Design and Analysis of Distributed Feed Solid Oxide Fuel ...

Department of Chemical and Environmental Engineering

Illinois Institute of Technology

Design and Analysis of Distributed

Feed Solid Oxide Fuel Cell Stacks

Donald Chmielewski

Ayman M. Al-Qattan

Presented at Argonne National Laboratory

January 21st, 2004


Illinois Institute of Technology 2

Outline

Motivation

Hydrogen Fed Case

Internal Reforming

Multi-Dimensional Analysis

Conclusions



Tubular Design SOFC

Fuel

Anode

Electrolyte

Cathode

Interconnect

Air

Air

Cathode

2 O=

V

-

+

Solid

Electrolyte

Anode

2H2

2H2O

O2+ 4 e- 2 O=

2H2+ 2 O= 2 H

2O +4 e-

O2

4 e-

4 e-

Heat



Flat-Plate Hydrogen Fed SOFC

Fuel Cell Stack

Anode

Flow

Cathode

Flow

Cathode

2 O=

V

-

+

Solid

Electrolyte

Anode

2H2

2H2O

O2+ 4 e- 2 O=

2H2+ 2 O= 2 H

2O +4 e-

O2

4 e-

4 e-

HEATRELEASED



Planar Design Characteristics

Advantages:

• Shorter current path => Lower ohmic loss

• Lower fabrication cost

Disadvantages

• Expensive seals

• Susceptible to thermal stresses

=> Shorter life-span



Review of SOFC Electrochemistry

OHOH 2221

2

OH

HH

C

CTTr

2

2

2ln)()(

Electrochemical Reaction:

Heat Generation:

FF

nhrjljGHn

jQ Hii 2

)()( 2

Reaction Rate:



Flow Configurations

Air Channel

Fuel Channel

InterconnectCathode

Anode

Electrolyte

Fuel

Flow

Air Flow



Plug Flow Reactor Analogy

Feed Exhaust

Reaction

Rate

Conventional Design



Figure taken from Selimovic Dissertation, Lund University, (2002).

Thermal Stresses in the Literature

Peters et al., state that

“ 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 that

“ … the internal stress would cause cracks or destruction of the electrolytes”



Fuel Cell Stack

Air Channel

Fuel Channel

InterconnectCathode

Anode

Electrolyte

Internal Reforming SOFC

CH4

Air Flow

H2O

CO2

H2 H

2O

O=

Fuel Flow

O2



Internal Reforming

44224 3 CHrefCH

kCkrHCOOHCH ref

eq

COH

COOHfshiftCO

k

K

CCCCkrHCOOHCO fshift 22

22

,

,222

is very large Endothermic

is also large Exothermic fshiftk ,

refk

2

1222

2 OHOH Hr Exothermic



Clarke et al, (1997) claim: “Internal reforming

offers:

• Reduced System Cost (reforming unit eliminated).

• Less Steam Required (anode reaction makes steam).

• More Uniform Temperature Distribution.

• Higher Conversions (equilibrium limiting products

consumed by the other reaction).”

The Promise of Internal Reforming



Figure taken from Selimovic Dissertation, Lund University, (2002).

Impact of Internal Reforming



Plug Flow Reactor Analogy (Internal Reforming)

ReformingReaction Rate

Reforming HeatGeneration

ElectrochemicalReaction Rate

ElectrochemicalHeat Generation

Combined HeatGeneration



Effective Structure of IR SOFC

• Heat and steam produced not used by reforming.

• Pre-heating steam is expensive.

• Steam in the feed lowers hydrogen utilization (reaction rate is a function of hydrogen to steam ratio).

ElectrochemicalSection

ReformingSection

Pre-Heater

222

224 3

COHOHCO

COHOHCH

OHOH 22

Methane

Steam



Additional Impacts of Non-Uniformity

• Electrolyte under-utilized at

low temperatures

• Hot-spots force the use of

more expensive high

temperature tolerant materials

• Large temperature range

restrict operational window



Exhaust

Feed

Feed

Distributed Feed Plug Flow Reactors

Distributed Feed Design

• Makes PFR act like a CSTR.

• Improves Yield and Selectivity.

• Improves Thermal Management.



Material Balance

Fz+ d z

, Tz+ d z

, vz+ d z

CH( ), C

H O( )z+d z

2z+d z

2

h

d z

Anode Channel

w

Fz , T

z , v

z, C

H (z),C

H O

(z)2 2

,F̂OHH CC

22

ˆ,ˆ,T̂

Control Volume

Side Feed Variables



Isothermal Model

22

2

22

2

ˆ)(

ˆ)(

HOHs

OH

HHs

H

s

rCfdV

FCd

rCfdV

FCd

fdV

dF

General Model:

channel. cell fuel the in rate flow Volumetric

feed.d distribute the in species of ionConcentrat

volumereactor per flowfeed d Distribute

:

:ˆ

).sec(: 313

F

iC

mmf

i

s

)()(

ln)()(

2

2

2

2

2

ii

H

OH

H

H

ljGHn

jQ

nhrj

C

CTTr

F

F

Rate Equations:



Achieving Uniform Heat Generation

OH

H

H

H

ii

C

CTTr

nhrj

ljGHn

jQ

2

2

2

2

ln)()(

)()( 2

F

F

QC

C

OH

H Constant Constant : HSR

2

2



Isothermal Design of

Distributed Feed Flow Rates

Define:

Set

This is achieved if

sp )(

)()(

2

2

zC

zCz

OH

H

Constant )ln( 02

spHrdz

d

)ˆˆ(

)]ln()[1(

22

*

spOHH

spsp

ssCC

ff

sp )0(

and = the desired HSR



Energy Model

)(

)ˆ(ˆˆ)(

)()(0

cschc

ccc

aaaasaha

aa

asahcsch

TTwhddz

dTCpCF

TTCpCFTTwhddz

dTCpFC

TThdTThdQw

Interconnect

Ta(z)

Tc(z)

ha

Q(z), Ts(z)

hc

d z

Anode

Cathode

Electrolyte

Adiabatic Wall

Fuel

z

Air



Hydrogen to Steam Ratio

Conventional vs. Side Feed



Electrolyte Temperature

Conventional vs. Side Feed



Continuous vs. Discrete

Fuel Injection

Exhaust

Feed L1

L2

L3

L4

F1

F2

F3

F4

F5

A

Exhaust

Feed

Feed



Hydrogen Fed Simulations

Hydrogen to Steam Ratio




Solid Temperature Profile




Fuel Temperature Profile




Air Temperature Profile



Variations in Air Side Flow Rate

Case 1:

Fuel to Air Flow Rate Ratio = 1:5000

Case 2:


Case 3:




Impact of Reducing Air Flow Rate

Fuel to Air Ratio 1:5000 Fuel to Air Ratio 1:50

Solid Temperature



Further Reduction in Air Flow Rate


Solid Temperature



Impact of Reducing Air Flow Rate

Air Gas Temperature




Impact of Injection Point Location

Exhaust

Feed L1

L2

L3

L4

F1

F2

F3

F4

F5

A




Solid Temperature at Fuel to Air Ratio of 1:5000



Full Energy Model

)(

)ˆ(ˆˆ)(

)()(2

2

cschc

ccc

aaaasaha

aa

asahcschs

s

TTwhddz

dTCpCF

TTCpCFTTwhddz

dTCpFC

TThdTThdQwdz

Tdak

Interconnect

Ta(z)

Tc(z)

ha

Q(z), Ts(z)

hc

d z

Anode

Cathode

Electrolyte

Adiabatic Wall

Fuel

z

Air

Solid Temperature

Boundary Conditions:

Zero Heat Flux at z = o and z = L



Impact of Heat Conduction Term


Without Conduction With Conduction



Fuel Utilization in the

Hydrogen Fed Case

inH

outHinH

C

CCU

,

,,

2

22

Changes in utilization achieved by variations in fuel feed flow rate



Summary of the Hydrogen Fed Case

• Continuous distributed feed will mitigated

temperature non-uniformity.

• Discrete injection and air side convection

will reduce uniformity.

• Utilization also impacted.



Internal Reforming SOFC

• Heat and steam produced not used by reforming.

• Pre-heating steam is expensive.

• Steam in the feed lowers hydrogen utilization (reaction rate is a function of hydrogen to steam ratio).

ElectrochemicalSection

ReformingSection

Pre-Heater

222

224 3

COHOHCO

COHOHCH

OHOH 22

Methane

Steam



Methane Fed Design Equations

22

2

24

2242

2

2242

2

44

4

4

ˆ)(

ˆ)(

ˆ)(

3ˆ)(

ˆ)(

2

COCOs

CO

COCHCOsCO

HCOCHOHs

OH

HCOCHHs

H

CHCHs

CH

CHs

rCfdV

FCd

rrCfdV

FCd

rrrCfdV

FCd

rrrCfdV

FCd

rCfdV

FCd

rC

fdV

dF

General Model:

)(

)(

ln )()(

2

,

2

2

22

22

44

2

2

2

iiHii

H

eq

COH

COOHfshiftCO

CHrefCH

OH

H

H

ljrSTrHQ

nhrj

K

CCCCkr

Ckr

C

CTTr

F

Rate Equations:



Carbon Deposition

OH

CHCO

C

CCCMMSR

OHCHCO

OHCHCO

COCCO

HCCH

2

4

222

22

2

24

22

2

2

CMMSR is a suggested measure for the risk of carbon deposition under SOFC operating conditions.

If CMMSR > 1: Carbon deposition risk

CMMSR < 1: No risk of carbon deposition



Methane Fed Design Scheme

Again define:

And set

This is achieved if

Constant )ln(02

spHrdz

d

)ˆˆ)(1()ˆˆ)((

)432()]ln()[1)((

222

*

4

2

*

spCOCOeqspspOHHeqsp

CHeqspeqspspspspeqsp

sCCKCCK

rKKKf

sp )0(

sp )(

)()(

2

2

zC

zCz

OH

H and = the desired HSR



Internal Reforming

Simulation Scenarios

Fuel to air flow rate ratio = 1:100

Inlet steam to carbon ratio (SCR)

Case 1: Conventional stack, inlet SCR = 2:1

Case 2: Conventional stack, inlet SCR = 1:1

Case 3: Distributed feed design, inlet SCR = 1:2

Case 4: Discrete injection, inlet SCR = 1:2

inCHinOH CC ,, 42:



Non-Isothermal Simulation of the

Internal Reforming Case



Non-Isothermal Simulation of the




Impact of Fuel Flow Rate

Fuel LHV Rate 3.28 J/sec Fuel LHV Rate 4.1 J/sec




Impact of Fuel Flow Rate

Fuel LHV Rate 3.28 J/sec Fuel LHV Rate 4.1 J/sec

CMMSR at Fuel to Air Ratio of 1:100



Impact of Air Flow Rate



Utilization in the


inHout

inCHout

outHout

outCHout

CFCF

CFCFU

24

24

4

41



Measures of Efficiency

StackFuel Feed

Power

Ko1195

(a)

Stack

Fuel FeedPower

Steam Feed

preH

Ko298

Ko1195

(b)

Stack

Power

Fuel

Exhaust

Burner

Fuel Feed

Steam Feed

Ko298

Ko1195

Ko373netH

(c)



Conventional Efficiency

LHV

Pe1inHout

inCHout

outHout

outCHout

CFCF

CFCFU

24

24

4

41



Modified Stack Efficiency

pre

e

HLHV

P

2

LHV

Pe1



System Efficiency

pre

e

HLHV

P

2

LHV

HHP preposte )(45.03



Summary of Internal Reforming Case

• Greater uniformity in temperature is

achieved.

• Less steam is required for CO protection.

• Utilization and efficiency improved.



Two Dimensional Analysis

Air Channel

Fuel Channel

Interconnect Rib

y

xz

Cathode

Anode

Electrolyte



2-D Distributed Feed Design



2-D Distributed Feed Design

Side FeedChannels

z1 z

2z

3z

4z

5

Active Area WallInactive Area

zx

Section of a stack layer



Sizing of the By-Pass Streams

3,

2,,

,

*

8

ˆ

ni

niniini

isi

A

pFzP

LAfF

Exhaust

Feed L1

L2

L3

L4

F1

F2

F3

F4

F5

A

Hagen-Poiseuille Equation:



Isothermal Velocity Profile for

Hydrogen Fed DFSOFC Stack



Isothermal Concentration Profile

Hydrogen Fed DFSOFC



Mixing Issues

0.08 0.09 0.1

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

Length (m)

Wid

th (

m)

Surface: Concentraion Arrow: [x velocity (u),y velocity (v)]

5

5.5

6

6.5

7

7.5

8

8.5

9Max: 9

Min: 5



Alternative Design



Isothermal Velocity Profile for




Isothermal Concentration Profile for




Mixing Issues

Concentration peaks at injection points could

cause high stress or carbon deposition regions.

Side FeedChannels

Hot Active Area

Wall

Cold Inactive Area



Summary

• Distributed feed design successfully mitigated

temperature non-uniformity.

• Utilization and efficiency was greatly improved

in the internal reforming case.

• 2-D simulations indicate that static mixers are

required to distribute fuel radially.



Acknowledgement

• Kuwait Institute for Scientific Research.

• Armour College of Engineering, IIT.

• Dr. Said Al-Hallaj and Dr. J. Robert Selman.

• Ali Zenfour, Nawwaf Al-Oraior

• Process System Engineering Laboratory



Power Load Transition Dynamics

How does the stack get from one operating point to

another?



Sensitivity Analysis

0.00E+00

5.00E-07

1.00E-06

1.50E-06

2.00E-06

2.50E-06

3.00E-06

3.50E-06

4.00E-06

800 900 1000 1100 1200

Temperature (K)

Reacti

on

Rate

(m

ol/

cm

2)

HSR = 0.1

HSR = 1

HSR = 10

Design and Analysis of Distributed Feed Solid Oxide Fuel ...

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