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GT hybrid systems: Stationary analysis
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Part load operation of SOFC/GT hybrid systems: Stationary analysis L. Barelli*, G. Bidini, A. Ottaviano Department of Industrial Engineering, University of Perugia, Via G. Duranti 1/A4, Perugia 06125, Italy
article info
abstract
Article history:
In a global energetic context characterized by the increasing demand of oil and gas, the
Received 7 June 2012
depletion of fossil resources and the global warming, more efficient energy systems and,
Received in revised form
consequently, innovative energy conversion processes are urgently required. A possible
2 August 2012
solution can be found in the fuel cells technology coupled with classical thermodynamic
Accepted 5 August 2012
cycle technologies in order to make hybrid systems able to achieve high energy/power
Available online 8 September 2012
efficiency with low environmental impact. Moreover, due to the synergistic effect of using a high temperature fuel cell such as solid oxide fuel cell (SOFC) and a recuperative gas
Keywords:
turbine (GT), the integrated system efficiency can be significantly improved. In this paper
Hybrid
a steady zero dimensional model of a SOFC/GT hybrid system is presented. The core of the
Gas turbine
work consists of a performance analysis focused on the influence of the GT part load
SOFC
functioning on the overall system efficiency maintaining the SOFC power set to the
Steady model
nominal one. Also the proper design and management of the heat recovery section is object of the present study, with target a global electric efficiency almost constant in part load functioning respect to nominal operation. The results of this study have been used as basis to the development of a dynamic model, presented in the following part of the study focused on the plant dynamic analysis. Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
The need of the reduction of power generation environmental impacts, both from economical than Earth health point of view, has motived the scientific community to research more efficient power generation solutions. In fact, today, the electrical power is mainly provided by conventional power plants that depend on fossil fuel combustion, which generates in relation to the particular feeding fuel soot, sulphur compounds, NOx together with other noxious emissions [1]. In this context, aiming to increase a clean electric production and considering the potential relevance of a distributed power generation market, the hybrid solid oxide fuel cell (SOFC) and
gas turbine (GT) system is an attractive option, with systems starting from few to hundreds kWs [2,3]. Fuel cells are electrochemical devices characterized by high electrical efficiencies (35e55% on a Lower Heating Value (LHV) basis) and low pollutant emissions. Different types of fuel cells are available today, differentiated by the electrolyte and their operating temperature. The high operating temperature (600e1000 C) and mature status of SOFC allow to combine, in order to improve the overall efficiency, such a technology with other conventional thermodynamic cycles. The importance of the development of hybrid power plants can be emphasized considering the interest and the research efforts that many multinational companies, e.g. Rolls-Royce,
* Corresponding author. Tel.: þ39 075 5853740; fax: þ39 075 5853736. E-mail address: [email protected] (L. Barelli). 0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2012.08.015
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Nomenclature Specific heat at constant pressure, kJ/(kg K) cp Fuelafterb Afterburner feeding methane flow rate, kg/s Fuelglobal Sum of SOFC and afterburner feeding methane flow rate, kg/s FuelSOFC SOFC feeding methane flow rate, kg/s GT Gas turbine I Current density, mA/cm2 k Specific heat at constant pressure and constant volume ratio _ m Mass flow rate, kg/s P Fuel cell operating pressure, bar Pref Reference operating pressure of the fuel cell, bar S/C Steam to carbon ratio SOFC Solid oxide fuel cell T Fuel cell operating temperature, C Reference operating temperature of the fuel cell, Tref C
GE Energy, Siemens Westinghouse and Mitsubishi Heavy Industries, are involving in their design. Moreover, in US, the integration of the fuel cell and GT hybrid system is considered to be the key technology to achieve the Vision 21st goals [4]. In [5] a general review of the integration strategies for solid oxide fuel cells has been presented. Specifically, in this work, the plant definable “direct thermal coupling scheme”, and more precisely “pressurized SOFC þ Brayton cycle” [5], described briefly in Section 2, has been adopted. Moreover the importance of the identification of the best configuration of hybrid system is central in many theoretical analysis and simulation works. Specifically in [6], considering a system configuration where the SOFC converts electrochemically the hydrogen, reformed from natural gas, producing both electrical power and high-grade waste heat for combined heat and power (CHP) system, it has been demonstrated that SOFC can achieve 50% net electrical efficiencies and have already been considered feasible for integration with multi-MW gas turbine engines to achieve more higher electrical efficiency. Anyway the achievable plant global efficiency isn’t estimated numerically and no indication are provided on a possible down scale. In this sense, more information are furnished in [7], concerning an advanced SOFC/GT hybrid system, developed by Siemens e Westinghouse Power Corporation, characterized by a pressurization of 3 atm, a global electrical power of 220 kW and a net electrical efficiency of 55%. An interesting hybrid system configuration, characterized by an IRSOFC (internal reforming SOFC) and two GT turbines, is presented in [8]. The first gas turbine is used to move the air and fuel compressors, while the second one, connected to the alternator, generates the electric power. Also in this work, where a sensitive analysis on the main parameters that influence the system behaviour has been carried out, the HS global electrical efficiency has been estimated around 60%. But in this study, except for the SOFC model based on Siemens Westinghouse data, system components as turbine, compressor and recuperators are modelled only considering
Ua Vref Wc Wglobal WGT WSOFC Wt b DVanode DVO2 DVP DVT hc hgen hglobal ht
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Air utilization factor Reference voltage, V Required compressor power, kW Sum of gas turbine and fuel cell generated power, kW Gas turbine power, kW Fuel cell generated power, kW Turbine output power, kW Pressure ratio Voltage loss due to hydrogen and water partial pressure variations, V Voltage loss due to oxygen partial pressure variation, V Voltage loss due to pressure variation, V Voltage loss due to temperature variation, V Compressor isentropic efficiency Generator mechanical efficiency First law efficiency of the hybrid plant Turbine isentropic efficiency
their thermodynamic characteristics without indicate factory datasheet. In order to confirm the high electrical efficiency achievable in the SOFC/GT plants, a value of 60% was found also in [9] where, beyond the energy analysis, an exergetic approach has been used to analysis the system behaviour under pressure, fuel utilization factor, fuel-to-air and steam-to-fuel ratios variations. The system configuration adopted is very similar to that of [8], characterized by an internal reforming SOFC. This configuration has been used by the authors as base for a subsequently work [10], in which a thermoeconomic model to investigate the better HS configurations is developed. In this work 48 synthesis/design (S/D) parameters are considered. The S/D optimization of the plant is carried out using a traditional single-level approach, based on a genetic algorithm. This optimization procedure shows that it’s possible to reduce dramatically the SOFC active area and the heat exchanger areas; consequently, it makes clear that the optimization of the only stack as an isolated device should be avoided, since inefficiencies in the turbomachinery and in the balance of plant can be significant. As said, it increases the importance of investigating the plant as a whole, analysing its behaviour at both design and part-load operation. In order to define the best HS configuration and the main parameters that influence the plant behaviour, in [11] a thermodynamic simulation of a high-temperature SOFC combined with a recuperated conventional GT is presented. Specifically, a second-law analysis of the cycle has been carried out through an algorithm that simulates the performance of a combined GTeSOFC cycle varying performance parameters, such as the compression ratio and turbine inlet temperature (TIT). It has been observed that an increase in either TIT or compression ratio leads to a higher rate of entropy production of the plant, whereas increasing the TIT improves the specific power output of the cycle. A new complex SOFC-GT hybrid configuration designed to operate over a 5:1 turndown ratio is presented in [12]. This configuration, composed by two gas turbine spools plus
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a separate gas turbine, consents to maintain high efficiencies in turndown condition. This result has been obtained maintaining the SOFC stack exit temperature at 1000 C, limiting the temperature across the stack to less than 200 C, keeping fuel utilization of 85% and thanks to the introduction of a variablegeometry nozzle turbine to directly influence system air flow. Moreover an auxiliary combustor, to control the thermal and power needs of the turbomachinery, has been adopted. An interesting model of hybrid SOFC/GT power system is developed to meet the electrical demand of an electrical power unit of a 300 passengers commercial aircraft in [13]. In a preliminary step, two simple types of models, varying the GT exhaust exploitation, have been presented. A sensitivity analysis, varying the heat exchangers transfer coefficient and the air mass flow rate, has allowed to define the better system configuration. This configuration, contrary to the studies discussed above, has been made to become more realistic basing on the turbine and compressor real performance maps. So, as result, it has been found that the fuel cell performance are strongly influenced by the operating temperature and, hence, when the heat exchanger properties are varied with the air mass flow rate, the HS performance improves. Moreover, the parameters that limit the cycle performance are the SOFC temperature, the turbine inlet and exhaust temperatures. This model doesn’t include the dynamic analysis but the authors refer to a future article in which this subject will be treated. So the purpose of the present paper, differently from the studies relative to stationary SOFC/GT hybrid plants [6e12] discussed above, is to develop a HS model based on datasheet, specifically for the fuel cell, or experimental data, for the gas turbine, to evaluate the nominal and the part load performance of the hybrid system. To this aim a 90 kW “ASC800 e SOFC Power” fuel cell and a 45 kW “Capston C30” micro turbine were chosen as basic components of modelling. Moreover, object of the present paper is also the definition of a proper thermal design and management of the heatrecovery section to optimize the global electric efficiency in part load operation. To this purpose, a zero-dimensional model of such a system has been developed in Aspen Plus environment. The analysis of its performance under different turbine operating points has been carried out taking constant the fuel cell power and the turbine inlet temperature. The model simulations have been conducted by setting the system pressurization and so, indirectly, the GT load. The first part of the study, described in Section 2 (hybrid system layout), has been focused on the identification of both plant layout and proper thermal recovery logic. Subsequently, in Section 3, the modelling of such a system (i.e. fuel cell, gas turbine and the heat exchanger) in Aspen Plus environment has been presented. Specifically in Section 3.1 it is presented the methodology adopted to calculate the turbine electric production, because the different working fluid used respect to the reference conditions indicated in the C30 datasheet. At this step, in Section 4, the attention has been devoted to the results of the Aspen Plus simulations and, in particular, to the energetic analysis of the system working with the GT choked. Finally, in Section 5, the model results have been discussed. The work presented here, descending from previous stationary and dynamic analysis of FC based system carried
out by the author [14e18], has to be considered part of a much larger research work that includes the dynamic modelling analysis of the entire SOFC/GT hybrid system. Because the large amount of data and information to detail and discuss, concerning system layout and components design, model development, simulations schedule and their results for both stationary and dynamic analysis, it has been necessary to divide the work into two separates articles to make the comprehension and its description easier. Then, in a separate paper titled “Part load operation of SOFC/GT hybrid systems: dynamic analysis” the second part of this research work, focused for the same hybrid system on the development of a Simulink dynamic model and on the execution of transients analysis, is described. Moreover, such a section of the study it includes a deep analysis on the heat exchangers blocks and their dynamic behaviour and the effect also on the SOFC operative point.
2.
Hybrid system layout
The choice of the plant layout, and then the coupling between its components, is considered essential by the thermodynamic point of view. The choice of a single working fluid or two can significantly change the performance in terms of efficiency and availability [5] and it can increase or decrease the plant complexity. In this discussion, in order to introduce the plant configuration selected in this work, it should be made an initial distinction between SOFC/GT systems directly and indirectly integrated. Specifically, in the first system configuration, the fuel cell and the gas turbine are connected through the working fluid, which is the same for both, implying also the same operating pressure. An example of an integrated cycle is supplied in Fig. 1 in the particular case of a pressurized system. As regards to the not integrated
Fig. 1 e Pressurized and integrated SOFC/GT configuration.
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configuration, the thermal energy is exchanged between the SOFC and the GT indirectly through a series of heat exchangers. In this case, therefore, as shown for example in Fig. 2, both working fluid and operating pressure are different. In Fig. 3 the system layout considered in this study is depicted. As evident in such a figure, it is characterized by three main sections: the fuel cell and reformer unit, the gas turbine, the heat recovery section. As it can be seen, the model layout shows a direct integration of SOFC and gas turbine system, in which the combustion chamber of the gas turbine has been replaced with a high temperature fuel cell and an afterburner. The choice of a direct integration system is due to two main considerations. The first is that a high operative pressure improves significantly the SOFC performance [19e21], while the second reason consists in the technological problems of an indirect integration. In fact in this last configuration, the gas turbine combustor is replaced with a heat exchanger in which the compressed air is heated by the fuel cell exhaust. But considering the difference of pressure present in this heat exchanger, between the SOFC atmospheric pressure and the compressor outlet stream, and taking into consideration that it works at very high temperature, it’s very onerous for the material used (sealant, mechanical vibrations). Moreover the optimum efficiency of this hybrid scheme is about 5% lower than the pressurized SOFC system [5]. The electrochemical model of the SOFC, developed in [22], uses, as reference, an experimental polarization curve at specified operating conditions. In particular the polarization curve, expressed by the Equation (1), is characteristic of the “ASC-800 SOFCPOWER” fuel cell [23] at 850 C (Fig. 4). Moreover the developed methodology, implemented through a Fortran routine in Aspen Plus, takes into account the voltage deviations from the reference one due to different operating conditions, in particular in term of pressure (DVP),
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temperature (DVT), fuel (DVanode) and oxidant composition (DVcathode), according to relations (2e5). Vref ¼ 5:419$1008 $I3 þ 2:083$1004 $I2 4:596,1001 $I þ 1:066$103
DVP ¼ 76$log
P Pref
(1)
(2)
DVT ¼ 0:008$ T Tref $I
(3)
DVanode ¼ 172$log
PH2 =PH2O ðPH2 =PH2O Þref
(4)
DVcathode ¼ 92$log
PO2 ðPO2 Þref
(5)
where: P, Pref are the operating pressure of the cell and the reference pressure respectively; T, Tref are the operating temperature of the cell and the reference temperature respectively; I is the current density; PH2, PH2O, PO2 are the partial pressures of hydrogen, water vapour and oxygen, respectively. Hereinafter in order to take a global overview of the hybrid plant a short description has been presented. The feeding streams of the hybrid system are: e “1F”: indicates the fuel feeding flow rate (methane, 100% CH4) needed to the cell to produce 90 kWe;
Fig. 2 e Non-pressurized and non-integrated SOFC/GT configuration.
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Fig. 3 e Hybrid system layout.
e “WATER”: is the water flow rate required by the steam methane reformer; such a flow rate is determined to meet the desired S/C ratio value, equal to 3.0, using a dedicated Design-spec function [24], e “1A”: is the inlet air flow rate processed by the compressor (79% N2, 21% O2), e “CH4BURN”: represents an auxiliary amount of fuel flow rate (methane, 100% CH4) directed in the afterburner block. Subsequently the streams “1F”, “Water” and “1A”, after their pressure rise, if necessary, are heated in the heat
recovery section by three heat exchangers (“REC1”, “REC2” and “REC3”) in which the thermal energy of the exhaust gases, coming from the turbine, is recovered. The temperature of the final exhaust stream “EXHAUST2” has been fixed at 153 C. In particular in “REC3”, and thanks to an auxiliary amount of thermal power (stream “Q5”) if the exhaust thermal energy is not enough, the water is brought to the steam conditions before the reforming section. Then, the fuel and steam flows (“2F” and “STEAM1”) are sent to the “REFORMER” block, maintained at its operating temperature thanks to the SOFC cooling thermal power “QCOOLING” and an auxiliary thermal flux coming from the “AFTERBUR” block.
Fig. 4 e ASC-800 polarization curve.
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The syngas, produced in the reformer, together with the oxidant reaches the fuel cell (modelled through the CATHODE, ANODE and HEATER1 units) where the electrochemical reaction takes place producing the demanded electrical power. The fuel cell exhaust gas “8M” is used to preheat the oxidant in the counter-current exchanger named “RIG”. Subsequently, in order to heat up the exhaust gas to the turbine inlet temperature, the cell exhaust “8N” is burned in the “AFTERBUR” block together with the stream “5C” (that is the part of oxidant not needed by the fuel cell) and the “CH4BURN”: the last is calculated through a Design Spec, with target to maintain the turbine inlet temperature constant and to ensure the water vaporization in the “Q5” unit. The fuel quantity provided by stream “1F” is calculated through a Fortran iterative procedure, with target the fuel cell electric power set by the user. The input of this procedure is the real polarization curve in function of the operating conditions (Equations (1)e(5)). The SOFC air input flow rate “4A” is determined considering an air utilization factor (Ua), defined as the ratio between stoichiometric air and introduced air, equal to 0.2. Whereas the inlet air flow rate of the system, upstream of the compressor, is fixed by the authors referring to the compressor map in order to match a defined GT electric power. In all heat exchanger units an amount of heat loss, equal to the 10% of the exchange heat, has been considered in analogy to the assumptions used in [25].
3.
Components model
3.1.
Gas turbine model
Parameters of the C30 gas turbine at design point
a It refers to the case of methane feeding.
WGT ¼ hgen ðht Wt Wc =hc Þ
(6)
where:
As just anticipated in Section 1, the gas turbine power calculated for the Capstone C30 used in the Aspen Plus model is more than 30 kW shown in the turbine datasheet (Table 1). It is due to the different type of gas expanded in the turbine in the SOFC/GT layout that, thank to its higher specific heat, permits to increase the produced turbine power (Equation (13)). In the following Fig. 6 the compressor map recalculated, basing on the real flow rate and GT power at nominal and part load conditions, is shown.
Table 2 e Model equations (the subscripts used in the equation refer to the Aspen Plus model streams of Fig. 1).
Table 1 e Capstone C30 nominal data.
Compressor isentropic efficiency Air flow rate Fuel flow rate Turbine inlet temperature Turbine isentropic efficiency Electric power generated Electric efficiency
nominal one, the thermodynamic equations shown in Table 2 for the compressor and the turbine have been used. The power output from the gas turbine has been calculated by:
- hgen is the generator mechanical efficiency set to 0.9; ht and hc are the turbine and the compressor isentropic efficiencies, equal to 0.9 and 0.8 respectively. - Wt, Wc are turbine output power and required compressor power.
The micro gas turbine selected in this work is CAPSTONE C30, which is a single-shaft micro GT equipped with a centrifugal compressor and a radial turbine. The main parameters of C30 gas turbine are summarized in Table 1. The pressure ratio in part load conditions is determined basing on the compressor performance map (Fig. 5), which shows the compressor introducing pressure as function of mass flow rate and shaft speed. In order to evaluate the pressure ratio and the air flow rate corresponding to a certain electric power demand far to the
Pressure ratio
Fig. 5 e Compressor performance map [26].
3.2 80% 0.31 kg s1 0.0024 kg s1 1173 K 90% 30 kWa 26%a
Thermodynamic equations used in the compressor and turbine model Compressor outlet pressure Compressor power Turbine pressure ratio Turbine power
P2A ¼ b$P1A _ 1A $cp;1A $T1A Wc ¼m $ðbg1A 1Þ bt ¼
P27 P27 ¼ P8 P2A
_ 8 $cp;8 $T8 $ð1 bt Þ Wt ¼ m
(10) K1A 1 K1A
(11)
where P27 ¼ 1.03 bar
(12)
where g1A ¼
where g8 ¼
k8 1 k8
(13)
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Fig. 6 e Pressure ratio (black lines) and GT power (grey lines) at different rotational speed (rpm) depending on compressor mass flow.
So, in Aspen Plus compressor model, the pressure ratio and the air flow rate calculated basing on the electric power required have been set. Instead, in the turbine model, only the outlet pressure value has been set, equal to the inlet compressor pressure, considering the entire working flow of the system as processed flow rate (i.e. cell exhaust plus auxiliary methane flow rate in the afterburner inlet). Moreover the turbine inlet temperature has been fixed at 900 C in every working conditions.
3.2.
Fuel cell and fuel processor model
As just anticipated in Section 2, the electrochemical model of SOFC is based on the experimental polarization curve, Equation (1), of a ASC-800 fuel cell produced by SOFCPOWER. Moreover in the zero dimensional model presented, in order to reach an electric power of 90 kW, a fuel cell stack made of 702 single cells, each characterized by an area of 144 cm2, has
been considered. The SOFC operating temperature has been set at 850 C, instead the pressure has been fixed as consequence of the pressure ratio required by the GT to meet the load demand. In Fig. 7 shows the model of the fuel cell section. Specifically, in the reactor module named “ANODE” the electrochemical reactions, that occur in the cell, have been simulated. The reactions considered in the block are: Electrochemical reaction : H2 þ 0:5O2 /H2 O
(7)
Methane steam reforming : CH4 þ H2 O4CO þ 3H2
(8)
Water gas shift reaction : CO þ H2 O4CO2 þ H2
(9)
Moreover, in order to send the oxidant flow rate that respects the air utilization factor (Ua), defined in Section 2, a separator block Sep, named “CATHODE”, has been
Fig. 7 e Fuel cell section.
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Fig. 8 e Reformer section. implemented. The SOFC produced electric power has been considered as an outlet stream of the block “HEATER1”, named “WE”. The final component “COOLER” represents the cooling system of the fuel cell, stream “QCOOLING”, that allows to maintain the cell temperature at 850 C. Furthermore on the anode side, before the mixing in the “MIXER” block between the anodic and cathodic exhaust streams, in the anodic stream “5F” the liquid water is drained in the block “SEP” (Fig. 7). The reformer model, as presented in [22], consists in Aspen Plus equilibrium reactor module Rgibbs (named “REFORMER”) in which the steam reforming reactions have been replicated. The module named “HEATER2” is a heater module used to bring the steam temperature (stream “STEAM1”) at the required inlet condition of the reformer (250 C) by a heat stream, “Q5”, calculated through a Design-spec function. The reforming temperature has been fixed at 750 C and its maintenance has been realized through the inlet thermal power streams, “QCOOLING” and “Q4” that represent the SOFC cooling thermal power and the auxiliary thermal power produced by the afterburner, “AFTERBURN” (Fig. 8).
3.3.
Heat recovery section model
As preliminary remark, it is evidenced as the heat-recovery section design and then its management strategy, as detailed in the following, has been performed aiming to an optimization of the global electric efficiency of the hybrid system in part load functioning. As anticipated in Section 2, the thermal power contained in the exhaust GT gas has been recovered by a series of three countercurrent heat exchangers.
In particular the first two, “REC1” and “REC2”, have been modelled by the Aspen Plus module HeatX, whereas the last “REC3” by the module MHeatX (Fig. 9). In order to consider, in “REC1” and “REC2”, a thermal loss equal to the 10% of the one exchanged, a Design-spec function has been used. Then the thermal power lost has been modelled with an outgoing stream, “QLOSS1”, that starts from the Heater block called “LOSS1”. Furthermore, in the heat exchanger “REC3”, the heat lost has been implemented directly in the Aspen Plus block. From the thermodynamic point of view, in “REC1” and “REC2” the difference between the hot inlet (“27B” and “28”) and the cold outlet (“3A” and “2F”) of the heat exchangers have been set to 30 C. Instead in the “REC3” only the hot outlet temperature (“EXHAUST2”) has been set at 153 C. Moreover it’s important to underline how a fundamental thermal power exchange takes place in the “RIG” block, as just said in Section 2, where the cathodic air flow rate is heated to the SOFC operating temperature exploiting the heat power contained in the fuel cell exhaust gas (“8M”). Also upstream of this recuperative heat exchanger, a thermal power loss, equal to 10%, has been considered in the “LOSSRIG” unit through the heat stream named “QLOSSRIG” (Fig. 3).
4.
Tests
4.1.
Conditions investigated
The analysis of the hybrid system performance has been carried out through simulations by varying: the pressure
Fig. 9 e Thermal power recovery section.
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Table 3 e Test conditions. Test
Compressor Compressor Gas turbine pressure ratio inlet air flow (kg/s) “1A” speed (rpm)
1 2 3 4
3.24 3.1 2.8 2.52
0.315 0.272 0.227 0.208
96,000 86,400 76,800 67,200
Table 4 e Simulations results. Test WGT WSOFC Wglobal hglobal FuelSOFC Fuelafterb Fuelglobal
1 2 3 4
kW
kW
kW
e
kg/s
kg/s
kg/s
45.4 38.3 30.1 25.0
90 90 90 90
135.4 128.3 120.1 115.0
59.23% 59.34% 59.18% 58.45%
0.00280 0.00281 0.00285 0.00289
0.00240 0.00210 0.00177 0.00158
0.00520 0.00491 0.00461 0.00447
conditions of the fuel and air feeding flows and, consequently, the air flow sucked by the compressor, maintaining a SOFC constant electric power (90 kW). In Table 3 the test conditions are shown: In particular in the Test 1 the gas turbine nominal functioning conditions have been replicated, instead in the other three tests the influence of the GT part load conditions on the hybrid system efficiency has been valuated. Furthermore, in each test, the temperature of reformer, SOFC and the turbine inlet temperature have been considered constant and equal to 750 C, 850 C and 900 C respectively.
4.2.
Simulations results
In the following Table 4 the simulations results obtained in the four tests indicated in Table 3 are presented. In particular the values of generated power, first law global efficiency and needed methane flow rates are listed.
Fig. 10 e Efficiency and hybrid power system trends.
Fig. 11 e Fuel streams in hybrid system.
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The trends of both global efficiency and total power generated by the hybrid system are shown in Fig. 10. It’s important to underline how the efficiency trend, varying the operative electric load (i.e. varying the gas turbine functioning point), is almost constant up to a GT load reduction of about 34% (Test 3). Moreover the efficiency maximum variation is 0.9% and occurs between the Test 2 and Test 4 (GT load reduction of 35%), while in the Test 4, in order to consider the maximum GT part load, the GT produced power has been reduced of 45% respect to the Test 1 with a very small efficiency variation (0.78%). Comparing the overall first law efficiency with other plants presented in technical works [6e9], it is possible to find a good agreement of the results obtained in term of efficiency values and their trends. Considering the trends of the feeding fuel flows, shown in Fig. 11, it is evident as a slight rise in the SOFC consumption, as anticipated in Section 2, corresponds to the decrease of the system pressure (from Test 1 to Test 4). The concomitant decrease of the fuel required by the afterburner block, due to both higher temperature of the fuel cell exhaust and lower thermal power required by the reformer (because the reduction of the “Q5” term), helps to maintain the global efficiency quite constant. The total amount of fuel consumed by the system reflects globally the hybrid power system trend (global produced power in Fig. 11) but it’s percentage variation between Test 1 and Test 4 is less respect to each of the generated power, 14% and 15% respectively. This difference influences the trend of hybrid system efficiency making it decreasing.
5.
Conclusions
In this paper a SOFC/GT hybrid system layout and its thermal management, concerning in particular the heat-recovery section, are presented and discussed by means of stationary analysis at nominal and part load operative conditions. In particular, the influence of the GT part load functioning on the overall system efficiency has been analysed maintaining the SOFC power set to the nominal one. To this aim, starting from the fuel cell (ASC-800) and the gas turbine (Capstone C30) datasheets, an Aspen Plus model that includes a heat recovery section, to properly exploit the hybrid system exhaust, has been implemented. The adopted philosophy, for the thermal management of such a section, consists of a greater heat recovery from the exhaust, in a suitable measure according to the particular GT load, in case of part load operation to compensate as much as possible the reduction of GT electric efficiency. Consequently, heating the system inlet feeding flows, the optimization of the system efficiency has been possible. Specifically, analysing the performance of GT/SOFC system at part load conditions (Fig. 10), the trend of the system efficiency is globally constant, with a maximum variation in any case less than 1% at a decreasing of the gas turbine load up to 45% respect to the nominal power. This result can be considered of primary importance in view of a possible utilizing of SOFC/GT system in a distributed power generation market where the load demand is far from
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be constant. Therefore, the research activity has concerned a more deep analysis of the proposed hybrid system layout in part load functioning, through the study of its dynamic behaviour during transients. This activity has required the development of a dynamic model of the system described, together with the main simulation results and consequent discussions, in a separate paper titled “Part load operation of SOFC/GT hybrid systems: dynamic analysis”. Relative to the possible effects of the electric load variation on the global system efficiency, it is evidenced as during transients in particular the proposed design of the heat-exchangers, and therefore their dynamic behaviour, is significant, influencing also the SOFC operative point.
references
[1] Borchiellini R, Massardo AF, Santarelli M. An analytical procedure for the carbon tax evaluation. Energy Conversion and Management 2000;41:1509e31. [2] Magistri L, Costamagna P, Massardo AF, Rodgers C, McDonald CF. A hybrid system based on a personal turbine (5 kW) and a solid oxide fuel cell stack: a flexible and high efficiency energy concept for the distributed power market. Journal of Engineering for Gas Turbines and Power 2002;124: 850e7. [3] Grillo O, Magistri L, Massardo AF. Hybrid systems for distributed power generation based on pressurisation and heat recovering of an existing 100 kW molten carbonate fuel cell. Journal of Power Sources 2003;115(2):252e67. [4] Vision 21 program plan-clean energy plants for the 21st century. U.S. Department of Energy; 1999. [5] Zhang X, Chan SH, Li G, Ho HK, Li J, Feng Z. A review of integration strategies for solid oxide fuel cells. Journal of Power Sources 2010;195:685e702. [6] Massardo AF, Lubelli F. Internal reforming solid oxide fuel cell and gas turbine combined cycles (IRSOFC-GT): part a e cell model and cycle thermodynamic analysis. Journal of Engineering for Gas Turbines and Power 2000;122:27e35. [7] Hirschenhofer JH, Stauler DB, Engleman RR, Klett MG. Fuel cell handbook. 4th ed. Parsons Corporation Reading P.A. for U.S. Department of Energy; 1998. [8] Chan SH, Ho HK, Tian Y. Modeling of simple hybrid solid oxide fuel cell and gas turbine power plant. Journal of Power Sources 2002;111:320e8. [9] Calise F, d’Accadia MD, Palombo A, Vanoli L. Simulation and exergy analysis of a hybrid solid oxide fuel cell (SOFC) e gas turbine system. Energy 2006;31:3278e99. [10] Calise F, d’Accadia MD, Vanoli L, von Spakovsky MR. Full load synthesis/designing optimization of a hybrid SOFC-GT power plant. Energy 2007;32:446e58. [11] Haseli Y, Dincer I, Naterer GF. Thermodynamic modeling of a gas turbine cycle combined with a solid oxide fuel cell. International Journal of Hydrogen Energy 2008;33:5811e22. [12] Burbank Jr W, Witmera D, Holcomb F. Model of a novel pressurized solid oxide fuel cell gas turbine hybrid engine. Journal of Power Sources 2009;193:656e64. [13] Chinda P, Brault P. The hybrid solid oxide fuel cell (SOFC) and gas turbine (GT) systems steady state modelling. International Journal of Hydrogen Energy 2012;37:9237e48. [14] Barelli L, Bidini G, Gallorini F, Ottaviano A. An energeticeexergetic analysis of a residential CHP system based on PEM fuel cell. Applied Energy 2011;88:4334e42. [15] Barelli L, Bidini G, Gallorini F, Ottaviano A. An energeticeexergetic comparison between PEMFC and SOFC-
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based micro-CHP systems. International Journal of Hydrogen Energy 2011;36:3206e14. Barelli L, Bidini G, Ottaviano A. Optimization of a PEMFC/ battery pack power system for a bus application. Applied Energy 2012;97:777e84. Barelli L, Bidini G, Gallorini F, Ottaviano A. Dynamic analysis of PEMFC-based CHP systems for domestic application. Applied Energy 2012;91:13e28. Barelli L, Bidini G, Gallorini F, Ottaviano A. Design optimization of a sofc-based chp system through dynamic analysis. Proceedings of EFC2011 European Fuel Cell e Piero Lunghi Conference & Exhibition December 14e16, 2011, Rome, Italy (selected for publication on International Journal of Hydrogen Energy, under review. Hussain MM, Li X, Dincer I. Mathematical modeling of planar solid oxide fuel cells. Journal of Power Sources 2006;161:1012e22. Meng N, Michael KHL, Dennis YCL. Parametric study of solid oxide fuel cell performance. Energy Conversion and Management 2007;48:1525e35.
[21] Seidler S, Henke M, Kallo J, Bessler WG, Maier U, Friedrich KA. Pressurized solid oxide fuel cells: experimental studies and modeling. Journal of Power Sources 2011;196: 7195e202. [22] Zhang W, Croiset E, Douglas PL, Fowler MW, Entchev E. Simulation of a tubular solid oxide fuel cell stack using Aspen Plus unit operation models. Energy Conversion and Management 2005;46:181e96. [23] URL: http://www.sofcpower.com/uploads/File/products/asc700_asc-800.pdf. [24] Aspen Plus version 2006 (20.0.3595) users guide. Cambridge MA, USA: Aspen Tech Ltd; 2006. [25] Traverso A, Massardo AF. Optimal design of compact recuperators for microturbine application. Applied Thermal Engineering 2005;25:2054e71. [26] Li Y, Weng Y. Performance study of a solid oxide fuel cell and gas turbine hybrid system designed for methane operating with non-designed fuels. Journal of Power Sources 2011;196: 3824e35.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Part load operation of SOFC/GT hybrid systems: Stationary analysis L. Barelli*, G. Bidini, A. Ottaviano Department of Industrial Engineering, University of Perugia, Via G. Duranti 1/A4, Perugia 06125, Italy
article info
abstract
Article history:
In a global energetic context characterized by the increasing demand of oil and gas, the
Received 7 June 2012
depletion of fossil resources and the global warming, more efficient energy systems and,
Received in revised form
consequently, innovative energy conversion processes are urgently required. A possible
2 August 2012
solution can be found in the fuel cells technology coupled with classical thermodynamic
Accepted 5 August 2012
cycle technologies in order to make hybrid systems able to achieve high energy/power
Available online 8 September 2012
efficiency with low environmental impact. Moreover, due to the synergistic effect of using a high temperature fuel cell such as solid oxide fuel cell (SOFC) and a recuperative gas
Keywords:
turbine (GT), the integrated system efficiency can be significantly improved. In this paper
Hybrid
a steady zero dimensional model of a SOFC/GT hybrid system is presented. The core of the
Gas turbine
work consists of a performance analysis focused on the influence of the GT part load
SOFC
functioning on the overall system efficiency maintaining the SOFC power set to the
Steady model
nominal one. Also the proper design and management of the heat recovery section is object of the present study, with target a global electric efficiency almost constant in part load functioning respect to nominal operation. The results of this study have been used as basis to the development of a dynamic model, presented in the following part of the study focused on the plant dynamic analysis. Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
The need of the reduction of power generation environmental impacts, both from economical than Earth health point of view, has motived the scientific community to research more efficient power generation solutions. In fact, today, the electrical power is mainly provided by conventional power plants that depend on fossil fuel combustion, which generates in relation to the particular feeding fuel soot, sulphur compounds, NOx together with other noxious emissions [1]. In this context, aiming to increase a clean electric production and considering the potential relevance of a distributed power generation market, the hybrid solid oxide fuel cell (SOFC) and
gas turbine (GT) system is an attractive option, with systems starting from few to hundreds kWs [2,3]. Fuel cells are electrochemical devices characterized by high electrical efficiencies (35e55% on a Lower Heating Value (LHV) basis) and low pollutant emissions. Different types of fuel cells are available today, differentiated by the electrolyte and their operating temperature. The high operating temperature (600e1000 C) and mature status of SOFC allow to combine, in order to improve the overall efficiency, such a technology with other conventional thermodynamic cycles. The importance of the development of hybrid power plants can be emphasized considering the interest and the research efforts that many multinational companies, e.g. Rolls-Royce,
* Corresponding author. Tel.: þ39 075 5853740; fax: þ39 075 5853736. E-mail address: [email protected] (L. Barelli). 0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2012.08.015
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Nomenclature Specific heat at constant pressure, kJ/(kg K) cp Fuelafterb Afterburner feeding methane flow rate, kg/s Fuelglobal Sum of SOFC and afterburner feeding methane flow rate, kg/s FuelSOFC SOFC feeding methane flow rate, kg/s GT Gas turbine I Current density, mA/cm2 k Specific heat at constant pressure and constant volume ratio _ m Mass flow rate, kg/s P Fuel cell operating pressure, bar Pref Reference operating pressure of the fuel cell, bar S/C Steam to carbon ratio SOFC Solid oxide fuel cell T Fuel cell operating temperature, C Reference operating temperature of the fuel cell, Tref C
GE Energy, Siemens Westinghouse and Mitsubishi Heavy Industries, are involving in their design. Moreover, in US, the integration of the fuel cell and GT hybrid system is considered to be the key technology to achieve the Vision 21st goals [4]. In [5] a general review of the integration strategies for solid oxide fuel cells has been presented. Specifically, in this work, the plant definable “direct thermal coupling scheme”, and more precisely “pressurized SOFC þ Brayton cycle” [5], described briefly in Section 2, has been adopted. Moreover the importance of the identification of the best configuration of hybrid system is central in many theoretical analysis and simulation works. Specifically in [6], considering a system configuration where the SOFC converts electrochemically the hydrogen, reformed from natural gas, producing both electrical power and high-grade waste heat for combined heat and power (CHP) system, it has been demonstrated that SOFC can achieve 50% net electrical efficiencies and have already been considered feasible for integration with multi-MW gas turbine engines to achieve more higher electrical efficiency. Anyway the achievable plant global efficiency isn’t estimated numerically and no indication are provided on a possible down scale. In this sense, more information are furnished in [7], concerning an advanced SOFC/GT hybrid system, developed by Siemens e Westinghouse Power Corporation, characterized by a pressurization of 3 atm, a global electrical power of 220 kW and a net electrical efficiency of 55%. An interesting hybrid system configuration, characterized by an IRSOFC (internal reforming SOFC) and two GT turbines, is presented in [8]. The first gas turbine is used to move the air and fuel compressors, while the second one, connected to the alternator, generates the electric power. Also in this work, where a sensitive analysis on the main parameters that influence the system behaviour has been carried out, the HS global electrical efficiency has been estimated around 60%. But in this study, except for the SOFC model based on Siemens Westinghouse data, system components as turbine, compressor and recuperators are modelled only considering
Ua Vref Wc Wglobal WGT WSOFC Wt b DVanode DVO2 DVP DVT hc hgen hglobal ht
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Air utilization factor Reference voltage, V Required compressor power, kW Sum of gas turbine and fuel cell generated power, kW Gas turbine power, kW Fuel cell generated power, kW Turbine output power, kW Pressure ratio Voltage loss due to hydrogen and water partial pressure variations, V Voltage loss due to oxygen partial pressure variation, V Voltage loss due to pressure variation, V Voltage loss due to temperature variation, V Compressor isentropic efficiency Generator mechanical efficiency First law efficiency of the hybrid plant Turbine isentropic efficiency
their thermodynamic characteristics without indicate factory datasheet. In order to confirm the high electrical efficiency achievable in the SOFC/GT plants, a value of 60% was found also in [9] where, beyond the energy analysis, an exergetic approach has been used to analysis the system behaviour under pressure, fuel utilization factor, fuel-to-air and steam-to-fuel ratios variations. The system configuration adopted is very similar to that of [8], characterized by an internal reforming SOFC. This configuration has been used by the authors as base for a subsequently work [10], in which a thermoeconomic model to investigate the better HS configurations is developed. In this work 48 synthesis/design (S/D) parameters are considered. The S/D optimization of the plant is carried out using a traditional single-level approach, based on a genetic algorithm. This optimization procedure shows that it’s possible to reduce dramatically the SOFC active area and the heat exchanger areas; consequently, it makes clear that the optimization of the only stack as an isolated device should be avoided, since inefficiencies in the turbomachinery and in the balance of plant can be significant. As said, it increases the importance of investigating the plant as a whole, analysing its behaviour at both design and part-load operation. In order to define the best HS configuration and the main parameters that influence the plant behaviour, in [11] a thermodynamic simulation of a high-temperature SOFC combined with a recuperated conventional GT is presented. Specifically, a second-law analysis of the cycle has been carried out through an algorithm that simulates the performance of a combined GTeSOFC cycle varying performance parameters, such as the compression ratio and turbine inlet temperature (TIT). It has been observed that an increase in either TIT or compression ratio leads to a higher rate of entropy production of the plant, whereas increasing the TIT improves the specific power output of the cycle. A new complex SOFC-GT hybrid configuration designed to operate over a 5:1 turndown ratio is presented in [12]. This configuration, composed by two gas turbine spools plus
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a separate gas turbine, consents to maintain high efficiencies in turndown condition. This result has been obtained maintaining the SOFC stack exit temperature at 1000 C, limiting the temperature across the stack to less than 200 C, keeping fuel utilization of 85% and thanks to the introduction of a variablegeometry nozzle turbine to directly influence system air flow. Moreover an auxiliary combustor, to control the thermal and power needs of the turbomachinery, has been adopted. An interesting model of hybrid SOFC/GT power system is developed to meet the electrical demand of an electrical power unit of a 300 passengers commercial aircraft in [13]. In a preliminary step, two simple types of models, varying the GT exhaust exploitation, have been presented. A sensitivity analysis, varying the heat exchangers transfer coefficient and the air mass flow rate, has allowed to define the better system configuration. This configuration, contrary to the studies discussed above, has been made to become more realistic basing on the turbine and compressor real performance maps. So, as result, it has been found that the fuel cell performance are strongly influenced by the operating temperature and, hence, when the heat exchanger properties are varied with the air mass flow rate, the HS performance improves. Moreover, the parameters that limit the cycle performance are the SOFC temperature, the turbine inlet and exhaust temperatures. This model doesn’t include the dynamic analysis but the authors refer to a future article in which this subject will be treated. So the purpose of the present paper, differently from the studies relative to stationary SOFC/GT hybrid plants [6e12] discussed above, is to develop a HS model based on datasheet, specifically for the fuel cell, or experimental data, for the gas turbine, to evaluate the nominal and the part load performance of the hybrid system. To this aim a 90 kW “ASC800 e SOFC Power” fuel cell and a 45 kW “Capston C30” micro turbine were chosen as basic components of modelling. Moreover, object of the present paper is also the definition of a proper thermal design and management of the heatrecovery section to optimize the global electric efficiency in part load operation. To this purpose, a zero-dimensional model of such a system has been developed in Aspen Plus environment. The analysis of its performance under different turbine operating points has been carried out taking constant the fuel cell power and the turbine inlet temperature. The model simulations have been conducted by setting the system pressurization and so, indirectly, the GT load. The first part of the study, described in Section 2 (hybrid system layout), has been focused on the identification of both plant layout and proper thermal recovery logic. Subsequently, in Section 3, the modelling of such a system (i.e. fuel cell, gas turbine and the heat exchanger) in Aspen Plus environment has been presented. Specifically in Section 3.1 it is presented the methodology adopted to calculate the turbine electric production, because the different working fluid used respect to the reference conditions indicated in the C30 datasheet. At this step, in Section 4, the attention has been devoted to the results of the Aspen Plus simulations and, in particular, to the energetic analysis of the system working with the GT choked. Finally, in Section 5, the model results have been discussed. The work presented here, descending from previous stationary and dynamic analysis of FC based system carried
out by the author [14e18], has to be considered part of a much larger research work that includes the dynamic modelling analysis of the entire SOFC/GT hybrid system. Because the large amount of data and information to detail and discuss, concerning system layout and components design, model development, simulations schedule and their results for both stationary and dynamic analysis, it has been necessary to divide the work into two separates articles to make the comprehension and its description easier. Then, in a separate paper titled “Part load operation of SOFC/GT hybrid systems: dynamic analysis” the second part of this research work, focused for the same hybrid system on the development of a Simulink dynamic model and on the execution of transients analysis, is described. Moreover, such a section of the study it includes a deep analysis on the heat exchangers blocks and their dynamic behaviour and the effect also on the SOFC operative point.
2.
Hybrid system layout
The choice of the plant layout, and then the coupling between its components, is considered essential by the thermodynamic point of view. The choice of a single working fluid or two can significantly change the performance in terms of efficiency and availability [5] and it can increase or decrease the plant complexity. In this discussion, in order to introduce the plant configuration selected in this work, it should be made an initial distinction between SOFC/GT systems directly and indirectly integrated. Specifically, in the first system configuration, the fuel cell and the gas turbine are connected through the working fluid, which is the same for both, implying also the same operating pressure. An example of an integrated cycle is supplied in Fig. 1 in the particular case of a pressurized system. As regards to the not integrated
Fig. 1 e Pressurized and integrated SOFC/GT configuration.
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configuration, the thermal energy is exchanged between the SOFC and the GT indirectly through a series of heat exchangers. In this case, therefore, as shown for example in Fig. 2, both working fluid and operating pressure are different. In Fig. 3 the system layout considered in this study is depicted. As evident in such a figure, it is characterized by three main sections: the fuel cell and reformer unit, the gas turbine, the heat recovery section. As it can be seen, the model layout shows a direct integration of SOFC and gas turbine system, in which the combustion chamber of the gas turbine has been replaced with a high temperature fuel cell and an afterburner. The choice of a direct integration system is due to two main considerations. The first is that a high operative pressure improves significantly the SOFC performance [19e21], while the second reason consists in the technological problems of an indirect integration. In fact in this last configuration, the gas turbine combustor is replaced with a heat exchanger in which the compressed air is heated by the fuel cell exhaust. But considering the difference of pressure present in this heat exchanger, between the SOFC atmospheric pressure and the compressor outlet stream, and taking into consideration that it works at very high temperature, it’s very onerous for the material used (sealant, mechanical vibrations). Moreover the optimum efficiency of this hybrid scheme is about 5% lower than the pressurized SOFC system [5]. The electrochemical model of the SOFC, developed in [22], uses, as reference, an experimental polarization curve at specified operating conditions. In particular the polarization curve, expressed by the Equation (1), is characteristic of the “ASC-800 SOFCPOWER” fuel cell [23] at 850 C (Fig. 4). Moreover the developed methodology, implemented through a Fortran routine in Aspen Plus, takes into account the voltage deviations from the reference one due to different operating conditions, in particular in term of pressure (DVP),
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temperature (DVT), fuel (DVanode) and oxidant composition (DVcathode), according to relations (2e5). Vref ¼ 5:419$1008 $I3 þ 2:083$1004 $I2 4:596,1001 $I þ 1:066$103
DVP ¼ 76$log
P Pref
(1)
(2)
DVT ¼ 0:008$ T Tref $I
(3)
DVanode ¼ 172$log
PH2 =PH2O ðPH2 =PH2O Þref
(4)
DVcathode ¼ 92$log
PO2 ðPO2 Þref
(5)
where: P, Pref are the operating pressure of the cell and the reference pressure respectively; T, Tref are the operating temperature of the cell and the reference temperature respectively; I is the current density; PH2, PH2O, PO2 are the partial pressures of hydrogen, water vapour and oxygen, respectively. Hereinafter in order to take a global overview of the hybrid plant a short description has been presented. The feeding streams of the hybrid system are: e “1F”: indicates the fuel feeding flow rate (methane, 100% CH4) needed to the cell to produce 90 kWe;
Fig. 2 e Non-pressurized and non-integrated SOFC/GT configuration.
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Fig. 3 e Hybrid system layout.
e “WATER”: is the water flow rate required by the steam methane reformer; such a flow rate is determined to meet the desired S/C ratio value, equal to 3.0, using a dedicated Design-spec function [24], e “1A”: is the inlet air flow rate processed by the compressor (79% N2, 21% O2), e “CH4BURN”: represents an auxiliary amount of fuel flow rate (methane, 100% CH4) directed in the afterburner block. Subsequently the streams “1F”, “Water” and “1A”, after their pressure rise, if necessary, are heated in the heat
recovery section by three heat exchangers (“REC1”, “REC2” and “REC3”) in which the thermal energy of the exhaust gases, coming from the turbine, is recovered. The temperature of the final exhaust stream “EXHAUST2” has been fixed at 153 C. In particular in “REC3”, and thanks to an auxiliary amount of thermal power (stream “Q5”) if the exhaust thermal energy is not enough, the water is brought to the steam conditions before the reforming section. Then, the fuel and steam flows (“2F” and “STEAM1”) are sent to the “REFORMER” block, maintained at its operating temperature thanks to the SOFC cooling thermal power “QCOOLING” and an auxiliary thermal flux coming from the “AFTERBUR” block.
Fig. 4 e ASC-800 polarization curve.
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The syngas, produced in the reformer, together with the oxidant reaches the fuel cell (modelled through the CATHODE, ANODE and HEATER1 units) where the electrochemical reaction takes place producing the demanded electrical power. The fuel cell exhaust gas “8M” is used to preheat the oxidant in the counter-current exchanger named “RIG”. Subsequently, in order to heat up the exhaust gas to the turbine inlet temperature, the cell exhaust “8N” is burned in the “AFTERBUR” block together with the stream “5C” (that is the part of oxidant not needed by the fuel cell) and the “CH4BURN”: the last is calculated through a Design Spec, with target to maintain the turbine inlet temperature constant and to ensure the water vaporization in the “Q5” unit. The fuel quantity provided by stream “1F” is calculated through a Fortran iterative procedure, with target the fuel cell electric power set by the user. The input of this procedure is the real polarization curve in function of the operating conditions (Equations (1)e(5)). The SOFC air input flow rate “4A” is determined considering an air utilization factor (Ua), defined as the ratio between stoichiometric air and introduced air, equal to 0.2. Whereas the inlet air flow rate of the system, upstream of the compressor, is fixed by the authors referring to the compressor map in order to match a defined GT electric power. In all heat exchanger units an amount of heat loss, equal to the 10% of the exchange heat, has been considered in analogy to the assumptions used in [25].
3.
Components model
3.1.
Gas turbine model
Parameters of the C30 gas turbine at design point
a It refers to the case of methane feeding.
WGT ¼ hgen ðht Wt Wc =hc Þ
(6)
where:
As just anticipated in Section 1, the gas turbine power calculated for the Capstone C30 used in the Aspen Plus model is more than 30 kW shown in the turbine datasheet (Table 1). It is due to the different type of gas expanded in the turbine in the SOFC/GT layout that, thank to its higher specific heat, permits to increase the produced turbine power (Equation (13)). In the following Fig. 6 the compressor map recalculated, basing on the real flow rate and GT power at nominal and part load conditions, is shown.
Table 2 e Model equations (the subscripts used in the equation refer to the Aspen Plus model streams of Fig. 1).
Table 1 e Capstone C30 nominal data.
Compressor isentropic efficiency Air flow rate Fuel flow rate Turbine inlet temperature Turbine isentropic efficiency Electric power generated Electric efficiency
nominal one, the thermodynamic equations shown in Table 2 for the compressor and the turbine have been used. The power output from the gas turbine has been calculated by:
- hgen is the generator mechanical efficiency set to 0.9; ht and hc are the turbine and the compressor isentropic efficiencies, equal to 0.9 and 0.8 respectively. - Wt, Wc are turbine output power and required compressor power.
The micro gas turbine selected in this work is CAPSTONE C30, which is a single-shaft micro GT equipped with a centrifugal compressor and a radial turbine. The main parameters of C30 gas turbine are summarized in Table 1. The pressure ratio in part load conditions is determined basing on the compressor performance map (Fig. 5), which shows the compressor introducing pressure as function of mass flow rate and shaft speed. In order to evaluate the pressure ratio and the air flow rate corresponding to a certain electric power demand far to the
Pressure ratio
Fig. 5 e Compressor performance map [26].
3.2 80% 0.31 kg s1 0.0024 kg s1 1173 K 90% 30 kWa 26%a
Thermodynamic equations used in the compressor and turbine model Compressor outlet pressure Compressor power Turbine pressure ratio Turbine power
P2A ¼ b$P1A _ 1A $cp;1A $T1A Wc ¼m $ðbg1A 1Þ bt ¼
P27 P27 ¼ P8 P2A
_ 8 $cp;8 $T8 $ð1 bt Þ Wt ¼ m
(10) K1A 1 K1A
(11)
where P27 ¼ 1.03 bar
(12)
where g1A ¼
where g8 ¼
k8 1 k8
(13)
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Fig. 6 e Pressure ratio (black lines) and GT power (grey lines) at different rotational speed (rpm) depending on compressor mass flow.
So, in Aspen Plus compressor model, the pressure ratio and the air flow rate calculated basing on the electric power required have been set. Instead, in the turbine model, only the outlet pressure value has been set, equal to the inlet compressor pressure, considering the entire working flow of the system as processed flow rate (i.e. cell exhaust plus auxiliary methane flow rate in the afterburner inlet). Moreover the turbine inlet temperature has been fixed at 900 C in every working conditions.
3.2.
Fuel cell and fuel processor model
As just anticipated in Section 2, the electrochemical model of SOFC is based on the experimental polarization curve, Equation (1), of a ASC-800 fuel cell produced by SOFCPOWER. Moreover in the zero dimensional model presented, in order to reach an electric power of 90 kW, a fuel cell stack made of 702 single cells, each characterized by an area of 144 cm2, has
been considered. The SOFC operating temperature has been set at 850 C, instead the pressure has been fixed as consequence of the pressure ratio required by the GT to meet the load demand. In Fig. 7 shows the model of the fuel cell section. Specifically, in the reactor module named “ANODE” the electrochemical reactions, that occur in the cell, have been simulated. The reactions considered in the block are: Electrochemical reaction : H2 þ 0:5O2 /H2 O
(7)
Methane steam reforming : CH4 þ H2 O4CO þ 3H2
(8)
Water gas shift reaction : CO þ H2 O4CO2 þ H2
(9)
Moreover, in order to send the oxidant flow rate that respects the air utilization factor (Ua), defined in Section 2, a separator block Sep, named “CATHODE”, has been
Fig. 7 e Fuel cell section.
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Fig. 8 e Reformer section. implemented. The SOFC produced electric power has been considered as an outlet stream of the block “HEATER1”, named “WE”. The final component “COOLER” represents the cooling system of the fuel cell, stream “QCOOLING”, that allows to maintain the cell temperature at 850 C. Furthermore on the anode side, before the mixing in the “MIXER” block between the anodic and cathodic exhaust streams, in the anodic stream “5F” the liquid water is drained in the block “SEP” (Fig. 7). The reformer model, as presented in [22], consists in Aspen Plus equilibrium reactor module Rgibbs (named “REFORMER”) in which the steam reforming reactions have been replicated. The module named “HEATER2” is a heater module used to bring the steam temperature (stream “STEAM1”) at the required inlet condition of the reformer (250 C) by a heat stream, “Q5”, calculated through a Design-spec function. The reforming temperature has been fixed at 750 C and its maintenance has been realized through the inlet thermal power streams, “QCOOLING” and “Q4” that represent the SOFC cooling thermal power and the auxiliary thermal power produced by the afterburner, “AFTERBURN” (Fig. 8).
3.3.
Heat recovery section model
As preliminary remark, it is evidenced as the heat-recovery section design and then its management strategy, as detailed in the following, has been performed aiming to an optimization of the global electric efficiency of the hybrid system in part load functioning. As anticipated in Section 2, the thermal power contained in the exhaust GT gas has been recovered by a series of three countercurrent heat exchangers.
In particular the first two, “REC1” and “REC2”, have been modelled by the Aspen Plus module HeatX, whereas the last “REC3” by the module MHeatX (Fig. 9). In order to consider, in “REC1” and “REC2”, a thermal loss equal to the 10% of the one exchanged, a Design-spec function has been used. Then the thermal power lost has been modelled with an outgoing stream, “QLOSS1”, that starts from the Heater block called “LOSS1”. Furthermore, in the heat exchanger “REC3”, the heat lost has been implemented directly in the Aspen Plus block. From the thermodynamic point of view, in “REC1” and “REC2” the difference between the hot inlet (“27B” and “28”) and the cold outlet (“3A” and “2F”) of the heat exchangers have been set to 30 C. Instead in the “REC3” only the hot outlet temperature (“EXHAUST2”) has been set at 153 C. Moreover it’s important to underline how a fundamental thermal power exchange takes place in the “RIG” block, as just said in Section 2, where the cathodic air flow rate is heated to the SOFC operating temperature exploiting the heat power contained in the fuel cell exhaust gas (“8M”). Also upstream of this recuperative heat exchanger, a thermal power loss, equal to 10%, has been considered in the “LOSSRIG” unit through the heat stream named “QLOSSRIG” (Fig. 3).
4.
Tests
4.1.
Conditions investigated
The analysis of the hybrid system performance has been carried out through simulations by varying: the pressure
Fig. 9 e Thermal power recovery section.
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Table 3 e Test conditions. Test
Compressor Compressor Gas turbine pressure ratio inlet air flow (kg/s) “1A” speed (rpm)
1 2 3 4
3.24 3.1 2.8 2.52
0.315 0.272 0.227 0.208
96,000 86,400 76,800 67,200
Table 4 e Simulations results. Test WGT WSOFC Wglobal hglobal FuelSOFC Fuelafterb Fuelglobal
1 2 3 4
kW
kW
kW
e
kg/s
kg/s
kg/s
45.4 38.3 30.1 25.0
90 90 90 90
135.4 128.3 120.1 115.0
59.23% 59.34% 59.18% 58.45%
0.00280 0.00281 0.00285 0.00289
0.00240 0.00210 0.00177 0.00158
0.00520 0.00491 0.00461 0.00447
conditions of the fuel and air feeding flows and, consequently, the air flow sucked by the compressor, maintaining a SOFC constant electric power (90 kW). In Table 3 the test conditions are shown: In particular in the Test 1 the gas turbine nominal functioning conditions have been replicated, instead in the other three tests the influence of the GT part load conditions on the hybrid system efficiency has been valuated. Furthermore, in each test, the temperature of reformer, SOFC and the turbine inlet temperature have been considered constant and equal to 750 C, 850 C and 900 C respectively.
4.2.
Simulations results
In the following Table 4 the simulations results obtained in the four tests indicated in Table 3 are presented. In particular the values of generated power, first law global efficiency and needed methane flow rates are listed.
Fig. 10 e Efficiency and hybrid power system trends.
Fig. 11 e Fuel streams in hybrid system.
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The trends of both global efficiency and total power generated by the hybrid system are shown in Fig. 10. It’s important to underline how the efficiency trend, varying the operative electric load (i.e. varying the gas turbine functioning point), is almost constant up to a GT load reduction of about 34% (Test 3). Moreover the efficiency maximum variation is 0.9% and occurs between the Test 2 and Test 4 (GT load reduction of 35%), while in the Test 4, in order to consider the maximum GT part load, the GT produced power has been reduced of 45% respect to the Test 1 with a very small efficiency variation (0.78%). Comparing the overall first law efficiency with other plants presented in technical works [6e9], it is possible to find a good agreement of the results obtained in term of efficiency values and their trends. Considering the trends of the feeding fuel flows, shown in Fig. 11, it is evident as a slight rise in the SOFC consumption, as anticipated in Section 2, corresponds to the decrease of the system pressure (from Test 1 to Test 4). The concomitant decrease of the fuel required by the afterburner block, due to both higher temperature of the fuel cell exhaust and lower thermal power required by the reformer (because the reduction of the “Q5” term), helps to maintain the global efficiency quite constant. The total amount of fuel consumed by the system reflects globally the hybrid power system trend (global produced power in Fig. 11) but it’s percentage variation between Test 1 and Test 4 is less respect to each of the generated power, 14% and 15% respectively. This difference influences the trend of hybrid system efficiency making it decreasing.
5.
Conclusions
In this paper a SOFC/GT hybrid system layout and its thermal management, concerning in particular the heat-recovery section, are presented and discussed by means of stationary analysis at nominal and part load operative conditions. In particular, the influence of the GT part load functioning on the overall system efficiency has been analysed maintaining the SOFC power set to the nominal one. To this aim, starting from the fuel cell (ASC-800) and the gas turbine (Capstone C30) datasheets, an Aspen Plus model that includes a heat recovery section, to properly exploit the hybrid system exhaust, has been implemented. The adopted philosophy, for the thermal management of such a section, consists of a greater heat recovery from the exhaust, in a suitable measure according to the particular GT load, in case of part load operation to compensate as much as possible the reduction of GT electric efficiency. Consequently, heating the system inlet feeding flows, the optimization of the system efficiency has been possible. Specifically, analysing the performance of GT/SOFC system at part load conditions (Fig. 10), the trend of the system efficiency is globally constant, with a maximum variation in any case less than 1% at a decreasing of the gas turbine load up to 45% respect to the nominal power. This result can be considered of primary importance in view of a possible utilizing of SOFC/GT system in a distributed power generation market where the load demand is far from
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be constant. Therefore, the research activity has concerned a more deep analysis of the proposed hybrid system layout in part load functioning, through the study of its dynamic behaviour during transients. This activity has required the development of a dynamic model of the system described, together with the main simulation results and consequent discussions, in a separate paper titled “Part load operation of SOFC/GT hybrid systems: dynamic analysis”. Relative to the possible effects of the electric load variation on the global system efficiency, it is evidenced as during transients in particular the proposed design of the heat-exchangers, and therefore their dynamic behaviour, is significant, influencing also the SOFC operative point.
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