Performance Evaluation of Organic Rankine Cycle Architectures: Application to Waste Heat Valorisation

Performantie-evaluatie van organische-Rankine-cyclusarchitecturen: toepassing op restwarmtevalorisatie

Steven Lecompte

Promotoren: prof. dr. ir. M. De Paepe, prof. dr. M. van den Broek Proefschrift ingediend tot het behalen van de graad van Doctor in de Ingenieurswetenschappen: Werktuigkunde-Elektrotechniek

Vakgroep Mechanica van Stroming, Warmte en Verbranding Voorzitter: prof. dr. ir. J. Vierendeels Faculteit Ingenieurswetenschappen en Architectuur Academiejaar 2015 - 2016 ISBN 978-90-8578-897-3 NUR 961 Wettelijk depot: D/2016/10.500/29 Universiteit Gent Faculteit Ingenieurswetenschappen en Architectuur Vakgroep Mechanica van Stroming, Warmte en Verbranding

Promotoren: Prof. dr. ir. Michel De Paepe Prof. dr. Martijn van den Broek

Universiteit Gent Faculteit Ingenieurswetenschappen en Architectuur

Vakgroep Mechanica van Stroming, Warmte en Verbranding Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgie¨

Tel.: +32-9-264.32.88 Fax.: +32-9-264.35.90

Proefschrift tot het behalen van de graad van Doctor in de Ingenieurswetenschappen: Werktuigkunde-Elektrotechniek Academiejaar 2015-2016

Dankwoord

Wanneer ik dit dankwoord schrijf is er een hele weg afgelegd. De ervaringen en kansen langs die weg culmineerden uiteindelijk in dit werk. Het was echter niet mogelijk om dit te doen zonder de steun van de mensen rondom mij. Eerst wil ik mijn promotoren prof. De Paepe en prof. van den Broek bedanken om me de kans te geven een doctoraat te starten. Bedankt om mij te steunen en om me bij te staan met wetenschappelijke raad en daad. De collega’s hebben me door deze vier aangename maar intensieve jaren ge- loodst. Ze waren een aanspreekpunt voor hulp en ontspanning. Sergei, bedankt om steeds klaar te staan om metingen te doen op de testopstellling. Bruno, bedankt voor de aangename samenwerking. Henk, bedankt om me intensief te begeleiden bij het begin van mijn doctoraat. Marijn, bedankt om een aantal administratieve taken over te nemen. Sven, bedankt voor je kritische blik. Bernd, bedankt voor de ideeen,¨ de wetenschappelijke raad, het nalezen en zoveel meer. Ook de vroe- gere collega’s waren een belangrijke inspiratiebron, bedankt hiervoor Marnix en Kathleen. Daarnaast ben ik ook dankbaar dat ik de fantastische mensen van het ORCNext project heb leren kennen. Ik wil ook graag al het technisch personeel bedanken. Dankzij de uitstekende administratieve hulp van Griet en Annie kwam ik niet in kafkaiaanse toestanden terecht, ook al durfde ik wel eens een ontvangst- bewijs vergeten. Mag ik ook niet vergeten, de hele dierentuin: Frakke, Eddy, Mieke, Godzilla, Soesje, Mufﬁn, Macaron. Jullie waren ideaal om mijn gedachten te verzetten, vooral wanneer er terug een van jullie uitgebroken was. Dankzij mijn ouders heb ik de vrijheid gehad om te doen wat ik graag deed, heel erg bedankt daarvoor. Tot slot wil ik mijn vrouw Jarissa bedanken voor haar geduld en eindeloze liefde. Sorry als ik soms koppig was en geen tijd had voor jullie. Maar de weg startte toen ik klein was. Elke dag kwam mijn opa mij ophalen van school. Ook onder de middag ging ik steevast naar daar. Bedankt oma en opa om me die kans te geven. Het minste wat ik kan doen is deze thesis opdragen aan m’n wijlen grootvader, Gaston De Clercq. Wat ik van jou geleerd heb is, nooit opgeven, blijven doorgaan.

Gent, mei 2016 Steven Lecompte

Table of Contents

Dankwoord i

List of Figures ix

List of Tables xv

Nomenclature xvii

Nederlandse Samenvatting xxv

English Summary xxix

1 Introduction 1 1.1 Towards renewable and sustainable energy ...... 1 1.2 Introducing the organic Rankine cycle ...... 4 1.2.1 ORC Working fluids ...... 5 1.2.1.1 Working fluid characteristics ...... 5 1.2.1.2 Environmentally friendly working fluids . . . .7 1.2.1.3 Working fluid safety constraints ...... 7 1.2.2 Challenges and opportunities ...... 8 1.3 Objective of the study ...... 8 1.4 Outline ...... 9 References ...... 10

I Organic Rankine cycle architectures and their evaluation criteria 15

2 Thermodynamic and thermo-economic evaluation criteria 17 2.1 Introduction ...... 17 2.2 Thermodynamic performance evaluation ...... 17 2.2.1 First law, energy balance criteria ...... 17 2.2.2 Second law, exergy balance criteria ...... 18 2.2.3 Performance criteria of pump and expander ...... 21 2.3 Thermo-economic performance evaluation ...... 23 2.3.1 Speciﬁc area ...... 24 iv

2.3.2 Speciﬁc investment cost ...... 24 2.3.3 Simple payback period ...... 25 2.3.4 Net present value ...... 25 2.3.5 Levelised cost of electricity ...... 26 2.3.6 Overview of thermo-economic criteria ...... 26 2.4 Conclusion ...... 28 References ...... 29

3 Review of organic Rankine cycle architectures 31 3.1 Introduction ...... 31 3.2 Thermodynamics of ideal cycles ...... 31 3.2.1 Comparison of the ideal cycles ...... 34 3.2.2 Heat recovery from industrial excess heat ...... 35 3.3 Overview of ORC architectures ...... 36 3.3.1 ORC with recuperator (RC) ...... 40 3.3.2 Regenerative feed heating ORC (RG) ...... 41 3.3.3 Organic ﬂash cycle (OFC) ...... 42 3.3.4 Trilateral (triangular) cycle (TLC) ...... 44 3.3.5 Zeotropic mixtures as ORC working ﬂuids (ZM) . . . . . 46 3.3.6 Transcritical ORC (TCORC) ...... 48 3.3.7 ORC with multiple evaporation pressures (MP) ...... 50 3.3.8 Vapour injector, reheater and cascade cycles ...... 52 3.3.9 Summary of ORC architectures ...... 52 3.4 Thermo-economic studies on ORC architectures ...... 54 3.5 Commercial and experimental prototypes ...... 57 3.6 Conclusions ...... 60 References ...... 63

II Comparison of organic Rankine cycles architectures: thermodynamic screening and thermo-economic appraisal 73

4 Thermodynamic performance evaluation and regression models of organic Rankine cycle architectures 75 4.1 Introduction ...... 75 4.2 Cycle arrangements ...... 75 4.3 Comparing the SCORC, TCORC and TLC ...... 76 4.4 Thermodynamic model and assumptions ...... 78 4.5 Optimisation algorithm and strategy ...... 80 4.6 Regression models ...... 84 4.6.1 Analysis of the full set of working ﬂuids (Case 1) . . . . . 86 4.6.2 Analysis of the environmentally friendly set of working ﬂuids (Case 2) ...... 91 4.6.3 Analysis of the restriction to a superheated state after the expander (Case 3) ...... 95 v

4.6.4 Analysis of the restriction with upper cooling limit (Case 4) 97 4.6.5 Analysis of the addition of a recuperator (Case 5) . . . . . 99 4.7 Example on the use of the regression models ...... 101 4.8 Overview and comparison with literature ...... 102 4.9 Conclusions ...... 105 References ...... 106

5 Thermo-economic performance evaluation of organic Rankine cycle architectures 113 5.1 Introduction ...... 113 5.2 Definition of the case study ...... 114 5.3 Model and assumptions ...... 114 5.3.1 Cycle assumptions ...... 114 5.3.2 Heat exchanger model ...... 115 5.3.3 Cost models ...... 117 5.3.4 Working fluid selection ...... 120 5.3.5 Expander considerations ...... 121 5.4 Optimisation strategy ...... 121 5.5 Specific investment costs of the Pareto front ...... 122 5.5.1 Analysis of the parameter space ...... 125 5.5.2 Turbine performance parameters ...... 129 5.5.3 Distribution of the costs ...... 129 5.6 Financial analysis and appraisal ...... 130 5.7 Conclusions ...... 132 References ...... 134

III Part-load operation of organic Rankine cycle heat engines 139

6 Part-load modelling of the organic Rankine cycle heat engine 141 6.1 Introduction ...... 141 6.2 Modelling approach ...... 142 6.2.1 The object-oriented paradigm ...... 142 6.2.2 Levels of modelling detail ...... 142 6.3 Heat exchangers ...... 143 6.3.1 Finite volume, moving boundary and hybrid model . . . . 143 6.3.2 Implementation ...... 144 6.3.3 Plate heat exchangers ...... 148 6.3.3.1 P-NTU correlations ...... 148 6.3.3.2 Connection equations ...... 149 6.3.3.3 Single phase heat and pressure drop correlations 149 6.3.3.4 Two phase heat and pressure drop correlations . 151 6.3.3.5 Supercritical heat and pressure drop correlations 152 6.4 Volumetric expanders ...... 153 vi

6.5 Centrifugal pump ...... 155 6.6 Cycle model ...... 156 6.7 Conclusions ...... 158 References ...... 159

7 Experimental validation and optimal operation under part-load conditions 163 7.1 Introduction ...... 163 7.2 The experimental ORC set-up ...... 164 7.3 Steady state analysis ...... 164 7.3.1 Steady state detection algorithm ...... 166 7.3.2 Acquiring the steady state points ...... 167 7.4 Heat exchanger heat balances ...... 170 7.5 Validation of the individual component models ...... 172 7.5.1 Evaporator and condenser ...... 172 7.5.2 Volumetric expander ...... 174 7.5.3 Centrifugal pump ...... 175 7.6 Validation of the full cycle model ...... 178 7.7 Optimal part-load operation ...... 182 7.7.1 Effect of the pump rotational speed ...... 182 7.7.2 Optimised pump rotational speed ...... 183 7.7.3 Comparison between the SCORC and PEORC ...... 184 7.8 Conclusions ...... 185 References ...... 187

8 Conclusions 189 8.1 Conclusions ...... 189 8.2 Future work ...... 191

A A Publications 193

B B Working ﬂuids list 197

C C Experimental ORC set-up 201 C.1 Components ...... 201 C.1.1 Measuring equipment ...... 201 C.1.2 Heat exchangers ...... 201 C.1.3 Centrifugal pump ...... 203 C.1.4 Volumetric double screw expander ...... 204 C.1.5 External loops ...... 204 C.1.5.1 Heating loop ...... 204 C.1.5.2 Cooling loop ...... 205 C.2 Uncertainty analysis ...... 206 References ...... 209 vii

D D Fin and tube heat exchangers 211 D.1 P-NTU correlations ...... 211 D.2 Connection equations ...... 212 D.3 Convective heat transfer correlations ...... 212 References ...... 214

E E On the use of zeotropic mixtures 215 E.1 Working fluid selection ...... 216 E.2 Model and assumptions ...... 216 E.2.1 Optimisation ...... 217 E.3 Effect of zeotropic mixtures ...... 218 E.3.1 Internal and external second law efficiency ...... 218 E.3.2 Analysis of the optimal pinch point temperature ...... 223 E.3.3 Glide slopes ...... 223 E.3.4 Effect of the recuperator ...... 225 E.4 Comparison of mixture compostitions ...... 227 E.4.1 Optimal mixture composition ...... 228 E.5 Sensitivity studies ...... 229 E.5.1 Sensitivity on inlet heat carrier temperature ...... 229 E.5.2 Sensitivity on pinch point temperature difference . . . . . 232 E.5.3 Sensitivity on cooling fluid glide slope ...... 232 E.6 Comparison to other work ...... 234 E.6.1 Irreversibility distribution ...... 234 E.7 Conclusions ...... 235 References ...... 237

List of Figures

1.1 World electricity generation from 1971 to 2013, ’other’ includes geothermal, solar, wind, etc., adapted from International Energy Agency (IEA) [2] ...... 2 1.2 Waste heat from a reheat furnace, volumetric flow rate and temperature profiles of the flue gas between 10-16/01/2011...... 3 1.3 (a) Component layout of the basic Rankine cycle. (b) T-s diagram of the basic Rankine cycle...... 4 1.4 T-s diagram of a dry, wet and isentropic fluid...... 6

2.1 Exergy ﬂow diagram of the basic ORC with recuperator...... 19 2.2 Pressure-volume diagram depicting (a) under-expansion and (b) over-expansion in the shaded region...... 23

3.1 T-s diagram. (a) Ideal Carnot cycle, infinite capacity heat source. (b) Externally irreversible Carnot cycle, finite capacity heat source. (c) Ideal triangular cycle, finite capacity heat source...... 32 3.2 Thermal efficiency, fraction of heat recovered and cycle efficiency of the Carnot cycle, externally irreversible Carnot cycle and TLC as a function of the temperature T1 for TL = 25 °C and TH = 200 °C. 34 3.3 Temperature-heat flow diagram at the evaporator of a subcritical ORC without superheating...... 35 3.4 (a) ORC with recuperator cycle layout. (b) ORC with recuperator T-s diagram...... 40 3.5 (a) ORC with regenerative feed heating cycle layout. (b) ORC with regenerative feed heating T-s diagram...... 41 3.6 (a) OFC cycle layout. (b) OFC T-s diagram...... 42 3.7 (a) Alternative OFC system. (b) Alternative OFC system T-s diagram...... 44 3.8 (a) TLC cycle layout. (b) TLC T-s diagram...... 45 3.9 (a) ORC with zeotropic mixtures cycle layout. (b) ORC with zeotropic mixtures T-s diagram...... 46 3.10 (a) Transcritical ORC cycle layout. (b) Transcritical ORC T-s diagram...... 48 3.11 (a) Multiple evaporation pressure ORC cycle layout. (b) Multiple evaporation pressure ORC T-s diagram...... 51 x

3.12 Example of a two-dimensional Pareto front...... 55

4.1 (a) Basic ORC layout. (b) ORC layout with recuperator...... 76 4.2 Discretisation modelling approach of the heat exchangers. . . . . 79 4.3 Second law efficiency ηII as a function of Fp and Fs for R1234yf, Tcf,in = 25 °C with (a) Thf,in = 140 °C and (b) Thf,in = 90 °C. 82 4.4 Contour plot of ηII,max for full set of working fluids (Case 1). . . 87 4.5 Vapour quality xexp,in for the PEORC...... 88 4.6 Relative ηII,max results: (a) Case 1, PEORC relative to TCORC, (b) Case 1, TCORC relative to SCORC, (c) Case 2, TCORC relative to SCORC, (d) Case 3, TCORC relative to SCORC, (e) Case 4, TCORC relative to SCORC, (f) Case 5, TCORC relative to SCORC. 89 4.7 Exergy content (a) case 1, (b) case 2, (c) case 3, (d) case 4, Tcf,in = 20 °C...... 90 4.8 Contour plot of ηII,max for environmentally friendly set of working fluids (Case 2)...... 92 4.9 Relative cycle results ηII,max for SCORC architecture, (a) (Case 1 - Case 2), (b) (Case2 - Case 3), (c) (Case 3 - Case 4), (d) (Case 4 - Case 5)...... 93 4.10 Relative cycle results ηII,max for TCORC architecture, (a) (Case 1 - Case 2), (b) (Case2 - Case 3), (c) (Case 3 - Case 4), (d) (Case 4 - Case 5)...... 94 4.11 Contour plot ηII,max, environmentally friendly set of working fluids and Tsup,exp,out > 0 (Case 3)...... 96 4.12 Contour plot ηII , environmentally friendly set of working fluids, Tsup,exp,out > 0 and Thf,out = 130 °C (Case 4)...... 98 4.13 ηII , ηII,int and ηII,ext for Case 4 with Thf,in = 160 °C...... 99 4.14 Contour plot ηII , environmentally friendly set of working fluids, Tsup,exp,out > 0, Thf,out = 130 °C and RC (Case 5)...... 100 4.15 Results of applying the regression models on waste heat recovery cases A and B...... 102

5.1 Schematic layout of a plate heat exchanger with two passes. . . . 116 5.2 SIC of the Pareto front versus net power output for the SCORC. . 123 5.3 SIC of the Pareto front versus net power output for the TCORC. . 123 5.4 Pinch point temperature differences as a function of SIC for the SCORC...... 126 5.5 Pinch point temperature differences as a function of W˙ net for the SCORC...... 126 5.6 Condensing and evaporating temperatures as a function of SIC for the SCORC...... 127 5.7 Condensing and turbine inlet temperatures as a function of SIC for the TCORC...... 127 5.8 Pinch point temperature differences as a function of SIC for the TCORC...... 128 xi

5.9 Pinch point temperature differences as a function of W˙ net for the TCORC...... 128 5.10 Turbine performance parameters SP and VR for the SCORC. . . . 129 5.11 Turbine performance parameters SP and VR for the TCORC. . . . 129 5.12 Distribution of the cost at minimum SIC for the SCORC. . . . . 130 5.13 Distribution of the cost at minimum SIC for the TCORC. . . . . 130 5.14 Cumulative cash ﬂow for minimum SIC of the SCORC, minimum SIC of the TCORC and maximum NPV of the SCORC. . 132

6.1 Outline of the hybrid discretisation approach for modelling the heat exchangers...... 144 6.2 UML class diagram of the classes associated to the heat exchanger. 145 6.3 UML ﬂowchart of the heat exchanger solver...... 147 6.4 Geometry of the plate heat exchanger wavy shape corrugation pattern...... 150 6.5 Dimensionless characteristic curves of the centrifugal pump. . . . 156 6.6 UML ﬂowchart of the cycle solver...... 157

7.1 Component layout and measurement equipment of the experimental 11 kWe ORC located at campus Kortrijk, Ghent University. . . 164 7.2 Picture of the experimental 11 kWe ORC (campus Kortrijk Ghent University)...... 165 7.3 Original dataset of the performed ORC experiments, plot of Thf,in, m˙ hf , V˙cf and W˙ exp,grid...... 168

7.4 Reference steady state operating regime, plot of Thf,in, m˙ hf , V˙cf and W˙ grid,el...... 169

7.5 Detected steady state operating zones, plot of Thf,in, m˙ hf , V˙cf and W˙ grid,el...... 169 7.6 Heat balance over the evaporator with error flags...... 171 7.7 Heat balance over the condenser with error flags...... 171 7.8 Parity plot of the heat flow rate of the evaporator, comparison between model and experiment...... 173 7.9 Parity plot of the heat flow rate of the condenser, comparison between model and experiment...... 174 7.10 Parity plot of the mass flow rate through the expander, comparison between model and experiment...... 176 7.11 Parity plot of the power output (W˙ exp,cycle in red and W˙ exp,grid in blue) of the volumetric expander, comparison between model and experiment...... 176 7.12 Parity plot of the mass flow rate through the pump, comparison between model and experiment...... 177 7.13 Parity plot of the power input of the pump, comparison between model and experiment...... 177 xii

7.14 Parity plot of the evaporation pressure, comparison between model and experiment...... 179 7.15 Parity plot of the condensation pressure, comparison between model and experiment...... 179 7.16 Parity plot of the working fluid mass flow rate, comparison between model and experiment...... 180 7.17 Parity plot of the cycle expander power output to grid, comparison between model and experiment...... 180 7.18 Parity plot of the net power output to grid, comparison between model and experiment...... 181 7.19 Illustration of pinch point shift, (line: model, star: experiment). . . 181 7.20 Model output variables xexp,in, W˙ net, W˙ exp,grid and W˙ pump,grid as a function of Npump for m˙ hf = 1.5 kg/s, Thf,in = 110 °C and 3 V˙cf = 13.4 m /h...... 182 7.21 Relative improvement in Wnet˙ of PEORC operation compared to SCORC operation with original and improved pump (original isentropic efficiency pump tripled), operating points from left to right correspond with the operating points in Table 7.7 from top to bottom...... 185

C.1 Plate heat exchanger of the ORC...... 202 C.2 Plate heat evaporator in the system...... 202 C.3 Centrifugal pump...... 203 C.4 3D picture of the volumetric double screw expander...... 204 C.5 Electrical thermal oil heater of 250 kWe...... 205 C.6 Air cooled cooler with glycol/water cooling loop...... 205

E.1 Second law efficiency of zeotropic mixtures in function of mixture concentration (optimal evaporation pressure)...... 219 E.2 Internal ηII,int and external ηII,ext second law efficiency of zeotropic mixtures in function of mixture concentration (optimal evaporation pressure)...... 219 E.3 ∆yD,cond and ∆yD,evap for zeotropic mixtures in function of mixture concentration (optimal evaporation pressure)...... 220 E.4 ∆yD,exp and ∆yD,pump for zeotropic mixtures in function of mixture concentration (optimal evaporation pressure)...... 220 E.5 QT diagram R245fa-isopentane (optimal concentration and evaporation pressure) and pure working fluid R245fa (optimal pressure). 221 E.6 QT diagram R245fa-isopentane (optimal concentration, fixed pinch point temperature 103.8 °C) and pure working fluid R245fa (optimal pressure)...... 222 E.7 Pinch point temperature and pressure in function of mixture concentration with optimal and reference pinch point temperature (=103.8 °C) (R245fa-isopentane)...... 224 xiii

E.8 ηII,ext and ηII,int in function of mixture concentration for optimal and reference pinch point temperature (=103.8 °C) (R245fa- isopentane)...... 224 E.9 Glide slope of R245fa-isopentane in evaporator and condenser in function of concentration...... 225 E.10 Relative difference in % between ORC with and without recuperator in function of mixture concentration for: ηII , ηII,int, ηII,ext (optimal evaporation pressure, R245fa-isopentane)...... 226 withoutrecuperator withrecuperator E.11 yD,component − yD,component in function of mixture concentration for: evaporator, condenser, recuperator (optimal evaporation pressure, R245fa-isopentane)...... 227 E.12 Relative improvement when using mixtures compared to the pure working fluids (optimal evaporation pressure and concentration). . 229 E.13 Irreversibility distribution for an ORC with zeotropic mixtures as working fluid (optimal evaporation pressure and concentration). . 230 E.14 Irreversibility distribution for an ORC with pure working fluids (optimal evaporation pressure and concentration)...... 231

List of Tables

2.1 List of objective functions used in thermo-economic optimisation. 27

3.1 List ORC architectures discussed in this chapter...... 36 3.2 Overview of papers about advanced ORC architectures showing power scale and application...... 38 3.3 Overview of papers on advanced ORC architectures showing the different boundary conditions...... 40 3.4 Thermo-economic analysis of transcritical cycles in open literature. 50 3.5 Summary of ORC architectures...... 53 3.6 Selection of scientiﬁc papers on thermo-economic optimisation of ORCs...... 57 3.7 Adaptations to the classical subcritical ORC by commercial manufacturers...... 57

3.8 Overview of experimental data about novel ORC architectures. . . 58

4.1 Research articles which investigate either the TLC or TCORC. . . 77 4.2 Assumptions and parameters for the thermodynamic model. . . . 79 4.3 Operating conditions at maximum second law efficiency for Thf,in = 90 °C and Thf,in = 140 °C for R1234yf with Tcf,in = 25 °C. . . 83 4.4 Description of the case studies with reference to their contour plots of ηII,max...... 84 4.5 Parameter estimates for ηII,max surface fits...... 85 4.6 Goodness-of-fit statistics for ηII,max surface fits...... 85 4.7 SCORC and TCORC working fluids with expansion ending in two-phase region...... 95 4.8 Description of two representative waste heat recovery cases A and B...... 101 4.9 Overview working fluid selection...... 103 4.10 Working fluid selection comparison with scientific literature. . . . 104

5.1 Main parameters of the thermodynamic cycle...... 114

5.2 Geometrical design parameters of the plate heat exchangers. . . . 116 5.3 Cost parameters by Turton et al. [28]...... 118 xvi

5.4 Pressure factor, material factor and bare module cost by Turton et al. [28]...... 118 5.5 Uncertainty for R245fa fundamental equation of state. [35] . . . . 120 5.6 Decision variables and their range for the thermo-economic optimisation...... 121 5.7 Parameter settings of the genetic optimisation algorithm...... 122 5.8 Results of minimum SIC and maximum W˙ net...... 124 5.9 Assumptions for the NPV calculations...... 131 5.10 Results of the NPV calculations...... 132

7.1 Steady state criteria according to Woodland et al. [1]...... 166 7.2 Reference values for detecting the steady state operating regime. . 170 7.3 Range of achieved operating conditions of the cycle validation dataset...... 170 7.4 Range of achieved operating conditions of the component calibration dataset...... 172 7.5 Model coefficients to determine the filling factor of the volumetric expander...... 175 7.6 Model coefficients to determine the isentropic efficiencies of the volumetric expander...... 175 7.7 Range of ORC boundary conditions, results of the optimisation of the pump speed with no constraint on superheating...... 183 7.8 Range of ORC boundary conditions, results of the optimisation of the pump speed with superheat constraint to 15 °C...... 184

C.1 Make of measurement equipment...... 201 C.2 Characteristics of the plate heat exchangers...... 203 C.3 Characteristics of the pump...... 204 C.4 Accuracy of measurement equipment...... 206 C.5 Absolute uncertainty values ...... 208

E.1 Thermophysical properties of the selected pure working fluids. . . 216 E.2 ORC, heat source and heat sink parameters...... 217 E.3 Results of the sensitivity analysis on the cooling fluid temperature glide ∆Ths: second law efficiency and working fluid temperature glide (optimal evaporation pressure and concentration)...... 233 E.4 Characteristic cycle parameters for heat carrier at 150 °C (optimal evaporation pressure and concentration)...... 236 xviii Nomenclature

A area m2 B capacity or size parameter W or m2 Bo boiling number - C cost C C heat capacity rate W/K CH dimensionless head - CV˙ dimensionless volume flow rate - cp specific heat capacity J/kg.K D diameter m E˙ exergy flow rate W e specific exergy J/kg F dimensionless optimisation parameter - G mass flux kg/m2.s Ha Hagen number - g gravitational acceleration m2/s h specific enthalpy J/kg hlg specific enthalpy of vaporisation J/kg I˙ irreversibility rate W i interest rate - K cost correlations coefficients - K number of passes - k thermal conductivity W/m.K LCOE levelised cost of electricity C/MWh M molar density kg/mol m˙ mass flow rate kg/s N number of paths - NPV net present value C NTU number of transfer units - Nu Nusselt number - P temperature effectiveness - pco corrugation pitch m PB simple payback period year P r Prandtl number - Q˙ heat transfer rate W R net cash flow over a fixed period C R heat capacity rate ratio - R2 coefficient of determination - Re Reynolds number - rv built-in volume ratio - xix

s specific entropy J/kg.K SA specific area m2/kWe SIC specific investment cost C/kWe SP size parameter - T temperature °C t thickness m U overall heat transfer coefficient W/m2.K U uncertainty / V˙ volume flow rate m3/s V volume m3 v specific volume m3/kg VC volume coefficient - VR volume ratio - W˙ power W p pressure Pa x vapour quality -

Greek symbols

α convective heat transfer coefficient W/m2.K β chevron angle ° ∆ difference - isentropic efficiency - ζ friction factor - η efficiency - κ thermal diffusivity m2/s ν kinematic viscosity m2/s σ standard deviation / ψ filling factor -

Subscripts

0 dead state I ﬁrst law II second law b bulk cf cold ﬂuid cn Carnot crit critical cond condenser D destruction evap evaporator eq equivalent exp expander xx

ext external extirr externally irreversible frac fraction g vapour state H high h hydraulic hf hot ﬂuid in inlet int internal L loss L low l liquid state max maximum min minimum out outlet prim primary rec recuperator sat saturated state sec secondary sub subcooling sup superheating th thermal w wall wf working ﬂuid

Acronyms

ASHREA American Society of Heating, Refrigerating, and Air- Conditioning Engineers AWF all working ﬂuids BM bare module CHP combined heat and power CEPCI chemical engineering plant cost index DDE Dynamic Data Exchange EES Engineering Equation Solver EWF environmentally friendly working ﬂuids GEO geothermal GR grass roots GWP global warming potential IEA International Energy Agency LMTD logarithmic mean temperature difference MP multiple evaporation pressures NFPA National Fire Protection Association NSGA Non-dominated Sorting Genetic Algorithm ODP ozone depletion potential xxi

OFC organic flash cycle ORC organic Rankine cycle PEC performance evaluation criterion PEC purchased equipment cost PP pinch point PEORC partial evaporating organic Rankine cycle RC recuperator RG regenerator RTD resistance temperature detector SCORC subcritical organic Rankine cycle SOL solar SSE sum of squared errors of prediction TCORC transcritical organic Rankine cycle TLC triangular cycle TM totale module UML Unified Modelling Language VC volume coefficient VPT variable phase turbine VR volume ratio WHR waste heat recovery ZM zeotropic mxitures

Nederlandse Samenvatting –Summary in Dutch–

In onze samenleving is er een steeds grotere vraag naar elektriciteit. De opwek- king van elektriciteit gebeurt vandaag echter voornamelijk door het verbranden van fossiele brandstoffen. Een vaak voorgestelde oplossing is om elektriciteit op te wekken vanuit hernieuwbare bronnen zoals wind, water of geothermie. Een aan- vullende aanpak is om efficienter¨ gebruik te maken van onze beschikbare energie. Er zijn bijvoorbeeld grote hoeveelheden aan overtollige warmte (i.e. restwarmte) beschikbaar op lage temperatuur (< 300 °C) die nu gewoon afgevoerd wordt naar de atmosfeer. Deze warmte kan nochtans nuttig gebruikt worden om elektriciteit te produceren. Dit is waar de organische-Rankine-cyclus (ORC) in het spel komt. Deze thermodynamische cyclus is analoog aan de Rankine cyclus die men vindt in klassieke thermische elektriciteitscentrales die werken op fossiele brandstoffen. In tegenstelling tot de Rankine cyclus, die water gebruikt als werkingsmiddel, gebruikt de ORC een alternatief werkingsmiddel. Dit werkingsmiddel is specifiek geselecteerd om kosteneffectief om te gaan met de lage temperatuur warmte. Om grootschalige integratie van ORCs te ondersteunen zijn er twee belangrijke vragen: hoe verder de performantie verbeteren en hoe de ORC te ontwerpen voor maximale financiele¨ opbrengst. Direct gerelateerd aan deze vragen is de keuze van performantieevaluatiecriteria. Daarom worden eerst de thermodynamische en financiele¨ criteria besproken die in de literatuur gebruikt worden. Voor de thermodynamische criteria is een analyse gebaseerd op de tweede hoofdwet het meest compleet. De tweede hoofdwet laat toe om kwantitatief te evalueren hoeveel potentieel de warmte heeft om arbeid te leveren. Voor de financiele¨ criteria wordt de netto actuele waarde aanzien als beste criterium. Het houdt rekening met de tijdswaarde van geld, de levensduur van het project en de kasstroom. Een ander criterium, dat veel gebruikt wordt in de literatuur, is de specifieke investeringskost. Dit criterium is gedefinieerd als de totale investeringskost gedeeld door het netto uitgaand elektrisch vermogen. Vandaag de dag is de subkritische ORC (SCORC) de de facto standaard in commerciele¨ toepassingen. Vanuit de literatuur is het nochtans duidelijk dat andere cyclusarchitecturen de mogelijkheid bieden op een groter netto uitgaand elektrisch vermogen met eenzelfde restwarmtebron. Om te begrijpen waar de betere performantie vandaan komt worden drie ideale thermodynamische cycli vergeleken. Daarnaast wordt ook het proces van de warmteoverdracht geanalyseerd voor een SCORC. Daaropvolgend wordt een literatuuronderzoek gepresenteerd waarbij xxvi NEDERLANDSE SAMENVATTING zeven architecturen besproken worden. Van deze architecturen zijn er twee die een hoog potentieel hebben voor restwarmte recuperatie: de transkritische ORC (TCORC) en de partiele¨ evaporatie cyclus (PEORC). Beide architecturen delen dezelfde opstelling van componenten als de SCORC, enkel het werkingsregime is anders. Voor de PEORC wordt het werkingsmiddel enkel gedeeltelijk verdampt in de verdamper. Voor de TCORC wordt het werkingsmiddel verhit tot een super- kritische temperatuur en druk. Omdat in de literatuur er verschillende modellen en randvoorwaarden gebruikt worden is het niet mogelijk om resultaten onderling te vergelijken. Bovendien is er een duidelijk gebrek aan experimentele studies. Meer bepaald modellen die experimenteel gevalideerd zijn, zijn schaars in de wetenschappelijke literatuur. Om de cyclusarchitecturen onder gelijke randvoorwaarden te vergelijken is er een uitgebreide thermodynamische screening opgezet met 67 werkingsmiddelen. De screening beschouwt de twee meest interessante ORC architecturen voor restwarmte valorisatie en de SCORC. Van de optimaliseringsresultaten worden re- gressiemodellen opgesteld. Deze maken het mogelijk om snel een inschatting te maken van de maximale thermodynamische performantie van de drie architecturen voor een grote verscheidenheid aan restwarmte temperaturen (100 °C-350 °C) en koelwatertemperaturen (15 °C-30 °C). De invloed van opeenvolgende extra randvoorwaarden is geanalyseerd: de beperking tot milieuvriendelijke werkingsmiddelen, een opgelegde oververhitting na expansie, het opleggen van een minimum uitgaande temperatuur bij afkoelen van de restwarmte, het toevoegen van een recuperator. Voor lage temperatuur restwarmte blijkt dat alternatieve architecturen zoals de PEORC en TCORC duidelijk grotere tweede hoofdwet rendementen geven in vergelijking tot de SCORC. Voor hoge restwarmte temperaturen (> 250 °C) wordt het verschil echter klein. Wanneer men de werkingsmiddelen beperkt tot milieuvriendelijke middelen is er een aanzienlijk verlies in tweede hoofdwet rendement, voornamelijk voor de lage restwarmte temperaturen. Er is dus potentieel voor een nieuwe generatie van werkingsmiddelen. Voor de eigenlijke dimensionering en de financiele¨ evaluatie wordt een raamwerk voorgesteld dat bestaat uit een multi-objectieve optimalisatie gebaseerd op investeringkost en netto uitgaand vermogen. Met deze twee waarden kan de netto actuele waarde bepaald worden. Dit raamwerk is toegepast op een restwarmte casus die de TCORC en SCORC vergelijkt. De resultaten tonen aan dat de TCORC een hoger uitgaand vermogen kan bereiken maar dit ten koste van een hogere specifieke investeringskost. Dit is te verklaren door de grotere kost van de warmte- wisselaars. Er is ook aangetoond dat het ontwerp dat de minimum specifieke investeringskost geeft niet noodzakelijk de grootste netto actuele waarde geeft. Het voorgesteld raamwerk kan eenvoudig aangepast worden voor toepassing op andere casus. Naast restwarmte zijn er ook andere warmtebronnen die aan de ORC kunnen gekoppeld worden zoals geothermie en zonne-energie. In tegenstelling tot deze hernieuwbare bronnen kan restwarmte een zeer grote variatie vertonen in temperatuur en capaciteit in een korte tijd. Daarom zijn deellastmodellen nodig om het werkelijk netto uitgaand vermogen te bepalen onder varierende¨ randvoorwaarden. SUMMARY IN DUTCH xxvii

Semi-empirische modellen, zogenaamde gray-box modellen, van de individuele ORC componenten worden voorgesteld op basis van de huidige literatuur. Een belangrijke poging is gedaan om de implementatie robuust, snel en modulair te maken. De modellen kunnen dus gebruikt worden in optimalisatie problemen maar zijn ook eenvoudig uitbreidbaar naar nieuwe conﬁguraties. De individuele component modellen worden ge¨ınterconnecteerd om zo het cyclus model te vormen. Dit is een simulatie model, wat betekend dat enkel de rotationele snelheid van pomp en expander als input gebruikt wordt. Experimentele gegevens van een 11 kWe ORC worden gebruikt om de modellen te kalibreren en valideren. De experimentele set-up is een verkleinde versie van een commercieel bestaande machine ontworpen voor lage temperatuur restwarmte (tussen 80 °C en 150 °C) met R245fa als werkingsmiddel. De belangrijkste componenten zijn de platenwarmtewisselaars die gebruikt worden als verdamper en condensor, een centrifugale pomp en een volumetrische dubbele schroef expander. Een robuust detectie algoritme is voorgesteld om uitschieters en transiente¨ gegevens te verwijderen. Het verkeerdelijk behouden van transiente¨ gegevens kan anders zorgen voor een vertekening in de resultaten. De resultaten van de experimentele validatie tonen een gesloten warmtebalans over verdamper en condensor met een onzekerheid van ±5% tussen primaire en secundaire warmtestroom. De belangrijke afhankelijke variabelen in het model zijn de verdampingsdruk, de con- densatiedruk en het massadebiet van het werkingsmiddel. Deze drie variabelen varieren¨ ±1% met de gemeten waarden. Het gemodelleerd uitgaand vermogen varieert ongeveer ±2% met de gemeten waarden. Dit kan aanzien worden als een aanvaardbaar resultaat. De gevalideerde modellen worden daarna gebruikt om de optimale snelheid van de pomp te bepalen. Als er geen extra beperkingen opge- legd worden is de optimale werking een PEORC cyclus. Wanneer de werking als PEORC vergeleken wordt met de werking als SCORC, blijkt dat de PEORC 2% to 12% meer netto vermogen geeft. Voor hoge warmte toevoer wordt de druk in het systeem hoog, dit belet een hoog uitgaand vermogen. Het variabel maken van het toerental van de expander kan hieraan verhelpen. Verder moet opgemerkt worden dat de vermogenswinst in PEORC werking sterk gerelateerd is aan de efﬁcientie¨ van de pomp. Dit is door de grotere invloed van de pump op het netto uitgaand vermogen door het vergroot massadebiet werkingsmiddel bij partiele¨ verdamping. Deze initiele¨ resultaten tonen aan dat er opportuniteiten zijn om SCORC installa- ties om te vormen naar PEORC werking.

English Summary

In our society, there is an ever increasing need for electricity. However, today most of the electricity is generated by burning fossil fuels. A frequently proposed solution, is to generate electricity from renewable energy sources like solar, wind, water or geothermal. An additional approach is to make more efficient use of our energy. For example, vast amounts of excess heat (i.e waste heat) at low temperature (< 300 °C) are currently discarded into atmosphere. Yet, part of this heat can still be used to generate electricity. This is where the organic Rankine cycle (ORC) comes into play. This thermodynamic cycle is analogous to the Rankine cycle found in classical thermal power plants running on fossil fuels. However, instead of using water as working fluid, an alternative fluid is employed. This fluid is chosen to cope in a technically feasible and cost effective way with the low-temperature heat. To support large scale adoption of ORCs driven by waste heat, two main questions should be addressed. Firstly, how to further increase the performance of the ORC and secondly, how to evaluate and size the ORC for maximum financial profit. Directly related to these questions, is the choice of performance evaluation criteria. As such, the thermodynamic and financial criteria used in literature are first introduced. For the thermodynamic criteria, an analysis based on the second law of thermodynamics was considered to be the most comprehensive, as it quantifies the potential of heat to produce power. For the financial criteria on the other hand, the net present value could be flagged as the best evaluation criterion. It considers the time value of money, the total lifetime of the project and the cash flow. A criterion that is however used frequently in literature, is the specific investment cost. This criterion is defined as total investment cost divided by the generated net power output. Currently, the subcritical ORC (SCORC) is the de facto standard in commercial applications. However from literature it is clear that other cycle architectures show increased net electrical power output from the same waste heat stream. To appre- ciate the source of the performance increase, three ideal thermodynamic cycles are first analysed and compared. In addition, the actual heat recovery process from a waste heat stream to a SCORC is depicted. Next, a literature review on ORC architectures is given. A total of seven architectures were identified. From these, two have high potential for waste heat recovery applications: the transcritical ORC (TCORC) and the partial evaporating ORC (PEORC). Both architectures share the same component arrangement with the SCORC. Only the operating regime is different. In a PEORC, the working fluid only partially evaporates in the evaporator. xxx ENGLISH SUMMARY

For the TCORC, the working fluid is heated to a supercritical temperature and pressure. However, because various boundary conditions and models are used, the results from literature are not cross-comparable. Furthermore, there is a clear lack of experimental results. Especially experimentally validated models are scarce. To evaluate the cycle architectures under equal boundary conditions, a comprehensive thermodynamic screening with 67 working fluids was performed. The presented screening considers the two most promising cycles for waste heat recovery and the SCORC. From the optimisation results, regression models were derived. These allow quickly assessing the maximum thermodynamic performance of the three cycle architectures for a large range of waste heat input temperatures (100 °C-350 °C) and condenser cooling temperatures (15 °C-30 °C). The impact of additional boundary conditions is analysed: limitation to environmentally friendly working fluids, enforced superheated state after the expander, upper cooling limit of the heat carrier and the addition of a recuperator. For low temperature waste heat, alternative architectures like the TCORC and PEORC clearly show higher maximum second law efficiencies compared to the SCORC. For high waste heat input temperatures (> 250 °C), the performance gain however becomes small. When restricting the working fluids to environmentally friendly ones, there is a significant decrease in power output for low temperature waste heat streams. As such, there is potential for a new generation of working fluids. The sizing and financial appraisal is tackled by proposing a framework that uses a multi-objective optimisation with as objectives investment cost and net power output. With these two values, the net present value can be calculated in a post-processing step. This framework was applied on a waste heat recovery case comparing the SCORC and TCORC. The results show that the TCORC allows for a higher net power output. However this is at the cost of a higher specific investment cost, due to the increased cost of the heat exchangers. It is also shown that the design that minimises the specific investment cost or the design that maximises the net present value are not necessarily the same. The proposed optimisation framework can easily be adapted to other cases. Besides waste heat, also other low temperature heat sources like geothermal or solar can also be coupled to the ORC. However, in contrast to these renewable sources, waste heat can have very large variations in capacity and temperature in a short time. Therefore part-load models are necessary to evaluate the actual power output under varying boundary conditions. Semi-empirical, so called gray- box models, of the individual ORC components are proposed based on the current state of the art. An important effort has been made to make the implementation fast, robust and highly modular. As such, the models can be used in optimisation problems but they are also easily extensible to new configurations. The individual components models are interconnected forming the cycle model. This is a simulation model, meaning that only the pump and expander speed are used as inputs. Experimental data from an 11 kWe ORC are used to calibrate and validate the models. This experimental set-up is a scaled-down version of a real commercial ORC designed for low heat source temperatures (between 80 °C and 150 °C) and uses R245fa as working fluid. The main components are the plate heat exchangers ENGLISH SUMMARY xxxi as evaporator and condenser, a centrifugal pump and a volumetric double screw expander. A robust steady state detection algorithm is proposed for removing outliers and transient behaviour in the data. False inclusion of transient data points could result in a bias of the results. The validation results show a closed heat balance of evaporator and condenser with a maximum deviation between secondary and primary heat flow rate of ±5%. The important dependent variables are the evaporation pressure, the condensation pressure and the working fluid mass flow rate. All three predicted parameters show a maximum deviation of less than ±1% from the measured values. The modelled net power output deviates less than ±2% from the measured values. In general, this is a satisfactory result. These validated models are subsequently used to identify the optimal pump speed during operation under different boundary conditions. If no extra constraints are imposed, the optimal operating point corresponds to PEORC operation. Comparing the operation as SCORC and PEORC, the PEORC shows an increased net power output between 2% to 12% over the SCORC. For high heat inputs, the pressure in the systems becomes too high, limiting the performance. Making the rotational speed of the expander variable could resolve this. It should also be noted that the increase in net power output is highly dependent on the efficiency of the pump. This due to the higher influence of the pump on the net power output due the higher working fluid mass flow rate when operating as a PEORC. These initial results nevertheless indicate that there are opportunities to retrofit existing SCORC installations to operate as PEORC.

1 Introduction

1.1 Towards renewable and sustainable energy

As the human population grows, it becomes increasingly dependent on energy. Especially electricity takes a central role, as can be seen from Figure 1.1. From 1971 till 2013 there is a steady increase in electricity generation worldwide. Most of this electricity still comes from burning fossil fuels in a thermal power plant. However, our non-renewable primary energy resources are finite. Furthermore, generation of electricity by burning fossil fuels puts a significant strain on the environment. A frequently proposed solution is to introduce renewable energy, coming from the sun, to provide a sustainable way to fulfil our energy needs. The sun’s energy potential can directly be captured by means of concentrated solar plants or photovoltaic systems. Indirectly, there are opportunities in wind, hydro or tidal energy. Yet, these renewable energy sources still amount for a low share of the electricity generated. In addition, it is essential to use our natural resources more efficiently to cope with the increasing demand for energy. This is directly reflected in the 20/20/20 targets [1] set out by the European Union. The EU not only aims at increased shares in renewable energy but also aims at a 20% improvement in energy efficiency. One way of doing this is by recovery of excess heat (i.e. waste heat) from industrial processes. This heat is typically a by-product and is discarded into the atmosphere. However, waste heat can be used more effectively. The most obvious and typically most cost effective way is to use this heat for heating other processes. 2 CHAPTER 1

28 000

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8 000

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World electricty generation [TWh] 0 1971 1975 1980 1985 1990 1995 2000 2005 2010 2013 Fossil thermal Nuclear Hydro Other . Figure 1.1: World electricity generation from 1971 to 2013, ’other’ includes geothermal, solar, wind, etc., adapted from International Energy Agency (IEA) [2]

If this is not an option, their are possibilities to upgrade the heat to higher temperatures with the help of a heat pump, to use the heat for cooling with the help of ab- or adsorption cooling or by converting the heat to electricity. There are still large amounts of waste heat available. For example, in Canada 70% [3] of the input energy from the eight largest manufacturing sectors is discarded to the atmosphere. For the U.S., estimates are between 20% and 50% [4] of industrial energy that is lost as waste heat. In Europe alone, 140 TWh/j [5] of waste heat is available. From an European perspective 2.5 GW [6] of gross electric power could be produced from available rejected industrial heat alone. However, in contrast to heat from most renewable sources like geothermal and solar, waste heat can have very large variations in a short time of capacity and temperature. In Figure 1.2 the flue gas temperature and volume flow rate of a reheat furnace is shown for one week (10-16/01/2011). In one hour, variations in temperature and volume flow rate are respectively in the order of 100 °C and 50 000 Nm3/h. Other examples of these capacity and temperature variations can amongst others be found in the cement industry (drying processes) [7], transportation sec- tor (mobile combustion engines) [8] and steel industry (electric arc furnaces, cokes ovens) [9]. As such care should be taken when doing an analysis on nominal values. Variations in the order of hours or days have an impact on the economics and the performance of waste heat recovery system. Therefore off-design models of the heat recovery systems are crucial to account for these effect. Waste heat and most renewable energy sources, like geothermal and solar, have the low temperature of the heat in common. For example, today’s large scale thermal power plants typically run at high temperatures (over 500 °C) and achieve INTRODUCTION 3

120000 100000 80000 60000 40000

tric flow rate [Nm³/h] 20000

0 20 40 60 80 100 120 140 160 Volume

450

400

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300 Temperature [°C] 250 0 20 40 60 80 100 120 140 160 Hours [h]

Figure 1.2: Waste heat from a reheat furnace, volumetric flow rate and temperature profiles of the flue gas between 10-16/01/2011.

efficiencies up to 60% [10] in modern combined-cycle gas power plants. However for lower temperatures, let us say below 200 °C, the ideal heat to power efficiency is inherently low. Considering waste heat at 200 °C with heat rejection at 20 °C, the maximum achievable heat to power efficiency (i.e Carnot efficiency) is 38%. Real heat to grid efficiencies are typically half of the reported Carnot efficiency values. The low efficiencies are thus an intrinsic factor that needs to be accounted for in order to provide cost-effective solutions.

This is the landscape where the organic Rankine cycle (ORC) comes into play. Although almost identical to a water/steam Rankine cycle used in today’s thermal power plants, the ORC converts heat at low temperature to electricity due to a careful selection of an advantageous working fluid. Further benefits include low maintenance, favourable operating pressures and autonomous operation. Systems installed in the past [11] have already proven these benefits associated with ORCs. Different low temperature heat sources are used as input to the ORC. Waste heat applications roughly consist of up to 20% [12] of the ORC market, preceded by geothermal and biomass installations. Yet, the share of waste heat recovery applications can be expected to increase just by considering the vast quantities available and the flexibility of the technology. 4 CHAPTER 1

1.2 Introducing the organic Rankine cycle

A thermodynamic cycle is a sequence of thermodynamic processes that ends in the same state as it started. These processes involve the transfer of heat and work during which state variables (e.g pressure and temperature) vary. A cycle with as purpose to convert heat to work is deﬁned as a power cycle. This in contrast to refrigeration and heat pump cycles which have as goal to provide cold and heat, respectively. For a more extensive discussion on thermodynamic cycles we refer to the textbook of Moran and Shapiro [13].

7 (a) (b) 2 Evaporator ṁWF Expander 2 ṁHTF 7 8 8 3 3 Generator T

ṁCF 6 1 1 4 6 4 5 Condenser

pump 5 S

Figure 1.3: (a) Component layout of the basic Rankine cycle. (b) T-s diagram of the basic Rankine cycle.

The Rankine cycle is a power cycle commonly found in today’s thermal power plants. This power cycle uses water as working fluid to convert heat to work. The basic component layout of the cycle is shown in Figure 1.3a, the corresponding temperature-entropy (T-s) diagram is given in Figure 1.3b. The cycle consists of a pump which pressurises the working fluid and transports it to the evaporator (1). In the evaporator, the working fluid is heated to the point of saturated or superheated vapour (2). Next, the working fluid expands (3) through an expander and produces mechanical work. This shaft power can then be converted to electricity by the generator. The superheated working fluid at the outlet of the expander is condensed to saturated liquid (4) in the condenser. The liquid working fluid is again pressurised by the pump, closing the cycle. The heat sink and heat source consist for most applications of a finite thermal reservoir and are indicated respectively as line (7)-(8) and (5)-(6). The organic Rankine cycle (ORC) is a commercially mature technology for converting low temperature heat to work. As the name suggests, is the working principle identical to the Rankine cycle discussed above. Yet an alternative working fluid instead of water is used. The primary benefit is that the cycle can be adapted to the low temperature of the heat source. More information about the INTRODUCTION 5 selection of the working fluid can be found in Section 1.2.1. To make a distinction with advanced cycle architectures introduced later, this cycle is named a subcritical ORC (SCORC). This means that the evaporator works under a pressure lower than the critical pressure of the working fluid. Most of the commercially available installations are of the SCORC type [14]. However, alternative cycle architectures have the ability to boost the thermodynamic performance of ORCs [15].

1.2.1 ORC Working fluids Organic Rankine cycles operate with so called organic fluids. In the context of ORCs this means a working fluid which has beneficial characteristics for low temperature heat conversion and typically excludes water which is used in the classical water/steam Rankine cycle. By using different fluids, the cycle can be tailored to specific needs. As this is a key characteristic of ORC systems, this topic is elaborated further in this section.

1.2.1.1 Working ﬂuid characteristics The properties that have an inﬂuence on the performance of the system are [16, 17]:

• The shape of the saturation vapour curve: As shown in Figure 1.4 the ﬂuids can be categorised as dry, wet and isentropic. A quantitative measure ∂s is the factor ξ = ∂T x [18]. With s the entropy, T the temperature and x the vapour fraction. The value of ξ is dependent on the temperature and pressure. Therefore this value is evaluated at the normal boiling point. This is the temperature at which a liquid’s vapour pressure equals one standard atmosphere (atm).

ξ < 0 : wet fluid (1.1) ξ > 0 : dry fluid (1.2) ξ = 0 : isentropic fluid (1.3)

A dry ﬂuid has the advantage of not needing superheating at the inlet of a turbine. The vapour is expanded in the superheated region, avoiding damage to the turbine blades [19]. However if the ﬂuid is highly superheated after expansion the condenser load increases. By using a recuperator, the heat of this superheated vapour can be used to preheat the liquid after the pump.

• The condensing pressure: A condensing pressure above atmospheric pressure reduces the risk of inﬁltration of non-condensable gases, which would lead to a performance decrease [20]. Thus no deaerator is needed. Still, the possibility of leakage remains. Furthermore a reduced volume ratio over the expander compared to water promotes smaller and hence cheaper expanders. 6 CHAPTER 1 T [K] T [K] T [K]

Dry Wet Isentropic s [J/kg] s [J/kg] s [J/kg]

Figure 1.4: T-s diagram of a dry, wet and isentropic ﬂuid.

• The evaporation pressure: A lower evaporation pressure is advantageous for component costs. Safety considerations will be less stringent with lower pressure. • The specific heat and latent heat: A high latent heat and low liquid specific heat promotes heat addition during phase change and reduces the mass flow rate of the working fluid [21, 22]. Hence, pumping power is reduced, resulting in a better thermal efficiency. However, other authors [23, 24] say that working fluids with a low latent heat are better. They explain that working fluids with low latent heat better follow the heat carrier profile. • The boiling point: A low boiling point allows the evaporation of the working fluid from low temperature heat sources. • The critical temperature: The temperature of the waste heat carrier is strongly related to the optimum value for the critical temperature of the working fluid [25]. Rayegan and Tao [26] conclude from their results that a higher critical temperature leads to a higher thermal efficiency. Quoilin et al. [27] states that in general the selected working fluid has a slightly larger critical temperature than the target evaporation temperature. The author mentions that the vapour density is very low if the evaporation is taken too far away from the critical point. This in turn leads to high pressure drops and larger components.

It is difficult to select the ideal working fluid just on an intrinsic set of qualitative characteristics. Therefore, the selection of working fluids for the ORC was early on triggered by thermodynamic simulations. Different objective functions for fluid selection have been used: thermal efficiency [17, 28], exergy efficiency [29], system efficiency [22, 30] and cost effective optimum design [31]. Because of the various criteria used, different optimal working fluids were selected. As such, no single fluid can be designated as best. INTRODUCTION 7

1.2.1.2 Environmentally friendly working ﬂuids

A key challenge is the availability of high performing ORC working fluids in the near future. From an environmental viewpoint several working fluids are a priori flagged as unsuitable. The ozone depletion potential (ODP) and global warming potential (GWP) are typically employed to assess respectively the impact on the ozone layer and the greenhouse effect. The GWP of a gas is a relative measure that indicates the contribution to global warming. This measure is defined as the ratio of the amount of heat trapped by 1 kg of gas during 100 years to the amount of heat trapped by the same mass of CO2 during the same period. The ODP is a measure of degradation of the ozone layer caused by a gas relative to the degradation of the ozone layer caused by CFC-11. Working fluids with an ODP larger than 0 are banned by the Montreal protocol [32]. In anticipation of new European F-gas regulations [33] the incentive is launched to ban fluids with a GWP value larger than 150. By 2015 this rule applies to domestic freezers and refrigerators and by 2022 in extension to some commercial installations. While the current rules apply for refrigerators and freezers, an analogous restriction can be expected for power producing cycles.

1.2.1.3 Working ﬂuid safety constraints

In addition to environmental constraints, safety is a main concern. The ASHRAE 34 standard provides a classification system which takes into account toxicity and flammability for refrigerants. Working fluids with a classification of A1 are preferred. These are non toxic and non flammable when tested in air at 21 °C and 101 kPa. However, in contrast to ODP and GWP regulations, there is no general consensus on acceptable or permitted working fluids concerning safety. For example, both n-pentane and toluene are commercially [12, 14] used in ORC installations but are not classified in the ASHRAE 34 database. However, they are classified under the NFPA 704 [34] standard. This standard categorises hazardous materials to quickly identify their risks. Under NFPA 704, toluene is marked as level 3 1 flammability and level 2 2 toxicity. Cyclopentane is marked as level 4 3 flammability and level 1 4 toxicity. Both are highly flammable, yet both are used in commercial ORC systems.

1Liquids and solids (including finely divided suspended solids) that can be ignited under almost all ambient temperature conditions. Liquids having a flash point below 23 °C and having a boiling point at or above 38 °C or having a flash point between 23 °C and 38 °C. 2Intense or continued but not chronic exposure could cause temporary incapacitation or possible residual injury 3Will rapidly or completely vaporise at normal atmospheric pressure and temperature, or is readily dispersed in air and will burn readily. Includes pyrophoric substances. Flash point below 23 °C 4Exposure would cause irritation with only minor residual injury 8 CHAPTER 1

1.2.2 Challenges and opportunities In the future ORC development path, two strategic questions remain: how to improve the performance and, secondly, how to evaluate and size the cycle for maximum profitability. In this regard four major research topics can be classified: the working fluids, the hardware components, the control strategy and the component layout and sizing. Numerous works in literature concentrate on fluid selection [17, 22, 28–31]. Besides the selection of the optimal working fluid, the development of new and improved expander designs gains a lot of attention [35–38]. Another research area which has bloomed is the optimal control strategy of ORCs [39–41]. In this respect, the off-design (i.e. part-load) operation [42, 43] is flagged as an important factor. Off-design operation means that the system operates at conditions different then the nominal conditions. Part-load operation, as defined in heat pump and refrigeration cycles typically relates to the capacity reduction at a certain operating condition. ORCs however almost always work at maximal power output. In literature on ORCs the word part-load is thus used as a general term which also includes off-design operation. Furthermore, alternative cycle architectures to the basic ORC are proposed and analysed [14, 15]. These advanced architectures show increased performance over the standard subcritical ORC. Yet, no single work provides insights on alternative cycle architectures from all of the three crucial steps of ORC system design, namely the initial fluid screening, the thermo-economic optimisation and the part-load operation. In each of these steps, several research opportunities remain to be addressed, see Chapter 3 for a detailed discussion. Most importantly, there is a need for a sound comparison between various cycle architectures. Different evaluation criteria are currently used in literature, making a comparison impossible. In addition, part-load behaviour is mostly neglected. In the rare instance that part-load behaviour is included, the part-load models are seldom validated with experimental results.

1.3 Objective of the study

The objective of this work is to investigate the potential of ORC architectures for waste heat recovery applications. In order to support increased adoption of ORC technology, the following topics are addressed:

1. Investigation of possible ORC performance improvements by looking at different cycle architectures.

2. Development of thermo-economic analysis tools to allow appraisals for waste heat recovery projects.

3. Investigation of the part-load behaviour of the ORC. INTRODUCTION 9

In this thesis, enhanced optimisation and modelling approaches are introduced that should in the near future lead to comprehensive tools for full virtual prototyping of ORCs.

1.4 Outline

The structure of the thesis is compiled on the basis of the objectives above. Part I, Organic Rankine cycle architectures and their evaluation criteria, provides a general introduction on ORC architectures and the evaluation criteria used for comparing ORC architectures. This part is composed of Chapters 2 and 3. In Chapter 2, the thermodynamic and thermo-economic performance evaluation criteria are introduced and critically compared. In Chapter 3, waste heat recovery with closed thermodynamic power cycles is explained and several alternative cycle architectures besides the basic SCORC are reviewed. Part II, Comparison of organic Rankine cycle architectures: thermodynamic screening and thermo-economic evaluation, investigates the potential of alternative ORC architectures based on the evaluation criteria and the selection of promising cycles from Part I. This part is composed of Chapters 4 and 5. In Chapter 4, a screening approach of working ﬂuids/architectures is introduced. The subcritical ORC, the transcritical ORC and the partial evaporating ORC are evaluated purely on thermodynamic criteria. In Chapter 5, a thermo-economic optimisation tool is presented. A multi- objective optimisation is on the basis of the analysis. Part III, Part-load operation of organic Rankine cycle heat engines, covers the last objective of this thesis. The investigation into the part-load operation of organic Rankine cycles. This part is composed of Chapters 6 and 7. In Chapter 6, part-load models for the ORC are introduced and the implementation of the different component models are described. In Chapter 7, the detailed part-load models are validated based on the experimental results of an 11 kWe ORC. This set-up is a scaled-down version of a real commercial ORC, designed for waste heat recovery under low heat source temperatures. The validated models are used to predict the optimal operating conditions for the subcritical operation (SCORC) and the newly introduced partial evaporating operation (PEORC). 10 CHAPTER 1

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Part I

Organic Rankine cycle architectures and their evaluation criteria

2 Thermodynamic and thermo-economic evaluation criteria

2.1 Introduction

In this chapter, the performance evaluation criteria concerning thermodynamic heat to power cycles are introduced. First, the performance evaluation criteria from the ﬁrst and second law of thermodynamics are explained. Next, the ﬁnan- cial criteria used in thermo-economic evaluation of waste heat recovery ORCs are explained.

2.2 Thermodynamic performance evaluation

2.2.1 First law, energy balance criteria

First law performance criteria are derived from the first law of thermodynamics. The first law of thermodynamics expresses the notion of conservation of energy. First law performance criteria [1, 2] are the net power output W˙ net, see Eq. 2.1 and the thermal efficiency ηth, see Eq. 2.2. In these equations, W˙ exp is the output power at the expander shaft, W˙ pump is the pumping power and Q˙ in is the heat flow from the heat carrier (e.g. waste heat stream) to the ORC. Important to note is that maximum net power output and maximum thermal efficiency are not necessarily reached by the same design. The effect of the denominator Q˙ in in the definition of 18 CHAPTER 2 the thermal efficiency leads the optimization to a different design. A comprehensive discussion on this topic can be found in Section 3.2.1. The net power output, as given in Eq. 2.1, only considers the thermodynamic cycle. When the full system is analysed, also auxiliary pumping or fan power can be subtracted from the expander output power.

W˙ net = W˙ exp − W˙ pump (2.1)

W˙ net ηth = (2.2) Q˙ in

2.2.2 Second law, exergy balance criteria According to DiPippo [3], exergy efficiency is the most appropriate indicator to compare thermodynamic performance. This criterion defines how well the incom- ing heat is converted into power and takes into account the characteristics of the heat source and the environment. The exergy flow rate, or potential work, at a state point i and a mass flow rate m˙ is given as:

E˙ i =m ˙ iei (2.3) with ei the speciﬁc exergy, disregarding the kinetic and potential energy changes:

ei = hi − h0 − T0(si − s0) (2.4)

The subscript 0 refers to the dead state, which can be reached spontaneously without any work input. In this work, the dead state is taken equal to the inlet condition of the condenser cooling medium. The exergy ﬂow rate expresses the maximum useful work possible when bringing the corresponding state in equilib- rium with the dead state. A detailed discussion about the fundamental principles of exergy can be found in the work of Kotas [4] and DiPippo [3]. The irreversibility rates I˙ of the components for a steady state ﬂow are evaluated using the exergy balance equation:

X T0 X X 0 = (1 − )Q˙ − W˙ + m˙ e − m˙ e − I˙ (2.5) T j in in out out component j j in out with the index j referring to an equal temperature section of the system boundary. This gives for the components under adiabatic conditions:

• Evaporator

I˙evap = (m ˙ hf ehf,in +m ˙ wf eevap,wf,in)−(m ˙ hf ehf,out +m ˙ wf eevap,wf,out) (2.6) THERMODYNAMICANDTHERMO-ECONOMIC EVALUATION CRITERIA 19

• Condenser

I˙cond = (m ˙ cf ecf,in +m ˙ wf econd,wf,in)−(m ˙ cf econd,cf +m ˙ wf econd,wf,out) (2.7)

• Recuperator

I˙rec =m ˙ wf [(epump,wf,out + eexp,wf,out) − (econd,wf,in + eevap,wf,in)] (2.8)

• Pump

I˙pump = W˙ pump − m˙ wf (epump,wf,out − epump,wf,in) (2.9)

• Expander

I˙exp =m ˙ wf (eexp,wf,in − eexp,wf,out) − W˙ exp (2.10)

Ė İ

Ẇ

Ė Ė

İ Ė Ẇ Ė İ

Figure 2.1: Exergy ﬂow diagram of the basic ORC with recuperator. 20 CHAPTER 2

The overall exergy balance for the system can also be written as follows, with E˙ hf,in the exergy ﬂow into the system:

E˙ hf,in = E˙ hf,out + E˙ cf,out − E˙ cf,in + I˙pump − W˙ pump

+ I˙exp + I˙cond + I˙evap + I˙rec + W˙ exp (2.11)

A qualitative exergy flow diagram of an ORC with recuperator is given in Fig- ure 2.1. The irreversibilities in the heat exchangers related to finite temperature heat transfer and pressure drops are given as I˙evap, I˙cond and I˙rec. The exergy flow E˙ evap,wf,out enters the turbine, work W˙ exp is generated and an exergy flow E˙ exp,out leaves. Part of this exergy goes to the recuperator, while the remaining part E˙ cond,wf,in goes to the condenser. The cooling water that enters the condenser has an exergy flow E˙ cf,in and an exergy flow E˙ cf,out is rejected to the ambient. Irreversibilities in the pump and turbine are indicated as I˙pump and I˙exp. Finally there is an internal exergy flow E˙ evap,wf,in to the evaporator. With a proper selection of the dead state, the output exergy of the hot fluid E˙ hf,out is always positive. Since irreversibilities are always positive, the attainable power production is then equal to the external exergy flow E˙ hf,in. The exergy efficiency is determined by the boundary region of the system. Therefore different forms of exergy efficiency are used in literature. If the waste heat after cooling in the evaporator is unused and only the power at the expander shaft is taken as utilisable output, the exergy efficiency is given as:

W˙ net ηII = (2.12) E˙ hf,in

In this equation, E˙ hf,in is the exergy of the waste heat source at the inlet of the evaporator:

E˙ hf,in =m ˙ wf [hhf,in − h0 − T0(shf,in − s0)] (2.13)

In some works ηII is called the utilisation exergy efficiency [3, 5, 6]. Quoilin et al. [7] defined the overall energy conversion efficiency as:

W˙ net ηoverall = (2.14) m˙ hf cp,hf (Thf,in − T0) which closely relates to the exergy efficiency ηII . The internal exergy efficiency [8] expresses what part of the exergy from the hot fluid is converted into work:

W˙ net ηII,int = (2.15) E˙ hf,in − E˙ hf,out THERMODYNAMICANDTHERMO-ECONOMIC EVALUATION CRITERIA 21

This parameter does not reflect how effective the cycle is in capturing the exergy flow from the heat source. The external exergy efficiency [8] expresses how much of the available exergy in the hot fluid is actually transferred to the ORC system. Note that the irreversibility due this exergy transfer over a finite temperature difference is considered internal.

E˙ hf,in − E˙ hf,out ηII,ext = (2.16) E˙ hf,in For some applications, such as combined heat and power (CHP), the waste heat after the ORC is reused. Minimisation of the internal irreversibilities (i.e maximisation of ηII,int) is key in optimising this type of cycle. An alternative definition is given by Ho et al. [5] and Long et al. [6] for ηII,int and ηII,ext. Here the term E˙ hf,in − E˙ hf,out is replaced with E˙ evap,wf,out − E˙ evap,wf,in. The difference is that the effect of irreversibilities due to finite temperature heat transfer can be found in ηII,ext instead of ηII,int. The second law efficiency ηII can however always be written as:

W˙ net ηII = = ηII,int.ηII,ext (2.17) E˙ hf,in Finally the exergy destruction and loss ratio are respectively given as:

I˙component yD = (2.18) Ehf,in and E˙ stream yL = (2.19) Ehf,in The exergy loss, subscript L, is defined as exergy which is unused and discarded into the atmosphere. There are two main exergy losses. The exergy loss associated to the hot stream outlet of the evaporator E˙ hf,out and the one associated to the cooling fluid outlet of the condenser E˙ cf,out. Unlike CHP applications, these streams are not used for heating purposes and thus are considered losses in this work. Exergy destruction, subscript D, is defined as exergy which is unavoidably lost in the cycle during the conversion from heat to electricity. These are the irreversibilities during finite temperature heat transfer (I˙cond, I˙evap, I˙rec) and the irreversibilities associated to the pump (I˙pump) and expander (I˙exp).

2.2.3 Performance criteria of pump and expander A thermodynamic efficiency for expanders and pumps is formed by making the comparison to an ideal process that is reversible, adiabatic and operates under 22 CHAPTER 2 steady state conditions. As such, this can be modelled as an isentropic process [1]. The corresponding efficiency is called an isentropic efficiency, the definitions for the pump and expander are respectively given in Eq. 2.20 and Eq. 2.21.

hexp,in − hexp,out exp = (2.20) hexp,in − hexp,out,isentropic

hpump,out,isentropic − hpump,in pump = (2.21) hpump,out − hpump,in In order to have an idea on the size of the expander, a set of thermodynamic criteria is introduced. These criteria are directly derived from the thermodynamic states. General design ranges can be associated to these thermodynamic criteria. They provides a rough means for pre-selection of working fluids and cycle architectures. The criteria are different for volumetric expanders (scroll, double/single screw, piston, etc.) and turbines (axial, radial, etc.). In the first type of machines, energy is exchanged directly by the changing volume of a working chamber. While for the turbine, energy is exchanged between the continuous flow of a fluid and a continuously rotating blade system. For the turbine, the parameters of importance are the size parameter (SP ) and the volume ratio (VR).

˙ 0.5 Vturbine,in SP = 0.25 (2.22) ∆hisentropic v VR = turbine,out (2.23) vturbine,in

In these definitions V˙ is the volume flow rate and v is the specific volume. The SP value directly correlates with the size of the expander and typically varies between 0.02 m and 1 m [9, 10]. For SP values between 0.2 m and 1 m the change in isentropic efficiency is small [9]. A lower SP results in higher losses associated to the relative increase in clearances and roughness. In contrast, a lower VR results in higher isentropic efficiencies. For a single stage machine, volume ratios lower than 50 are needed to get isentropic efficiencies in the range of 0.7 to 0.8 [9]. For the volumetric expander, the parameters of importance are the VR and the volume coefficient VC.

v VC = exp,out (2.24) hexp,in − hexp,out THERMODYNAMICANDTHERMO-ECONOMIC EVALUATION CRITERIA 23

The VC value directly correlates with the size of the expander. In refrigeration and heat pump applications the VC is typically between 0.25 and 0.6 m³/MJ [10]. To optimise the performance of the expander, the built-in volume ratio should match the system specific volume ratio for the ORC operating conditions. If the system specific VR is not equal to the expander built-in VR this leads to two types of possible losses: over- and under-expansion losses. In Figure 2.2 these losses are depicted in a pressure-volume diagram. For over-expansion losses, the built-in VR of the expander is higher than the system specific volume ratio. In this case, the pressure in the expansion chamber, when starting the discharge, has a higher pressure than the discharge line. For under-expansion losses, the built-in VR of the expander is lower than the system specific volume ratio. Then the pressure in the expansion chamber, when starting the discharge, is higher than in the discharge line. In this thesis, a double screw expander is used in the experimental campaign, see Appendix C. For these type of machines the maximum built-in VR is around 5. These expanders typically operate with a built-in VR lower than the system specific volume ratio. However this is not strongly impacting the performance, considering under-expansion is less detrimental than over-expansion [11]. Starting from the optimal pressure ratio of the volumetric expander, an increased outlet pressure (over-expansion) will lead to a higher decrease in expander isentropic efficiency compared to an identical decrease in outlet pressure (under-expansion) [12, 13].

(a) (b) p p

pexp,in pexp,in

pinternal pinternal

pexp,out pexp,out

vinternal vexp,out v vexp,out vinternal v

Figure 2.2: Pressure-volume diagram depicting (a) under-expansion and (b) over-expansion in the shaded region.

2.3 Thermo-economic performance evaluation

A combination of thermodynamic and ﬁnancial criteria are ultimately used as objectives in optimisation problems found in thermal energy systems. This is typically labelled as a thermo-economic study. From previous research on ORC thermo-economics follows that many different ﬁnancial criteria are used. A non- exhaustive literature overview on thermo-economic studies is provided in Section 24 CHAPTER 2

3.4. This sub-chapter details the ﬁnancial criteria employed in order to clarify their strengths and weaknesses.

2.3.1 Speciﬁc area

A SA = total (2.25) W˙ net The specific area (SA) is the most straightforward criterion to use under the assumption that the heat exchangers in the system account for the highest share in the cost. It is calculated by dividing the total heat exchange area of all heat exchangers in the system by the net power generated. In Chapter 5, it is shown that this assumption is valid, 50% of the cost is attributed to the heat exchangers for a SCORC. For a transcritical ORC (TCORC, see Chapter 3 for more information) this figure rises to 60%. Other studies confirm this and claim figures between approximately 51% and 80% [14, 15]. The highest share in heat exchanger cost is typically found when air cooled condensers are used [15]. However there are also studies which show that the expander accounts for the highest share in costs. For example, in a study by Astolfi et al. [16] a turbine has the highest cost. It is therefore arguable to say whether the expander or the heat exchangers are the most costly. However it is clear that the expander cost is not to be neglected. Furthermore it is shown that the relative share of component costs is also size dependent [17]. In addition, by using the area directly as figure of merit, the effects of economies of scale are neglected. Furthermore, the SA does not have a direct financial interpretation. It is only possible to compare different ORC systems and not to make investment decisions.

2.3.2 Speciﬁc investment cost

C SIC = inv (2.26) W˙ net The specific investment cost (SIC) is probably the single most used criterion in scientific literature. This criterion is calculated by dividing the total investment cost of the system by the net power output. Cost models are used to calculate the investment cost starting from the physical parameters of the individual components. The origins of these cost models are found in chemical engineering. The module factor approach discussed below is by far the most used. It was originally introduced by Guthrie [18, 19] and was later modified by Ulrich [20]. In this approach the costs are aggregated in several levels. On top you have the grass roots cost which includes the cost for site construction, preparation and the total module cost. The total module cost includes THERMODYNAMICANDTHERMO-ECONOMIC EVALUATION CRITERIA 25 contingency costs and fees in addition to the bare module cost. The bare module cost takes into account direct (installation of equipment, piping, instrumentation and control) and indirect costs (engineering and supervision, transportation) starting from the purchased equipment cost. The purchased equipment cost can be estimated with cost correlations for individual components. These are classified as ’preliminary’ or ’study’ estimates and gives accuracies in the range of +40% to -25% [21]. There are several recognised adaptations published based on this method. The most known ones are these of Bejan et al. [22] and of Turton et al. [21]. Both use a different set of assumptions and cost correlations. Therefore care should be taken not to mix these methods. In addition, in the definition of the SIC there is no agreement which of the aforementioned costs to use as the final investment cost. As such the results from literature cannot be easily compared or assessed. Another drawback is that the SIC as objective criterion in system optimisation does not necessarily result in the highest revenue in the long run. This is proven with a case in Chapter 5 and is further discussed below when introducing the simple payback period (PB) and the net present value (NPV ).

2.3.3 Simple payback period

C PB = inv (2.27) R The simple payback period indicates the number of years before the break even point. It is computed by dividing the investment cost Cinv by the yearly cash flow R. For a waste heat recovery ORC the yearly cash flow consists of operational expenditures (i.e maintenance and operating costs) and revenue from savings on electricity or selling of electricity. The yearly operational expenditures are typically simplified as a fixed percentage of the investment cost. The potential revenue is directly related to the net power output of the machine. Therefore usage of the SIC or PB as objective criterion results in the same optimisation results under the assumption that the operational cost is small compared to the revenues. There are some drawbacks to using the PB. The simple payback period does not take into account the time value of money. It furthermore ignores the cash flow generated after the break even point. As such, valuable long term projects can be overlooked.

2.3.4 Net present value

N X Rt NPV = (2.28) (1 + i)t t=1 26 CHAPTER 2

The net present value is considered to be the most comprehensive and complete criterion for making investment decisions [23]. It considers the time value of money, the total lifetime of the project and the cash flow. If the NP V > 0 the investment results in added value and a company should consider implementing the project. If the NP V < 0 the project results in a financial loss for the company. If however the NPV = 0 there is neither a financial loss or gain, acceptance of the project can be pursued due to other beneficial effects (environmental, social, etc.).

The way of calculating the NPV is found in Eq. 2.28. Here Rt is the net cash flow over a period t, i is the discount rate and N the number of time periods. Note that discount rate is not the same as inflation. The discount rate is taken the same as the rate of return that could be earned on the financial investment markets. Thus the project is compared to an investment on the financial market with an assumed fixed interest rate. The main drawback with the NPV is the many assumptions that are needed. These amongst others include the project lifetime and the discount rate. These are difficult to predict and are highly time and location depended. A sensitivity analysis on the results can however provide valuable insights and allows easing this weakness.

2.3.5 Levelised cost of electricity

NPV (C ,C ,C ) LCOE = t,inv t,fuel t,OM (2.29) NPV (Et,gen)

The levelised cost of electricity (LCOE) is commonly used to compare electricity generating services. The LCOE is the cost at which electricity needs to be sold to break even at the end of the project. The LCOE is calculated as the NPV of all the costs over the lifetime NPV (C) divided by the total discounted electricity output NPV (Et,gen). The costs can be fuel (Ct,fuel), operational and maintenance costs (Ct,OM ) and the initial investment cost (Ct,inv). The LCOE however cannot be used if the energy generating technology com- petes with other alternatives. For example the waste heat can also be used in a district heating network. Another possibility is that waste heat recovery is completely discarded and the investment capital goes to another project.

2.3.6 Overview of thermo-economic criteria

In Table 2.1 a summary with the strengths and weaknesses of the ﬁnancial performance evaluation criteria is compiled. From this list, the NPV can be considered the single best criterion because it gives a direct measure of the added value of a project [23]. However, several assumptions are needed in the calculation of the THERMODYNAMICANDTHERMO-ECONOMIC EVALUATION CRITERIA 27

NPV and many of these are time and location dependent. Thus, if these assumptions change, the complete design procedure needs to be repeated.

Criterion Comments Speciﬁc area (SA) Atotal ˙ Wnet • Easy to calculate • No direct ﬁnancial interpretation possible

Speciﬁc investment cost (SIC) Cinv ˙ Wnet • Easy to calculate • Frequently used • Minimum SIC does not necessarily result in highest NPV

Simple payback period (PB) Cinv R • Easy to calculate • Identical to min. SIC if the yearly cashﬂow is dominated by the electricity sold

Net present value (NPV ) Pyears t=1 Rt (1+i)t • Single best objective to make ﬁnan- cial appraisal • Many assumptions needed which are time and location depended

Levelised cost of electricity (LCOE) Pyears • Useful in comparing different en- t=1 NPV (Ct,inv ,Ct,fuel,Ct,OM ) Pyears t=1 NPV (Et,gen) ergy generating technologies • Not convenient for ﬁnancial appraisal of a single project

Table 2.1: List of objective functions used in thermo-economic optimisation. 28 CHAPTER 2

2.4 Conclusion

In this chapter, the different thermodynamic and financial criteria for evaluating organic Rankine cycles were introduced and critically discussed. Thermodynamic performance criteria based on the first and second law of thermodynamics were defined. A thermodynamic analysis based on the second law of thermodynamics is considered to be the most comprehensive as it quantifies the potential of heat to produce power. In each step, the losses (irreversibilities) can be evaluated and as such the critical points can be identified. In addition, thermodynamic criteria to assess the performance and relative size of the expander were presented. For the financial criteria, the net present value (NPV ) can be flagged as the best evaluation criterion. Compared to the specific area (SA), there is no assumption that the heat exchangers account for the largest cost. Compared to the specific investment cost (SIC) and the simple payback period (PB) it considers the profit during the full lifetime of the project. Compared to the levelised cost of electricity (LCOE) it allows comparing other alternative projects that not necessarily generate electricity. Both thermodynamic and financial criteria are used in optimisation problems. If a combination of thermodynamic and financial criteria are used as objectives or as boundary conditions, the term thermo-economic optimisation is used. The goal in a thermo-economic optimisation is to optimise the system on a component level while taking into account the financial appraisal. A further discussion on this topic, with examples from literature, is given in Section 3.4 of the next chapter. THERMODYNAMICANDTHERMO-ECONOMIC EVALUATION CRITERIA 29

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3.1 Introduction

Akin to the classic water/steam Rankine cycle, adaptations such as adding reheaters and recuperators or working in supercritical regime can improve the performance and cost-effectiveness of ORCs. This development path can also be noted in vapour compression cycles [1]. Therefore exploring cycle adaptations for ORCs is a logical next step. A brief overview of some ORC architectures can already be found in the review articles of Tchanche et al. [2] and Ziviani et al. [3]. In this chapter, the different cycle architectures are discussed, bearing in mind the performance evaluation criteria introduced in the previous chapter. First, ideal thermal cycles are introduced to indicate the optimisation potential of alternative cycle architectures compared to the subcritical ORC.

3.2 Thermodynamics of ideal cycles

In this section, three ideal thermodynamic cycles are analysed to give insight how to integrate power cycles in waste heat recovery applications. The cycles under consideration are the Carnot cycle, the externally irreversible Carnot cycle and the ideal trilateral cycle (TLC). A T-s diagram for each of the cycles is given in Figure 3.1. 32 CHAPTER 3

(a) (b) (c) 2 3

TH TH TH

2 2 3 T1 T1 T T T

TL TL TL 1 4 1 4 1 3

s s s

Figure 3.1: T-s diagram. (a) Ideal Carnot cycle, infinite capacity heat source. (b) Externally irreversible Carnot cycle, finite capacity heat source. (c) Ideal triangular cycle, finite capacity heat source.

The Carnot cycle (Figure 3.1a) is an idealisation of the Rankine cycle. The cycle receives and rejects heat reversibly respectively at TH and TL from an infinite thermal reservoir. Furthermore, the cycle includes compression and expansion processes that are isentropic. For the externally irreversible Carnot cycle (Figure 3.1b) a finite capacity heat source (with constant cp) is coupled to an ideal Carnot cycle. This finite capacity heat source therefore shows a temperature decrease from TH to T1 when heat is extracted. For the last thermodynamic cycle, a finite capacity heat source is coupled to the ideal trilateral cycle (Figure 3.1c). In contrast to the previous cycles, heat transfer to the TLC is not isothermal. An extension of the TLC is the Lorentz cycle [4]. In this cycle both the heat rejection and addition are non-isothermal. A Lorentz cycle can be approximated with the help of zeotropic mixtures or by using multiple evaporation and condensation pressures. A discussion and analysis on zeotropic mixtures in ORCs can be found in Appendix E. ∂Q From the thermodynamic relation dS = T , the thermal efficiency of the ideal Carnot cycle can be analytically derived as:

Wnet ηth,cn = (3.1) Qin Q − Q = in out (3.2) Qin (T − T )(S − S ) = H L 3 2 (3.3) TH (S3 − S2) T = 1 − L (3.4) TH

However, waste heat sources typically have a ﬁnite heat capacity. Therefore the situation in Figure 3.1b is analysed; a ﬁnite heat capacity source is introduced coupled to a reversible Carnot engine [5]. The fraction of heat recovered from this stream, ηfrac,cn, is given as: ORGANIC RANKINECYCLEARCHITECTURES 33

Qmax = cp(TH − TL) (3.5)

Qfrac = cp(TH − T1) (3.6)

Qfrac ηfrac,cn = (3.7) Qmax T − T = H 1 (3.8) TH − TL The net power output of this externally irreversible Carnot cycle is given by Eq. 3.9. A cycle efﬁciency ηcycle,extirr is introduced which relates the net power output to the maximum achievable heat input from the ﬁnite capacity heat stream, see also Eq. 3.5 and Eq. 3.7.

Wnet = ηcycle,extirrQmax (3.9)

= ηth,cnηfrac,cnQmax (3.10)

TL TH − T1 = (1 − ) cp(TH − TL) (3.11) T1 TH − TL The maximum power output is found by: ∂W net = 0 (3.12) ∂T1 ∗ p =⇒ T1 = Tcycle,extirr = TL.TH (3.13) This corresponds to a thermal efﬁciency:

∗ p ηth,cn = 1 − TL/TH (3.14) The thermal efficiency at maximum power output is also called the Curzon- Ahlborn efficiency [6]. For a finite capacity heat source, the best thermal match is made with an ideal triangular cycle as shown in Figure 3.1.c. The trilateral cycle is further discussed in section 3.3.4. The cycle efficiency for the ideal trilateral cycle [7] is given by:

Wnet ηcycle,T LC = (3.15) Qmax 0.5((T − T ).(S − S ) = 1 L 3 1 (3.16) 0.5((T1 − TL + 2TL)(S3 − S1) T − T = 1 L (3.17) T1 + TL

Because the heat source is always cooled to the lowest temperature TL, the fraction of heat recovered is equal to one and ηcycle,T LC = ηth,T LC . The maximum power output is found for:

∗ T1 = TT LC = TH (3.18) 34 CHAPTER 3

3.2.1 Comparison of the ideal cycles

In Figure 3.2 the above equations are plotted for TL = 25 °C and TH = 200 °C while T1 varies between 25 °C and 200 °C. It is clear that the thermal efficiency of the TLC is always lower than that of the Carnot cycle. It is however a different situation for the cycle efficiencies ηcycle that were introduced for finite capacity heat streams. For the externally irreversible Carnot cycle, the thermal efficiency increases for higher T1 but the fraction of heat recovered decreases. This results in ∗ a single maximum value for ηcycle,extirr with a temperature equal to Tcycle,extirr. Thus maximisation of the thermal efficiency will not necessarily correspond with maximisation of the cycle efficiency, or equivalently, the maximisation of the net power output from a given finite capacity heat stream [8, 9]. This in contrast to the TLC, here the thermal efficiency keeps increasing for higher T1 and the fraction of heat recovered is constant to one. This ultimately leads to higher cycle efficiencies, as seen in Figure 3.2. The temperature T1 where ηcycle,T LC is equal ∗ to the maximum ηcycle,extirr is designated Ttransition.

0.8

η ]

- th,cn 0.6 η frac,cn η cycle,extirr T* 0.4 TLC η frac,TLC * Efficiency [ Efficiency T cycle,extirr η cycle,TLC

0.2 Ttransition

0 25 50 75 100 125 150 175 200

T1 [°C]

Figure 3.2: Thermal efﬁciency, fraction of heat recovered and cycle efﬁciency of the Carnot cycle, externally irreversible Carnot cycle and TLC as a function of the temperature T1 for TL = 25 °C and TH = 200 °C.

∗ ∗ The difference Tdiff = Ttransition − Tcycle,extirr indicates how much higher the working fluid needs to be heated so that the TLC has higher cycle efficiency ∗ than the externally irreversible Carnot cycle. Tdiff increases from 0.7 °C for TH = 100 °C to 3.3 °C for TH = 200 °C and has an almost quadratic behaviour. The working fluids in an ideal TLC should therefore not be heated much higher than for a Carnot cycle to see an improvement in cycle efficiency. The benefit of alternative architectures, considering a more realistic heat recovery process, is further detailed in section 3.2.2. ORGANIC RANKINECYCLEARCHITECTURES 35

3.2.2 Heat recovery from industrial excess heat

Typical for industrial excess heat are the low temperatures (<350°C) and the low heat content. The heat carrier can be a fluid, steam or flue gasses. In contrast to solar or geothermal applications, the heat carrier often forms an open loop. As such the heat carrier is not recirculated but is exhausted into the atmosphere. There- fore, the main operational goal is maximisation of the net power output instead of maximisation of the thermal efficiency. In section 3.2, an infinite heat exchange area was assumed. For real systems however, the heat exchangers are not infinitely large. This results in a minimum temperature difference between the thermal streams. Secondly, with real working fluids, the slopes and shape of the saturation curve primarily influences the heat recovery process. The system can thus be optimised by selecting a proper working fluid and architecture, which operates at suitable working conditions [10].

Heat carrier

Irreversibility

ΔTPP Temperature [°C] Working fluid Heat loss

Ambient temperature 0% Heat transferred [%] 100%

Figure 3.3: Temperature-heat ﬂow diagram at the evaporator of a subcritical ORC without superheating.

By taking these considerations into account, the fundamentals of ORC waste heat recovery can be further explained with the help of Figure 3.3. The heat transfer rate as a function of temperature is given for an evaporator of a subcritical ORC. The heat transfer rate is expressed in percentage of total heat recovered; with as reference state the ambient. The pinch point (PP ), is the location of the minimum temperature difference (∆TPP ) between two streams. The pinch point location, the pinch point temperature difference and the working ﬂuid inlet temperature ﬁx the outlet temperature of the heat carrier and therefore the heat input Q˙ in:

Q˙ in =m ˙ hf .cp,hf .(Thf,in − Thf,out) (3.19) 36 CHAPTER 3

Two main losses are observed. Firstly, the heat that is still available at the exit of the ORC is usually lost to the environment. This loss is quantiﬁed in eq. 3.20. The ambient temperature is taken as reference for the lower cooling limit. The maximum theoretical work that can be provided with this heat is given by E˙ hf,out.

Q˙ loss =m ˙ hf .cp,hf .(Thf,out − Thf,ambient) (3.20)

Secondly, there are the irreversibilities (I˙evap) due to the finite temperature heat transfer. The larger these irreversibilities are, the less potential there is to provide work. Especially for low waste heat temperatures, these have a significant impact on the subcritical heat exchange process [11, 12]. Decreasing the exit losses, see Eq. 3.20, to the cycle is done by further cooling down the heat carrier. This can be done by adapting the location of the pinch point and by decreasing the working fluid inlet temperature of the evaporator. De- creasing the irreversibilities due to finite temperature heat transfer, is accomplished by minimising the average temperature difference during heat transfers. Thus, the temperature profiles of the waste heat carrier and the working fluid should be matched. The principles given above can be exploited to further increase the performance of ORCs. In this regard, the operating conditions and topology of the basic subcritical ORC can be extended to novel and more advanced cycle architectures. An example was already given with the comparison of the ideal TLC to the externally irreversible Carnot cycle in Section 3.2.1. In the next section a critical discussion on advanced ORC architectures is presented based on the current state of the art found in the scientific literature.

3.3 Overview of ORC architectures

An overview of all the ORC architectures introduced in this section is provided in Table 3.1.

Acronym Description Section SCORC Basic subcritical ORC 1.2 RC ORC with recuperator 3.3.1 RG ORC with regenerative feed heating 3.3.2 OFC Organic ﬂash cycle 3.3.3 TLC Triangular cycle 3.3.4 ZM ORC with zeotropic mixtures as working ﬂuids 3.3.5 TCORC Transcritical ORC 3.3.6 MP ORC with multiple pressure levels 3.3.7

Table 3.1: List ORC architectures discussed in this chapter. ORGANIC RANKINECYCLEARCHITECTURES 37

A summary of the papers discussed in this section is provided in Table 3.2. Besides waste heat recovery (WHR) also papers with as topic geothermal (GEO), combined heat and power (CHP) or solar (SOL) are included. Note that it is possible that cycle modifications are combined. The corresponding Table 3.3 lists the boundary conditions used in the modelling of the cycles. From this table it is directly clear that various boundary conditions are taken for isentropic efficiencies and pinch point temperature differences. Also the heat source inlet temperatures vary widely between 20 °C and 450 °C. This makes a direct and fair comparison difficult. Therefore, the performance evaluation criteria and boundary conditions are always clearly stated in this work.

Ref. Cycle Application Power scale [13] SCORC WHR n/a [13] SCORC WHR n/a [14] SCORC GEO 1 MW [15] SCORC WHR 7 MWe [16] SCORC+RC n/a 100 kWe [17] SCORC+RC WHR 140 kWe [11] SCORC+RC WHR 100 kWe [18] SCORC+RG WHR n/a [19] SCORC+RC & SCORC+RG WHR n/a [20] SCORC+RC & SCORC+RG WHR 50 MWe [21] SCORC+RC+RG SOL n/a [22] SCORC+RC+RG WHR 50-3300 kWe [23] SCORC & OFC & TCORC & ZM n/a n/a [24] OFC modiﬁcations n/a n/a [25] SCORC & OFC GEO n/a [25] SCORC & OFC GEO n/a [26] SCORC & TLC & TCORC n/a n/a [27] SCORC+RC & TCORC+RC & TLC+RC n/a n/a [28] SCORC & TLC & TCORC n/a n/a [29] SCORC & TLC+ZM n/a n/a [30] SCORC+RC & ZM+RC GEO n/a [31] SCORC+RC & ZM+RC SOL n/a [32] SCORC+RC & ZM+RC GEO n/a [33] SCORC+RC & ZM+RC WHR 200-300 kWe [33] SCORC+RC & ZM+RC WHR 200-300 kWe [34] SCORC+RC & ZM+RC WHR 50 kWe [35] SCORC+RC & ZM+RC WHR n/a [36] SCORC & MP & TCORC & ZM n/a n/a [36] SCORC & MP & TCORC & ZM n/a n/a [32] SCORC+RC & ZM & TCORC+ZM+RC WHR n/a [37] TCORC n/a 300 We [38] TCORC n/a n/a 38 CHAPTER 3

Ref. Cycle Application Power scale [39] SCORC+RC & TCORC+RC GEO n/a [40] SCORC+RC & TCORC+RC CHP 1 MWe [40] SCORC+RC & TCORC+RC WHR 1 MWe [40] SCORC+RC & TCORC+RC CHP 1 MWe [40] SCORC+RC & TCORC+RC CHP 1 MWe [40] SCORC+RC & TCORC+RC CHP 1 MWe [41] SCORC+RC & TCORC+RC WHR n/a [41] SCORC+RC & TCORC+RC CHP n/a [41] SCORC+RC & TCORC+RC GEO n/a [41] SCORC+RC & TCORC+RC GEO n/a [42] SCORC & TCORC n/a n/a [12] SCORC & TCORC GEO 5-10 kWe [43] SCORC & TCORC GEO n/a [44] MP n/a n/a [45] MP GEO 1.219 MWe [45] MP GEO 0.940 MWe [46] SCORC & MP & TCORC GEO 1 MWe [19] SCORC & TCORC & MP WHR n/a [47] SCORC+injector n/a n/a [48] SCORC+RC+reheater SOL 1 MWe [49] SCORC+cascade SOL n/a Table 3.2: Overview of papers about advanced ORC architectures showing power scale and application. ORGANIC RANKINECYCLEARCHITECTURES 39

Ref. Thf,in Tcf,in pump exp ∆TP P,evap ∆TP P,cond (°C) (°C) (-) (-) (°C) (°C) [13] 300 2 30 1 1 20 n/a [13] 200 2 30 1 1 20 n/a [14] 100-30 30 0.65 0.85 n/a n/a [15] 100 15 3 0.80 0.80 4 4 [16] 57-240 30 3 0.95 0.85 5 n/a [17] 145 253 0.60 0.85 8 n/a [11] 375-450 30 3 0.80 0.85 n/a n/a [18] 177 25 0.80 0.85 n/a n/a [19] 490 15 0.90 0.80 10 10 [20] 80-160 1 10-30 0.85 0.80 2-10 5 [21] 120 20 0.75 0.85 4 4 [22] 80-213 2 40-50 3 0.65 0.80 10 10 [23] 300 30 0.85 0.85 10 10 [24] 300 30 0.85 0.85 10 10 [25] 90-140 40 n/a n/a 10 10 [25] 90-140 40 n/a n/a 5 5 [26] 30-200 1 30 3 0.6 0.75 n/a n/a [27] 63-350 15-150 0.65 0.85 10 10 [28] 150-350 15-62 0.65 0.85 10 10 [29] 150 25 1.00 0.70 n/a n/a [30] 120 15 0.75 0.80 5 5 [31] 85 1 25 3 1.00 0.80 n/a n/a [32] 140 12 0.50 0.75 10 n/a [33] 150 25 0.80 0.65 20 10 [33] 250 35 0.80 0.65 30 20 [34] 177 42 3 1.00 0.85 4 n/a [35] 150 20 0.60 0.75 10 10 [36] 80-200 15 n/a n/a 10 10 [36] 80-200 15 n/a n/a 2.8 2.8 [32] 350 50 0.50 0.75 10 n/a [37] 100 20 0.80 0.80 4 4 [38] 220 n/a n/a n/a 10 n/a [39] 120-180 15 0.70 0.85 4 4 [40] 250 1 85 3 0.65 0.85 n/a n/a [40] 250 1 38 3 0.65 0.85 n/a n/a [40] 300 1 85 3 0.65 0.85 n/a n/a [40] 280 85 3 0.65 0.85 10 n/a [40] 350 85 3 0.65 0.85 10 n/a [41] 300 10 0.75 0.75 10 10 [41] 300 70 0.75 0.75 10 10 [41] 170 10 0.75 0.75 10 10 [41] 100 10 0.75 0.75 10 10 40 CHAPTER 3

Ref. Thf,in Tcf,in pump exp ∆TP P,evap ∆TP P,cond (°C) (°C) (-) (-) (°C) (°C) [42] 210 20 3 0.85 0.8 10 10 [12] 90 20 0.75 0.8 5 5 [43] 130-170 20-35 3 0.8 0.8 20 20 [44] 120 20 1 1 n/a n/a [45] 163 13 0.8 0.666 7.9 n/a [45] 163 13 0.8 0.708 2.9 n/a [46] 110-160 30-40 3 0.85 0.85 42284 42284 [19] 490 15 0.9 0.80 10 10 [47] 147 35 3 1 1 n/a n/a [48] 304 26.7 0.67 0.75 9.4 7.2 [49] 130-140 2 35 n/a n/a n/a n/a 1 Expander inlet temperature Texp,in is given instead of Thf,in. 2 Saturation evaporation temperature Tevap is given instead of Thf,in. 3 Saturation condensation temperature Tcond is given instead of Tcf,in. 4 Detailed heat transfer model. Table 3.3: Overview of papers on advanced ORC architectures showing the different boundary conditions.

3.3.1 ORC with recuperator (RC)

(a) (b) 7 2 Evaporator ṁwf Expander 2 ṁhf 7 8 9 8 3 3 Generator T Recuperator 9 4 4 6 ṁcf 6 5 1 5 1 Condenser 5 pump 5 S

Figure 3.4: (a) ORC with recuperator cycle layout. (b) ORC with recuperator T-s diagram.

Several authors [14, 50] suggest a recuperator (RC) to reuse the heat after the expander to preheat the working fluid. The cycle layout and T-s diagram are given in Figure 3.4. A recuperator essentially increases the thermal efficiency [14]. Thus a high power output can be maintained for a decreased heat input to the ORC. In order to implement a recuperator, a superheated state is necessary after the ORGANIC RANKINECYCLEARCHITECTURES 41 expander. In the case of dry fluids [10, 13, 16] a strongly superheated vapour exits the expander. This increases the load on the condenser. However, if there is no limitation on the temperature to which the flue gasses can be cooled, the net power output will not increase by adding a recuperator [17, 41]. The net work output will approximately be the same. Furthermore, in the cited studies the increased pressure drop and the extra cost of the recuperator are neglected. A recuperator can be beneficial [17, 34, 40] for waste heat recovery applications, if there is a higher cooling limit of the heat carrier. When flue gasses, con- taining water and sulphur trioxide, are cooled below the acid dew point, sulphuric acid vapour condenses. These acids potentially lead to corrosion and damage of the heat exchanger and should be avoided. The temperature of the acid dew point varies with the composition of the flue gas. Typical values range from around 100 °C to 130 °C [19, 51].

3.3.2 Regenerative feed heating ORC (RG)

(a) (b)

Evaporator ṁwf 2 8 Expander 7 ṁ hf 2 7 Direct contact heat exchanger Generator 8 10 T 1 10 3 3 1 11 9 cf 6 9 4 6 11 4 5 Condenser Pump II 5 Pump I S

Figure 3.5: (a) ORC with regenerative feed heating cycle layout. (b) ORC with regenerative feed heating T-s diagram.

ORCs with turbine bleeding, coupled to a direct contact heat exchanger, are typically designated as ORCs with regenerative feed heating. These cycles closely resemble the ORC with recuperator, as both pre-heat the working fluid before entering the evaporator. The schematic of the cycle and T-s diagram are shown respectively in Figure 3.5a and Figure 3.5b. Mago et al. [11] present an analysis of an ORC with regenerative feed heating and compared this with the basic ORC. Their results show that ORCs with regenerative feed heating have a higher thermal efficiency and lower irreversibilities. Furthermore, the authors note that the increase in thermal efficiency between cycle types depends strongly on the working fluid used. For some fluids, such as R245ca, the difference between the two cycle configurations is negligible. A cycle with both turbine bleeding and recuperator was analysed by Desai 42 CHAPTER 3 et al [22]. On average, a relative improvement of 16.5% in thermal efficiency is obtained when compared to the basic ORC cycle. Combining both modifications always gives a better thermal efficiency than the stand alone implementation of turbine bleeding or recuperation. Gang et al. [21] analysed an ORC with regenerative feed heating for use in conjunction with low temperature solar heat. There is an optimal regenerative temperature at which the ORC reaches maximum thermal efficiency. The maximum thermal efficiency is 9.2% higher than the thermal efficiency of the ORC without modifications. Meinel et al. [19] compared the basic ORC, the ORC with RC and the ORC with turbine bleeding. They too affirm the thermal efficiency gain compared to the basic ORC. Furthermore, for isentropic fluids the ORC with RG has a higher efficiency than that of the basic ORC and the ORC with RC. While for dry fluids the ORC with RC has a higher thermal efficiency than both the basic ORC and ORC with RG. Also Yari and Mahmoudi [20] compared the performance of the basic ORC, the ORC with RC and an ORC with RG. The application was waste heat recovery, with no constraint on the possible condensation of flue gasses. There- fore maximisation of the output power is crucial, not maximisation of the thermal efficiency. By using a recuperator or turbine bleeding less heat can be transferred to the cycle. As a result, the basic ORC was indicated as the best cycle design in both economic and thermodynamic perspective. The cycle with regenerative feed heating was found to have potential for cogeneration purposes.

3.3.3 Organic ﬂash cycle (OFC)

The organic ﬂash cycle (OFC) has its origin in geothermal energy generation [7]. There, liquid brine from a geothermal well is throttled down to a lower pressure in a ﬂash tank. The vapour fraction is fed to the turbine, the liquid phase is directly

(a) (b) 2 7 Flash tank Expander 9 ṁ Evaporator wf 9 10 2 ṁ 3 Generator hf 10 T 7 8 Mixer 8 3 Throttling 11 11 valve 1 ṁcf 6 6 1 4 4 5 Condenser 5 s Pump

Figure 3.6: (a) OFC cycle layout. (b) OFC T-s diagram. ORGANIC RANKINECYCLEARCHITECTURES 43 returned to the condenser. In order to increase the mass flow rate of vapour, several flash tanks can be connected in series. The liquid brine is mostly composed of water. However, the disadvantage of using the wet steam directly, is the significant amount of moisture that exits the expander [23]. An isentropic expansion of a wet fluid from the saturated vapour state inevitable ends in the two-phase state. Therefore special wet steam turbines are necessary with reinforced material to protect the turbine blades from erosion [7]. This in turn results in an increased production cost. Furthermore, it is known that the turbine isentropic efficiency reduces [52] with the moisture content. In the OFC, Figure 3.6, the liquid brine is not directly flashed, but is fed to a heat exchanger to heat an organic working fluid. In the heat exchanger, boiling of the working fluid is avoided, resulting in a better match between the temperature profiles of the heat carrier and the working fluid. This type of cycle is extensively discussed by Ho et al. [23, 24]. In a first paper by Ho et al. [23], the performance of the basic OFC is analysed and compared to the results of the transcritical cycle, and a cycle with zeotropic mixture as working fluid. The waste heat has a temperature of 300 °C. The results of this study indicate that the total output power for the OFC is slightly lower in comparison to an optimised ORC for the same conditions of the heat carrier. Still, the OFC captures more heat from the heat carrier compared to other investigated cycles. Because of the low thermal efficiency, this increased heat input does not lead to a higher mechanical power, but instead to a higher heat transfer to the cold fluid. The thermal efficiency is low as a result of the irreversibility introduced by the throttling valve. The optimised ORC has the highest power output, followed by the OFC, the transcritical CO2 cycle and the ORC with zeotropic mixtures. It should be stressed however, that only an ammonia/water mixture was included in the study. In a second study [24] about the OFC, the authors proposed and analysed enhancements to the OFC to increase power production. These modifications were: double flash OFC, two-phase OFC, modified OFC, two-phase OFC combined with a modified OFC. In the two-phase OFC the throttling valve is replaced by a two- phase expander. In this way the irreversibilities associated with the throttling valve are eliminated. In the double flash system, the working fluid is flashed in two stages and fed respectively to a high and low pressure expander. Because the working fluid is expanded at different pressure levels more vapour is available to produce work. The modified OFC also introduces a high and low pressure expander. Instead of flashing the working fluid at two different pressure levels, the superheated vapour after the high pressure expander is combined with the liquid coming from the flash tank. The resulting saturated vapour at intermediate pressure is then fed to a low pressure expander. There is 5% to 20% more power output when using the proposed enhancements in comparison to the optimised ORC with 44 CHAPTER 3

(a) (b) Flash tank 7 2 11 9 2 Separator 12 Expander 8 ṁ wf 12 Evaporator 9 10 Generator T ṁhf 3 8 11 10 3 7 8 1 4 6 ṁcf 6 Pump 2 5 5 4 1 Condenser s

Pump 1

Figure 3.7: (a) Alternative OFC system. (b) Alternative OFC system T-s diagram. hydrocarbons as working fluid. When using siloxanes, there is only a 2% to 4% increase. This is explained by the authors as caused by the smaller difference in specific entropy between saturated liquid and saturated vapour for siloxanes. This reduces the exergy destruction during isenthalpic throttling. Therefore, the overall effect of modifications to reduce exergy losses is small for siloxanes. Furthermore siloxanes are very dry fluids; hence the majority of exergy destruction is located in the condenser. A different type of OFC was investigated by Edrisi and Michaelides [25] and is shown in Figure 3.7. The working fluid in the investigated cycle evaporates to a certain dryness factor. After partial evaporation the vapour part is separated from the liquid and fed to the expander. The liquid part is flashed and the additionally produced vapour is again fed to an expander. The liquid after flashing goes directly to the heat exchanger for partial evaporation. The authors note that practical implementations of this cycle may require an extra expander and heat exchanger. The performance of the cycle is investigated for a heat carrier inlet temperature between 90 °C and 160 °C. The vapour quality and the evaporation temperature are optimised in order to maximise the power output. For the basic ORC, with saturated vapour at the inlet of the expander, only the evaporation temperature is optimised. The results indicate that the outlet temperatures of the heat carrier are significantly lower for the OFC than for the basic ORC. Therefore more heat is absorbed in the OFC to produce work. The optimum dryness factor increases with temperature but is significantly lower than one. The output power for this type of OFC can be up to 25% higher compared to the basic ORC.

3.3.4 Trilateral (triangular) cycle (TLC) The T-s-diagram of the trilateral cycle (TLC), Figure 3.8, closely resembles that of the OFC. Instead of ﬂashing the working ﬂuid to produce saturated vapour and ORGANIC RANKINECYCLEARCHITECTURES 45

(a) (b) 7 Evaporator ṁ wf Two-phase expander 2 ṁhf 2 7 8

3 Generator T 8 ṁ 6 1 cf 3 5 1 Condenser 4 4 6 5 pump s

Figure 3.8: (a) TLC cycle layout. (b) TLC T-s diagram. saturated liquid, the working fluid is directly fed to the expander. Boiling of the working fluid is avoided in order to shift the pinch point. Intrinsically the TLC has a lower thermal efficiency than the basic ORC [26]. Nevertheless, there is a higher potential to recover heat because of the better match between the temperature profiles of the heat carrier and the working fluid. The combined effect results in a better cycle efficiency. This was discussed in Section 3.2.2 and illustrated in Fig- ure 3.2. According to Schuster et al. [42], this match could best be realised with a transcritical cycle instead of a TLC. The results from the work of Fischer et al. [28] however showed that a TLC always has a better performance than the transcritical cycle. Yet, the challenge of triangular cycles is the availability of two-phase expander technology with high isentropic efficiency. According to DiPippo [53] isentropic efficiencies of at least 75% are necessary before adoption in geothermal plants is feasible. Fischer et al. [28] compared the performance of the TLC to sub- and transcritical ORCs. The working fluid for the TLC is water. For the sub- and transcritical ORCs the working fluid was cyclopentane (Thf,in = 250-350 °C), n-butane (Thf,in = 220 °C) or propane (Thf,in = 150 °C). The cycles are optimised for maximum power output. The exergy efficiency of the TLC is always higher than that of the sub- and transcritical ORC. For Thf,in = 350 °C to 220 °C the exergy efficiency is by 14% to 20% higher, while for Thf,in = 150 °C it is even 29% higher. Further- more the impact of the volume flow rate is discussed by the authors. The outgoing volume flows from the expander are a factor 2.8 higher for a TLC than for the ORC (Thf,in = 280 °C, Tcf,in = 85 °C). If Thf,in and Tcf,in are lowered to 150 °C and 38 °C respectively, this becomes a factor 70. The ratio of inlet to outlet volume flow rate over the expander is 100 to 1000 times larger than for the ORC depending on the temperature Tcf,in. The large volume flows are accounted to the low vapour pressure of water at ambient temperatures. Therefore the authors suggest using other working fluids than water for the TLC. In a subsequent study, Lai 46 CHAPTER 3 and Fischer [27] investigate Power Flash Cycles (PFC) with aromates, siloxanes, and alkanes as working fluids. The PFC is considered a generalisation of the TLC, also expansion into the superheated region is allowed. According to the authors, cyclopentane is to be preferred in a PFC because of the significantly smaller outlet volume flows than water while achieving a comparable high power production. The TLC and OFC are developed to improve heat transfer from the waste heat carrier. A next step can be the improvement of heat rejection at the condenser side. By incorporating a zeotropic mixture in the cycle a better match between working fluid and heat sink is possible. Zamfirescu and Dincer [29] analysed this idea for an ammonia-water trilateral cycle. However, Fischer et al. [28] noted that the advantage of a better temperature glide is small compared to the disadvantage of the corrosive behaviour of ammonia. A possible generalisation of the TLC, is a cycle which allows partial evaporation of the working fluid instead of just heating the working fluid to saturated liquid. In this work, such a cycle is named a partial evaporating ORC (PEORC). Research on these type of cycles has not been found in open scientific research.

3.3.5 Zeotropic mixtures as ORC working ﬂuids (ZM)

(a) (b) 7 2 Evaporator ṁwf Expander ṁhf 2 7 8 8 3 Generator T 3 6 1 ṁcf 5 6 4 1 Condenser 4 5 pump s

Figure 3.9: (a) ORC with zeotropic mixtures cycle layout. (b) ORC with zeotropic mixtures T-s diagram.

A different way of reducing irreversibilities associated to non-isothermal heat addition is the use of zeotropic mixtures. The general plant layout stays the same and is shown in Figure 3.9a. The non-isothermal phase change of these mixtures, shown in the T-s diagram of Figure 3.9b, permits a good match of the temperature profiles in the condenser and evaporator. Furthermore, zeotropic mixtures are already used in cryogenic refrigeration [54]. One of the earliest power cycle designs with a zeotropic mixture was the Kalina cycle [55]. The circuit of the Kalina cycle is different from the ORCs, because the ORGANIC RANKINECYCLEARCHITECTURES 47 mixture is only present in the heat exchangers and not in the expander. There- fore a separator and absorber are included in the cycle design. The working fluid used in the Kalina cycle is NH3-water. Lu et al. [56] assessed the performance of the Kalina cycle in comparison to an optimised ORC. They concluded that for low power and medium to high temperature the gains in overall efficiency are very small and this is obtained with a complicated plant layout, high maximum pressures, large surface heat exchangers and non-corrosive materials. Nonetheless, this cycle is commercially available and patented [57]. Besides NH3-water other organic mixtures are investigated in literature. From 1990 onwards there were crucial advances in predicting mixture thermodynamic properties. One of the key developments was the design of new computational methods. Colonna [58] made a survey of available methods for the estimation of mixture thermodynamic properties. A computer calculation (Stan- Mix) based on the model by Wong and Sandler [59] was developed. This laid the base for further simulation and analysis of zeotropic mixtures in organic Rankine cycles. Furthermore Angelino et al. [32] analysed an organic Rankine cycle with a zeotropic mixture of n-butane and n-hexane (50%/50%). The results showed that in particular air cooled condensers or cogeneration benefit from matching condensation temperatures (25% less air mass flow rate is needed). Two concerns are mentioned. The first is the prevention of fluid composition shift during operation. The second is the lack of information about heat transfer coefficients when using mixtures. Heberle et al. [30] investigated the exergy efficiency for zeotropic mixtures of isobutene-isopentane and R227ea-R245fa. For temperatures below 120 °C the exergy efficiency increased relatively with 4.3%-15% compared to using pure working fluids. The optimal exergy efficiency was found for the mixture concentration that results in matching temperature glide between working fluid and cooling water. Chys et al. [33] investigated zeotropic mixtures based on hydrocarbons and siloxanes as working fluids in ORCs. An increase in thermal efficiency of 15.7% and an increase in generated electricity of 12.3% was found for a temperature source of 150 °C. When using a higher temperature source of 250 °C the values decreased to 6.0% and 5.5% respectively. The influence of a third mixture component was analysed and considered to have a marginal effect. Wang and Zhao [31] investigated mixtures composed out of R245fa-R152a. As in the work of Heberle et al. [30], the volume flow rate and inlet/outlet volume flow ratio over the expander is decreased when using mixtures. Meanwhile the thermal efficiency is reduced, this is in contrast with the general trend observed [30, 33, 35]. This is explained by the chosen boundary conditions. The lowest and highest temperature of the cycle where fixed. Therefore the ability to match the temperature profile to an external heat carrier (evaporator) or cooling 48 CHAPTER 3 loop (condenser) is lost. Lecompte et al. [35] provided an exergy analysis on ORCs with zeotropic mixtures as working fluids (R245fa-pentane, R245fa-R365mfc, isopentane-isohexane, isopentane-cyclohexane, isopentane-isohexane, isobutene-isopentane and pentane- hexane), see also Appendix E for the results. The heat carrier inlet temperature Thf,in was 150 °C. Using mixtures resulted in an improvement of the exergy efficiency between 7.1% and 14.2% compared to pure working fluids. The source of this improvement is mainly ascribed to decreased irreversibilities in the condenser. This confirms the findings of Heberle et al. [30]. Exergy losses in the condenser are reduced by matching the glide slope of the working fluid with the glide slope of the cooling fluid. Consequently, an optimal mixture concentration exists which maximises the second law efficiency. The optimal condensing glide slope is however slightly smaller than the glide slope of the cooling fluid due to the exergy losses in the pump, expander and evaporator. The difference between the various optimised ORCs with zeotropic mixtures as working fluid is less than 3 percentage points. Therefore, thermo-economic criteria should be included when ranking working fluids. There are also important challenges related to possible composition shifts during operation [60] and lack of accurate convective heat transfer and pressure drop correlations.

3.3.6 Transcritical ORC (TCORC)

7 (a) (b)

2 Evaporator ṁwf 2 Expander ṁhf 7 8 T 3 Generator 3 8 ṁ 6 1 cf 5 4 6 Condenser 1 4 pump 5 s

Figure 3.10: (a) Transcritical ORC cycle layout. (b) Transcritical ORC T-s diagram.

When looking at the history of steam/water Rankine cycles and refrigeration cycles, the logical next step is incorporating a supercritical state. Starting from the 1950s, the first attempts to develop turbine power units based on supercritical states were made. As early as 1957 the first transcritical Rankine cycle was started up in the electric power station of Philo, USA [61]. In the USA alone 159 new transcriti- ORGANIC RANKINECYCLEARCHITECTURES 49 cal power plants were started up between 1960-1990. Furthermore, from the 1990s onwards there is a revival on the study of transcritical refrigeration [62] and heat pump cycles [63]. The importance of the supercritical cycles is further reflected by the more than 1000 patents on this subject. The major difference between a subcritical and a supercritical organic Rankine cycle lies in the heating process of the working fluid. The cycle layout is identical to that of the basic cycle of Figure 3.10a, the T-s diagram is shown in Figure 3.10b. Working fluids are compressed directly to supercritical pressure and heated to the supercritical state, effectively bypassing the two-phase region. By bypassing the isothermal boiling process, the temperature-glide of the transcritical Rankine cycle provides a good thermal match between working fluid and heat source [42]. Thus heat transfer is done more effectively compared to the basic ORC [14]. In a transcritical power cycle, the liquid to vapour phase transition is performed at supercritical pressure, while condensation takes place in the usual two-phase region. In contrast, for a pure supercritical cycle both heat addition and heat rejection occur in the supercritical state. Note that the difference between supercritical and transcritical is not always used rigorously. For example, the classic transcritical water/steam power cycle is often called a supercritical Rankine cycle. The thermodynamic performance benefits of a transcritical cycle were investigated by among others Angelino and Colonna [63], Saleh et al. [14] and Schuster et al. [42]. Schuster et al. [42] state that for the transcritical cycle an improved power output of 8% is possible compared to the basic subcritical cycle. The thermal efficiency is lower than that of the basic ORC but this is more than compensated by the increased heat addition to the cycle. This is in analogous to the TLC discussed in Section 3.3.4. A high power output of the system is linked with the choice of an appropriate organic medium. One of the first working fluids used in supercritical cycles was CO2 [64–66]. Because of the low critical temperature (31 °C) a supercritical state is easily achieved. Further desirable qualities are the small environmental impact and the low cost. However, because of the high critical pressure (73.8 bar) component costs are high and safety regulations are severe. Therefore also other working fluids are considered. A comparison between a transcritical cycle with working fluid R125 and CO2 shows an increased power output of 14% for R125 [37]. Even though the carbon dioxide cycle shows better heat transfer and pressure drop characteristics, the high pumping power required to manage the large pressure degrades the cycle’s power output. For this study, the total heat transfer area was fixed. The supercritical cycle with R125 was recommended for heat sources of about 100 °C [12, 37]. Astolfi et al. [39] compared the subcritical and transcritical ORC for the exploitation of medium to low temperature geothermal sources. They state that, as a general trend, the TCORC leads to the lowest electricity cost for most of the investigated cases. This is true as long as fluids with a critical temperature slightly lower 50 CHAPTER 3 than the temperature of the geothermal source are used. Vetter et al. [43] quantify that for optimal power output the working fluid should have a critical temperature of 0.8 times the heat source temperature. Karellas et al. [38] studied the design of plate heat exchangers for transcritical ORCs based on theoretical models. A calculation and dimensioning method was proposed by discretising the heat exchanger in various segments and employing the Jackson correlation [67] to calculate the convective heat transfer coefficient in the supercritical region. Their results show that the performance of the TCORC is higher than the basic ORC without a disproportioned rise of installation costs due to larger heat exchangers. However, they conclude that a techno-economic investigation of real-scale transcritical ORCs is vital before drawing final conclusions. Still, techno-economic studies on transcritical cycles are scarce and diverse performance evaluation criteria are used. A non-exhaustive list is given in Table 3.4. In Section 3.4 thermo-economics of ORCs are discussed in detail.

Ref. Performance criteria Conclusion [39] Plant total specific cost TCORC is in comparison to the SCORC the most cost effective solution under sufficient heat carrier temperature drop [12] Levelised energy cost [$/kWh] and TCORC with R125 provides the Heat exchange area per unit power most cost effective solution in com- [m²/kWe] parison with SCORC [15] Total specific cost of equipment TCORC with R125 most cost effec- (C/kWe) tive compared to TCORC with CO2 and ethane

Table 3.4: Thermo-economic analysis of transcritical cycles in open literature.

3.3.7 ORC with multiple evaporation pressures (MP)

Another way to decrease the irreversibilities involved in heat transfer over a ﬁnite temperature difference is to split the Rankine cycle in different pressure levels [68]. When introducing a second pressure level a new pinch point is created. It is clear from Figure 3.11 that for the low pressure loop the exhaust temperature of the heat carrier is lower. Therefore more heat is transferred into the cycle. There is a good match between the high temperature side of the heat carrier and the high pressure loop. Thus a high thermal efﬁciency can be achieved. The same principle is valid for the low temperature side of the heat carrier and the low pressure loop. The irreversibilities in the evaporators for dual pressure ORCs accounts for 26% of the ORGANIC RANKINECYCLEARCHITECTURES 51

(a) (b) ṁwf Evaporator II Expander I 7 8 7 ṁhf Expander II 3 8 8 3 4 Generator 9 4 5 T Evaporator I 10 9 2 1 6 2 5 cf 10 11 6 11 s 1 Condenser Pump II Pump I

Figure 3.11: (a) Multiple evaporation pressure ORC cycle layout. (b) Multiple evaporation pressure ORC T-s diagram. total irreversibilities [45]. This is relatively low compared to the values for a basic ORC in the work of Mago et al. [18], between 40.4% and 77%, and Shengjun et al. [12], between 30% and 51%. A careful selection of the pressure levels allows for a maximum exergy transfer. Stijepovic et al. [69] propose a methodology for the design of optimum multi- pressure organic Rankine cycle processes. By increasing the number of pressure levels the cycle approaches the theoretical Lorentz cycle. Lee and Kim [4] showed that for an finite thermal reservoir the maximum work output for the Lorentz cycle is twice that of the externally irreversible Carnot cycle for a given pinch point temperature difference. However, a lower mean temperature difference between the two streams means that a larger heat transfer area is needed for a given heat transfer rate. Multi-pressure organic Rankine plants are not analysed extensively in the open literature. Gnutek and Bryszewska-Mazurek [44] proposed a multi-pressure ORC with R123 as working fluid and a multi-segment sliding-vane expansion machine. Franco and Villani [46] analyzed the basic ORC, TCORC and MP for geothermal applications. The authors concluded that there is no single optimal working fluid/cycle combination. In some cases advanced cycle designs lead to higher performance, but not always. Only 6 working fluids where investigated: R134a, R152a, isobutene, n-pentane, R410A, R407C. Becquin and Freund [36] investigated several advanced power cycles for waste heat recovery: dual-pressure, transcritical and cycles with ammonia/water mixtures. The working fluids under consideration are: R125, R134a, isobutane and R245fa. The heat source temperature ranged from 80 °C to 200 °C and the cycles are optimised to produce the maximum net power output. Especially at the lower temperatures the modified cycles proved to significantly increase output power (up 52 CHAPTER 3 to 35%). The dual-pressure cycle was the only cycle which offered an increased power output over the whole range of heat source temperatures. Especially for the supercritical cycle and the cycle with zeotropic mixtures, the working fluid should ideally be custom- tailored to the cycle design. For the dual-pressure cycle the required overall thermal conductance UA (overall heat transfer coefficient (U) multiplied by heat transfer area (A)) is marginally higher than for the basic ORC. Meanwhile the net power output at a heat source inlet temperature of 100 °C is around 25% higher. The disadvantage lies in the complex layout with dual expanders and two pumps. In general the increased power output of the modified cycles is at the expense of a more complicated design and increased heat exchanger surface area.

3.3.8 Vapour injector, reheater and cascade cycles

In the open literature some other, less investigated, architecture modifications are mentioned. These are shortly presented in this section. A cycle with a vapour injector as regenerator is proposed by Xu and He [47]. The working fluid used was R123. The cycle consists of the basic ORC components, with the addition of turbine bleeding and an injector. High pressure vapour is extracted from the turbine and directed to the injector. The organic fluid from the condenser which enters the injector is pressurised and heated. The results indicate that the regenerative ORC with injector has a higher thermal efficiency than the basic ORC if the extraction pressure is lower than 390 kPa. An ORC with reheat for solar applications was considered in the work of Price and Hassani [48]. They determined that the thermal efficiency of the cycle with reheat is only slightly higher than the case without reheat. A same conclusion was made by Mago et al. [11]. Additionally, the cost of the cycle with reheat is considered higher because of the need of a low- and high pressure expander and an extra heat exchanger. Therefore the reheat cycle is discarded as a viable alternative. Another possibility is combining ORCs in a cascade. Each ORC is a separate stage. In contrast to the basic cycle, the condenser of the upper stage acts as the evaporator of the lower stage. By optimising the working fluid of each stage, the thermal efficiency can be increased [49]. The heat input however, is determined exclusively by the upper stage.

3.3.9 Summary of ORC architectures

From the discussion in section 3.2.2 follows that the power generated from a waste heat stream can be maximised by reducing the exit losses and decreasing the irreversibilities due to finite temperature heat transfer. In view of this, a variety of ORGANIC RANKINECYCLEARCHITECTURES 53 gasses Only beneficial ifgasses lower coolingRequirement of limit multi stage of expanders Performance simple flue OFC equals basicMany ORC additional components Stability working fluids Limited knowledge about heat exchange andsure pres- drop correlations for supercritical fluids Limited knowledge about heat exchange andsure pres- drop correlations for zeotropicRisk mixtures of fluid fraction Table 3.5: Summary of ORC architectures. pump extensions are possible: two-phase expander, multiple flash tanks, multiple expanders) MP Multiple expanders, pumps and heat exchangers Many additional components needed ZM Zeotropic mixtures No practical experience TLC Need for two-phase expander High efficiency two-phase expanders OFC Added flash tank, throttling valve, mixer (other Cycle Modifications Challenges TCORC Supercritical fluids High pressures SCORC+RC Additional heat exchanger Only beneficial if lower cooling limit of flue SCORC+RG Multi-stage expander, extra heat exchanger and 54 CHAPTER 3 advanced cycle architectures are proposed like the: TCORC, TLC, ZM, MP, OFC and cascaded cycles. If the goal is to maximise the thermal efficiency, this is achieved by maximising the mean temperature difference between heat addition and heat rejection. The following cycle modifications have exactly this as main objective: RC, RG, cycles with reheaters, cycles with vapour injector. The necessary modifications and challenges associated to each advanced cycle are shortly summarised in Table 3.5. It is important to realise that all the proposed modifications have an effect on the heat recovery process and thus on both the losses I˙evap and E˙ hf,out as discussed in Section 3.2.2. This necessitates a detailed thermodynamic analysis under various boundary conditions and operational regimes. Typically, a black box cycle analysis is employed; this black-box approach is advantageous because of its calculation speed. The optimisation objective and optimisation parameters are directly derived from first and second law thermodynamics. A broad selection of working fluids [10, 13, 14, 17, 26, 51] and cycle architectures [6, 23, 27, 28, 50], can be investigated in an acceptable time-frame. A comprehensive screening approach of working fluids/architectures is presented in Chapter 4. This optimisation approach however does not consider financial constraints.

3.4 Thermo-economic studies on ORC architectures

Thermo-economic or techno-economic optimisation approaches are rather scarce in scientific literature. A non-exhaustive overview of papers published on this topic is given in Table 3.6. From this list it is immediately clear that various objective functions are used in the optimisation process. Also the optimisation method used is very different among various publications, ranging from single objective optimisation with gradient based solvers to multi-objective optimisation with genetic algorithms. Furthermore, only six works from Table 3.6 investigate alternative cycles. Most of these are on the TCORC. Cayer et al. [15] studied transcritical power cycles for low temperature heat sources with working fluids R125, CO2 and ethane. They conclude that the choice of performance indicator has a significant impact on the optimisation results. R125 has the best thermal efficiency and lowest relative cost per unit of power produced while ethane has the highest specific net power output. Astolfi et al. [39] compared the SCORC and TCORC for the exploitation of medium-low temperature geothermal sources. They state that, as a general trend, the configurations based on supercritical cycles, employing fluids with a critical temperature slightly lower than the temperature of the geothermal source, leads to the lowest electricity cost for most of the investigated cases. Also Shengjun et al. [12] compared the subcritical ORC and transcritical ORC ORGANIC RANKINECYCLEARCHITECTURES 55 for low temperature geothermal power generation. From the large selection of pure working fluids investigated, R125 in a transcritical power cycle was indicated as cost effective solution for low-temperature geothermal ORC systems. The majority of the works listed in Table 3.6 have in common that they are limited to single objective criteria. This means that the objective to minimise or maximise is a single scalar value. This value is compiled from the model output variables. In contrast, a multi-objective optimisation optimises multiple objectives simultaneously, thus forming a Pareto front [70]. An example of a two dimensional Pareto front is shown in Figure 3.12. In a two-dimensional optimisation problem the Pareto front is a curve. On each point of the curve it is impossible to improve one objective without deteriorating the other objective. For example, if the two objectives are investment cost and net power output, the intuitive results would be that on the Pareto front it is impossible to increase the net power output without increasing the investment cost. Introduc- ing a multi-objective optimisation provides more flexibility in post-processing and interpretation of the results at the expense of an increased computational time.

Pareto frontier Obj 2 Obj

Feasible point

Infeasible point

Obj 1

Figure 3.12: Example of a two-dimensional Pareto front.

According to the author’s knowledge, the few multi-objective studies in open literature focus on the SCORC. Yet, the use of multi-objective optimisation techniques has some apparent benefits for thermo-economic optimisation. An interesting set of objectives to investigate, but still rarely employed in scientific literature, is the combination of net power output and investment cost. It is important to remark that the NPV is calculated solely based on the knowledge of the initial investment cost and the operational cash flow. The last being directly related to the net power output. Thus by having the Pareto front based on the objectives net power output and investment cost, the NPV can be calculated in a post-processing step. The SIC is also found on this Pareto front as the point with the lowest ratio of net power output over investment cost. The decision maker thus has the option 56 CHAPTER 3 to choose for a low payback time or a high NPV . This optimisation approach is further elaborated in chapter 5.

Reference Objective function Cycle Hettiarachchi et al. [71] Heat exchange area per unit power SCORC 2007 (m²/kWe) Cayer et al. [15] Relative cost per unit power TCORC 2010 (C/kWe) Shengjun et al. [12] Levelised energy cost ($/kWh) SCORC, 2011 Heat exchange area per unit power TCORC (m²/kWe) Quoilin et al. [72] Specific investment cost (C/kWe) SCORC 2011 Wang et al. [51] 1 Linear combination of area per unit SCORC 2012 power (m²/kWe) and heat recovery efficiency (%) Wang et al. [73] Heat exchange area per unit power SCORC 2013 (m²/kWe) Wang et al. [74] Exergy efficiency (%) vs. total in- SCORC 2013 vestment cost (C/kWe) Lecompte et al. [75] Specific investment cost (C/kWe) SCORC 2013 Pierobon et al. [76] 1 Net present value (C) vs. volume SCORC 2013 (m³) and volume (m³) vs. thermal efficiency (%) Astolfi et al. [39] Plant total specific cost (kC/kW) TCORC 2013 Shu et al. [77] Net present value ($) and Depre- SCORC, 2014 cated payback period (years) and TCORC Heat exchange area per unit power (m²/kWe) Li et al. [78] Electricity production cost ($/kWh) SCORC, 2014 ZM Muhammad et al. [79] Specific investment cost ($/kW) SCORC 2014 Nusiaputra et al. [80] Specific investment cost ($/kW) SCORC 2014 and Mean cash flow ($/year) Li et al. [81] Total area (m²) and Relative cost per SCORC 2014 unit power ($/W) and Ratio heat exchanger cost tot total cost (%) Toffolo et al. [82] Specific investment cost ($/kW) SCORC, 2014 and Levelised cost of electricity TCORC ($/kWh) ORGANIC RANKINECYCLEARCHITECTURES 57

Reference Objective function Cycle Meinel et al. [19] Speciﬁc costs per kilowatt hour SCORC 2014 (C/kWh) 1 These authors implement a multi-objective optimisation technique.

Table 3.6: Selection of scientiﬁc papers on thermo-economic optimisation of ORCs.

3.5 Commercial and experimental prototypes

Besides the already listed challenges, there is a general lack of new cycle architectures that are commercialised. An overview of adaptations to the classical subcritical ORC (with recuperator) by ORC manufacturers is given in Table 3.7. It is noteworthy that they all have their origin in low-temperature geothermal applications. Furthermore, the table suggests that new and complex cycle adaptations are, in first instance, only cost-effective for large installations. For large scale systems a small increase in efficiency already results in a significant increase in power output. Prototypes of three promising technologies where constructed: the TCORC, the MP and the TLC. In contrast to the TCORC or TLC, the MP [83] differs significantly in component layout from the basic ORC.

Manufacturer Installation Cycle Technical characteristics TAS [84] Neal Hot Springs TCORC Geothermal brine at 138 °C, (Oregon, USA) working fluid: R134a, net power output : 29.7 MWe Ormat 1[83] Ormesa I project MP Geothermal brine at 147 °C, (California, USA) 26 units in 3 level cascade, total power output 24 MWe Energent [85] Coso TLC Geothermal brine at 112 °C, (California, USA) total power output: 1 MWe Turboden [86] Livorno TCORC Geothermal brine at 150 °C, (Tuscany, Italy) total power output 500 kWe 1 Ormat has among others also MP type cycles in California, USA and Stillwater, USA. Table 3.7: Adaptations to the classical subcritical ORC by commercial manufacturers. Two manufacturers, namely Turboden [86] and TAS [84], invested in the development of transcritical cycles. Unalike TAS, the Turboden installation is an experimental prototype to assess the plant’s design criteria and thermodynamic performance. Turboden expects the plant to be 10-15% more efficient than cur- 58 CHAPTER 3 rently available commercial technology. The main challenge of designing a TLC is the availability of two-phase expanders. Energent [85] developed and patented the Variable Phase Turbine (VPT). The VPT can also be used in conditions where the working fluid is partially evaporated or even superheated. The VPT consists out of fixed nozzles and an axial impulse turbine. The inlet to the nozzle can be liquid, two-phase, supercritical or vapour. The two-phase nozzle efficiency is claimed to be between 90% and 97%, while the rotor efficiency is between 78% and 85%. An alternative for accomplishing two-phase expansion is the use of volumetric machines. Especially the screw expander technology looks promising. Smith et al. [87] report that expander isentropic efficiencies of 70% and more are attainable for screw expanders. In general, there is limited experimental data on ORCs available from open literature and most publications handle the basic SCORC. Yet this information is crucial to derive validated part-load models to assess the actual performance of ORCs. Notable publications that provide validated part-load models for the SCORC are those by Quoilin et al. [88], Ibarra et al. [89] and Bracco et al. [90]. All these papers cover systems smaller than 5 kWe and make use of a scroll expander. Even fewer publications give experimental results on novel cycle architectures. These papers mainly focus on the subcritical ORC with recuperator, the trilateral cycle, the subcritical ORC with zeotropic mixtures and transcritical cycles. An overview is given in Table 3.8.

Ref. Cycle Topic [91] ZM Heat transfer characteristics of siloxane mixtures [92] ZM Determination PP and maximum temperature difference [93] ZM On-site measurements with R245fa and R245fa/R152a [81] ZM Comparison of R245fa and R245fa/R601a [87] TLC Experiments on screw expanders in the range 5-850 kW [94] RC Comparison of ORC with and without RC [95] RC On-site results for ORC with RC in solar applications [96, 97] TCORC Heat transfer in the evaporator

Table 3.8: Overview of experimental data about novel ORC architectures.

Experiments on zeotropic mixtures focus on two major research questions: the effect on the heat transfer characteristics and the performance in real life setups. The first is addressed by Weith et al. [91] who analysed the heat transfer characteristics of siloxane mixtures during evaporation. They found heat transfer degrada- tions up to 46% compared to the available simple models. For R245fa/R365mfc, the degradation is even more severe. Wu et al. [92] investigated the pinch points and maximum temperature differences in a horizontal tube-in-tube evaporator for the mixtures R290/R600 (mass fraction: 0.15/0.85) and R245fa/R152a (mass frac- ORGANIC RANKINECYCLEARCHITECTURES 59 tion: 0.6/0.4). They demonstrate that the simplified models, where the apparent heat capacity is assumed to change linearly between saturated liquid and saturated vapour state, are insufficient to accurately predict the pinch point. Wang et al. [93] addressed the topic of the overall cycle performance, by performing an onsite experimental study of a low-temperature solar subcritical ORC. The pure fluid R245fa was compared to the zeotropic mixtures R245fa/R152a (mass fraction: 0.9/0.1) and R245fa/R152a (mass fraction: 0.7/0.3). The resulting overall cycle efficiency was respectively 0.88%, 0.92% and 1.28%. Li et al. [81] made an experimental comparison between R245fa and R245fa/R601a (mass fraction: 0.72/0.28) for ORCs using a scroll expander. Their results confirm the better match with the heat source profile when using zeotropic mixtures as working fluid. The TLC with a screw expander as expansion device is extensively studied in the experimental work of Smith et al [87]. Three different working fluids, varying rotor profiles and power outputs between 5-850 kW where investigated. The relatively large pressure drop at the inlet, associated with the initial filling between rotor and casing, was identified as a main factor contributing to the poor results of previous studies. They conclude that adiabatic efficiencies of 70% are possible at outputs of only 25 kW. Multi-megawatt machines are feasible with efficiencies of more than 80%. Experiments which compared the ORC versus the ORC with recuperator were performed by Li et al. [94]. Water of 130 °C is fed to the ORC. The working fluid is R123 and passes through a single stage axial flow turbine. This set-up gave a thermal efficiency of 7.98% and 6.15% for respectively the ORC with and without recuperator. This confirmed the expected results of a higher thermal efficiency for an ORC with recuperator. Wang et al. [95] describe experiments for a solar ORC with recuperator. With constant working fluid mass flow rate, the recuperator did not improve the thermal efficiency of the system. To the contrary, the preheating caused the collector inlet temperature to increase, which led to lower collector efficiencies and ultimately, lower overall cycle efficiencies. However, when changing the working fluid mass flow rate, improvements in the overall system efficiencies are reported. This result confirms the importance of comparing cycle architectures under optimal operating and design conditions. To the author’s knowledge no experimental data of a full transcritical cycle are available in literature. Bliem et al. [96, 97] published some data about supercritical heat exchangers working with pure isobutane and a butane/hexane mixture (mass fraction: 0.95/0.05). However, the developed computer code, HTRI (Heat Transfer Research, Inc.), is proprietary and no data about heat transfer correlations are shared. Furthermore, as the authors themselves note, the results are limited and insufficient to demonstrate the total system performance. In contrast, there are several works which provide experimental results on CO2 supercritical cycles. However these fall out of the scope of this work. 60 CHAPTER 3

A difficulty when comparing experimental studies on novel ORC architectures, is that the working fluids should be compared under their respective optimal conditions. Firstly, the components design (especially the expander) should be tuned for the specific working fluid. Additionally, the working fluids must be compared under optimal operating parameters. Otherwise biased conclusions could be drawn on which architecture or working fluid is the best. The lack of validated part-load models has been tackled in this work in Chapter 6 and Chapter 7. In Chapter 6 part-load models are introduced which are validated in Chapter 7 on experimental data of an 11 kWe waste heat recovery set-up with a double screw expander. Also in Chapter 7, the validated models are used to determine and compare the optimal operation of the set-up under SCORC and PEORC conditions.

3.6 Conclusions

In this chapter, the benefit of cycle modifications to the basic ORC was illustrated. The cycle configurations of interest are identified as:

• Transcritical cycles (TCORC)

• Trilateral cycles (TLC)

• Cycles with zeotropic mixtures as working ﬂuids (ZM)

• Cycles with multiple evaporation pressures (MP)

• Organic ﬂash cycles (OFC)

• Addition of a recuperator (RC)

• Regenerative cycle with turbine bleeding (RG)

• Cycle with vapour injector

• Cascade cycles

• Cycle with reheaters

Based on the insights gathered from the literature review two cycles types in particular show potential for waste heat recovery applications: the PEORC (including the TLC), and the TCORC. Both require little modiﬁcations to the original cycle layout while showing deﬁnite improvements to the net power output. Yet, there are several challenges that still need to be addressed. These are shortly summarised below: ORGANIC RANKINECYCLEARCHITECTURES 61

• Scientiﬁc papers published on alternative cycle architectures are not cross- comparable because of different assumptions used in modelling and different implementations of the performance evaluation criteria.

• In a ﬁnancial decision making scenario, the NPV is the single best criterion. Other ﬁnancial criteria have apparent drawbacks that can lead to sub optimal solutions. However the NPV depends on several assumptions which are time and place dependent. If these assumptions change, the complete design procedure needs to be repeated.

• Single objective optimisation approaches result in a single, possibly suboptimal choice for decision makers.

• Waste heat streams often are transient. While transient ORC models are available in literature [72, 98, 99], they have a high computational cost. Fur- thermore, the transient performance of the ORC will largely be determined by the control algorithm [100]. In this thesis, the focus is on the maximal attainable steady-state performance of different cycle architectures. Assuming that the control set-point is reached sufﬁciently fast compared to the dynam- ics of the waste heat stream, the ORC can be assumed to work in steady state conditions. For large capacity waste heat streams this is assumed to be true [101]. The operating point will however be shifted from nominal operation. As such part-load models are crucial to give an initial approxi- mation of the actual power output. However, validated part-load models are rather scarce in open literature, especially for alternative ORC architectures besides the SCORC.

The goal of this work is to investigate these opportunities and to address the challenges. This is done in the following chapters. First, in Chapter 4, a thermodynamic screening is performed considering the three most promising cycles identified from this chapter: SCORC, TCORC and PEORC. This step tackles the problem that fluid recommendations made in literature are based on different assumptions and thus not cross-comparable. Also only a limited number of working fluids and cycle architectures were previously investigated. The models implemented in this step are solely based on intrinsic thermodynamic parameters, no sizing or part-load is accounted for. As such the models have a low computational cost allowing to investigate several hypothetical cases. Regression models are compiled from the results, permitting us to quickly compare the achievable power output between different cycle architectures. Secondly, in Chapter 5, a thermo-economic optimisation framework is proposed where the sizing and subsequent financial appraisal is performed. In this framework the NPV is used as performance evaluation criterion. A multi-objective optimisation based on net power output and investment cost is first performed. 62 CHAPTER 3

With the resulting Pareto front from the multi-objective optimisation the NPV can be calculated in a post-processing step. A case study is presented comparing the SCORC and TCORC. Finally the effect of part-load operation is assessed in Chapter 7. The part-load models and their implementation are ﬁrst described in Chapter 6. These models are validated on an 11 kWe ORC set-up in Chapter 7. The optimal part-load operation is subsequently assessed for both the SCORC and the PEORC. ORGANIC RANKINECYCLEARCHITECTURES 63

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Part II

Comparison of organic Rankine cycles architectures: thermodynamic screening and thermo-economic appraisal

4 Thermodynamic performance evaluation and regression models of organic Rankine cycle architectures

4.1 Introduction

As indicated in Chapter 3, advanced cycle architectures have the potential to improve the performance of the subcritical ORC. Considering the above, advances in cycle architectures can further push adoption of ORC technologies for low temperature heat conversion. The subcritical ORC (SCORC), the partial evaporation ORC (PEORC) [1] and the transcritical ORC (TCORC) are further investigated in this chapter based purely on thermodynamic considerations. The advanced cycles all share the same component arrangement with the SCORC. Only the operating regime is different.

4.2 Cycle arrangements

In this section the different cycles under investigation are briefly re-introduced. Three closed cycle arrangements are investigated: the SCORC, the TCORC and the PEORC. The PEORC is a generalisation of the TLC. In contrast to a TLC, the working fluid in a PEORC is allowed to partially evaporate in the evaporator. The component arrangements are identical for all of these cycles and corresponds 76 CHAPTER 4 with that of Figure 4.1a.The working fluid passes successively trough the pump, evaporator, expander and condenser. For the TCORC, the evaporator is typically called a vapour generator because two-phase boiling is omitted. The working fluid is brought to supercritical pressure and heated to a supercritical state. The heat rejection process is still done by condensing the working fluid. For the PEORC, the evaporator only includes the pre-heating and ends at a state between saturated liquid and saturated vapour. Both the TLC and TCORC approach a triangular shape in a T-s diagram, pro- viding a good match with a finite capacity heat source [2]. An extensive discussion on these cycle architectures can be found in Chapter 3.

(a) 2 (b) ṁ 2 Evaporator WF Evaporator ṁWF Expander Expander ṁHTF ṁHTF 7 8 7 8 9 3 3 Generator Generator Recuperator ṁ 6 1 CF 4 6 5 ṁCF Condenser 5 1 Condenser 4 5 pump pump

Figure 4.1: (a) Basic ORC layout. (b) ORC layout with recuperator.

4.3 Comparing the SCORC, TCORC and TLC

While both the TCORC and TLC share the same triangular T-s diagram, there is no general consensus in scientific literature on which type of cycle architecture performs best. Smith et al. [3] were amongst the first to extensively investigate the TLC. The optimisation potential of modified ORC cycles can be appreciated by comparing the Carnot cycle and the ideal TLC. Evaluating the ideal TLC and Carnot cycle with finite heat capacity streams in their optimal upper cycle temperature results in an ideal conversion efficiency of the TLC which is roughly twice that of the Carnot cycle [3, 4]. An ideal TLC would have a perfect triangular shape with the expansion process stopping in the two-phase region. If the expansion process stops in the dry region, the TLC is sometimes called a quadrilateral cycle [5]. Schuster et al. [2] recommends a TCORC to approximate the ideal triangular cycle. On the other hand, in a study by Fischer et al. [6], the TLC had an improved net power output over both the SCORC and TCORC. In the latter study, the TLC worked with water as working fluid while the TCORC used R141b, R123, R245ca or R21. The inlet temperature pairs of heat carrier and condenser cooling THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 77

fluid were (350 °C, 62 °C), (280 °C, 62 °C), (280 °C, 15 °C), (220 °C, 15 °C) and (150 °C, 15 °C). Yamada et al. [7] also investigated the SCORC, TLC and TCORC for the working fluid R1234yf. However, in their simulations the heat carrier stream was not modelled. The highest thermal efficiency was found for a supercritical cycle, but nothing is mentioned about the point of maximum net power output. Furthermore, several other papers study only either the TCORC or TLC, see Table 4.1 for a non exhaustive overview.

Reference Cycle Topic [3, 8] TLC Analysis and working fluid selection [9] TLC Development of a screw expander [5] TLC Comparison of TLCs [10] TLC Piston engine as expander [11] TLC Analysis of an ammonia-water TLC [12] TCORC Parametric study [13] TCORC Plate heat exchanger design [14] TCORC Performance analysis in near-critical conditions [15] TCORC Working fluid selection [16] TCORC Working fluid selection

Table 4.1: Research articles which investigate either the TLC or TCORC.

To the author’s knowledge no paper:

• Compared and analysed the three cycle architectures; SCORC, TCORC and PEORC considering a large set of different boundary conditions.

• Includes a systematic analysis of the constraints: restriction to environmentally friendly working ﬂuids, superheated state after the expander, restriction on the heat carrier outlet temperature and the effect of the recuperator.

• Provides regression models for the three ORC architectures under consideration.

Because a large variety of boundary conditions and assumptions are used in literature, it is hard to make a fair comparison between different working ﬂuids and cycle architectures. Therefore the effort was set up to analyse a large set of working ﬂuids for several waste heat and cooling conditions in a methodological approach and this for the SCORC, PEORC and TCORC. In order to address the concerns listed above the following topics are tackled in this chapter: 78 CHAPTER 4

• The TCORC, PEORC, and SCORC are analysed and compared for heat sources with low to medium temperatures (100 °C - 250 °C) and high temperatures (250 °C - 350 °C).

• The performance potential of the TCORC, PEORC and SCORC is high- lighted by using an exergy analysis and rigorously applying the set of boundary conditions on each cycle type.

• A large set of 67 refrigerants is selected for the study.

• The PEORC is considered, investigating the region between the TLC and the SCORC.

• The impact of successive constraints is analysed: limitation to environmentally friendly working ﬂuids, enforced superheated state after the expander and upper cooling limit of the heat carrier.

• The addition of a recuperator to the SCORC and TCORC is discussed.

• Simple regression models are provided to quickly assess design implica- tions.

This work explicitly focuses on waste heat recovery applications. For these applications maximisation of the net power output is the main objective. Typical applications for the low to medium temperature regime are water jacket cooling [17], cooling of furnaces [18] or bottoming cycles [19]. The high temperature cases typically consist of cooling of high temperature ﬂue gas [20].

4.4 Thermodynamic model and assumptions

The boundary conditions and the modelling approach is elaborated in this section. The heat carrier inlet temperature varies between 100 °C and 350 °C. The cooling water inlet temperature ranges from 15 °C to 30 °C. A matrix with waste heat inlet temperature Thf,in and water cooling loop inlet temperature Tcf,in is constructed. Thf,in and Tcf,in respectively take the values [100, 120, 140, 160, 180, 200, 225, 250, 275, 300, 325, 350] °C and [15, 20, 25, 30] °C. The cycles are modelled under the assumption of steady state operation, no heat losses to the environment (i.e. well insulated heat exchangers) and no pressure drops in the heat exchangers, these pressure drops can in first instance be neglected compared to the pressure drop over the expander. The developed code supports a continuous transition between the three investigated cycles. The evaporators are modelled by discretising them in N segments, this is illustrated in Figure 4.2. In this way changing working fluid properties are taken into account. This is especially crucial for modelling the TCORC. The error analysis indicates that the THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 79 net power output of the TCORC changes less than 0.1 % when going from N = 20 to N = 100. To keep an acceptable calculation time a discretisation with N = 20 segments is chosen. The condenser is only divided into three zones: desuperheat- ing, condensing and subcooling zone. The working fluid exits the condenser as saturated liquid (xcond,wf,out = 0). The assumptions and parameters of the model are summarised in Table 4.2.

dhwf,1 dhwf,2 dhwf,i ….. dhwf,N

1 2 i dh N wf  cst dT hf constant heat capacity hot fluid ….. dThf,1 dThf,2 dThf,i dThf,N

Figure 4.2: Discretisation modelling approach of the heat exchangers.

Variable Description Value

pump (-) Isentropic efficiency pump 0.70 exp (-) Isentropic efficiency expander 0.80 ∆TP P,evap (°C) PP temperature difference evaporator 5 ∆TP P,cond (°C) PP temperature difference condenser 5 hf Heat carrier medium air cf Cooling loop medium water Thf,in (°C) Heat carrier inlet temperature 100-350 m˙ hf (kg/s) Heat carrier mass flow rate 1 Tcf,in (°C) Inlet temperature cooling water 15-30 Tcf,out (°C) Temperature rise cooling loop 10 xcond,wf,out (-) Vapour quality at exit condenser 0 rec (-) Effectiveness recuperator 0.8

Table 4.2: Assumptions and parameters for the thermodynamic model.

Thermophysical data is taken from CoolProp (version 4.2.5) [21]. Only pure working fluids are considered in this study, working fluid mixtures are out of scope. As additional criterion, the working fluids should have a critical temperature above 60 °C to make sure two-phase condensation occurs. Furthermore, for the SCORC the maximum pressure is 0.9 times the critical pressure [22, 23]. This to avoid 80 CHAPTER 4 unstable operation in near critical conditions. The complete list of working fluids and their characteristics are provided in Appendix B. The total heat input to the cycle follows from:

N−1 ˙ X Qevap = (hevap,wf,(x+1) − hevap,wf,x) · m˙ wf (4.1) x=1 with hevap,wf,x evaluated at the evaporation pressure pevap,wf . Furthermore, hwf,N is ﬁxed by the state variables pevap,wf and sevap,wf,out as discussed in section 4.5. The effectiveness of the recuperator is deﬁned as:

Q˙ rec hexp,wf,out − hcond,wf,in rec = = (4.2) Q˙ max hexp,wf,out − hmax with hmax evaluated at (p = pcond,wf , T = Tpump,wf,out). The expander and pump are characterised by their isentropic efﬁciency and are considered to be adiabatic. For volumetric machines the heat loss can be significant which would result in a lower shaft power output. Extensive details on the performance evaluation criteria and the second law efﬁciency calculations can be found in Section 2.2.

4.5 Optimisation algorithm and strategy

From the model in section 4.4 follows that there are two degrees of freedom left which can be optimised. These are generally fixed as follows: for the SCORC, evaporation pressure and superheating, for the TLC, evaporation pressure and vapour quality at the outlet of the evaporator and for the TCORC supercritical pressure and temperature at the outlet of the evaporator. In this work however, the degrees of freedom are fixed by defining two independent dimensionless parameters Fp and Fs:

pwf,evap − pmin Fp = (4.3a) pmax − pmin

pmin = pwf,sat(T = Tcf,out + ∆TP P,cond) (4.3b)

if (Thf,in − ∆TP P,evap > Twf,crit): (4.3c) pmax = 1.3 · pwf,crit

if (Thf n − ∆TP P,evap < Twf,crit): i (4.3d) pmax = pwf,sat(T = Thf,in − ∆TP P,evap) THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 81

swf,evap,out − smin Fs = (4.4a) smax − smin smax = swf (p = pwf,evap,T = Thf,in − ∆TP P,evap) (4.4b)

if (pwf,evap < pwf,crit): (4.4c) smin = swf,sat,l(p = pwf,evap)

if (pwf,evap > pwf,crit): (4.4d) smin = swf,crit

Both parameters have a range [0, 1]. The parameter Fp directly relates to the evaporation pressure. For a TCORC the maximum pressure is limited to 1.3 times the critical pressure. For the other cycles, the maximum pressure is limited to the saturation pressure at the heat input temperature corrected with the pinch point temperature difference. The parameter Fs determines the amount of superheating (SCORC), the vapour quality (PEORC) or the expander inlet temperature (TCORC). The maximum value corresponds to a pinch point which is located at the evaporator heat carrier inlet. For the SCORC, the minimum lies at the saturated liquid state at a given evaporation pressure. For the TCORC, the minimum corresponds to the critical point. The benefit of using these parameters is a more robust optimisation process. The model based on the parameters Fp and Fs permits defining the search space based on only two unique variables. The two state variables Fp and Fs fix the evaporator (or vapour generator) outlet state. In Figure 4.3 the effect of Fp and Fs on the second law efficiency is shown for the working fluid R1234yf. In Figure 4.3a and Figure 4.3b a waste heat carrier with Thf,in = 140 °C and Thf,in = 90 °C are used. The three different architectures: SCORC, TCORC and PEORC can be easily distinguished. For the case Thf,in = 90 °C, a supercritical regime is not attainable due to the critical temperature of R1234yf (Tcrit = 94.7 °C). This is because the waste heat inlet temperature corrected with the pinch point temperature difference is lower than the critical temperature. The supercritical regime is bounded by a straight line with a fixed value of Fp. The interface between PEORC and SCORC is explained by the saturation vapour curve, on which both Fp and Fs vary. The final goal is to optimise the second law efficiency ηII for different working fluids and cycle constraints. In Figure 4.3a (Thf,in = 140 °C) the global maximum for the second law efficiency is 0.437 and corresponds to a TCORC. In Figure 4.3b (Thf,in = 90 °C) the global maximum for the second law efficiency is 0.284 and corresponds to a PEORC. The optimal operating conditions for both cases are summarised in Table 4.3. However, as can be seen from Figure 4.3b, there is a risk that the optimisation algorithm gets stuck at a local optimum. Therefore a multi-start algorithm is 82 CHAPTER 4

F s [-] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(a)

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F F s [-] 90 = s 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 o R1234yf, for

(b)

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[-] 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 83

Variable Thf,in = 140 °C Thf,in = 90 °C Cycle type TCORC PEORC ηII (-) 0.437 0.284 Fs (-) 0.7205 0.1394 Fp (-) 1 0.6242 pwf,evap (bar) 43.97 21.23 pwf,cond (bar) 9.86 10.18 Texp,in (°C) 120.78 71.76

Table 4.3: Operating conditions at maximum second law efﬁciency for Thf,in = 90 °C and Thf,in = 140 °C for R1234yf with Tcf,in = 25 °C. employed [24]. This is a global optimisation algorithm which is partially heuris- tic. The fundamental idea is to construct an initial grid on which a local solver is applied. The global optimisation algorithm starts with a randomly distributed set of start points in the search space (Fs, Fp). Initially 20 start points were used. Subsequently, a local solver based on a trust-region algorithm [25] starts at these trail points and the best solution is retained. The investigated problem for the local solver is given below:

maximise ηII (Fs,Fp) Fs,Fp (4.5) subject to 0 ≤ (Fs,Fp) ≤ 1 The optimisation can also be limited to certain ORC architectures by further constraining Fs and Fp as illustrated in Figure 4.3. The termination conditions are as follows: 3000 maximum function evaluations, 1e-6 tolerance on objective function, 1e-6 tolerance on input variables. To assess the influence of the number of start points, the calculations were repeated with 40 start points. This however gave identical results. The investigation strategy consists of the following steps: first, all working fluids (AWF) from Appendix B are considered (Case 1). Afterwards the analysis is repeated for the subset which is assumed environmentally friendly (EWF) (Case 2). Next, the expander outlet is constrained to a superheated state, this results in an added constraint Tsup,exp,out > 0 (Case 3). In a following step the heat carrier outlet temperature is restricted, resulting in added constraint on Thf,out (Case 4). Finally, the addition of a recuperator is considered (Case 5). For each analysis, the second law efficiency ηII is maximised by employing the global optimisation algorithm. With this strategy a maximum attainable performance is reported in each consecutive step. As such, the consequence of each design choice is clearly analysed and this for the three different cycles under consideration. 84 CHAPTER 4

4.6 Regression models

First, regression models are compiled for each of the cycle types and cases under consideration. These regression models express the maximal second law efficiency ηII,max as function of temperatures Thf,in and Tcf,in. The proposed regression models are useful for predicting the impact of design constraints and this with a low computational cost. Several polynomial regression models up to third order were tried. However, the regression model which best captures the trends is not- polynomial: cTcf,in + 1 ηII,max = a + b (4.6) dThf,in + 1 Contour plots of these surface fits are plotted for the five different cases listed in Table 4.4. The marker type indicates the cycle architecture, while the colour of the marker indicates the working fluid name. Corresponding parameter estimates for each of the cycle types are provided in Table 4.5. Goodness-of-fit statistics [26] are provided in Table 4.6. A Sum of Squares Due to Error (SSE) closer to zero means that the fit is more useful for prediction (interpolation). While a high adjusted R2 value indicates a successful fit in explaining the variation of the data. The SSE and adjusted R2 ranges respectively between 0.0006-0.0041 and 0.992-0.999. Both SSE and adjusted R2 can be considered highly satisfactory. The residuals have been visually analysed on quantile-quantile (Q-Q) plots [26] and appear normally distributed around zero. All the coefficients are significant from a t-test [26] with 5% significance level.

Case Description ηII,max 1 Full set of working ﬂuids (AWF) Figure 4.4 2 Environmentally friendly set of working ﬂuids (EWF) Figure 4.8 3 EWF set with Tsup,exp,out > 0 Figure 4.11 4 EWF set with Tsup,exp,out > 0 and Thf,out = 130 °C Figure 4.12 5 EWF set with Tsup,exp,out > 0, Thf,out = 130 °C and RC Figure 4.14

Table 4.4: Description of the case studies with reference to their contour plots of ηII,max. THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 85

Type a b c d All working ﬂuids (AWF) SCORC 0.7548 1.315 0.01180 -0.04730 TCORC 0.7405 0.791 0.01265 -0.03490 PEORC 0.7408 0.479 0.01286 -0.02996 Environmentally friendly working ﬂuids (EWF) SCORC 0.7531 1.660 0.00933 -0.05206 TCORC 0.7247 0.371 0.01058 -0.01960 PEORC 0.7408 0.479 0.01286 -0.02996 EWF, Tsup,exp,out > 0 SCORC 0.7548 1.735 0.00911 -0.05345 TCORC 0.7228 0.306 0.01042 -0.01693 EWF, Tsup,exp,out > 0, Thf,out = 130 °C SCORC 0.7532 1.695 -0.002262 -0.02434 TCORC 0.8410 14.981 -0.001937 -0.13820 EWF, Tsup,exp,out > 0, Thf,out = 130 °C, RC SCORC 0.7303 1.433 -0.001919 -0.02230 TCORC 0.8303 9.997 -0.001922 -0.09669

Table 4.5: Parameter estimates for ηII,max surface ﬁts.

Cycle type Adjusted R2 (-) SSE (/) All working ﬂuids (AWF) SCORC 0.994 0.0032 TCORC 0.995 0.0022 PEORC 0.998 0.0006 Environmentally friendly working ﬂuids (EWF) SCORC 0.993 0.0040 TCORC 0.996 0.0023 PEORC 0.998 0.0006 EWF, Tsup,exp,out > 0 SCORC 0.992 0.0041 TCORC 0.994 0.0018 EWF, Tsup,exp,out > 0, Thf,out = 130 °C SCORC 0.999 0.0007 TCORC 0.996 0.0029 EWF, Tsup,exp,out > 0, RC, Thf,out = 130 °C SCORC 0.999 0.0006 TCORC 0.996 0.0030

Table 4.6: Goodness-of-ﬁt statistics for ηII,max surface ﬁts. 86 CHAPTER 4

4.6.1 Analysis of the full set of working ﬂuids (Case 1)

We start by discussing the results for the full set of working ﬂuids. From Figure 4.4 can be seen that the PEORC consistently has a higher ηII,max than the SCORC and TCORC. Up to Thf,in = 250 °C partial evaporation is largely omitted and the cycle corresponds to a TLC. The vapour quality at expander inlet for each of the calculated working points is visualised in Fig 4.5.

For increasing temperature Thf,in, the vapour quality at expander inlet increases slightly but does not exceed 9%. From a thermodynamic point of view, the pure TLC is thus a favourable choice. Furthermore, measuring the actual vapour quality for control purposes could be tedious in practical applications. The resulting optimal fluids for the PEORC are: D4, D6, MD2M, MD3M, water, n- dodecane, o-xylene. All these working fluids have a high critical temperature in common. As such there is a large increase in specific volume over the expander, indicating that optimal design of volumetric machines is challenging. While turbines can provide an alternative, there is the problem of the erosion of the turbine blades. Therefore, optimising solely ηII,max will not necessarily result in technically feasible solutions. Still, these results are valuable to define an upper region in which a technical solution can be found. The optimal fluids for the TCORC are: acetone, neopentane, R113, R218, R227ea, R236fa, R245fa, RC318, toluene and n-pentane. All these working fluids, except neopentane and toluene, are also found in the SCORC list of optimal fluids. Furthermore, the corresponding working fluids share the same boundary conditions. The resulting optimal fluids for the SCORC are highly sensitive to the heat carrier inlet temperature Thf,in. This is explained by the strong correlation between the critical temperature of the working fluid and the net power output for a fixed Thf,in [27–29]. A critical temperature closer to Thf,in results in larger net power output [27]. Due to the large variations in critical temperature for the working fluids under consideration, the resulting optimal working fluids often change for varying Thf,in. In total, 15 working fluids result from optimising the SCORC, compared to 10 and 7 for respectively the TCORC and PEORC. For the PEORC, typically siloxanes appear to give the best second law efficiency. Furthermore all of the optimal working fluids, except water, are very dry fluids [20]. For the TCORC several chemical groups of working fluids are found. These are amongst others: alkanes, chlorofluorocarbons, fluorocarbons, halocarbons and hydrofluo- rocarbons. However all of the resulting working fluids are of the dry type. Also for the SCORC most of the fluids are of the dry type. The only exceptions are R1234yf and acetone which are isentropic fluids and R143 which is a wet fluid.

For comparison purposes, the relative difference in ηII,max between PEORC- TCORC and TCORC-SCORC are given respectively in Figure 4.6a and Figure 4.6b. These plots clearly indicate a larger difference for low heat carrier inlet temperatures Thf,in. Comparing the TCORC with the PEORC, the relative difference THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 87 350 D4 D6 MD2M MD3M water n−dodecane o−xylene PEORC 300 250 [°C] acetone neopentane R113 R218 R227ea R236fa R245fa RC318 toluene n−pentane TCORC TCORC hf,in T 200 150 acetone cyclopentane R114 R123 R1233zde R1234yf R141b R143a R218 R227ea R236fa R245fa R365mfc RC318 n−pentane SCORC 100

30 25 20 15

cf,in

[°C] T 350 350 for full set of working ﬂuids (Case 1). II,max 300 η 300 250 250 [°C] [°C] hf,in hf,in PEORC SCORC T T 200 200 Figure 4.4: Contour plot of 150 150 100 100

30 25 20 15

cf,in 30 25 20 15

cf,in [°C] T

[°C] T

0.7 0.6 0.5 0.4 0.3 0.2 0.1 ,max II [-]

η 88 CHAPTER 4

0.0 0.0 0.0 0.0 0.0 1.4 0.0 0.0 2.7 3.9 8.3 7.3 30 8

7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.8 4.0 8.3 7.2 6 25

5 [°C] [%] cf,in

T 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.9 2.8 4.0 8.4 7.3 4 exp ,in

x 20

2 0.0 0.0 0.0 0.0 0.0 1.0 0.0 1.9 2.8 4.0 5.5 7.3 15 100 150 200 250 300 350 T [°C] hf,in

Figure 4.5: Vapour quality xexp,in for the PEORC.

in ηII,max is always lower than 26%. For temperatures Thf,in of 350 °C the relative difference in ηII,max already reduces to less than 5%. On the other hand, comparing the TCORC with the SCORC, the relative difference of ηII,max is always lower than 11%. While at temperatures of 350 °C the relative difference is less than 3%. Thus advanced cycle architectures like the PEORC and TCORC, have foremost potential in low temperature waste heat recovery applications. The exergy content for the processes of the three cycle types is shown in Fig- ure 4.7a for Tcf,in = 20 °C. With increasing Tcf,in mainly yD,condenser and yL,condenser increase while reducing ηII,max (see Figure 4.4). For high Thf,in, the expander is the main source of exergy destruction. In contrast, for decreasing Thf,in, the share yD,evaporator and yL,evaporator increase and become the dominant sources of exergy destruction and losses. This occurs around Thf,in = 140 °C. Consequently, for low Thf,in, it is beneficial to look further at strategies to decrease yD,evaporator and yL,evaporator. In contrast, for high Thf,in, the exergy loss yL,evaporator and exergy destruction yD,evaporator become insignificant. Improving the expander efficiency is thus more gainful. The increased ηII,max when going from SCORC to TCORC or from TCORC to PEORC can clearly be associated to a reduction in exergy desstruction yD,evaporator and exergy losses yL,evaporator. The PEORC always boosts the highest reduction in exergy losses yL,evaporator. As expected for the TCORC, the exergy destruction associated to the pump is always higher in comparison to the PEORC or the SCORC. Especially for low Thf,in the share of exergy destruction yD,pump is significant at the expense of a low ηII,max. THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 89

350 350 350 300 300 300 250 250 250 [°C] [°C] [°C] hf,in hf,in hf,in T T T 200 200 200 −14.4−11.3 −9.4−14.4−11.3 −11.6 −3.2 −0.8 −0.7 1.8 2.0 150 150 150 1.6 5.4 5.7 2.1 4.3 1.2 5.8 1.0 1.4 2.1 −7.7 −7.7−28.9−12.8 −9.7 −0.7 0.5 −0.1 2.1 −8.0 −9.0−25.1−13.3 −10.8 2.9 −2.3 0.4 −0.3 1.9−24.0 2.4 −8.8 −9.2−22.5−13.7 −12.2 −3.9 −1.5 −1.1 1.6 1.6 11.3 7.8 1.5 4.3 1.4 4.3 4.7 2.8 0.8 1.4 2.1 −0.5 2.5 7.3 7.4 1.9 5.6−1.3 1.7 1.3 6.3 6.5 5.5 2.0 0.6 4.9−1.3 1.7 1.3 2.7 5.8 0.5−1.8 1.7 1.6 4.7 4.8 2.3 2.2 3.8 1.2 5.4 1.1 1.3 2.0 10.8 10.3 8.6 1.8 4.6 1.8 9.0 4.2 10.6 8.5 5.0 1.5 4.4 3.4 1.6 6.9 0.9 4.2 1.7 4.8 2.7 3.1 5.3 0.9 11.2 6.9 1.6 1.6 4.5 2.3 1.2 3.8 4.4 2.6 0.9 1.3 2.0 100 100 100

30 25 20 15 30 25 20 15 30 25 20 15

cf,in cf,in

b cf,in d f [°C] T [°C] T [°C] T 350 350 350 relative to SCORC. 300 300 300 250 250 250 [°C] [°C] [°C] hf,in hf,in hf,in T T T 200 200 200 −13.4 −8.8 −8.7−13.4 −11.6 −4.2 −1.8 −0.3 0.7 1.8 results: (a) Case 1, PEORC relative to TCORC, (b) Case 1, TCORC relative to SCORC, (c) Case 2, 150 150 150 −29.0−13.6 −8.5 −7.9−29.0−13.6 −9.5 −2.2 −0.4 0.8 −8.3 1.0−28.7−14.5−10.4 −9.8 2.0 −3.9 −0.7 0.2 0.9−25.1 2.0 −9.2 −8.3−16.7−13.3 −11.9 −3.8 −2.8 −0.8 0.4 1.6 15.2 10.4 12.1 8.7 8.0 5.6 3.8 4.5 4.7 4.6 4.3 6.4 4.1 7.1 5.7 2.7 4.3 1.3 6.3 0.8 1.4 2.1 II,max η 25.6 18.4 12.4 13.9 9.5 9.0 5.923.9 16.7 11.3 4.4 13.0 9.1 4.8 8.4 5.0 5.722.0 5.0 4.0 4.3 4.6 4.820.1 14.0 9.6 4.8 11.2 8.2 4.4 7.5 5.4 3.7 6.6−15.3 4.4 4.1 9.1 7.5 4.5 2.3 5.6 4.5 1.3 5.1−13.6 4.2 3.7 6.1 8.1 6.6 2.5 0.9 4.9 1.7 1.3 2.7 −12.2 6.3 0.9 1.6 2.3 6.8−12.5 4.3 6.1 4.8 3.1 3.8 1.2 6.3 0.9 1.3 2.0 100 100 100

30 25 20 15 30 25 20 15 30 25 20 15

e cf,in cf,in cf,in c

a [°C] T [°C] T [°C] T

10 9 8 7 6 5 4 3 2 1 0

max, max, ,max, architecture y architecture II, y architecture II, x architecture II

η η η [%] )/ − ( TCORC relative to SCORC, (d) Case 3, TCORC relative to SCORC, (e) Case 4, TCORC relative to SCORC, (f) Case 5, TCORC Figure 4.6: Relative 90 CHAPTER 4

Exergy content [−] Exergy content [−] 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0 1 a 0 1 c

100 R1234YF 100 R218

120 R1234YF R218 R1234YF MD3M 140 R1234YF 120 R1234YF R1234ZEE R227EA 160 R1234ZEE MD3M

R1234ZEE 140 R227EA 180 Neopentane RC318

T IsoButane Water hf,in 200 Neopentane

160 R236FA

[°C] Neopentane iue47 xrycnet()cs ,()cs ,()cs ,()cs 4, case (d) 3, case (c) 2, case (b) 1, case (a) content Exergy 4.7: Figure

225 R236FA n−Pentane R1233ZDE D6 η 250 180 R114

II n−Pentane n−Pentane Neopentane 275 Cyclopentane MD2M T

n−Hexane 200 R245fa y hf,in 300 D,evaporator Cyclopentane R245fa Cyclopentane [°C] Water 325

Acetone 225 R1233ZDE Acetone n−Pentane 350 Acetone n−Dodecane Acetone

250 R123 R113

y Exergy content [−] Water 0.2 0.4 0.6 0.8 D,condenser d 0 1 275 R141b Acetone

140 Cyclopentane Water

300 Cyclopentane R152A 160 Acetone Acetone Butene Water 180

325 Acetone y Ethanol D,turbine cis−2−Butene Acetone 200 Ethanol o−Xylene

350 Acetone T cis−2−Butene 225 hf,in Ethanol Acetone [°C] cis−2−Butene Water 250 Ethanol y TCORC SCORC PEORC D,pump Cyclopentane 275 Ethanol Acetone 300 Ethanol Exergy content [−]

Acetone 0.2 0.4 0.6 0.8 325 b 0 1

y Ethanol

D,recuperator Ethanol 350 Methanol 100 R1234YF

Ethanol Propylene 120 R1234YF Exergy content [−] 0.2 0.4 0.6 0.8

T R1234YF 0 1 140 e cf,in R1234ZEE y L,evaporator

140 R1234ZEE

Cyclopentane 160 R1234ZEE 20 = R152A 160 Acetone IsoButane 180 Butene IsoButane 180

°C. Neopentane

Acetone T 200 cis−2−Butene hf,in Neopentane 200 y Ethanol [°C] L,condenser R1233ZDE 225

T cis−2−Butene R1233ZDE 225 hf,in Ethanol n−Pentane [°C] cis−2−Butene 250

250 n−Pentane Ethanol n−Pentane Cyclopentane 275 275 Ethanol Isohexane Acetone Acetone 300 300 Ethanol Cyclopentane Acetone Acetone 325 Ethanol 325 Acetone Ethanol Acetone 350 Ethanol 350 Acetone

Ethanol

Acetone THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 91 4.6.2 Analysis of the environmentally friendly set of working ﬂuids (Case 2)

In a following step, the working fluid set is constrained to environmentally friendly ones. This means an ODP equal to zero and a GWP equal or lower than 150. The results of the ηII maximisation are plotted in Figure 4.8. The results for the PE- ORC are completely identical to those discussed for the full set of working fluids. For the SCORC only 10 working fluids remain. This is to be expected considering the reduced variation in critical temperature along the remaining working fluids. From these working fluids acetone, cyclopentane, R1233zde, R1234yf and n-pentane are shared with Case 1. For the TCORC there are now 9 optimal working fluids. From these, 4 are shared with Case 1: acetone, neopentane, toluene and n-pentane. For the SCORC and TCORC most of the working fluids are of the dry type. The only exceptions are acetone (isentropic), R1234yf (isentropic), R1234zee (isentropic) and propylene (wet). Again several chemical categories of working fluids are found. Plots of the relative performance between the SCORC-TCORC are given in Figure 4.6c. For the temperature Thf,in = 100 °C, ηII,max for the TCORC is reduced by 15.3% relatively to the SCORC. Yet, when looking at Case 1, R218 was flagged as optimal and performed up to 10.8% better than a SCORC. Therefore an environmentally friendly working fluid resembling the characteristics of R218 could resolve this gap. The poor performance of the environmentally friendly equivalent, propylene, is partly due to the high supercritical pressure of 1.7 times that of R218. For Thf,in = 120 °C the TCORC again shows a relative ηII,max increase over the SCORC by up to 6.8%. The performance gain again gradually reduces for increasing heat carrier temperature. A detailed comparison between Case 1 and Case 2 is provided in Figure 4.9a for the SCORC and Figure 4.10a for the TCORC. For both the SCORC and TCORC there is a reduction in ηII,max for the low temperature regimes. Again, the highest reductions, up to 14.3% for the SCORC and 27.9% for the TCORC, are found for Thf,in = 100 °C. However, as can be seen from Figure 4.9a and Figure 4.10b, going to environmentally friendly working fluids does not necessarily lead to large decreases in performance. There are also some interesting changes in the exergy distribution shown in Figure 4.7b. For Thf,in = 100 °C, the poor performance of both the TCORC and SCORC can be linked to high exergy losses yL,evaporator. This indicates that both the SCORC and TCORC are not able to effectively cool down the heat carrier. In summary, there is still a gap for high performing environmentally friendly working fluids for low temperature applications (Thf,in = 100 °C) and this both for sub- and transcritical operation. 92 CHAPTER 4

η [−] II,max 0.1 0.2 0.3 0.4 0.5 0.6 0.7

T [°C] T [°C] cf,in cf,in 15 20 25 30 15 20 25 30

iue48 otu ltof plot Contour 4.8: Figure 100 100 150 150 η II,max 200 200 o niomnal redysto okn ud Cs 2). (Case ﬂuids working of set friendly environmentally for SCORC TCORC T T hf,in hf,in [°C] [°C] 250 250 300 300 350 350

SCORC n−Pentane n−Hexane R1234ZEE R1234YF R1233ZDE Neopentane Isohexane IsoButane Cyclopentane Acetone TCORC n−Pentane Toluene R1234ZEE R1234YF R1233ZDE Propylene Neopentane IsoButane Acetone THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 93

350 350 300 300 250 250 [°C] [°C] hf,in hf,in T T 200 200 150 150 0.3 1.5 1.9 1.1 1.6 2.3 1.4 3.1 0.9 1.0 3.3 1.4 0.3 3.4 0.5 2.3 1.6 1.1 1.3 0.4 −1.0 1.4 0.2 2.7 1.4 1.7 1.5−4.7 1.5 0.4 1.6 1.5 0.0 2.2 1.0 0.5 1.8 1.6 1.7 1.6 0.0 1.5 0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.2 2.4 0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 1.9 0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.3 2.0 0.0 0.4 0.0 0.0 0.0 0.1 0.0 0.0 0.0 0.1 0.6 0.0 0.0 100 100

30 25 20 15 30 25 20 15

cf,in

cf,in d [°C] [°C] T b T 350 350 300 300 (d) (Case 4 - Case 5). 250 250 [°C] [°C] for SCORC architecture, (a) (Case 1 - Case 2), (b) (Case2 - Case 3), (c) (Case 3 - Case 4), hf,in hf,in T T 200 200 II,max η 150 150 78.7 52.0 42.0 35.6 29.0 25.1 19.4 19.5 14.980.1 55.1 11.5 43.6 37.5 31.2 25.8 20.3 20.4 16.081.9 57.9 12.8 46.8 39.4 32.1 27.4 21.0 21.1 17.184.0 60.4 14.2 48.8 41.5 33.8 29.5 21.9 21.9 18.0 15.5 5.6 2.5 1.9 8.8 3.0 0.7 1.5 0.0 8.4 2.7 0.0 1.1 0.0 8.1 2.3 0.0 1.1 0.0 0.8 0.011.8 0.0 3.3 2.0 0.0 7.1 1.4 0.0 1.5 0.0 0.0 0.014.3 3.6 0.0 2.7 0.0 6.1 0.7 0.0 1.9 0.0 0.0 0.3 3.8 0.0 0.0 0.0 100 100

30 25 20 15 30 25 20 15

cf,in cf,in c a [°C] T [°C] T

10 9 8 7 6 5 4 3 2 1 0

II,case y II,case y II,case x II,case

η η η [%] )/ − ( Figure 4.9: Relative cycle results 94 CHAPTER 4 iue41:Rltv yl results cycle Relative 4.10: Figure

(η − η )/η [%] II,case,x II,case,y II,case,y 0 1 2 3 4 5 6 7 8 9 10

T [°C] T [°C] a

cf,in c cf,in 15 20 25 30 15 20 25 30 100 100 79 . 54 . 03 . 00 . 00 . 000.0 0.0 0.0 0.0 3.4 0.0 0.0 0.1 0.0 0.3 1.6 0.0 5.4 4.8 0.0 27.9 3.5 0.0 0.0 0.1 0.0 0.0 1.6 0.0 5.7 5.3 0.0 26.8 3.6 0.0 0.0 0.1 0.0 0.0 1.5 0.0 6.1 5.8 0.0 26.6 3.7 0.0 0.2 0.0 1.4 6.5 6.4 27.0 656. 544. 313. 812. 8815.8 18.8 23.4 28.1 32.9 43.1 47.1 55.4 14.5 66.7 86.5 17.7 22.1 26.8 31.2 41.8 45.4 53.9 13.1 64.9 85.7 16.6 20.7 25.5 29.5 40.4 43.5 52.2 12.1 63.3 84.8 15.4 19.3 24.1 27.7 38.7 41.5 50.5 60.8 83.9 150 150 η II,max 200 200 T T hf,in hf,in [°C] [°C] o CR rhtcue a Cs ae2,()(ae ae3,()(ae3-Case - 3 (Case (c) 3), Case - (Case2 (b) 2), Case - 1 (Case (a) architecture, TCORC for 250 250 ) d Cs ae5). Case - 4 (Case (d) 4), 300 300 350 350

T [°C] T [°C] d

cf,in cf,in b 15 20 25 30 15 20 25 30

100 100 02 . 15 . 08 . 00 . 03 . 0.0 0.0 0.3 1.0 0.0 0.0 0.0 0.8 0.0 0.0 1.5 0.3 2.6 10.2 0.8 0.0 0.0 0.0 0.6 0.0 0.0 1.7 0.3 2.4 9.4 0.6 0.0 0.0 0.0 0.5 0.0 0.0 1.9 0.3 2.2 8.6 0.4 0.0 0.0 0.4 0.0 2.1 1.9 8.4 02 . 12 . 13 . 05 . 041.6 0.4 1.9 0.5 0.6 1.3 2.0 0.9 0.3 1.2 0.7 1.8 0.2 0.5 0.7 1.3 2.4 0.9 0.3 1.3 1.3 1.8 0.2 0.5 0.8 1.4 2.5 0.9 0.3 1.2 0.0 1.8 0.2 0.5 0.8 1.8 0.9 1.1 0.8 0.2 150 150 200 200 T T hf,in hf,in [°C] [°C] 250 250 300 300 350 350

THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 95 4.6.3 Analysis of the restriction to a superheated state after the expander (Case 3)

In the foregoing discussion wet expansion was permitted. The SCORC and TCORC cycles which have wet vapour after the expander are listed in Table 4.7. For the full set of working fluids (Case 1), most of the SCORC and TCORC would end in a superheated state after the expander. However, when limited to environmentally friendly working fluids (Case 2), the expansion process of the TCORC mostly ends in the two-phase region. In general, the vapour quality at the outlet of the expander is consistently higher than 0.855 for the full set of working fluids and higher than 0.631 for the environmentally friendly set. While wet expansion is feasible for volumetric machines, it is not an option for turbo-machinery due to erosion of the turbine blades. Therefore, in a following step, the outlet of the expander is constrained to a superheated state.

Cycle Working Thf,in Tcf,in xexp,out type fluid (°C) (°C) (-) All working fluids (AWF) SCORC R1234yf 120 15, 20, 25 0.972, 0.9699, 0.957 TCORC R227ea 120 15, 20, 25, 30 0.913, 0.902, 0.891, 0.881 TCORC acetone 275 15, 20, 25, 30 0.855, 0.859, 0.861, 0.862 TCORC acetone 300 15, 20, 25, 30 0.931, 0.933, 0.936, 0.938 Environmentally friendly working fluids (EWF) SCORC R1234yf 120 15, 20, 25, 30 0.972, 0.970, 0.957, 0.996 SCORC R1234zee 140 15, 20 0.994, 0.992 TCORC propylene 100 15, 20, 25, 30 0.631, 0.676, 0.603, 0.631 TCORC R1234yf 120 15, 20, 25, 30 0.838, 0.835, 0.843, 0.846 TCORC R1234zee 140 15, 20, 25, 30 0.912, 0.908, 0.904, 0.911 TCORC isobutane 160 15, 20, 25, 30 0.920, 0.917, 0.917, 0.909 TCORC R1233zde 200 15, 20, 25, 30 0.968, 0.964, 0.961, 0.956 TCORC acetone 275 15, 20, 25, 30 0.855, 0.859, 0.861, 0.862 TCORC acetone 300 15, 20, 25, 30 0.931, 0.933, 0.936, 0.938

Table 4.7: SCORC and TCORC working ﬂuids with expansion ending in two-phase region.

The results of the ηII maximisation are plotted in Figure 4.11. The exergy distribution is given in Figure 4.7c. The optimal working ﬂuids for the SCORC are identical to those of Case 2. Only the operating parameters have changed so that a superheated stated is obtained after the expander. The results from Figure 4.9b conﬁrm that there is only a limited performance loss when restricting the ex- 96 CHAPTER 4

η [−] II,max 0.1 0.2 0.3 0.4 0.5 0.6 0.7

iue41:Cnorplot Contour 4.11: Figure T [°C] T [°C] cf,in cf,in 15 20 25 30 15 20 25 30

100 100 150 150 η II,max niomnal redysto okn ud and ﬂuids working of set friendly environmentally , 200 200 SCORC TCORC T T hf,in hf,in [°C] [°C] 250 250 300 300 T sup,exp,out 350 350 > 0 Cs 3). (Case

n−Pentane n−Hexane R1234ZEE R1234YF R1233ZDE Neopentane Isohexane IsoButane Cyclopentane Acetone SCORC n−Pentane Toluene R1234ZEE R1234YF Neopentane Cyclopentane Acetone TCORC THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 97 pander outlet to a superheated state. For the TCORC some of the working fluids have changed compared to Case 2 and 6 optimal working fluids remain. Isobutane, propylene and R1233zde are removed while cyclopentane is added. For both the TCORC and SCORC all the working fluids are of the dry or isentropic type. In contrast to the SCORC, ηII,max for the TCORC is further reduced for low Thf,in. This by up to 10.2% for Thf,in = 120 °C as noted in Figure 4.10b. Furthermore, there are no suitable transcritical fluids found for Thf,in = 100 °C. From Figure 4.6d a significant improvement of the TCORC over the SCORC is observed starting from Thf,in = 140 °C. Thus, while the TCORC is mainly beneficial in low temperature applications (Case 1), under the common restrictions applied in Case 3 only the smaller performance benefit at high Thf,in remains.

4.6.4 Analysis of the restriction with upper cooling limit (Case 4)

In heat recovery from hot flue gasses there is often a lower limit to the outlet temperature of the flue gases. When flue gasses, which contain water and sul- fur trioxide, are cooled below the acid dew point, sulfuric acid vapour condenses. These acids potentially lead to corrosion and damage of the heat exchanger. The temperature of the acid dew point varies with the composition of the flue gas. Typ- ical values range from around 100 °C to 130 °C [30–32]. In practice, manufactures want to reduce the risk of corrosion, therefore the higher value of Thf,out = 130 °C is chosen in this work.

The results of the ηII maximisation are plotted in Figure 4.12. Optimal working fluids for the SCORC are found found from Thf,in = 140 °C. Yet, many of the optimal SCORC working fluids from Case 3 have been replaced. Only acetone and cyclopentane remain. Furthermore the list of optimal SCORC working fluids has shrunk drastically to 5: acetone, cyclopentane, ethanol, m-xylene and n-nonane. For the TCORC, only acetone, cyclopentane and n-pentane are shared between case 3 and case 4. Seven working fluids are flagged as optimal for the TCORC: acetone, butene, cyclopentane, ethanol, R152a, cis-2-butene and n-pentane. For the SCORC most of the working fluids are still of the dry type, except ethanol (wet) and acetone (isentropic). For the TCORC, dry working fluids are not dominant anymore. Notable is the increased second law efficiency for increasing Tcf,in as opposed to the above cases. This is due to to choice of the dead state T0, which is equal to Tcf,in. Thus ηII,ext increases for rising Tcf,in because less of the available heat after the evaporator is considered useful. In contrast, ηII,int decreases as expected, corresponding with a lower cycle efficiency. Yet, the resulting product results in an increased second law efficiency as can be seen from Figure 4.13.

In Figure 4.6e the optimised ηII for SCORC and TCORC are compared for this case. There are very few boundary conditions for which the TCORC provides 98 CHAPTER 4

η [−] II,max 0.1 0.2 0.3 0.4 0.5 0.6 0.7 iue41:Cnorplot Contour 4.12: Figure

T [°C] T [°C] cf,in cf,in 15 20 25 30 15 20 25 30

150 150 η II niomnal redysto okn ﬂuids, working of set friendly environmentally , 200 200 SCORC TCORC T T 250 250 hf,in hf,in [°C] [°C] T sup,exp,out 300 300 > 0 and T hf,out 350 350 130 =

C(ae4). (Case °C n−Nonane m−Xylene Ethanol Cyclopentane Acetone SCORC n−Pentane cis−2−Butene R152A Ethanol Cyclopentane Butene Acetone TCORC THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 99 a thermodynamic benefit over the SCORC. Only starting from Thf,in = 300 °C there is a small improvement by going to a TCORC. This can be further explained with the help of the exergy distribution plot of Figure 4.7d. Up to Thf,in = 350 °C exergy loss to the environment of the evaporator yL,evaporator has the highest share in the exergy distribution. For a given dead state temperature, the absolute evaporator exergy losses are however fixed by the constant Thf,out. Thus cycle architectures which have as main effect a reduction in yL,evaporator, have no direct benefit under the constraints of this case. The only possible benefit can be associated to a reduction in yD,evaporator. For high temperatures Thf,in there is indeed a small reduction of yD,evaporator in comparison to the SCORC.

0.6

η 0.5 II,ext η II,int

[−] η 0.4 II II,ext η , II,int

η 0.3 , II η

0.2

0.1 15 20 25 30 T [°C] cf,in

Figure 4.13: ηII , ηII,int and ηII,ext for Case 4 with Thf,in = 160 °C.

4.6.5 Analysis of the addition of a recuperator (Case 5) Under the constraints of Case 4, a recuperator could be be beneficial according to the scientific literature [22, 33, 34]. A recuperator essentially increases the thermal efficiency [35]. Thus a high power output can be maintained for a decreased heat input to the ORC. The resulting contour plots of the regression model and the optimised working fluids are given in Figure 4.14. For the SCORC, acetone, cyclopentane, ethanol and methanol result from the optimisation. For the TCORC the optimal working fluids are acetone, butane, cyclopentane, ethanol, R152a and cis-2-butene. For both the TCORC and SCORC the optimal working fluids are either dry, isentropic or wet fluids. As in case 4, an increased second law efficiency is observed for increasing Tcf,in. The relative comparison of ηII with case 4 for the TCORC and SCORC is given in respectively Figure 4.10d and Figure 4.9d. For most boundary condition 100 CHAPTER 4

iue41:Cnorplot Contour 4.14: Figure η [−] II,max 0.1 0.2 0.3 0.4 0.5 0.6 0.7

T [°C] T [°C] cf,in cf,in 15 20 25 30 15 20 25 30

150 150 η II niomnal redysto okn ﬂuids, working of set friendly environmentally , 200 200 TCORC SCORC T T 250 250 hf,in hf,in [°C] [°C] T sup,exp,out 300 300 > 0 , T hf,out 350 350 130 = CadR Cs 5). (Case RC and °C

SCORC TCORC Methanol Ethanol Cyclopentane Acetone cis−2−Butene R152A Ethanol Cyclopentane Butene Acetone THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 101 pairs inclusion of a recuperator results in a decreased ηII,max. Maraver et al. [32] also reported similar decreased second law efficiencies in their cases. Yet, they state that the addition of a recuperator will in theory not decrease the second law efficiency of the cycle. It should at least be the same as for a non-recuperative cycle. They explain the observed reduction to discretisation errors. However, the observed reduction is a result of the fixed temperature glide of the secondary medium in the condenser. With a recuperator, to keep the outlet temperature of the secondary medium fixed, the condenser pressure rises. Even though also the condenser exergy destruction yD,condenser decreases slightly (see Figure 4.7d and Figure 4.7e), the net effect is a decrease in second law efficiency. This suggests that, when investigating the effect of the recuperator, the condenser side should also be optimised, taking into account fan and pumping power.

4.7 Example on the use of the regression models

The benefit of using the proposed regression models is the low computational cost in making an initial appraisal between different cycle architectures. Furthermore, the models can easily be used with a wide variety of cases. In this section, the effectiveness of the regression models based on Eq. 4.6 are assessed by application on two waste heat recovery cases. A medium temperature (Thf,in = 150-250 °C) and a high temperature (Thf,in = 250-350 °C) waste heat recovery group are defined. The low temperature group is representative for drying processes [36] and annealing furnaces [20]. The high temperature group includes, amongst others, exhaust gases from gas turbines or internal combustion engines [20] and electric arc furnaces [37]. One representative case is selected for each group. Details are provided in Table 4.8. The proposed cases and classification are based on data gathered from the industrial advisory board of the ORCNext project [38].

Case Description Tcf,in Thf,in (°C) Thf,out (°C) (°C) A Flue gas from drying 25 240 - process B Flue gas from electric arc 25 305 130 furnace

Table 4.8: Description of two representative waste heat recovery cases A and B.

For both cases, the performance potential of the different cycle architectures is investigated by employing the regression models. The regression models corre- 102 CHAPTER 4

0.7 SCORC TCORC 0.65 PEORC

0.6

[-] 0.55 II η

0.5

0.45

0.4 Case A Case B

Figure 4.15: Results of applying the regression models on waste heat recovery cases A and B. sponding to environmentally friendly working ﬂuids and a superheated state after the expander are used. An exception is made for the PEORC where no superheated state is required after the expander. For Case B, an additional minimum Thf,out of 130 °C is imposed. In this case the PEORC is not considered. The results are plotted in Figure 4.15. For Case A going to a TCORC or PEORC is clearly advantageous in terms of ηII,max. A respective increase of 3.51% and 10.66% in second law efﬁciency is attained compared to the SCORC. However, as expected from the discussion in section 4.6.4, in Case B the TCORC does not lead to an increased ηII compared to the SCORC. Therefore, going to advanced cycle architectures for case B could already be discouraged only from a thermodynamic viewpoint.

4.8 Overview and comparison with literature

An overview of the optimal working fluids with the corresponding cases and cycle architecture is listed in Table 4.9. Looking at the results, it is immediately clear that several combinations of cycle architecture and working fluid can be flagged as optimal. Many of these thermodynamically optimal combinations can also be retrieved from literature. A comparison with the working fluid/architecture recommendations made by other authors is given in Table 4.10. Note that only articles on waste heat recovery were considered. Due to different modelling constraints and assumptions between the works, it is not straightforward to interpret these results. In this work, a rigorous set of boundary conditions and assumptions was used which facilitated the analysis and discussion presented in the previous sections. THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 103

Working ﬂuid Case SCORC TCORC PEORC acetone 1,2,3,4,5 1,2,3,4,5 - butene 4,5 - cyclopentane 1,2,3,4 3,4,5 - cis-2-butene - 4,5 - D4 - - 1,2 D6 - - 1,2 ethanol 4 4,5 - isobutane 2,3 2 - isohexane 2,3 - - MD2M - - 1,2 MD3M - - 1,2 neopentane 3 1,3 - m-xylene 4 - - n-nonane 4 - - n-dodecane - - 1,2 n-hexane 2,3 - - n-pentane 1,3 1,3,4 - o-xylene - - 1,2 R113 - 1 - R114 1 - - R123 1 - - R1233zde 1,2,3 2 - R1234yf 1,2,3 2,3 - R1234zee 2,3 2,3 - R141b 1 - - R143a 1 - - R152a - 4,5 - R218 1 1 - R227ea 1 1 - R236fa 1 1 - R245fa 1 1 - R365mfc 1 - - RC318 1 1 - toluene 1 2,3 - water - - 1,2

Table 4.9: Overview working ﬂuid selection. 104 CHAPTER 4

Working ﬂuid Recommended as working ﬂuid for SCORC TCORC TLC or PEORC acetone [39, 40] - - butene - - - cyclopentane [22, 39, 41–43] [22] [5] cis-2-butene [44] - - D4 [45] [45] - D6 - - - ethanol [46, 47] - - isobutane [33, 35, 48] - - isohexane - - - MD2M [45] - - MD3M - - - neopentane - - - m-xylene - - - n-nonane - - - n-dodecane [49] - - n-hexane [28, 49] - - n-pentane [27, 49–51] - [3] o-xylene [52, 53] - - R113 [27, 46, 54, 55] - [3] R114 [27] - - R123 [27, 51, 53, 55–57] - - R1233zde [58] - - R1234yf [7, 59, 60] [7] - R1234zee [59] [61] - R141b [27, 34, 51, 55, 62, 63] - - R143a [60] [16, 35, 60, 64, 65] - R152a [17] [16] - R218 [66] [66, 67] - R227ea [50, 68, 69] [65] - R236fa [69, 70] [29] - R245fa [27, 43, 50, 55] - - R365mfc [43] [2] - RC318 [69] - - toluene [19, 49, 56] - - water - - [6]

Table 4.10: Working ﬂuid selection comparison with scientiﬁc literature. THERMODYNAMICPERFORMANCEEVALUATIONANDREGRESSIONMODELSOF ORGANIC RANKINECYCLEARCHITECTURES 105 4.9 Conclusions

In this chapter, regression models were formulated to quickly assess design constraints for the SCORC, TCORC and PEORC. The boundary conditions are a matrix with waste heat inlet temperature Thf,in and water cooling loop inlet temperatures Tcf,in that take respectively the values [100, 120, 140, 160, 180, 200, 225, 250, 275, 300, 325, 350] °C and [15, 20, 25, 30] °C. In the first step, all 67 working fluids were included in the optimisation. For low temperature waste heat, alternative architectures like the TCORC and PEORC clearly show higher maximum second law efficiencies compared to the SCORC. The PEORC outperforms the TCORC in second law efficiency by up to 25.6%, while the TCORC outperforms the SCORC in second law efficiency by up to 10.8%. For high Thf,in, the performance gain however becomes small. Further- more, the choice of optimal working fluid for the SCORC and TCORC is highly dependent on the boundary conditions of cooling loop and heat carrier. This is in contrast to the PEORC, for which a limited set of fluids covers the whole range of boundary conditions. The PEORC thus shows increased flexibility to cover different waste heat sources with a single working fluid. For the PEORC, typically siloxanes appear to give the best second law efficiency. Furthermore all of the optimal working fluids, except water, are strong dry fluids. Also for the SCORC and TCORC most of the optimal working fluids are of the dry type. There is however no clear chemical group of working fluids which provides the best performance. When restricting the working fluids to environmentally friendly ones, there is still a gap for high performing working fluids around Thf,in = 100 °C and this both for the SCORC and TCORC. For Thf,in = 100 °C the SCORC even outperforms the TCORC. There is only a small impact on ηII,max when further limiting the expander outlet to a superheated state. A significant improvement of the TCORC over the SCORC is again observed starting from Thf,in = 140 °C. Finally, restricting Thf,out to 130 °C results in an almost completely different set of optimal fluids. In this case the TCORC provides no benefit over a SCORC. Finally, the presented regression models allow to quickly compare the maximum achievable performance of the SCORC, TCORC and PEORC. An example was given with a medium and a low temperature case. Based on these results a first selection of working fluids and cycle architectures can be made. 106 CHAPTER 4

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5.1 Introduction

As pointed out in Chapter 3, the challenge remains to devise a thermo-economic ORC design strategy which is flexible enough to compare different cycle architectures while taking into account the sensitivity of economic parameters. A framework is proposed in this chapter which combines a multi-objective optimisation with a subsequent financial appraisal. The Pareto fronts from the optimisation process are effectively used as input for the financial appraisal. As the financial appraisal is now reduced to a post-processing step, no new design calculations are required when case dependant economic parameters vary. As such, several scenarios can be quickly evaluated. This novel way of optimising and interpreting results is applied on an incinerator waste heat recovery case. Both the TCORC and SCORC are investigated and compared. An extensive discussion on these cycle architectures can be found in Chapter 3. Wet expansion cycles are omitted at this stage because a turbine is used as expander due to the high power output associated to the case study. For high power outputs (∼ 1 MWe) typically turbines are preferred over volumetric machines [1]. The viability to implement a turbine under the given boundary conditions is also assessed. 114 CHAPTER 5

5.2 Deﬁnition of the case study

A representative waste heat recovery case was considered. Exhaust gasses from a waste incineration plant are cooled by an intermediate pressurised water loop. Originally, the waste heat was cooled by dry coolers. The pressurised cooling loop works at 15 bar and has a temperature of Thf,in=180 °C and a mass ﬂow rate of m˙ hf = 15 kg/s. Other examples in this temperature range are found in thermal oil loops and pressurised water loops in the chemical or steel industry [2]. In addition, these temperature levels are also found in ﬂue gasses from drying processes [3].

5.3 Model and assumptions

5.3.1 Cycle assumptions

The ORC cycle is evaluated assuming steady state conditions of all components. Pumps and turbines are characterised by their isentropic efficiency. Furthermore heat loss to ambient is assumed to be negligible. An overview of the fixed parameters and variables is given in Table 5.1. These values are chosen based on a literature survey. In this work conservative values are taken for the pump and turbine isentropic efficiencies.

Variable Description Value

exp (-) Isentropic efficiency turbine 0.7 pump (-) Isentropic efficiency pumps 0.6 ∆TP P,evap (°C) PP temperature difference evaporator Optimised ∆TP P,cond (°C) PP temperature difference condenser Optimised Tcf,in (°C) Inlet temperature cooling fluid condenser 25 2 Texp,in (°C) Inlet temperature turbine Optimised 1 pevap (bar) Evaporation pressure Optimised pcond (bar) Condensation pressure Optimised ηgenerator (-) Generator efficiency 0.98 ∆Tsub (°C) Condenser outlet subcooling 3 1 ∆Tsup (°C) Evaporator outlet superheating 5 1 For the SCORC 2 For the TCORC Table 5.1: Main parameters of the thermodynamic cycle. The same turbine isentropic efficiency used here is also found in the work of Wang et al. [4] and Vaja and Gambaroto [5], both consider applications on waste heat recovery. Other authors employed higher values of 0.75 [6, 7] or even 0.85 [8, 9]. But also turbine isentropic efficiencies of 0.65 [10] are found. The THERMO-ECONOMIC PERFORMANCE EVALUATION OF ORGANIC RANKINECYCLE ARCHITECTURES 115 pump isentropic efficiency found in literature typically ranges between 0.6 [11, 12] to 0.8 [13]. A certain amount of subcooling is added to better comply with real life cycles. Condensers typically have a minimal flooding resulting in subcooling. In addition, subcooling is beneficial to avoid cavitation by the working fluid pump. However, the subcooling should be maintained low to achieve a high power output. When a liquid receiver is installed, the condensers are not flooded and the amount of subcooling is negligible if the receiver is well insulated. To avoid cavitation in the pump, a separate subcooler can then be installed to achieve an optimal degree of subcooling. Furthermore, in an actual subcritical organic Rankine cycle design a certain amount of superheating is included, since the control strategy is almost always based on a fixed superheating setpoint. Furthermore, the risk of wet vapour entering the turbine is decreased. For dry fluids, several authors [14–16] suggest to keep superheating low in order to increase the power output. Also an upper pressure limit of 0.9pcrit [17, 18] is imposed to avoid unstable operation in the supercritical region. For the TCORC, the vapour generator pressure is kept constant to a value of 1.12pcrit to ensure safe operation. The pump and turbine are modelled by their isentropic efficiency. The net power output is found by subtract- ing from the expander power the pumping power required to circulate the working fluid, the heat carrier fluid and the water in the condenser cooling loop. Extensive details on the performance evaluation criteria used can be found in Section 2.2.

5.3.2 Heat exchanger model

Both the condenser and evaporator are of the plate heat exchanger type. A plate heat exchanger consists of a bundle of pre-formed metal plates, which shapes the channels. Trough these channels, the cold and hot stream flows while transferring heat. A schematic layout of a plate heat exchanger is given in Figure 5.1. In the example given, the working fluid side consists of two passes with two paths and the hot fluid side consists of one pass with four paths. Welded plate heat exchangers are reported to operate up to 300 bar [19]. This type of heat exchanger is also used in the part-load validation experiments in Chapter 7. A picture can be found in Appendix C Section C.1.2. The fixed values to model the plate heat exchanger are given in Table 5.2. The values reported in Table 5.2 are generally accepted values for the design of plate heat exchangers [11, 20–23]. With plate heat exchangers, the range of these parameters are greatly restricted due to manufacturing limitations [22]. The plate thickness is typically between 0.4 mm and 1.2 mm and the corrugation depth between 1.5mm and 5.4 mm. These limitations therefore constrain the optimisation potential. Further optimisation [23] is still possible by varying the corrugation angle [24]. In this work it was chosen to compare different cycles using identical 116 CHAPTER 5 assumptions on the plate heat exchanger geometry.

Figure 5.1: Schematic layout of a plate heat exchanger with two passes.

Variable Description Value

Dh (m) Hydraulic diameter 0.0035 t (m) Plate thickness 0.0005 β (°) Chevron angle 45 k (W/m.K) Plate thermal conductivity 13.56 pco (m) Corrugation pitch 0.007

Table 5.2: Geometrical design parameters of the plate heat exchangers.

The model is discussed here for the evaporator, but is analogous for the condenser. A distributed modelling approach is applied. The heat exchanger is divided into three zones: pre-heating, evaporating and superheating. In the pre-heating section the ﬂuid is heated to saturated vapour, afterwards it evaporates in the evaporation section and ﬁnally superheats in the superheating section. The evaporating zone, or the vapour generating zone in case of the TCORC, is further divided into I segments. The discritisation is similar to that in Figure 4.2 from Chapter 4. For the SCORC the evaporating zone is divided in I = 20 segments, while in the case of the TCORC the vapour generator is segmented in I = 60 segments. For these values, the net power output, resulting from the full cycle model, changes less than 0.01% when doubling the number of segments. The key equations of the model are shortly explained. Details about the build up of the model can be found in Section 6.3 of Chapter 6. Originally the modelling was done in Engineering Equation Solver (EES) [25]. These models were later ported to MATLAB, resulting in a more robust model with a modular structure. The results reported in this chapter come from the initial EES program. First, the Log Mean Temperature (LMTD) method [26] is applied to each of the segments to calculate the required heat transfer area: THERMO-ECONOMIC PERFORMANCE EVALUATION OF ORGANIC RANKINECYCLE ARCHITECTURES 117

Q˙ i = ∆TLMT DFUiAi (5.1) With A the heat transfer area, F the configuration correction factor and U the overall heat transfer coefficient. The value of F can be found from correlations [26] when knowing the flow arrangement. In later models, the LMTD method is replaced with the P-NTU method. This provides identical results but is more robust for numerical calculations, see also Chapter 6. The LMTD temperature difference is given as:

∆TA − ∆TB ∆TLMT D = (5.2) ln∆TA − ln∆TB

With ∆TA and ∆TB the temperature differences between the two streams at different ends of the heat exchanger. The overall heat transfer coefﬁcient U is given as:

1 1 1 = + + t/k (5.3) Ui αhf,i αwf,i With α the convective heat transfer coefﬁcients, t the plate thickness and k the thermal conductivity of the plate. The correlations to determine α are given in Section 6.3.3. Finally, the energy balance requires that:

Q˙ i =m ˙ wf (hwf,i+1 − hwf,i) =m ˙ hf (hhf,i+1 − hhf,i) (5.4) There is furthermore a relation between the number of paths and passes of the plate heat exchanger. When neglecting end plate effects, the product of number of passes (N) and paths (K) can be assumed equal for both sides [22]:

Nevap,wf .Kevap,wf = Nevap,hf .Kevap,hf (5.5)

5.3.3 Cost models The cost correlations are based on the exponential scaling law and are taken from Turton et al. [28]. Cost estimates performed with equipment cost correlations are classiﬁed as ’preliminary’ or ’study’ estimates, which gives accuracies in the range of +40% to -25% [28]. Data, from a survey of manufacturers during the period of May 2001 to September 2001, was ﬁtted to the following correlation:

0 2 log10(CPEC ) = K1 + K2 log10(B) + K3(log10(B)) (5.6) 118 CHAPTER 5 lcrclgnrtr[7 1.5 1.5 ------[27] generator Electrical pump motor Electrical up (centrifugal) Pumps ubn 3.5 ------(centrifugal) Pumps Turbine exchangers heat Plate Component ( area transfer Heat exchanger heat Plate Component ubn li oe k)227 .95-.681010 (kW) 100-1500 (kW) (kW) 1-300 75-2600 -0.1618 -0.1798 1.4965 0.1538 2.2476 1.4191 0.0536 2.4604 (kW) 3.3892 power Fluid (kW) (kW) power power Shaft Shaft (kW) power Shaft [27] generator Electrical pump drive Electrical (centrifugal) Pumps Turbine p 10 ( p bar ( p < bar ) al .:Pesr atr aeilfco n aemdl otb utne l [28]. al. et Turton by cost module bare and factor material factor, Pressure 5.4: Table K B ( < ) bar < 10 ) 19 < 100 .913 - 1 0 0 0 1.35 1.89 .913 033 .97-.02 - 1 -0.00226 0.3957 -0.3935 1.35 1.89 .612 - 1 0 0 0 1.21 0.96 al .:Cs aaeesb utne l [28]. al. et Turton by parameters Cost 5.3: Table B 1 m 2 .66-.57014 010 ( 10-1000 0.1547 -0.1557 4.6656 ) B 2 C EC P 0 1 C 1850000 = 1 K 2 C . 2 ( P/ 11800) K C 3 3 0 . 94 F m ai range Valid F BM m 2 ) THERMO-ECONOMIC PERFORMANCE EVALUATION OF ORGANIC RANKINECYCLE ARCHITECTURES 119

B is the capacity or size parameters, K1, K2 and K3 are parameters of the curve ﬁtting. For heat exchangers, B corresponds to the heat transfer area, while for pumps and turbines this corresponds with respectively the power input and output. These correlations were derived for a general Chemical Engineering Plant Cost Index (CEPCI) of 397. A multiplication with (CPCI2001/CPCI2013) is made to actualise the cost. The CPCI2013 is set to the value of August 2013 (564.7). The cost functions are provided in dollar. To convert the values to euro, a conversion factor of 0.731 (19/12/2013) is taken into account. Correction factors Fp and Fm take into account the operating pressure and type of material used. Fp is calculated by:

2 log10(Fp) = C1 + C2 log10(p) + C3(log10(p)) (5.7)

with p the pressure in bar. The coefﬁcients for the different components are given in Table 5.3 and Table 5.4. For plate heat exchangers, with pressures higher than 19 bar, no pressure correction factor is available. This could however increase the cost of the heat exchangers for the TCORC. The bare module cost takes into account direct (installation of equipment, piping, instrumentation and controls) and indirect costs (engineering and supervision, transportation):

0 CBM = CPEC FBM (5.8)

With FBM the bare module factor:

FBM = B1 + B2FpFm (5.9)

For some components the bare module factor is directly given. The total module cost additionally includes contingency costs and fees, here taken as respectively 15% and 3% according to Turton et al. [28]:

CTM = 1.18(CBM,c + CBM,e + CBM,turbine+

CBM,pump,wf + CBM,pump,hf + CBM,pump,cf + CBM,generator) (5.10)

The grass roots cost includes the costs for construction and site preparation. These costs are highly dependent on the speciﬁc site; here the proposed values by Turton et al. [28] were followed:

X 0 CGR = CTM + 0.5 CBM (5.11) components 120 CHAPTER 5

0 CBM is the bare module cost at base conditions (Fp = 1, Fm = 1). The speciﬁc investment cost (SIC) is in this work deﬁned as:

C SIC = GR (5.12) W˙ net

5.3.4 Working fluid selection The working fluid selected for this case must be able to give an acceptable expander design which can comply with the isentropic efficiency imposed. There- fore, R245fa is taken as reference working fluid for the SCORC and TCORC due to its de facto standard use in commercial ORC installations [3, 29]. Furthermore, R245fa has proven itself for various expander designs, either volumetric [6, 30] or turbine [31–34] technology. In Chapter 4, R245fa is flagged as the working fluid with the highest ηII for both the SCORC and TCORC under Thf,in = 200 °C. The selected working fluid is not necessarily the best for the investigated case, but provides a good benchmark for further study and comparison. The thermophysical data is taken from Engineering Equation Solver (EES) [25].

Density 0.1% (liquid phase, < 400 K and < 30 MPa) 0.2% (liquid phase, > 310 K and > 30 MPa) 1% (liquid phase, < 310 K and > 30 MPa) 1% (vapour phase, > 400 K)

Vapour pressure 0.2% (> 250 K) 0.35% (> 370 K)

Liquid phase heat 5% capacity

Table 5.5: Uncertainty for R245fa fundamental equation of state. [35]

EES implements the Fundamental Equations of State for R245fa presented by Lemmon and Span [35]. These correlations were derived in view of advanced technical applications for which very low uncertainties are not required [35]. The same Fundamental equations of State are found in REFPROP 9.1 [36]. Uncertainty data is provided in Table 5.5. In EES, the transport properties were obtained from the documentation provided by Honeywell. There is no information available on the uncertainty of these correlations. As such, caution should be taken when using EES for the ﬁnal design iteration. In REFPROP 9.1 [36] the viscosity and thermal conductivity are respectively derived from a correlation proposed by Huber et al. [37] and Marsh et al. [38]. In contrast to EES, uncertainty information is available in REFPROP 9.1 for the transport properties. THERMO-ECONOMIC PERFORMANCE EVALUATION OF ORGANIC RANKINECYCLE ARCHITECTURES 121 5.3.5 Expander considerations

To assess the feasibility of the fixed turbine isentropic efficiency given in Table 5.1, two expander evaluation criteria are used: the size parameter (SP ) and the volume ratio (VR). Both where introduced in section 2.2.3. In order to have an acceptable isentropic efficiency, these parameters should be constrained to a specific range. For a single stage machine, volume ratios lower than 50 are needed to get isentropic efficiencies in the range of 0.7 to 0.8 [39]. The SP values must range between 0.2 m and 1 m to limit the impact on the isentropic efficiency [39]. This will be verified when analysing the results of the optimisation.

5.4 Optimisation strategy

A multi-objective optimisation scheme with the optimisation variables from Table 5.6 is set up. The number of passes always relates to the side with the lowest mass ﬂow rate in order to balance pressure drops and heat transfer coefﬁcients [40]. The limits used have been chosen based on values found in literature [21, 23, 41]. The value range is chosen wide enough in order not to constrain the optimisation around the point of minimum SIC. The variables in the optimisation process affect the sizing and the power output of the cycle. They are however not directly constrained by manufacturing limitations. Manufacturing constraints are taken into account, as discussed above, trough the careful choice of parameters from Table 5.1 and Table 5.2.

Variable Description Lower Upper 2 Gcond,wf (kg/m .s) Mass flux working fluid condenser 20 100 2 1 1 Gevap,wf (kg/m .s) Mass flux working fluid evaporator 20 100 20 2 200 2 ∆TP P,cond (°C) PP temperature difference condenser 3 10 ∆TP P,evap (°C) PP temperature difference evaporator 3 10 Tcond (°C) Saturation temperature condenser 35 50 Tevap (°C) Saturation temperature evaporator 100 148.5 Texp,in (°C) Turbine inlet temperature 150 175 Nevap (-) Number of passes evaporator 1 3 Ncond (-) Number of passes condenser 1 3 1 For the SCORC 2 For the TCORC Table 5.6: Decision variables and their range for the thermo-economic optimisation. A genetic algorithm optimises two objective functions simultaneously. In this work this is W˙ net and Cinv. The benefit of working with a genetic algorithm 122 CHAPTER 5 includes searching for the global optimum while avoiding complex derivatives. An initial population of parameters is generated in the search area. The solutions are afterwards assessed, based on the objective criteria. The fittest are selected to construct a new population based on crossover and mutation operations [42]. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) was used in this work [42, 43]. The parameter settings of the genetic algorithm are provided in Ta- ble 5.7. A population of 120 can be considered a good default value for this type of optimisation. In other works population sizes of 40 [44], 30 [45, 46], 100 [47, 48] and 150 [49] are employed. A population size of 200 was also considered, but the changes on the Pareto front were marginal at the cost of doubling the calculation time. The optimisation was done in MATLAB [50] with the EES [25] models coupled by the Dynamic Data Exchange (DDE) protocol. Under the given parameters and assumptions the calculation time is approximately 6 hours on an E5-2736 v2 Intel processor. Due to limitations of the DDE protocol only a single core could be used.

Parameter Value Generations 50 Population size 120 Crossover rate 0.8 Migration rate 0.2 Mutation type Gaussian (shrink = 1, scale =1)

Table 5.7: Parameter settings of the genetic optimisation algorithm.

5.5 Speciﬁc investment costs of the Pareto front

The resulting SIC of the Pareto front as a function of the net power output are plotted in Figure 5.2 and Figure 5.3 for respectively the SCORC and TCORC. The approximate point of minimum SIC is visualised by a black rectangle. This black rectangle is also shown in Figure 5.4 to Figure 5.9. The corresponding optimised design parameters for the point of minimum SIC are given in Table 5.8. W˙ net,SIC is the net power output corresponding with the point of minimum SIC. With R245fa as working fluid, Quillin et al. [11] estimated the SIC at 2700 C/kWe for a 5 kWe ORC. Schuster et al. [51] made the assumption of a specific investment cost of 3755 C/kWe. Rettig et al. [52] compiled data of specific investment costs available from case studies and quotes from manufacturers. They showed that for ORC’s designed below 500 kWe the SIC rapidly increases. For 500 kWe and 250 kWe the SIC is respectively around 2250 C/kWe and 3000 C/kWe. In this work, the values of the SIC are higher, the reason is that the grass roots costs are used. THERMO-ECONOMIC PERFORMANCE EVALUATION OF ORGANIC RANKINECYCLE ARCHITECTURES 123

These costs additionally take into account the cost for integration, these are taken as 50% of the total component costs. The integration costs vary strongly from site to site but are known to be an important factor [53]. Removing this cost gives values of the SIC in the same range as in the cited papers.

4800 4800

4700 4700

4600 4600

4500 4500

4400 4400

4300 4300

4200 4200

4100 4100 550 600 650 700 750 800 . W [kW] net

Figure 5.2: SIC of the Pareto front versus net power output for the SCORC.

8500 8500

8000 8000

7500 7500

7000 7000

6500 6500

6000 6000

5500 5500

5000 5000 200 400 600 800 1000 1200 . W [kW] net

Figure 5.3: SIC of the Pareto front versus net power output for the TCORC.

It is clear that around W˙ net,SIC the SIC is not very sensitive to the net power output generated by the system and this for both the SCORC and TCORC. For in- 124 CHAPTER 5

Variable Minimum SIC Maximum W˙ net SCORC TCORC SCORC TCORC W˙ net,SIC (kWe) 681.8 681.3 791.5 1040 ηth (%) 10.47 11.20 10.90 11.10 ∆TP P,evap (°C) 5.9 8.2 3 3 ∆TP P,cond (°C) 8.0 7.0 3 3 Tevap (°C) 128.8 - 124.5 - Tcond (°C) 41.1 39.85 35.2 37.0 Texp,in (°C) 128.8 161.6 124.5 160.0 CGR (kC) 2805 3436 3725 8162 SIC (C/kWe) 4114 5044 4707 8137 2 Aevap (m ) 258 879 418 1205 2 Acond (m ) 398 385 888 756 Nevap (-) 2 2 2 2 Ncond (-) 2 2 2 2 m˙ wf (kg/s) 28.5 26.7 28.9 40.5 m˙ cf (kg/s) 205.30 150 217 255.0 2 Gevap,wf (kg/s.m ) 91.0 187 70.3 175.0 2 Gcond,wf (kg/s.m ) 54.0 53.5 22.4 46.1

Table 5.8: Results of minimum SIC and maximum W˙ net.

creasing W˙ net the SIC rises sharply for both the SCORC (W˙ net= 782.9 kW, SIC = 4482 C/kWe) and TCORC (W˙ net = 771.6 kW, SIC = 5463 C/kWe). While for decreasing W˙ net the SIC increases only gradually for the both the SCORC (W˙ net= 582.5 kW, SIC = 4176 C/kWe) and TCORC (W˙ net = 574 kW, SIC = 5187 C/kWe). The physical explanation is given in the Section 5.5.1 by investigating the resulting parameter space from the optimisation.

The point of W˙ net,SIC is almost equal for both cycles. In this point the TCORC has a higher thermal efficiency but also an increased heat transfer area for the vapour generator. The result is an increase in SIC of 22%. Interesting to note is that the resulting optimisation of the condenser side is almost identical for both cycles. Furthermore, the TCORC has the benefit of achieving higher net power output when solely optimising for maximum power output, see Table 5.8. As expected the maximum power output is found for the lower boundary on the pinch point temperature difference. However this is not necessarily true for the condensation saturation temperature as the auxiliary power for pumping the cooling fluid is taken into account. The maximum power output of the TCORC amounts to 1040 kW compared to 791.5 kW for the SCORC. This is a power increase up to 31.5%. However, this also comes with an increased SIC of 72.8%. THERMO-ECONOMIC PERFORMANCE EVALUATION OF ORGANIC RANKINECYCLE ARCHITECTURES 125 5.5.1 Analysis of the parameter space

In this paragraph, the parameter space resulting from the multi-objective optimisation is analysed. The different designs on the SIC of the Pareto front versus net power output are shown in terms of the design parameters. First the SCORC is discussed followed by the TCORC. The effect of the pinch point temperature difference on the SCORC is visualised in Figure 5.4. Around the point of minimum SIC the pinch point temperature difference of the evaporator ∆TP P,evap is relatively constant. However, the SIC increases sharply when ∆TP P,evap gets lower than 5 °C. This is explained by the large increase in heat surface area of the evaporator and the major share of the evaporator cost (see also Figure 5.12, which is discussed in section 5.5.3). A decrease in ∆TP P,evap thus directly results in a higher net power output, see Figure 5.5. However the increase in power does not offset the increase in investment cost. This also explains the sharp increase in SIC seen in Figure 5.2. The pinch point temperature difference of the condenser ∆TP P,cond is almost constant around the point of minimum SIC. For the condenser the sharp increase in SIC is noticeable starting from ∆TP P,cond = 4 °C. From Figure 5.5 follows that for increasing power output after the point W˙ net = 740 kW it is necessary to drastically decrease ∆TP P,cond. Before, this parameter remained almost unchanged. This indicates that from W˙ net = 740 kW a decreased ∆TP P,cond leads to a power increase with the lowest associated cost compared to the other optimisation parameters. The effect of the evaporation temperature and condensation temperature is shown in Figure 5.6. Between Tevap = 126.3 °C (SIC = 4139 C/kWh) and Tevap = 132.3 (SIC = 4132 C/kWh) the variation on the SIC is marginal, see Figure 5.6. This indicates that Tevap is not a sensitive factor in the optimisation process. In contrast, for Tcond there is a clear extremum visible at Tcond = 40 °C. Devia- tions around this point have a significant effect on the SIC. For changes in Tcond, not only the required heat transfer surface changes but also the required cooling water flow rate and thus auxiliary power. Overall, the results of the optimisation imply a large dependency between the parameters mutually and their objective functions. Furthermore, different parameters become dominant depending on the investigated point on the Pareto front. Analogous figures are made for the TCORC. In Figure 5.8 the effect of ∆TP P,evap and ∆TP P,cond on the SIC is shown for the TCORC. The clear relation found for the SCORC is not observed here. Low pinch points can lead to high specific investment costs but this is clearly not the dominant parameter in the optimisation. The effect of a low pinch point temperature difference on the SIC can plainly be offset by changing other parameters. The same trend is visible in Figure 5.9 for ∆TP P,evap and ∆TP P,cond as a function of W˙ net. The dominant factor in the optimisation is the temperature Texp,in and the condensation temperature Tcond. Both show clear extrema as a function of the SIC as shown in Figure 5.7. 126 CHAPTER 5

[°C] PP,evap 4100 4200 4300 4400 4500 4600 4700 4800 10 4 5 6 7 8 9 550 iue55 ic on eprtr ifrne safnto of function a as differences temperature point Pinch 5.5: Figure 4 iue54 ic on eprtr ifrne safnto of function a as differences temperature point Pinch 5.4: Figure 5 600 6 650 PP,evap W 7 . net [°C] [kW] 8 700 9 750 10 4100 4200 4300 4400 4500 4600 4700 4800 800

[°C] PP,cond 4100 4200 4300 4400 4500 4600 4700 4800 10 3 4 5 6 7 8 9 550 3 4 600 5 6 650 PP,cond W SIC ˙ W . net net [°C] 7 [kW] o h SCORC. the for o h SCORC. the for 700 8 9 750 10 4100 4200 4300 4400 4500 4600 4700 4800 800 THERMO-ECONOMIC PERFORMANCE EVALUATION OF ORGANIC RANKINECYCLE ARCHITECTURES 127 4800 4700 4600 4500 4400 4300 4200 4100 8500 8000 7500 7000 6500 6000 5500 5000 50 46 44 for the TCORC. for the SCORC. 45 42 SIC SIC [°C] [°C] cond cond T T 40 40 38 36 35 8500 8000 7500 7000 6500 6000 5500 5000 4800 4700 4600 4500 4400 4300 4200 4100 4800 4700 4600 4500 4400 4300 4200 4100 8500 8000 7500 7000 6500 6000 5500 5000 134 175 132 170 130 [°C] [°C] 165 evap exp,in T T 128 160 126 155 124 8500 8000 7500 7000 6500 6000 5500 5000 4800 4700 4600 4500 4400 4300 4200 4100 Figure 5.6: Condensing and evaporating temperatures as a function of Figure 5.7: Condensing and turbine inlet temperatures as a function of 128 CHAPTER 5

T [°C]

PP,evap 5000 5500 6000 6500 7000 7500 8000 8500 10 4 5 6 7 8 9 300 iue59 ic on eprtr ifrne safnto of function a as differences temperature point Pinch 5.9: Figure iue58 ic on eprtr ifrne safnto of function a as differences temperature point Pinch 5.8: Figure 4 400 5 500 6 600 PP,evap W 7 . net 700 [°C] [kW] 8 800 9 900 1000 10 5000 5500 6000 6500 7000 7500 8000 8500 1100

[°C]

PP,cond 5000 5500 6000 6500 7000 7500 8000 8500 4.5 5.5 6.5 7.5 8.5 9.5 5 6 7 8 9 300 4 400 5 500 6 600 PP,cond W SIC ˙ 7 W . net net 700 [°C] [°C] o h TCORC. the for o h TCORC. the for 8 800 9 900 1000 10 1100 5000 5500 6000 6500 7000 7500 8000 8500 THERMO-ECONOMIC PERFORMANCE EVALUATION OF ORGANIC RANKINECYCLE ARCHITECTURES 129 5.5.2 Turbine performance parameters

Both the SP and VR are plotted in Figure 5.10 and Figure 5.11 for respectively the SCORC and TCORC. Considering the discussion in Section 5.3.1, the fixed isentropic efficiency of 0.7 is deemed realistic, while higher isentropic efficiencies are clearly attainable. For both cycle types, the VR is consistently lower than 50, with the TCORC exhibiting the largest VR. For increased VR an increase in power output is noted. The size parameter becomes lower than 0.2 m for the TCORC. However the SP has a lower influence on the isentropic efficiency then the VR. Furthermore a conservative value of the isentropic efficiency was used.

0.034 800

750 0.032 700 [kW] net

SP [m] . 650 W 0.03 600

0.028 550 8 9 10 11 12 13 VR [-]

Figure 5.10: Turbine performance parameters SP and VR for the SCORC.

0.022 1000

0.02 800 0.018 [kW]

600 net SP [m] 0.016 . W 0.014 400

0.012 20 25 30 35 40 45 VR [-]

Figure 5.11: Turbine performance parameters SP and VR for the TCORC.

5.5.3 Distribution of the costs

Identifying the distribution of the costs is a primary step in determining the focus for further optimisation and development. Figure 5.12 shows the partition of the costs at minimum SIC for the SCORC while Figure 5.13 shows it for the TCORC. The distribution of the cost for the SCORC is in line with previous re- 130 CHAPTER 5 search done by the author [54]. For the SCORC the turbine amounts for the largest cost, followed by the condenser and evaporator. The sum of the generator, drives and pumps results in the lowest share of costs. In contrast, the vapour generator of the TCORC amounts for the largest cost followed by the turbine and condenser. Thus for the SCORC it is reasonable to consider the turbine a key component for further development. While for TCORC the vapour generator is the critical part, followed by the turbine.

Pumps 4% Drives 3% Evaporator 24%

Turbine 35%

Condenser 25%

Generator 9%

Figure 5.12: Distribution of the cost at minimum SIC for the SCORC.

Pumps 4% Drives 3% Vapour generator 43%

Turbine 26%

Generator 7%

Condenser 17%

Figure 5.13: Distribution of the cost at minimum SIC for the TCORC.

5.6 Financial analysis and appraisal

The SIC of the Pareto fronts from Figure 5.2 and Figure 5.3 can be effectively used as input for the ﬁnancial appraisal. As this is a post-processing step, no new design calculations are required. As such, several scenarios can be quickly THERMO-ECONOMIC PERFORMANCE EVALUATION OF ORGANIC RANKINECYCLE ARCHITECTURES 131 evaluated. The calculation time is less than 5 seconds. These Pareto fronts could also be directly used as input for decision makers. The complexity of the design model is thus avoided in this phase.

Parameter Value ORC lifetime (y) 20 discount rate (%) 6 production hours (h/y) 8000 price electricity (C/MWh) 69.6 increase electricity price (%/y) 0.50 maintenance cost (Cmaintenance/CTM) 0.02

Table 5.9: Assumptions for the NPV calculations.

A workshop [55] was organised between ORC manufacturers and end-users to verify the parameters of the NPV calculation listed in Table 5.9. The presented values are based on the market situation of Flanders, Belgium in 2013. The results of the NPV calculation are given in Table 5.10 for both the point of minimum SIC and maximum NPV . All points show a positive NPV value which means they would be cost-effective under the current assumptions. The simple payback period does not represent the best criterion for financial decision making, but is often used in practice and shown here for the sake of completeness. For the presented case the SCORC is flagged as the cycle of choice. The SCORC has an NPV which is 786 kC higher than the NPV of the TCORC. Furthermore, the payback time is roughly 2 years less than for the TCORC. Furthermore, the point of minimum SIC does not necessarily result in maximum NPV . For the SCORC an ORC with a net power output 7.3% larger than W˙ net,SIC provides an increase of the NPV of 5.2%. This is directly related to the cash flow shown in Figure 5.14. A higher investment cost with an associated higher power output can lead in the long term to higher profits. A lower SIC on the other hand obviously always leads to a lower payback time. For the TCORC, even in the long term, a higher power output than W˙ net,SIC does not result in improved NPV due to the very large increase in SIC (see Figure 5.3). The presented results are only valid under the assumptions presented here and for this specific case. This analysis provides by no means a general conclusion about the profitability of the TCORC or SCORC. Using another working fluid, changing the type of waste heat carrier or changing the cost structure could result in different conclusions. Also, installation of these systems in practice may induce different additional costs related to i.a. installation, contractor’s fees and contingencies. The aim of this analysis is to introduce the optimisation framework. 132 CHAPTER 5

Case W˙ net (kW) SIC (C/kWe) NPV (kC) Payback time (y) SCORC min. SIC 681.8 4114 1070 8.46 max. NPV 731.3 4138 1126 8.52 TCORC min. SIC 681.3 5044 284 10.70 max. NPV 681.3 5044 284 10.70

Table 5.10: Results of the NPV calculations.

5000 4000 3000 2000 1000 0

-1000 min. SIC SCORC -2000 max. NPV SCORC Cumulative cashflow ( k€ ) min. SIC TCORC -3000 -4000 1 3 5 7 9 11 13 15 17 19 years (y)

Figure 5.14: Cumulative cash ﬂow for minimum SIC of the SCORC, minimum SIC of the TCORC and maximum NPV of the SCORC.

5.7 Conclusions

In this chapter a novel framework for designing optimised ORC systems is proposed based on a multi-objective optimisation scheme in combination with ﬁnan- cial appraisal in a post-processing step. This novel way of optimising and interpreting results was applied to an incinerator waste heat recovery case. Both the SCORC and TCORC are investigated and compared using the suggested optimisation strategy. The conclusions are summarised below. The TCORC provides a 31.5% increase in net power output over the subcritical ORC but with an increased SIC of 72.8%. When comparing both the SCORC and TCORC at minimum SIC the net power output is almost equal. However, the SIC for the TCORC is increased by 22%. The SIC for the SCORC is highly sensitive to variations in the pinch point temperature difference and the condensation temperature. For the TCORC on the other hand, the value of the pinch point temperature difference is less inﬂuential. THERMO-ECONOMIC PERFORMANCE EVALUATION OF ORGANIC RANKINECYCLE ARCHITECTURES 133

For the TCORC, the turbine inlet temperature and the condensation temperature are the factors with the highest sensitivity on the SIC. For the SCORC the turbine amounts to the highest cost (35%), whereas for the TCORC this is the vapour generator (43%). This shows the high importance of the vapour generator design. In the ﬁnancial appraisal, the SCORC clearly outperforms the TCORC. Fur- thermore, even though the minimum SIC leads to the lowest payback time, this does not necessarily lead to the highest NPV . For the SCORC an ORC with a net power output 7.3% larger than the net power output at minimum SIC provides an increased NPV of 5.2%. The given results are only valid for the case and assumptions presented in this study. They do not count as general recommendations for cycle architectures. Other boundary conditions and working ﬂuid combinations will give different results. The optimisation framework however can still be used. At this point the inclusion of the part-load operation is missing, this topic is tackled in Chapters 6 and 7. 134 CHAPTER 5

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Part-load operation of organic Rankine cycle heat engines

6 Part-load modelling of the organic Rankine cycle heat engine

6.1 Introduction

Before analysing the part-load performance of ORCs, the part-load models are ﬁrst extensively discussed in this section. Validation of the component and cycle part-load performance is done in Chapter 7. Besides explaining the modelling choices and equations, the focus is on the actual implementation in MATLAB [1] and the solver strategy. The implementation details and modelling choices are decisive to have models with a low computational load that are robust and modular. This is important when executing optimisation problems. Robust and modular models further ensure the usefulness in future research and industrial projects. An important programming effort has thus been made to make sure that the code is:

• robust and fast, this is achieved by selecting an advantageous set of independent parameters, vectorization of the code and reduction of temporary variables and intermediate calculations.

• reused as much as possible, in this view the object-oriented programming paradigm was chosen. This not only reduces the programming effort but also reduces the risk of user errors.

• modular in the sense that different heat exchanger topologies, expanders and pumps can be investigated. Again, the beneﬁts of the object-oriented 142 CHAPTER 6

programming paradigm are exploited to implement this.

6.2 Modelling approach 6.2.1 The object-oriented paradigm Object-oriented programming allows to modularise the code based on re-occurring patterns. This programming paradigm was introduced in MATLAB [1] version 5.0 (1997) and completely revised in version 7.6 (2008). The object refers to a data structure which contains data (attributes) and code (methods). Objects can be seen as variables with an inherent internal structure. Thus objects can be manipulated in much the same way as variables of any programming language. The attributes and methods are deﬁned in a class, this is essentially a blueprint of the object. Methods and attributes from one class can be reused as initial blueprint for another class. This is called inheritance. Instances of the class are called objects. The power of object-oriented programming lies in the interaction between different objects and classes. This interaction and the structure of the classes can easily be visualised with the help of Uniﬁed Modelling Language (UML) diagrams. For the interested reader, more information about object-oriented programming and UML is found in the book of Register [2]. Finally, note that the actual implementation discussed in this chapter is easily portable to other programming languages that support object- oriented programming.

6.2.2 Levels of modelling detail Based on the purpose of the models, different levels of modelling detail is needed. In general, component models can be categorised in three groups: black box, grey box and white box models. In the black box models the characterising model outputs are set by a rule of thumb or are determined from experiments. Simple data regression directly relates the model inputs with the model outputs. A black- box approach is thus advantageous because of its fast calculation speed. A major drawback is that extrapolation to other operating or boundary conditions is not advisable. At the other side of the spectrum are white box models. These models are based on physical laws without any specific empirical dependency. These detailed models permit to perfectly optimise the component design. However, resolving each influence of geometry and operating conditions requires a computationally expensive model. Between these categories are the grey box models. These models are physics-based but are combined with empirical calibration. As expected, the benefits and drawbacks are situated between these of black and white box models. In this work, the calculation time is of importance due to the cost of optimisation. Furthermore the models should be scalable to different operating conditions and component sizes. In view of this, grey box models are the most suitable. PART-LOADMODELLINGOFTHEORGANIC RANKINE CYCLE HEAT ENGINE 143

6.3 Heat exchangers

First, the heat exchanger model is elaborated. The model developed is a hybrid between the finite volume and the moving boundary (i.e. three zone) models seen in literature. The main benefit of the moving boundary model is the fast calculation time, while the finite volume models shows increased accuracy at the expensive of increased computational time.

6.3.1 Finite volume, moving boundary and hybrid model In the moving boundary model, three zones are defined according to the state of the refrigerant: single phase liquid, two-phase liquid-vapour, single phase vapour. For a given geometry and inlet condition, the required heat exchange area for each zone is calculated. The outlet conditions follow from the equality of the calculated and the real heat exchange area in an iterative solving process (Aactual = AzoneI +AzoneII +AzoneIII ). The idea is that each zone can be adequately modelled with a set of lumped parameters. This assumption has been proven valid for heat exchangers used in various systems. Costa and Parise [3] report heat flow deviations less than 8.7% from the experimental results for complex air cooled condenser coils in air conditioning applications. Bansal and Tedford [4] implemented three zone heat exchangers in their model of a chiller plant, the outlet temperature deviations are predicted to within ± 5% compared to the experimental results. Cuevas et al. [5] presented an extensive validation of the pressure drop computed from the of the three zone model of a condenser. Their model is able to predict with a probability of 95% the condenser supply pressure within a confidence in- terval of +0.5 and −0.1 bar. Quoilin et al. [6] presented experimental results of an ORC using a scroll expander. Their result shows that the exhaust temperature is predicted with a maximum absolute error of 7 K, this corresponds to the prediction of the heat flux with an error of 2.5%. In the finite volume model, the heat exchange area is divided into a given number of equal volume parts. For each of these volumes the heat flow is calculated. Each volume consists of one zone, if there is a transition in the volume this introduces an error. A sufficient number of equal volume parts is thus necessary to reduce this error. Qiao et al. [7] developed a finite volume steady-state model of plate heat exchangers considering generalised flow configurations including phase- change on both sides. Three experimental cases were investigated. For the water- to-water case, the error of the heat load was within 2% while for the cases water- to-ammonia boiling and water-to-R22 boiling, the error of the heat load was within 5%. For all the cases, the discritisation was made on 15 elements. The finite volume steady state modelling approach is not frequently used. Yet, when modelling supercritical heat exchangers the assumption of a single supercritical zone would lead to large discrepancies. In this instance, the finite volume steady-state model is 144 CHAPTER 6 required [8, 9]. However experimental validations under supercritical conditions are according to the author’s knowledge not available in literature.

hsec,in ṁsec,in Segment (i+1)

hprim,in ṁprim,in Pass 1 Transition (i+1) Pass 2

Pass 3 Transition (i+1) hprim,out ṁprim,out Pass 4

hsec,out ṁsec,out

Figure 6.1: Outline of the hybrid discretisation approach for modelling the heat exchangers.

The presented hybrid model in this work is a combination of the finite volume and the moving boundary model. The heat exchanger is first discretised in a fixed set of volumetric segments. However, if a phase transition is detected during calculation of the heat transfer, additional segments are inserted. A visual representation of a four pass heat exchanger, subdivided in three segments per pass and with two transitions is given in Figure 6.1. The actual heat flow and the distribution of the mass flow rates between segments and passes are defined in the program. This is accomplished with a set of connection equations that are modularly defined on top of the main algorithm. The actual implementation is stated in the next section.

6.3.2 Implementation

The structure of the heat exchanger program can easily be derived from the UML class diagram given in Figure 6.2. There are four main classes: HEX, Geometry, FluidStruct and HeatPressureCorrelation. The Geometry class defines the geometrical structure of the heat exchanger. The HeatPressureCorrelation class acts as a parent class for all the convective heat transfer and pressure drop correlations. The FluidStruct class is essentially a data container with all the information of a fluid stream. This includes temperatures, pressures, mass flow rates and the fluid name. The HEX class is the main PART-LOADMODELLINGOFTHEORGANIC RANKINE CYCLE HEAT ENGINE 145 ) ) ) ) varargin varargin , , int int : : varargin varargin , , Tbulk int Tbulk int : : , , int int : : G G Tbulk Tbulk , , , , int int int int : : : : G G , , HeatPressureCorrelation [*] : int int : HeatPressureCorrelation : : int : [*] pressure pressure ( ( string int : [*] : [*] [*] int int pressure : int pressure : : ( ( name enthalpy Q m p singlephase twophase + + + + + + + FluidStruct lengthScales calculateAlpha calculatePdrop # + + HeatPressureCorrelation calculateAlpha calculatePdrop + + Han Wang Gnielinski Martin ... int ): int : ) pFractionExt , int int : ): int ): int : FluidStruct int : : int Cprim ): int , Cprim pFractionInt ): , int secFluid , : int , : int int : int : : int UA ): , UA , int int : : int index int , R ): : int , R FluidStruct out ): : int int , pFractionExt _ : : int , h : int pFractionExt : int , , : int : int int : : index in , index _ primFluid , index nextIndex h , ( int , , : index void int ( pFractionExt Q : ( int int , (): int int : : Q pFractionExt ( ): ): , int : int int int : : : int Geometry R R : ): , , void index Figure 6.2: UML class diagram of the classes associated to the heat exchanger. ( int int : int int : index nextPhase Geometry : : WFstruct ( : ( : P (...): WFstruct int ( pFractionExt : out ( _ NTU (..): ( h void geometry ( , ): int : geometry primFluid secFluid transitions HEX Solve initialize singlePhase twoPhase singlePhaseHeatTransfer twoPhaseHeatTransfer transition transitionSinglePhase transitionTwoPhase connectionEquations calcNTU calcP calcUA + + + # + + # # # # # # # # # # # # in string HEX _ : h , type int ( int int : ): ): int int : : R R , , int int int : : : int : P ( pFractionExt ( int : NTU int ( : Aprim Asec Aflowprim Aflowsec connectionEquations calcNTU calcP calcUA ... + + + + - # # # # Geometry PlateGeometry TubeFinGeometry ... TubeFinHEX PlateHEX ... 146 CHAPTER 6 component and consists of all the attributes and methods to calculate the performance of a heat exchanger. The actual interconnections between the segments and passes, the implementation of the P-NTU method [10] (see Section 6.3.3) and the calculation of the heat transfer area (A) multiplied with the overall heat transfer coefficient (U) depends on the heat exchanger type. Therefore four methods: con- nectionEquations, calcNTU, calcP and calcUA are classified as abstract. These methods can be used in the HEX class but need to be explicitly defined later on. This is done by making a new class which inherits the methods and attributes of the HEX class but also explicitly defines the implementation of these methods. Examples are the implementation of a plate heat exchanger (PlateHEX) and a tube and fin heat exchanger (TubeFinHEX). In addition, the HEX class needs objects from the FluidStruct and the Geometry class as input. The control flow cannot be seen from the UML class diagram, for this a flow- chart of the solver in the HEX class is presented in Figure 6.3. The depicted solver strategy is fully implemented in the HEX class. The solver calculates the heat transfer associated to the length of a single segment. This is repeated until there are no segments left. Note that it is possible that during the calculation a phase boundary is passed. If this is the case, the length associated to each zone is calculated. An additional intermediate segment is inserted and the heat transfer for the remaining area is then calculated as before. As shown in Figure 6.3, there are two main functions: the procedure to calculate the heat transfer and the procedure to determine the area of each phase under a phase transition. Both are calculated with the help of the P-NTU method [10]. The use of the P-NTU method has some direct benefits compared to other methods. Firstly, the calculation method does not depend on which fluid has the minimum heat capacity rate, as is the case in the -NTU method. If during part-load operation, the other fluid becomes the fluid with the minimum heat capacity rate, the same P-NTU relationship can be used. Secondly, the P-NTU method has the advantage that it is computationally more stable than the Log Mean Temperature (LMTD) method. The LMTD method has the risk that the sign of the log argument becomes negative. This gives an undefined function, resulting in an error of the numerical solver. First, the procedure to determine the heat transfer of a single segment, based on the P-NTU method is given. Assume in the next equations that the ORC working fluid corresponds with the primary fluid. Each segment has an inlet and an outlet side. These follow the direction of the iteration scheme, this is not necessarily the direction of the actual flow. The equation to calculate the heat transfer is given by:

Q˙ i = Cprim,iPprim,i(Tsec,in,i − Tprim,in,i)/(1 − Pprim,i) (6.1) with i iterating over the number of passes and segments, Cprim,i the heat capacity PART-LOADMODELLINGOFTHEORGANIC RANKINE CYCLE HEAT ENGINE 147

rate and Pprim,i the temperature effectiveness given by:

Tprim,out,i − Tprim,in,i Pprim,i = (6.2) Tsec,in,i − Tprim,in,i

Solve next segment

Set boundary conditions based on connection equations

[two-phase] [single-phase]

Inlet condition phase

Calculate heat Calculate heat Transition, calculate transfer based on transfer based on area available for two-phase single-phase single-phase correlations correlations

[single-phase] Transition, calculate area available for [two-phase] two-phase

[two-phase] [single-phase]

Outlet condition phase Outlet condition phase

[yes] [no]

iteration number = sum of segments + transitions

Figure 6.3: UML ﬂowchart of the heat exchanger solver.

The temperature effectiveness P is a function of the flow arrangement, the Number of Transfer Units (NTU) (Eq. 6.3) and the heat capacity ratio R (Eq. 6.4). Correlations for different flow configurations can be found in literature [10]. Correlations for parallel and counter-flow are given in Section 6.3.3.

UAprim,i NTUprim,i = (6.3) Cprim,i Cprim,i Rprim,i = (6.4) Csec,i Finally, the overall heat transfer coefficient U multiplied with the heat transfer area A needs to be calculated. For two fluids separated by a single wall this is computed 148 CHAPTER 6 as, 1 1 1 = + Rwall + (6.5) UAprim,i αprim,iAprim,i αsec,iAsec,i d Rwall = (6.6) kAm with Aprim,i and Asec,i the contact surface at respectively the primary and secondary side, αprim and αsec respectively the convective heat transfer coefficient at the primary and secondary side, Am the mean area over which conduction occurs, k the thermal conductivity and d the thickness of the wall. Next, to calculate the length until phase transition, an opposite scheme is used. Assume in this case that a transition occurs from a single-phase zone to a two- phase zone. First the heat transfer in the single phase zone is calculated up to the boundary with the two-phase zone:

Q˙ part,i = (hprim,transition,i − hprim,in,i)m ˙ prim,i (6.7)

Subsequently Ppart,prim,i is determined,

Q˙ part,i Ppart,prim,i = (6.8) (−Cprim,iTprim,in,i + Cprim,iTsec,in,i + Qpart,i) Now the NTU is a function of the flow arrangement, temperature effectiveness P and the heat capacity ratio R. Correlations for different flow configurations can again be found in literature [10]. As such the fraction UApart,prim,i is calculated as:

UApart,prim,i = NTUpart,prim,iCprim (6.9)

The relative part of the single phase region until the transition point is given by the ratio:

UApart,prim,i Lpart = (6.10) UAprim,i This general framework can be used to model several types of heat exchangers. The necessary closure equations for the plate heat exchangers that are used in this work are given in the next section. For the sake of completeness, the equations to model ﬁn and tube heat exchangers are given in Appendix D.

6.3.3 Plate heat exchangers 6.3.3.1 P-NTU correlations The P-NTU correlations used for modelling the plate heat exchanger are given below. PART-LOADMODELLINGOFTHEORGANIC RANKINE CYCLE HEAT ENGINE 149

For crossﬂow conﬁguration:

1 1 − RP NTU = log (6.11) 1 − R 1 − P 1 − exp[−NTU(1 − R)] P = (6.12) 1 − Rexp[−NTU(1 − R)]

For parallel ﬂow conﬁguration:

1 1 NTU = log (6.13) 1 + R 1 − P (1 + R) 1 − exp[−NTU(1 + R)] P = (6.14) 1 + R

6.3.3.2 Connection equations

For plate heat exchangers, the ﬂow equations are fully sequential. Each segment is directly linked with the next segment.

hprim,in,i+1 = hprim,out,i (6.15)

Tprim,in,i+1 = Tprim,out,i (6.16)

hsec,in,i+1 = hsec,out,i (6.17)

Tsec,in,i+1 = Tsec,out,i (6.18)

6.3.3.3 Single phase heat and pressure drop correlations

For the single phase, the well-known convective heat transfer and pressure drop correlations of Martin [11] are used. The heat transfer alpha follows from the Nusselt number Nu: αD Nu = h (6.19) k with α the convective heat transfer coefﬁcient and k the thermal conductivity of the working ﬂuid. The Nusselt number Nu is calculated from:

(1/3) (1/6) q Nu = cqP r (η/ηw) [2Hgsin2β] (6.20) with β the chevron angle of the plate corrugation pattern, cq and q take respectively the values 0.122 and 0.374. The Prandtl number P r is given as: ν P r = (6.21) κ 150 CHAPTER 6 with ν the kinematic viscosity and κ the thermal diffusivity. Hg is the Hagen number: Re2ζ Hg = (6.22) 2 with the Reynolds number Re deﬁned as GD Re = h (6.23) µl

In this equation G is the mass ﬂux entering the single phase zone, Dh the hydraulic diameter and µl the dynamic viscosity. The hydraulic diameter is calculated by: H D = (6.24) h Φ 1 p p Φ = (1 + 1 + X2 + 4 1 + X2/2) (6.25) 6 X = 2πH/(4Λ) (6.26) with H the corrugation depth and Λ the corrugation wavelength (= pco) and X the wavenumber of the wavy plate pattern, see Figure 6.4. The corrugation depth is typically between 1.5 mm and 5.4 mm [12].

H/2

Figure 6.4: Geometry of the plate heat exchanger wavy shape corrugation pattern.

The friction factor ζ is given by: 1 cosβ 1 − cos β √ = p + √ (6.27) ζ b tan β + c sin β + ζ0/ cos β ζ1 in this equation ζ1 = aζ1,0, the factors a,b,c are ﬁxed by: a = 3.8 (6.28) b = 0.18 (6.29) c = 0.36 (6.30)

If the ﬂow is laminar (Re < 2000) the factors ζ0 and ζ1,0 are given by: 64 ζ = (6.31) 0 Re 597 ζ = + 3.85 (6.32) 1,0 Re PART-LOADMODELLINGOFTHEORGANIC RANKINE CYCLE HEAT ENGINE 151

If the ﬂow is turbulent (Re ≥ 2000): 1 ζ = (6.33) 0 (1.8ln(Re) − 1.5)2 39 ζ = (6.34) 1,0 Re0.289 The pressure drop is calculated from the friction factor ζ:

LG2 ∆p = ζ (6.35) Dh2ρl

6.3.3.4 Two phase heat and pressure drop correlations

For the two-phase evaporation, the convective heat transfer correlations of Han et al. [13] are implemented:

Ge2,e 0.3 0.4 Nue = Ge1,eReeq Boeq P r (6.36)

Ge4,e fe = Ge3,eReeq (6.37)

The pressure drop is calculated from the friction factor ζ:

LG2 ∆p = ζ eq (6.38) Dhρl with L the channel length of the heat exchanger. Notice that the friction factor is deﬁned slightly different here compared to Eq. 6.35. The equivalent Reynolds number Reeq and boiling number Boeq are deﬁned as:

GeqDh Reeq = (6.39) µl q˙ Boeq = (6.40) Geqhlg with Geq the equivalent mass ﬂux:

ρl 1/2 Geq = G(1 − x + x( ) ) (6.41) ρg

The coefﬁcients are determined as:

−0.041 −2.83 Ge1,e = 2.81(pco/Dh ) (π/2 − β) (6.42) −0.082 0.61 Ge2,e = 0.746(pco/Dh ) (π/2 − β) (6.43) −5.27 −3.03 Ge3,e = 64710(pco/Dh ) (π/2 − β) (6.44) −0.062 −0.47 Ge4,e = −1.314(pco/Dh ) (π/2 − β) (6.45) 152 CHAPTER 6

These equations were derived from experimental measurements with Gwf = 13-34 kg/m2.s, q˙ = 2.5-8.5 kW/m2, x=0-0.95 and chevron angles 20°, 35°and 45°. For the two-phase condensation process the following equations by Han et al. [14] are used:

Ge2,c 1/3 Nuc = Ge1,cReeq P r (6.46)

Ge4,c fc = Ge3,cReeq (6.47)

The coefﬁcients are determined as:

−2.83 −4.5 Ge1,c = 11.2(pco/Dh ) (π/2 − β) (6.48) −0.23 1.48 Ge2,c = 0.746(pco/Dh ) (π/2 − β) (6.49) 4.17 −7.75 Ge3,c = 64710(pco/Dh ) (π/2 − β) (6.50) 0.0925 −1.3 Ge4,c = −1.314(pco/Dh ) (π/2 − β) (6.51)

These equations were derived from experimental measurements with Gwf = 13-34 kg/m2.s, q˙ = 4.7-5.3 kW/m2, x=0.15-0.95 and chevron angles 20°, 35°and 45°. The correlations by Han et al. [13, 14] can be applied in the range Reeq from 300 to 4000. When compared to the Hsieh and Lin correlation [15] the Nusselt numbers are very similar. In comparison with the Yan and Lin correlation [16], which is valid for higher Reynolds numbers, extrapolation gives Nusselt numbers which are lower. In general the implemented boiling and condensation heat transfer correlations give rather conservative values. While the above dimensionless correlations were derived for R410A or R134a they are frequently used to design heat exchangers using R245fa [17–19]. A detailed comparison of boiling and condensation heat transfer correlations can be found in the work of Garc´ıa-Cascales et al. [20]. However there is clearly a need for high accuracy heat transfer and pressure drop correlations speciﬁcally made for contemporary ORC working ﬂuids.

6.3.3.5 Supercritical heat and pressure drop correlations Both Cayer et al. [21] and Shenghjun et al. [22] used the Petukhov-Kranoschekov [23] correlations (Eq. 6.52-6.54) to calculate the convective heat transfer coefﬁ- cient and pressure drop in the supercritical state. The same correlations are also used in this work for simulation of the TCORC. Karellas et al. [8] used similar correlations for plate heat exchangers that are originally meant for tubular heat exchangers. In addition, almost all of the available supercritical correlations are made for water or CO2. Thus also here there is the need for high-accuracy heat transfer and pressure drop correlations, which are clearly lacking in current scien- tiﬁc literature. PART-LOADMODELLINGOFTHEORGANIC RANKINE CYCLE HEAT ENGINE 153

µb 0.11 kb Cp Nu = Nu0( )( )( ) (6.52) µw kw Cp,b

(f/8)RebP r Nu0 = (6.53) 12.7pf/8(P r2/3 − 1) + 1.07 −2 f = (1.82 log10 Reb − 1.64) (6.54)

6.4 Volumetric expanders

A model for the volumetric expander inherently has two degrees of freedom. One related to the volumetric performance the other to the work output. The volumetric performance is calculated from the inlet and outlet boundary conditions by the equation forming the filling factor: m˙ v ψ = wf exp,in (6.55) Vexp,internalNexp The isentropic efficiency relates the available energy of an adiabatic reversible process to the actual work output. In experimental works, several definitions circulate, thus care should be taken. For example, the electricity output at the grid can be used, resulting in Eq. 6.56. Another option, Eq. 6.57, is to use the energy difference of the working fluid over the expander. Be aware that ambient losses are included in the definition of Eq. 6.57, these are not separated.

W˙ exp,grid exp,grid = (6.56) W˙ exp,isentropic

m˙ wf (hexp,in − hexp,out) exp,cycle = (6.57) W˙ exp,isentropic

W˙ exp,isentropic =m ˙ wf (hexp,in − hexp,out,isentropic) (6.58) Several modelling approaches can be formulated. The first one is the constant- efficiency model. In this model a constant volumetric and isentropic efficiency are imposed independent of changing operating conditions. This type of model is useful in the design process where nominal values of specific equipment can be guessed. However part-load operation is completely discarded. Next, there are the polynomial based regression models [24, 25]. These are black box models with input parameters the pressure ratio over the expander and the supply density. The experimentally determined coefficients are fitted to a polynomial regression model. These kind of models show very good performance within the calibration range but care should be taken when extrapolating. A semi-empirical (i.e grey- box model) is proposed by Lemort et al. [26]. This physics-based model includes supply pressure drops, leakage flows and heat losses to the environment. 154 CHAPTER 6

The proposed model in this work is a hybrid between the polynomial regression models and the semi-empirical models. The ﬁlling factor is modelled by introducing non-dimensional working conditions as given by Declaye et al. [25]: r − 4 r∗ = p (6.59) p 4 p − 10 p∗ = exp,in (6.60) 10 N ψ = a + a ln exp + a r∗ + a p∗ (6.61) 1 2 5000 3 p 4

In these equations, rp is the pressure ratio over the expander, Nexp the rotational speed of the expander and pexp,in the inlet pressure of the expander in bar. The values of a1, a2, a3, a4 are fitted to calibration data. The model for the isentropic efficiency is adapted from Lemort et al. [26]. Both exp,cycle and exp,grid are predicted from a model which includes two parameters: the built-in volume ratio rv and a lumped thermo-mechanical loss coefficient ηloss. The built-in volume, rv, is the ratio of specific volume at the outlet on the specific volume at the inlet of the expander. The expansion model is split into an isentropic expansion (hexp,in-hexp,internal) and a constant volume expansion ((pexp,internal − pexp,out)vinrv), with vinternal the specific volume at the end of the isentropic expansion. The isentropic expansion fraction corresponds to a volume ratio increase rv. The constant volume expansion fraction accounts for the expansion (or recompression) to the final discharge pressure. As such the following relations are obtained:

W˙ exp,cycle = ηloss,exp,cyclem˙ wf [(hexp,in − hexp,internal)+ (6.62) (pexp,internal − pexp,out)vinternalrv,exp,cycle]

W˙ exp,grid = ηloss,exp,gridm˙ wf [(hexp,in − hexp,internal)+ (6.63) (pexp,internal − pexp,out)vinternalrv,exp,grid]

In these equations the coefficients rv and ηloss are determined by least squares model fitting. Volumetric expanders are considered suitable for two-phase expansion, yet limited experimental results are presented [27]. For example, Smith et al. [28], performed measurements on double screw expanders with inlet vapour qualities from 50% to 25%. They showed isentropic efficiencies ranging between 40% and 80%. Li et al. [29] studied a rolling piston-type two-phase expander reporting isentropic efficiencies of 58.7%. A trend, indicating reduced isentropic efficiencies under two-phase expansion for high efficiency single phase double screw machines and vice versa, was shown by Ohman¨ and Lundqvist [27]. They proposed a simplified model [30], see Eq. 6.64 and Eq. 6.65, that relates the isentropic efficiency of superheated or saturated inlet conditions to the isentropic efficiency for two-phase PART-LOADMODELLINGOFTHEORGANIC RANKINE CYCLE HEAT ENGINE 155

inlet. The cut-off point is found at single−phase,peak = 60%. For lower values of single−phase,peak the isentropic efficiency for two-phase inlet is increased over the isentropic efficiency under single phase inlet. They explain this due to a decrease in leakage because of the sealing of leakage paths by the liquid phase. However, they state that the available test data in literature is scarce and that the actual behaviour of the two-phase expansion is unknown. In this work, the isentropic efficiencies of the expander are generally lower than 60% so we prefer to analyse the worst case scenario without taking into account the possibly improved performance.

two−phase = single−phase,peak + ψtwo−phase(1 − xin)/10 (6.64)

ψtwo−phase = −0.15single−phase,peak + 0.09 (6.65)

6.5 Centrifugal pump

The centrifugal pump is typically described by characteristic curves. These depict the behaviour of head (i.e. pressure), power consumption and efficiency as function of the volume flow rate. For a fixed pumping speed there is a single curve relating the head with the volume flow rate and a second curve relating the efficiency with the volume flow rate. This data is shared by the manufacturer under normalised testing conditions [31].

These curves can also be written in terms of dimensionless parameters CV˙ (Eq. 6.66) and CH (Eq. 6.67). In these equations V˙ is the volume flow rate, N the rotor speed, D the impeller diameter, H the pressure head and g the gravitational acceleration. The benefit is that curves for different pumping speeds coincide due to kinematic similarity rules [32]. The dimensionless coefficients directly follow from rewriting the similarity rules for centrifugal pumps Eq. 6.68 to Eq. 6.70. The similarity rules relate the change of volume flow rate, head and efficiency to the change in impeller diameter and the change in rotational speed.

V˙ C = (6.66) V˙ ND3 gH C = (6.67) H N 2D2

V˙ ∝ ND3 (6.68) H ∝ N 2D2 (6.69) W˙ ∝ N 3D5 (6.70)

Again two isentropic efficiencies are defined pump,cycle (Eq. 6.71) and pump,grid (Eq. 6.72). The value pump,cycle is held fixed as the influence on the cycle state 156 CHAPTER 6

points is low. The value of pump,grid follows from the characteristic curve.

W˙ pump,isentropic pump,cycle = (6.71) m˙ wf (hpump,out − hpump,in)

W˙ pump,isentropic pump,grid = (6.72) W˙ pump,grid

W˙ pump,isentropic =m ˙ wf (hpump,out,isentropic − hpump,in) (6.73)

The centrifugal pump characteristic curve, as a function of two dimensionless variables, is shown in Figure 6.5. For the impeller diameter, D = 0.108m is assumed. In the dimensionless diagram only the results of a single stage are shown. The reported curve typically corresponds with low speciﬁc speed centrifugal pumps [33, 34]. The optimal operating point for this centrifugal pump would be around CV˙ = 0.011. Most of the operating points center around the point CV˙ = 0.0057. A similar modelling approach, that uses dimensionless curves to model centrifugal pumps in ORC systems, is seen in the work of Manente et al. [35].

Figure 6.5: Dimensionless characteristic curves of the centrifugal pump.

6.6 Cycle model

The full cycle model is built from the main components described above. In order to have a robust solving process, the choice of iteration variables and modelling equations are crucial. A decoupling of the mass and thermal balance provided a robust implementation. The ﬂow diagram of the cycle program is provided in PART-LOADMODELLINGOFTHEORGANIC RANKINE CYCLE HEAT ENGINE 157

Set guess values: hevap,wf,out and pcond,wf,,in

Solve mass balance [ṁwf, pevap,wf,out]

if |ṁwf-ṁwf,previous|<0.001 kg/s

[yes]

[no]

Solve thermal model [Cycle thermodynamic state points]

Figure 6.6: UML ﬂowchart of the cycle solver.

Figure 6.6. The main cycle iteration variables are the condenser saturation pressure pcond,wf,in and the enthalpy at the outlet of the evaporator hevap,wf,out. Starting from these iteration variables, with the given pump and expander rotational speed, the saturation pressure in the evaporator and the mass ﬂow rate of the working ﬂuid is calculated. This is achieved by numerically solving the mass balance of the pump and expander with as iteration variables the evaporator saturation pressure:

m˙ exp =m ˙ pump (6.74)

Next, the heat ﬂow rate from the heat exchanger models are calculated, this is Q˙ achieved. Subsequently, the cycle state points are calculated from the expander and pump models. As such the needed heat ﬂow rate to and from the cycle can be calculated, this is Q˙ needed. For a cycle with a single evaporator and condenser the set of equations thus become:

Q˙ cond,achieved = Q˙ cond,needed (6.75)

Q˙ evap,achieved = Q˙ evap,needed (6.76)

At this point, there is only one more degree of freedom left in the system. This is the degree of subcooling achieved in the condenser. During the experiments, the subcooling stayed approximately constant at 3 °C. Alternatively, this can be 158 CHAPTER 6 calculated from the charge in the system. The system of equations is solved using the Sequential Quadratic Programming (SQP) algorithm available in MATLAB [1]. Calculation time for a single set of input conditions is around 5 seconds on a single Intel Xeon E5-2640 v3 core.

6.7 Conclusions

Robust models of the individual cycle components are essential before any validation, optimisation or simulation can be performed. The models available in literature range from detailed physical white box to simple empirical black box models. Black box models are advantageous because of their low computational cost. In view of the optimisations that are performed in Chapter 7, this is an important benefit. However extrapolation to other operating points or cycle types is not advisable. Therefore hybrid approaches (i.e. grey box models) are proposed. The modelling choices made are extensively described in this chapter and are situated in the current state of the art. The heat exchanger models are a hybrid between the moving boundary and the finite volume modelling approach. The moving boundary approach is the faster of the two but is less accurate. This would pose a problem when for example modelling a transcritical ORC. The volumetric double screw expander is modelled by splitting the expansion process in an isentropic expansion and a constant volume expansion. As such the critical under- and over expansion losses are accounted for. A lumped correction factor accounts for leakages, mechanical and electrical losses. The centrifugal pump is modelled with the help of the characteristic dimensionless curves. Besides the model equations, the actual implementation determines the robust- ness and applicability. An object-oriented programming paradigm is proposed to easily extend and change the component models. Especially for modelling the heat exchangers this provides a lot of flexibility. Flowcharts are provided to explain the solving strategy. The complete cycle is solved by decoupling the mass and heat balances. This proved to be a very robust strategy that has a computational time of approximately 5 seconds for one operating point on a single Intel Xeon E5-2640 v3 core. PART-LOADMODELLINGOFTHEORGANIC RANKINE CYCLE HEAT ENGINE 159

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7 Experimental validation and optimal operation under part-load conditions

7.1 Introduction

In this chapter, the detailed component and cycle models from Chapter 6 are validated based on the results from an 11 kWe subcritical ORC. The purpose of the developed models is to investigate the part-load operation of the ORC. To achieve this, the models were developed to have a low computational cost and to be extensible to other operating points.

First, the procedure to detect steady state operation is elaborated in Section 7.3. A robust detection algorithm is vital for removing outliers and post-processing of the experimental data. False inclusion of transient data points makes the set of validation data useless. Next, the individual component models of the pump, expander and heat exchangers are validated based on the data from the experimental set-up. Subsequently, the results of the full cycle model are presented and compared with the experimental results. The cycle model is a simulation model, meaning that the only input values are external inputs like the pump and expander speed. Finally, the validated models are used to investigate and optimise the part-load behaviour of the set-up under SCORC and PEORC operation. 164 CHAPTER 7

7.2 The experimental ORC set-up

An 11 kWe organic Rankine cycle set-up is used for validating the part-load models described in Chapter 6. This experimental set-up is a scaled-down version of a real commercial ORC designed for low heat source temperatures (between 80 °C and 150 °C) and uses R245fa as working ﬂuid. The data capturing is done with a sample rate of 1 Hz. A schematic of the measurement equipment is given in Figure 7.1. A picture of the installation is given in Figure 7.2. In the presented tests, the recuperator is bypassed in order to reduce modelling errors on the cycle. Because partial condensation appears in the recuperator it is not possible to have a closed heat balance, as such it is impossible to assess the heat losses without accurate measurement of the vapour fraction. The recuperator in this system is also not insulated. Furthermore, on a component level, the addition of the recuperator provides little additional information as the condenser and evaporator are geometrically completely identical. Further details about the components, the measurement equipment used and the uncertainty analysis can be found in Appen- dix C.

Evaporator P T Generator Inverter

M T T

G Grid

T P Expander P

Recuperator

P T

M T P Pump T Condenser

Buffer tank T M

Figure 7.1: Component layout and measurement equipment of the experimental 11 kWe ORC located at campus Kortrijk, Ghent University.

7.3 Steady state analysis

The ﬁrst step in pre-processing the data is ﬁnding the steady-state points of operation. The strict meaning of steady state means that for a property K of a system the ∂K partial derivative with respect to time is zero ( ∂t ). In experimental data reduction this constraint is relaxed and a deviation during a time window is accepted. EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 165

Figure 7.2: Picture of the experimental 11 kWe ORC (campus Kortrijk Ghent University). 166 CHAPTER 7

7.3.1 Steady state detection algorithm Due to measurement errors and uncertainties, the strict deﬁnition of steady state is thus impractical to use. As such several approaches were formulated in literature. For example Woodland et al. [1] proposed a standard for an ORC steady state measurement detection. Measurements are made at 1 Hz intervals. These values are averaged over 30 consecutive recordings. This average is afterwards compared to averaged measurements taken 10 minutes later. The percentage change is then computed and compared to a predeﬁned threshold. These thresholds can be found in Table 7.1.

Measurement Steady state criteria Temperature Difference < 0.5 K Pressure Change < 2% Mass ﬂow rate Change < 2% Rotating equipment speed Change < 2%

Table 7.1: Steady state criteria according to Woodland et al. [1].

Other methods which make use of a time window are based on F-tests [2], t- tests [3], hotelling T2 tests [4] etc. Also wavelet transforms [5] are used, where the choice of the characteristic scale substitutes the role of the time window. The steady state algorithm used in this work is derived from the work by Kim et al. [6]. Their algorithm was applied on experimental data of a residential air conditioner. This algorithm is widely applicable and is applied on data coming from various thermodynamic cycles. They furthermore conclude that the evaporator superheat and condenser subcooling are sufficient for determining the onset of steady state. Also according to Gusev et al. [7] the time required for the temperatures in the condenser to stabilise is longer than for all others in the ORC system under consideration. However in determining the steady state points of the system it is not sufficient to look only at the condenser side. For example, consider the system is in steady state operation. When the setpoint of the expander rotational speed changes abruptly, it will take some time before the effect will be felt in the condenser. This however does not mean the system is in steady state operation. The procedure for finding the steady states points is outlined below:

• Manually identify a representative steady state zone. A representative steady state zone is identiﬁed after approximately one hour of operation. When the samples are taken, they should comply to the criteria of Woodland et al. [1], else a subsequent time window is used.

• Calculate the reference standard deviations based on 600 samples. This standard deviation multiplied with 2 is used as the threshold. A reference EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 167

standard deviation multiplied with 2 will remove less than 5% of the steady- state data assuming that the steady-state measurements are random and normally distributed [8].

• Calculate the forward-moving standard deviation over the dataset. The forward-moving average x¯k is deﬁned by Eq. 7.1, n is the window size and k the number of the calculation window. The difference between the moving average of two adjacent windows is given in Eq 7.2. The moving average of the subsequent window can thus be calculated with substraction and addition of two data points, see Eq. 7.3.

k+n−1 1 X x¯ = x (7.1) k n i k k+n k+n−1 1 X 1 X 1 x¯ − x¯ = x − x = (x − x ) (7.2) k+1 k n i n i n k+n k k+1 k 1 x¯ =x ¯ + (x − x ) (7.3) k+1 k n k+n k

The deﬁnition of the moving standard deviation σk is given in Eq 7.4. The difference between the moving standard deviation of two adjacent windows is given in Eq 7.5. The standard deviation of the subsequent window can thus be calculated as in Eq. 7.6.

k+n−1 "k+n−1 # 1 X 1 X σ2 = (x − x¯ )2 = x2 − x¯2 n (7.4) k n − 1 i k n − 1 i k k k "k+n k+n−1 # 1 X X σ2 − σ2 = x2 − x¯2 n − x2 +x ¯2 n (7.5) k+1 k n − 1 i k+1 i k k+1 k 1 σ2 = σ2 + n(¯x2 − x¯2 ) + (x2 − x2 ) (7.6) k+1 k n − 1 k k+1 k+n k

• Identify the steady state zones, these have a moving standard deviation which is lower than the identiﬁed threshold.

• Take the average of the identiﬁed data points in the steady state zones.

7.3.2 Acquiring the steady state points The goal of these experiments is to have validation data points over a large operating range, the initial sampling plan includes two levels of heat source mass 168 CHAPTER 7

flow rate (1.5 kg/s and 3 kg/s), two levels of cold water volume flow rate (7 m3/h and 13.4 m3/h) and two heat source temperature levels (110 °C and 120 °C). The expander speed is fixed at 5000 rpm. In Figure 7.3 these input values and the electrical power delivered to the grid by the expander W˙ exp,grid from the full dataset is shown.

ṁ exp,grid

Ẇ

Figure 7.3: Original dataset of the performed ORC experiments, plot of Thf,in, m˙ hf , V˙cf and W˙ exp,grid.

As indicators for steady state operation are taken: the speed of the rotating equipment, the mass flow rate and inlet temperature of the heat source, the inlet and outlet pressure of the expander, the working fluid outlet temperature of the condenser, the volume flow rate of the cooling fluid and the working fluid inlet temperature at the expander inlet. After an initial startup period of one hour the steady state reference values are acquired, these are shown in Figure 7.4. The corresponding mean, minimum, maximum and standard deviation values can be found in 7.2. A time window of 10 minutes is also used when calculating the moving standard deviation. The resulting steady zones are shown in Figure 7.5 and the achieved operating ranges are given in Table 7.3. EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 169

ṁ W

Ẇ

Figure 7.4: Reference steady state operating regime, plot of Thf,in, m˙ hf , V˙cf and W˙ grid,el.

ṁ

Ẇ

Figure 7.5: Detected steady state operating zones, plot of Thf,in, m˙ hf , V˙cf and W˙ grid,el. 170 CHAPTER 7

Variable Min. Max. Mean σ

Nexp (rpm) 4970 5027 5000 9.5296 Npump (rpm) 2229 2235 2234 2.0683 m˙ hf (kg/s) 1.517 1.597 1.573 0.0109 3 V˙cf (m /h) 12.811 14.229 13.620 0.2332 Thf,in (°C) 119.9 120.1 120.0 0.0267 pexp,in (bara) 11.435 11.525 11.496 0.0243 pexp,out (bara) 2.342 2.389 2.336 0.0148 Texp,in (°C) 115.9 116.4 116.3 0.1563 Tcond,out (°C) 34.7 35.1 35.0 0.1854

Table 7.2: Reference values for detecting the steady state operating regime.

Variable Minimum value Maximum value

m˙ hf (kg/s) 1.495 3.006 3 V˙cf (m /h) 7.038 14.465 Thf,in (°C) 110.0 120.0 Thf,out (°C) 83.0 103.4 Texp,in (°C) 107.8 119.5 Texp,out (°C) 78.3 88.0 Tsup (°C) 19.8 21.1 pexp,in (bara) 9.510 12.457 pexp,out (bara) 2.148 2.771 Npump (rpm) 1973 2340 m˙ wf (kg/s) 0.2902 0.3874

Table 7.3: Range of achieved operating conditions of the cycle validation dataset.

7.4 Heat exchanger heat balances

In Figure 7.6 and Figure 7.7 the parity plot between the heat flow rate of the primary and secondary fluid side is shown respectively for the evaporator and the condenser. The uncertainty flags are calculated for both the secondary and primary fluid side according to the information provided in Appendix C Section C.2. All of the points fall in a range of ±5% deviation relative to the parity line. For the evaporator, the largest uncertainty is found on the hot fluid side. This is due to the large uncertainty on the mass flow rate measurement with the orifice flow meter. The uncertainties on the secondary and primary heat flow rate combined almost always include the parity line. This means that with the current measurement equipment it is impossible to discriminate further between ambient EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 171 losses or the measurement uncertainties. For the condenser, the largest uncertainty is found on the cold fluid side. This is again due to the lower accuracy of the mass flow rate measurement at the secondary side. As such the same remarks apply here. In contrast to the evaporator, the condenser is not insulated. However, the results are acceptable due to the lower temperature difference between the ambient conditions and the primary and secondary fluid.

Figure 7.6: Heat balance over the evaporator with error ﬂags.

Figure 7.7: Heat balance over the condenser with error ﬂags. 172 CHAPTER 7

7.5 Validation of the individual component models

An elaborated description of the developed models, with the implementation details, can be found in Chapter 6. In general, the models developed proved to be very robust while having a low computational time. The heat exchanger model is computationally the most intensive and takes less than 3.5 seconds in order solve 11 data points on a single Intel Xeon E5-2640 v3 core. The heat exchanger, pump and expander models are modelled from the generic physical behaviour of these components. However, for the pump and expander, there remain coefﬁcients which need calibration for increased accuracy. In order not to over-ﬁt the models on the cycle validation dataset a second larger set of experimental data is preferred. In the ORCNext project [9] an aggregated dataset was available from the period between 24/08/2015 to 03/09/2015. The new 25 steady state points were again found as described in Section 7.3. The range of achieved operating conditions is given in Table 7.4. The results presented in this section are compiled from this dataset.

Variable Minimum value Maximum value

m˙ hf (kg/s) 1.305 3.047 3 V˙cf (m /h) 7.058 19.500 Thf,in (°C) 110.0 120.2 Thf,out (°C) 83.0 104.5 Texp,in (°C) 106.5 120.1 Texp,out (°C) 77.3 88.0 Tsup (°C) 12.2 21.1 pexp,in (bara) 9.264 12.444 pexp,out (bara) 1.952 2.692 Npump (rpm) 1939 2359 m˙ wf (kg/s) 0.2746 0.3910

Table 7.4: Range of achieved operating conditions of the component calibration dataset.

7.5.1 Evaporator and condenser

For the validation of the evaporator model, the input conditions of the model are chosen as: EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 173

• Mass ﬂow rate hot ﬂuid (m˙ hf )

• Mass ﬂow rate working ﬂuid (m˙ wf )

• Inlet enthalpy working ﬂuid (hevap,wf,in)

• Inlet enthalpy hot ﬂuid (hevap,hf,in)

The expected heat flow rate from the model compared to the experimental results is shown in Figure 7.8. Keep in mind that for making these plots the input measurements where handled as being exact. The uncertainties reported in Sec- tion 7.4 should thus not be forgotten when making claims about the performance. The heat flow rate generally deviates less than ±2% from the parity line. The evaporator model is thus able to predict the heat flow rate with satisfactory accuracy. Furthermore, the model accurately predicts pinch point shifts without any problem.

Figure 7.8: Parity plot of the heat ﬂow rate of the evaporator, comparison between model and experiment.

For the validation of the condenser model the input conditions of the model are chosen as: 174 CHAPTER 7

• Mass ﬂow rate cold ﬂuid (m˙ cf )

• Mass ﬂow rate working ﬂuid (m˙ wf )

• Inlet enthalpy working ﬂuid (hcond,wf,in)

• Inlet enthalpy cold ﬂuid (hcond,cf,in)

The expected heat ﬂow rate from the model compared to the experimental results is shown in Figure 7.9. As in the case with the evaporator, the expected heat ﬂow rate from the model deviates generally less than ±2% from the parity line. However, compared to the evaporator model, there are some more points which fall outside of the ±2% parity lines.

Figure 7.9: Parity plot of the heat ﬂow rate of the condenser, comparison between model and experiment.

7.5.2 Volumetric expander

In modelling the volumetric expander, two values are of importance, the predicted power output and the predicted mass flow rate through the expander. The expected mass flow through the expander is modelled based on the equations given by De- claye et al. [10]. Details are available in Chapter 6. The coefficients a1, a2, a3, a4 in the model are determined by least squares model fitting. The results are given in Table 7.5. The coefficient a2 is equal to zero because only one expander speed is tested, namely 5000 rpm. Furthermore a4 is zero, similar results are found in the work of Lemort et al. [11]. In their work, the authors explain that while an increased pressure would lead to increased leakage and higher filling factors there EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 175 is also an increase in the supply pressure drop which offsets this.

Coefﬁcient Value

a1 1.0632 a2 0 a3 0.0438 a4 0

Table 7.5: Model coefﬁcients to determine the ﬁlling factor of the volumetric expander.

The expander is modelled by splitting the expansion process into an isentropic expansion and a constant volume expansion. The model coefﬁcients are found via curve ﬁtting to the data and given in Table 7.6.

Coefﬁcient Value

ηloss,exp,cycle 0.6131 ηloss,exp,grid 0.5148 rv,exp,cycle 4.4953 rv,exp,grid 5.5674

Table 7.6: Model coefﬁcients to determine the isentropic efﬁciencies of the volumetric expander.

The results of the mass ﬂow rate modelling are shown in Figure 7.10. The model is able to predict most of the points with ±1% deviation. The proposed model can be considered very adequate for predicting the mass ﬂow in the cycle. In Figure 7.11 the results are shown for the grid power output. Here most of the data points fall in a range of ±2% deviation.

7.5.3 Centrifugal pump In the same way as for the volumetric expander, the two values of importance are the predicted power output and the predicted mass flow rate through the expander. Details about the modelling can again be found in Chapter 6. For the pump model, the isentropic efficiency pump,cycle, see Eq. 6.71, is kept fixed as the influence on the cycle state points is low. The value of pump,cycle directly follows from a least squares model fitting and is equal to 0.3482. The grid power input and mass flow rate are derived from the dimensionless characteristic curve given in Figure 6.5. The results of the mass flow rate modelling can be found in Figure 7.12. Most of the data points fall in the range of ±2% deviation however there is clearly more 176 CHAPTER 7 scattering of the data in comparison to the expander model. The same is noticeable for the net power input given in Figure 7.13. Most of the data points now only fall in the range of ±5% deviation from the parity line. Fortunately the impact of this error on the net power output is small.

Figure 7.10: Parity plot of the mass ﬂow rate through the expander, comparison between model and experiment.

Figure 7.11: Parity plot of the power output (W˙ exp,cycle in red and W˙ exp,grid in blue) of the volumetric expander, comparison between model and experiment. EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 177

Figure 7.12: Parity plot of the mass ﬂow rate through the pump, comparison between model and experiment.

Figure 7.13: Parity plot of the power input of the pump, comparison between model and experiment. 178 CHAPTER 7

7.6 Validation of the full cycle model

The individual component models are interconnected to form the full cycle model, bypassing the recuperator as depicted in Figure 7.1. The solving strategy is described in Chapter 6 Section 6.6. The only independent inputs to the cycle model are the pump speed Npump and the expander speed Nexp. The prevailing dependent model outputs are the evaporating pressure pevap, the condensing pressure pcond and the mass flow rate m˙ wf . These internal model values are influential in determining the net power output W˙ net of the ORC. The validation dataset described in Section 7.3.2 will now be used. First the parity plot of the evaporation pressure is given in Figure 7.14. A good match is seen between the resulting modelled pressure and the pressure measured before the expander. All of the points deviate less then ±1% from the experimental value. The parity plot for the condensing pressure is shown in Figure 7.15. In this case the resulting pressure from the model is compared with the measured pressure after the expander. Again a good match can be seen, with most of the modelled data points having a deviation less than ±1% compared to the measured pressure. The mass flow rate parity plot is given in Figure 7.16. Most of the modelled mass flow rates here have a deviation less than ±1% with the measured mass flow rate. Thus, based on the important internal variables pressure and mass flow rate, the modelled ORC gave satisfactory results. Finally the modelled versus measured electrical expander power output and net power output is depicted in respectively Figure 7.17 and Figure 7.18. The net power output can be considered the single most important value and is typically predicted within ±2% of the measured value. To show that the model is robust enough to resolve pinch point shifts, two sets of measurement data are selected and plotted in a T-s diagram. A first set with the pinch point at the superheated section and another where the pinch point shifts to the saturated liquid point. The T-s diagrams of the cycle simulations and of the measurements are given in Figure 7.19. Qualitatively seen there is a good match between the measured state points of the cycle and the simulation results. While for these two sets of data there was an exceptionally good match, other data points exhibited a similar trend. Yet, parity plots as shown above give a better quantitative understanding of the simulation results. EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 179

Figure 7.14: Parity plot of the evaporation pressure, comparison between model and experiment.

Figure 7.15: Parity plot of the condensation pressure, comparison between model and experiment. 180 CHAPTER 7

Figure 7.16: Parity plot of the working ﬂuid mass ﬂow rate, comparison between model and experiment.

Figure 7.17: Parity plot of the cycle expander power output to grid, comparison between model and experiment. EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 181

Figure 7.18: Parity plot of the net power output to grid, comparison between model and experiment.

Figure 7.19: Illustration of pinch point shift, (line: model, star: experiment). 182 CHAPTER 7

7.7 Optimal part-load operation

The validated models are now used to examine the optimal control set points of the experimental set-up. The control variables are the pump and the expander speed. As with most commercial ORC installations, the generator is assumed to be directly connected to the grid, so that the expander rotates at fixed speed. In this work, the expander speed and the cooling water inlet temperature are respectively fixed at 5000 rpm and 30 °C. Changes in the condensing pressure are imposed by changing the volumetric flow rate of the cooling loop.

7.7.1 Effect of the pump rotational speed To analyse the optimisation potential, the effect of the pump speed on the cycle operation is investigated. The typical trend of the expander inlet vapour quality, the pump inlet power, the expander outlet power and the net power output in function the pump speed is shown Figure 7.20. The expander output power rises sharply until approximately xexp,in = 0.5 and keeps steadily increasing after this point. For the net power output there is a steady increase until the point of saturated liquid. After this point the pumping power has a detrimental impact on the net power output. The maximum net power output is seen at xexp,in = 0.587 but the sensitivity on the pumping speed is low in this region. Thus slightly lower values of Npump corresponding with higher xexp,in are more interesting. Less working ﬂuid mass ﬂow rate circulates and the pumping power is lower while the effect on the net power output is negligible.

t t t

Figure 7.20: Model output variables xexp,in, W˙ net, W˙ exp,grid and W˙ pump,grid as a function of Npump for m˙ hf = 1.5 kg/s, Thf,in = 110 °C 3 and V˙cf = 13.4 m /h. EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 183 7.7.2 Optimised pump rotational speed

The optimal pump speed, that maximises the net power output, is determined for the list of boundary conditions in Table 7.7. This list comprises the typical working region of the system. The optimal pump speed and expander inlet vapour quality that corresponds with maximum W˙ net is added to Table 7.7.

m˙ hf Thf,in V˙cf Npump,opt m˙ wf xexp,in pexp,in W˙ net (kg/s) (°C) (m3/h) (rpm) (kg/s) (-) (bar) (kW) 1.5 110 7 2198 0.557 0.587 9.92 4.25 1.5 110 13.4 2295 0.630 0.509 9.83 4.94 1.5 120 7 2349 0.527 0.759 11.74 5.44 1.5 120 13.4 2456 0.617 0.634 11.63 6.25 3 110 7 2372 0.558 0.711 11.71 5.43 3 110 13.4 2536 0.700 0.551 11.61 6.28 3 120 7 2542 0.502 0.980 14.02 6.95 3 120 13.4 2603 0.541 0.916 13.97 7.84

Table 7.7: Range of ORC boundary conditions, results of the optimisation of the pump speed with no constraint on superheating.

The first thing to notice is that the optimised system always works as a PE- ORC. Yet, the vapour fraction at the inlet of the expander is high compared with the results from Chapter 4. There the conclusion was that a pure TLC, with vapour quality equal to zero, is thermodynamically the best for maximum net power generation. The explanation for this behaviour is found in the increasing mass flow rate when omitting the enthalpy of vaporisation. With a low isentropic efficiency of the pump, the required pumping power rises faster than the increase in expander power, see also Figure 7.20. The isentropic efficiency of the pump in the set-up is around 20%, this is a lot lower than the 70% in Chapter 4. This low value is however in line with other experimental results found in literature [12]. When artificially increasing the isentropic efficiency, the optimised cycle again shifts to lower vapour fractions as expected. Thus, when designing the PEORC, the importance of a high efficiency pump should be stressed. Secondly, for increased hot fluid mass flow rates and temperatures, the optimal pump speed will shift to higher values. The increased pump speed is associated with an increased pumping power and will again lead to an increase in the optimal xexp,in as explained before. The pressure in the system is comprised between 9.9 bar and 14 bar, with the higher values corresponding to higher waste heat input and lower cooling mass flow rates. Notice also that while the PEORC operation is simulated based on the detailed semi-empirical models, further validation in this operating regime is still necessary. 184 CHAPTER 7

7.7.3 Comparison between the SCORC and PEORC

Next, the ORC is optimised under the additional constraint of ﬁxed superheating. The level of superheat is commonly used as setpoint to control the SCORC. To make sure that under transient conditions a minimum superheat is attained, the setpoint is set to a safe value. During the experiments a value of 15 °C was the minimum superheat temperature under which robust control was achieved. This value is now imposed as additional constraint and the same optimisation was performed as in the previous section. The results are shown in Table 7.8.

m˙ hf Thf,in V˙cf Npump,opt m˙ wf pexp,in W˙ net (kg/s) (°C) (m3/h) (rpm) (kg/s) (bar) (kW) 1.5 110 7 2003 0.308 9.84 4.07 1.5 110 13,4 2029 0.309 9.83 4.55 1.5 120 7 2228 0.367 11.61 5.34 1.5 120 13.4 2255 0.368 11.59 5.93 3 110 7 2172 0.352 11.15 5.02 3 110 13.4 2199 0.353 11.14 5.59 3 120 7 2458 0.435 13.54 6.69 3 120 13.4 2483 0.433 13.47 7.39

Table 7.8: Range of ORC boundary conditions, results of the optimisation of the pump speed with superheat constraint to 15 °C.

Compared to the operation as a PEORC, the optimal rotational speed is around 200 rpm lower. This leads to working fluid mass flow rates which are roughly half that of the PEORC. The evaporation pressure in the SCORC system is slightly lower, in the order of a few 10 kPa. The relative increase in net power output for a PEORC compared to the SCORC is given in Figure 7.21. The relative net power improvements range between 2% and 12%. As already mentioned, the isentropic efficiency of the pump has a decisive impact on the achievable performance of the PEORC. Let us therefore assume a pump with thrice the isentropic efficiency of the set-up. Thus the isentropic efficiency goes up from approximately 20% to 60%. Under these conditions, the optimal mass flow rate in the PEORC is further increased leading to lower xexp,in. The relative performance increase of the PEORC compared to the SCORC can again be found in Figure 7.21. The comparison is made with the improved pump for both the SCORC and PEORC. The relative net power improvement now ranges between 6% to 40%. For the points with the high heat source mass flow rates of m˙ hf = 3 kg/s the increase in net power output with the improved pump is fairly low. This is due the high pressure in the system when the working fluid mass flow rate is increased. An increased pressure leads to a higher evaporation satu- EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 185

50 Original pump Improved pump

40 [%]

. net 30

10 Relative improvement W improvement Relative

0 1 2 3 4 5 6 7 8 Operating point [-]

Figure 7.21: Relative improvement in Wnet˙ of PEORC operation compared to SCORC operation with original and improved pump (original isentropic efficiency pump tripled), operating points from left to right correspond with the operating points in Table 7.7 from top to bottom. ration temperature and a lower heat input to the cycle. This optimisation effect was discussed in Section 3.2.1. A larger expander or using higher expander rotating speeds can increase the performance for these operating points. Performance benefits up to 40% are then attainable. Based on these results, there are clearly opportunities in retrofitting existing SCORC systems. With roughly the same maximum pressures, the same working fluid, and an adapted measuring and control strategy, significant net power improvements can be achieved. However the importance of the pump in a PEORC system should not be neglected.

7.8 Conclusions

In this chapter, experimental steady state data was gathered on a scaled-down version of a commercial 11 kWe ORC. An important aspect in the data processing, is the detecting of the steady state regions. Because of deviations in the measured data, due to the finite accuracy of the sensors and measuring equipment, the strict definition of steady state operation is not practical. As such a statistical detection algorithm was proposed based on the calculation of the moving standard deviation. Two experimental datasets were collected and processed. The first dataset was devised to gather information over a large operating range. The initial sampling plan includes two levels of heat source mass flow rate (1.5 kg/s and 3 kg/s), two levels of cold water volume flow rate (7 m3/h and 13.4 m3/h) and two heat 186 CHAPTER 7 source temperature levels (110 and 120 °C). The expander speed is fixed at 5000 rpm. This dataset is used to validate the full ORC model with interconnection of the individual components. The second dataset is an aggregation of all experiments performed during the ORCNext project in the period between 24/08/2015 to 03/09/2015. This larger dataset was used for calibration and validation of the component models that were described in Chapter 6. Results from the heat balance of evaporator and condenser indicate a closed heat balance with a maximum deviation between secondary and primary heat flow rate of ±5%. The dominant uncertainties are the uncertainty on the thermophysical properties and the uncertainty on the mass flow rate at the secondary side. Next, the detailed component models of evaporator, condenser, pump and expander were validated. Most of the heat flow rates of the condenser and evaporator are predicted within ±2% of the measured value. The mass flow rates at the expander are predicted within approximately ±1%, for the pump this is ±2%. The electrical power output of the expander is predicted within ±2%. The pump electrical power input is predicted within ±5%. Considering the relative low pumping power compared to the expander power this is not detrimental in determining the net power output. Finally, the validation results of the interconnected cycle model were presented. The important dependent model outputs are the evaporation pressure pevap, the condensation pressure pcond and the working fluid mass flow rate m˙ wf . All three predicted outputs show a maximum deviation of less than ±1% from the measured value. The modelled net power output deviates less than ±2% from the measured value. In general, this is a satisfactory results that gives confidence in using these models in the part-load analysis. Finally, the validated models were used to optimise the pump rotational speed during different operating regimes. For increased pump rotational speed, the expander power increases steadily. However, for the net power output, the high pumping power counteracts this effect. The high pumping power is partially due to the low isentropic efficiency (∼20%) of the pump in the set-up. The optimal expander inlet vapour fraction (xexp,in) that maximises the net power output, is always higher than 0.5. This is in contrast to Chapter 4, where was shown that the ideal operating point with a good performing pump (isentropic efficiency 70 %) and an optimised fluid selection, is a TLC (xexp,in = 0). Comparing the operation as SCORC and PEORC, the PEORC shows an increased net power output between 2% to 12% over the SCORC. When the pump is improved, with an isentropic efficiency of thrice the original value, the PEORC shows an increased performance between 6% to 40% compared to the SCORC. Both cycles were optimised with the same improved pump. To achieve optimal operating conditions under increased loads, it is advisable to increase the expander rotational speed. Based on these initial results, there are clearly opportunities available to retrofit existing SCORC systems to PEORC operation. EXPERIMENTAL VALIDATION AND OPTIMAL OPERATION UNDER PART-LOAD CONDITIONS 187 References

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[9] The Next Generation Organic Rankine Cycles (ORCNext), http://www.orcnext.be/, 2016.

[10] S. Declaye, S. Quoilin, L. Guillaume, and V. Lemort. Experimental study on an open-drive scroll expander integrated into an ORC (Organic Rankine Cycle) system with R245fa as working ﬂuid. Energy, 55:173–183, 2013.

[11] V. Lemort, S. Quoilin, C. Cuevas, and J. Lebrun. Testing and modeling a scroll expander integrated into an Organic Rankine Cycle. Applied Thermal Engineering, 29(14–15):3094–3102, 2009. 188 CHAPTER 7

8.1 Conclusions

ORCs are of interest to convert waste heat in industry to valuable power. In this moment in time, they are however only used in a few specific cases. Two strategic challenges remain to be addressed in order to increase adoption of ORC technology for waste heat valorisation. Firstly, a better understanding of the thermodynamic cycle architectures can lead to a better thermodynamic performance. Secondly, a sound method needs to be developed in order to evaluate and size the cycle for maximum financial profit. In this work these two challenges are tackled. To increase the power output of the ORC for a given waste heat stream, alternative cycle architectures besides the basic subcritical ORC (SCORC) are proposed. However, scientific papers published on alternative cycle architectures are not cross-comparable because of different assumptions used in modelling and different implementations of the performance evaluation criteria. Therefore a comprehensive thermodynamic screening with 67 working fluids was performed, considering the three most promising cycles for waste heat recovery: the SCORC, the transcritical ORC (TCORC) and the partial evaporating ORC (PEORC). From the optimisation results, regression models were derived. These allow quickly assessing the maximum performance of the three cycle architectures for a large range of waste heat input temperatures (100 °C-350 °C) and cooling water temperatures (15 °C-30 °C). For low temperature waste heat, alternative architectures like the TCORC and 190 CHAPTER 8

PEORC clearly show higher maximum second law efficiencies compared to the SCORC. The PEORC outperforms the TCORC in second law efficiency by up to 25.6%, while the TCORC outperforms the SCORC in second law efficiency by up to 10.8%. For high waste heat inlet temperatures, the performance gain however becomes small. When restricting the working fluids to environmentally friendly ones, there is still a gap for high-performing working fluids for waste heat streams around 100 °C and this both for the SCORC and TCORC. Furthermore, the choice of optimal working fluid for the SCORC and TCORC is highly dependent on the boundary conditions of cooling loop and heat carrier. This is in contrast to the PEORC, for which a limited set of fluids covers the whole range of boundary conditions. The PEORC thus shows increased flexibility to cover different waste heat sources with a single working fluid. The next question was how to optimise the cycle for maximum profitability. Based on the multi-objective optimisation of investment cost and net power output, a thermo-economic optimisation framework was introduced. This framework was applied on a waste heat recovery case comparing the SCORC and TCORC. The results showed that the TCORC can provide higher power outputs (+31.8%) but to the detriment of a higher SIC (+72.8%). The increased SIC is mainly due to the increased share of heat exchanger cost. For the TCORC, the vapour generator amounts to 43% of the total system cost, while for the SCORC the evaporator accounts for 24% of the total cost. As such, the vapour generator can be considered a key component in the TCORC. The results also indicate that the design corresponding to the minimum SIC does not necessarily give the highest NPV . It is possible that on the Pareto front a point with a better combination of net power output and investment cost is found that maximises the NPV . For the presented case, a SCORC with a net power output 7.3% larger than the net power output at minimum SIC provides an increased NPV of 5.2%. However, it should be noted, that the given results of the thermo-economic optimisation are only valid for the case and assumptions presented in this study. They do not count as general recommendations for cycle architectures. Other boundary conditions and working fluid combinations will give different results. The optimisation framework can however easily be adapted to other cases. Furthermore, when considering waste heat valorisation, the majority of applications have time varying waste heat streams. As such, the part-load operation of ORCs is of importance to accurately assess the electricity generated. To simulate this, semi-empirical gray box models were proposed. An effort has been made to make the implementation fast, robust and highly modular. As such, the models can be used in optimisation problems but they are also easily extensible to new configurations. The gray box models were validated and calibrated on datasets coming from an 11 kWe ORC. The first step in post-processing the datasets is identifying the steady-state points of operation. Inclusion of transient data would otherwise CONCLUSIONS 191 give a bias on the results. A methodology based on a moving time window gave an efficient tool to filter the large datasets. The validation results show a closed heat balance of evaporator and condenser with a maximum deviation between secondary and primary heat flow rate of ±5%. The only input parameters to the cycle model are pump and expander rotational speeds. The important dependent parameters are the evaporation pressure, the condensation pressure and the working fluid mass flow rate. All three predicted parameters show a maximum deviation of less than ±1% from the measured value. The modelled net power output deviates less than ±2% from the measured value. In general, this is a satisfactory results that gives confidence in using these models in the part-load analysis. The part-load analysis shows that increasing the pump rotational speed increases the expander power output. However, for the net power output, the high pumping power counteracts this effect. The optimal expander inlet vapour fraction that maximises the net power output, is always higher than 0.5. This corresponds to operation as a PEORC. Compared to operation as a SCORC, the net power output is increased between 2% to 12%, depending on the boundary conditions. For increased waste heat input, the pressure in the system increases, restricting the performance of the cycle. For high variations in waste heat input it would thus be advisable to also optimise the expander speed. For the PEORC, the efficiency of the pump is also important. When the isentropic efficiency of the pump in the set-up is artificially tripled, to a maximum of 60%, the PEORC shows an increased performance between 6% and 40%. The initial results thus indicate that there are opportunities to retrofit existing SCORC installations to operate under PEORC conditions.

8.2 Future work

As mentioned in the thesis, the convective heat transfer and pressure drop correlations used are derived for refrigerants and saturation pressures found in refrigeration applications. However it is not clear how accurate these are for the refrigerants and conditions used in ORCs. The saturation pressures found in ORCs are also higher than those of typical refrigeration applications. Furthermore, additional research is needed on heat transfer in the supercritical region. Almost all of the supercritical correlations are derived for water and CO2. On these topics new research is being performed at the Applied Thermodynamics & Heat Transfer research group at Ghent University. This already resulted in sub- and supercritical set-ups to derive accurate heat transfer correlations. Initial results are expected to follow soon. In the last chapter, the semi-empirical ORC model was validated with operating points in subcritical operation. The behaviour in partial evaporating regime 192 CHAPTER 8 is extrapolated by modelling the over- and under-expansion losses. The limited results from literature give confidence in the modelling approach. However these results should be validated with experimental data. To do this, some technical challenges need to be tackled. As the control algorithm is based on the level of superheating, a new control variable needs to be introduced to handle PEORC cycles. A possibility would be to predict the quality at the inlet of the expander by a heat balance over the evaporator. To have a good prediction of the quality, the mass flow rate and temperature measurements of the hot stream should have a low uncertainty. It is also not clear that the method with the heat balance will react fast enough under transient conditions, especially under (but not limited to) start-up and shutdown of the system. Another solution could be to integrate a capacitive void fraction sensor. The signal of the void fraction sensor can be used as input to the control algorithm. Because the change in void fraction would be measured instantaneously, this method would also work under transient conditions. This measurement can in turn be used to close the evaporator heat balance in validation experiments. Finally, to be interesting for industry, the three steps in the optimisation approach (fluid/architecture screening, thermo-economics, part-load operation) should be integrated in a single program. The three step exercise should be redone for each project because boundary conditions in waste heat recovery projects change considerably. It is therefore not possible to designate one design as the best. It is however possible to make a streamlined optimisation scheme. In addition, the program should be expanded with more validated models of different expander and heat exchanger types. As such, this effort should lead to virtual prototyping tools which helps the engineer in designing an optimal ORC. A Publications

Publications as ﬁrst author in peer-reviewed international journals

S. Lecompte, H. Huisseune, M. van den Broek, S. De Schampheleire, and M. De Paepe. Part load based thermo-economic optimization of the organic Rankine cycle (ORC) applied to a combined heat and power (CHP) system. Applied Energy, vol. 111, pp. 871-881, 2013.

S. Lecompte, B. Ameel, D. Ziviani, M. van den Broek, and M. De Paepe. Ex- ergy analysis of zeotropic mixtures as working ﬂuids in organic Rankine cycles. Energy Conversion and Management, vol. 85, pp. 727-739, 2014.

S. Lecompte, H. Huisseune, M. van den Broek, B. Vanslambrouck, and M. De Paepe. Review of organic Rankine cycle (ORC) architectures for waste heat recovery. Renewable & Sustainable Energy Reviews, vol. 47, pp. 448-461, 2015.

S. Lecompte, H. Huisseune, M. van den Broek, and M. De Paepe. Methodical thermodynamic analysis and regression models of organic Rankine cycle architectures for waste heat recovery. Energy, vol. 87, pp. 60-76, 2015.

S. Lecompte, S. Lemmens, H. Huisseune, M. van den Broek, and M. De Paepe. Multi-objective thermo-economic optimization strategy for ORCs applied to sub- 194 PUBLICATIONS critical and transcritical cycles for waste heat recovery. Energies, vol. 8, pp. 2714-2741, 2015.

Publications as co-author in peer-reviewed international journals

De Schampheleire, Sven, Peter De Jaeger, Robin Reynders, Kathleen De Kerpel, Bernd Ameel, Christophe T’Joen, Henk Huisseune, Steven Lecompte, and Michel De Paepe. Experimental Study of Buoyancy-driven Flow in Open-cell Aluminium Foam Heat Sinks. Applied Thermal Engineering 59 (1-2): 30-40, 2013.

Publications in proceedings of international confer- ences

S. Lecompte, H. Huisseune, S. De Schampeleire and M. De Paepe. Optimization of waste heat recovery using an orc in a large retail company 9th International Conference : Heat transfer, Fluid Mechanics and Thermodynamics, Proceedings, 540-546., Malta, 2012.

S. Lecompte, M. van den Broek and M. De Paepe. Second law analysis of zeotropic mixtures as working ﬂuids in organic Rankine cycles 26th International Confer- ence on Efﬁciency, Cost, Optimization, Simulation and Environmental Impact of Energy System, Proceedings, China, Guilin, 2013.

S. Lecompte, M. van den Broek, and M. De Paepe. Thermodynamic analysis of the partially evaporating trilateral cycle 2nd International Seminar on ORC Power Systems, Proceedings, Netherlands, Rotterdam, 2013.

S. Lecompte, H. Huisseune, M. van den Broek, and M. De Paepe. Thermo- economic optimization of organic rankine cycle CHP with low temperature waste heat 2nd International Seminar on ORC Power Systems, Proceedings, Nether- lands, Rotterdam, 2013.

A. Desideri, M. van den Broek, S. Gusev, S. Lecompte, V. Lemort, S. Quillin. Experimental study and dynamic modeling of a WHR ORC power system with screw expander 2nd International Seminar on ORC Power Systems, Proceedings, Netherlands, Rotterdam, 2013.

S. Lecompte, M. Lazova, M. van den Broek and M. De Paepe. Optimization of waste heat recovery using an orc in a large retail company 10th International APPENDIX A 195

Conference : Heat transfer, Fluid Mechanics and Thermodynamics, Proceedings, 372-377., Orlando, USA, 2014.

S. Lecompte, M. van den Broek and M. De Paepe. Optimal selection and sizing of heat exchangers for organic rankine cycles (ORC) based on thermo-economics Proceedings of the 15th International Heat Transfer Conference, Kyoto, Japan, 2014.

S. Lecompte, S. Lemmens, A. Verbruggen, M. van den Broek and M. De Paepe. Thermo-economic comparison of advanced organic rankine cycles. The 6 th In- ternational Conference on Applied Energy, Taipei, Taiwan, 2014.

D. Ziviani, A. Suman, S. Lecompte, M. De Paepe, M. van den Broek and, P. R. Spina, M. Venturini, A. Beyene. Comparison of a single-screw and a scroll expander under part-load conditions for low-grade heat recovery ORC systems. The 6 th International Conference on Applied Energy, Taipei, Taiwan, 2014.

A. Kaya, M. Lazova, S. Lecompte, and M. De Paepe. Design sensitivity analysis of a direct evporator for low-temperature waste heat recovery ORCs using various ﬂow boiling heat transfer correlations. The 24th IIR International Congress of Refrigeration, Yokohama, Japan, 2015.

A. Kaya, S. Lecompte, M. Lazova, K. De Kerpel and M. De Paepe. Design sensitivity analysis of a direct evaporator for low-temperature waste heat recovery ORCs using various ﬂow boiling heat transfer correlations. The 24th IIR Interna- tional Congress of Refrigeration, Yokohama, Japan, 2015.

S. Lecompte, H. Huisseune, M. van den Broek, and M. De Paepe. Thermody- namic optimization of organic rankine cycle architectures for waste heat recovery. The 24th IIR International Congress of Refrigeration, Pau, France, 2015.

S. Lecompte, M. van den Broek, and M. De Paepe. Techno-thermodynamic multi- objective optimization of organic rankine cycles for waste heat recovery. 11th International Conference on Heat Transfer, Fluid Mechanics and Thermodynam- ics, Proceedings, Kruger, South-Africa, 2015.

S. Lecompte, M. van den Broek, and M. De Paepe. Performance potential of ORC architectures for waste heat recovery taking into account design and environmental constraints. Proceedings of the 3rd International Seminar on ORC Power Systems., Brussels, Belgium, 2015.

B Working ﬂuids list

Working ﬂuid Tcrit (°C) pcrit (kPa) GWP ODP Environmentally friendly R11 197.91 4394 4750 1 - R113 214.06 3392 6130 1 - R114 145.68 3257 10000 1 - R12 111.97 4136 10900 1 - R123 183.67 3672 77 0.02 - R1233zde 165.60 3570 6 0 X R1234yf 94.70 3382 4 0 X R1234zee 109.37 3636 6 0 X R125 66.023 3617 3500 0 - R134a 101.06 4059 1430 0 - R141b 204.35 4212 725 0.12 - R142b 137.11 4055 2310 0.07 - R143a 72.707 3761 4470 0 - R152a 113.26 4520 124 0 X R161 102.10 5010 10 0 X R21 178.66 5181 151 0.04 - R218 71.87 2640 8830 0 - R22 96.14 4990 1810 0.05 - R227ea 101.75 2925 3220 0 - R236ea 139.29 342 1200 0 - R236fa 124.92 3200 9810 0 - R245fa 154.01 3651 1030 0 - R32 78.10 5782 675 0 - 198 WORKING FLUIDS LIST

R365mfc 186.85 3266 794 0 - RC318 115.23 2777 10300 0 - SES36 177.55 2849 3710 0 - ammonia 132.25 11333 0 0 X acetone 234.95 4700 0.5 0 X butene 146.14 4005 3 0 X cyclohexane 280.49 4075 n.a 0 X cyclopropane 125.15 5579 20 0 X cyclopentane 238.57 4571 11 0 X D4 313.35 1332 n.a n.a X D5 346.00 1160 n.a n.a X D6 372.63 961 n.a n.a X ethanol 241.56 6268 0 0 X HFE143m 104.77 3635 347 0 - isobutane 134.67 3629 3 0 X isobutene 144.94 4009 n.a n.a X isohexane 224.55 3040 n.a n.a X isopentane 187.20 3378 2 0 X MD2M 326.25 1227 0 0 X MD3M 355.21 945 0 0 X MD4M 380.05 877 0 0 X MDM 290.94 1415 0 0 X MM 245.60 1939 0 0 X methanol 239.35 8103 2.8 0 X neopentane 160.59 3196 n.a 0 X propylene 91.06 4555 3.1 0 X propyne 129.23 5626 n.a 0 X toluene 318.60 4126 3.3 0 X water 373.94 22064 0.2 0 X cis-2-butene 162.60 4225 2 0 X m-Xylene 343.74 3534 3 n.a X n-butane 151.97 3796 3 0 X n-decane 344.55 2103 2 0 X n-dodecane 384.95 1817 2 0 X n-heptane 266.98 2736 3 0 X n-hexane 234.67 3034 3.1 0 X n-nonane 321.40 2281 2 0 X n-octane 296.17 2497 3 0 X n-pentane 196.55 3370 2 0 X n-propane 96.74 4251 3 0 X n-undecane 365.65 1990 2 0 X o-xylene 357.11 3737 1 n.a X p-xylene 343.02 3531 3 n.a X trans-2-butene 155.46 4027 n.a n.a X APPENDIX B 199

C Experimental ORC set-up

C.1 Components C.1.1 Measuring equipment Details about the measuring equipment are provided in Table C.1. There is no measurement of the shaft torque. All of the equipment is connected trough a PROFIBUS [1] network to a Siemens S7-1200 PLC.

Measurement Type Equipment

m˙ wf Coriolis ﬂow meter E+H, Promass F m˙ hf Pressure oriﬁce Rosemount 3051 m˙ cf Ultrasonic Siemens Sitrans FUS 380 Twf RTD E+H, TST487 Thf RTD E+H, TR13 Tcf RTD E+H, TR90 pwf Absolute pressure sensor WIKA A-10

Table C.1: Make of measurement equipment.

C.1.2 Heat exchangers All of the heat exchangers (evaporator, condenser, recuperator) in the system are identical and of the brazed plate heat exchanger type. A picture of the such a heat 202 EXPERIMENTAL ORC SET-UP

Figure C.1: Plate heat exchanger of the ORC. exchanger installed in the system is shown in Figure C.1. Geometric details about the heat exchangers are provided in Table C.2. The evaporator is insulated with glass wool (thermal resistance value of 4.5 m2/K.W), see also Figure C.2. The other heat exchangers are not insulated. There is a bypass installed over the recuperator to support measurements without recuperator. Tests reported in this work are done without recuperator.

Figure C.2: Plate heat evaporator in the system. APPENDIX C 203

Characteristic Value Model SWEP B200T SC-M Number of plates (-) 150 Dimensions (mm) 525 x 353.5 x 243 Temperature range (°C) -196–225 Maximal pressures (bar) 45 at 135 °C and 36 at 225 °C Material (-) stainless steel Weight (kg) 69.8

Table C.2: Characteristics of the plate heat exchangers.

C.1.3 Centrifugal pump A centrifugal turbopump is chosen to pressurise the working ﬂuid. The characteristics are found in Table C.3. A picture is given in Figure C.3.

Figure C.3: Centrifugal pump. 204 EXPERIMENTAL ORC SET-UP

Characteristic Value Model Calpeda MXV 25-214 Nominal speed (rpm) 2900 Nominal power (kWe) 2.2 Head range (m) 59-149 Flow range (m3/h) 1-4.5 Number of stages (-) 14 Material (-) stainless steel AISI 304 Weight (kg) 26

Table C.3: Characteristics of the pump.

C.1.4 Volumetric double screw expander The expander is a volumetric double screw machine. Details about the expander are not disclosed. A 3D picture is given in Figure C.4.

Figure C.4: 3D picture of the volumetric double screw expander.

C.1.5 External loops The ORC system is composed of two main external loops: the heating and the cooling loop. The mass ﬂow rate of both secondary loops can be controlled by a three way valve.

C.1.5.1 Heating loop The heating loop consists of an Maxxtec®heater made up of 10 x 25 kWe electrical heaters, see Figure C.5. The maximum thermal oil ﬂow is 14 m3/h at a maximum temperature of 340 °C. The thermal oil used is Therminol 66. APPENDIX C 205

Figure C.5: Electrical thermal oil heater of 250 kWe.

C.1.5.2 Cooling loop

The cooling loop consists of an air cooled condenser with a rated capacity of 480 kW at 20 °C ambient and respectively water input and output temperature of 70 °C and 90 °C. The cooling medium is a mixture of water and glycol, with 33 vol% glycol. The maximum rated temperature and mass ﬂow rate are respectively 120 °C and 20 m3/h. It is not possible to independently impose the temperature of the water-glycol mixture that enters the ORC condenser. This temperature depends on the ambient conditions and the heat-load. A picture of the cooling loop is shown in Figure C.6.

Figure C.6: Air cooled cooler with glycol/water cooling loop. 206 EXPERIMENTAL ORC SET-UP

C.2 Uncertainty analysis

The uncertainty of each measurement equipment is given in Table C.4. For a well calibrated pressure oriﬁce (provided by Maxxtec®) according to the standards [2, 3], the uncertainty is approximately ±1% [4]. Uncertainties on the modelling of the thermophysical properties are given as:

Umodel,h,R245fa = 1.18%(gasious)

Umodel,h,R245fa = 0.10%(liquid)

Umodel,h,T herminol66 = 1%

Umodel,h,W aterGlycol = 1%

The data for R245fa is taken from Lemmon and Span [5]. For Therminol66 no speciﬁc data is available, however the regression model implemented in CoolProp shows a maximum error of 0.05%. For the water glycol mixture the regression model in CoolProp shows a maximum error of 0.02%. As such we assume a worst case scenario with an uncertainty of 1%. These uncertainties in the correlations should certainly not be neglected as they have a signiﬁcant impact in the error propagation.

Measurement Type Range Accuracy

m˙ wf Coriolis ﬂow meter 0 to 1.8 kg/s ±0.15% rate 3 m˙ hf Pressure oriﬁce 0 to 20 m /h ±1% rate m˙ cf Ultrasonic 0 to 6 l/s ±1% rate Twf RTD -50 to 300 °C ±0.2 °C Thf RTD -50 to 400 °C ±0.2 °C Tcf RTD 0 to 120 °C ±0.2 °C pwf Absolute pressure sensor 0 to 16 bar ±0.25% span

Table C.4: Accuracy of measurement equipment.

Assuming that each measured parameter is independent and random, the uncertainty on the variable y is calculated as function of the uncertainties Uxi on each measured variable xi [6]: v u 2 uX ∂y 2 Uy = t U (C.1) ∂x xi i i The accuracy of the measurement equipment used is given in Table C.4. The calculation of the heat ﬂow rate follows from: APPENDIX C 207

Q˙ =m ˙ (hin − hout) (C.2) Thus the uncertainty on Q˙ is calculated as:

v u !2 !2 !2 u ∂Q˙ ∂Q˙ ∂Q˙ UQ˙ = t Um˙ + Uhin + Uhout (C.3) ∂m˙ ∂hin ∂hout

q 2 2 2 UQ˙ = (∆hUm˙ ) + (mU ˙ hin ) + (mU ˙ hout ) (C.4)

With Uh calculated as: s 2 2 ∂h ∂h 2 Uh = UT + Up + U (C.5) ∂T ∂p hcorrelation

∂h ∂h The values of ∂T and ∂p can directly be derived from CoolProp [7] or alternatively by numerical differentiation. For calculating the mass ﬂow rate from a given volume ﬂow rate,

m˙ = ρV˙ (C.6) the uncertainty on m˙ is calculated as:

r 2 ˙ 2 Um˙ = VUρ + (ρUV˙ ) (C.7) s 2 2 ∂ρ ∂ρ 2 Uρ = UT + Up + U (C.8) ∂T ∂p ρcorrelation

The results of the uncertainty calculations can be found in Table C.5. 208 EXPERIMENTAL ORC SET-UP

Uncertainty U U U U U U U U U U U U U U U U m,cf ρ,cf evap, evap,h,out,hf evap,h,in,hf m,hf evap,h,in,cf cond, cond,h,out,wf cond,h,in,wf ρ,hf evap,h,in,wf evap,h,out,cf evap, evap,h,out,wf evap, ˙ ˙ ( Q,hf Q,wf Q,cf ( Q,wf k/)008 .42002 .42001 .71003 .80008 .710.0408 0.0791 0.0789 0.0840 0.0732 0.0721 0.0714 0.0422 0.0421 0.0422 0.0789 (kg/s) kg ˙ ˙ ˙ ˙ k/)001 .33001 .61000 .61000 .29009 .310.0301 0.0301 0.0299 0.0299 0.0601 0.0601 0.0601 0.0601 0.0313 0.0313 0.0314 (kg/s) kg / / m m k)37 .538 .968 .668 .434 .03.53 3.50 3.47 3.44 6.88 6.86 6.88 6.99 3.87 3.85 3.78 (kW) k)40 .640 .876 .876 .135 .43.53 3.54 3.52 3.51 7.69 7.68 7.68 7.68 4.06 4.06 4.07 (kW) k)23 .423 .825 .025 .119 .21.93 1.92 1.92 1.91 2.58 2.60 2.57 2.58 2.36 2.34 2.35 (kW) k)22 .722 .924 .125 .518 .51.86 1.85 1.86 1.85 2.50 2.51 2.49 2.49 2.28 2.27 2.26 (kW) 3 3 Jk)19 4710 4810 5810 4917 471473 1477 1477 1479 1509 1508 1508 1498 1501 1497 1490 (J/kg) Jk)19 8619 8419 8519 7711 771718 1717 1718 1717 1894 1895 1895 1894 1894 1896 1895 (J/kg) .70013 .89015 .87012 .87014 .72014 0.1776 0.1744 0.1742 0.1740 0.1827 0.1824 0.1827 0.1854 0.1849 0.1839 0.1780 ) Jk)28 0734 0533 0732 9224 942976 2944 2942 2942 3028 3027 3033 3065 3047 3037 2981 (J/kg) Jk)56 6157 7150 6759 6151 685621 5608 5611 5611 5697 5697 5706 5711 5679 5691 5664 (J/kg) .77020 .77021 .75021 .75029 .67029 0.2697 0.2697 0.2697 0.2697 0.2715 0.2715 0.2715 0.2715 0.2707 0.2707 0.2707 ) Jk)16 6815 6310 6410 5412 591582 1529 1528 1524 1606 1604 1607 1673 1658 1648 1561 (J/kg) Jk)17 3718 6310 6019 2217 211275 1271 1272 1272 1599 1600 1600 1603 1386 1387 1377 (J/kg) Jk)51 9250 9254 9154 8554 805841 5840 5842 5845 5940 5941 5942 5942 5908 5922 5917 (J/kg) Jk)25 0432 0329 9829 9221 942948 2914 2913 2912 2999 2998 2997 3033 3022 3014 2952 (J/kg) al .:Aslt netit values uncertainty Absolute C.5: Table taysaewrigpoints working state Steady APPENDIX C 209

References

[1] R. W. Mitchell. Proﬁbus: A Pocket Guide. ISA-The Instrumentation, Systems, and Automation Society, 2003.

[2] UNI EN ISO. Measurement of ﬂuid ﬂow by means of pressure differential devices inserted in circular cross section conduits running full - Part 1: General principles and requirements, 5167-2:2003.

[3] UNI EN ISO. Measurement of fluid flow by means of pressure differential devices inserted in circular cross section conduits running full - Part 2: Orifice Plates, 5167-2:2004.

[4] Z. D. Husain. Theoretical uncertainty of oriﬁce ﬂow measurement. Technical report, Univ. of Oklahoma, Oklahoma City, OK (United States), 1995.

[5] E. W. Lemmon and R. Span. Short fundamental equations of state for 20 industrial ﬂuids. Journal of Chemical & Engineering Data, 51(3):785–850, 2006.

[6] R. J. Moffat. Describing the uncertainties in experimental results. Experimen- tal Thermal and Fluid Science, 1(1):3 – 17, 1988.

[7] I. H. Bell, J. Wronski, S. Quoilin, and V. Lemort. Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp. Industrial & Engineering Chemistry Research, 53(6):2498–2508, 2014.

D Fin and tube heat exchangers

The implementation of a ﬁn and tube heat exchanger in the modelling approach is illustrated here for completeness. This code was used in consultancy projects but will not be further used in this thesis.

D.1 P-NTU correlations

The P-NTU correlations [1] for cross ﬂow heat exchangers with one pass and n parallel rows is given below:

n = 1 P = 1 − exp [−(1 − exp(R.NT U)/R)] (D.1) K2 n = 2 P = 1 − exp (−2K/R) 1 + (D.2) R K = 1 − exp(−NT U.R/2) (D.3) K2(3 − K) 3K4 n = 3 P = 1 − exp(−3K/R) 1 + + (D.4) R 2R2 K = 1 − exp(−NT U.R/3) (D.5) n = 4 P = 1 − exp(−4K/R) (D.6) K2(6 − 4K + K2) 4K4(2 − K) 8K6 1 + + + R R2 3R3 K = 1 − exp(−NT U.R/4) (D.7) 212 FINANDTUBEHEATEXCHANGERS

D.2 Connection equations

For a cross flow configuration with different passes the primary flow (i.e the working fluid) goes sequentially trough each segment while the secondary flow (i.e the hot flue gas) is assumed to be homogeneously divided over the cross-section area of the inlet. The resulting equations connection the segments are given below:

hprim,in,i+1 = hprim,out,i (D.8)

Tprim,in,i+1 = Tprim,out,i (D.9)

hsec,in,i+1 = hsec,in,i (D.10)

Tsec,in,i+1 = Tsec,in,i (D.11)

A homogeneous mixing of the secondary ﬂow is assumed over the segments composing the pass. As such, for the next pass, the inlet enthalpy and temperature of the secondary ﬂow is given as:

segments previous pass P hsec,out,im˙ sec,out,i h = i (D.12) sec,in,nextpass segments previous pass P m˙ sec,out,i i (D.13)

D.3 Convective heat transfer correlations

First the convective heat transfer correlations for single phase flow are given. Con- sidering a circular duct, the assumption of a constant heat flux and a fully developed laminar flow (Re < 2300) the local Nusselt number can be analytically [2] derived as:

Nu = 4.36 (D.14)

For turbulent ﬂow (Re > 2300) the Gnielinski [3] correlation is used: f P r Nu = (Re − 1000) (D.15) 2 1 + 12.7(f/2)1/2(P r2/3 − 1) with the friction factor f from the Bhatti-Shah [4] correlation:

f = 0.0054 + 2.3 ∗ 10−8Re−1/(−2/3) Re < 4000 (D.16) f = 0.00128 + 0.1143Re−1/3.2154 Re > 4000 (D.17) APPENDIX D 213

For the secondary side, the plain fin coil correlations from Wang [5] are used. The correlations are given in function of the fanning friction factor F and the Col- burn j factor and were derived from data on 74 coil configurations. The correlation has a dependency on the number of rows Nr, fin pitch Fp, hydraulic diameter Dh, transverse tube spacing Xt, collar diameter (Doutside + 2tfin) and longitudinal tube spacing Xl. P 5 P 6 P 7 P 3 P 4 Fp Fp Fp j = 0.086Re Nr (D.18) Dc Dh Xt X F 2 F F 3 f = 0.0267ReF 1 t p (D.19) Xl Dc X F 0.00758 F 1 = −0.764 + 0.739 t + 0.177 p − (D.20) Xl Dc Nt 64.021 F 2 = −15.689 + (D.21) ln(Re) 15.695 F 3 = 1.696 − (D.22) ln(Re) 0.41! 0.042Nt Fp P 3 = −0.361 − + 0.158ln Nt (D.23) ln(Re) Dc 1.42 Xl 0.076 D P 4 = −1.224 − h (D.24) ln(Re) 0.058N P 5 = −0.083 + t (D.25) ln(Re) Re P 6 = −5.735 + 1.21ln (D.26) N 214 FINANDTUBEHEATEXCHANGERS

References

[1] R. H. Avanço, R. Perussi, H. A. Navarro, and L. C. Gomez.´ Numerical compu- tation of the effectiveness-number of transfer units for several cross-flow heat exchangers with different flow arrangements. 2009.

[2] R. K. Shah and D. P. Sekulic. Fundamentals of Heat Exchanger Design. Wiley, 2003.

[3] V. Gnielinski. New equations for heat and mass transfer in the turbulent ﬂow in pipes and channels. NASA STI/Recon Technical Report A, 75:8–16, 1975.

[4] S. Kakac¸, R. K. Shah, and W. Aung, editors. Handbook of Single-Phase Con- vective Heat Transfer, chapter Laminar Convection Heat Transfer in Ducts. John Wiley & Sons, 1987.

[5] C. C. Wang, K. Y. Chi, and C. J. Chang. Heat transfer and friction characteristics of plain ﬁn-and-tube heat exchangers, part II: Correlation. International Journal of Heat and Mass Transfer, 43(15):2693 – 2700, 2000. E On the use of zeotropic mixtures

The use of zeotropic mixtures as working fluids for the ORC has gained interest recently. Zeotropic mixtures have a non-isothermal phase shift. As such, they have the ability to decrease the irreversibility associated with heat transfer over a finite temperature difference across the working fluid and the thermal heat source or heat sink reservoir. Zeotropic mixtures as working fluids have been investigated for heat pumps [1–3] and vapour compression cycles [3–5]. Several studies focus on the use of zeotropic mixtures for ORCs, their analysis is usually based on a first law analysis with a limited selection of zeotropic mixtures, see for examples the works of Wang and Zhao [6] (R245fa/R152a), Garg et al. [7] (R245fa/isopentane) and Borsukiewicz-Gozdur et al. [8] (propane/ethane) and Chys et al. [9]. Only a few studies investigate the ORC with zeotropic mixtures from a second law perspective. Furthermore, only a limited selection of working fluids are considered. Heberle et al. [10] investigated the second law efficiency of an ORC with zeotropic mixtures of isobutane/isopentane and R227ea/R245fa as working fluids. The results show that for temperatures below 120 °C the second law efficiencies increased in the range of 4.3% to 15%. The optimal second law efficiency was achieved when the temperature glide of condensation and cooling water matched. Ho et al. [11] compared the Organic Flash Cycle (OFC) to an optimised basic ORC cycle, a zeotropic rankine cycle with a binary ammonia-water mixture and a transcritical CO2 cycle. A distinction is made between utilisation efficiency and second law internal efficiency. The former definition assumes that the exergy which is left in the waste heat stream is discarded or unused, while the latter discards exergy 216 ONTHEUSEOFZEOTROPICMIXTURES destruction due to heat transfer in the evaporator. The definition of second law efficiency is therefore not unique; it is based on a carefully selected set of chosen input and output streams. The objective of this chapter is to analyse the performance of zeotropic working fluids based on a second law analysis. The work focusses on non-superheated subcritical cycles. Comparisons are made among a selection of zeotropic working fluids. Special care is taken to quantify the distribution of irreversibilities within the system. The ORC is optimised and the cause of the optimisation potential is further analysed.

E.1 Working ﬂuid selection

The selected pure working fluids are all hydrocarbons and can be found in Ta- ble E.1. The selection corresponds with that of a previous study by the authors [9]. Guidelines for mixture component selection in cryogenic applications are adopted [12, 13]. The first component is volatile at 1-1.5 bar and therefore, low temperatures after expansion can be obtained without the need to reach vacuum. The second component exceeds both the desired average condensation temperature and the boiling point of the first component. The final selection of mixtures is: isopentane-hexane, isopentane-cyclohexane, isopentane-isohexane, pentane- hexane, isobutane-isopentane, R245fa-pentane, R245fa-isopentane and R245fa- R365mfc. The most volatile component is always the first component in the mixtures name.

Fluid M (g/mol) Tcrit (°C) pcrit (bar) Tboiling (°C) cyclohexane 84.2 280.5 40.8 80.3 hexane 86.2 234.7 30.3 68.3 isobutane 58.1 134.7 36.3 -12.1 isohexane 86.2 224.6 30.4 59.8 isopentane 72.1 187.2 33.8 27.4 pentane 72.1 196.6 33.7 35.7 R245fa 134.0 154.0 36.5 14.8 R365mfc 148.1 186.9 32.7 39.8

Table E.1: Thermophysical properties of the selected pure working ﬂuids.

E.2 Model and assumptions

The ORC is evaluated assuming steady state conditions of all components. Fur- thermore, heat loss to ambient or pressure drops are neglected. An upper pressure APPENDIX E 217 limit of 90% of the critical pressure of the fluid is imposed in order to ensure a stable and safe operation. As each of the working fluids discussed are dry fluids and superheating is omitted. The ORC, heat source and heat sink parameters are summarised in Table E.2. The REFPROP 9.0 database [14] provides the thermophysical data of the studied mixtures and pure fluids.

Variable Description Value

pump (-) Isentropic efficiency pump 0.60 exp (-) Isentropic efficiency expander 0.75 ∆TP P,evap (°C) PP temperature difference evaporator 10 ∆TP P,cond (°C) PP temperature difference condenser 10 Thf,in (°C) Inlet temperature heat carrier 150 m˙ hf (kg/s) Mass flow rate heat carrier 65.5 hf Heat carrier medium Water cf Cooling medium Water phf (bar) Heat carrier pressure 5 Tcf,in (°C) Inlet temperature cooling water 20 Tcf,out (°C) Outlet temperature cooling water 30

Table E.2: ORC, heat source and heat sink parameters.

A comparative analysis is made by evaluating the exergy destruction ratio to reference values of a pure working ﬂuid. The most volatile component in the mixture is chosen as working ﬂuid for the reference case.

ref ∆yD,component = yD,component − yD,component (E.1)

The sum of ∆yD,component over the different components is a measure of the change in irreversibilities between a thermodynamic cycle with a zeotropic mixture as working ﬂuid and a pure working ﬂuid.

E.2.1 Optimisation

The second law efficiency ηII is maximised, unless otherwise stated. The optimisation variables are the evaporating pressure and the mixture concentration. If the mixture concentration is fixed, only the evaporation pressure is optimised. Opti- misation is done with a Generalised Reduced Gradient (GRG) nonlinear multistart algorithm [15]. Since E˙ hf,in is constant for a given heat source, optimisation of the second law efficiency is equal to optimisation of the net power output. 218 ONTHEUSEOFZEOTROPICMIXTURES

E.3 Effect of zeotropic mixtures

In this section R245fa-isopentane is used as a reference case to illustrate the different effects of zeotropic mixtures. Deviations and particularities for other mixtures (R245fa-pentane, R245fa-R365mfc, isopentane-isohexane, isopentane-cyclohexane, isopentane-isohexane, isobutane-isopentane, pentane-hexane) are discussed in section E.4.

In Fig. E.1c, ηII is plotted in function of the mixture concentration. An optimal mixture concentration of 0.28/0.72 gives an increase of 8.45% in second law efﬁciency compared to the pure working ﬂuid R245fa. Both are evaluated at their optimal evaporation pressure. The source of this increase and the underlying optimisation strategy are analysed further.

E.3.1 Internal and external second law efﬁciency

In a first step the absorbed heat and heat conversion to power are decoupled by plotting ηII,ext and ηII,int (see Fig. E.2c) for R245fa-isopentane. By using a mixture as working fluid more heat is transferred to the ORC (higher ηII,ext) and heat is converted more effectively to power (higher ηII,int). Furthermore, for R245fa- isopentane, the optimal concentration which maximises ηII,ext and ηII,int is equal and coincides with that of maximum second law efficiency ηII .

An increase in ηII,int is the result of a lower overall exergy destruction in the cycle. The source of the reduced exergy destruction is investigated by calculating ∆yD for all components. For R245fa-isopentane ∆yD,cond and ∆yD,evap are given in Fig. E.3c while ∆yD,exp and ∆yD,pump are given in Fig. E.4c. Note that the values of ∆yD,cond are generally larger than that of ∆yD,evap, ∆yD,exp or ∆yD,pump. Especially the pump has a low effect on the cycle internal performance when varying mixture concentration. Furthermore it is important to notice that the minimum value of ∆yD,cond is found at the same concentration that maximises ηII,int. Fig. E.5 gives the QT diagram for the optimised ORC with pure working ﬂuid (R245fa, full line) and with mixture (R245fa-isopentane, dashed line). The heat carrier is cooled down to a lower temperature when using a mixture. Firstly, this is due to the matching temperature glide in the condenser which lead to a decrease in working ﬂuid outlet temperature at the condenser. Also, the pinch point temperature is reduced, lowering the heat input limitation induced by the pinch point temperature difference. This is the further is discussed in section E.3.2. Furthermore, an increase in heat input follows when the latent heat capacity rate of the mixture is reduced [16]. This shifts the pinch point to the right in a QT diagram allowing a larger cooling of the heat carrier. APPENDIX E 219

II,int [%] η efficiency law Second

- 1 C 45 44 43 42 41 40 39 38 37 36 35

- 1

45 44 43 42 41 40 39 38 37 36 35

- 1 - 1

R245fa R365mfc

C R245fa R365mfc C 0.8 R245fa R365mfc 0.8 R245fa R365mfc 0.8 0.8

0.6

0.6 - 0.6 - - 0.6 - 0.4 0.4 R245fa isopentane 0.4 R245fa isopentane R245fa isopentane 0.4 R245fa isopentane 0.2

0.2

0.2 0.2

- - - Concentration most volatile component Concentration most volatile component 0 Concentration most volatile component 0 Concentration most volatile component 0 0

R245fa pentane

33 32 31 30 29 28 27 26

R245fa pentane II R245fa pentane

33 32 31 30 29 28 27 26 [%] η

Second law efficiency efficiency law Second R245fa pentane

II 83 80 77 74 71 68 [%] η efficiency law Second

83 II,ext 80 77 74 71 68 [%] η efficiency law Second

II,ext [%] η efficiency law Second

II,int

[%] η efficiency law Second

II,int [%] η efficiency law Second 1

B 45 44 43 42 41 40 39 38 37 36 35 45 44 43 42 41 40 39 38 37 36 35

- 1 -

0.8 -

0.8

B B Pentane hexane Pentane hexane 0.8 0.8 Pentane hexane Pentane hexane 0.6 0.6

0.6 0.6 0.4 0.4

- -

- - 0.4 0.4 0.2 0.2 Isobutane isopentane Isobutane isopentane 0.2 Concentration most volatile component Isobutane isopentane 0.2 Concentration most volatile component Isobutane isopentane 0 0

Concentration most volatile component

33 32 31 30 29 28 27 26

II II second law efﬁciency of zeotropic mixtures in function of mixture concentration [%] η Second law efficiency efficiency law Second 0 [%] η Second law efficiency efficiency law Second 0 (optimal evaporation pressure).

83 80 77 74 71 68

83 80 77 74 71 68 II,ext II,ext [%] η efficiency law Second [%] η efficiency law Second

II,ext

II,int II,int [%] η efficiency law Second [%] η Second law efficiency efficiency law Second η

1 1 - - A A - -

45 44 43 42 41 40 39 38 37 36 35 45 44 43 42 41 40 39 38 37 36 35 second law efficiency of zeotropic mixtures in function of concentration mixtures of zeotropic second law efficiency second law efficiency of zeotropic mixtures in function of concentration mixtures of zeotropic second law efficiency

1 1 ) )

II,ext II,ext 0.8 A 0.8 A η η Isopentane hexane Isopentane hexane Isopentane hexane Isopentane hexane 0.8 0.8 and external 0.6 0.6

- - - - 0.6 0.6 II,int η 0.4 0.4 ) and external ( ) ) and external ( ) 0.4 0.4 Isopentane cyclohexane Isopentane cyclohexane Isopentane cyclohexane II,int Isopentane cyclohexane II,int η η 0.2 0.2 0.2 - - 0.2 - -

Concentration most volatile component Concentration most volatile component Concentration most volatile component Concentration most volatile component 0 0 Second law efficiency of zeotropic mixtures of zeotropic law in function efficiency of concentration Second ( Internal 0 Second law efficiency of zeotropic mixtures of zeotropic law in function efficiency of concentration Second ( Internal 0 . .

. .

33 32 31 30 29 28 27 26 Figure E.1: Second law efﬁciency of zeotropic mixtures in function of mixture concentration (optimal evaporation pressure). 8 9

33 32 31 II 30 29 28 27 26 8 9 Isopentane isohexane

83 80 77 74 71 68

Isopentane isohexane [%] η efficiency law Second II II

II,ext Isopentane isohexane

83 80 77 74 71 68 Isopentane isohexane [%] η efficiency law Second [%] η efficiency law Second

II,ext [%] η Second law efficiency efficiency law Second Figure E.2: Internal Fig. Fig. Fig. Fig. 220 ONTHEUSEOFZEOTROPICMIXTURES Fig. Fig.

Δβ,turbine and Δβ,turbine 11. Fig. Δβ,pump 10. Fig. iueE.3: Figure iueE.4: Figure Δy [%] Δy [%]D,turbine -4 -3 -2 -1 Δy [%] -1.5 -1.0 -0.5 isohexane Isopentane D,cond -4 -3 -2 -1 D,exp Δy [%]0 1 2 3 4 11 10 -1.5 -1.0 -0.5 isohexane Isopentane 0.0 0.5 1.0 1.5 D,cond 0 1 2 3 4 isohexane Isopentane 0.0 0.5 1.0 1.5 isohexane Isopentane 0 . . 0

Δβ 0 Δ Δβ, 0 Concentration most volatile component volatile most Concentration Concentration most volatile component volatile most Concentration Concentration most volatile component volatile most Concentration β Concentration most volatile component volatile most Concentration ,cond ,cond turbine and Δβ,pump

0.2 -

- 0.2

- 0.2 and and ∆ ∆ y y cyclohexane Isopentane Δ cyclohexane Isopentane D,cond D,exp cyclohexane Isopentane Δβ cyclohexane Isopentane 0.4 β 0.4 0.4 0.4 ,evap ,evap

for zeotropic mixturesfor zeotropic of concentration in function for zeotropic mixtures in function of concentration mixturesfor zeotropic of concentration in function and 0.6 and 0.6 0.6 0.6 - - - -

∆

∆ for zeotropic mixturesfor zeotropic of concentration in function for zeotropic mixtures in function of concentration mixturesfor zeotropic of concentration in function y 0.8 0.8 0.8 y D,pump 0.8 hexane Isopentane hexane Isopentane D,evap hexane Isopentane hexane Isopentane A A A A

1 1 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 o etoi itrsi ucino itr ocnrto otmleaoainpressure). evaporation (optimal concentration mixture of function in mixtures zeotropic for o etoi itrsi ucino itr ocnrto otmleaoainpressure). evaporation (optimal concentration mixture of function in mixtures zeotropic for -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 - - -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 - -

ΔyD,evapΔyD,[%]evap [%] ΔyD,pumpΔyD, [%]pump [%] ΔyD,condΔyD,cond[%] [%] -4 -3 -2 -1 -4 -3 -2 -1 0 1 2 3 4 -1.5 -1.0 -0.5 0 1 2 3 4 -1.5 -1.0 -0.5 Δy Δy [%] [%] D, D,turbine0.0 0.5 1.0 1.5 exp0.0 0.5 1.0 1.5 0 0 Concentration most volatile component volatile mostConcentration ocnrto otvltl component volatile mostConcentration 0 0 Concentration most volatile component volatile most Concentration Concentration most volatile component volatile most Concentration 0.2 isopentane Isobutane 0.2 isopentane Isobutane 0.2 isopentane Isobutane 0.2 isopentane Isobutane 0.4 0.4 0.4 - 0.4 -

- -

0.6 0.6 0.6 0.6

hexane Pentane hexane Pentane 0.8 0.8 0.8 0.8 hexane Pentane hexane Pentane

B B B B - -

1 1 - - 1 1

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4

ΔyD,evapΔyD,evap[%] [%] ΔyD,pumpΔyD,pump [%] [%]

ΔyD,expΔy [%]D,turbine [%] ΔyD,condΔyD,cond[%] [%] -4 -3 -2 -1 -1.5 -1.0 -0.5 -4 -3 -2 -1 -1.5 -1.0 -0.5 pentane R245fa 0 1 2 3 4 0.0 0.5 1.0 1.5 pentane R245fa 0 1 2 3 4 0.0 0.5 1.0 1.5 pentane R245fa pentane R245fa 0 0 ocnrto otvltl component volatile mostConcentration Concentration most volatile component volatile mostConcentration 0 0 Concentration most volatile component volatile most Concentration Concentration most volatile component volatile most Concentration - -

- 0.2 - 0.2

0.2 0.2 isopentane R245fa 0.4 isopentane R245fa 0.4 isopentane R245fa 0.4 isopentane R245fa 0.4 - - 0.6 - 0.6 - 0.6 0.6

0.8 0.8 0.8 0.8 R365mfc R245fa R365mfc R245fa R365mfc R245fa R365mfc R245fa C C C C

1 1 1 1

- -

- -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -4 -3 -2 -1 0 1 2 3 4

Δy [%] D,evapΔyD,evap [%]

ΔyD,pumpΔy [%] [%]

D,pump APPENDIX E 221

21 041 kW 041 21

4 19 014 kW 014 19 20000

1 16 815 kW 815 16

19 899 kW 899 19

18 010 kW 010 18 15000 16 495 kW 495 16

10000 Enthalpy flow [kW] Enthalpyflow

(optimal pressure). 7 151 kW 151 7 7 189 kW 7 189 5000 ORC pure working working pure fluid ORC heat carrier (pure) (pure) water cooling ORC mixture carrier (mixture) heat (mixture) water cooling

6 7 2 Figure E.5: QT diagram R245fa-isopentane (optimal concentration and evaporation pressure) and pure working ﬂuid R245fa 0

3 0

80 60 40 20

160 140 120 100 C] ° [ Temperature 222 ONTHEUSEOFZEOTROPICMIXTURES

Temperature [°C] 100 120 140 160 20 40 60 80 iueE6 TdarmR4f-spnae(pia ocnrto,fie ic on eprtr 0. C n uewrigfluid working pure and °C) 103.8 temperature point pinch fixed concentration, (optimal R245fa-isopentane diagram QT E.6: Figure 0 3

0 6 2 7

cooling water (mixture) water cooling (mixture) heat carrier ORC mixture (pure) water cooling (pure) heat carrier fluid working ORC pure 5000 7151 kW 25a(pia pressure). (optimal R245fa 7269 kW

Enthalpy flowEnthalpy [kW] 10000

15 78115 kW 15000

17 99517 kW

16 49516 kW 1 8

18010 kW

4 20000

19899 kW 20017 kW

APPENDIX E 223

E.3.2 Analysis of the optimal pinch point temperature

In this section, the difference between the optimal pinch point temperature for pure fluids and zeotropic mixtures is discussed. The pinch point temperature TPP in this chapter, is defined as the temperature of the heat carrier at the point of minimum temperature difference between working fluid and heat carrier. The evaporation pressure unambiguously determines the pinch point temperature and vice versa. A cycle with R245-isopentane is constructed with as reference TPP the optimal TPP of an ORC with pure R245fa (103.8 °C). Only the second optimisation variable, the concentration, is optimised in this cycle. Fig. E.6 gives the QT diagram for this suboptimal reference cycle. The cycle with pure R245fa is shown as a full line. Again, the heat input to the cycle is increased due to matching temperature profiles in the condenser and the location of the pinch point. However, the heat input is lower than with an optimal pinch point temperature (see Fig. E.5). The discussion below explains what happens if the pinch point temperature is optimised. From Fig. E.7 it is clear that, between mixture concentrations 0 to 0.7 the optimal pinch point temperature is larger than that of the reference case. The results for external and internal second law efficiency for the reference case and the optimal case is given in Fig. E.8. Between mixture concentrations 0 to 0.7 the internal second law efficiency ηII,int is larger for the reference cycle while the external second law efficiency ηII,ext is lower. For the cycle with optimal pinch point temperature, internal second law efficiency is thus sacrificed for increased heat input. Mixture concentrations from 0.7 to 1 are optimised by increasing the pinch point temperature. Internal second law efficiency is increased in detriment of a decreased heat input. By optimising the evaporating pressure and thus the pinch point temperature an optimal balance is found between ηII,int and ηII,ext maximising the internal efficiency ηII .

E.3.3 Glide slopes

For the mixture R245fa-isopentane the optimal concentration (0.28/0.72) corresponds to the maximum glide slope possible in the condenser and evaporator (see Fig. E.9). As discussed earlier, matching the glide slope of the working fluid in the condenser to the glide slope of cooling fluid increases the heat input (ηII,ext) but also contributes considerably to the increase of conversion efficiency ηII,int. As a result matching the glide slopes in the condenser is crucial when optimising the power output. 224 ONTHEUSEOFZEOTROPICMIXTURES

105 104

103

° [

102

pp T 101 100 99 0 0.2 0.4 0.6 0.8 1 Concentration most volatile component

Reference Tpp Optimal Tpp

Figure E.7: Pinch point temperature and pressure in function of mixture concentration with optimal and reference pinch point temperature (=103.8 °C) (R245fa-isopentane).

81 41 80 40

78 39

[%] [%]

II,int II,int

II,ext 77 η η 38 76 37 75 74 36 0 0.2 0.4 0.6 0.8 1 Concentration most volatile component

Reference Tpp Optimal Tpp

Figure E.8: ηII,ext and ηII,int in function of mixture concentration for optimal and reference pinch point temperature (=103.8 °C) (R245fa-isopentane). APPENDIX E 225

7.0 6.0

5.0

C] ° 4.0 3.0

Glide Glide slope [ 2.0 1.0 0.0 0 0.2 0.4 0.6 0.8 1 Concentration most volatile component

Evaporator Condenser

Fig. 1. Glide slope of working fluid in condenser and evaporator Figure E.9: Glide slope of R245fa-isopentane in evaporator and condenser in function of concentration.

E.3.4 Effect of the recuperator

In this section, the influence of adding a recuperator to the basic ORC is analysed. The optimal pressure and concentration to maximise the net power output are approximately equal for an ORC with and without recuperator (pevap = 8.47 bar, C = 0.29/0.71 versus pevap = 8.43 bar, C = 0.28/0.72). However, compared to the ORC without recuperator, the internal second law efficiency (ηII,int) is higher while the external second law efficiency (ηII,ext) and second law efficiency (ηII ) are lower. This is illustrated in Fig. E.10 where the relative change of ηII,int, ηII,ext, and ηII is shown in function of the mixture concentration. An increase in ηII,int implies that the conversion from exergy to electric power occurs more efficiently. In contrast, a decrease in ηII,ext implies that the heat input to the ORC is reduced. The second law efficiency ηII is reduced, since the decrease in heat input is slightly larger than the increase in conversion efficiency. In Fig. E.10, the higher temperature glide of the working fluid (the glide slope peaks at a concentration of 0.2/0.8) result in a larger decrease of ηII . This is due to the imposed pinch point temperature difference at the recuperator. When the temperature glide gets higher, the temperature difference between the exit of the turbine and outlet of the condenser increases. As a result, the logarithmic mean temperature difference increases, leading to a higher heat recuperation and a decreased heat input at the evaporator. 226 ONTHEUSEOFZEOTROPICMIXTURES

4 2 0 -2 -4 -6

-8 andwithout recuperator [%] 0 0.2 0.4 0.6 0.8 1 Relative Relative difference ORC between with Concentration most volatile component

for ηII for ηII,ext for ηII,int

Figure E.10: Relative difference in % between ORC with and without recuperator in function of mixture concentration for: ηII , ηII,int, ηII,ext (optimal evaporation pressure, R245fa-isopentane).

The cause of the improved ηII,int is further explained by Fig. E.11 where without recuperator with recuperator yD,component − yD,component is plotted in function of the mixture concentration. This shows that the irreversibilities in the evaporator and condenser are lower for an ORC with a recuperator. This agrees with the general interpretation that the average heat rejection temperature is lowered and the average heat addition temperature is increased by the incorporation of a recuperator. As a result, the working ﬂuid better matches the temperature proﬁles of the cooling and heating medium, reducing the irreversibilities at the condenser and evaporator.

For other mixtures as working fluid, the effect is similar. The second law efficiency of an ORC with recuperator closely approximates the second law efficiency of the ORC without recuperator. Only when the cooling of the heat carrier is constrained or the heat after the ORC is used, a recuperator can be beneficial. This is the case in geothermal, combined heat and power, or in waste heat applications when condensation of the flue gas should be avoided. Furthermore, the recuperator adds an extra pressure drop, which is not taken into account in this study, but will further decrease the second law efficieny. In addition, the investment cost of the ORC is increased by adding a recuperator. Therefore, no recuperator is added to the ORC in the following discussions. APPENDIX E 227

1.5

1.0

0.5

0.0

without without recup

component β

-0.5

-1.0

-1.5

with recup with component

β -2.0

-2.5 0 0.2 0.4 0.6 0.8 1 Concentration most volatile component

Evaporator Condenser Recuperator

withoutrecuperator withrecuperator Figure E.11: yD,component − yD,component in function of mixture concentration for: evaporator, condenser, recuperator (optimal evaporation pressure, R245fa-isopentane).

E.4 Comparison of mixture compostitions

Besides R245fa-isopentane other mixtures are investigated: R245fa-pentane, R245fa- R365mfc, isopentane-isohexane, isopentane-cyclohexane, isopentane-isohexane, isobutane-isopentane, pentane-hexane. With the above discussion in mind the specifics of these mixtures are examined. For the mixtures isopentane-cyclohexane, isopentane-hexane and isobutane- isopentane two local maxima are observed for ηII in function of the mixture concentration (Fig. E.1). These maxima occur when the temperature glide of the mixture condensation exceeds the temperature glide of the cooling water. This leads to a decrease in ηII,int between these two maxima (Fig. E.2) due to an increase in irreversibilities in the condenser (∆yD,cond, Fig. E.3). The external second law efficiency is constant or increases and thus does not contribute to the creation of the local maxima. There is however only one global maximum. This is primarily accounted to the variation in pump irreversibilities, as can be noticed in Fig. E.4. High pump irreversibilities are found for large pumping powers. The large pumping power is a result of a high mass flow rate or a high pressure difference over the pump. Especially for isobutane-isopentane the irreversibilities in the pump have a noticeable effect when changing mixture concentration (Fig. E.4b). The cause is the large decrease of pressure difference over the pump: from 14.6 bar for pure isobutane to 4.62 bar for pure isopentane. For the other mixtures, the pressure dif- 228 ONTHEUSEOFZEOTROPICMIXTURES ference over the pump is only around 5 bar or lower. Furthermore, for the mixture isobutane-isopentane, there is a large increase in ∆yD,evap when going to higher concentrations of isopentane (Fig. E.3b). This is explained by the optimisation strategy. In order to maximise the second law efficiency, the pinch point temperature is strongly reduced (12 °C in comparison to pure isobutane). This in turn increases the irreversibilities in the evaporator.

E.4.1 Optimal mixture composition

In Table E.4 the results of the optimisation of pressure and mixture concentrations are summarised. It is clear that the use of zeotropic mixtures increases ηII . For working fluids with optimal mixture concentration and optimal pressure the variation in second law efficiency is low (between 30.94% and 32.05%). The best result (ηII = 32.05%) is found for a mixture of isobutane-isopentane with a concentration of 0.81/0.19. Both the internal and external second law efficiencies are higher for the ORC with mixtures as working fluid. The optimal condensing glide slope is slightly smaller than the glide slope of the cooling fluid. This is a result of the change in ∆yD for the evaporator, pump and turbine when changing mixture composition (Fig. E.3 and Fig. E.4). The optimal evaporation pressures for the mixtures are lower than those of the most volatile component in the mixture. This is favourable in view of construction and operation. The relative improvement in second law efficiency is within 7.1% to 14.2% and is presented in Fig. E.12. The increase of performance between pure working fluid and mixture is the largest for isopentane when mixing with isobutane (an increase of 14.2%). R245fa is best mixed with pentane to maximise the power output. The working fluid which is the least volatile in the mixture benefits most from adding a more volatile component. The irreversibility distributions are given for the working fluids with optimal mixture concentration (Fig. E.13) and for pure working fluids (Fig. E.14). The evaporator contributes the most to the losses in the ORC (around 50%) followed by the condenser (around 30%), turbine (around 19%) and pump (around 1%). For pure isobutane, but also for the mixture isobutane-isopentane, the pump takes a relatively large share of the total irreversibilities compared to other working fluids. The reason and effect of this was discussed in section E.4. Important to notice is the shift in irreversibility distribution between the pure working fluid and a mixture as working fluid. As discussed earlier, the improved performance is the result of a reduction in irreversibilities in the condenser. The result of the optimisation therefore reduces the share of condenser losses relative to the total losses in the cycle. For the current working fluids the reduction lies between 3 and 6 percentage points. APPENDIX E 229

15.0

12.0

9.0

improvement improvement [%] 6.0

II η 3.0

Relative Relative 0.0

most volatile component least volatile component

Fig. 1. Relative improvement when using mixtures compared to the pure working fluids (most volatile and least volFigureatile E.12:component) Relative improvement when using mixtures compared to the pure working ﬂuids (optimal evaporation pressure and concentration).

E.5 Sensitivity studies

E.5.1 Sensitivity on inlet heat carrier temperature

In a next step, the inlet temperature of the heat carrier is varied between 120 °C and 160 °C, while optimising the pressure and concentration in order to maximise the net output power. The second law efficiency in function of the inlet temperature shows an almost linear behaviour for all the investigated mixtures. The difference between the best and worst performing working fluid is between 1 to 3 percentage points. Therefore in order to further differentiate the best working fluid thermo-economic considerations [17] should be taken into account. A mixture of isopentane-isobutane has the highest second law efficiency in the range 130 °C to 160 °C. At 120 °C a mixture of isopentane-isohexane has the highest second law efficiency. For increasing heat carrier inlet temperatures the difference between second law efficiency of isopentane-isohexane and isopentane-isohexane increases. In contrast to the optimal evaporation pressure, the optimal concentration only changes slightly from the values given in Table E.4. Again, this indicates that primarily the condenser operating conditions affect the use of zeotropic mixtures. 230 ONTHEUSEOFZEOTROPICMIXTURES i mixtures using By 5. Fig. Fig. ncreased heat input input heat ncreased

Irreversibility distribution [%] 100% Irreversibility distribution [%] 100% Conclusion 10% 20% 30% 40% 50% 60% 70% 80% 90% 10% 20% 30% 40% 50% 60% 70% 80% 90% 14 13 0% 0% . . iueE1:Irvriiiydsrbto o nOCwt etoi itrsa okn ud(pia vprto rsueand pressure evaporation (optimal ﬂuid working as mixtures zeotropic with ORC an for distribution Irreversibility E.13: Figure Irreversibility distribution for Irreversibility for distribution Irreversibility for distribution 31.2% 47.9% 20.0% 0.8% 27.5% 51.1% 21.1% 0.3%

31.2% 49.0% 19.5% 27.6% 50.6% 21.6% 0.2% 0.2% s okn fluid working as ( s

30.1% 49.7% 20.1%

25.5% 52.1% 22.0%

0.1% 0.4%

) 31.0% 48.4% 20.0% 25.8% 51.9% 21.7% 0.6% 0.5% and heat conversion efficiency conversion heat and

31.5% 48.7% 19.5% 26.2% 50.1% 22.6% 0.3% 1.0% s an an o te ORC the for

31.0% 46.4% 21.2% ORC with purefluids working ORC with zeotropic 27.8% 49.1% 21.9% 1.4% 1.2%

31.6% 48.0% 19.8% 27.1% 49.9% 22.0% 0.6% 0.9%

concentration). nta o pr wrig fluids working pure of instead 25.4% 49.4% 23.0% 31.2% 42.6% 22.9% 2.2% 3.3%

( mixtures fluid as working

Irreversibility distribution [%] Irreversibility distribution [%] 25% 26% 27% 28% 29% 30% 31% 32% 33%

25% 26% 27% 28% 29% 30% 31% 32% 33% condenser evaporator pump turbine

condenser evaporator pump turbine . This .

results in an increased increased an in results

t ee s an is here APPENDIX E 231

turbine pump evaporator condenser

33% 32% 31% 30% 29% 28% 27% 26% 25% fluids [%] distribution Irreversibility

3.3% 22.9% 42.6% 31.2%

0.6% 19.8% 48.0% 31.6%

1.4% 21.2% 46.4% 31.0% ORC with pure working pure ORC with

an 0.3% 19.5% 48.7% 31.5%

0.6% 20.0% 48.4% 31.0%

0.1% 20.1% 49.7% 30.1%

0.2% 19.5% 49.0% 31.2%

0.8% 20.0% 47.9% 31.2% Irreversibility distribution Irreversibility for Figure E.14: Irreversibility distribution for an ORC with pure working ﬂuids (optimal evaporation pressure and concentration). .

90% 80% 70% 60% 50% 40% 30% 20% 10%

100% [%] distribution Irreversibility Fig. 232 ONTHEUSEOFZEOTROPICMIXTURES

E.5.2 Sensitivity on pinch point temperature difference

The convective heat transfer coefficient (α) of zeotropic mixtures is usually lower compared to pure fluids. An extensive overview of the degradation effects is found in the work of Rajapaksha [3]. If the convective heat transfer coefficient on the working fluid side is dominant, this results in an increased pinch point temperature difference for a fixed heat exchanger area and vice versa. Therefore, in a cost benefit analysis a thermo-economic approach is crucial. To have a first assessment, the sensitivity of the pinch point temperature difference on the second law efficiency is studied. The pinch point temperature difference in both the evaporator and condenser are incrementally increased from 10 °C tot 13 °C.

The results of this analsysis indicate that the decrease in ηII in the given range is approximately linear. For a decrease of 1 °C in both the condenser and evaporator, an absolute reduction of around 1 percentage point in second law efﬁciency is observed. It is interesting to note, that in general a pinch point temperature increase of 3 °C in the condenser and evaporator, already outweighs the observed performance beneﬁt associated to zeotropic mixtures. Furthermore, the ranking in terms of ηII stays the same for each calculated pinch point temperature difference.

E.5.3 Sensitivity on cooling ﬂuid glide slope

The sensitivity with respect to the temperature glide of the cooling fluid ∆Ths is evaluated by performing calculations for a variety of temperature glides, i.e. 5,10 and 15 °C. These correspond with a cooling fluid outlet temperature of 25, 30, 35 °C. In Table E.3 the results of the sensitivity analysis on the cooling fluid temperature glide are given. The working fluid with the highest second law efficiency is R245fa-R365mfc for ∆Ths = 5 °C, isobutane-isopentane for ∆Ths = 10 °C and isopentane-hexane for ∆Ths = 15 °C. Mixtures with R245fa have the lowest glide slope for the working fluid. They provide the highest second law efficiency for a ∆Ths = 5 °C. For larger ∆Ths these mixtures are not able to achieve a good match with the cooling fluid. Mix- tures with R245fa are therefore preferred for low ∆Ths. Isopentane-cyclohexane has as only working fluid a good match for ∆Ths = 15 °C. Still, isopentane-hexane has a larger second law efficiency due to a better temperature glide match in the evaporator associated to a lower latent heat of the mixture. In contrast to a change in pinch point temperature difference or heat carrier inlet temperature, the glide slope of the cooling fluid has a decisive effect on the selection of the optimal working fluid. This supports the importance of matching the cooling fluid glide slope in the condenser. For ∆Ths = 5 °C, all the mixtures provide a good temperature glide match. However, for larger ∆Ths not all the mixtures achieve a sufficient large glide slope in the condenser, which is reflected in a lower second law efficiency. APPENDIX E 233 hs (%) cond (°C) T II ∆ η : second law efficiency and working fluid hs T ∆ (%) cond (°C) II η Temperature glide cooling fluid condenser Slope Slope Slope 5 °C 10 °C 15 °C (%) cond (°C) II η temperature glide (optimal evaporation pressure and concentration). isopentane-hexaneisopentane-cyclohexaneisopentane-isohexane 32.30pentane-hexane 32.08isobutane-isopentane 32.65 5.6R245fa-pentane 4.4R245fa-isopentane 33.71 5.4R245fa-R365mfc 32.45 30.06 4.8 33.41 33.56 30.94 5.4 33.59 31.63 9.3 5.3 4.7 8.8 32.05 4.7 8.7 31.39 29.73 9.3 31.76 31.11 30.43 8.3 31.39 28.70 18.4 7.5 5.7 12.8 30.37 6.4 8.7 28.44 11.8 28.80 28.18 8.3 28.39 7.6 5.8 6.4 Working fluid Table E.3: Results of the sensitivity analysis on the cooling fluid temperature glide 234 ONTHEUSEOFZEOTROPICMIXTURES

E.6 Comparison to other work

Some noteworthy remarks from literature related to the presented results are listed in this section. First of all, Heberle et al. [10] investigated mixtures of R245fa-R227ea and isobutane-isopentane as working fluids for geothermal ORCs. Their results showed that for temperatures below 120 °C the second law efficiency increased in the range of 4.3% to 15% by using zeotropic mixtures. In this work, more fluids were investigated and a comparable improvement of second law efficiency is found for a heat carrier of 150 °C. In addition, the importance of matching the temperature glide at condensation with the temperature difference of the cooling water is supported. Garg et al. [7] investigated mixtures of isopentane and R245fa. A mixture concentration of 30% R245fa and 70% isopentane was specifically chosen to suppress flammability of isopentane. In this study, approximately the same mixture concentration leads to a maximisation of the second law efficiency under the conditions given in Table E.2.

E.6.1 Irreversibility distribution Several authors report a similar irreversibility distribution as in this work. Heberle et al. [10] indicates values around 25% for the share in condenser exergy losses, dependable on the mixture concentration of isobutane-isopentane. Zhu et al. [18] compares water, ethanol, R113, R123 and R245fa as working fluids in an ORC for engine exhaust heat recovery. Their values for the share in condenser exergy losses range between 20% and 30%. El-Emama and Dincer [19] provide an exergoeconomic analyses of a geothermal ORC. For an optimised ORC configuration with a heat carrier inlet temperature of 160 °C, the condenser accounts for 30.68% in the total exergy losses. Shengjun et al. [20] compared subcritical and transcritical ORCs for geothermal applications. Their results indicate that the share in condenser exergy losses lies between 18.6% and 23.2% for subcritical ORCs. In the works cited above, different boundary conditions are used, yet all of the values fall in a range between 18.6% and 30%. However, some studies report a lower share of condenser exergy destruction (between 2% and 5%). This is attributed to two reasons. Firstly, the exergy destruction in the condenser is low if an isothermal heat sink is used whose temperature is close to the condensation temperature of the working fluid [21]. However, this implies an infinite cooling fluid mass flow rate. Secondly, some papers impose unrealistic temperature profiles in the condenser. In the work of Tchanche et al. [22] the cooling fluid (water) exits the condenser at a higher temperature than the working fluid inlet temperature. Also in the work of Mago et al. [23] the temperature profiles cross in the condenser. As a result, exergy is locally generated in the condenser, in violation of the second law. As a consequence, the overall exergy APPENDIX E 235 destruction in the condenser is unrealistically low.

E.7 Conclusions

Using mixtures in subcritical ORCs as working fluids has been studied by using second law analysis. This result in some interesting conclusions. • Using mixtures results in an improvement of second law efficiency between 7.1% and 14.2% compared to pure working fluids. The source of this improvement lies in a combination of a higher heat input (ηII,ext) and a higher heat conversion efficiency (ηII,int) and is mainly ascribed to decreased irreversibilities in the condenser. • The distribution of irreversibilities has changed and the share of condenser losses is reduced with 3 to 6 percentage points relative to the pure working fluid. Exergy losses in the condenser are reduced by matching the glide slope of the working fluid with the glide slope of the cooling fluid. Consequently, an optimal mixture concentration exists which maximises the second law efficiency. The optimal condensing glide slope is slightly smaller than the glide slope of the cooling fluid due to the exergy losses in the pump, turbine and evaporator. • The difference in second law efficiency between optimised ORCs with zeotropic mixtures as working fluid is small (around 3 percentage points). As such, thermoeconomic criteria should be taken into account in order to further differentiate the optimal mixture. • A pinch point temperature decrease with only 3 °C has as result that pure working fluids have comparable performance to the zeotropic mixtures. • The second law efficiency of ORCs using zeotropic mixtures as working fluid with or without recuperator are approximately equal. • The second law efficiency in function of the heat carrier temperature between 120 °C and 160 °C shows an almost linear behaviour for all the investigated mixtures. Between 120 °C and 130 °C isopentane-isohexane has the highest second law efficiency. While between 130 °C and 160 °C isobutane- isopentane has the highest second law efficiency. There are also important challenges. In order to make a thermo-economic investigation heat transfer and pressure drop correlations are necessary. This is however difficult because of the lack of experimental data. Furthermore there are uncertainties on the actual operation related to possible composition shifts [24]. Therefore ORCs with zeotropic mixtures are not further assessed in the thermo- economic analysis. 236 ONTHEUSEOFZEOTROPICMIXTURES 25apnae03-.794 17 02 95 .515 . . 0925 72.8 2053 60.9 7.5 8.0 1.50 7.35 39.57 80.27 31.76 9.46 0.33-0.67 R245fa-pentane etn-eae05-.693 13 93 95 .905 . . 4318 30.6 1988 44.3 8.3 7.0 0.57 3.19 39.59 79.30 31.39 9.32 0.54-0.46 Pentane-hexane okn udC(oefrac.) (mole C fluid Working ylhxn .42.17.93.213 .400003. 659.5 1675 39.1 0.0 0.0 0.24 1.35 37.42 71.39 26.71 9.14 1 Cyclohexane cyclohexane Isopentane- Isopentane- Isopentane- spnae190 80 59 69 .814 . . 6511 59.6 1810 46.5 0.0 0.0 1.46 6.08 36.98 75.92 28.07 9.05 1 Isopentane isopentane isopentane Isobutane- shxn .12.77.63.824 .800004. 7123.6 1761 44.9 0.0 0.0 0.48 2.48 36.98 75.36 27.87 8.91 1 Isohexane isohexane sbtn 00 91 72 77 97 .900004. 80239.4 1810 46.5 0.0 0.0 5.19 19.78 37.74 77.20 29.14 10.04 1 Isobutane 35f .52.97.73.348 .600008. 8443.7 1814 82.8 0.0 0.0 0.96 4.85 37.03 76.67 28.39 8.95 1 R365mfc R365mfc R245fa- R245fa- etn .52.47.13.749 .200004. 7145.4 1781 43.5 0.0 0.0 1.12 4.91 37.07 75.11 27.84 9.05 1 Pentane eae189 76 45 70 .503 . . 2514 17.6 1741 42.5 0.0 0.0 0.36 1.95 37.08 74.57 27.65 8.94 1 Hexane 25a193 86 63 75 12 .300009. 8899.7 1888 90.8 0.0 0.0 2.43 11.29 37.58 76.31 28.67 9.39 1 R245fa hexane al .:Caatrsi yl aaeesfrha are t10° otmleaoainpesr n concentration). and pressure evaporation (optimal °C 150 at carrier heat for parameters cycle Characteristic E.4: Table .908 .93.47.03.224 .270884. 9223.2 1952 44.8 8.8 7.0 0.42 2.41 38.82 79.70 30.94 9.09 0.19-0.81 .105 .93.98.63.172 .757648. 0568.0 87.6 2025 2027 88.3 156.0 61.9 38.3 2154 6.4 11.9 5.7 52.0 2011 5.7 1886 47.5 9.3 6.4 41.7 1.37 8.7 1.85 6.9 7.20 9.3 8.43 39.01 7.1 3.36 38.88 80.46 7.4 13.48 0.72 31.39 80.01 39.13 9.29 0.26 31.11 3.75 81.91 9.38 0.41-0.59 1.56 39.29 32.05 0.28-0.72 39.11 80.52 9.61 31.63 76.88 0.81-0.19 9.22 30.06 9.27 0.44-0.56 0.08-0.92 (%) η th η (%) II η II,ext (%) η II,int (%) p (bar) evap p (bar) cond vp(°C) evap Slope od(°C) cond Slope (kg/s) m ˙ wf W (kW) ˙ exp W ˙ (kW) pump APPENDIX E 237

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