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

Sensitivity Analysis

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%

Micro TurbinesAllows for high efficiency at lower pressure ratios!

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

Hydrogen Recovery

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?