Modeling, Design and Control of Fuel Cell Systems

Modeling, Design and Control of Fuel Cell Systems Professor Donald J. Chmielewski ChEE Department Seminar September 1 st, 005

Outline Update on Other Research Fuel Cell Research SOFC Design PEMFC Control Fuel Processor Design and Control Future Efforts

Predictive Control s. t. N T min xk Qxk + u xk, uk k 0 Process M odel: Known Initial State : k + 1 Process Constraints : Cx T k x Ru k Du x 0 k k Ax k c d + Bu k k k 0 0

Infinite orizon Predictive Control s. t. T min xk Qxk + u xk, uk k 0 Process M odel: Known Initial State : k + 1 Process Constraints : Cx T k x Ru k Du x 0 k k Ax k c d + Bu k k k 0 0

Tuning Predictive Controllers s. t. T min xk Qxk + u xk, uk k 0 Process M odel: Known Initial State : k + 1 Process Constraints : Cx T k x Ru k Du x 0 k k Ax k c d + Bu k k k 0 0

Tuning Predictive Controllers s. t. T min xk Qxk + u xk, uk k 0 Process M odel: Known Initial State: k + 1 Process Constraints : Cx T k x Ru k Du x 0 k k Ax k c d + Bu k + k k Gd 0 0 k

Expected Dynamic Operating Region x 1 Expected Dynamic Operating Region (EDOR) x1 * x x

Closed-Loop Operating Region x Closed-Loop EDORs of different controllers * u L( Q, R ) 1 1 x u L( Q, R ) x u

Profit Based Tuning CV' s Constraint Polytope Baked-off Operating Points Expected Dynamic Operating Regions Optimal Steady-State Operating Point Goal: Bring the Backedoff Point as close as possible to the Optimal Steady-State. Constraint: Do not allow the EDOR outside the Constraint Polytope. MV' s

Sensor Selection Extensions of the Capital Cost Formulation Actuator Selection Simultaneous Sensor and Actuator Selection Distributed Parameter Systems Fault Recoverability Combined with Profit Based Tuning

Coal Fired Power Plants Coal In Air In Combustion Chamber Boiler Flue Gas: CO O eavy Metals and NO x s Pollution Control

Oxy-Combustion Coal In Air In Combustion Chamber Boiler O Flue Gas: CO O eavy Metals and NO x s Pollution Control

Oxy-Combustion Coal In Air In Combustion Chamber Boiler O Cryogenics Plant N Air Flue Gas: CO O eavy Metals and NO x s Pollution Control

eat and Power Integration Coal In Air In Combustion Chamber Boiler O Cryogenics Plant N Air Flue Gas: CO O eavy Metals and NO x s Pollution Control

Boiler Dynamics and Control Coal In Air In Combustion Chamber Boiler O Cryogenics Plant N Air Flue Gas: CO O eavy Metals and NO x s Pollution Control

Boiler Dynamics and Control

Outline Update on Other Research Fuel Cell Research SOFC Design PEMFC Control Fuel Processor Design and Control Future Efforts

What is a Fuel Cell? Fuel Cell Air O Answer: An electrochemical device that converts a fuel directly to electrical power Electric Power

Solid Oxide Fuel Cell (SOFC) e - e - O - O N N O O - O N N O O - O N O - O Anode Electrolyte Cathode

Solid Oxide Fuel Cell (SOFC) E cell E ner jr ( T cell ) e - e - O - O N O - O O N N E ner E o ja r F + RT cell F log P P P 1 O O N O O - O N O - O Anode Electrolyte Cathode

Solid Oxide Fuel Cell (SOFC) E cell E ner jr ( T cell ) e - e - O - O N O - O O N N E ner E o ja r F + RT cell F log P P P 1 O O N O Anode O - Electrolyte O - O O Cathode N r ( T + cell ) ( T cell ) log P P O

Resistance in the SOFC Zirconia Electrolyte Cathode (~30 μm) Electrolyte (10-00 μm) Anode ( up to 1 mm) R int = r (T ) * ( thickness / Area )

Cross Flow SOFC Stack Current Flow Fuel Flow Air Flow

Thermal Stresses Peters et al., state: Large temperature gradients in either direction can cause damage to one or of the components or interfaces due to thermal stresses Yakabe et al., state: the internal stress would cause cracks or destruction of the electrolytes From Selimovic, (00).

Exothermic Reactions in SOFC Fuel Flow Air Flow

Plug Flow Reactor Analogy O Feed Exhaust Reaction Rate

Internal Reforming SOFC C 4 O CO O Fuel Flow O = O Air Flow

Impact of Internal Reforming From Selimovic, (00).

Plug Flow Reactor Analogy (Internal Reforming) Reforming Reaction Rate Electrochemical Reaction Rate Reforming eat Generation Electrochemical eat Generation Combined eat Generation

Distributed Feed SOFC Continuous Feed Configuration Feed Feed Exhaust Discrete Injection Configuration Feed L 1 L L 3 L 4 F 1 F F 3 F 4 F 5 A Exhaust

Isothermal Model ˆ ) ( ˆ ) ( O s O s s r C f dv FC d r C f dv FC d f dv df + General Model: channel. cell flow rate in the fuel : Volumetric in the distributed feed. species : Concentration of ˆ ). sec : Distributed feed flow per reactor volume ( 3 1 3 F i C m m f i s + + + ) ( ) ( ) ln ( ) ( i i O l j G n j Q h n r j C C T T r F F Rate Equations:

Achieving Uniform eat Generation + O O C C T T r Q C C log ) ( ) ( since Constant Constant

Achieving Uniform eat Generation + O O C C T T r Q C C log ) ( ) ( since Constant Constant ) ( ) ( ) ( Define z C z C z O r 0 set Then dz dr

Achieving Uniform eat Generation + O O C C T T r Q C C log ) ( ) ( since Constant Constant ) ( ) ( ) ( Define z C z C z O r 0 set Then dz dr ) ˆ ˆ ( )] ln( 1)[ ( * sp O sp sp s s C C f f r r r + + r r sp (0) where

Energy Model Ts d ksa dz dta FCaCpa dz dtc FcCcCpc dz wq d d h h h h d a c h h c w( T w( T ( T s s s T T T a c ) + ) c ) d FC ˆ ˆ h a h a Cp ( T a s T a ( Tˆ T ) a Interconnect Adiabatic Wall Fuel ) h a T a (z) Anode Electrolyte Q(z), T s (z) Cathode Air z h c T c (z) d z

Simulations with a ydrogen Feed ydrogen to Steam Ratio

Simulations with a ydrogen Feed Solid Temperature Profile

Fuel Utilization ydrogen Case U C, in C C, in, out

Methane Fed Design Equations 4 4 4 4 4 4 4 ˆ ) ( ˆ ) ( ˆ ) ( 3 ˆ ) ( ˆ ) ( CO CO s CO CO C CO s CO CO C O s O CO C s C C s C C s r C f dv FC d r r C f dv FC d r r r C f dv FC d r r r C f dv FC d r C f dv FC d r C f dv df + + + + + + General Model: + + + ) ( ) ( ln ) ( ) (, 4 4 i i elec i i eq CO CO O f shift CO C ref C O l j r G r Q h n r j K C C C C k r C k r C C T T r F Rate Equations:

Methane Fed Design Scheme C ( z) Again define: r( z) and r sp = the desired SR C ( z) And set dr 0 dz This is achieved if O f * s ( r sp + K eq ( r sp )( r + sp K + 1)[ + ln( rsp)] ( r )( Cˆ Cˆ r ) + ( r eq O sp sp sp + r sp 1)( K K Cˆ eq eq + 3r Cˆ CO sp CO + 4K r sp ) eq ) r * C 4 r(0) r sp

Internal Reforming Case

Carbon Deposition O C CO O C CO CO C CO C C 4 + + + + + +

Carbon Deposition C CO CO + CO 4 C + + C + CO C + O C + O Steam to Carbon Ratio (SCR) C O in CC, in, : 4

Indicator of Carbon Deposition CMMSR C CO C + C O C 4 If CMMSR > 1: Carbon deposition risk CMMSR < 1: No risk of carbon deposition

Internal Reforming Case

Conventional Efficiency 1 P e LV

Measures of Efficiency

Modified Stack Efficiency LV P e + pre

System Efficiency 3 Pe + 0.45( post pre) LV

Polymer Electrolyte Membrane Fuel Cell (PEMFC) e - e - + O N N O + O N N O + O N + O Anode Electrolyte Cathode

Polymer Electrolyte Membrane Fuel Cell (PEMFC) e - e - Transportation Applications + O N N O + O N N O + O N + O Anode Electrolyte Cathode

Electrochemistry SOFC: E cell E P, P ) E ( j, T ) ner ( O ohm cell ja r F

Electrochemistry SOFC: E cell PEMFC: E P, P ) E ( j, T ) ner ( O ohm cell ja r F E cell Ener( PO, P E ( j, T ohm O cell ) E act (, R ) j) E mt ( j, K mt ( R )) r O ja F

PEMFC Polarization Curve 0 000

Ohmic Resistance Ionic conductivity,, increases with humidity

Ohmic Resistance Ionic conductivity,, increases with humidity R x w P P (T) sat x w = 0.35

Mass Transfer Resistance 1 ( s) Kmt ( xo xo ) r O C O ( s) C O j

Mass Transfer Resistance 1 ( s) Kmt ( xo xo ) r O C O ( s) C O j 0 000

Efficient Operation Ionic conductivity,, increases with humidity R x w P P (T) sat x w = 0.35

Mass Transfer Coefficient Flooding Resistance via the MTC K mt ( R ) K mt, o 1 ( ( R 1) e ) x 10-3 where is the porosity coef. 1.5 1 0.5 0 0 0 40 60 80 100 Relative umidity (%)

PEMFC Operating Window 80% R 100% Membrane Dried Out Membrane Flooded 0 60 C T cat 100 0 C

Dynamic Model of PEMFC Cooling Air In Anode In Solid Material + + Insulator Current Collector O Jacket Exhaust Cathode Air in Material and energy balances combined with PEMFC electrochemistry. + + + + + + N O Cathode Exhaust Parameters based on a 50 kw scale. MEA Air cooling is assumed. E cell

Power Set-Point Tracking Transportation Applications P e P e (sp) Power Controller MV PEMFC

Cell Voltage (V) Power Density (watts/cm ) Selecting the Power Output 1.4 1. 1 0.8 0.6 0.4 0. E P e cell 0.35 0.3 0.5 0. 0.15 0.1 0.05 0 0 00 400 600 Current Density (ma/cm 800 1000 0 )

Cell Voltage (V) Power Density (watts/cm ) Selecting the Power Output 1.4 1. 1 0.8 0.6 0.4 0. E P cell e 0.35 0.3 0.5 0. 0.15 0.1 0.05 0 0 00 400 600 Current Density (ma/cm 800 1000 0 )

+ - Power Controller PI j (sp) + - PI E cell PEMFC j P e P e (sp)

+ - Cell Voltage (V) Power Density (watts/cm ) Power Controller PI j (sp) + - PI E cell PEMFC j P e P e (sp) 1.4 1. 0.35 0.3 1 0.8 0.6 0.4 0. E P e cell 0.5 0. 0.15 0.1 0.05 0 0 00 400 600 Current Density (ma/cm 800 1000 0 )

Power Density (watts/cm ) Power Controller 0. 0.1 P e (sp) P e 0. 0.19 0.18 0 5 10 15 0 5 Time (seconds)

Cell Voltage (V) Power Density (watts/cm ) Power Controller Failure 1.4 1. 1 0.8 0.6 0.4 0. E P cell e 0.35 0.3 0.5 0. 0.15 0.1 0.05 0 0 00 400 600 Current Density (ma/cm 800 1000 0 )

Current Density (ma/cm ) Cell Voltage (V) Power Controller Failure 400 E cell 0.8 300 0.7 j 0.6 00 0 5 10 15 0 5 0.5 Time (seconds)

Temperature (Celsius) Relative umidity (%) Power Controller Failure 100 100 90 R 90 80 T cat 80 70 0 5 10 15 0 5 70 Time (seconds)

Temperature / R Controller P e (sp) Power Controller E cell P e, j PEMFC T cat (sp) PI + - PI F jac T cat R + - R (sp)

Power Density (watts/cm ) Temperature / R Controller 0.3 0.8 0.6 P e P (sp) e 0.4 0. 0. 0.18 0 0 40 60 80 Time (seconds)

Temperature (Celsius) Relative umidity (%) Temperature / R Controller 85 80 75 T cat R 100 95 90 70 (sp) T cat 65 0 0 40 60 80 Time (seconds) 85 80

Oxygen Controller P e (sp) Power Controller E cell P e, j PEMFC F jac R, T cat R (sp) R Controller PI F cat (sp) x O x O + -

Efficiency (%) Available Power and Efficiency 75 70 Power Control 65 60 55 0.17 0.18 0.19 0. 0.1 0. Power Density (watts/cm )

Efficiency (%) Available Power and Efficiency 75 70 Power Control 65 60 55 Power & umidity Control 0 0.05 0.1 0.15 0. 0.5 0.3 Power Density (watts/cm )

Efficiency (%) Available Power and Efficiency 75 70 Power Control Power, umidity & Oxygen Control 65 60 55 Power & umidity Control 0 0.1 0. 0.3 0.4 0.5 0.6 Power Density (watts/cm )

Outline Update on Other Research Fuel Cell Research SOFC Design PEMFC Control Fuel Processor Design and Control Future Efforts

Fuel Cell System Electric Power Conditioner Air Fuel Air Fuel Processor Fuel Cell Stack Spent-Fuel Burner Exhaust O CO Thermal & Water Management

ydrogen Storage vs. On-Board Reforming Transportation Applications ydrogen Storage Tank PEMFC Liquid Fuel Storage Tank C m n CO Reformer O CO PEMFC

PEMFC and CO Poisoning

Fuel Processing Reactors Reformer Water- Gas Shift (WGS) Preferential Oxidation (PrOx) PEMFC ydrocarbon Feed Large ydrocarbons Cracked: CO levels down to ~ 10 ppm Low to CO ratio Most CO converted to CO : ~ 1% CO remaining

Preferential Oxidation Desired Reaction: Parasitic Reaction: 1 1 CO + O CO + O O

Preferential Oxidation Desired Reaction: CO + 1 O CO Parasitic Reaction: 1 + O O Reformate CO ~1-% Air PrOx Reactor to PEMFC CO 10 ppm

PrOx Design Challenge Achieve an exit CO concentration less than 10 ppm Minimize the oxidation of Inlet concentration of CO is known

CO Selectivity Exit CO Concentration, % PrOx Modeling 1. 1.0 0.8.5% CO 0.6 0.4 1.3% CO 0. 0.% CO 0.0 0.0 0.5 1.0 1.5.0.5 3.0 Stoichiometry 1 0.8 0.6.6% CO 1.3% CO 0.4 GSV = 36,000/h 0.% CO 0. 0 0 0.5 1 1.5.5 l X 1/4

Stoichiometry CO Selectivity Optimal PrOx Design.5 1.0.0 0.8 l 1.5 0.6 S 1.0 0.4 0.5 0. 0.0 0.0 0.0 0. 0.4 0.6 0.8 1.0 1. Inlet CO Concentration (%)

Multistage PrOx Reactors Reformate Air Air Air Prox Stage 1 100 o C 100 o C Prox Stage Intercooler Intercooler Prox Stage 3

ydrogen Convereted (%) Optimal Multistage PrOx Designs.5 1.5 1 0.5 1-Stage -Stage 3-Stage 0 0 0.5 1 1.5.5 3 3.5 Inlet CO Concentration (%)

Optimal Oxygen Flow (mol/s) Optimal Air Flow Rates for the 3 Stage System 0.6 0.5 0.4 Overall 0.3 0. Stage 0.1 Stage 1 0 Stage 3 0 0.5 1 1.5.5 3 3.5 Inlet CO Concentration (%)

Partial Oxidation Total Oxidation: C + ( m + n/ ) O mco + n/ m n C m + m O mco + m + n/ ) ( Steam Reforming: n CO + + O CO Water Gas Shift: O ydrocarbon Fuel Air (at a substoichiometric rate) PO Reactor O CO CO

Partial Oxidation Oxidation: C + ( m + n/ ) O mco + n/ m n C m + m O mco + m + n/ ) ( Steam Reforming: n CO + + O CO Water Gas Shift: O ydrocarbon Fuel Air (at a substoichiometric rate) PO Reactor O CO CO

Water Gas Shift Reaction At igh temperatures equilibrium favors: CO + O + CO At Low temperatures equilibrium favors: CO + O + CO More O in the feed will also favor the forward direction

Autothermal Reforming Oxidation: C C + ( m + n/ ) O mco + n/ m n m + m O mco + m + n/ ) ( Steam Reforming: n CO + + O CO Water Gas Shift: O Steam ydrocarbon Fuel Air (at a substoichiometric rate) ATR Reactor O CO CO

Autothermal Reforming Oxidation: C C + ( m + n/ ) O mco + n/ m n m + m O mco + m + n/ ) ( Steam Reforming: n CO + + O CO Water Gas Shift: O ydrocarbon Fuel Air (at a substoichiometric rate) Steam ATR Reactor CO, O,, CO More Less CO

ATR Reactor Liquid water Vaporized gasoline, Steam Nozzle ot air igh Space Velocity (GSV ~ 50,000/h) Catalyst bed eater rod Thermocouple 7 mm 1 3 4 Noble Metal Catalyst Metal wall thickness=1.7 mm 1 mm 5 6 7 8 9 10 (Rh on a Gd-CeO substrate). 1 mm Operating Temperature 96 mm ~ 700 1000 o C Air (5 C) eat exchanger

Start-up the ATR Reactor 1. Partial Oxidation Mode to achieve desired operating temperature quickly (feed of fuel and air only). ATR Mode to achieve desired CO conversion (feed of fuel, air and steam)

Temperature ( C) CFD Model of the ATR Reactor Partial Oxidation Start-up: 1000 900 800 700 7 mm 19 mm 600 500 400 300 Inlet temperature 00 100 0 0 40 60 80 100 10 140 160 180 00 Time (s)

Temperature ( C) ATR Reactor Model Partial Oxidation Start-up: (Liquid Water Spray at 75 s) 900 800 700 7 mm 600 500 19 mm 400 300 00 Inlet temperature 100 0 0 40 60 80 100 10 140 160 180 Time (s)

Molar fractions wet (-) ATR Reactor Model Partial Oxidation Steady State: 0.5 0.0 CO 0.15 0.10 O 0.05 CO Fuel 0.00 0.0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Dimensionless x-axis (x/l)

Feedback Control of the ATR Reactor Temperature Fluctuations in Reactor T 3, set point Inlet Air Temperature T 1 + - PI Control Inlet Air Flow ATR Reactor T T 4 T 5 T 3, measured + + + + T 3 Sensor Noise

Feedback Control of the ATR Reactor Disturbances Temperature Fluctuations in Reactor T 3, set point Inlet Air Temperature T 1 Manipulated Variable + - PI Control Inlet Air Flow ATR Reactor T T 4 T 5 T 3, measured + + + + T 3 Sensor Noise Control Variable

ATR Temperature ( o C) ATR Temperature ( o C) Step Test Modeling 1050 1050 1000 T 1 1000 950 T 1 950 900 T T 3 T3 900 850 800 T T 5 850 T 4 T 5 750 700 T 3 T 4 800 0 0 40 60 80 100 time (sec) 650 0 0 40 60 80 100 time (sec) is Ti K ie FAir, in i s +1 is Ti K ie TAir, in i s +1 F T i Steam in is Kie, is +1

Temperature ( o C) Inlet Air Flow Rate (slpm) Analysis of the Feedback Controller Regulation During Partial Oxidation: 100 CV (T 3 ) Response: Open vs. Closed-loop MV (Air Flow) Response: Open-loop vs. Closed-loop 150 1100 Open-loop 100 Open-loop 1000 50 900 Closed-loop 0 Closed-loop 800 0 00 400 600 800 time (sec) -50 0 00 400 600 800 time (sec)

Temperature ( o C) Inlet Air Flow Rate (slpm) Analysis of the Feedback Controller Regulation During ATR Mode: 100 1100 1000 CV (T 3 ) Response: Open- vs. Closed-loop Open-loop MV (Air Flow) Response: Open vs. Closed-loop 00 Open-loop 150 Closed-loop 100 900 Closed-loop 50 800 0 00 400 600 800 time (sec) 0 0 00 400 600 800 time (sec)

T 3 Temperature ( o C) Steam Flow Rate (g/min) Transition from PO to ATR Mode Impact of Steam Injection 800 600 With Feedback Controller 400 Without Feedback Controller 100 Steam Flow Rate 50 0 0 50 100 150 00 0 time (sec)

T 3 Temperature ( o C) Steam Flow Rate (g/min) Transition from PO to ATR Mode Impact of Steam Injection Rate 800 600 400 With Feedback Controller Without Feedback Controller 100 Steam Flow Rate 50 0 50 100 150 00 0 time (sec)

Feed-forward Control Steam Flow Rate (Measured) TF w.r.t. Steam T 3, set point FF + - PI + + Air Flow TF w.r.t. Air Flow + + T 3

T 3 Temperature ( o C) T 3 Temperature ( o C) Impact of Model Mismatch 100 1000 Impact of Model Mismatch on Feed-forward Feed-forward With Model Mismatch Feed-forward Without Model Mismatch 1000 800 Impact of Model Mismatch on Feed-forward Feed-forward Without Model Mismatch 800 600 Feedback Controller Only 600 Feedback Controller Only 400 Feed-forward With Model Mismatch 400 0 0 40 60 80 100 time (sec) 00 0 0 40 60 80 100 time (sec)

Outline Update on Other Research Fuel Cell Research SOFC Design PEMFC Control Fuel Processor Design and Control Future Efforts

Computational Aspect of MPC

Temperature, o C Reduced Order Modeling 1000 @ z = 7 mm 800 600 @ z = 19 mm 400 00 0 Measured Inlet Temperature Experimental Measurements - "*" igh Order CFD Simulation - Solid Reduced Order Simulation - Dashed 0 40 60 80 100 10 140 160 180 00 Time, s Computational Effort: CFD: ~10 min ROM: ~30 sec

Mole Fraction, wet basis Reduced Order Modeling 0. 0.15 CO 0.1 0.05 0-0.05 CO O igh Order CFD Simulation - Solid Reduced Order Simulation - Dashed Fuel 0 0. 0.4 0.6 0.8 1 Dimensionless Axial Position, 1 unit =7mm Computational Effort: CFD: ~10 min ROM: ~30 sec

Acknowledgements Collaborators @ IIT: Said Al-allaj J. Robert Selman Vijay Ramani Satish Parulekar erek Clack Jai Prakash @ Argonne National Laboratory: Shabbir Ahmed Dennis Papadias Rajesh Ahluwalia Qizhi Zhang Michael Inbody (LANL)

Acknowledgements Students: Ayman Al-Qattan Amit Manthanwar Yongyou u Janet Ruettiger Jui-Kun Peng Kevin Lauzze Jotvinge Vaicekauskaite Ali Zenfour Funding: Argonne National Laboratory Illinois Clean Coal Institute American Air Liquide Kuwait Institute for Scientific Research Graduate and Armour Colleges, IIT Chemical & Environmental Engineering Department, IIT