Thermodynamic and economic evaluation of the organic Rankine cycle (ORC) and two-stage series organic Rankine cycle (TSORC) for flue gas heat recovery

Energy Conversion and Management 183 (2019) 816–829

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Thermodynamic and economic evaluation of the organic Rankine cycle (ORC) and two-stage series organic Rankine cycle (TSORC) for flue gas heat recovery

T

Tailu Lia, Nan Menga, Jian Liub, Jialing Zhuc, Xiangfei Konga,

⁎

a

School of Energy and Environmental Engineering, Hebei University of Technology, Tianjin 300401, PR China School of Energy and Safety Engineering, Tianjin Chengjian University, Tianjin 300384, PR China c Key Laboratory of Efficient Utilization of Low and Medium Grade Energy (Tianjin University), MOE, Tianjin 300072, PR China b

ARTICLE INFO

ABSTRACT

Keywords: ORC TSORC Thermodynamic-economic Electricity production cost

The flue gas heat can be recovered by organic Rankine cycle (ORC) or two-stage series organic Rankine cycle (TSORC), but their comprehensive performance should be compared in detail. In this paper, ORC and TSORC are compared from thermodynamic and economic points of view. The technical indicators include the net output power, efficiency, thermal conductance, volumetric flow ratio, and the economic indicators the electricity production cost (EPC), payback period (PBP) and rate of return on investment (ROROI). The results show that the TSORC can recover more heat in the low-pressure stage from the heat source so as to decrease the irreversible loss between the heat source and the working fluid in contrast with ORC, thereby enhancing the net output power and exergetic efficiency but decreasing the thermal efficiency. However, from the economic point of view, the TSORC declines the EPC, PBP and ROROI due to that the increased investment is higher than the earnings as a result of the installation of the second-stage evaporation. A higher flue gas temperature from 200 °C to 300 °C tends to enhance the tech-economic performance of the TSORC. As the manufacturing cost goes down over time, the TSORC will further improve its economic performance in the future.

1. Introduction At present, gas turbine (GT) has been widely used in ships, vehicles and electricity generators units because of its reliable operation, quick start-up and low noise. However, the performance of GT should be further improved due to a large amount of exhaust heat of flue gas, which also causes the thermal pollution, so the heat recovery from flue gas is beneficial to improving the overall efficiency of GT system. In this context, many researchers have been focused on the power generation performance enhancement of GT system. Fuel type is doubtlessly the key to improve the GT performance, and researchers have made a series comparison and analyses on liquid fuel [1], ammonia fuel [2], pyrolysis of bio-oil and mixed fuel [3], and the choice of fuel depending on its application conditions. Furthermore, the selection of material alloys for GT system components is another important factor affecting the life and performance of GTs. Subbarao et al. [4] compared the nickel, titanium, steel and other alloy materials which applied to the components of turbine blades alloy and found that the appropriate blade alloy material selected by the grain structure can improve the GT

⁎

Corresponding author. E-mail address: [email protected] (X. Kong).

https://doi.org/10.1016/j.enconman.2018.12.094 Received 14 October 2018; Accepted 24 December 2018 Available online 17 January 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

life and power generation performance. In addition, many scholars put forward the turbine inlet cooling technology [5,6], hybrid solar preheating [7] and other innovative technologies to improve the GT performance. The improvement of GT system covers the parametric optimization and the design of waste heat recovery. Santos et al. [8,9] proposed a closed reheat GT co-generation system and analyzed the performance difference between the GT cycle, steam cycle and combined-cycle GT (CCGT) cycle. Paepe et al. [10] reclaimed waste heat into the circulatory system and found that the electrical efficiency of micro GT (MGT) is considerably increased. The GT system is often combined with the waste heat recovery system to improve the system performance. Many researches have found that the Rankine cycle, Karina cycle, reheat ORC, ORC and TSORC are often applied to the waste heat recovery system [11,12]. Girgin et al. [13] studied the Rankine cycle system and found many limitations of the system. Larsen et al. [14–16] found that ORC has enormous potential to improve the thermal efficiency compared to the Kalina cycle. Braimakis et al. [17] discussed the ORC and reheat ORC in the thermal efficiency and utilization efficiency by thermodynamic

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Nomenclature Q I c W s K A m h ORC TSORC PBP VFR EPC ROROI CCGT GT

MGT ICE

heat quantity (kW) irreversible loss specific heat capacity power output (kW) specific entropy (J/kg·K) heat transfer coefficient (W/°C.m2) heat transfer area (m2) mass flow rate (kg/s) enthalpy (kJ/kg) organic Rankine cycle two-stage organic Rankine cycle payback period volumetric flow ratio electricity production cost rate of return on investment combined-cycle GT GT

micro GT internal combustion engine

Greek letters thermal efficiency (%) exergy efficiency (%)

ηth ηex Subscripts gain gamid gaout pp wf E C T P

theory. Braimakis et al. [18] compared and analyzed the ORC and TSORC by the thermodynamic evaluation, and the power generation performance of TSORC system is enhanced compared to the ORC. The ORC plays a major role in energy recovery from low-temperature waste heat due to its benefits of energy saving, investment savings, environmental friendliness, and it has great potential in improving engine performance [19,20]. In addition, for the heat recovery from a higher temperature heat source, the alkane working fluids have many benefits in the performance of ORC system [21–24]. Compared with the ORC, the TSORC system exhibited great advantages in the performance of power generation [25,26], but the economic performance of TSORC system is seldom studied. White et al. [27] suggested that the further development of ORC power system should be guided by the thermodynamic and the economic evaluations which balance the relationship between performance and cost. Yao et al. [28] carried out the thermodynamic economic performance analysis of the ORC by the net profit and payback period. Besides, Amirmohammad et al. [29,30] evaluated the economic impact of ORC from fuel savings, exergy efficiency and unit price. Furthermore, there are many scholars focused on maximizing the efficiency of system components. Qiu et al. [31] studied the optimization of compressed air driven scroll ex-pander and assessed the feasibility of using the expander in ORC. Nematollahi et al. [32] studied the effect of brazed

metal foam plate heat ex-changer (BMPHE) on the performance parameters of ORC and found that the power density of ORC system with the compact evaporator (BMPHE) is increased. The technical comparison has been conducted between the ORC and TSORC under different working conditions, but the economic evaluation is often ignored. Therefore, a comprehensive comparison between the ORC and TSORC for the flue gas recovery discharged by GTs from the viewpoint of thermodynamics and economy should be conducted in detail. In this paper, the thermodynamic-economic model of the TSORC has been constructed. The thermodynamic indicators include net output power (Wnet), thermal efficiency (ηth) and exergy efficiency (ηex), and the economic indicators are electricity production cost (EPC), payback period (PBP) and rate of return on investment (ROROI). The ORC and TSORC have been compared in the aspects of thermodynamics and economy. 2. System description The working principle diagram of flue gas recovery system by TSORC is shown in Fig. 1. The GT power generation system consists of a compressor, a combustor and a GT. Firstly, the filtered air is compressed by the compressor, and then enters the combustor to burn with the gas. The high temperature and high pressure gas produced in the

Evaporator1

Flue gas

Gas

flue gas inlet middle flue gas flue gas outlet pinch point working fluid evaporation phase condensation phase turbine phase pump phase

Combustor Compressor

Pump2

Gas Turbine Air Filter

Turbine

Evaporator2 Pump1

Cooling water

Working fluid

Condenser

Fig. 1. Flow chart of flue gas recovery system of TSORC. 817

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combustor drives the GT to do work. Finally, the flue gas exhausted by the GT flows into to the evaporators of TSORC system as the heat source to vaporize the working fluid. For the TSORC system, there are two evaporators and pumps, a condenser and a turbine. The working fluid from the condenser enters the low-pressure evaporator 2 driven by pump 1, and then divides into two parts: working fluid 1, and working fluid 2. The working fluid 2 continues is heated to the superheated state in the evaporator 2, and then flows into the turbine to output mechanical work. The liquid working fluid 1 at the saturated state of the evaporator 2 is pressurized by the pump 2 to enter the evaporator1 to be heated to the superheated state, and then flows into the turbine. The working fluid discharged by turbine flows into the condenser to be condensed by the cooling water, and finally it enters the evaporator 2 driven by the pump1 to complete a cycle. The evaporator 2 is a key component for the TSORC different from ORC. For the working fluid side, there are two outlets and one inlet, the working fluid at the superheated vapor sate from the evaporator 2 enters the middle class of the turbine through the outlet 1, and the liquid saturated working fluid is further pumped to evaporator 1 through the outlet 2 of the evaporator 2. The T-s diagram is shown in Fig. 2.

QE1,eva = mgas (hga,11

Q E1,eva = (KA)E1,eva [(t ga,11

hga,11) = mwf,1 (h11

Q E1,sup = (KA) E1,sup [(t ga,11

t17)]/ln[(t ga,11

t18)

(t ga,in

t11)]/ln[(t ga,11

t17)]

(t ga,12

t17)]/ln[(t ga,mid

t18)/(t ga,in (6)

AE1 = AE1,pre + AE1,eva + AE1,sup

(7)

QE1 = QE1,pre + Q E1,eva + Q E1,sup

(8)

The irreversible loss of high pressure evaporator is given by:

IE1 = T0 [mwf,1 (s11

s16)

mgas (sga,in

(9)

sga,mid)]

where the “IE1” is the irreversible loss of high pressure evaporator, the “T0” represents the ambient temperature, and the “s” represents the specific entropy the state points. The heat transfer equations of low pressure evaporator “E2” are given by:

QE2,pre = mgas (hga,22

hga,out) = mwf,2 (h27

(10)

h26)

where the “QE2” means the heat transfer quantity of low pressure evaporator, the “mwf,2” is the mass flow of working fluid2.

Q E2,pre = (KA)E2,pre [(t ga,out

t26)

(t ga,22

t27)]/ln[(t ga,out

t26)/(t ga,22 (11)

t27)]

where the “(KA)E2” is the product of heat transfer coefficient and area in low pressure evaporator.

QE2,eva = mgas (hga,21

hga,22) = mwf,2 (h28

Q E2,eva = (KA)E2,eva [(t ga,21

t28)

(t ga,22

(12)

h27) t27)]/ln[(t ga,21

t28)/(t ga,22 (13)

t27)]

QE2,sup = mgas (hga,mid

hga,21) = mwf,2 (h21

Q E2,sup = (KA) E2,sup [(t ga,mid

t21)

(t ga,21

(14)

h28) t28)]/ln[(t ga,mid

t21)/(t ga,21 (15)

t28)]

The total heat transfer area and heat transfer quantity of low pressure evaporator are given by:

AE2 = AE2,pre + AE2,eva + AE2,sup

(16)

QE2 = QE2,pre + Q E2,eva + Q E2,sup

(17)

The irreversible loss of low pressure evaporator is given by:

(1)

where the “QE1” represents the heat transfer quantity of high pressure evaporator, “mgas” and “mwf,1” represent the mass flow of flue gas and working fluid1, “h” represents the specific enthalpy of the state points. Besides, the subscripts of state points can be seen in Fig. 3.

t16)

(5)

h18)

The total heat transfer area and heat transfer quantity of the highpressure evaporator are given by:

The evaporating process between the flue gas and the working fluid can be divided into three parts: preheating section, evaporation section and superheating section, and the T-Q diagram of the evaporating process is shown in Fig. 3. The heat transfer coefficients for the evaporator and the condenser are 280 and 850 W/(m2 °C), respectively [36]. The heat transfer equations of high pressure evaporator “E1” are given by:

Q E1,pre = (KA)E1,pre [(t ga,mid

t18)/(t ga,12

t11)]

The working fluid at the inlet of pump is in saturated liquid state. The pinch temperature differences are set as 20 °C and 5 °C [33,34], and the condensation temperature of condenser is 30 °C. The working fluid at the outlet of two evaporators are superheated with a degree of superheat of 5 °C, and the outlet of condenser is super cooled liquid with a degree of super cooling of 5 °C [35]. The pressure drops of working fluid in evaporators, condenser and working fluid pump are all ignored. The energy losses from mixed applying of work by the high and low pressure steam in turbine are ignored. The temperature and friction losses of working fluids and the change of kinetic energy and potential energy are all ignored. The inlet temperature of flue gas is within the range of 200–300 °C, the ambient temperature is 20 °C, and the mass flow of flue gas is 10 kg/s.

h16)

(t ga,12

(4)

QE1,sup = mgas (hga,in

To facilitate establishing the thermodynamic model of TSORC system, following hypotheses are made based on the first law of thermodynamics and the second law of thermodynamics.

hga,mid) = mwf,1 (h17

t11)

(3)

h17)

t17)]

3. Thermodynamic modeling

QE1,pre = mgas (hga,12

hga,12) = mwf,1 (h18

t16)/(t ga,12 (2)

where the “(KA)E1” is the product of the heat transfer coefficient and area in the high-pressure evaporator, which represents the thermal conductance of evaporator.

Fig. 2. T-s diagram of TSORC system. 818

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tga,in

t(

)

T. Li et al.

tga,11

Flue gas High pressure loop Low pressure loop

tga,21 tga,out

t27

t17

t18

t16

t28

t26

E1,pre

t21

E2,sup E2,eva

E2,pre

t11

E1,eva

tga,mid

tga,22

E1,sup

tga,12

QE2

QE1 Q (kW)

Fig. 3. T-Q diagram of the heat transfer for the evaporation process.

IE2 = T0 [mwf,1 (s27

s26) + mwf,2 (s21

s27)

mgas (sga,mid

The irreversible loss of condenser is given by:

sga,out)] (18)

IC = T0 [mwf (s5

where the “IE2” is the irreversible loss of the low-pressure evaporator. The total heat transfer area and heat transfer rate of two evaporators are given by:

AE = AE1 + AE2

(19)

QE = Q E1 + Q E2

(20)

h5) = m cw (h cw,1

t cw,1)

(t5

t cw,in)]/ln[(t 4

t cw,1)/(t5

WP1 = m wf,1 (h16 WP2 = m wf (h26

QC,con = (KA)C,con [(t 4

t cw,1)

(t3

t cw,2)]/ln[(t 4

t cw,1)/(t3

IP2 = T0 mwf (s26

h3) = m cw (h cw,out

t cw,out)

(t3

t cw,2)]/ln[(t2

t cw,out)/(t3

WT = mwf,1 (h11

(26)

IT = T0 [mwf,1 (s12

The total heat transfer area and heat transfer quantity of condenser are given by: (27)

QC = QC1 + QC2 + QC3

(28)

(32)

(33) (34)

s27)

(35)

s5)

(36)

h12) + mwf,2 (h21

h22)

(37)

where the “WT” represents the power output of turbine. The irreversible loss of turbine is given by:

t cw,2)]

AC = A C1 + A C2 + A C3

(31)

The power output of turbine is given by:

where the subscript “cw,out” represents the outlet of cooling water.

QC,pre = (KA)C,pre [(t2

P2

IP = IP1 + IP2

(25)

h cw,2)

h5)/

P1

where the “IP1” and “IP2” are the irreversible loss of pump1 and pump2.

t cw,2)] (24)

QC,pre = m wf (h2

h5) = (h26s

h27)/

The irreversible losses of pumps are given by:

IP1 = T0 mwf,1 (s16

(23)

h cw,1)

h27) = (h16s

WP = WP1 + WP2

t cw,in)]

where the “(KA)C” is the product of heat transfer coefficient and area in condenser.

h 4) = m cw (h cw,2

(30)

where the “WP1”and “WP2” represent the power waste of pump1 and pump2, and the “ηP1” and “ηP1” represent the efficiency of pump1 and pump2, which are all 75% [37].

(22)

QC,con = m wf (h3

(29)

The power waste of pump1 and pump2 are given by:

where the “QC” means the heat transfer quantity of condenser, the “mcw” is the mass flow of cooling water, the “h4” and “h5” are the specific enthalpy of state points which can be seen in Fig. 2, and the subscript “cw,in” represents the inlet of cooling water.

QC,sup = (KA)C,sup [(t 4

scw,out)]

A = AE + A C

(21)

h cw,in)

m cw (scw,in

where the “IC” is the irreversible loss of condenser. The total heat transfer area of evaporators and condenser is given by:

The heat transfer equations of condenser “C” are given by:

QC,sup = m wf (h 4

s2)

s11) + mwf,2 (s22

s21)]

(38)

where the “IT” represents the irreversible loss of turbine. The volume flow ratio of turbine is given by:

VFR = (mwf,1v12 /v11 + mwf,2 v22 /v21)/(mwf,1 + mwf,2)

(39)

where the VFR is the volume flow ratio of turbine, which is a valuation 819

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Table 1 Correlation coefficient of components cost.

Exchanger Pump Turbine

Table 2 Thermodynamic properties of the selected fluids.

K1

K2

K3

C1

C2

C3

B1

B2

FM

Fbm

Working fluids

M (g/mol)

tb (°C)

tcri (°C)

Pcri (Mpa)

4.665 3.389 3.514

0.155 0.053 0.598

0.154 0.153 0

0 0 /

0 0 /

0 0 /

0.96 1.89 /

1.21 1.35 /

1 1.5 /

/ / 3.5

I-octane Cyclohex Heptane Octane Nonane

114.23 84.16 100.20 114.23 128.26

99.208 80.74 98.38 125.62 150.76

270.85 280.49 266.98 296.17 321.40

2.572 4.08 2.74 2.50 2.28

parameters of turbine, and the “v” represents the specific volume of state points. The net output power of system is given by:

Wnet =

T WT

350

(40)

WP

300

where the “Wnet” is the net output power of system, and the “ηT” represents the efficiency of turbine. The total irreversible loss of system is given by: The thermal efficiency is given by: th

(42)

= Wnet /QE

250

Wnet (kW)

(41)

I = IE1 + IE2 + IC + IT + IP

200

where the “ηth” is the thermal efficiency of system, which is a thermodynamic evaluation parameter. The exergy efficiency is given by: ex

= Wnet /(Ex ga,in

150

100

(43)

Ex ga,out )

60

where the “ηex” is the exergy efficiency of system, which is a thermodynamic evaluation parameter; And the “Ex” represents the exergy value of state points.

Ex ga,in = mgas (hga,in Ex ga,out = mgas (hga,out

(a) ORC

T0 sga,out)

(45)

Wnet (kW)

The economic evaluation of ORC system is mainly included the three aspects: electricity production cost (EPC), payback period (PBP) and rate of return on investment (ROROI). Besides, the cost of all components is also an important parameter of this economic study, which is defined as: (46)

EPC = [CRF Cost2018 + iCost2018]/(Wnet t op)

210

240

150

180

210

240

150

180

210

240

50 60 70 80 90 100

250

90

120

90

120

t e1 ( )

3.0

(47) 2.5

Wnet,TSORC/Wnet,ORC

1]

180

te2 ( )

300

150 60 (b) TSORC

Which CEPCI 2001 = 397, CEPCI 2018 = 648.7 [39,40]. The capital recovery factor (CRF) converts a present value into a stream of equal annual payments over a specified time, at a specified discount rate [41]. The electricity production cost (EPC) means that the system generates the net power output of 1 kWh, and it is the most important indicator of economic performance given by:

CRF = i (1 + i) LT /[(1 + i) LT

150

te ( )

200

where the “Cbm” is the cost of components. The Cost2001 means the cost of components in 2001, which introduced by the CEPCI (Chemical Engineering Plant Cost Index) [38]. Here, we converted it to the actual cost Cost2018 by the formula:

Cost2018 = Cost2001 CEPCI2018/ CEPCI2001

120

350

4. Economic modeling

Cost2001 = CbmE1 + CbmE2 + CbmC + CbmT + CbmP

90

400

(44)

T0 sga,in)

decane nonane cyclohex octane heptane i-octane

(48) (49)

where “i” is the annual loan interest rate, assumed to be 5%, “LT” is the life cycle time, assumed to be 15 year, and the “top” is the operation time, assumed as 7500 h [42]. The payback period (PBP) is the length of time required to recover the cost of an investment. The payback period of a given investment is an important determinant of whether to undertake the position or project, as longer payback periods are typically not desirable for investment [43].

2.0

1.5

1.0

60 (c)

te ( )

Fig. 4. Net power output for the flue gas temperature of 280 °C.

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PBP = ln[(Wnet Ce)/(Wnet Ce

iCost2018)]/ln(1 + i)

(50)

power output of 20.6 kW, whereas the relative difference in the thermal efficiency is 5.89%. Moreover, the absolute difference in the thermal efficiency is 0.83%. The VFR, the power output and the cycle efficiency for the actual engineering data are always lower than those for the numerical calculation. The differences mainly arise from the pressure drop of the working fluid in both the pipes the heat exchangers, and no pressure drop in both the pipes the heat exchangers was adopted for the numerical calculation while the pressure drop always exists in both the pipes the heat exchangers. On the other hand, the errors of the

where the “Ce” is the electricity price, assumed to be 0.15 $/kWh [44]. The rate of return on investment (ROROI) is a performance measure, used to evaluate the efficiency of an investment or compare the efficiency of a number of different investments. To calculate ROROI, the return of an investment is divided by the cost of the investment. The result is expressed as a percentage or a ratio: LT

[Wnet t opCe (1 + r) x/(1 + i) x]

ROROI1 = x= 1

(51)

LT

[k Cost2018 (1 + r) x/(1 + i) x + iCost2018]

ROROI2 = x=1

(52) (53)

ROROI = ROROI1/ROROI2

where the “r” means the inflation rate, assumed as 2%, and the “k” means the management cost of all components factor, assumed as 1.65% [45]. Besides, the cost price of components is calculated through the following formulas and the relevant parameters of cost as shown in Table 1 [38].

lg CpE1 = K1 + K2 lg(AE1) + K3 [lg(AE1)]2

(54)

lgFpE1 = C1 + C2 lg(PE1) + C3 [lg(PE1)]2

(55)

FbmE1 = B1 + B2 FMFpE1

(56) (57)

CbmE1 = CpE1 FbmE1 lgC pE2 = K1 + K2lg(AE2) +

K3 [lg(AE2)]2

(58)

lgFpE2 = C1 + C2 lg(PE2) + C3 [lg(PE2)]2

(59)

FbmE2 = B1 + B2 FMFpE2

(60) (61)

CbmE2 = CpE2 FbmE2 lgC pC = K1 + K2 lg(A C) +

K3 [lg(A C)]2

(62)

lgFpC = C1 + C2 lgPC + C3 [lg(PC)]2

(63)

FbmC = B1 + B2 FMFpC

(64) (65)

CbmC = CpC FbmC K3 [lg(WP)]2

(66)

lgFpP = C1 + C2 lg(WP) + C3 [lg(WP)]2

(67)

FbmP = B1 + B2 FMFpP

(68)

CbmP = CpP FbmP

(69)

lgC pP = K1 + K2 lg(WP) +

where the K1, K2, K3, C1, C2, C3, B1, B2, FM are the cost price correction factor of evaporators “E1” and “E2”, condenser “C” and pump “P”, as shown in Table 1.

lgC pT = K1 + K2 lg(WT) + K3 [lg(WT)]2

(70)

CbmT = CpT FbmT

(71)

where the K1, K2, K3, Fbm are the cost price correction factor of turbine “T”, as shown in Table 1. 5. Validation Numerical model constructed in this paper is validated by the actual engineering data from a R245fa-based ORC plant under the same heat source and heat sink. The numerical results show a very good agreement with the actual engineering, shown in Table 3. The rated power output of the actual plant is 350 kW, with the absolute difference of the

Fig. 5. Thermal efficiency for the flue gas temperature of 280 °C. 821

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800

50

600

40

30

I (kW)

ex (%)

decane nonane cyclohex octane heptane i-octane

200

20 60

(a) ORC

decane nonane cyclohex octane heptane i-octane

400

90

120

150

180

te ( )

210

240

60

(a) ORC

90

120

800

20 60 (b) TSORC

90

120

150

t e1 ( )

I (kW)

ex (%)

te2 ( )

30

210

240

150

180

210

240

150

180

210

240

50 60 70 80 90 100

700

50 60 70 80 90 100

180

te2 ( )

50

40

150

te ( )

600

500

180

210

400 60 (b) TSORC

240

90

120

90

120

t e1 ( )

4

1.15

1.10

ITSORC/IORC

ex,TSORC/ ex,ORC

3

1.05

1.00

0.95

0.90 60 (c)

2

1

90

120

150

180

210

60 (c)

240

te ( )

te ( )

Fig. 6. Exergy efficiency for the flue gas temperature of 280 °C.

Fig. 7. Irreversible loss for the flue gas temperature of 280 °C.

measuring instruments are another aspect that would lead to bring about errors.

Taken the flue gas at a temperature of 280 °C as an example, the thermodynamic and economic performances of ORC and TSORC are compared under different evaporation temperatures with different working fluids. Moreover, the ORC and TSORC with cyclohexane as the working fluid for the flue gas ranging from 200 °C to 300 °C is also analyzed.

6. Results and discussion For the recovery of 200–300 °C flue gas, the critical temperature is crucial for the selection of working fluids. In this study, the six working fluids with critical temperature > 250 °C are chosen, and their physical characteristics of six working fluids are shown in Table 2. 822

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1.0

400

0.9

decane nonane cyclohex octane heptane i-octane

200

VFR

KA (kW/

)

300

0.8

decane nonane cyclohex octane heptane i-octane

0.7

100

60

(a) ORC

90

120

150 te ( )

180

210

0.6 60

240

(a) ORC

90

120

150

180

te ( )

210

240

550

te2 ( ) 50 60 70 80 90 100

450

te2 ( )

0.93

50 60 70 80 90 100

0.90

VFR

KA (kW/

)

500

400

350 60 (b) TSORC

0.87

90

120

150

t e1 ( )

180

210

240

0.84 60 (b) TSORC

6

90

120

90

120

150

180

210

240

150

180

210

240

t e1 ( )

1.3

VFRTSORC/VFRORC

KATSORC/KAORC

5 4 3 2

1.2

1.1

1.0

1 60 (c)

90

120

150

te ( )

180

210

240 60 (c)

Fig. 8. Thermal conductance for the flue gas temperature of 280 °C.

te ( )

Fig. 9. Volumetric flow ratio for the flue gas temperature of 280 °C.

6.1. Net power output

Under a given te1, Wnet,TSORC increases with te2. This is similarly to the ORC, as the increasing of te1, the mass flow of working fluid in highpressure stage decreases but the inlet enthalpy of the turbine increases. In addition, Wnet,TSORC reaches the highest value of 408.6 kW when evaporation temperatures are 100 °C and 180 °C. Fig. 4(c) shows the comparison of ORC and TSORC on Wnet, as the increasing of te, the ratio of Wnet,TSORC/Wnet,ORC increases and is all higher than 1. Compared with the ORC, the TSORC significant promotes Wnet, and Wnet,TSORC/ Wnet,ORC = 1.81 for te1 = 240 °C and te2 = 80 °C.

Fig. 4(a) indicates the influence of evaporation temperature (te) on net power output Wnet,ORC. With the increasing of te, Wnet,ORC increases first and then decreases. The change trend of Wnet,ORC is due to the increase of the turbine inlet temperature and the decrease of mass flow of working fluids with the increasing te. The i-octane exhibites a good performance on Wnet,ORC, and Wnet,ORC reaches the highest value of 346.8 kW for te = 150 °C. Fig. 4(b) describes the influence of highpressure evaporation temperature (te1) and low-pressure evaporation temperature (te2) on Wnet,TSORC for cyclohexane. For the given te2, Wnet,TSORC increases first and then decreases with the increasing of te1. 823

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14

0.16 decane nonane cyclohex octane heptane i-octane

0.12

12

0.10

8

6

0.08

60

(a) ORC

90

120

150

180

te ( )

210

4 60

240

(a) ORC

te2 ( )

0.18

0.15

90

120

0.12

150

180

210

240

150

180

210

240

150

180

210

240

te ( )

te2 ( )

15

50 60 70 80 90 100

PBP (year)

EPC ($/kWh)

decane nonane cyclohex octane heptane i-octane

10

PBP (year)

EPC ($/kWh)

0.14

50 60 70 80 90 100

12

9

0.09

6

60 (b) TSORC

90

120

150

t e1 ( )

180

210

60 (b) TSORC

240

90

120

90

120

t e1 ( )

1.4

1.3

PBPTSORC/PBPORC

EPCTSORC/EPCORC

1.3

1.2

1.1

1.0

1.2

1.1

1.0

0.9 60 (c)

90

120

150

180

210

0.9 60

240

(c)

te ( )

te ( )

Fig. 11. Payback period for the flue gas temperature of 280 °C.

Fig. 10. Electricity production cost for the flue gas temperature of 280 °C.

influence of te1 and te2 on ηth,TSORC for cyclohexane. For a given te2, ηth,TSORC increases first and then decreases with the increasing of te1. For a given te1, ηth,TSORC increases with the increasing of te2. In addition, ηth,TSORC,opt = 16.66%. From Fig. 5(c), as the increasing of te, ηth,TSORC/ ηth,ORC increases first and then decreases and is always lower than 1. ηth,TSORC is lower than ηth,ORC. Fig. 6(a) illustrates the influence of te on ηex,ORC. With the increasing of te, ηex,ORC increases first and then decreases, and it is directly proportional to the net power output and the exergy input by the heat source. The cyclohexane exhibites a good performance on ηex,ORC,

6.2. Thermal and exergetic efficiencies Fig. 5(a) shows the influence of te on ηth,ORC. With the increasing of te, ηth,ORC increases first and then tends to a fixed value. ηth,ORC is directly proportional to the inlet enthalpy of evaporator as shown in Eqs. (5) and (42). The inlet enthalpy of evaporator begins to increase slowly, and this is why the thermal efficiency finally tends to a fixed value. For the working fluids, the cyclohexane exhibites a good performance on ηth,ORC, and ηth,ORC = 20.56% when te = 240 °C. Fig. 5(b) shows the 824

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is lower than that of ORC when te > 220 °C. Compared with the ORC, ηex,TSORC has the highest exergetic efficiency, 9.1%, for te1 = 160 °C and te2 = 110 °C.

3.0

6.3. Irreversible loss

ROROI

2.5

Fig. 7(a) indicates the influence of te on irreversible loss (I) of ORC. I is mainly consisted of four components: evaporator, condenser, turbine and pump, and the evaporator accounts for the largest proportion [46]. With the increasing of te, I decreases, and it is worth mentioning that the change tend becomes gentle for130°C < te < 190 °C. The reduction of irreversible loss is mainly due to the decrease of entropy of evaporator. Fig. 7(b) indicates the influence of te1 and te2 on I of TSORC with cyclohexane. For the given te2, with the increasing of te1, I decreases first and then increases, and for the given te1, I is inversely proportional to te2. Besides, there is the lowest value point for a given te2. For instance, when te2 = 50 °C, the lowest value of I, 585.07 kW, appears at te1 = 140 °C. In addition, the lowest value of I is 425.5 kW for te1 = 180 °C and te2 = 100 °C. From Fig. 7(c), as the increasing of te, ITSORC/IORC decreases first and then increases. ITSORC is lower than IORC for 110 °C < te < 160 °C, but ITSORC is higher than IORC for te < 100 °C and > 170 °C. Compared with the ORC, ITSORC has a lowest value of 6.0% for te1 = 240 °C and te2 = 120 °C.

decane nonane cyclohex octane heptane i-octane

2.0

1.5

60

(a) ORC

90

120

150

te ( )

180

210

240

2.4

ROROI

2.1

6.4. Thermal conductance

te2 ( )

1.8

50 60 70 80 90 100

1.5

1.2 60 (b) TSORC

90

120

150

t e1 ( )

Fig. 8(a) shows the influence of te on the thermal conductance (KA) KA is the product of heat transfer coefficient and heat transfer area, which is a valuation parameter of thermal conductance in evaporator. With the increasing of te, KA decreases. As the increasing of te, KA is directly proportional to the heat transfer area which will be decreased. The cyclohexane and decane have the lower values of KA for te < 170 °C. Fig. 8(b) describes the influence of te1 and te2 on (KA)TSORC with cyclohexane. For the given te2, KA decreases first and then increases with the increasing of te1. For the given te1, KA is proportional to te2. As the increase of te1, the heat transfer temperature difference will be decreased, which leads to increasing heat transfer area. In addition, (KA)TSORC,min = 358.48 kW/°C for te1 = 200 °C and te2 = 50 °C. From Fig. 8(c), (KA)TSORC/(KA)ORC increases with te and is higher than 1. (KA)TSORC is higher than (KA)ORC. ORC.

180

210

240

ROROITSORC/ROROIORC

1.1

1.0

6.5. Volumetric flow ratio Fig. 9(a) shows the influence of te on the volumetric flow ratio of turbine (VFR)ORC. The VFR is the volumetric flow ratio between the inlet and outlet of turbine. It can be observed in Fig. 9(a), with the increasing of te, VFR decreases, which is due to that VFR is inversely proportional to the inlet specific volume of turbine which will be increased as the Eq. (39) shown. The cyclohexane and heptane reach the lower values of VFR for te < 90 °C and te > 90 °C, respectively. Fig. 9(b) describes the influence of te1 and te2 on VFRTSORC with cyclohexane. For a given te2, with the increasing of te1, the VFR decreases first and then increases. For a given te1, the VFR decreases with the increasing of te2. From Fig. 9(c), as the increasing of te, VFRTSORC/ VFRORC increases and is all higher than 1. The VFR of TSORC is higher than that of ORC. Compared with the ORC, the TSORC on VFR has the lowest value when te is 60/70 °C. VFRTSORC reaches the lowest value of 0.849 for te1 = 180 °C and te2 = 60 °C.

0.9

0.8

60 (c)

90

120

150

180

210

240

te ( )

Fig. 12. Rate of return on investment for the flue gas temperature of 280 °C.

which reaches the maximum of 50.04% for te = 180 °C. Fig. 6(b) indicates the influence of te1 and te2 on ηex,TSORC with cyclohexane. For the given te2, the ηex,TSORC increases first and then decreases with the increasing of te1. For a given te1, ηex,TSORC increases with the increasing of te2. The change trend of ηex,TSORC is caused by the increase of outlet exergy value of flue gas and the Wnet, which as shown in Eq. (43). In addition, ηex,TSORC,opt reaches 54.45% for te1 = 100 °C and te2 = 80 °C, Fig. 6(c) shows the comparison of ORC and TSORC on ηex, as the increasing of te, the ηex,TSORC/ηex,ORC increases first and then decreases. ηex of TSORC is higher than that of ORC for te < 220 °C, but ηex of TSORC

6.6. Electricity production cost Fig. 10(a) indicates the influence of te on the electricity production cost (EPC) of ORC. With the increasing of te, the EPC decreases first and then increases. The change for EPC depends on the total components cost and the Wnet, as shown in Eq. (49). There is a proportional relationship between the total component costs and EPC, but the EPC is 825

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Table 3 Main parameters of ORC and TSORC with different flue gas temperature corresponding to the maximal net power output. tga,in/°C

Wnet,max/kW

ηth/%

ηex/%

EPC/$/kWh

PBP/year

ROROI/1

te/°C

200

ORC TSORC TSORC/ORC

135.61 192.51 1.42

12.02 13.29 1.11

40.83 50.51 1.24

0.1238 0.1359 1.10

9.33 10.52 1.13

1.73 1.58 0.91

105 90/140 1.08

220

ORC TSORC TSORC/ORC

176.83 240.15 1.36

12.94 14.37 1.11

42.20 51.77 1.23

0.1057 0.1280 1.21

7.67 9.74 1.27

2.03 1.67 0.83

115 100/140 1.09

240

ORC TSORC TSORC/ORC

224.16 292.17 1.30

13.77 15.06 1.09

43.53 52.52 1.21

0.0925 0.1188 1.28

6.54 8.86 1.35

2.32 1.80 0.78

125 100/150 1.07

260

ORC TSORC TSORC/ORC

278.18 347.41 1.25

14.84 15.78 1.06

45.41 53.30 1.17

0.0816 0.1089 1.34

5.65 7.96 1.41

2.63 1.97 0.75

140 100/160 1.02

280

ORC TSORC TSORC/ORC

339.55 408.63 1.20

15.45 16.66 1.08

46.82 54.45 1.16

0.0743 0.1093 1.47

5.08 7.99 1.57

2.88 1.96 0.68

150 100/180 1.04

300

ORC TSORC TSORC/ORC

409.09 472.54 1.16

16.25 17.57 1.08

48.79 55.45 1.14

0.0686 0.1002 1.46

4.64 7.20 1.55

3.12 2.14 0.68

165 100/200 1.05

Table 4 Parameters of ORC and TSORC with different flue gas temperature corresponding to the highest thermal efficiency. tga,in/°C

ηth,max/%

Wnet/kW

ηex/%

EPC/$/kWh

PBP/year

ROROI/1

te/°C

200

ORC TSORC TSORC/ORC

16.25 13.71 0.84

37.19 191.23 5.14

44.47 51.03 1.15

0.2331 0.1403 0.60

23.91 10.97 0.46

0.92 1.53 1.66

165 100/130 0.72

220

ORC TSORC TSORC/ORC

17.26 14.37 0.83

23.13 240.15 10.38

43.40 51.77 1.19

0.3157 0.1280 0.41

55.29 9.74 0.18

0.68 1.67 2.47

190 100/140 0.66

240

ORC TSORC TSORC/ORC

17.85 15.06 0.84

27.45 292.17 10.64

42.47 52.52 1.24

0.2762 0.1188 0.43

34.68 8.86 0.26

0.78 1.80 2.33

210 100/150 0.64

260

ORC TSORC TSORC/ORC

18.30 15.78 0.86

32.80 347.41 10.59

41.48 53.30 1.29

0.2413 0.1089 0.45

25.56 7.96 0.31

0.89 1.97 2.21

230 100/160 0.62

280

ORC TSORC TSORC/ORC

18.62 16.66 0.90

40.09 408.63 10.19

40.48 54.45 1.35

0.2083 0.1093 0.52

19.59 7.99 0.41

1.03 1.96 1.91

250 100/180 0.63

300

ORC TSORC TSORC/ORC

18.85 17.57 0.93

51.93 472.54 9.10

39.55 55.45 1.40

0.1740 0.1002 0.58

14.79 7.20 0.49

1.23 2.14 1.74

270 100/200 0.64

inversely proportional to Wnet. In addition, the cyclohexane reaches the lowest value of 0.0702 $/kWh for te = 170 °C. Fig. 10(b) describes the influence of te1 and te2 on EPCTSORC with cyclohexane. For a given te2, the EPC decreases first and then increases with te1. For a given te1, with the increasing of te2, the EPC increases for te1 < 160 °C and decreases first and then increases for te1 > 160 °C. The EPC reach the lowest value of 0.085 $/kWh. From Fig. 10(c), EPCTSORC/EPCORC decreases with te. EPCTSORC is higher than EPCORC for te < 240 °C, and it is lower than EPCORC for te = 240 °C. EPCTSORC reaches the lowest value for te1 = 180 °C and te2 = 60 °C. It is worth mentioning that the optimal EPC of TSORC is lower than the electricity price for the industrial use [47].

shown in Fig. 11(a). The cyclohexane reaches the lowest value of 4.77 years for te = 170 °C, which is 5.5% lower than i-octane. Fig. 11(b) shows the influence of te1 and te2 on PBPTSORC with cyclohexane. For a given te2, the PBP decreases first and then increases with te1. For a given te1, the PBP increases with te2 for te1 < 160 °C and decreases first and then increases for te1 > 160 °C. From Fig. 11(c), as the increasing of te, PBPTSORC/PBPORC decreases. PBPTSORC is higher than PBPORC for te < 240 °C, but it is lower than PBPORC for te = 240 °C. PBPTSORC reaches the lowest value for te1 = 180 °C and te2 = 60 °C. 6.8. Rate of return on investment Fig. 12(a) illustrates the influence of te on the rate of return on investment (ROROI) of ORC. With the increasing of te, the ROROI increases first and then decreases. The ROROI is an economic evaluation parameter the same as the EPC and PBP. The ROROI is directly proportional to Wnet and inversely proportional to the total component costs as shown in Eq. (53), so the ROROI is opposite to EPC. The cyclohexane reaches a higher ROROI for te < 190 °C, whereas the heptane has a higher ROROI for te > 190 °C. In addition, the cyclohexane

6.7. Payback period Fig. 11(a) shows the influence of te and working fluids on payback period (PBP) of ORC. With the increasing of te, the EPC decreases first and then increases. The PBP is directly proportional to Wnet and the total components cost as shown in Eq. (50). The factors of influence are same as the EPC, so the change trends of PBP and EPC are similar as 826

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Table 5 Main parameters of ORC and TSORC with flue gas temperature corresponding to the highest exergetic efficiency. tga,in/°C

ηex,max/%

Wnet/kW

ηth/%

EPC/$/kWh

PBP/year

ROROI/1

te/°C

200

ORC TSORC TSORC/ORC

44.90 51.03 1.14

80.84 191.23 2.37

15.47 13.71 0.89

0.1480 0.1403 0.95

11.78 10.97 0.93

1.45 1.53 1.05

150 100/130 0.79

220

ORC TSORC TSORC/ORC

45.20 51.77 1.15

135.66 240.15 1.77

15.75 14.37 0.91

0.1107 0.1280 1.16

8.12 9.74 1.20

1.93 1.67 0.86

155 100/140 0.81

240

ORC TSORC TSORC/ORC

45.72 52.52 1.15

195.43 292.17 1.50

16.01 15.06 0.94

0.0915 0.1188 1.30

6.46 8.86 1.37

2.34 1.80 0.77

160 100/150 0.83

260

ORC TSORC TSORC/ORC

46.50 53.30 1.15

260.33 347.41 1.33

16.26 15.78 0.97

0.0797 0.1089 1.37

5.50 7.96 1.45

2.69 1.97 0.73

165 100/160 0.86

280

ORC TSORC TSORC/ORC

47.58 54.45 1.14

330.60 408.63 1.24

16.49 16.66 1.01

0.0718 0.1093 1.52

4.89 7.99 1.63

2.98 1.96 0.66

170 100/180 0.92

300

ORC TSORC TSORC/ORC

49.06 55.45 1.13

403.35 472.54 1.17

16.93 17.57 1.04

0.0663 0.1002 1.51

4.47 7.20 1.61

3.23 2.14 0.66

180 100/200 0.96

Table 6 Main parameters of ORC and TSORC with flue gas temperature corresponding to EPCmin. tga,in/°C

EPCmin/$/kWh

Wnet/kW

ηth/%

ηex/%

PBP/year

ROROI/1

te/°C

200

ORC TSORC TSORC/ORC

0.1216 0.1333 1.0965

132.62 190.41 1.4358

12.95 12.87 0.9933

42.64 49.51 1.1610

9.12 10.26 1.1250

1.76 1.61 0.9120

115 80/130 0.93

220

ORC TSORC TSORC/ORC

0.1033 0.1176 1.1382

171.21 235.83 1.3774

14.15 13.64 0.9638

44.18 50.21 1.1365

7.46 8.74 1.1720

2.07 1.82 0.8786

130 80/140 0.88

240

ORC TSORC TSORC/ORC

0.0898 0.1049 1.1673

215.56 278.28 1.2910

15.16 14.06 0.9276

45.39 49.73 1.0957

6.32 7.60 1.2021

2.38 2.04 0.8567

145 70/150 0.82

260

ORC TSORC TSORC/ORC

0.0796 0.0943 1.1848

266.49 329.89 1.2379

16.01 14.94 0.9336

46.46 50.58 1.0886

5.49 6.69 1.2182

2.69 2.27 0.8440

160 70/170 0.81

280

ORC TSORC TSORC/ORC

0.0716 0.0851 1.1890

318.43 380.04 1.1935

16.92 15.66 0.9251

47.45 50.75 1.0697

4.87 5.94 1.2189

2.99 2.51 0.8411

180 60/180 0.77

300

ORC TSORC TSORC/ORC

0.0653 0.0772 1.1820

377.93 439.12 1.1619

17.64 16.59 0.9405

48.35 51.69 1.0690

4.39 5.31 1.2075

3.28 2.77 0.8460

200 50/190 0.76

exhibits a good performance on ROROI, reaching the largest ROROI of 3.013 for te = 170 °C, which is 2.8% higher than i-octane. Fig. 12(b) indicates the influence of te1 and te2 on the rate of return on investment (ROROI) of TSORC with cyclohexane. For a fixed te2, the ROROI increases first and then decreases with te1. For the given te1, with the increasing of te2, the ROROI decreases for te1 < 160 °C and increases first and then decreases for te1 > 160 °C. The change of ROROI is caused by the increase of total components cost, and it is opposite to the EPC. From Fig. 12(c), ROROITSORC/ROROIORC increases with te. ROROITSORC is lower than ROROIORC for te < 240 °C, but it is higher than ROROIORC for te = 240 °C. Compared with ORC, the TSORC promotes the ROROI by 7.4% for te1 = 240 °C and te2 = 70 °C. Finally, for the flue gas temperature in the range of 200–300 °C, the thermodynamic and economic results of ORC and TSORC with cyclohexane are listed in Tables 3–8. The optimal working conditions corresponding to the maximums of thermodynamic-economic parameters under each flue gas temperature have been found. Besides, the importance ranking of six evaluation parameters is given. From Table 3, with the increasing of flue gas temperature, Wnet is increases. Besides, Wnet,TSORC is higher than Wnet,ORC. Corresponding to Wnet,max, the

TSORC is better on ηth and ηex, but it is worse on EPC, PBP and ROROI. From Table 4, with the increasing of flue gas temperature, ηth increases. Besides, the ηth,TSORC is lower than ηth,ORC. Corresponding to ηth,max, the TSORC is better on Wnet, ηex, EPC, PBP and ROROI. From Table 5, with the increasing of flue gas temperature, ηex increases. Besides, ηex,TSORC is higher than ηex,ORC. Corresponding to ηex,max, the TSORC is better on Wnet, EPC, PBP and ROROI but worse on ηth. From Table 6, the EPC is decreases with the flue gas temperature, and the EPCTSORC is worse than EPCORC. The EPC can be obtained by combining the total components cost together with Wnet. The improvement on EPC is mainly caused by the increase of Wnet. Corresponding to EPCmax, the TSORC is better on Wnet and ηex but worse on ηth, PBP and ROROI. In addition, EPC TSORC is in the range of 0.077–0.133 $/kWh, which is lower than the electricity price for industrial use [47], the TSORC has a great application prospect. From Table 7, the PBP decreases with the flue gas temperature. Besides, PBP TSORC is higher than PBP ORC. The change of PBP is same as the EPC. Corresponding to maximum of the PBP, the TSORC is better on Wnet and ηex, but worse on ηth, EPC and RORO. From Table 8, with the increasing of flue gas temperature, the ROROI increases. Besides, the ROROI of TSORC is worse than that of ORC. Corresponding to the 827

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Table 7 Parameters of ORC and TSORC with flue gas temperature corresponding to PBPmin. tga,in/°C

PBPmin/year

Wnet/kW

ηth/%

ηex/%

EPC/$/kWh

ROROI/1

te/°C

200

ORC TSORC TSORC/ORC

9.12 10.26 1.12

132.62 190.41 1.44

12.95 12.87 0.99

42.64 49.51 1.16

0.1216 0.1333 1.10

1.76 1.61 0.91

115 80/130 0.93

220

ORC TSORC TSORC/ORC

7.46 8.74 1.17

171.21 235.83 1.38

14.15 13.64 0.96

44.18 50.21 1.14

0.1033 0.1176 1.14

2.07 1.82 0.88

130 80/140 0.88

240

ORC TSORC TSORC/ORC

6.32 7.60 1.20

215.56 278.28 1.29

15.16 14.06 0.93

45.39 49.73 1.10

0.0898 0.1049 1.17

2.38 2.04 0.86

145 70/150 0.82

260

ORC TSORC TSORC/ORC

5.49 6.69 1.22

266.49 329.89 1.24

16.01 14.94 0.93

46.46 50.58 1.09

0.0796 0.0943 1.18

2.69 2.27 0.84

160 70/170 0.81

280

ORC TSORC TSORC/ORC

4.87 5.94 1.22

318.43 380.04 1.19

16.92 15.66 0.93

47.45 50.75 1.07

0.0716 0.0851 1.19

2.99 2.51 0.84

180 60/180 0.77

300

ORC TSORC TSORC/ORC

4.39 5.31 1.21

377.93 439.12 1.16

17.64 16.59 0.94

48.35 51.69 1.07

0.0653 0.0772 1.18

3.28 2.77 0.85

200 50/190 0.76

Table 8 Main parameters of ORC and TSORC with different flue gas temperature corresponding to ROROImax. tga,in/°C

ROROImax/1

Wnet/kW

ηth/%

ηex/%

EPC/$/kWh

PBP/year

te/°C

200

ORC TSORC TSORC/ORC

1.76 1.61 0.91

132.62 190.41 1.44

12.95 12.87 0.99

42.64 49.51 1.16

0.1216 0.1333 1.10

9.12 10.26 1.12

115 80/130 0.93

220

ORC TSORC TSORC/ORC

2.07 1.82 0.88

171.21 235.83 1.38

14.15 13.64 0.96

44.18 50.21 1.14

0.1033 0.1176 1.14

7.46 8.74 1.17

130 80/140 0.88

240

ORC TSORC TSORC/ORC

2.38 2.04 0.86

215.56 278.28 1.29

15.16 14.06 0.93

45.39 49.73 1.10

0.0898 0.1049 1.17

6.32 7.60 1.20

145 70/150 0.82

260

ORC TSORC TSORC/ORC

2.69 2.27 0.84

266.49 329.89 1.24

16.01 14.94 0.93

46.46 50.58 1.09

0.0796 0.0943 1.18

5.49 6.69 1.22

160 70/170 0.81

280

ORC TSORC TSORC/ORC

2.99 2.51 0.84

318.43 380.04 1.19

16.92 15.66 0.93

47.45 50.75 1.07

0.0716 0.0851 1.19

4.87 5.94 1.22

180 60/180 0.77

300

ORC TSORC TSORC/ORC

3.28 2.77 0.85

377.93 439.12 1.16

17.64 16.59 0.94

48.35 51.69 1.07

0.0653 0.0772 1.18

4.39 5.31 1.21

200 50/190 0.76

ROROI, the TSORC is better on Wnet and ηex, but worse on ηth, EPC and PBP. In the above analysis, when flue gas temperature ranges from 200 °C to 300 °C, the higher the flue gas temperature is, the better the thermodynamic and economic performance is. Compared with the ORC, the TSORC promotes the net power output and exergetic efficiency, but the thermal efficiency, EPC, PBP and ROROI have been reduced. Therefore, the TSORC shows the better thermodynamic performance, the economic performance is worse than ORC.

exergetic efficiency under the same flue gas temperature in comparison to ORC, but with a lower thermal efficiency. (2) With the increase of flue gas temperature, the TSORC tends to weaken its thermodynamic advantage, due to that the heat recovery of flue gas for the low-pressure stage is becoming increasingly unworthy. (3) The overall economic performance of the ORC and TSORC is proportional to the grade of flue gas, and the ORC is more competitive than the TSORC. The EPC of TSORC with cyclohexane as the working fluid ranges from 0.077 $/kWh to 0.133 $/kWh, which is lower than commercial power. With the technical progress, the mechanical manufacturing cost tends to decline, so the TSORC will be more competitive in the future.

7. Conclusions The thermodynamic and economic performances of organic Rankine cycle (ORC) or two-stage series organic Rankine cycle (TSORC) were compared in this paper, with the flue gas temperature ranging from 200 to 300 °C. The main conclusions can be drawn from the present study can be summarized as follows:

Declaration of interest statement The authors declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could

(1) From the viewpoint of thermodynamics, the TSORC can recover more heat from the flue gas to enhance the net power output and 828

Energy Conversion and Management 183 (2019) 816–829

T. Li et al.

be construed as influencing the position presented in, or the review of, the manuscript entitled, “Thermodynamic and economic evaluation of the organic Rankine cycle (ORC) and two-stage series organic Rankine cycle (TSORC) for flue gas heat recovery”.

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