Parametric optimization and thermodynamic performance comparison of single-pressure and dual-pressure evaporation organic Rankine cycles

Parametric optimization and thermodynamic performance comparison of single-pressure and dual-pressure evaporation organic Rankine cycles

Applied Energy 217 (2018) 409–421 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Param...

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Applied Energy 217 (2018) 409–421

Contents lists available at ScienceDirect

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

Parametric optimization and thermodynamic performance comparison of single-pressure and dual-pressure evaporation organic Rankine cycles

T



Jian Lia, Zhong Gea, Yuanyuan Duana, , Zhen Yanga, Qiang Liua,b a Key Laboratory for Thermal Science and Power Engineering of MOE, Beijing Key Laboratory for CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084, PR China b Beijing Key Laboratory of Process Fluid Filtration and Separation, China University of Petroleum, Beijing 102249, PR China

H I G H L I G H T S

G RA P H I C A L AB S T R A C T

and dual-pressure eva• Single-pressure poration ORCs using pure fluids are studied.

evaporation pressures and • Optimized evaporator outlet temperatures are obtained.

performance for the 100–200 °C • System heat sources is analyzed and compared. power outputs of dual-pressure • Net evaporation ORCs can increase by 21.4–26.7%.

quantitative criterion is provided to • Aassess the optimal cycle type.

A R T I C L E I N F O

A B S T R A C T

Keywords: Organic Rankine cycle Dual-pressure evaporation Waste heat recovery Heat–power conversion Parametric optimization Performance comparison

Dual-pressure evaporation organic Rankine cycle (ORC) involves two evaporation processes with different pressures, and can significantly reduce the exergy loss in the heat absorption process compared with conventional single-pressure evaporation ORCs. However, the applicable heat source temperatures of dual-pressure evaporation ORCs and the effects of the working fluid thermophysical properties on the applicable conditions remain indeterminate. Optimal cycle parameters for various heat source temperatures also need to be studied. Solving these questions is crucial for the application and promotion of dual-pressure evaporation ORCs. This study focuses on a typical dual-pressure evaporation ORC driven by the 100–200 °C heat sources without a limit on the outlet temperature. Nine pure organic fluids were selected as working fluids. Evaporation pressures and evaporator outlet temperatures of the single-pressure and dual-pressure evaporation ORCs were optimized, and their optimized system thermodynamic performance was compared. Results show that the applicable heat source temperature range of the dual-pressure evaporation ORC (Wnet,dual > Wnet,single ) generally increases as the working fluid critical temperature increases. The upper limit of the applicable heat source temperatures (THS,in TP ), working fluid critical temperature and pinch point temperature difference generally conform to a linear relation. For the heat source temperature below THS,in TP , the maximized net power output of the dual-pressure evaporation ORC is larger than that of the single-pressure evaporation ORC. Furthermore, the increment generally increases as the heat source temperature decreases, and the maximum increments are 21.4–26.7% for nine working fluids. For the heat source temperature above THS,in TP , the dual-pressure evaporation ORC is unbefitting.



Corresponding author. E-mail address: [email protected] (Y. Duan).

https://doi.org/10.1016/j.apenergy.2018.02.096 Received 28 December 2017; Received in revised form 10 February 2018; Accepted 12 February 2018 0306-2619/ © 2018 Elsevier Ltd. All rights reserved.

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Nomenclature

g H h ṁ p Q s T W ΔT

in ip LL LP max min net O opt out P pp single sup sv sys T TP UL

gravitational acceleration (9.8 m s–2) pressure head (m) specific enthalpy (kJ kg–1) mass flow rate (kg s–1) pressure (MPa) heat flow rate (kW) specific entropy (J kg–1 K–1) temperature (°C) power (kW) temperature difference (°C)

Greek symbols

η

efficiency

Subscripts 1–11 c cond cool dual e HAP HP HS HS, 1 HS, 2

state points shown in Figs. 1 and 2 critical state condensation or condenser cooling water dual-pressure evaporation evaporation or evaporator heat absorption process high-pressure stage heat source fluid heat source fluid at the high-pressure stage outlet heat source fluid at the low-pressure stage outlet

inlet inflection point lower limit low-pressure stage maximum minimum net output organic working fluid optimal or optimized outlet feed pump pinch point single-pressure evaporation superheating or superheated saturation vapor curve system turbine transition point upper limit

Abbreviations GWP ODP ORC PPP PTORC STORC VPP

Global Warming Potential Ozone Depletion Potential Organic Rankine Cycle Pinch Point occurs at the Preheater inlet Parallel Two evaporator Organic Rankine Cycle Series Two evaporator Organic Rankine Cycle Pinch Point occurs at the Vaporization bubble point

evaporation pressure. The temperature match between the working fluid and heat source fluid is generally poor due to the pinch point temperature difference limitation and the working fluid isobaric heat absorption characteristics, which results in the considerable exergy loss [8,17–24]. Specifically, when the local heat capacity rate is not well matched between the working fluid and heat source fluid, a large temperature gradient will exist between them, which significantly increases the exergy losses. In other words, to be more direct viewing and vivid, when the working fluid of the subcritical ORC absorbs the heat from the heat source fluid, the curve of the working fluid is a polyline shape in the T-s diagram, whereas the curve of the heat source fluid is generally almost linear, which results in a poor temperature match and significantly increases the exergy losses. Furthermore, the heat release characteristics of various heat sources considerably vary [2,3,17,25,26], and the adaptability of conventional subcritical ORCs based on the single evaporation pressure is insufficient to meet the demand of temperature match [17,22,23,25]. Improving the temperature match between the working fluid and heat source fluid is necessary to achieve a high energy utilization efficiency. Several scholars have attempted to introduce zeotropic mixtures into the ORC system to increase the heat–power conversion efficiency, because the zeotropic mixture has a varying phase change temperature [5,7,13,27–32]. However, the temperature match between the working fluid and heat source fluid remains unsatisfactory, though the temperature match in the condensation process can be improved [5,7,29]. The limitations of the pinch point temperature difference and the working fluid isobaric heat absorption characteristics (e.g., the curve of the working fluid is the polyline shape in the T-s diagram) still exist for zeotropic mixtures [33]. Using the transcritical ORC is also an important approach to increasing the heat–power conversion efficiency [8,10,17,34–36]. For the transcritical ORC, the working fluid temperature increases continuously in the vapor generator, and that may provide a better temperature match between the working fluid and heat source fluid, compared to the conventional subcritical ORCs [10,17,35]. Therefore, the exergy loss in the cycle heat absorption process will be

1. Introduction To reduce CO2 emission and weaken greenhouse effect are global challenges. Renewable energy utilization and waste heat recovery are recognized key approaches to reducing CO2 emission and weakening greenhouse effect. Exploring the efficient utilization technology for renewable energy and waste heat resources has attracted the attention worldwide. The organic Rankine cycle (ORC) is an important and promising heat–power conversion technology that has been widely used in the renewable energy utilization (e.g., solar thermal, geothermal, and biomass energies) and waste heat recovery (e.g., internal combustion engine exhaust, industrial flue gas, and hot processed liquids) around the world [1–9]. ORC is based on the principle of the Rankine cycle and uses organic fluids as working fluids [8,10]. ORC has advantages of stability, flexibility, safety, as well as wider applicable ranges of the heat source temperature and installed capacity; compared to other heat–power conversion technologies utilizing the low and medium temperature (< 350 °C) thermal energy [2,3,9,11–15]. The more efficient utilization of the renewable energy and waste heat resources is the primary goal for the design and optimization of ORC systems. The design and optimization of the system is based on the cycle type of ORC, which significantly affects its energy utilization efficiency [8,10,16,17]. For the conventional subcritical ORCs, although the cycle concept is simple, their performance (e.g., the thermal efficiency, exergy efficiency, or net power output) is generally considerably lower than the theoretical ceiling for a given heat source and heat sink. Therein, the exergy loss during the finite temperature difference heat transfer between the working fluid and heat source fluid is generally the largest, and can exceed 40% of the total exergy loss [18–20]. Reducing the exergy loss during the finite temperature difference heat transfer between the working fluid and heat source fluid is crucial to increase the energy utilization efficiency for a conventional ORC system. Conventional subcritical ORCs are generally based on the single 410

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studies on the dual-pressure evaporation ORC are based on the specific heat source temperature [21,23,24,42–45]. As the heat source temperature increases, the variations in the optimal cycle parameters and thermodynamic performance of the dual-pressure evaporation ORC system remain indeterminate. Secondly, the optimal cycle type of an ORC system depends on the heat source temperature and working fluid thermophysical properties. For several certain heat source temperatures and working fluids, the thermodynamic performance of the dual-pressure evaporation ORC may be even worse than that of the singlepressure evaporation ORC. However, the applicable heat source temperatures of the dual-pressure evaporation ORC, where its thermodynamic performance is better than that of the single-pressure evaporation ORC, remain indeterminate thus far. Finally, the effects of the working fluid thermophysical properties on the applicable heat source temperatures of the dual-pressure evaporation ORC also need to be revealed. Solving these crucial questions is vital for the application and promotion of dual-pressure evaporation ORCs. This study focuses on a typical dual-pressure evaporation ORC (STORC [23]). Nine common pure organic fluids were selected as the working fluids, and the heat sources ranged from 100 °C to 200 °C without a limit on the outlet temperature. The heat sources with a temperature range of 100–200 °C are common and abundant in the renewable energy and waste heat resources [2,3,25,26]. In this study, for various heat source temperatures, the optimal evaporation pressures and evaporator outlet temperatures of the single-pressure and dualpressure evaporation ORCs were obtained, which could achieve the maximum net power output for per mass flow rate (kg s–1) heat source fluid. The thermodynamic performance of two ORC systems was analyzed and compared, and a quantitative criteria was provided to assess the applicable heat source temperatures of the dual-pressure evaporation ORC. The effects of the working fluid thermophysical properties on the applicable heat source temperatures of the dual-pressure evaporation ORC were also revealed. In addition, the effects of various heat source fluids on the optimal cycle parameters and thermodynamic performance of two ORC systems were also analyzed.

significantly reduced, and the system thermodynamic performance will be improved [8,35,37–39]. While, the heat source temperature should be high to achieve a transcritical ORC, otherwise the expansion process will pass through the two-phase region [8]. Moreover, the net power output of the transcritical ORC system will be even lower than that of the subcritical ORC system when the heat source temperature is low, mainly due to a high heat source outlet temperature of the transcritical ORC, which significantly increases the exergy loss in the heat absorption process [8,38,40,41]. In addition, the transcritical ORC has the single vapor generation pressure, and its adaptability is also generally insufficient to meet the demand of temperature match for heat sources with various characteristics [22,26]. In summary, a new-style cycle type of ORC is urgent, which can significantly reduce the exergy loss between the working fluid and heat source fluid; meanwhile, its adaptability is satisfactory for heat sources with various characteristics. Dual-pressure evaporation ORC involves two evaporation processes with different pressures and an isobaric condensation process. It is relatively emerging in the ORC field [17]. The dual-pressure evaporation ORC can significantly reduce the exergy loss during the finite temperature difference heat transfer between the working fluid and heat source fluid, because the number of optimizable cycle parameters is increased (e.g., the pressure, working fluid mass flow rate and superheat degree in each evaporation stage). Thus, the heat absorption process (including the processes of preheating, evaporation, and superheating) of the cycle can be designed more suitably to adapt the heat release characteristics of the heat source fluid, compared to the conventional single-pressure evaporation ORC [22]. The adaptability for heat sources with various characteristics is also improved. The advantages of dual-pressure evaporation ORCs in the thermodynamic performance have been proven by several studies. Li et al. [23] compared the thermodynamic performance of the series two evaporator ORC (STORC) and parallel two evaporator ORC (PTORC) with that of the single-pressure evaporation ORC for the 90–120 °C geothermal water and R245fa. Results showed that the net power output of the STORC system increased by 6.5–9.0%, and that of the PTORC system increased by 3.3–4.5% [23]. Shokati et al. [42] compared the thermodynamic performance of the single-pressure evaporation ORC, dualpressure evaporation ORC, cascade ORC and Kalina cycle based on a 175 °C heat source. Results indicated that the net power output of the dual-pressure evaporation ORC system was 15.2% larger than that of the single-pressure evaporation ORC system, 35.1% larger than that of the cascade ORC system, and 43.5% larger than that of the Kalina cycle system [42]. Manente et al. [43] compared the thermodynamic performance of the single-pressure and dual-pressure evaporation ORC systems for five specific heat source temperatures, and results indicated that the net power output of the dual-pressure evaporation ORC system could be 29% larger than that of the single-pressure evaporation ORC system. Moreover, zeotropic mixtures can also be used in the dualpressure evaporation ORC, and their advantages will be superposed. Sadeghi et al. [44] compared the thermodynamic performance of the single-pressure evaporation ORC, PTORC and STORC based on ten zeotropic mixtures for a 100 °C heat source. Results showed that the net power output of the STORC system was 34.3% larger than that of the single-pressure evaporation ORC system [44]. In addition, several scholars also introduced the concepts of the dual-pressure or even multi-pressure evaporation ORCs into their studies. For example, DiGenova et al. [25] used a set of ORC design concepts (e.g., the multipressure levels, reheat stages, and balanced recuperators) to customize an efficient thermodynamic cycle for the complex heat sources (demonstrated on a Fischer Tropsch plant). For the ORC technology, using the cycle type of the dual-pressure evaporation can further enhance the thermodynamic advantages compared with other heat–power conversion technologies utilizing the low and medium temperature (< 350 °C) thermal energy. That is helpful for the popularization of the ORC technology around the world. However, several crucial questions in the dual-pressure evaporation ORC remain indeterminate, and are urgent to be answered. Firstly, most of existing

2. Methodology 2.1. Single-pressure and dual-pressure evaporation ORCs For the single-pressure and dual-pressure evaporation ORCs using pure working fluids, the schematics of systems and their thermodynamic processes are shown in Figs. 1 and 2, respectively. The thermodynamic state points in Figs. 1 and 2 correspond for each ORC system. The detailed thermodynamic processes of the single-pressure evaporation ORC have been described in our previous work [8]. For the dual-pressure evaporation ORC, the saturated liquid working fluid is compressed to the evaporation pressure of the low-pressure stage ( pe,LP ) using a low-pressure feed pump (1–2 process). The low-pressure working fluid absorbs heat in the preheater (2–3 process) and is converted into saturated liquid. The liquid at the preheater outlet is divided into two flow paths. A portion of the liquid flows into the evaporator in the low-pressure stage and is converted into the saturated or superheated vapor (3–4 process). Another portion of the liquid is compressed to the evaporation pressure of the high-pressure stage ( pe,HP ) using a high-pressure feed pump (3–5 process), and then flows into the evaporator in the high-pressure stage and is converted into the saturated or superheated vapor (5–7 process). The working fluid vapor from the evaporator in the high-pressure stage initially flows into the highpressure turbine (7–8 process), and the vapor pressure decreases to the evaporation pressure of the low-pressure stage. The exhaust from the high-pressure turbine and the vapor from the evaporator in the lowpressure stage flow into the low-pressure turbine together (9–10 process), and the vapor pressure decreases to the condensation pressure. The exhaust from the low-pressure turbine flows into the condenser (10–1 process) and is cooled into saturated liquid, to complete a cycle. 411

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7

hot fluid

~

evaporator

10

3 preheater

THS,out 2

turbine

cooling tower circulating pump

condenser

feedpump

1

3

10

2 1 Tcool,in

(a) 7

THS,1 hot fluid THS,2 THS,out

high-pressure evaporator

5

~ 9 feed pump

low-pressure evaporator

3

feedpump

Tcool,out

(b)

Dual-pressure evaporation turbine cooling tower

7

.

mO,HP

6

circulating pump

condenser

preheater

2

~ 10

Tcool,pp

Cooling water

Entropy, s

8

4

11

turbine

High-Pressure

Temperature, T

THS,in

7

Temperature, T

THS,in

(a)

Single-pressure evaporation

1

Divided into two paths

.

5 3

4 10

Low-Pressure 2 1 Tcool,in

(b) Fig. 1. Schematics of the single-pressure and dual-pressure evaporation ORC systems: (a) Single-pressure evaporation ORC; (b) Dual-pressure evaporation ORC.

9 8

mO,LP

. m

O,HP

. m

11

O,LP

Tcool,pp

Cooling water

Tcool,out

Entropy, s

The schematic for the heat absorption process of the dual-pressure evaporation ORC is shown in Fig. 2(c).

Dual-pressure evaporation

2.2. Working fluids

THS,in

(c) Ho

Temperature, T

Nine common pure organic fluids, R227ea, R236ea, R245fa, R600, R600a, R601, R601a, R1234yf and R1234ze(E), were selected as the working fluids. All of the studied nine pure fluids are dry or isentropic fluids, which are popular to be used in ORC systems; moreover, previous studies have also shown that they can achieve an attractive thermodynamic performance in ORC systems [8,35,46–48]. Table 1 lists the major thermophysical properties of nine pure working fluids [49,50]. The entropy at the inflection point of the saturation vapor curve (sip ) is maximum in the two-phase region. The saturation vapor curve slope of an organic fluid is lower than 0 ((ds /dT )sv < 0 ) when the saturation vapor temperature is higher than its inflection point temperature (Tip ), and the organic fluid shows a “wet working fluid” property [51]. When the saturation vapor temperature is lower than its inflection point temperature, the saturation vapor curve slope is higher than 0 ((ds /dT )sv > 0 ) and the organic fluid shows a “dry working fluid” property [51].

THS,out

2

3

5

uid

7

6

THS,1 THS,2

t fl

Working fluid

4

Heat absorption process Heat flow rate, Q

Fig. 2. Schematics of thermodynamic processes for the single-pressure and dual-pressure evaporation ORCs: (a) Single-pressure evaporation ORC; (b) Dual-pressure evaporation ORC; (c) T-Q diagram for the heat absorption process of the dual-pressure evaporation ORC.

2.3. Boundary conditions, assumptions, and optimized parameters selection ranges of the model

temperature of the heat source fluid has no restriction, and it can theoretically decrease to the ambient temperature [26,52]. For example, the thermal oil and cooling liquid in refineries, the solar thermal energy with flat plate collectors, and several geothermal fields belong to this kind heat source [2,3,5,25,26,52]. To simplify the analysis, ORC systems are assumed to be in a steady state, the heat dissipation and pressure drop in the heat exchangers and pipes are assumed to be negligible, and heat exchangers are in a counter flow arrangement.

Boundary conditions of the single-pressure and dual-pressure evaporation ORC system models are listed in Table 2. The hot water is selected as the heat source fluid because it is common in the actual renewable energy and waste heat resources [2,5,7,26]. The pressure of the hot water maintains itself in a liquid state, where the pressures for the hot water inlet temperatures of 100–150 °C, 151–180 °C and 181–200 °C are 0.5 MPa, 1.2 MPa and 1.6 MPa, respectively. The outlet 412

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The heat absorption capacity of the dual-pressure evaporation ORC system is

Table 1 Major thermophysical properties of nine pure working fluids [49,50]. Working fluid

Tc /°C

pc /MPa

Tip /°C

ODP

GWP100

R227ea R236ea R245fa R600 R600a R601 R601a R1234yf R1234ze(E)

101.75 139.29 154.01 151.98 134.66 196.55 187.20 94.70 109.37

2.93 3.50 3.65 3.80 3.63 3.37 3.38 3.38 3.64

82.57 122.94 127.03 107.81 125.21 171.11 179.38 56.02 66.66

0 0 0 0 0 0 0 0 0

3220 1370 1030 ∼20 ∼20 ∼20 ∼20 4 6

Qsys = ṁ HS (hHS,in−hHS,out ),

where hHS,in and hHS,out are heat source fluid enthalpies at the heat source inlet and outlet, respectively. The working fluid mass flow rate in the high-pressure stage is

ṁ O,HP =

Symbol

Value

Heat source fluid inlet temperature/°C Heat source fluid mass flow rate/kg s–1 Heat source fluid pressure/MPa Heat absorption process pinch point temperature difference/°C Condenser pinch point temperature difference/°C

THS,in ṁ HS pHS ΔTHAP,pp

100–200 1 0.5, 1.2, 1.6 5

ΔTcond,pp

5

Cooling water inlet temperature/°C Cooling water temperature rise in the working fluid condensation process/°C Cooling water pressure/MPa Circulating pump pressure head/m Feed pump efficiency/% Turbine efficiency/%

Tcool,in Tcool,pp−Tcool,in

20 5

pcool H ηP ηT

0.101 10 75 80

ṁ HS (hHS,in−hHS,1) , h7−h5

(2)

where hHS,1 is the heat source fluid enthalpy at the high-pressure evaporator outlet; h5 and h 7 are working fluid enthalpies at the highpressure evaporator inlet and outlet, respectively. The working fluid mass flow rate in the low-pressure stage is

Table 2 Boundary conditions of the single-pressure and dual-pressure evaporation ORC system models. Parameter

(1)

ṁ O,LP =

ṁ HS (hHS,1−hHS,2) , h4−h3

(3)

where hHS,2 is the heat source fluid enthalpy at the low-pressure evaporator outlet; h3 and h4 are working fluid enthalpies at the low-pressure evaporator inlet and outlet, respectively. The mixing process of the exhaust from the high-pressure turbine and the vapor from the evaporator in the low-pressure stage is assumed as adiabatic, and the total enthalpy of the working fluid remains constant. The total power output of two turbines is

WT = ṁ O,HP (h 7−h8) + (ṁ O,HP + ṁ O,LP )(h 9−h10),

(4)

where h8 is the working fluid enthalpy at the high-pressure turbine outlet; h 9 and h10 are working fluid enthalpies at the low-pressure turbine inlet and outlet, respectively. The total power consumed by two feed pumps is

WP = ṁ O,HP (h5−h3) + (ṁ O,HP + ṁ O,LP )(h2−h1), For the single-pressure evaporation ORC, the evaporation pressure ( pe,single ) and evaporator outlet temperature (T7,single ) of the working fluid were optimized. Table 3 lists selection ranges of the evaporation pressure and evaporator outlet temperature for the single-pressure evaporation ORC. The upper limit of the evaporation pressure is set as 0.9pc to avoid the effect of the drastic variations in the working fluid thermophysical properties near the critical region. The method for determining the lower limit of the evaporator outlet temperature has been described in our previous work [8]. For the dual-pressure evaporation ORC, the evaporation pressures of two stages ( pe,LP and pe,HP ) and the evaporator outlet temperature in the high-pressure stage (T7 ) of the working fluid were optimized. The evaporator outlet temperature in the low-pressure stage (T4 ) of the working fluid was selected as the lower limit which corresponds to the evaporation pressure of the low-pressure stage [8]. Table 3 lists the selection ranges for the evaporation pressures of two stages and the evaporator outlet temperature in the high-pressure stage.

(5)

where h3 is the working fluid enthalpy at the preheater outlet; h1 and h2 are working fluid enthalpies at the low-pressure feed pump inlet and outlet, respectively. The power consumed by the cooling system is

Wcool = ṁ cool gH ,

(6)

where g is the gravity acceleration, and ṁ cool is the cooling water mass flow rate, which is calculated as follows:

ṁ cool =

(ṁ O,HP + ṁ O,LP )(h11−h1) , hcool,pp−hcool,in

(7)

where h11 is the working fluid enthalpy at the condensation dew point, hcool,pp is the cooling water enthalpy that corresponds to the condensation dew point of the working fluid, and hcool,in is the cooling water enthalpy at the condenser inlet. The net power output of the dual-pressure evaporation ORC system is calculated as (8)

Wnet = WT−WP−Wcool. 2.4. System model equations

The system efficiency is defined as

The detailed model equations of the single-pressure evaporation ORC system have been described in our previous work [8].

ηsys =

Wnet . Qsys

(9)

Table 3 Selection ranges of optimized cycle parameters for the single-pressure and dual-pressure evaporation ORCs. Cycle type Single-pressure evaporation

Dual-pressure evaporation

Optimized parameter

Lower limit

Upper limit

Evaporation pressure, pe,single

pcond + 100 kPa

0.9pc

Evaporator outlet temperature, T7,single

Expansion process does not pass through the two-phase region

THS,in−ΔTHAP,pp

0.9pc −100 kPa

Evaporation pressure of the low-pressure stage, pe,LP

pcond + 100 kPa

Evaporation pressure of the high-pressure stage, pe,HP

pe,LP + 100 kPa

0.9pc

Evaporator outlet temperature in the high-pressure stage, T7

Expansion process does not pass through the two-phase region

THS,in−ΔTHAP,pp

413

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source inlet temperature below 160 °C. For the heat source inlet temperature of 160–172 °C, the T7,single opt remains at 130.0 °C as the heat source inlet temperature increases. When the heat source inlet temperature is higher than 172 °C, the T7,single opt is higher than its lower limit, and increases from 130.0 °C to 154.7 °C as the heat source inlet temperature increases. For the single-pressure evaporation ORC, the reasons for the variations in the optimized evaporation pressure and evaporator outlet temperature as the heat source inlet temperature increases have been explained in our previous work [8]. For the single-pressure evaporation ORCs using R600a, the heat absorption process pinch point temperature difference, ΔTHAP,pp , occurs at the VPP (the evaporation bubble point of the working fluid) when the heat source inlet temperature is 100–171 °C. The slope of the heat source fluid curve in the T-s diagram increases as the heat source inlet temperature increases, and the position of ΔTHAP,pp will move from VPP to PPP (the heat source fluid outlet/the preheater inlet of the working fluid). Fig. 4 shows the schematic for various positions of ΔTHAP,pp in the single-pressure evaporation ORC. The ΔTHAP,pp occurs at the PPP when the heat source inlet temperature is higher than 171 °C. When the ΔTHAP,pp occurs at the PPP, the heat source outlet temperature of the single-pressure evaporation ORC system is mainly decided by the evaporation pressure. Meanwhile, the system heat absorption capacity can barely increase, because the decrement of the heat source outlet temperature is extremely low even if the evaporation pressure is reduced. The pe,single opt has generally reached its upper limit (0.9pc ); while, the T7,single opt can increase, which can further increase the efficiency and net power output of an ORC system. Therefore, the optimized evaporator outlet temperature (T7,single opt ) is generally higher than its lower limit (T7,single LL ) when the ΔTHAP,pp occurs at the PPP. Results show that: for the single-pressure evaporation ORCs, the heat source inlet temperatures where the ΔTHAP,pp occurs at the VPP, are almost equal to those of T7,single opt = T7,single LL (the upper limit of the former is generally 1 °C lower than that of the latter), as shown in Table 5. The critical temperatures of R601 and R601a are relatively high, and the optimized evaporation pressures are lower than their upper limits (0.9pc ). Moreover, the ΔTHAP,pp always occurs at the VPP for the heat source inlet temperature of 100–200 °C. Therefore, the variations in the optimized evaporation pressures and evaporator outlet temperatures of R601 and R601a are similar to those of R600a, which are driven by the 100–160 °C heat sources, as the heat source inlet temperature increases. For the dual-pressure evaporation ORCs using R600a, the optimized evaporation pressures for various heat source inlet temperatures are shown in Fig. 5. When the heat source inlet temperature is 100–154 °C, the optimized evaporation pressure of the high-pressure stage, pe,HP opt , increases from 1.21 MPa to 3.27 MPa (0.9pc ) and its increment also increases as the heat source inlet temperature increases. The pe,HP opt maintains its upper limit when the heat source inlet temperature is higher than 154 °C. The pe,HP opt is higher than pe,single opt for the heat source inlet temperature below 160 °C. The optimized evaporation pressure of the low-pressure stage, pe,LP opt , is always lower than that of

2.5. Process and details of optimization The optimized operation condition is the one that maximizes the system net power output. Thermophysical properties of organic fluids, heat source fluid and cooling water were calculated using REFPROP 9.1 [50]. The following was conducted for the dual-pressure evaporation ORC system driven by the heat source of a certain inlet temperature: The evaporation pressures of two stages ( p and p ) and the • evaporator outlet temperature in the high-pressure stage (T ) of the e,LP

e,HP

7

• •

working fluid were divided into 50 sections with equal pressure/ temperature intervals between their upper and lower limits, respectively. The heat absorption capacity, net power output and efficiency of the system were calculated for each pe,LP , pe,HP , and T7 . The method for determining the ΔTHAP,pp was similar to that in our previous work [8]. The operation condition which could not meet the requirement of ΔTHAP,pp was ignored. The system net power outputs for various cycle parameters ( pe,LP , pe,HP , and T7 ) were compared. The maximum system net power output and the optimized operation condition were then screened out for the given heat source inlet temperature.

The optimization process of the single-pressure evaporation ORC system is similar to that of the dual-pressure evaporation ORC system, and the details have been described in our previous work [8]. 2.6. Validation The single-pressure evaporation ORC is the conventional subcritical ORC, and the system model has been validated in our previous work [8]. The system model of the dual-pressure evaporation ORC was validated using the data listed in Manente et al. [43]. The same model assumptions were selected, and R600a was selected as the working fluid. Comparisons of the important calculation results between the present work and Manente et al. [43] are shown in Table 4. The maximum relative error is 1.2% ( pe,LP opt ), mainly due to the different calculation step lengths. Other relative errors are lower than 1%; moreover, the system net power outputs are almost the same. Therefore, the present system model of the dual-pressure evaporation ORC is also reliable. 3. Results and discussion 3.1. Optimized evaporation pressures and evaporator outlet temperatures For the single-pressure and dual-pressure evaporation ORCs, the variations of the optimized evaporation pressures and evaporator outlet temperatures are generally similar for various working fluids, as the heat source inlet temperature increases. R600a is taken as an example to introduce the detailed variations. Fig. 3 presents the optimized evaporation pressures ( pe,single opt ) and evaporator outlet temperatures (T7,single opt ) of the single-pressure evaporation ORCs using R600a for various heat source inlet temperatures. The pe,single opt increases from 0.95 MPa to 3.27 MPa (0.9pc , the upper limit of the evaporation pressure) and its increment also increases as the heat source inlet temperature increases, when the heat source inlet temperature is 100 °C–160 °C. When the heat source inlet temperature is higher than 160 °C, the pe,single opt remains at 3.27 MPa as the heat source inlet temperature increases. The lower limit of the evaporator outlet temperature (T7,single LL ) corresponds to the pe,single opt , and its variations are similar to those of the pe,single opt as the heat source inlet temperature increases. The T7,single opt is equal to its lower limit (T7,single LL ) when the heat source inlet temperature is lower than 172 °C. In detail, the T7,single opt increases from 63.7 °C to 130.0 °C, and its increment also increases as the heat source inlet temperature increases for the heat

Table 4 Validation of the calculation results from the present work with data listed in Manente et al. [43] for the dual-pressure evaporation ORC. Working fluid: R600a

414

THS,in = 100 °C

THS,in = 150 °C

Present work

Manente et al. [43]

Error

Present work

Manente et al. [43]

Error

1.2%

pe,LP opt /MPa

0.790

0.795

−0.7%

1.265

1.250

pe,HP opt /MPa

1.175

1.170

0.4%

2.545

2.530

0.6%

ΔTsup,LP opt /°C

0.01

0.01

0.0%

0.01

0.01

0.0%

ΔTsup,HP opt /°C

2

2

0.0%

2

2

0.0%

THS,out /°C Wnet max /kW

59.4 961.0

59.6 961.5

−0.4% −0.1%

60.9 3868

60.5 3871

0.6% −0.1%

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160

T7,single_opt 140

2.5

pe,single_opt

2.0

T7,single_LL

120 100

1.5

PPP 80

1.0 0.5 100

110

120

130

140

150

160

170

180

190

3.0

Evaporation pressure, pe(MPa)

VPP

3.0

Evaporator outlet temprature, T(ºC)

Evaporation pressure, pe(MPa)

3.5

180

3.5

60 200

THS,in 7

VPP 3

THS,out

PPP

Single-pressure evaporation

THS,out

10

11

2

1

Cooling water

Tcool,in

Tcool,pp

1.0

Tcool,out

R227ea R236ea R245fa R600 R600a R601 R601a R1234yf R1234ze(E)

100–131 °C 100–176 °C 100–191 °C 100–190 °C 100–171 °C 100–200 °C 100–200 °C 100–131 °C 100–149 °C

100–132 °C 100–177 °C 100–192 °C 100–191 °C 100–172 °C 100–200 °C 100–200 °C 100–132 °C 100–150 °C

130

140

150

160

170

180

190

200

T7_opt

120

T7_LL T7,single_opt

100 80 60

T4

40

110

120

130

140

150

160

170

180

190

200

Fig. 6. Optimized evaporator outlet temperatures of the dual-pressure evaporation ORCs using R600a for various heat source inlet temperatures.

Table 5 Heat source inlet temperatures where the heat absorption process pinch point temperature difference occurs at the VPP and T7,single opt = T7,single LL for the single-pressure evaporation ORC.

THS,in for T7,single opt = T7,single LL

120

Heat source inlet temperature, THS,in(ºC)

Fig. 4. Schematic for various positions of the heat absorption process pinch point temperature difference in the single-pressure evaporation ORC.

THS,in for VPP

110

140

20 100

Entropy, s

Working fluid

pe,LP_opt

0.5

160

Evaporator outlet temperature, T(ºC)

Temperature, T

H

fl

1.5

Fig. 5. Optimized evaporation pressures of the dual-pressure evaporation ORCs using R600a for various heat source inlet temperatures.

THS,in

ot

pe,single_opt

2.0

Heat source inlet temperature, THS,in(ºC)

Fig. 3. Optimized evaporation pressures and evaporator outlet temperatures of the singlepressure evaporation ORCs using R600a for various heat source inlet temperatures.

d ui

2.5

0.0 100

Heat source inlet temperature, THS,in(ºC)

pe,HP_opt

corresponds to the pe,HP opt when the heat source inlet temperature is lower than 172 °C. In detail, as the heat source inlet temperature increases, the T7 opt increases from 74.8 °C to 130.0 °C and its increment also increases for the heat source inlet temperature below 154 °C, whereas it remains at 130.0 °C for the heat source inlet temperature of 154–172 °C. When the heat source inlet temperature is higher than 172 °C, the T7 opt is higher than T7 LL , and increases from 130.0 °C to 154.7 °C as the heat source inlet temperature increases. In addition, the optimized evaporator outlet temperature of the high-pressure stage is higher than that of the single-pressure evaporation ORC for the heat source inlet temperature below 160 °C, and is almost equal to (slightly larger than) that of the single-pressure evaporation ORC for the heat source inlet temperature above 160 °C. The evaporator outlet temperature of the low-pressure stage, T4 , is lower than that of the single-pressure evaporation ORC, and the difference increases as the heat source inlet temperature increases. The variations of T4 are similar to those of pe,LP opt as the heat source inlet temperature increases. With the increase of the heat source inlet temperature, the T4 increases from 54.9 °C to 78.5 °C when the heat source inlet temperature is lower than 154 °C, and decreases when the heat source inlet temperature is 154–171 °C, and then remains at 38.1 °C when the heat source inlet temperature is higher than 171 °C. Results also show that: for the dual-pressure evaporation ORCs, the heat source inlet temperatures where T7 opt > T7 LL are almost equal to

the single-pressure evaporation ORC. As the heat source inlet temperature increases, the pe,LP opt increases from 0.77 MPa to 1.30 MPa and its increment also increases for the heat source inlet temperature below 154 °C; and it decreases for the heat source inlet temperature of 154–171 °C and maintains its lower limit ( pcond + 100 kPa ) for the heat source inlet temperature above 171 °C. Fig. 6 presents the optimized evaporator outlet temperatures of the dual-pressure evaporation ORCs using R600a for various heat source inlet temperatures. In the high-pressure stage, the optimized evaporator outlet temperature, T7 opt , is equal to its lower limit (T7 LL ) which 415

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evaporator outlet temperature of the high-pressure stage in the dualpressure evaporation ORC are equal to those of the single-pressure evaporation ORC; whereas the optimized evaporation pressure and evaporator outlet temperature of the low-pressure stage are significantly lower than those of the single-pressure evaporation ORC. Therefore, the system efficiency of the dual-pressure evaporation ORC is significantly lower than that of the single-pressure evaporation ORC. When the heat source inlet temperature is higher than 172 °C, the optimized evaporation pressure and evaporator outlet temperature of the low-pressure stage in the dual-pressure evaporation ORC are their lower limits, and significantly lower than those of the single-pressure evaporation ORC. However, the heat absorption capacity and power output of the low-pressure stage are extremely low compared with the total heat absorption capacity and power output of the dual-pressure evaporation ORC system; thus, the effect of the low-pressure stage on the system efficiency is relatively weak. Therefore, the system efficiency of the dual-pressure evaporation ORC is slightly lower than that of the single-pressure evaporation ORC, and the maximum relative decrement is lower than 1.5%. Fig. 8 presents the heat source outlet temperatures of the singlepressure and dual-pressure evaporation ORCs using R600a for the optimized operation conditions. The system heat absorption capacity increases with the decrease of the heat source outlet temperature for a given heat source inlet temperature. For the single-pressure evaporation ORC, when the heat source inlet temperature is lower than 160 °C, the ΔTHAP,pp occurs at the VPP and the optimized evaporation pressure increases as the heat source inlet temperature increases, as shown in Fig. 3. Although the slope of the heat source fluid curve in the T-s diagram generally increases as the heat source inlet temperature increases, which is beneficial in reducing the heat source outlet temperature. The effect of the increase in the optimized evaporation pressure on the heat source outlet temperature is relatively stronger. Therefore, the heat source outlet temperature increases from 59.0 °C to 67.2 °C as the heat source inlet temperature increases. When the heat source inlet temperature is 160–171 °C, the ΔTHAP,pp occurs at the VPP, and the optimized evaporation pressure and evaporator outlet temperature remain constant, as shown in Fig. 3. Therefore, the heat source outlet temperature decreases almost linearly as the heat source inlet temperature increases. When the heat source inlet temperature is higher than 171 °C, the ΔTHAP,pp occurs at the PPP and the optimized evaporation pressure remains constant; thus, the heat source outlet temperature also remains at approximately 37.2 °C. For the dual-pressure evaporation ORC, the heat source outlet temperature mainly depends on the evaporation pressure of the lowpressure stage ( pe,LP ) and the total working fluid mass flow rate

those where the pe,LP opt is the lower limit ( pcond + 100 kPa ), and are also almost equal to those where the ΔTHAP,pp in the single-pressure evaporation ORC occurs at the PPP. Although the system efficiency increases as the pe,LP increases, the heat source outlet temperature also increases. The results of the parameters optimization reveal that a low pe,LP with a high pe,HP can generally achieve a large net power output. When the pe,LP is the lower limit, the system heat absorption capacity can barely increase and the pe,HP opt has generally reached its upper limit. Thus, the evaporator outlet temperature of the high-pressure stage (T7 ) should be increased to further increase the system efficiency and net power output. Therefore, the T7 opt is generally higher than the T7 LL when pe,LP opt = pe,LP LL . In summary, the optimized cycle parameters in the single-pressure evaporation ORCs are as follows: when the ΔTHAP,pp occurs at the VPP, the pe,single opt increases as the heat source inlet temperature increases until its upper limit is reached; and the T7,single opt is generally equal to its lower limit which corresponds to the pe,single opt . When the ΔTHAP,pp occurs at the PPP, the pe,single opt is generally the upper limit; whereas the T7,single opt is generally higher than its lower limit, and increases as the heat source inlet temperature increases. The optimized cycle parameters in the dual-pressure evaporation ORCs are as follows: the pe,HP opt increases until its upper limit is reached; whereas the pe,LP opt initially increases (when pe,HP opt < pe,HP UL ) and then decreases until its lower limit is reached (when pe,HP opt = pe,HP UL ), as the heat source inlet temperature increases. The T7 opt is equal to its lower limit which corresponds to the pe,HP opt when pe,LP opt > pe,LP LL , whereas it is generally higher than its lower limit and increases as the heat source inlet temperature increases when pe,LP opt = pe,LP LL . The results can provide a great guiding value for the selections of the optimal evaporation pressures and evaporator outlet temperatures for the single-pressure and dual-pressure evaporation ORCs. That is beneficial and important for the design and optimization of two ORC systems in the practical applications. 3.2. Analyses and comparison of system thermodynamic performance R600a is taken as an example to analyze and compare the thermodynamic performance of the single-pressure and dual-pressure evaporation ORC systems for various heat source inlet temperatures. For other eight working fluids, the variations in the thermodynamic performance of two ORC systems are similar to those of R600a as the heat source inlet temperature increases. Fig. 7 presents the system efficiencies of the single-pressure and dual-pressure evaporation ORCs using R600a for the optimized operation conditions. The system efficiency generally increases as the evaporation pressure and evaporator outlet temperature increase because the cycle condensation temperature is constant. With the increase of the heat source inlet temperature, the efficiency of the single-pressure evaporation ORC system increases from 6.5% to 13.1% and its increment also increases for the heat source inlet temperature below 160 °C, and it remains at 13.1% for the heat source inlet temperature of 160–172 °C. For the heat source inlet temperature above 172 °C, the efficiency of the single-pressure evaporation ORC system increases but its increment decreases as the heat source inlet temperature increases; and reaches 13.5% when the heat source inlet temperature is 200 °C. The variations in the system efficiency of the single-pressure evaporation ORC have been explained in our previous work [8]. For the dual-pressure evaporation ORC, the system efficiency increases from 7.0% to 13.4% whereas its increment generally decreases for the heat source inlet temperature of 100–200 °C, as the heat source inlet temperature increases. In addition, the system efficiency of the dual-pressure evaporation ORC is higher than that of the single-pressure evaporation ORC when the heat source inlet temperature is lower than approximately 150 °C. When the heat source inlet temperature is approximately 150–172 °C, the optimized evaporation pressure and

15 14

System efficiency,

sys

(%)

13 12 11 10 9 Single-presssure Dual-pressure

8 7 6 5 100

110

120

130

140

150

160

170

180

190

200

Heat source inlet temperature, THS,in(ºC) Fig. 7. System efficiencies of the single-pressure and dual-pressure evaporation ORCs using R600a for the optimized operation conditions.

416

Applied Energy 217 (2018) 409–421

70

Maximized net power output, Wnet(kW)

Heat source outlet temperature, THS,out(ºC)

J. Li et al.

100

65 60 55 50 45

Single-pressure Dual-pressure

40 35 30 100

110

120

130

140

150

160

170

180

190

80

60

40

20

0 100

200

Single-pressure Dual-pressure

110

120

130

140

150

160

170

180

190

200

Heat source inlet temperature, THS,in(ºC)

Heat source inlet temperature, THS,in(ºC)

Fig. 9. Maximized net power outputs of the single-pressure and dual-pressure evaporation ORC systems using R600a for various heat source inlet temperatures.

Fig. 8. Heat source outlet temperatures of the single-pressure and dual-pressure evaporation ORCs using R600a for the optimized operation conditions.

than that of the single-pressure evaporation ORC, and the system heat absorption capacity only increases by approximately 0.5%. Fig. 9 presents the net power outputs of the single-pressure and dualpressure evaporation ORC systems using R600a for the optimized operation conditions. The values are also the maximized net power outputs for per mass flow rate (kg s–1) heat source fluid for various heat source inlet temperatures. The system net power output depends on the system efficiency and heat absorption capacity. For the single-pressure evaporation ORC, when the heat source inlet temperature is 100–160 °C, the system efficiency increases and its increment also increases as the heat source inlet temperature increases. The system heat absorption capacity also increases as the heat source inlet temperature increases because the temperature drop of the heat source fluid increases although its outlet temperature increases. When the heat source inlet temperature is 160–171 °C, the system efficiency remains constant, whereas the system heat absorption capacity increases and its increment also increases because the heat source outlet temperature decreases almost linearly. Therefore, for the heat source inlet temperature of 100–171 °C, the maximized net power output of the single-pressure evaporation ORC system increases from 11.3 kW to 72.9 kW and its increment also increases as the heat source inlet temperature increases. For the heat source inlet temperature above 171 °C, with the increase of the heat source inlet temperature, the system efficiency of the single-pressure evaporation ORC increases but its increment is low; and the system heat absorption capacity increases almost linearly because the heat source outlet temperature remains constant. Thus, the maximized system net power output increases almost linearly as the heat source inlet temperature increases, and reaches 94.0 kW when the heat source inlet temperature is 200 °C. For the dual-pressure evaporation ORC, the system efficiency increases whereas its increment decreases as the heat source inlet temperature increases. The variations of the heat source outlet temperature are relatively complex. While, with the increase of the heat source inlet temperature, the system heat absorption capacity increases and its increment also increases for the heat source inlet temperature below 171 °C, and it increases almost linearly for the heat source inlet temperature above 171 °C. Therefore, as the heat source inlet temperature increases, the maximized net power output of the dual-pressure evaporation ORC system increases from 14.3 kW to 93.4 kW for the heat source inlet temperature of 100–200 °C, and its variations are similar to those of the single-pressure evaporation ORC system. If the net power output of the dual-pressure evaporation ORC system is larger than that of the single-pressure evaporation ORC system, then the efficiency of the dual-pressure evaporation ORC system will be higher or its heat source outlet temperature will be lower (the heat absorption capacity will be larger), for the same heat source inlet temperature. When the heat source inlet temperature is 100–171 °C, the maximized net power output of

(ṁ O,HP + ṁ O,LP ) because of the preheating process (2–3 process), as shown in Fig. 1(b) and 2(b). The pe,LP determines the heat source fluid temperature at the preheater inlet (THS,2 ), whereas its effect on the total working fluid mass flow rate is relatively weak. THS,2 increases as the pe,LP increases, thereby increasing the heat source outlet temperature. The ṁ O,HP + ṁ O,LP determines the slope of the heat source fluid curve in the preheating process of the working fluid. The slope of the heat source fluid curve in the preheating process of the working fluid increases as the ṁ O,HP + ṁ O,LP increases, thereby reducing the heat source outlet temperature. When the heat source inlet temperature is lower than approximately 130 °C, the pe,LP opt and ṁ O,HP + ṁ O,LP increase as the heat source inlet temperature increases; and the heat source outlet temperature generally increases but with a low increment. When the heat source inlet temperature is approximately 130–154 °C, with the increase of the heat source inlet temperature, the pe,LP opt increases, and the ṁ O,HP + ṁ O,LP increases and its increment also increases. The effect of the increase in the ṁ O,HP + ṁ O,LP on the heat source outlet temperature is stronger. Thus, the heat source outlet temperature decreases as the heat source inlet temperature increases. When the heat source inlet temperature is 154–171 °C, the pe,LP opt decreases and its decrement increases; whereas the ṁ O,HP + ṁ O,LP increases and its increment also increases, as the heat source inlet temperature increases. Thus, the heat source outlet temperature decreases with the increase of the heat source inlet temperature. In conclusion, when the heat source inlet temperature is 130–171 °C, the heat source outlet temperature decreases from 52.1 °C to 36.4 °C and its decrement increases as the heat source inlet temperature increases. When the heat source inlet temperature is higher than 171 °C, the pe,LP opt and ṁ O,HP + ṁ O,LP remain constant; thus, the heat source outlet temperature remains at approximately 36.4 °C. However, the heat transfer temperature difference between the working fluid and the heat source fluid at the heat source outlet is still higher than the ΔTHAP,pp . The comparison between the heat source outlet temperatures of the single-pressure and dual-pressure evaporation ORCs shows that: when the heat source inlet temperature is 100–171 °C, the ΔTHAP,pp of the single-pressure evaporation ORC occurs at the VPP, and the heat source outlet temperature of the dual-pressure evaporation ORC is significantly lower than that of the single-pressure evaporation ORC. The maximum increment of the system heat absorption capacity is 22.6%. When the heat source inlet temperature is higher than 171 °C, the ΔTHAP,pp of the single-pressure evaporation ORC occurs at the PPP. Although the optimized evaporation pressure of the low-pressure stage ( pe,LP opt = pcond + 100 kPa ) is significantly lower than that of the singlepressure evaporation ORC ( pe,single opt = 0.9pc ), the heat source outlet temperature of the dual-pressure evaporation ORC is only 0.8 °C lower 417

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pressure evaporation ORC occurs at the VPP. Furthermore, the relative increment in the maximized net power output generally increases as the heat source inlet temperature decreases. When the heat source inlet temperature is higher than THS,in TP , the dual-pressure evaporation ORC system is unbefitting because its maximized net power output is generally lower than that of the single-pressure evaporation ORC system; and the ΔTHAP,pp of the singlepressure evaporation ORC occurs at the PPP. For the heat source inlet temperature slightly below THS,in TP , the difference in the efficiencies of the single-pressure and dual-pressure evaporation ORC systems is extremely low, and the heat source outlet temperature has a more significant effect on the relative superiority of their system net power outputs. The curve of the working fluid in the preheating process almost coincides with its saturation liquid curve, because the temperature increase of the working fluid in the compression process (1–2 and 3–5 processes) is low. Thus, the saturation liquid curve of the working fluid significantly affects the heat source outlet temperature. The shapes of the saturation liquid curves are similar for the studied nine working fluids, and that is the major reason for the relatively good linearity between THS,in TP and the working fluid critical temperature. The maximum deviation between the calculation of THS,in TP = 1.0416Tc + 30.629 °C and the actual THS,in TP is lower than 6 °C (occurs at R227ea), and the relative deviation is lower than 5%. Considering the effects of the temperature fluctuation in actual heat sources, and the limitation of the operation parameters control accuracy in the design and operation processes of an actual ORC system; the prediction accuracy of THS,in TP = 1.0416Tc + 30.629 °C is acceptable in the practical engineering. For the single-pressure and dual-pressure evaporation ORC systems, the maximized net power outputs and the optimal working fluids for the 100–200 °C heat sources are shown in Fig. 11(a) and (b), respectively. The results are beneficial for the ORC system to achieve a high heat–power conversion efficiency in the exploitation of the actual renewable energy and waste heat resources. Therein, the working fluid between two vertical dotted lines is the optimal working fluid in this heat source inlet temperature range. The critical temperature of the optimal working fluid generally increases as the heat source inlet temperature increases. For the single-pressure evaporation ORC system, the maximized net power output of R227ea is larger than that of R1234yf for the heat source inlet temperature below 115 °C. This result can be attributed to that the optimized evaporation pressure of R227ea is lower than that of R1234yf for the same heat source inlet temperature, although their system efficiencies are almost equal. Thus, the heat source outlet temperature of R227ea is lower, and its system heat absorption capacity is larger. In addition, the THS,in TP increases as the working fluid critical temperature increases, and the increment of the maximized system net power output ((Wnet,dual−Wnet,single)/Wnet,single ) increases with the increase of THS,in TP−THS,in . Thus, given a heat source inlet temperature, the working fluid critical temperature is higher, the (Wnet,dual−Wnet,single)/Wnet,single is larger. The critical temperature of the optimal working fluid generally

the dual-pressure evaporation ORC system is larger than that of the singlepressure evaporation ORC system. The relative increment increases as the heat source inlet temperature decreases, and the maximum increment is 25.6% for R600a. When the heat source inlet temperature is higher than 171 °C, the maximized net power output of the dual-pressure evaporation ORC system will be equal to that of the single-pressure evaporation ORC system. The single-pressure evaporation ORC can be considered as a special form of the dual-pressure evaporation ORC, which the evaporation pressure of the low-pressure stage (pe,LP ) is equal to the condensation pressure. In Fig. 9, the maximized net power output of the dual-pressure evaporation ORC system is slightly lower than that of the single-pressure evaporation ORC system (the maximum difference is lower than 0.7%), because of a minimum pressure difference (100 kPa) between the pe,LP and the condensation pressure (i.e., the lower limit of pe,LP is pcond + 100 kPa ) to distinguish them in the parametric optimization, and also to ensure that the expansive process of the low-pressure stage can be achieved. Table 6 lists the heat source inlet temperatures where the maximized net power output of the dual-pressure evaporation ORC system is larger than that of the single-pressure evaporation ORC system (Wnet,dual > Wnet,single ) and the maximum increment of the system net power output ([(Wnet,dual−Wnet,single)/ Wnet,single]max ) for various working fluids. For the studied nine pure working fluids, the increment of the maximized net power output ((Wnet,dual−Wnet,single)/ Wnet,single ) increases as the heat source inlet temperature decreases. The maximized net power output of the dual-pressure evaporation ORC system can increase by 21.4–26.7% at most compared with the single-pressure evaporation ORC system. Results also reveal that: the heat source inlet temperatures where Wnet,dual > Wnet,single are almost equal to those where the ΔTHAP,pp of the single-pressure evaporation ORC occurs at the VPP. In the single-pressure evaporation ORC, the optimized evaporation pressure is 0.9pc when the ΔTHAP,pp occurs at the PPP. Although the optimized evaporation pressure of the low-pressure stage is pcond + 100 kPa in the dual-pressure evaporation ORC, its heat source outlet temperature only decreases by 0.8 °C, and the increment of the system heat absorption capacity is relatively low, as shown in Fig. 8. Furthermore, in the dual-pressure evaporation ORC, the optimized evaporation pressure and evaporator outlet temperature of the high-pressure stage are almost equal to those of the single-pressure evaporation ORC. While, the optimized evaporation pressure of the low-pressure stage is lower, thereby reducing the efficiency of the dual-pressure evaporation ORC system, as shown in Fig. 7. The decrease in the system efficiency has a considerable effect on the system net power output. Thus, the maximized net power output of the dual-pressure evaporation ORC system is slightly lower than (almost equal to) that of the single-pressure evaporation ORC system when the ΔTHAP,pp of the single-pressure evaporation ORC occurs at the PPP. Otherwise, the maximized net power output of the dual-pressure evaporation ORC system is larger than that of the single-pressure evaporation ORC system when the ΔTHAP,pp of the single-pressure evaporation ORC occurs at the VPP. 3.3. Selections of the optimal cycle type and working fluid

Table 6 Heat source inlet temperatures where Wnet,dual > Wnet,single [(Wnet,dual−Wnet,single)/ Wnet,single]max for various working fluids.

The applicable heat source temperature range of the dual-pressure evaporation ORC (Wnet,dual > Wnet,single ) and [(Wnet,dual−Wnet,single)/ Wnet,single]max generally increase as the working fluid critical temperature increases. The upper limit of the applicable heat source temperatures and the working fluid critical temperature generally conform to THS,in TP = 1.0416Tc + 30.629 °C , as shown in Fig. 10. Given a certain working fluid, THS,in TP = 1.0416Tc + 30.629 °C can be used to assess the optimal cycle of ORC (i.e., the single-pressure or dual-pressure evaporation) for various heat source inlet temperatures. Moreover, THS,in TP can also be used to assess the position of ΔTHAP,pp in the single-pressure evaporation ORC. For a certain working fluid, when the heat source inlet temperature is lower than THS,in TP , the maximized net power output of the dual-pressure evaporation ORC system is larger than that of the single-pressure evaporation ORC system; and the ΔTHAP,pp of the single418

and

Working fluid

THS,in for Wnet,dual > Wnet,single

[(Wnet,dual−Wnet,single)/ Wnet,single]max

R227ea R236ea R245fa R600 R600a R601 R601a R1234yf R1234ze(E)

100–131 °C 100–175 °C 100–191 °C 100–189 °C 100–171 °C 100–200 °C 100–200 °C 100–131 °C 100–149 °C

21.4% 25.1% 26.3% 26.4% 25.6% 26.7% 26.5% 21.8% 24.3%

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120

(a) 190

Single-pressure evaporation PPP

180

R600

System net power output, Wnet(kW)

Heat source inlet temperature, THS,in(ºC)

200

R245fa R236ea

R600a

170 160 R1234ze(E)

THS,in_TP=1.0416Tc+30.629ºC

150 140

R2=0.986 R1234yf

120 90

Dual-pressure evaporation VPP

R227ea

130 100

110

120

130

140

150

100 R227ea R1234yf

R600a R236ea

R1234ze

R600

60

R245fa

40 20 0 100

160

R227ea

80

110

120

130

140

150

160

170

180

190

200

Heat source inlet temperature, THS,in(ºC)

Working fluid critical temperature, Tc(ºC)

120

(b) System net power output, Wnet(kW)

Fig. 10. Predictions for the optimal cycle type (single-pressure or dual-pressure evaporation) and the position of the heat absorption process pinch point temperature difference in the single-pressure evaporation ORC.

increases as the heat source inlet temperature increases. Therefore, in the dual-pressure evaporation ORC, the applicable heat source inlet temperatures of various working fluids decrease, compared to the single-pressure evaporation ORC. For example, the applicable heat source inlet temperatures of R600a are 164–175 °C for the singlepressure evaporation ORC, whereas those are 158–174 °C for the dualpressure evaporation ORC using R600a. For the 100–200 °C heat sources without a limit on the outlet temperature, the optimal cycle types, optimal working fluids, and maximized net power outputs are shown in Fig. 11(c). The total range of the heat source inlet temperature which the dual-pressure evaporation ORC is the optimal cycle type, is larger.

100 R600a

R1234ze

R227ea

R236ea

80 R600

60

R245fa

40 20 0 100

110

120

130

140

150

160

170

180

190

200

Heat source inlet temperature, THS,in(ºC) 120

System net power output, Wnet(kW)

3.4. Effect of the pinch point temperature difference on the optimal cycle type Given a heat source inlet temperature, as the pinch point temperature difference in the heat absorption process (ΔTHAP,pp ) increases, the optimized evaporation pressures, optimized evaporator outlet temperatures, and system efficiencies decrease, whereas the heat source outlet temperatures increase for the single-pressure and dual-pressure evaporation ORCs. Compared to the single-pressure evaporation ORC, the limitations of the pinch point temperature difference and the working fluid isobaric heat absorption characteristics are relatively weaker for the dual-pressure evaporation ORC. Thus, the decrement of the system efficiency and the increment of the heat source outlet temperature are lower. Fig. 12 shows the system efficiencies and heat source outlet temperatures of the single-pressure and dual-pressure evaporation ORCs using R600a for the optimized operation conditions when the ΔTHAP,pp is 10 °C. Compared to the results of ΔTHAP,pp = 5 °C (Figs. 7 and 8), the heat source inlet temperature ranges for ηsys,dual > ηsys,single and THS,out dual < THS,out single−1 °C significantly increase. Moreover, the (Wnet,dual−Wnet,single)/ Wnet,single increases as the ΔTHAP,pp increases for the same heat source inlet temperature. For example, for the single-pressure and dual-pressure evaporation ORCs using R600a driven by the 100 °C heat source, the (Wnet,dual−Wnet,single)/ Wnet,single is 25.6%, 26.4%, and 27.0% when the ΔTHAP,pp is 5 °C, 10 °C, and 15 °C, respectively. For the dual-pressure evaporation ORC, the upper limit of the applicable heat source temperatures (THS,in TP ) increases as the ΔTHAP,pp increases, and the increment of THS,in TP is generally equal to that of ΔTHAP,pp . The correlation of THS,in TP and the working fluid critical temperature (Tc ) should be further amended as THS,in TP = 1.0416Tc + ΔTHAP,pp + 25.629 °C to consider the effect of ΔTHAP,pp . The maximum relative deviation is lower than 5%, and the prediction accuracy is acceptable in the practical engineering.

(c)

100 80

R1234ze Dual

R227ea Dual

R600a Single

R1234ze Single

R227ea Single

R600a Dual

40

R236ea Dual

20

R245fa Dual

0 100

R245fa Single

R236ea Single

60

110

120

130

140

150

160

170

R600 Dual

180

190

200

Heat source inlet temperature, T HS,in(ºC) Fig. 11. Maximized net power outputs and optimal working fluids for various heat source inlet temperatures: (a) Single-pressure evaporation ORC; (b) Dual-pressure evaporation ORC; (c) Optimal cycle type (solid line: dual-pressure evaporation; dash line: singlepressure evaporation).

3.5. Heat release characteristics analysis of various heat source fluids To analyze the effects of various heat source fluids on the optimized cycle parameters and thermodynamic performance of the single-pressure and dual-pressure evaporation ORC systems, the 100–200 °C hot air is selected as the heat source fluid and the outlet temperature has no restriction. The methodology in Section 2 is also applicable for the hot air, except the pressure of the hot air is 101 kPa. Fig. 13 shows the heat release characteristics of the hot water and 419

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14

effects of the evaporation pressure and evaporator outlet temperature on the ηHS are almost the same for the hot water and hot air. In addition, for the single-pressure and dual-pressure evaporation ORCs, the power consumed by the cooling system is generally extremely low compared with the system power output, and its effect on the system efficiency is relatively weak. Thus, the system efficiency, ηHS , mainly depends on the evaporation pressures and evaporator outlet temperatures when the cycle condensation temperature is given. The effects of the evaporation pressures and evaporator outlet temperatures on the ηHS have a slight connection with the type of the heat source fluid. In summary, the effects of the evaporation pressures and evaporator outlet temperatures on the system net power output are almost the same for the hot water and hot air with the same temperature. Results reveal that: for the hot water and hot air with the same temperature, the optimized evaporation pressures (pe,single opt , pe,LP opt , and pe,HP opt ), optimized evaporator outlet temperatures (T7,single opt and T7 opt ), and the variations of the system efficiencies and heat source outlet temperatures are almost the same as the heat source inlet temperature increases. Therefore, for the 100–200 °C hot air without a limit on the outlet temperature, the fitting correlation, THS,in TP = 1.0416Tc + ΔTHAP,pp + 25.629 °C, is still applicable to assess the optimal cycle type of the working fluid and the ΔTHAP,pp position of the single-pressure evaporation ORC. The maximum relative deviation is lower than 5%.

12

System efficiency,

sys

(%)

(a)

10

8

Single-pressure Dual-pressure

6 100

110

120

130

140

150

160

170

180

190

200

Heat source outlet temperature, THS,out(ºC)

Heat source inlet temperature, THS,in(ºC) 80

(b)

75 70 65 60 55

4. Conclusions

50

This study focuses on a typical dual-pressure evaporation ORC driven by the 100–200 °C heat sources without a limit on the outlet temperature. Nine pure organic fluids were selected as working fluids. Evaporation pressures and evaporator outlet temperatures of the singlepressure and dual-pressure evaporation ORCs were optimized, and their optimized system thermodynamic performance was compared. Main results are detailed as follows. The applicable heat source temperature range of the dual-pressure evaporation ORC (Wnet,dual > Wnet,single ) generally increases as the working fluid critical temperature increases. The upper limit of the applicable heat source temperatures, the working fluid critical temperature, and the pinch point temperature difference generally conform to THS,in TP = 1.0416Tc + ΔTHAP,pp + 25.629 °C. Furthermore, the relative increment in the maximized net power output generally increases as the heat source inlet temperature decreases. The maximum increments are 21.4–26.7% (ΔTHAP,pp = 5 °C) for nine working fluids.

Single-pressure Dual-pressure

45 40 35 100

110

120

130

140

150

160

170

180

190

200

Heat source inlet temperature, THS,in(ºC) Fig. 12. System efficiencies and heat source outlet temperatures of the single-pressure and dual-pressure evaporation ORCs using R600a for the optimized operation conditions when the ΔTHAP,pp is 10 °C: (a) System efficiencies; (b) Heat source outlet temperatures.

Heat source outlet temperature,THS,out(ºC)

hot air for various heat source inlet temperatures. ηHS is the ratio of the actual specific enthalpy drop to the ideal specific enthalpy drop which the heat source outlet temperature is 25 °C. It represents the heat utilization ratio of the heat source. Although the specific heat capacities of the hot water and hot air are significantly different, the heat source outlet temperatures are almost equal to achieve the same ηHS for a given heat source inlet temperature. Furthermore, the outlet temperature difference generally decreases as the heat source inlet temperature decreases. The maximum temperature difference between the hot water and hot air is only 1.1 °C for the same ηHS when the heat source inlet temperature is 200 °C. The expression of the system net power output can be transformed as follows:

Wnet= Qsys·ηsys =

h −h ṁ HS (hHS,in−hHS,25 °C)· h HS,in− h HS,out ·ηsys HS,in HS,25 °C

= Q25 °C·ηHS ·ηsys,

(10)

where Q25 °C is the total heat release capacity of the heat source fluid when its temperature decreases to 25 °C. In this study, Q25 °C is constant given a type of the heat source fluid and inlet temperature. Thus, the cycle parameters which achieve the maximum ηHS ·ηsys are optimal because they also achieve the maximum system net power output. Results show that: given the evaporation pressures and evaporator outlet temperatures, the heat source outlet temperatures of the hot water and hot air are almost equal for the same heat source inlet temperature; thus, their ηHS are also almost equal, as shown in Fig. 13. Therefore, the

220 200

HS

180

=

hHS,in hHS,out

water-200ºC water-160ºC water-100ºC air-200ºC air-160ºC air-100ºC

hHS,in hHS,25 o C

160 140 120 100 80 60 40 20

0

10

20

30

40

50

60

70

Heat source utilization efficiency,

80

90

100

(%)

HS

Fig. 13. Heat release characteristics of the hot water and hot air for various heat source inlet temperatures.

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Acknowledgements

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