Two-stage evaporation strategy to improve system performance for organic Rankine cycle

Applied Energy 150 (2015) 323–334

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Two-stage evaporation strategy to improve system performance for organic Rankine cycle Tailu Li ⇑, Zhigang Zhang, Jian Lu, Junlan Yang, Yujie Hu School of Energy and Safety Engineering, Tianjin Chengjian University, Tianjin 300384, PR China

h i g h l i g h t s  The heat source is segmented in two temperature ranges.  We propose parallel and series two-stage organic Rankine cycle.  The objective function is the ratio of net power output to thermal conductance.  The STORC exceeds the PTORC.

a r t i c l e

i n f o

Article history: Received 26 May 2014 Received in revised form 21 October 2014 Accepted 6 April 2015

Keywords: Organic Rankine cycle Geothermal water Cascade evaporating Heat recovery Performance enhancement

a b s t r a c t The organic Rankine cycle (ORC) is a promising technology for heat recovery. However, evaporator leads to the highest irreversible loss and results in reducing cycle efficiency. In this paper, the heat source was segmented into two temperature ranges, which provides the possibility of two-stage evaporation. Based on cycle configuration, parallel two-stage organic Rankine cycle (PTORC) and series two-stage organic Rankine cycle (STORC) were put forward. The objective is to evaluate system performances, thereby elucidating their respective availability. Geothermal water inlet temperature (GWIT) ranges from 90 to 120 °C, with R245fa as the working fluid. The ratio of net power output to the total thermal conductance was chosen as the objective function. The results show that PTORC and STORC are significantly influenced by intermediate geothermal water temperature (IGWT) and evaporating temperatures. PTORC and STORC could evidently reduce the irreversible loss, and STORC is more significant. PTORC and STORC can output more net power, depending on cycle configuration and GWIT. STORC enhances the net power output with GWIT, whereas PTORC is just the opposite. The total thermal conductance of PTORC and STORC are almost equal with that of ORC. STORC presents more excellent system performance and deserves to be popularized in engineering applications. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction The global population growth together with the economic development results in the energy consumption acceleration. It is predicted that the energy demand will increase 33% by 2020 [1]. The electricity price has increased by about 12% over the past decade [2,3]. Furthermore, global warming, ozone layer depletion, and other environmental issues heave a great influence on energy policy. Therefore, the severe energy situation has attracted much attention on power generation from renewable sources and waste heat. The available solutions include organic Rankine cycle (ORC), Stirling cycle, Kalina cycle, et al. Among these cycles, ORC has been proposed due to its simplicity, reliability, and flexibility [4]. The ⇑ Corresponding author. Tel./fax: +86 22 23085107. E-mail address: [email protected] (T. Li). http://dx.doi.org/10.1016/j.apenergy.2015.04.016 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

ORC-based plants have been successfully adopted in recovering geothermal energy [5], solar energy [6], ocean thermal energy [7], and waste heat [8]. With respect to heat recovery, ORC is an effective way to recover low-medium grade heat, but the biggest problem is that the thermal efficiency is relatively low [9]. Mago et al. [10] calculated the exergy destruction using an exergy wheel. The evaporator has the highest exergy destruction rate, around 77%. Numerous studies have been carried out to reduce the irreversible loss, thereby improving the system performance. The correlative literatures can be summarized as the parametric optimization, and the hot topics can be classified into two aspects, i.e., the zeotropic mixtures and the cycle configuration improvement. The zeotropic mixtures have non-isothermal phase shift to decrease the irreversible loss in the evaporator and condenser. The screening of the working fluids have been studied by Wang et al. [11], Garg

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Nomenclature A C Ex f h I K M M0 m P Q s T t W DP

area (m2) specific heat (W/(kg °C)) exergy (kW) function specific enthalpy (kJ/kg) irreversibility rate (kW) heat transfer coefficient (W/(m2 °C)) molar mass (kg/kmol) amount of intermediate geothermal water temperature mass flow rate (kg/s) pressure (MPa) heat transfer rate (kW) specific entropy (kJ/(kg °C)) temperature (K) temperature (°C) power (kW) pressure difference (Pa)

Greek symbols g efficiency (%) q density (kg/m3) Subscripts c condenser con condensing cri critical cw cooling water e evaporator eva evaporating ex exergetic g generator

et al. [12], Borsukiewiczgozdur and Nowak [13], Chys et al. [14], and Heberle et al. [15]. However, we do not focus on the working fluid selection in this paper. The cycle configuration is another aspect that should be improved in order to enhance the system performance. ORC has already well known and successfully practised in engineering applications, but few literatures have paid attention on the cycle configuration to enhance the system performance. Based on ORC, a regenerator is installed to form the regenerative organic Rankine cycle (RORC). Many researchers have analyzed the RORC to focus on the cycle performance. Mago et al. [16] presented that RORC could not only produces higher efficiency but also reduces the heat absorption of the system to produce the same amount of power with a lower irreversibility. Pei et al. [17] designed an innovative of low temperature solar thermal electric generation with RORC. They found that RORC increases the thermal efficiency by about 4.9%. Xi et al. [18] investigated ORC, RORC, and the double-stage regenerative organic Rankine cycle (DRORC). The results indicate that the DRORC gives the highest efficiencies. Roy and Misra [19] analyzed and compared the RORC in order to select a better working fluid using the system efficiency as the objective function. Fernández et al. [20] compared the saturated and superheated, subcritical and supercritical RORCs and evaluated the influence of internal heat exchanger (IHX) on thermal efficiency. They found that the supercritical RORC is preferable for high temperatures heat source. Moreover, the thermal efficiency is directly related to the internal heat exchanger. Franco [21] utilized two different configurations, two basic cycle configurations, and two recuperated cycles to analyze the exploitation geothermal fluids dominated by low temperature water. The system performance

gw hw in m net obj out p pre pp s sup t th wf 0 10 , 100 , 2,

geothermal water hot water inlet mechanical net objective outlet pump pre-cooling or preheating pinch point isentropic superheating turbine thermal working fluid environment 3, 40 , 400 , 5, a, b, c, d, e state points

Acronyms ALT atmosphere life time (yr) CWIT cooling water inlet temperature GWIT geothermal water inlet temperature GWP global warming potential IGWT intermediate geothermal water temperature ODP ozone deletion potential ORC organic Rankine cycle PTORC parallel double cascade-evaporator organic Rankine cycle RORC regenerative organic Rankine cycle STORC series double cascade-evaporator organic Rankine cycle SORC solar organic Rankine cycle

increased a little, but significant reduction was found in cooling system surface area (up to 20%). Li et al. [22] constructed and experimentally analyzed the RORC with a geothermal source temperature of 130 °C. They found that the RORC has a thermal efficiency of 7.98%, which is higher than that of the ORC by 1.83%. In general, RORC not only decreases the thermal load of the condenser but also reduces the irreversible loss in the evaporator, but the system performance can be improved only to a small extent. Lecompte et al. [23] studied the ORC applied to a combined heat and power system. Kevin et al. [24] presented a set of concepts to create a customized including reheat stages, multiple pressure levels and balanced recuperators. Liu et al. [25] investigated the effect of condensing temperature glide on the performance of ORC with zeotropic mixtures. On the premise of ensuring the temperature difference at the pinch point, the single-evaporation in the evaporator is a major factor affecting the system irreversible loss. Many literatures have studied double-loop ORC to increase the system performance. Kosmadakis et al. [26] and Kosmadakis et al. [27] presented the parametric study and economic evaluation of a two-stage solar organic Rankine cycle (SORC) for reverse osmosis desalination. It was found that the two-stage SORC significantly improves the efficiency and reduces the system cost. Wang et al. [28] analyzed the combination of a gasoline engine with a dual loop ORC. The results indicate that the thermal efficiency increases by 3–6% throughout the operating region of the engine. Liu et al. [29] proposed a two-stage Rankine cycle consisting of a water steam Rankine cycle and an ORC for power generation. Zhang et al. [30] and Shu et al. [31–33] analyzed a dual-loop organic Rankine cycle (DORC) consisting of high- and low-temperature cycles. They found that

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1'

Turbine d

2 1" Evaporator1

Evaporator2 b

4'

4"

Condenser

3

c

Pump1

e

Pump2

Fig. 1. Schematic diagram of the PTORC.

Ge oth erm al wa

ter

1' 1"

4' 2 4" 3

Co oling wa ter

s (kJ/kg •K) Fig. 2. T  s diagram of the PTORC.

Generator

a

2. System description and working principle

1'

Turbine

2

d

1" Evaporator1

Evaporator2 Condenser

b

4'

4"

5

e

3

Pump1

Pump2

c Fig. 3. Schematic diagram of the STORC.

T (°C)

The heat source is segmented in two temperature ranges.1 Geothermal water from the production wells flows through the evaporator 1 and evaporator 2 successively. It is identified as a–b–c, which is shown by red lines from Figs. 1–4. Geothermal water from the outlet of the evaporator 2 will be reinjected. The cooling water goes into the condenser driven by the cooling water pump, and it can be identified as d–e–d, which is shown by green lines. The heat source and heat sink in the PTORC and STORC are completely the same. Moreover, the counter-current flow between the heat source and heat sink with the working fluid were adopted. The PTORC and STORC are both subcritical, and R245fa was chosen as the working fluid. Figs. 1 and 2 show the schematic diagram and the corresponding T  s diagram of the PTORC, respectively. The PTORC is almost the same with the basic ORC, and the main difference between them two is that the PTORC adopts double cascade-evaporating strategy whereas the basic ORC only has one. The PTORC consists of a high-pressure evaporator 1, a low-pressure evaporator 2, a high-pressure pump 1, a low-pressure pump 2, an induction turbine, a generator, a condenser, a cooling pump, and a cooling tower. The specific flowchart for the working fluid is as follows: The non-saturated liquid with a higher pressure and a lower temperature is pumped into the evaporator 1 by the pump 1, It could absorb heat from geothermal water (process a–b) coming from production wells to generate high-pressure saturated or superheated vapor (process 40 –10 ). Moreover, the nonsaturated liquid with relatively lower pressure temperature is

Generator

a

T (°C)

DORC with double regenerators performs better and that low condensation temperature of the high-temperature loop is beneficial to performance optimization better. Yang et al. [34] designed a set of dual-loop ORC to recover exhaust energy. The thermal efficiency is increased by 13% for the high load region and the brake specific fuel consumption can be reduced by a maximum 4%. Mohammadkhani et al. [35] utilized a gas turbine-modular helium reactor by two ORCs. Li et al. [36] presented a parallel doubleevaporator organic Rankine cycle (PDORC) to decrease the system irreversibility and to enhance the power output. Moreover, Stijepovic et al. [37] indicated that the multiple pressure system could have significant improvements in system performance. From the above-mentioned studies, it can be obtained that the two- or multi-stage ORC can indeed improve the system performance. However, it should be pointed out that the cycle configurations in literatures [26–37] are all parallel systems in essence, and this kind of configuration could adversely reduce the irreversible loss of the high-stage evaporator for the working fluid side. Moreover, no literature has been found to compare parallel and series two-stage organic Rankine cycles. The present paper focuses on the evaluation of the system performance improvement. The heat source is segmented in two temperature ranges. The parallel two-stage organic Rankine cycle (PTORC) and series two-stage organic Rankine cycle (STORC) are put forward to decrease the irreversible loss, especially in the evaporator. R245fa is adopted as the working fluid. The main objective is to compare the system performance of PTORC and STORC, thus elucidating their respective applicability. The dimensionless ratio of the exergetic efficiency to the total thermal conductance could act as the objective function. The parameters (mass flow rate, evaporating temperature, IGWT, VFR, net power output, cycle efficiency, thermal conductance, and objective function) of PTORC and STORC were compared with those of ORC.

1'

ter Ge oth erm al wa 5

4' 1" 2

4" 3

Co oling wa ter

s (kJ/kg •K) 1

For interpretation of color in Figs. 1–4, the reader is referred to the web version of this article.

Fig. 4. T  s diagram of the STORC.

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T. Li et al. / Applied Energy 150 (2015) 323–334

pumped into the evaporator 2 by the pump 2. The heat from geothermal water (process b–c) coming from the evaporator 1 can be absorbed to generate low-pressure saturated or superheated vapor (process 400 –100 ). The vapor at the state points 10 and 100 flow into the corresponding stages of the induction turbine where its enthalpy is converted into mechanical energy to drive the generator to produce electricity (process 10 (100 )–2). The discharging steam from the turbine outlet would come into the condenser where it is liquefied by the cooling water (process 2–3) driven by the cooling pump. The liquid at the condenser outlet is divided into two parts, which is pressurized by the pumps 1 and 2, and then another new cycle begins. The PTORC can be identified as 10 (100 )–2–3–40 (400 )–10 (100 ), which is shown by green lines. Figs. 3 and 4 depict the schematic diagram and the corresponding T  s diagram of the STORC, respectively. The STORC are almost the same with the PTORC, and the largest difference is that the high and low stages are connected to each other. The liquid working fluid from the condenser is first pressurized to flow into evaporator 2. This step could help to absorb heat from geothermal water (process b–c) coming from the evaporator 1 to generate low-pressure saturated or superheated vapor (process 400 –100 ). Then, a portion of the saturated liquid at the saturated pressure in the evaporator 2 is pumped to the evaporator 1 to absorb heat from geothermal water (process a–b) coming from production wells to generate high-pressure saturated or superheated vapor (process 40 –10 ). It should be clarified that the evaporators 1 and 2 in Fig. 1 and evaporator 2 in Fig. 3 can be the tube-shell heat exchanger or plate heat exchanger. Usually, the plate heat exchanger is more suitable for small scale systems due to the compactness and effectiveness, whereas the tube-shell heat exchanger is more suitable for large scale systems due to the high volumetric flow ratio of the working fluid. However, the evaporator 2 in Fig. 3 should be the tube-shell heat exchanger, because a portion of the working fluid, steam 5, is pumped from upper layer of the liquid working fluid in evaporator 2. Evaporator 2 in Fig. 3 adds an outlet pipe at the bottom based on the traditional tube-shell heat exchanger, so there are two inlet pipes (geothermal inlet pipe b and working fluid inlet pipe 400 ) and three outlet pipes (geothermal outlet pipe c, liquid fluid outlet pipe 5 and superheated vapor outlet pipe 100 ). 3. Mathematical model The energetic and exergetic analysis based on the first and second laws of thermodynamics were carried out for the working fluid. For simplicity, the following hypotheses were made: (1) Geothermal power plants operate in a steady-state condition. (2) Superheated vapor exists at the outlet of the evaporator, with a degree of superheat of 5 °C. Saturated liquid is also supposed to be at the condenser exit. (3) The working fluid at the inlet of the evaporator 1 for STORC is expected to stay at the saturated pressure in the evaporator 2. (4) Pressure would drop throughout the exchangers, while the exchangers and the pipelines could be neglected. (5) The kinetic and potential energy changes are negligible. (6) The temperature and friction losses are negligible. (7) Energy loss during the mixing process of the high- and lowpressure vapor in the turbine is negligible. The mathematical model for PTORC is expressed by the following equations:

Turbine:

gt ¼ ðh10  h2 Þ=ðh10  h2s Þ ¼ ðh100  h2 Þ=ðh100  h2s Þ

ð1Þ

where g and h denote the efficiency and the enthalpy, respectively; the subscript t stands for the turbine, and s means the isentropic process.

W t ¼ ðmwf;1 ðh10  h2s Þ þ mwf;2 ðh100  h2s ÞÞgt

ð2Þ

As the inlet and outlet temperatures of the heat source are given, Li et al. [38] found that there exists an optimal evaporating temperature maximizing the net power output. The heat source is segmented into two temperature ranges in this paper, so the mass flow rate of the working fluid for the two stages, mwf;1 and mwf;2 , can be calculated according to Li et al. [38]: mwf;1 ¼ minðmwf;11 ; mwf;12 Þ ¼

8 T gw;mid Þ < mwf;11 ¼ mgw cp;gwhðT gw;in ; T e;1 6 T e;1;opt h 10

:m

wf;12

¼

40

mgw cp;gw ðT gw;in T e DT pp Þ ;T e;1 h10 h40

> T e;1;opt ð3Þ

mwf;2 ¼ minðmwf;21 ; mwf;22 Þ ¼

8 T gw;out Þ < mwf;21 ¼ mgw cp;gwhðT gw;mid ; T e;2 6 T e;2;opt h 100

:m

wf;22 ¼

400

mgw cp;gw ðT gw;in T e DT pp Þ ;T e;2 h100 h400

> T e;2;opt ð4Þ

where W and m represent the power output and the mass flow rate, respectively; the subscript wf stands for the working fluid.

It ¼ T 0 ðmwf;1 ðs2  s10 Þ þ mwf;2 ðs2  s100 ÞÞ

ð5Þ

where I and s stand for the irreversible loss and the entropy, respectively; T 0 means the ambient temperature. Condenser:

Q c ¼ ðmwf;1 þ mwf;2 Þðh2  h3 Þ

ð6Þ

where Q stands for the thermal load; the subscript c stands for condenser.

Ic ¼ ðmwf;1 þ mwf;2 ÞT 0 ½ðs3  s2 Þ  ðh3  h2 Þ=T L 

ð7Þ

where T stands for the temperature; T L stands for the average temperature of the cooling water.

  W p;cw ¼ mcw DPcw = gp;cw qcw

ð8Þ

where q means for the density; the subscript p stands for the pump; DP cw represents the pressure loss in the cooling water circuit; the subscript cw stands for the cooling water.

ðKAÞc;pre ¼ Q c;pre =ðDT c;pre Þ

ð9Þ

ðKAÞc;con ¼ Q c;con =ðDT c;con Þ

ð10Þ

ðKAÞc;total ¼ ðKAÞc;pre þ ðKAÞc;con

ð11Þ

Q c ¼ Q c;pre þ ðKAÞc;con

ð12Þ

where K and A stand for the heat transfer coefficient and the area, respectively; the subscripts pre, and con stands for the pre-cooling from overheated to saturated vapor and condensing. The pre-cooling means the Pump 1:

gp1 ¼ ðh40 ;s  h3 Þ=ðh40  h3 Þ

ð13Þ

W p1 ¼ mwf;1 ðP e0  P c Þ=ðgp1 qwf Þ

ð14Þ

where P denotes the pressure; the subscripts e0 and c represent the evaporating pressure in the evaporator 2 and the condensing pressure, respectively.

T. Li et al. / Applied Energy 150 (2015) 323–334

Ip1 ¼ mwf;1 T 0 ðs40  s3 Þ

ð15Þ

Pump 2:

Itotal ¼ It þ Ic þ Ip1 þ Ip2 þ Ie1 þ Ie2  ¼ T 0 mwf;1 ððh40  h10 Þ=T H0 þ ðh2  h3 Þ=T L Þ  þmwf;2 ððh400  h100 Þ=T H00 þ ðh2  h3 Þ=T L Þ

327

ð37Þ

gp2 ¼ ðh400 ;s  h3 Þ=ðh400  h3 Þ

ð16Þ

W p2 ¼ mwf;2 ðPe00  Pc Þ=ðgp2 qwf Þ

ð17Þ

W net ¼ gm gg W t  W p1  W p2  W p;cw  W p;gw

Ip2 ¼ mwf;2 T 0 ðs400  s3 Þ

ð18Þ

where gm and gg are the conversion efficiency of the mechanical energy and the efficiency of the generator, respectively. Thermal efficiency:

Net power output:

Evaporator 1:

Q e1 ¼ mwf;1 ðh10  h40 Þ

ð19Þ

where the subscripts e1 and wf1 stand for the evaporator 1 and the working fluid evaporated in the evaporator 1.

Ie1 ¼ mwf;1 T 0 ½ðs10  s40 Þ  ðh10  h40 Þ=T H0 

ð20Þ

where T H0 represents the average temperature of the heat source in the evaporator 1.

W p;gw1 ¼ mgw DPgw1 =ðgp;gw qgw Þ

ð21Þ

where gw represents geothermal water; DPgw1 stands for the pressure drop in the evaporator 1.

gth ¼ W net =ðQ e1 þ Q e2 Þ

ð38Þ

ð39Þ

The exergy for geothermal water at the inlet and outlet of the evaporator can be expressed as:

mgw ðha  hc Þ ¼ mwf;1 ðh10  h40 Þ þ mwf;2 ðh100  h400 Þ

ð40Þ

where the subscripts a and c stand for the state points of geothermal water.

Exgw ¼ mgw ½ðha  hc Þ  T 0 ðsa  sc Þ

ð41Þ

Exergetic efficiency:

gex ¼ W net =Exgw

ð42Þ

ðKAÞe1;pre ¼ Q e1;pre =ðDT e1;pre Þ

ð22Þ

ðKAÞe1;eva ¼ Q e1;eva =ðDT e1;eva Þ

ð23Þ

F obj ¼ W net =ðKAÞtotal

ðKAÞe1;sup ¼ Q e1;sup =ðDT e1;sup Þ

ð24Þ

ðKAÞe1;total ¼ ðKAÞe1;pre þ ðKAÞe1;eva þ ðKAÞe1;sup

ð25Þ

Q e1 ¼ Q e1;pre þ Q e1;eva þ Q e1;sup

ð26Þ

The mathematical model for the STORC is similar with that for the PTORC. The parameters of geothermal water and cooling water for the STORC are quite the same with those for the PTORC. However, for the working fluid circuit, the mathematical models of the evaporator 2 and the pumps for the STORC are expressed as follows: Pump 1:

Objective function:

where the subscript e1 represents the evaporator 1; the subscripts pre, eva, and sup stands for the pre-heating, evaporating, and superheating. Evaporator 2:

Q e2 ¼ mwf;2 ðh100  h400 Þ

ð27Þ

where the subscripts e2 and wf2 stand for the evaporator 2 and the working fluid evaporated in the evaporator 2.

Ie2 ¼ mwf2 T 0 ½ðs100  s400 Þ  ðh100  h400 Þ=T H00 

ð28Þ

gp1 ¼ ðh40 ;s  h5 Þ=ðh40  h5 Þ

ð43Þ

ð44Þ

where the subscript 5 stands for the saturated liquid at the saturated temperature in the evaporator 2.

W p1 ¼ mwf;1 ðpe0  pe00 Þ=ðgp1 qwf Þ

ð45Þ

Ip1 ¼ mwf;1 T 0 ðs40  s5 Þ

ð46Þ

Pump 2:

where T H00 represents the average temperature of the heat source in the evaporator 2.

W p2 ¼ ðmwf;1 þ mwf;2 Þðpe00  pc Þ=ðgp2 qwf Þ

ð47Þ

  W p;gw2 ¼ mgw DPgw2 = gp;gw qgw

Ip2 ¼ ðmwf;1 þ mwf;2 ÞT 0 ðs400  s3 Þ

ð48Þ

ð29Þ

where DPgw1 stands for the pressure drop in the evaporator 2.

Evaporator 2:

Q e2 ¼ mwf;1 ðh5  h400 Þ þ mwf;2 ðh100  h400 Þ

ð49Þ

Ie2 ¼ mwf;2 T 0 ½ðs100  s400 Þ  ðh100  h400 Þ=T H00 

ð50Þ

ðKAÞe2;pre ¼ Q e2;pre =ðDT e2;pre Þ

ð30Þ

ðKAÞe2;eva ¼ Q e2;eva =ðDT e2;eva Þ

ð31Þ

ðKAÞe2;sup ¼ Q e2;sup =ðDT e2;sup Þ

ð32Þ

ðKAÞe2;total ¼ ðKAÞe2;pre þ ðKAÞe2;eva þ ðKAÞe2;sup

ð33Þ

ð51Þ

Q e2 ¼ Q e2;pre þ Q e2;eva þ Q e2;sup

ð34Þ

The other equations for the STORC are the same with those for the PTORC.

where the subscripts e stands for the evaporator. Total thermal conductance in the evaporator:

ðKAÞe ¼ ðKAÞe1 þ ðKAÞe2

Total thermal conductance:

mgw ðha  hc Þ ¼ mwf;1 ðh10  h40 Þ þ mwf;1 ðh5  h400 Þ þ mwf;2 ðh100  h400 Þ

4. Validation

ð35Þ

Total thermal conductance:

ðKAÞtotal ¼ ðKAÞe þ ðKAÞc

The exergy for geothermal water at the inlet and outlet of the evaporator for the STORC can be expressed as:

ð36Þ

Numerical model is validated by the experimental data for R245fa-based ORC under the same heat source and heat sink. The numerical results show a very good agreement with the experimental data results, as shown in Table 1. The rated power output of the experimental table is 500 W, with R245fa as the working

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T. Li et al. / Applied Energy 150 (2015) 323–334

Table 1 Validation of the numerical model with previous published data [34] for various fluids-based ORC. Fluids

T gw;inlet (°C)

T gw;outlet (°C)

mgw (kg/s)

T cw;inlet (°C)

T cw;outlet (°C)

mcw (kg/s)

VFR

W t (W)

gth (%)

Sources

R245fa R245fa

90 90

70 70

0.14 0.14

30 30

35 35

0.27 0.27

4.0 4.4

492 532

4.30 4.65

Experiment Present

Table 2 Simulation parameters and boundary conditions used in this study. Parameter

Value

Parameter

Value

GWIT (°C) Tail water outlet temperature (°C) Geothermal water flow rate (m3/h) Cooling water inlet temperature (°C) Cooling water outlet temperature (°C) Pinch point temperature difference (°C) Turbine inlet superheated degree (°C)

90–120 P70 69.45 25 35 5 5

Turbine isentropic efficiency (%) Pump isentropic efficiency (%) Cooling pump efficiency (%) Mechanical efficiency (%) Generator efficiency (%) Environmental temperature(°C) Environmental pressure (MPa)

75 60 75 97 98 25 0.101325

fluid. The absolute difference in the VFR is only 0.4, with a relative difference of 10.00%. The absolute difference in the power output is 40 W, whereas the absolute difference in the thermal efficiency is 0.35. Moreover, the relative difference in the power output and the thermal efficiency is almost the same, about 8.13%. The values of the VFR, the power output and the cycle efficiency for the experiment are always lower than those for the numerical calculation. The differences mainly arise from the pressure drop of the working fluid in both the pipes the heat exchangers, and no pressure drop in both the pipes the heat exchangers was adopted for the numerical calculation while the pressure drop always exists in both the pipes the heat exchangers. On the other hand, the errors of the measuring instruments are another aspect that would lead to bring about errors. 5. Results and discussion 5.1. Cycle independent parameter This study takes the subcritical ORC based on geothermal water as an example for low- and medium-grade heat source recovery. Table 2 shows the system parameters including the ORC, heat source, and heat sink, which is obtained from an existed practical ORC-based geothermal power plant in China. GWIT is varied at steps of 5 °C in the range of 90–120 °C, however, geothermal water outlet temperature is confined to be no less than 70 °C to prevent silica precipitation in the rejection wells [39]. It should be pointed out that the isentropic efficiency of the turbine is related to the property of the working fluid, the volumetric flow rate of the working fluid, the expansion ratio, and so on. Strictly, the isentropic efficiency of the turbine for the two stages is different, and it is difficult to ascertain the accurate values. To simplify the calculation, the same isentropic efficiency is adopted for each stage. R245fa belongs to the family of HFCs and is non-flammable, nontoxic, and thermally stable, and its ozone depletion potential (ODP) is zero. The evaporating pressure of the R245fa is appropriate and creates overpressure condensing. Moreover, R245fa was previously screened for its excellent performance in the low- to medium-temperature range [40–52]. Therefore, R245fa is selected as the working fluid, and its main physical properties are shown in Table 3. The first step for this study is an extensive thermodynamic optimization based on ORC, PTORC, and STORC with the purpose of ascertaining the optimal system performance of the working fluid and the cycle configuration for different GWITs. Once the parameters of the heat source and heat sink are determined, for the ORC,

the only decisive variable that should be ascertained to evaluate the other remaining dependent quantities is the evaporating temperature (evaporating pressure) or the mass flow rate of the working fluid. Moreover, there is strong corresponding relationship between the evaporating temperature and evaporating pressure for the pure working fluid. Therefore, these two parameters can be regarded as one parameter with respect to thermodynamics in essence. According to the law of energy conservation, the mass flow rate of the working fluid will be ascertained accordingly once the evaporating temperature is determined, and vice versa. However, for the PTORC and the STORC, the amount of the decisive variables increases due to the implementation of the double evaporating. The amount of the evaporating temperature equals to the quantity of the evaporating stage, whereas geothermal water has intermediate temperatures except for the inlet and outlet temperatures. On the other hand, the amount of the intermediate temperature depends on the quantity of the evaporating stage, and there exists an IGWT between every two evaporating stages. Hence, there also exists a linear function relationship between the amount of IGWT, M0 , and n, which can be expressed as the following equation:

M0 ¼ n  1

ð52Þ

Every increase in the evaporating stage will be in relation to two independent parameters, i.e., there exists a linear function relationship between the amount of the independent parameter, N, and the quantity of the evaporating stage, n, which is expressed as follows:

N ¼ 2n  1

ð53Þ

From Eq. (53), It can be calculated that PTORC and STORC have three independent variables that should be ascertained to optimize the system performance. They are the evaporating temperature in the high-pressure stage evaporator, T eva;high , the evaporating temperature in the low-pressure stage evaporator, T eva;low , and IGWT, T GWIT . Based on the three parameters, the other remaining dependent variables can be obtained. The net power output was employed as the objective function to optimize the systematic performance for the ORC, PTORC, and STORC. Hereafter, the system benefits of the PTORC and STORC are outlined with contrast to the ORC, with the dimensionless ratio of the exergetic efficiency to the total thermal conductance used as the objective function. 5.2. Mass flow rate of working fluid The mass flow rate of the working fluid, the evaporating temperature, and the condensing pressure with the highest net power

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T. Li et al. / Applied Energy 150 (2015) 323–334 Table 3 Thermodynamic properties of R245fa. Substance

Physical data

R245fa

Environmental data

Source

M (g/mol)

T b (°C)

T cri (°C)

P cri (MPa)

ALT (yr)

ODP

GWP (100 yr)

134.05

14.90

154.05

3.640

7.6

0

1030

[53]

Table 4 Mass flow rate, evaporating temperature, and condensing pressure for ORC, PTORC, and STORC. mwf (kg/s) ORC

90 95 100 105 110 115 120

25.83 32.77 39.12 45.40 51.61 57.77 63.25

T ev a (°C) PTORC

STORC

ORC

High

Low

High

Low

14.21 16.62 24.23 26.51 32.67 38.78 42.13

11.96 14.62 15.64 18.56 18.56 18.56 20.96

13.66 18.26 20.50 24.76 26.79 30.62 36.28

12.28 14.10 17.79 19.67 23.49 25.56 25.83

71 72 74 76 78 80 83

output for 90 6 T gw;in 6 120  C are shown in Table 4. The condensing pressure, P con , mainly relies on the ambient condition, and it varies from one place to another. Pcon equals to the pressure corresponding to the saturation temperature of 30 °C. Under the promise of a given geothermal water outlet temperature, the mass flow rate of the working fluid, mwf , is approximately linearly proportional to the GWIT, and it is calculated from Eqs. (3) and (4). Both mwf;1 and mwf;2 are inversely proportional to t e , but mwf;2 has a higher impact than mwf;1 . Increasing the evaporating temperature consistently could promote the specific enthalpy change of the working fluid in the evaporator. However, the heat provided by the heat source that is used to vaporize the working fluid is sharply shortened. Moreover, mwf is coupled with t e due to the one-to-one correspondence between the two parameters. The growth rate between the specific enthalpy at the inlet and outlet in the evaporator is shorter than that of the available heat provided by geothermal water. Overall, the mass flow rate of the working fluid for the ORC, mwf;ORC , are almost higher than those for the PTORC and STORC, mwf;PTORC , and mwf;STORC except for T gw;in = 90 °C. PTORC and STORC could increase the high-pressure evaporating temperature and lower the low-pressure evaporating temperature, in other words, the specific enthalpy increment in the high-pressure evaporator is increased, and that the specific enthalpy increment in the low-pressure evaporator is decreased. With the increment of T gw;in , the mass flow rate of the working fluid in the high-pressure evaporator increases faster than that in the low-pressure evaporator, thereby increasing the average specific enthalpy increment in the evaporator for the PTORC and STORC. 5.3. VFR The specific work of the working fluid is proportional to the evaporating temperature, whereas the mass flow rate of the working fluid is inversely proportional to the evaporating temperature. The high optimal evaporating temperature for the PTORC and STORC is higher than that for the ORC, whereas the lower evaporating temperature for the PTORC and STORC is lower than that for the ORC. On the premise of ensuring the temperature difference at the pinch point, it is necessary to have a comparison between the optimal evaporating temperature and the system performance. However, the PTORC and STORC implement a segmented utilization of the valuable geothermal water, which makes it feasible within the two segmented temperature range of geothermal water. Compared with the ORC, the two segmented temperature range of

IGWT (°C) PTORC

STORC

High

Low

High

Low

77 80 82 86 88 90 94

67 68 67 68 68 68 69

77 80 84 87 91 95 97

70 71 73 74 76 78 80

P con (MPa)

PTORC

STORC

79 81 82 84 84 84 86

82 84 88 90 94 97 99

0.1772 0.1772 0.1772 0.1772 0.1772 0.1772 0.1772

7.0

ORC PTORC-high PTORC-low STORC-high STORC-low

6.5

Volumetric flow ratio

T gw;in (°C)

6.0 5.5 5.0 4.5 4.0 3.5 3.0

90

95

100

105

110

115

120

Tgw,in ( oC) Fig. 5. VFR with the maximal power output with GWIT.

geothermal water is much shorter for the PTORC and STORC, meaning that the PTORC and STORC could make lower compromises and show better temperature matching between the heat source and the working fluid. The volumetric flow ratio (VFR) in function of T gw;in shows an approximately linear behavior for ORC, the high and low stages of the PTORC and the STORC in Fig. 5. Similar to the evaporating temperature shown in Table 3, the VFR for high stages of the PTORC and the STORC is evidently higher than that for the ORC, whereas the VFR for low stages of the PTORC and the STORC is evidently lower than that for the ORC. For a given ambient conditions, the system condensing pressure can be regarded as a constant, which implies that the VFR is only determined by T eva . Moreover, the VFR of high stages for the PTORC is higher than that for the STORC except for T gw;in > 95  C, but the VFR of low stages for the PTORC is consistently lower than that for the STORC. From Macchi and Perdichizzi [54], lower VFRs lead to higher turbine efficiencies. Moreover, according to Invernizzi et al. [55], the turbine efficiency can exceed 80% only for the VFRs below 50. The highest VFR in this study is only 6.74, thereby leading to a higher turbine efficiency. 5.4. Irreversible loss The system irreversible loss of ORC, PTORC, and STORC for different GWITs are similar to each other, so T gw;in = 100 °C is taken

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T. Li et al. / Applied Energy 150 (2015) 323–334

It=225.10kW

Irreversible loss (kW)

500 400

Ip=9.52kW

It=232.90kW Ip=10.44kW

Irreversible loss in the evaporator (kW)

600

It=240.50kW Ip=11.06kW

300 200

Ie=360.80kW

Ie=326.00kW

Ie=295.20kW

Ic=18.43kW

Ic=20.30kW

Ic=21.74kW

ORC Turbine

PDCORC Pump Evaporator

100 0

(a)

SDCORC Condenser

70

rt=36.68%

rt=39.50%

rt=42.30%

rp=1.55%

rp=1.77%

rp=1.95%

50

re=58.77%

re=55.29%

re=51.93%

30 20 10 0

(b)

500 400 300 200 100 0

90

1200

60

40

600

95

100

105

110

115

120

Fig. 7. Influence of the GWIT on the irreversible loss in the evaporator.

Total irreversible loss (kW)

Irreversible loss coefficient (%)

80

ORC PTORC STORC

Tgw,in ( oC)

100 90

700

rc=3.00%

rc=3.44%

ORC Turbine

PDCORC Pump Evaporator

rc=3.82% SDCORC Condenser

1000 800 600 400 200 0

Fig. 6. System irreversible loss versus GWIT when T gw;in ¼ 100  C.

ORC PTORC STORC

90

95

100

105

110

115

120

Tgw,in ( oC)

as an example, which is shown in Fig. 6. The total irreversible loss for ORC, PTORC, and STORC reduces sequentially, and the irreversible loss in the evaporator manifests a similar variation trend. However, the irreversible loss in the turbine, pump, and condenser for ORC, PTORC, and STORC are increased. For the evaporator, the PTORC and the STORC utilize geothermal water in segmented temperature range, thereby improving the matching between geothermal water and working fluid, so such the irreversible loss in the evaporator declines. A mew parameter, the equivalent evaporating temperature, is used to evaluate the PTORC and the STORC, which is expressed as follows:

T eva;eq ¼

mwf;high T eva;high þ mwf;low T eva;low mwf;high þ mwf;low

ð54Þ

For a given turbine efficiency, mwf and VFR are the decisive factors for the irreversible loss caused by the turbine. The highest difference of the working fluid between STORC and ORC is only 1.32%, indicating the irreversible loss caused by turbine is mainly influenced by the VFR. Moreover, among T eva;eq;SDRORC ; T eva;eq;PDRORC , and T eva;ORC ; T eva;eq;SDRORC is the highest, whereas T eva;ORC is the lowest. This is the main reason for more irreversible loss in the turbine for the STORC. It should be pointed out that the irreversible loss generated by the pump for the ORC, PTORC, and STORC ascends sequentially, and it is similar to each other for the irreversible loss caused by the turbine. STORC shows the highest irreversible loss in the condenser and the followed is PTORC. The working fluid at the outlet of the condenser is set to be 30 °C. Furthermore, the working fluid at the inlet of the condenser for the STORC has a higher temperature than that for the PTORC and ORC. Overall, the evaporator contributes the most to the total irreversible loss (above 50%) followed by the turbine (above 36%). However, the condenser only

Fig. 8. Influence of the GWIT on the total irreversible loss.

accounts for 3.82% in the PTORC, which is due to the low log mean temperature difference in it. The irreversible loss in the evaporator and the total irreversible loss in function of the GWIT are respectively shown in Figs. 7 and 8, respectively. They are proportional to the GWIT, which is consistent with ORC, PTORC, and STORC. Among the three cycles, STORC always generates the lowest irreversible loss in the evaporator and the total irreversible loss. The advantage of the STORC is more apparent for higher GWITs because the increase of the GWIT could enlarge the available temperature difference of geothermal water. The reduction of the irreversible loss in the evaporator for the STORC is proportional to the GWIT. Compared with ORC, the average reduction in the irreversible loss in the evaporator reaches 4.50% for PTORC, whereas it is 9.10% for STORC. Moreover, the highest reduction in the irreversible loss in the evaporator reaches 7.20% for PTORC, whereas it is 14.20% for STORC. Thus, STORC is more favorable with respect to reducing the irreversible loss in the evaporator and the system. 5.5. Net power output Fig. 9 shows the variation of the net power output with the GWIT. It is apparent that the net power output, W net , is approximately proportional to the GWIT for the three cycles. For the same GWIT, the STORC has the highest net power output, and the ORC is the lowest. However, the ratios of W net;PTORC =W net;ORC and W net;STORC =W net;ORC present different variation trends. W net;PTORC =W net;ORC is inversely proportional to the GWIT, whereas W net;STORC =W net;ORC is just the opposite. Within the range of the

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T. Li et al. / Applied Energy 150 (2015) 323–334

550

1400

ORC PTORC STORC

450

Wnet (kW)

1000 800 600

400 350 300 250 200

400

150 90

95

100

105

110

115

120

Tgw,in ( C)

ORC PDCORC SDCORC

( KA) con ( kW/ oC)

1200 1100 1000 900 800

600 90

95

100

110

115

120

110

115

120

1.40

1.38

1.38

1.36

1.36

1.34

1.34

1.32

1.32

1.30

1.30

1.28

1.28

1.26

1.26 95

100

105

110

115

120

Tgw,in ( oC)

Fig. 11. Thermal conductance in the evaporator with the GWIT.

Tgw,in ( oC)

1.00

1.00

0.98

0.98

0.96

0.96

0.94

0.94

0.92

0.92

0.90

0.90 90

95

100

105

110

115

5.6. Thermal conductance

( KA) con,SDCORC/( KA) con,ORC

( KA) con,PDCORC/( KA) con,ORC

105

105

1.40

(b)

(a)

100

Tgw,in ( oC)

90

700

(b)

95

( KA) eva,SDCORC/( KA) eva,ORC

( KA) eva,PDCORC/( KA) eva,ORC

Fig. 9. The variation of the net power output with GWIT.

1300

90

(a)

o

1400

ORC PDCORC SDCORC

500

( KA) eva ( kW/ oC)

1200

120

Tgw,in ( oC)

Fig. 10. Thermal conductance in the condenser versus GWIT.

GWIT in this study, W net;PTORC =W net;ORC decreases from 1.045 to 1.033, which signifying that the PTORC gradually losses its advantages with the GWIT. This happeded because the temperature difference between geothermal water and the working fluid at the evaporator inlet (the working fluid side) for the STORC becomes larger than that for the ORC, thereby resulting in larger and larger irreversibility with the GWIT. On the contrary, W net;STORC =W net;ORC ascends from 1.065 to 1.090. Compared with the PTORC, the STORC improves the matching between the heat source and the working fluid so that the STORC is more preferable for higher GWITs.

Fig. 10(a) depicts the thermal conductance in the condenser versus the GWIT. It is obvious that the thermal conductance in the condenser, ðKAÞcon , is also in direct proportion to the GWIT. ðKAÞcon for the ORC, PTORC, and STORC linearly increases with the GWIT. There are two reasons for this. Firstly, a higher evaporating temperature results in a higher temperature of the working fluid at the turbine outlet. It is a determinant factor to the log mean temperature difference in the condenser when the temperatures of the cooling water and the working fluid at the condenser outlet are given. The log mean temperature difference in the condenser for the PTORC and STORC is slightly higher than that for the ORC, and thus increases the log mean temperature difference in the condenser. On the other hand, the PTORC and STORC output more power in the turbine, and thereby reducing the thermal load in the condenser. From Fig. 10(b), both ðKAÞcon;PTORC =ðKAÞcon;ORC and ðKAÞcon;STORC Þ=ðKAÞcon;ORC initially decrease but then increase with the GWIT. ðKAÞcon;PTORC =ðKAÞcon;ORC (0.948) minimizes for T gw;in = 95 °C, whereas ðKAÞcon;STORC =ðKAÞcon;ORC (0.909) gets its minimum value for T gw;in = 115 °C. Fig. 11(a) elucidates the thermal conductance in the evaporator with the GWIT. Analogously, it is evident that the thermal conductance in the evaporator, ðKAÞeva , is also in direct relation with the GWIT. ðKAÞeva for the ORC, PTORC, and STORC linearly increases with the GWIT. The log mean temperature difference in the evaporator for the PTORC and STORC only varies a little, thus the thermal load in the evaporator is the main factor in determining the ðKAÞeva . Moreover, the log mean temperature difference in the high

332

T. Li et al. / Applied Energy 150 (2015) 323–334

44

1800

ORC PDCORC SDCORC

1700

1500

42

1400

η ex (%)

( KA) total ( kW/ oC)

1600

ORC PDCORC SDCORC

43

1300 1200 1100

41 40

1000 39

900 90

95

100

105

110

115

38

120

o

Tgw,in ( C) 1.10

1.08

1.08

1.06

1.06

1.04

1.04

1.02

1.02

1.00

1.00

90

95

(b)

100

105

95

100

110

115

120

0.98

Tgw,in ( C)

115

120

1.10

1.08

1.08

1.06

1.06

1.04

1.04

90

95

100

(b)

Fig. 12. Total thermal conductance versus the GWIT.

105

110

115

120

1.02

Tgw,in ( oC)

( Wnet/( KA) total) PDCORC/( Wnet/( KA) total) ORC

Fig. 13. Exergetic efficiency versus the GWIT.

1.10

1.10

1.08

1.08

1.06

1.06

1.04

1.04

1.02

1.02

1.00

1.00

0.98

0.98

0.96

0.96 90

95

100

105

Tgw,in ( oC)

110

115

120

( Wnet/( KA) total) SDCORC/( Wnet/( KA) total) ORC

stage evaporator for the PTORC is higher than that for the STORC, which adversely result in the fact that ðKAÞeva;STORC is a little higher than ðKAÞeva;PTORC . On the other hand, an increase in the GWIT could lead to a higher thermal load in the evaporator, thereby increasing the ðKAÞeva . From Fig. 11(b), ðKAÞeva;PTORC =ðKAÞeva;ORC is inversely proportional to the GWIT, and it gets a minimum value of 1.276 with T gw;in = 120 °C. However, ðKAÞeva;STORC =ðKAÞeva;ORC initially decreases but then increases with the GWIT. ðKAÞeva;PTORC =ðKAÞeva;ORC achieves its minimum value of 1.313 with T gw;in = 110 °C. Fig. 12(a) illustrates the variation trend of the total thermal conductance with the GWIT. Similar with (KA)con and (KA)eva, the total thermal conductance, (KA)total, is also proportional to the GWIT. (KA)total for the ORC, PTORC, and STORC linearly increases with the GWIT. (KA)total,PTORC is obviously higher than (KA)total,STORC and (KA)total,ORC. Furthermore, (KA)total,STORC evidently exceeds (KA)total,ORC with T gw;in 6 105  C, and the two parameters are pretty close when T gw;in P 105  C. From Fig. 12(b), (KA)total,PTORC/ (KA)total,ORC and (KA)total,STORC/(KA)total,ORC obtain their minimal values of 1.029 and 0.992 for T gw;in = 115 °C, respectively.

110

1.10

1.02

o

105

Tgw,in ( oC)

η ex,SDCORC/η ex,ORC

1.10

0.98

90

(a)

( KA) total,SDCORC/( KA) total,ORC

( KA) total,PDCORC/( KA) total,ORC

(a)

η ex,PDCORC/η ex,ORC

800

Fig. 14. Dimensionless ratio of the exergetic efficiency to the total thermal conductance versus the GWIT.

5.7. Exergetic efficiency

gex,STORC/gex,ORC is proportional to the GWIT, whereas gex,PTORC/ gex,ORC is inversely proportional to the GWIT. For 90  C 6 T gw;in 6 120  C, gex,STORC/gex,ORC increases from 1.065 to 1.089, however, gex,PTORC/gex,ORC decreases from 1.045 to 1.033.

Fig. 13(a) shows the exergetic efficiency with the GWIT. The exergetic efficiency, gex, for ORC, PTORC, and STORC can be approximately perceived as linearly proportional to the GWIT. Moreover, gex,STORC, gex,PTORC, and gex,ORC reduce in turn. From Fig. 13(b), it can be found out that the value of gex,STORC/gex,ORC and gex,PTORC/gex,ORC illustrate distinct variation trend with the GWIT, respectively, i.e.,

The irreversible loss in the high stage evaporator becomes larger due to the relatively high temperature difference at the inlet of the evaporator for the working fluid side. The STORC further enhances the system performance for higher GWITs, but the PTORC could gradually contribute less performance enhancement when GWIT becomes higher. Therefore, the STORC is also more advisable than the PTORC.

T. Li et al. / Applied Energy 150 (2015) 323–334

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5.8. Objective function

References

The ratio of the net power output to the total thermal conductance is chosen as the objective function. The numerator, W net , is related to the system earnings, and the denominator, (KA)total, is connected with the system cost. Fig. 14 depicts the dimensionless ratio of the net power output to the total thermal conductance versus the GWIT. The dimensionless ratio of (W net /(KA)total)STORC/(W net / (KA)total)ORC and (W net /(KA)total)PTORC/(W net /(KA)total)ORC initially increases but then decreases with the GWIT, the two parameters achieve their respective maximal values for T gw;in = 115 °C. The maximal values for the ratios of (W net /(KA)total)PTORC/(W net / (KA)total)ORC and (W net /(KA)total)STORC/(W net /(KA)total)ORC are 1.007 and 1.096, respectively. It should be pointed out that (W net /(KA)total)PTORC/(W net /(KA)total)ORC exceeds 1.000 for 105  C 6 T gw;in 6 115  C and is less than 1.000 for 105  CT gw;in 6 100  C and T gw;in = 120 °C, indicating that the PTORC could not have significantly difference with the ORC. On the contrary, (W net /(KA)total)STORC/(W net /(KA)total)ORC always surpass 1.000, illustrating that the STORC could evidently exceed the ORC. From the above-mentioned analysis, both the STORC and PTORC enhances the net power output, however, the PTORC deteriorates the matching between geothermal water and the working fluid in the high stage evaporator. The extent of deterioration is proportional to the GWIT, and this is the reason why the PTORC could not have better performance with the increase of the GWIT. On the contrary, the STORC pumps a portion of the saturated liquid in the low stage evaporator to the high stage evaporator, which could make it achieve better performance. The STORC absorbs a portion of heat from the lower temperature range to preheat the working fluid in the evaporator 1, whereas the working fluid in the evaporator 1 for the PTORC absorbs heat totally from the high temperature range. This is the main reason for their different performance. Therefore, the STORC manifests more excellent systematic performances, and it would be popular in engineering application in the future.

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6. Conclusions The heat source is segmented in two temperature ranges to realize two-stage evaporation in this study. Cycle configuration (PTORC and STORC) are evaluated and the optimal system parameters and the system irreversible loss are obtained. The main conclusions that can be drawn from the present study are summarized as follows: (1) The two-stage organic Rankine cycle segments the heat source in two segmented temperature ranges and realizes cascade evaporating, which reduces the system irreversible loss, especially in the evaporator. (2) Both the PTORC and the STORC can enhance the net power output within the range of this study, and the growth rate differs from the cycle configuration and the GWIT. (4) The STORC outputs more net power with the GWIT, but the STORC is just the opposite, illustrating that the STORC is more preferable. (5) The STORC presents excellent systematic performance, and it would be widely used in engineering applications in future.

Acknowledgments The authors gratefully acknowledge the support provided by the National Natural Science Foundation of China (Grant No. 51406130).

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[32]

[33]

[34]

[35]

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