Energy 38 (2012) 136e143
Contents lists available at SciVerse ScienceDirect
Energy
journal homepage: www.elsevier.com/locate/energy
The optimal evaporation temperature and working fluids for subcritical organic
Rankine cycle
Chao He a, Chao Liu a, *, Hong Gao a, Hui Xie a, Yourong Li a, Shuangying Wu a, Jinliang Xu b
a
b
Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400030, China
Renewable Energy School, North China Electric Power University, Beijing 102206, China
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 9 August 2011
Received in revised form
13 December 2011
Accepted 17 December 2011
Available online 16 January 2012
A theoretical formula is proposed to calculate the OET (optimal evaporation temperature) of subcritical
ORC (organic Rankine cycle) based on thermodynamic theory when the net power output is selected as
the objective function. The OETs of 22 working fluids including wet, isentropic and dry fluids are
determined under the given conditions. In order to compare the accuracy of these results, the quadratic
approximation method in EES (Engineering Equation Solver) is used to optimize the net power output
and the OETs are obtained by numerical simulation. The results show that the OETs calculated by the
theoretical formula are consistent with the numerical simulation results. In addition, the average
computational accuracy of OETs from the theoretical formula is higher than that from the simplified
formula recommended by the related literature. The larger net power output will be produced when the
critical temperature of working fluid approaches to the temperature of the waste heat source. According
to the maximum net power output, suitable working pressure, total heat transfer capacity and expander
SP (size parameter), R114, R245fa, R123, R601a, n-pentane, R141b and R113 are suited as working fluids
for subcritical ORC under the given conditions in this paper.
! 2011 Elsevier Ltd. All rights reserved.
Keywords:
Organic Rankine cycle
Optimal evaporation temperature
Working fluid
Waste heat recovery
1. Introduction
The low-grade energy sources are abundant in the world, such
as the solar energy, biomass energy, geothermal resources and
power plant waste heat. Therefore, how to utilize this kind of lowgrade energy has attracted more and more attentions for its
potential in relaxing the environmental pollution and reducing
fossil fuel consumption.
The ORC (organic Rankine cycle) technology was proposed to
recover the low-grade waste heat. The ORC performs better than
the conventional steam power cycle in converting the low-grade
waste heat energy into power [1e4]. Much research has been
done on the applications of ORC from different aspects. Vaja and
Gambarotta [5], Wang et al. [6] and Srinivasan et al. [7] focused on
recovering exhaust gas from internal combustion engine. Chinese
et al. [8] and Al-Sulaiman et al. [9] carried out the system analysis of
ORC for biomass-based power generation. Maizza et al. [10], Little
et al. [11] and Roy et al. [12] revolved around the general waste heat
recovery. Delgado-Torres et al. [13] and Tchanche et al. [14] examined the application of ORC for solar driven desalination. Zhang
* Corresponding author. Tel./fax: þ86 023 65112469.
E-mail address: [email protected] (C. Liu).
0360-5442/$ e see front matter ! 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.energy.2011.12.022
et al. [15] and Guo et al. [16] revolved about the low-temperature
geothermal power generation.
Furthermore, many efforts have been made on the choice of
working fluids and the performance analysis of the ORC. Hung et al.
[17] investigated ORC systems operated with refrigerant and
benzene-series fluids. Their work showed that isentropic (or nearly
isentropic) fluids were considered to be the best candidates of the
working fluids for ORC. Mago et al. [18] studied the thermodynamic
performance of different working fluids in ORC and pointed out that
the dry working fluids performed better than the wet working
fluids. Chen et al. [19] analyzed the working fluids selection criteria
for ORC such as types of working fluids, fluid density, specific heat,
latent heat, critical point, thermal conductivity and so on. Li et al.
[20] conducted the evaporation temperature optimization of ORC in
different areas through numerical simulation. Guo et al. [21]
compared the net power output of CO2-based transcritical
Rankine cycle and R245fa-based subcritical ORC with lowtemperature geothermal source. Manolakos et al. [22] compared
the mechanical work of a low-temperature solar ORC for RO (reverse
osmosis) desalination under the different conditions. Dai et al. [23]
investigated the effect of parameters of a novel combined power
and ejector refrigeration cycle on the net power output. Wei et al. [3]
explored the system performance analysis and optimization of ORC
with R245fa and found that it was a good way to improve the net
137
C. He et al. / Energy 38 (2012) 136e143
Nomenclature
ARD
Cp
h
DHH
DHs
_
m
OTE
Q_
qL
R
RD
Rg
s
SP
T
DTm
DT1
TrH
T1,f
T1,s
(UA)tot
V_
w
average relative deviation (dimensionless)
fluid specific heat capacity (kJ kg$1 K$1)
specific enthalpy (kJ kg$1)
enthalpy of vaporization in Eq. (19) (kJ kg$1)
isentropic enthalpy difference in the expander (J kg$1)
mass flow rate (kg s$1)
optimal evaporation temperature (K)
the heat rate injected and rejected (kW)
heat absorption per mass flow rate of fluid (kJ kg$1)
universal gas constant (kJ mol$1 K$1)
relative deviation (dimensionless)
specific gas constant (kJ kg$1 K$1)
specific entropy (kJ kg$1)
the expander size parameter
temperature (K)
the logarithmic mean temperature difference (K)
the pinch temperature difference in evaporator (K)
reduced temperature (K)
the OTE obtained with the formulas (K)
the OTE obtained with the simulation method (K)
the total heat transfer capacity (kW K$1)
volumetric flow rate (m3 s$1)
specific work (kJ kg$1)
power output of the system by maximizing the utilization of the
waste heat as much as possible. Baik et al. [24] compared the power
output of transcritical cycle with CO2 and the R125 for a low-grade
heat source of about 100 " C. The two cycles were optimized when
the power output of ORC is determined as the objective function.
The brief review above shows that the types of working fluids
have a significant influence on the performance of ORC. The net
power output is usually used to evaluate the performance of ORC
for the low-grade waste heat recovery. Normally, the net power
output of ORC is determined as an objective function. Numerical
simulation methods to calculate the OET (optimal evaporation
temperature) were adopted by almost all of the literatures. In this
paper, the theoretical formula for calculating the OET of subcritical
ORC is derived based on thermodynamic theory. The results obtained from the theoretical formula are compared with the
numerical simulation results for three types of working fluids.
According to the maximum net power output, suitable working
pressure, total heat transfer capacity and expander SP (size
parameter), a few working fluids are considered as the candidates
in subcritical ORC under the given conditions in this paper.
2. Thermodynamic analysis
_
W
power output or input (kW)
Greek symbols
latent heat of fluid (kJ kg$1)
efficiency (dimensionless)
correction factor (dimensionless)
acentric factor (dimensionless)
g
h
2
u
Subscripts
c
critical
co
condenser
evp
evaporator
g
generator
h
waste heat source
l
liquid
max
maximal
min
minimal
net
net
p
pump
s
isentropic
t
expander
wf
working fluid
1e8
state points
2s,4s
stat points for the ideal case
a new cycle begins. Fig. 2 illustrates the thermodynamic processes
on the Tes diagram for this ORC system. Generally, there are four
different processes: pumping process 3-4, isobaric heat absorption
process 4-1, expansion process 1-2 and isobaric condensation
process 2-3. For the ideal case, the processes 3-4 and 1-2 are the
isentropic processes 3-4s and 1-2s, respectively.
The ORC specifications considered in this paper are given in
Table 1. For the given conditions of the waste heat source, in order
to make full use of the low-grade waste heat, obtaining the
maximum net power output is desirable. The net power output of
the ORC can reflect the capability to recover the exhaust heat. And
so the net power output is selected as the objective function in this
paper. The evaporation temperature when the maximum net
power output was reached is defined as the OET.
The net power output of the ORC can be expressed as
_ net ¼ W
_ t$W
_ p
W
(1)
_ t and W
_ p are power generated by the expander and power
where W
consumed by the pump, respectively.
waste heat
source
1
5
2.1. System description
An elementary configuration of ORC for waste heat recovery is
shown in Fig. 1, which consists of a working fluid pump, an evaporator driven by low-grade waste heat, an expander, and a water
cooled condenser. Working fluid with low boiling point is pumped
to the evaporator, where it is heated and vaporized by the exhaust
heat. The generated high pressure vapor flows into the expander
and its heat energy is converted to work. Simultaneously, the
expander drives the generator and electric energy is generated.
Then, the exhaust vapor exits the expander and is led to the
condenser where it is condensed by the cooling water. The
condensed working fluid is pumped back to the evaporator and
expander
generator
6
evaporator
2
7
condenser
pump
4
Fig. 1. Schematic diagram of the ORC.
8
3
138
C. He et al. / Energy 38 (2012) 136e143
2.2. The theoretical formula of OET
T
The theoretical formula of the OET using the net power output
as the objective function is derived based on thermodynamic
theory.
The net power output of the ORC can be expressed as
5
waste heat
source
6
T1
!
"
_ net ¼ m
_ wf wnet ¼ m
_ wf wt $ wp
W
1
9
where wnet, wt and wp are the specific net power output and the
specific power of the expander and pump, respectively.
According to the Fig. 2, the specific net power output can be
determined as the area of 1-2-3-4-9-1. In fact, compared to the area
of 1-2-3-4-9-1, the area of 3-4-9-3 is so small that can be neglected.
Based on the analysis above, the specific net power output of ORC
can be expressed as
4
4s
2s
2
3
T2
8
7
cooling water
#
$
1
wt $ wp z ðT1 $ T3 Þðs1 $ s9 Þ þ ðT1 $ T3 Þðs9 $ s3 Þ hs hg
2
#
$
1
¼ ðT1 $ T3 Þ ðs1 $ s9 Þ þ ðs9 $ s3 Þ hs hg
2
S
Fig. 2. T$s diagram of the ORC.
The power generated by the expander is given by
_ t ¼ m
_ wf ðh1 $ h2 Þhg ¼ m
_ wf ðh1 $ h2s Þhs hg
W
(2)
where h1 and h2 are the specific enthalpies of the working fluid at
the inlet and outlet of the expander, respectively, h2s is the ideal
case of h2, hs and hg are the expander isentropic efficiency and the
_ wf is the mass flow rate of
generator efficiency, respectively, and m
working fluid.
The power consumed by the pump can be expressed as
_ p ¼
W
_ wf ðh4s $ h3 Þ
m
hp
_ wf ðh4 $ h3 Þ
¼ m
(3)
where hp is the isentropic efficiency of the pump, h4s and h4 are the
specific enthalpies of the working fluid at the outlet of the pump for
the ideal and actual condition, respectively, and h3 is the specific
enthalpy of the working fluid at the outlet of the condenser.
In this paper, the hypotheses are as follows: the system has
reached the steady state, there is no pressure drop in the evaporator, pipes and condenser, the heat losses in the components
are neglected, and isentropic efficiencies of the pump and the
expander are given. The working fluid at the expander inlet and
condenser outlet is saturated vapor and saturated liquid,
respectively.
The thermodynamic properties of working fluid and the ORC
performance are evaluated with EES (Engineering Equation
Solver) [25]. The quadratic approximation method is applied to
maximize the net power output by changing the evaporation
temperatures.
Table 1
Specifications of the ORC conditions.
(5)
where T1 and T3 are the evaporation temperature and condensation
temperature, respectively, s1 and s3 are the specific entropies of the
working fluid at the inlet of the expander and the pump, respectively, and s9 is the specific entropy of the saturated liquid working
fluid at the temperature of T1.
The mass flow rate of the working fluid is given by
_ wf ¼
m
_ h ðT5 $ T1 $ DT1 Þ
Cph m
g
(6)
where Cph is the specific heat of the waste heat source at constant
_ h is the mass flow rate of the waste heat source, T5 is the
pressure, m
inlet temperature of the waste heat, DT1 is the pinch temperature
difference in the evaporator and g is the latent heat of working fluid
at T1.
The latent heat can be expressed as:
(7)
g ¼ T1 ðs1 $ s9 Þ
The entropy change of the working fluid from the state point 3
to 9 can be approximately evaluated as:
s9 $ s3 zCpl ln
T1
T3
(8)
where Cpl is the specific heat of the liquid working fluid at constant
pressure.
Substituting Eqs. (5), (6), (7) and (8) into (4), the net power
output of the ORC can be approximately obtained as follows:
&
%
_ hh
D
_ net zCph mh s g ðT5 $ T1 $ T1 Þ ðT $ T Þ 1 þ Cpl T1 ln T1
W
1
3
T1
2g
T3
(9)
The Eq. (10) is used to determine the OET when the net power
output of ORC is considered as the objective function.
Parameter
Value
Unit
Waste heat source temperature
Mass flow rate of waste heat source
Cooling water temperature
Environment temperature
Environment pressure
Pinch temperature difference in evaporator
Pinch temperature difference in condenser
Isentropic efficiency of the expander
Generator efficiency
Pump isentropic efficiency
423.15a
1
293.15
293.15
100
5
5
80%
96%
75%
K
kg/s
K
K
kPa
K
K
a
(4)
The common temperature of the engineering waste heat.
_ net
dW
¼ 0
dT1
(10)
When the waste heat source temperature, the mass flow rate of
waste heat source, the cooling water temperature, the environment
temperature and pressure, the pinch temperature difference in
evaporator, the pinch temperature difference in condenser, the
isentropic efficiency of the expander, the generator efficiency and
the pump isentropic efficiency are given, the theoretical formula of
the OET of subcritical ORC is obtained as follows:
139
C. He et al. / Energy 38 (2012) 136e143
'
%
& %
&
Cpl
T3 ðT5 $ DT1 Þ
T1
T1
D
ðT
$1þ
$
T
þT
Þ
ln
þ1
$
2
ln
þ1
5
1
3
2g
T3
T3
T12
(
T ðT $ DT1 Þ 1 dg
T
$
ðT $T $ DT1 Þ ðT1 $T3 Þ ln 1 ¼ 0
'T1 $ 3 5
g dT1 5 1
T1
T3
(11)
The OET T1 can be obtained by solving the Eq. (11) with iterative
methods, if the correlative expression of latent heat of working
fluid is given.
Two expressions of latent heat of working fluid are selected:
One of the expressions [26] is
%
&
%
&
$
T 0:354
T 0:456
g ¼ Rg Tc 7:08$ 1 $ 1
þ10:95$u 1 $ 1
Tc
Tc
#
x ¼
(12)
and the other [27] is
g
RTc
¼
%
##%
&ðR1 Þ "
&
& $
%
u $ uðR1 Þ
g ðR2 Þ
g ðR1 Þ
þ
$
RTc
RTc
RTc
u $ uðR2 Þ
(13)
&
&
%
%
T 1=3
T 5=6
¼ 6:537$ 1$ 1
$2:467$ 1$ 1
Tc
Tc
%
%
&
&
T1 1:208
T
$77:251$ 1$
þ59:634$ 1$ 1
Tc
Tc
&2
&3
%
%
T
T
þ36:099$ 1$ 1 $14:606$ 1$ 1
Tc
Tc
(14)
g
where
%
%
g
RTc
&ðR1 Þ
are important factors for ORC [29e31]. In this paper, the maximum
net power output, suitable working pressure, total heat transfer
capacity and expander SP are considered as the criteria to screen
the working fluids of subcritical ORC.
According to the slope of the saturation vapor curve on the Tes
diagram (dT/ds), the working fluids can be classed as wet, isentropic or dry fluids. After defining x ¼ ds/dT, the types of working
fluids can be predicted. That is, x < 0: a wet fluid, x w 0: an isentropic fluid, and x > 0: a dry fluid. x can be calculated by using the
following equation presented in Ref. [32].
Cp ðn$TrH Þ=ð1 $ TrH Þ þ 1
DHH
$
TH
TH2
(19)
where x is the inverse of the slope of the saturated vapor curve on
the Tes diagram, TrH (¼TH/TC) denotes the reduced evaporation
temperature, DHH represents the enthalpy of vaporization, and n is
suggested to be 0.375 or 0.38 [33]. According to the given conditions, TH is set as 301.15 K (the condensation temperature of ORC)
for the investigated working fluids. Table 2 presents the physical
properties and the results determined by Eq. (19) for 22 pure
component working fluids.
The maximum working pressure, the total heat transfer area and
the expander size are three important technical and economic
factors in ORC system. The total heat transfer capacity (UA)tot,
which have been used to evaluate the cost of heat exchangers, can
approximately reflect the total heat transfer area of heat
exchangers in the ORC system [21,34]. The (UA)tot could be evaluated by the following equations:
&ðR2 Þ %
&
&
&
&
%
%
%
g ðR1 Þ
T 1=3
T 5=6
T 1:208
$
¼ $ 0:133$ 1 $ 1
$28:215$ 1 $ 1
$82:958$ 1 $ 1
RTc
RTc
Tc
Tc
Tc
&
%
&
&
%
%
T1
T1 2
T1 3
þ 19:105$ 1 $
þ 99:000$ 1 $
$2:796$ 1 $
Tc
Tc
Tc
g
(15)
uðR1 Þ ¼ 0:21 and uðR2 Þ ¼ 0:46
The Newton iteration method is adopted to solve the Eq. (11) by
combining Eq. (12) or (13) in matlab7.0.
2.3. Simplified formula
The simplified formula to determine the OET was presented by
Ref. [28].
T1 ¼ 2T *
(16)
where
T* ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
T3 ðT5 $ DT1 Þ
(17)
2 ¼ 0:999 þ 0:00041ðT5 $ T3 Þ=ðg0 =qL Þ
(18)
0
2 is the correction factor, g is the latent heat of working fluid at
the temperature of T* and qL is the heat the working fluid absorbs
from the condenser temperature to T*.
3. Choice of working fluids
The thermodynamic performance, stability, non-fouling, noncorrosiveness, non-toxicity, non-flammability of the working fluid
Table 2
Properties of working fluids.
Working fluids
x
Type of
fluids
Molecular
weight (g/mol)
Critical
temperature (K)
R717
Methanol
Ethanol
R600a
R142b
R114
R600
R245fa
R123
R601a
n-Pentane
R11
R141b
R113
n-Hexane
Toluene
n-Heptane
n-Octane
n-Dodecane
Cyclohexane
n-Decane
n-Nonane
$10.7
$11.55
$7.2
1.18
$0.13
0.62
0.55
0.52
0.19
1.08
0.99
$0.41
$0.27
0.37
1.88
$0.73
1.56
1.73
2.14
$0.17
278
1.84
Wet
Wet
Wet
Dry
Isentropic
Isentropic
Isentropic
Isentropic
Isentropic
Dry
Dry
Isentropic
Isentropic
Isentropic
Dry
Isentropic
Dry
Dry
Dry
Isentropic
Dry
Dry
17.03
32.04
46.07
58.12
100.5
170.92
58.12
134.05
152.93
72.15
72.15
137.37
116.95
187.38
86.17
92.14
100.2
114.2
170.3
84.16
142.28
128.26
405.4
513.4
513.9
407.8
410.3
418.9
425.1
427.2
456.8
460.4
469.7
471.2
477.4
487.3
507.9
591.8
540.1
569.3
658.1
553.6
617.7
594.6
140
C. He et al. / Energy 38 (2012) 136e143
Table 3
The OET and the RD by using different methods.
Working fluids
The simulation
results (K)
The results of Eqs.
(11) and (12) (K)
The results of Eqs.
(11) and (13) (K)
The results of Eq.
(16) (K)
RD of Eqs.
(11) and (12) (%)
RD of Eqs.
(11) and (13) (%)
RD of Eq.
(16) (%)
R717
Methanol
Ethanol
R600a
R142b
R114
R600
R245fa
R123
R601a
n-Pentane
R11
R141b
R113
n-Hexane
Toluene
n-Heptane
n-Octane
n-Dodecane
Cyclohexane
n-Decane
n-Nonane
363.7
360.6
359.2
366.2
366.7
365.6
365.3
365
362.6
362.9
362.4
360.4
361.4
361.6
362.3
362.1
360.9
360.6
360.4
360.5
360.3
360.4
362.8
357.5
358.6
368.4
366.4
367.1
365.1
365.6
362.7
363.3
362.8
360.8
361.3
362.1
361.8
359.4
361.7
361.6
361.4
360.4
361.4
361.4
362.8
356.8
358.2
367.3
366.0
367.0
364.3
367.9
363.2
363.0
362.8
360.3
361.2
362.3
363.0
359.8
364.3
368.4
360.0
360.2
357.6
352.1
360.3
357
357.8
364.8
363.3
364.8
363.2
363.7
361.7
362.4
362
360
360.6
361.5
361.6
359.1
361.4
361.3
361.2
359.9
361.2
361.2
$0.25
$0.86
$0.17
0.60
$0.08
0.41
$0.05
0.16
0.03
0.11
0.11
0.11
$0.03
0.14
$0.14
$0.75
0.22
0.28
0.28
$0.03
0.31
0.28
ARD
0.25
$0.25
$1.05
$0.28
0.30
$0.19
0.38
$0.27
0.79
0.17
0.03
0.11
$0.03
$0.06
0.19
0.19
$0.64
0.94
2.16
$0.11
$0.08
$0.75
$2.3
ARD
0.51
$0.94
$1.00
$0.39
$0.38
$0.93
$0.22
$0.58
$0.36
$0.25
$0.14
$0.11
$0.11
$0.22
$0.03
$0.19
$0.83
0.14
0.19
0.22
$0.17
0.25
0.22
ARD
0.36
ðUAÞtot ¼
Q_ evp
Q_
þ co
DTme DTmc
The ARD (average relative deviation) is expressed by
(20)
ARD ¼
_ wf ðh1 $ h4 Þ
Q_ evp ¼ m
(21)
_ wf ðh2 $ h3 Þ
Q_ co ¼ m
(22)
DTm ¼
DTmax $ DTmin
DTmax
ln
DTmin
(23)
where Q_ evp and Q_ co are the heat rate injected and rejected,
respectively, DTm is the logarithmic mean temperature difference,
DTmax and DTmin are the maximal and minimal temperature
differences at the ends of the heat exchangers, respectively.
Macchi [35] used the expander SP to evaluate the expander size.
SP ¼
qffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi
4
V_ 2s = DHs
(24)
where V_ 2s is the volume flow rate of the working fluid at the outlet
of the expander and DHs is the specific enthalpy drop in the
expander. And then the parameter (SP) have been used by other
researchers [24,36,37] to study the size character of the expander in
the ORC system.
4. Results and discussion
The OET and the RD (relative deviation) by using different
methods are shown in Table 3. The simulation results by EES are
regarded as reference value. And the RD is given by
RD ¼
T1;s $ T1;f
' 100%
T1;s
(25)
where T1,s and T1,f are the OET obtained from the numerical simulation and theoretical formulas, respectively.
Pn
i¼1
n
jRDi j
(26)
where i denotes the each working fluid.
The maximum RD of the OET is $2.3% for n-nonane with Eqs.
(11) and (13) as shown in Table 3. The ARDs of the OET are 0.25% and
0.51% respectively with Eqs. (11) and (12), Eqs. (11) and (13). This
shows that the theoretical formula is accurate to determine the OET
for the subcritical ORC. This formula is applicable to determine the
OET of ORC for wet, dry or isentropic fluids.
The ARD of the OET is 0.36% by using Eq. (16). Obviously, the
average accuracy to determine the OET for subcritical ORC with Eqs.
(11) and (12) is improved by 31% as compared with simplified Eq.
(16). The expression of latent heat of working fluid is needed when
the OET for the ORC is calculated using the theoretical formula
proposed, while the absorption heat and latent heat of the working
fluid using the simplified Eq. (16) are needed. Obviously, it is more
convenient to use the theoretical formula proposed to calculate the
OET for the subcritical ORC than using simplified Eq. (16).
Figs. 3 and 4 illustrate the maximal net power output and its
corresponding working pressure of ORC with different working
fluids by the numerical simulation, respectively. Higher net power
output means that more power could be obtained under the same
condition of waste heat source.
The maximal net power output values vary with the different
working fluids as shown in Fig. 3. For R600a, R142b, R114, R600 and
R245fa, the higher net power output will be obtained among the
investigated working fluids. These fluids are isentropic fluids
except R600a (dry fluid). The highest net power output of ORC is
about 9.61 kW when R114 is adopted. The net power outputs of ORC
are about 9.54 kW, 9.58 kW, 9.43 kW, 9.52 kW corresponding to
R600a, R142b, R600 and R245fa, respectively. Their critical
temperatures are very close to the waste heat source temperature
423.15 K. The lowest net power outputs of ORC are about 7.20 kW
and 7.79 kW when methanol and toluene are used as working
fluids. The critical temperatures of the two working fluids are much
higher than the temperature of the waste heat source. Therefore, it
141
C. He et al. / Energy 38 (2012) 136e143
The maximal net power output(kW)
10
9
8
7
n-Nonane
n-Decane
Cyclohexane
n-dodecane
n-octane
n-heptane
Toluene
n-Hexane
R113
R141b
R11
n-pentane
R601a
R123
R245fa
R600
R114
R142b
R600a
Ethanol
Methanol
R717
Working fluids
Fig. 3. The maximal net power output of ORC with different working fluids.
can be deduced that the larger net power output will be produced
when the critical temperature of working fluid approaches to the
temperature of the waste heat source.
As shown in Fig. 4, the highest working pressure at the maximal
net power output of ORC is about 5176 kPa when R717 is used as
working fluid. Higher working pressure in ORC means to increase
the investment of ORC system. The maximal net power output of
ORC for R717 is much smaller than that for R114. The working
pressures at the maximal net power output are about 1714 kPa,
1835 kPa, 1206 kPa, 1307 kPa, 1048 kPa for working fluids R600a,
R142b, R114, R600 and R245fa, respectively. For working fluids
R123, R601a, n-pentane, R11, R141b and R113, the range of working
pressures is from 300 kPa to 700 kPa. No matter the highest net
power output or lower working pressure in ORC, R114, R245fa,
R123, R601a, n-pentane, R141b and R113 are better working fluids.
For some working fluids investigated, such as toluene, n-heptane
and n-octane, the operation pressure could be much lower than
atmospheric pressure as shown in Fig. 4. This means that the system
needs a perfect sealing to avoid leakage, and it leads to more cost.
Figs. 5 and 6 illustrate the total heat transfer capacity and the
expander SP in ORC respectively when the maximum net power
output is obtained with different working fluids. For working fluids
R717, ethanol, methanol, R142b, R11 and R600a, the total heat
transfer capacity could change from 8 kW/K to 12 kW/K. Usually,
the higher total heat transfer capacity means the more cost of the
heat exchanger. For working fluids R141b, R600, R114, R245fa,
R123, toluene, R601a, R113, n-pentane and cyclohexane, the range
of total heat transfer capacity is between 6.2 kW/K and 7.5 kW/K.
For the remaining 6 working fluids, i.e., n-hexane, n-heptane, noctane, n-dodecane, n-decane and n-nonane, the total heat transfer
capacity is less than 6 kW/K. These six working fluids should be
better to use in ORC in terms of economic considerations. However,
the net power output and working pressure are not ideal for these
working fluids.
As shown in Fig. 6, for working fluids R717, methanol, R600a,
R142b, R114, R600, R245fa, R123, R601a, n-pentane, R11, R141b and
R113, the expander SP is smaller than 0.03 m. For working fluids
ethanol, n-hexane and cyclohexane, the range of the expander SP is
from 0.03 m to 0.05 m. The expander SP is greater than 0.05 m for
working fluids such as toluene, n-heptane, n-octane, n-dodecane,
n-decane and n-nonane.
Based on the above discussion, it could be concluded that the
lower total heat transfer capacity does not mean the smaller
expander SP. Therefore, the maximum net power output, suitable
working pressure, total heat transfer capacity and expander SP
should be completely taken into account, and then the better
working fluids for subcritical ORC could be determined.
5200
12
1800
1600
10
1400
(UA)tot (kW/K)
Pressure at the maximal net power output(kPa)
5150
1200
1000
8
800
600
6
400
200
0
n-Nonane
n-Decane
Cyclohexane
n-Dodecane
n-Octane
n-Heptane
Toluene
Working fluids
n-Hexane
R113
R141b
R11
n-pentane
R601a
R123
R245fa
R600
R114
R142b
R600a
Ethanol
Methanol
R717
n-Nonane
n-Decane
Cyclohexane
n-dodecane
n-octane
n-heptane
Toluene
n-Hexane
R113
R141b
R11
n-pentane
R601a
R123
R245fa
R600
R114
R142b
R600a
Ethanol
Methanol
R717
4
Working fluids
Fig. 4. The working pressure at the maximal net power output of ORC with different
working fluids.
Fig. 5. The total heat transfer capacity of the system with different working fluids.
142
C. He et al. / Energy 38 (2012) 136e143
and expander SP of ORC, R114, R245fa, R123, R601a, n-pentane,
R141b, and R113 are suited as working fluids in subcritical ORC
under the given conditions in this paper.
0.70
0.65
Acknowledgments
This work was supported by National Basic Research Program of
China (973 Program) under Grant No. 2011CB710701 and the
Fundamental Research Funds for the Central Universities under
Grant No. CDJXS10140005.
SP(m)
0.10
References
0.05
0.00
n-Nonane
n-Decane
Cyclohexane
n-Dodecane
n-Octane
n-Heptane
Toluene
n-Hexane
R113
R141b
R11
n-pentane
R601a
R123
R245fa
R600
R114
R142b
R600a
Ethanol
Methanol
R717
Working fluids
Fig. 6. The expander SP with different working fluids.
Working fluids, such as R114, R245fa, R123, R601a, n-pentane,
R141b and R113, are better ones under the given conditions in this
paper.
5. Conclusions
The theoretical formula is proposed to calculate the OET of the
subcritical ORC for waste heat recovery based on thermodynamic
theory. The OETs of 22 working fluids are investigated under the given
conditions. The quadratic approximation method supplied by EES is
used to optimize the net power output during the numerical simulation process. The calculation results from the theoretical formula
are compared with the results from numerical simulation and the
simplified formula in reference. The maximum net power output,
suitable working pressure, total heat transfer capacity and expander
SP are considered as the criteria to screen the working fluids.
The main conclusions are made as follows:
(1) The maximum RD of the OET determined by the theoretical
formula is $0.86% and 2.3% respectively for the two different
correlative expressions of latent heat of working fluid. The ARD
of the OET determined by the theoretical formula is less
than 1%.
(2) The maximum net power output of ORC varies with working
fluids at the given conditions. Under the conditions of this
paper, the maximum net power output of ORC will be changed
from 9.43 kW to 9.61 kW by using R600, R245fa, R600a, R142b
and R114. There exists 25% difference between the maximum
net power outputs for the investigated working fluids. When
the critical temperatures of the working fluids approach to the
temperature of the waste heat source, the greater net power
output will be produced.
(3) Based on the screening criteria of the maximum net power
output, suitable working pressure, total heat transfer capacity
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