Renewable Energy 54 (2013) 78e84
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A comparative study of power optimization in low-temperature geothermal heat source driven R125 transcritical cycle and HFC organic Rankine cycles Young-Jin Baik, Minsung Kim*, Ki-Chang Chang, Young-Soo Lee, Hyung-Kee Yoon High Efﬁciency and Clean Energy Research Division, Korea Institute of Energy Research, Daejeon 305-343, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 2 February 2012 Accepted 13 August 2012 Available online 28 September 2012
In order to compare the power output of an R125 transcritical cycle with that of HFC subcritical ORCs for a low-temperature geothermal heat source of about 100 C, an R125 transcritical cycle and subcritical ORCs using R134a, R245fa and R152a were optimized for power output by a simulation method. In contrast to previous studies, to fairly compare the power of different cycles, power optimizations were carried out for given heat source and sink inlet temperatures, and given ﬂow rates based on the typical power plant thermal-capacitance-rate ratio. The total overall conductance (TOC) which implies heat exchanger cost was ﬁxed, whereas the allocation of the overall conductance between the vapor generator and the condenser was optimized in the simulation. Results show that under simulation conditions considered in the present study, the power output of an R125 transcritical cycle was greater than that of subcritical ORCs when a TOC was higher than 35 kW/K. When a TOC was lower than that, transcritical cycle’s power output was slightly less than that of subcritical cycles. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Transcritical power cycle Low-temperature geothermal heat source ORC
1. Introduction Due to the worldwide energy crisis and environmental concerns, the utilization of a low-temperature geothermal heat source is drawing enormous attention. Several power cycles have been proposed for low-temperature heat source utilization. Among them, Organic Rankine Cycles (ORCs) using organic refrigerant as a working ﬂuid have been applied to geothermal binary power plants. Although ORC technology has improved greatly since its introduction, it is limited by its reliance on a constant-temperature evaporation process, which is unable to maximize power output from ﬁnite heat sources. Transcritical cycles, however, have a higher power output potential than do subcritical ORCs. The temperature glide above the critical point allows a better temperature proﬁle match to the temperature of the heat source than does constanttemperature subcritical evaporation. Although not a few studies on the transcritical cycle have been carried out, there are few comparative studies between subcritical cycles and transcritical cycles for a low-temperature heat source of about 100 C. Chen et al.  carried out an analysis of the lowtemperature driven carbon dioxide transcritical cycle and showed that it had a slightly higher power output than did the subcritical
* Corresponding author. Tel.: þ82 42 860 3062; fax: þ82 42 367 5067. E-mail address: [email protected]
(M. Kim). 0960-1481/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2012.08.055
cycle under the same mean thermodynamic heat rejection temperature. Zhang et al.  compared the solar-energy-powered carbon dioxide transcritical cycle with 4 different subcritical cycles and showed that the best is the carbon dioxide cycle. Saleh et al.  pointed out the potential of a transcritical cycle and recommended R143a for a geothermal application. More recently, Shengjun et al.  compared subcritical ORCs with transcritical power cycles from the viewpoint of thermodynamic and economic performance. They concluded that the R125 transcritical power cycle shows excellent economic and environmental performance. Previous studies are based on the following two simpliﬁcations. The ﬁrst is that the total overall conductance (TOC) (UA)v þ (UA)c for each cycle was not ﬁxed. It is necessary to ﬁx the TOC because it implies the cost of the heat exchanger required to implement the plant. To make a fair comparison of the performances of different cycles, it is best to take into account the identical constraint conditions of the total plant cost. However, because the actual assessment of the total plant cost inevitably involves some level of arbitrariness, we decided to avoid this by using the TOC value as the constraint condition. The TOC value reﬂects the cost of the heat exchanger, which accounts for the most signiﬁcant portion of the cost among ORC plant facilities [5e11]. The other is that the same heat rejection temperature was assumed regardless of the type of the cycle, or the cooling water ﬂow rates were different from each other. However, the power output of the cycle strongly depends on a TOC and the cooling water ﬂow rate. Thus, they need to be ﬁxed to fairly compare the power output of
Y.-J. Baik et al. / Renewable Energy 54 (2013) 78e84
different cycles. A heat rejection temperature, or a condensing temperature, should not be given, but needs to be determined by cycle’s characteristics at the ﬁxed cooling water ﬂow rate. In contrast to previous studies, the power output of different cycles were optimized and then compared at given heat source and sink inlet temperatures, and at given ﬂow rates based on the typical power plant thermal-capacitance-rate ratio. The total overall conductance (TOC) was ﬁxed, whereas the allocation of the overall conductance between the vapor generator and the condenser was optimized in the simulation. Because the performance of an ORC system is affected by the properties of working ﬂuids, in principle, these properties should be taken into account for an accurate study. However, as in the study of Jung et al. , Högberg et al.  and Jung et al. , under the assumption that a counterﬂow heat exchanger is used, using UA as a constraint condition to evaluate the performances of cycles using different working ﬂuids is regarded as an acceptable approach, which we decided to employ in this study. In order to form a transcritical cycle, the critical temperature of the working ﬂuid should be lower than the heat source temperature and higher than the condensing temperature. So far, a few working ﬂuids have been reported to show promise when used alongside a lowtemperature heat source of about 100 C: carbon dioxide, R125, R41, R170, R218, and R143a. In this study, only an R125 transcritical cycle was considered according to the recommendations from recent studies [4e15]. On the other hand, HFC (hydroﬂuorocarbon) subcritical cycles using R134a, R245fa and R152a, whose critical temperatures are higher than a heat source inlet temperature, were considered in accordance with recommendations [3,16]. The main objective of this study is to compare the power output of an R125 transcritical cycle with that of HFC subcritical ORCs for a low-temperature heat source of about 100 C. For this purpose, each cycle was optimized for power output under the same conditions and then compared. In general, the ﬁrst-law efﬁciency is used as the objective function of a fossil-fuel-based power cycle to improve economic feasibility. In contrast to fossil-fuel-based cycles, the power cycle considered in this study uses renewable energy, such as low-temperature geothermal heat source, which means little or no cost is incurred for reheating the source after its utilization. Therefore, the power output (the second-law efﬁciency, or exergy efﬁciency), which can be regarded as the actual product, was used as the performance index. Active research has been conducted for its improvement and maximization [5,9,15,17e19]. For these reasons, the objective of this study was to maximize power output by using it as the objective function.
Heat THI source inlet
Generator Turbine Vapor generator 2
Heat sink inlet
Pump Fig. 1. Schematic diagram of a power cycle.
components in the cycle are given below. The energy and exergy balances at the condenser and the vapor generator are
_ r ðh2 h3 Þ ¼ m _ CW cp;CW ðTCO TCI Þ ¼ ðUAÞc DTm;c Q_ c ¼ m
_ CW ðeCI eCO Þ þ m _ r ðe2 e3 Þ E_ D;c ¼ m
_ r ðh1 h4 Þ ¼ m _ HW cp;HW ðTHI THO Þ ¼ ðUAÞv DTm;v Q_ v ¼ m
_ HW ðeHI eHO Þ þ m _ r ðe4 e1 Þ: E_ D;v ¼ m
The rates of exergy loss, or the rates of exergy transportation to the environment, associated with a heat source exit and a heat sink exit are
_ HW eHO E_ L;v ¼ m
_ CW eCO : E_ L;c ¼ m
The pump and turbine isentropic efﬁciencies can be expressed as
hisen;p ¼ ðh4s h3 Þ=ðh4 h3 Þ
2. Thermodynamic analysis of the cycle
hisen;t ¼ ðh1 h2 Þ=ðh1 h2s Þ:
Fig. 1 shows a schematic diagram of a transcritical cycle in this study. A working ﬂuid leaves the condenser (state point 3 in Fig. 1; SP3), is pumped to a high pressure (SP4), and then heated up and changes to a superheated vapor (SP1). After expansion through the turbine to a low pressure (SP2), the vapor is completely condensed (SP3). A subcritical cycle has the same components as shown in Fig. 1, but there are liquid heating, evaporating and vapor superheating processes in the vapor generator during SP4 to SP1. An internal heat exchanger, which can be used between the turbine exit and the pump exit, was not considered in this study because a recent study  has shown that the internal heat exchanger increases the cycle efﬁciency, but has little inﬂuence on the net power output. Starling et al.  also pointed out that preheating is unnecessary in well-designed cycles. The system is assumed to be at steady state for the cycle simulations. Pressure drop and heat loss in each component are neglected. Heat exchangers are assumed to be in counterﬂow conﬁguration. The balances and heat transfer equations for
The exergy destruction rates in pumping and expanding processes are
_ r T0 ðs4 s3 Þ E_ D;p ¼ m
_ r T0 ðs2 s1 Þ: E_ D;t ¼ m
The power generated by the turbine and the power input to the pump is
_ t ¼ m _ r ðh1 h2 Þ W
_ p ¼ m _ r ðh4 h3 Þ: W
The net power output is determined as
_ net ¼ W _ t W _ p: W
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The power cycle has many design parameters: temperature, pressure at each part of the cycle, mass ﬂow rate, and so on. In this study, three independent variables are selected to maximize power output. The ﬁrst two are the turbine inlet pressure P1 and temperature T1 and the third is the (UA)c/((UA)v þ (UA)c) value, or the condenser fraction over the total overall conductance (TOC). Once the three independent variables are given, the cycle power output can be found as shown in Fig. 2. First, we assume the condenser pressure P3 and primary working ﬂuid mass ﬂow _ r . When the condensing pressure is provided, the state of rate m turbine outlet (SP2) is determined by the turbine isentropic efﬁciency. The condenser exit state (SP3) is also determined by the pressure and bubble point condition. The pump exit (SP4) is determined by the pump isentropic efﬁciency. From the energy balance in the vapor generator and the condenser, the heat source and the heat sink exit temperatures are determined. After this process, we can determine (UA) values for two heat exchangers from Eqs. (1) and (3), where the mean temperature difference DTm can be expressed as Eq. (14) by assuming the constant overall heat transfer coefﬁcient U [21,22].
1 Q_ i
ZQ_ i 0
dQ_ DT Q_
Fig. 2. Power output calculation procedure under the three given design variables.
After obtaining (UA)c and (UA)v values, the initially assumed P3 _ r are renewed. Then the above procedure is repeated until and m calculated (UA)c and (UA)v values reach predetermined (UA)c and (UA)v values from the given TOC and (UA)c/((UA)v þ (UA)c) value. Once the iterations are completed for given conditions, the power output and all other parameters are determined. The thermodynamic properties of the working ﬂuids are calculated by using REFPROP 8.0 . The following conditions are given: (1) The heat source inlet temperature THI ¼ 100 C and the mass _ HW ¼ 1 kg=s. ﬂow rate m (2) The heat sink inlet temperature TCI ¼ 20 C and a thermalcapacitance-rate ratio  is ﬁxed at 10, i.e., _ HW cp;HW Þ ¼ 10. _ CW cp;CW =m ðm (3) The total overall conductance (TOC) (UA)v þ (UA)c ranges from 20 to 80 kW/K. (4) The isentropic efﬁciency for the turbine and the pump is 0.8. (5) The condenser exit is at the saturated liquid state. 3. Results and discussion Fig. 3 shows the power output variations of R125 transcritical cycle over the change of three independent variables when a TOC is 50 kW/K. Once (UA)c/((UA)v þ (UA)c) is given, optimal P1 and T1 are capable of maximizing the power output. The reason why the optimum combination of P1, T1 and (UA)c/((UA)v þ (UA)c) exists is as follows. As P1 becomes lower and lower, an enthalpyetemperature relation in heating process approaches that of a subcritical cycle, which increases an average temperature difference between the heat source and the cycle, and exergy destruction rate E_ D;v . The turbine inlet and exit entropies also increase, causing a turbine exit superheating, i.e., condenser inlet temperature to increase, which in turn increases exergy destruction rate E_ D;c . If P1 is too high, _ p increases signiﬁcantly. These two competing pumping power W effects allow optimal P1 value to exist as shown in Fig. 3(b). Meanwhile, as T1 becomes lower, the working ﬂuid mass ﬂow rate _ r increases while the enthalpy difference between turbine inlet m and exit (h1 h2) decreases. Therefore, if T1 is too low, pumping power increases compared to the turbine power, which causes the _ r reduces, net power output to drop. Similarly, if T1 is too high, m also causing a drop in the net power output. These two competing effects make optimal T1 value as shown in Fig. 3(c). When (UA)c/ ((UA)v þ (UA)c) becomes too small, the condensing temperature becomes too high, increasing exergy destruction rate during the condensation E_ D;c . If (UA)c/((UA)v þ (UA)c) is too high, exergy destruction rate during the vapor generation process E_ D;v and an exergy loss rate associated with a heat source exit E_ L;v increase. These two competing effects allow optimal (UA)c/((UA)v þ (UA)c) value to exist as shown in Fig. 3(d). As we have seen, the net power output is determined by three independent variables under the given heat source and heat sink conditions. Therefore, it is necessary to optimize the three variables in order to maximize power output. For this purpose, the pattern search algorithm (PSA) [25,26] was employed in this study. The PSA, a method for solving optimization problems, has the advantage of wide ﬂexibility; it does not require any information about the gradient of the objective function. The PSA can be used even if the objective function is not differentiable or is not continuous. In this study, the PSA was implemented by using the Matlab software package . Table 1 shows the optimization results of R125 transcritical cycle and other subcritical ORCs when a TOC is 50 kW/K. An R125 transcritical cycle yields more power than subcritical ORCs. This is because the exergy destruction rate E_ D;v and exergy loss rate E_ L;v , which are related to the heating process, are
Y.-J. Baik et al. / Renewable Energy 54 (2013) 78e84
Fig. 3. Power of R125 transcritical cycle over the change of three independent variables ((UA)v þ (UA)c ¼ 50 kW/K).
signiﬁcantly smaller than that of subcritical ORCs. In contrast to subcritical ORCs, an R125 transcritical cycle has a better glide match in the vapor generator due to heating above the critical pressure. In the case of an R134a subcritical cycle, despite a very low DTmin,v (minimum temperature difference in the vapor generator) of approximately 1 C, an average temperature difference DTm,v is about 8.7 C. On the other hand, the DTmin,v and DTm,v of an R125 transcritical cycle are approximately 4.9 C and 8.5 C, respectively, indicating that the temperature difference during the vapor generation process of a transcritical cycle is relatively uniform. This can be seen in Figs. 4 and 5. A minimum temperature difference in the vapor generator of an R134a subcritical cycle occurs at a bubble point, while it resides in the middle of the vapor generator in the case of an R125 transcritical cycle. It should be mentioned that a ﬁxed value of 50 kW/K for the TOC of an R125 transcritical cycle is reasonable, considering that the DTmin,v and DTmin,c are about 4.9 C and 5.0 C respectively. In most studies on a low-temperature heat source driven power cycle, a DTmin of about 3e5 C has been taken into account. In addition, in the case of an R125 transcritical cycle, due to a smaller turbine inlet speciﬁc volume v1, the volumetric ﬂow rate
_ net is also smaller. Hence the size of the turbine per unit power v_ 1 =W could be smaller. However, since an R125 transcritical cycle is working at a higher pressure than subcritical ORCs, there is substantial exergy destruction during pumping and expansion (E_ D;p and E_ D;t ). Moreover, it is important to note that the large Q_ C of an R125 transcritical cycle causes its condensing temperature to be about 2 C higher than that of subcritical ORCs, which in turn increases exergy destruction rate E_ D;c and exergy loss rate E_ L;c . Here, it should be noted that if a conventional simpliﬁcation, in which the condensing temperature remains constant regardless of the type of the cycle, was employed, the performance of the R125 transcritical cycle would be overestimated. The optimal (UA)v value of an R125 transcritical cycle is greater than that of a subcritical cycle. This is because Q_ v of the R125 transcritical cycle, i.e., the amount of heat the cycle receives from the heat source, is greater than that of subcritical cycles. This signiﬁes that the actual implementation of an R125 transcritical cycle requires a vapor generator with a larger heat transfer area compared with that of the vapor generator for a subcritical cycle. Fig. 6 shows the power output variations of optimized R125 transcritical cycle and other subcritical ORCs over the change of
Y.-J. Baik et al. / Renewable Energy 54 (2013) 78e84
Table 1 Performance of R125 transcritical cycle and subcritical ORCs at maximum power output conditions ((UA)v þ (UA)c ¼ 50 kW/K).
Efﬁciency E_ D;c E_ D;v E_ L;c E_ L;v E_ D;p E_ D;t
66.02 91.82 46.90 28.83 31.99 1.496 3.618 4.291 1.522 2.819 0.0035 0.336 51.79 24.49 24.02 25.98 4.89 8.46 5.03 7.22 203.19 187.61 15.58 4.39 19.97 7.67 4.86 4.83 1.42 6.72 0.84 4.60
101.06 88.86 49.63 27.10 28.08 0.820 4.059 2.076 0.708 2.932 0.0107 0.592 57.82 23.90 20.52 29.48 1.11 8.67 3.65 5.53 177.77 162.95 14.83 1.17 15.99 8.34 3.43 6.24 1.07 9.40 0.23 3.66
113.26 95.96 53.27 26.86 27.66 0.510 4.517 1.774 0.630 2.815 0.0211 0.730 58.97 23.78 20.25 29.75 1.01 8.54 3.48 5.32 172.91 158.18 14.74 0.81 15.55 8.52 3.29 6.17 1.01 9.96 0.16 3.53
154.01 68.91 38.63 27.10 27.31 0.789 3.651 0.591 0.160 3.688 0.0306 1.653 59.08 23.77 19.71 30.29 0.98 8.75 3.53 5.21 172.48 157.87 14.61 0.32 14.93 8.47 2.88 6.74 1.01 10.01 0.06 3.54
C C C C C kg/s MPa MPa MPa e m3/kg m3/MJ C C kW/K kW/K C C C C kW kW kW kW kW e kW kW kW kW kW kW
a TOC. Under simulation conditions considered in the present study, transcritical cycle’s power output was greater when a TOC was approximately 35 kW/K or higher. When a TOC was lower than that, transcritical cycle’s power output was slightly less than that of subcritical cycles. At a TOC of 35 kW/K, the minimum temperature differences in the vapor generator and the condenser of an optimized R134 subcritical cycle were 2.4 C and 5.8 C, respectively, whereas they were calculated to be 7.2 C and 7.5 C, respectively, in the case of an optimized R125 transcritical cycle.
T [ C]
Tcrit T1 T2 T3 T4 _r m Pcrit Pv Pc Pv/Pc v1 _ net v_ 1 =W THO TCO (UA)v (UA)c DTmin,v DTm,v DTmin,c DTm,c Q_ v Q_ c _ net W _ p W _ t W
s [kJ/K-kg] Fig. 5. Optimized R134a subcritical Rankine cycle on a Tes diagram (Entropy values of heat source and sink ﬂuids are not on scale.).
In the case of subcritical ORCs (R134a, R152a, and R245fa subcritical cycles), previous studies [3,16] proposed their own optimal working ﬂuid from the cycle efﬁciency perspective. However, under simulation conditions considered in the present study where optimization was performed from the power output perspective, the maximum power outputs did not show signiﬁcant differences regardless of the kind of working ﬂuid. Although the power output increases along with a TOC, an increasing rate rapidly declines. This is because even though a high (UA) value is available, there is a limit in reducing E_ L;v due to the minimum temperature difference in the vapor generator, and E_ D;v increases with the increased Q_ v in the vapor generation process, as shown in Fig. 7. When a TOC is less than 35 kW/K, net power output of an R125 transcritical cycle is slightly lower than that of subcritical ORCs. This is because large E_ D;c , E_ L;c , E_ D;t and E_ D;p negate the increase in turbine power. A transcritical cycle has larger Q_ c and higher condensing temperature than subcritical ORCs, which cause E_ D;c and E_ L;c to increase. An increased turbine power and pumping power also increase E_ D;t and E_ D;p . However, the power output increases along with a TOC, and when a TOC reaches 80 kW/K, the power output
T [ C]
16 60 THO 2
s [kJ/K-kg] Fig. 4. Optimized R125 transcritical cycle on a Tes diagram (Entropy values of heat source and sink ﬂuids are not on scale.).
(UA)v +(UA)c [kW/K] Fig. 6. Power variations of optimized cycles in response to changes in TOC.
Y.-J. Baik et al. / Renewable Energy 54 (2013) 78e84
Fig. 7. Distribution of irreversibility and power of optimized cycles in response to changes in TOC.
becomes about 10% greater than the maximum power output of subcritical ORCs. As discussed earlier, this is due to a better glide match in the vapor generator, causing E_ L;v and E_ D;v (that account for most of the irreversibility occurring in subcritical ORCs) to be reduced more effectively than in subcritical ORCs, as shown in Fig. 7. In addition, since this study is based on a counterﬂow heat exchanger model that does not consider the properties of working ﬂuids, research on these properties in various types of heat exchangers should be conducted in the future. 4. Conclusions In order to compare the power output of an R125 transcritical cycle with that of HFC subcritical ORCs for a low-temperature geothermal heat source of about 100 C, an R125 transcritical cycle and subcritical ORCs using R134a, R245fa and R152a were optimized and then compared. In contrast to previous studies, power optimizations were carried out for given heat source and sink inlet temperatures, and given ﬂow rates. Under simulation conditions considered in the present study, the power output of an R125 transcritical cycle was greater than that of subcritical ORCs when a total overall conductance (TOC) was higher than 35 kW/K. In this case, the power output was improved by effectively reducing an exergy destruction rate and an exergy loss rate associated with a heating process, which account for most of the irreversibility occurring in subcritical ORCs, due to a better glide match in the vapor generator. On the other hand, when a TOC was less than 35 kW/K, a higher condensing temperature and a larger pumping power negate the increase in turbine power. In summary, it was shown that although an R125 transcritical cycle can potentially give a better power output performance than a subcritical cycle, it is not always the case, for a low-grade heat source of about 100 C. References  Chen Y, Lundqvist P, Johansson A, Platell P. A comparative study of carbon dioxide transcritical power cycle compared with an organic Rankine cycle with R123 as working ﬂuid in waste heat recovery. Applied Thermal Engineering 2006;26:2142e7.
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Nomenclature cp: speciﬁc heat (kJ/kg K) e: physical exergy (kJ/kg), e ¼ (h h0) T0(s s0) E_ D : rate of exergy destruction (kW) E_ L : rate of exergy loss (kW) h: enthalpy (kJ/kg) _ mass ﬂow rate (kg/s) m: P: pressure (kPa) Q_ : rate of heat transfer (kW) T: temperature ( C) TOC: total overall conductance (UA)v þ (UA)c (kW/K) UA: overall conductance (kW/K) v: speciﬁc volume (m3/kg)
84 _ volumetric ﬂow rate (m3/s) v: _ power (kW) W:
Y.-J. Baik et al. / Renewable Energy 54 (2013) 78e84
DTm: mean temperature difference in heat exchanger ( C) DTmin: minimum temperature difference in heat exchanger ( C) hisen: isentropic efﬁciency Subscripts c: condenser CI: cooling water (heat sink) inlet CO: cooling water (heat sink) exit crit: critical point
CW: cooling water HI: heat source inlet HO: heat source exit HW: heat source water p: pump r: the primary working ﬂuid t: turbine s: isentropic v: vapor generator 0: reference state, T ¼ 20 C and P ¼ 101.325 kPa 1e4: state points