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Abhinav Krishna
ORGANIC RANKINE CYCLE WITH SOLUTION CIRCUIT FOR LOW-GRADE
HEATRECOVERY
Master of Science in Mechanical Engineering
Eckhard A. Groll
Suresh V. Garimella
James E. Braun
W. Travis Horton
Eckhard Groll
David Anderson 07/25/2012
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ORGANIC RANKINE CYCLE WITH SOLUTION CIRCUIT FOR LOW-GRADE
HEATRECOVERY
Master of Science in Mechanical Engineering
Abhinav Krishna
07/12/2012
-
ORGANIC RANKINE CYCLE WITH SOLUTION CIRCUIT FOR LOW-GRADE HEAT
RECOVERY
A Thesis
Submitted to the Faculty
of
Purdue University
by
Abhinav Krishna
In Partial Fulfillment of the
Requirements for the Degree
of
Master of Science in Mechanical Engineering
August 2012
Purdue University
West Lafayette, Indiana
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-
ii
ACKNOWLEDGEMENTS
The contents of this work, and my personal growth during its
development, is due
in no small part to several people. My advisors Eckhard Groll
and Suresh Garimella
provided plenty of guidance and support, not to mention
commensurate intellectual
freedom, throughout my Masters studies. Jim Braun and Travis
Horton thank you for
all your useful insights during the course of this project.
I would like to thank everyone that helped in the design and
construction of the
challenging experimental setup for this project. Frank, Bob and
Gilbert thank you for
your efforts. Special thanks to two tireless students, Philipp
Danecker and Nick Czapla,
for the countless hours you spent working on the setup. Your
motivation and competence
went a long way in raising my enthusiasm for this project.
I have had the privilege of working with some of the best
graduate students
around. Brandon Woodland unassuming and soft spoken provided
plenty of brain
power for this work. Not that he represents a victory of
substance over style, because he
has plenty of both. Ian Bell and Craig Bradshaw provided quality
mentorship and plenty
of ideas. My other colleagues at Herrick Laboratories including
Bryce, Christian, Dong
Han, Howard, Huize, Simba, Stephen and several others have lent
me their time, of
which they had precious little. I have been lucky to foster
several friendships that extend
beyond professional interests during my time at Herrick
Laboratories.
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iii
Finally, I would like to thank the Cooling Technologies Research
Center, and
TORAD Engineering for funding this research and providing
customized equipment. I
would also like to thank ASHRAE for providing me with financial
support during my
Masters studies.
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iv
TABLE OF CONTENTS
Page
LIST OF TABLES
.............................................................................................................
vi LIST OF FIGURES
..........................................................................................................
vii NOMENCLATURE
..........................................................................................................
ix ABSTRACT
.................................................................................................................
xii CHAPTER 1. INTRODUCTION
......................................................................................1
1.1 Background
........................................................................................
1 1.2 Motivation
..........................................................................................
2 1.3 Objective
............................................................................................
3 1.4 Approach
............................................................................................
6
CHAPTER 2. CURRENT STATUS OF TECHNOLOGY
...............................................8 2.1 Organic
Rankine Cycles
....................................................................
8 2.2 Absorption Power Cycles
..................................................................
9 2.3 Working Fluid Mixtures
..................................................................
11
CHAPTER 3. THERMODYNAMIC MODEL DEVELOPMENT AND RESULTS
.......................................................................................13
3.1 Baseline Cycles
................................................................................
13 3.1.1 Organic Rankine Cycle
............................................................ 13
3.1.2 Vapor Compression Cycle with Solution Circuit
..................... 14 3.1.3 Organic Rankine Cycle with Solution
Circuit .......................... 16
3.2 Thermodynamic Features of Binary Mixtures
................................. 18 3.2.1 Phase Equilibrium
....................................................................
18 3.2.2 Absorption / Desorption Process
.............................................. 20 3.2.3 Temperature
Glide and Capacity Control ................................ 22
3.3 Cycle Model of an Organic Rankine Cycle with Solution
Circuit .. 25 3.3.1 Mass Balance
............................................................................
27 3.3.2 Energy Balance
.........................................................................
28
3.4 Organic Rankine Cycle with Solution Circuit Model Results
......... 32 CHAPTER 4. DESIGN OF EXPERIMENTAL TEST SYSTEM
..................................45
4.1 System
Sizing...................................................................................
45 4.2 System Design and Layout
.............................................................. 48
4.3 Design and Selection of Major Components
................................... 53
4.3.1 Pump
.........................................................................................
53 4.3.2 Heat Exchangers
.......................................................................
57 4.3.3 Expander
...................................................................................
60 4.3.4 Separator
...................................................................................
64
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Page
4.3.5 Receiver
....................................................................................
66 4.3.6 Expansion Valves
.....................................................................
66 4.3.7 Instrumentation and Data Acquisition
...................................... 67
4.4 Experimental Error and Uncertainty
................................................ 68 CHAPTER 5.
EXPERIMENTAL RESULTS AND ANALYSIS
...................................71
5.1 Experimental Program Overview
.................................................... 71 5.2
Experimental Performance Trends
.................................................. 75 5.3
Experimental Program Summary
..................................................... 81
CHAPTER 6. PERFORMANCE CHARACTERIZATION OF THE ORCSC SYSTEM
....................................................................................83
6.1 Parametric Analysis
.........................................................................
83 CHAPTER 7. CONCLUSIONS AND FUTURE WORK
...............................................90
7.1 Conclusion
.......................................................................................
90 7.2 Recommendations for Future
Work................................................. 92
LIST OF REFERENCES
...................................................................................................95
APPENDICES
Appendix A Instrument Calibration Procedures
.................................................. 98 Appendix B
Wiring Diagram for Data Acquisition
System............................... 105 Appendix C Procedures for
Charging and Discharging the ORCSC System .... 106 Appendix D
Procedures for Operating the ORCSC System
.............................. 108 Appendix E Data from
Experimental Testing
.................................................... 112
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vi
LIST OF TABLES
Table
..............................................................................................................................
Page
Table 3-1: Key assumptions used in the thermodynamic model.
..................................... 32 Table 4-1: Sample set of
input parameters used as a basis for system design.
................. 46 Table 4-2: Sample property values at each
state point in the
ORCSC cycle using the LKP EOS (refer to Figure 3-3).
................................46 Table 4-3: Capacities, flow
rates and cycle efficiencies used as a design
basis for the ORCSC.
.......................................................................................47
Table 4-4: Qualitative comparison for different pump types for an
ORCSC
application.
.......................................................................................................54
Table 4-5: Primary specifications of CAT PUMP MODEL 1051.CO2.
.......................... 56 Table 4-6: Data acquisition devices
and their output signals.
.......................................... 68 Table 4-7:
Measurement uncertainties.
.............................................................................
70 Table 5-1: Experimental test matrix.
................................................................................
72 Table 5-2: Key assumptions used in the thermodynamic model
for
experimental comparison.
................................................................................75
Table 6-1: Baseline conditions for parametric analysis.
................................................... 84 Table E-1:
Experimental temperature data.
....................................................................
112 Table E-2: Experimental temperature data continued.
................................................... 113 Table E-3:
Experimental pressure data.
..........................................................................
114 Table E-4: Experimental flow rate data.
.........................................................................
115 Table E-5: Experimental power, performance and heat transfer
data. ........................... 116
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vii
LIST OF FIGURES
Figure
.............................................................................................................................
Page
Figure 1-1: Heat sources, their temperature levels and heat
recovery technologies. .......... 4 Figure 3-1: Schematic
representation of the Organic Rankine Cycle.
.............................. 13 Figure 3-2: Schematic
representation of the Vapor Compression Cycle
with Solution Circuit.
.....................................................................................15
Figure 3-3: Schematic representation of the Organic Rankine
Cycle
with Solution Circuit.
.....................................................................................17
Figure 3-4: p, T, diagram for an arbitrary mixture (modified from
Kyle 1999). ........... 20 Figure 3-5: Variation of liquid and
vapor composition with temperature
for a binary mixture.
.......................................................................................21
Figure 3-6: Irreversibilities in heat transfer processes (modified
from Mulroy 1993). .... 24 Figure 3-7: Impact of ORCSC
concentration pairings on efficiency for a
source temperature of 100C and a sink temperature of 20C.
......................33 Figure 3-8: Variation of overall Second
Law Efficiency as a function of
Circulation Ratio.
...........................................................................................34
Figure 3-9: Impact of rich solution concentration on efficiency for
various source
temperatures. Plot is optimized for weak solution concentration.
.................35 Figure 3-10: Second Law efficiency as a
function of source temperature
for a basic ORC.
............................................................................................36
Figure 3-11: Second Law efficiency as a function of source
temperature
for an ORC with internal regeneration at the expander outlet.
.....................36 Figure 3-12: Second Law efficiency as a
function of source temperature
for the ORCSC.
.............................................................................................37
Figure 3-12: Variation of component capacities as a function of
Circulation Ratio. ....... 40 Figure 3-13: Variation of High-side
system Pressure as a function of
Circulation Ratio.
..........................................................................................41
Figure 3-14: Variation of Pressure Ratio as a function of
Circulation Ratio.................... 41 Figure 4-1: Detailed
schematic diagram of the secondary loop for heat input
temperature control.
........................................................................................49
Figure 4-2: Detailed schematic diagram of the primary ORCSC system.
........................ 49 Figure 4-3: Preliminary CAD
representation of ORCSC system arrangement. ............... 51
Figure 4-4: Top view of the primary ORCSC experimental load stand.
.......................... 52 Figure 4-5: Front view of the primary
ORCSC experimental load stand. ........................ 52 Figure
4-6: Secondary heat input loop load stand.
........................................................... 53
Figure 4-6: Sectional view of CAT PUMP MODEL 1051.CO2.
..................................... 56 Figure 4-7: Dual Coil Heat
Exchangers selected for use in the ORCSC. .........................
58
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viii
Figure
.............................................................................................................................
Page
Figure 4-8: Sanden TRS-105 scroll compressor housing.
................................................ 62 Figure 4-9:
Front view of Torad rotary spool expander housing.
..................................... 63 Figure 4-10: Design of the
Torad rotary spool expander.
................................................. 64 Figure 4-11:
Design and layout of separator and sight glass.
........................................... 65 Figure 4-12:
Receiver and sight glass selected for use in the ORCSC.
............................ 66 Figure 4-13: General overview of
the data aquistion system.
.......................................... 67 Figure 5-1:
Comparison of theoretical and experimental Second Law
efficiencies as a function of the Circulation Ratio.
........................................77 Figure 5-2: Comparison
of theoretical and experimental Desorber Heat
Input (System Capacity) as a function of the Circulation Ratio.
....................78 Figure 5-3: Comparison of theoretical and
experimental Second Law Efficiencies
as a function of the Desorber Exit Temperature.
............................................78 Figure 5-4:
Comparison of theoretical and experimental Expander Pressure
Ratio
as a function of the Circulation Ratio.
............................................................79
Figure 5-5: Comparison of theoretical and experimental Pump Work
Input as a
function of the Circulation Ratio.
...................................................................80
Figure 5-6: Comparison of theoretical and experimental Expander
Work Output as a
function of the Circulation Ratio.
..................................................................
80 Figure 6-1: Net power output and Second Law Efficiency as a
function of expander isentropic efficiency.
....................................................85 Figure 6-2:
Net power output and Second Law Efficiency as a function of
pump
efficiency.
.......................................................................................................86
Figure 6-3: Net power output and Second Law Efficiency as a
function of the
desorber pinch point temperature.
..................................................................87
Figure 6-4: Net power output and Second Law Efficiency as a
function of the
absorber pinch point temperature.
..................................................................88
Figure 6-5: Net power output and Second Law Efficiency as a
function of the
internal heat exchanger effectiveness.
............................................................89
Figure A 1: Sample calibration data for a thermocouple.
................................................. 99 Figure A 2:
Sample calibration data for a pressure transducer.
...................................... 101 Figure A 3: Sample
calibration data for a mass flow meter.
.......................................... 102 Figure A 4: Top view
of expander and torque cell.
........................................................ 103 Figure
A 5: Calibration of the torque cell.
......................................................................
104 Figure A 6: Sample calibration data for torque cell.
....................................................... 104
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ix
NOMENCLATURE
Symbols
A area CR Circulation Ratio,
F degrees of freedom
g gravitational acceleration
enthalpy
IHX Internal Heat Exchanger
K number of components
gm mass flow rate of glycol
rm mass flow rate of rich solution
wm mass flow rate of weak solution
vm mass flow rate of vapor
pressure
Q capacity
AQ absorber capacity
DQ desorber capacity
,h wQ heating capacity for water
,h totQ total heating capacity
T temperature V volumetric flow rate
h
p
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x
w overall uncertainty
W work
quality
z measured quantity
difference
heat exchanger effectiveness
efficiency
relative humidity density
number of phases
concentration
specific volume
Tor torque
rotational speed
Subscripts
a air
A absorber
c cold fluid
car carnot
comp compressor
cond condensing
crit critical
D desorber
h hot fluid
i inlet
IHX Internal Heat Exchanger
meas measured
o outlet
x
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xi
pump pump
pinch pinch-point temperature
r rich solution
ref refrigerant
s isentropic
sat saturation
sub sub-cooling
sup superheat
turb turbine
tot total
w weak solution
v vapor
Acronyms
DAQ Data Aquisition
EOS equation of state
EPDM Ethylene Propylene Diene Monomer
LKP Lee-Kesler-Plcker equation of state
ORC Organic Rankine Cycle
ORCSC Organic Rankine Cycle with Solution Circuit
PR Pressure Relief
PS Pressure Switch
PTFE Polytetrafluoroethylene
VCCSC Vapor Compression Cycle with Solution Circuit
VLE vapor-liquid-equilibrium
-
xii
ABSTRACT
Krishna, Abhinav. M.S.M.E., Purdue University, August 2012.
Organic Rankine Cycle with Solution Circuit for Low-Grade Heat
Recovery. Major Professors: Eckhard A. Groll, Suresh V.
Garimella.
Increasing interest in utilizing low-grade heat for power
generation has prompted
a search for ways in which the power conversion process may be
enhanced. A novel
Organic Rankine Cycle with Solution Circuit (ORCSC) using Carbon
Dioxide / Acetone
as the working fluid pair was studied for this purpose. A
thermodynamic simulation
model was developed and an experimental test stand was built to
serve as a proof of
concept for the technology.
The thermodynamic model showed that the ORCSC using Carbon
Dioxide /
Acetone as the working pair offers no significant efficiency
improvements over a
conventional Organic Rankine Cycle (ORC) using only Carbon
Dioxide as the working
fluid. Furthermore, the ORCSC with a Carbon Dioxide / Acetone
working pair has
significantly lower performance than an ORC using conventional
working fluids such as
pentane or R245fa. This may render the ORCSC unattractive since
the low-temperature
heat sources mean that the theoretical (Carnot) efficiency limit
is itself relatively low, and
achieving cycle efficiencies as close to the Carnot limit as
possible is necessary for
ensuring the economic feasibility of the technology. However,
the ORCSC was
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xiii
found to have significantly lower working pressures than an ORC,
provides the ability to
use temperature glide to match the temperature profiles of the
source and sink fluids and
facilitates intrinsic capacity control. This may lead to higher
overall system efficiencies
when coupled with sources that have varying heat input
temperatures or loads. More
application-specific studies that address the nature and
capacity of the source and sink
streams are required to identify where this ability may be most
advantageous.
The experimental tests showed good agreement with the simulation
data when all
the boundary conditions were matched. However, the efficiencies
of the system were
generally poor and many of the expected trends were skewed due
to design shortcomings
and the use of equipment that was not optimized for the ORCSC
system. Isolation of
individual parameters was an acute challenge due to the number
of variables that need to
be tightly controlled during system operation. Nevertheless, the
experimental results
provided a validation of the simulation model.
The simulation model was expanded to include a parametric study
of the various
components on the overall system performance. It showed that the
ORCSC is particularly
sensitive to the performance of the expander and pump. Amongst
the heat exchangers,
the performance of the absorber had the greatest impact on the
overall system
performance.
It is clear from this study that a range of practical
considerations need to be taken
into account and weighed together with the thermodynamic
analysis when evaluating the
feasibility of ORCSC technology. The ORCSC offers some potential
practical advantages
which may outweigh the added cost and complexity of these
systems in certain
applications. However, the maturity of the technology and
associated body of literature is
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xiv
limited, and further work needs to be pursued in this area
before widespread adoption of
the technology is possible.
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1
CHAPTER 1. INTRODUCTION
1.1 Background
The increasing cost of energy, coupled with the recent drive for
energy security
and climate change mitigation have provided the impetus for
harnessing renewable
energy sources as viable alternatives to conventional fossil
fuels. However, several of
these renewable energy sources, including geothermal, biomass
and solar, intrinsically
provide low-grade heat (at temperatures between 60C 300C).
Furthermore,
thermodynamic considerations mean that a large amount of
low-grade heat is discharged
from power plants and various other industrial processes. In
fact, in the United States,
over two-thirds of the primary energy supply is ultimately
rejected as low-grade waste
heat according to the World Energy Council (2006). Recovering
low-grade heat,
therefore, is increasingly becoming an economic and
environmental imperative.
Low-grade waste heat, largely at a temperature level between 30C
250C, is
primarily a product of thermo-mechanical energy conversion
losses. Thus far, waste heat
recovery systems have mainly been designed for thermal heat
recovery for process use
using recuperative heat exchangers. Conversions from waste heat
to higher forms of
energy, such as shaft work and/or electricity, have not been
viable due to technical and
cost impediments. Nevertheless, due to increasing energy costs
and available heat sources,
-
2
waste heat recovery systems are of increasing interest to
designers, engineers and society
at large (Little 2009).
1.2 Motivation
An increasing source of waste heat comes from growing technology
needs. In the
last twenty years, computer power consumption has increased
exponentially. Of the total
electricity consumption in the United States in 2006, more than
1 % was used to operate
large data centers (Koomey 2007). According to ASHRAE (2005),
datacom workload is
expected to rise further at a 40 to 50 % compound growth rate.
Additionally, the power
density of datacom equipment is expected to reach up to 8 kW/m2
for computer servers
and 15 kW/m2 for high density communication equipment by 2014.
In large data centers,
therefore, an enormous amount of electrical energy is consumed,
which is directly
converted into heat and ultimately rejected to the
environment.
The rejected heat represents a large energy stream that has
already been paid for;
however recovering and utilizing it represents a challenge. This
is primarily due to the
temperature level of the waste heat (50C 85C), which renders it
inefficient to convert
to a more usable form of an energy transport medium, such as
electricity, using
conventional power generation technology. Furthermore, several
renewable energy
sources face the same problem low source temperatures to the
point where the
application of steam Rankine Cycles, ubiquitous in power
generation, is grossly
inefficient and expensive.
Currently, technologies attempting to provide low-grade heat
recovery solutions
have seen very limited commercialization. This is broadly due to
two reasons: lack of
-
3
historical research and development in the area of waste heat
recovery due to technical
and cost impediments; and technical challenges associated with
scaling the technology
from utility scale to commercial scale, particularly with regard
to expansion machines
(turbines). However, due to rising primary energy costs and the
environmental premium
being placed on fossil fuels, the conversion from low-grade heat
to electrical energy is a
pressing societal challenge.
1.3 Objective
One way to recover low-grade heat, and use it in a power
generating capacity, is
to use Organic Rankine Cycle (ORC) technology. Organic Rankine
Cycles differ from
traditional steam Rankine Cycles in the use of an organic
working fluid as opposed to
water/steam as the working fluid, making them far better suited
for low temperature heat
sources. However, due to the low-temperature heat sources, the
theoretical (Carnot)
efficiency limit is relatively low. Therefore, achieving cycle
efficiencies as close to the
Carnot limit as possible remains a challenge, and is important
for ensuring the economic
feasibility of the technology. An overview of available heat
sources and their
temperature levels, as well as the technologies that could be
used for a given temperature
range to recover the available heat, is given in Figure 1-1.
-
4
Figure 1-1: Heat sources, their temperature levels and heat
recovery technologies.
In order to achieve cycle efficiencies as close to the Carnot
limit as possible, it
may be necessary to modify the Organic Rankine Cycle. One novel
modification,
proposed by Maloney and Robertson (1953) as well as Kalina
(1983), is to introduce
absorption technology for power generation. This modification is
termed the Organic
Rankine Cycle with Solution Circuit (ORCSC), also known as the
Absorption-Rankine
cycle. The ORCSC differs from the ORC primarily through the use
of a zeotropic
mixture, consisting of a refrigerant and an absorbent as the
working fluids. The
refrigerant and absorbent are characterized by a large boiling
point difference. This
enables the separation of the more volatile component (the
refrigerant) in the vapor phase
-
5
from the absorbent solution in the liquid phase. The refrigerant
vapor (and a small
quantity of the solution) then flows through the expansion
device, whereas the liquid
absorbent forms a solution circuit.
Aside from the possibility of higher exergetic conversion
efficiency than an ORC,
the ORCSC has several other inherent features that address
critical issues related to the
general applicability of low-grade heat recovery technology. For
example, the solution in
the ORCSC ensures significantly lower working pressures when
compared to a
conventional ORC. This allows for the use of high-pressure
natural refrigerants, such as
carbon dioxide, at moderate operating pressures which leads to
significant cost savings.
The use of natural refrigerants has numerous environmental
benefits, including negligible
Global Warming Potential (GWP), zero Ozone Depletion Potential
(ODP), and non-
toxicity. The use of a zeotropic mixture in the ORCSC also means
that the system
capacity can be easily adjusted by simply changing the
concentration of the refrigerant
used in the system. This offers a simple, cost-effective
solution for adapting the system
for peak and non-peak loads, which the system is bound to
encounter in practice.
Furthermore, as shown in Figure 1-1, the added system complexity
of the ORCSC can be
justified at two ends of the source temperature spectrum: at
extremely low source
temperatures (
-
6
temperature range is important because it fills an important
technology gap where
existing conversion systems cannot efficiently generate power.
Numerous exhaust heat
streams from industrial processes, as well as biomass and
certain solar concentration
techniques, fall into this spectrum.
Despite significant advantages, there have been few ORCSC
prototypes that have
been built. The few prototypes that exist have relied on using
an Ammonia / Water
working pair, which renders them unattractive in many
applications due to the corrosive
properties and toxicity of Ammonia. In this work, the objective
is to investigate an
ORCSC cycle that uses a natural refrigerant in the working pair,
and to demonstrate a
proof-of-concept experimental system.
1.4 Approach
In order to fulfill the objectives of this project, the
following approach was
adopted in the given order:
Literature and patent search of Organic Rankine Cycle
technology.
Identification of methods and measures from the literature to
increase the
efficiency and applicability of Organic Rankine Cycles,
including novel cycle
modifications.
Evaluation of different working fluids.
Thermodynamic simulations of possible cycles and assessment of
their feasibility.
Combination of the identified ideas for Organic Rankine Cycle
modifications,
including an Organic Rankine Cycle with Solution Circuit.
Selection of the most promising working pair.
-
7
Detailed simulations and selection of the most promising
concept.
Design and construction of an experimental bread board system
based on
simulation results to serve as a proof of concept for the
technology.
Implementation of the measurement system and development of the
test software.
Experimental tests according to a predetermined test matrix, and
determination of
several key system characteristics such as efficiency, capacity,
etc.
Comparison of measured performance to simulation results.
Model refinements based on test results.
Feasibility assessment of the technology, and recommendations
for improvements
to the system based on experimental experience.
Identification of future technology development needs.
-
8
CHAPTER 2. CURRENT STATUS OF TECHNOLOGY
2.1 Organic Rankine Cycles
Organic Rankine Cycles with low temperature heat input are
relatively well
known and have been investigated widely in the literature.
Theoretical investigations
were pursued as early as the 1970s by Davidson (1977) for
integration with solar
collectors, and further expanded by Probert et al. (1983).
Experimental investigations
were conducted by Monahan (1976), with reported First Law
thermal efficiencies usually
below 10% for small-scale systems. The experimental
investigations identified that
expansion turbines suitable for use in ORC systems have not been
widely studied, and
few commercial designs were available. In general, experimental
investigations have
largely involved the use of vane expanders (Badr et al. 1990,
Davidson 1977).
Hung et al. (1997) compared the efficiencies for various ORC
working fluids such
as benzene, ammonia, R11, R12, R134a and R113. The study
established correlations
between system efficiencies, source temperatures and system
pressures. Of the fluids
investigated, benzene was found to provide the highest
efficiency, followed by R113,
R11, R12, R134a, and Ammonia.
-
9
Despite the high Ozone Depletion Potential (ODP) and Global
Warming Potential
(GWP) of many of these fluids, the first commercial applications
appeared in the late 70s
and 80s with medium-scale power plants developed for geothermal
and solar applications.
Currently, over 300 ORC systems are in operation worldwide, with
over 1800 MWe of
installed capacity (and this number continues to grow at an ever
increasing pace). The
largest number of plants is installed for biomass Combined Heat
and Power (CHP)
applications, followed by geothermal plants and then Waste Heat
Recovery (WHR)
plants (Quoilin 2011). It should be noted, however, that the
largest application in terms of
installed power are geothermal applications. (Enertime
2011).
2.2 Absorption Power Cycles
The foundation for the Organic Rankine Cycle with Solution
Circuit (ORCSC),
also known as the Absorption-Rankine Cycle, is the Vapor
Compression Cycle with
Solution Circuit (VCCSC), first investigated by Altenkirch
(1950). Groll and
Radermacher (1994) carried out successful experimental testing
to demonstrate the
concept. Reversing the VCCSC creates a power generating cycle
similar to the Rankine
Cycle, but with higher potential efficiencies (Kalina 1983).
While Absorption-Rankine
Cycles have been known for more than 50 years, limited research
and even more limited
experimental investigations have been carried out in this
field.
One experimental investigation was performed by Maloney and
Robertson (1953)
using an Ammonia / Water pair as the working fluid. Their
results showed that the
absorption power cycle had no thermodynamic advantage over the
Rankine Cycle.
-
10
However, the authors encouraged further investigations in this
field, and proposed the use
of other binary mixtures.
Further investigations were conducted by Kalina (1983) with the
same working
fluid as Maloney and Robertson, but with a slightly different
experimental setup. Kalina
showed that the cycle has a thermal efficiency that is 30-60%
greater than comparable
steam power cycles at the same source temperature. In these
studies, the cycle was
coupled with relatively high turbine inlet temperatures of
180C.
Due to the diversity of potential applications, the Kalina cycle
was further studied
for different purposes with slightly different configurations.
Goswami and Xu (2000)
proposed a simple combined cycle using solar energy as the heat
source. Zheng et al.
(2006) modified the Kalina cycle in order to produce power as
well as provide
refrigeration simultaneously, but the investigations carried out
were numerical in nature,
without experimental validation.
Robbins and Garimella (2010) published theoretical
investigations of an Organic
Rankine Cycle with Solution Circuit using a novel binary mixture
of Amyl-Acetate and
Carbon Dioxide (CO2) as the working fluid. Their parametric
theoretical results showed
promising thermal efficiencies, but once again, experimental
validation was not carried
out.
In summary, while there have been a few experimental
investigations conducted
for Absorption-Rankine Cycles using Ammonia / Water as the
working pair, to the best
of the authors knowledge, no investigations to date have
considered novel working pairs
in an experimental investigation of the Absorption-Rankine
Cycle.
-
11
2.3 Working Fluid Mixtures
The choice of a working fluid mixture for the ORCSC is defined
by the
requirement that the two fluids have a large boiling point
difference. This enables the
more volatile component (refrigerant) to easily separate from
the liquid absorbent, and
for the system to accommodate a large range of source and sink
temperatures simply by
adjusting the composition of the mixture. Generally, the working
fluid mixtures found in
absorption cycles may also be used in the ORCSC. Ammonia / Water
mixtures have been
studied extensively in the literature; however, ammonia has the
obvious drawback of
being toxic and corrosive, which limits its potential
applications. An Amyl-Acetate /
Carbon Dioxide mixture was studied for use in an ORCSC (Robbins
and Garimella,
2010); however, the operating pressures were found to be too
high for this working pair.
Groll and Radermacher (1994) studied the use of a Carbon Dioxide
/ Acetone mixture in
a VCCSC application, and Carbon Dioxide was found to have the
following advantages:
Low Global Warming Potential and zero Ozone Depletion Potential
as compared
to conventional refrigerants. This is pertinent given that the
application of this
technology ultimately focuses on mitigating environmental
impact.
Non toxicity.
Non-flammability in this working pair, CO2 can be considered an
ideal fire
extinguishing medium for the Acetone. In case of a leak, a large
amount of CO2
and a small quantity of Acetone would escape from the system due
to the
difference in the vapor pressures of the two components.
Large volumetric heat capacity, which enables the use of smaller
turbines and
other components.
-
12
Compatibility with common component materials.
Simplicity of operation.
No recycling of working fluid required.
Furthermore, Acetone was chosen as the absorbent solution for
the following reasons:
Higher overall thermodynamic efficiencies due to its ability to
dissolve CO2.
Wide availability at low cost.
Lower flammability when compared to other hydrocarbon
solutions.
Given these advantages, a compelling case can be made for a
Carbon Dioxide / Acetone
working pair to be investigated in an ORCSC system.
-
13
CHAPTER 3. THERMODYNAMIC MODEL DEVELOPMENT AND RESULTS
3.1 Baseline Cycles
3.1.1 Organic Rankine Cycle
The conceptual foundation for the ORCSC lies in a combination of
a conventional
Organic Rankine Cycle with a Vapor Compression Cycle with
Solution Circuit (VCCSC).
A simplified schematic diagram of an ORC is shown in Figure 3-1
below.
Figure 3-1: Schematic representation of the Organic Rankine
Cycle.
The ORC is essentially made up of the four main components found
in traditional
steam Rankine Cycles: an evaporator, expander, condenser, and
pump. However, unlike
in steam Rankine cycles, there is usually no water-steam
separation drum connected to
Expander
Pump Condenser
Evaporator
Low-Grade Heat Source TH
Environment TL
(1)
(2)
(3)
(4)
-
14
the boiler, and one single heat exchanger is used to perform all
three evaporation phases:
preheating, vaporization and superheating. Due to a combination
of cost impediments,
system scale and thermodynamic properties of the chosen working
fluid, reheating and
turbine bleeding are generally not suitable for the ORC.
However, an internal regenerator
installed at the expander outlet is often used to preheat the
liquid from the pump outlet.
The working principle is as follows: the refrigerant leaves the
evaporator as a
supercritical gas (1), which then enters an expander. The
thermal expansion through the
expander produces mechanical shaft power (2), which can be
converted to electrical
energy in a generator. The refrigerant then enters the
condenser, where it is converted to
the liquid phase by rejecting heat to the ambient (3). The
liquid refrigerant is then
pumped back to the evaporator inlet to complete the cycle
(4).
3.1.2 Vapor Compression Cycle with Solution Circuit
The VCCSC combines absorption and compression technology, and
differs from the
conventional vapor compression cycle primarily by employing a
working fluid mixture
consisting of a refrigerant and an absorbent, instead of pure
components. A schematic
diagram of the VCCSC is provided in Figure 3-2.
-
15
Figure 3-2: Schematic representation of the Vapor Compression
Cycle with Solution Circuit.
The mixture is evaporated in the desorber using a heat source
(which may be the
conditioned space); however, the evaporation of the mixture is
not complete. Instead, a
liquid and vapor exist at the same temperature and pressure
(with differing concentrations)
in the desorber. The refrigerant-rich vapor and
low-concentration liquid (i.e. weak
solution) are separated at the desorber outlet. Note that an
additional separator may be
necessary to complete the separation process. While the vapor
(1) proceeds to the
mechanically driven compressor, the weak solution liquid (6) is
pumped to a recuperative
internal heat exchanger (7) where it is used to preheat the rich
solution from the absorber
(4). At the other end of the cycle, the compressed refrigerant
(2) and weak solution (8)
enter the absorber. Since absorption is an exothermic process, a
heat and mass exchange
process takes place in which heat is rejected to the environment
(or other appropriate heat
sink) and the refrigerant is simultaneously resorbed into the
absorbent, thereby forming a
Heat Source TH
Solution Pump
Absorber
Expansion Valve
Heat Sink TL
Compressor
(2)
(3)(4)
(5)
(6)
(7)
(1)
Desorber
Internal Heat Exchanger
Weak Solution
Rich Solution
(8)
-
16
rich solution (3). An expansion valve is used to equalize the
high-side and low-side
pressures (5).
3.1.3 Organic Rankine Cycle with Solution Circuit
The ORCSC reverses the VCCSC and applies the operating
principles of an ORC
to create a power generating cycle based on the use of a binary
mixture. Figure 3-3 shows
a schematic diagram of the Organic Rankine Cycle with Solution
Circuit. State (1)
represents the outlet of the desorber (note that a separator may
be used to separate the
vapor and liquid streams at the desorber outlet). At this state,
the heat source has heated
the mixture, and the primary working fluid is desorbed from the
solution. The CO2 vapor
stream then enters the expander, where it is expanded to its low
pressure state (2) while
producing mechanical shaft power. State (3) represents the
outlet of the absorber, where
the CO2 has been resorbed into the solution to form a rich
solution. Since absorption is an
exothermic process, the absorber rejects heat to the environment
during this process.
Following this, the rich solution is pumped to the high pressure
state (4) by means of a
solution pump, and is subsequently preheated by an internal heat
exchanger (5) before
entering the desorber. State (6) represents the liquid phase
weak solution at the desorber
outlet. The weak solution stream is then subcooled (7) through
the internal heat
exchanger, and expanded to the low pressure state (8) by an
expansion valve.
-
17
Figure 3-3: Schematic representation of the Organic Rankine
Cycle with Solution Circuit.
The main difference between the conventional vapor compression
cycle and ORC
when compared to the VCCSC and ORCSC, respectively, is the use
of a zeotropic
mixture with a large boiling point difference instead of a pure
fluid. By introducing such
a working fluid mixture, three important features are
accomplished:
1) Although desorption and absorption occur at constant
pressures, the saturation
temperatures are no longer constant but vary with the
composition changes of the
liquid and the vapor phases which occur during the phase change
processes. This
results in a temperature glide in the absorber and desorber.
These temperature
glides can be adjusted over a wide range or eliminated almost
entirely.
2) A change in the overall concentration of the mixture
circulating through the cycle
results in a change of the vapor pressures and densities at a
given temperature,
and therefore in a change of the capacity of the entire
unit.
Low-Grade Heat Source TH
Pump
Desorber
Expansion Valve
Environment TL
Expander
(2)
(3)
(4)
(5)(6)
(7)
(8)
(1)
Absorber
Internal Heat Exchanger
Weak Solution
Rich Solution
-
18
3) By introducing a solution in the cycle, the operating
pressures of the cycle are
significantly reduced. The solution allows the resorption
temperature of the
mixture to be higher than the critical temperature of the pure
refrigerant.
All of these features can be used to increase the overall COP
and expand the
flexibility of system operation. However, in order to understand
these features more fully
and evaluate their applicability in a power generating cycle, a
detailed study of
multiphase-multicomponent systems is necessary.
3.2 Thermodynamic Features of Binary Mixtures
This section provides a background on the thermodynamic
treatment of binary
mixtures. Since the proposed cycle utilizes a two component
mixture, emphasis is placed
on binary working fluids; however, the same concepts would hold
if multicomponent
mixtures were considered. A basic understanding of binary
mixture behavior is essential
to understand features such as temperature glide and capacity
control that are integral
facets of the ORCSC.
3.2.1 Phase Equilibrium
A single fluid is considered to be in phase equilibrium when
successive pressure
and temperature measurements of the liquid and vapor phase do
not vary with time. For a
binary mixture to be in phase equilibrium, in addition to
pressure and temperature, the
concentration of each component may not vary with time. In
general, the Gibbs phase
rule ( 3-1 ) gives the degrees of freedom of a system:
-
19
F K 2= + ( 3-1 )
The degrees of freedom (F) depends on the number of components
(K), and on the
number of phases ( ) that are prevalent. When F number of
intensive variables are
specified, the system is determinate. Therefore, in order to
visualize the phase behavior of
a binary system, three intensive variables need to be considered
when considering a
single-phase region (two intensive variables are needed when
considering the two-phase
region). Typically, the variables chosen are the temperature
(T), pressure (p) and the mass
concentration ( ). In the context of this work, when considering
a binary mixture
consisting of a primary working fluid and an absorbent, the mass
concentration may be
defined as:
liquidmass of primary working fluid in the liquid phase
mass of both componets in the liquid phase = ( 3-2 )
vapormass of primary working fluid in the vapor phase
mass of both componets in the vapor phase =
( 3-3 )
For the mass concentration of a binary mixture, the knowledge of
either the vapor
or liquid phase is sufficient, because the corresponding mass
fractions can be derived
from the knowledge of the other. Figure 3-4 represents a p, T,
diagram for an arbitrary mixture.
-
20
Figure 3-4: p, T, diagram for an arbitrary mixture (modified
from Kyle 1999).
The thick, solid line represents the saturated liquid boundary;
any point above the
line would indicate that the binary mixture is in the subcooled
region and a single liquid
phase exists. Similarly, the dashed line corresponds to the
saturated vapor boundary; any
point below the line would indicate that the binary mixture is
in the superheated phase.
For a point located in between the two boundaries, an
equilibrium between the liquid and
vapor phases exists. Therefore, the pressure and temperature are
the same for both phases,
while concentrations differ in each phase. This is discussed in
further detail below.
3.2.2 Absorption / Desorption Process
In order to understand the thermodynamic behavior of binary
mixtures more fully,
it is necessary to illustrate the absorption and desorption
processes in detail. Figure 3-5
-
21
shows a two-dimensional rendition of Figure 3-4 where the
pressure is held constant, i.e.,
the horizontal plane in Figure 3-4.
Figure 3-5: Variation of liquid and vapor composition with
temperature for a binary mixture.
Point 1 indicates a subcooled binary mixture in the liquid phase
for a given mass
concentration (1), temperature (T1) and pressure (p). As the
solution is heated at constant
pressure, point 1 moves up vertically until it reaches the
saturated liquid line. The first
vapor bubbles begin to form at temperature T2. At equilibrium, a
horizontal line ties
together the saturated liquid and vapor curves. These lines,
called tie lines, reflect the
-
22
equilibrium between liquid and vapor compositions (, and ,) at a
constant pressure and temperature for a binary mixture. At point 2,
the mass fraction of the liquid phase is
exactly the same as for the subcooled liquid at point 1(l). The
mass fraction of the vapor
phase is given by v,2, where the pressure and temperature are
the same as the liquid
phase as a condition for equilibrium. Note that the vapor
concentration is rich in the
primary fluid, because the boiling temperature ( boil,primary
fluidT ) of the pure refrigerant is
lower than the boiling point of the pure absorbent (
boil,absorbentT ). As the mixture is heated
further at constant pressure to state point 3, the amount of
primary fluid (l,3) remaining
in liquid phase is less than at state point 2 (l). Accordingly,
the vapor phase (v,3) also
contains a higher mass fraction of absorbent and a lower mass
concentration of the
primary fluid compared to state point (2). Continued heating
eventually moves the
mixture to point 4, where the last remaining droplet is
evaporated. At this point, the vapor
has exactly the same mass concentration (v,4) as the sub cooled
liquid (l). Further
heating leads to a superheated vapor (5) at the same
concentration.
To have a better analytical understanding of two-phase behavior,
the phase rule
( 3-1 ) can be applied. Given a binary mixture (K=2) and a
two-phase region ( = 2) at constant pressure, only one degree of
freedom remains. Therefore, either the temperature
(T) or the mass concentration () can be selected to fix the
equilibrium state.
3.2.3 Temperature Glide and Capacity Control
A key feature of utilizing a mixture-based cycle is that
although desorption and
absorption occur at constant pressures, the saturation
temperatures are no longer constant
-
23
but vary with the composition changes of the liquid and the
vapor phases that occur during
the phase change processes. For example, during the evaporation
process illustrated in
Figure 3-5, the saturation temperature changes from T2 to T4.
This temperature glide
becomes larger as the difference in the boiling points of the
pure components increases.
The temperature glide also depends on the mass fraction and the
shape of the vapor
bubble, which is an intrinsic property of the working fluid
mixture. In general, the
temperature glide is larger for intermediate values of initial
than for small or large
values of . An important feature is that the temperature glide
can be adjusted over a wide
range; for example, for a value of 1 in Figure 3-5, the first
bubbles form at a higher
saturation temperature (2) when compared to the initial case of
T2 and 1. Additionally,
the evaporation process is completed at a higher temperature (4
). As a result, the
saturation temperatures are shifted to higher temperature levels
with a smaller
temperature glide simply by varying the mass concentration. The
same effect can be
accomplished by having an incomplete evaporation process in
which a liquid and vapor
exist at the same temperature and pressure, but at different
concentrations.
A key feature of the temperature glide is that it can reduce
heat transfer
irreversibilities in the heat exchangers. This is accomplished
when the temperature profile
of the evaporating and condensing mixture matches that of
heat-source and heat-sink
fluids in the counter flow desorber and absorber (Mulroy 1993).
This is shown in Figure
3-6, which illustrates the Carnot and Lorenz cycles operating
with the same heat transfer
fluid temperature profiles at two different source
temperatures.
-
24
Figure 3-6: Irreversibilities in heat transfer processes
(modified from Mulroy 1993).
The Carnot cycle refers to a pure refrigerant, for which the
evaporation and
condensing process takes place at a constant temperature for a
fixed pressure. In
comparison to the Carnot cycle, the Lorenz cycle refers to the
evaporation and
condensation process of a mixture, with the temperature glide
clearly evident during
these phase change processes. If the profiles of the heat
transfer fluid (HTF) flowing
through a heat exchanger in counterflow is modeled with a
non-zero slope, the shaded
areas approximate the heat transfer irreversibilities. It can be
seen that the irreversibilities
are significantly lower for the Lorenz cycle due to the
temperature glide. Furthermore, if
the temperature of the heat source is increased for the same
operating cycle, it can be
seen from Figure 3-6 that the temperature profile of the HTF
changes. The new profile
can be matched by simply adjusting the mass concentration when
using a binary mixture
-
25
(e.g. to a value of 1 shown in Figure 3-5). A change in the
overall concentration of the
mixture circulating through the cycle results in a change of the
vapor pressures and
densities at a given temperature, and therefore in a change of
the capacity of the system.
It also shows that for a capacity adjustment, the heat transfer
irreversibilities remain
nearly constant for the Lorenz Cycle, while they increase
notably for the Carnot Cycle. It
is important to note, however, that the saturation temperatures
generally do not vary
linearly as a function of enthalpy for zeotropic mixtures, so
that Figure 3-6 can be
regarded as a simplification.
Nevertheless, the temperature glide and capacity control are two
key features of a
mixture-based cycle. The temperature glide can be used to reduce
heat transfer
irreversibilities when the source or sink fluids are not
approximated as reservoirs, i.e.,
they have temperature profiles with non-zero slopes through the
heat exchange processes.
Furthermore, since the temperature glide can be adjusted over a
wide range of heat-
source and heat-sink temperatures simply by varying the
concentration of` the mixture,
the capacity of the system can be adjusted for peak and non-peak
operation.
3.3 Cycle Model of an Organic Rankine Cycle with Solution
Circuit
In order to quantify the performance of the ORCSC, it is
necessary to build a
thermodynamic cycle model. To simplify the analysis of the
cycle, the following general
assumptions are made:
The pressure drop due to frictional losses through the piping
and fittings is
negligible. Therefore, the only pressure drops in the system are
across the turbine,
pump and expansion valve.
-
26
The rich solution exiting the absorber and the weak solution
exiting the desorber
are both saturated liquids.
The vapor stream exiting the desorber is a saturated vapor.
There is thermodynamic equilibrium between the vapor and liquid
phases during
the absorption and desorption processes.
All the piping in the system is perfectly insulated.
There is no oil present in the cycle.
A simulation model was developed to compute the thermodynamic
properties at
each state point. Since the working fluid is a binary mixture,
an equation of state (EOS) is
required to obtain extensive properties (enthalpy, entropy,
etc.) of the mixture at each
state point. Two equations of state were considered: the
correspondence method given by
the Lee-Kesler-Plcker (LKP) (Plcker et al. 1977), and the Wide
Range Equation of
State by Kunz and Wagner (Kunz et al. 2010). The LKP EOS is
given in a form that is
easily modifiable for several working pairs given appropriate
interaction parameters. It
was found to perform well for a Carbon Dioxide / Acetone mixture
in studies conducted
by Groll and Radermacher (1994). However, the LKP EOS was found
to have several
limitations as listed below:
Inability to calculate fluid properties accurately when given a
two-component
mixture in the two-phase region. This is particularly important
when fixing the
expander and expansion valve outlet states in the ORCSC
cycle.
Inability to calculate fluid properties accurately in the
superheated or subcooled
regions. This necessitated the assumption of either saturated
liquid or saturated
vapor at each state point.
-
27
Limitations in the range of pressures for which property data
were available
(accuracy was limited beyond 70 bars for the CO2 / Acetone
mixture).
Limitations in the range of concentrations for which property
data were available
(accuracy was limited outside the 0.15-0.6 [kgCO2/kgmixture]
range for the CO2 /
Acetone mixture).
Limitations in the range of temperatures for which property data
were available
(accuracy was limited beyond 150 C for the CO2 / Acetone
mixture).
Due to these limitations, it was found that the cycle
performance was significantly over-
predicted by the LKP EOS.
The Kunz and Wagner EOS was found to have a greater flexibility
of application,
particularly with regard to the range of temperatures, pressures
and concentrations for
which useful vapor-liquid-equilibrium (VLE) data were available.
Furthermore, the Kunz
and Wagner EOS is integrated with Refprop 9.0 (Lemmon et al.,
2012), allowing for easy
retrieval of the thermodynamic properties. The details of the
thermodynamic model are
given below.
3.3.1 Mass Balance
The mass balance for the ORCSC relates the mass flow rates of
the rich solution,
rm , weak solution, wm , and the vapor stream vm .
r w vm m m= + ( 3-4 )
Based on the mass concentrations of the rich and weak solutions,
the following mass
balance may be obtained:
-
28
r r w w v vm m m = + ( 3-5 )
A circulation ratio is defined as the ratio of the mass flow
rates of the rich solution and
vapor:
rv
v wk
r wk
mCRm
= =
( 3-6 )
3.3.2 Energy Balance
With reference to Figure 3-3, the heat capacity of the desorber
can be calculated using the
specific enthalpies evaluated at state points 1, 5 and 6:
( ) 6 1 51D vQ m CR h h CRh= + ( 3-7 )
Similarly, the heat capacity of the absorber can be calculated
using the specific enthalpies
evaluated at state points 2, 3 and 8:
( )2 8 31A vQ m h CR h CRh= + ( 3-8 )
The expansion across the expansion valve from state point 7 to 8
is assumed to be an
isenthalpic process:
7 8h h= ( 3-9 )
The energy balance across the internal heat exchanger gives the
following equation:
( )( )5 4 7 61v v vm CRh m CRh m CR h h= ( 3-10 )
Based on the isentropic turbine efficiency, turb , the enthalpy
at the turbine outlet can be
calculated as follows:
h2 = h1 turb h1 h2s( ) ( 3-11 )
The power output from the turbine is given by:
-
29
( )1 2turb vW m h h= ( 3-12 )
Similarly, based on the isentropic pump efficiency, pump , the
enthalpy at the pump outlet
can be calculated as follows:
4 34 3spump
h hh h
= + ( 3-13 )
The power input to the pump is given by:
( )4 3pump rW m h h= ( 3-14 )
Finally, the equations used for the thermal (first law) and
second law efficiencies are
given below:
turb pumpthermalD
W WW
= ( 3-15 )
sec
1
thermalond law
source
sink
TT
=
( 3-16 )
Note that sourceT and sinkT refer to the temperatures of the
heat-source and heat sink
temperature, respectively, assuming that they can be
approximated as constant
temperature reservoirs. The heat-source and heat-sink
temperatures cannot be reached
because of an incomplete heat transfer in the heat exchangers.
Given that the absorber
and desorber incorporate both heat and mass transfer, and the
fact that the working fluid
may traverse through the subcooled, two-phase and superheated
regions in these heat
exchangers, a traditional definition of heat exchanger
effectiveness may not be applied.
Consequently, pinch-point temperatures were used to predict the
heat exchanger outlet
temperatures. For the internal heat exchanger, however, the weak
solution and rich
-
30
solution streams remain in the liquid phase, and the traditional
heat exchanger
effectiveness definition is used.
With reference to Figure 3-3, the following steps were followed
to obtain the
requisite thermodynamic properties at each state point:
State point 6 is set by assuming a saturated liquid mixture at
the desorber outlet
(quality of zero), desorber outlet temperature, and a weak
solution concentration at
the desorber outlet. Since state points 6 and 1 are in
equilibrium in the two-phase
region, providing a temperature and the weak solution
concentration leaving the
desorber fixes the state. The vapor concentration is returned as
part of the outputs.
Note that a pinch-point is set between the heat source inlet
temperature and
maximum working fluid temperature:
1,6 1,6 source pinch source pinchT T T T T T= + = ( 3-17 )
Initially, this pinch-point temperature is set to 10 K.
State point 1 is set by assuming equilibrium with state point 6.
Given the two-
component two-phase condition that exists at the desorber, only
two intensive
properties need to be given to fix state point 1. These may be
the same temperature
and pressure as state point 6. The vapor concentration is
returned by assuming it to
be a saturated vapor in equilibrium with the saturated liquid
weak solution.
State point 3 is set by initially assuming a saturated liquid
mixture at the absorber
outlet, absorber outlet temperature, and a rich solution
concentration. This gives the
saturation pressure as one of the outputs. Using the saturation
pressure, the saturated
condition may be relaxed, and the state point can be adjusted to
incorporate some
subcooling at the same saturation pressure. Once again, a
pinch-point temperature is
-
31
applied between the heat sink inlet temperature and minimum
working fluid
temperature.
3, sin 3 sin sat k pinch sub k pinchT T T T T T T= += + + ( 3-18
)
Initially, the pinch-point and subcooling temperatures are set
to 5 K each.
State point 4 is set by assuming the same high side pressure
returned by state point 6,
the rich solution concentration as stated above, and the
definition of isentropic
efficiency given by equation ( 3-13 ).
State point 7 is set by assuming a saturated liquid mixture at
the internal heat
exchanger outlet, weak solution concentration as given by state
point 6, and the same
high side pressure given by state point 6.
State point 5 may be calculated by using the high side pressure
given by state point 6,
rich solution concentration calculated by the mass balance, and
the enthalpy given by
the internal heat exchanger energy balance in equation (7). Note
that an internal heat
exchanger effectiveness is defined based on fluid
enthalpies:
( )
( ), ,
max , , min
h h i h o
h i c i
h hQQ h h
m
m
= =
( 3-19 )
Initially, the heat exchanger effectiveness is set to 0.95.
State point 8 may be fixed by assuming the same enthalpy as
state point 7, weak
solution concentration as given by state point 6, and the same
pressure low side
pressure given by state point 3.
-
32
State point 2 is set by assuming the low side pressure set by
state point 3, the
concentration and the entropy given by state point 1, and the
definition of isentropic
efficiency given by equation ( 3-11 ).
By combining the above steps to calculate the thermodynamic
properties with the cycle
mass and energy balance equations, the properties at each state
point as well as an overall
solution to the cycle model is achieved.
3.4 Organic Rankine Cycle with Solution Circuit Model
Results
This section presents some of the key results from the
thermodynamic cycle
model. Table 3-1 summarizes some of the key assumptions
mentioned above. Unless
otherwise stated, these assumptions were applied when generating
the results described in
this section.
Table 3-1: Key assumptions used in the thermodynamic model.
Description Value
Condenser, absorber outlet subcooling 1. 5 C Temperature
difference between heat sink and condenser/absorber outlet
2. 5 C
Heat sink temperature 3. 20 C Temperature difference between
heat source and evaporator/desorber outlet
4. 10 C
Regenerator/internal heat exchanger effectiveness 5. 0.95 Pump
isentropic efficiency 6. 0.6 Expander isentropic efficiency 7. 0.8
Negligible pressure drop in lines, separators, and heat exchangers
8. Negligible heat loss in lines, mixer, separator, pumps, and
expander 9. Complete separation of liquid and gas phases 10.
Figure 3-7 shows that for a fixed source temperature, the ORCSC
has an ideal
concentration pairing which maximizes the efficiency. This means
that for a chosen rich
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33
solution concentration, there exists an optimal weak solution
concentration for which the
cycle performs the best. This is further illustrated in Figure
3-8. Furthermore, as expected,
the trend shows that higher rich solution concentrations lead to
higher efficiencies.
However, there are other tradeoffs such as high working
pressures that may constrain the
choice of concentration pairings.
Figure 3-7: Impact of ORCSC concentration pairings on efficiency
for a source temperature of 100C and a sink temperature of 20C.
Figure 3-8 clearly shows that there exists an optimal
Circulation Ratio for which
the cycle performs the best. Based on equation ( 3-6 ), it is
clear the Circulation Ratio is
analogous to the concentration pairing, and therefore confirms
the results shown in
Figure 3-7. The Circulation Ratio, however, is an important
physical parameter that is
essential to the control of an ORCSC system. It fixes the
relative mass flow rates of the
rich solution and vapor, and therefore fixes the relative speeds
of the pump and expander
in the system. By extension, it fixes the concentration pairing
of the system. Therefore
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34
the term Circulation Ratio is used in this text as opposed to
concentration pairing,
particularly when discussing the physical ORCSC system and the
experimental study.
Figure 3-8: Variation of overall Second Law Efficiency as a
function of Circulation Ratio.
Figure 3-9 illustrates the effect of rich solution concentration
on overall cycle
Second Law Efficiency for a Carbon Dioxide / Acetone working
pair. Note that the
chosen points have been optimized with respect to weak solution
concentration using
Engineering Equation Solver (EES) (Klein, 2012). From the
results shown in Figure 3-7,
and from a review of absorption studies in the literature, an
expected trend would show
that higher rich solution concentrations lead to higher the
efficiencies. The trend in Figure
3-9 matches this expected outcome for high concentration values.
Note that a peak value
may not occur in the high concentration region because the
two-phase concentration
range shrinks as the mixture critical point is approached. This
means that at extremely
high concentrations; it may not be possible to operate a
solution circuit. Furthermore, an
interesting overall result exists in which the peak efficiency
is achieved at extremely low
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35
concentration values. This means that a large fraction of the
absorbent, in this case
Acetone, participates in the expansion process. One reason for
this phenomenon, shown
in Figure 3-10, is that at extremely low concentrations the
absorbent, Acetone, is a better
working fluid than the absorbate, Carbon Dioxide as pure fluid.
Therefore, at extremely
low concentrations, the highest efficiencies are achieved
because the component with
better thermodynamic properties dominates the mixture, while the
overall cycle
simultaneously takes advantage of the internal regeneration
intrinsic to the solution
circuit. Achieving this optimal efficiency in the
low-concentration region, however, is a
practical challenge. Extremely tight tolerances in solution
concentrations are required to
realize these benefits. Nevertheless, the peak efficiencies that
occur at extremely low
concentrations have not been investigated in the literature, and
merits further
investigation in the future.
Figure 3-9: Impact of rich solution concentration on efficiency
for various source temperatures. Plot is optimized for weak
solution concentration.
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36
Figure 3-10: Second Law efficiency as a function of source
temperature for a basic ORC.
Figure 3-11: Second Law efficiency as a function of source
temperature for an ORC with internal regeneration at the expander
outlet.
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37
Figure 3-12: Second Law efficiency as a function of source
temperature for the ORCSC.
Figure 3-10 and Figure 3-11 compare the optimized performance of
various
working fluids for a basic ORC and an ORC with internal
regeneration, respectively,
using the parameters listed in Table 3-1. Figure 3-11 shows that
the addition of a
regenerator results in better performance for dry working
fluids, such as R245fa and
pentane, at high temperatures because the availability in the
expander exhaust stream is
not wasted. However, wet fluids like water and ammonia show no
improvement because
the expander exhaust temperature is not significantly higher
than the pump discharge
temperature.
Figure 3-12 shows the optimum performance of an ORCSC with
Ammonia /
Water and CO2 / Acetone working fluid pairs at two different
concentration ranges: at
extremely low absorbate concentrations (less than 1% by mass),
in which case a large
fraction of saturated water vapor or Acetone vapor participates
in the expansion process;
and at high concentrations (above 50% by mass), where only small
amounts of saturated
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38
Water vapor or Acetone vapor participates in the expansion
process. However, at a
200 C source temperature for the CO2 / Acetone working pair, it
was not possible to
operate at rich solution concentrations above 10% because the
two-phase concentration
range shrinks as the mixture critical point is approached. In
this case, the highest possible
concentration of 10% was used.
Note that in addition to the assumptions shown in Table 3-1,
there were no
restrictions on vapor quality at the expander exhaust, expander
pressure ratios,
Circulation Ratios, amount of charge required in the system for
a given capacity, or
specific volume of the working fluids at the expander discharge.
Therefore, the results
presented in Figure 3-10, Figure 3-11 and Figure 3-12 are highly
idealized and only
represent what is possible in the thermodynamic design space.
For example, Water
requires a pressure ratio of 296 for optimum efficiency at 200C.
It also has a specific
volume at the expander discharge of nearly 50 m3/kg at the same
design point. Designing
an expansion machine with multiple stages to accommodate the
high pressure ratios,
along with the cost of large components to accommodate the low
density renders Water
an impractical working fluid. Several of these practical
concerns are mitigated in the
ORCSC system.
The ORCSCs with high concentrations of ammonia or CO2 are
generally less
efficient than traditional ORCs using pure ammonia or CO2
respectively. In these cases
the temperature glide is detrimental to the Second Law
efficiency because it results in
higher irreversibilities against the assumed constant
temperature heat source. A real heat
source fluid will begin to cool as it heats the cycle working
fluid. This could severely
limit the maximum evaporating temperature of a traditional ORC
as the heat source
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39
stream reaches a pinch point against the liquid to two-phase
transition of the working
fluid. In contrast, the ORCSC may be able to reach higher
average working fluid
temperatures by being better able to match the temperature
profile of the heat source
stream with its two-phase temperature glide. A similar argument
can be made between
the working fluid and the heat sink fluid. Exceptions occur for
ammonia-water above
source temperatures of 160 C and for CO2-acetone at 200 C, where
the CO2
concentration is relatively low. The ORCSCs with low
concentrations of ammonia and
CO2 do not perform as well as traditional ORCs with pure water
and pure acetone
respectively (Woodland et al. 2012).
Figure 3-13 shows the desorber capacity along with the pump
power input as a
function of the Circulation Ratio for a fixed rich solution
concentration. Note that the
desorber capacity and pump power input have been normalized for
a 1 kW turbine design.
As the Circulation Ratio increases, the amount of CO2 in the
weak solution is increased
and the pump input power increases. More important, however, is
the fact that the
desorber capacity decreases as the Circulation Ratio is
increased. This illustrates a
solution for capacity control in this system during non-peak
loads, the Circulation Ratio
may be increased either by a concentration adjustment or, to
lesser extent, by varying the
relative speeds of the pump and expander to accommodate a
smaller heat input at the
source (Krishna et al. 2011).
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40
Figure 3-13: Variation of component capacities as a function of
Circulation Ratio.
Figure 3-14 indicates that the system pressures increase
considerably as the
Circulation Ratio is increased. Therefore, with reference to
Figure 3-8, it is clear that
there is a tradeoff between the efficiency and the operating
pressures seen in the system.
With reference to Figure 3-13, it can also be deduced that there
is a relationship between
capacity control and the system pressures. As the capacity is
lowered by increasing the
Circulation Ratio, the system sees higher pressures. Figure 3-15
shows the linear
variation of the Pressure Ratio with the Circulation Ratio. This
is an important design
consideration, particularly with regard to the expansion
machine. Depending on the
desired capacity range of the system, it would be advisable to
design and optimize the
expander for the corresponding Pressure Ratio.
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41
Figure 3-14: Variation of High-side system Pressure as a
function of Circulation Ratio.
Figure 3-15: Variation of Pressure Ratio as a function of
Circulation Ratio.
Based on the results shown in Figure 3-10 and Figure 3-12, it
may be tempting to
conclude that the ORCSC does not offer sufficient benefits, and
a basic ORC with the
best performing working fluid would be the ideal choice due to a
combination of
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42
simplicity and performance. However, it is important to note
that several practical
considerations should be weighed together with the thermodynamic
results presented
above. For example, the optimum efficiency for a basic ORC with
water as the working
fluid and a source temperature of 200 C is significantly higher
than the theoretical
efficiencies of the ORCSC. However, the use of water requires a
low vapor quality and
low density at the expander exhaust, vacuum pressure
condensation, and extremely high
expander pressure ratios. High pressure ratios require multiple
expansion stages. The sub-
atmospheric pressure makes air leakage into the system a
challenge. The low working
fluid density is a capacity concern, requiring large diameter
piping and a large expander
to achieve a capacity comparable to denser working fluids.
Therefore, despite the
promising efficiency of water as a working fluid for the source
temperatures considered,
the practical issues associated with its use may be
prohibitive.
The hydrocarbons acetone and pentane are very efficient, but
they are highly
flammable and pose challenges for sealing materials. This leads
to the widely accepted
view that R245fa is perhaps the best working fluid in an ORC.
However, the ORCSC
offers some potential practical advantages over an ORC with
regeneration using R245fa
as the working fluid that may outweigh the added complexity of
the system. The ORCSC
using ammonia-water as the working fluid at high concentrations
may have marginally
lower efficiencies than a R245fa ORC with regeneration, but the
use of a zeotropic
mixture in the ORCSC provides the ability to use the temperature
glide to match the
temperature profiles of the source and sink fluids. As shown in
Figure 3-13, the zeotropic
mixture also allows for capacity control simply by changing the
concentration of the
working fluid mixture. This may lead to higher overall system
efficiencies when coupled
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43
with sources that have varying heat input temperatures or loads,
such as waste heat
streams from diesel engines, power plants or other industrial
processes. The use of a
Carbon Dioxide / Acetone working pair is difficult to justify
from a performance
standpoint; its main advantage lies in the fact that aside from
CO2 being an inexpensive,
natural, non-flammable refrigerant, its high volumetric heat
capacity allows for the use of
smaller components which may lead to significant weight savings
in mobile applications.
The ORCSC is not without its challenges. The highest
efficiencies for the ORCSC
using Ammonia-Water require significantly low vapor quality in
the expander exhaust.
This is because the desorber outlet state point is modeled as a
saturated state, with liquid
and vapor existing at the same temperature and pressure (with
differing concentrations).
Therefore, since the vapor is at a saturated condition at the
expander inlet, the expansion
process has a tendency to generate significant quality at the
outlet condition. This is not
an issue with the Carbon Dioxide / Acetone working pair because
both Carbon Dioxide
and Acetone are dry working fluids. Therefore, the shape of the
vapor dome dictates that
the expander outlet condition will not fall into the two-phase
region. Control related
issues, which become significantly more complex with the ORCSC
compared to the
traditional ORC, have not been investigated in detail in the
literature, and require
rigorous examination.
Thus, a truly optimal choice of ORC and working fluid may be
highly
application-specific. Only two working fluid pairs were studied
out of a broad range of
possible binary mixtures. More binary mixture data is needed to
study the wide range of
working fluid combinations that may be possible with the ORCSC.
Appropriate system
selection, therefore, requires a much more thorough
investigation of the tradeoffs
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44
between efficiency, ability to match the heat source temperature
profile, cost of
implementation, and size constraints. Investigating these
tradeoffs, however, requires
experimental study. In this regard, an ORCSC experimental test
stand was constructed in
order to provide insight into the feasibility of the technology,
and further develop the
results of this study.
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45
CHAPTER 4. DESIGN OF EXPERIMENTAL TEST SYSTEM
An experimental test setup (breadboard system) was constructed
to serve as a
proof of concept for ORCSC technology. The system was fabricated
largely using off-
the-shelf parts harvested from the Liquid-Flooded Ericsson
Cooler experimental test
setup (Hugenroth 2006) at the Herrick Laboratories. Since the
breadboard system was
constructed before the computer modeling was complete, several
estimates pertaining to
system design were necessary. The timing for the design and
construction of the system
were largely dictated by needs of the project sponsor. In
addition to proof of concept
testing, the breadboard system was intended to validate the
results of the thermodynamic
cycle model, and to gain design-related experience.
4.1 System Sizing
The experimental breadboard system was designed for a nominal 1
kW power
output. Table 4-1 shows the key input parameters used in the
simulation model. The
values reflect initial expected performance of the equipment,
and were used as a basis for
system design and component selection.
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46
Table 4-1: Sample set of input parameters used as a basis for
system design. Symbol Value Description Unit
CR 5 Circulation Ratio [-] , 0.7 Isentropic turbine efficiency
[-] 0.5 Mechanical pump efficiency [-] 80 Temperature level of
heat-sink [ C] 20 Temperature level of heat-source [ C] 5 Pinch
Point temperature [ C] 0.21 Weak Solution Mass Concentration [-]
0.04 CO2 vapor mass flow rate [kg/s] 1.288 Heat Capacity ratio of
the working fluid [-]
Based on the data in Table 4-1, the conditions at each state
point in the cycle were
calculated as shown in Table 4-2. Note that these initial
calculations were performed
using the LKP EOS and contain significant sources of error as
described in Section 3.3.
However, these were used as the initial design basis and are
presented here to illustrate
the parameters taken into account when constructing the
experimental bread board
system.
Table 4-2: Sample property values at each state point in the
ORCSC cycle using the LKP EOS (refer to Figure 3-3).
State point T [ C] p [bar] h [kJ/kg] s [kJ/kg/K] [kg/m3]
1 75.00 29.85 579.0 2.4 49.7 2s 49.41 21.68 560.2 2.4 39.0 2
41.57 21.68 552.