Kinetic SMR

8/11/2019 Kinetic SMR

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CACHE Modules on Energy in the Curriculum

Fuel Cells

Module Title: Simulation of a Methane Steam Reforming Reactor

Module Author: Jason Keith

Author Affiliation: Michigan Technological University

Course: Kinetics and Reaction Engineering

Text Reference: Fogler (4thedition) Sections 4!" 4!# 4!$

Literature References% J! &u and '! Froment AIChE J. 35 ## ($#$) J! &u and '!

FromentAIChE J. 35 $" ($#$) F! ! *! Fernandes and ! +! Soares ,at! m! --l!Res! 3!3".. (/001)!

Conce#ts% 2evelo- a numerical model to -redict the conversion and hydrogen yield

3ithin a steam reforming reactor!

$ro%lem Moti&ation:

Fuel cells are a -romising alternative energy conversion technology! ne ty-e of fuel cell

a -roton e5change mem6rane fuel cell (7EMF8) reacts hydrogen 3ith o5ygen to -roduce

electricity (Figure )! Fundamental to a hydrogen economy -o3ered 6y fuel cells is thegeneration of high -urity hydrogen!

8onsider the schematic of a com-ressed hydrogen tan9 (/000 -si regulated to 0 -si)

feeding a -roton e5change mem6rane fuel cell as seen in Figure / 6elo3! The focus ofthis module is hydrogen generation 6y steam reforming of methane to fill the com-ressed

tan9!

st2raft J!M! Keith cto6er 4 /00#

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:/tan9 Fuel 8ell

8om-uter

(Electric

,oad)

:/out

ir in

ir ; :/ out

Figure /! 2iagram for fueling a la-to-!

7ressure

regulator

:/feed line

H2

H2

H2

H2

H2

O2

O2

H+

e- e-

AnodeElectrolyte

Cathode

O2

H2O

H2O

O2

H+

H+

H+H2

H2

H2

H2

H2O

H2O

Figure ! Reactions in the 7EMF8


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'ac(ground

*atural gas has 6een -ro-osed as a source of hydrogen for fuel cell vehicle a--lications6ecause of the e5isting infrastructure! ? :/= 8 ()

:/= 8/ (/)

dding together the steam reforming and 3ater gas shift reactions gives the overall

reaction%

8:4= / :/ > 4 :/= 8/ (?)

The e@uili6rium constants can 6e e5-ressed in terms of -artial -ressures (in atm) and

tem-erature in degrees Kelvin as AJ! R! Rostru-B*ielsen and K! as6ergB7etersen CSteamReforming TR 7artial 5idationD 8atalysts and Reaction Engineering 8h! 4 of

Handbook of Fuel Cells: Fundamentals, Technology, and Applications ol ?! G!

ielstich ! ,amm :! ! 'asteiger eds! Giley /00?H! The su6scri-t on the follo3ing

e@uili6rium constants refers to the e@uation num6er given a6ove%

);/"014/!?0e5-(/4

?

/ T

!

"HCH

C"H

== (4)

);410"$#!?e5-(/

/// T

!

"HC"

C"H +== (.)

);?/11/#!?4e5-(/

/4

/

4

/

? T

!

"HCH

C"H == (1)


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)( ?4

$$d#

dFCH += 3ith

0

44 )0( CHCH F#F == (")

)/(?/

/$$$

d#

dF"H ++=

3ith

0

//

)0("H"H

F#F ==

(#)

)4?( ?//

$$$d#

dFH ++= 3ith 0// )0( HH F#F == ($)

)( / $$d#

dFC" = 3ith

0)0(C"C"

F#F == (0)

)( ?//

$$d#

dFC" += 3ith

0

// )0( C"C" F#F == ()

0=d#

dFHe 3ith

0)0(HeHe

F#F == (/)

The reaction rates are given 6y%

/

?

//4.!/

/

%E&

!

k

$

C"H

"HCH

H

= (?)

/

/

///

/

/

/%E&

!

k

$

C"H

"HC"

H

= (4)

/

?

/

4

//

/4.!?

/

?

?%E&

!

k

$

C"H

"HCH

H

= (.)

/

//

//44

H

"H"H

HHC"C"CHCH

!!!!%E& ++++=

(1)

Furthermore the coefficients in E@uations ?B1 are given 6y the rrhenius relationshi-sas%

);/4000e5-(0//!4 . $Tk = (")


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);1"?0e5-(0$1! 1

/ $Tk = (#)

);/4?$00e5-(00/! .? $Tk = ($)

);?#/#0e5-(01.!1 44 $T!CH=

(/0)

);##1#0e5-(0""! ./ $T! "H =

(/)

);#/$00e5-(0/!1 $/ $T!H= (//)

);"01.0e5-(0/?!# . $T!C"

= (/?)

*ote that in the a6ove e5-ressions$I #!?4 J;(molBK) is the gas constant!

The reaction stoichiometry suggests that the num6er of moles 3ill increase 3ith the

distance do3n the reactor! Thus for a negligi6le -ressure dro- in the reactor the gase5-ands 6y increasing the volumetric flo3 rate! The -artial -ressure of a chemical s-ecies

is calculated from the total -ressure and the num6er of moles of that s-ecies!

tot

i

i

F

F = (/4)


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Exam#le $ro%lem )tatement: 8onsider a feed of 0000 mol;h 8:4 0000 mol;h :/

and 00 mol;h :/to a steam reforming reactor that o-erates at 000 K and a atm feed

-ressure! 2etermine the molar flo3 rates of 8:4 :/ 8/ 8 and :/as a function ofcatalyst 3eight u- to ?#/ g! lso determine the overall methane conversion!

Exam#le $ro%lem )olution:'tep () numerical model can 6e made to simulate E@uations " / 3ith the coefficients

determined in e@uations 4 1 and ? /?! Using a sim-le Euler discretiation of the

e@uations 3e have%

)( ?44 $$#FF iCHiCH +=+ (/.)

)/( ?/4// $$$#FF i"Hi"H ++=+ (/1)

)4?( ?/// $$$#FF iHiH +++=+ (/")

)( / $$#FF iC"iC" +=+ (/#)

)( //// $$#FF iC"iC" ++=+ (/$)

iHeiHe FF

( =

+

(?0)

su6Lect to the initial conditions 00000/04 == "HCH FF mol;h and 000/ =HF mol;h!

The other chemicals have ero initial molar flo3s% 0000/ === HeC"C" FFF mol;h!

These e@uations can 6e solved iteratively until the end of the reactor is reached! The-rocedure is as follo3s%

) 8alculate the rate constants k k/ k? !8:4 !:/ !8 !:/ and use them tocom-ute the reaction rates $ $/ $?at the feed conditions (location 0 total

catalyst 3eight #I 0)!

/) 8alculate chemical flo3 rates (location catalyst 3eight I #) using E@uations

/. ?0!?) 8alculate the total and -artial -ressures using E@uation /4!

4) 8alculate the rate constants k k/ k? !8:4 !:/ !8 !:/ and use them to

com-ute the reaction rates $ $/ $?at the feed conditions (location total

catalyst 3eight #I #)!.) Re-eat ste-s /B4 as you -rogress do3n the length of the reactor!

The system is simulated using a ste- sie of #I 0! g! For more detail -lease see the

MT,+ code at the end of the e5am-le -ro6lem solution! -lot of the s-ecies molarflo3 rates as a function of catalyst 3eight is sho3n in Figure ? 6elo3! There are some

o6servations to 6e made from this -lot! First of all as there is no helium -resent in the

feed the molar flo3 rate is ero every3here in the reactor! Secondly 6oth the 8 and


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8:4are sho3n as solid lines! The molar flo3 rate of 8:4decreases 3ith catalyst 3eight

3hile the molar flo3 rate of 8 increases 3ith catalyst 3eight! Ge also note that if #

I0!0 g the results are nearly identical!

Figure ?! S-ecies molar flo3 rates as a function of catalyst 3eight!

'tep *) The e5it 8:4molar flo3 rate is a6out /400 mol;h! This corres-onds to a 8: 4conversion of%

M"10000

/4000000

04

404 =

=

=CH

e+itCHCH

F

FF, (/)

)ummary: fter a @uic9 change in the first g of catalyst (see the : / molar flo3 rate)there is a slo3 a--roach to3ards e@uili6rium in the reactor!

Matla% Code% Follo3ing is the Matla6 code for this e5am-le -ro6lem!

%% steam reforming plug ow model% includes water-gas shift reaction and overall reaction%% this is an isothermal model with no pressure drop!%


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% CH4 + H2O


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for i$#12,dw+#w'i+#($w'i(+dw%/#$e"p'*342*-2#*5,0'i((/2$e"p'-36+4#5*,0'i((/$e"p'432#-#255,0'i((

%/CH4$5357e-4.e"p'2*,3#4,0'i((/CO$32e-7.e"p'*57*,3#4,0'i((/H2$53#2e-6.e"p'26**,3#4,0'i((/H2O$#3e7.e"p'-5*,3#4,0'i((%8in#$43224e#7.e"p'-24*#**,3#4,0'i((8in2$#3677e5.e"p'-5#*,3#4,0'i((8in$#3*2*2e#7.e"p'-246**,3#4,0'i((%9:;$#+/CH4.f'i(+/CO.c'i(+/H2.d'i(+/H2O.'i(,d'i(r#$8in#,d'i(237,9:;2.'f'i(.'i(-d'i(.a'i(,/#(r2$8in2,d'i(,9:;2.'a'i(.'i(-d'i(.c'i(,/2(r$8in,d'i(37,9:;2.'f'i(.'i(2-d'i(4.c'i(,/(%)a'i+#($)a'i(+'r#-r2(.dw)'i+#($)'i(-')*,)f*(.'r#+r2+2.r(.dw)c'i+#($)c'i(+'r2+r(.dw)d'i+#($)d'i(+'.r#+r2+4.r(.dw)e'i+#($)e'i()f'i+#($)f'i(-'r#+r(.dw)tot$)a'i+#(+)'i+#(+)c'i+#(+)d'i+#(+)e'i+#(+)f'i+#(%a'i+#( $ tot*.)a'i+#(,)tot'i+#( $ tot*.)'i+#(,)totc'i+#( $ tot*.)c'i+#(,)totd'i+#( $ tot*.)d'i+#(,)tote'i+#( $ tot*.)e'i+#(,)totf'i+#( $ tot*.)f'i+#(,)tot%end%&gure'#(plot'w=)a(hold onplot'w=)=>r-->(plot'w=)c=>g-3>(plot'w=)d=>81>(plot'w=)e=>c>(plot'w=)f=>>(

"lael'>Catal?st @eight= g>(?lael'>Aolar )low Bate mol,hr>(legend'>CO>=>H2O>=>CO2>=>H2>=>He>=>CH4>(


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Home $ro%lem )tatement: 8onsider a feed of 0000 mol;h 8:4 and 00 mol;h :/to a

steam reforming reactor that o-erates at $00 K and a / atm feed -ressure!

a" 2etermine the molar flo3 rates of 8:4 :/ 8/ 8 and :/as a function of catalyst

3eight u- to ?#/ g for :/ feed flo3 rates of /0000 mol;h ?0000 mol;h 40000 mol!h!

For each 3ater molar flo3 feed rate determine the methane conversion and the e5ithydrogen molar flo3 rate!

%"

Kinetic SMR

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