Energy 40 (2012) 107e115
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Fluid selection and parametric optimization of organic Rankine cycle using low temperature waste heat Z.Q. Wang a, b, *, N.J. Zhou b, J. Guo b, X.Y. Wang b a b
Institute of Mechanical Engineering, Xiang Tan University, No.13 North Xiangtan University Road, Xiangtan 411105, PR China School of Energy Science and Engineering, Central South University, No. 932 South Lushan road, Changsha 410083, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 November 2011 Received in revised form 8 February 2012 Accepted 11 February 2012 Available online 14 March 2012
The paper presented a working fluid selection and parametric optimization using a multi-objective optimization model by simulated annealing algorithm. The screening criteria considered included heat exchanger area per unit power output (A/Wnet) and heat recovery efficiency (V). The independent parameters are the evaporation and condensation pressures, working fluid and cooling water velocities in tubes. A comparison of optimized results for 13 working fluids shows that boiling temperature of working fluids will greatly affect the optimal evaporating pressure. R123 is the best choice for the temperature range of 100e180 C and R141b is the optimal working fluid when the temperature higher than 180 C. When the exhaust temperature ranges from 100 C to 220 C, the optimal pinch point at evaporator is about 15 C. Economic characteristic of system decreases rapidly with heat source temperature decrease. When the heat source temperature is lower than 100 C, ORC technology is uneconomical. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Optimization Organic Rankine cycle Working fluid Low temperature waste heat
1. Introduction More than 50% total heat generated in industry is the low grade heat and it is emitted in the range of 100e220 C. Recovering energy from this waste flue gas and convert it to electricity can reduce fossil fuel consumption and alleviate environmental problems. The organic Rankine cycle (ORC) is one of the promising technologies of converting low grade heat into electricity [1e3]. Therefore, more and more attention has been paid to the technology in recent years and many researches about it mainly focused on working fluid selection and parametric optimization of organic Rankine cycle. Saleh et al. [4] compared the thermodynamic performances of 31 pure working fluids for organic Rankine cycles on the basis of the BACKONE equation of state. Liu et al. [5] examined the effects of various working fluids on the thermal efficiency and total heat recovery efficiency. It showed that the wet fluid was regarded as inappropriate for ORC system. Hung et al. [6] did a comparative study between wet, dry, and isentropic fluids in ORC system and the isentropic fluids were considered to be the best. Tchanche et al. [7] analyzed the thermodynamic characteristics and performances of
* Corresponding author. Institute of Mechanical Engineering, Xiang Tan University, No.13 North Xiangtan University Road, Xiangtan 411105, PR China. Tel.: þ86 731 58292215; fax: þ86 731 58292210. E-mail address:
[email protected] (Z.Q. Wang). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.02.022
20 fluids in a low-temperature solar organic Rankine cycle and R134a was recommended. In the high-temperature organic Rankine cycles, Fernendez et al. [8] proposed that siloxanes can show good efficiencies and ensure thermal stability in regenerative ORCs. Based on the thermal efficiency, cyclopentane was recommended as the best working fluid [9]. Hung et al. [10] investigated the thermal efficiency and irreversibility of an organic Rankine cycle to recover waste heat. Results showed that p-xylene had the highest efficiency and the lowest irreversibility in recovering a high temperature waste heat. Aljundi et al. [11] compared the thermal and exergetic efficiencies of different working fluids in ORC system. The results showed that n-hexane was the best working fluid while R227ea was the worst. Quoilin et al. [12] studied the thermodynamic performance of a solar organic Rankine cycle. It showed that the most efficient fluid was Solkatherm. Chen et al. [13] showed that the CO2 transcritical organic Rankine cycle gave a slightly higher power output than the organic Rankine cycle using R123. Moreover, a series of mixtures [14e17], which could be used to reduce the system irreversibility, were also proposed in sub-critical ORC system. Hettiarachchi et al. [18] presented an optimum design of an ORC system utilizing low temperature geothermal water. Based on the screening criterion of total heat transfer area to the net power out, the ammonia was recommended among four pure fluids. Roy et al. [19] carried out a parametric optimization and performance analysis of a waste heat recovery system using ORC technology. The
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Z.Q. Wang et al. / Energy 40 (2012) 107e115
considered performance parameters were work output and efficiencies of the system and R123 was recommended. Rashidi et al. [20] presented a parametric optimization of the regenerative ORCs. In their research, thermal efficiency, exergy efficiency and specific work were selected as the objective functions. Guo et al. [21] examined the optimum working fluid and parameters for a lowtemperature geothermal ORC system. The results showed that optimum evaporation temperature and fluids vary with different screening criteria. When the net power output was selected as the objective function, Chao H. et al. [22] proposed the optimal evaporation temperature and working fluids for subcritical organic Rankine cycle. Wang et al. [23] presented the effects of thermodynamic parameters on the supercritical CO2 cycle performance and optimized the thermodynamic parameters by means of genetic algorithm. Choosing the exergy efficiency as an objective function, Dai et al. [24] compared the performance of 10 pure working fluids and R236EA was recommended. Cayer et al. [25] and Zhang et al. [26] conducted a parametric investigation for a trans-critical and sub-critical ORC system, respectively. They reported that the best working fluid and operation parameters varied with the objective function. The brief review presented above clearly shows that the screening criteria were very important to working fluid selection and parametric optimization for the ORC system. Many researchers conducted the studies limited to the first law efficiency [4e11,13e17,19,20,25,26] and second law efficiency [6e8,11,15,20,24e26]. A few researches considered the optimal parameters of ORC system with different criteria [19,20,25,26]. Although the optimal working fluid was recommended for a special indicator, these literature did not take two or more indicators in account at the same time. In fact, the ORC system should consider several indicators during the operation. Up to the present, none of the published studies focused on the working fluids selection and parameter optimization based on the multi-objective function. On the other hand, these works did not evaluate the effect of heat source temperature on the working fluids under the optimization condition. In this study, a multi-objective optimization model was proposed and the screening criteria considered included heat exchanger area for per unit power output (A/Wnet) and heat recovery efficiency (V). The main objective of this study was focused on finding a suitable working fluid of the ORC for waste heat recovery. The cycle parameters were optimized using a simulated annealing algorithm. The performances of the ORC with different working fluids were compared under the optimization condition. The effects of waste heat temperature and pinch temperature on cycle performance were discussed. And the economic characteristic analysis of system has also been performed.
3 3
4
2
4s 1
Fig. 1. The TeS diagram of ORC.
The typical temperature profile of the exhaust gas and working fluid in the evaporator is presented in Fig. 2. And the temperature profile in the condenser is similar to the evaporator. As shown in Fig. 2, the pinch point is the least temperature difference between the working fluid in evaporator and heating flue gas. And the pinch point in the evaporator can be either at the point where evaporation starts or at the exit of heat source (state 7). 2.2. Thermodynamic modeling 1) Evaporator According to Fig. 2, the evaporator can be divided into three sections: preheating, evaporating and superheating. Heat absorbed for different section is evaluated as:
Qe;j ¼ mg cp;g Tg;j Tg;jþ1 The pressure drop in the tube can be given as. 2
Dpe;j ¼ le;j
le;j rye;j De;j 2
(2)
The working fluid velocity is calculated using ::
ye ¼
__ 4m f Ne rf pD2e
2. System modeling 2.1. System description The basic components of a subcritical ORC system consist of an evaporator, a turbine, a condenser and a working fluid pump. The corresponding Tes diagram of ORC is shown in Fig. 1. The working fluid pump lets the liquid refrigerant (state 1) available at the exit of the condenser into the evaporator. The high pressure liquid (state 2) is heated and vaporized by the waste heat resource. Then the hot pressurized vapor is delivered to turbine inlet (state 3) and drives the expander to generate power. The low pressure vapor at the turbine outlet (state 4) is cooled to liquid refrigerant by cooling water when passing through the condenser.
(1)
Fig. 2. Typical temperature profiles for evaporator.
(3)
Z.Q. Wang et al. / Energy 40 (2012) 107e115
The heat exchanger area of the different section can be calculated by:
(4)
(5)
The mean temperature difference for different section in the evaporator is calculated by:
DTe;j ¼
::
__ ðh h Þ Wt ¼ m 3 4 f
de;j 1 1 1 ¼ þ þ þ Re;j ai;j ke;j ao;j Ke;j
3) Turbine The work done by the turbine can be expressed as:
Qe;j Ke;j DTe;j
Ae;j ¼
Tg;jþ1 Tf ;jþ1 Tg;j Tf ;j
The consumed power by working fluid pump and water pump are determined by [18]:
h i P mf ðp2 p1 Þ þ Dpe;j
Pf ¼
The Gnielinski equation is used for single-phase working fluid heat transfer [27]:
Pw ¼
f ¼
Tg;jþ1 Tf ;jþ1 Tg;j Tf ;j
ðf =8ÞRef Prf 2=3 Prf 1 þ 1:07 12:7ðf =8Þ
(7)
0:5
(8)
2 1:82lgRef 1:64
A correlation for the heat transfer of two-phase flows in a horizontal tube is defined as [28]
a ¼ a
8 9 0 0:37 2:2 >0:5 > r > > < ð1 xÞ þ 1:2x0:4 ð1 xÞ 00 = r
00 r0 0:67 2 > a 0:01 > 0:7 > > 1 þ 8ð1 xÞ þ rx : ; 0 00
a
(9)
(10)
2) Condenser The condenser consists of three section, superheating, condensing and subcooling, which is similar to the evaporator. Heat rejection at different section is determined by:
Qc ¼ mw cp;w Tw;jþ1 Tw;j
(11)
The pressure drop, water velocity in the tube and heat exchanger area of the condenser can be calculated by the following equations, respectively. 2
lc;j ryc;j ¼ lc;j Dc;j 2
(12)
::
__ w 4m yc ¼ Nc rw pD2c
(13)
Qc;j ¼ Kc;j DTc;j
(14)
The condensation heat transfer coefficient is calculated by [30]:
" Nu ¼ 0:725
(18)
Wnet ¼ Wt Pf Pw
(19)
When the pinch point stays at the exit of heat source, the evaporator will get the maximal energy from waste heat resource. The heat recovery efficiency is the ratio of the available energy to the maximum usable energy from waste heat.
Qe T5 T7 ¼ Qm T5 T2 Tpp
(20)
r
Nug ¼ 0:35Reg Prg
Ac;j
P
Dpc;j rw hp
mw
(17)
5) Cycle
f¼
Numerical correlations of the heat transfer coefficients between exhaust and evaporator is determined from [29]:
Dpc;j
rf hp
The net power of ORC system is defined as:
1
0
(16)
4) Pump
(6)
ln
Nuf ¼
109
k3f r0 ðr0 r00 Þgr
mf Dc ðTc Tb Þ
#0:25 (15)
2.3. Economic modeling In the low-temperature waste heat power plant, the heat exchangers (evaporator and condenser) contributes largely to the total cost. It is reasonable because 80e90% of the system capital cost was assigned on the heat exchangers [31]. The capital cost of each heat exchanger is determined by the following general correlation [26].
lgC ¼ F1 þ F2 lgA þ F3 ðlgAÞ2
(21)
CB ¼ C B1 þ B2 Fm Fp
(22)
lgFp ¼ C1 þ C2 lgp þ C3 ðlgpÞ2
(23)
The coefficients F1 ,F2 ,F3 ,B1 ,B2 ,C1 ,C2 ,C3 required for cost evaluation of each equipment can be obtained in Ref. [26]. Considering the cost of other system equipment (turbine and pump), there is a coefficient for the total cost of heat exchangers.
C1996 ¼ 1:15 CB;e þ CB;c
(24)
The cost of power plant is further converted from 1996 costs to 2008 costs by using Chemical Engineering Plant Cost Index (CEPCI) values.
C2008 ¼ C1996
CI;2008 CI;1996
(25)
where, CI;1996 ¼ 382; CI;2008 ¼ 575:4. The capital recovery cost (CRF) is estimated based on the following relation:
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Z.Q. Wang et al. / Energy 40 (2012) 107e115
Cr ¼
ið1 þ iÞts ð1 þ iÞts 1
(26)
The interest rate i and plant life time ts is set as 6% and 20 years, respectively. Electricity production cost could be calculated by:
CE ¼
Cr C2008 þ Cs Wnet Os
(27)
where, Cs is the operation and management cost of the system, which is 1.5% of the total cost. Os is the operation time of the plant, which is 7500 h/y. The payback period of system is determined by
lg
s¼
Wnet ,Os ,Cpri Cs Wnet ,Os ,Cpri Cs i,C2008 lgð1 þ iÞ
(28)
Table 1 Properties of considered working fluids. Working fluid
M/g$mol1 Tcrit /K
pcrit /MPa Tboil /K
cp /kJ$kg1$k1 ODP GWP
R123 R134a R141b R142b R152a R227ea R236ea R236fa R245ca R245fa R600 R600a n-pentane
152.93 102.03 116.95 100.5 66.05 170.03 152.04 152.04 134.05 134.05 58.122 58.122 72.149
3.662 4.059 4.460 4.07 4.516 2.926 3.502 3.2 3.925 3.64 3.796 3.64 3.37
1.023 1.280 1.163 1.219 1.625 1.077 1.219 1.205 1.332 1.318 2.297 2.236 2.367
456.83 374.21 479.96 410.26 386.41 374.8 412.44 398.07 447.57 427.2 425.13 407.82 469.7
300.97 247.08 305.2 264.0 249.13 256.7 279.34 271.71 298.28 288.05 272.6 261.48 309.21
0.02 0 0.11 0.06 0 0 0 0 0 0 0 0 0
120 1300 700 2400 120 3500 e 6300 560 950 20 20 11
2.4. optimization modeling 1) Objective function
where, CPri is the price of electricity and it is set to 0.5￥/kWh. In order to improve the power produced by per unit of heat exchanger area, the ratio of the total heat exchanger area to net power output is selected as the first objective function.
minf1 ðXÞ ¼ ðAe þ Ac Þ=Wnet
(29)
On the other hand, higher heat recovery efficiency means more energy recovered from wasted heat and more net power. Therefore, the second objective function is the heat recovery efficiency.
minf2 ðXÞ ¼ 1=f
(30)
Based on the two models, the evaluation function for the optimization is expressed by:
FðXÞ ¼ w1 f1 ðXÞ þ w2 f2 ðXÞ
(31)
2) Design variables The objective functions are closely correlated with the specific enthalpy of working fluid. And the specific enthalpy was tightly related with the pressures in evaporator and condenser. Therefore, the pressure is the important parameter which affected the system performance. Besides that, the heat transfer coefficient and pressure drop in tube varied with the velocities in evaporator and
0.24
Ref. results simulation results
thermal efficiency /%
0.20
0.16
0.12
0.08
0.04 320
340
360
380
400
evaporation temperature Fig. 3. Flow chart of simulation procedure annealing algorithm.
Fig. 4. Comparison of numerical results with Ref. results.
420
Z.Q. Wang et al. / Energy 40 (2012) 107e115 Table 2 Assumptions for the optimization. De /mm
de /mm
Tpp;e / C w1 T5 / C
32 3 10 0.6 140
Dc /mm
dc /mm
Tpp;c / C w2 Vg /m3h1
19 2.5 5 0.4 300,000
k /Wm1K1 R /m2KW1
hp ht
T8 / C
46.2 0.0004 0.8 0.8 20
condenser. Thus, the evaporating and condensing pressures, working fluids and cooling water velocities are the design variables.
X ¼ ½x1 ; x2 ; x3 ; x4 T ¼ ½Pe ; Pc ; ye ; yc T
(31)
3) Constraints In order to produce new solutions for the annealing algorithm, basic constrained conditions are given according to various demands. In order to avoid the air coming into the condenser, the condensing pressure should be greater than atmospheric pressure. So,x2 0:101 0. According to the characteristic of ORC system, the evaporation pressure should be higher than the condensing pressure. It meantx1 x2 > 0. In addition, the evaporating temperature must be lower than the inlet temperature of the heat source temperature. Similarly, the condensing temperature should be higher than the inlet temperature of cooling water. And the evaporating temperature and condensing temperature are functions of pressure in the evaporator and condenser, respectively. It indicates x1 < pmax andx2 < pmin . Besides that, the evaporating pressure should be lower than the critical pressure in a sub-critical cycle. So x1 < pcri . Lastly, the minimum velocity in tube should be larger than zero. So,x3 > 0; x4 > 0. 3. Optimization algorithm In the optimal design, there are many conventional methods such as the steepest descent method, powell method. Usually these methods acquires local optimization solutions easily but meets difficulty in obtaining global optimization solution. And another weak point is that its performance depends on the choice of initial solution. Compared with the conventional algorithms, the
111
simulated annealing (SA) method is recognized to have a better capability to find the global optimum solution. In addition to that, it has many other advantages in simple description, flexible usage, running efficiency and less restriction on initial conditions. As a result, the SA method was used in the parametric optimization for ORC. The SA is originated from the simulation of solid annealing process, such as growing silicon in the form of highly ordered, defect-free crystals. In order to accomplish this, the material is annealed. It is first heated to a temperature that permits many molecules to move freely with respect to each other. Then, it is cooled carefully and slowly until the material froze into a crystal, which is completely ordered and thus the system is at the state of minimum energy. In the optimum searching process, the objective function to a certain optimization problem is regarded as an equivalence of the energy, and the value of control parameter t which is reduced gradually and regarded as the temperature in solid annealing process. For each value of control parameter, the algorithm continues the iterative process to generate new solutions, judge it, then accept or abandon it, which corresponds to the heat balance process in a constant solid temperature. As the process is repeated and t tend to zero, the global optimal solution is obtained. The main idea of this algorithm is to first produce a series of relative optimization solutions by Metropolis algorithm, and continue the iterative process by the criterion of Metropolis, which decides whether to accept the transition from current solution n to a new solution k according to the transition probability B.
1 Bij t ¼ exp½ ðf ðkÞ f ðnÞÞ=t
f ðkÞ f ðnÞ f ðkÞ>f ðnÞ
(31)
Therefore, the simulated annealing algorithm can be considered as an iterative process of Metropolis algorithm with the decrease of controlling parameter valuet. The flow chart of the simulation procedure is shown in Fig. 3. 4. Working fluids The working fluid is an important part of an ORC system. For ORC applications, there are some general criteria like moderate vapor pressure in the evaporator, stability, suitable critical temperature, ozone-safe and so on [2,32]. As a result of these
Fig. 5. Variation of F(X) with the condensing pressure and evaporating pressure for R123.
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Z.Q. Wang et al. / Energy 40 (2012) 107e115
Fig. 6. Variation of F(x) with the velocity in evaporator and condenser for R123.
Table 3 Results of parameters optimization.
R123 R134a R141b R142b R152a R227ea R236ea R236fa R245ca R245fa R600 R600a n-pentane
Pe /MPa
ye /ms1
Pc /MPa
yc /ms1
hfir /%
A/m2
Wnet /KW
f/%
0.692 2.805 0.602 2.235 3.257 2.852 1.805 2.464 0.876 1.322 1.532 2.221 0.661
0.85 0.72 1.53 1.09 1.01 0.75 1.11 1.06 1.73 1.19 1.13 1.13 1.41
0.109 0.767 0.101 0.395 0.687 0.526 0.243 0.319 0.122 0.182 0.282 0.404 0.10
1.45 0.89 0.48 1.46 1.24 1.0 1.68 1.62 0.77 1.02 1.19 1.30 0.61
11.78 10.31 12.2 13.04 12.44 12.33 11.97 13.0 12.75 12.43 12.57 13.06 12.06
2448.6 4904.6 2424.6 2384.1 3245.5 6338.8 2390.7 2660.1 2558.7 2417.8 2520.9 2465.4 2581.7
446.4 565.4 416.4 404.5 523.6 743.5 420.6 459.7 444.9 428.6 447.8 436.5 340.4
53.7 88.14 50.87 49.2 66.87 100 49.0 54.15 45.8 49.7 51.6 50.47 42.9
criteria, 13 fluids presented in Table 1 are selected as potential candidates. 5. Parametric optimizations and studies 5.1. Validation According to the developed model, the ORC simulation was performed by using a simulation program written in Matlab. Numerical solution was validated with the results of Liu et al. [5] for the ideal Rankine cycle using R123 as the working fluid and for the same operating conditions. During the validation, waste heat temperature was 200 C and condenser temperature was 30 C. As shown in Fig. 4, the comparison shows very good agreement between present solution and the results of Liu et al. This accuracy is believed to be sufficient for most engineering applications.
with the evaporating pressure at first and then increases with it. The reason is that with the increase of pressure difference between evaporator and condenser, the enthalpy difference in turbine increases. It leads to more net power output. When the evaporating pressure increases further, the temperature difference between working fluid and heat source will decrease. It will result in a rapidly increase of heat exchanger area. So there will be an optimal evaporating pressure (0.692 MPa) and condensing pressure (0.109 MPa).
6 5 4
The working fluid at the exit of the evaporator is assumed to be saturated vapor and saturated liquid at the condenser exit. The main input data of organic Rankine cycle for simulation are listed in Table 2. Fig. 5 shows that the value of objective function of R123 increases with the condensing pressure obviously. And it decreases
2 1 0
R1 23 R1 34 a R1 41 b R1 42 b R1 52 R2 a 27 e R2 a 36 ea R2 36 f R2 a 45 c R2 a 45 fa R6 00 R6 0 n- 0a pe nt an e
5.2. Results and discussion
F(x)
3
Fig. 7. Objective function value of different working fluids.
Z.Q. Wang et al. / Energy 40 (2012) 107e115
3.5
8 R152a R134a R227ea
3.0
R142b R141b R123 R245fa R134a R152a
7 R236fa
2.5 R600a
6
R142b
2.0
R236ea
F(x)
Evaporating pressure /MPa
113
R600
1.5
R245fa
1.0
4
R245ca
n-pentane
R123
0.5 240
250
260
270 280 290 Boling temperature /K
5
3
R141b
300
310
2
100
120
Fig. 8. Effect of fluid’s boiling temperature on evaporating pressure.
As shown in Fig. 6, the objective function value of R123 of ORC reaches a minimum for specific values of velocity. It is because that lower velocity leads to lower heat transfer coefficient of heat exchanger. However, higher velocity will result in higher pressure drop in system and reduce the net power. The optimal velocity for evaporator and condenser is 0.85 m/s and 1.45 m/s, respectively. When the velocity in heat exchanger is greater than 0.5 m/s, the value difference of objective function is small. Table 3 and Fig. 7 show the value of the optimum operation parameters and objective function for different working fluids. The results indicate that the choice of working fluid can greatly affect the operation parameters and objective function. R123 has the minimum objective function value of 4.0 and R134a yields the highest objective function of 5.66, which is 41.5% higher that of R123. Fig. 8 shows that higher boiling temperature of the fluid the lower evaporating pressure in the cycle. N-pentane (309.2 K), R141b (305.2 K) and R123 (300.9 K) shows the lowest evaporating pressure. R152a (249.1 K) shows the highest evaporating pressure, followed by R134a (247.1 K) and R227ea (256.7 K). The evaporating pressure in the cycle for the three working fluids is more than 2.8 MPa. The high evaporating pressure may limit their usage. Therefore, the working fluid with higher boiling temperature is more suitable for the ORC system.
5
4
Heat recovery efficiency /%
F(x)
6
180
200
220
When heat source temperature is 140 C, Fig. 9 shows the objective function value for different working fluids. It is evident that objective function decreases with the increase of pinch point in evaporator. The main reason is that higher pinch point results in higher average temperature difference between waste heat and working fluid. And it results in less heat exchanger area. It can be seen from Fig. 9 that the value of objective function of R123 is 4.8 when pinch point is 5 C. It is 25% higher that of 15 C. When the pinch point increases from 15 C to 25 C, it only decreases by 8.3%. On the other hand, with the increase of the pinch point less heat is transferred to the ORC system, which leads to a decrease of the total net power. Therefore, the reasonable pinch point is about 15 C. Fig. 10 shows that when the heat source temperature ranges from 100 C to 180 C, the value of objective function of R123 is lowest. So R123 is the best choice for the temperature below 180 C. And R141b is the optimal working fluid when the temperature higher than 180 C. The Fig. 10 also shows that as the heat source temperature increases, the value of objective function decreases for R141b. However, it decreases first and then increases at a special temperature for other working fluids. At last, it decreases with the
R142b R141b R123 R245fa R134a R152a
1.0
7
160
Fig. 10. Variation of F(x) with heat source temperature under the optimized operation parameters.
8
R123 R600 R141b R152a n-pentane R227ea
140
Heat source temperature
0.8
0.6
0.4
3 100
5
10
15
20
25
30
120
140
160
180
200
220
Heat source temperature
Pinch point /K Fig. 9. Variation of F(x) with pinch point under the optimized operation parameters.
Fig. 11. Variation of heat recovery efficiency with heat source temperature under the optimized operation parameters.
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Z.Q. Wang et al. / Energy 40 (2012) 107e115
12
R123 R134a R141b R227ea R245fa n-pentane
10
Payback period /year
2) R123 is the best choice for the temperature ranges from 100 C to 180 C, and R141b is the optimal working fluid when the temperature higher than 180 C. 3) The value of objective function decreases with the increase of pinch point in evaporator, and the optimal pinch point for ORC system is about 15 C. 4) With the decrease of heat source temperature, the value of payback period increases. When the heat source temperature is lower than 100 C, the ORC technology is inappropriate.
8 6 4
Acknowledgment
2 100
120
140 160 180 Heat source temperature
200
220
Fig. 12. Variation of payback period with heat source temperature under the optimized operation parameters.
increase of heat source temperature. From Fig. 10, it can be see that the heat availability increases with the heat source temperature. It means that more heat is transferred from waste heat to evaporator and it leads to the decrease of the average temperature difference between them. When the heat recovery efficiency closes to maximum (1.0), the average temperature difference nears to minimum. It results in the rapidly increase of heat exchanger area of evaporator. Although the net power output increases with heat availability, the percentage of increase of net power is lower than the percentage of increase of heat exchanger area. Therefore, the evaluation function will increase rapidly under the heat source temperature. For R134a, R152a, R142b and R245fa, the corresponding temperatures of objective function increasing suddenly are 140 C, 160 C, 200 C and 220 C, respectively. It is consist with the boiling temperature of working fluids. Fig. 11 shows that when the heat source temperature is 140 C, the payback period for R123 is 3.68 years. Compared with R123, the payback period of R134a increases 59.8%. It indicates that the choice of working fluid can greatly affect the power plant cost. When heat source temperature is below 180 C, R123 shows the best economic performance. And when the temperature is higher than 180 C, R141b has better economy. It can be also seen from Fig. 12 that the heat source temperature is an important factor on the payback period. When the temperature is 120 C, the payback period of R123 is 5.25 years. It shows that the economy performance for ORC system under this temperature is good. While the temperature decreases to 100 C, the payback period reaches to 9.35 years, which is higher 76.6% than that of 120 C. The payback period is too long for the ORC system. Therefore, the ORC system is unsuitable to the heat source with temperature below 100 C. 6. Conclusions In this study, the working fluid and parameters of ORC system has been optimized by simulated annealing algorithm. The effect of waste heat temperature and pinch point on the performance and economic characteristics of ORC system has also been compared under the optimal conditions. According to the optimization and comparison, the following results are concluded. 1) The selection of working fluid can greatly affect the operation parameters and the evaporating pressure in the cycle increases with the decrease of the boiling temperature of working fluids.
The authors gratefully thank the financial support for this research from the Science and Technology Department of Hunan (2009Gk2009) and the Innovation Fund for Technology Based Firms of China (08C26224302178).
Nomenclature Q m h T cp Dp
l l D
r y N A K DT
a d P k R Nu Re Pr x r
m W
h f w C p
s
B i ts Os Cs CPri
heat flow rate, kW mass flow rate, kg s1 specific enthalpy, kJ kg1 temperature, C specific heat, kJ kg1 K1 pressure drop, Pa friction factor length of tube, m diameter of tube, m density, kg m3 velocity, m s1 number of tubes heat transfer surface area,m2 overall heat transfer coefficient, W m2 K1 mean temperature difference, C heat transfer coefficient, W m2 K1 thickness of tube, m power, kW thermal conductivity, W m1 K1 thermal resistance, W m2 K1 Nusselt number Reynolds number Prandlt number vapor quality latent heat, kJ kg1 viscosity, Pa s power, kW efficiency, % heat recovery efficiency, % the weight coefficients of objective functions cost, ﹩ pressure, MPa payback period, year probability for new solution, % interest rate, % plant life time, y operation time of the plant, h operation and management cost, ﹩ price of electricity, ￥/kWh
Superscripts 0 saturation liquid 00 saturation vapor
Z.Q. Wang et al. / Energy 40 (2012) 107e115
Subscripts f working fluid g exhaust gas t turbine p pump c condenser e evaporator m maximum w water i inside o outside b wall pp pinch point j number of section in evaporator and condenser I Chemical Engineering Plant Cost Index
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