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Economical evaluation and optimization of organic Rankine cycle with mixture working fluids using R245fa as flame retardant
Applied Thermal Engineering 113 (2017) 1056–1070
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Research Paper
Economical evaluation and optimization of organic Rankine cycle with mixture working fluids using R245fa as flame retardant Huan Xi a, Ming-Jia Li a, Ya-Ling He a,⇑, Yu-Wen Zhang a,b a b
Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA
h i g h l i g h t s Parametric optimization of ORC using mixture working fluids was carried out. R245fa was introduced as the flame retardant in the mixture working fluids. Fraction of R245fa was employed as one of optimized variables. Correlations between fraction of R245fa and heat source temperature were obtained.
a r t i c l e
i n f o
Article history: Received 17 May 2016 Revised 7 November 2016 Accepted 7 November 2016 Available online 9 November 2016 Keywords: Waste heat recovery (WHR) Organic Rankine cycle (ORC) Mixture working fluids Flame retardant Performance optimization
a b s t r a c t A detailed economic model of organic Rankine cycle (ORC) system using mixtures as working fluid has been built. By using R245fa as the flame retardant, R245fa/Isopentane, R245fa/Pentane, R245fa/ Cisbutene and R245fa/Butene were considered as the potential working fluids. The heat source temperatures investigated were 373.15–453.15 K. The optimization of 4 mixture and 5 pure working fluids were carried out with the objective function of minimizing the Electricity Production Cost (EPC). Genetic Algorithm (GA) was employed as the optimized method. Different from the most of the optimization researches about ORC with mixture working fluid, the mixture composition was set as one of the variables in the present work. The results show that the mixture working fluid is more economic-efficient than pure working fluid. The lower EPC value obtained by mixture working fluid was mainly due to the decrease of capital cost, which is essentially caused by the decrease of capital cost of the evaporator. R245fa/Isopentane and R245fa/Pentane were recommended as the optimal working fluids for their minimum EPC values. In addition, the correlations between the optimized mixture composition and heat source temperature were obtained. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Environmental issues like air pollution and global warming caused by the overuse of fossil fuel have become increasingly severe [1,2]. On the other hand, massive of low-temperature waste heat generated during different industry processes released to the environment caused a serious problem of energy waste. For these reasons, new environmentally-friendly technologies need to be developed to improve the overall energy utilization efficiency and recover heat from low-temperature heat sources. Organic Rankine cycles (ORCs) as one of the candidates for waste heat recovery has attracted increasing attention.
⇑ Corresponding author. E-mail address: [email protected] (Y.-L. He). http://dx.doi.org/10.1016/j.applthermaleng.2016.11.059 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
Organic Ranking cycle (ORC) is preferred as an efficient approach due to their flexibility, good thermodynamic performance, and simpler configuration. In the design of the ORC system, one important factor is the working fluid selection. Pure working fluids were generally utilized in ORC systems, for example, refrigerants such as R11, R141b, R113, R123, R245fa, R245ca [3], or some flammable hydrocarbons like n-pentane [4], Isobutane [5]. However, the most important limitation of pure working fluid is the constant temperature during the phase change process in the evaporator and condenser, which is not suitable for sensible heat sources. By contrast, by using mixture working fluid, the system performance can be improved by reducing the mismatch of temperature profiles between the heat transfer fluid and working fluid. Therefore, there is a significantly arising interest in mixture working fluids research. Zhao and Bao [6] discussed the influence of composition shift on ORC using R601/R600a as working fluid; the
H. Xi et al. / Applied Thermal Engineering 113 (2017) 1056–1070
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Nomenclature A B C cp CEPCI CRF de D EPC F GWP h H i k K L LTpl m mf p Pr T ODP Q q _ m VV
c
y Re W M v
heat transfer area (m2) correction factor of Table 5 cost ($) specific heat capacity (kJ/(kgK)) chemical engineering plant cost index capital recovery cost ($/(kWh)) equivalent diameter (mm) tube diameter (mm) electricity production cost ($/(kWh)) correction factor of Table 5 global warming potential specific enthalpy (kJ/kg) total wind pressure of the fan (Pa) interest rate heat transfer coefficient (W/(m2K)) correction factor of Table 5 length (m) plant life time (year) mass mass fraction pressure (kPa) Prandtl number temperature (K) zone depletion potential heat transfer flow rate (kW) heat flux (W/m2) mass flow rate (kg/s) volume low rate (m3/s) latent heat of vaporization (kJ/kg) mole fraction Reynolds number power (kW) molecular weight (kg/mole) specific volume (m3/kg)
fraction ratio was fixed at 31.56%/68.44% (mass fraction), and the heat source temperature was 90 °C. The results showed that the composition shift led to a lower output work of expander, the higher power consumption of the pump, lower net output work, and thermal efficiency. They also evaluated the output work, thermal efficiency and exergy efficiency of the ideal ORC systems for different zeotropic mixtures consisting of 5 components (i.e., R227ea, R245fa, R245ca, R236fa, and R236ea). The fractions of each mixture were evenly distributed between 0 and 1 with a steplength of 0.2. The influence of the heat source temperature on the optimal mass fraction of the different zeotropic mixture was emphasized [7]. Heberle et al. [8] presented a detailed simulation of ORC system. The second law efficiency was calculated for isobutane/isopentane and R227ea/R245fa depending on 5 different fraction ratios. Le et al. [9] carried out the thermodynamic and economic optimization of a subcritical ORC using n-pentane/ R245fa as working fluid under 5 different fraction ratios. The heat source temperature used in the calculated process was 423.15 K. N-pentane was recommended for the highest maximized exergy efficiency and the lowest minimized LCOE (Levelized Cost of Electricity). Garg et al. [10] investigated the system performance using isopentane/R245fa as the working fluid with a fixed mole fraction of 0.7/0.3. The heat source temperatures were in the range of 385– 425 K. The results showed that the mixture and the pure working fluid showed a comparable irreversibility at their optimum expansion ratios. Genetic algorithm was widely adopted for ORC optimization. Dai et al. [11] operated optimization calculating for ORC using GA, the exergy efficiency was employed as the objective
x the mole fraction of R245fa x (with subscripts l and L) dryness 4T pinch temperature (K) Greek symbols efficiency (%) dynamic viscosity (Pas) density (kg/m3)
g l q
Subscripts bm subscripts of correction factor in Table 5 bo boiling section C condenser cri critical cap capital cost co condoning section E evaporator F fan g gas H pinch point of the evaporator i&m insurance and maintenance cost L pinch point of the condenser m correction factor of Table 5 net net power ph phase change section Exp expender wall wall WF working fluid 1–9, 2a, 5a, 1⁄, 7⁄ state points in the cycle superscript elec electricity
function, the working fluid selection was also performed based on the calculation results. Wang et al. [12] operated a multi-objective optimization of the ORC with R134a as working fluid. Exergy efficiency and overall capital cost were employed as the objective functions. The effects of different optimized parameters on the exergy efficiency and capital cost were both examined according to the optimization results. The authors have also adopted GA as the optimization method for different ORC system comparison [13] and working fluid selection [14]. From the above literature review, it can be observed that for mixture working fluid, most works were carried out with fixed mixture composition. Few studies have reported about adopting the mixture composition as one of the optimized variables. In addition, the formulations of mixture fraction to heat source temperature were rarely mentioned. In view of this, in this paper, a number of mixtures consisting of inert (nonflammable) working fluids and flammable working fluids (hydrocarbons) were explored. The inert working fluid we selected was R245fa with high global warming potential (GWP) which was commonly adopted by the previous researches [15,16]; the flammable working fluids we selected were pentane [17], isopentane [18], butane [19] and cisbutene [20] according to previous researches, with low GWP. R245fa was motivated by the possibility of suppressing the flammability of the latter working fluids by blending with these working fluids, meanwhile, the mixture working fluid decreases the GWP relative to R245fa used alone, which enhanced the working fluids’ environmental performance. Properties of working fluids’ components are listed in Table 1. Based on the economic model, the economic
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performance of mixture and pure working fluids were both optimized and compared, and the formulations of mixture composition to heat source temperature were fitted on the basis of the optimized results. Optimal working fluids for different heat source temperatures were recommended based on the calculated results. 2. Modeling and calculation method
where the motor power input is:
W elec ¼ W P =gmotor P The net output power is defined as:
W net ¼ W Exp W elec WF P
ð5Þ
where WF is power consumption of the fan for waste gas and cooling air side, which can be calculated as [18]:
2.1. Thermodynamic model ORC system consists of at least five principal components: evaporator, expander, condenser, pump and working fluid. The working fluid is saturated liquid when passing out the condenser, then be pumped to the evaporator to gain energy from heating source fluid. Generated high pressure working fluid vapor could be saturated or superheated expands in the expander. The system layout and cycle T-s chart of ORC system are shown in Fig. 1. During the calculating process, several assumptions are introduced in this study: (1) the heat transfer and flow processes are in steady-state; (2) pipe pressure drop and heat losses from the components are all neglected; and (3) the parameters of working conditions are assumed as listed in Table 2, which is supplied by the waste heat recovery-related company based on the actual industry process in Xi’an, China. It is necessary to note that during the calculating process, the condensing temperature was assumed as 308.15 K except in the following circumstance: the condensing pressure decreases below atmosphere pressure under 308.15 K. In that case, the condensing temperature should be raised to set condensing pressure equal to the atmosphere pressure in order to avoid air getting into the cycle. It should be noted that steam turbines expand always work well below atmospheric pressure (as low as 35 mbar), however, there needs extra equipment to extract non-condensable fluid. We do not advocate to transplant the vacuum keeping system into ORC system. As a kind of green energy technology, ORC should be positioned as high applicability and simplification technology, any extra equipment which makes the system complex, bulky and with higher initial cost should not be recommended. For the ORC systems, the power of expander and pump can be expressed as:
_ WF ¼ gExp ðh1 h2 Þm_WF W Exp ¼ ðh1 h2a Þm
ð1Þ
_ WF =gP W P ¼ ðh5a h4 Þm_WF ¼ ðh5 h4 Þm
ð2Þ
where gExp and gP are the isentropic efficiency of expander and pump, which are both assumed as 0.8. m_WF is the mass flow rate of the working fluid. hi is the specific enthalpy of the working fluid at the state point i (as shown in Fig. 1). The pump motor efficiency (with the unit of 100%) is calculated from [21]:
h
ð4Þ
i
gmotor ¼ 75 þ 11:5logW P 1:5ðlogW P Þ2 =100
ð3Þ
WF ¼
2:778 107 H V V;g F L g1 g2 g3
ð6Þ
where H is the total wind pressure of the fan, VV,g is the gas flow rate with a unit of m3/h. g1, g2, g3 are fan efficiency, transmission efficiency, and electric efficiency, they are assumed as 0.7, 1.0, 0.9, respectively. FL is the altitude correction coefficient which can be calculated as [22]:
F L ¼ 0:98604 þ 0:01435 102 HL þ 2:495 109 H2L
ð7Þ
where HL in the above formula is altitude with the unit of meter. To calculate the net output power, the mass flow rate of working fluids and cooling air are indispensable. The mass flow rate is usually calculated according to the pinch points temperature and pinch point location. In this work, the pinch point temperature of the evaporator (DT H ) and condenser (DT L ) are both fixed at 8.0 K. For the mixture working fluids, the temperature glide during the evaporating and condensing processes perhaps make the pinch point location varying under different working conditions and different mixture compositions. To confirm the pinch point location and calculate mass flow rate, the following method should be adopted (take evaporator as example): In the evaporator, the possible location of pinch point should be at point (see Fig. 1): 7(1), 7⁄(1⁄), 8(6), 9(5a), then pinch point temperature should be calculated according to one of the following 4 equations:
DT H1 ¼ T g;7 T 1
ð8Þ
DT H2 ¼ T g;7 T 1
ð9Þ
DT H3 ¼ T g;8 T 6
ð10Þ
DT H3 ¼ T g;9 T 5a
ð11Þ
Step 1: point 7(1) is first assumed as the pinch point, then DT H1 is assigned the value of 8.0 K. Step 2: based on the above assumption, DT H2 , DT H3 , DT H4 are calculated according to the energy balance between (1–1⁄ and (7–7⁄), (7⁄–8) and (1⁄–6), (8–9) and (6–5a). Step 3: compare the four temperature differences above, if DT H2 , DT H3 , DT H4 are less than 8.0 K, the mass flow rate should be calculated as:
_ WF ¼ cp;g m _ g ðT 7 T 7 Þ=ðh1 h1 Þ m
ð12Þ
Table 1 Properties of the working fluids’ components.
a b c d
Working fluid
Tcria(K)
Pcrib (kPa)
Flammability
ODPc
GWPd
R245fa (C3H3F5) Cisbutene (C4H8) Butene (C4H8) Isopentane (C5H12) Pentane (C5H12)
427.16 418.09 419.29 460.35 469.7
3651.0 4009.8 4005.1 3378.0 3370.0
Nonflammable Flammable Flammable Flammable Flammable
0 n.a n.a 0 0
1030 n.a n.a 20 20
Pc: critical pressure. Tc: critical temperature. ODP: ozone depletion potential. GWP: global warming potential.
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Fig. 1. System layout and cycle T-s chart of ORC system.
Table 2 Assumed working conditions. Waste gas mass flow rate (kgs1) Environment temperature (K) Environment pressure (kPa) Condensing temperature (K) Expander isentropic efficiency Pump isentropic efficiency Pinch temperature difference in the evaporator (K) Pinch temperature difference in the condenser (K)
15.0 293.15 101.3 308.15 0.8 0.8 8.0 8.0
where cp;g is the specific heat capacity of the waste gas. Otherwise, if there exists a DT H less than DT H1 , the assumption in Step 1 is disproved, then DT H2 should be is assigned the value of 8.0 K and the Step 2–3 need to be repeated to calculate the temperature difference until one the assumption is proved right and the location of pinch point is determined. 2.2. Economic model
EPC ¼ ðCRF C cap þ C m&i Þ=ðh W net Þ
ð13Þ
where Ccap signifies the capital cost, comprising the investments for the evaporator, expander, condenser, pump, fans and working fluid.
CEPCI2014 ¼ ðC bm;E þ C bm;Exp þ C bm;P þ C bm;C Þ þ C bm;F CEPCI1996 CEPCI2014 þ C WF CEPCI2011
LT pl
.h
2 log C Exp ¼ K 1;Exp þ K 2;Exp log W Exp þ K 3;Exp log W Exp
ð18Þ
for the pump,
C bm;P ¼ C P F bm;P
ð19Þ 2
log C P ¼ K 1;P þ K 2;P log W P þ K 3;P ðlog W P Þ
ð20Þ
F bm;P ¼ B1;P þ B2;P F m;P F p;P
ð21Þ
LT pl
ð1 þ iÞ
i 1
log F P;P ¼ C 1;P þ C 2;P log prp þ C 3;P ðlog prp Þ
ð22Þ
prp ¼ pE pC
ð23Þ
for heat exchangers (take evaporator as an example),
C bm;E ¼ C E F bm;E
ð24Þ 2
ð25Þ
F bm;E ¼ B1;E þ B1;E F m;E F p;E ð14Þ
ð26Þ 2
log F p;E ¼ C 1 þ C 2 logðpE p0 Þ þ C 3 ðlogðpE p0 ÞÞ
ð16Þ
ð27Þ
for the fan of waste gas and cooling air,
C bm;F ¼ C F F bm;F F p;F
ð28Þ 2
ð15Þ
where i is the interest rate, assumed to be moderate at 5%, LTpl is the plant life time, assumed at 15 years. h is system working hours per annual operation period (h/year), in this work, it was assumed as 7500 h. Cm&i means the insurance and management cost of the system, which can be calculated as [24,25]:
C m&i ¼ 1:65%C cap
ð17Þ
log C E ¼ K 1;E þ K 2;E log AE þ K 3;E ðlog AE Þ
wherein CEPCI1996 = 382, CEPCI2011 = 582, CEPCI2014 = 586.77 (CEPCI means Chemical Engineering Plant Cost Index) [23]. CRF is the capital recovery cost, which is estimated based on the following equation.
CRF ¼ ið1 þ iÞ
C bm;Exp ¼ C Exp F bm;Exp
2
Electricity production cost (EPC) is the ratio of the total system cost to the net power output, which can be calculated by:
C cap
As the key factor of the cost estimation model, component investment cost provided by a current price quote from a suitable vendor (a seller of equipment), and adjusted using appropriate factors. Each component investment in Eq. (14) could be predicted by the following correlations and the corresponding coefficients K, B, C and F are listed in Table 3 [26,27]. For expander,
log C F ¼ K 1;F þ K 2;F log qV þ K 3;F ðlog qV Þ log F p;F ¼ C 1 þ C 2 log pF þ C 3 ðlog pF Þ
ð29Þ
2
ð30Þ 3
where qV is the gas flow rate with a unit of m /h. For the working fluid,
C WF ¼ cWF mWF
ð31Þ
where cWF is the unit price of working fluid with a unit of $/kg, mWF is the total working fluid charge the unit of kg, which will be intro-
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Table 3 Coefficients in equations evaluating the investment of system components [26,27]. Component
K1
K2
K3
B1
B2
C1
C2
C3
Fm
Fbm
Evaporator Condenser Expander Pump Fan (with electric device)
3.853 3.853 3.514 3.579 3.1761
0.424 0.424 0.598 0.321 0.1373
0 0 0 0.003 0.34314
1.53 1.53 / 1.8 0
1.27 1.27 / 1.51 0.20899
0 0 / 0.168 0.0328
0 0 / 0.348 /
0 0 / 0.484 /
2.8 2.8 / 1.8 /
/ / 3.5 / 1.12
Table 4 Configurations of genetic algorithms.
Optimal value of objective function(EPC)/ $·kWh -1
Population size Chromosome vector Crossover probability Mutation probability Elite count Stop generation
100 [T1, P1, x] 0.4 0.9 20 100
0.48
0.47
0.46
0.45
0.44
0.43
0
20
40
60
80
Evolution time
2.3. Calculation of the heat exchangers area To calculate the heat transfer area of evaporator and condenser, the heat transfer coefficient should be determined [29]. In the evaporator and condenser, the convective heat transfer coefficient of the organic working fluid side is generally more than 2000 W/ (m2K) [30,17] which is much great than that of the gas side. Thus, the overall heat transfer coefficient in the evaporator and condenser are mainly dependent on the convective heat transfer coefficient of gas side; in some related works, it was even assumed to be the constants to simplify the calculation [31,32]. Therefore, in this work the total heat transfer coefficient is estimated by employing the Kern formula [33]:
l lwall
ð33Þ
_ WF ðhWF;iþ1 hWF;i Þ Qi ¼ m
ð34Þ
Q i ¼ kAi
duced in part 2.4. Eqs. (17)–(30) are referred from Refs. [26,27], while Eq. (31) is referred from Ref.[28]. The cost estimation model used in this manuscript are widely adopted. The purchased cost is the key factor of the cost estimation mode, which is provided by a current price quote from a suitable vendor (a seller of equipment), and adjusted using appropriate scaling factors (such as K), and for inflation (such as CEPCI2014), to provide the estimated capital cost.
k 0:55 1=3 Re Pr de g
_ g ðhg;iþ1 hg;i Þ Qi ¼ m
100
Fig. 2. Variation of the optimal objective function value with the evolution times.
kph ¼ kbo ¼ kco ¼ 0:36
where kph, kbo and kco are the heat transfer coefficient during the phase change, boiling and condensing processes. l is the dynamic viscosity of the gas side. de is the equivalent diameter of the tube. k is heat conductivity coefficient, Re and Pr are the Reynolds number and Prandtl number, respectively. The logarithmic mean temperature difference (LMTD) method is widely used in heat exchanger design and calculation. Based on the above analysis, the overall heat transfer coefficient in the heat exchangers are mainly dependent on the convective heat transfer coefficient of the gas side. It is necessary to point out that the physical properties of waste gas were assumed as the fixed values in some related work [34]; even so, the physical properties of the gas are temperature-dependent, especially in the relatively high-temperature ranges [35]. Thus, the assumption of constant properties may lead to inaccurate results. An alternative solution is discretizing the heat exchangers so that the properties variation in each step is small and could be treated as an average constant value. The heat transfer for each step i as well as the corresponding properties of the waste gas and cooling air, and the fractional UAi values are calculated from the following equations (assumed as counter-flow configuration, take evaporator as an example):
0:14 ð32Þ
ðT g;iþ1 T WF;iþ1 Þ ðT g;i T WF;i Þ h i T T WF;iþ1 ln g;iþ1 T g;i T WF;i
ð35Þ
For evaporator, it can be divided into three regions: a superheated region, a two-phase region, and a supercooled region. For the condenser, the last two regions are applicable. Each region is then subdivided into 20 steps. For the calculating method of waste gas physical properties in this work, we adopt the formulas presented in Ref. [36], and for the cooling air, the physical properties calculating formulas were fitted based on the data from Refprop 9.0. 2.4. Working fluid charge estimation In the economic model described in Section 2.2, as seen in Eq. (14), the working fluid cost should be calculated. As we know, the working fluid cost is equal to the product of the unit price ($/ kg) and working fluid charge (kg). The unit price of the working fluids was obtained from the related manufacturers. To estimate the working fluid charge, the method presented in Ref. [37] were adopted. Take evaporator as an example, the mass flow rate of vaporized working fluid at the position with a distance of l from the inlet should be calculated as:
q00WF ¼ qpDl=c
ð36Þ
where q is the heat flux (W/m ), and c is the latent heat (J/kg), D is tube diameter. The total mass flow rate (for each tube) can be calculated as: 2
qWF ¼ qpDL=xL c
ð37Þ
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(a) Initial population
(b) Evolving for 25 times
(d) Evolving for 100 times
(c) Evolving for 75 times
Fig. 3. Population distributions under different evolution times.
Table 5 Calculating results of program stability evaluation. Calculation times
Value of objective function (EPC/$kWh1)
x of R245fa
T1 (K)
p1 (kPa)
1 2 3 4 5 Relative error
0.4283 0.4291 0.4296 0.4290 0.4291 0.295%
0.8552 0.8556 0.8532 0.8541 0.8535 0.285%
373.88 369.94 368.03 370.68 370.00 1.56%
1142.12 1144.94 1126.48 1141.96 1129.95 1.61%
where xL is the dryness at the evaporator outlet, L is tube length. Thus, the dryness at the position with a distance of l from the evaporator inlet can be expressed as:
xl ¼ q00WF qWF ¼ xL l=L
ð38Þ
It can be seen from Eq. (37) that xl is changed linearly with l. Thus, the working fluid charge (kg) is:
H. Xi et al. / Applied Thermal Engineering 113 (2017) 1056–1070 1.30 1.25 1.20 1.15 0.96 0.92 0.88 0.84 0.750 0.725 0.700 0.675 0.600 0.585 0.570 0.555 0.50 0.49 0.48 0.47 0.426 0.420 0.414 0.408
373.15 K 383.15 K 393.15 K 403.15 K 413.15 K
Tg/K
EPC/ $·kW-1
1062
423.15 K
0.365 0.360 0.355 0.350 0.32 0.31 0.30 0.29 0.285 0.280 0.275 0.270
433.15 K 443.15 K 453.15 K 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
xR245fa Fig. 4. Variation of the EPC with the mole fractions of R245fa for R245fa/Butene mixture under different heat source temperatures.
0
ln v 0 ln ðv 00 þ v 0 v 0 xL Þ L dx 000 xL ðv v Þ xL
ln v 0 ln ðv 00 xL þ v 0 v 0 xL Þ ¼ AE LE xL ðv v 000 Þ
mC ¼ AC LC
ð39Þ
1.4
1.0
4.0 3.5
0.8 0.6
3.0
0.4
0.0 393.15
413.15
R245fa/Isopentane R245fa
1.2
Isopentane
433.15
4.0
1.0
3.5
0.8 0.6
3.0 2.5 2.0
0.0 373.15
453.15
393.15
EPC/ $·kW -11
1.6
1.2
R245fa Butene
1.0
5.0
1.4
4.5
1.2
4.0 3.5
0.8 0.6
3.0
0.4 0.2 0.0
373.15
393.15
413.15
433.15
453.15
(b) R245fa/Isopentane
(a) R245fa/Pentane
R245fa/Butene
413.15
Tg/K
Tg/K
1.4
4.5
0.2
2.0 373.15
1.4
0.4
2.5
0.2
ð40Þ
5.0
4.5
R245fa/Pentane R245fa Pentane
1.2
ln v 0 ln ðv 00 xL þ v 0 v 0 xL Þ xL ðv v 000 Þ
1.6
5.0
1.6
EPC/ $·kW W h -1
The same procedure can be easily adopted to condenser:
433.15
Tg /K
(c) R245fa/Butene
453.15
4.5 R245fa/Cisbutene R245fa Cisbutene
1.0
4.0
3.5
0.8 0.6
3.0
0.4 2.5
2.5
0.2
2.0
0.0
2.0 373.15
393.15
413.15
433.15
453.15
Tg /K
(d) R245fa/Cisbutene
Fig. 5. Variations of the EPC and total cost with heat source temperatures for the mixture and pure working fluids.
Capital cost/ 106$
AE
Capital cost/ 10 6$
x0
EPC/ $·kWh -1
v
Z dl ¼
EPC/ $·kW -1
0
AE
Capital cost/ 106$
mE ¼
L
Capital cost/ 106$
Z
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where mE and mC are the working fluid charge in evaporator and condenser, respectively. AE and AC are total heat exchanger area of evaporator and condenser, respectively. v’ and v’’ are the specific volume of vapor and liquid working fluid, respectively. The working fluids charged in pump and expander possess a very low proportion. However, to make the calculation results more accurate, the ratio of this part of working fluids was set as 17.5%. We obtained this value from the experimental measurement in Ref. [38]. Based on the preceding description and analysis, the total working fluid charge is estimated by:
mWF ¼ ðmC þ mE Þ=ð1 17:5%Þ
ð41Þ
3. Description and evaluation of the optimization method 3.1. Description of the Genetic algorithm method
x is a randomly generated number between 0.05 and 0.95. The lower bound of T1 is 333.15 K, which is lower than all the optimal working conditions. The upper bound is given as the pinch point temperature and the critical temperature of the working fluid. The constraint (Tgas-8) is set according to the pinch point temperature, while the constraint (Tcrit-10) follows the rule that the highest temperature of the cycle should be 10 K lower than critical temperature [20]. To enable the state of [T1, p1, x] to be overheated or saturated, the lower bound of p1 is 200 kPa, which is low enough for all the working fluids and systems under the given conditions. The upper bound is generated by employing the saturation pressure psat,T associating with the generated T1 and x. When the EPC is chosen as the fitness function, the fitness function can be expressed as:
EPC ¼ f ðT 1 ; P1 ; xÞ
250
200
200
150 100
0.12
150 100 50
R245fa/Pentane R245fa Pentane
0.14
ð42Þ
The selection operator is used for selecting the excellent parents (with the better value of fitness function) among existing chromosomes to create the next generation. In this work, the selection
250
50
R245fa/Isopentane R245fa Isopentane
0.14 0.12
0.10
ηth
ηth
x 2 [0.05, 0.95]; T1 2 [333.15 K, Tmax], while Tmax = min{(Tcrit-10), (Tgas-8)}; p1 2 [200 kPa, psat,T].
Wnet /kW
Wnet /kW
Genetic algorithm (GA) is widely used as an optimizer for discontinuous, non-differentiable, or highly nonlinear problems. Inspired by Darwinian survival of the fittest principle, GA is a kind of bionics process. There are three basic and indispensable operators: selection operator, crossover operator, and mutation operator. In this work, fractions of working fluid, expander inlet pressure and temperature (i.e. T1 and P1), are selected as variables. The three-dimensional array [T1, P1, x] is chromosome. When generat-
ing the initial populations [T1n, p1n, x]n, the constraint conditions are:
0.10
0.08
0.08
0.06
0.06
0.04 373.15
393.15
413.15
433.15
0.04
453.15
373.15
393.15
T g /K
300
300
250
250
200 150 100
150 100
0.12
0.10
0.10
0.08
0.08
0.06
0.06
0.04
R245fa/Cisbutene R245fa Cisbutene
0.14
ηth
ηth
0.12
453.15
200
50
R245fa/Butene R245fa Butene
0.14
433.15
(b) R245fa/Isopentane
Wnet /kW
Wnet /kW
(a) R245fa/Pentane
50
413.15
T g /K
373.15
393.15
413.15
433.15
T g /K
(c) R245fa/Butene
453.15
0.04 373.15
393.15
413.15
433.15
453.15
T g/K
(d) R245fa/Cisbutene
Fig. 6. Variations of the net power and thermal efficiency with the heat source temperatures for the mixture and pure working fluids.
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operator we adopt is ‘‘deterministic sampling” method [39]. The crossover operator is responsible for generating new chromosomes by combining the selected two chromosomes. The simple arithmetic crossover is employed in this work. The fundamental of arithmetic crossover is presented as follows [40]:
c1 ¼ af1 þ ð1 aÞf 2
ð43Þ
c2 ¼ af2 þ ð1 aÞf 1
employed to protect the elites from crossover and mutation thus accelerating convergence [41]. Configurations of the GA in this work are listed in Table 4. Based on the above description, Genetic algorithm program was written by the authors with FORTRAN language. Subroutines contained in REFPROP 9.0 were called during the simulation process to calculate the thermodynamics properties of working fluids. 3.2. Evaluation of Genetic algorithm program
where c1 and c2 are offsprings, f1 and f2 are parents, a is a random number between 0 and 1. To avoid converging on local solutions, the mutation operator is used. The ‘‘elite-preservation strategy” is
Along with the evolving process, the individuals with worse fitness are weeded out, while the individuals with better fitness are
45
70
R245fa/Pentane R245fa Pentane
60
Pcon / %
Peva / %
40
R245fa/Pentane R245fa Pentane
65
35
55 50
30 45 25
373.15
393.15
413.15
433.15
40
453.15
373.15
393.15
413.15
T g/K
(a) evaporator
(b) condenser
3.0
453.15
16
R245fa/Pentane R245fa Pentane
2.5
R245fa/Pentane R245fa Pentane
Pexp / %
12
Ppump / %
433.15
T g/K
2.0
8 1.5
1.0
373.15
393.15
413.15
433.15
4
453.15
373.15
393.15
Tg/K
413.15
433.15
453.15
T g/K
(c) pump
(d) expander 0.8
15
R245fa/Pentane R245fa Pentane
0.6
Pfan / %
PWF / %
10
R245fa/Pentane R245fa Pentane
0.4
5 0.2
0
373.15
393.15
413.15
433.15
453.15
0.0
373.15
393.15
413.15
433.15
T g/K
Tg/K
(e) fans
(f) working fluid
453.15
Fig. 7. Percentage of each component in the total capital cost using R245fa, Pentane and their mixture under different heat source temperatures.
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assigned with high probabilities to survive to the next generation; the individuals should finally converge in a small area. The optimal individual with the minimum value of EPC could be singled out from the final population. The working condition of heat source temperature 413.15 K using working fluid R245fa/Isopentane is performed as an example to evaluate the feasibility and stability of the optimization method. Fig. 2 shows the variation of the optimal objective function value with the evolution times. It can be seen that as the evolution times increased, the optimal value of objective function updated by the smaller value until the iteration
is stopped (with the stop generation of about 100). Fig. 3 shows the population distribution under different evolution times. As shown in Fig. 3(a), the randomly generated individuals in the initial population are distributed dispersedly. Along with the evolution time increased, the degree of convergence of the individuals also increased. When the value of evolution time reaches 100, as can be seen in Fig 3(d), the individuals converge in a small area around the optimal individual. To evaluate the stability of the in-house Genetic algorithm program, calculations are performed 5 times repeatedly under the same parameter settings and the results are
45
70
R245fa/Isopentane R245fa Isopentane
40
Pcon / %
Peva / %
35 30
R245fa/Isopentane R245fa Isopentane
65
25
60 55 50
20 15
373.15
393.15
413.15
433.15
45
453.15
373.15
393.15
T g/K
16
R245fa/Isopentane R245fa Isopentane
3.5
2.5
12 10
2.0
8
1.5
6
373.15
393.15
413.15
433.15
R245fa/Isopentane R245fa Pentane
14
Pexp / %
Ppump / %
3.0
4
453.15
373.15
393.15
413.15
433.15
T g/K
T g/K
(c) pump
(d) expander
20
453.15
0.8
R245fa/Isopentane R245fa Isopentane
10
5
R245fa/Isopentane R245fa Isopentane
0.6
PWF / %
15
Pfan / %
453.15
(b) condenser
4.0
0
433.15
T g/K
(a) evaporator
1.0
413.15
0.4
0.2
373.15
393.15
413.15
T g/K
(e) fans
433.15
453.15
0.0
373.15
393.15
413.15
433.15
453.15
Tg/K
(f) working fluid
Fig. 8. Percentage of each component in the total capital cost using R245fa, Isopentane and their mixture under different heat source temperatures.
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listed in Table 5. It shows that for the 5 times calculations, optimized value of objective function and parameters relative errors were below 2%, which is enough to meet the requirement of the industrial demand. 4. Results and discussions 4.1. Comparison between the calculating methods In the most of the related work, the mixture compositions were usually discretely assumed as fixed values. Take R245fa/Butene as
an example, under the given heat source temperatures, the optimal EPC values under different mixture compositions (mole fractions of R245fa, varied from 0.1 to 0.9) were calculated. The calculated results are presented in Fig. 4. It can be seen from Fig. 4 that the ‘‘optimal mixture composition (corresponding with lowest EPC value for given heat source temperature)” under different heat source temperatures are distributed between 0.25 and 0.55, roughly showing an increasing trend along with the increase of heat source temperatures. Above method was commonly used to obtain the ‘‘optimal mixture composition” for mixture working fluid, however, several shortcomings exist about this method:
40
65
R245fa/Butene R245fa Butene
60
Pcon / %
Peva / %
35
R245fa/Butene R245fa Butene
55
30 50
25
373.15
393.15
413.15
433.15
45
453.15
373.15
393.15
(a) evaporator R245fa/Butene R245fa Butene
2.5
R245fa/Butene R245fa Butene
12
Pexp / %
Ppump / %
3.0
2.0
10 8 6
1.5
373.15
393.15
413.15
433.15
4
453.15
373.15
T g/K
393.15
413.15
433.15
453.15
T g/K
(d) expander
(c) pump 20
0.8
R245fa/Butene R245fa Butene
R245fa/Butene R245fa Butene
0.6
PWF / %
15
Pfan / %
453.15
14
3.5
10
5
0
433.15
(b) condenser
4.0
1.0
413.15
T g/K
T g/K
0.4
0.2
373.15
393.15
413.15
433.15
453.15
0.0
373.15
393.15
413.15
433.15
T g/K
T g/K
(e) fans
(f) working fluid
453.15
Fig. 9. Percentage of each component in the total capital cost using R245fa, Butene and their mixture under different heat source temperatures.
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40
65
R245fa/Cisbutene R245fa Cisbutene
60
Pcon / %
Peva / %
35
R245fa/Cisbutene R245fa Cisbutene
55
30 50
25
373.15
393.15
413.15
433.15
45
453.15
373.15
393.15
(a) evaporator
R245fa/Cisbutene R245fa Cisbutene
2.5
R245fa/Cisbutene R245fa Cisbutene
12
Pexp / %
3.0
Ppump / %
453.15
14
3.5
2.0
10 8 6
1.5
373.15
393.15
413.15
433.15
4
453.15
373.15
393.15
413.15
433.15
453.15
T g/K
T g/K
(d) expander
(c) pump 0.8
20
R245fa/Cisbutene R245fa Cisbutene
10
R245fa/Cisbutene R245fa Cisbutene
0.6
PWF / %
15
Pfan / %
433.15
(b) condenser
4.0
0.4
0.2
5
0
413.15
T g/K
T g/K
373.15
393.15
413.15
433.15
453.15
T g/K
(e) fans
0.0
373.15
393.15
413.15
433.15
453.15
T g/K
(f) working fluid
Fig. 10. Percentage of each component in the total capital cost using R245fa, Cisbutene and their mixture under different heat source temperatures.
firstly, the confirmed ‘‘optimal mixture composition” is essentially is an interval with accuracy of 0.1, not a unique value; secondly, the trends of objective function value (i.e. EPC value in the present work) and mixture composition are usually complex, singularity appears sometime [42], thus ulteriorly reducing the reliability of the calculated result. For these reasons described above, in this work, coupled with inlet temperature and pressure of expander, the mixture composition (i.e. mole fraction of R245fa) was set as one of the variables to be optimized. GA was recommended as an effective method to optimize the system performance and obtain the ‘‘optimal mixture composition”. When to obtain the optimal mixture compositions under certain heat source temperatures,
the calculating times were decreased 9 times. The reliability of the optimal program has been validated in Section 3.2. Based on this, compared with the above-motioned method showed in Fig. 4, the accuracy of the calculated optimal mixture composition was improved at the same time. 4.2. Comparison between mixtures and their components Fig. 5 shows the variations of the EPC and total cost with heat source temperatures for the mixture and pure working fluids. It can be seen that for all working fluids, the EPC value decreased with the increase of heat source temperature. For the capital cost,
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clearly showed that the mixture working fluid with a larger percentage of the condenser, pump, and expander in the capital cost, but a lower percentage of the capital cost of the evaporator in the most situations. Combined with the conclusion from Fig. 5, it can be inferred that for the mixture working fluid, the decrease of the EPC value is mainly due to the decrease of the capital cost, which is essentially caused by the decrease of the evaporator capital cost.
1.0
0.8
xR245fa
0.6
0.4
R245fa/ Isopentane R245fa/ Pentane R245fa/ Cisutene R245fa/ Butene
0.2
4.3. Analysis of the mixture working fluids behavior
0.0 373.15
393.15
413.15
433.15
453.15
Tg /K Fig. 11. Variations of the optimized mole fractions with heat source temperatures.
it showed a reverse tendency. As can be seen from Fig. 5 that the mixture working fluid showed a better economic performance (lower EPC and capital cost) compared to the pure working fluid. Lower capital cost obtained by the system using mixture working fluid means that under same heat source condition, using mixture working fluid leads to a smaller physical scale of ORC plant compared with the pure working fluid. From Fig. 5 it also can be seen that, for the pure and mixture working fluids, the operating condition for a lower EPC value always corresponds to a relative lower capital cost value. Fig. 6 shows the variations of the net power and thermal efficiency with the heat source temperature for the mixture and pure working fluids. It can be seen from Fig. 6 that when operated under the optimized working conditions, the net power of the mixture working fluid does not have a clear advantage compared with the pure working fluid, which illustrates that the decreased EPC value of mixture working fluid is mainly due to the decrease of the capital cost. Percentage of each system component (i.e. evaporator, condenser, pump, expander, working fluid and fans) in the total capital cost using different mixture and pure working fluids under different heat source temperature are showed in Figs. 7–10. It is interesting to note that in most situations, for the pure and mixture working fluids, the percentage of the evaporator and condenser in the total capital cost decreased with the increase of heat source temperature. For other components including pump, expander, working fluid, and fans, they showed opposite trends. Also, it
Fig. 11 shows the variations of the optimized mole fractions with heat source temperatures. It can be observed that the distribution of the optimized mixture compositions shows almost the linear behavior. In the process of actual application, the correlations should be useful to predict the mixture compositions with good accuracy, using only a few key design parameters and without the need of knowledge of working fluid properties and their use in ORCs. This method adopted in the present work could be used for making the correlations when the waste heat source scale and the working fluid are confirmed. In this work with the given working conditions, the correlation between optimized mole fractions of R245fa (xR245fa) and heat source temperature (Tg/K) for the selected 4 different mixtures are given by Eqs. (44)–(47): R245fa/Pentane:
xR245fa ¼ ð1096:63 0:9216T g Þ=1000 ðR ¼ 0:9209Þ R245fa/Isopentane:
xR245fa ¼ ð537:47 þ 0:7844T g Þ=1000 ðR ¼ 0:8769Þ
xR245fa ¼ ð731:62 þ 2:72T g Þ=1000 ðR ¼ 0:8947Þ
xR245fa ¼ ð1611:67 þ 5:27T g Þ=1000 ðR ¼ 0:9698Þ
443.15 K 433.15 K 423.15 K
T /K g
R245fa/Cisbutene R245fa/Butene R245fa/Isopentane R245fa/Pentane
393.15 K 383.15 K
373.15 K
-0.12
-0.08
-0.04
0.00
ð47Þ
It can be observed from the above formulas that as the critical temperature of the flammable working fluid increased, the slope of fitted straight line decreased. In the mixtures, act as the flame retardants, the mole fractions of R245fa increased as the increase of heat source temperature, this rule is correct except for R245fa/ Pentane. These formulas fitted from the optimized results using EPC as objective function should provide a reference for mixture composition determination for the recommended 4 mixtures.
403.15 K
-0.16
ð46Þ
R245fa/Cisbutene:
413.15 K
-0.20
ð45Þ
R245fa/Butene:
453.15 K
Cisbutene Butene Isopentane Pentane
ð44Þ
0.00
0.02
0.04
0.06
0.08
0.10
0.12
R Fig. 12. Variations of the characterization parameter R with heat source temperatures for pure and mixture working fluids.
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H. Xi et al. / Applied Thermal Engineering 113 (2017) 1056–1070
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4.4. Recommendation of working fluid for different heat source temperatures
(2013CB228304) and the Key Project of National Natural Science Foundation of China (No. 51436007).
By taking R245fa as the reference working fluid, a characterization parameter R is defined as:
References
RWF ¼ ðEPC R245fa EPC WF Þ=EPC R245fa
ð48Þ
where the subscripts ‘‘WF” in Eq. (48) represents different working fluids. RWF is inversely proportional to EPCWF, the lower value of EPC corresponds to the superior economic performance, therefore, the higher value of RWF, the better of the accordingly working fluid. Fig. 12 shows the variations of the characterization parameter R with heat source temperatures for pure and mixture working fluids. Fig. 12 should be divided into two parts, the left part is for pure working fluid and the right part is for mixture working fluid. Most of the R values for pure working fluids (on the left part) are negative. This illustrates that compared with the reference working fluid R245fa, pure working fluid with negative R value is poorly performed. As it to the mixture working fluid on the right part, the R value of them are all positive. They show superior economic performance compared with R245fa and other pure working fluids. It can be observed from Fig. 12 that under medium heat source temperature (i.e. 383.15–403.15 K), R245fa/Pentane is recommended as the optimal mixture working fluid for its maximum R value (represents minimum EPC value). While for relatively low (373.15 K) and high (413.15–453.15 K) heat source temperatures in this work, working fluid R245fa/Isopentane is recommended. As it to pure working fluids, Isopentane and Pentane are considered as the optimal working fluids when working under heat source temperature of 373.15–423.15 K and 433.15–453.15 K, respectively. Compared with the recommended pure working above, their mixtures with R245fa showed not only superior economic performances but also the lower flammability. Compared with the widely used working fluids R245fa, the economic performance and environment performance are both improved by using the recommended mixture working fluid.
5. Conclusions Optimized calculation for 5 pure working fluids and 4 mixture working fluids were performed by using GA as the optimization method. By using EPC as the objective function, the mixture composition was set as one of the variables during the calculating process. The main conclusions are as follows: (1) The mixture working fluid showed a better economic performance (lower EPC and capital cost). The lower EPC value obtained by mixture working fluid was mainly due to the decrease of the capital cost, which is essentially caused by the decrease of capital cost of the evaporator. (2) The correlations between optimized mixture composition (i.e. the mole fraction of R245fa) and heat source temperature (Tg) for the selected 4 mixture working fluids were fitted from the optimization results. (3) R245fa/Pentane and R245fa/Isopentane are recommended as the optimal mixtures working fluids for temperature range of (383.15–403.15 K) and (373.15, 413.15–453.15 K), respectively.
Acknowledgements The authors gratefully acknowledge the support from the National Key Basic Research Program of China (973 Program)
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Research Paper
Economical evaluation and optimization of organic Rankine cycle with mixture working fluids using R245fa as flame retardant Huan Xi a, Ming-Jia Li a, Ya-Ling He a,⇑, Yu-Wen Zhang a,b a b
Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA
h i g h l i g h t s Parametric optimization of ORC using mixture working fluids was carried out. R245fa was introduced as the flame retardant in the mixture working fluids. Fraction of R245fa was employed as one of optimized variables. Correlations between fraction of R245fa and heat source temperature were obtained.
a r t i c l e
i n f o
Article history: Received 17 May 2016 Revised 7 November 2016 Accepted 7 November 2016 Available online 9 November 2016 Keywords: Waste heat recovery (WHR) Organic Rankine cycle (ORC) Mixture working fluids Flame retardant Performance optimization
a b s t r a c t A detailed economic model of organic Rankine cycle (ORC) system using mixtures as working fluid has been built. By using R245fa as the flame retardant, R245fa/Isopentane, R245fa/Pentane, R245fa/ Cisbutene and R245fa/Butene were considered as the potential working fluids. The heat source temperatures investigated were 373.15–453.15 K. The optimization of 4 mixture and 5 pure working fluids were carried out with the objective function of minimizing the Electricity Production Cost (EPC). Genetic Algorithm (GA) was employed as the optimized method. Different from the most of the optimization researches about ORC with mixture working fluid, the mixture composition was set as one of the variables in the present work. The results show that the mixture working fluid is more economic-efficient than pure working fluid. The lower EPC value obtained by mixture working fluid was mainly due to the decrease of capital cost, which is essentially caused by the decrease of capital cost of the evaporator. R245fa/Isopentane and R245fa/Pentane were recommended as the optimal working fluids for their minimum EPC values. In addition, the correlations between the optimized mixture composition and heat source temperature were obtained. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Environmental issues like air pollution and global warming caused by the overuse of fossil fuel have become increasingly severe [1,2]. On the other hand, massive of low-temperature waste heat generated during different industry processes released to the environment caused a serious problem of energy waste. For these reasons, new environmentally-friendly technologies need to be developed to improve the overall energy utilization efficiency and recover heat from low-temperature heat sources. Organic Rankine cycles (ORCs) as one of the candidates for waste heat recovery has attracted increasing attention.
⇑ Corresponding author. E-mail address: [email protected] (Y.-L. He). http://dx.doi.org/10.1016/j.applthermaleng.2016.11.059 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.
Organic Ranking cycle (ORC) is preferred as an efficient approach due to their flexibility, good thermodynamic performance, and simpler configuration. In the design of the ORC system, one important factor is the working fluid selection. Pure working fluids were generally utilized in ORC systems, for example, refrigerants such as R11, R141b, R113, R123, R245fa, R245ca [3], or some flammable hydrocarbons like n-pentane [4], Isobutane [5]. However, the most important limitation of pure working fluid is the constant temperature during the phase change process in the evaporator and condenser, which is not suitable for sensible heat sources. By contrast, by using mixture working fluid, the system performance can be improved by reducing the mismatch of temperature profiles between the heat transfer fluid and working fluid. Therefore, there is a significantly arising interest in mixture working fluids research. Zhao and Bao [6] discussed the influence of composition shift on ORC using R601/R600a as working fluid; the
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Nomenclature A B C cp CEPCI CRF de D EPC F GWP h H i k K L LTpl m mf p Pr T ODP Q q _ m VV
c
y Re W M v
heat transfer area (m2) correction factor of Table 5 cost ($) specific heat capacity (kJ/(kgK)) chemical engineering plant cost index capital recovery cost ($/(kWh)) equivalent diameter (mm) tube diameter (mm) electricity production cost ($/(kWh)) correction factor of Table 5 global warming potential specific enthalpy (kJ/kg) total wind pressure of the fan (Pa) interest rate heat transfer coefficient (W/(m2K)) correction factor of Table 5 length (m) plant life time (year) mass mass fraction pressure (kPa) Prandtl number temperature (K) zone depletion potential heat transfer flow rate (kW) heat flux (W/m2) mass flow rate (kg/s) volume low rate (m3/s) latent heat of vaporization (kJ/kg) mole fraction Reynolds number power (kW) molecular weight (kg/mole) specific volume (m3/kg)
fraction ratio was fixed at 31.56%/68.44% (mass fraction), and the heat source temperature was 90 °C. The results showed that the composition shift led to a lower output work of expander, the higher power consumption of the pump, lower net output work, and thermal efficiency. They also evaluated the output work, thermal efficiency and exergy efficiency of the ideal ORC systems for different zeotropic mixtures consisting of 5 components (i.e., R227ea, R245fa, R245ca, R236fa, and R236ea). The fractions of each mixture were evenly distributed between 0 and 1 with a steplength of 0.2. The influence of the heat source temperature on the optimal mass fraction of the different zeotropic mixture was emphasized [7]. Heberle et al. [8] presented a detailed simulation of ORC system. The second law efficiency was calculated for isobutane/isopentane and R227ea/R245fa depending on 5 different fraction ratios. Le et al. [9] carried out the thermodynamic and economic optimization of a subcritical ORC using n-pentane/ R245fa as working fluid under 5 different fraction ratios. The heat source temperature used in the calculated process was 423.15 K. N-pentane was recommended for the highest maximized exergy efficiency and the lowest minimized LCOE (Levelized Cost of Electricity). Garg et al. [10] investigated the system performance using isopentane/R245fa as the working fluid with a fixed mole fraction of 0.7/0.3. The heat source temperatures were in the range of 385– 425 K. The results showed that the mixture and the pure working fluid showed a comparable irreversibility at their optimum expansion ratios. Genetic algorithm was widely adopted for ORC optimization. Dai et al. [11] operated optimization calculating for ORC using GA, the exergy efficiency was employed as the objective
x the mole fraction of R245fa x (with subscripts l and L) dryness 4T pinch temperature (K) Greek symbols efficiency (%) dynamic viscosity (Pas) density (kg/m3)
g l q
Subscripts bm subscripts of correction factor in Table 5 bo boiling section C condenser cri critical cap capital cost co condoning section E evaporator F fan g gas H pinch point of the evaporator i&m insurance and maintenance cost L pinch point of the condenser m correction factor of Table 5 net net power ph phase change section Exp expender wall wall WF working fluid 1–9, 2a, 5a, 1⁄, 7⁄ state points in the cycle superscript elec electricity
function, the working fluid selection was also performed based on the calculation results. Wang et al. [12] operated a multi-objective optimization of the ORC with R134a as working fluid. Exergy efficiency and overall capital cost were employed as the objective functions. The effects of different optimized parameters on the exergy efficiency and capital cost were both examined according to the optimization results. The authors have also adopted GA as the optimization method for different ORC system comparison [13] and working fluid selection [14]. From the above literature review, it can be observed that for mixture working fluid, most works were carried out with fixed mixture composition. Few studies have reported about adopting the mixture composition as one of the optimized variables. In addition, the formulations of mixture fraction to heat source temperature were rarely mentioned. In view of this, in this paper, a number of mixtures consisting of inert (nonflammable) working fluids and flammable working fluids (hydrocarbons) were explored. The inert working fluid we selected was R245fa with high global warming potential (GWP) which was commonly adopted by the previous researches [15,16]; the flammable working fluids we selected were pentane [17], isopentane [18], butane [19] and cisbutene [20] according to previous researches, with low GWP. R245fa was motivated by the possibility of suppressing the flammability of the latter working fluids by blending with these working fluids, meanwhile, the mixture working fluid decreases the GWP relative to R245fa used alone, which enhanced the working fluids’ environmental performance. Properties of working fluids’ components are listed in Table 1. Based on the economic model, the economic
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performance of mixture and pure working fluids were both optimized and compared, and the formulations of mixture composition to heat source temperature were fitted on the basis of the optimized results. Optimal working fluids for different heat source temperatures were recommended based on the calculated results. 2. Modeling and calculation method
where the motor power input is:
W elec ¼ W P =gmotor P The net output power is defined as:
W net ¼ W Exp W elec WF P
ð5Þ
where WF is power consumption of the fan for waste gas and cooling air side, which can be calculated as [18]:
2.1. Thermodynamic model ORC system consists of at least five principal components: evaporator, expander, condenser, pump and working fluid. The working fluid is saturated liquid when passing out the condenser, then be pumped to the evaporator to gain energy from heating source fluid. Generated high pressure working fluid vapor could be saturated or superheated expands in the expander. The system layout and cycle T-s chart of ORC system are shown in Fig. 1. During the calculating process, several assumptions are introduced in this study: (1) the heat transfer and flow processes are in steady-state; (2) pipe pressure drop and heat losses from the components are all neglected; and (3) the parameters of working conditions are assumed as listed in Table 2, which is supplied by the waste heat recovery-related company based on the actual industry process in Xi’an, China. It is necessary to note that during the calculating process, the condensing temperature was assumed as 308.15 K except in the following circumstance: the condensing pressure decreases below atmosphere pressure under 308.15 K. In that case, the condensing temperature should be raised to set condensing pressure equal to the atmosphere pressure in order to avoid air getting into the cycle. It should be noted that steam turbines expand always work well below atmospheric pressure (as low as 35 mbar), however, there needs extra equipment to extract non-condensable fluid. We do not advocate to transplant the vacuum keeping system into ORC system. As a kind of green energy technology, ORC should be positioned as high applicability and simplification technology, any extra equipment which makes the system complex, bulky and with higher initial cost should not be recommended. For the ORC systems, the power of expander and pump can be expressed as:
_ WF ¼ gExp ðh1 h2 Þm_WF W Exp ¼ ðh1 h2a Þm
ð1Þ
_ WF =gP W P ¼ ðh5a h4 Þm_WF ¼ ðh5 h4 Þm
ð2Þ
where gExp and gP are the isentropic efficiency of expander and pump, which are both assumed as 0.8. m_WF is the mass flow rate of the working fluid. hi is the specific enthalpy of the working fluid at the state point i (as shown in Fig. 1). The pump motor efficiency (with the unit of 100%) is calculated from [21]:
h
ð4Þ
i
gmotor ¼ 75 þ 11:5logW P 1:5ðlogW P Þ2 =100
ð3Þ
WF ¼
2:778 107 H V V;g F L g1 g2 g3
ð6Þ
where H is the total wind pressure of the fan, VV,g is the gas flow rate with a unit of m3/h. g1, g2, g3 are fan efficiency, transmission efficiency, and electric efficiency, they are assumed as 0.7, 1.0, 0.9, respectively. FL is the altitude correction coefficient which can be calculated as [22]:
F L ¼ 0:98604 þ 0:01435 102 HL þ 2:495 109 H2L
ð7Þ
where HL in the above formula is altitude with the unit of meter. To calculate the net output power, the mass flow rate of working fluids and cooling air are indispensable. The mass flow rate is usually calculated according to the pinch points temperature and pinch point location. In this work, the pinch point temperature of the evaporator (DT H ) and condenser (DT L ) are both fixed at 8.0 K. For the mixture working fluids, the temperature glide during the evaporating and condensing processes perhaps make the pinch point location varying under different working conditions and different mixture compositions. To confirm the pinch point location and calculate mass flow rate, the following method should be adopted (take evaporator as example): In the evaporator, the possible location of pinch point should be at point (see Fig. 1): 7(1), 7⁄(1⁄), 8(6), 9(5a), then pinch point temperature should be calculated according to one of the following 4 equations:
DT H1 ¼ T g;7 T 1
ð8Þ
DT H2 ¼ T g;7 T 1
ð9Þ
DT H3 ¼ T g;8 T 6
ð10Þ
DT H3 ¼ T g;9 T 5a
ð11Þ
Step 1: point 7(1) is first assumed as the pinch point, then DT H1 is assigned the value of 8.0 K. Step 2: based on the above assumption, DT H2 , DT H3 , DT H4 are calculated according to the energy balance between (1–1⁄ and (7–7⁄), (7⁄–8) and (1⁄–6), (8–9) and (6–5a). Step 3: compare the four temperature differences above, if DT H2 , DT H3 , DT H4 are less than 8.0 K, the mass flow rate should be calculated as:
_ WF ¼ cp;g m _ g ðT 7 T 7 Þ=ðh1 h1 Þ m
ð12Þ
Table 1 Properties of the working fluids’ components.
a b c d
Working fluid
Tcria(K)
Pcrib (kPa)
Flammability
ODPc
GWPd
R245fa (C3H3F5) Cisbutene (C4H8) Butene (C4H8) Isopentane (C5H12) Pentane (C5H12)
427.16 418.09 419.29 460.35 469.7
3651.0 4009.8 4005.1 3378.0 3370.0
Nonflammable Flammable Flammable Flammable Flammable
0 n.a n.a 0 0
1030 n.a n.a 20 20
Pc: critical pressure. Tc: critical temperature. ODP: ozone depletion potential. GWP: global warming potential.
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Fig. 1. System layout and cycle T-s chart of ORC system.
Table 2 Assumed working conditions. Waste gas mass flow rate (kgs1) Environment temperature (K) Environment pressure (kPa) Condensing temperature (K) Expander isentropic efficiency Pump isentropic efficiency Pinch temperature difference in the evaporator (K) Pinch temperature difference in the condenser (K)
15.0 293.15 101.3 308.15 0.8 0.8 8.0 8.0
where cp;g is the specific heat capacity of the waste gas. Otherwise, if there exists a DT H less than DT H1 , the assumption in Step 1 is disproved, then DT H2 should be is assigned the value of 8.0 K and the Step 2–3 need to be repeated to calculate the temperature difference until one the assumption is proved right and the location of pinch point is determined. 2.2. Economic model
EPC ¼ ðCRF C cap þ C m&i Þ=ðh W net Þ
ð13Þ
where Ccap signifies the capital cost, comprising the investments for the evaporator, expander, condenser, pump, fans and working fluid.
CEPCI2014 ¼ ðC bm;E þ C bm;Exp þ C bm;P þ C bm;C Þ þ C bm;F CEPCI1996 CEPCI2014 þ C WF CEPCI2011
LT pl
.h
2 log C Exp ¼ K 1;Exp þ K 2;Exp log W Exp þ K 3;Exp log W Exp
ð18Þ
for the pump,
C bm;P ¼ C P F bm;P
ð19Þ 2
log C P ¼ K 1;P þ K 2;P log W P þ K 3;P ðlog W P Þ
ð20Þ
F bm;P ¼ B1;P þ B2;P F m;P F p;P
ð21Þ
LT pl
ð1 þ iÞ
i 1
log F P;P ¼ C 1;P þ C 2;P log prp þ C 3;P ðlog prp Þ
ð22Þ
prp ¼ pE pC
ð23Þ
for heat exchangers (take evaporator as an example),
C bm;E ¼ C E F bm;E
ð24Þ 2
ð25Þ
F bm;E ¼ B1;E þ B1;E F m;E F p;E ð14Þ
ð26Þ 2
log F p;E ¼ C 1 þ C 2 logðpE p0 Þ þ C 3 ðlogðpE p0 ÞÞ
ð16Þ
ð27Þ
for the fan of waste gas and cooling air,
C bm;F ¼ C F F bm;F F p;F
ð28Þ 2
ð15Þ
where i is the interest rate, assumed to be moderate at 5%, LTpl is the plant life time, assumed at 15 years. h is system working hours per annual operation period (h/year), in this work, it was assumed as 7500 h. Cm&i means the insurance and management cost of the system, which can be calculated as [24,25]:
C m&i ¼ 1:65%C cap
ð17Þ
log C E ¼ K 1;E þ K 2;E log AE þ K 3;E ðlog AE Þ
wherein CEPCI1996 = 382, CEPCI2011 = 582, CEPCI2014 = 586.77 (CEPCI means Chemical Engineering Plant Cost Index) [23]. CRF is the capital recovery cost, which is estimated based on the following equation.
CRF ¼ ið1 þ iÞ
C bm;Exp ¼ C Exp F bm;Exp
2
Electricity production cost (EPC) is the ratio of the total system cost to the net power output, which can be calculated by:
C cap
As the key factor of the cost estimation model, component investment cost provided by a current price quote from a suitable vendor (a seller of equipment), and adjusted using appropriate factors. Each component investment in Eq. (14) could be predicted by the following correlations and the corresponding coefficients K, B, C and F are listed in Table 3 [26,27]. For expander,
log C F ¼ K 1;F þ K 2;F log qV þ K 3;F ðlog qV Þ log F p;F ¼ C 1 þ C 2 log pF þ C 3 ðlog pF Þ
ð29Þ
2
ð30Þ 3
where qV is the gas flow rate with a unit of m /h. For the working fluid,
C WF ¼ cWF mWF
ð31Þ
where cWF is the unit price of working fluid with a unit of $/kg, mWF is the total working fluid charge the unit of kg, which will be intro-
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Table 3 Coefficients in equations evaluating the investment of system components [26,27]. Component
K1
K2
K3
B1
B2
C1
C2
C3
Fm
Fbm
Evaporator Condenser Expander Pump Fan (with electric device)
3.853 3.853 3.514 3.579 3.1761
0.424 0.424 0.598 0.321 0.1373
0 0 0 0.003 0.34314
1.53 1.53 / 1.8 0
1.27 1.27 / 1.51 0.20899
0 0 / 0.168 0.0328
0 0 / 0.348 /
0 0 / 0.484 /
2.8 2.8 / 1.8 /
/ / 3.5 / 1.12
Table 4 Configurations of genetic algorithms.
Optimal value of objective function(EPC)/ $·kWh -1
Population size Chromosome vector Crossover probability Mutation probability Elite count Stop generation
100 [T1, P1, x] 0.4 0.9 20 100
0.48
0.47
0.46
0.45
0.44
0.43
0
20
40
60
80
Evolution time
2.3. Calculation of the heat exchangers area To calculate the heat transfer area of evaporator and condenser, the heat transfer coefficient should be determined [29]. In the evaporator and condenser, the convective heat transfer coefficient of the organic working fluid side is generally more than 2000 W/ (m2K) [30,17] which is much great than that of the gas side. Thus, the overall heat transfer coefficient in the evaporator and condenser are mainly dependent on the convective heat transfer coefficient of gas side; in some related works, it was even assumed to be the constants to simplify the calculation [31,32]. Therefore, in this work the total heat transfer coefficient is estimated by employing the Kern formula [33]:
l lwall
ð33Þ
_ WF ðhWF;iþ1 hWF;i Þ Qi ¼ m
ð34Þ
Q i ¼ kAi
duced in part 2.4. Eqs. (17)–(30) are referred from Refs. [26,27], while Eq. (31) is referred from Ref.[28]. The cost estimation model used in this manuscript are widely adopted. The purchased cost is the key factor of the cost estimation mode, which is provided by a current price quote from a suitable vendor (a seller of equipment), and adjusted using appropriate scaling factors (such as K), and for inflation (such as CEPCI2014), to provide the estimated capital cost.
k 0:55 1=3 Re Pr de g
_ g ðhg;iþ1 hg;i Þ Qi ¼ m
100
Fig. 2. Variation of the optimal objective function value with the evolution times.
kph ¼ kbo ¼ kco ¼ 0:36
where kph, kbo and kco are the heat transfer coefficient during the phase change, boiling and condensing processes. l is the dynamic viscosity of the gas side. de is the equivalent diameter of the tube. k is heat conductivity coefficient, Re and Pr are the Reynolds number and Prandtl number, respectively. The logarithmic mean temperature difference (LMTD) method is widely used in heat exchanger design and calculation. Based on the above analysis, the overall heat transfer coefficient in the heat exchangers are mainly dependent on the convective heat transfer coefficient of the gas side. It is necessary to point out that the physical properties of waste gas were assumed as the fixed values in some related work [34]; even so, the physical properties of the gas are temperature-dependent, especially in the relatively high-temperature ranges [35]. Thus, the assumption of constant properties may lead to inaccurate results. An alternative solution is discretizing the heat exchangers so that the properties variation in each step is small and could be treated as an average constant value. The heat transfer for each step i as well as the corresponding properties of the waste gas and cooling air, and the fractional UAi values are calculated from the following equations (assumed as counter-flow configuration, take evaporator as an example):
0:14 ð32Þ
ðT g;iþ1 T WF;iþ1 Þ ðT g;i T WF;i Þ h i T T WF;iþ1 ln g;iþ1 T g;i T WF;i
ð35Þ
For evaporator, it can be divided into three regions: a superheated region, a two-phase region, and a supercooled region. For the condenser, the last two regions are applicable. Each region is then subdivided into 20 steps. For the calculating method of waste gas physical properties in this work, we adopt the formulas presented in Ref. [36], and for the cooling air, the physical properties calculating formulas were fitted based on the data from Refprop 9.0. 2.4. Working fluid charge estimation In the economic model described in Section 2.2, as seen in Eq. (14), the working fluid cost should be calculated. As we know, the working fluid cost is equal to the product of the unit price ($/ kg) and working fluid charge (kg). The unit price of the working fluids was obtained from the related manufacturers. To estimate the working fluid charge, the method presented in Ref. [37] were adopted. Take evaporator as an example, the mass flow rate of vaporized working fluid at the position with a distance of l from the inlet should be calculated as:
q00WF ¼ qpDl=c
ð36Þ
where q is the heat flux (W/m ), and c is the latent heat (J/kg), D is tube diameter. The total mass flow rate (for each tube) can be calculated as: 2
qWF ¼ qpDL=xL c
ð37Þ
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(a) Initial population
(b) Evolving for 25 times
(d) Evolving for 100 times
(c) Evolving for 75 times
Fig. 3. Population distributions under different evolution times.
Table 5 Calculating results of program stability evaluation. Calculation times
Value of objective function (EPC/$kWh1)
x of R245fa
T1 (K)
p1 (kPa)
1 2 3 4 5 Relative error
0.4283 0.4291 0.4296 0.4290 0.4291 0.295%
0.8552 0.8556 0.8532 0.8541 0.8535 0.285%
373.88 369.94 368.03 370.68 370.00 1.56%
1142.12 1144.94 1126.48 1141.96 1129.95 1.61%
where xL is the dryness at the evaporator outlet, L is tube length. Thus, the dryness at the position with a distance of l from the evaporator inlet can be expressed as:
xl ¼ q00WF qWF ¼ xL l=L
ð38Þ
It can be seen from Eq. (37) that xl is changed linearly with l. Thus, the working fluid charge (kg) is:
H. Xi et al. / Applied Thermal Engineering 113 (2017) 1056–1070 1.30 1.25 1.20 1.15 0.96 0.92 0.88 0.84 0.750 0.725 0.700 0.675 0.600 0.585 0.570 0.555 0.50 0.49 0.48 0.47 0.426 0.420 0.414 0.408
373.15 K 383.15 K 393.15 K 403.15 K 413.15 K
Tg/K
EPC/ $·kW-1
1062
423.15 K
0.365 0.360 0.355 0.350 0.32 0.31 0.30 0.29 0.285 0.280 0.275 0.270
433.15 K 443.15 K 453.15 K 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
xR245fa Fig. 4. Variation of the EPC with the mole fractions of R245fa for R245fa/Butene mixture under different heat source temperatures.
0
ln v 0 ln ðv 00 þ v 0 v 0 xL Þ L dx 000 xL ðv v Þ xL
ln v 0 ln ðv 00 xL þ v 0 v 0 xL Þ ¼ AE LE xL ðv v 000 Þ
mC ¼ AC LC
ð39Þ
1.4
1.0
4.0 3.5
0.8 0.6
3.0
0.4
0.0 393.15
413.15
R245fa/Isopentane R245fa
1.2
Isopentane
433.15
4.0
1.0
3.5
0.8 0.6
3.0 2.5 2.0
0.0 373.15
453.15
393.15
EPC/ $·kW -11
1.6
1.2
R245fa Butene
1.0
5.0
1.4
4.5
1.2
4.0 3.5
0.8 0.6
3.0
0.4 0.2 0.0
373.15
393.15
413.15
433.15
453.15
(b) R245fa/Isopentane
(a) R245fa/Pentane
R245fa/Butene
413.15
Tg/K
Tg/K
1.4
4.5
0.2
2.0 373.15
1.4
0.4
2.5
0.2
ð40Þ
5.0
4.5
R245fa/Pentane R245fa Pentane
1.2
ln v 0 ln ðv 00 xL þ v 0 v 0 xL Þ xL ðv v 000 Þ
1.6
5.0
1.6
EPC/ $·kW W h -1
The same procedure can be easily adopted to condenser:
433.15
Tg /K
(c) R245fa/Butene
453.15
4.5 R245fa/Cisbutene R245fa Cisbutene
1.0
4.0
3.5
0.8 0.6
3.0
0.4 2.5
2.5
0.2
2.0
0.0
2.0 373.15
393.15
413.15
433.15
453.15
Tg /K
(d) R245fa/Cisbutene
Fig. 5. Variations of the EPC and total cost with heat source temperatures for the mixture and pure working fluids.
Capital cost/ 106$
AE
Capital cost/ 10 6$
x0
EPC/ $·kWh -1
v
Z dl ¼
EPC/ $·kW -1
0
AE
Capital cost/ 106$
mE ¼
L
Capital cost/ 106$
Z
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where mE and mC are the working fluid charge in evaporator and condenser, respectively. AE and AC are total heat exchanger area of evaporator and condenser, respectively. v’ and v’’ are the specific volume of vapor and liquid working fluid, respectively. The working fluids charged in pump and expander possess a very low proportion. However, to make the calculation results more accurate, the ratio of this part of working fluids was set as 17.5%. We obtained this value from the experimental measurement in Ref. [38]. Based on the preceding description and analysis, the total working fluid charge is estimated by:
mWF ¼ ðmC þ mE Þ=ð1 17:5%Þ
ð41Þ
3. Description and evaluation of the optimization method 3.1. Description of the Genetic algorithm method
x is a randomly generated number between 0.05 and 0.95. The lower bound of T1 is 333.15 K, which is lower than all the optimal working conditions. The upper bound is given as the pinch point temperature and the critical temperature of the working fluid. The constraint (Tgas-8) is set according to the pinch point temperature, while the constraint (Tcrit-10) follows the rule that the highest temperature of the cycle should be 10 K lower than critical temperature [20]. To enable the state of [T1, p1, x] to be overheated or saturated, the lower bound of p1 is 200 kPa, which is low enough for all the working fluids and systems under the given conditions. The upper bound is generated by employing the saturation pressure psat,T associating with the generated T1 and x. When the EPC is chosen as the fitness function, the fitness function can be expressed as:
EPC ¼ f ðT 1 ; P1 ; xÞ
250
200
200
150 100
0.12
150 100 50
R245fa/Pentane R245fa Pentane
0.14
ð42Þ
The selection operator is used for selecting the excellent parents (with the better value of fitness function) among existing chromosomes to create the next generation. In this work, the selection
250
50
R245fa/Isopentane R245fa Isopentane
0.14 0.12
0.10
ηth
ηth
x 2 [0.05, 0.95]; T1 2 [333.15 K, Tmax], while Tmax = min{(Tcrit-10), (Tgas-8)}; p1 2 [200 kPa, psat,T].
Wnet /kW
Wnet /kW
Genetic algorithm (GA) is widely used as an optimizer for discontinuous, non-differentiable, or highly nonlinear problems. Inspired by Darwinian survival of the fittest principle, GA is a kind of bionics process. There are three basic and indispensable operators: selection operator, crossover operator, and mutation operator. In this work, fractions of working fluid, expander inlet pressure and temperature (i.e. T1 and P1), are selected as variables. The three-dimensional array [T1, P1, x] is chromosome. When generat-
ing the initial populations [T1n, p1n, x]n, the constraint conditions are:
0.10
0.08
0.08
0.06
0.06
0.04 373.15
393.15
413.15
433.15
0.04
453.15
373.15
393.15
T g /K
300
300
250
250
200 150 100
150 100
0.12
0.10
0.10
0.08
0.08
0.06
0.06
0.04
R245fa/Cisbutene R245fa Cisbutene
0.14
ηth
ηth
0.12
453.15
200
50
R245fa/Butene R245fa Butene
0.14
433.15
(b) R245fa/Isopentane
Wnet /kW
Wnet /kW
(a) R245fa/Pentane
50
413.15
T g /K
373.15
393.15
413.15
433.15
T g /K
(c) R245fa/Butene
453.15
0.04 373.15
393.15
413.15
433.15
453.15
T g/K
(d) R245fa/Cisbutene
Fig. 6. Variations of the net power and thermal efficiency with the heat source temperatures for the mixture and pure working fluids.
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operator we adopt is ‘‘deterministic sampling” method [39]. The crossover operator is responsible for generating new chromosomes by combining the selected two chromosomes. The simple arithmetic crossover is employed in this work. The fundamental of arithmetic crossover is presented as follows [40]:
c1 ¼ af1 þ ð1 aÞf 2
ð43Þ
c2 ¼ af2 þ ð1 aÞf 1
employed to protect the elites from crossover and mutation thus accelerating convergence [41]. Configurations of the GA in this work are listed in Table 4. Based on the above description, Genetic algorithm program was written by the authors with FORTRAN language. Subroutines contained in REFPROP 9.0 were called during the simulation process to calculate the thermodynamics properties of working fluids. 3.2. Evaluation of Genetic algorithm program
where c1 and c2 are offsprings, f1 and f2 are parents, a is a random number between 0 and 1. To avoid converging on local solutions, the mutation operator is used. The ‘‘elite-preservation strategy” is
Along with the evolving process, the individuals with worse fitness are weeded out, while the individuals with better fitness are
45
70
R245fa/Pentane R245fa Pentane
60
Pcon / %
Peva / %
40
R245fa/Pentane R245fa Pentane
65
35
55 50
30 45 25
373.15
393.15
413.15
433.15
40
453.15
373.15
393.15
413.15
T g/K
(a) evaporator
(b) condenser
3.0
453.15
16
R245fa/Pentane R245fa Pentane
2.5
R245fa/Pentane R245fa Pentane
Pexp / %
12
Ppump / %
433.15
T g/K
2.0
8 1.5
1.0
373.15
393.15
413.15
433.15
4
453.15
373.15
393.15
Tg/K
413.15
433.15
453.15
T g/K
(c) pump
(d) expander 0.8
15
R245fa/Pentane R245fa Pentane
0.6
Pfan / %
PWF / %
10
R245fa/Pentane R245fa Pentane
0.4
5 0.2
0
373.15
393.15
413.15
433.15
453.15
0.0
373.15
393.15
413.15
433.15
T g/K
Tg/K
(e) fans
(f) working fluid
453.15
Fig. 7. Percentage of each component in the total capital cost using R245fa, Pentane and their mixture under different heat source temperatures.
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assigned with high probabilities to survive to the next generation; the individuals should finally converge in a small area. The optimal individual with the minimum value of EPC could be singled out from the final population. The working condition of heat source temperature 413.15 K using working fluid R245fa/Isopentane is performed as an example to evaluate the feasibility and stability of the optimization method. Fig. 2 shows the variation of the optimal objective function value with the evolution times. It can be seen that as the evolution times increased, the optimal value of objective function updated by the smaller value until the iteration
is stopped (with the stop generation of about 100). Fig. 3 shows the population distribution under different evolution times. As shown in Fig. 3(a), the randomly generated individuals in the initial population are distributed dispersedly. Along with the evolution time increased, the degree of convergence of the individuals also increased. When the value of evolution time reaches 100, as can be seen in Fig 3(d), the individuals converge in a small area around the optimal individual. To evaluate the stability of the in-house Genetic algorithm program, calculations are performed 5 times repeatedly under the same parameter settings and the results are
45
70
R245fa/Isopentane R245fa Isopentane
40
Pcon / %
Peva / %
35 30
R245fa/Isopentane R245fa Isopentane
65
25
60 55 50
20 15
373.15
393.15
413.15
433.15
45
453.15
373.15
393.15
T g/K
16
R245fa/Isopentane R245fa Isopentane
3.5
2.5
12 10
2.0
8
1.5
6
373.15
393.15
413.15
433.15
R245fa/Isopentane R245fa Pentane
14
Pexp / %
Ppump / %
3.0
4
453.15
373.15
393.15
413.15
433.15
T g/K
T g/K
(c) pump
(d) expander
20
453.15
0.8
R245fa/Isopentane R245fa Isopentane
10
5
R245fa/Isopentane R245fa Isopentane
0.6
PWF / %
15
Pfan / %
453.15
(b) condenser
4.0
0
433.15
T g/K
(a) evaporator
1.0
413.15
0.4
0.2
373.15
393.15
413.15
T g/K
(e) fans
433.15
453.15
0.0
373.15
393.15
413.15
433.15
453.15
Tg/K
(f) working fluid
Fig. 8. Percentage of each component in the total capital cost using R245fa, Isopentane and their mixture under different heat source temperatures.
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listed in Table 5. It shows that for the 5 times calculations, optimized value of objective function and parameters relative errors were below 2%, which is enough to meet the requirement of the industrial demand. 4. Results and discussions 4.1. Comparison between the calculating methods In the most of the related work, the mixture compositions were usually discretely assumed as fixed values. Take R245fa/Butene as
an example, under the given heat source temperatures, the optimal EPC values under different mixture compositions (mole fractions of R245fa, varied from 0.1 to 0.9) were calculated. The calculated results are presented in Fig. 4. It can be seen from Fig. 4 that the ‘‘optimal mixture composition (corresponding with lowest EPC value for given heat source temperature)” under different heat source temperatures are distributed between 0.25 and 0.55, roughly showing an increasing trend along with the increase of heat source temperatures. Above method was commonly used to obtain the ‘‘optimal mixture composition” for mixture working fluid, however, several shortcomings exist about this method:
40
65
R245fa/Butene R245fa Butene
60
Pcon / %
Peva / %
35
R245fa/Butene R245fa Butene
55
30 50
25
373.15
393.15
413.15
433.15
45
453.15
373.15
393.15
(a) evaporator R245fa/Butene R245fa Butene
2.5
R245fa/Butene R245fa Butene
12
Pexp / %
Ppump / %
3.0
2.0
10 8 6
1.5
373.15
393.15
413.15
433.15
4
453.15
373.15
T g/K
393.15
413.15
433.15
453.15
T g/K
(d) expander
(c) pump 20
0.8
R245fa/Butene R245fa Butene
R245fa/Butene R245fa Butene
0.6
PWF / %
15
Pfan / %
453.15
14
3.5
10
5
0
433.15
(b) condenser
4.0
1.0
413.15
T g/K
T g/K
0.4
0.2
373.15
393.15
413.15
433.15
453.15
0.0
373.15
393.15
413.15
433.15
T g/K
T g/K
(e) fans
(f) working fluid
453.15
Fig. 9. Percentage of each component in the total capital cost using R245fa, Butene and their mixture under different heat source temperatures.
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40
65
R245fa/Cisbutene R245fa Cisbutene
60
Pcon / %
Peva / %
35
R245fa/Cisbutene R245fa Cisbutene
55
30 50
25
373.15
393.15
413.15
433.15
45
453.15
373.15
393.15
(a) evaporator
R245fa/Cisbutene R245fa Cisbutene
2.5
R245fa/Cisbutene R245fa Cisbutene
12
Pexp / %
3.0
Ppump / %
453.15
14
3.5
2.0
10 8 6
1.5
373.15
393.15
413.15
433.15
4
453.15
373.15
393.15
413.15
433.15
453.15
T g/K
T g/K
(d) expander
(c) pump 0.8
20
R245fa/Cisbutene R245fa Cisbutene
10
R245fa/Cisbutene R245fa Cisbutene
0.6
PWF / %
15
Pfan / %
433.15
(b) condenser
4.0
0.4
0.2
5
0
413.15
T g/K
T g/K
373.15
393.15
413.15
433.15
453.15
T g/K
(e) fans
0.0
373.15
393.15
413.15
433.15
453.15
T g/K
(f) working fluid
Fig. 10. Percentage of each component in the total capital cost using R245fa, Cisbutene and their mixture under different heat source temperatures.
firstly, the confirmed ‘‘optimal mixture composition” is essentially is an interval with accuracy of 0.1, not a unique value; secondly, the trends of objective function value (i.e. EPC value in the present work) and mixture composition are usually complex, singularity appears sometime [42], thus ulteriorly reducing the reliability of the calculated result. For these reasons described above, in this work, coupled with inlet temperature and pressure of expander, the mixture composition (i.e. mole fraction of R245fa) was set as one of the variables to be optimized. GA was recommended as an effective method to optimize the system performance and obtain the ‘‘optimal mixture composition”. When to obtain the optimal mixture compositions under certain heat source temperatures,
the calculating times were decreased 9 times. The reliability of the optimal program has been validated in Section 3.2. Based on this, compared with the above-motioned method showed in Fig. 4, the accuracy of the calculated optimal mixture composition was improved at the same time. 4.2. Comparison between mixtures and their components Fig. 5 shows the variations of the EPC and total cost with heat source temperatures for the mixture and pure working fluids. It can be seen that for all working fluids, the EPC value decreased with the increase of heat source temperature. For the capital cost,
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clearly showed that the mixture working fluid with a larger percentage of the condenser, pump, and expander in the capital cost, but a lower percentage of the capital cost of the evaporator in the most situations. Combined with the conclusion from Fig. 5, it can be inferred that for the mixture working fluid, the decrease of the EPC value is mainly due to the decrease of the capital cost, which is essentially caused by the decrease of the evaporator capital cost.
1.0
0.8
xR245fa
0.6
0.4
R245fa/ Isopentane R245fa/ Pentane R245fa/ Cisutene R245fa/ Butene
0.2
4.3. Analysis of the mixture working fluids behavior
0.0 373.15
393.15
413.15
433.15
453.15
Tg /K Fig. 11. Variations of the optimized mole fractions with heat source temperatures.
it showed a reverse tendency. As can be seen from Fig. 5 that the mixture working fluid showed a better economic performance (lower EPC and capital cost) compared to the pure working fluid. Lower capital cost obtained by the system using mixture working fluid means that under same heat source condition, using mixture working fluid leads to a smaller physical scale of ORC plant compared with the pure working fluid. From Fig. 5 it also can be seen that, for the pure and mixture working fluids, the operating condition for a lower EPC value always corresponds to a relative lower capital cost value. Fig. 6 shows the variations of the net power and thermal efficiency with the heat source temperature for the mixture and pure working fluids. It can be seen from Fig. 6 that when operated under the optimized working conditions, the net power of the mixture working fluid does not have a clear advantage compared with the pure working fluid, which illustrates that the decreased EPC value of mixture working fluid is mainly due to the decrease of the capital cost. Percentage of each system component (i.e. evaporator, condenser, pump, expander, working fluid and fans) in the total capital cost using different mixture and pure working fluids under different heat source temperature are showed in Figs. 7–10. It is interesting to note that in most situations, for the pure and mixture working fluids, the percentage of the evaporator and condenser in the total capital cost decreased with the increase of heat source temperature. For other components including pump, expander, working fluid, and fans, they showed opposite trends. Also, it
Fig. 11 shows the variations of the optimized mole fractions with heat source temperatures. It can be observed that the distribution of the optimized mixture compositions shows almost the linear behavior. In the process of actual application, the correlations should be useful to predict the mixture compositions with good accuracy, using only a few key design parameters and without the need of knowledge of working fluid properties and their use in ORCs. This method adopted in the present work could be used for making the correlations when the waste heat source scale and the working fluid are confirmed. In this work with the given working conditions, the correlation between optimized mole fractions of R245fa (xR245fa) and heat source temperature (Tg/K) for the selected 4 different mixtures are given by Eqs. (44)–(47): R245fa/Pentane:
xR245fa ¼ ð1096:63 0:9216T g Þ=1000 ðR ¼ 0:9209Þ R245fa/Isopentane:
xR245fa ¼ ð537:47 þ 0:7844T g Þ=1000 ðR ¼ 0:8769Þ
xR245fa ¼ ð731:62 þ 2:72T g Þ=1000 ðR ¼ 0:8947Þ
xR245fa ¼ ð1611:67 þ 5:27T g Þ=1000 ðR ¼ 0:9698Þ
443.15 K 433.15 K 423.15 K
T /K g
R245fa/Cisbutene R245fa/Butene R245fa/Isopentane R245fa/Pentane
393.15 K 383.15 K
373.15 K
-0.12
-0.08
-0.04
0.00
ð47Þ
It can be observed from the above formulas that as the critical temperature of the flammable working fluid increased, the slope of fitted straight line decreased. In the mixtures, act as the flame retardants, the mole fractions of R245fa increased as the increase of heat source temperature, this rule is correct except for R245fa/ Pentane. These formulas fitted from the optimized results using EPC as objective function should provide a reference for mixture composition determination for the recommended 4 mixtures.
403.15 K
-0.16
ð46Þ
R245fa/Cisbutene:
413.15 K
-0.20
ð45Þ
R245fa/Butene:
453.15 K
Cisbutene Butene Isopentane Pentane
ð44Þ
0.00
0.02
0.04
0.06
0.08
0.10
0.12
R Fig. 12. Variations of the characterization parameter R with heat source temperatures for pure and mixture working fluids.
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4.4. Recommendation of working fluid for different heat source temperatures
(2013CB228304) and the Key Project of National Natural Science Foundation of China (No. 51436007).
By taking R245fa as the reference working fluid, a characterization parameter R is defined as:
References
RWF ¼ ðEPC R245fa EPC WF Þ=EPC R245fa
ð48Þ
where the subscripts ‘‘WF” in Eq. (48) represents different working fluids. RWF is inversely proportional to EPCWF, the lower value of EPC corresponds to the superior economic performance, therefore, the higher value of RWF, the better of the accordingly working fluid. Fig. 12 shows the variations of the characterization parameter R with heat source temperatures for pure and mixture working fluids. Fig. 12 should be divided into two parts, the left part is for pure working fluid and the right part is for mixture working fluid. Most of the R values for pure working fluids (on the left part) are negative. This illustrates that compared with the reference working fluid R245fa, pure working fluid with negative R value is poorly performed. As it to the mixture working fluid on the right part, the R value of them are all positive. They show superior economic performance compared with R245fa and other pure working fluids. It can be observed from Fig. 12 that under medium heat source temperature (i.e. 383.15–403.15 K), R245fa/Pentane is recommended as the optimal mixture working fluid for its maximum R value (represents minimum EPC value). While for relatively low (373.15 K) and high (413.15–453.15 K) heat source temperatures in this work, working fluid R245fa/Isopentane is recommended. As it to pure working fluids, Isopentane and Pentane are considered as the optimal working fluids when working under heat source temperature of 373.15–423.15 K and 433.15–453.15 K, respectively. Compared with the recommended pure working above, their mixtures with R245fa showed not only superior economic performances but also the lower flammability. Compared with the widely used working fluids R245fa, the economic performance and environment performance are both improved by using the recommended mixture working fluid.
5. Conclusions Optimized calculation for 5 pure working fluids and 4 mixture working fluids were performed by using GA as the optimization method. By using EPC as the objective function, the mixture composition was set as one of the variables during the calculating process. The main conclusions are as follows: (1) The mixture working fluid showed a better economic performance (lower EPC and capital cost). The lower EPC value obtained by mixture working fluid was mainly due to the decrease of the capital cost, which is essentially caused by the decrease of capital cost of the evaporator. (2) The correlations between optimized mixture composition (i.e. the mole fraction of R245fa) and heat source temperature (Tg) for the selected 4 mixture working fluids were fitted from the optimization results. (3) R245fa/Pentane and R245fa/Isopentane are recommended as the optimal mixtures working fluids for temperature range of (383.15–403.15 K) and (373.15, 413.15–453.15 K), respectively.
Acknowledgements The authors gratefully acknowledge the support from the National Key Basic Research Program of China (973 Program)
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