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A comparison between conventional recuperative gas turbine and hybrid solid oxide fuel cell –gas turbine systems with direct/indirect integration D Sa´nchez1*, R Chacartegui1, T Sa´nchez1, J Martı´nez2, and F Rosa3 1 Universidad de Sevilla, Escuela Te´cnica Superior de Ingenieros de Sevilla, Camino de los descubrimientos s/n, Sevilla, Spain 2 AICIA, Camino de los descubrimientos s/n, Sevilla, Spain 3 ˜ as, Mazago´n, Spain Instituto Nacional de Te´cnica Aerospacial INTA, Carretera San Juan del Puerto – Matalascan The manuscript was received on 7 May 2007 and was accepted after revision for publication on 23 November 2007. DOI: 10.1243/09576509JPE472

Abstract: Conventional recuperative micro gas turbines have a 30 per cent low heating value (LHV) maximum efficiency at full load. Therefore, if they are to be used in a potential distributed energy scenario, solutions must be developed that increase efficiency. An innovative gas turbine-based technology is the fuel cell – gas turbine hybrid system. This work is aimed at studying how the basic performance of a conventional Brayton cycle changes when heat addition is done at a fuel cell. Two layouts are considered: a direct system where the compressor feeds the fuel cell directly and an indirect system where only heat is transferred between subsystems. Direct and indirect systems have been studied at full and part load, concluding that the efficiency versus pressure ratio curves of hybrid systems change substantially with respect to a traditional gas turbine; part-load efficiency hardly decreases. Maximum efficiency of hybrid systems doubles the efficiency of state of the art micro gas turbine and remains high at part load. Furthermore, the benefit of a certain increase in temperature is higher for hybrid systems than for conventional engines. Finally, a simple economic analysis shows that the total installation and operation/maintenance costs of hybrid systems make them competitive against conventional gas turbines. Keywords: fuel cell, gas turbine, hybrid system

1

INTRODUCTION

Small scale gas turbines have usually lacked efficiency either at full or part load, this being a major disadvantage when compared with piston engines or other power devices. Using a recuperative gas turbine can counteract this fact partially, increasing rated efficiency to over 25 per cent and approaching the milestone 30 per cent. However, in any cases, running at part load significantly reduces these figures and means a penalty over the performance of the system. *Corresponding author: Thermal Power Group, Universidad de Sevilla, Grupo de Motores Te´rmicos, Escuela Te´cnica Superior de Ingenieros, Camino de los descubrimientos s/n, Sevilla 41092, Spain. email: [email protected] JPE472 # IMechE 2008

The reason for this poor performance is found in a very low turbine inlet temperature [1]. Low power is coupled to low air mass flow and, hence, to radial turbomachinery which cannot be cooled. Current materials can withstand temperatures of up to 1000 8C for continuous operation and, occasionally, rise to 1100 8C for a temporary peak load demand. After years of focusing all efforts in developing new materials capable of withstanding temperatures over 1000 8C, a new interest for innovative cycles has recently grown up parallel to the increasing notoriety of fuel cells in the power sector. In a similar way to gas and steam combined cycles in the industrial power generation market, where the combination of gas and steam turbines can lead to efficiencies over 50 per cent low heating value (LHV), hybrid cycles Proc. IMechE Vol. 222 Part A: J. Power and Energy

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composed of high temperature fuel cells and microgas turbines are being considered for distributed power applications. Recent analyses of this kind of hybrid systems report efficiencies over 60 per cent LHV [2]. A lot of research in the analysis of fuel cell – gas turbine hybrid systems has been done in recent years, covering different types of fuel cells and a number of integration schemes, and conclusions have been drawn about the capabilities of this sort of devices. However, although many different system layouts have been presented in these works, most studies concentrate in a particular integration sketch, usually neglecting other layouts, and have developed a full set of characteristics curves which describe the performance of the system under different working conditions, either at full or part load. The present work covers the fundamentals of integrating a solid oxide fuel cell and a micro gas turbine. An analysis is made about the impact of modifying a basic recuperative gas turbine cycle with a fuel cell for the external heat addition process. Optimal pressure ratio, cell temperature, and other parameters are studied in order to establish a maximum efficiency for each of the systems considered. After this basic thermodynamic study, a comparison of part-load behaviour is done and conclusions are drawn about which of the systems is more convenient for different working environments. A brief description of the model used is presented – a full description of the model is out of the scope of this work – and, later, the three systems considered in the analysis are described. To complete this technical study, a simplified economic analysis of installation and operation costs of the systems presented is included. Conclusions are written in the final section. 2

with the protons to form water. Water joins the anodic gas and is exhausted from the cell. A flow of electrons is established from the anode to the cathode through an external circuit, i.e. electrical load. This electric current is coupled to a voltage difference between electrodes, which appears as a consequence of the reaction taking place in the cell. It can be ideally described by the Nernst equation, equation (2) pH2
p1=2 Rg
T O2 ln E ¼ E0 þ ne
F pH2 O

! ð2Þ

E is the Nernst or ideal potential established between electrodes and it depends only on temperature and composition as shown in equation (2). E0 is the standard potential which is the potential at reference conditions. The power developed by the cell is the product of voltage and electric current Wideal ¼ E
I

ð3Þ

Regrettably, not all this power Wideal is useful due to irreversibilities arising in the process described above. In fact, a voltage drop DV takes place. Therefore, the real work produced by the cell is Wreal ¼ ðE  DV Þ
I

ð4Þ

There are three contributors to the voltage drop: ohmic losses, activation losses, and concentration losses; these losses are usually called polarizations. The ohmic polarization is caused by the resistance to the flow of electric current in electrodes and electrolyte and it can be easily described by the following equation

DESCRIPTION OF THE FUEL CELL MODEL DVohm ¼ Z
I

Fuel cells are devices where hydrogen is oxidized to water electrochemically, i.e. no combustion takes place, in a strongly exothermic reaction (Dhf ¼ 2242 kJ/mol), equation (1) 1 H2 þ O2 ! H2 O 2

ð1Þ

A hydrogen stream enters the anode where hydrogen molecules are dissociated into protons at the anodic surface. These protons migrate through the electrode towards the contact surface between anode and electrolyte, usually called three-phase layer, where the oxidation takes place. At the same time, an oxygen stream feeds the cathode. At this electrode, oxygen ions are formed which migrate through the electrolyte to the three-phase layer where they react Proc. IMechE Vol. 222 Part A: J. Power and Energy

ð5Þ

Z is the equivalent resistance of the cell. It depends mainly on materials and temperature through the electronic/ionic resistivity and, secondarily, on the cell internal configuration, i.e. planar, tubular, mixed. The calculation of Z is not complex although it involves very large equations which are not of interest for this work. Readers who wish to know the process to evaluate the ohmic polarization are referred to reference [3]. Activation losses are related to the need to overcome the activation energy of the half reactions taking place at each anode. They depend on materials, temperature, composition, and intensity. The calculation of the activation loss is more complex than the previous one and it involves evaluating some necessary material properties, which is not an JPE472 # IMechE 2008

Comparison between conventional recuperative gas turbine and hybrid SOFC–GT systems

easy task. Therefore, simplified methods are used to predict activation losses, Tafel equations being the most common. Equation (6) shows the aspect of a Tafel line relating current intensity and voltage drop DVact ¼ a þ b
lnð jÞ

ð6Þ

However, using Tafel equations can lead to a not negligible error at low current densities, up to 20 per cent, so, for the present work, a more general equation has been used. This expression is derived from a general Butler Volmer equation after assuming the commonly accepted hypothesis of symmetric transfer coefficients equal to 0.5 [4] DVact ¼


 Rg
T j0 sinh1 F 2
j

ð7Þ

Equation (7) is applicable to both anode and cathode as j0, which stands for the so called exchange current density, is different for each of them. The sum of the activation loss at both electrodes is the total activation loss. A more detailed analysis of the method to calculate activation losses and the hypotheses made to obtain equation (7) is given in reference [4]. Concentration losses are related to the velocity at which species diffuse through the porous electrodes and are consumed at the active sites where the oxidation reaction takes place. Its calculation is therefore related to the capacity of feeding the reaction with hydrogen and oxygen at a high enough rate. If the concentration of any of the species reacting were too low or if their rate of reaction were too high or if they diffused slowly, the concentration losses would increase. However, this type of polarization is very low compared with the previous ones; in fact, one order of magnitude smaller. Thus, most authors dismiss the concentration polarization and only consider ohmic and activation losses. This has been done in the present work. 3 3.1

FUEL CONDITIONING Prereforming

Up to now, hydrogen has been considered to be the only component of the fuel stream feeding the anode. This is not usual. Hydrogen is not found as a free gas in nature and it has to be obtained as a product from an industrial process. There are several techniques to produce hydrogen from other compounds such as water, natural gas or other and all of them imply a waste of energy. Among these, natural gas is extensively used as fuel for power producers, such as gas turbines or even JPE472 # IMechE 2008

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large piston engines, and a very vast supply network is already available at almost any site where a power plant is set. In addition, the process where hydrogen is formed from natural gas, mainly methane, is well known in heavy industries and its application to fuel cells is therefore easy. When dealing with natural gas, it is quite usual to assume that it is formed exclusively by methane. If longer chained hydrocarbons appear, they are converted to equivalent methane. Thus, the following reforming process is considered to take place inside the cell CH4 þ H2 O ! 3H2 þ CO

ð8Þ

Equation (8) is called the reforming reaction and is strongly endothermic (Dhf ¼ 206 kJ/mol). In addition, the following water–gas shift reaction occurs, which is slightly exothermic (Dhf ¼ 241 kJ/mol) CO þ H2 O ! H2 þ CO2

ð9Þ

As deduced from equations (8) and (9), hydrogen is obtained from methane if water is present. To guarantee the presence of water and avoid undesirable reactions that would form atomic carbon and block the catalyst, part of the gases exhausting the anode is recirculated and joins the raw fuel. This exhaust stream contains up to 50 per cent (vol) of water coming from the oxidation of hydrogen. Recirculating exhaust gases not only supplies water but also promote the endothermic reforming reaction. Note that the exhaust gases are at a very high temperature and can be used as a heat source for the reforming process, which is favoured by high temperatures. Despite this, not all the methane feeding the cell can be reformed inside it. If pure methane entered the anode, the endothermic behaviour of the reforming process, which is not balanced by the exothermicity of both hydrogen oxidation and shift reactions, would cause a strong decrease in temperature. In this situation, high stresses would appear in the elements of the cell which would eventually deteriorate its performance noticeably and, eventually, break it. Thus, a prereforming reactor is placed outside the cell in order to have part of the methane reformed before entering it. This prereforming reactor is considered to be adiabatic and both reactions, reforming and shift, are supposed to reach chemical equilibrium at its exit. The equilibrium constant of both reactions is related to the temperature at which equilibrium is reached and it can be obtained from the following equation log kp;i ¼ aT 4 þ bT 3 þ cT 2 þ dT þ e

ð10Þ

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where T is temperature in K and kp,i stands for the equilibrium constant of both reactions kp;ref


 p3 pCO n3 nCO p 2 ¼ H2 ¼ H2 pCH4 pH2 O nCH4 nH2 O ntot

kp;shift ¼

pH2 pCO2 nH2 nCO2 ¼ pCO pH2 O nCO nH2 O

Uf ¼ ð11Þ

ð12Þ

Internal reforming

About 20 – 40 per cent of the methane in the raw fuel is prereformed outside the cell, the rest of it being completely reformed at the anode. For the water – gas shift reaction, chemical equilibrium is assumed again, this time at the operating temperature of the cell. Equations (10) and (12) can be used to evaluate the rate of the latter reaction.

4

FUEL CELL MASS AND ENERGY BALANCE

Section 3 has shown the procedure to evaluate how much methane and carbon monoxide react according to equations (8) and (9). In order to apply a mass balance equation, the rate of hydrogen being oxidized to water must still be evaluated. The amount of hydrogen demanded by the cell is related directly with the current intensity between electrodes through Faraday’s law nH2 ¼

j
A 2
F

nH2 ; oxidized nH2 ; oxidized  ¼ nH2 ; supplied 3
nCH4 þ nCO þ nH2 raw fuel ð14Þ

Molar flows are evaluated at the prereformer exit in equations (11) and (12). Coefficients a to e in equation (10) are different for each reaction as shown in Table 1 [5].

3.2

fuel utilization factor

ð13Þ

where j is the current density and A the active cell area. However, in order to avoid a lack of hydrogen in a sudden change in the operational conditions and to improve the performance of the cell, hydrogen is supplied in excess with respect to what equation (13) establishes. This excess is defined through the

As long as natural gas, methane, is used in most cases as raw fuel, an equivalent hydrogen flow must be calculated to determine how much fuel feeds the cell. This equivalent hydrogen flow is shown in the denominator of the rightmost term in equation (14). Finally, the amount of anodic exhaust gases being recirculated to the prereforming reactor is determined by the steam to carbon ratio (STCR), equation (15). This parameter measures the ratio of water molecules to atomic carbon at the entrance of the prereformer and its value must be in the range from 1.5 to 3. A too high STCR would ensure a high degree of prereforming but would dilute the hydrogen flow and lower the efficiency at the same time. Oppositely, if STCR were too low, atomic carbon would probably be formed and block the catalyst, causing a decrease in efficiency as well.  nH2 O  STCR ¼ nCH4 þ nCO prereformer inlet

ð15Þ

A mass balance equation can now be applied to the fuel cell in order to calculate the outlet flow and composition of the exhaust gas at both electrodes. However, as said in the introductory section of this work, air is supplied to the cathode well in excess with respect to stoichiometry in order to cool down the cell. The precise air flow is obtained by applying a heat balance equation to the cell, not the prereformer, and calculating the amount of air needed to maintain the operating temperature of the cell at the desired value. Compositions, molar flows, and temperatures are the result of the application of both heat and mass balance equations to prerefroming reactor and cell, equations (16) and (17), respectively Hfuel þ Hrecirculation  nref Dhref  nshift Dhshift ¼ Href effluent

Table 1

a b c d e

ð16Þ

Coefficients in equation (10)

Reforming

Shift

22.6312  10211 1.2406  1027 22.2523  1024 1.9503  1021 266.1395

5.47  10212 22.5748  1028 4.6374  1025 3.9150  1022 13.2097

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Href effluent þ Hair  nref Dhref  nshift Dhshift  noxid Dhoxid ¼ Hexhaust þ Welec þ Qloss

ð17Þ

All total enthalpies considered in equations (16) and (17) are temperature and composition dependent. In addition, a heat loss to the surroundings has been JPE472 # IMechE 2008

Comparison between conventional recuperative gas turbine and hybrid SOFC–GT systems

Fig. 1

Prereformer and fuel cell block diagram

considered as Qloss. A block diagram of the whole system to which equations apply is depicted in Fig. 1.

5 5.1

HYBRID SYSTEMS Configurations

A conventional micro gas turbine has been taken as reference system in this work. These gas turbines comprise a centrifugal compressor, backflow single combustion chamber, radial turbine, and recuperator. Radial turbines cannot be cooled internally, what means that turbine inlet temperature is relatively low in comparison with heavy duty axial flow turbines. As a result, efficiency decreases, this being a major disadvantage of this kind of power generators. To offset this characteristic of micro gas turbines, hybrid systems are proposed. The heat addition to the system is not done through a conventional combustion process as in the former system, but through an electrochemical process. During this controlled oxidation not only heat is released but a considerable amount of work is done, i.e. electrical work. The electrical work is about three to five times higher than the gas turbine if turbine inlet and cell temperatures are the same. This means a remarkable boost in efficiency, which reaches values close to 65 per cent depending on the configuration of the hybrid system. Figures 2 and 3 show two different layouts for integrating gas turbines and fuel cells. Figure 2 is representative of the direct hybrid system. The air

Fig. 2

SOFC – GT direct hybrid system

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Fig. 3

153

SOFC – GT indirect hybrid system

leaving the compressor feeds the cathode of the fuel cell after being preheated by the exhaust gas of the turbine. The exhaust gas of the cell enters the turbine where power is produced. Under this configuration, the fuel cell is pressurized to up to 3 or 4 bar, increasing useful power and efficiency considerably. In this sense, the efficiency of the cell depends on the pressure ratio of the turbine. Figure 3 shows an indirect hybrid system. In this case, there is no mass exchange between fuel cell and gas turbine and only heat is transferred between subsystems. The air leaving the compressor is heated up by the exhaust gas of the cell at a heat exchanger. This hot air enters directly into the gas turbine where it is expanded to produce power. Once expanded, the exhaust air of the turbine is used to raise the temperature of the air feeding the fuel cell, which works at atmospheric pressure. Thus, the efficiency of the cell is lower than in the previous case but, on the other hand, does not depend on the pressure ratio of the turbine.

5.2

Microturbine model

The operation of heavy duty gas turbines is difficult to model as long as many parameters are involved. Firing temperature, inlet guide vanes position, inlet air temperature and moisture, gas generator rotating speed, variations of compressor and turbine efficiencies, inlet filters pressure drop, and turbine backpressure are just some of the factors which have to be considered. However, micro gas turbines are much easier to model as most of its technology comes from the piston engine supercharging industry. In the present work, a high speed compressor – turbine coupling has been considered whose characteristic curves are shown in Fig. 4. A variable speed operating line is shown dashed in Fig. 4, where horizontal axis is the ratio of actual to design point corrected mass flows, see equation (18), and vertical axis is the pressure ratio. Corrected speed curves have been drawn for completion of the model, Proc. IMechE Vol. 222 Part A: J. Power and Energy

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Fig. 4

Characteristic curves of a compressor-turbine coupling

equation (19) pffiffiffiffiffiffiffiffi m Tair _c¼ m pair

ð18Þ

N Nc ¼ pffiffiffiffiffiffiffiffi Tair

ð19Þ

Efficiency lines have not been considered. Constant efficiency lines for centrifugal compressors are ellipses whose major axe is almost parallel to the surge line and with a large major to minor axe ratio [6]. Therefore, efficiency does not change substantially with corrected mass flow as long as operation follows the dashed line shown in Fig. 4. Thus, constant efficiency is assumed for both compressor and turbine. Mechanical and electrical efficiencies are considered constant as well. 6 6.1

MODEL RESULTS

Fig. 5

Useful work versus pressure ratio conventional recuperative gas turbine

for

a

engineer. Maximum work and efficiency are reached at different pressure ratios. Some aspects of Figs 5 and 6 must be pointed out. First, a maximum efficiency of 30 per cent LHV is expected for the highest turbine inlet temperature; slightly lower values can be obtained for state of the art engines. Second, choosing the pressure ratio for the highest possible efficiency leads to a reduction in useful work and conversely. However, for recuperative engines, this is a minor effect as pressure ratios for maximum work and efficiency are very close; for the 900 8C case shown in Figs 5 and 6, these are 2.5 and 3.2, respectively. Finally, it is very important to notice that, without being concerned about which of the two parameters is to be maximized, both optimum pressure ratios are in the working range of state of the art single stage radial turbomachinery. This is not the case for nonrecuperative engines. Figure 7 shows the power ratio between fuel cell and gas turbine for both types of hybrid systems and for

Full-load operation

Graphics in this section are design figures and, therefore, the use of performance maps like Fig. 4 is not applicable [6]. Instead, a characteristic efficiency is chosen for both compressor and turbine and, after, a sensitivity analysis to pressure ratio and turbine inlet temperature is carried on. The objective of this ‘design analysis’ is to identify the optimum performance parameters, if any, of a hybrid system in order to adopt a particular design point. Once the design point is chosen, performance maps are generated for the part-load analysis presented in section 6.2. The analysis has been done from the gas turbine perspective. Figures 5 and 6 show the useful work and efficiency versus pressure ratio curves of a recuperative gas turbine for different turbine inlet temperatures which are well known for any gas turbine Proc. IMechE Vol. 222 Part A: J. Power and Energy

Fig. 6

Efficiency versus pressure conventional gas turbine

ratio

for

a

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different cell temperatures. Curves are referred to the same active area of the fuel cell, i.e. number of unit cells in the stack. It is shown that the fuel cell produces between three to five times more power than the gas turbine for direct and indirect integrations, respectively. Therefore, it is concluded that the pressure ratio for maximum useful work at the turbine is not of interest any more, since most of the power of the system is produced by the fuel cell. Instead, global efficiency is the main concern. Substituting the combustion chamber with a fuel cell affects the shape of the efficiency curves depicted in Fig. 6. As shown in Fig. 8 for direct hybrid systems, a rapid increase in efficiency is followed by stabilization. This trend is very close to that which characterizes fuel cells, for which pressure increases efficiency in an asymptotic pattern. This behaviour is enhanced initially by the improvement in gas turbine efficiency with pressure ratio. The inversion of this trend for the gas turbine, which is shown in Fig. 7, causes a slight

decrease in efficiency which is visible in Fig. 8. There is still an influence of temperature on the value of optimum pressure ratio but, once stabilization is reached, the efficiency is almost independent of pressure ratio. Therefore, the following conclusion is drawn from a practical point of view. Optimum pressure ratios are out of the working range of state of the art single stage centrifugal compressors, which is limited to 4 or 5. However, for this maximum affordable working pressure ratio, efficiency is quite close to its maximum value. This statement is less true as temperature increases over 1000 8C as working temperature increases. Figure 9 is similar to Fig. 8 but it applies to indirect hybrid systems. As it was expected, these hybrid systems are less efficient than direct ones as long as the fuel cell works at atmospheric pressure; i.e. the power and efficiency enhancement caused by the effect of pressure over the cell is not present now. Thus, the general shape of the curve is closer to the custom engine shown in Fig. 6, though shifted upwards. As a consequence, the value of the optimum pressure ratio for maximum efficiency at each cell temperature is well defined and there is a considerable decrease in efficiency when working pressure ratios differ from that optimum value. However, there is a characteristic of indirect hybrid systems that make them very interesting. It is shown in Fig. 9 that the value of pressure ratio which gives maximum efficiency is almost independent of temperature. Therefore, it is guaranteed that although gas turbine technology develops, and as a consequence turbines can withstand higher temperatures, optimum pressure ratios will still be attainable for single stage radial compressors. This is an advantage of this kind of integration that is not present in direct systems except for the almost stabilized fashion of the curves at current working temperatures.

Fig. 8

Fig. 9

Fig. 7

Power ratio from fuel cell to gas turbine for direct and indirect hybrid systems

Efficiency versus pressure ratio for a direct hybrid system

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Efficiency versus pressure ratio for an indirect hybrid system Proc. IMechE Vol. 222 Part A: J. Power and Energy

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6.2

Part-load operation

A comparison has been done in the previous section for gas-turbine-based power systems working at design conditions. Among other advantages, hybrid systems have shown to be capable of reaching higher efficiencies than custom recuperative gas turbines. Part-load operation will be analysed now. Part-load operation of gas turbine engines is very difficult to describe. Several strategies for load control are available and, generally, the same engine can be fitted with any of them depending on the turbine duty. Furthermore, the load control system of a particular running engine can be changed upon request to the OEM at a major overhaul. Figure 10 shows the efficiency– load curves for conventional gas turbine, direct, and indirect hybrid systems. For the first case, a 4.5 MW, 38.5 per cent LHV efficiency, single shaft recuperated gas turbine working at part load and fitted with a two step load control system is considered. For the first 10 per cent load change, variable inlet guide vanes are used to decrease air mass flow through the compressor. Pressure ratio decreases, improving the effectiveness of the recuperating process at constant shaft speed. Below 90 per cent load demand, and with IGVs at its closest position, turbine inlet temperature is reduced. By using this sequential load control system, part-load efficiency is kept at its best for slight load reductions. However, if load is to be reduced to a very low level, say between 50 and 75 per cent, a dramatic decrease in efficiency cannot be avoided. Working at variable speed balances this effect partially but an efficiency reduction will still be present. The behaviour reflected in Fig. 10 is expected from the next generation micro gas turbine equipped with variable geometry centrifugal compressors. Direct hybrid systems are now considered. For them, the efficiency – load curves in Fig. 10 show a

Fig. 10

Part-load efficiency for the systems considered

Proc. IMechE Vol. 222 Part A: J. Power and Energy

smooth quadratic shape that leads to an initial increase in efficiency followed by a slight reduction. This quadratic shape is due to the effect of pressure on the cell. When reducing the load initially, a decrease in mass flow is followed by both a reduction in pressure ratio and current density for compressor and fuel cell, respectively. The latter effect prevails and, as a consequence, efficiency increases. However, a further load reduction reverses this trend. The effect of pressure, which increases exponentially towards low pressures, is more important and cannot be balanced by the improved efficiency of the cell. Indirect hybrid systems do not follow the same pattern at part load as indirect systems. The fuel cell runs permanently at ambient pressure and its performance is only influenced by the reduction in current density. The effect of pressure ratio is now almost limited to the gas turbine and therefore, reducing the load will always increase the global efficiency at a similar rate as for standalone fuel cells.

7

ECONOMIC ANALYSIS

A brief economic analysis has been done in order to complete the previous technical study. It is well known that both fuel cells and micro gas turbines are presently very expensive technologies and, therefore, they do not share a big piece of the electricity market yet. However, as long as environmental issues are promoting cleaner technologies and the general layout of the electricity chain from supplier to consumer is evolving towards a decentralized net – commonly referred to as distributed generation – the interest for these power systems is increasing. In order to develop an economic analysis, cost estimators for the costliest components of the power systems exposed previously are considered. These estimators are taken from reference [7], though correction factors have been applied to adjust the turnkey cost of each technology to the value suggested by the International Energy Agency in reference [8]. Thus, the reference installation cost for the micro gas turbine is around 1000 USD/kW for a 150 kW rated power engine, 1000– 1300 USD/ kW suggested in reference [8], while for the fuel cell cost, it increases to 2000 USD/kW for the same power capacity, 1900 – 3500/USD/kW suggested in reference [8]. Note that these are reference values that are expected to change with rated power. The cost of auxiliary or secondary equipment – inverters, combustors, and fuel compressors – is calculated as a percentage of the cost of major equipment, Table 2, as suggested in reference [7]. For the case of heat exchangers, a difference is made depending on whether they are part of a standalone fuel cell or gas turbine or a complete hybrid JPE472 # IMechE 2008

Comparison between conventional recuperative gas turbine and hybrid SOFC–GT systems

Table 2

Installation cost estimators

Component

Cost (USD)

Gas turbine

Cturb ¼ 0.6(298.328 ln(Pturb) þ 1318.5) Pturb Pcomp 0.67 Ccomp ¼ 0.6.915 62( ) 445 Caux ¼ 0.15(Cturb þ Ccomp)

Compressor GT auxiliary equipment Solid oxide fuel cell Inverter SOFC auxiliary equipment

Table 3

(20) (21) (22)

CSOFC ¼ 1.7 . p . Nt . Dcell . Lcell (2.96 . Tcell 2 1907) PSOFC 0.7 Ccomp ¼ 105 ( ) 500 Caux,sa ¼ 0.1 . CSOFC

(23)

Caux,hs ¼ 0.4 . CSOFC

(26)

Installation cost versus rated power

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Performance assumptions for O&M cost calculation

Parameter

Reference value

GT efficiency SOFC efficiency Direct hybrid system efficiency Indirect hybrid system efficiency Natural gas cost Rated power

27 per cent 40 per cent 60 per cent 45 per cent 39 USD/MWh HHV 150 kW

(24) (25)

system. For the former, the cost of this equipment is considered to be a 10 per cent of the major equipment cost. For the latter, this value increases to 40 per cent of the fuel cell cost. From data in Table 2, a calculation of the installation cost is done and presented in Fig. 11. The plot shows that, as expected, the cost of standalone gas turbines is significantly lower than any of the systems incorporating fuel cells. Furthermore, for the case of hybrid systems, it is shown that the indirect system is more expensive than the standalone fuel cell, due to the high cost of heat exchangers while hardly any revenue in terms of increased power is obtained. A second issue is now considered in the economic analysis as it is not only the installation cost that influences the adopted technology but also the operation and maintenance (O&M) cost. This second analysis has been carried out with the assumptions shown in Table 3, related to performance parameters and fuel cost. Efficiency data are taken from the analysis in section 6.1. The cost of natural gas is assumed to be 39 USD/MWh high heating value (HHV), which is the average value of the industrial price in Spain for 2006.

Fig. 11

157

Figure 12 shows the effect of the operating time on the total, installation and O&M, costs for the different technologies considered in this work. It is very interesting to see that, due to the enhanced efficiency and despite the higher installation cost, fuel-cell-based technologies are economically attractive in the mid and long term. If a moderate 50 per cent load factor is assumed, which is equivalent to 4380 full load equivalent working hours a year, the increased initial investment of installing a direct hybrid system is counterbalanced after 2 years with respect to conventional microgas turbine technology. If, on the other hand, an indirect hybrid system is considered, or a standalone fuel cell, the time needed to offset the initial investment increases to more than 4 years. These compensation periods are shorter for higher power factors. The comparison shown in this section is a simplified economic analysis that does not include the consideration of how the investment is done – initial equity, interest rate. . .– but allows for some general conclusions to be drawn. In this sense, although fuel-cell-based power systems are more expensive than conventional gas turbines by a factor of 2, Fig. 11, the enhanced efficiency of such hybrid systems leads to reduced O&M costs that offset their higher initial investment. Furthermore, this compensation time is even shorter than shown in Fig. 12 if the difference in part-load efficiency, Fig. 10, is taken into

Fig. 12

Total cost versus operating hours

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account for derated operation. It can be assumed therefore that hybrid systems are competitive technically and economically as long as reliability problems that are currently affecting them are solved.

8

CONCLUSIONS

Hybrid systems are not a new concept for the scientific community. Studies have been done on integration layouts and pilot plants are running with highly satisfactory performance [2]. However, a mature technology has still to be developed, even though these systems enter a commercial phase. Despite this, hybrid systems are frequently studied from the fuel cell perspective. The cell is considered as a power system which is overcharged by means of a turbocharger which, in addition, generates a small amount of power. Thus, the global efficiency is increased by around 15 points. The work presented here adopts a new perspective. The gas turbine user considers the hybrid system as a gas turbine engine where the combustion chamber has been substituted by a fuel cell. It is expected that such a system performs similarly to a conventional gas turbine with some deviations which must be identified. This work is aimed at finding the differences between three different concepts of small scale gas turbines by applying the principles of traditional gas turbine theory. The following particular conclusions are drawn. 1. At the moment, hybrid systems cannot be considered for base load due to the high manufacturing cost and low power density of the fuel cell. 2. However, for small scale applications, particularly distributed generation, hybrid systems are much more efficient than state of the art conventional recuperative gas turbines. 3. Hybrid systems of any kind are between 50 and 100 per cent more efficient than recuperative gas turbine engines. 4. SOFC – GT hybrid systems have a pressure ratio for maximum efficiency like conventional gas turbines. 5. The efficiency curve for a direct hybrid system is almost independent of pressure ratio near its maximum point. 6. The pressure ratio for maximum efficiency of an indirect hybrid system is almost independent of cell temperature. 7. The part-load efficiency of a hybrid system is remarkably higher than in the gas turbine engine and it keeps close to the rated value independently of the load demand. 8. For an indirect hybrid system, efficiency is higher at part load than at full load. Proc. IMechE Vol. 222 Part A: J. Power and Energy

9. The initial investment or installation cost of a hybrid system is around two times higher than a conventional gas turbine engine of the same rated power. However, when operation and maintenance costs are included, the total cost of a fuel-cell-based plant is lower in the mid – direct hybrid systems – or long term – indirect hybrid systems. 10. Increasing the load factor shortens the compensation period needed for the hybrid system to be more interesting economically than a recuperated gas turbine. Readers might find contradictory the last conclusion. Reducing the current density increases efficiency but, at the same time, increases substantially the active area, i.e. number of cells in the stack, which is needed to generate the same power. From an economical perspective, it is more interesting to reduce the installation cost of the system, i.e. cell area, although operating cost increases due to a lower efficiency.

ACKNOWLEDGEMENT The authors wish to acknowledge the Spanish National Institute for Aerospace Technology (INTA) for funding this research project.

REFERENCES 1 Romier, A. Small gas turbine technology. Appl. Thermal Eng., 2004, 24, 1709–1723. 2 Veyo, S. E., Shockling, A., Dederer, J. T., Gillett, J. E., and Lundberg, W. L. Tubular solid oxide fuel cell/gas turbine hybrid cycle power systems status. J. Eng. Gas Turbines Power, 2002, 124, 845– 849. 3 Nisancioglu, K. Ohmic losses. In Proceedings of the IEA Workshop on Mathematical Modelling, Charmey, 1998, pp. 87 –98. ˜oz, A., and Sa´nchez, T. 4 Sa´nchez, D., Chacartegui, R., Mun Thermal and electrochemical modelling of internal reforming solid oxide fuel cell with tubular geometry. J. Power Sources, 2006, 160, 1074–1087. 5 Massardo, A. F. and Lubelli, F. Internal reforming solid oxide fuel cells – gas turbines combined cycle (IRSOFC-GT): part A – cell model and cycle thermodynamic analysis. J. Eng. Gas Turbines Power, 2000, 122, 27–35. 6 Cohen, H., Rogers, G. F. C., and Saravanamootoo, H. I. H. Gas turbine theory, 2001 (Prentice Hall, Harlow). 7 Calise, F., Dentice d’Accadia, M., Vanoli, L., and von Spakovsky, M. R. Full load synthesis/design optimization of a hybrid SOFC-GT power plant. Energy, 2007, 32, 446 –458. 8 Various authors. Distributed generation in liberalised electricity markets, International Energy Agency, Paris, 2002, p. 26. JPE472 # IMechE 2008

Comparison between conventional recuperative gas turbine and hybrid SOFC–GT systems

APPENDIX Notation A DHS E F GT h H I IGV IHS j j0 kp m n ne N OEM p P

cell active area (m2) direct hybrid system Nernst potential (V) Faraday constant gas turbine specific molar enthalpy (J/mol) total enthalpy (J) current intensity (A) inlet guide vanes indirect hybrid system current density (A/m2) exchange current density (A/m2) equilibrium constant mass flow (kg/s) molar flow (mol/s) number of exchanged electrons rotating speed (r/min) original equipment manufacturer partial pressure (bar) power (kW)

JPE472 # IMechE 2008

Q Rg STCR T Uf V W Z

total heat flow (J) ideal gas constant (J/mol K) steam to carbon ratio temperature (K) fuel utilization factor (per cent) voltage (V) work (J/mol) ohmic resistance (V)

DV

voltage loss (V)

159

Subscripts 0 act aux comp hs ohm ref sa shift turb

standard activation auxiliary compressor hybrid system ohmic reforming standalone water – gas shifting turbine

Proc. IMechE Vol. 222 Part A: J. Power and Energy