Modeling, Design and Control of Fuel Cell Systems

Transcription

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

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

3 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

4 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

5 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

6 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

7 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

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

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

10 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

11 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

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

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

14 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

15 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

16 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

17 Boiler Dynamics and Control

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

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

20 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

21 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

22 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

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

24 Cross Flow SOFC Stack Current Flow Fuel Flow Air Flow

25 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).

26 Exothermic Reactions in SOFC Fuel Flow Air Flow

27 Plug Flow Reactor Analogy O Feed Exhaust Reaction Rate

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

29 Impact of Internal Reforming From Selimovic, (00).

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

31 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

32 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 ( 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:

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

34 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

35 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

36 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

37 Simulations with a ydrogen Feed ydrogen to Steam Ratio

38 Simulations with a ydrogen Feed Solid Temperature Profile

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

40 Methane Fed Design Equations 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:

41 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

42 Internal Reforming Case

43 Carbon Deposition O C CO O C CO CO C CO C C

44 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

45 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

46 Internal Reforming Case

47 Conventional Efficiency 1 P e LV

48 Measures of Efficiency

49 Modified Stack Efficiency LV P e + pre

50 System Efficiency 3 Pe ( post pre) LV

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

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

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

54 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

55 PEMFC Polarization Curve 0 000

56 Ohmic Resistance Ionic conductivity,, increases with humidity

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

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

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

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

61 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 Relative umidity (%)

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

63 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

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

65 Cell Voltage (V) Power Density (watts/cm ) Selecting the Power Output E P e cell Current Density (ma/cm )

66 Cell Voltage (V) Power Density (watts/cm ) Selecting the Power Output E P cell e Current Density (ma/cm )

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

68 + - Cell Voltage (V) Power Density (watts/cm ) Power Controller PI j (sp) + - PI E cell PEMFC j P e P e (sp) E P e cell Current Density (ma/cm )

69 Power Density (watts/cm ) Power Controller P e (sp) P e Time (seconds)

70 Cell Voltage (V) Power Density (watts/cm ) Power Controller Failure E P cell e Current Density (ma/cm )

71 Current Density (ma/cm ) Cell Voltage (V) Power Controller Failure 400 E cell j Time (seconds)

72 Temperature (Celsius) Relative umidity (%) Power Controller Failure R T cat Time (seconds)

73 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)

74 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)

75 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)

76 Power Density (watts/cm ) Temperature / R Controller P e P (sp) e Time (seconds)

77 Temperature (Celsius) Relative umidity (%) Temperature / R Controller T cat R (sp) T cat Time (seconds) 85 80

78 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 + -

79 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 + -

80 Efficiency (%) Available Power and Efficiency Power Control Power Density (watts/cm )

81 Efficiency (%) Available Power and Efficiency Power Control Power & umidity Control Power Density (watts/cm )

82 Efficiency (%) Available Power and Efficiency Power Control Power, umidity & Oxygen Control Power & umidity Control Power Density (watts/cm )

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

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

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

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

87 PEMFC and CO Poisoning

88 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

89 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

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

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

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

93 CO Selectivity Exit CO Concentration, % PrOx Modeling % CO % CO 0. 0.% CO Stoichiometry % CO 1.3% CO 0.4 GSV = 36,000/h 0.% CO l X 1/4

94 Stoichiometry CO Selectivity Optimal PrOx Design l S Inlet CO Concentration (%)

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

96 ydrogen Convereted (%) Optimal Multistage PrOx Designs Stage -Stage 3-Stage Inlet CO Concentration (%)

97 Optimal Oxygen Flow (mol/s) Optimal Air Flow Rates for the 3 Stage System Overall Stage 0.1 Stage 1 0 Stage Inlet CO Concentration (%)

98 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

99 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

100 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

101 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

102 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

103 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

104 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

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

106 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)

107 Temperature ( C) CFD Model of the ATR Reactor Partial Oxidation Start-up: mm 19 mm Inlet temperature Time (s)

108 Temperature ( C) ATR Reactor Model Partial Oxidation Start-up: (Liquid Water Spray at 75 s) mm mm Inlet temperature Time (s)

109 Molar fractions wet (-) ATR Reactor Model Partial Oxidation Steady State: CO O 0.05 CO Fuel Dimensionless x-axis (x/l)

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

111 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

112 ATR Temperature ( o C) ATR Temperature ( o C) Step Test Modeling T T T T 3 T T T T 4 T T 3 T time (sec) 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

113 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 Open-loop 100 Open-loop Closed-loop 0 Closed-loop time (sec) time (sec)

114 Temperature ( o C) Inlet Air Flow Rate (slpm) Analysis of the Feedback Controller Regulation During ATR Mode: CV (T 3 ) Response: Open- vs. Closed-loop Open-loop MV (Air Flow) Response: Open vs. Closed-loop 00 Open-loop 150 Closed-loop Closed-loop time (sec) time (sec)

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

116 T 3 Temperature ( o C) Steam Flow Rate (g/min) Transition from PO to ATR Mode Impact of Steam Injection Rate With Feedback Controller Without Feedback Controller 100 Steam Flow Rate time (sec)

117 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

118 T 3 Temperature ( o C) T 3 Temperature ( o C) Impact of Model Mismatch Impact of Model Mismatch on Feed-forward Feed-forward With Model Mismatch Feed-forward Without Model Mismatch Impact of Model Mismatch on Feed-forward Feed-forward Without Model Mismatch Feedback Controller Only 600 Feedback Controller Only 400 Feed-forward With Model Mismatch time (sec) time (sec)

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

120 Computational Aspect of MPC

121 Temperature, o C Reduced Order Modeling z = 7 mm 800 z = 19 mm Measured Inlet Temperature Experimental Measurements - "*" igh Order CFD Simulation - Solid Reduced Order Simulation - Dashed Time, s Computational Effort: CFD: ~10 min ROM: ~30 sec

122 Mole Fraction, wet basis Reduced Order Modeling CO CO O igh Order CFD Simulation - Solid Reduced Order Simulation - Dashed Fuel Dimensionless Axial Position, 1 unit =7mm Computational Effort: CFD: ~10 min ROM: ~30 sec

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

124 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