Rigorous mathematical model for reactive absorption

Development and Demonstration of a New NonEquilibrium Rate-Based Process Model for the Hot Potassium Carbonate Process by

Su Ming Pamela Ooi

Thesis submitted for the degree of Doctor of Philosophy

in

The University of Adelaide School of Chemical Engineering July 2008

Summary

Summary Chemical absorption and desorption processes are two fundamental operations in the process industry. Due to the rate-controlled nature of these processes, classical equilibrium stage models are usually inadequate for describing the behaviour of chemical absorption and desorption processes. A more effective modelling method is the non-equilibrium rate-based approach, which considers the effects of the various driving forces across the vapour-liquid interface.

In this thesis, a new non-equilibrium rate-based model for chemical absorption and desorption is developed and applied to the hot potassium carbonate process CO2 Removal Trains at the Santos Moomba Processing Facility. The rate-based process models incorporate rigorous thermodynamic and mass transfer relations for the system and detailed hydrodynamic calculations for the column internals.

The enhancement factor approach was used to represent the effects of the chemical

reactions.

The non-equilibrium rate-based CO2 Removal Train process models were implemented in the Aspen Custom Modeler® simulation environment, which enabled rigorous thermodynamic and physical property calculations via the Aspen Properties® software. Literature data were used to determine the parameters for the Aspen Properties® property models and to develop empirical correlations when the default Aspen Properties® models were inadequate. Preliminary simulations indicated the need for adjustments to the absorber column models, and a sensitivity analysis identified the effective interfacial area as a suitable model parameter for adjustment. Following the application of adjustment factors to the absorber column models, the CO2 Removal Train process models were successfully validated against steady-state plant data.

The success of the Aspen Custom Modeler® process models demonstrated the suitability of the nonequilibrium rate-based approach for modelling the hot potassium carbonate process. Unfortunately, the hot potassium carbonate process could not be modelled as such in HYSYS®, Santos’s preferred simulation environment, due to the absence of electrolyte components and property models and the limitations of the HYSYS® column operations in accommodating chemical reactions and nonequilibrium column behaviour. While importation of the Aspen Custom Modeler® process models into HYSYS® was possible, it was considered impractical due to the significant associated computation time.

To overcome this problem, a novel approach involving the HYSYS® column stage efficiencies and hypothetical HYSYS® components was developed.

Stage efficiency correlations, relating various

operating parameters to the column performance, were derived from parametric studies performed in Aspen Custom Modeler®. Preliminary simulations indicated that the efficiency correlations were only necessary for the absorber columns; the regenerator columns were adequately represented by the default equilibrium stage models.

Hypothetical components were created for the hot potassium

carbonate system and the standard Peng-Robinson property package model in HYSYS® was i

Summary

modified to include tabular physical property models to accommodate the hot potassium carbonate system. Relevant model parameters were determined from literature data. As for the Aspen Custom Modeler® process models, the HYSYS® CO2 Removal Train process models were successfully validated against steady-state plant data.

To demonstrate a potential application of the HYSYS® process models, dynamic simulations of the two most dissimilarly configured trains, CO2 Removal Trains #1 and #7, were performed. Simple firstorder plus dead time (FOPDT) process transfer function models, relating the key process variables, were derived to develop a diagonal control structure for each CO2 Removal Train. The FOPDT model is the standard process engineering approximation to higher order systems, and it effectively described most of the process response curves for the two CO2 Removal Trains. Although a few response curves were distinctly underdamped, the quality of the validating data for the CO2 Removal Trains did not justify the use of more complex models than the FOPDT model.

While diagonal control structures are a well established form of control for multivariable systems, their application to the hot potassium carbonate process has not been documented in literature. Using a number of controllability analysis methods, the two CO2 Removal Trains were found to share the same optimal diagonal control structure, which suggested that the identified control scheme was independent of the CO2 Removal Train configurations. The optimal diagonal control structure was tested in dynamic simulations using the MATLAB® numerical computing environment and was found to provide effective control.

This finding confirmed the results of the controllability analyses and

demonstrated how the HYSYS® process model could be used to facilitate the development of a control strategy for the Moomba CO2 Removal Trains. In conclusion, this work addressed the development of a new non-equilibrium rate-based model for the hot potassium carbonate process and its application to the Moomba CO2 Removal Trains. Further work is recommended to extend the model validity over a wider range of operating conditions and to expand the dynamic HYSYS® simulations to incorporate the diagonal control structures and/or more complex control schemes.

ii

Statement

Statement This work contains no material which has been accepted for the award of any other degree or diploma in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text.

I give consent to this copy of my thesis, when deposited in the University Library, being made available for loan and photocopying, subject to the provisions of the Copyright Act 1968.

Su Ming Pamela Ooi Adelaide, 16/07/2008

iii

Acknowledgements

Acknowledgements I wish to express my sincere appreciation to all organisations and persons who have contributed council and assistance during this work.

In particular, I would like to thank Santos for providing funding and technical support for this project. Special thanks are extended to Keith Humphris, Len Cowen, Ian Smith, Ross Mullner, Claire Barber, Randall Yeates and Mark Moss for their advice and assistance with providing technical data.

I would also like to thank my academic supervisors, Associate Professor Brian O’Neill, Dr Chris Colby and Professor Keith King, for their encouragement, advice and guidance.

Special thanks are

extended to Dr Robin Thiele who provided invaluable advice regarding rate-based modelling.

Finally, I would like to express my deepest gratitude to my boyfriend Simon and to my parents for providing endless support and encouragement, without which I could not have completed this thesis.

iv

Table of Contents

Table of Contents Nomenclature

…...........

xvii

Chapter 1: Introduction

…...........

1

1.1 Project Objectives

…...........

2

1.2 Thesis Structure

…...........

2

…...........

4

2.1 The Hot Potassium Carbonate Process

…...........

5

2.2 The Non-Equilibrium Rate-Based Approach

…...........

18

2.3 Electrolyte Thermodynamics

…...........

30

2.4 Process Simulation Platform

…...........

32

2.5 Multivariable Process Control

…..........

34

2.6 Summary

…..........

45

…..........

46

3.1 Summary of Property Models

…..........

47

3.2 The Electrolyte NRTL Model

…..........

50

3.3 Summary

…..........

58

…..........

59

4.1 Process Model Equations

…..........

60

4.2 Preliminary CO2 Train Simulations

…..........

69

4.3 Column Model Adjustments

…..........

73

4.4 CO2 Train Model Validation

…..........

83

4.5 Summary

…..........

91

…..........

92

5.1 Solution Operating Parameters

…..........

93

5.2 Raw Gas Operating Parameters

…..........

97

5.3 Column Operating Parameters

…..........

100

5.4 Summary

…..........

107

…..........

108

6.1 The Modelling Approach

…..........

109

6.2 Thermodynamic and Physical Property Models

…..........

115

6.3 Summary

…..........

120

…..........

121

7.1 Absorber Column Models

…..........

122

7.2 Regenerator Column Models

…..........

124

7.3 Preliminary Column Model Simulations

…..........

127

7.4 Column Stage Efficiency Correlations

…..........

135

Chapter 2: Literature Review

Chapter 3: Thermodynamic and Physical Properties of the Hot Potassium Carbonate System

Chapter 4: Aspen Custom Modeler® Process Model Development

Chapter 5: Aspen Custom Modeler® CO2 Removal Train Parametric Studies

Chapter 6: Modelling the Hot Potassium Carbonate System in HYSYS®

Chapter 7: The Absorber and Regenerator Column Models

v

Table of Contents

7.5 Summary

…..........

141

…..........

142

8.1 Ancillary Operation Models

…..........

143

8.2 Steady-State CO2 Train Models

…..........

147

8.3 Model Validation

…..........

151

8.4 Summary

…..........

158

…..........

159

9.1 Dynamic CO2 Train Models

…..........

160

9.2 Process Case Studies

…..........

169

9.3 Summary

…..........

175

…..........

176

10.1 Selection of Diagonal Control Structure

…..........

177

10.2 Selection of Diagonal Control Structure Configuration

…..........

184

10.3 Analysis of Diagonal Control Structure Performance

…..........

187

10.4 BLT Tuning

…..........

190

10.5 Diagonal Control Structure Dynamic Simulations

…..........

192

10.6 Summary

…..........

198

….........

199

11.1 Conclusions

….........

200

11.2 Recommendations

….........

203

References

….........

204

Appendix A: Thermodynamic Model Equations

…..........

A-1

A.1 Reference States

…..........

A-2

A.2 The Electrolyte NRTL Model

…..........

A-3

A.3 Cubic Equations of State

…..........

A-8

…..........

A-10

B.1 Thermodynamic Property Models

…..........

A-11

B.2 Physical and Transport Property Models

…..........

A-17

…..........

A-38

C.1 Parameter Values

…..........

A-39

C.2 Data Regression Procedure

…..........

A-41

C.3 Data Regression Results

…..........

A-44

…..........

A-49

D.1 The Different Modelling Approaches

…..........

A-50

D.2 Model Adjustments

…..........

A-52

D.3 CO2 Train Model Validation

…..........

A-56

…..........

A-62

Chapter 8: HYSYS® CO2 Removal Train Process Model Development

Chapter 9: Dynamic HYSYS® Simulations of CO2 Removal Trains #1 and #7

Chapter 10: Process Control Studies for CO2 Trains #1 and #7

Chapter 11: Conclusions and Recommendations

Appendix B: Property Models for Aspen Custom Modeler®

Appendix C: Electrolyte NRTL Adjustable Parameters

Appendix D: Aspen Custom Modeler® Simulation Results

Appendix E: Hypothetical K2CO3* HYSYS® Component Properties

vi

Table of Contents

E.1 Base Properties

…..........

A-63

E.2 Additional Point Properties

…..........

A-66

E.3 Temperature Dependent Properties

…..........

A-67

Appendix F: Property Models for HYSYS®

…..........

A-70

F.1 Thermodynamic Property Models

…..........

A-71

F.2 Physical and Transport Property Models

…..........

A-72

…..........

A-84

G.1 Data Regression Procedure

…..........

A-85

G.2 Data Regression Results

…..........

A-87

…..........

A-88

H.1 Preliminary Column Model Simulations

…..........

A-89

H.2 Steady-State CO2 Train Models

…..........

A-95

H.3 CO2 Train Model Validation

…..........

A-101

…..........

A-107

I.1 Selection of Diagonal Control Structure

…..........

A-108

I.2 Selection of Diagonal Control Structure Configuration

…..........

A-111

I.3 Analysis of Diagonal Control Structure Performance

…..........

A-114

I.4 BLT Tuning

…..........

A-115

I.5 Diagonal Control Structure Dynamic Simulations

…..........

A-117

Appendix G: Enhanced PR Binary Interaction Parameters

Appendix H: HYSYS® Simulation Results

Appendix I: Process Control Studies of the CO2 Trains

vii

List of Figures

List of Figures Figure 2.1.1:

A simple form of the hot potassium carbonate process.

…..........

5

Figure 2.1.2:

Basic CO2 train process flow diagrams.

…..........

7

Figure 2.1.3:

Reaction flow scheme for the hot potassium carbonate process.

…..........

10

Figure 2.2.1:

The two-film model for simultaneous mass and energy transfer.

…..........

20

Figure 3.2.1:

Comparison between the Electrolyte NRTL predictions and the experimental data.

…..........

54

CO2 partial pressure over K2CO3 solution as a function of CO2 loading.

…..........

54

Comparison between the Electrolyte NRTL predictions and the experimental data.

…..........

57

H2S partial pressure over K2CO3 solution as a function of equivalent H2S content.

…..........

57

Figure 4.1.1:

Equilibrium stage for Model 1 (adapted from Thiele (2007)).

…..........

62

Figure 4.1.2:

Non-equilibrium stage for Model 2 (adapted from Thiele (2007)).

…..........

63

Figure 4.1.3:

Non-equilibrium stage for Model 3 (adapted from Thiele (2007)).

…..........

64

Figure 4.2.1:

Preliminary Aspen Custom Modeler® simulation column configurations.

…..........

69

Results of the absorber discretisation simulation runs for CO2 train #1.

…..........

70

Results of the regenerator discretisation simulation runs for CO2 train #1.

…..........

70

Results of the different modelling approaches for CO2 trains #1 and #7.

…..........

72

Figure 4.3.1:

Temperature profiles for CO2 trains #1 and #7.

…..........

74

Figure 4.3.2:

Effect of the liquid phase enthalpy correction on the absorber profiles.

…..........

75

Sensitivity analysis results for the absorber column model (Model 2).

…..........

79

Sensitivity analysis results for the regenerator column model (Model 2).

…..........

80

Effect of the solution reboiler steam flow on the regenerator column model (Model 2).

…..........

81

Effect of the effective interfacial area adjustment factor on the absorber CO2 and H2S vapour phase profiles.

…..........

82

Simplified CO2 train configurations for the Aspen Custom Modeler® simulations.

…..........

83

CO2 and H2S vapour and liquid phase profiles for the first set of plant data.

…..........

88

CO2 and H2S vapour and liquid phase profiles for the second set of plant data.

…..........

87

Vapour and liquid phase temperature profiles for the two sets of plant data.

…..........

88

Effect of the solution flow rate on the performance of the CO2 trains.

…..........

94

Figure 3.2.2: Figure 3.2.3: Figure 3.2.4:

Figure 4.2.2: Figure 4.2.3: Figure 4.2.4:

Figure 4.3.3: Figure 4.3.4: Figure 4.3.5: Figure 4.3.6: Figure 4.4.1: Figure 4.4.2: Figure 4.4.3: Figure 4.4.4: Figure 5.1.1:

viii

List of Figures

Figure 5.1.2:

Effect of the solution strength on the performance of the CO2 trains.

…..........

95

Effect of the solution CO2 loading on the performance of the CO2 trains.

…..........

96

Effect of the raw gas flow rate on the performance of the CO2 trains.

…..........

98

Effect of the raw gas CO2 content on the performance of the CO2 trains.

…..........

99

Effect of the absorber temperature on the performance of the CO2 trains.

…..........

101

Effect of the regenerator temperature on the performance of the CO2 trains.

…..........

102

Figure 5.3.3:

Effect of pressure on the performance of the CO2 trains.

…..........

104

Figure 5.3.4:

Effect of the steam flow rate to the regenerator solution reboilers on the performance of the CO2 trains.

…..........

105

Effect of the makeup water flow rate to the regenerator overhead catchpots on the performance of the CO2 trains.

…..........

106

The different definitions of the column stage efficiency in HYSYS®.

…..........

114

Comparison between the enhanced PR predictions and the experimental data.

…..........

118

Comparison between the enhanced PR predictions and the experimental data.

…..........

119

Figure 7.1.1:

Process flow diagram of an absorber column model in HYSYS®.

…..........

122

Figure 7.2.1:

Process flow diagrams of the two most dissimilar regenerator column models in HYSYS®.

…..........

126

Equilibrium stage simulation results for the absorber and regenerator columns.

…..........

128

Figure 7.3.2:

Sensitivity analysis results for the absorber models.

…..........

130

Figure 7.3.3:

Effect of the column stage efficiencies on the absorber composition and temperature profiles.

…..........

131

Figure 7.3.4:

Sensitivity analysis results for the regenerator models.

…..........

132

Figure 7.3.5:

Effect of the column stage efficiencies on the regenerator composition and temperature profiles.

…..........

133

Effect of the reboiler steam flow on the regenerator column performance.

…..........

134

Effect of the correlated overall stage efficiencies on the steadystate absorber columns.

…..........

137

Effect of the correlated overall stage efficiencies on the steadystate behaviour of the dynamic absorber columns.

…..........

137

An example HYSYS® spreadsheet for calculating the absorber overall stage efficiencies.

…..........

139

HYSYS® process flow diagram of the CO2 train absorption circuits.

…..........

143

Figure 8.1.2:

HYSYS® process flow diagram of the solution pumpset model.

…..........

144

Figure 8.1.3:

HYSYS® spreadsheet for the pumpset calculations.

…..........

145

Figure 5.1.3: Figure 5.2.1: Figure 5.2.2: Figure 5.3.1: Figure 5.3.2:

Figure 5.3.5: Figure 6.1.1: Figure 6.2.1: Figure 6.2.2:

Figure 7.3.1:

Figure 7.3.6: Figure 7.4.1: Figure 7.4.2: Figure 7.4.3: Figure 8.1.1:

ix

List of Figures

Figure 8.2.1:

Process flow diagram for the steady-state HYSYS® model of CO2 train #1.

…..........

149

Process flow diagram for the steady-state HYSYS® model of CO2 train #7.

…..........

150

CO2 and H2S vapour and liquid phase profiles for the first set of data.

…..........

153

CO2 and H2S vapour and liquid phase profiles for the second set of data.

…..........

154

Vapour and liquid phase temperature profiles for the two sets of plant data.

…..........

155

Process flow diagram of the simplified dynamic HYSYS® model for CO2 train #1.

…..........

163

Process flow diagram of the simplified dynamic HYSYS® model for CO2 train #7.

…..........

164

Figure 9.1.3:

Flow control loop responses.

…..........

166

Figure 9.1.4:

Temperature control loop responses.

…..........

167

Figure 9.1.5:

Liquid level control loop responses.

…..........

168

Figure 9.2.1:

Process response curves for a 2% magnitude step change in the raw gas flow rate at 0 min.

…..........

171

Process response curves for a 2% magnitude step change in the lean solution flow rate at 0 min.

…..........

171

Process response curves for a 2% magnitude step change in the reboiler steam flow rate at 0 min.

…..........

172

Process response curves for a 2% magnitude step change in the regenerator liquid level at 0 min.

…..........

172

Process response curves for a 2% magnitude step change in the raw gas CO2 content at 0 min.

…..........

173

Figure 10.1.1:

Frequency plots of the MRI and CN.

…..........

181

Figure 10.1.2:

Frequency plots of DCN and DC for CO2 train #1.

…..........

182

Figure 10.1.3:

Frequency plots of DCN and DC for CO2 train #7.

…..........

183

Figure 10.2.1:

Frequency plots for the RGA elements.

…..........

185

Figure 10.3.1:

Frequency plots for |PRGAij| and |CLDGij|.

…..........

189

Figure 10.4.1:

Plots of the scalar function W.

…..........

191

Figure 10.5.1:

Frequency plots of |1+GOL,i(s)| and |PRGAij|.

…..........

195

Figure 10.5.2:

CO2 train #1 closed-loop step response curves at the high gas throughput conditions.

…..........

196

CO2 train #7 closed-loop step response curves at the high gas throughput conditions.

…..........

197

Comparison between the predicted and experimental solution heat capacities.

…..........

A-16

Comparison between the predicted and experimental solution mass densities.

…..........

A-20

Comparison between the predicted and experimental solution viscosities.

…..........

A-25

Comparison between the predicted and experimental solution surface tensions.

…..........

A-28

Figure 8.2.2: Figure 8.3.1: Figure 8.3.2: Figure 8.3.3: Figure 9.1.1: Figure 9.1.2:

Figure 9.2.2: Figure 9.2.3: Figure 9.2.4: Figure 9.2.5:

Figure 10.5.3: Figure B.1.1: Figure B.2.1: Figure B.2.2: Figure B.2.3:

x

List of Figures

Figure B.2.4:

Comparison between the predicted and experimental solution thermal conductivities.

…..........

A-33

Results of the different modelling approaches for CO2 trains #2 to #4.

…..........

A-50

Results of the different modelling approaches for CO2 trains #5 and #6.

…..........

A-51

Figure D.2.1:

Temperature profiles for CO2 trains #2 to #4.

…..........

A-52

Figure D.2.2:

Temperature profiles for CO2 trains #5 and #6.

…..........

A-53

Figure D.2.3:

Effect of the effective interfacial area adjustment factor on the absorber CO2 and H2S vapour phase profiles.

…..........

A-55

CO2 and H2S vapour and liquid phase column profiles for the first set of plant data.

…..........

A-56


…..........

A-57

CO2 and H2S vapour and liquid phase column profiles for the second set of plant data.

…..........

A-58


…..........

A-59

Figure D.3.5:

Column temperature profiles for the first set of plant data.

…..........

A-60

Figure D.3.6:

Column temperature profiles for the second set of plant data.

…..........

A-61

Figure F.2.1:

Comparison between the predicted and experimental solution mass densities.

…..........

A-74

Comparison between the predicted and experimental solution viscosities.

…..........

A-77

Comparison between the solution surface tensions predicted by the tabular model and the empirical correlation.

…..........

A-79

Comparison between the solution thermal conductivities predicted by the tabular model and the empirical correlation.

…..........

A-83


…..........

A-89


…..........

A-90


…..........

A-91


…..........

A-92


…..........

A-93


…..........

A-94

Figure H.2.1:

Process flow diagram for the steady-state model of CO2 train #2.

…..........

A-96

Figure H.2.2:


…..........

A-97

Figure H.2.3:


…..........

A-98

Figure H.2.4:


…..........

A-99

Figure H.2.5:


…..........

A-100

Figure D.1.1: Figure D.1.2:

Figure D.3.1: Figure D.3.2: Figure D.3.3: Figure D.3.4:

Figure F.2.2: Figure F.2.3: Figure F.2.4: Figure H.1.1: Figure H.1.2: Figure H.1.3: Figure H.1.4: Figure H.1.5: Figure H.1.6:

xi

List of Figures

Figure H.3.1:


…..........

A-101


…..........

A-102


…..........

A-103


…..........

A-104

Figure H.3.5:

Column temperature profiles for the first set of plant data.

…..........

A-105

Figure H.3.6:

Column temperature profiles for the second set of plant data.

…..........

A-106

Figure I.5.1:

CO2 train #1 closed-loop step response curves at the medium gas throughput conditions.

…..........

A-121

CO2 train #7 closed-loop step response curves at the medium gas throughput conditions.

…..........

A-122

CO2 train #1 closed-loop step response curves at the low gas throughput conditions.

…..........

A-123

CO2 train #7 closed-loop step response curves at the low gas throughput conditions.

…..........

A-124

Figure H.3.2: Figure H.3.3: Figure H.3.4:

Figure I.5.2: Figure I.5.3: Figure I.5.4:

xii

List of Tables

List of Tables Table 2.1.1:

Nameplate capacity of the CO2 trains.

…..........

8

Table 2.1.2:

Typical operating data for the CO2 trains from 2002.

…..........

9

Table 2.1.3:

Acid gas absorption reactions in the hot potassium carbonate process.

…..........

10

Table 2.1.4:

Ion contribution factors (Pohorecki and Moniuk, 1988).

…..........

13

Table 2.1.5:

Acid gas desorption reactions in the hot potassium carbonate process.

…..........

13

…..........

15

Temperature dependence of the equilibrium and Henry’s Law constants.

…..........

16

Table 2.1.8:

Liquid phase relations and vapour-liquid equilibria expressions.

…..........

16

Table 2.2.1:

The MESH equations for a stage i and j = 1…NC components.

…..........

19

Table 2.2.2:

Mass transfer relations (Taylor and Krishna, 1993).

…..........

21

Table 2.2.3:

Mass transfer coefficient and effective interfacial area correlations (Onda et al., 1968ab).

…..........

27

Table 2.2.4:

Hydrodynamic relations (Stichlmair et al., 1989).

…..........

29

Table 2.2.5:

Packing characteristics and constants for metal random packings.

…..........

29

Common dynamic process behaviour (Stephanopoulos, 1984; Wade, 2004).

…..........

35

Table 2.5.2:

Ziegler-Nichols and Tyreus-Luyben controller tuning rules.

…..........

37

Table 2.5.3:

Liquid level PID controller tuning rules (Wade, 2004).

…..........

37

Table 3.1.1:

Vapour phase thermodynamic and physical property models.

…..........

47

Table 3.1.2:

Liquid phase thermodynamic and physical property models.

…..........

48

Table 3.1.3:

Property data sources for the hot potassium carbonate system.

…..........

49

Table 3.2.1:

Adjustable binary parameters for the Electrolyte NRTL model.

…..........

50

Table 3.2.2:

Electrolyte NRTL parameters for the CO2-K2CO3-KHCO3-H2O system.

…..........

53

Electrolyte NRTL parameters for the CO2-H2S-K2CO3-KHCO3KHS-K2S-H2O system.

…..........

56

The average variation associated with the model parameter values for the CO2 train absorbers and regenerators.

…..........

77

Effective interfacial area adjustment factor values and their effect on the CO2 train absorbers.

…..........

82

CO2 train simulation results for the first set of plant data in Table 2.1.2.

…..........

89

CO2 train simulation results for the second set of plant data in Table 2.1.2.

…..........

90

Property estimation methods for the Miscellaneous class of hypothetical components.

…..........

110

Thermodynamic and physical property models.

…..........

115

Table 2.1.6: Table 2.1.7:

Table 2.5.1:

Table 3.2.3: Table 4.3.1: Table 4.3.2: Table 4.4.1: Table 4.4.2: Table 6.1.1: Table 6.2.1:

CO2-H2S-K2CO3-KHCO3-KHS-K2S-H2O system equilibria.

xiii

List of Tables

Table 6.2.2:

Enhanced PR parameter values for the CO2-K2CO3-H2O system.

…..........

117

Table 6.2.3:

Enhanced PR parameter values for the CO2-H2S-K2CO3-H2O system.

…..........

119

Coefficients for the steady-state column stage efficiency correlations.

…..........

136

Coefficients for the dynamic column stage efficiency correlations.

…..........

136

An example HYSYS® macro for updating the absorber overall stage efficiencies.

…..........

140

CO2 train simulation results for the first set of plant data in Table 2.1.2.

…..........

156

CO2 train simulation results for the second set of plant data in Table 2.1.2.

…..........

157

Flow control loop characteristics and controller settings for CO2 trains #1 and #7.

…..........

166

Temperature control loop characteristics and controller settings for CO2 trains #1 and #7.

…..........

167

Table 9.1.3:

Liquid level controller settings for CO2 trains #1 and #7.

…..........

167

Table 9.2.1:

Process transfer functions for CO2 train #1.

…..........

173

Table 9.2.2:

Process transfer functions for CO2 train #7.

…..........

174

Table 10.1.1:

Process transfer function matrices for the diagonal control structures.

…..........

179

Table 10.1.2:

Sensitivity analysis indices at steady-state.

…..........

180

Table 10.2.1:

Steady-state results for the interaction and stability analyses for the RGF-RSF control structure.

…..........

185

Reordered process transfer function matrices for the RGF-RSF diagonal control structure.

…..........

186

Steady-state values for the PRGA and CLDG for the selected configuration for the RGF-RSF diagonal control structure.

…..........

188

BLT tuning parameters for the RGF-RSF diagonal control structures for CO2 trains #1 and #7.

…..........

191

Table B.1.1:

Component critical properties (Poling et al., 2001).

…..........

A-11

Table B.1.2:

Ideal gas heat capacity coefficients and enthalpies of formation (Poling et al., 2001).

…..........

A-12

Table B.1.3:

Ionic species thermodynamic properties (Zemaitis et al., 1986).

…..........

A-15

Table B.1.4:

Temperature dependence of Henry’s Law constants.

…..........

A-15

Table B.1.5:

Criss-Cobble entropy parameters (Criss and Cobble, 1964ab).

…..........

A-16

Table B.1.6:

Atmospheric solution heat capacity data.

…..........

A-16

Table B.1.7:

Parameter values for the Aspen Properties® heat capacity polynomial.

…..........

A-16

Table B.2.1:

Antoine equation coefficients (Rowley et al., 1998).

…..........

A-17

Table B.2.2:

Parameter values for the modified Rackett equation (Spencer and Danner, 1972).

…..........

A-19

Atmospheric solution mass density data.

…..........

A-19

Table 7.4.1: Table 7.4.2: Table 7.4.3: Table 8.3.1: Table 8.3.2: Table 9.1.1: Table 9.1.2:

Table 10.2.2: Table 10.3.1: Table 10.4.1:

Table B.2.3:

xiv

List of Tables

Table B.2.4:

Pair parameter values for the Clarke Aqueous Electrolyte Volume model.

…..........

A-19

Table B.2.5:

Component characteristic volumes.

…..........

A-21

Table B.2.6:

Coefficients for the DIPPR vapour viscosity model (Rowley et al., 1998).

…..........

A-23

Coefficients for the Andrade liquid viscosity equation (Reid et al., 1977).

…..........

A-24

Table B.2.8:

Atmospheric solution viscosity data.

…..........

A-25

Table B.2.9:

Parameter values for the Jones-Dole viscosity equation.

…..........

A-25

Table B.2.10:

Coefficients for the DIPPR surface tension equation (Rowley et al., 1998).

…..........

A-27

Table B.2.11:

Atmospheric solution surface tension data.

…..........

A-28

Table B.2.12:

Surface tension correlation coefficients.

…..........

A-28

Table B.2.13:

Coefficients for the DIPPR vapour thermal conductivity model (Rowley et al., 1998).

…..........

A-30

Coefficients for the DIPPR liquid thermal conductivity equation (Rowley et al., 1998).

…..........

A-32

Table B.2.15:

Atmospheric solution thermal conductivity data.

…..........

A-32

Table B.2.16:

Liquid phase thermal conductivity correlation coefficients.

…..........

A-32

Table B.2.17:

Normal boiling points and the corresponding liquid molar volumes (Poling et al., 2001).

…..........

A-35

Table B.2.18:

Ionic conductivities at infinite dilution.

…..........

A-37

Table B.2.19:

Diffusivities in water at 25°C.

…..........

A-37

Table C.1.1:

The Electrolyte NRTL adjustable parameters used in this work.

…..........

A-39

Table C.1.2:

The Electrolyte NRTL adjustable parameters used in this work.

…..........

A-40

Table C.3.1:

Statistical results for the CO2-K2CO3-KHCO3-H2O system data regression runs.

…..........

A-45

Suitable parameter value sets for the CO2-K2CO3-KHCO3-H2O system.

…..........

A-46

Statistical results for the CO2-H2S-K2CO3-KHCO3-KHS-K2S-H2O system data regression runs.

…..........

A-47

Suitable parameter value sets for the CO2-H2S-K2CO3-KHCO3KHS-K2S-H2O system.

…..........

A-48

Alternative mass transfer coefficient and effective interfacial area correlations.

…..........

A-54

Table E.3.1:

Temperature dependent property correlation coefficients.

…..........

A-67

Table F.2.1:

Coefficient values for the HYSYS® liquid density tabular model.

…..........

A-73

Table F.2.2:

Coefficient values for the HYSYS® liquid viscosity tabular model.

…..........

A-77

Coefficient values for the HYSYS® liquid surface tension tabular model.

…..........

A-79

Coefficient values for the HYSYS® liquid thermal conductivity tabular model.

…..........

A-83

Statistical results for the CO2-K2CO3-H2O system data regression runs.

…..........

A-87

Table B.2.7:

Table B.2.14:

Table C.3.2: Table C.3.3: Table C.3.4: Table D.2.1:

Table F.2.3: Table F.2.4: Table G.2.1:

xv

List of Tables

Table G.2.2: Table I.2.1:

Statistical results for the CO2-H2S-K2CO3-H2O system data regression runs.

…..........

A-87

System poles and zeros for the SGC-RSF control structure.

…..........

A-111

xvi

Nomenclature

Nomenclature Latin Letters A

–

*

Step size or amplitude of limit cycle

–

A

Latini component parameter 3

Aca

m /kmol

Clarke Aqueous Electrolyte Volume parameter

AI

–

Debye-Hückel parameter

AAD

%

Average absolute deviation

a

–

a

m ·bar/kmol

Cubic equation of state mixture parameter

Activity

a

2 3 m /m

Specific surface area

6

2

2

Riedel anion parameter

2

Riedel cation parameter

W·m /K·kmol

aa

W·m /K·kmol

ac

2

aI

m /m 6

3

Effective interfacial area 2

aj

m ·bar/kmol

Cubic equation of state parameter for species j

aT,j

kJ/kmol·K

Criss-Cobble entropy parameter

Bca

L/mol

Breslau-Miller electrolyte parameter

3

Cubic equation of state mixture parameter

3

Ion contribution factor

3

Breslau-Miller anion parameter

3

m /kmol

b

m /kmol

b ba,1

m /kmol

ba,2

m /kmol·K

Breslau-Miller anion parameter

bc,1

m3/kmol

Breslau-Miller cation parameter

3

Breslau-Miller cation parameter

3

m /kmol·K

bc,2 bj

m /kmol

Cubic equation of state parameter for species j

bT,j

–

Criss-Cobble entropy parameter 3

C

kmol/m 3 mol/cm

ˆ C H2S

mol/m

Cj

–

Electrolyte NRTL parameter (zj for ions and 1 for molecular species)

C $jw

–

Reduced volume integral of species j at infinite dilution in water

Cp

kJ/kmol·K cal/mol·K kJ/kg·K Btu/lbmol·°R

Heat capacity

ˆ C p

kJ/kg·K

Mass heat capacity

kJ/kmol·K

Average value of C p between 25°C and temperature T

CR

–

Reduced molar density

Cv

J/mol·K

Heat capacity at constant volume

Cp

T

3

Molar concentration or molar density Equivalent H2S content

25

CLDG

–

Closed-loop disturbance gain matrix

CN

–

Condition number

ct

kmol/m

Total mole concentration

D

m

Diameter

D

3

2

cm /s m2/s

Effective diffusion coefficient or diffusivity

xvii

Nomenclature

Djk Dw

2

m /s

Binary diffusion coefficient for species pair j-k

2

cm /s

Diffusion coefficient in water

2

jk

m /s

Maxwell-Stefan diffusivity for the binary species pair j-k

DC

–

Disturbance cost

DCN

–

Disturbance condition number

DR

–

Decay ratio

DRGA

–

Dynamic relative gain array

d

–

Height of first overshoot

d

–

Process load or disturbance

d(s)

–

Vector of process disturbances

dh

m

Hydraulic diameter

dN

m

Nominal packing size

dp

m

Particle diameter

df

–

Degrees of freedom 2

Energy flux across the vapour-liquid interface

E

kW/m

Estage

–

HYSYS® column overall stage efficiency

EMurph

–

Murphree vapour efficiency

EF

–

Enhancement factor

e

C

Charge of an electron (1.60219×10

F

C/mol

Faraday’s constant (96 485 C/mol)

F

kmol/s

Feed molar flow

F

kmol/s

Flow rate

F

–

F-Test result

F

–

BLT detuning factor

F1, F2,F3

–

Chung functions

Fc

–

Fractional conversion of K2CO3 to KHCO3 and KHS

FCO2

–

CO2 loading

Fj

–

Fractional conversion of CO3 to HCO3 due to species j absorption

Fmax

m3/min

Maximum flow through control valve

'Fin

%

Maximum percentage step change in inflow

f

atm bar Pa

Fugacity

fo

–

Particle friction factor

fT

–

Twu function at temperature T

fx,0

–

Ely-Hanley function

G

–

Electrolyte NRTL parameter

G

kmol/s

Vapour phase molar flow

G

–

Transfer function

G(s)

–

-19

C)

2-

-

Transfer function matrix 3

ˆ G

sm /h

Vapour phase standard volumetric flow

G(s)

–

Transfer function matrix with paired elements along the diagonal

G

E

kJ/kmol

Symmetric excess Gibbs energy

G

E*

kJ/kmol

Un-symmetric excess Gibbs energy

–

Process transfer function

G(s)

xviii

Nomenclature

g

m/s

H

m

2

2

Gravitational acceleration (9.81m/s ) Height 3

Hj

bar·m /kmol

Henry’s Law constant for species j in solution

Hj

bar

Henry’s Law constant for species j in pure water 3

H wj

bar·m /kmol

Henry’s Law constant for species j in water

Ha

–

Hatta number

HETP

m

Height of packing equivalent to a theoretical plate

h

kJ/kmol kJ/kg

Enthalpy

h

–

Height of relay

h

–

Twu function

–

Ely-Hanley function

f

'h

kJ/kmol kJ/mol

Enthalpy or heat of formation

'hvap

kJ/kmol

Enthalpy of vaporisation

'hfk

kJ/mol

Joback contribution for group k to the enthalpy of formation

I

–

hx,0

Identity matrix 3

Ic

kmol/m

Molar concentration based ionic strength

Ix

–

Mole fraction based ionic strength

IAE

–

Integral of the absolute error

J

–

J

kmol/m ·s

Diffusion flux

K

– kmol/m3 2 6 kmol /m

Chemical equilibrium constant

K

–

Gain

K’

–

Pseudo-equilibrium constant

K’p

–

Integrator gain

k

J/K erg/K

Boltzmann constant (1.38066×10-23 J/K or 1.38066×10-16 erg/K)

k

m/s

Mass transfer coefficient

k

1/s m3/kmol·s 6 2 m /kmol ·s

Reaction rate constant

kjk

–

Cubic equation of state binary interaction parameter for species pair j-k

k’

1/s

Pseudo-first-order reaction rate constant

k’’

1/s

Kinetic coefficient

L

kmol/s

Liquid phase molar flow

Lc

–

Closed-loop log modulus

'Lmax

%

Objective function for the linear quadratic regulator problem 2

3

Maximum allowable percentage deviation from setpoint

Lˆ

m /h

Liquid phase volumetric flow

Le

–

Lewis number

M

kmol

Material holdup

MAD

%

Maximum absolute deviation

MIC

–

Morari index of integral controllability

MRI

–

Morari Resiliency Index

xix

Nomenclature

MW

kg/kmol g/mol

Molecular weight

m

–

Manipulated variable 3

Solution molarity (total K2CO3 concentration)

2

m

kmol/m

N

kmol/m ·s

Molar flux across the vapour-liquid interface

N

–

Number

N

–

Order of multivariable system

Neqm

–

Number of equilibrium stages

Nk

–

Number of UNIFAC groups of type k for Joback method

No

1/mol

Avogadro’s number (6.02205×1023 1/mol)

NC

–

Number of components

ND

–

Number of data points

NI

–

Niederlinski index

n

kmol

Number of moles

n

–

Number of species in the system

P

atm bar Pa psia

Pressure or partial pressure

P

s

bar

Vapour pressure

Po

min

Period of oscillation

Pu

min

Ultimate period or limit cycle period

'P

Pa kPa

Pressure drop

PRGA

–

Performance relative gain array

p

–

Pitzer-Debye-Hückel closest approach parameter (14.9)

p

–

p-value

Q

–

Objective function for the data regression runs

Q

kJ/s kW

Heat flow or duty

QDR

–

Quarter decay ratio

R

kJ/kmol·K 3 m ·bar/K·kmol 3 atm·cm /mol·K

Gas constant (8.3144 kJ/kmol·K or 0.0831447 m3·bar/K·kmol or 82.06 atm·cm3/mol·K)

R

kmol/m3·s

Molar reaction rate

RSP

–

Ratio setpoint

RGA

–

Relative gain array

RRMSQE

–

Residual root mean square error

Re

–

Reynolds number

rj

m

Born radius of species j

S f25

kJ/kmol·K

Infinite dilution entropy at 25°C

S fT

kJ/kmol·K

Infinite dilution entropy at temperature T

SG

–

Specific gravity

SSQ

–

Sum of squared errors

'SG

–

Change in specific gravity

s

–

Laplace transform variable (s = i·Z)

xx

Nomenclature

T

K °C °R °F

Temperature

Tref

K

Reference temperature (298.15 K)

T*

–

Dimensionless temperature

t

min

Time

U

kJ

Energy holdup

U(s)

–

Process input transfer function

u

–

V

m

Process input 3

Volume 3

V

cm /mol 3 m /kmol

Molar volume

f Vca

m3/kmol

Clarke Aqueous Electrolyte Volume parameter

Ve

L/mol

Breslau-Miller effective volume

VRo , VRG

–

COSTALD reduced volumes

v

m/s

*

3

v ~ v

f

Velocity

cm /mol

Characteristic volume

–

Reduced molar volume 3

cm /mol m3/kmol

Partial molar volume at infinite dilution in pure water

W

–

Scalar BLT function

Wi

–

Weight of data group i

WSSQ

–

Weighted sum of squares

wf

–

Weight fraction

wfK 2CO3

–

Equivalent weight fraction of K2CO3

X

–

Effective local mole fraction

x

–

Liquid phase mole fraction

x

–

Component mole fraction

Y(s)

–

Process output transfer function

y

–

Vapour phase mole fraction

y

–

Component mass fraction

y

–

Process output or response

Z

–

Compressibility

Z

–

Chung parameter

Z

cSt

Twu kinematic viscosity parameter

v

Z°

1/atm

Isothermal compressibility at infinite dilution in water

Z

(0)

–

Pitzer compressibility function for spherical molecules

Z

(1)

–

Pitzer compressibility deviation function

ZRA

–

Rackett parameter

z

–

Charge number

z

–

Feed mole fraction

z

–

Ionic charge

z

–

Secondary process variable

xxi

Nomenclature

Greek Letters D

–

Chung parameter

D

–

Electrolyte NRTL non-randomness factor

D

–

Latini component parameter 2

D

kW/m ·K

Heat transfer coefficient

Dc

–

Riedel critical point parameter

Dj

–

Cubic equation of state alpha function for species j

E

–

Chung parameter

E

–

Latini component parameter

E

–

Packing specific constant 3

E CO2

m /kmol

Contribution factor for CO2 absorption

G

m

Film thickness

G

Debye

Dipole moment

Gp

–

Chapman-Enskog-Brokaw polar parameter

H

–

Error 2

H

C /J·m

Dielectric constant

H

erg

Characteristic energy

I

°

Phase lag

rad I

m3/m3 3

3

Phase volumetric holdup

I

m /m

Ijk

–

Wilke viscosity function for species pair j-k

*

m·K/W

Stiel-Thodos parameter

J

–

Activity coefficient

J

–

Latini component parameter

J

Packing voidage

–

Symmetric activity coefficient

*

–

Un-symmetric activity coefficient

K

–

Dimensionless film coordinate

K

–

Column stage efficiency

M

kV

Electrical potential

M

–

Fugacity coefficient

N

–

Chung association factor

O

–

Relative gain

O

–

Eigenvalue

O

min

IMC tuning parameter

O

W/m·K

Thermal conductivity

O

–

Vector of eigenvalues

O'

W/m·K

Ely-Hanley translational thermal conductivity contribution

O”

W/m·K

Ely-Hanley internal thermal conductivity contribution

J

2

Of

m /·kmol

Ionic conductivity at infinite dilution in water

P

kJ·m/kmol

Chemical potential

xxii

Nomenclature P

cP kg/m·s Pa·s

Dynamic viscosity

'Pca

cP

Jones-Dole viscosity contribution term for electrolyte ca

Q

cSt 2 m /s

Kinematic viscosity

T

min

Dead time 3

U

g/m 3 kg/m

Mass density

V

–

Standard error associated with a data point

V(s)

–

Singular value

V

Å

Characteristic length

Vc

N/m

Critical surface tension parameter

'Vca

N/m

Onsager-Samaras surface tension contribution term for electrolyte ca

VL

N/m dyne/cm

Surface tension

W

–

Electrolyte NRTL binary interaction energy parameter

W

min

Natural period of oscillation

W

min

Time constant

X

–

Stoichiometric coefficient

:D,jk

–

Diffusion coefficient integral for species pair j-k

Z

–

Acentricity

Z

rad/min 1/6

Frequency 1/2

1/2

2/3

[

K ·kmol /kg ·atm

Dean-Stiel parameter

8 atm) absorber countercurrent to the lean hot potassium carbonate solution which is fed to the top of the absorber. Within the column, contact between the two phases results in the transfer of the acid gases from the gas phase into the liquid phase. The sweet gas leaves through the top of the absorber while the rich potassium carbonate solution, containing the absorbed acid gases, leaves from the bottom. The rich solution is depressurised, causing some of the absorbed acid gas to flash off, before entering the low pressure (1 – 3 atm) regenerator. The remaining acid gas is then removed in the regenerator through reboil stripping. The removed acid gas is vented from the top of the regenerator while the regenerated potassium carbonate solution is pumped back to the absorber.

The high pressure in the absorber is required to ensure that the acid gas partial pressure in the raw gas exceeds the equilibrium pressure of the acid gas over the potassium carbonate solution (Benson and Field, 1959). This is necessary for the absorption of the acid gas to take place. The high operating pressure also enables the absorber to be run at temperatures close to the atmospheric boiling point of the potassium carbonate solution (100° – 140°C) without excessive evaporation of the 5


solution, thereby eliminating the need to heat the rich solution before it enters the regenerator. Another advantage of the elevated absorber temperature is the increased solubility of potassium carbonate and potassium bicarbonate. This enables the use of concentrated solutions between 20 to 40 wt% potassium carbonate, which facilitates greater acid gas removal. Kohl and Nielson (1997) recommend a solution concentration of 30 wt% potassium carbonate as a suitable design value for most applications.

Further research and development work has introduced many enhancements that have substantially improved the process economics and extended the applicability of the hot potassium carbonate process. One such enhancement is the addition of small quantities of amine or inorganic activators to the potassium carbonate solution to increase the rate of acid gas absorption (Bartoo, 1984; Kohl and Nielson, 1997). Other improvements involve modifications to the process flow scheme, such as the inclusion of more complex split-flow absorbers and two-stage regenerators to increase the sweet gas purity (Field et al., 1962; Benson and Parrish, 1984), and energy conservation features to improve the process economy (Benson and McCrea, 1979; Grover, 1987).

To date, there are over 700 commercial installations of the hot potassium carbonate process worldwide (UOP Gas Processing, 2000). Seven of these comprise the Raw Gas Conditioning (RGC) Plant at the Santos Moomba Processing Facility.

Located in the Central Australian desert, the

Moomba facility processes raw natural gas to reduce its CO2 and water content and to recover ethane and heavier hydrocarbons. The removal of CO2 occurs in the RGC Plant, which consists of seven parallel hot potassium carbonate process trains known as the CO2 Removal Trains (CO2 trains). The configuration and operation of these CO2 trains are outlined in the following section.

2.1.2 The Santos Moomba CO2 Trains The seven parallel Moomba CO2 trains are not identical, but share similar layouts, which are depicted in Figure 2.1.2. The CO2 trains are based on a simple single-stage packed absorber and single-stage packed regenerator configuration, similar to the flow scheme in Figure 2.1.1.

Some energy

conservation features have been incorporated: power recovery turbines are coupled to the main solution pumps for all seven trains, while gas-gas heat exchangers have been included for heat recovery in CO2 trains #3 to #7. A proprietary amine activator, ACT-1, was previously added to the potassium carbonate solutions for CO2 trains #1 to #5, but Santos has since discontinued its use. The purpose of the Moomba CO2 trains is to remove sufficient CO2 to prevent the formation of dry ice (solid CO2) in the cold sections of the downstream Liquids Recovery Plant (LRP) and to meet the quality specification for sales gas, the final gas product from the Moomba Processing Facility. H2S removal also occurs within the CO2 trains, but this is of minor consequence due to the relatively insignificant levels of H2S in the raw gas.

6


Potassium Carbonate Solution

Flash Steam Acid Gas

Condenser

Overhead Catchpot

Sour Water (Trains #3 & #4) Water Cooler

REGENERATOR th (4 bed only in Trains #3 )

ABSORBER (Only 1 bed in Trains #1 & #2)

Makeup Water

Raw Gas Gas-Gas Heat Exchanger (Trains #3 & #4)

Solution Reboiler

Sweet Gas

LP Steam

Sweet Gas Separator Condensate Receiver Power Recovery Turbine

Sour Water

Main Solution Pump

Steam Turbine Condensate

(a)

Potassium Carbonate Solution

Flash Steam (Trains #5 & #6)

Acid Gas

Condenser Overhead Catchpot

Sour Water

ABSORBER (Only 2 beds in Train #5)

Makeup Water

REGENERATOR

Flash Steam (Train #7)

LP Steam

Raw Gas Gas-Gas Heat Exchanger

Solution Reboiler

Sweet Gas

Sweet Gas Separator Condensate Receiver

Sour Water

Power Recovery Turbine

Main Solution Pump

Steam Turbine Condensate

(b) Figure 2.1.2: Basic CO2 train process flow diagrams. (a) CO2 trains #1 to #4. (b) CO2 trains #5 to #7.

The raw gas entering the RGC Plant typically contains 16 to 20 mol% CO2 and 5 to 20 ppm H2S. This variation is due to changes in the proportions of the raw gas supplied to Moomba from various gas fields, whose individual CO2 content range from 5 to 45 mol%. The sweet gas leaving the RGC Plant typically contains 2.5 to 3 mol% CO2 and 0.5 to 1 ppm H2S. However, due to the different absorber designs, the CO2 content of sweet gas streams produced by the individual trains can vary between 0.1 7


and 8 mol% depending on the operating conditions. The combined sweet gas from the RGC Plant is fed to the LRP for separation into sales gas (which is predominantly methane), ethane, liquefied petroleum gas (LPG) and condensate.

Due to the high CO2 content of the raw gas, the processing capacity of the CO2 trains is normally limited by the CO2 removal capacity of the hot potassium carbonate process. Table 2.1.1 gives an indication of the maximum capacities of each train for processing raw gas to produce sweet gas that meets the Santos specification of 2.5 mol% CO2, and two sets of typical operating data from 2002 are presented in Table 2.1.2. The performance of the CO2 trains is critical to the successful operation of the Moomba Processing Facility since the RGC Plant is one of the facility’s bottlenecks. The gas flow through the RGC Plant sets the gas flow through the Moomba Processing Facility and therefore the sales gas, ethane and LPG production rates. Table 2.1.1: Nameplate capacity of the CO2 trains. CO2 Removal Capacity (106 sm3/d) Train #1 Train #2 Train #3 Train #4 Train #5 Train #6 Train #7 Total 3

0.30 0.30 0.50 0.54 0.58 0.69 0.96 3.87

Raw Gas CO2 Content (mol%) 16

18

20

Maximum Raw Gas Capacity (106 sm3/d) 2.17 2.17 3.61 3.90 4.19 4.98 6.93 27.95

3

1.89 1.89 3.15 3.40 3.65 4.34 6.04 24.34

1.67 1.67 2.79 3.01 3.23 3.84 5.35 21.56

Note: sm /d refers to m /d at standard conditions, i.e. dry gas at 15°C and 1 atm.

8

9

Raw Gas a mol% CO2 ppm H2S 6 3 b Flow (10 sm /d) Temperature (°C) Sweet Gas a mol% CO2 ppm H2S Temperature (°C) Acid Gas 6 3 b CO2 (10 sm /d) c Temperature (°C) Lean Solution e CO2 loading e H2S loading f wt% K2CO3 3 Flow (m /h) Temperature (°C) Rich Solution e CO2 loading e H2S loading 3 Flow (m /h) Temperature (°C) Sour Water ppm CO2 3 Flow (m /h) Absorber Pressure (bar) Pressure drop (bar) Regenerator Pressure (bar) Pressure drop (bar) Cooling Water Circuit 3 Water Flow (m /h) Cooler Duty (MW) Overhead Condenser Temperature (°C) Pressure (bar) Solution Reboiler g Steam flow (t/h) a

CO2 Train Data Set #1 #3 #4 #5

#1

#2

18.5 20 1.95 38

18.5 20 1.65 38

18.5 20 2.93 95

18.5 20 3.35 95

2.5 10) imply unbalanced sensitivity to process uncertainties and may indicate control problems (Skogestad and Postlethwaite, 1996). Consequently, the set of manipulated variables with the smallest CN should be selected.

It should be noted that CN and the MRI are scale-dependent and are therefore functions of the units of Gp(s). To circumvent this problem, Gp(s) should be scaled based on physical grounds, e.g. by dividing

each variable by its allowed range (Skogestad and Postlethwaite, 1996). 38


2.5.3.2 The Disturbance Condition Number and the Disturbance Cost The sensitivity of a MIMO process to disturbances also affects the control system behaviour, and should also be considered in the selection of the manipulated variables. Two useful indices are the disturbance condition number (DCN) (Skogestad and Morari, 1987) and the disturbance cost (DC) (Lewin, 1996): 1

DCN

DC

Gp (s) Gd (s) d(s)

2

Gd (s) d(s) 2

Vmax (s)

(2.5.5)

1

Gp (s) Gd(s) d(s)

(2.5.6) 2

where Gd(s) is the process disturbance transfer function matrix, and d(s) is the process disturbance vector. Both DCN and DC provide an indication of the extent of control action required to reject a disturbance. Small values for DCN (~1) and DC indicate the system is relatively insensitive to the disturbance and hence less control action is needed to eliminate its effect. Consequently, the set of manipulated variables should be selected to give the smallest DCN and DC. Like CN and the MRI, DCN and DC are scale-dependent, so it is important that Gd(s) and d(s) are well-scaled. It should be noted that the above four indices are dependent on the choice of controlled and manipulated variables, but are unaffected by permutations in the control loop pairings. Therefore, these indices can only be used to discriminate between alternative diagonal control structures and are not applicable for selecting the configuration (variable pairings) for the diagonal control structure.

2.5.4 Selection of Diagonal Control Structure Configuration Ideally, the diagonal control structure resulting from the selected controlled and manipulated variables should have minimal interaction between its SISO control loops (Svrcek et al., 2006). Since there are N! feasible control loops for an N×N MIMO system, the following analysis methods are used to identify suitable diagonal control structure configurations.

2.5.4.1 The Relative Gain Array The most well-known and extensively applied variable pairing tool is the relative gain array (RGA), which was proposed by Bristol (1966) as a measure of the SISO control loop interactions in a diagonal control structure. For an N×N MIMO process, the RGA is a dimensionless matrix whose ijth element Oij is the relative gain of a controlled variable yi to a manipulated variable mj:

Oij

§ wyi · ¨ ¸ m w j © ¹m · § wyi ¸ ¨ m w j¹ ©

(s)

Gp,ij (s) Gp

1 T ij

for i,j = 1, …, N

y

39

(2.5.7)


The relative gains are unaffected by scaling and provide a quantitative comparison of how each manipulated variable affects each controlled variable. In general, variable pairings should be selected such that the relative gains are positive and as close to 1 as possible over the frequency range of interest (Skogestad and Postlethwaite, 1996).

This minimises the interaction between the loops,

thereby preventing stability problems caused by interaction.

2.5.4.2 The Niederlinski Index and the Morari Index of Integral Controllability Once suitable SISO control loop pairings have been determined from the RGA, the rows and columns of Gp(s) can be reordered such that the paired elements are located along the diagonal to correspond with the diagonal control structure.

The reordered process transfer matrix Gp(s) enables the

application of the Niederlinski index (NI) (Niederlinski, 1971):

det Gp (0)

NI

(2.5.8)

N

G

p,ii (0)

i 1

to analyse the stability of the selected control loop pairings at steady-state (s=0). If all the SISO controllers contain integral action and have positive loop gains, a negative NI proves that the specified diagonal control structure will definitely be closed-loop unstable (Grosdidier et al., 1985). Therefore, any variable pairings that give a negative NI should be eliminated. For a 2×2 system, a positive NI satisfies the necessary conditions for closed-loop stability. However, for higher order systems, a positive NI indicates the system may or may not be unstable, and its stability should therefore be tested by dynamic simulation.

An alternative measure of the stability of a diagonal control structure is the Morari index of integral controllability (MIC) (Grosdidier et al., 1985; Yu and Luyben, 1986): MIC O G

p

where O G

p

(0)

(2.5.9)

(0)

is the vector of the eigenvalues of the matrix Gp+(0), which is obtained from Gp(0) by

adjusting the signs so that all the diagonal elements are positive. If all the SISO controllers contain integral action and have positive loop gains, a negative eigenvalue for Gp+(0) will produce an unstable diagonal control structure. Consequently, any variable pairings that result in a negative MIC element should be eliminated.

2.5.5 Analysis of Diagonal Control Structure Performance After an appropriate diagonal control structure configuration has been identified from the above methods, its performance can be analysed through the use of the performance relative gain array (PRGA) and the closed-loop disturbance gain (CLDG) matrix (Skogestad and Postlethwaite, 1996): PRGA

1

Gp,diag(s) Gp (s)

(2.5.10)

40


CLDG

1

Gp,diag(s) Gp (s) Gd (s)

(2.5.11)

where Gp,diag(s) is a diagonal matrix consisting of the diagonal elements of Gp(s). For acceptable disturbance rejection and setpoint tracking performance, the following condition must be satisfied for each control loop i, disturbance k and setpoint j (Skogestad and Postlethwaite, 1996):

^

1 GOL,i (s) ! max CLDG ik , PRGA ij k, j

`

(2.5.12)

GOL,i (s) Gp,ii(s) Gc,i (s)

(2.5.13)

where GOL,i(s) is the open-loop transfer function and Gc,i(s) is the controller transfer function for loop i. Consequently, disturbances and setpoint changes corresponding to large CLDG and PRGA elements will be more difficult to control. It should be noted that |1+GOL,i(s)| need only be larger than |PRGAij| at frequencies where the setpoints are tracked, which is usually limited to low frequencies (Z1 1T T

c, j

2 / 7 @

(B.2.8)

where R is the gas constant, T is the absolute temperature, Tc is the critical temperature, Pc is the critical pressure, and ZRA is the Rackett parameter, for which values are presented in Table B.2.2. The liquid phase electrolyte molar densities CL,ca were calculated using the Clarke Aqueous Electrolyte Volume model (Chen et al., 1983): 1 C L,ca

f A ca Vca

x ca

(B.2.9)

1 x ca

A-18

Appendix B: Property Models for Aspen Custom Modeler® f where xca is the apparent electrolyte mole fraction for the electrolyte ca. Databank values for Vca and

Aca were available in Aspen Properties® for a number of cation-anion pairs, but not for the four key pairs of interest: (K+,CO32-), (K+,HCO3-), (K+,HS-) and (K+,S2-). Given the relatively negligible quantities of HS- and S2- ions present in the liquid phase for the process of interest, it was considered reasonable to neglect the effect of the (K+,HS-) and (K+,S2-) pairs on the liquid phase density. The parameter values for the (K+,CO32-) and (K+,HCO3-) pairs were regressed from the literature data in Table B.2.3 using the Aspen Properties® DRS, and are presented in Table B.2.4. Figure B.2.1 compares the solution mass densities predicted by equations (B.2.6) to (B.2.9) against the literature values. The average absolute deviation between the predicted and literature values is 0.4%. Table B.2.2: Parameter values for the modified Rackett equation (Spencer and Danner, 1972).

Component CO2 H2S H2O N2 CH4 C2H6 C3H8 n-C4H10 i-C4H10 n-C5H12 i-C5H12 n-C6H14 n-C7H16

ZRA 0.2736 0.2851 0.2432 0.2905 0.2876 0.2789 0.2763 0.2728 0.2750 0.2685 0.2716 0.2635 0.2611

Table B.2.3: Atmospheric solution mass density data.

Solution K2CO3 a K2CO3 b KHCO3 b K2CO3–KHCO3 c K2CO3–KHCO3 d a d

Concentration 20 – 40 wt% K2CO3 20 – 40 wt% K2CO3 1 – 30 wt% KHCO3 22 – 30 wt% K2CO3 e 30 wt% K2CO3 e

CO2 Loading 0 – 0.6 0–1

b

Temperature Range 30 – 100°C 30 – 90°C 30 – 80°C 70 – 115°C 70 – 130°C c

Armand Products Company (1998) Chernen’kaya and Revenko (1975) Bocard and Mayland (1962) e UOP Gas Processing (1998) These concentrations are in terms of equivalent K2CO3 weight percent.

Table B.2.4: Pair parameter values for the Clarke Aqueous Electrolyte Volume model.

Parameter

Component j

f Vca f Vca

+

K

a

Standard Deviation

2-

0.007465

0.001818

+

HCO3

-

0.018397

0.002006

+

2-

0.136841 0.077836

0.009026 0.009483

K

Aca Aca

Parameter Value a

Component k

K K+

CO3

CO3 HCO3-

3

Molar volume in m /kmol.

A-19


1600 Potassium carbonate (Armand Product Company, 1998) Potassium carbonate (Chernen'kaya & Revenko, 1975) Potassium bicarbonate (Chernen'kaya & Revenko, 1975) Potassium carbonate-bicarbonate (Bocard & Mayland, 1962) Potassium carbonate-bicarbonate (UOP, 1998)

Predicted Solution Mass Density (kg/m 3)

1500

1400

1300

1200

1100

1000

900

800 800

900

1000

1100

1200

1300

1400

1500

1600

3

Experimental Solution Mass Density (kg/m )

Figure B.2.1: Comparison between the predicted and experimental solution mass densities. The dashed lines (---) represent the ± 1% lines.

B.2.3.3 Partial Molar Volume The partial molar volume v fj of a component j at infinite dilution in water is required to determine the effect of pressure on its Henry’s Law constant. The method of Brelvi and O’Connell (1972) was used in this work to calculate v fj : v fj Z $j

R T

1 C $jw

(B.2.10)

where v fj is in cm3/mol, Z $j is the isothermal compressibility at infinite dilution in water in 1/atm: § VLs,H O ·¸ ¨ ln¨1 $ 2 ¸ ¨ Zj R T ¸ © ¹

(B.2.11)

2 3 0.42704 ~ v j 1 2.089 ~ v j 1 0.42367 ~ vj 1

C$jw is the reduced volume integral of component j at infinite dilution in water: § ¨ ln¨ C $jw ¨ ©

§ v* ¨ w* ¨v © j

· ¸ ¸ ¹

0.62

§ ¨ ln¨ C $jw ¨ ©

§ v* ¨ w* ¨v © j

· ¸ ¸ ¹

0.62

· ¸ ¸ ¸ ¹

2.4467 2.12074 ~ vj

for 2.0 d ~ v j d 2.785

(B.2.12)

· ¸ ¸ ¸ ¹

2 3.02214 1.87085 ~ v j 0.71955 ~ v j for 2.785 d ~ v j d 3 .2

(B.2.13)

A-20


T is the system temperature in K, R is the gas constant (82.06 atm·cm3/mol·K), VLs,H2O is the liquid phase molar volume of water in at its saturation pressure in cm3/mol, v *j is the characteristic volume for which values are listed in Table B.2.5, and ~ v j is the dimensionless reduced molar volume: ~ vj

v *j

(B.2.14)

VLs,H O 2

Table B.2.5: Component characteristic volumes.

v* (cm3/mol) 93.94 88.74 46.40 89.64 99.21 148.17 203.49 254.92 263.24 303.16 306.51 369.44 431.76

Component CO2 a H2S a H2O a N2 b CH4 b C2H6 b C3H8 b n-C4H10 b i-C4H10 b n-C5H12 b i-C5H12 b n-C6H14 b n-C7H16 b a b

Austgen and co-workers (1989) Zemaitiis and co-workers (1986)

B.2.4 Viscosity B.2.4.1 Vapour Phase Viscosity In this work, the vapour phase viscosity PG was determined in two steps. First, the low pressure vapour phase viscosity P LP G was determined from the Wilke method (Wilke, 1950): NC

P LP G

¦ j 1

y j P LP G, j

(B.2.15)

NC

¦y

k

I jk

k 1

I jk

0.5 0.25 º ª § LP · P § MWk · G , j » «1 ¨ ¸ ¨ ¸ MW j ¹ ¸ » « ¨© P LP © G,k ¹ ¼ ¬

ª § MW j ·º ¸» «8 ¨1 MW k ¹¼ ¬ ©

2

0 .5

(B.2.16)

LP where yj and yk are the vapour phase mole fractions of components j and k, P LP G, j and P G,k are the

component low pressure vapour phase viscosities, MWj and MWk are the component molecular

A-21


weights, and NC is the number of vapour phase components. The Dean-Stiel pressure correction (Dean and Stiel, 1965) was then applied to P LP G to give PG: PG

[

1.858 § §V · V 1.111¨ c ,G ¸ 1.08 u 10 4 ¨ 1.439 c ,G VG V G¹ © ¨e e [ ¨ ©

P LP G

Tc,G MWG

1/ 2

· ¸ ¸ ¸ ¹

(B.2.17)

1/ 6

Pc,G

(B.2.18)

2/3

where PG and P LP G are in cP, MWG is the vapour phase molecular weight in kg/kmol, VG is the vapour phase molar volume, Vc,G is the vapour phase critical molar volume, Tc,G is the vapour phase critical temperature in K, and Pc,G is the vapour phase critical pressure in atm. The vapour phase critical properties were obtained as follows: NC

Vc,G

¦y

j

Vc, j

(B.2.19)

j

Tc, j

(B.2.20)

j

Z c, j

(B.2.21)

j 1

NC

Tc,G

¦y j 1

NC

Z c,G

¦y j 1

Pc,G

Z c,G R Tc,G

(B.2.22)

Vc,G

where R is the gas constant, Zc,G is the vapour phase critical compressibility, and Vc,j, Tc,j and Zc,j are the component critical molar volume, temperature and compressibility, respectively.

The component low pressure vapour phase viscosities P LP G, j were calculated using the DIPPR vapour viscosity model (Rowley et al., 1998): P LP G, j

A TB 1 C D 2 T T

(B.2.23)

where P LP G, j is in cP and T is the system temperature in K. The relevant coefficients are given in Table B.2.6.

A-22


Table B.2.6: Coefficients for the DIPPR vapour viscosity model (Rowley et al., 1998).

NOTE: This table is included on page A-23 of the print copy of the thesis held in the University of Adelaide Library.

B.2.4.2 Liquid Phase Viscosity In this work, the liquid phase viscosity PL was determined from the Jones-Dole equation (Jones and Dole, 1929): PL

§ P L,solvent ¨1 ¨ ©

¦ 'P ca

ca

· ¸ ¸ ¹

(B.2.24)

where PL,solvent is the viscosity of the solvent, which was determined from the mole-fraction-weighted sum of the component liquid viscosities PL,j for H2O and any molecular species present in the liquid phase: NC

P L,solvent

¦x

j

P L, j

(B.2.25)

j 1

x is the liquid phase mole fraction and NC is the number of molecular species present in the liquid phase. The values of PL,j were calculated from the Andrade equation (Reid et al., 1977) with the coefficients given in Table B.2.7: ln P L, j

Aj

Bj

(B.2.26)

T

where PL,j is in cP and T is in K. The contribution term 'Pca was determined using the Breslau-Miller equation (Breslau and Miller, 1972; Breslau et al., 1974): 'P ca

2.5 Ve C L,ca 10.05 Ve C L,ca

2

where CL,ca is the molar concentration of the apparent electrolyte ca:

A-23

(B.2.27)


C L,ca

x ca C L

(B.2.28)

Ve is the effective volume in L/mol: Ve

B ca 0.002 2.60

for electrolytes involving univalent ions

(B.2.29)

Ve

B ca 0.011 5.06

for other electrolytes

(B.2.30)

B ca

b c,1 b c,2 T b a,1 b a,2 T

(B.2.31)

xca is the apparent electrolyte mole fraction, CL is the liquid phase molar density, and T is the system absolute temperature.

Databank values for the parameters bc,1, bc,2, ba,1 and ba,2 were available in Aspen Properties® for a number of cations and anions, but not for the K+, HCO3-, CO32-, HS- and S2- ions. Given the relatively negligible quantities of HS- and S2- ions present in the liquid phase for the process of interest, it was considered reasonable to neglect the effect of these two ions on the liquid phase viscosity. The parameter values for the K+, HCO3- and CO32- ions were regressed from the literature data in Table B.2.8 using the Aspen Properties® DRS, and are given in Table B.2.9. Figure B.2.1 compares the solution viscosities predicted by equations (B.2.24) to (B.2.31) against the literature values. The average absolute deviation between the predicted and literature values is 3.1%. Table B.2.7: Coefficients for the Andrade liquid viscosity equation (Reid et al., 1977).


A-24


Table B.2.8: Atmospheric solution viscosity data.

Solution K2CO3 a K2CO3 b K2CO3 c K2CO3 d KHCO3 a K2CO3–KHCO3 e

Concentration 20 – 40 wt% K2CO3 20 – 25 wt% K2CO3 28 – 40 wt% K2CO3 22 – 30 wt% K2CO3 10 – 30 wt% KHCO3 30 wt% K2CO3 f

a

CO2 Loading 0.6

b

Temperature Range 35 – 90°C 75 – 90°C 30 – 60°C 70 – 130°C 35 – 75°C 70 – 130°C

c

Chernen’kaya and Revenko (1975) Correia and co-workers (1980) Gonçalves and Kestin (1981) e f Bocard and Mayland (1962) UOP Gas Processing (1998) This concentration is in terms of equivalent K2CO3 weight percent . d

Table B.2.9: Parameter values for the Jones-Dole viscosity equation.

K+

Parameter

Value 13.0705 -0.0295 -

a

bc,1 bc,2 b ba,1 a ba,2 b a

3

Parameter in m /kmol.

b

Std. Dev. 4.7165 0.0113 -

HCO3Value Std. Dev. -12.7297 4.7312 0.02893 0.01138

CO32Value Std. Dev. -25.1305 9.3835 0.0576 0.0225

3

Parameter in m /kmol·K.

3.5 Potassium carbonate (Chernen'kaya & Revenko, 1975) Potassium carbonate (Correia et al, 1980) Potassium carbonate (Gonçalves & Kestin, 1981) Potassium carbonate (Bocard & Mayland, 1962) Potassium bicarbonate (Chernen'kaya & Revenko, 1975) Potassium carbonate-bicarbonate (UOP, 1998)

Predicted Solution Viscosity (cP)

3.0

2.5

2.0

1.5

1.0

0.5

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Experimental Solution Viscosity (cP)

Figure B.2.2: Comparison between the predicted and experimental solution viscosities. The dashed lines (---) represent the ± 5% lines.

A-25


B.2.5 Surface Tension In Aspen Properties®, the Onsager-Samaras model (Onsager and Samaras, 1934) is used to determine the liquid phase surface tension V L for an electrolyte system: VL

V L,solvent

¦x

ca

'V ca

(B.2.32)

ca

where VL,solvent is the surface tension of the solvent, which is determined from the mole-fractionweighted sum of the component surface tensions VL,j for H2O and any molecular species present in the liquid phase: NC

V L,solvent

¦x

j

V L, j

(B.2.33)

j 1

x is the liquid phase mole fraction and NC is the number of molecular species present in the liquid phase. The component surface tensions VL,j are calculated from the DIPPR surface tension equation (Rowley et al., 1998): 2

V L, j

§ T ·¸ A j ¨1 ¨ Tc, j ¸¹ ©

B j C j T

Tc , j

§ · § · D j ¨¨ T ¸¸ E j ¨¨ T ¸¸ © Tc , j ¹ © Tc , j ¹

3

(B.2.34)

where VL,j is in N/m, the temperature T and the component critical temperature Tc,j are in K, and the relevant coefficients are given in Table B.2.10. The contribution term 'Vca is defined as (Horvath, 1985): 'V ca

§ 1.13 u 10 13 H H O T 80.0 2 C L,ca log ¨¨ C L,ca H H2O ©

3 ·¸ ¸ ¹

(B.2.35)

where H H2O is the dielectric constant of water (Harned and Owen, 1958): H H2O

1 · §1 78.540 31989.380 ¨ ¸ © T 298.15 ¹

(B.2.36)

CL,ca is the molar concentration of the apparent electrolyte ca, and T is the system temperature in K. When equations (B.2.32) to (B.2.36) were applied to carbonate-bicarbonate solutions, the predicted surface tensions were found to be inconsistent with the literature data in Table B.2.11. Since there were no adjustable parameters which could be regressed to give a better fit to the data, it was decided to extrapolate the literature data to develop an empirical surface tension correlation of the form:

A-26


VL

A A wf >B B T B 0

0

1

1

K 2CO3 2

A 2 wf K 2CO3

2

T 2 FCO2 0.35

2 C 0 C1 T @

(B.2.37)

where VL is in N/m, T is the temperature in °C, wf K 2CO3 is the equivalent K2CO3 weight fraction, and F CO2 is the CO2 loading. The correlation coefficients were determined via the simple unweighted

least squares method in a Microsoft® Excel spreadsheet, and the resulting values are given in Table B.2.12. Since the surface tension of water is not affected by pressure within the pressure range of interest (Haar et al., 1984), VL was assumed to be similarly unaffected by pressure. The above correlation is valid for temperatures between 20° and 130°C, equivalent K2CO3 concentrations of 20 to 40 wt% and CO2 loadings between 0 and 1. These conditions encompass the typical absorber and regenerator operating conditions for the Moomba CO2 trains. It was considered reasonable to neglect the effect of the H2S loading on the surface tension since relatively negligible quantities of H2S are absorbed in the CO2 trains. The typical H2S loading is of the order of 10-4, which is several orders of magnitude less than the CO2 loading for the CO2 trains. Similarly, it was also considered reasonable to disregard the presence of other gases (such as N2, CH4 and other hydrocarbons) as negligible amounts of these gases are dissolved into the liquid phase.

Figure B.2.3 compares the surface tension values predicted by equation (B.2.37) against the literature values. The average absolute deviation is 0.4%, compared to 7.6% for the values predicted by the Onsager-Samaras model and the DIPPR equation. As a result, the empirical correlation was used in this work. Table B.2.10: Coefficients for the DIPPR surface tension equation (Rowley et al., 1998).


A-27


Table B.2.11: Atmospheric solution surface tension data.

Solution K2CO3 a K2CO3–KHCO3 b Na2CO3–NaHCO3 c

Concentration 0 – 50 wt% K2CO3 27 – 30 wt% K2CO3 d 20 wt% Na2CO3 e

a

CO2 Loading 0 – 0.35 0 – 0.9

b

Temperature Range 20°C 20 – 130°C 25°C c

d

Armand Products Company (1998) UOP Gas Processing (1998) Bedekar (1955) These e concentrations are in terms of equivalent K2CO3 weight percent. This concentration is in terms of equivalent Na2CO3 weight percent.

Table B.2.12: Surface tension correlation coefficients.

Coefficient A0 A1 A2 B0 B1 B2 C0 C1

Value 8.7129×10-1 0 1.4250 2.3859×10-2 4.9160×10-5 6.0020×10-7 8.2563×10-2 -1.4361×10-4

Predicted Solution Surface Tension (N/m)

0.12

0.11

Potassium carbonate Potassium carbonate-bicarbonate

0.10

0.09

0.08

0.07

0.06 0.06

0.07

0.08

0.09

0.10

0.11

0.12

Experimental Solution Surface Tension (N/m)

Figure B.2.3: Comparison between the predicted and experimental solution surface tensions. The dashed lines (---) represent the ± 1% lines.

A-28


B.2.6 Thermal Conductivity B.2.6.1 Vapour Phase Thermal Conductivity Like the vapour phase viscosity, the vapour phase thermal conductivity OG was determined in two steps in this work. First, the low pressure vapour phase thermal conductivity OLP G was determined from the Wassiljewa-Mason-Saxena method (Mason and Saxena, 1958): y j OLP G, j

NC

OLP G

¦ j 1

(B.2.38)

NC

¦y

I jk

k

k 1

I jk

0.5 0.25 º ª § LP · § MWk · » «1 ¨ P G, j ¸ ¨ ¸ ¸ MW » « ¨© P LP j © ¹ G,k ¹ ¼ ¬

ª § MW j ·º ¸» «8 ¨1 MW k ¹¼ ¬ ©

2

(B.2.39)

0 .5

where OLP G, j is the component low pressure thermal conductivity, yj and yk are the component vapour LP phase mole fractions, P LP G, j and P G,k are the component low pressure vapour phase viscosities, MWj

and MWk are the component molecular weights, and NC is the number of vapour phase components. The Stiel-Thodos pressure correction (Stiel and Thodos, 1964) was then applied to OLP G to give OG:

O O O

5

5

5

G

OLP G * Z c,G

G

OLP G * Z c,G

G

OLP G * Z c,G

*

· § 0.535Vc,G VG 1.22 u 10 2 ¨ e 1¸ ¸ ¨ ¹ ©

for

· § 0.67Vc,G VG 1.14 u 10 2 ¨ e 1.069 ¸ ¸ ¨ ¹ ©

for 0.5

Vc,G VG

0. 5

Vc,G

(B.2.40)

2. 0

(B.2.41)

· § 1.155Vc ,G Vc,G VG 2.60 u 10 3 ¨ e 2. 8 2.016 ¸ for 2.0 ¸ ¨ VG ¹ ©

(B.2.42)

§ Tc,G MWG 3 210 ¨ 4 ¨ Pc,G ©

· ¸ ¸ ¹

VG

1/ 6

(B.2.43)

Zc,G, Vc,G, Tc,G and Pc,G are the vapour phase critical compressibility, critical molar volume, critical temperature in K and critical pressure in bar, respectively, and the parameter * is in m·K/W . VG is the vapour phase molar volume, and MWG is the vapour phase molecular weight in kg/kmol. The vapour phase critical properties were obtained as follows (Poling et al., 2001): NC NC

Vc,G

¦¦ y

j

y k Vc, jk

(B.2.44)

j 1 k 1

A-29


NC NC

¦¦ y Tc,G

j

y k Vc, jk Tc, jk

j 1 k 1

(B.2.45)

Vc,G NC

ZG

¦y

j

Zj

(B.2.46)

j 1

Z c,G Pc,G

Vc, jk Tc, jk

0.291 0.08 Z G

(B.2.47)

Z c,G R Tc,G

(B.2.48)

Vc,G

V

1/ 3

c, j

Vc,k

1/ 3 3

(B.2.49)

8

Tc,j Tc,k 0.5

(B.2.50)

where ZG is the vapour phase acentricity, R is the gas constant, Vc,j and Vc,k are the component critical molar volumes, Tc,j and Tc,k are the component critical temperatures, Zj is the component acentricity, and Zc,j is the component critical compressibility. The component low pressure vapour phase thermal conductivities OLP G, j are calculated using the DIPPR vapour thermal conductivity model (Rowley et al., 1998): Aj T

OLP G, j 1

Cj T

Bj

(B.2.51)

Dj T2

where OLP G, j is in W/m·K and T is the system temperature in K. The relevant coefficients are given in Table B.2.13. Table B.2.13: Coefficients for the DIPPR vapour thermal conductivity model (Rowley et al., 1998).


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B.2.6.2 Liquid Phase Thermal Conductivity In Aspen Properties®, the liquid phase thermal conductivity OL for an electrolyte system is determined from the Riedel equation (Riedel, 1951): OL

§ ¨ O L,solvent (293K ) O L,solvent (293K ) ¨© O L,solvent

¦ a ca

c

· a a C L,ca ¸ ¸ ¹

(B.2.52)

where OL,solvent is the solvent thermal conductivity at the system temperature T, OL(293K) is the solvent thermal conductivity at 293 K, CL,ca is the molar concentration of the apparent electrolyte ca, and ac and aa are the cationic and anionic Riedel parameters. The solvent thermal conductivity is determined from the component thermal conductivities OL,j of H2O and any molecular species present in the liquid phase via the Vredeveld mixing rule (Reid et al., 1977): § ¨ ¨ ©

O L,solvent

¦ wf

j

O L, j

2

j

· ¸ ¸ ¹

0.5

(B.2.53)

where wfj is the component weight fraction and NC is the number of molecular species present in the liquid phase. The values of OL,j are calculated from the DIPPR equation (Rowley et al., 1998) with the coefficients given in Table B.2.14: O L, j

A j B j T C j T2 D j T3 E j T 4

(B.2.54)

where OL,j is in W/m·K and T is in K. Using the Aspen Properties® databank values for the parameters ac and aa, equations (B.2.52) to (B.2.54) were applied to potassium carbonate-bicarbonate solutions.

The resulting liquid phase

thermal conductivity values were found to be inconsistent with the literature data in Table B.2.15. The ac and aa values were re-regressed from the literature data using the Aspen Properties® DRS, but this did not improve the performance of equations (B.2.52) to (B.2.54). Consequently, it was decided to extrapolate the literature data to develop an empirical liquid phase thermal conductivity correlation of the form: OL

A B

0

A 1 wf K 2CO3 A 2 FCO2 A 3 T A 4 T 2

0

B1 T B 2 T 2 B 3 P

(B.2.55)

where OL is in W/m·K, T is the temperature in °C, P is the pressure in bar, wf K 2CO3 is the equivalent K2CO3 weight fraction, and F CO2 is the CO2 loading. The correlation coefficients were determined via the simple unweighted least squares method in a Microsoft® Excel spreadsheet, and the resulting values are given in Table B.2.16. The dependence of OL on pressure was assumed to be the same as

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that for the thermal conductivity of water, which increases linearly with pressure within the pressure range of interest (Haar et al., 1984). The correlation is valid for temperatures between 20° and 130°C, pressures between 1 and 75 bar, equivalent K2CO3 concentrations of 20 to 40 wt% and CO2 loadings between 0 and 1.

Figure B.2.4 compares the solution thermal conductivity values predicted by equation (B.2.56) against the literature values. The average absolute deviation is 0.5%, compared to 10.6% for the values predicted by the Riedel and DIPPR equations. As a result, the empirical correlation was used in this work. Table B.2.14: Coefficients for the DIPPR liquid thermal conductivity equation (Rowley et al., 1998).


Table B.2.15: Atmospheric solution thermal conductivity data.

Solution K2CO3 a K2CO3–KHCO3 b a

Concentration 20 – 40 wt% K2CO3 27 – 30 wt% K2CO3 c

Chernen’kaya and Revenko (1973) of equivalent K2CO3 weight percent.

b

CO2 Loading 0 – 0.75

UOP Gas Processing (1998)

c

These concentrations are in terms

Table B.2.16: Liquid phase thermal conductivity correlation coefficients.

Coefficient A0 A1 A2 A2 A4 B0 B1 B2 B3

Value 6.2933×10-1 -1.8732×10-1 -2.3768×10-2 1.2144×10-3 -4.9031×10-6 9.9983×10-1 1.1860×10-5 1.0952×10-7 8.0807×10-5

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Temperature Range 20 – 90°C 70 – 130°C


Predicted Solution Thermal Conductivity (W/m·K)

0.68 Potassium carbonate 0.66

Potassium carbonate-bicarbonate

0.64

0.62

0.60

0.58

0.56

0.54 0.54

0.56

0.58

0.60

0.62

0.64

0.66

0.68

Experimental Solution Thermal Conductivity (W/m·K)

Figure B.2.4: Comparison between the predicted and experimental solution thermal conductivities. The dashed lines (---) represent the ± 1% lines.

B.2.7 Diffusivities B.2.7.1 Vapour Phase Diffusivities In this work, the vapour phase component diffusivities Dc,j were calculated using Blanc’s Law (Reid et al., 1977): § ¨ NC D G, jk y k ¨ ¨ k 1 yk k 1 ¨ kz j kz j © NC

D G, j

¦

¦

· ¸ ¸ ¸ ¸ ¹

(B.2.56)

where yj and yk are the component vapour phase mole fractions, NC is the number of vapour phase components, and Dg,jk is the vapour phase binary diffusivity for the component pair j-k, which was determined from the corresponding binary diffusivity D LP G, jk at atmospheric pressure using the DawsonKhoury-Kobayashi expression (Reid et al., 1977): D G, jk C G D LP G, jk

C LP G

2

1 0.053432 C R 0.030182 C R 0.029725 C R

3

(B.2.57)

CG and C LP G are the vapour phase molar densities at the system pressure P and at atmospheric pressure, respectively. CR is the reduced molar density, which was determined from the relation: CR

C G Vc, jk

§ y j Vc, j y k Vc,k CG ¨ ¨ y j yk ©

· ¸ ¸ ¹

where Vc,j and Vc,k are the component critical volumes.

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(B.2.58)


The atmospheric vapour phase binary diffusivities D LP G, jk were obtained from the Chapman-EnskogBrokaw model (Poling et al., 2001): 0.00266 T 3 / 2

D LP G, jk

P MW jk

MW jk

1/ 2

(B.2.59)

2

V jk : D, jk 1

§ 1 1 ·¸ 2¨ ¨ MW j MWk ¸ © ¹

(B.2.60)

2 where D LP G, jk is in cm /s, T is the system temperature in K, P is the system pressure in bar, MWj and

MWk are the component molecular weights in kg/kmol, Vjk is the characteristic length in Å, and :D,jk is the diffusion collision integral. The characteristic length Vjk was obtained from the following relations: V jk

V j V k 1/ 2

Vj

§ 1.585 Vb, j ¨ ¨ 1 1 .3 G 2 p, j ©

G p, jk G p, j

(B.2.61) · ¸ ¸ ¹

1/ 3

(B.2.62)

G p,j G p,k 1/ 2 1.94 u 10 3 G j

(B.2.63) 2

(B.2.64)

Vb, j Tb, j

where Tb,j is the normal boiling point in K, Vb,j is the component liquid molar volume at Tb,j in cm3/mol, and Gp,j is the component polar parameter, Gj is the component dipole moment in Debye. Values of Vb,j and Tb,j are given in Table B.2.17. The diffusion collision integral :D,jk was determined from the correlation: : D, jk

A T*

B

C e DT

*

E e FT

*

G e HT

*

0.19 G p, jk

2

T*

(B.2.65)

where A is 1.06036, B is 0.15610, C is 0.19300, D is 0.47635, E is 1.03587, F is 1.52996, G is 1.76474 and H is 3.89411. The dimensionless temperature T* was calculated from: T* H jk k Hj k

kT H jk

(B.2.66)

§ H j Hk · ¨ ¸ ¨k k ¸ © ¹

1/ 2

1.18 1 1.3 G p, j

(B.2.67)

2

T

(B.2.68)

b, j

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where Hj and Hk are the component characteristic energies and k is the Boltzmann constant. Table B.2.17: Normal boiling points and the corresponding liquid molar volumes (Poling et al., 2001).


B.2.7.2 Liquid Phase Diffusivities For ionic and electrolyte species, the liquid phase species diffusivities DL,j were determined in this work using the Stokes-Einstein relation (Poling et al., 2001): D L, j P L

D fw, j P L25,H O

T

298.15K

2

(B.2.69)

where T is the system temperature in K, PL is the liquid phase viscosity, D fw, j is the species diffusivity at infinite dilution in water at 25°C, and P L25,H2O is the viscosity of water at 25°C. P L25,H2O was calculated from (Bingham, 1922): 1 P L,H2O

2 0.021482 ª«T 8.435 8078.4 T 8.435 º» 1.2 ¼ ¬

(B.2.70)

where P L,H2O is in cP and T is in °C. The Nernst equation (Horvath, 1985) was used to obtain the values of D fw, j : D fw, j

D fw, j

Ofj R T z j F2

z c

z a Ofc Ofa R T

z c z a Ofc Ofa F 2

for j = ionic species

(B.2.71)

for j = electrolyte species ca

(B.2.72)

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where Ofj is the ionic conductivity at infinite dilution, zj is the charge number (or the absolute value of the species ionic charge), R is the gas constant, T is 298.15 K, and F is Faraday’s constant. The subscripts a and c refer to the anions and cations comprising the electrolyte species ca. Values of Ofj are listed in Table B.2.18.

For molecular species, the liquid phase species diffusivities DL,j were determined using the correlation suggested by Ratcliff and Holdcroft (1963): § D w, j log¨ ¨ D L, j ©

· ¸ ¸ ¹

§ PL 0.637 log¨ ¨ P L,H O 2 ©

· ¸ ¸ ¹

(B.2.73)

where PL is the liquid phase viscosity, Dw,j is the species diffusivity in water, and P L,H2O is the viscosity of water.

The values of Dw,j for CO2 and H2S were calculated from the following correlations, which were derived from the data presented by Versteeg and van Swaaij (1988) and Tamimi and co-workers (1994): D w,CO2

2.9294 u 10 2 e

D w,H2S

8.7161 u 10 3 e

2184 .8

1839 .7

T

(B.2.74)

T

(B.2.75)

where D w,CO2 and D w,CO2 are in cm2/s and T is the temperature in K. For the other molecular species present in the liquid phase, Dw,j was determined using the Stokes-Einstein relation: D w, j P L,H2O T

25 D 25 w , j P L,H

2O

(B.2.76)

298.15K

where D 25 w, j is the species diffusivity in water at 25°C, values of which are given in Table B.2.19, and PL25,H2O is the viscosity of water at 25°C.

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Table B.2.18: Ionic conductivities at infinite dilution. 2 Of (m /·kmol)

Ionic Species H3O+ K+ OHHCO3CO32HSS2-

35.010 a 7.352 a 19.830 a 4.450 a 6.930 a 6.500 b 9.990 b

a

Robinson and Stokes (1965) co-workers (1971)

b

Onda and

Table B.2.19: Diffusivities in water at 25°C. 5

2.57 a 2.01 b 1.88 c 1.52 c 1.21 c 1.05 d 1.04 d 0.93 d 0.93 d 0.84 d 0.77 d

H2O N2 CH4 C2H6 C3H8 n-C4H10 i-C4H10 n-C5H12 i-C5H12 n-C6H14 n-C7H16 a

2

D 25 w , j ×10 (cm /s)

Component

b

Wang (1965) Ferrell and Himmelblau c d (1967) Witherspoon and Saraf (1965) Determined from the equation proposed by Hayduk and Laudie (1974).

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APPENDIX C

ELECTROLYTE NRTL ADJUSTABLE PARAMETERS This appendix outlines the procedure followed for the regression of the model parameters for the Electrolyte NRTL model. The results of the data regression are analysed and the complete set of model parameters is included within.

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C.1 Parameter Values The Electrolyte NRTL adjustable parameters for determining the energy parameter W from equation (3.2.4) are presented in Tables C.1.1 and C.1.2.

The listed values were taken from the Aspen

Properties® databanks, unless indicated otherwise. The default values for W and the non-randomness factor D were set as 0 and 0.2, respectively. Table C.1.1: The Electrolyte NRTL adjustable parameters used in this work.

Component i CO2 (H3O+,OH-) CO2 (H3O+,CO32-) CO2 (H3O+,HCO3-) CO2 (H3O+,HS-) CO2 (H3O+,S2-) CO2 (K+,OH-) CO2 (K+,CO32-) CO2 + (K ,HCO3-) CO2 (K+,HS-) CO2 (K+,S2-) H2S (H3O+,OH-) H2S (H3O+,CO32-) H2S (H3O+,HCO3-) H2S (H3O+,HS-) H2S (H3O+,S2-) H2S (K+,OH-) H2S (K+,CO32-) H2S (K+,HCO3-) H2S (K+,HS-) H2S (K+,S2-)

Component j (H3O+,OH-) CO2 (H3O+,CO32-) CO2 (H3O+,HCO3-) CO2 (H3O+,HS-) CO2 (H3O+,S2-) CO2 (K+,OH-) CO2 (K+,CO32-) CO2 (K+,HCO3-) CO2 (K+,HS-) CO2 (K+,S2-) CO2 (H3O+,OH-) H2S (H3O+,CO32-) H2S (H3O+,HCO3-) H2S (H3O+,HS-) H2S (H3O+,S2-) H2S (K+,OH-) H2S (K+,CO32-) H2S (K+,HCO3-) H2S (K+,HS-) H2S (K+,S2-) H2S

A 15.000 -8.000 15.000 -8.000 15.000 -8.000 15.000 -8.000 15.000 -8.000 10.000 -2.000 10.000 -2.000 10.000 -2.000 10.000 -2.000 10.000 -2.000 15.000 -8.000 15.000 -8.000 15.000 -8.000 15.000 -8.000 15.000 -8.000 10.000 -2.000 10.000 -2.000 10.000 -2.000 10.000 -2.000 10.000 -2.000

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B 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

C 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

D 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2


Table C.1.2: The Electrolyte NRTL adjustable parameters used in this work.

Component i H2O (H3O+,OH-) H2O (H3O+,CO32-) H2O (H3O+,HCO3-) H2O (H3O+,HS-) H2O (H3O+,S2-) H2O (K+,OH-) H2O (K+,CO32-) H2O (K+,HCO3-) H2O (K+,HS-) H2O (K+,S2-) CO2 H2O H2S H2O

Component j (H3O+,OH-) H2O (H3O+,CO32-) H2O (H3O+,HCO3-) H2O (H3O+,HS-) H2O (H3O+,S2-) H2O (K+,OH-) H2O (K+,CO32-) H2O (K+,HCO3-) H2O (K+,HS-) H2O (K+,S2-) H2O H2O CO2 H2O H2S

A 8.045 -4.072 8.045 -4.072 8.045 -4.072 8.045 -4.072 8.045 -4.072 7.841 -4.259 -5.020 a -0.176 a 6.250 a -3.728 a 3.076 a -3.253 a 3.438 a -6.305 a 10.064 10.064 -3.674 -3.674

a These values were regressed from literature data.

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B 0 0 0 0 0 0 0 0 0 0 773.360 -305.651 -250.640 a -864.400 a 0a 0a 0a -226.148 a 4206.772 a -267.739 a -3268.135 -3268.135 1155.9 1155.9

C 0 0 0 0 0 0 0 0 0 0 0 0 0a 0a 0a 0a 0a 0a 0a 0a 0 0 0 0

D 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2


C.2 Data Regression Procedure The Electrolyte NRTL adjustable parameter values not taken from the Aspen Properties® databanks were determined using the Aspen Properties® Data Regression System (DRS). +

-

+

parameter values for the H2O-(K ,HCO3 ) and H2O-(K

,CO32-)

The adjustable

binary interaction pairs were first

determined from Tosh and co-workers’ (1959) data for CO2 solubility in aqueous potassium carbonate solutions. Adjustable parameter values for the H2O-(K+,HS-) and H2O-(K+,S2-) binary interaction pairs were then determined using Tosh and co-workers’ (1960) H2S solubility data in aqueous potassium carbonate solutions. Both sets of data regressions were performed using the general procedure outlined below.

1.

Where available, the Aspen Properties® databank values were set as the initial values for the adjustable parameters to be regressed from the data. Otherwise, the following default values were applied: Binary Interaction Pair Water-Electrolyte Electrolyte-Water

2.

A 8 -4

B 0 0

C 0 0

The full set of twelve adjustable parameters was regressed from the data. The resulting set of parameter values was labelled “Full”.

3.

One of the four C parameters (designated as C1) was excluded from regression (i.e. it was fixed at its initial value) and the remaining adjustable parameters were regressed from the data. The resulting set of parameter values was labelled “C1”. Another C parameter (C2) was then excluded instead of C1 to give the parameter value set “C2”. This step was repeated with the remaining C parameters (C3 and C4) to give the parameter values sets “C3” and “C4”.

4.

C1 and C2 were excluded from regression and the remaining adjustable parameters were regressed from the data. The resulting set of parameter values was labelled “C12”. C3 was then excluded instead of C2 to give the parameter value set “C13”. C4 was then excluded instead of C3 to give the parameter value set “C14”.

5.

C2 and C3 were excluded from regression and the remaining adjustable parameters were regressed from the data. The resulting set of parameter values was labelled “C23”. C4 was then excluded instead of C3 to give the parameter value set “C24”.

6.

C3 and C4 were excluded from regression and the remaining adjustable parameters were regressed from the data. The resulting set of parameter values was labelled “C34”.

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7.

C1, C2 and C3 were excluded from regression and the remaining adjustable parameters were regressed from the data. The resulting set of parameter values was labelled “C123”. C4 was then excluded instead of C3 to give the parameter value set “C124”. C3 was then excluded instead of C2 to give the parameter value set “C134”.

8.

C2, C3 and C3 were excluded from regression and the remaining adjustable parameters were regressed from the data. The resulting set of parameter values was labelled “C234”.

9.

All four C parameters were excluded from regression and the remaining adjustable parameters were regressed from the data.

The resulting set of parameter values was

labelled “C”.

10. Excluding all four C parameters from regression, steps 3 to 9 were repeated with the four B parameters (B1, B2, B3 and B4) to give the parameter value sets “B1C”, “B2C”, “B3C”, “B4C”, “B12C”, “B13C”, “B14C”, “B123C”, “B124C”, “B134C”, “B234C” and “BC”.

11. Excluding all C and B parameters from regression, steps 3 to 9 were repeated with the four A parameters (A1, A2, A3 and A4) to give the parameter value sets “A1BC”, “A2BC”, “A3BC”, “A4BC”, “A12BC”, “A13BC”, “A14BC”, “A123BC”, “A124BC”, “A134BC”, “A234BC” and “ABC”.

12. Each simplified set of parameter values obtained from steps 3 to 11 was compared against the “Full” parameter value set via an F-Test to determine the reliability of the simplified set. The corresponding one-tail p-value was also calculated to determine the probability of observing the F-Test value if the null hypothesis was true. Null hypothesis:

The simplified set fits the data better than the “Full” set. F 1 or p > 0.05

where WSSQ Simplified WSSQ Full df Simplified df Full

F

p df

(C.2.1)

WSSQ Full dfFull

f F, df Simplified dfFull , dfFull

(C.2.2)

NData NParameters

(C.2.3)

WSSQFull and WSSQSimplified are the weighted sum of squares for the full and simplified parameter value sets, respectively, dfFull and dfSimplified are the corresponding degrees of freedom, NData is the number of data points used in the regression, and NParameters is the number of parameters regressed.

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13. The simplified parameter value sets which passed the above F-Test were sorted according to their weighted sum of squares. A logic test was then performed on each parameter set to tabulate the number of parameters with a standard error greater than the associated regressed value. The parameter value set with the lowest logic test result and the lowest weighted sum of squares was labelled the optimal set.

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C.3 Data Regression Results The statistical results for the data regression runs for the CO2-K2CO3-KHCO3-H2O system are given in Table C.3.1. The weighted sum of squares (WSSQ), residual root mean square error (RRMSQE), degrees of freedom (df), F-value and p-value are listed for each parameter set. The data set used in the regression runs consisted of 120 data points, and the number of parameters regressed ranged from 0 to 12, depending on the parameter set. Using the F-Test, 25 simplified parameter sets were identified as being more suitable than the “Full” set. These are sorted in ascending order according to their WSSQ in Table C.3.1. The corresponding logic test results are also presented.

Of the 25 simplified parameter sets in Table C.3.1, set “B34C” was the only set to have all its regressed parameter values greater than the associated standard error.

Consequently, it was

selected as the optimal parameter value set and was used in the next series of data regression runs for the CO2-H2S-K2CO3-KHCO3-KHS-K2S-H2O system. The regressed parameter values and standard errors associated with this optimal set are given in Table 3.2.2.

Table C.3.3 presents the statistical results for the data regression runs for the CO2-H2S-K2CO3KHCO3-KHS-K2S-H2O system. The data set used in this series of regression runs consisted of 127 data points, and the number of parameters regressed ranged from 0 to 12, depending on the parameter set. Only 6 simplified parameter sets were determined to be more suitable than the “Full” set via the F-Test, and these are sorted in ascending order according to their WSSQ in Table C.3.4. The corresponding logic test results are also presented.

Of the 6 simplified parameter sets in Table C.3.4, set “B1C” was the only set to have all its regressed parameter values greater than the associated standard error. It was therefore selected as the optimal parameter value set for the CO2-H2S-K2CO3-KHCO3-KHS-K2S-H2O system. The regressed parameter values and standard errors associated with this optimal set are given in Table 3.2.3.

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Table C.3.1: Statistical results for the CO2-K2CO3-KHCO3-H2O system data regression runs.

Parameter Set Full C1 C2 C3 C4 C12 C13 C14 C23 C24 C34 C123 C124 C134 C234 C B1C B2C B3C B4C B12C B13C B14C B23C B24C B34C B123C B124C B134C B234C BC A1BC A2BC A3BC A4BC A12BC A13BC A14BC A23BC A24BC A34BC A123BC A124BC A134BC A234BC ABC

WSSQ 1143.4 1378.6 1223.8 1129.1 1160.7 1230.6 1279.8 1230.8 1199.3 1100.3 1198.3 1178.2 1214.5 1192.0 1191.1 1188.6 1105.0 1178.2 1178.4 1206.7 1142.6 1180.1 1198.3 1194.0 1207.2 1201.7 1194.9 1198.1 1204.7 1195.4 1195.8 1471.3 1467.2 7246.8 3356.2 1889.7 8143.4 4755.4 1577.1 6965.0 8706.5 9897.8 10029.4 9693.6 9920.5 10032.7

RRMSQE 3.254 3.573 3.366 3.233 3.278 3.376 3.442 3.376 3.332 3.192 3.331 3.303 3.353 3.322 3.321 3.317 3.199 3.303 3.303 3.343 3.253 3.306 3.331 3.325 3.343 3.336 3.326 3.331 3.340 3.327 3.328 3.691 3.686 8.191 5.575 4.183 8.683 6.636 3.821 8.031 8.979 9.573 9.637 9.474 9.584 9.638

df 108 109 109 109 109 110 110 110 110 110 110 111 111 111 111 112 113 113 113 113 114 114 114 114 114 114 115 115 115 115 116 117 117 117 117 118 118 118 118 118 118 119 119 119 119 120

a

F 22.21 7.59 -1.36 1.63 4.12 6.44 4.12 2.64 -2.03 2.59 1.10 2.24 1.53 1.50 1.07 -0.73 0.66 0.66 1.19 -0.01 0.58 0.86 0.80 1.00 1.04 0.69 0.74 0.83 0.70 0.62 3.44 3.40 64.05 23.22 7.05 66.12 34.12 4.10 54.99 71.44 75.17 76.30 73.42 75.37 69.97

p 7.3×10-6 6.9×10-3 n/a a 2.0×10-1 1.9×10-2 2.3×10-3 1.9×10-2 7.6×10-2 n/a a 8.0×10-2 3.5×10-1 8.8×10-2 2.1×10-1 2.2×10-1 3.8×10-1 n/a a 6.6×10-1 6.5×10-1 3.2×10-1 n/a a 7.5×10-1 5.2×10-1 5.7×10-1 4.3×10-1 4.0×10-1 6.8×10-1 6.4×10-1 5.7×10-1 6.7×10-1 7.6×10-1 9.2×10-4 1.0×10-3 3.2×10-39 1.5×10-21 1.9×10-8 2.1×10-41 5.4×10-29 8.5×10-5 8.9×10-38 6.0×10-43 2.1×10-45 1.0×10-45 6.4×10-45 1.9×10-45 3.2×10-45

Null Hypothesis False False True True False False False True True True True True True True True True True True True True True True True True True True True True True True False False False False False False False False False False False False False False False

No p-value was calculated as the F-value was negative due to the WSSQ being smaller than that of the “Full” parameter set, indicating the null hypothesis is true.

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Table C.3.2: Suitable parameter value sets for the CO2-K2CO3-KHCO3-H2O system.

Parameter Set

WSSQ

Logic Test

C24 B1C C3 B12C FULL C4 C123 B2C B3C B13C C C234 C134 B23C B123C B234C BC B124C C34 B14C C23 B34C B134C B4C B24C C124

1100.3 1105.0 1129.1 1142.6 1143.4 1160.7 1178.2 1178.2 1178.4 1180.1 1188.6 1191.1 1192.0 1194.0 1194.9 1195.4 1195.8 1198.1 1198.3 1198.3 1199.3 1201.7 1204.7 1206.7 1207.2 1214.5

7 3 9 2 8 8 6 5 5 4 5 6 6 3 2 2 1 3 7 3 7 0 2 4 4 6

A-46


Table C.3.3: Statistical results for the CO2-H2S-K2CO3-KHCO3-KHS-K2S-H2O system data regression runs.

Parameter Set Full C1 C2 C3 C4 C12 C13 C14 C23 C24 C34 C123 C124 C134 C234 C B1C B2C B3C B4C B12C B13C B14C B23C B24C B34C B123C B124C B134C B234C BC A1BC A2BC A3BC A4BC A12BC A13BC A14BC A23BC A24BC A34BC A123BC A124BC A134BC A234BC ABC

WSSQ 2006.6 3221.7 1962.6 3225.1 3850.9 1985.1 3860.6 3860.6 1981.6 3224.0 3851.0 1995.6 1991.8 3860.6 3227.9 3259.7 2014.7 3314.8 3892.1 3892.1 3363.3 3980.0 3980.0 3319.9 3317.9 3892.1 4035.0 3366.4 3980.0 3689.0 3718.5 3898.5 4906.3 4027.1 4031.1 255230.6 4445.9 4466.3 5648.7 5730.4 22110.0 255249.6 255255.3 24056.8 23051.6 268481.8

RRMSQE 4.177 5.293 4.131 5.296 5.787 4.155 5.794 5.794 4.151 5.295 5.787 4.166 4.162 5.794 5.298 5.324 4.186 5.369 5.818 5.818 5.408 5.883 5.883 5.373 5.371 5.818 5.923 5.410 5.883 5.664 5.686 5.822 6.532 5.918 5.921 47.110 6.218 6.232 7.009 7.059 13.866 47.112 47.113 14.463 14.158 48.318

df 115 116 116 116 116 117 117 117 117 117 117 118 118 118 118 119 120 120 120 120 121 121 121 121 121 121 122 122 122 122 123 124 124 124 124 125 125 125 125 125 125 126 126 126 126 127

a

F 69.63 -2.53 69.83 105.69 -0.62 53.12 53.12 -0.72 34.88 52.85 -0.21 -0.28 35.42 23.33 17.95 0.09 14.99 21.61 21.61 12.96 18.85 18.85 12.54 12.52 18.01 16.61 11.13 16.16 13.77 12.26 12.05 18.46 12.87 12.89 1451.21 13.98 14.10 20.87 21.34 115.21 1319.39 1319.41 114.88 109.64 1272.63

p 1.8×10-13 n/a a 1.7×10-13 5.6×10-18 n/a a 4.6×10-17 4.6×10-17 n/a a 1.4×10-12 5.3×10-17 n/a a n/a a 2.8×10-16 7.2×10-12 1.8×10-11 9.9×10-1 2.6×10-11 3.4×10-15 3.4×10-15 3.8×10-11 3.5×10-15 3.5×10-15 7.7×10-11 7.9×10-11 1.2×10-14 5.5×10-15 1.1×10-10 1.2×10-14 7.5×10-13 1.4×10-12 3.1×10-13 1.1×10-18 5.4×10-14 5.1×10-14 5.2×10-116 7.1×10-16 5.5×10-16 1.4×10-21 6.2×10-22 4.4×10-55 1.8×10-115 1.8×10-115 1.2×10-56 1.4×10-55 3.5×10-116

Null Hypothesis False True False False True False False True False False True True False False False True False False False False False False False False False False False False False False False False False False False False False False False False False False False False False

No p-value was calculated as the F-value was negative due to the WSSQ being smaller than that of the “Full” parameter set, indicating the null hypothesis is true.

A-47


Table C.3.4: Suitable parameter value sets for the CO2-H2S-K2CO3-KHCO3-KHS-K2S-H2O system.

Parameter Set C2 C23 C12 C124 C123 FULL B1C

WSSQ 1962.6 1981.6 1985.1 1991.8 1995.6 2006.6 2014.7

A-48

Logic Test 4 7 5 6 7 12 0


APPENDIX D

ASPEN CUSTOM MODELER® SIMULATION RESULTS This appendix presents the results for the Aspen Custom Modeler® simulations. The column profiles generated from the preliminary column simulations are provided; along with the column profiles produced by the Aspen Custom Modeler® CO2 train process models. Also included is a table of alternative correlations for estimating the mass transfer coefficients and effective interfacial area.

A-49


D.1 The Different Modelling Approaches The absorber CO2 and H2S vapour phase profiles and the regenerator liquid phase CO2 and H2S loading profiles for CO2 trains #2 to #6 are presented below for the three different modelling approaches.

Model 2

Model 3

Data

Cond 1.2 WS

1.0

Fraction of Total Packed Height


Model 1

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0

5

CO2 (mol%)

10

15

20

25

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 0.3

H2S (ppm)

0.4

0.5

0.6

0.7

0

(a)

30

(d)

1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

15

0

20

5

CO2 (mol%)

10

15

20

25

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 0.3

H2S (ppm)

0.4

0.5

0.6

0.7

0

5

10

15

20

25

30

H2S Loading (×106)

CO2 Loading

(b)

(e) Cond 1.2 WS

1.0



20

1.2 Cond WS



10

H2S Loading (×106)

CO2 Loading

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0

CO2 (mol%)

5

10

15

20

25

H2S (ppm)

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 0.3

0.4

0.5

0.6

0.7

(c)

0

5

10

15

20

25

30

H2S Loading (×106)

CO2 Loading

(f)

Figure D.1.1: Results of the different modelling approaches for CO2 trains #2 to #4. Absorber CO2 and H2S vapour phase profiles for (a) train #2, (b) train #3 and (c) train #4. Regenerator liquid phase CO2 and H2S loading profiles for (d) train #2, (e) train #3 and (f) train #4 (Cond = condenser, WS = wash section, Reb = reboiler).

Model 1

Model 2

A-50

Model 3

Data




Cond 1.2 1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0

5

CO2 (mol%)

10

15

20

25

WS 1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

H2S (ppm)

0.3

0.4

0.5

0.6

0.7

0

5

(a)

10

15

20

25

H2S Loading (×106)

CO2 Loading

(c)

1.0



Cond 1.2

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

CO2 (mol%)

0

5

10

15

20

25

WS 1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 0.3

H2S (ppm)

0.4

0.5

0.6

0.7

0

(b)

5

10

15

20

25

30

H2S Loading (×106)

CO2 Loading

(d)

Figure D.1.2: Results of the different modelling approaches for CO2 trains #5 and #6. Absorber CO2 and H2S vapour phase profiles for (a) train #5 and (b) train #6. Regenerator liquid phase CO2 and H2S loading profiles for (c) train #5 and (d) train #6 (Cond = condenser, WS = wash section, Reb = reboiler).

A-51


D.2 Model Adjustments D.2.1 Liquid Phase Enthalpy Correction The temperature profiles predicted by Model 2 for the absorber and regenerator columns in CO2 trains #2 to #6 are presented below. The effect of the liquid phase enthalpy correction on the absorber temperature profiles is also included.

Vapour Phase

Liquid Phase

Vapour Data

Liquid Data

Uncorrected enthalpy

1.0 0.8 0.6 0.4 0.2 0.0 Reb

0.8

0.6

0.4

0.2

0.0

-0.2

30 30

50

70

90

110

130

60

Absorber Temperature (°C)

70

80

90

100

110

50

70

90

110

130 100

Vapour Phase Temperature (°C)

Regenerator Temperature (°C)

(a)

120

130

Liquid Phase Temperature (°C)

(d) 1.0



110

120

1.2 Cond WS 1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 90

100

110

120

130


60

70

80

90

100

110

0.8

0.6

0.4

0.2

0.0 90

120

100

110

120

130 100



(b)

110

120

130


(e)

1.2 Cond WS

1.0



Data

1.0



1.2 Cond WS

Corrected enthalpy

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 90

100

110

120

130


60

70

80

90

100

110

0.8

0.6

0.4

0.2

0.0 90

120

100

110

120

130 100



(c)

110

120

130


(f)

Figure D.2.1: Temperature profiles for CO2 trains #2 to #4. Temperature profiles predicted by Model 2 for (a) train #2, (b) train #3 and (c) train #4 (Cond = condenser, WS = wash section, Reb = reboiler). Effect of the liquid phase enthalpy correction on the absorber temperatures for (d) train #2, (e) train #3 and (f) train #4.

A-52


Vapour Phase

Liquid Phase

Vapour Data

Liquid Data

Uncorrected enthalpy

1.0 0.8 0.6 0.4 0.2 0.0 Reb

0.8

0.6

0.4

0.2

0.0

-0.2

90 90

100

110

120

130

60


70

80

90

100

110

100

110

120

130 100

110

120

130

120



(a)


(c)

Cond 1.2 WS

1.0



Data

1.0



Cond 1.2 WS

Corrected enthalpy

1.0 0.8 0.6 0.4 0.2 0.0 Reb

0.8

0.6

0.4

0.2

0.0

-0.2

90 90

100

110

120

130

60


70

80

90

100

110

100

110

120

130 100

110

120

130

120



(b)


(d)

Figure D.2.2: Temperature profiles for CO2 trains #5 and #6. Temperature profiles predicted by Model 2 for (a) train #5 and (b) train #6 (Cond = condenser, WS = wash section, Reb = reboiler). Effect of the liquid phase enthalpy correction on the absorber temperatures for (c) train #5 and (d) train #6.

A-53


D.2.2 Sensitivity to Model Parameters Table D.2.1 lists some alternative correlations for estimating the mass transfer coefficients and the effective interfacial area. Table D.2.1: Alternative mass transfer coefficient and effective interfacial area correlations.

Mass Transfer Coefficient Correlations 0. 8

§ PG · ¸ ¨ ¨ UG DGj ¸ © ¹

k Gj

DGj § UG v G · ¸ 0 .2 ¨ dN ¨© a PG ¸¹

kLj

§U 2 g· 0.015 DLj ¨ L 2 ¸ ¸ ¨ P © L ¹

k Gj

§ dp UG v G · ¸ 1.195 v G ¨¨ ¸ © PG 1 I ¹

kLj

DLj § dp UL vL · ¸ ¨ 25.1 dp ¨© aI PL ¸¹

k Gj

· § a ¸ EG DGj ¨¨ ¸ I I d L ¹ © h

kLj

§U g· EL ¨¨ L ¸¸ © PL ¹

Van Krevelen and Hoftijzer (1948)

Shulman and co-workers (1955)

Billet and Schultes (1999)

1 6

1 3

§ DLj · ¸ ¨¨ ¸ © dh ¹

§U v · ¨¨ L L ¸¸ © aI PL ¹

0.45

0 .5

0 .5

0. 8

1 3

2

3

§ PL · ¸ ¨ ¨ UL DLj ¸ ¹ ©

§ UG DGj · ¸ ¨¨ ¸ © PG ¹

§ PL · ¸ ¨ ¨ UL DLj ¸ ¹ ©

§U v · ¨¨ G G ¸¸ © a PG ¹

§v · ¨ L ¸ © a ¹

2

(D.2.1)

1 3

3

(D.2.2)

0 .5

0.75

§ PG · ¸ ¨ ¨ UG DGj ¸ © ¹

1 3

(D.2.3)

1 3

Effective Interfacial Area Correlations 0.041

§U v 2 · ¨ L L ¸ ¨ a VL ¸ © ¹

Puranik and Vogelpohl (1974)

aI a

§U v · 1.045 ¨¨ L L ¸¸ © a PL ¹

Kolev (1976)

aI a

§ U g · ¸ 0.583 ¨¨ 2L ¸ © a VL ¹

Bravo and Fair (1982)

aI a

§v P U v · 19.76 ¨¨ L L G G ¸¸ a PG ¹ © VL

Billet and Schultes (1999)

aI a

1 .5

a dh 0.5

0.49

§v 2 a· ¸ ¨ L ¨ g ¸ ¹ ©

§U v d · ¨¨ L L h ¸¸ PL ¹ ©

0.196

0.392

0.2

0.133

§V · ¨¨ c ¸¸ © VL ¹

a dp

VL

0.5

Hc

0.4

0.182

(D.2.4)

0.42

§ U v 2 dh · ¸ ¨ L L ¸ ¨ V L ¹ ©

(D.2.5)

(D.2.6) 0.75

§ v 2 · ¨ L ¸ ¨ g dh ¸ ¹ ©

0.45

(D.2.7)

Note: All variables are in SI units. Notation: Dj is the component diffusivity; is the mass density; is the viscosity; a is the packing specific surface area; v is the phase flow velocity; g is the gravitational constant; dN is the nominal packing size; dp is the packing particle diameter; dh is the packing hydraulic diameter; I is the voidage; IL is the liquid phase volumetric holdup; E is a packing-specific constant; VL is the surface tension; Vc is the critical surface tension parameter; Hc is the column height; Dc is the column diameter; G and L are the vapour and liquid phase molar flow rates; Ct is the molar density; and the subscripts G and L denote the vapour and liquid phases.

A-54


D.2.3 Effective Interfacial Area Adjustment Factor The effect of the effective interfacial area adjustment factor on the absorber CO2 and H2S vapour phase profiles for CO2 trains #2 to #6 are presented below.

Unadjusted Model

Adjusted Model 1.0



1.0

Data

0.8

0.6

0.4

0.2

0.0 0

5

10

15

0

20

5

CO2 (mol%)

10

15

20

0.8

0.6

0.4

0.2

0.0

25

0

5

H2S (ppm)

10

15

20

5

10

15

20

25

20

25

H2S (ppm)

(a)

(b) 1.0

1.0



0

CO2 (mol%)

0.8

0.6

0.4

0.2

0.0 0

5

10

15

0

20

5

CO2 (mol%)

10

15

20

0.8

0.6

0.4

0.2

0.0

25

0

5

H2S (ppm)

10

15

20

5

10

15

H2S (ppm)

(c) Fraction of Total Packed Height

0

CO2 (mol%)

(d)

1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0

CO2 (mol%)

5

10

15

20

25

H2S (ppm)

(e) Figure D.2.3: Effect of the effective interfacial area adjustment factor on the absorber CO2 and H2S vapour phase profiles. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4. (d) CO2 train #5. (e) CO2 train #6.

A-55


D.3 CO2 Train Model Validation The vapour and liquid phase composition profiles and the temperature profiles for the absorber and regenerator columns in the Aspen Custom Modeler® models for CO2 trains #2 to #6 are presented below.

CO2 CO2

CO2 CO2 Data Data

H2S H2S

H H2S Data 2S Data

Regenerator H2S (ppm) Absorber H2S (ppm) 0

10

20

0

Absorber H2S Loading 30

0.E+00

2.E-05

4.E-05



0.8

0.6

0.4

0.2

0.0 5

10

15

20

0.2

Absorber CO2 (mol%)

0.4

0.6

0.8

50

75

100

0.E+00

1.E-05

2.E-05

3.E-05

30

50

70

90

0.2

0.4

0.6

0.8

Cond 1.2 WS

6.E-05

1.0

0

Regenerator H2S Loading

25

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0

10

Absorber CO2 Loading

Regenerator CO2 (mol%)

Regenerator CO2 Loading

(a) Regenerator H2S (ppm) Absorber H2S (ppm) 0

10

20

0


0.E+00

2.E-05

4.E-05



0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0.2

Absorber CO2 (mol%)

0.4

0.6

0.8

50

75

100

0.E+00

1.E-05

2.E-05

3.E-05

30

50

70

90

0.2

0.4

0.6

0.8

1.2 Cond WS

6.E-05

1.0


25

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0

10




(b) Regenerator H2S (ppm) Absorber H2S (ppm) 0

10

20

0


0.E+00

2.E-05

4.E-05



0.8

0.6

0.4

0.2

0.0 0

5

10

15

Absorber CO2 (mol%)

20

0.2

0.4

0.6

0.8

50

75

100

0.E+00

1.E-05

2.E-05

3.E-05

30

50

70

90

0.2

0.4

0.6

0.8

Cond 1.2 WS

6.E-05

1.0


25

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0

10




(c) Figure D.3.1: CO2 and H2S vapour and liquid phase column profiles for the first set of plant data. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4. (Cond = condenser, WS = wash section, Reb = reboiler)

A-56


CO2 CO2

CO2 CO2 Data Data

H2S H2S

H H2S Data 2S Data


10

20


0.E+00

2.E-05

4.E-05

0



0.8

0.6

0.4

0.2

0.0 5

10

15

20

0.2

Absorber CO2 (mol%)

0.4

0.6

0.8

50

75

100

0.E+00

30

50

70

90

0.2

1.E-05

2.E-05

3.E-05

1.2 Cond WS

6.E-05

1.0

0


25

1.0

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 10



0.3

0.4

0.5

0.6



10

20

0


0.E+00

2.E-05

4.E-05



0.8

0.6

0.4

0.2

0.0 0

5

10

15

Absorber CO2 (mol%)

20

0.2

0.4

0.6

0.8

50

75

100

0.E+00

1.E-05

2.E-05

3.E-05

30

50

70

90

0.2

0.4

0.6

0.8

1.2 Cond WS

6.E-05

1.0


25

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0

10




(b) Figure D.3.2: CO2 and H2S vapour and liquid phase column profiles for the first set of plant data. (a) CO2 train #5. (b) CO2 train #6. (Cond = condenser, WS = wash section, Reb = reboiler)

A-57


CO2 CO2

CO2 CO2 Data Data

H2S H2S

H H2S Data 2S Data


5

10

15


0.E+00

1.E-05

2.E-05

3.E-05

0 4.E-05



1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0.2

Absorber CO2 (mol%)

0.4

0.6

0.8

1.0


20

40

60

80

0.E+00

30

50

70

90

0.2

5.E-06

1.E-05

2.E-05

2.E-05

1.2 Cond WS 1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 10



0.4

0.6

0.8



5

10

15


0.E+00

2.E-05

4.E-05

0



0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0.2

Absorber CO2 (mol%)

0.4

0.6

0.8

40

60

80

0.E+00

30

50

70

90

0.2

5.E-06

1.E-05

2.E-05

2.E-05

1.2 Cond WS

6.E-05

1.0


20

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0

10



0.4

0.6

0.8


(b) Regenerator H2S (ppm) Absorber H2S (ppm) 0

5

10

15


0.E+00

2.E-05

4.E-05

0



0.8

0.6

0.4

0.2

0.0 0

5

10

15

Absorber CO2 (mol%)

20

0.2

0.4

0.6

0.8

40

60

80

0.E+00

30

50

70

90

0.2

5.E-06

1.E-05

2.E-05

2.E-05

Cond 1.2 WS

6.E-05

1.0


20

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0

10



0.4

0.6

0.8


(c) Figure D.3.3: CO2 and H2S vapour and liquid phase column profiles for the second set of plant data. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4. (Cond = condenser, WS = wash section, Reb = reboiler)

A-58


CO2 CO2

CO2 CO2 Data Data

H2S H2S

H H2S Data 2S Data


5

10

15


0.E+00

1.E-05

2.E-05

3.E-05

0



0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0.2

Absorber CO2 (mol%)

0.4

0.6

0.8

40

60

80

0.E+00

5.E-06

1.E-05

2.E-05

30

50

70

90

0.2

0.4

0.6

0.8

1.2 Cond WS

4.E-05

1.0


20

1.0

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 10





5

10

15


0.E+00

2.E-05

4.E-05

0



0.8

0.6

0.4

0.2

0.0 0

5

10

15

Absorber CO2 (mol%)

20

0.2

0.4

0.6

0.8

40

60

80

0.E+00

30

50

70

90

0.2

5.E-06

1.E-05

2.E-05

2.E-05

1.2 Cond WS

6.E-05

1.0


20

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0

10



0.4

0.6

0.8


(b) Figure D.3.4: CO2 and H2S vapour and liquid phase column profiles for the second set of plant data. (a) CO2 train #5. (b) CO2 train #6. (Cond = condenser, WS = wash section, Reb = reboiler)

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Vapour Phase

Liquid Phase

Vapour Data

1.2 Cond WS


1.2 Cond WS


Liquid Data

1.0 0.8 0.6 0.4 0.2 0.0 Reb

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

-0.2 30

50

70

90

110

60

130


70

80

90

100

110

90

120

100

110

120

130



(a)

70

80

90

100

110

120


(b)

1.2 Cond WS

1.2 Cond WS



60

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

90

100

110

120

130

60


70

80

90

100

110

120

90


100

110

120

130


(c)

60

70

80

90

100

110

120


(d)


1.2 Cond WS 1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 90

100

110

120

130


60

70

80

90

100

110

120


(e) Figure D.3.5: Column temperature profiles for the first set of plant data. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4. (d) CO2 train #5. (e) CO2 train #6. (Cond = condenser, WS = wash section, Reb = reboiler)

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Liquid Phase

Vapour Data

1.2 Cond

Cond 1.2

WS 1.0

WS



Vapour Phase

0.8 0.6 0.4 0.2 0.0 Reb

Liquid Data

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

-0.2 30

50

70

90

110

130

60


70

80

90

100

110

90

120

100

110

120

130



(a)

70

80

90

100

110

120


(b)

1.2 Cond WS

1.2 Cond WS



60

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

90

100

110

120

130

60


70

80

90

100

110

120

90


100

110

120

130


(c)

60

70

80

90

100

110

120


(d)


1.2 Cond WS 1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 90

100

110

120

130


60

70

80

90

100

110

120


(e) Figure D.3.6: Column temperature profiles for the second set of plant data. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4. (d) CO2 train #5. (e) CO2 train #6. (Cond = condenser, WS = wash section, Reb = reboiler)

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APPENDIX E

HYPOTHETICAL K2CO3* HYSYS® COMPONENT PROPERTIES This appendix presents the various physical and thermodynamic properties required for the creation of the hypothetical K2CO3* HYSYS® component.

A-62


E.1 Base Properties E.1.1 Normal Boiling Point When the normal boiling point is unknown for a hypothetical component, HYSYS® uses a proprietary method to estimate this property (Hyprotech Ltd, 2001a). In the case of the hypothetical K2CO3* component, the potassium carbonate melting point of 900.85°C (Chase, 1998) was used as the hypothetical component’s normal boiling point since potassium carbonate does not boil, but instead begins to decompose at temperatures close to its melting point.

E.1.2 Molecular Weight HYSYS® has two default methods for estimating the molecular weight of hypothetical components: the Bergman method (Bergman et al., 1975) and the Lee-Kesler model (Kesler and Lee, 1976). The former method is applied only to components with boiling points less than 155°F (68.3°C) and is based on tabulated molecular weights of gas condensate carbon number fractions from C5 to C45 that were obtained from a study of US gas condensate mixtures by Bergman and co-workers (1975). The latter estimation method is used for all other hypothetical components and gives the molecular weight MW as a function of the boiling point Tb in °R and the specific gravity SG: MW

12272.6 9486.4 SG 4.6523 3.3287 SG T b

§ 720.79 · 10 7 ¸ 1 0.77084 SG 0.02058 SG 2 ¨¨1.3437 Tb ¸¹ Tb © § 181.9 · 10 12 ¸ 1 0.80882 SG 0.02226 SG 2 ¨¨1.8828 Tb ¸¹ Tb 3 ©

(E.1.1)

It should be noted that SG refers to 60°F/60°F specific gravity, i.e. the mass ratio of equal volumes of the component of interest and water at 60°F.

For the hypothetical K2CO3* component, neither estimation method was used since the molecular weight was taken to be that of potassium carbonate: 138.2058 kg/kmol (Chase, 1998).

E.1.3 Ideal Liquid Density The default estimation method for determining the ideal liquid density of a hypothetical component in HYSYS® is the following correlation proposed by Yen and Woods (1966): j

Vc VLs

§ T ·3 ¸ K j ¨¨1 Tc ¸¹ © 1

4

1

¦ j

(E.1.2) 2

3

K1

17.4425 214.578 Z c 989.625 Z c 1522.06 Z c

K2

3.28257 13.6377 Z c 107.4844 Z c 384.211 Z c

K2

60.2091 402.063 Z c 501.0 Z c 641.0 Z c

2

2

A-63

3

(E.1.3) 3

if Z c d 0.26

(E.1.4)

if Z c ! 0.26

(E.1.5)


K3

0

(E.1.6)

K4

0.93 K 2

(E.1.7)

where Vc is the critical molar volume, VLs is the saturated liquid molar volume, T is the temperature, Tc is the critical temperature, and Zc is the critical compressibility. For the hypothetical K2CO3* component, the ideal liquid density was not estimated by the above method, but was instead taken to be 2423.11 kg/m3, the density of solid potassium carbonate (Perry and Green, 1997).

E.1.4 Critical Temperature and Critical Pressure Three default methods are available in HYSYS® for estimating the critical temperatures and critical pressures of hypothetical components: the Lee-Kesler model (Kesler and Lee, 1976), the Bergman method (Bergman, 1976) and the Cavett relations (Cavett, 1964).

The first method is used for

components with liquid densities greater than 1067 kg/m3 or boiling points above 800 K, and consists of the following correlations: 341.7 811 SG 0.4244 0.1174 SG T b 0.4669 3.2623 SG

Tc

10 5 Tb

(E.1.8)

0.0566 § 2.2898 0.11857 · ¨¨ 0.24244 ¸¸ 10 3 T b SG SG SG 2 ¹ © 1.6977 · 3.648 0.47227 · § 2 § 3 ¨¨1.4685 ¸ 10 10 T b ¸ 10 7 T b ¨¨ 0.42019 ¸ ¸ 2 2 SG SG ¹ SG © ¹ © 8.3634

ln Pc

(E.1.9)

where the critical temperature Tc and the boiling point Tb are in °R, Pc is the critical pressure in psia, and SG is the 60°F/60°F specific gravity. The second method by Bergman (1976) is only applied to components with low densities (< 850 kg/m3) and low boiling points (< 548.316 K), and was therefore not of interest in this work. The last method by Cavett (1964) is used for all other hypothetical components and is of the following form: 768.071 1.7134 T b 0.10834 u 10 2 T b 0.3889 u 10 6 T b 2

Tc

3

· · § 141.5 2 § 141.5 131.5 ¸ 0.89213 u 10 2 T b ¨ 131.5 ¸ 0.53095 u 10 6 T b ¨ ¹ © SG ¹ © SG · 2 § 141.5 0.32712 u 10 7 T b ¨ 131.5 ¸ SG ¹ ©

log Pc

(E.1.10)

2

2.829 0.9412 u 10 3 T b 0.30475 u 10 5 T b 0.15141 u 10 8 T b 2

3

· § 141.5 · 2 § 141 .5 131.5 ¸ 0.20876 u 10 4 T b ¨ 131.5 ¸ 0.11048 u 10 7 T b ¨ © SG ¹ © SG ¹ 2

· § 141.5 · 2 § 141.5 0.1395 u 10 9 T b ¨ 131.5 ¸ 0.4827 u 10 7 T b ¨ 131.5 ¸ SG SG © ¹ © ¹

A-64

2

(E.1.11)


where Tc and Tb are in °F, Pc is in psia, and SG is the 60°F/60°F specific gravity. Since the critical temperature and critical pressure of potassium carbonate were not available in literature, the Lee-Kesler model was used to estimate these two critical properties for the hypothetical K2CO3* component.

The critical temperature was estimated to be 1645.10°C while the critical

pressure was estimated to be 4507.57 kPa.

E.1.5 Critical Volume and Acentricity In HYSYS®, the correlations proposed by Pitzer and co-workers (1955) are the default estimation method for determining the critical volume and acentricity of hypothetical components belonging to the Miscellaneous class of components. These correlations take the following form: Zc

Pc Vc R Tc

Z

§ Ps log¨ ¨P © c

§ T P · § T P · ¸ Z ( 0 ) ¨¨ , ¸¸ Z Z (1) ¨¨ , ¸ © Tc Pc ¹ © Tc Pc ¹ · ¸ 1.000 ¸ ¹

at

T Tc

1 and

at

T Tc

0. 7

P Pc

1

(E.1.12)

(E.1.13)

where Zc is the critical compressibility, Pc is the critical pressure , Vc is the critical molar volume, Tc is the critical temperature, P is the pressure, T is the temperature, Z is the acentricity, and Ps is the vapour pressure. Z(0) and Z(1) are functions of T, P, Tc and Pc. As literature values for the critical volume and acentricity of potassium carbonate were unavailable, the Pitzer model was used to estimate these two properties for the hypothetical K2CO3* component. The critical volume was estimated to be 0.997346 m3/kmol while the acentricity was estimated to be 0.107562.

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E.2 Additional Point Properties E.2.1 Heat of Formation Two default methods are available for the estimation of the heat (or enthalpy) of formation at 25°C for hypothetical HYSYS® components. If the component’s structure can be defined in terms of UNIFAC groups, the method proposed by Joback (1984) is applied; otherwise, a simple ratio with respect to octane (Hyprotech Ltd, 2001a) is used instead. The Joback method is a group contribution method that takes the form: f 'h 25 qC

68.29

¦N

k

'hfk

(E.2.1)

k

f where 'h 25 qC is the heat of formation at 25°C in kJ/mol, Nk is the number of UNIFAC groups of type k

and 'hfk is the contribution for group k to the heat of formation in kJ/mol. The alternative HYSYS® default method takes the form: f 'h 25 qC

f 'h 25 qC,oc tan e MW

(E.2.2)

MW oc tan e

where MW is the molecular weight.

For the hypothetical K2CO3* component, the heat of formation was not estimated by either of the above two methods, but was instead taken to be that for potassium carbonate: -1144610 kJ/kmol (Chase, 1998).

E.2.2 Dipole Moment No default estimation method for the dipole moment of a hypothetical component is currently available in HYSYS®. Instead, the dipole moments for such components are set equal to zero (Hyprotech Ltd, 2001a). Consequently, the dipole moment for the hypothetical K2CO3* component was set as 0.00 Debye.

E.2.3 Radius of Gyration To estimate the radius of gyration for a hypothetical component, HYSYS® uses a proprietary method (Hyprotech Ltd, 2001a). For the hypothetical K2CO3* component, the radius of gyration estimated by this method was 2.64138 Å.

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E.3 Temperature Dependent Properties E.3.1 Ideal Gas Enthalpy In HYSYS®, the ideal gas enthalpy hIG of a component is calculated from the following temperature dependent relation: a b T c T2 d T3 e T4 f T5

hIG

(E.3.1)

where hIG is in kJ/kg, T is in K, and the reference point is an ideal gas at 0 K. If not provided, the coefficients a to f are estimated from the ideal gas heat capacity correlation proposed by Cavett (1964): § § T 13 ¨ ¨ b ¨ 0.036863384 ¨¨ SG ¨ © ©

C pIG

§ ¨ ¨ 3.1865 u 10 5 ¨ ©

· · ¸ 0.4673722 ¸ MW ¸ ¸¸ ¸ ¹ ¹

§ T 13 ¨¨ b ¨ SG ©

· · ¸ 0.001045186 ¸ MW T ¸ ¸¸ ¸ ¹ ¹

(E.3.2)

4.9572 u 10 7 MW T 2

where CpIG is the ideal gas heat capacity in Btu/lbmol·°R, Tb is the boiling point in °R, SG is the 60°F/60°F specific gravity, MW is the molecular weight, and T is the temperature in °R.

No thermochemical data were available for potassium carbonate in the ideal gas state. Consequently, heat capacity and enthalpy data from the NIST-JANAF Thermochemical Tables (Chase, 1998) for crystalline potassium carbonate were instead used to derive the coefficients for equation (E.3.1) for the hypothetical K2CO3* component. After the data had been corrected to account for the different reference temperatures (0 K for equation (E.3.1) and 25°C for the NIST-JANAF tables), the following relationship between heat capacity Cp and enthalpy h was used to regress the coefficient values given in Table E.3.1: Cp

§ wh · ¸ ¨ © wT ¹ P

b 2 c T 3 d T2 4 e T3 5 f T4

(E.3.3)

where Cp is in kJ/kg·K, h is in kJ/kg, and T is in K. Table E.3.1: Temperature dependent property correlation coefficients.

Coefficient a b c d e f

Ideal Gas Enthalpy -19.8419 0.365850 9.80515×10-4 -5.86603×10-7 2.49532×10-10 -3.99650×10-14

Ideal Gas Gibbs Free Energy -1142180 246.572 4.51346×10-2 0.00 0.00 –

A-67

Vapour Pressure 22.0529 -27345.9 0.00 -0.515316 2.08489 0.00


E.3.2 Ideal Gas Gibbs Free Energy The ideal gas Gibbs free energy GIG of a component in HYSYS® is calculated from the following temperature dependent relation: GIG

a b T c T2 d T3 e T4

(E.3.4)

where GIG is in kJ/kmol, T is in K, and the reference point is an ideal gas at 25°C. If not provided, the coefficients a to e are estimated from a HYSYS® proprietary method (Hyprotech Ltd, 2001a).

As mentioned above, no thermochemical data were available for potassium carbonate in the ideal gas state. Consequently, Gibbs free energy data from the NIST-JANAF Thermochemical Tables (Chase, 1998) for crystalline potassium carbonate were instead used to regress the coefficients for equation (E.3.4) for the hypothetical K2CO3* component. The resulting coefficient values are given in Table E.3.1.

E.3.3 Vapour Pressure In HYSYS®, the vapour pressure of a component is calculated from the Modified Antoine equation: lnP s

a

b d ln T e T f Tc

(E.3.5)

where Ps is the vapour pressure in kPa and T is the temperature in K. If the coefficients a to f are not provided, HYSYS® estimates these based on the vapour pressures calculated from the correlation proposed by Riedel (1954): § Ps ln¨ ¨P © c

· ¸ ¸ ¹

§T 2.933 3.758 D c 3.0168 3.758 D c ¨¨ c © T § T 3.5196 3.758 D c D c ln¨¨ © Tc

Dc

\b

· § T ¸ 0.0838 3.758 D c ¨ ¸ ¨T ¹ © c

0.315 \ b ln Pc §T 0.0838 \ b ln¨¨ b © Tc §T 35 36 ¨¨ c © Tb

· ¸ ¸ ¹

6

(E.3.6)

(E.2.7)

· ¸ ¸ ¹

· §T ¸ 42 ln¨ b ¸ ¨T ¹ © c

· ¸¸ ¹

· § Tb ¸¨ ¸ ¨T ¹ © c

· ¸ ¸ ¹

6

(E.3.8)

where Ps and the critical pressure Pc are in atm, and T, the critical temperature Tc and the boiling point Tb are in K. Since vapour pressure data for potassium carbonate was unavailable in literature, data for an inorganic compound with a melting point similar to that for potassium carbonate was used instead to derive the coefficients for equation (E.3.5). The compound selected was lead oxide PbO which has a

A-68


melting point of 890°C (c.f. 900.85°C for potassium carbonate) and the coefficient values in Table E.3.1 were regressed from its vapour pressure data provided by Perry and Green (1997).

A-69


APPENDIX F

PROPERTY MODELS FOR HYSYS® This appendix presents the various thermodynamic and physical property models utilised in the HYSYS® process models for the CO2 trains. Where necessary, model parameters are regressed from literature data.

A-70


F.1 Thermodynamic Property Models F.1.1 Enthalpy For the HYSYS® simulations, the vapour and liquid phase enthalpies h were calculated from the rigorous thermodynamic relation: h hIG RT

V

º ª § wP · 1 «T ¨ ¸ P» dV R T ¬ © wT ¹ V ¼ f

³

Z 1

(F.1.1)

which in terms of the enhanced PR equation of state is: h hIG RT

Z 1

da · §¨ V § ¨a T ¸ ln dt ¹ ¨© V b R T © 1

1. 5

2

2 1 b ·¸ 2 1 b ¸¹

(F.1.2)

hIG is the ideal gas enthalpy (the ideal gas enthalpy of formation at 25°C), R is the gas constant, T is the absolute temperature, Z is the compressibility, V is the molar volume, P is the pressure, and a and b are the PR parameters.

F.1.2 Heat Capacity The heat capacity Cp was calculated from the rigorous relation: 2

Cp

§ dP · § dV · Cv T ¨ ¸ ¨ ¸ © dV ¹ T © dT ¹ P

2

§ dU · § dP · § dV · ¨ ¸ T¨ ¸ ¨ ¸ © dT ¹ V © dV ¹ T © dT ¹ P

(F.1.3)

where U is the total internal energy. If a solution could not be obtained for this equation, the ideal gas method was applied instead: Cp

Cp

Cv

Cp R

(F.1.4)

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F.2 Physical and Transport Property Models F.2.1 Molecular Weight For the HYSYS® simulations, the molecular weight MW of a phase was determined from the molefraction-weighted sums of the individual component molecular weights: NC

MW

¦x

j

MW j

(F.2.1)

j 1

where x is the mole fraction and NC is the number of components.

F.2.2 Density F.2.2.1 Vapour Phase Density The vapour phase mass density UG was determined from: UG

P MW G Z R T

(F.2.2)

where P is the pressure, MWG is the vapour phase molecular weight, Z is the vapour phase compressibility factor calculated from the enhanced PR equation of state, R is the gas constant, and T is the absolute pressure.

F.2.2.2 Liquid Phase Density F.2.2.2.1 Sour PR Property Package For the Sour PR property package, the liquid phase mass density UL was determined from the corresponding states liquid density (COSTALD) equation by Hankinson and Thomson (1979): UL

NC

¦U j 1

VL, j VRo

1 xj

NC

¦

L, j

j 1

1 x j VL, j MW j

v *j VRo 1 Z j VRG

(F.2.4)

§ T ·¸ 1 1.52816 ¨1 ¨ Tc, j ¸¹ © § T ·¸ 0.190454 ¨1 ¨ Tc, j ¸¹ ©

VRG

(F.2.3)

4

1 3

§ T ·¸ 1.43907 ¨1 ¨ Tc, j ¸¹ ©

2

3

§ T ·¸ 0.81446 ¨1 ¨ Tc, j ¸¹ ©

(F.2.5)

3

§ T 0.296123 0.386914 ¨ ¨ Tc, j ©

· § ¸ 0.0427258 ¨ T ¸ ¨ Tc, j ¹ © T 1.00001 Tc, j

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2

· § ¸ 0.0480645 ¨ T ¸ ¨ Tc, j ¹ ©

· ¸ ¸ ¹

2

(F.2.6)


where x is the liquid phase mole fraction, VL is the liquid phase molar volume, MW is the molecular weight, v* is the characteristic volume, Z is the acentricity, T is the absolute temperature, Tc is the critical temperature, and NC is the number of components.

F.2.2.2.2 PR Property Package In the PR property package, the HYSYS® tabular model was used instead of the default COSTALD equation to facilitate the more accurate prediction of the liquid phase density.

The temperature

dependence of the pure component liquid mass densities UL,j was described by polynomials of the form: U L, j

A B T C T2 D T3 E T4

(F.2.7)

where UL,j is in kg/m3 and T is the absolute temperature in K, and the overall liquid phase density was calculated from equation (F.2.3).

The default HYSYS® coefficient values for H2O were used for H2O and the hypothetical water component H2O*. The effect of H2S and other gases (such as N2, CH4 and other hydrocarbons) on the liquid phase density was disregarded due to their negligible liquid phase concentrations compared to that of CO2, and these gases were assigned the same coefficient values as H2O. The coefficient values for the hypothetical potassium carbonate component K2CO3* were regressed from the literature data in Table B.2.3 for pure potassium carbonate solutions while the coefficient values for CO2 were regressed from the data for pure potassium bicarbonate and potassium carbonate-bicarbonate solutions. The K2CO3* and CO2 coefficients were determined via the simple unweighted least squares method in a Microsoft® Excel spreadsheet, and the resulting values are listed in Table F.2.1.

Figure F.2.1 compares the liquid phase mass density values predicted by the tabular model against the literature values. The average absolute deviation between the predicted and literature values is 0.8%, compared to 4.3% for the values predicted by the COSTALD equation. Table F.2.1: Coefficient values for the HYSYS® liquid density tabular model.

Coefficient A B C D E

K2CO3* 3.4050×101 -2.1173×10-2 0 0 0

CO2 -7.5735×102 7.2698 -2.1830×10-2 2.1418×10-5 0

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H2O and other components 5.8305×101 -5.3842×10-3 -2.4881×10-5 4.7481×10-8 -6.5125×10-11


Predicted Solution Mass Density (kg/m3)

1450

1350

Potassium carbonate Potassium bicarbonate Potassium carbonate-bicarbonate

1250

1150

1050

950 950

1050

1150

1250

1350

1450 3

Experimental Solution Mass Density (kg/m )

Figure F.2.1: Comparison between the predicted and experimental solution mass densities. The dashed lines (---) represent the ± 1% lines.

F.2.3 Viscosity F.2.3.1 Vapour Phase Viscosity The vapour phase dynamic viscosity was determined from a proprietary modification of the model proposed by Ely and Hanley (1981). In the original model, the viscosity P of a mixture at density U, temperature T and composition x is equated to the viscosity Px of a hypothetical pure fluid: PU, T

P x U, T

(F.2.8)

This enables the use of the following corresponding states argument to determine P from the viscosity P0 of a reference fluid: P x U, T P0 U0 , T0

fx,0 MWx MW0 h 2 3 x,0

(F.2.9)

T0

T f x,0

(F.2.10)

U0

U h x,0

(F.2.11)

MW is the molecular weight. The subscript x refers to the fluid of interest while the subscript 0 refers to the reference fluid. fx,0 and hx,0 are functions of the critical parameters and the acentricities of the reference fluid and the fluid of interest.

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F.2.3.2 Liquid Phase Viscosity F.2.3.2.1 Sour PR Property Package In the Sour PR property package, the liquid phase viscosity was determined in one of three ways: via the proprietary modified Ely-Hanley model for light hydrocarbons; via the Twu model (Twu, 1985) for heavy hydrocarbons; or via the proprietary modified Letsou-Stiel model (Letsou and Stiel, 1973) for all other chemicals. In the original model proposed by Letsou and Stiel (1973), the liquid phase dynamic viscosity PL is determined from the following equations: § NC 1 · ¨ x j P L, j 3 ¸ ¨ ¸ ©j1 ¹

3

¦

PL

Tc, j

P L, j Pc, j

2

3

1 6

MW j

(F.2.12)

§ T T 0.015174 0.02135 0.0075 ¨ ¨ Tc, j Tc, j ©

· ¸ ¸ ¹

2

§ § T T ¨ Z j ¨ 0.042552 0.07674 0.0340 ¨ ¨ Tc, j Tc, j ¨ © ©

· ¸ ¸ ¹

2

· ¸ ¸ ¸ ¹

(F.2.13)

where PL is in cP, x is the mole fraction, NC is the number of components, Tc is the critical temperature in K, Pc is the critical pressure in atm, MW is the molecular weight, and Z is the acentricity. The Twu model is more complex, first requiring the calculation of the component kinematic viscosities at 100°F and 210°F from their boiling points Tb and specific gravities SG: § 450 ·¸ ln¨ Q L, j,T ¨ Tb, j ¸¹ ©

§ 450 ·¸ §¨ 1 2 f T, j ln¨ Q Lo, j,T ¨ Tb, j ¸¹ ¨© 1 2 f T, j ©

f100qF, j

1.33932 1.99873

56.7394

f 210qF, j

1.99873

56.7394

'SG j

'SG j

hj

SG

j

SG oj

Tb, j

Tb, j

· ¸ ¸ ¹

2

'SG j

for T = 100°F, 210°F 21.1141 'SG j

2

(F.2.16)

· ¸ ¸ ¹

2

(F.2.17)

· § 844.687 ¸ ¨ o 21 . 6364 ¸ SG j SG j 1.49546 SG j ¨¨ Tb, j ¸ ¹ © · § 2 7543.00 ¸ ¨ SG j SG oj 1.49546 SG j ¨ 458.199 ¸ ¨ Tb, j ¸ ¹ ©

>

(F.2.15)

Tb, j

2

Tb, j

21.1141 'SG j

§1 2 hj 1.49546 SG j ¨ ¨1 2 hj ©

(F.2.14)

A-75

@

(F.2.18)


where QL is the kinematic viscosity in cSt , T is the temperature in °F, and Tb is in °R. The reference variables, denoted by the superscript o, are obtained from:

ln

Q Lo,210qF, j

ln Q Lo,100qF, j

1 .5

§ Tbo, j 4.73227 27.0975 ¨1 o ¨ Tc, j ©

§ Tbo, j ¨ 50.4706 1 o ¨ Tc, j ©

§ Tbo, j 13749 .5 ¨1 o ¨ Tc, j ©

· ¸ ¸ ¹

· ¸ ¸ ¹

2

4

0.801621 1.37179 ln Q Lo,210qF, j

§ Tbo, j ¨ 0.843593 0.128624 1 o ¨ Tc, j ©

SG oj

Tco, j

· ¸ ¸ ¹

o · § ¸ 49.4491 ¨1 Tb, j ¸ ¨ Tco, j ¹ ©

(F.2.19)

(F.2.20)

o · § ¸ 3.36129 ¨1 Tb, j ¸ ¨ Tco, j ¹ ©

· ¸ ¸ ¹

3

12

Tbo, j § 0.533272 0.191017 u 10 3 T o 0.779681 u 10 7 T o 2 · ¨ b, j b, j ¸ ¸ ¨ 3 13 10 o 28 o ¸ ¨ 0.284376 u 10 T 0 . 959468 10 T u b , j b , j ¹ ©

(F.2.21)

(F.2.22)

The two calculated kinematic viscosities are then substituted into the following equations to determine the component dynamic viscosities PL,j at temperature T, which are then used to calculate the liquid phase dynamic viscosity from equation (F.2.12):

Q L,T, j 0.7 e

Z T, j

ln ln Z j

1.47 1.84Q L,T, j 0.51Q L,T, j 2

ln ln Z 100qF, j

Q L, j

Z j 0. 7 e

P L, j

U L, j Q L, j

for T = 100°F, 210°F

ln ln Z 100qF, j ln ln Z 210qF, j ln 100qF ln 210qF

ln T ln 100qF

0.7487 3.295 Z j 0.7 6.119 Z j 0.7 2 0.3193 Z j 0.7

3

(F.2.23) (F.2.24) (F.2.25) (F.2.26)

It should be noted that in equation (F.2.26), PL,j is in kg/m·s, QL,j is in m2/s and the density UL,j is in kg/m3.

F.2.3.2.2 PR Property Package In the PR property package, the HYSYS® tabular model was used, instead of the above-mentioned default HYSYS® models, to facilitate the more accurate prediction of the liquid phase viscosity. The temperature dependence of the pure component liquid dynamic viscosities PL,j was described by polynomials of the form: ln P L, j

A

B C ln T D T E T

(F.2.27)

A-76


where PL,j is in cP and T is the absolute temperature in K, and the overall liquid phase viscosity PL was calculated from equation (F.2.12).

As for the liquid density tabular model, the default HYSYS® coefficient values for H2O were used for H2O, the hypothetical water component H2O* and H2S and other gases (such as N2, CH4 and other hydrocarbons). The coefficient values for the hypothetical potassium carbonate component K2CO3* were regressed from the literature data in Table B.2.8 for pure potassium carbonate solutions while the coefficient values for CO2 were regressed from the data for pure potassium bicarbonate and potassium carbonate-bicarbonate solutions. The K2CO3* and CO2 coefficients were determined via the simple unweighted least squares method in a Microsoft® Excel spreadsheet, and the resulting values are listed in Table F.2.2.

Figure F.2.2 compares the liquid phase dynamic viscosity values predicted by the tabular model against the literature values. The average absolute deviation between the predicted and literature values is 4.6%, compared to 7.5% for the values predicted by the default HYSYS® models. Table F.2.2: Coefficient values for the HYSYS® liquid viscosity tabular model.


K2CO3* -2.3878×102 9.7635E×103 3.8379E×101 -4.2743×10-2 1.0000

CO2 -2.7937E+03 8.0287E+04 4.8288E+02 -7.3978E-01 1.0000

H2O and other components -1.1213×10-1 -2.4004×10-4 -3.1123 0 0

3.5 Potassium carbonate

Predicted Solution Viscosity (cP)

3.0

Potassium bicarbonate Potassium carbonate-bicarbonate

2.5

2.0

1.5

1.0

0.5

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Experimental Solution Viscosity (cP)

Figure F.2.2: Comparison between the predicted and experimental solution viscosities. The dashed lines (---) represent the ± 5% lines.

A-77


F.2.4 Surface Tension F.2.4.1 Sour PR Property Package In the Sour PR property package, the liquid phase surface tension VL was determined in one of two ways: via a proprietary modification of the correlation proposed by Brock and Bird (1955) for hydrocarbon systems or via a proprietary polynomial for aqueous systems. The original form of the Brock-Bird model is as follows: VL

NC

1 xj

¦V j 1

V L, j

Pc, j

2

(F.2.28)

L, j

3

Tc, j

1 3

§ Tb, j § ¨ ¨ ln Pc, j ¨ Tc, j ¨ ¨ 0.1207 ¨1 Tb, j ¨ ¨ 1 ¨¨ ¨ Tc, j © ©

· · ¸ ¸ 11 ¸ § · 9 ¸ T ¸ ¸ 0.281¸ ¨¨1 Tc, j ¸¹ ¸ © ¸ ¸¸ ¸ ¹ ¹

(F.2.29)

where VL is in dyne/cm, x is the mole fraction, NC is the number of components, Pc is the critical pressure in atm, Tc is the critical temperature in K, and Tb is the boiling point in K.

F.2.4.2 PR Property Package In the PR property package, the HYSYS® tabular model was used, instead of the above-mentioned default HYSYS® models, to facilitate the more accurate prediction of the liquid phase surface tension. The temperature dependence of the pure component liquid surface tensions VL,j was described by polynomials of the form: V L, j

A B T C T2 D T3 E T4

(F.2.30)

where VL,j is in dyne/cm and T is the absolute temperature in K, and the overall liquid phase surface tension VL was calculated from equation (F.2.28). Like the liquid density and liquid viscosity tabular models, the default HYSYS® coefficient values for H2O were used for H2O, the hypothetical water component H2O* and H2S and other gases (such as N2, CH4 and other hydrocarbons). The coefficient values for the hypothetical potassium carbonate component K2CO3* and for CO2 were regressed from a set of values generated using the empirical surface tension correlation (B.2.37). The K2CO3* and CO2 coefficients were determined via the simple unweighted least squares method in a Microsoft® Excel spreadsheet, and the resulting values are listed in Table F.2.3.

Figure F.2.3 compares the liquid phase surface tension values predicted by the tabular model against those generated by the empirical correlation. The average absolute deviation between the two sets of values is 3.8%, compared to 94.4% for the values predicted by the modified Brock-Bird model.

A-78


Table F.2.3: Coefficient values for the HYSYS® liquid surface tension tabular model.


K2CO3*

CO2

H2O and other components

2.5209×102 -1.4077 4.4242×10-3 -6.9349×10-6 3.9069×10-9

-3.0588×102 1.2235 -1.2345×10-3 0 0

1.8277×104 -9.3402×101 1.1945×10-1 0 0

Tabular Model Solution Surface Tension (dyne/cm)

100 Potassium carbonate Potassium bicarbonate Potassium carbonate-bicarbonate 90

80

70

60 60

70

80

90

100

Empirical Correlation Solution Surface Tension (dyne/cm)

Figure F.2.3: Comparison between the solution surface tensions predicted by the tabular model and the empirical correlation. The dashed lines (---) represent the ± 5% lines.

F.2.5 Thermal Conductivity F.2.5.1 Vapour Phase Thermal Conductivity The vapour phase thermal conductivity was determined from a proprietary modification of the model proposed by Ely and Hanley (1983). In the original model, the thermal conductivity O of the fluid of interest (a pure fluid or a mixture) at density U and temperature T is divided into two contributory terms: OU, T

O' U, T O" T

(F.2.31)

The first term O’ represents the transfer of energy from purely collisional or translational effects, while the second term O” is due to the transfer of energy via the internal degrees of freedom.

The

translational contribution O’ for a mixture of composition x is equated to the contribution O’x for a hypothetical pure fluid: O' U, T

O' x U, T

(F.2.32)

A-79


Consequently, from the corresponding states argument, O’x is obtained from the translational contribution O’0 of a reference fluid: O' x U, T

O' 0 U 0 , T0

f x,0

MW 0 MW x h 2 3 x,0

ª§ T § wf x,0 «¨¨1 ¨ « f x,0 ¨© wT ¬©

· ¸ ¸ ¹ Vx

· Z º ¸ c,0 » ¸ Z » ¹ c, x ¼

3

2

(F.2.33)

MW is the molecular weight and Zc is the critical compressibility. The subscript x refers to the fluid of interest while the subscript 0 refers to the reference fluid. T0 and U0 are given by equations (F.2.10) and (F.2.11). fx,0 and hx,0 are functions of the critical parameters and the acentricities of the reference fluid and the fluid of interest. The internal contribution O” is given by: 5 R · P § 1.32 ¨ C pIG ¸ 2 ¹ MW ©

O" T

(F.2.34)

where CpIG is the ideal gas heat capacity, R is the gas constant, and P is the viscosity from equation (F.2.8).

Two other methods were also used to calculate the vapour phase thermal conductivities in the HYSYS® simulations: the simple set of correlations proposed by Misic and Thodos (1961, 1963) and the more complex model by Chung and co-workers (1988). The Misic-Thodos correlations are based on dimensional analysis and assume that the vapour phase thermal conductivity OG is described by a function with the general form: OG

B

D

E

F

f MW A Tc T C Pc Vc Cp RG §§ T f ¨¨ ¨¨ 1 Tc 6 MW ¨© © Tc Pc

2

3

C F 5 · · § Cp · 5 ¸ ¨ ¸ Z c 6 G F R 6 ¸ ¸ ¨ R ¸ ¸¸ ¹ © ¹ ¹

(F.2.35)

where OG is in cal/cm·s·K, MW is the molecular weight in g/mol, Tc is the critical temperature in K, T is the temperature in K, Pc is the critical pressure in atm, Vc is the critical volume in cm3/mol, Zc is the critical compressibility, Cp is the heat capacity in cal/mol·K, and R is the gas constant in atm·cm3/mol·K.

Several functions, based on the equation (F.2.35), were obtained by Misic and

Thodos (1961, 1963) for different types of compounds over various reduced temperature ranges.

While the Misic-Thodos correlations are suitable only for low pressures, the Chung model is applicable to both high and low pressures: OG

31.2 u 10 3 P LP G < MW 3.586 u 10 3

V · § ¨¨ F1 F2 c ¸¸ 6V¹ ©

10 3 Tc 2 Vc 3 F1 F3 MW

A-80

2

§ V · T ¨¨ c ¸¸ Tc ©6V¹

(F.2.36)

0.05

where A-85


SSQ Simplified SSQ Full df Simplified dfFull

F

p df

(G.1.1)

SSQ Full df Full

f F, df Simplified df Full , df Full

(G.1.2)

NData NParameters

(G.1.3)

SSQFull and SSQSimplified are the sum of squares for the full and simplified parameter value sets, respectively, dfFull and dfSimplified are the corresponding degrees of freedom, NData is the number of data points used in the regression, and NParameters is the number of parameters regressed.

7. The simplified parameter value sets which passed the above F-Test were sorted according to their sum of squares. A logic test was then performed on each parameter set to tabulate the number of parameters with a standard error greater than the associated regressed value. The parameter value set with the lowest logic test result and the lowest weighted sum of squares was labelled the optimal set.

A-86


G.2 Data Regression Results The statistical results for the data regression runs for the CO2-K2CO3-H2O system are given in Table G.2.1. The sum of squares (SSQ), residual root mean square error (RRMSQE), degrees of freedom (df), F-value and p-value are listed for each parameter set. The data set used in the regression runs consisted of 120 data points, and the number of parameters regressed ranged from 0 to 3, depending on the parameter set. From the F-Test, none of the simplified parameter sets were identified as being more suitable than the “Full” set. Consequently, the “Full” set was selected as the optimal parameter value set and was used in the next series of data regression runs for the CO2-H2S-K2CO3-H2O system. The regressed parameter values and standard errors associated with this optimal set are given in Table 6.2.2.

Table G.2.2 presents the statistical results for the data regression runs for the CO2-H2S-K2CO3-H2O system. The data set used in this series of regression runs consisted of 127 data points, and the number of parameters regressed ranged from 0 to 2, depending on the parameter set. As for the previous set of regressions, none of the simplified parameter sets were determined to be more suitable than the “Full” set via the F-Test. Consequently, the “Full” set was selected as the optimal parameter value set for the CO2-H2S-K2CO3-H2O system, and its regressed parameter values and standard errors are given in Table 6.2.3. Table G.2.1: Statistical results for the CO2-K2CO3-H2O system data regression runs.

Parameter Set Full Fixed k H O* K CO * 2 2 3 Fixed k CO K CO * 2 2 3 Fixed k CO H O* 2 2 Fixed k H O* K CO * 2 2 3 and k CO K CO * 2 2 3 Fixed k H O* K CO * 2 2 3 and k CO H O* 2 2 Fixed k CO K CO * 2 2 3 and k CO H O* 2 2 All Fixed

SSQ 150.9

RRMSQE 1.290

df 117

F -

p -

185.9

1.255

118

27.18

8.1×10-7

False

47.04

-10

False

-25

211.5

1.339

118

Null Hypothesis -

3.5×10

375.2

1.783

118

173.93

6.8×10

False

220.9

1.363

119

27.16

2.0×10-10

False

385.4

1.800

119

90.93

1.5×10-24

False

1160.3

3.123

119

391.37

1.5×10-52

False

2704.5

4.747

120

660.07

4.0×10-73

False

Table G.2.2: Statistical results for the CO2-H2S-K2CO3-H2O system data regression runs.

Parameter Set

SSQ

RRMSQE

df

Full Fixed kH S K CO * 2 2 3

1611.9

3.591

125

2361.1

4.329

Fixed kH S K CO * 2 2 3

2971.0

4.856

All Fixed

5113.9

6.346

F

p

Null Hypothesis

126

58.10

5.4×10-12

False

126

105.39

2.6×10-18

False

135.78

-32

False

127

A-87

-

4.6×10


APPENDIX H

HYSYS® SIMULATION RESULTS This appendix presents the results of the HYSYS® simulations for CO2 trains #2 to #6. Included are the column profiles generated by the preliminary column simulations and the column profiles predicted by the full CO2 trains process models. Also presented are the process flow diagrams for the HYSYS® process models for CO2 trains #2 to #6.

A-88


H.1 Preliminary Column Model Simulations H.1.1 Equilibrium Stage Model Approach The composition and temperature profiles predicted by the equilibrium stage models for the absorber and regenerator columns in CO2 trains #2 to #6 are presented below.

CO2 CO2 CO2 Data CO2 Data

H2S H2S H2S Data Data H2S

VapourPhase Phase Vapour VapourData Data Vapour

LiquidPhase Phase Liquid LiquidData Data Liquid

Regenerator H2S Loading 0.E+00 Cond 1.2

Absorber H2S (ppm) 10

20

1.0


2.E-05

3.E-05

WS

30


0

1.E-05

0.8

0.6

0.4

0.2

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

0.0 0

5

10

15

20

30

Absorber CO2 (mol%)

50

70

90

110

0.0

130

0.2

0.4

0.6

0.8



60

70

80

90

100 110 120


(a) Regenerator H2S Loading 0.E+00 Cond 1.2


20

1.0


2.E-05

3.E-05

WS

30


0

1.E-05

0.8

0.6

0.4

0.2

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

0.0 0

5

10

15

20

Absorber CO2 (mol%)

90

100

110

120

0.0

130

0.2

0.4

0.6

0.8



60

70

80

90

100 110 120


(b) Regenerator H2S Loading 0.E+00 Cond 1.2


20

30


0 1.0


1.E-05

2.E-05

3.E-05

WS

0.8

0.6

0.4

0.2

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

0.0 0

5

10

15

Absorber CO2 (mol%)

20

90

100

110

120

130

0.0

0.2

0.4

0.6

0.8



60

70

80

90

100 110 120


(c) Figure H.1.1: Equilibrium stage simulation results for the absorber and regenerator columns. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4. (Cond = condenser, WS = wash section, Reb = reboiler)

A-89


CO2 CO2 CO2 Data CO2 Data

H2S H2S H2S Data Data H2S

VapourPhase Phase Vapour VapourData Data Vapour

LiquidPhase Phase Liquid LiquidData Data Liquid

Regenerator H2S Loading 0.E+00 Cond 1.2


20

1.0


2.E-05

3.E-05

WS

30


0

1.E-05

0.8

0.6

0.4

0.2

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

0.0 0

5

10

15

20

90

Absorber CO2 (mol%)

100

110

120

0.0

130

0.2

0.4

0.6

0.8



60

70

80

90

100 110 120


(a) Regenerator H2S Loading 0.E+00 Cond 1.2


20

1.0


2.E-05

3.E-05

WS

30


0

1.E-05

0.8

0.6

0.4

0.2

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

0.0 0

5

10

15

Absorber CO2 (mol%)

20

90

100

110

120

130

0.0

0.2

0.4

0.6

0.8



60

70

80

90

100 110 120


(b) Figure H.1.2: Equilibrium stage simulation results for the absorber and regenerator columns. (a) CO2 train #5. (b) CO2 train #6. (Cond = condenser, WS = wash section, Reb = reboiler)

A-90


H.1.2 Column Stage Efficiency Correlations The composition and temperature profiles predicted using the correlated overall stage efficiencies for the steady-state and dynamic absorber columns in CO2 trains #2 to #6 are presented below.


Default Efficiencies

Correlated Efficiencies

Data

1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0

10

CO2 (mol%)

20

30

H2S (ppm)

30

50

70

90

110

130

90


100

110

120

130



(a) 1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0

CO2 (mol%)

10

20

30

H2S (ppm)

90

100

110

120


90

100

110

120

130



(b) 1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

CO2 (mol%)

15

20

0

10

20

30

H2S (ppm)

90

100

110

120


90

100

110

120

130


(c) Figure H.1.3: Effect of the correlated overall stage efficiencies on the steady-state absorber columns. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4.

A-91




Correlated Efficiencies

Data

1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0

10

CO2 (mol%)

20

30

H2S (ppm)

90

100

110

120

90

100

110

120

130



90

90


(a) 1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

CO2 (mol%)

15

20

0

10

20

30

H2S (ppm)

100

110

120


100

110

120

130


(b) Figure H.1.4: Effect of the correlated overall stage efficiencies on the steady-state absorber columns. (a) CO2 train #5. (b) CO2 train #6.

A-92




Steady-State Efficiencies

Dynamic Efficiencies

Data

1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0

CO2 (mol%)

10

20

30

H2S (ppm)

30

50

70

90

110

130


90

100

110

120

130



(a) 1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0

CO2 (mol%)

10

20

30

H2S (ppm)

90

100

110

120


90

100

110

120

130



(b) 1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

CO2 (mol%)

15

20

0

10

20

30

H2S (ppm)

90

100

110

120


90

100

110

120

130


(c) Figure H.1.5: Effect of the correlated overall stage efficiencies on the steady-state behaviour of the dynamic absorber columns. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4.

A-93




Steady-State Efficiencies

Dynamic Efficiencies

Data

1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0

10

CO2 (mol%)

20

30

H2S (ppm)

90

100

110

120

90

100

110

120

130



90

90


(a) 1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

CO2 (mol%)

15

20

0

10

20

30

H2S (ppm)

100

110

120


100

110

120

130


(b) Figure H.1.6: Effect of the correlated overall stage efficiencies on the steady-state behaviour of the dynamic absorber columns. (a) CO2 train #5. (b) CO2 train #6.

A-94


H.2 Steady-State CO2 Train Models The process flow diagrams for the steady-state HYSYS® models of CO2 trains #2 to #6 are provided on the following pages.

A-95


A-96 Figure H.2.1: Process flow diagram for the steady-state model of CO2 train #2.










H.3 CO2 Train Model Validation The vapour and liquid phase composition profiles and the temperature profiles for the absorber and regenerator columns in the steady-state HYSYS® models for CO2 trains #2 to #6 are presented below.

CO2 CO2

CO2 CO2 Data Data

H2S H2S

H H2S Data 2S Data


10

20


0.E+00

2.E-05

4.E-05

0



0.8

0.6

0.4

0.2

0.0 5

10

15

20

0.2

Absorber CO2 (mol%)

0.4

0.6

0.8

50

75

100

0.E+00

1.E-05

2.E-05

3.E-05

30

50

70

90

0.2

0.4

0.6

0.8

Cond 1.2 WS

6.E-05

1.0

0


25

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0

10





10

20


0.E+00

2.E-05

4.E-05

0



0.8

0.6

0.4

0.2

5

10

15

20

0.2

0.4

0.6

0.8

75

100

0.E+00

1.E-05

2.E-05

3.E-05

30

50

70

90

0.2

0.4

0.6

0.8

1.0 0.8 0.6 0.4 0.2 0.0 Reb

0.0

Absorber CO2 (mol%)

50

Cond 1.2 WS

6.E-05

1.0

0


25

-0.2

1.0

10




(b) Regenerator H2S (ppm)


10

20


0.E+00

2.E-05

4.E-05

0



0.8

0.6

0.4

0.2

0.0 0

5

10

15

Absorber CO2 (mol%)

20

0.2

0.4

0.6

0.8

50

75

100

0.E+00

1.E-05

2.E-05

3.E-05

30

50

70

90

0.2

0.4

0.6

0.8

Cond 1.2 WS

6.E-05

1.0


25

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0

10




(c) Figure H.3.1: CO2 and H2S vapour and liquid phase column profiles for the first set of plant data. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4. (Cond = condenser, WS = wash section, Reb = reboiler)

A-101


CO2 CO2

CO2 CO2 Data Data

H2S H2S

H H2S Data 2S Data

Regenerator H2S (ppm)


10

20


0.E+00

2.E-05

4.E-05

0



0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

0.2

Absorber CO2 (mol%)

0.4

0.6

50

75

100

0.E+00

1.E-05

2.E-05

3.E-05

30

50

70

90

0.2

0.4

0.6

0.8

Cond 1.2 WS

6.E-05

1.0


25

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

0.8

10





10

20


0.E+00

2.E-05

4.E-05

0



0.8

0.6

0.4

0.2

0.0 0

5

10

15

Absorber CO2 (mol%)

20

0.2

0.4

0.6

0.8

50

75

100

0.E+00

1.E-05

2.E-05

3.E-05

30

50

70

90

0.2

0.4

0.6

0.8

Cond 1.2 WS

6.E-05

1.0


25

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0

10




(b) Figure H.3.2: CO2 and H2S vapour and liquid phase column profiles for the first set of plant data. (a) CO2 train #5. (b) CO2 train #6. (Cond = condenser, WS = wash section, Reb = reboiler)

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CO2 CO2

CO2 CO2 Data Data

H2S H2S

H H2S Data 2S Data


5

10

15


0.E+00

1.E-05

2.E-05

3.E-05

0



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1.E-05

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Absorber CO2 (mol%)

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Cond 1.2 WS

6.E-05

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(b) Regenerator H2S (ppm)


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Cond 1.2 WS

6.E-05

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1.0

10



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0.8


(c) Figure H.3.3: CO2 and H2S vapour and liquid phase column profiles for the second set of plant data. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4. (Cond = condenser, WS = wash section, Reb = reboiler)

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CO2 CO2

CO2 CO2 Data Data

H2S H2S

H H2S Data 2S Data

Regenerator H2S (ppm)


5

10

15


0.E+00

1.E-05

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3.E-05

0



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Absorber CO2 (mol%)

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0.E+00

30

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90

0.2

5.E-06

1.E-05

2.E-05

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Cond 1.2 WS

4.E-05

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20

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

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10



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2.E-05

3.E-05

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Absorber CO2 (mol%)

20

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5.E-06

1.E-05

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Cond 1.2 WS

4.E-05

1.0


20

1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2

1.0

10



0.4

0.6

0.8


(b) Figure H.3.4: CO2 and H2S vapour and liquid phase column profiles for the second set of plant data. (a) CO2 train #5. (b) CO2 train #6. (Cond = condenser, WS = wash section, Reb = reboiler)

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Vapour Phase

Liquid Phase

Vapour Data

1.2 Cond WS



1.2 Cond WS

Liquid Data

1.0 0.8 0.6 0.4 0.2 0.0 Reb

1.0 0.8 0.6 0.4 0.2 0.0 Reb

-0.2

-0.2 30

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1.2 Cond WS


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1.0 0.8 0.6 0.4 0.2 0.0 Reb

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90

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60


70

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(e) Figure H.3.5: Column temperature profiles for the first set of plant data. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4. (d) CO2 train #5. (e) CO2 train #6. (Cond = condenser, WS = wash section, Reb = reboiler)

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Vapour Phase

Liquid Phase

Vapour Data

1.2 Cond WS



1.2 Cond WS

Liquid Data

1.0 0.8 0.6 0.4 0.2 0.0 Reb

1.0 0.8 0.6 0.4 0.2 0.0 Reb

-0.2

-0.2 30

50

70

90

110

60

130


70

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120

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(a)

70

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(b) 1.2 Cond WS


1.2 Cond WS


60

130


1.0 0.8 0.6 0.4 0.2 0.0 Reb

1.0 0.8 0.6 0.4 0.2 0.0 Reb

-0.2

-0.2 80

90

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(c)

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(d)


1.2 Cond WS 1.0 0.8 0.6 0.4 0.2 0.0 Reb -0.2 80

90

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70

80

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100

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(e) Figure H.3.6: Column temperature profiles for the second set of plant data. (a) CO2 train #2. (b) CO2 train #3. (c) CO2 train #4. (d) CO2 train #5. (e) CO2 train #6. (Cond = condenser, WS = wash section, Reb = reboiler)

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APPENDIX I

PROCESS CONTROL STUDIES OF THE CO2 TRAINS This appendix provides examples of the MATLAB® scripts used in the process control studies for CO2 trains #1 and #7. Also included are the step response curves generated from the closed-loop testing of the optimal diagonal control structures for the two CO2 trains.

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I.1 Selection of Diagonal Control Structure An example of the MATLAB® scripts used to calculate the various sensitivity analysis indices is provided below.

% Program sensitivity.m % Compares alternative diagonal control structures for CO2 Train #1 % at high gas throughput % Calculates CN, MRI, DCN and DC % % Notation: % alt1 = SGC-LSF % alt2 = SGC-RSF % alt3 = SGC-RLL % y1 = Sweet gas CO2 content % y2 = Sweet gas flow rate % d1 = Raw gas CO2 content % clear % % Process gain matrices KpH1alt1=[1.1695 -0.0635; 1.0881 -0.0026]; KpH1alt2=[1.1695 -0.9885; 1.0881 -0.0262]; KpH1alt3=[1.1695 0.0412; 1.0881 0.0032]; % % Process time constant matrices TpH1alt1=[8.2231 2.2825; 1.6168 3.3742]; TpH1alt2=[8.2231 13.1691; 1.6168 16.0241]; TpH1alt3=[8.2231 10.2357; 1.6168 9.4975]; % % Process dead time matrices DTH1alt1=[0.1667 0.1667; 0.1667 0.1667]; DTH1alt2=[0.1667 0.6667; 0.1667 0.8333]; DTH1alt3=[0.1667 51.9408; 0.1667 69.1521]; % % Disturbance gain, time constant and dead time vectors KdH1=[0.5757; -0.0735]; TpdH1=[6.1206; 3.4381]; DTdH1=[0.1667; 0.1667]; % % Unit magnitude disturbance in d1 and unit magnitude setpoint changes % in y1 and y2 Dd1=[1]; Dy=eye(2); % for i=1:2 for j=1:2 % 3rd order Pade approximations for dead times [DTH1alt1num(i,:,j),DTH1alt1den(i,:,j)]=pade(DTH1alt1(i,j),3); [DTH1alt2num(i,:,j),DTH1alt2den(i,:,j)]=pade(DTH1alt2(i,j),3); [DTH1alt3num(i,:,j),DTH1alt3den(i,:,j)]=pade(DTH1alt3(i,j),3); % [DTdH1num(i,:),DTdH1den(i,:)]=pade(DTdH1(i),3); % % Process transfer functions GpH1alt1(i,j)=tf(KpH1alt1(i,j)*DTH1alt1num(i,:,j), conv([TpH1alt1(i,j) 1],DTH1alt1den(i,:,j))); GpH1alt2(i,j)=tf(KpH1alt2(i,j)*DTH1alt2num(i,:,j), conv([TpH1alt2(i,j) 1],DTH1alt2den(i,:,j))); GpH1alt3(i,j)=tf(KpH1alt3(i,j)*DTH1alt3num(i,:,j), conv([TpH1alt3(i,j) 1],DTH1alt3den(i,:,j))); % % Disturbance transfer functions GdH1(i,1)=tf(KdH1(i)*DTdH1num(i,:),conv([TpdH1(i) 1],DTdH1den(i,:)));

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end end % % Steady-state analysis % Singular value decomposition SVDH1(:,1)=svd(KpH1alt1); SVDH1(:,2)=svd(KpH1alt2); SVDH1(:,3)=svd(KpH1alt3); % % MRI values MRIH1(1)=min(SVDH1(:,1)); MRIH1(2)=min(SVDH1(:,2)); MRIH1(3)=min(SVDH1(:,3)) % % CN values CNH1(1)=cond(KpH1alt1); CNH1(2)=cond(KpH1alt2); CNH1(3)=cond(KpH1alt3) % % DCN and DC values DCH1(1,1)=norm(inv(KpH1alt1)*KdH1*Dd1); DCH1(1,2)=norm(inv(KpH1alt2)*KdH1*Dd1); DCH1(1,3)=norm(inv(KpH1alt3)*KdH1*Dd1); % DCNH1(1,1)=DCH1(1,1)/norm(KdH1*Dd1)*max(SVDH1(:,1)); DCNH1(1,2)=DCH1(1,2)/norm(KdH1*Dd1)*max(SVDH1(:,2)); DCNH1(1,3)=DCH1(1,3)/norm(KdH1*Dd1)*max(SVDH1(:,3)); % for i=1:2 DCH1(i+1,1)=norm(inv(KpH1alt1)*Dy(:,i)); DCH1(i+1,2)=norm(inv(KpH1alt2)*Dy(:,i)); DCH1(i+1,3)=norm(inv(KpH1alt3)*Dy(:,i)); % DCNH1(i+1,1)=DCH1(i+1,1)/norm(Dy(:,i))*max(SVDH1(:,1)); DCNH1(i+1,2)=DCH1(i+1,2)/norm(Dy(:,i))*max(SVDH1(:,2)); DCNH1(i+1,3)=DCH1(i+1,3)/norm(Dy(:,i))*max(SVDH1(:,3)); end DCNH1, DCH1 % % Frequency analysis w=logspace(-5,2,100); % % Evaluate process and disturbance transfer functions over frequency range GpH1alt1_w=freqresp(GpH1alt1,w); GpH1alt2_w=freqresp(GpH1alt2,w); GpH1alt3_w=freqresp(GpH1alt3,w); GdH1_w=freqresp(GdH1,w); % % Calculate indices over frequency range and print to text file for i=1:length(w) % Singular value decomposition SVDH1_w(:,1,i)=svd(GpH1alt1_w(:,:,i)); SVDH1_w(:,2,i)=svd(GpH1alt2_w(:,:,i)); SVDH1_w(:,3,i)=svd(GpH1alt3_w(:,:,i)); % % MRI values for j=1:3 MRIH1_w(j,i)=min(SVDH1_w(:,j,i)); end % % CN values CNH1_w(1,i)=cond(GpH1alt1_w(:,:,i)); CNH1_w(2,i)=cond(GpH1alt2_w(:,:,i)); CNH1_w(3,i)=cond(GpH1alt3_w(:,:,i)); % % DCN and DC values DCH1alt1_w(1,i)=norm(inv(GpH1alt1_w(:,:,i))*GdH1_w(:,:,i)*Dd1); DCH1alt2_w(1,i)=norm(inv(GpH1alt2_w(:,:,i))*GdH1_w(:,:,i)*Dd1);

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DCH1alt3_w(1,i)=norm(inv(GpH1alt3_w(:,:,i))*GdH1_w(:,:,i)*Dd1); % DCNH1alt1_w(1,i)=DCH1alt1_w(1,i)/norm(GdH1_w(:,:,i)*Dd1)*max(SVDH1_w(:,1,i)); DCNH1alt2_w(1,i)=DCH1alt2_w(1,i)/norm(GdH1_w(:,:,i)*Dd1)*max(SVDH1_w(:,2,i)); DCNH1alt3_w(1,i)=DCH1alt3_w(1,i)/norm(GdH1_w(:,:,i)*Dd1)*max(SVDH1_w(:,3,i)); % for j=1:2 DCH1alt1_w(j+1,i)=norm(inv(GpH1alt1_w(:,:,i))*Dy(:,j)); DCH1alt2_w(j+1,i)=norm(inv(GpH1alt2_w(:,:,i))*Dy(:,j)); DCH1alt3_w(j+1,i)=norm(inv(GpH1alt3_w(:,:,i))*Dy(:,j)); % DCNH1alt1_w(j+1,i)=DCH1alt1_w(j+1,i)/norm(Dy(:,j))*max(SVDH1_w(:,1,i)); DCNH1alt2_w(j+1,i)=DCH1alt2_w(j+1,i)/norm(Dy(:,j))*max(SVDH1_w(:,2,i)); DCNH1alt3_w(j+1,i)=DCH1alt3_w(j+1,i)/norm(Dy(:,j))*max(SVDH1_w(:,3,i)); end end y=[w; MRIH1_w;]; fid=fopen('MRIH1_w.txt','w'); fprintf(fid,'%12.8f %12.8f %12.8f %12.8f\n',y); fclose(fid); y=[w; CNH1_w]; fid=fopen('CNH1_w.txt','w'); fprintf(fid,'%12.8f %12.8f %12.8f %12.8f\n',y); fclose(fid); y=[w; DCNH1alt1_w; DCNH1alt2_w; DCNH1alt3_w]; fid=fopen('DCNH1_w.txt','w'); fprintf(fid,'%12.8f %12.8f %12.8f %12.8f %12.8f %12.8f %12.8f %12.8f %12.8f %12.8f\n',y); fclose(fid); y=[w; DCH1alt1_w; DCH1alt2_w; DCH1alt3_w]; fid=fopen('DCH1_w.txt','w'); fprintf(fid,'%12.8f %12.8f %12.8f %12.8f %12.8f %12.8f %12.8f %12.8f %12.8f %12.8f\n',y); fclose(fid);

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I.2 Selection of Diagonal Control Structure Configuration I.2.1 MATLAB® Script for Stability Analysis An example of the MATLAB® scripts used to analyse system stability is provided below.

The

calculated system poles and zeros are given in Table I.2.1.

% Program Stability.m % Determines the system poles and zeros for CO2 train #1 at high gas throughput % clear % % Process gain, time constant and dead time matrices KpH1=[1.1695 -0.9885; 1.0881 -0.0262]; TpH1=[8.2231 13.1691; 1.6168 16.0241]; DTH1=[0.1667 0.6667; 0.1667 0.8333]; % for i=1:2 for j=1:2 % Find 3rd order Pade approximations for dead times [DTH1num(i,:,j),DTH1den(i,:,j)]=pade(DTH1(i,j),3); % % Create system transfer function matrices GpH1(i,j)=tf(KpH1(i,j)*DTH1num(i,:,j),conv([TpH1(i,j) 1],DTH1den(i,:,j))); end end % % Obtain state-space model coefficient matrices % and calculate system poles and zeros [AH1,BH1,CH1,DH1]=ssdata(GpH1); PH1=eig(AH1) ZH1=tzero(AH1,BH1,CH1,DH1)

Table I.2.1: System poles and zeros for the SGC-RSF control structure.

CO2 Train #1

CO2 Train #7

High Gas Throughput

Medium Gas Throughput

Low Gas Throughput

High Gas Throughput

Medium Gas Throughput

Low Gas Throughput

System Poles

-0.12 -0.62 -22.06±21.05i -27.86 -5.52±5.26i -6.97 -0.08 -4.41±4.21i -5.57 -0.06

-0.07 -0.43 -22.06±21.05i -27.86 -5.52±5.26i -6.97 -0.06 -4.41±4.21i -5.57 -0.05

-0.04 -0.36 -22.06±21.05i -27.86 -5.52±5.26i -6.97 -0.05 -4.41±4.21i -5.57 -0.05

-0.23 -0.48 -22.06±21.05i -27.86 -5.52±5.26i -6.97 -0.10 -11.03±10.53i -13.93 -0.10

-0.10 -0.36 -22.06±21.05i -27.86 -5.52±5.26i -6.97 -0.07 -11.03±10.53i -13.93 -0.07

-0.05 -0.34 -22.06±21.05i -27.86 -5.52±5.26i -6.97 -0.05 -11.03±10.53i -13.93 -0.06

System Zeros

-4.41±4.20i -5.57 5.53±5.26i 6.97 -0.06 -0.12 22.06±21.05i 27.86

-4.41±4.20i 5.52±5.26i 6.97 -5.57 -0.05 -0.07 22.06±21.05i 27.86

-4.41±4.21i -5.57 5.52±5.26i 6.97 -0.05 -0.04 22.06±21.05i 27.86

-15.33 -11.83±9.70i 5.89±4.90i 6.18 -0.09 -0.21 22.06±21.05i 27.86

-11.27±10.34i -14.25 5.61±5.16i 6.77 -0.07 -0.09 22.06±21.05i 27.86

-11.09±10.48i -14.01 5.54±5.24i 6.92 -0.06 -0.05 22.06±21.05i 27.86

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I.2.2 MATLAB® Script for RGA Calculations An example of the MATLAB® scripts used for the RGA calculations is provided below.

% Program RGA.m % Calculates the RGA for CO2 train #1 at high gas throughput % clear % % Process gain, time constant and dead time matrices for SGC-RSF control structure KpH1=[1.1695 -0.9885; 1.0881 -0.0262]; TpH1=[8.2231 13.1691; 1.6168 16.0241]; DTH1=[0.1667 0.6667; 0.1667 0.8333]; % for i=1:2 for j=1:2 % 3rd order Pade approximations for dead times [DTH1num(i,:,j),DTH1den(i,:,j)]=pade(DTH1(i,j),3); % % Process transfer functions GpH1(i,j)=tf(KpH1(i,j)*DTH1num(i,:,j),conv([TpH1(i,j) 1],DTH1den(i,:,j))); end end % % Steady-state RGA RGAH1=KpH1.*inv(KpH1).' % % Calculate RGA over frequency range and print to text file w = logspace(-5,2,100); % GpH1_w=freqresp(GpH1,w); % for i=1:length(w) RGAH1_w(:,:,i)=GpH1_w(:,:,i).*inv(GpH1_w(:,:,i)).'; end % for i=1:2 RGAH1r1(i,:)=sign(RGAH1(1,i))*abs(RGAH1_w(1,i,:)); RGAH1r2(i,:)=sign(RGAH1(2,i))*abs(RGAH1_w(2,i,:)); end % y=[w; RGAH1r1; RGAH1r2]; fid=fopen('RGAH1_w.txt','w'); fprintf(fid,'%12.8f %12.8f %12.8f %12.8f %12.8f\n',y); fclose(fid);

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I.2.3 MATLAB® Script for Stability Index Calculations An example of the MATLAB® scripts used for the stability index calculations is provided below.

% Program StabilityIndices.m % Completes variable pairing analysis for CO2 Train #1 at high gas throughput % Calculates NI and MIC stability indices % clear % % Reordered process gain matrices for SGC-RSF control structure % i.e. paired variables according to RGA along diagonal KpH1=[-0.9885 1.1695; -0.0262 1.0881]; % % % Reordered process gain matrices with positive diagonal elements KpH1p=[0.9885 1.1695; 0.0262 1.0881]; % % Calculate NI values NIH1=det(KpH1)/(KpH1(1,1)*KpH1(2,2)) % % Determine eigenvectors and eigenvalues for positive diagonal gain matrices [KpH1pEVec, KpH1pEVal] = eig(KpH1p); % % Calculate MIC values MICH1=diag(KpH1pEVal)

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I.3 Analysis of Diagonal Control Structure Performance An example of the MATLAB® scripts used for the PRGA and CLDG calculations is provided below.

% Program PerformanceAnalysis.m % Analyses performance of control structure for CO2 Train #1 at high gas throughput % Calculates PRGA and CLDG % clear % % Reordered process gain, time constant and dead time matrices % i.e. paired variables according to RGA along diagonal KpH1=[-0.9885 1.1695; -0.0262 1.0881]; TpH1=[13.1691 8.2231; 16.0241 1.6168]; DTH1=[0.6667 0.1667; 0.8333 0.1667]; % % Disturbance gain, time constant and dead time vectors KdH1=[0.5757; -0.0735]; TpdH1=[6.1206; 3.4381]; DTdH1=[0.1667; 0.1667]; % for i=1:2 for j=1:2 % 3rd order Pade approximations for dead times [DTH1num(i,:,j),DTH1den(i,:,j)]=pade(DTH1(i,j),3); [DTdH1num(i,:),DTdH1den(i,:)]=pade(DTdH1(i),3); % % Process and disturbance transfer functions GpH1(i,j)=tf(KpH1(i,j)*DTH1num(i,:,j),conv([TpH1(i,j) 1],DTH1den(i,:,j))); GdH1(i,1)=tf(KdH1(i)*DTdH1num(i,:),conv([TpdH1(i) 1],DTdH1den(i,:))); end end % % Steady-state PRGA and CLDG PRGAH1=diag(diag(KpH1))*inv(KpH1) CLDGH1=PRGAH1*KdH1 % % Frequency analysis w=logspace(-5,2,100); % % Evaluate process and disturbance transfer functions over frequency range GpH1_w=freqresp(GpH1,w); GdH1_w=freqresp(GdH1,w); % % Calculate PRGA and CLDG over frequency range and print to text file for i=1:length(w) % PRGA PRGAH1_w(:,:,i)=diag(diag(GpH1_w(:,:,i)))*inv(GpH1_w(:,:,i)); % for j=1:2 PRGAH1r1_w(j,i)=PRGAH1_w(1,j,i); PRGAH1r2_w(j,i)=PRGAH1_w(2,j,i); end % % CLDG CLDGH1_w(:,i)=PRGAH1_w(:,:,i)*GdH1_w(:,:,i); end y=[w; PRGAH1r1_w; PRGAH1r2_w fid=fopen('PRGAH1_w.txt','w'); fprintf(fid,'%12.8f %12.8f %12.8f %12.8f %12.8f\n',y); fclose(fid); y=[w; CLDGH1_w]; fid=fopen('CLDGH1_w.txt','w'); fprintf(fid,'%12.8f %12.8f %12.8f\n',y); fclose(fid);

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I.4 BLT Tuning An example of the MATLAB® scripts used to perform BLT tuning is provided below.

% Program BLT.m % Performs BLT tuning for CO2 Train #1 at high gas throughput % clear % % Reordered process gain, time constant and dead time matrices % i.e. paired variables according to RGA along diagonal KpH1=[-0.9885 1.1695; -0.0262 1.0881]; TpH1=[13.1691 8.2231; 16.0241 1.6168]; DTH1=[0.6667 0.1667; 0.8333 0.1667]; % % Ziegler-Nichols PI settings KcZNH1=diag([-14.3942 7.2173]); TiZNH1=diag([1.1883 0.2914]); % % Set up tuning parameters i=sqrt(-1); w=logspace(-3,2,500); s=i*w; f=2.1; df=0.01; loop=0; flagm=-1; flagp=-1; dbmax=-100; % for i=1:2 for j=1:2 % 3rd order Pade approximations for dead times [DTH1num(i,:,j),DTH1den(i,:,j)]=pade(DTH1(i,j),3); [DTdH1num(i,:),DTdH1den(i,:)]=pade(DTdH1(i),3); % % Process transfer functions GpH1(i,j)=tf(KpH1(i,j)*DTH1num(i,:,j),conv([TpH1(i,j) 1],DTH1den(i,:,j))); end end % % BLT tuning: vary f until dbmax=4 (because 2x2 system) while abs(dbmax-4)>0.01 KcH1=KcZNH1/f; TiH1=TiZNH1*f; % % Controller transfer function for i=1:2 GcH1(i,i)=tf(KcH1(i,i)*[TiH1(i,i) 1],[TiH1(i,i) 0]); end % % Evaluate Gp and Gc over frequency range GpH1_w=freqresp(GpH1,w); GcH1_w=freqresp(GcH1,w); % % Calculate W function for i=1:length(w) WnyquistH1(i)=-1+det(eye(2)+GpH1_w(:,:,i)*GcH1_w(:,:,i)); lc(i)=WnyquistH1(i)/(1+WnyquistH1(i)); dbcl(i)=20*log10(abs(lc(i))); end % % Identify peak in closed-loop log modulus [dbmax,nmax]=max(dbcl); wmax=w(nmax); %

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loop=loop+1; if loop>50, break, end % % Test if +4 dB criterion is satisfied, if not get new value for f if dbmax>4 if flagp>0 df=df/2; end flagm=1; f=f+df; else if flagm>0 df=df/2; end flagp=1; f=f-df; if f

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