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Exergoeconomic comparison of TLC (trilateral Rankine cycle), ORC (organic Rankine cycle) and Kalina cycle using a low grade heat source
Energy 83 (2015) 712e722
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Exergoeconomic comparison of TLC (trilateral Rankine cycle), ORC (organic Rankine cycle) and Kalina cycle using a low grade heat source M. Yari a, *, A.S. Mehr a, V. Zare b, S.M.S. Mahmoudi a, M.A. Rosen c a
Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran Department of Mechanical Engineering, Urmia University of Technology, Urmia, Iran c Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe, Street North, Oshawa, Ontario L1H 7K4, Canada b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 September 2013 Received in revised form 16 November 2014 Accepted 23 February 2015 Available online 18 March 2015
Recently, the TLC (trilateral power cycle) has attracted significant interest as it provides better matching between the temperature profiles in the evaporator compared to conventional power cycles. This article investigates the performance of this cycle and compares it with those for the ORC (organic Rankine cycle) and the Kalina cycle, from the viewpoints of thermodynamics and thermoeconomics. A low-grade heat source with a temperature of 120 C is considered for all the three systems. Parametric studies are performed for the systems for several working fluids in the ORC and TLC. The systems are then optimized for either maximum net output power or minimum product cost, using the EES (engineering equation solver) software. The results for the TLC indicate that an increase in the expander inlet temperature leads to an increase in net output power and a decrease in product cost for this power plant, whereas this is not the case for the ORC system. It is found that, although the TLC can achieve a higher net output power compared with the ORC and Kalina (KCS11 (Kalina cycle system 11)) systems, its product cost is greatly affected by the expander isentropic efficiency. It is also revealed that using n-butane as the working fluid can result in the lowest product cost in the ORC and the TLC. In addition, it is observed that, for both the ORC and Kalina systems, the optimum operating condition for maximum net output power differs from that for minimum product cost. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Trilateral cycle ORC Kalina cycle Ammonia-water Exergoeconomic Low-grade heat source
1. Introduction An enduring area of interest for engineers, in which lots of work has been performed, is the conversion of heat to electricity. Recently, there is growing interest in utilizing low and moderate temperature heat sources, which are available via solar, geothermal and biogenic energy systems, and as waste heat from industries. For producing power, one can consider such cycles as ORCs (organic Rankine cycles) [1e12], Kalina cycles [13e21] and TLCs (trilateral cycles) [22e27]. These have been extensively investigated. For example, the performance has been investigated of ORCs using low-grade heat sources and focusing on selecting proper working fluids [3e8], while the performance of the Kalina cycle has been analyzed and compared with conventional power systems [13e16], and TLC performance has been analyzed using ammonia-water as a
* Corresponding author. Tel.: þ98 41 33392477. E-mail address: [email protected] (M. Yari). http://dx.doi.org/10.1016/j.energy.2015.02.080 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
working fluid [23] and ORCs and TLCs have been thermodynamically compared [27]. Whilst ORC and Kalina cycles are used already in existing power plants, the TLC is still in a state of technical development and less known [22]. The components in the TLC system are the same as those in the ORC system except that the working fluid at the entrance of the TLC expander (turbine) is a saturated liquid. Consequently, the state of the working fluid at the expander exit is a two-phase mixture. As the thermodynamic mean temperature at which heat is received is comparatively lower for the TLC, the thermal efficiency for this cycle is lower than that for the ORC, for the same temperature limits. Similar to transcritical cycles, the design of a reliable and efficient two-phase expander is still ongoing, although significant efforts have been made recently for screw-type and scroll-type expanders and reciprocating engines [28]. Compared to the case of the ORC, better temperature matching between the brine as a heat source and the TLC working fluid is observed in the TLC system. The expander in a TLC system is a key element. In general, two types of expansion devices exist: turbo-machines and positive
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Fig. 1. Schematic diagram for basic ORC and corresponding T-s diagram.
displacement (or volumetric) machines. The former uses the kinetic energy of an expanding flow to turn a shaft at a high rotational speed and the latter operates by expanding a fixed volume of fluid per one revolution. At low capacities, the turbines suffer from a high-pressure drop in each stage due to the free space between the blade tips and housing. A problem with screw expanders, however, is their complicated 3D geometry in which the rotor mating line is relatively long and allows for large flow leakage. On the other hand, the geometry of scroll machines is simpler, reducing leakage problems [23]. To the best of our knowledge there is lack of information on the thermodynamic behavior of TLC systems, particularly from the viewpoint of exergoeconomics. The issue is more significant when TLC performance is compared with other well-known power plants such as the ORC and Kalina systems. The present paper aims to satisfy this need for information and to provide results that help efforts to better utilize heat sources at low temperatures. 2. Description of the cycles
heat sources while KCS5 is used for gas turbine power plants [19]. Each system has its own distinct features. For example, KCS11 does not have a distillation arrangement, but one is found in KCS5. Nevertheless, the working fluid in all Kalina cycle systems is an ammoniaewater mixture, which has the advantage of having varying boiling and condensing temperatures. This phenomenon reduces lower exergy destructions. Fig. 2 shows a schematic diagram of the KCS11 system. A saturated liquid ammonia-water mixture exiting the condenser is pumped to the regenerator where it is preheated before entering the evaporator. Hot water heats the ammonia-water mixture in the evaporator after which the liquid and vapor phases are separated in the separator unit. The obtained vapor enters the turbine and produces power, as it expands, before entering the absorber. The liquid ammonia-water mixture exiting the separator flows to the regenerator and then is throttled in the expansion valve. The low pressure ammonia-water mixture then flows to the absorber and is mixed with the turbine exit flow. The mixed flow exiting the absorber is condensed in the condenser and then passes through the pump to complete the cycle.
2.1. Organic Rankine cycle 2.3. TLC (Trilateral cycle) The ORC basically consists of an evaporator (heater), a turbine, a condenser and a pump. A schematic diagram for this cycle is shown in Fig. 1. A hot water stream (120 C) with a flow rate of 100 kg/s is used to heat the working fluid in the evaporator. 2.2. KCS11 (Kalina cycle system 11) The Kalina power cycle has various configurations, each of which is appropriate for some applications. KCS11 (Kalina cycle system 11) is suitable for producing power using low-temperature
The TLC (Trilateral Cycle) system is basically a power plant in which expansion starts from the saturated liquid rather than the saturated, superheated or supercritical vapor phase. In such a configuration, the transfer of heat from a heat source stream to the working fluid is achieved with a high degree of temperature matching (see Fig. 3). A TLC system to which heat is supplied from the heat source and removed by the cooling agent is shown in Fig. 4. The system consists of a pump, a heater, a twophase expander and a condenser.
Fig. 2. Schematic diagram of Kalina cycle system 11 (KCS11) and corresponding T-s diagram.
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Low pressure saturated liquid at the condenser exit is pumped to the heater where it is heated and becomes a saturated liquid at higher pressure. The liquid then expands in the expander after which it is condensed in the condenser. 3. Modeling methodology and assumptions 3.1. Assumptions In modeling the systems, the power plants are assumed to operate under steady conditions. Pressure losses due to the friction in heat exchangers and connecting pipes are taken as negligible. The systems reject heat to cooling water in the condenser. For the considered systems, an isentropic efficiency value of 0.85 is assumed for the pumps. For the ORC and KCS1, the turbine isentropic efficiency is considered to be 0.85 [29,30]. For the TLC system, however, the expander isentropic efficiency is varied in the range of 0.65e0.85 [23]. Table 1 summarizes the input parameter values for the cycles. 3.2. Thermodynamic analysis In the thermodynamic analyses, each component is considered as a control volume and the principles of mass and energy conservations as well as the second law of thermodynamics are applied. These equations and thermodynamic property relations are solved using the EES (engineering equation solver) software [34] to simulate the performance for each cycle. For each component the conservation of mass can be expressed as follows:
X X
m_ i ¼
X
m_ i xi ¼
m_ e
X
(1)
m_ e xe
(2)
Here, m_ is the mass flow rate and xi is the ammonia concentration in the solution. Note that equation (2) is applied only when the working fluid is an ammonia-water mixture (for the case of KCS11). The first law of thermodynamics yields the energy balance for each component as follows [35]:
_ ¼ Q_ k W k
X
m_ e he
X
m_ i hi
(3)
The second law of thermodynamics is used to evaluate the cycle performance based on an exergy perspective. In the absence of magnetic, electrical, nuclear and surface tension effects, and ignoring the kinetic and potential energies, the total exergy rate of a stream is the sum of physical and chemical exergy rates [36,37]:
E_ ¼ E_ ph þ E_ ch
(4)
The former part in the right side of equation (4) can be obtained written as follows:
_ h0 Þ T0 ðs s0 Þ E_ ph ¼ m½ðh
(5)
When the working fluid is an ammonia-water mixture, E_ ch cannot be neglected (i.e., for the Kalina power plant). The chemical exergy for an ammonia-water mixture can be calculated approximately as follows [38,39]:
X 1X 0 e0ch;NH3 þ ech;H2 O E_ ch zm_ MNH3 MH2 O
Fig. 3. Variation in heat carrier and working fluid temperatures during heat addition process for a) ORC, b) KCS11, c) TLC.
where e0ch;NH3 and e0ch;H2 O are the standard chemical exergies of ammonia and water, respectively. These are given by Ahrendts [40]. The thermal efficiency of the systems are expressed as
hth ¼
_ net W Q_
(7)
in
(6)
_ net is the net output power and Q_ is the supplied heat where W in rate in the evaporator/heater of the systems. A more meaningful
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Fig. 4. Schematic diagram for trilateral cycle (TLC) and corresponding T-s diagram.
criterion to assess the performance of an energy converting system is the second law efficiency, which can be defined as the ratio of output to input exergy. For the considered systems the second law efficiency can be expressed as
hex ¼
_ net W E_
(8)
in
where E_ in is the exergy rate of heat source, which is defined as
3.3. Cost equations Parameters such as the type of financing, the required capital and the expected life of a component influence the costs for owning and operating a system (non-exergy related cost rates). To calculate the costs of components at a specific size or capacity, a power law relation is used, such as [41e44]:
E_ hs ¼ m_ hs ½ðhhs h0 Þ T0 ðshs s0 Þ
(9)
In order to evaluate the performance of a system from the second law point of view, it is necessary to identify both the product and the fuel for each component of the system. The product represents the desired result produced by the component or the system. The fuel represents the resource expended to generate the product, and is not necessarily an actual fuel such as natural gas, oil or coal. Both the product and the fuel are expressed in terms of exergy. The exergy destruction rate in a component is calculated from the exergy rate balance for a component [37]:
E_ D ¼ E_ F E_ P E_ L
(10)
Cost at reference year ¼ Original cos t
Here, E_ F , E_ P and E_ L are the exergy flow rates associated with the fuel, the product and the losses for the component, respectively.
a
Zk ¼ ZR;K
AK AR
ZP ¼ ZR;P
_P W _ W R;P
(11) !mp
_n ZT ¼ ZR;T W t
Parameter
Value
Cycle
Reference
P0 (kPa) T0 ( C) Ths ( C) m_ hs ðkg:s1 Þ DTPP (K) hP (%) hT (%) hexp (%) Q3 () Q3 () Q6 () DTReg (K)
101.325 25 120 100 10 85 85 65e85 1 0 1 5
ORC, KCS11,TLC ORC, KCS11,TLC ORC, KCS11,TLC ORC, KCS11,TLC ORC, KCS11,TLC ORC, KCS11,TLC ORC, KCS11 TLC ORC TLC KCS11 KCS11
e e [31,32] [31,32] [23,30,33] [29,30] [27] [23] [23,27] [23,27] [20] [20]
np (12)
(13)
Here, the subscript R represents the reference components and the powers in the equations take on the following values [41e44]: a ¼ 0.514, mp ¼ 0.26, np ¼ 0.5, nt ¼ 0.7. Also, hp is the isentropic pump efficiency which is assumed to be 0.85. The cost data involved in an economic analysis at different years must be brought to the reference year according to the following relation:
Cost index for the reference year Cost index for the original year
Table 1 Parameters used in the simulation.
1 hP hP
(14)
For updating all costs to the year 2012, the Marshall and Swift equipment cost index [45] is used in the present work. Using the CRF (capital recovery factor) and the number of hours per year that the unit operates, the capital investment of a component is converted to the cost rate. The CRF is determined as follows:
CRF ¼
ir ð1 þ ir Þn ð1 þ ir Þn 1
(15)
where i is the interest rate and the n is the lifetime of the system in years. These parameters are considered fixed at 0.15 and 20 years, respectively [46].
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Table 2 Validation of present model for KCS11. P ¼ 2.0 MPa
Parameters
Optimum ammonia fraction (kg/kg) Maximum thermal efficiency (%)
P ¼ 2.5 MPa Hettiarachchi et al. [20]
Present model
Hettiarachchi et al. [20]
Present model
Hettiarachchi et al. [20]
0.598 9.15
0.609 9.02
0.677 9.6
0.685 9.5
0.752 10.24
0.754 10.20
Table 3 Validation of present model for TLC. Parameters
C_ L;K ¼ cF;K E_ L;K
Case IV
_ Q 56 (kW)
Fischer [27]
Present model
Fischer [27]
Present model
5862
5889
8800
8860
11.36 86.33
11.29 86.91
For each component of the systems operating at steady state condition, the entering and exiting exergy streams are in the form of heat and work interactions as well as material streams. The associated costs with these exergy terms are related through the following equations [36]:
C_ i ¼ ci E_ i
X
C_ i þ C_ q þ Z_
C_ e ¼ ce E_ e
(16)
_ C_ w ¼ cw W
C_ q ¼ cq E_ q
(17)
where C_ i and C_ e are the cost rates associated with entering and exiting exergy streams, respectively, and C_ w and C_ q are the cost rates associated with the exergy transfer in the form of heat and work, respectively. In equation (16), Z_ is the appropriate charge due to capital investment and operating and maintenance expenses for each component. Also, ci, ce, cw and cq denote average costs per unit exergy. In a thermoeconomic analysis of a thermal system, the average unit cost of fuel, cF, the average unit cost of product, cP, the cost rate of exergy destruction rate, C_ D and the exergoeconomic factor f each play a vital role. These parameters are expressed as follows:
C_ F;K E_ F;K
(18)
cP;K ¼
C_ P;K E_
(19)
P;K
E_ P;K is considered to be constant
(20)
Table 4 Comparison of results from present model with those reported by Ref. [23] for ORC, Kalina and TLC. Parameter
(21)
fk ¼
Z_ k
(22)
Z_ k þ C_ D;k þ C_ L;k
In order to validate the simulation results, available data in the literature are used. Table 2 compares the results obtained from the present model for KCS11 and those reported by Hettiarachchi et al. [20]. For each value of generator pressure, the obtained ammonia fraction for maximum efficiency, from the present work, is seen to be close to the value reported by Hettiarachchi et al. [20]. For the case of the TLC, data of two studied cases (case IV (T5 ¼ 220 C, T7 ¼ 15 C) and case V (T5 ¼ 150 C, T7 ¼ 15 C)) reported by Fischer are used [27]. As Table 3 demonstrates, there is a good agreement between the results obtained by our model and those reported by Fischer. Note that the model for the ORC has been validated in our previously published work [9]. Also, a comparison is presented between the data obtained from present models to that of Zamfirescu and Dincer [23] (Table 4). The comparison shows that the thermodynamic efficiency values from the present work agree well with those reported by Ref. [23]. For the ORC with R134a as a working fluid, assuming an interest rate of 5%, the unit product cost given in the literature is 0.056 $/ kWh [10]. The calculated value for this parameter in the present work is found to be 0.0557 $/kWh which is in a good agreement with the reported value. Also, for some other working fluids (Table 5), it is found that the cost values found with present model are close to those reported in literature [10]. 4. Results and discussion 4.1. Parametric study
cF;K ¼
C_ D;K ¼ cF;K E_ D;K
E_ P;K is considered to be constant
3.5. Model validation
3.4. Exergy costing and exergoeconomic evaluation
C_ e þ C_ w ¼
Case V
h (%) 17.06 16.98 th _ 34.14 34.29 C HC (kW/K) _ W ¼ 1MW, DT ¼ 10 K, hp ¼ 0.65, ht ¼ 0.85.
X
P ¼ 3.0 MPa
Present model
ORC
NH3eH2O cycles
R141b R123 R245ca R21
Kalina
TLC
3
8
10 Thermal efficiency given by Ref. [23], hth (%) Thermal efficiency calculated 10.06 by present model, hth (%)
9
9
9
9.02
9.11
8.91 3.09
8.08
4.1.1. ORC A similar trend to that which occurs in published works [7] is observed here for the variation of net output power with turbine inlet temperature. Indeed, as the turbine inlet temperature increases the net output power is maximized at some special temperature. The variation of net output power with turbine inlet temperature for the ORC is shown in Fig. 5 for several working fluids. Table 5 Comparison of results from present model with those reported by Ref. [10] for ORC, i ¼ 0.05, hT ¼ 0.8, hP ¼ 0.75 Parameter
Unit product cost found from present model ($/kWh) Unit product cost reported by Ref. [10] ($/kWh)
Working fluid R123
R245fa
R152a
CO2
R134a
0.0641
0.0578
0.0566
0.0773
0.0577
0.063
0.059
0.053
0.077
0.056
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Fig. 5. ORC net output power versus turbine inlet temperature for several working fluids.
Fig. 7. Product cost versus turbine inlet temperature of the ORC for several working fluids.
Referring to Fig. 5, for almost all the studied working fluids, as the turbine inlet temperature increases there is an optimum value for turbine inlet temperature at which the net output power is maximized. This is due to the variations of mass flow rate and enthalpy drop through the turbine of ORC (as the turbine inlet temperature increases the mass flow rate decreases and the enthalpy drop increases). However, for R1234yf as a working fluid, the turbine inlet temperature cannot be raised beyond a particular value due to the lower value of critical temperature. The figure also indicates that for R1234yf the output power is higher than that obtained for the other studied working fluids. Variations of thermal and exergy efficiencies of ORC with turbine inlet temperature are shown in Fig. 6 for the studied working fluids. As the turbine inlet temperature increases the thermal efficiency of the cycle is observed to increase almost steadily for all of the studied working fluids. This is in accordance with the Carnot principle. It is shown in Fig. 6 that the highest thermal efficiency is achieved with ammonia as a working fluid. However, the variation trend of exergy efficiency with turbine inlet temperature is similar to that for the net output power, primarily because a constant value is assumed for the cycle inlet exergy. Fig. 7 shows the variation of ORC product cost with turbine inlet temperature. For each of the studied working fluids, there is an optimum value for the turbine inlet temperature at which the product cost is minimized. Comparing Figs. 5 and 7 indicates an
interesting point: the turbine inlet temperature at which the product cost is minimized is higher than the corresponding value for maximum net output power. 4.1.2. KCS11 For the case of the Kalina cycle, a parametric study is performed considering the effect of such parameters as turbine inlet temperature and pressure as well as ammonia concentration (X1) on the net output power, the thermal efficiency and the product cost. Similar to the ORC case, the heat source is a stream of hot water with a mass flow rate of 100 kg/s at a temperature of 120 C. The condenser temperature in this case is 40 C. For turbine inlet temperatures of 80 C, 90 C and 100 C and ammonia concentrations of 60%, 75% and 90% the variation of net output power with turbine inlet pressure is shown in Fig. 8. For a given value of ammonia concentration, an optimum turbine inlet pressure is observed at which the net output power is maximized. In addition, an increase in the ammonia concentration results in an increase in the net output power. It can be seen that as the turbine inlet temperature increases from 80 to 100 C (at a particular ammonia concentration) the net output power increases. Note that the effect is more pronounced at lower turbine inlet temperatures. The influence of turbine inlet pressure on the thermal efficiency of the Kalina cycle system is depicted in Fig. 9. At each ammonia concentration there is an optimum value of turbine inlet pressure at
Fig. 6. ORC thermal and exergy efficiencies versus turbine inlet temperature for several working fluids.
Fig. 8. KCS11 net output power versus turbine inlet temperature.
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Fig. 9. Kalina thermal efficiency versus turbine inlet pressure.
Fig. 11. TLC net output power versus turbine inlet temperature for several working fluids.
which the thermal efficiency is maximized. Comparing Figs. 8 and 9 reveals that the optimum values of turbine inlet pressure for maximum thermal efficiency are higher than the optimum values for maximum net output power. The variation of product cost with the turbine inlet pressure is shown in Fig. 10. For clarity, only ammonia concentrations of 60% and 90% are shown in this figure. As the figure indicates, at a particular value of turbine inlet pressure the cycle product cost is minimized. Note that the optimum values of turbine inlet pressures differ for minimum product cost, maximum net power and maximum thermal efficiency. 4.1.3. TLC Fig. 11 shows the variation of net output power with expander inlet temperature for the case of a TLC with several working fluids. As the expander inlet temperature increases the net output power is observed to increase. This trend is not similar to that of the ORC for which the net output power is maximized at a particular value of turbine inlet temperature. The variation of the thermal efficiency of the TLC with expander inlet temperature is shown in Fig. 12. As the figure indicates, the trend is similar to that of the net output power. An interesting point for the TLC case is the better performance for the n-butane working fluid considering both the net output power and thermal efficiency. This was not the case for the ORC.
Fig. 10. Product cost versus turbine inlet temperature.
Fig. 12. TLC thermal efficiency versus turbine inlet temperature for several working fluids.
Fig. 13 shows the variation of TLC product cost with expander turbine temperature for several working fluids. As the expander inlet temperature increases the product cost is seen to decrease for all the studied working fluids.
Fig. 13. Product cost versus turbine inlet temperature of the TLC for several working fluids.
M. Yari et al. / Energy 83 (2015) 712e722
As the key component in the TLC is the expander, the effect of its isentropic efficiency is presented in Fig. 14. The results presented only for the n-butane as the working fluid. In Fig. 14, as the expander isentropic efficiency increases from 65% to 85%, the TLC net output power increases by 40% and the product cost is reduced by 25%. Thus, the expander efficiency has a great impact on the TLC performance. 4.2. Optimization results The studied systems are optimized from the viewpoints of thermodynamics and thermoeconomics using the EES software. The objectives are to maximize the net output power and thermal efficiency as well as to minimize the unit exergy cost of the system product. Tables 6 and 7 show the optimization results for the ORC based on the maximum net power and minimum product cost, respectively. According to Table 6, when the optimization is based on the maximum net power, the highest net output power is achieved with R1234yf as the working fluid. However, the highest thermal efficiency and lowest product cost are obtained using the R134a. On the other hand, using the ammonia and n-butane as working fluids in the ORC exhibited the best result considering the product cost which is 16.49$/GJ. Comparing the results shown in Tables 6 and 7 reveals that, for each of the working fluids (R1234yf or propane or R134a), the maximum net output power and the minimum product cost are achieved with identical values of turbine inlet temperature. For the KCS11 case, the optimization results, based on maximizing the net output power and minimizing the product cost, for three values of ammonia concentrations, are shown in Tables 10 and 11, respectively. It is found that the turbine inlet pressure at which the product cost is minimized is higher than the corresponding value at which the net power is maximized. It is also observed that both the maximum net output power and minimum product cost occurs at the highest ammonia concentration. Finally, the results of the parametric study for the case of TLC show that unlike the ORC and KCS11 cases there are no maximum and minimum values for either the net output power or product cost. However, the highest value of the net output power or the lowest product cost is achieved with the highest turbine inlet temperature. Table 9 shows the highest values of net output power, thermal efficiency and exergy efficiency as well as the lowest value of product cost for the TLC system with an expander isentropic efficiency of 0.75. Comparing the results in Tables 6e10 reveals that using n-butane in the TLC results the highest net output power
719
Table 6 Optimization results for having maximum net output power of ORC. Working fluid
T3 ( C)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
R1234yf n-butane Isobutene Propane R134a R152a Ammonia
84 76.32 77.33 86.9 94.9 77.77 75.53
1816 1450 1479 1635 1448 1476 1377
7.787 7.72 7.715 8.318 9.19 7.806 7.883
34.37 27.44 28 30.95 27.4 27.94 26.07
17.7 18.14 18.19 17.96 17.43 18.32 18.34
Table 7 Optimization results for having minimum product cost of ORC. Working fluid
T3 ( C)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
R1234yf n-butane Isobutene Propane R134a R152a Ammonia
84 93.21 92.49 86.9 94.9 91.83 93.06
1816 1110 1189 1635 1448 1252 1042
7.787 10.2 9.823 8.318 9.19 9.667 10.68
34.37 21.01 22.5 30.95 27.4 23.69 19.72
17.7 16.49 16.8 17.96 17.43 17.1 16.49
Table 8 Optimization results for TLC with expander isentropic efficiency of 0.75. Working fluid
T3 ( C)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
R1234yf n-butane Isobutene Propane R134a R152a Ammonia
84 109 109 93.9 94.9 109 109
1288 2034 2016 1591 1626 2070 1931
4.458 7.005 6.96 5.625 5.688 7.284 6.771
24.38 38.5 38.16 30.12 30.77 39.18 36.55
27.89 18.19 18.63 23.72 22.81 18.57 19.99
Table 9 Optimization results for TLC with expander isentropic efficiency of 0.85. Working fluid
T3 ( C)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
R1234yf n-butane Isobutene Propane R134a R152a Ammonia
84 109 109 93.9 94.9 109 109
1557 2368 2364 1934 1947 2452 2308
5.389 8.151 8.16 6.837 6.813 8.629 8.093
29.47 44.8 44.74 36.6 36.86 46.41 43.69
23.55 16.01 16.27 19.98 19.47 16.06 17.13
Table 10 Optimization results for having maximum net output power of KCS11. Ammonia concentration
T5 ( C)
P5 (bar)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
60% 75% 90%
109 109 109
18.14 26.47 32.34
1046 1165 1321
6.243 6.885 7.549
19.79 22.06 25
22.16 20.37 18.65
Table 11 Optimization results for having minimum product cost of KCS11.
Fig. 14. Effect of expander isentropic efficiency of TLC system on the net output power and product cost.
Ammonia concentration
T5 ( C)
P5 (bar)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
60% 75% 90%
109 109 109
25.23 35.79 43.48
851.7 957.8 1108
8.28 8.887 9.501
16.12 18.13 20.98
19.91 18.57 17.14
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Table 12 Exergoeconomic analysis results for ORC in minimized product cost working condition. Components
cF,k ($GJ1)
cP,k ($GJ1)
C_ D;k ($h1)
C_ L;k ($h1)
Z_ k ($h1)
C_ D;k þ C_ L;k þ Z_ k ($h1)
fk (%)
Evaporator Condenser Turbine Pump
5 11.29 10.08 15.56
11.29 18.71 16.49 15.97
0.737 1.124 6.829 0.4539
91.8 0.2481 e e
0.3419 0.3665 20.02 0.8737
92.88 1.739 26.85 1.328
0.3681 21.07 74.56 65.81
Working fluid: n-butane, m_ hs ¼ 100 kg=s, Tcond ¼ 40 C, T3 ¼ 93.21 C, chw
¼
5 $/GJ.
Table 13 Exergoeconomic analysis results for KCS11 in minimized product cost working condition. Components
cF,k ($GJ1)
cP,k ($GJ1)
C_ D;k ($h1)
C_ L;k ($h1)
Z_ k ($h1)
C_ D;k þ C_ L;k þ Z_ k ($h1)
fk (%)
Evaporator Condenser Turbine Pump Regenerator Absorber
5 10.653 10.65 10.68 10.65 10.65
10.65 10.68 17.14 10.685 10.69 10.653
7.74 13.36 7.363 0.6252 3.084 0.062
50.22 11.86 e e e e
1.313 0.5765 20.2 1.094 0.2775 0.0482
59.27 25.8 27.57 1.72 3.366 0.1111
2.215 2.235 73.29 63.64 8.389 43.45
X1 ¼ 0.9,m_ hs ¼ 100 kg=s, Tcond ¼ 40 C, T5 ¼ 109 C, P5 ¼ 43.48 bar, chw
¼
5 $/GJ.
Table 14 Exergoeconomic analysis results for TLC in minimized product cost working condition. Components
cF,k ($GJ1)
cP,k ($GJ1)
C_ D;k ($h1)
C_ L;k ($h1)
Z_ k ($h1)
C_ D;k þ C_ L;k þ Z_ k ($h1)
fk (%)
Evaporator Condenser Turbine Pump
5 10.92 10.92 13.62
10.92 13.62 18.19 14.35
11.51 42.13 31.14 4.357
8.205 8.805 e e
4.05 3.177 34.16 4.922
23.77 54.11 65.3 9.279
17.07 5.87 52.31 53.04
Working fluid: n-butane, m_ hs ¼ 100 kg=s, hexpander ¼ 0.75, Tcond ¼ 40 C, T3 ¼ 109 C, chw
with a product cost comparable to the other cycles. In addition, it is found that using the n-butane as working fluid for the case of ORC can yield the lowest product cost among the other working fluids. It can be concluded that the highest output power and the lowest product cost can be obtained with TLC and ORC, respectively. However, from the results in Table 9 (for expander isentropic efficiency of 0.85), it is observed that the isentropic efficiency of the expander has a great impact on the TLC performance. It can be concluded that the TLC power plant could compete economically with the other studied power producing systems. Detailed exergoeconomic analyses are carried out for the components of the systems. The results are shown in Tables 12e14 for the ORC, KCS11 and TLC, respectively. In all systems, the turbine and pump have higher exergoeconomic factor, f, indicating higher investment costs for these components. On the other hand, the evaporator and condenser have lower exergoeconomic factor values, indicating that for these components the cost rates associated with the exergy destruction and/or exergy losses are higher. Therefore, it can be concluded that engineers should focus on reducing the exergy losses and exergy destruction in evaporator and condenser. In addition, to reduce the overall product cost of the systems designers should pay more attention on lowering the investment cost of the turbine. 5. Conclusions The performances of three power generating systems (ORC, KCS11 and TLC) are investigated and compared from the viewpoints of thermodynamics and exergoeconomics. The obtained results reveal that, considering both thermodynamic and economic viewpoints, the TLC power system can be useful if the TLC expander has an isentropic efficiency close to that of conventional turbines. However, the good temperature match in the evaporator of the TLC
¼
5 $/GJ.
is the main advantage of this cycle. In addition, considering the cp values for the ORC, TLC and KC11 from Tables 6e11, it can be concluded that using an ORC for low grade heat utilization, to produce power, is the most advantageous among the three options investigated, from the viewpoint of economics. This is an important result because it has been reported in literature previously that the TLC is superior to the ORC from the viewpoint of thermodynamics [23,27]. Also, following conclusions could be drawn: For the case of the ORC, there is a particular turbine inlet temperature at which the net output power is maximized while for the case of TLC the output power increases with increasing expander inlet temperature. For the case of the ORC, the optimum value of turbine inlet temperature for minimum product cost is different from the corresponding value for maximum net output power. For the case of the Kalina system, for a given value of ammonia concentration, the net output power is maximized at a particular value of turbine inlet pressure. This value is different from the turbine inlet pressure at which the product cost is minimized. For the case of the TLC system, when the expander inlet temperature approaches the temperature of heat source, the net output power and the thermal efficiency increase and the product cost decreases. This is not the case for the ORC system. The optimization results, based on minimizing the product cost, indicate that the n-butane can yield the lowest product cost in the ORC and TLC systems. The optimization results indicate that the net output power of TLC system could be higher than that in the ORC and/or KCS11 systems. However, the superiority of the TLC system relative to the ORC or KCS11 depends on the value of expander isentropic efficiency.
M. Yari et al. / Energy 83 (2015) 712e722
Nomenclature c C_ E_ h ir m_ P Q_ rp s T Z _ W X Z_
cost per exergy unit ($ GJ1) cost rate ($ h1) exergy rate [kW] specific enthalpy [kJ kg1] interest rate mass flow rate [kg s1] pressure [bar] heat transfer rate [kW] compressor pressure ratio specific entropy [kJ kg1 K1] temperature [ C] investment cost of components ($) power [kW] ammonia concentration (kg/kg) investment cost rate of components ($ h1)
Abbreviations and subscripts 0 ambient ch chemical CI capital investment cond condenser CRF capital recovery factor cw cold water D destruction evap evaporator gen generator HC heat carrier Hs heat source (hot water) i, in input out output P pump ph physical Reg regenerator TLC trilateral cycle Greek symbols hex exergy efficiency [%] hth thermal efficiency [%] j specific flow exergy [kJ kg1] References [1] ORC-HP-technology. VDI- Berichte 539. VDIeVerlag Düsseldorf. In: Proceedings of VDI-Seminar 10-12 Sept. 1984 ETH Zürich, ISBN 3180905395. [2] DiPippo R. Second law assessment of binary plants generating power from low - temperature geothermal fluids. Geothermics 2004;33:565e86. [3] Tchanche BF, Papadakis G, Lambrinos G, Frangoudakis A. Fluid selection for a low-temperature solar organic Rankine cycle. Appl Therm Eng 2009;29: 2468e76. [4] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for low temperature organic Rankine cycles. Energy 2007;32:1210e21. [5] Hettiarachchia HDM, Golubovica M, Worek WM, Ikegami Y. Optimum design criteria for an organic Rankine cycle using low-temperature geothermal heat sources. Energy 2007;32:1698e706. [6] Lakew AA, Bolland O. Working fluids for low-temperature heat source. Appl Therm Eng 2010;30:1262e8. [7] Dai YP, Wang JF, Gao L. Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery. Energy Convers Manage 2009;50:576e82. [8] Wang XD, Zhao L. Analysis of zeotropic mixtures used in low-temperature solar Rankine cycles for power generation. Sol Energy 2009;83:605e13. [9] Yari M. Exergetic analysis of various types of geothermal power plants. Renew Energy 2010;35:112e21. [10] Shengjun Zh, Huaixin W, Tao G. Performance comparison and parametric optimization of subcritical organic Rankine cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Appl Energy 2011;29:2740e54.
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[11] Wei DH, Lu XS, Lu Z, Gu J. Performance analysis and optimization of organic Rankine cycle (ORC) for waste heat recovery. Energy Convers Manage 2007;48:1113e9. [12] Aghahosseini S, Dincer I. Comparative performance analysis of lowtemperature organic Rankine cycle (ORC) using pure and zeotropic working fluids. Appl Therm Eng 2013;54:35e42. [13] Kalina AI. Combined-cycle system with novel bottoming cycle. J Eng Gas Turbines Power Trans ASME 1984;106:737e42. [14] Kalina AI, Leibowitz HM. Kalina cycle promises improved efficiency. Mod Power Syst Rev 1987;7:19e23. [15] Park YM, Sonntag RE. A preliminary study of the Kalina power cycle in connection with a combined cycle system. Int J Energy Res 1990;14:153e62. [16] Lolos P, Rogdakis ED. A Kalina power cycle driven by renewable energy sources. Energy 2009;34:457e64. [17] Bombarda P, Ivernizzi CM, Pietra C. Heat recovery from diesel engines: a thermo-dynamic comparison between Kalina and ORC cycles. Appl Therm Eng 2010;30:212e9. [18] Fu Wencheng, Zhu Jialing, Zhang Wei, Lu Zhiyong. Performance evaluation of Kalina cycle subsystem on geothermal power generation in the oilfield. Appl Therm Eng 2013;54:497e506. [19] Zh Xinxin, He Maogang, Zh Ying. A review of research on the Kalina cycle. Renew Sustain Energy Rev 2012;16:5309e18. [20] Hettiarachchi HDM, Golubovic M, Worek WM, Ikegami Y. The performance of the Kalina cycle system 11 (KSC-11) with low-temperature heat sources. J Energy Resour Technol Trans ASME 2007;129:243e7. [21] Qiu K, Hayden ACS. Integrated thermoelectric and organic Rankine cycles for micro-CHP systems. Appl Energy 2012;97:667e72. [22] Smith IK. Development of the trilateral flash cycle system: fundamental considerations. J Power Energy Proc IMechE 1993;207:179e94. [23] Zamfirescu C, Dincer I. Thermodynamic analysis of a novel ammonia-water trilateral Rankine cycle. Thermochim Acta 2008;447:7e15. € ffler M. Kreisprozess mit Flashverdampfung im Arbeitsraum einer Kolben[24] Lo maschine. VGB PowerTech. Int J Electr Heat Gen 2007;7:92e7 [in German)]. [25] DiPippo R. Ideal thermal efficiency for geothermal binary plants. Geothermics 2007;36:276e85. € ffler M. Flash evaporation in cyclones. Chem Eng Technol 2008;31:1062e5. [26] Lo [27] Fischer J. Comparison of trilateral cycles and organic Rankine cycles. Energy 2011;36:6208e19. [28] Huff HJ, Radermacher R, Praissner M. Experimental investigation of a scroll expander in a carbon dioxide air-conditioning system. In: Proceedings of the International Congress of Refrigeration 2003, Washington, D.C; 2003. Paper 485. [29] Ho T, Mao SS, Greif R. Comparison of the organic Flash cycle (OFC) to other advanced vapor cycles for intermediate and high temperature waste heat reclamation and solar thermal energy. Energy 2012;42:213e23. [30] Soroureddin A, Mehr AS, Mahmoudi SMS, Yari M. Thermodynamic analysis of employing ejector and organic Rankine cycles for GT-MHR waste heat utilization: a comparative study. Energy Convers Manage 2013;67:125e37. [31] Heberle F, Bassermann P, Preißinger M, Brüggemann D. Exergoeconomic optimization of an organic rankine cycle for low-temperature geothermal heat sources. Int J Thermo (IJoT) 2012;15(2):119e26. [32] Bertrand F, Tchanche Gr, Lambrinos A, Frangoudakis Papadakis G. Lowgrade heat conversion into power using organic Rankine cycles e a review of various applications. Renew Sustain Energy Rev 2011;15: 3963e79. [33] Yari M, Mehr AS, Mahmoudi SMS. Simulation study of the combination of absorption refrigeration and ejector-expansion systems. Renew Energy 2013;60:370e81. [34] Klein SA, Alvarda F. Engineering equation solver (EES). WI: F-chart software. 2008. [35] Çengel YA, Boles MA. Thermodynamics: an engineering approach. Chapter 7e8. 5th ed. McGraw-Hill; 2006. [36] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. New York: John Wiley & Sons, Inc; 1996. [37] Kotas TJ. The exergy method of thermal plant analysis. Melbourne, FL, USA: Krieger Publishing; 1995. [38] Misra RD, Sahoo PK, Gupta A. Thermoeconomic evaluation and optimization of an aqua-ammonia vapour-absorption refrigeration system. Int J Ref 2006;29:47e59. [39] Rossa JA, Bazzo E. Thermodynamic modeling of an ammonia-water absorption system associated with a microturbine. Int J Thermodyn 2009;12:38e43. [40] Ahrendts J. Reference states. Energy 1980;5:667e77. [41] Rodríguez CEC, Palacio JCE, Venturini OJ, Lora EES, Cobas VM, dos Santos DM, et al. Exergetic and economic comparison of ORC and Kalina cycle for low temperature enhanced geothermal system in Brazil. Appl Therm Eng 2013;52: 109e19. [42] Zh Guo-Yan, En W, Shan-Tung T. Techno-economic study on compact heat exchangers. Int J Energy Res 2008;32:1119e27. [43] Rodríguez CEC, Palacio JCE, Venturini OJ, Lora EES, Cobas VM, dos Santos DM, et al. Exergetic and economic analysis of Kalina cycle for low temperature geothermal sources in Brazil. 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[44] Misra RD, Sahoo PK, Sahoo S, Gupta A. Thermoeconomic optimization of a single effect water/LiBr vapour absorption refrigeration system. Int J Ref 2003;26:158e69. [45] Economic Indicators. Marshall & Swift equipment cost index. Chem Eng September 2011:72.
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Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Exergoeconomic comparison of TLC (trilateral Rankine cycle), ORC (organic Rankine cycle) and Kalina cycle using a low grade heat source M. Yari a, *, A.S. Mehr a, V. Zare b, S.M.S. Mahmoudi a, M.A. Rosen c a
Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran Department of Mechanical Engineering, Urmia University of Technology, Urmia, Iran c Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe, Street North, Oshawa, Ontario L1H 7K4, Canada b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 September 2013 Received in revised form 16 November 2014 Accepted 23 February 2015 Available online 18 March 2015
Recently, the TLC (trilateral power cycle) has attracted significant interest as it provides better matching between the temperature profiles in the evaporator compared to conventional power cycles. This article investigates the performance of this cycle and compares it with those for the ORC (organic Rankine cycle) and the Kalina cycle, from the viewpoints of thermodynamics and thermoeconomics. A low-grade heat source with a temperature of 120 C is considered for all the three systems. Parametric studies are performed for the systems for several working fluids in the ORC and TLC. The systems are then optimized for either maximum net output power or minimum product cost, using the EES (engineering equation solver) software. The results for the TLC indicate that an increase in the expander inlet temperature leads to an increase in net output power and a decrease in product cost for this power plant, whereas this is not the case for the ORC system. It is found that, although the TLC can achieve a higher net output power compared with the ORC and Kalina (KCS11 (Kalina cycle system 11)) systems, its product cost is greatly affected by the expander isentropic efficiency. It is also revealed that using n-butane as the working fluid can result in the lowest product cost in the ORC and the TLC. In addition, it is observed that, for both the ORC and Kalina systems, the optimum operating condition for maximum net output power differs from that for minimum product cost. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Trilateral cycle ORC Kalina cycle Ammonia-water Exergoeconomic Low-grade heat source
1. Introduction An enduring area of interest for engineers, in which lots of work has been performed, is the conversion of heat to electricity. Recently, there is growing interest in utilizing low and moderate temperature heat sources, which are available via solar, geothermal and biogenic energy systems, and as waste heat from industries. For producing power, one can consider such cycles as ORCs (organic Rankine cycles) [1e12], Kalina cycles [13e21] and TLCs (trilateral cycles) [22e27]. These have been extensively investigated. For example, the performance has been investigated of ORCs using low-grade heat sources and focusing on selecting proper working fluids [3e8], while the performance of the Kalina cycle has been analyzed and compared with conventional power systems [13e16], and TLC performance has been analyzed using ammonia-water as a
* Corresponding author. Tel.: þ98 41 33392477. E-mail address: [email protected] (M. Yari). http://dx.doi.org/10.1016/j.energy.2015.02.080 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
working fluid [23] and ORCs and TLCs have been thermodynamically compared [27]. Whilst ORC and Kalina cycles are used already in existing power plants, the TLC is still in a state of technical development and less known [22]. The components in the TLC system are the same as those in the ORC system except that the working fluid at the entrance of the TLC expander (turbine) is a saturated liquid. Consequently, the state of the working fluid at the expander exit is a two-phase mixture. As the thermodynamic mean temperature at which heat is received is comparatively lower for the TLC, the thermal efficiency for this cycle is lower than that for the ORC, for the same temperature limits. Similar to transcritical cycles, the design of a reliable and efficient two-phase expander is still ongoing, although significant efforts have been made recently for screw-type and scroll-type expanders and reciprocating engines [28]. Compared to the case of the ORC, better temperature matching between the brine as a heat source and the TLC working fluid is observed in the TLC system. The expander in a TLC system is a key element. In general, two types of expansion devices exist: turbo-machines and positive
M. Yari et al. / Energy 83 (2015) 712e722
713
Fig. 1. Schematic diagram for basic ORC and corresponding T-s diagram.
displacement (or volumetric) machines. The former uses the kinetic energy of an expanding flow to turn a shaft at a high rotational speed and the latter operates by expanding a fixed volume of fluid per one revolution. At low capacities, the turbines suffer from a high-pressure drop in each stage due to the free space between the blade tips and housing. A problem with screw expanders, however, is their complicated 3D geometry in which the rotor mating line is relatively long and allows for large flow leakage. On the other hand, the geometry of scroll machines is simpler, reducing leakage problems [23]. To the best of our knowledge there is lack of information on the thermodynamic behavior of TLC systems, particularly from the viewpoint of exergoeconomics. The issue is more significant when TLC performance is compared with other well-known power plants such as the ORC and Kalina systems. The present paper aims to satisfy this need for information and to provide results that help efforts to better utilize heat sources at low temperatures. 2. Description of the cycles
heat sources while KCS5 is used for gas turbine power plants [19]. Each system has its own distinct features. For example, KCS11 does not have a distillation arrangement, but one is found in KCS5. Nevertheless, the working fluid in all Kalina cycle systems is an ammoniaewater mixture, which has the advantage of having varying boiling and condensing temperatures. This phenomenon reduces lower exergy destructions. Fig. 2 shows a schematic diagram of the KCS11 system. A saturated liquid ammonia-water mixture exiting the condenser is pumped to the regenerator where it is preheated before entering the evaporator. Hot water heats the ammonia-water mixture in the evaporator after which the liquid and vapor phases are separated in the separator unit. The obtained vapor enters the turbine and produces power, as it expands, before entering the absorber. The liquid ammonia-water mixture exiting the separator flows to the regenerator and then is throttled in the expansion valve. The low pressure ammonia-water mixture then flows to the absorber and is mixed with the turbine exit flow. The mixed flow exiting the absorber is condensed in the condenser and then passes through the pump to complete the cycle.
2.1. Organic Rankine cycle 2.3. TLC (Trilateral cycle) The ORC basically consists of an evaporator (heater), a turbine, a condenser and a pump. A schematic diagram for this cycle is shown in Fig. 1. A hot water stream (120 C) with a flow rate of 100 kg/s is used to heat the working fluid in the evaporator. 2.2. KCS11 (Kalina cycle system 11) The Kalina power cycle has various configurations, each of which is appropriate for some applications. KCS11 (Kalina cycle system 11) is suitable for producing power using low-temperature
The TLC (Trilateral Cycle) system is basically a power plant in which expansion starts from the saturated liquid rather than the saturated, superheated or supercritical vapor phase. In such a configuration, the transfer of heat from a heat source stream to the working fluid is achieved with a high degree of temperature matching (see Fig. 3). A TLC system to which heat is supplied from the heat source and removed by the cooling agent is shown in Fig. 4. The system consists of a pump, a heater, a twophase expander and a condenser.
Fig. 2. Schematic diagram of Kalina cycle system 11 (KCS11) and corresponding T-s diagram.
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Low pressure saturated liquid at the condenser exit is pumped to the heater where it is heated and becomes a saturated liquid at higher pressure. The liquid then expands in the expander after which it is condensed in the condenser. 3. Modeling methodology and assumptions 3.1. Assumptions In modeling the systems, the power plants are assumed to operate under steady conditions. Pressure losses due to the friction in heat exchangers and connecting pipes are taken as negligible. The systems reject heat to cooling water in the condenser. For the considered systems, an isentropic efficiency value of 0.85 is assumed for the pumps. For the ORC and KCS1, the turbine isentropic efficiency is considered to be 0.85 [29,30]. For the TLC system, however, the expander isentropic efficiency is varied in the range of 0.65e0.85 [23]. Table 1 summarizes the input parameter values for the cycles. 3.2. Thermodynamic analysis In the thermodynamic analyses, each component is considered as a control volume and the principles of mass and energy conservations as well as the second law of thermodynamics are applied. These equations and thermodynamic property relations are solved using the EES (engineering equation solver) software [34] to simulate the performance for each cycle. For each component the conservation of mass can be expressed as follows:
X X
m_ i ¼
X
m_ i xi ¼
m_ e
X
(1)
m_ e xe
(2)
Here, m_ is the mass flow rate and xi is the ammonia concentration in the solution. Note that equation (2) is applied only when the working fluid is an ammonia-water mixture (for the case of KCS11). The first law of thermodynamics yields the energy balance for each component as follows [35]:
_ ¼ Q_ k W k
X
m_ e he
X
m_ i hi
(3)
The second law of thermodynamics is used to evaluate the cycle performance based on an exergy perspective. In the absence of magnetic, electrical, nuclear and surface tension effects, and ignoring the kinetic and potential energies, the total exergy rate of a stream is the sum of physical and chemical exergy rates [36,37]:
E_ ¼ E_ ph þ E_ ch
(4)
The former part in the right side of equation (4) can be obtained written as follows:
_ h0 Þ T0 ðs s0 Þ E_ ph ¼ m½ðh
(5)
When the working fluid is an ammonia-water mixture, E_ ch cannot be neglected (i.e., for the Kalina power plant). The chemical exergy for an ammonia-water mixture can be calculated approximately as follows [38,39]:
X 1X 0 e0ch;NH3 þ ech;H2 O E_ ch zm_ MNH3 MH2 O
Fig. 3. Variation in heat carrier and working fluid temperatures during heat addition process for a) ORC, b) KCS11, c) TLC.
where e0ch;NH3 and e0ch;H2 O are the standard chemical exergies of ammonia and water, respectively. These are given by Ahrendts [40]. The thermal efficiency of the systems are expressed as
hth ¼
_ net W Q_
(7)
in
(6)
_ net is the net output power and Q_ is the supplied heat where W in rate in the evaporator/heater of the systems. A more meaningful
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715
Fig. 4. Schematic diagram for trilateral cycle (TLC) and corresponding T-s diagram.
criterion to assess the performance of an energy converting system is the second law efficiency, which can be defined as the ratio of output to input exergy. For the considered systems the second law efficiency can be expressed as
hex ¼
_ net W E_
(8)
in
where E_ in is the exergy rate of heat source, which is defined as
3.3. Cost equations Parameters such as the type of financing, the required capital and the expected life of a component influence the costs for owning and operating a system (non-exergy related cost rates). To calculate the costs of components at a specific size or capacity, a power law relation is used, such as [41e44]:
E_ hs ¼ m_ hs ½ðhhs h0 Þ T0 ðshs s0 Þ
(9)
In order to evaluate the performance of a system from the second law point of view, it is necessary to identify both the product and the fuel for each component of the system. The product represents the desired result produced by the component or the system. The fuel represents the resource expended to generate the product, and is not necessarily an actual fuel such as natural gas, oil or coal. Both the product and the fuel are expressed in terms of exergy. The exergy destruction rate in a component is calculated from the exergy rate balance for a component [37]:
E_ D ¼ E_ F E_ P E_ L
(10)
Cost at reference year ¼ Original cos t
Here, E_ F , E_ P and E_ L are the exergy flow rates associated with the fuel, the product and the losses for the component, respectively.
a
Zk ¼ ZR;K
AK AR
ZP ¼ ZR;P
_P W _ W R;P
(11) !mp
_n ZT ¼ ZR;T W t
Parameter
Value
Cycle
Reference
P0 (kPa) T0 ( C) Ths ( C) m_ hs ðkg:s1 Þ DTPP (K) hP (%) hT (%) hexp (%) Q3 () Q3 () Q6 () DTReg (K)
101.325 25 120 100 10 85 85 65e85 1 0 1 5
ORC, KCS11,TLC ORC, KCS11,TLC ORC, KCS11,TLC ORC, KCS11,TLC ORC, KCS11,TLC ORC, KCS11,TLC ORC, KCS11 TLC ORC TLC KCS11 KCS11
e e [31,32] [31,32] [23,30,33] [29,30] [27] [23] [23,27] [23,27] [20] [20]
np (12)
(13)
Here, the subscript R represents the reference components and the powers in the equations take on the following values [41e44]: a ¼ 0.514, mp ¼ 0.26, np ¼ 0.5, nt ¼ 0.7. Also, hp is the isentropic pump efficiency which is assumed to be 0.85. The cost data involved in an economic analysis at different years must be brought to the reference year according to the following relation:
Cost index for the reference year Cost index for the original year
Table 1 Parameters used in the simulation.
1 hP hP
(14)
For updating all costs to the year 2012, the Marshall and Swift equipment cost index [45] is used in the present work. Using the CRF (capital recovery factor) and the number of hours per year that the unit operates, the capital investment of a component is converted to the cost rate. The CRF is determined as follows:
CRF ¼
ir ð1 þ ir Þn ð1 þ ir Þn 1
(15)
where i is the interest rate and the n is the lifetime of the system in years. These parameters are considered fixed at 0.15 and 20 years, respectively [46].
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Table 2 Validation of present model for KCS11. P ¼ 2.0 MPa
Parameters
Optimum ammonia fraction (kg/kg) Maximum thermal efficiency (%)
P ¼ 2.5 MPa Hettiarachchi et al. [20]
Present model
Hettiarachchi et al. [20]
Present model
Hettiarachchi et al. [20]
0.598 9.15
0.609 9.02
0.677 9.6
0.685 9.5
0.752 10.24
0.754 10.20
Table 3 Validation of present model for TLC. Parameters
C_ L;K ¼ cF;K E_ L;K
Case IV
_ Q 56 (kW)
Fischer [27]
Present model
Fischer [27]
Present model
5862
5889
8800
8860
11.36 86.33
11.29 86.91
For each component of the systems operating at steady state condition, the entering and exiting exergy streams are in the form of heat and work interactions as well as material streams. The associated costs with these exergy terms are related through the following equations [36]:
C_ i ¼ ci E_ i
X
C_ i þ C_ q þ Z_
C_ e ¼ ce E_ e
(16)
_ C_ w ¼ cw W
C_ q ¼ cq E_ q
(17)
where C_ i and C_ e are the cost rates associated with entering and exiting exergy streams, respectively, and C_ w and C_ q are the cost rates associated with the exergy transfer in the form of heat and work, respectively. In equation (16), Z_ is the appropriate charge due to capital investment and operating and maintenance expenses for each component. Also, ci, ce, cw and cq denote average costs per unit exergy. In a thermoeconomic analysis of a thermal system, the average unit cost of fuel, cF, the average unit cost of product, cP, the cost rate of exergy destruction rate, C_ D and the exergoeconomic factor f each play a vital role. These parameters are expressed as follows:
C_ F;K E_ F;K
(18)
cP;K ¼
C_ P;K E_
(19)
P;K
E_ P;K is considered to be constant
(20)
Table 4 Comparison of results from present model with those reported by Ref. [23] for ORC, Kalina and TLC. Parameter
(21)
fk ¼
Z_ k
(22)
Z_ k þ C_ D;k þ C_ L;k
In order to validate the simulation results, available data in the literature are used. Table 2 compares the results obtained from the present model for KCS11 and those reported by Hettiarachchi et al. [20]. For each value of generator pressure, the obtained ammonia fraction for maximum efficiency, from the present work, is seen to be close to the value reported by Hettiarachchi et al. [20]. For the case of the TLC, data of two studied cases (case IV (T5 ¼ 220 C, T7 ¼ 15 C) and case V (T5 ¼ 150 C, T7 ¼ 15 C)) reported by Fischer are used [27]. As Table 3 demonstrates, there is a good agreement between the results obtained by our model and those reported by Fischer. Note that the model for the ORC has been validated in our previously published work [9]. Also, a comparison is presented between the data obtained from present models to that of Zamfirescu and Dincer [23] (Table 4). The comparison shows that the thermodynamic efficiency values from the present work agree well with those reported by Ref. [23]. For the ORC with R134a as a working fluid, assuming an interest rate of 5%, the unit product cost given in the literature is 0.056 $/ kWh [10]. The calculated value for this parameter in the present work is found to be 0.0557 $/kWh which is in a good agreement with the reported value. Also, for some other working fluids (Table 5), it is found that the cost values found with present model are close to those reported in literature [10]. 4. Results and discussion 4.1. Parametric study
cF;K ¼
C_ D;K ¼ cF;K E_ D;K
E_ P;K is considered to be constant
3.5. Model validation
3.4. Exergy costing and exergoeconomic evaluation
C_ e þ C_ w ¼
Case V
h (%) 17.06 16.98 th _ 34.14 34.29 C HC (kW/K) _ W ¼ 1MW, DT ¼ 10 K, hp ¼ 0.65, ht ¼ 0.85.
X
P ¼ 3.0 MPa
Present model
ORC
NH3eH2O cycles
R141b R123 R245ca R21
Kalina
TLC
3
8
10 Thermal efficiency given by Ref. [23], hth (%) Thermal efficiency calculated 10.06 by present model, hth (%)
9
9
9
9.02
9.11
8.91 3.09
8.08
4.1.1. ORC A similar trend to that which occurs in published works [7] is observed here for the variation of net output power with turbine inlet temperature. Indeed, as the turbine inlet temperature increases the net output power is maximized at some special temperature. The variation of net output power with turbine inlet temperature for the ORC is shown in Fig. 5 for several working fluids. Table 5 Comparison of results from present model with those reported by Ref. [10] for ORC, i ¼ 0.05, hT ¼ 0.8, hP ¼ 0.75 Parameter
Unit product cost found from present model ($/kWh) Unit product cost reported by Ref. [10] ($/kWh)
Working fluid R123
R245fa
R152a
CO2
R134a
0.0641
0.0578
0.0566
0.0773
0.0577
0.063
0.059
0.053
0.077
0.056
M. Yari et al. / Energy 83 (2015) 712e722
717
Fig. 5. ORC net output power versus turbine inlet temperature for several working fluids.
Fig. 7. Product cost versus turbine inlet temperature of the ORC for several working fluids.
Referring to Fig. 5, for almost all the studied working fluids, as the turbine inlet temperature increases there is an optimum value for turbine inlet temperature at which the net output power is maximized. This is due to the variations of mass flow rate and enthalpy drop through the turbine of ORC (as the turbine inlet temperature increases the mass flow rate decreases and the enthalpy drop increases). However, for R1234yf as a working fluid, the turbine inlet temperature cannot be raised beyond a particular value due to the lower value of critical temperature. The figure also indicates that for R1234yf the output power is higher than that obtained for the other studied working fluids. Variations of thermal and exergy efficiencies of ORC with turbine inlet temperature are shown in Fig. 6 for the studied working fluids. As the turbine inlet temperature increases the thermal efficiency of the cycle is observed to increase almost steadily for all of the studied working fluids. This is in accordance with the Carnot principle. It is shown in Fig. 6 that the highest thermal efficiency is achieved with ammonia as a working fluid. However, the variation trend of exergy efficiency with turbine inlet temperature is similar to that for the net output power, primarily because a constant value is assumed for the cycle inlet exergy. Fig. 7 shows the variation of ORC product cost with turbine inlet temperature. For each of the studied working fluids, there is an optimum value for the turbine inlet temperature at which the product cost is minimized. Comparing Figs. 5 and 7 indicates an
interesting point: the turbine inlet temperature at which the product cost is minimized is higher than the corresponding value for maximum net output power. 4.1.2. KCS11 For the case of the Kalina cycle, a parametric study is performed considering the effect of such parameters as turbine inlet temperature and pressure as well as ammonia concentration (X1) on the net output power, the thermal efficiency and the product cost. Similar to the ORC case, the heat source is a stream of hot water with a mass flow rate of 100 kg/s at a temperature of 120 C. The condenser temperature in this case is 40 C. For turbine inlet temperatures of 80 C, 90 C and 100 C and ammonia concentrations of 60%, 75% and 90% the variation of net output power with turbine inlet pressure is shown in Fig. 8. For a given value of ammonia concentration, an optimum turbine inlet pressure is observed at which the net output power is maximized. In addition, an increase in the ammonia concentration results in an increase in the net output power. It can be seen that as the turbine inlet temperature increases from 80 to 100 C (at a particular ammonia concentration) the net output power increases. Note that the effect is more pronounced at lower turbine inlet temperatures. The influence of turbine inlet pressure on the thermal efficiency of the Kalina cycle system is depicted in Fig. 9. At each ammonia concentration there is an optimum value of turbine inlet pressure at
Fig. 6. ORC thermal and exergy efficiencies versus turbine inlet temperature for several working fluids.
Fig. 8. KCS11 net output power versus turbine inlet temperature.
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M. Yari et al. / Energy 83 (2015) 712e722
Fig. 9. Kalina thermal efficiency versus turbine inlet pressure.
Fig. 11. TLC net output power versus turbine inlet temperature for several working fluids.
which the thermal efficiency is maximized. Comparing Figs. 8 and 9 reveals that the optimum values of turbine inlet pressure for maximum thermal efficiency are higher than the optimum values for maximum net output power. The variation of product cost with the turbine inlet pressure is shown in Fig. 10. For clarity, only ammonia concentrations of 60% and 90% are shown in this figure. As the figure indicates, at a particular value of turbine inlet pressure the cycle product cost is minimized. Note that the optimum values of turbine inlet pressures differ for minimum product cost, maximum net power and maximum thermal efficiency. 4.1.3. TLC Fig. 11 shows the variation of net output power with expander inlet temperature for the case of a TLC with several working fluids. As the expander inlet temperature increases the net output power is observed to increase. This trend is not similar to that of the ORC for which the net output power is maximized at a particular value of turbine inlet temperature. The variation of the thermal efficiency of the TLC with expander inlet temperature is shown in Fig. 12. As the figure indicates, the trend is similar to that of the net output power. An interesting point for the TLC case is the better performance for the n-butane working fluid considering both the net output power and thermal efficiency. This was not the case for the ORC.
Fig. 10. Product cost versus turbine inlet temperature.
Fig. 12. TLC thermal efficiency versus turbine inlet temperature for several working fluids.
Fig. 13 shows the variation of TLC product cost with expander turbine temperature for several working fluids. As the expander inlet temperature increases the product cost is seen to decrease for all the studied working fluids.
Fig. 13. Product cost versus turbine inlet temperature of the TLC for several working fluids.
M. Yari et al. / Energy 83 (2015) 712e722
As the key component in the TLC is the expander, the effect of its isentropic efficiency is presented in Fig. 14. The results presented only for the n-butane as the working fluid. In Fig. 14, as the expander isentropic efficiency increases from 65% to 85%, the TLC net output power increases by 40% and the product cost is reduced by 25%. Thus, the expander efficiency has a great impact on the TLC performance. 4.2. Optimization results The studied systems are optimized from the viewpoints of thermodynamics and thermoeconomics using the EES software. The objectives are to maximize the net output power and thermal efficiency as well as to minimize the unit exergy cost of the system product. Tables 6 and 7 show the optimization results for the ORC based on the maximum net power and minimum product cost, respectively. According to Table 6, when the optimization is based on the maximum net power, the highest net output power is achieved with R1234yf as the working fluid. However, the highest thermal efficiency and lowest product cost are obtained using the R134a. On the other hand, using the ammonia and n-butane as working fluids in the ORC exhibited the best result considering the product cost which is 16.49$/GJ. Comparing the results shown in Tables 6 and 7 reveals that, for each of the working fluids (R1234yf or propane or R134a), the maximum net output power and the minimum product cost are achieved with identical values of turbine inlet temperature. For the KCS11 case, the optimization results, based on maximizing the net output power and minimizing the product cost, for three values of ammonia concentrations, are shown in Tables 10 and 11, respectively. It is found that the turbine inlet pressure at which the product cost is minimized is higher than the corresponding value at which the net power is maximized. It is also observed that both the maximum net output power and minimum product cost occurs at the highest ammonia concentration. Finally, the results of the parametric study for the case of TLC show that unlike the ORC and KCS11 cases there are no maximum and minimum values for either the net output power or product cost. However, the highest value of the net output power or the lowest product cost is achieved with the highest turbine inlet temperature. Table 9 shows the highest values of net output power, thermal efficiency and exergy efficiency as well as the lowest value of product cost for the TLC system with an expander isentropic efficiency of 0.75. Comparing the results in Tables 6e10 reveals that using n-butane in the TLC results the highest net output power
719
Table 6 Optimization results for having maximum net output power of ORC. Working fluid
T3 ( C)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
R1234yf n-butane Isobutene Propane R134a R152a Ammonia
84 76.32 77.33 86.9 94.9 77.77 75.53
1816 1450 1479 1635 1448 1476 1377
7.787 7.72 7.715 8.318 9.19 7.806 7.883
34.37 27.44 28 30.95 27.4 27.94 26.07
17.7 18.14 18.19 17.96 17.43 18.32 18.34
Table 7 Optimization results for having minimum product cost of ORC. Working fluid
T3 ( C)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
R1234yf n-butane Isobutene Propane R134a R152a Ammonia
84 93.21 92.49 86.9 94.9 91.83 93.06
1816 1110 1189 1635 1448 1252 1042
7.787 10.2 9.823 8.318 9.19 9.667 10.68
34.37 21.01 22.5 30.95 27.4 23.69 19.72
17.7 16.49 16.8 17.96 17.43 17.1 16.49
Table 8 Optimization results for TLC with expander isentropic efficiency of 0.75. Working fluid
T3 ( C)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
R1234yf n-butane Isobutene Propane R134a R152a Ammonia
84 109 109 93.9 94.9 109 109
1288 2034 2016 1591 1626 2070 1931
4.458 7.005 6.96 5.625 5.688 7.284 6.771
24.38 38.5 38.16 30.12 30.77 39.18 36.55
27.89 18.19 18.63 23.72 22.81 18.57 19.99
Table 9 Optimization results for TLC with expander isentropic efficiency of 0.85. Working fluid
T3 ( C)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
R1234yf n-butane Isobutene Propane R134a R152a Ammonia
84 109 109 93.9 94.9 109 109
1557 2368 2364 1934 1947 2452 2308
5.389 8.151 8.16 6.837 6.813 8.629 8.093
29.47 44.8 44.74 36.6 36.86 46.41 43.69
23.55 16.01 16.27 19.98 19.47 16.06 17.13
Table 10 Optimization results for having maximum net output power of KCS11. Ammonia concentration
T5 ( C)
P5 (bar)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
60% 75% 90%
109 109 109
18.14 26.47 32.34
1046 1165 1321
6.243 6.885 7.549
19.79 22.06 25
22.16 20.37 18.65
Table 11 Optimization results for having minimum product cost of KCS11.
Fig. 14. Effect of expander isentropic efficiency of TLC system on the net output power and product cost.
Ammonia concentration
T5 ( C)
P5 (bar)
_ net (kW) W
hth (%)
hex (%)
cp ($/GJ)
60% 75% 90%
109 109 109
25.23 35.79 43.48
851.7 957.8 1108
8.28 8.887 9.501
16.12 18.13 20.98
19.91 18.57 17.14
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M. Yari et al. / Energy 83 (2015) 712e722
Table 12 Exergoeconomic analysis results for ORC in minimized product cost working condition. Components
cF,k ($GJ1)
cP,k ($GJ1)
C_ D;k ($h1)
C_ L;k ($h1)
Z_ k ($h1)
C_ D;k þ C_ L;k þ Z_ k ($h1)
fk (%)
Evaporator Condenser Turbine Pump
5 11.29 10.08 15.56
11.29 18.71 16.49 15.97
0.737 1.124 6.829 0.4539
91.8 0.2481 e e
0.3419 0.3665 20.02 0.8737
92.88 1.739 26.85 1.328
0.3681 21.07 74.56 65.81
Working fluid: n-butane, m_ hs ¼ 100 kg=s, Tcond ¼ 40 C, T3 ¼ 93.21 C, chw
¼
5 $/GJ.
Table 13 Exergoeconomic analysis results for KCS11 in minimized product cost working condition. Components
cF,k ($GJ1)
cP,k ($GJ1)
C_ D;k ($h1)
C_ L;k ($h1)
Z_ k ($h1)
C_ D;k þ C_ L;k þ Z_ k ($h1)
fk (%)
Evaporator Condenser Turbine Pump Regenerator Absorber
5 10.653 10.65 10.68 10.65 10.65
10.65 10.68 17.14 10.685 10.69 10.653
7.74 13.36 7.363 0.6252 3.084 0.062
50.22 11.86 e e e e
1.313 0.5765 20.2 1.094 0.2775 0.0482
59.27 25.8 27.57 1.72 3.366 0.1111
2.215 2.235 73.29 63.64 8.389 43.45
X1 ¼ 0.9,m_ hs ¼ 100 kg=s, Tcond ¼ 40 C, T5 ¼ 109 C, P5 ¼ 43.48 bar, chw
¼
5 $/GJ.
Table 14 Exergoeconomic analysis results for TLC in minimized product cost working condition. Components
cF,k ($GJ1)
cP,k ($GJ1)
C_ D;k ($h1)
C_ L;k ($h1)
Z_ k ($h1)
C_ D;k þ C_ L;k þ Z_ k ($h1)
fk (%)
Evaporator Condenser Turbine Pump
5 10.92 10.92 13.62
10.92 13.62 18.19 14.35
11.51 42.13 31.14 4.357
8.205 8.805 e e
4.05 3.177 34.16 4.922
23.77 54.11 65.3 9.279
17.07 5.87 52.31 53.04
Working fluid: n-butane, m_ hs ¼ 100 kg=s, hexpander ¼ 0.75, Tcond ¼ 40 C, T3 ¼ 109 C, chw
with a product cost comparable to the other cycles. In addition, it is found that using the n-butane as working fluid for the case of ORC can yield the lowest product cost among the other working fluids. It can be concluded that the highest output power and the lowest product cost can be obtained with TLC and ORC, respectively. However, from the results in Table 9 (for expander isentropic efficiency of 0.85), it is observed that the isentropic efficiency of the expander has a great impact on the TLC performance. It can be concluded that the TLC power plant could compete economically with the other studied power producing systems. Detailed exergoeconomic analyses are carried out for the components of the systems. The results are shown in Tables 12e14 for the ORC, KCS11 and TLC, respectively. In all systems, the turbine and pump have higher exergoeconomic factor, f, indicating higher investment costs for these components. On the other hand, the evaporator and condenser have lower exergoeconomic factor values, indicating that for these components the cost rates associated with the exergy destruction and/or exergy losses are higher. Therefore, it can be concluded that engineers should focus on reducing the exergy losses and exergy destruction in evaporator and condenser. In addition, to reduce the overall product cost of the systems designers should pay more attention on lowering the investment cost of the turbine. 5. Conclusions The performances of three power generating systems (ORC, KCS11 and TLC) are investigated and compared from the viewpoints of thermodynamics and exergoeconomics. The obtained results reveal that, considering both thermodynamic and economic viewpoints, the TLC power system can be useful if the TLC expander has an isentropic efficiency close to that of conventional turbines. However, the good temperature match in the evaporator of the TLC
¼
5 $/GJ.
is the main advantage of this cycle. In addition, considering the cp values for the ORC, TLC and KC11 from Tables 6e11, it can be concluded that using an ORC for low grade heat utilization, to produce power, is the most advantageous among the three options investigated, from the viewpoint of economics. This is an important result because it has been reported in literature previously that the TLC is superior to the ORC from the viewpoint of thermodynamics [23,27]. Also, following conclusions could be drawn: For the case of the ORC, there is a particular turbine inlet temperature at which the net output power is maximized while for the case of TLC the output power increases with increasing expander inlet temperature. For the case of the ORC, the optimum value of turbine inlet temperature for minimum product cost is different from the corresponding value for maximum net output power. For the case of the Kalina system, for a given value of ammonia concentration, the net output power is maximized at a particular value of turbine inlet pressure. This value is different from the turbine inlet pressure at which the product cost is minimized. For the case of the TLC system, when the expander inlet temperature approaches the temperature of heat source, the net output power and the thermal efficiency increase and the product cost decreases. This is not the case for the ORC system. The optimization results, based on minimizing the product cost, indicate that the n-butane can yield the lowest product cost in the ORC and TLC systems. The optimization results indicate that the net output power of TLC system could be higher than that in the ORC and/or KCS11 systems. However, the superiority of the TLC system relative to the ORC or KCS11 depends on the value of expander isentropic efficiency.
M. Yari et al. / Energy 83 (2015) 712e722
Nomenclature c C_ E_ h ir m_ P Q_ rp s T Z _ W X Z_
cost per exergy unit ($ GJ1) cost rate ($ h1) exergy rate [kW] specific enthalpy [kJ kg1] interest rate mass flow rate [kg s1] pressure [bar] heat transfer rate [kW] compressor pressure ratio specific entropy [kJ kg1 K1] temperature [ C] investment cost of components ($) power [kW] ammonia concentration (kg/kg) investment cost rate of components ($ h1)
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