Mohammad Ali Fanaei Shykholeslami, Assistant Professor in Ferdowsi University,Chemical Engineering Department

Transcription

1 Non-na Contol o Ba's Yas Boacto Basd on a Kntc and Mass Tans Modl Alh shahmohammad, MS d n Chmcal nnn,tach n Homozan Unvsty, Mchancal Ennn Dpatmnt Mohammad Al Fana Shyholslam, Assstant Posso n Fdows Unvsty,Chmcal Ennn Dpatmnt Abstact A stuctud unsatd cybntc modl abl to dscb a dauxc owth phnomna o clls colony n aobc conon. In ths pap, th modl has bn povn n th smulaton o th bhavo o a batch and d-batch boactos achvn satsactoy sults. Fo smulatn d batch systm, at st, th optmal substat dn n to boacto has bn obtand by solvn optmal contol poblm. Applyn ths pol to pocss modl shows that thanol concntaton s much lss n compason wth a constant d at. Also, bcaus n many mntaton pocsss, yn tans s th at lmtn stp, so o pvntn om yn stavaton that causs thanol poducton, yn mass tans cocnt s smulatd on th uncton o mpll spd and a low at and thn, contol o yn concntaton by PI and GC contoll hav bn consdd. Rsults show that two contolls hav a sam pomanc, but bcaus o smpl stuctu n PI contolls, PI contoll s btt than GC o ths pocss. Also cll concntaton wthout usn contoll hav bn bouht and shown that poductvty s small n compason wth usn contolls. Kywods: cybntc modl; d-batch boacto; optmal contol; Sacchaomycs cvsa. Intoducton Th Sacchaomycs cvsa bomass, manly n th om o ba s yast, psnts th last bul poducton o any snl-cll mcooansm n th wold. Sval mllon tons o sh ba s yast clls a poducd yaly o human ood us []. Th poducton o ba s yast nvolvs th mult-sta popaaton o th slctd yast stan on sua as cabon souc. Ba s yast s usually poducd om a small quantty o S. cvsa addd to a lqud soluton o ssntal nutnts, at sutabl tmpatu and ph. Th ct o vaabls, such as ph and tmpatu, s wll nown and th optmal st-ponts can b asly dnd. On th contay, yld and poductvnss can b laly actd om th concntaton o bomass, sua, yn and thanol omaton, any. Th optmal conons vn mum yld and poductvnss chan alon wth tm toth wth th bomass owth: consquntly, th d at o nutnts n th d-batch boacto must b chand too. Tho, th dn at o th molasss s th most ctcal vaabl and th poblm s to ndvduat th bst dn at squnc. Ths poblm could b solvd by dvlopn a stuctud unsatd modl to dscb a owth at abl to povd nomaton about th mtabolc outs pvaln at any momnt o th clls colony l and about how th owth s nluncd om opaton conons. Such a modl, namd cybntc modl, has bn poposd o th st tm by Staht and Ramshna [] and Van and Ramshn [,4]. Mo cntly, Jons and Kompala [5,6], D So t al. [7,8] hav xtndd th us o ths modl o dscbn th owth o S. cvsa n boactos. In ths pap, at st, th sult o smulaton n batch boacto has bn bouht and shown that amnts a qut satsactoy wht xpmntal data. As w sad Also, th dn at o th molasss plays a vy mpotant ol n th batch posson as wll as th nal poduct concntaton that s obtand at th nd o th batch. Snc ach acto un s ollowd by a psonnl ntnsv, clann and stlzaton opaton, dtmnaton o th bst possbl pol may b conomcally xpnsv. A pocss modl n such a scnao, could b vy usul. Usn tools om contol thoy, optmum substat pols could b dtmnd n much lss tm compad to xpmntal dtmnaton, thby sultd n conomc savns. So n ths pap, o smulatn d batch systm, th optmal substat dn n to boacto has bn obtand by solvn optmal contol poblm [9,]. Althouh cybntc modl mpows mcooansms to allocat cllula soucs o th upta o thos substats that bst t th cllula qumnts, but n ths pap, o pvntn om yn stavaton that causs thanol poducton, yn mass tans cocnt s smulatd on th uncton o mpll spd and a low at and thn, contol o yn concntaton by PI and GC contoll and ct o usn contolls on bomass concntaton hav bn consdd.. Th smulaton modl Dun th aobc owth o S. cvsa, suas and thanol can b usd as cabon and ny soucs, whas Emal: a_shamohammad@yahoo.com -Tl: 97677

2 nton and oth mno nutnt qumnts a satsd by noanc salts. Sua can b mtabolzd va two dnt ny poducn pathways, mntaton () o daton (), dpndn on th sua concntaton n th mdum. Bomass ylds on lucos a stonly latd to th pvaln mtabolc pathway, bn mal only whn sua s dzd. Fo ths ason, n d-batch pocsss o yast poducton, th cabon souc d must stctly b contolld to nsu a bomass yld as clos as possbl to th thotcal valu obtanabl. Und yn stavaton conons, th mntatv mtabolc pathway always pdomnats; at a low sua concntaton, thanol s poducd, too. Ethanol poducd dun th mntatv mtabolc pathway n a batch cultu s consumd whn lucos s no lon avalabl n th mdum. Ths phnomna s namd dauxc bhavo o S. cvsa. On th bass o abov consdatons, t s vdnt that S. cvsa has ntnal ulatn mchansms whch dct th mcooansm towads th most convnnt mtabolc pathway abl to optmz th us o avalabl soucs. Th cybntc modln amwo s basd on th hypothss that mcooansms optmz th utlzaton o avalabl substats to mz th owth at at all tms. Th cybntc vaabls u and v psntn th optmal stats o th synthss and actvty, spctvly, o th y nzym o th mtabolc pathway,. Th valu o u can b assssd assumn that cll soucs wll b allocatd n such a way to obtan th mum bomass owth at. Th vaabl whch contols th nhbton/actvaton mchansm o (v ) s dtmnd consdn th nhbton ct null whn th mcooansm ows on th substat whch acclats th bomass owth at to th utmost, whas th nhbton ct possvly ncass at a dcasn owth at [7]. Tho, u () () ν ( j ) Sua can b mtabolzd va two dnt ny poducn pathways, mntaton o daton, dpndn on th sua concntaton n th mdum. So, th ntc modln o th owth bhavo o S. cvsa qus a dtald nowld o th ntacllula contol mchansms and th Monod classcal modl s not nouh. In ths modl, spcc owth ats o th dnt mtabolc ways a modld accodn to a modd Monod at quaton, wh th modcaton conssts n th act that ach owth at has bn assumd popotonal to, th latv ntacllula pop y nzym concntaton. S sua mntton () µ V S + S thanol daton(4) µ V + S + µ S V + S + sua daton(5) Ths choc ntoducs an advanta n manan th cybntc modl bcaus th atos can chan n th an, only. Wh S and S psnt, spctvly, th quantty o sua and thanol n th boacto, Ox th concntaton o dssolvd yn, V th volum o th lqud n th boacto, K th satuaton constants o th substat o ach mtabolc pathway () and KO x psnts th satuaton constant o th dssolvd yn. Wth ths owth at quatons, th common balanc quatons o batch (F n ) and d-batch (F n ) boactos can b wttn as dx ( ν ) balanc on bomass(6) ds ν F n s X Y Y ν balanc on sua(7) + ds ν X ν Y Y balanc on thanol(8) φ dv F balanc on lqud volum(9) n

3 d S ( + ) + µ ( + ) ε εu ν V + S balanc on mntaton y nzym() latv concntaton d S ( ) µ + + ( + ) ε εu ν V + + S balanc on thanol daton y() nzym latv concntaton d S ( ) µ + + ( + ) ε εu ν V + S + balanc on sua daton y() nzym latv concntaton wh α ε α + α d ν ν X Ka( ) φ + Y Y φ V balanc on yn lqud concntaton() Paamt valus Unt φ ν + φ ν ( ) + φ ν 46 Y Y Y RQ φ ν φ + ν Y Y spatoy quotnt(4) wh X, Fn, S, Ka, a, spctvly, th bomass quantty n th acto, th valu o th sua d stam, th sua concntaton n th d, th cocnt o as lqud mass tans and th concntaton o yn at th as lqud ntac, and α and a, spctvly, th nzym dcay and synthss at constant; α s a small consttutv synthss tm o all th nzyms and s mpotant n pdctn th nducton o nzyms whch hav bn pssd o lon pods o tm and Y and φ th ylds and stochomtc cocnts o th dnt mtabolc pathways, spctvly. Th spatoy quotnt (RQ) s th ato o CO mols poducd on th yn mols consumd. RQ s hh than whn th mntatv lucos mtabolc pathway pdomnats, aound whn th datv lucos mtabolc pathway pdomnats, and small than n th cas o thanol consumpton.. Batch Smulaton sults In F.a, th volutons wth tm o concntaton o spctvly bomass, lucos and thanol a potd. In F. b, th voluton o th spatoy quotnt s potd. As t can b sn n both cass amnts a qut satsactoy wth xpmntal data. Tabl Modl paamts valus usd o th smulaton sults ε.99. µ.45 µ. µ. Y Y Y φ φ φ K ( ) ( ) ( ) ±..8.4 ± ( h ) ( h ) ( h ) ( h ) ( dm ) ( dm ) ( dm ) ( dm ) Concntaton[/] Modl Smulaton Glucos Ethanol Cll Mass Tm(hous)

4 (a) 8 Modl Smulaton Expmntal Valus 6 4 RQ 8 6 (b) (c) Tm(hous) F.. Expmntal data [7] and modl smulaton o cll mass, lucos, thanol concntaton (F. a) and spatoy quotnt (F. b). (F. c) Th tnds o th latv y nzym concntaton o th th mtabolc pathways o S. cvsa Optmal Contol In th cas o a d-batch boacto, on oal s to mz/mnmz an appopat pomanc objctv. Towads achvn ths oal, t s mpotant to not that dcsons mad adn th nput dun th cous o th batch play an mpotant ol on th objctv uncton. Th systm dynamcs a dscbd by x ( x, u, t) that x(t) and u(t) a vcto valud stat and nput spctvly and t s th ntal tm. Th objctv uncton o th optmal contol poblm s th mnmzaton o thanol concntaton at th nd o th batch. Th nal omulaton o th objctv uncton s vn as, t J ( t ) ϕ ( x( t ), t ) + ( x, u, t) (5) t Th uncton ϕ accounts o th contbuton o th nal stat, whas, accounts o th path dpndnc n th objctv uncton wth t as th nal tm o opaton. Intally, th ncssay conon o u to b optmal s H. u Hamltonan s mathmatcally dscbd as, T H[ x( u( λ ( t] [ x( u( t] + λ ( t) [ x( u( t] (6)

5 In ths quaton, λ s th co-stat vaabl and s usd to ncopoat th systm dynamcs nto th objctv uncton. Th onal optmal contol poblm s thn tansomd nto a two-pont bounday valu poblm, as th dntal quatons o th stat and th nw co-stat vaabls hav bounday conons dnd at t ( x t )) and at t T ( ϕ λ ( t ) ), spctvly []. x 5. Optmal Contol Rsults In F., th sult o solvn o optmal contol poblm o d at has bn potd. F., shows th nlunc o ths pol on thanol concntaton and RQ n compa wth constant d at. (.5.8 Flow RQ Constant d at ***** Optmal d at Tm[hous] ( m )F. Optmal d at pol h F n 6. Fd-batch Smulaton sults Bcaus n many mntaton pocsss, yn tans s th at lmtn stp, coct masumnt o th volumtc mass tans cocnt s a cucal stp n th dsn pocdu o boactos. In od to nsu ull aobc conons, both a low and stn at a vad to p th dssolvd yn concntaton hh than a ctcal valu. So, by usn a low and stn at valus, an quaton o masun yn mass tans cocnt, has bn poposd. Fo all nds o actos wh th sol pupos s mass tans, multpl-mpll systms a advantaous and th wll b la savns on an ndustal scal, spcally o th boactos wh th acton pods a lon and th pow consumpton cost can b a sncant componnt to th ovall poducton costs []. So, a std tan( Dcm,H4cm) wth two dsc tubn atatos(d7.5cm,spacncm) has bn supposd. In act yast suspnsons n th an o 5- m - a classd as Nwtonan lquds. So th vscosty and dnsty o th both a masud dun th whol pod o mntaton by quatons: µ.9 ρ ρ + W X Wh ρ W and ρ X a th dnsty o pu wat and dy yast and X s th yast concntaton []. Wth computn pow numb [4], th al as pow consumpton s calculatd 5 P N ρ. N D (9) P ρ ρ W X X Tm[hous] By tal and o, th ollown quaton has bn poposd o computn th al as pow consumpton that pdcts th Kla valus, wll. Ethanol F. Ethanol concntaton and RQ wth constant and optmal d at (7) (8) P.448 P N Q.56 D. 4 () It s obvous that Kla s latd to as pow consumpton p unt volum o both and th supcal vlocty: K P a V α ( V ) S

6 A low at[/mn] Wh th valus o α and dpndn on th systm omty. Th ollown quaton o Kla has bn poposd. As t has bn shown n F 5, th poposd quaton, has a satsactoy colaton wth xpmntal data..45 P K.8 * ( ). 4 a VS V () Tm(hous) F 4. Expmntal data o th a low and st spd ats[7] By usn ths quaton, Kla valus a calculatd and appld to pocss modl. In F. 6, th volutons wth tm o concntaton o bomass and dssolvd yn hav bn potd * Cll Mass concntaton[/] o Dssolvd Oxyn Concntaton[%sat] Modl Smulaton R.P.M [m n - ] M.T co * Expmntal valus Modl smulaton 5 5 Tm[hous] F 5. Expmntal data [7] and modl smulaton o th Kla 5 4 F 6. Expmntal data [7] and modl smulaton o th bomass and yn concntaton 5 5 Tm[hous] 7. Dssolvd yn contol Oxyn tans n aobc bopocsss s ssntal. So any shota o yn dastcally acts th pocss pomanc. Almost always, bopocsss a cad out n aquous mda wh th solublty o yn s vy low own to th psnc o onc salts and nutnts and th at o yn utlzaton by th mcooansms s ath hh. As t's shown n pvous stp, mpll spd and a low at, a two vaabl that act on yn mass tans cocnt. Bcaus convntonal popotonal-ntal (PI) has a snl nput-snl output stuctu, ths two vaabls must combn n th om o on paamt. Wth substtuton th valus o P and V s n poposd quaton o Kla, ths quaton can b stablshd:.4 (.4 ( N P. ρ. D ) ) K a. N. Q.45.4 V. A.45 K K C a c( ρ ). K N and Q must b dnd as a unctons o K C. Wht havn mnmum and mum o N and Q and naton som numbs btwn thm, valus o K C t. Fttn quatons to ths data a th om o blow: N.9668KC () 5 QG.6KC N α. Q C ()

7 Now, wth havn Ka valus that t om contol law and ρ by solvn stat unctons and th K C valus, N and Q valus can b ound and apply to pocss modl. 8. GC Mthod a lobally lnazn contol (GC) and a convntonal popotonal-ntal (PI) contoll hav bn dsnd o contolln th total yn concntaton, and pomanc o ths contolls hav bn compad thouh smulaton. Th GC mthod s a nonlna contol alothm basd on dntal omtc appoach. Th st stp n th GC synthss s th calculaton o a stat dbac, und whch th closd loop nput/output systm s xactly lna. Thn o lnazd systm, a contoll wth ntal acton such as PI can b dsnd. To mplmnt th stat dbac o th GC, all th pocss stat vaabls must b masud o stmatd. Consd SISO pocsss wth th ollown modl: x ( x, d ) + ( x, d ) u y h ( x ) wth a nt latv od (th latv od s th smallst nt o whch h ( x ) ). x and d a th vcto o stat vaabls and dstubancs, spctvly. u and y a th manpulatd nput and th contolld output, spctvly. Und th stat dbac: u ν h ( x ) h ( x ) h ( x ) wh 's a tunabl paamts, th closd loop v-y bhavo s lna and dscbd by th ollown quaton: dy d y y ν (5) Som udlns o tunn o 's paamts and oth mas o usn GC mthod hav bn dscbd by Sooush and Kavas [5]. Th nput o th lnazd systm (v) can b natd by a PI contoll as blow: t c ν ν s + c ( ) + ( ) (56) τ I Wh * s th dsd pol o yn concntaton n th boacto and Kc and τ I a an and ntal tm constant o PI contoll, spctvly. 9. Thotcal sults In ths scton, pomanc o GC and PI contolls on cll concntaton, hav bn compad. Also, how ths contolls pom on contol o yn amount n boacto has bn suvyd. Also cll concntaton wthout usn contoll hav bn bouht and shown that poductvty s small than usn contolls. Ects o unctanty n pocss modl on pomanc o contol mthods, hav bn bouht, and amp uncton as an nput, has bn appld to pocss modl. Th sultn contol alothm (GC), has th paamts, K c and τ I that must b tund by tal and o. (4) 6 x PI Contol GC Contol 5 4 Wth GC Contoll Wth PI Contoll Wthout Contoll concntaton[/] 4.5 Concntaton[/] Tm[hous] F 7. Closd loop spons o yn concntaton, GC mthod (dash ln), PI contoll (ln) 5 5 Tm[hous] F 8. Closd loop spons o cll concntaton, GC mthod (ln), PI contoll (ln-sta), wthout contoll (ln- squa)

8 . Conclusons Smulaton sults show that amnts a qut satsactoy wth xpmntal data. In patcula, t can b sn that th cybntc modl poms wll n th smulaton o th la-phass and th dauxc owth. In batch systm, whn owth bns at an ntal la-phas, th yast has a hh owth at manly wth a mntatv mtabolc pathway wth thanol poducton; ths s conmd om th hh valus o th spatoy quotnt. At th whol avalabl lucos s consumd and at a nw la-phas, S. cvsa stats mtabolzn thanol. All ths aspcts o yast owth a wll smulatd om th modl. Intally, n th psnc o a hh lucos concntaton, th latv y nzym concntaton, pomotn lucos mntaton s manly synthszd. At th total lucos consumpton dun th dauxc la-phas, th y nzym that just pomot thanol daton, s synthszd and thanol consumpton stats wth a dnt at. In d-batch systm, applyn th optmal substat dn n to boacto caus th thanol concntaton and th spatoy quotnt bcom much lss n compa wth a constant d at. Rsults o usn contolls on yn concntaton show that althouh pomanc o GC on th contol o yn s mo smooth than PI contoll, but bcaus o th man oal s ach to mum o cll mass and ths contolls hav appmatly th sam pomanc to ach t and as a PI contoll dosn't nd th pocss modl and has a smpl stuctu than GC, so t sms that PI contoll s btt than GC o ths pocss. Also th ct o yn contol on cll concntaton shows that by usn contoll, at o bomass poducton dun th opaton and also concntaton at th nd o th pocss s hh than natual conon. On th oth hand, t s obvous that wth passn th tm, dnc btwn two mod bcoms hh and t's bcaus o th bul lqud yn concntaton dcass wth tm; so th yn mass tans at bcoms nsucnt as a consqunc o th ncasn bomass concntaton. Tho, t s possbl to conclud that n spt o th cybntc modl mpows mcooansms to allocat cllula soucs o th upta o thos substats that bst t th cllula qumnts, o nsun ull aobc conons; t s ncssay to us asonabl contoll n od to optmz th bomass poducton n a boacto. Rncs [] A. Son," A Mult-Scal Appoach to Fd-Batch Boacto Contol", PhD thss, Dpatmnt o Chmcal Ennn, Unvcty o Pttsbuh, -8, (). [] J. V. Staht, and D. Ramshna," Cybntc Modln and Rulaton o Mtabolc Pathways. Gowth on Complmntay Nutnts", Botch. Po.,, , (994). [] J. Van, and D. Ramshna," Mtabolc Ennn om a Cybntc Pspctv-I. Thotcal Plmnas", Botch. Po., 5, 47-45, (999). [4] J. Van, and D. Ramshna," Mtabolc Ennn om a Cybntc Pspctv:. Aspatat Famly o Amno Asd", Mtabolc En.,, 88-6, (999). [5] Knnth D. Jons, and Dhnaa S. Kompala," Cybntc Modl o th Gowth Dynamcs o Sacchaomycs cvsa n Batch and Contnuous Cultus", Botch. J., 7, 5-, (999). [6] D. S. Kompala," Cybntc Modln o Spontanous Oscllatons n Contnuous Cultus o Sacchaomycs cvsa", 7, 67-74, (999). [7] M. D So, R. Tss, and E. Santacsaa," A Kntc and Mass Tans Modl to Smulat thgowth o Ba's Yast n Industal Boacto", Chm. En., 8, 47-54, (). [8] M. D So, E. D Alts, and P. Paascandola," A Gnal Kntc and Mass Tans Modl to Smulat th Ba's Yast Gowth n Boactos", Catalyss Today., 66, , (). [9] E. Balsa-Canto, J. R. Bana, A. A. Alonso, and V. S. Vasslads," Ecnt Optmal Contol o Bopocss Usn Scond-od Inomaton", Ind. En. Chm. Rs., 9, , (). [] R. uus, and D. Hnnssy," Optmzaton o Fd-Batch Ractos by th uus-jaaola Optmzaton Pocdu," Ind. En. Chm. Rs., 8, , (998). [] A. E. Byson, and Yu-Ch Ho," Appld Optmal Contol", [] P. R. Goat, Anthony A.C.M. Bnacs and A. B. Pan," Multpl-mpll systms wth a spcal mphass on boactos: a ctcal vw", Bochm En J., 6, 9 44, ().

9 [] M. Mancn, and M. Mos," Rholocal Bhavou o Ba's Yast Suspnsons", Food En. J., 44, 5-, (). [4] W.. McCab, J. C. Smth, and P. Haott," Unt Opatons o Chmcal Ennn. Chapt 9", 6, 8-8. [5] M. Sooush, and C. Kavas, "Nonlna contol o a batch polymzaton acto: An xpmntal study", AIChE J., 8, p49-44, 99