- Email: [email protected]
Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis
Energy xxx (2014) 1e10
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis You-Rong Li a, *, Mei-Tang Du a, Chun-Mei Wu a, Shuang-Ying Wu a, Chao Liu a, Jin-Liang Xu b a Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400044, China b Beijing Key Laboratory of New and Renewable Energy, North China Electric Power University, Beijing 102206, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 July 2013 Received in revised form 17 December 2013 Accepted 10 February 2014 Available online xxx
This paper presents an economical evaluation and parametric optimization on subcritical ORC (organic Rankine cycle) system for recovering the low-temperature waste heat of flue gas which is released from industrial boilers. First, the effects of the PPTD (pinch point temperature difference) in evaporator and condenser, and evaporating temperature on the system performance are examined with the EPC (electricity production cost) as the evaluation criterion. The optimal evaporating temperature, PPTDs in evaporator and condenser, as well as condensing temperature corresponding to the minimum EPC are provided simultaneously for the subcritical ORC system under different heat source temperatures. Then, the optimal parameter values are compared for nine potential organic working fluids with the critical point temperature from 124 C to 235 C. Results show that there exists a possible relationship between the critical temperature of working fluids and the economical performance of the system. Furthermore, it is suggested that the working fluids including R123, n-pentane, R11 and R141b, whose critical temperature range from 180 C to 210 C, are preferable for recovering the low-temperature waste heat of flue gas. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine cycle Economic evaluation Parameter optimization Electricity production cost
1. Introduction Along with the sharp growth of the world population and the rapid development of economy, the environmental pollution and energy shortage have become the bottleneck problems, which restrict the human social advancement. Exploiting new energy resources and improving the utilization ratio of conventional energy are two fundamental approaches to alleviate the severe situation. The ORC (organic Rankine cycle) has large technical potential and wide applications to generate the electricity by making use of a variety of different low-temperature heat sources, including renewable energy, such as solar energy, geothermal and biomass energy [1e3], and industrial waste heat from internal combustion engine, micro-gas turbine and boiler etc. [4e6]. In addition to its high thermal efficiency and simple structure, the ORC system offers the easiness of the application to the local small-scale power
* Corresponding author. Tel.: þ86 23 65112284. E-mail address: [email protected] (Y.-R. Li).
generation system, which has an advantage in recovering the distributed heat resource. During the past several decades, many researches on the ORC system have been done to improve the system performance and enhance the energy utilization rate. Selecting the suitable working fluids has been greatly concerned as an important factor which affects the cycle performance. The slope of the saturation vapor curve of the working fluid in Tes diagram is directly relevant to its behavior in the ORC system. Based on the different slope of the saturation vapor curve, the working fluids are classified into three categories, such as wet, isentropic, and dry fluids [7]. Roy et al. [8] conducted the performance analysis of ORC system by using R-12, R-123, R-134a and R-717 as working fluids under different heat source conditions. Results showed that the R123 appears to be a preferable selection as the working fluid for its good performance which is exhibited in the ORC system. Wang et al. [9] evaluated the performance of the ORC system with nine different working fluids in recovering the waste heat of the engine exhaust gas. It is found that the ORC system using R11, R141b, R113 and R123 as the working fluids has slightly the high thermal efficiency and the low exergy destruction rate. However, while considering the safety
http://dx.doi.org/10.1016/j.energy.2014.02.038 0360-5442/Ó 2014 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
2
Y.-R. Li et al. / Energy xxx (2014) 1e10
Nomenclature A heat transfer area, m2 B1, B2 coefficients for equipment cost C cost, $ C1, C2, C3 coefficients for equipment cost CBM bare module cost, $ CEPCI chemical engineering’s plant cost index COM cost of operation and maintenance, $ CRF capital recovery factor Cp purchased cost, $ EPC electricity production cost, $/(kW$h) FM material factor Fp pressure factor h specific enthalpy, kJ/kg K heat transfer coefficient, W/(m2$K) K1, K2, K3 coefficients for equipment cost LTpl life time of the plant, years M molecular weight, kg/kmol m mass flow rate, kg/s P pressure, MPa Pr Prandtl number Q heat flow rate, kW Re Reynolds number T temperature, C top operation time, hours
level and environmental impacts of the working fluids, R245fa and R245ca are the most suitable candidates. Guo et al. [10] compared the performance of the ORC-based power generation system for 27 organic working fluids with the critical point temperature that ranges from 71.95 to 214.06 C under a given geothermal source condition. The results indicated that R236ea presented the largest net power output, while E170, R600 and R141b presented the lowest A/Wnet and EPC value. Obviously, the preferable organic working fluid in the ORC system depends on various parametric conditions, for example, heat resource condition, evaluation criteria, as well as physical properties of the fluid, safety, technological feasibility and environmental harmony etc. Besides selecting suitable working fluids, modifying basic ORC and optimizing the operating parameters are two major measures to improve the performance of the ORC system. Rayegan and Tao [11] used the regenerative ORC instead of the basic ORC to reduce the irreversible loss of a solar ORC system. It was found that the regeneration could enhance the thermal and exergy efficiency of the cycle and it tended to be more effective for high molecular complexity working fluids in most instances. Pei et al. [12] designed a solar power generating system with the regenerative ORC system. The results showed that the cycle efficiency and overall system efficiency could reach the maximum values at appropriate regenerative temperatures, and both the maximum values are higher than the basic ORC system. Meanwhile, some new Rankine power systems equipping with vapor injector-based novel, thermal driven pump, and SVM (switching valves method) are proposed to improve the performance of the ORC system by reducing the power consumption of the working fluid pump [13e15]. The combined power and the cooling cycle system with different combination ways have also been investigated, such as the combinations of the ORC with ejector refrigeration cycle, vapor compression cycle and absorption refrigeration cycle [16e20]. On the other hand, the operating parameters are closely connected to the power output and efficiency of the ORC system. Wei
W
power output or input, kW
Greek symbols isentropic efficiency thermal conductivity, W/(m$K) viscosity, kg/(m$s)
his l m
Subscripts a air bo boiling section c condenser co condensing section cri critical e evaporator g glue gas i inlet m mean o outlet opt optimal p pump pc precooling section ph preheating section pp pinch point t turbine tot total wf working fluid
et al. [21] analyzed the effects of the mass flow rate and the inlet temperature of heat source and cold source on the power output and system efficiency. Li et al. [22] discussed the effects of evaporating temperature on the thermal efficiency, exergy efficiency, output power, exergy loss and outlet temperature of exhaust gas in detail. Wang et al. [23] presented the maximum net power output and the optimal evaporating temperature at different inlet temperature of heat source. And the influences of the turbine inlet temperature and Jacob number on the net power output and thermal efficiency were also investigated. Zhou et al. [24] studied the cycle efficiency, heat recovery efficiency, output power and exergy efficiency with respect to the evaporating pressure, heat source temperature and superheat degree through system experiments. Different researchers may evaluate the performance by different performance criterions, such as the net power output, the thermal efficiency, the exergy efficiency, the ratio of total heat transfer area to net power output, and EPC (electricity production cost), etc. [23e 26]. The most suitable working fluid, ORC structure, and the optimal operation parameters are not all the same when different performance criteria are adopted. Since the EPC attaches the importance to the total cost of the ORC system, as well as concerning the power output, it is considered as a reasonable evaluation criterion which can really reflect the economical and thermodynamic performance of the ORC system under a given heat source. The parameter matching relation between the internal parameters of the ORC system and the outside heat source condition plays a critical role in effectively utilizing low temperature waste heat. However, the present parameter optimization is primarily concerned with the choice of evaporating temperature, turbine inlet temperature, turbine inlet pressure and the degree of superheat at the turbine inlet, etc. [26e29]. Few studies dealt with the detailed analysis and optimization on the PPTD (pinch point temperature difference) in evaporator and condenser simultaneously. In fact, the
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
Y.-R. Li et al. / Energy xxx (2014) 1e10
PPTD in heat exchanger has a direct effect on the irreversible loss in the ORC system [30e32], and is closely related with heat transfer area, heat flow rate and outlet temperature of heat source in the evaporator. In this work, the PPTDs in evaporator and condenser, evaporating temperature, and condensing temperature are simultaneously analyzed and optimized at different heat source temperature by using the EPC as the performance evaluation criterion. The aim is to seek the optimal parameters and suitable working fluids to achieve the optimum balance between the energy utilization rate and the investment cost of the ORC system for recovering the low-temperature waste heat of flue gas released from industrial boilers. 2. System description and modeling The Tes diagram of a basic subcritical ORC system is depicted in Fig. 1. In the evaporator, the sub-cooled liquid working fluid absorbs heat from the flue gas and turns into saturated vapor. Then the saturated vapor under the high pressure flows into the turbine to do work, and drives a generator to produce the electricity. The expanded superheated vapor is cooled down and condensed to the saturated liquid state under the condensing pressure by the cooling air that comes from the environment. After the liquid working fluid is pumped to the evaporator, it absorbs heat in evaporator again to continue the next loop. The isentropic efficiencies of working fluid pump and turbine are taken into account during the real processes (1-2 and 4-5) of compression and expansion, which are 80% and 85% in this work, respectively. In order to perform the thermodynamic calculation and performance analysis for a basic subcritical ORC system, a set of relevant parameters of heat source and sink, and some cycle parameters are assumed, which is shown in Table 1. Because the present ORC system is designed for recovering waste heat of the flue gas that is released from industrial boilers, the temperature of the heat source varies from 150 C to 200 C, and the cold source is the air from the environment [33,34]. In the subcritical ORC system, the pinch limitations in evaporator and condenser are respectively located at the saturated liquid point and saturated vapor point of the working fluids, which has been verified by the subsequent calculation. The thermodynamics properties of the working fluids are calculated by the software of EES [35].
3
Table 1 Conditions of heat source and sink and the ORC parameters. Term
Value
The inlet temperature of exhaust gas, C The inlet temperature of cooling air, C The mass flow rate of exhaust gas, kg/s The mass flow rate of cooling air, kg/s Isentropic efficiency of turbine, % Isentropic efficiency of working fluids pump, %
150e200 20 10 50 85 80
Furthermore, some assumptions are also considered as follows: each component in the ORC system works in a steady state; heat loss in heat exchangers and pipelines is small enough to be neglected [32,33]; working fluids at the condenser outlet and turbine inlet are respectively saturated liquid and saturated vapor; the temperature difference at the pinch point in heat changer is not less than 3 C. With the above assumptions, the thermodynamic model of the subcritical ORC system can be described as follows: (1) Pump The isentropic efficiency of the working fluid pump is defined by
his;p ¼
h2s h1 : h2 h1
(1)
The pressure raise that is supplied by the working fluid pump is determined by the pressure difference between condensation and evaporation, and the work input is
Wp ¼ mwf ðh2 h1 Þ:
(2)
(2) Turbine The working fluid comes to pass an adiabatic expansion in the turbine, and the isentropic efficiency and the power output are, respectively
his;t ¼
h4 h5 ; h4 h5s
Wt ¼ mwf ðh4 h5 Þ:
(3)
(4)
(3) Evaporator The evaporator is divided into two parts: preheating section and boiling section. The pinch point occurs at the point where the boiling section starts. The temperature Tg,pp of the flue gas at the pinch point is determined by the bubbling point temperature and the pinch point temperature difference,
Tg;pp ¼ T3 þ DTe :
(5)
The mass flow rate of the organic working fluid can be calculated as
mwf ¼
Fig. 1. Tes diagram of a basic subcritical ORC system.
mg cp;g Tg;i Tg;pp : h4 h3
(6)
The heat balance equations in the evaporator are expressed as follows,
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
4
Y.-R. Li et al. / Energy xxx (2014) 1e10
Qph ¼ mwf ðh3 h2 Þ ¼ mg hg;pp hg;o ;
(7a)
Qbo ¼ mwf ðh4 h3 Þ ¼ mg hg;i hg;pp :
(7b)
The heat transfer areas in preheating section and boiling section can be respectively calculated by
Aph ¼
Qph Qbo ; A ¼ : Kph DTm;ph bo Kbo DTm;bo
(8a-b)
where, DTm is the logarithmic mean heat transfer temperature difference,
DTm;ph ¼
Tg;o T2 DTe T
T2
ln g;oDT e
; DTm;bo ¼
Tg;i T4 DTe T T
ln g;iDT 4 e
:
(9a-b)
l de
1=3
m mw
Re0:55 Prg g
0:14 :
(10)
The condenser also consists of two sections: the precooling section and the condensing section, without considering the subcooling of working fluids [25,28,29]. The pinch point limitation is at the boundary of the two sections, and the condensing temperature can be derived through iterating the following relation,
ma cp;a Tc DTc Ta;i ¼ mwf ðh6 h1 Þ:
(11)
The heat balance equations in condenser can be given as follows,
Qpc ¼ mwf ðh5 h6 Þ ¼ ma ha;o ha;pp ;
(12b)
Qpc Qco ; Aco ¼ : Kpc DTm;pc Kco DTm;co T5 Ta;o DTc T T
ln 5DT a;o c
log Cp ¼ K1 þ K2 log W þ K3 ðlog WÞ2 :
(16)
In above equations, Cp is a basic cost concerning with the heat transfer area of heat exchangers, or the mechanical work of pump and turbine operating at ambient pressure. Eq. (15) is used to calculate the cost of evaporator and condenser, and Eq. (16) to calculate the cost of pump and turbine. And considering the specific material of the construction and operating pressure, the cost should be corrected as:
CBM ¼ Cp B1 þ B2 FM Fp :
; DTm;co ¼
log Fp ¼ C1 þ C2 log P þ C3 ðlog PÞ2 :
(17)
(18)
In Eqs. 15e18, K1, K2, K3, B1, B2, C1, C2, and C3 are coefficients for the cost evaluation of system components. It should be noted that the actual capital cost must be converted from the cost of 1996 by introducing the CEPCI (Chemical Engineering Plant Cost Index). The CEPCI is widely used to adjust the plant construction costs at different periods and its value is published at intervals in the Chemical Engineering Journal [27],
CBM;2011 ¼ CBM;1996 $CEPCI2011 =CEPCI1996 :
Similar to the evaporator, the heat transfer area and the logarithmic mean heat transfer temperature difference in each section can be expressed as, respectively
DTm;pc ¼
For pump and turbine,
(12a)
¼ mwf ðh6 h1 Þ ¼ ma ha;pp ha;i :
Apc ¼
(15)
In the above formula, CBM is the corrected cost, FM is the material correction factor, and Fp is a measure that reflects the pressure factor since the system components work at the pressure much higher than the ambient pressure, which is determined by
(4) Condenser
Qco
A complete detailed economic analysis relies on several particular parameters, and the process is much complicated, even different from location to location and time to time. However, the total investment cost of an ORC system is mainly determined by the cost of the major components, including evaporator, turbine, condenser and pump. It should be pointed that the effect of the fluid cost on the total investment cost is slight and the variation of the mass flow rate of the working fluid with the PPTDs of evaporator and condenser and the evaporation temperature is small. Therefore, the cost of the fluid is not considered in this work, as shown in Refs. [25,27,40]. The current calculation method about the capital cost generally adopted the following correlations [10,25,27]. For heat exchangers,
log Cp ¼ K1 þ K2 log A þ K3 ðlog AÞ2 :
In the evaporator, the convective heat transfer coefficient of the organic working fluid side is generally more than 2000 W/(m2$K) [36e38]. So the thermal resistance of the flue gas side is much greater than that of the working fluid side, the convective heat transfer coefficient of flue gas is much smaller than that of organic working fluids. The overall heat transfer coefficient in the evaporator is mainly dependent on the convective heat transfer coefficient of the flue gas side, and even assumed to be the constants in Ref. [17]. Therefore, the total heat transfer coefficient is estimated by employing the Kern formula [39]
Kph ¼ Kbo ¼ Kog ¼ 0:36
3. Economical model
(13a-b)
T1 Ta;i DTc T T
ln 1DT a;i c
:
(14a-b)
In condenser, the precooling section is a small region, and the heat transfer in condenser is mainly limited by the thermal resistance of the air side. The convective heat transfer coefficient of the air side practically determines the total heat transfer coefficient, which also can be obtained by the Kern formula.
(19)
Then the total investment cost can be estimated by:
Ctot ¼ CBM;e þ CBM;c þ CBM;t þ CBM;p :
(20)
To take the effective operation time, the capital recovery cost and the COM (cost of operation and maintenance) into account, the electricity production cost, which is considered as the performance evaluation criteria used in the following optimization process, can be given by
EPC ¼ ðCtot CRF þ COMÞ= top Wt Wp ;
(21)
h i CRF ¼ ið1 þ iÞLTpl = ð1 þ iÞLTpl 1 ;
(22)
where, the interest rate (i) is set as 5%, the plant life time (LTpl) as 20 years, the operation time (top) as 8000 h, and COM is 1.5% of the investment cost.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
Y.-R. Li et al. / Energy xxx (2014) 1e10
5
In this model, the evaporating temperature and the pinch point temperature differences in evaporator and condenser are variables to be optimized, and the condensing temperature can be correspondingly calculated when the three independent variables are determined. After inputting a set of data for the independent variables within a certain range, the state parameters at each point in the ORC system can be estimated. Then, the heat transfer areas of heat exchangers and some cycle performance parameters are obtained. Obviously, the electricity production cost can be minimized by taking the partial derivatives of EPC in Eq. (21) with respect to Te, DTe and DTc, respectively, and setting them equal to zero
vEPC vEPC vEPC ¼ 0; ¼ 0; ¼ 0: vTe vDTe vDTc
(23a-c)
4. Results and discussion 4.1. The economical analysis The economical calculation shows that a large part of the total investment cost comes from the heat exchangers, which is mainly affected by the heat transfer area. While the PPTD (pinch point temperature difference) in heat exchanger is directly relative to the heat transfer area, thus it has a significant impact on the economical performance of the system. In the meantime, the PPTD in the heat exchanger immediately relates to the heat transfer capability, and therefore it concerns the thermodynamic performance of system as well. As a result, the optimization of PPTD has important implications for the performance improvement of the ORC system. Taking R245fa and R123 as the working fluids, Fig. 2 presents the variation of EPC with the PPTDs (DTe and DTc) in evaporator and condenser at Tg,i ¼ 180 C and Te ¼ 125 C. It can be found that the EPC decreases at first, and then increases with the increase of DTe and DTc, respectively, and the EPC of the ORC system reaches the minimum value at a specific combination of PPTDs in evaporator and condenser. From Eq. (21), the variation of EPC is mainly caused by the change of the investment cost and the power output of the ORC system. In evaporator, with the increase of DTe at certain evaporating temperature, the mean heat transfer temperature difference increases, leading to a decrease in the heat transfer area, which results in a reduction of the system investment cost. On the other hand, the increase of DTe yields a decrease in the heat transfer rate, and then the mass flow rate of the working fluid decreases, which leads to a reduction of power output. The reduction of the system investment has a greater effect than the reduction of power output on the EPC at a small DTe, and the value of EPC decreases with the increase of DTe; while with the further increase of DTe, the decrease of the mass flow rate of the working fluid becomes gradually obvious, and thus the reduction of power output weighs more and contributes to an increase of EPC. As for the condenser, the increase of DTc enables the heat transfer area of condenser to decrease, which results in a reduction of the investment cost, and thus the EPC decreases firstly. Meanwhile, the condensing temperature increases with the increase of DTc, and the enthalpy drop of unit working fluid in turbine becomes lesser, which results in a decrease in power output. When the DTc becomes high enough, the effect of the decreasing power output outweighs that of the decreasing investment cost. As a result, the EPC displays an increase later with the further increase of DTc. Therefore, it can be concluded that the EPC can achieve the minimum value at appropriate values of PPTDs in evaporator and condenser under given heat source temperature and evaporating temperature. As shown in Fig. 2, at Tg,i ¼ 180 C, Te ¼ 125 C, the
Fig. 2. Variation of EPC with DTe and DTc.
optimal combined PPTDs for R245fa and R123 are DTe,opt ¼ 15.2 C, DTc,opt ¼ 12.9 C and DTe,opt ¼ 11.3 C, DTc,opt ¼ 14.3 C, respectively. The minimum EPC with respect to the evaporating temperature at various heat source temperatures for R245fa and R123 have been shown in Fig. 3. It can be found that the EPC of the ORC system first decreases, and then increases with the increase of the evaporating temperature, and there exists an optimal evaporating temperature at a certain heat source temperature. The evaporating temperature determines the enthalpy difference of working fluid in the phase change region of evaporator, which affects the mass flow rate of working fluid under the certain heat transfer rate. On the other hand, evaporating temperature is closely related to the enthalpy drop per unit mass flow rate during expansion. As the power output of turbine is the product of the mass flow rate of working fluid and the enthalpy drop, the evaporating temperature determines the net work output to a large extent. Meanwhile, the evaporating PPTD and the heat transfer rate are changing with the evaporating
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
6
Y.-R. Li et al. / Energy xxx (2014) 1e10
Fig. 3. Variation of EPC with Te at different heat source temperature. Fig. 4. Variation of DTe,opt with Te at different heat source temperature.
temperature, which results in a variation of the total investment cost of system. The comprehensive effects of these factors contribute to the variation of EPC with the evaporating temperature as Fig. 3. From Figs. 2 and 3, an eventually minimum value of EPC exists at a combination of optimal values of the evaporating temperature, and PPTDs in evaporator and condenser. From Fig. 3, it is obvious that the EPC is greatly affected by the heat source temperature, and a higher heat source temperature can effectively reduce the electricity production cost of the ORC system owing to the remarkable increase of the net power output. It is also found that the optimal evaporating temperature corresponding to the minimum EPC appears an increasing trend toward the critical temperature with the increase of the heat source temperature. It hints that a trans-critical ORC may be more favorable, and is needed to be further studied. 4.2. The parametric optimization As mentioned above, there exist a couple of optimal PPTDs in evaporator and condenser that minimize the EPC at a certain evaporating temperature. Figs. 4 and 5 present respectively the variation of optimal PPTDs in evaporator and condenser with the
evaporating temperature at the different heat source temperature for R245fa and R123. Obviously, the optimal evaporating PPTD approximately linearly decreases with the evaporating temperature. With the increase of the evaporating temperature, the heat transfer rate in evaporator has a decreasing trend, and thus leads to a large reduction of power output, which may result in an increasing EPC. The decrease of evaporating PPTD can restrain the decrease of the heat transfer rate in evaporator, and then the reduction of power output to some degree. Therefore, a reasonable decrease of PPTD in evaporator can keep the EPC consistently lowest with the increase of the evaporating temperature. On the other hand, the increase of the heat source temperature yields a more remarkable increase of the investment cost than the increase of power output. Thus, a slight increase of optimal PPTD can finally balance the two-side effects of the heat source temperature on the value of EPC, and thereby keep the EPC minimum as possible. Therefore a higher heat source temperature results in a higher optimal PPTD in evaporator at the same evaporating temperature, as shown in Fig. 4. The variations of optimal PPTD in condenser and the corresponding optimal condensing temperature have been shown in
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
Y.-R. Li et al. / Energy xxx (2014) 1e10
7
Fig. 5. Variation of DTc,opt and Tc with Te at different heat source temperature.
Fig. 5. It can be found that the optimal PPTD in condenser and the condensing temperature almost keep constant with the increase of the evaporating temperature. With the increase of the heat source temperature, the optimal condensing temperature appears a slight increase, while the optimal condensing PPTD still remains almost unchanged, more or less at 12 C for R245fa while 14 C for R123. The optimal values of PPTDs in evaporator and condenser, evaporating temperature and condensing temperature for R245fa and R123 at different heat source temperature are presented in Fig. 6. It can be seen that the optimal evaporating temperature is notably influenced by the heat source temperature, while the other three parameters have only slight variations with the increase of the heat source temperature. It should be pointed that, in our previous work [6], the ratio of the net power output to total heat transfer area is used as the performance evaluation criterion to analyze the effect of the PPTDs and the evaporation temperature on the cost-effective performance of the ORC system in recovering the low temperature waste heat of the flue gas. In this case, the total pinch point temperature difference of evaporator and condenser should be given. Obviously, it is arbitrary and random. Therefore, the best cost-effective performance is not always corresponding to the minimum EPC.
Fig. 6. The optimal values of Te, Tc, DTe,opt and DTc,opt with respect to Tg,i.
4.3. The comparison for different working fluids To avoid the wet corrosion to turbine blades during the expansion of wet working fluids [8,9,25], nine dry or isentropic working fluids with the critical temperature from 124 C to 235 C are investigated, considering the heat source condition, as well as the physical properties and environmental friendliness of working fluids. The main properties of the working fluids are listed in Table 2. The economical optimization has been done for the subcritical ORC system with above nine working fluids when the heat source temperature maintains at 180 C. The minimum EPC of the nine working fluids are shown in Fig. 7. It can be found that four working fluids including R123, n-pentane, R11 and R141b, whose critical temperature range from 183.68 C to 204.21 C, possess the relative low EPC approaching 0.07$/(kW$h), while the ORC system with R236fa yields the highest EPC approaching 0.09$/(kW$h). Therefore, it is clear that the selection of working fluids has a significant influence on the economic performance of the subcritical ORC system.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
8
Y.-R. Li et al. / Energy xxx (2014) 1e10
Table 2 Main properties of the working fluids.
35
Working fluids
M (kg/kmol)
Tcri ( C)
Pcri (MPa)
1 2 3 4 5 6 7 8 9
R236fa R600a R114 R245fa R123 n-pentane R11 R141b n-hexane
152.0 58.1 170.9 134.1 152.9 72.2 137.4 117.0 86.2
124.92 134.70 145.68 154.05 183.68 196.55 198.96 204.21 234.67
3.20 3.63 3.29 3.65 3.67 3.36 4.41 4.25 3.06
ΔTe,opt ΔTc,opt
30 25 20
ΔTopt ºC
No.
15 10 5
When the minimum EPC is reached, Fig. 8 shows the corresponding net power output. Obviously, R245fa yields the highest net power output (112.6 kW) and R236fa the lowest (92.3 kW). Combining with Fig. 7, it indicates that the working fluid with the best economical performance may not own the largest net power by the effect of the investment cost of the system. For the selection of working fluids under a certain heat source condition, not only the waste heat recovery efficiency and power output but also the total investment cost of the heat recovery system should be taken into account. Figs. 9 and 10 present the optimal PPTDs in evaporator and condenser, evaporating temperature and condensing temperature
0.10
EPCmin ($/kWh)
0.08
0.06
0.04
0.02
0.00
R23 R R 6fa 600a 114
R24 R 5fa 123
n-pe R ntan 11 e
n R14 1b -hexan e
Fig. 7. The minimum EPC of different working fluids at Tg,i ¼ 180 C.
0
R236fa R600a R114 R245fa R123 n-pentane R11
R141bn-hexane
Fig. 9. The DTe,opt and DTc,opt of different working fluids at Tg,i ¼ 180 C.
of different working fluids at Tg,i ¼ 180 C. As shown in Fig. 9, the working fluid with higher critical temperature displays a smaller optimal evaporating PPTD and a larger optimal condensing PPTD. From Fig. 10, the optimal evaporating temperatures of different working fluids have a gradually increasing trend with the increase of the critical temperature, while the optimal condensing temperatures have no significant difference among the different working fluids. It indicates that the condensing temperature is insensitive to the economical performance, which further validates the rationality of parameter optimization at a given condensing temperature in some researches [10,22,25]. The minimum EPC with respect to the corresponding critical temperature of working fluids at different heat source temperature are shown in Fig. 11. It is found that the EPC of the ORC system presents a general trend, which decreases first and then increases with the increase of the critical temperature of working fluids. The results show that the working fluids with the critical temperature between 180 C and 210 C have the lower EPC. Therefore, the working fluids including R123, n-pentane, R11 and R141b are more suitable for recovering the waste heat of the flue gas. Meanwhile, the EPC decreases with the increase of the heat source temperature, and the higher critical temperature of working fluids, the EPC decreases the more dramatic. For instance, when the heat source temperature rises from 160 C to 200 C, the minimum EPC of the 236fa system decreases by 13.5%, while the n-hexane system decreases by 32%.
120
160
100
140 80
Wnet (kW)
120
60
Topt ºC
100
40 20 0 R 2
Te,opt Tc,opt
80 60 40
36f a
R6 00a
R1 14
R1 R2 23 45f a
n-p R1 1 ent ane
n R1 41b -hex ane
Fig. 8. Net power output of different working fluids at the minimum EPC at Tg,i ¼ 180 C.
20 0
R236fa R600a R114 R245fa R123 n-pentane R11
R141bn-hexane
Fig. 10. The Te,opt and Tc,opt of different working fluids at Tg,i ¼ 180 C.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
Y.-R. Li et al. / Energy xxx (2014) 1e10
Fig. 11. The influence of critical temperature on the minimum EPC at different heat source temperature.
5. Conclusion In the present study, the economical model of the subcritical ORC system for recovering the waste heat of the low-temperature flue gas has been presented. The effects of main parameters (Te, DTe and DTc) on the system performance were simultaneously analyzed combining the thermodynamics and economics. The optimal parameters were obtained for different working fluids at different heat source temperature. According to the analysis and optimization, the following conclusions can be summarized: (1) The performance criterion EPC decreases firstly, and then increases with the increase of Te, DTe and DTc respectively at certain heat source temperature. There exists an optimal combination of these parameters to minimize the EPC. (2) The optimal PPTD in evaporator decreases, while that in condenser almost keeps constant with the increase of the evaporating temperature. (3) The optimal parameters depend on the working fluids and the heat source temperature. A higher heat source temperature results in a better economical performance. With the increase of the heat source temperature, the optimal evaporating temperature and evaporating PPTD increase, the condensing temperature and condensing PPTD change little. (4) With the increase of the critical temperature of the working fluids, the EPC decreases first and then increases. The working fluids with the critical temperature within the range from 180 C to 210 C possess lower EPC, and therefore, R123, n-pentane, R11 and R141b are recommended as the working fluids to recover the waste heat of flue gas. Acknowledgment This work is supported by National Basic Research Program of China (973 Program, Grant No. 2011CB710701) and the Natural Science Foundation of China of International Cooperation Project (51210011). References [1] Tempesti D, Fiaschi D. Thermo-economic assessment of a micro CHP system fuelled by geothermal and solar energy. Energy 2013;58:45e51. [2] Ghasemi H, Paci M, Tizzanini A, Mitsos A. Modeling and optimization of a binary geothermal power plant. Energy 2013;50:412e28.
9
[3] Al-Sulaiman FA, Dincer I, Hamdullahpur F. Energy and exergy analyses of a biomass trigeneration system using an organic Rankine cycle. Energy 2012;45(1):975e85. [4] Shu GQ, Zhao J, Tian H, Liang XY, Wei HQ. Parametric and exergetic analysis of waste heat recovery system based on thermoelectric generator and organic Rankine cycle utilizing R123. Energy 2012;45(1):806e16. [5] Invernizzi C, Iora P, Silva P. Bottoming micro-Rankine cycles for micro-gas turbines. Appl Therm Eng 2007;27(1):100e10. [6] Li YR, Wang JN, Du MT. Influence of coupled pinch point temperature difference and evaporation temperature on performance of organic Rankine cycle. Energy 2012;42(1):503e9. [7] Hung TC, Shai TY, Wang SK. A review of organic Rankine cycles (ORCs) for the recovery of low-grade waste heat. Energy 1997;22(7):661e7. [8] Roy JP, Mishra MK, Misra A. Performance analysis of an organic Rankine cycle with superheating under different heat source temperature conditions. Appl Energy 2011;88(9):2995e3004. [9] Wang EH, Zhang HG, Fan BY, Ouyang MG, Zhao Y, Mu QH. Study of working fluid selection of organic Rankine cycle (ORC) for engine waste heat recovery. Energy 2011;36(5):3406e18. [10] Guo T, Wang HX, Zhang SJ. Fluids and parameters optimization for a novel cogeneration system driven by low-temperature geothermal sources. Energy 2011;36(5):2639e49. [11] Rayegan R, Tao YX. A procedure to select working fluids for solar organic Rankine cycles (ORCs). Renew Energy 2011;36(2):659e70. [12] Pei G, Li J, Ji J. Analysis of low temperature solar thermal electric generation using regenerative organic Rankine cycle. Appl Therm Eng 2010;30(8):998e 1004. [13] Xu RJ, He YL. A vapor injector-based novel regenerative organic Rankine cycle. Appl Therm Eng 2011;31(6):1238e43. [14] Lakew AA, Bolland O, Ladam Y. Theoretical thermodynamic analysis of Rankine power cycle with thermal driven pump. Appl Energy 2011;88(9): 3005e11. [15] Yamada N, Minami T, Anuar Mohamad MN. Fundamental experiment of pumpless Rankine-type cycle for low-temperature heat recovery. Energy 2011;36(2):1010e7. [16] Zheng B, Weng YW. A combined power and ejector refrigeration cycle for low temperature heat sources. Sol Energy 2010;84(5):784e91. [17] Little AB, Garimella S. Comparative assessment of alternative cycles for waste heat recovery and upgrade. Energy 2011;36(7):4492e504. [18] Aphornratana S, Sriveerakul T. Analysis of a combined Rankine-vapourcompression refrigeration cycle. Energy Convers Manag 2010;51(12):2557e64. [19] Vijayaraghavan S, Goswami DY. On evaluating efficiency of a combined power and cooling cycle. J Energy Resour Technol 2003;125(3):221e7. [20] Wang H, Peterson R, Herron T. Design study of configurations on system COP for a combined ORC (organic Rankine cycle) and VCC (vapor compression cycle). Energy 2011;36(8):4809e20. [21] Wei DH, Lu XS, Lu Z, Gu JM. Performance analysis and optimization of organic Rankine cycle (ORC) for waste heat recovery. Energy Convers Manag 2007;48(4):1113e9. [22] Li W, Feng X, Yu LJ, Xu J. Effects of evaporating temperature and internal heat exchanger on organic Rankine cycle. Appl Therm Eng 2011;31(17e18):4014e23. [23] Wang DX, Ling X, Peng H. Cost-effectiveness performance analysis of organic Rankine cycle for low grade heat utilization coupling with operation condition. Appl Therm Eng 2013;58(1e2):571e84. [24] Zhou NJ, Wang XY, Chen Z, Wang ZQ. Experimental study on organic Rankine cycle for waste heat recovery from low-temperature flue gas. Energy 2013;55: 216e25. [25] Zhang SJ, Wang HX, Guo T. Performance comparison and parametric optimization of subcritical organic Rankine cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Appl Energy 2011;88(8):2740e54. [26] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic Rankine cycles. Appl Therm Eng 2011;31(14): 2885e93. [27] Cayer E, Galanis N, Nesreddine H. Parametric study and optimization of a transcritical power cycle using a low temperature source. Appl Energy 2010;87(4):1349e57. http://www.sciencedirect.com/science/help/doi.htm. [28] Wang JF, Dai YP, Gao L. Exergy analyses and parametric optimizations for different cogeneration power plants in cement industry. Appl Energy 2009;86(6):941e8. [29] Wang DX, Ling X, Peng H, Liu L, Tao LL. Efficiency and optimal performance evaluation of organic Rankine cycle for low grade waste heat power generation. Energy 2013;50:343e52. [30] Venkatarathnam G, Mokashi G, Murthy SS. Occurrence of pinch points in condensers and evaporators for zeotropic refrigerant mixtures. Int J Refrig 1996;19(6):361e8. [31] Venkatarathnam G, Mokashi G, Murthy SS. Effect of mixture composition on the formation of pinch points in condensers and evaporators for zeotropic refrigerant mixtures. Int J Refrig 1999;22(3):205e15. [32] Heberle F, Preißinger M, Brüggemann D. Zeotropic mixtures as working fluids in organic Rankine cycles for low-enthalpy geothermal resources. Renew Energy 2012;37:364e70. [33] Dai YP, Wang JF, Gao L. Exergy analysis, parametric analysis and optimization for a novel combined power and ejector refrigeration cycle. Appl Therm Eng 2009;29(10):1983e90.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
10
Y.-R. Li et al. / Energy xxx (2014) 1e10
[34] Sun J, Li WH. Operation optimization of an organic Rankine cycle (ORC) heat recovery power plant. Appl Therm Eng 2011;31(11):2032e41. [35] Klein SA, et al. Borland reference fluid thermodynamic and transport properties EES. Commercial and professional versions; 2001. [36] Baik YJ, Kim M, Chang KC, Kim SJ. Power-based performance comparison between carbon dioxide and R125 transcritical cycles for a low-grade heat source. Appl Energy 2011;88(3):892e8. [37] Madhawa Hettiarachchi HD, Golubovic M, Worek WM, Ikegami Y. Optimum design criteria for an organic Rankine cycle using low-temperature geothermal heat sources. Energy 2007;32(9):1698e706.
[38] Dalkilic AS, Laohalertdecha S, Wongwises S. Experimental investigation of heat transfer coefficient of R134a during condensation in vertical downward flow at high mass flux in a smooth tube. Int Commun Heat Mass Transf 2009;36(10):1036e43. [39] Kern DQ. Process heat transfer. McGraw-Hill College; 1950. [40] Wang ZQ, Zhou NJ, Guo J, Wang XY. Fluid selection and parametric optimization of organic Rankine cycle using low temperature waste heat. Energy 2012;40(1):107e15.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis You-Rong Li a, *, Mei-Tang Du a, Chun-Mei Wu a, Shuang-Ying Wu a, Chao Liu a, Jin-Liang Xu b a Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400044, China b Beijing Key Laboratory of New and Renewable Energy, North China Electric Power University, Beijing 102206, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 July 2013 Received in revised form 17 December 2013 Accepted 10 February 2014 Available online xxx
This paper presents an economical evaluation and parametric optimization on subcritical ORC (organic Rankine cycle) system for recovering the low-temperature waste heat of flue gas which is released from industrial boilers. First, the effects of the PPTD (pinch point temperature difference) in evaporator and condenser, and evaporating temperature on the system performance are examined with the EPC (electricity production cost) as the evaluation criterion. The optimal evaporating temperature, PPTDs in evaporator and condenser, as well as condensing temperature corresponding to the minimum EPC are provided simultaneously for the subcritical ORC system under different heat source temperatures. Then, the optimal parameter values are compared for nine potential organic working fluids with the critical point temperature from 124 C to 235 C. Results show that there exists a possible relationship between the critical temperature of working fluids and the economical performance of the system. Furthermore, it is suggested that the working fluids including R123, n-pentane, R11 and R141b, whose critical temperature range from 180 C to 210 C, are preferable for recovering the low-temperature waste heat of flue gas. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Organic Rankine cycle Economic evaluation Parameter optimization Electricity production cost
1. Introduction Along with the sharp growth of the world population and the rapid development of economy, the environmental pollution and energy shortage have become the bottleneck problems, which restrict the human social advancement. Exploiting new energy resources and improving the utilization ratio of conventional energy are two fundamental approaches to alleviate the severe situation. The ORC (organic Rankine cycle) has large technical potential and wide applications to generate the electricity by making use of a variety of different low-temperature heat sources, including renewable energy, such as solar energy, geothermal and biomass energy [1e3], and industrial waste heat from internal combustion engine, micro-gas turbine and boiler etc. [4e6]. In addition to its high thermal efficiency and simple structure, the ORC system offers the easiness of the application to the local small-scale power
* Corresponding author. Tel.: þ86 23 65112284. E-mail address: [email protected] (Y.-R. Li).
generation system, which has an advantage in recovering the distributed heat resource. During the past several decades, many researches on the ORC system have been done to improve the system performance and enhance the energy utilization rate. Selecting the suitable working fluids has been greatly concerned as an important factor which affects the cycle performance. The slope of the saturation vapor curve of the working fluid in Tes diagram is directly relevant to its behavior in the ORC system. Based on the different slope of the saturation vapor curve, the working fluids are classified into three categories, such as wet, isentropic, and dry fluids [7]. Roy et al. [8] conducted the performance analysis of ORC system by using R-12, R-123, R-134a and R-717 as working fluids under different heat source conditions. Results showed that the R123 appears to be a preferable selection as the working fluid for its good performance which is exhibited in the ORC system. Wang et al. [9] evaluated the performance of the ORC system with nine different working fluids in recovering the waste heat of the engine exhaust gas. It is found that the ORC system using R11, R141b, R113 and R123 as the working fluids has slightly the high thermal efficiency and the low exergy destruction rate. However, while considering the safety
http://dx.doi.org/10.1016/j.energy.2014.02.038 0360-5442/Ó 2014 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
2
Y.-R. Li et al. / Energy xxx (2014) 1e10
Nomenclature A heat transfer area, m2 B1, B2 coefficients for equipment cost C cost, $ C1, C2, C3 coefficients for equipment cost CBM bare module cost, $ CEPCI chemical engineering’s plant cost index COM cost of operation and maintenance, $ CRF capital recovery factor Cp purchased cost, $ EPC electricity production cost, $/(kW$h) FM material factor Fp pressure factor h specific enthalpy, kJ/kg K heat transfer coefficient, W/(m2$K) K1, K2, K3 coefficients for equipment cost LTpl life time of the plant, years M molecular weight, kg/kmol m mass flow rate, kg/s P pressure, MPa Pr Prandtl number Q heat flow rate, kW Re Reynolds number T temperature, C top operation time, hours
level and environmental impacts of the working fluids, R245fa and R245ca are the most suitable candidates. Guo et al. [10] compared the performance of the ORC-based power generation system for 27 organic working fluids with the critical point temperature that ranges from 71.95 to 214.06 C under a given geothermal source condition. The results indicated that R236ea presented the largest net power output, while E170, R600 and R141b presented the lowest A/Wnet and EPC value. Obviously, the preferable organic working fluid in the ORC system depends on various parametric conditions, for example, heat resource condition, evaluation criteria, as well as physical properties of the fluid, safety, technological feasibility and environmental harmony etc. Besides selecting suitable working fluids, modifying basic ORC and optimizing the operating parameters are two major measures to improve the performance of the ORC system. Rayegan and Tao [11] used the regenerative ORC instead of the basic ORC to reduce the irreversible loss of a solar ORC system. It was found that the regeneration could enhance the thermal and exergy efficiency of the cycle and it tended to be more effective for high molecular complexity working fluids in most instances. Pei et al. [12] designed a solar power generating system with the regenerative ORC system. The results showed that the cycle efficiency and overall system efficiency could reach the maximum values at appropriate regenerative temperatures, and both the maximum values are higher than the basic ORC system. Meanwhile, some new Rankine power systems equipping with vapor injector-based novel, thermal driven pump, and SVM (switching valves method) are proposed to improve the performance of the ORC system by reducing the power consumption of the working fluid pump [13e15]. The combined power and the cooling cycle system with different combination ways have also been investigated, such as the combinations of the ORC with ejector refrigeration cycle, vapor compression cycle and absorption refrigeration cycle [16e20]. On the other hand, the operating parameters are closely connected to the power output and efficiency of the ORC system. Wei
W
power output or input, kW
Greek symbols isentropic efficiency thermal conductivity, W/(m$K) viscosity, kg/(m$s)
his l m
Subscripts a air bo boiling section c condenser co condensing section cri critical e evaporator g glue gas i inlet m mean o outlet opt optimal p pump pc precooling section ph preheating section pp pinch point t turbine tot total wf working fluid
et al. [21] analyzed the effects of the mass flow rate and the inlet temperature of heat source and cold source on the power output and system efficiency. Li et al. [22] discussed the effects of evaporating temperature on the thermal efficiency, exergy efficiency, output power, exergy loss and outlet temperature of exhaust gas in detail. Wang et al. [23] presented the maximum net power output and the optimal evaporating temperature at different inlet temperature of heat source. And the influences of the turbine inlet temperature and Jacob number on the net power output and thermal efficiency were also investigated. Zhou et al. [24] studied the cycle efficiency, heat recovery efficiency, output power and exergy efficiency with respect to the evaporating pressure, heat source temperature and superheat degree through system experiments. Different researchers may evaluate the performance by different performance criterions, such as the net power output, the thermal efficiency, the exergy efficiency, the ratio of total heat transfer area to net power output, and EPC (electricity production cost), etc. [23e 26]. The most suitable working fluid, ORC structure, and the optimal operation parameters are not all the same when different performance criteria are adopted. Since the EPC attaches the importance to the total cost of the ORC system, as well as concerning the power output, it is considered as a reasonable evaluation criterion which can really reflect the economical and thermodynamic performance of the ORC system under a given heat source. The parameter matching relation between the internal parameters of the ORC system and the outside heat source condition plays a critical role in effectively utilizing low temperature waste heat. However, the present parameter optimization is primarily concerned with the choice of evaporating temperature, turbine inlet temperature, turbine inlet pressure and the degree of superheat at the turbine inlet, etc. [26e29]. Few studies dealt with the detailed analysis and optimization on the PPTD (pinch point temperature difference) in evaporator and condenser simultaneously. In fact, the
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
Y.-R. Li et al. / Energy xxx (2014) 1e10
PPTD in heat exchanger has a direct effect on the irreversible loss in the ORC system [30e32], and is closely related with heat transfer area, heat flow rate and outlet temperature of heat source in the evaporator. In this work, the PPTDs in evaporator and condenser, evaporating temperature, and condensing temperature are simultaneously analyzed and optimized at different heat source temperature by using the EPC as the performance evaluation criterion. The aim is to seek the optimal parameters and suitable working fluids to achieve the optimum balance between the energy utilization rate and the investment cost of the ORC system for recovering the low-temperature waste heat of flue gas released from industrial boilers. 2. System description and modeling The Tes diagram of a basic subcritical ORC system is depicted in Fig. 1. In the evaporator, the sub-cooled liquid working fluid absorbs heat from the flue gas and turns into saturated vapor. Then the saturated vapor under the high pressure flows into the turbine to do work, and drives a generator to produce the electricity. The expanded superheated vapor is cooled down and condensed to the saturated liquid state under the condensing pressure by the cooling air that comes from the environment. After the liquid working fluid is pumped to the evaporator, it absorbs heat in evaporator again to continue the next loop. The isentropic efficiencies of working fluid pump and turbine are taken into account during the real processes (1-2 and 4-5) of compression and expansion, which are 80% and 85% in this work, respectively. In order to perform the thermodynamic calculation and performance analysis for a basic subcritical ORC system, a set of relevant parameters of heat source and sink, and some cycle parameters are assumed, which is shown in Table 1. Because the present ORC system is designed for recovering waste heat of the flue gas that is released from industrial boilers, the temperature of the heat source varies from 150 C to 200 C, and the cold source is the air from the environment [33,34]. In the subcritical ORC system, the pinch limitations in evaporator and condenser are respectively located at the saturated liquid point and saturated vapor point of the working fluids, which has been verified by the subsequent calculation. The thermodynamics properties of the working fluids are calculated by the software of EES [35].
3
Table 1 Conditions of heat source and sink and the ORC parameters. Term
Value
The inlet temperature of exhaust gas, C The inlet temperature of cooling air, C The mass flow rate of exhaust gas, kg/s The mass flow rate of cooling air, kg/s Isentropic efficiency of turbine, % Isentropic efficiency of working fluids pump, %
150e200 20 10 50 85 80
Furthermore, some assumptions are also considered as follows: each component in the ORC system works in a steady state; heat loss in heat exchangers and pipelines is small enough to be neglected [32,33]; working fluids at the condenser outlet and turbine inlet are respectively saturated liquid and saturated vapor; the temperature difference at the pinch point in heat changer is not less than 3 C. With the above assumptions, the thermodynamic model of the subcritical ORC system can be described as follows: (1) Pump The isentropic efficiency of the working fluid pump is defined by
his;p ¼
h2s h1 : h2 h1
(1)
The pressure raise that is supplied by the working fluid pump is determined by the pressure difference between condensation and evaporation, and the work input is
Wp ¼ mwf ðh2 h1 Þ:
(2)
(2) Turbine The working fluid comes to pass an adiabatic expansion in the turbine, and the isentropic efficiency and the power output are, respectively
his;t ¼
h4 h5 ; h4 h5s
Wt ¼ mwf ðh4 h5 Þ:
(3)
(4)
(3) Evaporator The evaporator is divided into two parts: preheating section and boiling section. The pinch point occurs at the point where the boiling section starts. The temperature Tg,pp of the flue gas at the pinch point is determined by the bubbling point temperature and the pinch point temperature difference,
Tg;pp ¼ T3 þ DTe :
(5)
The mass flow rate of the organic working fluid can be calculated as
mwf ¼
Fig. 1. Tes diagram of a basic subcritical ORC system.
mg cp;g Tg;i Tg;pp : h4 h3
(6)
The heat balance equations in the evaporator are expressed as follows,
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
4
Y.-R. Li et al. / Energy xxx (2014) 1e10
Qph ¼ mwf ðh3 h2 Þ ¼ mg hg;pp hg;o ;
(7a)
Qbo ¼ mwf ðh4 h3 Þ ¼ mg hg;i hg;pp :
(7b)
The heat transfer areas in preheating section and boiling section can be respectively calculated by
Aph ¼
Qph Qbo ; A ¼ : Kph DTm;ph bo Kbo DTm;bo
(8a-b)
where, DTm is the logarithmic mean heat transfer temperature difference,
DTm;ph ¼
Tg;o T2 DTe T
T2
ln g;oDT e
; DTm;bo ¼
Tg;i T4 DTe T T
ln g;iDT 4 e
:
(9a-b)
l de
1=3
m mw
Re0:55 Prg g
0:14 :
(10)
The condenser also consists of two sections: the precooling section and the condensing section, without considering the subcooling of working fluids [25,28,29]. The pinch point limitation is at the boundary of the two sections, and the condensing temperature can be derived through iterating the following relation,
ma cp;a Tc DTc Ta;i ¼ mwf ðh6 h1 Þ:
(11)
The heat balance equations in condenser can be given as follows,
Qpc ¼ mwf ðh5 h6 Þ ¼ ma ha;o ha;pp ;
(12b)
Qpc Qco ; Aco ¼ : Kpc DTm;pc Kco DTm;co T5 Ta;o DTc T T
ln 5DT a;o c
log Cp ¼ K1 þ K2 log W þ K3 ðlog WÞ2 :
(16)
In above equations, Cp is a basic cost concerning with the heat transfer area of heat exchangers, or the mechanical work of pump and turbine operating at ambient pressure. Eq. (15) is used to calculate the cost of evaporator and condenser, and Eq. (16) to calculate the cost of pump and turbine. And considering the specific material of the construction and operating pressure, the cost should be corrected as:
CBM ¼ Cp B1 þ B2 FM Fp :
; DTm;co ¼
log Fp ¼ C1 þ C2 log P þ C3 ðlog PÞ2 :
(17)
(18)
In Eqs. 15e18, K1, K2, K3, B1, B2, C1, C2, and C3 are coefficients for the cost evaluation of system components. It should be noted that the actual capital cost must be converted from the cost of 1996 by introducing the CEPCI (Chemical Engineering Plant Cost Index). The CEPCI is widely used to adjust the plant construction costs at different periods and its value is published at intervals in the Chemical Engineering Journal [27],
CBM;2011 ¼ CBM;1996 $CEPCI2011 =CEPCI1996 :
Similar to the evaporator, the heat transfer area and the logarithmic mean heat transfer temperature difference in each section can be expressed as, respectively
DTm;pc ¼
For pump and turbine,
(12a)
¼ mwf ðh6 h1 Þ ¼ ma ha;pp ha;i :
Apc ¼
(15)
In the above formula, CBM is the corrected cost, FM is the material correction factor, and Fp is a measure that reflects the pressure factor since the system components work at the pressure much higher than the ambient pressure, which is determined by
(4) Condenser
Qco
A complete detailed economic analysis relies on several particular parameters, and the process is much complicated, even different from location to location and time to time. However, the total investment cost of an ORC system is mainly determined by the cost of the major components, including evaporator, turbine, condenser and pump. It should be pointed that the effect of the fluid cost on the total investment cost is slight and the variation of the mass flow rate of the working fluid with the PPTDs of evaporator and condenser and the evaporation temperature is small. Therefore, the cost of the fluid is not considered in this work, as shown in Refs. [25,27,40]. The current calculation method about the capital cost generally adopted the following correlations [10,25,27]. For heat exchangers,
log Cp ¼ K1 þ K2 log A þ K3 ðlog AÞ2 :
In the evaporator, the convective heat transfer coefficient of the organic working fluid side is generally more than 2000 W/(m2$K) [36e38]. So the thermal resistance of the flue gas side is much greater than that of the working fluid side, the convective heat transfer coefficient of flue gas is much smaller than that of organic working fluids. The overall heat transfer coefficient in the evaporator is mainly dependent on the convective heat transfer coefficient of the flue gas side, and even assumed to be the constants in Ref. [17]. Therefore, the total heat transfer coefficient is estimated by employing the Kern formula [39]
Kph ¼ Kbo ¼ Kog ¼ 0:36
3. Economical model
(13a-b)
T1 Ta;i DTc T T
ln 1DT a;i c
:
(14a-b)
In condenser, the precooling section is a small region, and the heat transfer in condenser is mainly limited by the thermal resistance of the air side. The convective heat transfer coefficient of the air side practically determines the total heat transfer coefficient, which also can be obtained by the Kern formula.
(19)
Then the total investment cost can be estimated by:
Ctot ¼ CBM;e þ CBM;c þ CBM;t þ CBM;p :
(20)
To take the effective operation time, the capital recovery cost and the COM (cost of operation and maintenance) into account, the electricity production cost, which is considered as the performance evaluation criteria used in the following optimization process, can be given by
EPC ¼ ðCtot CRF þ COMÞ= top Wt Wp ;
(21)
h i CRF ¼ ið1 þ iÞLTpl = ð1 þ iÞLTpl 1 ;
(22)
where, the interest rate (i) is set as 5%, the plant life time (LTpl) as 20 years, the operation time (top) as 8000 h, and COM is 1.5% of the investment cost.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
Y.-R. Li et al. / Energy xxx (2014) 1e10
5
In this model, the evaporating temperature and the pinch point temperature differences in evaporator and condenser are variables to be optimized, and the condensing temperature can be correspondingly calculated when the three independent variables are determined. After inputting a set of data for the independent variables within a certain range, the state parameters at each point in the ORC system can be estimated. Then, the heat transfer areas of heat exchangers and some cycle performance parameters are obtained. Obviously, the electricity production cost can be minimized by taking the partial derivatives of EPC in Eq. (21) with respect to Te, DTe and DTc, respectively, and setting them equal to zero
vEPC vEPC vEPC ¼ 0; ¼ 0; ¼ 0: vTe vDTe vDTc
(23a-c)
4. Results and discussion 4.1. The economical analysis The economical calculation shows that a large part of the total investment cost comes from the heat exchangers, which is mainly affected by the heat transfer area. While the PPTD (pinch point temperature difference) in heat exchanger is directly relative to the heat transfer area, thus it has a significant impact on the economical performance of the system. In the meantime, the PPTD in the heat exchanger immediately relates to the heat transfer capability, and therefore it concerns the thermodynamic performance of system as well. As a result, the optimization of PPTD has important implications for the performance improvement of the ORC system. Taking R245fa and R123 as the working fluids, Fig. 2 presents the variation of EPC with the PPTDs (DTe and DTc) in evaporator and condenser at Tg,i ¼ 180 C and Te ¼ 125 C. It can be found that the EPC decreases at first, and then increases with the increase of DTe and DTc, respectively, and the EPC of the ORC system reaches the minimum value at a specific combination of PPTDs in evaporator and condenser. From Eq. (21), the variation of EPC is mainly caused by the change of the investment cost and the power output of the ORC system. In evaporator, with the increase of DTe at certain evaporating temperature, the mean heat transfer temperature difference increases, leading to a decrease in the heat transfer area, which results in a reduction of the system investment cost. On the other hand, the increase of DTe yields a decrease in the heat transfer rate, and then the mass flow rate of the working fluid decreases, which leads to a reduction of power output. The reduction of the system investment has a greater effect than the reduction of power output on the EPC at a small DTe, and the value of EPC decreases with the increase of DTe; while with the further increase of DTe, the decrease of the mass flow rate of the working fluid becomes gradually obvious, and thus the reduction of power output weighs more and contributes to an increase of EPC. As for the condenser, the increase of DTc enables the heat transfer area of condenser to decrease, which results in a reduction of the investment cost, and thus the EPC decreases firstly. Meanwhile, the condensing temperature increases with the increase of DTc, and the enthalpy drop of unit working fluid in turbine becomes lesser, which results in a decrease in power output. When the DTc becomes high enough, the effect of the decreasing power output outweighs that of the decreasing investment cost. As a result, the EPC displays an increase later with the further increase of DTc. Therefore, it can be concluded that the EPC can achieve the minimum value at appropriate values of PPTDs in evaporator and condenser under given heat source temperature and evaporating temperature. As shown in Fig. 2, at Tg,i ¼ 180 C, Te ¼ 125 C, the
Fig. 2. Variation of EPC with DTe and DTc.
optimal combined PPTDs for R245fa and R123 are DTe,opt ¼ 15.2 C, DTc,opt ¼ 12.9 C and DTe,opt ¼ 11.3 C, DTc,opt ¼ 14.3 C, respectively. The minimum EPC with respect to the evaporating temperature at various heat source temperatures for R245fa and R123 have been shown in Fig. 3. It can be found that the EPC of the ORC system first decreases, and then increases with the increase of the evaporating temperature, and there exists an optimal evaporating temperature at a certain heat source temperature. The evaporating temperature determines the enthalpy difference of working fluid in the phase change region of evaporator, which affects the mass flow rate of working fluid under the certain heat transfer rate. On the other hand, evaporating temperature is closely related to the enthalpy drop per unit mass flow rate during expansion. As the power output of turbine is the product of the mass flow rate of working fluid and the enthalpy drop, the evaporating temperature determines the net work output to a large extent. Meanwhile, the evaporating PPTD and the heat transfer rate are changing with the evaporating
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
6
Y.-R. Li et al. / Energy xxx (2014) 1e10
Fig. 3. Variation of EPC with Te at different heat source temperature. Fig. 4. Variation of DTe,opt with Te at different heat source temperature.
temperature, which results in a variation of the total investment cost of system. The comprehensive effects of these factors contribute to the variation of EPC with the evaporating temperature as Fig. 3. From Figs. 2 and 3, an eventually minimum value of EPC exists at a combination of optimal values of the evaporating temperature, and PPTDs in evaporator and condenser. From Fig. 3, it is obvious that the EPC is greatly affected by the heat source temperature, and a higher heat source temperature can effectively reduce the electricity production cost of the ORC system owing to the remarkable increase of the net power output. It is also found that the optimal evaporating temperature corresponding to the minimum EPC appears an increasing trend toward the critical temperature with the increase of the heat source temperature. It hints that a trans-critical ORC may be more favorable, and is needed to be further studied. 4.2. The parametric optimization As mentioned above, there exist a couple of optimal PPTDs in evaporator and condenser that minimize the EPC at a certain evaporating temperature. Figs. 4 and 5 present respectively the variation of optimal PPTDs in evaporator and condenser with the
evaporating temperature at the different heat source temperature for R245fa and R123. Obviously, the optimal evaporating PPTD approximately linearly decreases with the evaporating temperature. With the increase of the evaporating temperature, the heat transfer rate in evaporator has a decreasing trend, and thus leads to a large reduction of power output, which may result in an increasing EPC. The decrease of evaporating PPTD can restrain the decrease of the heat transfer rate in evaporator, and then the reduction of power output to some degree. Therefore, a reasonable decrease of PPTD in evaporator can keep the EPC consistently lowest with the increase of the evaporating temperature. On the other hand, the increase of the heat source temperature yields a more remarkable increase of the investment cost than the increase of power output. Thus, a slight increase of optimal PPTD can finally balance the two-side effects of the heat source temperature on the value of EPC, and thereby keep the EPC minimum as possible. Therefore a higher heat source temperature results in a higher optimal PPTD in evaporator at the same evaporating temperature, as shown in Fig. 4. The variations of optimal PPTD in condenser and the corresponding optimal condensing temperature have been shown in
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
Y.-R. Li et al. / Energy xxx (2014) 1e10
7
Fig. 5. Variation of DTc,opt and Tc with Te at different heat source temperature.
Fig. 5. It can be found that the optimal PPTD in condenser and the condensing temperature almost keep constant with the increase of the evaporating temperature. With the increase of the heat source temperature, the optimal condensing temperature appears a slight increase, while the optimal condensing PPTD still remains almost unchanged, more or less at 12 C for R245fa while 14 C for R123. The optimal values of PPTDs in evaporator and condenser, evaporating temperature and condensing temperature for R245fa and R123 at different heat source temperature are presented in Fig. 6. It can be seen that the optimal evaporating temperature is notably influenced by the heat source temperature, while the other three parameters have only slight variations with the increase of the heat source temperature. It should be pointed that, in our previous work [6], the ratio of the net power output to total heat transfer area is used as the performance evaluation criterion to analyze the effect of the PPTDs and the evaporation temperature on the cost-effective performance of the ORC system in recovering the low temperature waste heat of the flue gas. In this case, the total pinch point temperature difference of evaporator and condenser should be given. Obviously, it is arbitrary and random. Therefore, the best cost-effective performance is not always corresponding to the minimum EPC.
Fig. 6. The optimal values of Te, Tc, DTe,opt and DTc,opt with respect to Tg,i.
4.3. The comparison for different working fluids To avoid the wet corrosion to turbine blades during the expansion of wet working fluids [8,9,25], nine dry or isentropic working fluids with the critical temperature from 124 C to 235 C are investigated, considering the heat source condition, as well as the physical properties and environmental friendliness of working fluids. The main properties of the working fluids are listed in Table 2. The economical optimization has been done for the subcritical ORC system with above nine working fluids when the heat source temperature maintains at 180 C. The minimum EPC of the nine working fluids are shown in Fig. 7. It can be found that four working fluids including R123, n-pentane, R11 and R141b, whose critical temperature range from 183.68 C to 204.21 C, possess the relative low EPC approaching 0.07$/(kW$h), while the ORC system with R236fa yields the highest EPC approaching 0.09$/(kW$h). Therefore, it is clear that the selection of working fluids has a significant influence on the economic performance of the subcritical ORC system.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
8
Y.-R. Li et al. / Energy xxx (2014) 1e10
Table 2 Main properties of the working fluids.
35
Working fluids
M (kg/kmol)
Tcri ( C)
Pcri (MPa)
1 2 3 4 5 6 7 8 9
R236fa R600a R114 R245fa R123 n-pentane R11 R141b n-hexane
152.0 58.1 170.9 134.1 152.9 72.2 137.4 117.0 86.2
124.92 134.70 145.68 154.05 183.68 196.55 198.96 204.21 234.67
3.20 3.63 3.29 3.65 3.67 3.36 4.41 4.25 3.06
ΔTe,opt ΔTc,opt
30 25 20
ΔTopt ºC
No.
15 10 5
When the minimum EPC is reached, Fig. 8 shows the corresponding net power output. Obviously, R245fa yields the highest net power output (112.6 kW) and R236fa the lowest (92.3 kW). Combining with Fig. 7, it indicates that the working fluid with the best economical performance may not own the largest net power by the effect of the investment cost of the system. For the selection of working fluids under a certain heat source condition, not only the waste heat recovery efficiency and power output but also the total investment cost of the heat recovery system should be taken into account. Figs. 9 and 10 present the optimal PPTDs in evaporator and condenser, evaporating temperature and condensing temperature
0.10
EPCmin ($/kWh)
0.08
0.06
0.04
0.02
0.00
R23 R R 6fa 600a 114
R24 R 5fa 123
n-pe R ntan 11 e
n R14 1b -hexan e
Fig. 7. The minimum EPC of different working fluids at Tg,i ¼ 180 C.
0
R236fa R600a R114 R245fa R123 n-pentane R11
R141bn-hexane
Fig. 9. The DTe,opt and DTc,opt of different working fluids at Tg,i ¼ 180 C.
of different working fluids at Tg,i ¼ 180 C. As shown in Fig. 9, the working fluid with higher critical temperature displays a smaller optimal evaporating PPTD and a larger optimal condensing PPTD. From Fig. 10, the optimal evaporating temperatures of different working fluids have a gradually increasing trend with the increase of the critical temperature, while the optimal condensing temperatures have no significant difference among the different working fluids. It indicates that the condensing temperature is insensitive to the economical performance, which further validates the rationality of parameter optimization at a given condensing temperature in some researches [10,22,25]. The minimum EPC with respect to the corresponding critical temperature of working fluids at different heat source temperature are shown in Fig. 11. It is found that the EPC of the ORC system presents a general trend, which decreases first and then increases with the increase of the critical temperature of working fluids. The results show that the working fluids with the critical temperature between 180 C and 210 C have the lower EPC. Therefore, the working fluids including R123, n-pentane, R11 and R141b are more suitable for recovering the waste heat of the flue gas. Meanwhile, the EPC decreases with the increase of the heat source temperature, and the higher critical temperature of working fluids, the EPC decreases the more dramatic. For instance, when the heat source temperature rises from 160 C to 200 C, the minimum EPC of the 236fa system decreases by 13.5%, while the n-hexane system decreases by 32%.
120
160
100
140 80
Wnet (kW)
120
60
Topt ºC
100
40 20 0 R 2
Te,opt Tc,opt
80 60 40
36f a
R6 00a
R1 14
R1 R2 23 45f a
n-p R1 1 ent ane
n R1 41b -hex ane
Fig. 8. Net power output of different working fluids at the minimum EPC at Tg,i ¼ 180 C.
20 0
R236fa R600a R114 R245fa R123 n-pentane R11
R141bn-hexane
Fig. 10. The Te,opt and Tc,opt of different working fluids at Tg,i ¼ 180 C.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
Y.-R. Li et al. / Energy xxx (2014) 1e10
Fig. 11. The influence of critical temperature on the minimum EPC at different heat source temperature.
5. Conclusion In the present study, the economical model of the subcritical ORC system for recovering the waste heat of the low-temperature flue gas has been presented. The effects of main parameters (Te, DTe and DTc) on the system performance were simultaneously analyzed combining the thermodynamics and economics. The optimal parameters were obtained for different working fluids at different heat source temperature. According to the analysis and optimization, the following conclusions can be summarized: (1) The performance criterion EPC decreases firstly, and then increases with the increase of Te, DTe and DTc respectively at certain heat source temperature. There exists an optimal combination of these parameters to minimize the EPC. (2) The optimal PPTD in evaporator decreases, while that in condenser almost keeps constant with the increase of the evaporating temperature. (3) The optimal parameters depend on the working fluids and the heat source temperature. A higher heat source temperature results in a better economical performance. With the increase of the heat source temperature, the optimal evaporating temperature and evaporating PPTD increase, the condensing temperature and condensing PPTD change little. (4) With the increase of the critical temperature of the working fluids, the EPC decreases first and then increases. The working fluids with the critical temperature within the range from 180 C to 210 C possess lower EPC, and therefore, R123, n-pentane, R11 and R141b are recommended as the working fluids to recover the waste heat of flue gas. Acknowledgment This work is supported by National Basic Research Program of China (973 Program, Grant No. 2011CB710701) and the Natural Science Foundation of China of International Cooperation Project (51210011). References [1] Tempesti D, Fiaschi D. Thermo-economic assessment of a micro CHP system fuelled by geothermal and solar energy. Energy 2013;58:45e51. [2] Ghasemi H, Paci M, Tizzanini A, Mitsos A. Modeling and optimization of a binary geothermal power plant. Energy 2013;50:412e28.
9
[3] Al-Sulaiman FA, Dincer I, Hamdullahpur F. Energy and exergy analyses of a biomass trigeneration system using an organic Rankine cycle. Energy 2012;45(1):975e85. [4] Shu GQ, Zhao J, Tian H, Liang XY, Wei HQ. Parametric and exergetic analysis of waste heat recovery system based on thermoelectric generator and organic Rankine cycle utilizing R123. Energy 2012;45(1):806e16. [5] Invernizzi C, Iora P, Silva P. Bottoming micro-Rankine cycles for micro-gas turbines. Appl Therm Eng 2007;27(1):100e10. [6] Li YR, Wang JN, Du MT. Influence of coupled pinch point temperature difference and evaporation temperature on performance of organic Rankine cycle. Energy 2012;42(1):503e9. [7] Hung TC, Shai TY, Wang SK. A review of organic Rankine cycles (ORCs) for the recovery of low-grade waste heat. Energy 1997;22(7):661e7. [8] Roy JP, Mishra MK, Misra A. Performance analysis of an organic Rankine cycle with superheating under different heat source temperature conditions. Appl Energy 2011;88(9):2995e3004. [9] Wang EH, Zhang HG, Fan BY, Ouyang MG, Zhao Y, Mu QH. Study of working fluid selection of organic Rankine cycle (ORC) for engine waste heat recovery. Energy 2011;36(5):3406e18. [10] Guo T, Wang HX, Zhang SJ. Fluids and parameters optimization for a novel cogeneration system driven by low-temperature geothermal sources. Energy 2011;36(5):2639e49. [11] Rayegan R, Tao YX. A procedure to select working fluids for solar organic Rankine cycles (ORCs). Renew Energy 2011;36(2):659e70. [12] Pei G, Li J, Ji J. Analysis of low temperature solar thermal electric generation using regenerative organic Rankine cycle. Appl Therm Eng 2010;30(8):998e 1004. [13] Xu RJ, He YL. A vapor injector-based novel regenerative organic Rankine cycle. Appl Therm Eng 2011;31(6):1238e43. [14] Lakew AA, Bolland O, Ladam Y. Theoretical thermodynamic analysis of Rankine power cycle with thermal driven pump. Appl Energy 2011;88(9): 3005e11. [15] Yamada N, Minami T, Anuar Mohamad MN. Fundamental experiment of pumpless Rankine-type cycle for low-temperature heat recovery. Energy 2011;36(2):1010e7. [16] Zheng B, Weng YW. A combined power and ejector refrigeration cycle for low temperature heat sources. Sol Energy 2010;84(5):784e91. [17] Little AB, Garimella S. Comparative assessment of alternative cycles for waste heat recovery and upgrade. Energy 2011;36(7):4492e504. [18] Aphornratana S, Sriveerakul T. Analysis of a combined Rankine-vapourcompression refrigeration cycle. Energy Convers Manag 2010;51(12):2557e64. [19] Vijayaraghavan S, Goswami DY. On evaluating efficiency of a combined power and cooling cycle. J Energy Resour Technol 2003;125(3):221e7. [20] Wang H, Peterson R, Herron T. Design study of configurations on system COP for a combined ORC (organic Rankine cycle) and VCC (vapor compression cycle). Energy 2011;36(8):4809e20. [21] Wei DH, Lu XS, Lu Z, Gu JM. Performance analysis and optimization of organic Rankine cycle (ORC) for waste heat recovery. Energy Convers Manag 2007;48(4):1113e9. [22] Li W, Feng X, Yu LJ, Xu J. Effects of evaporating temperature and internal heat exchanger on organic Rankine cycle. Appl Therm Eng 2011;31(17e18):4014e23. [23] Wang DX, Ling X, Peng H. Cost-effectiveness performance analysis of organic Rankine cycle for low grade heat utilization coupling with operation condition. Appl Therm Eng 2013;58(1e2):571e84. [24] Zhou NJ, Wang XY, Chen Z, Wang ZQ. Experimental study on organic Rankine cycle for waste heat recovery from low-temperature flue gas. Energy 2013;55: 216e25. [25] Zhang SJ, Wang HX, Guo T. Performance comparison and parametric optimization of subcritical organic Rankine cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Appl Energy 2011;88(8):2740e54. [26] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic Rankine cycles. Appl Therm Eng 2011;31(14): 2885e93. [27] Cayer E, Galanis N, Nesreddine H. Parametric study and optimization of a transcritical power cycle using a low temperature source. Appl Energy 2010;87(4):1349e57. http://www.sciencedirect.com/science/help/doi.htm. [28] Wang JF, Dai YP, Gao L. Exergy analyses and parametric optimizations for different cogeneration power plants in cement industry. Appl Energy 2009;86(6):941e8. [29] Wang DX, Ling X, Peng H, Liu L, Tao LL. Efficiency and optimal performance evaluation of organic Rankine cycle for low grade waste heat power generation. Energy 2013;50:343e52. [30] Venkatarathnam G, Mokashi G, Murthy SS. Occurrence of pinch points in condensers and evaporators for zeotropic refrigerant mixtures. Int J Refrig 1996;19(6):361e8. [31] Venkatarathnam G, Mokashi G, Murthy SS. Effect of mixture composition on the formation of pinch points in condensers and evaporators for zeotropic refrigerant mixtures. Int J Refrig 1999;22(3):205e15. [32] Heberle F, Preißinger M, Brüggemann D. Zeotropic mixtures as working fluids in organic Rankine cycles for low-enthalpy geothermal resources. Renew Energy 2012;37:364e70. [33] Dai YP, Wang JF, Gao L. Exergy analysis, parametric analysis and optimization for a novel combined power and ejector refrigeration cycle. Appl Therm Eng 2009;29(10):1983e90.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038
10
Y.-R. Li et al. / Energy xxx (2014) 1e10
[34] Sun J, Li WH. Operation optimization of an organic Rankine cycle (ORC) heat recovery power plant. Appl Therm Eng 2011;31(11):2032e41. [35] Klein SA, et al. Borland reference fluid thermodynamic and transport properties EES. Commercial and professional versions; 2001. [36] Baik YJ, Kim M, Chang KC, Kim SJ. Power-based performance comparison between carbon dioxide and R125 transcritical cycles for a low-grade heat source. Appl Energy 2011;88(3):892e8. [37] Madhawa Hettiarachchi HD, Golubovic M, Worek WM, Ikegami Y. Optimum design criteria for an organic Rankine cycle using low-temperature geothermal heat sources. Energy 2007;32(9):1698e706.
[38] Dalkilic AS, Laohalertdecha S, Wongwises S. Experimental investigation of heat transfer coefficient of R134a during condensation in vertical downward flow at high mass flux in a smooth tube. Int Commun Heat Mass Transf 2009;36(10):1036e43. [39] Kern DQ. Process heat transfer. McGraw-Hill College; 1950. [40] Wang ZQ, Zhou NJ, Guo J, Wang XY. Fluid selection and parametric optimization of organic Rankine cycle using low temperature waste heat. Energy 2012;40(1):107e15.
Please cite this article in press as: Li Y-R, et al., Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.02.038