Mathematical modeling and analysis of dynamic behaviour of a fed-batch penicilin G fermentation process

Mathematical

Modelling

Praceadings of I'{enotiahol ConfeEn e on chehtical an l Biopn.es E\iaceting 27' 2q A4u!2003, Uniwrsiti Malqria Sabah Kotu Kintua l

and Anatysis of Dynamic Behaviour of a Fed'batch Penicillin

G Fermentation

Process

Arshad Ahmadl Noor Asma Fazli Abdul Samad2 Chow Ai Wei:

'Depdrtment aJ chenical Engi@enng

Unireniti Teknalosi Malarsia, 8 1 3 1 0 UTM Skudai, Jahoa Mata)sia TeL +6A-7 553-5610 Far: +60'7'558'1463, Enait: a\hdd@fl<kba-utm mv

'1lnboruko' oJPrccess Contnl, Depadnent of Chenical EngikeetnLs Uin'e rcili TeLrola|i M.tlalsia, 8 1 3 10 UTM Skudai, Johot, MaLalsia Tel: +60-7 553 5858. Enail: [email protected] ai|u chaw@vth.'o.con1

Abstract

This paper .liscusses the charucteristics aJ Peni.illin C ferhlentations wilh subslrute inhibition using d)hanic simuLatiott. The feffientation Ptocess tras situuLated in MATIAB e innftett aM anab'se' of the dYatuic behariaut ol the pncess \|ere carried out to pnti.le the necettury pncess insiShts. Dltami( sinuLdtiotls rereated raridtians in the sensitiriry oJ the tnodeL to subsiate concnttutiors, dependinq on the operctiry poi l This vaiation indicates non-lineatit! in d)nanic behaviour PID co rol was ako ewluate.l dnd resuht are deftonstruted

Keywords:

Peniciuin Gi Femenlation; Dynamic simulaiioni PID

Introduction

Penicjllin is an anlibiotic that is categorised as a secondary menbolite product thar hs played impo.tant roles

'n pharmaceudcal field for years. Genemlly. fte industrial prodDction of penicillin is characlerised by two dislinct regim€s. The initialphase is lo grow cells in a batch culture. Thh is $en followed by a fed-batch operalion ro promote the b;osynthesis ofpenicillin. ln fermenlation, substrate is very impo.lanl for cell growft. mainGnance of the microbial population and fo.malion of products. Howevea for some prccesses. prcduct fo.mations may be suppressed when subskale concenlradon exceeds certain value. As a result, conlrolled supply ofsubstrate is nec€ssary.

ln order to explore fte effect! of process variables and analyse the sensitivily of these variables, the use ofdynamic simulalion tecbniqu$ is advantageous- This has motivated some actiie researchers. Fof example, mechanistic models ofp€nicillin fermentarion had been developed by Bajpai and ReuB I1l. In addition, there were also researchers workiDs on developins software packase t21, hybrid modelling (t3l.tal,tsl) and dynamic optimization t6l.

In this work, we concenlmle on the development ol a complete mathematical model and sinulation test-bed for process control studies on a Penicillin G fennentalion process. The mechanistic model ofBajpai andReuol1l, and the extended model by Biml et al.[2] were ulilized as the basis ofourmodelling effons. These models are classified as unstruclured model and they are simpler than slruclured models. In unstruclurcd models, all cellular physiology ;nformation is galhered in a single biomas term so that $ere is no explicit strudural information abolt the ceuular aclivity t2l. On the othe. hand, slructured models for penicillin-pmducdon include the effects of cell physiology on penicillin production.

Mathematical Modelling

MalhematicalModellingof Penicillin Fermenlation In a fed-batch operation, there is no removal of producls f.om the fermenter until the end of the process. The outpu! of a fermenter during penicillin produclion. fd. is therefore equal to zerc Gee Eqlation (l)). The nutrienb arc fed at a variable rate to the cullure broth in a fed-balch process I7l.

F - , = 0 ( 1 )

The .eactions involved are simplified as follow:

5 -r X:.t -+ Pi (2)

ln this case. the manipulaied variable is the feed raie of S, which is the subst.ate.

Ovetdv Ma$ Balance

The overall mass balance for ihe fermentation process was simplifien and shown in Equation (3) where v represents the culture volume, and F is the fe€d rate of subslmle.

(3) above indicares that a constant densily made. Because penicillin production is an

aerobic fermenirtion process. the lbrmentat'on cuLure rs continuously sparged with air. The air leaves tho fementer through the exhdust gas line lf the a;r enlering the ferment€r is dry. water is conlinually stfipped from lhe mednnn and Ieaves the system as vapour. Evaporative water losr can be significant over a period oldays [8]. Typically, l0-2oc' of

h e r o r a l o r o r h c a r o e o \ . d u e I n e \ a P o r a l i o n d u n n g o n e week of femenration. the actual amount depending on the lempemrure ofthe iementalion [2]. Hence, evaPorative loss. FL* shoLrld be taken into accoun! in modelling ofatermenter. ln addilion. the eftbcl of ac;d,4rase addition on the loral volume change of the cuhure b.olh. Fdb should also be included in Equrlion (3). By including all these erms' the olenll nrass balancc fo.a ftfmenlercan be expressed as:

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For the Bajpai and Reup model til. distolved oxlgen concentration C. and oxygen limitalion constant (ox are included in Equation (8) to sivel

,=,,@i;o,.#.c,

_(e)

According 10 Birol e, al. t2l, effects of environmental vadables such as pH and lemperature should also be taken into account in the specific Srowth expression- These variables play impoftnnt roles on lhe qualily and quantily of the final product. Considering these vadables, lhe specific growth rate is now given byl

C .

- Lr+l(4H l'LH ,K ll{^.x+"),/(.Y+r '

.

_{^ . r l}

l l i

" , J - 1 1 -

i * J : . l l f

'

_{' R / l l}

8 r ' l

_{, . ,}

,

Ellec. oJ pH

Another term to consider in the specific growth rate expression is the hyd.ogen ion concenttation [H'] l2l The pH of the culture medium becomes acidic. as lhe concentration of biomass increases. lhe amounl of NH4OH added into the cullure medium aho incfeases in order to keep rh€ pH constant duliDg the pe.icillin fermentrtion. Based on lhis observation, the hyd.ogen ion concentfation is related to biomass formation as [2]:

d t H ' t , . . r x , I a * J I a , q J o L , , , , 1 r

- - ' A N -

- ' l - I n j ;

, . / / \

_{" , 1}

( l l)

a is given

as:

^ [ro* rla't- ta'tiv - c,,"1F

+ F")^t

"=--

n+lF;TE,

The suggested evapo.ative loss can follo$ing rela!ionships [2]:

Ft,., = V )G51o rdt^ _{'') \}

(4) be represented by the

(5)

Here, f. and I, are the frcezing and boiling enPerature of the culture medium lbat were asslmed io have rhe same properties as water, respeclively, and ,l is a sugg€sEd evapomtion rale of2.5 x 10" l/h al the operation tempemlure of 25 'C I2l. Here, the mte of evapomdon apProaches infinity at the boiling point, and for engineering purposes the exponent 5 h large enougb to represent _{this [2]}

Mass Aalance ot Biomass

The equadon for mass balanceon biomass is simplified as:

dt v dt (6)

where X is ihe biomass concent.ation _{and I is lhe specific} growth rale ofthe biomass. The specific growth mtd can be described by Monod model (Equation (7)). where fte microorganisms' growth .ale depetds on the concentmtlo. o f l i m i t i n g n u r . i e n t ( [ 8 ] i t 9 l ; l l 0 l : [l ll)

s

'

r K . + s )

_{0 )}

H€re, tx represents the maximum specific growth rate, and Kl is the substfate satumtion constant. However the Monod model is inaccurate to describe the growtb under certa'n condilion' Ll2l. Ite modeti' only valid lor balanced SrowIh and should not be applied when grolvlh conditions are changing rapidty t8l. Numerous modifications we€ made to Monod model to improve accuracy of the kinetic model. one example is the Conlois kinetics thal is used to rcpresent the diffusioral limitations thai occur at high biomass concentrations (tlOlitlzl). The Conrois kinetics nodel is given by equation (8) below.

s

'

' ' ( K , X + S l

Here, 4 and 16 rcpresent acid and base flow rates in Uh' fespecdvely, where the conc€ntration in both soLurions, C$ are assumed €qual to be 3 M. Besides that, Birol et al. [2] aho suggesled rhal undet pH conlrol. (he hydrcSen ion concenlration can be calculated by taking the disassociaion of water and acid.4)ase into account as well as the hydrogen production. The propo.tionality constant, _{7 is estjmated} as

l0' mol [r]/s biomass. Efect o! TenPqatwe

According to Doran [8], temperature hd a significant kinetic effect on reactions. The effe.t of temperature on the specific growih rate can be represen!€d by an Anhenius type of

' "'{l-'

".'(

*l'l l-".'('#)li

( 1 3 )

( t 2 )

3 8 8

(8)

He€, & and A! are lhe constant and dctivation energy fof grc*lh. $hile td ,nd td arc the conslant rnd activation e.er8y ior dealh. respectively.

Tenpercture Contrcl

The tempefatu.e ofthe culture medium was keptconstanl ar 25 "C. It was conlrolled by a sptit-mnge PID controller lhat .llors lhe hcating or cooling water flow mte to be rnanipula|ed. The velociry form ofthe digital PID algorithm (as shown ;n Equation (14)) was used.

A M y . = A , ( 8 , E " + : : : 8 . - ! | , N

x ( c v N

_{- z c v N )+cvN )DMVN}

( t4)

Here. Kc is the proporrional gain, ./ is the inte8ral consran t, .i is rhe derivarive constanr _{and Cyr, -tP, and My! represent} fie cuflent values of rhe conrolled variable, set poinl and conlroller ou tput al lhe cunent saorple N, respectivety, with the curenr lalueoleftor. ttr (=SPr- Cy,).

Mats Aabnee on Peticillitl

For a fed batch fermeniatjon prccess wilh peniciltin concentradon. P and culrure volume, y. specific penicillin production ra!e, _{tpp, and penicillin hydrolysis constanr, &} tbe mass balance equation on penicillin is reduced rc:

d P . . . . - P d v d t V d ,

, l s t The specific penicillin p.oduclion mre, tpp is defined as E q u a r i o n _{( I6) t ll.}

s

c , "

t'"' = t'"p<"+s

+ii K),--;;i5

_{( 1 6 )}

where4pis the maximum specific peniciltin production rate, (F is the inhibition constant, (iis theinhibirion constanl for product formnrion, (op is the oxygen limitation constanr, and C.'is thedissolved oxygen conc€ntmrion.

Mass Balonce on Substrate

A m.ss b?lance on substmre is sbown as followl

*!!=

_f,x-fix

-,,,x*l:t

v dt

s d v

_]:')

Herc, S and X is the subsrrate and biomass concenrration respectively, fs is rhe yield coefficienr (g biomass/g substrate), rp is rhe yield coefficieDr (g p€nicillin/g subslrale), I is the specific growth raie of biomars. tpp 6 me s p e c i f i c p r o d L c l i o n r d , e o f p e n i c i L n , ln \ i r r h e m c i n l e n a n L e coefficienr. F is the feed flow mte of subst.ate, _{$is the feed} substrare conc€ntration. and yis the culrure volumc.

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Mass Daknce on Dissolved Orl|et

Mass balance on dissolved oxygen car be writren rs

! : -

_{. r - r - ! .}

_{x - , . x K l , . . ) - . d J}

r p , I J l

( t 8 ) where / is the specific growrh rate, /pp is the specific production rare of penicillin, CL is rhe concenimlon or dissolved-oxygen _{and y is the cuhure yolume. fv, is dre} yield constant wilh unit (g biomass/g oxlgen), ypl, is the yield connant with unir {g penicillin/g oxygen), ,(/. is the ove.aU mass rmnsfer coefricienr. The diffe.ence {cL' - C.) be.ween the maximun possible and aclual oxygen concenrrur;ons _{in rhe liqLrid cuhu.e rep.esenls the} c o n c c r r f i .on dr'\ i.g tu.(. for md. . r!.\rer.

The overall mass rranste. coefficienr trh is conslant rn the original model of Balpai rnd Reup [l]. However, in $is $ork, K,. is assumed to be a funcrion of agitation polvei i n p u r P "

" n d n o t r r " r e o f o x ) g e n /. a..LBge.reJ o ) B J , e y

a n d

_{o r i ( ttI. rhi\ i.5ho{n}

_{i n r q i " . o n i i " r rl.," -" or}

a and I are assigned so rhar the dependence of penicillin concentrar;on _{on &. marches ctosety !o rbe predicrjons of} Bajpai and Reup tll.

".=".k"\+)'

( 1 9 ) Mass Balance on Carbo Dioxide (CO,)

Du.ing a fermenhtion process, CO, is produced. The CO, evolution mle can be represented by :

dco.

dx

d t

= a ) i + a t x _{+ a l}

(20) Here, c.r is rhe constant rclaing CO, 10 grcwth, (r: is the consllnt relating CO, 10 maintenance energy. and ar is the constant relating CO, ro penjcillin production. The vatues of o1, c& and sr are cbosen _{lo give CO, profiles simila. to the} pr€dicLions oi Monrdgue _{and Lo,trort erslsl. .\ \uggesred b)} B i m l e , d l [2].

Energy Balance

In fe.menBtion, changes _{in beah of mixing of subst.ate and} producLs _{wirh rhe brorh are generaly negtig,bte srnce} cell-culture _{media are uruatt) ditule .queous sotu ons wrrh} behaviour _{close to ideal t8l. In addition, tbe effecb of hear} gener ion due ro mechanicat agiration and aemdon power mput are also assum€d ro be negligible €ompared to rhe hear generaton caused by microbial metabolism. rhe sunoundings, heat exchanger, _{and rate ofsensible enthalpy} gain by lhe flow system srream\. Tle energy batance nn a c o i l e d r y p e h e a r e { c h r ' n g e r . { h i c h i. s u i l a b l e f o r J t d b o m r o D scale fermenter has been suSgesled as follow l2ll

ISBN:983-2643-15-5

q

I l

" ' - ' ( r .

_{t u}

- t ) . -lrt

_{- ? + . , -}

- - \

' . v p .l t | \ a r l z P | . . I J \ 2 t l Here, ?l is lhe feed remperature of lbe subsraie. f is lhe ieed now raie of the substlale, F. is the flow rate oi the cooling liquid, p is the density of lhe cullure medium pc rs the d;nsny of lhe cooling liquid, c,, and .F reprcsent the heat capacity of the culture nledium 3nd the cooling liquad rcspectively. 0.,, is the heat of reaction, a and b areconstants' Forft;s panicular equation, fte u.il of Fis g/(l-hr)

Reacdons i. bioprocesses occur as a result of enzvme aclivitv and cell metabolism For heat generalion caused bv nicrobial reactions/metabolism, Birol er dl. t2l has suggesed the following eqtratron:

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(./0.,,"/d0 is the volumetric heal ptuduction rate. rqr is assumed rc be coneant and might be rfeated as a yield coeffrcienr, and rq, is a constart for hear produclion durirg mainlenance. Thc second lenn in Equation (22) is impodant to lake account for the heat ptuduclion du.ing malntenance since melabolic mainlenance activities give a siSniiicant effect on the heat generahon.

Process

Simulation

The model developed herc was simulated using MATLAB software. The o.dinafy differenlial equalrons were solved using Fourth-Order Runge'Kuta algoilhm wjth adapl've slep size mechankm. Sampling time was fixed at 0.02 hour a s s l r g g e s l e d b y B i r o l e r u 1 . t 2 l . T h e w o r k o f B i r o l , T . / i v ' ( regarded as the benchmark for the simLrlatlon slud) and as such. the kinelic pafamelers as well asthein;tial values were based on their work. These lre tabulated in Tables I and 2

! 9 - = , 4 L v

* , , x v

122)

Trbl, I Kutett. Panntete5 t Vdnbles [2]

Time, t (h) Time, t (h)

Heat transfer coefficienl of heatins/cooling liquid (caUtr."C)

1000

Constant;nheatgenerntion (catg

i . 6 7 8 3

x l 0 a

0.60

rt

Fed subsrare concenlLalion (g/l)

600

Acdvation energy for cell dealh

50 000

Tl Feed Emperature of subslrate (K)

298

Aclivation energy for groath lc!l/mol)

5 i0 0

Yield constant (g penicillin/g oxysen)

o.20

Anhenius constant for cell death l03l Yield constant (s penicillin/g glucose)

0.90

Anhenius conslanl for growth

7 x l 0 r

Yield conslanr

(s biomass/g

oxysen)

0.04

K

P e n i c r l l ' n h y d r o l y s i s r a t e c o n s t a n t ( h ' )

0.04

Yield constant (s biomass/g glucose)

0.45

Constant

(mon)

t 0 r 0

Constant in Kh

1 0

K,

ConslBot(moYl) 7 x l 0 I Constant r€lating CO, to growlh (mnol CO,/g biomss)

0 . 1 4 1

Inhibilion constant for Produci formation (g/l)

0 . 1 0

Conslant relaling CO, to maintenance

enersy (rnnol CO,/g bionass.h)

t 0 l

Oxygen limitation constml (with limitat'on)

5 x 1 0 5 Constant relating COr lo penicill;n production {mmol COl /l.h)

1 0 4

Oxygen limitation conslant (with limitation)

2 x lo-'?

Constanr

in Kb

0 . 4

Inhibition constant (g/h)

0.0002

_v

Proportionality constanl (mol

trrl/g biomast

1 0 5

Saturation constant (g/l)

0 . 1 5

Maximum specific growth late (h-')

0.092

Maintenance coefficient on oxygen

(h')

o.467

Specific rate ofpenicillin produclion (hr)

0.005

Maintenancecoefficient on substrate

o r )

0 . 0 1 4

I Constant _{in F|d, ft} r)

2 . 5 x 1 0 '

Constant

3

Density ofmedium (g/l) x Heat capacity of medium (caug."C)

1 / 1 5 0 0

Yield of heat generalion (cayg biomass)

60

Densily ofcooling liquid (g/l) x H€it capacity of €ooling liquid (cavg."C)

l/2000

Tabte 2 - Initial Conditions [2) Tim€, t (h)

CL Dissolved oxygen concentration (= CL

saruratior) (g/l)

l . l 6

Coz

Ca$on dioxide concenradon (mmol/l)

0 . 5

Hydrosen

ion concent.ation

(mon)

l 0 r I

Penicillin coDcentration (s/l)

0

4",,

0

s

Substrare concenlmtion (91)

t 5

T

2 9 7

Cultufe !olume (l)

1 0 0

Biomlss concentmlion (g/1)

0 . 1

The sludy was divided inlo lwo partsl 1 dynamic simulation of batcb culture

2. closed-loop ope.ation of fed'batch iementalion Here. pH and lemperature were cottrolled using

Results and DiscussioD

The profiles of the outpul variables under Dominal operating conditions for batch ferrenlation process are shown rn Figurc I to Figurc 8. The production of Peoicillin started only rfter a lag-phase. According to Doran [8], cells use the iag phase to adapt to their new environmert Following the lag period, the growth enered the acceleration phase. After the substrate in the culture medium depleted, cell growth slowed down, showing a decreasing trend as shown rn Figur€ 2. The penicillin concentration started lo increase at this stage due the increas€ amount ofpenicillin (see Figure 3).This indicates tha! rhe prccess was in the producl

PnreIlinq: nJ hturatianal ConfeEn . On Atenicol a l Sialocc$ ErSnEerntg 21 2q^ A4!!2ID3. UniwBiti MaLaJsia Sabah K.to KL&hdtu

Fisare 2 PrafLe oJ bianast cohc.ntrdttun

Fieure 3 Prclile of pehicillin concentdtion

Fisurc a Prolile ofdL\oLrcd oryBen con.?ntrutioi E

a

5

E

E

s

Fisure I - ProJile

ofsabstrate

ISBNr983-2643-15-5

FiB ure 5 - P tofi le of tenpe nt"re

9

Pn(edrrys aI Intfltarionat ConIe?n.e An Chenicol and Bio ads:Ensineetins 27' ?q' AqN2003, Uniteari Mdhy:ia Sabah Kota Kinabah

6

-a

Fi8urc9 - Substrate concettrdtion at initial substate cancentrations of |0, 15 1nd 25 9t'l

FiBurc t0 - Penicillin Concentration at inititll subsrrate concennatkhr oJ 10, I 5 dnd 25 8,4

F€d-batch Fermentation

Fed'balch fermentation was accomplished by contin'rousv feeding the substrate to promoie rhe biosvnthesis of lhe product- Here, a threshold value of 0.5 8/l was assignerl to the subslmte concentration. Substm|e fe€ding was acxvated once the strbslrate concentration reached this threshold value However, high concentration of substrate mav inhibit the ceu growth. Hence, controlled supPly of carbon source (slucose) was practiced in this study.

Fisue 6 Prcrtle ofpH

a "

o \ f f i . ; ; - E d

Fi7ure 7 - Prafile ulcatu"n dioxi.le cohcentr'!ion

F isure 8 - P ro.Jile oI NLture _'otune

During lhe fermenlation P.ocess, dissolved oxyget was lrilised for cellrespiration (see Figure 4) andcarbon dioxide was released by the ceUs. Theconcentrations ofgasses in the systenr aho seLve as good indicators on problem slatement. It can also be observed thal tempemture and pH were reduced with time (see Figure 5 md 6). Tbis nav directiv affect the quality of the prccess. A control svsr€m rs therefore required to maintain these values

The simulation rsults for different values of initial substrate concenLadon are illustmted inFigure9 and Figure l0 Here. it can be seen ahat the penicillin production increases wrth an increase in tbeinitial substrateconcentmtion, and then levels off due to substmte limitadon in batch fermentation

E "

6 ' "

Fiswe ll - ProJile oJ substrute

concentation

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E

a

FiEurc l5 Profle of tenperuture

%-- 6-- i6-

- - "m

Fryrrt t2 Prvlile oJbrcnttr concentdtiun _{FiBute t6 ProfLe of pH}

FiSure 13 - P rafiLe of peaicillin conceniation _{Figurc 17 - Prolle ol carbon .Iioride corce\tatian}

5

_{g ,}

8

":t

"l

Fisute 14 - Prolile of dissohied oDsen concentrction

_{Fisurc 18 - Profle ol'otume}

E*.

ISBN:983-2643-15-5

Fisure 19 Profile oJsubstatefeed

nte

I

ln rhis wo.k, the substrale fbed rale. pH, and temperatufe sere conrrolled using PID conrolleE The profiles of the outpul vadables under nominal opemting condition where constdi glucose feed are used duritg the fed-batch opemtion. are illustrated in Figure ll lo Figure 19. Noletbat both biomass and penicillin concentmtions had been improved by adding a slow glucose lbed into the batch fermenter. The controlled supply of gl cose enabled bolb giowrh and penicillin production ro lake place simultaneously Ii].

By including PID contolle.s in ftesystem, fte values ofPH and temperalure were ma;nlained close !o their desired set poinrs. Compared io the results withoul controllers, rbe variaiions from the set-point values had been reduced As I result, the overall perfonnance of lbe fe.mentation Process was improved.Thh proved the importaice ofcontmlsystenr

Conclusion

An unstructurcd model for a fed'barch Penic;llin G fe.mentatioo process had been develo!€d in this sludy Tbis mathematical model includes additional inpul va.iables like feed flow rale of substmte. pH, temperature. aemirot rate, agitalion power as well as oxtput lariables such as CO, evolution and heat generation terms. The model was simulated in MATLAB environmenl and analyses of lhe dynamic behaviou.of fie process were carried our. F.om fte observation, a good agreement was shown bellveen the r$ultsobtaired in this study and lbe literalure

Acknowledgements

The aurhors wish to thank Prol Ali Cinar and Dr Cenk Undey for rheir rechnical support on rhis work This prcject is funded by the Ministry of Science, Te.hnology and the Envircnment alrd UniveN;d Teknoiogi Malaysia through UTM'PrP Schola$hjps and IRPA research granr.

Relerences

tll

Bajpai,

R. K. and ReuP,

M. 1980.

A Mechanistic

Modelfor Penicillin Production. Joumal of Chenic&l Te chno lo ey @d R i o I e ch n o I o s t. 301332-344.

P n , c c J : . e t . t t 1 , 4 n a t a r n t c r 4 l c . . n r A 1 \ L . a t a l a r t R , t r ' r4e r r . t

2/' 2q Ausun 2AAi , Uhirt\ni MaLafla Subah, K.la Kinabalk

l2l Birol, G., Undey, C. rnd Cinat, A. 2002. A Modular Simulation Package lor Fed balch Fennentation: Penicillin Production. Canquters anl Chenical En\ine e ring. 26: t553 t565.

[3] Palnaik. P. R. 1999. NeuralControl orAn Imperfecdy Mixed Fed balch Bioreactof fof Recombinanr B-Ealacrose. DiochemicaL EnSineerinS JawndL 3 : 1 1 3 - 1 2 0 .

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