Research ArticleOptimal Operation Conditions for a Methane Fuelled SOFCand Microturbine Hybrid System
Vincenzo De Marco Gaetano Florio and Petronilla Fragiacomo
Department of Mechanical Energy and Management Engineering University of Calabria Arcavacata Rende 87036 Cosenza Italy
Correspondence should be addressed to Petronilla Fragiacomo petronillafragiacomounicalit
Received 30 June 2015 Revised 15 October 2015 Accepted 18 October 2015
Academic Editor Wei-Hsin Chen
Copyright copy 2015 Vincenzo De Marco et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
The study of a hybrid system obtained coupling a methane fuelled gas microturbine (MTG) and a solid oxide fuel cell (SOFC)was performed The objective of this study is to evaluate the operation conditions as a function of the independent variables ofthe system which are the current density and fuel utilization factor Numerical simulations were carried out in developing a C++computer code in order to identify the preferable plant configuration and both the optimal methane flow and the current densityOperation conditions are able to ensure elasticity and the most suitable fuel utilization factor To confirm the reliability of themodels results of the simulations were compared with reference results found in literature
1 Introduction
The question of energy savings and optimization of resourcesis nowadays of primary importance in both economic andenvironmental fields In order to respect the Kyoto protocolit is important to invest in new forms of livelihood energy[1 2] The present work lies as part of these problems Anassigned hybrid system resulting from the coupling of a solidoxide fuel cell (SOFC) with a gas microturbine (MTG) wasanalyzed For this purpose a C++ code was developed so thatit was possible to define the optimal conditions of operationof the system as a function of the current density dfc of thefuel cell and the fuel utilization (119880119891) It has to be pointedout that only by developing such C++ code taking intoaccount both chemical and physical phenomena (ie balanceof power chemical reactions and change in the composition)was it possible to appreciate the difference in performance bycomparing different plant schemes Such calculations matchwith the current direction taken by the state of the art (ie thepresence of an afterburner in place of a direct stream fromthe SOFC stack to the turbine) Although it is still difficultto find experimental data to validate the model completelythis was subjected to comparison with anothermodel presentin the literature It is important to highlight that this kind
of approach can be easily adapted to other kinds of plantsonly by changing the parameters utilized and by correctlydefining the events considered In this specific case for theanalysis of the gas turbine the data plate of the MTGAnsaldo100 kW was taken as a reference as well as in [3ndash7] Thistype of system can reach values comparable to those of largesize from an efficiency point of view This is why manyresearchers have been working for years in order to assess themost appropriate type of application [8ndash11] Other types ofsimilar systems studied with the same approach are thosethat focus more on evaluating the potential for residentialcogeneration systems (SOFC-CHP) [12] those that evaluatecoupling between SOFC and gas turbine of greater power(SOFC-GT) [13ndash15] or those that take into account moltencarbonates fuel cell (MCFC) instead of SOFC [16ndash22] In thesame field specific SOFC-MTG can vary the nature of the fuel(which in this case is pure methane but which may be egsynthesis gas or biomass) [14 21ndash27] and there are also thosethat try despite the fact that the state-of-the-art technologyin question is not consolidated a first economic evaluation[27 28] Even the samemathematical model can see differentapproaches In this work for example a linear law is assumedas a function of temperature for the calculation of the currentdensity of anodic and cathodic exchange necessary for the
Hindawi Publishing CorporationJournal of Renewable EnergyVolume 2015 Article ID 508138 13 pageshttpdxdoiorg1011552015508138
2 Journal of Renewable Energy
calculation of activation losses while in other works this isconsidered constant [23] With regard to the current densitylimit valid for the calculation of losses due to concentrationin this paper we consider the same for cathode and anodewhile elsewhere in spite of slight differences of the resultsa diversification is operated [14] Another approach for thecalculation of the cell voltage is the use of a polynomialfunction of the current by which it calculates a referencevoltage and the next calculation of the deviation from thisvoltage due to the temperature the operating pressure andthe molars fractions of the different components [29] In thiscase from the definition of the limits of physical chemicaland technological achievements of different components theparameters ldquofreerdquo of the system and the range within whichthe values should vary were identified
2 System Configurations
The system used as reference in this work is a hybrid system(MTG + SOFC) described in [3] Here in addition to theSOFC and MTG there are a prereformer an afterburnerand an ejector in which methane is mixed with the gasrecirculation This type of system is capable of providing atthe design point an electric power to the axis equal to 428 kWdivided into 319 kW produced by the fuel cell and 109 kWby gas turbine The power spent by the two compressors(air and fuel) is respectively of 148 kW and 13 kW for anefficiency of 061 and a TIT of 1240K Table 1 shows the maintechnical and thermodynamic data of the gas turbine and thecell and themeaning of both streams andblocks present in thefollowing plant schemes In this work three different systemconfigurations were analyzed namely the ldquobase systemrdquo theldquosystem with prereformerrdquo and the ldquocomplete systemrdquo Inboth the second and the third configuration a componentis added with respect to the previous scheme Compared tothe system studied in [3] there is no ejector The workingpressure of the methane is assumed to be the same as thatof the SOFC
21 Base System Figure 1 shows the diagram of the basesystem The anode exhaust (in red) is divided into two partsthe left side exhaust is sent to the recirculation while the rightside flow enters the gas turbine This stream finally unifiesthe cathode exhaust to make its entry in the expander Theexit gas from the turbine reaches the heat exchanger whereit provides thermal energy to preheat the air drawn from theMTGcompressorThe ldquoregeneratedrdquo air (in black) then entersthe fuel cell from the cathode sideThe recirculation is mixedwith the pressurized methane (yellow) to enter then togetherthe anode of the fuel cell (green)
22 System with Prereformer The operation of the systemwith prereformer (Figure 2) differs with respect to the hybridsystem shown in Figure 1 only because of the presence of theprereformer In the latter component themixture ofmethaneand gas recirculation enters so that a part of the methane isconverted into hydrogen externally to the cell
Table 1 Basic parameters of the components of the hybrid systemand streams and blocks meaning in plant schemes
Turbomachineryconfiguration Radial
Compression ratio 39Compressor isentropicefficiency 075
Stream 1 Cold compressed air entering theheat exchanger
Stream 2 Hot compressed air entering thecathode
Stream 3 Uncompressed CH4Stream 4 Compressed CH4
Stream 5 CH4 and anode outlet mixtureentering the anode
Stream 6 Anode outletStream 7 Anode outlet mixing with CH4
Stream 8 Anode outlet mixing with cathodeoutlet
Stream 9 Cathode outletStream 10 Mixture entering the turbine
Stream 11 Turbine outlet entering the heatexchanger
Stream 12 Heat exchanger outlet
Stream 13 CH4 and anode outlet mixtureentering the prereformer
Stream 14 Prereformer outlet entering theanode
Stream 15 Afterburner outlet entering theturbine
Stream 16 Mixer outletBlock A Air compressorBlock B TurbineBlock C AlternatorBlock D CH4 compressorBlock E Heat exchangerBlock F InverterBlock G Solid oxide fuel cellBlock H PrereformerBlock I AfterburnerBlock J Mixer
Journal of Renewable Energy 3
A B C
D
E
G
A C
F
SOFC DcAc
12
11
3
1 4 76
89
10
5
2
Figure 1 Technical scheme of the base system
A CSOFC
DcAc
14
H
Figure 2 Technical scheme of the system with prereformer
23 Complete System In the case of complete system(Figure 3) the difference from the previous configurationis that the anode exhaust not sent to recirculation is sentdownstream of SOFC where an afterburner (or postcom-bustor) provides for oxidization of the hydrogen and carbonmonoxide residuesThe cathode exhaust provides the oxygento the afterburner while the products of the postcombustorconstitute the working fluid of the expander of MTG Therest of the system is entirely analogous to the previousconfigurations
3 Mathematical Model
Here the procedures used for the calculation of the mainvariables of the hybrid system as a function of 119880119891 anddfc are described recirculation flow temperatures of mix-ing between recirculation and methane input anode celloperation of afterburning and of inlet air to the cathodepercentage of methane converted from the prereformer andvarious performance parameters that is power output and
efficiency Calculation of flow recirculation we calculate theair recirculation rate according to
119899ric =119899H2 ric119891H2
(1)
where the calculation of 119899H2 ric is done using
119899H2 ric =
119911119880119891 minus 3119899CH4
(1 + 03119891CO119891H2
)
(2)
where 119911 is given by
119911 =
dfc sdot 1198601198912119865
(3)
So once 119880119891 and dfc are assigned the recirculation flow istherefore uniquely defined Calculation of the temperature ofmixing between recirculation anodic and pressurized methane(119879mix block A in Figure 5) a mixture formed by gas recircu-lation and methane out from the compressor enters the fuel
4 Journal of Renewable Energy
A CSOFC
15I
DcAc
Figure 3 Technical scheme of complete system
Electricalpower cathode
SOFC
power (Tfc )
power (Tcat)power (Tan)Inlet anode Inlet cathode
power (Tfc )
sum power of reactions
Outlet anode Outlet
Figure 4 Flow input power and output from the fuel cell
cell The anode inlet temperature is calculated by attempts bythe balance of thermal power expressed by
When (4) reaches convergence the same 119879mix represents theunknown searchedCalculation ofmoles ofmethane convertedfrom the prereformer (119909 block A in Figure 5) this parameteris obtained by attempts starting from 119909 of hypotheses toobtain the one that satisfies the power balance to prereformerInside the prereformer coupled reactions of steam reforming
reaction and that coupled to it of Water Gas Shift Reaction(WGSR) occur expressed by
CH4 +H2Olarrrarr 3H2 + CO (5)
CO +H2Olarrrarr CO2 +H2 (6)
The ratio between (6) and (5) speed of reaction is unknownWe proceeded by calculating the speed of reactions for theoperating temperatures of the SOFC and for different per-centages of reforming using as a parameter the convergenceof equilibrium constants defined by
119870ref =[H2]3sdot [CO]
[CH4] sdot [H2O]1198752 (7)
119870shif =[H2] sdot [CO2][CO] sdot [H2O]
(8)
Journal of Renewable Energy 5
New Tcatlowast
New
Tcatlowast
Calc dr =minus
middot 100
Calc dr =Tcat
lowast minus TcatTcat
lowast
A
B
C
D
E
F
Tan = Tmix
x gt nCH4
If dr gt01
If dr gt 01
middot 100
Stop
Tmix lt 873
Tan = 873
Tcatlowast= Tcat
HYP
If
If
Recursionand new attempt
( )
( )Tfc Tfclowast
Tfclowast
Tfclowast
minusTfc Tfclowast
TfcTfclowast
Figure 5 Flow diagram for the calculation of the parameters of the complete system
and comparing (7) and (8) with the values of the equilibriumconstants calculated as a function of the temperature accord-ing to
Table 2 shows the values of the constants relating to (9) forthe two reactionsThe average ratio between speed of (6) andspeed of (5) is equal on average to about 03 Equations (7) and(8) are taken from [31] while (9) is taken from [30]Thereforein the calculations of the mass balance and thermal powerbalance we consider that for each mole of CH4 converted03 moles of H2 is also generated from the conversion of COproduced by (6) In light of this approximation the powerbalance to the prereformer appears to be expressed by
Table 2 Values for the calculation of the equilibrium constant 119870[30]
Reforming ShiftingA 26312 sdot 10
minus11547 sdot 10
minus12
B 12406 sdot 10minus7
minus2574 sdot 10minus8
C minus22523 sdot 10minus4
46374 sdot 10minus5
D 512749 sdot 10minus1
minus3915 sdot 10minus2
E minus66139488 13209723
Operating Temperature of the Cell (119879fc Block C in Figure 5)An iterative method for the calculation of the operatingtemperature of the cell is used as well We start froma temperature of attempt until the convergence of powerbalance is reached This last is expressed by
119899CH4
sdot ℎCH4
(119879an) + 119899H2Oifc
sdot ℎH2O (119879an) + 119899H
2 ifcsdot (119879an)
+ 119899COifcsdot ℎCO (119879an) + 119899CO
2 ifcsdot ℎCO
2
(119879an) + 119899O2 ifc
sdot ℎO2
(119879cat) + 119899N2
sdot ℎN2
(119879cat) minus 119899CH4
sdot Δℎref
minus 03119899CH4
sdot Δℎshif minus 119911 sdot ΔℎH2O
= 119899H2Oofc
sdot ℎH2O (119879fc) + 119899H
2ofcsdot (119879fc) + 119899COofc
sdot ℎCO (119879fc) + 119899CO2ofcsdot ℎCO
2
(119879fc) + 119899O2ofc
sdot ℎO2
(119879fc) + 119899N2
sdot ℎN2
(119879fc) +
(11)
6 Journal of Renewable Energy
It is interesting to observe graphically the power flow ofFigure 4 in which the contributions present in (11) are visibleIt is nowpossible at this stage to calculate the power generatedby the cell through
119888 = 119881 sdot 119868 (12)
To calculate 119868 the following equation is used
119868 = dfc sdot 119860119891 (13)
119881 is obtained by
119881 = 1198810 minus 119881Nernst minus 119881att minus 119881ohm minus 119881conc (14)
while (15) is used to calculate 1198810
1198810 =minusΔ1198660
2119865 (15)
119881Nernst is given by
119881Nernst =119877119879
2119865ln(
119891H2O
119891H2
sdot 119891O2
05sdot 11987505) (16)
119881att is provided by
119881act = 119881act119886
+ 119881act119888
(17)
To calculate 119881act119886
we resort to
119881act119886
= (119877119879
119865) sinhminus1 ( dfc
21198940119886
) (18)
Analogous calculation of 119881act119888
results by
119881act119888
= (119877119879
119865) sinhminus1 ( dfc
21198940119888
) (19)
Once losses for activation have been defined we calculatethose for concentration 119881conc by
119881conc = (119877119879
119865) ln(1 minus dfc
119894119897) (20)
The voltage loss due to the ohmic resistance is obtained by
119881ohm = dfc sdot4
sum
119894=1
119871 119894
120590119894
(21)
From (12) to (15) are taken from [3] whereas the equationsin (16) to (21) are taken from [4] Calculation of afterburningtemperature (block D in Figure 5) once it has left the cell thegas mixture reaches a postcombustor Here since the oxida-tion of both hydrogen and carbon monoxide still present inthe anode exhaust the temperature of the gas rises furtherThen the following occur
H2 +1
2O2 997888rarr H2O (22)
CO + 12O2 997888rarr CO2 (23)
By varying 119879pc the balance of thermal power is solvedexpressed by
119899H2 ipcsdot ℎH2
(119879fc) + 119899H2Oipc
sdot ℎH2O (119879fc) + 119899COipc
sdot ℎCO (119879fc) + 119899CO2 ipcsdot ℎCO
2
(119879fc) + 119899O2 ipc
sdot ℎO2
(119879fc) + 119899N2 ipcsdot ℎN2
(119879fc)
minus 120578comb [(119899H2 ipcsdot ΔℎH
2O) minus (119899COipc
sdot ΔℎCO2
)]
= 119899H2Oopc
sdot ℎH2O (119879pc) + 119899CO
2opcsdot ℎCO
2
(119879pc)
+ 119899O2opcsdot ℎO2
(119879pc) + 119899N2 ipcsdot ℎN2
(119879pc)
(24)
Once 119879pc is known which also corresponds to the TIT sincewe know the isentropic efficiency of the expander MTG wecan easily calculate the temperature of the turbine outlet (119879outblock E in Figure 5) by
119879out = TIT minus 120578is (TIT minus 119879is) (25)
Calculation of the inlet air temperature at the cathode (119879catblock F in Figure 5) gas mixture of known composition andtemperature 119879out once expanded is sent to a countercurrentheat exchanger (or regenerator) Here as the hot fluid andas the cold respectively the mixture under examination andthe outlet air from the compressor (at a flow rate equal to0808Kgs and at a temperature of 404K) enter The balanceequation of thermal power into the regenerator is expressedby
It starts from 1198791198901 attempted and the calculation is iterateduntil (26) is satisfied 1198791198901 represents the temperature at whichthe hot gases exiting the regenerator give part of their thermalpower to cogeneration purposes Once this first phase iscompleted the calculation of 119879cat through (27) is effected
Thus after calculating 119879cat the circuit is completely definedAt the following iteration this temperature 119879cat is the inputfor the calculation of 119879fc The cycle continues until all the
Journal of Renewable Energy 7
parameters arrive at convergence Then the evaluation ofperformance parameters is made as follows
Useful Power of the Cell Calculation (uc) Consider
Gas Turbine Useful Power Calculation (tg) Consider
tg = ut minus ac (31)
where
ut = 119905 sdot Δℎ (32)
Gas Turbine Efficiency Calculation (120578tg) Consider
120578tg =tg
CH4
sdot LHVCH4
(33)
The efficiency and useful power of the entire system are thencalculated as the sum of efficiency and useful power of SOFCandMTGWe then calculate the cogeneration indices that isIRE
IRE = 1 minustot
SI120578SI + cog (34)
and the thermal limit LT
LT =cog sdot 120578term
tot (35)
It was assumed that the heat available downstream of theregenerator was transferable with an efficiency of 40 to athermodynamic cycle downstream to calculate the cogener-ative values The procedure described already is summarizedin Figure 5
4 Constraints Definition
ldquoSettingrdquo defines a given combination of parameters dfc and119880119891 with which it is possible to operate the hybrid systemTherefore the set of all the possible settings by the rangewithin which the parameters themselves can vary is defined(Table 1) By defining the constraints we proceed to identifythe settings that are eligible for a given value of the flowof methane so as to adequately assess the elasticity designconnected to the same flow Steam to Carbon Ratio (STCR)the lower limit of Steam toCarbonRatio is the first restrictionto be taken into account defined as
STCR =119899H2O
119899CO + 119899CH4
(36)
The said parametermust remain above 2 In the event that thislimit is not respected the humidification of the anodemay notbe satisfactory and itmay cause cracking of bothmethane andcarbon dioxide molecules according to the reactions
CH4 997888rarr C + 2H2 (37)
CO2 997888rarr C +O2 (38)
Consequently we face the catalyst deactivation caused by thepresence of carbonaceous deposits
Constraint on Maximum Current Density The methane isconverted to hydrogen by (5) and (6) Given the assumptionspreviously made on the kinetics of these reactions we havethat the total conversion of one mole of methane per secondgives rise to 33 moles of hydrogen per second Simultane-ously according to (3) 119911 moles of hydrogen per second isinstead consumed Thus the consumption of hydrogen isdirectly proportional to the current density Therefore thesettings that provide a value of 119911 higher with respect tohydrogen product are considered ineligible
Constraints on the Operating Temperature of the Fuel Cell(119879fc) and the Turbine Inlet Temperature (119879119868119879) Constraintsrelating to temperature are the last to be taken into accountWe excluded the settings that generate temperatures of thestack higher than typical operating temperatures of SOFCsand have turbine inlet temperatures above 1250K (currenttechnological limit of MTG) Thus we summarize the con-ditions as follows
(a) 873K lt 119879fc lt 1200K(b) TIT lt 1250K
5 Results
In this section we proceed to the choice of the optimalconfiguration with which the hybrid system works and thento define the methane flow and the operative current densityThe next step is sensitivity analysis of the main parametersat varying 119880119891 whereas at the end a first validation ofthe calculation model is operated Selection of the optimalconfiguration the optimum configuration is that of completesystem This choice stems from the following reasoningAccording to (2) recirculation flow decreases at increasing119880119891 and the recirculation being at a temperature higher thancompressed methane this implies a lowering of 119879mix whichthen propagates on all operating parameters of the plantusing as a parameter to control the fall percentage 119879fc atvarying 119880119891 defined by
See Tables 3 and 4In the case of the base system the fall of temperature is
higher than 5 This is considered excessive By comparing
8 Journal of Renewable Energy
Table 3 Fall of temperature for increasing 119880119891 for base system
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 96392500 082 9137 521
Table 4 Fall of temperature for increasing 119880119891 for system withprereformer
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 94552500 082 9113 366
Table 5 Comparison between the gas turbine power plant withprereformer and complete system for dfc = 2500Am2
119880119891 System with prereformer Complete system081 1011 16674082 9238 15487083 8302 14483
Tables 3 and 4 it is evident how for homologous settingsin the case of system with prereformer the condition hasimproved Having higher temperatures with lower values 119880119891implies that a significant part of the fuel is not properlyused a phenomenon that has an impact on the values ofgas turbine power Therefore to remedy this gap is necessaryto insert an afterburner downstream of the fuel cell so thatthe configuration of the complete system becomes necessaryTable 5 shows how for homologous conditions the completesystem ensures a significant increase of the gas turbine power
Definition of Optimum Operating Conditions The optimumoperating conditions that is flow ofmethane and the currentdensity to operate with are chosen using design flexibility asthe criterion The model developed has been applied to thecalculation of the conditions resulting from three differentvalues of flow rate of methane low (119887 = 0012 kgs)medium (119898 = 0015 kgs) and high (119886 = 0018 kgs)In the case of high flow rate of methane there is no settingcompatible with all the constraints In contrast from acomparison between Tables 6(a) and 6(b) it is shown thatthe medium flow rate ensures greater design flexibility thusresulting in a specific value (asterisks are the settings eligible)Table 6(b) shows how for dfc = 2900Am2 there is agreater choice of the possible settings that satisfy all theconstraints outlined above so that this value is identified asthe operating current density and is used in the followingsensitivity analysis
Sensitivity of Operating Parameters and Performance at Vary-ing 119880119891 A sensitivity analysis is performed to determine theeffect of varying 119880119891 on the operating parameters and perfor-mance According to (2) the recirculation flow decreases atincreasing 119880119891 (first effect) Consequently all operating tem-peratures of the plant should decrease However the decreaseof recirculation flow implies a greater flow to the afterburner
Table 6 Plan of the possible settings for low and medium flow rateof methane
Figure 6 Percentage of prereforming at varying 119880119891
1000
1050
1100
1150
1200
1250
1300
T (K
)
076 077 078 079 080 081 082075
TIT (
Uf (mdash)
dfc = 2900 Am2)
Figure 7 TIT at varying 119880119891
as well (second effect) so that temperatures should increaseThe first effect prevails on the second one Therefore theoverall effect is a lowering of all operating temperatures of thehybrid system Consequently the temperature being lowerto keep the anode inlet temperature at the desired value aninferior amount of methane flow has to be reformed beforeentering the cellThus the percentage of reforming decreasesas Figure 6 shows Figure 7 owing to the already describedeffects shows how the temperature at the turbine inletmonotonically decreases and the turbogas power dependingon the TIT (TIT decrease means a decreasing in Δℎ thus areduction in useful power according to (31) and (32)) thismeans also a decreasing in terms of MTG power as one canobserve in Figure 8 Instead a nonmonotonous trend is thatconcerning the power of the cell In fact this is affected forlow values of 119880119891 by a prereforming effect which changesthe composition in the anode input (reactions (5) and (6))Therefore according to (16) the composition change meansthat the percentage of reforming decreases while Nernst-losses increase causing an overall power decrease in thestack Therefore when it is no longer necessary to reformthe Nernst-loss decreases with decreasing temperature sothat the power of the cell starts growing (Figure 9) Finally
140
150
160
170
180
190
200
P (k
W)
076 077 078 079 080 081 082075
MTG power (kW)
Uf (mdash)
Figure 8 Turbogas power at varying 119880119891
075 076 077 078 079 080 081 082
Fuel cell power (kW)
360
361
362
363
364
365
366
367
368
369
370
P (k
W)
Uf (mdash)
Figure 9 Fuel cell power at varying 119880119891
it is interesting to note that with increasing119880119891 while overallperformance parameters decrease there is an increase in theindex IRE (Figure 10) whereas the thermal limit remainsnearly constant
6 Discussion
61 First Validation of the Calculation Model A first testingof the model calculation was carried out both of a qualitativeand of a quantitative nature The ldquotrendrdquo of some fundamen-tal parameters with respect to developments known from theliterature was evaluated and the results obtained here werecompared with those calculated in [3]
62 Qualitative Validation First for purpose of qualitativemodel validation the data obtained were compared for thesame 119880119891 for different values of dfc As we expected Table 7shows that an increase of the current density causes anincrease of the operating temperature of the hybrid systemand consequently an increase in the percentage of methaneon which it performs the prereforming Table 8 shows that
10 Journal of Renewable Energy
075 076 077 078 079 080 081 08205
151520253035404550
()
IREThermal limit
dfc = 2900 Am2
Uf (mdash)
Figure 10 IRE (blue) and LT (red) at varying 119880119891
A CSOFC
DcAc
J16
Figure 11 Hybrid system studied in [3]
with the increase of dfc both the cell (despite an increasein voltage losses) and the gas turbine power rise the secondbeing directly dependent on the turbine inlet temperature
63 Quantitative Validation To end the first validationprocess the model was applied to the system of Figure 15studied in [3] and results were compared In [3] the methaneis compressed to 30 bars instead of the operating pressureof the MTG and then joined in a mixer and blend withassociated losses from the anode recirculation The mixer isthe only difference compared to the complete system Thethermodynamic modeling of the mixer and of the ejectorinside it would be very complex In homologous conditionsthe results turn out better for the complete system (consistentwith the physical principles) Thus one objective was toevaluate in a first approximation how the ejector affects thelosses using equivalent useful area as a parameter This isdefined as the percentage of usable area of Figure 3 hybridsystem compared with that of Figure 11 (without ejector)such that in homologous operating conditions both systemsproduce the same power The results are as shown in Table 9
It is seen that when the area is reduced up to 85 of thegiven ldquoplaterdquo the relative difference between the referencedata and the data provided by the model remains around 1thus lending credibility to the mathematical model describedin this paper
7 Conclusions
The objective set at the beginning was to define the optimalconditions of operation of the hybrid system by developinga C++ code and to evaluate the suitability of this approachwith the physical and chemical process present inside theSOFC-MTGplant In the first instancewe see that the optimalconfiguration of the hybrid system is that of the completesystem This ensures both a satisfactory temperature man-agement and good values of gas turbine power The flow rateof methane is excellent given the guaranteed high designflexibility which is defined as 119898 that is 0015 kgs Forthe said value of the flow rate of methane current densitythat ensures the best compromise between performance anddegrees of freedom to the designer (varying 119880119891 eligible
Journal of Renewable Energy 11
Table 7 Operating parameters in equal value 119880119891 for different dfc
dfc [Am2] 119880119891 Voltage [V] Voltage losses [V] uc [kW] tg [kW] tot [kW]2900 082 06788 05058 36278 14128 504063000 082 06619 05227 36596 18078 54674
Table 9 Comparison of the data obtained with the model andexperimental data studied by evaluating an equivalent useful areaequal to 85 of the effective area (dfc = 3200Am2)
Model data Reference data Relative difference[]
Hybrid systempower [kW] 43147 428 080
Fuel cell power[kW] 32052 319 047
Gas turbinepower [kW] 11095 109 176
Hybrid systemefficiency [kW] 062 061
Fuel cellefficiency [kW] 046 045
Gas turbineefficiency [kW] 016 016
between 075 and 082) is that of 2900Am2 The last stepis the choice of operating 119880119891 which may vary dependingon the objective it set out choosing a low 119880119891 if there isdirected towards energy optimization 119880119891 high if the goalis to maximize the cogeneration yield and a medium 119880119891 ifseeking a compromise between the two requirements Sincesystems of this type are still under study of the 3 optionsdescribed above at the current state of the art it seemsto make sense to focus on energy optimization and whenconsolidated on the market there will be consideration laterwith the economic scenario of the moment This factor isclosely related to the evaluation of the investment fromthe perspective of cogeneration The developed C++ codematches with both the state of the art and reference datataken from the literature suggesting the suitability of thisapproach to evaluate and describe SOFC-MTG and otherkinds of plants
Nomenclature
119860119891 Useful area of the fuel cell [m2]
119888119901 Specific heat at constant pressure[J(molsdotK)]
119888119901119898 Average specific heat of the mixture in the
course of expansion [J(kgsdotK)]119888V Specific heat at constant volume
[J(molsdotK)]dfc Current density with which it operates
within the fuel cell [Am2]119865 Faraday constant that is 96485 [Cmol]119891CO Molar fraction of carbon monoxide
dimensionless119891H2
Molar fraction of hydrogen dimensionlessℎair Molar enthalpy of the air [Jmol]ℎCH4
Molar enthalpy of methane [Jmol]ℎCO Molar enthalpy of carbon monoxide
[Jmol]ℎCO2
Molar enthalpy of carbon dioxide [Jmol]ℎH2
Molar enthalpy of hydrogen [Jmol]ℎH2O Molar enthalpy of the water vapor [Jmol]
ℎO2
Molar enthalpy of oxygen [Jmol]ℎN2
Molar enthalpy of nitrogen [Jmol]119868 Operation current [A]IRE ldquoEnergy saving indexrdquo dimensionless1198940119886 Current density exchange anode side
[Am2]1198940119888 Current density exchange cathode side
[Am2]119894119897 Limit current density [Am2]119870ref Equilibrium constant of the reaction of
steam reforming dimensionless119870shif Equilibrium constant of the reaction of
Water Gas Shift Reaction dimensionless Air mass flow rate [kgs]CH
4
Methane mass flow rate [kgs]119905 Mass flow rate in the expander [kgs]119899CH4
Electric power obtained through theelectrochemical reaction of waterformation [W]
ac Power absorbed by the compressor gasturbine system [W]
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
2 Journal of Renewable Energy
calculation of activation losses while in other works this isconsidered constant [23] With regard to the current densitylimit valid for the calculation of losses due to concentrationin this paper we consider the same for cathode and anodewhile elsewhere in spite of slight differences of the resultsa diversification is operated [14] Another approach for thecalculation of the cell voltage is the use of a polynomialfunction of the current by which it calculates a referencevoltage and the next calculation of the deviation from thisvoltage due to the temperature the operating pressure andthe molars fractions of the different components [29] In thiscase from the definition of the limits of physical chemicaland technological achievements of different components theparameters ldquofreerdquo of the system and the range within whichthe values should vary were identified
2 System Configurations
The system used as reference in this work is a hybrid system(MTG + SOFC) described in [3] Here in addition to theSOFC and MTG there are a prereformer an afterburnerand an ejector in which methane is mixed with the gasrecirculation This type of system is capable of providing atthe design point an electric power to the axis equal to 428 kWdivided into 319 kW produced by the fuel cell and 109 kWby gas turbine The power spent by the two compressors(air and fuel) is respectively of 148 kW and 13 kW for anefficiency of 061 and a TIT of 1240K Table 1 shows the maintechnical and thermodynamic data of the gas turbine and thecell and themeaning of both streams andblocks present in thefollowing plant schemes In this work three different systemconfigurations were analyzed namely the ldquobase systemrdquo theldquosystem with prereformerrdquo and the ldquocomplete systemrdquo Inboth the second and the third configuration a componentis added with respect to the previous scheme Compared tothe system studied in [3] there is no ejector The workingpressure of the methane is assumed to be the same as thatof the SOFC
21 Base System Figure 1 shows the diagram of the basesystem The anode exhaust (in red) is divided into two partsthe left side exhaust is sent to the recirculation while the rightside flow enters the gas turbine This stream finally unifiesthe cathode exhaust to make its entry in the expander Theexit gas from the turbine reaches the heat exchanger whereit provides thermal energy to preheat the air drawn from theMTGcompressorThe ldquoregeneratedrdquo air (in black) then entersthe fuel cell from the cathode sideThe recirculation is mixedwith the pressurized methane (yellow) to enter then togetherthe anode of the fuel cell (green)
22 System with Prereformer The operation of the systemwith prereformer (Figure 2) differs with respect to the hybridsystem shown in Figure 1 only because of the presence of theprereformer In the latter component themixture ofmethaneand gas recirculation enters so that a part of the methane isconverted into hydrogen externally to the cell
Table 1 Basic parameters of the components of the hybrid systemand streams and blocks meaning in plant schemes
Turbomachineryconfiguration Radial
Compression ratio 39Compressor isentropicefficiency 075
Stream 1 Cold compressed air entering theheat exchanger
Stream 2 Hot compressed air entering thecathode
Stream 3 Uncompressed CH4Stream 4 Compressed CH4
Stream 5 CH4 and anode outlet mixtureentering the anode
Stream 6 Anode outletStream 7 Anode outlet mixing with CH4
Stream 8 Anode outlet mixing with cathodeoutlet
Stream 9 Cathode outletStream 10 Mixture entering the turbine
Stream 11 Turbine outlet entering the heatexchanger
Stream 12 Heat exchanger outlet
Stream 13 CH4 and anode outlet mixtureentering the prereformer
Stream 14 Prereformer outlet entering theanode
Stream 15 Afterburner outlet entering theturbine
Stream 16 Mixer outletBlock A Air compressorBlock B TurbineBlock C AlternatorBlock D CH4 compressorBlock E Heat exchangerBlock F InverterBlock G Solid oxide fuel cellBlock H PrereformerBlock I AfterburnerBlock J Mixer
Journal of Renewable Energy 3
A B C
D
E
G
A C
F
SOFC DcAc
12
11
3
1 4 76
89
10
5
2
Figure 1 Technical scheme of the base system
A CSOFC
DcAc
14
H
Figure 2 Technical scheme of the system with prereformer
23 Complete System In the case of complete system(Figure 3) the difference from the previous configurationis that the anode exhaust not sent to recirculation is sentdownstream of SOFC where an afterburner (or postcom-bustor) provides for oxidization of the hydrogen and carbonmonoxide residuesThe cathode exhaust provides the oxygento the afterburner while the products of the postcombustorconstitute the working fluid of the expander of MTG Therest of the system is entirely analogous to the previousconfigurations
3 Mathematical Model
Here the procedures used for the calculation of the mainvariables of the hybrid system as a function of 119880119891 anddfc are described recirculation flow temperatures of mix-ing between recirculation and methane input anode celloperation of afterburning and of inlet air to the cathodepercentage of methane converted from the prereformer andvarious performance parameters that is power output and
efficiency Calculation of flow recirculation we calculate theair recirculation rate according to
119899ric =119899H2 ric119891H2
(1)
where the calculation of 119899H2 ric is done using
119899H2 ric =
119911119880119891 minus 3119899CH4
(1 + 03119891CO119891H2
)
(2)
where 119911 is given by
119911 =
dfc sdot 1198601198912119865
(3)
So once 119880119891 and dfc are assigned the recirculation flow istherefore uniquely defined Calculation of the temperature ofmixing between recirculation anodic and pressurized methane(119879mix block A in Figure 5) a mixture formed by gas recircu-lation and methane out from the compressor enters the fuel
4 Journal of Renewable Energy
A CSOFC
15I
DcAc
Figure 3 Technical scheme of complete system
Electricalpower cathode
SOFC
power (Tfc )
power (Tcat)power (Tan)Inlet anode Inlet cathode
power (Tfc )
sum power of reactions
Outlet anode Outlet
Figure 4 Flow input power and output from the fuel cell
cell The anode inlet temperature is calculated by attempts bythe balance of thermal power expressed by
When (4) reaches convergence the same 119879mix represents theunknown searchedCalculation ofmoles ofmethane convertedfrom the prereformer (119909 block A in Figure 5) this parameteris obtained by attempts starting from 119909 of hypotheses toobtain the one that satisfies the power balance to prereformerInside the prereformer coupled reactions of steam reforming
reaction and that coupled to it of Water Gas Shift Reaction(WGSR) occur expressed by
CH4 +H2Olarrrarr 3H2 + CO (5)
CO +H2Olarrrarr CO2 +H2 (6)
The ratio between (6) and (5) speed of reaction is unknownWe proceeded by calculating the speed of reactions for theoperating temperatures of the SOFC and for different per-centages of reforming using as a parameter the convergenceof equilibrium constants defined by
119870ref =[H2]3sdot [CO]
[CH4] sdot [H2O]1198752 (7)
119870shif =[H2] sdot [CO2][CO] sdot [H2O]
(8)
Journal of Renewable Energy 5
New Tcatlowast
New
Tcatlowast
Calc dr =minus
middot 100
Calc dr =Tcat
lowast minus TcatTcat
lowast
A
B
C
D
E
F
Tan = Tmix
x gt nCH4
If dr gt01
If dr gt 01
middot 100
Stop
Tmix lt 873
Tan = 873
Tcatlowast= Tcat
HYP
If
If
Recursionand new attempt
( )
( )Tfc Tfclowast
Tfclowast
Tfclowast
minusTfc Tfclowast
TfcTfclowast
Figure 5 Flow diagram for the calculation of the parameters of the complete system
and comparing (7) and (8) with the values of the equilibriumconstants calculated as a function of the temperature accord-ing to
Table 2 shows the values of the constants relating to (9) forthe two reactionsThe average ratio between speed of (6) andspeed of (5) is equal on average to about 03 Equations (7) and(8) are taken from [31] while (9) is taken from [30]Thereforein the calculations of the mass balance and thermal powerbalance we consider that for each mole of CH4 converted03 moles of H2 is also generated from the conversion of COproduced by (6) In light of this approximation the powerbalance to the prereformer appears to be expressed by
Table 2 Values for the calculation of the equilibrium constant 119870[30]
Reforming ShiftingA 26312 sdot 10
minus11547 sdot 10
minus12
B 12406 sdot 10minus7
minus2574 sdot 10minus8
C minus22523 sdot 10minus4
46374 sdot 10minus5
D 512749 sdot 10minus1
minus3915 sdot 10minus2
E minus66139488 13209723
Operating Temperature of the Cell (119879fc Block C in Figure 5)An iterative method for the calculation of the operatingtemperature of the cell is used as well We start froma temperature of attempt until the convergence of powerbalance is reached This last is expressed by
119899CH4
sdot ℎCH4
(119879an) + 119899H2Oifc
sdot ℎH2O (119879an) + 119899H
2 ifcsdot (119879an)
+ 119899COifcsdot ℎCO (119879an) + 119899CO
2 ifcsdot ℎCO
2
(119879an) + 119899O2 ifc
sdot ℎO2
(119879cat) + 119899N2
sdot ℎN2
(119879cat) minus 119899CH4
sdot Δℎref
minus 03119899CH4
sdot Δℎshif minus 119911 sdot ΔℎH2O
= 119899H2Oofc
sdot ℎH2O (119879fc) + 119899H
2ofcsdot (119879fc) + 119899COofc
sdot ℎCO (119879fc) + 119899CO2ofcsdot ℎCO
2
(119879fc) + 119899O2ofc
sdot ℎO2
(119879fc) + 119899N2
sdot ℎN2
(119879fc) +
(11)
6 Journal of Renewable Energy
It is interesting to observe graphically the power flow ofFigure 4 in which the contributions present in (11) are visibleIt is nowpossible at this stage to calculate the power generatedby the cell through
119888 = 119881 sdot 119868 (12)
To calculate 119868 the following equation is used
119868 = dfc sdot 119860119891 (13)
119881 is obtained by
119881 = 1198810 minus 119881Nernst minus 119881att minus 119881ohm minus 119881conc (14)
while (15) is used to calculate 1198810
1198810 =minusΔ1198660
2119865 (15)
119881Nernst is given by
119881Nernst =119877119879
2119865ln(
119891H2O
119891H2
sdot 119891O2
05sdot 11987505) (16)
119881att is provided by
119881act = 119881act119886
+ 119881act119888
(17)
To calculate 119881act119886
we resort to
119881act119886
= (119877119879
119865) sinhminus1 ( dfc
21198940119886
) (18)
Analogous calculation of 119881act119888
results by
119881act119888
= (119877119879
119865) sinhminus1 ( dfc
21198940119888
) (19)
Once losses for activation have been defined we calculatethose for concentration 119881conc by
119881conc = (119877119879
119865) ln(1 minus dfc
119894119897) (20)
The voltage loss due to the ohmic resistance is obtained by
119881ohm = dfc sdot4
sum
119894=1
119871 119894
120590119894
(21)
From (12) to (15) are taken from [3] whereas the equationsin (16) to (21) are taken from [4] Calculation of afterburningtemperature (block D in Figure 5) once it has left the cell thegas mixture reaches a postcombustor Here since the oxida-tion of both hydrogen and carbon monoxide still present inthe anode exhaust the temperature of the gas rises furtherThen the following occur
H2 +1
2O2 997888rarr H2O (22)
CO + 12O2 997888rarr CO2 (23)
By varying 119879pc the balance of thermal power is solvedexpressed by
119899H2 ipcsdot ℎH2
(119879fc) + 119899H2Oipc
sdot ℎH2O (119879fc) + 119899COipc
sdot ℎCO (119879fc) + 119899CO2 ipcsdot ℎCO
2
(119879fc) + 119899O2 ipc
sdot ℎO2
(119879fc) + 119899N2 ipcsdot ℎN2
(119879fc)
minus 120578comb [(119899H2 ipcsdot ΔℎH
2O) minus (119899COipc
sdot ΔℎCO2
)]
= 119899H2Oopc
sdot ℎH2O (119879pc) + 119899CO
2opcsdot ℎCO
2
(119879pc)
+ 119899O2opcsdot ℎO2
(119879pc) + 119899N2 ipcsdot ℎN2
(119879pc)
(24)
Once 119879pc is known which also corresponds to the TIT sincewe know the isentropic efficiency of the expander MTG wecan easily calculate the temperature of the turbine outlet (119879outblock E in Figure 5) by
119879out = TIT minus 120578is (TIT minus 119879is) (25)
Calculation of the inlet air temperature at the cathode (119879catblock F in Figure 5) gas mixture of known composition andtemperature 119879out once expanded is sent to a countercurrentheat exchanger (or regenerator) Here as the hot fluid andas the cold respectively the mixture under examination andthe outlet air from the compressor (at a flow rate equal to0808Kgs and at a temperature of 404K) enter The balanceequation of thermal power into the regenerator is expressedby
It starts from 1198791198901 attempted and the calculation is iterateduntil (26) is satisfied 1198791198901 represents the temperature at whichthe hot gases exiting the regenerator give part of their thermalpower to cogeneration purposes Once this first phase iscompleted the calculation of 119879cat through (27) is effected
Thus after calculating 119879cat the circuit is completely definedAt the following iteration this temperature 119879cat is the inputfor the calculation of 119879fc The cycle continues until all the
Journal of Renewable Energy 7
parameters arrive at convergence Then the evaluation ofperformance parameters is made as follows
Useful Power of the Cell Calculation (uc) Consider
Gas Turbine Useful Power Calculation (tg) Consider
tg = ut minus ac (31)
where
ut = 119905 sdot Δℎ (32)
Gas Turbine Efficiency Calculation (120578tg) Consider
120578tg =tg
CH4
sdot LHVCH4
(33)
The efficiency and useful power of the entire system are thencalculated as the sum of efficiency and useful power of SOFCandMTGWe then calculate the cogeneration indices that isIRE
IRE = 1 minustot
SI120578SI + cog (34)
and the thermal limit LT
LT =cog sdot 120578term
tot (35)
It was assumed that the heat available downstream of theregenerator was transferable with an efficiency of 40 to athermodynamic cycle downstream to calculate the cogener-ative values The procedure described already is summarizedin Figure 5
4 Constraints Definition
ldquoSettingrdquo defines a given combination of parameters dfc and119880119891 with which it is possible to operate the hybrid systemTherefore the set of all the possible settings by the rangewithin which the parameters themselves can vary is defined(Table 1) By defining the constraints we proceed to identifythe settings that are eligible for a given value of the flowof methane so as to adequately assess the elasticity designconnected to the same flow Steam to Carbon Ratio (STCR)the lower limit of Steam toCarbonRatio is the first restrictionto be taken into account defined as
STCR =119899H2O
119899CO + 119899CH4
(36)
The said parametermust remain above 2 In the event that thislimit is not respected the humidification of the anodemay notbe satisfactory and itmay cause cracking of bothmethane andcarbon dioxide molecules according to the reactions
CH4 997888rarr C + 2H2 (37)
CO2 997888rarr C +O2 (38)
Consequently we face the catalyst deactivation caused by thepresence of carbonaceous deposits
Constraint on Maximum Current Density The methane isconverted to hydrogen by (5) and (6) Given the assumptionspreviously made on the kinetics of these reactions we havethat the total conversion of one mole of methane per secondgives rise to 33 moles of hydrogen per second Simultane-ously according to (3) 119911 moles of hydrogen per second isinstead consumed Thus the consumption of hydrogen isdirectly proportional to the current density Therefore thesettings that provide a value of 119911 higher with respect tohydrogen product are considered ineligible
Constraints on the Operating Temperature of the Fuel Cell(119879fc) and the Turbine Inlet Temperature (119879119868119879) Constraintsrelating to temperature are the last to be taken into accountWe excluded the settings that generate temperatures of thestack higher than typical operating temperatures of SOFCsand have turbine inlet temperatures above 1250K (currenttechnological limit of MTG) Thus we summarize the con-ditions as follows
(a) 873K lt 119879fc lt 1200K(b) TIT lt 1250K
5 Results
In this section we proceed to the choice of the optimalconfiguration with which the hybrid system works and thento define the methane flow and the operative current densityThe next step is sensitivity analysis of the main parametersat varying 119880119891 whereas at the end a first validation ofthe calculation model is operated Selection of the optimalconfiguration the optimum configuration is that of completesystem This choice stems from the following reasoningAccording to (2) recirculation flow decreases at increasing119880119891 and the recirculation being at a temperature higher thancompressed methane this implies a lowering of 119879mix whichthen propagates on all operating parameters of the plantusing as a parameter to control the fall percentage 119879fc atvarying 119880119891 defined by
See Tables 3 and 4In the case of the base system the fall of temperature is
higher than 5 This is considered excessive By comparing
8 Journal of Renewable Energy
Table 3 Fall of temperature for increasing 119880119891 for base system
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 96392500 082 9137 521
Table 4 Fall of temperature for increasing 119880119891 for system withprereformer
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 94552500 082 9113 366
Table 5 Comparison between the gas turbine power plant withprereformer and complete system for dfc = 2500Am2
119880119891 System with prereformer Complete system081 1011 16674082 9238 15487083 8302 14483
Tables 3 and 4 it is evident how for homologous settingsin the case of system with prereformer the condition hasimproved Having higher temperatures with lower values 119880119891implies that a significant part of the fuel is not properlyused a phenomenon that has an impact on the values ofgas turbine power Therefore to remedy this gap is necessaryto insert an afterburner downstream of the fuel cell so thatthe configuration of the complete system becomes necessaryTable 5 shows how for homologous conditions the completesystem ensures a significant increase of the gas turbine power
Definition of Optimum Operating Conditions The optimumoperating conditions that is flow ofmethane and the currentdensity to operate with are chosen using design flexibility asthe criterion The model developed has been applied to thecalculation of the conditions resulting from three differentvalues of flow rate of methane low (119887 = 0012 kgs)medium (119898 = 0015 kgs) and high (119886 = 0018 kgs)In the case of high flow rate of methane there is no settingcompatible with all the constraints In contrast from acomparison between Tables 6(a) and 6(b) it is shown thatthe medium flow rate ensures greater design flexibility thusresulting in a specific value (asterisks are the settings eligible)Table 6(b) shows how for dfc = 2900Am2 there is agreater choice of the possible settings that satisfy all theconstraints outlined above so that this value is identified asthe operating current density and is used in the followingsensitivity analysis
Sensitivity of Operating Parameters and Performance at Vary-ing 119880119891 A sensitivity analysis is performed to determine theeffect of varying 119880119891 on the operating parameters and perfor-mance According to (2) the recirculation flow decreases atincreasing 119880119891 (first effect) Consequently all operating tem-peratures of the plant should decrease However the decreaseof recirculation flow implies a greater flow to the afterburner
Table 6 Plan of the possible settings for low and medium flow rateof methane
Figure 6 Percentage of prereforming at varying 119880119891
1000
1050
1100
1150
1200
1250
1300
T (K
)
076 077 078 079 080 081 082075
TIT (
Uf (mdash)
dfc = 2900 Am2)
Figure 7 TIT at varying 119880119891
as well (second effect) so that temperatures should increaseThe first effect prevails on the second one Therefore theoverall effect is a lowering of all operating temperatures of thehybrid system Consequently the temperature being lowerto keep the anode inlet temperature at the desired value aninferior amount of methane flow has to be reformed beforeentering the cellThus the percentage of reforming decreasesas Figure 6 shows Figure 7 owing to the already describedeffects shows how the temperature at the turbine inletmonotonically decreases and the turbogas power dependingon the TIT (TIT decrease means a decreasing in Δℎ thus areduction in useful power according to (31) and (32)) thismeans also a decreasing in terms of MTG power as one canobserve in Figure 8 Instead a nonmonotonous trend is thatconcerning the power of the cell In fact this is affected forlow values of 119880119891 by a prereforming effect which changesthe composition in the anode input (reactions (5) and (6))Therefore according to (16) the composition change meansthat the percentage of reforming decreases while Nernst-losses increase causing an overall power decrease in thestack Therefore when it is no longer necessary to reformthe Nernst-loss decreases with decreasing temperature sothat the power of the cell starts growing (Figure 9) Finally
140
150
160
170
180
190
200
P (k
W)
076 077 078 079 080 081 082075
MTG power (kW)
Uf (mdash)
Figure 8 Turbogas power at varying 119880119891
075 076 077 078 079 080 081 082
Fuel cell power (kW)
360
361
362
363
364
365
366
367
368
369
370
P (k
W)
Uf (mdash)
Figure 9 Fuel cell power at varying 119880119891
it is interesting to note that with increasing119880119891 while overallperformance parameters decrease there is an increase in theindex IRE (Figure 10) whereas the thermal limit remainsnearly constant
6 Discussion
61 First Validation of the Calculation Model A first testingof the model calculation was carried out both of a qualitativeand of a quantitative nature The ldquotrendrdquo of some fundamen-tal parameters with respect to developments known from theliterature was evaluated and the results obtained here werecompared with those calculated in [3]
62 Qualitative Validation First for purpose of qualitativemodel validation the data obtained were compared for thesame 119880119891 for different values of dfc As we expected Table 7shows that an increase of the current density causes anincrease of the operating temperature of the hybrid systemand consequently an increase in the percentage of methaneon which it performs the prereforming Table 8 shows that
10 Journal of Renewable Energy
075 076 077 078 079 080 081 08205
151520253035404550
()
IREThermal limit
dfc = 2900 Am2
Uf (mdash)
Figure 10 IRE (blue) and LT (red) at varying 119880119891
A CSOFC
DcAc
J16
Figure 11 Hybrid system studied in [3]
with the increase of dfc both the cell (despite an increasein voltage losses) and the gas turbine power rise the secondbeing directly dependent on the turbine inlet temperature
63 Quantitative Validation To end the first validationprocess the model was applied to the system of Figure 15studied in [3] and results were compared In [3] the methaneis compressed to 30 bars instead of the operating pressureof the MTG and then joined in a mixer and blend withassociated losses from the anode recirculation The mixer isthe only difference compared to the complete system Thethermodynamic modeling of the mixer and of the ejectorinside it would be very complex In homologous conditionsthe results turn out better for the complete system (consistentwith the physical principles) Thus one objective was toevaluate in a first approximation how the ejector affects thelosses using equivalent useful area as a parameter This isdefined as the percentage of usable area of Figure 3 hybridsystem compared with that of Figure 11 (without ejector)such that in homologous operating conditions both systemsproduce the same power The results are as shown in Table 9
It is seen that when the area is reduced up to 85 of thegiven ldquoplaterdquo the relative difference between the referencedata and the data provided by the model remains around 1thus lending credibility to the mathematical model describedin this paper
7 Conclusions
The objective set at the beginning was to define the optimalconditions of operation of the hybrid system by developinga C++ code and to evaluate the suitability of this approachwith the physical and chemical process present inside theSOFC-MTGplant In the first instancewe see that the optimalconfiguration of the hybrid system is that of the completesystem This ensures both a satisfactory temperature man-agement and good values of gas turbine power The flow rateof methane is excellent given the guaranteed high designflexibility which is defined as 119898 that is 0015 kgs Forthe said value of the flow rate of methane current densitythat ensures the best compromise between performance anddegrees of freedom to the designer (varying 119880119891 eligible
Journal of Renewable Energy 11
Table 7 Operating parameters in equal value 119880119891 for different dfc
dfc [Am2] 119880119891 Voltage [V] Voltage losses [V] uc [kW] tg [kW] tot [kW]2900 082 06788 05058 36278 14128 504063000 082 06619 05227 36596 18078 54674
Table 9 Comparison of the data obtained with the model andexperimental data studied by evaluating an equivalent useful areaequal to 85 of the effective area (dfc = 3200Am2)
Model data Reference data Relative difference[]
Hybrid systempower [kW] 43147 428 080
Fuel cell power[kW] 32052 319 047
Gas turbinepower [kW] 11095 109 176
Hybrid systemefficiency [kW] 062 061
Fuel cellefficiency [kW] 046 045
Gas turbineefficiency [kW] 016 016
between 075 and 082) is that of 2900Am2 The last stepis the choice of operating 119880119891 which may vary dependingon the objective it set out choosing a low 119880119891 if there isdirected towards energy optimization 119880119891 high if the goalis to maximize the cogeneration yield and a medium 119880119891 ifseeking a compromise between the two requirements Sincesystems of this type are still under study of the 3 optionsdescribed above at the current state of the art it seemsto make sense to focus on energy optimization and whenconsolidated on the market there will be consideration laterwith the economic scenario of the moment This factor isclosely related to the evaluation of the investment fromthe perspective of cogeneration The developed C++ codematches with both the state of the art and reference datataken from the literature suggesting the suitability of thisapproach to evaluate and describe SOFC-MTG and otherkinds of plants
Nomenclature
119860119891 Useful area of the fuel cell [m2]
119888119901 Specific heat at constant pressure[J(molsdotK)]
119888119901119898 Average specific heat of the mixture in the
course of expansion [J(kgsdotK)]119888V Specific heat at constant volume
[J(molsdotK)]dfc Current density with which it operates
within the fuel cell [Am2]119865 Faraday constant that is 96485 [Cmol]119891CO Molar fraction of carbon monoxide
dimensionless119891H2
Molar fraction of hydrogen dimensionlessℎair Molar enthalpy of the air [Jmol]ℎCH4
Molar enthalpy of methane [Jmol]ℎCO Molar enthalpy of carbon monoxide
[Jmol]ℎCO2
Molar enthalpy of carbon dioxide [Jmol]ℎH2
Molar enthalpy of hydrogen [Jmol]ℎH2O Molar enthalpy of the water vapor [Jmol]
ℎO2
Molar enthalpy of oxygen [Jmol]ℎN2
Molar enthalpy of nitrogen [Jmol]119868 Operation current [A]IRE ldquoEnergy saving indexrdquo dimensionless1198940119886 Current density exchange anode side
[Am2]1198940119888 Current density exchange cathode side
[Am2]119894119897 Limit current density [Am2]119870ref Equilibrium constant of the reaction of
steam reforming dimensionless119870shif Equilibrium constant of the reaction of
Water Gas Shift Reaction dimensionless Air mass flow rate [kgs]CH
4
Methane mass flow rate [kgs]119905 Mass flow rate in the expander [kgs]119899CH4
Electric power obtained through theelectrochemical reaction of waterformation [W]
ac Power absorbed by the compressor gasturbine system [W]
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of Renewable Energy 3
A B C
D
E
G
A C
F
SOFC DcAc
12
11
3
1 4 76
89
10
5
2
Figure 1 Technical scheme of the base system
A CSOFC
DcAc
14
H
Figure 2 Technical scheme of the system with prereformer
23 Complete System In the case of complete system(Figure 3) the difference from the previous configurationis that the anode exhaust not sent to recirculation is sentdownstream of SOFC where an afterburner (or postcom-bustor) provides for oxidization of the hydrogen and carbonmonoxide residuesThe cathode exhaust provides the oxygento the afterburner while the products of the postcombustorconstitute the working fluid of the expander of MTG Therest of the system is entirely analogous to the previousconfigurations
3 Mathematical Model
Here the procedures used for the calculation of the mainvariables of the hybrid system as a function of 119880119891 anddfc are described recirculation flow temperatures of mix-ing between recirculation and methane input anode celloperation of afterburning and of inlet air to the cathodepercentage of methane converted from the prereformer andvarious performance parameters that is power output and
efficiency Calculation of flow recirculation we calculate theair recirculation rate according to
119899ric =119899H2 ric119891H2
(1)
where the calculation of 119899H2 ric is done using
119899H2 ric =
119911119880119891 minus 3119899CH4
(1 + 03119891CO119891H2
)
(2)
where 119911 is given by
119911 =
dfc sdot 1198601198912119865
(3)
So once 119880119891 and dfc are assigned the recirculation flow istherefore uniquely defined Calculation of the temperature ofmixing between recirculation anodic and pressurized methane(119879mix block A in Figure 5) a mixture formed by gas recircu-lation and methane out from the compressor enters the fuel
4 Journal of Renewable Energy
A CSOFC
15I
DcAc
Figure 3 Technical scheme of complete system
Electricalpower cathode
SOFC
power (Tfc )
power (Tcat)power (Tan)Inlet anode Inlet cathode
power (Tfc )
sum power of reactions
Outlet anode Outlet
Figure 4 Flow input power and output from the fuel cell
cell The anode inlet temperature is calculated by attempts bythe balance of thermal power expressed by
When (4) reaches convergence the same 119879mix represents theunknown searchedCalculation ofmoles ofmethane convertedfrom the prereformer (119909 block A in Figure 5) this parameteris obtained by attempts starting from 119909 of hypotheses toobtain the one that satisfies the power balance to prereformerInside the prereformer coupled reactions of steam reforming
reaction and that coupled to it of Water Gas Shift Reaction(WGSR) occur expressed by
CH4 +H2Olarrrarr 3H2 + CO (5)
CO +H2Olarrrarr CO2 +H2 (6)
The ratio between (6) and (5) speed of reaction is unknownWe proceeded by calculating the speed of reactions for theoperating temperatures of the SOFC and for different per-centages of reforming using as a parameter the convergenceof equilibrium constants defined by
119870ref =[H2]3sdot [CO]
[CH4] sdot [H2O]1198752 (7)
119870shif =[H2] sdot [CO2][CO] sdot [H2O]
(8)
Journal of Renewable Energy 5
New Tcatlowast
New
Tcatlowast
Calc dr =minus
middot 100
Calc dr =Tcat
lowast minus TcatTcat
lowast
A
B
C
D
E
F
Tan = Tmix
x gt nCH4
If dr gt01
If dr gt 01
middot 100
Stop
Tmix lt 873
Tan = 873
Tcatlowast= Tcat
HYP
If
If
Recursionand new attempt
( )
( )Tfc Tfclowast
Tfclowast
Tfclowast
minusTfc Tfclowast
TfcTfclowast
Figure 5 Flow diagram for the calculation of the parameters of the complete system
and comparing (7) and (8) with the values of the equilibriumconstants calculated as a function of the temperature accord-ing to
Table 2 shows the values of the constants relating to (9) forthe two reactionsThe average ratio between speed of (6) andspeed of (5) is equal on average to about 03 Equations (7) and(8) are taken from [31] while (9) is taken from [30]Thereforein the calculations of the mass balance and thermal powerbalance we consider that for each mole of CH4 converted03 moles of H2 is also generated from the conversion of COproduced by (6) In light of this approximation the powerbalance to the prereformer appears to be expressed by
Table 2 Values for the calculation of the equilibrium constant 119870[30]
Reforming ShiftingA 26312 sdot 10
minus11547 sdot 10
minus12
B 12406 sdot 10minus7
minus2574 sdot 10minus8
C minus22523 sdot 10minus4
46374 sdot 10minus5
D 512749 sdot 10minus1
minus3915 sdot 10minus2
E minus66139488 13209723
Operating Temperature of the Cell (119879fc Block C in Figure 5)An iterative method for the calculation of the operatingtemperature of the cell is used as well We start froma temperature of attempt until the convergence of powerbalance is reached This last is expressed by
119899CH4
sdot ℎCH4
(119879an) + 119899H2Oifc
sdot ℎH2O (119879an) + 119899H
2 ifcsdot (119879an)
+ 119899COifcsdot ℎCO (119879an) + 119899CO
2 ifcsdot ℎCO
2
(119879an) + 119899O2 ifc
sdot ℎO2
(119879cat) + 119899N2
sdot ℎN2
(119879cat) minus 119899CH4
sdot Δℎref
minus 03119899CH4
sdot Δℎshif minus 119911 sdot ΔℎH2O
= 119899H2Oofc
sdot ℎH2O (119879fc) + 119899H
2ofcsdot (119879fc) + 119899COofc
sdot ℎCO (119879fc) + 119899CO2ofcsdot ℎCO
2
(119879fc) + 119899O2ofc
sdot ℎO2
(119879fc) + 119899N2
sdot ℎN2
(119879fc) +
(11)
6 Journal of Renewable Energy
It is interesting to observe graphically the power flow ofFigure 4 in which the contributions present in (11) are visibleIt is nowpossible at this stage to calculate the power generatedby the cell through
119888 = 119881 sdot 119868 (12)
To calculate 119868 the following equation is used
119868 = dfc sdot 119860119891 (13)
119881 is obtained by
119881 = 1198810 minus 119881Nernst minus 119881att minus 119881ohm minus 119881conc (14)
while (15) is used to calculate 1198810
1198810 =minusΔ1198660
2119865 (15)
119881Nernst is given by
119881Nernst =119877119879
2119865ln(
119891H2O
119891H2
sdot 119891O2
05sdot 11987505) (16)
119881att is provided by
119881act = 119881act119886
+ 119881act119888
(17)
To calculate 119881act119886
we resort to
119881act119886
= (119877119879
119865) sinhminus1 ( dfc
21198940119886
) (18)
Analogous calculation of 119881act119888
results by
119881act119888
= (119877119879
119865) sinhminus1 ( dfc
21198940119888
) (19)
Once losses for activation have been defined we calculatethose for concentration 119881conc by
119881conc = (119877119879
119865) ln(1 minus dfc
119894119897) (20)
The voltage loss due to the ohmic resistance is obtained by
119881ohm = dfc sdot4
sum
119894=1
119871 119894
120590119894
(21)
From (12) to (15) are taken from [3] whereas the equationsin (16) to (21) are taken from [4] Calculation of afterburningtemperature (block D in Figure 5) once it has left the cell thegas mixture reaches a postcombustor Here since the oxida-tion of both hydrogen and carbon monoxide still present inthe anode exhaust the temperature of the gas rises furtherThen the following occur
H2 +1
2O2 997888rarr H2O (22)
CO + 12O2 997888rarr CO2 (23)
By varying 119879pc the balance of thermal power is solvedexpressed by
119899H2 ipcsdot ℎH2
(119879fc) + 119899H2Oipc
sdot ℎH2O (119879fc) + 119899COipc
sdot ℎCO (119879fc) + 119899CO2 ipcsdot ℎCO
2
(119879fc) + 119899O2 ipc
sdot ℎO2
(119879fc) + 119899N2 ipcsdot ℎN2
(119879fc)
minus 120578comb [(119899H2 ipcsdot ΔℎH
2O) minus (119899COipc
sdot ΔℎCO2
)]
= 119899H2Oopc
sdot ℎH2O (119879pc) + 119899CO
2opcsdot ℎCO
2
(119879pc)
+ 119899O2opcsdot ℎO2
(119879pc) + 119899N2 ipcsdot ℎN2
(119879pc)
(24)
Once 119879pc is known which also corresponds to the TIT sincewe know the isentropic efficiency of the expander MTG wecan easily calculate the temperature of the turbine outlet (119879outblock E in Figure 5) by
119879out = TIT minus 120578is (TIT minus 119879is) (25)
Calculation of the inlet air temperature at the cathode (119879catblock F in Figure 5) gas mixture of known composition andtemperature 119879out once expanded is sent to a countercurrentheat exchanger (or regenerator) Here as the hot fluid andas the cold respectively the mixture under examination andthe outlet air from the compressor (at a flow rate equal to0808Kgs and at a temperature of 404K) enter The balanceequation of thermal power into the regenerator is expressedby
It starts from 1198791198901 attempted and the calculation is iterateduntil (26) is satisfied 1198791198901 represents the temperature at whichthe hot gases exiting the regenerator give part of their thermalpower to cogeneration purposes Once this first phase iscompleted the calculation of 119879cat through (27) is effected
Thus after calculating 119879cat the circuit is completely definedAt the following iteration this temperature 119879cat is the inputfor the calculation of 119879fc The cycle continues until all the
Journal of Renewable Energy 7
parameters arrive at convergence Then the evaluation ofperformance parameters is made as follows
Useful Power of the Cell Calculation (uc) Consider
Gas Turbine Useful Power Calculation (tg) Consider
tg = ut minus ac (31)
where
ut = 119905 sdot Δℎ (32)
Gas Turbine Efficiency Calculation (120578tg) Consider
120578tg =tg
CH4
sdot LHVCH4
(33)
The efficiency and useful power of the entire system are thencalculated as the sum of efficiency and useful power of SOFCandMTGWe then calculate the cogeneration indices that isIRE
IRE = 1 minustot
SI120578SI + cog (34)
and the thermal limit LT
LT =cog sdot 120578term
tot (35)
It was assumed that the heat available downstream of theregenerator was transferable with an efficiency of 40 to athermodynamic cycle downstream to calculate the cogener-ative values The procedure described already is summarizedin Figure 5
4 Constraints Definition
ldquoSettingrdquo defines a given combination of parameters dfc and119880119891 with which it is possible to operate the hybrid systemTherefore the set of all the possible settings by the rangewithin which the parameters themselves can vary is defined(Table 1) By defining the constraints we proceed to identifythe settings that are eligible for a given value of the flowof methane so as to adequately assess the elasticity designconnected to the same flow Steam to Carbon Ratio (STCR)the lower limit of Steam toCarbonRatio is the first restrictionto be taken into account defined as
STCR =119899H2O
119899CO + 119899CH4
(36)
The said parametermust remain above 2 In the event that thislimit is not respected the humidification of the anodemay notbe satisfactory and itmay cause cracking of bothmethane andcarbon dioxide molecules according to the reactions
CH4 997888rarr C + 2H2 (37)
CO2 997888rarr C +O2 (38)
Consequently we face the catalyst deactivation caused by thepresence of carbonaceous deposits
Constraint on Maximum Current Density The methane isconverted to hydrogen by (5) and (6) Given the assumptionspreviously made on the kinetics of these reactions we havethat the total conversion of one mole of methane per secondgives rise to 33 moles of hydrogen per second Simultane-ously according to (3) 119911 moles of hydrogen per second isinstead consumed Thus the consumption of hydrogen isdirectly proportional to the current density Therefore thesettings that provide a value of 119911 higher with respect tohydrogen product are considered ineligible
Constraints on the Operating Temperature of the Fuel Cell(119879fc) and the Turbine Inlet Temperature (119879119868119879) Constraintsrelating to temperature are the last to be taken into accountWe excluded the settings that generate temperatures of thestack higher than typical operating temperatures of SOFCsand have turbine inlet temperatures above 1250K (currenttechnological limit of MTG) Thus we summarize the con-ditions as follows
(a) 873K lt 119879fc lt 1200K(b) TIT lt 1250K
5 Results
In this section we proceed to the choice of the optimalconfiguration with which the hybrid system works and thento define the methane flow and the operative current densityThe next step is sensitivity analysis of the main parametersat varying 119880119891 whereas at the end a first validation ofthe calculation model is operated Selection of the optimalconfiguration the optimum configuration is that of completesystem This choice stems from the following reasoningAccording to (2) recirculation flow decreases at increasing119880119891 and the recirculation being at a temperature higher thancompressed methane this implies a lowering of 119879mix whichthen propagates on all operating parameters of the plantusing as a parameter to control the fall percentage 119879fc atvarying 119880119891 defined by
See Tables 3 and 4In the case of the base system the fall of temperature is
higher than 5 This is considered excessive By comparing
8 Journal of Renewable Energy
Table 3 Fall of temperature for increasing 119880119891 for base system
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 96392500 082 9137 521
Table 4 Fall of temperature for increasing 119880119891 for system withprereformer
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 94552500 082 9113 366
Table 5 Comparison between the gas turbine power plant withprereformer and complete system for dfc = 2500Am2
119880119891 System with prereformer Complete system081 1011 16674082 9238 15487083 8302 14483
Tables 3 and 4 it is evident how for homologous settingsin the case of system with prereformer the condition hasimproved Having higher temperatures with lower values 119880119891implies that a significant part of the fuel is not properlyused a phenomenon that has an impact on the values ofgas turbine power Therefore to remedy this gap is necessaryto insert an afterburner downstream of the fuel cell so thatthe configuration of the complete system becomes necessaryTable 5 shows how for homologous conditions the completesystem ensures a significant increase of the gas turbine power
Definition of Optimum Operating Conditions The optimumoperating conditions that is flow ofmethane and the currentdensity to operate with are chosen using design flexibility asthe criterion The model developed has been applied to thecalculation of the conditions resulting from three differentvalues of flow rate of methane low (119887 = 0012 kgs)medium (119898 = 0015 kgs) and high (119886 = 0018 kgs)In the case of high flow rate of methane there is no settingcompatible with all the constraints In contrast from acomparison between Tables 6(a) and 6(b) it is shown thatthe medium flow rate ensures greater design flexibility thusresulting in a specific value (asterisks are the settings eligible)Table 6(b) shows how for dfc = 2900Am2 there is agreater choice of the possible settings that satisfy all theconstraints outlined above so that this value is identified asthe operating current density and is used in the followingsensitivity analysis
Sensitivity of Operating Parameters and Performance at Vary-ing 119880119891 A sensitivity analysis is performed to determine theeffect of varying 119880119891 on the operating parameters and perfor-mance According to (2) the recirculation flow decreases atincreasing 119880119891 (first effect) Consequently all operating tem-peratures of the plant should decrease However the decreaseof recirculation flow implies a greater flow to the afterburner
Table 6 Plan of the possible settings for low and medium flow rateof methane
Figure 6 Percentage of prereforming at varying 119880119891
1000
1050
1100
1150
1200
1250
1300
T (K
)
076 077 078 079 080 081 082075
TIT (
Uf (mdash)
dfc = 2900 Am2)
Figure 7 TIT at varying 119880119891
as well (second effect) so that temperatures should increaseThe first effect prevails on the second one Therefore theoverall effect is a lowering of all operating temperatures of thehybrid system Consequently the temperature being lowerto keep the anode inlet temperature at the desired value aninferior amount of methane flow has to be reformed beforeentering the cellThus the percentage of reforming decreasesas Figure 6 shows Figure 7 owing to the already describedeffects shows how the temperature at the turbine inletmonotonically decreases and the turbogas power dependingon the TIT (TIT decrease means a decreasing in Δℎ thus areduction in useful power according to (31) and (32)) thismeans also a decreasing in terms of MTG power as one canobserve in Figure 8 Instead a nonmonotonous trend is thatconcerning the power of the cell In fact this is affected forlow values of 119880119891 by a prereforming effect which changesthe composition in the anode input (reactions (5) and (6))Therefore according to (16) the composition change meansthat the percentage of reforming decreases while Nernst-losses increase causing an overall power decrease in thestack Therefore when it is no longer necessary to reformthe Nernst-loss decreases with decreasing temperature sothat the power of the cell starts growing (Figure 9) Finally
140
150
160
170
180
190
200
P (k
W)
076 077 078 079 080 081 082075
MTG power (kW)
Uf (mdash)
Figure 8 Turbogas power at varying 119880119891
075 076 077 078 079 080 081 082
Fuel cell power (kW)
360
361
362
363
364
365
366
367
368
369
370
P (k
W)
Uf (mdash)
Figure 9 Fuel cell power at varying 119880119891
it is interesting to note that with increasing119880119891 while overallperformance parameters decrease there is an increase in theindex IRE (Figure 10) whereas the thermal limit remainsnearly constant
6 Discussion
61 First Validation of the Calculation Model A first testingof the model calculation was carried out both of a qualitativeand of a quantitative nature The ldquotrendrdquo of some fundamen-tal parameters with respect to developments known from theliterature was evaluated and the results obtained here werecompared with those calculated in [3]
62 Qualitative Validation First for purpose of qualitativemodel validation the data obtained were compared for thesame 119880119891 for different values of dfc As we expected Table 7shows that an increase of the current density causes anincrease of the operating temperature of the hybrid systemand consequently an increase in the percentage of methaneon which it performs the prereforming Table 8 shows that
10 Journal of Renewable Energy
075 076 077 078 079 080 081 08205
151520253035404550
()
IREThermal limit
dfc = 2900 Am2
Uf (mdash)
Figure 10 IRE (blue) and LT (red) at varying 119880119891
A CSOFC
DcAc
J16
Figure 11 Hybrid system studied in [3]
with the increase of dfc both the cell (despite an increasein voltage losses) and the gas turbine power rise the secondbeing directly dependent on the turbine inlet temperature
63 Quantitative Validation To end the first validationprocess the model was applied to the system of Figure 15studied in [3] and results were compared In [3] the methaneis compressed to 30 bars instead of the operating pressureof the MTG and then joined in a mixer and blend withassociated losses from the anode recirculation The mixer isthe only difference compared to the complete system Thethermodynamic modeling of the mixer and of the ejectorinside it would be very complex In homologous conditionsthe results turn out better for the complete system (consistentwith the physical principles) Thus one objective was toevaluate in a first approximation how the ejector affects thelosses using equivalent useful area as a parameter This isdefined as the percentage of usable area of Figure 3 hybridsystem compared with that of Figure 11 (without ejector)such that in homologous operating conditions both systemsproduce the same power The results are as shown in Table 9
It is seen that when the area is reduced up to 85 of thegiven ldquoplaterdquo the relative difference between the referencedata and the data provided by the model remains around 1thus lending credibility to the mathematical model describedin this paper
7 Conclusions
The objective set at the beginning was to define the optimalconditions of operation of the hybrid system by developinga C++ code and to evaluate the suitability of this approachwith the physical and chemical process present inside theSOFC-MTGplant In the first instancewe see that the optimalconfiguration of the hybrid system is that of the completesystem This ensures both a satisfactory temperature man-agement and good values of gas turbine power The flow rateof methane is excellent given the guaranteed high designflexibility which is defined as 119898 that is 0015 kgs Forthe said value of the flow rate of methane current densitythat ensures the best compromise between performance anddegrees of freedom to the designer (varying 119880119891 eligible
Journal of Renewable Energy 11
Table 7 Operating parameters in equal value 119880119891 for different dfc
dfc [Am2] 119880119891 Voltage [V] Voltage losses [V] uc [kW] tg [kW] tot [kW]2900 082 06788 05058 36278 14128 504063000 082 06619 05227 36596 18078 54674
Table 9 Comparison of the data obtained with the model andexperimental data studied by evaluating an equivalent useful areaequal to 85 of the effective area (dfc = 3200Am2)
Model data Reference data Relative difference[]
Hybrid systempower [kW] 43147 428 080
Fuel cell power[kW] 32052 319 047
Gas turbinepower [kW] 11095 109 176
Hybrid systemefficiency [kW] 062 061
Fuel cellefficiency [kW] 046 045
Gas turbineefficiency [kW] 016 016
between 075 and 082) is that of 2900Am2 The last stepis the choice of operating 119880119891 which may vary dependingon the objective it set out choosing a low 119880119891 if there isdirected towards energy optimization 119880119891 high if the goalis to maximize the cogeneration yield and a medium 119880119891 ifseeking a compromise between the two requirements Sincesystems of this type are still under study of the 3 optionsdescribed above at the current state of the art it seemsto make sense to focus on energy optimization and whenconsolidated on the market there will be consideration laterwith the economic scenario of the moment This factor isclosely related to the evaluation of the investment fromthe perspective of cogeneration The developed C++ codematches with both the state of the art and reference datataken from the literature suggesting the suitability of thisapproach to evaluate and describe SOFC-MTG and otherkinds of plants
Nomenclature
119860119891 Useful area of the fuel cell [m2]
119888119901 Specific heat at constant pressure[J(molsdotK)]
119888119901119898 Average specific heat of the mixture in the
course of expansion [J(kgsdotK)]119888V Specific heat at constant volume
[J(molsdotK)]dfc Current density with which it operates
within the fuel cell [Am2]119865 Faraday constant that is 96485 [Cmol]119891CO Molar fraction of carbon monoxide
dimensionless119891H2
Molar fraction of hydrogen dimensionlessℎair Molar enthalpy of the air [Jmol]ℎCH4
Molar enthalpy of methane [Jmol]ℎCO Molar enthalpy of carbon monoxide
[Jmol]ℎCO2
Molar enthalpy of carbon dioxide [Jmol]ℎH2
Molar enthalpy of hydrogen [Jmol]ℎH2O Molar enthalpy of the water vapor [Jmol]
ℎO2
Molar enthalpy of oxygen [Jmol]ℎN2
Molar enthalpy of nitrogen [Jmol]119868 Operation current [A]IRE ldquoEnergy saving indexrdquo dimensionless1198940119886 Current density exchange anode side
[Am2]1198940119888 Current density exchange cathode side
[Am2]119894119897 Limit current density [Am2]119870ref Equilibrium constant of the reaction of
steam reforming dimensionless119870shif Equilibrium constant of the reaction of
Water Gas Shift Reaction dimensionless Air mass flow rate [kgs]CH
4
Methane mass flow rate [kgs]119905 Mass flow rate in the expander [kgs]119899CH4
Electric power obtained through theelectrochemical reaction of waterformation [W]
ac Power absorbed by the compressor gasturbine system [W]
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
When (4) reaches convergence the same 119879mix represents theunknown searchedCalculation ofmoles ofmethane convertedfrom the prereformer (119909 block A in Figure 5) this parameteris obtained by attempts starting from 119909 of hypotheses toobtain the one that satisfies the power balance to prereformerInside the prereformer coupled reactions of steam reforming
reaction and that coupled to it of Water Gas Shift Reaction(WGSR) occur expressed by
CH4 +H2Olarrrarr 3H2 + CO (5)
CO +H2Olarrrarr CO2 +H2 (6)
The ratio between (6) and (5) speed of reaction is unknownWe proceeded by calculating the speed of reactions for theoperating temperatures of the SOFC and for different per-centages of reforming using as a parameter the convergenceof equilibrium constants defined by
119870ref =[H2]3sdot [CO]
[CH4] sdot [H2O]1198752 (7)
119870shif =[H2] sdot [CO2][CO] sdot [H2O]
(8)
Journal of Renewable Energy 5
New Tcatlowast
New
Tcatlowast
Calc dr =minus
middot 100
Calc dr =Tcat
lowast minus TcatTcat
lowast
A
B
C
D
E
F
Tan = Tmix
x gt nCH4
If dr gt01
If dr gt 01
middot 100
Stop
Tmix lt 873
Tan = 873
Tcatlowast= Tcat
HYP
If
If
Recursionand new attempt
( )
( )Tfc Tfclowast
Tfclowast
Tfclowast
minusTfc Tfclowast
TfcTfclowast
Figure 5 Flow diagram for the calculation of the parameters of the complete system
and comparing (7) and (8) with the values of the equilibriumconstants calculated as a function of the temperature accord-ing to
Table 2 shows the values of the constants relating to (9) forthe two reactionsThe average ratio between speed of (6) andspeed of (5) is equal on average to about 03 Equations (7) and(8) are taken from [31] while (9) is taken from [30]Thereforein the calculations of the mass balance and thermal powerbalance we consider that for each mole of CH4 converted03 moles of H2 is also generated from the conversion of COproduced by (6) In light of this approximation the powerbalance to the prereformer appears to be expressed by
Table 2 Values for the calculation of the equilibrium constant 119870[30]
Reforming ShiftingA 26312 sdot 10
minus11547 sdot 10
minus12
B 12406 sdot 10minus7
minus2574 sdot 10minus8
C minus22523 sdot 10minus4
46374 sdot 10minus5
D 512749 sdot 10minus1
minus3915 sdot 10minus2
E minus66139488 13209723
Operating Temperature of the Cell (119879fc Block C in Figure 5)An iterative method for the calculation of the operatingtemperature of the cell is used as well We start froma temperature of attempt until the convergence of powerbalance is reached This last is expressed by
119899CH4
sdot ℎCH4
(119879an) + 119899H2Oifc
sdot ℎH2O (119879an) + 119899H
2 ifcsdot (119879an)
+ 119899COifcsdot ℎCO (119879an) + 119899CO
2 ifcsdot ℎCO
2
(119879an) + 119899O2 ifc
sdot ℎO2
(119879cat) + 119899N2
sdot ℎN2
(119879cat) minus 119899CH4
sdot Δℎref
minus 03119899CH4
sdot Δℎshif minus 119911 sdot ΔℎH2O
= 119899H2Oofc
sdot ℎH2O (119879fc) + 119899H
2ofcsdot (119879fc) + 119899COofc
sdot ℎCO (119879fc) + 119899CO2ofcsdot ℎCO
2
(119879fc) + 119899O2ofc
sdot ℎO2
(119879fc) + 119899N2
sdot ℎN2
(119879fc) +
(11)
6 Journal of Renewable Energy
It is interesting to observe graphically the power flow ofFigure 4 in which the contributions present in (11) are visibleIt is nowpossible at this stage to calculate the power generatedby the cell through
119888 = 119881 sdot 119868 (12)
To calculate 119868 the following equation is used
119868 = dfc sdot 119860119891 (13)
119881 is obtained by
119881 = 1198810 minus 119881Nernst minus 119881att minus 119881ohm minus 119881conc (14)
while (15) is used to calculate 1198810
1198810 =minusΔ1198660
2119865 (15)
119881Nernst is given by
119881Nernst =119877119879
2119865ln(
119891H2O
119891H2
sdot 119891O2
05sdot 11987505) (16)
119881att is provided by
119881act = 119881act119886
+ 119881act119888
(17)
To calculate 119881act119886
we resort to
119881act119886
= (119877119879
119865) sinhminus1 ( dfc
21198940119886
) (18)
Analogous calculation of 119881act119888
results by
119881act119888
= (119877119879
119865) sinhminus1 ( dfc
21198940119888
) (19)
Once losses for activation have been defined we calculatethose for concentration 119881conc by
119881conc = (119877119879
119865) ln(1 minus dfc
119894119897) (20)
The voltage loss due to the ohmic resistance is obtained by
119881ohm = dfc sdot4
sum
119894=1
119871 119894
120590119894
(21)
From (12) to (15) are taken from [3] whereas the equationsin (16) to (21) are taken from [4] Calculation of afterburningtemperature (block D in Figure 5) once it has left the cell thegas mixture reaches a postcombustor Here since the oxida-tion of both hydrogen and carbon monoxide still present inthe anode exhaust the temperature of the gas rises furtherThen the following occur
H2 +1
2O2 997888rarr H2O (22)
CO + 12O2 997888rarr CO2 (23)
By varying 119879pc the balance of thermal power is solvedexpressed by
119899H2 ipcsdot ℎH2
(119879fc) + 119899H2Oipc
sdot ℎH2O (119879fc) + 119899COipc
sdot ℎCO (119879fc) + 119899CO2 ipcsdot ℎCO
2
(119879fc) + 119899O2 ipc
sdot ℎO2
(119879fc) + 119899N2 ipcsdot ℎN2
(119879fc)
minus 120578comb [(119899H2 ipcsdot ΔℎH
2O) minus (119899COipc
sdot ΔℎCO2
)]
= 119899H2Oopc
sdot ℎH2O (119879pc) + 119899CO
2opcsdot ℎCO
2
(119879pc)
+ 119899O2opcsdot ℎO2
(119879pc) + 119899N2 ipcsdot ℎN2
(119879pc)
(24)
Once 119879pc is known which also corresponds to the TIT sincewe know the isentropic efficiency of the expander MTG wecan easily calculate the temperature of the turbine outlet (119879outblock E in Figure 5) by
119879out = TIT minus 120578is (TIT minus 119879is) (25)
Calculation of the inlet air temperature at the cathode (119879catblock F in Figure 5) gas mixture of known composition andtemperature 119879out once expanded is sent to a countercurrentheat exchanger (or regenerator) Here as the hot fluid andas the cold respectively the mixture under examination andthe outlet air from the compressor (at a flow rate equal to0808Kgs and at a temperature of 404K) enter The balanceequation of thermal power into the regenerator is expressedby
It starts from 1198791198901 attempted and the calculation is iterateduntil (26) is satisfied 1198791198901 represents the temperature at whichthe hot gases exiting the regenerator give part of their thermalpower to cogeneration purposes Once this first phase iscompleted the calculation of 119879cat through (27) is effected
Thus after calculating 119879cat the circuit is completely definedAt the following iteration this temperature 119879cat is the inputfor the calculation of 119879fc The cycle continues until all the
Journal of Renewable Energy 7
parameters arrive at convergence Then the evaluation ofperformance parameters is made as follows
Useful Power of the Cell Calculation (uc) Consider
Gas Turbine Useful Power Calculation (tg) Consider
tg = ut minus ac (31)
where
ut = 119905 sdot Δℎ (32)
Gas Turbine Efficiency Calculation (120578tg) Consider
120578tg =tg
CH4
sdot LHVCH4
(33)
The efficiency and useful power of the entire system are thencalculated as the sum of efficiency and useful power of SOFCandMTGWe then calculate the cogeneration indices that isIRE
IRE = 1 minustot
SI120578SI + cog (34)
and the thermal limit LT
LT =cog sdot 120578term
tot (35)
It was assumed that the heat available downstream of theregenerator was transferable with an efficiency of 40 to athermodynamic cycle downstream to calculate the cogener-ative values The procedure described already is summarizedin Figure 5
4 Constraints Definition
ldquoSettingrdquo defines a given combination of parameters dfc and119880119891 with which it is possible to operate the hybrid systemTherefore the set of all the possible settings by the rangewithin which the parameters themselves can vary is defined(Table 1) By defining the constraints we proceed to identifythe settings that are eligible for a given value of the flowof methane so as to adequately assess the elasticity designconnected to the same flow Steam to Carbon Ratio (STCR)the lower limit of Steam toCarbonRatio is the first restrictionto be taken into account defined as
STCR =119899H2O
119899CO + 119899CH4
(36)
The said parametermust remain above 2 In the event that thislimit is not respected the humidification of the anodemay notbe satisfactory and itmay cause cracking of bothmethane andcarbon dioxide molecules according to the reactions
CH4 997888rarr C + 2H2 (37)
CO2 997888rarr C +O2 (38)
Consequently we face the catalyst deactivation caused by thepresence of carbonaceous deposits
Constraint on Maximum Current Density The methane isconverted to hydrogen by (5) and (6) Given the assumptionspreviously made on the kinetics of these reactions we havethat the total conversion of one mole of methane per secondgives rise to 33 moles of hydrogen per second Simultane-ously according to (3) 119911 moles of hydrogen per second isinstead consumed Thus the consumption of hydrogen isdirectly proportional to the current density Therefore thesettings that provide a value of 119911 higher with respect tohydrogen product are considered ineligible
Constraints on the Operating Temperature of the Fuel Cell(119879fc) and the Turbine Inlet Temperature (119879119868119879) Constraintsrelating to temperature are the last to be taken into accountWe excluded the settings that generate temperatures of thestack higher than typical operating temperatures of SOFCsand have turbine inlet temperatures above 1250K (currenttechnological limit of MTG) Thus we summarize the con-ditions as follows
(a) 873K lt 119879fc lt 1200K(b) TIT lt 1250K
5 Results
In this section we proceed to the choice of the optimalconfiguration with which the hybrid system works and thento define the methane flow and the operative current densityThe next step is sensitivity analysis of the main parametersat varying 119880119891 whereas at the end a first validation ofthe calculation model is operated Selection of the optimalconfiguration the optimum configuration is that of completesystem This choice stems from the following reasoningAccording to (2) recirculation flow decreases at increasing119880119891 and the recirculation being at a temperature higher thancompressed methane this implies a lowering of 119879mix whichthen propagates on all operating parameters of the plantusing as a parameter to control the fall percentage 119879fc atvarying 119880119891 defined by
See Tables 3 and 4In the case of the base system the fall of temperature is
higher than 5 This is considered excessive By comparing
8 Journal of Renewable Energy
Table 3 Fall of temperature for increasing 119880119891 for base system
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 96392500 082 9137 521
Table 4 Fall of temperature for increasing 119880119891 for system withprereformer
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 94552500 082 9113 366
Table 5 Comparison between the gas turbine power plant withprereformer and complete system for dfc = 2500Am2
119880119891 System with prereformer Complete system081 1011 16674082 9238 15487083 8302 14483
Tables 3 and 4 it is evident how for homologous settingsin the case of system with prereformer the condition hasimproved Having higher temperatures with lower values 119880119891implies that a significant part of the fuel is not properlyused a phenomenon that has an impact on the values ofgas turbine power Therefore to remedy this gap is necessaryto insert an afterburner downstream of the fuel cell so thatthe configuration of the complete system becomes necessaryTable 5 shows how for homologous conditions the completesystem ensures a significant increase of the gas turbine power
Definition of Optimum Operating Conditions The optimumoperating conditions that is flow ofmethane and the currentdensity to operate with are chosen using design flexibility asthe criterion The model developed has been applied to thecalculation of the conditions resulting from three differentvalues of flow rate of methane low (119887 = 0012 kgs)medium (119898 = 0015 kgs) and high (119886 = 0018 kgs)In the case of high flow rate of methane there is no settingcompatible with all the constraints In contrast from acomparison between Tables 6(a) and 6(b) it is shown thatthe medium flow rate ensures greater design flexibility thusresulting in a specific value (asterisks are the settings eligible)Table 6(b) shows how for dfc = 2900Am2 there is agreater choice of the possible settings that satisfy all theconstraints outlined above so that this value is identified asthe operating current density and is used in the followingsensitivity analysis
Sensitivity of Operating Parameters and Performance at Vary-ing 119880119891 A sensitivity analysis is performed to determine theeffect of varying 119880119891 on the operating parameters and perfor-mance According to (2) the recirculation flow decreases atincreasing 119880119891 (first effect) Consequently all operating tem-peratures of the plant should decrease However the decreaseof recirculation flow implies a greater flow to the afterburner
Table 6 Plan of the possible settings for low and medium flow rateof methane
Figure 6 Percentage of prereforming at varying 119880119891
1000
1050
1100
1150
1200
1250
1300
T (K
)
076 077 078 079 080 081 082075
TIT (
Uf (mdash)
dfc = 2900 Am2)
Figure 7 TIT at varying 119880119891
as well (second effect) so that temperatures should increaseThe first effect prevails on the second one Therefore theoverall effect is a lowering of all operating temperatures of thehybrid system Consequently the temperature being lowerto keep the anode inlet temperature at the desired value aninferior amount of methane flow has to be reformed beforeentering the cellThus the percentage of reforming decreasesas Figure 6 shows Figure 7 owing to the already describedeffects shows how the temperature at the turbine inletmonotonically decreases and the turbogas power dependingon the TIT (TIT decrease means a decreasing in Δℎ thus areduction in useful power according to (31) and (32)) thismeans also a decreasing in terms of MTG power as one canobserve in Figure 8 Instead a nonmonotonous trend is thatconcerning the power of the cell In fact this is affected forlow values of 119880119891 by a prereforming effect which changesthe composition in the anode input (reactions (5) and (6))Therefore according to (16) the composition change meansthat the percentage of reforming decreases while Nernst-losses increase causing an overall power decrease in thestack Therefore when it is no longer necessary to reformthe Nernst-loss decreases with decreasing temperature sothat the power of the cell starts growing (Figure 9) Finally
140
150
160
170
180
190
200
P (k
W)
076 077 078 079 080 081 082075
MTG power (kW)
Uf (mdash)
Figure 8 Turbogas power at varying 119880119891
075 076 077 078 079 080 081 082
Fuel cell power (kW)
360
361
362
363
364
365
366
367
368
369
370
P (k
W)
Uf (mdash)
Figure 9 Fuel cell power at varying 119880119891
it is interesting to note that with increasing119880119891 while overallperformance parameters decrease there is an increase in theindex IRE (Figure 10) whereas the thermal limit remainsnearly constant
6 Discussion
61 First Validation of the Calculation Model A first testingof the model calculation was carried out both of a qualitativeand of a quantitative nature The ldquotrendrdquo of some fundamen-tal parameters with respect to developments known from theliterature was evaluated and the results obtained here werecompared with those calculated in [3]
62 Qualitative Validation First for purpose of qualitativemodel validation the data obtained were compared for thesame 119880119891 for different values of dfc As we expected Table 7shows that an increase of the current density causes anincrease of the operating temperature of the hybrid systemand consequently an increase in the percentage of methaneon which it performs the prereforming Table 8 shows that
10 Journal of Renewable Energy
075 076 077 078 079 080 081 08205
151520253035404550
()
IREThermal limit
dfc = 2900 Am2
Uf (mdash)
Figure 10 IRE (blue) and LT (red) at varying 119880119891
A CSOFC
DcAc
J16
Figure 11 Hybrid system studied in [3]
with the increase of dfc both the cell (despite an increasein voltage losses) and the gas turbine power rise the secondbeing directly dependent on the turbine inlet temperature
63 Quantitative Validation To end the first validationprocess the model was applied to the system of Figure 15studied in [3] and results were compared In [3] the methaneis compressed to 30 bars instead of the operating pressureof the MTG and then joined in a mixer and blend withassociated losses from the anode recirculation The mixer isthe only difference compared to the complete system Thethermodynamic modeling of the mixer and of the ejectorinside it would be very complex In homologous conditionsthe results turn out better for the complete system (consistentwith the physical principles) Thus one objective was toevaluate in a first approximation how the ejector affects thelosses using equivalent useful area as a parameter This isdefined as the percentage of usable area of Figure 3 hybridsystem compared with that of Figure 11 (without ejector)such that in homologous operating conditions both systemsproduce the same power The results are as shown in Table 9
It is seen that when the area is reduced up to 85 of thegiven ldquoplaterdquo the relative difference between the referencedata and the data provided by the model remains around 1thus lending credibility to the mathematical model describedin this paper
7 Conclusions
The objective set at the beginning was to define the optimalconditions of operation of the hybrid system by developinga C++ code and to evaluate the suitability of this approachwith the physical and chemical process present inside theSOFC-MTGplant In the first instancewe see that the optimalconfiguration of the hybrid system is that of the completesystem This ensures both a satisfactory temperature man-agement and good values of gas turbine power The flow rateof methane is excellent given the guaranteed high designflexibility which is defined as 119898 that is 0015 kgs Forthe said value of the flow rate of methane current densitythat ensures the best compromise between performance anddegrees of freedom to the designer (varying 119880119891 eligible
Journal of Renewable Energy 11
Table 7 Operating parameters in equal value 119880119891 for different dfc
dfc [Am2] 119880119891 Voltage [V] Voltage losses [V] uc [kW] tg [kW] tot [kW]2900 082 06788 05058 36278 14128 504063000 082 06619 05227 36596 18078 54674
Table 9 Comparison of the data obtained with the model andexperimental data studied by evaluating an equivalent useful areaequal to 85 of the effective area (dfc = 3200Am2)
Model data Reference data Relative difference[]
Hybrid systempower [kW] 43147 428 080
Fuel cell power[kW] 32052 319 047
Gas turbinepower [kW] 11095 109 176
Hybrid systemefficiency [kW] 062 061
Fuel cellefficiency [kW] 046 045
Gas turbineefficiency [kW] 016 016
between 075 and 082) is that of 2900Am2 The last stepis the choice of operating 119880119891 which may vary dependingon the objective it set out choosing a low 119880119891 if there isdirected towards energy optimization 119880119891 high if the goalis to maximize the cogeneration yield and a medium 119880119891 ifseeking a compromise between the two requirements Sincesystems of this type are still under study of the 3 optionsdescribed above at the current state of the art it seemsto make sense to focus on energy optimization and whenconsolidated on the market there will be consideration laterwith the economic scenario of the moment This factor isclosely related to the evaluation of the investment fromthe perspective of cogeneration The developed C++ codematches with both the state of the art and reference datataken from the literature suggesting the suitability of thisapproach to evaluate and describe SOFC-MTG and otherkinds of plants
Nomenclature
119860119891 Useful area of the fuel cell [m2]
119888119901 Specific heat at constant pressure[J(molsdotK)]
119888119901119898 Average specific heat of the mixture in the
course of expansion [J(kgsdotK)]119888V Specific heat at constant volume
[J(molsdotK)]dfc Current density with which it operates
within the fuel cell [Am2]119865 Faraday constant that is 96485 [Cmol]119891CO Molar fraction of carbon monoxide
dimensionless119891H2
Molar fraction of hydrogen dimensionlessℎair Molar enthalpy of the air [Jmol]ℎCH4
Molar enthalpy of methane [Jmol]ℎCO Molar enthalpy of carbon monoxide
[Jmol]ℎCO2
Molar enthalpy of carbon dioxide [Jmol]ℎH2
Molar enthalpy of hydrogen [Jmol]ℎH2O Molar enthalpy of the water vapor [Jmol]
ℎO2
Molar enthalpy of oxygen [Jmol]ℎN2
Molar enthalpy of nitrogen [Jmol]119868 Operation current [A]IRE ldquoEnergy saving indexrdquo dimensionless1198940119886 Current density exchange anode side
[Am2]1198940119888 Current density exchange cathode side
[Am2]119894119897 Limit current density [Am2]119870ref Equilibrium constant of the reaction of
steam reforming dimensionless119870shif Equilibrium constant of the reaction of
Water Gas Shift Reaction dimensionless Air mass flow rate [kgs]CH
4
Methane mass flow rate [kgs]119905 Mass flow rate in the expander [kgs]119899CH4
Electric power obtained through theelectrochemical reaction of waterformation [W]
ac Power absorbed by the compressor gasturbine system [W]
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
Table 2 shows the values of the constants relating to (9) forthe two reactionsThe average ratio between speed of (6) andspeed of (5) is equal on average to about 03 Equations (7) and(8) are taken from [31] while (9) is taken from [30]Thereforein the calculations of the mass balance and thermal powerbalance we consider that for each mole of CH4 converted03 moles of H2 is also generated from the conversion of COproduced by (6) In light of this approximation the powerbalance to the prereformer appears to be expressed by
Table 2 Values for the calculation of the equilibrium constant 119870[30]
Reforming ShiftingA 26312 sdot 10
minus11547 sdot 10
minus12
B 12406 sdot 10minus7
minus2574 sdot 10minus8
C minus22523 sdot 10minus4
46374 sdot 10minus5
D 512749 sdot 10minus1
minus3915 sdot 10minus2
E minus66139488 13209723
Operating Temperature of the Cell (119879fc Block C in Figure 5)An iterative method for the calculation of the operatingtemperature of the cell is used as well We start froma temperature of attempt until the convergence of powerbalance is reached This last is expressed by
119899CH4
sdot ℎCH4
(119879an) + 119899H2Oifc
sdot ℎH2O (119879an) + 119899H
2 ifcsdot (119879an)
+ 119899COifcsdot ℎCO (119879an) + 119899CO
2 ifcsdot ℎCO
2
(119879an) + 119899O2 ifc
sdot ℎO2
(119879cat) + 119899N2
sdot ℎN2
(119879cat) minus 119899CH4
sdot Δℎref
minus 03119899CH4
sdot Δℎshif minus 119911 sdot ΔℎH2O
= 119899H2Oofc
sdot ℎH2O (119879fc) + 119899H
2ofcsdot (119879fc) + 119899COofc
sdot ℎCO (119879fc) + 119899CO2ofcsdot ℎCO
2
(119879fc) + 119899O2ofc
sdot ℎO2
(119879fc) + 119899N2
sdot ℎN2
(119879fc) +
(11)
6 Journal of Renewable Energy
It is interesting to observe graphically the power flow ofFigure 4 in which the contributions present in (11) are visibleIt is nowpossible at this stage to calculate the power generatedby the cell through
119888 = 119881 sdot 119868 (12)
To calculate 119868 the following equation is used
119868 = dfc sdot 119860119891 (13)
119881 is obtained by
119881 = 1198810 minus 119881Nernst minus 119881att minus 119881ohm minus 119881conc (14)
while (15) is used to calculate 1198810
1198810 =minusΔ1198660
2119865 (15)
119881Nernst is given by
119881Nernst =119877119879
2119865ln(
119891H2O
119891H2
sdot 119891O2
05sdot 11987505) (16)
119881att is provided by
119881act = 119881act119886
+ 119881act119888
(17)
To calculate 119881act119886
we resort to
119881act119886
= (119877119879
119865) sinhminus1 ( dfc
21198940119886
) (18)
Analogous calculation of 119881act119888
results by
119881act119888
= (119877119879
119865) sinhminus1 ( dfc
21198940119888
) (19)
Once losses for activation have been defined we calculatethose for concentration 119881conc by
119881conc = (119877119879
119865) ln(1 minus dfc
119894119897) (20)
The voltage loss due to the ohmic resistance is obtained by
119881ohm = dfc sdot4
sum
119894=1
119871 119894
120590119894
(21)
From (12) to (15) are taken from [3] whereas the equationsin (16) to (21) are taken from [4] Calculation of afterburningtemperature (block D in Figure 5) once it has left the cell thegas mixture reaches a postcombustor Here since the oxida-tion of both hydrogen and carbon monoxide still present inthe anode exhaust the temperature of the gas rises furtherThen the following occur
H2 +1
2O2 997888rarr H2O (22)
CO + 12O2 997888rarr CO2 (23)
By varying 119879pc the balance of thermal power is solvedexpressed by
119899H2 ipcsdot ℎH2
(119879fc) + 119899H2Oipc
sdot ℎH2O (119879fc) + 119899COipc
sdot ℎCO (119879fc) + 119899CO2 ipcsdot ℎCO
2
(119879fc) + 119899O2 ipc
sdot ℎO2
(119879fc) + 119899N2 ipcsdot ℎN2
(119879fc)
minus 120578comb [(119899H2 ipcsdot ΔℎH
2O) minus (119899COipc
sdot ΔℎCO2
)]
= 119899H2Oopc
sdot ℎH2O (119879pc) + 119899CO
2opcsdot ℎCO
2
(119879pc)
+ 119899O2opcsdot ℎO2
(119879pc) + 119899N2 ipcsdot ℎN2
(119879pc)
(24)
Once 119879pc is known which also corresponds to the TIT sincewe know the isentropic efficiency of the expander MTG wecan easily calculate the temperature of the turbine outlet (119879outblock E in Figure 5) by
119879out = TIT minus 120578is (TIT minus 119879is) (25)
Calculation of the inlet air temperature at the cathode (119879catblock F in Figure 5) gas mixture of known composition andtemperature 119879out once expanded is sent to a countercurrentheat exchanger (or regenerator) Here as the hot fluid andas the cold respectively the mixture under examination andthe outlet air from the compressor (at a flow rate equal to0808Kgs and at a temperature of 404K) enter The balanceequation of thermal power into the regenerator is expressedby
It starts from 1198791198901 attempted and the calculation is iterateduntil (26) is satisfied 1198791198901 represents the temperature at whichthe hot gases exiting the regenerator give part of their thermalpower to cogeneration purposes Once this first phase iscompleted the calculation of 119879cat through (27) is effected
Thus after calculating 119879cat the circuit is completely definedAt the following iteration this temperature 119879cat is the inputfor the calculation of 119879fc The cycle continues until all the
Journal of Renewable Energy 7
parameters arrive at convergence Then the evaluation ofperformance parameters is made as follows
Useful Power of the Cell Calculation (uc) Consider
Gas Turbine Useful Power Calculation (tg) Consider
tg = ut minus ac (31)
where
ut = 119905 sdot Δℎ (32)
Gas Turbine Efficiency Calculation (120578tg) Consider
120578tg =tg
CH4
sdot LHVCH4
(33)
The efficiency and useful power of the entire system are thencalculated as the sum of efficiency and useful power of SOFCandMTGWe then calculate the cogeneration indices that isIRE
IRE = 1 minustot
SI120578SI + cog (34)
and the thermal limit LT
LT =cog sdot 120578term
tot (35)
It was assumed that the heat available downstream of theregenerator was transferable with an efficiency of 40 to athermodynamic cycle downstream to calculate the cogener-ative values The procedure described already is summarizedin Figure 5
4 Constraints Definition
ldquoSettingrdquo defines a given combination of parameters dfc and119880119891 with which it is possible to operate the hybrid systemTherefore the set of all the possible settings by the rangewithin which the parameters themselves can vary is defined(Table 1) By defining the constraints we proceed to identifythe settings that are eligible for a given value of the flowof methane so as to adequately assess the elasticity designconnected to the same flow Steam to Carbon Ratio (STCR)the lower limit of Steam toCarbonRatio is the first restrictionto be taken into account defined as
STCR =119899H2O
119899CO + 119899CH4
(36)
The said parametermust remain above 2 In the event that thislimit is not respected the humidification of the anodemay notbe satisfactory and itmay cause cracking of bothmethane andcarbon dioxide molecules according to the reactions
CH4 997888rarr C + 2H2 (37)
CO2 997888rarr C +O2 (38)
Consequently we face the catalyst deactivation caused by thepresence of carbonaceous deposits
Constraint on Maximum Current Density The methane isconverted to hydrogen by (5) and (6) Given the assumptionspreviously made on the kinetics of these reactions we havethat the total conversion of one mole of methane per secondgives rise to 33 moles of hydrogen per second Simultane-ously according to (3) 119911 moles of hydrogen per second isinstead consumed Thus the consumption of hydrogen isdirectly proportional to the current density Therefore thesettings that provide a value of 119911 higher with respect tohydrogen product are considered ineligible
Constraints on the Operating Temperature of the Fuel Cell(119879fc) and the Turbine Inlet Temperature (119879119868119879) Constraintsrelating to temperature are the last to be taken into accountWe excluded the settings that generate temperatures of thestack higher than typical operating temperatures of SOFCsand have turbine inlet temperatures above 1250K (currenttechnological limit of MTG) Thus we summarize the con-ditions as follows
(a) 873K lt 119879fc lt 1200K(b) TIT lt 1250K
5 Results
In this section we proceed to the choice of the optimalconfiguration with which the hybrid system works and thento define the methane flow and the operative current densityThe next step is sensitivity analysis of the main parametersat varying 119880119891 whereas at the end a first validation ofthe calculation model is operated Selection of the optimalconfiguration the optimum configuration is that of completesystem This choice stems from the following reasoningAccording to (2) recirculation flow decreases at increasing119880119891 and the recirculation being at a temperature higher thancompressed methane this implies a lowering of 119879mix whichthen propagates on all operating parameters of the plantusing as a parameter to control the fall percentage 119879fc atvarying 119880119891 defined by
See Tables 3 and 4In the case of the base system the fall of temperature is
higher than 5 This is considered excessive By comparing
8 Journal of Renewable Energy
Table 3 Fall of temperature for increasing 119880119891 for base system
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 96392500 082 9137 521
Table 4 Fall of temperature for increasing 119880119891 for system withprereformer
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 94552500 082 9113 366
Table 5 Comparison between the gas turbine power plant withprereformer and complete system for dfc = 2500Am2
119880119891 System with prereformer Complete system081 1011 16674082 9238 15487083 8302 14483
Tables 3 and 4 it is evident how for homologous settingsin the case of system with prereformer the condition hasimproved Having higher temperatures with lower values 119880119891implies that a significant part of the fuel is not properlyused a phenomenon that has an impact on the values ofgas turbine power Therefore to remedy this gap is necessaryto insert an afterburner downstream of the fuel cell so thatthe configuration of the complete system becomes necessaryTable 5 shows how for homologous conditions the completesystem ensures a significant increase of the gas turbine power
Definition of Optimum Operating Conditions The optimumoperating conditions that is flow ofmethane and the currentdensity to operate with are chosen using design flexibility asthe criterion The model developed has been applied to thecalculation of the conditions resulting from three differentvalues of flow rate of methane low (119887 = 0012 kgs)medium (119898 = 0015 kgs) and high (119886 = 0018 kgs)In the case of high flow rate of methane there is no settingcompatible with all the constraints In contrast from acomparison between Tables 6(a) and 6(b) it is shown thatthe medium flow rate ensures greater design flexibility thusresulting in a specific value (asterisks are the settings eligible)Table 6(b) shows how for dfc = 2900Am2 there is agreater choice of the possible settings that satisfy all theconstraints outlined above so that this value is identified asthe operating current density and is used in the followingsensitivity analysis
Sensitivity of Operating Parameters and Performance at Vary-ing 119880119891 A sensitivity analysis is performed to determine theeffect of varying 119880119891 on the operating parameters and perfor-mance According to (2) the recirculation flow decreases atincreasing 119880119891 (first effect) Consequently all operating tem-peratures of the plant should decrease However the decreaseof recirculation flow implies a greater flow to the afterburner
Table 6 Plan of the possible settings for low and medium flow rateof methane
Figure 6 Percentage of prereforming at varying 119880119891
1000
1050
1100
1150
1200
1250
1300
T (K
)
076 077 078 079 080 081 082075
TIT (
Uf (mdash)
dfc = 2900 Am2)
Figure 7 TIT at varying 119880119891
as well (second effect) so that temperatures should increaseThe first effect prevails on the second one Therefore theoverall effect is a lowering of all operating temperatures of thehybrid system Consequently the temperature being lowerto keep the anode inlet temperature at the desired value aninferior amount of methane flow has to be reformed beforeentering the cellThus the percentage of reforming decreasesas Figure 6 shows Figure 7 owing to the already describedeffects shows how the temperature at the turbine inletmonotonically decreases and the turbogas power dependingon the TIT (TIT decrease means a decreasing in Δℎ thus areduction in useful power according to (31) and (32)) thismeans also a decreasing in terms of MTG power as one canobserve in Figure 8 Instead a nonmonotonous trend is thatconcerning the power of the cell In fact this is affected forlow values of 119880119891 by a prereforming effect which changesthe composition in the anode input (reactions (5) and (6))Therefore according to (16) the composition change meansthat the percentage of reforming decreases while Nernst-losses increase causing an overall power decrease in thestack Therefore when it is no longer necessary to reformthe Nernst-loss decreases with decreasing temperature sothat the power of the cell starts growing (Figure 9) Finally
140
150
160
170
180
190
200
P (k
W)
076 077 078 079 080 081 082075
MTG power (kW)
Uf (mdash)
Figure 8 Turbogas power at varying 119880119891
075 076 077 078 079 080 081 082
Fuel cell power (kW)
360
361
362
363
364
365
366
367
368
369
370
P (k
W)
Uf (mdash)
Figure 9 Fuel cell power at varying 119880119891
it is interesting to note that with increasing119880119891 while overallperformance parameters decrease there is an increase in theindex IRE (Figure 10) whereas the thermal limit remainsnearly constant
6 Discussion
61 First Validation of the Calculation Model A first testingof the model calculation was carried out both of a qualitativeand of a quantitative nature The ldquotrendrdquo of some fundamen-tal parameters with respect to developments known from theliterature was evaluated and the results obtained here werecompared with those calculated in [3]
62 Qualitative Validation First for purpose of qualitativemodel validation the data obtained were compared for thesame 119880119891 for different values of dfc As we expected Table 7shows that an increase of the current density causes anincrease of the operating temperature of the hybrid systemand consequently an increase in the percentage of methaneon which it performs the prereforming Table 8 shows that
10 Journal of Renewable Energy
075 076 077 078 079 080 081 08205
151520253035404550
()
IREThermal limit
dfc = 2900 Am2
Uf (mdash)
Figure 10 IRE (blue) and LT (red) at varying 119880119891
A CSOFC
DcAc
J16
Figure 11 Hybrid system studied in [3]
with the increase of dfc both the cell (despite an increasein voltage losses) and the gas turbine power rise the secondbeing directly dependent on the turbine inlet temperature
63 Quantitative Validation To end the first validationprocess the model was applied to the system of Figure 15studied in [3] and results were compared In [3] the methaneis compressed to 30 bars instead of the operating pressureof the MTG and then joined in a mixer and blend withassociated losses from the anode recirculation The mixer isthe only difference compared to the complete system Thethermodynamic modeling of the mixer and of the ejectorinside it would be very complex In homologous conditionsthe results turn out better for the complete system (consistentwith the physical principles) Thus one objective was toevaluate in a first approximation how the ejector affects thelosses using equivalent useful area as a parameter This isdefined as the percentage of usable area of Figure 3 hybridsystem compared with that of Figure 11 (without ejector)such that in homologous operating conditions both systemsproduce the same power The results are as shown in Table 9
It is seen that when the area is reduced up to 85 of thegiven ldquoplaterdquo the relative difference between the referencedata and the data provided by the model remains around 1thus lending credibility to the mathematical model describedin this paper
7 Conclusions
The objective set at the beginning was to define the optimalconditions of operation of the hybrid system by developinga C++ code and to evaluate the suitability of this approachwith the physical and chemical process present inside theSOFC-MTGplant In the first instancewe see that the optimalconfiguration of the hybrid system is that of the completesystem This ensures both a satisfactory temperature man-agement and good values of gas turbine power The flow rateof methane is excellent given the guaranteed high designflexibility which is defined as 119898 that is 0015 kgs Forthe said value of the flow rate of methane current densitythat ensures the best compromise between performance anddegrees of freedom to the designer (varying 119880119891 eligible
Journal of Renewable Energy 11
Table 7 Operating parameters in equal value 119880119891 for different dfc
dfc [Am2] 119880119891 Voltage [V] Voltage losses [V] uc [kW] tg [kW] tot [kW]2900 082 06788 05058 36278 14128 504063000 082 06619 05227 36596 18078 54674
Table 9 Comparison of the data obtained with the model andexperimental data studied by evaluating an equivalent useful areaequal to 85 of the effective area (dfc = 3200Am2)
Model data Reference data Relative difference[]
Hybrid systempower [kW] 43147 428 080
Fuel cell power[kW] 32052 319 047
Gas turbinepower [kW] 11095 109 176
Hybrid systemefficiency [kW] 062 061
Fuel cellefficiency [kW] 046 045
Gas turbineefficiency [kW] 016 016
between 075 and 082) is that of 2900Am2 The last stepis the choice of operating 119880119891 which may vary dependingon the objective it set out choosing a low 119880119891 if there isdirected towards energy optimization 119880119891 high if the goalis to maximize the cogeneration yield and a medium 119880119891 ifseeking a compromise between the two requirements Sincesystems of this type are still under study of the 3 optionsdescribed above at the current state of the art it seemsto make sense to focus on energy optimization and whenconsolidated on the market there will be consideration laterwith the economic scenario of the moment This factor isclosely related to the evaluation of the investment fromthe perspective of cogeneration The developed C++ codematches with both the state of the art and reference datataken from the literature suggesting the suitability of thisapproach to evaluate and describe SOFC-MTG and otherkinds of plants
Nomenclature
119860119891 Useful area of the fuel cell [m2]
119888119901 Specific heat at constant pressure[J(molsdotK)]
119888119901119898 Average specific heat of the mixture in the
course of expansion [J(kgsdotK)]119888V Specific heat at constant volume
[J(molsdotK)]dfc Current density with which it operates
within the fuel cell [Am2]119865 Faraday constant that is 96485 [Cmol]119891CO Molar fraction of carbon monoxide
dimensionless119891H2
Molar fraction of hydrogen dimensionlessℎair Molar enthalpy of the air [Jmol]ℎCH4
Molar enthalpy of methane [Jmol]ℎCO Molar enthalpy of carbon monoxide
[Jmol]ℎCO2
Molar enthalpy of carbon dioxide [Jmol]ℎH2
Molar enthalpy of hydrogen [Jmol]ℎH2O Molar enthalpy of the water vapor [Jmol]
ℎO2
Molar enthalpy of oxygen [Jmol]ℎN2
Molar enthalpy of nitrogen [Jmol]119868 Operation current [A]IRE ldquoEnergy saving indexrdquo dimensionless1198940119886 Current density exchange anode side
[Am2]1198940119888 Current density exchange cathode side
[Am2]119894119897 Limit current density [Am2]119870ref Equilibrium constant of the reaction of
steam reforming dimensionless119870shif Equilibrium constant of the reaction of
Water Gas Shift Reaction dimensionless Air mass flow rate [kgs]CH
4
Methane mass flow rate [kgs]119905 Mass flow rate in the expander [kgs]119899CH4
Electric power obtained through theelectrochemical reaction of waterformation [W]
ac Power absorbed by the compressor gasturbine system [W]
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
6 Journal of Renewable Energy
It is interesting to observe graphically the power flow ofFigure 4 in which the contributions present in (11) are visibleIt is nowpossible at this stage to calculate the power generatedby the cell through
119888 = 119881 sdot 119868 (12)
To calculate 119868 the following equation is used
119868 = dfc sdot 119860119891 (13)
119881 is obtained by
119881 = 1198810 minus 119881Nernst minus 119881att minus 119881ohm minus 119881conc (14)
while (15) is used to calculate 1198810
1198810 =minusΔ1198660
2119865 (15)
119881Nernst is given by
119881Nernst =119877119879
2119865ln(
119891H2O
119891H2
sdot 119891O2
05sdot 11987505) (16)
119881att is provided by
119881act = 119881act119886
+ 119881act119888
(17)
To calculate 119881act119886
we resort to
119881act119886
= (119877119879
119865) sinhminus1 ( dfc
21198940119886
) (18)
Analogous calculation of 119881act119888
results by
119881act119888
= (119877119879
119865) sinhminus1 ( dfc
21198940119888
) (19)
Once losses for activation have been defined we calculatethose for concentration 119881conc by
119881conc = (119877119879
119865) ln(1 minus dfc
119894119897) (20)
The voltage loss due to the ohmic resistance is obtained by
119881ohm = dfc sdot4
sum
119894=1
119871 119894
120590119894
(21)
From (12) to (15) are taken from [3] whereas the equationsin (16) to (21) are taken from [4] Calculation of afterburningtemperature (block D in Figure 5) once it has left the cell thegas mixture reaches a postcombustor Here since the oxida-tion of both hydrogen and carbon monoxide still present inthe anode exhaust the temperature of the gas rises furtherThen the following occur
H2 +1
2O2 997888rarr H2O (22)
CO + 12O2 997888rarr CO2 (23)
By varying 119879pc the balance of thermal power is solvedexpressed by
119899H2 ipcsdot ℎH2
(119879fc) + 119899H2Oipc
sdot ℎH2O (119879fc) + 119899COipc
sdot ℎCO (119879fc) + 119899CO2 ipcsdot ℎCO
2
(119879fc) + 119899O2 ipc
sdot ℎO2
(119879fc) + 119899N2 ipcsdot ℎN2
(119879fc)
minus 120578comb [(119899H2 ipcsdot ΔℎH
2O) minus (119899COipc
sdot ΔℎCO2
)]
= 119899H2Oopc
sdot ℎH2O (119879pc) + 119899CO
2opcsdot ℎCO
2
(119879pc)
+ 119899O2opcsdot ℎO2
(119879pc) + 119899N2 ipcsdot ℎN2
(119879pc)
(24)
Once 119879pc is known which also corresponds to the TIT sincewe know the isentropic efficiency of the expander MTG wecan easily calculate the temperature of the turbine outlet (119879outblock E in Figure 5) by
119879out = TIT minus 120578is (TIT minus 119879is) (25)
Calculation of the inlet air temperature at the cathode (119879catblock F in Figure 5) gas mixture of known composition andtemperature 119879out once expanded is sent to a countercurrentheat exchanger (or regenerator) Here as the hot fluid andas the cold respectively the mixture under examination andthe outlet air from the compressor (at a flow rate equal to0808Kgs and at a temperature of 404K) enter The balanceequation of thermal power into the regenerator is expressedby
It starts from 1198791198901 attempted and the calculation is iterateduntil (26) is satisfied 1198791198901 represents the temperature at whichthe hot gases exiting the regenerator give part of their thermalpower to cogeneration purposes Once this first phase iscompleted the calculation of 119879cat through (27) is effected
Thus after calculating 119879cat the circuit is completely definedAt the following iteration this temperature 119879cat is the inputfor the calculation of 119879fc The cycle continues until all the
Journal of Renewable Energy 7
parameters arrive at convergence Then the evaluation ofperformance parameters is made as follows
Useful Power of the Cell Calculation (uc) Consider
Gas Turbine Useful Power Calculation (tg) Consider
tg = ut minus ac (31)
where
ut = 119905 sdot Δℎ (32)
Gas Turbine Efficiency Calculation (120578tg) Consider
120578tg =tg
CH4
sdot LHVCH4
(33)
The efficiency and useful power of the entire system are thencalculated as the sum of efficiency and useful power of SOFCandMTGWe then calculate the cogeneration indices that isIRE
IRE = 1 minustot
SI120578SI + cog (34)
and the thermal limit LT
LT =cog sdot 120578term
tot (35)
It was assumed that the heat available downstream of theregenerator was transferable with an efficiency of 40 to athermodynamic cycle downstream to calculate the cogener-ative values The procedure described already is summarizedin Figure 5
4 Constraints Definition
ldquoSettingrdquo defines a given combination of parameters dfc and119880119891 with which it is possible to operate the hybrid systemTherefore the set of all the possible settings by the rangewithin which the parameters themselves can vary is defined(Table 1) By defining the constraints we proceed to identifythe settings that are eligible for a given value of the flowof methane so as to adequately assess the elasticity designconnected to the same flow Steam to Carbon Ratio (STCR)the lower limit of Steam toCarbonRatio is the first restrictionto be taken into account defined as
STCR =119899H2O
119899CO + 119899CH4
(36)
The said parametermust remain above 2 In the event that thislimit is not respected the humidification of the anodemay notbe satisfactory and itmay cause cracking of bothmethane andcarbon dioxide molecules according to the reactions
CH4 997888rarr C + 2H2 (37)
CO2 997888rarr C +O2 (38)
Consequently we face the catalyst deactivation caused by thepresence of carbonaceous deposits
Constraint on Maximum Current Density The methane isconverted to hydrogen by (5) and (6) Given the assumptionspreviously made on the kinetics of these reactions we havethat the total conversion of one mole of methane per secondgives rise to 33 moles of hydrogen per second Simultane-ously according to (3) 119911 moles of hydrogen per second isinstead consumed Thus the consumption of hydrogen isdirectly proportional to the current density Therefore thesettings that provide a value of 119911 higher with respect tohydrogen product are considered ineligible
Constraints on the Operating Temperature of the Fuel Cell(119879fc) and the Turbine Inlet Temperature (119879119868119879) Constraintsrelating to temperature are the last to be taken into accountWe excluded the settings that generate temperatures of thestack higher than typical operating temperatures of SOFCsand have turbine inlet temperatures above 1250K (currenttechnological limit of MTG) Thus we summarize the con-ditions as follows
(a) 873K lt 119879fc lt 1200K(b) TIT lt 1250K
5 Results
In this section we proceed to the choice of the optimalconfiguration with which the hybrid system works and thento define the methane flow and the operative current densityThe next step is sensitivity analysis of the main parametersat varying 119880119891 whereas at the end a first validation ofthe calculation model is operated Selection of the optimalconfiguration the optimum configuration is that of completesystem This choice stems from the following reasoningAccording to (2) recirculation flow decreases at increasing119880119891 and the recirculation being at a temperature higher thancompressed methane this implies a lowering of 119879mix whichthen propagates on all operating parameters of the plantusing as a parameter to control the fall percentage 119879fc atvarying 119880119891 defined by
See Tables 3 and 4In the case of the base system the fall of temperature is
higher than 5 This is considered excessive By comparing
8 Journal of Renewable Energy
Table 3 Fall of temperature for increasing 119880119891 for base system
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 96392500 082 9137 521
Table 4 Fall of temperature for increasing 119880119891 for system withprereformer
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 94552500 082 9113 366
Table 5 Comparison between the gas turbine power plant withprereformer and complete system for dfc = 2500Am2
119880119891 System with prereformer Complete system081 1011 16674082 9238 15487083 8302 14483
Tables 3 and 4 it is evident how for homologous settingsin the case of system with prereformer the condition hasimproved Having higher temperatures with lower values 119880119891implies that a significant part of the fuel is not properlyused a phenomenon that has an impact on the values ofgas turbine power Therefore to remedy this gap is necessaryto insert an afterburner downstream of the fuel cell so thatthe configuration of the complete system becomes necessaryTable 5 shows how for homologous conditions the completesystem ensures a significant increase of the gas turbine power
Definition of Optimum Operating Conditions The optimumoperating conditions that is flow ofmethane and the currentdensity to operate with are chosen using design flexibility asthe criterion The model developed has been applied to thecalculation of the conditions resulting from three differentvalues of flow rate of methane low (119887 = 0012 kgs)medium (119898 = 0015 kgs) and high (119886 = 0018 kgs)In the case of high flow rate of methane there is no settingcompatible with all the constraints In contrast from acomparison between Tables 6(a) and 6(b) it is shown thatthe medium flow rate ensures greater design flexibility thusresulting in a specific value (asterisks are the settings eligible)Table 6(b) shows how for dfc = 2900Am2 there is agreater choice of the possible settings that satisfy all theconstraints outlined above so that this value is identified asthe operating current density and is used in the followingsensitivity analysis
Sensitivity of Operating Parameters and Performance at Vary-ing 119880119891 A sensitivity analysis is performed to determine theeffect of varying 119880119891 on the operating parameters and perfor-mance According to (2) the recirculation flow decreases atincreasing 119880119891 (first effect) Consequently all operating tem-peratures of the plant should decrease However the decreaseof recirculation flow implies a greater flow to the afterburner
Table 6 Plan of the possible settings for low and medium flow rateof methane
Figure 6 Percentage of prereforming at varying 119880119891
1000
1050
1100
1150
1200
1250
1300
T (K
)
076 077 078 079 080 081 082075
TIT (
Uf (mdash)
dfc = 2900 Am2)
Figure 7 TIT at varying 119880119891
as well (second effect) so that temperatures should increaseThe first effect prevails on the second one Therefore theoverall effect is a lowering of all operating temperatures of thehybrid system Consequently the temperature being lowerto keep the anode inlet temperature at the desired value aninferior amount of methane flow has to be reformed beforeentering the cellThus the percentage of reforming decreasesas Figure 6 shows Figure 7 owing to the already describedeffects shows how the temperature at the turbine inletmonotonically decreases and the turbogas power dependingon the TIT (TIT decrease means a decreasing in Δℎ thus areduction in useful power according to (31) and (32)) thismeans also a decreasing in terms of MTG power as one canobserve in Figure 8 Instead a nonmonotonous trend is thatconcerning the power of the cell In fact this is affected forlow values of 119880119891 by a prereforming effect which changesthe composition in the anode input (reactions (5) and (6))Therefore according to (16) the composition change meansthat the percentage of reforming decreases while Nernst-losses increase causing an overall power decrease in thestack Therefore when it is no longer necessary to reformthe Nernst-loss decreases with decreasing temperature sothat the power of the cell starts growing (Figure 9) Finally
140
150
160
170
180
190
200
P (k
W)
076 077 078 079 080 081 082075
MTG power (kW)
Uf (mdash)
Figure 8 Turbogas power at varying 119880119891
075 076 077 078 079 080 081 082
Fuel cell power (kW)
360
361
362
363
364
365
366
367
368
369
370
P (k
W)
Uf (mdash)
Figure 9 Fuel cell power at varying 119880119891
it is interesting to note that with increasing119880119891 while overallperformance parameters decrease there is an increase in theindex IRE (Figure 10) whereas the thermal limit remainsnearly constant
6 Discussion
61 First Validation of the Calculation Model A first testingof the model calculation was carried out both of a qualitativeand of a quantitative nature The ldquotrendrdquo of some fundamen-tal parameters with respect to developments known from theliterature was evaluated and the results obtained here werecompared with those calculated in [3]
62 Qualitative Validation First for purpose of qualitativemodel validation the data obtained were compared for thesame 119880119891 for different values of dfc As we expected Table 7shows that an increase of the current density causes anincrease of the operating temperature of the hybrid systemand consequently an increase in the percentage of methaneon which it performs the prereforming Table 8 shows that
10 Journal of Renewable Energy
075 076 077 078 079 080 081 08205
151520253035404550
()
IREThermal limit
dfc = 2900 Am2
Uf (mdash)
Figure 10 IRE (blue) and LT (red) at varying 119880119891
A CSOFC
DcAc
J16
Figure 11 Hybrid system studied in [3]
with the increase of dfc both the cell (despite an increasein voltage losses) and the gas turbine power rise the secondbeing directly dependent on the turbine inlet temperature
63 Quantitative Validation To end the first validationprocess the model was applied to the system of Figure 15studied in [3] and results were compared In [3] the methaneis compressed to 30 bars instead of the operating pressureof the MTG and then joined in a mixer and blend withassociated losses from the anode recirculation The mixer isthe only difference compared to the complete system Thethermodynamic modeling of the mixer and of the ejectorinside it would be very complex In homologous conditionsthe results turn out better for the complete system (consistentwith the physical principles) Thus one objective was toevaluate in a first approximation how the ejector affects thelosses using equivalent useful area as a parameter This isdefined as the percentage of usable area of Figure 3 hybridsystem compared with that of Figure 11 (without ejector)such that in homologous operating conditions both systemsproduce the same power The results are as shown in Table 9
It is seen that when the area is reduced up to 85 of thegiven ldquoplaterdquo the relative difference between the referencedata and the data provided by the model remains around 1thus lending credibility to the mathematical model describedin this paper
7 Conclusions
The objective set at the beginning was to define the optimalconditions of operation of the hybrid system by developinga C++ code and to evaluate the suitability of this approachwith the physical and chemical process present inside theSOFC-MTGplant In the first instancewe see that the optimalconfiguration of the hybrid system is that of the completesystem This ensures both a satisfactory temperature man-agement and good values of gas turbine power The flow rateof methane is excellent given the guaranteed high designflexibility which is defined as 119898 that is 0015 kgs Forthe said value of the flow rate of methane current densitythat ensures the best compromise between performance anddegrees of freedom to the designer (varying 119880119891 eligible
Journal of Renewable Energy 11
Table 7 Operating parameters in equal value 119880119891 for different dfc
dfc [Am2] 119880119891 Voltage [V] Voltage losses [V] uc [kW] tg [kW] tot [kW]2900 082 06788 05058 36278 14128 504063000 082 06619 05227 36596 18078 54674
Table 9 Comparison of the data obtained with the model andexperimental data studied by evaluating an equivalent useful areaequal to 85 of the effective area (dfc = 3200Am2)
Model data Reference data Relative difference[]
Hybrid systempower [kW] 43147 428 080
Fuel cell power[kW] 32052 319 047
Gas turbinepower [kW] 11095 109 176
Hybrid systemefficiency [kW] 062 061
Fuel cellefficiency [kW] 046 045
Gas turbineefficiency [kW] 016 016
between 075 and 082) is that of 2900Am2 The last stepis the choice of operating 119880119891 which may vary dependingon the objective it set out choosing a low 119880119891 if there isdirected towards energy optimization 119880119891 high if the goalis to maximize the cogeneration yield and a medium 119880119891 ifseeking a compromise between the two requirements Sincesystems of this type are still under study of the 3 optionsdescribed above at the current state of the art it seemsto make sense to focus on energy optimization and whenconsolidated on the market there will be consideration laterwith the economic scenario of the moment This factor isclosely related to the evaluation of the investment fromthe perspective of cogeneration The developed C++ codematches with both the state of the art and reference datataken from the literature suggesting the suitability of thisapproach to evaluate and describe SOFC-MTG and otherkinds of plants
Nomenclature
119860119891 Useful area of the fuel cell [m2]
119888119901 Specific heat at constant pressure[J(molsdotK)]
119888119901119898 Average specific heat of the mixture in the
course of expansion [J(kgsdotK)]119888V Specific heat at constant volume
[J(molsdotK)]dfc Current density with which it operates
within the fuel cell [Am2]119865 Faraday constant that is 96485 [Cmol]119891CO Molar fraction of carbon monoxide
dimensionless119891H2
Molar fraction of hydrogen dimensionlessℎair Molar enthalpy of the air [Jmol]ℎCH4
Molar enthalpy of methane [Jmol]ℎCO Molar enthalpy of carbon monoxide
[Jmol]ℎCO2
Molar enthalpy of carbon dioxide [Jmol]ℎH2
Molar enthalpy of hydrogen [Jmol]ℎH2O Molar enthalpy of the water vapor [Jmol]
ℎO2
Molar enthalpy of oxygen [Jmol]ℎN2
Molar enthalpy of nitrogen [Jmol]119868 Operation current [A]IRE ldquoEnergy saving indexrdquo dimensionless1198940119886 Current density exchange anode side
[Am2]1198940119888 Current density exchange cathode side
[Am2]119894119897 Limit current density [Am2]119870ref Equilibrium constant of the reaction of
steam reforming dimensionless119870shif Equilibrium constant of the reaction of
Water Gas Shift Reaction dimensionless Air mass flow rate [kgs]CH
4
Methane mass flow rate [kgs]119905 Mass flow rate in the expander [kgs]119899CH4
Electric power obtained through theelectrochemical reaction of waterformation [W]
ac Power absorbed by the compressor gasturbine system [W]
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
Gas Turbine Useful Power Calculation (tg) Consider
tg = ut minus ac (31)
where
ut = 119905 sdot Δℎ (32)
Gas Turbine Efficiency Calculation (120578tg) Consider
120578tg =tg
CH4
sdot LHVCH4
(33)
The efficiency and useful power of the entire system are thencalculated as the sum of efficiency and useful power of SOFCandMTGWe then calculate the cogeneration indices that isIRE
IRE = 1 minustot
SI120578SI + cog (34)
and the thermal limit LT
LT =cog sdot 120578term
tot (35)
It was assumed that the heat available downstream of theregenerator was transferable with an efficiency of 40 to athermodynamic cycle downstream to calculate the cogener-ative values The procedure described already is summarizedin Figure 5
4 Constraints Definition
ldquoSettingrdquo defines a given combination of parameters dfc and119880119891 with which it is possible to operate the hybrid systemTherefore the set of all the possible settings by the rangewithin which the parameters themselves can vary is defined(Table 1) By defining the constraints we proceed to identifythe settings that are eligible for a given value of the flowof methane so as to adequately assess the elasticity designconnected to the same flow Steam to Carbon Ratio (STCR)the lower limit of Steam toCarbonRatio is the first restrictionto be taken into account defined as
STCR =119899H2O
119899CO + 119899CH4
(36)
The said parametermust remain above 2 In the event that thislimit is not respected the humidification of the anodemay notbe satisfactory and itmay cause cracking of bothmethane andcarbon dioxide molecules according to the reactions
CH4 997888rarr C + 2H2 (37)
CO2 997888rarr C +O2 (38)
Consequently we face the catalyst deactivation caused by thepresence of carbonaceous deposits
Constraint on Maximum Current Density The methane isconverted to hydrogen by (5) and (6) Given the assumptionspreviously made on the kinetics of these reactions we havethat the total conversion of one mole of methane per secondgives rise to 33 moles of hydrogen per second Simultane-ously according to (3) 119911 moles of hydrogen per second isinstead consumed Thus the consumption of hydrogen isdirectly proportional to the current density Therefore thesettings that provide a value of 119911 higher with respect tohydrogen product are considered ineligible
Constraints on the Operating Temperature of the Fuel Cell(119879fc) and the Turbine Inlet Temperature (119879119868119879) Constraintsrelating to temperature are the last to be taken into accountWe excluded the settings that generate temperatures of thestack higher than typical operating temperatures of SOFCsand have turbine inlet temperatures above 1250K (currenttechnological limit of MTG) Thus we summarize the con-ditions as follows
(a) 873K lt 119879fc lt 1200K(b) TIT lt 1250K
5 Results
In this section we proceed to the choice of the optimalconfiguration with which the hybrid system works and thento define the methane flow and the operative current densityThe next step is sensitivity analysis of the main parametersat varying 119880119891 whereas at the end a first validation ofthe calculation model is operated Selection of the optimalconfiguration the optimum configuration is that of completesystem This choice stems from the following reasoningAccording to (2) recirculation flow decreases at increasing119880119891 and the recirculation being at a temperature higher thancompressed methane this implies a lowering of 119879mix whichthen propagates on all operating parameters of the plantusing as a parameter to control the fall percentage 119879fc atvarying 119880119891 defined by
See Tables 3 and 4In the case of the base system the fall of temperature is
higher than 5 This is considered excessive By comparing
8 Journal of Renewable Energy
Table 3 Fall of temperature for increasing 119880119891 for base system
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 96392500 082 9137 521
Table 4 Fall of temperature for increasing 119880119891 for system withprereformer
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 94552500 082 9113 366
Table 5 Comparison between the gas turbine power plant withprereformer and complete system for dfc = 2500Am2
119880119891 System with prereformer Complete system081 1011 16674082 9238 15487083 8302 14483
Tables 3 and 4 it is evident how for homologous settingsin the case of system with prereformer the condition hasimproved Having higher temperatures with lower values 119880119891implies that a significant part of the fuel is not properlyused a phenomenon that has an impact on the values ofgas turbine power Therefore to remedy this gap is necessaryto insert an afterburner downstream of the fuel cell so thatthe configuration of the complete system becomes necessaryTable 5 shows how for homologous conditions the completesystem ensures a significant increase of the gas turbine power
Definition of Optimum Operating Conditions The optimumoperating conditions that is flow ofmethane and the currentdensity to operate with are chosen using design flexibility asthe criterion The model developed has been applied to thecalculation of the conditions resulting from three differentvalues of flow rate of methane low (119887 = 0012 kgs)medium (119898 = 0015 kgs) and high (119886 = 0018 kgs)In the case of high flow rate of methane there is no settingcompatible with all the constraints In contrast from acomparison between Tables 6(a) and 6(b) it is shown thatthe medium flow rate ensures greater design flexibility thusresulting in a specific value (asterisks are the settings eligible)Table 6(b) shows how for dfc = 2900Am2 there is agreater choice of the possible settings that satisfy all theconstraints outlined above so that this value is identified asthe operating current density and is used in the followingsensitivity analysis
Sensitivity of Operating Parameters and Performance at Vary-ing 119880119891 A sensitivity analysis is performed to determine theeffect of varying 119880119891 on the operating parameters and perfor-mance According to (2) the recirculation flow decreases atincreasing 119880119891 (first effect) Consequently all operating tem-peratures of the plant should decrease However the decreaseof recirculation flow implies a greater flow to the afterburner
Table 6 Plan of the possible settings for low and medium flow rateof methane
Figure 6 Percentage of prereforming at varying 119880119891
1000
1050
1100
1150
1200
1250
1300
T (K
)
076 077 078 079 080 081 082075
TIT (
Uf (mdash)
dfc = 2900 Am2)
Figure 7 TIT at varying 119880119891
as well (second effect) so that temperatures should increaseThe first effect prevails on the second one Therefore theoverall effect is a lowering of all operating temperatures of thehybrid system Consequently the temperature being lowerto keep the anode inlet temperature at the desired value aninferior amount of methane flow has to be reformed beforeentering the cellThus the percentage of reforming decreasesas Figure 6 shows Figure 7 owing to the already describedeffects shows how the temperature at the turbine inletmonotonically decreases and the turbogas power dependingon the TIT (TIT decrease means a decreasing in Δℎ thus areduction in useful power according to (31) and (32)) thismeans also a decreasing in terms of MTG power as one canobserve in Figure 8 Instead a nonmonotonous trend is thatconcerning the power of the cell In fact this is affected forlow values of 119880119891 by a prereforming effect which changesthe composition in the anode input (reactions (5) and (6))Therefore according to (16) the composition change meansthat the percentage of reforming decreases while Nernst-losses increase causing an overall power decrease in thestack Therefore when it is no longer necessary to reformthe Nernst-loss decreases with decreasing temperature sothat the power of the cell starts growing (Figure 9) Finally
140
150
160
170
180
190
200
P (k
W)
076 077 078 079 080 081 082075
MTG power (kW)
Uf (mdash)
Figure 8 Turbogas power at varying 119880119891
075 076 077 078 079 080 081 082
Fuel cell power (kW)
360
361
362
363
364
365
366
367
368
369
370
P (k
W)
Uf (mdash)
Figure 9 Fuel cell power at varying 119880119891
it is interesting to note that with increasing119880119891 while overallperformance parameters decrease there is an increase in theindex IRE (Figure 10) whereas the thermal limit remainsnearly constant
6 Discussion
61 First Validation of the Calculation Model A first testingof the model calculation was carried out both of a qualitativeand of a quantitative nature The ldquotrendrdquo of some fundamen-tal parameters with respect to developments known from theliterature was evaluated and the results obtained here werecompared with those calculated in [3]
62 Qualitative Validation First for purpose of qualitativemodel validation the data obtained were compared for thesame 119880119891 for different values of dfc As we expected Table 7shows that an increase of the current density causes anincrease of the operating temperature of the hybrid systemand consequently an increase in the percentage of methaneon which it performs the prereforming Table 8 shows that
10 Journal of Renewable Energy
075 076 077 078 079 080 081 08205
151520253035404550
()
IREThermal limit
dfc = 2900 Am2
Uf (mdash)
Figure 10 IRE (blue) and LT (red) at varying 119880119891
A CSOFC
DcAc
J16
Figure 11 Hybrid system studied in [3]
with the increase of dfc both the cell (despite an increasein voltage losses) and the gas turbine power rise the secondbeing directly dependent on the turbine inlet temperature
63 Quantitative Validation To end the first validationprocess the model was applied to the system of Figure 15studied in [3] and results were compared In [3] the methaneis compressed to 30 bars instead of the operating pressureof the MTG and then joined in a mixer and blend withassociated losses from the anode recirculation The mixer isthe only difference compared to the complete system Thethermodynamic modeling of the mixer and of the ejectorinside it would be very complex In homologous conditionsthe results turn out better for the complete system (consistentwith the physical principles) Thus one objective was toevaluate in a first approximation how the ejector affects thelosses using equivalent useful area as a parameter This isdefined as the percentage of usable area of Figure 3 hybridsystem compared with that of Figure 11 (without ejector)such that in homologous operating conditions both systemsproduce the same power The results are as shown in Table 9
It is seen that when the area is reduced up to 85 of thegiven ldquoplaterdquo the relative difference between the referencedata and the data provided by the model remains around 1thus lending credibility to the mathematical model describedin this paper
7 Conclusions
The objective set at the beginning was to define the optimalconditions of operation of the hybrid system by developinga C++ code and to evaluate the suitability of this approachwith the physical and chemical process present inside theSOFC-MTGplant In the first instancewe see that the optimalconfiguration of the hybrid system is that of the completesystem This ensures both a satisfactory temperature man-agement and good values of gas turbine power The flow rateof methane is excellent given the guaranteed high designflexibility which is defined as 119898 that is 0015 kgs Forthe said value of the flow rate of methane current densitythat ensures the best compromise between performance anddegrees of freedom to the designer (varying 119880119891 eligible
Journal of Renewable Energy 11
Table 7 Operating parameters in equal value 119880119891 for different dfc
dfc [Am2] 119880119891 Voltage [V] Voltage losses [V] uc [kW] tg [kW] tot [kW]2900 082 06788 05058 36278 14128 504063000 082 06619 05227 36596 18078 54674
Table 9 Comparison of the data obtained with the model andexperimental data studied by evaluating an equivalent useful areaequal to 85 of the effective area (dfc = 3200Am2)
Model data Reference data Relative difference[]
Hybrid systempower [kW] 43147 428 080
Fuel cell power[kW] 32052 319 047
Gas turbinepower [kW] 11095 109 176
Hybrid systemefficiency [kW] 062 061
Fuel cellefficiency [kW] 046 045
Gas turbineefficiency [kW] 016 016
between 075 and 082) is that of 2900Am2 The last stepis the choice of operating 119880119891 which may vary dependingon the objective it set out choosing a low 119880119891 if there isdirected towards energy optimization 119880119891 high if the goalis to maximize the cogeneration yield and a medium 119880119891 ifseeking a compromise between the two requirements Sincesystems of this type are still under study of the 3 optionsdescribed above at the current state of the art it seemsto make sense to focus on energy optimization and whenconsolidated on the market there will be consideration laterwith the economic scenario of the moment This factor isclosely related to the evaluation of the investment fromthe perspective of cogeneration The developed C++ codematches with both the state of the art and reference datataken from the literature suggesting the suitability of thisapproach to evaluate and describe SOFC-MTG and otherkinds of plants
Nomenclature
119860119891 Useful area of the fuel cell [m2]
119888119901 Specific heat at constant pressure[J(molsdotK)]
119888119901119898 Average specific heat of the mixture in the
course of expansion [J(kgsdotK)]119888V Specific heat at constant volume
[J(molsdotK)]dfc Current density with which it operates
within the fuel cell [Am2]119865 Faraday constant that is 96485 [Cmol]119891CO Molar fraction of carbon monoxide
dimensionless119891H2
Molar fraction of hydrogen dimensionlessℎair Molar enthalpy of the air [Jmol]ℎCH4
Molar enthalpy of methane [Jmol]ℎCO Molar enthalpy of carbon monoxide
[Jmol]ℎCO2
Molar enthalpy of carbon dioxide [Jmol]ℎH2
Molar enthalpy of hydrogen [Jmol]ℎH2O Molar enthalpy of the water vapor [Jmol]
ℎO2
Molar enthalpy of oxygen [Jmol]ℎN2
Molar enthalpy of nitrogen [Jmol]119868 Operation current [A]IRE ldquoEnergy saving indexrdquo dimensionless1198940119886 Current density exchange anode side
[Am2]1198940119888 Current density exchange cathode side
[Am2]119894119897 Limit current density [Am2]119870ref Equilibrium constant of the reaction of
steam reforming dimensionless119870shif Equilibrium constant of the reaction of
Water Gas Shift Reaction dimensionless Air mass flow rate [kgs]CH
4
Methane mass flow rate [kgs]119905 Mass flow rate in the expander [kgs]119899CH4
Electric power obtained through theelectrochemical reaction of waterformation [W]
ac Power absorbed by the compressor gasturbine system [W]
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
8 Journal of Renewable Energy
Table 3 Fall of temperature for increasing 119880119891 for base system
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 96392500 082 9137 521
Table 4 Fall of temperature for increasing 119880119891 for system withprereformer
dfc [Am2] 119880119891 119879fc [K] Fall of temperature []2500 081 94552500 082 9113 366
Table 5 Comparison between the gas turbine power plant withprereformer and complete system for dfc = 2500Am2
119880119891 System with prereformer Complete system081 1011 16674082 9238 15487083 8302 14483
Tables 3 and 4 it is evident how for homologous settingsin the case of system with prereformer the condition hasimproved Having higher temperatures with lower values 119880119891implies that a significant part of the fuel is not properlyused a phenomenon that has an impact on the values ofgas turbine power Therefore to remedy this gap is necessaryto insert an afterburner downstream of the fuel cell so thatthe configuration of the complete system becomes necessaryTable 5 shows how for homologous conditions the completesystem ensures a significant increase of the gas turbine power
Definition of Optimum Operating Conditions The optimumoperating conditions that is flow ofmethane and the currentdensity to operate with are chosen using design flexibility asthe criterion The model developed has been applied to thecalculation of the conditions resulting from three differentvalues of flow rate of methane low (119887 = 0012 kgs)medium (119898 = 0015 kgs) and high (119886 = 0018 kgs)In the case of high flow rate of methane there is no settingcompatible with all the constraints In contrast from acomparison between Tables 6(a) and 6(b) it is shown thatthe medium flow rate ensures greater design flexibility thusresulting in a specific value (asterisks are the settings eligible)Table 6(b) shows how for dfc = 2900Am2 there is agreater choice of the possible settings that satisfy all theconstraints outlined above so that this value is identified asthe operating current density and is used in the followingsensitivity analysis
Sensitivity of Operating Parameters and Performance at Vary-ing 119880119891 A sensitivity analysis is performed to determine theeffect of varying 119880119891 on the operating parameters and perfor-mance According to (2) the recirculation flow decreases atincreasing 119880119891 (first effect) Consequently all operating tem-peratures of the plant should decrease However the decreaseof recirculation flow implies a greater flow to the afterburner
Table 6 Plan of the possible settings for low and medium flow rateof methane
Figure 6 Percentage of prereforming at varying 119880119891
1000
1050
1100
1150
1200
1250
1300
T (K
)
076 077 078 079 080 081 082075
TIT (
Uf (mdash)
dfc = 2900 Am2)
Figure 7 TIT at varying 119880119891
as well (second effect) so that temperatures should increaseThe first effect prevails on the second one Therefore theoverall effect is a lowering of all operating temperatures of thehybrid system Consequently the temperature being lowerto keep the anode inlet temperature at the desired value aninferior amount of methane flow has to be reformed beforeentering the cellThus the percentage of reforming decreasesas Figure 6 shows Figure 7 owing to the already describedeffects shows how the temperature at the turbine inletmonotonically decreases and the turbogas power dependingon the TIT (TIT decrease means a decreasing in Δℎ thus areduction in useful power according to (31) and (32)) thismeans also a decreasing in terms of MTG power as one canobserve in Figure 8 Instead a nonmonotonous trend is thatconcerning the power of the cell In fact this is affected forlow values of 119880119891 by a prereforming effect which changesthe composition in the anode input (reactions (5) and (6))Therefore according to (16) the composition change meansthat the percentage of reforming decreases while Nernst-losses increase causing an overall power decrease in thestack Therefore when it is no longer necessary to reformthe Nernst-loss decreases with decreasing temperature sothat the power of the cell starts growing (Figure 9) Finally
140
150
160
170
180
190
200
P (k
W)
076 077 078 079 080 081 082075
MTG power (kW)
Uf (mdash)
Figure 8 Turbogas power at varying 119880119891
075 076 077 078 079 080 081 082
Fuel cell power (kW)
360
361
362
363
364
365
366
367
368
369
370
P (k
W)
Uf (mdash)
Figure 9 Fuel cell power at varying 119880119891
it is interesting to note that with increasing119880119891 while overallperformance parameters decrease there is an increase in theindex IRE (Figure 10) whereas the thermal limit remainsnearly constant
6 Discussion
61 First Validation of the Calculation Model A first testingof the model calculation was carried out both of a qualitativeand of a quantitative nature The ldquotrendrdquo of some fundamen-tal parameters with respect to developments known from theliterature was evaluated and the results obtained here werecompared with those calculated in [3]
62 Qualitative Validation First for purpose of qualitativemodel validation the data obtained were compared for thesame 119880119891 for different values of dfc As we expected Table 7shows that an increase of the current density causes anincrease of the operating temperature of the hybrid systemand consequently an increase in the percentage of methaneon which it performs the prereforming Table 8 shows that
10 Journal of Renewable Energy
075 076 077 078 079 080 081 08205
151520253035404550
()
IREThermal limit
dfc = 2900 Am2
Uf (mdash)
Figure 10 IRE (blue) and LT (red) at varying 119880119891
A CSOFC
DcAc
J16
Figure 11 Hybrid system studied in [3]
with the increase of dfc both the cell (despite an increasein voltage losses) and the gas turbine power rise the secondbeing directly dependent on the turbine inlet temperature
63 Quantitative Validation To end the first validationprocess the model was applied to the system of Figure 15studied in [3] and results were compared In [3] the methaneis compressed to 30 bars instead of the operating pressureof the MTG and then joined in a mixer and blend withassociated losses from the anode recirculation The mixer isthe only difference compared to the complete system Thethermodynamic modeling of the mixer and of the ejectorinside it would be very complex In homologous conditionsthe results turn out better for the complete system (consistentwith the physical principles) Thus one objective was toevaluate in a first approximation how the ejector affects thelosses using equivalent useful area as a parameter This isdefined as the percentage of usable area of Figure 3 hybridsystem compared with that of Figure 11 (without ejector)such that in homologous operating conditions both systemsproduce the same power The results are as shown in Table 9
It is seen that when the area is reduced up to 85 of thegiven ldquoplaterdquo the relative difference between the referencedata and the data provided by the model remains around 1thus lending credibility to the mathematical model describedin this paper
7 Conclusions
The objective set at the beginning was to define the optimalconditions of operation of the hybrid system by developinga C++ code and to evaluate the suitability of this approachwith the physical and chemical process present inside theSOFC-MTGplant In the first instancewe see that the optimalconfiguration of the hybrid system is that of the completesystem This ensures both a satisfactory temperature man-agement and good values of gas turbine power The flow rateof methane is excellent given the guaranteed high designflexibility which is defined as 119898 that is 0015 kgs Forthe said value of the flow rate of methane current densitythat ensures the best compromise between performance anddegrees of freedom to the designer (varying 119880119891 eligible
Journal of Renewable Energy 11
Table 7 Operating parameters in equal value 119880119891 for different dfc
dfc [Am2] 119880119891 Voltage [V] Voltage losses [V] uc [kW] tg [kW] tot [kW]2900 082 06788 05058 36278 14128 504063000 082 06619 05227 36596 18078 54674
Table 9 Comparison of the data obtained with the model andexperimental data studied by evaluating an equivalent useful areaequal to 85 of the effective area (dfc = 3200Am2)
Model data Reference data Relative difference[]
Hybrid systempower [kW] 43147 428 080
Fuel cell power[kW] 32052 319 047
Gas turbinepower [kW] 11095 109 176
Hybrid systemefficiency [kW] 062 061
Fuel cellefficiency [kW] 046 045
Gas turbineefficiency [kW] 016 016
between 075 and 082) is that of 2900Am2 The last stepis the choice of operating 119880119891 which may vary dependingon the objective it set out choosing a low 119880119891 if there isdirected towards energy optimization 119880119891 high if the goalis to maximize the cogeneration yield and a medium 119880119891 ifseeking a compromise between the two requirements Sincesystems of this type are still under study of the 3 optionsdescribed above at the current state of the art it seemsto make sense to focus on energy optimization and whenconsolidated on the market there will be consideration laterwith the economic scenario of the moment This factor isclosely related to the evaluation of the investment fromthe perspective of cogeneration The developed C++ codematches with both the state of the art and reference datataken from the literature suggesting the suitability of thisapproach to evaluate and describe SOFC-MTG and otherkinds of plants
Nomenclature
119860119891 Useful area of the fuel cell [m2]
119888119901 Specific heat at constant pressure[J(molsdotK)]
119888119901119898 Average specific heat of the mixture in the
course of expansion [J(kgsdotK)]119888V Specific heat at constant volume
[J(molsdotK)]dfc Current density with which it operates
within the fuel cell [Am2]119865 Faraday constant that is 96485 [Cmol]119891CO Molar fraction of carbon monoxide
dimensionless119891H2
Molar fraction of hydrogen dimensionlessℎair Molar enthalpy of the air [Jmol]ℎCH4
Molar enthalpy of methane [Jmol]ℎCO Molar enthalpy of carbon monoxide
[Jmol]ℎCO2
Molar enthalpy of carbon dioxide [Jmol]ℎH2
Molar enthalpy of hydrogen [Jmol]ℎH2O Molar enthalpy of the water vapor [Jmol]
ℎO2
Molar enthalpy of oxygen [Jmol]ℎN2
Molar enthalpy of nitrogen [Jmol]119868 Operation current [A]IRE ldquoEnergy saving indexrdquo dimensionless1198940119886 Current density exchange anode side
[Am2]1198940119888 Current density exchange cathode side
[Am2]119894119897 Limit current density [Am2]119870ref Equilibrium constant of the reaction of
steam reforming dimensionless119870shif Equilibrium constant of the reaction of
Water Gas Shift Reaction dimensionless Air mass flow rate [kgs]CH
4
Methane mass flow rate [kgs]119905 Mass flow rate in the expander [kgs]119899CH4
Electric power obtained through theelectrochemical reaction of waterformation [W]
ac Power absorbed by the compressor gasturbine system [W]
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of Renewable Energy 9
0
10
20
30
40
50
60
70
Refo
rmin
g (
)
076 077 078 079 080 081 082075Uf (mdash)
Reforming (dfc = 2900 Am2) ()
Figure 6 Percentage of prereforming at varying 119880119891
1000
1050
1100
1150
1200
1250
1300
T (K
)
076 077 078 079 080 081 082075
TIT (
Uf (mdash)
dfc = 2900 Am2)
Figure 7 TIT at varying 119880119891
as well (second effect) so that temperatures should increaseThe first effect prevails on the second one Therefore theoverall effect is a lowering of all operating temperatures of thehybrid system Consequently the temperature being lowerto keep the anode inlet temperature at the desired value aninferior amount of methane flow has to be reformed beforeentering the cellThus the percentage of reforming decreasesas Figure 6 shows Figure 7 owing to the already describedeffects shows how the temperature at the turbine inletmonotonically decreases and the turbogas power dependingon the TIT (TIT decrease means a decreasing in Δℎ thus areduction in useful power according to (31) and (32)) thismeans also a decreasing in terms of MTG power as one canobserve in Figure 8 Instead a nonmonotonous trend is thatconcerning the power of the cell In fact this is affected forlow values of 119880119891 by a prereforming effect which changesthe composition in the anode input (reactions (5) and (6))Therefore according to (16) the composition change meansthat the percentage of reforming decreases while Nernst-losses increase causing an overall power decrease in thestack Therefore when it is no longer necessary to reformthe Nernst-loss decreases with decreasing temperature sothat the power of the cell starts growing (Figure 9) Finally
140
150
160
170
180
190
200
P (k
W)
076 077 078 079 080 081 082075
MTG power (kW)
Uf (mdash)
Figure 8 Turbogas power at varying 119880119891
075 076 077 078 079 080 081 082
Fuel cell power (kW)
360
361
362
363
364
365
366
367
368
369
370
P (k
W)
Uf (mdash)
Figure 9 Fuel cell power at varying 119880119891
it is interesting to note that with increasing119880119891 while overallperformance parameters decrease there is an increase in theindex IRE (Figure 10) whereas the thermal limit remainsnearly constant
6 Discussion
61 First Validation of the Calculation Model A first testingof the model calculation was carried out both of a qualitativeand of a quantitative nature The ldquotrendrdquo of some fundamen-tal parameters with respect to developments known from theliterature was evaluated and the results obtained here werecompared with those calculated in [3]
62 Qualitative Validation First for purpose of qualitativemodel validation the data obtained were compared for thesame 119880119891 for different values of dfc As we expected Table 7shows that an increase of the current density causes anincrease of the operating temperature of the hybrid systemand consequently an increase in the percentage of methaneon which it performs the prereforming Table 8 shows that
10 Journal of Renewable Energy
075 076 077 078 079 080 081 08205
151520253035404550
()
IREThermal limit
dfc = 2900 Am2
Uf (mdash)
Figure 10 IRE (blue) and LT (red) at varying 119880119891
A CSOFC
DcAc
J16
Figure 11 Hybrid system studied in [3]
with the increase of dfc both the cell (despite an increasein voltage losses) and the gas turbine power rise the secondbeing directly dependent on the turbine inlet temperature
63 Quantitative Validation To end the first validationprocess the model was applied to the system of Figure 15studied in [3] and results were compared In [3] the methaneis compressed to 30 bars instead of the operating pressureof the MTG and then joined in a mixer and blend withassociated losses from the anode recirculation The mixer isthe only difference compared to the complete system Thethermodynamic modeling of the mixer and of the ejectorinside it would be very complex In homologous conditionsthe results turn out better for the complete system (consistentwith the physical principles) Thus one objective was toevaluate in a first approximation how the ejector affects thelosses using equivalent useful area as a parameter This isdefined as the percentage of usable area of Figure 3 hybridsystem compared with that of Figure 11 (without ejector)such that in homologous operating conditions both systemsproduce the same power The results are as shown in Table 9
It is seen that when the area is reduced up to 85 of thegiven ldquoplaterdquo the relative difference between the referencedata and the data provided by the model remains around 1thus lending credibility to the mathematical model describedin this paper
7 Conclusions
The objective set at the beginning was to define the optimalconditions of operation of the hybrid system by developinga C++ code and to evaluate the suitability of this approachwith the physical and chemical process present inside theSOFC-MTGplant In the first instancewe see that the optimalconfiguration of the hybrid system is that of the completesystem This ensures both a satisfactory temperature man-agement and good values of gas turbine power The flow rateof methane is excellent given the guaranteed high designflexibility which is defined as 119898 that is 0015 kgs Forthe said value of the flow rate of methane current densitythat ensures the best compromise between performance anddegrees of freedom to the designer (varying 119880119891 eligible
Journal of Renewable Energy 11
Table 7 Operating parameters in equal value 119880119891 for different dfc
dfc [Am2] 119880119891 Voltage [V] Voltage losses [V] uc [kW] tg [kW] tot [kW]2900 082 06788 05058 36278 14128 504063000 082 06619 05227 36596 18078 54674
Table 9 Comparison of the data obtained with the model andexperimental data studied by evaluating an equivalent useful areaequal to 85 of the effective area (dfc = 3200Am2)
Model data Reference data Relative difference[]
Hybrid systempower [kW] 43147 428 080
Fuel cell power[kW] 32052 319 047
Gas turbinepower [kW] 11095 109 176
Hybrid systemefficiency [kW] 062 061
Fuel cellefficiency [kW] 046 045
Gas turbineefficiency [kW] 016 016
between 075 and 082) is that of 2900Am2 The last stepis the choice of operating 119880119891 which may vary dependingon the objective it set out choosing a low 119880119891 if there isdirected towards energy optimization 119880119891 high if the goalis to maximize the cogeneration yield and a medium 119880119891 ifseeking a compromise between the two requirements Sincesystems of this type are still under study of the 3 optionsdescribed above at the current state of the art it seemsto make sense to focus on energy optimization and whenconsolidated on the market there will be consideration laterwith the economic scenario of the moment This factor isclosely related to the evaluation of the investment fromthe perspective of cogeneration The developed C++ codematches with both the state of the art and reference datataken from the literature suggesting the suitability of thisapproach to evaluate and describe SOFC-MTG and otherkinds of plants
Nomenclature
119860119891 Useful area of the fuel cell [m2]
119888119901 Specific heat at constant pressure[J(molsdotK)]
119888119901119898 Average specific heat of the mixture in the
course of expansion [J(kgsdotK)]119888V Specific heat at constant volume
[J(molsdotK)]dfc Current density with which it operates
within the fuel cell [Am2]119865 Faraday constant that is 96485 [Cmol]119891CO Molar fraction of carbon monoxide
dimensionless119891H2
Molar fraction of hydrogen dimensionlessℎair Molar enthalpy of the air [Jmol]ℎCH4
Molar enthalpy of methane [Jmol]ℎCO Molar enthalpy of carbon monoxide
[Jmol]ℎCO2
Molar enthalpy of carbon dioxide [Jmol]ℎH2
Molar enthalpy of hydrogen [Jmol]ℎH2O Molar enthalpy of the water vapor [Jmol]
ℎO2
Molar enthalpy of oxygen [Jmol]ℎN2
Molar enthalpy of nitrogen [Jmol]119868 Operation current [A]IRE ldquoEnergy saving indexrdquo dimensionless1198940119886 Current density exchange anode side
[Am2]1198940119888 Current density exchange cathode side
[Am2]119894119897 Limit current density [Am2]119870ref Equilibrium constant of the reaction of
steam reforming dimensionless119870shif Equilibrium constant of the reaction of
Water Gas Shift Reaction dimensionless Air mass flow rate [kgs]CH
4
Methane mass flow rate [kgs]119905 Mass flow rate in the expander [kgs]119899CH4
Electric power obtained through theelectrochemical reaction of waterformation [W]
ac Power absorbed by the compressor gasturbine system [W]
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
10 Journal of Renewable Energy
075 076 077 078 079 080 081 08205
151520253035404550
()
IREThermal limit
dfc = 2900 Am2
Uf (mdash)
Figure 10 IRE (blue) and LT (red) at varying 119880119891
A CSOFC
DcAc
J16
Figure 11 Hybrid system studied in [3]
with the increase of dfc both the cell (despite an increasein voltage losses) and the gas turbine power rise the secondbeing directly dependent on the turbine inlet temperature
63 Quantitative Validation To end the first validationprocess the model was applied to the system of Figure 15studied in [3] and results were compared In [3] the methaneis compressed to 30 bars instead of the operating pressureof the MTG and then joined in a mixer and blend withassociated losses from the anode recirculation The mixer isthe only difference compared to the complete system Thethermodynamic modeling of the mixer and of the ejectorinside it would be very complex In homologous conditionsthe results turn out better for the complete system (consistentwith the physical principles) Thus one objective was toevaluate in a first approximation how the ejector affects thelosses using equivalent useful area as a parameter This isdefined as the percentage of usable area of Figure 3 hybridsystem compared with that of Figure 11 (without ejector)such that in homologous operating conditions both systemsproduce the same power The results are as shown in Table 9
It is seen that when the area is reduced up to 85 of thegiven ldquoplaterdquo the relative difference between the referencedata and the data provided by the model remains around 1thus lending credibility to the mathematical model describedin this paper
7 Conclusions
The objective set at the beginning was to define the optimalconditions of operation of the hybrid system by developinga C++ code and to evaluate the suitability of this approachwith the physical and chemical process present inside theSOFC-MTGplant In the first instancewe see that the optimalconfiguration of the hybrid system is that of the completesystem This ensures both a satisfactory temperature man-agement and good values of gas turbine power The flow rateof methane is excellent given the guaranteed high designflexibility which is defined as 119898 that is 0015 kgs Forthe said value of the flow rate of methane current densitythat ensures the best compromise between performance anddegrees of freedom to the designer (varying 119880119891 eligible
Journal of Renewable Energy 11
Table 7 Operating parameters in equal value 119880119891 for different dfc
dfc [Am2] 119880119891 Voltage [V] Voltage losses [V] uc [kW] tg [kW] tot [kW]2900 082 06788 05058 36278 14128 504063000 082 06619 05227 36596 18078 54674
Table 9 Comparison of the data obtained with the model andexperimental data studied by evaluating an equivalent useful areaequal to 85 of the effective area (dfc = 3200Am2)
Model data Reference data Relative difference[]
Hybrid systempower [kW] 43147 428 080
Fuel cell power[kW] 32052 319 047
Gas turbinepower [kW] 11095 109 176
Hybrid systemefficiency [kW] 062 061
Fuel cellefficiency [kW] 046 045
Gas turbineefficiency [kW] 016 016
between 075 and 082) is that of 2900Am2 The last stepis the choice of operating 119880119891 which may vary dependingon the objective it set out choosing a low 119880119891 if there isdirected towards energy optimization 119880119891 high if the goalis to maximize the cogeneration yield and a medium 119880119891 ifseeking a compromise between the two requirements Sincesystems of this type are still under study of the 3 optionsdescribed above at the current state of the art it seemsto make sense to focus on energy optimization and whenconsolidated on the market there will be consideration laterwith the economic scenario of the moment This factor isclosely related to the evaluation of the investment fromthe perspective of cogeneration The developed C++ codematches with both the state of the art and reference datataken from the literature suggesting the suitability of thisapproach to evaluate and describe SOFC-MTG and otherkinds of plants
Nomenclature
119860119891 Useful area of the fuel cell [m2]
119888119901 Specific heat at constant pressure[J(molsdotK)]
119888119901119898 Average specific heat of the mixture in the
course of expansion [J(kgsdotK)]119888V Specific heat at constant volume
[J(molsdotK)]dfc Current density with which it operates
within the fuel cell [Am2]119865 Faraday constant that is 96485 [Cmol]119891CO Molar fraction of carbon monoxide
dimensionless119891H2
Molar fraction of hydrogen dimensionlessℎair Molar enthalpy of the air [Jmol]ℎCH4
Molar enthalpy of methane [Jmol]ℎCO Molar enthalpy of carbon monoxide
[Jmol]ℎCO2
Molar enthalpy of carbon dioxide [Jmol]ℎH2
Molar enthalpy of hydrogen [Jmol]ℎH2O Molar enthalpy of the water vapor [Jmol]
ℎO2
Molar enthalpy of oxygen [Jmol]ℎN2
Molar enthalpy of nitrogen [Jmol]119868 Operation current [A]IRE ldquoEnergy saving indexrdquo dimensionless1198940119886 Current density exchange anode side
[Am2]1198940119888 Current density exchange cathode side
[Am2]119894119897 Limit current density [Am2]119870ref Equilibrium constant of the reaction of
steam reforming dimensionless119870shif Equilibrium constant of the reaction of
Water Gas Shift Reaction dimensionless Air mass flow rate [kgs]CH
4
Methane mass flow rate [kgs]119905 Mass flow rate in the expander [kgs]119899CH4
Electric power obtained through theelectrochemical reaction of waterformation [W]
ac Power absorbed by the compressor gasturbine system [W]
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
dfc [Am2] 119880119891 Voltage [V] Voltage losses [V] uc [kW] tg [kW] tot [kW]2900 082 06788 05058 36278 14128 504063000 082 06619 05227 36596 18078 54674
Table 9 Comparison of the data obtained with the model andexperimental data studied by evaluating an equivalent useful areaequal to 85 of the effective area (dfc = 3200Am2)
Model data Reference data Relative difference[]
Hybrid systempower [kW] 43147 428 080
Fuel cell power[kW] 32052 319 047
Gas turbinepower [kW] 11095 109 176
Hybrid systemefficiency [kW] 062 061
Fuel cellefficiency [kW] 046 045
Gas turbineefficiency [kW] 016 016
between 075 and 082) is that of 2900Am2 The last stepis the choice of operating 119880119891 which may vary dependingon the objective it set out choosing a low 119880119891 if there isdirected towards energy optimization 119880119891 high if the goalis to maximize the cogeneration yield and a medium 119880119891 ifseeking a compromise between the two requirements Sincesystems of this type are still under study of the 3 optionsdescribed above at the current state of the art it seemsto make sense to focus on energy optimization and whenconsolidated on the market there will be consideration laterwith the economic scenario of the moment This factor isclosely related to the evaluation of the investment fromthe perspective of cogeneration The developed C++ codematches with both the state of the art and reference datataken from the literature suggesting the suitability of thisapproach to evaluate and describe SOFC-MTG and otherkinds of plants
Nomenclature
119860119891 Useful area of the fuel cell [m2]
119888119901 Specific heat at constant pressure[J(molsdotK)]
119888119901119898 Average specific heat of the mixture in the
course of expansion [J(kgsdotK)]119888V Specific heat at constant volume
[J(molsdotK)]dfc Current density with which it operates
within the fuel cell [Am2]119865 Faraday constant that is 96485 [Cmol]119891CO Molar fraction of carbon monoxide
dimensionless119891H2
Molar fraction of hydrogen dimensionlessℎair Molar enthalpy of the air [Jmol]ℎCH4
Molar enthalpy of methane [Jmol]ℎCO Molar enthalpy of carbon monoxide
[Jmol]ℎCO2
Molar enthalpy of carbon dioxide [Jmol]ℎH2
Molar enthalpy of hydrogen [Jmol]ℎH2O Molar enthalpy of the water vapor [Jmol]
ℎO2
Molar enthalpy of oxygen [Jmol]ℎN2
Molar enthalpy of nitrogen [Jmol]119868 Operation current [A]IRE ldquoEnergy saving indexrdquo dimensionless1198940119886 Current density exchange anode side
[Am2]1198940119888 Current density exchange cathode side
[Am2]119894119897 Limit current density [Am2]119870ref Equilibrium constant of the reaction of
steam reforming dimensionless119870shif Equilibrium constant of the reaction of
Water Gas Shift Reaction dimensionless Air mass flow rate [kgs]CH
4
Methane mass flow rate [kgs]119905 Mass flow rate in the expander [kgs]119899CH4
Electric power obtained through theelectrochemical reaction of waterformation [W]
ac Power absorbed by the compressor gasturbine system [W]
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
12 Journal of Renewable Energy
119888 Power generated by the cell [W]cog Cogeneration power transmitted to the
thermodynamic cycle placed downstreamof the hybrid system [W]
1198901 Thermal power transferred to air in theevent that the regenerator has efficiency1 [W]
SI Hybrid system power [W]term Thermal power transferred to air [W]tg Gas turbine useful power [W]tot Total power supplied by the hybrid system
[W]119875uc Useful power generated by the cell [W]ut Gas turbine expander useful power [W]119877 Universal gas constant 8314 [J(molsdotK)]STCR Steam to Carbon Ratio dimensionless119879an Anode inlet temperature [K]119879cat Cathode inlet temperature [K]1198791198901 Temperature efficiency 1 [K]119879fc Operating temperature of the cell [K]119879is Isentropic temperature of the turbine
outlet [K]119879mix Temperature mixing
recirculation-methane [K]119879out Turbine outlet temperature [K]119879pc Afterburning temperature [K]TIT Turbine inlet temperature [K]119880119891 Fuel utilization factor dimensionless119881 Cell operating voltage [V]1198810 Maximum voltage obtained in standard
conditions at a pressure of 1 atm and at atemperature of 25∘C [V]
119881att Voltage activation losses [V]119881act119886
Voltage activation losses anode side [V]119881act119888
Voltage activation losses cathode side [V]119881conc Voltage concentration losses [V]119881Nernst Nernst-loss [V]119881ohm Voltage ohmic losses [V]119911 Number of moles of hydrogen which react
in a second inside the fuel cell [mols]
Greek Alphabet
120573 Compression ratio dimensionlessΔ1198660 Variation in Gibbs free energy in
formation water reaction minus228600 [Jmol]ΔℎCO
2
Standard enthalpy of formation of carbonmonoxide oxidation reaction [Jmol]
ΔℎH2O Enthalpy of formation of electrochemical
water formation reaction [Jmol]Δℎref Enthalpy of formation in reforming
reaction [Jmol]Δℎshif Enthalpy of formation in shifting reaction
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] A Demirbas ldquoFuel cells as clean energy convertersrdquo EnergySources Part A Recovery Utilization and Environmental Effectsvol 29 no 2 pp 185ndash191 2007
[2] Z Ziaka and S Vasileiadis ldquoPretreated landfill gas conversionprocess via a catalytic membrane reactor for renewable com-bined fuel cell-power generationrdquo Journal of Renewable Energyvol 2013 Article ID 209364 8 pages 2013
[3] A Pontecorvo R Tuccillo and F Bozza Studio di una micro-turbina a gas per sistemi cogenerativi ed ibridi [PhD thesis]Universita degli Studi di Napoli Federico II Napoli Italy 2010
[4] F Bozza M C Cameretti and R Tuccillo ldquoAdapting themicro-gas turbine operation to variable thermal and electricalrequirementsrdquo ASME Paper 2003-GT-38652 2003
[5] F Bozza and R Tuccillo ldquoTransient operation analysis of acogenerating micro-gas turbinerdquo ASME Paper ESDA 2004-58079 2004
[6] MC Cameretti andR Tuccillo ldquoComparing different solutionsfor the micro-gas turbine combustorrdquo ASME Paper 2004-GT-53286 2004
[7] R Tuccillo ldquoPerformance and transient behaviour of MTGbased energy systemsrdquo Tech Rep RTO-MP-AVT-131 VKILSMicro Gas Turbines 2005
[8] S H Chan H K Ho and Y Tian ldquoModelling of simple hybridsolid oxide fuel cell and gas turbine power plantrdquo Journal ofPower Sources vol 109 no 1 pp 111ndash120 2002
[9] S K Nayak and D N Gaonkar ldquoModeling and perfor-mance analysis of microturbine generation system in gridconnectedislanding operationrdquo Journal of Renewable Energyvol 2 no 4 pp 750ndash757 2012
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of Renewable Energy 13
[10] C Stiller B Thorud and O Bolland ldquoSafe dynamic operationof a simple SOFCGT hybrid systemrdquo ASME Paper 2005-GT-68481 ASME 2005
[11] S H Chan H K Ho and Y Tian ldquoMulti-level modelingof SOFCndashgas turbine hybrid systemrdquo International Journal ofHydrogen Energy vol 28 no 8 pp 889ndash900 2003
[12] L Barelli G Bidini F Gallorini and P A Ottaviano ldquoDesignoptimization of a SOFC-based CHP system through dynamicanalysisrdquo International Journal of Hydrogen Energy vol 38 no1 pp 354ndash369 2013
[13] H-W D Chiang C-N Hsu W-B Huang C-H Lee W-PHuang and W-T Hong ldquoDesign and performance study ofa solid oxide fuel cell and gas turbine hybrid system appliedin combined cooling heating and power systemrdquo Journal ofEnergy Engineering vol 138 no 4 pp 205ndash214 2012
[14] L Barelli G Bidini and P A Ottaviano ldquoPart load operationof SOFCGT hybrid systems stationary analysisrdquo InternationalJournal of Hydrogen Energy vol 37 no 21 pp 16140ndash16150 2012
[15] P Chinda and P Brault ldquoThe hybrid solid oxide fuel cell(SOFC) and gas turbine (GT) systems steady state modelingrdquoInternational Journal of Hydrogen Energy vol 37 no 11 pp9237ndash9248 2012
[16] X Zhang J Guo and J Chen ldquoInfluence ofmultiple irreversiblelosses on the performance of a molten carbonate fuel cell-gas turbine hybrid systemrdquo International Journal of HydrogenEnergy vol 37 no 10 pp 8664ndash8671 2012
[17] L Leto C Dispenza A Moreno and A Calabro ldquoSimulationmodel of a molten carbonate fuel cell-microturbine hybridsystemrdquo Applied Thermal Engineering vol 31 no 6-7 pp 1263ndash1271 2011
[18] O Corigliano G Florio and P Fragiacomo ldquoA numericalsimulation model of high temperature fuel cells fed by biogasrdquoEnergy Sources Part A Recovery Utilization and EnvironmentalEffects vol 34 no 2 pp 101ndash110 2011
[19] GDe Lorenzo andP Fragiacomo ldquoTechnical analysis of an eco-friendly hybrid plant with a microgas turbine and an MCFCsystemrdquo Fuel Cells vol 10 no 1 pp 194ndash208 2010
[20] G De Lorenzo and P Fragiacomo ldquoAmethodology for improv-ing the performance of molten carbonate fuel cellgas turbinehybrid systemsrdquo International Journal of Energy Research vol36 no 1 pp 96ndash110 2012
[21] S Wongchanpai H I Wai M Saito and H Yoshida ldquoPerfor-mance evaluation of a direct biogas solid oxide fuel cellmdashmicrogas turbine (SOFC-MTG) hybrid combined heat and power(CHP) systemrdquo Journal of Power Sources vol 223 pp 9ndash17 2013
[22] R Toonssen S Sollai P V Aravind NWoudstra and A H MVerkooijen ldquoAlternative system designs of biomass gasificationSOFCGT hybrid systemsrdquo International Journal of HydrogenEnergy vol 36 no 16 pp 10414ndash10425 2011
[23] Y Zhao J Sadhukhan A Lanzini N Brandon and N ShahldquoOptimal integration strategies for a syngas fuelled SOFC andgas turbine hybridrdquo Journal of Power Sources vol 196 no 22pp 9516ndash9527 2011
[24] P V Aravind C Schilt B Turker and T Woudstra ldquoTher-modynamic model of a very high efficiency power plant basedon a biomass gasifier SOFCs and a gas turbinerdquo InternationalJournal of Renewable Energy Development vol 1 no 2 pp 51ndash55 2012
[25] C Bang-Moslashller and M Rokni ldquoThermodynamic performancestudy of biomass gasification solid oxide fuel cell andmicro gasturbine hybrid systemsrdquo Energy Conversion and Managementvol 51 no 11 pp 2330ndash2339 2010
[26] C Bao N Cai and E Croiset ldquoA multi-level simulationplatform of natural gas internal reforming solid oxide fuel cell-gas turbine hybrid generation systemmdashpart II Balancing unitsmodel library and system simulationrdquo Journal of Power Sourcesvol 196 no 20 pp 8424ndash8434 2011
[27] S Douvartzides and P Tsiakaras ldquoThermodynamic and eco-nomic analysis of a steam reformer-solid oxide fuel cell systemfed by natural gas and ethanolrdquo Energy Sources vol 24 no 4pp 365ndash373 2002
[28] D F Cheddie and R Murray ldquoThermo-economic modelingof a solid oxide fuel cellgas turbine power plant with semi-direct coupling and anode recyclingrdquo International Journal ofHydrogen Energy vol 35 no 20 pp 11208ndash11215 2010
[29] Y Zhao N Shah and N Brandon ldquoComparison betweentwo optimization strategies for solid oxide fuel cell-gas turbinehybrid cyclesrdquo International Journal of Hydrogen Energy vol 36no 16 pp 10235ndash10246 2011
[30] U G Bossel and B C H Swiss Final Report on SOFCData factsand Figures Federal Office of Energy 1992
[31] O Levenspiel Ingegneria delle reazioni chimiche Casa EditriceAmbrosiana Milano Italy 1972
