Thermodynamic and Kinetic Study of Carbon Dioxide and Mercury

Removal from Flue Gas in Coal Combustion Power Plants

Kun Liu

B.Sc. Chemical Engineering, Tianjin University, 2007

A Dissertation

submitted in partial fulfillment of the requirements for the degree

Doctor of Philosophy

in the School of Energy, Environmental, Biological & Medical Engineering of the College of Engineering and Applied Science

University of Cincinnati Cincinnati, OH

2012

Dissertation Committee:

Stephen W. Thiel, Ph.D (Chair) Junhang Dong, Ph.D Yuen-Koh Kao, PhD Neville G. Pinto, Ph.D Drew C. McAvoy, Ph.D Abstract Carbon dioxide and mercury from anthropogenic emissions pose a significant threat to our environment and human health. Removal from their major source – coal- fired power plants – is one of the most effective approaches to control their emissions.

Traditional removal technologies are usually cost-intensive and low-efficient. Many studies have been focused on the novel capture approaches that are cost-effective while keeping a high performance. Thermodynamics and kinetics are critical to these studies as they provide fundamental knowledge of the capture process. In this work, the thermodynamics and kinetics of CO2 and Hg capture through absorption using aqueous

amines solutions and adsorption using supported ionic liquid sorbents were investigated.

A vapor-liquid equilibrium (VLE) data reduction method developed by Barker [1]

that simplifies experimental measurements while maintaining accuracy was applied for

the first time to the thermodynamic study of CO2 absorption in aqueous amine systems.

The method eliminates the measurements of speciation in liquid phase and vapor phase by applying a layer of mass balance iteration in the correlation. Incorporating the

electrolyte non-random two liquid (eNRTL) model and the Soave–Redlich–Kwong

(SRK) model, the data reduction method was used to correlate VLE and heat of absorption data collected in a modified batch calorimeter for ethanolamine (MEA) - H2O

- CO2 system and piperazine (PZ) - H2O - CO2 systems. The optimized model with the

best-fit eNRTL model parameters was used to predict vapor pressures under the

conditions reported in the literature; the predicted values were consistent with the

independent literature results, indicating successful application of the Barker data reduction method and the mathematical model in the thermodynamic study of CO2-

ii aqueous amine systems. The importance of combined correlation of VLE and heat of absorption data in the accurate prediction of the two properties was also confirmed by comparing the prediction from single and multiple data sets correlation.

With the current technologies, capture of CO2 and Hg from coal combustion flue

gas requires additional air pollution control devices that can only do a single task (for

example, a gas scrubber for CO2 or duct entrainment adsorption for Hg). To reduce the

cost, a new approach to capture both CO2 and Hg from coal combustion flue gas in an

integrated adsorbent system was discovered. In this approach, a task-specific amino acid

ionic liquid is supported on silica gel particles with high surface area and pore volume.

CO2 capture for these sorbents was studied in simplified fixed-bed experiments. The CO2

capacity for was found to be 0.4 mol of CO2/ mol of ionic liquid. The ionic liquid loading

was optimal for CO2 capture at 40 wt%. Mass transfer in fixed-bed trials was slow at high

ionic liquid loadings due to the decreasing in contact surface area. Limited change of CO2

capacity was observed after four adsorption/desorption cycles, which indicates good

regenerability. Hg capture performance was assessed for the same material in fixed-bed

adsorption tests under a nitrogen environment. These sorbent systems had a total Hg

uptake of more than 14 mg/g. Slipstream testing of the sorbents, along with other novel

Hg sorbents developed previously, using coal combustion flue gas showed promising and competitive results in Hg removal rate and Hg capacity compared with competing

technologies. When both CO2 and Hg are present in the gas phase, it is expected that Hg

(present in trace quantities in flue gas) accumulates and fixes in the sorbent via strong

chemical bonding over an extended time, while CO2 (present in large quantities in flue

gas) can reversibly be adsorbed and desorbed on the sorbent. This hypothesis was

iii

validated by the experimental evidence that the present of CO2 has limited effect on the capture of elemental Hg vapor and the theoretical evidence that oxidized Hg has a stronger bonding with the ionic liquid than CO2.

In summary, the thermodynamic and kinetic behaviors of CO2 and Hg capture

from coal combustion flue gas were successfully investigated through experimental and theoretical methods. The obtained experimental results and modeling framework will advance the design and optimization of pollution control process.

[1] Barker, J., Determination of activity coefficients from total pressure measurements.

Australian Journal of Chemistry, 1953. 6(3): p. 207-210.

Acknowledgements I would like to express my deep appreciation and gratitude to my academic

advisor, Dr. Stephen W. Thiel, for all the support, instruction, and encouragement that he

provided to me throughout my graduate study. His in-depth knowledge and experience in

chemical engineering is a tremendous help in my research. In 2008 and 2009 when my

research had some resistance, his patience and continuous encouragement helped me overcome the difficulties. In the stage of dissertation writing, his timely and helpful

comments and suggestions are also greatly appreciated. I am truly fortunate to have had

the opportunity to work with Dr. Thiel.

I would also like to express my heartfelt appreciation to Dr. Neville G. Pinto for his valuable suggestion and encouragement to my research. His effort on helping the slipstream testing of mercury sorbent project moving forward is also greatly appreciated.

I would like to thank the other members in my dissertation committee: Dr.

Junhang Dong, Dr. Yuen-Koh Kao, and Dr. Drew C. McAvoy for their helpful comments and suggestions to my research work and their valuable time on reviewing my dissertation.

This work was supported by the following agencies, companies, and organizations: Ohio Coal Development Office, Babcock & Wilcox Co., US

Environmental Protection Agency, Duke Energy Co., Oxford Mining Inc, ARCADIS

Co., and The University of Cincinnati. Their financial and technical supports are gratefully acknowledged.

I highly appreciate and would like to thank my research colleagues: Juan He,

Rebecca J. Desch, Amina Darwish, Jungseung Kim, Poornima Rao, Shada Salem, Taylor

Robie, Ali Gitipour, and Salem Shehadeh. The experience of working with them was enjoyable and memorable. I greatly appreciate the help by Juan on the bench-scale mercury adsorption tests. Her excellent work provided very valuable support to the slipstream tests in this work.

Finally, I would like to thank my family: my parents, the loveliest couple in the world, and my wife, the most beautiful woman in the world. Their trust and love are the greatest momentums to my graduate study.

vii

Table of Content

List of Figures ...... xiii

List of Tables ...... xviii

List of Symbols ...... xx

Chapter 1 - Introduction and Objectives ...... 1

1.1 Major flue gas pollutants and control technologies ...... 3

1.1.1 Carbon dioxide ...... 3

1.1.2 Mercury ...... 15

1.1.3 Other pollutants ...... 18

1.1.4 Process Integration ...... 20

1.2 Key thermodynamic and kinetic properties in pollutant gas removal from flue gas

...... 21

1.2.1 Vapor liquid equilibrium ...... 22

1.2.2 Energy demand for regeneration ...... 23

1.2.3 Heat capacity ...... 23

1.2.4 Mass transfer and dispersion in fixed-bed adsorption ...... 24

1.3 Objectives ...... 26

Chapter 2 - Materials and Methods ...... 28

2.1 Materials and Preparation ...... 28

2.1.1 Aqueous CO2 solvents ...... 28

2.1.2 Amino acid (AA)-based room temperature ionic liquid (RTIL)-coated silica

gel ...... 28

viii

2.1.3 RTIL-coated 3-mercaptopropyltrimethoxysilane (MPTS) - silica gel ...... 29

2.2 Characterization Techniques ...... 30

2.2.1 Fourier Transform Infra-Red (FTIR) ...... 30

2.2.2 BET Analysis ...... 30

2.2.3 Thermo-Gravimetric Analysis (TGA) ...... 31

2.2.4 Scanning Electron Microscopy (SEM) ...... 31

2.2.5 Elemental Analysis ...... 31

2.3 Apparatus and Procedure ...... 31

2.3.1 VLE measurement for aqueous amine systems ...... 31

2.3.2 Heat capacity measurement ...... 33

2.3.3 VLE and heat of absorption measurement for CO2 – aqueous amine systems 34

2.3.4 Fixed-bed CO2 adsorption measurement ...... 36

2.3.5 Fixed-bed mercury adsorption measurement for slipstream testing ...... 37

2.3.6 Mercury Sampling using modified Ontario Hydro method ...... 38

2.3.7 Bench-scale fixed-bed mercury adsorption measurement ...... 40

2.3.8 Entrained-flow mercury capture testing ...... 41

Chapter 3 - Thermodynamics of Amine-H2O Systems ...... 44

3.1 Introduction ...... 44

3.2 Theory ...... 45

3.2.1 Chemical Equilibrium ...... 45

3.2.2 Activity coefficient model ...... 46

3.2.3 Phase equilibrium ...... 53

3.2.4 Heat capacity ...... 53

3.3 Experimental methods ...... 54

3.4 Experimental results and data correlation ...... 54

3.4.1 Vapor liquid equilibrium ...... 54

3.4.2 Heat capacity ...... 55

3.4.3 Activity coefficient model correlation ...... 55

3.5 Model Prediction ...... 59

3.5.1 Vapor liquid equilibrium prediction ...... 59

3.5.2 Heat capacity prediction...... 61

3.5.3 Activity coefficient prediction ...... 62

3.6 Conclusion ...... 64

Chapter 4 - Thermodynamics of CO2 - Aqueous Amine Systems ...... 65

4.1 Introduction ...... 65

4.2 Objectives ...... 66

4.3 Theory ...... 67

4.3.1 Chemical Equilibrium ...... 67

4.3.2 Heat of absorption ...... 71

4.3.3 Baker Reduction Theory ...... 72

4.4 Experimental results and data correlation ...... 74

4.4.1 Vapor liquid equilibrium ...... 74

4.4.2 Heat of Absorption ...... 75

4.4.3 Activity coefficient model correlation with VLE and heat of absorption data 75

4.4.4 CO2 vapor pressure prediction and comparison ...... 77

4.4.5 Heat of absorption prediction and comparison ...... 83

4.4.6 Validation of combined correlation of VLE and heat of absorption ...... 87

4.5 Speciation prediction ...... 89

4.6 Conclusion ...... 90

Chapter 5 - Thermodynamics and Kinetics of CO2 Capture Using Room

Temperature Ionic Liquids ...... 92

5.1 Introduction ...... 92

5.2 Objectives ...... 93

5.3 Characterization results ...... 93

5.3.1 Characterization of CO2 reaction with RTILs ...... 94

5.3.2 Vapor liquid equilibrium and heat of absorption ...... 94

5.3.3 Surface area and pore size distribution of [P(C4)4][Tau] coated silica gels ..... 98

5.3.4 Thermal Stability of Ionic Coating Layer ...... 101

5.4 Experimental results for CO2 capture using silica supported RTILs ...... 103

5.4.1 Effect of RTIL loading on CO2 capacity ...... 104

5.4.2 Effect of RTIL loading on mass transfer ...... 106

5.4.3 Effect of temperature ...... 108

5.4.4 Regenerability ...... 109

5.5 Conclusion ...... 111

Chapter 6 - Room Temperature Ionic Liquid-Coated Sorbents for Hg and

Combined Hg -CO2 Capture from Coal Combustion Flue Gas ...... 112

6.1 Introduction ...... 112

6.2 Objectives ...... 114

6.3 Results and Discussion ...... 114

6.3.1 Hg capture ...... 114

6.3.2 Hg capture in low vapor concentration ...... 119

6.3.3 Hg and CO2 combined capture ...... 127

6.4 Conclusion ...... 132

Chapter 7 - General Conclusions...... 134

Chapter 8 - Future Work ...... 140

8.1 Assessment of other activity coefficient models ...... 140

8.2 Fugacity approach in thermodynamic study of CO2 capture ...... 141

8.3 Expended solvent systems in thermodynamic study of CO2 absorption ...... 142

8.4 Study the effect of other components on CO2 ...... 142

8.5 Long-term assessment of RTIL-coated sorbents for Hg capture in coal combustion

flue gas ...... 143

8.6 Alternative substrate for RTIL coated sorbents ...... 143

Reference ...... 144

Appendix A - Raw Data ...... 172

Appendix B - Calculation ...... 186

Appendix C - MATLAB® Code ...... 190

xii

List of Figures

Figure 1.1 2002 Electricity generation fuel mix in the United States [2] ...... 1

Figure 1.2 Process flow diagram for the CO2 separation process by absorption [14] ...... 5

Figure 1.3 Calculated equilibrium isotherms for CO2 solubility XCO2 (in mol CO2 per kg

solvent) in methanol (MeOH) and in an aqueous solution with 0.3 g/g MEA

(property data model) at various temperatures [15] ...... 8

Figure 1.4 Adsorbent materials for carbon dioxide capture from large anthropogenic point

sources [37] ...... 11

Figure 1.5 Portion of global anthropogenic mercury emissions to air in 2005 from

different sectors [49] ...... 16

Figure 1.6 Heat of regeneration versus CO2 delta loading for various capture reactor

designs [100] ...... 24

Figure 1.7 Schematic of fixed-bed breakthrough curve ...... 25

Figure 2.1 Schematic of equilibrium cell for VLE measurement (top: aqueous amines

systems; bottom: CO2 – aqueous amine systems) ...... 32

Figure 2.2. Schematic of fixed bed apparatus for CO2 adsorption measurements ...... 36

Figure 2.3 Location of slipstream testing unit in power plant ...... 37

Figure 2.4 Schematic of fixed-bed adsorption apparatus for slipstream mercury capture

testing ...... 38

Figure 2.5. Schematic of modified Ontario Hydro Method for mercury measurement ... 39

Figure 2.6 Fixed-bed apparatus for determination of Hg capture characteristics [103] .. 41

Figure 2.7 Schematic of entrained-flow reactor system [106] ...... 42

xiii

Figure 3.1 Comparison of correlated and experimental vapor pressure above aqueous

amine systems (top: PZ system (xPZ = 0.04, 0.09, 0.14, and 0.32) at 313K to 393K,

bottom: MEA system (xMEA = 0.05, 0.11, 0.31, and 0.54) at 313K to 393K) ...... 58

Figure 3.2 Comparison of total vapor pressures of PZ – H2O system by model prediction

(lines) and experiments (squares: this work, circles: [124], and diamonds: [125]) .. 60

Figure 3.3 Comparison of total vapor pressures of MEA – H2O system by model

prediction (lines) and experiments (circles: this work, diamonds: [126]) ...... 60

Figure 3.4 Comparison of heat capacity of PZ – H2O system by model prediction (lines)

and experiments (squares: this work, circles: [49], and triangles: [14]) ...... 61

Figure 3.5 Comparison of heat capacity of MEA – H2O system by model prediction

(lines) and experiments (squares: this work, triangles: [127], cross: [98], circles:

[92]) ...... 62

Figure 3.6 Predictions of activity coefficient of PZ at 313 K and 393 K ...... 63

Figure 3.7 Predictions of activity coefficient of MEA at 313 K and 393 K ...... 63

-5 -3 Figure 4.1 Data reduction method flow chart (ε1 = 1×10 , and ε2 = 1×10 ) ...... 76

Figure 4.2 Comparison of correlated and experimental vapor pressure above aqueous

amine – CO2 systems (top: PZ system (bPZ = 2m, 3.6m, and 5m) at 313K to 373K,

bottom: MEA system (30 wt% and 40 wt% MEA) at 313K to 373K) ...... 79

Figure 4.3 Comparison of model predicted and reported CO2 pressure at 2m (top) and 4m

aqueous piperazine (bottom) (line: predicted; solid circle: Lit. [134]; open circle: Lit.

[14]) ...... 81

Figure 4.4 Comparison of model predicted and reported CO2 partial pressure at 3.6m

(top) and 5m (bottom) aqueous piperazine (line: predicted; open circle: Lit. [14]) . 82

xiv

Figure 4.5 Comparison of model predicted and reported CO2 partial pressure at 30wt%

MEA (line: predicted; solid diamond: Lit. [21]) ...... 83

Figure 4.6 Comparison of model predicted and reported CO2 partial pressure at 3.5m

(top) and 7m (bottom) MEA (line: predicted; solid circle: Lit. [14]) ...... 84

Figure 4.7 Comparison of model predicted (lines) and reported enthalpy of absorption at

313 K (green squares) and 353 K (red circles) for 2.4 m PZ [14] ...... 86

Figure 4.8 Comparison of model predicted (lines) and reported enthalpy of absorption at

313 K (green squares) and 353 K (red circles) for 30 wt% MEA [137] ...... 86

Figure 4.9 Comparison of model predicted (line) and reported enthalpy of absorption

(squares: [136], diamonds: [139], and circles: [138]) for 30 wt% MEA ...... 87

Figure 4.10 Comparison of model predicted (lines) (using VLE data only) and reported

CO2 vapor pressure (left) and enthalpy of absorption (right) [14, 134] ...... 88

Figure 4.11 Comparison of model predicted (lines) (using heat of absorption data only)

and reported CO2 vapor pressure (left) and enthalpy of absorption (right) [14, 134] 89

Figure 4.12 Calculated liquid phase speciation (top: 5m PZ at 313K, bottom: 30 wt%

MEA at 313K) ...... 90

Figure 5.1 FTIR spectra of fresh and spent ILs (top: [P(C4)4][Met]; bottom:

[P(C4)4][Tau]) ...... 95

Figure 5.2 Vapor pressure of CO2 above [P(C4)4][Tau] RTIL at different temperatures . 97

Figure 5.3 Heat of absorption of CO2 by [P(C4)4][Tau] and 30 wt% aqueous MEA ...... 97

Figure 5.4 Calculated pore volumes for different [P(C4)4][Tau] loading silica gels ...... 99

Figure 5.5 Calculated pore diameter distribution from BET analysis (scatter) and

Gaussian distribution fit (line) for different [P(C4)4][Tau] loading silica gels (mean

pore diameters from the fitting are shown in the inset graph) ...... 100

Figure 5.6 Possible distribution of RTIL in pores ...... 100

Figure 5.7 Weight loss (top) and derivative weight loss (bottom) for 20 wt%

° ° [P(C4)4][Tau] coated silica gel by TGA upon heating to 700 C at a rate of 10 C/min

...... 102

Figure 5.8 Comparison of SEM micrographs of uncoated silica gel (A) and silica gel

coated with 20 wt% [P(C4)4][Tau] (B) ...... 103

Figure 5.9 CO2 capacities for [P(C4)4][Tau] (top) and [P(C4)4][Met] (bottom) at different

loadings ...... 105

Figure 5.10 Experimental and calculated breakthrough curve for CO2 capture with

[P(C4)4][Tau] coated silica gels in different RTIL loadings (■: 15wt%, ■: 25wt%,

and ■: 40wt%) ...... 108

Figure 5.11 Breakthrough curve for 40 wt% [P(C4)4][Tau]-silica at different temperatures

...... 109

Figure 5.12 Breakthrough curve for 40 wt% [P(C4)4][Tau] coated silica after each

regeneration cycle ...... 110

Figure 6.1 Entrained-flow breakthrough curve for Hg0 capture using 25 wt% [bmim]-

MPTS-Silica gel sorbent ...... 117

Figure 6.2 Hg removal percentages over time for [bmim]Cl-MPTS-silica (top: total Hg,

bottom: oxidized Hg (red) and elemental Hg (green)) ...... 120

xvi

Figure 6.3 Hg removal percentages over time for MEC-MPTS-silica (top: total Hg,

bottom: oxidized Hg (red) and elemental Hg (green)) ...... 121

Figure 6.4 Hg removal percentages over time for [(P4)4][Tau][Cys] - silica (top: total Hg,

bottom: oxidized Hg (red) and elemental Hg (green)) ...... 122

Figure 6.5 Hg removal percentages over time for [(P4)4][Tau] - silica (top: total Hg,

bottom: oxidized Hg (red) and elemental Hg (green)) ...... 123

Figure 6.6 Calculated structures of possible Hg2+ — DMPS complexes which shows the

4:1 complex that forms in the presence of excess DMPS [155] ...... 125

Figure 6.7 Calculated isotherm of elemental Hg adsorption by 20 wt% [(P4)4][Tau]

coated silica sorbent at 298 K and 101 kPa ...... 127

2+ Figure. 6.8 Possible reaction routes among amino acids, CO2 and Hg molecules ...... 130

0 Figure. 6.9 Possible reaction routes among amino acids, CO2 and Hg molecules ...... 130

- - 2+ - 0 - Figure. 6.10 Optimized molecular structure of Met -CO2, Met -Hg , Met -Hg , and Met -

2+ - 0 CO2-Hg , Met -CO2-Hg ...... 131

- - 2+ - 0 - Figure. 6.11 Optimized molecular structures of Tau -CO2, Tau -Hg , Tau -Hg , and Tau -

2+ - 0 CO2-Hg , Tau -CO2-Hg complexes ...... 132

xvii

List of Tables

Table 1.1. Contributions of electricity generation to total USA air emission [2] ...... 2

Table 1.2 Examples of commercially used solvents for CO2 separation [15] ...... 6

Table 1.3 Portion of U.S. air pollution that comes from power plants [66] ...... 19

Table 2.1. Textural characteristics of silica substrate particles ...... 28

Table 2.2. Comparison of measured mercury concentration by sorbent trap method and

modified Ontario Hydro method ...... 40

Table 3.1 Parameters for calculating reaction equilibrium constants for amine

dissociation on the mole fraction scale ...... 46

Table 3.2 Regression results of binary interaction parameters for PZ-H2O system ...... 57

Table 3.3 Regression results of binary interaction parameters for MEA-H2O system ..... 57

Table 4.1 Parameters for calculating reaction equilibrium constants for CO2 reaction with

aqueous amine on the mole fraction scale ...... 70

Table 4.2. Best-fit binary interaction parameters for PZ-CO2-H2O system ...... 78

Table 4.3. Best-fit binary interaction parameters for MEA-CO2-H2O system ...... 78

Table 5.1 Best-fit parameters for VLE relationship of CO2 and [P(C4)4][Tau] expressed

by Eq. (5.1) ...... 96

Table 5.2 Textural properties of RTIL-coated sorbents with different RTIL loadings .... 99

Table 5.3 Fitted axial dispersion coefficient Da and the effective mass transfer coefficient

k for [P(C4)4][Tau]-Si with different RTIL loadings at room temperature ...... 107

Table 6.1 Hg capacities (Hg0 and Hg2+) of studied sorbents and activated carbon ...... 115

xviii

Table 6.2 Bench scale fixed-bed testing results for 40 wt% [(P4)4][Tau] and [(P4)4][Met]

coated silica gels (Testing Conditions: 30 – 48 ppb Hg in N2 carrier gas at ~ 80 ˚C)

...... 128

Table 6.3 Calculated enthalpy for each routine shown in Figure. 6.8 ...... 130

Table 6.4 Calculated enthalpy for each routine shown in Figure. 6.9 ...... 130

xix

List of Symbols

CI: confidence interval

D: dielectric constant

F: degrees of freedom

H: Henry’s constant

K: equilibrium constant

I: ionic strength

Ms: solvent molecular weight

N: number of experimental points

P: pressure

0 Ps : saturation pressure of the solvent

R: gas constant

T: temperature (K)

Vcell: volume of equilibrium cell

X: effective mole fraction

Z: absolute value of the ionic charge

e: electron charge

g: Gibbs energy

k: Boltzmann constant

n: number of moles

r: Born radius

tinv: inverse of Student's t cumulative distribution function,

v: molar volume

x: liquid phase mole fraction y: vapor phase mole fraction

Greek Letters

α: CO2 loading (mol CO2/mol amine)/ NRTL nonrandomness factor

σ: standard error

γ : activity coefficient

ρ : closest approach parameter in the Pitzer-Debye-Huckel equation

τ : NRTL interaction parameter

0 ϕˆ : pure solvent vapor phase fugacity coefficient at saturation pressure

ϕˆ : vapor phase fugacity coefficient

Subscripts

i,j: any species

c: cation

a: anion

m: molecule t: summation of all species l: liquid phase v vapor phase s: solvent

w: water x: true mole fraction ub: upper bound lb: lower bound

xxi new: updated value

Superscripts cal: calculated pressure exp: experimental pressure

T: summation of liquid phase and vapor phase

Abbreviations

AA: amino acid

ACI: activated carbon injection

CA: carbonic anhydrase

Cys: Cysteine eNRTL: electrolyte Non-random Two-liquid

ESP: electrostatic precipitator

FF: fabric filter

FGD: flue-gas desulfurization

IGCC: coal gasification combined cycle

IL: ionic liquid

MEA: monoethanolamine

Met: methionine

MTZ: mass transfer zone

NRTL: Non-random Two-liquid

PM: particulate matter

PZ: piperazine

RTIL: room temperature ionic liquid

xxii

SCR: selective catalytic reduction

SRK: Soave-Redlich-Kwong

Tau: Taurine

VLE: vapor liquid equilibrium

xxiii

Chapter 1 - Introduction and Objectives

Coal combustion has been the primary power source to supply the rapidly

growing energy demands of the United States for decades. In 2011, there were more than

1,300 coal-fired power plants generating 315 gigawatts during peak time in the United

States [1]. Coal was reported to account for 50% of the total energy generation

nationwide, as shown in Figure 1.1 [2]. From a worldwide standpoint, coal combustion provides 40% of the total energy, and its use is expected to grow 65% by the year of 2035

[3].

Figure 1.1 2002 Electricity generation fuel mix in the United States [2]

While people have long benefited from coal energy, emissions from coal-fired power plants are a major source of air pollution in North America. Table 1.1 presents the total emission of several major flue gas pollutants in the United States [2]. Pollutants from coal combustion are great threats to the global environment and human health.

Carbon dioxide, a major component in flue gas, has been identified as a greenhouse gas which is responsible for global climate change. Acid gases, including hydrogen chloride

(HCl), sulfur dioxide (SO2), and nitrogen oxides (NOx), dramatically increase the acidity

of atmosphere and water environment. Trace metal vapor emission that bio-accumulates

gradually in lake, river, and ground water may damage the whole ecosystem. Low

visibility due to haze can be caused by particulate matter (PM) from coal combustion [4].

Thus, control of flue gas pollutants has been an important topic in both the industrial and

the academic worlds.

Table 1.1. Contributions of electricity generation to total USA air emission [2] Total annual Total electricity Collective Number of emissions from production from emission rate Pollutant facilities included included of included included facilities facilities (GWh) facilities 2,178 million Carbon dioxide 899 2.4 million 893 kg/MWh tonnes 0.023 Mercury 44,231 kg 376 1.9 million kg/GWh 9.2 million Sulfur dioxide 836 2.4 million 3.79 kg/MWh tonnes 4.0 million Nitrogen oxides 897 2.4 million 1.66 kg/MWh tonnes

In addition to environmental damage, pollution from coal-fired power plants also

has direct and indirect effects on human health. According to a 2004 report, pollutants

from coal-fired power plant are responsible for nearly 38,200 non-fatal heart attacks and numerous asthma attacks, cardiac problems, and respiratory problems each year in the

United States [5]. Some of these diseases can be easily recognized as the result of power plant pollution. For example, a high respiratory disease rate among the people who live around a power plant may be attributed to the ash from incomplete combustion of fossil

fuels. On the other hand, indirect effects could be as severe as the direct effects but less

noticeable. Carbon dioxide was not recognized as a pollutant until recent studies

discovered that climate change resulting of CO2 accumulation in atmosphere has great

effects on heat- and cold-related illnesses such as heat stress, arterial thrombosis and respiratory disease. [6]

1.1 Major flue gas pollutants and control technologies

Typical flue gas from coal-fired power plants includes N2, CO2, H2O, O2, CO,

H2S, NH3, nitrogen oxides (NOx), sulfur oxides (SOx), hydrocarbons, hydrocyanic acid,

hydrogen halides, heavy metal vapor, and fly ash. Most of the emission components are

pollutants which are regulated by government agencies. In this section, several of the

most significant pollutants (CO2, Hg, SOx, NOx, and fly ash) along with their control

technologies are introduced.

1.1.1 Carbon dioxide

Global climate change is currently the subject of intense discussion. Daily

observations and records show that the average global temperature is rising, glaciers are

shrinking, and global land precipitation is increasing due to climate change. It is widely accepted that man-made carbon dioxide is a primary contributor to global climate change

[7]. Emissions from coal-fired power plants account for more than 32% of total

anthropogenic CO2 emissions in the U.S., and are considered to be the largest stationary source of carbon dioxide emissions [8]. With the growing evidence for the negative effects of CO2, the U.S. EPA realized the urgency of CO2 emission control and proposed

for the first time a standard to limit the CO2 emission from power plants [9]. The new rule requires new power plants to generate less than 1,000 lb of CO2 per megawatt hour

of electricity produced on average over a 30-year period, much less than the current coal- fired power plant CO2 emission rate of averaging 893 kg (1,968 lb) of CO2 per megawatt

hour as shown in Table 1.1.

Many techniques have been developed to capture carbon dioxide in coal-fired

power plants. These carbon control technologies can be divided into three categories: oxy-combustion capture, pre-combustion capture, and post-combustion capture.

Oxy-combustion capture technology eliminates the carbon dioxide separation

from nitrogen in flue gas by using high-purity oxygen in coal combustion. Prior to the

combustor, nitrogen in air is removed, leaving the flue gas “nitrogen free”. Since the

major flue gas component, nitrogen, is not present in the flue gas generated by oxy-

combustion, separation of carbon dioxide is dramatically simplified. However, the

production of oxygen and the special requirements for equipment material for high-

temperature oxygen service impose a significant amount of cost to the capture process.

Pre-combustion capture is a promising approach for CO2 separation in coal

gasification combined cycle (IGCC) power plants. In this technology, fossil fuels are

first gasified into a mixture of water, hydrogen, carbon monoxide, and carbon dioxide,

followed by a water shift reaction in which carbon monoxide is reacted with steam to

produce hydrogen and carbon dioxide. The CO2 can be then easily separated from the

hydrogen, which is then used for power generation [10, 11]. Even though pre-combustion

capture has great advantages over oxy-combustion and post-combustion capture technologies, its implementation is limited to IGCC power plants, which have not yet

been widely deployed.

Post-combustion capture is the most attractive option for existing power plants

because of its maturity and good prospects for retrofitting. This approach uses absorption

or adsorption to remove CO2 from flue gas to liquid or solid, followed by desorption of

CO2 and regeneration of solvents or sorbents. The desorbed CO2 can be compressed and

stored in a concentrated form [12, 13].

1.1.1.1 Absorption Absorption of carbon dioxide using liquid solvents has drawn great attention due to its similarity to well-established gas desulfurization processes. It can be easily retrofitted and applied to existing power plants without much modification. Similar to desulfurization processes, absorption of carbon dioxide is based on the high solubility of

weakly-acidic carbon dioxide in a liquid (for example, a physical or chemical solvent) in

an absorber. The captured CO2 in the liquid phase is released at a higher temperature in

the regenerator. The regenerated solvent is sent back to the absorber for another cycle of

absorption, and the concentrated CO2 stripped out of the solvent is pressurized for further

use or storage. Energy is needed in the process to pump the materials, heat and cool

solvent between the absorber and regenerator, and release CO2 from solvents. A

schematic of the absorption process is shown in Figure 1.2.

Figure 1.2 Process flow diagram for the CO2 separation process by absorption [14]

Table 1.2 Examples of commercially used solvents for CO2 separation [15] Solvent Absorber conditions

I. Physical solvents T ≈ -70 °C to -10 °C, p > 20 Methanol (RectisolTM) bar T ≈ -20 °C to 40 °C, p > 20 N-Methyl-2-pyrrolidone (NMP) (PurisolTM) bar Dimethyl ether of polyethylene glycol (DMPEG) T ≈ -40 °C to 0 °C, p > 20 bar (SelexolTM)

IIa. Organic chemical solvents (amine-based) Monoethanolamine (MEA) 2-amino-2-methyl-1-propanol (AMP) diethanolamine (DEA) diisopropanolamine (DIPA) methyldiethanolamine(MDEA) T ≈ 40-60 °C, p ≈ 1-65 bar triethanolamine (TEA) piperazine (PZ) Commercial solvent (for example, KS-1TM by Mitsubishi)

IIb. Inorganic chemical solvents Hot potash T ≈ 70-120 °C, p ≈ 20-70 bar potassium carbonate (+ activators) (Benfield ProcessTM) Potassium/sodium carbonate (aqueous solution) T ≈ 20-40 °C Ammonia (chilled ammonia) T ≈ 0-20 °C, p ≈ 1 bar Ammonia T ≈ 40 °C, p = 1 bar

III. Mixture of physical and chemical solvents Sulfolane + DIPA/MDEA (SulfinolTM) T ≈ 20-80 °C, p = 5 bar Methanol + secondary alkylamine (AmisolTM)

Table 1.2 lists several representative CO2 solvents that have been widely used or commercialized. These solvents can be categorized as physical and chemical solvents. A physical solvent absorbs CO2 gas purely through physical dissolution. The vapor liquid equilibrium in such case can be simply expressed by Henry’s law which states that over a limited range the fugacity of the solute is proportional to its concentration in the liquid

[16]. Due to the intrinsically low physical solubility, absorption into a physical solvent

must usually be done at low temperature and high pressure. Chemical solvents, on the

other hand, take the advantages of fast reversible reactions between weakly-acidic CO2

and an alkaline solvent that can absorb much more CO2 at low pressure and high

temperature. Figure 1.3 compares a linear isotherm of a physical solvent (methanol) and a

nonlinear isotherm of a chemical solvent (30 wt% MEA); the chemical solvent gives a

much lower CO2 partial pressure at the same CO2 loading (mol CO2/kg solvent) in the

solvent. Given the conditions of flue gas in coal-fired power plants, chemical solvents are

the preferred choice for CO2 absorption.

One major class of chemical solvent is aqueous amines. Aqueous

monoethanolamine (MEA) has been used as a general acid gas (for example, CO2 and

H2S) solvent for more than 80 years due to its high reaction rate and high capacity. MEA,

as well as other primary and secondary amines, reacts with bicarbonate (R (1.3)) and a hydronium ion (R (1.4)) to form carbamate and pronated amine respectively. One mole of

CO2 reacts with two moles of amine, which indicates a theoretical CO2 capacity of 0.5

mol CO2/mol amine for primary and secondary amines.

+− 2H23 O← → H O + OH R (1.1)

+− 2H22 O+ CO ← → H 3 O + HCO 3 R (1.2)

−− R2 NH+ HCO 32 ← → R NCOO+ H 2 O R (1.3)

++ R2 NH+ H 3 O ← → H2 O + R 22 NH R (1.4)

The thermodynamics [17-22] and kinetics [23-26] of CO2 capture using aqueous

solutions of MEA have been studied extensively, making it a benchmark material for

aqueous amine studies. The drawback of using primary amines, such as MEA, is the high

enthalpy of reaction which may cause high regeneration cost. Tertiary amines (for

example, N-methyl-diethanolamine (MDEA)) have no hydrogen bonded to the nitrogen

atom on the amine site, which prevents formation of carbamate with CO2 (R (1.3)) and doubles the CO2 capacity to 1 mol of CO2 by 1 mol of amine. In addition, the total heat of

absorption is reduced because the carbamation reaction (R (1.3)), which has a high

reaction enthalpy, is eliminated. Thus, tertiary amines are reasonable alternatives to

primary and secondary amines. Because the amine group is sterically hindered, tertiary

amines may react slowly with CO2. To address this problem, promoters that facilitate the reaction of CO2 and amines can be added to the system.

Figure 1.3 Calculated equilibrium isotherms for CO2 solubility XCO2 (in mol CO2 per kg solvent) in methanol (MeOH) and in an aqueous solution with 0.3 g/g MEA (property data model) at various temperatures [15]

Piperazine (PZ), a weak base, can facilitate CO2 absorption into aqueous solution.

In addition, piperazine itself was reported react rapidly with CO2 to form carbamate due

to the limited steric hindrance of the cyclic di-amine structure [27]. Recently, it has been

found that piperazine also has great advantages of greater thermal and oxidative stability

over the other amines [28]. Even though the boiling point of piperazine is not high (419.2

K [29]), its volatility is comparable to that of MEA because of its low activity coefficient in the CO2-loaded solution [30]. One drawback of PZ is its low solubility in water at

room temperature, which limits its further application in flue gas CO2 capture. It was

proposed that this limitation could be overcome by running the absorption/stripping

cycles at high CO2 loading so that most of the PZ exists in ionic form [30]. Another drawback of PZ is low capacity; consequently, in this application it is usually mixed with other amines to combine their individual advantages [31, 32].

As CO2 hydration (R (1.2)) is the rate-controlling step in CO2 absorption using

aqueous amine [33], much work has been done to facilitate this step by introducing a

catalyst to the system. The biological catalyst carbonic anhydrase (CA), an enzyme found

in animals, plants, and bacteria, is another promising route to increase the CO2 absorption

rate. CA is used by many organisms to maintain acid-base balance in blood and other

tissues by converting carbon dioxide to bicarbonate. These enzymes efficiently catalyze

the CO2 hydration reaction: 1.3 g of CO2 can be hydrated in 1 second using only 1 mg of

carbonic anhydrase. This hydration reaction is freely reversible, depending only on

partial pressure gradients, and does not benefit from increasing temperature [34]. To

apply CA to CO2 capture from flue gas, much work has been focused on stabilizing the

enzyme under the harsh conditions and high temperature in flue gas. For example,

Dilmore et al. [35] have proposed absorption of CO2 into water containing CA; the

enzyme facilitates conversion to bicarbonate that is adsorbed onto polyacrylamide beads.

Once loaded with bicarbonate, the polyacrylamide is removed from the system, thermally

regenerated, and recycled to the capture process. In this way the CA is protected from the

elevated temperature used in the regeneration operation.

Even though liquid solvent systems have been widely studied and have great potential in CO2 capture application, they have several intrinsic drawbacks:

• High energy consumption in heating and cooling cycles. The absorption and

stripping processes require heating and cooling to the optimal process

temperatures. Due to the high heat capacity of liquids, the energy used on

heating/cooling cycles is relatively high.

• Limited amine concentration. To prevent the possible high viscosity and

precipitation at high amine concentrations in aqueous phase, the solvent must

include a large amount of water to dilute the amine.

• Corrosion to the equipment. Heat-stable salts in the amine solution may cause

increased corrosion on the surface of the steel equipment [36].

1.1.1.2 Adsorption Solid adsorbents can solve the problems encountered using liquid solvents as mentioned above. Through physisorption, chemisorption, or both, CO2 can be directly

captured on the active sites of a solid surface. Solid sorbents can be used at temperatures

from room temperature to as high as 900K with a maximum CO2 capacity of 11 mmol

CO2 per gram of sorbent. Figure 1.4 summarizes the operating temperatures and working

CO2 capacities (mol CO2 per gram of sorbent) of a number of solid adsorbents [37].

Amine-based adsorbents, one of the most studied CO2 solid adsorbent, are analogues the

liquid amine solutions used for CO2 absorption. In these adsorbents, amines (active site

for CO2 capture) are concentrated and immobilized on a solid support which can be

10 chosen from a materials ranging from polymeric resins to inorganic silica. Due to the high concentration of amine, the CO2 capacity per unit volume of sorbent is much higher than that of the corresponding liquid amine solutions. Immobilization on a chemically stable substrate also enhances stability of these adsorbents. In addition, mass transfer of

CO2 from gas phase to the active site is dramatically simplified due to the absence of water.

Figure 1.4 Adsorbent materials for carbon dioxide capture from large anthropogenic point sources [37] There are basically two approaches to integrate amine into a solid substrate: physical coating and chemical grafting. Physical coating of amines onto the surface of a porous material is a simple but effective approach to immobilize amines on a solid

substrate. Such coating can be done by completely mixing the substrate and the organic

amines in a properly selected solvent, followed by the evaporation of the solvent. The

simplicity of this adsorbent preparation method can decrease the cost of the adsorbent

material and advance commercialization of the technology. The choice of amine is

usually based on maximizing the number of amine groups per unit volume of solid. Thus,

molecules that contain multiple amine groups (for example, tetraethylenepentamine,

pentaethylenehexamine, and polyethyleneimine) have been widely studied. Another type

of amine-containing material that is suitable for impregnation on solid substrate is task-

specific room temperature ionic liquids (RTILs). RTILs are liquids that only contain ions

at or below room temperature [38]. Proper functionalization of the RTILs, often by amine tethering, can make them task-specific for CO2 capture. The features of low volatility and

high stability at elevated temperature, and environmental friendliness make task-specific

RTILs a promising candidate in CO2 capture. Bates et al. tethered a primary amine to an

imidazolium-based ionic liquid, and observed a capacity of one mole CO2 per mole of

RTIL [39]. Fukumoto et al. synthesized twenty types of amino acid based ionic liquids

[40], some of which were found to be effective in CO2 capture [41-44]. Due to their high viscosity, it is impractical to apply RTILs in traditional scrubbing/stripping processes.

Chemical grafting of amine on the surface of substrates is another approach for amine immobilization. The advantage of chemical grafting over physical coating is that the leaching of amine is minimized because of the strong chemical bonding between the amine and the substrate. Another advantage of chemical grafting is enhanced mass transfer. Unlike impregnated amines which accumulate on the surface, most of the grafted amines form a single layer and are directly exposed to gas-phase CO2; this

arrangement eliminates mass transfer resistance in the liquid phase. Chemical grafting is

usually realized on oxide supports (for example, silica particles) using the reaction

between an amine-containing silane and a hydroxide group on the substrate surface. The

most common amine-containing silanes are 3-aminopropyltrimethoxysilane, 3-(2-

aminoethyl)aminopropyltrimethoxysilane, and 3-[2-(2- aminoethyl)aminoethyl] aminopropyltrimethoxysilane which are mono, bi, and tri amines respectively. The CO2

loading ranges from 1.27 to 5.07 mmol per gram of adsorbent [37].

1.1.1.3 Key technical factors in CO2 capture

Both absorption and adsorption have merits and drawbacks in CO2 capture

applications. In the design and optimization of CO2 capture process, a proper selection of

these two methods should be made according to their individual features and design

demands. Nevertheless, there are several common key factors that can be applied to both

methods:

CO2 capacity. CO2 capacity is usually defined as the amount of captured CO2 per

unit mass or mole of solvent or sorbent. It determines the required solvent or sorbent

quantity needed in the process. A low CO2 capacity usually requires a large quantity of

solvent or sorbent for a target CO2 removal rate. The cost for the large quantity of material and related costs for handling and regeneration make those low-capacity materials unattractive. Thus, selection of a material that has high CO2 uptake is critical in

CO2 removal design and optimization. A common criterion for judging the CO2 uptake

capability of a liquid solvent is its vapor liquid equilibrium (VLE) behavior. VLE defines

the saturation partial vapor pressure of CO2 above a loaded liquid solvent at a certain

temperature. VLE behavior also defines the maximum CO2 loading that can be obtained at a specified temperature and CO2 partial pressure.

Regenerability. A 1300 net MWe power plant can generate more than 7 million tons of CO2 per year [45]. Reuse of high-cost solvent or sorbent is necessary to remove such a large amount of CO2 from flue gas at a reasonable cost. Two factors are important

to regenerability: (1) regeneration temperature and pressure, and (2) desorption enthalpy.

At the regeneration temperature and pressure in a stripper most of the CO2 should be

released from the solvent. From an energy standpoint, close-to-feed-gas temperature and close-to-process pressure are preferred to minimize the energy required for heating.

Knowledge of VLE behavior is necessary to determine the regeneration temperature and

pressure, as it can define the relationship of the vapor pressure of CO2 and CO2 loading

of liquid solvent at the process temperature. The heat capacity of the solvent is another

important factor in determining the energy required to heat the solvent to the targeted

temperature for regeneration. A low heat capacity for the solvent is usually welcome as it

means less energy is needed for heating and cooling. The regeneration energy also

includes energy for disassociation of CO2 from the chemical solvent, which is 17% of

total regeneration energy demand [46]. A study of the heat of CO2 absorption of a solvent

determines the amount of energy associated with the exothermic reaction in absorption

and the endothermic reaction in desorption of CO2.

Mass transfer rate. Rapid mass transfer not only helps reduce the amount of solvent but also allows a shorter scrubber and stripper, which reduces capital costs in a space-constrained plant. Mass transfer in the CO2 capture process can be enhanced by

increasing the contacting area between gas phase and liquid or solid phase. For liquid

14 solvents, this can be acquired by careful design of the packing and liquid distributors.

Solid sorbents often have the advantage in contacting area due to the high surface area of porous materials. The other key parameter in the determination of mass transfer rate is the mass transfer coefficient. As discussed in section 1.1.1.1, some of the promoters, such as PZ, and catalysts, such as CA have been found to enhance the mass transfer of CO2 into solvent phase by facilitating the slow reaction step in the absorption process [31, 32].

Stability. Even though regeneration can extend the use of solvents/sorbents, oxidative degradation can in some cases dramatically decrease operating life of the material and increase the operating cost in CO2 capture. For this reason, many solvents that were once considered promising (for example, monoethanolamine) are being reconsidered and improved.

1.1.2 Mercury

In addition to CO2, mercury emissions from power plants are another great environmental and health threat. Although mercury concentration in atmosphere is extremely low, mercury can enter rivers, lakes and estuaries through rain or snow. Once there, the mercury be transformed to methylmercury and accumulate in fish tissue. When these fish are eaten by human beings, the methylmercury may kill nerve cells, and cause lack of coordination, slurred speech, and even death. Mercury in human body may also damage the kidneys and immunological system, and affect the brain and neurological system. Particularly, newborns are at very high risk of mercury toxicity if their mothers have exposure to mercury.

By far, coal combustion is blamed to be the primary sectorial source of mercury emission. A report issued by United Nations Environment Programme (UNEP) pointed

that fossil fuel combustion for power and heating generated 878 tons of mercury in the

year of 2005, which is about 46% of global anthropogenic mercury emission to the

atmosphere as shown in Figure 1.5 [47]. In the U.S., coal-fired power plants are responsible for 50% of the total mercury emissions as shown in Table 1.3. To reduce the effect of mercury on health and environment, the U.S. government has committed to reduce the mercury emission from its major source – coal-fired power plants. U.S.

Environmental Protection Agency (US EPA) issued the Clean Air Mercury Rule in 2005 to cap mercury emission for the first time in the US. In 2011, US EPA issued more aggressive Mercury and Air Toxics Standards (MATS) that require power plants to eliminate 90% of atmospheric mercury emission in five years [48]. While such standards are estimated to provide $90 billion in health benefits [48], they also stimulate the urgent demand for high–performance, cost-effective mercury control technologies.

Figure 1.5 Portion of global anthropogenic mercury emissions to air in 2005 from different sectors [49] Flue gas from coal combustion typically contains 1 – 20 parts per billion of mercury existing in three states: oxidized form, elemental form, and particulate-

associated form [50]. Particulate-associated mercury can be removed from the gas phase

by the particulate removal device (for example, electrostatic precipitator or fabric filter)

in the treatment process of flue gas. Thus, oxidized mercury and elemental mercury are

more frequently the subject of mercury control studies.

Progress has been made on mercury emission control through several promising

technologies. Currently, activated carbon injection (ACI) is one of the most

commercialized technologies that have been adopted by the power plants. Activated

carbon injected at upstream of a particulate removal device can capture 67% to 92%

percentage of mercury in the flue gas by entrained-flow adsorption [51]. The low cost of

activated carbon and the simplicity in implementation made the technology easily accepted by the industry. But this technology has the limitation of (1) great consumption of activated carbon due to low capacity and adsorbent loss by dust cleaning, and (2) negative effect of trace amount of carbon in fly ash on the reuse of ash in concrete production [52]. Improved ACI technologies (for example, TOXECON™ process [53])

isolate the mercury capture process from the particulate control process so as to minimize

the interference and maximize the capture effectiveness. However, the addition of

another control device imposes extra capital and operating cost to the total cost of mercury capture.

Another large portion of research has been focused on the oxidization of mercury

[54-57]. Because oxidized mercury has high solubility in water and is easily reduced to

elemental mercury, it is widely accepted that oxidized mercury is much easier to remove

from the gas phase. Capturing oxidized mercury in the flue gas desulfurization (FGD)

operation is an attractive technology for existing power plants equipped with FGD. With

a proper selection of oxidant and oxidant injection point, mercury can be nearly 100%

oxidized and removed in wet scrubbing process [58]. But, dissolved oxidized mercury in

the FGD slurry can be reduced re-emitted as elemental mercury [59, 60], and the captured

mercury can be released as secondary pollution to water resource. In addition, only a

small fraction of power plants are equipped with wet scrubbers.

Researchers at the University of Cincinnati have developed a novel

environmentally-friendly adsorbent system by introducing a chelating group (thiol) and a

layer of ionic liquid to the silica substrate [61-64]. Two ionic liquids,

(Methylpolyoxyethylene(15)octadecanammonium chloride (MEC) and 1-butyl-3-methylimidazolium chloride ([bmim]Cl)), were found to be good physical solvents for oxidized and elemental mercury vapor. The dissolved mercury is then immobilized by chelation with the thiol groups. The capacity of such adsorbents is so high that they can be used for extended time, and the spent adsorbent carrying the captured mercury can be landfilled.

Most of the research on this technology was conducted in the laboratories using simulated flue gas. Pilot testing of these novel mercury adsorbents is needed to assess their performance in real-world environments in advance of commercialization.

1.1.3 Other pollutants Sulfur oxide is another pollutant that can cause dramatic damage to the

environment and health. Exposure to high levels of sulfur oxide can cause respiratory

symptoms and decrease in lung function to people with asthma history [65]. Sulfur oxide

is also a major source of fine particulates that have diameter smaller than 2.5 micrometers

(known as PM2.5). The small size of these particles make them easy to be inhaled into the

human body, causing heart or lung disease. Sulfur oxide can also damage the

environment through formation of acid rain, which is harmful to trees, crops, and aquatic

life. Due to their negative effects on health and environment, efforts have been made to

control sulfur oxides emission from coal-fired power plants, which are the major

emission source of acid gases as shown in Table 1.3. Desulfurization methods, including

wet scrubbing and spray dry scrubbing, use the reaction of sulfur oxides and an alkaline

slurry, by which 80 – 90% of SOx can be removed from flue gas.

Table 1.3 Portion of U.S. air pollution that comes from power plants [66] Flue Gas Pollutants Percentage of total national emissions SO2 60% NOx 13% Mercury 50% Arsenic 62% Nickel 28% Chromium 22%

Nitrogen oxides emitted from coal-fired power plant have health and environmental effects similar to those of sulfur oxides due to the similarity in chemical and physical properties. More importantly, nitrogen oxides are considered to be the most important substances reducing ground-level ozone [67], a criteria pollutants and a major

component of smog. High level of smog may cause respiratory problems and reduce

visibility. It has been reported that about 20% of the man-made nitrogen oxides emission

in the US is from power plants [68]. The benchmark technology, selective catalytic

reduction (SCR) using a reductant such as anhydrous ammonia, aqueous ammonia, or

urea [69], is the most effective approach on NOx control in coal-fired power plants. NOx

is converted to N2 and H2O with the help of a catalyst at elevated temperature. The application of SCR in coal combustion power plants is reported to reduce 80 - 90% of

NOx in the exhaust gas. Further removal can be attained using improved technologies

[70].

As discussed previously, particulate matter can be a product of the reaction

between sulfur oxides and other components, or other organic and inorganic particulates that are small enough to cause health and environmental concern. Particulate matter can be controlled using either a fabric filter (FF) bag house, which uses a fine mesh filter to stop the particulates, or an electrostatic precipitator (ESP), in which particulates are trapped by electrostatic force. Activated carbon as mentioned in section 1.1.2 is also captured with fly ash in the particulate control devices.

In addition to SOx, NOx, O3, and PM, there are other two criteria pollutants – lead

and CO – in coal-fired power plant emissions. However, as their emissions from coal-

fired power plants are much less than their major sources [71], control of these two

pollutants has received less attention than control of the other pollutants.

1.1.4 Process Integration Currently, high cost is still a major obstacle to the implementation of flue gas

treatment process for power plants. For example, the cost to capture CO2 in flue gas from

a coal-fired power plant with the current technologies is estimated to be $42 per metric ton of CO2 which will increase the electricity price by 30 – 40% [72]. The cost of mercury

removal with ACI technology is estimated to range from $33,000 to $131,000 per pound of

Hg for bituminous coal-fired power plants and $18,000 to $55,000 per pound of Hg for subbituminous coal-fired power plants, which corresponds to the incremental increase in cost of electricity between 0.37 mills/kWh to 5.72 mills/kWh [73].

Several approaches to reduce the cost of emission control, including development

of low-cost materials, optimization of process design, and integration of multiple

treatment processes into a single unit operation, have been proposed and developed.

Process integration is of great interest because of the tremendous potential reduction in

both capital and operating costs. In addition, integrated processes are favored for

retrofitting existing power plants that have limited floor plans.

Sulfur oxides and nitrogen oxides have similar chemical and physical properties.

Success has been achieved in combining the capture of these two components in a single

process by using catalytic sorbents [74-76] and wet scrubbing [77]. By providing energetic free electrons to the flue gas, SO2 and NOx can be dissociated into radicals and

converted into solids that can be removed along with particulates through the

conventional approaches [78]. Since greenhouse gases have drawn great attention in the

environmental protection, further effort has been made to integrate CO2 into the

combined capture processes mentioned above [79, 80]. Current mercury removal technologies also provide great opportunities for process integration. Particulate control

devices are combined with active carbon injection as mentioned above, SCR is used for

mercury oxidation [81, 82], and wet scrubber is integrated with oxidized mercury

removal.

1.2 Key thermodynamic and kinetic properties in pollutant gas removal

from flue gas

Thermodynamic and kinetic properties of a solvent or sorbent system in pollutant

removal from flue gas are valuable and convenient criteria in candidate screening and in

21 process design and optimization. Thus, the study of thermodynamic and kinetic properties is an important activity in pollutant control.

1.2.1 Vapor liquid equilibrium When a liquid solvent is involved in the removal of a pollutant gas from gas, vapor liquid equilibrium is important as it describes the maximum solubility of pollutant gas in the liquid solvent at the process temperature and pressure. Such properties can also be used in process design for the determination of solvent/solution flow rate, scrubber/stripper length, and absorption/desorption temperature and pressure.

In the case of gas-liquid absorption, phase equilibrium describes the distribution of each component in the vapor phase and the liquid phase. Three criteria should be reached at equilibrium between liquid and vapor [83]:

• The temperature of the two phases is the same at equilibrium.

• The partial pressure of every component in the two phases is the same at

equilibrium.

• The chemical potential of every component in the two phases is the same

at equilibrium.

Because of the relationship between chemical potential and fugacity as expressed in Eq. (1.1) and Eq. (1.2), the third criterion can be converted to the equation of fugacity, which can be conveniently written as a function of measurable properties. The equation is so important that establishes a bridge between the theory and practice, which can be used for mathematical modeling of experimental data.

µii= G (1.1)

dGii= RTdln f (1.2)

Most of the high performance solvents currently used for pollutant gas removal

are based on chemisorption, which has the advantages of fast and reversible/irreversible

chemical reactions. Due to the chemical reactions, chemical equilibrium has to be added

into the VLE thermodynamic framework, which complicates theoretical study. For

example, in the case of CO2 absorption by using aqueous monoethanolamine, there are

five reactions that can occur in the liquid phase, and there can be more reactions when

other chemicals are added to the solvent.

1.2.2 Energy demand for regeneration For most of the gas removal process, the sorption step is exothermic and the

desorption step is endothermic, which leads to heat generation and demand respectively.

Unfortunately, such energy costs are the dominant factors in CO2 capture by absorption and adsorption process. Heat of absorption or adsorption can provide useful and accurate information on the exact amount of energy that the sorption process requires. Therefore, the determination of absorption enthalpy is one of the required activities in pollutant control study [84-87].

1.2.3 Heat capacity Flue gas pollutants are usually desorbed from the solvent or sorbent by

temperature swing, which takes the advantage of lower solubility at higher temperature.

The energy used to heat and cool the solvent/sorbent material to the target

desorption/sorption temperature is a large contribution to the total capture cost. This

energy is determined by the heat capacity of the material. Therefore, finding a low heat

capacity solvent/sorbent system is a priority in material screening. For example, many

studies have investigated the use of liquid solvents for CO2 capture [49, 88-98]. On the

other hand, it has been reported that solid sorbent has advantages over aqueous MEA in

terms of energy consumption when the CO2 loading is above 1.5 mol CO2/kg of sorbent

as shown in Figure 1.6 [99, 100].

Figure 1.6 Heat of regeneration versus CO2 delta loading for various capture reactor designs [100]

1.2.4 Mass transfer and dispersion in fixed-bed adsorption Fixed-bed adsorption is a common technique in pollution control as it offers the

advantage of simplicity and ease of operation [101]. Ideally, pollutant gas in contact with

a solid sorbent can be adsorbed in the fixed-bed until the sorbent bed is saturated. In

practice, internal mass transfer resistance and axial dispersion result in broad

concentration profiles along the length of the bed. The segment of the bed that corresponds to a broad concentration front is defined as the mass transfer zone (MTZ) as shown in Figure 1.7 [102]. The sorbent along the length of MTZ is not practically useful as adsorbate is not sufficiently captured.. Hence, the study of mass transfer and axial dispersion in fixed-bed adsorption is critical to process design and optimization.

Saturated zone

Mass transfer zone

Fresh sorbent

Figure 1.7 Schematic of fixed-bed breakthrough curve

Mass transfer in the a gas-porous particle adsorption process includes four steps

[102]: (1) external (interphase) mass transfer by convection; (2) internal (intraphase) mass transfer by pore diffusion; (3) surface diffusion; and (4) adsorption of solute onto the porous surface. Modern high performance adsorbents are usually chemically-treated on the surface for high capacity. In such case, the fourth step has been proven to be the slowest and controlling step due to the low diffusivity in liquid [103]. Thus, the relationship between surface functionalization and mass transfer becomes an interesting topic in the development of new adsorbent systems.

Axial dispersion in a fixed-bed is caused by two mechanisms: (1) mechanical dispersion due to the convective mixing in the bed, and (2) diffusive dispersion due to the

25 molecular diffusion with the fluid phase [104]. The first mechanism is often dominant in practice. The effect of axial dispersion is more obvious for a bed with a high aspect ratio

(the ratio of diameter to length) and low velocity, which is preferred in the design of fixed beds due to the low pressure drop. Therefore, attention must be paid to the effects of axial dispersion in fixed-bed studies.

1.3 Objectives The overall objective of this research is to study the key thermodynamic and kinetic properties of carbon dioxide and mercury removal from flue gas using bench- scale and pilot-scale experimental testing and mathematical modeling. The specific objectives of this work are to:

1. Establish a thermodynamic framework within which key thermodynamic properties (vapor liquid equilibrium (VLE), heat of absorption, and heat capacity) can be investigated for CO2 absorption;

2. Measure the VLE, heat of absorption, and heat capacity for CO2 removal by aqueous amine system and ionic liquid systems;

3. Correlate the experimental data using the thermodynamic framework to obtain best-fit model parameters, and to validate the experimental result and mathematical modeling by comparing the predicted results with independent literature data;

4. Establish a model within which the key kinetic properties including mass transfer rate, axial dispersion, and sorbent capacity can be studied for fixed-bed CO2 adsorption;

5. Assess the CO2 capture performance of ionic liquid coated solid sorbents in fixed- bed operation;

6. Correlate the adsorption experimental data in the fixed-bed model to obtain the

26 best-fit kinetic parameters;

7. Study the mercury capture performance of ionic liquid coated solid sorbents in pilot scale testing;

8. Evaluate the feasibility of simultaneous capture of CO2 and mercury from flue gas with ionic liquid coated solid sorbents.

Chapter 2 - Materials and Methods

2.1 Materials and Preparation

2.1.1 Aqueous CO2 solvents

Two benchmark CO2 solvents were used in this work: aqueous monoetholamine

(MEA) and aqueous piperazine (PZ). Both MEA (≥98%) and PZ (99%) were obtained

from Sigma-Aldrich, Inc (Milwaukee, WI). Aqueous solvent with desired amine

concentration was prepared by mixing DI water and amine in a sealed beaker at room

temperature with stirring for 15 min.

2.1.2 Amino acid (AA)-based room temperature ionic liquid (RTIL)-coated silica gel L-methionine (98%) were purchased from Fisher Scientific, Inc (Pittsburg, PA).

Taurine (99%) was purchased from Alfa Aesar Co (Ward Hill, MA).

Tetrabutylphosphonium hydroxide solution (40 wt% in H2O) and silica gel substrates

(Davisil Grade 646) were purchased from Sigma-Aldrich, Inc (Milwaukee, WI). The

textural properties of the silica gel substrates determined in previous investigations [61]

are summarized in Table 2.1.

Table 2.1. Textural characteristics of silica substrate particles Silica Particle Size Pore Size BET Surface Pore Volume Substrate (µm) (Å) Area (m2/g) (cm3/g) Grade # 646 250-500 163 311 1.18 62 75-250 163 283 1.18

Pure amino acid-based RTILs were prepared by reacting equal numbers of moles of amino acid and tetrabutylphosphonium hydroxide (in 40 wt% aqueous solution) under

stiring for three hours at room temperature. In this work, 1.9 g of methionine or 1.6 g of

taurine was reacted with 9 g of tetrabutylphosphonium hydroxide solution to synthesize

approximately 5 g of AA-based RTIL. The solvent (water) was evaporated in a rotary

vacuum evaporator (Büchi Rotavapor R-205, Brinkmann Instruments, Inc, Westbury,

NY) under vacuum at 60oC and 80 rpm for half hour, and dried in a vacuum oven at 60oC

for three days.

Supported AA-RTIL silica gel was prepared with a one-step method which

combines ionic liquid preparation and substrate coating in a single step. Such low-cost preparation is expected to be favorable in large-scale sorbent production. The detailed preparation steps are discussed as followed: equal molar of amino acid and tetrabutylphosphonium hydroxide solution (1.9 g of methionine or 1.6 g of taurine with

9.0 g of tetrabutylphosphonium hydroxide solution in this work) were mixed in 20 g of

DI water under stirring at room temperature until amino acid is fully dissolved. The solution is further mixed with 15 g silica gel particles to achieve a final 25 wt% RTIL loading level. The amount of silica gel can be adjusted according to the desired RTIL loading level. To achieve a uniform ionic liquid and substrate distribution, the mixture was mixed at room temperature in a rotary vacuum evaporator at 80 rpm for one-half hour before the water was removed under vacuum at 60°C and 80 rpm. The product was

further dried at 60°Cin a vacuum oven for three days before any test or characterization.

2.1.3 RTIL-coated 3-mercaptopropyltrimethoxysilane (MPTS) - silica gel Two RTILs were used for mercury capture in this work:

methylpolyoxyethylene(15)octadecanammonium chloride (MEC) and 1-butyl-3-methyl-

imidazolium chloride ([bmim]Cl). MEC was a gift from Akzo Nobel Chemicals

(McCook, IL). [bmim]Cl and 3-mercaptopropyltrimethoxysilane (MPTS) (95%) were

purchased from Sigma-Aldrich, Inc (Milwaukee, WI). The detailed preparation procedure

for RTIL coated MPTS - silica gel was introduced by the previous investigators [105].

Briefly, 50 ml MPTS was grafted on 25 g acid-washed silica gel surface in 500 ml of dry

toluene under nitrogen protection at 100°C for 20 hours. The product was washed with

500 ml of toluene to remove unreacted MPTS and then filtered to remove toluene

solvent. Residual toluene was removed by placing the product under vacuum at 100oC for

overnight. To achieve 25 wt% RTIL coating, 15 g of MPTS-grafted silica gel was then mixed with 5 g of RTIL and 50 ml of dichloromethane in a rotary vacuum evaporator at

80 rpm for one-half hour before the dichloromethane was removed under vacuum at 60°C

and 80 rpm. The product was placed at room temperature in ambient air overnight.

2.2 Characterization Techniques

2.2.1 Fourier Transform Infra-Red (FTIR) The chemistry of reacted and unreacted RTILs was characterized by attenuated

total reflectance FTIR (ATR-FTIR) (Agilent Technologies Inc., Santa Clara, CA)

analysis for spectrum range of 600 – 3600 cm-1. RTIL samples were placed at the FTIR

for analysis without pre-treatment.

2.2.2 BET Analysis The textural characteristics of particles, including surface area, pore volume, and

pore size distribution, were determined by a volumetric adsorption analyzer (TriStar

3000, Micromeritics Instrument Co., Norcross, GA). Prior to BET analysis, samples were

degassed at 100oC for 12 hours to remove unwanted gas and vapor absorbed on particle

surface. The N2 absorption and desorption isotherm was fit with the BET model to

calculate the BET surface area. The BJH model was used to calculate pore size, volume

and distribution.

2.2.3 Thermo-Gravimetric Analysis (TGA) Thermo-gravimetric analysis was used to assess the thermal stability of studied

materials using a simultaneous DSC-TGA (SDT-Q600, TA Instruments, New Castle,

DE). Approximate 23 mg of sample was heated up to 700oC at 10oC/min under 100 ml/min nitrogen protection.

2.2.4 Scanning Electron Microscopy (SEM) The coating uniformity and surface characteristics of the coated particles were

examined by a scanning electron microscope (S-4300, Hitachi High Technologies

America Inc., Lexington, KY).

2.2.5 Elemental Analysis Elemental analysis was used to determine the concentration of active site in

functionalized particles. The weight percent of C, N, O, and S was measured by an

external laboratory (Robertson Microlit Laboratories Inc., Ledgewood, NJ).

2.3 Apparatus and Procedure

2.3.1 VLE measurement for aqueous amine systems A modified batch calorimeter (C80D, Setaram Inc., Hillsborough, NJ) was used for vapor-liquid equilibrium measurements as shown in Figure 2.1. The aqueous amine is

placed in the equilibrium cell, and allowed to equilibrate with the vapor in the cell. The

outlet of the equilibrium cell is connected to a pressure transducer (0 to 30 psia, Model

PX409-030AV-XL, OMEGA Engineering, Inc., Stamford, CT) with 0.03% linearity to

31 monitor the total pressure inside the cell. The other outlet of the cell is connected through a solenoid valve (Cv = 0.10, Model SV3301, OMEGA Engineering, Inc., Stamford, CT) to a vacuum pump (Maxima C Plus M4C, Thermo Fisher Scientific Inc., Pittsburgh, PA).

Figure 2.1 Schematic of equilibrium cell for VLE measurement (top: aqueous

amines systems; bottom: CO2 – aqueous amine systems)

In a typical measurement, approximately 7 g of pre-prepared solvent in (section

2.1.1) is weighed in the equilibrium cell of the calorimeter and frozen to minimize solvent evaporation during cell installation. After the equilibrium cell is installed and connected in the calorimeter, the equilibrium cell is evacuated using a vacuum pump. The

temperature in the calorimeter is then raised to the desired value and held for the entire

experiment. The system is allowed to equilibrate until both pressure and heat flow vary

less than 0.5% within 15 min. Vapor pressures and temperature are continuously monitored and logged using a data acquisition device (USB-TEMP-AI, Measurement

Computing Co., Norton, MA) and an in-house data acquisition program during a scan. A

complete scan consists of measurements made at several temperatures that cover the

whole targeted temperature range.

The uncertainty of the VLE measurement is estimated from the accuracy of the

pressure transducers (0.06%) and the temperature (0.1%) to be less than 0.2%.

2.3.2 Heat capacity measurement Heat capacities of studied aqueous amines were measured using the batch

calorimeter (Setaram C80D) described in section 2.3.1. Vendor-supplied batch cells were

used for heat capacity measurements. These batch cells are sealed stainless steel

containers with no outlet. In a typical measurement, one of the batch cells is charged with

about 7 g aqueous amine, which occupies about 95% of the cell volume. The 5% free

space allows for volumetric expansion of the liquid during the measurement. As the

thermal expansion coefficient for a liquid is extremely low (for example 69×10-6 °C-1 for

water at 20°C), it is reasonable to assume the work can be ignored (W=0). Therefore, the

measured heat flow is the change of internal energy (Q = ∆U). Since the molar volume of

liquid solution is very small (for example 18×10-6 m3/mol for water at 20°C), it is also reasonable to assume ∆PV = 0 and ∆U = ∆H for the studied systems which have a small to moderate pressure change. In addition, minimized vapor volume allows the assumption that the enthalpy of vaporization is negligible. Thus, based on the discussion above, the

measured heat capacity of the liquid can be considered as the heat capacity at constant

pressure (Cp=(∂H/∂T)P).

2.3.3 VLE and heat of absorption measurement for CO2 – aqueous amine systems

When a non-condensable component (for example, CO2) is involved in the system, the VLE measurement apparatus used in section 2.3.1 must be further modified as shown

in Figure 2.1. The apparatus consists of an equilibrium cell in the calorimeter system and

a CO2 injection system. Aqueous CO2 solvent prepared in section 2.1.1 is placed in the

equilibrium cell, and allowed to equilibrate with vapor phase in the cell. One outlet of the

equilibrium cell is connected to a pressure transducer (0 to 30 psia, Model PX409-

030AV-XL, OMEGA Engineering, Inc., Stamford, CT) with 0.03% linearity to monitor

the total pressure inside the cell. The other outlet of the cell is connected through a

solenoid valve (Cv = 0.10, Model SV3301, OMEGA Engineering, Inc., Stamford, CT) to a CO2 reservoir (Teflon, Zeus Industrial Products, Orangeburg, SC) that is maintained at

room temperature. The pressure of the CO2 reservoir is monitored by another pressure transducer (0 to 30 psia, Model PX409-030AV-XL, OMEGA Engineering, Inc.,

Stamford, CT) with 0.03% linearity and controlled by another solenoid valve (Cv = 0.10,

Model SV3301, OMEGA Engineering, Inc., Stamford, CT) that is connected to a 3-way

valve (Swagelok, Cincinnati, OH). Either CO2 gas (Tech. grade, Wright Brothers Co.,

Cincinnati, OH) or vacuum by a vacuum pump (Maxima C Plus M4C, Thermo Fisher

Scientific Inc., Pittsburgh, PA) can be applied to the system through the 3-way valve. The

volumes of the CO2 reservoir and the equilibrium cell are precisely measured to ensure an accurate data reduction. In the VLE measurement, the equilibrium cell is securely placed

in the batch calorimeter (Setaram C80D) which provides precise temperature control for the cell. Using the batch calorimeter in the thermodynamic study of CO2 absorption also

allows measurement of both pressure and heat flow in a single operation and so allows

simultaneous measurement of VLE and heat of absorption.

In a typical measurement, approximately 0.4 g of pre-prepared solvent is weighed

in the equilibrium cell and frozen to minimize solvent evaporation during cell

installation. The equilibrium cell and the CO2 reservoir are then installed and connected in the calorimeter, and the whole system is evacuated using a vacuum pump, The CO2

reservoir is then charged with pure CO2 to about 5 psig and the equilibrium cell remains

at vacuum. The temperature in the calorimeter is then raised to the desired value and held

for the entire experiment. A small amount of CO2 gas is then injected into the system

from the CO2 reservoir by switching the solenoid valve on for about 0.1 second. The

pressure drop in the CO2 reservoir is then used to calculate the number of moles of

injected CO2 (ninj) through the equation of state. After the injection, the system is allowed

to equilibrate until both the pressure and heat flow vary by less than 0.5% within 15 min.

The total pressure, temperature, and heat flow are continuously monitored and logged by

a data acquisition device (USB-TEMP-AI, Measurement Computing Co., Norton, MA)

and an in-house data acquisition software during the scan. A complete scan consists of

several CO2 injections that cover the whole targeted CO2 loading range. The integration of ninj from each injection represents the total number of moles of CO2 in the system.

The uncertainty of the VLE measurement is estimated from the accuracy of the

pressure transducers (0.06%), the volume of the cells (3%), and the temperature (0.1%) to

be less than 5%.

2.3.4 Fixed-bed CO2 adsorption measurement

A fixed-bed adsorption system was set up for the CO2 capture tests as shown in

Figure 2.2. A heat-traced 25 mm ID borosilicate glass column (Diba Industries, Danbury,

CT) was used as the adsorber. Uniform heating was achieved using a wire mesh layer

between the adsorber and heat tracing. Temperature was monitored and controlled using

a J-type thermocouple (KMTSS-125G-6, OMEGA Engineering, Inc., Stamford, CT) and

a temperature controller (CSC32J, OMEGA Engineering, Inc., Stamford, CT). The effluent CO2 concentration was measured using a CO2 Analyzer (WMA-4, PP-System,

Amesbury, MA). In each experiment, a sorbent sample of approximate 4 g was packed

into the column. The feed to the adsorber was a 1 L/min gas stream containing 3% of

CO2 in air. The feed initially bypassed the adsorber for inlet CO2 concentration

determination. Afterwards, the gas flow was switched to the adsorber by adjusting a 3- way valve. The CO2 effluent concentration was continuously logged to a computer via

RS232 protocol.

Figure 2.2. Schematic of fixed bed apparatus for CO2 adsorption measurements

2.3.5 Fixed-bed mercury adsorption measurement for slipstream testing A fixed-bed mercury adsorption testing unit was designed and installed as shown in Figure 2.3 at one of the induced draft fans at Zimmer Station (Moscow, OH), operated by Duke Energy Co. The apparatus, shown schematically in Figure 2.4, has a 1-inch ID borosilicate glass column (Ace Glass Inc., Vineland, NJ) as an adsorber that holds 3 to 6 grams of sorbents and operates at 0.3 to 0.5 cfm flue gas. The flow rate of flue gas in the system is monitored by measuring the pressure drop of a manifold at downstream of the adsorber. The flow rate - pressure drop relation of the manifold was calibrated in the lab.

Sample gases are drawn from the inlet and the outlet of the adsorber for mercury analysis, which is discussed in section 2.3.6. A round bottom flask was installed upstream of the apparatus to function as a cyclone separator for fly ash removal. Fine ashes not removed by the separator were stopped by glass wool immediately upstream of the sorbent. All the parts that have flue gas flow are maintained at 300F by heat tracing and insulation. To insure that there is enough mercury in the flue gas for the test, a mercury(II) chloride permeation tube (Valco Instruments Co., Poulsbo, WA) with a generation rate of ~3

µg/min is added upstream of the apparatus, making the mercury concentration at the inlet

150 to 260 µg/m3. The high mercury concentration in this test was used to expedite saturation of the sorbent.

Figure 2.3 Location of slipstream testing unit in power plant

Figure 2.4 Schematic of fixed-bed adsorption apparatus for slipstream mercury capture testing

2.3.6 Mercury Sampling using modified Ontario Hydro method Mercury rates were determined using a real-time mercury speciation analysis method based on the standard Ontario Hydro Method. The sampling system setup is schematically shown in Figure 2.5. The sampling system has two channels for the measurement of elemental mercury and total mercury respectively. The elemental mercury measurement channel uses a KCl midget impinge (Chemglass, Vineland, NJ) that captures all the oxidized mercury followed by a KOH impinger that removes acidic gases. The total mercury measurement channel has a SnCl2 impinger that reduces oxidized mercury to elemental state and a KOH impinger that removes acid gas. The effluent gas from the impinger train goes to a cold vapor atomic absorption analyzer (VM

3000 Mercury Vapor Analyzer, Mercury Instruments USA, Littleton, CO) for concentration determination. The elemental mercury concentration can be read directly from the elemental mercury measurement channel, and the oxidized mercury

concentration can be calculated by subtracting the elemental mercury reading from the

total mercury reading.

The modified Ontario Hydro method was validated by comparing measurement results with EPA Method 30B which uses commercial sorbent traps for mercury determination. Mercury in the inlet flue gas was collected at a speciation sorbent trap

(Ohio Lumex Co., Twinsburg, OH) at a flow rate of 1 L/min for 15 minutes. Afterwards, the mercury concentration at the same point was measured by the modified Ontario

Hydro method described above. The total amount of oxidized and elemental mercury on the sorbent trap was later analyzed by the sorbent trap manufacturer. The results from the two methods are compared in Table 2.2. The proximity of mercury concentrations by the two methods validates the accuracy of the modified Ontario Hydro method.

Figure 2.5. Schematic of modified Ontario Hydro Method for mercury measurement

Table 2.2. Comparison of measured mercury concentration by sorbent trap method and modified Ontario Hydro method

Modified Ontario Sorbent Trap Difference Hydro

Oxidized Mercury Conc. (µg/m3) 226 201 11% Elemental Mercury Conc. (µg/m3) 61 70 15% Total Mercury Conc. (µg/m3) 287 271 5%

2.3.7 Bench-scale fixed-bed mercury adsorption measurement A fixed-bed adsorber, schematically shown in Figure 2.6, was used to evaluate Hg

adsorbent performance in simulated flue gas. The adsorber and determination method

was described in details in the previous study [61]. Briefly, Hg vapor was generated from

a Hg permeation tube (Dynacal® tube, Valco Instruments Co., Poulsbo, WA) in a Hg

evaporator oven (Dynacalibrators® Model 150, Valco Instruments Co., Poulsbo, WA)

through which N2 carrier gas (pp Grade, Wright Brothers Inc., Cincinnati, OH) passed at

a total flow rate of 15 ml/min. The Hg concentration at upstream of the adsorber was

about 18 ppbm, which is much higher than the typical Hg concentration in coal

combustion flue gas. The high Hg concentration helps to reduce the time to reach

breakthrough and expedite the experiments. The mercury-laden gas was then introduced into the fixed-bed adsorber which is maintained at 60 to 80oC. The Hg concentration at

inlet and outlet of the adsorber was analyzed every several hours using the modified

Ontario Hydro Method until sorbents were saturated with Hg. Hg capacity can be

calculated by integrating the breakthrough curve.

Figure 2.6 Fixed-bed apparatus for determination of Hg capture characteristics [103]

2.3.8 Entrained-flow mercury capture testing The entrained-flow mercury capture test was conducted using an Entrained Flow

Reactor located in the US EPA facility at Research Triangle Park, NC. A detailed

description of the reactor setup can be found in the literature [106]; a schematic of the reactor setup is shown in Figure 2.7. Briefly, a methane-air mixture is combusted in an electric furnace to generate the major flue gas components, including CO2, O2, CO, and

H2O vapor. The other flue gas components, including HCl, NO, and SO2 are supplied

from gas cylinders and mixed with the methane combustion flue gas at upstream of the

reactor. Elemental mercury generated from a permeation system (Dynacalibrator® Model

190, Valco Instruments Co., Poulsbo, WA) is purged into the flue gas with N2 carrier gas.

The flow rate of each component is controlled by a mass flow controller. Sorbents are

injected into the flue gas upstream of the reactor using a nitrogen carrier stream. The

reactor is made from a 4 m long by 4 cm ID Pyrex column, which ensures uniform

mixing of flow and sorbent in the reactor. The temperature at the reactor was maintained

at 140oC using heat tracing to simulate the temperature in real flue gas. The spent sorbent

is removed by a filter at downstream of the reactor; the gas flow is analyzed by a mercury

Continuous Emission Monitor (CEM) (DM-6B, Nippon Instruments Co., Japan) for

elemental mercury determination.

Figure 2.7 Schematic of entrained-flow reactor system [106]

Chapter 3 - Thermodynamics of Amine-H2O Systems

3.1 Introduction

Aqueous amine solvent systems are commonly used for CO2 capture. These

systems have the advantages of fast reaction, high CO2 capacity, and low enthalpy of absorption, and are easy to handle. The thermodynamic properties of aqueous amines are critical to the design of CO2 removal systems. In addition, these thermodynamic properties determine the energy required for solvent heating/cooling, solvent loss during the scrubbing and stripping processes and other process parameters. In this chapter, key thermodynamic properties, including vapor liquid equilibrium (VLE) and heat capacity, of two benchmark solvents (monoethanolamine (MEA) and piperazine (PZ)) are investigated. Experimental data was collected using a modified calorimeter, and the data were fit with a mathematical model which includes the electrolyte Non-Random Two-

Liquid (eNRTL) activity coefficient model and Soave-Redlich-Kwong (SRK) fugacity coefficient model to obtain a set of best-fit interaction parameters. The optimized model was further used to predict vapor pressure and heat capacity, and the predictions were compared to independently-measured literature data. Model predictions agree well with literature data, validating both the experimental approach and the mathematical model.

The thermodynamic model and the best-fit interaction parameters established in this chapter provide fundamental knowledge that will be applied to the study in Chapter 4, in which ternary systems of CO2-aqueous amine are investigated.

3.2 Theory

3.2.1 Chemical Equilibrium

Aqueous amine solvents for CO2 capture usually are single or mixed alkanolamines in water. Alkanolamines, which are bases, exist in a protonated form in an aqueous environment. The chemical equilibria involved in the dissolution of MEA in water include

K3.1 +− 2H23 O←  → H O + OH R (3.1)

++K3.2 H23 O+ MEAH ←  → H O + MEA R (3.2)

Dissolution of the diamine PZ in water includes the following reactions in addition to R (3.1).

++K3.3 H23 O+ MEAH ←  → H O + MEA R (3.3)

++K3.4 H23 O+ PZH ←  → H O + PZ R (3.4)

2+K3.5 ++ H22 O+ PZH ←  → H 3 O + PZH R (3.5)

The equilibrium constants Kr that describes the balance of reactants and products for the reactions above can be expressed as

νν =αγri,, = ri Kxr∏∏ i ()ii (3.1) ii where the subscript r denotes the reaction and the subscript i denotes the species; αi, γi, and νi are activity and activity coefficient, and stoichiometric number of species i, respectively. Note that the equilibrium constants in this work are based on mole fractions.

The equilibrium constants are expressed as functions of temperature as described by Eq. (3.2). The parameters in Eq. (3.2) for each reaction were obtained from the literature and listed in Table 3.1.

Br Kr = exp A r ++ C rr ln( T) + D T (3.2) T

Table 3.1 Parameters for calculating reaction equilibrium constants for amine dissociation on the mole fraction scale A B C D Source K3.1 132.899 -13445.9 -22.4773 0 [107] K3.2 -22.82 -6997 3.26 0 [14] K3.3 -64.4 -4899 8.90 0 [14] K3.4 -67.8 -3091 10.2 0 [14] *A, B, C, and D are parameters in Eq. (3.2) Since the amine concentration used in this work span a wide range, both water and unreacted amine are treated as solvent species in this chapter. Based on this choice, a symmetric reference state is used for water and amine as described by Eq. (3.3), while an asymmetric reference state is used for the other species (ions) as shown in Eq. (3.4). The parameter values in Table 3.1 are consistent with these choices for reference state [14].

γ ss→→1 as x 1 (3.3)

γ ii→→1 as x 0 (3.4)

3.2.2 Activity coefficient model The activity coefficient of a species, which is a function of temperature, pressure, and composition, quantitatively describes the non-ideality of that species in the system.

As a low to moderate pressure range is used in this work (6kPa – 200kPa), activity coefficients are assumed to be independent of pressure as suggested in the literature

[108].

There are a number of models that describes the dependence of activity

coefficient on temperature and composition for non-electrolyte liquid mixtures (for

example, the Wilson Model [109], the Non-Random Two-Liquid (NRTL) Model [110], and the UNIQUAC Model [111]). When electrolytes are involved, interactions among cations, anions, and molecules increase system non-ideality; the traditional activity coefficient models which were built for non-electrolyte systems are not applicable. Thus, several models have been developed for electrolyte systems, including the Debye-Hückel model, the Pitzer model, the Deshmukh-Mather model, and the Electrolyte Non-Random

Two-Liquid (eNRTL) model [112-114].

A major challenge of modeling an electrolyte solution is how to address the electrostatic forces from molecule-ion and ion-ion interactions, which are greater than the

van der Waals forces in non-electrolyte solutions. Debye and Hückel proposed a model to describe the non-ideality of an infinitely dilute solution by considering the ∆G to charge a spherical and neutral atom to an ion in pure solvent and the additional ∆G to charge the neutral atom in the presence of all other ions [115]. The Debye–Hückel model has the form of

2 0.5 lnγ ii= −Az I (3.5)

in which zi is the charge of species i, I is the solution ionic strength (mol/kg) defined by

1 all ionis = 2 6 T 1.5 -0.5 0.5 I∑ mzii , A = 1.8244×10 /(Ds ) (mol kg ), and Ds is the dielectric constant of 2 i

solvent.

The Debye–Hückel model is valid up to an ionic strength of 0.005 mol/kg [116],

which is too low to make the model to be used for many electrolyte solutions. Therefore,

an extension of Debye–Hückel model was proposed by Davies [117] as shown in (3.6).

−Az z I0.5 γ = +− ln 0.5 (3.6) 1+ Br0 I

11 T 0.5 -0.5 0.5 in which B = 5.0292×10 /(Ds ) (mol kg ), and r0 is the ion radius.

Even though the Debye–Hückel model and extended Debye-Hückel model

successfully accounts for long-range electrostatic forces in dilute electrolyte solutions,

performance at high ion strength is not as good as at infinitely dilute. Several

improvements have been made to make the model applicable over a wider range of ion

strength. A common feature of these improved models is separation the non-ideality into

different contributions, usually including a long-range term for the electrostatic forces

and a short-range term for the interactions among ions and molecule.

One of the successful examples is the Pitzer model [118]. It improved the Debye–

Hückel model and used it as the long-range interaction term and included an extension of

Guggenheim’s model [119] to count for short-range interactions. The model can be expressed in terms of Gibbs free energy by Eq. (3.7).

gex all species all species all species all species all species =f() I ++∑∑mmi jλµ ij () i ∑∑∑mmi j m k ijk (3.7) ww RT ij ijk

in which f(I) is the Debye-Hückel term for long range interaction, ww is the mass of water

(kg), mi is the molality of speicies i (mol/kg), and λ and μ are viral coefficients.

The activity coefficient of species i can be obtained by differentiating gex as

expressed by (3.8).

ex 1 ∂ (ngt ) lnγ i =  (3.8) RT∂ ni T,, Pnji≠

Pitzer extended the Debye-Hückel term for long-range interaction and recommended a formulation based on mole-fraction-based ionic strength Ix. It has a

excess Gibbs free energy form as shown by (3.9).

1 ex,PDH all non-inert species 2 1 g 1000 4AIΦ X 2 =−+∑ xkXln1 ρ I (3.9) RT k M S ρ 

in which subscript k denotes any non-inert species, Ms is molecular weight of solvent, Ix

1 all ionis = 2 is ionic strength based on mole fraction defined by Ix ∑ xzii , ρ is a “closest 2 i approach” parameter. Aϕ is the Debye-Hückel parameter, which can be expressed as

1 3 2 2 2 12π Ndo  e Aφ =  (3.10) 3 1000 Dw kT

-1 3 where No is Avogadro’s number (mol ), d is the solvent density (mol/m ), e is the charge

of an electron (esu), Dw is the dielectric constant for water, and k is the Boltzmann

constant (erg/K).

The other representing model is the Deshmukh-Mather model [120] which also

uses Debye–Hückel theory for long-range interaction term. The short range term is

simplified by taking the mass-average of the binary interaction parameters. The

mathematical expression of Deshmukh-Mather model for activity coefficient of species k

is shown by Eq. (3.11).

−Az z I0.5 all species γβ= +− + ln k 0.5 2 ∑ kim i (3.11) 1+ Br0 I i

in which the subscript i denotes any species, mi is the molality of species i (mol/kg), and

βkj is the binary interaction parameter for species k and j.

One of the advantages of Deshmukh-Mather model over other similar models is

the computational simplicity which is important in fast screening studies.

The eNRTL model proposed by Chen and Evans is another activity coefficient

model for electrolyte systems [121]. The model is based on Pitzer’s model, which accounts for long range ionic interaction. A Born correction is included for mixed solvent systems to convert the reference state from infinite dilution in solvent to infinite dilution in water. Local ionic interactions are calculated by a term based on the Non-Random

Two-Liquid (NRTL) theory which accounts the non-ideality from the contributions of binary interactions. . When all of the terms above are considered, the excess Gibbs free energy in the eNRTL model can be expressed as

gex =g ex,PDH +g ex,Born+ g ex,NRTL (3.12)

The first term, which comes from the Pitzer-Debye-Hückel (PDH) model, has the expression of Eq. (3.9).

The second term in Eq. (3.12) is a Born correction, expressed as

1 ex,Born 2 2 all species 2 ge  11 Xz  −2 = − ∑ ii 10 (3.13) RT2 kT Dsw D i ri 

in which subscript i denotes any species, Xi = Cxi (C = zi for ions or C = 1 for molecules),

ri is the Born radius (m) and Ds is the dielectric constant of mixed solvent.

The last term accounts for local ion interaction using the NRTL approach has the

form

ττ ex, NRTL ∑∑XGj jm jm XGj jc,, a'' c jc a c g jjX a' = ∑XXmc+ ∑∑ '  RT mc∑XGk km a  ∑∑Xa'' XGk kc, a' c kka'' (3.14)  τ ∑ XGj ja,, c'' a ja c a X c' j + ∑∑X a '  a c ∑∑Xc'' XGk ka, c' a c'' k in which subscript m, a, and c denote any molecule, anion, and cation in the solution, and subscript i, j, k represent any species in the solution. The parameter G in Eq. (3.14)

G jm =exp( −ατjm jm ) (3.15)

G jc, ac =exp( −ατjc,, ac jc ac ) (3.16)

G ja, ca =exp( −ατja,, ca ja ca ) (3.17)

∑ XGa ca, m a Gcm = (3.18) ∑ X a' a'

∑ XGc ca, m c Gam = (3.19) ∑ X c' c' in which α is the nonrandomness parameter and τ is binary energy interaction parameter that have the relationship as

∑ X aα ca, m a αcm = (3.20) ∑ X a' a'

∑ X cα ca, m c αam = (3.21) ∑ X c' c'

τmc, ac=−+ ττ cm ca ,, m τ m ca (3.22)

τma, ca=−+ ττ am ca ,, m τ m ca (3.23)

B τ =A + (3.24) T

Finally, activity coefficient of species i can be obtained by differentiating gex in

Eq. (3.12) through Eq. (3.8).

One of the advantages of eNRTL model is that the model can describe the non-

ideality of an electrolyte system with relatively few parameters (binary interaction

parameters) [115]. In addition, the commercialization of eNRTL model in ASPEN Plus®

software (Aspen Technology, Inc.) makes it one of the most popular activity coefficient models for electrolyte systems. For the same reason, eNRTL has been widely adopted and successfully used in the thermodynamic study of CO2 capture. Therefore, the eNRTL

model is adopted in this work to account the non-ideality of electrolyte systems.

In the mathematical expression of the eNRTL model above, the only parameters

that are not available from the literature are the nonrandomness parameters α and the

binary energy interaction parameters τ. Due to the complexity of the systems studied, the

number of binary interaction parameters will be so large that the computational effort

required to complete the correlation calculation for those parameters becomes extremely

large. According to the literature [20], the non-randomness parameters are usually set to a

default value for each system in the correlation. The default values for the systems

studied in this work can be found in the corresponding sections. In addition, the

interaction parameters for ion – ion binary pairs are usually set to zero. Those binary

pairs that do not show significant impact on system non-ideality can be selected by

performing a screening correlation which includes a wide selection of binary pairs. 52

Detailed assumptions and default values for the thermodynamic parameters are discussed

in 3.4.3 for aqueous amine systems.

3.2.3 Phase equilibrium The relationship between the compositions of the liquid and vapor phases of an

aqueous amine system is described by Eq. (3.25). The vapor pressures of ionic species are assumed to negligible in this work because ionic species do not exist at significant concentrations in the vapor phase. Because both water and amine are treated as solvents,

the activity coefficient γ i in Eq. (3.25) is subject to symmetric reference state for these

two components.

∞ 0 vPii(P − ) yPϕγˆ = xP00ϕ exp (3.25) i i iii i   RT

in which yi and are the mole fraction and fugacity coefficient of component i,

푖 0 0 respectively, in the휑� vapor phase; P is total pressure; xi, γi, Pi , φi are the mole fraction, activity coefficient, pure component saturation vapor pressure, and pure component

∞ fugacity coefficient of component i in the liquid phase, respectively; and vi is the partial

molar volume of the solvent.

3.2.4 Heat capacity The heat capacities of an aqueous amine solution is expressed by Eq. (3.26), in

which the first term on the right side represents the ideal solution heat capacity and the second term represents the excess heat capacity due to non-ideality.

all species = + E Cp ∑ Cpi, Cx p i (3.26) i

in which subscript i denotes any species, Cp,i is the heat capacity for pure component i

E (kJ/mol/K), and Cp is the excess heat capacity of the system (kJ/mol/K).

The excess heat capacity and activity coefficient are related to the excess enthalpy

through Eq. (3.27) and Eq. (3.28), respectively.

all species ∂H E E = i Cxpi∑ (3.27) i ∂T

E E H ∂(GTi / ) ∂lnγ ii=−=− (3.28) T 2 ∂∂TT px, i px, i

3.3 Experimental methods The apparatus and procedure for VLE and heat capacity determination of aqueous

amine are described in detail in section 2.3.1 and section 2.3.2 respectively.

3.4 Experimental results and data correlation

3.4.1 Vapor liquid equilibrium

The vapor liquid equilibrium was measured for PZ - H2O systems (xPZ = 0.04,

0.09, 0.14, and 0.32) and MEA - H2O systems (xMEA = 0.05, 0.11, 0.31, and 0.54) at

temperatures ranging from 313 K to 393 K. The total vapor pressure, liquid composition,

and temperature at equilibrium are presented in Appendix A.1 and A.3 for the PZ and

MEA systems, respectively. It should be noted that PZ has limited solubility in water, above which piperazine hexahydrate and anhydrous piperazine will precipitate.

Therefore, only PZ concentrations below the solubility limit were investigated in this

work. In addition, the amine concentrations in Appendix A.1 and A.3 are the initial amine

concentrations determined by solution preparation. This approximation is valid because

54 the numbers of moles of water and amine in the vapor phase are less than 2% of those in the liquid phase.

3.4.2 Heat capacity Following the procedures described in section 2.3.2, heat capacities at constant pressure were measured for the PZ - H2O system and the MEA - H2O system. The results are listed in Appendix A.2 and A.4. Heat capacities were measured at temperatures from

313 K to 393 K at 10 K intervals. The heat capacities of the pure components (amines and water) were also measured as a baseline check.

3.4.3 Activity coefficient model correlation One of the most important reasons to study the thermodynamics of aqueous amine solutions is to assess quantitatively the non-ideality of the liquid phase, which is represented by activity coefficients. In the capture of CO2 using aqueous amines, the pressure is usually close to atmospheric. Therefore, vapor phase non-ideality is often less significant than that of liquid phase. In this work, SRK model, which was reported to predict accurately the phase behavior of mixtures [122], was used for vapor phase non- ideality calculations.

To obtain the activity coefficient of each species in a solvent system, the experimental data were fit with the thermodynamic model described in section 3.2 using the approach similar to that in Hilliard’s work [14]. As both vapor pressure and heat capacity are related to activity coefficients, both sets of experimental data were included in the correlation. The problem was realized as the minimization of objective function in

Eq. (3.29) which is the summation of squared difference in calculated and experimental

total vapor pressures and heat capacities, normalized based on the magnitudes of the

calculated and experimental values.

exp cal 22N exp cal NP Cp 11(PPi−− i ) ( CCpk,, pk) = + f ∑∑exp cal exp cal (3.29) N PP N CC P iki i Cp pk,, pk

in which Np and NCp are the number of experimental data points for vapor pressure and

heat capacity repectively.

For this purpose, an in-house correlation package was developed using

MATLAB®. The local optimization function fmincon was used to find the minimum of

Eq. (3.29) by adjusting the binary interaction parameters. Even though global minimization was not used in this work, it was included as an available option in the

correlation package. However, global optimization takes much longer to converge as it

employs multiple starting points. 95% confidence intervals were determined using the

function nlpredci; standard errors for the parameter estimates were determined using Eq.

(3.30).

CI-1 CI s =ub lb ⋅ (3.30) e 2tinv( 0.975, F )

where CIub and CIlb are the upper and lower bounds of the 95% lever confidence interval

of the estimation calculated by function nlpredci, tinv is the inverse of Student's t

cumulative distribution function, and F is the degrees of freedom.

In the MEA – H2O binary system, there are two molecules, two cations, and one

anion, as indicated by the chemical reactions in R (3.1) and R (3.2). Ten binary

interaction pairs can thus be formed. In the PZ – H2O binary system, there is an

+ additional cation, PZH2 , in the system due to the two amine groups in the PZ. Eighteen

binary pairs can thus be formed in this case. However, most of the interaction pairs can

be neglected due to their low concentrations in the system. In this work, only the

interaction pairs listed in Table 3.2 and Table 3.3 were estimated in the regression. The rest of the interaction pairs, which have insignificant impact on the system non-ideality, were ignored in the correlation and set to the default values listed in Table 3.2 and Table

3.3. In addition, as suggested by the literature [20, 121], the non-randomness parameters for molecule - molecule interaction and molecule – ion pair interaction were fixed at a default value of 0.2.

The final fitted parameter values and the corresponding standard errors are listed in Table 3.2 and Table 3.3. A comparison of the final calculated and the experimental total vapor pressure is shown in Figure 3.1. The correlation coefficients, R2, of 0.99 and

0.98 for the two systems indicate a successful correlation of the experimental data using

the thermodynamic model for PZ and MEA aqueous solution systems.

Table 3.2 Regression results of binary interaction parameters for PZ-H2O system A B -3 H2O - PZ / PZ - H2O -0.45 ± 2.55×10 31.52 ± 1.91 Default molecule - ion pair and ion pair - molecule parameters Molecule - ion pair 10 ion pair - molecule -2 Water - ion pair 8 ion pair - water -4 *A and B are parameters in Eq. (3.24)

Table 3.3 Regression results of binary interaction parameters for MEA-H2O system A B

H2O - MEA / MEA - H2O -0.27 ± 0.11 53.11 ± 38.44 Default molecule - ion pair and ion pair - molecule parameters Molecule - ion pair 10 Molecule - ion pair -2 Water - ion pair 8 Water - ion pair -4 *A and B are parameters in Eq. (3.24)

12 2 PZ-H2O (R = 0.99)

11 /Pa) p x

e 10

Log(P 9

8 8 9 10 11 12 Log(P /Pa) cal

2 12 MEA-H2O (R = 0.98)

11 /Pa) p x

e 10

9 Log(P 8 8 9 10 11 12 Log(P /Pa) cal Figure 3.1 Comparison of correlated and experimental vapor pressure above aqueous amine systems (top: PZ system (xPZ = 0.04, 0.09, 0.14, and 0.32) at 313K to

393K, bottom: MEA system (xMEA = 0.05, 0.11, 0.31, and 0.54) at 313K to 393K)

3.5 Model Prediction

3.5.1 Vapor liquid equilibrium prediction Solvent vapor pressure is an important consideration in design and optimization as it influences the rates of water and amine loss during the scrubbing and stripping process and their content in the scrubber lean gas flow. Using the interaction parameters presented in Table 3.2 and Table 3.3, the model can be used to predict the vapor pressures of water and amine for specified overall liquid compositions and temperatures.

The total vapor pressures for PZ solutions and MEA solutions at different temperatures and concentrations predicted using the model are compared with literature data in Figure 3.2 and Figure 3.3 respectively. The model adequately predicts the total vapor pressure above PZ solution over the whole concentration range. The high agreement is consistent with the good correlation indicated by the small error of fitted parameters as shown in Table 3.2. On the other hand, total vapor pressure over MEA solution can be predicted adequately for MEA concentrations less than 0.5 mole fraction but shows some degree of deviation above 0.5. Since the maximum MEA concentration used in the experiments of this work is xMEA = 0.54, the model parameters regressed from these experimental data is only valid up to a MEA mole fraction of 0.54. This could lead to the discrepancy in the comparison of prediction and literature data above 0.5 mole fraction. In addition, the typical amine concentration in industrial practice is below 50 wt% (mole fraction of 0.2 for MEA) due to the corrosion concern at a concentration above 50 wt%[123]. For these typical amine concentrations, the best-fit parameters obtained from this work can predict the vapor pressures adequately.

7 10

6 10 472K

393K 5 10 386K

373K

4 353K 10 333K Total Pressure (Pa) 313K 3 10 0 0.2 0.4 0.6 0.8 1 PZ Concentraction (mole fraction)

Figure 3.2 Comparison of total vapor pressures of PZ – H2O system by model prediction (lines) and experiments (squares: this work, circles: [124], and diamonds: [125])

6 10

5 10 393 K

4 373 K 10 353 K 308 K 333 K 3 10 298 K

Total Pressure (Pa) Pressure Total 2 10

1 10 0 0.2 0.4 0.6 0.8 1 MEA Concentraction (mole fraction)

Figure 3.3 Comparison of total vapor pressures of MEA – H2O system by model prediction (lines) and experiments (circles: this work, diamonds: [126])

3.5.2 Heat capacity prediction With the fitted interaction parameters in Table 3.2, the eNRTL model was used to predict the heat capacities of aqueous PZ and MEA systems from 293 K to 393 K for different amine concentrations; results are shown in Figure 3.4 and Figure 3.5, respectively. Experimental data reported in the literature and in work at are also shown.

As the experimental data used for the interaction parameter regression is selected from this work as mentioned in section 3.4.3, the predicted heat capacities generally show better agreement with the data from this work than with the independent literature data.

Even though no correlation was performed with those literature data, the model can still adequately predict the heat capacities for both PZ and MEA systems.

4.2

4.1

4.0 x = 0.05 3.9

3.8

3.7 x = 0.09 Heat Capacity (kJ/kg-K)Heat 3.6 40 60 80 100 120 o Temerature ( C)

Figure 3.4 Comparison of heat capacity of PZ – H2O system by model prediction (lines) and experiments (squares: this work, circles: [49], and triangles: [14])

5.0

4.5 x = 0.1 4.0 x = 0.5 3.5 x = 0.6

3.0 x = 0.8

Heat Capacity (kJ/Kg-K) Capacity Heat 2.5

2.0 20 40 60 80 100 120 o Temperature ( C)

Figure 3.5 Comparison of heat capacity of MEA – H2O system by model prediction (lines) and experiments (squares: this work, triangles: [127], cross: [98], circles: [92])

3.5.3 Activity coefficient prediction Activity coefficients that describe the deviation from Raoult’s Law were also calculated using the model. Due to the lack of experimental data, prediction from a model with high accuracy could provide valuable information on the trend of activity coefficient over concentration and temperature.

0.9

0.8

0.7 393 K 313 K 0.6

PZ Activity Coefficient0.5

0.4 0 0.2 0.4 0.6 0.8 1 PZ Concentraction (mole fraction) Figure 3.6 Predictions of activity coefficient of PZ at 313 K and 393 K

0.95

313 K 0.9

0.85 393 K

0.8 MEA Activity Coefficient

0.75 0 0.2 0.4 0.6 0.8 1 3 MEA Concentraction (mole fraction) Figure 3.7 Predictions of activity coefficient of MEA at 313 K and 393 K

Figure 3.6 and Figure 3.7 show the activity coefficients of PZ and MEA respectively at 313 K and 393 K over the whole concentration range. As a symmetric reference state was selected for both systems, the activity coefficient of unreacted amine approaches unity as the amine concentration approaches one. The trend of the calculated

PZ activity coefficient is consistent with that in Hilliard’s work [14], in which extensive experimental data were used. Even though the binary interaction parameter in Eq. (3.24) is temperature dependent, the temperature dependence of the PZ activity coefficient, shown in Figure 3.6, is not obvious because of the small value of B determined in the correlation (Table 3.2). On the other hand, the dependence of the MEA activity coefficient, shown in Figure 3.7, is more significant due to a larger value of B in Table

3.3.

3.6 Conclusion Thermodynamic properties including VLE and heat capacity of two aqueous

amines (PZ and MEA) were investigated by experimental measurement and mathematical

modeling. The consistency of experimental and calculated results suggested a successful

correlation. The model was further used to predict vapor pressures and heat capacities under the conditions reported in the literatures. The high agreement of the prediction and the independent literature data validates the experimental measurements and the correlation with the thermodynamic model. This work provides fundamental information for the study of tertiary system (CO2 – aqueous amine) which will be discussed in

Chapter 4.

Chapter 4 - Thermodynamics of CO2 - Aqueous Amine Systems

4.1 Introduction

Vapor liquid equilibrium (VLE) is a critical factor in absorptive CO2 capture process design and optimization. A typical study of VLE properties includes collection of experimental VLE data and correlation of the data using a thermodynamic model that can be used for prediction. The collection of experimental VLE data for a CO2 - aqueous amine system usually requires measurement of temperature, vapor pressure, and speciation in liquid and vapor phases at equilibrium. While measurements of temperature and pressure are simple and straightforward, the measurement of speciation in the vapor and liquid phases usually requires sampling the system, which may potentially break the equilibrium and force the system move to a new equilibrium.

Barker [128] introduced a VLE determination method that minimizes experimental measurements but has accuracy comparable to traditional measurements.

Under the assumption that the activity coefficient model can predict the bubble point

pressure with accuracy comparable to the experimental error of the measured total

pressure [129], the Barker data reduction method calculates the speciation using the

thermodynamic model with the constraint of total mass balance. The Barker reduction

method requires only the equilibrium temperature, total pressure, and total number of

moles of each component in the system. Since no speciation measurement is required

with this method, the errors in speciation measurements are eliminated.

The heat of absorption is another important property in the CO2 capture process as

it determines the energetics of the absorption and desorption processes. There are

basically two approaches for heat of absorption determination: theoretical approach and

experimental approach. In the theoretical approach, the heat of absorption is calculated

from pressure data, which is usually obtained from VLE experiments. This approach was

welcomed by many researchers because of its simplicity, but the error of the calculated

heat of absorption is ten times higher than the pressure data. The experimental approach,

on the other hand, solves the problems encountered in the theoretical approach by

measuring the heat of absorption data directly through calorimetry.

In this work, both VLE and heat of absorption data were experimental measured

using a modified batch calorimeter. The experimental data obtained were correlated

simultaneously with a thermodynamic model using the Barker reduction method. The

predictions of the optimized model were compared with independently-measured literature data to confirm the effectiveness of model.

4.2 Objectives In this work, the Barker data reduction combined with a thermodynamic

framework that uses electrolyte Non-Random Two-Liquid (eNRTL) activity coefficient

model and Soave-Redlich-Kwong (SRK) fugacity coefficient model is applied to the

study of VLE and heat of absorption in CO2-aqueous amine systems. Ethanolamine

(MEA)-H2O-CO2 and piperazine (PZ)-H2O-CO2 are used as model solvent systems in

this work because of their high reaction rates, high capacities, and abundance of

published data.

The specific objectives of this work are to (1) design experiments according to the

thermodynamic framework; (2) collect experimental VLE and heat of absorption data and

correlate the results with the thermodynamic model using Barker data reduction method;

66 and (3) validate the method and results by comparing independently-measured literature data with the predicted data from the optimized thermodynamic model.

4.3 Theory

4.3.1 Chemical Equilibrium

The following chemical equilibria are considered in the liquid phase for CO2 absorption by aqueous MEA solvent:

K4.1 +− 2H23 O←  → H O + OH R (4.1)

K4.2 +− 2H22 O+ CO ←  → H 3 O + HCO 3 R (4.2)

−K4.3 +−2 H2 O+ HCO 3 ←  → H 33 O + CO R (4.3)

++K4.4 H23 O+ MEAH ←  → H O + MEA R (4.4)

−−K4.5 RNHCOO+ HO2 ←  → RNH23 + HCO R (4.5)

CO2 absorption by aqueous PZ includes reactions R (4.6) to R (4.9) in addition to

2+ reactions R (3.1) to R (4.3). PZH2 is ignored in this work as its concentration in the studied CO2 loading range is negligible.

++K4.6 H23 O+ PZH ←  → H O + PZ R (4.6)

+ − K4.7 −+ H PZCOO+ H23 O ←  → PZCOO + H O R (4.7)

K4.8 −+ PZ+ CO22 + HO ←  → PZCOO + HO3 R (4.8)

− K4.9 −− PZCOO()22+ HO ←  → PZCOO + HCO3 R (4.9)

The equilibrium constants Kr that describes the balance of reactants and products

for the reactions above have can be expressed through Eq. (4.1).

νν =αγri,, = ri Kxr∏∏ i ()ii (4.1) ii

in which subscript r denotes any reactions from R (3.1) to R (4.9), subscript i denotes species, αi, γi, and νr,i are activity, activity coefficient, and stoichiometric number of species i in reaction r, respectively.

The equilibrium constants are based on mole fraction and have a dependence with

temperature as described by Eq. (4.2). Values of the parameters in Eq. (4.2) for reactions

R (3.1) to R (4.9) are adopted from the literature as listed in Table 4.1.

Br Kr = exp A r ++ C rr ln( T) + D T (4.2) T

in which subscript r denotes any reaction from R (3.1) to R (4.9).

Because the equilibrium constants adopted from the literature are measured at

infinite dilution of amine in water, only water is treated as a solvent species; the other

species, including unreacted amine, CO2 molecules and ions, are treated as solutes in this

chapter. A symmetric reference state is used for water as shown by Eq. (4.3) while an

asymmetric reference state is used for the other species as shown by Eq. (4.4).

γ →→1 as x 1 ww (4.3)

γ ii→→1 as x 0 (4.4)

Such reference state choice is consistent with the studied systems in which the

amine concentrations were very low (below a mole fraction of 0.17). Note that this choice

is different from that in the study of H2O-amine system in Chapter 3 where both water

and amine were selected as solvent. The difference in reference choice does not affect the

model calculation and parameter estimation because the activity coefficients with

asymmetric reference state was converted from the activity coefficients with symmetric

reference state by Eq. (4.5).

* ∞ lnγi= ln γγ ii − ln (4.5)

* in which γi is the activity coefficient for species i using asymmetric reference state

* (lim lnγ i = 1) ,γi is the activity coefficient for species i using symmetric reference state xi →0

∞ (lim lnγ i = 1) , and γγii= lim ln . xi →1 xi →0

The relationship between the liquid and vapor phases is described by Eq. (4.6) for

water and amine and Eq. (4.7) for CO2 molecules. It should be noted that the activity

coefficient γi in Eq. (4.6) is subject to symmetric reference state for water and asymmetric reference state for amine.

∞ 0 vPss(P − ) yPϕγˆ = xP00ϕ exp i i iii i  RT   (4.6)

∞ 0 vPi (P − ) yPxϕˆ = γ *0 Hϕ exp i i ii ii  RT   (4.7) in which yi and are the mole fraction and fugacity coefficient of component i,

푖 0 0 respectively, in the휑� vapor phase; P is vapor pressure; xi, γi, Pi , φi are the mole fraction,

activity coefficient, pure component saturation vapor pressure, and pure component

fugacity coefficient of component i in the liquid phase, respectively, v∞ is the partial

molar volume of the solvent or solute; and Hi is the Henry’s law constant for CO2.

The Henry’s law constant for CO2 in solvent is estimated to be the same as that in

water for PZ - H2O - CO2 system due to the low concentration of PZ. The Henry’s law

constants used for the MEA - H2O - CO2 system were mass-averaged Henry’s law constants in pure MEA and pure water proposed by Liu and Zhang [130]. The temperature dependence is adopted from the literature [20, 130] and is listed in Table 4.1.

The activity coefficients in Eqs. (4.6) and (4.7) are calculated using the eNRTL model, which is discussed in detail in section 3.2.2.

The fugacity coefficients in Eqs. (4.6) and (4.7) are computed using the Redlich-

Kwong-Soave (SRK) equation of state,

RT a P = − (4.8) VbVVbm−− mm()

in which Vm is molar volume, and a and b are SRK model parameters.

Table 4.1 Parameters for calculating reaction equilibrium constants for CO2 reaction with aqueous amine on the mole fraction scale

Ar Br Cr Dr Source

K4.1 132.899 -13445.9 -22.4773 0 [107]

K4.2 231.465 -12092.1 -36.7816 0 [107]

K4.3 216.049 -12431.7 -35.4819 0 [107]

K4.4 2.1211 -8189.38 0 -0.007484 [20]

K4.5 2.8898 -3635.09 0 0 [20]

K4.6 18.135 3814.4 0 -0.0151 [131]*

K4.7 -4.6185 3616.1 0 0 [132]*

K4.8 0.3615 1322.3 0 0 [132]*

K4.9 14.043 3493.1 0 0 [131]*

Hwater 170.7126 -8477.71 -21.9574 0.005781 [20]

HMEA 89.452 -2934.6 -11.592 0.01644 [130] * converted from molality scale **A, B, C, and D are parameters in Eq. (4.2)

4.3.2 Heat of absorption

There are two approaches to obtain the heat of absorption of CO2 in aqueous

amines: (1) estimation from solubility data using the Gibbs-Helmholtz equation and (2)

calorimetric measurement.

Heat of absorption of CO2 can be estimated from the Gibbs-Helmholtz equation

as shown by Eq. (4.9). This is a convenient way to obtain heat of absorption data as no additional experimental data are required except for solubility data.

∂∂ln fPln ∆=HRii ≈ R (4.9) abs ∂∂(1/TT) (1/ ) xx

in which fi is the fugacity of species i (Pa).

The disadvantage of using Gibbs-Helmholtz method is that: the accuracy of

calculated heat of absorption data significantly depends on the accuracy of CO2 partial

pressure measurement, because the uncertainty of ∆H from the equation is one order of magnitude greater of the uncertainty of the CO2 partial pressure measurement [1]. In

addition, from a regression point of view, the lack of experimental heat of absorption data

could lead to inaccuracy in the parameter values obtained in theeactivity coefficient

model regression. Solubility measurements are usually performed under isothermal

conditions, and a set of solubility data could cover only scattered temperature points but

many CO2 loading points. In the regression of A and B in the activity coefficient model parameter τ = A + B/T, the scatter in temperature data and redundancy in CO2 loading

data could lead to a high error in B which is decisive in the estimation by Gibbs-

Helmholtz equation.

The direct measurement of the heat of absorption of CO2 is usually done using a calorimeter. The uncertainty of this method comes from the measurements of heat flow

71 and CO2 loading. These two uncertainties can be minimized using a reliable instrument and a good measurement method. Ultimately, calorimetric measurement has a lower uncertainty than estimation using the Gibbs-Helmholtz equation. In this work, the heat of absorption of CO2 was measured using a batch calorimeter. The experimental data were used with the solubility data in the activity coefficient model correlation.

It should be noted that the measurement environment in this work is constant volume, which requires an addition term (∆P∙V) that accounts the pressure increase in the

Gibbs-Helmholtz equation. Thus, the final expression for heat of absorption calculation at constant volume can be written as Eq. (4.10). In addition, the heat of absorption data reported in this work is integral in loadings, which requires the integration of Eq. (4.10) from zero loading. Since the pressure is a complex function of loading, numerical integration is needed.

∂∂ln fP ln ∆HR = ii+∆PV ⋅ ≈ R +∆PV ⋅ (4.10) abs ∂∂(1/TT) (1/ ) Vx,, Vx

4.3.3 Baker Reduction Theory Barker data reduction correlates the experimental VLE and heat of absorption data with a thermodynamic model through an efficient and effective approach. The raw data collected from the VLE and heat of absorption measurements are (1) the total number of moles of CO2 and solvent in the equilibrium cell, (2) the equilibrium pressure,

(3) the equilibrium temperature, and (4) the integral heat of absorption. Within the framework of the data reduction introduced by Barker [128], the raw data can be fit with a thermodynamic model by varying the interaction parameters in the activity coefficient model.

The data reduction and model correlation process is similar to that used by Uusi-

Kyyny et al. [129], and shown schematically Figure 4.1. Generally, the process starts by

assuming all the solvents are in the liquid phase and initiating a CO2 loading α (defined

as α = nn/ ) and a set of interaction parameters for the activity coefficient model. co2 amine

Starting from the initial solvent composition and the CO2 loading, a trial and error

variation of activity coefficient model parameters is performed to minimize the sum-of- squares difference between the calculated and experimental total vapor pressure and heat of absorption. This process is represented by the inner iteration layer in Figure 4.1. In each iteration, the liquid phase speciation and the corresponding activity coefficients can be calculated using the non-stoichiometric method which is discussed Appendix B.1 [133] and the electrolyte NRTL model respectively. The partial pressure of each component and the corresponding fugacity coefficients can be calculated through the phase equilibrium with the Soave-Redlich-Kwong (SRK) model.

Following the inner iteration, the molar volume of each component is then calculated by

v cal vtt= ZRT/ p (4.11)

v 3 where v t is the molar volume of vapor phase (m /mol), Z is the compressibility factor,

cal and p t is the calculated total pressures (Pa).

The total number of moles in vapor phase is then calculated by

ll v Vcell- vn t t nt = vl (4.12) vvtt-

v l where n t and n t are the total number of moles in vapor phase and liquid phase

l 3 respectively (mol), v t is the molar volume of liquid phase (m /mol), Vcell is the volume of

the equilibrium cell (m3).

The number of moles of each component in vapor phase can be derived from

vv ni= yn it (4.13)

v where n i is the number of moles of i component in the vapor phase (mol).

The number of moles of each component in liquid phase then can be updated

through

l Tv ni, new= nn i − i (4.14)

l T where n i,new is the updated number of moles in the liquid phase (mol), and n i is the total

number of moles of component i in both phases (mol). The CO2 loading can also be

updated with the new composition.

Additional iterations follow using the updated liquid compositions until the

changes of number of moles of each component in the liquid phase are below tolerance.

The values of tolerance in this work were picked to be small so that high accuracy in the

parameter regression can be obtained while keeping the calculation time reasonably short.

4.4 Experimental results and data correlation 4.4.1 Vapor liquid equilibrium

Pressure, temperature, and total number of moles of CO2 and solvent at each equilibrium was measured for the PZ – H2O – CO2 system (bPZ = 2m, 3.6m, and 5m) and

MEA – H2O – CO2 system (30 wt% and 40 wt% MEA) at temperatures ranging from 313

K to 393 K following the procedures in section 2.3.3. The results are presented in

Appendix A.5 and A.7. The data are further used with the heat of absorption data for

mathematical model correlation discussed in the following section.

4.4.2 Heat of Absorption

Heat of absorption of CO2 by aqueous PZ (2m, 3.6m, and 5m) and MEA (30 wt%

and 40 wt%) was also measured using the method discussed in section 2.3.3. The results

are listed in Appendix A.6 and A.8. The data are further used with the VLE data for mathematical model correlation discussed in the following section.

4.4.3 Activity coefficient model correlation with VLE and heat of absorption data To describe the non-ideality of the solvent systems, the collected VLE and heat of

absorption experimental data were fit with a thermodynamic model following the

procedure discussed in section 4.3. For this purpose, an in-house correlation package was

developed using MATLAB®. The local optimization function fmincon was used to

estimate the values of the interaction parameters at each iteration. Even though global

minimization was not used in this work, it was included as an available option in the

correlation package. However, global optimization takes much longer to converge as it

employs multiple starting points. 95% confidence intervals were determined using the

function nlpredci; standard errors for the parameter estimates were determined using Eq.

(3.30).

CI-1 CI s =ub lb ⋅ (4.15) e 2tinv( 0.975, F )

where CIub and CIlb are the upper and lower bounds of the 95% lever confidence interval

of the estimation calculated by function nlpredci, tinv is the inverse of Student's t

cumulative distribution function, and F is the degrees of freedom.

n , T, pexp , H , p 0, K i t i i i Assume all the solvents are in liquid

state, and initiate CO2 loading α and

interaction parameters in eNRTL model

Update xi,new exp xi, T, p t, α, τ

Adjust eNRTL Chemical Equilibrium interaction parameters xi and γi

Phase Equilibrium

yi and φi ∂ln Pcal ∆HRcal ≈ CO2 +∆PV ⋅ abs ∂(1/T ) cal Vx, P t

exp cal 22exp cal No 11(PPt−− t ) ( HHabs abs ) ε >+ If 1 ∑∑exp cal exp cal N PP⋅⋅ N HH Pt t t Habs abs abs

yes ll v Vcell- vn t t v cal nt = vl vtt= ZRT/ p vvtt-

l Tv vv ni, new= nn i − i ni= yn it

xi,new

ll2 1 (nni, new− i ) ε > Yes Output No If 2 ∑ ll N nni, new i

-5 -3 Figure 4.1 Data reduction method flow chart (ε1 = 1×10 , and ε2 = 1×10 )

Preliminary trials were carried out with a wide selection of interaction pairs in the

eNRTL model. The pairs that showed the most statistical significance in the preliminary

trials were selected for the final correlation and are listed in Table 4.2 and Table 4.3.

Parameter values for the H2O – amine interaction pairs were obtained from Chapter 3.

The parameters of the rest of the interaction pairs that were not included in the regression

were set to default values, as suggested by Hilliard [14] and Liu et al. [130]. The final

fitted parameters and the corresponding standard errors are listed in Table 4.2 and Table

4.3. The correlations coefficients (r2) were 0.83 for both the PZ and the MEA systems,

which indicates a successful correlation of the experimental data using the

thermodynamic model and the Barker data reduction. The relatively high error of

parameter B obtained from the correlations could be attributed to the fact that the number

of variables in temperature is much less than that in liquid composition in the

experiments (for example, 77 data points were collected at 4 different temperatures for

PZ system; 37 data points were collected at 4 different temperatures for MEA system).

4.4.4 CO2 vapor pressure prediction and comparison By applying the best-fit parameter values in Table 4.2 and Table 4.3 to the

thermodynamic model, the model can be used to predict CO2 partial pressure for the PZ-

H2O-CO2 and MEA-H2O-CO2 systems. To validate the application of the Barker data reduction in VLE and heat of absorption study of CO2 – aqueous amine system, CO2

partial pressures under several conditions reported by the literature were predicted using

the parameters Table 4.2 and Table 4.3, and compared with independently-measured

values from the literature [14, 21, 134, 135] as shown from Figure 4.3 to Figure 4.6. It should be noted that the predicted values calculated from the model used here and the literature data are independent.

Table 4.2. Best-fit binary interaction parameters for PZ-CO2-H2O system A B

H2O - CO2 6.45 ± 2.86 -206.6 ± 1019.6

CO2 - H2O 6.45 ± 2.86 -206.6 ± 1019.6 -3 * * H2O - PZ -0.45 ± 2.55×10 31.52 ± 1.91 -3 * * PZ - H2O -0.45 ± 2.55×10 31.52 ± 1.91 + - H2O - PZH HCO3 0.82 ± 38.96 + - PZH HCO3 - H2O -0.57 ± 14.42 + - H2O - PZH PZCOO 5.47 ± 1.45 + - PZH PZCOO - H2O -2.91 ± 0.82 Default molecule-ion pair (ion pair-molecule) parameters Molecule-electrolyte 10 Electrolyte-molecule -2 Water-electrolyte 8 Electrolyte-water -4

* Obtained from the thermodynamic study of H2O – PZ system in section 3.4.3 ** A and B are parameters in binary interaction parameter expressed as τ = A + B/T

Table 4.3. Best-fit binary interaction parameters for MEA-CO2-H2O system A B

H2O - CO2 0.18 ± 4.80 -1508.3 ± 1713.1

CO2 - H2O 0.18 ± 4.80 -1508.3 ± 1713.1

H2O - MEA -0.27 ± 0.11 * 53.11 ± 38.44 * MEA - H2O -0.27 ± 0.11 * 53.11 ± 38.44 * + - H2O - MEAH HCO3 5.14 ± 0.45 + - MEAH HCO3 - H2O -5.35 ± 0.47 + - H2O - MEAH MEACOO 1.51 ± 0.81 + - MEAH MEACOO - H2O -4.77 ± 0.54 Defaulting molecule-ion pair (ion pair-molecule) parameters

CO2-electrolyte 15 Electrolyte-CO2 -8 Water-electrolyte 8 Electrolyte-water -4

* Obtained from the thermodynamic study of H2O – MEA system in section 3.4.3 ** A and B are parameters in binary interaction parameter expressed as τ = A + B/T

13 2 PZ-H2O-CO2 (R = 0.83) 12 /Pa)

p 11 x e 10

Log(P 9

8 8 9 10 11 12 13 Log(P /Pa) cal

13 2 MEA-H2O-CO2 (R = 0.83) 12 /Pa)

p 11 x e 10

Log(P 9

8 8 9 10 11 12 13 Log(P /Pa) cal Figure 4.2 Comparison of correlated and experimental vapor pressure above aqueous amine – CO2 systems (top: PZ system (bPZ = 2m, 3.6m, and 5m) at 313K to 373K, bottom: MEA system (30 wt% and 40 wt% MEA) at 313K to 373K) 79

For PZ-H2O-CO2 system, the optimized model was compared with literature data

from two works [14, 134] at different temperatures and PZ concentrations as shown in

Figure 4.3 and Figure 4.4. The predicted CO2 partial pressure agrees well with the

literature data even for the set at 393K which is outside of the regression temperature

range used here. Even though total pressure was used as the objective function in the

correlation, the strong agreement with literature data suggests that accurate model

parameters can still be obtained with the proper selection of regression method (Barker

reduction in our case).

For the MEA-H2O-CO2 system, the predicted CO2 partial pressures are also in

line with the experimental data reported by Shen and Li [21], and show slight

discrepancy with the data reported by Hilliard [14]. As the same set of parameters in

Table 4.3 was used for the predictions in both cases, the inconsistency of prediction

performance suggests an inconsistency among the literature data. There is a common

concern for the correlation that uses the objective function of total vapor pressure, which

includes contributions from three components – CO2, H2O, and MEA: in the low CO2

loading (low CO2 partial vapor pressure) range, the vapor pressures of water and MEA

are dominant over CO2 partial pressure, which decreases the sensitivity and accuracy of

CO2 partial pressure in the correlation. Fortunately, in the comparison with

independently-measured literature shown in Figure 4.5 and Figure 4.6, there is no

significant discrepancy in the low CO2 loading range between the predicted and literature values. This may also suggest the successful application of Barker reduction in the VLE study of CO2 – aqueous amine systems.

6 10

5 10

4 393 K 10

3 10 353 K 333 K 2 10 313 K Vapor Pressure/Pa

2 1 10 CO

0 10 0 0.2 0.4 0.6 0.8 1 CO Loading (mol CO /mol amine) 2 2

6 10

5 10

393 K 4 10

3 10 353 K

Vapor Pressure/Pa 2 2 10 CO

1 10 0 0.2 0.4 0.6 0.8 1 CO Loading (mol CO /mol amine) 2 2

Figure 4.3 Comparison of model predicted and reported CO2 pressure at 2m (top) and 4m aqueous piperazine (bottom) (line: predicted; solid circle: Lit. [134]; open circle: Lit. [14])

6 10

5 10

4 10

3 10 333 K

2 10 313 K Vapor Pressure/Pa

2 1 10 CO

0 10 0 0.2 0.4 0.6 0.8 1 CO Loading (mol CO /mol amine) 2 2

6 10

5 10

4 10

3 10 333 K

2 10

Vapor Pressure/Pa 313 K 2 1 10 CO

0 10 0 0.2 0.4 0.6 0.8 1 CO Loading (mol CO /mol amine) 2 2

Figure 4.4 Comparison of model predicted and reported CO2 partial pressure at 3.6m (top) and 5m (bottom) aqueous piperazine (line: predicted; open circle: Lit. [14])

4.4.5 Heat of absorption prediction and comparison The heat of absorption, another key thermodynamic property in addition to VLE,

can also be calculated with the activity coefficient parameters in Table 4.2 and Table 4.3.

To validate the application of Barker data reduction in heat of absorption study of CO2 -

liquid amine system, reaction enthalpies under several conditions reported by the

literature were predicted using the parameters obtained from this work and compared

with independent literature data.

For the PZ-H2O-CO2 system, there are scattered heat of absorption data in the

literature. Hilliard reported several sets of heat of absorption data for PZ-H2O-CO2

system from a personal communications with Kim [14]. These experimental data were

compared with the predictions from this work as shown in Figure 4.7. For MEA-H2O-

CO2 system, the predicted enthalpy of absorption from this work is compared with

several sets of independent literature data [136-139] in Figure 4.8 and Figure 4.9.

5 10

373 K

4 10

353 K

Vapor Pressure/Pa 3

2 10 313 K 333 K CO

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 CO Loading (mol CO /mol amine) 2 2

Figure 4.5 Comparison of model predicted and reported CO2 partial pressure at 30wt% MEA (line: predicted; solid diamond: Lit. [21]) 83

4 10

3 10 333 K

313 K 2 10 Vapor Pressure/Pa 2 CO

1 10 0.1 0.2 0.3 0.4 0.5 0.6 CO Loading (mol CO /mol amine) 2 2

4 10

3 333 K 10

2 313 K 10 Vapor Pressure/Pa 2 CO

1 10 0.1 0.2 0.3 0.4 0.5 0.6 CO Loading (mol CO /mol amine) 2 2

Figure 4.6 Comparison of model predicted and reported CO2 partial pressure at 3.5m (top) and 7m (bottom) MEA (line: predicted; solid circle: Lit. [14])

Generally, the predicted enthalpy of absorption agrees well (within ±25%) with independently-measured literature data for both aqueous PZ and aqueous MEA systems.

The predicted enthalpy of absorption tends to be constant at low CO2 loading and

gradually decreases with increasing CO2 loading. This result is consistent with the

reported literature values as shown in the figures. In addition, the prediction slightly

overestimates the enthalpy of absorption at low CO2 loadings and low temperature. This

could be due to the calculation error in liquid phase speciation, as the uncertainty of

calculated enthalpy is one order of magnitude higher than that of the solubility data [138].

The uncertainty in the literature data is another contributor to the discrepancy between

the calculated results and the previously published results. Since some of the literature

values were calculated from pressure data using the Gibbs- Helmholtz equation, the uncertainty of the reported enthalpy data was up to ±20% [138]. Another possible reason is that the number of experimental enthalpy of absorption data used for correlation is less than that of the solubility data, which makes the fitted parameters more accurate in solubility prediction than enthalpy of absorption prediction.

40 Enthalpy (kJ/mol) Enthalpy 30

20 0 0.2 0.4 0.6 0.8 1 CO Loading (mol CO /mol amine) 2 2 Figure 4.7 Comparison of model predicted (lines) and reported enthalpy of absorption at 313 K (green squares) and 353 K (red circles) for 2.4 m PZ [14]

120

100

40 Enthalpy (kJ/mol) Enthalpy 20

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 CO Loading (mol CO /mol amine) 2 2 Figure 4.8 Comparison of model predicted (lines) and reported enthalpy of absorption at 313 K (green squares) and 353 K (red circles) for 30 wt% MEA [137] 86

120

100

40 Enthalpy (kJ/mol) Enthalpy 20

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 CO Loading (mol CO /mol amine) 2 2 Figure 4.9 Comparison of model predicted (line) and reported enthalpy of absorption (squares: [136], diamonds: [139], and circles: [138]) for 30 wt% MEA

4.4.6 Validation of combined correlation of VLE and heat of absorption Both vapor pressure and heat of absorption can be related to activity coefficient as discussed in section 4.3.3. Therefore, both data sets were correlated with the thermodynamic model using the Barker reduction to obtain best-fit interaction parameters in the eNRTL model as shown in Figure 4.1. The fitted parameters were expected to predicting accurately both the CO2 vapor pressure and the heat of absorption of CO2. The comparison of prediction and independent literature data confirmed this expectation in section 4.4.4 and 4.4.5. In addition, it is interesting to see the prediction performance with parameters fitted from individual data sets. Taking the PZ-H2O-CO2 system as an example, two correlations were performed using VLE data and heat of absorption respectively. Vapor pressure and heat of absorption were predicted using the optimized

model from the two correlations. The comparison of independent literature data and

prediction using VLE data set is shown in Figure 4.10. The comparison of independent literature data and prediction using heat of absorption data set is shown in Figure 4.11. It

can been seen in Figure 4.10 that the model obtained using VLE data can predict CO2

vapor pressure adequately, but does not predict either the plateau in the heat of absorption

in the low CO2 loading range and the sharp decrease of the heat of absorption in the high

loading range. On the other hand, it can be seen from Figure 4.11 that the model obtained

using the heat of absorption data in can predict the heat of absorption behavior along CO2

range very well, but fails to predict accurately the CO2 vapor pressure over the solvent.

The combined correlation of VLE and heat of absorption data is important and necessary to accurately predict the two properties.

8 10 90 2m PZ 7 2.4m PZ 10 80 353K 6 10

5 70 10 393K 4 10 60 313K 3 353K 10 50

Vapor Pressure/Pa 2 2

10 333K (kJ/mol) Enthalpy

313K 40 CO 1 10

0 10 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 CO Loading (mol CO /mol amine) CO Loading (mol CO /mol amine) 2 2 2 2 Figure 4.10 Comparison of model predicted (lines) (using VLE data only) and

reported CO2 vapor pressure (left) and enthalpy of absorption (right) [14, 134]

6 10 90 2m PZ 2.4m PZ 5 353K 10 80 393K 4 10 70 353K 3 10 60 313K

2 333K 10 50 313K Vapor Pressure/Pa 2

1 (kJ/mol) Enthalpy 10 40 CO 0 10 30 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 CO Loading (mol CO /mol amine) CO Loading (mol CO /mol amine) 2 2 2 2 Figure 4.11 Comparison of model predicted (lines) (using heat of absorption data

only) and reported CO2 vapor pressure (left) and enthalpy of absorption (right) [14, 134]

4.5 Speciation prediction Even though the speciation experimental data is not required using the Barker

data reduction method in this work, the thermodynamic model can be used to predict

speciation in liquid phase. Figure 4.12 shows two examples of the calculated speciation for PZ - H2O - CO2 and MEA - H2O - CO2 systems. This provides a calculation pathway

in the determination of chemical composition at certain operation conditions.

0.14

0.12 PZ H+PZCOO- 3 0.1

0.08

0.06 Speciation 0.04 PZH+ - 0.02 PZCOO HCOO- 3 0 0 0.2 0.4 0.6 0.8 1 CO Loading (mol CO /mol amine) 2 2

0.14 MEA 0.12

0.1

0.08 MEAH+

0.06 HCO- 3 Speciation 0.04

0.02 PZCOO-

0 0 0.1 0.2 0.3 0.4 0.5 0.6 CO Loading (mol CO /mol amine) 2 2 Figure 4.12 Calculated liquid phase speciation (top: 5m PZ at 313K, bottom: 30 wt% MEA at 313K)

4.6 Conclusion

Thermodynamic properties including VLE and heat of absorption of two CO2 solvent systems (CO2 in aqueous PZ and CO2 in aqueous MEA) were investigated.

Experimental data were collected using a modified calorimeter, and the data were fit with a mathematical model using Barker reduction. The consistency of experimental and calculated results suggested a successful correlation and application of the Barker

reduction. The model was further used to predict CO2 partial pressures and heat of absorption under the conditions reported in the literature. Model predictions agree well with the literature data of CO2 partial pressure, validating the correlation method used in

this work. The predicted heat of absorption showed a consistent trend with literature data.

The slight discrepancy in values between the two could be due to the error in speciation

calculation and heat of absorption calculation. The comparison of model predictions

using single data set and multiple data sets confirmed the importance of combined

correlation of VLE and heat of absorption data to accurately predict the two properties.

Finally, the model was able to successfully predict the speciation in liquid phase, which is

useful to determine the liquid composition at a certain CO2 loading.

Chapter 5 - Thermodynamics and Kinetics of CO2 Capture Using Room Temperature Ionic Liquids

5.1 Introduction Chemical absorption by aqueous amine is one of the m ost effective approaches to

remove CO2 from coal combustion flue gas [140]. Some of the thermodynamic properties of CO2 capture by aqueous amines were discussed in Chapter 3 and Chapter 4. Despite of

the successful application of aqueous amines in CO2 capture, there are several challenges

and difficulties for this solvent system, including high energy consumption for the

separation, oxidative degradation of the amines, volatilization of the amines, and

corrosion of the equipment [141].

Aqueous amino acids (AAs) have been found to be a promising alternative to the

aqueous amines in CO2 capture from flue gas because of their amine functionality. In

addition, AAs have the advantages of resistance to oxidative degradation, negligible

volatility, and close-to-water surface tension and viscosity in aqueous solution [41, 142-

144]. However, similar to aqueous amines, aqueous AAs also suffer the problems of low

CO2 loading and high energy requirements for solvent heating and cooling. Ionic liquids

are another form in which AAs can be used for CO2 capture. When reacted with a

Brønsted base, AAs can form into anions. With the correct choice of base, the product of

this reaction will be a room temperature ionic liquid (RTIL), a liquid that contains only ions at or below room temperature [38]. Because of the amine groups of AAs, AA-based

RTILs were reported to have good performance in CO2 capture. Fukumoto et al. synthesized twenty AA-based ionic liquids [40], some of which was found to be effective in CO2 capture [41-44]. Compared with traditional aqueous amine solvent systems, AA-

based RTILs have the advantages of high CO2 capacity, good thermo-stability, low vapor

pressure, and environmental friendliness [42, 43, 145].

However, RTILs usually have high viscosity, which may cause difficulties in material handling and slow absorption rate. In this work, supporting RTILs on porous solid substrate is proposed to overcome those difficulties as the porous solid particles have high surface area and can be operated in a fixed bed. Two sulfur-containing AAs were used to synthesize RTILs, which were supported on silica particles; the thermodynamic and kinetic properties for CO2 capture were studied. It is worth noting that sulfur-containing AAs provide the potential for simultaneous capture of CO2 and

mercury, which will be discussed in Chapter 6.

5.2 Objectives The objectives of the work reported in this chapter are to (1) evaluate the thermodynamic properties of AA-based RTILs for CO2 capture, including VLE and heat

of absorption; (2) investigate the kinetic properties of AA-based RTILs supported on

silica gel in fixed-bed operation.

5.3 Characterization results Two AA-based RTILs were synthesized using sulfur-containing AAs. One is tetrabutylphosphonium methionine ([P(C4)4][Met]), which was synthesized by the

reaction of methionine (Met) and tetrabutylphosphonium hydroxide ([P(C4)4]OH) solution. The other RTIL is tetrabutylphosphonium taurine ([P(C4)4][Tau]) synthesized

from taurine (Tau) and [P(C4)4]OH solution. Detailed synthesis procedures are provided

in section 2.1.2. The CO2 absorption by pure RTIL was characterized using FTIR spectra

and thermodynamically studied using a batch calorimeter. The RTILs were also

supported on silica gel particles and characterized for textural properties and thermal

stability.

5.3.1 Characterization of CO2 reaction with RTILs

The reaction of CO2 and amino acid based RTILs was characterized by the FTIR spectrum of unreacted and reacted RTILs; spectra are shown in Figure 5.1. The weak peaks at 3360 cm-1 and 3290 cm-1 on the fresh RTILs represent the symmetric and asymmetric stretches of NH2 group. Furthermore, the fresh RTILs were equilibrated with

CO2 at room temperature and 30 psia for overnight, and characterized by FTIR. After the

-1 absorption of CO2, there was a new peak at 1670 cm , corresponding to the formation of

a COO-H bond, and a new peak at 3410 cm-1, indicating an N-H stretch. Reaction with

-1 -1 CO2 also resulted in the disappearance of NH2 peaks at 3360 cm and 3290 cm

indicates that almost all of the amine groups reacted with CO2.

5.3.2 Vapor liquid equilibrium and heat of absorption

Vapor liquid equilibrium were measured for the CO2 - [P(C4)4][Tau] system at

temperatures from 333K to 373K; the results are shown in Figure 5.2. It can be seen that

VLE behavior of [P(C4)4][Tau] is similar to that of aqueous amine such as

monoethanolamine in Figure 4.5 because of their similarity in the amine functionality. To

make the VLE results usable for the fixed-bed adsorption study in section 5.4.2, the CO2

concentrations in vapor and liquid phases in Figure 5.2 was fit with a power function:

α =KP ⋅ η (5.1)

in which α is the CO2 loading (mol CO2/mol RTIL), P is the vapor pressure of CO2 in gas phase (MPa), K is the equilibrium constant defined as K = exp(E/T+F).

Fresh Spent

Figure 5.1 FTIR spectra of fresh and spent ILs (top: [P(C4)4][Met]; bottom:

[P(C4)4][Tau])

The power parameter η and the parameters (E and F) in K were determined by

minimizing the least-square difference of calculated and experimental CO2 loadings. The

results are shown in Table 5.1. The relationship and the best-fit parameters will be used in the kinetic study of fixed-bed operation discussed in section 5.4.2.

Table 5.1 Best-fit parameters for VLE relationship of CO2 and [P(C4)4][Tau] expressed by Eq. (5.1) Parameter Best-fit value E 1451 ± 434 F 6.3 ± 2.1 η 0.19 ± 0.12

The heat of absorption of CO2 by the RTILs was measured simultaneously with

the VLE measurement. It can be seen that the heat of absorption with the RTILs is

comparable to the benchmark aqueous amine: Both of the solvents have a heat of

absorption of 100 kJ per mole of CO2 absorbed at low CO2 loading. It decreases

gradually when the solvent is saturated with CO2.

The non-ideality of the CO2-RTIL system is of great interest to the thermodynamic study of CO2 capture. However, the activity coefficient models

developed for dilute aqueous electrolyte system (for example, the electrolyte NRTL

model and the Pitzer model) are not applicable to the non-aqueous RTIL system. Success

has been made on modeling physical absorption of CO2 in RTIL systems using Equation

of State models [146-148], but the chemical reactions between CO2 and AA-based RTIL

in this work complicates the problem. The thermodynamic modeling of CO2 capture using RTILs is excluded from this work, but is recommended for future study.

300

100

373 K 353 K

Vapor Pressure (kPa) Pressure Vapor 333 K 313 K 10 0.2 0.3 0.4 0.5 CO Loading (mol CO / mol IL) 2 2

Figure 5.2 Vapor pressure of CO2 above [P(C4)4][Tau] RTIL at different temperatures 120 ) 2

90 kJ/ mol CO 60 MEA 353K Tau 373K Tau 353K 30 Tau 333K

Heat of Sorption ( 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 CO Loading (mol CO / mol IL) 2 2

Figure 5.3 Heat of absorption of CO2 by [P(C4)4][Tau] and 30 wt% aqueous MEA

5.3.3 Surface area and pore size distribution of [P(C4)4][Tau] coated silica gels

The surface area, pore volume, and pore size distribution of silica gels coated

were determined as functions of RTIL loading using the method described in section

2.2.2 and summarized in Table 5.2. As the RTILs studied in this work have similar

physical and chemical properties, [P(C4)4][Tau]-coated silica gel was used as a representative material for textural characterization. The pore volume of [P(C4)4][Tau]- coated silica gel is shown as a function of RTIL loading in Figure 5.4.The pore volume decreases linearly with increasing RTIL loading. This trend is reasonable because the pores in silica gels are occupied by RTIL as the RTIL loading increases. The pore volumes were also fit with a line in Figure 5.4; the y-intercept of the linear fit suggests a maximum RTIL loading of 49 wt% which is quantitatively consistent with the measured total pore volume.

The RTIL in the pores could be distributed in at least two ways: evenly distributed on the surface (Figure 5.6A) or accumulated at the bottom of the pores (Figure 5.6B). In

the former case, both pore size and pore volume decrease linearly with the increase of

RTIL loading. In the latter case, only pore volume decrease linearly with the increase of

RTIL loading while pore size should remain unchanged. To study the RTIL distribution

in this work, the pore size distributions at different RTIL loadings were fit to a Gaussian

distribution as shown in Figure 5.5. The mean pore sizes are shown in the same graph. It

can be seen that the particles have similar pore sizes for all the loading levels above zero

and slightly larger pore size for silica substrate. The result is consistent with the RTIL

distribution shown in Figure 5.6B and indicates that the RTIL is accumulated at the

bottom of pores.

Table 5.2 Textural properties of RTIL-coated sorbents with different RTIL loadings BJH Mean Particle Size BET Surface Pore Volume RTIL Loading Pore Size (µm) Area (m2/g) (cm3/g) (Å) Substrate 250-500 151 311 1.18 15 wt% 250-500 92 184 0.78 25 wt% 250-500 88 136 0.58 40 wt% 250-500 94 50 0.23

1.2 Calculated pore volumes Linear Fit 1.0 /g) 3 0.8

0.6

0.4 y = -0.023 x+1.16 2 R = 0.99

Pore Volume (cm 0.2

0.0 0 10 20 30 40 50 IL Loading (wt%)

Figure 5.4 Calculated pore volumes for different [P(C4)4][Tau] loading silica gels

4.0 No Loading 3.5 15 wt% Loading 3.0 25 wt% Loading 40 wt% Loading 2.5

130

2.0 125

120

1.5 115

110

1.0 105

Mean Pore Diameter (A) Mean Pore Diameter 0 10 20 30 40 RTIL Loading (wt%) 0.5 Diff. Pore Volume (cc/g*A) 0.0 0 100 200 300

Pore Diameter (A) Figure 5.5 Calculated pore diameter distribution from BET analysis (scatter) and

Gaussian distribution fit (line) for different [P(C4)4][Tau] loading silica gels (mean pore diameters from the fitting are shown in the inset graph)

A B

Figure 5.6 Possible distribution of RTIL in pores

100

5.3.4 Thermal Stability of Ionic Coating Layer

As a potential adsorbent system applied in flue gas from coal combustion, RTIL-

coated silica gels must be thermally stable at high temperature. The thermal stability of a

representative adsorbent, 20 wt% [P(C4)4][Tau]-coated silica gel, was exanimated using

TGA as described in section 2.2.3. TGA results are shown in Figure 5.7. As water was used as solvent in the preparation of RTIL, the 3 wt% loss observed at 100oC in Figure

5.7 should be attributed to the residual water in RTIL. As water in RTIL is reported to be

favorable to CO2 capture [44], such a small amount of water residue in this work does not

o reduce CO2 capacity. An additional weight loss of 18 wt% at 700 C is attributed to the

evaporation or decomposition of the RTIL coating. The consistency of the measured

weight loss by TGA (18 wt%) with the desired RTIL loading (20 wt%) indicates a

successful preparation of [P(C4)4][Tau]-coated silica gel using the one-step method

described in section 2.1.2. The success of RTIL coating was also confirmed by the

uniform coating seen in SEM micrographs of uncoated silica gel and silica gel coated

with 20 wt% [P(C4)4][Tau], shown in Figure 5.8. The uniform coating also implies good

wettability of the silica surface by the RTIL using the one-step method. Poor wettability

is suggested by the patchy surface appearance in the image [64].

The derivative weight in Figure 5.7 shows an upper temperature limit of 300oC

for 20 wt% [P(C4)4][Tau]-coated silica gel, which is higher than the temperature at the

target flue gas treatment locations (downstream of particulate removal device: ~160oC or downstream of flue-gas desulfurization (FGD): ~60oC). The TGA results above confirm

that AA-based RTIL coated silica gel can have sufficient thermal stability to be used for the treatment of flue gas from coal combustion.

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Weight Loss (wt%) 5

0 0 100 200 300 400 500 600 700

Temperature (°C)

0.25

0.20

0.15

0.10

0.05 Derivative Weight (wt%/°C) Weight Derivative 0.00 100 200 300 400 500 600 700

Temperature (°C) Figure 5.7 Weight loss (top) and derivative weight loss (bottom) for 20 wt% ° ° [P(C4)4][Tau] coated silica gel by TGA upon heating to 700 C at a rate of 10 C/min

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2 μm

Figure 5.8 Comparison of SEM micrographs of uncoated silica gel (A) and silica gel

coated with 20 wt% [P(C4)4][Tau] (B)

5.4 Experimental results for CO2 capture using silica supported RTILs As noted in the introduction to this chapter, RTILs were supported on porous silica gel particles to increase the surface area for contacting with CO2 and to make the

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material easy to handle. RTIL-coated silica sorbents with loadings from 15 wt% to 50

wt% were tested in fixed-bed operation. Typical CO2 effluent concentration curves

(breakthrough curves) are shown in Figure 5.11. The area above each curve corresponds

to the amount of captured CO2, which in turn was used to calculate adsorbent capacity.

The slope of curve provides useful information about mass transfer; a steeper slope indicates faster mass transfer from the gas phase to the adsorbed phase.

5.4.1 Effect of RTIL loading on CO2 capacity

CO2 capacities from the breakthrough curves were calculated for [P(C4)4][Tau]-

and [P(C4)4][Met]-coated silica gels at 15 wt% to 50 wt% RTIL loadings; results are

shown in Figure 5.9. It is expected that the CO2 capacity per unit mass of adsorbent

should increase linearly with increasing RTIL loading, which was confirmed by the

results from the experiments as shown in Figure 5.9. The CO2 capacity is

thermodynamically determined by the VLE of the CO2–RTIL system. This theoretical

capacity is shown as lines in Figure 5.9. The measured capacities are close to the

theoretical capacities. Since the pore volume of the silica particle substrate (determined

by BET characterization) is limited, there is a maximum loading of RTIL of about 50

wt%, beyond which the RTIL will accumulate on the external surface of the particles and

cause particle aggregation. Such aggregation could dramatically decrease the surface area

for contacting with CO2 and block access of CO2 to some of the active site on RTIL.

Therefore, a decrease of CO2 capacity beyond 40 wt% was observed in Figure 5.9.

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)

Exp. 0.42 Theo. / g sorbent 2 0.28

mmol CO 0.14 (

0.00 0 10 20 30 40 50 60 Capacity IL Loading (wt%)

) 0.64 Exp. Theo. 0.48 /sorbent g 2 0.32

mmolCO 0.16 (

0.00 0 10 20 30 40 50 60 Capacity IL Loading (wt%)

Figure 5.9 CO2 capacities for [P(C4)4][Tau] (top) and [P(C4)4][Met] (bottom) at different loadings

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5.4.2 Effect of RTIL loading on mass transfer

To obtain mass transfer coefficients and axial dispersion coefficients for the

adsorbents at different RTIL loadings, the breakthrough curves of CO2 adsorption were

fit with an unsteady state fixed-bed model:

∂C1 ∂∂2 CC ∂ q = −−λ (5.2) ∂τPe ∂∂ ηη2 ∂ τ

∂⋅q kL =()qq* − (5.3) ∂τ u

accompanied with boundary and initial conditions:

C(τ, η) = 0, q*(τ, η) = 0 at τ = 0

∂C =Pe( C − 1) at η = 0 ∂η 1 η=0

∂C = 0 at η = 1 ∂η η=1

tu 1− ε L uL z where τ = , λ = k , Pe = , η = , C is the normalized CO2 concentration in L ε u Da L

the gas phase (C = c/c0), t is the time (s), u is the superficial gas velocity (m/s), L is the

length of bed (m), ε is the bed void fraction, k is the overall mass transfer coefficient (s-1),

2 K is the equilibrium constant, Da is the axial dispersion coefficient (m /s), q is the

normalized adsorbate concentration on the particles, and q* is the normalized adsorbate

concentration in equilibrium with gas phase concentration C.

The equilibrium of CO2 concentration in vapor phase and solid phase was determined from the VLE study in section 5.3.2.

The partial differential equations in eq. (5.2) and eq. (5.3) were solved numerically in MATLAB® using finite element method. The method is discussed in

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detail in Appendix B.2. Breakthrough curves were fit with the model to obtain the axial

dispersion coefficient Da and the overall volumetric mass transfer coefficient k associated with total surface area. The best-fit results are shown in Table 5.3; the fitted and

experimental breakthrough curves are shown in Figure 5.10. It can be seen that the

overall mass transfer coefficient decreases with increasing RTIL loading because of the

loss of surface area at high loadings as indicated in Table 5.2. In contrast, the axial

dispersion coefficient is independent with RTIL loading due to the similarity in bed and

flow patterns. The molecular diffusivity of CO2 in the RTIL was estimated from the

correlation of Wilke and Chang [149], Eq. (5.4)

TM()φ 0.5 = × −16 B DAB 1.173 10 0.6 (5.4) µBAV

in which MB is the molecular weight of solvent, μB is the viscosity of solvent (cP), VA is

the molar volume of solute at boiling point, (m3/mol), and ϕ is the association parameter

of solvent and set to be 1 as suggested by the literature [150]. The estimated diffusivity,

3.9×10-9 m2/s, is four orders of magnitude lower than the axial dispersion coefficient.

This comparison indicates that the axial dispersion is not the major resistance in CO2

mass transfer.

Table 5.3 Fitted axial dispersion coefficient Da and the effective mass transfer

coefficient k for [P(C4)4][Tau]-Si with different RTIL loadings at room temperature -1 D /m2 s-1 RTIL wt% k/s a 15 0.35 ± 0.04 25 0.17 ± 0.01 1.23×10-4 ± 0.01×10-4 40 0.08 ± 0.01

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0.8

0.6 0 c/c 0.4

0.2

0 0 100 200 300 400 500

Bed Volume

Figure 5.10 Experimental and calculated breakthrough curve for CO2 capture with

[P(C4)4][Tau] coated silica gels in different RTIL loadings (■: 15wt%, ■: 25wt%, and ■: 40wt%)

5.4.3 Effect of temperature

The effect of temperature on the fixed-bed absorption was investigated by

comparing the breakthrough curves at 298K and 333K for [P(C4)4][Tau]-coated silica gel.

It can be seen that raising the temperature causes the total capacity to drop by 25%. This

trend is consistent with the VLE study that shows a decrease in liquid phase CO2

concentration with increasing temperature. However, the sorbents can capture almost 100%

of CO2 at both temperatures for the first 250 bed volumes which is the primary working

portion in the CO2 capture process. On the other hand, the mass transfer rate at high temperature is faster than at low temperature due to the decrease in viscosity. Therefore, there is a trade-off between CO2 capacity and mass transfer rate in terms of operating

temperature.

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5.4.4 Regenerability

Due the differences in sorbent capacity and CO2 production rate in a power plant,

the CO2 sorbent is necessary to be reusable to make the process cost efficient. The regeneration of sorbent is usually done by temperature swing or pressure swing depending on sorbent’s temperature and pressure sensitivity. Because the VLE of

[P(C4)4][Tau] and CO2 has sharp gradients in both temperature and pressure, as

determined in section 5.3.2, both temperature and pressure swing can be used as

regeneration methods.

Start Point 1.00

0.75 333K (0.31 mol CO2/mol IL)

298K (0.40 mol CO2/mol IL) Flow Rate: 1 l/min

0 0.50 CO2 Inlet Conc.: 3% c/c

0.25

0.00 0 500 1000 1500 2000 2500 3000

Bed Volume

Figure 5.11 Breakthrough curve for 40 wt% [P(C4)4][Tau]-silica at different temperatures

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Start Point 1.00 Regen

0.75 Dash line: fresh sorbent Fresh Solid lines: regen. sorbent

0 0.50 Flow Rate: 1 l/min CO Inlet Conc.: 3% c/c 2

0.25

0.00 0 500 1000 1500 2000 2500 3000

Bed Volume

Figure 5.12 Breakthrough curve for 40 wt% [P(C4)4][Tau] coated silica after each regeneration cycle

The regenerability of the [P(C4)4][Tau]-coated silica sorbent was studied by

conducting the adsorption/desorption process five times. Here, to ensure complete CO2

desorption, CO2 saturated sorbents were heated at 333K under vacuum for 15 minutes

before the adsorption cycle. The regenerability of the [P(C4)4][Tau]-coated sorbent was studied by running the adsorption/desorption process five times. The breakthrough curves for the five adsorption cycles are shown in Figure 5.12. It can be seen that the capacity of sorbent decreased about 20% after the first regeneration cycle but was unchanged during the subsequent cycles. In addition, the mass transfer indicated by the slope of the breakthrough curves remained unchanged in all the regeneration cycles, which suggested a good stability of the RTIL. In sum, the results above showed an acceptable regenerability of the RTIL coated silica sorbent in CO2 adsorption/desorption cycles.

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5.5 Conclusion

AA-based RTILs were studied for CO2 capture in a batch calorimeter and a fixed- bed apparatus. BET analysis revealed that most of the RTIL coated on the sorbent surface accumulated at the bottom of the pores and was not evenly distributed on the surface.

This is important in the kinetic study, which requires knowledge of the mass transfer pathway. TGA analysis confirms the thermal stability of the sorbents up to 300°C, which is higher than the temperature at the most of the flue gas treatment locations. Fixed-bed adsorption studies showed maximum CO2 capacities of 0.45 and 0.60 mol CO2/mol of IL for [P(C4)4][Tau] and [P(C4)4][Met] coated silica sorbents respectively. The trend of CO2 capacity with RTIL loading suggested that there is an interaction between the hydroxyl group on silica surface and the amine groups which decreases the CO2 capacity. The maximum RTIL loading was also determined to be 50 wt%. Mathematical modeling of the breakthrough curves indicated that the overall mass transfer coefficients decreases with increasing RTIL loading because of the loss of contacting surface area. The axial dispersion coefficient, on the other hand, is independent with RTIL loading. High temperature was determined to reduce the solubility of CO2 in the RTIL coating layer but enhanced mass transfer in the layer. The regenerability of the sorbents was also confirmed to be acceptable after the five adsorption/desorption cycles. In summary, AA- based RTIL coated silica sorbents are promising solid sorbents for CO2 capture from flue gas in coal combustion power plants.

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Chapter 6 - Room Temperature Ionic Liquid-Coated Sorbents

for Hg and Combined Hg -CO2 Capture from Coal Combustion Flue Gas

6.1 Introduction Ionic liquids (ILs) are liquids composed only of ions. They can be simply produced by heating metallic salts to above their melting point. For example, NaCl will become an IL above its melting point of 801°C [151]. Such high melting temperatures

limit their application. However, ILs that remain in liquid form at or below room

temperature were found by Walden in 1914 [152] and have been developed since then.

These room temperature ionic liquids (RTILs) usually consist of a large, asymmetric cation such as 1-butyl-3-methylimidazolium, 1-alkylpyridinium, N-methyl-N- alkylpyrrolidiniumand, or tetraalkylphosphonium and an anion; there are a wide range of anions used in RTILs. RTILs have a number of properties that make them promising solvents for flue gas treatment. First, RTILs have very low vapor pressures compared with many other organic and inorganic solvents. This feature can minimize solvent loss during long-term gas treatment process and can guarantee a low solvent concentration in the lean gas stream. Second, RTILs have excellent thermal stability at elevated temperatures. For example, 1-butyl-3-methyl-imidazolium chloride is stable up to 200°C, and 1-butyl-1-methyl pyrrolidinium chloride does not decompose until 325°C [63]. This high temperature limit gives RTILs an edge over traditional solvents in elevated temperature application such as flue gas treatment.

RTILs have been reported to be good solvents for a number of gas pollutants present in flue gas from coal combustion. Pinto and coworkers found several ILs that are

112

good solvents for oxidized Hg and elemental Hg in simulated flue gas at 160oC. These

RTILs were coated on the surface of porous particles that have sulfur-contained chelating ligands to make nanostructured chelating adsorbents; in these materials, Hg from the vapor phase dissolves in the IL and subsequently bonds to the chelating ligands.

Laboratory-scale tests using simulated flue gas have shown that these adsorbents have higher Hg capacities than current commercially available adsorbents [61, 63, 64]. A pilot- scale trial is needed to test the performance of these novel Hg adsorbents in capturing both oxidized and elemental Hg from an actual coal combustion flue gas. For this purpose, a slipstream of flue gas from coal-fired power plant is a proper gas source for the testing.

Some functionalized ILs have also been reported to have high CO2 solubility

compared to traditional organic solvents [42, 44, 153]. The work presented in Chapter 5 discussed the effectiveness of amino acid (AA)-based RTILs for CO2 capture. Since

sulfur has been identified as the active site for Hg capture in nanostructured chelating

adsorbents, it is hypothesized that, with proper selection and design, AA-based RTILs

that contain both amine and sulfur can capture CO2 and Hg simultaneously.

Since RTILs were identified to be good solvents for heavy metal vapors, their Hg

capture performance under different conditions needs to be assessed. Therefore, the first

part of this chapter discusses the testing of RTIL-coated sorbents for Hg capture from

simulated and coal combustion flue gases, followed by a discussion of Hg capacity of

studied sorbents under low Hg vapor concentration. To validate the hypothesis of

simultaneous capture of Hg and CO2, the combined capture of Hg and CO2 using an AA-

based RTIL that contain both amine and sulfur groups was investigated.

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6.2 Objectives The objectives of this research reported in this section are to (1) design and set up

a properly scaled apparatus for slipstream testing of Hg sorbents; (2) assess the Hg

capture performance of RTIL-coated sorbents under simulated and real flue gas

conditions; (3) determine the Hg capacity of RTIL-coated sorbents at low Hg vapor concentration via adsorption isotherms; and (4) assess the feasibility of simultaneous CO2

and Hg removal using AA-based RTILs that contain both amine and sulfur groups, and to identify the potential competition between CO2 and Hg.

6.3 Results and Discussion

6.3.1 Hg capture Four RTIL-based sorbents were prepared for Hg capture: 1-Butyl-3-methylimidazolium chloride ([bmim]Cl)-coated 3-mercaptopropyltrimethoxy-silane (MPTS)- silica gel ([bmim]-MPTS-Si), methylpolyoxyethylene(15)octadecanammonium chloride

(MEC) coated MPTS-silica gel (MEC-MPTS-Si), tetrabutylphosphonium taurine

((P4)4[Tau]) coated silica gel ((P4)4[Tau]-Si), and tetrabutylphosphonium methionine

((P4)4[Met]) coated silica gel ((P4)4[Met]-Si). The detailed synthesis procedure for each sorbent can be found in section 2.1.2 and 2.1.3. Characterization of the sorbents was discussed by Ji and coworkers [105] and in section 5.4 in this work. These sorbents were tested for Hg capture in a fixed-bed testing unit using simulated flue gas, an entrained- flow testing unit using simulated flue gas, and a fixed-bed test unit using real flue gas

from coal combustion.

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6.3.1.1 Bench-scale testing in fixed-bed Hg sorbents, including 25 wt% [bmim]-MPTS-Si, 25 wt% MEC-MPTS-Si, 40 wt% (P4)4[Tau]-Si, and 40 wt% (P4)4[Met]-Si, were tested in a bench-scale fixed-bed

apparatus to determine their Hg capacity. The measurement method is described in

section 2.3.7. Hg capacities were determined from the breakthrough curves. These

capacities, along with the capacity of activated carbon (one of the most mature Hg

control technologies) are compared in Table 6.1. It can be seen that under simulated flue

gas conditions all of the studied sorbents have very high oxidized Hg capacities

compared with that of activated carbon. The capacity for elemental Hg is slightly lower

than that of oxidized Hg because elemental Hg is less soluble in the RTIL layer than is

oxidized Hg. On the other hand, when both oxidized and elemental Hg are present in gas

phase, the measured total Hg capacities were lower than the summation of the capacities

of single species. This could be due to a limitation of the total number of active sites –

sulfur – in the sorbents for oxidized Hg and elemental Hg.

Table 6.1 Hg capacities (Hg0 and Hg2+) of studied sorbents and activated carbon 25 wt% [bmim]- 25 wt% MEC- 40 wt% 40 wt% Activated Adsorbent MPTS-Si MPTS-Si (P4)4[Tau]-Si (P4)4[Met]-Si Carbon[154] Hg2+ Capacity 17 >58 12 10 0.1 – 3.3* (mg/g) Hg0 Capacity 5 No capacity 10 9 0.2 – 1.4* (mg/g) Measured Hg2+ Hg0 19 Not tested 14 Not tested N/A Capacity (mg/g) 0 * The experiments in this work were conducted in simulated flue gas with a Hg (Hg or HgCl2) 3 concentration of ~300 mg/Nm in N2 carrier gas. The experiments for activated carbon were 0 3 conducted in simulated flue gas with a Hg (Hg or HgCl2) concentration of ~50 mg/Nm with simulated flue gases containing O2 (~6 vol%), CO2 (~12 vol%), H2O (~7 vol%), select concentrations of HCl, SO2 , and NOx , and balance N2 [154].

115

6.3.1.2 Bench-scale testing in entrained flow Hg capture performance of 25 wt% [bmim]-MPTS-Silica gel sorbent in entrained flow was investigated in an entrained-flow reactor. The apparatus and measurement method was introduced in section 2.3.8. In this test, the reactor temperature was maintained at 140oC, and the sorbent injection rate was at 0.5 g/hr. Prior to the test, the sorbents were ground to a smaller size (around 50 – 100 µm) for high contacting area.

The elemental Hg concentration at the inlet of the reactor was 22 μg/Nm3. The effluent

Hg concentration was recorded and shown in Figure 6.1. The Hg concentration steadily decreased after sorbents were injected into the flow, and did not reach a steady-state concentration after 25 min. This could be due to slow mass transfer of Hg in the RTIL coating layer; a longer residence time is needed. Over the course of the experiment, sorbent accumulated gradually on the particle filter at downstream of the reactor and built a pancake fixed bed on the filter. The Hg removal rate increased with the accumulation of sorbents on the filter due to the increasing of contacting time between Hg vapor and sorbents in the pancake bed on the filter. The intercept of breakthrough curve at x axis indicates that removal may reach 100% at 40 min. With the assumption that all of the adsorption was occurred at the fixed bed on the filter, the minimum residence time for

100% Hg0 removal in a fixed bed can be calculated by

L t = 40 min (6.1) v in which L40min is the bed length at 40 min (cm), and v is gas superficial velocity (cm/s).

A L40min of 0.08 cm was calculated from the sorbent injection rate, the filter surface area, and the bed density. At a gas velocity of 0.47 m/s, the minimum residence time for 100%

Hg0 removal in a fixed bed was determined to be 0.17 ms. The residence time in the

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laboratory fixed-bed tests discussed in section 6.3.1.1 was approximately 10 ms which is

long enough for 100% Hg removal.

Injection Point 25

20 ) 3

g/m 15 µ

10 Conc. ( 0

Hg 5

0 0 5 10 15 20 25

Time (min) Figure 6.1 Entrained-flow breakthrough curve for Hg0 capture using 25 wt% [bmim]-MPTS-Silica gel sorbent

6.3.1.3 Slipstream testing in fixed-bed In this trial, a slipstream of flue gas was pulled downstream of the electrostatic precipitator of a 1,300-megawatt coal-fired power plant (operated by Duke Energy Co.).

For each adsorbent test, a fixed bed (1 inch inside diameter and 0.6 inch deep) was packed and continuously tested in the flue gas stream for approximately two weeks. Flue

gas samples were drawn at inlet and outlet of the bed for Hg determination with modified

Ontario Hydro method as described in section 2.3.6.

Two categories of Hg adsorbents were tested in the trial: (1) AA-based RTIL- coated sorbents that were used in the CO2 capture study in Chapter 5 and (2) RTIL coated

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chelating sorbents which has been studied in previous work [61, 63, 64]. The first category includes 40 wt% [(P4)4][Tau]-silica, 40 wt% [(P4)4][Met]-silica, and 40 wt%

[(P4)4][Tau][Cys]-silica ([Tau]:[Cys] = 4:1). The second category includes 25 wt% MEC-

MPTS-silica and 25 wt% [bmim]Cl-MPTS-silica. For each test, three to six grams of sorbent were loaded in the adsorber and run with flue gas for a maximum time of two weeks. The Hg removal rate histories for each sorbent are shown in Figure 6.2 to Figure

6.5. Generally, all tested sorbents could capture more than 80% of oxidized Hg in the first day of the test, which suggested that the tested sorbents are effective for capturing

oxidized Hg from actual flue gas. [(P4)4][Tau]-silica and [bmim]Cl-MPTS-silica continuously removed more than 80% of the total Hg for an extended period of time. The fast breakthrough of other sorbents is attributed to the oxidation and degradation of RTIL by acidic components in the flue gas at elevated temperature.

Mercury capture performance was better for oxidized Hg than for elemental Hg. It

is widely accepted that elemental Hg is more difficult to capture than oxidized Hg

because of its high chemical stability and low solubility in water. The removal of

elemental Hg by the sorbents in this work depends on physical solubility in ionic liquid

layer. It has been discovered that elemental Hg can dissolve in [bmim]Cl but not in MEC

[64], which was confirmed in this trial.

The test validated the performance and stability of the sorbent under the true flue gas conditions. Slipstream testing will also advance commercial-scale implementation of these adsorbents. For example, one of the potential issues in implementation is the accumulation of fly ash on sorbent bed. Depending on the efficiency of the particulate removal device at upstream of the Hg removal operation, a certain amount of fly ash is

118 present in the flue gas and accumulates on the sorbent bed. The accumulated fly ash can reduce or even block the gas flow. An extra particulate removal device is recommended for implementation of this technology. In addition, since the slipstream testing in this work lasted less than two weeks, which is much shorter than the proposed working cycle for this type of sorbent (2-6 months), a longer term is recommended in future testing.

6.3.2 Hg capture in low vapor concentration To expedite the experiments, the inlet Hg concentrations in the bench-scale fixed- bed testing and the slipstream testing in this work were higher than the typical Hg concentration in coal combustion flue gas. Because Hg is captured through chemisorption in this work, a favorable isotherm is expected. In such case, capacity at low Hg vapor concentration is close to the measured capacities at high concentration. This hypothesis can be validated by the isotherm of Hg adsorption using the RTIL coated sorbents.

However, there are great difficulties in the experimental measurement for Hg isotherm as the Hg vapor source is difficult to control at the 1 - 5 ppb level and the concentration determination has significant error at such low concentration. Therefore, the isotherm was calculated through chemical equilibrium and phase equilibrium as discussed in the following.

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100

(%) 40

Total Hg Removal Percentage Percentage Removal Hg Total 0 1 2 3 4 5 6 7 8 9 10 Time (Day)

Figure 6.2 Hg removal percentages over time for [bmim]Cl-MPTS-silica (top: total Hg, bottom: oxidized Hg (red) and elemental Hg (green))

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100

60 (%) 40

20 Total Hg Removal Percentage Percentage Removal Hg Total 0 2 3 4 Time (Day)

Figure 6.3 Hg removal percentages over time for MEC-MPTS-silica (top: total Hg, bottom: oxidized Hg (red) and elemental Hg (green))

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Figure 6.4 Hg removal percentages over time for [(P4)4][Tau][Cys] - silica (top: total Hg, bottom: oxidized Hg (red) and elemental Hg (green))

122

Figure 6.5 Hg removal percentages over time for [(P4)4][Tau] - silica (top: total Hg, bottom: oxidized Hg (red) and elemental Hg (green))

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The capture of Hg by AA-based RTIL coated solid sorbents can be considered

into two steps: (1) solution of Hg in the RTIL coating layer, and (2) chelating with active

sites (sulfur). The solution of Hg in the RTIL coating layer can be described by Henry’s

law:

PHg= Hx Hg (6.2)

in which PHg is the partial pressure of Hg vapor, H is the Henry’s law constant, and xHg is the mole fraction of Hg in liquid. There is very limited data on Henry’s law constants for

Hg in RTILs. Ji and coworkers reported 2.7 mg of Hg dissolved in 0.25 g of RTIL above a Hg concentration of 66 ppbv [62], which can be converted to a Henry’s low constant of

0.08. This value is adopted in this work for the estimation of Hg isotherm in AA-based

RTIL.

The chelating mechanism between Hg and sulfur in AA-based RTIL is still unknown. It is reasonable to adapt the mechanism Hg chelation by sulfur in aqueous systems to this work. George and coworkers studied the structures of Hg -

dimercaptopropanesulfonic acid (DMPS), which has a similar active site structure to the

species used in this work [155]. One of the possible coordination structures is shown in

Figure 6.6; this structure suggests a S:Hg ratio of 4:1. The chelation of Hg by S was also

characterized and confirmed by Abu-Daabes and Pinto through Far-FTIR analysis [64].

Based on structure proposed by George and coworkers, the following reversible reaction can be suggested for the chelation reaction.

K Hg+4 S ← → HgS4 (6.3)

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Figure 6.6 Calculated structures of possible Hg2+ — DMPS complexes which shows the 4:1 complex that forms in the presence of excess DMPS [155]

Literature data for the equilibrium constant K of the reaction in Eq. (6.3) are not available, but the equilibrium constant can be calculated from the standard Gibbs free energy change of the chelation reaction using Eq. (6.4). The standard Gibbs free energy change was obtained from the molecular simulation using Gaussian® 93. The structures of AA, Hg and their chelating complex were optimized by using DFT/Becke3LYP method with 6-311+G(d,p) basis. LANL2DZ basis was added to the set when Hg is present in the molecule structure. Using [(P4)4][Tau] as an example, the calculated ∆G at

298 K and 101 kPa for one mole of elemental Hg chelating with one mole of Tau- is -17 kJ/mol. For oxidized Hg, the calculated ∆Go is -1434 kJ/mol.

∆Go lnK = − (6.4) RT

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With the chemical equilibrium and phase equilibrium discussed above, the isotherm of elemental Hg adsorption by 20 wt% [(P4)4][Tau] coated silica sorbent at 298

K and 101 kPa was calculated and shown in Figure 6.7. The conditions used in the calculation were different from that in a typical flue gas due to limitations of time. In addition, the exclusion of the cation in the calculation for simplification purpose may also bring error in the calculation. However, since the purpose of using molecular simulation in this work was to qualitatively describe the shape of the isotherm, the error resulting from these assumptions should be acceptable. From the isotherm it can be seen that the isotherm is favorable because of chemisorption (chelating between Hg and S). Based on these calculations, the Hg capacity under typical coal combustion flue gas condition (1-5 ppb of Hg) is about 30% lower than the capacity under the experimental condition in this work (~ 66 ppb of Hg), which is still acceptable. In case of oxidized Hg, since the calculated ∆Go is two orders of magnitude higher than elemental Hg, the isotherm will be a rectangular isotherm and the capacity at typical flue gas condition will be close to the value measured in this work.

126

18 Hg conc. in this work

10 Typical Hg conc. in coal 8 combustion flue gas 6

Capacity (mg Hg/g sorbent) 2

0 10 20 30 40 50 60 70 80 90

Hg vapor concentration (ppb)

Figure 6.7 Calculated isotherm of elemental Hg adsorption by 20 wt% [(P4)4][Tau] coated silica sorbent at 298 K and 101 kPa

6.3.3 Hg and CO2 combined capture Two sulfur-contained AAs (taurine and methionine) were synthesized into RTIL-

coated sorbents ([(P4)4][Tau] and [(P4)4][Met]) by following the procedure in section

2.1.2. Their potential capability of simultaneous capture of Hg and CO2 will be discussed

via experimental evidence and theoretical evidence.

6.3.3.1 Experimental Evidence The ideal approach to assess the feasibility of simultaneous capture is to test the

adsorption performance of CO2 and Hg in the presence of both two species in the gas

phase. However, such simultaneous measurements could not be performed due to the

limitation of the existing instruments. Given the fact that the concentration of Hg in flue

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gas is about one billion orders of magnitude lower than CO2, it is reasonable to expect

that the influence on Hg capture caused by the potential competition should be much

more dramatic than that on CO2. Thus, this study focused on the impact of CO2 on Hg

capture.

Bench scale of [(P4)4][Tau] and [(P4)4][Met] with and without CO2 was performed

in a fixed-bed apparatus. The results, shown in Table 6.2, indicate that adding CO2 to the

gas phase reduced capacities by only 30%.

Table 6.2 Bench scale fixed-bed testing results for 40 wt% [(P4)4][Tau] and

[(P4)4][Met] coated silica gels (Testing Conditions: 30 – 48 ppb Hg in N2 carrier gas at ~ 80 ˚C) 0 0 Ionic Liquid Hg Capacity Hg Capacity with 20% CO2 [(P4)4][Tau] 10 mg/g 6 mg/g [(P4)4][Met] 9 mg/g 6 mg/g

The Hg capture performance using real flue gas was assessed for [(P4)4][Tau] and

[(P4)4][Tau] in the slipstream test apparatus as discussed in section 6.3.1.3. Since the flue gas contains about 15% CO2, the slipstream results can also provide more practical

information to the combined capture study. From Figure 6.5, it can be seen that the

[(P4)4][Tau] had a total Hg removal rate above 80% for eight days, a promising

performance for Hg capture in the presence of CO2 in the flue gas.

6.3.3.2 Theoretical Evidence

The difference of concentration in the flue gas for CO2 and Hg requires the

sorbents to have the ability of continuous Hg capture and regeneration for CO2 sorption.

This process depends on the strong chemical bonding of Hg and weak bonding of CO2 to the adsorbent, which would make the adsorbed Hg remain on the sorbent during the CO2 128

regeneration process. Molecular simulation was used to validate the hypothesis. The

binding energy of CO2 and Hg to the RTIL species was determined by calculating the

enthalpy of reaction through molecular simulation with Gaussian® 93. Two possible

routes were considered for combined capture based on the reactions sequences shown in

Figure. 6.8 and Figure. 6.9 for elemental Hg and oxidized Hg respectively. The problem

was simplified by considering only the AA molecule, which is the reactive part of an AA-

based RTIL The structures of amino acids, CO2, Hg and their chelating complexes were

optimized by using DFT/Becke3LYP method with 6-311+G(d,p) basis and shown in

Figure. 6.10 and Figure. 6.11. LANL2DZ basis was added to the set when Hg is present

in the molecule structure. The calculated enthalpies for the reactions between amino acid,

oxidized Hg, and CO2 at 298K are listed in Table 6.3. The enthalpy of carbamate formation for [(P4)4][Tau] is of the same order of magnitude of the experimental heat of

adsorption values in 4.4.5. The absorption of oxidized Hg, either from amino acid or

carbamate, is exothermic with an enthalpy of reaction that is three orders of magnitude

larger than that of the formation of carbamate, which indicates a much stronger bonding

between the amino acid and oxidized Hg. The calculated reaction enthalpy suggests that

it is possible to run the process with continuous oxidized Hg removal while capturing the

CO2 on an adsorption/desorption cycle basis. However, in case of elemental Hg, as

shown in Table 6.4, the bonding between Hg and amino acid or Hg and carbamate is

comparable to CO2 –amino acid bonding. This molecular simulation result suggests that

the captured elemental Hg might be released from the sorbent system during a CO2

regeneration process.

129

- ΔH3 ΔH1 AA -CO2

- 2+ - AA Hg -AA -CO2

- 2+ ΔH2 AA -Hg ΔH4

2+ Figure. 6.8 Possible reaction routes among amino acids, CO2 and Hg molecules

Table 6.3 Calculated enthalpy for each routine shown in Figure. 6.8 Calculated enthalpy (kJ/mol) Sorbent ΔH1 ΔH2 ΔH3 ΔH4 [(P4)4][Met] -54 -1630 -1502 73 [(P4)4][Tau] -46 -1465 -1346 73

- ΔH6 ΔH1 AA -CO2

- 0 - AA Hg -AA -CO2

- 0 ΔH5 AA -Hg ΔH7

0 Figure. 6.9 Possible reaction routes among amino acids, CO2 and Hg molecules

Table 6.4 Calculated enthalpy for each routine shown in Figure. 6.9 Calculated enthalpy (kJ/mol) Sorbent ΔH1 ΔH5 ΔH6 ΔH7 [(P4)4][Met] -54 -21 -12 -45 [(P4)4][Tau] -46 -19 -13 -40

130

- - Met Met -CO2

- 2+ Met -Hg Met--Hg0

0 - 2+ - Hg -Met -CO2 Hg -Met -CO2

- - 2+ - 0 Figure. 6.10 Optimized molecular structure of Met -CO2, Met -Hg , Met -Hg , and - 2+ - 0 Met -CO2-Hg , Met -CO2-Hg

131

- - Tau Tau -CO2

- 0 Tau -Hg Tau--Hg2+

0 - 2+ - Hg -Tau -CO2 Hg -Tau -CO2

- - 2+ - 0 Figure. 6.11 Optimized molecular structures of Tau -CO2, Tau -Hg , Tau -Hg , and - 2+ - 0 Tau -CO2-Hg , Tau -CO2-Hg complexes

6.4 Conclusion Several RTIL-coated silica sorbents, including 25 wt% [bmim]-MPTS-Si, 25 wt%

MEC-MPTS-Si, 40 wt% (P4)4[Tau]-Si, and 40 wt% (P4)4[Met]-Si, were investigated for

Hg capture in both simulated flue gas and coal combustion flue gas. In the bench-scale fixed-bed tests using simulated flue gas, all of the studied sorbents showed higher oxidized Hg capacity than activated carbon. For elemental Hg, the studied sorbents, except 25 wt% MEC-MPTS-Si, also have higher capacity than activated carbon. It was

132

also confirmed that 25 wt% [bmim]-MPTS-Si sorbent has the ability of capturing

elemental Hg in entrained flow. But the slow mass transfer rate requires a longer

residence time in the entrained flow for the sorbent. Slipstream testing indicated that all

of the studied sorbents are capable of capture oxidized Hg under the condition of coal

combustion flue gas. 25 wt% [bmim]-MPTS-Si and 40 wt% (P4)4[Tau]-Si have the best performance as they could capture more than 80% of total Hg for five days and eight days respectively. The Hg speciation history from the slipstream testing suggested that the studied sorbents work better for oxidized Hg than elemental Hg.

Hg capacity under the condition of low Hg vapor concentration was studied through calculating the adsorption isotherm from chemical and phase equilibrium. The isotherm showed an approximately 30% decrease in elemental capacity from the high Hg vapor concentration in this work to a low Hg concentration in the typical coal combustion flue gas. Oxidized Hg, however, does not change significantly because of the high ∆Go

for the chelating of Hg and RTIL.

The possibility of simultaneous capture of Hg and CO2 using AA-based RTIL

sorbents was assessed through experimental and theoretical routes. Experimental

evidence suggests that there is limited competition between the two species in the

adsorption. Theoretical evidence confirmed that the bonding between oxidized Hg and

AA is much stronger than that of CO2 and AA. The results suggest that combined capture

can be carried out using continuous Hg capture while CO2 is captured through

adsorption/desorption cycles.

133

Chapter 7 - General Conclusions

The thermodynamics and kinetics of carbon dioxide and mercury removal using

organic solvents and ionic liquid coated particles were investigated in this work.

Specifically, thermodynamic properties, including vapor liquid equilibrium, heat of

absorption, and heat capacity were studied for aqueous amine systems for CO2 capture;

an amino acid (AA)-based room temperature ionic liquid (RTIL) adsorbent system was

developed for CO2 and Hg removal; and the Hg capture performance of RITL coated

adsorbents was assessed in a slipstream trial using coal combustion flue gas.

The thermodynamics of aqueous amine solvent systems, aqueous piperazine (PZ)

and aqueous ethanolamine (MEA), were investigated in Chapter 3. The purpose of the

study was to obtain a fundamental thermodynamic knowledge of the solvent systems and

provide supporting information for the study of the ternary systems (water – amine –

CO2). Total vapor pressures and heat capacities of aqueous PZ and aqueous MEA at

different concentrations and temperatures were measured using a modified batch

calorimeter. These experimental data were fit with a thermodynamic model incorporating

the electrolyte non-random two liquid (eNRTL) model as an activity coefficient model

and Soave-Redlich-Kwong (SRK) equation of state as fugacity coefficient model. Binary

interaction parameters in eNRTL model were obtained and used in the ternary system

study. Comparison with independent literature data confirms the accuracy in

experimental measurement and mathematical modeling.

In Chapter 4, the thermodynamics of CO2 absorption in two aqueous amine

systems – PZ-H2O and MEA-H2O – were studied. To simplify the experimental measurement but still keeps a high accuracy on the results, the Barker reduction method

134

was, for the first time, applied to the study of CO2 – aqueous amine systems. The vapor pressure and heat of absorption for CO2 – aqueous amine systems were measured using a

modified batch calorimeter. Using the Barker reduction, the experimental data were fit in

a thermodynamic model which includes the eNRTL model as activity coefficient model

and the SRK equation of state as fugacity coefficient model. The best-fit value of the

parameters in the activity coefficient model and their confidence intervals were

calculated using an in-house calculation package. Partial pressure of CO2 and heat of

absorption predictions were compared with independent literature data. The agreement of

prediction and independent literature data indicates a successful application of the Barker

reduction to the thermodynamic study of CO2 – aqueous amine system. The importance of combined correlation of VLE and heat of absorption data in the accurate prediction of the two properties was also confirmed by comparing the prediction from single and multiple data sets correlation. Using the Barker reduction, which involves more complicated calculations but simpler measurements, can minimize experimental error and benefits from the fast-growing computing resources. The results from this work will provide a basis of experimental and correlation method for the screening of other novel

CO2 solvent systems.

Two of the major concerns from the coal combustion industries regarding

deploying new pollution control devices are high capital and operating costs and the limited space available for the installation of addition pollution control devices. To solve

these problems, an amino acid-based room temperature ionic liquid (AA-based RTIL)

system supported on porous silica substrate was developed to combine the control of two

critical pollutants – mercury vapor and carbon dioxide - into a single process. In this

135

adsorbent system, an ionic liquid layer that contains both amine and sulfur groups is

supported on mesoporous silica particles. BET analysis showed that these RTIL-coated

sorbents have high surface area and pore volume thanks to the porosity of the substrate.

With the increasing of RTIL loading, both surface area and pore volume decrease linearly

due to the occupation of pores by RTIL. Pore size, on the other hand, does not drop significantly with increasing RTIL loading, which suggests that most of the RTIL accumulates across the pores instead of being evenly distributed on the surface. TGA analysis confirmed the thermal stability of the RTILs at temperatures up to 300°C.

Together with SEM micrographs, TGA analysis also confirmed successful one-step

synthesis of AA-based RTIL coated silica gel.

To understand the basis of AA-based RTIL on CO2 and Hg capture, these sorbent

systems were firstly investigated for CO2 removal. The reaction between a representative

AA-based RTIL and CO2 was confirmed by FTIR analysis. The thermodynamic

properties for sorption of CO2 in representative AA-based RTIL were studied in a

modified batch calorimeter. The AA-based RTIL had high CO2 capacity and similar heat

of absorption comparable to that of a benchmark solvent – monoethanolamine. The AA-

based RTIL was also supported on porous silica and packed in a fixed-bed apparatus.

Maximum CO2 capacities of 0.45 and 0.55 mmol CO2 per gram of sorbent were found for

[P(C4)4][Tau]- and [P(C4)4][Met]-coated silica gel respectively at room temperature with

3% of CO2 mixed in air. The capacity increases with the increasing of RTIL loading due to the addition availability of amine active sites. CO2 capacity reaches a maximum at

around 40 wt% RTIL loading beyond which all the available pore volume is filled by

RTIL and the excess RTIL on the external surface of particle causes aggregation. The

136

overall mass transfer coefficients for adsorbents with different RTIL loadings were

obtained by fitting the breakthrough curves with an un-steady fixed-bed model. The

calculated overall mass transfer coefficient decrease with increasing RTIL loading

because of the loss of surface area at high loading. The axial dispersion coefficient is

independent of RTIL loading due to the similarity in fixed-bed and flow patterns.

Temperature was found to reduce CO2 capacity but increase the mass transfer rate. An

AA-based RTIL had good regenerability in CO2 capture through several

adsorption/desorption cycles. The capacity of sorbent decreased about 20% after the first

regeneration cycle but was unchanged during subsequent cycles.

The mercury adsorption performance of several RTIL-coated solid sorbents were

studied in a fixed-bed testing unit using simulated flue gas, an entrained-flow testing unit using simulated flue gas, and a fixed-bed testing unit using real flue gas from coal combustion. Fixed-bed tests using simulated flue gas showed a maximum oxidized Hg capacity of more than 58 mg Hg2+/g sorbent using 25 wt% MEC-MPTS-Si and a

0 maximum elemental Hg capacity of 10 Hg /g sorbent using 40 wt% (P4)4[Tau]-Si. When

both oxidized and elemental Hg are present in gas phase, the measured total Hg

capacities were lower than the sum of the capacities of the single components, which

indicates a possible competition for active sites on the sorbents. The Hg capacities for all

sorbents studied are higher than that of activated carbon, one of the most widely used Hg

sorbents.

The Hg capture performance of 25 wt% [bmim]-MPTS-Si in entrained flow was

assessed in an entrained-flow reactor located in US EPA, Research Triangle Park, NC.

Gradually-increased elemental Hg removal was observed from the breakthrough curve,

137

which indicates that the sorbent is capable of capturing elemental Hg in the entrained

flow. The breakthrough curve also suggests that the residence time of sorbent during

entrained-flow may not be long enough and some of capture may occur at the filter

located at downstream of the reactor.

Slipstream testing using coal combustion flue gas for 40 wt% [(P4)4][Tau]-Si, 40

wt% [(P4)4][Met]-Si, 40 wt% [(P4)4][Tau][Cys]-Si ([Tau]:[Cys] = 4:1), 25wt% MEC-

MPTS-Si, and 25wt% [bmim]Cl-MPTS-Si showed that all studied Hg sorbents are capable of capture oxidized mercury in a fixed-bed operation. [(P4)4][Tau]-Si and

[bmim]Cl-MPTS-Si have the best Hg removal performance and can remove more than

80% of total Hg for at least five days. The speciation removal history indicates that the

studied sorbents have higher removal rate for oxidized Hg than elemental Hg, which can

be attributed to the low solubility of elemental Hg in ILs. The results from the slipstream

testing will advance commercial scale implementation of the adsorbents.

The feasibility of simultaneous capture of Hg and CO2 were investigated using

both experimental evidence and theoretical arguments. Experimental results for Hg

capture in the presence of CO2 indicated that Hg capacity dropped by 30% when 15%-

20% of CO2 is present in the gas phase. This could be due to the decrease of free space in

RTIL when CO2 is dissolved in the IL, which in turn decreases the solubility of Hg in the

IL. The other possible explanation for the Hg capacity drop is the competition between

Hg and CO2 for amine groups. The hypothesis that CO2 can be captured on the basis of

adsorption/desorption cycles while mercury can undergo a continuous adsorption process

because of its extremely low concentration in flue gas was validated by calculating the

bonding energy of active site, CO2, and/or Hg through molecular simulation. The

138 encouraging results suggest that the studied system is promising on simultaneous capture of CO2 and mercury from coal fired flue gas.

In summary, to help solve existing problems and improve the current technologies for CO2 and Hg capture from coal combustion flue gas, the thermodynamics and kinetics of CO2 and Hg capture were investigated through innovative experimental and theoretical methods in this work. Through experiments at different scales, the thermodynamic and kinetic behaviors of the capture processes were revealed. The mathematical modeling of the experimental results generalized and quantified the behavior, providing a pathway to estimate the thermodynamic and kinetic properties through the theoretical method. The combination of experimental and theoretical methods in the study of thermodynamics and kinetics in this work facilitates the design and optimization of the processes of CO2 and

Hg capture from coal combustion flue gas.

139

Chapter 8 - Future Work

Based on the results and conclusions from this work, the following

recommendations are offered to explore the other models and approaches in the

thermodynamic study of CO2 capture, apply the studied model and method to new

solvent systems, and assess the long-term performance of Hg sorbents in coal combustion flue gas.

8.1 Assessment of other activity coefficient models Electrolyte Non Random Two Liquid (eNRTL) model was used as activity

coefficient model in this work to study the thermodynamic properties of CO2 solvents because of its popularity and availability in published data. There are a number of other activity coefficient models designed for electrolyte solutions, including the refined eNRTL model [156], the extended UNIQUAC model [157], and the Mixed Solvent

Electrolyte model [158]. Refined eNRTL was established on the basis of the original eNRTL and eliminates the assumptions of constant ionic charge fraction. Although the refinement increases the complexity, it provides a more rigorous framework to the study of multi-electrolyte systems. The extended UNIQUAC model uses the UNIQUAC model as short-range ionic interaction term and the extended Debye-Huckel model as long- range interaction term. Even though the extended UNIQUAC model is applied less often than the eNRTL model, its successful use for CO2 – aqueous amine systems was reported

[159]. Mixed Solvent Electrolyte (MSE) model is a commercialized model designed for

electrolyte solution by OLI Systems, Inc. The MSE model uses the UNIQUAC model for

the short-range term and Pitzer Debye-Hückel model for the long-range term. However, different from the extended UNIQUAC model, the MSE model uses quadratic

140

temperature dependence in the short-range term. Although these activity coefficient

models mentioned above have proven to be effective for electrolyte solutions, their

performance in the thermodynamic study of CO2-aqueous amine systems using the

Barker reduction merits investigation. Modules of the corresponding activity coefficient

models can be built and merged to the calculation package for assessment.

8.2 Fugacity approach in thermodynamic study of CO2 capture The thermodynamic modeling framework in this work uses an activity coefficient

model to describe the non-ideality in liquid phase. An alternative approach is to use an

Equation of State (EoS) to represent the fugacity coefficients in liquid phase. To apply

EoS to an electrolyte system like CO2-loaded aqueous amine, EoS models must consider the ionic interaction in liquids. Several electrolyte EoS models have been developed and used in the thermodynamic study of CO2 absorption [160-163]. Integration of EoS models into the Barker reduction framework is recommended. The result and the comparison with activity coefficient method will provide an assessment of the performance for each method.

EoS models can also be applied to non-aqueous systems, such as the ionic liquid systems in this work, and have successfully modeled the physical solution of CO2 in ILs

[146-148]. Chemical reactions of CO2 and functionalized IL may complicate the

modeling, but it is recommended for further study as functionalized IL shows promising

performance in CO2 capture. In addition, thermodynamic modeling using EoS models for

IL systems will extend fundamental understanding of these systems.

141

8.3 Expended solvent systems in thermodynamic study of CO2 absorption This work focused the application of Barker reduction in the thermodynamic

study of CO2, thus only two benchmark CO2 solvent systems (piperazine and

monoethanolamine) were used in this work because of their availability in published data.

Since the Barker reduction has been validated in this work, it is recommended to apply

this method to the other promising aqueous amine systems. For example, Dubois and

coworkers identified aqueous piperidine (PIP) to have the best overall CO2 capture

performance (high absorption rate and good regenerability) [164]. In addition, some amine blends, including tertiary amine N-methyldiethanolamine (MDEA) + absorption activator piperazine (PZ), sterically hindered amine 2-amino-2-methyl-1-propanol (AMP)

+ PZ, and AMP + PIP were also recommended in Dubois’s work [164].

8.4 Study the effect of other components on CO2

The thermodynamic and kinetic study of CO2 capture in this work focuses on the

methodology and the fundamental properties of the process. Therefore, the vapor phase in

this study contains pure CO2 or CO2 mixed in air. But, there are many more components

(for example, SO2, NOx, O2, and water vapor) in the flue gas that could impact CO2

capture. It is well known that SO2 in flue gas can also be absorbed by alkanolamine

solutions; work has been done to study the absorption of those acidic gases in the

presence of CO2 [165]. In addition to SO2, it is necessary to study the effect of other

components in the flue gas on CO2 capture.

142

8.5 Long-term assessment of RTIL-coated sorbents for Hg capture in coal combustion flue gas Due to the schedule constraints, the mercury sorbents studied in this work were tested in coal combustion flue gas for a relatively short period of time. Their long-term

stability needs to be assessed as the sorbents have a high capacity which enables them to

be used for an extended period of time. Potential engineering problems, such as fly ash

blockage, should be addressed in the long-term tests.

8.6 Alternative substrate for RTIL coated sorbents Porous silica was used as the substrate for RTIL coating in this work for two major reasons: (1) the hydroxyl groups on the surface can be easily functionalized, and

(2) using silica as substrate keeps the consistency with previous work on Hg capture. But,

due to the high cost of silica and the reactivity of hydroxyl on silica surface, it is

recommended to explore other low cost, chemically inert materials as substrates. Carbon was studied as a substrate to support RTIL for Hg capture [105]. The high Hg capacity and the low cost of the carbon-based sorbent showed very promising results. It is recommended to adapt it as the substrate for AA-based RTILs.

143

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Science, 2000. 55(15): p. 2975-2988.

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Equation of State. Industrial & Engineering Chemistry Research, 1999. 38(9): p.

3473-3480.

170

164. Dubois, L. and D. Thomas, Screening of Aqueous Amine-Based Solvents for

Postcombustion CO2 Capture by Chemical Absorption. Chemical engineering &

technology, 2012. 35(3): p. 513-524.

165. Huy, P.Q., K. Sasaki, Y. Sugai, T. Kiga, M. Fujioka, and T. Adachi, Effects of

SO2 and pH Concentration on CO2 Adsorption Capacity in Coal Seams for CO2

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171

Appendix A - Raw Data

A.1 VLE data for H2O-PZ system

T P /Pa T/K xPZ 7143 313 0.04 18202 333 0.04 42816 353 0.04 95148 373 0.04 6964 313 0.09 17788 333 0.09 41369 353 0.09 88253 373 0.09 6688 313 0.14 16547 333 0.14 38611 353 0.14 83427 373 0.14 12717 333 0.30 19980 343 0.30 30478 353 0.30 45265 363 0.30 65611 373 0.30

A.2 Heat capacity of H2O-PZ system

Cp /(kJ/kg/K) T/K xPZ 3.89 338 0.05 3.92 348 0.05 3.95 358 0.05 3.96 368 0.05 3.98 378 0.05 4.02 388 0.05 3.79 338 0.09 3.83 348 0.09 3.86 358 0.09 3.89 368 0.09 3.91 378 0.09 3.96 388 0.09

A.3 VLE data for H2O-MEA system

172

T P /Pa T/K xMEA 6247 313 0.11 9184 323 0.11 15259 333 0.11 41369 353 0.11 80503 373 0.11 3351 303 0.31 4633 313 0.31 5916 323 0.31 13279 333 0.31 31068 353 0.31 59033 373 0.31 120796 393 0.31 8481 313 0.05 20133 333 0.05 44057 353 0.05 93838 373 0.05 176644 393 0.05 10618 333 0.54 23304 353 0.54 47988 373 0.54 93286 393 0.54

A.4 Heat capacity of H2O-MEA system

Cp /(kJ/kg/K) T/K xMEA 3.82 313 0.11 3.91 333 0.11 3.95 338 0.11 3.97 348 0.11 3.97 353 0.11 4.00 358 0.11 4.03 368 0.11 4.02 373 0.11 4.08 393 0.11 3.32 338 0.5 3.36 348 0.5 3.40 358 0.5 3.48 368 0.5 3.54 378 0.5 3.03 338 0.8

173

3.06 348 0.8 3.10 358 0.8 3.15 368 0.8 3.22 378 0.8 3.82 313 0.11

A.5 VLE data for CO2-H2O-PZ system 2m PZ T nT /mmol T nT /mmol P /Pa HO2 namine /mmol CO2 9086 33.05 1.41 0.34 313K 11021 33.05 1.41 0.66 13503 33.05 1.41 0.97 31094 33.05 1.41 1.36 86387 33.05 1.41 1.73 23737 21.85 0.93 0.39 30662 21.85 0.93 0.71 57910 21.85 0.93 0.98 333K 114349 21.85 0.93 1.30 142183 21.85 0.93 1.45 178987 21.85 0.93 1.63 49273 20.64 0.88 0.28 67383 20.64 0.88 0.64 353K 101432 20.64 0.88 0.90 119172 20.64 0.88 1.00 155129 20.64 0.88 1.19 104203 18.75 0.80 0.43 126509 18.75 0.80 0.60 373K 150521 18.75 0.80 0.79 165497 18.75 0.80 0.90 3.6m PZ T nT /mmol T nT /mmol P /Pa HO2 namine /mmol CO2 6602 8.84 1.40 0.49 7678 8.84 1.40 0.82 8438 8.84 1.40 0.98 313K 23380 8.84 1.40 1.35 41971 8.84 1.40 1.56 68559 8.84 1.40 1.69 82801 8.84 1.40 1.72 100894 8.84 1.40 1.78 17286 10.09 1.60 0.47 333K 18293 10.09 1.60 0.63

174

19359 10.09 1.60 0.87 23826 10.09 1.60 1.22 48812 10.09 1.60 1.52 68559 10.09 1.60 1.72 105381 10.09 1.60 1.88 127808 10.09 1.60 2.08 43245 11.66 1.10 0.52 52348 11.66 1.10 0.75 78417 11.66 1.10 1.00 102943 11.66 1.10 1.16 353K 114464 11.66 1.10 1.23 133992 11.66 1.10 1.33 151537 11.66 1.10 1.43 170023 11.66 1.10 1.53 108770 11.10 1.04 0.54 116505 11.10 1.04 0.66 123775 11.10 1.04 0.74 138698 11.10 1.04 0.86 373K 148152 11.10 1.04 0.93 162483 11.10 1.04 1.02 176148 11.10 1.04 1.10 192055 11.10 1.04 1.19 5m PZ T nT /mmol T nT /mmol P /Pa HO2 namine /mmol CO2 18969 16.69 1.57 0.75 21224 16.69 1.57 0.99 23747 16.69 1.57 1.13 30404 16.69 1.57 1.37 333K 43554 16.69 1.57 1.45 53313 16.69 1.57 1.54 63808 16.69 1.57 1.68 83551 16.69 1.57 1.72 109402 16.69 1.57 1.96 140069 16.69 1.57 2.15 38214 9.11 1.45 0.37 40178 9.11 1.45 0.63 46624 9.11 1.45 0.91 62301 9.11 1.45 1.15 353K 93318 9.11 1.45 1.40 114627 9.11 1.45 1.53 137290 9.11 1.45 1.66 155044 9.11 1.45 1.76 173962 9.11 1.45 1.86 373K 122328 9.30 1.48 1.02

175

132190 9.30 1.48 1.12 146517 9.30 1.48 1.24 161144 9.30 1.48 1.34

A.6 Heat of absorption for CO2-H2O-PZ system

-Qint/(kJ/mol of CO2) α ( nn/ ) T/K CO2 CO2 PZ xPZ 82.69 313 0.44 0.04 79.21 313 0.80 0.04 77.22 313 0.93 0.04 77.36 313 0.97 0.04 77.45 313 0.98 0.04 77.71 313 0.98 0.04 77.58 313 1.00 0.04 86.66 333 0.40 0.04 88.62 333 0.70 0.04 84.51 333 0.85 0.04 83.93 333 0.91 0.04 84.80 333 0.92 0.04 85.38 333 0.93 0.04 99.53 353 0.53 0.04 97.53 353 0.73 0.04 96.71 353 0.76 0.04 96.61 353 0.78 0.04 96.24 353 0.80 0.04 118.21 373 0.20 0.04 119.31 373 0.27 0.04 112.64 373 0.34 0.04 114.89 373 0.37 0.04 114.43 373 0.41 0.04 89.86 313 0.30 0.09 87.32 313 0.56 0.09 83.26 313 0.80 0.09 82.03 313 0.89 0.09 81.98 313 0.92 0.09 81.80 313 0.93 0.09 81.49 313 0.93 0.09 98.90 333 0.26 0.09 97.03 333 0.47 0.09 93.67 333 0.70 0.09 92.74 333 0.80 0.09 93.05 333 0.84 0.09

176

93.21 333 0.86 0.09 93.52 333 0.86 0.09 93.63 333 0.87 0.09 103.01 353 0.21 0.09 101.62 353 0.44 0.09 99.55 353 0.61 0.09 98.53 353 0.73 0.09 98.70 353 0.77 0.09 98.81 353 0.79 0.09 99.10 353 0.81 0.09 99.25 353 0.82 0.09 98.98 353 0.84 0.09 126.64 373 0.15 0.09 120.53 373 0.28 0.09 120.71 373 0.43 0.09 121.84 373 0.51 0.09 122.05 373 0.55 0.09 121.78 373 0.61 0.09 121.57 373 0.64 0.09 121.38 373 0.67 0.09 120.78 373 0.69 0.09 119.89 373 0.72 0.09 99.23 333 0.21 0.14 97.36 333 0.43 0.14 94.58 333 0.62 0.14 92.55 333 0.78 0.14 92.44 333 0.83 0.14 92.79 333 0.86 0.14 92.91 333 0.87 0.14 91.81 333 0.89 0.14 100.04 353 0.25 0.14 99.57 353 0.41 0.14 97.43 353 0.59 0.14 96.05 353 0.71 0.14 95.07 353 0.78 0.14 95.05 353 0.81 0.14 94.83 353 0.83 0.14 94.59 353 0.84 0.14 94.39 353 0.85 0.14 119.00 373 0.12 0.14 117.19 373 0.22 0.14 117.24 373 0.35 0.14 118.15 373 0.43 0.14

177

117.63 373 0.49 0.14 116.50 373 0.55 0.14 117.03 373 0.59 0.14 116.29 373 0.62 0.14 115.56 373 0.65 0.14

A.7 VLE data for CO2-H2O-MEA system 30 wt% MEA T nT /mmol T nT /mmol P /Pa HO2 namine /mmol CO2 40876 16.61 2.10 1.21 76096 16.61 2.10 1.43 313K 110491 16.61 2.10 1.62 139632 16.61 2.10 1.78 157922 16.61 2.10 1.87 184672 16.61 2.10 2.02 18257 17.50 2.21 0.27 19938 17.50 2.21 0.58 23983 17.50 2.21 1.02 333K 55572 17.50 2.21 1.20 90650 17.50 2.21 1.40 123405 17.50 2.21 1.57 41782 10.77 1.36 0.20 43437 10.77 1.36 0.39 353K 61639 10.77 1.36 0.71 101767 10.77 1.36 0.95 204361 10.77 1.36 1.44 81082 11.47 1.45 0.17 101353 11.47 1.45 0.61 122037 11.47 1.45 0.76 373K 146858 11.47 1.45 0.89 173334 11.47 1.45 1.03 187813 11.47 1.45 1.10 198155 11.47 1.45 1.15 40 wt% MEA T nT /mmol T nT /mmol P /Pa HO2 namine /mmol CO2 6164 6.47 1.27 0.08 313K 6784 6.47 1.27 0.22 37314 6.47 1.27 0.84 80545 6.47 1.27 1.09 14520 7.05 1.39 0.07 333K 204692 7.05 1.39 1.61 353K 45257 7.23 1.42 0.70

178

105779 7.23 1.42 1.05 172010 7.23 1.42 1.35 212055 7.23 1.42 1.54 102884 8.65 1.70 0.83 373K 168370 8.65 1.70 1.28 191950 8.65 1.70 1.39

A.8 Heat of absorption for CO2-H2O-MEA system

α ( nn/ ) -Qint/(kJ/mol of CO2) T/K CO2 CO2 MEA xMEA 89.86 298 0.17 0.11 88.41 298 0.36 0.11 85.92 298 0.55 0.11 82.13 298 0.63 0.11 79.78 298 0.66 0.11 92.50 313 0.34 0.11 86.68 313 0.54 0.11 82.47 313 0.60 0.11 80.67 313 0.62 0.11 78.02 313 0.66 0.11 92.51 333 0.45 0.11 93.47 333 0.52 0.11 93.44 333 0.54 0.11 90.92 333 0.57 0.11 90.05 333 0.58 0.11 95.26 353 0.17 0.11 95.49 353 0.30 0.11 94.16 353 0.40 0.11 93.84 353 0.46 0.11 93.11 353 0.49 0.11 92.29 353 0.51 0.11 99.32 313 0.17 0.16 91.31 313 0.47 0.16 86.93 313 0.54 0.16 86.50 313 0.57 0.16 86.28 313 0.58 0.16 84.15 313 0.61 0.16 83.40 313 0.63 0.16 108.67 333 0.30 0.16 104.38 333 0.48 0.16 104.32 333 0.50 0.16 104.52 333 0.51 0.16 104.42 333 0.53 0.16

179

117.08 353 0.43 0.16 113.82 353 0.49 0.16 114.53 353 0.50 0.16 113.66 353 0.51 0.16

A.9 VLE data for CO2 - [P(C4)4][Tau] system P /Pa α ( nn/ ) CO2 T/K CO2 CO2 IL 20392.74 313 0.40297 63073.16 313 0.46408 91384.75 313 0.48951 13732.26 333 0.31584 55801.09 333 0.38229 78097.33 333 0.40271 90621.95 333 0.42464 117141.9 333 0.44137 138875.3 333 0.45133 164613.2 333 0.4612 31167.12 353 0.26947 75366.77 353 0.32757 102328.6 353 0.34298 148839.8 353 0.37999 44976.31 373 0.18672 99670.84 373 0.25478 129047.3 373 0.2735 156215.8 373 0.2943

A.10 Heat of absorption data for CO2 - [P(C4)4][Tau] system

α ( nn/ ) -Qint/(kJ/mol of CO2) T/K CO2 CO2 IL 93.84419 333 0.31584 92.55624 333 0.38229 91.32826 333 0.40271 88.25204 333 0.42464 97.62017 353 0.26947 96.4729 353 0.32758 94.71314 353 0.34299 88.87668 353 0.38001 102.2127 373 0.18672 102.1449 373 0.25478 101.328 373 0.2735 100.1737 373 0.2943

180

A.11 Hg concentration histories from slipstream testing

181

Sorbent: 40wt% (P4)4[Tau]-Si Sorbent weight: 6 g Hg0 Time Hg2+ Removal % Removal % Captured Hg0 Captured Hg2+ Flow rate ∆P (in Inlet/outlet (ug/m3 (Day) (ug/m3) (Hg0) (Hg2+) (mg/g/min) (mg/g/min) (acfm) w.c.) ) In 56±14 209±17 1 0% 99% 0.00 0.71 0.5 7.5 Out 61±9 1±13 In 42±5 200±10 3 57% 90% 0.08 0.49 0.4 6.5 Out 18±3 20±7 In 52±4 160±18 6 71% 83% 0.11 0.45 0.5 8 Out 15±7 27±8 In 30±6 191±14 8 83% 96% 0.11 0.63 0.5 9 Out 5±1 7±4 In 5±1 233±33 16 40% 52% 0.00 0.33 0.4 8 Out 3±0 113±17

Est. Capacity (mg Hg/g sorbent): 1.0 mg Hg0/g sorbent; 7.5 mg Hg2+/g sorbent; 8.5 mg HgT/g sorbent.

182

Sorbent: 25wt% MEC-MPTS-Si Sorbent weight: 6 g Hg0 Time Hg2+ Removal % Removal % Captured Hg0 Captured Hg2+ Flow rate ∆P (in Inlet/outlet (ug/m3 (Day) (ug/m3) (Hg0) (Hg2+) (mg/g/min) (mg/g/min) (acfm) w.c.) )

In 3±1 259±15 2 0% 95% 0.00 0.59 0.4 12.5 Out 15±1 13±5

In 7±3 202±8 4 0% 50% 0.00 0.24 0.4 12.5 Out 54±5 101±15

Est. Capacity (mg Hg/g sorbent): 0.0 mg Hg0/g sorbent; 1.4 mg Hg2+/g sorbent; 1.4 mg HgT/g sorbent.

183

Sorbent: 25wt% BmimCl-MPTS-Si Sorbent weight: 6 g Hg0 Time Hg2+ Removal % Removal % Captured Hg0 Captured Hg2+ Flow rate ∆P (in Inlet/outlet (ug/m3 (Day) (ug/m3) (Hg0) (Hg2+) (mg/g/min) (mg/g/min) (acfm) w.c.) ) In 2±1 153±11 1 0% 93% 0.00 0.64 0.3 9.5 Out 3±2 10±3 In 4±2 25±1 3 75% 80% 0.00 0.09 0.3 9.8 Out 1±1 5±2 In 14±1 30±2 5 86% 87% 0.02 0.11 0.3 9.8 Out 2±1 4±2 In 10±2 198±4 10 0% 64% 0.00 0.55 0.3 10.3 Out 54±1 71±2

Est. Capacity (mg Hg/g sorbent): 0.1 mg Hg0/g sorbent; 2.6 mg Hg2+/g sorbent; 2.7 mg HgT/g sorbent.

184

Sorbent: 40wt% (P4)4[Tau][Cys]-Si ([Tau]:[Cys]=4:1) Sorbent weight: 6 g Hg0 Time Hg2+ Removal % Removal % Captured Hg0 Captured Hg2+ Flow rate ∆P (in Inlet/outlet (ug/m3 (Day) (ug/m3) (Hg0) (Hg2+) (mg/g/min) (mg/g/min) (acfm) w.c.) )

In 45±1 107±5 1 47% 80% 0.04 0.30 0.3 12.2 Out 24±8 21±10

In 55±1 102±11 5 5% 45% 0.00 0.15 0.3 12.7 Out 52±2 56±2

Est. Capacity (mg Hg/g sorbent): 0.1 mg Hg0/g sorbent; 0.9 mg Hg2+/g sorbent; 1.0 mg HgT/g sorbent.

185

Appendix B - Calculation

B.1 Calculation for chemical equilibrium There are two approaches to solve the chemical equilibrium of a system at

constant temperature and pressure: stoichiometric and non-stoichiometric approaches.

The stoichiometric approach utilizes the relationship of equilibrium constant K and the

activity of each species in a reaction r as shown in Eq. (B.1)

υ = γ ri, Kxr∏( ii) (B.1)

in which γi is the activity coefficient of species i, xi is the mole fraction of species i, and

υr,i is the stoichiometric number of species i in reaction r.

K is a function of temperature at a certain standard state for a reaction r. For a well-established reaction, there is usually available literature data for its equilibrium constant. For a system that has R reactions and N species, R chemical equilibrium equations of Eq. (B.1) plus N-R mass balance and charge balance equations can be solved

simultaneously for the composition of the system.

Non-stoichiometric approach is to find the composition of a system by

minimizing the Gibbs free energy G at constant temperature and pressure with the

constraints of total mass balance. This approach can be mathematically represented by

Eq. (B.2) and Eq. (B.3)

all species

min Gn= ∑ iiµ (B.2) i

all species

∑ anki i= b k k=1,2,... M (B.3) i

186

in which ni is the number of moles for species i, μi is the chemical potential of species i,

M is the number of elements in the system, aki is the subscript of element k in species i, and bk is the total number of moles for element k in the system.

The problem of system composition is now converted to a optimization problem of Eq. (B.2) with the constraint of Eq. (B.3). μi in Eq. (B.2) is suggested to be expressed

° by a function of standard state chemical potential μ i, activity coefficient γi, and mole

fraction xi of species i [1]:

 µµii=++(T , P ) RT ln γi ( T , P , n ) RT ln xi (B.4)

° For a system that has R reactions and N species, μ i can be calculated from

chemical equilibrium constant K through solving the linear equations in vector form:

NK''T    µ = −RT  (B.5) I  0

’ in which N is a N×R matrix containing elements of υr,i, I is a (N-R) ×R identity matrix,

’ and K is a R×1 array containing elements of lnKr.

Thus, with the chemical equilibrium constants and the stoichiometric numbers for

each reaction in a system available, the composition of a system can be calculated

through simultaneous solving Eq. (B.1) to (B.5). The optimization can be performed in

MATLAB® using function fmincon.

B.2 Numerical calculation for one-dimensional fixed-bed model

The CO2 adsorption process by solid sorbents in a fixed bed was mathematically modeled by a one-dimensional fixed-bed model: ∂C1 ∂∂2 CC ∂ q = − −⋅λ (B.6) ∂τPe ∂∂ ηη2 ∂ τ

187

∂⋅q kL =()qq* − (B.7) ∂τ u

accompanied with boundary and initial conditions:

C(τ, η) = 0, q*(τ, η) = 0 at τ = 0 (B.8)

∂C =Pe( C − 1) at η = 0 ∂η 1 (B.9) η=0

∂C = 0 at η = 1 ∂η (B.10) η=1

tu 1− ε L uL z where τ = , λ = k , Pe = , η = , C is the normalized CO2 concentration in L ε u Da L

the gas phase (C = c/c0), t is the time (s), u is the superficial gas velocity (m/s), L is the

length of bed (m), ε is the bed void fraction, k is the overall mass transfer coefficient (s-1),

2 , Da is the axial dispersion coefficient (m /s), q is the normalized adsorbate concentration

on the particles, and q* is the normalized adsorbate concentration in equilibrium with gas

phase concentration C.

In addition, the equilibrium isotherm for the studied system was determined in

section 5.3.2 as q = KC0.19, in which K is the equilibrium constant obtained from the

integration of breakthrough curves.

To solve the partial differential equations above, the length dimension in z was

numerically divided into N elements. Therefore, Eq. (B.6) and Eq. (B.7) were differentiated to 2N of ordinary differential equations as shown in Eq. (B.11) and

Eq.(B.12). Meanwhile, the boundary conditions in Eq. (B.9) and Eq. (B.10) can be

converted to the ordinary differential equation form in Eq. (B.13) and Eq. (B.14). The

188

2N+2 ordinary differential equations were solved simultaneously for 2N+2 variables (Cn

* and C n, n = 0 to N) in MATLAB® using function ode15s.

dC12 C−+ C C C − C  =n+1 nn − 1− n +− 11 n −−λ 0.19 * 0.19  2   KC()nn C (B.11) dτη Pe  ∆∆2 η 

dC* k⋅− L() C0.19 C * 0.19 n= nn *− 0.81 (B.12) duτ 0.19C n

1 (C−= C) Pe( C − 1) (B.13) 2∆z 20 1

1 (CC+ −=) 0 (B.14) 2∆z nn1

Reference

1. Smith, W.R. and R.W. Missen, Chemical reaction equilibrium analysis: theory

and algorithms 1982, New York: Wiley.

189

Appendix C - MATLAB® Code

Explanation for Subroutines: ObjFunc – Calculation of Objective function Enthalpy – Calculation of enthalpy of reaction Liq – Calculation of liquid composition Optnew – Chemical equilibrium calculation with non-stoichiometry method Activity – Activity coefficient model calculation Vap – Calculation of vapor phase composition Fug - Fugacity coefficient model calculation

% Written by Kun Liu % Revision Date: Jun 19 2012 % Revision Comment: % Correlation package for PZ-H2O-CO2 system

% Features for this version: % 1. Deshmukh-Mather model and eNRTL model for liquid phase nonideality % 2. SRK and PR model for vapor phase nonideality % 3. Choice of data screening, correlation, and presentation % 4. Choice of global minima search and local minima search % 5. Choice of total pressure and partial pressure methods % 6. Send email function available after correlation

% x_N0 = initial mole fraction of amine % x_H2O = initial mole fraction of water % alpha = CO2 loading at equilibrium % Pexp = the experimental data of total pressure, kPa % T = temperature,K % K = [K_w;K_CO2;K_HCO3;K_AmA;K_1;K_AmACO;K_2]; % K_CO2 = equilibrium constant for carbon dioxide hydration % K_HCO3 = equilibrium constant for dissociation of bicarbonate % K_AmA = equilibrium constant for dissociation of protonated PZ % K_1 = equilibrium constant for carbamate reversion to bicarbonate % K_w = equilibrium constant for ionization of water

% xl = mole fractions for H2O, PZ, CO2, PZH+, H+, PZCOO-,

190

% HCO3-, OH-, CO3--, H+PZCOO3+, PZ(COO3)+ % n = number of mole for H2O, PZ, CO2, PZH+, H+, PZCOO-, % HCO3-, OH-, CO3--, H+PZCOO3+, PZ(COO3)+ % nt = total number of mole of all species % Gamma = activitiy coefficents for H2O, PZ, CO2, PZH+, H+, PZCOO-, % HCO3-, OH-, CO3--, H+PZCOO3+, PZ(COO3)+ % vl = molar volume, m3/mol % Ps = satuation pressure, Pa

% Note: If multi-core processor is available, please enable parallel computation to increase computing speed.

clear all clc global T n Pexp NP lnK N r v ra z a b H_amine act m N_m N_c N_a A vl... Ac NDelH NP_P deltaHcor alpha0 Hexp fugmod totalP

act = 2; % Activity Coefficient Model (1 for DM; 2 for eNRTL) fugmod = 1; %Fugacity Coefficient Model (1 for SRK; 2 for PR) cor = 1; %1 for correlation; 2 for presentation scr = 2; % 1: raw data screening; 2: no screening gsearch = 2; % Global search options deltaHcor = 3; % 1: include absorption enthalpy in the correlation; 2: not included ScLb = 0.5; %screening lower bound ScUb = 2; %screening upper bound Bn = [15;5]; %interaction parameter bounds TotalIt = 3; %total pressure method iteration (set 1 for partial pressure cor) totalP = 1; %total or partial pressure (1: total; 2: partial) betacor = zeros(1,6); if act == 2 betapresent =[6.45315973844639 0.817743619199898 5.47002398507998 -0.206554348632208 -0.573954675157455 -2.91394705904942];%PZVLEH %eNRTL else

191 betapresent = [-10.69177636 16.31278223 -16.38199027 3.086197111 5.436369252 - 5.454800385]; %DM end if deltaHcor == 1 disp('Screening is disabled because the correlation of enthalpy is enabled.') disp('') disp('') end

Data Input

%======%======Data Inupt======%======

%Parameters Input ------v = [-1,0,0,0,1,0,0,1,0,0,0;-1,0,-1,0,1,0,1,0,0,0,0;... 0,0,0,0,1,0,-1,0,1,0,0;0,-1,0,1,-1,0,0,0,0,0,0;... 1,-1,0,0,0,1,-1,0,0,0,0;1,0,0,0,0,-1,-1,0,0,0,1;... 0,0,0,0,-1,-1,0,0,0,1,0];%Stoichiometry in the reactions a = [2,10,0,11,1,9,1,1,0,10,8;1,0,2,0,0,2,3,1,3,2,4;... 0,4,1,4,0,5,1,0,1,5,6;0,2,0,2,0,2,0,0,0,2,2];%number of element (row) in i component (column) ra = 3e-10*ones(1,size(v,2)); %ionic radius(30 nm by default, m) ra(7) = 4e-10; ra(4) =3.5e-10; ra(2) = 3.5e-10; ra(6) = 4.5e-10; ra(9) = 5e-10; z = [0 0 0 1 1 -1 -1 -1 -2 0 -2]; % charge r = size(v,1); N = size(v,2); m = size(a,1);

N_m = 3; %number of molecules

192

N_c = 2; %number of cations N_a = 6; %number of anions

A1 = [132.899 -13445.9 -22.4773 0 ;...%K_w 231.465 -12092.1 -36.7816 0 ;...%K_CO2 216.049 -12431.7 -35.4819 0 ;...%K_HCO3 18.135 3814.4 0 -0.015096;...%K_AmA -4.6185 3616.1 0 0 ;...%K_1 0.3615 1322.3 0 0 ;...%K_AmACO 14.043 3493.1 0 0 ;...%K_2 ];

B1 = [170.7126 -8477.711 -21.95743 0.005780748]; %Henry's law constant vl = [1.80691e-5;6.03415e-5]; %molar volume (m3/mol)

Vcell = 13.13e-6; %cell volume

A = [72.55 -7207 0 0 -7.139 4.046E-6 2;... 70.5 -7915 0 0 -6.646 5.21E-18 6;... ];%saturation vapor pressure

Ac = [647.096,2.20640e7,0.344861;...%Tc 638.0,6.87e6,0.4138;...%Pc 304.21,7.38300e6,0.223621];%W

%------

%Experimental Data Input------disp('Correlation Begins') disp('') disp('Loading data from spreadsheet') if cor == 1

if totalP == 1 Data = xlsread('PZ_totaldata3.xls')'; else Data = xlsread('PZ_partial.xls')'; end

193

if deltaHcor == 1 dim = size(Data,1) - 1; NDelH = find(Data(size(Data,1),:)>0); NPDelH = length(NDelH); Hexp = Data(size(Data,1),NDelH); else dim = size(Data,1); end

NP_P = size(Data,2); NP = size(Data,2); %number of data points

Pexp = Data(1,:); %experimental data T = Data(2,:); %temperature alpha0 = Data(3,:); %CO2 loading n_H2O = Data(4,:); %number of mole for water n_N0 = Data(5:dim-1,:); %number of mole for amine n_CO2 = Data(dim,:); %number of mole for CO2

if deltaHcor == 1 T(NP_P+1:NP_P+NPDelH) = T(NDelH)+5; alpha0(NP_P+1:NP_P+NPDelH) = alpha0(NDelH); n_N0(NP_P+1:NP_P+NPDelH) = n_N0(NDelH); n_H2O(NP_P+1:NP_P+NPDelH) = n_H2O(NDelH); n_CO2(NP_P+1:NP_P+NPDelH) = n_CO2(NDelH); Pexp(NP_P+1:NP_P+NPDelH) = Pexp(NDelH); NP = length(T); end x_N0 = sum(n_N0,1)./(sum(n_N0,1)+n_H2O); %mole fraction of amine x_H2O = n_H2O./(sum(n_N0,1)+n_H2O); %mole fraction of water else

beta0 = betapresent;

if totalP ==1 %Data1 = xlsread('PZ_totaldata.xls'); Data1 = xlsread('Kampstot.xls');

else Data1 = xlsread('Ermatchkov.xls'); Data2 = xlsread('Hiliards.xls');

194

end

T0 = [298;313;333;353;393;313;333;353;393;313;333;353;393]*ones(1,20); T = [T0(1,:),T0(2,:),T0(3,:),T0(4,:),T0(5,:),T0(6,:),T0(7,:),T0(8,:),T0(9,:)... ,T0(10,:),T0(11,:),T0(12,:),T0(13,:)]; alpha = linspace(.001,1,20); alpha = [alpha,alpha,alpha,alpha,alpha,alpha,alpha,alpha,alpha,alpha,alpha,alpha,alpha]; %x_N0 = [0.041*ones(1,100) 0.0858623869743579*ones(1,80) 0.136508418019111*ones(1,80)]; x_N0 = [0.041*ones(1,100) 0.099*ones(1,80) 0.136508418019111*ones(1,80)];

T = [T,T+8]; x_N0 = [x_N0, x_N0]; x_H2O = 1 - x_N0; alpha0 = [alpha, alpha];

NP = size(alpha0,2); %number of data points

Pexp1 = Data1(:,1)'; alpha1 = Data1(:,3)'; T1 = Data1(:,2)'; end

%------

%Equilibrium Constants and Henry's Law constants------TT = ones(r,1)*T; AA1 = A1(:,1)*ones(1,NP); AA2 = A1(:,2)*ones(1,NP); AA3 = A1(:,3)*ones(1,NP); AA4 = A1(:,4)*ones(1,NP); K = exp(AA1+AA2./TT+AA3.*log(TT)+AA4.*TT); lnK = log(K);

BB1 = B1(:,1)*ones(1,NP); BB2 = B1(:,2)*ones(1,NP); BB3 = B1(:,3)*ones(1,NP); BB4 = B1(:,4)*ones(1,NP); H_amine = exp(BB1+BB2./T+BB3.*log(T)+BB4.*T);

195

%Initialize values------n = 0*ones(N,NP); n(1,:) = 1000*x_H2O; n(2:N_m-1,:) = 1000*x_N0; n(N_m,:) = sum(n(2:N_m-1,:),1).*alpha0; b = a*n; n = 0.001*ones(N,NP); n(1,:) = 1000*x_H2O; n(2:N_m-1,:) = 1000*x_N0; n(N_m+N_c+1,:) = sum(n(2:N_m-1,:),1).*alpha0;

%Solve for mole fraction ------xl = Liq(0,T,n,NP,lnK,N,r,v,ra,z,a,b,m,N_m,N_c,N_a,act); n = 1000*xl; if cor == 1 if deltaHcor ~= 1 && scr ==1

Screening Test Calculation

%Solve activity coefficients ------Gamma = ones(r,NP); %Solve for gas phase composition------yv = Vap(xl,Gamma,T,NP);

% Screening ------ratio = (yv(1,1:NP_P)./Pexp); count = 0;

for q = 1:NP_P if ratio(:,q)ScLb count = count+1; end end

sub = find(ratioScLb); %screening criterion (factor of three)

196

percentage = count/NP_P;

% Output and Save "good" data ------disp('Screening Test Report') disp(' ') fprintf('\tTotal Data Points = %d\n',NP_P) fprintf('\t"Good" Data Points = %d\n',count) fprintf('\tTest Pass Rate = %.2f\n',percentage) disp(' ') disp(' ')

Pexpgood = Pexp(sub); alphagood = alpha0(sub); Tgood = T(sub); n_H2Ogood = n_H2O(sub); n_N0good = n_N0(sub); n_CO2good = n_CO2(sub); lnKgood = lnK(:,sub); H_aminegood = H_amine(sub); save MEA_VLE_SCR_test.mat disp ('Data Screening Test Finished.') %------disp(' ') disp ('Please enter the number of data points you want to run in the correlation') disp (' Note 1: The smaller the number, the shorter computation time and the less accurate result') fprintf('\tNote 2: It has to be less than the total number of good data points: %d\n',count) demoNum = input ('please enter here: '); sub = 1:1:demoNum;

Pexp = Pexpgood(sub); alpha0 = alphagood(sub); T = Tgood(sub); n_H2O = n_H2Ogood(sub); n_N0 = n_N0good(sub); n_CO2 = n_CO2good(sub); lnK = lnKgood(:,sub); H_amine = H_aminegood(sub);

197

NP_P = length(T); NP = NP_P;

end disp ('Do you want to run a global minimization first? Yes:1; No:2.') demo = input('please enter here: '); disp(' ') disp('Correlation is running. Please wait...') disp('If you wish to abort this running, please press ctrl+c') disp(' ') n_t = [n_H2O;n_N0;n_CO2]; n_lnew = [n_H2O;n_N0;n_N0.*alpha0]; beta0 = betacor; beta1 = beta0; for total = 1:TotalIt

n_l = 0*ones(N,NP); n_l(1:N_m,:) = n_lnew;

n_lt = sum(n_l(1:N_m-1,:),1); xx = n_l(1:N_m-1,:)./(ones(N_m-1,1)*n_lt); alpha = n_l(N_m,:)./sum(n_l(2:N_m-1,:),1);

n = 0*ones(N,NP); n(1,:) = 1000*xx(1,:); n(2:N_m-1,:) = 1000*xx(2:N_m-1,:); n(N_m,:) = sum(n(2:N_m-1,:),1).*alpha;

b = a*n;

n = 0.001*ones(N,NP); n(1,:) = 1000*xx(1,:); n(2:N_m-1,:) = 1000*xx(2:N_m-1,:); n(N_m+N_c+1,:) = sum(n(2:N_m-1,:),1).*alpha;

198

xl = Liq(0,T,n,NP,lnK,N,r,v,ra,z,a,b,m,N_m,N_c,N_a,act); n = 1000*xl;

%format interaction parameters betaleng = length(beta0)/length(Bn); p = 1;Bnbeta = zeros(1,length(beta0)); for i=1:betaleng:length(beta0) Bnbeta(1,i:i+betaleng-1) = Bn(p).*ones(1,betaleng); p = p+1; end

%lb = 0 - Bnbeta; %upper bound %ub = 0 + Bnbeta; %lower bound

lb = [-5 0 0 -15 -5 -5]; ub = [5 5 5 15 0 0];

if demo == 1 %global search %Below provides four global minima search options:

if gsearch == 1 options = saoptimset('TimeLimit',8*3600,'Display','iter','PlotFcns',{@saplotbestx,@saplotf},'TolFun',1e-3); [beta1] = simulannealbnd(@ObjFunc,beta0,lb,ub,options); % find the global minimum by changing the parameters elseif gsearch == 2 opts = optimset('Algorithm','interior-point'); problem = createOptimProblem('fmincon','x0',beta0,... 'objective',@(x)ObjFunc(x),'lb',lb,'ub',ub,... 'options',opts); gs = GlobalSearch('MaxTime',3600*8,'Display','iter'); [beta1] = run(gs,problem);

elseif gsearch == 3 options = psoptimset('PlotFcns',{@psplotbestf,@psplotmeshsize,@psplotbestx},... 'Display','iter','TimeLimit',8*3600); [beta1] = patternsearch(@ObjFunc,beta0,[],[],[],[],lb,ub,[],options); elseif gsearch == 4 options = gaoptimset('Display','iter'); [beta1] = ga(@ObjFunc,length(beta0),[],[],[],[],lb,ub,[],options); end

199 end if demo == 2 %local minima search with full data sample size options = optimset ('MaxIter',200,'Display','iter','Algorithm','interior-point',... 'PlotFcns',{@optimplotx,@optimplotfval,@optimplotstepsize},'TolX',1e-5,'TolFun',1e-5,... 'FinDiffType','forward');

[beta1] = fmincon(@ObjFunc,beta0,[],[],[],[],lb,ub,[],options); end xl = Liq(beta1,T,n,NP,lnK,N,r,v,ra,z,a,b,m,N_m,N_c,N_a,act); %liquid speciation calculation [LnGamma,Gamma] = Activity(beta1,T,xl,ra,z,N,N_m,N_c,N_a,act); %activity coefficient calculation yv = Vap(xl,Gamma,T,NP); %vapor pressure calculation vlt = sum((vl*ones(1,NP)).*xl(1:N_m-1,:),1); % total pressure

V_cell = Vcell*ones(1,NP); R = 8.314; v_vt = yv(2,:).*R.*T./Pexp; n_vtnew = (V_cell-vlt.*sum(n_l(1:N_m-1,:),1))./(v_vt-vlt); %calculate total mole in vapor phase

%calculate the amount of mole for each component in vapor phase------n_vnew = yv(3:3+N_m-1,:).*(ones(N_m,1)*n_vtnew);

%calculate the amount of mole for each component in liquid phase------n_lnew = n_t - n_vnew;

%check for accuracy------error = abs((n_lnew(1:N_m,1:NP_P) - n_l(1:N_m,1:NP_P))./n_l(1:N_m,1:NP_P)); count = length(find(error<0.05)); n_error(total) = mean(mean(error,2)); if n_error(total)<0.003 && mod(total,2) ~= 0 break end fprintf('\tMean Error%.4f\n',n_error) if total==TotalIt && TotalIt~=1 disp('Possible inaccurate result detected, please increase "total" value') end

200 end save correlation.mat

% least square fitting for 95% confidence intervals options = optimset ('MaxIter',200,'Display','iter'); lb = beta1 - Bnbeta./10; %upper bound ub = beta1 + Bnbeta./10; %lower bound [beta3,resnorm,residual,exitflag,output,lambda,jacobian] = lsqnonlin(@ObjFuncls,beta1,lb,ub,options); alpha = 0.05; % 95% confidence interval ci = nlparci(beta3,residual,jacobian,alpha); if deltaHcor == 1 lengy = length(Pexp)+length(Hexp); else lengy = length(Pexp); end t = tinv(1-alpha/2,lengy-length(beta3)); nlinfit_se = (ci(:,2)-ci(:,1)) ./ (2*t); % Standard Error

xl = Liq(beta3,T,n,NP,lnK,N,r,v,ra,z,a,b,m,N_m,N_c,N_a,act); %liquid phase composition [LnGamma,Gamma] = Activity(beta3,T,xl,ra,z,N,N_m,N_c,N_a,act); %activity coefficient calculation yv = Vap(xl,Gamma,T,NP); %vapor phase composition ratio = (yv(1,:)./Pexp); meanv = mean(ratio); standv = std(ratio); R2 = 1 - (sum((Pexp-yv(1,:)).^2)/sum((Pexp-mean(Pexp)).^2 )); %R square

Save data & output save ModelCorrelate.mat %save data

% Output------disp(' ')

%sendemail(['Correlation Finished. R2 is ' num2str(R2)]) fprintf('Estimated Parameters:\n')

201 for i = 1:length(beta0) %fprintf('\tInteraction Parameter %d: %.3f ?%.5f\n',i,beta3(i),ci(i,2)-beta3(i)) fprintf('\tInteraction Parameter %d: %.3f ?%.5f\n',i,beta3(i),nlinfit_se(i)) end disp(' ') fprintf('\tThe mean value of the ratio of Pcal_C_O_2 to Pexp_C_O_2 = %.2f\n',meanv) fprintf('\tThe standard deviation of the ratio of Pcal_C_O_2 to Pexp_C_O_2 = %.2f\n',standv) fprintf('\tR Square = %.2f\n',R2) disp(' ') figure(2) loglog([10e2,10e5],[10e2,10e5],'-k','LineWidth',2);hold on loglog ((yv(1,:)),Pexp,'LineStyle','none','Marker','s','MarkerFaceColor','r','MarkerEdgeColor','r','MarkerSize',5) xlabel('P_c_a_l /kPa','FontSize',20,'FontName','Times New Roman') ylabel('P_e_x_p /kPa','FontSize',20,'FontName','Times New Roman') hold off figure(3) plot (alpha0(1,:),ratio,'LineStyle','none','Marker','s','MarkerFaceColor','r','MarkerEdgeColor','r','MarkerSize',5) xlabel('CO_2 Loading (mol CO_2/mol amine)','FontSize',20,'FontName','Times New Roman') ylabel('P_c_a_l/P_e_x_p','FontSize',20,'FontName','Times New Roman')

else xl = Liq(beta0,T,n,NP,lnK,N,r,v,ra,z,a,b,m,N_m,N_c,N_a,act); [LnGamma,Gamma] = Activity(beta0,T,xl,ra,z,N,N_m,N_c,N_a,act); yv = Vap(xl,Gamma,T,NP);

[deltaH,deltaHIn] = Enthalpy(yv(end,1:(NP/2)),yv(end,(NP/2+1):NP),T(1:(NP/2)),T((NP/2+1):NP),alpha);

NP_Pr = length(alpha1);alpha1(1,NP_Pr+1)=alpha1(1,NP_Pr)-0.01;T1(1,NP_Pr+1)=T1(1,NP_Pr)-0.01; cc = 1;Tcount = 1;Ccount = 1;figure(1);Pcount = 1;

Pexp2 = Data2(:,1)'; alpha2 = Data2(:,3)'; semilogy(alpha2(1,1:6),Pexp2(1,1:6),'og','MarkerSize',7); hold on semilogy(alpha2(1,7:14),Pexp2(1,7:14),'ob','MarkerSize',7); for dp = 1:NP_Pr

202 alphaplot(1,cc) = alpha1(1,dp); yvplot(1,cc) = Pexp1(1,dp); if alpha1(1,dp+1)

if T1(1,dp) == 313 colorcode = 'og';mf = 'g'; elseif T1(1,dp) == 333 colorcode = 'ob';mf = 'b'; elseif T1(1,dp) == 353 colorcode = 'or';mf = 'r'; elseif T1(1,dp) == 373 colorcode = 'ok';mf = 'k'; elseif T1(1,dp) == 393 colorcode = 'ok';mf = 'k'; elseif T1(1,dp) == 314 colorcode = 'ow';mf = 'w'; elseif T1(1,dp) == 298 colorcode = 'ow';mf = 'w'; end

semilogy(alphaplot(1,1:cc),yvplot(1,1:cc),colorcode,'MarkerSize',7,'MarkerFaceColor',mf);

if Tcount == 1 hold on end

cc = 1;Tcount = Tcount + 1; if T1(1,dp+1)<=T1(1,dp)

pls = 21+80*(Ccount-1); semilogy(alpha(1,pls:pls+19),yv(1,pls:pls+19),'-g','LineWidth',2); semilogy(alpha(1,pls+20:pls+39),yv(1,pls+20:pls+39),'-b','LineWidth',2); semilogy(alpha(1,pls+40:pls+59),yv(1,pls+40:pls+59),'-r','LineWidth',2); semilogy(alpha(1,pls+60:pls+79),yv(1,pls+60:pls+79),'-k','LineWidth',2); %legend('313K','313K','333K','333K','353K','353K','373K','373K'); xlabel('CO_2 Loading (mol CO_2/mol amine)','FontSize',20,... 'FontName','Times New Roman') ylabel('CO_2 Vapor Pressure /Pa','FontSize',20,'FontName','Times New Roman') hold off Ccount = Ccount + 1;Tcount = 1;Pcount = Pcount + 1;

203

if dp ~=NP_Pr figure(Ccount); end end else cc = cc + 1; end

end

DataH = xlsread('HPZ_ref1.xls'); Hexp = DataH(:,1)'; %experimental data T1 = DataH(:,2)'; %T alpha1 = DataH(:,3)'; %CO2 loading

NP_Pr = length(alpha1);alpha1(1,NP_Pr+1)=alpha1(1,NP_Pr)-0.01;T1(1,NP_Pr+1)=T1(1,NP_Pr)-0.01; cc = 1;Tcount = 1;figure(Pcount);Ccount = 1;

for dp = 1:NP_Pr

alphaplot(1,cc) = alpha1(1,dp); yvplot(1,cc) = Hexp(1,dp);

if alpha1(1,dp+1)

if T1(1,dp) == 313 colorcode = 'og';mf = 'g'; elseif T1(1,dp) == 333 colorcode = 'sb';mf = 'b'; elseif T1(1,dp) == 353 colorcode = 'dr';mf = 'r'; elseif T1(1,dp) == 373 colorcode = 'pk';mf = 'k'; end

plot(alphaplot(1,1:cc),yvplot(1,1:cc),colorcode,'MarkerSize',7,'MarkerFaceColor',mf);

if Tcount == 1 hold on end

204

cc = 1;Tcount = Tcount + 1; if T1(1,dp+1)<=T1(1,dp)

pls = 21+80*(Ccount-1); plot(alpha(1,pls:pls+19),deltaH(1,pls:pls+19),'-g','LineWidth',2); plot(alpha(1,pls+20:pls+39),deltaH(1,pls+20:pls+39),'-b','LineWidth',2); plot(alpha(1,pls+40:pls+59),deltaH(1,pls+40:pls+59),'-r','LineWidth',2); plot(alpha(1,pls+60:pls+79),deltaH(1,pls+60:pls+79),'-k','LineWidth',2); %legend('313K','313K','333K','333K','353K','353K','373K','373K'); xlabel('CO_2 Loading (mol CO_2/mol amine)','FontSize',20,... 'FontName','Times New Roman') ylabel('Vapor Pressure /Pa','FontSize',20,'FontName','Times New Roman') hold off Ccount = Ccount + 1;Tcount = 1;Pcount = Pcount + 1; if dp ~=NP_Pr figure(Pcount); end end else cc = cc + 1; end

end figure(Pcount) plot(alpha(1,21:40),Gamma(2,21:40),'-b');hold on plot(alpha(1,21:40),Gamma(3,21:40),'-r'); plot(alpha(1,21:40),Gamma(4,21:40),'-k'); plot(alpha(1,21:40),Gamma(5,21:40),'-c'); plot(alpha(1,21:40),Gamma(6,21:40),'-m'); plot(alpha(1,21:40),Gamma(7,21:40),'--b'); plot(alpha(1,21:40),Gamma(8,21:40),'--r'); plot(alpha(1,21:40),Gamma(9,21:40),'--g'); plot(alpha(1,21:40),Gamma(10,21:40),'--c'); plot(alpha(1,21:40),Gamma(11,21:40),'--m'); xlabel('CO_2 Loading (mol CO_2/mol amine)','FontSize',20,... 'FontName','Times New Roman') ylabel('Activity Coefficient','FontSize',20,'FontName','Times New Roman')

205 hold off figure(Pcount+1) %semilogy(T(1,101:120),yv(1,101:120),'-y');hold on %plot(alpha(1,1:20),deltaH(1,1:20),'-y') %semilogy(alpha1(1,28:35),Pexp1(1,28:35),'oy');

%semilogy(T(1,21:40),yv(1,21:40),'-b'); plot(alpha(1,21:40),deltaHIn(1,21:40),'-g');hold on %semilogy(alpha1(1,7:11),Pexp1(1,7:11),'ob'); %semilogy(alpha2(1,1:12),Pexp2(1,1:12),'xb');

%semilogy(T(1,41:60),yv(1,41:60),'-r'); plot(alpha(1,41:60),deltaHIn(1,41:60),'-b'); %semilogy(alpha1(1,12:16),Pexp1(1,12:16),'or'); %semilogy(alpha2(1,13:24),Pexp2(1,13:24),'xr');

%semilogy(T(1,61:80),yv(1,61:80),'-g'); plot(alpha(1,61:80),deltaHIn(1,61:80),'-r'); %semilogy(alpha1(1,17:22),Pexp1(1,17:22),'og'); %semilogy(alpha2(1,25:36),Pexp2(1,25:36),'xg');

%semilogy(T(1,81:100),yv(1,81:100),'-k'); plot(alpha(1,81:100),deltaHIn(1,81:100),'-k'); %semilogy(alpha1(1,23:29),Pexp1(1,23:29),'ok'); %semilogy(alpha2(1,37:48),Pexp2(1,37:48),'xk'); xlabel('CO2 Loading (mol CO2/mol amine)','FontSize',20,... 'FontName','Times New Roman') ylabel('Enthalpy (kJ/mol)','FontSize',20,'FontName','Times New Roman') hold off figure(Pcount+2) plot(alpha(1,181:200),xl(2,181:200),'-b','LineWidth',2);hold on plot(alpha(1,181:200),xl(3,181:200),'-r','LineWidth',2); plot(alpha(1,181:200),xl(4,181:200),'-k','LineWidth',2); plot(alpha(1,181:200),xl(5,181:200),'-c','LineWidth',2); plot(alpha(1,181:200),xl(6,181:200),'-m','LineWidth',2); plot(alpha(1,181:200),xl(7,181:200),'--b','LineWidth',2);

206 plot(alpha(1,181:200),xl(8,181:200),'--r','LineWidth',2); plot(alpha(1,181:200),xl(9,181:200),'--g','LineWidth',2); plot(alpha(1,181:200),xl(10,181:200),'--c','LineWidth',2); plot(alpha(1,181:200),xl(11,181:200),'--m','LineWidth',2); xlabel('CO_2 Loading (mol CO_2/mol amine)','FontSize',20,'FontName','Times New Roman') ylabel('Speciation','FontSize',20,'FontName','Times New Roman') %legend('PZ','CO_2','PZH^+','H_3O^+','PZCOO^-','HCO_3^-','OH^-','CO_3^-^-','H^+PZCOO_3^-', 'PZ(COO_3)_2^2+') hold off for i = 1:Pcount+2 saveas (figure(i),['PZ_fig',num2str(i),'.fig']) end exportEPS(Pcount+2) save ModelPresenteNRTL.mat end

function f = ObjFunc(BETA) %objective function for fmincon global T n Pexp NP lnK N r v ra z a b m N_m N_c N_a act NP_P NDelH deltaHcor alpha0 Hexp xl = Liq(BETA,T,n,NP,lnK,N,r,v,ra,z,a,b,m,N_m,N_c,N_a,act); %solve for liquid composition [LnGamma,Gamma] = Activity(BETA,T,xl,ra,z,N,N_m,N_c,N_a,act); %solve for activity coefficient yv = Vap(xl,Gamma,T,NP); %solve for vapor composition if deltaHcor == 3 %[deltaH,deltaHIn] = Enthalpy(yv(end,NDelH),yv(end,NP_P+1:NP),T(1,NDelH),T(1,NP_P+1:NP),alpha0(1,NP_P+1:NP));

%f = sum(abs((yv(1,1:NP_P)-Pexp)./Pexp))+sum(abs((deltaHIn-Hexp)./Hexp)); %f = f/(NP); [g,~] = HcalPZ(BETA); f = sum(((yv(1,:)-Pexp).^2./Pexp./yv(1,:)))/NP + g; else f = sum(((yv(1,:)-Pexp).^2./Pexp./yv(1,:))); f = f/(NP);

207 end

function f = ObjFuncls(BETA) %objective function for lsqnonlin global T n Pexp NP lnK N r v ra z a b m N_m N_c N_a act NP_P NDelH deltaHcor alpha0 Hexp xl = Liq(BETA,T,n,NP,lnK,N,r,v,ra,z,a,b,m,N_m,N_c,N_a,act); %solve for liquid composition [LnGamma,Gamma] = Activity(BETA,T,xl,ra,z,N,N_m,N_c,N_a,act); %solve for activity coefficient yv = Vap(xl,Gamma,T,NP); %solve for vapor composition if deltaHcor == 3 %[deltaH,deltaHIn] = Enthalpy(yv(end,NDelH),yv(end,NP_P+1:NP),T(1,NDelH),T(1,NP_P+1:NP),alpha0(1,NP_P+1:NP)); %f = [sqrt(abs((yv(1,1:NP_P)-Pexp)./Pexp)./NP_P),sqrt(abs((deltaHIn-Hexp)./Hexp))./(NP-NP_P)]; [~,g] = HcalPZ(BETA); f = [sqrt(abs((yv(1,1:NP_P)-Pexp)./Pexp)./NP_P),g]; else f = sqrt(abs((yv(1,:)-Pexp)./Pexp)./NP); end function [deltaH,deltaHIn] = Enthalpy(yv1,yv2,T1,T2,alpha) %objective function for lsqnonlin

NP = length(T1); deltaH = -8.314.*(log(yv2)-log(yv1))./(1./T2-1./T1)./1000; if nargout > 1 HIn = deltaH(1,1)*alpha(1,1);

deltaHIn(1,1) = deltaH(1,1); for i=2:NP if alpha(1,i)>alpha(1,i-1) HIn = HIn+deltaH(1,i)*(alpha(1,i)-alpha(1,i-1)); deltaHIn(1,i) = HIn./alpha(1,i); else HIn = deltaH(1,i)*alpha(1,i); deltaHIn(1,i) = deltaH(1,i); end end end

208

function xl = Liq(beta0,T,n,NP,lnK,N,r,v,ra,z,a,b,m,N_m,N_c,N_a,act) %Solve for liquid composition

R = 8.314; Zero = zeros((N-r),1); I = eye((N-r),N); LHS = [v;I]; xl = zeros(N,NP);

%reserved for equilibrium constant correlation------if length(beta0) == 160 betalength = (length(beta0))/2; K_AmA = exp(beta0(betalength-1)+beta0(2*betalength-1)*1000./T); K_1 = exp(beta0(betalength)+beta0(2*betalength)*1000./T); lnK(4,:) = log(K_AmA); lnK(5,:) = log(K_1); elseif length(beta0) == 14 betalength = (length(beta0))/2; K_AmA = exp((beta0(betalength-1)-644)/10+(beta0(betalength)-489.9)*10./T+(beta0(2*betalength- 1)+890)/100.*log(T)+beta0(2*betalength)/10000.*T); lnK(4,:) = log(K_AmA); end %------parfor i = 1:NP RHS = -R*T(:,i)*[lnK(:,i);Zero]; u0 = LHS\RHS; %solve for u0 from equilibrium constants nn = Optnew(n(:,i),u0,N,beta0,T(:,i),ra,z,m,a,b(:,i),N_m,N_c,N_a,act); totn = sum(nn); %total amount of mole xl(:,i) = nn/totn; %mole fraction end function n = Optnew(n,u0,N,BETA,T,r,z,m,a,b,N_m,N_c,N_a,act) %nonstoichiometric chemical equilibrium calculation

Gamma = ones(N,1); for p = 1:300

R = 8.314;

209

term1 = zeros(m+1,m+1); term2 = zeros(m+1,1); term3 = zeros(m+1,1); n_t = sum(n); x = n./n_t; u01 = u0 + (R*T*log(Gamma)); u = u01 + R*T*log(x); bb = a*n; term1(1:m,1:m) = ones(m,1)*n'.*a*a'; term2(1:m,:) = sum((a.*(ones(m,1)*n').*(ones(m,1)*u')),2); term3(1:m,:) = b-bb; term1(m+1,1:m) = bb'; term2(m+1,:) = n'*u; term1(1:m,m+1) = bb;

RHS = term2./(R*T)+term3; LHS = term1; soln = LHS\RHS; theta = soln(1:m,1); uu = soln(m+1,1)*ones(N,1); diffn = (-u./R./T+(theta'*a)'+uu); deltan = n.*diffn; if max(abs(diffn))<0.01 && p ~=1 n = n + ww.*deltan; break end

210

if max(abs(diffn))>1 ww = 0.8/max(abs(diffn)); else ww = 1; end n = n + ww.*deltan; totn = sum(n); %total amount of mole x = n/totn; %mole fraction if length(BETA) ~= 1 [LnGamma,Gamma] = Activity(BETA,T,x,r,z,N,N_m,N_c,N_a,act); %solve for activity coefficient else Gamma = 1; end if p==300 disp('Possible inaccurate result detected, please increase the max iteration cycle') end end function [LnGa,Ga]=Activity(BETA,T,x,r,z,N,N_m,N_c,N_a,act) %solve for activity coefficients

%Input------Mw = [18;86.14]; %Damine = 36.76 + 14836.*(1./T'-1./273.15);%MEA Damine = 4.25 + 1532./T'.*(1./T'-1./298.15);%PZ %------

%Set up parameter variables if size(BETA,1)==1 && length(BETA)~=1 betalength = (length(BETA))/2; BETA_1(1,:) = BETA(1,1:betalength); BETA_1(2,:) = BETA(1,betalength+1:2*betalength); BETA = BETA_1; end

%DM Model act=1

211 if act ==1

%Setup interaction parameters beta = zeros(size(x,1),size(x,2),size(x,1)); %set all interaction parameters to be zeros if length(BETA)~=1 BETA = [1 0; 0 1000]*BETA; %beta(4,:,7) = BETA(1,6)+BETA(2,6)./T'; %beta(7,:,4) = beta(4,:,7); beta(6,:,3) = BETA(1,1)+BETA(2,1)./T'; beta(3,:,6) = beta(6,:,3); beta(7,:,3) = BETA(1,2)+BETA(2,2)./T'; beta(3,:,7) = beta(7,:,3); %beta(2,:,7) = BETA(1,4)+BETA(2,4)./T'; %beta(7,:,2) = beta(2,:,7); %beta(4,:,6) = BETA(1,5)+BETA(2,5)./T'; %beta(6,:,4) = beta(4,:,6); beta(2,:,3) = BETA(1,3)+BETA(2,3)./T'; beta(3,:,2) = beta(2,:,7); end

%Setup constants F = 96485.3415; %Faraday constant = 96 485.3415 C / mol rou = 1; %solvent density (kg/L) e = 8.854187817e-12; %Vacuum permittivity = 8.854187817e-12 F/m Dw = 78.54*(1-4.579e-3*(T-298.15)+1.19e-5*(T-298.15).^2-2.8e-7*(T-298.15).^3); %water dielectric constant Dmix = x(1,:).*Dw + sum(x(2:(N_m-1),:).*Damine',1);%mixture dielectric constant R = 8.314; % Gas constant J/K/mol NA = 6.0221415e23; %Avogadro's Constant = 6.0221415e23 mol-1

A = (F^3*(2000*rou)^0.5)./(2.303.*(8*pi*NA).*(e*R.*T.*Dmix).^(3/2)); %limit slope of Debye?H?ckel B = (2000*F^3./(e*R.*T.*Dmix)).^0.5; %parameter in DM model

I = 0.5*z.^2*x./Mw(1)*1000; %ionic stength (molarity)

%Solve for Gammas Gamma = ones(size(x)); for i = 1:size(x,1); if i>1 Gamma(i,:) = 2./Mw(1)*sum((beta(:,:,i).*x),1); else Gamma(i,:) = -A*z(i)^2.*I.^0.5./(1+B*r(i).*I.^0.5)+2./Mw(1)*sum((beta(:,:,i).*x),1);

212

end end

%eNRTL Model act=2 elseif act == 2

NP = size(x,2); NC = N+1; X = zeros(NP,NC);

alp = zeros(NP,NC,NC,NC,NC); G = ones(NP,NC,NC,NC,NC); tau = zeros(NP,NC,NC,NC,NC);

zz = abs(z)'; zzl = z==0; zz(zzl) = 1; X(:,2:N+1) = ((zz*ones(1,NP)).*x)';

S_m = 2; S_c = N_m+S_m; S_a = N_c+S_c;

%LnGammaPDH & LnGammaBorn------LNGammaLC = zeros(NP,(NC)); LNGammaPDH = zeros(NP,(NC)); LNGammaBorn = zeros(NP,(NC));

Ms = sum((Mw*ones(1,NP)).*x(1:(N_m-1),:),1)'; d = Ms.^-1; %solvent density (mol/cm3) Dw = 78.54*(1-4.579e-3.*(T'-298.15)+1.19e-5.*(T'-298.15).^2-2.8e-7*(T'-298.15).^3); %water dielectric constant Dmix = x(1,:)'.*Dw + sum(x(2:(N_m-1),:)'.*Damine,1);%mixture dielectric constant NA = 6.0221415e23; %Avogadro's Constant = 6.0221415e23 mol-1 k = 1.38e-16; %Boltzmann constant (erg/K) Q = 4.803e-10; %electronic charge (esu) rou = 14.9; %distance of closest approach

A = 1/3.*((2.*pi.*1e-3.*NA.*d).^0.5).*(Q.^2./(Dmix.*k.*T')).^1.5;

213

z(1,2:N+1) = z; r(1,2:N+1) = r; I = sum(0.5*(x.*(zz*ones(1,NP)).^2),1)'; for j = S_m:(S_m+N_m+N_c+N_a-1) LNGammaPDH(:,j) = -(1000./Ms).^0.5.*A.*((2.*z(j).^2./rou).*log(1+... rou.*I.^0.5)+((z(j).^2.*I.^0.5-2*I.^1.5)./(1+rou.*I.^0.5)));

LNGammaBorn(:,j) = Q.^2./(2.*k.*T').*(1./Dmix-1./Dw).*(z(j).^2./r(j)).*10^-2; end

% solve for alp(m,m)------for B = S_m:(S_m+N_m-1) for BB = S_m:(S_m+N_m-1) if BB~=B||(B~=3&&BB~=4)||(B~=4&&BB~=3) alp(:,B,1,BB,1) = 0.2*ones(NP,1); end end end

% solve for alp(m,ca),alp(ca,m),alp(mc,ca),alp(ma,ca),tau(m,ca),tau(ca,m)-- for ct = S_c:(S_c+N_c-1) for an = S_a:(S_a+N_a-1) for BB = S_m:(S_m+N_m-1) alp(:,BB,1,ct,an) = 0.2*ones(NP,1); alp(:,BB,ct,ct,an) = alp(:,BB,1,ct,an); alp(:,BB,an,ct,an) = alp(:,BB,1,ct,an); alp(:,ct,an,BB,1) = 0.2*ones(NP,1); alp(:,ct,an,BB,ct) = alp(:,ct,an,BB,1); alp(:,ct,an,BB,an) = alp(:,ct,an,BB,1); tau(:,BB,1,ct,an) = 10*ones(NP,1); tau(:,ct,an,BB,1) = -2*ones(NP,1); end

tau(:,2,1,ct,an) = 8*ones(NP,1); tau(:,ct,an,2,1) = -4*ones(NP,1);

end end

214 if length(BETA)~=1 if size(BETA,1)==3 BETA = [1 0 0; 0 1000 0; 0 0 1000]*BETA; Tref = 298.25; % load tau(m,m), tau(m,ca),tau(ca,m) tau(:,2,1,3,1) = BETA(1,1)+BETA(2,1)./T'+ BETA(3,1).*((Tref-T')./T'+log(T'./Tref)); tau(:,3,1,2,1) = BETA(1,2)+BETA(2,2)./T'+ BETA(3,2).*((Tref-T')./T'+log(T'./Tref)); tau(:,2,1,4,1) = BETA(1,3)+BETA(2,3)./T'+ BETA(3,3).*((Tref-T')./T'+log(T'./Tref)); tau(:,4,1,2,1) = BETA(1,4)+BETA(2,4)./T'+ BETA(3,4).*((Tref-T')./T'+log(T'./Tref));

tau(:,2,1,5,7) = BETA(1,5)+BETA(2,5)./T'+ BETA(3,5).*((Tref-T')./T'+log(T'./Tref)); tau(:,2,1,5,8) = BETA(1,6)+BETA(2,6)./T'+ BETA(3,6).*((Tref-T')./T'+log(T'./Tref)); tau(:,5,7,2,1) = BETA(1,7)+BETA(2,7)./T'+ BETA(3,7).*((Tref-T')./T'+log(T'./Tref)); tau(:,5,8,2,1) = BETA(1,8)+BETA(2,8)./T'+ BETA(3,8).*((Tref-T')./T'+log(T'./Tref));

tau(:,3,1,5,7) = BETA(1,9)+BETA(2,9)./T'+ BETA(3,9).*((Tref-T')./T'+log(T'./Tref)); tau(:,3,1,5,8) = BETA(1,10)+BETA(2,10)./T'+ BETA(3,10).*((Tref-T')./T'+log(T'./Tref)); tau(:,5,7,3,1) = BETA(1,11)+BETA(2,11)./T'+ BETA(3,11).*((Tref-T')./T'+log(T'./Tref)); tau(:,5,8,3,1) = BETA(1,12)+BETA(2,12)./T'+ BETA(3,12).*((Tref-T')./T'+log(T'./Tref));

tau(:,4,1,5,8) = BETA(1,13)+BETA(2,13)./T'+ BETA(3,13).*((Tref-T')./T'+log(T'./Tref)); tau(:,5,8,4,1) = BETA(1,14)+BETA(2,14)./T'+ BETA(3,14).*((Tref-T')./T'+log(T'./Tref));

else BETA = [1 0; 0 1]*BETA;

tau(:,2,1,3,1) = -0.45+31.52./T'; tau(:,3,1,2,1) = -0.45+31.52./T';

tau(:,2,1,4,1) = BETA(1,1)+BETA(2,1)*1000./T'; tau(:,4,1,2,1) = tau(:,2,1,4,1);

tau(:,2,1,5,8) = BETA(1,2); tau(:,5,8,2,1) = BETA(2,2);

tau(:,2,1,5,7) = BETA(1,3); tau(:,5,7,2,1) = BETA(2,3);

end end

215

% solve G(m,m) = exp(-alp(m,m)*tau(m,m))------for B = S_m:(S_m+N_m-1) for BB = S_m:(S_m+N_m-1) G(:,B,1,BB,1) = exp(-alp(:,B,1,BB,1).*tau(:,B,1,BB,1)); end end

% solve G(ca,m) = exp(-alp(ca,m)*tau(ca,m))------for B = S_m:(S_m+N_m-1) for ct = S_c:(S_c+N_c-1) for a = S_a:(S_a+N_a-1) G(:,ct,a,B,1) = exp(-alp(:,ct,a,B,1).*tau(:,ct,a,B,1)); end end end

% solve G(c,m) from X(a),G(ca,m) ------for B = S_m:(S_m+N_m-1) for ct = S_c:(S_c+N_c-1) term1 = zeros(NP,1); term2 = zeros(NP,1); for a = S_a:(S_a+N_a-1) term1 = term1 + X(:,a).*G(:,ct,a,B,1); term2 = term2 + X(:,a); end G(:,ct,1,B,1) = term1./term2; end end

% solve G(a,m) from X(c),G(ca,m) ------for B = S_m:(S_m+N_m-1) for an = S_a:(S_a+N_a-1) term1 = zeros(NP,1); term2 = zeros(NP,1); for c = S_c:(S_c+N_c-1) term1 = term1 + X(:,c).*G(:,c,an,B,1); term2 = term2 + X(:,c); end G(:,an,1,B,1) = term1./term2; end end

216

% solve alp(c,m),alp(m,c) from X(a),alp(m,ca) ------% solve tau(c,m) from G(c,m) and alp(c,m) ------for B = S_m:(S_m+N_m-1) for ct = S_c:(S_c+N_c-1) term1 = zeros(NP,1); term2 = zeros(NP,1); for a = S_a:(S_a+N_a-1) term1 = term1 + X(:,a).*alp(:,B,1,ct,a); term2 = term2 + X(:,a); end alp(:,ct,1,B,1) = term1./term2; alp(:,B,1,ct,1) = alp(:,ct,1,B,1); tau(:,ct,1,B,1) = -log(G(:,ct,1,B,1))./alp(:,ct,1,B,1); end end

% solve alp(a,m),alp(m,a) from X(c),alp(m,ca) ------% solve tau(a,m) from G(a,m) and alp(a,m) ------for B = S_m:(S_m+N_m-1) for an = S_a:(S_a+N_a-1) term1 = zeros(NP,1); term2 = zeros(NP,1); for c = S_c:(S_c+N_c-1) term1 = term1 + X(:,c).*alp(:,B,1,c,an); term2 = term2 + X(:,c); end alp(:,an,1,B,1) = term1./term2; alp(:,B,1,an,1) = alp(:,an,1,B,1); tau(:,an,1,B,1) = -log(G(:,an,1,B,1))./alp(:,an,1,B,1); end end

% solve tau(ma,ca),tau(mc,ac),G(ma,ca),G(mc,ac) from tau(a,m),tau(c,m), % tau(ca,m),tau(m,ca),alp(mc,ac),alp(ma,ca),tau(mc,ac),tau(ma,ca) for B = S_m:(S_m+N_m-1) for a = S_a:(S_a+N_a-1) for c = S_c:(S_c+N_c-1) tau(:,B,a,c,a) = tau(:,a,1,B,1)-tau(:,c,a,B,1)+tau(:,B,1,c,a); tau(:,B,c,a,c) = tau(:,c,1,B,1)-tau(:,c,a,B,1)+tau(:,B,1,c,a); G(:,B,c,a,c) = exp(-alp(:,B,c,a,c).*tau(:,B,c,a,c)); G(:,B,a,c,a) = exp(-alp(:,B,a,c,a).*tau(:,B,a,c,a)); end

217

end end

%LnGammaLC(m)------for B = S_m:(S_m+N_m-1)

term_MM1 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a- 1),1,B,1).*tau(:,S_m:(S_m+N_m+N_c+N_a-1),1,B,1),2); term_MM2 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a-1),1,B,1),2); term_M1 = term_MM1./term_MM2;

term_M2 = zeros(NP,1);

for m = S_m:(S_m+N_m-1)

term_MM3 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a-1),1,m,1),2); term_MM4 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a- 1),1,m,1).*tau(:,S_m:(S_m+N_m+N_c+N_a-1),1,m,1),2); term_MM5 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a-1),1,m,1),2);

term_M2 = term_M2 + (X(:,m).*G(:,B,1,m,1)./term_MM3.*(tau(:,B,1,m,1)-term_MM4./term_MM5));

end

term_MA1 = sum(X(:,S_a:(S_a+N_a-1)),2);

term_M3 = zeros(NP,1); for c = S_c:(S_c+N_c-1) term_M31=zeros(NP,1); for a = S_a:(S_a+N_a-1) term_MA2 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a-1),c,a,c),2); term_MA3 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a- 1),c,a,c).*tau(:,S_m:(S_m+N_m+N_c+N_a-1),c,a,c),2); term_MA4 = term_MA2;

term_M31 = term_M31 + (X(:,a)./term_MA1.*(X(:,c).*G(:,B,c,a,c))./term_MA2.*(tau(:,B,c,a,c)- term_MA3./term_MA4)); end term_M3 = term_M3 + term_M31; end

218

term_MC1 = sum(X(:,S_c:(S_c+N_c-1)),2); term_M4 = zeros(NP,1); for a = S_a:(S_a+N_a-1) term_M41=zeros(NP,1); for c = S_c:(S_c+N_c-1)

term_MC2 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a-1),a,c,a),2); term_MC3 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a- 1),a,c,a).*tau(:,S_m:(S_m+N_m+N_c+N_a-1),a,c,a),2); term_MC4 = term_MC2;

term_M41 = term_M41 + (X(:,c)./term_MC1.*(X(:,a).*G(:,B,a,c,a))./term_MC2.*(tau(:,B,a,c,a)- term_MC3./term_MC4)); end term_M4 = term_M4 + term_M41; end

term_M = term_M1 + term_M2 + term_M3 + term_M4;

if B == S_m LNGammaLC(:,B) = term_M; else LNGammaLC(:,B) = term_M - tau(:,2,1,B,1) - G(:,B,1,2,1).*tau(:,B,1,2,1); end end

%LnGammaLC(c)------

for ct = S_c:(S_c+N_c-1)

term_C11 = sum(X(:,S_a:(S_a+N_a-1)),2);

term_C1=zeros(NP,1); for a = S_a:(S_a+N_a-1)

term_C12 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a-1),ct,a,ct),2); term_C13 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a- 1),ct,a,ct).*tau(:,S_m:(S_m+N_m+N_c+N_a-1),ct,a,ct),2);

term_C1 = term_C1 + (X(:,a)./term_C11.*term_C13./term_C12);

219

end

term_C2=zeros(NP,1); for m = S_m:(S_m+N_m-1)

term_C22 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a-1),1,m,1),2); term_C23 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a- 1),1,m,1).*tau(:,S_m:(S_m+N_m+N_c+N_a-1),1,m,1),2);

term_C2 = term_C2 + ((X(:,m).*G(:,ct,1,m,1))./term_C22.*(tau(:,ct,1,m,1)-term_C23./term_C22)); end

term_C31 = sum(X(:,S_c:(S_c+N_c-1)),2);

term_C3 = zeros(NP,1); term_Ce1 = zeros(NP,1); for a = S_a:(S_a+N_a-1) term_CC3=zeros(NP,1); for c = S_c:(S_c+N_c-1)

term_C32 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a-1),a,c,a),2); term_C33 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a- 1),a,c,a).*tau(:,S_m:(S_m+N_m+N_c+N_a-1),a,c,a),2); term_C34 = term_C32;

term_CC3 = term_CC3 + (X(:,c)./term_C31.*(X(:,a).*G(:,ct,a,c,a))./... term_C32.*(tau(:,ct,a,c,a)-term_C33./term_C34));

end term_C3 = term_C3 + term_CC3; term_Ce1 = term_Ce1 + X(:,a).*tau(:,2,ct,a,ct); end

term_Ce2 = sum(X(:,S_a:(S_a+N_a-1)),2); term_Ce3 = term_Ce1./term_Ce2;

term_C = term_C1 + term_C2 + term_C3; LNGammaLC(:,ct) = z(ct).*(term_C - G(:,ct,1,2,1).*tau(:,ct,1,2,1) - term_Ce3);

end

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%LnGammaLC(a)------

for an = S_a:(S_a+N_a-1)

term_A11 = sum(X(:,S_c:(S_c+N_c-1)),2);

term_A1=zeros(NP,1); for c = S_c:(S_c+N_c-1)

term_A12 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a-1),an,c,an),2); term_A13 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a- 1),an,c,an).*tau(:,S_m:(S_m+N_m+N_c+N_a-1),an,c,an),2);

term_A1 = term_A1 + (X(:,c)./term_A11.*term_A13./term_A12); end

term_A2=zeros(NP,1); for m = S_m:(S_m+N_m-1)

term_A22 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a-1),1,m,1),2); term_A23 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a- 1),1,m,1).*tau(:,S_m:(S_m+N_m+N_c+N_a-1),1,m,1),2);

term_A2 = term_A2 + ((X(:,m).*G(:,an,1,m,1))./term_A22.*(tau(:,an,1,m,1)-term_A23./term_A22)); end

term_A31 = sum(X(:,S_a:(S_a+N_a-1)),2);

term_A3 = zeros(NP,1); term_Ae1 = zeros(NP,1); for c = S_c:(S_c+N_c-1) term_AA3=zeros(NP,1); for a = S_a:(S_a+N_a-1)

term_A32 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a-1),c,a,c),2); term_A33 = sum(X(:,S_m:(S_m+N_m+N_c+N_a-1)).*G(:,S_m:(S_m+N_m+N_c+N_a- 1),c,a,c).*tau(:,S_m:(S_m+N_m+N_c+N_a-1),c,a,c),2); term_A34 = term_A32;

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term_AA3 = term_AA3 + (X(:,a)./term_A31.*(X(:,c).*G(:,an,c,a,c))./term_A32.*(tau(:,an,c,a,c)- term_A33./term_A34)); end term_A3 = term_A3 + term_AA3; term_Ae1 = term_Ae1 + X(:,c).*tau(:,2,an,c,an);

end

term_A = term_A1 + term_A2 + term_A3;

term_Ae2 = sum(X(:,S_c:(S_c+N_c-1)),2); term_Ae3 = term_Ae1./term_Ae2;

LNGammaLC(:,an) = z(an).*(term_A - G(:,an,1,2,1).*tau(:,an,1,2,1) - term_Ae3); end

%solve for GammaNRTL------GammaNRTL = ones(NP,(10)); for j = S_m:(S_m+N_m+N_c+N_a-1) GammaNRTL(:,j) = LNGammaPDH(:,j)+LNGammaBorn(:,j)+LNGammaLC(:,j); end

Gamma(1:N,:) = GammaNRTL(:,2:N+1)'; end

LnGa = Gamma; if nargout > 1 Ga = exp(Gamma); end

% Solve for pure component fugacity coefficients------function Yv=Vap(x,Gamma,T,NP) global H_amine A N_m vl totalP

A1 = A(:,1)*ones(1,NP); A2 = A(:,2)*ones(1,NP); A3 = A(:,3)*ones(1,NP); A4 = A(:,4)*ones(1,NP); A5 = A(:,5)*ones(1,NP); A6 = A(:,6)*ones(1,NP); A7 = A(:,7)*ones(1,NP);

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Ps=exp(A1+A2./((ones(N_m-1,1)*T)+A3)+A4.*(ones(N_m-1,1)*T)+A5.*log((ones(N_m-1,1)*T))+A6.*(ones(N_m- 1,1)*T).^A7);

Ptnew = 0; fhi0 = ones(N_m-1,NP); fhi = ones(N_m,NP); P = ones(N_m,NP); Pnew = ones(N_m,NP); for i = 1:N_m-1 for q = 1:NP y = 1; Tg = T(:,q); p = Ps(i,q); fhi0(i,q) = Fug(i,Tg,p,y); end end %------for k = 1:8

for i = 1:N_m-1 P(i,:) = Ps(i,:).*x(i,:).*Gamma(i,:).*fhi0(i,:).*exp(vl(i).*(Ptnew-Ps(i,:))./8.314./T)./fhi(1,:); end P(N_m,:) = H_amine.*x(N_m,:).*Gamma(N_m,:)./fhi(N_m,:);

Pt = sum(P,1);

y = P./(ones(N_m,1)*Pt);

for j = 1:5

for i = 1:N_m-1 Pnew(i,:) = Ps(i,:).*x(i,:).*Gamma(i,:).*fhi0(i,:).*exp(vl(i).*(Ptnew-Ps(i,:))./8.314./T)./fhi(1,:); end Pnew(N_m,:) = H_amine.*x(N_m,:).*Gamma(N_m,:)./fhi(N_m,:); Ptnew = sum(Pnew,1);

Ptm = max(abs((Ptnew - Pt)./Pt));

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if Ptm<0.005 break end

if j==5 disp('Possible inaccurate result detected, please increase j') fprintf('\tError code (percentage)%.4f\n',Ptm) end Pt = Ptnew; %Iteration end

%Evaluate composition for outter iteration------

ynew = P./(ones(N_m,1)*Pt);

ym = max(max(abs(ynew - y)./ynew)); % Solve for fugacity coefficients------y = ynew; Z = ones(N_m,NP); fhinew = zeros(N_m,NP); for q = 1:NP Tg = T(:,q); p = Ptnew(:,q); [fhinew(:,q),Z(:,q)] = Fug(N_m,Tg,p,y(:,q)); end %------fhi = fhinew; if ym<0.03&&k~=1 break end end if k==8 disp('Possible inaccurate result detected, please increase k') fprintf('\tError code (percentage)%.4f\n',ym) end if totalP == 1 Yv=[sum(Pnew(1:N_m,:));Z(1,:);y;Pnew(N_m,:)]; else Yv=[Pnew(N_m,:);Z(1,:);y;Pnew(N_m,:)];

224 end function [fhi,ZZ] = Fug(BETA,T,P,y) global Ac fugmod

R = 8.314; % gas constant [=] J/(mol K)

N=length(y); %Number of components delta = zeros(N,N);

%Critical Properties------if N>1 Q = Ac; end if N==1 Q = Ac(BETA,:); % Water end %------

% Reduced variables and parameters of the model------for j=1:N; Tc(j)=Q(j,1); Pc(j)=Q(j,2); w(j)=Q(j,3); Tr(j)= T/Tc(j); Pr(j)= P/Pc(j); m(j) = 0.48 + 1.574*w(j) - 0.176*w(j)^2; alfa(j) = (1 + m(j)*(1 - sqrt(Tr(j))))^2; a(j) = 0.42748*((R*Tc(j))^2/Pc(j))*alfa(j); b(j) = 0.08664*R*Tc(j)/Pc(j); A(j)= a(j)*P/(R*T)^2; B(j)= b(j)*P/(R*T); end %------

%Parameters of the EOS based on the mixing rule ------for j=1:N for i=1:N

225

E(i,j)=y(i)*y(j)*(1-delta(i,j))*(A(i)*A(j))^0.5; EE(i,j)=(1-delta(i,j))*(A(i)*A(j))^0.5; end F(j)=B(j)*y(j); end e=sum(E); AA=sum(e); BB=sum(F); %------

% Compressibility factor ------if isnan(AA) || isnan(BB) Z = [1 0 0]; else Z = roots([1 -1 (AA-BB-BB^2) (-AA*BB)]); end ZR = []; for i = 1:3; if isreal(Z(i)); ZR(i) = Z(i); end end

ZZ = max(ZR); %max root for vapour phase %------

%Fugacity Coefficient------if fugmod == 1

for i=1:N;

for k=1:N; Ay(k)=y(k)*EE(i,k); AY=sum(Ay); end

fhi = exp((ZZ-1).*(B(i)/BB)-log(ZZ-BB)-AA/BB*log((ZZ+BB)/ZZ).*(2*(AY^2/AA^2)-(B(i)/BB)));

end

226

elseif fugmod == 2 for i=1:N;

for k=1:N; Ay(k)=y(k)*EE(i,k); AY=sum(Ay); end

fhi = exp((B(i)/BB)*(ZZ- 1)- log(ZZ-BB) -(AA/(2*BB*sqrt(2)))*log((ZZ+(1+sqrt(2))*BB)... /(ZZ+(1-sqrt(2))*BB))*((2*(AY/AA)-(B(i)/BB)))); end end function sendemail(subject) % Define these variables appropriately: mail = '[email protected]'; %Your GMail email address password = 'xxx'; %Your GMail password

% Then this code will set up the preferences properly: setpref('Internet','E_mail',mail); setpref('Internet','SMTP_Server','smtp.gmail.com'); setpref('Internet','SMTP_Username',mail); setpref('Internet','SMTP_Password',password); props = java.lang.System.getProperties; props.setProperty('mail.smtp.auth','true'); props.setProperty('mail.smtp.socketFactory.class', 'javax.net.ssl.SSLSocketFactory'); props.setProperty('mail.smtp.socketFactory.port','465');

% Send the email. Note that the first input is the address you are sending the email to sendmail('[email protected]','',subject)

227