The Impact of Hydration Dynamics on the Control of a PEM Fuel Cell

Transcription

1 The Impact of Hydration Dynamics on the Control of a PM Fuel Cell Syed K. Ahmed Donald J. Chmielewski Department of Chemical and nvironmental ngineering Illinois Institute of Technology Presented at the Annual Meeting of the AICh: November 006

2 Outline PMFC Model Mat. & nergy Balances and lectrochemistry Membrane Model Controller Analysis Feedback Control Feedback/Feed-forward Control

3 Polymer lectrolyte Membrane Fuel Cell (PMFC) H H H H e - e - O H + N H H + O H + H O N O O N H O H O O N H O N H O Generated power due to enthalpy released by the reaction: H + ½ O H O H Anode H + lectrolyte O Cathode H O (H ~ 58 kcal/mole H )

4 Dynamic Model of PMFC Cooling Air In Anode In (H, H O) Solid Material H H O H + H + H + H + H + Insulator Current Collector O N Jacket xhaust Cathode Air in Parameters based on 1 kw scale. Humidified hydrogen feed Anode xhaust H + H + H + MA H O Cathode xhaust Air cooling is assumed. cell

5 Material Balances in the Anode Gas V V F an an an dc C H dt dc ( an) dt F in an C F in an F C in an H C ( r H, in ( an), in J F an ( an) F C an H ) A C ( an) mem r H A J mem ( an) A mem lectrochemical Reaction Rate ----> Flux of Water to the Membrane ----> r H ( an) J

6 Material Balances in the Cathode Gas V V F ca ca ca dc O dt dc C ( ca) dt F in ca F C in ca F C in ca r O C O, in ( ca), in J F ca ( ca) C F O ca C A mem r O ( ca) A mem J ( ca) A mem lectrochemical Reaction Rate ----> Flux of Water to the Membrane ----> r O ( ca) J

7 nergy Balances (Reaction Chamber Gases) Cathode Chamber Gas V ca dt dt ca F in ca T in ca F ca T ca UA C p ca ( T Tca ) sol Anode Chamber Gas V an dt dt an F in an T in an F an T an UA C p an ( Tsol Tan)

8 nergy Balances (Cooling Jacket and Solid Material) Cooling Jacket Gas V jac dt dt jac F in jac T in jac F jac T jac UA C p jac ( T T ) jac sol Solid Material sol C V UA ( T T ) UA p sol sol dt dt ca UA ( Tan Tsol) QgenAmem an ca sol jac ( T jac T sol )

9 Reaction, Heat & Power Rates lectrochemical Reaction Rates: (molar generation per area of membrane) r H j r O F j 4F Heat Generation Rate: (per area of membrane) Q gen ( H f, ) r H P e Power Generation Rate: (electrical energy generation rate per area of membrane) Pe j cell

10 lectrochemistry Why we need it Reaction rates depend on j, current Heat Generation depen on current Need cell ( j) cell cell

11 lectrochemistry cell ner act ohm mt

12 lectrochemistry (Ideal Voltage) cell ner act ohm mt Nernst Potential: ner o RT sol F ln P H P H P 1/ O O

13 lectrochemistry (Kinetic Losses) cell ner act ohm mt Activation Loss: xchange Current Density: 1 RT sol ln j / act F j o j o o ( ( ca) C / o O C O ) j o

14 lectrochemistry (Loss Due to Ionic Resistance) cell ner act ohm mt Ohmic Loss: ohm IR j t mem Membrane Thickness: t mem Ionic Conductivity:

15 lectrochemistry (Mass Transfer Losses) cell ner act ohm mt Mass Transfer Loss: mt 1 1 RT sol F ln j L j L j Limiting Current Density: j F K L mt C ( ca) O Mass Transfer Coefficient: K mt D ( ca) GDL t GDL

16 Outline PMFC Model Mat. & nergy Balances and lectrochemistry Membrane Model Controller Analysis Feedback Control Feedback/Feed-forward Control

17 Hydration Model for MA Anode Solid Material Current Collector In Cathode (H, H O) H Air in O H + H + H O H + H + H + N Anode xhaust H + H + H + H O Cathode xhaust MA

18 Hydration Model for MA Anode Solid Material Current Collector In Cathode (H, H O) H Air in O H + H + H O H + H + H + N Anode xhaust H + H + H + H O Cathode xhaust MA

19 Water Transport in the Membrane LCTRO-OSMOTIC DRAG DIFFUSION

20 Water Transport in the Membrane Water Flux Mechanisms: J diff D e C ( mem) z J drag j F

21 Hydration Model for MA quations of Change: C ( mem) J ( mem) t z J mem) J diff J drag D C ( ( mem) z j F

22 Hydration Model for MA quations of Change: C ( mem) J ( mem) t z J mem) J diff J drag D C ( ( mem) z j F

23 Hydration Model for Membrane Boundary Conditions ) ( ) ( z C D t C mem O H e mem O H m O H ca O H mem O H e an O H mem O H e z r J F j z C D z J F j z C D at 0 0 at 0 ) ( ) ( ) ( ) (

24 Concentration Profiles ( mem C ) ( ) m ( mem) C H O 0 ( an) C HO ˆ ( mem ) C o ( ca) ˆ ( mem) C C HO m ( mem C ) ( z) HO Anode Gas GDL Membrane GDL Cathode Gas τ a τ m τ c

25 Water Fluxes Into the Membrane ( C ) ( ) mem HO m ( an) C HO ˆ ( mem ) C o ( mem) C H O 0 ( ca) ˆ ( mem) C C HO m ( C ) ( z) mem HO Anode Gas GDL Membrane GDL Cathode Gas δ a δ m δ c J ( an) k ( an) gdl [ C ( an) Cˆ ( an/ mem) ] J ( ca) k ( ca) gdl [ C ( ca) Cˆ ( mem / ca) ]

26 Water Vapor at Membrane Surface a an, mem aan, gas aca, mem a ca, gas

27 Water Vapor at Membrane Surface a an, mem aan, gas aca, mem a ca, gas Activity in Membrane: C ( mem) N s ( 0) C ( a ) an, mem ( a ) a ( mem) N 39.85a ( s mem ) ( a 36.0a 3 ca, mem )

28 Water Vapor at Membrane Surface a an, mem aan, gas aca, mem a ca, gas Activity in Membrane: C ( mem) Activity in Gas: a Cˆ N s ( 0) C ( a ) ( an/ mem) an, gas vap sol ( mem / ca) CH O RTsol ( T p an, mem ( a ) a ) ( mem) 39.85a ˆ N ( s mem ) ( a 36.0a a 3 ca, gas ca, mem p RT vap sol ) ( T sol )

29 Steady-State Water Content A/cm A/cm λ=ho/so A/cm Length Across PM (cm)

30 Dynamic Model of PMFC Cooling Air In Anode In (H, H O) Solid Material H H O H + H + H + H + H + Insulator Current Collector O N Jacket xhaust Cathode Air in Parameters based on 1 kw scale. Humidified hydrogen feed Anode xhaust H + H + H + MA H O Cathode xhaust Air cooling is assumed. cell

31 λ=ho/so3 - Membrane Conductivity A/cm A/cm A/cm Length Across PM (cm) z) z0.0036

32 lectrochemistry (Loss Due to Ionic Resistance) cell ner act ohm mt Ohmic Loss: ohm IR j t mem dz ( z) 0 Ionic Conductivity: z) z0.0036

33 Outline PMFC Model Mat. & nergy Balances and lectrochemistry Membrane Model Controller Analysis Feedback Control Feedback/Feed-forward Control

34 Current Set-Point Tracking Transportation Applications j j (sp) Current Controller MV PMFC

35 Current Controller

36 Current Controller

37 Current Controller

38 Current Controller

39 Current Controller

40 Current Controller

41 Water Fluxes Into the Membrane

42 Current Controller

43 Current/Temperature Controller T s(sp) j (sp) Current Controller + - PI cell j PMFC T s F j

44 Current/Temperature Controller

45 Current/Temperature Controller

46 Current/Temperature Controller

47 Current/Temperature Controller

48 Feed-forward Controller Feed-forward Controller F c o, F a o j (sp) T s(sp) Current Controller + - PI cell j PMFC T s F j

49 Feed-forward Controller

50 Feed-forward Controller

51 Feed-forward Controller

52 Feed-forward Controller

53 Water Content by the Cathode GDL

54 Feed-forward Controller

55 Conclusion What is the Impact of Hydration Dynamics on the Fuel Cell? Fuel cell is unpredictable and a better controller needs to be attached

56 Acknowledgements Argonne National Laboratory Department of Chemical & nvironmental ngineering, IIT