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Effect of condensation temperature glide on the performance of organic Rankine cycles with zeotropic mixture working fluids
Applied Energy 115 (2014) 394–404
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Effect of condensation temperature glide on the performance of organic Rankine cycles with zeotropic mixture working fluids Qiang Liu, Yuanyuan Duan ⇑, Zhen Yang ⇑ Key Laboratory of Thermal Science and Power Engineering of MOE, Beijing Key Laboratory for CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084, PR China
h i g h l i g h t s A condensation pressure determination method for ORC with zeotropic mixture is given. The effects of condensation temperature glide on the ORC performance are analyzed. Mixture mole fractions for the maximum power output of a geothermal ORC are identified. The biomass ORC performance with part of the latent heat transferred in the IHE is analyzed.
a r t i c l e
i n f o
Article history: Received 20 July 2013 Received in revised form 5 October 2013 Accepted 12 November 2013 Available online 5 December 2013 Keywords: Organic Rankine cycle (ORC) Zeotropic mixture Condensation temperature glide Thermal performance Geothermal energy Biomass energy
a b s t r a c t The organic Rankine cycle (ORC) has been widely used to convert low-grade (<300 °C) thermal energy to electricity. Use of zeotropic mixtures as the working fluids improves the thermodynamic performance of ORC systems due to better matches of the temperature profiles of the working fluid and the heat source/ sink. This paper presents a method to determine the optimal ORC condensation pressure when using a zeotropic mixture. This study also investigates the effects of the condensation temperature glide of the zeotropic mixture on the ORC thermodynamic performance. Geothermal water and biomass are used as the heat sources. Zeotropic mixtures of butane/pentane (R600/R601), butane/isopentane (R600/ R601a), isobutane/pentane (R600a/R601) and isobutane/isopentane (R600a/R601a) were selected as the working fluids for the geothermal ORC with octane/decane, nonane/decane and octamethyltrisiloxane/decamethyltetrasiloxane (MDM/MD2M) selected as working fluids for the cogenerative ORC driven by the biomass energy. Two optimal working fluid mole fractions maximize the cycle efficiency, exergy efficiency and net power output for cooling water temperature increases less than the maximum condensation temperature glide, while the highest net power output appears at the higher mole fraction of the more volatile component for the geothermal ORC when the condensation temperature glide of the working fluid mixture matches the cooling water temperature increase. Higher condensation temperature glides result in large thermal loss to the heat sink and exergy destruction in the condenser. There is only one optimal working fluid mole fraction that maximizes the thermal efficiency, exergy efficiency and net power output when the cooling water temperature increase is greater than the condensation temperature glide. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Over 80% of the world’s current total primary energy supply is from fossil fuels [1] which has led to increasing air pollution and global warming. Use of low-grade thermal energy, such as geothermal heat, solar energy, biomass energy and industrial waste heat, has received more attention recently and systems have been developed to supply electricity to reduce the environmental stresses caused by fossil fuel consumption. ⇑ Corresponding authors. Tel.: +86 10 62796318; fax: +86 10 62770209. E-mail addresses: [email protected] (Q. Liu), [email protected] (Y. Duan), [email protected] (Z. Yang). 0306-2619/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2013.11.036
ORC systems are preferred for use with this abundant lowgrade thermal energy in low and medium temperature (<300 °C) heat sources as an efficient approach due to their higher thermal efficiencies, reliability and flexibility as well as simpler control and lower maintenance costs [2–6] relative to the conventional steam Rankine cycle. For instance, ORC systems have been extensively used to generate electricity from geothermal and biomass heat sources. Some of the critical challenges with ORCs are the working fluid selection and the cycle design [7–14]. Pure fluids consisting of CFCs [7–9], HFCs [9–13,15], hydrocarbons [9,10,12,13,16–18] and siloxanes [14,19,20] are generally chosen as the working fluids for ORC systems. An ideal ORC should have a perfect match between the temperatures of the working
Q. Liu et al. / Applied Energy 115 (2014) 394–404
395
Nomenclature E h m p Q s T W x
exergy (kW) specific enthalpy (kJ/kg) mass flow rate (kg/s) pressure (MPa) heat flow rate (kW) specific entropy (kJ/kg K) temperature (°C) power (kW) mole fraction
Acronyms CFCs chlorofluorocarbons CHP combined heat and power HFCs hydrofluorocarbons HTF heat transfer fluid IHE internal heat exchanger ORC organic Rankine cycle Greek symbols g efficiency D difference of temperature
fluid and the heat source and heat sink to reduce exergy losses during the heat transfer. Subcritical ORCs, which are operated at pressures below the critical point, have isothermal evaporation and condensation processes that result in bad temperature matches between the working fluid and the heat source and sink which lead to large heat transfer irreversibilities [21,22]. In contrast, supercritical ORCs can have better temperature matches with the heat source; however, their operating pressures are much higher than for the subcritical cycles. The heat exchangers in supercritical ORC systems are also larger since the overall heat transfer coefficient decreases as the operating pressure increases [23]. Zeotropic mixtures have non-isothermal evaporation and condensation. During the evaporation and condensation, the mixture temperature glides (changes) due to the changing component concentrations in each phase of the mixture. Thus, the use of zeotropic mixtures instead of pure fluids as the ORC working fluids can provide better temperature matches with the heat source and sink temperatures which will reduce the exergy losses and increase the cycle efficiency. Chen et al. [22] proposed a supercritical ORC using R134a/R32 as the working fluid and analyzed its performance with an average condensation temperature of 309.5 K. They found that the cycle efficiency was increased by 10–30% with R134a/R32 compared to a cycle with R134a. Angelino and Colonna di Paliano [24,25] investigated ORCs with mixtures of hydrocarbons for a low temperature heat source and with mixtures of siloxanes for waste heat recovery. Their results showed that the mixture working fluids have better thermodynamic performance than pure fluids. Wang and Zhao [26] analyzed the performance of a low-temperature solar ORC using zeotropic mixtures of R245fa and R152a at a fixed condensation bubble point temperature of 25 °C. Their experimental results [27] showed that the zeotropic mixtures of R245fa and R152a had higher collector and thermal efficiencies than those with pure R245fa. The thermal efficiency was then significantly increased when the cycle was combined with an internal heat exchanger (IHE). Heberle et al. [28] investigated the second law efficiencies of zeotropic mixtures as the working fluids for geothermal ORCs. The results showed that the efficiency increased by up to 15% using mixtures as the working fluids compared to the most efficient pure fluid for heat source temperatures below 120 °C. Chys et al. [29] discussed a mixture
X
exergy destruction rate
Subscripts 0–4 points corresponding to Figs. 1–4 C condenser E evaporator en environment ex exergy efficiency glide temperature glide H heat transfer fluid IHE internal heat exchanger in inlet O organic working fluid ORC organic Rankine cycle out outlet p pump s isentropic T turbine th thermal efficiency w cooling water
selection method and optimized the mixture concentrations to get the maximum ORC thermal efficiency. Their results showed that the cycle efficiency and power output increased significantly for lower temperature heat sources and when the temperature change in the heat source heat exchanger was relatively large. Li et al. [30] optimized the performance of an ORC condenser using a binary mixture. They theoretically analyzed the performance for fixed dew point and bubble point temperatures. Yin et al. [31] investigated the influences of SF6 concentration on the cycle efficiency, heat exchanger size and heat transfer coefficients in the evaporator and condenser for a geothermal ORC using a mixture of SF6 and CO2. Their results demonstrated how zeotropic binary mixtures can increase the thermal efficiencies of geothermal ORC. These previous studies have analyzed the effect of the evaporation temperature glide on the cycle performance with little consideration of the effect of the condensation temperature glide. The condensation temperature glide is higher than the evaporation temperature glide for a zeotropic mixture, but the temperature increase in the heat sink is less than for the heat transfer fluid temperature drop in the heat source for ORC systems. Therefore, the temperature match of the condensation process strongly affects the ORC performance because the mixture temperature glide and coolant temperature increase determine the condensation pressure (temperature) that then affects the cycle performance. This work focuses on the effect of the condensation temperature glide of zeotropic mixtures on ORC performance. This study analyzes the dependency of the cycle thermal efficiency, net power output and exergy efficiency on the condensation temperature glide. 2. Methodology 2.1. System model A schematic of the o2 ORC [10] considered in this study is shown in Fig. 1. The o2 cycle is a subcritical cycle with saturated vapor at the turbine inlet [10]. The cycle has a relatively high thermal efficiency for turbine inlet temperatures below 90% of the critical temperature of the working fluid [17]. Cycles operated at supercritical pressures have better temperature matches with the
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(a)
TH1
(a) butane Heat source Temperature, T
TH2 ΔTE
4
TH3
0
1 3 2
ΔTw
2'
ΔTC
Tw,in
Tw,out
Heat sink
(b)
Entropy, s
(b) butane/pentane (0.9/0.1)
TH1
Temperature, T
Heat source
X
_ in ¼ m
_ ¼ Q_ W
X
X
_ ¼ E_ heat W
_ out m
ð1Þ
_ out hout m
X
E_ out
X
X
_ in hin m
E_ in þ I_
ΔTC
Tw,out Heat sink
ΔTw
TH1
Heat source
Temperature, T
TH2 Δ TE
TH3
0
4 1
Tglide
3 2 Tw,in
2' Tw,out Heat sink
Δ Tw
Entropy, s
ð3Þ
ð4Þ
1 2'
(c) butane/pentane (0.5/0.5)
ð2Þ
The turbine inlet temperature, T0, is equal to T4 for pure fluids and is equal to the dew point temperature for zeotropic mixtures at the turbine inlet pressure (also the pressure of point 4). TH2 is the HTF temperature at the evaporator outlet.
0
4
Entropy, s
Δ TC
_ _ is the mass flow rate of the fluid, Q_ is the net heat input, W where m is the net power output, h is the specific enthalpy, the subscripts in and out stand for inlet and outlet, E_ heat is the net heat exergy input and I_ is the exergy destruction. _ O , is determined by the energy The working fluid flow rate, m balance in the evaporator. At the pinch point in the evaporator (Fig. 2), the temperature difference between the heat source heat transfer fluid (HTF) and the working fluid, DTE, is
DT E ¼ T H2 T 4
ΔTE
TH3
Tglide 3 2 Tw,in
Fig. 1. Schematic of an o2 ORC: (a) without an IHE and (b) with an IHE.
heat sources than the o2 cycles, but the operating pressures are much higher and the heat transfer area is much larger (due to the lower heat transfer coefficients at supercritical conditions); thus, they are not considered in this paper. Only the thermal performance of the o2 cycle is studied. Two types of heat sources are considered with geothermal water at 140 °C and thermal oil at 300 °C heated by biomass energy. The thermal performance characteristics of the ORC including the thermal efficiencies, net power outputs and exergy efficiencies are analyzed for the two heat sources, especially the effects of the condensation temperature glide. Mass, energy and exergy balances for any control volume at steady state with negligible potential and kinetic energy changes can be expressed as
TH2
Fig. 2. Temperature-entropy diagrams of an ORC without an IHE.
The work generated by the turbine is
_ T¼m _ O ðh0 h1s ÞgT ¼ m _ O ðh0 h1 Þ W
ð5Þ
where gT is the turbine isentropic efficiency, h0 is the enthalpy of the working fluid at the evaporator outlet, h1s is the turbine outlet enthalpy for an isentropic expansion process and h1 is the real enthalpy at the turbine outlet. The power consumed by the pump can be defined as
_ O ðh3s h2 Þ _ p¼m _ O ðh3 h2 Þ W ¼m
gps
ð6Þ
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(a)
(a)
octane/decane (0.9/0.1)
octane/decane (0.5/0.5)
Heat source
0
4
1
3a
Tglide 3 2 Tw,in
2'
u Liq
1a
3
n rbi
ork id w
Heat sink Entropy, s
1
por
3a
fl i ng
Tw,out
(b)
Temperature, T
Tu
ΔTC
Tw,in
1
xh ee
1a 2'
3 2
ΔTw
t va a us
1
3a
ΔTC Tw,out
Heat sink Entropy, s
0
4
1a
(b)
Temperature, T
Temperature, T
Temperature, T
Heat source
u id
i ne rb Tu
or vap ust a exh
Two phase region
1a
2'
ui Liq
i flu ng rki o dw
3a
d
Δ TIHE
Δ TIHE
3' 3 Heat flow, Q
Heat flow, Q
Fig. 3. ORC conditions with an IHE for Tglide 6 DTIHE + DTp: (a) temperature–entropy diagram and (b) IHE temperature profiles.
where gps is the pump isentropic efficiency, h3s is the working fluid enthalpy after the pump for an isentropic process, h2 and h3 are the enthalpies at the pump inlet and outlet. The net power generated by the ORC is defined as
_ net ¼ W _ TW _p W
ð7Þ
The energy transferred to the ORC from the HTF is defined as
_ H ðhH1 hH3 Þ Q_ H ¼ m
ð8Þ
_ H is the heat transfer fluid (HTF) flow rate, hH1 and hH3 are where m the HTF enthalpies at the evaporator inlet and preheater outlet. The ORC thermal efficiency is defined as
_ W
gth ¼ _ net QH
ð9Þ
The thermal efficiency of the cogenerative ORC driven by the biomass energy does not consider the heat supplied to the cogeneration heating system [14,32]. The ORC exergy efficiency is defined as
_ W
gex ¼ _ net EH
ð10Þ
where E_ H is the exergy input to the ORC. For the geothermal ORC, E_ H is calculated as
_ H ½ðhH1 hen Þ T en ðsH1 sen Þ E_ H ¼ m
Fig. 4. ORC conditions with an IHE for Tglide > DTIHE + DTp: (a) temperature–entropy diagram and (b) IHE temperature profiles.
Table 1 Operating parameters for the geothermal ORC without an IHE. Parameter
Value
_ H /kgs1 Geothermal water flow rate, m Geothermal water inlet temperature, TH1/°C Evaporator inlet temperature, T4/°C Evaporator pinch temperature, DTE/°C Condenser pinch temperature, DTC/°C Cooling water inlet temperature, Tw,in/°C Cooling water outlet temperature, Tw,out/°C Turbine efficiency, gT/% Pump isentropic efficiency, gps/%
1 140 80 10 5 20 25 85 65
For the cogenerative ORC, E_ H is calculated as
_ H cp ½ðT H1 T H3 Þ T en lnðT H1 =T H3 Þ E_ H ¼ m
where cp is the isobaric specific heat of the thermal oil, TH1 and TH3 are the HTF temperatures at the evaporator inlet and preheater outlet. The exergy destruction rate, Xi, in each component of the ORC is defined as
Xi ¼ ð11Þ
where hen and sen are the reference values of the enthalpy and entropy at the reference (environment) temperature, Ten.
ð12Þ
Ii E_ H
ð13Þ
The heat sink uses water to cool the working fluid. The condensation temperature should always be as low as possible to increase the cycle efficiency and power output. However, this is not possible
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(a) . mH , TH1 , T4 , ΔTE , ΔTC , Tw,in , Tw,out , c p ,w , Ten , x1 , x2 ,ηT ,η ps
pC
0.5
Condensation pressure, pC (MPa)
(a)
p2′ = pC
. . mO , mw , T2 , T2′, T0 , T1 , ΔTw
T2′ = Tw,in + ΔTw + ΔTC
0.4
0.3
0.2
0.1
0.0 0.0
Condensation pressure, pC (MPa)
. mO , T0 , T1 , p1 , η th ,ηex , Wnet , ΩC
(b)
0.6
0.8
1.0
Octane/Decane MDM/MD2M Nonane/Decane
0.025
0.000 0.0
. mH , TH1 , ΔTH3 , T4 , ΔTC , Tw,in , Tw,out , c p ,th , Ten , x1 , x2 ,ηT ,η ps
0.2
0.4
0.6
0.8
1.0
Mole fraction of the more volatile component, x1 Fig. 6. Condensation pressures of the mixtures for various mole fractions of the more volatile component.
T2′ = 100o C, pC = p2′ pC
20
o
Condensation temperature glide, Tglide ( C)
Tglide ≤ ΔTIHE + ΔTp
0.4
(b) 0.050
T2 = Tw,in + ΔTC , pC = p2
. mO , T0 , T1 , T2 , T3 , p1
0.2
Mole fraction of the more volatile component, x1
T2′ − T2 ≤ ΔTw
η th ,ηex , Wnet , ΩC
R600/R601 R600/R601a R600a/R601 R600a/R601a
T2 , T2′, T3 , T3′, T1a , T3a
T1a = Tw,out + ΔTC η th ,ηex , Wnet , ΩC η th ,ηex , Wnet , ΩC
Fig. 5. Flow charts for the condensation pressure determination.
15
R600/R601 R600/R601a R600a/R601 R600a/R601a
Octane/Decane MDM/MD2M Nonane/Decane
10
5
0 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction of the more volatile component, x1 in cogenerative applications due to the temperature requirements of the subsequent heat use (80 °C for industrial or domestic heating, 100 °C for thermally activated cooling). Therefore, the cooling water temperature increase for an ORC driven by geothermal heat was set to 5 °C while for a cogenerative ORC driven by the biomass heat was set to 20 °C due to the cogeneration heating demand. Fig. 2 shows the temperature–entropy diagrams of o2 cycles without an IHE using a pure fluid (butane) and mixtures (butane and pentane) for a geothermal heat source with a geothermal water inlet temperature, TH1, of 140 °C. When the working fluid is a pure fluid, the condensation temperature is constant at:
T 2 ¼ T 02 ¼ T w;in þ DT w þ DT C
ð14Þ
Fig. 7. Condensation temperature glides of zeotropic mixtures for various mole fractions of the more volatile component.
where Tw,in is the cooling water inlet temperature, DTw is defined here as the cooling water temperature increase just due to the latent heat (DTw – Tw,out Tw,in for a superheated working fluid at the condenser inlet) and DTC is the pinch point temperature difference required by the heat transfer conditions in the condenser. The cooling water inlet temperature, Tw,in, depends on the environmental conditions and the pinch point temperature difference, DTC, which is generally 5–10 °C. These two parameters are assumed to not change much when the influences of weather or
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Thus, the condensation pressure is the dew point pressure of the mixture working fluid when Tglide 6 DTw. When Tglide > DTw, the pinch point appears at the bubble point of the mixture working fluid (Fig. 2c) where the working fluid temperature at this point, T2, can be expressed as
Table 2 Operating parameters for the cogenerative ORC with an IHE. Parameter
Value
Thermal oil inlet temperature, TH1/°C Thermal oil outlet temperature, TH3/°C Evaporator inlet temperature, T4/°C Condenser pinch temperature, DTC/°C IHE pinch temperature, DTIHE/°C Cooling water inlet temperature, Tw,in/°C Cooling water outlet temperature, Tw,out/°C Turbine efficiency, gT/% Pump isentropic efficiency, gps/%
300 240 240 10 10 70 90 85 65
T 2 ¼ T w;in þ DT C
ð16Þ
Thus, the condensation pressure is the bubble point pressure of the mixture working fluid when Tglide > DTw. With the biomass heat source, the turbine exhaust vapor temperature is relatively high and an IHE can be used to recover the waste heat to improve the cycle thermal efficiency [29,32]. DTIHE denotes the minimum temperature difference between the turbine exhaust vapor and the liquid working fluid in the IHE. When Tglide 6 DTIHE + DTp (DTp = T3 T2 denotes the working fluid temperature increase in the pump), DTIHE is the difference between the IHE exit vapor temperature and the IHE inlet liquid temperature as shown in Fig. 3,
climate change are neglected. Thus, the cooling water temperature increase, DTw, needs to be low to obtain a lower condensation temperature that will increase the cycle efficiency and power output. Water is used here as the condenser coolant due to its high heat capacity that reduces the temperature increase during the cooling of the working fluid. In this study, the cooling water temperature increase was set to 5 °C for the ORCs driven by the geothermal water. When a zeotropic mixture working fluid is used, the temperature glide of the working fluid during condensation and the pinch point temperature difference between the mixture and the cooling water need to be carefully evaluated. When the temperature glide, Tglide, is lower than the cooling water temperature increase, DTw, the pinch point occurs at the dew point of the mixture (Fig. 2b) with its temperature, T 02 , expressed as
where T1a is the exit vapor temperature after being cooled in the IHE and T3 is the inlet liquid temperature as shown in Fig. 3b. The pinch point in the condenser occurs at the dew point of the mixture. When Tglide > DTIHE + DTp, the working fluid may condense in the IHE and the pinch point will occur at the dew point, 20 , as shown in Fig. 4, resulting in a wet exiting vapor (point 1a is in the two-phase region) as shown in Fig. 4b. Then, the pinch point in the IHE is determined by
T 02 ¼ T w;in þ DT w þ DT C
DT IHE ¼ T 02 T 03
6
10.4
4
10.2
2
0.6
0.8
0 1.0
8 10.6 6 10.4 4 10.2
10.0 0.0
2
0.2
10.8
12
10.4
9
10.2
6
10.0
3
0.4
0.6
Mole fraction of R600a, xR600a
0.8
0 1.0
Cycle thermal efficiency, ηth(%)
o
Condensation temperature glide, Tglide( C)
Cycle thermal efficiency, ηth(%)
15
10.6
0.2
0.4
0.6
0.8
0 1.0
Mole fraction of R600, xR600
(c) R600a/R601a
9.8 0.0
o
10
10.8
Mole fraction of R600, xR600 10.8
12
(b) R600/R601
20
(d) R600a/R601
o
0.4
ð18Þ
10.6
15
10.4 10 10.2 5
10.0
9.8 0.0
0.2
0.4
Condensation temperature glide, Tglide( C)
0.2
Cycle thermal efficiency, ηth(%)
o
10.6
10.0 0.0
11.0
ð17Þ
Condensation temperature glide, Tglide( C)
8
(a) R600/R601a
Condensation temperature glide, Tglide( C)
Cycle thermal efficiency, ηth(%)
10.8
ð15Þ
DT IHE ¼ T 1a T 3
0.6
0.8
0 1.0
Mole fraction of R600a, xR600a
Fig. 8. Thermal efficiencies of the geothermal ORC without an IHE for various mole fractions of the more volatile component (evaporator inlet temperature is 80 °C and geothermal inlet temperature is 140 °C).
Cycle thermal efficiency, ηth(%)
60
55
50
R600/R601 R600/R601a R600a/R601 R600a/R601a
45
40 0.0
0.2
0.4
0.6
0.8
T1a
20.5
T'2 10
20.0 5 19.5
0.2
0.4
0.6
0.8
0 1.0
Mole fraction of octane, xoctane
Cycle thermal efficiency, ηth(%)
o
200
o
15
21.0
210
20
T1a< T'2
21.0
1.0
(b) 220
Octane/Decane MDM/MD2M Nonane/Decane
(b) MDM/MD2M
15
20.5 10 20.0 5 19.5
19.0 0.0
0.2
0.4
0.6
0.8
0 1.0
Mole fraction of MDM, xMDM
180 0.0
0.2
0.4
0.6
0.8
1.0 20.6
Fig. 9. Turbine outlet temperatures for various mole fractions of the more volatile component.
T 03
where is the temperature of the liquid working fluid after being heated by part of the latent heat (20 1a) of the working fluid in the IHE and T 02 is the dew point temperature at the condensation pressure of the working fluid. 2.2. Working fluids Isobutane (R600a) and isopentane (R601a) have been used as pure working fluids in geothermal ORC systems [33] and are used here as representative examples of pure fluids. Zeotropic mixtures of butane/pentane (R600/R601), butane/isopentane (R600/R601a), isobutane/pentane (R600a/R601) and isobutane/isopentane (R600a/R601a) were selected as the mixture working fluids for the geothermal ORC in this paper. Complex working fluids with higher critical temperatures, like decane, octane, toluene, benzene and siloxane, are generally used as the working fluid for cogenerative ORC [14,32,34–36]. Zeotropic mixtures of octane/decane, nonane/decane and MDM/MD2M were selected as the working fluids for the cogenerative ORC driven by the biomass energy. The thermodynamic properties of the selected zeotropic mixtures were calculated using the REFPROP 9.0 software [37]. The condensation temperature glide of mixtures varies with the component mole fractions. The mole fractions in this study were varied from 0.1 to 0.9. The component mole fractions may differ from the nominal values due to the component differential hold up of the two-phase flow in the condenser and evaporator [28]. This difference increases as the temperature glide of the mixture increases [38–40]. In this paper, the selected mole fractions caused temper-
Cycle thermal efficiency, ηth(%)
Mole fraction of the more volatile component, x1
6
(c) Nonane/Decane
o
Turbine outlet temperature, T1 ( C)
(a) Octane/Decane
19.0 0.0
Mole fraction of the more volatile component, x1
190
21.5
o
o
Turbine outlet temperature, T1 ( C)
65
20.4 4 20.2 2 20.0
19.8 0.0
0.2
0.4
Condensation temperature glide, Tglide( C)
(a)
Condensation temperature glide, Tglide( C)
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Condensation temperature glide, Tglide( C)
400
0.6
0.8
0 1.0
Mole fraction of nonane, xnonane Fig. 10. Thermal efficiencies of the cogenerative ORC with an IHE for various mole fractions with an evaporator inlet temperature of 240 °C.
ature glides of less than 17.5 °C. The effect of the mole fraction difference due to hold up is not considered in the calculations. 2.3. Study cases The condensation pressure and temperature should be as low as possible to increase the thermal efficiency and power output of a geothermal ORC. The total cooling water temperature increase was set to 5 °C, which is representative of many real systems. An internal heat exchanger (IHE) can be used to improve the cycle thermal efficiency to recover part of the waste heat when the turbine exhaust vapor is superheated [41]. However, the net power output is not affected by the IHE for a fixed evaporation temperature [13] (the evaporator inlet temperature was 80 °C for the geothermal ORC cases used here) because the working fluid flow rate and specific work are not changed. Thus, an IHE is not used for the
401
6
32
4
31
2
0.6
0.8
0 1.0
9
32
6
31
3
30 0.0
0.2
Mole fraction of R600, xR600
33
8
32 4 31
0.4
0.6
0.8
0 1.0
Mole fraction of R600a, xR600a
Net power output, Wnet (kW)
12 34
0.2
35
o
(c) R600a/R601a
30 0.0
0.6
0.8
0 1.0
Mole fraction of R600, xR600 Condensation temperature glide, Tglide( C)
Net power output, Wnet (kW)
35
0.4
20
(d) R600a/R601
o
0.4
33
34 15 33 32
10
31 5 30 29 0.0
0.2
Condensation temperature glide, Tglide ( C)
0.2
12
(b) R600/R601
o
o
33
30 0.0
34
Condensation temperature glide, Tglide( C)
8
(a) R600/R601a
Net power output, Wnet (kW)
Net power output, Wnet (kW)
34
Condensation temperature glide, Tglide( C)
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0.4
0.6
0.8
0 1.0
Mole fraction of R600a, xR600a
Fig. 11. Net power outputs of the geothermal ORC without an IHE for various mole fractions of the more volatile component.
geothermal ORC to reduce the system complexity and cost. The operating parameters and boundary conditions for the geothermal ORC are listed in Table 1. The flow chart for the pressure zdetermination process is shown in Fig. 5a. The condensation pressures are shown in Fig. 6a for the various mole fractions of the working fluid, with the corresponding condensation temperature glides shown in Fig. 7. The cogenerative ORC driven by biomass energy has received increasing attention for applications related to combined heat and power (CHP) generation and small scale distributed electricity generation. A typical cogenerative ORC system driven by biomass energy includes a thermal oil boiler and an ORC. The thermal oil circuit operating temperature is generally between 240 °C and 300 °C. The selected working fluids for the cogenerative ORC have relatively high normal boiling temperatures with high condensation temperatures close to 100 °C. In the cogenerative ORC, the cooling water is heated to a relatively high temperature and used to supply heat. In this analysis, the cooling water temperature at the condenser inlet was set to 70 °C with the water outlet temperature set to 90 °C. The operating parameters and boundary conditions for the cogenerative ORC are listed in Table 2. The temperature drop in the turbine is lower with the complex fluid as the working fluid, while the turbine outlet temperature is higher. Thus, an IHE is used to recover the heat in the exhaust vapor to improve the cycle thermal efficiency. The total cooling water temperature increase was set to 20 °C, the same as for the pure fluids, which is higher than the maximum condensation temperature glide of the selected mixtures for the cogenerative ORC. Therefore, the condensation pressure was
determined based on the dew point pressure at temperature T 02 or the pressure at T1a for Tglide > DTIHE + DTp with part of the latent heat recovered in the IHE. The pinch point temperature differences in the condenser and IHE were both set to 10 °C. Since the cooling water temperature at the condenser outlet is 90 °C, T 02 is 100 °C (DTw = Tw,out Tw,in because the superheat degree is very small for the mixtures) for Tglide 6 DTIHE + DTp and T1a is 100 °C for Tglide > DTIHE + DTp. The flow chart for the pressure determination process is shown in Fig. 5b. The condensation pressures are shown in Fig. 6b with the condensation temperature glides shown in Fig. 7. The maximal condensation temperature glide is about 17.5 °C. Note that the maximum temperature glide does not always occur at a mole fraction of x1 = 0.5 due to the non ideal behavior of each component. In addition, the temperature glides for each mixture shown in Fig. 7 are at different condensation pressures. The major aim of a power plant is to output the maximum power with the highest thermal efficiency and exergy efficiency. Thus, the thermal efficiency, net power output and exergy efficiency are generally used to evaluate the power plant thermal performance. The effects of the condensation temperature glide on the thermal efficiency, net power output and exergy efficiency will be analyzed in the next section. 3. Results and discussion 3.1. Effect of the condensation temperature glide on the cycle thermal efficiency Fig. 8 shows the thermal efficiency of the geothermal ORC without an IHE for mixtures with various mole fractions at an
Q. Liu et al. / Applied Energy 115 (2014) 394–404
o
20
(a) Octane/Decane
T1a< T'2
35
15
34
T1a
T'2
10
33 5
32
31 0.0
0.2
0.4
0.6
0.8
0 1.0
Cycle exergy efficiency, ηex (%)
Net power output, Wnet (kW)
36
Condensation temperature glide, Tglide( C)
402
33 5 32
0.6
0.8
0 1.0
Net power output, Wnet (kW)
5
(c) Nonane/Decane
o
34.0
4 33.5 3
2 33.0 1
32.5 0.0
0.2
0.4
Condensation temperature glide, Tglide ( C)
Mole fraction of MDM, xMDM
0.6
0.8
0 1.0
Mole fraction of nonane, xnonane Fig. 12. Net power outputs of the cogenerative ORC for various mole fractions of the more volatile component.
evaporator inlet temperature of 80 °C and geothermal water inlet temperature of 140 °C. The maximum condensation temperature glides for R600/R601a, R600/R601, R600a/R601a and R600a/R601 all occur at a mole fraction of 0.5 and are higher than the cooling water temperature increase. For the mixture of R600 and R601a, the cycle thermal efficiency first increases with increasing condensation temperature glide when the condensation temperature glide is less than the cooling water temperature increase for xR600 < 0.2. The maximum thermal efficiency at about xR600 = 0.2 occurs when the condensation temperature glide is about equal to the cooling water temperature increase and then begins to decrease to a minimum at about xR600 = 0.5 where the condensation temperature glide is 6.48 °C. At xR600 = 0.8, the thermal efficiency reaches another maximum when the condensation temperature glide drops to about 5 °C. Note that for both efficiency maxima,
Exergy destruction rate in the condenser, ΩC (%)
o
10
0.4
0.2
0.4
0.6
0.8
1.0
Fig. 13. Exergy efficiency of the geothermal ORC for various mole fractions.
18
R600/R601 R600/R601a R600a/R601 R600a/R601a
16
14
12
10
8 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction of more volatile component, x1 Fig. 14. Exergy destruction rate in the condenser for the geothermal ORC as a function of mole fraction.
47
Cycle exergy efficiency, ηex (%)
Condensation temperature glide, Tglide( C)
Net power output, Wnet (kW)
15
34
0.2
38
Mole fraction of more volatile component, x1
(b) MDM/MD2M
31 0.0
R600/R601 R600/R601a R600a/R601 R600a/R601a
40
36 0.0
Mole fraction of octane, xoctane 35
42
46 45 44 43 Octane/Decane MDM/MD2M Nonane/Decane
42 41 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction of more volatile component , x 1 Fig. 15. Exergy efficiency of the cogenerative ORC for various mole fractions.
the condensation temperature glides are both close to the cooling water temperature increase and the heat transfer irreversibility in the condenser is minimized [28]. When the condensation temperature glide does not match the cooling water temperature increase, the cycle thermal efficiency decreases. Similar conclusions can be
403
drawn for the other mixtures in Fig. 8b–d. Note that the mixtures will have lower cycle thermal efficiencies than pure fluids when the condensation temperature glide is much higher than the cooling water temperature increase. The turbine outlet temperature reaches a maximum at 0.3–0.4 mole fraction of the more volatile component for the selected mixtures, as shown in Fig. 9a. Thus, the thermal loss to the heat sink also reaches a maximum at 0.3– 0.4 mole fraction of the more volatile component resulting in a lower thermal efficiency and power output. Fig. 10 shows the cycle thermal efficiency as a function of the mole fraction of the more volatile component for the cogenerative ORCs with an IHE. The dashed line in Fig. 10a shows the cycle thermal efficiency with the turbine exhaust vapor only cooled to the dew point temperature in the IHE while the solid line shows the efficiency with the turbine exhaust vapor cooled to a wet vapor (vapor and liquid) when the condensation temperature glide is greater than 10 °C + DTp (see the analysis about the IHE pinch point in Section 2). Since more waste heat is recovered, cycles with the turbine exhaust vapor cooled to a wet vapor in the IHE have higher efficiencies than those with the vapor only cooled to the dew point. For instance, the thermal efficiency with 0.5/0.5 (octane/decane) is 21.6% when the turbine exhaust vapor is condensed into a wet vapor in the IHE, an increase of about 2.9% relative to the efficiency of 21% when the turbine exhaust vapor is only cooled to the dew point. Fig. 10 also shows that the cycle thermal efficiency is generally higher with a larger temperature glide. For instance in Fig. 10a, the cycle efficiency is 20.6% when Tglide is 6 °C at xoctane = 0.1 and increases to 21.6% when Tglide is 15.7 °C at xoctane = 0.5. At xoctane = 0.5, the cycle thermal efficiency reaches a maximum and the condensation temperature glide is also about the largest. Thus, mixtures will have better cycle efficiencies than pure fluids for the right conditions. 3.2. Effect of the condensation temperature glide on the power output The net power output of the geothermal ORC without an IHE is shown in Fig. 11 as a function of the component mole fraction. Two local maxima also appear in the net power output when the condensation temperature glide is almost equal to the cooling water temperature increase, with the higher maximum at a higher mole fraction of the more volatile component which gives a higher geothermal heat utilization. The geothermal water exhaust temperature, TH3, is higher at lower mole fractions of the more volatile component which reduces the geothermal heat utilization. The mole fraction of the more volatile component should be greater with the condensation temperature glide close to the cooling water temperature increase to give a higher geothermal heat utilization and a higher net power output for a geothermal ORC. The net power output of the geothermal ORC with R600/R601a reaches a minimum at a mole fraction 0.4 of R600 in Fig. 11, when the turbine outlet temperature reaches the maximum as shown in Fig. 9a. The net power output with the R600a/R601 mixture is even lower than with pure R601 for R600a mole fractions between 0.2 and 0.5 due to the relatively large condensation temperature glide as shown in Fig. 11d. The power output of the geothermal ORC with pure R600a is higher than that with pure R600, R601 or R601a. The net power output is 7.7% higher with the R600a/ R601a (0.9/0.1) mixture than with pure R600a and 8.1% higher with the R600a/R601 (0.94/0.06) mixture. The net power output of the cogenerative ORC is shown in Fig. 12 as a function of the mole fraction of the more volatile component. The heat utilized by the cogenerative ORC is constant given the fixed operating parameters of the thermal oil circuit. Therefore, the net power output of the cogenerative ORC corresponds to the cycle thermal efficiency. More power is then generated with a larger temperature glide.
Exergy destruction rate in the condenser, ΩC (%)
Q. Liu et al. / Applied Energy 115 (2014) 394–404
9
8
7
6
5
4 0.0
Octane/Decane MDM/MD2M Nonane/Decane 0.2
0.4
0.6
0.8
1.0
Mole fraction of more volatile component , x1 Fig. 16. Exergy destruction rate in the condenser for the cogenerative ORC as a function of mole fraction.
3.3. Effect of the condensation temperature glide on the exergy efficiency The exergy efficiency corresponds to the net power output according to Eq. (10). Fig. 13 shows the exergy efficiency of the geothermal ORC for various mole fractions. Two local maxima also appear in the exergy efficiency when the condensation temperature glide is almost equal to the cooling water temperature increase with the highest exergy efficiency at a higher mole fraction of the more volatile component. The exergy efficiency decreases significantly at mole fractions with higher condensation temperature glides (Tglide > DTw). The exergy destruction rate in the condenser for the geothermal ORC is shown in Fig. 14 as a function of the mole fraction. The exergy destruction rate first decreases with increasing condensation temperature glide when the condensation temperature glide is less than the cooling water temperature increase, because the temperature difference between the working fluid and the cooling water decreases. The minimum exergy destruction rate occurs when the condensation temperature glide is about equal to the cooling water temperature increase. The exergy destruction rate then begins to increase to the maximum when the condensation temperature glide is higher than the cooling water temperature increase as the temperature difference between the working fluid and cooling water increases. The mixtures with higher condensation temperature glides have higher exergy destruction rates when the condensation temperature glide is higher than the cooling water temperature increase. The exergy efficiency of the cogenerative ORC is shown in Fig. 15 with the exergy destruction rate in the condenser is shown in Fig. 16 for various mole fractions. The cooling water temperature increase is higher than the condensation temperature glide of the working fluid; thus, the exergy efficiency increases as the condensation temperature glide increases, while the exergy destruction rate decreases. The condensation temperature glide is higher, the increase in exergy efficiency is higher but the exergy destruction rate is lower. 4. Conclusions The thermodynamic performance of ORC systems can be improved by using zeotropic mixtures as the working fluid. This paper presents a method to determine the ORC condensation pressure with zeotropic mixtures. When the condensation temperature glide is less than the cooling water temperature increase, the condensation pressure is determined by the mixture dew point and
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the cycle thermal efficiency increases as the condensation temperature glide increases. When the condensation temperature glide is greater than the cooling water temperature increase, the condensation pressure is determined by the mixture bubble point and the cycle thermal efficiency decreases as the condensation temperature glide increases. Higher condensation temperature glides also cause large exergy destruction rates and lower exergy efficiencies. When the cooling water temperature increase is less than the maximum condensation temperature glide of the mixture, two maxima appear in the cycle thermal efficiency, exergy efficiency and net power output at the points where the condensation temperature glide matches the cooling water temperature increase at two different mole fractions of the more volatile component, with the higher power output at the higher mole fraction. When the cooling water temperature increase is higher than the maximum condensation temperature glide of the mixture, the efficiency and power output curves have only one maximum. Higher condensation temperature glides are not better with mixture working fluids for lower cooling water temperature increase. ORC systems have better thermodynamic performance when the condensation temperature glide is nearly equal to the cooling water temperature increase. If the maximum condensation temperature glide is higher than the cooling water temperature increase, the mole fraction of the more volatile component should be high with the condensation temperature glide nearly equal to the cooling water temperature increase to obtain the maximum net power for a geothermal ORC. Acknowledgement This work was supported by the National Natural Science Foundation of China (Grant Nos. 51076074, 51236004 and 51321002). References [1] International Energy Agency (IEA). Key world energy statistics; 2012. [accessed 06.05.13]. [2] Ammar Y, Joyce S, Norman R, Wang YD, Roskilly AP. Low grade thermal energy sources and uses from the process industry in the UK. Appl Energy 2012;89:3–20. [3] Aneke M, Agnew B, Underwood C. Performance analysis of the Chena binary geothermal power plant. Appl Therm Eng 2011;31:1825–32. [4] Stoppato A. Energetic and economic investigation of the operation management of an organic Rankine cycle cogeneration plant. Energy 2012;41:3–9. [5] Roy JP, Mishra MK, Misra A. Performance analysis of an organic Rankine cycle with superheating under different heat source temperature conditions. Appl Energy 2011;88:2995–3004. [6] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic Rankine cycles. Appl Therm Eng 2011;31:2885–93. [7] Badr O, Probert SD, O’Callaghan PW. Selecting a working fluid for a Rankinecycle engine. Appl Energy 1985;21:1–42. [8] Hung TC, Shai TY, Wang SK. A review of organic Rankine cycles (ORCs) for the recovery of low-grade waste heat. Energy 1997;22:661–7. [9] Tchanche BF, Papadakis G, Lambrinos G, Frangoudakis A. Fluid selection for a low-temperature solar organic Rankine cycle. Appl Therm Eng 2009;29:2468–76. [10] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy 2007;32(7):1210–21. [11] Yari M. Exergetic analysis of various types of geothermal power plants. Renew Energy 2010;35:112–21. [12] Lakew AA, Bolland O. Working fluids for low-temperature heat source. Appl Therm Eng 2010;30(10):1262–8.
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Effect of condensation temperature glide on the performance of organic Rankine cycles with zeotropic mixture working fluids Qiang Liu, Yuanyuan Duan ⇑, Zhen Yang ⇑ Key Laboratory of Thermal Science and Power Engineering of MOE, Beijing Key Laboratory for CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084, PR China
h i g h l i g h t s A condensation pressure determination method for ORC with zeotropic mixture is given. The effects of condensation temperature glide on the ORC performance are analyzed. Mixture mole fractions for the maximum power output of a geothermal ORC are identified. The biomass ORC performance with part of the latent heat transferred in the IHE is analyzed.
a r t i c l e
i n f o
Article history: Received 20 July 2013 Received in revised form 5 October 2013 Accepted 12 November 2013 Available online 5 December 2013 Keywords: Organic Rankine cycle (ORC) Zeotropic mixture Condensation temperature glide Thermal performance Geothermal energy Biomass energy
a b s t r a c t The organic Rankine cycle (ORC) has been widely used to convert low-grade (<300 °C) thermal energy to electricity. Use of zeotropic mixtures as the working fluids improves the thermodynamic performance of ORC systems due to better matches of the temperature profiles of the working fluid and the heat source/ sink. This paper presents a method to determine the optimal ORC condensation pressure when using a zeotropic mixture. This study also investigates the effects of the condensation temperature glide of the zeotropic mixture on the ORC thermodynamic performance. Geothermal water and biomass are used as the heat sources. Zeotropic mixtures of butane/pentane (R600/R601), butane/isopentane (R600/ R601a), isobutane/pentane (R600a/R601) and isobutane/isopentane (R600a/R601a) were selected as the working fluids for the geothermal ORC with octane/decane, nonane/decane and octamethyltrisiloxane/decamethyltetrasiloxane (MDM/MD2M) selected as working fluids for the cogenerative ORC driven by the biomass energy. Two optimal working fluid mole fractions maximize the cycle efficiency, exergy efficiency and net power output for cooling water temperature increases less than the maximum condensation temperature glide, while the highest net power output appears at the higher mole fraction of the more volatile component for the geothermal ORC when the condensation temperature glide of the working fluid mixture matches the cooling water temperature increase. Higher condensation temperature glides result in large thermal loss to the heat sink and exergy destruction in the condenser. There is only one optimal working fluid mole fraction that maximizes the thermal efficiency, exergy efficiency and net power output when the cooling water temperature increase is greater than the condensation temperature glide. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Over 80% of the world’s current total primary energy supply is from fossil fuels [1] which has led to increasing air pollution and global warming. Use of low-grade thermal energy, such as geothermal heat, solar energy, biomass energy and industrial waste heat, has received more attention recently and systems have been developed to supply electricity to reduce the environmental stresses caused by fossil fuel consumption. ⇑ Corresponding authors. Tel.: +86 10 62796318; fax: +86 10 62770209. E-mail addresses: [email protected] (Q. Liu), [email protected] (Y. Duan), [email protected] (Z. Yang). 0306-2619/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2013.11.036
ORC systems are preferred for use with this abundant lowgrade thermal energy in low and medium temperature (<300 °C) heat sources as an efficient approach due to their higher thermal efficiencies, reliability and flexibility as well as simpler control and lower maintenance costs [2–6] relative to the conventional steam Rankine cycle. For instance, ORC systems have been extensively used to generate electricity from geothermal and biomass heat sources. Some of the critical challenges with ORCs are the working fluid selection and the cycle design [7–14]. Pure fluids consisting of CFCs [7–9], HFCs [9–13,15], hydrocarbons [9,10,12,13,16–18] and siloxanes [14,19,20] are generally chosen as the working fluids for ORC systems. An ideal ORC should have a perfect match between the temperatures of the working
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Nomenclature E h m p Q s T W x
exergy (kW) specific enthalpy (kJ/kg) mass flow rate (kg/s) pressure (MPa) heat flow rate (kW) specific entropy (kJ/kg K) temperature (°C) power (kW) mole fraction
Acronyms CFCs chlorofluorocarbons CHP combined heat and power HFCs hydrofluorocarbons HTF heat transfer fluid IHE internal heat exchanger ORC organic Rankine cycle Greek symbols g efficiency D difference of temperature
fluid and the heat source and heat sink to reduce exergy losses during the heat transfer. Subcritical ORCs, which are operated at pressures below the critical point, have isothermal evaporation and condensation processes that result in bad temperature matches between the working fluid and the heat source and sink which lead to large heat transfer irreversibilities [21,22]. In contrast, supercritical ORCs can have better temperature matches with the heat source; however, their operating pressures are much higher than for the subcritical cycles. The heat exchangers in supercritical ORC systems are also larger since the overall heat transfer coefficient decreases as the operating pressure increases [23]. Zeotropic mixtures have non-isothermal evaporation and condensation. During the evaporation and condensation, the mixture temperature glides (changes) due to the changing component concentrations in each phase of the mixture. Thus, the use of zeotropic mixtures instead of pure fluids as the ORC working fluids can provide better temperature matches with the heat source and sink temperatures which will reduce the exergy losses and increase the cycle efficiency. Chen et al. [22] proposed a supercritical ORC using R134a/R32 as the working fluid and analyzed its performance with an average condensation temperature of 309.5 K. They found that the cycle efficiency was increased by 10–30% with R134a/R32 compared to a cycle with R134a. Angelino and Colonna di Paliano [24,25] investigated ORCs with mixtures of hydrocarbons for a low temperature heat source and with mixtures of siloxanes for waste heat recovery. Their results showed that the mixture working fluids have better thermodynamic performance than pure fluids. Wang and Zhao [26] analyzed the performance of a low-temperature solar ORC using zeotropic mixtures of R245fa and R152a at a fixed condensation bubble point temperature of 25 °C. Their experimental results [27] showed that the zeotropic mixtures of R245fa and R152a had higher collector and thermal efficiencies than those with pure R245fa. The thermal efficiency was then significantly increased when the cycle was combined with an internal heat exchanger (IHE). Heberle et al. [28] investigated the second law efficiencies of zeotropic mixtures as the working fluids for geothermal ORCs. The results showed that the efficiency increased by up to 15% using mixtures as the working fluids compared to the most efficient pure fluid for heat source temperatures below 120 °C. Chys et al. [29] discussed a mixture
X
exergy destruction rate
Subscripts 0–4 points corresponding to Figs. 1–4 C condenser E evaporator en environment ex exergy efficiency glide temperature glide H heat transfer fluid IHE internal heat exchanger in inlet O organic working fluid ORC organic Rankine cycle out outlet p pump s isentropic T turbine th thermal efficiency w cooling water
selection method and optimized the mixture concentrations to get the maximum ORC thermal efficiency. Their results showed that the cycle efficiency and power output increased significantly for lower temperature heat sources and when the temperature change in the heat source heat exchanger was relatively large. Li et al. [30] optimized the performance of an ORC condenser using a binary mixture. They theoretically analyzed the performance for fixed dew point and bubble point temperatures. Yin et al. [31] investigated the influences of SF6 concentration on the cycle efficiency, heat exchanger size and heat transfer coefficients in the evaporator and condenser for a geothermal ORC using a mixture of SF6 and CO2. Their results demonstrated how zeotropic binary mixtures can increase the thermal efficiencies of geothermal ORC. These previous studies have analyzed the effect of the evaporation temperature glide on the cycle performance with little consideration of the effect of the condensation temperature glide. The condensation temperature glide is higher than the evaporation temperature glide for a zeotropic mixture, but the temperature increase in the heat sink is less than for the heat transfer fluid temperature drop in the heat source for ORC systems. Therefore, the temperature match of the condensation process strongly affects the ORC performance because the mixture temperature glide and coolant temperature increase determine the condensation pressure (temperature) that then affects the cycle performance. This work focuses on the effect of the condensation temperature glide of zeotropic mixtures on ORC performance. This study analyzes the dependency of the cycle thermal efficiency, net power output and exergy efficiency on the condensation temperature glide. 2. Methodology 2.1. System model A schematic of the o2 ORC [10] considered in this study is shown in Fig. 1. The o2 cycle is a subcritical cycle with saturated vapor at the turbine inlet [10]. The cycle has a relatively high thermal efficiency for turbine inlet temperatures below 90% of the critical temperature of the working fluid [17]. Cycles operated at supercritical pressures have better temperature matches with the
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(a)
TH1
(a) butane Heat source Temperature, T
TH2 ΔTE
4
TH3
0
1 3 2
ΔTw
2'
ΔTC
Tw,in
Tw,out
Heat sink
(b)
Entropy, s
(b) butane/pentane (0.9/0.1)
TH1
Temperature, T
Heat source
X
_ in ¼ m
_ ¼ Q_ W
X
X
_ ¼ E_ heat W
_ out m
ð1Þ
_ out hout m
X
E_ out
X
X
_ in hin m
E_ in þ I_
ΔTC
Tw,out Heat sink
ΔTw
TH1
Heat source
Temperature, T
TH2 Δ TE
TH3
0
4 1
Tglide
3 2 Tw,in
2' Tw,out Heat sink
Δ Tw
Entropy, s
ð3Þ
ð4Þ
1 2'
(c) butane/pentane (0.5/0.5)
ð2Þ
The turbine inlet temperature, T0, is equal to T4 for pure fluids and is equal to the dew point temperature for zeotropic mixtures at the turbine inlet pressure (also the pressure of point 4). TH2 is the HTF temperature at the evaporator outlet.
0
4
Entropy, s
Δ TC
_ _ is the mass flow rate of the fluid, Q_ is the net heat input, W where m is the net power output, h is the specific enthalpy, the subscripts in and out stand for inlet and outlet, E_ heat is the net heat exergy input and I_ is the exergy destruction. _ O , is determined by the energy The working fluid flow rate, m balance in the evaporator. At the pinch point in the evaporator (Fig. 2), the temperature difference between the heat source heat transfer fluid (HTF) and the working fluid, DTE, is
DT E ¼ T H2 T 4
ΔTE
TH3
Tglide 3 2 Tw,in
Fig. 1. Schematic of an o2 ORC: (a) without an IHE and (b) with an IHE.
heat sources than the o2 cycles, but the operating pressures are much higher and the heat transfer area is much larger (due to the lower heat transfer coefficients at supercritical conditions); thus, they are not considered in this paper. Only the thermal performance of the o2 cycle is studied. Two types of heat sources are considered with geothermal water at 140 °C and thermal oil at 300 °C heated by biomass energy. The thermal performance characteristics of the ORC including the thermal efficiencies, net power outputs and exergy efficiencies are analyzed for the two heat sources, especially the effects of the condensation temperature glide. Mass, energy and exergy balances for any control volume at steady state with negligible potential and kinetic energy changes can be expressed as
TH2
Fig. 2. Temperature-entropy diagrams of an ORC without an IHE.
The work generated by the turbine is
_ T¼m _ O ðh0 h1s ÞgT ¼ m _ O ðh0 h1 Þ W
ð5Þ
where gT is the turbine isentropic efficiency, h0 is the enthalpy of the working fluid at the evaporator outlet, h1s is the turbine outlet enthalpy for an isentropic expansion process and h1 is the real enthalpy at the turbine outlet. The power consumed by the pump can be defined as
_ O ðh3s h2 Þ _ p¼m _ O ðh3 h2 Þ W ¼m
gps
ð6Þ
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Q. Liu et al. / Applied Energy 115 (2014) 394–404
(a)
(a)
octane/decane (0.9/0.1)
octane/decane (0.5/0.5)
Heat source
0
4
1
3a
Tglide 3 2 Tw,in
2'
u Liq
1a
3
n rbi
ork id w
Heat sink Entropy, s
1
por
3a
fl i ng
Tw,out
(b)
Temperature, T
Tu
ΔTC
Tw,in
1
xh ee
1a 2'
3 2
ΔTw
t va a us
1
3a
ΔTC Tw,out
Heat sink Entropy, s
0
4
1a
(b)
Temperature, T
Temperature, T
Temperature, T
Heat source
u id
i ne rb Tu
or vap ust a exh
Two phase region
1a
2'
ui Liq
i flu ng rki o dw
3a
d
Δ TIHE
Δ TIHE
3' 3 Heat flow, Q
Heat flow, Q
Fig. 3. ORC conditions with an IHE for Tglide 6 DTIHE + DTp: (a) temperature–entropy diagram and (b) IHE temperature profiles.
where gps is the pump isentropic efficiency, h3s is the working fluid enthalpy after the pump for an isentropic process, h2 and h3 are the enthalpies at the pump inlet and outlet. The net power generated by the ORC is defined as
_ net ¼ W _ TW _p W
ð7Þ
The energy transferred to the ORC from the HTF is defined as
_ H ðhH1 hH3 Þ Q_ H ¼ m
ð8Þ
_ H is the heat transfer fluid (HTF) flow rate, hH1 and hH3 are where m the HTF enthalpies at the evaporator inlet and preheater outlet. The ORC thermal efficiency is defined as
_ W
gth ¼ _ net QH
ð9Þ
The thermal efficiency of the cogenerative ORC driven by the biomass energy does not consider the heat supplied to the cogeneration heating system [14,32]. The ORC exergy efficiency is defined as
_ W
gex ¼ _ net EH
ð10Þ
where E_ H is the exergy input to the ORC. For the geothermal ORC, E_ H is calculated as
_ H ½ðhH1 hen Þ T en ðsH1 sen Þ E_ H ¼ m
Fig. 4. ORC conditions with an IHE for Tglide > DTIHE + DTp: (a) temperature–entropy diagram and (b) IHE temperature profiles.
Table 1 Operating parameters for the geothermal ORC without an IHE. Parameter
Value
_ H /kgs1 Geothermal water flow rate, m Geothermal water inlet temperature, TH1/°C Evaporator inlet temperature, T4/°C Evaporator pinch temperature, DTE/°C Condenser pinch temperature, DTC/°C Cooling water inlet temperature, Tw,in/°C Cooling water outlet temperature, Tw,out/°C Turbine efficiency, gT/% Pump isentropic efficiency, gps/%
1 140 80 10 5 20 25 85 65
For the cogenerative ORC, E_ H is calculated as
_ H cp ½ðT H1 T H3 Þ T en lnðT H1 =T H3 Þ E_ H ¼ m
where cp is the isobaric specific heat of the thermal oil, TH1 and TH3 are the HTF temperatures at the evaporator inlet and preheater outlet. The exergy destruction rate, Xi, in each component of the ORC is defined as
Xi ¼ ð11Þ
where hen and sen are the reference values of the enthalpy and entropy at the reference (environment) temperature, Ten.
ð12Þ
Ii E_ H
ð13Þ
The heat sink uses water to cool the working fluid. The condensation temperature should always be as low as possible to increase the cycle efficiency and power output. However, this is not possible
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Q. Liu et al. / Applied Energy 115 (2014) 394–404
(a) . mH , TH1 , T4 , ΔTE , ΔTC , Tw,in , Tw,out , c p ,w , Ten , x1 , x2 ,ηT ,η ps
pC
0.5
Condensation pressure, pC (MPa)
(a)
p2′ = pC
. . mO , mw , T2 , T2′, T0 , T1 , ΔTw
T2′ = Tw,in + ΔTw + ΔTC
0.4
0.3
0.2
0.1
0.0 0.0
Condensation pressure, pC (MPa)
. mO , T0 , T1 , p1 , η th ,ηex , Wnet , ΩC
(b)
0.6
0.8
1.0
Octane/Decane MDM/MD2M Nonane/Decane
0.025
0.000 0.0
. mH , TH1 , ΔTH3 , T4 , ΔTC , Tw,in , Tw,out , c p ,th , Ten , x1 , x2 ,ηT ,η ps
0.2
0.4
0.6
0.8
1.0
Mole fraction of the more volatile component, x1 Fig. 6. Condensation pressures of the mixtures for various mole fractions of the more volatile component.
T2′ = 100o C, pC = p2′ pC
20
o
Condensation temperature glide, Tglide ( C)
Tglide ≤ ΔTIHE + ΔTp
0.4
(b) 0.050
T2 = Tw,in + ΔTC , pC = p2
. mO , T0 , T1 , T2 , T3 , p1
0.2
Mole fraction of the more volatile component, x1
T2′ − T2 ≤ ΔTw
η th ,ηex , Wnet , ΩC
R600/R601 R600/R601a R600a/R601 R600a/R601a
T2 , T2′, T3 , T3′, T1a , T3a
T1a = Tw,out + ΔTC η th ,ηex , Wnet , ΩC η th ,ηex , Wnet , ΩC
Fig. 5. Flow charts for the condensation pressure determination.
15
R600/R601 R600/R601a R600a/R601 R600a/R601a
Octane/Decane MDM/MD2M Nonane/Decane
10
5
0 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction of the more volatile component, x1 in cogenerative applications due to the temperature requirements of the subsequent heat use (80 °C for industrial or domestic heating, 100 °C for thermally activated cooling). Therefore, the cooling water temperature increase for an ORC driven by geothermal heat was set to 5 °C while for a cogenerative ORC driven by the biomass heat was set to 20 °C due to the cogeneration heating demand. Fig. 2 shows the temperature–entropy diagrams of o2 cycles without an IHE using a pure fluid (butane) and mixtures (butane and pentane) for a geothermal heat source with a geothermal water inlet temperature, TH1, of 140 °C. When the working fluid is a pure fluid, the condensation temperature is constant at:
T 2 ¼ T 02 ¼ T w;in þ DT w þ DT C
ð14Þ
Fig. 7. Condensation temperature glides of zeotropic mixtures for various mole fractions of the more volatile component.
where Tw,in is the cooling water inlet temperature, DTw is defined here as the cooling water temperature increase just due to the latent heat (DTw – Tw,out Tw,in for a superheated working fluid at the condenser inlet) and DTC is the pinch point temperature difference required by the heat transfer conditions in the condenser. The cooling water inlet temperature, Tw,in, depends on the environmental conditions and the pinch point temperature difference, DTC, which is generally 5–10 °C. These two parameters are assumed to not change much when the influences of weather or
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Q. Liu et al. / Applied Energy 115 (2014) 394–404
Thus, the condensation pressure is the dew point pressure of the mixture working fluid when Tglide 6 DTw. When Tglide > DTw, the pinch point appears at the bubble point of the mixture working fluid (Fig. 2c) where the working fluid temperature at this point, T2, can be expressed as
Table 2 Operating parameters for the cogenerative ORC with an IHE. Parameter
Value
Thermal oil inlet temperature, TH1/°C Thermal oil outlet temperature, TH3/°C Evaporator inlet temperature, T4/°C Condenser pinch temperature, DTC/°C IHE pinch temperature, DTIHE/°C Cooling water inlet temperature, Tw,in/°C Cooling water outlet temperature, Tw,out/°C Turbine efficiency, gT/% Pump isentropic efficiency, gps/%
300 240 240 10 10 70 90 85 65
T 2 ¼ T w;in þ DT C
ð16Þ
Thus, the condensation pressure is the bubble point pressure of the mixture working fluid when Tglide > DTw. With the biomass heat source, the turbine exhaust vapor temperature is relatively high and an IHE can be used to recover the waste heat to improve the cycle thermal efficiency [29,32]. DTIHE denotes the minimum temperature difference between the turbine exhaust vapor and the liquid working fluid in the IHE. When Tglide 6 DTIHE + DTp (DTp = T3 T2 denotes the working fluid temperature increase in the pump), DTIHE is the difference between the IHE exit vapor temperature and the IHE inlet liquid temperature as shown in Fig. 3,
climate change are neglected. Thus, the cooling water temperature increase, DTw, needs to be low to obtain a lower condensation temperature that will increase the cycle efficiency and power output. Water is used here as the condenser coolant due to its high heat capacity that reduces the temperature increase during the cooling of the working fluid. In this study, the cooling water temperature increase was set to 5 °C for the ORCs driven by the geothermal water. When a zeotropic mixture working fluid is used, the temperature glide of the working fluid during condensation and the pinch point temperature difference between the mixture and the cooling water need to be carefully evaluated. When the temperature glide, Tglide, is lower than the cooling water temperature increase, DTw, the pinch point occurs at the dew point of the mixture (Fig. 2b) with its temperature, T 02 , expressed as
where T1a is the exit vapor temperature after being cooled in the IHE and T3 is the inlet liquid temperature as shown in Fig. 3b. The pinch point in the condenser occurs at the dew point of the mixture. When Tglide > DTIHE + DTp, the working fluid may condense in the IHE and the pinch point will occur at the dew point, 20 , as shown in Fig. 4, resulting in a wet exiting vapor (point 1a is in the two-phase region) as shown in Fig. 4b. Then, the pinch point in the IHE is determined by
T 02 ¼ T w;in þ DT w þ DT C
DT IHE ¼ T 02 T 03
6
10.4
4
10.2
2
0.6
0.8
0 1.0
8 10.6 6 10.4 4 10.2
10.0 0.0
2
0.2
10.8
12
10.4
9
10.2
6
10.0
3
0.4
0.6
Mole fraction of R600a, xR600a
0.8
0 1.0
Cycle thermal efficiency, ηth(%)
o
Condensation temperature glide, Tglide( C)
Cycle thermal efficiency, ηth(%)
15
10.6
0.2
0.4
0.6
0.8
0 1.0
Mole fraction of R600, xR600
(c) R600a/R601a
9.8 0.0
o
10
10.8
Mole fraction of R600, xR600 10.8
12
(b) R600/R601
20
(d) R600a/R601
o
0.4
ð18Þ
10.6
15
10.4 10 10.2 5
10.0
9.8 0.0
0.2
0.4
Condensation temperature glide, Tglide( C)
0.2
Cycle thermal efficiency, ηth(%)
o
10.6
10.0 0.0
11.0
ð17Þ
Condensation temperature glide, Tglide( C)
8
(a) R600/R601a
Condensation temperature glide, Tglide( C)
Cycle thermal efficiency, ηth(%)
10.8
ð15Þ
DT IHE ¼ T 1a T 3
0.6
0.8
0 1.0
Mole fraction of R600a, xR600a
Fig. 8. Thermal efficiencies of the geothermal ORC without an IHE for various mole fractions of the more volatile component (evaporator inlet temperature is 80 °C and geothermal inlet temperature is 140 °C).
Cycle thermal efficiency, ηth(%)
60
55
50
R600/R601 R600/R601a R600a/R601 R600a/R601a
45
40 0.0
0.2
0.4
0.6
0.8
T1a
20.5
T'2 10
20.0 5 19.5
0.2
0.4
0.6
0.8
0 1.0
Mole fraction of octane, xoctane
Cycle thermal efficiency, ηth(%)
o
200
o
15
21.0
210
20
T1a< T'2
21.0
1.0
(b) 220
Octane/Decane MDM/MD2M Nonane/Decane
(b) MDM/MD2M
15
20.5 10 20.0 5 19.5
19.0 0.0
0.2
0.4
0.6
0.8
0 1.0
Mole fraction of MDM, xMDM
180 0.0
0.2
0.4
0.6
0.8
1.0 20.6
Fig. 9. Turbine outlet temperatures for various mole fractions of the more volatile component.
T 03
where is the temperature of the liquid working fluid after being heated by part of the latent heat (20 1a) of the working fluid in the IHE and T 02 is the dew point temperature at the condensation pressure of the working fluid. 2.2. Working fluids Isobutane (R600a) and isopentane (R601a) have been used as pure working fluids in geothermal ORC systems [33] and are used here as representative examples of pure fluids. Zeotropic mixtures of butane/pentane (R600/R601), butane/isopentane (R600/R601a), isobutane/pentane (R600a/R601) and isobutane/isopentane (R600a/R601a) were selected as the mixture working fluids for the geothermal ORC in this paper. Complex working fluids with higher critical temperatures, like decane, octane, toluene, benzene and siloxane, are generally used as the working fluid for cogenerative ORC [14,32,34–36]. Zeotropic mixtures of octane/decane, nonane/decane and MDM/MD2M were selected as the working fluids for the cogenerative ORC driven by the biomass energy. The thermodynamic properties of the selected zeotropic mixtures were calculated using the REFPROP 9.0 software [37]. The condensation temperature glide of mixtures varies with the component mole fractions. The mole fractions in this study were varied from 0.1 to 0.9. The component mole fractions may differ from the nominal values due to the component differential hold up of the two-phase flow in the condenser and evaporator [28]. This difference increases as the temperature glide of the mixture increases [38–40]. In this paper, the selected mole fractions caused temper-
Cycle thermal efficiency, ηth(%)
Mole fraction of the more volatile component, x1
6
(c) Nonane/Decane
o
Turbine outlet temperature, T1 ( C)
(a) Octane/Decane
19.0 0.0
Mole fraction of the more volatile component, x1
190
21.5
o
o
Turbine outlet temperature, T1 ( C)
65
20.4 4 20.2 2 20.0
19.8 0.0
0.2
0.4
Condensation temperature glide, Tglide( C)
(a)
Condensation temperature glide, Tglide( C)
Q. Liu et al. / Applied Energy 115 (2014) 394–404
Condensation temperature glide, Tglide( C)
400
0.6
0.8
0 1.0
Mole fraction of nonane, xnonane Fig. 10. Thermal efficiencies of the cogenerative ORC with an IHE for various mole fractions with an evaporator inlet temperature of 240 °C.
ature glides of less than 17.5 °C. The effect of the mole fraction difference due to hold up is not considered in the calculations. 2.3. Study cases The condensation pressure and temperature should be as low as possible to increase the thermal efficiency and power output of a geothermal ORC. The total cooling water temperature increase was set to 5 °C, which is representative of many real systems. An internal heat exchanger (IHE) can be used to improve the cycle thermal efficiency to recover part of the waste heat when the turbine exhaust vapor is superheated [41]. However, the net power output is not affected by the IHE for a fixed evaporation temperature [13] (the evaporator inlet temperature was 80 °C for the geothermal ORC cases used here) because the working fluid flow rate and specific work are not changed. Thus, an IHE is not used for the
401
6
32
4
31
2
0.6
0.8
0 1.0
9
32
6
31
3
30 0.0
0.2
Mole fraction of R600, xR600
33
8
32 4 31
0.4
0.6
0.8
0 1.0
Mole fraction of R600a, xR600a
Net power output, Wnet (kW)
12 34
0.2
35
o
(c) R600a/R601a
30 0.0
0.6
0.8
0 1.0
Mole fraction of R600, xR600 Condensation temperature glide, Tglide( C)
Net power output, Wnet (kW)
35
0.4
20
(d) R600a/R601
o
0.4
33
34 15 33 32
10
31 5 30 29 0.0
0.2
Condensation temperature glide, Tglide ( C)
0.2
12
(b) R600/R601
o
o
33
30 0.0
34
Condensation temperature glide, Tglide( C)
8
(a) R600/R601a
Net power output, Wnet (kW)
Net power output, Wnet (kW)
34
Condensation temperature glide, Tglide( C)
Q. Liu et al. / Applied Energy 115 (2014) 394–404
0.4
0.6
0.8
0 1.0
Mole fraction of R600a, xR600a
Fig. 11. Net power outputs of the geothermal ORC without an IHE for various mole fractions of the more volatile component.
geothermal ORC to reduce the system complexity and cost. The operating parameters and boundary conditions for the geothermal ORC are listed in Table 1. The flow chart for the pressure zdetermination process is shown in Fig. 5a. The condensation pressures are shown in Fig. 6a for the various mole fractions of the working fluid, with the corresponding condensation temperature glides shown in Fig. 7. The cogenerative ORC driven by biomass energy has received increasing attention for applications related to combined heat and power (CHP) generation and small scale distributed electricity generation. A typical cogenerative ORC system driven by biomass energy includes a thermal oil boiler and an ORC. The thermal oil circuit operating temperature is generally between 240 °C and 300 °C. The selected working fluids for the cogenerative ORC have relatively high normal boiling temperatures with high condensation temperatures close to 100 °C. In the cogenerative ORC, the cooling water is heated to a relatively high temperature and used to supply heat. In this analysis, the cooling water temperature at the condenser inlet was set to 70 °C with the water outlet temperature set to 90 °C. The operating parameters and boundary conditions for the cogenerative ORC are listed in Table 2. The temperature drop in the turbine is lower with the complex fluid as the working fluid, while the turbine outlet temperature is higher. Thus, an IHE is used to recover the heat in the exhaust vapor to improve the cycle thermal efficiency. The total cooling water temperature increase was set to 20 °C, the same as for the pure fluids, which is higher than the maximum condensation temperature glide of the selected mixtures for the cogenerative ORC. Therefore, the condensation pressure was
determined based on the dew point pressure at temperature T 02 or the pressure at T1a for Tglide > DTIHE + DTp with part of the latent heat recovered in the IHE. The pinch point temperature differences in the condenser and IHE were both set to 10 °C. Since the cooling water temperature at the condenser outlet is 90 °C, T 02 is 100 °C (DTw = Tw,out Tw,in because the superheat degree is very small for the mixtures) for Tglide 6 DTIHE + DTp and T1a is 100 °C for Tglide > DTIHE + DTp. The flow chart for the pressure determination process is shown in Fig. 5b. The condensation pressures are shown in Fig. 6b with the condensation temperature glides shown in Fig. 7. The maximal condensation temperature glide is about 17.5 °C. Note that the maximum temperature glide does not always occur at a mole fraction of x1 = 0.5 due to the non ideal behavior of each component. In addition, the temperature glides for each mixture shown in Fig. 7 are at different condensation pressures. The major aim of a power plant is to output the maximum power with the highest thermal efficiency and exergy efficiency. Thus, the thermal efficiency, net power output and exergy efficiency are generally used to evaluate the power plant thermal performance. The effects of the condensation temperature glide on the thermal efficiency, net power output and exergy efficiency will be analyzed in the next section. 3. Results and discussion 3.1. Effect of the condensation temperature glide on the cycle thermal efficiency Fig. 8 shows the thermal efficiency of the geothermal ORC without an IHE for mixtures with various mole fractions at an
Q. Liu et al. / Applied Energy 115 (2014) 394–404
o
20
(a) Octane/Decane
T1a< T'2
35
15
34
T1a
T'2
10
33 5
32
31 0.0
0.2
0.4
0.6
0.8
0 1.0
Cycle exergy efficiency, ηex (%)
Net power output, Wnet (kW)
36
Condensation temperature glide, Tglide( C)
402
33 5 32
0.6
0.8
0 1.0
Net power output, Wnet (kW)
5
(c) Nonane/Decane
o
34.0
4 33.5 3
2 33.0 1
32.5 0.0
0.2
0.4
Condensation temperature glide, Tglide ( C)
Mole fraction of MDM, xMDM
0.6
0.8
0 1.0
Mole fraction of nonane, xnonane Fig. 12. Net power outputs of the cogenerative ORC for various mole fractions of the more volatile component.
evaporator inlet temperature of 80 °C and geothermal water inlet temperature of 140 °C. The maximum condensation temperature glides for R600/R601a, R600/R601, R600a/R601a and R600a/R601 all occur at a mole fraction of 0.5 and are higher than the cooling water temperature increase. For the mixture of R600 and R601a, the cycle thermal efficiency first increases with increasing condensation temperature glide when the condensation temperature glide is less than the cooling water temperature increase for xR600 < 0.2. The maximum thermal efficiency at about xR600 = 0.2 occurs when the condensation temperature glide is about equal to the cooling water temperature increase and then begins to decrease to a minimum at about xR600 = 0.5 where the condensation temperature glide is 6.48 °C. At xR600 = 0.8, the thermal efficiency reaches another maximum when the condensation temperature glide drops to about 5 °C. Note that for both efficiency maxima,
Exergy destruction rate in the condenser, ΩC (%)
o
10
0.4
0.2
0.4
0.6
0.8
1.0
Fig. 13. Exergy efficiency of the geothermal ORC for various mole fractions.
18
R600/R601 R600/R601a R600a/R601 R600a/R601a
16
14
12
10
8 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction of more volatile component, x1 Fig. 14. Exergy destruction rate in the condenser for the geothermal ORC as a function of mole fraction.
47
Cycle exergy efficiency, ηex (%)
Condensation temperature glide, Tglide( C)
Net power output, Wnet (kW)
15
34
0.2
38
Mole fraction of more volatile component, x1
(b) MDM/MD2M
31 0.0
R600/R601 R600/R601a R600a/R601 R600a/R601a
40
36 0.0
Mole fraction of octane, xoctane 35
42
46 45 44 43 Octane/Decane MDM/MD2M Nonane/Decane
42 41 0.0
0.2
0.4
0.6
0.8
1.0
Mole fraction of more volatile component , x 1 Fig. 15. Exergy efficiency of the cogenerative ORC for various mole fractions.
the condensation temperature glides are both close to the cooling water temperature increase and the heat transfer irreversibility in the condenser is minimized [28]. When the condensation temperature glide does not match the cooling water temperature increase, the cycle thermal efficiency decreases. Similar conclusions can be
403
drawn for the other mixtures in Fig. 8b–d. Note that the mixtures will have lower cycle thermal efficiencies than pure fluids when the condensation temperature glide is much higher than the cooling water temperature increase. The turbine outlet temperature reaches a maximum at 0.3–0.4 mole fraction of the more volatile component for the selected mixtures, as shown in Fig. 9a. Thus, the thermal loss to the heat sink also reaches a maximum at 0.3– 0.4 mole fraction of the more volatile component resulting in a lower thermal efficiency and power output. Fig. 10 shows the cycle thermal efficiency as a function of the mole fraction of the more volatile component for the cogenerative ORCs with an IHE. The dashed line in Fig. 10a shows the cycle thermal efficiency with the turbine exhaust vapor only cooled to the dew point temperature in the IHE while the solid line shows the efficiency with the turbine exhaust vapor cooled to a wet vapor (vapor and liquid) when the condensation temperature glide is greater than 10 °C + DTp (see the analysis about the IHE pinch point in Section 2). Since more waste heat is recovered, cycles with the turbine exhaust vapor cooled to a wet vapor in the IHE have higher efficiencies than those with the vapor only cooled to the dew point. For instance, the thermal efficiency with 0.5/0.5 (octane/decane) is 21.6% when the turbine exhaust vapor is condensed into a wet vapor in the IHE, an increase of about 2.9% relative to the efficiency of 21% when the turbine exhaust vapor is only cooled to the dew point. Fig. 10 also shows that the cycle thermal efficiency is generally higher with a larger temperature glide. For instance in Fig. 10a, the cycle efficiency is 20.6% when Tglide is 6 °C at xoctane = 0.1 and increases to 21.6% when Tglide is 15.7 °C at xoctane = 0.5. At xoctane = 0.5, the cycle thermal efficiency reaches a maximum and the condensation temperature glide is also about the largest. Thus, mixtures will have better cycle efficiencies than pure fluids for the right conditions. 3.2. Effect of the condensation temperature glide on the power output The net power output of the geothermal ORC without an IHE is shown in Fig. 11 as a function of the component mole fraction. Two local maxima also appear in the net power output when the condensation temperature glide is almost equal to the cooling water temperature increase, with the higher maximum at a higher mole fraction of the more volatile component which gives a higher geothermal heat utilization. The geothermal water exhaust temperature, TH3, is higher at lower mole fractions of the more volatile component which reduces the geothermal heat utilization. The mole fraction of the more volatile component should be greater with the condensation temperature glide close to the cooling water temperature increase to give a higher geothermal heat utilization and a higher net power output for a geothermal ORC. The net power output of the geothermal ORC with R600/R601a reaches a minimum at a mole fraction 0.4 of R600 in Fig. 11, when the turbine outlet temperature reaches the maximum as shown in Fig. 9a. The net power output with the R600a/R601 mixture is even lower than with pure R601 for R600a mole fractions between 0.2 and 0.5 due to the relatively large condensation temperature glide as shown in Fig. 11d. The power output of the geothermal ORC with pure R600a is higher than that with pure R600, R601 or R601a. The net power output is 7.7% higher with the R600a/ R601a (0.9/0.1) mixture than with pure R600a and 8.1% higher with the R600a/R601 (0.94/0.06) mixture. The net power output of the cogenerative ORC is shown in Fig. 12 as a function of the mole fraction of the more volatile component. The heat utilized by the cogenerative ORC is constant given the fixed operating parameters of the thermal oil circuit. Therefore, the net power output of the cogenerative ORC corresponds to the cycle thermal efficiency. More power is then generated with a larger temperature glide.
Exergy destruction rate in the condenser, ΩC (%)
Q. Liu et al. / Applied Energy 115 (2014) 394–404
9
8
7
6
5
4 0.0
Octane/Decane MDM/MD2M Nonane/Decane 0.2
0.4
0.6
0.8
1.0
Mole fraction of more volatile component , x1 Fig. 16. Exergy destruction rate in the condenser for the cogenerative ORC as a function of mole fraction.
3.3. Effect of the condensation temperature glide on the exergy efficiency The exergy efficiency corresponds to the net power output according to Eq. (10). Fig. 13 shows the exergy efficiency of the geothermal ORC for various mole fractions. Two local maxima also appear in the exergy efficiency when the condensation temperature glide is almost equal to the cooling water temperature increase with the highest exergy efficiency at a higher mole fraction of the more volatile component. The exergy efficiency decreases significantly at mole fractions with higher condensation temperature glides (Tglide > DTw). The exergy destruction rate in the condenser for the geothermal ORC is shown in Fig. 14 as a function of the mole fraction. The exergy destruction rate first decreases with increasing condensation temperature glide when the condensation temperature glide is less than the cooling water temperature increase, because the temperature difference between the working fluid and the cooling water decreases. The minimum exergy destruction rate occurs when the condensation temperature glide is about equal to the cooling water temperature increase. The exergy destruction rate then begins to increase to the maximum when the condensation temperature glide is higher than the cooling water temperature increase as the temperature difference between the working fluid and cooling water increases. The mixtures with higher condensation temperature glides have higher exergy destruction rates when the condensation temperature glide is higher than the cooling water temperature increase. The exergy efficiency of the cogenerative ORC is shown in Fig. 15 with the exergy destruction rate in the condenser is shown in Fig. 16 for various mole fractions. The cooling water temperature increase is higher than the condensation temperature glide of the working fluid; thus, the exergy efficiency increases as the condensation temperature glide increases, while the exergy destruction rate decreases. The condensation temperature glide is higher, the increase in exergy efficiency is higher but the exergy destruction rate is lower. 4. Conclusions The thermodynamic performance of ORC systems can be improved by using zeotropic mixtures as the working fluid. This paper presents a method to determine the ORC condensation pressure with zeotropic mixtures. When the condensation temperature glide is less than the cooling water temperature increase, the condensation pressure is determined by the mixture dew point and
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the cycle thermal efficiency increases as the condensation temperature glide increases. When the condensation temperature glide is greater than the cooling water temperature increase, the condensation pressure is determined by the mixture bubble point and the cycle thermal efficiency decreases as the condensation temperature glide increases. Higher condensation temperature glides also cause large exergy destruction rates and lower exergy efficiencies. When the cooling water temperature increase is less than the maximum condensation temperature glide of the mixture, two maxima appear in the cycle thermal efficiency, exergy efficiency and net power output at the points where the condensation temperature glide matches the cooling water temperature increase at two different mole fractions of the more volatile component, with the higher power output at the higher mole fraction. When the cooling water temperature increase is higher than the maximum condensation temperature glide of the mixture, the efficiency and power output curves have only one maximum. Higher condensation temperature glides are not better with mixture working fluids for lower cooling water temperature increase. ORC systems have better thermodynamic performance when the condensation temperature glide is nearly equal to the cooling water temperature increase. If the maximum condensation temperature glide is higher than the cooling water temperature increase, the mole fraction of the more volatile component should be high with the condensation temperature glide nearly equal to the cooling water temperature increase to obtain the maximum net power for a geothermal ORC. Acknowledgement This work was supported by the National Natural Science Foundation of China (Grant Nos. 51076074, 51236004 and 51321002). References [1] International Energy Agency (IEA). Key world energy statistics; 2012.
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