9 fuel cell mass transport final version
TRANSCRIPT
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Fuel Cell Mass Transport
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Basic Operation
H2+1/2O2 = H2OH2 = 2H+ + 2e-
1/2O2 + 2H+ + 2e- = H2Ohttp://www.odec.ca/projects/2007/truo7j2/fuel_cell_small.JPG
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Concentration Lossor Mass Transport Loss
• Reactant/product concentrations � fuel cell performance
• Reactant/product concentrations within the catalyst layer, not the fuel cell inlet, matter
• Reactant depletion/product accumulation adversely affects performance
• Can be minimized by optimization of mass transport and flow structures
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• Transport in flow structure– mm ~ cm scale– convection
• Transport in fuel cell electrode structure– nm ~ µm scale– diffusion
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Diffusion Layer
• H2 concentration falls from the bulk value Co
H2into at the flow
channel to a much lower value C*
H2at the catalyst layer
http://pubs.acs.org/cen/img/83/i05/8305bus2fuel.gifhttp://www.directindustry.com/prod/tech-etch/fuel-cell-plate-30189-212422.html
H2H+
flow channelanode electrolyte
diffusion layerH
2co
ncen
trat
ion
CoH2
C*H2
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Convection vs. Diffusion
• Convection driven by the pressure we apply to introduce fuel or oxidant to the fuel cell
• Diffusion driven by the concentration difference which is developed by consumption of reactant species at the catalyst layer
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Convection vs. Diffusion• Boundary between the convective and diffusive flow is
around where the gas channel and porous electrode meet
• Gas channel � gas stream well mixed � no concentration gradients – the velocity of the moving gas stream tends toward zero at
the electrode-channel boundary
• Thickness of diffusion layer is not well defined and dependent on flow conditions, flow channel geometry or electrode structures– Extremely high gas velocity � convective mixing may
penetrate into the electrode– Very low gas velocity � diffusion layer may stretch out into
the middle of the flow channel
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Diffusive Transport
• Transport in electrode is based on diffusion
• Assumption– Electrode thickness = diffusion layer
thickness
• Electrochemical reaction drives the diffusion
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Mass Transport• Electrochemical reaction
leads to reactant depletion (and product accumulation) at the catalyst layer
• C*R < Co
R and C*P > Co
P– C*
R and C*P : reactant and
product concentration at the catalyst layer
– CoR and Co
P : bulk reactant and product concentration (flow channel)
• Concentration loss (or mass transport loss)– Nernstian Losses– Reaction Losses
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Concentration Loss(or mass transport loss)
• Nernstian Losses: reversible fuel cell voltage will decrease
• Reaction Losses: reaction rate (activation) losses will increase
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Reactant concentration & Current density
• j: current density (a measure of the electrochemical reaction rate)
• Jdiff: diffusion flux of reactants to the catalyst layer
• nF: conversion factor from molar diffusion flux into the current density
• Deff: effective reactant diffusivity (Deff = ετD) (pore structure)
• δ: electrode (diffusion layer) thickness
• C*R: catalyst layer reactant
concentration• C0
R: bulk reactant concentrationeffRR
RReff
RReff
diff
diff
diff
nFD
jCC
ccnFDj
ccDJ
dx
dcDJ
nFJj
δ
δ
δ
−=
−−=
−−=
−=
=
0*
0*
0*
Reactant concentration in the catalyst layer is less than the bulk concentration� Low current density ( j) � low concentration loss� Thin diffusion layer (δ) � low concentration loss� High effective diffusivity (Deff) � low concentration loss
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Flux
• Positive J means matter (or energy) flows towards positive z
• Matter flows from high to low concentration
ATKINS’ Physical Chemistry 8th Ed.
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Limiting Current Density• When the reactant concentration in the catalyst layer is zero �
limit maximum current density
• Mass transport design strategies– High C0
R (by designing good flow structures that evenly distribute reactants)
– Deff is large and δ is small (by carefully optimizing fuel cell operating conditions, electrode structure, and diffusion layer thickness)
• Typically– δ = 100 ~ 300 µm– Deff = 10-2 cm2/s– jL = 1 ~ 10 A/cm2
• Fuel cell will never be able to produce a higher current density than that determined by its limiting current density
δ
δ
Reff
L
effRR
CnFDj
nFD
jCC
0
0* 0
=
=−=
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Nernstian Loss
– ηconc: voltage loss due to reactant depletion in the catalyst layer– E0
Nernst: Nernst voltage using c0 values– E*
Nernst: Nernst voltage using c* values– C0
R: bulk reactant concentration– C*
R: catalyst layer reactant concentration
– (product accumulation is neglected)
R
R
RR
NernstNernstconc
R
P
C
C
nF
RT
CnF
RTE
CnF
RTE
EE
C
C
nF
RTEE
*
0
*
0
0
0
*0
0
ln
)1
ln()1
ln(
ln
=
−−−=
−=
−=
η
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Nernstian Loss
• This expression is valid only for j < jL
• For j << jL– concentration loss
will be minor
• For j � jL– concentration loss
will increase sharply
jj
j
nF
RT
C
C
nF
RT
jj
j
nFDjnFDj
nFDj
C
C
nFD
j
nFD
j
nFD
jCC
nFD
jC
CnFDj
L
Lconc
R
Rconc
L
L
effeff
L
eff
L
R
R
effeff
L
effRR
eff
LR
Reff
L
−=
=
−=
−=
−=
−=
=
=
ln
ln
//
/
*
0
*
0
0*
0
0
η
η
δδ
δ
δδ
δ
δ
δ
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Reaction Loss
• J00 is measured at the reference reactant and product concentration values C0*R
and C0*P
• J00 is exchange current density at “standard concentration”• C*
R and C*P are arbitrary concentrations
)eC
C- e
C
C( j = j
e j - e j = j
/RT)nF-(1-
*0
P
*
P /RTnF
*0
R
*
R0
0
/RT)nF--(1
0
/RTnF
0
actact
actact
ηαηα
ηαηα
*0
0
*0
ln
)
R
Ract
/RT nF
*0
R
*
R0
0
Cj
jC
nF
RT
eC
C( j =j act
αη
ηα
=
Butler-Volmer equation
• High current density region, the 2nd term in the Butler-Volmer equation drops out
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Reaction Loss
• η0act activation loss using c0
• η*act activation loss using c*
jj
j
jj
j
C
C
C
C
Cj
jC
Cj
jC
L
Lonc
L
L
R
R
R
R
R
R
R
R
actactonc
−=
−=
=
−=
−=
lnnF
RT
lnnF
RT
)lnnF
RT()ln
nF
RT(
c
*
*0
*
0
00
0
*0
*0
0
*0
0*
c
αη
α
αα
ηηη
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Concentration Loss
• Total concentration loss = Nernstian Loss + Reaction Loss
jj
jc
jj
j
nF
RT
jj
j
nF
RT
jj
j
nF
RT
L
Lconc
L
L
L
L
L
Lconc
−=
−+=
−+
−=
ln
ln)1
1)((
lnln
η
α
αη
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Summary
ηact = (aA + bB lnj) + (aA + bB lnj): activation losses from both the anode (A) and the cathode (C)
ηohmic = j ASR
ηconc = c ln[ jL/( jL – j)]
6 7 8
9
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Application of a small signal voltage perturbation confines the impedance measurement to
a pseudolinear portion of a fuel cell’s i-V curve
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Nyquist plot (Fuel Cell)
• Example Nyquist plot from a hypothetical fuel cell
• Relative size of the three regions ~ relative magnitude of the three losses
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Merging
In many fuel cells, cathode impedance is significantly larger than the
anode impedance
� RC loops for the cathode overwhelms the RC loop for the anode
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Equivalent Circuit
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EIS at Different Points
(a) low current density: activation kinetics dominate and R is large
(b) intermediate current, activation loops decrease since R decreases with increasing ηact
(c) high current density, activation loops may continue to decrease, but the mass transport effects begin to
intercede.