Thermo-economic analysis and comparison of a CO2 transcritical power cycle and an organic Rankine cycle

Geothermics 50 (2014) 101–111

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Thermo-economic analysis and comparison of a CO2 transcritical power cycle and an organic Rankine cycle Maoqing Li, Jiangfeng Wang, Saili Li, Xurong Wang, Weifeng He, Yiping Dai ∗ Institute of Turbomachinery, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China

a r t i c l e

i n f o

Article history: Received 28 January 2013 Accepted 18 September 2013 Keywords: CO2 transcritical power cycle Organic Rankine cycle Low temperature geothermal source Thermo-economic analysis

a b s t r a c t CO2 transcritical power cycle (CDTPC) and organic Rankine cycle (ORC) can effectively recover low grade heat due to their excellent thermodynamic performance. This paper conducts thermo-economic analysis and comparison of a CDTPC and an ORC using R123, R245fa, R600a and R601 as the working fluids driven by the low temperature geothermal source with the temperature ranging from 90 ◦ C to 120 ◦ C. The two power cycles are evaluated in terms of five indicators: net power output, thermal efficiency, exergy efficiency, cost per net power output (CPP) and the ratio of the heat exchangers’ cost to the overall system’s cost (ROC). Results indicate that the regenerator can increase the thermodynamic performance of the two power cycles. The ORC working with R600a presents the highest net power output while the highest thermal and exergy efficiencies are obtained by the regenerative ORC working with R601. The maximum net power output of the regenerative CDTPC is slightly higher than that of the basic CDTPC. The CDTPC has a better economic performance than ORC in terms of CPP and under a certain turbine inlet pressure the CPP of the regenerative CDTPC is even lower than that of the basic CDTPC. © 2013 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, accelerated consumption of fossil fuels has caused serious environmental problems and energy shortage. This makes urgent the use of environmentally friendly renewable energy technologies that have near-zero greenhouse gas emissions. Among several types of the renewable energy, geothermal energy appears to be the most attractive energy source since it is huge, independent of weather condition and easily utilized by conventional technologies. However, most of the geothermal resources are obtained at temperatures lower than 150 ◦ C and are therefore designated as “low temperature” or “low enthalpy” geothermal resources (Barbier, 2002). Moreover, the utilization of low temperature resources can be achieved with binary plants. About 44% of the existing units are binary plants which, however, produce less than 10% of the world geothermal electricity because of their lower average size (Bertani, 2012). In binary plants, the working fluid, other than geothermal fluid, undergoes a closed cycle. Most of the binary plants are based on Rankine or Kalina cycles (Guzovic et al., 2010). Since the temperature “glide” for CO2 is above the critical point, the so-called pinching problem, which may occur in ORC’s counter

∗ Corresponding author at: Institute of Turbomachinery, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an 710049, PR China. Tel.: +86 029 82668704; fax: +86 029 82668704. E-mail address: [email protected] (Y. Dai). 0375-6505/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.geothermics.2013.09.005

current heat exchanger, could be avoided in CDTPC (Chen et al., 2005). Moreover, compared with Kalina cycle, CO2 as a pure working fluid has better heat transfer performance than fluid mixtures (Chen et al., 2007). Therefore, much research has been conducted on the CDTPC system. (Yamaguchi et al., 2006; Zhang et al., 2006a, b; Zhang et al., 2007a,b) conducted an experimental investigation and thermodynamic analysis of basic CDTPC powered by solar energy. It was found that CO2 could efficiently convert the low-temperature solar energy into electricity and the power generation efficiency was higher than that of a solar cell. Cayer et al. (2009) presented a detailed analysis of a CDTPC using an industrial low-grade heat source. They found that a regenerator (or internal heat exchanger, IHX) could improve marginally the thermal efficiency, the exergy efficiency and the total heat exchange surface. Yari (2010) also founded that an IHX could increase the system efficiency by analyzing seven types of geothermal power plant. Kim et al. (2012) analyzed the thermodynamic performance of the transcritical CO2 cycle using both low and high temperature heat source. Wang et al. (2010) discussed the effects of the thermodynamic parameters on the cycle performance and the exergy destruction in each component was examined for the CDTPC in waste heat recovery. Velez et al. (2011) presented the thermodynamic analysis of a CDTPC using a low temperature heat source for power generation and discussed the effect of an IHX on the system performance. The result revealed that the IHX could increase the energy and exergy efficiency of the cycle, while they also pointed out that the

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Nomenclature A b B Bo cp C D E F FS G HX h s f L I k K M N Nu P Pr q Q rfg Re t U W xm GWP ODP

cross sectional area, m2 ; heat transfer surface area, m2 channel spacing, m constant boiling number specific heat, J kg−1 K−1 wetted perimeter of the cross-section, m; capital cost, 104 USD; constant diameter, m exergy, kJ s−1 factor additional factor mass velocity, kg m−2 s−1 heat exchanger enthalpy, kJ kg−1 convection heat transfer coefficient, W m−2 K−1 entropy kJ kg−1 K−1 friction factor length from center of inlet port to center of exit port, m exergy destruction, kJ kg−1 thermal conductivity, W m−2 K−1 constant mass flow rate, kg s−1 number Nusselt number pressure, MPa Prandtl number average imposed wall heat flux, W m−2 heat transfer rate, kW enthalpy of vaporization, J kg−1 Reynolds number temperature, K overall heat transfer coefficient, W m−2 K−1 channel width, m; Power, kW vapor quality global warming potential. Relative to CO2 . ozone depletion potential. Relative to R11

Greek letters ␤ Chevron angle ı thickness, cm log mean temperature difference between hot side tm and cold side, K  viscosity, kg s−1 m−1 ; efficiency, % P pressure difference density kg/m3   thermal conductivity, W m−1 k−1 Subscripts c cold channel ch eq equivalent h hydraulic; hot in inlet liquid l m mean M material factor material and pressure factor MP max maximum minimum min

out P PP ge eva wf con reg tur gw cw net exg eng 0 1–10 S tot

v

outlet pressure factor pump generator evaporator working fluid condenser regenerator turbine geothermal water cooling water net exergy energy dead state state point single-phase flow total vapor

raise of the capital cost of the overall system and the complexity of the flow scheme would have to be analyzed deeply in future works. In addition, the comparison of the CDTPC and the ORC has also been conducted by many researchers. Chen et al. (2005) used a CDTPC to recover the energy of the vehicle engine’s exhaust. They found that about 20% of energy in the exhaust could be converted into useful work. They also compared the CDTPC with an ORC working with R123 in Ref. Chen et al. (2006) and pointed out that a CDTPC gave a slightly higher power output than the ORC. Cayer et al. (2010) studied a basic transcritical power cycle using a sensible low temperature heat source and the performance of CO2 , ethane and R125 were compared. The results showed that the CO2 performed better in transfer coefficient. Baik et al. (2011) compared the power output of the CO2 transcritical and R125 transcritical cycles for a low-grade heat source of about 100 ◦ C, and the two cycles were optimized to maximize the power output under the same conditions. But the regenerator was not introduced and the economic performance was not evaluated. Guo et al. (2010) presented a comparative analysis of a CDTPC and an ORC working with R245fa but the economic performance of the two cycles were not evaluated. Zhang et al. (2011) presented the thermodynamic and economic analysis of both ORC and transcritical power cycle utilizing low-temperature geothermal source and optimized them using five indicators. But the data of the complete system cost were rough, since they assumed the total cost of the heat exchangers to be the total system cost. Moreover, the effect of the regenerator on the system was not evaluated. A review of the literature reveals that information is seldom available about the thermo-economic analysis and comparison between the regenerative CDTPC and ORC. This paper conducts a comparative analysis between a CDTPC and an ORC using R123, R245fa, R600a and R601 as the working fluids driven by the lowtemperature geothermal source ranging from 90 ◦ C to 120 ◦ C. The regenerator (internal heat exchanger, IHX) is introduced to both of the cycles to evaluate the effect of the configuration on the thermo-economic performance of the power cycles. Thermodynamic, economic and the heat exchanger models are established. Net power output, thermal efficiency, exergy efficiency, the ratio of the heat exchangers’ cost to the whole system’s cost (ROC) and cost per net power output (CPP) are used as the objective functions and the optimum value of each performance indicator is evaluated and compared.

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Fig. 1. Schematic diagram of the basic ORC and basic CDTPC.

Table 1 Mathematical model of the basic cycle system. Component

Energy relations

Exergy destruction

Pump Evaporator Turbine Condenser

WPP,wf = Mwf (h2 − h1 ) = Mwf (h2s − h1 )/PP Qeva = Mwf (h3 − h2 ) = Mgw (h5 − h6 ) Wtur = Mwf (h3 − h4 ) = Mwf (h3 − h4s )tur Qcon = Mwf (h4 − h1 ) = Mcw (h8 − h7 )

Ipp,wf = Wpp,wf + E1 − E2 Ieva = E5 + E2 − E6 − E3 Itur = E3 − Wtur − E4 Icon = E4 − E1

2. System modeling 2.1. System description The power cycles analyzed here include a basic ORC, a basic CDTPC, a regenerative ORC and a regenerative CDTPC. Both of the basic cycles have the similar components, consisting of a working fluid pump, an evaporator, a turbine and a condenser. The schematic diagrams of the basic cycles are shown in Fig. 1. The liquid (state 1) available at the condenser outlet is pumped into high pressure (state 2) and then flows into the evaporator where it is heated and vaporized by the geothermal water. The high pressure and temperature vapor (state 3) flows into the turbine and its enthalpy is converted into power. The low pressure vapor (state 4) is led to the condenser where it is liquefied by cooling water. The above described processes are presented in the T-s diagrams shown in Fig. 2. The schematic diagrams of the regenerative cycles are shown in Fig. 3 and the T-s diagrams are shown in Fig. 4. In the regenerative cycles, the working fluid is preheated in the regenerator before it is heated in the evaporator.

2.2. Thermodynamic modeling The energy and exergy analysis based on the first and second laws of the thermodynamics are evaluated. For simplicity, the pressure drops in evaporator, condenser, regenerator and pipes are ignored. And the system is assumed to be at steady-state. The thermodynamic properties of the working fluids are calculated by REFPROP 9.0. The mathematical models of the basic cycle system and the regenerative cycle system are listed in Table 1 and Table 2, respectively.

Fig. 2. T-s diagram of the basic ORC and basic CDTPC. (a) T-s diagram of the basic ORC, (b) T-s diagram of the basic CDTPC.

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Fig. 3. Schematic diagram of the regenerative ORC and regenerative CDTPC.

Table 2 Mathematical model of the regenerative cycle system. Component

Energy relations

Exergy destruction

Pump Regenerator Evaporator Turbine Condenser

WPP,wf = Mwf (h2 − h1 ) = Mwf (h2s − h1 )/PP Qreg = Mwf (h3 − h2 ) = Mwf (h5 − h6 ) Qeva = Mwf (h4 − h3 ) = Mgw (h7 − h8 ) Wtur = Mwf (h4 − h5 ) = Mwf (h4 − h5s )tur Qcon = Mwf (h6 − h1 ) = Mcw (h9 − h10 )

Ipp,wf = Wpp,wf + E1 − E2 Ireg = E5 + E2 − E6 − E3 Ieva = E7 + E3 − E8 − E4 Itur = E4 − Wtur − E5 Icon = E6 − E1

The net power output of the power cycle systems can be given by: Wnet = Wtur − WPP,wf − Wpp,gw − WPP,cw

(1)

in which WPP,gw =

Mgw Pgw (gw gw )

(2)

WPP,cw =

Mcw Pcw (cw cw )

(3)

The exergy is given by: E = M [h − h0 − T0 (s − s0 )]

(4)

The energy and exergy efficiencies are generally defined as: eng =

exg =

Wnet Qeva Ein −

(5)



I

Ein

(6)

2.3. Calculation of the heat exchange area

Fig. 4. T-s diagram of the regenerative ORC and regenerative CDTPC. (a) T-s diagram of the regenerative ORC, (b) T-s diagram of the regenerative CDTPC.

Numerical correlations are used to calculate the heat transfer coefficients in the heat exchangers. The pressure drops in heat exchangers are set as the condition of convergence in the calculation of the heat transfer area and are designated as 10 kPa. The heat exchangers in the power cycle systems are plate heat exchange (PHE) type for its high efficiency and compact structure. The heat transfer processes for single-phase flow and two-phase flow are respectively discussed below. (1) Single-phase flow

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The heat transfer in the single-phase region is given by: QS = US AS tm

(7)

where US is the overall heat transfer coefficient, AS is heat transfer surface area, tm is the log mean temperature difference (LMTD) between the hot side and cold side.The overall heat transfer coefficient is given by: 1 1 ı 1 = + + US hh m hc

(8)

where hh and hc are respectively the convection heat transfer coefficients for the hot side and cold side. The Chisholm and Wanniarachchi correlation is employed to calculate the Nusselt number for both hot side and cold side, being expressed by Ref. Garcia-Cascales et al. (2007):



Nu = 0.724

6ˇ 

0.646

Re0.583 Pr 1/3

105

transfer areas and the pressure drops of the evaporator and the condenser are the sum of all the sections.The heat transfer for each section is given by: Qi = Ui Ai ti

(18)

The overall heat transfer coefficient for each section is given by: 1 1 ı 1 = + + Ui hh,i m hc,i

(19)

The condensation heat transfer coefficient on the hot side of each section in the condenser is expressed as Yan et al. (1999): Nui,h =

hf,i Dh i

1/3

0.4 = 4.118Reeq,i Pri

(20)

The evaporation heat transfer coefficient on the cold side of each section in the evaporator is expressed as Yan and Lin (1999):



(9) Nui,c =

1/3 1.926Prl Bo0.3 Reeq,i 0.5 eq,i

(1 − xm,i ) + xm,i

The Reynolds number is given by: GDh 

Re =

(10)

where G denotes the mass velocity through the plate channels and Dh denotes the hydraulic diameter of the flow channel, being expressed as: G=

m Nch bW

Dh =

The Prandtl number is given by: (13)

The convection heat transfer coefficient for single-phase flow (superheated and subcooled regions) is expressed as: Nu Dh

(14)

The pressure drops are given by: (15)

where f is the friction factor, calculated with the Ventas correlations shown in Zacarias et al. (2010). These correlations were obtained during the calibration of the PHE using a single-phase flow throughout both sides:

f = 2.21 · Re−0.097

(21)

(22)

l q Geq,i · rfg

(23)



  0.5  l

(24)

v

The pressure drops in each section of the condenser and the evaporator are calculated in the same manner as in Eq. (23). Kuo correlation (Kuo et al., 2005) is used to calculate the friction factor of the condenser. −1.14 fcon,i = 21, 500 · Reeq · Bo−0.085 eq,i

(25)

Hsieh correlation (Sun et al., 2012) is used to calculate the friction factor of the evaporator.

2fG2 p = L Dh

f = 14.62 · Re−0.514

where

Geq,i Dh

Geq,i = G 1 − xm,i + xm,i

cp  Pr = 

h=

Reeq,i = Boeq,i =

(12)

l

v

where Prl is the Prandtl number of saturated liquid for the organic working fluid, xm,i s the vapor quality for each section, Reeq,i and Boeq,i is the equivalent Reynolds and Boiling numbers for each section, which are

(11)

4Wb 4A = C 2(W + b)

  1/2 

Re ≤ 50

(16)

Re≥180

(17)

(2) Two-phase flow The heat transfer process in the two-phase region is divided into relatively small sections, with so slight property variations in each section that constant properties can be assumed. The total heat

−1.25 feva,i = 61, 000 · Reeq,i

(26)

2.4. Economical modeling The overall capital cost of the cycle system is determined from a sum of the cost of individual component which is discussed below. The cost of the heat exchanger is expressed as Atrens et al. (2011): CHX =

527.7 0 (B1,HX + B2,HX FM,HX FP,HX )FS CHX 397

(27)

where FS is an additional factor considering material, additional piping, freight, labor and other overheads, B1,HX and B2,HX are

Table 3 Calculation parameters. Constant

Value

Constant

Value

Constant

Value

Constant

Value

B1,HX B2,HX FM,HX FS K1,HX K2,HX

0.96 1.21 2.4 1.7 4.6656 −0.1557

K3,HX C1,HX C2,HX C3,HX B1,PP B2,PP

0.1547 0 0 0 1.89 1.35

FM,PP K1,PP K2,PP K3,PP C1,PP C2,PP

2.2 3.3892 0.0536 0.1538 −0.3935 0.3957

C3,PP FMP K1,tur K2,tur K3,tur

−0.00226 3.5 2.2659 1.4398 −0.1776

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Table 4 Assumptions for simulation. Item

Value

Temperature of the geothermal water, ◦ C Temperature of the cooling water, ◦ C Pinch temperature difference in all the heat exchangers, ◦ C Mass flow rate of the geothermal water, kg s−1 Turbine isentropic efficiency Pump isentropic efficiency Generator efficiency

120 15 5 10 0.75 0.7 0.96

constants for the heat exchange type, FM,HX is the material factor (for stainless steel) of the heat exchanger, FP,HX is the pressure fac0 is the basic cost for the heat exchanger made from tor, and CHX carbon steel operating at ambient pressure. The numbers are the ratio of Chemical Engineering Plant Cost Indices (CEPCI) which are used to update the basic cost. The basic cost of heat exchanger made from carbon steel is given by Turton et al. (2009): 0 log CHX = K1,HX + K2,HX log AHX + K3,HX (log AHX )2

(28)

where K1,HX , K2,HX and K3,HX are constants for the heat exchange type, and AHX is the heat transfer area.Pressure factor of the heat exchanger is given by: log FP,HX = C1,HX + C2,HX log PHX + C3,HX (log PHX )2

(29)

where C1,HX , C2,HX and C3,HX are constants for the heat exchange type, and PHX is the design pressure of the heat exchanger. The pumps used in the power cycle systems are centrifugal type and the costs of the pumps can be calculated by: CPP =

527.7 0 (B1,PP + B2,PP FM,PP FP,PP )FS CPP 397

(30)

where B1,PP and B2,PP are constants for pump type (centrifugal), FM,PP is the material factor of the pump, FP,PP is the pressure factor of the 0 is the basic cost of the pump made from carbon steel. pump, and CPP The basic cost of the pump made from carbon steel is given by: 0 log CPP = K1,PP + K2,PP log WPP + K3,PP (log WPP )2

(31)

where K1,PP , K2,PP and K3,PP are constants for pump type, and WPP is the consumption power in the pump.Pressure factor of the pump is given by: log FP,PP = C1,PP + C2,PP log PPP + C3,PP (log PPP )2

(32)

where C1,PP , C2,PP and C3,PP are constants for pump type, and PPP is the design pressure of the pump.The cost of the turbine is given by: Ctur =

527.7 0 FMP FS Ctur 397

(33)

where FMP is the material and the pressure factor (for stainless steel) 0 is the basic cost of the turbine made from of the turbine, and Ctur carbon steel, which is determined by: 0 log Ctur = K1,tur + K2,tur log Wtur + K3,PP (log Wtur )2

(34)

where K1,tur , K2,tur and K3,tur are constants for turbine, and Wtur is the turbine output power. The values of these constants are given in Table 3. 3. Simulation procedure The inlet temperature of the geothermal water and the cooling water, the pinch temperature difference, the flow rate of the geothermal water, the isentropic efficiencies of the pumps and the turbine were listed in Table 4. The flow chart of the simulation procedure is shown in Fig. 5. The initial step is to specify the values of all the fixed parameters

Fig. 5. Flow chart of the simulation procedure.

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Table 5 List of considered working fluids.

CO2 R123 R245fa R600a R601

ASHRE 34a

Molecular mass

GWP

ODP

tbp (◦ C)

tcrit (◦ C)

pcrit (MPa)

A1 B1 B1 A3 A3

44.01 152.93 134.05 58.12 72.15

1 77 7.6 ∼20 20

0 0.02 0 0 0

−78.4 27.82 14.9 −11.67 36.0

30.98 183.68 154.05 134.67 196.6

7.3 3.6 3.6 3.6 3.37

a ASHRAE Standard 34-Refrigerant safety group classification. 1: No flame propagation; 2: Lower flammability; 3: Higher Flammability; A: Lower Toxicity; B: Higher Toxicity.

and the range of the variable ones. In the power cycle systems, the parameters for optimization are the turbine inlet pressure and the turbine inlet temperature. Once the values of the independent variables are given, the state of each point can be calculated and the cycle performance of the system is evaluated. The economic objective function value of the CPP and ROC can be obtained. The optimum value of the power cycle system can be found by particle swarm optimization (PSO) (Sun et al., 2012). To compare the CDTPC with the ORC, several organic working fluids were selected. Table 5 lists some properties of the CO2 and various organic working fluids of the ORC considered here. 4. Results and discussion 4.1. Energy analysis Fig. 6 shows the variation of the net power output with the turbine inlet pressure for the CDTPC and the ORC. Fig. 6(a) and (b) show a parabola-like behavior and thus the existence of a maximum for the net power output. For a constant turbine inlet temperature, the net power output was determined by the specific enthalpy drop in the turbine, the working fluid mass flow rate and the pump power consumption. For CDTPC, with increasing turbine inlet pressure, the evaporating temperature in the evaporator increased and these enabled the specific enthalpy to drop in the turbine. They also enabled both the working fluid mass flow rate and the pump power consumption to increase. The pump power consumption of CDTPC was large due to the high pump output pressure. Therefore, with increasing turbine inlet pressure the net power increased firstly (caused by the increasing specific enthalpy drop and the working fluid mass flow rate) and then decreased (caused by the increasing pump power consumption), existing a maximum value. The maximum net power outputs of 129.5 kW, 152.7 kW and 173.5 kW were yielded with the turbine inlet temperature at 359 K, 371 K and 383 K, respectively. When an IHX was added the net power output of the CDTPC increased. CO2 was preheated in the IHX before it

entered into the evaporator and this increased the CO2 mass flow rate and led to an increment in the net power output. The maximum net power outputs could be increased to 131.7 kW, 156.1 kW and 177.24 kW with the turbine inlet temperature at 359 K, 371 K and 383 K, respectively. For pressures higher than approximately 11.6 MPa, 13 MPa and 14.4 MPa with the turbine inlet temperature at 359 K, 371 K and 383 K, respectively, the IHX couldn’t be used because the temperature difference between the turbine exhaust and the pump outlet was less than 5 K which was the design pinch point of the IHX. For the ORC, with increased turbine inlet pressure the specific enthalpy drop and the pump power consumption increased while the working fluid mass flow decreased. The pump power consumption was very small in the ORC due to the low pump outlet pressure and the net power was mainly decided by the specific enthalpy drop and the working fluid mass flow rate. The net power increased firstly (caused by the increasing specific enthalpy drop) and then decreased (caused by the decreasing working fluid mass flow rate). With turbine inlet temperature of 383 K, the maximum net powers for R123, R245fa, R600a and R601 were 192.2 kW, 192.7 kW, 190.9 kW and 186.7 kW, respectively, independent of the IHX. The reason is that the IHX can’t increase the working fluid mass flow rate due to the pinch point in the evaporator. Fig. 6 also shows that the ORC working with R245fa yields the maximum net power of 192.7 kW. Fig. 7 shows the variation of the thermal efficiency with the turbine inlet pressure for both power cycles. For the CDTPC, the thermal efficiency increased firstly and then decreased with a maximum. When the turbine inlet temperatures were 359 K, 371 K and 383 K the maximum thermal efficiencies of the basic systems were 3.9%, 4.7% and 5.5%, respectively. When an IHX was used, the corresponding maximum thermal efficiencies were increased to 4.1%, 5.1%, and 6.1%, respectively. For pressures higher than approximately 11.6 MPa, 13 MPa and 14.4 MPa with the turbine inlet temperature at 359 K, 371 K and 383 K, respectively, the IHX couldn’t be used and the thermal efficiency became equal to that of the basic one. For the ORC, the thermal efficiency increased with the

Fig. 6. Net power output vs. turbine inlet pressure. (a) CDTPC, (b) ORC.

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Fig. 7. Thermal efficiency vs. turbine inlet pressure. (a) CDTPC, (b) ORC.

turbine inlet pressure and the maximum thermal efficiencies of the basic systems were 12.4%, 11.8%, 11.2% and 12.1% when the working fluids were R123, R245fa, R600a and R601, respectively. When an IHX was used, the corresponding maximum thermal efficiencies were increased to 13.3%, 12.8%, 11.9%, and 13.8%, respectively. The variations of the thermal efficiency of the CDTPC and the ORC were different. Due to high turbine inlet pressure, the pump power consumption of the CDTPC was high and this enabled the thermal efficiency to decrease after it reached the maximum. However, for the ORC when the turbine inlet pressure increased, the enthalpy drop in the turbine increased and this led to an increment in the thermal efficiency. Fig. 7 also shows that with the turbine inlet temperature of 383 K, the highest increment of 14.05% in the thermal efficiency is obtained for the ORC working with R601, followed by the CDTPC which is 10.9%.

4.2. Exergy results Fig. 8 shows the variation of the exergy efficiency with the turbine inlet pressure for both power cycles. The exergy efficiency increased with the turbine inlet pressure for both basic CDTPC and ORC. Heat-transfer temperature difference in the evaporator reduced with increasing evaporating temperature caused by the increasing turbine inlet pressure and this enabled the exergy loss to lower in the evaporator. As the heat-transfer irreversibility in the evaporator was very large (Li et al., 2012; Mago et al., 2008), the reduction of exergy loss in the evaporator enabled the system

exergy efficiency to increase. The exergy efficiency of the CDTPC had no maximum when the turbine inlet pressure rose (with the similar results to those mentioned in (Velez et al., 2011)). However, the exergy efficiency of the basic ORC increased and the maximum exergy efficiency was obtained when the turbine inlet was saturated vapor. The IHX could increase the exergy efficiency for both power cycles. As Fig. 8 shown, the highest exergy efficiency of the basic ORC was obtained for R123, the highest exergy efficiency of the regenerative cycle and the highest exergy efficiency increment of 14.55% (from 49.41% to 56.6%) were observed for R601.

4.3. Heat exchange area Fig. 9 shows the variation of the total area of the heat exchangers with the turbine inlet pressure for both power cycles. For the basic CDTPC, the total heat exchange area increased with increasing turbine inlet pressure and turbine inlet temperature (TIT). While it was opposite to the ORC, the increasing turbine inlet pressure decreased the total heat exchange area. With increasing turbine inlet pressure, the working fluid mass flow rate increased for the CDTPC while decreased for the ORC. Therefore, changing with the working fluid mass flow rate the total heat exchange area increased for the CDTPC and decreased for the ORC. When an IHX was used, the total heat exchange area increased for both CDTPC and ORC and with increasing turbine inlet pressure, the total heat exchange area difference of the regenerative cycle and the basic one decreased. For the regenerative CDTPC, the total heat exchange area decreased firstly and then

Fig. 8. Exergy efficiency vs. turbine inlet pressure. (a) CDTPC, (b) ORC.

M. Li et al. / Geothermics 50 (2014) 101–111

109

Fig. 9. Total area vs. turbine inlet pressure. (a) CDTPC, (b) ORC.

increased with the minimums of 129.1 m2 , 133.7 m2 and 147.3 m2 when the turbine inlet temperatures were 359 K, 371 K and 383 K, respectively. For the regenerative ORC, the total heat exchange area decreased with increasing turbine inlet pressure. When the turbine inlet pressure increased to a certain value, the total heat exchange areas of the regenerative cycles were almost the same as the basic one.

4.4. Economic analysis Fig. 10 shows the variation of the ratio of the heat exchangers’ cost to the whole system’s cost with the turbine inlet pressure for both power cycles. For the CDTPC, the ROC decreased and at most operating points the ROC was lower than 0.625. For the regenerative CDTPC, the cost of the heat exchangers decreased firstly and then increased with the heat exchange area (shown in Fig. 9(a)). When the turbine inlet pressure increased, the CO2 mass flow rate increased and these enabled the cost of the pump and turbine to increase and finally led to an increment in the total cost of the whole system. As the increment in the whole system’s cost was larger than that of the heat exchangers’ cost, the ROC of the CDTPC decreased. For the ORC, the ROC decreased firstly and then increased with minimums and at most operating points the ROC was higher than 0.625. With increasing turbine inlet pressure, the heat exchanger’s cost and the working fluid mass flow rate both decreased. The decreased mass flow rate enabled the pump and turbine costs to decrease and finally enabled the whole cost of the system to decrease. Therefore, for pressures higher than 0.59 MPa, 0.64 MPa, 0.60 MPa and 0.62 MPa for R123, R245fa, R600a and R601, the ROC increased with

minimums of 0.65, 0.64, 0.60 and 0.62, respectively. Fig. 10 also shows that the ROC of the ORC is generally higher than that of the CDTPC. For both cycles, the IHX could increase the ROC significantly. This illustrates that though the total areas of the regenerative cycles are finally almost the same as the basic ones, the total cost of the whole system could be increased significantly as a new component (IHX) is introduced. Fig. 11 shows the variation of the CPP with the turbine inlet pressure for both power cycles. With turbine inlet temperature of 383 K, the CPP of the regenerative CDTPC was lower than that of the basic one when the turbine inlet pressure was lower than 9.3 MPa. However, when the turbine inlet pressure was higher than 9.3 MPa, the CPP of the regenerative cycle was higher than that of the basic one. And with the turbine inlet temperature of 359 K, the CPP of the basic CDTPC was equal to that of the regenerative one when the turbine inlet pressure was 8.5 MPa. However, for the ORC when an IHX was added, the CPP increased. This is because that with an IHX the total cost and the net power output both increase for the CDTPC, while for the ORC the total cost increases and the net power output is unchanged. Fig. 11 also reveals that, compared with the ORC, the IHX can increase the economic efficiency of the CDTPC.

4.5. Optimization results The CDTPC and the ORC system are evaluated and compared in terms of five performance indicators. The optimal values of the five indicators of the basic and the regenerative low-temperature (i.e. 90–120 ◦ C) geothermal power cycles are listed in Table 6. The regenerative CDTPC had the highest CPP and followed by the basic

Fig. 10. ROC vs. turbine inlet pressure. (a) CDTPC, (b) ORC.

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M. Li et al. / Geothermics 50 (2014) 101–111

Fig. 11. CPP vs. turbine inlet pressure. (a) CDTPC, (b) ORC.

Table 6 Optimal values of the five indicators of the basic and the regenerative low-temperature geothermal power cycles.

CPP ($/W) ROC Wnet (kW) eng exg

CO2

CO2 (IHX)

R123

R123 (IHX)

R245fa

R245fa (IHX)

R600a

R600a (IHX)

R601

R601 (IHX)

1750 0.31 173.57 5.50 54.40

1870 0.50 177.24 6.10 51.09

1380 0.65 198.39 12.40 50.42

1820 0.75 198.39 13.30 54.19

1360 0.64 203.50 11.80 48.95

1670 0.71 203.50 12.81 53.72

1250 0.60 204.86 11.22 48.55

1600 0.69 204.86 12.24 53.60

1270 0.62 198.43 12.10 49.41

1540 0.72 198.43 13.80 56.60

CDTPC. For the ORC, higher CPP were also obtained for the regenerative cycles and the highest CPP was presented for R123. As most of the system capital costs are assigned on the heat exchangers (Zhang et al., 2011; Papadopoulos et al., 2010), lower ROC means better heat transfer in the heat exchangers and relative smaller heat exchange area. It was obvious that with a regenerator the ROC of the power cycles all increased and the lowest ROC was observed for the basic CDTPC followed by the regenerative CDTPC. Compared with the ORC, the higher working pressure of the CDTPC led to the higher capital cost of the pumps, turbine and other components. Therefore, the ROC of the CDTPC was lower than that of the ORC. The highest net power output was obtained for the ORC working with R600a which was 204.86 kW, higher than that of the regenerative CDTPC by about 27.62 kW. For the CDTPC, an IHX increased the maximum of the net power output by about 3.67 kW. The maximum of the thermal and exergy efficiencies could be both increased when an IHX was introduced. The highest thermal efficiency was obtained for the regenerative ORC working with R601 and the highest exergy efficiency was presented also for the regenerative ORC working with R601 followed by the CDTPC.

which is 10.9% when the turbine inlet temperature is 383 K. The highest exergy efficiency of the basic ORC was obtained for R123 and the highest exergy efficiency of the regenerative one was presented for R601a. (3) With increasing turbine inlet pressure, the total heat exchange area of the CDTPC increases while the total heat exchange area of the ORC decreases. The IHX can increase the total heat exchange area and the total capital cost significantly for both CDTPC and ORC. For the two power cycle systems, the cost per net power output (CPP) decreased to the minimum and then increased.

5. Conclusions

Atrens, A.D., Gurgenci, H., Rudolph, V., 2011. Economic optimization of a CO2 -based EGS power plant. Energ. Fuel. 25, 3765–3775. Baik, Y.J., Kim, M., Chang, K.C., Kim, S.J., 2011. Power-based performance comparison between carbon dioxide and R125 transcritical cycles for a low-grade heat source. Appl. Energ. 88, 892–898. Barbier, E., 2002. Geothermal energy technology and current status: an overview. Renew. Sust. Energ. Rev. 6, 3–65. Bertani, R., 2012. Geothermal power generation in the world 2005–2010 update report. Geothermics 41, 1–29. Cayer, E., Galanis, N., Desilets, M., Nesreddine, H., Roy, P., 2009. Analysis of a carbon dioxide transcritical power cycle using a low temperature source. Appl. Energy 86, 1055–1063. Cayer, E., Galanis, N., Nesreddine, H., 2010. Parametric study and optimization of a transcritical power cycle using a low temperature source. Appl. Energy 87, 1349–1357. Chen, Y., Lundqvist, P., Platell, P., 2005. Theoretical research of carbon dioxide power cycle application in automobile industry to reduce vehicle’s fuel consumption. Appl. Therm. Eng. 25, 2041–2053. Chen, Y., Lundqvist, P., Johansson, A., Platell, P., 2006. A comparative study of the carbon dioxide transcritical power cycle compared with an organic rankine cycle with R123 as working fluid in waste heat recovery. Appl. Therm. Eng. 26, 2142–2147. Chen, Y., Pridasawas, W., Lundqvist, P., 2007. ASME Low-Grade Heat Source Utilization by Carbon Dioxide Transcritical Power Cycle.

In this paper, the thermo-economic performance of the CO2 transcritical power cycle (CDTPC) and organic Rankine cycle (ORC) are examined in terms of five indicators for low temperature geothermal power plant. The regenerator (internal heat exchanger, IHX) is introduced to both power cycles to evaluate the effect of the configuration on the thermo-economic performance of the power cycle. The main conclusions can be summarized as follows: (1) The ORC working with R245fa yields the maximum net power of 192.7 kW, though the IHX can’t increase ORC’s net power output. However, for the CDTPC the net power output can be increased by the IHX and when the turbine inlet pressure increases the effect of the IHX on the net power out decreases. (2) The IHX can increase the thermal efficiency of CDTPC and ORC. The highest increment of 14.05% in the thermal efficiency is obtained for the ORC working with R601, followed by the CDTPC

Acknowledgements The authors gratefully acknowledge the financial support by the National Key Technology R&D Program (Grant No. 2011BAA05B03) and the National high-tech Research and development (Grant No. SS2012AA053002). References

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