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Energy 42 (2012) 503e509
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Influence of coupled pinch point temperature difference and evaporation
temperature on performance of organic Rankine cycle
You-Rong Li*, Jian-Ning Wang, Mei-Tang Du
Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400044, China
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 15 January 2012
Accepted 4 March 2012
Available online 11 April 2012
This paper presented the analysis on the influence of the pinch point temperature difference (PPTD) and
the evaporation temperature on the performance of organic Rankine cycle (ORC) in recovering the low
temperature waste heat of the flue gas. Both the net power output and the heat transfer area of the
evaporator and condenser were evaluated for dry and isentropic working fluids. When the heat and cold
source conditions were given, the maximum net power output and the heat transfer area were obtained.
The results show that some organic working fluids cannot reach the maximum net power output to avoid
the low temperature corrosion. With the increase of the PPTD of the evaporator at a given total
temperature difference, the total heat transfer area decreases first and then increases, while the corresponding cost-effective performance (ratio of the net power output to total heat transfer area) displays
almost the opposite variation tendency. The PPTD of the evaporator for the optimization cost-effective
performance is approximately the same for different organic working fluids. Meanwhile, the isentropic
working fluids show better cost-effective performance than dry working fluids.
Ó 2012 Elsevier Ltd. All rights reserved.
Keywords:
Organic Rankine cycle
Pinch point temperature difference
Evaporation temperature
Low temperature waste heat
Flue gas
1. Introduction
Due to the rapid increase of the energy consumption in recent
years, how to effectively utilize the low temperature waste heat,
which was directly discharged to atmosphere in the industrial
production, has attracted the considerable interest. It has been
found that more than half of the total industrial waste heat was the
low temperature heat energy and most of that was wasted in the
form of flue gas [1]. Therefore, converting waste heat into electricity not only saves the fossil fuel but also contributes to reduce
the thermal pollution. Nevertheless, a great quantity of waste heat
with the temperature below 200 C is not suitable to be recovered
by the traditional Rankine cycle [2]. As one of the most promising
technologies in recovering this kind of waste heat, the organic
Rankin cycle (ORC) with organic working fluids, which occurs
phase change at relative low temperature, has been increasingly
paid attention and gradually used in practical industrial applications. In addition, the ORC system has many advantages in making
full use of the low temperature waste heat, for example, flexibility,
safety and maintenance requirements etc [3,4].
So far, many investigations on the ORC system has been performed, including the working fluid selection [5e9], the optimum
* Corresponding author. Tel.: þ86 23 6511 2284; fax: þ86 23 6510 2473.
E-mail address: [email protected] (Y.-R. Li).
0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved.
doi:10.1016/j.energy.2012.03.018
design for improving the system efficiency [10e13] and the system
operating optimization etc [14e18]. Internal heat exchanger (IHE)
was suggested to be equipped to improve the ORC efficiency in
some conditions, however, Dai and Li pointed out that the IHE could
not increase the net power output at a given heat source condition
[19e22] and even not consider the extra investment. Besides, it was
also certified that the superheating and supercooling of the
working fluids lead to an increase of the system irreversibility
[23,24]. Therefore, the basic ORC system was considered in present
study.
Evaporation temperature and condensation temperature are
two main control parameters and have an important impact on the
ORC performance. According to the second law of thermodynamics,
both the higher evaporation temperature and the lower condensation temperature lead to an increase of the system thermal efficiency [25]. However, the evaporation temperature and
condensation temperature are restricted by the critical temperature of the organic working fluid and the ambient temperature,
respectively. The increasing evaporation temperature will reduce
the heat transfer flux in the evaporator, which may lead to
a decrease of the net power output finally. At the same time, the
PPTD of the heat exchanger not only influences the evaporation
temperature and condensation temperature but also plays an
essential role in the cost-efficiency tradeoff [26]. With the decrease
of the PPTD, higher evaporation temperature and lower condensation temperature can be achieved between the inlet temperature
504
Y.-R. Li et al. / Energy 42 (2012) 503e509
Nomenclature
A
cp
h
m
Ja
K
Q
T
W
heat transfer area (m2)
specific heat capacity (J kg1 K1)
specific enthalpy (J kg1)
mass flow rate (kg s1)
Jacob number ()
heat transfer coefficient (W m2 K1)
heat transfer flux (W)
temperature ( C)
power (W)
Greek symbols
h
isentropic efficiency
of waste heat and the heat sink temperature. Meanwhile, more heat
transfer area is required with the decrease of the PPTD, which
results in an increase of cost for the ORC system.
Although there were many investigations associated with the
optimization of the ORC system, detailed influence of the PPTD on
the ORC performance was rarely found. Hence the main objective of
this study is to analyze the influences of the coupled evaporation
temperature and the PPTD on the net power output and the costeffective performance. The lowest temperature of the flue gas at
the evaporator outlet should exceed 90 C in order to avoid the low
temperature corrosion. At the given external heat and cold source
conditions, the optimum performance of the ORC system is evaluated with different working fluids including R123, R11, R245fa and
R113 etc. The physical properties of organic working fluids and the
system performance were calculated with Engineering Equation
Solver (EES) [27].
ε
ratio of the net power output to heat transfer area
(W m2)
Subscripts
a
cooling air
c
condenser
e
evaporator
g
flue gas
p
pump
s
single-phase region
t
two-phase region
T
total
tur
turbine
wf
working fluid
The heat transfer area can be obtained when the heat transfer
coefficient and state parameters of the organic working fluid
are determined. Meanwhile, cost-effective performance for the
ORC system would be worked out.
A simple description of the thermodynamic modeling procedure of the basic ORC system, as shown in Ref. [20], was summarized as following:
2. Thermodynamic model of the ORC system
The layout of the basic ORC system and the T-S diagram are
shown in Fig. 1. It can be found that the ORC system uses the same
thermodynamic principles as the traditional steam Rankine cycle.
The difference is that the ORC system employs the low boiling point
organic working fluid to recover the low temperature waste heat.
The organic working fluid absorbs heat from the flue gas in the
evaporator and becomes saturated vapor used to drive turbine.
After leaving turbine, the organic working fluid is condensed to
saturated liquid in the condenser and pumped back to the evaporator to close the cycle. The steady operation state of the cycle is
assumed in this work and pressure drop in the evaporator,
condenser and pipes can be neglected. Specific heat capacities of
the flue gas and cooling air are assumed to be constant. The ORC
specifications in this work are listed in Table 1.
The detailed procedures of calculation are outlined as follows:
At the given conditions of heat and cold sources, the physical
properties at the two-phase region of the evaporator and the
mass flow rate of the working fluid are obtained from the
prescribed evaporation temperature and the PPTD of the
evaporator.
The state of the organic working fluid at condenser outlet is
assumed to be saturated liquid. Therefore, the condensation
temperature can be calculated after iterating to meet the PPTD
of the condenser and the given isentropic efficiencies of turbine
and pump. In addition, the outlet temperatures of the flue gas
and cooling air, and the net power output are determined by
state parameters of the working fluid at operation points.
Fig. 1. The basic ORC system.
Y.-R. Li et al. / Energy 42 (2012) 503e509
Ref.
The calculation method is completely adapted to the condenser
and the heat released of the organic working fluid in condenser can
be obtained easily as:
[20,25]
Qc ¼ ma cpa Tc DTc Ta;in ð1 þ Jac Þ;
Table 1
Specifications of the ORC considered.
Items
Value
Ambient temperature ( C)
Flue gas temperature ( C)
Flue gas flow rate (kg s1)
Cooling air temperature ( C)
Cooling air flow rate (kg s1)
Pump isentropic efficiency
Turbine isentropic efficiency
Minimum allowed discharge temperature ( C)
Heat transfer coefficient in evaporator (W m2 K1)
Heat transfer coefficient in condenser (W m2 K1)
20
160
10.47
20
52.35
0.8
0.85
90
70
50
Jac ¼
(1)
h1 h1a
Ta;out Tc þ DTc
¼
:
h1a h2
Tc DTc Ta;in
(12)
DTc is the PPTD of the condenser and the Jac denotes the ratio of
the sensible heat to the latent heat of the working fluid in
condenser.
Therefore, the net power output of the ORC system can be
determined as following:
Wnet ¼ Wtur Wp ¼ Qe Qc :
Pump, 2-3,
Wp ¼ mwf ðh3 h2 Þ ¼ mwf ðh2a h2 Þ=hp :
(11)
where,
[31]
[3]
[3]
[31]
[30]
[30]
Condenser, 1-2,
Qc ¼ mwf ðh1 h2 Þ:
505
(13)
Substituting Eqs. (10) and (11) into Eq. (13) yields:
(2)
Wnet ¼ mg cpg Tg;in Te DTe ð1 þ Jae Þ
ma cpa Tc DTc Ta;in ð1 þ Jac Þ:
ð14Þ
Evaporator, 3-4,
2.2. Heat transfer area
Qe ¼ mwf ðh4 h3 Þ:
(3)
mwf ðh4 h3a Þ ¼ mg cpg Tg;in Tg;e ;
(5)
There have been many formulas which used to calculate the
heat transfer coefficient of the heat exchanger in the published
literatures [2,15,28,29]. Shell-and-tube heat exchanger of the
counter-current design is employed, and the heat transfer coefficients in evaporator and condenser are directly given in Table 1.
Both heat transfer procedures of the single-phase region and the
two-phase region were considered in evaporator and condenser. As
the thermal resistances of gas side and air side in evaporator and
condenser are much larger than those of the working fluid side,
respectively, heat transfer coefficients of evaporator and condenser
could be regarded as constant [30].
Based on the heat transfer equations, the heat transfer area of
the single-phase region in the evaporator can be calculated as
following:
mwf ðh3a h3 Þ ¼ mg cpg Tg;e Tg;out ;
(6)
Ae;s ¼
Turbine, 4-1,
Wtur ¼ mwf ðh4 h1 Þ ¼ mwf ðh4 h4a Þhtur :
(4)
2.1. Net power output
When the viscous dissipation and heat losses of the heat
exchanger are neglected, energy balance in single-phase and twophase region of evaporator can be expressed as following,
respectively,
where
(15)
where,
Tg;e ¼ Te þ DTe :
(7)
The h4 and h3a are the enthalpies of the organic working fluid at
the saturated vapor and saturated liquid conditions, respectively.
DTe is the smallest temperature difference in evaporator, which is
defined as the difference between the flue gas temperature where
the organic fluid begins to evaporate and the evaporation
temperature.
In evaporator, the ratio of the sensible heat to the latent heat of
the working fluid is defined as
Jae ¼
mg cpg Te þ DTe Tg;out
:
Ke DTm;e;s
Te þ DTe Tg;out
h3a h3
¼
:
h4 h3a
Tg;in Te DTe
(8)
The total absorbed heat of the organic working fluid in the
evaporator can be expressed as:
Qe ¼ mwf ðh4 h3 Þ ¼ mg cpg Tg;in Tg;out :
Ae;s ¼
(16)
mg cpg Te þ DTe Tg;out
Tg;out T3
ln
:
DTe
Ke Tg;out Tc DTe
(17)
Set ze ¼ Jae ðTg;in Te DTe Þ, the above equation can be written
as:
Ae;s ¼
(10)
Tg;out T3 DTe
:
Tg;out T3
ln
DTe
DTm,e,s is the logarithmic mean temperature difference of the
single-phase region in evaporator and Ke is the heat transfer coefficient. In the basic ORC system, Tc is very close to T3 and the
difference between Tc and T3 is negligible, and therefore, using Tc to
replace T3 is reasonable. In this case, the heat transfer area can be
determined as:
(9)
Substituting Eqs. (5), (6) and (8) into Eq. (9) yields:
Qe ¼ mg cpg Tg;in Te DTe ð1 þ Jae Þ:
DTm;e;s ¼
mg cpg
ze
ðTe Tc þ DTe Þ ze
ln
:
DTe
Ke Te Tc ze
(18)
Using the similar method, the heat transfer area of the singlephase region in the condenser can be expressed as
506
Ac;s
Y.-R. Li et al. / Energy 42 (2012) 503e509
ma cpa
zc
ðT þ Tc DTc Þ zc
¼
ln 1
;
DTc
Kc T1 Tc zc
(19)
where, zc ¼ Jac ðTc DTc Ta;in Þ.
T1 mainly depends on Te and Tc with the constant isentropic
efficiency of turbine. The value of T1 will slightly increase with the
increase of Te and the decrease of Tc. For a near-isentropic fluid, the
difference between T1 and Tc can be neglected [7].
In two-phase region, the areas of the heat exchanger for the
evaporator and condenser can be written as, respectively,
Ae;t
Tg;in Te
mg cpg
¼
ln
;
DTe
Ke
(20)
Tc Ta;in
ma cpa
ln
:
DTc
Kc
(21)
Ac;t ¼
The total heat transfer area in the evaporator and condenser can
be obtained as:
AT ¼ Ae þ Ac :
(22)
where, Ae ¼ Ae,s þ Ae,t and Ac ¼ Ac,s þ Ac,t.
Thereby, the net power output per heat transfer area can be
obtained as:
ε ¼ Wnet =AT :
(23)
Based on above analyses, it can be known that both the net
power output and the heat transfer area of the ORC system are
mainly associated with Te, Tc, DTe and DTc. At the given heat and cold
sources, matching those key parameters to improve the ORC system
performance is the main target of this work. The previous published papers have researched the ORC at some certain PPTD, as
shown in Table 2, however, the effect of the PPTD on the ORC
performance is not considered. Consequently, this paper will focus
much attention on the influence of the PPTD of the evaporation on
the cost-effective optimization at a given total PPTD (DTT).
In order to check the validation of the present model, we carried
out some calculations of the basic ORC for the various fluids under
the same operation conditions as Dai et al. [22]. The comparison of
the net power output was shown in Table 3. A good agreement was
achieved and the relative error was less 1%.
Table 3
The comparison of the net power output.
Working fluids
R11
R123
R141b
R113
Wnet (kW)
149.9
151.34
0.95
157.8
156.91
0.57
152.4
152.8
0.26
155.8
155.77
0.02
This work
Dai et al. [22]
Relative error (%)
3.1. Effect of the PPTD on the net power output
Fig. 2 shows the variation of the net power output with the PPTD
of the evaporator at DTT ¼ 20 C. It can be found that the net power
output increases first, and then decreases with the increase of the
PPTD of the evaporator at a fixed evaporation temperature Te. This
is mainly because the increase of the PPTD of the evaporator causes
the decrease of the heat transfer flux, which results in a reduction
of the mass flow rate of the organic working fluids. On the other
hand, at a given total PPTD (DTT), the condensation temperature
decreases to meet the decrease of the PPTD of the condenser. As
a result, the difference between the evaporation temperature and
the condensation temperature increases, which leads to the
increase of the specific enthalpy drop in turbine. Therefore, there is
an optimal PPTD of the evaporator to maximize the net power
output.
Comparison with other waste heat resources like the
geothermal energy, the low temperature flue gas has several
distinct features in the waste heat recovery system. Of which, the
temperature of the flue gas at the evaporator outlet should exceed
90 C to avoid the low temperature corrosion. Therefore, organic
a
3. Results and discussion
The cost-effective performance is determined by the electric
energy production and investment of the ORC system, which can be
measured by the net power output and the heat transfer area. In
this work, we focused on the dry and isentropic organic working
fluids.
b
Table 2
Selections of pinch point temperature difference in references.
Fluids
Heat source
Cold
source
DTe DTc Ref.
R134a, R123, R227ea, R245fa, R290,
n-pentane
R113, R245ca, isobutene, R123
Water, ammonia, Butane, Isobutene,
R11, R236EA R123, R141B, R113,
R245CA
R134a
R227ea, Isobutane, R245fa, opentane
Hot air
Water
10
5
[6]
Water
Flue gas
Water
e
15
8
15
e
[14]
[22]
Water/steam
Hot water
11
5
6
5
[31]
[13]
R123
Flue gas
Air
Cold
water
e
10
10
[20]
Fig. 2. Variation of the net power output with the PPTD of the evaporator at
DTT ¼ 20 C. Solid lines correspond to Tg,out 90 C and dashed lines Tg,out < 90 C.
(a) R245fa; 1: Te ¼ 108 C; 2: Te ¼ 110 C; 3: Te ¼ 112 C; (b) R123; 1: Te ¼ 105 C; 2:
Te ¼ 107 C; 3: Te ¼ 109 C.
Y.-R. Li et al. / Energy 42 (2012) 503e509
Fig. 3. The variations of the maximum net power output and the optimal evaporation
temperature with the PPTD of the evaporator at DTT ¼ 20 C. Solid line: Wnet,max;
Dashed line: Te,opt. 1: R245fa; 2: R114; 3: R123; 4: R11.
working fluids can be categorized into two groups at the given
operation conditions according to whether they can achieve the
maximum net power output. With the increase of the PPTD of the
evaporator, isentropic working fluids, for example R245fa and R114,
cannot achieve the maximum value of the net power output at the
restrict condition, as shown in Fig. 2(a). Some attention should be
paid when they are used to recovery the low temperature waste
heat of the flue gas. On the contrary, R123 and R11 belong to the
kind of organic working fluids which can achieve the maximum net
power output at certain evaporation temperature, as shown in
Fig. 2(b).
When the PPTD is determined, the net power output
increases first, and then decreases with the increase of the
evaporation temperature [25]. Therefore, there has been an
optimal evaporation temperature for each PPTD of the evaporator to maximize the net power output at a fixed total PPTD. The
linear relations of the maximum net power output and the
optimal evaporation temperature with the PPTD of the evaporator at DTT ¼ 20 C are shown in Fig. 3. It can be found that the
organic working fluids including R114 and R245fa which cannot
achieve the maximum net power output present better performance than R123 and R11.
The area of heat exchangers contributes largely to the total cost
of the ORC system, therefore, it is necessary to discuss the effect of
the PPTD on the heat transfer area, which has the advantage to
analyze the performance of the ORC. When the total PPTD is given,
with the variation of the PPTD of the evaporator, the heat transfer
area of evaporator and condenser would change simultaneously. It
means that the variation of the PPTD of the evaporator affects the
area of not only evaporator but also condenser.
The heat transfer areas corresponding to the maximum net
power output are calculated at the given conditions shown in
Table 1. In general, the area of the heat exchanger decreases with
the increase of the PPTD at the same heat transfer flux. The rational
allocation of the PPTDs in evaporator and condenser to achieve
more net power output with less heat transfer area by reducing the
system irreversibility is the main task in the optimization process.
As shown in Fig. 4, the area of the evaporator decreases and the area
of condenser increases with the increase of the PPTD of the evaporator. Because the heat transfer coefficient of evaporator is
generally larger than that of condenser, and the temperature variation of cooling air between the inlet and outlet is less than that of
the flue gas in evaporator, and therefore, the area of condenser is
the major source of the total heat transfer area. As a result, the total
area of the heat exchanger is decreasing slightly first and then
increasing gradually after reaching the minimum value at the PPTD
of the evaporator about 7 C.
507
Fig. 4. Variation of the heat transfer area with the PPTD of the evaporator at
DTT ¼ 20 C.
Fig. 5 shows that the variation tendencies of the heat transfer
area for different organic working fluids are the approximate same.
The difference of the total area of the heat exchanger between two
arbitrary organic working fluids decreases with the increase of the
PPTD of the evaporator. It means the choice of the organic working
fluid has a little influence on the heat transfer area. The total area of
the heat exchanger decreases with the increase of the total PPTD for
all organic working fluids. This is because the increase of the PPTD
of the condenser reduces the area of condenser, which is the major
factor of the total heat transfer area.
The good linear relationship between the maximum net power
output and the PPTD of the evaporator is found in the previous part.
However, the growth rate of the total heat transfer area is
a
b
Fig. 5. Variation of the heat transfer area with the PPTD of the evaporator.
(a) DTT ¼ 20 C; (b) DTT ¼ 30 C. 1: R123; 2: R11; 3: R245fa; 4: R114.
508
Y.-R. Li et al. / Energy 42 (2012) 503e509
Fig. 6. Variations of the total heat transfer area and the net power output with the
PPTD of the evaporator at DTT ¼ 20 C.
increasing gradually with the increase of the PPTD of the evaporator. Both the above relationships for R123 can be seen in Fig. 6.
3.2. Cost-effective optimum
Pure pursuit of the net power output is meaningless without
considering the investment in utilizing the low temperature waste
heat effectively. The optimum of the net power output per heat
transfer area has a very important practical significance. The heat
transfer area can be reduced to some extent by matching the
system parameter with the exterior condition for the same power
output. In addition, the above analyses show that both the total
area of heat exchangers and the net power output increase with the
increase of the PPTD of the evaporator. Therefore, it’s necessary to
evaluate the cost-effective performance of the ORC system by ε,
a
b
which is defined as the ratio of the net power output to the total
heat transfer area.
The ratio of the net power output to heat transfer area increases
first, and then decreases for all organic working fluids, as shown in
Fig. 7. Meanwhile, we can see that the ORC system using R11 as the
working fluid always has the best cost-effective performance
although it presents the lowest net power output, as shown in
Fig. 3, compared to other organic working fluids.
It hints that the maximum net power output and the best costeffective performance cannot be achieved at the same time. Those
two aspects should be considered simultaneously in choosing the
most suitable organic working fluids in different designs. Further,
the less system irreversibility is generated in condenser when
isentropic fluids are used. Therefore, we can come to a conclusion
that isentropic fluids show better cost-effective performance than
dry fluids. As shown in Fig. 7, the isentropic fluids including R11 and
R123 present better cost-effective performance than dry working
fluids including R114 and R245fa. The differences of the performance for organic working fluids are reducing along with the
increase of the PPTD of the evaporator. Taking the total PPTD of
20 C as an example, when the PPTD of the evaporator exceeds to
14 C, the difference of ε among the isentropic and dry working
fluids is very small.
4. Conclusions
In this study, we have analyzed the influence of the evaporation
temperature and the PPTD on the performance of the ORC system
in recovering the low temperature waste heat of the flue gas. Based
on the present analysis, the main conclusions can be summarized
as follows:
(1) In order to avoid the low temperature corrosion, some organic
working fluids, such as R114 and R245fa, cannot achieve their
maximum net power output, which should be paid attention to
recover waste heat of the flue gas. Furthermore, it is found that
there has been a linear relationship between the PPTD of the
evaporator and the corresponding maximum net power
output.
(2) The total heat transfer area is decreasing first and then
increasing with the increase of the PPTD of the evaporator. The
differences of the heat transfer area between two arbitrarily
organic working fluids diminish gradually with the increase of
the PPTD of the evaporator. In this case, the choice of organic
working fluids has little difference.
(3) The ratio of the net power output to the heat transfer area is
increasing first, and then decreasing after reaching its
maximum value at an optimal PPTD of the evaporator which
are almost equal to all the organic working fluids studied in the
work. The calculation presents that the ORC system using R11
as the working fluid achieves the largest value of the net power
output per heat transfer area, followed by R123, R245fa and
R114.
Acknowledgment
This work is supported by National Basic Research Program of
China (973 Program, Grant No. 2011CB710701).
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Fig. 7. Variations of ε with the PPTD of the evaporator. (a) DTT ¼ 20 C; (b) DTT ¼ 30 C.
1: R123; 2: R11; 3: R245fa; 4: R114.
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