Dynamics and Control of Chemical Reactors, Distillation Columns and Batch Processes. Selected Papers from the 3rd IFAC Symposium, Maryland, USA, 26–29 April 1992

372 Pages·1993·14.39 MB·English

AC SYMPOSIAS ERIES
IF
JanGoerst lEedri,t or-in-GCehoierMfg,ae s oUnn iverSscihtooyof,Il n formTaetcihonno alnoEdgn yg ineering,
FairVfAa2 x2,30 044-44,U SA
DHURJTAI& STEPAHNOPOUOLS:O n-lFianueDl ett ecatniSdou npe rviisni oCtnhh eem ical
ProcIensudss tr(i1e99s3N, o .I)
BALCHEeNta l:D ynamiacnsCd o ntrooflC hemiRceacalt oDrisis,lt tliaoCno lumnsB atacnhd
Proces(1s9e9s3 ,No.2)
OLLER&O CAMACHOI:n telCloimgpoennetn atnsId n strumenCtosn trfAooplpr l ications
(1993,No3)
ZAREMBA: InfoCromnatrtPoirloo nb lienMm asn ufactTuercihnngo l(1 o9g93yN,o .4)
STASSENA:n alyDseissi,ag nnEd v aluaotfMi ano-nM cahiSnyes te(m19s9 N3o,5 )
RODD& VERBRUGGEANr:t ciifIainlt elliinRg eelan-cTei Cmoen tro(1 l9 93N,o .6)
FUESS:N onliCnoenatrrSo yles mtsD esi(g1n9 9N3o,. 7)
DUGARDM,' SAA&D L ANDAUA:d aipvtSey steimnC so ntraonlSd g inaPlr oces(1s 9i9n3Ng,o .8)
TUX UYANM:o deilnanlgd C ontrooflN atioEncaoln om(i1e9s9N3 o,. 9)
LIUC,H EN& ZHENGL:a regS caSlyes teTmhse:oa rnyAd pplicat(1 i99o3,nN os. JO)
GUYA N& CHENZ HEN-YAUu:t omaitnMi ionn iMnign,e raanldM etParlo ces(1s 9i9n3Ng,o .II)
DEBRA& GOTTZEIN:A utomaCtoinctri onAl e rosp(a1c99eN3 o,. 12)
ALBERTO&S K OPACELoKw: CosAtu tomat(1i9o9nN3o ,. 13)
HARVE&Y EMSPAKA:u tomated BSasyesodtn He ummsa Snk i(lalnI dn telli(g19e9nN3co,.e 1)4 )
BARKERC:o mpuAtiedre Dde siignCn o ntSryoslt e(1m 9s9 2N,o .I)
KHEIeRta l:A dvanicnCe osn trEodlu ca(t1i9o9Nn2o ,. 2)
BANYAS&Z K EVICZKIYd:e ntifaincdSa ytsitoPenam r amEestteirm a(1t 9i9o2Nn,o .3)
LEVI&S S TEPHANODUis:t uritbeIdn tellSiygsentcee(m1 9s9 N2o,. 4)
FRANK&E KRAUSD:e siMgent hoodfCs o ntrSoyls te(1m 9s9 2N,o 5)
ISERMANN& FREYERMUTFHa:u Dlett ectSiuopenr,v iasniSdo afent yf oTre chnPircoasclse es
(199N2o,. 6)
TROCH eta l:R oboCto ntro(1l9 9N2o,. 7)
NAJI&M DUFOURA:d vanCcoendtr ooflC hemiPcraoelcs s(e1 9s9 2N,o .8)
WELFONDELRA,U STER&E WRE BERC:o ntroofl PoPwlearna tnsPd o weSry ste(1m 9s9 2N,o .9)
KARIM& STEPHANOPOULMOoSd:e lainndCg o ntrooflB itoechnPircoacle (s1 s99e2Ns,o .JO)
FREYS:a feotfCy o mputer SCyosntte1rm9os9l 2
NOTICER ETAOD ERS
youlri briansryo a tl reaas dtya nding/coorndcteuirsn tuooamrste uirbon s ctroti hbsieesrr miaeyws e,r ecommend
If
thyaotpu l aacs et agn/dcionntionrsu uabtsicoronir pdtteorir eon c eiimvmee diuapotnpe ulbyl iaclanlte ivwoo nl umes.
Shouylofdui tnhdta hte vsoel unmole onsg seerrv yeo unre eydosuo rr dcearn c ancealatln teyid mw ei thnooutti ce.
be
Copioefas llp reviouslvyo lpuuambrealesvi asihleAadf b ulldele.ys crciapttaliowvgieul elg l asdelonyntr equest.
be
AUTOMATICanAd CONTROLE NGINEERINPGR ACTICE
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Deputy Editor-in-Chief Editor-in-Chief, CEP
AUTOMATICA InstifotrIu ntdeu strial
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FullilosI ftF publiacpapteiaatotrnh sse o tefh nvidos l ume
DYNAMICASN DC ONTROLO F
CHEMICARLE ACTORSD,I STIALTLION
COLUMNSA ND BATCHP ROCESSES
(DYCORD'+9 2)
SelecPtaepde frrso mt h3er dI FACS ymposiMuamry,l andU,S A,
26- 29A pri1l9 92
Editebdy
J.GB.A LCHEN
DepartmoefEn ntg ineCeyrbirennge tics,
ThNeo wregiIanns toitfTue cthen ology,
TrondihmeN,o rway
Co-edited by
E.DG.I LLES K.VW.A LLER J.BR.A WLINGS
(Germany) (Finland) (USA)
Published
forth e
INIBRNATIONFAELD ERATIOOFNA UTOMATICCO NTROL
by
PERGAMONP RESS
OXFORD • NEW YORK • SEOUL TOKYO
•
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AlRli ghRtess ervNeodp .a rotf t hipsu blicamtaiyo nbr ee producsetdo,r eda r ient riseyvsatleo mr
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photopcyiongr,e cordoirno gt herw,iw siethopuetr missiionwn r itifrnogm thceo pyrihgohltdr es.
Firesdti t1i9o39n
LibroafrC yo ngrCeasst aloignPi unbglt iicoDana ta
Dynmaicansd controolfc hemicraealc tordsi,s tillcoaltuimonnas n d
batcphr ocessseelse:c ptaepde frrosm t he3 rdI FACS ymposiuMma,ry land,
USA,2 6-2A9p ri1l99 2/edibtyeJ d. GB.a lch-en1.s etd .
p.c m.- (IFACs ympossiear i1e9s9;3 n,o .2A) s electoifpo anp ers af rom
symposiuomr ganiaztte hdUe n iversoifMt ayr yland.
Incluidnedse xes.
1.C hemicparlo cecsosn trol-CgornessIe.Bs a.l cheJensn,G .I II.n ternational
FederatioofAn u tomatCiocn troIDl..S eries
TP155.759.5D 1993 660'. 2851-dc20 92-44352
BritLiisbhrr yCa ataloignuP iulnbigc aDtaitoan
A catalorgeuceo frodtr h iboso k isa vailafbrlotemh eB ritLiisbhr ary
ISB0N- 048-170161 -
Thesper oceediwnegrsre e produbcyem de anso ft hpeh otoffs-eotp roceusssi ntgh ema nuscrpitss upplied
byt haeu thoorftsh ed ifefrenpatpe rsT.h ema nuscrpitsh avbee etny peusdi ngd ifefrentptye writaenrds
typaecfes. lTayh-eo uftiug.reasn dt abloefss o mepa persd id not agcroempel etewliyt thh es tandard
requiremecnotnss:e quetnhtrele yp rodtuicodno esn odtis play compulneitfeo r.mT iot eynsurraep id
publicatthiiso nd iscrecpoaunlncdoy t cbhea negd:n orc oultdh Een glibsehc heckceodmp let.e ly
Thereofret,h ree aderasr ea sketdo e xcusaen yd eficienocfit ehsisp ublicawthiiocnmah y bed uet ot he
abovmee ntionreeads o.n s
TheE ditors
PrintienGd r eaBtr itabiyBn P CCW heatoUnds, Ex eter
3rIdF ASCY MPOSIUOMN DYNAMICASN DC ONTROOLF
CHEMICARLE ACTORDSI,S TILLATCIOOLNU MNASN D
BATCHP ROCESS(EDSYC ORD+' 92)
Sponsobrye d
InternatiFoendaelr atoifAo unt omatCiocn tr(oIlF AC)
-WorkinGgr ouopn C hemicPalr ocess Control
Cop-osnsobrye d
AmerincA automatCiocn trCoolu ncil
ChemicParlo ceSsyss teLmasbo ratoar cyo,n stitLuaebonrta tory
oft heS ysteRmess earCcehn teUrn,i versoifMt ayr yland
Organbiyze d
ChemicParlo ceSsyss teLmasb oratoofrt yh eU niversoifMt ayr yland
onb ehaolff t hAem ericAaunt omatCiocn trCoolu ncil
InternatPiroongarlaC mommem ittee
J.GB.a lch(eNn) (Chairman)
SubcommiotntC ehee micRaela ctors SubcommiotntB eaet cPhr ocesses
E.DG.i ll(eDs) (Co-Chairman) J.BR.a wlings (US(AC)o -Chairman)
D.B onvi(nC H) N.J erom(eUS A)
M.F riedr(iDc)h H.L eegwater
(NL)
I.H ashimo(tJo) H.P reis(iAgU S)
S.BJ.o rgen(sDeKn) G.R eklai(tUiSsA )
J.CK.a nto(rU SA) D.R ippi(nC H)
J.FM.a cGreg(oCrA N) T.T akamat(sJu)
W.H.R ay( USA) P.D rone(nS F)
H.S chul(eDr) E.Z afirio(uU SA)
SubcommiotntD eies tillation Columns
K.V.W alle(rS F) (Co-Chairman)
L.H ammarstr(oSmF )
W.L uyben (USA)
J.ER.i jnsdorp
(NL)
D.ES.e bor(gU SA)
S.S kogest(aNd)
B.T yreu(sU SA)
NationOargla nizCionmgm ittee
T.JM.c Avoy (Chairman)
K.Y.C hoi
M.M avrovouniotis
E.Zafiriou
INTRODUCCTON The decidteoid n viftoeu wre ll-knowns pecialitsots
IPC
presents urveyp aperons thmeai n themeso ft hsey mpo­
This volumcoen taianse sl ectioofnp aperpsr esentaettd h e siumT.h eses urvepya persar e incluidnedt hivso lume.
3rIdF AC Symposioun m and ControolfC hemi­
Dynamics
caRle actorDsi.s tillCaotliuomnnan sd BatcPhr ocess-es, Furthermtowroetu torial sessions werteop roesrgeaninzetd
DYC ORD+' 9-2o rganiaztedU niversoifMt aryy land, thset aotfet he oft woim portantte chnical sTechteosres .
art
CollePgarek ,M arylanUdS,A A pril2 6-2199,9 2T.h is are:
symposiubeml ongisn sae quenocftrie e nnicaoln ferences
Professor Ljung( LinkapUinnigv ers(iSty) ):
Lennart
plannebdy t hWe orkinGgr ouopn C hemicParlo cess
ProcesIsd entificThaeotriyo nan.d Practise.
ControolfIF AC -IntetrniaonFaeld eratoifAo unt omatic
ControlT.h ef irDsYtC ORD symposiuwma so rganized ainnd
198i6n B ournemouthU,K andt hseec ondi n1 98i9n
ProfesSstoerp hIen.M arcus( UniversoifMt aryy land
MaastricThhteN, e therlands.
(USA)M)od:e llianndg ControolfD iscretEev enSty s­
Allt hessey mposihaa vbeeen verwye lalt tenbdyepe do ple tems.
frombo th academirces earcanhd indusantryd many very
Botho ft hestuet oriwaelrsve e ryw elplr esentanedd
signifipcaanpetr hsa ve contributed.
been
accepteHdo.w evethre,y ar e notr eprintiend volume.
this
Thec hemicparloc esisnd ustry placed higphr iorointa y
has
betteunrd erstandingo fc hemicraela ctdoyrn amiancds th e Thesep roceediarnego sr ganizedas follows:
ofs uchkn owledgefo rt hdee sign beottfe rc ontrosly s­
use
Secti1o:Sn urv ey papers.
temsI.nr eceynetar st herhea vbeee ns omem ajoard vances
inthis fieTlhde.se ar er eportiendthis volume. Secti2o:Cn h emicraela ctmorosd ellinesgtim,a tion and
control.
Systefomrsh igpehr formance distillaartveei ryos ni gnifi­
cantp arotfsth ec hemicailn dustryE.v ent houdgihs tillatiSoenc ti3o:Dn i stillactioolnumns modellinegs,t imatanido n.
modellianndg c ontrohla vbeeen actifiveel dfso r researchc ontrol.
developmfoernm tan y decadesi,m portannte wc ontri­
and
Secti4o:Bn a tcprho cessemso dellianndg c,o ntrol.
butiotnobs as icu nderstaanndd icnogn trosly stedme sign
havneo wbe enm adean d arepr esentedh ereThe. availabil­Secti5o:Gnen erasly stemMso.d elliensgt,im atianodn
itoyf hi ghc apacimtoyd em computmearsk etsh e control.
implementaotifos nu chhi ghsolpyh isticactoendtr oslt ruc­
turesf easibtlodea yth atco uldo nlhya vbeee ndr eamed of
somey earasg o.
In genertahler heas be ena t endenciynt hper ocesisn dustry
durinrgec endtec adest oco nvertpr ocesseq uipmenftr om
theo ld-fashibonaetdcs ht ytloeco ntinuouospelrya tiunngi t
operatianodn sr eactoAr nse.w i ntereisnbt a tcphr ocesses
has howeveevro lved, its eemthsa tb atcohpe ra­
because
JenGs. B alchen
tionusn ders triccotn tromla yh avseo mee xtraordinary
Professor
advantagients er mso fe conomy, conveanndi qeunacle.i ty
Chairmano fI nternatioPnraolg rCamo mmittee
Topiccosn cerning modelliensgt,i maantdi ocno ntroolf
ProceediEndgist or
batcprho cesstheuss p laany importranotli enth e present
volume.
Ina ddittiotho neth reem aitnh emecsh:e micraela ctdoirss­,
tillactoilounmn san,d batcphr ocesses;v olumael so
this
addressess omeo ft hnee wtr endisn d ynamics control
and
methodolosguyc ahs m odebla sedp redicctoinvtreo nle,w
methodfso ird entificaotfdi yonnam imco delnso,n linear
controthleo ryan d thaep plicaotifno enur anle twortkos
identificatianodn co ntrol.
In 199,0IF AC establians Ihnedt ernatioPnraolg rCamo m­
mittfeoret hpel anninogfth esc ientiprfiocgr am for
DYCORD+'92Th.i sc ommtteie had2 6h ighqluya lified
membersfr omt hien ternaticoonmmauln itoyfs pecialists.
Threeo ft hmee mberss erveasd co-chairfomsreu nbc om­
mitteeosnc hemicraela ctdoirsslt,ai tlicoonl and batch
umns
procesTsehses.e w ereP:r ofessoEr. DG.i ll(eDs)P ,r ofessor
K.VW.a ll(eSrF )P,ro fesJs.oBRr.a wlin(gUsS Ar)e spec­
tively.i nternatiopnraolg ram committee
This and
particuliartlcsyo -chairdmiedan ni mpressjiovbie nfi rst
review1i0n3ga bstractsl,a treerv iewainndge valuaatliln g
thep apertsh awte rsee lecftoedprr e sentaatlith oenc onfer­
ence and tfihnseae lllecyt iotnh peoa fpe rtos bep ublished
int hesPer oceedings.
Copyrigh©t IFADCy namiacnsd C ontroolf C hemical SURVEYP APERS
Reacto(rDsY CORD'+92M)a,r ylaUnSdA,, 1 992
STABILITYC RITERIAF OR CHEMICALR EACTORS
V.B aloatkaiaanhDd . K odra
DepartmeonftC hemicEanlg ineerUinnigv,e rosfiH toyus tonH,o ustonTX, 77204-4,U7 S9A2
Abstract: Stability acrrepi rteesreinaft oersd i xm ostc ommont ypeosf c hemicraela ctoar s:
batcrhe actor, a cfolnotswit niurotruaesndr k e actaot ru,b ulflaorw r eactaof rl,u idibzeedrd e actor,
a tubular catalytica truebaucltaorr aauntdo thermal reactoerx tewrniahtleh a ti nternal or
exchanTghee.c ritermiaayb eu setdo d etermtihnebe o undaorfty h er egioofnp arametvearl uiens
whicthh eb ehavioofar reactionrw ,h icah s ingelxeo therrmeiacc toicocnu rissi, n sensittoi ve
smalple rturbations.
Keyw ordsS:t abilbiatyt;cre ha ctosrt;i rtraendrk e acttourb;u lraera ctfolru;i dibzeedrd e actor;
tubulcaart alyrteiacc tor; autothermal reactorp;a raimgneitstreiinocsn i;t ievxittiyn.c tion;
INfRODUCTION ratoefh earte movaatla nyi nstaisng ti vebny
Iti sa w elkln owfna ctth acth emicraela ctoirnws h,i ch Q=U A(T-Tc) (2)
oneo rm oree xotherrmeiacc tioocncsu ra,r eh ighly
sensittiosv mea lclh angienst hed esigonro peratingw herUe ist heo verahlelat tr anscfoeerf ficAi iesnt th,e
variablTehse. s ensitiivsim tayi nldyu et ot he heattr ansafreeraT , i st het emperatiuntr heer eactor
exponentdieaple ndenocfe t her eacti(ohne at and Tc ist hec oolantte mperatuNreeg.l ecting
generatriaotnoe)n thet emperataunrdfe e edbaocfk variatiinod nesn siatnydo ther phypsriopcearlt tihees ,
energeyi thbeyrc onducticoonn,v ectoirotr na nsfer dimensionelqeusast idoenssc ribtihneeg v olutoifo n
acroas bso undarIynp .r actiicti esi, m porttaond te sign thec onversainodtn e mperaatruegr iev ebny
ando peraat ree actoourt siidters e gioofns ensitivity.
Thusi,ti so fi nterteods ett ermtihneeb oundaorfyt he
rreeagciotoifonspi r an rsaemnesvtitaetolrsi u mvieaesnl wp lhe irctthuh rebb eahtaivoinoosfar. ddxt= (1- xn )exp[ 1 9 9 / yJ H(l- x) (3)
+
A consideraamboluen t woofr kh asb eenr eportoend
d9 9
pcahsestmi ixcrtyaeyela a crtRssoe.erc n esnritet viaivneaidwrt tyis ctblayebdR siua lrziiotanntyng h d e dt= B (-1x )n exp[1 9/yJ H(1 x-)- a( 9 - 9c)
Schmit(z1 987)M,o rbideelltia l.( 1987), and (4)
+
monograpbhys A ris( 1975a)n dZ eldoviectha l.
(1985s)u mmaritzheei mportcaonntt ributDiuoetn os . 0,9 0 (5)
spaclei mitatitohness c,o poef t hiasr ticwliel ble x = =
limitteodr eviewitnhges tabilcirtiyt efroirva a rious
where
typeos f chemicarle actoirns w hicha single
exotherrmieca ction oIctci ushr osp.e d tthhaits
E T-T0
collectoifor ne sulwtisl plr ovindeew i nsighatnsd 9=
RT -T0-
stimulfautret hreers earocnht hes tabialnidtc yo ntrol o
ofc hemicraela ctors.
STA BILITCYRI TERIOFNO RA BATCHR EACTOR
We considanei rd ewale lslt irbraetdc rhe actionwr h ich
a singlier,r everseixboltehe rmrieca ctiAo n-- ---) B
occurWse. a ssumthea tt her atiesg ivebny
n�O (1)
UA
where H(iCstA h)e H eavisiudnei'stst efpu nction. We (6)
furthaesrs umteh atth er eactioscr o olesdu cthh atth e
HerBe ist hea diabatteimcp erartiusreei, s t he
y
dimenslieosansc tivaetnieorng 0yci, s t hec oolant (8)
temperant uirste h,er eactoirodnea rn d ist he
a
dimensiohnelaretes mso vpaalr ameTtyepri.cr aaln ge
Eliminoaft0i a onndx f roEmq s. (7()8g )ia vntedhs e
ofv alueofsp arametfeorrhs i ghelxyo thermic
stabibloiutnyd a(rryu nawlaoyc uisn)t h ep arameter
reactairoenB:s i s1 0 to i1s001 ,0 to i3s-0 1,t o0 c
y spacOen. o nes idoef t hibso unda(riyn sensitive
0. regiod2n0)/ d2xi sn egateivveery whoenrt eh ree action
patwhh iolnet hoet hseird (er unarweagyi odn2)0,/2 d x
Thet imceo ordimnaaybt eee liminfartoeEmdq s(.3 -4)
isp ositoinav s ee gmeonftt h ree actpiaotnh .
byd ividEiqn(.g 4b )y( )3.T higsi ves
Fotrh sep ecciaasolef 0 c= 0( equcaolo laanndit n ilt ia
d0= B- a (0- 0c) temperataunrdye= s oo )( laragcet ivaetnieorngt yh)e
dx eigenvparloubel deemf inbeyEd q s. a(n7d) takes
(1- x n )exp[ 0 JH( l- x) thfoer m( AdlaenrdE ni1g,9 64) ()8
1 0+/ y
d0 0 e-0
(7a) = B[ 1 a (9)
dx B (l - xn)H(l -x)J
(7b)
8=0 @ X=O (Ola)
IntegroaftE iqos(n.7 g)i vtehsre e actpiaotinhn t he
tempera-tcuornev erpsliaonnFe i.g u1r seh owsso me 8=1+ @X= Xe (lbO)
{;;
reactpiaotnhf so rt ypical ovfpa alruaemse ters. All
wherXeei s roootft heeq uation
reactpiaotnha sr ec onfitnoea d t riangruelgairo n the
formbeydt hies other=m ala nd atdhiea ba=t ic
(a ) (a
0)r eactpiaotnah nsdt heeq uooililbirn(iex=u m1 .) n (n n-1
(1- Xe)- (1c-)x -
+BTu )
�(1+ ex-p-1( )=0 (1)1
{;); Tu
Figurseh owas p olto ft her unawlaoyc uisnt he
(a/B2,pB l)a nfeo rz eroth fiarnosdrt d erre actions
(=nO,lT)h.i rsu nawlaoyc cuas nb ed escrbiybt ewdo
asymptoFtoerst .h ea diabactaisc(e a = 0)i,t
approatchhaees sy mptote
e
B B=a=
2
1+Tu ) 12)
( (
whilfeot rh set roncgoloylc eads( eB a 1)i t
1,
approatchhaees sy mptote >> »
13)
(
x
Fi1g: R eactpiaotnfh osar homogeneoruesa cbtaotrc h
Int hei sothecramsaelt, h et emperarteumraei ns
constaatn0 t =0 ,w hilteh ec onverisnicorne ases
monootnicaflrloyzm e rtoo u nitFyo.rt hea diabatic
casteh,e t emperaitnucrree amsoenosot nicafrlolmy
zertoo B .I nm anyp ractsiictaula ttihoaend si,a batic
temperartiusiresue n accephtiagbahln ydt hpeu rpose
ofc ooliinstg o l imtihtet emperaitnucrree Tahsee .
manneirnw hicthh tee mperacthuarnegd eest ermines
theb oundabreyt ween (soarif ne sensiatnidv e)
runawabye havAidolrae.nr d E ni(g1 9d6e4f)ia nb ea tch
reacttoobr e i nsensiiftt ihvere e acttiroanj ectory
(definbeyEd q s7.)i ss ucthh ad2t0 /d2xi sn egataitv e
allp ointis.,ei .n tihnes ensirteigvieot nh,e
temperamtauyir nec rewaistecho nverbsuito nw ai th Fig. Boundary betweena ndir nusneanwsaiyt ive
negatsievceo ndde rivatTihvet er.a nsiftrioomn reg2ifo:onars b atcrhe actor
insenstiotr iuvnea wbaeyh avoicocru wrhse nt wo Fort hsep ecciaasloe fa z erootrhd reera ctiitmo any,
inflexpiooinnb tesg itno a ppeairnt her eactionb es howtnh atth een tirruen awbaoyu ndiasrg yi veinn
trajecTthoibrsoy u.n diasdr eyfi nbeydE q(.7 a)n d ap arameftorri(mcBa lakot1a9i8ah9,)
2
A_mm! Aistn h eoa f crbateasoatrercce ,ha catlilo n
(m+l+ l)m traacjroeetnca toft r iorinreafeignodeigr soum nle udr
btyh ea anidsdrio eatpabhaacaettnttrhhdiimes uc a n l
equli(ill)xnHi.=eob wurenitvlubhiemaekrt e,c h
(4)r etarhceetpa oafcratotC ,hriSm s oTca nRoy n tain
1 lipmo(iiwdtn/hd0= tex asr in esd bo rlaantcehde s.
Fi3sg husororwemesp ea af cttotyhrvips aoi lncu aels
Usaisnymgme TpththooomtGdairsasca,n oy dpf a rAac mooo )emc tplelaorestfstsh .eie f ication
Leea Knads s(o19hy61sa ),hva eond wdin tfL yfoirpefneer paaseanc( nte tot(hqir 1suo 9 in7v 7a)l ently,
t(ah1e9na6x5 t)ac, peplorltforeh xunelint oma cbawuitasfiyd uo irnoacc fgoa rntvaviemDeorswarns a)s us is o n
fotrch oecm oamBfs1o i eg0ns i b vye n gibZvyee alnZnd y(dos1 vBi9ian4cl 1ha) k,o taiah and
Lusasmn aodnth ye rs.
e >
(1981)
aB [ 12 .(9f32134])6
(15)
=
+
A cootfrmh upelna odarcewibufEasys(iqyo 9ns n-e. d
witothEfhaq ts. h tothwlhasaieta ts t er
c11)o naspe(p1r5r)iv io.atnxeith i.inem vs aeet1 ni5so int,i ve
redgebifEyoiq nn.b e aradtei dcasehc f tionri tely
insMeon(r1ns5e)ui,o mctveaierlvhricea,cu.v al ela tions
shtothmwhaanettx ritamenumsrmpiii esesr neat t ure
litumonii iiftts ety dthl vhaaapenrlr gueeed0 1r i cted
bEyq . 0
a
(15).
Fora nfdiE( nqm1i.ba5tg ey)ee ,n eralized
-1 5
0c� y to
e1+9c
= (16)
aB [ +2 9 .(4l 6 ( )!!_2/3
1 + �B) ] 0.2 0.4 0.6 0.8 1.0
x
I F3iR:gte .pia afoocatrnh h o sm ogeneous CSTR
SATB ILFIATO YRC SCTRRI TERION
Tshtese ctaoadntaytven ee dmr iapsninei d roeWadnaete l tufs hritesene tb eaae dothaCyfea S vTiRo rt o be
CSiwTnhaR si iecnxhgon lto-ehrrt edehrea imrcni tstciseo ompn naes lriiltttfr uhi erevpab eaca ttthii oonn s
AB o cadcreeu bsrtycash rl eeig qbeuebacdrto ainitponchonxe eis0 c 9n ,=t at ix=nsn 9d =0g d =o e0s
ncootan lntiypam oiTiinhttn1 ,ub h tsoes,u . n dary
� Bx beitnwsaereneundnrns eaiidgwsteia ifoyvin en ed by
F(xDx (a)-1e -xxapa)D H ln-(x 0) tohceco tuflwrr ipoemo intiincrhtn eee tpa sac tthi on
[ ] contpnhoeexic0 9nt,=0 ati xnsn d9 g=0 .
= 1+ = (17T)dh eiifsdsi i nfrfiotfothmeabfia r 1ar ,ote ten nca thc tor.
Hoiwmtebas veyhe ort= cw,hrn =e avi aattltihu caeat l
Bx
9--=-- (18w)hl iipcmodhiii tniso tsanss pll phyieig aghrht elry
aaD tthahawtanhi t in cpfhold ieincsttasip opne ar.
1
+
whtDeharemkne ou Dhmiadlbs,eeeb frryi , n Terhdeeo Bs fau llaLaktn(uosd1st m9sabau8 ieys1a e)hd
toobt tfhaoeil nl oftwobhiroen u gn deaxrpyr essions
otfrh eeoig fni sooepnne sriattiivoen :
Tbdhyie m hetenrascation oeisdnfsfelf efeiiiris[ c1 n s(i1 +e B e--JdnJ�( 1t+)2 nenx+l (p22( 0la )
f= or {;t;I-n {;);
aanoldtpl ha eraarards mee e ftienresd previously. In
wrEiqtas(in.i1ndh t8gb a) aes,se sniu sm ed that
(20b)
laaBnr(0e1(gd7 =)ee c q oauofnaltedlaee nmdtp erature).
y
Ftorhraoe vnf aog Bldfe ue befEys(iq 2nt.0ew bdo) ,
Trheeta rcaittjnihe opecn lmt a(abonxyere, y9 )
lipmomiieatnarct t gu ses pb Eypq o.i nt defined
obbteyal iitnrmheeiedtsn (iiaaDmfrdt)eoei nmnc ge
Eqas(n.T1d gh8 ii)vs.e s and (17)
(17)
aFa 2F
ax(9B( xxn1e9)-H -l -9(x)) (19a)=xa = x0 2 (20c)
=
3
E(q2.0 a). prbeEyd(q3) i2t. mch ,ate txe eidmmr ipuisems r ea ture
litumoni itteyd.
FBo( r+1 )3 tfhoelp laorwaimnegtr ic
repgritesvhsteeebas nob tuianltdiiatoryny
2! ABCIRUIIFTTA OTE RUR BRIUEOLANAC RT OR
.y-;/"V-;;;,
(+n xx21) -
B = (la2)TST shtese tcaaodtnayevtn eedrm ispanie orna ture
n2(x-1)x homtougrbeeuniawlenchao atsiru oic srnh g le
exortehoaeccarctdrmuieeirosb cstncy h r ei bed
a (l-n2x+ )n 1-x x orddiifenfqaeurrayet nitoinasl
= exp
B( +n xx1) [ 2- x]; d=xD ( a-x1ne )H 9-x( )l (24)
d�
t-
O<X1< (lb2)d -D0da =2e D (aB-x1 )H l-nx( -a )eD 9a
1--=- + d�d �2
- - <i>ii2 e (25)
Otnlh odece bufEysi(q n2t.el1w d)ipo ,mo iitn ts
.y-;; wbiotcuhon nddairtyi ons
meaaritng(s ebo ilpfaou ibrnEyc(tq a1 .t7d i)eo fni)n ed
and
X=O (26a)
d0
(21c-)-= O (26b)
<dl>b�2
Da
ed -0
Ftoshrpe ce aocafszi eeoa rrlrod etteahhrc -e t= i0o n�=,1 (26c)
ensttliaoribdcesieu lbssEiyc( qt r2w.yi0h b)ide,c�d h
@
sitmop lifies
wh�iet sdrh ieem leecnnosgoitrohdn ilneastse ,
(22)
(27)
aanoldtpl ha eraarards mee pe frtieeInvrneis do usly.
arraiEt(vq a2is(n4n.i2d)gh 5tb a ) aes,se t snhu amte d
madsissin psee grillssaii 0rgco=0gi n .eb laen,d
When mtoh<!>dhe2iu vsltle uharsery rg mea l Thiele
(h2<!> E(q-22sa45.iyr ) de tet oenh vteoi lcuatli on
eqfuaoab rtar itewocatinhcdhts tihe om re nsionless
le� �00p)n, lgtatrhyhooeid fl ni egm t eitnm.se i onless
Thtsuhtseca, rb fiaioht lroei mrttoiuygob enun leaoru s
reiiasdc tettonooha trbfa i a trct eiactanlhhc et or
l<l>ih2m (ipftll Wuoh<l>h2gwe1 )(nh2 .<l> 0 ),
ttheem bpeeicrnoadmopteefoups asre niendt d ieonnt
Eq(�s2 aoo (.4n2 )d5 b i)en « ttmgeo�a itg yvhr eea ted
foalllegoqewubiarntagii ocn s
l+l(Da0)nlel(l--;nD )a</(e 119- n)
1xl )=({
O[ ; ] Dal/(e19- n)
B _
> (28a)
F4iR:gu .bn oaufwanoa dryCa SrTiRe= s x l)B(
0 (28b)
1+ Daa
Fi4sg huapor oltwefoshs tte b a obfuitonlhrdie at ryy
coazfsea erfin oordtrrs hdet Aea isrctnc th aieso en s.
E(qm2sba8.uey) tsc oeo dtnr hseepta arictunthc isto n
oabf a rtetcab!iehco- tusonattrdtaah,a rde rti i aebsa tic
asBy( m+1=np 2a )t bnoedatc seoy tmtmoehp t et(h lo0)ept,) liIx mact(ban seyeh .ot wshnte e tahdayt
sbteaohtEfae(q iv 2svsi8.seo ) irtr tmyo ohi t falh tae r
stcroaoosnlayg/Bemle dFpy.l ot arvroga otelfe u es
BE,q( s2m"\/.1ab u )yest oeobd tf aoilnCl SoetTwqhRiAuie nsatn cg th oa ieCfso St enTrh sRue.,n away
loccoountfsssw ieosgw tmisfet oinhnrt esst t,h e
apparnoeaxxl= ipfymtrotbaheriotes cue san ildo anr y
gibvye n
a e
B= (3)2 =n n/1-n)( e{xn-p n/(- +,n1 )n}
� ( -)k
BBa< < B* (29a)
Tehxipsiar sple lsisFoonsit 4 iIgti.ostues ne rd ee n
thfaBot r1 E0(q,3)2. p raog voiowBddnhante(l- ae=hsnldr e )aie s a yBba,imga spitb t(viyo2ec t9n eb ,)
approtofrhx ueiln moaNacwutuaimsyoe. nr ical
sims>u htloahatwtacth trie io tonaifs c aanld value
4
n2n1)_l n (<n2--n1-)l )i(n usedt od etermitnheet ransibteitowne einn sensitive
B" (29c)
n/n-(1)-n (n1+) andr unawabye havifoorr all three homogeneous
reactmoord els.
*
(Notet haBta= ea ndB = ee(-1)/(e-f2o)ra firosrtd er
reactainodnB a = 1,B *= foarz eroth roeradcetri on).
oo STA BILITCYR ITREION FORA FLUIDIZED BED
Thes econsde gmenmta yb ed escriibnea d p arametric REACTOR
form
We considae frl uidibzeedrd e actionwr h icthhe fluid
ands olipdha saers ew elmli xedW.e furthears sumteh at
�=� [1 + (n-)l]tn/ (l-n) there naor tee mperatourrc eo ncentragtrdiaioenn ts
withitnh ep articWlietsh.t hesaes sumptitohnes ,
steasdtya ctoen versainodtn e mperaitnut rheef luaindd
92 1 solpihda seasr ed escribbyet dh ee quations
B=S-11 -[l+n(-l}tl](tl-n) (30)
(32)
={[+l+(-n l)t](nn-li)- [l+(-nl])}t, 0 1
e d < D� )
Xs= (1+ Da x (33)
ForB 1,th er unawalyo cudse finbeydE q.( 30)
appro» acthheess t roncgoloyl eads ymptao/tBe e.
= (1+ aDaS)= BDae xp(9(81-) x n.H )(-lXs ) (34)
Eqs.( 29- 30)m ay beu sedt oo btaitnh ef ollowing
analyteixcparle ssfioortn h er unawalyo cufso,rl arge (35)
valuoefsB :
where
a e
= [ (31)
B
1 +1.414( �)1'2]
(36)
insseintive anda lolt hepra rametaerreas s d efinperde viouEsqlsy..
(3-235)m ayb ec ombinteodg ivteh ef ollowsiinngg le
equationt heff olru icdo nversion:
{ }
a./B Bx Da
F(x)=x-Deaxp1 + aD+ Bax � ah x
0.1 (1 - xD �- x) n -x- � x) (37a)
runaway Da H(l Da
Whent hep artei hcelaatn dm assD amkohlneurm bers
arez ero( Dpah= D�pm = O)._ thec onvei_rosn� nd
temperaitnut rheef luiadn ds olipdh aseasr ei dentical
B (0s= 0,Xs = x)a ndE q.( 37ar)e ducteots h aotfa s ingle
phasCeS TR (Eq(.1 7)).
Fig5.: R unawabyo undarfioeras fi rsotr derre actiino n Thes teasdtya bteeh avioofEr q .( 37am)a yb ea nalyzed
at ubulrare actor byc onstructthiern ega ctpiaotnh isn t he( 0,x) plane
byu sinrge lation
Fig5. s howas p lootf t hes tabibloiutnyd afroyra first
oofrad erzree arcottofihroo dr<l>nhe 2rr �e a0c atnidt%o hn2e, �r uoon. aFwoalrtyo h cecu ass e is0 =1 +B axD a (37b)
independoefn<l> th 2 andi sg ivebny E q.( 22)I.n Oncea gaiwne,d efine a fbleudri edaiczte(odtr w poh ase
generfaolra, n yn 0, thed ifference betweenC StThR}et sobe e i nsensittosi mvael ple rrtbuatiiofnt sh ere
twol imitciansgei ss>s malaln di tm ayb ec onclutdheadt
exisat rse actpiaotnch o nnectxi n=0g , 0 = t0o x =1 ,
axiadli spersoifoh ne ath asa small efofne tchte
0 = 0c ontainnion gl imipto intUss.i ngt his
stabilbiotuyn dary.
definittihoeen x,a cbto undabreyt weetnh ei nsensitive
andr unaway remgaiyob nesd etermibnyea dn alyzing
A compariosfotn h er unawacyr itefroirta h et hree
Eqs(.3 7)I.tc anb es howtnh afto trh es pecicaalso ef a
homogeneroeusa ctmoord els sthhoawttsh ed ifferences
zerootrhd erre actitohnet, r ansiftrioomn insentsoi tive
betweetnh ec ritearriea muschm alltehr ant he
runawabye havioocrc urwsh ena hysterepsoiisn t
uncertaiinntvyo lviendt hed eterminaotfi tohne
appeairnst her eaction Ipnta htihcs.a set,h ee ntire
kinetaincd h eattr ansfer parametae srisn.g leT hus,
runawayl ocumsa yb ee xpresisnea dn alytfiocraml:
univercsrailt edreifoinn beydE qs. (a2n0d() 2 1m)a yb e
5