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_____________________________________________________________________________________________________ This report may only be used wordily or entirely for publication purposes. Texts or publications where this report is issued have to be approved by the authors before submission.
report Nr. 00000
Literature Study
The transcritical organic Rankine cycle
Author(s): Catternan Tom
University/department: Ghent University - Department of Flow, Heat and
Combustion Mechanics
Address: Sint-Pietersnieuwstraat 41, 9000 Gent, Belgium
11/04/2013
SBO project funded by
_____________________________________________________________________________________________________ This report may only be used wordily or entirely for publication purposes. Texts or publications where this report is issued have to be approved by the authors before submission.
Frame
This report is composed in the frame of the IWT SBO-110006 project The Next
Generation Organic Rankine Cycles (www.orcnext.be), funded by the Institute for
the Promotion and Innovation by Science and Technology in Flanders (IWT).
The presented work is part of WP4 ‘Development of supercritical technologies’. In
particular a literature survey is made in agreement with subtask D4.2. In this
report the possible benefits of using SC fluids in ORCs and acceptable ranges of
the different operational parameters are presented.
The goal of this report is to communicate the advantages using supercritical
fluids and recent progress in research about convective heat transfer to fluids
working at a supercritical pressure towards the research partners and advisory
board of the ORCNext project. As such, this work should not be considered a
scientific article.
_____________________________________________________________________________________________________ This report may only be used wordily or entirely for publication purposes. Texts or publications where this report is issued have to be approved by the authors before submission.
Content Frame ....................................................................................................... 2
Content ..................................................................................................... 3
Nomenclature ............................................................................................ 6
Chapter 1 Introduction ................................................................................ 8
Chapter 2 The organic Rankine cycle ......................................................... 10
1. Introduction ................................................................................. 10
2. Components ................................................................................. 12
3. Applications of organic Rankine cycles ............................................. 14
2.1 Biomass [10] ............................................................................. 14
2.2 Geothermal heat sources [10] ...................................................... 15
2.3 Solar energy [20] ....................................................................... 16
2.4 Waste heat recovery from internal combustion engines [10] ............ 17
2.5 Industrial waste heat [22] ........................................................... 18
2.5.1 Cement industry ................................................................... 18
2.5.2 Steel industry ....................................................................... 19
2.5.3 Glass industry ...................................................................... 19
Chapter 3 Transcritical organic Rankine cycle .............................................. 20
1. Introduction ................................................................................. 20
2. Temperature profile in the heat exchanger ....................................... 23
3. The transcritical cycle .................................................................... 25
Chapter 4 Classification of working fluids-Selection criteria ........................... 28
1. Introduction ................................................................................. 28
2. Classification and selection criteria of working fluids .......................... 29
2.1 Screening criteria ....................................................................... 29
2.1.1 Safety criterion (ASHRAE 34) ................................................. 29
2.1.2 Environmental criterion ......................................................... 30
2.1.3 Stability of the working fluid and compatibility with materials in
contact 32
2.1.4 Thermophysical properties ..................................................... 32
2.1.5 Availability and cost of working fluids ...................................... 40
2.2 Cycle criteria - Selection by performance indicator .......................... 41
2.2.1 Thermodynamic performance indicators ................................... 41
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2.2.2 Heat exchanger performance indicators ................................... 51
2.2.3 Cost performance indicators ................................................... 53
3. Working fluids for organic Rankine cycles ......................................... 55
3.1 Fluid candidates ......................................................................... 55
3.1.1 Group 1: Fluids ammonia, benzene and toluene ........................ 58
3.1.2 Group 2: Fluids R170, R744, R41, R23, R116, R32, R125 and
R143a 58
3.1.3 Group 3: Fluids propyne, HC270, R152a, R22 and R1270........... 59
3.1.4 Group 4: Fluids R21, R142b, R134a, R290, R141b, R123, R245ca,
R245fa, R236ea, R124, R227ea, R218 ................................................ 59
3.1.5 Group 5: Fluids R601, R600, R600a, FC-4-1-12, RC318, R-3-1-10
59
3.2 Working fluids for transcritical organic Rankine cycles ..................... 59
Chapter 5 Modelling .................................................................................. 63
1. Introduction .................................................................................... 63
2. Energy balances .............................................................................. 63
3.3 Pump ........................................................................................ 64
3.4 Vapour generator ....................................................................... 64
3.5 Expander ................................................................................... 64
3.6 Condenser ................................................................................. 65
3.7 Regenerator (Internal Heat Exchanger) ......................................... 65
3. Heat transfer ................................................................................... 66
3.1 Vapour generator ....................................................................... 68
3.1.1 Working fluid – heat transfer coefficient ................................... 68
3.1.2 Heat source.......................................................................... 70
3.2 Condenser ................................................................................. 71
3.2.1 Working fluid ........................................................................ 71
3.2.2 Cooling fluid ......................................................................... 72
3.3 Evaporator (subcritical) ............................................................... 72
3.3.1 Working fluid single-phase heat transfer coefficient ................... 72
3.3.2 Working fluid two-phase heat transfer coefficient ...................... 73
4. Pressure drop ............................................................................... 73
4.1 Vapour generator ....................................................................... 73
4.1.1 Working fluid ........................................................................ 73
4.2 Condenser ................................................................................. 73
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4.2.1 Working fluid ........................................................................ 73
4.2.2 Cooling fluid - single-phase pressure drop ................................ 74
4.3 Evaporator (subcritical) ............................................................... 74
Chapter 6 Fluid selection and cycle optimization ........................................... 76
1. Parametric study and cycle optimization ........................................... 76
1.1 Energy analysis .......................................................................... 78
1.2 Exergy analysis .......................................................................... 82
1.3 Recovery efficiency ..................................................................... 86
1.4 Total heat transfer capacity UA .................................................... 87
1.5 Heat exchanger surface ............................................................... 88
1.6 Thermo-economic analysis........................................................... 90
2. Fluid selection ............................................................................... 95
Chapter 7 Heat exchanger design ............................................................... 96
References .............................................................................................. 97
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Nomenclature H Enthalpy (kJ)
h Specific enthalpy (kJ/kg)
m Mass (kg)
Mass flow rate (kg/s)
P Power (kW)
Q Heat (kJ)
q Specific heat (kJ/kg)
Heat flow rate (kJ/s)
T Temperature (°C)
S Entropy (kJ/K)
s Specific entropy (kJ/kg-K)
W Work (kJ)
w Specific work (kJ/kg)
Greek symbols
Efficiency (%)
Thermal efficiency (%)
Total heat-recovery efficiency (%)
Heat availability (-)
Sub- and superscripts
s Isentropic
crit Critical
CS Cold Source
Mech Mechanical
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WH Waste heat
Evap Evaporator
Exp Expander
Cond Condenser
Vap-gen Vapour Generator
WH Waste heat
In Inlet
Out Outlet
1,2,3… State points
Acronyms
ORC Organic Rankine Cycle
IHE Internal Heat Exchanger
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Chapter 1
Introduction During the last 100 years, the world’s population and industrial activity increased
considerably. As a consequence, the energy demand during this period has risen
almost exponentially.
Fossil fuels have been used to achieve great technological and economic
progress. However, the increasing consumption of these limited resources has
led to more and more environmental problems such as global warming, ozone
depletion and atmospheric pollution. Furthermore, along with the fast
development of industry, energy shortages and blackouts have appeared more
and more frequently all over the world.
This situation illustrates the necessity of developing new clean energy sources
and also the necessity of decreasing the energy intensity in all sectors of the
economy.
There is much effort in using renewable energy sources like solar, water and
wind energy. But also biomass and the utilization of low-grade heat sources,
such as geothermal resources, exhaust gas of gas turbines and waste heat from
industrial plants can be used for the production of electricity. These resources
have potential in reducing consumption of fossil fuels and in relaxing
environmental problems.
The valorisation of industrial thermal wastes seems to offer an important
potential. As an example, 71% of the 3,220 PJ annually consumed by the eight
principal industrial sectors in Canada are thrown away in the form of thermal
wastes and represent an annual recovery potential of 2,280 PJ of thermal energy
[1].
Experts assume that the annual unused industrial waste heat potential amounts
to 140TWh in Europe alone, implying a CO2-reduction potential of about 14Mton
of CO2 per annum [2]. In Flanders alone, several studies indicate the enormous
amount (order of several hundreds of MWth) of available thermal power at low
temperatures (± 100°). Such ‘waste’ heat is available in the steel, cement, glass,
paper, plastic, chemical and food industry in the form of cooling water, exhaust
air of drying installations, flue gasses, afterburners, … [3]. In fact today only the
first steps are being made to recover the energy present in the waste heat and
the driving force for doing so is energy efficiency:
Rising energy prices force industry to make their processes more energy
efficient from a purely economic point of view [4].
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EU (and regional) legislation related to CO2-emission reductions (the
202020-goals) force industry to reduce their CO2-emissions in order to be
compliant to the rules [EU17215/08].
The organic Rankine cycle (short: ORC) is a promising process for conversion of
low and medium temperature heat to electricity. Hence, ORC technology has a
big economical potential and can help to realize the 202020 goals. However,
there are only few applications that can use this energy directly as heat.
Furthermore, transportation of large quantities of heat over long distances is not
practical. In situ utilization of this heat as the source of a power cycle is thus a
concept generating a lot of interest.
In chapter 2 an introduction about organic Rankine cycles and an overview of the
main components are given. Further, the main applications of organic Rankine
cycles are discussed.
In chapter 3 the transcritical Rankine cycle and its advantages are explained.
Chapter 4 gives an overview of the selection criteria for the working fluids and
lists the potential candidates for transcritical Rankine cycles.
In chapter 5 the thermodynamic and heat exchanger models are described,
which will be used in the numerical simulations with EES.
In chapter 6 an overview is given of parametric studies done by several
researchers and the influence of the key parameters on different performance
indicators are studied.
Chapter 7 describes principles of the heat exchanger design.
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Chapter 2
The organic Rankine cycle
1. Introduction
The process of an organic Rankine cycle works like the traditional Clausius-
Rankine steam power cycle, but instead of water it uses an organic working fluid.
Advantages presented by water as working fluid are [5]:
very good thermal/chemical stability (no risk of decomposition);
very low viscosity (less pumping work required);
good energy carrier (high latent and specific heat);
non-toxic, non-flammable and no threat to the environment (zero ODP,
zero GWP);
cheap and abundant (present almost everywhere on earth).
However, many problems are encountered when using water as working fluid
[6]:
need of superheating to prevent condensation during expansion;
risk of erosion of turbine blades;
excess pressure in the evaporator;
complex and expensive turbines.
The traditional steam cycle does not give a satisfying performance when utilizing
low-grade waste heat because of its low thermal efficiency and large volume
flows (Hung et al. [7]). For low-temperature waste heat recovery in small to
medium scale power plants, organic fluids have been proposed, because of its
several advantages over conventional steam (Tchanche et al. [8]):
less heat is needed during the evaporation process;
the evaporation process takes place at lower pressure and temperature;
the expansion process ends in the vapour region and hence the
superheating is not required and the risk of blade erosion is avoided;
the smaller temperature difference between evaporation and condensation
also means that the pressure drop/ratio will be much smaller and thus
simple single stage turbines can be used.
In contrast to water, the expansion in the turbine ends for most organic fluids
not in the wet steam regime but in the gas phase above condenser temperature.
Thus, often an internal heat exchanger (or regenerator) is used to improve
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efficiency by preheating the liquid working fluid with the expanded superheated
vapour before the condenser.
The difference between water and several organic fluids is shown in a T,s-
diagram in Figure 1.
Figure 1: Comparison T,s-diagram of water and an organic fluid.
The diagram shows the saturation lines for water and a few organic fluids. It can
be clearly seen, that the critical point (top of the saturation curve) of an organic
fluid is reached at lower pressures and temperatures compared with water.
A comparison of the fluid properties between an organic fluid and steam is
presented in Table 1 [8].
Table 1: Summary of fluid properties comparison in steam and organic Rankine cycles
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A big challenge for optimizing an organic Rankine cycle for waste heat recovery
is the choice of the proper organic working fluid and the design of the cycle for
variable heat input and waste heat temperature.
A configuration and the cycle plotted in a T,s-diagram of an organic Rankine
cycle is shown in Figure 2.
Figure 2: Demonstration of an organic Rankine cycle: (a) Configuration of an organic Rankine cycle; (b) An organic Rankine cycle process in T–s diagram.
2. Components
A general description of an organic Rankine cycle can be found in Figure 3. As
can be seen, the cycle exists out of several components, which are similar to a
normal cooling cycle. The main components are:
a feeding pump of the organic fluid;
a vapour generator;
a turbine or expander;
a condenser;
and if necessary an internal heat exchanger or regenerator.
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Figure 3: Organic Rankine Cycle a) without IHE b) with IHE
An advantage of organic working fluids is that the turbine built for ORCs typically
requires only a single-stage expander, which results in a simpler, more
economical system in terms of capital costs and maintenance [9].
The power range of ORC process applications can vary from a few kW up to 1
MW. The most commonly used turbines which are available in the market cover a
range above 50 kW. Therefore, expanders in the power range below 10 kW have
to be found.
Schuster et al. gives a short overview of the used expanders in ORC technology
in [10], as summarized below.
A very promising solution to this turbine market problem is to use the scroll
expander. This expander works in a reverse way as the scroll compressor, which
is a positive displacement machine used in air conditioning technologies. Scroll
machines have two identical coils, one of which is fixed and the other is orbiting
with 180° out of phase forming crescent-shaped chambers, whose volumes
accelerate with increasing angle of rotation.
Another promising machine for the expansion of the working fluid is the screw
type compressor. Rotary screw compressors are also positive displacement
machines. The mechanism for gas compression utilizes either a single screw
element or two counter rotating intermeshed helical screw elements housed
within a specially shaped chamber. As the mechanism rotates, the meshing and
rotation of the two helical rotors produces a series of volume-reducing cavities.
Gas is drawn in through an inlet port in the casing, captured in a cavity,
compressed as the cavity reduces in volume, and then discharged through
another port in the casing. Screw type compressors can work in the reverse
direction also as expanders providing similar efficiencies. The effectiveness of the
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screw mechanism is dependent on close fitting clearances between the helical
rotors and the chamber for sealing of the compression cavities.
Recently, Gerotor and scroll expanders were experimentally tested for
performance in organic Rankine cycles [11].
3. Applications of organic Rankine cycles
Organic Rankine cycles can be used with several (renewable) energy sources:
biomass;
geothermal heat sources;
waste heat recovery of internal combustion engines or industrial plants;
solar energy.
2.1 Biomass [10]
Combustion is the most common process for energy production from this
renewable fuel. The fact that it is CO2-free has lead the countries to the financial
support of biomass combustion technologies. Some countries, for example
Germany, support extra the use of innovative technologies such as ORC process.
Therefore, many examples of ORC powered Combined Heat and Power plants are
working in central Europe like Stadtwärme Lienz Austria 1000 kWel, Sauerlach
Bavaria 700 kWel, Toblach South Tyrol 1100 kWel, Fußach Austria 1500 kWel
[12].
The main reason why the construction of new ORC plants increases is the fact
that it is the only proven technology for decentralized applications for the
production of power up to 1 MWel from solid fuels like biomass. The electrical
efficiency of the ORC process lies between 6-17 % [13].
However, even if the efficiency of the ORC is low, it has advantages, like the fact
that the system can work without maintenance, which leads to very low
personnel costs. Furthermore the organic working fluid has, in comparison with
water, a relatively low enthalpy difference between high pressure and expanded
vapour. This leads to higher mass flows compared with water. The application of
larger turbines due to the higher mass flow reduces the gap losses compared to
a water-steam turbine with the same power. The efficiency of an organic Rankine
cycle turbine is up to 85 % and it has outstanding part load behaviour [14].
The exhaust gas from biomass combustion has a temperature of about 1000°C.
For the use of the exhaust heat in the ORC process, the working fluid which is
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used in most of the biomass applications is octamethyltrisiloxane (OMTS).
Drescher et al. [15] discuss the use of other organic fluids and calculated an
efficiency rise of around three percentage points in the case where Butylbenzene
(C10H14) is used.
For biomass applications, the temperature levels are significantly higher than
low-grade heat applications (see Table 2 for typical temperatures of ORC for
biomass application).
Table 2: Typical temperatures of ORC for biomass application
Flame temperature 1200 K
Maximum thermal oil temperature 630 K
Maximum ORC fluid temperature 600 K
Condenser temperature 370 K
2.2 Geothermal heat sources [10]
Geothermal heat sources vary in temperature from 50 to 350°C, and can either
be dry, mainly steam, a mixture of steam and water, or just liquid water. The
temperature of the resource is a major determinant of the type of technologies
required to extract the heat and the uses to which it can be applied [16] [17].
Generally, the high-temperature reservoirs are the ones most suitable for
commercial production of electricity. Dry steam and flash steam systems are
widely used to produce electricity from high-temperature resources. Dry steam
systems use the steam from geothermal reservoirs as it comes from wells, and
route it directly through turbine/generator units to produce electricity. Flash
steam plants are the most common type of geothermal power generation plants
in operation today. In flash steam plants, hot water under very high pressure is
suddenly released to a much lower pressure, allowing some of the water to
convert into steam, which is then used to drive a turbine.
Medium-temperature geothermal resources, where temperatures are typically in
the range of 100–220°C, are by far the most commonly available resource.
Binary cycle power plants are the most common technology for utilizing such
resources for electricity generation. There are many different technical variations
of binary plants including the organic Rankine cycles. Binary cycle geothermal
power generation plants differ from dry steam and flash steam systems in that
the water or the steam from the geothermal reservoir never comes in contact
with the turbine/generator units. In binary systems, the water from the
geothermal reservoir is used to heat a secondary fluid which is vaporized and
used to turn the turbine/generator units. The geothermal water and the working
fluid are each confined in separate circulating systems and never come in contact
with each other.
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Although binary power plants are generally more expensive to build than steam-
driven plants, they have several advantages. The working fluid boils and flashes
to a vapour at a lower temperature than water does, so electricity can be
generated from reservoirs with lower temperatures.
An example of a geothermal plant using the ORC process is the plant Neustadt-
Glewe in Germany [18], which was the first geothermal power plant in Germany
[19]. This plant is a simple organic Rankine cycle plant which uses n-
Perfluorpentane (C5F12) as working fluid. It uses water of approximately 98°C
located at a depth of 2250 m and converts this heat to 210 kW electricity by
means of an organic Rankine cycle (ORC) turbine. Another well-known
geothermal plant using ORC process is the Altheim Rankine Cycle Turbogenerator
in the upper Austrian city Altheim. This plant produces 1 MWel power and supply
heat to a small district heating system. The thermal power input from the
geothermal water is equal to 12.4 MWth.
2.3 Solar energy [20]
Concentrating solar power is a well-proven technology: the sun is tracked and
reflected on a linear or on a punctual collector, transferring heat to a fluid at high
temperature. The heat is then transferred to a power cycle generating electricity.
The three main concentrating technologies are the parabolic dish, the solar
tower, and the parabolic trough. Parabolic dishes and solar towers are punctual
concentration technologies, leading to a higher concentration factor and to higher
temperatures. The best suited power cycles for these technologies are the
Stirling engine (small-scale plants), the steam cycle, or even the combined cycle,
for solar towers.
Parabolic troughs work at a lower temperature (300°C to 400°C). Up to now,
they were mainly coupled to traditional steam Rankine cycles for power
generation (Müller-Steinhagen & Trieb, 2004). The same limitation as in
geothermal or biomass power plants remains: steam cycles require high
temperatures, high pressures, and therefore high installed power to be
profitable.
Organic Rankine cycles seem to be a promising technology to decrease
investment costs at small scale: they can work at lower temperatures, and the
total installed power can be reduced down to the kW scale. The working principle
of solar energy powered Rankine cycle for combined heat recovery and power
generation is presented in Figure 4. Technologies such as Fresnel linear
concentrators (Ford, 2008) are particularly suitable for solar ORCs since they
require lower investment cost, but work at a lower temperature.
Up to now, very few CSP plants using ORC are available on the market:
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A 1MWe concentrating solar power ORC plant was completed in 2006 in
Arizona. The ORC module uses n-pentane as the working fluid and shows
an efficiency of 20 %. The overall solar to electricity efficiency is 12.1% on
the design point (Canada, 2004).
Some very small-scale systems are being studied for remote off-grid
applications. The only available proof-of-concept is a 1 kWe system
installed in Lesotho by “STG International” for rural electrification. The
goal of this project is to develop and implement a small scale solar thermal
technology utilizing medium temperature collectors and an ORC to achieve
economics analogous to large-scale solar thermal installations. This
configuration aims at replacing or supplementing Diesel generators in off-
grid areas of developing countries, by generating clean power at a lower
levelized cost.
Figure 4: Solar energy powered Rankine cycle using supercritical CO2 for combined
power generation and heat recovery
2.4 Waste heat recovery from internal combustion engines
[10]
A typical example of ORC powered waste heat recovery units can be found in the
field of internal combustion (IC) engines, for example in biomass digestion
plants. In this case, biogas coming out from the biomass digester is burned in an
internal combustion engine. The waste heat from this engine operates the ORC
cycle. Depending on the size of the digestion plant and the standard of the
insulation of the plant, the thermal need is between 20 … 25 % of the waste heat
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of the motor [21]. According to the low temperature level, the digester can be
heated with the cooling water of the motor and the turbocharger. For driving the
ORC, the heat of the exhaust gas can be used.
A coupling of the ORC process with internal combustion engines can be also
found in first prototypes for on-road-vehicle applications, where the condition for
waste heat is variable. Figure 5 shows the schematic setup of such a system.
Figure 5: Schematic representation of waste heat recovery for combustion engines
2.5 Industrial waste heat [22]
Heat recovery from ORC power plants can have many applications in the
industrial sector, especially in fields where energy has an impact on the
production process. Below is a list of potential fields for the ORC heat recovery
systems.
2.5.1 Cement industry
The cement production process involves lime decarbonizing reactions, which
being endothermic, requires great amounts of heat and high temperatures to
take place.
The unused heat supplied for these reactions can be found in the combustion gas
– or kiln gas – (after the raw material pre-heating) and in the clinker cooler air
flow (an air stream used to cool down the clinker after it exits the kiln). These
flows could, via thermal oil heat recovery circuits, be the heat sources feeding
the ORC for power generation purposes.
Typical cement production plants have a production capacity between 2000 and
8000 tons per day, with energy consumption ranging from 3.5 to 5 GJ/ton of
clinker produced (10%–15% of it in the form of electricity).
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As an indication, the power that can be produced by a Turboden [14] ORC
system in a typical cement making process can range from 0.5 to 1 MW/kilotons
per day of clinker production capacity (assuming heat recovery from both kiln
and cooler waste flows).
Using these figures, it can be estimated that the energy produced by an ORC can
account for around 10%–20% of the total electricity consumed by a cement
plant.
Additionally, in the case of heavy fuel oil (or similar liquid fuels) being used as a
fuel (either primary or as a back-up), some of the recovered heat can also be
used to keep the system at the correct working temperature.
2.5.2 Steel industry
Metallurgical industry is the major energy-consuming industry, whether in
nonferrous metallurgy or ferrous metallurgy industry, there is problem of big
energy waste. In the steel production and processing industry, there are multiple
waste heat sources where energy recovery with the ORC is possible. They can be
divided into relatively ‘clean’ sources (fumes from rolling pre-heating furnaces,
forging pre-heating furnaces, thermal treatments that are typically methane-
fuelled and have a relatively low dust content) and relatively ‘unclean’ ones
(fumes from blast furnaces, electric arc furnaces …).
For the clean sources, heat recovery processes can rely on established
technology to interface with the process (heat recovery exchangers); the second
option, the exhaust characteristics (very high flows, high temperatures, high dust
content, large variations in operating loads, environmental constraints) requires
significant development to be carried out on the heat recovery exchangers.
2.5.3 Glass industry
Glass production involves the melting and refining of raw materials which takes
place at high temperatures.
The unused heat supplied for glass production can be found in the combustion
gas exiting the oven. This flow can be used by the ORC to generate electricity,
sometimes via an intermediate thermal oil circuit.
Glass production processes can vary, i.e. the kind of product (float or hollow
glass), fuel employed (methane, HFO …), raw materials, size, etc. This makes it
difficult to develop a general rule of thumb to guess the quantity of power
producible with ORC heat recovery. Generally speaking, the exhaust gas
temperatures are relatively high (400°C–500°C), leading to high conversion
efficiencies (up to 25%), with related economic advantages.
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Chapter 3
Transcritical organic Rankine cycle
1. Introduction
The ideal thermal efficiency of a power cycle operating between a constant heat
source and cold source temperature is the Carnot efficiency, defined as follows:
| |
| |
The Carnot cycle consists of the four reversible processes shown in the T,s-
diagram of Figure 6. The processes are:
1→2: Isentropic expansion during which work is produced by the cycle
working fluid.
2→3: Isothermal heat rejection from the working fluid to a cooling
medium.
3→4: Isentropic compression during which work is performed on the cycle
working fluid.
4→1: Isothermal heat addition to the working fluid from a heating
medium.
Figure 6: Ideal Carnot cycle
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Due to the fact that in power production cycles, for example using waste heat,
the heat source is cooled down in the heat exchange process, the Carnot
efficiency and the maximum amount of transferred heat are competing
objectives (Figure 7).
Figure 7: Heat exchanger efficiency for a cooled down heat source, for a ideal Carnot
cycle with Tmax = 130°C and 160°C [23].
DiPippo [24] reviewed the Carnot cycle to its appropriateness to serve as the
ideal model for geothermal binary power plants. It was shown that the Carnot
cycle sets an unrealistically high upper limit on the thermal efficiency of these
plants. A more useful model is the triangular or trilateral cycle (Figure 8) because
binary plants, for example operating on geothermal hot water, use a non-
isothermal heat source. The triangular cycle imposes a lower upper bound on the
thermal efficiency and serves as a more meaningful ideal cycle against which to
measure the performance of real binary cycles.
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Figure 8: Triangular cycle
The thermal efficiency of a triangular cycle is lower than the ideal Carnot cycle
for the same upper and lower temperature.
The triangular cycle consists out of three processes (Figure 8):
The first two are the same as in the ideal Carnot cycle.
The heating process (state point 3 to state point 1) now is non-isothermal.
The thermal efficiency of the ideal triangular cycle is defined by (DiPippo [24]):
The cycle 1561 (Figure 8) represents the maximum-efficiency triangular
cycle, given the temperature of the heat source and the prevailing dead-state
temperature. The thermal efficiency for this cycle is:
Schuster et al. [23] compared the influence of a rectangular Carnot cycle and a
triangular cycle for two different initial heat source temperatures on the system
efficiency and found that for a rectangular cycle the system efficiency starts to
decline at a certain point with the increasing maximum cycle temperature. This
happens because the influence of the lower amount of heat exchanged in the
cycle, exceeds the benefit from the higher cycle efficiency. For a triangular cycle,
the system efficiency keeps on increasing with rising maximum cycle
temperature, because the transferred heat is only depended on the cycle
condensing temperature.
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Figure 9: System efficiency calculated for a rectangular (R) and triangular (T) process for initial heat source temperatures of 210°C and 150°C [23].
From Figure 9 it is visible that the cycle efficiency is optimized by maximizing the
maximum cycle temperature and keeping the isothermal heat transfer part to a
minimum.
2. Temperature profile in the heat exchanger
As mentioned before, when utilizing the energy of a low-grade heat source, the
enthalpy of the heat source fluid will drop with a gliding temperature profile in
the main heat exchanger during the energy transfer process. Larjola et al. [25]
pointed out that for a cycle that uses waste heat at a moderate inlet temperature
(80–200°C) as heat source, the best efficiency and highest power output is
usually obtained when the working fluid temperature profile can match the
temperature profile of the heat source fluid. This means, the system will have a
better performance if the temperature difference between the heat source and
the temperature of the working fluid in an evaporator (or vapour generator) is
reduced, because then the system has a lower irreversibility.
One of the limitations of a conventional subcritical ORC is the constant
temperature evaporation, which makes it less suitable for sensible heat sources
such as waste heat [26]. Therefore, some proposed cycles use mixtures as
working fluid [27] or a supercritical pressure to achieve variable temperature
heat addition to the working fluid for a better thermal fit with the heat source
(approach of a triangular cycle) (Figure 10).
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Figure 10: Temperature profile of heat source and working fluid for a subcritical ORC, subcritical ORC with a zeotropic mixture as working fluid and a transcritical ORC
In a transcritical power cycle, the liquid vapour phase transition is performed at a
continuously variable temperature at a supercritical pressure, while condensation
takes place in the usual constant temperature mode at subcritical pressure.
Thus, the major difference between a subcritical and a transcritical organic
Rankine cycle lies in the heating process of the working fluid. Working fluids with
relatively low critical temperatures and pressures can be compressed directly to
their supercritical pressures and heated to their supercritical state, bypassing the
two-phase region (no phase-transition). By bypassing the isothermal boiling
process, the temperature-glide (temperature change during take-up of heat
energy) of a transcritical Rankine cycle allows the working fluid to have a better
thermal match with the heat source compared to a subcritical organic fluid,
resulting in less exergy losses and exergy destruction. Furthermore, by avoiding
the boiling process, the configuration of the heating system can be potentially
simplified.
Figure 11 shows the different thermal match for R152a in a conventional organic
Rankine cycle and R134a in a transcritical Rankine cycle for the same maximum
temperature and pinch limitation [28].
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Figure 11: -diagram demonstrating the thermal match in a subcritical and transcritical
organic Rankine cycle. (a) Heating R152a in a subcritical ORC at 20 bar from 31.16°C to 100°C. (b) Heating R134a in a transcritical ORC at 40 bar from 33.93°C to 100°C [28].
The transcritical cycle, where heat rejection takes place at a subcritical pressure
and heat addition at a supercritical pressure, must not be confused with the
entirely supercritical cycle proposed by Feher [29].
Studies about low-temperature heat sources in transcritical cycles are quite rare
and were first being considered for geothermal power generation (Gu et al. [30]
[31]). Later, transcritical cycles have also been studied for solar energy (Zhang
X.R. et al. [32] [33]) and waste heat applications (Chen Y et al. [34]).
3. The transcritical cycle
A conceptual configuration and a p,h- and T,s-diagram of a transcritical Rankine
cycle are shown in Figure 12. The working fluid is pumped above its critical
pressure (from state point 1 until state point 2) and then heated with a constant
supercritical pressure from liquid directly to supercritical vapour (state point 3).
The supercritical vapour is expanded in the turbine to extract mechanical work
(from state point 3 until state point 4). After expansion, the fluid is condensed in
the condenser by dissipating heat to a heat sink (state point 4 until state point 1)
and the condensed liquid is then pumped to the high pressure again, which
completes the cycle.
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Figure 12: A typical transcritical organic Rankine cycle – configuration (left) and p,h-
diagram (right)
The cycle is composed of following processes:
Process 1–2: a non-isentropic compression process in the pump;
Process 2–3: a constant-pressure heat absorption process in the vapour
generator;
Process 3–4: a non-isentropic expansion process in the expander/turbine;
Process 4–1: a constant-pressure heat rejection process in the condenser;
The main advantage of the transcritical process is the fact that the average high
temperature, in which the heat input is taking place, is higher than in the case of
the subcritical process. Therefore, according to Carnot, the efficiency is higher.
Figure 13 shows the process of a sub- and transcritical ORC for the organic
working fluid R245fa in a T,s-diagram. Even for the same maximum superheated
vapour temperature, the heat input occurs at a higher average temperature
level. The superheating as shown in the diagram cannot be realized in reality for
a subcritical cycle due to the tremendous heat exchange area needed due to the
low heat exchange coefficient for the gaseous phase (Schuster et al. [10]).
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Figure 13: Sub- and transcritical ORC (R245fa)
As also can be seen in Figure 13, is that for a transcritical process, the enthalpy
fall is much higher than in the subcritical one for the same condensing
pressure, whereas the feed pump’s additional specific work to reach the
supercritical pressure, corresponding to the enthalpy rise , is very low.
Therefore, according to the first law of thermodynamics, the efficiency of a
transcritical cycle can become higher compared to a subcritical cycle. Thus, if the
heat transfer between the power cycle and the heat source is taken into account
properly, a transcritical power cycle should have a better performance than a
subcritical ORC.
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Chapter 4
Classification of working fluids-
Selection criteria
1. Introduction
The selection of working fluids and operating conditions are very important to the
system performance. The thermodynamic properties of working fluids will affect
the system efficiency and operation.
However, the thermodynamic parameters of the fluid are not the only criteria for
selection of an appropriate working fluid. The Montreal Protocol on Substances
that Deplete the Ozone Layer [35] and the EC regulation 2037/2000 restrict the
use of ozone depleting substances (European Parliament and council, 2004).
Therefore, the cycle designer should always be aware of the global warming
potential and the low ozone depletion of the working fluid before designing the
ORC-application.
In order to identify the most suitable organic fluids, several general criteria have
to be taken into consideration, namely:
safety and health aspects:
o toxicity (MAC = Maximum Allowable Concentration)
o explosion limit
o flammability
o small potential of decomposition
o stability of the fluid
o compatibility with materials in contact (non-corrosive)
environmental aspects:
o low ozone depletion potential (ODP)
o low global warming potential (GWP)
o low atmospheric life time
thermophysical aspects (shape of saturated vapour line, low critical
pressure and temperature, high density, low viscosity, high thermal
conductivity …)
thermodynamic aspects (efficiency, net power output, low specific volumes
…)
working range of waste heat (temperature, heat flux …)
availability and cost of the working fluid
cost of the system
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The two main parameters for fluid selection are the maximum and minimum
process temperature. The upper limit of the maximum process temperature is
the fluid stability and material compatibility. The melting temperature should be
below ambient temperature, because else the fluid may solidify during shutdown
time.
An important aspect for the choice of the working fluid is the temperature of the
available heat source, which can range from low temperatures of about 90°C to
medium temperatures of about 400°C for ORC-applications.
For low-temperature heat sources the advantage of organic fluids is obvious
because of higher molecular mass and the volume ratio of the working fluid at
the turbine outlet and inlet (or the vapour expansion ratio VER). The latter can
be smaller by an order of magnitude for organic fluids than for water and thus
allows the use of simpler and cheaper turbines [36].
2. Classification and selection criteria of working fluids
There is a wide selection of organic fluids which can be used in organic Rankine
cycles. Despite all the research activities that are going on in this field, there is
no consensus concerning the best working fluid. This is due to the fact that the
working fluids have to be subjected to a number of criteria and also due to the
wide range of applications. Refrigerants are the most promising fluids for ORC
cycles according to Mago et al. [37], especially with the view of their low toxicity.
The fluid selection affects the system efficiency, operating conditions,
environmental impact and economic viability. Selection criteria are set out in this
section to locate the potential working fluid candidates for different cycles at
various conditions. Some of these criteria can only be used after evaluation of
the cycle by simulation. A difference can be made between criteria that can be
evaluated without simulation of the cycle, called “screening criteria”, and criteria
after simulation of the cycle, called “cycle criteria”. The working fluids will
eventually be selected by a combination of all these criteria.
2.1 Screening criteria
2.1.1 Safety criterion (ASHRAE 34)
The American Society of Heating, Refrigerating and Air-Conditioning Engineers
(ASHRAE) focuses on building systems, energy efficiency, indoor air quality,
refrigeration and sustainability within the industry. ASHRAE also publishes a well-
recognized series of standards and guidelines relating to HVAC systems and
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issues. The standard ASHRAE 34 describes the “Designation and Safety
Classification of Refrigerants” and gives an indication of the safety level of the
used refrigerant [38].
Table 3: The standard AHRAE 34 classification
Toxicity:
Class A represents refrigerants for which the toxicity has not been
identified at concentrations less than or equal to 400 ppm by volume.
Class B represents refrigerants for which there is evidence of toxicity at
concentrations below 400 ppm by volume.
Flammability:
Class 1 indicates refrigerants that do not show flame propagation when
tested in air at 101.3 kPa and 21°C.
Class 2 represents refrigerants having a lower flammability limit (LFL) of
more than 0.10 kg/m³ at 101.3 kPa and 21°C and the heat of combustion
(HOC) less than 19 MJ/kg.
Class 3 represents refrigerants which are highly flammable and having a
lower flammability limit (LFL) of less than 0.10 kg/m³ at 101.3 kPa and
21°C or the heat of combustion (HOC) greater than or equal to 19 MJ/kg.
2.1.2 Environmental criterion
The most important environmental criteria are the global warming potential
(GWP), ozone depletion potential (ODP) and the atmospheric lifetime (ALT).
Global-warming potential (GWP) is a relative measure of how much heat a
greenhouse gas traps in the atmosphere. It compares the amount of heat
trapped by a certain mass of the gas in question to the amount of heat trapped
by a similar mass of carbon dioxide. A GWP is calculated over a specific time
interval, commonly 20, 100 or 500 years. For example, the 20 year GWP of
methane is 72, which means that if the same mass of methane and carbon
dioxide were introduced into the atmosphere, that methane will trap 72 times
more heat than the carbon dioxide over the next 20 years [39].
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The ozone depletion potential (ODP) of a chemical compound is the relative
amount of degradation to the ozone layer it can cause, with
trichlorofluoromethane (R11) being fixed at an ODP of 1. Chlorodifluoromethane
(R22), for example, has an ODP of 0.055 x R11, or R11 has the maximum
potential amongst chlorocarbons because of the presence of three chlorine atoms
in the molecule [40].
The atmospheric lifetime (ATL) of a chemical compound is the period of time
required to restore the equilibrium after a sudden increase or decrease in its
concentration in the atmosphere. The time depends on the chemical reactions
that the gas goes through and the natural buffering capabilities. Individual atoms
or molecules may be lost or deposited to sinks such as the soil, the oceans and
other waters, or vegetation and other biological systems, reducing the excess to
background concentrations [41].
An important statement here, as mentioned before, is the Montreal Protocol [35].
This determines the phasing out of chlorofluorocarbon (CFC) and
hydrochlorofluorocarbon compounds (HCFC). The use and production of CFCs has
been banned since 2010. For HCFCs the following transition rules are:
2004: reduction of 35% from the reference;
2010: reduction of 75% from the reference;
2015: reduction of 90% from the reference;
2020: reduction of 99.5% from the reference;
2030: complete phase out.
The reference for developed countries is set at 2.8% of that country's 1989
chlorofluorocarbon consumption + 100% of that country's 1989 HCFC
consumption [35].
Some working fluids have been phased out, such as R11, R12, R113, R114, and
R115, while some others are being phased out in 2020 or 2030 (such as R21,
R22, R123, R124, R141b and R142b).
The hydrofluorocarbons (HFCs: a compound consisting of hydrogen, fluorine, and
carbon) are a class of replacements for CFCs. Because they do not contain
chlorine or bromine, they do not deplete the ozone layer. All HFCs have an ozone
depletion potential of 0, but some of them have a high GWP!
The ORC system can take the advantage of reducing the consumption of fossil
fuels and the emission of the greenhouse gas.
For example if a geothermal power plant is used instead of a petroleum-fired
power plant, the saved petroleum ( in kiloliter/year) and reduced CO2
emission ( in kg/year) per year can be simply estimated as [42]:
( )
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( )
Where:
is the operating time per day (e.g. 24h);
is the amount of petroleum consumed to produce 1 kWh of electrical
energy (e.g. 0.266 l/kWh);
is the amount of CO2 emission if 1 kWh of electrical energy produced
by a petroleum fire power plant (e.g. 0.894 kg/kWh).
2.1.3 Stability of the working fluid and compatibility with materials in
contact
Unlike water, organic fluids usually suffer chemical deterioration and
decomposition at high temperatures [43]. The maximum operating temperature
is thus limited by the chemical stability of the working fluid. Additionally, the
working fluid should be noncorrosive and compatible with engine materials and
lubricating oil. Calderazzi and Paliano [44] studied the thermal stability of R134a,
R141b, R13I1, R7146 and R125 associated with stainless steel as the container
material. Andersen and Bruno [9] presented a method to assess the chemical
stability of potential working fluids by ampule testing techniques. The method
allows the determination of the decomposition reaction rate constant of simple
fluids at the temperatures and pressures of interest.
2.1.4 Thermophysical properties
The several thermophysical properties for evaluation of the suitability of a
working fluid for ORC-applications are:
the type of fluids;
the influence of latent heat, density and specific heat;
the critical temperature and pressure;
the use of mixtures as working fluid;
and the availability and cost of the working fluids.
2.1.4.1 Type of fluids
The working fluids can be classified into three categories according to the shape
of the saturated vapour line in the T,s-diagram (Figure 14). Since the value of
⁄ leads to infinity for isentropic fluids, the inverse is used to express how
‘dry’ or ‘wet’ a fluid is.
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Define ⁄ , the 3 types of working fluids can be classified by the value of
:
dry fluids ( ),
isentropic fluids ( ),
and wet fluids ( ).
Liu et al. [45] derived an expression to calculate , which is:
Where:
⁄ denotes the reduced evaporating temperature;
represents the enthalpy of vaporization;
the exponent n is suggested to be 0.375 or 0.38 [46].
Chen H. et al. [47] made calculations and discovered that large deviations can
occur when using this equation at off-normal boiling points. Therefore, it is
recommended to use the entropy and temperature data directly to calculate .
Figure 14: T,s-diagram for the three types of working fluids
The working fluids of dry or isentropic type are more appropriate for ORC
systems. This is because dry or isentropic fluids are superheated after isentropic
expansion, thereby eliminating the concerns of impingement of liquid droplets on
the turbine blades. However, if the liquid is “too dry”, the expanded vapour will
leave the turbine with substantial superheat, which is a waste and adds to the
cooling load in the condenser [48]. The cycle efficiency can be increased using
this superheat to preheat the liquid after it leaves the feed pump and before it
enters the vapour generator.
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Liu et al. [45] investigated the effect of working fluids in organic Rankine cycles
for waste heat recovery and found that the presence of a hydrogen bond in
certain molecules such as water, ammonia and ethanol may result in ‘wet’ fluid
conditions due to larger vaporizing enthalpy, and is regarded unsuitable for
ORCs.
Furthermore, it can be observed from literature, that the fluids consisting of
simpler molecules are mostly of the ‘wet’ type, while those consisting of more
complicated molecules are mostly of the ‘dry’ type.
In the next paragraphs the basic types of organic Rankine cycles will be
described according to the type of working fluid. The state points of the used T,s-
diagrams (Figure 16 and Figure 18) correspond with the cycle architecture of
Figure 15.
Figure 15: Organic Rankine Cycle a) without IHE b) with IHE
2.1.4.1.1 Trans – and subcritical ‘wet’ cycles
On Figure 16, the T,s-diagram is shown of a subcritical organic Rankine cycle
using a ‘wet’ fluid as working fluid.
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Figure 16: T,s-diagram of an ORC with a wet organic fluid and saturated vapour at the turbine inlet (left) and superheated vapour at the turbine inlet (right)
The working fluid leaves the condenser as saturated fluid with temperature
and condenser pressure (state point 1). The liquid is then
compressed to the subcritical evaporator pressure by the
feed pump (state point 2). The working fluid is then heated in the evaporator at
constant pressure untill it reaches the saturated vapour line (state point 3). In
the expander or turbine the saturated vapour is expanded to the
condensor pressure (state point 4). This point lies in the two-phase region.
Finally, the fluid passes through the condenser where the rest of the heat is
removed at a constant pressure, untill it becomes sturated liquid (state point 1).
An other type of ORC (Figure 16 right) is one where superheated vapour is
presented at the inlet of the expander. Starting from state point 2, the fluid is
heated, evaporized and superheated in the evaporator at constant subcritical
pressure (state point 3). The saturated vapour is then expanded with an
isentropic efficiency to state point 4, which is in the superheated vapour
region.
Figure 17 shows a ‘wet’ fluid (propyne), used in a transcritical Rankine cycle. If
the expansion is carried out such that the expansion does not go into the two-
phase region (the dashed lines in Figure 17), a ‘wet’ fluid will need a higher
turbine inlet temperature, without concerns about de-superheating after the
expansion. If the process is allowed to pass through the two-phase region (the
solid lines in Figure 17), the ‘wet’ fluid stays in the two-phase region at the
turbine exit.
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Figure 17: T,s-diagram of a transcritical ORC with a 'wet' organic fluid
Bakhtar et al. [49] [50] [51] [52] found that for a ‘wet’ fluid, such as water, the
fluid first subcools and then nucleates to become a two-phase mixture. The
formation and behavior of the liquid in the turbine create problems that would
lower the performance of the turbine.
2.1.4.1.2 Trans – and subcritical ‘dry’ cycles
Figure 18 presents a T,s-diagram of a subcritical organic Rankine cycle using a
‘dry’ fluid as working fluid. The difference here is that due to the positive slope of
the saturated vapour line, the state of the fluid after expansion is always in the
superheated vapour region located on the condenser pressure isobar (state point
4), also if the working fluid is superheated in the evaporator.
Figure 18: T,s-diagram of an ORC with a 'dry' organic fluid and saturated vapour at the turbine inlet
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Figure 19 shows a ‘dry fluid (pentane), used in a transcritical Rankine cycle. If
the expansion is carried out such that the expansion does not go into the two-
phase region (the dashed lines in Figure 19), ‘dry’ fluids may leave the turbine
with substantial amount of superheat, which adds to the burden for the
condensation process or a recovery system (IHE) is needed. If the process is
allowed to pass through the two-phase region (the solid lines in Figure 19), the
‘dry’ fluid can still leave the turbine at superheated state. Goswami et al. [53]
and Demuth [54] [55] found that only extremely fine droplets (fog) were formed
in the two-phase region and no liquid was actually formed to damage the turbine
before it started drying during the expansion. Demuth [54] also found that the
turbine performance should not degrade significantly as a result of the turbine
expansion process passing through and leaving the moisture region if no
condensation occurs.
Figure 19: T,s-diagram of a transcritical ORC with a 'dry' organic fluid
Saleh et al. [28] compared ‘dry’ and ‘wet’ organic fluids and noticed that the
highest values of thermal efficiency are obtained for the high-boiling substances
with overhanging (‘dry’) saturated vapour line in subcritical processes with an
internal heat exchanger. For the ‘wet’ cycles it was found that the increase of the
thermal efficiency by superheating is only small in the case without an internal
heat exchanger and hence not really rewarding. A more significant increase can
be achieved if superheating is combined with an internal heat exchanger. At the
contrary, for the ‘dry’ cycles a decrease of the thermal efficiency was found by
superheating.
To this end, dry fluids may serve better than wet fluids in supercritical states if
the turbine expansion involves two-phase region [48].
2.1.4.2 Influence of latent heat, density and specific heat
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Chen H. et al [48] conducted a theoretical analysis by deriving the expression of
the enthalpy change through the turbine expansion and it was found that
working fluids with a high density, low liquid specific heat and high latent heat
are expected to give high turbine work output.
[ ⁄
⁄ ⁄]
Where:
T1 and T2 are the saturation temperatures of two points on the coexistence
line and T1 > T2;
T’in is the turbine inlet temperature;
and L is the latent heat.
2.1.4.3 Critical temperature and pressure
Besides the shape of the saturated vapour line, the pressure at which the
working fluid exchanges heat is also an important classification parameter. A
difference can be made between subcritical and transcritical cycles.
For a subcritical cycle, the working fluid undergoes a liquid-vapour phase
transition, while for the transcritical cycle such a phase transition does not occur
(Figure 20).
Figure 20: T,s-diagram - comparison between a sub- and supercritical fluid
In order to reject heat to the ambient in the condenser, the critical temperature
must be above 300K (design condensation temperature). Furthermore, the
critical point of a working fluid should not be too high to use in transcritical
Rankine cycles.
Moreover, as in general, the molecularly simpler fluids have lower critical
temperatures , so lower can be found for mostly ‘wet’-fluids and for
higher mostly ‘dry’-fluids.
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2.1.4.4 Mixtures
As mentioned in Chapter 3 – section 2 Temperature profile in heat exchanger,
mixtures of working fluids [27] can be used to achieve variable temperature heat
addition in the vapour generator and heat rejection in the condenser for a better
thermal fit with the heat source (cfr. triangular cycle).
Chen H. et al. [47] [56] stated that the use of zeotropic mixtures can approach
an “ideal” working fluid for transcritical ORCs, as these mixtures have the
property of a temperature-glide during phase-change, which decreases the
exergy destruction during condensation (Figure 21Figure 20).
Figure 21: A transcritical Rankine cycle with an "ideal" working fluid
A comparison between subcritical R134a and a transcritical zeotropic mixtures of
R32 and R134a (0.3/0.7 mass fraction) shows that due to the thermal glide the
zeotropic mixtures has a 22.67% higher exergy efficiency during the
condensation process than pure R134a (Chen H. et al. [56], Figure 22).
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Figure 22: Condensing process of R134a (left) and the zeotropic mixture of R134a and R32 (right) and their thermal match with the cooling fluid.
2.1.5 Availability and cost of working fluids
The availability and cost of the working fluids are among the considerations when
selecting working fluids. Traditional refrigerants used in organic Rankine cycles
are expensive. This cost could be reduced by a more massive production of those
refrigerants, or by the use of low cost hydrocarbons.
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2.2 Cycle criteria - Selection by performance indicator
In order to choose an appropriate working fluid and operating conditions for a
waste heat stream with a specific temperature and mass flow rate, several
indicators have to be evaluated. A distinction can be made between
thermodynamic indicators, heat exchanger design indicators and economic
indicators.
2.2.1 Thermodynamic performance indicators
Using the first and second law of thermodynamics [57], a first performance
evaluation can already be made of an organic Rankine cycle under diverse
working conditions for different working fluids. The state points correspond with
the organic Rankine cycle of Figure 15.
2.2.1.1 First law efficiency - Thermal efficiency of the cycle – Net power
output
The thermal efficiency of the cycle is defined as the net mechanical power
produced with an ORC to the heat input to the working fluid of the ORC.
The net mechanical power produced with an ORC can be written as:
| |
[ ]
With the enthalpy fall in the expander and the enthalpy rise
necessary for pumping the working fluid.
The heat input to the working fluid of the ORC by heat exchange in the vapour
generator is equal to:
For an ORC with an internal heat exchanger or regenerator the input heat is
given as:
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Working with a regenerator, the average temperature of heat transfer to the
cycle (from to ) is higher than without IHE (from to ) while the average
temperature of heat transfer to the environment (from to ) is lower than in
case without IHE (from to ). Also the heat transferred in the regenerator
does not need to be supplied from outside. All these aspects result according to
Carnot in a higher thermal efficiency.
Much research has been conducted on the ORC system using the first law as a
selection criterion. Saleh et al. [28] screened 31 pure component working fluids
for ORCs and noticed a general trend that the thermal efficiency increases with
the fluids critical temperature.
Chen Y. et al. [58] compared a carbon dioxide transcritical power cycle with a
subcritical ORC using R123 as working fluid for low-grade waste heat recovery
(exhaust gas of 150°C and a mass flow rate of 0.4 kg/s) and found that the
transcritical CO2 cycle has a higher system efficiency when taking into account
the heat transfer behaviour between the heat source and the working fluid.
Furthermore, the transcritical CO2 cycle shows a higher power output, when
using the same thermodynamic mean heat-rejection temperature of 25°C. The
thermodynamic mean temperature is used as reference, because of non-
isothermal heat addition and rejection. They also noted that only comparing the
thermodynamic efficiencies of cycles might be misleading, since the highest
power output is not achieved at maximum cycle thermal efficiency when utilizing
a certain heat source.
Gu et al. [30] [31]) compared propane, R125 and R134a in a transcritical cycle
for geothermal power generation by optimization of the cycle state parameters,
especially the condensing temperatures or pressures. Propane and R134a are
found to be more suitable as the working fluids of transcritical cycles because of
their higher power output from the same geothermal resource compared to
R125.
Baik et al. [59] compared optimized cycles of transcritical CO2 and R125 with the
power output as objective function for a low-grade heat source of 100°C. They
were also one of the first who took the pressure drop characteristics into account
and didn’t fix the cycle minimum temperature, as in actual practice. A simple
double-pipe heat exchanger was chosen for convenience under the assumption
that if the working fluid performs better in a double-pipe heat exchanger it will
perform better in other types of heat exchangers. It was found that R125 has
around 14% more net power than CO2, because the CO2 cycle requires a higher
pumping due to the higher pressure. Even though, CO2 has better heat transfer
and pressure drop characteristics. It should be noted that if a conventional
approach, in which the cycle minimum temperature is fixed, were employed, the
performance of the R125 cycle would be overestimated.
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It can be concluded that in a lot of cases the overall thermal efficiency can be
improved using transcritical cycles instead of subcritical cycles (e.g. +5% [60]),
but this also happens at the expense of a bigger vapour generator (Mickielewicz
et al. [60]).
As the thermal efficiency cannot reflect the ability to convert energy from low-
grade waste heat into usable work, we need to consider the exergy efficiency,
which can evaluate the performance for waste heat recovery.
2.2.1.2 Second law efficiency - Exergy efficiency
From the viewpoint of the first law of thermodynamics and energy conservation,
used to determine the overall thermal efficiency, work and heat are equivalent.
On the other hand, based on the second law of thermodynamics, exergy
quantifies the difference between work and heat in terms of irreversibility.
Because of the thermodynamic irreversibility occurring in each of the
components, such as non-isentropic expansion, non-isentropic compression and
heat transfer over a finite temperature difference, the exergy analysis method
can be employed to evaluate the performance for low-grade waste heat
recovery.
Consider p0 and T0 to be the ambient pressure and temperature as the specified
dead reference state. In most of the studies the conditions of the ambient
environment are taken as the dead state.
The following assumptions are made to calculate the exergy of each state point:
It is assumed that only physical exergies are used for flue gas and steam
flows.
Chemical exergies of the substances are neglected.
Kinetic and potential exergies of materials are ignored.
The exergy of the state point can be considered as [57]:
[ ]
The exergy balance for an open thermodynamic system can be expressed as
[57]:
∑ ∑
With the exergy destruction or irreversibility.
The objective of this parameter is to show the use of the exergy concept in
assessing the effectiveness of energy source utilization.
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Exergy efficiency indicates the percentage of usable energy conserved during a
process (e.g. condensation or heating process).
In literature several equations can be found for defining the exergy efficiency.
The three most suitable definitions are discussed below (Ho et al. [61]).
The internal second law efficiency is defined as the ratio of the net work
produced to the potential work (or exergy) added [61].
( )
With and the specific exergy of the working fluid before and after heat
addition, respectively.
The major problem with this equation is that it doesn’t give a good
representation of the performance of the cycle in a waste heat recovery system,
because the exergy in the heat source stream is afterwards discarded or not
used anymore (the amount of unused exergy or exergy loss is noted as ).
Since the focus of this work is on waste heat recovery, the aim should be to
optimize the heat transfer from the waste heat source to the working fluid and
simultaneously optimize the net output power from this heat transfer.
The internal second law only says something about how efficient the cycle
produces work from a certain amount of exergy that is added to the system
during the heat addition, but it doesn’t say something about how efficient the
cycle is at absorbing the exergy from the waste heat source.
In other words, a cycle can have a high internal second law efficiency, but only
producing little power because only a small amount of exergy is added to the
system.
If the heat energy of the heat source is still to be used after the heat transfer
process to the power cycle (e.g. in combined heat and power cycles), it is better
to define a second law efficiency that also includes the exergy destruction due to
the heat transfer from the heat source to the working fluid.
( )
This is also called the external second law efficiency [61].
For applications where the energy of the heat source is unused after the heat
transfer process (e.g. some waste heat and solar power applications), the
remaining exergy will eventually be lost to the environment. In this case it is
better to define a more appropriate parameter that expresses the ratio of how
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much power is produced to the theoretical amount of potential work from a given
finite heat source. This parameter is also called the utilisation efficiency [61].
( )
Where represents the heat source’s exergy at the dead state.
The advantage of this non-dimensional parameter is that is can be used to
compare different cycles.
The heat addition exergy efficiency can be defined as:
( )
( )
The utilisation efficiency then can be written as [61]:
It is clear that the utilisation efficiency can be maximized when the system is
efficient at absorbing heat energy ( ) and simultaneously efficient at
concerting it to useful work ( ).
Several authors use different definitions for exergy efficiency, which makes it
difficult to make a comparison between efficiencies listed in papers. An overview
is listed below:
Cayer et al. [62]
With the total exergy destruction:
∑
∑
Wang et al. [63]
∑
With ∑ the total system irreversibility and the exergy losses to the
environment:
Chen H et al. [47]
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With the exergy of the working fluid obtained by absorbing heat from the heat
source and the exergy input by the pump.
Zhang XR et al. [64]
⇒
⁄
Another expression can be:
With
Schuster and Karellas (2010) [23] studied the efficiency optimization potential in
transcritical ORCs for various working fluids (water, R1234a, R227ea, R152a,
RC318, R236fa, iso-butene, R245fa, R365mfc, iso-pentane, iso-hexane and
cyclo-hexane) and found that an improvement of about 8% in system efficiency
is possible due to a better exergy efficiency. Furthermore it was also noticed that
good system efficiencies and low exergy losses are not directly followed by low
values for the heat transfer capacity UA.
Chen H. et al (2011) [47] performed an energetic and exergy analysis of a CO2-
and R32 based transcritical Rankine cycle. R32 has the advantage that it has a
higher thermal conductivity and condenses more easily than CO2. Furthermore,
the thermal efficiency of R32 was about 12.6-18.7% higher than CO2 and works
at much lower pressures. The exergy efficiency of R32 was also found to be
higher over a wide range of the maximum pressure of the cycle.
2.2.1.2.1 System total irreversibility
Irreversibility is the cause of inefficiency and exergy loss/destruction. An
exergetic analysis is necessary to know the extent of irreversibility in each
process, and therefore the potential for improvement.
The work developed by the overall system can be written as [57]:
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The exergy change of the system can be written as [57]:
Energy and entropy balance for a closed system can be written as [57]:
∫
∫ (
)
The closed system exergy balance can then be written as [57]:
∫
⇒ ∫
[ ]
⇒ ∫
[∫ (
)
] [ ]
⇔
∫ (
)
[ ]
The aim is to minimise the exergy destruction or irreversibility of each
component.
⇒ [ ∫ (
)
]
⇒ [
]
The irreversibility of the pump is defined as:
( )
or
The irreversibility of the vapour generator is defined as:
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( ) ( )
With the irreversibility equation and , the irreversibility
can be written as:
[
]
The irreversibility of the expander is defined as:
( )
or
The irreversibility of the condenser is defined as:
With the irreversibility equation and
[
]
The irreversibility of the IHE is defined as:
( ) ( )
or
[ ]
The irreversibility of a process, , is the sum of all of available exergy
destruction of all the streams in the system:
∑
The major exergy destruction in the vapour generator or the condenser is due to
heat transfer over a finite temperature difference, and the exergy destruction in
the turbine or pump is due to the friction losses of the flow through the turbine
or the pump, the non-ideal adiabatic expansion or compression in the turbine or
the pump, and the corresponding irreversibilities.
As the heat source is not cooled down to the dead state temperature , the rest
of exergy after the heat exchanger that is not used, is regarded as losses.
Figure 23 [23]shows the hatched exergy destruction due to heat transfer and
losses (exergy transportation to the environment) due to incomplete cooling
down of the heat source for sub- and supercritical conditions.
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Figure 23: Exergy losses and destruction in subcritical (left) and supercritical (right)
heating process.
2.2.1.2.2 Exergy destruction factor (EDF)
The exergy destruction factor of a component can be defined as the ratio of the
exergy destruction of the component to the net power produced by the cycle.
2.2.1.3 Other efficiencies
Some authors use also other efficiencies to express the performance of the
power cycle, but these are less used because the external exergy efficiency and
utilisation efficiency already give a very good representation of the performance
of the cycle.
2.2.1.3.1 Heat-exchanger and system efficiency [10] [23]
One of the main goals of an optimal working organic Rankine cycle is not to have
the maximum thermal efficiency, but to maximize the power output from a given
heat source.
The efficiency of the heat exchanger, which transfers the heat from the waste
heat source to the organic fluid, is defined as:
The efficiency of the whole system then can be defined as:
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As the efficiency of the ORC system is directly linked with the efficiency of the
heat-exchanger, it is our goal to maximize the transferred heat.
Schuster and Karellas (2008) [10] performed simulations with subcritical and
supercritical fluid parameters for applications of waste heat recovery from
internal combustion engines and a geothermal power plant. Using R245fa as
working fluid for the waste heat recovery from IC engines (thermal oil at 240°C);
a 13% higher system efficiency was found in the case of supercritical fluid
parameters.
2.2.1.3.2 Recovery efficiency [65]
The thermal efficiency represents the ORC itself, neglecting the thermal
behaviour of heat sources and sinks. The recovery efficiency takes this influence
into consideration and is a more meaningful parameter.
With is the maximum theoretical power produced by a Carnot engine
operating between the heat source inlet temperature and the ambient
temperature.
Net power output of the system can be given:
2.2.1.3.3 Rankine cycle efficiency
The Rankine cycle efficiency is defined as:
With:
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Heat supply in vapour generator:
Heat rejection in the condenser:
2.2.2 Heat exchanger performance indicators
Besides the thermal and exergy efficiency and net power output, another
objective for optimization can be the performance indicators related to the heat
exchangers used in the cycle.
The two objective functions considered in literature are the heat transfer capacity
and the total heat exchanger area.
2.2.2.1 Heat transfer capacity UA capacity
Schuster et al. [23] uses the heat transfer capacity in his research to investigate
the influence of the maximum cycle temperature (turbine inlet temperature) on
UA for a selection of working fluids. It has to be noted that good system
efficiencies and low exergy losses are not directly followed by low values for the
heat transfer capacity UA [23]. This indicates again the importance of a good
choice of the objective function.
Cayer et al. [62] [66] uses the heat transfer capacity as an objective function
and checks the influence of the turbine inlet temperature, turbine inlet pressure
and the net work output on the value of UA for a transcritical cycle using CO2,
ethane and R125.
The general results can be found in Chapter 6 Fluid selection and cycle
optimization.
A better objective function as heat exchange performance indicator can be the
minimization of the total area needed for heat exchange. A low value for UA can
indicate on a small heat exchange surface, which is positive, but it can also
indicate on a low overall heat transfer coefficient.
2.2.2.2 Total heat exchanger surface
Cayer et al. [62] [66] also investigated the influence of the turbine inlet
temperature, turbine inlet pressure and the net work output on the value of UA
for a transcritical cycle using CO2, ethane and R125.
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The general results can be found in Chapter 6 Fluid selection and cycle
optimization.
The gap between two consecutive points of the temperature profiles of the heat
source and sink with the working fluid say something about the heat transfer
rate and consequently the heat transfer surface.
Figure 24: Optimized carbon dioxide transcritical cycle (left) and optimized R125 transcritical cycle (right).
A wide gap indicates that the segment has a high heat transfer rate compared
with points having a narrow gap.
In the case of the carbon dioxide in the vapour generator (Figure 24), the
segments near the exit have relatively low heat transfer rates due to the low
temperature difference. In contrast, a larger heat transfer area is occupied by
the middle range of the R125 vapour generator.
2.2.2.3 Heat exchanger efficiency
For the calculation of the heat exchanger efficiency, the -NTU method cannot be
used, as in some parts of the heat transfer procedure, neither the temperature
nor the specific heat capacity are constant. In a subcritical heat transfer process
one of the two values is constant. In the sensible heat transfer procedures, is
considered constant, where in latent heat transfer procedures (evaporation) the
temperature remains constant. Therefore, the following definition was used for
the efficiency of the heat exchanger [67]:
With the heat transferred to the organic working fluid and the maximum
transferable heat, defined as:
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( )
{( ) ( )
}
2.2.3 Cost performance indicators
A complete economic analysis is rather complex, because it is dependent on
several parameters which are influenced by future local and global events.
Zhang S. et al. [65] and Cayer et al. [66] were one of the first who performed a
thermo-economic parameter analysis for a selection of working fluids in
transcritical organic Rankine cycles (R134a, R143a, R218, R125, R41, R170,
ethane and CO2).
The general results can be found in Chapter 6 Fluid selection and cycle
optimization.
Cayer et al. [66] uses well-estimated purchase prices for the major components
of the cycle (pump, turbine and heat exchangers) as the representative of the
complete life cycle cost, even if it is just a fraction of the actual total cost.
Zhang S et al. [65] considers the total cost of the heat exchangers
representative of the complete system cost of an ORC, because 80-90% of the
system capital cost can be assigned on the heat exchangers [68] [69] [70].
Two economic performance indicators can be used for evaluation of a power
system:
APR
LEC
2.2.3.1 APR
As it is stated that the total cost of a heat exchanger is representative for the
complete system cost [68] [69] [70], the APR can be used as a performance
indicator for evaluation of an organic Rankine cycle.
APR is the ratio of the total heat transfer area to the total net power output [69].
The result of the APR doesn’t give an economical value, but it says something
about the heat exchange area needed for a certain amount of net power output.
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The goal is to minimize this function to obtain as much power with as less heat
exchange surface.
2.2.3.2 Levelized energy cost LEC
The levelized energy cost is defined as the ratio of the system cost to the total
net power output [70].
The purchase price of the components can be calculated by the following general
correlation [71]:
With:
the basic cost of the equipment assuming ambient operating pressure
and carbon steel construction in the year of 1996 (US dollar).
is a dimensional parameter which corresponds to the total area in m2 for
the heat exchangers, the power output in kW for the turbine and the
power input in kW for the pump.
and are component and material specific coefficients.
Cayer et al. [66] chose the following specifications for his case:
an axial gas turbine in cast steel;
an electric centrifugal pump in cast steel;
a fixed head shell and tube vapour generator in cast steel;
and a fixed head shell and tube condenser in stainless steel.
Zhang S et al. [65] chose:
a fixed head shell and tube vapour generator in cast steel;
a fixed head shell and tube condenser in stainless steel;
and the operating pressure of both heat exchanger are much higher than
the ambient pressure.
This basic cost then has to be corrected for the chosen material and for the
working pressures by following correlation:
The corrected cost than be defined as:
With:
the material correction factor;
the pressure correction factor;
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and and the coefficients characterising each type of equipment.
The total is calculated by summating the of each component.
The cost of the power plant also needs to be converted from the costs in 1996 to
the present day by using Chemical Engineering Plant Cost Index (CEPCI) values,
which are published in the Chemical Engineering Journal and allows adjusting
process plant construction costs from one period to another [71].
All the coefficients ( , , , and ) are available in literature [72].
Taking into account the interest rate ( , e.g. 5%) and the lifetime of the plant
( , e.g. 20 years), the capital recovery cost can be defined [73]:
The levelized energy cost then can be calculated by [70]:
Where:
is the present capital cost of the power plant in US dollar;
the operations and maintenance cost of the power plant US dollar
(e.g. 1.5% of );
the annual net power output of the power plant in kW.
3. Working fluids for organic Rankine cycles
3.1 Fluid candidates
More than 50 working fluids have been suggested in the literature, among which
some have been phased out as required by the protocols, and some are not
practical for application due to their properties (e.g. methane). Based on the
criteria of safety, environmental issues, critical temperature and availability, a
list of pure working fluids that could be used in for organic Rankine cycles and
transcritical Rankine cycles is presented in Table 4. Multi-component fluids are
not completely included in this table, because the mixing rule is rather
complicated and there are a lot of combinations possible.
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Table 4: Overview of potential working fluids for ORCs
Physical data Safety data
Environmental data
Name Type Tcrit (°C)
pcrit
(bar)
ASHRAE 34 safety group
ATL (yr) ODP
GWP (100 yr)
R-116
19,88 30,50
0 11900
R-23
26,14 48,30
0 n.a.
R-747 - CO2 WET 31,10 73,80 A1 >50 0 1
R-170 WET 32,18 48,00 A3 0,21 0 ~20
R-41 WET 44,13 59,00 n.a. 2,4 0 92
R-125 WET 66,02 36,20 A1 29 0 3500
R-410A
70,20 47,90 A1 16,95 0 2088
R-218 DRY 71,89 26,80 A1 2600 0 8830
R-143a WET 72,73 37,64 A2 52 0 4470
R-32 WET 78,11 57,83 A2 4,9 0 550
R-E125 WET 81,34 33,51 R-407C
86,79 45,97 A1 n.a. 0 1800
R-1270 WET 92,42 46,65 R-22
96,15 49,90
0,03 1700
R-290 - propane WET 96,65 42,47 A3 0,041 0 ~20
R-134a Isentropic 101,03 40,56 A1 14 0 1430
R-227ea DRY 101,74 29,29 A1 42 0 3220
R-500
105,50 44,55 A1 n.a. 0,738 8100
R-12
112,00 41,14 A1 100 1000 10890
R-3-1-10
113,18 23,20
0 8600
R-152a WET 113,50 44,95 A2 1,4 0 124
R-C318
115,20 27,78 A1 3200 0 10250
R-124
122,28 36,20
0,03 620
CF3I WET 123,29 39,53 R-C270 - cyclopropane WET 124,65 54,90 R-236fa DRY 125,55 32,00 A1 240 0 9810
R-E170 WET 126,85 52,40 R-717 - Ammonia
132,30 113,33 B2 0,01 0 <1
R-E245mc DRY 133,68 28,87
R-600a - iso-butane DRY 135,05 36,47 A3 0,019 0 ~20
R-142b
137,11 40,60
0,04 2400
R-236ea DRY 139,22 34,12 n.a. 8 0 1370
R-114
145,70 32,89 A1 300 0 10040
R-E134 DRY 147,10 42,28 FC-4-1-12
147,41 20,50
0 9160
C5F12 DRY 148,85 20,40 R-600 - n-butane DRY 152,00 37,95 A3 0,018 0 ~20
R-245fa Isentropic 154,05 36,40 B1 7,6 0 900
R-338mccq DRY 158,80 27,26 neo-C5H12 - neo-pentane DRY 160,65 32,00 R-E347mcc DRY 164,55 24,76
R-E245 DRY 170,88 30,48 R-245ca DRY 174,42 39,25 A1 62 0 560
R-21
178,33 51,80
0,01 210
R-123 Isentropic 183,70 36,68 B1 1,3 0,02 120
R-601a - iso-pentane DRY 187,75 33,86
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R-601 - n-pentane DRY 196,50 33,64 - 0,01 0 ~20
R-11 Isentropic 197,96 44,08 A1 45 1 1400
R-141b
204,20 42,49 n.a. 9,3 0,12 725
R-113
214,10 34,39 A1 85 1000 6130
n-hexane DRY 234,67 30,10 Methanol
240,20 81,04 n.a. n.a. n.a. n.a.
Ethanol Wet 240,80 61,48 n.a. n.a. n.a. n.a.
Cyclo-hexane
280,50 40,75 A3 n.a. n.a. n.a.
OMTS
290,85 14,40 Toluene Dry 318,85 41,10
R-718 - Water Wet 374,00 220,64 A1 n.a. 0 <1
Chen H. et al [48] made a distribution of 35 pure working fluids in a -diagram
(Figure 25, Figure 26), from which the critical temperature and the type of each
working fluid is shown. The fluids are divided into 5 groups based on their
locations in the -diagram.
Figure 25: Distribution of the screened 35 working fluids in -diagram [48]
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Figure 26: Close-up look of the distribution of the remaining 31 working fluids in -diagram [48]
3.1.1 Group 1: Fluids ammonia, benzene and toluene
Water is located in the upper left of the chart, which indicates it is the wettest
fluid and has the highest critical temperature among all the fluids plotted, which
makes it unsuitable for low-temperature heat conversion. Ammonia is a very wet
fluid, which needs superheating when used in an organic Rankine cycle.
Ammonia is not recommended in transcritical Rankine cycles, since the critical
pressure is relatively high (11.33MPa). Benzene and toluene are considered as
isentropic fluids with relatively high critical temperatures, which are desirable
characteristics for organic Rankine cycles. Benzene and toluene are chemically
stable in these potential operating conditions [9].
3.1.2 Group 2: Fluids R170, R744, R41, R23, R116, R32, R125 and R143a
Fluids R170, R744, R41, R23, R116, R32, R125 and R143a are wet fluids with
low critical temperatures and reasonable critical pressures (Table 4), which are
desirable characteristics for transcritical Rankine cycles. Carbon dioxide (R744)
and R134a have been studied in transcritical Rankine cycles in the literature.
Among these fluids, R170, R744, R41, R23 and R116 have critical temperatures
below 320 K, which require low condensing temperatures, not achievable under
many circumstances. The critical temperatures of R32, R125 and R143a are
above 320 K, so the design of condensers for these fluids is not a big concern.
Provided other aspects are satisfied, R32, R125 and R143a could be promising
working fluids for transcritical Rankine cycle.
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3.1.3 Group 3: Fluids propyne, HC270, R152a, R22 and R1270
Propyne, HC270, R152a, R22 and R1270 are wet fluids with relatively high
critical temperatures. Superheat is usually needed for this group of fluids when
applied in organic Rankine cycles. They might be applied in transcritical Rankine
cycles if the temperature profile of the heat source meets the requirements.
However, propyne, HC270 (cyclopropane) and R1270 (propene) are not normally
used in their supercritical state due to the stability concerns. Propyne, HC270
and R1270 have relatively low molecular weight (Table 4). Applying these fluids
implies a larger system size compared to those fluids with higher molecular
weight.
3.1.4 Group 4: Fluids R21, R142b, R134a, R290, R141b, R123, R245ca,
R245fa, R236ea, R124, R227ea, R218
This group of fluids can be considered isentropic fluids. They can be applied in
organic Rankine cycle or transcritical Rankine cycle depending on the
temperature profile of the heat source. Since the isentropic expansion would not
cause wet fluid problems, superheat is not necessary in organic Rankine cycle
with these fluids. Among these fluids, R141b, R123, R21, R245ca, R245fa,
R236ea and R142b have critical temperature above 400 K, making them more
likely to be used in organic Rankine cycle than in transcritical cycle for low-
temperature heat sources, while the rest may be used in either cycle, depending
on the heat source profile.
3.1.5 Group 5: Fluids R601, R600, R600a, FC-4-1-12, RC318, R-3-1-10
Fluids R601, R600, R600a, FC-4-1-12, RC318, R-3-1-10 are considered dry
fluids. Based on the analysis before, dry fluids may be used in transcritical
Rankine cycles and organic Rankine cycles. Since superheat has a negative effect
on the cycle efficiency when dry fluids are used in organic Rankine cycle,
superheating is not recommended. The decision on which fluids could be used
may be based on how the operating temperature is tailored to cope with the heat
source temperature profile.
Later, these fluids will be evaluated on their thermodynamic performances,
depending waste heat source.
3.2 Working fluids for transcritical organic Rankine cycles
In order to form a transcritical cycle, the critical temperature of the working fluid
should be lower than the heat source temperature and higher than the
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condensing temperature. A part of the cycle will be located in the supercritical
region.
Much research has already been done using carbon dioxide in transcritical power
cycles (Chen H. et al. [47]; Chen Y. et al. [58]; Cayer E. et al. [62] [66]; Wang
J. et al. [63]). This mainly due to the fact that CO2 has a low critical temperature
(31.1°C), is compact, non-toxic, inexpensive, abundant in nature and
environmental friendly. Recycling or recovery of CO2 would not be necessary,
either for environmental or economic reasons. CO2 is also thermally stable and
behaves inertly, thus eliminating material problems or chemical reactions in the
system. A transcritical CO2 power cycle shows a high potential to recover low-
grade waste heat, because of the low critical temperature and the better
temperature glide matching between the heat source and working fluid in the
vapour generator. Transcritical CO2 also doesn’t have a pinch limitation in the
vapour generator. Although, it should be noted that condensation of carbon
dioxide can be difficult in some places because of its low critical temperature.
Furthermore, an operating condition of 60-160 bar is a safety concern.
Research in the use of supercritical CO2 is mainly found in solar energy powered
Rankine cycles, either for power generation, heat generation or a combined cycle
of power and heat (Zhang X.R. et al.). Numerical simulations show that the
proposed system may have an annual average power generation efficiency and
heat recovery efficiency as high as 11.4% up to 20.0% and 36.2% up to 68.0%,
respectively. The cycle efficiencies and outputs can be significantly increased by
increasing the CO2 mass flow rate (Zhang X.R. et al. [32] [33]).
Furthermore, Zhang X.R. et al. designed and constructed an experimental
prototype of a solar energy powered Rankine cycle using supercritical CO2. The
system performance was evaluated based on daily, monthly and yearly
experiment data. The experimental results show that CO2 works stable in the
transcritical region and the estimated power generation efficiency is 8.78%-
9.45% and heat recovery efficiency is 65.0%-70.0% [42] [64]. Supercritical CO2
actually has physical properties somewhere between those of a liquid and a gas.
So it is difficult to decide whether a turbine of a gas or a liquid type should be
used for the Rankine cycle using supercritical CO2. Therefore, in the prototype, a
throttling valve was used, instead of a turbine, in order to study the cycle
performance. The throttling valve can provide various extents of opening for the
cycle loop in order to simulate pressure drop occurring in realistic turbine
condition and consequently a thermodynamic cycle can be achieved.
Besides CO2, also organic fluids like isobutene, propane, propylene,
difluoromethane and R245fa (Schuster et al. [10]) have been suggested for
transcritical Rankine cycles. It was found that supercritical fluids can maximize
the efficiency of the system (Schuster et al. [10]).
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Not only pure substances show a better performance in a transcritical cycle, but
also mixtures can be used. Chen H. et al [47] [56] made a comparative study
between a subcritical ORC with R134a and a transcritical ORC with a zeotropic
mixture of R134a and R32 (0.7R134a/0.3R32). Due to the better thermal match
during heating and condensing, an overall better performance for the transcritical
working zeotropic mixture (thermal efficiency, net work output and exergy
efficiency) was accomplished. An improvement of 10% to 30% in thermal
efficiency was found for Tmax-range between 120 and 200°C and the exergy
efficiency improved about 60% compared to the subcritical cycle. At Tmax 200°C
the transcritical ORC provides 38.9% more net work compared to the subcritical
ORC.
Table 5 shows an overview of the working fluids that can be used in transcritical
cycles, according to the temperature range of the waste heat stream.
Table 5: Overview of potential working fluids for transcritical ORCs
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Physical data Safety data Environmental data
Name Type Tcrit (°C)
pcrit
(bar)
Molecular weight (g/mol)
ASHRAE 34 safety group
ATL (yr) ODP
GWP (100 yr)
PFC-116 Wet 19,88 30,50 138,02 A1 10000 0 11900
HFC-23 Wet 26,14 48,30 70,01 A1 270 0 14800
R-744 (CO2) Wet 31,10 73,80 44,01 A1 >50 0 1
HC-170 (ethane) Wet 32,18 48,00 8,70 A3 0,21 0 ~20
HFC-41 Wet 44,13 59,00 34,03 Flammable 2,4 0 92
HFC-125 Wet 66,02 36,20 120,02 A1 29 0 3500
HFC-410A - 70,20 47,90 72,58 A1 16,95 0 2088
PFC-218 Isentropic 71,89 26,80 188,02 A1 2600 0 8830
HFC-143a Wet 72,73 37,64 84,04 A2 52 0 4470
HFC-32 Wet 78,11 57,83 52,02 A2 4,9 0 550
HFC-407C - 86,79 45,97 86,20 A1 15657 0 1800
HC-290 (propane) Wet 96,65 42,47 44,10 A3 0,041 0 ~20
HFC-134a Isentropic 101,03 40,56 102,03 A1 14 0 1430
HFC-227ea Dry 101,74 29,29 170,03 A1 34,2 0 3220
PFC-3-1-10 Dry 113,18 23,20 238,03 - 2600 0 8600
HFC-152a WET 113,50 44,95 66,05 A2 1,4 0 124
PFC-C318 Dry 115,20 27,78 200,03 A1 3200 0 10250
HCFC-124 Isentropic 122,28 36,20 136,47 A1 5,8 0,03 620
HC-600a (isobutane) DRY 135,05 36,47 58,12 A3 0,019 0 ~20
HCHF-142b Isentropic 137,11 40,60 100,49 A2 17,9 0,04 2400
HFC-236ea Dry 139,22 34,12 152,04 - 10,7 0 1370
PFC-4-1-12 Dry 147,41 20,50 288,03 - 4100 0 9160
HC-600 (n-butane) Dry 152,00 37,95 58,12 A3 0,018 0 ~20
HFC-245fa Isentropic 154,05 36,40 134,05 B1 7,6 0 900
HFC-245ca Dry 174,42 39,25 134,05 A1 6,2 0 693
HCFC-21 Wet 178,33 51,80 102,92 B1 1,7 0,01 210
HCFC-123 Isentropic 183,70 36,68 152,93 B1 1,3 0,02 77
HC-601 (n-pentane) Dry 196,50 33,64 72,15 A3 0,01 0 ~20
HCFC-141b Isentropic 204,20 42,49 116,95 A2 9,3 0,12 725
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Chapter 5
Modelling
1. Introduction
The first step towards a fundamental understanding and estimation of the
performance and characteristics of the system is a mathematical model that
simulates the behaviour of the Rankine cycle.
To define the thermodynamic state of each point, the energy balances will be
made. With these balances, the first conclusions can already be made concerning
efficiency and power output. Because our interest is in the heat transfer from the
waste heat source to the supercritical working fluid, a second step in the analysis
is the heat transfer modelling. Here the heat exchangers will be discretized, due
to the variable properties of the supercritical fluid during heating. To determine
the local heat transfer in each section, experimental correlations will be used for
the heat transfer coefficients.
In most of the research done, friction and the pressure drop are neglected. Baik
et al. [59] and Zhang S. et al. [65] were the first who took the pressure drop in
the system into account.
Besides the thermodynamic modelling, an economic analysis will be done using
the cost performance indicators mentioned in Chapter 4 section 2.2.3.
2. Energy balances
The energy balance is made for all the components in the ORC system: the
pump, the vapour generator, the expander, the condenser and if necessary the
regenerator or internal heat exchanger.
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Figure 27: ORC with IHE (regenerator) and T,s-diagram
3.3 Pump
To bring the working fluid from the condensing pressure to the pressure present
in the vapour generator, a feed pump is required. The required work is .
⁄
⁄
With the isentropic efficiency of the pump, this is defined as:
is the mechanical efficiency of the pump.
3.4 Vapour generator
Between state point 2 and 3, there is heat exchanged between the working fluid
and the waste heat source. The added heat to the working fluid is .
3.5 Expander
During the following expansion process work is delivered in the expander. The
delivered power is given by:
The maximum temperature in the cycle occurs at the expander inlet.
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The isentropic efficiency of the expander is defined as:
The volume flow rate of the working fluid at the expander inlet and outlet are
defined as:
The vapour expansion ratio VER of the expander is defined as:
⁄
3.6 Condenser
The excess heat flow rate is then removed in the condenser during process
(4-1) and is defined as:
The minimum temperature in the cycle occurs at the condenser outlet.
3.7 Regenerator (Internal Heat Exchanger)
In case that the endpoint of the expander (state point 4) is located in the
superheated vapour region, the temperature will be higher than the
temperature . If this temperature difference is remarkable, it could be
interesting [74] to add an extra internal heat exchanger (IHE or regenerator) to
the cycle. But, as an internal heat exchanger increases the cycle efficiency,
recent studies have shown that it has little influence on the net power output and
significantly increases the heat exchange surface and consequently the cost [62]
[65].
This heat exchange is presented in the cycles by state point 4a and 2a. The
saturated vapour cools down in the internal heat exchanger in the process (4–
4a) by transferring the heat to the already compressed liquid which is
heated up in the process (2–2a) by the heat .
Due to the variable specific heat of a supercritical fluid near the critical
temperature, the traditional definition of the effectiveness cannot be used,
because this assumes a constant value for the specific heat. Instead of
considering a constant specific heat and working with the temperature
differences as in the traditional approach, the enthalpy difference is used to
express the effectiveness.
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The heat exchanged between the two streams in the regenerator is:
In an ideal heat exchanger, one of the following two situations can occur
depending on which of the two streams in the regenerator has the smaller heat
capacity: either T4a tends towards T2 or T2a tends towards T4. In this way, the
maximum heat exchange is given by the smaller of the following two
quantities:
{
The regenerator effectiveness is then expressed as:
The use of variable properties in the regenerator by applying above equations
instead of the traditional ones obtained by replacing the enthalpy differences by
the product of temperature differences and a constant specific heat has a very
significant effect on the cycle thermal efficiency. For example, for a transcritical
CO2-cycle [62] with a high pressure of 7.5 MPa and maximum and minimum
cycle temperatures of 95°C and 15°C, respectively, the thermal efficiency
obtained with the traditional method is 25.8% versus 6.3% when considering
variable properties. Since the corresponding Carnot efficiency is 21.7%, it is
obvious that the traditional definition of the effectiveness leads to unacceptable
results. By extension, the LMTD and –NTU methods, which are also based on
the assumption of constant properties, should not be used in transcritical
analyses.
3. Heat transfer
A widely used method of calculating the heat transfer capacity UA is by applying
the logarithmic mean temperature difference (LMTD) between the inlet and
outlet of the heat exchanger.
(
)
However, the LMTD-method is based on constant properties, an assumption
leading to incorrect results in the case of supercritical fluids. An alternative
solution consists in discretizing the heat exchangers so that the properties
variation in each step is small and an average constant value, different for each
step, can be assigned to each of them. The discretization is performed by
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dividing the overall enthalpy change for one of the streams in N equal differences
(Cayer et al. [62]). Without partitioning, the calculation error will be
unacceptable [67].
Figure 28 presents the heat transfer between the heat source and the
supercritical organic working fluid.
Figure 28: Q,T-diagram of a supercritical heat exchange process.
By discretizing the heat exchanger, assuming a counter-flow configuration, the
heat transfer for each step i and the fractional heat transfer capacity UAi are
calculated with the following equations:
{
( )
( )
( )
Heat flow of the heat source is supposed to be linear. A dependence of the heat
capacity with the temperature is not considered.
(
)
With
The overall heat transfer coefficient for a tube with inner diameter din and outer
diameter dout, calculated on the inner diameter is defined by:
(
)
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⇒
(
)
With
{
Implemented on a discretized section, the sectional overall heat transfer
coefficient calculated on the inner diameter, , can be written as:
(
)
⇒
(
)
To calculate the sectional overall heat transfer coefficient, the local heat transfer
coefficients need to be known. In the following section, several correlations are
given for the local convection heat transfer coefficients.
Once the sectional overall eat transfer coefficient is calculated, then the
corresponding surface (or equivalent length ) can be calculated.
The total surface A of the heat exchangers can be calculated by adding the
surfaces of all individual sections .
3.1 Vapour generator
3.1.1 Working fluid – heat transfer coefficient
The correlations for the convection heat transfer coefficient of the supercritical
working fluid are discussed in the literature study about supercritical heat
transfer. Here an overview is given of the correlations used in research for
transcritical organic Rankine cycles.
The classical heat transfer correlations for the calculation of the Nusselt number
cannot be used due to the variations around the critical point. Krasnoshchekov
and Protopopov (1966) and Jackson et al [75] [76] developed in correlations for
supercritical fluid parameters. The correlations have a correction factor which
neutralizes the effect of the variations of the thermo-physical properties around
the pseudo-critical point and provides more stable and accurate results.
Baik et al. [59] use a Nusselt-correlation proposed by Krasnoshchekov and
Protopopov (1966) in [77] for carbon dioxide in the supercritical range at high
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temperature drops, which take the difference is properties between the wall and
the bulk into account.
(
)
(
)
Where refers to the bulk fluid temperature and to the wall temperature.
is calculated using the Petukhov-Kirillov correlation [78] (1958) and the
bulk temperature of the fluid. The average specific heat is defined as:
The exponent is expressed as a function of the pseudo-critical , wall and
bulk temperature of the fluid [77].
Cayer et al. [62] [66], Song Y et al. [79] and Zhang S. et al. [65] also use the
correlation of Krasnoshchekov, Protopopov and Petukhov [80] in a slightly
different form.
(
)
(
)
(
)
With
(
( )
( )
)
Where the Darcy friction factor is expressed as
Schuster and Karellas [81] use the Jackson correlation [82] (1979):
(
)
(
)
The exponent of the equation is defined as follows [83]:
For:
For:
(
)
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For:
(
)( (
))
3.1.2 Heat source
Several researchers use different correlations to determine the convective heat
transfer on the hot side. An overview is given below.
Cayer et al. [62] [66] use the Petukhov correlation [84] to calculate the
convection heat transfer coefficient on the hot side using hot air as heat source.
[
( )
(
)
]
It is to be noted that the equivalent diameter of the shell must be used in this
equation and that the air flow is supposed parallel to the tubes.
Zhang S. et al. [65] use hot water as heat source and the following correlation
for the convection heat transfer coefficient:
(
)
Schuster and Karellas [81] and Song Y et al. [79] use the Dittus-Boelter
correlation from [84]:
With n=0.3 for cooling of the heat source.
Baik et al. [59] use the Gnielinski correlation for turbulent flow in tubes [84] for
the calculation of the convection heat transfer coefficient on the heat side.
( )
( )
(
)
Where f is the Darcy friction factor that can be obtained from the Moody chart or
for smooth tubes from the correlation by Petukhov [84].
The Gnielinski correlation is valid for [84]:
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3.2 Condenser
The condenser requires a more detailed analysis for the calculation of the UA
value. As mentioned before, two situations are conceivable depending on the
state of the working fluid at the turbine outlet. First, when the working fluid is at
a superheated vapour state, the condenser is divided into a single-phase region
and a two-phase region. Each region is then subdivided in a number of steps
with equal enthalpy differences for the working fluid. Second, when the state of
the working fluid at the exit of the turbine falls in the two-phase region, this
region is subdivided in a sufficient number of steps with equal enthalpy
differences and the first one ignored (Cayer et al. [62]).
3.2.1 Working fluid
3.2.1.1 Single-phase heat transfer coefficient
Baik et al. [59] use the Gnielinski correlation for turbulent flow in tubes [84] for
the calculation of the convection heat transfer coefficient of the single-phase
working fluid in the condenser.
( )
( )
(
)
Where f is the Darcy friction factor that can be obtained from the Moody chart or
for smooth tubes from the correlation by Petukhov [84].
The Gnielinski correlation is valid for [84]:
Cayer et al. [62] [66] use the Petukhov correlation [84] to calculate the
convection heat transfer coefficient of the single-phase working fluid in the
condensing stage.
[
( )
(
) ]
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It is to be noted that the equivalent diameter of the shell must be used in this
equation and that the air flow is supposed parallel to the tubes.
3.2.1.2 Two-phase heat transfer coefficient
If the expansion in the turbine or expander ends in the two-phase region, the
most common used correlation by researchers (Cayer et al. [62] [66], Zhang S.
et al. [65], Song Y [79]) for the convection heat transfer coefficient is the
Cavallini and Zecchin correlation [85].
Where the equivalent Reynolds number is defined as:
(
)(
)
Baik et al. [59] uses the general correlation for heat transfer during film
condensation inside pipes by Shah [86].
3.2.2 Cooling fluid
For the calculation of the convection heat transfer of the cooling fluid Baik et al.
[59] use the Gnielinski correlation for turbulent flow in tubes [84], where all
water properties are assumed to be a function of temperature only. Cayer et al.
[62] [66] use the Petukhov correlation [84] and Zhang S. et al. [65] the Cavallini
and Zecchin correlation [85].
3.3 Evaporator (subcritical)
In case a comparison is made between a subcritical and transcritical cycle, the
correlations for the calculation of the convection heat transfer coefficient of the
single-phase and two-phase region are given below.
3.3.1 Working fluid single-phase heat transfer coefficient
Zhang S. et al. [65] use the normal Dittus-Boelter correlation for single-phase
heat transfer [85].
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3.3.2 Working fluid two-phase heat transfer coefficient
For the two-phase region Zhang S. et al. [65] use the Wang-Touber correlation
[87].
{
| (
)
( | )
(
)
√(
)
(
) (
)
4. Pressure drop
4.1 Vapour generator
4.1.1 Working fluid
Baik et al. [59] uses the following equation for the pressure drop in the vapour
generator:
Where the friction factor f is calculated by using the Blasius correlation, which
works well for supercritical frictional pressure drop of carbon dioxide [88].
Zhang S. et al. [65] calculate the friction factor using the Kang correlation [89]:
4.2 Condenser
4.2.1 Working fluid
4.2.1.1 Single-phase pressure drop
4.2.1.2 Two-phase pressure drop
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Baik et al. [59] formulates the two-phase pressure drop in terms of the frictional
effect and the acceleration effect only, neglecting the gravitational effect.
The frictional pressure drop is calculated by the Müller-Steinhagen and Heck
correlation [90] and the acceleration pressure drop is expressed in terms of
the qualities, void fractions, and specific volumes of the vapour and the liquid in
their saturated states [91].
Zhang S. et al. [65] use the Kedzierski correlation [92].
(
)
(
)
[
] [
]
(
)
4.2.2 Cooling fluid - single-phase pressure drop
For the pressure drop in the cooling fluid of the condenser, Zhang S. et al. [65]
use also the Kedzierski correlation [92].
4.3 Evaporator (subcritical)
In case a comparison is made between a subcritical and transcritical cycle, the
correlations for the calculation of the pressure drop of the single-phase and two-
phase region are given below.
4.3.1.1 Single-phase pressure drop
Zhang S. et al. [65] use the Wang-Touber correlation for single-phase pressure
drop [87].
The friction factor is:
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{
4.3.1.2 Two-phase pressure drop
Zhang S. et al. [65] use also the Wang-Touber correlation for the two-phase
pressure drop [87].
(
)(
)
, and are the entering, leaving and average vapour quality respectively.
(
)
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Chapter 6
Fluid selection and cycle
optimization
1. Parametric study and cycle optimization
To adequately compare different working fluids, parametric studies, optimization
of the cycle parameters and a proper choice of the objective functions are
required.
A parametric analysis is performed to evaluate the effects of each key parameter
on the transcritical power cycle, such as turbine inlet pressure and temperature.
Most studies done on transcritical cycles were limited to applying the first law of
thermodynamics. A more detailed approach was necessary and Cayer et al.
(2009) [62] presented a methodology using 4 performance indicators to analyse
a transcritical CO2 power cycle using an industrial low-grade stream of process
gases (100°C and a mass flow rate of 314.5kg/s). The used indicators were: the
thermal and exergy efficiency, the total heat transfer capacity UA and the heat
exchange surface. The variable parameters were the maximum cycle pressure
(turbine inlet pressure) and the net power output. It was noticed that for each
performance indicator, there was an optimum maximum cycle pressure, not
necessarily all identical. Furthermore an augmentation of the net power output
has no influence on the results of the energy analysis, but it decreases the
exergy efficiency and increases the heat exchanger’s surface and has no
significant effect on the optimizing maximum cycle pressure.
Cayer et al. [62] use a dimensionless parameter to compare the net power
output of several cycles. Define as the fraction of the net power output to the
maximum reversible power produced by a Carnot engine operating between the
heat source and sink temperatures.
With:
In the last term (Carnot efficiency) the temperatures are in K.
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The mass flow rate of the organic working fluid can then be calculated as:
With the specific net output.
The advantage of this approach is that is always positive and less than the
unit.
Later Cayer et al. [66] expanded his model for CO2, ethane and R125 and added
2 more performance indicators: specific net output and relative system cost. The
independent parameters were the maximum cycle pressure and temperature and
the net power output. The parametric studies revealed that it is not possible to
simultaneously optimize all performance indicators and that the design value
must be a matter of choice. A comparison of optimum indicators for the three
fluids shows that none outperforms the other two on all counts. Thus, R125 had
the best thermal efficiency, ethane the highest specific net power output and
R125 the lowest UA, surface and cost. The CO2 had a higher total UA but a lower
specific net output than ethane.
Wang J. et al. [63] performed a parametric exergy analysis for transcritical CO2
by means of a genetic algorithm to recover as much waste heat as possible. They
found that key thermodynamic parameters, such as turbine inlet pressure,
turbine inlet temperature and environment temperature have significant effects
on the performance of the supercritical CO2 power cycle and exergy destruction.
Zhang S. et al. [65] did a parameter optimization and performance comparison
of 16 working fluids in subcritical and transcritical ORCs for low-temperature
geothermal power generation. Five performance indicators were used as
objective functions: thermal efficiency, exergy efficiency, recovery efficiency,
heat exchanger area per unit power output (APR) and levelized energy cost
(LEC). The transcritical cycles had a lower thermal efficiency, but a much lower
vapour expansion ratio, which indicates less turbine stages, smaller expanders
and no supersonic flows. Also fluids in transcritical cycles recovered more
available thermal power and could maximize the utilization of the geothermal
heat source. The transcritical cycle working with R125 has excellent economic
and environmental performance.
To compare cycles under equal operating conditions it is common to use the
same boiling and condensing temperatures. However, for a cycle with sensible
heat addition or rejection temperature, such as a transcritical power cycle, the
heating (and cooling) processes take place with gliding temperature instead of
isothermal. Therefore, an equal reference temperature is needed to compare
subcritical and transcritical cycles equally. For a cycle with gliding temperatures,
the mean heat addition temperature will be lower than the maximum heat
addition temperature, while the mean heat rejection temperature will be higher
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than the minimum heat rejection temperature as well. Consequently, the
thermodynamic mean temperatures can be used to define the reference
temperature in heat addition or heat rejection process for such a cycle [81]. The
thermodynamic mean temperatures for the heating and cooling processes of a
cycle with gliding temperature can be defined as follows, respectively:
And
1.1 Energy analysis
In the energy analysis, the objective is to determine the thermal efficiency and
the specific net power output. The first law of thermodynamics only depends on
the states of the working fluid at different points in the cycle and is not
influenced by the working fluid mass flow rate and the net power output.
Cayer et al. [66] found that the thermal efficiency and specific net power output
increase with increasing maximum cycle temperature (turbine inlet
temperature). An optimization for the maximum cycle temperature is not
required, because it will lead a value equal to the inlet temperature of the heat
source, and will require an infinitely large transcritical heater for this
temperature.
Varying the maximum cycle pressure (turbine inlet pressure), it clear as can be
seen in Figure 29 and Figure 30 a maximum occurs for the thermal efficiency and
specific net power output. The corresponding optimizing maximum pressure
increases with increasing maximum cycle temperature. Furthermore, the
optimum specific output is at a lower maximum pressure than the optimum
thermal efficiency.
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Figure 29: Transcritical CO2: Thermal efficiency versus maximum pressure for different Tmax [66].
Figure 30: Transcritical CO2: Specific net power output versus maximum pressure for different Tmax [66].
For free heat sources, the focus should be in maximizing the specific output,
rather than the thermal efficiency.
A comparison between transcritical CO2, R125 and ethane is given in Figure 31
and Figure 32.
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Figure 31: Thermal efficiency: comparison between CO2, R125 and ethane (Tmax=95°C) [66].
Figure 32: Specific net power output: comparison between CO2, R125 and ethane (Tmax=95°C) [66].
Figure 31 shows that R125 achieves a maximum thermal efficiency above 10%,
which is significantly higher than for CO2 and ethane and also corresponds with a
lower maximum cycle pressure. The ethane and the carbon dioxide achieve
similar maximum thermal efficiencies near 8.5% but the ethane needs a lower
pressure.
The maximum outputs (Figure 32) for CO2 and R125 are significantly lower than
the output for ethane as working fluid. The pressure at which the maximum
outputs are obtained is lowest for R125 and highest for CO2.
Wang J. et al. [63] investigated the net power output of transcritical CO2 and
R125 (Figure 33).
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Figure 33: Optimized carbon dioxide transcritical cycle (left) and optimized R125 transcritical cycle (right) [63].
The net power of the R125 transcritical cycle is around 14% greater than that of
the carbon dioxide cycle. The main reasons are the higher cycle pressure of CO2,
because the increased turbine power of the carbon dioxide cycle cannot
compensate for the pumping power increase and also the CO2 cycle has a greater
exergy destruction of the pump.
Chen H. et al. [47] found that the thermal efficiency of transcritical R32 is higher
than carbon dioxide for the same temperature and at a lower maximum working
pressure (Figure 34). R32 has a maximum limiting pressure for each turbine inlet
temperature, because of the allowed vapour quality in the turbine (here x ≥
95%).
Figure 34: Thermal efficiencies of a CO2- and R32-based transcritical Rankine cycles [47].
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1.2 Exergy analysis
The energy analysis does not take the quality of the heat exchange in the vapour
generator and condenser into account, so a second law analysis is required. To
characterize the heat transfer process, the mass flow rate of the working fluid,
heat source and cold source are necessary.
An exergy destruction distribution analysis showed that around 50% of the
irreversibility takes place in the vapour generator, 27% in the turbine, 11% in
the condenser, 7% in the pump and less than 5% in the regenerator. This
distribution is essentially the same for all values of the high pressure and . In
view of these results, efforts should be made to improve the temperature
matching between the heat source and the working fluid in the evaporator
Cayer et al. [66] investigated the influence of the turbine inlet temperature and
pressure and the net power output of the exergy efficiency
( ). For a fixed net power output , the exergy efficiency
increases with increasing maximum cycle pressure and maximum cycle
temperature. The optimizing maximum pressure is almost identical for the
thermal and exergy efficiency.
For a fixed maximum cycle temperature (95°C), the exergy efficiency increases
with increasing net power output. Moreover, the high pressure which maximizes
is relatively independent of .
Figure 35: Exergy efficiency versus maximum pressure for > 0.21 with Tmax = 95°C
[66].
For high values of an important phenomenon occurs at low and high values of
the maximum pressure: the specific net output for such pressures being low, the
working fluid mass flow rate and the heat extracted from the heat source
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increase in order to generate the high net power output corresponding to .
Since the heat source capacity is limited, extracting more heat results in a
reduction of its temperature throughout the vapour generator. However this
temperature cannot be lower than the corresponding temperature of the carbon
dioxide. This condition limits the acceptable range of values for the maximum
pressure.
An exergy destruction distribution analysis showed that around 50% of the
irreversibility takes place in the vapour generator, 27% in the turbine, 11% in
the condenser, 7% in the pump and less than 5% in the regenerator. This
distribution is essentially the same for all values of the high pressure and . In
view of these results, efforts should be made to improve the temperature
matching between the heat source and the working fluid in the evaporator
Wang J. et al. [63] investigated the effect of turbine inlet pressure, turbine inlet
temperature and environment temperature on the exergy efficiency for different
heat source temperatures.
Figure 36: Exergy efficiency versus turbine inlet pressure for various heat source temperatures [63].
The effect of the turbine inlet pressure shows a maximum exergy efficiency. As
the enthalpy drop across the turbine increases as the pressure ratio increases,
the turbine power output increases. By subtracting pump input from the turbine
power output, the net power output increases. From a certain value for the
turbine inlet pressure, a decrease in vapour flow rate is generated by vapour
generator, resulting in a decrease of the net power output and so also the exergy
efficiency.
As can be seen on Figure 36 the exergy efficiency increases as heat source
temperature increases.
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Furthermore, the exergy efficiency increases as the turbine inlet temperature
increases (Figure 37).
Figure 37: Exergy efficiency versus turbine inlet temperature for various heat source temperatures [63].
By studying the effect of the environment temperature on exergy efficiency, it
was noticed that the exergy efficiency decreases with an increase in environment
temperature. The reason for this is that an increase in environment temperature
results in an increase in condensing pressure, which reduces the turbine power
Figure 38: Exergy efficiency versus environment temperature for various heat source temperatures [63].
Wang et al. took a close look at the exergy destruction for each component in
function of the thermodynamic parameter turbine inlet pressure and temperature
and environment temperature and found that the biggest exergy destruction
occurs in vapour generator, followed by the turbine, then the condenser and at
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last the pump. The turbine inlet pressure had the biggest effect on exergy
destruction as can be seen in Figure 39.
Figure 39: Exergy destruction in each component versus turbine inlet pressure [63].
As turbine inlet pressure increases, the exergy destruction in the vapour
generator decreases. The exergy destruction in the pump and turbine increase,
because an increase in the turbine inlet pressure results in an increase in
pressure difference through the turbine or pump. In the condenser a decrease in
exergy destruction is noticed, because the turbine outlet temperature decreases.
This could result in a decrease in heat transfer temperature difference for the
condenser.
Figure 40: Exergy destruction in each component versus turbine inlet temperature [63].
As the turbine inlet temperature increases (Figure 40), the exergy destruction in
the vapour generator decreases, because an increase in the turbine inlet
temperature can result in a decrease in the heat transfer temperature difference
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for the vapour generator. Further, the exergy destruction in the pump and
turbine decreases and in the condenser an increase is noticeable, because
turbine outlet temperature increases, thus, the heat transfer temperature
difference in the condenser increases.
The influence on the exergy destruction as the environment temperature
increases (Figure 41) is visible as a decrease in exergy destruction in the pump
and turbine, because the condensing pressure increases, thus, the pressure
differences through the turbine and the pump decrease. In the condenser itself,
the exergy destruction increases, because the turbine outlet temperature
increases, and this results in an increase in the heat transfer temperature
difference for the condenser.
Figure 41: Exergy destruction in each component versus environment temperature [63].
1.3 Recovery efficiency
The recovery efficiency is an indicator for evaluating the ratio of available energy
recovered from the heat source.
Zhang S. et al. [65] used this performance indicator for different working fluids
(Figure 42). The highest recovery efficiency was delivered by R218 followed by
R41 and R125. These fluids in transcritical power cycle recovered much more
available thermal power and could maximize the utilization of the geothermal
source. So the favoured working fluids in terms of geothermal utilization were
the fluids in transcritical power cycle with R218, R41 and R125.
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Figure 42: Recovery efficiency of different working fluids under their optimized operation parameters [65].
1.4 Total heat transfer capacity UA
As mentioned before the heat exchangers are discretized so that the variations of
the properties can be considered constant in each step. The discretization is
performed by dividing the overall enthalpy change for one of the streams in N
equal differences .
By analysing the heat transfer capacity as performance indicator, Cayer et al.
[62] showed that the use of an internal heat exchanger is in most of the cases
not practical, because the new UA added by the internal heat exchanger does not
fully compensate the obtained reduction at the vapour generator.
For a fixed net power output, Cayer et al. [66] saw that the total UA varies
significantly with the maximum cycle pressure and temperature. The optimizing
maximum cycle temperature is not equal to the inlet temperature of the heat
source (as in the thermal and exergy analysis), because this would yield an
infinitely large vapour generator. Low values of the maximum cycle temperature
also doesn’t provide low values for the total UA, because in order to obtain the
net power output, a higher mass flow rate is required (due to the lower values of
the specific output at low Tmax). If the mass flow rate increases, the temperature
difference between the fluids decrease and the total heat transfer capacity
increased accordingly.
There exists an optimum maximum cycle temperature as well as an optimum
maximum cycle pressure that minimizes the total UA.
Cayer et al. [66] compared three working fluids (CO2, R125 and ethane) and
found that the lowest values of the total heat transfer capacity is obtained with
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R125, followed by ethane which shows a slightly lower UA than carbon dioxide
except for very high net power outputs.
Schuster and Karellas [23] found that maximum cycle temperatures with good
system efficiencies and low exergy losses need the highest heat transfer
capacities.
1.5 Heat exchanger surface
To determine the surface A of the heat exchangers, the heat transfer coefficients
for the fluids need to be calculated using the correlations presented in Chapter 5
and the literature study about supercritical heat transfer.
Each heat exchanger is considered as a counter-flow shell and tubes with one
pass for all the streams. The vapour generator transfers the heat from the waste
heat source to the working fluid. The high pressure working fluid flows inside the
tubes and the air flows in the shell. Because of the poor heat transfer coefficient
of air, longitudinal fins can be added on the outside of each tube. The number of
tubes and the shell diameter are obtained from the mass balance equations by
fixing the minimum velocity for example at 0.5 m/s for the liquid working fluid
and the maximum velocity for example at 30 m/s for the hot entering air.
The condenser modelling is similar to the vapour generator with a few
exceptions. The working fluid still flows inside the tubes because of its higher
pressure and the water in the shell. However, this time the longitudinal fins are
positioned inside the tubes because of the good transfer properties of water and
the risk of fouling if fins are installed on the water side. The number of tubes and
the shell diameter are obtained by assuming a minimum velocity of for example
1.5 m/s for the saturated liquid working fluid and a maximum velocity of for
example 3 m/s for the cooling water. The condenser is still divided into two
sections as in the finite size analysis.
Modelling of the regenerator (if applicable) follows the same methodology as the
two preceding heat exchangers. The higher pressure working fluid from the
pump circulates inside the tubes and the lower pressure one from the turbine in
the shell. The fins are located inside the tubes to reduce the regenerator size and
facilitate assembly. The minimum velocity of the cold stream working fluid is set
for example to 1.5 m/s and the maximum velocity of the supersaturated working
fluid for example at 10 m/s.
Cayer et al. [62] use the Petukhov’s correlation [84] for the low pressure
working fluid and Krasnoshchekov–Protopopov’s correlation (see literature study
for supercritical heat transfer) for the supercritical working fluid coming from the
pump.
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The effect of the maximum cycle pressure on the total heat transfer area A is
quasi the same as on the total heat transfer capacity UA, but the maximum cycle
temperature to minimize the total area is not the same as for minimising the
total heat transfer capacity (Cayer et al. [66]).
Figure 43: Total area versus maximum pressure for different Tmax with =0.2 [66].
As can be seen on Figure 44, the minimum total surface behaves linear for low
values of the net power output and exponential for higher . The linearity is
due to the presence of the condenser. A significant difference is noticed in the
relative importance of the two heat exchangers. The vapour generator surface is
higher for a large range of and definitely dominant for above 0.2 while its UA
exceeds that of the condenser only when approaches its upper limit. This can
be explained by the significantly greater heat transfer coefficients in the
condenser which reduce the relative importance of its area despite its higher UA
value.
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Figure 44: Optimized total area and corresponding values for the heat exchanger [66].
However, in opposition to the results for the total heat transfer capacity UA,
carbon dioxide as working fluid requires a smaller heat exchanger surface than
ethane, which indicates that the carbon dioxide has better heat transfer
properties. The smallest heat transfer area was found for R125.
Figure 45: Comparison of minimum total heat exchange surface [66].
1.6 Thermo-economic analysis
The economics of an ORC system is linked to the thermodynamic properties of
the working fluid. A bad choice of working fluid can lead to a less efficient and
expensive power unit.
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As mentioned already in Chapter 4, Zhang S. et al. [65] and Cayer et al. [66]
were one of the first who performed a thermo-economic parameter analysis for a
selection of working fluids in transcritical organic Rankine cycles (R134a, R143a,
R218, R125, R41, R170, ethane and CO2).
Cayer et al. [66] use well-estimated purchase prices for the major components
of the cycle (pump, turbine and heat exchangers) as the representative of the
complete life cycle cost, even if it is just a fraction of the actual total cost.
Zhang S et al. [65] consider the total cost of the heat exchangers representative
of the complete system cost of an ORC, because 80-90% of the system capital
cost can be assigned on the heat exchangers [68] [69] [70].
Two economic performance indicators can be used for evaluation of a power
system:
APR
LEC
The relative total cost in over a range of maximum cycle pressures and
maximum cycle temperatures (for a fixed net power output) can be seen in
Figure 46.
Figure 46: The relative total cost in over a range of maximum cycle pressures and maximum cycle temperatures with = 0.2 [66].
The optimising maximum pressure is significantly lower than the corresponding
values determined in all the previous analyses (energy, exergy, total heart
transfer capacity and heat exchange surface). The reason for this result is the
important dependence of the turbine and pump costs on the pressure, because
their prices rapidly increase when the pressure is augmented. On the other hand,
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at low pressures the heat exchangers’ surface increases and consequently so
does their cost.
By varying the net power output (Figure 47) under optimized conditions, it can
be observed that the total relative cost increases linearly with the net power
output for low values of and exponentially for higher values of . This
behaviour is similar to that observed in the analysis of the heat exchange area.
Furthermore, the total cost tends towards infinity as approaches its
maximum value. This rapid augmentation of the cost is mainly due to the vapour
generator. Nevertheless, for most of the acceptable values of , the relative cost
of the turbine is definitely dominant, because the price of this component is
highly dependent on the maximum pressure.
Figure 47: Optimised relative cost and corresponding values for each component [66].
Furthermore, Cayer et al. [66] compared the relative cost per net power output
for CO2, R125 and ethane (Figure 48) and it shows that the relative cost per kW
with R125 is about 20% lower than the other two fluids.
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Figure 48: Comparison of minimum relative cost per kW [66].
Zhang S et al. [65] also compared a series of working fluids (Figure 49) and it
was found that in a transcritical power cycle system, the LEC was the lowest for
R143a, R125 and R41 and was similar with that of R152a in a subcritical ORC.
The carbon dioxide had a much higher operating pressure, which resulted in
additional expenses in the plant design, leading to a high objective function
value.
Figure 49: The LEC value of different working fluids under their optimised operation conditions [65].
Among the fluids in transcritical power cycle, R143a was not acceptable because
the heating pressure range was limited by the turbine outlet quality. R41 showed
favourable performance except for its flammability. These comparisons indicated
that R125 in the transcritical power cycle system was preferable since it offered
lower LEC, reduced more CO2-emission and cuts down more petroleum
consumption.
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Zhang S et al. [65] also use the APR as objective function, which is the ratio of
total heat exchanger area to net power output (Figure 50).
Figure 50: The APR value of different working fluids under their optimised operation conditions [65].
In transcritical power cycle, R143a exhibited the least APR value and was a cost-
effective fluid. R170 provided the highest APR value, about 59% larger than that
of R143a. Among the fluids considered, R41 produced the highest net power
output, but the heat exchanger area was 82.5% larger than that of R143a. As a
result, R41 gave the APR value of 31.7% higher than that of R143a. To
demonstrate the differences in the subcritical ORC and the transcritical power
cycle, the economic performance comparison was conducted and it was observed
that the choice of working fluid could greatly affect the power plant cost. Fluids in
a transcritical power cycle system took the advantage of high net power output.
For example, the net output power of R143a was 28.7% and 23.8% larger than
that of R152a and R123, respectively. However, due to the large heat absorption
capacity, more heat exchanger area was required in transcritical power cycle.
The heat exchanger area required for R143a was 57.4% and 9.8% larger than
that of R152a and R123, respectively. As a result, the objective function value of
R143a was 23% larger than that of R152a, but 14.8% smaller than R123.
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2. Fluid selection
In Table 5 (chapter 4) an overview of working fluids was given suitable for a
transcritical power cycle. Table 6 shows a reduced overview of the working fluids
that can be used in transcritical cycles, according to the temperature range of
the waste heat stream. Working fluids which will be phased out, working fluids
with a low molecular weight, a very low critical temperature and a high
flammability have been deleted.
Table 6: Overview of potential working fluids for transcritical ORCs
Physical data Safety data
Environmental data
Name Type Tcrit (°C)
pcrit
(bar)
Molecular weight (g/mol)
ASHRAE 34 safety group
ATL (yr) ODP
GWP (100 yr)
HFC-23 Wet 26,14 48,30 70,01 A1 270 0 14800
R-747 (CO2) Wet 31,10 73,80 44,01 A1 >50 0 1
HFC-125 Wet 66,02 36,20 120,02 A1 29 0 3500
HFC-410A - 70,20 47,90 72,58 A1 16,95 0 2088
PFC-218 Isentropic 71,89 26,80 188,02 A1 2600 0 8830
HFC-143a Wet 72,73 37,64 84,04 A2 52 0 4470
HFC-32 Wet 78,11 57,83 52,02 A2 4,9 0 550
HFC-407C - 86,79 45,97 86,20 A1 15657 0 1800
HFC-134a Isentropic 101,03 40,56 102,03 A1 14 0 1430
HFC-227ea Dry 101,74 29,29 170,03 A1 34,2 0 3220
PFC-3-1-10 Dry 113,18 23,20 238,03 - 2600 0 8600
HFC-152a WET 113,50 44,95 66,05 A2 1,4 0 124
PFC-C318 Dry 115,20 27,78 200,03 A1 3200 0 10250
HFC-236ea Dry 139,22 34,12 152,04 - 10,7 0 1370
PFC-4-1-12 Dry 147,41 20,50 288,03 - 4100 0 9160
HFC-245fa Isentropic 154,05 36,40 134,05 B1 7,6 0 900
HFC-245ca Dry 174,42 39,25 134,05 A1 6,2 0 693
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Chapter 7
Heat exchanger design Schuster and Karellas (2012) [67] were the first to investigate the influence of
ORC parameters on the heat exchanger design. The basic parameters of the
design were defined in the cases of supercritical fluid parameters and the
convective coefficients. The used working fluids were R134a, R227ea and
R245fa.
The general conclusion was that the heat transfer coefficient decreases with
increasing supercritical pressure and temperature, consequently the heat
exchanger area increases (Figure 51).
Figure 51: Mean overall heat transfer coefficient versus pressure for three fluids and superheating temperatures [67].
Further research is necessary in understanding the heat transfer mechanism in
the critical region. In the literature study about supercritical heat transfer, this
section will be examined more in detail.
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References
[1] Stricker Associates Inc. Market study on waste heat and requirements for
cooling and refrigeration in Canadian industry.2006.
[2] TeTra-Symposium 2009.
[3] Mckinsey 2009.
[4] Masokin 2007.
[5] „ORCycle,” [Online]. Available: www.orcycle.be. [Geopend 05 11 2012].
[6] Wali E. Optimum working fluids for solar powered Rankine cycle cooling of
buildings. Solar Energy 1980;25:235–41.
[7] Hung TC, Shai TY, Wang SK. A review of organic rankine cycles (ORCs) for the
recovery of low-grade waste heat. Energy 1997; 22(7):661e7.
[8] B.F. Tchanche et al. Low-grade heat conversion into power using organic
Rankine cycles – A review of various applications Renewable and Sustainable
Energy Reviews 15 (2011) 3963–3979.
[9] Andersen WC, Bruno TJ. Rapid screening of fluids for chemical stability in
organic Rankine cycle applications. Industrial and Engineering Chemistry
Research 2005;44:5560–6.
[10] Schuster A, Karellas S, Supercritical Fluid Parameters in Organic Rankine Cycle
Applications, International Journal of Thermodynamics 2008; 11(3): 101-108.
[11] Mathias JA et al., Experimental testing of gerotor and scroll expanders used in,
and energetic and exergetic modeling of, an organic Rankine cycle. Journal of
Energy Resources Technology 2009;131(3):012201–12209.
[12] Duvia, A., Gaia M. (2002): ORC plants for power production from 0,4 MWe to
1,5 MWe: technology, efficiency, practical experiences and economy. 7th
Holzenergie Symposium, Zürich, Switzerland, 18. October 2002.
[13] Karl, J. (2004): Decentralised energy systems, new technologies in liberalised
energy market Dezentrale Energiesysteme , (Neue Technologien im
liberalisierten Energiemarkt) Oldenbourg Wissensschaftsverlag, München,. (in
German).
Page 98/104 Literature Study - The transcritical organic Rankine cycle
Report no. 00000
_____________________________________________________________________________________________________ This report may only be used wordily or entirely for publication purposes. Texts or publications where this report is issued have to be approved by the authors before submission.
[14] Turboden High Efficiency Rankine for Renewable Energy and Heat Recovery
available at: http://www.turboden.it/orc.asp (Date of access 22.10.2012).
[15] Drescher I., Brüggemann D. (2007): Fluid selection for the Organic Rankine
Cycle (ORC) in biomass power and heat plants, Applied Thermal Engineering 27
(2007) 223-228..
[16] Barbier E. Nature and technology of geothermal energy: a review. Renewable
Sustainable Energy Rev 1997;1(1–2):1–69.
[17] Barbier E. Geothermal energy technology and current status: an overview.
Renewable Sustainable Energy Rev 2002;6:3–65.
[18] Broßmann E, Eckert F, Möllmann G, Technical concept of the geothermal power
plant Neustadt-Glewe. (technisches Konzept des geothermischen Kraftwerks
Neustadt-Gelewe).Berlin, Germany;
http://www.geothermie.de/gte/gte43/technisches_konzept_des_geotherm.htm.
[19] Lund, J (2005). W.: Combined Heat and Power plant Neustadt-Glewe,
Germany. GHC, Bulletin June.
[20] Sylvain Quoilin, Sustainable Energy Conversion Through the Use of Organic
Rankine Cycles for Waste Heat Recovery and Solar Applications, Liège, October
2011.
[21] Fachagentur nachwachsende Rohstoffe e.V. (2004) (ed.): Assistance for Biogas
production and use (Handreichung Biogasgewinnung und – nutzung). Leipzig,.
(in German).
[22] R. Vescovo, „Cogeneration and on-site power production,” Turboden, 01 03
2009. [Online]. Available: http://www.cospp.com/articles/print/volume-
10/issue-2/features/orc-recovering-industrial-heat-power-generation-from-
waste-energy-streams.html. [Geopend 22 10 2012].
[23] Schuster A, Karellas S, Efficiency optimization potential in supercritical Organic
Rankine Cycles, Energy 2010 (35): 1033-1039.
[24] DiPippo R. Ideal thermal efficiency for geothermal binary plants. Geothermics
2007;36(3):276–85.
[25] Larjola J. Electricity from industrial waste heat using high-speed organic
Rankine cycle (ORC). Int J Prod Econ.
[26] Chen Y. Novel cycles using carbon dioxide as working fluid. Licentiate thesis.
Stockholm, Sweden: School of Industrial Engineering and Management; 2006.
Page 99/104 Literature Study - The transcritical organic Rankine cycle
Report no. 00000
_____________________________________________________________________________________________________ This report may only be used wordily or entirely for publication purposes. Texts or publications where this report is issued have to be approved by the authors before submission.
[27] Kalina AI. Combined-cycle system with novel bottoming cycle. J Eng Gas Turb
Power 1984;106:737–42.
[28] Saleh B. Working fluids for low-temperature organic Rankine cycles; Energy 32
(2007): 1210–1221.
[29] Feher EG. The supercritical thermodynamic power cycle. Energy Convers
1968;8:85–90.
[30] Gu Z, Optimization of cyclic parameters of a supercritical cycle for geothermal
power generation, Energy Conversion and Management 42 (2001) 1409-1416.
[31] Gu Z, Sato H. Performance of supercritical cycles for geothermal binary design.
Energy Conversion and Management 43 (2002) 961–971.
[32] Zhang XR, Yamaguchi H, Analysis of a novel solar energy-powered Rankine
cycle for combined power and heat generation using supercritical carbon
dioxide, Renewable Energy 31 (2006) 1839–1854.
[33] Zhang XR. Theoretical analysis of a thermodynamic cycle for power and heat
production using supercritical carbon dioxide, Applied Thermal Engineering 26
(2006) 2142–2147.
[34] Chen Y, Lundqvist P, Platell P. Theoretical research of carbon dioxide power
cycle application in automobile industry to reduce vehicle’s fuel consumption.
Appl Therm Eng 2005;25(14–15):2041–53.
[35] UNEP, „Montreal protocol on substances that deplete the ozone layer,” 1987,
reviewed in 2000.
[36] Rogers G, Mayhew Y. Engineering thermodynamics, work and heat transfer, 4th
ed. Harlow: Longman Scientific &Technical; 1992 (p. 239–243).
[37] P.J. Mago, L.M. Chamra, K. Srinivasan, C. Somayaji, An examination of
regenerative organic Rankine cycles using dry fluids. Applied Thermal
Engineering 28 (8-9) (2008) 998e1007.
[38] ANSI/ASHRAE Standard 34, Number Designation and Safety Classification of
Regfrigerants, 2008.
[39] "Global Warming Potentials". Contribution of Working Group I to the Fourth
Assessment Report of the Intergovernmental Panel on Climate Change, 2007.
2007. Retrieved 2012-10-26.
[40] „Wikipedia - Ozone depletion potential,” 30 08 2012. [Online]. Available:
http://en.wikipedia.org/wiki/Ozone_depletion_potential. [Geopend 26 10
Page 100/104 Literature Study - The transcritical organic Rankine cycle
Report no. 00000
_____________________________________________________________________________________________________ This report may only be used wordily or entirely for publication purposes. Texts or publications where this report is issued have to be approved by the authors before submission.
2012].
[41] „Wikipedia - Atmospheric lifetime,” 23 10 2012. [Online]. Available:
http://en.wikipedia.org/wiki/Greenhouse_gas#Atmospheric_lifetime. [Geopend
26 10 2012].
[42] Zhang XR, Yamaguchi H. Solar energy powered Rankine cycle using
supercritical CO2. Applied Thermal Engineering 26 (2006): 2345–2354.
[43] Quoilin S. Experimental study and modeling of a low temperature Rankine cycle
for small scale cogeneration. Thesis, University of Liege; 2007.
[44] Calderazzi L, di Paliano PC. Thermal stability of R-134a, R-141b, R-13I1, R-
7146, R-125 associated with stainless steel as a containing material.
International Journal of Refrigeration 1997;20:381–9.
[45] Liu BT. Effect of working fluids in organic Rankine cycle for waste heat
recovery, Energy 29 (2004): 1207–1217.
[46] Poling BE, Prausnitz JM, O’Connell JP. The properties of gases and liquids, 5th
ed. New York: McGraw-Hill; 2001.
[47] Chen H, Goswami DY, Rahman M, Stefanakos EK. Energetic and exergetic
analysis of CO2- and R32-based transcritical Rankine cycles for low-grade heat
conversion, Applied Energy 2011; 88: 2802-2808.
[48] Chen H. et al. A review of thermodynamic cycles and working fluids for the
conversion of low-grade heat. Renewable and Sustainable Energy Reviews 14
(2010) 3059–3067.
[49] Bakhtar F, Mahpeykar MR. On the performance of a cascade of turbine rotor tip
section blading in nucleating steam. Part 3: theoretical treatment. Proceedings
of the Institution of Mechanical Engineers Part C Mechanical Engineering
Science 1997;211:195–210.
[50] Bakhtar F. On the performance of a cascade of turbine rotor tip section blading
in wet steam. Part 1: generation of wer steam of prescribed droplet sizes.
Proceedings of the Institution of Mech Engineers Part C Mech Engineering
Science 2005;209:115–24.
[51] Bakhtar F. On the performance of a cascade of turbine rotor tip section blading
in wet steam. Part 2: surface pressure distributions. Proceedings of the
Institution of Mech Engineers Part C Journal of Mech Engineering Science
1997;211:531–40.
Page 101/104 Literature Study - The transcritical organic Rankine cycle
Report no. 00000
_____________________________________________________________________________________________________ This report may only be used wordily or entirely for publication purposes. Texts or publications where this report is issued have to be approved by the authors before submission.
[52] Bakhtar F. On the performance of a cascade of turbine rotor tip section blading
in wet steam. Part 4: droplet measurements. Proceedings of the Institution of
Mech Engineers Part C Journal of Mech Engineering Science 1997;211:639–48.
[53] Goswami DY, Hingorani S, Mines G. A laser-based technique for particle sizing
to study two-phase expansion in turbines. Journal of Solar Energy Engineering
1991;113:211–8.
[54] Demuth OJ. Analyses of mixed hydrocarbon binary thermodynamic cycles for
moderate temperature geothermal resources, Idaho; 1981.
[55] Demuth OJ, Preliminary assessment of condensation behavior for hydrocarbon–
vapor expansions which cross the saturation line near the critical point, Idaho;
1983.
[56] Chen H, Goswami DY, Rahman M, Stefanakos EK. A supercritical Rankine cycle
using zeotropic mixture working fluids for the conversion of low-grade heat into
power, Energy 2011; 36: 549-555.
[57] Moran MJ (2011), Fundamentals of engineering thermodynamics (7th edition).
John Wiley & Sons.
[58] Chen Y, Lundqvist P, Johansson A, Platell P, A comparative study of the carbon
dioxide transcritical power cycle compared with an organic Rankine cycle with
R123 as working fluid in waste heat recovery, Applied Thermal Engineering
2006 (26): 2142-2147.
[59] Baik YJ, Kim M, Chang KC, Kim SJ; Power-based performance comparison
between carbon dioxide and R125 transcritical cycles for a low-grade heat
source; Applied Energy 88 (2011) 892–898.
[60] Mikielewicz D, Mikielewicz J. A thermodynamic criterion for selection of working
fluid for subcritical and supercritical domestic micro CHP, Applied Thermal
Engineering 30 (2010) 2357e2362.
[61] Ho et al, Comparison of the Organic Flash Cycle (OFC) to other advanced vapor
cycles for intermediate and high temperature waste heat reclamation and solar
thermal energy, Energy 42 (2012) 213e223.
[62] Cayer, Galanis. Analysis of a CO2 transcritical power cycle using a low
temperature source; Applied Energy 86 (2009): 1055–1063.
[63] Wang J, Sun Z, Dai Y, Ma S. Parametric optimization design for supercritical
CO2 power cycle using genetic algorithm and artificial neural network, Applied
Energy 87 (2010) 1317–1324.
Page 102/104 Literature Study - The transcritical organic Rankine cycle
Report no. 00000
_____________________________________________________________________________________________________ This report may only be used wordily or entirely for publication purposes. Texts or publications where this report is issued have to be approved by the authors before submission.
[64] Zhang XR, Yamaguchi H, Experimental study on the performance of solar
Rankine system using supercritical CO2, Renewable Energy 32 (2007) 2617–
2628.
[65] Zhang S, Wang H, Guo T. Performance comparison and parametric optimization
of subcritical Organic Rankine Cycle (ORC) and transcritical power cycle system
for low-temperature geothermal power generation, Applied Energy 2011; 88:
2740-2754.
[66] Cayer E, Galanis N, Nesreddine H. Parametric study and optimization of a
transcritical power cycle using a low temperature source, Applied Energy 2010;
87: 1349-1357.
[67] Schuster A, Karellas S, Leontaritis AD. Influence of supercritical ORC
parameters on plate heat exchanger design, Applied Thermal Engineering
2012; 33-34: 70-76.
[68] Papadopoulos AI, Stijepovic M, Linke P. On the systematic design and selection
of optimal working fluids for Organic Rankine Cycles. Appl Therm Eng
2010;30:760–9.
[69] Uehara H, Ikegami Y. Optimization of a closed-cycle OTEC plant system. J Solar
Eng 1990;112:247–56.
[70] Bliem C, Zangrando F, Hassani V. Value analysis of advanced heat rejection
systems for geothermal power plants. Energy Conver Eng Conf 1996.
[71] Turton R, Bailie RC, Whiting WB, Shaeiwitz JA. Analysis, synthesis and design
of chemical processes. New Jersey: Prentice Hall PTR; 1998.
[72] Calm JM, Hourahan GC. Refrigerant data summary. Eng Syst 2001;18(11):74–
88.
[73] Nafey AS, Sharaf MA. Combined solar Organic Rankine Cycle with reverse
osmosis desalination process: energy, exergy, and cost evaluations. Renew
Energy 2010.
[74] Hammer H, Röhmfeld M. Abwärmenutzung zur Krafterzeugung mittels neuer
Kreislaufmedien. VDI-Bericht 415, 81–87, VDI-Verlag Düsseldorf; 1981 (in
German).
[75] Jackson, J D and Hall, W B, Forced convection heat transfer to fluids at
supercritical pressure, Turbulent Forced Convection in Channels and Rod
Bundles, 1979, Vol.2, 563-611, published by Hemisphere Publishing
Corporation.
Page 103/104 Literature Study - The transcritical organic Rankine cycle
Report no. 00000
_____________________________________________________________________________________________________ This report may only be used wordily or entirely for publication purposes. Texts or publications where this report is issued have to be approved by the authors before submission.
[76] Jackson, J D and Hall, W B, Influences of buoyancy on heat transfer to fluids
flowing in vertical tubes under turbulent conditions, Turbulent Forced
Convection in Channels and Rod Bundles, 1979, Vol2., 613-640, published by
Hemisphere Publishing Corporat.
[77] Krasnoshchekov EA, Protopopov VS. Experimental study of heat exchange in
carbon dioxide in the supercritical range at high temperature drops. Teplofiz
Vys Temp 1966;4:389–98.
[78] Petukhov BS, Kirillov VV. On heat exchange at turbulent flow of liquid in pipes.
Teploenergetika 1958;4:63–8.
[79] Song Y, Thermodynamic analysis of a transcritical CO2 power cycle driven by
solar energy with liquified natural gas as its heat sink; Applied Energy 92
(2012) 194–203.
[80] Petukhov BS, Krasnoshchekov EA, Protopopov VS. An investigation of heat
transfer to fluids flowing in pipes under supercritical conditions. ASME.
University of Colorado, Boulder, CO, USA; 1961. p. 569–78.
[81] A. Bejan, Entropy Generation Minimization, CRC Press, Inc., 2004, ISBN 0-
8493-9651-4.
[82] J.D. Jackson, W.B. Hall, Influences of buoyancy on heat transfer to fluids
flowing in vertical tubes under turbulent conditions. in: S. Kakac, D.B. Spalding
(Eds.), Turbulent Forced Convection in Channels and Bundles, vol. 2, 1979, p.
640.
[83] Kyoung-Ho Kang, Soon-Heung Chang. Experimental study on the heat transfer
characteristics during the pressure transients under supercritical pressures,
International Journal of Heat and Mass Transfer 52 (2009) 4946–4955.
[84] Incropera FP, Dewitt DP. Fundamentals of heat and mass transfer. 5th ed. New
York: John Wiley and Sons; 2002.
[85] Cavallini A, Del CD, Doretti L, Longo GA, Rossetto L. Heat transfer and pressure
drop during condensation of refrigerants inside horizontal enhanced tubes. Int J
Refrig 2000;23:4–25.
[86] Shah MM. A general correlation for heat transfer during film condensation
inside pipe. Int J Heat Mass Transfer 1979;22:547–56.
[87] Wang-Touber correlation in Wang H, Touber S. Distributed and non-steady-
state modelling of an air cooler. Int J Refrig 1991; 14(2):98–111.
Page 104/104 Literature Study - The transcritical organic Rankine cycle
Report no. 00000
_____________________________________________________________________________________________________ This report may only be used wordily or entirely for publication purposes. Texts or publications where this report is issued have to be approved by the authors before submission.
[88] Cheng L, Ribatski G, Thome JR. Analysis of supercritical CO2 cooling in macro
and micro-channels. Int J Refrig 2008;31:1301–16.
[89] Kyoung-Ho Kang, Soon-Heung Chang. Experimental study on the heat transfer
characteristics during the pressure transients under supercritical pressures. Int
J Heat Mass Transfer 2009;52:4946–55.
[90] Müller-Steinhagen H, Heck K. A simple pressure drop correlation for twophase
flow in pipes. Chem Eng Process 1986;20:297–308.
[91] Collier JG, Thome JR. Convective boiling and condensation. Third ed. Oxford:
Clarendon Press; 1994.
[92] Kedzierski MA, Goncalves JM. Horizontal convective condensation of alternative
refrigerants within a micro-fin tube. NISTIR 6095. US Dept. Commerce; 1997.