyl ether. Catalysis letters, 96(1-2), 23-28.

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[75] Peng, X. D., Wang, A. W., Toseland, B. A., & Tijm, P. J. A. (1999). Single-step syngas-to-dimethyl ether processes for optimal productivity, minimal emissions, and natural gas-derived syngas. Industrial & engineering chemistry research, 38(11), 4381- 4388.

[76] Hu, J., Wang, Y., Cao, C., Elliott, D. C., Stevens, D. J., & White, J. F. (2005). Conversion of biomass syngas to DME using a microchannel reactor. Industrial & engineering chemistry research, 44(6), 1722-1727.

[77] Lu, W. Z., Teng, L. H., & Xiao, W. D. (2004). Simulation and experiment study of dimethyl ether synthesis from syngas in a fluidized-bed reactor. Chemical Engineering Science, 59(22), 5455-5464.

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41

CHAPTER 3: METHODOLOGY

3.1 Introduction

Thermodynamics is a remarkable intellectual structure, for it deals with the scientific relationships amongst observations and is independent of the hypothetical models of the infinitesimal nature of matter; because of this independence and immediacy, it is remarkably useful. From diverse experiments (and so now from tabulated data), one can predict properties such as the direction of spontaneous chemical and physical change and the composition of reaction mixtures at equilibrium, and the response of these properties to changes in operating conditions. Hence, thermodynamic analysis if properly utilized can predict what happens in a chemical reactor. Taking into account the dependence of equilibrium conversions of chemical reactions on temperature, pressure and initial compositions, one can develop a methodology to analyse and consequently understand the performance of chemical systems [1]-[2].

3.2 Thermodynamic Analysis of the Process

Here, the basic idea was to synthesise the process flowsheet based on fundamental thermodynamic principles to optimise some objective such as producing DME from syngas, while minimising carbon dioxide emissions. There are essentially three principles that can be used to synthesise flowsheets: these are an overall mass balance (the composition of each species in the reactor must remain positive), a constraint called the energy balance (determines heat requirements of a chemical process) and another called work/entropy balance which is associated with the ΔG of a process (the trend will always be in the direction for which ΔG ≤ 0) [1], [3]-[4].

The objective in this case was to find a region where any reaction in the reactor becomes thermodynamically viable, even under altered process parameters. It is assumed that the chemical species involved in the said reactions are completely pure and in a gas phase as shown in Figure 3.2-1. The system was considered to be ideal hence the equations of state were used to estimate the thermodynamic properties.

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Figure 3.2-1: Representation of this typical process showing feed and product streams.

Selectivity issues become crucial when considering systems containing multiple reactions because that raises questions like: (1) which reaction is dominant? And (2) how do varying process conditions like temperature; pressure and initial composition affect the status of such a reaction?

Considering the significance of decisions taken in the early stages of a design process, it then becomes crucial that the above questions are answered as early as possible since the attainment of the process is generally determined by the conceptual design.

The principal idea is that the feed materials have chemical potential which based on how efficient the is, must be conserved during the transformation of reactants into products, whether they are chemicals or direct work outputs such as electricity. To be able to do this, researchers [3] invented the Gibbs free energy vs. Enthalpy plot. This is a two- dimensional plot which can be used to represent all possible processes including their efficiencies no matter how complex the process is. Using this plot enables one to synthesise processes that satisfy all the applicable constraints that have the highest efficiencies.

We therefore adapted and extended the methodology invented by these leading researchers in the field of process synthesis to analyse and understand the principles governing the production of DME from syngas so as to gain an insight into the inner workings of this chemical system.

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3.2.1 Effect of Temperature on the Equilibrium Conversions of Chemical Reactions

Temperature dependence of heat capacity

The interpretation of heat as energy in transit is preceded by the idea that a body has a capacity for heat. The smaller the temperature change in a body instigated by the transfer of a given amount of heat, the greater its capacity [2]. The constant-pressure heat capacity is defined as:

∂H Cp = ( ) (3.1) ∂T P

The definition accommodates both specific and molar heat capacities, depending on whether enthalpy is molar or specific. This heat capacity relates in a simple way to a constant- pressure, closed-system process, for which Equation (3.1) is equally well written:

dH = CpdT (3.2)

On integrating,

T2 ∆H = ∫ CpdT (3.3) T1

Evaluating the integral in Equation (3.3) requires knowledge of how heat capacity is affected by a change in temperature and this is usually given by an empirical Equation (3.4):

C p = A + BT + CT2 + DT−2 (3.4) R

Where A, B, C and D are constants characteristic of the specific substance. The units of Cp are governed by the choice of R because the ratio Cp⁄R is dimensionless.

Substituting Cp as a function of temperature for temperature limits of T0 and T:

44

T Cp B 2 2 C 3 3 D τ−1 ∫ = AT0(τ − 1) + T0 (τ − 1) + T0 (τ − 1) + ( ) (3.5) T0 R 2 3 T0 τ

T Where: τ = (3.51) T0

T−T Since: τ − 1 = 0 , Equation (3.5) may be written as: T0

T CP B C 2 2 D ∫ dT = [A + T0(τ + 1) + T0 (τ + τ + 1) + 2] (T − T0) (3.5.2) T0 R 2 3 τT0

The expression in square brackets is identified as 〈CP〉H⁄R, and 〈CP〉H it’s called mean heat capacity:

〈CP〉H B C 2 2 D = A + T0(τ + 1) + T0 (τ + τ + 1) + 2 (3.6) R 2 3 τT0

Equation (3.6) may be simplified to:

∆H = 〈Cp〉H(T − T0) (3.7)

Temperature dependence of ∆푯ퟎ

We then treated the calculation of standard heats of reaction at different temperatures from knowledge of the value at the reference temperature of 298.15 K. The heat of reaction can be calculated as follows:

∆H = Hp − Hr (3.8)

Where: subscripts p and r represent products and reactants respectively.

Differentiating Equation (3.8) with respect to temperature at constant pressure:

∂(∆H) ∂H ∂H ( ) = ( p) − ( r) (3.8.1) ∂T P ∂T P ∂T P

45

But: (∂H⁄ ∂T )P = Cp, therefore:

∂(∆H) ( ) = Cp,p − Cp,r = ∆Cp (3.8.2) ∂T P

Referring to Equation (3.3) and recalling Equation (3.2), the standard heat of reaction can be expressed as:

0 0 dHi = Cp,i dT (3.9)

Multiplying by the stoichiometric numbers and summing the overall products and reactants gives:

0 0 d ∑i 푣푖Hi = ∑i 푣푖Cp,i dT (3.9.1)

0 0 The term ∑i 푣푖Hi is the standard heat of reaction, defined by Equation (3.6) as ∆H . The standard heat capacity change of reaction is defined similarly as: 0 0 ∆Cp = ∑i 푣푖Cp,i (3.9.2)

As a result of this:

0 0 d∆H = ∆Cp dT (3.9.3)

This is the central equation linking heat of reaction to temperature, which upon integration becomes:

0 0 o T CP ∆H = ∆H0 + R ∫ dT (3.10) T0 R

0 0 Where ∆H0 and ∆H are heats of reaction at reference temperature T0 and temperature T respectively. Given the temperature and heat capacity dependence of each product and reactant, the integral is then given by the analog of Equation (3.5) as:

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0 T ∆Cp ∆B 2 ∆C 3 3 ∆D τ−1 ∫ = ∆AT0(τ − 1) + (τ − 1) + T0 (τ − 1) + ( ) (3.11) T0 R 2 3 T0 τ

Where by definition, ∆A = ∑i 푣푖Ai, with analogous definitions for ∆B, ∆C, and ∆D.

The enthalpy change in a reaction (∆H) as a function of temperature at constant pressure can subsequently be determined by:

0 o 0 ∆H = ∆H0 + 〈∆Cp 〉H(T − T0) (3.12)

Where: ∆H0 Represents the change in enthalpy at a particular temperature o 0 ∆H0 Indicates the change in enthalpy at standard conditions (1 Bar and 25 C) 0 〈∆Cp 〉H Shows the mean heat capacity as a function of temperature

Temperature dependence of ∆푮ퟎ

This section looks at how ΔG change during the course of a reaction where material constantly react to form new products. As mentioned earlier, the trend will always be in the direction for which the free energy is negative. We can therefore conclude that ΔG plays a very important role in reaction analysis although it cannot tell how fast the reaction will occur which can be very slow at times hence the significance of a catalyst and proper reaction conditions.

Before measuring the changes of ΔG as a result of changes in temperature during the course of a reaction, we must first find the relation concerning Gibbs free energy (G) and pressure. Looking first at the definition of G:

G = (U + PV) − TS = H − TS (3.13) Such that: G = U + PV − TS (3.13.1)

47

Differentiating Equation (3.13.1) gives: dG = dU + PdV + VdP − TdS − SdT (3.13.2)

However: dU = dq − PdV (3.14)

And also: dS = dq/T (3.15)

We may then substitute: dU = TdS − PdV (3.16)

This then promisingly looks as: dG = (TdS − PdV) + PdV + VdP − TdS − SdT (3.17)

Or: dG = VdP − SdT (3.18) At constant pressure (dP) = 0: dG = −SdT (3.19)

Partially differentiating at constant pressure yields:

∂G ( ) = −S (3.20) ∂T P

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Substituting Equation (3.20) into Equation (3.13) gives:

∂G G = H + T ( ) (3.21) ∂T P

Dividing throughout by T2 and rearranging yields:

G 1 ∂G H − 2 + ( ) = − 2 (3.22) T T ∂T P T

Since:

퐺 휕( ) G 1 ∂G 푇 − 2 + ( ) = [ ] (3.23) T T ∂T P 휕푇 푃

Then:

∆G ∂( ) ∆H [ T ] = − (Gibbs-Helmholtz equation) (3.24) ∂T T2 P

Interpreting and rearranging Equation (3.24) gives:

∆G,T ∆G0,T 1 1 2 − 1 = ∆H0 × ( − ) (3.25) T2 T1 T2 T1

This can also be expressed as:

∆G,T ∆G0 1 1 2 = + ∆H0 × ( − ) (3.26) T2 T1 T2 T1

At standard temperature and pressure (298.15 K and 1.01325 bar), Equation (3.26) makes it possible to calculate ∆G of a reaction at any temperature T2

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3.2.2 Effect of Pressure on the Equilibrium Conversions of Chemical Reactions

Pressure dependence of ∆푮ퟎ dG = VdP − SdT as shown by Equation (3.18). At constant temperature: dG = VdP (3.27)

Partially differentiating at constant temperature gives:

∂G ( ) = V (3.28) ∂P T

For n moles of a perfect gas:

PV = nRT (3.29)

Equation (3.27) then reduces to:

dP dG = nRT (3.30) P

Integrating from P1 to P2:

P2 dP P2 ∆G = G2 − G1 = nRT ∫ = nRTln (3.31) P1 P P1

The free energy of a gas is usually related to the standard free energy G0, which is defined as the free energy of one mole of a gas at one atmospheric pressure [2].

For standard states therefore:

o o P G = G + RT × ln ( o) (3.32) P0

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Where G is the free energy at some pressure (P); G0 is the free energy at a particular absolute temperature; R is the universal gas constant; To is that particular absolute temperature; and o P0 is the standard ambient pressure.

3.3.3 Effect of Initial Composition on the Equilibrium Conversions of Chemical Reactions

The reaction coordinate

The general chemical reaction may be written as:

푣1A1 + 푣2A2 + ⋯ ↔ 푣3A3 + 푣4A4 + ⋯ (3.33)

Where: 푣푖 is a stoichiometric coefficient and Ai stands for a chemical formula/species. The species on the left are reactants and the ones on the right are products. The generalised stoichiometric coefficients for the above reaction may be written as:

0 = 푣퐵A1 + 푣퐶A2 + ⋯ + 푣푆A3 + 푣푇A4 + ⋯

Where

푣퐵 = −푣1 푣푆 = 푣3

푣퐶 = −푣2 푣푇 = 푣4

This leads to the generalisation of stoichiometric coefficients as positive (+) quantities for the products of the reaction and negative (-) for the reactants.

As the reaction represented by Equation (3.33) takes place, the changes in the numbers of moles of species present in the reaction are in direct proportion to the stoichiometric numbers [2]. Applying this principle to a differential amount of reaction leads to:

dN dN dN dN 2 = 1 3 = 1 Etc. v2 v1 v3 v1

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Including all species yields:

dN dN dN dN 1 = 2 = 3 = 4 = ⋯ v1 v2 v3 v4

With all terms being equal; a single quantity representing an amount of reaction can be used to collectively identify these terms. Thus a definition of dε is given by the equation: dN dN dN dN 1 = 2 = 3 = 4 = ⋯ = dε (3.34) v1 v2 v3 v4

This can also be written as:

dNi = 푣푖 dε (i = 1, 2 … N) (3.35)

Where ε is called the reaction coordinate and characterizes the extent or degree to which a reaction has taken place. Simply put, ε can be determined by the amount of reactant and product available in the reactor at any time. The reaction coordinate is also known as either: degree of reaction, degree of advancement, extent of reaction, or process variable. Equation (3.35) represents only the changes in ε with respect to changes in a mole numbers. The definition of ε depends for a specific application on setting it equal to zero at an initial state of the reaction, setting it to a negative value when the reaction turns towards reactants and positive when the reaction turns towards products. Integrating Equation (3.35) from an initial 0 unreacted state where ε = 0 and Ni = Ni to a state reached after a random amount yields:

Ni ε ∫ 0 dNi = 푣푖 ∫ dε (3.36) Ni 0

Or

0 Ni = Ni + 푣푖ε (i = 1, 2 … N) (3.37)

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Multi-reaction stoichiometry

When multiple independent reactions proceed simultaneously, subscript j serves as the reaction index. A separate extent of reaction εj then applies to each reaction. The stoichiometric numbers are also subscripted to distinguish each species per reaction.

Thus, 푣푖,푗 designates the stoichiometric number of species i in reaction j. The fact that a number of moles of a species Ni may change because of several reactions, the general equation analogous to Equation (3.35) includes a sum:

dNi = ∑ 푣푖,푗dεjj (i = 1,2,…,N) (3.38)

0 Integrating from Ni = Ni and εj = 0 to arbitrary Ni and εj gives:

0 Ni = Ni + ∑ 푣푖,푗dεjj (i = 1,2,…,N) (3.39)

0 Where Ni is the molar flowrate at some point in the reactor, Ni is the molar flowrate of the specie input to the reactor, and 푣푖,푗 is the stoichiometric coefficients of species i in the reaction.

Process mass balance

Assuming that the system is allowed to reach equilibrium, the number of moles Ni of component i in the product stream can be obtained using the relationship between the number 0 of mole Ni of component i in the feed stream and the extent of reaction (ε) as shown by Equation (3.39).

Since the requirement is a positive molar flow rate of the reactants, then:

0 Ni = Ni + ∑j 푣푖,푗dεj ≥ 0 (3.40)

The inequality of all species thus determines the achievable area in the space of constraints described by the vector N, within which the system can operate thermodynamically without violating the laws governing mass balance [3].

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Process energy

Despite the fact that mass balance is such a useful tool, its aspects of the process cannot be isolated because energy and work aspects also must be considered. The energy aspects can be taken into account using an energy balance as shown by Equation (3.41) and the work aspect of it can be taken into account by using the Gibbs free energy balance as shown by Equation (3.42).

∆H = (∑ 푣 ∆H ) − (∑ 푣 ∆H ) (3.41) (reaction j) 푗 i,j products 푗 i,j reactants

∆G = (∑ 푣 ∆G ) − (∑ 푣 ∆G ) (3.42) (reaction j) 푗 i,j products 푗 i,j reactants

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References

[1] Smith, E. B. (1990). Basic chemical thermodynamics. 4th edition. Oxford.

[2] Smith, J. M., Van Ness, H. C., & Abbott, M. M. (2005). Introduction to chemical engineering thermodynamics. 7th ed. McGraw-Hill, New York.

[3] Okonye, L. U., Hildebrandt, D., Glasser, D., & Patel, B. (2012). Attainable regions for a reactor: Application of ∆H − ∆G plot. Chemical Engineering Research and Design, 90, 1590-1609.

[4] Warn, J. R. W., & Peters, A. P. H. (1996). Concise Chemical Thermodynamics. 2nd edition.

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CHAPTER 4: RESULTS, ANALYSIS AND DISCUSSION

4.1 Introduction

This chapter outlines the application of thermodynamic reaction equilibrium theory to the analysis of DME synthesis process. The feasibility of this process is then discussed in terms of the AR build via thermodynamic principles and graphical representations.

4.2 Thermodynamically Attainable Region

Chemical processes are analysed in terms of their heat and work requirements using the analogy of heat engine and a graphical approach [1]. This project adapted a graphical approach which looks at processes holistically. Processes are represented and classified in different thermodynamic regions in the ΔH-ΔG space (GH-diagram) which helps understand how process conditions such as pressure and temperature can be manipulated in order to meet heat and work requirements more reversibly.

Understanding the relationship between the heat and work as functions of temperature and pressure can provide insights into the process and also give an indication of what the process structure would be. We therefore derived thermodynamic equations (section 3.2) which would then be used to calculate the heat and work requirements of this process.

Enthalpy (heat) as a function of temperature

Heat, like work, is energy in transit and is not a function of the state of a system. Heat and work are interconvertible. A steam engine is an example of a machine designed to convert heat into work. The turning of a paddle wheel in a tank of water to produce heat from friction represents the reverse process, the conversion of work into heat.

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Heat capacity: When the flow of heat into or out of a system causes a temperature change, the heat is calculated from the heat capacity CP defined as:

∂H Cp = ( ) (4.1) ∂T P

Where: ∂H is the flow of heat resulting in a temperature change ∂T. Rearranging and integrating gives:

T2 ∆H = ∫ CP dT (4.2) T1

Equation (4.2) is an example of a line integral, demonstrating that ∂H is not an exact differential. To calculate ∆H, one must know the heat capacity as a function of temperature. If one graphs Cp against T as shown in Figure 4.1-1, the area under the curve is ∆H. The dependence of Cp upon T is determined by the path followed, hence the calculation of ∆H requires that we specify the path.

Figure 4.1-1: Area under the curve or heat added in raising the temperature from T1 to T2.

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As can be seen from this Figure, heat capacity varies in a nonlinear fashion with temperature.

The number of terms commonly used to describe Cp varies from two to four. High temperature reactions are becoming increasingly important, and as a result, wider variations in Cp are encountered [2].

To integrate the line integral in Equation (4.2), heat capacity is often expressed as a power series expansion in T of the type shown in Equation (4.3), which corresponds better with reality since it proved to sufficiently hold at higher temperatures [2].

C C = a + bT + + dT2 + ⋯ (4.3) P T2

The number of terms required in Equation (4.3) depends upon the substance and the temperature interval. For small temperature differences, heat capacity changes with temperature are small and CP can be represented reasonably well by:

T2 ∆H = Cp ∫ dT = CP(T2 − T1) (4.4) T1

For larger and over very large temperature changes, higher power terms in Equation (4.3) are included. Tables of the coefficients for Equation (4.3) for a number of substances are summarized in the literature [2]-[3].

As an example: In the temperature range of 50 to 1000 K and at a pressure of 1.01325 bar, the heat capacity of CO2 (g) in J/mol.K with coefficients obtained from [3], is given by:

C 0 P = 3.26 + 1.36 × 10−3T + 1.50 × 10−5T2 − 2.37 × 10−8T3 + 1.06 × 10−11T4 R

Calculating the amount of heat necessary to isobarically raise the temperature of one mole of

CO2 from 289 K to 523 K at 1.01325 bar would be calculated as follows:

A graph of CP against T for this temperature range is shown in Figure 4.1-2. The area under the curve is again ∆H. It can be obtained by integrating Equation (4.2) with CP expression/equation extracted from [3].

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T2 1 ∆H = R ∫ (a + a T + a T2 + a T3 + a T4) dT R 0 1 2 3 4 T1

T a T2 a T3 a T4 a T5 2 ∆H = [a T + 1 + 2 + 3 + 4 ] × R 0 2 3 4 5 T1

a a a a ∆H = a (T − T ) + 1 (T 2 − T 2) + 2 (T 3 − T 3) + 3 (T 4 − T 4) + 4 (T 5 − T 5)R 0 2 1 2 2 1 3 2 1 4 2 1 5 2 1

With:

a0 = 3.259

−3 a1 = 1.356 × 10

−5 a2 = 1.502 × 10

−8 a3 = −2.374 × 10

−11 a4 = 1.056 × 10

T1 = 298.15 K

T2 = 523.15 K

∆H = 9335,348 J/mol

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Figure 4.1-2: Area under the curve or heat added in raising the temperature from 298 to 523 K.

The enthalpies calculated by the procedure given above are significantly different from the ones calculated by Equation (4.5) due to the fact that Equation (4.5) has the enthalpy of formation of compounds in it. Energy balance depends on the basis and elements are generally considered as such (basis), hence factoring the enthalpy of formation of compounds into the procedure above gives an error of about 899 J/mol. We acknowledge the difference brought by this two procedures but for reasons of simplicity, we will make use of Equation (4.5) derived in section 3.2.1.

0 0 ∆H = ∆H0 + 〈∆Cp 〉H(T − T0) (4.5)

To effectively utilise Equation (4.5), we then had to find the enthalpies of formation for all the chemical species involved in this reaction system. This thermodynamic data was extracted from [2].

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Heat capacity is also a function of temperature hence we had to find its expression expressed as such. The heat capacity constants were rather taken from [3] and heat capacity equation presented as follows:

C p = a + a T + a T2 + a T3 + a T4 (4.6) R 0 1 2 3 4

Where: R is the universal gas constant which was taken as 8.314 J⁄ mol. K

For illustration purposes, we then calculated the thermodynamic properties of only one component (DME) in this section, with the rest presented in appendix A. The heat capacity was calculated at 25 ℃ as shown in Table 4.1-1.

Table 4.1-1: Heat capacity constants and sample calculations.

Component a0 a1 a2 a3 a4 4,361 6,07E-03 2,90E-05 -3,581E-08 1,282E-11

CH3OCH3 2 3 4 a0 a1T a2T a3T a4T 4,361 1,80977 2,57702 -0,949093 0,101304

CP = (4.361 + 1.810 + 2.577 − 0.949 + 0.101) × 8.314 = 65.68 J⁄ mol. K

This then made it possible for us to calculate the changes in enthalpy at any temperature. We therefore moved from standard conditions and calculated ΔH rather at 250 ℃ (Table 4.1-2). Heat capacity at this temperature would be different from the one calculated above but the calculation will not be shown this time since the procedure is the same.

Table 4.1-2: Part of enthalpy calculation as a function of temperature.

o Component ΔHo [J/mol] Cp [J/mol.K] T - T0 [K]

CH3OCH3 -184100 93,9791 225

∆H0 = −184100 + (93,9791 × 225) = −162955 J⁄ mol

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Gibbs free energy (work) as a function of both temperature and pressure

Gibbs free energy determines the work requirements of a chemical process and the derived Equations for temperature dependence (Equation 4.7) and pressure dependence (Equation 4.8) look as follows:

∆G,T2 ∆G0 1 1 = + ∆H0 × ( − ) (4.7) T2 T1 T2 T1

P G = Go + RTo × ln ( ) (4.8) P0

We then applied Equation (4.7) in calculating the Gibbs free energy as a function of temperature as shown in Table 4.1-3 (at 250 ℃).

Table 4.1-3: Part of Gibbs free energy calculation as a function of temperature.

-1 -1 Component ΔH0 [J/mol] ΔG0 [J/mol] ΔG0/T [J/mol.K] 1/T0 [K ] 1/T2 [K ]

CH3OCH3 -184100 -112800 -378,333 0,00335 0,00191

∆G0 = [−378.333 + (−184100 × (0.00191 − 0.00335)] × 523.15 = −58993 J⁄ mol

This was followed by the Gibbs free energy calculation as a function of pressure (Equation 4.8). We again moved from standard temperature and pressure and used 90 bar and 250 0C instead (Table 4.1-4).

Table 4.1-4: Part of Gibbs free energy calculation as a function of pressure.

0 0 Component ΔG [J/mol] RT [J/mol] P/P0 ln (P/P0)

CH3OCH3 -58993 4349,469 88,823 4,4866

G = −58993 + (4349.469 × 4.4866) = −39479 J⁄ mol

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These results obtained through this procedure would then assist in mapping the extent plot, hence it became necessary to validate them and that was done by calculating the overall ΔH and ΔG for the reactions involved at standard conditions and then compared the results with literature. The resulting properties are given in Table 4.1-5.

Table 4.1-5: Enthalpy and Gibbs free energy at standard conditions.

At standard temperature and pressure

Component Cp [J/mol.K] ΔH [J/mol] ΔG [J/mol]

H2 28,7731 0 0 CO 29,0298 -110530 -137150

CO2 37,0199 -393510 -394370

CH3OH 44,2153 -200940 -162320

H2O 33,5164 -241814 -228590

CH3OCH3 65,6806 -184100 -112800

The overall reaction ΔH and ΔG would be given by:

∆H = (∑ 푣 ∆H ) − (∑ 푣 ∆H ) (4.9) (reaction j) 푗 i,j products 푗 i,j reactants

∆G = (∑ 푣 ∆G ) − (∑ 푣 ∆G ) (4.10) (reaction j) 푗 i,j products 푗 i,j reactants

Recalling our overall reactions:

CO + 2H2 ↔ CH3OH (4.11)

∆Hrxn = −200940 − (−110530 + (2 × 0)) = −90.41 kJ⁄mol

∆Grxn = −162320 − (−137150 + (2 × 0)) = −25.17 kJ⁄mol

CO + H2O ↔ CO2 + H2 (4.12)

∆Hrxn = [(−393510 + (1 × 0))] − [−110530 + (−241814)] = −24.03 kJ⁄mol

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∆Grxn = [(−394370 + (1 × 0))] − [−137150 + (−228590)] = −28.63 kJ⁄mol

2CH3OH ↔ CH3OCH3 + H2O (4.13)

∆Hrxn = [−184100 + (−241814)] − [2(−200940)] = −24.03 kJ⁄mol

∆Grxn = [−112800 + (−22859)] − [2(−162320)] = −16.75 kJ⁄mol

These results compare very closely to the work by [4], [5] and [6], and therefore the calculated enthalpies and Gibbs free energies were used for developing the thermodynamic attainable region.

4.2.1 Stoichiometric subspace for a single reaction

0 Equation (3.40) [Ni = Ni + ∑j 푣푖,푗dεj ≥ 0] provided a theoretical basis on which to build the graphical analysis. The reaction coordinate (ɛ) is independent of any reaction species and as such, allows for the relation between species with changing mole numbers. This can be presented as an extent plot which will eventually be interpreted in terms of a GH plot. Methanol dehydration reaction presented below will be used as an example.

kJ 2CH OH ↔ CH OCH + H O (∆H = −24.03 and ∆G = −16.75 kJ/mol) 3 3 3 2 mol

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Chemical species mass balance (stoichiometric feed)

For methanol (CH3OH):

0 NCH3OH = N CH3OH − 2ε ≥ 0 (4.1)

0 Where: NCH3OH is methanol output in moles, N CH3OH represent the moles of methanol fed into the chemical process, and ε is the reaction coordinate.

0 0 Equation (4.1) can be written as: N CH3OH − 2ε ≥ 0 where N CH3OH = 2

This then reduces to: 2(1 − ε) ≥ 0

Therefore: ε ≤ 1

For dimethyl ether (CH3OCH3):

0 NCH3OCH3 = N CH3OCH3 + ε ≥ 0 (4.2)

0 Where: NCH3OCH3 is DME output in moles, N CH3OCH3 represent the moles of DME fed into the chemical process, and ε is the reaction coordinate.

0 0 Equation (4.2) can be written as: N CH3OCH3 + ε ≥ 0 where N CH3OCH3 = 0 since we are not feeding DME into the process.

Hence: ε ≥ 0

For (H2O):

0 NH2O = N H2O + ε ≥ 0 (4.3)

0 Where: NH2O is water output in moles, N H2O is water input into the process in moles, and ε is the reaction coordinate.

0 0 Equation (4.3) can be written as: N H2O + ε ≥ 0 where N H2O = 0 since we are not feeding water into the process.

Hence: ε ≥ 0

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Figure 4.1-3 (an extent plot) is a result of the above mass balance for the three chemical species involved, where point zero (0) denotes the feed point with an extent of zero since the reaction (methanol dehydration) has not taken place. Points A and B are anywhere along the extent line between the feed and products with an overall feed conversion of 40% and 80% respectively. The reaction has not yet completed at these two points hence methanol would still be expected in the reactor and would be completely converted to products at an extent equalling 1.

Figure 4.1-3: An extent plot for a single reaction.

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4.2.2 Presenting the stoichiometric subspace in terms of the GH space

The objective was to establish the performance of this system in terms of the heat (enthalpy) and work (Gibbs free energy) requirements. It then became necessary to express the extent of the reactions as a function of these thermodynamic variables and this is how the resulting equations look:

∆H = ε∆Hf (4.4)

∆G = ε∆Gf (4.5)

Where ∆Hf and ∆Gf are the enthalpy and Gibbs free energy change of formation of a compound from its elements respectively. Critically analysing these equations makes it clear that plotting ΔH against ΔG for each chemical species by varying ε would result in a linear relationship as shown in Figure 4.1-4.

Figure 4.1-4: Depiction of a chemical process using the G-H plot for one reaction at standard conditions (1 bar and 25 0C).

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In Figure 4.1-4, point (0, 0) or origin indicates the feed point with an extent of zero since none of the reactions in the system has taken place at this point; hence the system heat and work requirements are also zero. Similar to the extent plots, points along the line between feed and products represent the product output with an overall incomplete reaction (40% and 80% conversions respectively) for the definite feed. The reaction will likely proceed in the direction of the arrow and terminate when the extent equal 1 with the net ΔG and ΔH values of the reacting system.

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4.2.3 Energy and work balances in the GH space

Considering that the value of ΔH determines heat requirements of a chemical process while ΔG corresponds to the work requirements (with the trend always in the direction for which ΔG ≤ 0), an analysis of a simple energy and work balance can be plotted as shown in Figure 4.1-5 and Figure 4.1-6.

Figure 4.1-5: Energy balance analysis by means of the G-H plot.

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Figure 4.1-6: Work balance analysis by means of the G-H plot.

This analysis leads to conclusions that complete methanol dehydration at standard conditions (25 ℃ and 1 bar) is spontaneous and exothermic which is technically termed feasible. However, available catalysts impose constraints even stronger than those of thermodynamics on the achievable set of composition spaces since there is presently no catalyst that promotes this dehydration reaction at standard conditions [7], hence the reactor is forced to operate at elevated temperatures, which is ideal since the conversion of methanol strongly depends on the operating temperature of the reactor [8].

4.2.4 Effects of changes in temperature and pressure on GH space for a one reaction

H and G are functions of temperature, hence elevating temperature at constant pressure allows us to analyse its effects on a G-H plot as depicted in Figure 4.1-7. The variation was done at the current industrial temperature range.

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Figure 4.1-7: The effects of temperature variations on methanol dehydration reaction at 1 bar.

As seen in Figure 4.1-7, temperature variation at constant pressure has negligible effects on the feasibility of the reaction since the reaction remains spontaneous (ΔG of the reaction slightly decreases) and requires the release of heat (ΔH slightly decreasing with temperature increase). This reaction is exothermic in nature, which means increasing temperatures favours the reverse reaction (also according to Le Chatelier’s principle) which in this case is nonspontaneous. This would be seen by mass balance lines shifting into the positive ΔG region. Comparing the slopes at 25 ℃ and 300 ℃ supports this theory.

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Temperature increase also affects methanol synthesis which could adversely influence DME production. It therefore became necessary to consider this temperature variation on the analysis of methanol synthesis and the results are illustrated as shown in Figure 4.1-8.

Figure 4.1-8: The effects of temperature variations on methanol synthesis reaction.

From Figure 4.1-8, we notice that temperature increase increases the positive slope of the reaction which results in G being more positive resulting in the mass balance moving into the positive ΔG space. This therefore suggests that elevated temperatures are unfavourable for the forward reaction since it will thermodynamically choose the most stable position which in this case will be the feed point since it has lower ΔG.

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Increasing the pressure (which is the same as putting work into the system) makes this reaction feasible again. At increased pressures nonetheless, the effects of pressure changes while the system temperature is fixed as seen in Figure 4.1-9 can be found to have a substantial influence, but only on G of the reaction at the specified pressure variations since enthalpy is pressure insensitive.

Figure 4.1-9: The effects of pressure variations on methanol synthesis reaction.

As can be seen in Figure 4.1-9, ΔH expectedly remains constant with pressure increase while ΔG increased significantly becoming more negative, thereby leading to a more spontaneous forward reaction. Therefore, increased pressure seems to support the forward reaction, as it will thermodynamically follow the path with a maximum change in G, as a result of its smaller ΔG. The reaction at 90 bars would therefore be anticipated to be more thermodynamically stable. Variation of these process variables resulted in rotation of the

73 mass balance line, with the length in H staying more constant compared to G. At higher temperatures, the system can be made feasible by putting work (in the form of pressure) into the system.

Since methanol dehydration does not have a change in the number of moles for both reactants and products, pressure variations at different temperatures have a negligible effect on the mass balance lines with slopes at different temperatures staying constant as shown in Figure 4.1-10.

Figure 4.1-10: Effects of pressure variations on a methanol dehydration reaction.

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4.2.5 Stoichiometric subspace and GH space involving three reactions

We now can contemplate a more intricate case in which:

 Multiple reactions take place in a single unit (reactor)

 Specie(s) appears in one or two chemical reactions

The reaction coordinates of these reactions can be used to compute values for ΔH and ΔG of the combined process while enthalpy and Gibbs free energy of formation are extracted from the published literature. According to Hess’s law;

∆H = ε1∆H1 + ε2∆H2 + ε3∆H3 (4.6)

∆G = ε1∆G1 + ε2∆G2 + ε3∆G3 (4.7)

Where, Ɛ1, Ɛ2, and Ɛ3 are the reaction coordinates of reactions 1, 2, and 3; ΔH1, ΔH2, ΔH3,

ΔG1, ΔG2 and ΔG3 are the enthalpy and Gibbs free energies of reactions 1, 2 and 3 respectively; and ΔH and ΔG are the enthalpy and Gibbs free energy of the combined process.

In an attempt to ascertain the performance of both reactants and product species during this synthesis, we now consider the graphical technique to analyse the concurrent reactions that occur in DME synthesis from syngas. The synthesis reactions are indicated by Equations 4.8, 4.9 and 4.10 below, which presume the use of a stoichiometric feed. We chose −2 to +2 as the reaction coordinates. The reactions involved in DME synthesis are as follows.

CO + 2H2 ↔ CH3OH [… ε1] (4.8)

CO + H2O ↔ CO2 + H2 [… ε2] (4.9)

2CH3OH ↔ CH3OCH3 + H2O [… ε3] (4.10)

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4.2.5.1 Mass balance calculations for chemical species

Carbon monoxide (CO) mass balance when the three reactions are considered:

0 NCO = N CO − ε1 − ε2 ≥ 0 (4.11)

0 ε2 = N CO − ε1

0 Where: NCO is carbon monoxide output in moles, N CO represents the moles of carbon monoxide fed into the chemical process, and ε1 and ε2 are extents of reactions 1 and 2 respectively. Considering the stoichiometric feed, it follows that:

ε2 = 1 − ε1

Hydrogen (H2) mass balance when all three reactions are considered:

0 NH2 = N H2 − 2ε1 + ε2 ≥ 0 (4.12)

0 ε2 = 2ε1 − N H2

0 Where: NH2 is hydrogen output in moles, N H2 symbolizes the moles of hydrogen fed into the chemical process, and ε1 and ε2 are extents of reaction 1 and 2 respectively. Considering the stoichiometric feed, it follows that:

ε2 = 2ε1 − 2

Water (H2O) mass balance when all three reactions are considered:

0 NH2O = N H2O − ε2 + ε3 ≥ 0 (4.13)

0 ε3 = ε2 − N H2O

0 Where: NH2O is water output in moles, N H2O denotes the moles of water fed into the chemical process, and ε2 and ε3 are extents of reaction 2 and 3 respectively. Considering the stoichiometric feed, it follows that:

ε3 = ε2 − 1

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Methanol (CH3OH) mass balance when the three reactions are considered:

0 NCH3OH = N CH3OH + ε1 − 2ε3 ≥ 0 (4.14)

0 2ε3 = N CH3OH + ε1

0 Where: NCH3OH is methanol output in moles, N CH3OH is the moles of methanol fed into the chemical process, and ε1 and ε3 are extents of reaction 1 and 3 respectively. Considering the stoichiometric feed, it follows that:

ε3 = ε1⁄2

Carbon dioxide (CO2) mass balance when the three reactions are considered:

0 NCO2 = N CO2 + ε2 ≥ 0 (4.15)

ε = −N0 2 CO2

0 Where: NCO2 is carbon dioxide output in moles, N CO2 represents the moles of carbon dioxide fed into the chemical process, and ε2 is the extent of reaction 2. Since the moles of carbon dioxide fed into the process equal zero, it follows that:

ε2 = −1

Dimethyl ether (CH3OCH3) mass balance when the three reactions are considered:

0 NCH3OCH3 = N CH3OCH3 + ε3 ≥ 0 (4.16)

ε = −N0 3 CH3OCH3

0 Where: NCH3OCH3 is dimethyl ether output in moles, N CH3OCH3 represents the moles of dimethyl ether fed into the chemical process, and ε3 is the extent of reaction 3. With the initial moles of DME as zero (since it is not in the feed), it follows that:

ε3 = 0

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Figure 4.1-11 (surfaces in three dimensional space) is obtained when plotting the summation of this mass balance on an extent plot with the extent of reaction taken from -2 to +2.

Figure 4.1-11: Extent plot for the summation of three reactions using a stoichiometric feed.

Evaluating extents for the three equations result in a linear relationship for the individual species involved. Plotting the summation of these mass balance limiting lines on an extent plot depicts how dimethyl ether synthesis reaction depends on both the methanol synthesis and the water gas shift reactions (ε3 = f(ε1, ε2)). This function is viewed as a surface obtained by erecting elevations corresponding to values of ε3 at different points (ε1, ε2) and this helps in visualising the volume of the region above the ε1ε2-plane.

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4.2.5.2 Extent plot transformation to the GH space

Transforming the extent plot implies expressing the reaction coordinates and molar flow rates in terms of the overall ΔH and ΔG of the reactions. Section 4.2.5.1 introduced the general procedure for performing the species mass balances. We could then calculate the point in the reactor at which the molar flowrate is greater than or equal to zero. This enables solving for reaction extents with their elimination leading to linear relationships for respective species at different feeds.

The reaction system we are considering in this dissertation involves three equations occurring simultaneously. It would then be more relevant to first consider the GH diagram for two reactions (methanol synthesis (4.8) and WGS (4.9)) and then add the methanol dehydration (4.10) separately so that we could properly understand its influence on the AR. Eliminating

ε1 , ε2 , and ε3 and Ni for each species in terms of the overall ΔH and ΔG allows for plotting a linear relationship that would meet the reactor’s AR. The resulting ΔH and ΔG limits can be presented in a GH plot as shown in Figure 4.1-12 which is similar to that of a single reaction (Figure 4.1-4) with the reaction happening from point a to c where the reactants are completely transformed to products at an extent corresponding to 1.

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Figure 4.1-12: Depiction of the GH plot showing methanol and water gas shift reactions at 25°C and 1 bar using a stoichiometric feed.

As part of the project to arrive at a better understanding of this process synthesis, we then assumed in this case that both the methanol synthesis reaction (Equation 4.8) and the dimethyl ether synthesis reaction (Equation 4.10) occurred simultaneously while the WGS (Equation 4.9) reaction did not take place because the nature of the catalyst set kinetic limits on the reaction. This limitation would hold even if the reaction was thermodynamically feasible. Jia et al. [9] cited a comparable situation while working on Fischer-Tropsch synthesis where the use of cobalt catalyst for carbon monoxide hydrogenation did not result in water conversion to hydrogen. This assumption resulted in Figure 4.1-13 as shown below.

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Figure 4.1-13: Depiction of the GH plot showing MeOH synthesis and DME synthesis reactions, at 25°C and 1 bar, using a stoichiometric feed.

The resulting polygon (abc) is expected to contain the number of sides equal to the reacting species but this is not the case as seen in Figure 4.1-13. This is due to the mass balance calculations being the same for some species (NCO sharing the mass balance with NH2 while

NH2O shares the mass balance with NDME) hence causing the limiting lines to collapse into each other. During the course of a reaction, materials are constantly reacting and reforming and therefore bring about changes in ΔG with the trend always in the direction for which ΔG is negative. The objective was to ascertain the performance of this reaction system in terms of the reaction extent and work requirement (ΔG). It therefore became necessary to present G as a function of the reaction extent in order to sufficiently discuss this system. A large negative ΔG0 gives a minimum on the right hand side of the curve in Figure 4.1-14, as is the case in Figure 4.1-13 (ΔG = −63.25 kJ/mol compared to Figure 4.1-12 (ΔG = −28.63 kJ/mol.

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Figure 4.1-14: The Gibbs free energy as a function of the extent of the reaction.

A large positive ΔG0, however, gives a minimum on the left hand side, and leads to a very small equilibrium constant. It seems plausible that a large negative value of ΔG0 should lead to near complete reaction from left to right, and also to a large equilibrium constant. We can therefore conclude that DME synthesis alleviates the methanol synthesis thermodynamic equilibrium limitation and leads to a more thermodynamically stable process synthesis, resulting in higher once-through conversion of syngas.

4.2.6 Feed analysis on the GH space

Normally, the water gas shift reaction (Equation 4.9) occurs on methanol synthesis reaction catalysts. We now examine the impact of the water gas shift reaction on the mass balance region when both the methanol synthesis reaction (Equation 4.8) and the dimethyl ether synthesis reaction (Equation 4.10) are also occurring at the same time.

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Using a feed comprising of CO (2 mol), H2 (3 mols), H2O (0.5 mols), and 2 moles of

CH3OH, we did the species mass balances and eliminated Ɛ1, Ɛ2, and Ɛ3 and the resulting Ni in terms of the ΔH and ΔG of the combined process. The aim was to establish the performance of the reactant and product species. The result, represented in a G-H domain, is presented in Figure 4.1-15.

Figure 4.1-15: Depiction of a chemical process using the G-H plot for DME synthesis reactions using a four component feed containing CO (2 mols), H2 (3 mols), H2O (0.5 mol), and CH3OH (2 mols).

The G-H plot presented in Figure 4.1-16 below records the results of a five-component feed of CO (1 mol), H2 (2 mols), H2O (0.5 mols), CO2 (1 mol), and 2 moles of CH3OH. We again performed the mass balance for all species and eliminated Ɛ1, Ɛ2, Ɛ3 and Ni in terms of the ΔH

83 and ΔG of the combined process. The aim was still to establish the performance of the reactant and species.

Figure 4.1-16: Depiction of a chemical process using the G-H plot for DME synthesis using a five- feed component of CO (2 mol), CO2 (1 mol), H2 (3 mols), H2O (0.5 mol), and CH3OH (2 mols).

Comparing Figure 4.1-15 and Figure 4.1-16 in terms of the mass balance region, it is clear that the introduction of CO2 in the feed changes the shape and size of this region and results in a greater number of reaction pathways. The mass balance AR would then be interpreted in terms of the boundaries set by these limits, but this is not as clear looking at Figure 4.1-16. To aid in our analysis, we therefore opted to reduce the number of components involved by considering only the methanol synthesis (Equation 4.8) and WGS (Equation 4.9) reactions. This was done with the sole aim of properly showing the region we are trying to define so that it could be easier to understand the one more cluttered as seen in Figure 4.1-16 since that is the system this dissertation aims to analyse.

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4.2.6.1 Mass balance for chemical species

With the overall objective of explaining the reactor’s AR and also identifying how the Gibbs free energy is minimised within the reactor, the mass balance was therefore performed for the following two equations as explained.

CO + 2H2 ↔ CH3OH [… ε1] (4.8)

CO + H2O ↔ CO2 + H2 [… ε2] (4.9)

Carbon monoxide (CO) mass balance when only two reactions (Equation (4.8) and Equation (4.9)) are considered can be expressed as:

0 NCO = N CO − ε1 − ε2 ≥ 0

0 ε2 ≤ N CO − ε1

0 Where: NCO is carbon monoxide output in moles, N CO is carbon monoxide fed into the process in moles, and ε1 and ε2 are extents of reaction 1 and 2 respectively. Considering the 0 stoichiometric feed (N CO = 1), it follows that:

ε2 ≤ 1 − ε1

The mass balance for hydrogen (H2) when only two reactions (Equation (4.8) and Equation (4.9)) are considered can be expressed as:

0 NH2 = N H2 − 2ε1 + ε2 ≥ 0

0 ε2 ≥ 2ε1 − N H2

0 Where: NH2 is hydrogen output in moles, N H2 represent the initial moles of hydrogen, and

ε1 and ε2 are extents of reaction 1 and 2 respectively. With the moles of hydrogen fed into the 0 process taken as 3 (N H2 = 3), we therefore get:

ε2 ≥ 2ε1 − 3

Water (H2O) mass balance when only two reactions (Equation (4.8) and Equation (4.9)) are considered can be expressed as:

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0 NH2O = N H2O − ε2 ≥ 0

0 ε2 ≤ N H2O

0 Where: NH2O is water output in moles, N H2O represent the moles of water fed into the chemical process, and ε2 is the extent of reaction 2. Taking the initial moles to be 0 0.5 (N H2O = 0.5), it follows that:

ε2 ≤ 0.5

Methanol (CH3OH) mass balance when only two reactions (Equation (4.8) and Equation (4.9)) are considered can be expressed as:

0 NCH3OH = N CH3OH + ε1 ≥ 0

0 ε1 ≥ −N CH3OH

0 Where: NCH3OH is methanol output in moles, N CH3OH represent the moles of methanol fed, and ε1 is the extent of reaction 1. With the initial moles of CH3OH fed into the process taken 0 as zero (N CH3OH = 0), we can reason that:

ε1 ≥ 0

Carbon dioxide (CO2) mass balance when only two reactions (Equation (4.8) and Equation (4.9)) are considered can be expressed as:

0 NCO2 = N CO2 + ε2 ≥ 0

ε ≥ −N0 2 CO2

0 Where: NCO2 is carbon dioxide output in moles, N CO2 represent the moles of carbon dioxide 0 fed, and ε2 is the extent of reaction 2. Assuming CO2 fed into the process to be 1 (N CO2 = 1), it follows that:

ε2 ≤ −1

As shown in Figure 4.1-17, plotting the above mass balance calculations on an extent plot results in a polygon with the number of sides equal to the chemical species involved.

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Figure 4.1-17: Extent plot for MeOH and WGS reactions, with a feed consisting of CO (1 mol), H2 (3 mols), CO2 (1 mol) and 0.5 mols of H2O.

The pentagonal region shaded in blue (Figure 4.1-17) is the mass balance attainable region, which characterises all the probable extents for the specified feed. As such, methanol synthesis would be feasible within this region. The problem space became limited by the number of components considered for developing this region, which was only meant to familiarise us with this concept. We now applied these principles to the analysis of DME synthesis as discussed in section 4.2.6.2.

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4.2.6.2 Transforming to GH space

Recalling the mass balances for the respective chemical species for the three equations involved in DME synthesis:

For carbon monoxide (CO) species, 0 NCO = N CO − ε1 − ε2 ≥ 0

For hydrogen (H2) species, 0 NH2 = N H2 − 2ε1 + ε2 ≥ 0

For water (H2O) species, 0 NH2O = N H2O − ε2 + ε3 ≥ 0

For carbon dioxide (CO2) species, 0 NCO2 = N CO2 + ε2 ≥ 0

For methanol (CH3OH) species, 0 NCH3OH = N CH3OH + ε1 − 2ε3 ≥ 0

For methanol (CH3OCH3) species, 0 NDME = N DME + ε3 ≥ 0

The limits for each species have been represented in a G-H space. ΔH and ΔG results of the altered chemical species are plotted on the G-H space. As seen in Figure 4.1-16, the resulting polygon has the same number of sides equal to those in the extent plot. However, the region constrained by these mass balance lines defines the attainable boundaries in a G-H plot. Enclosed in these boundaries is the space of thermodynamically feasible DME synthesis and can then be termed the thermodynamic AR.

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As previously discussed, the AR in this dissertation refers to the thermodynamically achievable region in the state space within which the reactor can function without violating thermodynamic boundaries, using only the process of reactions. This region should contain the feed point, which should be equal to zero at the intersection of the species, and it should represent all the possible combinations of the species taking part in the reactions.

Figure 4.1-18: G-H plot for DME synthesis reactions, with a feed of CO (2 mols), CO2 (1 mol), H2 (3 mols), H2O (0.5 mol), and CH3OH (2 mols).

As seen in Figure 4.1-18, the mass balance region resembles the sides of the extent plot in Figure 4.1-17. This is the area where there are feasible reactions, because the conditions required to optimize the process in a steady state system are satisfied and all the species are positive. (In other words, this region contains the feed point, it is zero on the boundaries, and it represents all the possible combinations of the species involved in the reactions). It can therefore be referred to as the mass balance attainable region.

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Looking at the boundaries of this region (Figure 4.1-18), we now solved for reaction extents and substituted the results into the general equations as follows:

At point a: NDME = NH2O = 0. Recalling Equations 4.13 and 4.16,

0 0 N DME + ε3 = N H2O − ε2 + ε3 = 0

Since the feed contains: N0 = 0 and N0 = 1⁄ , it follows therefore that: DME H2O 2

1 ε1 = 1, ε2 = ⁄2 and ε3 = 0

Substituting these extents in Equations 4.8 to 4.9, one deduces that methanol at this point is produced via the hydrogenation of carbon monoxide in the presence of water, with the general formula:

3CO + 3H2 + H2O ↔ 2CH3OH + CO2

This reaction will proceed until all the water is used up since we are feeding 0.5 moles of water compared to two moles of CO which then makes water the limiting reactant.

At point b: NDME = NCO = 0. Remembering Equations 4.11 and 4.16,

0 0 N DME + ε3 = N CO − ε1 + ε2 = 0

0 0 Since the feed contains: N DME = 0 and N CO = 2, solving for the three reaction coordinates leads to:

ε1 = 0, ε2 = 0 and ε3 = 0

These reaction extents suggest that none of the reactions (Equations 4.8, 4.9, and 4.10) occurs at this point. We made an assumption earlier that methanol synthesis from CO2 (Equation 2.2) would be ignored in this analysis, but that could be the reaction happening at this point or one of the side reactions proposed by [11] or possibly the overall reaction occurring at point a. This will be the most stable reaction at this point due to its low ΔG.

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At point c: NCO = NH2 = 0. Recalling Equations 4.11 and 4.12,

0 0 N CO − ε1 − ε2 = N H2 − 2ε1 + ε2 = 0

0 0 Since the feed contains: N CO = 2 and N H2 = 3, solving for reaction extents gives:

5 1 ε1 = ⁄3, ε2 = ⁄3 and ε3 = 1

Substituting these extents in equations 4.8 to 4.9 leads to the general formula:

6CO + 9H2 + CH3OH → 3CH3OCH3 + 2H2O

Apart from a characteristic change in ΔG between point b and c, there is also some DME being produced at this point which will happen until all the methanol is finished looking at the stoichiometric coefficients of this reaction.

At point d: NH2 = NCO2 = 0. Recalling Equations 4.12 and 4.15,

0 0 N H2 + ε2 − 2ε1 = N CO2 + ε2 = 0

0 0 Since the feed contains: N H2 = 3 and N CO2 = 1, therefore:

ε1 = 1, ε2 = −1 and ε3 = −1

The negative sign on extent 2 simply means that the RWGS is favoured at this point. Substituting these reaction extents leads to the general formula:

CO2 + 3H2 + CH3OH → CH3OCH3 + 2H2O

We now see DME being produced from the hydrogenation of carbon dioxide at point d, with DME slightly less than the one produced at point c, and this is expected based the Gibbs free energies at these two points.

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At point e: NH2O = NCO2 = 0. Recalling Equations 4.13 and 4.15,

0 0 N CO2 + ε2 = N H2O − ε2 + ε3 = 0

Since the feed contains: N0 = 1 and N0 = 1⁄ , it follows therefore that: CO2 H2O 2

1 1 ε1 = − ⁄2, ε2 = − ⁄2 and ε3 = −1

Substituting these extents in equations 4.8 to 4.9 leads to:

CO2 + H2O + 2CH3OCH3 → 3CH3OH + 2CO + H2

The negative ε3 implies the reverse reaction being supported, which means the methanol synthesis rather than dehydration is being favoured at this point. Thermodynamically, this point is in the positive ΔG space and therefore makes sense that the reverse reaction is the one supported. This reaction could be made feasible again by adding work to the system.

For each limiting line, the difference between two successive points lead to the following general equations:

Between points a and b (the NDME = 0 line), methanol is produced via the hydrogenation of carbon monoxide in the presence of water as follows:

3CO + 3H2 + H2O → 2CH3OH + CO2

Between points b and c (the NCO = 0 line), dimethyl ether production begins with the general equation as:

3CH3OH + 3CO + 6H2 + CO2 → 3CH3OCH3 + 3H2O

Between points c and d (the NH2 = 0 line), dimethyl ether is produced directly from syngas and also produces carbon dioxide as shown:

6CO + 6H2 → 2CH3OCH3 + 2CO2

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Between points d and e (the NCO2 = 0 line), dimethyl ether is produced from synthesis gas in the presence of methanol with the general equation:

4CH3OH + 2CO + 4H2 → 3CH3OCH3 + 3H2O

Between points e and a (the NH2O = 0 line), methanol is produced non-spontaneously from dimethyl ether as follows:

2CH3OCH3 + 2CO2 → CH3OH + 5CO + 4H2

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4.2.7 The attainable region for the reactor

As a general necessity for feasibility, the ΔG of all the reactions (excluding the mixing) happening through the reactor should be ≤ 0, then its attainable region for the specified feed can be represented as shown in Figure 4.1-19 with the area below the ΔG = 0 line as the region of feasible DME synthesis with minimum work requirement.

Figure 4.1-19: Attainable region for DME synthesis in GH space at 25 0C and 1 bar, using a feed of

CO (2 mol), CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol).

According to May and Rudd [12], the reaction path will follow the maximum change in G as a result of a large area of the negative Gibbs free energy pointing towards the relative stability of the intermediates, hence the more thermodynamically stable overall reaction is expected to be at point c as seen in Figure 4.1-19 (with a value of -78.52 kJ/mol). This is the

94 point expected to yield the maximum possible conversion under the current process conditions. As seen from this figure, the reactor’s AR is part of the mass balance region.

Taking the origin as the feed point, the synthesis reaction would be expected to go through point a and stop at point c, with the overall reaction as 3CH3OH + 3CO + 6H2 + CO2 →

3CH3OCH3 + 3H2O. This reaction would be the most likely to occur of all the possibilities obtained in the reactor under the given process conditions.

From the above, one can deduce what the reaction pathway will be, and predict its boundary in terms of the likely limiting extents of reaction. This in turn helps us to find the reactor’s AR, and to see the results of changes in the process feed and operating conditions.

4.2.8 Effect of changes in operating conditions

A GH plot for the combined methanol synthesis, WGS and methanol dehydration reactions can be drawn up for any given temperature and pressure. The objective was to analyse the effect of optimum temperature and pressure on the mass balance AR. Instead of randomly picking and varying these conditions until establishing the ones giving the maximum possible DME yield, we rather opted for varying conditions around the ones given as optimum in [11] for this reaction synthesis. These conditions (50 bar and 260 0C) are considered optimal in both the thermodynamic and economic point of view. They were chosen after the observation that while high pressure and low temperature favour DME’s production, lower temperatures favour the formation of CO2 and H2O which in turn would raise the operating costs of both tail gas and waste water.

4.2.8.1 Effect of changes in operating temperature

The central idea of the GH-space is that any that can have their change in enthalpy and Gibbs-free energy defined (this actually includes all unit processes, since all units can have mass, energy and entropy balances performed on them) can be represented as vectors on the GH-space and can be manipulated as vectors where the change in enthalpy represents the flow of heat and the change in Gibbs-free energy represents the flow of work.

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These thermodynamic variables are both temperature dependent and the effect of the change in temperature at a fixed pressure (50 bar) is depicted in Figure 4.1-20 to Figure 4.1-22.

Figure 4.1-20: Reactor’s AR for DME synthesis in GH space at 200 0C and 50 bar, with a feed of CO

(2 mol), CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol).

As seen in Figure 4.1-20, the increase in temperature and pressure from standard conditions slightly changed the shape and size of the AR since the region boundaries is now defined by four points (a-d) rather than five as seen in Figure 4.1-19. The other notable change is in the ΔG of the reaction which now increased to −63 kJ/mol and therefore making this synthesis less stable at these conditions compared to standard conditions. This is in agreement with Le Chatelier’s principle that increasing temperature in an exothermic reaction will push the system towards making reactants, which in this case will be favouring the non-spontaneous endothermic reaction hence an increase in Gibbs free energy.

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Increasing the temperature to 260 0C with the pressure still fixed at 50 bar resulted in Figure 4.1-20 shown below.

Figure 4.1-21: Reactor’s AR for DME synthesis in GH space at 260 0C and 50 bar, with a feed of CO

(2 mol), CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol).

Temperature variation at constant pressure for this reaction synthesis has a significant effect only on the Gibbs free energy (which shifts into the positive ΔG with an increase in temperature) as seen in Figure 4.1-21 and Figure 4.1-22. This behaviour is already discussed and therefore it is also interesting to look at the effect temperature variation has on the enthalpy of this reaction network. The temperature dependence of ΔH is seen to be very small (increasing from -216.35 kJ/mol to -206.66 kJ/mol within this temperature range) in comparison to the heats of reaction. This is in agreement with the work by [13]-[14], and therefore supports the procedure we took for this analysis.

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Figure 4.1-22: AR for DME synthesis in GH space at 300 0C and 50 bar, using a feed of CO (2 mol),

CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol).

4.2.8.2 Effect of changes in system pressure

The operating pressure of the system is found to have significant effects on the ΔG of reaction as discussed already. It is not a surprise therefore that, different ΔG values were obtained when taking the mass balance for each of the chemical species involved. The results for pressure variation at a constant temperature of 260 °C presented on the GH-space are discussed below.

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Figure 4.1-23: AR for DME synthesis in GH space at 260 0C and 30 bar, using a feed of CO (2 mol),

CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol).

As seen in Figure 4.1-23 and Figure 4.1-24, the increase in pressure (which is the same as putting work into the system) seems to be counteracting the effects of increases in temperature by shifting the mass balance AR back into the negative (feasible) ΔG space. It is also noteworthy that pressure increase at constant temperature has a significant effect only on the G of the reaction.

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Figure 4.1-24: AR for DME synthesis in GH space at 260 0C and 70 bar, using a feed of CO (2 mol),

CO2 (1 mol), H2 (3 mols), MeOH (2 mols) and H2O (0.5 mol).

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References

[1] Sempuga, B. R., Patel, B., Hildebrandt, D., & Glasser, D. (2011). The Relationship between Heat, Temperature, Pressure and Process Complexity. Industrial & Engineering Chemistry Research Journal, 50 (14), 8603-8619.

[2] Perry's chemical engineers' handbook. Volume 7. New York: McGraw-Hill, 1997.

[3] Reid, R. C., Prausnitz, J. M., & Poling, B. E. (1987). The properties of gases and liquids.

[4] Mpela, A. N. (2008). A process synthesis approach to low-pressure methanol/dimethyl ether co-production from syngas over gold-based catalysts. PhD Thesis, Republic of South Africa: University of the Witwatersrand, Johannesburg.

[5] Okonye, L. U., Hildebrandt, D., Glasser, D., & Patel, B. (2012). Attainable regions for a reactor: Application of ∆H − ∆G plot. Chemical Engineering Research and Design, 90, 1590-1609.

[6] Chen, W., Lin, B., Lee, H., & Huang M. (2012). One-step synthesis of dimethyl ether

from the gas mixture containing CO2 with high space velocity. Applied Energy, 98, 92- 101.

[7] Shinnar, R., & Feng, C. A. (1985). Structure of complex catalytic reactions: thermodynamic constraints in kinetic modeling and catalyst evaluation. Industrial & engineering chemistry fundamentals, 24 (2), 153-170.

[8] Raoof, F., Taghizadeh, M., Eliassi, A., & Yaripour, F. (2008). Effects of temperature and feed composition on catalytic dehydration of methanol to dimethyl ether over γ- alumina. Fuel, 87 (13), 2967-2971.

[9] Jia, G., Tan, Y., & Han, Y. (2005). Synthesis of dimethyl ether from CO hydrogenation: a thermodynamic analysis of the influence of water gas-shift reaction. Journal of Natural Gas Chemistry, 14, 47-53.

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[10] Warn, J. R. W., & Peters, A. P. H. (1996). Concise Chemical Thermodynamics. 2nd edition.

[11] Chen, H. J., Chei, W. F., & Yu, C. S. (2013). Analysis, synthesis, and design of a one- step dimethyl ether production via a thermodynamic approach. Applied Energy, 101, 449-456.

[12] May, D. and Rudd, F. D., (1976), Development of Solvay clusters of chemical reactions. Chemical Engineering Science, 31 (1), 1976, 59 - 69.

[13] Sempuga, B.C., Hausberger, B., Patel, B., Hildebrandt, D., Glasser, D. (2010) Classification of Chemical Processes: A Graphical Approach to Process Synthesis to Improve Reactive Process Work Efficiency. Ind. Eng. Chem. Res. 49 (17), 8227-8237

[14] Oaki, H. and Ishida, M. (1982) Study of Chemical Process Structures for Process Synthesis. Journal of Chemical Engineering of Japan. 15(1), 51-56

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CHAPTER 5: CONCLUSION AND RECOMMENDATIONS

Industrial processes pose a serious threat to the world’s natural resources for they consume them in high proportions as sources of energy for driving chemical processes that provide raw materials for many industrial chemicals. The responsibility for cutting back on the amount of energy needed for chemical processes rests on improving the efficiency of the processes used.

This research aimed at applying a graphical technique to assess the feasibility of processes occurring within chemical reactors. Considering the competitive nature of reactions occurring within the reactor per product run, we used thermodynamic analysis and mass balance calculations to show the interaction between these reactions, which ultimately made it possible to identify which of the many reactions happening will most likely dominate in that particular process. The technique accomplishes this by considering the thermodynamic properties of the feed material and products to assess the probable transformation in the separate co-existing reactions, and to establish the AR in that particular chemical process.

The prime objective was to evaluate the direct synthesis of dimethyl ether from syngas using a simple graphical approach which could identify the space of all possibilities, and in particular visualizing what that space looks like so as to gain better insights into the inner workings of this chemical system. This technique provides a systematic way for process designers to not only determine process targets or achieve optimal efficiency but also understand what could be essential to meeting these targets.

In the context of this dissertation, the AR refers to a thermodynamic region within which any reactor functions without violating thermodynamic boundaries. The procedure was to find the AR and then use mass balance calculations to interpret its edge in terms of the prospective limiting extents. The technique is a two dimensional plot of ΔH against ΔG, which respectively represents heat and work flows. While the principles applied may appear to be simple thermodynamics, this can be somewhat deceptive since the technique provides an elegant method of building flowsheets, allowing for easy and rapid interpretation of the results.

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5.1 Summary of Results

The results summarized below are not intended to be an absolute final solution to the problems of emissions and energy efficiency. These results represent an ideal case; they represent the best case, the “target” for the process. Obviously a real process would never perform as well as the ideal but knowing what the ideal actually is provides a basis for comparison. How far is a design from the ideal? Is it possible or practical to attempt to improve the real case? The ideal solution provides valuable information in answering those questions, amongst others.

Work began with establishing the ideal relationship between temperature and enthalpy of a reaction. To calculate ∆H, one would be expected to know the heat capacity as a function of temperature. Plotting Cp against T gives ∆H as the area under this curve. The dependence of

Cp upon T is determined by the path followed, hence the calculation of ∆H requires that we specify the path. The enthalpies calculated via this graphical approach are significantly 0 0 different from the ones calculated by ∆H = ∆H0 + 〈∆Cp 〉H(T − T0). This is due to the fact that this Equation has the enthalpy of formation in it and also assumes small temperature ranges. We acknowledged the differences brought by these two procedures but made use of this equation for reasons of simplicity.

This was followed by the introduction of an extent plot which was subsequently transformed to the GH space, where we found that variation of the temperature of the operating system affected both the ΔH and the ΔG of the reaction. In the case of methanol dehydration reaction, temperature variation had negligible effect on the feasibility of this reaction. The difference was observed with methanol synthesis reaction where temperature increase resulted in an increase in the positive slope G hence making this synthesis unfavourable. This situation could be reversed by putting work into the system in the form of pressure. Pressure variations at constant temperature were seen to have significant effects only on the G (ΔH remained unchanged) of the methanol synthesis reaction due to mole-number reducing stoichiometry of this reaction.

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We then plotted the GH space for the combined DME synthesis reactions and this resulted in a polygon with the number of sided similar to that of an extent plot a result of the mass balances on the different chemical species (Ni). The region bounded by these lines represented the mass balance boundaries (AR) that establishes the conditions within which the reactor would function without violating the thermodynamic relations. Temperature increase was seen to shift AR into the unfavourable positive ΔG space, while the increase in pressure reserved this situation which is in agreement with Le Chatelier’s principle.

This dissertation also shows that the introduction of either water or CO2, or both, to the feed opens up the mass balance region, resulting in WGS activity and generating more reaction path alternatives. Therefore, the RWGS/WGS reactions also determine the routes reactions can take. Again, the change in Gibbs free energy across the reactor and the reaction pathways leading to product are interlinked.

All of these factors are useful to the engineer who is setting performance targets for chemical processes. They enable designers to find the reactor’s AR, deduce the process reaction pathways, and interpret their boundaries in terms of the likely limiting extents of reaction. The GH model makes the results of changing the process feed and operating conditions of reactions clear in an easily accessible manner that makes it an indispensable tool in the conceptual design phase of a chemical process.

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5.2 Recommendations and Future Work

This approach offers a benefit of not only evaluating projects at design phase but also evaluating the efficiency of actual processes, identifying sources of inefficiencies within the process. The method can be applied to the Fischer-Tropsch synthesis and other industrial processes to obtain optimal results, to identify possible means of saving energy, and devise methods of supplying or recovering energy from the processes so as to improve process reversibility and efficiency.

An avenue of further research is to develop algorithms for the use of the GH-space that can be programmed into a computer model. The caveat here is that excluding the human element too much from the use of the GH-space has the danger of removing what is perhaps the greatest advantage of the method, the room for constant innovation.

For all the strengths of the GH-space, the technique is not without its weaknesses. As a thermodynamic tool, the GH-space gives little to no information in regards to kinetics and catalysis. Additionally the GH-space cannot handle the heat exchanger unit, this is not a weakness of the technique precisely but rather a gap for more research. Dealing with heat exchangers will require additional research and development of the technique.

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APPENDIX A: THERMODYNAMIC DATA

This section shows how the thermodynamic data used to analyse the performance of the DME synthesis process was calculated.

Table A-1: Enthalpy and Gibbs free energy of formation extracted from Perry’s Chemical Engineers’ Handbook, 7th ed.

THERMODYNAMIC PARAMETERS J/kmol J/mol ΔH0 -200940000 -200940 Methanol ΔG0 -162320000 -162320 J/kmol J/mol ΔH0 -110530000 -110530 Carbon monoxide ΔG0 -137150000 -137150 J/kmol J/mol ΔH0 -393510000 -393510 Carbon dioxide ΔG0 -394370000 -394370 J/kmol J/mol ΔH0 -241814000 -241814 Water ΔG0 -228590000 -228590 J/kmol J/mol ΔH0 -184100000 -184100 Dimethyl ether ΔG0 -112800000 -112800 J/kmol J/mol ΔH0 0 0 Hydrogen ΔG0 0 0

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Table A-2: Heat capacity constants taken from the ‘properties of gases and liquids, 5th ed.’

HEAT CAPACITY CONSTANTS

Component 퐚ퟎ 퐚ퟏ 퐚ퟐ 퐚ퟑ 퐚ퟒ

H2 2,883 0,003681 -0,00000772 6,92E-09 -2,130E-12 CO 3,912 -0,003913 0,00001182 -1,302E-08 5,150E-12

CO2 3,259 0,001356 0,00001502 -2,374E-08 1,056E-11

CH3OH 4,714 -0,006986 0,00004211 -4,443E-08 1,535E-11

H2O 4,395 -0,004186 0,00001405 -1,564E-08 6,320E-12

CH3OCH3 4,361 0,006070 0,00002899 -3,581E-08 1,282E-11

Equation A-1 was used to calculate the heat capacities as shown in Table A-3.

C p = a + a T + a T2 + a T3 + a T4 (A-1) R 0 1 2 3 4

Table A-3: Heat capacity calculations at standard conditions

2 3 4 Component T [K] a0 a1T a2T a3T a4T 퐂퐏 [퐉/퐦퐨퐥. 퐊] H2 298,15 2,883 1,0975 -0,6863 0,1834 -0,0168 28,7731 CO 298,15 3,912 -1,1667 1,0507 -0,3451 0,0407 29,0298

CO2 298,15 3,259 0,4043 1,3352 -0,6292 0,0834 37,0199

CH3OH 298,15 4,714 -2,0829 3,7433 -1,1776 0,1213 44,2153

H2O 298,15 4,395 -1,2481 1,249 -0,4145 0,0499 33,5164

CH3OCH3 298,15 4,361 1,8098 2,577 -0,9491 0,1013 65,6806

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Temperature dependence of ∆퐇ퟎ

Equation A-2 was used to calculate the enthalpies as a function of temperature as shown in Table A-4.

0 0 ∆H = ∆H0 + 〈∆Cp 〉H(T − T0) (A-2)

T = 250 ℃

T0 = 25 ℃

Table A-4: Enthalpy calculations at 250 ℃

0 Component ΔH0 [J/mol] 퐂퐏 [퐉/퐦퐨퐥. 퐊] T - T0 [K] ΔH [J/mol]

H2 0 29,3244 225 0 CO -110530 30,1087 225 -103756

CO2 -393510 45,4865 225 -383276

CH3OH -200940 61,2952 225 -187149

H2O -241814 35,6210 225 -233799

CH3OCH3 -184100 93,9791 225 -162955

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Temperature dependence of ∆퐆ퟎ

Equation A-3 was used to calculate the Gibbs free energies as a function of temperature as shown in Table A-5.

∆G,T2 ∆G0 1 1 = + ∆H0 × ( − ) (A-3) T2 T1 T2 T1

T2 = 250 ℃

T0 = 25 ℃

Table A-5: Gibbs free energy calculations at 250 ℃

-1 -1 Component ΔH0 [J/mol] ΔG0 [J/mol] 1/T0 [K ] 1/T2 [K ] ΔG [J/mol]

H2 0 29,3244 0,00335 0,00191 0 CO -110530 30,1087 0,00335 0,00191 -157239

CO2 -393510 45,4865 0,00335 0,00191 -395019

CH3OH -200940 61,2952 0,00335 0,00191 -133175

H2O -241814 35,6210 0,00335 0,00191 -218610

CH3OCH3 -184100 93,9791 0,00335 0,00191 -58993

110

Pressure dependence of ∆퐇ퟎ

Equation A-4 was used to calculate the Gibbs free energies as a function of pressure (with temperature fixed at 25 ℃) as shown in Table A-6.

P G = Go + RTo × ln ( ) (A-4) P0

T = 25 ℃ P = 90 bar

Table A-6: Gibbs free energy calculations at 25 ℃ and 90 bar

0 0 Component ΔG [J/mol] RT [J/mol] P/P0 ln (P/P0) G [J/mol]

H2 0 4349,47 88,8231 4,48665 19515 CO -157239 4349,47 88,8231 4,48665 -137724

CO2 -395019 4349,47 88,8231 4,48665 -375504

CH3OH -133175 4349,47 88,8231 4,48665 -113661

H2O -218610 4349,47 88,8231 4,48665 -199096

CH3OCH3 -58993.0 4349,47 88,8231 4,48665 -39479.0

111

Enthalpies of reactions

Equation A-5 was used to calculate the overall enthalpies at standard conditions as shown in Table A-7.

∆H = (∑ 푣 ∆H ) − (∑ 푣 ∆H ) (A-5) (reaction j) 푗 i,j products 푗 i,j reactants

Table A-7: Overall enthalpy calculations at standard conditions

Reaction Balanced Equation ∑ΔHProducts ∑ΔHReactants Overall ΔH [kJ/mol]

1 CO + 2H2 = CH3OH -200940 -110530 -90,41

2 CO + H2O = CO2 + H2 -393510 -352344 -41,17

3 2CH3OH = CH3OCH3 + H2O -425914 -401880 -24,03

112

Gibbs free energies of reactions

Equation A-6 was used to calculate the overall Gibbs free energies at standard conditions as shown in Table A-8.

∆G = (∑ 푣 ∆G ) − (∑ 푣 ∆G ) (A-6) (reaction j) 푗 i,j products 푗 i,j reactants

Table A-8: Overall Gibbs free energy calculations at standard conditions

Reaction Balanced Equation ∑ΔGProducts ∑ΔGReactants Overall ΔG [kJ/mol]

1 CO + 2H2 = CH3OH -162320 -137150 -25,17

2 CO + H2O = CO2 + H2 -394370 -365740 -28,63

3 2CH3OH = CH3OCH3 + H2O -341390 -324640 -16,75

113