Supercritical and Other High-pressure Solvent Systems

Andrew J Hunt; Thomas M Attard

BOOK

Supercritical and Other High-pressure Solvent Systems

Andrew J Hunt | Thomas M Attard

(2018)

Additional Information

Book Details

ISBN: 978-1-78801-354-3
Edition: 1
Language: English
Pages: 678
Subjects: Sustainability
Industrial chemistry & chemical engineering
Environmental science, engineering & technology

Abstract

Exploring the range and utility of high-pressure solvent systems across a variety of different chemical applications, this book brings together recent advances in supercritical technology and other pressurised-solvent systems. It provides an in-depth overview of the latest advances and developments and discusses the limitations and drawbacks that need to be addressed. Wherever possible, the greenness and economic viability of the different solvent systems is highlighted. This book is ideal for researchers and industrialists working in environmental science, green chemistry and biorefineries.

Section Title	Page	Action	Price
Cover	Cover
Supercritical and Other High-pressure Solvent Systems: For Extraction, Reaction and Material Processing	i
Preface	vii
Contents	ix
Chapter 1 - Introduction to High-pressure Solvent Systems	1
1.1 Green Chemistry	1
1.2 Supercritical Fluids	3
1.2.1 Supercritical Fluids: Physical Properties	6
1.2.2 Supercritical Carbon Dioxide	7
1.2.3 Subcritical and Supercritical Water	8
1.2.4 Pressurised Solvent Systems	9
1.3 Conclusions	11
References	11
Chapter 2 - Understanding Entrainer Effects in Supercritical CO2	14
2.1 Introduction	14
2.1.1 Increasing Solubility	14
2.2 The Key Ideas	16
2.2.1 Too Many (Non-)Explanations	16
2.2.2 The Right Explanation	17
2.2.3 Getting the Numbers	18
2.2.4 How Not to Do It	19
2.3 The Difficulty of Prediction	20
2.3.1 What Gives Large Gu2 Values	21
2.3.2 Modelling the Baseline Solubility in Pure scCO2 via the Chrastil Formula	21
2.3.3 Linear Enhancement Factor per Entrainer Concentration (the Sovová kav Factor)	24
2.3.4 Database of Linear Solubility Enhancement Factors	26
2.3.5 From the Linearised Sovová Enhancement Factor Model to KBIs	26
2.3.6 Entrainer Effect Viewed from kav	31
2.3.7 As Good as It Gets	32
2.4 A Plausible Theory	33
2.5 Conclusions	36
References	37
Chapter 3 - Supercritical Carbon Dioxide Extraction of Lipophilic Molecules	40
3.1 Introduction	40
3.2 Solvent Extraction Problems	41
3.3 Supercritical Fluid Extraction	45
3.3.1 Choosing the Appropriate Operating Conditions for Extraction	45
3.3.2 Pressure and Temperature	46
3.3.3 Density and Solvent Power	47
3.3.4 Use of Modifiers/Co-solvents	48
3.3.5 Flow Rate	48
3.3.6 Particle Size	48
3.3.7 Optimisation of scCO2 Extraction Processes: Experimental Design	49
3.3.8 Screening Experimental Designs	50
3.3.9 Two-level Factorial Design	51
3.3.10 Two-level Full Factorial Design	51
3.3.11 Two-level Fractional Factorial Design	52
3.3.12 Two-level Plackett–Burman Design	53
3.3.13 Optimisation Design	53
3.3.14 Taguchi Design	54
3.3.15 Star Design	55
3.3.16 Central Composite Design	55
3.3.17 Box–Behnken Design (BBD)	55
3.4 Supercritical Extraction of Waxes and Bioactive Compounds	57
3.4.1 Bioactive Compounds	62
3.5 scCO2 Fractionation	65
3.6 scCO2 Extraction of Lipids as Part of a Holistic Biorefinery	67
3.7 Supercritical Extraction in Industry: Recent Advances in the Past Few Years	68
3.8 Conclusion	70
References	70
Chapter 4 - Subcritical Water: Current Status, Advances, and Applications for Extractions, Reactions and Separations	77
4.1 Introduction	77
4.2 Subcritical Water	78
4.3 Use of Subcritical Water: Current Status	80
4.4 Water for Extractions, Reactions and Separations	83
4.4.1 Extractions	83
4.4.1.1 Phenolic Compounds	83
4.4.1.2 Carbohydrates	85
4.4.1.3 Other Compounds	88
4.4.2 Mass Transfer During Extraction	90
4.4.2.1 Main Extraction Parameters	92
4.4.2.1.1\rSolubility (Thermodynamic State).The high solubility of a solute in a solvent indicates that less amount of solvent is needed to...	92
4.4.2.1.2\rSolvent Flow Rate.The solvent flow rate parameter is directly associated with the mass transfer mode when the flow is large enou...	93
4.4.2.1.3\rProperties of Plant Matrices.The knowledge of the raw material characteristics and the solute is crucial for efficient extractio...	93
4.4.3 Separations and Decompositions	94
4.4.4 Reactions	95
4.5 Economic Issues of Subcritical Water Processes	97
4.6 Patents Survey	99
4.7 Conclusions and Future Perspectives	99
Acknowledgements	101
References	101
Chapter 5 - Supercritical Fluid Chromatography (SFC)	106
5.1 Introduction	106
5.2 Early Packed Columns	107
5.3 SFC Instrumentation	108
5.4 Mobile Phase	108
5.5 Additives	109
5.6 Solid Phase	110
5.7 Detectors	112
5.7.1 Detectors: Mobile Phase	112
5.7.1.1 Mobile Phase – No Modifier	112
5.7.1.2 Mobile Phase – Modifier	112
5.7.1.3 SFC-MS	114
5.7.2 Detectors: Type of Extract	115
5.8 Two-dimensional SFC (2D SFC)	115
5.9 Polymer Separations	117
5.9.1 Polystyrene	117
5.9.2 Polyethylene Glycol (PEG)	119
5.9.3 Polyprenol	119
5.10 Natural Product Separations	120
5.10.1 Complex Lipid Systems	120
5.10.2 Triacylglycerols (TAGs)	121
5.10.3 Carotenoids	122
5.10.4 Terpenes	122
5.10.5 Alkaloids	124
5.10.6 Phenolic Compounds	125
5.10.6.1 Coumarins	126
5.10.6.2 Cannabinoids	126
5.10.6.3 Anthraquinones	126
5.10.6.4 Flavonoids	127
5.11 Green Credentials	128
5.12 Conclusion	128
References	128
Chapter 6 - Heterogeneous Catalysis in Supercritical Carbon Dioxide	132
6.1 Introduction	132
6.2 Reactions over Heterogeneous Catalysts	137
6.2.1 Hydrogenation	137
6.2.1.1 The –C=O Bond of α,β-unsaturated Aldehydes	138
6.2.1.2 Conjugated and Isolated –C=C Bonds	147
6.2.1.3 Nitrile to Amine	151
6.2.1.4 Nitroaromatics	153
6.2.1.5 Aromatic Ring Hydrogenation	156
6.2.2 Oxidation	159
6.2.2.1 Alcohol Oxidation	160
6.2.2.2 Other Oxidising Agents	165
6.2.3 Hydrogenolysis	168
6.2.3.1 Hydrogenolysis of the Ethereal C–O Bond	168
6.2.3.2 Hydrogenolysis of the Carbonyl C–O Bond	173
6.2.3.3 Hydrogenolysis of the Carbonyl C–O Bond of Tetrahydrofurfuryl Alcohol	174
6.2.4 Dehydrogenation of Alcohols	176
6.2.5 Current Status of Some Industrially Important Reactions	178
6.2.5.1 Alkylation	178
6.2.5.2 Hydroformylation	181
6.2.5.3 Reductive Amination	182
6.3 Conclusion	183
References	184
Chapter 7 - Biocatalysis in Supercritical and Liquid Carbon Dioxide and Carbon Dioxide-expanded Liquids	191
7.1 Introduction	191
7.1.1 Supercritical and Liquid CO2	192
7.1.2 CO2-expanded Liquids	193
7.2 Biocatalyst Behaviour in High-pressure CO2-related Solvents	194
7.2.1 Nature of Enzymes	195
7.2.2 Effect of Water Content	195
7.2.3 Solubility of Enzymes and Coenzymes	197
7.2.4 Carbamate and Carbonic Acid Formation	198
7.2.5 Thermodynamic Equilibrium of Reactions	199
7.2.6 Effect of Temperature and Pressure	200
7.2.7 Effect of Changes in the Solvent Properties Caused by Tuning the Pressure and Temperature	201
7.3 Biocatalytic Reactions in Liquid and Supercritical CO2	203
7.3.1 Lipase-catalysed (Trans)Esterification, Hydrolysis and Polymerisation	203
7.3.2 Galactosidase-catalysed Transgalactosylation	206
7.3.3 Alcohol Dehydrogenase-catalysed Reduction	207
7.3.4 Carboxylase-catalysed Carboxylation	207
7.4 Biocatalytic Reactions in CO2-expanded Liquids	208
7.4.1 Conventional Organic Liquids as the Solvent Component	208
7.4.2 Green Liquids as the Solvent Component: Bio-based Liquids	210
7.4.3 Green Liquids as the Solvent Component: Water	212
7.4.4 Green Liquids as the Solvent Component: Ionic Liquids	215
7.5 Conclusions	215
References	216
Chapter 8 - Selective Hydrogenation in Carbon Dioxide-dissolved Expanded Liquid Phases	221
8.1 Introduction	221
8.2 Hydrogenation of α,β-unsaturated Carbonyl Compounds	223
8.2.1 Cinnamaldehyde	223
8.2.2 Citral	230
8.2.3 Furfural and Furfuryl Alcohol Analogues	231
8.2.4 Isophorone Analogues	234
8.2.5 Maleic Anhydride	236
8.3 Hydrogenation of Nitro Compounds	237
8.3.1 Hydrogenation in CO2-dissolved Expanded Substrates	238
8.3.2 Hydrogenation in CO2-dissolved Expanded Liquid Solvents	242
8.4 Hydrogenation of Nitrile Compounds	245
8.5 Hydrogenation of Aromatic Rings, Alkenes, Alkynes and Other Compounds	250
8.5.1 Hydrogenation of Phenol	250
8.5.2 Hydrogenation of Biphenyl, Naphthalene and Tetralin	252
8.5.3 Hydrogenation of Alkenes and Alkynes	253
8.5.4 Hydrogenation of Other Compounds	255
8.6 Conclusion	255
Acknowledgements	256
References	256
Chapter 9 - Electrochemistry in Supercritical Fluids	262
9.1 Introduction	262
9.2 A Brief Historical Review of Electrochemistry in Supercritical Fluids	263
9.3 Supercritical Fluids	264
9.3.1 Polar Supercritical Fluids	270
9.3.2 Supercritical CO2	270
9.3.3 Supercritical Hydrofluorocarbons	271
9.4 Electrolytes	272
9.4.1 Phase Behaviour	272
9.4.2 Conductivity of SCF Electrolytes	272
9.4.3 Viscosity	280
9.5 Electrodes	280
9.6 High Pressure and Temperature Systems for Supercritical Fluid Electrochemistry	282
9.7 Electrochemistry	291
9.7.1 The Double Layer in SCF Electrolytes	291
9.7.2 Electrode Kinetics and Mass Transport	292
9.8 Applications of Supercritical Fluid Electrochemistry	295
9.8.1 Electrodeposition	295
9.8.2 Electrosynthesis	297
9.9 Conclusions	297
Acknowledgements	298
References	298
Chapter 10 - Materials Processing and Recycling with Near- and Supercritical CO2-based Solvents	304
10.1 Introduction	304
10.2 Thermodynamics and Phase Behaviour Data for CO2-based Solvents	306
10.2.1 Equation of State for the Estimation of the Vapour–Liquid Equilibrium and Thermodynamic Properties	308
10.2.2 Solubility of Reagents	310
10.3 Organic Materials Processing Using CO2-based Systems	311
10.3.1 Required Equipment	312
10.3.1.1 Pumps	312
10.3.1.2 Contactor	313
10.3.1.3 Precipitation Vessel	313
10.3.1.4 Back-pressure Regulator	313
10.3.1.5 Particle Separator	314
10.3.1.6 Fluid Separator	314
10.3.2 Principles of Processes Using CO2 for Organic Material Precipitation	314
10.3.2.1 CO2 as a Solvent	314
10.3.2.2 CO2 as an Antisolvent	316
10.3.2.3 CO2 as a Solute	318
10.4 Inorganic Materials Processing Using CO2-based Systems	320
10.4.1 Continuous Synthesis of Inorganic Nanostructures in CO2-based Solvents	321
10.4.2 Deposition of Films with a Supercritical Fluid Chemical Deposition Process in a Cold Wall Reactor	323
10.4.3 Surface Engineering of Materials in CO2-based Solvents	326
10.5 Materials Recycling with Supercritical CO2	327
10.5.1 LIB Electrolyte Recovery	328
10.5.2 Heavy Metal Extraction	330
10.5.3 Polymer Recycling, Case Study of PS	331
10.5.4 New Recycling Procedures based on the Use of scCO2	331
10.5.4.1 Supercritical CO2 Leaching	331
10.5.4.2 Supercritical CO2 Delamination	332
10.6 Conclusions	333
Acknowledgements	334
References	334
Chapter 11 - Solubility and Synthesis of Polymers Using Supercritical Carbon Dioxide	340
11.1 Introduction	340
11.2 Solubility of Polymers in scCO2	341
11.2.1 Predicting the CO2 Solubility in Polymers: Theoretical and Experimental Approaches	342
11.2.1.1 Henry's Law	343
11.2.1.2 Flory–Huggins Cell Model	343
11.2.1.3 Sanchez–Lacombe Model	344
11.2.1.4 Statistical Association Fluid Theory (SAFT)	344
11.2.2 Experimental Techniques to Measure Solubility	344
11.2.2.1 Gravimetric Method	344
11.2.2.2 Manometric Method	345
11.2.2.3 Piezoelectric Method	345
11.2.2.4 Gas Chromatography (GC)	345
11.2.2.5 Spectroscopic Method	346
11.3 Plasticising Effect of CO2	346
11.4 Overview of the Synthesis of Polymers in scCO2	348
11.4.1 Step-growth Polymerisation	348
11.4.2 Chain-growth Polymerisation in scCO2	349
11.4.2.1 Homogeneous Radical Polymerisation in scCO2	350
11.4.2.2 Heterogeneous Polymerisation in scCO2	352
11.4.2.2.1\rPrecipitation Polymerisation.In precipitation polymerisation, the monomers and other components start off completely soluble in ...	352
11.4.2.2.2\rDispersion Polymerisation.This is similar to precipitation polymerisation, whereby the monomer and the initiator are completely ...	354
11.4.2.2.3\rSuspension Polymerisation.Contrary to precipitation polymerisation and dispersion polymerisation, both the monomers and resultin...	356
11.4.2.2.4\rEmulsion Polymerisation.Emulsion polymerisations typically involve a biphasic mixture (that is stirred) of water–organic solvent...	357
CO2-in-H2O Emulsion Polymerisation: Examples. As stated previously, CO2-in-H2O emulsion polymerisation leads to the formation of...	359
H2O-in-CO2 Emulsion Polymerisation: Examples. Inverse emulsion polymerisation was first reported by Beckman1397969777s group in ...	360
11.4.2.2.5\rCLRP Polymerisation in Heterogeneous Systems Involving scCO2.scCO2 is ideal for conducting heterogeneous CLRP since the monomer,...	360
RAFT. There is significant work reported in the literature covering RAFT-mediated dispersion polymerisation in scCO2, which was ...	360
NMP. Initially, NMP polymerisation in scCO2 was solely reported using styrene as the monomer in dispersion (use of a stabiliser)...	363
ATRP. Both precipitation and dispersion ATRP polymerisations have been carried out in scCO2, but in the case of the former, ther...	364
CLRP Mini-emulsion Polymerisation in scCO2. Cheng et al. performed the RAFT mini-emulsion polymerisation of styrene with trithio...	364
Other CLRP in scCO2. A dispersion reversible chain transfer catalysed polymerisation (dispersion RTCP) of MMA in scCO2 was condu...	365
11.5 Conclusion	365
References	366
Chapter 12 - Incorporation of Drugs and Metals into Aerogels Using Supercritical Fluids	374
12.1 Aerogels	374
12.2 Supercritical Impregnation	376
12.2.1 Silica Aerogels	378
12.2.2 Polysaccharide and Protein Aerogels	383
12.3 Supercritical Fluid Deposition	386
12.4 Conclusion	389
References	390
Chapter 13 - Mathematical Modelling and Computation for Rapid Expansion of Supercritical Solutions	395
13.1 Introduction	395
13.2 Ideal-gas Flow Model	396
13.2.1 Compressible Navier–Stokes Equations	396
13.2.2 Preconditioned Equations	398
13.2.3 Numerical Methods	398
13.3 Thermophysical Flow Model	399
13.3.1 Modification of Preconditioned Equations	399
13.3.2 Thermophysical Model	399
13.4 Condensation Model	401
13.4.1 General Dynamic Equation	401
13.4.2 Method of Moments	401
13.4.3 Nucleation Model	403
13.4.4 Growth Rate Model	406
13.4.5 Coagulation Model	407
13.5 RESS Simulation	409
13.6 Concluding Remarks	414
References	415
Chapter 14 - The Engineering of Continuous Hydrothermal/Solvothermal Synthesis of Nanomaterials	416
14.1 Introduction	416
14.2 Hydrothermal Synthesis	417
14.2.1 Nucleation and Growth Mechanisms during Hydrothermal Synthesis	418
14.3 The Case for Continuous Flow Methods for the Synthesis of Nanomaterials	419
14.3.1 The Road from Batch to Continuous	420
14.4 Reactor Modelling	423
14.4.1 Pseudo-fluid Modelling	423
14.4.2 Computational Fluid Dynamics (CFD) Modelling	426
14.4.3 Neutron and X-ray Measurements	428
14.4.4 Reactor Design Principles	430
14.4.4.1 Essential Features	430
14.4.4.2 Important Features	432
14.4.4.3 Desirable Features	434
14.5 Beyond T-piece Reactors	436
14.5.1 Y-piece Reactors	436
14.5.2 Tangential Swirl Reactors	436
14.5.3 Pipe-in-pipe Reactors	438
14.5.4 Mechanical Hybrid Designs	439
14.6 Scale Up	439
14.7 Economics and Life Cycle Assessment (LCA)	442
14.7.1 Production Benefits and Opportunities for CHS	443
14.8 Conclusions and Future Outlook	444
References	445
Chapter 15 - The Chemistry of Continuous Hydrothermal/Solvothermal Synthesis of Nanomaterials	449
15.1 Introduction	449
15.2 Metal Oxides	450
15.3 Metal Sulphides and Chalcogenides	455
15.4 Phosphates	460
15.5 Metals	461
15.6 Zeolites and Metal Organic Frameworks	464
15.7 Layered Double Hydroxides	467
15.8 Other Materials	468
15.9 Conclusions	468
References	469
Chapter 16 - Supercritical Water Oxidation: The Next Generation for Abatement of Unrecyclable Waste of Hazardous Nature and Complex Composition	476
16.1 Background	476
16.2 The Chemistry of Supercritical Water	479
16.3 Features and Design Considerations for the Supercritical Water Oxidation Process	480
16.3.1 Feedstock	481
16.3.2 Reactor Design and Configuration	482
16.3.3 Energy Recovery and Integration	483
16.4 Operational Problems Associated with Supercritical Water Oxidation	486
16.4.1 Salt Precipitation	486
16.4.1.1 Pressure Manipulation	487
16.4.1.2 Reactor Design Solutions	488
16.4.2 Corrosion	489
16.5 Enhancement of the SCWO Process	492
16.5.1 Multi-port Oxidant Injection	492
16.5.2 Co-fuel Assisted SCWO System	494
16.5.3 Effects of Process Enhancements on SCWO Kinetics	499
16.5.3.1 Case Study 1: Supercritical Water Oxidation of DBU in an IPA-added System	500
16.5.3.2 Case Study 2: Supercritical Water Oxidation of NH4+ in an IPA-added System	501
16.6 Performance of the SCWO System for the Treatment of Complex Waste	506
16.6.1 Case Study: Use of SCWO for Treatment of Complex Wastewater	506
16.7 Conclusions	508
References	508
Chapter 17 - Gas Expanded-liquids	512
17.1 Introduction	512
17.2 Carbon Dioxide-expanded Liquids (CXLs)	515
17.2.1 Properties	515
17.2.2 Instrumentation	518
17.3 Applications	519
17.3.1 Extraction and Biorefinery	520
17.3.2 Particle Formation	521
17.3.2.1 CO2 Acting as the Solute: Particles from a Gas-saturated Solution (PGSS)	522
17.3.2.2 CO2 Acting as an Antisolvent	523
17.3.2.2.1\rGas Antisolvent (GAS) Technique.The simplest process that uses CO2 as an antisolvent is the GAS process.9 It is particularly use...	523
17.3.2.2.2\rPrecipitation with Compressed Antisolvent (PCA) and Aerosol Solvent Extraction System (ASES).The PCA process is the reverse of t...	524
17.3.2.3 CO2 Acting as a Co-solvent: Depressurisation of an Expanded Liquid Organic Solution (DELOS)	526
17.3.2.4 Enhanced Oil Recovery	527
17.3.2.5 Other Applications	528
17.4 Conclusions and Future Trends	528
Acknowledgements	529
References	529
Chapter 18 - Use of Water and Supercritical Carbon Dioxide in Novel Methodologies for Biomass Processing	532
18.1 Introduction	532
18.2 Biomass Hydrolysis	536
18.2.1 Effect of Pre-treatment on Hemicellulose Hydrolysis	536
18.2.2 Influence of Pre-treatment on Cellulose Hydrolysis	538
18.2.3 Effect of Pre-treatment on Starchy Materials	538
18.3 Conversion of Biomass-related Monosaccharides into Value-added Products	539
18.3.1 Hexose-derived Products	540
18.3.2 Pentose-derived Products	543
18.3.3 Lignin Extraction with scCO2	547
18.4 Effect of Pre-treatment on Enzymatic Hydrolysis	548
18.5 Conclusions	554
Acknowledgements	554
References	555
Chapter 19 - Hydrothermal Events Occurring During Gasification in Supercritical Water	560
19.1 Introduction	560
19.2 Thermo-physical Properties of Supercritical Water	563
19.3 Supercritical Water Gasification	566
19.4 Degradation of Model Compounds in Hydrothermal Gasification	570
19.4.1 Carbohydrates	570
19.4.2 Lignin	572
19.4.3 Proteins	573
19.4.4 Lipids and Fatty Acids	575
19.4.5 Alcohols	576
19.4.6 Sewage Sludge	578
19.5 Conclusions	581
Acknowledgements	581
References	581
Chapter 20 - Sub- and Supercritical Water Hydrolysis Applied to Agri-food Residues	588
20.1 Introduction	588
20.2 Sub/supercritical Water Hydrolysis Process	590
20.3 Novel Developments in Sub/supercritical Water Hydrolysis Applied to Agri-food Residues	597
20.4 Future Perspectives	614
20.5 Conclusions	615
References	616
Chapter 21 - Applications of Fluids at Supercritical Pressure in the Area of Power Generation – Movements Towards Economically-viable Clean Energy	620
21.1 The Properties of Fluids at Supercritical Pressure	620
21.2 Supercritical Pressure Fluids in Power Generation Plants	622
21.2.1 How it all Began – Supercritical Pressure ‘Steam’ Generators	622
21.2.2 Power Stations Operating at Supercritical Pressure – The Benson Boiler	622
21.3 Early Research on Heat Transfer with Fluids at Supercritical Pressure	623
21.4 A Unique Study of Heat Transfer to Carbon Dioxide at Supercritical Pressure	624
21.4.1 Diffusion of Heat with Strong Non-uniformity of Fluid Properties but in the Absence of any Advection of Heat	624
21.4.2 The Initial Experiments	626
21.4.3 Further Experiments	626
21.4.4 Experiments with the Cooled Surface Uppermost	629
21.4.5 Direct Numerical Simulation of the Experiments	629
21.5 Localised Deterioration of Heat Transfer in Vertical Heated Tubes	629
21.5.1 An Early Experiment Using Supercritical Water	629
21.5.2 Experiments with Supercritical Pressure Carbon Dioxide	631
21.5.3 Examples of Localised Deterioration of Heat Transfer with Heated Tubes of Smaller Diameter	633
21.5.4 Experiments at Pressures Just Below the Critical Value	633
21.6 A Simple Model of Buoyancy-induced Partial Laminarisation	634
21.6.1 Introduction	634
21.6.2 Effect of Buoyancy in Modifying the Distribution of Shear Stress	635
21.6.3 Effect of Shear Stress Modification on the Turbulent Diffusion Heat	636
21.6.4 Explanation of the Localised Nature of the Heat Transfer Deterioration	637
21.6.5 A Simple Criterion for Partial Laminarisation	637
21.7 Turbulent Forced Convection Heat Transfer with Fluids at Supercritical Pressure	638
21.7.1 Introduction	638
21.7.2 Empirical Equations for Turbulent Forced Convection Heat Transfer to Fluids at Supercritical Pressure	639
21.7.3 An Evaluation of Some Early Equations	639
21.7.4 Similarity and Scaling in the Case of Forced Convection Heat Transfer to Fluids at Supercritical Pressure	641
21.7.5 Correlating Buoyancy-influenced and Acceleration-influenced Heat Transfer Data	641
21.8 Development of Physically Based Semi-empirical Models of Heat Transfer to Supercritical Pressure Fluids	644
21.8.1 A Revival of Interest after the Millennium in Heat Transfer to Fluids at Supercritical Pressure	644
21.8.2 A Physically Based, Semi-empirical Model of Buoyancy-influenced Turbulent Flow and Heat Transfer in Supercritical Pressure...	644
21.8.3 A Physically Based Semi-empirical Model of Impairment of Heat Transfer due to Thermally Induced Bulk Flow Acceleration	646
21.8.4 Recent Work on the Development of Extended Semi-empirical Models	648
21.9 Supercritical Transformational Electric Power Cycles	648
21.9.1 Background	648
21.9.2 Advantages of Power Conversion Cycles using Supercritical Pressure Carbon Dioxide	649
21.9.3 The Supercritical CO2 Re-compression Cycle	649
21.9.4 Other Applications of scCO2 Power Cycles	650
21.9.5 Ongoing Studies of Applications Involving scCO2 Cycles	650
21.9.6 Ongoing Work	651
21.9.7 Where are we Heading Clean Energy Production Using scCO2 Power Cycles	652
Nomenclature	652
Greek symbols	653
Subscripts	653
Superscripts	654
Appendix: Steady Turbulent Flow and Heat Transfer in Tubes	654
1 Introduction	654
2 Historical Background – Analogy Between Friction and Heat Transfer	654
3 Reynolds’s Ground Breaking Experimental Study of Turbulent Flow in Tubes	657
4 The Basis of our Present Day Approach to Turbulent Flow –Reynolds’s Dynamical Theory of Incompressible Viscous Fluids	660
5 Turbulent Flow and Heat Transfer in Tubes – the Present Picture	662
References	665
Subject Index	667

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