Model P edic i e Con ol o E hanol S eam
Re o me s wi h Memb ane Sepa a ion
Ma ia Se a, Ca los Ocampo-Ma inez, Mingming Li and Jo di Llo ca
Ins i u de Rob`
o ica i In o m`
a ica Indus ial (CSIC - UPC)
Uni e si a Poli `
ecnica de Ca alunya
Llo ens i A igas 4-6, 08028 Ba celona, Spain
Ins i u de T`
ecniques Ene g`
e iques
Uni e si a Poli `
ecnica de Ca alunya
Diagonal 647, Ed. ETSEIB, 08028 Ba celona, Spain
Abs ac
This pape ocuses on he dynamic modelling and he p edic i e con ol o an
e hanol s eam e o me (ESR) wi h Pd-Ag memb ane sepa a ion s age o he gen-
e a ion o pu e hyd ogen. Hyd ogen pu i y necessa y o eed a p o on exchange
memb ane uel cell (PEMFC) is equi ed. A non-linea dynamic model o he
ESR is de eloped oge he wi h a p ocedu e o adjus ing he model pa ame e s
in o de o i a bank o expe imen al da a o a eal ESR sys em. S a ic and dy-
namic analysis o he non-linea ESR model is p esen ed. F om his non-linea
model, a linea , educed o de and disc e ised model is de i ed and a model p e-
dic i e con olle (LMPC) is designed o he ESR sys em. Con ol objec i es a e
pu e hyd ogen low a e acking and e hanol inle minimiza ion. Compa isons be-
ween he non-linea and linea models a e ca ied ou o de e mine he con ol
cons ain s. Finally, simula ion esul s o he implemen ed LMPC con olle a e
p esen ed and discussed.
E hanol s eam e o me , s aged-sepa a ion memb ane eac o , con ol-o ien ed model,
linea model p edic i e con ol
1 In oduc ion
Nowadays hyd ogen has eme ged as an in e es ing ene gy ec o which may be used
o s o e ene gy om enewable sou ces. Th ough uel cells his hyd ogen may be con-
e ed in o elec ici y when necessa y a a high e iciency. Fo ins ance, uel cell e-
hicles ha e e iciencies mo e han wo imes highe han hose o combus ion engines.
The mos ma u e uel cell echnology, wi h a wide ange o applica ions, is PEMFC
1
[1]. Du abili y, eliabili y and e iciency o PEMFC a e signi ican ly imp o ed when
pu e hyd ogen is supplied o hem.
Due o i s physical p ope ies, hyd ogen is di icul o anspo and s o e, which
makes he echniques o in si u hyd ogen p oduc ion inc easingly in e es ing o many
applica ions. Hyd ogen can be ob ained om many di e en sou ces such as wa e ,
e hanol, na u al gas o o he ossil uels. Among hese sou ces, e hanol has been chosen
o gene a ing hyd ogen in he las decades o se e al ad an ages: high con en o
hyd ogen, easy po abili y and s o abili y, enewable na u e and low oxici y.
Nowadays, he e a e h ee common echniques o hyd ogen p oduc ion om e hanol:
s eam e o ming (SR), pa ial oxida ion (POX) and au o- he mal e o ming (ATR). The
bes o hese op ions is SR because o i s lowe ope a ing empe a u e and highe hy-
d ogen yield. Howe e , his echnique gene a es he highes emission o CO, which
can poison he anode ca alys o PEMFCs i he quan i y is mo e han 100 pa s pe
million (ppm). I high empe a u e PEMFC a e used, he ole ance o CO is highe , as
explained in [2], whe e he in eg a ion o an e hanol s eam e o me o a high empe -
a u e PEMFC is s udied. In any case, hyd ogen pu i ica ion is essen ial be o e eeding
PEMFCs.
Con en ional me hods o pu e hyd ogen gene a ion include wa e gas shi (WGS),
CO p e e en ial oxida ion (COP Ox), and p essu e-swing adso p ion (PSA), among
o he s. Addi ionally, memb ane sepa a ion echniques ha e al eady been applied o
ob ain pu e hyd ogen om he gas mix u e [3, 4, 5, 6]. Especially, palladium-based
memb anes ha e gained g ea in e es wi h mo e han 6000 scien i ic a icles [7] in-
ol ed since Juenke e al. [8] analysed he use o palladium memb anes o hyd ogen
pu i ica ion in 1955. The ema kable p og ess achie ed in he ield o palladium-based
memb ane eac o s (MRs) is due o hei comple e hyd ogen pe m-selec i i y wi h e-
spec o all o he gases [7]. Fu he mo e, only one hea ing uni is equi ed o bo h
he e o me s age and sepa a ion s age. In [9], an exe ge ic s udy o an e hanol s eam
e o me wi h a palladium-based memb ane has been p esen ed and he bes ope a ing
condi ions ega ding he exe ge ic and he mal e iciency ha e been de e mined.
The ca alys plays an impo an ole in he e hanol s eam e o ming (ESR) p o-
cess, since i can accele a e he eac ion a e and imp o e he pe o mance o he ESR.
Cobal -based ca alys s ha e been conside ed o be a sui able choice o hei low cos ,
high ac i i y and selec i i y [10, 11, 12], especially o he ESR o p oduce hyd ogen
a mode a e empe a u e [11, 13, 14]. Ca alys s se up is also a ele an issue. In [15],
ESR o hyd ogen gene a ion o e s uc u ed ca alys s is desc ibed based on di e en
expe imen al es s.
Dynamic modelling o ESRs wi h memb ane sepa a ion is e y limi ed. In [16], he
way o ob ain a con ol-o ien ed model om a dynamic simula ion-o ien ed model o
an ESR wi hou memb ane sepa a ion s age is p esen ed, while [5] p esen s he model
o a s aged-sepa a ion memb ane eac o o s eam e o ming o me hane. Only [17]
p esen s he modelling o he ESR wi h memb ane sepa a ion o he gene a ion o pu e
hyd ogen. In he pape , he ESR model is ob ained acco ding o he phenomenological
kine ic model wi h powe law [18] and expe imen al da a. On he o he hand, so a ,
he e ha e been e y ew wo ks in ol ed in o designing con olle s o ESR. In spi e o
he non-linea ESR na u e, linea con olle s a e designed in wo wo ks [19, 20] since
hey can yield a sa is ac o y pe o mance i he p ocess is ope a ed close o a nominal
2
ope a ing poin . Speci ically, in [20], a linea model p edic i e con olle (LMPC) is
designed o he ESR wi hou memb ane sepa a ion.
Model p edic i e con ol (MPC) is an ad anced s a egy o p ocess con ol ha has
been widely used in indus y and chemical p ocesses since he 1980s[21, 22]. The
MPC s a egy is a se o con ol me hodologies ha use a ma hema ical model o a
conside ed sys em o ob ain con ol ac ions h ough minimizing a cos unc ion ela ed
o selec ed con ol objec i es conside ing he desi ed sys em pe o mance.
MPC has p esen ed ob ious ad an ages o e o he me hods [21]: mul i-objec i es
easy o deal wi h he mul i- a iable sys em, eed- o wa d con ol been used in a na u-
al way o compensa e measu able dis u bances and bene icial o acking u u e e -
e ences. Howe e , he s a egy has also i s own d awbacks: i s uning, which is no
a gene al heo y ha can be implemen ed in a gene ic way, and he high compu a-
ional ime de i ed om he numbe o a iables and cons ain s, mainly in la ge-scale
sys em. In [20], an LMPC scheme has been p esen ed o an ESR p ocess wi hou
memb ane sepa a ion.
The main con ibu ion o his pape is o ob ain a dynamic model o an ESR wi h
memb ane sepa a ion and o use his model o design a LMPC able o ope a e he
sys em p ope ly a ound a nominal ope a ing poin .
The eminde o his pape is o ganized as ollows: Sec ion 2 gi es a b ie de-
sc ip ion o he ESR sys em wi h memb ane sepa a ion s udied in his wo k. Sec ion
3 i s ly p esen s he non-linea ma hema ical model o he ESR and secondly p esen s
he con ol-o ien ed model o he MPC con olle design. Sec ion 4 p esen s he MPC
design o he ESR, including he o mula ion o he co esponding op imiza ion p ob-
lem and he LMPC con olle con igu a ion wi h ou pu eedback. Sec ion 5 shows
and discusses he main simula ion esul s. Finally, he main conclusions a e d awn in
Sec ion 6.
2 Sys em desc ip ion
2.1 Expe imen al se up
Fo he pu pose o simpli ying he sys em se up, he p ocess o gene a ing hyd ogen
ia ESR and pu i ying hyd ogen using selec i e memb ane may be adop ed in a single
eac ion and sepa a ion module, named S aged-Sepa a ion Memb ane Reac o (SSMR)
[17]. In his pape , he ESR was conduc ed in o a SSMR using a cobal -based ca alys
o e co die i e monoli hs ha we e implemen ed in se ies in o a s ainless-s eel Pd-Ag
memb ane s age [23]. A scheme o he SSMR is shown in Figu e 1. The SSMR mod-
elled in his wo k co esponds o a eal labo a o y sys em wi h he ollowing cha ac e -
is ics: he eac ion-sepa a ion chambe measu es 230 mm high and 22 mm o ou side
diame e and has a lowe head o allow he exi o he sepa a ed s eams, which a e
e en a e and pe mea e s eams. A eed e apo a ion condui is used o e apo a e bo h
e hanol and wa e be o e en e ing he eac o . Fi e ca aly ic honeycomb pieces o 2
cm leng h each a e disposed in se ies in o he eac o ollowed by a Pd-Ag memb ane
ube. The ca aly ic honeycomb pieces a e loaded wi h a o al o 1.32 g o cobal -based
ca alys . The pine-hole ee and dead-end memb ane ube measu es 76 mm high, 1/8
3
inch diame e and a o al a ea o 7.1 cm2. The Pd-Ag ac i e laye is 30 µm hick o e
a po ous s ainless s eel suppo . The liquid mix u e o he e hanol and wa e a e ed
di ec ly om he s o age ank by a high-pe o mance liquid ch oma og aphy (HPLC)
pump. The e en a e p essu e is adjus ed and con olled by a manually-ope a ed back-
p essu e egula o and he pe mea e p essu e is main ained a a mosphe ic p essu e.
Figu e 1: S aged-sepa a ion memb ane eac o
The expe imen al da a used in his wo k was ob ained a di e en p essu es in
he ange 1 ba –14 ba , di e en empe a u es in he ange 500°C–600°Cand di e -
en s eam o ca bon (S/C) a ios. The s eam o ca bon a io is de ined as he numbe o
wa e molecules di ided by he numbe o ca bon a oms, and i is applied in his case
o he inle low a e mix u e o bo h e hanol and wa e . Also, wo se s o expe imen s
we e done in o de o cha ac e ise he beha iou o he sys em: expe imen s wi hou he
sepa a ion s age (wi hou memb ane) and expe imen s wi h he sepa a ion s age (wi h
memb ane). A ull-con e sion a e (100%) o e hanol and ace aldehyde we e measu ed
in he e o me s age.
4
Figu e 2: Scheme o he ESR
2.2 Chemical eac ion
The ESR eac ions o e cobal -based ca alys s a e exp essed as ollows [12, 24, 25]:
C2H5OH −−→ CH3CHO + H2,(1a)
C2H5OH −−→ CO + CH4+ H2,(1b)
CO + H2O−−*
)−− CO2+ H2,(1c)
CH3CHO + 3 H2O−−→ 2 CO2+ 5 H2.(1d)
These ou eac ions a e aking place in he same space and condi ions simul ane-
ously. Fi s ly, e hanol dehyd ogena es in o hyd ogen and ace aldehyde (1a), which is
u he e o med wi h wa e o ca bon dioxide (1d). In addi ion, cobal ca alys s a e
ac i e o he Wa e Gas Shi (WGS) eac ion (1c) unde ypical ope a ing condi ions.
The undesi ed eac ion is he e hanol decomposi ion o p oduce ca bon monoxide and
me hane (1b). In he memb ane sepa a ion s age, he Pd-Ag memb ane pe mea es only
he hyd ogen and lea es he was e gases in he e en a e side [26, 27]. Figu e 2 shows
a scheme o he p ocess wi h he wo s ages in se ies.
2.3 Ene gy s udy
An ene gy s udy has been done in o de o quan i y he global ene gy balance o he
SSMR desc ibed in Sec ion 2.1 a s eady s a e and o some speci ic ope a ing condi-
ions. In pa icula , 8 ba o p essu e, 813.15 K (540¨
ı¿½ C) o empe a u e, an inle wa-
e low o 0.0108 mol/min and an inle e hanol low o 0.0018 mol/min a e conside ed.
The ela ionship be ween hese wa e and e hanol inle lows is 6 o 1, o equi alen ly
S/C =3. The ene gy supplied is calcula ed aking in o accoun he powe necessa y
o apo ize and hea he eac an s o 813.15 K, he ene gy necessa y o p essu ize he
gases and he hea consumed by he eac ion. The ene gy o he hyd ogen p essu isa-
ion is no conside ed. The supplied ene gy esul s in 14.78 Wa s. On he o he hand,
o he selec ed ope a ing poin , 3.4 mols o hyd ogen a e ob ained om each mole
o e hanol in he e o ming s age and he e o e, he ou le hyd ogen low a e o m he
e o ming s age is 6.2 ×10−3mol/min. This low a e could be ans o med in o 29.5
Wa s o hea i combus ed (High Hea ing Value used o he calcula ion). Conside ing
he sepa a ion s age as well o he same ope a ing condi ions, he hyd ogen low a e in
he e en a e side is 4.65 ×10−3mol/min and he pu e hyd ogen low a e in he pe me-
a e side is 1.55 ×10−3mol/min. These low a es could be ans o med in o 22.15 Wa s
5

o hea and 3.57 Wa s o elec ici y, espec i ely, conside ing ha he pu e hyd ogen
eeds a PEM uel cell wi h a s oichiome y o 1.1 and 0.8 Vol s. This numbe s, co e-
sponding o he expe imen al se up desc ibed in Sec ion 2.1, could easily be imp o ed
i imp o ed designs we e conside ed.
3 Ma hema ical modelling
3.1 Main assump ions
In his pape , wo plug- low kind eac o s a e assumed o ep esen he dynamic beha -
io o he ESR wi h memb ane sepa a ion. The i s eac o is he e o me s age, and
he second is he memb ane sepa a ion s age. The main modelling assump ions a e:
• Iso he mal ope a ion condi ions wi hin each s age
• Isoba ic ope a ion condi ions assumed due o he high oid ac ion o monoli hic
s uc u es
• Comple ely mixed luid inside he plug- low eac o (PFR) in any c oss-sec ion
a any posi ion
• Neglec ed di usion e ms due o he p edominance o con ec ion ac ion o e
di usion ac ion
• Ideal gases due o he low ope a ing p essu e
• Fluid eloci y depending only on he axial posi ion
• 1D model due o he small diame e o he eac o
3.2 Mass balance o he e o me s age
The mole balance equa ion oge he wi h he ini ial and bounda y condi ions o he
plug low eac o model a e exp essed as [16]
∂Cj
∂ + Cj
∂υ
∂z +υ∂Cj
∂z =X
i
νj,i i,(2a)
Cj(0, z)=Cj,0(z),∀z∈[in, ou ](2b)
Cj( , 0) = Cj,in ( ),∀ > 0(2c)
i= 1,...,4,(2d)
j= 1,...,7,(2e)
whe e jdeno es he componen , which could be C2H5OH, H2O, CH4, CO, CO2,
CH3CHO o H2and ideno es he eac ion acco ding o (1a)-(1d). Mo o e , Cjis
he concen a ion o he j- h componen , iis he eac ion a e o eac ion i,υis he
linea eloci y o he gases, in is he se o inle condi ions while ou is he se o ou le
6
condi ions, νj,i is he s oichiome ic coe icien o componen jin eac ion iand zis
he axial posi ion a iable.
In o de o sol e he se o pa ial di e en ial equa ions (PDEs) p esen ed in (2a),
υand a e exp essed as unc ions o Cj. In he PFR wi h isoba ic and iso he mal con-
di ions, i is assumed ha υ a ies wi h ime and posi ion wi hin he eac o acco ding
o he ollowing exp essions [16]:
υ=υin (1 + εX),(3a)
X=1−Cj
Cj,in
1 + Cj
Cj,in
,(3b)
whe e Xis he con e sion a e o he e hanol while εis he mola ela ion o he
conside ed eac ion. Mo eo e , he olume ic low a e (Q) and mola low a e o he
di e en componen s (Fi), which a e assumed measu ed a iables o he con ol p ob-
lem, a e compu ed as
Q=A1υ, (4a)
Fj=QCj,(4b)
whe e A1is he sec ion a ea o he ubula eac o . Reac ion a es depend on concen-
a ion, empe a u e and p essu e. Acco ding o [18], he ollowing phenomenological
kine ics ha e been conside ed o he ou modeled eac ions:
1=k1(PC2H5OH)m(P),(5a)
2=k2PC2H5OH,(5b)
3=k3PCOPH2O−PCO2PH2
kW GS ,(5c)
4=k4PCH3CHOPH2O3,(5d)
ki=k∞,iexp −Ea,i 1
RT −1
RT e ,(5e)
kW GS =exp 4577.8
T−4.33,(5 )
m(P)=1.2+0.23(P−4),(5g)
whe e k∞,i a e he p e-exponen ial ac o s, ki he kine ic cons an s and Ea,i he ac i-
a ion ene gies o each eac ion. The e e ence empe a u e T e has been selec ed o
be 873.15 K, which is he highes empe a u e o he expe imen . Besides, m(P)is an
exponen ial ac o depending on p essu e and PC2H5OH,PCO,PH2O,PCO2,PCH3CHO
a e he pa ial p essu es o each componen .
3.3 Mass ans e o he memb ane sepa a ion s age
In his s age, he p ocess o he hyd ogen selec i e sepa a ion wi hou chemical eac-
ions akes place. A Pd-Ag me allic memb ane is used o pe mea e only he hyd ogen
7
lea ing he es o he gas on he e en a e side. The mass ans e mechanism can be
exp essed using he Sie e s’ law as [4]
JH2=Pe
δA2pPH2 e en a e −pPH2pe mea e,(6)
wi h Pe=Pe0·exp −Ea
RT ,(7)
whe e Peco esponds wi h he gas pe meabili y, Pe0is he p e-exponen ial ac o , Ris
he ideal gas cons an , Tis empe a u e, PH2 e en a e is he hyd ogen pa ial p essu e
in he e en a e side, PH2pe mea e is he hyd ogen pa ial p essu e in he pe mea e side,
Eais he appa en ac i a ion ene gy, A2is he su ace a ea o he memb ane and JH2
is he pe mea ing hyd ogen lux.
3.4 Spa ial disc e iza ion
Each s age is di ided in o 20 slices o smalle size and each slice is conside ed as a
con inuous s i ed ank eac o wi h homogeneous condi ions. Backwa d ini e di e -
ences a e applied o ans o m he PDEs in o o dina y di e en ial equa ions (ODEs),
which a e exp essed as
∂Cj
∂z ∼
=Cj(z)−Cj(z−1)
4z.(8)
3.5 Pa ame e s adjus men
The model pa ame e s ha e been adjus ed o sa is y a se o s a ic expe imen al da a.
Speci ically, he mola low a es o he di e en componen s Fiwe e collec ed. Pa-
ame e s o he e o me s age ha e been adjus ed using expe imen al da a ob ained
wi hou he sepa a ion s age. Once hese pa ame e s ha e been ixed, he pa ame e s
o he sepa a ion s age ha e been adjus ed using expe imen al da a ob ained wi h he
whole ( e o me s age plus sepa a ion s age) sys em. The p e-exponen ial ac o s and
ac i a ion ene gies in (5) we e adjus ed in o de ha all he e hanol and ace aldehyde
a e comple ely ans o med and he ou le mola low a es o he es o componen s
a e close o he expe imen al da a. Speci ically, he ollowing s eps we e ollowed o
i he eal da a:
• Fi s o all, adjus k∞,2and Ea,2 o i he quan i y o CH4, which is only p o-
duced in eac ion (1b)
• Then, adjus k∞,1and Ea,1 o ensu e ha he whole con e sion o e hanol is
100%
• Then, adjus k∞,4and Ea,4 o ensu e ha he con e sion o ace aldehyde is 100%
• Finally, adjus k∞,3and Ea,3acco ding o he quan i y o H2 om he expe i-
men al da a.
8
Fo each k∞,i-Ea,i pai , k∞,i was i s adjus ed a T=T e and hen Ea,i was adjus ed
using expe imen al da a a di e en empe a u es. The alues o all he ob ained pa-
ame e s a e shown in he Appendix. On he o he hand, i m(P)= 1, he kine ic model
in (5) only i s o p essu e a 1 ba . In o de ha i is sui able o p essu es be ween
1 ba o 14 ba , a powe -law exp ession is equi ed. The e o e, an exponen ial numbe
m(P)in (5a) was added. Equa ion (5g) shows he ela ionship be ween he cons an
m(P)and he p essu e. The accu acy o he model wi h espec o he expe imen al
da a is assessed h ough he e o s shown in Figu e 3. I can be seen ha he ag eemen
be ween he expe imen al and simula ed da a is sa is ac o y. Finally, pa ame e s Pe0
and Eain (7) we e also adjus ed acco ding o he eal da a o pu e hyd ogen ob ained
in he expe imen s. Exac alues o bo h pa ame e s a e also gi en in he Appendix.
Figu e 3: Model da a e sus expe imen al da a. Red line shows a 1:1 co espondence
3.6 S a ic analysis o he non-linea model
The s a ic and dynamic beha iou o he non-linea ESR model has been analysed in
open loop. This in o ma ion plays a signi ican ole in he MPC con olle design ac ing
as a guidance o he manual uning o he MPC con olle .
The s a ic esul s a e ob ained by sol ing he di e en ial algeb aic equa ions in (2)
un il all he de i a i es wi h espec o ime a e equal o ze o. S a ic low a e p o iles
o each componen wi h espec o he posi ion in he axial di ec ion o he eac o a e
shown in Figu es 4(a) and 4(b) o he i s and second s age o he eac o , espec i ely.
9
Figu e 6: LMPC-based closed-loop con igu a ion
5 Simula ion esul s
Some pa ame e s in ol ed in he MPC con olle can be uned o mee he con ol ob-
jec i es, which a e he p edic ion ho izon (HP), he con ol ho izon (HC), and he
weigh s o each con ol objec i e (Mand N). In his wo k, HChas been gi en he
same alue as HP. E en ually, HP= 50 (25 minu es), which ensu es an adequa e
ho izon o he closed-loop p edic ion. Rega ding Mand N, wo op ions a e imple-
men ed in o de ha bo h con ol objec i es can be weigh ed di e en ly.
The i s op ion is o assign he same weighs o Mand Nin o de ha bo h con ol
objec i es ha e he same p io i y. Figu e 7 shows he esul s o his con olle uning
case wi h se poin changes o ±10%. In o de o sa is y bo h con ol objec i es a he
same ime, he con olle sea ches he op imal inpu s o wa e and p essu e. Howe e ,
i can be seen ha , since e hanol minimiza ion is gi en he same weigh as hyd ogen
acking, he hyd ogen is always less han i s e e ence wi hin he simula ion ime (see
Figu e 7(b)). This shows ha he capaci y o mee bo h con ol objec i es h ough
he manipula ion o wa e and p essu e is limi ed. The e o e, i we conside ha he
p incipal con ol objec i e is o ack he e e ence o hyd ogen, he weigh ing op ion
should be changed.
Conside ing he hyd ogen low a e se poin acking as he main objec i e, i is nec-
essa y o assign much mo e weigh on M han N. Figu e 8 shows he simula ion esul s
ela ed o his uning case. In pa icula , Figu e 8(a) shows he con ol ac ions applied
o he eal ESR sys em. The empe a u e is always main ained a i s nominal alue
because i is no conside ed a manipula ed inpu . Figu e 8(b) shows he pu e hyd ogen
low a e and i s e e ence. The se poin is changed ±10% a ime 10 minu es, 25
minu es and 40 minu es. The pu e hyd ogen p oduced p ope ly ollows i s e e ence.
Fu he mo e, con ol ac ions change qui e smoo hly du ing he se poin acking in
16

o de o ind he new s eady s a e. The e o e, conside ing di e en dynamic and s a ic
aspec s, i can be concluded ha he con ol objec i e has been success ully achie ed.
6 Conclusions
This pape p esen s an LMPC con olle o he con ol o an e hanol s eam e o me
wi h memb ane sepa a ion. The wo k is based on a non-linea dis ibu ed model whose
pa ame e s ha e been adjus ed using expe imen al da a. Howe e , he LMPC con-
olle is designed based on a linea , o de educed and disc e ised model ha has been
de i ed om he non-linea model. A compa ison be ween he non-linea and linea
models shows ha he linea model is capable o ep esen ing he impo an dynamics
o he ESR in a neighbou hood o he selec ed nominal ope a ing poin . Finally, he
designed LMPC con olle has been shown o be app op ia e o se poin acking o
hyd ogen p oduc ion o posi i e and nega i e changes up o 10%. Also, he LMPC
has shown i s capabili y o op ionally ake in o accoun he minimiza ion o e hanol in-
low h ough he uning o some weigh ing pa ame e s, al hough o physical easons,
he minimiza ion o he e hanol in low implies limi a ions in he achie able hyd ogen
p oduc ion. Fu u e wo k will add ess he analysis o he sys em a di e en ope a ing
condi ions and he conside a ion o non linea MPC con olle s. Also, i will add ess
he mal model inclusion, unce ain y conside a ion as well as se up design imp o e-
men .
Acknowledgemen
This pape has pa ially suppo ed by he Spanish esea ch p ojec MICAPEM ( e .
DPI2015-69286-C3-2-R, MINECO/FEDER). Mingming Li has been suppo ed by he
China Schola ship Council (CSC). Jo di Llo ca is Se a H´
un e Fellow and is g a e ul
o ICREA Academia p og am.
Ac onyms
ATR Au o- he mal Re o ming
ESR E hanol S eam Re o me
HPLC High-pe o mance Liquid
Ch oma og aphy
LMPC Linea Model P edic i e Con ol
LRDsys Linea Reduced Disc e e Model
LRsys Linea Model wi h O de Reduc ion
Lsys Linea Full-o de Con inuous Model
MI Manipula ed Inpu s
MO Measu ed Ou pu s
MPC Model P edic i e Con ol
MRs Memb ane Reac o s
NLsys Non-linea Con inuous Model
17
NMPC Non-linea Model P edic i e Con ol
ODEs O dina y Di e en ial Equa ions
PDEs Pa ial Di e en ial Equa ions
PEMFC Polyme Elec oly e Memb ane
Fuel Cell
PFR Plug Flow Reac o
PID P opo ion In eg a ion Di e en ia ion
POX Pa ial Oxida ion
ppm Pa s pe million
PSA P essu e-swing Adso p ion
SR S eam Re o ming
WGS Wa e Gas Shi
Nomencla u e
V1Volume, m3
A1Sec ion a ea o eac o , m2
εMola ela ion, dimensionless
V2Volume, m3
δThickness o Pd-Ag memb ane, m
A2Su ace a ea o Pd-Ag memb ane, m2
DDiame e o Pd-Ag memb ane, m
RIdeal gas cons an , J mol−1K−1
TTempe a u e inside he eac o , K
T e Tempe a u e e e ence, K
υLinea eloci y o gases, m min−1
Reac ion a es, mol m−3min−1
νS oichiome ic coe icien , dimensionless
CConcen a ion, mol/m−3
QVolume ic low a e, m3min−1
FMola low a e, mol min−1
PH2 e en a e Hyd ogen p essu e in e en a e side, Pa
PH2pe mea e Hyd ogen p essu e in pe mea e side, Pa
PeGas pe meabili y, mol m−1min−1Pa−0.5
JH2Flux o pe mea ing hyd ogen, mol min−1
PP essu e in he e o me s age, ba
PC2H5OH Pa ial p essu e o C2H5OH, Pa
PH2OPa ial p essu e o H2O, Pa
PCO Pa ial p essu e o CO, Pa
PCO2Pa ial p essu e o CO2, Pa
PCH3CHO Pa ial p essu e o CH3CHO, Pa
in Reac o inle
ou Reac o ou le
TsSampling ime, minu es
18
HPP edic ion ho izon
MWeigh ing ma ix (con ol uning)
NWeigh ing ma ix (con ol uning)
umin Minimum alues o manipula ed inpu s
umax Maximum alues o manipula ed inpu s
ymin Minimum alues o measu ed ou pu s
ymax Maximum alues o measu ed ou pu s
Appendix: Adjus ed pa ame e s
Re o me s age
Ac i a ion ene gies o each eac ion:
Ea1= 7.0×103
J mol−1
Ea2=1.3×104J mol−1
Ea3=7.0×103J mol−1
Ea4=8.9×103J mol−1
P e-exponen ial ac o s o each eac ion:
k∞1=5.025 ×103
mol m−3min−1ba −1
k∞2=4.788 ×104
mol m−3min−1ba −1
k∞3=4.548 ×103
mol m−3min−1ba −2
k∞4=4.788 ×104
mol m−3min−1ba −4
Memb ane sepa a ion s age
Ea=8.8 ×103J mol−1
Pe0=9.0 ×10−7mol m−3min−1Pa−0.5
Re e ences
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(a) Con ol ac ions o he closed-loop sys em wi h a posi i e e e ence
(b) Hyd ogen ou pu o he closed-loop sys em wi h a
posi i e e e ence
Figu e 7: Simula ion esul s o he i s case o con olle uning (M=N)
23
(a) Con ol ac ions o he closed-loop sys em wi h a posi i e e e ence
(b) Hyd ogen ou pu o he closed-loop sys em wi h a
posi i e e e ence
Figu e 8: Simula ion esul s o he second case o con olle uning (M > N)
24