Techno-economic performance of two-stage series evaporation organic Rankine cycle with dual-level heat sources

Journal Pre-proofs Techno-economic performance of two-stage series evaporation organic Rankine cycle with dual-level heat sources Qiulin Wang, Jianqiang Wang, Tailu Li, Nan Meng PII: DOI: Reference:

S1359-4311(19)37306-5 https://doi.org/10.1016/j.applthermaleng.2020.115078 ATE 115078

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Applied Thermal Engineering

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23 October 2019 9 February 2020 11 February 2020

Please cite this article as: Q. Wang, J. Wang, T. Li, N. Meng, Techno-economic performance of two-stage series evaporation organic Rankine cycle with dual-level heat sources, Applied Thermal Engineering (2020), doi: https://doi.org/10.1016/j.applthermaleng.2020.115078

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Techno-economic performance of two-stage series evaporation organic Rankine cycle with dual-level heat sources Qiulin Wanga, Jianqiang Wangb, Tailu Lic, Nan Mengc* a

School of Electric Power, Shanxi University, Taiyuan, 030006, China；

b

College of Energy and Environmental Engineering, Hebei University of engineering, Handan 056038,

PR China c

School of Energy and Environmental Engineering, Hebei University of Technology, Tianjin 300401,

China；

Abstract:

With the increasing of fossil energy crisis and environmental pollution, the development and utilization of renewable energy has become a hot spot in recent years. Based on two-stage serial organic Rankine cycle system of single heat source, the twostage series organic Rankine cycle system of double heat source is proposed in this paper to realize cascade utilization of heat sources with different temperatures. The composite heat source grade is correlated with the two-stage series evaporation temperature to improve the power generation power and economic benefit of the system. Taking R245fa as an example, the mass flow rate of heat source is 10kg/s, and the effects of evaporation temperature and heat source temperature on the net output power, thermal efficiency, exergy efficiency, electricity production cost and investment *

Corresponding author: Tel: +86-22-60435787. E-mail address: [email protected]

payback period of organic Rankine cycle, two-stage serial organic Rankine cycle system of single heat source and two-stage series organic Rankine cycle system of double heat source are optimized and analyzed. It is found that the electricity production cost and investment payback period of two-stage series organic Rankine cycle system of double heat source are always the smallest, followed by two-stage serial organic Rankine cycle system of single heat source, and the largest is the electricity production cost and investment payback period of organic Rankine cycle system. At the same time, it is found that two-stage series organic Rankine cycle system of double heat source is more suitable for low-temperature heat source.

Keywords: organic Rankine cycle; two-stage series organic Rankine cycle; power generation; economic performance

1. Introduction Energy is the basis of human survival and sustainable development. The development and utilization of energy has an important impact on the social and economic development of a country or region [1]. Fossil energy crisis and environmental pollution are becoming more and more serious, which makes the improvements in new technologies for renewable energy power plants, exploitation of renewables and a broader use of energy-saving systems are crucial matters, both to reduce greenhouse gas emissions and to meet the increasing world energy demand [2]. However, most renewable energy sources are intermittent and non-programmable, failing to provide consistently stable heat supply, and there is no guarantee that the matching between the high energy production cycle and its needs [3]. Geothermal

energy, as a kind of renewable energy, is rich in reserves and unaffected by weather and climate change. In recent years, it has received widespread attention from researchers [4]. As a common system for converting medium-low temperature geothermal energy into electric energy, organic Rankine cycle (ORC) has been widely studied by a large number of researchers, which mainly focuses on the optimization of system structure, working fluid and cycle parameter. In terms of system structure, Braimakis et al. [5] compared and analyzed three kinds of regenerated organic Rankine cycle structures, including CF-ORC, O-ORC and CB-ORC, and the results showed that CF-ORC had the highest energy efficiency. Iodice et al. [6] Proposed an innovative solar power generation system based on the steam Rankine cycle, and found that direct steam generation solar systems with screw expanders as power machines are more suitable for the use of low and medium temperature heat sources. Baccioli et al. [7] in order to solve the coupling problem between seawater desalination multi-effect distillation system and waste heat recovery ORC, a comparative analysis was made on the mixed series cascade structures, and it was found that the mixed structure greatly improved the economic profit of the system. Bao et al. [8] studied the effects of working fluids and four system configurations on system performance and found that steam turbines had a significant impact on the net output power of the system, and the maximum net output power of the system with npentane is increased by 17%. Wang et al. [9] compared the single-stage evaporation system with the two-stage evaporation system. The results showed that the irreversible loss of two-stage evaporation is lower and the performance of the system is improved.

Guo et al. [10] proposed a new cogeneration system based on the traditional ORC, and studied the effects of eight working fluids on the system. It was found that the system with R236ea and R245ca as working fluid had the optimal performance. From the perspective of flue gas waste heat recovery, Li et al. [11] found that TSORC could recover more heat from the heat source at low pressure stage, thus reducing the irreversible loss between the heat source and the working medium and improving the net output power. Meng et al. [12] found that the double-flash organic Rankine cycle based combined heating and power system had the highest efficiency under the coupling of geothermal fluid temperature and dryness. Garcia-Saez et al. [13] proposed a coupling system of solar energy and ORC and evaluated the technical and economic performance of the new system. It was found to increase the utilization of solar equipment and reduce the payback period. From the literature, it can be seen that researchers mainly optimized the performance and structure of ORC system based on a single heat source, while in this study, the concept of double heat sources is proposed for cascade utilization of heat sources at different temperatures. For the selection of the working medium of the system, Yu et al. [14] compared and analyzed the effects of different working fluids on the system performance. It was found that the system using R125, R143a, R290 and R1270 as working fluids had relatively good performance without waste heat utilization, while the system using R170, R134a and R290 with waste heat utilization had better performance. Barse et al. [15] found a strong correlation between the critical temperature of the working fluid and the efficiency of the working fluid by analyzing 12 working fluids. For R600, the

optimized system design can improve the thermal efficiency by 25%. The study of Kumar et al. [16] showed that the ORC system with benzene as circulating working fluid had better economic performance and higher system efficiency. Li et al. [17] studied and analyzed the influence of 10 kinds of working fluids on the associated geothermal ORC in oil field. The results showed that the system benefit of using R601a as organic working fluid was the best. Thurairaja et al. [18] revealed that the suitable temperature range of MD2M and cyclopentane was 50-100℃, that of butane, neopentane and R245fa was 100-150℃, and the suitable temperature range of ethanol, methanol and acetone was 150-200℃, that of water, m-Xylene and p-Xylene was 200320℃. Eyerer et al. [19] found that R1224yd (Z) and R1233zd (E) could be used as substitutes for R245fa. Li et al. [20] believed that R123, n-pentane, R11, R141b and other working fluids with critical temperature between 180℃ and 210℃ were more suitable for recovering low-temperature waste heat of flue gas. Moreover, as an important evaluation index to measure whether the ORC system can be commercialized, the economic parameter has also been studied by scholars at home and abroad. Braimakis et al. [21] used a new comprehensive thermal economic optimization method to optimize the ORC and the regenerated ORC system, and the results showed that the regenerative ORC has good adaptability to high temperature, closed loop system and open loop system. Karimia et al. [22] selected levelized cost of electricity (LCOE), return on investment (ROI) and payback period (PBP) as economic indicators to focus on the economic benefits of three ORC configurations, and the results showed that LCOE of RORC-R123 was the minimum value. Navongxay et al. [23] evaluated the system optimization model by using energy efficiency, exergy efficiency, levelized electricity cost (LEC) and exergy cost (EC). It was found that the

model 1 had the lowest economics, with LEC and EC values of $0.074 /kWh and $0.080 /kWh, respectively. Arabkoohsar et al. [24] proposed a new waste heat recovery method for waste-CHP-ORC plant. The results showed that the payback period of the parallel project is reduced by about 10%. Michael et al. [25] proposed a new organic Rankine cycle system for waste heat recovery in internal combustion engines and found that the best ORC designs had a discount recovery period (DPP) of 4-5 years. Ahmadi et al. [26, 27] studied a new multi-objective function optimization method to optimize the total cost rate and exergy efficiency of the system. Wang et al. [28] selected exergy efficiency and overall capital cost as objective functions and found that under given waste heat conditions, the optimal exergy efficiency was 13.98% and the total investment cost was 129.28×104 USD. The evaluation and analysis of the system's economics in the literature provides a theoretical basis for the establishment of the economic model of this study From the above literature, it can be found that the improvement of basic ORC structure can effectively improve the utilization rate of medium and low temperature heat sources. As one of the most important factors affecting system performance, the matching between heat source and working fluid needs to be studied. In view of the diversity of the temperature of the geothermal source, the two-stage series organic Rankine cycle system of double heat source (TSORC-DHS) system is proposed in this study, which aims to optimize the system performance by matching the heat source temperature diversity with the working fluid. At the same time, the energy, exergy analyses model is established and compared with the organic Rankine cycle (ORC) system and two-stage serial organic Rankine cycle system of single heat source (TSORC-SHS) system in detail. In addition, two economic parameters, electricity production cost (EPC) and payback period (PBP), are selected to evaluate the

economics of the system. 2. System description Fig. 1 shows the flow chart of the two-stage serial organic Rankine cycle system of the organic Rankine cycle (ORC) system, two-stage serial organic Rankine cycle system of single heat source (TSORC-SHS) system and double heat source (TSORCDHS) system, respectively. The ORC system consists of five parts: evaporator A, turbine B, generator C, condenser D and working fluid pump P. In addition, the red line a-b stands for the geothermal source, the blue line e-f stands for the cooling water, and the green line represents the working fluid. The operation process of ORC system is shown in the Fig. 1(a). The low-temperature and low-pressure organic working fluid is pressurized by the working fluid pump P and exchanges heat with the geothermal source in the evaporator A, so as to be converted into a high-temperature and high-pressure vapor. The vapor drives the turbine B to perform work while driving the generator to output electric energy. After working, the working fluid is cooled to low-temperature and low-pressure by the cooling water in the condenser D, and then enters the working fluid pump P again to complete a cycle process (process 5-6-1-2-5). As shown in Fig. 1(b), the components of the TSORC-SHS system and the TSORC-DHS system are exactly the same, and the operation process of the system is also consistent, except that the TSORC-SHS adopts the form of a single heat source at the geothermal source, which is indicated by the red line a-b-c. The following is a detailed description of the TSORC-DHS system. From the Fig. 1(c), it can be seen that the TSORC-DHS system consists of highpressure evaporator A1, low-pressure evaporator A2, two turbines B1 and B2, generator C, condenser D, high-pressure pump P1 and low-pressure pump P2. In addition, the red

line a-b stands for the high-temperature geothermal source, c-d represents the lowtemperature geothermal source, the blue line e-f stands for the cooling water, and the green line represents the process of working fluid circulation. The specific operation process of the TSORC-DHS system is described as follows: The low-temperature and low-pressure liquid working fluid is first pressurized by the low-pressure working fluid pump P2, and then enters into the low-pressure evaporator A2 to exchange heat with the low-temperature heat source. During this process, part of the working fluid is converted into high-temperature and high-pressure vapor to drive the turbine B2 (process 2-5-26-21). The other part of working fluid flows into the highpressure working fluid pump P1 and is pressurized again into the high-pressure evaporator A1 to exchange heat with the high-temperature source, and then into the high-pressure turbine B1 (process 27-16-11). The vapor working fluid entering the two turbines B2 and B1 drives the generator to obtain electricity. The vapor working fluid discharged by the turbine enters the condenser is cooled by the cooling water by heat exchange, and is transformed into the low-temperature and low-pressure liquid (process 21-22-2, 11-12-2). And then enters the low-pressure working fluid pump P2 again to start a new cycle. Fig. 2 shows the T-s diagrams of the ORC, TSORC-SHS and TSORC-DHS system, where the trends of TSORC-SHS and TSORC-DHS are consistent.

Fig. 1 Schematic diagram of (a) ORC system; (b) TSORC-SHS system; (c) TSORC-DHS system

Fig. 2 T-s diagram of (a) ORC system; (b) TSORC-SHS/TSORCDHS system

3. Mathematical model 3.1. Assumptions In order to facilitate the establishment of the mathematical model of the system, based on the first law of thermodynamics and the second law of thermodynamics, the following assumptions are made for the model: (1) The cooling and heat sources of the two systems and the components of the system

operate stably [34]. (2) The organic working fluid at the inlet of the working fluid pump is in a saturated liquid state. The pinch temperature difference at state points 17 and 27 in the cycle is 5℃ [35]. (3) The cold and heat source temperature is constant, and the cooling water temperature at the inlet and outlet of the condenser is 35℃ and 45℃, respectively [12]. (4) The organic working fluid is superheated steam and supercooled liquid at the inlet of steam turbine and the outlet of condenser, respectively, and the super-heat and subcooling are 5℃ [36]. (5) The change of kinetic energy and potential energy of organic working fluid are ignored [37]. (6) The pressure drop and friction loss of organic working fluid in evaporator, condenser and pipe are ignored, as well as the heat loss in pipeline [34]. (7) The energy loss of organic working fluid in the mixing process of steam turbine is ignored [36].

3.2. Governing equations 3.2.1. Thermodynamic model The thermodynamic model of TSORC system (including TSORC-DHS and TSORCSHS systems) is shown below： The high-pressure evaporator： 𝑄𝐴1 = 𝑚wf1(ℎ11 ― ℎ16) = 𝑚gw(ℎgw ,in ― ℎhw,out)

(1)

Where ℎ, 𝑚 and Q stand for the enthalpy, the mass flow rate and the heat transfer rate, respectively. The subscript wf and gw means the working fluid and hightemperature geothermal water, respectively. 11 and 16 stand for inlet and outlet of highpressure evaporator. The subscripts in and out stand for inlet and outlet, respectively.

Preheating section: 𝑄A1,pre

𝑚wf1(ℎ17 ― ℎ16)

𝐾𝐴A1,pre = ∆𝑇A1,pre = ∆𝑇A1,pre =

∆𝑇A1,pre

𝑡gw ,out ― 𝑡16 ― 𝛥𝑡𝑝𝑝 𝑙𝑛

𝑡gw ,out ― 𝑡16 𝛥𝑡𝑝𝑝

(2) (3)

Where the KA represents the thermal conductivity, the t stands for the temperature, and the subscript pp stands for pinch point. The Δ T stands for the logarithmic mean temperature difference. Evaporation section: 𝑄A1,eva

𝑚wf1(ℎ18 ― ℎ17)

𝐾𝐴A1,eva = 𝛥𝑇A1,eva =

𝛥𝑇A1,eva

(4)

Where the subscript eva means the evaporator. 𝛥𝑇𝐴1,eva =

𝑡gw ,1 ― 𝑡18 ― 𝛥𝑡𝑝𝑝 𝑙𝑛

𝑡gw ,1 ― 𝑡18 𝛥𝑡𝑝𝑝

(5)

Super-heating section: 𝑄A1,sup

𝐾𝐴A1,sup = ∆𝑇A1,sup = 𝛥𝑇𝐴1,sup =

𝑚wf1(ℎ11 ― ℎ18) ∆𝑇A1,sup

(𝑡gw ,in ― 𝑡11) ― (𝑡gw ,1 ― 𝑡18) 𝑡gw ,in ― 𝑡11 gw ,1 ― 𝑡18

(6) (7)

𝑙𝑛 𝑡

The low-pressure evaporator： 𝑄𝐴2 = 𝑚wf(ℎ27 ― ℎ26) + 𝑚wf2(ℎ21 ― ℎ27) = 𝑚lw(ℎlw,in ― ℎlw,out)

(8)

The subscript 26 and 21 stand for inlet and outlet of low-pressure evaporator. The subscript gw stands for the low-temperature geothermal water. Preheating section: 𝑄𝐴2,pre

𝐾𝐴𝐴2,pre = 𝛥𝑇𝐴2,pre =

𝑚wf(ℎ27 ― ℎ26) 𝛥𝑇𝐴2,pre

(9)

𝑡lw,out ― 𝑡26 ― 𝛥𝑡𝑝𝑝

𝛥𝑇𝐴2,pre =

𝑙𝑛

𝑡lw,out ― 𝑡26 𝛥𝑡𝑝𝑝

Evaporation section:

(10)

𝑄A2,eva

𝐾𝐴A2,eva = 𝛥𝑇A2,eva = 𝛥𝑇𝐴2,pre =

𝑚wf2(ℎ28 ― ℎ27) 𝛥𝑇A2,eva

𝑡lw,2 ― 𝑡28 ― 𝛥𝑡𝑝𝑝 𝑙𝑛

𝑡lw,2 ― 𝑡28 𝛥𝑡𝑝𝑝

(11) (12)

Super-heating section: 𝑄A2,sup

𝑚wf2(ℎ21 ― ℎ28)

𝐾𝐴A2,sup = 𝛥𝑇A2,sup = 𝛥𝑇𝐴2,𝑠𝑢𝑝 =

𝛥𝑇A2,sup

(𝑡lw,in ― 𝑡21) ― (𝑡lw,2 ― 𝑡28) 𝑡lw,in ― 𝑡21 lw,2 ― 𝑡28

(13) (14)

𝑙𝑛 𝑡

Where subscripts A1 and A2 stand for the high-pressure evaporator and the lowpressure evaporator, respectively. Condenser： 𝑄𝑐 = 𝑚wf(ℎ2 ― ℎ5) = 𝑐 ⋅ 𝑚cw(𝑡cw,out ― 𝑡cw,out)

(15)

The subscript c and cw stand for condenser and cooling water. The c represents specific heat capacity. Pre-cooling section: 𝑄𝑐,pre

(𝐾𝐴) c,pre = 𝛥𝑇𝑐,pre =

𝑚wf(ℎ2 ― ℎ3) 𝛥𝑇𝑐,pre

(16)

The subscript pre stands for pre-cooling. 𝛥𝑇𝑐,pre =

(𝑡cw,out ― 𝑡2) ― (𝑡cw,2 ― 𝑡3) 𝑡cw,out ― 𝑡2 cw,2 ― 𝑡3

(17)

ln 𝑡

Condensing section: 𝑄𝑐,con

(𝐾𝐴) c,con = 𝛥𝑇𝑐,con =

𝑚wf(ℎ3 ― ℎ4) 𝛥𝑇𝑐,con

(18)

The subscript con stands for condensing. 𝛥𝑇𝑐,con =

(𝑡3 ― 𝑡cw,2) ― (𝑡4 ― 𝑡cw,1) 𝑡3 ― 𝑡cw,2 4 ― 𝑡cw,1

(19)

𝑙𝑛 𝑡

Sub-cooled section: 𝑄𝑐,sub

(𝐾𝐴) c,sub = 𝛥𝑇𝑐,sub =

𝑚wf(ℎ4 ― ℎ5) 𝛥𝑇𝑐,sub

(20)

The subscript sub stands for sub-cooling. 𝛥𝑇𝑐,sub =

(𝑡4 ― 𝑡cw,1) ― (𝑡5 ― 𝑡cw,in) 𝑡4 ― 𝑡cw,1 5 ― 𝑡cw,in

(𝐾𝐴) c = (𝐾𝐴) c,pre + (𝐾𝐴) c,con + (𝐾𝐴) c,sub 𝑚cw =

𝑚wf(ℎ2 ― ℎ5) 𝑐 ⋅ 𝛥𝑡cw

𝑚wf1 = 𝑚wf2 =

𝑚gw𝑐p,gw(𝑡gw,in ― 𝑡pp ― 𝑡e1) ℎ11 ― ℎ17 𝑚lw𝑐p,lw(𝑡lw,in ― 𝑡pp ― 𝑡e2)

𝑚wf22 =

(21)

ln𝑡

ℎ21 ― ℎ27 𝑚lw ⋅ 𝑐 ⋅ (𝑡lwmid ― 𝑡𝑏2) ℎ21 ― ℎ27

(22) (23) (24) (25) (26)

𝑚wf = 𝑚wf1 + 𝑚wf2

(27)

𝑊𝑃 = 𝑊𝑃1 + 𝑊𝑃2 = 𝑚wf1(ℎ16 ― ℎ27) + 𝑚wf(ℎ26 ― ℎ5)

(28)

Where the subscript P stands for the working fluid pump. 𝑊𝑡 = 𝜂𝑡[𝑚𝑤𝑓1(ℎ11 ― ℎ12𝑠) + 𝑚𝑤𝑓2(ℎ21 ― ℎ22𝑠) ]

(29)

= 𝑚𝑤𝑓1(ℎ11 ― ℎ12) + 𝑚𝑤𝑓2(ℎ21 ― ℎ22) Where 𝑊 expresses the power output, the subscript t represents the turbine. 𝑊hp =

(𝑚gw + 𝑚lw)𝑔 ⋅ 𝐻hp 1000𝜂hp

(30)

Where 𝐻 and g stand for the pressure head and acceleration of gravity. The subscript hp represents the heat source water pump. 𝑊cp =

𝑚cw ⋅ 𝑔 ⋅ 𝐻cp 1000𝜂cp

(31)

The subscript cp represents the cooling water pump. The efficiency of heat source water pump 𝜂hp and cooling water pump 𝜂cp are set to 0.75. The following is the mathematical model of net power output. 𝑊net = 𝜂𝑚 ⋅ 𝜂𝑔 ⋅ 𝑊𝑡 ― 𝑊𝑃 ― 𝑊hp ― 𝑊cp

(32)

Where 𝜂𝑚 and 𝜂𝑔 stand for the mechanical efficiency and the generating efficiency.

𝜂th =

𝑊net 𝑄1

𝑊net

(33)

⋅ 100 = 𝑄𝑒1 + 𝑄𝑒2 ⋅ 100%

The 𝜂th stands for the thermal efficiency. 𝐸𝑥net = 𝐸𝑥lw,in ―𝐸𝑥lw,out + (𝐸𝑥gw,in ― 𝐸𝑥gw,out)

(34)

Where 𝐸𝑥 represents exergy. 𝑊net

(35)

𝜂ex = 𝐸𝑥net ⋅ 100% Where the 𝜂ex stands for exergy efficiency. The thermodynamic model of ORC system is shown below： Evaporator：

(36)

𝑄𝐴 = 𝑚wf(ℎ1 ― ℎ6) = 𝑚gw(ℎgw ,in ― ℎgw ,out) Condenser： 𝑄𝑐 = 𝑚wf(ℎ2 ― ℎ5) = 𝑐 ⋅ 𝑚cw(𝑡cw,out ― 𝑡cw,out) 𝑚wf =

(37)

𝑚gw𝑐p,gw(𝑡gw ,in ― 𝑡pp ― 𝑡e)

(38)

ℎ1 ― ℎ7

𝑊𝑃 = 𝑚wf(ℎ6 ― ℎ7)

(39)

𝑊𝑡 = 𝑚wf(ℎ1 ― ℎ2)

(40)

𝑊cp = 𝑊hp =

𝑚cw ⋅ 𝑔 ⋅ 𝐻cp

(41)

1000𝜂cp 𝑚gw𝑔 ⋅ 𝐻hp

(42)

1000𝜂hp

𝑊net = 𝜂𝑚 ⋅ 𝜂𝑔 ⋅ 𝑊𝑡 ― 𝑊𝑃 ― 𝑊cp ― 𝑊hp (

4

𝜂th =

𝑊net 𝑄

⋅ 100

3

) (44)

3.2.2. Economic model Economic analysis is a common technique for evaluating the overall performance of systems. System total equipment base module cost Cbm consists of the module cost

of each component, and the module cost per component is the product of the component cost Cp of each component and the module cost factor Fbm. The Cp represents equipment capacity cost which depends on the coefficient K and the surface area or power of the component. The modular cost factor Fbm is determined by the coefficients B and C. Moreover, the material coefficient Fm and pressure coefficient Fp also have some influence on it. Total cost for each component of the system: 𝐶𝑜𝑠 𝑡2001 = 𝐶bm,eva + 𝐶bm,con + 𝐶bm,𝑝 + 𝐶bm,tur

(45)

Where Cbm represents the cost of components, Cost2001 refers to the cost of 2001 (introduced by the chemical plant cost index CEPCI) [29]. Convert it to the actual cost: 𝐶𝐸𝑃𝐶𝐼2018

𝐶𝑜𝑠 𝑡2018 = 𝐶𝑜𝑠 𝑡2001 ⋅ 𝐶𝐸𝑃𝐶𝐼2001

(46)

Among them, CEPCI2001=397, CEPCI2018=648.7[30, 31]. Capital recovery factor: 𝑖 ⋅ (1 + 𝑖)𝐿𝑇

𝐶𝑅𝐹 = (1 + 𝑖)𝐿𝑇 ― 1

(47)

Where i is the annual loan rate, and is supposed to be 4.9% (refer to Bank of China loan rate in 2018), 𝐿𝑇 is the life cycle time, and is supposed to be 15 years. Electricity Production Cost (EPC): 𝐸𝑃𝐶 = (𝐶𝐹𝑅 × 𝐶𝑜𝑠 𝑡2018 + 𝑘 × 𝐶𝑜𝑠 𝑡2018)/(𝑊𝑛𝑒𝑡 × 𝑡op)

(48)

Where k represents the insurance and management cost factors, and is supposed to be 1%. The subscript top represents the running time of the machine, and is supposed to be 7500h. Payback period [32] (PBP):

𝑃𝐵𝑃 =

𝑊𝑛𝑒𝑡 ⋅ 𝐶𝑒 ― 𝑘 ⋅ 𝐶𝑜𝑠 𝑡2018 ⋅ 𝐶 𝑛𝑒𝑡 𝑒 ― 𝑘 ⋅ 𝐶𝑜𝑠 𝑡2018 ― 𝑖 ⋅ 𝐶𝑜𝑠 𝑡2018

ln𝑊

(49)

𝑙𝑛 (1 + 𝑖)

Where 𝐶𝑒 represents the price of electricity. The following is the cost of the components of the ORC system, including steam turbines, pumps, evaporators and condensers. Evaporator: 𝐶bm,eva = 𝐶𝑝,eva × 𝐹bm,eva

(50)

𝑙𝑔 𝐶𝑝,eva = 𝐾1 + 𝐾2 ⋅ 𝑙𝑔 (𝐴eva) + 𝐾3 ⋅ [𝑙𝑔 (𝐴eva)]2

(51)

𝐹bm,eva = 𝐵1 + 𝐵2 ⋅ 𝐹𝑀 ⋅ 𝐹𝑝,eva

(52)

𝑙𝑔 𝐹𝑝,eva = 𝐶1 + 𝐶2 ⋅ 𝑙𝑔 (𝑝𝑒) + 𝐶3 ⋅ [𝑙𝑔 (𝑝𝑒)]2 (

5

3

)

Among them, K1=4.6656, K2=-0.1557, K3=0.1547; B1=0.96, B2=1.21; FM=1.0; C1=0, C2=0, C3=0. Condenser: (54)

𝐶bm,con = 𝐶𝑝,con × 𝐹bm,con 𝑙𝑔 𝐶𝑝,con = 𝐾1 + 𝐾2 ⋅ 𝑙𝑔 (𝐴con) + 𝐾3 ⋅ [𝑙𝑔 (𝐴con)]2 (

5

5

) (56)

𝐹bm,con = 𝐵1 + 𝐵2 ⋅ 𝐹𝑀 ⋅ 𝐹𝑝,con 𝑙𝑔 𝐹𝑝,con = 𝐶1 + 𝐶2 ⋅ 𝑙𝑔 (𝑝𝑐) + 𝐶3 ⋅ [𝑙𝑔 (𝑝𝑐)]2 (

5

7

)

The condenser has the same coefficients as the evaporator. Pump: 𝐶bm,𝑝 = 𝐶𝑝,𝑝 × 𝐹bm,𝑝

(58)

𝑙𝑔 𝐶𝑝,𝑝 = 𝐾1 + 𝐾2 ⋅ 𝑙𝑔 (𝑊𝑝) + 𝐾3[𝑙𝑔 (𝑊𝑝)]2 (

5

9

)

𝐹bm,𝑝 = 𝐵1 + 𝐵2 ⋅ 𝐹𝑀 ⋅ 𝐹p,p

(60)

𝑙𝑔 𝐹𝑝,𝑝 = 𝐶1 + 𝐶2 ⋅ 𝑙𝑔 (𝑝𝑝) + 𝐶3 ⋅ [𝑙𝑔 (𝑝𝑝)]2

(61)

Among them, K1=3.3892, K2=-0.0536, K3=0.1538; B1=1.89, B2=1.35; FM=1.5; C1=0, C2=0, C3=0. Turbine: 𝐶bm,tur = 𝐶𝑝,tur ⋅ 𝐹bm,tur

(62)

𝑙𝑔 𝐶𝑝,tur = 𝐾1 + 𝐾2 ⋅ 𝑙𝑔 (𝑊net) + 𝐾3[𝑙𝑔 (𝑊net)]2

(63)

Among them, K1=3.514, K2=0.598, K3=0; Fbm=3.5. The following are the costs of the components of the TSORC system, where the cost model of the turbine, pump and condenser is the same as that of the ORC system. High-pressure evaporator: 𝐶bm,eva1 = 𝐶𝑝,eva1 × 𝐹bm,eva1

(64)

𝑙𝑔 𝐶𝑝,eva1 = 𝐾1 + 𝐾2 ⋅ 𝑙𝑔 (𝐴eva1) + 𝐾3 ⋅ [𝑙𝑔 (𝐴eva1)]2

(65)

𝐹bm,eva1 = 𝐵1 + 𝐵2 ⋅ 𝐹𝑀 ⋅ 𝐹𝑝,eva1

(66)

𝑙𝑔 𝐹𝑝,eva1 = 𝐶1 + 𝐶2 ⋅ 𝑙𝑔 (𝑝e1) + 𝐶3 ⋅ [𝑙𝑔 (𝑝e1)]2

(67)

Among them, K1=4.6656, K2=-0.1557, K3=0.1547; B1=0.96, B2=1.21; FM=1.0; C1=0, C2=0, C3=0. Low-pressure evaporator: 𝐶bm,eva2 = 𝐶𝑝,eva2 × 𝐹bm,eva2

(68)

𝑙𝑔 𝐶𝑝,eva2 = 𝐾1 + 𝐾2 ⋅ 𝑙𝑔 (𝐴eva2) + 𝐾3 ⋅ [𝑙𝑔 (𝐴eva2)]2

(69)

𝐹bm,eva2 = 𝐵1 + 𝐵2 ⋅ 𝐹𝑀 ⋅ 𝐹𝑝,eva2

(70)

𝑙𝑔 𝐹𝑝,eva2 = 𝐶1 + 𝐶2 ⋅ 𝑙𝑔 (𝑝e2) + 𝐶3 ⋅ [𝑙𝑔 (𝑝e2)]2

(71)

Total evaporator cost: (72)

𝐶bm,eva = 𝐶bm,eva1 + 𝐶bm,eva2

Table 1. Condition of simulation for the three systems. Items

Parameters

Ambient temperature/ Dead state temperature (℃)

20

Ambient pressure/ Dead state pressure (kPa)

101.3

Heat source temperature (℃)

110 ~150

Pinch point temperature difference of evaporator (℃)

5

Pinch point temperature difference of condenser (℃)

5

Condensation temperature of condenser (℃)

50

Inlet temperature of cooling water

35

Outlet temperature of cooling water

45

Isentropic efficiency of turbine (%)

75

Isentropic efficiency of working fluid pump (%)

60

Isentropic efficiency of cooling water pump (%)

75

Turbine mechanical efficiency (%)

95

Generator efficiency (%)

95

Condenser efficiency (%)

95

4. Validation The experimental data of Li et al. [33] are used to verify the numerical model of this study. In the case of consistent initial parameter setting, the ORC numerical model of this study is in good agreement with the experimental data compared with the ORC test device with R123 as the working fluid, as shown in Table 2. However, the theoretical values of net output power Wnet and thermal efficiency ηth are slightly higher than the experimental values. This is because the theoretical model does not take into account the pressure drop of the working fluid in the heat exchanger and tube, and the measurement instrument in the actual engineering will also produce some errors.

Table 2 Validation results compared with previously published data of ORC system Fluids

Tgw,in

Tgw,out

mgw

Tcw,in

Tcw,out

mcw

Wnet

ηth

Sources

(℃)

(℃)

(kg/s)

(℃)

(℃)

(kg/s)

(kW)

(%)

R123

110.9

87.4

69.44

28

38

162.5

270

3.96

Ref. [33]

R123

110.9

87.4

69.44

28

38

162.5

288.1

4.10

Present study

5. Results and discussion 5.1 Net power output The effect of different evaporation temperatures on the net output power (Wnet) of the three systems is shown in Fig.3. From Fig. 3 (a), with the increase of evaporation temperature (te), the net output power of ORC system increases first and then decreases, and there is a peak value in the middle. It can be seen from Fig.3 (b) that when the low-

pressure evaporation temperature (te2) is fixed, the net output work of the TSORC-SHS system first increases and then decreases with the increase of the high-pressure evaporation temperature (te1), and there is a peak value in the middle. For another, when the high-pressure evaporation temperature is fixed and higher than 71℃, the net output power of the system decreases with the increase of the low-pressure evaporation temperature. On the contrary, when the high-pressure evaporation temperature is lower than 71℃, the net output power of the system increases with the rise of the low-pressure evaporation temperature. From Fig. 3 (c), when the high-pressure evaporation temperature is fixed and lower than 79℃, the trend of net output power of TSORCDHS system increases at first and then decreases with the increase of the low-pressure evaporation temperature, which is similar to the TSORC-SHS system. On the contrary, when the high-pressure evaporation temperature is fixed and higher than 79℃, the net output power tends to decrease with the increase of low-pressure evaporation temperature. When the low-pressure evaporation temperature is constant, the net output power increases first and then decreases with the rise of the high-pressure evaporation temperature, but the evaporation temperature of low-pressure evaporator should be less than that of high-pressure evaporator. It can be concluded that there is a coupling relationship between the high-pressure evaporation temperature and the low-pressure evaporation temperature of the TSORC system. One of the main purposes of this study is to find the coupling relationship between the two evaporation temperatures so as to achieve the optimal operating performance of the system. Because the output power of ORC, PDORC and SDORC systems is related to the

mass flow of the working fluid and the enthalpy difference of the working fluid at the inlet and outlet of the turbine. With the increase of evaporation temperature, the mass flow of ORC system gradually decreases, while the specific enthalpy difference increases. Therefore, the net output power of systems increases first and then decreases. Similarly, the working fluid mass flow of the TSORC-SHS and TSORC-DHS systems is opposite to the specific enthalpy difference at the inlet and outlet of the turbine, and there is a coupling relationship between the high-pressure evaporation temperature and the low-pressure evaporation temperature. By comparing the three systems, it can be concluded that the net output power of TSORC-DHS system is the highest, followed by the TSORC-SHS system, and the net output power of ORC system is the lowest. The optimal evaporation temperature of ORC is 80℃, and its corresponding optimal net output power is 58.98 kW. The optimal high-pressure evaporation temperature and the low-pressure evaporation temperature of TSORC-SHS are 88℃ and 71℃, respectively. At this time, its optimal net output power reaches the 75.72kW. When the high-pressure evaporation temperature and the low-pressure evaporation temperature are 80℃ and 74℃, respectively, the net output power of the TSORC-DHS system reaches the maximum value of 96.18 kW. By comparing the three systems, it can be concluded that the net output power of TSORC-DHS system is the highest, followed by the TSORC-SHS system, and the net output power of ORC system is the lowest. The maximum net output power of the TSORC-DHS system is 27.3% higher than that of the TSORC-SHS system and 63.1% higher than that of the ORC system.

Fig. 3 the net output power of three systems with different evaporation temperatures at 110℃

5.2 Exergy efficiency Fig. 4 illustrates the effects of different evaporation temperatures on the exergy efficiency (ηex) of the systems. As shown in Fig. 4 (a), the exergy efficiency of ORC system increases at first and then decreases with the increase of evaporation temperature (te), and there is a maximum value in the middle. From the Fig. 4 (b), when the lowpressure evaporation temperature (te2) is fixed, the exergy efficiency of the TSORCSHS system increases first and then decreases with the increase of the high-pressure evaporation temperature (te1), and there is a maximum value. When the high-pressure evaporation temperature is constant, the exergy efficiency of the TSORC-SHS system increases gradually with the rise of the low-pressure evaporation temperature. As shown in Fig. 4 (c), the variation trend of TSORC-DHS system exergy efficiency is similar to TSORC-SHS. The change trend of the exergy efficiency is similar to that of the net output power of the system. Exergy efficiency is the ratio of the net system output power to the exergy difference between the system inlet and outlet, that is, exergy efficiency is proportional to the net system output power. When the evaporation temperature is 97℃, the exergy efficiency of ORC system reaches the maximum, which is 26.76%. When the highpressure evaporation temperature and low-pressure evaporation temperature are 99℃ and 92℃, respectively, the maximum exergy efficiency of TSORC-SHS system is 27.92%. When the high-pressure evaporation temperature and the low-pressure evaporation temperature are 96℃ and 89℃, respectively, the maximum exergy

efficiency of TSORC-DHS system is 26.21%. Comparing the three systems, the exergy efficiency of TSORC-DHS system is 6.1% lower than that of TSORC-SHS system and 2.1% lower than that of ORC system.

Fig. 4 variation of exergy efficiency of three systems with different evaporation temperatures at 110℃

5.3 Thermal efficiency Fig. 5 describes the effects of different evaporation temperatures on the thermal efficiency of the three systems. It can be seen from Fig. 5 (a) that the thermal efficiency of ORC system increases at first and then decreases with the evaporation temperature (te), and there is a maximum value in the middle. As shown in the Fig. 5 (b), when the low-pressure evaporation temperature (te2) is fixed, the thermal efficiency of the TSORC-SHS system increases first and then decreases with the rise of the high-pressure evaporation temperature (te1). It can be seen from Fig.5 (c) that the variation trend of thermal efficiency of the TSORC-DHS system is similar to the TSORC-SHS, but the curve of the thermal efficiency of the TSORC-DHS system changes more slowly. According to Eqs. (33) and (42), the thermal efficiency of the system is related to the net output power and the heat transfer between the heat source and the working fluid.

When the available temperature difference of heat source increases gradually, the mass flow rate of working fluid also increases, which further increases the heat exchange capacity. In other words, when the mass flow rate of the heat source is constant, the enthalpy difference at the inlet and outlet of the heat exchanger increases, which is also an important factor affecting the thermal efficiency of the system. Therefore, the coupling relationship between the net output power and the enthalpy difference between the inlet and outlet of the evaporator leads to the variation law of the thermal efficiency of the system. When the evaporation temperature is 98℃, the thermal efficiency of ORC system reaches the maximum, which is 6.097%. The thermal efficiency of TSORC-SHS system reaches the maximum value of 6.04% when the high-pressure evaporation temperature and the low-pressure evaporation temperature are 99℃ and 92℃, respectively. When the high-pressure evaporation temperature and the low-pressure evaporation temperature are 97℃ and 92℃, respectively, the thermal efficiency of TSORC-DHS system reaches the maximum, which is 5.645%. Compared with the thermal efficiency of TSORC-SHS system, the maximum thermal efficiency of TSORC-DHS system is reduced by 6.5%, while compared with the thermal efficiency of ORC system, which of TSORC-DHS system is reduced by 7.1%. It is found that the thermal efficiency of ORC system is the highest, while that of TSORC-DHS system is the lowest. Therefore, it can be concluded that although the net output power of TSORC system is higher than that of ORC system, the heat energy absorbed by the heat source is much higher than that absorbed by ORC system. Therefore, in general, the thermal

and exergy efficiency of TSORC is lower than that of ORC system, especially the TSORC-DHS system.

Fig. 5 variation of the efficiency of three systems with different evaporation temperatures at 110℃ 5.4 Electricity production cost

Fig. 6 shows the variation of electricity production cost (EPC) with evaporation temperature for three systems with heat source temperature of 110℃. From Fig.6 (a), with the increase of evaporation temperature (te), the electricity production cost (EPC) of the ORC system decreases at first and then increases. There is a minimum value of 0.325$/kWh when the evaporation temperature of ORC is 88℃. As shown in Fig.6 (b), for the TSORC-SHS, when the low-pressure evaporation temperature (te2) is fixed and lower than 79℃, the electricity production cost of the system first decreases and then increases with the rise of high-pressure evaporation temperature (te1). When the lowpressure evaporation temperature is higher than 79℃, the electricity production cost of the system shows a decreasing trend with the increase of the high pressure evaporation temperature. So the TSORC-SHS system has the lowest electricity generation cost of 0.2764$/kWh when the high and low pressure evaporation temperature is 104℃ and 91℃ respectively. Fig.6 (c) shows that for the TSORC-DHS, with the rise of the highpressure evaporation temperature, the electricity production cost of the system shows a

tendency of decreasing first and then increasing when the low-pressure evaporation temperature is fixed and lower than 83℃. When the low-pressure evaporation temperature is higher than 83℃, the electricity production cost of the system shows an increasing trend with the rise of high-pressure evaporation temperature. The electricity production cost of TSORC-DHS system is the lowest with 0.0835$/kWh when the high and low pressure evaporation temperature is 82℃ and 77℃, respectively. From the Eq. (39), it can be seen that the electricity production cost of the system is mainly affected by the total cost of each component (Cost2018) and the net output power (Wnet) of the system, which is positively proportional to the total cost of each component and is inversely proportional to the net output power of the system. As can be seen from Fig. 3, the net output power of the system increases first and then decreases, while the total cost of each component of the system decreases with the increase of evaporation temperature. Therefore, most of the electricity production costs of these three systems have a trend of decreasing at first and then increasing. By comparing the three figures, it is found that the electricity production cost of ORC system is the largest, followed by TSORC-SHS system, while the electricity production cost of TSORC-DHS system is relatively low. Compared with TSORC-SHS system, the lower electricity production cost of TSORC-DHS system is mainly affected by the net output power of the system. When the heat source temperature is 110℃, the net output power of TSORC-DHS system is larger than that of TSORC-SHS system, which makes the electricity production cost of TSORC-DHS system relatively low. Compared with the TSORC-SHS and TSORC-DHS system, the ORC system has only one evaporator and one working fluid pump, which makes the total cost of the system components lower, but the reduction of net output power accounts for a relatively large proportion, so the electricity production cost is relatively high.

Fig. 6 variation of electricity production costs of three systems with different evaporation temperatures at 110℃

5.5 Payback period Fig. 7 shows the payback period (PBP) of the three systems with the heat source temperature of 110℃ at different evaporation temperatures. It can be seen from Fig. 7 (a) that with the increase of evaporation temperature (te), the payback period of ORC system decreases at first and then increases, and when the evaporation temperature is 88℃, the payback period of ORC system obtains the minimum value with 8.02 years. Fig.7 (b) shows that when the low-pressure evaporation temperature is fixed and lowers than 81℃, the investment payback period of TSORC-SHS system decreases at first and then increases with the high-pressure evaporation temperature. When the low-pressure evaporation temperature is higher than 81℃, with the increase of high-pressure evaporation temperature, the payback period of TSORC-SHS system shows a decreasing trend. When the evaporation temperatures of high and low pressure are 104℃ and 86℃, the investment payback period of TSORC-SHS system is the minimum, which is 6.22 years. From the Fig. 7 (c), when the low-pressure evaporation temperature is higher than 80℃, the payback period of TSORC-DHS system shows an increasing trend with the increase of high-pressure evaporation temperature. When the evaporation temperatures of high and low pressure are 82℃ and 77℃, respectively, the payback period of TSORC-DHS system is the minimum, which is 1.71 years. For the TSORCDHS system and ORC system, when the minimum value of system electricity production cost is obtained, the payback period is also the minimum value.

From the Eq. (40), it can be seen that the payback period of system is also affected by the total cost of each component (Cost2018) and the net output power (Wnet) of the system, so its change law is consistent with electricity production cost. Compared with the three diagrams, it is found that the payback period of ORC system is the largest, followed by that of TSORC-SHS system, while the payback period of TSORC-DHS system is the lowest. Compared with TSORC-SHS system, the lower payback period of TSORC-DHS system is mainly due to the relatively large net output power of the system. Although the component cost and net output power of ORC system are lower than other systems, the proportion of net output power of the system is relatively large, which makes the payback period of the ORC system relatively large.

Fig. 7 variation of payback period of three systems with different evaporation temperature of 110℃

The effect of different heat source temperatures on the maximum net output power (Wnet) of the three systems is shown in Fig. 8. It can be seen that with the increase of heat source temperature (tgwin), the maximum net output power of ORC, TSORC-SHS and TSORC-DHS systems also increases gradually. The net output power of the system is mainly affected by steam turbine power (Wt). However, the power of steam turbine

is affected by the mass flow rate of circulating working fluid and the enthalpy difference between inlet and outlet of steam turbine. When the heat source temperature increases, the mass flow rate of the circulating working fluid will also increase, which makes the steam turbine power also increase, and the net output power of the system also increase with it. As shown in the Fig. 8, when the heat source temperature is higher than 140℃, the maximum net output power of the TSORC-SHS system is the highest, and that of the ORC system is the lowest. On the contrary, when the heat source temperature is lower than 140℃, the maximum net output power of the TSORC-DHS system is the highest, and that of the ORC system is the lowest. With the increase of the heat source temperature, the difference between the maximum net output powers of the TSORCSHS system TSORC-DHS system gradually decreases. The results show that when the heat source temperature is 110℃, the difference between the maximum net output power of the TSORC-DHS system and TSORC-SHS system is 20.46 kW. At this time, the maximum net output power of the TSORC-DHS system increased by 27.3% with respect to the TSORC-SHS system. When the heat source temperature is 140℃, the difference between the maximum net output power of the TSORC-DHS system and TSORC-SHS system is the minimum and its value is 0.6 kW. At this time, compared with the TSORC-SHS system, the maximum net output power of the TSORC-DHS system is increased by 0.31%.

TSORC-DHS TSORC-SHS ORC

240

236

W net,max (kW)

200

242.4

199.5

192.3 191.7

160

154.8

155.6 147.2

122.9

120

117.8 108.5

96.18

80

85.76 75.72 58.98

40

110

120

130

140

150

tgwin(℃)

Fig. 8 the maximum net output power of three systems at different heat source temperatures

The effect of different heat source temperatures on the maximum exergy efficiency of the three systems is shown in Fig.9. It can be seen that with the increase of heat source temperature (tgwin), the maximum exergy efficiencies (ηex) of ORC, TSORCSHS and TSORC-DHS systems also increase gradually, while the growth rate of the three systems slowed down. When the heat source temperature is lower than 120℃, the maximum exergy efficiency of the TSORC-SHS system is the largest, followed by the ORC system, and the maximum exergy efficiency of the TSORC-DHS system is lowest. When the heat source temperature is higher than 120℃, the maximum exergy efficiency of the TSORC-SHS system is the largest, followed the TSORC-DHS system, and that of the ORC system is lowest. As the inlet temperature of the heat source increases, the difference between the maximum exergy efficiency of the TSORC-SHS system and the TSORC-DHS system gradually decreases. The results show that when the heat source temperature is 110℃, the difference between the maximum exergy efficiency of the

TSORC-SHS system and TSORC-DHS system is the largest, which is 1.87%. When the heat source temperature is 150℃, the difference between the maximum exergy efficiency of the TSORC-SHS system and TSORC-DHS system is the lowest, which is 0.15%. Fig. 10 shows the effect of different heat source temperature on the maximum thermal efficiency (ηth) of the three systems. It can be seen that with the increase of the heat source temperature, the maximum thermal efficiency of the TSORC-SHS system is always the highest, followed by the ORC system, and that of TSORC-DHS system is lowest. The difference between the maximum thermal efficiencies of the three systems remains almost constant with the heat source temperature. With the increase of the heat source temperature, the maximum thermal efficiency of ORC, TSORC-SHS and TSORC-DHS systems is gradually improved. This is because the thermal efficiency of the system is related to the net output power. When the inlet temperature of the heat source increases, both the net output power and the thermal efficiency of the system increase.

Fig. 9 variation of exergy efficiency of three systems at different heat source temperatures

Fig. 10 variation of thermal efficiency of three systems at different heat source temperatures

Fig.11 illustrates the variation of electricity production cost (EPC) of the three systems at different heat source temperatures. It can be seen from that when the heat source temperature (tgwin) is the same, the electricity production cost (EPC) of the three systems is the smallest in the TSORC-DHS system, followed by the TSORC-SHS

system, and that of the ORC system is the largest. The electricity production costs of the three systems gradually decrease with the increase of the heat source temperature, and the difference between the three systems are also decrease. TSORC-SHS system has the largest reduction in electricity production cost, while TSORC-DHS system has the smallest reduction. When the heat source temperature increases from 110℃ to 150℃, the electricity production cost of TSORC-SHS system is reduced by 56.5%, that of TSORC-SHS system is reduced by 50.8%, and that of TSORC-DHS system is reduced by 40.4%. It can be seen from Fig. 8 that with the increase of the heat source temperature, the net output power of the TSORC-SHS system is also gradually increasing. And when the heat source temperature exceeds 140℃, the net output power of the TSORC-SHS system will exceed the net output power of the TSORC-DHS system. The growth rate of net output power of TSORC-DHS system is the smallest, while the increase rate of net output power of ORC system is the largest. However, the total cost of each component of ORC system is lower than that of the other two systems. Because the cost of electricity production is inversely proportional to the net output power of the system, the reduction of electricity production cost of TSORC-DHS system is the lowest. The electricity production cost of TSORC-SHS system is the largest, which makes the electricity production cost of TSORC-SHS system closer and closer to that of TSORCDHS system. At the same time, it is indirectly proved that the higher the heat source temperature, the weaker the advantages of TSORC-DHS system.

Fig. 11 variation of electricity production cost of three systems under different heat source temperatures

Fig. 12 shows the change of the payback period of the three systems when the heat source temperature changes from 110℃ to 150℃. It can be seen that when the heat source temperature (tgwin) is fixed, the payback period (PBP) of ORC system is relatively large, followed by TSORC-SHS system, and the payback period of the TSORC-DHS system is lowest. With the increase of heat source inlet temperature, the payback periods of the three systems are gradually decreasing, and the difference between the payback periods of three systems is also gradually decreasing. When the heat source temperature is 150℃, the difference between the payback periods of the three systems is the lowest. At this time, there is a difference of 2.42 years between ORC system and TSORC-DHS system, and 1.41 years between TSORC-SHS system and TSORC-DHS system. When the heat source temperature is 110℃, the difference between the payback periods of the three systems are the largest, and the difference between the payback period of the ORC system and the TSORC-DHS system is 6.30 years. The difference between the payback period of TSORC-SHS system and TSORCDHS system is 4.50 years. With the increase of heat source inlet temperature, the

reduction in these three systems is also gradually decreasing. Among them, the payback period of TSORC-SHS system is the largest, while the decrease of TSORC-DHS system investment payback period is the smallest. With the change of heat source inlet temperature from 110℃ to 150℃, the payback period of TSORC-SHS system is reduced by 61.3%, the payback period of TSORC system investment is reduced by 57.4%, and the investment payback period of TSORC-DHS system is reduced by 41.8%. The payback period of system is mainly affected by the total cost of each component and the net output power of the system. When the inlet temperature of the heat source of the system increases, the net output power difference between three systems gradually decreases.

Fig. 12 variation of investment payback period of three systems under different heat source temperatures

6. Conclusions To improve the power generation performance of organic Rankine cycle system

and realize the cascade utilization of different temperature heat sources, the two-stage series organic Rankine cycle system of double heat source system is proposed based on two-stage serial organic Rankine cycle system of single heat source system. The optimum evaporation temperature of organic Rankine cycle, two-stage serial organic Rankine cycle system of single heat source and two-stage series organic Rankine cycle system of double heat source systems is selected to improve the power generation and economic performance. The heat source temperature changes from 110℃ to 150℃, and the power generation performance and economic benefit of the three systems are optimized. The main conclusions are as follows: (1) When the heat source temperature is lower than 130℃, the thermodynamic performance of two-stage series organic Rankine cycle system of double heat source system is better than that of organic Rankine cycle system and two-stage serial organic Rankine cycle system of single heat source system. When the heat source temperature is higher than 130℃, the advantage of two-stage series organic Rankine cycle system of double heat source system is weakened, while that of two-stage serial organic Rankine cycle system of single heat source system is relatively improved. With the increasing of heat source temperature, the influence of composite heat source on the performance of the system decreases gradually, so two-stage series organic Rankine cycle system of double heat source is more suitable for low temperature heat source. (2) When the heat source temperature is 110℃, the effect of evaporation temperature on the performance of organic Rankine cycle, two-stage serial organic Rankine cycle system of single heat source and two-stage series organic Rankine cycle

system of double heat source systems is studied. Based on the net output power of the system, the optimum evaporation temperature of organic Rankine cycle system is 80℃, and the optimum high-pressure evaporation temperature and low-pressure evaporation temperature of two-stage serial organic Rankine cycle system of single heat source system are 88℃ and 71℃, respectively. The optimum high-pressure evaporation temperature and low-pressure evaporation temperature of two-stage series organic Rankine cycle system of double heat source system are 80℃ and 74℃, respectively. (3) The electricity production costs of organic Rankine cycle, two-stage serial organic Rankine cycle system of single heat source and two-stage series organic Rankine cycle system of double heat source systems decrease at first and then increase with the increasing of evaporation temperature, and there are three minimum value. Among the three systems, the electricity production cost of two-stage series organic Rankine cycle system of double heat source system is the smallest, while that of organic Rankine cycle system is the largest. (4) For organic Rankine cycle system, when the evaporation temperature is 88℃, the electricity production cost and payback period of the system are the minimum, which are 0.323$/kWh and 8.02 years, respectively. For two-stage series organic Rankine cycle system of double heat source system, when the high and low pressure evaporation temperature is 82℃ and 77℃, the electricity production cost and payback period of the system are the minimum, which are 0.084$/kWh and 1.71 years, respectively. (5) During the change of heat source inlet temperature from 110℃ to 150℃, it is found that the electricity production cost and payback period of two-stage series organic

Rankine cycle system of double heat source system are always the smallest, followed by those of two-stage serial organic Rankine cycle system of single heat source system, and the largest is the electricity production cost and investment payback period of organic Rankine cycle system.

Acknowledgments The authors gratefully acknowledge the support provided by the National Key Research and Development Program of China (Grant No. 2018YFB1501805) and the Opening Funds of State Key Laboratory of Building Safety and Built Environment And National Engineering Research Center of Building Technology (Grant No. BSBE2018-06).

Nomenclature

A

Area (m2)

C

Cost ($)

c

Specific heat (kJ/kg)

Ex

Exergy flow rate (kW)

e

Specific flow exergy (kJ/kg)

h

Specific enthalpy (kJ/kg)

m

Mass flow rate (kg/s)

P

Pressure (MPa)

Q

Heat flow rate (kW)

s

Specific entropy (kJ/(kg ℃))

T

Temperature (K)

ΔT

Temperature difference (K)

t

Temperature (℃)

U

Intrinsic energy (kJ)

W

Mechanical work (kW)

Greek symbols η

Efficiency

Subscripts

　

c

Condenser

e

Evaporator

ex

Exergetic

g

Generator

gw

High-temperature geothermal water

he

Heat exchanger

in

Inlet of each component

lw

Low-temperature geothermal water

out

Outlet of each component

p

Pump

pp

Pinch point

s

Isentropic

t

Turbine

th

Thermal

wf

Working fluid

2~5, 11, 16, 17, 18, 21, State points 26, 27, 28, 12s. Acronyms

　

CB

Regenerative cycle with closed preheater and bleed stream throttling

CF

Regenerative

cycle with

closed preheater and

bleed

stream recirculation CRF

Capital recovery factor

EPC

Electricity production cost

LEC

Horizontal energy cost

O

Regenerative cycle with open preheater

ORC

Organic rankine cycle

PBP

The payback period

ROROI

Rate of return on investment Two-stage series organic Rankine cycle system of double

TSORC-DHS heat source Two-stage serial organic Rankine cycle system of single TSORC-SHS heat source

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Highlights



Two-stage evaporation is proposed.



Energetic, exergetic and economic performances are compared.



Two-stage serial organic Rankine cycle is advisable for double-level heat sources.