Steady State Modeling and Analysis of a De-Coupled Fuel Cell – Gas Turbine Hybrid for Clean Power Generation
Steady State Modeling and Analysis
of a De-Coupled Fuel Cell – Gas Turbine Hybrid for Clean Power
Generation
What?? Why??
• What is a solid oxide fuel cell?
– Direct conversion of chemical energy to power
• What is a heat engine?
– Combustion Heat Spins something Power
• Loses efficiency at each step
Anode
Ceramic
Cathode
Power
Air
Fuel
Oions
What is a FC-GT?
• Combination of systems
– Improve on existing systems
– Heat generated by fuel cell drives turbomachinery
• Fuel Cell (Heat) Spin something Power
Fuel Cell
Outline
• Background
• Literature Review
• Modeling Considerations
• Results
– Design Space Investigation
– Economic Analysis
• Conclusions
Real World Examples
GE 2003
UC Irvine – Siemens/
Westinghouse
Mitsubishi
De-Coupled FC-GT
Fuel Cell Power Combustion Heat Spin Something Added Power
SOFC
Fuel Humidification
Heat
Outline
• Background
• Literature Review
• Modeling Considerations
• Results
– Design Space Investigation
– Economic Analysis
• Conclusions
Literature Review
• Fuel Cell Modeling Approaches
– Fuel cell modeling
• Bulk/Spatially Resolved 1, 2
– Simplest
• Equivalent Circuit/Physical– Black Box 3
– Nodal4
[1] Wolfgang Winkler, Pedro Nehter, Mark C Williams, David Tucker, and Randy Gemmen, "General Fuel Cell
Hybrid Synergies and Hybrid System Testing Status," Power Sources, vol. 159, no. 1, pp. 656-666, September
2006.
[2] James Larminie, Fuel Cell Systems Explained, 2nd ed.: Oxford Brookes University, 2003.
[3] Dayadeep S. Monder, K. Nandakumar, and Karl T. Chuang, "Model development for a SOFC button cell using
H2S as fuel," Journal of Power Sources, vol. 162, no. 1, November 2006.
[4] Jens Palsson, Azra Selimovic, and Lars Sjunnesson, "Combined Solid Oxide Fuel Cell and Gas Turbine Systems
for Efficient Power and Heat Generation," Power Sources, vol. 86, no. 1-2, pp. 442-448, March 2000.
Literature Review Cont..
• Gas Turbine Modeling
– Brayton Cycle
• Isentropic Relations 5
– Refined w/ real world data
• Compressor/Turbine maps6
[5] Penyarat Chinda and Pascal Brault, "The Hybrid Solid Oxide Fuel
Cell (SOFC) and Gas Turbine (GT) Systems Steady State Modeling,"
Hydrogen Energy, vol. 37, no. 11, pp. 9237-9248, June 2012.
[6] Jason Kupecki, "Considerations Regarding Modeling of MW-scale
IG-SOFC Hybrid Power System," Thesis 2009.
FC-GT Hybrids
• Modeling studies cite balance of of mass and energy into systems7, 8
– Maintaining thermal tolerance of SOFC
– Mass flow of GT
• Most modeling based on system configurations9
– Bottoming cycle
– Topping cycle[7] M.L. Ferrari, Matteo Pascenti, Roberto Bertone, and Loredana Magistri,
"Hybrid Simulation Facility Based on Commercial 100 kWe Micro Gas
Turbine," Fuel Cell Science and Technology, vol. 6, no. 3, May 2009.
[8] Nischal Srivastava, "Modeling of Solid Oxide Fuel Cell/Gas Turbine
Hybrid System," Mechanical Engineering, Florida State University, Thesis
2006.
[9] A. Palombo, L. Vanoli F. Calise, "Design and partial load exergy
analysis of a hybrid SOFC-GT power plant," 2005.
Topping Cycle: Benefits and Challenges
• Benefits:– Higher pressure ratios – higher OCV 8
• Drawbacks:
– GT operates at constant mass flux – temp changes• Surge Margin 9
– FC temp constant – changing mass flux
– FC pressurization within turbine• No way to control temperature gradient – Tightly coupled10
[8] Dustin McLarty, Yusuke Kuniba, Jack Brouwer, and Scott Samuelson, "Experimental and Theoretical Evidence for
Control Requirements in Solid Oxide Fuel Cell Gas Turbine Hybrid Systems," Power Sources, vol. 209, March 2012.
[9] A Traverso, L. Magistri, and A.F Massardo, "Turbomachinery For the Air Management and Energy Recovery in Fuel Cell
Gas Turbine Hybrid Systems," Energy, vol. 35, no. 2, February 2010.
[10] F. Mueller, Jack Brouwer, F. Jabbari, and Scott Samuelson, "Dynamic SImulation of an Integrated Solid Oxide Fuel
Cell System including Current-Based Fuel Flow Control," Fuel Cell Science and Technology, vol. 3, pp. 144-154, October
2006.
Solutions
• Decoupling the system?11
– Additional control
– Reduce risk
– Hard to accomplish
• Thermal management12
– Internal reformation13
• Eliminate auxiliary systems
[11] Dustin McLarty, Jack Brouwer, and Scott Samuelson, "Hybrid Fuel Cell Gas Turbine System Design and
Optimization," Journal of Fuel Cell Science and Technology, vol. 10, 2013.
[12] S.K. Park,T.S. Kim, J.H. Kim, J.L. Sohn W.J Yang, "Design Performance Analysis of Pressurized Solid Oxide
Fuel Cell/Gas Turbine Hybrid Systems Considering Temperature Constraints," Power Sources, vol. 160, no. 1,
September 2006.
[13] Kasra Nikooyeh, Ayodeji A. Jeje, and Josephine M. Hill, "3D Modeling of Anode-Supported Planar
SOFC with Internal Reforming of Methane," Power Sources, vol. 171, no. 2, September 2007.
Outline
• Background
• Literature Review
• Modeling Considerations
• Results
– Design Space Investigation
– Economic Analysis
• Conclusions
Models using First Principles
• Compressor/Turbine:
– Isentropic Relations:
• ሶ𝑊 = ሶ𝑚(ℎ𝑖𝑛 − ℎ𝑜𝑢𝑡)
• 𝜂𝐶 =ℎ𝑠−ℎ𝑖𝑛
ℎ𝑜𝑢𝑡−ℎ𝑖𝑛, 𝜂𝑇 =
ℎ𝐼𝑛−ℎ𝑜𝑢𝑡
ℎ𝑖𝑛−ℎ𝑠,
Compressor Turbine
ሶ𝑚𝑖𝑛
ℎ𝑖𝑛
ሶ𝑚𝑜𝑢𝑡
ℎ𝑠ℎ𝑜𝑢𝑡
ሶ𝑚𝑜𝑢𝑡
ሶ𝑊𝑜𝑢𝑡
OTM Modeling
• OTM:
– 𝑄𝑃𝑟𝑒ℎ𝑒𝑎𝑡 = ሶ𝑚 ℎ800°𝐶 − ℎ𝐶,𝑂𝑢𝑡
– 𝑅𝑇 = 1 −1−𝑋𝑓𝑒𝑒𝑑 ∗𝑃𝑂𝑇𝑀
𝑋𝑓𝑒𝑒𝑑(𝑃𝑖𝑛−𝑃𝑂𝑇𝑀)
• ሶ𝑛𝑂2 = 𝛼𝑅𝑇 ∙ 𝑋𝑓𝑒𝑒𝑑 ∙ሶ𝑚𝐶,𝑜𝑢𝑡
ℳ
𝑃𝑂𝑇𝑀
𝑃𝑖𝑛
Fuel Cell Modeling
• Heat generated = Cooling of Steam Reforming
– Δ𝐸 = ሶ𝑄𝐺𝑒𝑛 − ሶ𝑄𝑅𝑒𝑓𝑜𝑟𝑚
• Nernst Equation:
– 𝐸 𝑥 =−∆𝐺𝑟𝑥𝑛
2𝐹−
𝑅𝑇
𝐹ln
𝑋𝐻2𝑂 𝑥
𝑋𝐻2 𝑥 ∙𝑋𝑂2∙𝑃𝐺𝑇
100𝑘𝑃𝑎
12
• Mass Balance
– 𝑋𝐻2(𝑥) = 1 +𝜀𝑊𝐺𝑆
3−
2 ሶ𝑛𝑂2∙𝑟
3 ሶ𝑛𝐶𝐻4−
𝑊(1−𝑟)
6𝐹∙ ሶ𝑛𝐶𝐻40𝑥𝑖 𝑥 𝑑𝑥
– 𝑋𝐻2𝑂 𝑥 =2 ሶ𝑛𝑂2∙𝑟
3 ሶ𝑛𝐶𝐻4−
1+𝜀𝑊𝐺𝑆
3+
𝑊(1−𝑟)
6𝐹∙ ሶ𝑛𝐶𝐻40𝑥𝑖 𝑥 𝑑𝑥
• Define current distribution along (x)
– 𝑖 𝑥 =𝐸 𝑥 −𝑉
𝐴𝑆𝑅
Nodal Fuel CellAverage
Current
Density
(A/cm2)
Operating
Voltage
(V)
Hydrogen
Utilization
(%)
1.50 .77 .488
1.37 .791 .510
1.23 .815 .536
1.09 .840 .568
0.950 .863 .603
0.810 .887 .642
0.669 .910 .685
0.528 .936 .731
0.387 .951 .777
0.246 .965 .815
.105 .973 .831
Combustor Model
• Energy balance with products from OTM and FC
– Δ𝐸 = ሶ𝑛𝑎𝑖𝑟ℎ𝑎𝑖𝑟 + ሶ𝑛𝐴𝑛𝑜𝑑𝑒൫ℎ𝐴𝑛𝑜𝑑𝑒 + 𝑋𝐶𝑂 𝐿 ∙
Outline
• Background
• Literature Review
• Modeling Considerations
• Results
– Design Space Investigation
– Economic Analysis
• Conclusions
Design Space Investigation
·Operating Voltage ·Hydrogen Utilization
0.46 0.49 0.52 0.55 0.58 0.61 0.64 0.67 0.73 0.78 0.81
ResultsDesign Variable Value Range Units
Current Density 0.50 0.105 – 1.5 A/cm2
Turbine Press. 1.5 0.3-2.5 MPa
Permeate Press. 50 50-250 kPa
ηC80 70-85 %
ηT88 75-90 %
Turbine Inlet 1200 1000-1700 K
ASR .25 .18-.30 Ω·cm2
Value RangeSOFC Voltage 0.936V 0.77-0.97V
Hydrogen Utilization 74.0% 48.8-83.1%
Anode Recirculation 59.6% 85.1-53.6%
Oxygen Recovered 49.7% of RT 16.5-82.5%
dFC-GT Efficiency 75.4% 55.0-82.1%
Potential Hydrogen RecoverySOFC Operating Voltage (Volts) SOFC Exhaust H2 Concentration (%)
0.972 9.10
0.951 16.4
0.910 28.7
0.863 39.7
0.815 48.4
0.770 55.0
Economic Analysis
• Cost Assumptions:
– Fuel - $4.50/therm
– Grid - $0.05/kWh
– Demand - $3.00/kW
• Emission Assumptions:
– Fuel – 879 lb/therm
– Grid – 116.39 lb/MWh
0.0997…
3.8675…
25.396…
59.235…
91.928…98.358… 99.643… 99.866… 100
0
20
40
60
80
100
120
0
2000
4000
6000
8000
10000
12000
14000
10 12 14 16 18 20 22 24 26
Freq
uen
cy (
#)
Demand (MW)
Meeting Peak Demand• Efficiency Curves
– Peaker vs dFC-GT
– Varying efficiencies
• Operation at near design conditions > 95% of time
25.00
35.00
45.00
55.00
65.00
75.00
85.00
10.00 15.00 20.00 25.00 30.00
GT
Effi
cien
cy (
%)
GT Power (MW)
dFC-GT
Peaker
Economic Conclusions
$0.00
$1,000,000.00
$2,000,000.00
$3,000,000.00
$4,000,000.00
$5,000,000.00
$6,000,000.00
$7,000,000.00
$8,000,000.00
Grid Only Base + Grid Peaker dFC-GT
An
nu
al C
ost
s ($
)
Annual Mortage Payment
Annual Operating Costs
Technology Capital
Financing Costs
On-Site Fuel
Costs
Grid energy &
demand costs
Total annual
costs
Grid dependent - - $7,059,206 $7,059,206
Base-load CC + grid $953,825 $2,249,604 $2,666,855 $5,870,285
‘Peaker’ GT $1,192,281 $5,685,589 - $6,877,871
dFC-GT $2,384,563 $3,236,865 - $5,621,428
Technology On-Site Emissions
of CO2 (tons)
Grid related
Emissions (tons)
Total Emissions
(tons)
Grid dependent - 55,336 55,336
Base-load CC + grid 29,254 19,888 49,142
‘Peaker’ GT 73,879 - 73,879
dFC-GT 42,079 - 42,079
Outline
• Background
• Literature Review:
• Modeling Considerations
• Results
– Design Space Investigation
– Economic Analysis
• Conclusions
Outlook/Next Steps
• Pressurized/Pure Oxygen cathode tests:
– Currently being worked on at CESI Lab
• Steam Reformation Tests:
– Internal steam reformation able to thermally balance pressurized FC
• OTM Tests:
– Ability to operate at lower pressure ratios
– Pre-heating
• Transient Response
– Dynamic modeling
Conclusions
• dFC-GT:
– Retro-Fit capable
– De-Coupling – Extra Control
– Highly efficient hybrid – 75.4% FTE• .936V FC Operating Voltage
• 74% H2 utilization
– Micro-Turbine Scaling
– Economically feasible • Lower investment
• Lower fuel costs
• The future is bright!
• QUESTIONS?