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Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cell–supercritical CO2 Brayton cycle hybrid system
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Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system Emin Ac¸ıkkalp* Department of Mechanical and Manufacturing Engineering, Engineering Faculty, Bilecik S.E. University, Bilecik, Turkey
article info
abstract
Article history:
In last decade, there has been increasing interest about fuel cell-heat engine or refrigerator
Received 26 September 2016
hybrid systems. Molten carbonate fuel cells (MCFC) provides an opportunity to be used in a
Received in revised form
hybrid system because of high temperature heat obtained from the system. Brayton cycles
5 December 2016
may be an alternative to use with MCFC as bottom cycle. In this paper, e MCFCesuper-
Accepted 22 December 2016
critical CO2 (SCO2) Brayton cycle hybrid heat engine is investigated as a promising power
Available online xxx
generation option. SCO2 Brayton cycle is chosen because of some advantages like higher efficiency comparing with conventional (air) Brayton cycle. This hybrid system is investi-
Keywords:
gated ecological criteria involving ecological function and exergetic sustainability index as
Molten carbonate fuel cell
well as basic thermodynamic parameters. Results are obtained numerically and perfor-
Supercritical Brayton cycle
mance limits are tried to define for designing more environmental friendly system.
Exergetic sustainability index
© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Exergy-based ecological function
Introduction Hybrid systems of high temperature fuel cell with thermal systems are an alternative for obtaining high efficient systems and offer a solution to utilize of heat rejected by the fuel cell. High temperature fuel cells like solid oxide fuel cells (SOFC) and molten carbonate fuel cells (MCFC) are two of the suitable ones to be used in hybrid system. In near future, studies about irreversible fuel cells have been presented to the literature. In Refs. [1e5], irreversible SOFC, MCFC, proton exchange membrane (PEM) fuel cell, phosphoric acid fuel cell (PAFC) and direct carbon fuel cell (DCFC) are modeled. Hybrid fuel cell - heat engine or refrigeration systems involving, Brayton, Stirling, Braysson heat
engines, thermoelectric generator, absorption refrigerator were researched in Refs. [6e25]. Brayton cycles are an option to use waste heat produced from the fuel cell and supercritical CO2 (SCO2) Brayton cycles have gained attention for last decades. Their working fluid is CO2 above the critical point. Significant reduction in the compressor work is occurred in this cycle and this causes to increase at the thermal efficiency. This system is smaller when it compares with a steam system, that's why, smaller capital costs are provided, and less greenhouses gases arereleased. However, temperature at the outlet of the turbine is high and recuperation process at this stage affects thermal efficiency importantly. Because of their advantages, it might be an efficient alternative for the hybrid applications. In the
* Fax: þ90 (228) 216 05 88. E-mail addresses: [email protected], [email protected]. http://dx.doi.org/10.1016/j.ijhydene.2016.12.110 0360-3199/© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
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Nomenclature A C e esi E En exd Exd F g G h H j k K ne p P Q_ R SCO2 T U x
2
area, m heat capacity, W K1 ecological function density, W m2 exergetic sustainability index ecological function, W activation energy, J mol1 exergy destruction density, W m2 exergy destruction rate, W Faraday constant, C mol1 molar Gibbs free energy, J mol1 molar Gibbs free energy, J molar enthalpy, J mol1 enthalpy, J current density, A m2 ratio of specific heats heat conductance, W K1 number of electron pressure, atm, kPa, power density, W m2 power, W heat rate, W universal gas constant, J mol1 K1 supercritical carbon dioxide cycle temperature, K potential, V isentropic temperature
Subscripts A air Brayton cycle an anode B Brayton
literature, some papers can be found [26e30] about hybrid MCFCeSCO2 Brayton heat engines. In Refs. [26,27], comparison between SCO2 and air Brayton e MCFC hybrid systems are conducted and it is found that SCO2 Brayton cycle-MCFC hybrid system is more advantageous in terms of efficiency and net power output. Mahmoudi and Ghavimi [28], analyzed MCFCeSCO2 Brayton-organic Rankine cycle hybrid system by using thermoeconomic and multi objective optimization methods. Their results show that exergy efficiency might reach to 65.3% and product unit cost might be reduced to 0.039 cent (US)/kWh. Baronci et al., compared MCFCeSCO2 Brayton hybrid system with MCFC-organic Rankine cycle hybrid system [29]. They found that using SCO2 Brayton hybrid system as a bottoming cycle provides nearly 5% increasing at the energy efficiency than organic Rankine cycle does. In Ref. [30], MCFCeSCO2 Brayton cycle is investigated by means of exergy analysis. Result shows that overall efficiency of the system is 78% and overall exergy efficiency is 50% and it is determined that exergy efficiency of reformer is minimum while exergy efficiency of E-101 heat exchanger is maximum. Finite-Time-Thermodynamics (FTT) is very useful tool to asses actual thermodynamic cycles and systems. Contrast to classical thermodynamics, internal external irreversibilities
cp C CO2 cat e esi ex h H H2 H2O i l max o O2 ohm p r rc rev S SCO2 t h
compression fuel cell carbon dioxide cathode ecological function, W exergetic sustainability index expansion hot side hybrid hydrogen water ideal standard cold side maximum environment condition oxygen ohm overpotential power regenerator recuparator reversible isentropic conditions supercritical carbon dioxide cycle theoretical maximum potential efficiency
Greek letters h efficiency 4 exergy efficiency ε effectiveness
or both of them are taken into account and more realistic results and optimization conditions can be obtained. There are many example of thermal cycles analyzed wit FTT [31e51]. In the literature, some ecological and environmental criteria were proposed to evaluate actual thermal systems too. Angulo -Brown presented an ecological function [52] and it was improved by Yan [53]. This function was applied to Brayton cycles and some examples of it may be shown in Refs. [54e64]. Another criterion is exergetic sustainability index. This index enables us to evaluate sustainability range of thermal cycles. Exergetic sustainability index was researched by several authors in Refs. [49,65e76]. In this paper, MCFCeSCO2 Brayton heat engine is taken into account. Novelty of this research is to investigate the considered system by using ecological function and exergetic sustainability index. Purpose of this research is to design more ecological and less environmental harmful systems. The basic thermodynamic parameters including power output, energy and exergy efficiencies and exergy destructions are investigated as well as ecological function and exergetic sustainability index. It is tried to define the performance limits of the considered system. Results are obtained numerically and they are plotted in figures, finally, they are discussed and evaluated.
Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
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Thermodynamic analysis Combined MCFC and supercritical CO2 Brayton heat engine is shown in Fig. 1. Heat rejected from the MCFC is used for heating working fluid of the Brayton cycle. Anode potential (Uan), cathode potential (Ucat), ohm overpotential (Uohm) and theoretical maximum potential (Ut) of MCFC, these potentials can be calculated as follows respectively [3]:
Uan ¼ 2:27 109 je
Enact;an RT
pH0:42 p0:17 p1 2 ;an CO2 ;an H2 O;an
Ucat ¼ 7:505 1010 je
(1)
Enact;cat RT
0:09 p0:43 O2 ;cat pCO2 ;cat
(2)
Uohm ¼ 0:5 104 je
3016
3
1 1 T923
0 1 0:5 pCO2 ;cat C RT BpH2 ;an pO2 ;cat ln@ Ut ¼ Ei þ A ne F pH2 ;an pCO2 ;an
(3)
(4)
where, j is the current density, pH2 ;an is partial pressure of hydrogen at the anode, pCO2 ;an is the partial pressure of carbon dioxide at the anode, pH2 O;an is the partial pressure of water at the anode, pO2 ;cat is the partial pressure of oxygen at the cathode, pCO2 ;cat is the partial pressure of carbon dioxide at the cathode, R is the universal gas constant, T is the operating temperature of the MCFC, Enact is the activation energy, F is the Faraday constant, ne is the number of electrons and Ui is the ideal standard potential.
Fig. 1 e a: MCFC e Brayton hybrid heat engine. b: Tes diagram of Brayton cycle. Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
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Dgo Ui ¼ ne F
(5)
Cell voltage is written by using eqs. (1)e(5) [3]: Ucell ¼ ðUt Uan Ucat Uohm Þ
(6) hB ¼ 1
Power and efficiency of the fuel cell are [3]: PC ¼ Ucell jA hC ¼
(7)
PC
(8)
DH_
Dh Ucell jA ne F
(10)
Heat exchange at the regenerator can be described as: Q_ r ¼ Kr ð1 εr ÞðT To Þ
Q_ h ¼ DH_ PC Q_ r
(11)
(21)
Q_ h ¼ Cεh ðT T5 Þ ¼ CðT3 T5 Þ
(13)
where C is the heat capacity and εh is the effectiveness of the hot side. T2 and T4 temperatures can be calculated by using compression (hcp ) and expansion (hex ) efficiencies. k1 T2s T1 T3 T4 T2S T3 p2 k ; hex ¼ ; ¼ ¼x¼ T2 T1 T3 T4s T1 T4S p1 T2S T1 þ T1 hcp
PB ¼ Q_ h Q_ l
(22)
ExdB ¼ To
_ Q l Q_ h Tl T
(23)
Exergy efficiency of any thermal cycle is rate energy efficiency to reversible (Carnot) efficiency or rate of power output to reversible power and it can be expressed for Brayton cycle as: hB PB ¼ hrev;B Prev;B
(24)
where hB;rev is: hrev;B ¼ 1
Tl T
(25)
reversible power for Brayton cycle can be obtained from eq (24) as:
(12)
Another heat input expression to the bottom cycle is shown in eq. (13):
T2 ¼
Q_ l ¼ Q_ h ð1 hB Þ
4B ¼
where, Kr is the heat conductance of the regenerator, εr is the regenerator effectiveness and To is the environment temperature. Heat input to the bottom cycle (SCO2 Brayton cycle) is written as eq. (12):
hcp ¼
Heat rejection from the Brayton engine is:
(9)
where, A is the area of the interconnect plate and Dh is the molar enthalpy change. Exergy destruction rate of fuel cell is [3]:
(20)
Exergy destruction rate of the Brayton engine is:
jADh DH_ ¼ ne F
ðT6 T1 Þ Q_ l ¼1 ðT3 T5 Þ Q_ h
Power output of the Brayton cycle is:
where DH is the maximum possible power from the fuel cell and it can be described as [3]:
ExdC ¼
For making easier of the calculations, a correlation between x and j can be obtained by using eqs. (12), (13) and (17). This correlation is plotted in Fig. 2. Energy efficiency of the Brayton cycle, under assumption of constant specific heats, is written as following:
Prev;B ¼
PB 4B
(26)
Power output, energy efficiency, exergy efficiency and exergy destruction rate of the hybrid system are described in eqs. (27)e(30) respectively.
(14)
!
T4 ¼ ðT3 hex ðT3 T4S ÞÞ
(15)
(16)
where k is ratio of specific heats and x is the isentropic temperature. T3, T5 and T6 are expressed in eqs. (17)e(19): T3 ¼ T5 ð1 εrc Þ þ εh T
(17)
T5 ¼ T4 εrc þ ð1 εrc ÞT2
(18)
T6 ¼ T2 εrc þ ð1 εrc ÞT4
(19)
where εrc is the recuparator effectiveness.
Fig. 2 e Isentropic temperature versus current density for SCO2 and air Brayton cycles.
Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e9
PH ¼ PC þ PB
(27)
hH ¼
PC þ PB DH_
(28)
4H ¼
PC þ PB Prev;C þ Prev;B
(29)
ExdH ¼ ExdC þ ExdB
(30)
After the basic thermodynamic parameters, environmental criteria may be explained. Fist criterion is exergetic sustainability index. Exergetic sustainability index is ratio of exergy output of the system to lost exergy that is described as difference of exergy input from the useful exergy output. This provides us information about sustainability of the considered system. Its physical meaning is that ratio of exergy output from the system, maximum power output of a heat engine, to the waste exergy that is not used by the system. It can be described as: esiH ¼
Prev;C þ Prev;B ΔG_ PH
5
Fig. 3 e Power density change with current density for SCO2 and air Brayton cycles.
(31)
Another criterion considered in this paper is ecological function. Ecological function is difference of power output and exergy destruction originated from the entropy generation. It provides an opportunity to maximize power output while reducing exergy destruction and this causes to decrease at the environmental impact of the researched system: EH ¼ ðPH Þ ExdH
(32)
Results and discussion Variables used in calculations of MCFC are; pH2 ;an ; pH2 O;an ; pCO2 ;an , pO2 ;cat; pCO2 ;cat ; pH2 O;cat are 0.6, 0.342, 0.058, 0.08, 0.08, 0.25 (atm) respectively, ne is 2, Eact,an is 53,500 (J mol2), Eact,cat is 77,300 (J mol2), F is 96,485 (C mol1), R is 8.314 (J mol1 K1), finally, Dg, Dh and T are 197000 (J mol1), 247430 (J mol1) and 923 (K) respectively [3,11,18,21,22,24]. Compressor, turbine efficiencies and effectiveness of recuperator for the SCO2 Brayton and air Brayton cycles are taken from ref. [27]. Compression efficiency, expansion efficiency and recuparator efficiency are assumed as 0.91, 0.94 and 0.98 for SCO2 Brayton cycle and 0.85, 0.90 and 0.92 for Air Brayton cycle respectively [27]. Finally, Kr and εr, εh, εrc, TL and To are 10 (W K1), 0.85, 0.95, 0.98, 300 (K) and 298.15 (K). In comparison of these two type of Brayton cycles, mass flows are assumed as same with each other and, according to this assumption, CSCO2 and CA are taken as 400 (W K1) and 475.47 (W K1). Relation between isentropic temperature and current density is shown in Fig. 2. Power density (p ¼ P/A), exergy density (exd ¼ Exd/A), ecological function density (e ¼ E/A), sustainability index, energy and exergy efficiencies are investigated according to current density and their curves are plotted in Figs. 3e7. Variations with p ecological function, exergetic sustainable index and h for the hybrid heat engine are shown in Figs. 8 and 9.
Fig. 4 e Energy efficiencies variations with current density for SCO2 and air Brayton cycles.
Power density values for MCFC, SCO2 and air Brayton cycles and hybrid heat engines are illustrated in Fig. 3. Main purpose of any heat engine or power generation system is to produce power output as high as possible. That's why, obtaining maximum power from these systems is crucial. It can be seen that hybrid systems, SCO2 Brayton cycle, air Brayton cycle and MCFC have optimum points. SCO2 e hybrid system gets it maximum value that is equal to 3101.13 (W m2) at j ¼ 4150 (A m2), MCFC and SCO2 Brayton cycle get their maximum values at j ¼ 3750 (A m2) and j ¼ 4350 (A m2), corresponding values to these optimum points are 1885.13(W m2) and 1251.07 (W m2) respectively. When, maximum points of SCO2 hybrid system and air-hybrid system are compared, SCO2 hybrid system is 5% more advantageous in terms of maximum power output than air hybrid system. Energy efficiencies curves are indicated in Fig. 4. Energy efficiency is ratio of acquired product that is mostly
Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
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Fig. 5 e Exergy efficiencies variations with current density for SCO2 and air Brayton cycles.
Fig. 6 e Exergy destruction densities according to current density for SCO2 and air Brayton cycles.
Fig. 7 e Variation of ecological function and exergetic sustainability index with current density for MCFCeSCO2 Brayton hybrid cycle.
Fig. 8 e Efficiency-power density curve for MCFCeSCO2 Brayton hybrid cycle.
Fig. 9 e Ecological function density and exergetic sustainability index changes with power density for MCFCeSCO2 Brayton hybrid cycle.
power or work output to fuel provided to the system. It means that one can produce much power with same fuel by using an energy efficient system compared with a system that has same capacity however less energy efficient one. As it is seen, hybrid systems and Brayton cycles have optimum points while MCFC has no optimum. Optimum points of the SCO2 hybrid system and SCO2 Brayton cycle are equal to 0.79 and 0.46 and corresponding current densities are 1150 (W m2) and 2300 (W m2). Maximum energy efficiencies of air hybrid system and air Brayton system correspond to 82.8% and 72.6% of SCO2 hybrid system and SCO2 Brayton cycle. Exergy efficiency represents how considered system is close to the ideal one. So, if exergy efficiency increases, irreversibilities existed in the system will be reduced. As it can be seen in Fig. 5, there is no optimum point for exergy efficiency of the MCFC while hybrid systems and Brayton cycles have. Optimum values of the SCO2 hybrid system and SCO2 Brayton cycles are 0.79 and 0.68 and their current densities at the maximum points are j ¼ 850 (W m2) and 2300 (W m2). Maximum exergy
Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
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efficiencies of air hybrid system and air Brayton cycle are equal to 76.7% of SCO2 hybrid system and 72.7% of the SCO2 Brayton cycle. Exergy destruction rate shows us the lost work in the system resulting from the irreversibilities or entropy generation. According to Fig. 6, exergy destruction density values of considered systems increase with current density and there is no minimum. This means that current density is required to be as minimum as possible to obtain smaller exergy destruction values. However, air-hybrid system and air Brayton cycle have higher exergy destruction rates at the same current densities. Fig. 7 shows variation of e and esi with current density for the SCO2 hybrid system. e reaches its maximum that is equal to 650.795 (W m2) at j ¼ 1850 (A m2) and esi reaches its maximum at j ¼ 1350 (A m2) with 4.92 value. Fig. 8 can be called as performance curve of the SCO2 hybrid system. Current densities at maximum power and maximum energy efficiency are jP and jh respectively. In the design studies, current density is chosen as jh j jP. In Fig. 8, pmax is the maximum power density, ph is the power density at the maximum efficiency, hP is the efficiency at the maximum power and hmax is the maximum efficiency. As it shown, efficiency and power values should be chosen as hP h hmax and ph p pmax. hP is 0.58 and ph is 1166.3(W m2). If they are compared with their maximum values, hP is 73% of the maximum efficiency and ph is the 38% of the maximum power density. Changes of e and esi with power density for SCO2 hybrid system is plotted in Fig. 9. Where, emax is the maximum ecological function, ep is ecological function at the maximum power density, esip is the exergetic sustainability index at the maximum power density, esimax is the maximum exergetic sustainability index, pe is the power density at the maximum ecological function and pesi is the power density at the maximum exergetic sustainability index. ep, esip, pe, pesi are equal to 1443.97 (W m2), 2.96 and 3043.06 (W m2), 1837.27 (W m2), esip is 60% of the esimax, pe is equal to 59% of pmax and, finally, pesi is 44% of. pmax, however ep cannot be compared with emax, because of negative value of ep. It can be seen that je and jesi, which are current density at maximum ecological function and exergetic sustainability index, are between values of jh and jP. Power output value is bigger at the maximum ecological function than the maximum exergetic sustainability index and vice a versa is true for the energy efficiency. eh is ecological function at the maximum efficiency, esih is the exergetic sustainability index at the maximum efficiency, esimax is the maximum exergetic sustainability index, he is the energy efficiency at the maximum ecological function and hesi is the energy efficiency at the maximum exergetic sustainability index. eh, esih, he, hesi are equal to 526.72 (W m2), 4.88, 0.77 and 0.79. These values are equal to nearly 81%, 99%, 98% and 99% of their maximum values.
Conclusion This paper aims to investigate and optimize MCFCeSCO2 Brayton hybrid cycle with exergetic based ecological and sustainability criteria. MCFCeSCO2 Brayton hybrid system is optimized for power output, exergy destruction, energy and exergy efficiencies as well as criteria mentioned above. Ecological and sustainable operation conditions are described
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by using ecological function and exergetic sustainability index. Results show that ecological function should be chosen as objective function to obtain higher power output compared with exergetic sustainability index, however, exergy destruction density is bigger too. In spite of this, optimum ecological function represents the point where difference of power output and exergy destruction rate is the maximum. For the future studies, it is recommended that ecological function and exergetic sustainable index should be used for designing more environmental fuel cell-heat engine hybrid systems.
Acknowledgments The authors would like to thank the reviewers for their valuable comments, which have been utilized in improving the quality of the paper.
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Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
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Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system Emin Ac¸ıkkalp* Department of Mechanical and Manufacturing Engineering, Engineering Faculty, Bilecik S.E. University, Bilecik, Turkey
article info
abstract
Article history:
In last decade, there has been increasing interest about fuel cell-heat engine or refrigerator
Received 26 September 2016
hybrid systems. Molten carbonate fuel cells (MCFC) provides an opportunity to be used in a
Received in revised form
hybrid system because of high temperature heat obtained from the system. Brayton cycles
5 December 2016
may be an alternative to use with MCFC as bottom cycle. In this paper, e MCFCesuper-
Accepted 22 December 2016
critical CO2 (SCO2) Brayton cycle hybrid heat engine is investigated as a promising power
Available online xxx
generation option. SCO2 Brayton cycle is chosen because of some advantages like higher efficiency comparing with conventional (air) Brayton cycle. This hybrid system is investi-
Keywords:
gated ecological criteria involving ecological function and exergetic sustainability index as
Molten carbonate fuel cell
well as basic thermodynamic parameters. Results are obtained numerically and perfor-
Supercritical Brayton cycle
mance limits are tried to define for designing more environmental friendly system.
Exergetic sustainability index
© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Exergy-based ecological function
Introduction Hybrid systems of high temperature fuel cell with thermal systems are an alternative for obtaining high efficient systems and offer a solution to utilize of heat rejected by the fuel cell. High temperature fuel cells like solid oxide fuel cells (SOFC) and molten carbonate fuel cells (MCFC) are two of the suitable ones to be used in hybrid system. In near future, studies about irreversible fuel cells have been presented to the literature. In Refs. [1e5], irreversible SOFC, MCFC, proton exchange membrane (PEM) fuel cell, phosphoric acid fuel cell (PAFC) and direct carbon fuel cell (DCFC) are modeled. Hybrid fuel cell - heat engine or refrigeration systems involving, Brayton, Stirling, Braysson heat
engines, thermoelectric generator, absorption refrigerator were researched in Refs. [6e25]. Brayton cycles are an option to use waste heat produced from the fuel cell and supercritical CO2 (SCO2) Brayton cycles have gained attention for last decades. Their working fluid is CO2 above the critical point. Significant reduction in the compressor work is occurred in this cycle and this causes to increase at the thermal efficiency. This system is smaller when it compares with a steam system, that's why, smaller capital costs are provided, and less greenhouses gases arereleased. However, temperature at the outlet of the turbine is high and recuperation process at this stage affects thermal efficiency importantly. Because of their advantages, it might be an efficient alternative for the hybrid applications. In the
* Fax: þ90 (228) 216 05 88. E-mail addresses: [email protected], [email protected]. http://dx.doi.org/10.1016/j.ijhydene.2016.12.110 0360-3199/© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
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Nomenclature A C e esi E En exd Exd F g G h H j k K ne p P Q_ R SCO2 T U x
2
area, m heat capacity, W K1 ecological function density, W m2 exergetic sustainability index ecological function, W activation energy, J mol1 exergy destruction density, W m2 exergy destruction rate, W Faraday constant, C mol1 molar Gibbs free energy, J mol1 molar Gibbs free energy, J molar enthalpy, J mol1 enthalpy, J current density, A m2 ratio of specific heats heat conductance, W K1 number of electron pressure, atm, kPa, power density, W m2 power, W heat rate, W universal gas constant, J mol1 K1 supercritical carbon dioxide cycle temperature, K potential, V isentropic temperature
Subscripts A air Brayton cycle an anode B Brayton
literature, some papers can be found [26e30] about hybrid MCFCeSCO2 Brayton heat engines. In Refs. [26,27], comparison between SCO2 and air Brayton e MCFC hybrid systems are conducted and it is found that SCO2 Brayton cycle-MCFC hybrid system is more advantageous in terms of efficiency and net power output. Mahmoudi and Ghavimi [28], analyzed MCFCeSCO2 Brayton-organic Rankine cycle hybrid system by using thermoeconomic and multi objective optimization methods. Their results show that exergy efficiency might reach to 65.3% and product unit cost might be reduced to 0.039 cent (US)/kWh. Baronci et al., compared MCFCeSCO2 Brayton hybrid system with MCFC-organic Rankine cycle hybrid system [29]. They found that using SCO2 Brayton hybrid system as a bottoming cycle provides nearly 5% increasing at the energy efficiency than organic Rankine cycle does. In Ref. [30], MCFCeSCO2 Brayton cycle is investigated by means of exergy analysis. Result shows that overall efficiency of the system is 78% and overall exergy efficiency is 50% and it is determined that exergy efficiency of reformer is minimum while exergy efficiency of E-101 heat exchanger is maximum. Finite-Time-Thermodynamics (FTT) is very useful tool to asses actual thermodynamic cycles and systems. Contrast to classical thermodynamics, internal external irreversibilities
cp C CO2 cat e esi ex h H H2 H2O i l max o O2 ohm p r rc rev S SCO2 t h
compression fuel cell carbon dioxide cathode ecological function, W exergetic sustainability index expansion hot side hybrid hydrogen water ideal standard cold side maximum environment condition oxygen ohm overpotential power regenerator recuparator reversible isentropic conditions supercritical carbon dioxide cycle theoretical maximum potential efficiency
Greek letters h efficiency 4 exergy efficiency ε effectiveness
or both of them are taken into account and more realistic results and optimization conditions can be obtained. There are many example of thermal cycles analyzed wit FTT [31e51]. In the literature, some ecological and environmental criteria were proposed to evaluate actual thermal systems too. Angulo -Brown presented an ecological function [52] and it was improved by Yan [53]. This function was applied to Brayton cycles and some examples of it may be shown in Refs. [54e64]. Another criterion is exergetic sustainability index. This index enables us to evaluate sustainability range of thermal cycles. Exergetic sustainability index was researched by several authors in Refs. [49,65e76]. In this paper, MCFCeSCO2 Brayton heat engine is taken into account. Novelty of this research is to investigate the considered system by using ecological function and exergetic sustainability index. Purpose of this research is to design more ecological and less environmental harmful systems. The basic thermodynamic parameters including power output, energy and exergy efficiencies and exergy destructions are investigated as well as ecological function and exergetic sustainability index. It is tried to define the performance limits of the considered system. Results are obtained numerically and they are plotted in figures, finally, they are discussed and evaluated.
Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e9
Thermodynamic analysis Combined MCFC and supercritical CO2 Brayton heat engine is shown in Fig. 1. Heat rejected from the MCFC is used for heating working fluid of the Brayton cycle. Anode potential (Uan), cathode potential (Ucat), ohm overpotential (Uohm) and theoretical maximum potential (Ut) of MCFC, these potentials can be calculated as follows respectively [3]:
Uan ¼ 2:27 109 je
Enact;an RT
pH0:42 p0:17 p1 2 ;an CO2 ;an H2 O;an
Ucat ¼ 7:505 1010 je
(1)
Enact;cat RT
0:09 p0:43 O2 ;cat pCO2 ;cat
(2)
Uohm ¼ 0:5 104 je
3016
3
1 1 T923
0 1 0:5 pCO2 ;cat C RT BpH2 ;an pO2 ;cat ln@ Ut ¼ Ei þ A ne F pH2 ;an pCO2 ;an
(3)
(4)
where, j is the current density, pH2 ;an is partial pressure of hydrogen at the anode, pCO2 ;an is the partial pressure of carbon dioxide at the anode, pH2 O;an is the partial pressure of water at the anode, pO2 ;cat is the partial pressure of oxygen at the cathode, pCO2 ;cat is the partial pressure of carbon dioxide at the cathode, R is the universal gas constant, T is the operating temperature of the MCFC, Enact is the activation energy, F is the Faraday constant, ne is the number of electrons and Ui is the ideal standard potential.
Fig. 1 e a: MCFC e Brayton hybrid heat engine. b: Tes diagram of Brayton cycle. Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
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Dgo Ui ¼ ne F
(5)
Cell voltage is written by using eqs. (1)e(5) [3]: Ucell ¼ ðUt Uan Ucat Uohm Þ
(6) hB ¼ 1
Power and efficiency of the fuel cell are [3]: PC ¼ Ucell jA hC ¼
(7)
PC
(8)
DH_
Dh Ucell jA ne F
(10)
Heat exchange at the regenerator can be described as: Q_ r ¼ Kr ð1 εr ÞðT To Þ
Q_ h ¼ DH_ PC Q_ r
(11)
(21)
Q_ h ¼ Cεh ðT T5 Þ ¼ CðT3 T5 Þ
(13)
where C is the heat capacity and εh is the effectiveness of the hot side. T2 and T4 temperatures can be calculated by using compression (hcp ) and expansion (hex ) efficiencies. k1 T2s T1 T3 T4 T2S T3 p2 k ; hex ¼ ; ¼ ¼x¼ T2 T1 T3 T4s T1 T4S p1 T2S T1 þ T1 hcp
PB ¼ Q_ h Q_ l
(22)
ExdB ¼ To
_ Q l Q_ h Tl T
(23)
Exergy efficiency of any thermal cycle is rate energy efficiency to reversible (Carnot) efficiency or rate of power output to reversible power and it can be expressed for Brayton cycle as: hB PB ¼ hrev;B Prev;B
(24)
where hB;rev is: hrev;B ¼ 1
Tl T
(25)
reversible power for Brayton cycle can be obtained from eq (24) as:
(12)
Another heat input expression to the bottom cycle is shown in eq. (13):
T2 ¼
Q_ l ¼ Q_ h ð1 hB Þ
4B ¼
where, Kr is the heat conductance of the regenerator, εr is the regenerator effectiveness and To is the environment temperature. Heat input to the bottom cycle (SCO2 Brayton cycle) is written as eq. (12):
hcp ¼
Heat rejection from the Brayton engine is:
(9)
where, A is the area of the interconnect plate and Dh is the molar enthalpy change. Exergy destruction rate of fuel cell is [3]:
(20)
Exergy destruction rate of the Brayton engine is:
jADh DH_ ¼ ne F
ðT6 T1 Þ Q_ l ¼1 ðT3 T5 Þ Q_ h
Power output of the Brayton cycle is:
where DH is the maximum possible power from the fuel cell and it can be described as [3]:
ExdC ¼
For making easier of the calculations, a correlation between x and j can be obtained by using eqs. (12), (13) and (17). This correlation is plotted in Fig. 2. Energy efficiency of the Brayton cycle, under assumption of constant specific heats, is written as following:
Prev;B ¼
PB 4B
(26)
Power output, energy efficiency, exergy efficiency and exergy destruction rate of the hybrid system are described in eqs. (27)e(30) respectively.
(14)
!
T4 ¼ ðT3 hex ðT3 T4S ÞÞ
(15)
(16)
where k is ratio of specific heats and x is the isentropic temperature. T3, T5 and T6 are expressed in eqs. (17)e(19): T3 ¼ T5 ð1 εrc Þ þ εh T
(17)
T5 ¼ T4 εrc þ ð1 εrc ÞT2
(18)
T6 ¼ T2 εrc þ ð1 εrc ÞT4
(19)
where εrc is the recuparator effectiveness.
Fig. 2 e Isentropic temperature versus current density for SCO2 and air Brayton cycles.
Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e9
PH ¼ PC þ PB
(27)
hH ¼
PC þ PB DH_
(28)
4H ¼
PC þ PB Prev;C þ Prev;B
(29)
ExdH ¼ ExdC þ ExdB
(30)
After the basic thermodynamic parameters, environmental criteria may be explained. Fist criterion is exergetic sustainability index. Exergetic sustainability index is ratio of exergy output of the system to lost exergy that is described as difference of exergy input from the useful exergy output. This provides us information about sustainability of the considered system. Its physical meaning is that ratio of exergy output from the system, maximum power output of a heat engine, to the waste exergy that is not used by the system. It can be described as: esiH ¼
Prev;C þ Prev;B ΔG_ PH
5
Fig. 3 e Power density change with current density for SCO2 and air Brayton cycles.
(31)
Another criterion considered in this paper is ecological function. Ecological function is difference of power output and exergy destruction originated from the entropy generation. It provides an opportunity to maximize power output while reducing exergy destruction and this causes to decrease at the environmental impact of the researched system: EH ¼ ðPH Þ ExdH
(32)
Results and discussion Variables used in calculations of MCFC are; pH2 ;an ; pH2 O;an ; pCO2 ;an , pO2 ;cat; pCO2 ;cat ; pH2 O;cat are 0.6, 0.342, 0.058, 0.08, 0.08, 0.25 (atm) respectively, ne is 2, Eact,an is 53,500 (J mol2), Eact,cat is 77,300 (J mol2), F is 96,485 (C mol1), R is 8.314 (J mol1 K1), finally, Dg, Dh and T are 197000 (J mol1), 247430 (J mol1) and 923 (K) respectively [3,11,18,21,22,24]. Compressor, turbine efficiencies and effectiveness of recuperator for the SCO2 Brayton and air Brayton cycles are taken from ref. [27]. Compression efficiency, expansion efficiency and recuparator efficiency are assumed as 0.91, 0.94 and 0.98 for SCO2 Brayton cycle and 0.85, 0.90 and 0.92 for Air Brayton cycle respectively [27]. Finally, Kr and εr, εh, εrc, TL and To are 10 (W K1), 0.85, 0.95, 0.98, 300 (K) and 298.15 (K). In comparison of these two type of Brayton cycles, mass flows are assumed as same with each other and, according to this assumption, CSCO2 and CA are taken as 400 (W K1) and 475.47 (W K1). Relation between isentropic temperature and current density is shown in Fig. 2. Power density (p ¼ P/A), exergy density (exd ¼ Exd/A), ecological function density (e ¼ E/A), sustainability index, energy and exergy efficiencies are investigated according to current density and their curves are plotted in Figs. 3e7. Variations with p ecological function, exergetic sustainable index and h for the hybrid heat engine are shown in Figs. 8 and 9.
Fig. 4 e Energy efficiencies variations with current density for SCO2 and air Brayton cycles.
Power density values for MCFC, SCO2 and air Brayton cycles and hybrid heat engines are illustrated in Fig. 3. Main purpose of any heat engine or power generation system is to produce power output as high as possible. That's why, obtaining maximum power from these systems is crucial. It can be seen that hybrid systems, SCO2 Brayton cycle, air Brayton cycle and MCFC have optimum points. SCO2 e hybrid system gets it maximum value that is equal to 3101.13 (W m2) at j ¼ 4150 (A m2), MCFC and SCO2 Brayton cycle get their maximum values at j ¼ 3750 (A m2) and j ¼ 4350 (A m2), corresponding values to these optimum points are 1885.13(W m2) and 1251.07 (W m2) respectively. When, maximum points of SCO2 hybrid system and air-hybrid system are compared, SCO2 hybrid system is 5% more advantageous in terms of maximum power output than air hybrid system. Energy efficiencies curves are indicated in Fig. 4. Energy efficiency is ratio of acquired product that is mostly
Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
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Fig. 5 e Exergy efficiencies variations with current density for SCO2 and air Brayton cycles.
Fig. 6 e Exergy destruction densities according to current density for SCO2 and air Brayton cycles.
Fig. 7 e Variation of ecological function and exergetic sustainability index with current density for MCFCeSCO2 Brayton hybrid cycle.
Fig. 8 e Efficiency-power density curve for MCFCeSCO2 Brayton hybrid cycle.
Fig. 9 e Ecological function density and exergetic sustainability index changes with power density for MCFCeSCO2 Brayton hybrid cycle.
power or work output to fuel provided to the system. It means that one can produce much power with same fuel by using an energy efficient system compared with a system that has same capacity however less energy efficient one. As it is seen, hybrid systems and Brayton cycles have optimum points while MCFC has no optimum. Optimum points of the SCO2 hybrid system and SCO2 Brayton cycle are equal to 0.79 and 0.46 and corresponding current densities are 1150 (W m2) and 2300 (W m2). Maximum energy efficiencies of air hybrid system and air Brayton system correspond to 82.8% and 72.6% of SCO2 hybrid system and SCO2 Brayton cycle. Exergy efficiency represents how considered system is close to the ideal one. So, if exergy efficiency increases, irreversibilities existed in the system will be reduced. As it can be seen in Fig. 5, there is no optimum point for exergy efficiency of the MCFC while hybrid systems and Brayton cycles have. Optimum values of the SCO2 hybrid system and SCO2 Brayton cycles are 0.79 and 0.68 and their current densities at the maximum points are j ¼ 850 (W m2) and 2300 (W m2). Maximum exergy
Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110
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efficiencies of air hybrid system and air Brayton cycle are equal to 76.7% of SCO2 hybrid system and 72.7% of the SCO2 Brayton cycle. Exergy destruction rate shows us the lost work in the system resulting from the irreversibilities or entropy generation. According to Fig. 6, exergy destruction density values of considered systems increase with current density and there is no minimum. This means that current density is required to be as minimum as possible to obtain smaller exergy destruction values. However, air-hybrid system and air Brayton cycle have higher exergy destruction rates at the same current densities. Fig. 7 shows variation of e and esi with current density for the SCO2 hybrid system. e reaches its maximum that is equal to 650.795 (W m2) at j ¼ 1850 (A m2) and esi reaches its maximum at j ¼ 1350 (A m2) with 4.92 value. Fig. 8 can be called as performance curve of the SCO2 hybrid system. Current densities at maximum power and maximum energy efficiency are jP and jh respectively. In the design studies, current density is chosen as jh j jP. In Fig. 8, pmax is the maximum power density, ph is the power density at the maximum efficiency, hP is the efficiency at the maximum power and hmax is the maximum efficiency. As it shown, efficiency and power values should be chosen as hP h hmax and ph p pmax. hP is 0.58 and ph is 1166.3(W m2). If they are compared with their maximum values, hP is 73% of the maximum efficiency and ph is the 38% of the maximum power density. Changes of e and esi with power density for SCO2 hybrid system is plotted in Fig. 9. Where, emax is the maximum ecological function, ep is ecological function at the maximum power density, esip is the exergetic sustainability index at the maximum power density, esimax is the maximum exergetic sustainability index, pe is the power density at the maximum ecological function and pesi is the power density at the maximum exergetic sustainability index. ep, esip, pe, pesi are equal to 1443.97 (W m2), 2.96 and 3043.06 (W m2), 1837.27 (W m2), esip is 60% of the esimax, pe is equal to 59% of pmax and, finally, pesi is 44% of. pmax, however ep cannot be compared with emax, because of negative value of ep. It can be seen that je and jesi, which are current density at maximum ecological function and exergetic sustainability index, are between values of jh and jP. Power output value is bigger at the maximum ecological function than the maximum exergetic sustainability index and vice a versa is true for the energy efficiency. eh is ecological function at the maximum efficiency, esih is the exergetic sustainability index at the maximum efficiency, esimax is the maximum exergetic sustainability index, he is the energy efficiency at the maximum ecological function and hesi is the energy efficiency at the maximum exergetic sustainability index. eh, esih, he, hesi are equal to 526.72 (W m2), 4.88, 0.77 and 0.79. These values are equal to nearly 81%, 99%, 98% and 99% of their maximum values.
Conclusion This paper aims to investigate and optimize MCFCeSCO2 Brayton hybrid cycle with exergetic based ecological and sustainability criteria. MCFCeSCO2 Brayton hybrid system is optimized for power output, exergy destruction, energy and exergy efficiencies as well as criteria mentioned above. Ecological and sustainable operation conditions are described
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by using ecological function and exergetic sustainability index. Results show that ecological function should be chosen as objective function to obtain higher power output compared with exergetic sustainability index, however, exergy destruction density is bigger too. In spite of this, optimum ecological function represents the point where difference of power output and exergy destruction rate is the maximum. For the future studies, it is recommended that ecological function and exergetic sustainable index should be used for designing more environmental fuel cell-heat engine hybrid systems.
Acknowledgments The authors would like to thank the reviewers for their valuable comments, which have been utilized in improving the quality of the paper.
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Please cite this article in press as: Ac¸ıkkalp E, Ecologic and sustainable objective thermodynamic evaluation of molten carbonate fuel cellesupercritical CO2 Brayton cycle hybrid system, International Journal of Hydrogen Energy (2017), http://dx.doi.org/10.1016/ j.ijhydene.2016.12.110