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INTERNATIONAL JOURNAL OF ENERGY RESEARCH
Int. J. Energy Res. 2012; 36:871
885
Published online 9 March 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/er.1839
–
Thermodynamic analysis and optimization of power
cycles using a
temperature heat source
Mohammed Khennich and Nicolas Galanis
*
,
†
nite low
‐
Faculté de génie, Université de Sherbrooke, Sherbrooke, QC, Canada J1K 2R1
SUMMARY
The analysis of a subcritical Rankine cycle with superheating, operating between a constant
owrate low-
temperature heat source and a
nite size
thermodynamics, is presented. The results show the existence of two optimum evaporation pressures: one
minimizes the total thermal conductance of the two heat exchangers, whereas the other maximizes the net power
output. A comparison of such results for
xed temperature sink, according to the principles of classical and
ve working
uids leads to the selection of R141b for a system generating
10% of a reference power which depends on the speci
ed source and sink characteristics; for the conditions under
consideration this reference power is 6861kW. The results for this particular system show that the minimum total
thermal conductance of the two heat exchangers is 1581kWK
−
1
;
the corresponding thermal ef
ciency is 12.6%
and the total exergy losses are 13.8% of the source
s exergy. Slightly more than 50% of the exergy destruction
occurs in the vapor generator. Copyright © 2011 John Wiley & Sons, Ltd.
’
KEY WORDS
waste heat; energy analysis; exergy analysis; heat exchanger conductance; turbine size parameter; Rankine cycle
Correspondence
*
Nicolas Galanis, Faculté de génie, Université de Sherbrooke, Sherbrooke, QC, Canada J1K 2R1.
†
E-mail: Nicolas.Galanis@USherbrooke.ca
Received 21 October 2010; Revised 11 January 2011; Accepted 23 January 2011
1. INTRODUCTION
thermal energy in combustion gases. Traditional exam-
ples of such applications are the heating of the combus-
tion air supplied to the boilers of steam plants by the ue
gases and the cogeneration installations using the exhaust
gases of a gas turbine plant to produce steam for
industrial processes or for electricity generation.
The energy of thermal engine exhaust gases is not
the only source of low (80
–
150°C) or intermediate
(up to 350°C) temperature heat. Such thermal energy
abounds in nature (geothermal and solar energy) and is
also available as waste heat from industry (pulp and
paper, aluminum production, etc.). The potential
contribution of these sources to our energy needs is
important. An MIT report [1] estimated that it would
be possible to develop 100GW of generating capacity
from geothermal sources in the United States by in-
vesting 1 billion dollars over a period of 15 years.
Another study [2], which analyzed manufacturing
processes within the eight largest Canadian manu-
facturing sectors accounting for approximately 2/3 of
the total energy used by Canadian industries, indicates
that approximately 70% of the input energy is released
to the environment as waste heat. The use of these
energy sources would reduce the dependence on
imported ones and could have a benecial environmental
The availability of abundant quantities of energy is an
essential condition for the well being and development
of our modern industrial societies. As the population
and economic activity increase, the global consump-
tion of energy rises continuously. The principal
primary energy sources that are used to satisfy this
ever
‐
increasing demand in all the economic sectors are
fossil fuels. Although available in large quantities, they
are neither innite nor renewable. Furthermore, the
conversion of their chemical energy into useful work
by combustion and thermal engines, which is almost
the only method used for their exploitation, is subject
to the fundamental laws of thermodynamics which
severely limit the efciency of such systems and results
in undesirable side effects, such as greenhouse gases
(GHGs), urban smog, thermal pollution and acidica-
tion of lakes and rivers. It is therefore imperative
to seek and adopt alternate renewable energy sources
as well as methods, which improve the conversion
efciency and diminish the negative impacts of fossil
‐
fuelled engines. One way of increasing the performance
and decreasing the environmental impact of stationary
thermal engines is by recuperating and utilizing low
‐
grade
871
Copyright © 2011 John Wiley & Sons, Ltd.
M. Khennich and N. Galanis
Thermodynamic analysis and optimization of power cycles
effect. Thus, the theoretical GHG reduction that can be
achieved by recovering the above
‐
mentioned waste heat
from the eight largest Canadian manufacturing sectors is
2.5 times the target of 45Mt of GHG suggested by the
Kyoto protocol.
The methods that can be used to convert this thermal
energy into mechanical energy and electricity include
thermodynamic cycles using organic uids (ORC),
mixtures of pure uids (NH
3
/H
2
O) and uids with very
low critical temperatures (CO
2
). Some power
‐
generating
plants using such uids have been built [3] but in most
cases the published literature consists of semi
‐
analytical
or numerical studies. A 2006 analysis of solar trough
ORC electricity generating systems (available at
concluded that
such plants with 1
–
10MW capacity would be economi-
cally attractive for isolated communities in Africa and the
Middle East. Grid connected customers in the US
with large loads concerned about reliability and paying
high prices for peak electricity are also potential custo-
mers for such systems. Liu et al. [4] analyzed the effect
of working uids (wet: water, ethanol; dry: HFE7100,
n
‐
results show the existence of an optimum evaporation
pressure for each of the four steps. They also indicate
that an increase of the net power output decreases the
exergetic efciency and increases the heat exchangers
’
surface. On the other hand, Cayer et al. [8] analyzed
the performance of a transcritical CO
2
cycle with
specied heat source temperature (100°C) and mass
owrate as well as heat sink temperature (10°C). They
used six performance indicators (thermal efciency,
specic net output, exergetic efciency, total UA and
surface of the heat exchangers as well as the relative
cost of the system) and three independent parameters
(maximum temperature and pressure of the cycle as
well as the net power output). Their results show that it
is impossible to simultaneously optimize all six per-
formance indicators. They nally optimized the cycle
parameters by minimizing the acquisition cost of major
components per unit output
($kW
−
1
) and compared
such optimum cycles for
three working
uids (CO
2
,
ethane, R125).
Recently, Lakew and Bolland [9] analyzed the per-
formance of the following working uids: R134a,
R123, R227ea, R245fa, R290 and n
‐
pentane. Their
evaluation is based on power production capability
and equipment size requirements. They used a sub-
critical Rankine cycle without superheating, specied
the heat source temperature in the range of 80
–
200°C
and used the evaporator pressure as independent
parameter. The performance parameters examined are
power output, exergetic efciency, heat exchanger area
and turbine size factor. The results of this study show
that the selection of working uids depends on the type
of heat source, the temperature level and the design
objective. The latter can be either the maximum power
output or the smallest component size (heat exchanger
or turbine). It was shown that maximum power
is obtained for an optimal evaporator pressure.
Furthermore, a working uid may have the smallest
turbine size factor but require a large heat exchanger
area. The authors concluded that an economic study is
necessary to determine which working uid is the most
appropriate.
Mago et al. [10] calculated the exergy destroyed in
an ORC using R113. They established that most of the
exergy destruction occurs in the evaporator. They also
showed that the total exergy destruction decreases with
increasing evaporator pressure and with decreasing
difference between the temperatures of the heat source
and the working uid in the evaporator. Guo et al. [11]
presented a comparative analysis of natural and
conventional working uids for use in transcritical
Rankine cycles using a low
‐
temperature (80
–
120°C)
geothermal source. Their results show that R125 gives
the best thermodynamic and techno
‐
economic perfor-
mance. For source temperatures above 100°C, R32 and
R134a also show better performances than CO
2
, which
was used as a base line. Chen et al. [12] presented a
review of the organic and supercritical Rankine cycles
pentane and isentropic: R11, R123,
benzene) on the performance of ORCs and reported
that the thermal efciency of such cycles is a weak
function of the critical temperature. They also indicated
that using a constant heat source temperature can
result in considerable design differences with respect to
the actual variable temperature of nite heat sources
such as geothermal or waste streams. Madhawa
Hettiarachchi et al. [5] used the ratio of the total heat
exchanger area to the net power output as the criterion
for the ORC design and evaluated the optimum cycle by
varying the evaporation and condensation temperatures
as well as the velocities of the geothermal source and the
cooling water. They compared the optimum cycle per-
formances for four working uids by xing the gross
power output of the cycle and found that ammonia
minimizes the chosen design criterion but its corres-
ponding rst and second law efciencies are lower than
those obtained with HCFC 123 and n
‐
pentane. These
two studies do not consider superheating of the working
uid. On the other hand, Saleh et al. [6] performed
a thermodynamic analysis of 31 pure working uids
for ORCs with and without superheating, operating
between 100 and 30°C. They found that the highest
thermal efciencies are obtained with dry uids in
subcritical cycles with regenerator. They also performed
a pinch analysis for the heat transfer between the source
and the working uid and reported that the largest
amount of heat can be transferred to a super
‐
critical
pentane,
iso
‐
uid.
Similarly, Roy et al. [7] analyzed the performance of
a Rankine cycle with superheating using a mixture of
ammonia and water for
uid and the least to a high
‐
boiling subcritical
xed source and sink temper-
atures. Their methodology includes four steps: energy
and exergy analyses,
nite size thermodynamics and
calculation of
the heat exchangers
’
surfaces. Their
872
Int. J. Energy Res. 2012; 36:871
–
885 © 2011 John Wiley & Sons, Ltd.
DOI: 10.1002/er
Thermodynamic analysis and optimization of power cycles
M. Khennich and N. Galanis
for the conversion of low
‐
grade heat as well as selec-
tion criteria for working uids. Types of working
uids, the inuence of latent heat, density, specic heat
and other thermodynamic properties (at the critical
and freezing points) as well as the effectiveness of super-
heating, the stability, safety and environmental impact
were discussed. They considered 35 potential working
uids and grouped them based on the values of their
critical temperature and the inverse of the slope of
the saturation vapor curve on the T
−
s diagram. They
concluded that there is no uid that meets all the criteria
for heat sources with different temperatures.
Despite these and other analogous studies, the thermo-
dynamic analysis of power cycles using low
‐
temperature
heat sources with a specied mass owrate (such as
industrial waste heat) and a heat sink of xed inlet tem-
perature is not complete. In the present paper, we illus-
trate certain properties of such cycles with both saturated
and superheated conditions at the turbine inlet through a
case study using ve working uids (R134a, R123,
R141b, ammonia and water). Their potential for power
production in a speci
evaporator. Turbine and pump efciency is 0.80, which
is assumed to be the same for all considered working
uids. The temperature at the turbine inlet and the
condensation temperature are varied by changing the
value of the temperature difference DT. The tempera-
ture
–
entropy diagram of the system used to recover
energy from the low
‐
temperature gas stream is shown in
Figure 2, which illustrates a case with superheated uid
at the turbine exit. It should be noted however that for
some working uids and high values of the evaporating
pressure state 2 can be in the two
‐
phase region.
The basic equations used to model the cycle express
mass and energy balances for each component. The
assumptions are the following:
•
Each component is considered as an open system
in steady
‐
state operation;
c range of evaporation pressure is
evaluated. Speci
cally, we show that for these conditions
the acceptable range of evaporation pressures has upper
and lower bounds, which approach each other as the net
power output of the cycle increases. As a result, the net
power output of the cycle cannot exceed an upper limit
W
n
;
max
. It is also shown that for each possible value
of the net power output there exists an optimum value
of the evaporation pressure, which minimizes the total
thermal conductance of the two heat exchangers.
Furthermore, the turbine size factor and the effect of the
temperature difference DT on the volume ow ratio
at the turbine inlet and outlet are determined for the
conditions minimizing the total thermal conductance
UA
t
. Finally, an exergy analysis of the optimum cycle
identies the major irreversibility sources.
Figure 1. Schematic diagram of system under consideration.
2. SYSTEM DESCRIPTION
AND MODEL
Figure 1 illustrates the schematic diagram of a basic
system (ORC,
critical cycle or system using a
mixture of uids) used to recover energy from a low
‐
temperature gas stream. It is similar to the superheated
Rankine cycle. The heat source is an industrial waste
gas idealized as air at a temperature of T
s,in
= 100°C
with a volumetric owrate of 1.2millionm
3
h
−
1
(for
atmospheric pressure and 100°C the corresponding
mass owrate is M
s
¼
314
:
5kgs
1
). The cooling uid
in the condenser is water at T
p,in
= 10°C (the annual
average temperature of the water of the St. Lawrence
river). The working uid receives heat at a relatively
high pressure in the evaporator, expands in a turbine,
thereby producing useful work, and rejects heat at a low
pressure in the condenser.
trans
‐
It
is then pumped to the
Figure 2. Temperature
–
entropy diagram.
873
Int. J. Energy Res. 2012; 36:871
–
885 © 2011 John Wiley & Sons, Ltd.
DOI: 10.1002/er
M. Khennich and N. Galanis
Thermodynamic analysis and optimization of power cycles
•
The kinetic and potential energies as well as the
friction and heat losses are neglected;
•
At the exit from the condenser the working uid is
saturated liquid;
depend on those of
the two independent parameters
P
ev
and DT.
For the exergy analysis of the system, the mass
owrate of the working uid in the cycle is required.
The latter is calculated by xing the net power output
W
n
of the system or, more specically, its non
‐
dimensional value
α
which is obtained by dividing
•
The pinch for the condenser, equal to (T
g
–
T
p,pr
)
when state 2 is superheated vapor and to
(T
2
–
T
p,out
)whenitisatwo
‐
phase mixture, is set
equal to DT/2 while that for the evaporator,
DT
5*
=(T
s,sc
–
T
5*
), is required to be greater than,
or equal, to DT/2;
W
n
by the following reference quantity:
W
ref
¼
M
s
Cp
s
T
s
;
in
T
p
;
in
1
T
p
;
in
=
T
s
;
in
(9)
•
The specic heat of
the source and sink is
W
ref
is evaluated by considering a Carnot process
operating between the inlet temperatures of the heat
source and sink. With the adopted conditions, the
value of this reference quantity is 6861kW. The pro-
duct of the mass owrate, the specic heat and the
temperature difference is higher than the actual heat
extracted from the heat source, whereas the Carnot
efciency is higher than that of the actual cycle using
the specied heat source and sink. Therefore, the
values of
α
will be considerably lower than one. From
the previous energy analysis, which determines the
specic net power output, the mass owrate of the
working uid is calculated for a given value of
α
:
m
¼ a
W
ref
assumed to be constant;
•
The specic volume of the working uid remains
constant during pumping;
•
Finally, the liquid content at the exit of the
turbine is required to be less than 5% to limit the
effect of liquid droplets on the turbine blades.
Since the quantities M
s
, T
s,in
, T
p,in
,
η
T
and
η
P
are
xed, the choice of a value for DT determines state 4
and T
1
. Under these conditions the evaporation pres-
sure can vary but its value is constrained by the im-
posed restrictions on the quality at the exit from the
turbine and the evaporator pinch. For any value of this
pressure that satises these two requirements the entire
cycle is xed and its performance can be calculated
using the following equations taking into consideration
the assumptions already presented:
=
w
n
(10)
The mass owrate of the working uid is therefore
proportional to
α
(or, equivalently, to the net power
output) and inversely proportional to w
n
which, as
established earlier, is a function of P
ev
and DT. Thus
m =
α
f(P
ev
,DT).
The mass owrate of the cooling water is obtained
from the energy balance for the phase change in the
condenser:
Q
4g
¼
_
mh
g
h
4
•
For the pump:
η
P
¼
n
4
ð
P
ev
P
C
Þ
_
(1)
h
5
h
4
w
P
¼
h
5
h
4
ð
Þ
(2)
¼
M
p
Cp
p
T
p
;
pr
T
p
;
in
(11)
•
For the turbine:
The thermal conductance UA
4g
for this part of the
condenser can then be obtained using the corres-
ponding logarithmic difference:
Q
4g
¼
UA4
g
Δ
T
ln
;
4g
(12)
An analogous approach is applied to the desuper-
heating part of the condenser and results in the
determination of T
p,out
and UA
2g
. When state 2 is a
two
‐
phase mixture the temperature difference
(T
2
–
T
p,out
) is set equal to DT/2. The mass owrate
of the cooling water and the thermal conductance of
the condenser are obtained from the corresponding
energy balance and logarithmic temperature difference
(equations similar to Equation (11) and (12)). Similarly,
the three unknown temperatures (T
s,pr
, T
s,sc
, T
s,out
)and
the corresponding thermal conductances for
h
1
h
ð Þ
h
1
h
2
;
is
η
T
¼
(3)
w
T
¼
h
1
h
2
ð
Þ
(4)
•
For the evaporator:
q
ev
¼
h
1
h
5
ð
Þ
(5)
•
For the condenser:
q
C
¼
h
2
h
4
ð
Þ
(6)
•
The specic net power output is:
w
n
¼
w
T
w
P
(7)
the three
•
The thermal ef
ciency of the cycle is:
parts of
the vapor generator
(UA
11*
,UA
1*5
,UA
5*
5)
can
be
determined
from equations
similar
to
w
n
q
ev
η
th
¼
(8)
Equations (11) and (12).
Since the potential and kinetic energies have been
neglected, the exergy of the working and external uids
at any state can be calculated from:
e
¼
h
h
0
According to the arguments in the paragraph pre-
ceding Equation (1), the thermodynamic properties of
the working uid as well as the values of w
n
and
η
th
ð
Þ
T
0
s
s
0
ð
Þ
(13)
874
Int. J. Energy Res. 2012; 36:871
–
885 © 2011 John Wiley & Sons, Ltd.
DOI: 10.1002/er
 Thermodynamic analysis and optimization of power cycles
M. Khennich and N. Galanis
3. WORKING FLUIDS
The dead state, indicated by the subscript 0, is at
atmospheric pressure and the xed temperature
T
p,in
= 10°C of the water entering the condenser. The
exergy destruction rate in any of the system
’
s compo-
nents is then calculated from the following exergy
balance equation:
E
d
¼
X
in
The choice of the working uids was based on their
thermodynamic characteristics and their environmen-
tally benign nature. Working uids for systems with
low or intermediate temperature sources must satisfy
several safety, environmental, performance and eco-
nomic criteria [12]. Among the safety aspects, amm-
ability, toxicity and auto
‐
ignition are particularly
important. Environmental criteria include the ozone
depletion potential
Þ
X
out
Þ
W
ð
m
in
e
in
ð
m
out
e
out
(14)
The total exergy destruction E
d
;
t
, i.e. the summation
of the exergy destruction by all its components, is non
‐
dimensionalized by dividing it by the exergy of the heat
source:
(ODP) and the global warming
potential (GWP).
Based on these considerations, the following working
uids R134a, R123, R141b, ammonia and water are
used in the present study. Their thermophysical, safety
and environmental properties are compared and pre-
sented in Table I. It should be noted that R123 and
R141b will be phased out by 2030 due to their non
‐
zero
ODP [12]. From a safety point of view water and R134a
are the best, while ammonia is the worst. From an
environmental point of view ammonia and water are the
best. Water has been included in the present study for
the purpose of comparison although it is known that it
is not a good working uid for low
‐
temperature systems
such as the one under consideration.
b ¼
E
d
;
t
=
M
s
e
s
;
in
Þ
(15)
A small value of
β
is an indication that the system
approaches thermodynamic perfection.
The preliminary design of the turbine can be obtained
following a study by Macchi and Perdichizzi [13] by
calculating the turbine size parameter SP, which accounts
for the actual turbine dimensions, and the turbine isen-
tropic volume ow ratio V
RT,is
, which accounts for
compressibility effects during the expansion:
0
:
5
0
:
25
SP
¼
V
T
;
2is
= ð
1000
Δ
h
is
Þ
(16)
V
RT
;
is
¼
V
T
;
2is
=
V
T
;
1
(17)
The study by Macchi and Perdichizzi [13] states that
the results obtained by optimizing a particular turbine
can be used for other turbines with the same specic
speed, provided they have the same SP and V
RT,is
parameters.
Based on the previously presented relations between
the dependent variables (P
C
, thermodynamic proper-
ties of the working uid, w
n
, m) and the independent
parameters (
α
, P
ev
, DT) it follows that for the condi-
tions under consideration all the UAs, the mass ow
rate of the sink,
β
and SP are functions of the same
three independent variables which can take different
values compatible with the previously specied con-
straints on x
2
and DT.
The numerical model of the system was solved using
the EES code [14], which includes thermodynamic
properties for a large number of natural and manu-
factured uids. The present model and calculation pro-
cedure were successfully validated by comparing their
results with those published by Liu et al. [4] and by
Madhawa Hettiarachchi et al. [5] (see the Appendix).
4. RESULTS AND DISCUSSION
The results presented here have been calculated for the
ve previously mentioned working uids with T
s,in
=
100°C, M
s
¼
314
:
5kgs
1
, T
p,in
= 10°C. The range of
values for the temperature difference DT is 5
–
15°C.
The efciency of the turbine and pump is xed at 0.80.
4.1. Effect of the evaporation pressure
and DT
Figure 3 shows the effect of the evaporator pressure on
x
2
(when x
2
<
1 this ratio is the quality of the working
uid at the exit of the turbine) and on the temperature
pinch in the evaporator (DT) for R134a,
α
= 0.05 (or
equivalently W
n
¼
343
:
1kW ) and DT = 5°C. When
P
ev
is low the working uid at state 2 is superheated
vapor (this is indicated by x
2
>
1). As P
ev
increases
state 2 approaches the saturation curve and eventually
the uid at 2 becomes a mixture of vapor and liquid; its
Table I. Thermophysical, environmental and safety characteristics of working
uids.
Molecular weight
(kgk
−
1
mol
−
1
)
ASHRAE 34
safety group
GWP
(100 year)
Fluid
Formula
NBP (°C)
T
cr
(°C)
P
cr
(MPa)
ODP
Nature
R134a
CH
2
FCF
3
102.03
−
26.1
101.03
4.06
A1
0
1300
Isentropic
R123
CHCl
2
CF
3
152.93
27.8
183.68
3.67
B1
0.012
120
Isentropic
R141b
CH
3
CCl
2
F
116.95
32.0
204.20
4.25
A2
0.086
700
Isentropic
Ammonia
NH
3
17.03
−
33.3
132.25
11.33
B2
0
<
1
Wet
Water
H
2
O
18.02
100.0
373.98
22.06
A1
0
<
1
Wet
875
Int. J. Energy Res. 2012; 36:871
–
885 © 2011 John Wiley & Sons, Ltd.
DOI: 10.1002/er
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