Thermodynamic and thermo-economic analysis of dual-pressure and single pressure evaporation organic Rankine cycles

Energy Conversion and Management 177 (2018) 718–736

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

Thermodynamic and thermo-economic analysis of dual-pressure and single pressure evaporation organic Rankine cycles

T

Mingtao Wanga, , Yiguang Chenb, Qiyi Liua, Zhao Yuanyuana ⁎

a b

School of Energy and Power Engineering, Ludong University, 186 Middle Honqi Road, Zhifu District, Yantai 264025, China College of Civil Engineering & Architecture, Jiaxing University, Jiaxing 314001, China

ARTICLE INFO

ABSTRACT

Keywords: Dual pressure Organic Rankine cycle Performance evaluation Electricity production cost

The goal of this paper is to study and evaluate the thermodynamic and the thermo-economic performance of dual-pressure and single pressure evaporation organic Rankine cycle (DORC and SORC) using isobutane as the working fluid. The effects of the two-stage pressures and the heat source inlet temperature on the system performances have been investigated. Then the performance comparisons between SORC and DORC have been conducted at the optimized condition. Results show that the DORC yields more net power than the SORC when the heat source temperature is between 100 and 177.2 °C, and the net power output gains of the DORC are higher at lower heat source temperature. The DORC no longer has the performance advantage as the heat source temperature is above 177.2 °C. The thermo-economic evaluations show that the optimized electricity production cost (EPC) decreases as the heat source temperature rises. Furthermore, optimized EPC of SORC and DORC are nearly equal at the same heat source temperature. For the heat source temperature of 100–177.2 °C, the DORC can significantly increase the net power output, but the thermo-economic performance of DORC is not reduced by system complexity compared to the SORC.

1. Introduction The main energy consumption fields of the world are industry [1] and building [2]. Due to the emission regulations and the increasing of energy prices, waste heat recovery [3] and application of renewable energy [4] have received more and more attention. Organic Rankine cycle (ORC) has been considered as an effective and promising method for translating low-media temperature heat to power [5]. Therefore, it has been widely used in the waste heat recovery [6,7]. However, the thermodynamic performance of the ORC is limited by the cycle structure. Lecompte et al. [8] pointed out that there is a mismatch between the working fluid isothermal phase change process and the heat source temperature linear drop process in the subcritical ORC, which means a large heat transfer difference and increases the exergy loss in the evaporator. In order to improve the temperature match in the evaporator, some scholars introduced the modified ORC, such as the recuperated cycles [9]. Maraver et al. [10] investigated the ORC performance with and without a recuperator. The result showed that the recuperated ORC could improve the thermal efficiency, but reduce the utilization rate of heat source. Therefore it could not increase the net power output. Furthermore, using zeotropic mixtures as working fluids is also an ⁎

approach to improve the temperature match between heat source and working fluid, because the zeotropic mixtures have temperature glides during the phase change process [11,12]. Nevertheless, the temperature match between the zeotropic mixtures and heat source is still not satisfactory, especially when the temperature drop of heat source is much larger than the temperature glide of the zerotropic mixtures in the evaporation process, as shown in Ref. [13]. Liu et al. [14] also found that ORC system using zeotropic mixtures showed better cycle performance when the temperature increase of cooling water was nearly equal to condensation temperature glide; however, there is still large exergy loss in the evaporator. In the transcritical ORC (TORC), the working fluid temperature continues to rise by absorbing heat at the pressure above the critical pressure in the evaporator [15,16]. That will improve the temperature match in the evaporator. Therefore, the average heat transfer temperature difference will be decreased, and the cycle performance would be improved, compared with the subcritical ORC [17,18]. Besides the performance advantages, TORC also have some drawbacks. Li et al. [19] investigated the performances of the subcritical and transcritical ORCs using R1234ze (E) as working fluid. They found that the TORC had better thermal efficiency; however its heat absorption capacity decreased compared to the subcritical ORC. Maraver et al. [10]

Corresponding author. E-mail address: [email protected] (M. Wang).

https://doi.org/10.1016/j.enconman.2018.10.017 Received 15 August 2018; Received in revised form 21 September 2018; Accepted 7 October 2018 0196-8904/ © 2018 Published by Elsevier Ltd.

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Nomenclature A Ash Cai Cp Cbm Ctot cps Dsh do di F Fb Fcr Fp Fbm Fk Gs h he2 ho hi hd hnb hnc hl hload ht hs Jl Jb Js ji m n Nu Pr Pt q Q Re T U v W y

Xtt x ΔT

heat exchanger surface area, m2 bundle cross flow area, m2 annuity of the investment cost, k$ purchased cost, k$ bare module cost, k$ total investment cost, k$ specific heat, kJ/(kg·K) the shell diameter, m diameters of outside tube, m diameters of inside tube, m cost factor correction factor for the effect of convection capital recovery factor pressure factor bare module cost factor maintenance cost factor shell side mass velocity, kg/(m2·s) enthalpy, kJ/(kg·K) boiling heat transfer coefficient, W/(m2·K) heat transfer coefficients, W/(m2·K) heat transfer coefficients for inside flow, W/(m2·K) ideal transfer coefficient for pure cross flow, W/(m2·K) nucleate boiling coefficient, W/(m2·K) natural convection heat transfer coefficient, W/(m2·K) heat-transfer coefficient of the liquid phase, W/(m2·K) annual operation hours, h heat transfer coefficient of tube-side, W/(m2·K) condensation heat transfer coefficient, W/(m2·K) correlation factor for baffle leakage correction factor for bundle bypassing effects correlation factor for variable baffle spacing Colburn j-factor mass flow rate, kg/s economic life time, year Nusselt number Prandtl number tube pitch heat flux, kW/m2 heat capacity, kW Reynolds number temperature, °C overall heat transfer coefficient, W/(m2·K) velocity, m/s power, kW interest rate

Lockhart–Martinelli parameter vapor mass fraction temperature difference, °C

Greek symbols δbb

k µ

bypass clearance, m thermal efficiency heat recovery effectiveness thermal conductivity, W/(m·K) viscosity, kg/(m·s) density, kg/m3

Abbreviations DORC EPC SORC ORC

dual-pressure ORC electricity production cost single-pressure ORC organic Rankine cycle

Subscript a amb bm c cool con d eva h hs i in LMTD l o pp out pum s sub sh tur tot t w

absorption ambient bare module critical cooling water condensation dual-pressure evaporator High-state pressure Heat source inside inlet log-mean temperature difference low-state pressure outside pinch point outlet pump single pressure sub-cooling shell turbine total tube tube wall

recovering the engine waste heat. They found that the dual-loop ORC system could provide a maximum net power output (23.62 kW) and a minimum EPC (0.41 $/kW h) at the rated condition. The thermal efficiency of the system is between 8.97% and 10.19% over the whole operating range. Indeed, dual-loop ORC was more suitable for two or more heat sources heat recovery, as also shown in Ref. [22]. However, this kind of cycle still had high exergy destruction in the evaporator, especially in the high-stage pressure, on account of the isothermal phase change of the working fluid. Different from the dual-loop ORC, the DORC (dual-pressure ORC) system splits the pure working fluid into two evaporation process with different pressure values, which could reduce the heat transfer

researched performances of subcritical and transcritical ORC systems. It was found that the highest second law efficiency was achieved by transcritical ORC using R134a when the geothermal heat source temperature was 170 °C. However, Maraver et al. [10] also emphasized that there were also some drawbacks for the TORC, such as high pressure and high expansion ratios. Besides, dual-loop ORC, also called cascade ORC, was also proposed for heat recovery. Shu et al. [20] investigated the dual-loop ORC to recovery both the flue gas waste heat and cylinder cooling water waste heat. The proposed cycle achieved a power output higher than that of the Steam Rankin cycle. Yang et al. [21] recently analyzed the thermodynamic and economic performance of dual-loop ORC system for

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temperature difference in the evaporator. The advantages of the DORC have been presented by some researches. Franco et al. [23] evaluated the system performance improvement potential of the DORC system. They found that the DORC using isobutene or n-pentane as working fluid could increase the exergy efficiency by 15–21% compared to the SORC in the recovery of geothermal water at 160 °C. Peris et al. [24] investigated system performances of the 6 ORC layouts using 10 working fluids for recovering the jacket water waste heat from the engines. The results showed that the dual-pressure layout using SES36 as working fluids achieved the maximum efficiency of 7.15%. Stijepovic et al. [25] investigated the potential of multi-pressure ORC for recovering the waste heat of a 320 °C heat source using the exergy composite curves approach. The results indicated that, because of the rise of the heat capacity absorbed from the heat source, the power output of the multi-pressure ORC was higher than that of the SORC. It was also found that the third-pressure ORC improved a marginal system performance compared with the DORC system. Guzovic et al. [26] evaluated the feasibility of the DORC for recovering a 175 °C geofluid. The authors showed that the DORC system increased the exergy

efficiency from 52% to 65%, and brought an obvious increase in the net power output from 5270 to 6371 kW. Li et al. [27] investigated and compared the system performances of SORC and DORC (two-stage ORC) for recovering the geothermal heat source of 100 °C. The results showed that the DORC improved the net power output from 622.7 to 669.7 kW compared to the SORC. And the irreversible loss in the evaporator decreased from 360.8 to 295.2 kW. Thierry et al. [28] analyzed the performance of the DORC using mixture as working fluid for recovering waste heat of 90–110 °C. The results indicated that the DORC improved efficiency from 6.85% to 7.70% compared to the SORC when heat source temperature was 90 °C. Li et al. [29] investigated and evaluated system performances of series two-stage ORC (STORC), parallel two-stage ORC (PTORC) and single pressure ORC (SORC) using 90–120 °C geothermal water as heat source. The results showed that PTORC and STORC could reduce exergy loss in the evaporator and improve the net power output. Moreover, it also found that STORC showed best system performance, and could be widely used in engineering. Shokati et al. [30] compared the SORC, DORC, dual-loop ORC and Kalina cycle from the viewpoints of energy, exergy and

90 80

Isobutane

Temperature/K

70

5

3

4

60 50 40

6

2

7

1 8

30 20 10 1.0

1.2

1.4

a) SORC

1.6 1.8 2.0 Entropy/kJ(kg K)-1

2.2

2.4

c) T-s diagram of SORC 90 80

Isobutane

8

Temperatrue/K

70 60

5

50

3

4

2 1

30 1.2

13

12

1.4

1.6

1.8

2.0

Entropy/kJ kg K)-1

b) DORC

d) T-s diagram of DORC Fig. 1. Schematic and T-s diagrams of SORC and DORC.

720

9 10 11

40

20

7

6

2.2

2.4

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performances. In addition, the reasons behind the advantages of DORC system are also investigated.

Table 1 System parameters of the SORC and DORC system models. Parameters

Value

Heat source temperature, Ths Heat source pressure, Phs Heat source mass flow rate, mhs Pinch point temperature difference in the evaporator, ΔTeva Condenser sub-cooling, ΔTsub Cooling water inlet temperate, Tcool Cooling water pressure, Pcool Condensation temperature, Tcon Pinch point temperature difference in the condenser, ΔTcon Turbine efficiency, ηt Pump efficiency, ηp Ambient temperature, Tamb

100–200 °C 0.5–1.6 MPa 5 kg/s 10 °C 2 °C 20 °C 0.101 MPa 35 °C 5 0.85 0.7 25 °C

2. Methodology This section introduces the SORC and DORC systems using isobutane as the working fluid for the following thermodynamic and thermo-economic comparisons. Moreover, boundary conditions, assumptions and optimization process are also presented for the analysis of the cycle performances. 2.1. SORC and DORC Fig. 1 shows the schematic diagrams of SORC and DORC using pure working fluids, and the corresponding T-s diagrams respectively. For the SORC system (Fig. 1a and c), the high pressure working fluid from the pump flows into the evaporator, where it absorbs heat and converts to the superheated vapor (2–5). Then, the superheated vapor enters the turbine to generate power (5–6). The exhausted vapor from turbine goes through the condenser and condenses to the liquid. At last, the liquid working fluid is compressed and enters the evaporator to complete a cycle. For the DORC system (Fig. 1b and d), the working fluid from the preheater 1 is split into two sections. One part enters the vaporizer and absorbs heat (3–4). The other part flows into the pump 2 and is further compressed to the high-stage pressure (3–5). Then it flows into the high-stage evaporator (preheater1, vaporizer 2 and superheater 2), absorbs heat and then becomes superheated (5–8). The superheated vapor expands in the high-pressure turbine (8–9) and then mixes with the working fluid from the vaporizer 1 in the inlet of the turbine 1. The mixed working fluid flows into the turbine 1 and undergoes the second expansion (10–11). The exhaust vapor from the turbine 1 enters into the condenser and condenses to the liquid (12–1). At last, the liquid working fluid is compressed and enters the preheater1, where the whole cycle is completed.

exergoeconomic. They found that the net power output of the DORC was maximum, 15.22% higher than the SORC. Manente et al. [31] proposed and compared the SORC and DORC using geothermal heat source of 100–200 °C. The results indicated whether the thermodynamic performance of the DORC was better than that of SORC depended on the working fluid and heat source temperature. The increment of the power output of the DORC decreased, and at last disappeared as the temperature of heat source increased. Sadeghi et al. [32] analyzed and compared the performances of the simple ORC, PTPRC and STORC using zeotropic working fluids for heat recovery from geothermal water. The minimum turbine size parameter (TSP) and maximum net power output were chosen as the optimized goals. It was observed that STORC yielded the maximum net power and R407A was the most suitable working fluid candidate. Li et al. [33] studied the applicable range of the DORC and investigated the influences of the working fluid critical temperature on the suitable heat source temperature range. Results showed that the SORC and DORC systems had different heat source temperature applicable range, which was closely relevant to the working fluid critical properties. In addition, they found that there was a linear relationship between applicable range of heat source temperature and the critical temperature of the working fluid. Li et al. [34] investigated and evaluated the thermal economic performance of the separate and induction turbine layouts, and analyzed the effects of high-stage and low-stage pressure on the thermal economic performance. They found that induction layout produced more net power, and the maximum decrement of the specific investment cost was 34.2%. However, the existing researches on DORC mainly concentrated on the system parameters optimization or the performance comparisons with other ORC layouts, and few published researches focus on the DORC thermo-economic performance. In fact, the DORC system is more complex because of the two evaporation process, two turbines and pumps. Although the thermodynamic performance of the DORC is better than that of the SORC, components investment of the DORC also increases simultaneously. Therefore, it is essential to investigate the applicability of the DORC from the aspect of the thermo-economic. In this paper, the thermodynamic and the economic performances of DORC and SORC are investigated and compared. The thermodynamic and economic models of the SORC and DORC systems are built by the Matlab software. The influences of the high-stage and low-stage pressures on SORC and DORC systems parameters (Outlet temperature of heat source, working fluid mass flow rate, thermal efficiency, net power output, investment cost and electricity production cost) are investigated. On the basic of this, the optimization processes are carried out to compare the thermodynamic and economic performances of DORC and SORC systems. Then the feasibility and advantage of the DORC system is discussed in view of thermodynamic and economic

2.2. System parameters and assumptions The models of the SORC and DORC are established using Matlab software and the REFPROP 9.0. System parameters of SORC and DORC are listed in the Table 1. For simplifying the analysis, the assumptions of the models are presented as follows. (1) The SORC and DORC systems operate at a steady state; (2) The pressure drop of exchangers and the pipe heat dissipating capacity could be neglected; (3) The input power of the cooling pump is calculated as 1% of the total capacity of the heat release in the condenser [35]; (4) The counter-current flow exchangers are adopted; (5) The maximum pressure (Pe,max) is set as 0.9Pc for the SORC and Table 2 The ranges of the optimized parameters of the SORC and DORC systems [31,33].

721

Cycle layout

Parameters

Maximum value

Minimum value

SORC

Evaporation pressure, Peva Superheat degree, ΔTeva

0.9 Pc /

Pcon + 100 kPa 2K

DORC

High-stage pressure of, P,h Low-stage pressure of, P,l Superheat degree of the highstage, ΔTh Superheat degree of the low stage, ΔTl

0.9 Pc 0.9Pc-100 kPa /

Pe,l + 100 kPa Pcon + 100 kPa 2K

/

0.01 K

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Heat

Ts1 Temperature

are the enthalpies of the heat source water in the evaporator inlet and outlet respectively, kJ/kg. Thus, the mass flow rate of the working fluid of SORC is

Tin

SORC ce sour

msw =

Tsout Working fluid

3

(2)

The equations used to analyze the performance of SORC are shown in Table 3. The net power of the SORC system can be calculated as follows:

5 4

(3)

Wsnet = Wstur Wspum Wscool

where Wscool is the pump power, assumed as 1% of the heat rejection in the condenser, kW. According to Fig. 2b, the mass flow rate of the working fluid in the vaporizer 2 and vaporizer 1 are

2 Heating capacity

mdh =

mhs (hdin hd2 ) h7 h5

(4)

mdl =

mhs ·(h d2 h dout ) h 4 h2

(5)

a) SORC Tdin

DORC

Temperature

Qa (h5 h2 )

Heat

Td3

s

e ourc

Td2

Td1 7 6

Tdout

where hd2 is the enthalpy of heat source water at the temperature of Td2 in Fig. 2b, kJ/kg. The equations used to analyze the performance of DORC are shown in Table 4. The net power of the DORC system is calculated as:

Working fluid

Therefore, the thermal efficiency of SORC and DORC can be determined by:

4

3

(6)

Wdnet = Wdtur1 + Wdtur2 Wdpum1 Wdpum1 Wdcool

5

(7)

= Wnet / Qa

2

by

Heating capacity

=

b) DORC

Table 3 Equations used in the energy analysis of SORC. Equation

Turbine

Wstur = msw ·(h5 h6) = m sw ·(h5 h6s)·

Pump

Evaporator Condenser

Wspum = msw ·(h2 h1) = msw ·(h2s h1)/

(8)

2.4. Economic models 2.4.1. Heat transfer calculation The shell and tube heat exchanger is used in this paper. The heat source water and cooling water flow in the tube side, and the working fluid flows in the shell side. The heat-transfer surface of the exchangers can be obtained by:

tur pum

Qeva = mhs·(h sin h sout ) Qcon = m sw ·(h7 h1)

A= DORC [33]; (6) The working fluid from turbine is superheated; (7) The ranges of the optimized parameters are shown in Table 2.

Q U · TLMTD

(9)

Table 4 Equations used in the energy analysis of DORC.

2.3. Thermodynamic models

Component

Equation

Turbine1

Wdtur1 = (mdh + mdl )·(h10 h11) = (mdh + mdl )·(h10 h11s)·

Turbine2 Pump 1

Fig. 2 shows the temperature profiles in the evaporators of the SORC and DORC. According to Fig. 2a, the heat absorption of the SORC from the heat source is

Qa = mhs ·(hsin hsout )

Qa mhs ·(hsin hamb)

where hamb is the enthalpy of heat source water at the ambient temperature, kJ/kg.

Fig. 2. Temperature profiles in the evaporator of SORC and DORC.

Component

And the heat recovery effectiveness of SORC and DORC is calculated

(1)

where mhs is the mass flow rate of the heat source, kg/s; hsin and hsout

722

Wdtur2 = m dh ·(h8 h 9) = mdh (h8 h 9s)·

Wdpum1 = (mdh + mdl)·(h2 h1) = (mdh + mdl )·(h2s h1)/

Pump 2

Wdpum2 = mdh ·(h5 h3) = m dh (h5s h3)/

Evaporator Condenser

Qeva = mhs·(h din h dout ) Qcon = (mdh + m dl )·(h12 h1)

tur

tur

pum

pum

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where A is the heat transfer area, m2; Q is the heat transfer capacity of the heat exchanger, kW; ΔTLMTD is the log-mean temperature difference of the heat exchanger, given by

Tmax

TLMTD =

ln(

Tmin Tmax ) Tmin

where y is the interest rate, and assumed as 5%; n is economic life time, assumed as 15 years [40]. 2.5. Optimization process

(10)

The net power output and EPC are used to evaluate the system performance. For SORC system, the decision variables of the optimization process are the evaporation pressure and the superheating degree. For the DORC system, the high and low stage evaporation pressures along with the superheat degrees are optimized. The following procedure is the optimization process for the DORC system, which is shown in Fig. 3. The optimization process of the DORC system is similar.

The overall heat transfer coefficient of the heat exchanger is

1 1 1 d d d = + · o + o ·lg o U ho hi di 2µ µ

(11)

where μ is the tube thermal conductivity, W/(m·K); do and di are the outside and inside diameters of the tube, m; ho and hi are the heat transfer coefficients for outside and inside flows, respectively, W/ (m2·K).

(1) The high-stage pressure and low-stage pressures are divided into 50 equal parts between the maximum and minimum values respectively; (2) The initial superheat degree of the high stage evaporator is set as 2 K. The system performances are calculated according to the above conditions; (3) With the calculation results to determine whether the working fluid from turbine 2 is superheated. If the result is satisfactory, go to step 4; otherwise, increasing superheat degree of the evaporator 2 and repeating the calculation until the working fluids is superheated. (4) According to the superheat degree obtained from step 3, the system performances at different pressures are calculated. The operation pressures which could not meet the demand of pinch point temperature difference (PPTD) in the evaporator are ignored.

2.4.1.1. Heat transfer calculation of shell side. The single phase heat transfer coefficient of the shell side is calculated by the correlation of Bell-Dlaware [36]:

ho1 = h id Jc Jl Jb Js

(12)

The boiling heat transfer coefficient of the evaporator is calculated as [37]:

he2 = h nb Fb + h nc

(13)

The condensation heat transfer coefficient for the two-phase fluid in the condenser is calculated as the following [38]:

hs / hl = 1.26Xtt 0.78

(14)

The parameters of Eqs. (12)–(14) are given in Appendix A.1–3. 2.4.1.2. Heat transfer of the tube side. The correlation of Petukhow and Popov [39] required for the calculation of the single phase heat transfer coefficient of the tube side can be shown in the following equation.

ht =

Nu·k di

(15)

The parameters of Eq. (14) are given in Appendix A.4 2.4.2. Investment cost calculation The total investment cost of the systems in 2014 is calculated by [40]:

Ctot2014 =

Ctot2001 CEPCI2014 CEPCI2014

Ctot2001 = Cbm,eva + Cbm,con + Cbm,tur + Cbm,pum

(16) (17)

where CEPCI stands for Chemical Engineering Plant Cost Index; CEPCI2001 = 382, CEPCI2014 = 586.77 [41]. The bare module cost for evaporator, condenser, turbine, and pump are given in Appendix B. The electricity production cost (EPC) can be calculated by:

EPC =

Cai + Fk Ctot2014 Wnet ·hload

(18)

where Fk is the maintenance cost factor, assumed as 1.65% [41]; hload is the annual operation hours, and its value is 7446 h/year [42]; Cai is the annuity of the investment cost, estimated as:

Cai = Ctot2014· Fcr

(19)

where Fcr is the capital recovery factor, and is calculated as:

Fcr =

y (1 + y )n (1 + y )n 1

Fig. 3. Diagram of the optimization process of DORC.

(20)

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position of the pinch point temperature difference (ΔTpp) in the evaporator occurs at ΔTpp1, as shown in Fig. 5. In case of satisfying the ΔTpp, rising evaporation pressure could lead to increase of the heat source outlet temperature, as shown in Fig. 6, which means the utilization rate of the heat source decreases. On the other hand, increasing Pe means the increase of the thermal efficiency. Therefore, there exists an optimal Pe for the SORC system to obtain the maximum Wnet (Wmax). When Ths increases to 180–200 °C, the position of the ΔTppwill move from ΔTpp1 to ΔTpp2, as shown in Fig. 5. Tout depends on the working fluid temperature from the pump1, and it keeps basically constant as shown in Fig. 6. In other words, the utilization of the heat source almost remains unchanged. Therefore, Wnet is basically proportional to the thermal efficiency of SORC, and increases with the rise of Pe. Moreover, it is apparent that Wnet increase with the rise of Ths, due to the increase of Ths and the decrease of Tout. The green five stars points in the Figs. 4 and 6 are Wmax and the corresponding Pe and Tout at different Ths. In this paper, parameters of the system corresponding to the maximum Wnet are called optimized parameters.

Table 5 System input parameters and boundary conditions of the system models [31]. Parameters

Value

Working fluid Heat source temperature, Ths Heat source mass flow rate, mhs Pinch point temperature difference, ΔTeva Condenser sub-cooling, ΔTsub Condensation temperature, Tcon Turbine efficiency, ηt Pump efficiency, ηp Ambient temperature, Tamb

Isobutane 100 or 150 °C 100 kg/s 10 °C 2 °C 35 °C 0.85 0.7 20 °C

3. Model verification The calculation results of this paper were compared with the data presented by Manente et al. [31] for SORC and DORC. The same input parameters and boundary conditions are shown in Table 5. The output parameters and comparison results of the SORC and DORC at heat source temperature of 100 °C and 150 °C are presented in Tables 6 and 7 respectively. It can be seen that the maximum relative error is 3.56%, which is the mass flow rate of the working fluid in the SORC, followed by 3.42%, which is the heat recovery effectiveness. Other relative errors are usually less than 3%. Moreover, it should be noted that the relative errors of the net power output are less than 0.2%. The error reasons are as follows. In this paper, the models of the SORC and DORC are built using Matlab software and the REFPROP 9.0, whereas in Ref. [33], the models are established using the EES (Engineering Equation Solver) software and its internal fluids properties library. Therefore, the relative errors are mainly caused by the different fluids properties library (EES 10.101 vs. REFPROP 9.0) and different calculation step lengths. From the comparison results, it can be seen that the calculation models of this paper are reliable.

4.1.2. DORC Compared with the SORC system, the DORC system is more complex which is affected by the high stage pressure (Ph) and the low stage pressure (Pl) simultaneously. As Ths increases, the variations of Tout, thermal efficiency (ηth), working fluid mass flow rate (M) and Wnet are similar. Therefore, take Ths = 100 °C as an example to analyze the parameters variations of the DORC. 4.1.2.1. Outlet temperature of the heat source. Fig. 7 shows the variations of Tout with Ph and Pl of the DORC system when Ths is 100 °C. It is apparent that Tout increases with the increase of Pl, while basically remains unchanged with the increase of Ph. The reason is as follows: for the DORC system, when Ths is 100 °C, the optimized Ph and Pl are 572.9 kPa and 1160.1 kPa respectively, and the position of ΔTpp in low stage evaporator occurs between Point 1 and Point 2 in Fig. 8a. If Pl decreases from 772.9 kPa to 572.9 kPa, the position of ΔTpp will move from 1–2 to 1′–2′. With the limitation of ΔTpp, Tout decreases from 58.6 °C to 49.3 °C. If Ph increases from 1160.1 kPa to 1360.1 kPa, the position of ΔTpp in the higher evaporator will move from 3–4 to 3′–4′. While Tout basically remains unchanged (58.5 °C −58.6 °C), because of the fact that the position of ΔTpp in the high stage evaporator is more far away from the heat source outlet, as shown in Fig. 8b. Therefore, the variations of Ph have little effect on Tout.

4. Results and discussions 4.1. Thermodynamic performance analysis 4.1.1. SORC Fig. 4 presents the influences of the heat source inlet temperature (Ths) and evaporation pressure (Pe) on the variation of the net output power (Wnet) of the SORC. It is obvious that, when Ths is 100–160 °C, Wnet firstly increases and then decreases as Pe increases. When Ths is higher than 160 °C (180 and 200 °C), Wnet increases with the rise of Ths. The reason is as follows: When Ths is between 100 and 160 °C, the

4.1.2.2. Net power output of turbines. Fig. 9 shows net power output of the two turbines over the Ph and Pl when Ths is 100 °C. The variations of Mh, Ml and Mtot are presented in Fig. 10. Increasing Pl has two conflicting influences on Wtur1, one is increasing the pressure

Table 6 Comparison of the results in this paper and the data presented by Manente et al. [31] for SORC. Isobutane

Pe (kPa) m (kg/s) T3 (°C) Tout (°C) Wnet (kW) Φ (%) ηth (%) ηsys (%)

Ths = 100 °C

Ths = 150 °C

This paper

Manente et al.

Relative error

This paper

Manente et al.

Relative error

996.98 35.92 66.05 68.75 755.1 39.16 5.75 2.253

975 37.2 65.1 67.7 756.0 40.5 5.58 2.257

2.2% −3.56% 1.44% 1.53% 0.12% 3.42% 3.0% 0.18%

1861.4 82.35 96.53 72.75 3269.9 59.74 10 5.97

1860 82.3 96.6 72.7 3270 59.7 9.99 5.969

0.07% 0.06% −0.07% 0.07% 0 0.07% 0.1% 0.017%

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Table 7 Comparison of the results in this paper and the data presented by Manente et al. [31] for DORC. Isobutane

Ths = 100 °C

Php (kPa) Php (kPa) mhp (kg/s) mlp (kg/s) Tsat_hp (°C) Tsat_lp (°C) Tout (°C) Wnet (kW) Φ (%) ηth (%) ηsys (%)

450 400 350

This paper

Manente et al.

Relative error

This paper

Manente et al.

Relative error

1160.1 772.89 26.56 21.44 72.99 55 58.6 960.16 51.85 5.53 2.87

1170 795 26.0 20.8 73.5 56.2 59.6 961.5 50.6 5.67 2.87

−0.08% −2.86% 2.1% 2.98% −0.7% −2.18% −1.7% −0.14% 2.4% −2.5% 0

2534.6 1241.1 62.61 33.16 113.5 76.18 60.37 3868.1 69.2 10.21 7.06

2530 1250 62.9 32.8 113.3 76.6 60.5 3871 69.2 10.22 7.066

0.18% −0.7% −0.463% 1.09% 0.18% −0.55% 0.21% 0.075% 0 0.1% 0.09%

Ths=100 oC

Ths=180 oC

Ths=120 oC

Ths=200 oC

420 410

413.9

Ths=140 oC

400

358.3

Ths=160 oC

300

390 380

250 200

206.3

150

1000

Ths=180 oC Ths=200 oC

360

1500

2000

2500

3000

310 300 600 900 1200 1500 1800 2100 2400 2700 3000 3300 Pe/kPa

3500

Fig. 4. Wnet of the SORC system.

Fig. 6. Tout of the SORC system.

180

Tout/oC

1500

160

Isobutane Heat source

140 120

1400 1300 1200

pp1

Ph/kPa

Temperature/oC

Ths=160 oC

320

Pe/kPa

100 80

40

0

400

800

1200

1600

2000

2400

2800

1000 Ths=100 oC

800

pp2

-400

1100

900

Isobutane Heat source

60

20

Ths=140 oC

330

37.8 500

Ths=120 oC

340

75.2

50

370

Ths=100 oC

350

128.8

100

0

Tout/oC

Wnet/kW

Ths = 150 °C

700

3200

48.0 50.6 53.3 55.9 58.5 61.1 63.8 66.4 69.0 71.6 74.3 76.9 79.5 82.1 84.8 87.4 90.0

600 700 800 900 1000 1100 1200 1300 1400

Heat absorption capacity/kW

Pl/kPa

Fig. 5. Temperature profiles in the evaporator of SORC.

Fig. 7. Outlet temperature of heat source of DORC.

difference of turbine1 which has a positive influence on Wtur1, and the other is the reduction of total mass flow rate (Mtot) that has a negative effect on Wtur1. Therefore, Wtur1 increases firstly and then decreases as Pl increases, as shown in Fig. 9a. Moreover, it can be seen that Wtur1 most remain unchanged as Ph increases. This is because the Mtot and pressure difference of pump1

remain basically unchanged, which leads to no considerable variation in Wtur1, as Ph increases. As shown in Fig. 9b, the power output of turbine 2 (Wtur2) increases firstly and then decreases as Ph increases. Same as Pl in Fig. 9a, increasing Ph would lead to the increase of the pressure difference of

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Isobutane Heat source Isobutane Heat source

90

Temperature/oC

80 70

o

Tout=58.6 C

60 50 40

2' Tout=49.3 oC

3' Ph=1160.1 kPa

Pl=772.9 kPa

33.40 36.06 38.72

900

Pl=572.9 kPa

41.38

800

o

Ths=100 C

700

Isobutane Heat source Isobutane Heat source

90 80

4'

Tout=58.6 oC

3 2'

2

o

Tout=58.5 C

1

1'

Wt2/kW

1500

Ph=

1400 1300

3'

1200

Ph=1160.1 kPa

Pe=772.9 kPa

1100 1000 Ths=100 oC

900

40

800

30 -200 -100

0

46.70

a ) Turbine 1

1360.1 kPa

4

44.04

600 700 800 900 1000 1100 1200 1300 1400 Pl/kPa

Ph/kPa

100

Temperature/oC

30.74

1000

a) Decreasing Pl

50

28.08

1100

-200 -100 0 100 200 300 400 500 600 700 800 900 10001100 Qe/kW

60

25.42

1200

30

70

22.76

1300

3

1'

20.10

1400

4'

4

2

1

Wt1/kW

1500

Ph/kPa

100

700

100 200 300 400 500 600 700 800 900

0.50 2.63 4.75 6.88 9.00 11.13 13.25 15.38 17.50 19.63 21.75 23.88 26.00 28.13 30.25 32.38 34.50

600 700 800 900 1000 1100 1200 1300 1400

Qe/kW

Pl/kPa

b) Increasing Ph

b) Turbine2

Fig. 8. Temperature profiles in the evaporator of DORC.

Fig. 9. The power output of two turbines of DORC over Ph and Pl.

turbine 2 and the decrease of the Mh. It also can be seen that Wt1 decreases with the increase of Pl. This is because of the turbine1 pressure difference and Mtot decrease as the Pl increases, which leads to reduction of Wtur1. 4.1.2.3. Thermal efficiency. Fig. 11 illustrates the effects of Ph and Pl on the thermal efficiency (ηth) of the DORC. As above analysis, Wt2 increases firstly and then decreases, whereas Wt1 (Fig. 9a) and Tout (Fig. 7) most remain unchanged with the increase of Ph. Therefore, ηth increases firstly and then decreases with the rise of Ph. Moreover, it is apparent that ηth increases as Pl increases. The main reason is that the increase of Pl leads to the rise of Tout, which decreases the utilization rate of the heat source.

and Wt2: Wt1 increases firstly and then decreases, whereas Wt2 remains basically unchanged with the increase of the Ph. Increasing of Pl also has the similar effects on the Wt1 and Wt2. Consequence of above mentioned effects leads to change trend in Wnet. The higher Wnet can be seen in the range of 1000 kPa < Ph < 1400 kPa and 650 kPa < Pl < 1000 kPa from Fig. 12a. When Ths is 100 °C, the maximum Wnet (Wmax) is 48.0 kW, and the optimized pressures (Ph and Pl) are 1160 kPa and 773 kPa respectively. Fig. 12b–d are the Wnet contours when Ths are 120 °C, 140 °C and 160 °C respectively. The contours show that it has the same tendency of changes, and the reason is also similar. Moreover, the maximum Wnet markedly increases from 48.0 kW to 241.7 kW as Ths rises from 100 °C to 160 °C due to the rise of the optimized Ph, Pl and Mtot.

4.1.2.4. Net power output. Fig. 12a shows the variations of Wnet of the DORC system over Ph and Pl, when Ths is 100 °C. It is apparent that the Wnet increases firstly and then decreases as Ph and Pl increases. The reason is explained as follows. Increasing Ph has different effects on Wt1

4.1.3. Thermodynamic performance comparison Fig. 13a presents maximized net power outputs (Wmax) of SORC and DORC under the optimized operation conditions. For the Ths of 100–160 °C, Wmax of the SORC increases from 37.8 to 206.3 kW,

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Mh/kg s-1

1400 1300

Ph/kPa

1200 1100 1000 Ths=100 oC

900 800 700

1400 1300 1200

700

Ph/kPa

Fig. 11. Thermal efficiency of DORC.

Ml/kg s-1

1200 1100 1000

Ths=100 oC

900 800 700

0.26 0.43 0.59 0.76 0.93 1.10 1.26 1.43 1.60 1.77 1.93 2.10 2.27 2.44 2.60 2.77 2.94

whereas that of the DORC rises from 48 to 241.7 KW. It is apparent that Wmax of DORC is larger than that of SORC at the same heat source inlet temperature. The reason for the gains of Wnet in DORC is as follows. The Wmax depends on the heat absorption capacity and the thermal efficiency. Fig. 13b shows the thermal efficiency of the SORC and DORC. It is found that the thermal efficiency of DORC show no obvious advantages, even slightly lower than that of SORC at heat source temperature of 100 °C (5.53% vs. 5.75%). However, the heat absorption capacity of the DORC increases significantly compared to the SORC at the same Ths, as shown in Fig. 13c. Therefore, the DORC system yields more net power than SORC system under the same heat source inlet temperature. Moreover, it can be found from Fig. 13a that the increment of Wmax decreases from 21.3% to 14.6% when Ths increases from 100 °C to 160 °C. That is to say that the Wmax increment of DORC decrease with the increase of the Ths, and DORC system has more advantage at lower Ths. From the exergy point of view, the average heat transfer temperature difference in the evaporator of DORC is smaller than that of SORC, which leads to the lower exergy loss in the evaporator. Accordingly, DORC shows better thermodynamic performance than SORC at the same heat source inlet temperature of 100 to 160 °C. It should be noted that when Ths increases to 177.2 °C, the thermal match in the evaporator of DORC and SORC are almost equal, as shown in Fig. 14. When Ths is higher than 177.2 °C, DORC system no longer has performance advantage, while its layout will be more complex. In a word, for the working fluids of isobutene, the SORC system is beneficial for Ths of 177.2 °C to 200 °C, while DORC system would show better performance for Ths of 100 °C to 177.2 °C under the boundary conditions of this paper. Therefore, in the next part, the thermo-economic performance comparisons of SORC and DORC are conducted at Ths of 100–160 °C.

600 700 800 900 1000 1100 1200 1300 1400 Pl/kPa

b) Low-stage pressure Mtot(kg/s)

1500

0.53 0.70 0.86 1.03 1.20 1.36 1.53 1.70 1.87 2.03 2.20 2.37 2.53 2.70 2.87 3.03 3.20

1400 1300

Ph/kPa

1200 1100 1000 900 800 700

0.016 0.021 0.025 0.029 0.034 0.038 0.043 0.047 0.051 0.056 0.060 0.065 0.069 0.073 0.078 0.082 0.087

600 700 800 900 1000 1100 1200 1300 1400 Pl/kPa

a) High-stage pressure

1300

Ths=100oC

1000

800

Pl/kPa

1400

1100

900

600 700 800 900 1000 1100 1200 1300 1400

1500

th

1500

0.19 0.36 0.52 0.69 0.85 1.02 1.19 1.35 1.52 1.69 1.85 2.02 2.19 2.35 2.52 2.68 2.85

Ph/kPa

1500

600 700 800 900 1000 1100 1200 1300 1400 Pl/kPa

4.2. Thermo-economic performance analysis 4.2.1. SORC According to the above analysis, it could be found that Wmax of DORC is larger than that of SORC when Ths is 100–177.2 °C. However, the layout of DORC is more complex and expensive. Therefore, it is essential to make a thermo-economic comparison between DORC and SORC.

c) Total mass flow rate

Fig. 10. Mass flow rate of working fluid of DORC.

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Wnet/kW

1400 1300 48.0 kW

Ph=1160kPa

Ph/kPa

1200 1100 1000 900 800

Ths=100 oC

700 600

Pl=773kPa

25 27 28 30 31 33 34 36 38 39 41 42 44 45 47 48 50

Wnet/kPa

3200 2800 2400

155.1kW

Ph/kPa

1500

2000

Ph=2130 kPa

1600 1200 800 800

600 700 800 900 1000 1100 1200 1300 1400 Pl/kPa

1200

1600

1800 93.3 kW

Ph/kPa

1600

Ph=1566 kPa

1400 1200 1000

Ths=120 oC

800

Pl=929 kPa 600

2400

2800

c) Ths=140 oC Wnet/kW

3600

40 43 47 50 53 57 60 63 67 70 73 77 80 83 87 90 93

3200

Wnet/kW

Ph=3266.1 kPa 241.7 kW

2800 2400 Ph/kPa

2000

2000

Pl/kPa

a) Ths=100 oC 2200

Ths=140 oC

Pl=1137 kPa

65.0 70.7 76.3 82.0 87.6 93.3 98.9 104.6 110.3 115.9 121.6 127.2 132.9 138.5 144.2 149.8 155.5

2000 1600 1200

Pl=1397.2 kPa

Ths=160 oC

800

800 1000 1200 1400 1600 1800 2000 Pl/kPa

800

1200

b) Ths=120 oC

1600 2000 Pl/kPa

2400

150 156 162 167 173 179 185 190 196 202 208 213 219 225 231 236 242

2800

d) Ths=160 oC Fig. 12. The net power output of DORC over Ph and Pl.

Fig. 15 shows the total investment cost (Ctot) of SORC over Pe for different Ths. As can be seen, the changing trends for Ctot and Wnet are the same as the Pe increases. The reasons are as follows. The investment cost of the turbine accounts for more than 50% of Ctot. Therefore, Wnet is the most important factor affecting Ctot. Consequently, Ctot increases firstly and then decreases as Pe increases. Moreover, it can be seen that Ctot increases dramatically with the increase of Ths due to the increase of the system capacity. Fig. 16 presents the EPC of SORC system over Pe for different Ths. The change tendency of the EPC is opposite to the Ctot, and reasons are similar. It should be noted that EPC decreases with the increase of Ths, which means that the SORC shows better thermo-economic performance at higher Ths. The points of the green five stars in Figs. 15 and 16 are the system parameters corresponding to Wmax. It can be seen than the optimized EPC decreases from 0.24 $/kW h to 0.13 $/kW h, and the optimized Ctot increases from 607.5 k$ to 1785.6 k$ as Ths increases from 100 to 160 °C

4.2.2. DORC Fig. 17a shows the variation of the investment cost of pump1 (Cpum1) over Ph and Pl when Ths is 100 °C. Increasing Pl has two conflicting effects on the input power of pump1 (Wpum1), one is increasing the pressure difference of pump1 which leads to the increase of Wpum1 and the other is that it has a negative impact on Wpum1 by the reduction of the Mtot. And Wpum1 is the main factor affecting Cpum1. Therefore, as Pl increases, Cpum1increases firstly and then decreases. In addition, the increase of Ph has little effect on the pressure difference of pump1 and Mtot. So Wtur1 and Cpum1 basically remains unchanged as Ph increases. Fig. 17b outlines the effect of Ph and Pl on the investment cost of pump 2 (Cpum2). By raising Pl, the pressure difference of pump 2 decreases and Mh basically remains unchanged. Therefore, Cpum2 decreases as Pl increases. Same as Pl in Fig. 16a, the increase of Ph also has two opposite effects on the Wpum2: increasing the pressure difference of pump 2 and decreasing Mh. Therefore, Wpum2 and Cpum2 firstly increase and then decrease with the increase of Ph. The effect of Ph and Pl on the variation of investment cost of two pumps (Cpum) is depicted in Fig. 18a. It is obvious that Cpum firstly

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160

160

128.8

140

17.1%

75.2 93.3 19.4% 37.8

100

48.0 0

50

SORC DORC

37.8

21.3%

48.1

100

Ths1

140

155.5

120

Tin=177.2 oC

180

14.6%

241.7

Temperature/oC

Heat source inlet temperature/oC

200

206.3

150 Wnet/kW

120

3

100 80 60

Tout

40

200

20

250

2 0

400

800

a) Maximum net power output of SORC and DORC

7.53 7.48

100

SORC DORC

5.53 0

2

4

6

8

Ths1

140 Temperature/oC

Heat source inlet temperature /oC

160

9.35

5.75

10

120

80 60 40 20

12

7

6

T T hs2 Tout hs3 2 0

34

5

400

800

b) Thermal efficiency of SORC and DORC

1200 1600 Q/kW

2000

2400

2800

b) DORC Fig. 14. Temperature profiles in the evaporator of SORC and DORC when Tin = 177.2 °C.

2141.4 1875.8 656.13kW 1423.1

140

1657.9

2800

998.4

120

1246.1

SORC DORC

867.7 0

400

800

1200

Ths=120oC Ths=140oC

2000

656.1

100

Ths=100oC

2400

1600

2000

Ths=160oC

1600 Ctot/k$

Heat sourece inlet temperature/oC

2800

100

Thermal efficiency/%

160

2400

Tin=177.2 oC

Isobutane

180

9.0

120

2000

200

11.29

140

1200 1600 Q/kW

a) SORC

11.0

160

7

2400

Heat absorption capacity/kW

1785.6

1200

1320

800

c) Heat absorption capacity of SORC and DORC Fig. 13. Wmax and corresponding heat recovery capacity and thermal efficiency of SORC and DORC.

939.5

400 0

increases and then decreases with the increase of Ph and Pl. As discussed above, it is the combined effect of Cpum1 and Cpum2. Fig. 18b presents the effect of Ph and Pl on the variation of the investment cost of turbine (Ctur). It is apparent that the variation tendency of Ctur is similar to that of Wtur, and the reason is also analogous.

607.5 400

800

1200

1600 2000 Pe/kPa

Fig. 15. Ctot of SORC over Pe.

729

2400

2800

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M. Wang et al.

0.7 0.6

Ths=100 oC

Ths=140 oC

1500

Ths=120 oC

Ths=160 oC

1400 1300

0.5 EPC($ kWh)

Cpum/k$

1200 Ph/kPa

0.4

1100

0.3

1000

0.24 0.19

0.2

0.16

900

0.13

800

0.1

Ths=100 oC

700

600

600 700 800 900 1000 1100 1200 1300 1400 Pl/kPa

900 1200 1500 1800 2100 2400 2700 3000 3300 Pe/kPa

a) Pump

Fig. 16. EPC of SORC over Pe.

Ctur/k$

1500

1500

Cpum1/k$

1400

1400 1300

48.30

1300

51.01

1200

53.72

1200

Ph/kPa

56.42

1100

59.13

1100

Ph/kPa

61.84

1000

64.55

1000

67.26

900

69.97

900

72.67

800

75.38

800

80.80

600

700

800

b) Turbine

a) Pump 1 Cpum2/k$ 38.30 41.46 44.62 47.77 50.93 54.09 57.25 60.41 63.57 66.72 69.88 73.04 76.20

Ph/kPa

1100 1000 900 800 700 700

800

1400

70.90

1300

77.05

73.98 80.13

1200

83.20

1100

86.28

1000

92.42

900

98.58

Ph/kPa

1200

600

Cexc/k$

1500

1500

1300

123.0 134.9 146.8 158.6 170.5 182.4 194.3 206.1 218.0 229.9 241.8 253.6 265.5 277.4 289.3 301.1 313.0

600 700 800 900 1000 1100 1200 1300 1400 Pl/kPa

900 1000 1100 1200 1300 1400 Pl/kPa

1400

Ths=100 oC

700

78.09

700

63.60 65.18 66.76 68.34 69.92 71.51 73.09 74.67 76.25 77.83 79.41 80.99 82.58 84.16 85.74 87.32 88.90

89.35 95.50 101.7

800

Ths=100 oC

700

104.7 107.8

600 700 800 900 1000 1100 1200 1300 1400 Pl/kPa

900 1000 1100 1200 1300 1400 Pl/kPa

c) Heat exchanger

b) Pump 2

Fig. 18. Investment cost of DORC component.

Fig. 17. Investment cost of pump 1 and pump 2.

The variation of the investment cost of the heat exchanger by increasing Ph and Pl is demonstrated in Fig. 18c. It can be seen that Cexc maintains within a narrow range as Ph increases, and decreases as Pl decreases. Cexc is mainly determined by the heat exchanger surface

areas. According to Eq. (9), there is a direction correlation between the heat exchanger area and absorbed heat from the evaporator. The absorbed heat is decided by Tout, which is shown in Fig. 7. Therefore, Cexe has the opposite variation trend with Tout, whereas the reason is similar.

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1500

403.0 426.0 449.0 472.0 495.0 518.0 541.0 564.0 587.0 610.0 633.0 656.0 679.0 702.0 725.0 748.0 771.0

1300 1200

770 k$

Ph=1160 kPa

1100 1000 900 800

o

Ths=100 C

Pl=773kPa

700 600

700

800

Ctot(k$)

2400

1587 k$

1600

Pl=1137 kPa

800

Pl/kPa

a) Ths=100 C

c) Ths=140oC

2200

Ctot/k$

1800

Ph/kPa

Ph=1566 kPa

1400 1200 Ths=120oC Pl=929 kPa

800 600

482 524 566 608 651 693 735 777 819 861 903 945 988 1030 1072 1114 1156

Ph=3266.1kPa

3300

Ctot(k$)

2172 k$

3000 2700 2400 Ph/kPa

2000

1000

Th=140 oC

600 900 1200 1500 1800 2100 2400 2700 3000

o

1600

Ph=2130 kPa

2000

1200

900 1000 1100 1200 1300 1400 Pl/kPa

1154 k$

670.0 727.8 785.6 843.4 901.3 959.1 1017 1075 1133 1190 1248 1306 1364 1422 1479 1537 1595

2800

Ph/kPa

1400

Ph/kPa

3200

Ctot(k$)

2100 1800 1500 Ths=160 oC

1200 900

800 1000 1200 1400 1600 1800 2000 Pl/kPa

600

b) Ths=120oC

Pl=1397 kPa

985 1059 1134 1208 1283 1357 1431 1506 1580 1654 1729 1803 1878 1952 2026 2101 2175

900 1200 1500 1800 2100 2400 2700 3000 Pl/kPa

d) Ths=160oC Fig. 19. Contours of Ctot of the DORC.

Fig. 19a shows the investment cost of DORC (Ctot) variations with the increase of Ph and Pl when Ths is 100 °C. Consequence of above mentioned reasons leads to the variations trend of Ctot: Ctot firstly increases and then decreases with the increase of Ph and Pl. Fig. 19b–d present variations of Ctot with the increase of the Ph and Pl when Ths is 120 °C, 140 °C and 160 °C respectively. The variation trend of Ctot is similar, and the reason is also same. It can be seen than the optimized Ctot increases from 770 k$ to 2172 k$ as Ths increases from 100 °C to160 °C The effect of Ph and Pl on the EPC variation is shown in Fig. 20. From Fig. 20a, it can be observed that EPC decreases firstly, and then increases with the increase of Ph and Pl. The lower values of EPC can be seen in the range of 1000 kPa < Ph < 1400 kPa and 680 kPa < Pl < 1050 kPa. Consequently, the value of EPC is 0.241 at the corresponding optimized conditions of Ph = 1160 kPa and Pl = 773 kPa. Combined with Fig. 12, we could found that the range of Ph and Pl of higher Wnet is basically included by that of lower EPC. That is to say,

the DORC could show better thermodynamic and thermo-economic performances in the optimized two-stage pressures. Fig. 20b–d show the variations of EPC with the increase of Ph and Pl when Ths is 120 °C, 140 °C, and 160 °C respectively. It is obvious that EPC decreases from 0.24 $/kW h to 0.14 $/kW h when Ths increases from 100 °C to 160 °C. In a word, DORC system possesses better thermoeconomic performance at higher Ths. 4.2.3. Thermo-economic performance comparison Fig. 21a presents the optimized Ctot of SORC and DORC over different Ths. It is apparent the optimized Ctot of DORC is larger than that of the SORC. Moreover, optimized Ctot increases as Ths increases on account of the increase of the system capacity. Fig. 21b shows the optimized EPC of SORC and DORC over different Ths. It can be seen that the optimized EPC of SORC and DORC show little change. From Figs. 21b and 12, we could find that the DORC can significantly increase net power output, but the thermo-economic

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EPC($/kWh)

1500 1400

0.2592 0.2773 0.2864

Ph/kPa

Ph/kPa

1160 kPa

1100

0.2955

1000

0.3046

900

0.3227

800

Ths=100 C

773 kPa

700

0.1860

2100 1800

0.3409

0.2980 0.3140

Pl=1137 kPa

0.3460

Pl/kPa

EPC($/kWh)

0.2142 0.2278

1400

0.2549 0.2685 0.2821

1200

Ph/kPa

Ph=1566 kPa

0.2413

0.2957

o

Ths=120 C

0.1320

2700

0.1368

2400

0.1465

2100

0.1562

0.1417 0.1513 0.1610

1800

0.1658 0.1707

1500

0.3092

1000

EPC($/kWh)

0.14 $/kWh

3000

0.2006

1800

Ph=1397 kPa

3300

0.1870

2000

Ph/kPa

Th=140 C

c) Ths=140oC

2200

600

0.3300

o

600 900 1200 1500 1800 2100 2400 2700 3000

a) Ths=100 C

800

0.2500 0.2820

o

Pl=929 kPa

0.2340 0.2660

900

600 700 800 900 1000 1100 1200 1300 1400 Pl/kPa

1600

0.2180

Ph=2130 kPa

1200

0.3318 0.3500

0.19$/kWh

0.2020

0.16 $/kWh

1500

0.3137

o

0.1700

2400

0.2682

0.24$/kWh

1200

0.1540

2700

0.2501

1300

EPC($/kWh)

3000

0.2410

0.1755

1200

0.3228 0.3364

Pl=1397 kPa

900

0.3500

600

800 1000 1200 1400 1600 1800 2000 Pl/kPa

0.1803

Ths=160oC

0.1852 0.1900

900 1200 1500 1800 2100 2400 2700 3000 Pl/kPa

d) Ths=160oC

b) Ths=120oC

Fig. 20. Contours of EPC of DORC system.

performance is not reduced by increased system complexity compared to the SORC. This well confirms that DORC has a good prospect for application at lower temperature (100–177.2 °C) heat source for isobutane.

21.3% to 14.6% when Ths increases from 100 °C to 160 °C. DORC system has more advantage at lower Ths. (c) Both SORC and DORC show better thermo-economic performances at higher heat source inlet temperature. Optimized EPC of SORC decreases from 0.24 $/kW h to 0.13 $/kW h, that of DORC decreases from 0.24 $/kW h to 0.14 $/kW h as Ths increases from 100 to 160 °C (d) Optimized EPC of SORC and DORC at the same heat source inlet temperature are nearly equal. The DORC can significantly increase net power output, but the thermo-economic performance is not reduced by increased system complexity compared to the SORC.

5. Conclusions The thermodynamic and thermo-economic performances of SORC and DORC using isobutane as working fluids were investigated and evaluated. The effects of the two-stage pressures and the heat source temperature on the system performances are also analyzed. Main conclusions obtained are listed as follows: (a) Thermodynamic performance of DORC using isobutane as working fluid is better than that of SORC as the heat source temperature is lower than 177.2 °C; DORC system no longer has performance advantage if the heat source temperature is higher than 177.2 °C. (b) The optimized net power output increment of DORC decreases from

Acknowledgement This work has been supported by the Natural Science Foundation of Shandong Province (Nos. ZR2014EEP026 and ZR2016AP07) and the Scientific Research Foundation of Ludong University (No. 27860301).

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M. Wang et al.

Heat source temperature/oC

2795.1

1785.6

160

2172.3

2605

1320

140

1586.6 939.5

120

1154.2 607.5

100

770 0

SORC DORC

770

300 600 900 1200 1500 1800 2100 2400 2700 3000 Ctot/k$

a) Ctot

Heat source temperature/oC

160

140

0.1312

DORC SORC

0.1362 0.1553 0.1875

0.1551

0.1875 0.1894

120

0.1875

0.1875 0.2438

100

0.1875

0.2431

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30 EPC($/kWh)

b) EPC Fig. 21. Thermo-economic comparisons of SORC and DORC.

Appendix A. . Heat transfer A.1. Single phase heat transfer coefficient in the shell side The single phase heat transfer coefficient of shell side is calculated by the correlation of Bell-Dlaware [36]: (A1)

ho = h id Jc Jl Jb Js

where Jc is the correction factor for baffle cut and spacing; Jl is the correlation factor for baffle leakage; Jb is the correction factor for bundle bypassing effects; Js is the correlation factor for variable baffle spacing at the inlet and outlet; The combined effects of all these correction factors for a reasonable well-designed shell-and-tube heat exchanger is of the order of 0.60 [36]. hd is the ideal transfer coefficient for pure cross flow,

hd = ji cps

m sh Ash

k sh c psh µsh

2/3

µsh µsh,w

0.14

(A2)

where cps is the specific heat of the working fluid, kJ/(kg·K); sh stands for shell; msh is the mass flow rate of working fluid, kg/s; ksh is the thermal conductivity of the working fluid, W/(m·K); μsh is the dynamic viscosity of working fluid, Pa·s; Ash is the cross flow area at the centerline of the shell for one cross flow between two baffles, m; ji is the Colburn j-factor for an ideal tube bank. A.2. The boiling heat transfer coefficient in the shell-side The boiling heat transfer coefficient in the evaporator of the shell-side is given as follows [37]: (A3)

he = h nb Fb + h nc 2

where Fb is a correction factor for the effect of convection; hnb is the nucleate boiling coefficient, W/(m ·K); hnc is the natural convection heat transfer coefficient, W/(m2·K). The parameters are calculated as follows:

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M. Wang et al. 0.7 h nb = 0.00417p0.69 c q Fp

Fp = 0.7 + 2pr (4 +

1 ) 1 pr

(A5)

0.785Dotl 1 Ct (Pt / do )2d o

Fb = 1 + 0.1

Dotl = Dsh

(A4)

0.75

(A6) (A7)

bb

(A8)

= 0.017Ds + 0.256m

bb

2

where Pc is the working fluid critical pressure, MPa; q is the heat flux, kW/m ; pr = P/Pc; Pt is the tube pitch, m; Dsh is the diameter of the shell, m; δbb is the bypass clearance; Ct is a constant decided by the tube bundle configuration [37]. A.3. The condensation heat transfer coefficient in the shell side The condensation heat transfer coefficient for the two-phase fluid in the condenser is calculated by [38] (A9)

hs / hl = 1.26Xtt 0.78 hl = ji Gs· cps·Pr (

Xtt =

1 x x

2/3) (µ

0.25

(A10)

1 /µ w )

v

µl

l

µv

0.1

(A11) 2

where hl is the heat-transfer coefficient for the liquid phase flowing alone through the bundle, W/(m ·K); Xtt is the Lockhart–Martinelli parameter, Eq. (A11); Gs is the shell side mass velocity of the working fluid, kg/(m2·s); cps is the specific heat capacity of the working fluid, kJ/(kg·K); Pr is the Prandtl number of the working fluid; x is the vapor mass fraction in the liquid-vapor mixture; V and L stand for vapor and liquid, respectively; μ is the viscosity of the working fluids, kg/(m·s). The Colburn j-factor for an ideal tube bank is given as follows:

ji = a1

1.33 PT/ d o

a

(Resh )a2

(A12)

where Res is the Reynolds number of working fluids:

Resh =

m sh d 0 Ash µsh

(A13)

where Ash is the bundle cross flow area, m2. where

a=

a3 1 + 0.14(Resh ) a4

(A14)

Table A.1 gives the coefficients of Eqs. (A12) and (A14).

Table A1 Correlation coefficients for ji in Eqs. (A12) and (A14). Layout angle

Reynolds number

a1

a2

a3

a4

30°

4

10 -10 104-103 103-102 102-10 < 10

0.321 0.321 0.593 1.360 1.4

−0.388 −0.388 −0.477 −0.657 −0.667

1.450

0.519

45°

105-104 104-103 103-102 102-10 < 10

0.370 0.370 0.73 0.498 1.550

−0.396 −0.396 −0.500 −0.667 −0.667

1.930

0.500

90°

105-104 104-103 103-102 102-10 < 10

0.370 0.107 0.408 0.900 0.97

−0.395 −0.266 −0.460 −0.631 −0.667

1.187

0.370

5

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M. Wang et al.

A.4. Single phase heat transfer coefficient in the tube side The correlation of Petukhow and Popov [39] is used to calculate the single phase heat transfer coefficient and is given by:

ht =

Nu·k di

(A15)

where the Nusselt number can be calculated by

Nu =

(f /8) Ret ·Prt [1.27·(f /8)0.5·(Pr 2/3 1) + 1.07]

(A16)

And

Ret =

Prt =

t vt d i

(A17)

µt

cpt µt

(A18)

kt

f = (0.782· lgRet 1.51)

(A19)

2

where t stands for tube; Ret and Prt are the Reynolds number and the Prandtl number of the heat source water, respectively; ρt, vt, kt, μt are the density, mass velocity, thermal conductivity and viscosity of the heat source water respectively. Appendix B. . Total investment cost The bare module cost for each component is calculated by (B1)

Cbm = Cp Fbm

where Cp is the purchased cost for base conditions: equipment made of carbon steel and operating at near ambient pressures, which is calculated by (B2)

log10 Cp = K1 + K2log10 (X ) + K3 (log10 X ) 2

where X refer to the output net power for the turbine, input net power for the pump, or surface area for heat exchanger respectively. The values for K1, K2 and K3 are given in the Table B1. Fbm is the factor of bare module cost, which is given as follows: (B3)

Fbm = B1 + B2 FM FP where the values of B1and B2 are given in Table B1; Fp is the pressure factor, which is calculated by the following equation:

(B4)

log10 Fp = C1 + C2 log10 P + C3 (log10 P ) 2 where P is the operating pressure and the units of P is bar gauge. The values of C1, C2 and C3 are given in Table B1. Table B1 Component bare module cost parameters [41]. Components

K1

K2

K3

C1

C2

C3

B1

B2

FM

FBM

Pump Turbine Condenser Evaporator

3.87 2.705 4.325

0.316 1.44 −0.303

0.122 −0.177 0.163

−0.245 / −0.039

0.259 / 0.082

−0.014 / −0.012

1.89 / 1.63

1.35 / 1.66

2.35 / 1.35

/ 6.2 /

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