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Generalized pinch point design method of subcritical-supercritical organic Rankine cycle for maximum heat recovery
Energy 143 (2018) 141e150
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Generalized pinch point design method of subcritical-supercritical organic Rankine cycle for maximum heat recovery Jahar Sarkar* Department of Mechanical Engineering, Indian Institute of Technology (B.H.U.), Varanasi, UP 221005, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 May 2017 Received in revised form 16 August 2017 Accepted 14 October 2017 Available online 2 November 2017
Novel methodology for pinch point design and optimization of subcritical and supercritical organic Rankine cycles is proposed for maximum heat recovery. The proposed method is able to predict pinch point locations in both evaporator and condenser simultaneously. As a main advantage, both evaporator and condenser pressures can be optimized simultaneously by optimizing only working fluid mass flow rate to get maximum net work output or heat recovery efficiency for given heating fluid and cooling fluid inlet conditions using selected working fluids. Working fluids have been selected based on thermodynamic and environmental criteria and compared based on various performance parameters (net work output, thermal efficiency, heat recovery efficiency, irreversibility, exergetic efficiency, turbine size parameter and heat transfer requirement). The present method seems to be better than previous pinch point design methods as it optimize the cycle by considering both source and sink. At optimum operation, ammonia is best in terms of lower mass flow rate requirement, higher exergetic efficiency, lower turbine staging and turbine size, whereas, isopentane is best in terms of higher power output and heat recovery efficiency. Novel contour plots are presented as well to select optimum ORC design parameters for available heat source and sink. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Waste heat recovery Organic Rankine cycle Pinch point temperature difference Pinch analysis Exergy destruction Optimization
1. Introduction Within last two decades, the organic Rankine cycle (ORC) has gained widespread attention and researches especially for waste heat recovery. However, the selection of proper working fluid as well as operating parameters for the ORC system is very crucial and still challenging issue as it will affect energy efficiency and economy as well as operational and environmental safeties. As the available waste heats are widely varied with its different combinations of temperature and mass flow rate [1], the ORC system needs to be designed with individual combination of working fluid and operating parameters for maximum heat recovery. To avoid the rigorous system simulation (also depends on component type), the primary design of ORC system is generally done by pinch point analysis. The pinch point in the evaporator is the point where the temperature difference between the source and working fluids is the least. Similarly, the same in the condenser is the temperature difference between the working and sink fluids is the least. As
* Corresponding author. E-mail address: [email protected]. https://doi.org/10.1016/j.energy.2017.10.057 0360-5442/© 2017 Elsevier Ltd. All rights reserved.
important operating parameter, the value of pinch point temperature difference (PPTD) is usually chosen according to the manufacturer experience. The pinch point plays an important role in the cycle design and the pinch point position is strongly dependent on source and sink conditions and working fluids [2]. Hence, pinch point analysis based proper coupling with heat source fluid and sink fluid is very essential for maximum waste heat recovery. With the increase in PPTD, lower evaporation temperature and higher condensation temperature can be achieved, which leads to decrease in cycle efficiency; and on the other hand, heat transfer area also decreases, which results in a decrease of cost for the ORC system. Hence, the PPTD of the heat exchanger not only influences the evaporation and condensation temperatures but also plays an essential role in the cost-efficiency tradeoff. Determination of the location of pinch point makes notable impact on the optimal design of ORC system [3,4]. Several researches introduced the methods of determining pinch point for subcritical ORC. Chen et al. [5] proposed a design method for organic Rankine cycles with constraint of inlet and outlet heat carrier fluid temperatures coupling with the heat source and studied the optimal running parameters of ORCs using benzene for given PPTD. Li et al. [6] theoretically studied the influence of the
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J. Sarkar / Energy 143 (2018) 141e150
Nomenclature cp Ex h I m p PPTD Q s SP T T0 UA v VFR W
specific isobaric heat capacity, kJ/kgK exergy rate, W specific enthalpy, kJ/kg irreversibility, W mass flow rate, kg/s pressure, bar pinch point temperature difference, oC heat transfer rate, W specific entropy, kJ/kgK size parameter, m temperature, oC reference temperature, K heat transfer requirement, kW/K specific volume, m3/kg volume flow ratio work transfer rate, W
PPTD and the evaporation temperature on the performance of ORC in recovering the low temperature waste heat of the flue gas. They concluded that there exists an almost same optimal evaporating PPTD to achieve their respective optimal cost-effective performance for different organic working fluids under the same condition [7]. Tian et al. [8] proposed a method to determine the pinch point in evaporator by evaporator pressure as constraint and done techno-economical analysis based on various working fluids for engine exhaust. Zebian and Mitsos [9] introduced a double-pinch criterion for closed feed water heaters of regenerative Rankine cycles and claimed that it simplifies the optimization procedure and results in significant efficiency increase for fixed heat exchanger area. Wang et al. [10] studied effect of PPTD and approach temperature difference on the net power output and surface areas of both the evaporator and the condenser using R123, R245fa and isobutane. Guo et al. [11] studied the effect of outlet temperature of heat source on ORC performance and showed that subcritical cycle performs better at higher outlet temperature. Ryms et al. [12] developed an algorithm to attain the parametric match enabling quick estimation of the possible heat reception by the specific working fluid. Yu and Feng [13] used pinch analysis to find out the proper way to increase the amount of heat recovered. Liu et al. [14] optimized the heat source temperature for given evaporator temperature. Yu et al. [15] proposed the method to determine working fluid mass flow rate for given evaporator pressure and then optimized. Wu et al. [16] analyzed the effects of PPTDs in evaporator and condenser on the exergo-economic performance of ORCs. Yang et al. [17] also studied the effect of PPTD on economic performance of ORCs. Pan and Shi [18] concluded that the pinch point locates at the bubble point for the evaporator in most cases and may shift to the subcooled liquid state in the near critical conditions. Pinch point with fluid mixture also had been determined by taking evaporator pressure as constraint in some investigation [19,20]. Unlike to the subcritical cycle, the pinch point in the evaporator of supercritical cycle has no certain locations; the pinch point may be anywhere depending on the temperature glides and the evaporator pinch point had been determined by taking evaporator pressure as constraint in most of the investigations [21e23]. Literature review shows that the PPTD had been located by taking either heat source parameters or evaporator and condenser pressures or double pinch points as constraints, which may be best
his hth hsys hII
isentropic efficiency thermal efficiency system or heat recovery efficiency exergetic efficiency
Subscripts 1e5 state points c condenser cf cooling fluid (heat sink) in condenser e evaporator hf heating fluid (heat source) in evaporator i inlet o outlet p pump t turbine wf working fluid
for individual certain source and sink. Furthermore, only evaporator pressure has been optimized by keeping condenser pressure as constraint for both subcritical and supercritical cycles. However, with best of the authors' knowledge, no general method has been proposed for simultaneous determination of pinch points in both evaporator and condenser for optimum design of the subcritical as well as supercritical ORC systems. In this study, a novel method is proposed to determine the location of PPTD in evaporator and condenser simultaneously for both subcritical and supercritical organic Rankine cycles. Single parameter (working fluid mass flow rate) has been optimized, which leads to optimize evaporator and condenser pressures simultaneously for maximum heat recovery. Comparison of selected low GWP working fluids (can be considered as next generation fluids) based on various energy-exergy performances is presented. Novel contour plots are presented as well to select optimum cycle operating parameters and performance for available heat source and sink.
2. Proposed methodology Temperature-enthalpy rate diagrams of subcritical ORC are shown in Figs.1 and 2 for wet fluid and dry fluid respectively. For ORC with superheating (wet fluid), the pinch point in evaporator would appear at three possible positions, the start point of preheating, namely Preheating Pinch Point (PPP) [14], the start point of vaporization, namely Vaporization Pinch Point (VPP) [14] and the end point of superheating, which can be defined as Superheating Pinch Point (SPP), whereas, the pinch point in condenser appears at saturated vapor point, namely Condensation Pinch Point (CPP). For ORC without superheating (dry fluid), the pinch point in evaporator would appear at two possible positions, the start point of preheating (PPP) and the start point of vaporization (VPP), whereas the pinch point in condenser appears at saturated vapor point (CPP) or turbine exit point. It is interesting to note that the profile matching between source and working fluids in evaporator is strongly dependent on source fluid to working fluid mass flow rate ratio (MR). By increasing MR, the following cases are possible:A e PPTD at PPP only, B e double PPTD at PPP and VPP, C e PPTD at VPP only, D e double PPTD at VPP and SPP (wet fluid) and E PPTD at SPP only (wet fluid). The proposed model is based on the energy balance of individual component or component segment of subcritical or
J. Sarkar / Energy 143 (2018) 141e150
Temperature
Profiles of heating fluid A: PPP only B: PPP and VPP C: VPP only D: VPP and SPP E: SPP only
B
(1)
h4 h5 ¼ his;t ½h4 hðpc ; s4 Þ
(2)
Now, the 5 enthalpy rate equations in evaporator and condenser are given by,
C
E
4' VPP PPP
his;p ðh2 h1 Þ ¼ hðpe ; s1 Þ h1 A
4 D
143
SPP
Organic Rankine Cycle 5
Cooling fluid
Enthalpy rate
mwf ðh3 h2 Þ ¼ mhf cp;hf Thf 3 Thf 2
(3)
mwf ðh40 h3 Þ ¼ mhf cphf Thf 40 Thf 3
(4)
mwf ðh4 h40 Þ ¼ mhf cphf Thfi Thf 40
(5)
mwf ðh5 h50 Þ ¼ mcf cpcf Tcf 5 Tcf 50
(6)
mwf ðh50 h1 Þ ¼ mcf cpcf Tcf 50 Tcfi
(7)
Fig. 1. Temperature-enthalpy rate diagram of ORC with source and sink for wet fluid.
The conditions for pinch point analysis are given by, supercritical organic Rankine cycle. The following general assumptions have been made for the present model: ➢ Each component is considered as a steady-state steady-flow system ➢ Pressure drop in all the heat exchangers is negligibly small ➢ Changes in kinetic and potential energies in each component are negligible ➢ Expansion and compression processes have given isentropic efficiencies ➢ Heat transfer in the cycle occurs with heat source and heat sink only ➢ Saturated liquid is supposed at the condenser exit ➢ Turbine inlet condition is saturated vapor for dry fluid whereas turbine exit condition is saturated vapor for wet fluid
(8)
i h PPTDc ¼ Min T50 Tcf 50 ; T5 Tcf 5
(9)
For given heat source mass flow rate, heat source inlet temperature, heat sink mass flow rate, heat sink inlet temperature, PPTD of evaporator and PPTD of condenser, and integrating pump and turbine energy equations, above equations can be expressed by 8 variables (condenser pressure, evaporator pressure, working fluid mass flow rate, 5 temperature differences at 2, 3, 4, 40 and 5 for wet fluid or 2, 3, 4, 50 and 5 for dry fluid). Hence, for any working fluid mass flow rate (or MR), other seven parameters can be calculated by using above seven equations (3)e(9), which will yield the pinch point locations in both evaporator and condenser. Above methodology can be used for ORC with zeotropic mixture also (only difference is that apart from PPP, VPP and SPP, another possible pinch
Profiles of heating fluid A: Point 2 only C: Point 3 only D: Points 3 and 4 E: Point 4 only
A
Profiles of heating fluid A: PPP only B: PPP and VPP C: VPP only
B C
4 VPP
3
5'
5
A
C
4
E
Organic Rankine Cycle PPP
Temperature
Temperature
For subcritical cycle, energy balances in pump and turbine are given by, respectively,
i h PPTDe ¼ Min Thfi T4 ; Thf 3 T3 ; Thf 2 T2
D
3
Supercritical heat addition
Cooling fluid
Enthalpy rate Fig. 2. Temperature-enthalpy rate diagram of ORC with source and sink for dry fluid.
Enthalpy rate Fig. 3. Temperature-enthalpy rate diagram for supercritical heat addition of ORC.
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J. Sarkar / Energy 143 (2018) 141e150
point may be saturated vapor point in the evaporator). For supercritical operation (Fig. 3), the evaporator has been divided into large number of segments (say N, which will give Nþ1 terminals or possible pinch points) and energy balance has been applied in each segment to get temperature difference in each terminal. Similar to the subcritical cycle, for N segment of evaporator, there will be total (Nþ4) equations and same variables for given working fluid mass flow rate and can be solved. The evaporator pressure has been iterated based on the criteria that the minimum temperature difference is equal to PPTD. As shown in Fig. 4, the maximum saturation entropy has been made equal to the entropy at the corresponding saturation pressure during expansion to confirm the dry expansion for dry fluid. Hence, the operating parameters and pinch location can be determined in evaporator and condenser simultaneously based on the solution.
the main criterion for further performance evaluations due to the advantage that it combines both thermal efficiency (hth ) and heat transfer efficiency (hHE ) of an ORC system. The global system efficiency is expressed by Ref. [24]:
hsys ¼ hth hHE ¼
Wnet mhf cp;hf Thf ;i T0
(16)
The turbine isentropic volume flow ratio, which is used to measure of turbine size and staging, is given by Ref. [24],
VFR ¼ v5s =v4
(17)
Furthermore, the turbine size parameter is given by Ref. [25],
SP ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q 4 ðh4 h5s Þ mwf v5s
(18)
3. Performance evaluation For given working fluid mass flow rate, after finding all the state points using above methodology, pump work and turbine work rates are given by, respectively,
Wp ¼ mwf ðh2 h1 Þ
(10)
Wt ¼ mwf ðh4 h5 Þ
(11)
The total conductance (UA) of two heat exchangers (evaporator and condenser) is directly related to the heat exchanger surfaces and is often used to give a global idea of their dimensions. Applying LMTD method, the total conductance or heat transfer requirement, which can be used to measure compactness of heat exchangers, can be approximated as:
UA ¼
The heat input and heat rejection rates are given by, respectively,
Qe ¼ mwf ðh4 h2 Þ
(12)
Qc ¼ mwf ðh5 h1 Þ
(13)
mwf ðh3 h2 Þ mwf ðh40 h3 Þ mwf ðh4 h40 Þ þ þ LMTD2/3 LMTD3/40 LMTD40 /4 mwf ðh5 h50 Þ mwf ðh50 h1 Þ þ þ LMTD5/50 LMTD50 /1
(19)
According to the first law of thermodynamics, the net power output is given by,
It can be noted that for supercritical Ranking cycle, calculation of UA for condenser is same and UA for evaporator is the summation of UAs for all segments calculated based on LMTD method. Neglecting pressure drop of heating fluid, the exergy input to the system is given by,
Wnet ¼ Wt Wp ¼ Qe Qc
. Exi ¼ Qh T0 mhf cp;hf ln Thfi Thfo
(14)
Finally, the thermal efficiency of cycle is given by,
hth ¼ Wnet =Qe
(15)
Heat recovery efficiency or global system efficiency is used as
(20)
Using exergy balance, the exergy destruction rates of evaporator, pump, turbine and condenser can be found from, respectively [26]:
h i . Ie ¼ T0 mwf ðs4 s2 Þ mhf cp;hf ln Thfi Thfo
(21)
Ip ¼ mwf T0 ½s2 s1
(22)
It ¼ mwf T0 ½s5 s4
(23)
Ic ¼ Qc mwf T0 ½s5 s1
(24)
Overall exergy balance of the cycle is given by,
Exi þ Wp Wt ¼
X
I
(25)
Hence, the second law (exergetic) efficiency is expressed by:
hII ¼
P Wnet I ¼1 Exi Exi
(26)
Combining Eqs. (15), (20) and (26),
hII ¼ Fig. 4. Temperature-entropy diagram for turbine expansion process of supercritical ORC.
hth
.
1 T0 Tlm;hf
where; Tlm;hf ¼
Thfi Thfo . ln Thfi Thfo
(27)
J. Sarkar / Energy 143 (2018) 141e150
4. Simulation and optimization An EES [27] simulation code has been developed for the subcritical-supercritical Rankine cycle to analyze the energetic and exergetic performances employing the novel methodology and relations presented above. Based on the methodology presented above, the code searches for the state point values for all the components of the cycle using the input parameters: heat source flow rate and inlet temperature, heat sink flow rate and inlet temperature, working fluid flow rate, pump and turbine isentropic efficiencies. Effective iteration technique and suitable tolerances for convergence have been used to calculate the state points of the cycle. In-build property subroutines have been used for the thermodynamic properties of selected working fluids. It may be noted that the following two criteria have been used in simulation: (i) turbine exit condition is saturated for wet fluids; (ii) turbine inlet condition is saturated for dry fluids. Utilizing the state point values, the various energetic and exergetic performance parameters have been evaluated. For the simulation, the pump and turbine isentropic efficiencies have been taken as 80% and 85%, respectively [7]. The EES simulation code has been verified with the available literature data of ORC for toluene [7]. For heat source flow rate of 10.47 kg/s and inlet temperature of 160 C, heat sink flow rate of 52.35 kg/s and inlet temperature of 20 C, evaporator PPTD of 13 C, condenser PPTD of 17 C and evaporator temperature of 110 C, the predicted net work is 66.7 kW, which is fairly matched with literature data 66.2 kW [7]. Similar match has been observed for n-Pentane also with same literature. To cover the industry application as widely as possible, the heat source temperatures were assumed as 160 Ce300 C. In present study, PPTD in evaporator and PPTD in condenser have been taken as 10 C and 5 C, respectively [14].
145
In the present methodology, based on the assumptions, the net work output is dependent on source, sink and working fluid mass flow rate. The working fluid mass flow rate can be optimized for maximum net work output or heat recovery efficiency. The flowchart for present simulation and optimization is shown in Fig. 5. The present code is able to predict maximum possible power generation and corresponding design and operating parameters for available source and sink conditions. Hence, optimum working fluid mass flow rate or mass flow rate ratio and corresponding maximum net work output or heat recovery efficiency are given by,
mwf ;opt ; MRopt ¼ f mhf ; Thfi ; mcf ; Tcfi
(28)
Wnet;max ; hrec;max ¼ f mhf ; Thfi ; mcf ; Tcfi
(29)
5. Results and discussion 5.1. Working fluid selection The selection of suitable working fluids for the ORC systems is very crucial as it will affect both energy economy as well as operational and environmental safeties. The chemical, physical, thermal and environmental properties of the selected working fluids are shown in Table 1. For the working fluid selection, the following criteria have been considered: negligible ozone layer depletion (ODP), negligible global warming potential (GWP), considerably higher auto-ignition temperature (AIT) than heat source temperature for thermal stability and higher critical temperature. 5.2. Comparison with other methods
Fig. 5. Flowchart for simulation and optimization.
As shown in Figs. 1 and 2, it is clearly understood that the slope of heating (heat source) fluid as well as the location of pinch point are strongly dependent on the mass flow rate ratio between heating and working fluid. With increase in heating fluid to working fluid mass flow rate ratio the following cases are possible: A, B, C, D (wet fluid) and E (wet fluid). With the increase in mass flow rate ratio, the evaporator temperature increases monotonically initially very fast and then slowly and hence based on the basic thermodynamic principles, the thermal efficiency increases monotonically initially quickly and then slowly (Fig. 6). However, interestingly, the net power output increases and decreases, leading to some maximum value at optimum MR as shown in Fig. 6. Hence, the heat recovery efficiency also increases and decreases by giving some maximum value. This can be attributed by the fact that the thermal efficiency increases and heat exchanger efficiency decreases and combined effect of these opposite trend leads to this trend of system efficiency. Condition of optimum MR leading to maximum system or heat recovery efficiency signifies the best coupling or best matching with the given heat source and sink. This also implies the best design of ORC system to get maximum heat recovery (flowchart to determine optimal condition is given in Fig. 5). This optimal design condition of ORC is also dependent on the working fluid and PPTD. It may be noted that the optimum design for maximum net power output will lead to minimum payback period for given source, sink, PPTD and component type. Various pinch point design methods of subcritical and supercritical ORC systems used in literature for given PPTD can be summarized as: Method 1: Design for given source fluid flow rate, inlet and exit temperatures [5,26]; Method 2: Double pinch point design for given source fluid flow rate and inlet temperature [9]; Method 3:
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J. Sarkar / Energy 143 (2018) 141e150
Table 1 Selected working fluids for organic Rankine cycle. Fluids
Composition
Type
NBP (oC)
Tcr (oC)
CP (bar)
ODP
GWP
AIT (oC)
Ammonia R-1233zd Iso-pentane n-Pentane Iso-hexane Benzene Toluene
NH3 C3H2F3Cl C5H12 C5H12 C6H14 C6H6 C7H8
Wet Dry Dry Dry Dry Dry Dry
33.05 18.32 27.00 36.06 60.21 80.06 110.4
133.0 165.6 187.2 196.5 226.6 288.9 318.6
113.3 35.73 33.78 33.70 30.40 48.94 41.26
0 0.0002 0 0 0 0 0
<1 7 20 20 e 2 3
651 380 420 309 306 560 535
175
20
165
18
155
16
145
14
135
12
125
10
115
8
Isopentane
Ammonia
105
6 2
4
6
8
10
12
14
Thermal efficiency, Recovery efficiency (%)
Net power output (kW)
CP e Critical pressure, GWP e Global warming potential, AIT e autoignition temperature.
16
Mass flow rate ratio Fig. 6. Variation of performances with mass flow rate ratio.
Design for given evaporator pressure, source fluid flow rate and inlet temperature [15e23]. Whereas, in the present method, pinch point design has been done for given working fluid flow rate, source fluid flow rate and inlet temperature (dissimilar to the previous cases, condenser temperature has been iterated based on the available sink condition). Similar to the present method, optimization is possible for both Method 1 and 3, however, Method 1 is less studied and no optimization has been done, whereas, optimization of ORC with Method 3 has been done for various target parameters. However, optimization is not possible with Method 2 due to more constraint parameters. In fact, Method 2 is a special case of the proposed method. Similarity between Method 1, Method 3 and present method is that same results are expected after optimization, although approaches are different (optimum parameters are different; source fluid exit temperature, evaporator temperature and working fluid mass flow rate, respectively). Furthermore, the method of case 3 only optimized the evaporator pressure, whereas
the present method yields the optimization of both evaporator and condenser pressures, which can be done by optimizing a single parameter (MR) only for maximum heat recovery. 5.3. Case studies The following three heat source conditions have been considered for the performance comparison of selected working fluids: (i) heat capacity rate of 10.784 kW/K and inlet temperature of 160 C, (ii) heat capacity rate of 8.387 kW/K and inlet temperature of 200 C, and (iii) heat capacity rate of 6.315 kW/K and inlet temperature of 250 C. For all cases, cooling water flow rate and inlet temperature have been taken as 50 kg/s and 20 C, respectively. Working fluid mass flow rate has been optimized to get maximum heat recovery and results are presented for optimal condition. Optimum working fluid mass flow rate and corresponding mass flow rate ratio, thermal efficiency, net work output, heat recovery efficiency and second law efficiency are shown in Figs. 7e12. Higher enthalpy change of ammonia leads to lower mass flow rate. Due to
J. Sarkar / Energy 143 (2018) 141e150
300
4.5 4
Thf,i = 160oC, Chf = 10784W/K
280
Thf,i = 200oC, Chf = 8387W/K
260
Thf,i =
3.5
250oC,
Chf = 6315W/K
3 2.5 2 1.5 1
Net work output (kW)
Working fluid mass flow rate (kg/s)
5
220 200 180 160 140 120
0
100
Fig. 10. Comparison of maximum net work output.
Fig. 7. Comparison of working fluid mass flow rate.
24
Mass flow rate ratio
Thf,i =
Chf = 10784W/K
14
Thf,i =
200oC,
Chf = 8387W/K
12
Thf,i = 250oC, Chf = 6315W/K
10 8 6 4
Heat recovery efficiency (%)
18 16
2
21 18 15 12 9 6 3
Fig. 11. Comparison of maximum heat recovery efficiency.
Fig. 8. Comparison of optimum mass flow rate ratio.
90
30
Thermal efficiency (%)
160oC,
Chf = 10784W/K
Thf,i = 200oC, Chf = 8387W/K Thf,i =
250oC,
80
Chf = 6315W/K
15 10 5
Exergetic efficiency (%)
Thf,i =
20
Thf,i = 160oC, Chf = 10784W/K Thf,i = 200oC, Chf = 8387W/K Thf,i = 250oC, Chf = 6315W/K
0
0
25
Thf,i = 160oC, Chf = 10784W/K Thf,i = 200oC, Chf = 8387W/K Thf,i = 250oC, Chf = 6315W/K
240
0.5
160oC,
147
70
Thf,i = 160oC, Chf = 10784W/K Thf,i = 200oC, Chf = 8387W/K Thf,i = 250oC, Chf = 6315W/K
60 50 40 30 20 10 0
0
Fig. 12. Comparison of optimum exergetic efficiency. Fig. 9. Comparison of optimum thermal efficiency.
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J. Sarkar / Energy 143 (2018) 141e150
temperature for supercritical Rankine cycle. Isopentane has comparatively lower pressure ratio and lower volume flow ratio, which leads to lower turbine staging and hence lower turbine cost. However, the operating pressure is higher for ammonia leads to higher density and hence lower turbine size leads to lower cost. It can be noted that the effect on heat conductance or heat transfer requirement is not so significant. Component irreversibilities show similar trend for all working fluids. Exergetic efficiency increases with increase in heat source temperature. Although isopentane has comparatively higher GWP than other chosen working fluids, it is in-general negligible or low-GWP fluid and has been considered as next generation fluid. Furthermore other fluids have some individual safety problem such as ammonia is toxic, R-1233zd is mild ozone layer depleter, benzene and toluene are carcinogens, and n-pentane and isohexane have lower auto ignition temperature. Based on above discussion, isopentane has been considered as best fluid and taken for further analysis. Most of the cases, it can be assumed that heat source is limited but sufficient cooling fluid is available. Hence, for a same amount of available heat (mhf cp;hf ðThf ;i T0 Þ¼ constant), the heating fluid mass flow rate is a function of heating fluid inlet temperature. According to these arguments, the optimum cycle parameters will be as function of heating and cooling fluid inlet temperatures only. Contours of optimum mass flow rate ratio, maximum work output and maximum heat recovery efficiency are shown in Figs. 13e15 for 1500 kW available heat. It can be noted that the working fluid mass flow rate is nearly unchanged due to same available heat and ratio decreases with increase in heating fluid inlet temperature. However, the net power as well as heat recovery efficiency is significantly influenced by both heating and cooling inlet temperatures due to the effect of these on temperature profile matching in both evaporator and condenser. Optimum parameter contours can be useful tools to
Table 2 Optimum operating parameters and energetic performances. Fluids
pe pc
VFR
SP (m)
UA (kW/K)
ie (%)
ic (%)
it (%)
ip (%)
Ammonia R-1233zd Iso-pentane n-Pentane Iso-hexane Benzene Toluene
8.037 19.97 11.15 11.70 14.23 16.79 23.47
5.513 20.85 12.07 12.08 14.06 13.72 19.30
0.0116 0.0484 0.0522 0.0575 0.0855 0.1085 0.1881
152.2 167.5 170.7 165.3 163.6 144.3 144.0
20.03 17.33 22.46 23.93 24.94 20.08 20.08
8.08 9.17 12.03 11.73 12.46 8.26 8.53
10.99 10.81 8.91 8.73 8.31 9.25 8.97
0.77 0.76 0.32 0.24 0.12 0.04 0.02
near critical operation of R1233zd, the temperature gradient of heat source is more (due to better matching of temperature profile) and also enthalpy change of R1234zd is less (lower average heat capacity due to mostly single phase heat transfer), which leads to higher R1233zd mass flow rate. As a result, the mass flow rate ratio gives opposite trend (Fig. 8). It can be noted that the effect of working fluid is more predominant than that of heat source condition as it is strongly dependent on specific enthalpy change. As shown, mass flow rate ratio decreases with increase in heat source temperature. Thermal efficiency of ORC is strongly dependent on working fluid as well as heat source temperature (Fig. 9). Increase in heat source temperature leads to increase in cycle temperature lift and it is well known fact that thermal efficiency increases with temperature lift. Due to same reason, the net power output also increases with increase in heat source temperature (Fig. 10). As shown in Fig. 11, isopentane and R1233zd are best choice due to higher heat recovery efficiency and isopentane may be a better choice due to lower cost and zero ODP compared to R1233zd. Table 2 presents the comparison of some other performance parameters. It may be noted that the PPTD occurs at VPP for subcritical Rankine cycle and it is very close to pseudocritical
220 Heating fluid inlet temperature ( oC)
Mass flow rate ratio
210
3.2 3.4
200
3.6
190
3.8 4
180
4.2 4.4
170
4.6 4.8
160
12
16 20 24 o Cooling fluid intel temperature ( C) Fig. 13. Contours of optimum mass flow rate ratio for isopentane.
5
28
J. Sarkar / Energy 143 (2018) 141e150
149
220 Heating fluid inlet temperature ( oC)
210
200 190
210
180 170
200
160 150
190
140
180
130 120
170 110
Net power (kW)
160 10
14
18
22
26
30
o
Cooling fluid intel temperature ( C) Fig. 14. Contours of maximum net power output for isopentane.
220 14
Heating fluid inlet temperature (oC)
210
13.5
13 12.5 12 11.5
200
11 10.5 10
190
9.5 9
180
8.5 8
170
160 10
7.5 Recovery efficiency (%)
15
20
25
30
o
Cooling fluid intel temperature ( C) Fig. 15. Contours of maximum heat recovery efficiency for isopentane.
choose optimal operating and design parameters of ORC system for maximum heat utilization.
6. Conclusions A general methodology is proposed to determine the location of PPTD in evaporator and condenser simultaneously of both
subcritical and supercritical organic Rankine cycles and optimized for maximum waste heat recovery. Working fluids have been selected based on various thermodynamic, environmental and safety criteria and compared for various heat source and sink conditions. For available heating fluid and cooling fluid, net work output as well as heat recovery efficiency first increases and then decreases
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J. Sarkar / Energy 143 (2018) 141e150
with working fluid mass flow rate, leading to some maximum value. Hence, the optimum working fluid mass flow rate leads best design condition to get maximum waste heat recovery for a certain working fluid. Comparison with previous pinch point design methods shows that the proposed method is able to optimize the ORC for both available heat source and sink. Comparison of selected working fluids for various heat source conditions at optimum ORC operation shows that lowest mass flow rate and hence highest mass flow rate ratio is need for ammonia. Ammonia also yields highest thermal efficiency for given conditions. At optimum operation, the net power output as well as heat recovery efficiency increases with increase in heat source temperature and isopentane and R1233zd yield maximum values. However, isopentane may be a better choice due to lower cost and zero ODP compared to R1233zd. Isopentane is also best in terms of lower pressure ratio and lower volume flow ratio. Whereas, ammonia is best in term of lower turbine size and hence lower cost. Exergetic efficiency increases with increase in heat source temperature. The net power as well as heat recovery efficiency is significantly influenced by both heating and cooling inlet temperatures. Presented optimum parameter contours can be useful for design engineer to select best operating parameters for maximum heat recovery. References [1] Sarkar J, Bhattacharyya S. Potential of organic Rankine cycle technology in India: working fluid selection and feasibility study. Energy 2015;90:1618e25. [2] Pang K-C, Chen S-C, Hung T-C, Feng Y-Q, Yang S-C, Wong K-W, et al. Experimental study on organic Rankine cycle utilizing R245fa, R123 and their mixtures to investigate the maximum power generation from low-grade heat. Energy 2017;133:636e51. [3] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy 2007;32:1210e21. € [4] Ohman H, Lundqvist P. Theory and method for analysis of low temperature driven power cycles. Appl Therm Eng 2012;37:44e50. [5] Chen Q, Xu J, Chen H. A new design method for Organic Rankine Cycles with constraint of inlet and outlet heat carrier fluid temperatures coupling with the heat source. Appl Energy 2012;98:562e73. [6] Li Y-R, Wang J-N, Du M-T. Influence of coupled pinch point temperature difference and evaporation temperature on performance of organic Rankine cycle. Energy 2012;42:503e9. [7] Li Y-R, Wang J-N, Du M-T, Wu S-Y, Liu C, Xu J-L. Effect of pinch point temperature difference on cost effective performance of organic Rankine cycle. Int J Energy Res 2013;37:1952e62. [8] Tian H, Shu G, Wei H, Liang X, Liu L. Fluids and parameters optimization for
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[24] [25] [26] [27]
the organic Rankine cycles (ORCs) used in exhaust heat recovery of Internal Combustion Engine (ICE). Energy 2012;47:125e36. Zebian H, Mitsos A. A double-pinch criterion for regenerative Rankine cycles. Energy 2012;40:258e70. Wang J, Yan Z, Wang M, Maa S, Dai Y. Thermodynamic analysis and optimization of an (organic Rankine cycle) ORC using low grade heat source. Energy 2013;49:356e65. Guo C, Du X, Yang L, Yang Y. Performance analysis of organic Rankine cycle based on location of heat transfer pinch point in evaporator. Appl Therm Eng 2014;62:176e86. Ryms M, Pys T, Klugmann-Radziemska E. Adapting the pinch point analysis to improve the ORC design process. Int. J Energy Res 2014;38:29e40. Yu H, Feng X. Pinch position between heat carrier and working fluid in organic Rankine cycle for waste heat recovery. Chem Eng Trans 2014;39:61e6. Liu W, Meinel D, Gleinser M, Wieland C, Spliethoff H. Optimal heat source temperature for thermodynamic optimization of sub-critical organic Rankine cycles. Energy 2015;88:897e906. Yu H, Feng X, Wang Y. A new pinch based method for simultaneous selection of working fluid and operating conditions in an ORC (Organic Rankine Cycle) recovering waste heat. Energy 2015;90:36e46. Wu S-Y, Zhou S-M, Xiao L. The determination and matching analysis of pinch point temperature difference in evaporator and condenser of organic Rankine cycle for mixed working fluid. Int J Green Energy 2016;13:470e80. Yang M-H, Yeh R-H. Economic performances optimization of an organic Rankine cycle system with lower global warming potential working fluids in geothermal application. Renew Energy 2016;85:1201e13. Pan L, Shi W. Investigation on the pinch point position in heat exchangers. J Therm Sci 2016;25:258e65. Kim KH, Han CH, Kim K. Effects of ammonia concentration on the thermodynamic performances of ammonia-water based power cycles. Thermochim Acta 2012;530:7e16. Mohammadkhani F, Ranjbar F, Yari M. A comparative study on the ammoniawater based bottoming power cycles: the exergoeconomic viewpoint. Energy 2015;87:425e34. Shu G, Liu L, Tian H, Wei H, Xu X. Performance comparison and working fluid analysis of subcritical and transcritical dual-loop organic Rankine cycle (DORC) used in engine waste heat recovery. Energy Convers Manag 2013;74: 35e43. Shu G, Liu L, Tian H, Wei H, Liang Y. Analysis of regenerative dual-loop organic Rankine cycles (DORCs) used in engine waste heat recovery. Energy Convers Manag 2013;76:234e43. Xu H, Gao N, Zhu T. Investigation on the fluid selection and evaporation parametric optimization for sub- and supercritical organic Rankine cycle. Energy 2016;96:59e68. Sarkar J. Comprehensive study on the role of eco-friendly working fluid properties on ORC performances. Int J Thermodyn 2016;19:198e204. Invernizzi C, Iora P, Silva P. Bottoming micro-Rankine cycles for micro-gas turbines. Appl Therm Eng 2007;27:100e10. Sarkar J. Property-based selection criteria of low GWP working fluids for organic Rankine cycle. J Braz Soc Mech Sci Eng 2017;39:1419e28. Klein SA. Engineering equation solver professional. 2017. Version 10.221.
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Generalized pinch point design method of subcritical-supercritical organic Rankine cycle for maximum heat recovery Jahar Sarkar* Department of Mechanical Engineering, Indian Institute of Technology (B.H.U.), Varanasi, UP 221005, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 May 2017 Received in revised form 16 August 2017 Accepted 14 October 2017 Available online 2 November 2017
Novel methodology for pinch point design and optimization of subcritical and supercritical organic Rankine cycles is proposed for maximum heat recovery. The proposed method is able to predict pinch point locations in both evaporator and condenser simultaneously. As a main advantage, both evaporator and condenser pressures can be optimized simultaneously by optimizing only working fluid mass flow rate to get maximum net work output or heat recovery efficiency for given heating fluid and cooling fluid inlet conditions using selected working fluids. Working fluids have been selected based on thermodynamic and environmental criteria and compared based on various performance parameters (net work output, thermal efficiency, heat recovery efficiency, irreversibility, exergetic efficiency, turbine size parameter and heat transfer requirement). The present method seems to be better than previous pinch point design methods as it optimize the cycle by considering both source and sink. At optimum operation, ammonia is best in terms of lower mass flow rate requirement, higher exergetic efficiency, lower turbine staging and turbine size, whereas, isopentane is best in terms of higher power output and heat recovery efficiency. Novel contour plots are presented as well to select optimum ORC design parameters for available heat source and sink. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Waste heat recovery Organic Rankine cycle Pinch point temperature difference Pinch analysis Exergy destruction Optimization
1. Introduction Within last two decades, the organic Rankine cycle (ORC) has gained widespread attention and researches especially for waste heat recovery. However, the selection of proper working fluid as well as operating parameters for the ORC system is very crucial and still challenging issue as it will affect energy efficiency and economy as well as operational and environmental safeties. As the available waste heats are widely varied with its different combinations of temperature and mass flow rate [1], the ORC system needs to be designed with individual combination of working fluid and operating parameters for maximum heat recovery. To avoid the rigorous system simulation (also depends on component type), the primary design of ORC system is generally done by pinch point analysis. The pinch point in the evaporator is the point where the temperature difference between the source and working fluids is the least. Similarly, the same in the condenser is the temperature difference between the working and sink fluids is the least. As
* Corresponding author. E-mail address: [email protected]. https://doi.org/10.1016/j.energy.2017.10.057 0360-5442/© 2017 Elsevier Ltd. All rights reserved.
important operating parameter, the value of pinch point temperature difference (PPTD) is usually chosen according to the manufacturer experience. The pinch point plays an important role in the cycle design and the pinch point position is strongly dependent on source and sink conditions and working fluids [2]. Hence, pinch point analysis based proper coupling with heat source fluid and sink fluid is very essential for maximum waste heat recovery. With the increase in PPTD, lower evaporation temperature and higher condensation temperature can be achieved, which leads to decrease in cycle efficiency; and on the other hand, heat transfer area also decreases, which results in a decrease of cost for the ORC system. Hence, the PPTD of the heat exchanger not only influences the evaporation and condensation temperatures but also plays an essential role in the cost-efficiency tradeoff. Determination of the location of pinch point makes notable impact on the optimal design of ORC system [3,4]. Several researches introduced the methods of determining pinch point for subcritical ORC. Chen et al. [5] proposed a design method for organic Rankine cycles with constraint of inlet and outlet heat carrier fluid temperatures coupling with the heat source and studied the optimal running parameters of ORCs using benzene for given PPTD. Li et al. [6] theoretically studied the influence of the
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J. Sarkar / Energy 143 (2018) 141e150
Nomenclature cp Ex h I m p PPTD Q s SP T T0 UA v VFR W
specific isobaric heat capacity, kJ/kgK exergy rate, W specific enthalpy, kJ/kg irreversibility, W mass flow rate, kg/s pressure, bar pinch point temperature difference, oC heat transfer rate, W specific entropy, kJ/kgK size parameter, m temperature, oC reference temperature, K heat transfer requirement, kW/K specific volume, m3/kg volume flow ratio work transfer rate, W
PPTD and the evaporation temperature on the performance of ORC in recovering the low temperature waste heat of the flue gas. They concluded that there exists an almost same optimal evaporating PPTD to achieve their respective optimal cost-effective performance for different organic working fluids under the same condition [7]. Tian et al. [8] proposed a method to determine the pinch point in evaporator by evaporator pressure as constraint and done techno-economical analysis based on various working fluids for engine exhaust. Zebian and Mitsos [9] introduced a double-pinch criterion for closed feed water heaters of regenerative Rankine cycles and claimed that it simplifies the optimization procedure and results in significant efficiency increase for fixed heat exchanger area. Wang et al. [10] studied effect of PPTD and approach temperature difference on the net power output and surface areas of both the evaporator and the condenser using R123, R245fa and isobutane. Guo et al. [11] studied the effect of outlet temperature of heat source on ORC performance and showed that subcritical cycle performs better at higher outlet temperature. Ryms et al. [12] developed an algorithm to attain the parametric match enabling quick estimation of the possible heat reception by the specific working fluid. Yu and Feng [13] used pinch analysis to find out the proper way to increase the amount of heat recovered. Liu et al. [14] optimized the heat source temperature for given evaporator temperature. Yu et al. [15] proposed the method to determine working fluid mass flow rate for given evaporator pressure and then optimized. Wu et al. [16] analyzed the effects of PPTDs in evaporator and condenser on the exergo-economic performance of ORCs. Yang et al. [17] also studied the effect of PPTD on economic performance of ORCs. Pan and Shi [18] concluded that the pinch point locates at the bubble point for the evaporator in most cases and may shift to the subcooled liquid state in the near critical conditions. Pinch point with fluid mixture also had been determined by taking evaporator pressure as constraint in some investigation [19,20]. Unlike to the subcritical cycle, the pinch point in the evaporator of supercritical cycle has no certain locations; the pinch point may be anywhere depending on the temperature glides and the evaporator pinch point had been determined by taking evaporator pressure as constraint in most of the investigations [21e23]. Literature review shows that the PPTD had been located by taking either heat source parameters or evaporator and condenser pressures or double pinch points as constraints, which may be best
his hth hsys hII
isentropic efficiency thermal efficiency system or heat recovery efficiency exergetic efficiency
Subscripts 1e5 state points c condenser cf cooling fluid (heat sink) in condenser e evaporator hf heating fluid (heat source) in evaporator i inlet o outlet p pump t turbine wf working fluid
for individual certain source and sink. Furthermore, only evaporator pressure has been optimized by keeping condenser pressure as constraint for both subcritical and supercritical cycles. However, with best of the authors' knowledge, no general method has been proposed for simultaneous determination of pinch points in both evaporator and condenser for optimum design of the subcritical as well as supercritical ORC systems. In this study, a novel method is proposed to determine the location of PPTD in evaporator and condenser simultaneously for both subcritical and supercritical organic Rankine cycles. Single parameter (working fluid mass flow rate) has been optimized, which leads to optimize evaporator and condenser pressures simultaneously for maximum heat recovery. Comparison of selected low GWP working fluids (can be considered as next generation fluids) based on various energy-exergy performances is presented. Novel contour plots are presented as well to select optimum cycle operating parameters and performance for available heat source and sink.
2. Proposed methodology Temperature-enthalpy rate diagrams of subcritical ORC are shown in Figs.1 and 2 for wet fluid and dry fluid respectively. For ORC with superheating (wet fluid), the pinch point in evaporator would appear at three possible positions, the start point of preheating, namely Preheating Pinch Point (PPP) [14], the start point of vaporization, namely Vaporization Pinch Point (VPP) [14] and the end point of superheating, which can be defined as Superheating Pinch Point (SPP), whereas, the pinch point in condenser appears at saturated vapor point, namely Condensation Pinch Point (CPP). For ORC without superheating (dry fluid), the pinch point in evaporator would appear at two possible positions, the start point of preheating (PPP) and the start point of vaporization (VPP), whereas the pinch point in condenser appears at saturated vapor point (CPP) or turbine exit point. It is interesting to note that the profile matching between source and working fluids in evaporator is strongly dependent on source fluid to working fluid mass flow rate ratio (MR). By increasing MR, the following cases are possible:A e PPTD at PPP only, B e double PPTD at PPP and VPP, C e PPTD at VPP only, D e double PPTD at VPP and SPP (wet fluid) and E PPTD at SPP only (wet fluid). The proposed model is based on the energy balance of individual component or component segment of subcritical or
J. Sarkar / Energy 143 (2018) 141e150
Temperature
Profiles of heating fluid A: PPP only B: PPP and VPP C: VPP only D: VPP and SPP E: SPP only
B
(1)
h4 h5 ¼ his;t ½h4 hðpc ; s4 Þ
(2)
Now, the 5 enthalpy rate equations in evaporator and condenser are given by,
C
E
4' VPP PPP
his;p ðh2 h1 Þ ¼ hðpe ; s1 Þ h1 A
4 D
143
SPP
Organic Rankine Cycle 5
Cooling fluid
Enthalpy rate
mwf ðh3 h2 Þ ¼ mhf cp;hf Thf 3 Thf 2
(3)
mwf ðh40 h3 Þ ¼ mhf cphf Thf 40 Thf 3
(4)
mwf ðh4 h40 Þ ¼ mhf cphf Thfi Thf 40
(5)
mwf ðh5 h50 Þ ¼ mcf cpcf Tcf 5 Tcf 50
(6)
mwf ðh50 h1 Þ ¼ mcf cpcf Tcf 50 Tcfi
(7)
Fig. 1. Temperature-enthalpy rate diagram of ORC with source and sink for wet fluid.
The conditions for pinch point analysis are given by, supercritical organic Rankine cycle. The following general assumptions have been made for the present model: ➢ Each component is considered as a steady-state steady-flow system ➢ Pressure drop in all the heat exchangers is negligibly small ➢ Changes in kinetic and potential energies in each component are negligible ➢ Expansion and compression processes have given isentropic efficiencies ➢ Heat transfer in the cycle occurs with heat source and heat sink only ➢ Saturated liquid is supposed at the condenser exit ➢ Turbine inlet condition is saturated vapor for dry fluid whereas turbine exit condition is saturated vapor for wet fluid
(8)
i h PPTDc ¼ Min T50 Tcf 50 ; T5 Tcf 5
(9)
For given heat source mass flow rate, heat source inlet temperature, heat sink mass flow rate, heat sink inlet temperature, PPTD of evaporator and PPTD of condenser, and integrating pump and turbine energy equations, above equations can be expressed by 8 variables (condenser pressure, evaporator pressure, working fluid mass flow rate, 5 temperature differences at 2, 3, 4, 40 and 5 for wet fluid or 2, 3, 4, 50 and 5 for dry fluid). Hence, for any working fluid mass flow rate (or MR), other seven parameters can be calculated by using above seven equations (3)e(9), which will yield the pinch point locations in both evaporator and condenser. Above methodology can be used for ORC with zeotropic mixture also (only difference is that apart from PPP, VPP and SPP, another possible pinch
Profiles of heating fluid A: Point 2 only C: Point 3 only D: Points 3 and 4 E: Point 4 only
A
Profiles of heating fluid A: PPP only B: PPP and VPP C: VPP only
B C
4 VPP
3
5'
5
A
C
4
E
Organic Rankine Cycle PPP
Temperature
Temperature
For subcritical cycle, energy balances in pump and turbine are given by, respectively,
i h PPTDe ¼ Min Thfi T4 ; Thf 3 T3 ; Thf 2 T2
D
3
Supercritical heat addition
Cooling fluid
Enthalpy rate Fig. 2. Temperature-enthalpy rate diagram of ORC with source and sink for dry fluid.
Enthalpy rate Fig. 3. Temperature-enthalpy rate diagram for supercritical heat addition of ORC.
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J. Sarkar / Energy 143 (2018) 141e150
point may be saturated vapor point in the evaporator). For supercritical operation (Fig. 3), the evaporator has been divided into large number of segments (say N, which will give Nþ1 terminals or possible pinch points) and energy balance has been applied in each segment to get temperature difference in each terminal. Similar to the subcritical cycle, for N segment of evaporator, there will be total (Nþ4) equations and same variables for given working fluid mass flow rate and can be solved. The evaporator pressure has been iterated based on the criteria that the minimum temperature difference is equal to PPTD. As shown in Fig. 4, the maximum saturation entropy has been made equal to the entropy at the corresponding saturation pressure during expansion to confirm the dry expansion for dry fluid. Hence, the operating parameters and pinch location can be determined in evaporator and condenser simultaneously based on the solution.
the main criterion for further performance evaluations due to the advantage that it combines both thermal efficiency (hth ) and heat transfer efficiency (hHE ) of an ORC system. The global system efficiency is expressed by Ref. [24]:
hsys ¼ hth hHE ¼
Wnet mhf cp;hf Thf ;i T0
(16)
The turbine isentropic volume flow ratio, which is used to measure of turbine size and staging, is given by Ref. [24],
VFR ¼ v5s =v4
(17)
Furthermore, the turbine size parameter is given by Ref. [25],
SP ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q 4 ðh4 h5s Þ mwf v5s
(18)
3. Performance evaluation For given working fluid mass flow rate, after finding all the state points using above methodology, pump work and turbine work rates are given by, respectively,
Wp ¼ mwf ðh2 h1 Þ
(10)
Wt ¼ mwf ðh4 h5 Þ
(11)
The total conductance (UA) of two heat exchangers (evaporator and condenser) is directly related to the heat exchanger surfaces and is often used to give a global idea of their dimensions. Applying LMTD method, the total conductance or heat transfer requirement, which can be used to measure compactness of heat exchangers, can be approximated as:
UA ¼
The heat input and heat rejection rates are given by, respectively,
Qe ¼ mwf ðh4 h2 Þ
(12)
Qc ¼ mwf ðh5 h1 Þ
(13)
mwf ðh3 h2 Þ mwf ðh40 h3 Þ mwf ðh4 h40 Þ þ þ LMTD2/3 LMTD3/40 LMTD40 /4 mwf ðh5 h50 Þ mwf ðh50 h1 Þ þ þ LMTD5/50 LMTD50 /1
(19)
According to the first law of thermodynamics, the net power output is given by,
It can be noted that for supercritical Ranking cycle, calculation of UA for condenser is same and UA for evaporator is the summation of UAs for all segments calculated based on LMTD method. Neglecting pressure drop of heating fluid, the exergy input to the system is given by,
Wnet ¼ Wt Wp ¼ Qe Qc
. Exi ¼ Qh T0 mhf cp;hf ln Thfi Thfo
(14)
Finally, the thermal efficiency of cycle is given by,
hth ¼ Wnet =Qe
(15)
Heat recovery efficiency or global system efficiency is used as
(20)
Using exergy balance, the exergy destruction rates of evaporator, pump, turbine and condenser can be found from, respectively [26]:
h i . Ie ¼ T0 mwf ðs4 s2 Þ mhf cp;hf ln Thfi Thfo
(21)
Ip ¼ mwf T0 ½s2 s1
(22)
It ¼ mwf T0 ½s5 s4
(23)
Ic ¼ Qc mwf T0 ½s5 s1
(24)
Overall exergy balance of the cycle is given by,
Exi þ Wp Wt ¼
X
I
(25)
Hence, the second law (exergetic) efficiency is expressed by:
hII ¼
P Wnet I ¼1 Exi Exi
(26)
Combining Eqs. (15), (20) and (26),
hII ¼ Fig. 4. Temperature-entropy diagram for turbine expansion process of supercritical ORC.
hth
.
1 T0 Tlm;hf
where; Tlm;hf ¼
Thfi Thfo . ln Thfi Thfo
(27)
J. Sarkar / Energy 143 (2018) 141e150
4. Simulation and optimization An EES [27] simulation code has been developed for the subcritical-supercritical Rankine cycle to analyze the energetic and exergetic performances employing the novel methodology and relations presented above. Based on the methodology presented above, the code searches for the state point values for all the components of the cycle using the input parameters: heat source flow rate and inlet temperature, heat sink flow rate and inlet temperature, working fluid flow rate, pump and turbine isentropic efficiencies. Effective iteration technique and suitable tolerances for convergence have been used to calculate the state points of the cycle. In-build property subroutines have been used for the thermodynamic properties of selected working fluids. It may be noted that the following two criteria have been used in simulation: (i) turbine exit condition is saturated for wet fluids; (ii) turbine inlet condition is saturated for dry fluids. Utilizing the state point values, the various energetic and exergetic performance parameters have been evaluated. For the simulation, the pump and turbine isentropic efficiencies have been taken as 80% and 85%, respectively [7]. The EES simulation code has been verified with the available literature data of ORC for toluene [7]. For heat source flow rate of 10.47 kg/s and inlet temperature of 160 C, heat sink flow rate of 52.35 kg/s and inlet temperature of 20 C, evaporator PPTD of 13 C, condenser PPTD of 17 C and evaporator temperature of 110 C, the predicted net work is 66.7 kW, which is fairly matched with literature data 66.2 kW [7]. Similar match has been observed for n-Pentane also with same literature. To cover the industry application as widely as possible, the heat source temperatures were assumed as 160 Ce300 C. In present study, PPTD in evaporator and PPTD in condenser have been taken as 10 C and 5 C, respectively [14].
145
In the present methodology, based on the assumptions, the net work output is dependent on source, sink and working fluid mass flow rate. The working fluid mass flow rate can be optimized for maximum net work output or heat recovery efficiency. The flowchart for present simulation and optimization is shown in Fig. 5. The present code is able to predict maximum possible power generation and corresponding design and operating parameters for available source and sink conditions. Hence, optimum working fluid mass flow rate or mass flow rate ratio and corresponding maximum net work output or heat recovery efficiency are given by,
mwf ;opt ; MRopt ¼ f mhf ; Thfi ; mcf ; Tcfi
(28)
Wnet;max ; hrec;max ¼ f mhf ; Thfi ; mcf ; Tcfi
(29)
5. Results and discussion 5.1. Working fluid selection The selection of suitable working fluids for the ORC systems is very crucial as it will affect both energy economy as well as operational and environmental safeties. The chemical, physical, thermal and environmental properties of the selected working fluids are shown in Table 1. For the working fluid selection, the following criteria have been considered: negligible ozone layer depletion (ODP), negligible global warming potential (GWP), considerably higher auto-ignition temperature (AIT) than heat source temperature for thermal stability and higher critical temperature. 5.2. Comparison with other methods
Fig. 5. Flowchart for simulation and optimization.
As shown in Figs. 1 and 2, it is clearly understood that the slope of heating (heat source) fluid as well as the location of pinch point are strongly dependent on the mass flow rate ratio between heating and working fluid. With increase in heating fluid to working fluid mass flow rate ratio the following cases are possible: A, B, C, D (wet fluid) and E (wet fluid). With the increase in mass flow rate ratio, the evaporator temperature increases monotonically initially very fast and then slowly and hence based on the basic thermodynamic principles, the thermal efficiency increases monotonically initially quickly and then slowly (Fig. 6). However, interestingly, the net power output increases and decreases, leading to some maximum value at optimum MR as shown in Fig. 6. Hence, the heat recovery efficiency also increases and decreases by giving some maximum value. This can be attributed by the fact that the thermal efficiency increases and heat exchanger efficiency decreases and combined effect of these opposite trend leads to this trend of system efficiency. Condition of optimum MR leading to maximum system or heat recovery efficiency signifies the best coupling or best matching with the given heat source and sink. This also implies the best design of ORC system to get maximum heat recovery (flowchart to determine optimal condition is given in Fig. 5). This optimal design condition of ORC is also dependent on the working fluid and PPTD. It may be noted that the optimum design for maximum net power output will lead to minimum payback period for given source, sink, PPTD and component type. Various pinch point design methods of subcritical and supercritical ORC systems used in literature for given PPTD can be summarized as: Method 1: Design for given source fluid flow rate, inlet and exit temperatures [5,26]; Method 2: Double pinch point design for given source fluid flow rate and inlet temperature [9]; Method 3:
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J. Sarkar / Energy 143 (2018) 141e150
Table 1 Selected working fluids for organic Rankine cycle. Fluids
Composition
Type
NBP (oC)
Tcr (oC)
CP (bar)
ODP
GWP
AIT (oC)
Ammonia R-1233zd Iso-pentane n-Pentane Iso-hexane Benzene Toluene
NH3 C3H2F3Cl C5H12 C5H12 C6H14 C6H6 C7H8
Wet Dry Dry Dry Dry Dry Dry
33.05 18.32 27.00 36.06 60.21 80.06 110.4
133.0 165.6 187.2 196.5 226.6 288.9 318.6
113.3 35.73 33.78 33.70 30.40 48.94 41.26
0 0.0002 0 0 0 0 0
<1 7 20 20 e 2 3
651 380 420 309 306 560 535
175
20
165
18
155
16
145
14
135
12
125
10
115
8
Isopentane
Ammonia
105
6 2
4
6
8
10
12
14
Thermal efficiency, Recovery efficiency (%)
Net power output (kW)
CP e Critical pressure, GWP e Global warming potential, AIT e autoignition temperature.
16
Mass flow rate ratio Fig. 6. Variation of performances with mass flow rate ratio.
Design for given evaporator pressure, source fluid flow rate and inlet temperature [15e23]. Whereas, in the present method, pinch point design has been done for given working fluid flow rate, source fluid flow rate and inlet temperature (dissimilar to the previous cases, condenser temperature has been iterated based on the available sink condition). Similar to the present method, optimization is possible for both Method 1 and 3, however, Method 1 is less studied and no optimization has been done, whereas, optimization of ORC with Method 3 has been done for various target parameters. However, optimization is not possible with Method 2 due to more constraint parameters. In fact, Method 2 is a special case of the proposed method. Similarity between Method 1, Method 3 and present method is that same results are expected after optimization, although approaches are different (optimum parameters are different; source fluid exit temperature, evaporator temperature and working fluid mass flow rate, respectively). Furthermore, the method of case 3 only optimized the evaporator pressure, whereas
the present method yields the optimization of both evaporator and condenser pressures, which can be done by optimizing a single parameter (MR) only for maximum heat recovery. 5.3. Case studies The following three heat source conditions have been considered for the performance comparison of selected working fluids: (i) heat capacity rate of 10.784 kW/K and inlet temperature of 160 C, (ii) heat capacity rate of 8.387 kW/K and inlet temperature of 200 C, and (iii) heat capacity rate of 6.315 kW/K and inlet temperature of 250 C. For all cases, cooling water flow rate and inlet temperature have been taken as 50 kg/s and 20 C, respectively. Working fluid mass flow rate has been optimized to get maximum heat recovery and results are presented for optimal condition. Optimum working fluid mass flow rate and corresponding mass flow rate ratio, thermal efficiency, net work output, heat recovery efficiency and second law efficiency are shown in Figs. 7e12. Higher enthalpy change of ammonia leads to lower mass flow rate. Due to
J. Sarkar / Energy 143 (2018) 141e150
300
4.5 4
Thf,i = 160oC, Chf = 10784W/K
280
Thf,i = 200oC, Chf = 8387W/K
260
Thf,i =
3.5
250oC,
Chf = 6315W/K
3 2.5 2 1.5 1
Net work output (kW)
Working fluid mass flow rate (kg/s)
5
220 200 180 160 140 120
0
100
Fig. 10. Comparison of maximum net work output.
Fig. 7. Comparison of working fluid mass flow rate.
24
Mass flow rate ratio
Thf,i =
Chf = 10784W/K
14
Thf,i =
200oC,
Chf = 8387W/K
12
Thf,i = 250oC, Chf = 6315W/K
10 8 6 4
Heat recovery efficiency (%)
18 16
2
21 18 15 12 9 6 3
Fig. 11. Comparison of maximum heat recovery efficiency.
Fig. 8. Comparison of optimum mass flow rate ratio.
90
30
Thermal efficiency (%)
160oC,
Chf = 10784W/K
Thf,i = 200oC, Chf = 8387W/K Thf,i =
250oC,
80
Chf = 6315W/K
15 10 5
Exergetic efficiency (%)
Thf,i =
20
Thf,i = 160oC, Chf = 10784W/K Thf,i = 200oC, Chf = 8387W/K Thf,i = 250oC, Chf = 6315W/K
0
0
25
Thf,i = 160oC, Chf = 10784W/K Thf,i = 200oC, Chf = 8387W/K Thf,i = 250oC, Chf = 6315W/K
240
0.5
160oC,
147
70
Thf,i = 160oC, Chf = 10784W/K Thf,i = 200oC, Chf = 8387W/K Thf,i = 250oC, Chf = 6315W/K
60 50 40 30 20 10 0
0
Fig. 12. Comparison of optimum exergetic efficiency. Fig. 9. Comparison of optimum thermal efficiency.
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J. Sarkar / Energy 143 (2018) 141e150
temperature for supercritical Rankine cycle. Isopentane has comparatively lower pressure ratio and lower volume flow ratio, which leads to lower turbine staging and hence lower turbine cost. However, the operating pressure is higher for ammonia leads to higher density and hence lower turbine size leads to lower cost. It can be noted that the effect on heat conductance or heat transfer requirement is not so significant. Component irreversibilities show similar trend for all working fluids. Exergetic efficiency increases with increase in heat source temperature. Although isopentane has comparatively higher GWP than other chosen working fluids, it is in-general negligible or low-GWP fluid and has been considered as next generation fluid. Furthermore other fluids have some individual safety problem such as ammonia is toxic, R-1233zd is mild ozone layer depleter, benzene and toluene are carcinogens, and n-pentane and isohexane have lower auto ignition temperature. Based on above discussion, isopentane has been considered as best fluid and taken for further analysis. Most of the cases, it can be assumed that heat source is limited but sufficient cooling fluid is available. Hence, for a same amount of available heat (mhf cp;hf ðThf ;i T0 Þ¼ constant), the heating fluid mass flow rate is a function of heating fluid inlet temperature. According to these arguments, the optimum cycle parameters will be as function of heating and cooling fluid inlet temperatures only. Contours of optimum mass flow rate ratio, maximum work output and maximum heat recovery efficiency are shown in Figs. 13e15 for 1500 kW available heat. It can be noted that the working fluid mass flow rate is nearly unchanged due to same available heat and ratio decreases with increase in heating fluid inlet temperature. However, the net power as well as heat recovery efficiency is significantly influenced by both heating and cooling inlet temperatures due to the effect of these on temperature profile matching in both evaporator and condenser. Optimum parameter contours can be useful tools to
Table 2 Optimum operating parameters and energetic performances. Fluids
pe pc
VFR
SP (m)
UA (kW/K)
ie (%)
ic (%)
it (%)
ip (%)
Ammonia R-1233zd Iso-pentane n-Pentane Iso-hexane Benzene Toluene
8.037 19.97 11.15 11.70 14.23 16.79 23.47
5.513 20.85 12.07 12.08 14.06 13.72 19.30
0.0116 0.0484 0.0522 0.0575 0.0855 0.1085 0.1881
152.2 167.5 170.7 165.3 163.6 144.3 144.0
20.03 17.33 22.46 23.93 24.94 20.08 20.08
8.08 9.17 12.03 11.73 12.46 8.26 8.53
10.99 10.81 8.91 8.73 8.31 9.25 8.97
0.77 0.76 0.32 0.24 0.12 0.04 0.02
near critical operation of R1233zd, the temperature gradient of heat source is more (due to better matching of temperature profile) and also enthalpy change of R1234zd is less (lower average heat capacity due to mostly single phase heat transfer), which leads to higher R1233zd mass flow rate. As a result, the mass flow rate ratio gives opposite trend (Fig. 8). It can be noted that the effect of working fluid is more predominant than that of heat source condition as it is strongly dependent on specific enthalpy change. As shown, mass flow rate ratio decreases with increase in heat source temperature. Thermal efficiency of ORC is strongly dependent on working fluid as well as heat source temperature (Fig. 9). Increase in heat source temperature leads to increase in cycle temperature lift and it is well known fact that thermal efficiency increases with temperature lift. Due to same reason, the net power output also increases with increase in heat source temperature (Fig. 10). As shown in Fig. 11, isopentane and R1233zd are best choice due to higher heat recovery efficiency and isopentane may be a better choice due to lower cost and zero ODP compared to R1233zd. Table 2 presents the comparison of some other performance parameters. It may be noted that the PPTD occurs at VPP for subcritical Rankine cycle and it is very close to pseudocritical
220 Heating fluid inlet temperature ( oC)
Mass flow rate ratio
210
3.2 3.4
200
3.6
190
3.8 4
180
4.2 4.4
170
4.6 4.8
160
12
16 20 24 o Cooling fluid intel temperature ( C) Fig. 13. Contours of optimum mass flow rate ratio for isopentane.
5
28
J. Sarkar / Energy 143 (2018) 141e150
149
220 Heating fluid inlet temperature ( oC)
210
200 190
210
180 170
200
160 150
190
140
180
130 120
170 110
Net power (kW)
160 10
14
18
22
26
30
o
Cooling fluid intel temperature ( C) Fig. 14. Contours of maximum net power output for isopentane.
220 14
Heating fluid inlet temperature (oC)
210
13.5
13 12.5 12 11.5
200
11 10.5 10
190
9.5 9
180
8.5 8
170
160 10
7.5 Recovery efficiency (%)
15
20
25
30
o
Cooling fluid intel temperature ( C) Fig. 15. Contours of maximum heat recovery efficiency for isopentane.
choose optimal operating and design parameters of ORC system for maximum heat utilization.
6. Conclusions A general methodology is proposed to determine the location of PPTD in evaporator and condenser simultaneously of both
subcritical and supercritical organic Rankine cycles and optimized for maximum waste heat recovery. Working fluids have been selected based on various thermodynamic, environmental and safety criteria and compared for various heat source and sink conditions. For available heating fluid and cooling fluid, net work output as well as heat recovery efficiency first increases and then decreases
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J. Sarkar / Energy 143 (2018) 141e150
with working fluid mass flow rate, leading to some maximum value. Hence, the optimum working fluid mass flow rate leads best design condition to get maximum waste heat recovery for a certain working fluid. Comparison with previous pinch point design methods shows that the proposed method is able to optimize the ORC for both available heat source and sink. Comparison of selected working fluids for various heat source conditions at optimum ORC operation shows that lowest mass flow rate and hence highest mass flow rate ratio is need for ammonia. Ammonia also yields highest thermal efficiency for given conditions. At optimum operation, the net power output as well as heat recovery efficiency increases with increase in heat source temperature and isopentane and R1233zd yield maximum values. However, isopentane may be a better choice due to lower cost and zero ODP compared to R1233zd. Isopentane is also best in terms of lower pressure ratio and lower volume flow ratio. Whereas, ammonia is best in term of lower turbine size and hence lower cost. Exergetic efficiency increases with increase in heat source temperature. The net power as well as heat recovery efficiency is significantly influenced by both heating and cooling inlet temperatures. Presented optimum parameter contours can be useful for design engineer to select best operating parameters for maximum heat recovery. References [1] Sarkar J, Bhattacharyya S. Potential of organic Rankine cycle technology in India: working fluid selection and feasibility study. Energy 2015;90:1618e25. [2] Pang K-C, Chen S-C, Hung T-C, Feng Y-Q, Yang S-C, Wong K-W, et al. Experimental study on organic Rankine cycle utilizing R245fa, R123 and their mixtures to investigate the maximum power generation from low-grade heat. Energy 2017;133:636e51. [3] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy 2007;32:1210e21. € [4] Ohman H, Lundqvist P. Theory and method for analysis of low temperature driven power cycles. Appl Therm Eng 2012;37:44e50. [5] Chen Q, Xu J, Chen H. A new design method for Organic Rankine Cycles with constraint of inlet and outlet heat carrier fluid temperatures coupling with the heat source. Appl Energy 2012;98:562e73. [6] Li Y-R, Wang J-N, Du M-T. Influence of coupled pinch point temperature difference and evaporation temperature on performance of organic Rankine cycle. Energy 2012;42:503e9. [7] Li Y-R, Wang J-N, Du M-T, Wu S-Y, Liu C, Xu J-L. Effect of pinch point temperature difference on cost effective performance of organic Rankine cycle. Int J Energy Res 2013;37:1952e62. [8] Tian H, Shu G, Wei H, Liang X, Liu L. Fluids and parameters optimization for
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