Effect of operating parameters on a hybrid system of intermediate-temperature solid oxide fuel cell and gas turbine

Energy 91 (2015) 10e19

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Effect of operating parameters on a hybrid system of intermediatetemperature solid oxide fuel cell and gas turbine Xiaojing Lv, Chaohao Lu, Yuzhang Wang, Yiwu Weng* School of Mechanical Engineering, Key Laboratory for Power Machinery and Engineering of Ministry of Education, Shanghai Jiao Tong Univ., 800 Dong Chuan Rd., Shanghai 200240, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 11 November 2014 Received in revised form 14 July 2015 Accepted 23 July 2015 Available online xxx

In this work, detailed mathematical models of a hybrid system of an IT-SOFC (intermediate-temperature solid oxide fuel cell) and a GT (gas turbine) that is fueled by gasified biomass gas are built. Under the constraints of the working temperature of the fuel cell, mean axial temperature gradient, compressor surge, and turbine inlet temperature, the effects of operating parameters on the hybrid system are investigated mainly including RS (rotational speed), F/A (fuel/air) ratio, and S/C (steam/carbon) ratio. The electrical efficiency is 59.24% under the design condition. The power and efficiency of the system both decrease as the RS increases, with the latter decreasing from 60.95% to 49.08%. If the RS is too low, the system operation goes beyond the safety zone. In this situation, both the fuel cell and the turbine may be subjected to excess temperatures, and the compressor may easily surge. The efficiency increases from 56.5% to 61.34% with increasing F/A ratio, but an extremely high F/A ratio can cause the turbine to suffer from excess temperature. The efficiency decreases from 61.12% to 56.8% with increasing S/C ratio. The following two conclusions are drawn. First, the F/A ratio has the greatest influence on the performance of the hybrid system, i.e., its adjustment can effectively change the load in a wide range. Second, the RS and S/C ratio are suitable for load adjustment in a narrow range. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Intermediate temperature solid oxide fuel cell Gas turbine Hybrid system Gasified biomass gas Operating parameter

1. Introduction IT-SOFCs (intermediate-temperature solid oxide fuel cells) can operate between 873 K and 1073 K. They can not only maintain the advantages of conventional HT-SOFCs (high-temperature solid oxide fuel cells, 1073 Ke1273 K), such as high efficiency and zero emission, but also decrease starting temperature and time, and improve stability performance and lifetime. Moreover, the use of stainless steel as connection material for IT-SOFCs further reduces manufacturing costs and thus boosts the commercialization feasibility of these fuel cells [1,2]. Studies on electrode materials and mathematic models for IT-SOFCs have been extensively carried out [3e7], thereby providing a fundamental basis for their wide application. Bedogni et al. [8e10] conducted a theory analysis and experimental tests on the electrochemical performance, distribution of temperature field, and durability of fuel cells. Their work serves as a reference for improving the electrical performance of ITSOFCs. At present, the applied research on IT-SOFCs mainly focuses

* Corresponding author. Tel./fax: þ86 21 3420 6342. E-mail address: [email protected] (Y. Weng). http://dx.doi.org/10.1016/j.energy.2015.07.100 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

on vehicles [2,11,12] and power stations [13e15]. Zhu et al. [13] built an IT-SOFC/GT model to carry out an energy balance analysis and exergy analysis and provided reference data for the application of IT-SOFCs in small-scale power stations. Campanari et al. [14] evaluated the performance of an IT-SOFC on the basis of the gasification combined cycle fueled by coal gas. The system consisted of two steam shift reactors, a methanation reactor, and CO2 capture and other equipment; its electrical efficiency can reach up to 51.6%. Paepe et al. [15] studied the performance of a two-stage hybrid system consisting of an HT-SOFC and an IT-SOFC fueled by CH4 and analyzed the effect of the operation temperature, pressure, and current density of the fuel cells. Several researchers have carried out studies on integrated systems based on biomass gasification and HT-SOFC/GT [16e19]. These works provide the research foundation for the utilization of biomass gas in hybrid systems. Integrated systems can overcome biomass dispersion and transport challenges while satisfying the varied fuel requirements of SOFC/GT hybrid systems. In addition, integrated systems cover relatively small areas; thus, the investment cost is low [20,21]. However, because of their high complexity, the coordination control technologies of the integrated system are extremely difficult [22,23].

X. Lv et al. / Energy 91 (2015) 10e19

As for the commercial development of hybrid systems integrated with HT-SOFCs, it remains limited by the high working temperature and by other factors, including difficult component matching, short system lifespan, and high generation cost. The aforementioned issues can be successfully overcome with the hybrid system consisting of an IT-SOFC and a micro GT. In addition to its high efficiency and low NOX emission, the IT-SOFC/GT hybrid system is also adaptable to resources such as natural gas, coal gas, biomass gas, methanol, ethyl alcohol, and other hydrocarbons [14,24]. China has abundant biomass energy resources with great potential for commercial development. The IT-SOFC/GT hybrid system can utilize these biomass resources according to local conditions and form small-scale off-grid or grid-connected distributed power stations. Thus, this hybrid system shows high application potential [25]. Current research on the hybrid system fueled with biomass gas is mainly focused on system modeling [17,26], system integration and optimization design [19,27,28], effect of biomass fuel [29e31], selection of component operation parameters [32], etc. However, the hybrid system is a complicated system with various parameters, nonlinearity, strong thermodynamic coupling, and multiple objectives. It is thus essential to study the system performance and load change caused by varying operation parameters, such as fuel and air flows, fuel utilization, and RS. Assuming a constant RS, Costamagna et al. [33e36] investigated the performance of the hybrid system using natural gas and discussed the effect of fuel and air flows, current density, and fuel utilization. However, they ignored the variation of air flow, compressor SM (surge margin), and FTG (fuel cell temperature gradient). Stiller et al. [37] studied the methods for safely operating a hybrid SOFC/GT system under part load and load change without considering the influence of SM and FTG on each RS. Diamantis et al. [32] studied the matching relation between GTs and fuel cells with consideration of system lifespan. They thus proposed two types of operating strategies used in the condition of constant fuel cell temperature or TIT (turbine inlet temperature). At present, the studies on the safe operation of hybrid systems mainly focus on natural gas or HT-SOFCs. The effects of operation parameters such as FWT (fuel cell working temperature), SM, and TIT on system safety are serious because biomass gas has a lower heat value than natural gas. On the one hand, compressors easily surge because of extremely low TIT. On the other hand, system performance can easily decline because of extremely low FWT. Therefore, the effects of GT RS, fuel/air (F/A) ratio, and steam/carbon (S/C) ratio on the IT-SOFC/GT hybrid system fueled by biomass gas must be investigated with consideration of the constraints of SM, FWT, FTG, and TIT. In the present work, detailed mathematic models of the hybrid IT-SOFC/GT system fueled by gasified biomass gas were built in MATLAB SIMULINK. Accordingly, the performance of the hybrid system under design and off-design conditions was analyzed. The operation parameters of RS, F/A ratio, and S/C ratio were modified to quantify the output and electrical efficiency of the system, with the constraints of FWT, FTG, SM, and TIT. The simulated results can benefit the design and application of IT-SOFC/GT hybrid systems fueled by biomass gas.

11

the reformer. Then, the reformed gas enters the SOFC anode to trigger an electrochemical reaction. The air pressurized by the compressor is heated by the heat exchanger and then enters the SOFC cathode to provide O2 for the electrochemical reaction. The exhaust gas from the SOFC anode contains incompletely reacted fuels, which will continue to be combusted in the catalytic combustor. The high-temperature gas enters the turbine to generate power. The exhaust gas from the turbine preheats the fuel and air and then heats the evaporator before being released into the atmosphere. 2.2. Mathematical models of IT-SOFC A 2D anode-supported IT-SOFC model was introduced in the literature [6]; this model includes an electrochemical model and a thermodynamic model based on mass and energy balance equations. The electrochemical model describes the function relation between the fuel cell voltage, various polarization losses, and current density. These models consider the influence of reactant and product concentrations on the Nernst potential and the mass/ heat transfer and diffusion limitations. On the basis of these two models, we form two assumptions: 1) zero leakage exists, and 2) only H2 is involved in the electrochemical reaction, and the electrochemical reaction of CO is not considered. Fuel cell output voltage can be reduced because of irreversible losses caused by ohm, activation, and concentration [38]. Open-circuit voltage can be calculated with a Nernst equation, which describes the relationship between reversible electrochemical voltage, chemical substance concentration, and gas pressure. This phenomenon occurs on the boundary between electrodes and electrolyte. The equations for the anode-supported IT-SOFC model are listed in Table 1. Ohm loss is caused by the movement of ions and electrons along the component resistance and contact resistance between cell components. The phenomenon is closely related to electrode material, geometrical property, and electronic conduction characteristics [6]. Activation polarization is the over-potential needed to overcome the activation energy of the electrochemical reaction on surfaces [24,38]. It is represented by the non-linear ButlereVolmer equation. The polarizations of the anode and cathode can be solved by the equations [6] in Table 1 because of the effect of the reactant and product concentrations on electrode/electrolyte interfaces.

2. Mathematical models 2.1. IT-SOFC/GT hybrid system structure An IT-SOFC/GT hybrid system mainly consists of an IT-SOFC, a GT, a catalytic combustor, a reformer, and a heat exchanger (Fig. 1). Biomass gas is heated and then mixed with steam before it enters

Fig. 1. Schematic of IT/SOFC-GT hybrid system.

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X. Lv et al. / Energy 91 (2015) 10e19

Table 1 Equations for mathematical model in Anode-supported IT-SOFC. NO. 1

Equation U¼

OCP UTPB

Comment 

 hOhm þ hconc;anode þ hconc;cathode þ hact;anode þ hact;cathode 0

2

OCP 0 ¼ UH  UTPB 2

3

hOhm ¼ jROhm


Open-circuit potential

A

Ohmic losses

telectrolyte tcathode t ¼ anode þ þ sanode selectrolyte scathode

4

ROhm

5

j ¼ j0;anode

6

j0;anode ¼

"

Internal resistance of the fuel cell



# pH O;TPB pH2 ;TPB anF ð1  aÞnF hact;anode  2 hact;anode exp exp 







 anF ð1  aÞnF hact;cathode  exp  hact;cathode j ¼ j0;cathode exp
8

j0;cathode ¼

Mi;in þ

X

Cathode current density




pH2 O;TPB pH2 ;f
hconc ¼

! þ

pO2 ;a
Anode current density

Exchange current density for anode

7

10

Fuel cell potential

1

o2 ;TPB

2

9



Exchange current density for cathode

!

Total concentration over-potential losses

Mass balance equation in fuel cell fuel and air channels Ci;k rk ¼ Mi;out

k

P

11 Tout ¼

i

Energy balance equation in fuel cell fuel and air channels

Mi;in cp:i Tin þ rele ðDHele Þ  Pout  Qrad P Mi;out cp;i i

12

PSOFC ¼ UðjÞ,j,L,W

13

hSOFC ¼

Fuel cell output power

PSOFC

Fuel cell electric efficiency

0 þy0 ,LHV 0 þy0 ,LHV 0 Þ,M ðy0CH4 ,LHVCH H2 H2 CO CO 4

When the reactant inlet flux and product outlet flux from an electrode are slower than the discharged current, concentration profiles are developed across the electrodes, and concentration over-potential is produced [6]. The mass and energy balance equations of fuel cells consider anode and cathode channels. The model also includes the change in gas composition caused by an electrochemical reaction and the change in specific heat value with temperature. 2.3. Gas turbine The GT model used in this study mainly consists of a centrifugal compressor and a radial turbine, which are represented by the characteristic maps of a compressor and turbine, respectively. The compressor characteristic maps are shown in Figs. 2 and 3 [39e41]. Each speed curve in the compressor characteristic map corresponds to a wide range of mass flow rates and pressure ratios. Thus, when operation condition changes, the two parameters under different speed curves could overlap. To determine a unique operating status, the relationship between mass flow rate and pressure ratio should be established. As shown in Fig. 2, b lines are used as an auxiliary coordinate to determine an operating

status. These lines obtained by a second-order polynomial are used to determine the mass flow rate, pressure ratio, and efficiency [33]. Generally, compressor characteristic maps can be obtained through experiments in a standard state. In practice, introducing reduced parameters to calculate the variable operation conditions of GTs is necessary [39,40]. According to similarity theory, compressor characteristic curves can be described by apset ffiffiffiffiffi of functions of pressure ratio p , reduced mass flow m T1 =P1, a pffiffiffiffiffi reduced RS n= T1 and efficiency hc:

ma

 .pffiffiffiffiffi pffiffiffiffiffi. T1 T1 P1 ¼ f1 p; n

 .pffiffiffiffiffi T1 hc ¼ f2 p; n   1  la p 1 T2 ¼ T1 1 þ hc  . Pc ¼ cpa ma T1 pla  1 hc

(1)

(2)

(3)

(4)

X. Lv et al. / Energy 91 (2015) 10e19

Dks ¼

13



h . pffiffiffiffiffi. i ma T1 P1 ps

surge

h . pffiffiffiffiffi. i pw ma T1 P1

work

1

(9)  100%

In this model, the surge line and the corresponding values of mass flow and pressure ratio at each RS on the compressor and turbine characteristic maps are obtained using the GetData software. An operation database is built to find corresponding operating points and evaluate whether the SM meets the safety requirement. 2.4. Reformer model Wood chip gasified gas, composed of 4.53% CH4, 23.64% H2, 13.87% CO, 17.92% CO2, and 40.04% N2, is chosen in this study as fuel. The composition of this gasified gas is obtained through a twostage gasification experiment developed by the Institute of Thermal Engineering, Shanghai Jiao Tong University, Shanghai, China [41]. The reformed model includes a strong endothermic steam reforming reaction (10) and a weak exothermic water gas shift reaction (11). The heat needed for the reforming reaction is provided by GT exhaust gas.

Fig. 2. Compressor pressure ratio curve.

CH4 þ H2 O⇔CO þ 3H2

(10)

CO þ H2 O⇔CO2 þ H2

(11)

Reformer output H2 is defined by the H2 production from the CH4 reforming reaction and the water shift reaction in the equilibrium state. It is calculated as follows:

nH2 ;tot ¼ nH2 ;in þ nCO;eq þ 3nCH4 ;eq

(12)

2.5. Catalytic combustor model

Fig. 3. Compressor efficiency curve.

Turbine characteristic curves can be described pffiffiffiffiffiby a set of functions of expand ratio l, reduced mass flow mg T3 =P3, reduced RS pffiffiffiffiffi n= T3 and efficiency ht:

The exhaust gas from the SOFC anode contains incompletely reacted compositions (CO, CH4, H2) with extremely low values. Thus, complete combustion in the catalytic combustor is necessary to improve system energy utilization [39]. The main chemical reactions in the combustor are as follows:

CH4 þ2O2 ¼ CO2 þ2H2 O þ Q CH4

(13)

(5)

1 CO þ O2 ¼ CO2 þQ CO 2

(14)

 .pffiffiffiffiffi T3 ht ¼ f4 l; n

(6)

1 H2 þ O2 ¼ H2 O þ Q H2 2

(15)

h   i T4 ¼ T3 1  1  llg $ht

(7)

  Pt ¼ cpg mg T3 1  llg $ht

(8)

mg

 .pffiffiffiffiffi pffiffiffiffiffi. T3 T3 P3 ¼ f3 l; n

Surge boundary is important for compressor. A compressor easily enters a surge state by increasing p at a constant flow rate or by decreasing flow rate at a constant p [40]. In this case, the air flow in the compressor could yield intense pulsation and produce a reverse flow, which can cause the blade to vibrate and even break. The compressor SM Dks is used to evaluate the distance from the working point to the surge boundary. When the SM is small, the compressor could easily surge. The computational formula is:

The combustor inlet enthalpy Dh at a standard state and the combustor outlet temperature T could be calculated using the following equations [39]:

DH ¼

X i

ZTstd cp;i dT þ

ni T0;i

X

ZTstd nj

j

cp;j dT

(16)

T0;j

X   nm DH þ QH2 þ QCO $εcomb ¼ m

ZTout cp;m dT Tstd

(17)

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X. Lv et al. / Energy 91 (2015) 10e19

Table 2 IT-SOFC operation parameter [6]. Fuel cell working temperature, Tworking:fc Fuel cell stack pressure loss, floss;sofc Single cell number, n

973 K

Table 4 Hybrid system operation constraint. Average current density, j

5000 A m2

1%

Pressure, p

0.4 MPa

912

Fuel utilization, Ufuel

75%

Fuel cell Temperature gradient (TG) Working temperature (WT)

Gas turbine <10 K/cm

873 K < T < 1123 K

Compressor surge margin (SM) Turbine inlet temperature (TIT)

>15%

1023 K < TIT < 1223 K

2.6. Hybrid system design parameter and operation constraint The SOFC geometry and physical parameters are obtained from Ref. [6]. The operation parameters are shown in Table 2. A certain type of 30 kW micro GT performance map is built using the similar method under various operations. The design parameters of the GT are shown in Table 3. The parameter selection for the heat exchanger, mixer, and other parts of the model is presented in Ref. [39]. The efficiency of a hybrid system is defined as:

hSOFC ¼

PSOFC þ PGT 0 0 0 0 Þ,M ðyCH4 ,LHVCH4 þyH2 ,LHVH0 2 þy0CO ,LHVCO fuel

(18)

To ensure that the hybrid IT-SOFC/GT system can work safely, several constraints are added to it. 1) The FTG should be smaller than the limit, and the working temperature must be below the maximum tolerable temperature of the material [6]. 2) The operation points of the compressor should be away from the surge line, and the SM must be greater than 15% to prevent surge under offdesign conditions. 3) The TIT must be smaller than the maximum tolerable temperature of the material [42]. The specific parameter thresholds are shown in Table 4.

3. Results and analysis 3.1. System performance under the design condition By using the aforementioned IT-SOFC/GT mathematical models, the operation performance and calculation value for each node at the design point are determined, as shown in Table 5. The output power of the hybrid system is 177.68 kW, and the electrical efficiency is 59.24%. The TIT and FWT are 1173 K and 1026 K, respectively. The temperature difference between the inlet and the outlet of the fuel cell is 231 K. The corresponding mean axial temperature gradient of the fuel cell is 5.77 K/cm. The compressor SM is 18.41%. This operation point can meet the requirement in Table 4. The results conform to the data given in Refs. [6,39,40]. Hence, the chosen parameters for the IT-SOFC and GT hybrid system are reasonable. The turbine expansion ratio is approximately 3.04, which is smaller than the compressor pressure ratio by 0.16 because of the pressure loss in the system components, such as the compressor, fuel cell, heat exchanger, and combustor. The catalytic combustor temperature does not exceed 1200 K and changes homogeneously. NOx emission is very low (nearly zero), and CO is completely converted to CO2 [39]. The results illustrate that the hybrid system features attractive emission characteristics.

3.2. Effect of rotational speed on system performance The performance of GTs mainly relies on RS because this factor closely affects the pressure and flow rate of compressors. In this study, b coordinate ranges from 0 to 1, and the corresponding reduced RS ranges from 0.6 to 1.1. The intersections of these curves are the operation points under variable speed, as shown by the black points in Fig. 2. The performance of the hybrid system with variable speed is shown in Figs. 4e7. Fig. 4 shows that the FWT and FTG decrease with the increase in reduced RS. This effect can be explained as follows. At a constant fuel flow rate, the heat released by the electrochemistry reaction remains unchanged, but the fuel cell is cooled by more air as a result of the increasing compressor RS. The FWT and FTG increase as b increases because at a constant RS, a rising b can cause the pressure ratio to increase and the air flow to decrease. Therefore, the increased pressure ratio raises the inlet temperature of the fuel cell, and the decreased air flow weakens the cooling effect of the fuel cell. The combined effects increase the working temperature and temperature gradient of the fuel cell. The FWT and FTG change drastically with the variation of b in the reduced RS range of 0.6e0.8. When the reduced RS range is 0.8e1.1, the fuel cell can safely work. We should note that under operation points (reduced RS ¼ 0.6 or 0.7, corresponding b ¼ 0.8 or 1), the FWT and FTG increase drastically beyond the safety range. This change is caused by the air flow decreasing sharply when the RS decreases and b increases; in this case, a weak cooling effect is observed. Consequently, both the FWT and the FTG increase remarkably. Under this condition, the electrode material is easy to crack because of high internal thermal stress. Fig. 5 illustrates that when b increases from 0 to 0.6, the voltage and power of the fuel cell decrease with increasing RS. When b increases from 0.8 to 1, it initially increases and then decreases when the maximum values are reached because increasing reduced RS leads to a decrease in FWT. Under this condition, increasing the electrolyte ion resistivity results in increasing ohm loss and activation loss. The consequence is the decreased output voltage of the fuel cell. Therefore, when the current density is constant, the output power of the fuel cell decreases. In Fig. 6, the TIT decreases with the increase in reduced RS and b. The corresponding acceptable operation points of the TIT are shown in the figure. The SM reaches the maximum at the rated RS in all b, except in 0.8 and 1. When b is not greater than 0.4, the SM is greater than 15%, which indicates that the compressor works in the safety zone. When b is greater than 0.4, the SM is less than 15%, which indicates that the compressor surges easily. The operation

Table 3 GT designed parameter [39,40]. Compressor Pressure ratio, pc Isentropic efficiency, hc Inlet pressure loss, floss;c Air mass flow rate, Mair

Turbine 3.2 80% 1% 0.185 kg s1

Inlet temperature, TTIT Isentropic efficiency, ht Outlet pressure loss, floss;t Gas mass flow rate, Mgas

Others 1173 K 82% 1% 0.269 kg s1

Combustor loss, floss;comb HE efficiency, hHE HE gas side pressure loss, floss;gas HE air side pressure loss, floss;air

1% 95% 3% 1%

X. Lv et al. / Energy 91 (2015) 10e19

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Table 5 IT-SOFC/GT hybrid system performance and each node parameter. IT-SOFC/GT hybrid system performance SOFC voltage/V GT power/kW System electrical efficiency/% IT-SOFC/GT Node T/K M/kg/s P/MPa H2/% CH4/% CO/% CO2/ O2/% N2/% H2O/%

each node parameter 1 2 298 442 0.185 0.185 0.101 0.321 0 0 0 0 0 0 0 0 21 21 79 79 0 0

3 729.7 0.185 0.315 0 0 0 0 21 79 0

0.70 49.78 59.24 4 1026 0.169 0.310 0 0 0 0 14.68 85.32 0

5 298 0.055 0.320 23.64 4.53 13.87 17.92 0 40.04 0

6 533.5 0.030 0.317 0 0 0 0 0 0 100

SOFC power/kW System power/kW

7 403.1 0.085 0.313 13.69 2.62 8.03 10.38 0 23.19 42.07

8 901.8 0.085 0.311 13.69 2.62 8.03 10.38 0 23.19 42.07

9 795.2 0.085 0.307 24.88 0.19 5.09 14.78 0 22.12 32.93

10 1026 0.100 0.304 1.87 0.19 5.09 14.78 0 22.12 55.95

127.90 177.68

11 1173 0.269 0.305 0 0 0 8.34 7.19 60.27 24.2

12 969.8 0.269 0.101 0 0 0 8.34 7.19 60.27 24.2

13 594.9 0.269 0.101 0 0 0 8.34 7.19 60.27 24.2

14 349.4 0.269 0.101 0 0 0 8.34 7.19 60.27 24.2

Fig. 4. FWT and FTG variation with RS.

Fig. 6. TIT and SM variation with RS.

points of the GT gradually approaches the surge boundary line with increasing b. This condition can lead to an increase in pressure ratio and a decrease in SM. Under this condition, the GT cannot operate safely. The potential reason is that the air flow will strongly pulsate and even flow back, causing the compressor blade to periodically vibrate and even break. As shown in Fig. 7, the power and efficiency of the hybrid system are reduced with the increased reduced RS. The reason is that the power and efficiency of cell decrease gradually with rising reduced

RS, which is similar to the system performance. With increasing b, these factors reach their maximum values at the operation point of the reduced RS, that is, 0.7 and 0.8. However, under these conditions, the compressor will enter the surge state, and the turbine would suffer from over-temperature. With increasing b, efficiency decreases sharply at the operation points, with the reduced RS varying from 1 to 1.1. The potential reason is that when the reduced RS is high, the air flow slightly

Fig. 5. IT-SOFC output voltage and power variation with RS.

Fig. 7. Hybrid system output power and electrical efficiency variation with RS.

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X. Lv et al. / Energy 91 (2015) 10e19

Fig. 8. FWT and FTG variation with F/A ratio.

Fig. 10. TIT and SM variation with F/A ratio.

changes, but the pressure ratio significantly changes. This condition will cause the cathode of the fuel cell to work at high pressure, causing the oxygen to be consumed quickly. As a result, fuel concentration and fuel cell reaction both disappear. Therefore, the power and efficiency of the fuel cell will be reduced, resulting in poor system performance. When safety is considered, the hybrid system can operate in the reduced RS range of 0.8e1.1. The corresponding power range is 147.3 kWe195.9 kW, and the efficiency range is 49.08%e60.95%, as shown in Fig. 7.

As shown in Fig. 9, the output voltage and power of the fuel cell increase when the F/A ratio increases. The fuel cell voltage rises sharply when it is less than 0.2 and changes relatively flat when it is greater than 0.2. The output power of the fuel cell increases monotonously. This is because, for the anode-supported SOFC, the ohm loss and cathode activation over-potentials play a significant role when current density is low. The polarization losses decrease rapidly due to increasing fuel cell working temperature, thereby leading to increasing voltage. These phenomena have similar variation trends compared with the results provided in Ref. [6]. In Fig. 10, increasing the F/A ratio increases the combustible composition that enters the catalytic combustion, which leads to an increase in the TIT. When the F/A ratio is less than 0.19, the TIT is below the lower limit value, but when the F/A ratio is greater than 0.44, the TIT is above 1224 K, which causes over-temperature in the turbine. Additionally, the compressor SM increases as the F/A ratio increases. When the F/A ratio is less than 0.27, the compressor operation point is close to the surge boundary line, in which the SM is less than 15% and the compressor easily surges. Fig. 11 shows that as the F/A ratio increases, the system output power increases linearly. Efficiency changes in a large range when the F/A ratio is lower than 0.17, and it is relatively flat when the F/ A ratio is greater than 0.17 because the fuel cell is the major power component of the hybrid system. Thus, when the F/A ratio is small, the PGT =PSOFC is large, and when the F/A ratio is large, the PGT =PSOFC decreases. These conditions reflect the advantages of the fuel cell.

3.3. Effect of F/A ratio on system performance The F/A ratio is an important parameter in operating the hybrid system. Two approaches can be used to adjust the F/A ratio: 1) keeping the air flow constant and changing fuel flow and 2) keeping the fuel flow constant and changing the air flow [30]. In this work, the second method is used. When the fuel flow varies within 0.3e1.3 times of the rated value, the F/A ratio changes in the range of 0.11e0.46. The performance of the hybrid system is shown in Figs. 8e11. Fig. 8 shows that the FWT and FTG increase gradually with increasing F/A ratio. The reasons are as follows. For rising FWT, the increasing F/A ratio requires more fuel for the electrochemical reaction. Thus, more heat is released. For rising FTG, the temperature difference between the inlet and the outlet of the fuel cell increases. The maximum mean axial temperature gradient is 8.34 K/cm, which meets the working requirement of the fuel cell.

Fig. 9. IT-SOFC output voltage and power variation with F/A ratio.

Fig. 11. Hybrid system output power and electrical efficiency variation with F/A ratio.

X. Lv et al. / Energy 91 (2015) 10e19

17

Fig. 12. FWT and FTG variation with S/C ratio.

Fig. 14. TIT and SM variation with S/C ratio.

According to aforementioned analysis, when the F/A ratio ranges from 0.27 to 0.43, the hybrid system is under safe operation conditions. The corresponding range of the system power is 126 kWe220 kW, and the load adjustable range is relatively large. In this case, the system efficiency ranges from 56.5% to 61.34%.

concentration in the fuel cell, thereby reducing the Nernst potential [38]. Therefore, the output voltage and power of the fuel cell are reduced. In Fig. 14, the TIT decreases from 1195 K to 1140 K as the S/C ratio increases. The operation point is close to the surge boundary, and the SM decreases. However, the SM of all the operation points is greater than 15%, which indicates that the safety requirement is met. The increase in water strengthens the cooling effect of the fuel cell and the combustor, which further reduces the TIT. This phenomenon also appears in the fuel cell inlet, causing the temperature difference between both ends of the fuel cell to increase. The same is observed in the case of the FTG, as show in Fig. 11. Fig. 15 shows that the power and electrical efficiency of the hybrid system decrease with growing S/C ratio. When the S/C ratio is large, a decrease in fuel cell power overwhelms the increase in GT power. Additionally, the increase in PGT =PSOFC decreases the electrical efficiency of the system. Therefore, in the S/C ratio variation range, the system can safely operate with a power range of 183.9 kWe170.4 kW and an electrical efficiency range of 61.12%e56.8%.

3.4. Effect of S/C ratio on system performance The selection of a reasonable S/C ratio is important to prevent carbon deposition. A change in S/C ratio can lead to variations in fuel composition concentration, fuel cell temperature, and Nernst potential. These variations will ultimately change the system performance, as shown in Fig. 12e15. Fig. 12 shows that the FWT decreases with increasing S/C ratio because a large amount of H2 is produced from CH4 and CO reforming as the S/C ratio increases. This condition causes more heat to be absorbed by CH4 steam reforming and increases the cooling effect from H2O on the fuel cell stack. Obviously, the FTG increases from 6.99 K/cm to 8.05 K/cm, which is within the safe operation range. As shown in Fig. 13, the output voltage and power of the fuel cell decrease as the S/C ratio increases because a large amount of H2O cause working temperature of the fuel cell to decrease. Consequently, the resistance of ohm polarization and electrode polarization increases. On the one hand, the inner voltage loss caused by the polarization resistance of the fuel cell increases. On the other hand, the increase in H2O dilutes the composition

Fig. 13. IT-SOFC output voltage and power variation with S/C ratio.

3.5. Influence analysis of the operation parameter Under the constraints of the FWT, FTG, TIT, and SM, the operation parameters will cause the system power to change to a different extent. If the reduced RS changes at the constant fuel flow

Fig. 15. Hybrid system output power and electrical efficiency variation with S/C ratio.

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rate, the system power range is 147.3 kWe183.3 kW, and the relative power range is 82%e104%. In this case, the system load adjustment range is moderate. If the F/A ratio changes at the constant air flow rate, the system power range is 126 kWe220 kW, and the relative power range is 70%e130%. In this condition, the system load adjustment range is wide. If the S/C ratio changes, the system power range is 170.4 kWe183.9 kW, and the relative power range is 96%e104%. This condition produces a narrow system load adjustment range, as shown in Fig. 16. When changing the RS, the FWT and SM fluctuate safely in a certain zone. The main reason is that the speed variation in different b can cause the operation point to change and the system operation to deviate from the design point and to a certain zone (Fig. 2). When the F/A ratio or the S/C ratio is modified, these parameters monotonously vary. In the safe operation range, the F/A ratio has the greatest effect on the performance of the hybrid system. It is thus suitable for a wide range of load adjustment. The second largest effect is from the RS, followed by that from the S/C ratio. Both parameters are suitable for a narrow range of load adjustments. According to the above analysis, the influence of the operation parameters on the performance of the hybrid system is summarized in Table 6. If a larger safe operation range of variable speed is needed, other adjustment measures should be adopted. By reducing the fuel flow rate or by increasing the air flow rate to prevent the system from overheating, the fuel cell and turbine can both work effectively in the safe zone. A low S/C ratio could increase the electrical efficiency and output power of the system, but carbon deposition can be easily triggered. Thus, the S/C ratio should be selected appropriately to consider both the safety and operating lifetime of the reformer, fuel cell stack, and GT. 4. Conclusions Detailed mathematical models of a hybrid IT-SOFC/GT system fueled by wood chip gasified gas are built, and the effects of operation parameters on the system are investigated. The main conclusions are: (1) The electrical efficiency of the hybrid IT-SOFC/GT system fueled by a wood chip gasified gas could reach up to 59.24% under design conditions with extremely low NOx and CO emissions.

Table 6 Summary of the influence of operating parameter Operating parameter

Hybris System Performance

Safety

Reduced RS

1) Its influence on the hybrid system is moderate. 2) The system efficiency range is 60.95% ~ 49.08%. 3) The relative power range is 82% ~ 104%. 1) Its influence on the hybrid system is biggest. 2) The system efficiency range is 56.5% ~ 61.34%. 3)The relative power range is 70% ~ 130% 1) Its influence on the hybrid system is minimal. 2) The system efficiency range is 61.12% ~ 56.8%. 3) The relative power range is 96% ~ 104%.

1) Its influence on the hybrid system safety is moderate. 2) The system safety operation range is moderate.

F/A ratio

S/C ratio

1) Its influence on the hybrid system safety is serious. 2) The system safety operation range is minimal.

1) Its influence on the hybrid system safety is small. 2) The system safety operation range is biggest.

(2) The power and efficiency of the hybrid system decrease with increasing reduced RS. In the safety zone, the operation parameters fluctuate in a certain zone. When the reduced RS is less than 0.8, both the fuel cell and the turbine are prone to over-temperature, and the compressor surges easily. These conditions indicate an unsafe system operation. (3) The F/A ratio has the greatest effect on the performance of the hybrid system. With increasing F/A ratio, the system power and efficiency increase. When the F/A ratio ranges from 0.27 to 0.43, the system can work safely and efficiently. This parameter is thus suitable for a wide range of load adjustment. The system cannot operate safely outside this range. (4) The S/C ratio has a minimal effect on the performance of the hybrid system. As it increases, the system power and efficiency decrease. When the S/C ratio is increased from 1 to 4, the efficiency decreases from 61.12% to 56.8%, which is suitable for a narrow range of load adjustment. The system can operate safely in this variation range. Acknowledgments The research is supported by National Natural Science Foundation of China under grant No. 51376123 and 863 Program of China (No. 2014AA052803). References

Fig. 16. Hybrid system relative output power and electrical efficiency.

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Glossary A: fuel cell stack surface area (m2) Ci,k: stoichiometric coefficient of component i in reaction k cp: specific heat capacity (kJ kg1 K1) E: activation energy (kJ mol1) F: Faraday constant (C) ha, hf: air and fuel channel height (mm) i: current density (A) j: average current density (A cm2) k: corresponding coefficients (A m2) L: cell length (m) l: adiabatic coefficient LHV: lower heating value (kJ mol1) M: mass flow rate (kg s1) n: molar flow (mol s1) p: pressure (MPa) P: output power (kW) pi: partial pressure of component i in the relevant gas channel (MPa) Pload: load power (kW) PSOFC: power of SOFC (kW) r: reaction rate Qrad: radiation heat (kJ) R: gas constant(J mol1 K1) Ranode, Rcathode: anode resistance and cathode resistance (U m2) ROhm: total cell resistance, including both ionic and electronic resistance (U m2) T: temperature (K) U0: potential (V) UOCP: open circuit potential (OCP) (V) OCP : actual open circuit potential (V) Uactual W: cell width (m) TIT: turbine inlet temperature FWT: fuel cell working temperature FTG: fuel cell temperature gradient CSM: compressor surge margin RS: rotational speed Greek letters

DG: change of Gibbs free energy (kJ mol1) DH: enthalpy change of reaction (kJ mol1) Dks: surge margin DPw: power working on the rotor l: expansion ratio

p: pressure ratio ps: pressure ratio on compressor surge line pw: compressor working ratio ε: SOFC stack surface radiation coefficient εcomb : combustor efficiency j: pressure loss hSOFC: electrical efficiency of SOFC hc, ht: adiabatic compression efficiency and adiabatic expansion efficiency hgen, hm: electrical efficiency and mechanical efficiency s: StefaneBoltzmann constant (W m2 K4) sanode, scathode: electronic conductivity of anode and cathode (U1 m1) selectrolyte: ionic conductivity of electrolyte (U1 m1) tanode, tcathode, telectrolyte, tI…: thickness (mm) Superscripts *: stagnation state Subscripts a: air c: compressor comb: combustor ele: electrochemical g: gas i,j,k: Components from SOFC anode and cathode exhaust gas and chemical reaction m: Components of combustor outlet gas sur: Environment temperature (K) std: Standard conditions t: turbine