2009 American Control ConferenceHyatt Regency Riverfront, St. Louis, MO, USAJune 10-12, 2009

ThA20.1

Dynamics and Control of Membrane Hydration in a PEMFC*

Syed Ahmed and Donald J. Chmielewski t

alhode,.(llir)

CathodeE"haust

JackelExhaustlr In '\ , - /

/C-- * -~-) "\ ik' OJ

- m'(. 'K_ ~ f-

V i& 1/:0

, ,

:;.;:;~~ cl,._--, c... ,

CoolingA·

AnodeExhaus

Abstract

The Jllbject ofwater IIIallagement is a key is!ille illthe design and operation of Polymer Electrolyte Mem­brane Fllel Cells (PEMFC). In this paper we presenra dynamic model central to understanding the watermanagemellf and flooding issue. First we considermembrane hydration and show how the interplay be­tween electro-osmaric drag alld back-diffusioll deter­mille iOllic condllctil'it)'. The model is t!lel/used to idell­tifY appropriate manipulated variables for controllingthe location and shape of the hydration profile withillthe membrane.

Figure 1. Schematic of the PEMFC System.1. Introduction

The overall objective of a PEM~C control systemis to deliver power at levels equal to that requested by acommand signal (presumably coming from the cell useror a higher level controller), which suggests that achiev­ing a wide range of possible power conditions is of fun­damental concern. In this note we illustrate how thephenomena of membrane dehydration and GDL nood­ing create limitations to the set of available power con­ditions. We also pUl'.iue the question of finding new ma­nipulated variables capable of changing the membranehydration profile.

As one would expect the literature on fuel cell mod­eling is quite large, for an overview please see the fol­lowing texts: [1,21. Concerning membrane hydrationmodels Ihe work of Springer el.al [3J is fundamental.In addilion to [31, Ihe current hydration model employstechniques from [4-7J. For a variety of pel'.ipecliveson the analysis and design of control systems for thePEMFC application, please see l8-14J and the refer­ences therein.

'Center for Etectrochemical Science & Engineering Depanmentof Chemical &. Biological F.ogin""ring,11Iiooi~ Inslimle of T,--chool_ogy. Chicago. IL 60616

'Co~ponding aUl1Jor.phonc: 312-567-3537. fax: 312-567-8874.email: chrnielewski@iil.edu

2. The Dynamic Model

The $y$tem $Cen<tno i$ $imilar to .hat ofl.a1l7.ze andChmielewski [9). In contrast 10 [9J, the new model willconsider a non-pure hydrogen feed (with an exit flow)as well as hydration dynamics within the membrane.

The unit cell of the model consist of two gaschambers separated by a membrane ek.-ctrode assem­bly (MEA), see figure I. On the anode side. hydro­gen is split into hydrogen ions and electrons. While theions travel through the membrane, the electrons travelthrough the anode to the current collector and on to theload. These electrons then travel back to the cathodewhere they combine with the hydrogen ions and oxygento produce waler. The rate of reaction is proporlional tothe currenl density ;j, = -rll, = -!ro1=rlJ,o where ri rep­resents the generation of species i per unit area. Whilethe membrane is designed to be impermeable 10 H! andO!. it is capable of significant water uptake. As suchrH,O cannot be used for the gas phase material balances.Instead we define a pair of water transfer nuxeS 10 themembrane from the anode and cathode gas chambers,J~,()andY",(),

978-1-4244-4524-0/09/$25.00 ©2009 MGG 2648

...15

...............................

MilS t."M'mb....... Length (em)"

H I.!

•••• 1.4

r__c·o':·'o'c':'·:"C"Cl-dO'O":""::;.''''''=="__--," --r._........n"..'

A water balance within the membrane yields:

aen 0 aJii 0~=-~ (12)

d' d;where e:1o is the concentration of water in the mem­brane and Jli10 is the flux of water through the mem­brane. Water transport within the membrane is dueto two separate mechanisllls- diffusion and electro­osmotic drag. r,;jO =JJf +Jdr, where

ac:: .J'" --u ---!!J!!..+'-'- (13)1110- • dz ., §

If we assume the diffusion and drag coefficients (D",and~)are constant, the following model will arise.

de: Q a2c;; 0f =D.. ---i/.F (14)

ae:,o j~1'f/1o+Dm ----;r:--.., =Oatz=O (15)

aC;;lQ j~-D"'----;r:-+ ..,+J/'lO+rlJ,Q=Oatz=c. (16)

The flux of water entering the membrane from the gaschambers is

2.3. Membrane Hydration Model

i'tt,o ""pli [CJ,10-t-"] (17)

JH10 k'"pli [CH1o-c-] (t8)

where C = d... [(p....p(P)/RP)] and d,.. satisfies the gas /mcmbrane C<Juilibrium relation at thc chamber intcr­faces, dctcnmned by

N, (0.043+ 17.81a::. +39.S5(a::.)2 +36.0(a::Y) = q;,ol~-o(19)

N, (0.043 + 17.81<. + 39.85(<<,;.)2 + 36.0«<,;.)3) = C;;zol~_.J20)

Figure 2 illustrates typical water content profiles,all at stcady statc and a solid tempcraturcof800C. At thelow power condition, we see that diffusion dominates(indicated by the nearly horizontal profile). However,at the higher power condition we St-."C the combined ef­fect of water generation on the cathode side along witheleclro-osmutic dr.tg. also Iowaruthe calhode side.

Figure 2. Typical water content profiles.

(7)

(8)

(6)

(I)

(S)

(2)

(3)

(4)

(11)

~T,~-F[TC+ (UA)~ (T'-r)CisCp.ir

+(rozr -.!ftzoT')A../Cis

F; + (ro, - JI/zo)A./Cir

F;C/110~ - Ff'Cj/zo -J/izoA",

F;r: - I'fT" + (U~)d (1" - T")C~Cpir

+(rll, T" -1'/11oT")A"/C;r

":+ (rHz - J/11o)A./Cir

E",II = EM' - E..-l:.-E""

In the anode chamber:

dC'J,v·f

dC'ft 0VdfdP

v· tiI

The cell voltage is the ideal losses

2.1. Material and Energy Balances

in the calhodc chamber:

de;," ---"'­C d,

de;, 0"--'­C d,

dFV~tiI

At the solid material and coolingjackct:

Thc heal generation teml Q~ is the amount of heat pro­duced by the electrochemical reaction, given by Q,.,. =(AH/.llzO)rH10- P" where P~ = jE",I/'

2.2. Electrochemical Model

(UA),,(T" - T') + (UA)c(r - T')

I (UA)j(Ti - T') 1 (UA),(T'" - T')

-(rlJ,r'+rozr -J//10 r'

-J'lloT')AmCpir+Qg,.A.. (10)

, .E_ = E" + (NT(') /fl"')ln(PII,P~/PlljO) IS the Nemst poten-tial. The activation loss is E.. = (l/a)(RT(') /n§)I,,(jjj,,),

where j" = t:(CfJ,IC'/J,V is the exchange current density...The ohmic loss is EoJun '" jA",!Ii, wherc !Ii '" f dz/a(:.).,a(:.) =0.005193A(:,) - 0.00326exp( 1269.0( 1/303 - I/T)). A(:') =C:,o(z)/N. and e:,o(:') is the membrane hydration levelwithin the membrane (defined in the next section). &.. isthe membrane thick.ness (:. = 0 is anode side and z = &.is the cathode side). Thc mass transfer loss is E_ =(1/2+ ria) (RT(') /nY)/,,(h./UI. - i»), where h. = 2nYk'"l'i'C"O:!

is the limiting current density. The mass transfer coef­ficient across the GDL is ~l'il = V'~"slO~, where O~, is thethickness of the GDL. o'gd/ = £1.50.1775(T/273.15) I.lill. £i isthe GDL vuid fr.action and i =cora.

2649

90,--------------,3<100

600600

,,,,

200 300 400Time (se<:onds)

100

,,,r--~',

" ,,----~

,[5:J---~..) I,

,

,,o.

..- 0.45o~; O.~

.::' 0.3~

~ 0.3

i"- 0.2

o.

~ F;,F.:lip)

I Eff/{ IpE!\IF"CL

P,~ I PI _.

I PI I J

p/"'}

P (sp)F,,~ ,F,,·

...:.... Power Ecell

ControllerPoj PEMFC

T. ('PJ I Isol -" r-IPI

I fjac T,

Figure 3. Power I Temperature Control Loops

(21)

Figure 4. Response to Power Increases

'------,IOO=----,'''00,-----=300=----,..,=----,6OO=--6OiITIme (seconds)

600'00

.......... ..........

200 300 400Time (sccond§)

........

100

,,, ....... ~--.

75

I'

12

·• 10•at 8"0•, ,~

,where Api = ¢Nf1iois the surface area available for wa­ter evaporation from the GDL. The flux of liquid waterbeing ejected from the membrane is given by 1ft = Kit.

m.uIO.(Q;,o/N.-14)]. To complete the flooding modelwe need only subtract J11 from the left side of (16).Fo,lJf,/fJ,Kfl and N;;t are parameters of the COL to bedetenninL'd elnpirically.

In the event of flooding (0::, <::: I) , the mass transfercoefficient at the cathode. ~I' is modified to

.l!gJl = (LYgdtl8~1)[1 - Fo~_(p((N:.llo !N';/O - 1)/tI')]

where Fo, and If! arc porosity and anti flooding coeffi­cients, N;lf is amount of water prescnt in the GDL andN;:t is the maximum the GDL can hold. The amount ofwater in thc GDL is given by:

J dN'iJ~o •- -- =J/l-Agdlk'"gJl*(C' -G'ty,)A.. ((I -

3. Temperature Control

Using the feedback struclUre of figure 3, we simu­late the fuel cell responses to increasing and decreasingstep changes in the power set-point. Consider the 10­200 second interval of figure 4. The increase in powercauses the solid temperature 10 increase, which causesIhe controller to increase jackctllow, and thus bring thetemperature back to scI-point.

This retum to the sct-point causes the water re­moval driving forces to remain aboul constant, whichresults in a nel inL'TCasc in water cunlent wilhin the

membrane, due to increased generation and elcctro­osmotic drag. In the second two intervals (200 - 450and450-600 seconds), similar responses arc observed, withthe exception of the flooding event at about 600 sec­onds, which results in the unstable behavior observed.

In figure 5, the opposite responses occur. Althoughthe cell is not expected 10 fail, the Fairly low hydrationlevel within the membrane (and thus low ionic conduc­tivity) suggests faifty inefficient operation. It is alsonoted that the c1oscd-loop settling time with respect totell1pt:r.lturc is around 50 seconds, and Ihe upen-loop

2650

,.,

,.,, .', .. ', ...

I."-----' ..

" ,-----------,-~-~-~-...,............., •• ,;;c",;;;.c-"1

,,t:=':OO==200~---'-JOOC"c-c..c----'-JOOC"c-J""•

, --',- - - rl....

,

,

5

::..,". ,.i

1! 0.1

Figure 5. Response to Power Decreases

'00 ""

.'. .... .............. ,.... ,

,, , ,"'--------

100 200 300 400'.

E .~ 6

~f----,, '"

4. In addition to an increase in average water con­tent, we sce an increasc in the slope. From an ohmicloss/efficiency perspective, the ideal profile has zeroslope and is just below the flooding condition ).=14.This brings us to a fundamental question: Does thereexist a set of manipulated variables that can influencethe position and slope of Ihe hydration profile?

To address this question we identified a number po­tential manipulations. These include: anode bubblertemperature, cathode bubbler temperature, and the solidsclpoim temperature. In the step tests to follow we im­pose a constant current condition U=O.2 Ncm2) so asto decouple the reaction rate and ionic conductivity re­lationship.

In figure 6, an increase in anode bubbler tempera­ture (from 86uC 10 90"C) not only increases the averagewater content, it also n..>duccs the !\lope. Since it is as­sumed that gas leaving the bubbler is saturated, an in­crease in bubbler temperature has the effect of increas­ing gas water content at the anode inlet. This eausesan increase in the flux of water from the anode gas toanode side of the membrane. The net effect is a liftingof the anode side water content which also serves to in­crease the average. It should be noted that an increasein bubblef tempcfature will increase the inlet and thusanode gas temperature, which will decrease the waternux driving force. Basel! on the simulation results, this

Figure 6. Step responses due to anode bubblertemperature (upper plot, 86QC to 900C, lowerplot, 86"C to 82"C )

'00

400100 200 300Tlm~ (uwnds)

100 200 300Time (Iifl<:ond~)

"

',-----r===c=o==;]}.(O)

....... ,J,fJ_n)

- - -,J,fJ_)

4. Manipulation of the Hydration Profile

,.. -------,'. .I, \,_. •

76 ,:-----,'OO;;c------:,OOO,---C,:::OO,----"'7.'Time (~econd~l

settling time for membrane hydration is around 200 sec­onds.

"'------'1::::'='T*=;(l

As indicated in the previous section. changes inpower output will dramatically influence the water con­lent profile within the membrane. The first concern isaverage waleI' content. At high power, the average in­creases, while al low it decreases. Both of these condi­lions have detrimental results, flooding in the fitSt caseand dehydralion in the second. The second concern isprofile shape. Cunsider the high power case of figure

2651

----- .."

~ 7

l~ 6.S ." .

.: ,

"--­ --------

.... , ..... " ..

8,-------------,

•1 •

U~ , ,'

o .... ' ...LI-----. '. --------I """"

"

.,--------------,

---------- -- - - --'

"~~~So 100 200 JOG 400 SOO 600

------...... ,

,­,,-----, ..'

"~ 10

~ ')

~ 8," ,,

,ot==:'~OO;=:2~OO~.JOO;;;---;""""-"JOO.---d'"

3O\---;'~OO'-2~OO.--;JOO;;;---;"'';;O-''soo;;;---.i,'"

",------------,

•

.......... , .............., .........•....

]l:! 7;,"

'~~5~ 200 300 400 SOO 600

Figure 7. Step responses due to cathode bub·bier temperature (upper plot. 40°C to 50'-'C.lower plot, 40"C to 30"C)

Figure 8. Step responses due to set·point tem·perature (upper plot, 80"C to 70"C, lower plot,8O"C to 90"C)

change has a much smaller impact compared to the wa­ter content of the gas.

Concerning the cathode bubbler (figure 7), the im­pact is much less dramatic and the gain is of oppositesign. We allribute this to the larger impact of chang­ing inlet gas temperature verses that of water content.In essence the two competing effects of bubbler tem­per.tture almost caned each other at the cathode. Thisstronger impact of inlet gas temperature at the cathodeis due 10 the larger cathode gas flow which results inmore influence on gas temperature within the chamber.

Changes to the solid temperature set-point will im­pact the average membrane water content, but will leavethe slope essentially unchanged (see figure 8). Thisstems from the fact that the gas temperature in bothchambers will be influenced equally. Tllus, the waterflux driving force will be impacted equally on both sidesof the membrane.

Summarizing the step responses, we find that theanode bubbler temperature can decrease slope, but willalso increase average membrane water content. Thecathode bubbler temperature can also change averagewater content, but docs so at a much smaller gain andhas little impact on slope. Finally, solid temperaturehas a strong influence on average water content with al­most no change to the slope. This suggests the follow­ing upen-loop control scheme; simultaneously increase

13 • , I"~~~~;~~~~~~~~~~

- 12 ,~,

! 11

i 10 ..•..•....•....•....

" .,-----'70O-~,COO~c200=-300=-"'=-csoo~--7soo-

Figure 9. Combined anode bubbler and set­point temperature increase

anode bubbler tcmperature (to flattcn slope). while de­creasing solid temperature (to Slay out of the floodingregime). Figure 9 shows such simulation.

5. Conclusions

Clearly this is only a portion of the puzzle. Be­fore one can close the loop, a suitable set of measure­ments (capable ofinfening the hydration profile) wouldneed to be identified. Such a measurement scheme willlikely include a combination of online impedance spec­troscopy (to measure ionic resistance and infer averagewater in the membrane) along wilh a IIH.xlcl based Slale

2652

estimator, driven by more traditional measurements oftemperature, relative humidity and gas now rales. Anadditional complication is the along thc channel com­ponent of the fuel cell. Clearly, the conclusions of thisCSTR based sludy would need to be revalidated withinsuch a configuration.

6. Acknowledgements

This work was supported by the Department ofChemical and Biological Engineering and the GraduateCollege at the Illinois Institute of Tl.-chnology.

7. Notation

References

III Larminie. L and A Dicl.:s. Fuel Ctll S)'$relll$ £.lp/ailltd. 2nded. We.~l Sussex: John Wiley & Son!>. 2003.

[21 O·Hayre. R.• S-W. Chao W. Colella. and F. Prinz. FIltl CellFUI/(UlmCll/als. New Ym: John Wiley & Sons. 2006.

[3] Springer. T.E.. T.A. Z1wodzinski. ~nd S. Gouesfeld. "Polyn>erElectrolyle Flk'i Cell Model." Journal of EI~'nxhe",ica/SQ­citly 138 (1991):2334-2342

[4] zawod7..inksi. TA., J Davey. J. V~lerio. and S. Gouesfeld'The Water Comem Dependence of Elt:ctro-oslHOIic Drngin PrOIon-Conducting Polymer Electrolytes." Elcc/rochimicaAcra40 (1995):297-302.

[51 Weber. A.Z.. and J. Newman. 'Transport in Polymer­Electrolyle Membranes:' Joumal of The EleclnxhemicaJ SQ­dny 151 (2()()4):A311-A325.

super­a,c,j,eS,1II

CT

FO,F]rH2,razAV

AU

Cig

Cp.ig

N.Qgell

JEcruI1Hj.H20

"aJ.J~

CO,r!IfaOm

~d/F.

'I'Jf'KflN H20

r/'N 2°·1110.1",d<

and sub-scriptsanode, cathode, jacket, ambient gassolids, membrane

Concentrations(mollcm3)Ternpcralure(K)Inlet and Outlet F1ows(cm3/s)Reaction rale of Hydrogen, OxygenArea(cm2)Volume(cmJ)

Water Profile in MembraneHeat Exchanger Coef.(J/s-cm2-K)Ideal Gas Concentration(mo]lcmJ )

Ideal Gas Heat Capacity(J/mol-K)Number of Sulfonic Sites(mol/cmJ)

Heat GenerationCurrent Density(Alcm2)Voltage of Fuel Ccll(V)Heat of Formation of Water(J/mol)No. of electrons transferred in reactionCharge transfer coefficientExchange current densityExchange current density

at reference concentrationReference ConcentrationActivityeoefficienlResistance of MembraneConductivity in MembraneMembrane diffusion CoefficientDiffusion constant across GDLEmpirical Parameter for GDLEmpirical Parameter for GDLFlux of liquid ejected from MembraneEmpirical Parameter for GDL

Mo]es of Water in GDL

Maximum Moles of Water in GDL

2653

[61 Weber. A.Z., and J. Newman. "Modeling Transport inPolYlHer-Electrolyle Fuel Cells." Amuicall Chemical Soci..,)'104 {20(4):4679-4726.

[71 Chen. F..H.S. Chu. c.Y. Soong, and W.M. Yan. "EffectiveSchemes 10 Cootrollhe Dynamic Bellavior of lhe WmerTrans­ron in the Membrane of PEM Fuel Cell." Joumal of Po"'erSollrces 140 (2005):243- 249.

[8] Pul.:rushpan, J.T.. A.G SlefanopoulOll, and H. Peng. Control ofFuel Cell Ptm'er SJJlems: PlillCipleJ, Modeling. AmllJJi$ andFudback IHsign. London: Springer-Verlag, 2004.

[9] Lauzzc. Ke.. DJ. Chmielewski. "Power Coolrol of a Poly­mer Electrolyle Membrane Fuel Cell." fndus/rial & Ellgineer.illS Chtmi.flry Ruearr:h 45 {2(06):4661--4670.

[10] Golben. J., D.R. Lewin. "Model-Based Control of Fuel Cells(2): Optimal Efficieocy:' Joumal of I'ower SOlfrets 173(2007):298-309.

[II] Melhcbr, R.N., V. Pra'iad. and R.D. Gudi. "Dynamic Analy­sis and Linear Comrol Slrategies for Prolon Exchange Mem­brane Fuel Cell using a Distributed Parameler Model" JoumolojPower SOllrces 165 (2007): 152-170.

[12] Yang. Y.. F.e. Wang, H.P. Chang. Y.W. Ma. and B.J. Weng."Low Power PrOIon Exchange Membrane Fuel Cell Systemldentificmioo and Adaptive Comrol:' JOllrnal ofPower SQlIrces164 (2007):761-771.

[131 Zenith. F. COll/ral ofFIlei Cells. Dis,,- Norwegian Univ. of Sci­ence and Technology, 2007. Trondheim: NTNU-Tryl.:l.:.2OO7.

[141 Zhang. L.. M. Pan. and S. Quan. "Model predictive conlrol of

water managemenl in PEMFe." Jou",al of I'ower SOllrCts ISO

(2008):322-329.