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Thermo-economic comparison of subcritical organic Rankine cycle based on different heat exchanger configurations
Energy 123 (2017) 728e741
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Energy journal homepage: www.elsevier.com/locate/energy
Thermo-economic comparison of subcritical organic Rankine cycle based on different heat exchanger configurations Cheng Zhang a, Chao Liu a, *, Shukun Wang a, Xiaoxiao Xu a, Qibin Li b a Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400030, China b College of Aerospace Engineering, Chongqing University, Chongqing 400030, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 July 2016 Received in revised form 3 January 2017 Accepted 25 January 2017 Available online 30 January 2017
The cost of heat exchangers account for a large proportion of total investment in organic Rankine cycle (ORC). In this paper, plate heat exchanger (P), shell-and-tube heat exchanger (S) and finned-tube heat exchanger (F) are used as evaporator and condenser of four subcritical ORC configurations: ORC-PP, ORCSS, ORC-FP and ORC-FS. The thermo-economic models are built and a thermo-economic evaluation and comparison of four ORC configurations is presented in order to recover the low-temperature waste heat. The optimal evaporating pressure, pinch point temperature difference, net power output and dynamic payback period corresponding to the minimum electricity production cost (EPC) are obtained for different ORC configurations under different heat source temperatures. Results show that the EPCs of ORC-PP and ORC-SS are apparently higher than that of ORC-FP and ORC-FS. Among them, ORC-FS is the most cost-effective configuration. The optimal pinch point temperature difference in evaporator has a decreasing trend with the increase of critical temperature of working fluid for ORC-FS and ORC-FP, while the optimal pinch point temperature difference in condenser keeps nearly constant. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine cycle Thermo-economic evaluation Electricity production cost Plate heat exchanger Shell-and-tube heat exchanger Finned-tube heat exchanger
1. Introduction Along with the rapid development of economy, a large amount of low-temperature waste heat sources is generated by existing industrial process. Meanwhile, environmental pollution and energy shortage have significantly deteriorated. Survey data shows that low/medium grade waste heat accounts for 50% or more proportion of the total heat produced in industrial processes [1]. A lot of approaches have been proposed for the recovery of the waste heat [2] for reducing environmental pollution and energy shortage problems. Among the conversion technologies, organic Rankine cycle (ORC) is the most widely used [3], which can be driven directly by low grade energy such as solar energy [4e7], biomass energy [8e10], geothermal energy [6,11e14], waste heat from gas turbine [15], and exhaust gases from vehicle engines or marine diesel engines [16,17] to electricity. ORC has the same system components as steam Rankine cycle (a
* Corresponding author. Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, Chongqing University, Chongqing 400030, China. E-mail address: [email protected] (C. Liu). http://dx.doi.org/10.1016/j.energy.2017.01.132 0360-5442/© 2017 Elsevier Ltd. All rights reserved.
boiler, a condenser, an expansion device and a pump) but uses organic fluid. However, the conversion efficiency is relatively low due to low heat source temperature [18]. In order to maximize the electricity generation efficiency of ORCs, many researches have been carried out. To sum up previous work focused on in the following aspects: selection criteria of optimal organic working fluids (pure or zeotropic working fluids [19]), thermodynamic and physical properties [20], various thermodynamic cycles (basic cycle, trans-/supercritical cycle [14,21e23], regenerative cycle [18,24], reheated cycle, recuperative cycle [24e26] and combined cycle [8,15,27,28]), selection of primary components and geometric dimensions [19,28], and environmental concerns [29]. In addition, commercial applications of ORC have a rapid development in Europe and the US. Among them, Turboden and ORMAT are primarily representative companies for recovering biomass and geothermal energy, respectively [2]. Researchers have increasingly focused on the ORCs' feasibility in terms of views on technical, economic and environmental point in recent years. Li et al. [30] conducted an economical model of the subcritical ORC system for the use of low-temperature flue gas. The electricity production cost was selected as the evaluation criterion. Quoilin et al. [1] investigated the thermodynamic and economic
C. Zhang et al. / Energy 123 (2017) 728e741
Nomenclature A Bo C Co D Fr G H K Nu Pr Re U V Y cp dt db g m p pp q x
heat transfer surface area (m2) boiling number cost ($)/constant relative to equipment cost correlation convection number diameter (m) Froude number mass velocity (k gm2 s1) fin height (m) constant relative to equipment cost correlation Nuselt number Prandtl number Reynolds number overall heat transfer coefficient (Wm2 K1) volume flow rate (m3/s) Fin pitch (m) specific heat (J kg1 K1) fin collar outside diameter (m) fin root diameter (m) acceleration due to gravity (m/s2) mass flow rate (kg/s) pressure (kPa) payback period (year) average imposed wall heat flux (kW/m2) dryness fraction
Abbreviations COM Cost of Operation and Maintenance CRF Capital Recovery Factor GWP Global Warming Potential relative to CO2 HX-P Plate Heat Exchanger HX-S Shell-and-tube Heat Exchanger HX-F Finned tube Heat Exchanger ORC-PP Both evaporator and condenser using plate heat exchanger ORC-FP Finned tube bundles as evaporator and plate heat exchanger as condenser ORC-SS Both evaporator and condenser using shell-and-tube heat exchanger
optimization of a small scale ORC for recovering waste heat. Plat heat exchanger was used in their model and economic profitability. Lecompte et al. [28] developed a thermo-economic design methodology of ORC based on CHP system, taking into account partial load behavior. A plate heat exchanger and a finned tube heat exchanger with circular fins were selected as evaporator and condenser, respectively. Zeotropic mixtures are used as working fluids for better temperature profiles match of heat source and heat sink [31]. Wu et al. [32] calculated and compared the performance of ORC using zeotropic mixtures with corresponding pure fluids. The result showed that the economic performance of that system was worse in some extent compared to corresponding pure fluid cycles. However, Kheiri et al. [19] found that the ORC using zeotropic mixture of npentane and R245fa could not only weaken flammability of npentane well but also made the system reached a good economic profitability. In addition, thermo-economic assessment for different ORC applications was conducted. Astolfi et al. [11] presented a detailed analysis of binary ORC power plants for recovering low-medium
ORC-FS
729
Finned tube bundles as evaporator and shell-and-tube heat exchanger as condenser
Greek letters pressure difference (kPa) temperature difference (K) convection heat transfer coefficient (Wm2 K1) Chevron angle/finned ratio thickness (m) efficiency density (kg/m3) thermal conductivity (Wm1 K1) dynamic viscosity (Ns/m2)
Dp DT a b d h r l m
Subscripts/superscripts LT lifetime c cold/condensation cond condenser crit critical e evaporating evap evaporator eq equivalent gen generator fg flue gas h heat source/hot/hydraulic in inlet/inside l liquid g gas max maximum min minimum out outlet pp pump sp single-phase t turbine tot total tp two-phase wf working fluid 1e8 state points
temperature geothermal sources. Walraven et al. [12] performed an economic optimization of air-cooled ORC driven by geothermal heat sources. Yang et al. [13] investigated the economic optimization of an ORC with lower GWP working fluids in geothermal application. A review of the literature reveals that the thermo-economic comparisons of different ORC systems are of great difference and complicated. Consequently, this paper aims to conducts a comparative analysis of thermo-economic concerning four ORC configurations. In the models, four ORC configurations are: both evaporator and condenser using plate heat exchanger (ORC-PP), a finned tube bundles with circular fins as evaporator and a plate heat exchangers as condenser (ORC-FP), both evaporator and condenser using shell-and-tube heat exchanger (ORC-SS), and a finned tube bundles with circular fins as evaporator and a shelland-tube heat exchanger as condenser (ORC-FS). The cost of heat exchanger, turbine, electricity generator, working fluid pump and cooling water pump is considered. Then the evaporating pressure, pinch point temperature differences in evaporator and condenser are analyzed and optimized at different heat source temperatures
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C. Zhang et al. / Energy 123 (2017) 728e741 Table 1 Given conditions and ORC parameters.
Fig. 1. Schematic diagram of an ORC.
and different heat exchanger configurations by using the EPC (electricity production cost) and ppd (dynamic payback period) as the objective function. Furthermore, the thermo-economic comparison of subcritical ORC provides detailed information to evaluate the thermo-economic viability of ORC, and then seek the optimal heat exchanger configuration, parameters and suitable working fluids for the ORC system to achieve the goal of high efficiency utilization of energy and energy savings. 2. System configurations and assumptions 2.1. System description The schematic diagram of the ORC is shown in Fig. 1. In the models, superheat is not considered for dry and isentropic fluids. However, for wet fluids, superheat is necessary to avoid liquid droplet impingement in turbine during the expansion, and it is assumed that the state of expander outlet is saturated. In addition, the internal heat exchanger (IHX) will not be taken into account in the ORC models due to larger capital investment. The working fluid absorbs heat from the exhaust flue gas in the evaporator and then continuously vaporizes into saturated vapor (dry and isentropic fluid) or overheated vapor (wet fluid). Then the high pressure vapor flows into the turbine to expand and convert into shaft work to drives the generator to generate electricity. After that, the expanded superheated vapor flows into to condenser, in which it is condensed to saturated liquid by the cooling water. The saturated liquid is pumped into the evaporator again to continue the next cycle. Fig. 2 shows Tes diagram of different working fluids. In the thermodynamic modeling, the given conditions and ORC parameters are shown in Table 1. In order to prevent from corrosion
Parameter and unit
Value
The flue gas temperature, C The temperature constraint of discharged flue gas, C The flow rate of flue gas, kg/s Condensing temperature, C The inlet temperature of cooling water, C Pinch point temperature in evaporator, C Pinch point temperature in condenser, C Turbine isentropic efficiency Pump isentropic efficiency Generator efficiency The operating time top,hour life cycle time LT, year annual loan interest rate i on-grid electricity price Celec, $/kWh
120e200 82 10 30 20 5e30 5e30 0.80 0.75 0.95 8000 20 0.04, 0.05, 0.06 0.10, 0.15, 0.20
of low-temperature flue gas, the temperature constraint of discharged flue gas is set to 82 C [33]. The condensing temperature is usually assumed to be 30e36 C when water is used as cooling medium [13,15,34]. Therefore the condensing temperature is assumed to be 30 C in present paper. In addition, the following assumptions are also taken into consideration: (1)ORC system works in a steady state; (2)There is no pressure drop in the evaporator, pipes and condenser; (3)The heat losses in the components are neglected; (4)Working fluids at the condenser outlet is saturated liquid; (5)Dry and isentropic working fluid at the turbine inlet is saturated vapor; (6)Temperature difference at the pinch point in heat changer is not less than 3 C [30].
2.2. Heat exchanger configurations It is found that the capital cost of heat exchanger accounts for a large proportion of ORC, and even reaches about 80% in case of aircooled condenser[ [12]. Therefore, the selection of heat exchanger in ORC is very important. In the evaporator the heat transfer process happens between gas phase and liquid phase and in the condenser heat transfer process does in vapor/liquid-liquid. Therefore, four kinds of heat exchanger configurations (PP, FP, SS and FS) are simulated in the model. The geometric parameters of the heat exchangers are given in Table 2.
Fig. 2. Tes diagram of working fluids: (a) dry or isentropic and (b) wet.
C. Zhang et al. / Energy 123 (2017) 728e741
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Table 2 Heat exchangers parameters. Heat exchanger
Parameter and unit
Value
Heat exchanger
Parameter and unit
Value
Plate heat exchanger
Effective channel length, LEff(m) Width of flow channel, w(m) Plate thickness, d(mm) Mean flow channel gap, b(mm) Corrugation pitch, l(mm) Chevron angle, b(degrees) Material Pressure drop allowance, (kPa) Inner tube diameter, di(mm) Outer tube diameter, do(mm) Tube pitch, S(mm) Tube material Shell material Pressure drop allowance, (kPa) Shell Tube
1.25 0.55 0.5 5 15 p/6 CS 10 15 19 25 CS CS
Finned tube heat exchanger
Inner tube diameter, di(mm) Outer tube diameter, do(mm) Fin collar outside diameter, dt(mm) Fin root diameter, db(mm) Fin pitch, Y(mm) Fin height, H(mm) Fin thickness, df(mm) Transversal tube pitch, S1(mm) Longitudinal tube pitch, S2(mm) Tube length, L(m) Tube material Fin material Pressure drop allowance, (kPa) Air Tube
10 13 25.3 10.55 2.6 5 0.15 25 21 3 CS Al
Shell-and-tube heat exchangera
a
30 20
30 20
Tube side for working fluid and shell-side for heat transfer fluid.
2.3. Working fluids
Wt ¼ mwf ðh1 h2 Þ ¼ mwf ðh1 h2s Þht
The thermophysical properties of working fluids largely affects the performance of ORC system, such as conversion efficiency, economic viability, environmental impact and operating conditions [35]. Therefore, 11 substances are selected as working fluids of ORC system, as shown in Table 3. Furthermore, two refrigerant evaluation indexes ODP being zero and GWP being lower than 150 [19] are considered except for R245fa. The properties of working fluids are calculated by using REFPROP Version 9.0 [36] in the software MATLAB Version 7.10.0.
(3)
The work consumed by pump is
Wpp ¼ mwf ðh4 h3 Þ ¼ mwf ðh4s h3 Þhpp
(4)
The net power output can be expressed as
Wnet ¼ Wt Wpp
(5)
3.2. Heat exchanger area 3. Thermodynamic and economic models 3.1. Thermodynamic model Energy analysis of ORC is as follows: The heat transfer flow rate in the evaporator is
Qevap ¼ mwf ðh1 h4 Þ ¼ mwf ðh5 h6 Þ
(1)
The heat transfer flow rate in the condenser is
Qcond ¼ mwf ðh2 h3 Þ ¼ mwf ðh8 h7 Þ
(2)
Evaporator is divided into three regions, i.e. preheating, evaporation and superheating region while condenser is divided into two regions, i.e. cooling and condensation region, as shown in Fig. 3. For two-phase flow region, the process is divided into finite small elements so that constant properties are be able to assumed in each element [14]. In the heat exchange models, the log mean temperature difference (LMTD) method is employed. The fouling heat resistance in the process of heat transfer is ignored. Thus, the heat transfer and heat transfer coefficients are given by: Single-phase region:
Qsp ¼ Usp Asp DTLM;sp
The work produced by the turbine is
(6)
Table 3 Properties of 11kinds of working fluids. ASHRAE 34
Classification
Molecular mass
TNBP( C)
Tcrit( C)
pcrit(MPa)
Safetya
Life/yr
ODP
GWP
R1234fy R161 R152a RC270 R600a R600 R245fab R601b R601a R601 Cyclopentane
HFO HFC HFC HC HC HC HFC HC HC HC HC
114.04 48.04 66.05 42.08 58.12 58.12 134.05 72.15 72.15 72.15 70.13
29.5 37.06 24 31.5 11.7 0.5 15.1 9.5 27.8 36.1 49.4
94.7 102.2 113.3 125.2 134.7 152 154 160.6 187.2 196.6 238.6
3.38 5.09 4.52 5.58 3.63 3.8 3.65 3.2 3.38 3.37 4.51
A2L
0.029 0.18 1.5 0.44 0.016 0.018 7.7
0 0 0 0 0 0 0 0 0 0 0
<4.4 12 133 ~20 ~20 ~20 1050 ~20 ~20 ~20 11
a b
A2 A3 A3 A3 B1 A3 A3 A3 A3
0.009 0.009 0.007
Refrigerant safety group classification. 1: No flammability; 2: Lower flammability; 3: Higher Flammability; A: Lower Toxicity; B: Higher Toxicity. R245fa with GWP being higher than 150, which is used to compare with other working fluids due to its remarkable thermodynamic properties and wide researches.
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Fig. 3. Three-zone modeling of an evaporator (a) and two-zone modeling of a condenser (b).
The overall heat transfer coefficient of single phase for plate, finned tube and shell-and-tube heat exchanger, respectively:
The Yan-Lio-Lin correlation [37] is used to calculate the condensation heat transfer coefficient for two-phase flow.
1 1 d 1 ¼ þ þ Usp asp;h l asp;c
(7a)
a ¼ 4:118
1 1 d 1 ¼ þ þ Usp asp;h l asp;c bhf
(7b)
1 1 do do do 1 ¼ þ ln þ Usp atp;fl din 2l din atp;wf
(7c)
ll Dh
1=3 Re0:4 eq Pr
(11a)
where
Reeq ¼ Geq Dh hl
(11b)
. Boeq ¼ q Geq $rfg
(11c)
i h Geq ¼ G 1 xm þ xm ðrl =rv Þ1=2
(11d)
Two-phase flow:
Qtp;i ¼ Utp;i Atp;i DTLM;tp;i
(8)
1 1 d 1 ¼ þ þ Utp;i atp;h;i l atp;c;i
(9a)
The pressure drops are expressed as [14]:
Dp ¼ 1 1 d 1 ¼ þ þ Utp atp;h;i l atp;c;i bhf
(9c)
where i denotes each section of two-phase region, hf denotes finned efficiency, b denotes finned ratio. The heat transfer correlations of heat exchangers used in the models are given as follow: (1) Plate heat exchanger The Chisholm-Wanniarachchi correlation [37] is used to calculate the convection heat transfer coefficient for single-phase flow.
Dh a
ll
¼ 0:724
0:646 6b
p
Re0:583 Pr1=3
(10)
The boiling heat transfer coefficient for two-phase flow is calculated by the Yan-Lin correlation [37].
Nu ¼
Dh a
ll
1=3
¼ 1:926Prl
(12)
(9b)
1 1 do do do 1 ¼ þ ln þ Utp;i asp;fl;i din 2l din asp;wf ;i
Nu ¼
2fG2 rDh
h i 1=2 0:5 Bo0:3 eq Reeq 1 xm þ xm ðrl =rv Þ (11)
f ¼ 14:62Re0:514
Re 50
(12a)
f ¼ 2:21Re0:0:097
Re 180
(12b)
(2) Finned tube heat exchanger and shell-and-tube heat exchanger The Young correlation [38] is employed to calculate the air-side heat transfer coefficient in the finned tube heat exchanger for single-phase flow. For high-fin tube bundle, i.e. dt/db ¼ 1.2~1.6, and db ¼ 13.5~16 mm:
!0:075 db a db Gmax 0:667 cp m1=3 Y 0:164 Y ¼ 0:1507 H k m k df
(13)
For high-fin tube bundle, i.e. dt/db ¼ 1.7~2.4, db ¼ 12~41 mm:
db a d Gmax 0:718 cp m1=3 Y 0:296 ¼ 0:1378 b H k m k The pressure drops of tube outside are expressed as:
(14)
C. Zhang et al. / Energy 123 (2017) 728e741
Dp ¼
nfG2max 2r
(15)
Gmax db 0:316 S1 0:297 S1 0:515 f ¼ 37:86 m db S2
Co ¼
733
1 x 8 rg 0:5 x rl
(17c)
Froude number with all flow as liquid:
(15a) Frl0 ¼ G2
where n is the tube row number along flow direction The Gnielinski correlation [39] is used to calculate in-tube heat transfer coefficient both in the finned tube heat exchanger and shell-and-tube exchanger for single-phase flow:
i h ðf =8ÞðRe 1000ÞPrf da 1 þ ðd=lÞ2=3 ct ¼ Nu ¼ pffiffiffiffiffiffiffiffi 2=3 k 1 þ 12:7 f =8 Prf 1
(16)
where f is Darcy resistance coefficient, which is calculated by Filonenko equation
f ¼ ð1:821gRe 1:64Þ2
(16a)
.
r2l gd
(17d)
Liquid Reynolds number:
Rel ¼ Gdð1 xÞ=ml
(17e)
The Gungor-Winterton correlation [41,42] is employed to calculate the boiling heat transfer coefficient in the shell-and-tube heat exchanger for two-phase flow:
atp
8 9 ! < x 0:75 r 0:41 = l ¼ al 1 þ 3000Bo:896 þ 1:12 : ; 1x rg
(18)
where
For liquid, ct is given by:
ct ¼
Prf Prw
0:11
Prf ¼ 0:05 20 Prw
0:4 al ¼ 0:023Re0:8 l Prl ðkl =dÞ
(16b)
For gas, ct is given by:
ct ¼
Tf Tw
0:45
Tf ¼ 0:5 1:5 Tw
(16c)
al ¼ 0:023ðGð1 xÞd=mÞPr0:4 l ðkl =dÞ
gas: 0.6
o
(19)
o
(17)
0:4 al ¼ 0:023Re0:8 l Prl ðll =dÞ
(19a)
The shell-side pressure drop is calculated in the shell-and-tube heat exchanger by the following equation [19].
The Kandlikar correlation [40] is used to calculate the boiling heat transfer coefficient in the finned tube heat exchanger for twophase flow:
n
.
atp ¼ al ð1 xÞ0:8 þ 3:8x0:76 ð1 xÞ0:04 Pr0:38 where
which is valid for a range of
atp ¼ al C1 CoC2 ð25Frl0 ÞC5 þ C3 BoC4 Ffl
The Shah correlation [43] is used to calculate the in-tube condensation heat transfer correlation both in the finned tube heat exchanger and shell-and-tube exchanger for two-phase flow:
n
(18a)
(17a)
where value of C1, C2, C3, C4 and C5 in Kandlikar correlation is given in Table 4, and Co is determined as following:
Dp ¼
fDG2 ðNb 1Þ 2rDe ðm=mw Þ0:14
(20)
Table 5 shows the heat transfer correlations for different heat exchangers at different regions. In the modeling, the pressure drops in the heat exchangers are balanced by pump power compensation as following equation.
Wpp;offset ¼ Dp$Vwf
(21)
Co < 0.65: convection boiling Co > 0.65: nucleate boiling 3.3. Economic model
Boiling number:
Bo ¼ q Giig
(17b)
Convection number:
log Cp0 ¼ K1 þ K2 log10 ðAÞ þ K3 ½log10 ðAÞ2
Table 4 Value of constant for Kandlikar heat transfer correlation [40]. Constant
Convection boiling
Nucleate boiling
C1 C2 C3 C4 C5 a
1.136 0.9 667.2 0.7 0.3
0.6683 0.2 1058.0 0.7 0.3
a
For vertical tube or horizontal tube (Frl > 0.04) C5 ¼ 0.
The cost of the equipment using carbon steel construction and at ambient operating pressure is calculated as following equation [30,44]. For heat exchanger:
(22)
For pump and turbine:
log Cp0 ¼ K1 þ K2 log10 ðWÞ þ K3 ½log10 ðWÞ2
(23)
When taking the specific material of equipment and operating pressure into account, the correction for bare module cost is presented as
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Table 5 Heat transfer correlations for different heat exchangers at different regions. Heat exchanger configuration
Heat exchange region
Heat transfer correlation for flue gas or water
Heat transfer correlation for working fluid
PP
Preheating Boiling Superheating Cooling Condensation Preheating Boiling Superheating Cooling Condensation Preheating Boiling Superheating Cooling Condensation Preheating Boiling Superheating Cooling Condensation
Chisholm-Wanniarachchi Chisholm-Wanniarachchi Chisholm-Wanniarachchi Chisholm-Wanniarachchi Chisholm-Wanniarachchi Young Young Young Chisholm-Wanniarachchi Chisholm-Wanniarachchi Gnielinski Gnielinski Gnielinski Gnielinski Gnielinski Young Young Young Gnielinski Gnielinski
Chisholm-Wanniarachchi Yan-Lin Chisholm-Wanniarachchi Chisholm-Wanniarachchi Yan-Lio-Lin Gnielinski Kandlikar Gnielinski Chisholm-Wanniarachchi Yan-Lio-Lin Gnielinski Gungor-Winterton Gnielinski Gnielinski Shah Gnielinski Kandlikar Gnielinski Gnielinski Shah
High-pressure side
Low-pressure side FP
High-pressure side
Low-pressure side SS
High-pressure side
Low-pressure side FS
High-pressure side
Low-pressure side
CBM ¼ CP B1 þ B2 Fm Fp
(24)
viability, EPC optimization:
where Fm and Fp are the material and pressure correction factor, respectively. Fm is given in Table 6 and Fp is determined by 2
logFP ¼ C1 þ C2 log10 ðpÞ þ C3 ½log10 ðpÞ
(25)
K1, K2, K3, B1, B2, C1, C2 and C3 are fitting cost coefficients for different equipment. The values are given in Table 6. The cost of the electricity generator is calculated by following equation [19]. 0 Cp;gen
0:95 ¼ 60 Wgen
(26)
The actual cost need to be converted from the cost of 2001 by introducing the CEPCI (Chemical Engineering Plant Cost Index) [44]. The cost of 2014 should be corrected as:
CBM;2014 ¼ CBM;2001 CEPCI2014 =CEPCI2001
(27)
where CEPCI2001 ¼ 397, CEPCI2014 ¼ 586.77. The total capital cost is mainly determined by the cost of main equipment, including heat exchanger, turbine, electricity generator, working fluid pump and cooling water pump. Then the total investment capital cost can be approximately presented as:
Ctot ¼ CBM;evap þ CBM;cond þ CBM;tur þ CBM;gen þ CBM;pp þ CBM;wp (28) Furthermore, the COM (cost of operation and maintenance) should be considered and is set as 1.5%. To evaluate the economic
EPC ¼
is employed
as evaluation
criteria in
the
ðCtot CRF þ COMÞ top Wnet
(29)
where CRF is the capital recovery factor:
CRF ¼ h
ið1 þ iÞLT ð1 þ iÞLT 1
i
(30)
where top denote the operating time, i is annual loan interest rate and LT denotes the life cycle time. All electricity is supplied to the power grid. Hence the investment return time ppd can be calculated by the following equation:
ppd ¼ ln
Wnet Celec COM Wnet Celec COM i,Ctot
lnð1 þ iÞ
(31)
The thermo-economic model is calculated in the MATLAB software. The flow chart of the thermo-economic modeling is shown in Fig. 4. In the modeling, optimization is carried out by using EPC as objective function. Evaporating temperature and pressure, pinch point temperature differences in the evaporator and condenser, temperature of discharged flue gas and working fluid mass flow rate can be obtained according to corresponding optimal EPC.
Table 6 Values of constants for different equipments [44]. Equipment
K1
K2
K3
C1
C2
C3
B1
B2
Fm
Fbm
HX-P HX-S
4.6656 4.8306
0.1557 0.8509
/ /
1.63
1.66
1.25
/
Pump
3.3892
0.0536
1.89
1.35
1.50
/
Turbine
2.2476
1.4965
0 0 0.08183 0 0.0123 0 0.00226 /
1.0 1.30
0.3030
0 0 0.11272 0 0.00627 0 0.3957 /
1.21 1.66
4.3247
0 0 0.03881 0 0.00164 0 0.3935 /
0.96 1.63
HX-F
0.1547 0.3187 (5 < p < 140barg) 0.1634 (5 < p < 140barg) 0.1538 (10 < p < 100barg) 0.1618
/
/
/
3.30
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Fig. 4. Flow chart of the thermo-economic modeling.
Fig. 5. Variation of EPC with pe for different heat exchanger configurations at Tfg,out > 82 C: (a) and (b), Tfg,out < 82 C: (c) and (d).
735
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4. Results and discussion 4.1. Economic analysis This paper takes R600 and R601 as a case study. As shown in Fig. 5, the variation of EPC with evaporating pressure (pe) is presented for different ORC configurations at Th ¼ 160 C and DTe ¼ DTc ¼ 8 C. It can be found that EPC decreases first smoothly and then increases steeply with the pe. That is to say there exists a minimum EPC at a specific pe. This phenomenon is also found in the literature [14,19,30]. In addition, the EPCs of ORC-PP and ORC-SS are apparently higher than that of ORC-FP and ORC-FS, of which ORCFS keeps the lowest EPC with the variation of pe. However, the difference of different ORC configurations shrinks gradually with the increase of pe. As shown in Fig. 6, the reason is that when pe increases, total investment cost (Ctot) decreases with the decrease of heat exchanger area caused by the decrease of heat transfer of the heat source, while Wnet increases firstly in a small pressure range and then decreases sharply. This comprehensive variation of Ctot and Wnet results in a minimum EPC due to EPC being proportional to Ctot and inversely proportional to Wnet. Moreover, Fig. 5 also presents that EPC increases with pe starting from a specific point when constraint of discharged flue gas temperature is considered. The same trend exists in the Variation of ppd with pe, as shown in Fig. 7. It is noted that EPC and ppd have the same independent variables of Ctot and Wnet, as expressed in Eqs. (29) and (31). That is reason why the variation of EPC and ppd keep
Fig. 6. Effect of pe on the Ctot and Wnet for different heat exchanger configurations.
same. Therefore, it can be concluded that EPC and ppd can achieve a minimum value at an appropriate pe. Fig. 8 presents the variation of EPC with the pinch point temperature in the evaporator (DTe) at Th ¼ 160 C and Te ¼ 106 C, using R600 and R601 as working fluid, respectively. It can be seen that EPC decreases at first and then increases with DTe. Thus, there also exists an optimal DTe corresponding to a minimum EPC, as the same optimal result for pinch point temperature difference in the condenser (DTc). On one hand, the mean heat transfer temperature difference increases with the increase of DTe, which results in a reduction of heat transfer area and capital cost. On the other hand, the heat transfer decreases due to the increase of DTe at a given evaporating temperature (Te), which results in a reduction of power output. At first, in a lower DTe range, the reduction of capital cost has a greater effect than the reduction of power output on the EPC. Hence EPC decreases with the DTe. And with further increase of DTe, the reduction of power output turns into a dominant factor due to rapid reduction of heat input, and results in the increase of EPC. In this work, because ambient temperature water is used as coolant the DTc is limited in a small range of 5e10 C, and the optimal results almost are 8 C. For ORC-PP, ORC-FP and ORC-FS, the variation of EPC is relatively smooth while the EPC varies sharply for ORC-SS, which leads to a greater pinch point temperature difference with respect to a minimum EPC. 4.2. Optimization results The best thermodynamic performance may not always meet the optimal economic performance. Table 7 shows the optimization results for R601 due to its good economic benefits and wider scope of heat source temperatures. The lowest EPC 0.074$/kWh and lowest ppd 6.7 years are obtained for ORC-FS at Th ¼ 140 C. The value is just slightly lower than that of ORC-FP. While the largest EPC 0.132$/kWh is obtained for ORC-PP, and the largest Wnet 70.6 kW for ORC-FP are found. At Th ¼ 160 C and Th ¼ 180 C, the same results can be found for different configurations. Through comparative analysis, ORC-FP and ORC-FS look promising for recovering waste heat of flue gas. Moreover, ORC-FS shows the most attractive. In addition, the optimal pe or Te increases with the increase of heat source temperature. For more optimization results on different ORC configurations and different working fluids, please browse Table S1- S4 in the Supplementary data of Appendix A. The DTe and DTc, play an important role in the design process of heat exchanger. As presented in Fig. 8, there exists optimal DTe, and DTc in the evaporator and condenser to minimize the EPC. Fig. 9 presents the optimal DTe (DTe,opt) at Th ¼ 160 C with different working fluids. For ORC-PP and ORC-SS, the DTe,opt has no obvious regularity and fluctuates with different working fluids as shown in Fig. 9(a). For ORC-FP and ORC-FS, as shown in Fig. 9(b), the DTe,opt has a decreasing trend with the increase of critical temperature of working fluids. While the DTc,opt keeps nearly a constant value of about 8 C for different ORC configurations. As shown in Figs. 10e12, the minimum EPC, and the corresponding Wnet and ppd for different working fluids at Th ¼ 160 C are presented. The EPC for ORC-PP using different working fluids is the largest, followed by ORC-SS, ORC-FP and ORC-FS. The EPC of ORC-PP and ORC-SS ranging from 0.085 to 0.150$/kWh are apparently higher than that of ORC-FP and ORC-FS ranging from 0.055 to 0.070$/kWh for different working fluids. In addition, the ranges of ppd are 6.5e8.4 years for ORC-PP and ORC-SS, and 4.3e5.6years for ORC-FP and ORC-FS. Among them, ORC-FS is the most cost-effective ORC configuration. It can be seen that ORC-PP is 60%e70%, ORC-SS is 47%e51%, and ORC-FP is about 14% higher EPC than that of ORC-FS. It is also found that the EPC and ppd have
Fig. 7. Variation of ppd with pe for different heat exchanger configurations at Tfg,out > 82 C: (a) and (b), Tfg,out < 82 C: (c) and (d).
Fig. 8. Variation of EPC with DTe for different heat exchanger configurations ((a) & (b)).
Table 7 Optimization results for working fluid R601. Th ( C)
PP 140
160
180
140
160
180
140
160
180
140
160
180
Teva ( C) peva (kPa) pcon (kPa) mwf (kg/s) mcs (kg/s) DTe ( C) DTc ( C) Tfg,out( C) Wnet (kW) EPC ($/kWh) ppd (year)
90 470.3 82.0 1.285 55.66 11 8 82.1 68.8 0.132 12.3
100 592.7 82.0 1.576 68.28 14 8 86.7 96.5 0.104 8.1
112 769.1 82.0 1.843 79.82 17 8 90.9 129.0 0.085 7.2
96 541.2 82.0 1.213 52.52 8 8 84.2 70.6 0.085 8.2
106 676.6 82.0 1.315 69.97 8 8 83.2 106.1 0.068 6.0
120 906.7 82.0 1.952 84.57 8 8 83.2 147.6 0.057 4.9
86 427.1 82.0 1.203 52.09 17 8 86.5 60.6 0.109 11.6
94 516.7 82.0 1.441 62.40 23 8 94.2 81.6 0.088 8.4
104 647.7 82.0 1.641 71.08 29 8 102.7 105.3 0.074 6.7
90 470.3 82.0 1.285 55.66 11 8 82.1 68.8 0.074 6.7
106 676.6 82.0 1.615 69.97 8 8 83.2 106.1 0.059 5.1
114 801.9 82.0 2.005 86.86 11 8 82.4 143.2 0.050 4.2
FP
SS
FS
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Fig. 9. The DTe,opt of different working fluid for different heat exchanger configurations ((a) & (b)).
Fig. 10. The minimum EPC of different working fluid for different heat exchanger configurations.
a same trend, which decreases with the increase of critical temperature of working fluids except for ORC-PP. For ORC-PP, EPC and ppd increase firstly and then decrease with the increase of critical temperature of working fluid. For ORC-FS using different working fluids, the lowest EPC 0.058$/kWh and lowest ppd 4.3years for cyclopentane, and the highest Wnet 111.8 kW for RC270 are
Fig. 11. The ppd of different working fluid for different heat exchanger configurations at the minimum EPC.
Fig. 12. The Wnet of different working fluids for different heat exchanger configurations at the minimum EPC.
obtained. It is demonstrated that the heat exchanger configuration and working fluid have a significant influence on the economic performance of ORC systems.
Fig. 13. The minimum EPC of different working fluids at different heat source temperatures in FS ORC.
C. Zhang et al. / Energy 123 (2017) 728e741
Fig. 14. The ppd of different working fluids at different heat source temperatures and minimum EPC for ORC-FS.
4.3. Sensitive analysis: electricity price and annual loan interest rate It has been mentioned above that Th has a great influence on the pinch point temperature difference. Nevertheless, the influence of Th on economic performance is more evident. As shown in Fig. 13,
739
the minimum EPC and ppd are greatly affected by Th for ORC-FS. However, the difference of minimum EPC and ppd between two heat source temperatures will become much smaller with the increase of Th. Taking R600 as example, the minimum EPC is 0.104, 0.075, 0.06, 0.051 and 0.043$/kWh with respect to ranges of Th from 120 to 200 C, which shows a reduction rate of 27.9%, 20%, 15% and 15.5%, respectively. The influence of Th on ppd has the same influence on EPC, as shown in Fig. 14. In addition, the working fluid with lower or higher critical temperature cannot meet the temperature constraint of discharged flue gas at some specific Th. That is to say, not all working fluids are suitable for all heat source temperature. In this paper, RC270, R600a, R600, R601b, R601a and R601, critical temperature ranging from 152.2 to 196.6 C, are suitable for the heat temperature ranging from 120 to 200 C. Similarly, the optimization results for different ORC configurations and different working fluids are found in the Supplementary data of Appendix A. The grid price of state grid company is a ranges of 0.03e0.152$/ kWh in China [45], including traditional energy power plant and new energy power plant. Therefore, three kinds of electricity price are selected in the modeling as shown in Table 1. In addition, electricity price of 0.2$/kWh should take the government subsidies into consideration. For ORC-PP, as show in Fig. 15, the EPC are 0.098, 0.0105 and 0.113$/kWh with respect to the annual loan interest rate of 4, 5 and 6% [46], which shows an average increase rate of 7%. And the ppd are 22.2, 10.9 and 7.3years with respect to the on-grid electricity price of 0.10, 0.15 and 0.20$/kWh, showing a reduction rate of 51% and
Fig. 15. Sensitivity analysis of electricity price and loan interest rate on the EPC and ppd ((a), (b), (c) & (d)).
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33%, which makes a great reduction in ppd. Therefore, the government subsidies or the lower loan interest rate can greatly encourage the development of ORC program when plate or shell-and-tube heat exchanger must be used in the condition of gas-liquid heat exchange. 5. Conclusion The present paper performs a comparative analysis of an ORC based on four different kinds of heat exchanger configurations for recovering low-temperature waste heat of flue gas, ranges from 120 to 200 C. The evaporating temperature, pinch point temperature differences in evaporator and condenser are analyzed and optimized based on different heat exchanger configurations by using EPC and ppd as the objective function. Meanwhile, the sensitivity analysis is performed to analyze the effects of electricity price and annual loan interest rate on thermo-economic performance of ORC. The main conclusions can be drawn: (1) The EPCs of ORC-PP and ORC-SS are apparently higher than that of ORC-FP and ORC-FS. For different working fluids, the EPC of former two configuration ranges from 0.085 to 0.150$/ kWh and the latter two configuration from 0.055 to 0.070$/ kWh. Among them, ORC-FS is the most cost-effective ORC configuration. (2) It is found that the ppd has the same variation trend with EPC. For different working fluids, the ranges of ppd of are 6.5e8.4 years for ORC-PP and ORC-SS, and 4.3e5.6years for ORC-FP and ORC-FS. (3) The DTe,opt has a decreasing trend with the increase of critical temperature of working fluids at a certain heat source temperatures for ORC-FS and ORC-FP. But the DTc,opt keeps nearly constant value of about 8 C. (4) On-gird electricity price and lower loan interest rate, especially the subsidies of on-gird electricity price can make great reductions in EPC and ppd. The fluids RC270, R600a, R600, R601b, R601a and R601 are recommended as working fluids due to considerable economic benefits and the wider scope of heat source temperatures. Acknowledgements This work is supported by “National Natural Science Foundation of China” (No. 51576019) and “International Science & Technology Cooperation Program of China” (No. 2015DFG62270). Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.energy.2017.01.132. References [1] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic Rankine cycles. Appl Therm Eng 2011;31(14): 2885e93. lez F, Segovia JJ, Martín MC, Antolín G, Chejne F, Quijano A. A technical, [2] Ve economical and market review of organic Rankine cycles for the conversion of low-grade heat for power generation. Renew Sustain Energy Rev 2012;16(6): 4175e89. [3] Quoilin S, Lemort V. Technological and economical survey of organic Rankine cycle systems. 2009. [4] Kosmadakis G, Manolakos D, Kyritsis S, Papadakis G. Economic assessment of a two-stage solar organic Rankine cycle for reverse osmosis desalination. Renew Energy 2009;34(6):1579e86. [5] Kosmadakis G, Manolakos D, Papadakis G. Simulation and economic analysis of a CPV/thermal system coupled with an organic Rankine cycle for increased power generation. Sol Energy 2011;85(2):308e24.
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Thermo-economic comparison of subcritical organic Rankine cycle based on different heat exchanger configurations Cheng Zhang a, Chao Liu a, *, Shukun Wang a, Xiaoxiao Xu a, Qibin Li b a Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400030, China b College of Aerospace Engineering, Chongqing University, Chongqing 400030, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 July 2016 Received in revised form 3 January 2017 Accepted 25 January 2017 Available online 30 January 2017
The cost of heat exchangers account for a large proportion of total investment in organic Rankine cycle (ORC). In this paper, plate heat exchanger (P), shell-and-tube heat exchanger (S) and finned-tube heat exchanger (F) are used as evaporator and condenser of four subcritical ORC configurations: ORC-PP, ORCSS, ORC-FP and ORC-FS. The thermo-economic models are built and a thermo-economic evaluation and comparison of four ORC configurations is presented in order to recover the low-temperature waste heat. The optimal evaporating pressure, pinch point temperature difference, net power output and dynamic payback period corresponding to the minimum electricity production cost (EPC) are obtained for different ORC configurations under different heat source temperatures. Results show that the EPCs of ORC-PP and ORC-SS are apparently higher than that of ORC-FP and ORC-FS. Among them, ORC-FS is the most cost-effective configuration. The optimal pinch point temperature difference in evaporator has a decreasing trend with the increase of critical temperature of working fluid for ORC-FS and ORC-FP, while the optimal pinch point temperature difference in condenser keeps nearly constant. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine cycle Thermo-economic evaluation Electricity production cost Plate heat exchanger Shell-and-tube heat exchanger Finned-tube heat exchanger
1. Introduction Along with the rapid development of economy, a large amount of low-temperature waste heat sources is generated by existing industrial process. Meanwhile, environmental pollution and energy shortage have significantly deteriorated. Survey data shows that low/medium grade waste heat accounts for 50% or more proportion of the total heat produced in industrial processes [1]. A lot of approaches have been proposed for the recovery of the waste heat [2] for reducing environmental pollution and energy shortage problems. Among the conversion technologies, organic Rankine cycle (ORC) is the most widely used [3], which can be driven directly by low grade energy such as solar energy [4e7], biomass energy [8e10], geothermal energy [6,11e14], waste heat from gas turbine [15], and exhaust gases from vehicle engines or marine diesel engines [16,17] to electricity. ORC has the same system components as steam Rankine cycle (a
* Corresponding author. Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Ministry of Education, Chongqing University, Chongqing 400030, China. E-mail address: [email protected] (C. Liu). http://dx.doi.org/10.1016/j.energy.2017.01.132 0360-5442/© 2017 Elsevier Ltd. All rights reserved.
boiler, a condenser, an expansion device and a pump) but uses organic fluid. However, the conversion efficiency is relatively low due to low heat source temperature [18]. In order to maximize the electricity generation efficiency of ORCs, many researches have been carried out. To sum up previous work focused on in the following aspects: selection criteria of optimal organic working fluids (pure or zeotropic working fluids [19]), thermodynamic and physical properties [20], various thermodynamic cycles (basic cycle, trans-/supercritical cycle [14,21e23], regenerative cycle [18,24], reheated cycle, recuperative cycle [24e26] and combined cycle [8,15,27,28]), selection of primary components and geometric dimensions [19,28], and environmental concerns [29]. In addition, commercial applications of ORC have a rapid development in Europe and the US. Among them, Turboden and ORMAT are primarily representative companies for recovering biomass and geothermal energy, respectively [2]. Researchers have increasingly focused on the ORCs' feasibility in terms of views on technical, economic and environmental point in recent years. Li et al. [30] conducted an economical model of the subcritical ORC system for the use of low-temperature flue gas. The electricity production cost was selected as the evaluation criterion. Quoilin et al. [1] investigated the thermodynamic and economic
C. Zhang et al. / Energy 123 (2017) 728e741
Nomenclature A Bo C Co D Fr G H K Nu Pr Re U V Y cp dt db g m p pp q x
heat transfer surface area (m2) boiling number cost ($)/constant relative to equipment cost correlation convection number diameter (m) Froude number mass velocity (k gm2 s1) fin height (m) constant relative to equipment cost correlation Nuselt number Prandtl number Reynolds number overall heat transfer coefficient (Wm2 K1) volume flow rate (m3/s) Fin pitch (m) specific heat (J kg1 K1) fin collar outside diameter (m) fin root diameter (m) acceleration due to gravity (m/s2) mass flow rate (kg/s) pressure (kPa) payback period (year) average imposed wall heat flux (kW/m2) dryness fraction
Abbreviations COM Cost of Operation and Maintenance CRF Capital Recovery Factor GWP Global Warming Potential relative to CO2 HX-P Plate Heat Exchanger HX-S Shell-and-tube Heat Exchanger HX-F Finned tube Heat Exchanger ORC-PP Both evaporator and condenser using plate heat exchanger ORC-FP Finned tube bundles as evaporator and plate heat exchanger as condenser ORC-SS Both evaporator and condenser using shell-and-tube heat exchanger
optimization of a small scale ORC for recovering waste heat. Plat heat exchanger was used in their model and economic profitability. Lecompte et al. [28] developed a thermo-economic design methodology of ORC based on CHP system, taking into account partial load behavior. A plate heat exchanger and a finned tube heat exchanger with circular fins were selected as evaporator and condenser, respectively. Zeotropic mixtures are used as working fluids for better temperature profiles match of heat source and heat sink [31]. Wu et al. [32] calculated and compared the performance of ORC using zeotropic mixtures with corresponding pure fluids. The result showed that the economic performance of that system was worse in some extent compared to corresponding pure fluid cycles. However, Kheiri et al. [19] found that the ORC using zeotropic mixture of npentane and R245fa could not only weaken flammability of npentane well but also made the system reached a good economic profitability. In addition, thermo-economic assessment for different ORC applications was conducted. Astolfi et al. [11] presented a detailed analysis of binary ORC power plants for recovering low-medium
ORC-FS
729
Finned tube bundles as evaporator and shell-and-tube heat exchanger as condenser
Greek letters pressure difference (kPa) temperature difference (K) convection heat transfer coefficient (Wm2 K1) Chevron angle/finned ratio thickness (m) efficiency density (kg/m3) thermal conductivity (Wm1 K1) dynamic viscosity (Ns/m2)
Dp DT a b d h r l m
Subscripts/superscripts LT lifetime c cold/condensation cond condenser crit critical e evaporating evap evaporator eq equivalent gen generator fg flue gas h heat source/hot/hydraulic in inlet/inside l liquid g gas max maximum min minimum out outlet pp pump sp single-phase t turbine tot total tp two-phase wf working fluid 1e8 state points
temperature geothermal sources. Walraven et al. [12] performed an economic optimization of air-cooled ORC driven by geothermal heat sources. Yang et al. [13] investigated the economic optimization of an ORC with lower GWP working fluids in geothermal application. A review of the literature reveals that the thermo-economic comparisons of different ORC systems are of great difference and complicated. Consequently, this paper aims to conducts a comparative analysis of thermo-economic concerning four ORC configurations. In the models, four ORC configurations are: both evaporator and condenser using plate heat exchanger (ORC-PP), a finned tube bundles with circular fins as evaporator and a plate heat exchangers as condenser (ORC-FP), both evaporator and condenser using shell-and-tube heat exchanger (ORC-SS), and a finned tube bundles with circular fins as evaporator and a shelland-tube heat exchanger as condenser (ORC-FS). The cost of heat exchanger, turbine, electricity generator, working fluid pump and cooling water pump is considered. Then the evaporating pressure, pinch point temperature differences in evaporator and condenser are analyzed and optimized at different heat source temperatures
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C. Zhang et al. / Energy 123 (2017) 728e741 Table 1 Given conditions and ORC parameters.
Fig. 1. Schematic diagram of an ORC.
and different heat exchanger configurations by using the EPC (electricity production cost) and ppd (dynamic payback period) as the objective function. Furthermore, the thermo-economic comparison of subcritical ORC provides detailed information to evaluate the thermo-economic viability of ORC, and then seek the optimal heat exchanger configuration, parameters and suitable working fluids for the ORC system to achieve the goal of high efficiency utilization of energy and energy savings. 2. System configurations and assumptions 2.1. System description The schematic diagram of the ORC is shown in Fig. 1. In the models, superheat is not considered for dry and isentropic fluids. However, for wet fluids, superheat is necessary to avoid liquid droplet impingement in turbine during the expansion, and it is assumed that the state of expander outlet is saturated. In addition, the internal heat exchanger (IHX) will not be taken into account in the ORC models due to larger capital investment. The working fluid absorbs heat from the exhaust flue gas in the evaporator and then continuously vaporizes into saturated vapor (dry and isentropic fluid) or overheated vapor (wet fluid). Then the high pressure vapor flows into the turbine to expand and convert into shaft work to drives the generator to generate electricity. After that, the expanded superheated vapor flows into to condenser, in which it is condensed to saturated liquid by the cooling water. The saturated liquid is pumped into the evaporator again to continue the next cycle. Fig. 2 shows Tes diagram of different working fluids. In the thermodynamic modeling, the given conditions and ORC parameters are shown in Table 1. In order to prevent from corrosion
Parameter and unit
Value
The flue gas temperature, C The temperature constraint of discharged flue gas, C The flow rate of flue gas, kg/s Condensing temperature, C The inlet temperature of cooling water, C Pinch point temperature in evaporator, C Pinch point temperature in condenser, C Turbine isentropic efficiency Pump isentropic efficiency Generator efficiency The operating time top,hour life cycle time LT, year annual loan interest rate i on-grid electricity price Celec, $/kWh
120e200 82 10 30 20 5e30 5e30 0.80 0.75 0.95 8000 20 0.04, 0.05, 0.06 0.10, 0.15, 0.20
of low-temperature flue gas, the temperature constraint of discharged flue gas is set to 82 C [33]. The condensing temperature is usually assumed to be 30e36 C when water is used as cooling medium [13,15,34]. Therefore the condensing temperature is assumed to be 30 C in present paper. In addition, the following assumptions are also taken into consideration: (1)ORC system works in a steady state; (2)There is no pressure drop in the evaporator, pipes and condenser; (3)The heat losses in the components are neglected; (4)Working fluids at the condenser outlet is saturated liquid; (5)Dry and isentropic working fluid at the turbine inlet is saturated vapor; (6)Temperature difference at the pinch point in heat changer is not less than 3 C [30].
2.2. Heat exchanger configurations It is found that the capital cost of heat exchanger accounts for a large proportion of ORC, and even reaches about 80% in case of aircooled condenser[ [12]. Therefore, the selection of heat exchanger in ORC is very important. In the evaporator the heat transfer process happens between gas phase and liquid phase and in the condenser heat transfer process does in vapor/liquid-liquid. Therefore, four kinds of heat exchanger configurations (PP, FP, SS and FS) are simulated in the model. The geometric parameters of the heat exchangers are given in Table 2.
Fig. 2. Tes diagram of working fluids: (a) dry or isentropic and (b) wet.
C. Zhang et al. / Energy 123 (2017) 728e741
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Table 2 Heat exchangers parameters. Heat exchanger
Parameter and unit
Value
Heat exchanger
Parameter and unit
Value
Plate heat exchanger
Effective channel length, LEff(m) Width of flow channel, w(m) Plate thickness, d(mm) Mean flow channel gap, b(mm) Corrugation pitch, l(mm) Chevron angle, b(degrees) Material Pressure drop allowance, (kPa) Inner tube diameter, di(mm) Outer tube diameter, do(mm) Tube pitch, S(mm) Tube material Shell material Pressure drop allowance, (kPa) Shell Tube
1.25 0.55 0.5 5 15 p/6 CS 10 15 19 25 CS CS
Finned tube heat exchanger
Inner tube diameter, di(mm) Outer tube diameter, do(mm) Fin collar outside diameter, dt(mm) Fin root diameter, db(mm) Fin pitch, Y(mm) Fin height, H(mm) Fin thickness, df(mm) Transversal tube pitch, S1(mm) Longitudinal tube pitch, S2(mm) Tube length, L(m) Tube material Fin material Pressure drop allowance, (kPa) Air Tube
10 13 25.3 10.55 2.6 5 0.15 25 21 3 CS Al
Shell-and-tube heat exchangera
a
30 20
30 20
Tube side for working fluid and shell-side for heat transfer fluid.
2.3. Working fluids
Wt ¼ mwf ðh1 h2 Þ ¼ mwf ðh1 h2s Þht
The thermophysical properties of working fluids largely affects the performance of ORC system, such as conversion efficiency, economic viability, environmental impact and operating conditions [35]. Therefore, 11 substances are selected as working fluids of ORC system, as shown in Table 3. Furthermore, two refrigerant evaluation indexes ODP being zero and GWP being lower than 150 [19] are considered except for R245fa. The properties of working fluids are calculated by using REFPROP Version 9.0 [36] in the software MATLAB Version 7.10.0.
(3)
The work consumed by pump is
Wpp ¼ mwf ðh4 h3 Þ ¼ mwf ðh4s h3 Þhpp
(4)
The net power output can be expressed as
Wnet ¼ Wt Wpp
(5)
3.2. Heat exchanger area 3. Thermodynamic and economic models 3.1. Thermodynamic model Energy analysis of ORC is as follows: The heat transfer flow rate in the evaporator is
Qevap ¼ mwf ðh1 h4 Þ ¼ mwf ðh5 h6 Þ
(1)
The heat transfer flow rate in the condenser is
Qcond ¼ mwf ðh2 h3 Þ ¼ mwf ðh8 h7 Þ
(2)
Evaporator is divided into three regions, i.e. preheating, evaporation and superheating region while condenser is divided into two regions, i.e. cooling and condensation region, as shown in Fig. 3. For two-phase flow region, the process is divided into finite small elements so that constant properties are be able to assumed in each element [14]. In the heat exchange models, the log mean temperature difference (LMTD) method is employed. The fouling heat resistance in the process of heat transfer is ignored. Thus, the heat transfer and heat transfer coefficients are given by: Single-phase region:
Qsp ¼ Usp Asp DTLM;sp
The work produced by the turbine is
(6)
Table 3 Properties of 11kinds of working fluids. ASHRAE 34
Classification
Molecular mass
TNBP( C)
Tcrit( C)
pcrit(MPa)
Safetya
Life/yr
ODP
GWP
R1234fy R161 R152a RC270 R600a R600 R245fab R601b R601a R601 Cyclopentane
HFO HFC HFC HC HC HC HFC HC HC HC HC
114.04 48.04 66.05 42.08 58.12 58.12 134.05 72.15 72.15 72.15 70.13
29.5 37.06 24 31.5 11.7 0.5 15.1 9.5 27.8 36.1 49.4
94.7 102.2 113.3 125.2 134.7 152 154 160.6 187.2 196.6 238.6
3.38 5.09 4.52 5.58 3.63 3.8 3.65 3.2 3.38 3.37 4.51
A2L
0.029 0.18 1.5 0.44 0.016 0.018 7.7
0 0 0 0 0 0 0 0 0 0 0
<4.4 12 133 ~20 ~20 ~20 1050 ~20 ~20 ~20 11
a b
A2 A3 A3 A3 B1 A3 A3 A3 A3
0.009 0.009 0.007
Refrigerant safety group classification. 1: No flammability; 2: Lower flammability; 3: Higher Flammability; A: Lower Toxicity; B: Higher Toxicity. R245fa with GWP being higher than 150, which is used to compare with other working fluids due to its remarkable thermodynamic properties and wide researches.
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Fig. 3. Three-zone modeling of an evaporator (a) and two-zone modeling of a condenser (b).
The overall heat transfer coefficient of single phase for plate, finned tube and shell-and-tube heat exchanger, respectively:
The Yan-Lio-Lin correlation [37] is used to calculate the condensation heat transfer coefficient for two-phase flow.
1 1 d 1 ¼ þ þ Usp asp;h l asp;c
(7a)
a ¼ 4:118
1 1 d 1 ¼ þ þ Usp asp;h l asp;c bhf
(7b)
1 1 do do do 1 ¼ þ ln þ Usp atp;fl din 2l din atp;wf
(7c)
ll Dh
1=3 Re0:4 eq Pr
(11a)
where
Reeq ¼ Geq Dh hl
(11b)
. Boeq ¼ q Geq $rfg
(11c)
i h Geq ¼ G 1 xm þ xm ðrl =rv Þ1=2
(11d)
Two-phase flow:
Qtp;i ¼ Utp;i Atp;i DTLM;tp;i
(8)
1 1 d 1 ¼ þ þ Utp;i atp;h;i l atp;c;i
(9a)
The pressure drops are expressed as [14]:
Dp ¼ 1 1 d 1 ¼ þ þ Utp atp;h;i l atp;c;i bhf
(9c)
where i denotes each section of two-phase region, hf denotes finned efficiency, b denotes finned ratio. The heat transfer correlations of heat exchangers used in the models are given as follow: (1) Plate heat exchanger The Chisholm-Wanniarachchi correlation [37] is used to calculate the convection heat transfer coefficient for single-phase flow.
Dh a
ll
¼ 0:724
0:646 6b
p
Re0:583 Pr1=3
(10)
The boiling heat transfer coefficient for two-phase flow is calculated by the Yan-Lin correlation [37].
Nu ¼
Dh a
ll
1=3
¼ 1:926Prl
(12)
(9b)
1 1 do do do 1 ¼ þ ln þ Utp;i asp;fl;i din 2l din asp;wf ;i
Nu ¼
2fG2 rDh
h i 1=2 0:5 Bo0:3 eq Reeq 1 xm þ xm ðrl =rv Þ (11)
f ¼ 14:62Re0:514
Re 50
(12a)
f ¼ 2:21Re0:0:097
Re 180
(12b)
(2) Finned tube heat exchanger and shell-and-tube heat exchanger The Young correlation [38] is employed to calculate the air-side heat transfer coefficient in the finned tube heat exchanger for single-phase flow. For high-fin tube bundle, i.e. dt/db ¼ 1.2~1.6, and db ¼ 13.5~16 mm:
!0:075 db a db Gmax 0:667 cp m1=3 Y 0:164 Y ¼ 0:1507 H k m k df
(13)
For high-fin tube bundle, i.e. dt/db ¼ 1.7~2.4, db ¼ 12~41 mm:
db a d Gmax 0:718 cp m1=3 Y 0:296 ¼ 0:1378 b H k m k The pressure drops of tube outside are expressed as:
(14)
C. Zhang et al. / Energy 123 (2017) 728e741
Dp ¼
nfG2max 2r
(15)
Gmax db 0:316 S1 0:297 S1 0:515 f ¼ 37:86 m db S2
Co ¼
733
1 x 8 rg 0:5 x rl
(17c)
Froude number with all flow as liquid:
(15a) Frl0 ¼ G2
where n is the tube row number along flow direction The Gnielinski correlation [39] is used to calculate in-tube heat transfer coefficient both in the finned tube heat exchanger and shell-and-tube exchanger for single-phase flow:
i h ðf =8ÞðRe 1000ÞPrf da 1 þ ðd=lÞ2=3 ct ¼ Nu ¼ pffiffiffiffiffiffiffiffi 2=3 k 1 þ 12:7 f =8 Prf 1
(16)
where f is Darcy resistance coefficient, which is calculated by Filonenko equation
f ¼ ð1:821gRe 1:64Þ2
(16a)
.
r2l gd
(17d)
Liquid Reynolds number:
Rel ¼ Gdð1 xÞ=ml
(17e)
The Gungor-Winterton correlation [41,42] is employed to calculate the boiling heat transfer coefficient in the shell-and-tube heat exchanger for two-phase flow:
atp
8 9 ! < x 0:75 r 0:41 = l ¼ al 1 þ 3000Bo:896 þ 1:12 : ; 1x rg
(18)
where
For liquid, ct is given by:
ct ¼
Prf Prw
0:11
Prf ¼ 0:05 20 Prw
0:4 al ¼ 0:023Re0:8 l Prl ðkl =dÞ
(16b)
For gas, ct is given by:
ct ¼
Tf Tw
0:45
Tf ¼ 0:5 1:5 Tw
(16c)
al ¼ 0:023ðGð1 xÞd=mÞPr0:4 l ðkl =dÞ
gas: 0.6
o
(19)
o
(17)
0:4 al ¼ 0:023Re0:8 l Prl ðll =dÞ
(19a)
The shell-side pressure drop is calculated in the shell-and-tube heat exchanger by the following equation [19].
The Kandlikar correlation [40] is used to calculate the boiling heat transfer coefficient in the finned tube heat exchanger for twophase flow:
n
.
atp ¼ al ð1 xÞ0:8 þ 3:8x0:76 ð1 xÞ0:04 Pr0:38 where
which is valid for a range of
atp ¼ al C1 CoC2 ð25Frl0 ÞC5 þ C3 BoC4 Ffl
The Shah correlation [43] is used to calculate the in-tube condensation heat transfer correlation both in the finned tube heat exchanger and shell-and-tube exchanger for two-phase flow:
n
(18a)
(17a)
where value of C1, C2, C3, C4 and C5 in Kandlikar correlation is given in Table 4, and Co is determined as following:
Dp ¼
fDG2 ðNb 1Þ 2rDe ðm=mw Þ0:14
(20)
Table 5 shows the heat transfer correlations for different heat exchangers at different regions. In the modeling, the pressure drops in the heat exchangers are balanced by pump power compensation as following equation.
Wpp;offset ¼ Dp$Vwf
(21)
Co < 0.65: convection boiling Co > 0.65: nucleate boiling 3.3. Economic model
Boiling number:
Bo ¼ q Giig
(17b)
Convection number:
log Cp0 ¼ K1 þ K2 log10 ðAÞ þ K3 ½log10 ðAÞ2
Table 4 Value of constant for Kandlikar heat transfer correlation [40]. Constant
Convection boiling
Nucleate boiling
C1 C2 C3 C4 C5 a
1.136 0.9 667.2 0.7 0.3
0.6683 0.2 1058.0 0.7 0.3
a
For vertical tube or horizontal tube (Frl > 0.04) C5 ¼ 0.
The cost of the equipment using carbon steel construction and at ambient operating pressure is calculated as following equation [30,44]. For heat exchanger:
(22)
For pump and turbine:
log Cp0 ¼ K1 þ K2 log10 ðWÞ þ K3 ½log10 ðWÞ2
(23)
When taking the specific material of equipment and operating pressure into account, the correction for bare module cost is presented as
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Table 5 Heat transfer correlations for different heat exchangers at different regions. Heat exchanger configuration
Heat exchange region
Heat transfer correlation for flue gas or water
Heat transfer correlation for working fluid
PP
Preheating Boiling Superheating Cooling Condensation Preheating Boiling Superheating Cooling Condensation Preheating Boiling Superheating Cooling Condensation Preheating Boiling Superheating Cooling Condensation
Chisholm-Wanniarachchi Chisholm-Wanniarachchi Chisholm-Wanniarachchi Chisholm-Wanniarachchi Chisholm-Wanniarachchi Young Young Young Chisholm-Wanniarachchi Chisholm-Wanniarachchi Gnielinski Gnielinski Gnielinski Gnielinski Gnielinski Young Young Young Gnielinski Gnielinski
Chisholm-Wanniarachchi Yan-Lin Chisholm-Wanniarachchi Chisholm-Wanniarachchi Yan-Lio-Lin Gnielinski Kandlikar Gnielinski Chisholm-Wanniarachchi Yan-Lio-Lin Gnielinski Gungor-Winterton Gnielinski Gnielinski Shah Gnielinski Kandlikar Gnielinski Gnielinski Shah
High-pressure side
Low-pressure side FP
High-pressure side
Low-pressure side SS
High-pressure side
Low-pressure side FS
High-pressure side
Low-pressure side
CBM ¼ CP B1 þ B2 Fm Fp
(24)
viability, EPC optimization:
where Fm and Fp are the material and pressure correction factor, respectively. Fm is given in Table 6 and Fp is determined by 2
logFP ¼ C1 þ C2 log10 ðpÞ þ C3 ½log10 ðpÞ
(25)
K1, K2, K3, B1, B2, C1, C2 and C3 are fitting cost coefficients for different equipment. The values are given in Table 6. The cost of the electricity generator is calculated by following equation [19]. 0 Cp;gen
0:95 ¼ 60 Wgen
(26)
The actual cost need to be converted from the cost of 2001 by introducing the CEPCI (Chemical Engineering Plant Cost Index) [44]. The cost of 2014 should be corrected as:
CBM;2014 ¼ CBM;2001 CEPCI2014 =CEPCI2001
(27)
where CEPCI2001 ¼ 397, CEPCI2014 ¼ 586.77. The total capital cost is mainly determined by the cost of main equipment, including heat exchanger, turbine, electricity generator, working fluid pump and cooling water pump. Then the total investment capital cost can be approximately presented as:
Ctot ¼ CBM;evap þ CBM;cond þ CBM;tur þ CBM;gen þ CBM;pp þ CBM;wp (28) Furthermore, the COM (cost of operation and maintenance) should be considered and is set as 1.5%. To evaluate the economic
EPC ¼
is employed
as evaluation
criteria in
the
ðCtot CRF þ COMÞ top Wnet
(29)
where CRF is the capital recovery factor:
CRF ¼ h
ið1 þ iÞLT ð1 þ iÞLT 1
i
(30)
where top denote the operating time, i is annual loan interest rate and LT denotes the life cycle time. All electricity is supplied to the power grid. Hence the investment return time ppd can be calculated by the following equation:
ppd ¼ ln
Wnet Celec COM Wnet Celec COM i,Ctot
lnð1 þ iÞ
(31)
The thermo-economic model is calculated in the MATLAB software. The flow chart of the thermo-economic modeling is shown in Fig. 4. In the modeling, optimization is carried out by using EPC as objective function. Evaporating temperature and pressure, pinch point temperature differences in the evaporator and condenser, temperature of discharged flue gas and working fluid mass flow rate can be obtained according to corresponding optimal EPC.
Table 6 Values of constants for different equipments [44]. Equipment
K1
K2
K3
C1
C2
C3
B1
B2
Fm
Fbm
HX-P HX-S
4.6656 4.8306
0.1557 0.8509
/ /
1.63
1.66
1.25
/
Pump
3.3892
0.0536
1.89
1.35
1.50
/
Turbine
2.2476
1.4965
0 0 0.08183 0 0.0123 0 0.00226 /
1.0 1.30
0.3030
0 0 0.11272 0 0.00627 0 0.3957 /
1.21 1.66
4.3247
0 0 0.03881 0 0.00164 0 0.3935 /
0.96 1.63
HX-F
0.1547 0.3187 (5 < p < 140barg) 0.1634 (5 < p < 140barg) 0.1538 (10 < p < 100barg) 0.1618
/
/
/
3.30
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Fig. 4. Flow chart of the thermo-economic modeling.
Fig. 5. Variation of EPC with pe for different heat exchanger configurations at Tfg,out > 82 C: (a) and (b), Tfg,out < 82 C: (c) and (d).
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4. Results and discussion 4.1. Economic analysis This paper takes R600 and R601 as a case study. As shown in Fig. 5, the variation of EPC with evaporating pressure (pe) is presented for different ORC configurations at Th ¼ 160 C and DTe ¼ DTc ¼ 8 C. It can be found that EPC decreases first smoothly and then increases steeply with the pe. That is to say there exists a minimum EPC at a specific pe. This phenomenon is also found in the literature [14,19,30]. In addition, the EPCs of ORC-PP and ORC-SS are apparently higher than that of ORC-FP and ORC-FS, of which ORCFS keeps the lowest EPC with the variation of pe. However, the difference of different ORC configurations shrinks gradually with the increase of pe. As shown in Fig. 6, the reason is that when pe increases, total investment cost (Ctot) decreases with the decrease of heat exchanger area caused by the decrease of heat transfer of the heat source, while Wnet increases firstly in a small pressure range and then decreases sharply. This comprehensive variation of Ctot and Wnet results in a minimum EPC due to EPC being proportional to Ctot and inversely proportional to Wnet. Moreover, Fig. 5 also presents that EPC increases with pe starting from a specific point when constraint of discharged flue gas temperature is considered. The same trend exists in the Variation of ppd with pe, as shown in Fig. 7. It is noted that EPC and ppd have the same independent variables of Ctot and Wnet, as expressed in Eqs. (29) and (31). That is reason why the variation of EPC and ppd keep
Fig. 6. Effect of pe on the Ctot and Wnet for different heat exchanger configurations.
same. Therefore, it can be concluded that EPC and ppd can achieve a minimum value at an appropriate pe. Fig. 8 presents the variation of EPC with the pinch point temperature in the evaporator (DTe) at Th ¼ 160 C and Te ¼ 106 C, using R600 and R601 as working fluid, respectively. It can be seen that EPC decreases at first and then increases with DTe. Thus, there also exists an optimal DTe corresponding to a minimum EPC, as the same optimal result for pinch point temperature difference in the condenser (DTc). On one hand, the mean heat transfer temperature difference increases with the increase of DTe, which results in a reduction of heat transfer area and capital cost. On the other hand, the heat transfer decreases due to the increase of DTe at a given evaporating temperature (Te), which results in a reduction of power output. At first, in a lower DTe range, the reduction of capital cost has a greater effect than the reduction of power output on the EPC. Hence EPC decreases with the DTe. And with further increase of DTe, the reduction of power output turns into a dominant factor due to rapid reduction of heat input, and results in the increase of EPC. In this work, because ambient temperature water is used as coolant the DTc is limited in a small range of 5e10 C, and the optimal results almost are 8 C. For ORC-PP, ORC-FP and ORC-FS, the variation of EPC is relatively smooth while the EPC varies sharply for ORC-SS, which leads to a greater pinch point temperature difference with respect to a minimum EPC. 4.2. Optimization results The best thermodynamic performance may not always meet the optimal economic performance. Table 7 shows the optimization results for R601 due to its good economic benefits and wider scope of heat source temperatures. The lowest EPC 0.074$/kWh and lowest ppd 6.7 years are obtained for ORC-FS at Th ¼ 140 C. The value is just slightly lower than that of ORC-FP. While the largest EPC 0.132$/kWh is obtained for ORC-PP, and the largest Wnet 70.6 kW for ORC-FP are found. At Th ¼ 160 C and Th ¼ 180 C, the same results can be found for different configurations. Through comparative analysis, ORC-FP and ORC-FS look promising for recovering waste heat of flue gas. Moreover, ORC-FS shows the most attractive. In addition, the optimal pe or Te increases with the increase of heat source temperature. For more optimization results on different ORC configurations and different working fluids, please browse Table S1- S4 in the Supplementary data of Appendix A. The DTe and DTc, play an important role in the design process of heat exchanger. As presented in Fig. 8, there exists optimal DTe, and DTc in the evaporator and condenser to minimize the EPC. Fig. 9 presents the optimal DTe (DTe,opt) at Th ¼ 160 C with different working fluids. For ORC-PP and ORC-SS, the DTe,opt has no obvious regularity and fluctuates with different working fluids as shown in Fig. 9(a). For ORC-FP and ORC-FS, as shown in Fig. 9(b), the DTe,opt has a decreasing trend with the increase of critical temperature of working fluids. While the DTc,opt keeps nearly a constant value of about 8 C for different ORC configurations. As shown in Figs. 10e12, the minimum EPC, and the corresponding Wnet and ppd for different working fluids at Th ¼ 160 C are presented. The EPC for ORC-PP using different working fluids is the largest, followed by ORC-SS, ORC-FP and ORC-FS. The EPC of ORC-PP and ORC-SS ranging from 0.085 to 0.150$/kWh are apparently higher than that of ORC-FP and ORC-FS ranging from 0.055 to 0.070$/kWh for different working fluids. In addition, the ranges of ppd are 6.5e8.4 years for ORC-PP and ORC-SS, and 4.3e5.6years for ORC-FP and ORC-FS. Among them, ORC-FS is the most cost-effective ORC configuration. It can be seen that ORC-PP is 60%e70%, ORC-SS is 47%e51%, and ORC-FP is about 14% higher EPC than that of ORC-FS. It is also found that the EPC and ppd have
Fig. 7. Variation of ppd with pe for different heat exchanger configurations at Tfg,out > 82 C: (a) and (b), Tfg,out < 82 C: (c) and (d).
Fig. 8. Variation of EPC with DTe for different heat exchanger configurations ((a) & (b)).
Table 7 Optimization results for working fluid R601. Th ( C)
PP 140
160
180
140
160
180
140
160
180
140
160
180
Teva ( C) peva (kPa) pcon (kPa) mwf (kg/s) mcs (kg/s) DTe ( C) DTc ( C) Tfg,out( C) Wnet (kW) EPC ($/kWh) ppd (year)
90 470.3 82.0 1.285 55.66 11 8 82.1 68.8 0.132 12.3
100 592.7 82.0 1.576 68.28 14 8 86.7 96.5 0.104 8.1
112 769.1 82.0 1.843 79.82 17 8 90.9 129.0 0.085 7.2
96 541.2 82.0 1.213 52.52 8 8 84.2 70.6 0.085 8.2
106 676.6 82.0 1.315 69.97 8 8 83.2 106.1 0.068 6.0
120 906.7 82.0 1.952 84.57 8 8 83.2 147.6 0.057 4.9
86 427.1 82.0 1.203 52.09 17 8 86.5 60.6 0.109 11.6
94 516.7 82.0 1.441 62.40 23 8 94.2 81.6 0.088 8.4
104 647.7 82.0 1.641 71.08 29 8 102.7 105.3 0.074 6.7
90 470.3 82.0 1.285 55.66 11 8 82.1 68.8 0.074 6.7
106 676.6 82.0 1.615 69.97 8 8 83.2 106.1 0.059 5.1
114 801.9 82.0 2.005 86.86 11 8 82.4 143.2 0.050 4.2
FP
SS
FS
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Fig. 9. The DTe,opt of different working fluid for different heat exchanger configurations ((a) & (b)).
Fig. 10. The minimum EPC of different working fluid for different heat exchanger configurations.
a same trend, which decreases with the increase of critical temperature of working fluids except for ORC-PP. For ORC-PP, EPC and ppd increase firstly and then decrease with the increase of critical temperature of working fluid. For ORC-FS using different working fluids, the lowest EPC 0.058$/kWh and lowest ppd 4.3years for cyclopentane, and the highest Wnet 111.8 kW for RC270 are
Fig. 11. The ppd of different working fluid for different heat exchanger configurations at the minimum EPC.
Fig. 12. The Wnet of different working fluids for different heat exchanger configurations at the minimum EPC.
obtained. It is demonstrated that the heat exchanger configuration and working fluid have a significant influence on the economic performance of ORC systems.
Fig. 13. The minimum EPC of different working fluids at different heat source temperatures in FS ORC.
C. Zhang et al. / Energy 123 (2017) 728e741
Fig. 14. The ppd of different working fluids at different heat source temperatures and minimum EPC for ORC-FS.
4.3. Sensitive analysis: electricity price and annual loan interest rate It has been mentioned above that Th has a great influence on the pinch point temperature difference. Nevertheless, the influence of Th on economic performance is more evident. As shown in Fig. 13,
739
the minimum EPC and ppd are greatly affected by Th for ORC-FS. However, the difference of minimum EPC and ppd between two heat source temperatures will become much smaller with the increase of Th. Taking R600 as example, the minimum EPC is 0.104, 0.075, 0.06, 0.051 and 0.043$/kWh with respect to ranges of Th from 120 to 200 C, which shows a reduction rate of 27.9%, 20%, 15% and 15.5%, respectively. The influence of Th on ppd has the same influence on EPC, as shown in Fig. 14. In addition, the working fluid with lower or higher critical temperature cannot meet the temperature constraint of discharged flue gas at some specific Th. That is to say, not all working fluids are suitable for all heat source temperature. In this paper, RC270, R600a, R600, R601b, R601a and R601, critical temperature ranging from 152.2 to 196.6 C, are suitable for the heat temperature ranging from 120 to 200 C. Similarly, the optimization results for different ORC configurations and different working fluids are found in the Supplementary data of Appendix A. The grid price of state grid company is a ranges of 0.03e0.152$/ kWh in China [45], including traditional energy power plant and new energy power plant. Therefore, three kinds of electricity price are selected in the modeling as shown in Table 1. In addition, electricity price of 0.2$/kWh should take the government subsidies into consideration. For ORC-PP, as show in Fig. 15, the EPC are 0.098, 0.0105 and 0.113$/kWh with respect to the annual loan interest rate of 4, 5 and 6% [46], which shows an average increase rate of 7%. And the ppd are 22.2, 10.9 and 7.3years with respect to the on-grid electricity price of 0.10, 0.15 and 0.20$/kWh, showing a reduction rate of 51% and
Fig. 15. Sensitivity analysis of electricity price and loan interest rate on the EPC and ppd ((a), (b), (c) & (d)).
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33%, which makes a great reduction in ppd. Therefore, the government subsidies or the lower loan interest rate can greatly encourage the development of ORC program when plate or shell-and-tube heat exchanger must be used in the condition of gas-liquid heat exchange. 5. Conclusion The present paper performs a comparative analysis of an ORC based on four different kinds of heat exchanger configurations for recovering low-temperature waste heat of flue gas, ranges from 120 to 200 C. The evaporating temperature, pinch point temperature differences in evaporator and condenser are analyzed and optimized based on different heat exchanger configurations by using EPC and ppd as the objective function. Meanwhile, the sensitivity analysis is performed to analyze the effects of electricity price and annual loan interest rate on thermo-economic performance of ORC. The main conclusions can be drawn: (1) The EPCs of ORC-PP and ORC-SS are apparently higher than that of ORC-FP and ORC-FS. For different working fluids, the EPC of former two configuration ranges from 0.085 to 0.150$/ kWh and the latter two configuration from 0.055 to 0.070$/ kWh. Among them, ORC-FS is the most cost-effective ORC configuration. (2) It is found that the ppd has the same variation trend with EPC. For different working fluids, the ranges of ppd of are 6.5e8.4 years for ORC-PP and ORC-SS, and 4.3e5.6years for ORC-FP and ORC-FS. (3) The DTe,opt has a decreasing trend with the increase of critical temperature of working fluids at a certain heat source temperatures for ORC-FS and ORC-FP. But the DTc,opt keeps nearly constant value of about 8 C. (4) On-gird electricity price and lower loan interest rate, especially the subsidies of on-gird electricity price can make great reductions in EPC and ppd. The fluids RC270, R600a, R600, R601b, R601a and R601 are recommended as working fluids due to considerable economic benefits and the wider scope of heat source temperatures. Acknowledgements This work is supported by “National Natural Science Foundation of China” (No. 51576019) and “International Science & Technology Cooperation Program of China” (No. 2015DFG62270). Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.energy.2017.01.132. References [1] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic Rankine cycles. Appl Therm Eng 2011;31(14): 2885e93. lez F, Segovia JJ, Martín MC, Antolín G, Chejne F, Quijano A. A technical, [2] Ve economical and market review of organic Rankine cycles for the conversion of low-grade heat for power generation. Renew Sustain Energy Rev 2012;16(6): 4175e89. [3] Quoilin S, Lemort V. Technological and economical survey of organic Rankine cycle systems. 2009. [4] Kosmadakis G, Manolakos D, Kyritsis S, Papadakis G. Economic assessment of a two-stage solar organic Rankine cycle for reverse osmosis desalination. Renew Energy 2009;34(6):1579e86. [5] Kosmadakis G, Manolakos D, Papadakis G. Simulation and economic analysis of a CPV/thermal system coupled with an organic Rankine cycle for increased power generation. Sol Energy 2011;85(2):308e24.
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