uncertainty analysis of penicillin vproduction using monte carlo simulation

7/22/2019 Uncertainty Analysis of Penicillin VProduction Using Monte Carlo Simulation

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Uncertainty Analysis of Penicillin VProduction Using Monte Carlo Simulation

Arno Biwer,

1

Steve Griffith,

1,2

Charles Cooney

1

1

Department of Chemical Engineering, Massachusetts Institute of Technology,Massachusetts

02139; telephone: 617-253-3108; fax: 617-258-6876;e-mail: ccooney

@

mit.edu

2

Light Pharma, Cambridge, Massachusetts 02139Rec eived 8 July 2004; accept ed 1 O ctober 2004Published online 28 February 2005 in

Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/bit.20359

Abstract:

Uncertainty and variability affect economic andenvironmental performance in

the production of biotech-nology and pharmaceutical products. However, commer-cial

process simulation software typically provides analysisthat assumes deterministic rather than

stochastic processparameters a nd thus is not c apable o f de aling with

thecomplexities created by variance that arise in the decision-making process. Using the

production of penicillin V as acase study, this article shows how uncertainty can

bequantified and evaluated. The first step is construction ofa process model, as well asanalysis of its cost structureand environmental impact. The second step is identifica-

ti on of un ce rt ai nv ar ia bl e sa nd de te rm in at io no ft he ir pr ob a -bility distributions

based on available process and literaturedata. Finally, Monte Carlo simulations are run to see

howthese uncertainties propagate through the model and af-fect key economic

and environmental outcomes.

Thus,theoverallvariationoftheseobjectivefunctionsarequantified,the technical, su

pply chain, and market parameters thatcontribute most to the existing variance are

identified andthe di ffere nces between economic and ecol ogical eval -uation are

analyzed. In our case study analysis, we showthat final penicillin and biomass concentrations

in the fer-menter have the highest contribution to variance for bothunit production cost andenvironmental impact. The pen-

icill in sell ing pric e domin ates return on investment variance as well as the variance

for other revenue-dependentparameters.

B

2004 Wiley Periodicals, Inc.

Keywords:

M o n t e C a r l o s i m u l a t i o n ; u n c e r t a i n t y ; v a r i -

abili ty; penicill in; economic asses sment ; envi ronmental assessment

INTRODUCTION

Commercial process simulation software usuallyprov ides a na lys i s t ha t a s s umes det ermin i s t i c proces s pa ra met ers .The


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software does not consider existing variations of tech-nic al , su pp ly ch ai n,

a n d m a r k e t p a r a m e t e r s t h a t c a n s i g -

n i f i c a nt ly a l t er o pera t ing de c i s ion s a nd b a t ch- t o-ba t chexpect at ions .

However, an understanding of these param-

e t e r s a n d t h e i r u n c e r t a i n t y i s e s s e n t i a l f o r t h e e c o n o m i c s u c c e s s o f a

pro ces s des ign and the ana lys is of exi st i ngprocesses. Thus, a methodologyis needed that combinesstandard process simulation software with uncertainty anal-ysis.

In this article, we use a well-characterized process, theproduction of penici ll in , to

illustrate how this goal mightbe accomplished.Penicillins produced by

Penicillium chrysogenum

arestill among the most important antibiotics. Penicillins be-long to a family of

hydrophobic

h

-lactams. Each

containsa d i f f e r e n t a c y l s i d e c h a i n a t t a c h e d b y a n a m i d e l i n k -

a g e t o t h e a m i n o g r o u p o f t h e p e n i c i l l i n n u c l e u s , t h e 6 -a m i n o p en i c i l l an i c ac i d . P e n i c i l l in G a n d p e n i c i l l in V a r e t h e m a i n c o m

m e r c i a l p e n i c i l l i n s . M o s t o f t h e p e n -

i c i l l i n V ( p h e n o x y m e t h y l p e n i c i l l i n ) i s c o n v e r t e d t o 6 -

a m i n o p e n i c i l l a n i c a c i d ( 6 -

A P A ) , w h i c h i n t u r n i s u s e d t o m a k e a m o x i c i l l i n a n d a m p i c i l l i n ( M c C o y , 2

0 00 ). I na d d i t i o n , p e n i c i l l i n V i s u s e d d i r e c t l y a s a n a n t i b i o t i c (

f

1 , 6 0 0 t o n s p e r y e a r ) ( V a n N i s t e l r o o i j e t a l . , 1 9 9 8 ) a n d r a n k s a m o

n g t h e 1 0 0 t o p p r e s c r i b e d d r u g s i n t h e U nited States (American

Druggist, http://www.rxlist.com/ top200a.htm, May 2004).h

-

L a c t a m a n t i b i o t i c s a m o u n t t o a b o u t 6 0 % o f t h e w o r l d wi d e a n

t ib iot ics mar ket ; th i s was app rox imat ely $5 b il lion per year in sales in 1999

(Demain and Elander,1999). The global demand for

h

-lactams grows by around2% annually, mainly because of rising demand

in countriess u c h a s C h i n a a n d I n d i a ( M i l m o , 2 0 0 3 ) . L o w e ( 2 0 0 1 ) e s t

i m a t e s t h a t t h e w o r l d p r o d u c t i o n o f p e n i c i l l i n w a s 6 5 , 0 0 0 t o n s i

n 2 0 0 1 . A s a r e s u l t o f l a r g e o v e r c a p a c i t y in the market, penicillinprices have been under continu-ous pressure for several years. Prices have

fallen signifi-cantly during the last several years from $20/billion units(B U )

d u r in g t he m i d- 1 9 90 s t o $1 2 / BU i n 1 99 7 t o $9 / B U i n 2 0 0 0 ( M c C o y ,

2 0 0 0 ) . A s o f 2 0 0 3 , t h e p r i c e o f p e n i - c illi n G was app rox imate ly $ 11 /BU,

which is $1718/kg(Milmo, 2003).Improvements in the penicillin production process

resultprimarily from ge netic-based strain i mprovements,

whilet h e p r o c e s s f l o w s h e e t h a s c h a n g e d v e r y l i t t l e ( V a

n Nistelrooij et al., 1998). Although some improvement

h asb e e n r e a l i z e d f r o m r e f i n e m e n t i n o p e r a t i n g c o n d i t i o n s ,

B2004 Wiley Periodicals, Inc.


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Correspondence to:

C. CooneyThis article includes supplementary material available via the Internet

athttp://www.interscience.wiley.com/jpages/0006-3592/suppmat.

these changes are often difficult to observe because vari-ance in the overall

process masks small improvements inproduction. As such, i t takes manymo re ex pe ri me nt s or production runs to statistically verify the impact of a

par-ticular process change. In the present work, we assess howvariance in strain

and proces s parameters affects key eco -nomic and environmental impact metrics.

Because environ-mental concerns have become increasingly important,

weinclude an envir onme ntal evaluation in our analysis.Using a process model for

penicillin V, Monte Carlo sim-ulations are performed to investigate the effect of

param-eter uncertainty on overall process performance. Thereby,we use a new

a p p r o a c h t h a t p r o v i d e s a g e n e r a l m e t h o d -

o l o g y f o r c o m b i n i n g p r o c e s s s i m u l a t i o n s o f t w a r e a n d s p r e a d s h e e t

modeling to conduct high-leverageu n c e r t a i n t y a n a l y s i s . T h i s o f f e r s a f u n d a m e n t a l b a s i s f o r d e c i s i o n m a

king in the design and analysis of bioprocesses.

MATERIALS AND METHODS

The proce s s m odel for pen ic i l l in V pro duct i on wa s b u i l t using t he process

simulator SuperPro Designer version 5.1(Intelligen, Scotch Plain, NJ), which

provides the materialbalance and key economic parameters of the process.

Toper fo rm t he Mont e C a r lo s imula t ions , key p a r t s o f t hemodel were

transferred to Microsoft Excel and

a n a l y z e d v i a M o n t e C a r l o s i m u l a t i o n , u s i n g C r y s t a l B a l l 2 0 0 0 ( D e c i s i o

neering, Denver, CO). Crystal Ball is an Add-inf o r M S E x c e l t h a t e n a b l e s t h edefinition of the probabil-ity distributions of stochastic variables, generates

randomnumbe rs ba s ed on t h es e d i s t r ib ut ions , a nd s t ore s t he re-s ul ts o f

MS Excel calculations for each trial. Monte Carlosimulations with 100,000

tr ia ls ta ke aro un d 20 min (P C: Pentium I II processor, 512 MB RAM). Each run

requ i res a round 5 MB d i s c s pa ce. We not e , however , t ha t a

g oo de s t i m a t e o f t h e s a m p l i n g d i s t r i b u t i o n o f t h e m e a n f o r primary

forecast variables can often be achieved with thedefault Crystal Ball setting of

1,000

trials.A l l S u p e r P r o m o d e l p a r t s t h a t a r e a f f e c t e d b y t h e uncer

tain parameters were transferred to MS Excel. Sincemost computations inSuperPro can also be done in spread-

s h e e t c a l c u l a t i o n s , t h i s t r a n s f e r i s p o s s i b l e , b u t i t i s t h e m o s t t i m e

con sum ing par t and has a c ert a in r is k o f t ran -script ion errors. Therefore,

it is currently necessary to vali-date the constructed base case spreadsheet

model

againstS u p e r P r o r e s u l t s t o e n s u r e t h a t a l l i n p u t s a r e c o r r e c t . Furth

er work is necessary to develop a direct linkage be-tween the simulation

software and the Monte Carlo simu-lation tool.For the environmental

assessment, a method developedby B iw er and Hei nz l e (20 04) i s use d. In

t h i s m e t h o d , a w e i g h t i n g f a c t o r i s c a l c u l a t e d f o r e v e r y i n p u t a n do u t p u t component representing the environmental relevance of thecompound.


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These environmental factors (EF) are multi-plied by the amount of the

compound in the mass balanceto o bta i n the env iro nme nta l ind ex (EI ) . The

su m of al l input, respectively, output components gives the EIs of theprocess.

These indices, like the economic indicators, rep-

res en t one of s ev era l pos s i b le i nd ica t ors t o des c r ibe t heenvi ronmenta l p

erformance of a process. For the economicevaluation, generally acceptedindicators are used

a nd t he irdef in i t ion s ca n be found in a p propr ia t e t ext b ooks ( e .g . , Pet ers

et al., 2003).

MODELING BASE CASEFermentation Model

In commerc ia l proces s es , pen ic i l l in V i s produced a s a fed-ba t ch

fermentation (Ohno et al., 2002). Regardless of whether a penicillin producer

uses its own unique strain orone acquired from a common club, fermentation

conditionsand downstream step s are established that are optimal fort h e

producer s s t ra in and f i t with in the context of a par-t icu lar faci l i ty .

However, most processes follow a similarstructure and variance is introducedfrom opera ting con-d i t ions . A t yp ica l medium i s compo s ed of g luco s e,

c o r n s t e e p l i q u o r , o r a n o t h e r c o m p l e x s o u r c e ( f o r o t h e r p o s s i - b le

sources, see Lowe, 2001), mineral salts, and phenoxy-ac et ic ac id as a

p r e c u r s o r f o r p e n i c i l l i n V ( D e m a i n a n d E l a n d e r , 1 9 9 9 ; V a n N i s t e l r o o i j e t

a l . , 1 998 ; Per ry et a l . ,1997).

P. chrysogenum

has diff iculty synthesizing the phe-nol ic s ide chain for penici l l in and

ph en ox ya ce ti c ac id is added continuously to the culture

medium.Peni c i l l in s are sec ond ary met abo l i t es , gen era l ly pro -duced at low

growth rates (Strohl, 1999). Penicillin synthe-sis starts from three activated amino acids,involves

s e v e r a l e n z y m e s a n d i s o p e n i c i l l i n N a s a m a j o r i n t e r m e d i a t e ( S t r o h l ,

1999). More details about the penicil l in synthesiscan be found in Paradkar et

al . (19 97 ) and St ro hl (1 99 7) .Key operat ing parameters requir ing optimizat ion

are tem-perature, pH, dissolved oxygen, and assimilable

n it rogen,precurs o r , re duc in g s uga rs , a n d b iom a s s co ncent ra t ion s ( Va n

Nistelrooij et a l. , 1998). In the pre sen t stud y, we use a s imp l i f ied

f e r m e n t a t i o n m o d e l t o d e s c r i b e t h e d e p e n d e n c e o f f i n a l p r o d u c t a n d b io

mass concent rations on the cell yield and maint enancecoefficient and the specific

product formation rate and yieldcoefficient. The values for the model parameters( Ta ble I )a re de r ive d f rom a combi na t ion of l i t era t ure a nd

p r o c e s s d a t a . T w o f e r m e n t a t i o n s t a g e s ( g r o w t h a n d p r o d u c t i o n p h a s e )

a r e a s s u m e d , a l t h o u g h i n s o m e o f today s highlyproductive fermentations,

such a separation no longer exists(Lowe, 2001). The first (primary) phase lasts about

50 h,and during this time mainly biomass is produced in a batchculture. After the

biomass formation slows down, penicillinV is produc ed in the second ary pha se (10 6

h). During theproduction phase, glucose is fed continuously.

Process Model

The production process model for penicil l in V is based onth e av ai la bl e

l i t e r a t u r e ( O h n o e t a l . , 2 0 0 2 ; P e r r y e t a l . ,


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1 6 8 B I O T E C H N O L O G Y A N D B I O E N G I N E E R I N G , V O L . 9 0 , N O . 2 , A P R

I L 2 0 , 2 0 0 5

1 9 9 7 ; L o w e , 2 0 0 1 ; V a n N i s t e l r o o i j e t a l . , 1 9 9 8 ) . A s p e n B a t c h P l u s a n d I n

te l l i gen s S u p e r P r o D e si g n e r w e r e t h e software packages considered for the

implementation of theprocess model. Altho ugh both packa ges are robust simu-lation tools, SuperPro Designer was chosen based on theintuitive relationship

between its process representationa n d t h e s p r e a d s h e e t m o d e l t h a t

w a s c o n s t r u c t e d f o r Monte Carlo analysis.F i g ur e 1 s h ow s t he p r o ce s s

flow diagram created withthe software SuperPro Designer. Fermenters with a

totalcapacity of 40200 m

3

are used for production (Ohno et al.,2002; Lowe, 2001; Falbe and Regni tz, 1999;

Perry et al.,1997). We chose a facility with 11 fermenters, each with avolume of

100 m

3, optimizing the usage of the downstreamequipment. Penicillin V sodium salt is

the final

product .The media components (pharmamedia , t race metals ,phenoxyacet

ate; S-102 to S-104) are blended in tank P-1and sterilized in the continuous

heat sterilizer P-4. The glu-cose solution is prepared in tank P-2. Medium and

g lucoses o lut ion a re fe d t o t he fe rment e r P -7 ( g luco s e s o lut ion i s fed

continuously only during the production phase). The air(S-113) is compresse d (P-5) and

filter sterilized (P-6). Theexhaust air, containing mainly carbon dioxide, is

filtered(P-8) to prevent release of by-products to the environment.

Figure 1.Process flow diagram of the penicillin V production model (SuperPro Designer, version 5.1).

Table I.

Parameter values of the fermentation model of penicillin V

production.P a r a m e t e r V a l u e Y i e l d c o

e f f i c i e n t s V a l u e

t

exp

(time of exponential growth) (h)50

Y

X/pharmamedia( g / g ) 2 . 1 4

t

prod

( t i m e o f p r o d u c t i o n ) ( h ) 1 0 6

Y

X/gluc.

( g / g ) 0 . 4 5

X

f

(biomass concentration at texp


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) ( g / L ) 3 0

Y

pen./gluc.

( g / g ) 0 . 8 1

X

nl( f i n a l b i o m a s s c o n c e n t r a t i o n ) ( g / L ) 4 5

Y

pen./phenoxyacetic acid

( g / g ) 2 . 0 0

V

in

( i n i t i a l v o l u m e ) ( L ) 5 5 , 0 0 0

Y

X/O2

( g / g ) 1 . 5 6V

final

( f i n a l v o l u m e ) ( L ) 7 5 , 0 0 0

m

gluc.

(maintenance coefficient)(g glu./g dcw h)0.022

P

final

( f i n a l p r o d u c t c o n c e n t r a t i o n ) ( g / L ) 6 3 . 3

mO2

(maintenance coefficient)(g/g dcw h)0.023

B I W E R E T A L . : U N C E R T A I N T Y A N A L Y S I S P E N I C I L L I N P R O D U C T I O N

1 6 9


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In t he ag itated fe rmenter, bioma ss and pe nici llin V are pro-duced consuming the

carbon sources, the precursor, and themineral sal ts.After the fermentatio n, the

fermenter content is fed to aharvest tank (P-

9).A t y p i c a l d o w n s t r e a m p r o c e s s i s d i v i d e d i n t o t h e following

unit processes: biomass removal, extraction, re-extraction, and crystallization,

filtration and crystal washingand drying (Van Nistelrooij et al., 1998). The

f e r m e n t a - t i o n b r o t h f l o w s t o t h e r o t a r y v a c u u m f i l t e r P - 2 0 , w h e r e w ash

water (S-150) is used to recover product for the re-tained biomass. The retainedfungal biomass is discharged(S-151).Before extraction, the cell-

f ree b rot h i s a c id i f ied t o a pH of

f

3 in P-22, using sulfuric acid (S-154) and

cooledt o m in imiz e d egra da t ion dur ing a c id ext ra ct ion . I n t he centr ifugal

extract ion step (P-23), the penici ll in is trans-ferr ed in to the or ga ni c ph as e

( b u t y l a c e t a t e , S - 1 5 7 ) . T h e remaining aqueous solution is discharged and neutralized

inP - 2 4 w i t h s o d i u m h y d r o x i d e ( 1 0 % w / w , S - 1 5 9 ) . T h e penicillin is re-

extracted (P-25) into acetone/water (S-162),where sodium acetate is added (S-

16 3) . T he so di um sa lt of penicil l in V then precipitates. The crystals (S-165)areseparated and washed in the basket centrifugation (P-26)and conveyed to


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the fluid bed dryer (P-31). The remainingwashing solution is discharged (S-173).

The solut ion sep-arated in the centr i fuge (S-168) i s lead to P-

2 7 , w h e r e m o s t o f t h e b u t y l a c e t a t e i s s p l i t o f f i n a r e c y c l i n g

s te p( n o t s h o w n i n d e t a i l ) . T h e r e s t i s d i s c h a r g e d a n d n e u -

t r a l i z e d i n P - 2 8 ( N a O H , 1 0 % w / w ; S - 1 7 0 ) . T h e b u t y l a ce ta t e

is reu sed in t he ext rac t ion . In P -29 , f res h b uty lacetate is added (S-156) . Inthe dryer (P-31), the penic il linis dr i ed wit h a i r (S- 175 ) and the f in a l

pro duc t s t ore d i ntank P-32.

EVALUATION BASE CASE

A p r o c e s s s i m u l a t i o n w a s r u n a s a b a s e c a s e t o

es t a b l i s ha r efere nce p o int f or bot h econ omic a nd env i ronm ent a l assessm

ent.

Base Case Analysis

T h e a v e r a g e p r o d u c t i o n r a t e f r o m t h e f a c i l i t y i s a p p r o x - i m a t e l y

263 kg penic i l l in V sodium sa lt per hour . Thisresults in an annual

production of 2,090 tons with the as-s u mp t io n o f 3 3 0 o p e ra t in g d a y s. T h e i n it i a l f e r me n t er v o l u m e i s 5 5

m

3

a n d 2 0 m

3

are added as nutrient andprecursor feeds (36%). The volume added in the

model iswithin the range given by Lowe (2001). Annual productioni s 5 4 6

b a t c h e s a n d i t i s a s s u m e d t h a t 1 6 f a i l ( 3 % ) . T h e o ve ra l l

y i e l d o f t h e f e r m e n t a t i o n i s 0 . 2 1 g p e n i c i l l i n / g g l u c o s e . T h e y i e l d a c r o s s

do wn str eam re co ve ry is 90 %. The carbon balance shows that around 25% oft he C -a toms a re conve rt ed t o pen i c i l l i n , 17% t o b iom a s s , a n d 60%

tocarbon dioxide.Table II presents the summary material balance for

t heba s e ca s e proce s s . A l t oget her , 7 ,880 kg/h ra w ma t er ia l s a re needed,

which is 30 kg per k g final product (kg/kg P).The input includes a number of

mater ia ls that are typical for fer men tat i on pro ces ses : a h i gh amou nt of

w a t e r , g l u - c o s e a s c a r b o n s o u r c e , o x y g e n , m e d i a , a n d t r a c e

m e t a l s . S p e c i f i c t o t h e p e n i c i l l i n p r o d u c t i o n i s t h e d e m a n d f o r p he nox yac

etic acid. Furthermore, relevant amounts of thesolvents butyl acetate and

acetone are needed for extrac-t io n, and a smal ler amo unt of sodi um

ac et at e th at fo rm sthe final product with the penicill in is needed in the crys-tallization step.Besides the product, the fermentation output consists

o f l a r g e a m o u n t s o f c a r b o n d i o x i d e a n d b i o m a s s . F u r t h e r -

mo re , s ig ni f i ca nt am ou nt s o f u nu se d r aw mat er ia ls and unrecovered product

leave the process. This model assumesan 80 % re cy cl in g o f bu ty l ac e ta te (s ee

al so Ch an g et al ., 2002). Acetone (S-167, S-173) is also recycled (70%)

(notshown in Fig.

1).T h e p r o c e s s c o n s u m e s 4 1 G W h e l e c t r i c a l p o w e r (20

kWh/kg P); 4,400 tons steam (2.1 kg/kg P); 6.4 millionm

3

chilled water (3.1 m3


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/ k g P ) , a n d 3 m i l l i o n m

3

coolingwater (1.4 m

3

/k g P ) . The com pre ssor and the fe rmen ter consume 90% of the electr ical

energy required. The ster-i l iz at i on pro ce ss (P -4 ) i s t h e m a i n c o n s u m e r o f s t e a m , a l t h o u g h s o m e s t e a m i s a l s o r e q u i r e d

f o r d r y i n g . C h i l l e d w a t e r i s u s e d m a i n l y i n t h e f e r m e n t e r a n d

t h e s t e r i l i z a -

t i o n s t e p ; a d d i t i o n a l c o o l i n g w a t e r i s u s e d i n t h e c o m - p re ss or P -

5 . I n t h e e x t r a c t i o n s t e p , f r e o n i s u s e d a s h e a t t r a n s f e r a g e n t . T h e

e n e r g y d e m a n d f o r t h e r e c y c l i n g o f t h e f r e o n i s a d d e d t o t h e e l e c t r i c i t y

d e m a n d . T h e

r e s u l t s o f t h e e n e r g y a n a l y s i s a r e c o n s i s t e n t w i t h O h n o e t a l . ( 2 0 0

2), who state the energy requirement per kg product

Table II.Material balance of the model of the penicillin V

production.*C o m p o n e n t I n p u t [ k g / k g P ] O u t p u t [

k g / k g P ] A c e t i c a c

i d

0 . 1 6 A c e t o n

e 0 . 1 2 0 . 1 2 B

i o m a s s ( d c w )

0 . 8 6 B u t y l a c e t

a t e 0 . 2 8 0 . 2 8 C a r

b o n d i o x i d e 5 . 3 1 G l u c o s e

4 . 9 5 0 . 1 0 O

x y g e n 2

. 5

P e n i c i l l i n V ( l o s s )

0 . 1 0 P e n i c i l l i n V s o d i u

m s a l t

1 . 0 0 P h a r m a m e d i a

0 . 4 6 0 . 0 6 P h e n o x y a ce t i c a c i d 0 . 5 8 0 . 0 1 S o d

i u m a c e t a t e 0 . 2 3

0 . 0 1 S u l f u r i c a c i

d 0 . 0 5 0 . 0 5 T r a c e

m e t a l s 0 . 6 7 0 .

0 9 S o d i u m h y d r o x i d e

0 . 1 2 0 . 1 2 W a t e r

2 0 . 0 2 1 . 8

T o t a l 3 0 .

0 3 0 . 0 *The recycling of butyl acetate andacetone is already considered. Fromthe amount of air transport ed through the


12/12

fermenter, only the amount of oxygen consumed is compiled in (kg/kg P) = kg

component per kg finalproduct; final product = penicillin V sodium salt; dcw =

dry cell weight.

1 7 0 B I O T E C H N O L O G Y A N D B I O E N G I N E E R I N G , V O L . 9 0 , N O . 2 , A P

uncertainty analysis of penicillin vproduction using monte carlo simulation

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