Master Thesis - DTU Electronic Theses and Dissertationsetd.dtu.dk/thesis/268604/Speciale.pdfSoldrevet Fjernkøling Master Thesis Su Cheong Ho MEK-TES-EP-2010-07 May 2010 Industrial

Soldrevet Fjernkøling

Ma

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Su Cheong Ho

MEK-TES-EP-2010-07

May 2010

Industrial Heat Pumps, Optimizationand Application.

Christen Malte MarkussenTorben Schmidt OmmenMEK-TES-EP-2010-18September 2010

This report is part of the requirements to achieve the M.Sc.Eng degree at the TechnicalUniversity of Denmark.

This report represents 35 ECTS points for each of the indicated authors.

Delivery date: 05.09.2010

This report was prepared by:

Christen Malte MarkussenDTU student number: s042311

and

Torben Schmidt OmmenDTU student number: s042912

SupervisorsBrian Elmegaard, Head of Section, Lector, DTU Mechanical EngineeringMartin Ryhl Kærn, Industrial Ph.D. Student, DTU Mechanical Engineering

External SupervisorLars Reinholdt, Senior Consultant, Energy and Climate, DTI Technological Institute

Section of Thermal Energy SystemsDepartment of Mechanical Engineering - DTU MEKTechnical University of Denmark

Nils Koppels AlléBygning 403DK-2800 Kgs. LyngbyDenmark

www.tes.mek.dtu.dkTel: (+45) 4525 4131Fax: (+45) 4588 4325

Abstract

This project aims at identifying the current status of industrial grade heat pumps usingnatural working fluids and their potential in the future Danish energy system. Fourspecific cycles have been investigated, namely a condensing vapor (R717 and R718), atranscritical (R744) and a compression absorption hybrid (R717/R718). It is attempted tosubstantiate or reject a claim that industrial grade heat pumps should be developed andimplemented as a part of the Danish energy make up. Litterature studies are conductedin scientific papers and technical publications to establish the working limits of thesecycles as well as the current status and direction of research within the field of industrialgrade heat pumps. Based on exergy analysis an economic evaluation is performed.

Based on scenario analysis in STREAM indications are observed to support, thatlarge scale thermal production using heat pumps has an alleviating effect on thefuture Danish energy system. It has been quantified what consumption and emissionreductions are to be expected if the Danish industry were to get an incentive forrecovery of waste heat. Average reduction values are estimated at 40 % for all harmfullemissions considered. This is accomplished by recovering as much as 20 PJ of wasteheat.

All four working cycles have had their working domains established based on currentdata from industry. Given working constraints such as Tsink and Tlift the modelsare able to identify the process with the lowest cost per heat unit and dimension theindividual components using thermoeconomic principles. All sink temperatures from50-125 °C can be achieved with todays equipment and 150°C will be realistic within aforeseeable number of years.

For a specific case the waste heat potential was sought verified. An apparent savingpotential of almost half the continuous consumption of the specific facility wasestablished, amounting to 300 kW. Furthermore a heat pump potential for externalsale of approximately 61 kW was found on the basis of the developed thermodynamicmodels.

It is the recommendation of this study that large measures should be taken in orderto mature and implement heat pumps as an integral part of the Danish heat productionsystem. Furthermore it is vital that government and legislators take initiative andproduce incentives for implementing such systems in all sectors where large amountsof waste heat are generated. These technologies are vital if emission goals are to be metand society’s dependence on fossil fuels is to be reduced.

CONTENTS i

Contents

1 Preface 1

2 Introduction 2

3 Problem statement 3

4 Heat pumps in Denmark - application and potential 44.1 STREAM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44.2 Waste heat in Danish industry . . . . . . . . . . . . . . . . . . . . . . . . . 84.3 International reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.4 Customers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.5 Legal issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 Constraints of the heat pump models 14

6 Working Fluids 156.1 Safety and environmental impact of Working Fluids . . . . . . . . . . . . 16

7 Basic simulation models 187.1 Condensing vapor heat pump cycle . . . . . . . . . . . . . . . . . . . . . 187.2 Transcritical heat pump cycle . . . . . . . . . . . . . . . . . . . . . . . . . 207.3 Compression/absorption heat pump cycle . . . . . . . . . . . . . . . . . 21

8 Heat Exchange between Heat Pump and Industrial Process 23

9 Compressors and their operating limits 269.1 Current status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269.2 Approaches to lowering compressor outlet temperature . . . . . . . . . . 32

10 Comparison of working domains 34

11 Exergy analysis and Thermoeconomics 3711.1 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3711.2 Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

12 Verification of models - General observations 4312.1 Condensing vapor heat pump . . . . . . . . . . . . . . . . . . . . . . . . . 4512.2 Transcritical heat pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5212.3 Hybrid heat pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

13 General solution 62

14 Case Study 6614.1 Berendsen - Industrial laundry services . . . . . . . . . . . . . . . . . . . 6614.2 Pinch analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

15 Discussion 86

16 Conclusion 88

CONTENTS ii

A STREAM 93

B Integration of Heat Pumps 97B.1 Pinch Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97B.2 Heat pumps in Pinch analysis . . . . . . . . . . . . . . . . . . . . . . . . . 99

C Compressors 101C.1 General concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101C.2 The reciprocating piston compressor . . . . . . . . . . . . . . . . . . . . . 102C.3 The screw compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103C.4 The centrifugal turbine compressor . . . . . . . . . . . . . . . . . . . . . . 105C.5 The axial turbine compressor . . . . . . . . . . . . . . . . . . . . . . . . . 106

D Exergy concepts 107D.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107D.2 Exergy destruction/loss ratios and exergy efficiencies . . . . . . . . . . . 109D.3 Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

E EES Code 112

LIST OF FIGURES iii

List of Figures

4.1 Duration curves for boilers . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.2 Duration curves for four of the different scenarios . . . . . . . . . . . . . 64.3 Heat pump characteristic in the scenarios . . . . . . . . . . . . . . . . . . 74.4 System characteristic for the different scenarios. . . . . . . . . . . . . . . 74.5 Economic and environmental characteristics of the different scenarios . . 84.6 Characteristics of IHP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.7 Typical IHP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.8 Industrial waste heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.9 Fuel saving potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.10 Emission reduction potential . . . . . . . . . . . . . . . . . . . . . . . . . 115.1 Heat pump and heat exchange nomenclature . . . . . . . . . . . . . . . . 146.1 Vapor pressure vs. temperature . . . . . . . . . . . . . . . . . . . . . . . . 157.1 State points for Condensing Vapor Heat Pump . . . . . . . . . . . . . . . 187.2 State points for Transcritical Heat Pump . . . . . . . . . . . . . . . . . . . 207.3 State points for Hybrid Heat Pump . . . . . . . . . . . . . . . . . . . . . . 218.1 Theoretical temperature profile in condensing vapor heat pump . . . . . 238.2 Theoretical temperature profile in transcritical heat pump . . . . . . . . . 248.3 Theoretical temperature profile of hybrid heat pump . . . . . . . . . . . 249.1 Compressor characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 269.2 Isentropic and volumetric efficiency . . . . . . . . . . . . . . . . . . . . . 319.3 State points for CVHP with oil injection . . . . . . . . . . . . . . . . . . . 329.4 State points in two-stage CVHP . . . . . . . . . . . . . . . . . . . . . . . . 3310.1 Working domain of heat pump with R717 . . . . . . . . . . . . . . . . . . 3410.2 Differences in characteristic values . . . . . . . . . . . . . . . . . . . . . . 3510.3 Working domain of R717 and R718 . . . . . . . . . . . . . . . . . . . . . . 3510.4 Working domain of hybrid heat pump . . . . . . . . . . . . . . . . . . . . 3510.5 Simple comparison of working domains . . . . . . . . . . . . . . . . . . . 3611.1 Example of exergy calculations . . . . . . . . . . . . . . . . . . . . . . . . 3912.1 Table of parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4412.2 Isentropic efficiency correlations for R717 vs. constant isentropic efficiency 4512.3 Impact of volumetric efficiency on compressor size . . . . . . . . . . . . . 4612.4 Maximisation of COP in CVHP with R717 . . . . . . . . . . . . . . . . . . 4712.5 COP and HEX area with changes in sink and source media . . . . . . . . 4812.6 Heat exchanger area and COP as a function of pinch temperatures . . . 4812.7 Example of exergy destruction in CVHP . . . . . . . . . . . . . . . . . . . 4912.8 Example of exergetic efficiency in CVHP . . . . . . . . . . . . . . . . . . . 5012.9 Heat price at different operating hours a year . . . . . . . . . . . . . . . . 5012.10PBP and COP with changes in operating hours . . . . . . . . . . . . . . . 5112.11PBP and COP with changes in temperature lift . . . . . . . . . . . . . . . 5112.12COP of R744 with changes in isentropic efficiency . . . . . . . . . . . . . 5212.13Heat exchange in gas cooler . . . . . . . . . . . . . . . . . . . . . . . . . . 5312.14Pinch-point consideration in gas cooler . . . . . . . . . . . . . . . . . . . 5312.15Cost of heat from TCHP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5412.16Changes in TCHP-model with variations in sink temperature . . . . . . 5412.17Optimisation of PBP with different number of operating hours . . . . . . 5512.18COP as a function of different isentropic efficiencies . . . . . . . . . . . . 5612.19Variation in solution strenght in CAHP . . . . . . . . . . . . . . . . . . . 57

LIST OF FIGURES iv

12.20CAHP with changes in solution of working fluid . . . . . . . . . . . . . . 5812.21Impact of pinch temperature on the hybrid heat pump . . . . . . . . . . 5912.22Temperature variation in sink . . . . . . . . . . . . . . . . . . . . . . . . . 5912.23Impact of changing sink temperatures . . . . . . . . . . . . . . . . . . . . 6012.24Best CAHP with different temperature lifts . . . . . . . . . . . . . . . . . 6113.1 Parameters used in figures 13.2 - 13.4 . . . . . . . . . . . . . . . . . . . . 6213.2 Cost of heat and COP at temperature lifts of 20 K . . . . . . . . . . . . . . 6313.3 Cost of heat and COP at temperature lifts of 30 K . . . . . . . . . . . . . . 6413.4 Cost of heat and COP at temperature lifts of 40 K . . . . . . . . . . . . . . 6513.5 Approaches for lowering compressor outlet temperatures . . . . . . . . . 6514.1 Flowchart of flatwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6714.2 Plant overview - nomenclature . . . . . . . . . . . . . . . . . . . . . . . . 6814.3 Plant overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6814.4 Plant overview - liquid string . . . . . . . . . . . . . . . . . . . . . . . . . 6914.5 Ironing roll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7014.6 Wax deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7114.7 Textiles after press . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7114.8 Daily consumption data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7214.9 Berendsen data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7314.10Water consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7314.11Flow measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7414.12Flow profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7514.13heat flow diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7514.14Time series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7614.15Waste heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7614.16Pinch - streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7714.17Pinch - CC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7714.18Pinch - GCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7814.19Alternative composite curves . . . . . . . . . . . . . . . . . . . . . . . . . 7914.20Sensitivity of TCI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8014.21Heat Exchanger network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8114.22Sink temperature levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8114.23Source temperature levels . . . . . . . . . . . . . . . . . . . . . . . . . . . 8214.24Contour plot of PBP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8314.25Optimisation of HEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8314.26Recovered heat for minimum PBP . . . . . . . . . . . . . . . . . . . . . . 8414.27Response from source media . . . . . . . . . . . . . . . . . . . . . . . . . 84A.1 Duration curves for the different STREAM scenarios. . . . . . . . . . . . 93A.2 Boiler operation for the different STREAM scenarios. . . . . . . . . . . . 94A.3 Cost overview for STREAM scenarios. . . . . . . . . . . . . . . . . . . . . 95A.4 Carbondioxide reductions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 96B.1 Composite and Grand Composite Curves . . . . . . . . . . . . . . . . . . 98B.2 Heat pump placement relative to pinch . . . . . . . . . . . . . . . . . . . 99C.1 Characteristic reciprocating compressor . . . . . . . . . . . . . . . . . . . 102C.2 Screw compressor considerations . . . . . . . . . . . . . . . . . . . . . . . 104C.3 Maximum pressure ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Nomenclature

Abbreviations

bn. Billion

C Variable cost [DKK/year]

CAHP Compression Absorption Heat Pump Cycle

CC Composite Curve

CFC Chloro Fluoro Carbon

CHP Combined Heat and Power

CIP Cleaning In Place

COP Coefficient Of Performance

CPI Chemical Plant cost Index

CRF Capital Recovery Factor

CVHP Condensing Vapour Heat Pump

DKK Currency in Denmark

DTU Technical University of Denmark

EES Engineering Equation Solver

GCC Grand Composite Curve

GREEN Title of STREAM scenario from Energinet.dk

GWP Greenhouse Warming Potential

HCFC Hydro Chloro Fluoro Carbon

HEN Heat Exchanger Network

HEX Heat Exchanger

HFC Hydro Fluoro Carbon

HP Heat Pump

IEA International Energy Agency

IHP Industrial Heat Pump

LMTD Logarithmic Mean Temperature Difference [K]

MVR Mechanical Vapor Recompression

NG Natural gas

mill. Million

NPV Net Present Value [DKK]

PBP Payback Period [year(s)]

PEC Purchased Equipment Cost [DKK]

REF Title of STREAM scenario from Energinet.dk

STREAM Modelling tool www.eaea.dk

TCHP Transcritical Heat Pump

TCI Total Capital Investment [DKK]

TSO Transmission System Operator

V HC Volumetric Heating Capacity [kJ/m3]

W Title of STREAM scenario with increased wind turbine capacity

WHP Title of STREAM scenario with heat production from heat pumps

WHPS2x Title of STREAM scenario with double thermal storage

WHPS2xF Title of STREAM scenario with flexible heat pump production

Greek Symbols

∆ Difference or ratio from inlet to outlet

ε Exergetic efficiency [/]

η Efficiency [/]

Superscripts

˙[ ] Time dependent rate [/s]

CH Chemical (exergy)

KN Kinetic (exergy)

PH Physical (exergy)

PT Potential (exergy)

j Index refering to part of system

Subscripts

0 Dead state

b Boundary

comp Refering to compressor

cond Condenser

cv Control volume

D Destruction (exergy)

DL Destruction/Loss (exergy)

e Exit (exergy analysis)

eff Effective

evap Evaporator

expa Expansion valve (exergy)

F Fuel (exergy)

GC Gas Cooler

high State after high stage compressor

i Component indice (exergy)

i In (exergy analysis)

in Inlet state

int Intermediate state (before high stage compressor)

is/isentropic Isentropic

k Component indice (exergy)

L Loss (exergy)

lm Logarithmic Mean

oil Oil

out Exit state

P Product (exergy)

p Phase gas, two-phase, liquid

pump Refering to pump

q Exergy as heat (exergy)

rev Reversible

s Superheated state (after evaporator) or subcooled state (after condenser)

tot Total

vol/volumetric Volumetric

w Work

w water

Mathematical Symbols

∆p Pressure ratio [/]

∆Tmin Minimum temperature difference in heat exchanger [K]

C Cost rate for product and fuel (exergy) [DKK/s]

Q Thermal energy transfer rate [kW ]

Z Cost rate for capital investment and operation (exergy) [DKK/s]

γ Specific heat ratio [/]

ν Specific volume [m3/kg]

πvolume Ratio between swept volume and lubricant flow rate [/]

E Standard exergy [kJ ]

Q Dimensionless total energy transfer by heat [/]

A Area [m2]

c Cost of exergy stream [DKK/kJ ]

d Difference

e Specific exergy [kJ/kg]

g acceleration of gravity (exergy) [m/s2]

h Enthalpy [kJ/kg]

hop Number of operating hours per year [hours/year]

I Investment [DKK]

i Interest rate

M Mass [kg]

n Technical lifetime of installation [DKK]

P Pressure [kPa]

p Pressure [bar]

Q Thermal energy [kJ ]

q Ratio of heat source and heat sink energy levels, q=COP(COP-1)

r Inflation rate

S Savings [DKK/year]

s Entropy [kJ/(kg ·K)]

T Temperature [K]

t Temperature [°C]

t Time [s]

Tlift Temperature difference between source inlet and sink outlet [K]

Tsink Delivery temperature of heat pump [K]

Tsource Temperature of source at evaporator inlet [K]

U Heat transfer coefficient [kW/(m2K)]

V Volume [m3]

W Work (electric) [kJ ]

x Mass fraction of R717/R718 mixture [kg/kg]

yD Exergy destruction ratio

z Elevation (exergy) [m]

1 PREFACE 1

1 Preface

This master thesis is a part of the requirement for achieving the M.Sc.Eng degree fromthe Technical University of Denmark.

We would like to thank a number of people who assisted us throughout the courseof this project.

Head supervisor, Brian Elmegaard who has offered time and guidance wheneverneeded, which has been highly appreciated. Furthermore Brian assisted with projectideas and various contacts.Martin Ryhl Kærn for providing insight and help with assumptions and calculations,especially regarding heat exchangers.Lars Reinholdt for the idea behind the project, and subsequently providing input oncutting edge developments within the field of heat pumps.

A part of the project addresses a specific industrial plant. The intended industrial plantfell through, and a new case had to be found. Especially two people were helpfull withthis compelling problem.Tomas Skov Hansen from JENSEN-GROUP for conveying the contact to Berendsenin Roskilde that provided data for a case study. Tomas has been available to clarifyquestions regarding the equipment, and helped with an engineering approach toindustrial laundry facilities.Steen W. Jørgensen for helping us to understand the inner workings of the specificindustrial laundry facility.

2 INTRODUCTION 2

2 Introduction

Heat pumps are machines that can extract thermal energy from a source, upgrade it toa usefull level and deliver it to a new location using mechanical work. The potentialof producing heat without consuming fossil energy has recieved renewed interest inrecent years due to increasing fuel prices.

In 2007 the Danish government presented a motion for Danish energy policy towards2025 [Statsministeriet, 2007]. The idea behind the proposal is to make Denmarkindependent from the use of fossil fuels on a long term basis. One of the short termgoals is to increase the use of sustainable energy to more than 30 % of the combinedenergy consumption before 2025. The idea is to maintain the total consumptionof energy in Denmark at the current level, while changing the composition of bothelectricity production and the amount of biofuels within transportation. One of thepartial goals specified in the motion is to increase the amount of energy from wind.

Increasing the sustainable energy supply in Denmark to 30 % means 50 % of the totalelectricity consumption [Ea Energianalyse A/S, 2007]. A jump from 27 % (18% wind)to 50 % of the total electricity consumption will have a considerable influence on theDanish electricity grid and place demands on all sectors of the network. New andunforeseen problems are expected to challenge both the producer, distributor and end-user along with the infrastructure of the transmission network itself.

An important point of interest is the district heating networks, where surplus heat frompower plants is distributed to the daily needs of the citizens. Danish power producershave untill now been able to build a large share of Combined Heat and Power plants(CHP). A decreasing share of traditional thermal power production can become aproblem with increased electricity production from wind, due to the variability inproduction from windturbines. Problems can arise in the situations where heat isneeded without additional electricity. Heat pumps in the district heating network couldeliminate the need for burning valuable fuel to achieve low grade heat, by either usingwaste heat from industrial processes, or even upgrading heat from fx. soil.

Another application of these heat pumps is to directly implement them in the industrialprocesses, in order to reuse the waste heat on site. The usefullness of a heat pumpis increased for industrial purposes the higher temperatures it can achieve, makingthis upper limit a point of interest. Some adjustments are also needed to make heatpumps cope with the variety of heat sources possible. An assessment on the useof heat pumps in its dynamic enviroment is preferable, as many industrial plantstend to produce batch by batch rather than continuous production. This creates anincongruency between when there is a demand for heating and when there is wasteheat available.

In all applications the primary point of interest is whether or not the technologyis economically feasible. Danish industry demands a (very) short pay back rate inorder to invest in "nice to have"-technologies (technologies with high sums of netpresent value, but also high investment cost). Legislation and subsidies can furtherthe implementation of heat pumps, which could potentially reduce the use of fossilfuels (and subsequently harmfull emission) and increase security of supply.

3 PROBLEM STATEMENT 3

3 Problem statement

The aim of the work done in this project, is to perform a preliminary evaluation offour industrial grade heat pump cycles using natural working fluids. This is done inorder to determine the ideal heat pump within a given working regime, consideringthermodynamic and economical operating criteria.

A study is also carried out to establish what contribution heat pumps could have inalleviating a number of expected challenges due to increased share of renewables inthe future energy system.

Furthermore an estimate is made of the potential for reduction in fossil fuel consump-tion and subsequent harmfull emissions. This is done by assuming that an incentiveexists for waste heat recovery, through the use of process integration and heat pumpsin Danish industry.

Finally an actual industrial facility will be investigated and an energy optimisationattempted. This will serve as a verification of the assumptions regarding waste heatand energy savings potential in industry.

4 HEAT PUMPS IN DENMARK - APPLICATION AND POTENTIAL 4

4 Heat pumps in Denmark - application and poten-tial

An overview of the potential for utilising heat pumps as part of the Danish energymakeup will be provided in this section. This is done to justify the effort of developingthe technologies from a system and socioeconomic viewpoint. Several scenarioshave been considered using the STREAM modelling tool to investigate the effect ofintroducing large scale thermal production using heat pumps in the future.

Furthermore a litterature study has been undertaken to uncover the potential forwaste heat recovery from Danish and international industry. Denmark did notparticipate in the last international survey regarding industrial heat pumps, IEA’sAnnex 21, however several sources have attempted to map the waste heat in Danishindustries ([Viegand, 2009],[SKAT, 2006],[dkTEKNIK, 2002]). From this data a wasteheat potential for use in industrial heat pumps can be aggregated and subsequentsaving potential verified or dismissed.

This section will conclude by providing a brief overview and explanation of the relevantparameters in Danish tax regulations for the utilisation of waste heat in industry.

4.1 STREAM model

Stream is a comprehensive but simple spreadsheet based planning tool, allowingsimple and fast calculations of what impact specific parameters have on a very complexsystem. A total of six different scenarios were investigated in the STREAM model.All scenarios are compared to a reference - business as usual - (which does not complywith the 2030 reduction targets). Both of the initial scenarios are based on those madeavailable in the course 45004 at DTU during the fall semester of 2009. Both scenarioswere produced by the Danish TSO, Energinet.dk.

Based on Energinet.dk’s ambitious GREEN scenario, four additional scenarios havebeen developed progressively so that each subsequent scenario is based on theprevious. The first senario increases the amount of intermittent windpower in thesystem in order to reach the goals of increased wind [Statsministeriet, 2007]. Byimplementing heat pumps in large scale in the consecutive scenarios, it is attemptedto substantiate a hypothesis that heat pumps can in fact help alleviate the technical andeconomical problems associated with an energy scenario largely based on intermittentressources. All relevant figures have been documented in appendix A.

Wind scenario - W From Energinet.dk’s ambitious GREEN scenario the approachhas been to introduce a substantial disturbance in the system. This is achieved byincreasing the share of wind power in the total consumption of electrical energy from30 to 50 %. Even though this is a drastic change in the energy mix its justification liesin the decreased reliability of fossil fuel supplies. That Denmark needs to incorporatea greater fraction of sustainable ressources for energy in the future is widely regardedas a valid assumption. These ressources (wind, solar, wave etc.) have the inherentcharacteristic of intermittency producing a large number of overrun hours where the


electricity generation is larger than the consumption, as can be seen in figure 4.2 onpage 6.

Because of the much increased share of wind energy in the system there is a large dropin thermal power production. A large investment is therfore needed for individualboilers to produce heat (see figure 4.1(a)). Among other results are the tendencyfor large amounts of forced export together with an increasing share of thermalpower plants needing to run in condensing mode (see figure 4.4). A high shareof condensing power plants is an expression of a low overall system efficiency andtherfore low utilisation of expensive ressources. Currently due to the large extentof interconnnection between Denmark and the surrounding countries, any electricityoverrun can be exported without much difficulty. In the future however all of thesecountries may experience overrun in the same time periods resulting in bottlenecksand overloads in the transmission network.

(a) Wind scenario

(b) Flex scenario

Figure 4.1: Comparison between the load duration curve for boiler production in thewind scenario and the one with flexible heat pumps. No attempt has been made tooptimise the distribution of different fossil fuel types, meaning that the ratio of therespective boiler fuels remains unchanged


Additional heat pumps - WHP A large share of heat pumps is imposed on thescenario with increased wind capacity. In the tertiary and residential sector the shareis increased from 5 to 20 %. A reduction in the share of district heating is alsoimplemented from 60 % to 59 and 50 % in the tertiary and residential sector respectively.STREAM currently does not support using heat pumps in industry. For districtheating heat pumps are implented as 20 % of the total district heating demand. Thisdevelopment reduces the total annuitised cost slightly, mainly because the individualheat pumps almost completely neglect the increased fuel cost and need for investmentin individual boilers (see figure 4.1(b)). Total investment costs are however increasedbecause the heat pumps are more expensive than conventional boiler technology, butthe reduction in fuel consumption makes up for this. Using heat pumps for thermalproduction also increases the total electricity consumption reducing the number ofoverrun hours and subsequent need for forced export of electricity.

Figure 4.2: Duration curves for four of the different scenarios. NB. some intermediatescenarios have been omitted.

Increased thermal storage - WHPS2x Because the heat pumps are tied to a thermalconsumption time series in STREAM, which differs from the electrical consumptiontime series, the heat pumps actually increase the peak export need. In order tocounteract this problem a scenario with increased thermal storage is developed.Energinet.dk’s GREEN scenario uses a storage capacity equal to three hours averagethermal production. In the WHPS2x scenario this is expanded to twice the storagecapacity, ie. equal to six hours of average production.

Even though the heat pumps are not allowed access to the storage capacity in STREAM,the increase actually has the desired effect to some extent. Electricity overflow isreduced both in maximum amplitude, quantity and in number of hours. STREAM hasa non-trivial decision routine to avoid operating district heating heat pumps in a waythat increases the need for peak thermal power. As can be seen in figure 4.2 none of theheat pump scenarios raise the intersection of the duration curve and the ordinate axis.Increasing the thermal storage allows STREAM to operate the heat pumps for a greater


number of hours, as can be seen in figure 4.3. That the model finds relief in increasedthermal storage also indicate that there is a problem with thermal power plants beingoperated in order to cover heat demand, even though the demand for power is verylow. Both the total annuitised cost and the total investment cost are decreased slightlyas can be seen in figure 4.5.

Figure 4.3: Heat pump characteristic for the different scenarios. It is important to notethat the apparant drop in electricity consumption for heat pumps in the flexible scenariohas simply been allocated to hours with less stress on the system.

Demand response - WHPS2xF Due to the relatively slow response time of thermalsystems their demand is considered non-acute. As a consequence electrically driventhermal production such as heat pumps, could potentially be used to stabilise thepower sector by providing a flexible demand response. A scenario is developed where50% of the electricity for the individual and district heating heat pumps is considereddemand responsive. In the GREEN scenario this is a readily implementable optionsince some of the elctricity consumption is already allocated to hydrogen electrolysisand the charging of electric vehicles.

Figure 4.4: System characteristic for the different scenarios.

Throughout the scenarios the ratio between demand response classes has been keptconstant at: 40% inflexible, 40% very flexible and 20% during night hours. Due tothe relatively high degree of intermittency in the predicted system, the share of veryflexible demand responsive consumption has been increased. This is done to reflectthe fact that these consumers will predict many hours with very low power prices andadjust their production and storage capabilities accordingly. Adding HP demand to thegeneral power consumption may also seem conflicting since the seasonal variation ofthe two time series differs. An underlying argument for this approach is that all HPscould be devised so that they during the summer months are able to provide cooling.This could further help balance the system by replacing a portion of the non-responsiveair conditioning installations. This is however not reflected in the model.


Of all the scenario variations this version is the one coming closest to the originalGREEN scenario when it comes to total annuitised cost, almost completely neglectingthe extra cost of the additional wind power. Compared to the previous scenario theflexibility of the heat pumps means a reduction in forced electricity export of 77 % from1.23 PJ to 0.28 PJ. The share of CHP production forced to run in condensing mode isreduced from 12.5% in the WIND scenario (10.78% in GREEN) to 2.31%.

Figure 4.5: Economic and environmental characteristics of the different scenarios

Even given the primitive nature of the STREAM model some interesting tendencies canbe observed. It is worth noting that despite the massive shock to the system in the formof heavily increased wind power, it was possible to achieve a system approximatingthe GREEN scenario using a straigthforward and intuitive approach. With referenceto figure 4.5 it can be seen that the flex scenario only surpasses the total cost of theGREEN scenario by 9.3% (1260 MW installed HP capacity) while at the same timedistancing Denmark from the CO2 reduction target with a further 5.6 mill. tonne. Thisis an increase of 74.7% compared to the GREEN scenario. Of course such a reduction inemissions carries with it a range of local environmental benefits, and more prominentlyalso an alleged stabilising effect on the global climate. Technically a more tangiblesideeffect is the very real reduction in reliance on import from the increasingly unstablefossil fuel market.

4.2 Waste heat in Danish industry

The last comprehensive study into the amount and quality of Danish waste heat fromindustry quantified that 7.3 PJ/year could theoretically be utilised [dkTEKNIK, 2002].Available statistics are based on questionnaire answers from mainly energy intensiveprocess oriented Danish companies.

Out of discretion for the involved companies the temperature levels remain undis-closed. However the responses are said to encompass both heat potential for directrecovery through process integration, and also low grade heat which can be consideredusefull for district heating. A theoretical potential can therefore be said to exist in theorder of 6.6% of the total district heating production in Denmark [dkTEKNIK, 2002]. Ifall of this potential was realised it would correspond to a tripling of the current amountof district heating from industrial waste heat.

The share of documented waste heat comprises 5.3% of the total energy consumptionin industry, and as much as 17.3% of the energy consumption in the companies whoresponded to the questionaire. In the report it is heavily underlined that the feedback


from Danish companies was very limited (34 responses out of 134 questionaires), andonly in a select few cases was it possible to actually determine the economic feasiblity ofpotential projects. The share of this waste energy that could be documented to a levelwhere an economic payback period could be calculated comes from nine companiesand comprise 33% or 2.3 PJ/year (2.4 year PBP on average). The investment cost isestimated at 152 mio. DKK.

This report was revised in [SKAT, 2006] and later in [Viegand, 2009] where it was es-timated that the heat price would be 100.7 DKK/MWh excl. tax and 280.6 DKK/MWhincl. tax, compared to the average production price in the district heating network of387 DKK/MWh in 2002. These revisions were carried out to determine whether theDanish tax system was as big a hindrance for waste heat recovery as the responsesin the intial 2002 report had indicated. Both of the later reports agreed that the taxlegislation still allows for a profit, however as long as the profit margin is larger forother investments, the possibility of waste heat recovery is simply not explored.

4.3 International reports

In 1995 IEA published the Annex 21 report which was an international survey ofthe potential for industrial heat pumps including statistics of how many existed andwhere they were being used. Many aspects were considered regarding for instance thepotential of the technology including maturity, expected improvements in economiccompetitiveness along with environmental side effects such as emission reductionpotential. The participating countries were: Canada, France, Japan, Norway, Sweden,UK and US. It should be noted that the types of considered working fluids in the Annexinclude mostly substances which are now either banned or being phased out globally(CFCs and HCFCs). Statistics from Annex 21 have been adapted as representative forthe number and characteristics of heat pumps suited for Danish industry. In figure 4.6a summary of the country specific data from [Annex-21, 1995] is presented.

Figure 4.6: Summary of statistics on industrial heat pumps installed in the Annex 21countries.

According to [Annex-21, 1995] the numbers presented in figure 4.7 are representativefor a typical heat pump in the listed industries. All numbers for sink temperature, tem-perature lift and installed size listed, are achievable today with the natural refrigerantsfrom this study. Total Q indicates the amount of installed HP capacity per industrycompared to the total number of reported installations. Missing numbers for wood and


miscellaneous are due to either very few reports or an incongruent mix of installationsthat the authors did not deem fit to generalise.

Figure 4.7: Typical characteristics for heat pumps in specific industries [Annex-21, 1995]

When observing indicators for industry such as share of thermal energy of totalconsumption, share of consumption in different industries, and net energy savingpotential, similar numbers are obtained from the Annex as was observed in theSTREAM model and in [dkTEKNIK, 2002]. It is therfore assumed that it is reasonableto extrapolate results from calculations based on both surveys.

Initially it was investigated what the potential reduction in thermal energy consump-tion would be, when assuming that a theoretical potential of 17.3% waste heat recovery[dkTEKNIK, 2002] was realised (figure 4.8). This is the equivalent of 861 MW ofcontinuously generating thermal production. If the same investment cost for heatexchange is assumed as that implemented in the heat pump models, an initial capitalcost of 916.9 mio. DKK is obtained.

Figure 4.8: Energy consumption in industry from STREAM, with percentiledistribution. Percentage of energy consumption that is heat using 40% average valuefrom [Annex-21, 1995]. Waste heat potential as 17.3% of total energy consumption[dkTEKNIK, 2002].

In the Annex findings an average of 5.4% of the thermal energy consumed in industrycould be replaced by heat pumps. Even though it was stated that the percentagevalue of 17.3 was based on heat of a quality suited for direct process integration orDH, a calculation example is carried out where 5.4% of the recovered heat needsto be produced by heat pumps. Using the average investment cost from figure 4.7extrapolated to 2010 prices using the chemical plant cost index (CPI) [CE, 2006], acombined investment cost of 1.469 bn. DKK is obtained. Using the price of naturalgas [DKK/kWh] as cost of heat, the annual savings for thermal energy becomes 1.214bn. DKK. With an annual expense of 54 mill. DKK for electricity to heat pumps the PBP(see section 11.2) of this investment becomes 1.20 years.

These findings constitute a substantial saving in fossil fuel consumption. Using the


energy mix for industry from the STREAM model and lower heating values from[DGC, 2004] the reduction in fuel consumption can be calculated. Results are shownin figure 4.9.

Figure 4.9: Saving potential related to waste heat recovery with heat pumps distributedon fuel type.

Quantifying this in environmental terms the annual savings in harmfull emissions havebeen estimated. Emission factors for the fuels used in industry are from [DMU, 2008]and the energy mix of electricity (public generation) is from [Energinet.dk, 2010].Results are shown in figure 4.10.

Figure 4.10: Reduction in harmfull emissions from waste heat recovery in industry.

It must be emphasised again that these calculations rely heavily on a number ofassumptions. Inherently this implies that the results have a high degree of uncertaintyconnected to them. Because however the amount of waste heat, which the calculationsuse as point of origin, are based on heat of a quality much higher than what is needed assource medium for heat pumps, it could be argued that the existing potential is greateryet. In section 14 a case study is performed, where it is shown that the saving potentialfor a process oriented Danish company is very much consistent with the statistics,assumptions and results of this section.

Appertaining to the assumptions regarding market penetration of savings from: ther-modynamic optimisation, waste heat recovery and usage of heat pumps, in Danishindustry, is that the price of realising the potential is calculated without adding taxes tothe waste heat. Even given the uncertainties involved, the gain to society from realisingeven a fraction of the proposed reduction, are still substantial. Considering a yearlypotential saving of 1.2 bn. DKK for heat by reusing 20[PJ] waste heat along with averagereductions in harmfull emissions above 40%, legislative incentives must be advocatedfrom a socioeconomic viewpoint.


4.4 Customers

Currently the external consumers for industrial waste heat would obviously be thedistrict heating networks. Some of the reasons why this possibility is not moreextensively exercised are mentioned in [Viegand, 2009] and [SKAT, 2006]. Thesereasons include for instance high variability in the industrial activity making the heatproduction unreliable and therefore unattractive for the district heating operators. Lowprices in the district heating network due to either close proximity to large centralheating plants, or biomass/waste fired plants with low fuel costs. Additionally usingthe waste heat to provide a temperature increase in either the return or the supply linefrom a power plant is associated with some thermodynamical issues [Viegand, 2009].

According to "Danske Fjernvarmeværkers Forening (DFF)" the recent rise in energyprices has made the option of using industrial waste heat in district heating networksincreasingly attractive [Viegand, 2009]. Combine this with the scenarios used by theDanish TSO, Energinet.dk, where no less than 50% of the gross energy consumptioncomes from sustainable energy in 2030 [Energinet.dk, 2007] the incentive to increasethe share of waste heat becomes abundantly clear. There is a consensus that the energymarket must move away from the large central power plants and that wind powerwill have a substantial share in the future energy makeup. The first forecast cancelsthe industry’s problem of competing on prices, and means that the operators willhave to meet heating demand by combining several smaller decentralised providers.The second forecast predicts the end of the large fossil fuel based thermal units andthe coming of electrically driven space heating and utility. Both forecasts indicatesignificantly improved market conditions for large heat pumps operating on industrialwaste heat.

4.5 Legal issues

The Danish legislation refunds a large portion of the taxes on energy for process usein industry. To avoid that the companies produce cheap heat on purpose by operatingtheir processes inefficiently energy wise, the waste heat intended for internal spaceheating or external sale is taxed. The argument for taxing waste energy is that it wouldotherwise displace the energy from power plants that is subject to fuel taxes. Thiswould both remove the incentive for companies to invest in energy-efficient equipmentbut also make the government guilty of anti-competitive subsidies according to theEuropean Commission, and harm the overall environmental goal [SKAT, 2006]. Thereis however still an economic incentive to use this energy in most cases, but due tothe industries’ current business planning policies, many heat recovery investments arerejected even with PBP as low as 1-2 years [Viegand, 2009].

Current legislation however create a number of counterintuitive instances of howenergy should be priced. Because a cheap immersion heater does not need any wasteheat to function and all the electric input is assumed to be converted to heat, companiesare only obligated to pay the price of the electricity consumed. A heat pump is able todeliver the same amount of heat but with a third or a quarter of the electric input.Because however it also needs a thermal input which, if being industrial process wasteheat, was not subjected to the full tax burden initially, the current situation implies


that if reused (for purposes other than process) this heat must be taxed. Assigningtaxes to heat on a quantitative basis becomes absurd when a company is forced to payfull taxes on a kWh basis for heat at for instance 40°C, when they can get better heatby simply consuming new fuel with cheaper equipment. It is therefore this study’srecommendation that legislation needs to be altered so that taxation is attributed tothe fuel and not the product (heat/electricity). This would send a more direct pricesignal to the owners and operators of equipment as to what the actual impact of theirconsumption is.

Recent studies have indicated that a previously overlooked potential may exist becausethe energy consumption for heating water for cleaning purposes (Cleaning In Place:CIP) is much greater than previously assumed. Since this usage can be classified asprocess, if it is separate from any hot utility water (which is normally classified as spaceheating), no additional taxes must be paid [Viegand, 2009].

In general the cited sources state that the lack of utilised potential is due to a variety ofdifferent reasons, and not principally taxes. There is both a low economic incentive, butalso a lack of knowledge in industry of how to identify and utilise the existing potential.For external sale, a long number of unique and unforeseen reasons can appear makingprojects unattractive.

5 CONSTRAINTS OF THE HEAT PUMP MODELS 14

5 Constraints of the heat pump models

Based on the previous sections it is possible to set a frame for the solutions concerningthe choice of heat pump for a set state. Solutions will be based on the following fourparameters.

• Sink temperature Tsink (the obtained output temperature of sink media leavingthe heat exchanger on the high temperature side of the heat pump.)

• Temperature lift Tlift between sink and source (the sink temperature Tsink minusthe temperature of the available source media Tsource further elaborated on insection 8)

• COP - Heat output of condenser (or alike) in proportion to the consumption ofwork in compressor and pump components.

• Production cost of heat from heat pump.

An overview of the nomenclature with regard to heat pumps and industrial streams inthe project is displayed in figure 5.1 as an elaboration of the above.

Figure 5.1: Overview of nomenclature in heat exchangers of a single stage condensingheat pump. The temperature lift is defined as the difference between sink (outlet) andsource (inlet) temperatures.

From section 4.3 an equitable range of delivery temperatures with appertainingtemperature lift and size can be used as point of origin for the study. Due to newmaterial constraints and possibilities sink temperatures are expanded to vary between50 °C to 150 °C, with temperature lift normally between 15 and 60.

6 WORKING FLUIDS 15

6 Working Fluids

A working fluid has to satisfy a number of criteria, which will be specified as ingeneral refrigeration textbooks (e.g. in [Paul, 2003a] and [Granryd, 2005]). Besidesthe thermodynamic and physical criteria, the ideal working fluid has to be thermallyand chemically stable (also towards the materials for containment), safe and readilyavailable at a low price. It is also critical, that an escape/spill of working fluid to thesurroundings does not harm the environment. Especially damage to the atmospherehas been discussed, banning HCFC and CFC from the 1990ies due to ozone depletion.Today HFCs are also being discussed due to their Greenhouse Warming Potential.

Most of the thermal properties are easily read in different property-diagrams for theworking fluids in question. Both (t,s)- and (log(p),h)-diagrams provide this informationregarding Ammonia (R717), Water Vapor (R718) and Carbon Dioxide (R744). Theworking fluid of the fourth cycle - the hybrid cycle - is a mixture of both R717 andR718, where the vapor pressure not only changes with temperature, but also with theconcentration of the solution. Vapor pressure as a function of temperatures for the fourdifferent working fluids are shown in figure 6.1. It is worth noticing that x = 1 andx = 0 in figure 6.1 (b) corresponds to R717 and R718 in figure 6.1 (a).

(a) Vapor pressure of Ammonia (R717), WaterVapor (R718) and Carbon Dioxide (R744). R717corresponds to x=1 and R718 corresponds tox=0 in 6.1 (b).

(b) Vapor pressure of NH3H2O at differentconcentrations of ammonia in water.

Figure 6.1: Vapor pressure vs. temperature of the four working fluids in this project.

As can be seen in both a (t, s)-, (log(p), h)-diagram, and when calculating the vaporpressure, the four working fluids are quite different with respect to the correspondingtemperature and pressure levels. Without considering dimensioning of componentsnecessary it is clear that all four working fluids (but especially Carbon Dioxide(R744) and Water Vapor (R718)) will have difficulties covering the entire range of sinktemperatures.

• Ammonia - R717 - has a critical temperature of 132 °C at 11.3 [MPa]. R717is well known for its disadvantage towards compressors with low isentropicefficiency which cause very high outlet temperatures of the working fluid. This is

6 WORKING FLUIDS 16

easily identified from the layout of isentropic and isothermal lines in a (log(p), h)-diagram.

• Water Vapor - R718 - critical temperature at 374 °C at 22.0 [MPa]. Evaporationtemperatures below 100 °C will require equipment suitable for low (vacuum)pressures and very high volume flows. Water vapor (like R717) requires specialattention regarding high temperatures at the outlet of the compressor.

• Carbon Dioxide - R744 - has a critical temperature of 31 °C at 7.3 [MPa]. In orderto use Carbon Dioxide as a working fluid in industrial heat pumps, transcriticaloperation is necessary, at pressures above 9.0 [MPa] [Nekså et al., 1998]. Trans-critical operation indicates a temperature glide in the sink.

• Non-azeotropic working fluids (in this case a mixture of Ammonia (R717) andWater Vapor (R718)) provide the posibility to cover temperature levels wherethere is a lack of pure refrigerants. As can be seen in figure 6.1 (b) vapor pressurechanges with concentration of R717.The heat exchange temperature profiles are also changed when using non-azeotropic working fluids. Temperature "glide" is the result of a volatile com-ponent (R717) absorbed into (or out of) the solution.

6.1 Safety and environmental impact of Working Fluids

The four working fluids are commonly known as "natural refrigerants" within thecooling industry. They are all chosen due to their low environmental impact andhigh availability while still being thermodynamically and physically interesting. Eventhough the four working fluids are all labeled "natural" there is still some considerationsto cover before investment in an industrial plant.

Ammonia Of the three natural working fluids discussed in this report, Ammonia isthe only toxic and combustible working fluid, even though high concentrations arenecessary in both cases [Lorentzen, 1995].

• The lower ignition limit of ammonia is at 15.5 % by volume, which is considerablehigher than that of hydrocarbons and natural gas [Granryd, 2005]. At the sametime the heat of combustion is less than half of natural gas, minimising thedamage of an explosion

• The toxicity of Ammonia is in reality considerably lower than that of chlorine. Atthe same time Ammonia has a built in safety factor due to easy detection (smell).Detection is easy as low as 5 [ppm], while tissue damage starts around a thousandtimes higher concentration.

• Ammonia has no ozone depleting potential or green house warming potential.

The utilisation of Ammonia in industrial plants requires ventilation, but due to the lowweight of Ammonia this only requires venting in the ceiling.

Water Vapor Water vapor as a working fluid is harmless with regards to safety andenviroment [Yuan and Blaise, 1988] and [Sharon E. Wright, 2000]. It is worth noticingthat use of water as working fluid will require a level of treatment due to clogging ofresidue in heat exchangers.

6 WORKING FLUIDS 17

Ammonia and Water Vapor mixtures The mixture of Ammonia and Water Vapor istreated in this project as having the same impact as the two working fluids individualy.If a leak occurs Ammonia and Water will remain mixed, but due to the non-azeotropicproperty, Ammonia may evaporate changing the mixture. A mixture of Ammonia andWater will remain toxic but not combustible.

Carbon Dioxide Carbon Dioxide is non-toxic, non-flammable and it has a very lowgreenhouse warming potential (it is the benchmark of warming potential for othergreenhouse gasses). Carbon Dioxide as a working fluid, is a by-product from industrialproduction, and therefore a spill will not contribute further to global greenhousewarming [Nekså et al., 1998].

Carbon Dioxide is in many respects considered the ideal working fluid with regards toharmlessness to the environment [Lorentzen, 1995]. A spill can cause problems withpersonal safety due to suffocation, since Carbon Dioxide is heavier than air. Thismay be problematic when installation is made in close proximity to the workspaceof employees, depending of course on the size of the installation and the amount ofworking fluid. As described in section 7.2 Carbon Dioxide heat pumps require a veryhigh working pressure on the high pressure side, and with risk of a leak, higher safetyfactors must be considered.

7 BASIC SIMULATION MODELS 18

7 Basic simulation models

During the construction of the basic models for comparison of the different types of heatpumps, only major effects are considered. The impact of pressure drop from variouscomponents, non-usefull superheat/subcooling and heat loss etc. is not considered. Inthe construction of a specific plant, the magnitude of all these effects can all togetherhave a significant impact on the performance.

7.1 Condensing vapor heat pump cycle

A simple thermodynamic model have been produced for the simulation of a condens-ing vapor heat pump [CVHP]. The model is used with the working fluids Ammonia(R717) and Water Vapor (R718). The heat pump is based on sub-critical heat exchangein both the evaporator and the condenser.

Figure 7.1: Example of state points in the condensing vapor heat pump. The modelis utilised with the working fluids (Ammonia (R717) and Water Vapor (R718)). Theappertaining example of heat exchange can be found in section 8.

In the simple one-stage heat pump steady state is assumed and heat loss from both thecompressor and the expansion valve is neglected. The cycle is modeled as follows:

• Heating of the working fluid in the evaporator follows two steps: evaporationand superheating. Evaporation occurs at constant pressure (neglecting pressurelosses) which implies constant temperature evaporation.Superheating of the working fluid vapor (in the evaporator) is a constant-pressureprocess (discussed in section 12.1).The continuous cooling of the source is calculated from the change in enthalpyfrom point 4 to point 1s in figure 7.1 multiplied by the massflow.


• The compressor (and expansion device) build up a pressure difference betweenthe low and the high pressure, thereby enabling the working fluid on the lowpressure side to vaporise in the evaporator, and condense in the condenser on thehigh pressure side at appropriate temperatures for the process.The compression is considered adiabatic - but not reversible - due to an isentropiccompression efficiency defined to compensate for friction and other losses.

• After compression to the condensing pressure, the superheated vapor entersthe condenser, where it rejects heat to the heat sink at constant pressure. Heatrejection in the condenser will follow 3 steps: desuperheating, condensationand subcooling. When neglecting pressure losses condensation is a constanttemperature process. The amount of subcooling is found in section 12.1. Heatingof the sink medium is calculated as the change in enthalpy from state 2 and untilstate 3s times the massflow of working fluid.

• The expansion device is considered isenthalpic - neglecting any changes inpotential and kinetic energy.

The coupling of the heat rejection between working fluid and heat exchange mediais modelled according to figure 5.1. The symbol for minimum driving temperaturedifference (∆Tmin) is used for both the sink and source, but not necessarily at the samevalue. On the evaporator side the pinch temperature with respect to the source mediais defined at state point 4 in figure 7.1.In the condenser, the outlet temperature depends on the temperature variation of thesink and the location of the pinch point. The pinch point of a subcritical cycle couldpotentially be located at three different positions in the heat exchanger (the inlet, thepoint of saturated vapor and the outlet). As the two working fluids considered in thecondensing vapor heat pump have (very) high (compressor) outlet temperatures, onlythe point of saturated vapor and the outlet of the working fluid is considered (figure5.1).

The critical point of the working fluid is crucial; as it is the highest temperature theheat pump can deliver heat energy at. According to the saturation curve, the latent heatof evaporation is at its minimum just below the critical temperature. The condensingtemperature should therefore be sufficiently below the critical point in order to reducethe mass flow at a set heat pump capacity. Condensation just below the critical pointwill affect the COP due to increased mass flow though the compressor and can affectthe size of the heat pump due to material constraints at high pressures [Eisa et al., 1986].

Pressure levels can also be a problem at the evaporator side of the heat pump, especiallywhen considering one of the working fluids (R 718). Pressures lower than atmosphericcan lead to malfunctioning due to air leaks into the working fluid.Another effect of low pressure in the evaporator is the higher specific volume at theinlet of the compressor, as discussed later on. Volumetric thermodynamic properties areoften more relevant than the mass based properties. This is due to compressor friction,because work needed in the compressor increase as the volume flow increases. In manystudies the latent heat of condensation per unit vapor volume is considered as being ofprimary interest in the design and performance of heat pumps [Eisa et al., 1986].


7.2 Transcritical heat pump cycle

As shown in figure 6.1 (a) on page 15 high pressure can be expected when using CarbonDioxide.

The cycle of a transcritical heat pump is characterised by heat rejection at highertemperatures (and pressures) than the critical point of the working fluid. Heat is nolonger being rejected while the working fluid condensates, but from the changingtemperatures of a dense vapor in the gas cooler.

Figure 7.2: Example of state points in the Transcritical heat pump. Compared to theCVHP the temperature variation is increased in the heat sink as also shown in figure8.2.

The following changes have been implemented in the transcritical heat pump model.

• The superheated vapor enters the gas cooler, where heat is rejected at constantpressure. The fluid will follow constant pressure until it reaches the desiredtemperature for throttling. Heating of the sink is calculated as the change inenthalpy from state 2 and until state 3 times the massflow of the heat pump.Additional subcooling is neglected.

• Introduction of an internal heat exchanger between state points 1 to 1s and 3 to 4if cost effective.

Compression of Carbon Dioxide takes place at low pressure ratios compared to R717and R718 due to the high mean pressure of the cycle. The limiting factor of thistechnology is the high pressure difference to the surroundings in both compressor andgas cooler.

Heat exchange on the evaporator side of the transcritical heat pump is modeledequivalent to the heat exchange of the condensing vapor heat pump. A numerical


differentiation is used to find the optimum pinch point in the gas cooler, in order tominimise compressor shaft power (see figure 8.2).

An important point is the possible regulation of a transcritical cycle by changing the op-timum discharge pressure for varying heat output of the heat pump [Nekså et al., 1998].The regulation of a R744 heat pump provides higher efficiencies when heat demand ischanged, but at the same time the outlet pressure (of course) influence the temperaturerange [Miljøstyrelsen, 2001].

7.3 Compression/absorption heat pump cycle

The Compression/Absorption Heat Pump cycle [CAHP] is a combination of the CarréAbsorption heat pump cycle and a regular CVHP cycle. It was invented by Osenbrückin 1895, but little researched until the 1970’ies. [Hultén and Berntsson, 1999].

Figure 7.3: Example of state points in the Hybrid heat pump. In the example theworking fluid mixture is 0, 75 [R717/R718] on mass basis. The mixture of Ammoniaand Water is split in state point 10 and mixed in state point 9. State 1 is saturated vapor,while state 6 is saturated liquid. Appertaining heat exchange can be found in figure 8.3.

The design of a CAHP is based on the difference in vapor pressure of the two workingfluids in the mixture. State points and design of CAHP is modelled according to figure7.3. The modeling of a CAHP cycle is more complex compared to eg. the CVHP, due tothe ratio of the two working fluids makes for an additional level of freedom. As can beseen in 6.1 (b) the mixing of Ammonia and Water Vapor facilitate a large span in sinktemperatures.

• The mixture of working fluids is considered known at state-point 3, as is thetemperature of the working fluid. The fluid in state 3 is assumed saturated liquid


(quality = 0). This is sufficient information to calculate the pressure on the highpressure side (neglecting pressure losses).

• Internal heat exchanger, absorber and desorber are constant pressure heat ex-changers (neglecting pressure losses). Cooling and heating of the mixture ofAmmonia and Water Vapor is not constant temperature processes due to the non-azeotropic properties. Heat transfer is calculated from inlet and outlet enthalpiestimes the massflow of the heat exchanger.

• The expansion device is considered isenthalpic, neglecting any changes in poten-tial and kinetic energy.

• Pressure on the low pressure side is calculated based on a mass balance of themixture through both the compressor, the solution pump and expansion valve.

• Both the (weak) liquid solution entering the solution pump and the vaporentering the compressor is assumed saturated.

• Compression is considered adiabatic and irreversible, due to an isentropic com-pression efficiency defined to compensate for friction and other losses. Thesolution pump has similar assumptions. The ratio of work between pumpand compressor: Wpump/Wcomp is at most 5%. The working fluid entering thecompressor is at minimum 99% ammonia.

• The internal heat exchanger increases the temperature of the weak solution (fromstate point 7 to 8) with heat from the strong solution in state point 3. The internalheat exchanger has a separately defined ∆Tmin.

• Mixture of the streams 2 and 8 is from [Poul Scheel Larsen, 2005], neglectingchanges in kinetic and potential energy.

Changing the mixture of the cycle will change the temperature lift and temperaturesin both the absorber and desorber. Acording to [Åhlby et al., 1991] the optimal cycle isachived with the highest possible pressure on the high pressure side, minimising thewater content in the compressed vapor. Effects of pressure and mixture are investigatedin section 12.3.

[Hultén and Berntsson, 2002] expects application in industrial plants and as districtheating within the temperature range of 80 − 130 °C. Higher temperatures can bereached with the working fluid, but will require awareness regarding compressorlubrication.

Heat exchange in the compression/absorption heat pump is different from the twoother types. Due to changes in temperature profile with changes in the mixture of theworking fluid, rather large temperature variation in the sink/source media can be aconsequence. In the evaporator the pinch is placed at the working fluid outlet (withspecial attention paid to the temperature variation in the source media) , while thecondenser pinch point is placed by numerical intergration (see figure 8.3).

8 HEAT EXCHANGE BETWEEN HEAT PUMP AND INDUSTRIAL PROCESS 23

8 Heat Exchange between Heat Pump and IndustrialProcess

Applying pinch analysis to the heat exchangers of an industrial heat pump is reasonableas a first guess calculation, assuring that the second law of thermodynamics is notviolated. This matematical approach is particulary good when phase change in theheat exchanger is considered, which is the case in most heat pumps. A more detailedanalysis of the heat exchanger will be required before finishing the design studies of aheat pump for installation [G. Nellis, 2008].

A walkthrough of pinch technology and heat pumps in pinch analysis is presentedin Appendix B.1. In pinch analysis (equation (B.2)) heat loss and heat exchanger pricesare already correlated with respect to the payback period of the HEN.

Pinch Heat Exchange The correlation between heat exchanger price (and size) andirreversibilities is also applicable when introducing heat pumps into industrial plants.The size of ∆Tmin in the case of a heat pump is in most cases lower than whatwould be experienced in equation (B.2) due to a payoff between increased investmentcost of the heat pump and investment cost in the heat exchangers. ∆Tmin can belower than 2K, but in most cases the economically interesting range is (according to[Brunin et al., 1997] and [Annex-21, 1995]):

2K ≤ ∆THEX ≤ 8K (8.1)

A simple overview of some of the nomenclature used in this report can be seen infigure 5.1, and an example of heat exchange using pinch technology is presented infigure 8.1. In figure 8.1 QC is used as a relation between enthalpy in the inlet of the heatexchanger and the outlet. It is the relative duty (dimensionless) of both the evaporatorand condenser (on basis of the temperature lift of the sink fluid QH → 1). In theexample in figure 8.1 q = 1.19 (see equation B.3)

Figure 8.1: Theoretical temperature profile of both working fluid and sink/source fluidin the crossflow heat exchangers of a single stage condensing vapor heat pump. Thisexample matches the calculations in figure 7.1


Besides conventional condensing vapor heat pumps, two other types of heat pumpsare modeled (transcritical- and compression/absorption heat pumps) which have asomewhat different temperature profile in the heat exchanger. The temperature glidesof transcritical- and compression/absorption heat pumps is caused by the workingfluids.

A temperature glide in the working fluid is beneficial in applications where sink and/orsource media require heating/cooling over a temperature range. The temperature glideallows for a steeper gradient of the sink and source in the heat pump, by shifting thepinch point towards lower values of relative duty. At the same time irreversibilitiesin the heat exchanger are minimised compared to heat exchange with evapora-tion/condensation. Temperature profiles of transcritical- and compression/absorptioncan be seen in figure 8.2 and 8.3.

Figure 8.2: Temperature profile of working fluid and sink/source fluid of a transcriticalheat pump. Condensation of working fluid will not occur in the heat exchanger, whichmatches figure 8.2.

Figure 8.3: Theoretical profile of the temperatures in desorber and absorber of thecompression/absorption heat pump model. Absoption/desorption of ammonia inwater changes the condensation/evaporation characteristics. This figure matches theexample of figure 8.3.


Calculation of corresponding heat exchanger area In order to determine the priceof heat exchange between the industrial process and the heat pump for the economiccomparison, a more accurate calculation is needed. This can be done on the basis of theassumptions used in pinch technology.

It is clear, that when designing a heat pump for a specific application, the type ofheat exchanger must fit the application. A calculation of the price of a specific heatexchanger require consideration with regard to working pressure, heat exchanger areaand price.

A calculation of the Log-Mean Temperature Difference (LMTD) of each seperate partof a heat exchanger (eg. subcooling, condensation (two phase) and de-superheatingin the CVHP) is used to calculate an overall heat exchanger area for each of the heatexchangers in the models. A subsequent change in the pinch analysis will change theheat exchanger area, based on the change in driving temperature difference (LMTD)[G. Nellis, 2008] .

Q = UA ∆Tlm (8.2)

In each part of the heat exchanger a seperate U-value is chosen to allow for differencesin the state of the fluid. These values are based on overall considerations from[Granryd, 2005] and [Bejan, 1996] and heat exchanger areas. The sink and sourcemedia is assumed to be liquid water, pressurised to avoid effects from evapora-tion/condensation.

As a special case, the U-value of the transcritical Gas Cooler is found from specificexperimental data from [DTI, ]. It has not been possible to obtain a seperate U-valueof heat rejection from a transcritical vapor from litterature. The overall heat exchangebetween R744 and water is calculated according to the same principles (equation 8.2)and is set to a value of Uoverall = 0, 95 [kW/ (m2 K)]. The calculation of the U-value canbe found in appendix E.

Hulten uses a varying U-value for the calculations of the hybrid model, which issomewhat higher in the absorber than the one used in this project (two phase).

Prices matching the calculated area are correlated in section 11.2.

9 COMPRESSORS AND THEIR OPERATING LIMITS 26

9 Compressors and their operating limits

Observing historical trends within refrigeration, practical constraints of cooling plantshave changed, if economically interesting, due to research and engineering within thesefields. Many of these changes and inventions are applicable in heat pumps as well,although not necessarily intended in research, indicating that problematic constraintsmight change when economically interesting.

This section will give an introduction to the limitations and present status for com-pressor technology, with a focus on the most relevant compressor types. Each distinctcompressor technology is described in a dedicated section in appendix C along withcertain important concerns requiring special attention during a design process.

There are two primary groups of compressors, namely the dynamic and the positivedisplacement type [Granryd, 2005].

• Positive displacement compressors work by trapping the gas in a space which issubsequently reduced in volume. This increases the pressure as the axis of thecompressor turns. At some point the gas will be delivered to the high pressureside when an exit port is uncovered.

• A dynamic compressor works by an impeller giving the gas high speed. For anaxial turbine the pressure is increased by a diffuser, which reduces the speed. Fora radial turbine the centrifugal field further enhances the compression.

Since this project aims at industrial applications the relevant compressor types are inthe range of high output and efficiency (physical size is not parameter). The typesconsidered are: reciprocating piston-, screw compressors and turbines (both centrifugaland axial).

9.1 Current status

Figure 9.1: Characteristics for different compressor types from [Annex-21, 1995] inits original form. Volumetric flow rates are to be updated by recent values from[Granryd, 2005].


The last major international survey of industrial heat pumps [Annex-21, 1995] reportedthe numbers shown in figure 9.1. More recent numbers indicate that developmentsof the screw compressor technology have displaced the high capacity reciprocatingcompressor in this market segment [Granryd, 2005]. The same source states thatcentrifugal and screw compressors are now competitive at volume flow rates as lowas 2,000 and 180 m3/h, respectively.

Reliability is a major consern with regards to the different types of compressors.

• The mechanical interaction between moving parts are lowest in the dynamiccompressors, however with high forces on each blade. Small amounts of liquiddroplets in the working fluid vapor are not harmfull. Excessive amount can causeerrosion and unbalancing of the impellers.

• In reciprocating compressors, liquid droplets are a huge problem and manyprecautions are taken to avoid this problem. Increased superheating of theworking fluid is one of the means to avoid "liquid hammering".

• Screw compressors and the like are less sensitive to droplets than reciprocatingpiston compressors. With these compressor types no superheating is necessary.At the same time oil-injection can decrease outlet temperatures of the compressor.

9.1.1 Limitations

The driving force for high temperature heat pumps is the increasing fossil fuel prices.Historically production of thermal energy has largely been based on simple andinexpensive technical solutions which are cost effective due to low oil/gas prices.Expectations of increased prices of these resources, have driven the development ofheat pump technology towards higher temperature applications.

One of the inherent issues with newer heat pumps is that the high temperatures desiredare accompanied by high pressures. Traditional design pressure for refrigerationapplication has been 2.5 [MPa], due to the large spectrum of different evaporating andcondensation temperatures from working fluids in traditional refrigeation (CFCs andHCFCss). However the desire to make heat pumps (for higher temperature applica-tions with natural working fluids) lead to an increase in design pressure up to 3.5-4[MPa] on the high pressure side in the early nineties [Korfitsen and Kristensen, 1998].Development has been most explicit within CO2 heat pumps. Presently these heatpumps are reaching high pressures of up to 12-13 [MPa] [Nekså et al., 1998].

The next step for this development is one of the incentives behind this project, namelythe potential of using heat pump technology to produce process steam for industrialapplications. This means approaching temperatures of 220 °C for steam between 1-2[MPa]. Problems arise on a number of fronts when dealing with these temperatures:

• Current levels of design pressures are no longer sufficient, however the me-chanical solutions for dealing with high pressures have already been solvedin other fields of engineering, most prominently the petro-chemical industries.[Burckhardt Compression, 2010]

• Attainable outlet temperatures for oil-lubricated machinery are limited to 160 °C(320 ◦F ) , due to the instability/breakdown of the lubricating media [Lewis, 2009].


Oil-free solutions exist, but at a substantially increased cost. This is at the momentone of the fields of work within the compressor-industry. Possible solutionsinclude:

– Increasing the breakdown temperatures is possible at increased cost, refiningthe synthetic oil for the specific needs.

– Increasing the flow of oil through the compressor will lower the temperatureof the working fluid leaving the compressor. A specific oil loop canbe designed to utilise the excess heat attained in the lubrication (hightemperatures). This specific solution is possible in most screw-compressorsand is discussed in section 9.2.1.

• Pressure differences and temperature levels are also limited by the materials usedfor seals and gaskets in the compressors.

For niche applications mostly all of these problems can be solved technically, but aspreviously mentioned this is a costly affair.

Lubrication of bearings and moving parts in a compressor is necessary. As discussed inthe following, several solutions do exsist. Generally the compressor requires lubricant,where an oil free solution is favourable in the rest of the system, (eg. due to fouling ofthe heat exchangers). In industrial plants an oil separator is installed which extract theoil from the working fluid.

According to the websites of the companies Grasso and Johnson Controls (Sabroe andFrick) compression of R717 is today limited at respectively 5.2 [MPa] and 5.0 [MPa][GEA Grasso, 2010] and [Johnson Controls Denmark ApS. Sabroe, 2010] for screw andreciprocating compressors respectively. Johnson Controls use test pressures of above8.0 [MPa] indicating a possible lift in working pressure [Korfitsen and Kristensen, 1998].The magnitude of the volumetric flow rate matches that of figure 9.1 with volumetricflow rates between 50 − 10000 [m3/h] (which is approx. 20 − 4000 [kW]) from thetwo rival companies (pressure ratios below 10 : 1). Other players in the market havebeen inspected without further results. Vilters are reaching 5.0 [MPa] and similar flowrates with their single screw compressors [Vilter Manufacturing, 2010]. Vilter describes7.6 [MPa] as the design limit due to material considerations. 5.2 [MPa] is consideredmaximum working pressures of R717 henceforth.

The spectrum of pressure and volumetric flow rates is different with regard tocompressors for transcritical operation. Bitzer produces reciprocating compressors forR744 at 10.0 [MPa] and 25 [m3/h] (22 [kW]) [BITZER Kühlmaschinenbau, 2010]. TheDanish company Advansor have used Bitzer compressors at 12.0 [MPa] at similar flowrates [Advansor, 2010]. Both Danfoss and Bock produces reciprocating compressors(13.0+ [MPa]) for commercial use around flowrates less than 14 [m3/h] (25 [kW])([Danfoss, 2010] and [Bock Kältemaschinen, 2010]). Only one example of a compressorwith an industrial grade output is found, a screw compressor from GEA Grassoreaching 12.0 [MPa] (160 [kW]) [GmbH, 2010]. Several examples exist of small recip-rocating compressors in series in order to reach higher outputs. The design pressure oftranscritical compressors for R744 will be considered as 13.0 [MPa] henceforth.

Compression of water vapor (steam) in industry is usually handled by dynamic- or


oil-free screw compressors. With the scope of this project, screw compressors areconsidered the reasonable choice. Examples of compressors for steam have been foundin the range of 2.000−26.000 [m3/h] ([Atlas Copco, 2010] and [Howden Process, 2010])with attainable outlet pressures of 2.6 [MPa] (pressure ratios up to 7 : 1 in one stage)and reasonable isentropic efficiencies (as discussed in section 9.1.2).

Combinations of ammonia and water vapor can use both conventional ammoniacompressors and compressors for steam according to [Hultén and Berntsson, 1999]and [Ferreira et al., 2006]. Neither of the above mentioned compressor producers,manufacture compressors specifically designed for hybrid heat pumps.

The compressors for R717 and R744 are in both cases considered lubricated. In thecase of working fluids containing water (the mixture of R717 and R718 and the pureR718) operating oil-free compressors under wet conditions can improve the isentropicefficiencies by 2, 5 − 13 % due to liquid refrigerant droplets performing as lubricant[Ferreira et al., 2006]. If compressors with oil is considered, a soluble oil must be chosenin order to avoid problems with mixing water and oil, and fouling from oil on heatexchanger surfaces [Hultén and Berntsson, 1999].

9.1.2 Efficiencies

The working condition of a given heat pump (with the stated limitations from section9.1.1) will be affected by the compressor efficiency. Especially the compressor outlettemperature is effected, extending the range of some heat pumps using a compressorwith a high isentropic efficiency. From litterature studies several different expressionsfor isentropic efficiencies are found.

A general agreement is that isentropic efficiencies of positive displacement compressorslie in the range of 0, 85[/] − 0, 65[/] (e.g. [Granryd, 2005], [Brunin et al., 1997] and[Degueurce et al., 1984]). In cases where the focus is expressing the differences inworking fluids, several sources use a constant level efficiency for all pressure ratios(e.g. [Eisa et al., 1986]). More detailed descriptions are found in comparisons ofdifferent heat pump types. A characteristic feature of these sources is a fallingisentropic efficiency with increasing pressure ratio. The built in volume ratio of acompressor must match the specific application to maximise the isentropic efficiency(screw: [Brendeng, 1979], piston: [Villadsen, 1985]). A general correlation for isentropicefficiency can therefore not be found. A short elaboration on the factors that influencecompressor efficiency and compressor work, can be found in Appendix C.

When relating the developed models to the flow regimes of figure 9.1 it is apparentthat dynamic compressors will not be interesting for installations below a couple ofMW. Looking at the possible compression ratios of figure 9.1 and comparing the rangeand price of the different technologies the radial turbine would be the next choice forlarger installations.

The correlations of isentropic and volumetric efficiency is commented in the followingfor each working fluid. The correlations are from experimental data. A graphicalpresentation of the correlations are found in figure 9.2 on page 31.


R744 (Carbon Dioxide) - Reciprocating compressor The correlations for the CO2compressor have been obtained from Nekså [Nekså et al., 1998]. The expression isderived from empirical data for a small piston compressor matching the compressorsfound in section 9.1.1. It is assumed that the isentropic efficiency will not be effectedfrom changes in capacity (using a larger compressor).

1, 5 < ∆p < 2, 5 : ηisentropic = −0, 72 + 1, 32∆p− 0, 28∆p2

2, 5 < ∆p < 4, 5 : ηisentropic = 0, 91− 0, 03∆p

1, 5 < ∆p < 4, 5 : ηvolumetric = 1, 00− 0, 05∆p

R717 (Ammonia) - Reciprocating and screw compressor According to Hulten &Berntsson efficiency correlations matching a lubricated screw compressor with R717as working fluid can be formulated as below[Hultén and Berntsson, 1999]:

1, 5 < ∆p < 3, 5 : ηisentropic = −0, 05 + 0, 55∆p− 0, 09∆p2

3, 5 < ∆p < 7, 0 : ηisentropic = 0, 82− 0, 01∆p

1, 5 < ∆p < 3, 0 : ηvolumetric = 0, 91

3, 0 < ∆p < 7, 0 : ηvolumetric = 0, 93− 0, 01∆p

R718 (Water vapor) - Screw compressor Degueurce gives an expression for oil free(dry) compression of steam at inlet temperatures around 100 − 120 °C and pressureratios between 1, 5 − 3, 7. Commercial units are operating with a single stagepressure ratio of up to 8 [Degueurce et al., 1984]. A maximum single stage pressureratio of 6 is adopted in this paper. As stated in section 9.1.1, Ferreira outline anincrease in isentropic efficiency between 2, 5 − 13 % if lubricated by droplets of water[Ferreira et al., 2006]. A general increase of 5 % in isentropic efficiency is adopted in thefollowing.

1, 5 < ∆p < 2, 5 : ηisentropic = −0, 39 + 0, 96∆p− 0, 20∆p2

2, 5 < ∆p < 7, 0 : ηisentropic = 0, 79− 0, 01∆p

1, 5 < ∆p < 7, 0 : ηvolumetric = 0, 81

Hybrid mixture (Ammonia and Water vapor) - Screw Compressor Regarding thehybrid process, Hulten & Berntsson states that the expression for R717 is also validfor a hybrid process using a mixture of R717 and R718, with an efficiency reductionof 5% for both ηvol and ηis [Hultén and Berntsson, 1999]. Ferreira uses isentropic


efficiencies from a wet twin screw oil-free compressor equivalent to that used for R718[Ferreira et al., 2006]. The correlations are quite similar, indicating that the achievablehigh pressure corresponding to the correlations are more important. Correlationscorresponding to Hulten are used for the calculations.

1, 5 < ∆p < 3, 5 : ηisentropic = −0, 10 + 0, 55∆p− 0, 09∆p2

3, 5 < ∆p < 7, 0 : ηisentropic = 0, 77− 0, 01∆p

1, 5 < ∆p < 3, 0 : ηvolumetric = 0, 86

3, 0 < ∆p < 7, 0 : ηvolumetric = 0, 89− 0, 01∆p

(a) Correlations for isentropic efficiency

(b) Correlations for volumetric efficiency

Figure 9.2: Isentropic and volumetric efficiency of compressors from litterature atdifferent pressure ratios. The correlations and boundries are from [Nekså et al., 1998],[Hultén and Berntsson, 1999], [Degueurce et al., 1984] and [Brunin et al., 1997]. Corre-lations are based on experimental data.


9.2 Approaches to lowering compressor outlet temperature

New problems emerge with the increased attainable pressures discussed in section9.1.1. Especially breakdown of oil due to higher outlet temperatures of the workingfluid is a problem. Utilising a compressor with a high isentropic efficiency reduces theimpact of the problem, but this is not always possible and does not reduce invesmentcost of the compressor.

9.2.1 Oil Injection

Injection of surplus lubrication into the inlet mainfold of a screw compressor can reducethe temperature of the working fluid leaving the compressor. The temperature ofthe lubrication, the surface area of the lubrication (spray of particles) and the typeof screw compressor has an influence on the outlet temperature [Stosic et al., 2003].The previously mentioned oil separator becomes imperative with injection of surpluslubrication. A heat exchanger is used to utilise the heat contained in the oil return line.A revision of the example of a condensing vapor heat pump from figure 7.1 can befound in figure 9.3 with increased oil injection and heat exchanger on the oil return line.Compressor cooling by oil injection is implemented in the condensing vapor heat pumpand the compression/absorption heat pump (where high temperatures is a problem).

Figure 9.3: Revision of state points for ammonia CVHP with oil injection. The changein compressor outlet temperature changes the attained sink temperature due to a loweramount of superheat in the condenser.

According to Brunin a reasonable value of the amount of oil injection is πvolume = 138[/](ratio between compressor volumeflow and lubricant [Brunin et al., 1997]).

The simple model assumes that the lubrication particles attain the temperature of theworking fluid (infinite surface area) prior to the segregation in the oil separator.

To simplify the calculation of heat rejection in both the oil heat exchanger andthe condenser, assumptions are made that two streams (with appropriate massflowaccording to the amount of heat) are heated parallel to each other. This also simplifiesthe calculation of heat exchanger area in both cases.The temperature of the oil added before the compressor is assumed to match the


temperature of the working fluid. This imply that a portion of the heat attained inthe oil is rejected to the suroundings, without assisting the process. This energy couldbe used as a supplementary heating of the source medium.

9.2.2 Two stage heat pump

A two-stage heat pump allows for higher possible pressure differences betweensink and source and in some cases higher overall COP, while lowering the outlettemperature of the compressor compared to the one stage cycle. The model is named"two-stage with flash intercooler" [Annex-21, 1995], and is modelled according to theschematics of figure 9.4.

Figure 9.4: Two-stage CVHP state points. The model reduces high temperatures at thecompressor outlet and permit higher pressure ratios.

An additional compressor and expansion valve is introduced, in order to mix thesuperheated vapor from the low stage compressor with the mixture of liquid and flashgas from the high pressure expansion valve.

• The ekstra Compressor and Expansion Valve is modelled according to the simpleone-stage cycle. The pressure ratio for the two stages is not equal, but a variablefor optimisation.

• The mixing of the two streams is considered without heat exchange to thesurroundings. By direct contact between the two flows (superheated vapor andliquid with flash gas) the vapor out will have a temperature close to saturation[Granryd, 2005]. State 5 in 9.4 has a quality of 0 (saturated liquid). State 2int isvapor with a quality of 1 (saturated vapor).

The use of the two-stage cycle expand the technical possibilities of a heat pump givena certain workin fluid. According to Granryd, problems with flash intercoolers havebeen experienced, due to pressure drop through the flash intercooler (pressure dropfrom flash intercooler is not in the model). In order to avoid liquid in the high stagecompressor, management of the two compressors must be considered, or superheatingof vapor from the flash intercooler is needed.

10 COMPARISON OF WORKING DOMAINS 34

10 Comparison of working domains

A quick comparison of the different heat pumps is conducted, in order to evaluate theworking domain of each heat pump type. The comparison is based on an idea from anarticle by Brunin [Brunin et al., 1997], and will at the same time act as a validation ofthe models.

Brunin does not consider a transcritical heat pump with R744 and uses a a generalcorrelation of isentropic and volumetric compressor efficiency (which can be seen infigure 9.2). The comparison of the heat pump models is conducted using the differentefficiency correlations found in section 9.1.2.

The working domain of the four working fluids is restricted by a set of factors.

• Low pressure - Absolute pressure above 101.3 [kPa]

• High pressure - Absolute pressure below the high pressure dictated by the choiceof compressor from section 9.1.1.

• COP - Higher values than COP = 4

• VHC - Volumetric Heating Capcity is the ratio between usefull heat and sweptvolume flow of the compressor. VHC is a (very) simple expression of investmentcost of heat pump.

Curves displaying the limits of R717 are shown in figure 10.1.

The temperature variation in the sink and source media is kept constant (15 [K]) inboth the hybrid and condensing vapor heat pump. In the transcritical heat pump onlythe temperature variation of the source is limited.

Figure 10.1: Working domain of Heat pump with R717 with limits according to theabove items.

A comparison of the CVHP model created in this project and the model used inBrunin is done in figure 10.3. The models match even though different correlationsof compressor efficiencies and different pinch considerations are used. Most of thedifferences are presented in figure 10.2.


Figure 10.2: Differences in characteristic values used in this project and in Brunin[Brunin et al., 1997]. Only key variables are presented. Also the correlations ofcompressor efficiencies are different in the two models.

The high pressure limit is set to match the compressors considered in section 9.1.1,while Brunin uses a set upper limit of 2.5 [MPa], even though specific comments aremade with regard to higher attainable pressures with R717 [Brunin et al., 1997].

(a) Working domain of R717 and R718 in theheat pump models of this project.

(b) Working domain of R717 and R718 fromBrunin.

Figure 10.3: Comparison of the working domain (CVHP) of R717 and R718. The twomodels match well, even though the high pressure limit is changed (figure (a)).

(a) Working domain of hybrid heat pumpmodels of this project.

(b) Working domain of hybrid heat pump fromBrunin.

Figure 10.4: Comparison of the working domain of the hybrid heat pump from thisproject and [Brunin et al., 1997]. The calculations from Brunin are with cooling ofthe working fluid with oil injection. Calculation of figure (a) does not include theseconsiderations.

A comparison of the two hybrid models is also possible, although the models are notdirectly comparable. The increased high pressure in the model of this project changesthe possible temperature lift and sink temperatures. The calculations in Brunin is


with oil injection for cooling of the working fluid, while the calculations of the hybridprocess in this part of the project is without cooling (even though high temperaturesare reached).

With all four models collected into one figure (figure 10.5), the possibilities whenconsidering the four chosen working fluids are shown. The working domain of thesefour heat pumps cover the requirements of heat pumps stated in Annex 21 and severalother sources (including Brunin) [Annex-21, 1995].

In figure 10.5, the hybrid model only reflect one solution of the working fluid (x=0.65).As shown in figure 10.4 the attainable sink temperatures can be changed, without asignificant impact on possible temperature lifts.

Figure 10.5: A simple comparison of working domains of four working fluids. Withdifferent solutions of the working fluid in the hybrid model, the temperature spectrumconsidered is easily covered. The solution of Ammonia/Water in this figure is x = 0.65.All calculations in this comparison is without consideration of the temperatures of theworking fluid after the compressor.

The above comparison covers plain thermodynamic considerations with regard toeconomy, mode of operation and sink/source media. More detailed reflections aredisregarded.

11 EXERGY ANALYSIS AND THERMOECONOMICS 37

11 Exergy analysis and Thermoeconomics

The concept of exergy is based on the departure of the system from that of a suitablydefined environment. When applied to streams of matter or energy, the exergy of thesystem is the maximum theoretical useful work that can be obtained when the systeminteracts to equilibrium with the environment. This analysis is based primarily onthe exergy definitions presented in [Bejan, 1996]. Because some ambiguity exists inlitterature a detailed explanation of the concepts is provided in appendix D.

In exergy terms the environment is differentiated from the systems immediate sur-roundings, and will in this study be defined as ambient temperature and pressure(T0=20 [°C], p0=101.3 [kPa]). The systems immediate surroundings are chosen so thatthey encompass enough of the environment to ensure that heat loss occurs at T0. Thisis an assumption to simplify the amount of information needed by eliminating the firstterm in equation (11.1) enabling the evaluation of the systems internal losses and thedestruction of exergy. This assumption neglects inefficiencies due to heat loss betweencomponents and piping along with irreversibilities due to fluid friction. This is areasonable assumption when comparing models and is used throughout this report[Bejan, 1996].

Because exergy is a qualitative measure it can be utilised to optimise a system froma thermoeconomic viewpoint. By assigning a cost to all streams in the system andsupplying the model with economic correlations for the different components, it ispossible to find the optimal economic operating point and equipment dimensions givencertain external constraints. This is done in the models using cost minimisation withrespect to the heat produced.

11.1 Calculations

Control volume analysis is applied on a component and on a system level, usingequation (11.1).

dEcvdt

=∑j

(1− T0

Tj

)Qj −

(W − p0

dVcvdt

)+∑i

miei −∑e

meee − ED (11.1)

Efficiencies In order to define meaningful efficiencies, equally meaningful consid-erations are necessary as to what can be regarded as the fuel and the product of thesystem/component.

System Generally for a heat pump system, the product is the increase in exergy of thesink medium flowing through the heat rejecting unit (ie. condenser etc.). The fuel forsuch a system will be the decrease in exergy of the source medium as it flows throughthe evaporator, in addition to the fuel of the fluid machinery (electricity or other for thecompressor and pump drive).

εsystem =∆Esink

∆Esource +∑(

Wcomp + Wpump

) (11.2)


If however the heat pump functions in dual mode, i.e. providing heat and at the sametime providing cooling to a source medium which otherwise would have requiredventing or even additional cooling efforts, the exergy removed from the source mediummay be counted as a product. This definition is valid for pinch analysis applicationseven though the heat transfer takes place above T0 as long as it is below the pinchtemperature.

εsystem =∆Esink + ∆Esource∑(Wcomp + Wpump

) (11.3)

Components For fluid machinery (compressor/pump):

εcomp =Ee − EiW

(11.4)

The product of the component is the increase in exergy of the flow from inlet, i, to exit,e, and the fuel is the shaft power needed to drive the compressor.

For heat exchangers the purpose is assumed to be the heating of a cold stream, by ahot stream. That is the product of the component is the change in exergy of the coldstream from inlet to exit, and the fuel is the change in exergy of a hot stream from inletto exit.

εHEX =Ecold,e − Ecold,iEhot,i − Ehot,e

(11.5)

For evaporators the cold stream is the working fluid, and the hot stream is the sourcemedium. For condensers/gas coolers, the cold stream is the sink medium and the hotstream is the working fluid.

For an expansion valve different approaches can be chosen, depending on what isconsidered the fuel and the product in the exergy balance for the component. To isolatethe component and give a clearer definition of the impact of an expansion valve on thesystem, the following definition can be chosen:

εexpa =Eexpa,i − Eexpa,e

Wcomp

(11.6)

That is, the product of the expansion valve is the pressure drop over it, and hence thechange in exergy from inlet to outlet. The fuel for this process is the compression work.Another approach assumes that nothing can be done to improve on the componentitself, and the exergy destruction related to it should be reduced by optimisation of thecomponents it serves. This is described in for instance [Morosuk and Tsatsaronis, 2008]and [Misra et al., 2006], where, in the latter, the expansion valve is included in what iscalled the "evaporator assembly" along with a number of other slave components to theevaporator. The argument being that the expansion valve is necessary for this group ofcomponents to function, and the loss of exergy over it, must be considered as a fuel forthe evaporator. Following this line of reasoning, this project only reflects on the exergydestruction in the valve in comparison to the other components and no attempt is madeto calculate an efficiency.


Special case For the CAHP cycle, an expression was developed to account for theexergy destruction due to chemical irreversibilities (the underlined term in equation(11.7)). It is based on a system observation where the efficiency from a componentcalculation is subtracted from the efficiency derived from a system calculation. Identi-fying the difference between the two as the exergy destruction related to the remainingcomponents yields:

0 =EP

EF−

(1−

∑k (ED,k + EL,k)

EF,k−ECHDL,i

EF,i

)(11.7)

It is considered beyond the scope of the project to describe the irreversibilites dueto chemical affinity in the mixing and distilation process of the hybrid cycle. Theexpression provided in equation (11.7) gives a measure of scale for this chemicalphenomenon, but cannot assign a seperate value for the mixing/unmixing unitsrespectively.

Example In figure 11.1 the results af a representative calculation has been summarisedto demonstrate how the results for a given operating condition may look whenrepresented in exergy terms. The figure depicts the two stage R717 process with adelivery temperature of 100 °C and a source temperature of 50 °C.

Figure 11.1: Results of exergy calculations for the 2 stage R717 process at specificoperating conditions.

11.2 Economics

For the purpose of benchmarking the modeled heat pump cycles with respect toeach other, their cost optimal operating conditions have been calculated using exergycosting. Economy provides an impartial basis for comparison and the exergy conceptprovides the means for a qualtiative representation of the cycles.

Constructing exergoeconomic cost balances for all streams enables an evaluation of therunning cost for heat production taking into account the quality of the heat consumedand produced. This is an objective function for minimisation. The cost rate balance ofequation (11.8) expresses the cost rate associated with the product of the system as afunction of the fuel consumed in the process and the cost rate of the capital cost andoperation and maintenance.

CP,tot = CF,tot + ZCItot + ZOMtot (11.8)


Ci = ciEi = ci(miei) (11.9)

Costing of each stream is apportioned to it using the exergy rate it represents and thecost needed to obtain it. For the heat pump cycles a general expression can be obtainedas: ∑

e

(ceEe)k + cq,kEq,k = cw,kWk +∑i

(ciEi)k + Zk (11.10)

Note that the sign convention from equation (11.1) is adapted so that work being doneto the system is positive. To obtain the necessary number of expressions to solve thisset of linear equations some auxiliary relations are needed.

• For all cycles it is assumed that the cost rate of the exergy stream leaving thecondenser equals the cost rate entering it.

• For cycles with internal heat exchange it is assumed that the cost rate of the fuelstream remains constant over the heat exchanger.

• The cost of all entering streams (input) is assumed to be known:

Price of compression work is set as the electricity price (corrected with anefficiency of the electric motor).

Source heat entering the evaporator is assigned zero cost (see commentbelow).

Assuming the heat produced is used for process, no additional tax must be payedaccording to Danish legislation. Alternatively the heat must be accounted at the fullduty of the fuel used to obtain it. This is of course a strong incentive against recoveringwaste heat (for elaboration on internal use/external sale see section 4.5), and for thepurpose of this calculation it is assumed that if the legislators find it prudent toimplement heat pumps in the Danish energy sector in the future, these rules must besubject to revision.

Using the above approach in concordance with the exergy costing principles proposedin [Bejan, 1996] it is ensured that all costs in connection to owning and operating theplant is assigned to the heat produced.

Cost balance for heat pump cycle - single stage R717

ce,compEe,comp = cw,compWcomp + ce,evapEe,evap + Zcomp + 14 Zplant

ce,condEe,cond = ce,compEe,comp − cq,cond∆Esink + Zcond + 14 Zplant

ce,EV Ee,EV = ce,condEe,cond + 14 Zplant

ce,evapEe,evap = ce,EV Ee,EV + Zevap + 14 Zplant

Auxiliary relations: ce,cond = ce,comp and cw,comp = electricity price


It is not possible to obtain a general solution for the minimum of the objective function(cq,cond) since it involves the partial differential of a number of decision variables,making the problem strongly non-linear. Instead a nummerical solver has been applied.

Some preliminary economic relations was provided to the models in order to estimatecosts related to capital investment and operation. First a purchased equipment cost forcomponent k (PECk) is calculated using economic correlations from litterature whichwere adjusted using current price examples. Secondly the total capital investment(TCIk) is calculated using a factor which accounts for all the additional costs relatedto a new investment. For this purpose it is assumed that the heat pump is an expansionto an existing installation, which mainly neglects the costs related to purchase of landand site preparation (TCIk = PECk · 4.16 from [Elmegaard, 2009] and [Bejan, 1996]).A small modification was made to make the model more sensitive to changes in theindividual components:

TCIk = PECkTCIplant = 3.16 ·

∑k PECk

A capital recovery factor (CRF ) is used to distribute the initial investment as anannuitised cost (Zk) which corrects for the time value of money.

CRF =(ieff ·(1+ieff )n)((1+ieff )n−1)

[Bejan, 1996],

where n = 15 : plant lifetime [Paul, 2003b] and:

ieff = 1+ri+i − 1 [Elmegaard, 2009],

where i = 7.0% : interest rate [Paul, 2003b] and r = 2.13% : inflation rate[Energistyrelsen, 2005].

To achieve the final cost rate (Zk), the annuitised cost is distributed over the numberof operating hours on a per second basis. An estimate for number of operating hourscould be based on the value calculated in the STREAM analysis and used as input(hop = 6100 hours for the scenario with flexible consumption). In the results sectionthe number will be evident, but as a general rule 2500 hours are used corresponding toeight hours a day, six days a week (representative for the case study).

Correlations for estimating PEC of component k

PECcomp = k1V2h + k2Vh + k3 [1]

PECcomp,R744 = k4 ∗ Vh + k5 [2]

PECelec.motor = k6Wcomp − k7 [3]

PECcond = k8Acond + k9 [4]

PECevap = k8Aevap + k9 [4]

Acond =∑

pQcond,p

Uoverall,p·lmtdcond,p [5]


Aevap =∑

pQevap,p

Uoverall,p·lmtdevap,p [5]

Uoverall,p =(

1Up

+ 1Uw

)−1[5]

k1−9 = {0.03558 [DKK·h2/m6], 355.72 [DKK·h/m3], 30645 [DKK],2126.4 [DKK/m3], 37245 [DKK], 648.6 [DKK/kW ], -1388.6 [DKK],

1548.2 [DKK/m2], 16817 [DKK]}

• Subscripts

p = {gas, two-phase, liquid}

w = {water}

• References

[1-5]: [Jessen Jürgensen A/S, 2010a],[Jessen Jürgensen A/S, 2010b],[Maskin-Elektro, 2010],[Jessen Jürgensen A/S, 2010c],[Bejan, 1996]

Not all of the components for which prices have been found comply with the pressurerequirements set forth as operating limits. This is in part due to the fact that highpressure heat pump components are new products with few retailers, making it timeconsuming to find prices. It is however assumed that the data is valid to be usedfor comparison and to demonstrate the thermoeconomic method. To evaluate thefeasibility of each project a payback period (PBP) is also calculated [Elmegaard, 2009].

PBP = −ln(

1− ieff IS−C

)ln(1 + ieff )

(11.11)

I : investment, S : savings, C : costs

Here the savings are calculated as the amount of displaced gas consumption by thedelivered heat, and the cost is the yearly expenses for electricity. An underlyingassumption for these evaluations is, that the scrap value of the equipment balances thecost related with disposing of the installation. Furthermore regarding capitalised costin the calculations no requirement is made for perpetual replacement of equipment.

12 VERIFICATION OF MODELS - GENERAL OBSERVATIONS 43

12 Verification of models - General observations

In order to achieve a satisfactory solution and an optimal heat pump configuration inall of the different conditions possible for industial application, a closer look on eachmodel, and some of the parameters, is appropriate.

The models constructed in this project are made to fulfill the same set of characterisicparameters in order for the reader to compare the different solutions straightforward.In this way the models are expected to produce the optimal result based on a variationof parameter sets (presented in section 5) and the model corresponding to a specificworking fluid.

A few comments regarding general effects in heat pumps are stated in the following.Other effects are also treated in the subsections regarding the individual heat pumps.

Effects of subcooling and superheating From coursebooks in refrigeration it is clearthat superheating and subcooling can be important parameters in the heat pump typesconsidered [Granryd, 2005] and [Paul, 2003a].

The effects of subcooling and superheating is only beneficial if the decreased tempera-ture difference between the working fluid and the sink/source media affects the price ofthe heat exchangers less than the corresponding decrease in price related to the powerdemand of the heat pump.

Subcooling results in both increased temperature variation in the heat exchanger and ahigher amount of heat rejection per unit mass of working fluid. Subcooling will lowerthe massflow needed through the compressor at a given load and thus increase COP.Without consideration of heat exchanger price, the increase in COP from increasingsubcooling is in the range of 0, 2 − 0, 5%/ °C in the models. This is not applicable inthe transcritical heat pump, where subcooling is not a possibility (but rather wouldcontinue the heat rejection as before hand).

Superheating will in most cases have a negative effect on the COP of the system(depending on the working fluid) [Granryd, 2005]. Increased superheating affectsthe temperature of the working fluid after the compressor, reducing the operationaltemperature span of the heat pump. The effect of increased superheating on COPis negative ( −0, 5%/ °C.) for R717, R718 and the hybrid. When considering R744superheating is worth further consideration. Inspection of the parameters whichinfluence the constant pressure temperature glide reveals the explanation. A reductionin pressure ratio for the heat pump cycle is possible (lower pressures in the gascooler can be achieved), if a larger share of the source temperature lift is utilised assuperheating.

Compressor efficiency and size The different correlations of isentropic and volumet-ric efficiency presented in section 9.1.2 and their impact on the system is examined,in order to validate the impact of the correlations on the model. It is necessary witha concise survey of the impact of compressor isentropic efficiency on COP in orderto understand the impact of compressor efficiency on the solution. Values of COPare calculated for different constant values of isentropic efficiency alongside with the


correlation from litterature (and section 9.1.2).

Due to the origin of the correlations (experimental data from specific compressors),it is likely that set values of isentropic and volumetric efficiencies are more accurateas expectations of a specific compressor for the job at hand. As seen in figure 9.2 (a)on page 31, isentropic efficiencies are quite low at compression ratios below 2, 5 [/](presumably due to data from a specific compressor). Using the correlations describedin section 9.1.2 could very well illustrate the use of a compressor built for a specificcompression ratio (volume ratio), but used for the entire span of possible pressure ratiosin a heat pump.

The correlations from litterature are chosen since they represent actual data collectedfrom compressors and at the same time differentiate the four working fluids appropri-ately. Considerations regarding higher isentropic efficiency in the low pressure ratiorange can be reasonable, but is not utilised in this project, as no evidence of betterpossibilities are found in litterature.

Impact of heat exchange on price As discussed in section 8 and section 11.2 the priceof heat exchange is dependent on a collection of variables. The price of heat exchangehas a big effect on both the investment and PBP of the plant. Increased investmentallows for higher values of COP (decrease in running cost) due to lower pressure ratios,while a reduced investment in heat exchange will require higher running cost, due toincreased work in the compressor (neglecting pressure losses in heat exchange whichhas the opposite effect).

In order to present a reasonable estimate on the size of investment, an optimisationof ∆Tmin with regard to the investment of a heat pump is a necessary consideration.

The considerations are also valid for the small heat exchangers (as used when consider-ing oil injection or internal heat exchangers), but as these are in the scale of (maximum)1 : 10 times the size of the high temperature heat exchanger (condenser, gas cooler andabsorber), the assumptions regarding ∆Tmin in this HEX will also be imposed on thesmaller heat exchangers.

Parameters A set of parameters is chosen for the calculations in section 12.1 - 12.3.Variation of these parameters do occur, but will be evident in the separate section.

Figure 12.1: Table of the most important parameters used in sections (12.1 - 12.3).

Even though sink temperature variation in both TCHP and CAHP is allowed to change,a stringent eye is keept on the laws of thermodynamics throughout the report. The most


general observations will be emphasised in section 12.1, in order to reduce repetition insection 12.2 and 12.3.

12.1 Condensing vapor heat pump

A general example of the temperature profiles in a R717 single stage heat pumpis presented on page 23. As five different models of CVHP exist with similarconsiderations the figures will primarily illustrate the single stage R717 heat pump.Similar results are obtained from the remaining models unless further discussed.

Isentropic efficiency Figure 12.2 (a) illustrates the change in COP of a single stageR717 heat pump due to changes in isentropic efficiency. Varying the temperaturelift affects the pressure ratio, which affects the isentropic efficiency. It is clear thatthe impact on COP (in relation to constant isentropic efficiency) is highest with lowtemperature lifts (low pressure ratios). The figure correspond well with trends fromfigure 9.2 (a).

(a) Correlation and set values of isentropic efficiency.

(b) Increased sink temperature affects the pressure ratio.

Figure 12.2: Impact of isentropic efficiency correlations (R717) versus constantisentropic efficiency on COP at different temperature lifts and sink temperatures.


In the two figures, the previously described limits (mainly concerning compressors)in the heat pumps, outline the limits of the figures. As an example, the sourcetemperatures in figure 12.2 (a) are limited (the temperature lift of the heat pump islimited) and the line ends where the appropriate limit dictates it (in this example dueto high temperatures after the compressor). If needed, considerations like this, will beevident from comments in respective sections.

Different values of sink temperatures with varying temperature lift is plotted in figure12.2 (b) along with a set value of isentropic efficiency ηis = 0, 75 in order to comparethe two figures. The figure clearly shows the trends from varying isentropic efficiencyin increasing sink temperature levels.

An increase in sink temperature will lead to a decrease in the pressure ratio for at settemperature lift. The effect is an increased impact from the low isentropic efficienciesof the correlation (low pressure ratios). The figures indicate, that two-stage heat pumpswill only be competitive in applications with high temperature lifts when using thecorrelation of varying isentropic efficiency.

Volumetric efficiency This is only a vital parameter with regard to the economy ofthe heat pump system and the size of the compressor. The volumetric efficiency doesnot affect the calculation of COP, temperatures or mode of operation. The volume ofthe working fluid vapor at the inlet and the volumetric efficiency defines the size of thecompressor necessary for the job at hand.

As can be seen in figure 9.2 (b) on page 31 volumetric efficiencies are fairly constantwhen considering R717 and R718. In order to compare the two volumetric efficiencies aconstant ηvolumetric = 0.85 is considered. A simple outline on the impact of volumetricefficiency on compressor size can be seen in figure 12.3.

Figure 12.3: The impact of volumetric efficiency correlations on compressor sizecompared to constant volumetric efficiency. Broken lines show a constant volumetricefficiency for comparison.

When considering size and price of the compressor in the CVHP, R718 is worse off


compared to R717, as a result of the higher volume required through the compressorwhich increases the effect of a volumetric efficiency. At the same time the specificcorrelations of volumetric efficiency result in a lower overall efficency in the R718 heatpump increasing the gap, which leads to an additional increase in investment.

Single, Two-stage or Oil Injection - Impact on COP The different models of CVHPwith R717 and their influence on COP is compared. The comparison does not take intoconsideration the differences in investment of the different solutions.

As described in section 9.1.1, the compressor lubrication (as well as seals and gaskets)may not exceed 160 °C . An example of the possible solutions are presented in figure12.4, where an increase in temperature lift rules out the single stage heat pump modeldue to high temperatures. The optimal solutions (with respect to COP) is emphasisedfor each of the two temperature lifts.

A similar reflection can be made for the two models concerning R718 (one- & two-stage). Pressure ratio between high and low pressure side is greater for R718 models,which enlarge the requirement of the two stage cycle.

Figure 12.4: Maximisation of COP in CVHP at two different temperature lifts andvariable sink temperatures. The solutions with the highest COP, which at the sametime satisfy the set limitations of the project, are emphasised.

Temperature variations in sink and source media The temperature variation in thereceiving sink and heat rejecting source media has an influence on several factors inthe CVHP. Both COP and the necessary heat exchanger area are directly related to thedifference between temperatures in the inlet and outlet of a heat exchanger. The impactof these variables on the performance of the heat pump is directly related to the pinchpoint.

In figure 12.5 (a), a small increase in COP is visible with an increase in temperaturevariation in the sink media. An increase in temperature variation in the source media isnot beneficial with respect to COP due to increased pressure difference between lowand high pressure heat exchangers (see figure 5.1), but will (as will the increase invariation of sink media) decrease the necessary heat exchanger area.


(a) COP as a function of different temperaturevariations in sink and source media.

(b) Heat exchanger area as a function of differenttemperature variations in sink and source media.

Figure 12.5: The influence of different temperature variations on COP and heatexchanger area in CVHP. Incrased temperature variation in the sink media trigger asmall increase in COP due to the location of the pinch point (see figure 8.1). Theparameter not being varied is kept constant.

An increase in source media variation will effectively increase the necessary tempera-ture lift in the heat pump, while the coresponding increase in sink media variation tosome extent will decrease the necessary condensation pressure (effectively reduce thetemperature lift)

Impact of changes in pinch temperature An increase in pinch temperature willincrease the driving temperature difference in the calculations of heat exchanger area.The impact of this change is examined for further understanding of the model.

(a) Influence from pinch temperature ∆Tmin onCOP in both condenser and evaporator

(b) Influence from pinch tempeature on heatexchanger area in condenser and evaporator

Figure 12.6: Heat exchanger area and COP as a function of pinch temperatures inthe CVHP-model. An increase in pinch temperature will decrease COP and heatexchanger area in both the condenser and the evaporator. The effect of increased pinchtemperature on PBP is most favorable in the condenser.


An increase in pinch temperature (in both condenser and evaporator) leads to adecrease in COP and a reduction of the necessary heat exchanger area. The negativeeffect on COP from an increased pinch temperature in the evaporator is greater thanin the condenser. The reduction in heat exchanger area is comparatively greater in thecondenser. An economic optimisation of these two variables will consequently result ina lower pinch temperature in the evaporator than in the condenser for these conditions.

Exergy considerations In figure 9.2 a representation of the overall performance ofthe CVHP was presented, where changes due to the variable isentropic efficiency waspresented. In the following two figures (12.7 - 12.8), a different representation of thesame data is made with respect to the exergy destruction rate,ED [kW], and exergeticefficiency, ε [/].

The four destruction rates (one-stage heat pump components) are presented togetherwith the compressor destruction rate of the constant isentropic efficiency ηisentropic =0.75 heat pump. Small changes do appear in the other components with changes inisentropic efficiency (especially in the condenser due to changes in inlet temperature),but these are omitted to simplify the presentation.

Figure 12.7: Quantification of thermodynamic irreversibilities in CVHP with changesin temperature lift and isentropic efficiency.

The changes in thermodynamic irreversibilities (exergy destruction) due to changesin temperature lift, are clear in the compressor, condenser and expansion valve. Thechanges due to temperature lift does not change the destruction of exergy in theevaporator (does not change the temperature distribution between source and workingfluid in the heat exchanger). Destruction of exergy in the expansion valve is directlylinked to the pressure differences between high and low pressure heat exchange in theheat pump.


Figure 12.8: Exergetic efficiency of the destruction losses from figure 12.7. The efficiencyof the system, and especially of the evaporator decrease as the temperatures of theevaporator approaches T0.

The exergetic efficiency of the system (figure 12.8) decrease as a result of increasedtemperature lift in the heat pump. This is mainly due to the decrease in efficiency inthe evaporator as the temperatures of the heat exchange approaches T0. The exergeticefficiency of the compressor increase due to the correlation of isentropic efficiency.

Heat price and PBP As price is a decision parameter in the comparison betweendifferent heat pumps, a brief review of the important factors is required. The optimalprice of a given plant is found as a minimisation of the cost of heat. An example ofthis is given in figure 12.9, where the heat exchange area (∆Tmin) is varied. The fixedHEX-area in figure 12.9 correspond to ∆Tmin = 2 in both condenser and evaporator.A calculation of the corresponding heat produced in a boiler is only based on the cost ofthe natural gas and an assumed efficiency of ηboiler = 0.8. A reference gas price of 275.6[DKK/MWh] from the case study is assumed representative. The prices of natural gasand electricity are from section 14, and they are relativly low - due to old long termagreements. It is assumed that the ratio of cost between electricity and natural gas isstill reasonable. Models are compared with an intention of retrofit, meaning that a heatprice from heat pump lower than the gas price indicates the possibility of retiring afunctioning gas boiler in exchange for a heat pump, with a profit.

Figure 12.9: Heat price at different operating hours a year. Investment cost of the heatpump is distributed as a constant annuity in the technical lifetime of the heat pump.


In the case at hand (figure 12.9) a heat demand of 1 [MW] in more than 1200 hours ayear - in fifteen years - is cheaper with a heat pump than with the natural gas boiler.Only variable cost are assumed for the boiler.

Both figure 12.10 and 12.11 shows PBP and COP with variable operating hours andtemperature lift. The calculations are executed as a minimisation of the price of theproduced heat, thus not minimising the PBP of the plant.

Figure 12.10: Impact on possible PBP and appertaining COP with changes in operatinghours. Investment cost are decreased in cases with a low number of operating hours(pr. year).

The lowest cost of heat is dependent on the sink temperature, the temperature liftbetween sink and source and the amount of operating hours a year. In figure 12.11 thenumber of operating hours is kept constant to consider the impact of sink temperatureson the lowest running cost of a CVHP.

Figure 12.11: Impact on possible PBP and resulting COP with different temperaturelift (a set amount of operating hours). Investment cost increase with an increase intemperature lift in order to minimise running cost.


12.2 Transcritical heat pump

A general example of the temperature profiles in a transcritical heat pump is presentedon page 24 (figure 8.2) .

Isentropic efficiency A representation of the transcritical heat pump and the impacton COP from changes in isentropic efficiency can be found in Figure 12.12.

As can be seen, COP decreases as the source temperature reaches the critical tempera-ture of the working fluid. The observations from the CVHP do apply, especially withregard to temperature lift and isentropic efficiency. The drop in COP is greater with thevarying isentropic efficiency correlation than for a constant, with source temperaturesof 35 °C or higher.

Figure 12.12: Impact on COP with different correlations of isentropic efficiency.

Comparing the COP of a TCHP with that of CVHP, half of figure 12.12 matches theperformance from figure 2(a). In the remaining part, the impact of reaching the criticalpoint is crucial, indicating that comparison of the two types will only be interestingwith high temperature lifts.

Heat exchange in the gas cooler As "transcitical" means across the critical point, theperformance of the evaporator in a TCHP is much alike that of a CVHP. The heatexchange area is increased, which can be a reflection of the amount of source heatnecessary for superheating the working fluid.

The trends for changes in ∆Tmin on the Gas Cooler area seem small, although the heatexchange area is increased. As can be seen in figure 12.13 (a), the impact on COP ishigher than in 12.6 (a), which is due to an increased pressure ratio.


(a) Influence from pinch temperature ∆Tmin onCOP in both Gas Cooler and Evaporator.

(b) Influence from pinch tempeature ∆Tmin onheat exchanger area in condenser and evaporator.

Figure 12.13: Inspection of trends from changes in ∆Tmin on heat exchange and COP inthe gas cooler of a transcritical heat pump.

In the gas cooler, the pinch point depends on the shape of constant pressure heatrejection as discussed in section 7.2. The model calculates the pinch based ontemperature differences between the transcritical heat rejection and the sink media.

Figure 12.14 displays the COP of the TCHP from the calculated pinch along with twoset values. The impact on COP reflects changes in the necessary derived high pressure,which changes the pressure ratio. A value of higher importance in this project is theabsolute pressure for heat rejection, as it directly influence the limitations of the heatpump.

Figure 12.14: Impact on COP with different manually set pinch point placementscompared to the calculated.

Economy of TCHP As with the CVHP, a segment of the economy calculations areshown in three different figures. Figure 12.15 is the actual calculated (minimised) cost


of heat in two different operating conditions with changes in operation hours a year.

Figure 12.15: Cost of heat in the transcitical heat pump at different operating conditions.Both an increase in sink temperatures and in the temperature lift increase the price ofheat.

Both figure 12.16 and figure 12.17 show the shift in heat pump price (as a simplifiedPBP) with changes in sink temperatures and operating hours.

Figure 12.16: COP and PBP with variations in sink temperature. Both COP and thesimple PBP favours the lower sink temperatures. The combined heat exchanger areais fairly constant, but the marginal change shifts from sink to source as the deliverytemperature is increased.


Figure 12.17: Optimisation of pay back period with changes in the number of operatinghours per year. As the number of operating hours are reduced COP decreases withinvestment.

12.3 Hybrid heat pump

An example of the temperature profiles in hybrid heat pump is presented on page 24(figure 8.3).As discussed in section 7.3, the CAHP introduces an extra degree of freedom, as theconcentration of Ammonia in Water change the relation between vapor pressure andtemperature. Different segments of the relations between temperature, pressure, COPand the solution will be presented.

Isentropic Efficiency At a set mixture, the mode of operation of the hybrid heat pumpmatches that of the CVHP. As a first example, a set ratio between Ammonia and Wateris presented. COP is presented with a variety of isentropic efficiencies, enabling acomparison with both the CVHP and TCHP.


Figure 12.18: COP as a function of different isentropic efficiencies. xstrong defines theamount of Ammonia in the Ammonia/Water mixture. Higher sink temperatures canbe optained whith a decrease in xstrong.

Effects from changing the mixture of Ammonia The extra degree of freedomincreases the posibilities of the heat pump system. At the same time, the degree offreedom complicates the ability of capturing only one effect on the system at a time.

As can be seen in figure 12.18, a 85 % solution easily reaches sink temperatures of 105°C even with large temperature lifts, which normally is a consideration with compres-sion of Ammonia (according to the model, more than 99% of the compressed workingfluid is Ammonia). The hybrid process decrease the necessary pressure difference,mainly due to the temperature slope in heat rejection (not constant temperature). In thisway, a lower amount of work is needed for compression, reducing the temperatures ofthe Ammonia after the compressor .

A variation of xstrong is possible with constant sink temperature, and an examinationof the influence is conducted in the following figures (12.19 & 12.20). It should benoted, that the higher the concentration of Ammonia in the solution, the higher thetemperature change of the working fluid. In the figures 12.19 and 12.20 the temperaturevariation of the sink media is keept constant, even though this is not necessarilythe optimal solution. Inspection of ∆Tsink can be found in figure 12.22 and will bediscussed later on.


(a) Impact on massflow, pressure ratio and COP.

(b) Impact on pressure and HEX Area.

Figure 12.19: As solution strengh varies CAHP cycle changes with respect to massflow,pressures, heat exchanger area and overall COP.

It is clear that COP increases with higher contents of Ammonia in the working fluid.This is mainly due to the decrease in pressure ratio between sink and source at highersolutions (increase in both low and high pressures). At lower Ammonia concentrationsthe mass flow of the solution pump increases, which matches expectations from 7.3.

In figure 12.20 destruction rates and exergetic efficiencies are shown, which can becompared directly with figure 12.19. Not all of the calculated rates and efficienciesare shown, as some are quite trivial. Two exergetic efficiencies of the system are shown.The difference between these two is the destruction rate from the mixing/unmixing ofAmmonia and Water due to chemical affinity.


(a) Destruction rate in a CAHP with 1 MW capasity.

(b) Exergetic efficiencies in a CAHP.

Figure 12.20: Exergetic efficiencies and destruction rates of Compression/AbsorbtionHeat Pump with changes in solution of working fluid. Compared to CVHP the ratesare generally lower and more stable, this is due to less varation in pressure levels. Onlythe most interesting components are shown.

As the concentration of Ammonia has an impact on the temperature variation in theAbsorber, a evaluation of the inpact of the pinch temperature is needed. Figure 12.21can be directly compared to the matching figures in CVHP and TCHP.

xstrong is presented as both 0.8 and 0.9. From experience with the model it is noted,that the change in temperature variation in the Absorber is greater for values of xabove 0.8 (meaning that a figure representing xstrong = 0.7 would approximate thatof xstrong = 0.8).


(a) Changes in COP when varying ∆Tmin inAbsorber and Desorber.

(b) Changes in HEX-area when varying ∆Tminin Absorber and Desorber.

Figure 12.21: Impact of pinch temperature on the hybrid heat pump.

Variation in sink media In the CAHP ∆Tsink is yet another variable for optimisation,as the temperature variation in the Absorber changes with changes in the working fluidand temperatures. An examination of the influence is conducted in the following figure.The impact on COP from changes in ∆Tsink is presented in figure 12.22 at different sinktemperatures. It is clear that changes in sink variation might also change the necessaryheat exchanger area of the heat pump.

From the figure it is clear that it is not possible to chose one optimal ∆Tsink basedon three different opperating conditions.

Figure 12.22: Different sink temperatures and different sink temperature variations andtheir impact on COP.

Sink temperatures In order to present another dimension of the hybrid heat pump,a set value of xstrong and ∆Tsink is chosen, in order to experience the changes fromvarying sink temperatures.

It is clear, that xstrong defines the inner workings of the heat pump (massflowdistribution is constant with a set value of xstrong) and that it is possible to produce


almost constant values of COP with changes in solution and sink temperature.

The destruction rate of the Expansion Valve follows the pressure ratio, as does thecompressor (observing the effect of isentropic efficiency). The destruction rate in bothAbsorber and Desorber is dependent on the temperature variation in the working fluid,which follows the sink temperature and solution of the working fluid.

(a) Massflow and pressures with changes in sink temperature.

(b) Destruction rates and COP in a 1 MW plant

Figure 12.23: Impact on CAHP with changes in sink temperatures.

Economy and COP As many parameters change throughout the calculation of theoptimal CAHP, both as a function of the amount of operating hours a year and the sinktemperatures, a different approach is chosen, where the different calculations are madebased on 3 different fixed xstrong (0.7, 0.8 and 0.9). The three values are chosen as theycover sink temperatures from 70 - 130 °C (from figure 10.5.


In order to assess the different heat pumps in a simple and intuitive manner, onlythe solutions deemed best are presented. The solutions are presented in the entiretemperature span possible with the respective concentration of Ammonia.

(a) Best CAHP with temperature lift of 20 K

(b) Best CAHP with temperature lift of 30 K

(c) Best CAHP with temperature lift of 40 K

Figure 12.24: The best CAHP with different temperature lifts. The input parametersand variables can be found in the figures.

As in the CVHP the price of heat from natural gas is constant 275, 6[DKK/MWh]. Ascan be seen in figure 12.24 most of the possible solutions are still sufficiently below thisnumber.

13 GENERAL SOLUTION 62

13 General solution

As discussed in section 5, the solution is based on four different parameters:

• Tsink

• Tlift

• COP

• Cost of heat (production)

These four parameters are presented in the figures 13.2 - 13.4. Each of these figuresrepresent a temperature lift between 20 [K] and 40 [K]. In the figures the optimal heatpump is presented at the sink temperature and temperature lift needed.

The different heat pumps overlap, to show the different possibilities of the fourtechnologies. Only heat pumps which are superior in a spectrum of the solution areshown. The heat pumps are evaluated with the cost of producing heat as the majorinfluence.

As in section 12, a list of different parameters are set for the calculation of thecomparison. These are presented in figure 13.1

Figure 13.1: Parameters used in figure 13.2 - 13.4.

In figure 13.1 the parameter "lift" indicates, that the parameter ∆Tsink is set to matchthe temperature lift of the TCHP. This is the maximum posible sink variation in a pinchanalysis.

The possible heat pump characteristics with different sink temperatures and threedifferent temperature lifts are presented. The four working fluids all cover up to 125 °Cin all three cases.


(a) COP.

(b) Cost of heat.

Figure 13.2: Cost of heat and the corresponding COP at temperature lifts of 20 K. Resultsare optimised to produce heat at the minimum cost at the given number of operatinghours a year, using the four working fluids of the project.


(a) COP.

(b) Cost of heat.

Figure 13.3: Cost of heat and the corresponding COP at temperature lifts of 30 K. Resultsare optimised to produce heat at minimum cost at the amount of operating hours a year,using the four working fluids of the project.

In figure 13.4 a temperature gap emerge between the R717 CVHP and the CAHP. Thehigh temperature lift decrease the working span of R717 due to the high temperaturein the compressor. The two alternatives to R717 have not been introduced in the figure,in order to see the impact of the simple heat pump.

The alternatives can be seen in figure 13.5. In this case the two stage heat pump isthe cheaper choice, and would be the preferable solution for selection.


(a) COP.

(b) Cost of heat.

Figure 13.4: Cost of heat and the corresponding COP at temperature lifts of 40 K. Resultsare optimized to produce the minmum cost at the given amount of operating hours ayear, using the four working fluids of the project. Further calculations regarding atemperature lift of 40 K can be found in figure 13.5

Figure 13.5: R717 and the two approaches for lowering compressor outlet temperatures- oil injection and two stage cycle.

14 CASE STUDY 66

14 Case Study

A case study has been performed to establish the validity of the assumption thata saving potential exists from recovering waste heat in industry. To achieve anunderstanding of the way energy flows in the system a general assessment of theoverall facility and individual components was carried out. All relevant thermalstreams have been mapped so that a trust worthy pinch analysis could be performed.From available data and additional measurements, a time dependent heat load hasbeen developed for the case. If the results indicate a saving potential, a more detailedanalysis should be conducted to verify this. For the concrete dimensioning of theequipment more details regarding operation would be preferable. An evaluation of thepinch analysis will determine whether a heat pump could provide a savings potential.A detailed explanation of the pinch concepts is provided in appedix B.

14.1 Berendsen - Industrial laundry services

The chosen case is an industrial laundry facility located in Roskilde, DK. This particularfacility is a franchise of Berendsen Group, which is a provider of textile services.Contact was arranged through the JENSEN-GROUP who provide textile handlingequipment to Berendsen among others.

Large amounts of heat are consumed at the facility for both washing, drying andironing. Currently the heat is produced by means of a boiler, fired with naturalgas, producing low pressure steam. Although much effort is spent to optimise thesystem and utilise waste heat, significant quantities are still being vented directly onthe roof. An apparant potential therefore exists for both heat recovery and possiblyalso for the implementation of a heat pump. Berendsen is currently connected to thedistrict heating network because the company has previously sold their waste heatexternally. These heat exchangers were installed prior to 1995 when the tax legislationwas changed with respect to the recovery of industrial waste heat (see section 4.5). Theywere kept in place after the change and the reason why they are no longer in operationis because they started leaking. No effort has been made to replace them because theeconomic potential no longer exists.

Overview of plant Treating the textiles consists of a number of steps and is dependenton the type of textile. Different classes include clothing (uniforms, jackets, aprons),flat textiles (dish cloths, towels, linens such as: bed sheets, pillow and duvet covers)and bedding (duvets and pillows). On figure 14.1 an overview of the handling andprocessing is diplayed. The image is from JENSENs flatworks section which is almostcompletely automated. Actual plants may choose to use personel for some of thehandling steps to increase flexibility.

14 CASE STUDY 67

Figure 14.1: Flowchart of flatwork system courtesy of JENSEN.

Basic process

1. Arrival of unsorted textiles

2. Sorting

3. Washing

4. Drying

Semi-drying

Full drying

5. Ironing

6. Folding - Handling - Shipping

To accomplish the task of treating the textiles, the Berendsen facility has a large numberand variety of equipment. For the purpose of this study the focus will be on thecomponents that have a thermal input or output.

Components of interest

• Washing

Traditional washing machines

8 units: Group A

7 units: Group clothes

Continuous Batch Washer

1 unit: Lavatec tube (13 compartments)

1 unit: Voss tube (8 compartments)

• Drying - Tumble driers (direct burner, NG)

3 units: Group full-dry

5 units: Group semi-dry

14 CASE STUDY 68

• Ironing

5 units: Ironing rolls (specialized for handling different textiles - input fromsemi-dry tumbler units)

2 units: Body-presses (Chef jackets - negligable throughput)

Of the components on the above list only the traditional washing machines do not haveoutputs that are vented directly to the roof.

Figure 14.2: Nomenclature for figure 14.3 and figure 14.4.

Figure 14.3: Overview of the plant facilities at Berendsen. Some liquid distributionlines and exhaust vents have been omitted for the sake of clarity. Placement andsplitting/joining of distribution lines are symbolical and is not based on the actualpiping. Nomenclature as per figure: 14.2.

Both the washing tubes and the traditional washing machines reject a rather substantialamount of water directly to the sewers. Some heat recovery is performed from thisrejected water. Accomplishing the heat recovery allows for preheating of the new waterinput for the washing lines. These modern washing tubes however also recycle a largeportion of the water.

14 CASE STUDY 69

Figure 14.4: Liquid distribution strings for condensate, raw water and soft water. Samereservations apply as for figure 14.3. Specifically for RW the distribution lines also goto the washing lines, however only in limited amounts.

Both washing tubes also have exhaust lines on the roof to remove the humid air frominside the tubes. This is done for two reasons, firstly to avoid the heat/moisture inthe work area, secondly because the air contains a rather high concentration of thechemicals from the washing process. Although this air is quite humid, the flow ratesand temperatures are too low to be considered usefull.

When observing the exhaust ducts on the roof of such an industrial laundry facilityit is important to distinguish between the different types of processes that create theexhaust. Intuitively a very large waste heat potential would be assumed when noticingthe heat shimmers and condensate coming from the streams. During investigationsit became apparent however, that the condensate came from the washing tubes, andthe relative humidities of the high temperature, high volume flow streams were muchlower.

In hinsight this is obviously because the latter streams adhere from the tumble driersand ironing rolls, the purpose of which is to remove water from the textiles. Thesestreams have high temperatures and flow rates so that their relative humidity canbe very low in close proximity to the textiles. That is, in order to remove the waterat a significant rate these components need a high input of very dry air. This isaccomplished by heating the atmospheric air, which is used as input, as it passesthrough the component.

Initially it was indicated that condensing the moisture from these exhausts would be asubstantial contribution to the potential waste heat recovery. Measurements howeverreveal that the dewpoint of the high flow rate streams ranges from 20-40 °C making itpractically infeasible to utilise.

14 CASE STUDY 70

Ironing rolls One of the major consumers of thermal energy in the process is theironing roll (figure: 14.5). At the Berendsen facility 5 individual ironing rolls are inoperation, each fitted with a different feeding mechanism. This allows for processinga range of different textiles without interruption. After ironing, different automatedfolding mechanisms deliver the finished product to the personel. Automated handlingand shipping solutions exit, but since the bulk input at this facility covers a widespectre, human personal provides greater flexibility.

Figure 14.5: Working principle and flow input/output for ironing roll.

By means of suction, the textiles are held in place as they are transported by conveyorbelts, through every step of the process. Drying and ironing of the textiles is achievedby rotating them with a cylinder, where the lower half of the cylinder is exposed to aheated steel chest. Suction is applied to the cylinder to keep the textiles in place. Thissuction air containing the evaporated water, is then what is vented on the roof.

Heating of the steel chest can be achieved by heat exchange with either low pressuresteam, or oil. The steam method requires a centralised boiler and distribution linesfor the steam (usually 1.0-1.2 MPa - 190-200 °C). Using oil as thermal transport media(230 °C) is achieved with a local gas burner. A decentralized solution provides greaterflexibility, higher fuel efficiency and increased productivity. The reasoning behind thesteam heated rolls is principally tradition because centralised boilers have always beenused extensively for thermal energy in the laundry industry.

Data from the exhaust streams has been obtained experimentally for all 5 steam firedrolls at Berendsen. Inside the heated steel chest, the steam condenses as it delivers itsenergy to the wet clothes. A condensate return line runs from the individual rolls (190kPa - 125 °C). This return line is injected into the soft water string for use in the washingline.

A gas fired roll located at A-vask in Taastrup was also investigated experimentally.Additionally to the venting of the suction air, the gas fired roll is interesting becausethe combustion products from the burner is vented immediately next to the suctionair vent. These combustion products are of significantly higher temperature than thesuction air (>190 °C). Many new laundry facilities are focusing on these decentralisedironing rolls, and because these have no condensate output all heating of the washinglines require additional heat. This is an obvious opportunity for WHR.

14 CASE STUDY 71

Figure 14.6: Wax deposits on exhaust vent.

A problem with utilising the waste heat from the suction air, is that this stream hasa content of wax. Wax is used for reducing friction in connection with the conveyingmechanism. Otherwise the textiles would tend to stick to the surfaces in an uninten-tional fashion, blocking the production line and forcing an interruption/intervention.No data is available for how much wax is deposited on the clothes as opposed tobeing vented with the suction air. Clear deposits can however be observed wheninvestigating the exhaust vents from the ironing rolls 14.6. Heat exchanger foulingwould consequently be an issue.

Washing tubes - Continuous Batch Washer Another prime consumer of thermalenergy is the washing tubes. Berendsen have two different systems installed, a Voss anda Lavatec tube. The prime argument behind washing tubes is a significant reductionin water consumption and the requirement for manual labour. After the textiles havecompleted a full cycle in the tube, they are placed in a press which extracts the bulkportion of the water (see figure: 14.7).

Figure 14.7: A textile ’cake’ after having water extracted in the press at the end of thewashing tube cycle.

The tubes are fed with treated soft water. This water is preheated by the waste water,and the final temperature lift is achieved by injecting condensate from the ironingrolls. If there is insufficient condensate available, steam from the boiler can be injecteddirectly. The latter solution is of course the more expensive choice since it is a stream ofconsiderably higher quality and therefore value.

14 CASE STUDY 72

Gas fired tumble driers Two groups of tumble driers are in operation at the Berend-sen facility. Refering to the assigned designations as presented in figure 14.2, tumblers2.1-5 run semi-drying cycles and tumblers 2.6-8 run mostly full-drying cycles. Semi-dry textiles are subsequently sent through the ironing rolls for finishing. One of theprincipal justifications for tumbling the textiles before ironing is to break up the textile’cake’ after the water extraction press at the end of the washing tube (figure: 14.7).

Based on observations it can be assumed that 1-2 units from either group are inoperation at any one time throughout the duration of a working day. All tumblersare equipped with a local gas burner for heating the air which is sucked through thetumbling chamber. As previously stated this is done to lower the relative humidity,making the air drier, allowing it to absorb the water from the textiles at a higher rate.

Time series In order to perform a reliable pinch analysis of the thermal flows, thegathered data must be aggregated to a time dependent data series. A distributedheat load has been estimated from production and consumption numbers along withexperimental data. Initially it is assumed that all the detected waste heat is availablefor process integration or as source media for a heat pump.

Available data Fortunately Berendsen keeps detailed records of consumption /production numbers as well as usage time of the different machines (the first tooptimise production, the latter because it relates to the working hours of the personel).In constructing a reliable heat load any substantial cyclic variations must be addressed.Because the production only takes place in a limited number of hours per day it isalso necessary to consider the discontinuous load profile. Available data must beinvestigated for fluctuations over different time intervals to estimate how long a periodthe time series must run and at what resolution, to provide a reliable solution.

(a) Fluctuations in gas consumption on adaily basis.

(b) Fluctuations in soft water consumptionon a daily basis.

Figure 14.8: Consumption data over a three month period.

On figures 14.8(a) and (b) the daily readings for gas and soft water consumption aredepicted. It can be seen that the production varies significantly on a day to daybasis. Outlying readings can be attributed to a number of different circumstancesother than varying intensities in production. High values may be due to a weekendof production where no technician read the meters, making the monday readingsomewhat misleading. Low values may be due to two readings on the same day.

14 CASE STUDY 73

Production and consumption numbers for 2009 have been made available to identifyany clear periodic tendencies. The trends can be observed on figure 14.9 (a). As canbe seen there are clear variations, but no discernable patterns may be established. Forproduction numbers may is the month of highest intensity, and is therefore chosen asdimensioning reference.

Operational hours of the ironing rolls have been made available for may 2009, and atypical week for roll 1 can be seen in figure 14.9 (b). A value of 1 indicates a full hour ofoperation, 0.5 indicates half an hour of operation, and so forth.

(a) Variations in production on a monthlybasis for 2009.

(b) Operational hours for roll 1.

Figure 14.9: Production and operational data from Berendsen.

In order to define load data for the washing line, a simple algorithm has beenformulated. From this it is stated that if the ironing rolls are in operation, so is thewashing line. The load in the washing line is stated as a number between 0-1, so thatthe sum for all washing equipment for that month equals the actual measured waterconsumption. The load intensity is defined from the number of ironing rolls that are inoperation. This is an assumption of correlation between the load on the ironing rollsand on the washing line.

Depending on the washing group, a percentage value defines the amount of waterconsumption pertaining to the group. This percentage value is calculated as theaverage consumption given from a series of data for 5 representative days providedby Berendsen. It is an assumption that the percentile distribution remains constant.

Figure 14.10: Estimated values for water consumption in the washing line.

From this a heat load for the washing line can be estimated since all the preheated watermust reach 60 °C.

Experimental measurements Two different series of experiments were carried out toprovide the final data for constructing a heat load profile for the facility.

14 CASE STUDY 74

Firstly the amount of vapor separated per kg of ironed clothes was measured for threeof the different rolls. Between 5-10 pieces of clothes were ironed and the mass wasmeasured before and after ironing. Then the duration for treatment of the given amountof clothes was measured. This provides an estimate of how much water is transferedto the suction air per time unit. Knowing the intial humidity of the suction air therelative humidity of the exhaust air on the roof can be calculated. Knowing the rateof processing of clothes and using a standard heat capacity of wool, the rate of heattransfer from the ironing rolls to the clothes and exhaust air can be estimated. Thisagain yields the boiler work needed for the operation of the rolls.

Secondly the exhaust flow temperatures and velocities were measured using a thermalunit and a pitot tube (see figure 14.11). For the tumble driers a measurement was donefor one unit in either of the two groups, and these values are considered representativefor the remaining units. Flow measurements for the washing tube exhausts were belowthe measuring regime of the pitot tube (∆P < 0.002kPa) indicating stream velocitiesbelow 2 metres per second.

Figure 14.11: Measurements of the exhaust flows from the different units.

Due to apertures in the exhausts the flow profile was not even over the entire area ofthe exhaust tube. Measuring 25 values across a centerline proved that the flow washighest app. 2-3 cm from the edge and lowest in the center. A linear flow profile wasestimated with the highest value as the average of four measurements around the edgeand the lowest in the center. Here the edge values were taken where the flow washighest. This gives a negligible discrepancy and makes integration over the entire areastraightforward (figure 14.12).

14 CASE STUDY 75

Figure 14.12: Flow profile (black) and assumed linear profile (red).

Heat load and waste heat potential With reference to figure 14.13 the heat that needsto be produced by the boiler equals the heat consumed in the ironing rolls and thewashing line.

Figure 14.13: Flow of heat from boiler through system.

Based on the collected data and the experimental measurements, the following relationsare constructed.

Qironing = m2(hsteam − hcondensate) (14.1)

Qwash = m2(hcondensate − hwash) + m6(hsteam − hwash) (14.2)

Qboiler = Qironing + Qwash (14.3)

It is now possible to construct a time series of the thermal work performed by the boiler.On figure 14.14 the developed time series is plotted for the second week of may.

14 CASE STUDY 76

Figure 14.14: Time dependent heat load for one week in the series.

From the measurements the waste heat from the different units can be estimated. Onfigure 14.15 the total waste heat is overlayed on the same plot as the total thermal workdone by the boiler. Again the figure focuses on the same single week.

Figure 14.15: Time dependent waste heat and boiler work for a single week.

14.2 Pinch analysis

A pinch analysis is a valuable tool when evaluating whether installing a heat pump isan economically viable investment. Firstly a pinch analysis can reveal if the waste heatis available at usefull temperatures. Secondly the pinch temperature must be knownto decide how much and at what temperature the heat pump should provide heat.Considering the pinch temperature is important because otherwise a heat pump mightbe considered for a delivery temperature where process integration could provide acheaper alternative (this is further discussed in appendix B).

14 CASE STUDY 77

Figure 14.16: Stream overview for pinch calculations (∆Tmin = 10K).

All gathered data on streams needing heating or cooling is condensed into figure 14.16assuming static operating conditions. For the purpose of this analysis a minimumtemperature difference of 10K is considered representative. Using this data the pinchtemperature and the minimum hot and cold utility can be calculated.

Figure 14.17: Composite curve for the Berendsen facility. Red line indicates hot streamsand blue cold. The different enthalpy rate intervals are marked by dotted lines endingon the curve which impose the interval border.

In the interval where the cold and the hot composite curves overlap horizontally,considering a ∆Tmin = 10K, it is possible to heat exchange between the two (figure14.17). If this is done optimally then one arrives at the Grand Composite Curve as canbe seen on figure 14.18. Here the minimum hot utility of 537 kW is indicated by thered arrow. This means that an apparant reduction potential exist which constitutes asignificant share when compared to the peak heat load from figure 14.17 (1020 kW ).

14 CASE STUDY 78

Figure 14.18: Grand composite curve from a pinch analysis of the thermal flows at theBerendsen facility. Blue and red arrows indicate minimum cold and hot utility.

If one observes the boiler load time series on figure 14.14 it is apparant that the averageheat load probably is closer to 700-800 kW due to the dynamics of the system. Thispinch case is of course attempted to match, but the analysis is still static. Thesediscrepencies are simply a result of the fact that the equipment is operated in differentintervals in the time series. No comment is tied to the minimum cold utility since theexcess waste heat can simply be vented directly with negligible cost.

Below the pinch temperature (108°C) a rather large quantity of waste heat still exist.The reason why this waste heat cannot be utilised fully is because all of the remainingneed for hot utility is required for producing the steam for the ironing rolls. This ismostly a cost connected with phase change that due to the pressure in the system firststarts to happen at temperatures above 180-190°C. It is this phase change spike that canbe observed as the top line in the GCC and constitutes almost all of the remaining hotutility.

Because none of the heat pump cycles modeled can achieve the relevant outlettemperatures (waste heat of significant amounts are now only available below sub 80°C,making the needed temperature lift infeasible) it was investigated whether the ironingand drying of the clothes could be achieved at a lower temperature. According to thetechnical personel at Berendsen no reduction in process temperature is possible, and thegap of variation is quite narrow (190-170°C). The clothes could easily be dried at a lowertemperature, but for the ironing to provide an acceptable result, higher temperaturesare needed. If the temperature drops the clothes will get an unwanted pleating effect.This is an important factor, since it rules out a heat pump as a substitution for the boilerand reduces it to at most a supplement. Instead it will be investigated whether a heatpump can be used to upgrade the remaining waste heat after process integration forutility water or district heating.

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Saving potential A preliminary estimate can be made for the necessary heat ex-changer area to accomplish the indicated reduction in heating utility, using a relationfrom [Bejan, 1996] which takes into account the multiple streams per enthalpy rateinterval j, given as:

AHEN =∑j

1

∆Tlm,j

(hot∑i

Qjihi

+

cold∑k

Qjkhk

)(14.4)

Estimating the profitability of this approach is done using the economic principleof PBP as described in section 11.2. With a total investment cost of 58,000.00 DKK(AHEX = 47[m2]) the savings of the project yields 428,363.00 DKK annually and aPBP of 0.13 years. This is the optimal theoretical solution as described by the pinchconventions, an actual solution might not be able to provide the indicated savings fromthe prescribed configuration. Optimisation of the Heat Exchanger Network (HEN) issummarised in figure 14.25. In this scenario of ideal integration the condensate stringis used to preheat the water before the boiler as opposed to the actual situation whereit is used for heating the washing line. This ideal approach should improve overallefficiency by reducing irreversibilites due to heat exchange with large temperaturedifferences.

Because it is unlikely that Berendsen would change their current mode of operationwith regard to the condensate, an additional configuration will be calculated, whereonly the exhausts are available for process integration. This involves two steps wherefirst preheating of the boiler water will be considered and next heating of the washingline. It is assumed that two heat exchangers are necessary to achieve this, due to thedifference in quality of the sink medium (treated soft water for washing is not of thenecessary quality for steam production in a boiler).

(a) Composite Curve - Boiler. (b) Composite curve - Washing line.

Figure 14.19: Composite curves for the two heat exchangers excluding the condensatestring.

A new required heat exchanger area is calculated at 51.5m2 which is an increase of 9.5%.Total investment cost is increased by 26.45% to 76,231.00 DKK resulting in a PBP of 0.20years.

Both solutions are theoretical and the indicated investment cost may prove to behigher because the physical distance between the boiler/washing line and exhaust

14 CASE STUDY 80

vents involve a considerable amount of piping, or because the price example of theheat exchanger is chosen for a less than ideal type. Additional costs will also occur as aresult of cleaning the heat exchanger from wax and other unwanted elements. Howeverthe PBP is sufficiently low to warrent a recomendation of pursuing this investment. Toensure that the result is not highly influenced by unknown factors the calculated capitalinvesment is varied by ±20% to estimate the sensitivity of the PBP to additional capitalcost.

Figure 14.20: Sensitivity analysis of investment cost on PBP.

On figure 14.20 the PBP is plotted as a function of a percentile change in investment costbetween -20 and 20 %. Changes in PBP are limited to ±20% showing a linear relation.

As can be seen from figure 14.18 the amount of hot utility that cannot be covered byprocess integration is limited to an interval between 108−150°C, before the temperaturelift becomes impossible. This adds up to approximately 27kW. On the basis of thislimited savings potential it is deamed unwise to start rerouting all current processstreams in order to integrate a heat pump. Because the price examples of the models donot apply to heat pumps this small, another approach is used to determine the viabilityof a heat pump project. Setting a (generous) maximum PBP of 5 years and using a COPof 4.0 the highest allowable capital investment can be calculated. This yields a TCIof 37,354.00 DKK and based on previous assumptions the allowable equipment costbecomes less than 10,000.00 DKK. Current prices of separate components or packagedheat pump solutions confirm that such a project is economically infeasible for internalprocess use. Alternatively it is possible to use any remaining waste heat for utility wateror district heating. This will be investigated in the following.

Verification and remaining potential Because the initial calculations reveal that pro-cess integration would be profitable for Berendsen, detailed calculations are warrentedto establish the specific investment necessary. In appendix E these calculations areincluded and here the temperature of the remaining waste stream is also calculated.

14 CASE STUDY 81

Figure 14.21: A proposal for a simple heat exchanger network with two units.

All gaseous waste streams are utilised and the proposed HEN can be seen on figure14.21. By using the hottest streams in the first heat exchanger it is possible to preheatthe boiler water almost to the pinch temperature (108 °C). All remaining waste streamsare included in the second heat exchanger, which in effect eliminates the need to injectsteam for heating the washing lines in all the considered time intervals.

Figure 14.22: Sink temperature levels - inlet of boiler water is 20 °C and inlet of softwater for washing line is estimated to 35 °C after preheat.

In figure 14.22 two sets of sink exit temperatures are presented. The blue and greenseries are made from a calculation where the HEX area needed to achieve the desiredsink exit temperature is found for every time interval. This value fluctuates a greatdeal, and the red and purple values are therefore calculated from representative valuesof heat exchanger area. No optimisation has been performed at this stage, the chosen

14 CASE STUDY 82

value is simply the most frequently occuring. Because ironing roll number 4 andthe tumble driers, that only run semi-dry cycles, have outlet temperatures that aresignificantly lower than the other waste heat streams, these are directed around thefirst heat exchanger and joined with the source outlet of the first heat exchanger.

Figure 14.23: Source temperature levels - second waste heat string is added after thefirst heat exchanger.

As can be seen from figure 14.23 the temperature of the source outlet after the secondheat exchanger is still around 40 °C. If the energy is extracted from this stream downto ambient conditions this would amount to approximately 100-130 kW continuouslyduring operation hours.

Based on economic correlations the HEN with the most economically interestinginvestment is now found by minimising the PBP of the investment. Like with anyother optimisation the minimum of the objective function can have a rather large spanof solutions of almost constant value with respect to the decision variable(s). Thisis illustrated in figure 14.24 where the PBP is shown as a function of the two heatexchanger areas.

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Figure 14.24: PBP of heat exchanger investment as a contour plot.

It is therfore possible to consider a slightly less than optimal investment and achieve asolution with relatively greater fuel savings.

Figure 14.25: Optimal dimensions of the proposed heat exchangers with respect to thePBP of the investment.

Strictly considering the project with the fastest return on investment, the economicalgorithm chooses a solution which reject an amount of heat in a number of timeintervals. This is illustrated in figure 14.26 as the intervals where the blue and greencurves are below the red and purple curves respectively. In the intervals where thecurves designated (min PBP) are above their counterpart, extra heat is extracted fromthe streams. It is assumed that this additional heat can simply be stored in a thermalresevoir.

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Figure 14.26: Link between recovered heat and the optimised heat exchanger area.

As a result of the reduced heat exchanger area (as opposed to full recovery) the finaltemperature of the waste stream has increased in general. The extent of this impact isillustrated with figure 14.27.

Figure 14.27: Response from source media (waste heat stream) due to fixed heatexchanger areas. Choice of areas are based on minimum PBP.

A continuous saving potential in all operating hours of approximately 300 kW can beachieved. This yields 750 MWh a year. From figure 13.4 (b) it is clear, that there are

14 CASE STUDY 85

possibilities in connecting the residual exhaust gas to the district heating network inRoskilde, or even to Berendsens own hot water utility. Estimating a sink temperatureof 87 °C enables the use of a CAHP with a corresponding heat price of approx. 240[DKK/MWh] (as Berendsen has 2495 operational hours a year). This will, with the∆Tsource = 10[K] indicate a heat pump capacity of 61.6 [kW].

15 Discussion

Approach Using the STREAM models it was initially established that using heatpumps for thermal production both in individual boilers and in the district heatingnetworks, had a beneficial influence on the proposed future energy system. Next apotential for reduction of energy consumption and harmfull emissions was estimated.

A number of detailed thermodynamic models were constructed to establish the currentstatus of, and possibilities for heat pumps.

Through a case study the validity of a savings potential was sought established whichyielded results corresponding to or exceeding those found in previous studies.

Assumptions It was prioritised that the thermodynamic heat pump models had toinclude some simplifying assumptions so that results could be achieved within theproject timeframe. This meant neglecting a number of issues such as heat and pressurelosses in the system. Omitting these factors may influence the marginal results but inreturn the models are reasonably stable and can perform calculations/optimisationswithin acceptable time limits (2-15 min).

With respect to the optimisation procedure it has to be noted that firstly it is an essentialassumption that the cost related to balance of plant, piping and regulation can bebased on a ratio calculated from the cost of the main components. Validating thisassumption is a matter of experience and statistics which is why this report has beenbased on the recommendations in litterature. Secondly the pricing functions are basedon component examples from a single supplyer (of the shelf ) which have been veryfiedas representative. Optimally such inputs should of course be extracted from updateddatabases via a comprehensive supplyer network.

Using EES as a solver has enabled a comprehensive study of a variety of parameters.If it is desired to proceed with a more detailed study where more decision variablesare considered, it is recommended to choose a higher level programming language.It is estimated that it would require the formulation of a dedicated solver to expandthe problem much further. A stand alone module should improve stability, speed andreliability of results.

Optimisation using the proposed thermoeconomic method has proven most succesfull.It is however somewhat optimistic with regard to what is ideal. Because the economicinput is based on aggregation and annuitisation of cost the method approachesa maximisation of NPV. The NPV value is of course known to overestimate theprofitability of projects and neglect the value of liquidity. When comparing the cost ofheat from the models with that of heat from fossil fuels, the results may show savingsin many regions. However care must be taken when advocating such a solution, sincethe initial investment still is a very big threshold, and not many things can go wrongbefore a project becomes an expense.

15 DISCUSSION 87

Choosing a variable compressor efficiency negates the fact that most industrial heatpumps are tailored to their application, meaning not many operating hours are spentoutside the domain of highest efficiency. It was considered more prudent to choose aconservative approach that reflected the slightly less than optimal situation in minorcompanies and/or future experiments aimed at validating the results from this report.To get a more accurate estimate of what a specific investment in a heat pump will yieldit is necessary to consider how much actual part load and yearly operation the unit willrecieve.

All heat cost from HP production are calculated as duty free, based on a sink mediumintended for process or a change in tax legislation. Meaning that in effect the sourcemedium comes at no additional cost.

Results It comes as no surprise that the STREAM model indicates that electricallydriven thermal production benefits an energy system with more intermittent gener-ation. Validating the extent of the effect needs more detailed modelling, especiallyconcerning the demand response.

Even given the level of detailing in the models, the lower level of uncertainty connectedwith the thermodynamic parameters (as opposed to the economic calculations), makethe results relevant for evaluating the potential of the investigated heat pump cycles.Working domains and attainable temperatures have been verified through comparisonwith scientific litterature and matches performance characteristics and prices of listedproducts from leading european companies.

Results from the case study validates the existence of large amounts of waste heat inindustry. It also demonstrates the strength of Pinch analysis. It was concluded that theboiler could not be replaced by a heat pump, but that does not mean that heat pumps asa general rule cannot be used to replace industrial boilers. It has to be considered thatthe load profile and temperature demands of this particular facility were somewhatunususal, with a high demand in two quite different temperature intervals.

JENSEN states that many new facilities resort to the decentralised oil heated ironingrolls because of their greater flexibility and higher productivity. However not mucheffort is spent in recovering the waste heat from these local burners. Without the properguidance such a project requires additional planning and seems cumbersome. It istherefore more obvious to choose a conventional turn-key solution such as a centralboiler for heating the washing lines.As with all projects with many results based on extrapolated and aggregated data,significant uncertainties are involved. Given the stated assumptions in the respectivesections the produced results and conclusions are expected to hold.

On this basis it should be emphasised that a potential for displacing the consumption offossil fuels exist with the recovery of waste heat. The case at hand is a prime example ofpresumed situation in Danish industry where waste heat is abundant and no measuresare taken to utilise the potential.

16 CONCLUSION 88

16 Conclusion

Findings Thermal production from heat pumps have an alleviating effect on anumber of the expected future challenges in the proposed energy scenarios. This isaccomplished by relieving CHP plants from undue thermal production, providing easyenergy storage and demand response.

An estimation was made of the possible energy savings and potential emissionreduction through waste heat recovery and use of heat pumps in industry. It can beconcluded that as of yet no obvious economic potential exists, because the fuel pricesare still too low. This factor is however a subjugate to change and combined with aneed for security of supply, the outlook for heat pump projects are improving. Anotheruncovered problem was simply that the knowledge of how to exploit the existingpotential is lacking in industry at present. For industry to exploit the possibility ofrecovering waste heat the profit margins need to increase. Incentives are needed if it isdeamed inappropriate to wait until fossil fuel prices rise to levels where project becomeurgently interesting.

Through thermodynamic modelling the mapping of working domains for the individ-ual heat pumps cycles have been obtained. A correlation for an optimal heat price hassimilarly been calculated based on the temperature lift and delivery temperature. Thisenables the selection of the ideal heat pump cycle and mode of operation based ona specific need. An autonomous cost minimisation procedure have been formulatedusing thermoeconomics. When observing the calculated heat prices these appearcompetitive with the heat prices found for current Danish heating network. With thefour documented heat pump cycles achievable delivery temperatures are in the rangeof 50-150°C. Only in the range 125-150 issues could arise with problematic temperaturelifts.

Of the parameters considered in this project, the one having the most prominentinfluence on the viability of a heat pump project is the number of yearly full load hours.

From the optimisation of a specific industrial facility a yearly savings potential of 750MWh was found. Additionally a heat pump potential of 61[kW ] was found. Thisexceeds the expectations based on litterature studies, including that for heat pumppotential. A heat price could be found for this facility using the thermodynamic modelsthat is competitive with the current prices in the district heating networks. Fromobserving this specific laundry facility it can be assumed that this is an industry wichgenerally produce large amounts of waste heat and have a vested interest in recoveringit. As mentioned many new facilities use oil heated ironing rolls, and very few seem torealise the potential in recovering the waste heat.

REFERENCES 89

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A STREAM 93

A STREAM

A full documentation of the most important results from the STREAM scenario analysisare presented next. To get an even better overview of the changes in the system theExcel file appended to the project could be usefull. In ’comparison.xlsx’ a macro is usedto import, resize and place the figures also found below. By changing back and forthbetween the different scenarios the differences from one scenario to the next are moreevident.

(a) Reference scenario. (b) Green scenario.

(c) Wind scenario. (d) Heat Pump scenario.

(e) Thermal storage scenario. (f) Flexible scenario.

Figure A.1: Duration curves for the different STREAM scenarios.

A STREAM 94




Figure A.2: Duration curves for individual boilers in the different STREAM scenarios.

A STREAM 95




Figure A.3: Economic impact of variations in the different STREAM scenarios.

A STREAM 96




Figure A.4: Changes in CO2 emissions.

B INTEGRATION OF HEAT PUMPS 97

B Integration of Heat Pumps

When discussing integration of heat pumps in Danish industry, the important pointof interest is investment cost and the resulting payback period. Heat pumps have thepossibility to provide both heating and cooling of processes using minimal electricityor available fuels due to high values of Coefficient Of Performance [COP], whichminimises the running cost of a plant.

A possible lack of operating heat pumps in Danish industry seems most likely to bedue to high investment cost. Integration of energy- and Carbon Dioxide-reducingtechnologies in Danish industrial plants could be forced by the legislators as discussedin section 4.5. Evening out legislation might address the problems, where regulationand taxes today can even be biased towards traditional heating and cooling in industrialplants. Through the use of heat pumps, incentives in legislation could reduce energyconsumption in Danish industry.

In order for heat pumps to assist in reducing energy cost in industrial plants, theintegration must be well planned and thought through. Heat pumps in industry isnot a package deal, but when well integrated within the existing plant, they may savea significant part of existing process heating and cooling energy.

B.1 Pinch Analysis

Management of energy-streams in industrial plants is normally done using pinchanalysis. This analysis focuses on heating and cooling streams in an industrial plantusing only heat exchange between hot and cold streams. A pinch analysis characterisesevery single steam in an industrial process with their start and final temperatures andby the amount of heat required for the flow to change temperature (the mass flowmultiplied by the heat capacity).

In a simple pinch analysis a general heat exchanger temperature change, ∆Tmin is set,representing the size and price of heat exchangers within the system. [Rokni, 2006]

∆Tmin → 0⇒ Heat Exchanger size and price →∞ (B.1)

For this assumption to be valid, the cost of energy and the capital cost of the heatexchanger must be considered. Heat exchanger design changes dramatically withfluids, temperature ranges and heat loads, and the optimal correlation between priceand heat loss can be comprehensive to determine. According to [Rokni, 2006] thefollowing assumption is reasonable when looking at industrial plants (heat exchangeas a general term) within chemical industries:

5K ≤ ∆THEX ≤ 20K (B.2)

When performing a pinch analysis a temperature (the pinch) is identified. The pinchtemperature is defined as being the temperature where the net heat needed is zero


(the amount of cooling meets the amount of heating necessary). Above the pinchtemperature there is at net heat deficit and below the pinch temperature a net heatsurplus. This implies that cooling of a stream above the pinch temperature must beconducted from a stream requiring heat. Additional cooling above the pinch willdirectly affect the amount of heating above the pinch by the same amount. Thesimilar problem will occur below the pinch, where (unnecessary) heating will resultin additional cooling.

The pinch analysis results in both Composite Curves and Grand Composite Curves,both of which are useful tools within process integration [Annex-21, 1995]:

• Composite Curves (CC) are cold and hot streams collected respectively over theentire temperature interval of the process and plotted in a temperature/heatcontent diagram. Heat exchange is possible where the two curves overlaphorizontally, which implies additional heat and cooling where they do notoverlap.

• Grand Composite Curves (GCC) are cold and hot streams collected (net heatneeded) in each temperature interval. Heat must be added at QH and removed atQC . The pinch is (as stated earlier) where the net heat needed is zero.

(a) (b)

Figure B.1: Composite and Grand Composite Curves of a industrial plant equivalent to[Annex-21, 1995].

Pinch analysis can be used in both new projects and retrofit situation. Besides the pinchanalysis a few important considerations should be noted, which are not within thecalculation itself. These considerations also impact the overall cost-optimal solution[Bengtsson et al., 2002]:

• The physical distance between the hot and cold streams is important. This ismainly due to heat and pressure losses in piping.

• Depending on the industry some of the streams can have different demands withrespect to heat exchangers. This could be with respect to materials, pressure,pressure loss etc.


• Heat transfer coefficients change as the stream changes between vapor and liquid,different media etc.

Basic pinch technology covers only continuous production processes or steady stateproblems. This is not necessarily the case for all industrial heat pump installations,where the heat pump may need to produce heat (and cooling) even when the heatsource temperature changes thoughout the working hours. The entire GCC changes,and in these situations both (or all) pinch temperatures, cooling and heating demandsmust be (re-)considered.

B.2 Heat pumps in Pinch analysis

The introduction of a heat pump in an industrial plant is done based on a completepinch analysis for that specific plant. The pinch temperature, the total cooling andheating demands and temperature lifts are all necessary for the dimensioning of theheat pump. In most literature (e.g. [Annex-21, 1995] and [Wallin, 1996]) concerningindustrial heat pumps the relation between cooling and heating demands are definedas q:

q =HeatSink

HeatSource=

COP

COP − 1(B.3)

Values of q are typically between 0.5 (heat transformers) and 1.5 (Vapor CompressionHeat Pump). The traditional absorption cycle has a q-value of up to 2.7. [Wallin, 1996].

Figure B.2: Heat pump placement relative to pinch

Figure B.2 shows the three different ways of integrating a heat pump into a plant[Annex-21, 1995].

(a) Integration of a heat pump with both the heat sink and heat source below the pinchwill require additional cooling corresponding to the work needed to run the heatpump (in an ideal situation -> overall COP of heat pump = -1).

(b) A heat pump with both heat sink and heat source above the pinch temperature willreduce heat demand with the heat equivalent to the work input of the heat pump(in an ideal situation -> overall COP of heat pump = 1)


(c) When integrating a heat pump with the heat source below the pinch temperatureand the heat sink above the pinch, the heat pump will reduce heat demand abovethe pinch, while reducing the cooling demand below the pinch. (overall COP ofheat pump » 1). This integration is consequently the only viable thermoeconomicsolution.

Most of the Grand Composite Curve will be affected from the changes of integratinga heat pump, except for the temperature interval between the heat sink and heat source.

A change in the pinch temperature is possible when introducing a heat pump (depend-ing on heat pump characteristics), but it is of course essential, that the pinch tempera-ture does not cross heat sink or source temperature, resulting in either integration a orb from figure B.2.

A change in the GCC will affect the Heat Exchanger Network (HEN) within the similartemperature range, making a retrofit installation less economically attractive, in the casewhere a complete pinch analysis with appertaining HEN is already utilised.

C COMPRESSORS 101

C Compressors

C.1 General concepts

For a given compressor a range of parameters are defined with the purpose ofcomparing component characteristics. For displacement compressors a swept volume,Videal, can be defined, being the geometrical volume which is filled with gas at thecompressor inlet, the unit will be [m3/revolution]. The swept volume flow, Videal, is thetheoretical gas flow in [m3/sec], giving the relation Videal = Videal · n/60, where n is thenumber of revolutions per minute. For a piston compressor with z cylinders, stroke Sand cylinder diameter D, the theoretical swept volume flow would be [Granryd, 2005]:

Videal = z · n · π ·D2

4 · 60· S (C.1)

Due to a number of losses the actual flow will be smaller than the theoretical. Avolumetric efficiency can be defined as:

ηvol =m · ν2,compVideal

(C.2)

Where ν2,comp is the specific volume of the working fluid at the compressor inlet, andm is the mass flow of the working fluid [kg/s]. Because dynamic compressors have noideal swept volume the concept of a volumetric efficiency does not apply to this typeof compressors.The isentropic efficiency is defined as the ratio of the isentropic work per unit mass tothe actual shaft work:

ηis =εcomp,isεcomp

(C.3)

Where εcomp,is = h1,comp,is−h2,comp, is the isentropic compression work in [kJ/kg]. Theideal work of compression per kg of gas is:

|ε| =∣∣∣∣∫ ex

inν · dp

∣∣∣∣ (C.4)

Written for an ideal gas under isentropic conditions, this expression can be formulatedas:

|ε| = γ

(γ − 1)R · Tin

[pexpin

(γ−1)γ − 1

](C.5)

The actual work delivered at the compressor shaft, W [kW ], can be estimated by:

W =m(hout,comp,is − hin,comp)

ηis(C.6)

Where h is the enthalpy of the gas at the compressor out- and inlet respectively. Thisexpression can be further developed so that one may find the maximum compressorpower needed for a process. Such an expression is useful for dimensioning the electric

C COMPRESSORS 102

motor to drive the compressor. According to [Granryd, 2005] the following expressionis valid in the case of an ideal gas:

W =ηisηvol

γ

γ − 1pin

[pexpin

γ−1γ − 1

]Videal (C.7)

Here gamma, γ, is a fluid property known as the specific heat ratio.

C.2 The reciprocating piston compressor

This type of compressor is advantageous for low to medium/high applications. Thetechnology is well known and proven. Most components are easily fabricated (withexception of the valves) and can be serviced in situ. The service intervals are shorterbut less expensive than for a screw compressor, which normally needs to be shippedback to the factory. The technology has relatively high off-design efficiency, making itideal for applications with many part-load hours [York, 2001].

(a) Two stage piston compressor(low stage in V-arrangement)[Department of Energy, 1985].

(b) Theoretical volumetric efficiency as af func-tion of pressure ratio and dead space ra-tio(gamma=1.3).

Figure C.1: Illustrative technical drawing of a reciprocating compressor and the typicalimpact of a characteristic drawback, the dead space ratio.

One important aspect of the piston compressor that influences the volumetric efficiencyand limits the attainable pressure ratio, is the dead volume. The dead volume is thenecessary clearance between the piston top and the cylinder head, needed principally toaccommodate the valves. This volume will not be evacuated when the exit valve opens,and the remaining gas will consequently displace new gas when the cylinder is filled inthe next cycle, thereby lowering the volume flow rate compared to the theoretical value.According to [Granryd, 2005] an expression for the theoretical volumetric efficiency canbe formulated as:

ηvol,th = 1− V0Vswept

·

((pexpin

) 1γ

− 1

)(C.8)

Where V0 is the dead volume (V0/Vswept: dead space ratio), and pex/pin is the pressureratio over the compressor. The most important losses in this type of compressor arepressure drop over the valves, leakage and heat exchange between the gas and the

C COMPRESSORS 103

cylinder walls. The construction furthermore has some issues regarding sensitivity tocorrosive properties of some working fluids. Condensate on the relatively cold inletvalves from insufficient superheat can damage the parts. Poor designs can result in anaccumulation of droplets in the cylinder, and if left unchecked, the tendency can leadto liquid hammering. That is, if the amount of liquid in the chamber is greater thanthe dead volume, pressure many times that of the design, will result when the pistonapproaches the top of the cylinder.

The piston compressor can be operated relatively efficient at part load by eitherfrequency control, or by operating the inlet valve during the compression part of thecycle. For the last technique simply maintaining an open inlet valve, will reduce thepumping work in the relevant cylinders considerably.

Only very few piston compressors function without lubrication because of the higherproduction costs related to the demand for tighter tolerances. When operatingcompressors using oil for lubrication and/or cooling one should observe the need forcompatible working fluids. Most lubricating oils can dissolve an amount of the typicalworking fluids in them. If the compressor is not in operation for periods of time (forinstance in connection with seasonal variation for A/C units for office buildings) theoil should be heated before starting operation. Otherwise the high concentration ofworking fluid in the oil could compromise its ability to function as lubrication andmechanical failure may result.

C.3 The screw compressor

The screw compressor is an attempt to combine the advantages of the displacement andthe dynamic compressor. The first patents were issued to Alf Lysholm in the 1930-ties.The principle is to trap a number of gas volumes between two matching screw profilesin a housing. As the screws are rotated by a motor (usually only one screw is connectedto the motorshaft, and the other screw is driven by the first or rotated by gears), thegas volumes are compressed. The inlet and outlet port are fixed machined openings ineither end of the housing, matching the profiles of the screw lobes. The rotating screwsare the only moving parts in this design.

C COMPRESSORS 104

(a) Screw compressor. (b) The effect of built in volume ratio onisentropic efficiency [Brendeng, 1979].

Figure C.2: Schematic of screw compressor and the effect of built in volume ratio oncompressor efficiency.

The screw compressor can function both with and without oil injection. Injecting oilboth seal the space between the lobes and the housing and decrease leakage, it can alsocool the gas so higher pressure ratios can be achieved in a single stage. Oil free com-pressors have higher tolerance requirements to the machining (to avoid leakage) andalso require precision gears (to avoid contact), both of which increase manufacturingcosts. Because the screw compressor is able to function with considerable amounts ofliquid in the compression volume, the requirements for sufficient superheat are lesscritical. Since rather large quantities of oil are added, oil separation after compressionis crucial to avoid fouling of heat exchangers.

The design of the discharge port represents a built-in volume ratio, and should be madeto accommodate both axial and radial flow. It should also be constructed to deliver thegas as close to the pressure of the discharge line as possible, to avoid shocks into eitherthe compressor or discharge line.

Ideally the discharge port should be uncovered precisely at the moment the compressedgas pocket reaches the pressure in the discharge line, otherwise unnecessary work isbeing performed. The effect of this principle has been illustrated in [Granryd, 2005]and the effect on the isentropic efficiency can be summarised as:

ηis =(∆p)

(κ−1)κ − 1

πκ−1κ

i − κ−1κ · π

−( 1κ)

i · (π −∆p)− 1(C.9)

Where πi = νki is the built in pressure ratio, k is the polytropic exponent and νi isthe built in volume ratio. The volume ratio is defined in a similar way as for pistoncompressors, using the volume of gas at the inlet, Vs and the volume of gas when thedischarge port is uncovered, Vi, giving νi = Vs/Vi.

The effect of (C.9) can be seen in figure C.2 for varying volume ratios.

C COMPRESSORS 105

C.4 The centrifugal turbine compressor

A dynamic compressor widely in use for industrial applications is the centrifugalcompressor. In this type of compressor the volume flow and pressure ratio, is achievedby accelerating the gas both radially and tangentially. It can be shown that the idealwork of compression for a gas is proportional to the square of the speed of the outerimpeller tip [Granryd, 2005]:

|ε| = constant · u22 (C.10)

From this a characteristic factor for the impeller geometry can be related. It is defined asa dimensionless head factor, and its numerical size determines how large a compressionwork can be achieved from a given impeller geometry:

ψ =2 |ε|isu22

(C.11)

A larger value is desirable in order to avoid multistaging. Another useful parameter isthe volume flow factor which is defined as:

φ = 4 · Vin(πD2u2)

(C.12)

Where Vin is the incoming volume flow rate, D is the outer impeller diameter and u2the tip speed. An example is given in [Granryd, 2005] of how one can approximatethe highest possible pressure ratio from these dimensionless factors. If one considersa normal tip speed of 220 m/s, and also that the head factor is limited to φ = 1, thisyields:

|εis,max| =γ

(γ − 1)· 8314

M· Tin

(pexpin

)(γ−1γ

)− 1

⇒ (C.13)

(pexpin

)=

[|ε|is · (γ − 1) ·Mγ · 8314 · Tin

+ 1

]( γγ−1

)(C.14)

Using the indicated maximum isentropic compression work and an inlet temperature,Tin, of 313K (NB. This value is changed from that in the reference due to this being HPapplication rather than for refrigeration), the function can be plotted to illustrate therelation between molecular weight and the attainable pressure ratio:

C COMPRESSORS 106

Figure C.3: Attainable pressure ratio as a function of molecular weight

C.5 The axial turbine compressor

Axial compressors are best known for their role in jet airplane propulsion. It is acompact, lightweight and durable design; however the material requirements for theblades make it a very expensive solution. Developments in recent years have helpedbring down the costs of axial turbines but their use is still strictly limited to very highvolume flow applications with limited requirements for pressure ratio. In an axialturbine the flow is induced by the spinning of impellers. When the flow passes theimpellers it is reduced in velocity over the stationary diffuser vanes, this also buildspressure. Multi-staging for an axial turbine consists of placing a sequence of impellersand diffusers in turn until the required pressure ratio is achieved.

D EXERGY CONCEPTS 107

D Exergy concepts

For many years the goal of energy conservation and system optimisation has beenbased primarily on a first law of thermodynamics approach. That is, from anengineering standpoint the conservation of energy means that a system only needs tobe optimised on a quantitative basis.

First law optimisation techniques like for instance the COP used extensively inrefrigeration and heat pump industries, does not take into account the inequalityin value of 1 kWh of electricity and heat respectively. For comparative studiesthis may also be sufficient for evaluating what equipment to invest in for a specificapplication. However for grassroot and retrofit situations it is essential to implementthermodynamic principles that reveal a system’s inefficiencies and enable the designerto evaluate them qualitatively from a thermodynamic and economical viewpoint.

Irreversibilities and unacceptable inefficiencies means wasting scarce and increasinglyvaluable fuel input. The ability of a given amount of energy to do work is a qualitativemeasure that is not constrained by conservation. It gives a realistic measure of thepotential value of a fuel, fluid stream or process, and in classical thermodynamicsit provides the means to explain the degradation in value of energy subjected toirreversibilities. This is a second law approach and the extensive property associatedwith a system described, is called exergy [Bejan, 1996].

D.1 Definitions

The standard formulation of the total exergy in a system can be formulated as:

E = EPH + EKN + EPT + ECH [kJ ] (D.1)

where PH, KN, PT and CH denotes physical, kinetic, potential and chemical exergyrespectively. Another useful form is to look at this equation on a unit-of-mass basis,where the total specific exergy becomes:

e = ePH + eKN + ePT + eCH [kJ/kg] (D.2)

Usually the kinetic and potential terms are neglected but in principle they are convert-ible to work, whereby they equal the potential and kinetic energies:

eKN =1

2V 2 (D.3)

where V denotes velocity

ePT = gz (D.4)

where g denotes acceleration of gravity and z elevation.

The chemical exergy does not necessarily require a chemical reaction, mixing actionsalso influence this term. For heat pump considerations this chemical exergy term cantherefore be neglected except for the case where the working fluid consists of more thanone component with varying concentrations through the cycle.


According to [Bejan, 1996] the obtainable work from a system is given by:

Wc = (U − U0) + p0(V − V0)− T0(S − S0)− T0Sgen (D.5)

Where U denotes the internal energy of the system, V − V0 denotes the volume changeof the closed system, S − S0 denotes the entropy of the closed system at the given andat the dead state, T0 and p0 are the dead state conditions. The underlined terms aregiven by the initial and the dead state of the system and are independent of the processconsidered. The last term includes Sgen and is process dependent, the term is thereforepositive when irreversibilities are present. The physical exergy, EPH , is defined asthe maximum obtainable work when a closed system passes to a dead state, and thisexpression is given as the limiting case for Sgen → 0, which is the case for a process freeof irreversibilities.

EPH = (U − U0) + p0(V − V0)− T0(S − S0) (D.6)

For any actual process irreversibilities means that Wc < EPH , and this loss ofavailability for doing work is known as exergy destruction, ED. This principle oflimited efficiency is named the Gouy-Stodola theorem, and expresses the discrepancybetween the actual work and the theoretical work:

ED = T0Sgen (D.7)

The proportionality between lost work and entropy generation was first proposed byFrench physicist G. Gouy in 1889 and again by Swiss engineer A. Stodola in 1905, buthas not received the deserved attention until almost a century later [Bejan, 1989].

Concerning engineering applications, a more convenient form is the change in physicalexergy, E2 − E1. In this form the terms concerning the physical and chemical make-upof the environment disappears except for T0 and p0 which still have to be specified.In a form convenient for evaluating closed systems and control volumes (assumingnegligible change in potential, kinetic and chemical exergy) the equation becomes:

E2 − E1 =

((U2 − U0) + p0(V2 − V0)− T0(S2 − S0))−((U1 − U0) + p0(V1 − V0)− T0(S1 − S0)))

→ ((U2 − U1) + p0(V2 − V1)− T0(S2 − S1)) (D.8)

The closed system exergy balance can be shown to be:

(E2 − E1) =

∫ 2

1

(1− T0

Tb

)δQ− [W − p0(V2 − V1)]− T0Sgen (D.9)

The first term concerns the exergy transfer related to heat transfer into or out of thesystem during the process. Here the subscript b denotes the temperature of the chosenboundary at which the heat transfer is accounted:

Eq =

∫ 2

1

(1− T0

Tb

)δQ (D.10)


The second term relates to the exergy transfer associated with the transfer of energy asa result of work being done to or by the system:

EW = W − p0(V2 − V1) (D.11)

The time rate change of exergy form of the balance equation is given as:

dEdt

=∑j

(1− T0

Tj

)Qj −

(W − p0

dV

dt

)− ED (D.12)

Relating this to a control volume form there is need to account for exergy transfer bymass entering and exiting the system. This is given as:

dEcvdt

=∑j

(1− T0

Tj

)Qj −

(W − p0

dVcvdt

)+∑i

miei −∑e

meee − ED (D.13)

Choosing the boundary for heat transfer as the dead state temperature means that thefirst term, Eq, disappears. This is useful for theoretical considerations where there is noknowledge of the heat loss in the different parts of the system. It is beyond the scope ofthis project to provide detailed simulations that can account for the exergy destructionand losses due to heat losses and friction.

To evaluate the control volume form of the exergy balance a way of accounting forthe exergy entering and exiting the system is needed. This is provided in [Bejan, 1996]:

e = (h− h0)− T0(s− s0) +1

2V 2 + gz + eCH (D.14)

using: (Wcv

m

)int,rev

= (hi − he)− Tb(si − se) +1

2(V 2i − V 2

e ) + g(zi − ze) (D.15)

and identifying the underlined term in equation (D.14) as the physical exergy:

ePH = (h− h0)− T0(s− s0) (D.16)

D.2 Exergy destruction/loss ratios and exergy efficiencies

Because the systems modeled exclude losses connected with heat loss and friction, andthere is no physical test data, no meaningful distinction can be made between exergydestruction and exergy loss. If in a retrofit situation the calculations should aim atidentifying the components of greater theoretical exergetic inefficiency. This can bedone by analysing two different ratios:

y∗D =ED,k

ED,tot(D.17)


This ratio relates the exergy destruction of component k, to the sum of all exergydestruction in the system. Alternatively the destruction rate can be compared to thetotal fuel input.

yD =ED,k

EF,tot(D.18)

These ratios are useful for comparing alternate components in the same system, andfor identifying candidates for optimisation. They are however not meaningful incomparing between systems, here the magnitude of the exergy destruction providesbetter insight. For systems and components an exergetic efficiency can be defined asthe ratio between the fuel input and the generated products. An exergy balance for asystem or a component can be written as:

EF = EP + ED + EL (D.19)

If it is possible to define a product then the efficiency is given as:

ε =EP

EF= 1− ED + EL

EF(D.20)

Otherwise the difference between the accountable destruction/loss of exergy and100% provides the efficiency, as also shown. In the special case of the compres-sion/absorption hybrid heat pump, the chemical exergy of the mixing and separationof the streams with different concentrations is not negligible. A detailed account of thischemical exergy is outside the aim of this project. The destruction ratio of exergy dueto chemical reactions can however still be found because the inefficiencies of all othercomponents are calculated.

0 =EP

EF−

(1−

∑k (ED,k + EL,k)

EF,k−ECHDL,i

EF,i

)(D.21)

Where k are the components with destruction of physical exergy and i are thecomponents with destruction of chemical exergy. The expression for calculating the

destruction of exergy from chemical irreversibilities,ECHDL,iEF,i

, gives a percentage valueand provides the order of magnitude. For more detailed calculations this approachcannot be recommended.

D.3 Programming

The approach has been to create a number of subroutines in a seperate EES library. Thecalculations are component based and can be called directly from any EES worksheetas a subprogram. Although the intention has been to make the exergy scripts as genericas possible, three different variations were needed to accomodate for the difference incomponents.

• 1 stage: [Evaporator - Compressor - Condenser - Expansion valve]

• 2 stage: [Evaporator - Low Stage Compressor - Internal HEX - Low StageExpansion Valve- High Stage Compressor - Condenser - High Stage ExpansionValve]


• hybrid: [Desorber - Boil Off Unit/Mixing Unit - Compressor - Liquid Pump -Internal HEX - Absorber - Expansion Valve]

These library files can be called for any simulation having a similar structure ofcomponents. Because the model was initially intended to run transient cycles overlarge timeseries it was chosen to use subprograms instead of procedures. Embeddedprocedures function faster but the number of possible equations and variables arelimited to 6000 and 12000 respectively. This becomes relevant if the model needs tooptimise in a resolution down to individual hours. Subprograms call a new worksheetincreasing the maximum number of equations and variables allowed.

In special cases the heat pump can cool a stream at a temperature below that ofthe reference environment, T0. Under these circumstances attention must be paid tosigns and the directions of the exergy flows since exergy is transferred in the oppositedirection of the heat transfer. A change in the exergy library files will be necessary, sinceno logic statements where included in these to reduce calculation time.

E EES CODE 112

E EES Code

On the following pages the thermodynamic models on which this project is basedare documented. Along with each separate cycle are library files where the definedsubprograms are documented. The details of the modeling is not extensively describedin the code, it is simply labeled what function each section of code performs. Details ofthe modeling approach is described in the appropriate sections of the report.

Each cycle is labeled with a header so that the cycle may be identified. The sequence ofthe code is as follows.

• R717 single stage

• R717 two stage

• R718 single stage

• R718 two stage

• R744 transcritical

• NH3H2O hybrid

Additionally to the section labels, some of the important parameters have a commentstating their function. This comment is located below the parameter.

In addition to the models additional calculations are enclosed.

• U-value for transcritical R744 operation

• Validation of Pinch HEN calculations for Berendsen

File:HEAT_PUMP_R717.EES 8/30/2010 10:15:06 AM Page 1

EES Ver. 8.596: #0780: Department of Energy Engineering, Tech. Univ. of Denmark

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"----------------------------- Heat pump simulation - R717 Condensing Vapor Heat Pump------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

$INCLUDE HEX_R717.LIB

$INCLUDE Exergy_func_R717.LIB

PROCEDURE isentropic(DELTAp:eta_is)

IF DELTAp =< 3.0 THEN

eta_is=-0.05+0.55*DELTAp-0.09*DELTAp^2

ELSE

eta_is=0.82-0.01*DELTAp

ENDIF

END

PROCEDURE volumetric(DELTAp:eta_vol)

IF DELTAp =< 3 THEN

eta_vol=0.91

ELSE

eta_vol=0.94-0.01*DELTAp

ENDIF

END

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- INPUT DATA ----------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"This section defines the working conditions of the heat pump."

R$='R717'

"Definition of working fluid"

Q_dot_heat+Q_dot_oil_usefull=1000

"Heat output"

t_out=75 [C]

"Delivery temperature"

t_lift=20 [K]

"Temperature lift"

DELTAt_sink=10 [K]

"Temperature change in sink medium"

DELTAt_source=10 [K]

"Temperature change in source medium"

t_superheat=5 [k]

"Superheat"

DELTAT_COND=2 [K]

"DELTAT_min that defines the temperature difference at the pinch point in the condenser"

DELTAT_EVAP=2 [K]

"DELTAT_min that defines the temperature difference at the pinch point in the evaporator"

t_source=t_out-t_lift

"Temperature of source medium into evaporator"

R_sink$='R718'

"Definition of sink medium"

p_sink=10100 [kPa]

"Pressure on sink medium side: set above ambient to avoid 2phase conditions"

R_source$='R718'

"Definition of source medium"

p_source=101 [kPa]



"Pressure on source medium side"

c_oil=2.00 [kJ/kgK]

"Heat capacity of lubricating oil"

rho_oil=800 [kg/m^3]

"Density of lubricating oil"

Q_dot_oil=0

"Heat output from lubrication oil: values should be between 0 and 50-100 "

eta_gas=0.8

"Efficiency of gas burner for comparing with heat pump"

c_q_gas_kWh=22.05

"Example: Price of gas"

c_F_elec_kWh=69.94 [Øre/kWh]

"Example: Price of electricity"

h_op=2500

"Number of operating hours"

eta_elec=0.9

"Efficiency of electric motor"

r_n=0.0213

"Inflation rate"

n=15

"Technical lifetime of heat pump project"

r=0.07

"Interest rate"

{eta_is=0,75}

CALL isentropic(DELTAp:eta_is)

"Varying isentropic efficiency - as a function of pressure ratio"

CALL volumetric(DELTAp:eta_vol)

"Varying volumetric efficiency - as a function of pressure ratio"

{eta_vol=0,85}

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"----------------------------------------------------------- CYCLE CALCULATION ----------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

t_cond_out=converttemp(C,K,t_out)

t_cond_in=converttemp(C,K,t_out-DELTAt_sink)

t_evap_in=converttemp(C,K,t_out-t_lift)

t_evap_out=converttemp(C,K,t_out-t_lift-DELTAt_source)

"Temperature conversions"

VHC=(h_2-h_3s)*m_dot/(V_dot_s*1000)

"Volumetric heating capacity"

DELTAp=p_3/p_1

"Pressure ratio"

h_int=enthalpy(R$,p=p_3s,x=x_vapor)

x_int=(h_int-h_3s)/(h_2-h_3s)

t_cond=(t_cond_out-t_cond_in)*x_int+t_cond_in

T_3=t_cond+DELTAT_COND

x_vapor=1

x_liquid=0



h_3=Enthalpy(R$,T=T_3,x=x_liquid)

h_3s=h_4

t_3s=t_cond_in+DELTAT_COND

t_subcool=t_3-t_3s

p_3s=pressure(R$,t=t_3s+t_subcool,x=x_liquid)

p_3s=p_3

h_3s=Enthalpy(R$,T=T_3s,p=p_3)

x_4=quality(R$,T=t_4,h=h_4)

t_1=t_evap_out-DELTAT_EVAP

t_1s=t_evap_in-DELTAT_EVAP-DELTAt_source+t_superheat

p_1=p_4

t_1=t_4

p_1=pressure(R$,x=x_vapor,t=t_1)

h_1=Enthalpy(R$,x=x_vapor,p=p_1)

h_1s=Enthalpy(R$,T=t_1s,p=p_1)

s_1s=Entropy(R$,T=t_1s,p=p_1)

p_2=p_3

s_1s=s_2is

t_2is=temperature(R$,p=p_2,s=s_2is)

h_2is=Enthalpy(R$,p=p_2,s=s_2is)

t_2=temperature(r$,p=p_2,h=h_2)

Q_dot_heat=(h_2-h_3s)*m_dot

rho_1s=Density(R$,T=T_1s,P=P_1)

rho_2=Density(R$,T=T_2,P=P_2)

rho_3s=Density(R$,T=T_3s,P=P_3)

rho_4=Density(R$,T=T_4,h=h_4)

v_1s=Volume(R$,T=T_1s,P=P_1)

V_dot_1=m_dot*v_1s

eta_vol=V_dot_1/V_dot_s

W_d=(h_2is-h_1s)*m_dot

epsilon_v=W_d/V_dot_1

W_comp=(eta_vol/eta_is)*V_dot_s*epsilon_v

"same as W_comp=m_dot*(h_2-h_1s)"

V_dot_h=V_dot_s*3600

p_4=p_low

p_2=p_high

COP=(Q_dot_heat+Q_dot_oil_usefull)/W_comp

"Coefficient Of Performance"

Q_dot_cool-(Q_dot_oil_usefull-Q_dot_oil)=(h_1s-h_4)*m_dot

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- OIL INJECTION --------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

t_2=t_oil_out

t_1s=t_oil_in



h_2_oil=h_1s+(h_2is-h_1s)/(eta_is)

Q_dot_oil=(h_2_oil-h_2)*m_dot

{h_2=h_2_oil-Q_dot_oil*m_dot}

Q_dot_oil=(t_oil_out-t_oil_in)*m_dot_oil*c_oil

V_dot_oil=m_dot_oil/rho_oil*1000*60

Q_dot_oil_usefull=(t_oil_out-(t_cond_in+DELTAT_COND))*m_dot_oil*c_oil

v_dot_h_oil=m_dot_oil/rho_oil*3600

deltat_oil_small=(t_cond_in+DELTAT_COND)-t_cond_in

deltat_oil_great=t_oil_out-t_cond_out

lmtd_oil=(deltat_oil_great-deltat_oil_small)/LN(deltat_oil_great/deltat_oil_small)

A_oil=Q_dot_oil_usefull/(U_overall_l*lmtd_oil)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- HEAT TRANSFER ---------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"Calls subprograms that contains heat exchanger calculations where duplicate commands are used to establish and verify pinch

point assumptions"

CALL EVAP_R718(R_source$,t_evap_in,t_evap_out,p_source,Q_dot_cool:t_evap_R718[1..51],x_evap_R718[1..51]

,h_evap_R718[1..51],m_dot_evap_R718)

CALL EVAP_R717(R$,h_1s,h_4,t_4,p_1:t_evap_R717[1..51],x_evap_R717[1..51],h_evap_R717[1..51])

CALL cond_R717(R$,h_2,h_3s,t_3s,p_2:t_cond_R717[1..51],x_cond_R717[1..51],h_cond_R717[1..51])

CALL cond_R718(R_sink$,p_sink,t_cond_out,t_cond_in,Q_dot_heat:x_cond_R718[1..51],t_cond_R718[1..51]

,h_cond_R718[1..51],m_dot_cond)

t_evap_g=t_evap_out+(t_evap_in-t_evap_out)*((h_1-h_4)/(h_1s-h_4))

t_cond_2p=t_cond_in+(t_cond_out-t_cond_in)*((h_3-h_3s)/(h_2-h_3s))

t_cond_g=t_cond_in+(t_cond_out-t_cond_in)*((h_int-h_3)/(h_2-h_3s))

Q_dot_heat=Q_dot_cond_l+Q_dot_cond_2p+Q_dot_cond_g

Q_dot_cond_2p=m_dot*(h_int-h_3)

Q_dot_cond_g=m_dot*(h_2-h_int)

Q_dot_cool=Q_dot_evap_2p+Q_dot_evap_g

Q_dot_evap_g=m_dot*(h_1s-h_1)

"Calls lmtd values for economic calculation regarding heat exchanger area"

CALL lmtdsource1(R$, t_evap_out, t_evap_g, h_4, h_1, p_low: lmtd_source_2p)

CALL lmtdsource2(R$, t_evap_g, t_evap_in, h_1, h_1s, p_low: lmtd_source_g)

CALL lmtdsink1(R$, t_cond_in, t_cond_2p, h_3s, h_3, p_high: lmtd_sink_l)

CALL lmtdsink2(R$, t_cond_2p, t_cond_g, h_3, h_int, p_high: lmtd_sink_2p)

CALL lmtdsink3(R$, t_cond_g, t_cond_out, h_int, h_2, p_high: lmtd_sink_g)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------ EXERGY ANALYSIS ------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

CALL Compressor(m_dot,t_1s,t_2,h_1s,h_2,R$,W_comp:epsilon_comp,E_dot_D_comp,DELTAE_comp,E_dot_comp_in

,E_dot_comp_out)

CALL Condenser(m_dot,t_cond_R717[1],t_cond_R717[51],h_cond_R717[1],h_cond_R717[51],R$,W_comp,R_sink$,m_dot_cond

,t_cond_R718[51],t_cond_R718[1],h_cond_R718[51],h_cond_R718[1]:DELTAE_R_cond,epsilon_cond,DELTAE_sink_cond

,E_dot_D_cond,E_dot_cond_out,E_dot_cond_in)

CALL Evaporator(m_dot,t_evap_R717[51],t_evap_R717[1],h_evap_R717[51],h_evap_R717[1],R$,R_source$,m_dot_evap_R718



,t_evap_R718[1],t_evap_R718[51],h_evap_R718[1],h_evap_R718[51]:epsilon_evap,DELTAE_R_evap,DELTAE_source_evap

,E_dot_D_evap,E_dot_evap_out,E_dot_evap_in)

CALL Expansion(m_dot,t_3s,t_4,h_3s,h_4,R$,W_comp:DELTAE_expa,E_dot_D_expa,E_dot_EV_out,E_dot_EV_in)

CALL EPSILON(DELTAE_sink_cond,DELTAE_source_evap,W_comp,E_dot_D_comp,E_dot_D_cond,E_dot_D_expa

,E_dot_D_evap:epsilon_system,epsilon_system_DL,E_dot_F_tot,E_dot_DL_tot,y_DL_comp,y_DL_cond,y_DL_expa,y_DL_evap

,y|star_DL_comp,y|star_DL_cond,y|star_DL_expa,y|star_DL_evap,y|star_DL_sum)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"----------------------------------------------------------- THERMOECONOMICS ----------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

c_F_elec=(c_F_elec_kWh)/3600 [Øre/kJ]

c_F_gas=(c_q_gas_kWh)/3600 [Øre/kJ]

"! Exergy costing definitions"

CRF=(r_eff*(1+r_eff)^n)/((1+r_eff)^n-1)

r_eff=(1+r)/(1+r_n)-1

"! Investment calculations"

Z_dot=(Z_dot_comp+Z_dot_cond+Z_dot_evap)

"Total annuitized cost rate for all components"

Z_dot_comp=(Z_CI_comp+Z_OM_comp)/(h_op*3600)

Z_dot_cond=(Z_CI_cond+Z_OM_cond)/(h_op*3600)

Z_dot_evap=(Z_CI_evap+Z_OM_evap)/(h_op*3600)

Z_dot_plant=(Z_CI_plant+Z_OM_plant)/(h_op*3600)

"Total annuitized cost rate related to the different components"

Z_CI_comp=CRF*TCI_comp

Z_CI_cond=CRF*TCI_cond

Z_CI_evap=CRF*TCI_evap

Z_CI_plant=CRF*TCI_plant

"Total annuitized cost from capital investment related to the different components"

Z_OM_comp=0.05*Z_CI_comp

Z_OM_cond=0.05*Z_CI_cond

Z_OM_evap=0.05*Z_CI_evap

Z_OM_plant=0.05*Z_CI_plant

"Total annual cost from operation and maintenance related to the different components - given as fraction of capital investment"

TCI_comp=(PEC_comp_R717+PEC_motor)*100

TCI_cond=(PEC_cond+PEC_oil)*100

TCI_evap=PEC_evap*100

"Total capital investment for the different components"

TCI_plant=(TCI_comp+TCI_cond+TCI_evap)*3.16

"Total capital investment for remaining plant"

"!PEC - Purchased Equipment Cost"

"Compressor"

PEC_comp_R717=30645 + 355.719*V_dot_h - 0.0355803*V_dot_h^2

"Motor drive"

PEC_motor=-1388.63 + 648.64*W_comp

"Heat Exchangers"



U_w=2

U_l=5

U_2p=2

U_g=0.6

U_overall_l=(1/U_l+1/U_w)^(-1)

U_overall_2p=(1/U_2p+1/U_w)^(-1)

U_overall_g=(1/U_g+1/U_w)^(-1)

"Heat transfer coefficients to estimate needed heat exchanger area"

PEC_cond=16817 + 1548.17*A_cond

A_cond=Q_dot_cond_l/(U_overall_l*lmtd_sink_l)+Q_dot_cond_2p/(U_overall_2p*lmtd_sink_2p)+Q_dot_cond_g/(U_overall_g

*lmtd_sink_g)

PEC_evap=16817 + 1548.17*A_evap

A_evap=Q_dot_evap_2p/(U_overall_2p*lmtd_source_2p)+Q_dot_evap_g/(U_overall_g*lmtd_source_g)

PEC_oil=2000*A_oil

"! Costing functions"

c_w_comp=c_F_elec

c_e_comp=c_e_cond

c_e_comp*E_dot_comp_out=c_w_comp*W_comp/eta_elec+c_e_evap*E_dot_evap_out+Z_dot_comp+(Z_dot_plant/4)

c_e_cond*E_dot_cond_out+c_q_cond*DELTAE_sink_cond=c_e_comp*E_dot_comp_out+Z_dot_cond+(Z_dot_plant/4)

c_e_EV*E_dot_EV_out=c_e_cond*E_dot_cond_out+(Z_dot_plant/4)

c_e_evap*E_dot_evap_out=c_e_EV*E_dot_EV_out+Z_dot_evap+(Z_dot_plant/4)

c_q_cond_kWh=c_q_cond*3600

"! Project Comparison - NPV & PBP"

A=(TCI_cond+TCI_evap+TCI_comp+TCI_plant)/100

c_heat_HP=c_q_cond*DELTAE_sink_cond*3600/100

c_heat_gas=c_F_gas/eta_gas*Q_dot_heat*3600/100

b=Q_dot_heat/1000*h_op*c_heat_gas

d=(h_op*(W_comp/eta_elec)*c_F_elec_kWh)/100

c=b-d

PBP=(A/c)

File:Exergy_func_R717.LIB 8/30/2010 10:13:26 AM Page 1


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------ Library file - R717 Condensing Vapor Heat Pump------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"! Library file containing subprograms for exergy analysis of R717 HP"

" REF: TDO (Thermal Design and Optimization - Bejan, Tsatsaronis, Moran)"

"!Compressor"

SUBPROGRAM Compressor(massflow,T_in,T_out,h_in,h_out,R$,W_comp:epsilon_comp,E_dot_D_comp,DELTAE_comp

,E_dot_comp_in,E_dot_comp_out)

T_0=ConvertTemp(C,K,20)

"Temperature at dead state: for this application ambient temperature [20C](R744)"

P_0=101.3

"Pressure for reference condition at dead state"

h_0=Enthalpy(R$,T=T_0,P=P_0)

"Enthalpy at dead state conditions"

s_0=Entropy(R$,T=T_0,P=P_0)

"Entropy at dead state conditions"

s_in=Entropy(R$,T=T_in,h=h_in)

"Entropy of working fluid at compressor inlet"

s_out=Entropy(R$,T=T_out,h=h_out)

"Entropy of working fluid at compressor outlet"

E_dot_comp_in=massflow*(h_in-h_0-T_0*(s_in-s_0))

"Exergy flow into compressor [Ref: TDO: eq. (3.13) p. 126+Ex 3.1 p. 127]"

E_dot_comp_out=massflow*(h_out-h_0-T_0*(s_out-s_0))

"Exergy flow out of compressor [Ref: TDO: eq. (3.13) p. 126+Ex 3.1 p. 127]"

DELTAE_comp=(E_dot_comp_out-E_dot_comp_in)

"Change in exergy flow over compressor"

epsilon_comp=(E_dot_comp_out-E_dot_comp_in)/W_comp

"Exergetic efficiency of compressor [Ref: TDO: eq. (3.30) p. 151]"

W_dot_cv=-W_comp

"Time rate of energy transfer by work other than flow work. Negative due to compression work transferred into the control volume

[cf.: Ref: TDO: fig 3.1 p. 118 + eq. (3.10c) p. 124]"

0=-W_dot_cv+E_dot_comp_in-E_dot_comp_out-E_dot_D_comp

"E_dot_D_comp: Exergy destruction from losses and irreversibilities over compression stage [Ref: TDO: eq. 3.11(a+b) p. 125+

eq. 3.28 p. 150]"

END

"!Condenser"

SUBPROGRAM Condenser(massflow,T_in,T_out,h_in,h_out,R$,W_comp,R_sink$,massflow_sink,T_sink_in,T_sink_out

,h_sink_in,h_sink_out:DELTAE_R_cond,epsilon_cond,DELTAE_sink_cond,E_dot_D_cond,E_dot_cond_out,E_dot_cond_in)



P_0=101.3



"Entropy of working fluid at dead state conditions"

s_1=Entropy(R$,T=T_in,h=h_in)

"Entropy of working fluid at Gascooler inlet"

s_2=Entropy(R$,T=T_out,h=h_out)

"Entropy of working fluid at Gascooler outlet"


"Enthalpy of working fluid at dead state conditions"



E_dot_cond_in=massflow*(h_in-h_0-T_0*(s_1-s_0))

"Exergy flow of working fluid into Gascooler [Ref: TDO: eq. (3.13) p. 126+Ex 3.1 p. 127]"

E_dot_cond_out=massflow*(h_out-h_0-T_0*(s_2-s_0))

"Exergy flow of working fluid out of Gascooler [Ref: TDO: eq. (3.13) p. 126+Ex 3.1 p. 127]"

s_sink_0=Entropy(R_sink$,T=T_0,P=P_0)

"Entropy of sink fluid at dead state conditions"

s_sink_in=Entropy(R_sink$,T=T_sink_in,h=h_sink_in)

"Entropy of sink fluid at Gascooler inlet"

s_sink_out=Entropy(R_sink$,T=T_sink_out,h=h_sink_out)

"Entropy of sink fluid at Gascooler outlet"

h_sink_0=Enthalpy(R_sink$,T=T_0,P=P_0)

E_dot_sink_in=massflow_sink*(h_sink_in-h_sink_0-T_0*(s_sink_in-s_sink_0))

"Exergy flow of sink fluid into Gascooler"

E_dot_sink_out=massflow_sink*(h_sink_out-h_sink_0-T_0*(s_sink_out-s_sink_0))

"Exergy flow of sink fluid out of Gascooler"

epsilon_cond=(E_dot_sink_out-E_dot_sink_in)/(E_dot_cond_in-E_dot_cond_out)

"Exergetic efficiency of Gascooler [Ref: TDO: eq. (3.32) p. 153]"

DELTAE_R_cond=E_dot_cond_out-E_dot_cond_in

"Change in exergy of working fluid flow over Gascooler (NB. value changes sign when regarded as fuel input)"

DELTAE_sink_cond=E_dot_sink_out-E_dot_sink_in

"Change in exergy of sink fluid flow over Gascooler"

E_dot_cond_in-E_dot_cond_out=E_dot_sink_out-E_dot_sink_in+E_dot_D_cond

"Rate of exergy destruction/loss over Gascooler [Ref: TDO: eq. (3.11a) p. 125]"

END

"!Evaporator"

SUBPROGRAM Evaporator(massflow,T_in,T_out,h_in,h_out,R$,R_source$,massflow_source,T_source_in,T_source_out

,h_source_in,h_source_out:epsilon_evap,DELTAE_R_evap,DELTAE_source_evap,E_dot_D_evap,E_dot_evap_out

,E_dot_evap_in)



P_0=101.3





"Entropy of working fluid at evaporator inlet"


"Entropy of working fluid at evaporator outlet"



E_dot_evap_in=massflow*(h_in-h_0-T_0*(s_1-s_0))

"Exergy flow of working fluid into evaporator"

E_dot_evap_out=massflow*(h_out-h_0-T_0*(s_2-s_0))

"Exergy flow of working fluid out of evaporator"

s_source_0=Entropy(R_source$,T=T_0,P=P_0)

"Entropy of source fluid at dead state conditions"

s_source_in=Entropy(R_source$,T=T_source_in,h=h_source_in)

"Entropy of source fluid at evaporator inlet"

s_source_out=Entropy(R_source$,T=T_source_out,h=h_source_out)

"Entropy of source fluid at evaporator outlet"



E_dot_source_in=massflow_source*(h_source_in-h_0-T_0*(s_source_in-s_source_0))

"Exergy flow of source fluid into evaporator"

E_dot_source_out=massflow_source*(h_source_out-h_0-T_0*(s_source_out-s_source_0))

"Exergy flow of source fluid out of evaporator"

epsilon_evap=(E_dot_evap_out-E_dot_evap_in)/(E_dot_source_in-E_dot_source_out)

"Exergetic efficiency of evaporator [Ref: TDO: eq. (3.32+3.33) p. 153]. NB. if cycle works in dual mode ie. if T_source_in<T_0 the

change of exergy flow in source fluid counts as a product. The fuel input here is the difference in exergy flow rate of the working

fluid. The Exergy in this case flows in the opposite direction of the heat transfer"

DELTAE_R_evap=E_dot_evap_out-E_dot_evap_in

"Change in exergy of working fluid flow over evaporator (NB. value changes sign when regarded as fuel input)"

DELTAE_source_evap=E_dot_source_out-E_dot_source_in

"Change in exergy of source fluid flow over Gascooler (NB. value changes sign when regarded as product)"

E_dot_D_evap=E_dot_evap_in+E_dot_source_in-E_dot_evap_out-E_dot_source_out

"Rate of exergy destruction/loss over Evaporator [Ref: TDO: eq. (3.11a) p. 125]"

END

"!Expansion"

SUBPROGRAM Expansion(massflow,T_in,T_out,h_in,h_out,R$,W_comp:DELTAE_expa,E_dot_D_expa,E_dot_EV_out

,E_dot_EV_in)



P_0=101.3





"Entropy of working fluid at expansion valve inlet"


"Entropy of working fluid at expansion valve outlet"



E_dot_EV_in=massflow*(h_in-h_0-T_0*(s_1-s_0))

"Exergy flow of working fluid into expansion valve"

E_dot_EV_out=massflow*(h_out-h_0-T_0*(s_2-s_0))

"Exergy flow of working fluid out of expansion valve"

DELTAE_expa=E_dot_EV_out-E_dot_EV_in

"Change in exergy over expansion valve"

E_dot_D_expa=-DELTAE_expa

"Exergy flow out of working fluid over expansion valve"

END

"!Exergetic efficiency of system and ratios for exergy Loss and Destruction"

SUBPROGRAM EPSILON(DELTAE_sink_cond,DELTAE_source_evap,W_comp,E_dot_D_comp,E_dot_D_cond,E_dot_D_expa



epsilon_system=DELTAE_sink_cond/(W_comp+(-DELTAE_source_evap))

"Product vs. Fuel input [electricity for compressor and heat input in evaporator] [Ref: TDO: eq. (3.29) p. 150]"

epsilon_system_DL=1-(E_dot_DL_tot/E_dot_F_tot)

"Same as above, but calculated from Exergy destruction and losses[Ref: TDO: eq. (3.29) p. 150]"

E_dot_F_tot=W_comp-DELTAE_source_evap



"Fuel input for heat pump [Electricity for compressor and heat input in evaporator. Could be expanded to include pumping of

source and sinke media. If the source temperature is lower than ambiant T_0 the heat pump is assumed to function in dual mode

and the heat removed in the evaporator counts as a product instead of a fuel]"

E_dot_DL_tot=E_dot_D_comp+E_dot_D_cond+E_dot_D_expa+E_dot_D_evap

"Total Exergy destruction/loss in the system components "

y_DL_comp=E_dot_D_comp/E_Dot_F_tot

"Exergy destruction/loss ratio in component compared to the rate of exergy provided to the system [Ref: TDO: eq. (3.25) p. 149]"

y_DL_cond=E_dot_D_cond/E_dot_F_tot

"Exergy destruction/loss ratio in component compared to the rate of exergy provided to the system"

y_DL_expa=E_dot_D_expa/E_dot_F_tot


y_DL_evap=E_dot_D_evap/E_dot_F_tot


y|star_DL_comp=E_dot_D_comp/E_dot_DL_tot

"Exergy destruction/loss ratio in component compared to the total exergy destruction/loss in the system [Ref: TDO: eq. (3.26)

p.149]"

y|star_DL_cond=E_dot_D_cond/E_dot_DL_tot

"Exergy destruction/loss ratio in component compared to the total exergy destruction/loss in the system"

y|star_DL_expa=E_dot_D_expa/E_dot_DL_tot


y|star_DL_evap=E_dot_D_evap/E_dot_DL_tot


y|star_DL_sum=y|star_DL_comp+y|star_DL_cond+y|star_DL_expa+y|star_DL_evap

"Sum of exergy destruction/loss ratios. Check to see if value equals 1"

END

File:HEAT_PUMP_R717_2stage.EES 8/30/2010 10:19:45 AM Page 1


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"----------------------------- Heat pump simulation - R717 - 2 Stage Condensing Vapor Heat Pump------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

PROCEDURE isentropiclow(DELTAp_low:eta_is_low)

IF DELTAp_low =< 3.0 THEN

eta_is_low=-0.05+0.55*DELTAp_low-0.09*DELTAp_low^2

ELSE

eta_is_low=0.82-0.01*DELTAp_low

ENDIF

END

PROCEDURE isentropichigh(DELTAp_high:eta_is_high)

IF DELTAp_high =< 3.0 THEN

eta_is_high=-0.05+0.55*DELTAp_high-0.09*DELTAp_high^2

ELSE

eta_is_high=0.82-0.01*DELTAp_high

ENDIF

END

PROCEDURE volumetriclow(DELTAp_low:eta_vol_low)

IF DELTAp_low =< 3 THEN

eta_vol_low=0.91

ELSE

eta_vol_low=0.94-0.01*DELTAp

ENDIF

END

PROCEDURE volumetrichigh(DELTAp_high:eta_vol_high)

IF DELTAp_high =< 3 THEN

eta_vol_high=0.91

ELSE

eta_vol_high=0.94-0.01*DELTAp

ENDIF

END

$INCLUDE HEX_R717_2stage.LIB


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- INPUT DATA ----------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


Q_dot_heat=1000 [kW]

"Heat output"

R$='R717'


PR=0.75

"Pressure ratio between high and low stage"

DELTAT_COND=5


DELTAT_EVAP=5


t_out=90 [C]




t_lift=37.5 [K]

"Temperature lift"

DELTAt_sink=10 [K]




t_superheat=5[k]

"Superheat"



R_sink$='R718'


p_sink=10100 [kPa]

"Pressure on sink medium side: above ambient pressure is to avoid two phase conditions in heat exchanger"

R_source$='R718'


p_source=101 [kPa]


eta_gas=0.8


c_q_gas_kWh=22.05




h_op=2500


eta_elec=0.9


r_n=0.0213

"Inflation rate"

n=15


r=0.07

"Interest rate"

{eta_is_low=0,75

eta_is_high=0,75

eta_vol_low=0,85

eta_vol_high=0,85}

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

CALL isentropiclow(DELTAp_low:eta_is_low)

CALL isentropichigh(DELTAp_high:eta_is_high)


CALL volumetriclow(DELTAp_low:eta_vol_low)

CALL volumetrichigh(DELTAp_high:eta_vol_high)









DELTAP=p_3/p_1

"Pressure ratio"


x_int=(h_int-h_3s)/(h_2_high-h_3s)



x_vapor=1

x_liquid=0


h_3s=h_4


t_subcool=t_3-t_3s


p_3s=p_3


p_4=p_3-(p_3-p_1)*(PR)

x_4=quality(R$,p=p_4,h=h_4)

p_5=p_4

t_4=temperature(R$,p=p_4,h=h_4)

s_4=Entropy(R$,h=h_4,T=t_4)

x_5=0

h_5=enthalpy(R$,x=x_5,p=p_5)

t_5=temperature(R$,x=x_5,p=p_5)



t_1s=t_evap_in-DELTAT_EVAP-DELTAt_source+t_superheat

p_1=p_6

t_1=t_6

h_6=h_5


h_1=Enthalpy(R$,x=x_vapor,t=t_1)

h_1s=Enthalpy(R$,T=t_1s,p=p_1)

s_1s=Entropy(R$,T=t_1s,p=p_1)

p_2_low=p_4

p_2_high=p_3

DELTAp_low=p_2_low/p_1

DELTAp_high=p_2_high/p_2_low

s_1s=s_2_low_s

t_2_low_s=temperature(R$,p=p_2_low,s=s_2_low_s)

h_2_low_s=Enthalpy(R$,p=p_2_low,s=s_2_low_s)



h_2_low=h_1s+(h_2_low_s-h_1s)/(eta_is_low)

t_2_low=temperature(R$,p=p_2_low,h=h_2_low)

s_2_low=Entropy(R$,T=t_2_low,h=h_2_low)

t_2_int=temperature(R$,p=p_2_low,x=x_vapor)

h_2_int=enthalpy(R$,p=p_2_low,x=x_vapor)

s_2_int=entropy(R$,p=p_2_low,x=x_vapor)

s_2_int=s_2_high_s

t_2_high_s=temperature(R$,p=p_2_high,s=s_2_high_s)

h_2_high_s=Enthalpy(R$,p=p_2_high,s=s_2_high_s)

h_2_high=h_2_int+(h_2_high_s-h_2_int)/(eta_is_high)

t_2_high=temperature(r$,p=p_2_high,h=h_2_high)

v_inlet_low=Volume(R$,T=T_1s,P=P_1)

V_dot_low=m_dot_low*v_inlet_low

eta_vol_low=V_dot_low/V_dot_s_low

w_d_low=(h_2_low_s-h_1s)*m_dot_low

epsilon_v_low=w_d_low/V_dot_low

W_comp_low=(eta_vol_low/eta_is_low)*V_dot_s_low*epsilon_v_low


v_inlet_high=Volume(R$,x=x_vapor,P=P_2_low)

V_dot_high=m_dot_high*v_inlet_high

eta_vol_high=V_dot_high/V_dot_s_high

w_d_high=(h_2_high_s-h_2_int)*m_dot_high

epsilon_v_high=w_d_high/V_dot_high

W_comp_high=(eta_vol_high/eta_is_high)*V_dot_s_high*epsilon_v_high


V_dot_h_low=V_dot_s_low*3600

V_dot_h_high=V_dot_s_high*3600

W_comp=W_comp_low+W_comp_high

COP=Q_dot_heat/(W_comp_low+W_comp_high)

Q_dot_heat=(h_2_high-h_3s)*m_dot_high

Q_dot_cool=(h_1s-h_6)*m_dot_low

h_5*m_dot_low=((h_2_low*m_dot_low)-(h_2_int*m_dot_high)+(h_4*m_dot_high))

rho_1s=density(R$,h=h_1s,p=p_1)

rho_2low=density(R$,h=h_2_low,p=p_2_low)

rho_2int=density(R$,h=h_2_int,p=p_2_low)

rho_2high=density(R$,h=h_2_high,p=p_2_high)

rho_3s=density(R$,h=h_3s,p=p_3)

rho_4=density(R$,h=h_4,p=p_4)



"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- HEAT TRANSFER ---------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


point assumptions"



t_evap_g=t_evap_out+(t_evap_in-t_evap_out)*((h_1-h_6)/(h_1s-h_6))

t_cond_2p=t_cond_in+(t_cond_out-t_cond_in)*((h_3-h_3s)/(h_2_high-h_3s))

t_cond_g=t_cond_in+(t_cond_out-t_cond_in)*((h_int-h_3)/(h_2_high-h_3s))


Q_dot_cond_2p=m_dot_high*(h_int-h_3)

Q_dot_cond_g=m_dot_high*(h_2_high-h_int)


Q_dot_evap_g=m_dot_low*(h_1s-h_1)

p_6=p_low

p_2_high=p_high



CALL EVAP_R717(R$,h_1s,h_6,t_6,p_1:t_evap_R717[1..51],x_evap_R717[1..51],h_evap_R717[1..51])

CALL cond_R717(R$,h_2_high,h_3s,t_3s,p_2_high:t_cond_R717[1..51],x_cond_R717[1..51],h_cond_R717[1..51])





CALL lmtdsource2(R$, t_evap_g, t_evap_in, h_1, h_1s, p_low: lmtd_source_g)



CALL lmtdsink3(R$, t_cond_g, t_cond_out, h_int, h_2_high, p_high: lmtd_sink_g)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------ EXERGY ANALYSIS ------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

CALL Compressor_low(m_dot_low,t_1s,t_2_low,h_1s,h_2_low,R$,W_comp_low:epsilon_comp_low,E_dot_D_comp_low

,DELTAE_comp_low,E_dot_comp_low_in,E_dot_comp_low_out)

CALL Compressor_high(m_dot_high,t_2_int,t_2_high,h_2_int,h_2_high,R$,W_comp_high:epsilon_comp_high

,E_dot_D_comp_high,DELTAE_comp_high,E_dot_comp_high_in,E_dot_comp_high_out)

CALL Condenser(m_dot_high,t_cond_R717[1],t_cond_R717[51],h_cond_R717[1],h_cond_R717[51],R$,W_comp,R_sink$

,m_dot_cond,t_cond_R718[51],t_cond_R718[1],h_cond_R718[51],h_cond_R718[1]:DELTAE_R_cond,epsilon_cond

,DELTAE_sink_cond,E_dot_D_cond,E_dot_cond_in,E_dot_cond_out)

Call Expansion_high(m_dot_high,t_3s,t_4,h_3s,h_4,R$,W_comp_high:DELTAE_expa_high,E_dot_D_expa_high

,E_dot_EVhigh_in,E_dot_EVhigh_out)

CALL Internal_HEX(m_dot_low,t_2_low,t_2_int,h_2_low,h_2_int,s_2_low,s_2_int,m_dot_high,t_4,t_5,h_4,h_5,s_4,s_5

,R$:DELTAE_hot_HEX,DELTAE_cold_HEX,E_dot_D_HEX,E_dot_cold_in,E_dot_cold_out,E_dot_hot_in,E_dot_hot_out)

CALL Expansion_low(m_dot_low,t_5,t_6,h_5,h_6,R$,W_comp_low:DELTAE_expa_low,E_dot_D_expa_low,E_dot_EVlow_in

,E_dot_EVlow_out)

CALL Evaporator(m_dot_low,t_evap_R717[51],t_evap_R717[1],h_evap_R717[51],h_evap_R717[1],R$,R_source$

,m_dot_evap_R718,t_evap_R718[1],t_evap_R718[51],h_evap_R718[1],h_evap_R718[51]:epsilon_evap,DELTAE_R_evap

,DELTAE_source_evap,E_dot_D_evap,E_dot_evap_in,E_dot_evap_out)

CALL Exergy(W_comp,DELTAE_sink_cond,DELTAE_source_evap,E_dot_D_comp_low,E_dot_D_comp_high,E_dot_D_cond

,E_dot_D_expa_high,E_dot_D_HEX,E_dot_D_expa_low,E_dot_D_evap:epsilon_system,epsilon_system_DL,E_dot_F_tot

,E_dot_DL_tot,y_DL_comp_low,y_DL_comp_high,y_DL_cond,y_DL_expa_high,y_DL_HEX,y_DL_expa_low,y_DL_evap

,y|star_DL_comp_low,y|star_DL_comp_high,y|star_DL_cond,y|star_DL_expa_low,y|star_DL_expa_high,y|star_DL_evap



,y|star_DL_HEX,y|star_DL_sum)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"





r_eff=(1+r)/(1+r_n)-1


Z_dot=(Z_dot_comp_low+Z_dot_comp_high+Z_dot_cond+Z_dot_evap)


Z_dot_comp_low=(Z_CI_comp_low+Z_OM_comp_low)/(h_op*3600)

Z_dot_comp_high=(Z_CI_comp_high+Z_OM_comp_high)/(h_op*3600)





Z_CI_comp_low=CRF*TCI_comp_low

Z_CI_comp_high=CRF*TCI_comp_high





Z_OM_comp_low=0.05*Z_CI_comp_low

Z_OM_comp_high=0.05*Z_CI_comp_high





TCI_comp_low=(PEC_comp_low+PEC_motor_low)*100

TCI_comp_high=(PEC_comp_high+PEC_motor_high)*100

TCI_cond=(PEC_cond)*100



TCI_plant=(TCI_comp_low+TCI_comp_high+TCI_cond+TCI_evap)*3.16


"! PEC - Purchased Equipment Cost"

"Compressor"

PEC_comp_low=30645 + 355.719*V_dot_h_low - 0.0355803*V_dot_h_low^2

PEC_comp_high=30645 + 355.719*V_dot_h_high - 0.0355803*V_dot_h_high^2

"Elec, Motor"

PEC_motor_low=-1388.63 + 648.64*W_comp_low

PEC_motor_high=-1388.63 + 648.64*W_comp_high

"Heat Exchangers"

U_w=2



U_l=5

U_2p=2

U_g=0.6





PEC_cond=16817 + 1548.17*A_cond


*lmtd_sink_g)

PEC_evap=16817 + 1548.17*A_evap



c_w_comp=c_F_elec

c_e_comp_high=c_e_cond

c_e_EVhigh=c_e_intHEX_low

c_e_cond*E_dot_cond_out+c_q_cond*DELTAE_sink_cond=c_e_comp_high*E_dot_comp_high_out+Z_dot_cond+(Z_dot_plant/7

)

c_e_comp_high*E_dot_comp_high_out=c_e_intHEX_high*E_dot_comp_high_in+c_w_comp*W_comp_high+Z_dot_comp_high

+(Z_dot_plant/7)

c_e_intHEX_high*E_dot_comp_high_in+c_e_intHEX_low*E_dot_EVlow_in=c_e_EVhigh*E_dot_EVhigh_out+c_e_comp_low

*E_dot_comp_low_out+(Z_dot_plant/7)

c_e_EVhigh*E_dot_EVhigh_out=c_e_cond*E_dot_cond_out+(Z_dot_plant/7)

c_e_comp_low*E_dot_comp_low_out=c_w_comp*W_comp_low+c_e_evap*E_dot_evap_out+Z_dot_comp_low+(Z_dot_plant/7)

c_e_evap*E_dot_evap_out=c_e_EVlow*E_dot_EVlow_out+Z_dot_evap+(Z_dot_plant/7)

c_e_EVlow*E_dot_EVlow_out=c_e_intHEX_low*E_dot_EVlow_in+(Z_dot_plant/7)



A=(TCI_comp_low+TCI_comp_high+TCI_evap+TCI_cond+TCI_plant)/100




d=(h_op*((W_comp_low+W_comp_high)/eta_elec)*c_F_elec_kWh)/100

c=b-d

PBP=(A/c)



"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"----------------------------- Library file - R717 - 2 Stage Condensing Vapor Heat Pump------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"! Library file containing subprograms for exergy analysis of R717 - 2 stage HP"


"!Compressor 1st stage"

SUBPROGRAM Compressor_low(massflow,T_in,T_out,h_in,h_out,R$,W_comp_low:epsilon_comp_low,E_dot_D_comp_low



"Temperature at dead state: for this application ambient temperature [20C]"

P_0=101.3










E_dot_comp_low_in=massflow*(h_in-h_0-T_0*(s_in-s_0))


E_dot_comp_low_out=massflow*(h_out-h_0-T_0*(s_out-s_0))


DELTAE_comp_low=(E_dot_comp_low_out-E_dot_comp_low_in)


epsilon_comp_low=(E_dot_comp_low_out-E_dot_comp_low_in)/W_comp_low


W_dot_cv=-W_comp_low



0=-W_dot_cv+E_dot_comp_low_in-E_dot_comp_low_out-E_dot_D_comp_low


eq. 3.28 p. 150]"

END

"!Compressor 2nd stage"

SUBPROGRAM Compressor_high(massflow,T_in,T_out,h_in,h_out,R$,W_comp_high:epsilon_comp_high,E_dot_D_comp_high

,DELTAE_comp_high,E_dot_comp_high_in,E_dot_comp_high_out)



P_0=101.3












E_dot_comp_high_in=massflow*(h_in-h_0-T_0*(s_in-s_0))


E_dot_comp_high_out=massflow*(h_out-h_0-T_0*(s_out-s_0))


DELTAE_comp_high=(E_dot_comp_high_out-E_dot_comp_high_in)


epsilon_comp_high=(E_dot_comp_high_out-E_dot_comp_high_in)/W_comp_high


W_dot_cv=-W_comp_high



0=-W_dot_cv+E_dot_comp_high_in-E_dot_comp_high_out-E_dot_D_comp_high


eq. 3.28 p. 150]"

END

"!Condenser"


,h_sink_in,h_sink_out:DELTAE_R_cond,epsilon_cond,DELTAE_sink_cond,E_dot_D_cond,E_dot_cond_in,E_dot_cond_out)



P_0=101.3





"Entropy of working fluid at condenser inlet"


"Entropy of working fluid at condenser outlet"




"Exergy flow of working fluid into condenser [Ref: TDO: eq. (3.13) p. 126+Ex 3.1 p. 127]"


"Exergy flow of working fluid out of condenser [Ref: TDO: eq. (3.13) p. 126+Ex 3.1 p. 127]"




"Entropy of sink fluid at condenser inlet"


"Entropy of sink fluid at condenser outlet"


"Enthalpy of sink fluid at dead state conditions"


"Exergy flow of sink fluid into condenser"


"Exergy flow of sink fluid out of condenser"


"Exergetic efficiency of condenser [Ref: TDO: eq. (3.32) p. 153]"


"Change in exergy of working fluid flow over condenser (NB. value changes sign when regarded as fuel input)"




"Change in exergy of sink fluid flow over condenser"


"Rate of exergy destruction/loss over condenser [Ref: TDO: eq. (3.11a) p. 125]"

END

"!Expansion"

SUBPROGRAM Expansion_high(massflow,T_in,T_out,h_in,h_out,R$,W_comp:DELTAE_expa_high,E_dot_D_expa_high




P_0=101.3










E_dot_EVhigh_in=massflow*(h_in-h_0-T_0*(s_1-s_0))


E_dot_EVhigh_out=massflow*(h_out-h_0-T_0*(s_2-s_0))


DELTAE_expa_high=E_dot_EVhigh_out-E_dot_EVhigh_in


E_dot_D_expa_high=-DELTAE_expa_high


END

"!Internal HEX"

SUBPROGRAM Internal_HEX(m_dot_hot,t_hot_in,t_hot_out,h_hot_in,h_hot_out,s_hot_in,s_hot_out,m_dot_cold,t_cold_in

,t_cold_out,h_cold_in,h_cold_out,s_cold_in,s_cold_out,R$:DELTAE_hot_HEX,DELTAE_cold_HEX,E_dot_D_HEX,E_dot_cold_in

,E_dot_cold_out,E_dot_hot_in,E_dot_hot_out)



P_0=1




E_dot_cold_in=m_dot_cold*(h_cold_in-h_0-T_0*(s_cold_in-s_0))

"Exergy flow of working fluid into internal heat exchanger"

E_dot_cold_out=m_dot_hot*(h_cold_out-h_0-T_0*(s_cold_out-s_0))

"Exergy flow of working fluid out of internal heat exchanger"

E_dot_hot_in=m_dot_hot*(h_hot_in-h_0-T_0*(s_hot_in-s_0))

"Exergy flow of hot fluid into internal heat exchanger"

E_dot_hot_out=m_dot_cold*(h_hot_out-h_0-T_0*(s_hot_out-s_0))

"Exergy flow of hot fluid out of internal heat exchanger"



DELTAE_hot_HEX=E_dot_hot_out-E_dot_hot_in

"Change in exergy of working fluid flow over internal heat exchanger"

DELTAE_cold_HEX=E_dot_cold_in-E_dot_hot_out

"Change in exergy of hot fluid flow over internal heat exchanger "

E_dot_D_HEX=E_dot_cold_in+E_dot_hot_in-E_dot_cold_out-E_dot_hot_out

"Rate of exergy destruction/loss over internal heat exchanger [Ref: TDO: eq. (3.11a) p. 125]"

END

"!Expansion"

SUBPROGRAM Expansion_low(massflow,T_in,T_out,h_in,h_out,R$,W_comp:DELTAE_expa_low,E_dot_D_expa_low

,E_dot_EVlow_in,E_dot_EVlow_out)



P_0=101.3










E_dot_EVlow_in=massflow*(h_in-h_0-T_0*(s_1-s_0))


E_dot_EVlow_out=massflow*(h_out-h_0-T_0*(s_2-s_0))


DELTAE_expa_low=E_dot_EVlow_out-E_dot_EVlow_in


E_dot_D_expa_low=-DELTAE_expa_low


END

"!Evaporator"


,h_source_in,h_source_out:epsilon_evap,DELTAE_R_evap,DELTAE_source_evap,E_dot_D_evap,E_dot_evap_in

,E_dot_evap_out)



P_0=101.3




































END


SUBPROGRAM Exergy(W_comp,DELTAE_sink_cond,DELTAE_source_evap,E_dot_D_comp_low,E_dot_D_comp_high

,E_dot_D_cond,E_dot_D_expa_high,E_dot_D_HEX,E_dot_D_expa_low,E_dot_D_evap:epsilon_system,epsilon_system_DL

,E_dot_F_tot,E_dot_DL_tot,y_DL_comp_low,y_DL_comp_high,y_DL_cond,y_DL_expa_high,y_DL_HEX,y_DL_expa_low

,y_DL_evap,y|star_DL_comp_low,y|star_DL_comp_high,y|star_DL_cond,y|star_DL_expa_low,y|star_DL_expa_high

,y|star_DL_evap,y|star_DL_HEX,y|star_DL_sum)









E_dot_DL_tot=E_dot_D_comp_low+E_dot_D_comp_high+E_dot_D_cond+E_dot_D_expa_low+E_dot_D_expa_high

+E_dot_D_evap+E_dot_D_HEX

"Total Exergy destruction/loss in the system components"

y_DL_comp_high=E_dot_D_comp_high/E_dot_F_tot


y_DL_comp_low=E_dot_D_comp_low/E_dot_F_tot



y_DL_expa_high=E_dot_D_expa_high/E_dot_F_tot


y_DL_expa_low=E_dot_D_expa_low/E_dot_F_tot



y_DL_HEX=E_dot_D_HEX/E_dot_F_tot



y|star_DL_comp_high=E_dot_D_comp_high/E_dot_DL_tot


p.149]"

y|star_DL_comp_low=E_dot_D_comp_low/E_dot_DL_tot



y|star_DL_expa_high=E_dot_D_expa_high/E_dot_DL_tot


y|star_DL_expa_low=E_dot_D_expa_low/E_dot_DL_tot



y|star_DL_HEX=E_dot_D_HEX/E_dot_DL_tot

y|star_DL_sum=y|star_DL_comp_high+y|star_DL_comp_low+y|star_DL_cond+y|star_DL_expa_high+y|star_DL_evap

+y|star_DL_expa_low+y|star_DL_HEX


END



"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"----------------------------- Heat pump simulation - R718 Condensing Vapor Heat Pump------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"






ELSE


ENDIF

END

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- INPUT DATA ----------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"



"Heat output"

R$='R718'


DELTAT_EVAP=5 [K]


DELTAT_COND=5 [K]


t_out=150 [C]


t_lift=40 [K]

"Temperature lift"

DELTAt_sink=10 [K]


DELTAt_source=5 [K]


t_superheat=0 [k]

"Superheat"



R_sink$='R718'


p_sink=10100 [kPa]


R_source$='R718'


p_source=10100 [kPa]


eta_gas=0.8


c_q_gas_kWh=22.05




h_op=2500




eta_elec=0.9


r_n=0.0213

"Inflation rate"

n=15


r=0.07

"Interest rate"

{eta_is=0,75}

CALL isentropic(DELTAp:eta_is)


eta_vol=0.81

"Constant volumetric efficiency"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"







x_int=(h_int-h_3s)/(h_2-h_3s)



DELTAp=p_3/p_1

"Pressure ratio"

x_vapor=1

x_liquid=0


h_3s=h_4


t_subcool=t_3-t_3s


p_3s=p_3


x_4=quality(R$,T=t_4,h=h_4)


p_1=p_4

t_1=t_4


h_1=Enthalpy(R$,x=x_vapor,p=p_1)



s_1=Entropy(R$,x=x_vapor,p=p_1)

p_2=p_3

s_1=s_2is

t_2is=temperature(R$,p=p_2,s=s_2is)

h_2is=Enthalpy(R$,p=p_2,s=s_2is)

h_2=h_1+(h_2is-h_1)/(eta_is)

t_2=temperature(r$,p=p_2,h=h_2)

Q_dot_heat=(h_2-h_3s)*m_dot

v_inlet=Volume(R$,x=x_vapor,P=P_1)

V_dot_1=m_dot*v_inlet


W_d=(h_2is-h_1)*m_dot

epsilon_v=W_d/V_dot_1

W_comp=(eta_vol/eta_is)*V_dot_s*epsilon_v


COP=Q_dot_heat/W_comp

Q_dot_cool=(h_1-h_4)*m_dot

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- HEAT TRANSFER ---------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


point assumptions"



CALL EVAP_R(R$,h_1,h_4,t_4,p_1:t_evap_R[1..51],x_evap_R[1..51],h_evap_R[1..51])

CALL cond_R(R$,h_2,h_3s,t_3s,p_2:t_cond_R[1..51],x_cond_R[1..51],h_cond_R[1..51])




Q_dot_cond_2p=m_dot*(h_int-h_3)

Q_dot_cond_g=m_dot*(h_2-h_int)

Q_dot_cool=q_dot_evap_2p

t_cond_2p=t_cond_in+(t_cond_out-t_cond_in)*((h_3-h_3s)/(h_2-h_3s))

t_cond_g=t_cond_in+(t_cond_out-t_cond_in)*((h_int-h_3)/(h_2-h_3s))

p_4=p_low

p_2=p_high


CALL lmtdsource1(R$, t_evap_out, t_evap_in, h_4, h_1, p_low: lmtd_source_2p)



CALL lmtdsink3(R$, t_cond_g, t_cond_out, h_int, h_2, p_high: lmtd_sink_g)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------ EXERGY ANALYSIS ------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"



CALL Compressor(m_dot,t_1,t_2,h_1,h_2,R$,W_comp:epsilon_comp,E_dot_D_comp,DELTAE_comp,E_dot_comp_in

,E_dot_comp_out)

CALL Condenser(m_dot,t_cond_R[1],t_cond_R[51],h_cond_R[1],h_cond_R[51],R$,W_comp,R_sink$,m_dot_cond


,E_dot_D_cond,E_dot_cond_out,E_dot_cond_in)

CALL Evaporator(m_dot,t_evap_R[51],t_evap_R[1],h_evap_R[51],h_evap_R[1],R$,R_source$,m_dot_evap_R718,t_evap_R718[1

],t_evap_R718[51],h_evap_R718[1],h_evap_R718[51]:epsilon_evap,DELTAE_R_evap,DELTAE_source_evap,E_dot_D_evap

,E_dot_evap_out,E_dot_evap_in)

CALL Expansion(m_dot,t_3s,t_4,h_3s,h_4,R$,W_comp:DELTAE_expa,E_dot_D_expa,E_dot_EV_out,E_dot_EV_in)




"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"





r_eff=(1+r)/(1+r_n)-1



















TCI_comp=(PEC_comp_R717+PEC_motor)*100









"Compressor"

PEC_comp_R717=30645 + 355.719*V_dot_h - 0.0355803*V_dot_h^2

"Motor drive"

PEC_motor=-1388.63 + 648.64*W_comp

"Heat Exchangers"

U_w=2

U_l=5

U_2p=2

U_g=0.6





PEC_cond=16817 + 1548.17*A_cond


*lmtd_sink_g)

PEC_evap=16817 + 1548.17*A_evap

A_evap=Q_dot_evap_2p/(U_overall_2p*lmtd_source_2p)


c_w_comp=c_F_elec

c_e_comp=c_e_cond












c=b-d

PBP=(A/c)



"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------ Library file - R718 Condensing Vapor Heat Pump-------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"! Library file containing subprograms for exergy analysis of R718 HP"


"!Compressor"





P_0=101.3


















W_dot_cv=-W_comp





eq. 3.28 p. 150]"

END

"!Condenser"


,h_sink_in,h_sink_out:DELTAE_R_cond,epsilon_cond,DELTAE_sink_cond,E_dot_D_cond,E_dot_cond_out,E_dot_cond_in)



P_0=101.3



































END

"!Evaporator"


,h_source_in,h_source_out:epsilon_evap,DELTAE_R_evap,DELTAE_source_evap,E_dot_D_evap,E_dot_evap_out

,E_dot_evap_in)



P_0=101.3




































END

"!Expansion"

SUBPROGRAM Expansion(massflow,T_in,T_out,h_in,h_out,R$,W_comp:DELTAE_expa,E_dot_D_expa,E_dot_EV_out

,E_dot_EV_in)



P_0=101.3


















END



























p.149]"









END



"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"----------------------------- Heat pump simulation - R718 - 2 Stage Condensing Vapor Heat Pump------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

PROCEDURE isentropiclow(DELTAp_low:eta_is_low)

IF DELTAp_low =< 2.5 THEN

eta_is_low=-0.39+0.96*DELTAp_low-0.20*DELTAp_low^2

ELSE

eta_is_low=0.79-0.01*DELTAp_low

ENDIF

END

PROCEDURE isentropichigh(DELTAp_high:eta_is_high)

IF DELTAp_high =< 2.5 THEN

eta_is_high=-0.39+0.96*DELTAp_high-0.20*DELTAp_high^2

ELSE

eta_is_high=0.79-0.01*DELTAp_high

ENDIF

END

$INCLUDE HEX_R718_2stage.LIB


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- INPUT DATA ----------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"



"Heat output"

R$='R718'


PR=0.7

"Pressure ratio between high and low stage"

DELTAT_COND=5


DELTAT_EVAP=5


t_out=150 [C]


t_lift=30 [K]

"Temperature lift"

DELTAt_sink=10 [K]




{t_superheat=5 [K]}

R_sink$='R718'


p_sink=10100 [kPa]

"Pressure on sink medium side: above ambient pressure is to avoid two phase conditions in heat exchanger"

R_source$='R718'


p_source=202 [kPa]

"Pressure on source medium side: above ambient pressure is to avoid two phase conditions in heat exchanger"



eta_gas=0.8


c_q_gas_kWh=22.05




h_op=2500


eta_elec=0.9


r_n=0.0213

"Inflation rate"

n=15


r=0.07

"Interest rate"

{eta_is_low=0,75

eta_is_high=0,75}

eta_vol=0.85

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

CALL isentropiclow(DELTAp_low:eta_is_low)

CALL isentropichigh(DELTAp_high:eta_is_high)









DELTAP=p_3/p_1

"Pressure ratio"


x_int=(h_int-h_3s)/(h_2_high-h_3s)



x_vapor=1

x_liquid=0


h_3s=h_4


t_subcool=t_3-t_3s


p_3s=p_3




p_4=p_3-(p_3-p_1)*(PR)

x_4=quality(R$,p=p_4,h=h_4)

p_5=p_4



x_5=0

h_5=enthalpy(R$,x=x_5,p=p_5)

t_5=temperature(R$,x=x_5,p=p_5)



t_1s=t_evap_in-DELTAT_EVAP-DELTAt_source

p_1=p_6

t_1=t_6

h_6=h_5


h_1=Enthalpy(R$,x=x_vapor,t=t_1)

h_1s=Enthalpy(R$,x=x_vapor,p=p_1)

s_1s=Entropy(R$,x=x_vapor,p=p_1)

p_2_low=p_4

p_2_high=p_3

DELTAp_low=p_2_low/p_1

DELTAp_high=p_2_high/p_2_low

s_1s=s_2_low_s

t_2_low_s=temperature(R$,p=p_2_low,s=s_2_low_s)

h_2_low_s=Enthalpy(R$,p=p_2_low,s=s_2_low_s)

h_2_low=h_1s+(h_2_low_s-h_1s)/(eta_is_low)

t_2_low=temperature(R$,p=p_2_low,h=h_2_low)

s_2_low=Entropy(R$,T=t_2_low,h=h_2_low)

t_2_int=temperature(R$,p=p_2_low,x=x_vapor)

h_2_int=enthalpy(R$,p=p_2_low,x=x_vapor)

s_2_int=entropy(R$,p=p_2_low,x=x_vapor)

s_2_int=s_2_high_s

t_2_high_s=temperature(R$,p=p_2_high,s=s_2_high_s)

h_2_high_s=Enthalpy(R$,p=p_2_high,s=s_2_high_s)

h_2_high=h_2_int+(h_2_high_s-h_2_int)/(eta_is_high)

t_2_high=temperature(r$,p=p_2_high,h=h_2_high)

v_inlet_low=Volume(R$,x=x_vapor,P=P_1)

V_dot_low=m_dot_low*v_inlet_low

eta_vol=V_dot_low/V_dot_s_low

w_d_low=(h_2_low_s-h_1s)*m_dot_low

epsilon_v_low=w_d_low/V_dot_low

W_comp_low=(eta_vol/eta_is_low)*V_dot_s_low*epsilon_v_low


v_inlet_high=Volume(R$,x=x_vapor,P=P_2_low)

V_dot_high=m_dot_high*v_inlet_high

eta_vol=V_dot_high/V_dot_s_high

w_d_high=(h_2_high_s-h_2_int)*m_dot_high



epsilon_v_high=w_d_high/V_dot_high

W_comp_high=(eta_vol/eta_is_high)*V_dot_s_high*epsilon_v_high


W_comp=W_comp_low+W_comp_high

V_dot_h_low=V_dot_s_low*3600

V_dot_h_high=V_dot_s_high*3600

V_dot=V_dot_h_high+V_dot_h_low

COP=Q_dot_heat/(W_comp_low+W_comp_high)

Q_dot_heat=(h_2_high-h_3s)*m_dot_high

Q_dot_cool=(h_1s-h_6)*m_dot_low

h_5*m_dot_low=((h_2_low*m_dot_low)-(h_2_int*m_dot_high)+(h_4*m_dot_high))

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- HEAT TRANSFER ---------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


point assumptions"

t_cond_2p=t_cond_in+(t_cond_out-t_cond_in)*((h_3-h_3s)/(h_2_high-h_3s))

t_cond_g=t_cond_in+(t_cond_out-t_cond_in)*((h_int-h_3)/(h_2_high-h_3s))


Q_dot_cond_2p=m_dot_high*(h_int-h_3)

Q_dot_cond_g=m_dot_high*(h_2_high-h_int)

Q_dot_cool=Q_dot_evap_2p

p_6=p_low

p_2_high=p_high



CALL EVAP_R(R$,h_1s,h_6,t_6,p_1:t_evap_R[1..51],x_evap_R[1..51],h_evap_R[1..51])

CALL cond_R(R$,h_2_high,h_3s,t_3s,p_2_high:t_cond_R[1..51],x_cond_R[1..51],h_cond_R[1..51])




CALL lmtdsource1(R$, t_evap_out, t_evap_in, h_4, h_1, p_low: lmtd_source_2p)



CALL lmtdsink3(R$, t_cond_g, t_cond_out, h_int, h_2_high, p_high: lmtd_sink_g)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------ EXERGY ANALYSIS ------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

CALL Compressor_low(m_dot_low,t_1s,t_2_low,h_1s,h_2_low,R$,W_comp_low:epsilon_comp_low,E_dot_D_comp_low


CALL Compressor_high(m_dot_high,t_2_int,t_2_high,h_2_int,h_2_high,R$,W_comp_high:epsilon_comp_high

,E_dot_D_comp_high,DELTAE_comp_high,E_dot_comp_high_in,E_dot_comp_high_out)



CALL Condenser(m_dot_high,t_cond_R[1],t_cond_R[51],h_cond_R[1],h_cond_R[51],R$,W_comp,R_sink$,m_dot_cond


,E_dot_D_cond,E_dot_cond_in,E_dot_cond_out)

Call Expansion_high(m_dot_high,t_3s,t_4,h_3s,h_4,R$,W_comp_high:DELTAE_expa_high,E_dot_D_expa_high


CALL Internal_HEX(m_dot_low,t_2_low,t_2_int,h_2_low,h_2_int,s_2_low,s_2_int,m_dot_high,t_4,t_5,h_4,h_5,s_4,s_5

,R$:DELTAE_hot_HEX,DELTAE_cold_HEX,E_dot_D_HEX,E_dot_cold_in,E_dot_cold_out,E_dot_hot_in,E_dot_hot_out)

CALL Expansion_low(m_dot_low,t_5,t_6,h_5,h_6,R$,W_comp_low:DELTAE_expa_low,E_dot_D_expa_low,E_dot_EVlow_in

,E_dot_EVlow_out)

CALL Evaporator(m_dot_low,t_evap_R[51],t_evap_R[1],h_evap_R[51],h_evap_R[1],R$,R_source$,m_dot_evap_R718


,E_dot_D_evap,E_dot_evap_in,E_dot_evap_out)

CALL Exergy(W_comp,DELTAE_sink_cond,DELTAE_source_evap,E_dot_D_comp_low,E_dot_D_comp_high,E_dot_D_cond

,E_dot_D_expa_high,E_dot_D_HEX,E_dot_D_expa_low,E_dot_D_evap:epsilon_system,epsilon_system_DL,E_dot_F_tot

,E_dot_DL_tot,y_DL_comp_low,y_DL_comp_high,y_DL_cond,y_DL_expa_high,y_DL_HEX,y_DL_expa_low,y_DL_evap

,y|star_DL_comp_low,y|star_DL_comp_high,y|star_DL_cond,y|star_DL_expa_low,y|star_DL_expa_high,y|star_DL_evap

,y|star_DL_HEX,y|star_DL_sum)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"





r_eff=(1+r)/(1+r_n)-1


Z_dot=(Z_dot_comp_low+Z_dot_comp_high+Z_dot_cond+Z_dot_evap)


Z_dot_comp_low=(Z_CI_comp_low+Z_OM_comp_low)/(h_op*3600)

Z_dot_comp_high=(Z_CI_comp_high+Z_OM_comp_high)/(h_op*3600)





Z_CI_comp_low=CRF*TCI_comp_low

Z_CI_comp_high=CRF*TCI_comp_high





Z_OM_comp_low=0.05*Z_CI_comp_low

Z_OM_comp_high=0.05*Z_CI_comp_high







TCI_comp_low=(PEC_comp_low+PEC_motor_low)*100

TCI_comp_high=(PEC_comp_high+PEC_motor_high)*100




TCI_plant=(TCI_comp_low+TCI_comp_high+TCI_cond+TCI_evap)*3.16



"Compressor"

PEC_comp_low=30645 + 355.719*V_dot_h_low - 0.0355803*V_dot_h_low^2

PEC_comp_high=30645 + 355.719*V_dot_h_high - 0.0355803*V_dot_h_high^2

"Elec, Motor"

PEC_motor_low=-1388.63 + 648.64*W_comp_low

PEC_motor_high=-1388.63 + 648.64*W_comp_high

"Heat Exchangers"

U_w=2

U_l=5

U_2p=2

U_g=0.6





PEC_cond=16817 + 1548.17*A_cond


*lmtd_sink_g)

PEC_evap=16817 + 1548.17*A_evap

A_evap=Q_dot_evap_2p/(U_overall_2p*lmtd_source_2p)


c_w_comp=c_F_elec

c_e_comp_high=c_e_cond

c_e_EVhigh=c_e_intHEX_low

c_e_cond*E_dot_cond_out+c_q_cond*DELTAE_sink_cond=c_e_comp_high*E_dot_comp_high_out+Z_dot_cond+(Z_dot_plant/7

)

c_e_comp_high*E_dot_comp_high_out=c_e_intHEX_high*E_dot_comp_high_in+c_w_comp*W_comp_high+Z_dot_comp_high

+(Z_dot_plant/7)

c_e_intHEX_high*E_dot_comp_high_in+c_e_intHEX_low*E_dot_EVlow_in=c_e_EVhigh*E_dot_EVhigh_out+c_e_comp_low

*E_dot_comp_low_out+(Z_dot_plant/7)

c_e_EVhigh*E_dot_EVhigh_out=c_e_cond*E_dot_cond_out+(Z_dot_plant/7)

c_e_comp_low*E_dot_comp_low_out=c_w_comp*W_comp_low+c_e_evap*E_dot_evap_out+Z_dot_comp_low+(Z_dot_plant/7)

c_e_evap*E_dot_evap_out=c_e_EVlow*E_dot_EVlow_out+Z_dot_evap+(Z_dot_plant/7)

c_e_EVlow*E_dot_EVlow_out=c_e_intHEX_low*E_dot_EVlow_in+(Z_dot_plant/7)



A=(TCI_comp_low+TCI_comp_high+TCI_evap+TCI_cond+TCI_plant)/100






d=(h_op*((W_comp_low+W_comp_high)/eta_elec)*c_F_elec_kWh)/100

c=b-d

PBP=(A/c)



"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"--------------------------------- Library file - R718 - 2 Stage Condensing Vapor Heat Pump------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"! Library file containing subprograms for exergy analysis of R718 - 2 stage HP"


"!Compressor 1st stage"

SUBPROGRAM Compressor_low(massflow,T_in,T_out,h_in,h_out,R$,W_comp_low:epsilon_comp_low,E_dot_D_comp_low




P_0=101.3










E_dot_comp_low_in=massflow*(h_in-h_0-T_0*(s_in-s_0))


E_dot_comp_low_out=massflow*(h_out-h_0-T_0*(s_out-s_0))


DELTAE_comp_low=(E_dot_comp_low_out-E_dot_comp_low_in)


epsilon_comp_low=(E_dot_comp_low_out-E_dot_comp_low_in)/W_comp_low


W_dot_cv=-W_comp_low



0=-W_dot_cv+E_dot_comp_low_in-E_dot_comp_low_out-E_dot_D_comp_low


eq. 3.28 p. 150]"

END

"!Compressor 2nd stage"

SUBPROGRAM Compressor_high(massflow,T_in,T_out,h_in,h_out,R$,W_comp_high:epsilon_comp_high,E_dot_D_comp_high

,DELTAE_comp_high,E_dot_comp_high_in,E_dot_comp_high_out)



P_0=101.3










E_dot_comp_high_in=massflow*(h_in-h_0-T_0*(s_in-s_0))




E_dot_comp_high_out=massflow*(h_out-h_0-T_0*(s_out-s_0))


DELTAE_comp_high=(E_dot_comp_high_out-E_dot_comp_high_in)


epsilon_comp_high=(E_dot_comp_high_out-E_dot_comp_high_in)/W_comp_high


W_dot_cv=-W_comp_high



0=-W_dot_cv+E_dot_comp_high_in-E_dot_comp_high_out-E_dot_D_comp_high


eq. 3.28 p. 150]"

END

"!Condenser"





P_0=101.3



































END

"!Expansion"

SUBPROGRAM Expansion_high(massflow,T_in,T_out,h_in,h_out,R$,W_comp:DELTAE_expa_high,E_dot_D_expa_high




P_0=101.3










E_dot_EVhigh_in=massflow*(h_in-h_0-T_0*(s_1-s_0))


E_dot_EVhigh_out=massflow*(h_out-h_0-T_0*(s_2-s_0))


DELTAE_expa_high=E_dot_EVhigh_out-E_dot_EVhigh_in


E_dot_D_expa_high=-DELTAE_expa_high


END

"!Internal HEX"

SUBPROGRAM Internal_HEX(m_dot_hot,t_hot_in,t_hot_out,h_hot_in,h_hot_out,s_hot_in,s_hot_out,m_dot_cold,t_cold_in

,t_cold_out,h_cold_in,h_cold_out,s_cold_in,s_cold_out,R$:DELTAE_hot_HEX,DELTAE_cold_HEX,E_dot_D_HEX,E_dot_cold_in

,E_dot_cold_out,E_dot_hot_in,E_dot_hot_out)



P_0=1




E_dot_cold_in=m_dot_cold*(h_cold_in-h_0-T_0*(s_cold_in-s_0))


E_dot_cold_out=m_dot_hot*(h_cold_out-h_0-T_0*(s_cold_out-s_0))


E_dot_hot_in=m_dot_hot*(h_hot_in-h_0-T_0*(s_hot_in-s_0))


E_dot_hot_out=m_dot_cold*(h_hot_out-h_0-T_0*(s_hot_out-s_0))


{epsilon_HEX=(E_dot_hot_in-E_dot_hot_out)/(E_dot_cold_out-E_dot_cold_in)}

"Exergetic efficiency of internal heat exchanger [Ref: TDO: eq. (3.32+3.33) p. 153]. This efficiency becomes quite complicated



because the hot flow receives exergy by being cooled, but also in the form of increased mass flow from boil-off"

DELTAE_hot_HEX=E_dot_hot_out-E_dot_hot_in


DELTAE_cold_HEX=E_dot_cold_in-E_dot_hot_out


E_dot_D_HEX=E_dot_cold_in+E_dot_hot_in-E_dot_cold_out-E_dot_hot_out


{ epsilon_HEX_DL=(1-(E_dot_D_HEX)/(FUEL))}

END

"!Expansion"

SUBPROGRAM Expansion_low(massflow,T_in,T_out,h_in,h_out,R$,W_comp:DELTAE_expa_low,E_dot_D_expa_low

,E_dot_EVlow_in,E_dot_EVlow_out)



P_0=101.3










E_dot_EVlow_in=massflow*(h_in-h_0-T_0*(s_1-s_0))


E_dot_EVlow_out=massflow*(h_out-h_0-T_0*(s_2-s_0))


DELTAE_expa_low=E_dot_EVlow_out-E_dot_EVlow_in


E_dot_D_expa_low=-DELTAE_expa_low


epsilon_expa_low=E_dot_D_expa_low/W_comp

"Exergetic efficiency of expansion valve assuming that the fuel input is the compression work"

END

"!Evaporator"


,h_source_in,h_source_out:epsilon_evap,DELTAE_R_evap,DELTAE_source_evap,E_dot_D_evap,E_dot_evap_in

,E_dot_evap_out)



P_0=101.3




































END

SUBPROGRAM Exergy(W_comp,DELTAE_sink_cond,DELTAE_source_evap,E_dot_D_comp_low,E_dot_D_comp_high

,E_dot_D_cond,E_dot_D_expa_high,E_dot_D_HEX,E_dot_D_expa_low,E_dot_D_evap:epsilon_system,epsilon_system_DL

,E_dot_F_tot,E_dot_DL_tot,y_DL_comp_low,y_DL_comp_high,y_DL_cond,y_DL_expa_high,y_DL_HEX,y_DL_expa_low

,y_DL_evap,y|star_DL_comp_low,y|star_DL_comp_high,y|star_DL_cond,y|star_DL_expa_low,y|star_DL_expa_high

,y|star_DL_evap,y|star_DL_HEX,y|star_DL_sum)

{!Exergetic efficiency of system and ratios for exergy Loss and Destruction}









E_dot_DL_tot=E_dot_D_comp_low+E_dot_D_comp_high+E_dot_D_cond+E_dot_D_expa_low+E_dot_D_expa_high

+E_dot_D_evap+E_dot_D_HEX

"Total Exergy destruction/loss in the system components"

y_DL_comp_high=E_dot_D_comp_high/E_dot_F_tot


y_DL_comp_low=E_dot_D_comp_low/E_dot_F_tot





y_DL_expa_high=E_dot_D_expa_high/E_dot_F_tot


y_DL_expa_low=E_dot_D_expa_low/E_dot_F_tot




y|star_DL_comp_high=E_dot_D_comp_high/E_dot_DL_tot


p.149]"

y|star_DL_comp_low=E_dot_D_comp_low/E_dot_DL_tot



y|star_DL_expa_high=E_dot_D_expa_high/E_dot_DL_tot


y|star_DL_expa_low=E_dot_D_expa_low/E_dot_DL_tot




y|star_DL_sum=y|star_DL_comp_high+y|star_DL_comp_low+y|star_DL_cond+y|star_DL_expa_high+y|star_DL_evap

+y|star_DL_expa_low+y|star_DL_HEX


END

File:heat_pump_r744.EES 8/30/2010 10:26:51 AM Page 1


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"----------------------------- Heat pump simulation - R744 Transcritical Heat Pump------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"






ELSE


ENDIF

END

PROCEDURE integra(t_GC_R744[1..51],t_GC_R718[1..51],x_GC_R744[1..51],delta_t_min:x_int)

j:=1

REPEAT

j=j+1

t_minimum[j]=t_GC_R744[j]-t_GC_R718[j]

UNTIL (t_minimum[j]=delta_t_min)

x_int=x_GC_R744[j]

End

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- INPUT DATA ----------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


$REFERENCE R744 IIR

R$='R744'



"Heat output"

DELTAT_GC=5 [K]

"DELTAT_min that defines the temperature difference at the pinch point in the GasCooler (GC)"

DELTAT_EVAP=5 [K]

t_out=75 [C]


t_lift=30 [K]

"Temperature lift"

DELTAt_sink=t_lift




x_int2=0.4

t_superheat=5 [K]

"Superheat"

R_sink$='R718'


p_sink=801 [kPa]


R_source$='R718'




p_source=801 [kPa]

"Pressure on source medium side: set above ambient to avoid 2phase conditions"

eta_gas=0.8


c_q_gas_kWh=22.05




h_op=2500


eta_elec=0.9


r_n=0.0213

"Inflation rate"

n_econ=15


r=0.07

"Interest rate"

{eta_is=0,75}

Call isentropic(DELTAp:eta_is)


eta_vol=1-0.05*DELTAp


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

DELTAp=p_2/p_1

"Pressure ratio"

t_GC_out=converttemp(C,K,t_out)

t_GC_in=converttemp(C,K,t_out-DELTAt_sink)

t_evap_in_c=t_out-t_lift

t_evap_in=converttemp(C,K,t_evap_in_c)

t_evap_out=converttemp(C,K,t_evap_in_c-DELTAt_source)


VHC=(h_2-h_3)*m_dot/(V_dot_s*1000)

"Volumetric heating capacity"

t_GC_int=t_GC_in+(t_GC_out-t_GC_in)*x_int2

{x_int=x_int2}

t_3=t_GC_in+DELTAT_GC

Q_dot_heat=(h_2-h_3)*m_dot

p_3=p_2s

p_3=p_high

h_3=enthalpy(R$,t=t_3,p=p_3)

t_int=t_GC_int+DELTAT_GC

h_int=enthalpy(R$,t=t_int,p=p_3)

p_2=p_2s

h_2=h_int+(h_int-h_3)*((1/x_int2)-1)



t_2=temperature(R$,P=p_2,h=h_2)

h_2s=h_1+(h_2-h_1)*eta_is

s_2s=s_1

t_2s=temperature(R$,h=h_2s,s=s_2s)

p_2s=pressure(R$,h=h_2s,s=s_2s)

x_vapor=1

t_6=T_evap_out-DELTAT_EVAP

h_6=enthalpy(R$,t=t_6, x=x_vapor)

p_6=pressure(R$,h=h_6,t=t_6)

p_6=p_1

p_6=p_low

t_1=T_evap_in-DELTAT_EVAP

h_1=enthalpy(R$,t=t_1,p=p_1)

s_1=entropy(R$,h=h_1,t=t_1)

Q_dot_superheat=(h_1-h_6)*m_dot

h_3=h_5

p_5=p_6

x_5=quality(R$,h=h_5,p=p_5)


v_inlet=Volume(R$,T=T_1,P=P_1)

V_dot_1=m_dot*v_inlet



W_comp=m_dot*(h_2-h_1)

COP=Q_dot_heat/W_comp

Q_dot_cool=(h_1-h_5)*m_dot




rho_5=Density(R$,T=T_5,h=h_5)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- HEAT TRANSFER ---------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


point assumptions"



CALL EVAP_R744(R$,h_1,h_5,t_5,p_1:t_evap_R744[1..51],x_evap_R744[1..51],h_evap_R744[1..51])

CALL GC_R744(R$,h_2,h_3,t_3,p_2:t_GC_R744[1..51],x_GC_R744[1..51],h_GC_R744[1..51])

CALL GC_R718(R_sink$,p_sink,t_GC_in,t_GC_out,Q_dot_heat:x_GC_R718[1..51],t_GC_R718[1..51],h_GC_R718[1..51]

,m_dot_GC)

CALL integra(t_GC_R744[1..51],t_GC_R718[1..51],x_GC_R744[1..51],delta_t_min:x_int)

t_evap_g=t_evap_out+(t_evap_in-t_evap_out)*((h_6-h_5)/(h_1-h_5))




Q_dot_evap_g=m_dot*(h_1-h_6)



CALL lmtdsource2(R$, t_evap_g, t_evap_in, h_6, h_1, p_low: lmtd_source_g)

CALL lmtdsink(R$, t_GC_out, t_GC_in, h_3, h_2, p_high: lmtd_sink_tc)

N=50

Duplicate j=1,N+1

t_minimum[j]=t_GC_R744[j]-t_GC_R718[j]

END

delta_t_min=MIN(t_minimum[1..51])

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------ EXERGY ANALYSIS ------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

CALL Compressor(m_dot,t_1,t_2,h_1,h_2,R$,W_comp:epsilon_comp,E_dot_D_comp,DELTAE_comp,E_dot_comp_in

,E_dot_comp_out)

CALL Condenser(m_dot,t_GC_R744[1],t_GC_R744[51],h_GC_R744[1],h_GC_R744[51],R$,W_comp,R_sink$,m_dot_GC

,t_GC_R718[51],t_GC_R718[1],h_GC_R718[51],h_GC_R718[1]:DELTAE_R744_cond,epsilon_cond,DELTAE_sink_cond

,E_dot_D_cond,E_dot_cond_in,E_dot_cond_out)

CALL Evaporator(m_dot,t_evap_R744[51],t_evap_R744[1],h_evap_R744[51],h_evap_R744[1],R$,R_source$,m_dot_evap_R718

,t_evap_R718[1],t_evap_R718[51],h_evap_R718[1],h_evap_R718[51]:epsilon_evap,DELTAE_R744_evap,DELTAE_source_evap


CALL Expansion(m_dot,t_3,t_5,h_3,h_5,R$,W_comp:DELTAE_expa,E_dot_D_expa,E_dot_EV_in,E_dot_EV_out)




"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"




CRF=(r_eff*(1+r_eff)^n_econ)/((1+r_eff)^n_econ-1)

r_eff=(1+r)/(1+r_n)-1


{Z_dot=(Z_dot_comp+Z_dot_cond+Z_dot_evap)}



















TCI_comp=(PEC_comp+PEC_motor)*100







"Compressor"

PEC_comp=37245.2 + 2126.39*V_dot_h

"Motor"

PEC_motor=-1388.63 + 648.64*W_comp

"Heat Exchangers"

U_w=2

U_2p=2

U_g=0.6



U_overall_tc=0.95


PEC_cond=16817 + 1548.17*A_cond

A_cond=Q_dot_heat/(U_overall_tc*lmtd_sink_tc)

PEC_evap=16817 + 1548.17*A_evap



c_w_comp=c_F_elec

c_e_comp=c_e_cond














c=b-d

PBP=(A/c)



"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"----------------------------------------------- Library file - R744 Transcritical Heat Pump---------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

$REFERENCE R744 IIR

"! Library file containing subprograms for exergy analysis of R744 transcritical HP"


"!Compressor"





P_0=101.3


















W_dot_cv=-W_comp





eq. 3.28 p. 150]"

END

"!Condenser"


,h_sink_in,h_sink_out:DELTAE_R744_cond,epsilon_cond,DELTAE_sink_cond,E_dot_D_cond,E_dot_cond_in,E_dot_cond_out)



P_0=101.3





























DELTAE_R744_cond=E_dot_cond_in-E_dot_cond_out






END

"!Evaporator"


,h_source_in,h_source_out:epsilon_evap,DELTAE_R744_evap,DELTAE_source_evap,E_dot_D_evap,E_dot_evap_in

,E_dot_evap_out)



P_0=101.3






























DELTAE_R744_evap=E_dot_evap_out-E_dot_evap_in






END

"!Expansion"

SUBPROGRAM Expansion(massflow,T_in,T_out,h_in,h_out,R$,W_comp:DELTAE_expa,E_dot_D_expa,E_dot_EV_in

,E_dot_EV_out)



P_0=101.3


















END



























p.149]"









END

File:HEAT_PUMP_NH3H2O.EES 8/30/2010 9:58:28 AM Page 1


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------ Heat pump simulation - NH3H2O compression/absorption (hybrid)------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"




ELSE


ENDIF

END

$INCLUDE HEX_NH3H2O.LIB

$INCLUDE Exergy_func_NH3H2O.LIB

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- INPUT DATA ----------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"



"Heat output"

t_out_C=100


DELTAT_sink=20


t_source_in_C=80


t_lift=t_out_C-T_source_in_C

"Temperature lift"

DELTAT_INT_HEX=5

"DELTAT_min that defines the temperature difference at the pinch point in the internal heat exchanger"

DELTAT_COND=5


DELTAT_EVAP=5


x_strong=0.75

"Mass fraction of strong solution"

R_source$='R718'


p_source=10 [bar]

"Pressure on source medium side: set above ambient to avoid 2phase conditions"

R_sink$='R718'


p_sink=20 [bar]


{eta_is=0,7}

"Constant isentropic compressor efficiency"

Call isentropic(DELTAp:eta_is)


eta_vol=0.81

"Volumetric efficiency"



eta_pump=0.8

"Efficiency of liquid pump"

t_subcool=2

"Amount of subcooling"

t_max2=1.5

"Iteration parameter - compensates for heat exchanger profile compared to pinch"

eta_gas=0.8


c_q_gas_kWh=22.05




"Input prices for exergy calculations XX.XX [øre/kWh] must be provided for thermoeconomic calculations"

h_op=2500


eta_elec=0.9


r_n=0.0213

"Inflation rate"

n=15


r=0.07

"Interest rate"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

t_sink_out=converttemp(C,K,t_out_C)

t_sink_in=converttemp(C,K,t_out_C-DELTAT_sink)

t_source_in=converttemp(C,K,t_source_in_C)

t_source_out=t_5o+DELTAT_EVAP


t_int=t_3os+(t_9o-t_3os)/2

DELTAp=P_high/P_low

"Pressure ratio"

COP=Q_dot_heat/(W_comp+W_pump)

"Coefficient Of Performance"

{Q_dot_heat=Q_dot_cool+w_comp+w_pump}

m_dot=m_dot_comp+m_dot_pump

"Massflow"

m_dot_comp=q_10o*m_dot

h_9o=(h_2o*m_dot_comp+(h_8o*m_dot_pump))/m_dot

"!High pressure heat exchanger"

Q_dot_heat=m_dot*(h_9o-h_3os)

t_3s=t_sink_in+DELTAT_COND+t_max2

p_3s=p_high

x_3s=x_strong

CALL NH3H2O(123,t_3s,p_3s,x_3s:t_3os,p_3os,x_3os,h_3os,s_3os,u_3os,v_3os,q_3os)

p_3o=p_high

x_3=x_strong

t_3=t_sink_in+t_subcool+DELTAT_COND+t_max2

q_3=0



CALL NH3H2O(138,t_3,x_3,q_3:t_3o,p_3o,x_3o,h_3o,s_3o,u_3o,v_3o,q_3o)

t_9=t_sink_out+DELTAT_COND+t_max2

p_9=p_high

x_9=x_strong

CALL NH3H2O(123,t_9, p_9,x_9:t_9o,p_9o,x_9o,h_9o,s_9o,u_9o,v_9o,q_9o)

"!Internal heat exchanger - hot fluid"

Q_dot_HEX=(h_3os-h_4)*m_dot

x_4=x_strong

p_4=p_high

CALL NH3H2O(234,p_4,x_4,h_4:t_4o,p_4o,x_4o,h_4o,s_4o,u_4o,v_4o,q_4o)

"! Expansion"

x_5=x_strong

p_5=p_1o

p_5=p_low

h_5=h_4o


"!Low pressure heat exchanger"

Q_dot_cool=(h_10o-h_5o)*m_dot

t_10=t_source_in-DELTAT_EVAP

x_10=x_strong

p_10=p_1o

CALL NH3H2O(123,t_10,p_10,x_10:t_10o,p_10o,x_10o,h_10o,s_10o,u_10o,v_10o,q_10o)

"!Seperation"

x_strong*m_dot=(x_1o*m_dot_comp+x_6*m_dot_pump)

p_6=p_1o



x_comp=x_1o


s_1o=s_2os

q_1=1

CALL NH3H2O(128,t_1,p_1,q_1:t_1o,p_1o,x_1o,h_1o,s_1o,u_1o,v_1o,q_1o)

V_dot_h=v_1o*m_dot_comp*3600/eta_vol

"! Pump"

p_7s=p_high

s_7s=s_6o

x_7s=x_6o

CALL NH3H2O(235,p_7s,x_7s,s_7s:t_7os,p_7os,x_7os,h_7os,s_7os,u_7os,v_7os,q_7os)

p_7=p_high

x_7=x_6o

h_7=h_6o+(h_7os-h_6o)/eta_pump


"! Internal heat exchanger - cold fluid"

Q_dot_HEX=(h_8o-h_7o)*m_dot_pump

t_8=t_3os-DELTAT_INT_HEX

p_8=p_high

x_8=x_6o




"! Compressor"

p_2s=p_high

h_2s=h_1o+(h_2_oil-h_1o)*eta_is

x_2s=x_comp

CALL NH3H2O(234,p_2s,x_2s,h_2s:t_2os,p_2os,x_2os,h_2os,s_2os,u_2os,v_2os,q_2os)

p_2=p_high

x_2=x_comp


W_comp=(h_2_oil-h_1o)*m_dot_comp

W_pump=(h_7o-h_6o)*m_dot_pump

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- OIL INJECTION --------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

c_oil=2.00 [kJ/kgK]

rho_oil=800 [kg/m^3]

Q_dot_oil=0

t_2o=t_oil_out

t_1o=t_oil_in

h_2o=h_2_oil-Q_dot_oil*m_dot_comp

{h_2o=h_2_oil}

Q_dot_oil=(t_oil_out-t_oil_in)*m_dot_oil*c_oil

V_dot_oil=m_dot_oil/rho_oil*1000*60

Q_dot_oil_usefull=(t_oil_out-(t_sink_in+DELTAT_COND))*m_dot_oil*c_oil

deltat_oil_small=(t_sink_in+DELTAT_COND)-t_sink_in

deltat_oil_great=t_oil_out-t_sink_out

lmtd_oil=(deltat_oil_great-deltat_oil_small)/LN(deltat_oil_great/deltat_oil_small)

A_oil=Q_dot_oil_usefull/(U_overall_l*lmtd_oil)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- INTERNAL HEX ------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

deltat_HEX_small=t_3o-t_8o

deltat_HEX_great=t_4o-t_7o

lmtd_HEX=(deltat_HEX_great-deltat_HEX_small)/LN(deltat_HEX_great/deltat_HEX_small)

A_HEX=Q_dot_HEX/(U_overall_l*lmtd_HEX)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------------- HEAT TRANSFER ---------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


point assumptions"



CALL EVAP_R718(R_source$,t_source_out, t_source_in, p_source,Q_dot_cool:h_evap_R718[1..21],t_evap_R718[1..21]

,x_evap_R718[1..21],m_dot_source_R718)

CALL EVAP_NH3H2O(h_10o,h_5o,t_5o,p_5o,x_5o:x_evap_[1..21],t_evap[1..21],h_evap[1..21])

CALL COND_NH3H2O(h_9o,h_3os,t_3os,p_3os,x_3os:x_cond_[1..21],t_cond[1..21],h_cond[1..21])

CALL COND_R718(R_sink$,t_sink_in,t_sink_out,p_sink,Q_dot_heat:h_cond_R718[1..21],t_cond_R718[1..21]

,x_cond_R718[1..21],m_dot_sink_R718)

CALL COND_max(t_3os,t_9o,t_cond[1..21]:t_max)


CALL lmtdsink(t_cond_R718[1], t_cond_R718[21], t_cond[1..21]: lmtd_sink)

CALL lmtdsource(t_evap_R718[21], t_evap_R718[1], t_evap[1..21]: lmtd_source)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------------------ EXERGY ANALYSIS ------------------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"Calls subprograms for exergy calculations, see separate library file"

CALL Compressor(m_dot_comp,t_1o,t_2o,h_1o,h_2o,s_1o,s_2o,x_1o,W_comp:epsilon_comp,E_dot_D_comp,DELTAE_comp


CALL Pump(m_dot_pump,t_6o,t_7o,h_6o,h_7o,s_6o,s_7o,x_6o,W_pump:epsilon_pump,E_dot_D_pump,DELTAE_pump

,E_dot_pump_in,E_dot_pump_out)

CALL Condenser(m_dot,t_9o,t_3os,h_9o,h_3os,s_9o,s_3os,x_9o,R_sink$,m_dot_sink_R718,t_cond_R718[21],t_cond_R718[1]

,h_cond_R718[21],h_cond_R718[1]:DELTAE_R_cond,epsilon_cond,DELTAE_sink_cond,E_dot_D_cond,E_dot_cond_in

,E_dot_cond_out)

CALL Internal_HEX(m_dot_pump,t_7o,t_8o,h_7o,h_8o,s_7o,s_8o,x_8o,m_dot,t_3os,t_4o,h_3os,h_4o,s_3os,s_4o

,x_3os:epsilon_HEX,DELTAE_pump_HEX,DELTAE_m_HEX,E_dot_D_HEX,E_dot_HEX_in,E_dot_HEX_out,E_dot_HEXhot_in

,E_dot_HEXhot_out)

CALL Expansion(m_dot,t_4o,t_5o,h_4o,h_5o,s_4o,s_5o,x_4o:DELTAE_expa,E_dot_D_expa,E_dot_EV_in,E_dot_EV_out)

CALL Evaporator(m_dot,t_evap[21],t_evap[1],h_evap[21],h_evap[1],s_5o,s_10o,x_5o,R_source$,m_dot_source_R718



CALL Exergy(DELTAE_sink_cond,W_comp,W_pump,DELTAE_source_evap,E_dot_D_comp,E_dot_D_cond,E_dot_D_expa

,E_dot_D_evap,E_dot_D_pump,E_dot_D_HEX:epsilon_system,epsilon_system_DL,E_dot_F_tot,E_dot_DL_tot,y_DL_comp

,y_DL_cond,y_DL_expa,y_DL_evap,y|star_DL_comp,y|star_DL_cond,y|star_DL_expa,y|star_DL_evap,y_DL_pump,y_DL_HEX

,y|star_DL_pump,y|star_DL_HEX,y|star_DL_sum)

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"





r_eff=(1+r)/(1+r_n)-1







"Total annuitized cost rate related to the compressor"


"Total annuitized cost rate related to the condenser"


"Total annuitized cost rate related to the evaporator"


"Total annuitized cost rate related to remaining plant construction"


"Total annuitized cost from capital investment related to the compressor"


"Total annuitized cost from capital investment related to the condenser"


"Total annuitized cost from capital investment related to the evaporator"


"Total annuitized cost from capital investment related to remaining plant construction"


"Total annual cost from operation and maintenance related to the compressor - given as fraction of capital investment"


"Total annual cost from operation and maintenance related to the condenser - given as fraction of capital investment"


"Total annual cost from operation and maintenance related to the evaporater - given as fraction of capital investment"


"Total annual cost from operation and maintenance related to remaining plant - given as fraction of capital investment"

TCI_comp=(PEC_comp+PEC_motor)*100

"Total capital investment for compressor and drive motor"

TCI_cond=(PEC_cond+PEC_oil+PEC_HEX)*100

"Total capital investment for condenser"


"Total capital investment for evaporator"




"Compressor"

PEC_comp=30645 + 355.719*V_dot_h - 0.0355803*V_dot_h^2

"Motor"

PEC_motor=-1388.63 + 648.64*W_comp

"Heat Exchangers"

U_w=2

U_l=5

U_2p=2




PEC_cond=16817 + 1548.17*A_cond

A_cond=Q_dot_heat/(U_overall_2p*lmtd_sink)

PEC_evap=16817 + 1548.17*A_evap

A_evap=Q_dot_cool/(U_overall_2p*lmtd_source)

PEC_oil=2000*A_oil



PEC_HEX=2000*A_HEX


c_w_elec=c_F_elec

c_e_HEXhot=c_e_cond

c_e_cond=c_e_mixer

c_e_mixer=c_e_HEX+c_e_comp

c_e_mixer * E_dot_cond_in=c_e_HEX*E_dot_HEX_out+c_e_comp*E_dot_comp_out+(Z_dot_plant/8)

c_e_cond * E_dot_cond_out+c_q_cond*DELTAE_sink_cond=c_e_mixer*E_dot_cond_in+Z_dot_cond+(Z_dot_plant/8)

c_e_HEXhot*E_dot_HEXhot_out+c_e_HEX*E_dot_HEX_out=c_e_cond*E_dot_cond_out+c_e_pump*E_dot_pump_out

+(Z_dot_plant/8)

c_e_EV*E_Dot_EV_out=c_e_HEXhot*E_dot_HEXhot_out+(Z_dot_plant/8)


c_e_liquid*E_dot_pump_in+c_e_gas*E_dot_comp_in=c_e_evap*E_dot_evap_out+(Z_dot_plant/8)

c_e_pump*E_dot_pump_out=c_e_liquid*E_dot_pump_in+c_w_elec*W_pump+(Z_dot_plant/8)

c_e_comp*E_dot_comp_out=c_e_gas*E_dot_comp_in+c_w_elec*W_comp+Z_dot_comp+(Z_dot_plant/8)






d=(h_op*((W_comp+W_pump)/eta_elec)*c_F_elec_kWh)/100

c=b-d

PBP=(A/c)

File:Exergy_func_NH3H2O.LIB 8/30/2010 9:51:05 AM Page 1


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"-------------------------------------- Library file - NH3H2O compression/absorption (hybrid)------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"! Library file containing subprograms for exergy analysis of hybrid HP"


"!Compressor"

SUBPROGRAM Compressor(massflow,T_in,T_out,h_in,h_out,s_in,s_out,x_0,W_comp:epsilon_comp,E_dot_D_comp

,DELTAE_comp,E_dot_comp_in,E_dot_comp_out)



P_0=1


CALL NH3H2O(123,T_0,P_0,x_0: T_0o,P_0o,x_0o,h_0o,s_0o,u_0o,v_0o,q_0o)

"Determining NH3H2O properties"

E_dot_comp_in=massflow*(h_in-h_0o-T_0o*(s_in-s_0o))


E_dot_comp_out=massflow*(h_out-h_0o-T_0o*(s_out-s_0o))






W_dot_cv=-W_comp





eq. 3.28 p. 150]"

END

"!Pump"

SUBPROGRAM Pump(massflow,T_in,T_out,h_in,h_out,s_in,s_out,x_0,W_pump:epsilon_pump,E_dot_D_pump,DELTAE_pump

,E_dot_pump_in,E_dot_pump_out)



P_0=1




E_dot_pump_in=massflow*(h_in-h_0o-T_0o*(s_in-s_0o))

"Exergy flow into pump [Ref: TDO: eq. (3.13) p. 126+Ex 3.1 p. 127]"

E_dot_pump_out=massflow*(h_out-h_0o-T_0o*(s_out-s_0o))

"Exergy flow out of pump [Ref: TDO: eq. (3.13) p. 126+Ex 3.1 p. 127]"

DELTAE_pump=(E_dot_pump_out-E_dot_pump_in)

"Change in exergy flow over pump"

epsilon_pump=(E_dot_pump_out-E_dot_pump_in)/W_pump

"Exergetic efficiency of pump [Ref: TDO: eq. (3.30) p. 151]"

W_dot_cv=-W_pump



"Time rate of energy transfer by work other than flow work. Negative due to pumping work transferred into the control volume [cf.:

Ref: TDO: fig 3.1 p. 118 + eq. (3.10c) p. 124]"

0=-W_dot_cv+E_dot_pump_in-E_dot_pump_out-E_dot_D_pump

"E_dot_D_pump: Exergy destruction from losses and irreversibilities over pumping stage [Ref: TDO: eq. 3.11(a+b) p. 125+ eq.

3.28 p. 150]"

END

"!Condenser"

SUBPROGRAM Condenser(massflow,T_in,T_out,h_in,h_out,s_in,s_out,x_0,R_sink$,massflow_sink,T_sink_in,T_sink_out




P_0=1


x_0=x_1o

"Defining mixture of concentration"



E_dot_cond_in=massflow*(h_in-h_0o-T_0o*(s_in-s_0o))

"Exergy flow of working fluid into condenser [Ref: TDO: eq. (3.13) p. 126+Ex 3.1 p. 127]"

E_dot_cond_out=massflow*(h_out-h_0o-T_0o*(s_out-s_0o))

"Exergy flow of working fluid out of condenser [Ref: TDO: eq. (3.13) p. 126+Ex 3.1 p. 127]"


"Enthalpy of sink fluid at dead state conditions"




"Entropy of sink fluid at condenser inlet"


"Entropy of sink fluid at condenser outlet"


"Exergy flow of sink fluid into condenser"


"Exergy flow of sink fluid out of condenser"


"Exergetic efficiency of condenser [Ref: TDO: eq. (3.32) p. 153]"


"Change in exergy of working fluid flow over condenser (NB. value changes sign when regarded as fuel input)"


"Change in exergy of sink fluid flow over condenser"


"Rate of exergy destruction/loss over condenser [Ref: TDO: eq. (3.11a) p. 125]"

END

"!Evaporator"

SUBPROGRAM Evaporator(massflow,T_in,T_out,h_in,h_out,s_in,s_out,x_0,R_source$,massflow_source,T_source_in

,T_source_out,h_source_in,h_source_out:epsilon_evap,DELTAE_R_evap,DELTAE_source_evap,E_dot_D_evap,E_dot_evap_in

,E_dot_evap_out)



P_0=1






E_dot_evap_in=massflow*(h_in-h_0o-T_0*(s_in-s_0o))


E_dot_evap_out=massflow*(h_out-h_0o-T_0*(s_out-s_0o))








h_source_0=Enthalpy(R_source$,T=T_0,P=P_0)

"Enthalpy of source fluid at dead state conditions"

E_dot_source_in=massflow_source*(h_source_in-h_source_0-T_0*(s_source_in-s_source_0))


E_dot_source_out=massflow_source*(h_source_out-h_source_0-T_0*(s_source_out-s_source_0))












END

"!Internal HEX"

SUBPROGRAM Internal_HEX(m_dot_pump,T_in,T_out,h_in,h_out,s_in,s_out,x_0,m_dot,T_hot_in,T_hot_out,h_hot_in,h_hot_out

,s_hot_in,s_hot_out,x_0_hot:epsilon_HEX,DELTAE_pump_HEX,DELTAE_m_HEX,E_dot_D_HEX,E_dot_HEX_in,E_dot_HEX_out

E_dot_HEXhot_in,E_dot_HEXhot_out)



P_0=1




E_dot_HEX_in=m_dot_pump*(h_in-h_0o-T_0*(s_in-s_0o))


E_dot_HEX_out=m_dot_pump*(h_out-h_0o-T_0*(s_out-s_0o))


CALL NH3H2O(123,T_0,P_0,x_0_hot: T_hoto,P_hoto,x_hoto,h_hoto,s_hoto,u_hoto,v_hoto,q_hoto)


E_dot_HEXhot_in=m_dot*(h_hot_in-h_hoto-T_0*(s_hot_in-s_hoto))


E_dot_HEXhot_out=m_dot*(h_hot_out-h_hoto-T_0*(s_hot_out-s_hoto))




epsilon_HEX=(E_dot_HEX_out-E_dot_HEX_in)/(E_dot_HEXhot_in-E_dot_HEXhot_out)

"Exergetic efficiency of internal heat exchanger [Ref: TDO: eq. (3.32+3.33) p. 153]. "

DELTAE_pump_HEX=E_dot_HEX_out-E_dot_HEX_in


DELTAE_m_HEX=E_dot_HEXhot_out-E_dot_HEXhot_in


E_dot_D_HEX=E_dot_HEX_in+E_dot_HEXhot_in-E_dot_HEX_out-E_dot_HEXhot_out


END

"!Expansion"

SUBPROGRAM Expansion(massflow,T_in,T_out,h_in,h_out,s_in,s_out,x_0:DELTAE_expa,E_dot_D_expa,E_dot_EV_in

,E_dot_EV_out)



P_0=1




E_dot_EV_in=massflow*(h_in-h_0o-T_0*(s_in-s_0o))


E_dot_EV_out=massflow*(h_out-h_0o-T_0*(s_out-s_0o))






END


SUBPROGRAM Exergy(DELTAE_sink_cond,W_comp,W_pump,DELTAE_source_evap,E_dot_D_comp,E_dot_D_cond

,E_dot_D_expa,E_dot_D_evap,E_dot_D_pump,E_dot_D_HEX:epsilon_system,epsilon_system_DL,E_dot_F_tot,E_dot_DL_tot

,y_DL_comp,y_DL_cond,y_DL_expa,y_DL_evap,y|star_DL_comp,y|star_DL_cond,y|star_DL_expa,y|star_DL_evap,y_DL_pump

,y_DL_HEX,y|star_DL_pump,y|star_DL_HEX,y|star_DL_sum)

epsilon_system=DELTAE_sink_cond/(W_comp+W_pump+(-DELTAE_source_evap))




E_dot_F_tot=W_comp+W_pump-DELTAE_source_evap




E_dot_DL_tot=E_dot_D_comp+E_dot_D_cond+E_dot_D_expa+E_dot_D_evap+E_dot_D_pump+E_dot_D_HEX












y_DL_pump=E_dot_D_pump/E_dot_F_tot






p.149]"







y|star_DL_pump=E_dot_D_pump/E_dot_DL_tot




y|star_DL_sum=y|star_DL_comp+y|star_DL_cond+y|star_DL_expa+y|star_DL_evap+y|star_DL_pump+y|star_DL_HEX


END

File:U_value_R744.EES 9/1/2010 11:24:23 AM Page 1


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"-------------------------- Calculation of U value to be used in R744 Transcritical Heat Pump------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"Because of the special characteristics of a transcritical fluid, a U-value different from the standard

(gas, two-phase, liquid) is calculated. This is done on the basis of experimental data from an article published by DTI."

"! Input"

$REFERENCE R744 IIR

R$='R744'

R_source$='R718'

P_1=10100

t_1=105

h_1=enthalpy(R$,p=p_1,t=t_1)

p_1=p_2

t_2=45

h_2=enthalpy(R$,p=p_2,t=t_2)

p_source=101

t_3=40

h_3=enthalpy(R_source$,p=p_source,t=t_3)

t_4=80

h_4=enthalpy(R_source$,p=p_source,t=t_4)

Q_dot= 65 [kW]

"! Calculation"

Q_dot=(h_1-h_2)*m_dot_r

Q_dot=(h_4-h_3)*m_dot_h2o

N=20

h_wf[0]=h_1

t_wf[0]=t_1

DELTAh_wf=(h_1-h_2)/N

h_h2o[0]=h_4

t_h2o[0]=t_4

DELTAh_h2o=(h_4-h_3)/N

Duplicate i=1,N

h_wf[i]=h_wf[i-1]-DELTAh_wf

t_wf[i]=temperature(R$,p=p_1,h=h_wf[i])

h_h2o[i]=h_h2o[i-1]-DELTAh_h2o

t_h2o[i]=temperature(R_source$,p=p_source,h=h_h2o[i])

DELTAT_high[i]=t_wf[i-1]-t_h2o[i-1]

DELTAT_low[i]=t_wf[i]-t_h2o[i]

lmtd[i]=(DELTAT_high[i]-DELTAT_low[i])/LN(DELTAT_high[i]/DELTAT_low[i])

END

LMTD=SUM(lmtd[1..20])/N

Q_dot=U*A*LMTD

A=0.70*0.3*50

File:hex.EES 9/1/2010 11:17:04 AM Page 1


"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"------------------------------------------------ Pinch HEN Calculation - Berendsen ----------------------------------------------------"

"!--------------------------------------------------------------------------------------------------------------------------------------------------------"

"In this file the calculation of necessary heat exchanger area for process integration at Berendsen is validated.

In this calculation a more precise temperature out of the last heat exchanger is calculated and it is this value

that could potentially be used as input for a heat pump."

"! Input"

DELTAT_min=10

F$='AirH2O'

p_in=101 [kPa]

A_HEX1=6

{A_HEX1=max(A_HEX1[3..N])}

{A_HEX3=max(A_HEX3[3..N])}

A_HEX3=40

T_sink1_in=Converttemp(C,K,20)

T_sink3_in=Converttemp(C,K,35)

T_wash=Converttemp(C,K,60)

T_cond=Converttemp(C,K,125)


U_g=0.6

U_w=2

N=40

"! Data import"

DUPLICATE i=1, 40

Hour[i]=Lookup('WH',i,'Hour')

m_dot_HEX1[i]=Lookup('WH',i,'m_dot_HEX1')

m_dot_HEX2[i]=Lookup('WH',i,'m_dot_HEX2')

T_source1_in[i]=Lookup('WH',i,'T_HEX1')

T_source2_in[i]=Lookup('WH',i,'T_HEX2')

h_source1_in[i]=Lookup('WH',i,'h_HEX1')

h_source2_in[i]=Lookup('WH',i,'h_HEX2')

m_dot_cond[i]=Lookup('WH',i,'m_dot_cond')

m_dot_wash[i]=Lookup('WH',i,'m_dot_wash')

omega_HEX1[i]=Lookup('WH',i,'omega_HEX1')

omega_HEX2[i]=Lookup('WH',i,'omega_HEX2')

"! AREA 1"

T_sink1_out[i]=t_source1_in[i]-DELTAT_min

Q_dot_source1[i]=m_dot_cond[i]*4.12*(T_sink1_out[i]-t_sink1_in)

Q_dot_source1[i]=m_dot_HEX1[i]*(h_source1_in[i]-h_source1_out[i])

t_source1_out[i]=temperature(F$,h=h_source1_out[i],w=omega_HEX1[i],P=p_in)

lmtd_hex1[i]=((T_source1_out[i]-T_sink1_in)-(T_source1_in[i]-T_sink1_out[i]))/LN((T_source1_out[i]-T_sink1_in)/(T_source1_in[i]

-T_sink1_out[i]))

Q_dot_source1[i]=U_overall_g*A_hex1[i]*lmtd_hex1[i]

"! REAL 1"

C_dot_source1[i]=m_dot_HEX1[i]*1.05

C_dot_sink1[i]=m_dot_cond[i]*4.12

C_dot_1_min[i]=MIN(C_dot_sink1[i],C_dot_source1[i])

C_dot_1_max[i]=MAX(C_dot_sink1[i],C_dot_source1[i])

NTU1[i]=U_overall_g*A_HEX1/C_dot_1_min[i]

epsilon1[i]=HX('crossflow_both_unmixed',NTU1[i],C_dot_source1[i],C_dot_sink1[i],'epsilon')

q_dot_1_max[i]=C_dot_1_min[i]*(T_source1_in[i]-T_sink1_in)

q_dot_1_real[i]=q_dot_1_max[i]*epsilon1[i]

File:hex.EES 9/1/2010 11:17:05 AM Page 2


T_real_source1_out[i]=T_source1_in[i]-q_dot_1_real[i]/C_dot_source1[i]

T_real_sink1_out[i]=T_sink1_in+q_dot_1_real[i]/C_dot_sink1[i]

h_real_source1_out[i]=enthalpy(F$,t=T_real_source1_out[i],w=omega_HEX1[i],P=p_in)

"! NEW STATES"

h_source3_in[i]*m_dot_HEX3[i]=h_real_source1_out[i]*m_dot_HEX1[i]+h_source2_in[i]*m_dot_HEX2[i]

m_dot_HEX3[i]=m_dot_HEX1[i]+m_dot_HEX2[i]

m_dot_HEX3[i]*omega_HEX3[i]=m_dot_HEX1[i]*omega_HEX1[i]+m_dot_HEX2[i]*omega_HEX2[i]

T_source3_in[i]=temperature(F$,h=h_source3_in[i],w=omega_HEX3[i],P=p_in)

"! AREA 3"

Q_dot_wash[i]=m_dot_cond[i]*4.12*(T_cond-T_wash)

Q_dot_wash[i]=m_dot_wash[i]*4.12*(T_wash-T_sink3_out[i])

"Calculation of temperature 3 necessary out of hex"

Q_dot_source3[i]=m_dot_HEX3[i]*(h_source3_in[i]-h_source3_out[i])

Q_dot_source3[i]=m_dot_wash[i]*4.12*(T_sink3_out[i]-t_sink3_in)

T_source3_out[i]=temperature(F$,h=h_source3_out[i],w=omega_HEX3[i],P=p_in)

Q_dot_source3[i]=U_overall_g*A_hex3[i]*lmtd_hex3[i]

lmtd_hex3[i]=((t_source3_out[i]-t_sink3_in)-(t_source3_in[i]-t_sink3_out[i]))/LN(ABS((t_source3_out[i]-t_sink3_in)/(t_source3_in[i]

-t_sink3_out[i])))

"! REAL 3"

C_dot_source3[i]=m_dot_HEX3[i]*1.05

C_dot_sink3[i]=m_dot_wash[i]*4.12

C_dot_3_min[i]=MIN(C_dot_sink3[i],C_dot_source3[i])

C_dot_3_max[i]=MAX(C_dot_sink3[i],C_dot_source3[i])

NTU3[i]=U_overall_g*A_HEX3/C_dot_3_min[i]

epsilon3[i]=HX('crossflow_both_unmixed',NTU3[i],C_dot_source3[i],C_dot_sink3[i],'epsilon')

q_dot_3_max[i]=C_dot_3_min[i]*(T_source3_in[i]-T_sink3_in)

q_dot_3_real[i]=q_dot_3_max[i]*epsilon3[i]

T_real_source3_out[i]=T_source3_in[i]-q_dot_3_real[i]/C_dot_source3[i]

T_real_sink3_out[i]=T_sink3_in+q_dot_3_real[i]/C_dot_sink3[i]

h_real_source3_out[i]=enthalpy(F$,t=T_real_source3_out[i],w=omega_HEX3[i],P=p_in)

END

"----------------------------------------------------------------------------lookup---------------------------------------------------------------------------"

DTU Mechanical Engineering

Section of Thermal Energy Systems

Technical University of Denmark

Nils Koppels Allé, Bld. 403

DK- 2800 Kgs. Lyngby

Denmark

Phone (+45) 45 25 41 31

Fax (+45) 45 88 43 25

www.mek.dtu.dk

Documents

Master Thesis - DTU Electronic Theses and Dissertationsetd.dtu.dk/thesis/268604/Speciale.pdfSoldrevet Fjernkøling Master Thesis Su Cheong Ho MEK-TES-EP-2010-07 May 2010 Industrial