uncertainty analysis of penicillin v production using monte carlo simulation

Uncertainty Analysis of Penicillin VProduction Using Monte Carlo Simulation

Arno Biwer,1 Steve Griffith,1,2 Charles Cooney1

1Department of Chemical Engineering, Massachusetts Institute of Technology,Massachusetts 02139; telephone: 617-253-3108; fax: 617-258-6876;e-mail: [email protected] Pharma, Cambridge, Massachusetts 02139

Received 8 July 2004; accepted 1 October 2004

Published 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 and thus is not capable of dealing 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 as analysis of its cost structureand environmental impact. The second step is identifica-tion of uncertain variables and determination of their proba-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, theoverall variation of these objective functions are quantified,the technical, supply chain, and market parameters thatcontribute most to the existing variance are identified andthe differences between economic and ecological 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 and environmental impact. The pen-icillin selling price dominates return on investment vari-ance as well as the variance for other revenue-dependentparameters. B 2004 Wiley Periodicals, Inc.

Keywords: Monte Carlo simulation; uncertainty; vari-ability; penicillin; economic assessment; environmentalassessment

INTRODUCTION

Commercial process simulation software usually provides

analysis that assumes deterministic process parameters.

The software does not consider existing variations of tech-

nical, supply chain, and market parameters that can sig-

nificantly alter operating decisions and batch-to-batch

expectations. However, an understanding of these param-

eters and their uncertainty is essential for the economic

success of a process design and the analysis of existing

processes. Thus, a methodology is needed that combines

standard process simulation software with uncertainty anal-

ysis. In this article, we use a well-characterized process, the

production of penicillin, to illustrate how this goal might

be accomplished.

Penicillins produced by Penicillium chrysogenum are

still among the most important antibiotics. Penicillins be-

long to a family of hydrophobic h-lactams. Each contains

a different acyl side chain attached by an amide link-

age to the amino group of the penicillin nucleus, the

6-aminopenicillanic acid. Penicillin G and penicillin V

are the main commercial penicillins. Most of the pen-

icillin V (phenoxymethylpenicillin) is converted to 6-

aminopenicillanic acid (6-APA), which in turn is used

to make amoxicillin and ampicillin (McCoy, 2000). In

addition, penicillin V is used directly as an antibiotic

(f1,600 tons per year) (Van Nistelrooij et al., 1998)

and ranks among the 100 top prescribed drugs in the

United States (American Druggist, http://www.rxlist.com/

top200a.htm, May 2004).

h-Lactam antibiotics amount to about 60% of the

worldwide antibiotics market; this was approximately

$5 billion per year in sales in 1999 (Demain and Elander,

1999). The global demand for h-lactams grows by around

2% annually, mainly because of rising demand in countries

such as China and India (Milmo, 2003). Lowe (2001)

estimates that the world production of penicillin was

65,000 tons in 2001. As a result of large overcapacity

in the market, penicillin prices have been under continu-

ous pressure for several years. Prices have fallen signifi-

cantly during the last several years from $20/billion units

(BU) during the mid-1990s to $12/BU in 1997 to $9/BU

in 2000 (McCoy, 2000). As of 2003, the price of peni-

cillin G was approximately $11/BU, which is $17–18/kg

(Milmo, 2003).

Improvements in the penicillin production process result

primarily from genetic-based strain improvements, while

the process flowsheet has changed very little (Van

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

been realized from refinement in operating conditions,

B 2004 Wiley Periodicals, Inc.

Correspondence to: C. Cooney

This article includes supplementary material available via the Internet at

http://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 in

production. As such, it takes many more experiments or

production runs to statistically verify the impact of a par-

ticular process change. In the present work, we assess how

variance in strain and process parameters affects key eco-

nomic and environmental impact metrics. Because environ-

mental concerns have become increasingly important, we

include an environmental 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 approach that provides a general method-

ology for combining process simulation software and

spreadsheet modeling to conduct high-leverage uncertainty

analysis. This offers a fundamental basis for decision

making in the design and analysis of bioprocesses.

MATERIALS AND METHODS

The process model for penicillin V production was built

using the process simulator SuperPro Designer version 5.1

(Intelligen, Scotch Plain, NJ), which provides the material

balance and key economic parameters of the process. To

perform the Monte Carlo simulations, key parts of the

model were transferred to Microsoft Excel and analyzed

via Monte Carlo simulation, using Crystal Ball 2000

(Decisioneering, Denver, CO). Crystal Ball is an ‘‘Add-in’’

for MS Excel that enables the definition of the probabil-

ity distributions of stochastic variables, generates random

numbers based on these distributions, and stores the re-

sults of MS Excel calculations for each trial. Monte Carlo

simulations with 100,000 trials take around 20 min (PC:

Pentium III processor, 512 MB RAM). Each run requires

around 5 MB disc space. We note, however, that a good

estimate of the sampling distribution of the mean for

primary forecast variables can often be achieved with the

default Crystal Ball setting of 1,000 trials.

All SuperPro model parts that are affected by the

uncertain parameters were transferred to MS Excel. Since

most computations in SuperPro can also be done in spread-

sheet calculations, this transfer is possible, but it is the

most time consuming part and has a certain risk of tran-

scription errors. Therefore, it is currently necessary to vali-

date the constructed base case spreadsheet model against

SuperPro results to ensure that all inputs are correct.

Further 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 developed

by Biwer and Heinzle (2004) is used. In this method, a

weighting factor is calculated for every input and output

component representing the environmental relevance of the

compound. These environmental factors (EF) are multi-

plied by the amount of the compound in the mass balance

to obtain the environmental index (EI). The sum of all

input, respectively, output components gives the EIs of the

process. These indices, like the economic indicators, rep-

resent one of several possible indicators to describe the

environmental performance of a process. For the economic

evaluation, generally accepted indicators are used and their

definitions can be found in appropriate textbooks (e.g.,

Peters et al., 2003).

MODELING BASE CASE

Fermentation Model

In commercial processes, penicillin V is produced as a

fed-batch fermentation (Ohno et al., 2002). Regardless of

whether a penicillin producer uses its own unique strain or

one acquired from a common club, fermentation conditions

and downstream steps are established that are optimal for

the producer’s strain and fit within the context of a par-

ticular facility. However, most processes follow a similar

structure and variance is introduced from operating con-

ditions. A typical medium is composed of glucose, corn

steep liquor, or another complex source (for other possi-

ble sources, see Lowe, 2001), mineral salts, and phenoxy-

acetic acid as a precursor for penicillin V (Demain and

Elander, 1999; Van Nistelrooij et al., 1998; Perry et al.,

1997). P. chrysogenum has difficulty synthesizing the phe-

nolic side chain for penicillin and phenoxyacetic acid is

added continuously to the culture medium.

Penicillins are secondary metabolites, generally pro-

duced at low growth rates (Strohl, 1999). Penicillin synthe-

sis starts from three activated amino acids, involves several

enzymes and isopenicillin N as a major intermediate

(Strohl, 1999). More details about the penicillin synthesis

can be found in Paradkar et al. (1997) and Strohl (1997).

Key operating parameters requiring optimization are tem-

perature, pH, dissolved oxygen, and assimilable nitrogen,

precursor, reducing sugars, and biomass concentrations

(Van Nistelrooij et al., 1998).

In the present study, we use a simplified fermentation

model to describe the dependence of final product and

biomass concentrations on the cell yield and maintenance

coefficient and the specific product formation rate and yield

coefficient. The values for the model parameters (Table I)

are derived from a combination of literature and process

data. Two fermentation stages (growth and production

phase) are assumed, although in some of today’s highly

productive 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 batch

culture. After the biomass formation slows down, penicillin

V is produced in the secondary phase (106 h). During the

production phase, glucose is fed continuously.

Process Model

The production process model for penicillin V is based on

the available literature (Ohno et al., 2002; Perry et al.,

168 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 90, NO. 2, APRIL 20, 2005

1997; Lowe, 2001; Van Nistelrooij et al., 1998). Aspen

Batch Plus and Intelligen’s SuperPro Designer were the

software packages considered for the implementation of the

process model. Although both packages are robust simu-

lation tools, SuperPro Designer was chosen based on the

intuitive relationship between its process representation

and the spreadsheet model that was constructed for

Monte Carlo analysis.

Figure 1 shows the process flow diagram created with

the software SuperPro Designer. Fermenters with a total

capacity of 40–200 m3 are used for production (Ohno et al.,

2002; Lowe, 2001; Falbe and Regnitz, 1999; Perry et al.,

1997). We chose a facility with 11 fermenters, each with a

volume of 100 m3, optimizing the usage of the downstream

equipment. Penicillin V sodium salt is the final product.

The media components (pharmamedia, trace metals,

phenoxyacetate; S-102 to S-104) are blended in tank P-1

and sterilized in the continuous heat sterilizer P-4. The glu-

cose solution is prepared in tank P-2. Medium and glucose

solution are fed to the fermenter P-7 (glucose solution is

fed continuously only during the production phase). The air

(S-113) is compressed (P-5) and filter sterilized (P-6). The

exhaust 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.

Parameter Value Yield coefficients Value

texp (time of exponential growth) (h) 50 YX/pharmamedia (g/g) 2.14

tprod (time of production) (h) 106 YX/gluc. (g/g) 0.45

Xf (biomass concentration at texp) (g/L) 30 Ypen./gluc. (g/g) 0.81

Xnl (final biomass concentration) (g/L) 45 Ypen./phenoxyacetic acid (g/g) 2.00

Vin (initial volume) (L) 55,000 YX/O2 (g/g) 1.56

Vfinal (final volume) (L) 75,000 mgluc. (maintenance coefficient)

(g glu./g dcw h)

0.022

Pfinal (final product concentration) (g/L) 63.3 mO2 (maintenance coefficient)

(g/g dcw h)

0.023

BIWER ET AL.: UNCERTAINTY ANALYSIS PENICILLIN PRODUCTION 169

In the agitated fermenter, biomass and penicillin V are pro-

duced consuming the carbon sources, the precursor, and the

mineral salts.

After the fermentation, the fermenter content is fed to a

harvest tank (P-9).

A typical downstream process is divided into the

following unit processes: biomass removal, extraction, re-

extraction, and crystallization, filtration and crystal washing

and drying (Van Nistelrooij et al., 1998). The fermenta-

tion broth flows to the rotary vacuum filter P-20, where

wash water (S-150) is used to recover product for the re-

tained biomass. The retained fungal biomass is discharged

(S-151).

Before extraction, the cell-free broth is acidified to a

pH of f3 in P-22, using sulfuric acid (S-154) and cooled

to minimize degradation during acid extraction. In the

centrifugal extraction step (P-23), the penicillin is trans-

ferred into the organic phase (butyl acetate, S-157). The

remaining aqueous solution is discharged and neutralized in

P-24 with sodium hydroxide (10% w/w, S-159). The

penicillin is re-extracted (P-25) into acetone/water (S-162),

where sodium acetate is added (S-163). The sodium salt

of penicillin V then precipitates. The crystals (S-165) are

separated and washed in the basket centrifugation (P-26)

and conveyed to the fluid bed dryer (P-31). The remaining

washing solution is discharged (S-173). The solution sep-

arated in the centrifuge (S-168) is lead to P-27, where

most of the butyl acetate is split off in a recycling step

(not shown in detail). The rest is discharged and neu-

tralized in P-28 (NaOH, 10% w/w; S-170). The butyl

acetate is reused in the extraction. In P-29, fresh butyl

acetate is added (S-156). In the dryer (P-31), the penicillin

is dried with air (S-175) and the final product stored in

tank P-32.

EVALUATION BASE CASE

A process simulation was run as a base case to establish

a reference point for both economic and environmental

assessment.

Base Case Analysis

The average production rate from the facility is approx-

imately 263 kg penicillin V sodium salt per hour. This

results in an annual production of 2,090 tons with the as-

sumption of 330 operating days. The initial fermenter

volume is 55 m3 and 20 m3 are added as nutrient and

precursor feeds (36%). The volume added in the model is

within the range given by Lowe (2001). Annual production

is 546 batches and it is assumed that 16 fail (3%). The

overall yield of the fermentation is 0.21 g penicillin/g

glucose. The yield across downstream recovery is 90%.

The carbon balance shows that around 25% of the C-atoms

are converted to penicillin, 17% to biomass, and 60% to

carbon dioxide.

Table II presents the summary material balance for the

base case process. Altogether, 7,880 kg/h raw materials

are needed, which is 30 kg per kg final product (kg/kg P).

The input includes a number of materials that are typical

for fermentation processes: a high amount of water, glu-

cose as carbon source, oxygen, media, and trace metals.

Specific to the penicillin production is the demand for

phenoxyacetic acid. Furthermore, relevant amounts of the

solvents butyl acetate and acetone are needed for extrac-

tion, and a smaller amount of sodium acetate that forms

the final product with the penicillin is needed in the crys-

tallization step.

Besides the product, the fermentation output consists of

large amounts of carbon dioxide and biomass. Further-

more, significant amounts of unused raw materials and

unrecovered product leave the process. This model assumes

an 80% recycling of butyl acetate (see also Chang et al.,

2002). Acetone (S-167, S-173) is also recycled (70%) (not

shown in Fig. 1).

The process consumes 41 GWh electrical power

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

m3 chilled water (3.1 m3/kg P), and 3 million m3 cooling

water (1.4 m3/kg P). The compressor and the fermenter

consume 90% of the electrical energy required. The ster-

ilization process (P-4) is the main consumer of steam,

although some steam is also required for drying. Chilled

water is used mainly in the fermenter and the steriliza-

tion step; additional cooling water is used in the com-

pressor P-5. In the extraction step, freon is used as heat

transfer agent. The energy demand for the recycling of

the freon is added to the electricity demand. The results

of the energy analysis are consistent with Ohno et al.

(2002), who state the energy requirement per kg product

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

Component Input [kg/kg P] Output [kg/kg P]

Acetic acid — 0.16

Acetone 0.12 0.12

Biomass (dcw) — 0.86

Butyl acetate 0.28 0.28

Carbon dioxide — 5.31

Glucose 4.95 0.10

Oxygen 2.5 —

Penicillin V (loss) — 0.10

Penicillin V sodium salt — 1.00

Pharmamedia 0.46 0.06

Phenoxyacetic acid 0.58 0.01

Sodium acetate 0.23 0.01

Sulfuric acid 0.05 0.05

Trace metals 0.67 0.09

Sodium hydroxide 0.12 0.12

Water 20.0 21.8

Total 30.0 30.0

*The recycling of butyl acetate and acetone is already considered. From

the amount of air transported through the fermenter, only the amount of

oxygen consumed is compiled in (kg/kg P) = kg component per kg final

product; final product = penicillin V sodium salt; dcw = dry cell weight.


to be 108 MJ (30 kWh) electrical energy, 40 kg steam

and 9 m3 cooling water. However, the demand of steam

is only 5% of that amount. In Ohno et al. (2002), most

of the steam is needed for batch sterilization. In our mod-

el, continuous sterilization is used, and it requires much

less steam.

Economic Assessment

The base case model provides an estimate of the costs

involved in penicillin manufacture. Combined with the

current market price of penicillin, these estimates allow us

to calculate a number of financial measures that indicate

the economic value of an investment in penicillin manu-

facture. Although in a rigorous capital budgeting process,

we would seek to determine the net present value of the

estimated investment, we use the basic financial metrics of

earnings before interest and taxes (EBIT), earnings before

interest, taxes, depreciation, and amortization (EBITDA),

and return on investment (ROI) in the analyses that follow.

The justification for the use of these metrics is that our

primary objective is illustration of uncertainty analysis

rather than project valuation.

In the model, the total purchased equipment costs is

$9.1 million. Based on data from Peters et al. (2003), it

was assumed that the purchased equipment cost is 27.5%

of fixed capital investment (FCI) leading to a FCI of

$44.1 million and a total capital investment (TCI) of

$51.4 million. The fermenters with $5.5 million dominate

the purchase costs. All other equipment costs less than

$1 million; thus, the fermenters and related equipment dom-

inate the equipment costs, in agreement with the analysis

of Swartz (1979).

The total operating costs are $33.8 million per year. The

raw material costs, mainly glucose, phenoxyacetic acid and

butyl acetate (including recycling costs), have the biggest

share (37%); this is consistent with results from Lowe

(2001). They are followed by equipment-dependent costs

(24%) (mainly depreciation and maintenance) and the labor

costs (14%). Utility costs (11%, mainly electricity) and

plant overhead cost (11%) also play an important role,

while laboratory/QC/QA, waste treatment, and consum-

ables (altogether 3%) have only a small impact. Seven

single operating cost parameters capture each by them-

selves more than 2% of the global operating costs. The

fermenter-related costs of glucose (6.3%), phenoxyacetic

acid (12.9%), and electricity for fermenter (2.0%) and

compressor (3.0%) constitute 25% of the total operating

costs. Furthermore, basic labor cost (11.5%), butyl acetate

(9.1%, including recycling cost), and chilled water demand

(3.1%) contribute considerably to the operating cost. Here

we note that the price of glucose and assumed hourly labor

rates play an important role. This explains why today most

penicillin producing plants are located in countries where

sugar and labor costs are low but are capable of supplying a

stable source of energy given the high energy requirements

of the process.

Based on an annual production of 2,090 tons, the unit

production costs in the model are $16.2/kg final prod-

uct, which equals $10.3/BU. The selling price is set to be

$17.3/kg (Milmo, 2003). Hence, the annual revenue is

$36 million. Since the cost of operations is $32 million per

year, this results in EBITDA of $4.0 million. Including

depreciation leads to negative EBIT of �$350,000 and

the ROI is negative (�0.5%). Note that the ROI number

assumes a 35% tax rate and no financial leverage for the

project (i.e., no interest payments).

Environmental Assessment

Environmental aspects have become increasingly important

in pharmaceutical production and should be considered

together with the economic assessment (DeSimone and

Popoff, 1997). The method used, which was recently

developed by Biwer and Heinzle (2004), aggregates the

whole range of possible environmental impacts to two per-

formance figures that enable an appropriate comparison

with the economic key figures and the examination of

how uncertainty affects the environmental impact. They

are therefore more suitable for this purpose than complex

methods such as the life cycle assessment.

Wastewater is discharged mainly from the extraction

step (remaining broth after penicillin removal) and after the

separation of the crystals in the basket centrifugation,

where a mixture of butyl acetate, acetone, water and some

impurities are discharged. After a partial removal of the

butyl acetate (P-27) and acetone (not shown), both waste

streams (S-171, S-173) are assumed to pass to a biological

wastewater treatment plant. Solid waste is produced in the

biomass removal. The only relevant emission is the exhaust

air of the fermenter, which includes a large amount of

carbon dioxide (S-117). We have not attempted to assess

fugitive emissions from the process.

Figure 2 shows the EI of the input and output

compounds. On the input side, the media components

Figure 2. Environmental indices (EI) of the input and output

components of the penicillin V production model. [IP/kg P] = index

points per kg final product.


(mainly ammonium sulfate), the precursor phenoxyacetic

acid, butyl acetate (extraction), and acids and bases (used

for pH control of the extraction and neutralization of

waste streams) have the highest indices. Although glu-

cose and pharmamedia are used in large amounts, they

are not relevant in any of the input impact categories

(for further details, see Biwer and Heinzle, 2004). Hence,

their environmental factor is EFIn = 0, and they do not

appear in the evaluation of the input. The output EIs

are strongly dominated by the carbon dioxide produced

during the fermentation. Furthermore, the biomass, the

butyl acetate used in the extraction, acids + bases and

the acetic acid formed in the re-extraction step (P-25) have

some impact.

The overall EI, which describes the environmental

performance of the process, for the input is EIIn =

0.45 Index Points/kg P (= IP/kg P), for the output EIOut =

0.72 IP/kg P. Thus, from an environmental point of

view, the output has a higher relevance than the input. In

addition to the material balance, the energy consumption

also contributes significantly to the environmental impact

of a process (Castells et al., 1994). The supply of energy

affects the input side by consuming fossil energy sources

and the output side by generating air pollution (e.g., carbon

dioxide, sulfur dioxide).

OBJECTIVE FUNCTIONS, VARIABLES, ANDPROBABILITY DISTRIBUTIONS

One of the inherent problems in fermentation process de-

velopment is the variability associated with both the biol-

ogy and the process itself. We set out to understand how

variance in key biological and process parameters would

impact the final result. Using the process model as the basis

for a Monte Carlo simulation (MCS), we can explore how

variance propagates through the entire process to impact

both economic and environmental results. A crucial step in

this analysis is selecting the objective functions, the input

variables, and their probability distributions.

Several output parameters are useful as economic

objective functions. These include the unit production

costs (UPC); the EBIT; the EBITDA; and the ROI. Also

relevant is the input and output EI of the process. In our

analysis, the investment cost and the plant overhead cost

are kept constant to represent an existing facility.

From the process model, a number of technical, supply

chain, and market parameters routinely exhibit uncertain-

ty. Table III summarizes these parameters and their prob-

ability distribution. The probability distributions shown

there are derived from experimental data and are assumed

to reflect the expected uncertainty in a process. For a more

detailed discussion of these terms, see Vose (2003). For

simplification, all variables chosen are assumed inde-

pendent. This assumption is true for most parameters.

For those parameters, where a known correlation exists,

e.g., biomass concentration and agitator power, the im-

pact on the objective functions is small and so Crystal

Ball’s correlation capability was not used in the Monte

Carlo simulations.

Technical Parameters

Technical parameters are all process parameters that affect

the fermentation and the downstream steps on a batch-

to-batch basis. In our analysis of technical parameter

variability, we take the perspective of product development

and assume that the true mean of each parameter is

unknown but described by a distribution. This allows us to

calculate economic parameters, such as ROI, for each

Monte Carlo trial in a meaningful way. We recognize,

however, that the penicillin process is quite well charac-

terized, so we could have performed technical parameter

uncertainty analysis with regard to process capabilities,

which are defined by operating specifications, means, and

standard deviations.

In this work, variability is described for values that

determine the biomass and product formation. For all such

parameters (see Table III) we have assumed a normal

distribution and their mean values and coefficients of

variation are derived from experimental data. Additionally,

minimum and, for some parameters, maximum values as

well, are defined, since in reality many distributions that

are normal within a few standard deviations of the mean

never assume values that are many standard deviations

from the mean and so should not be sampled during

simulation. The mean value of the final product concen-

tration is based on the work of Demain and Elander (1999)

and Van Nistelrooij et al. (1998). Fermentation time and

initial and final broth volumes are assumed to be deter-

ministic. Fermentation conditions do vary, as represented in

the MCS by the aeration rate and the power consumption of

the stirrer.

In the base case, the overall yield of the separation and

purification section is 90%. In the MCS, the variation in

overall recovery is achieved by varying the yield of indi-

vidual steps (P-20, P-25, P-26, P-31) and the partition co-

efficient (KPen) of the extraction step (P-23). For these

parameters, a set of probability distributions is assumed

that results in variability of the overall purification yield

equal to the variability usually observed in actual processes.

For the yield parameters, a normal distribution is assumed,

while for the partition coefficient, a uniform distribution is

chosen (see Table III). Depending on minor variations of

pH value, the KPen varies between the two values defined.

Under environmental and economic aspect the recycling of

butyl acetate and acetone is crucial. Mean values and stan-

dard deviations are defined based on yields and variability

usually occurring in the recycling of organic solvent.

Supply Chain and Market Parameters

The technical parameters are largely defined by the process

and are under the control of the manufacturer (e.g., strain


used, fermentation or purification conditions). Supply chain

and market parameters are not influenced by the process

conditions and display variance that affects the economics

of the process over an extended period.

The raw material costs account for a large part of the unit

production costs. They are dominated by the costs for

glucose and phenoxyacetic acid. Therefore, the prices of

these materials are considered in the MCS. The mean

glucose price was calculated from monthly average prices

on the world market from 1996 to 2001. Using the ‘‘batch

fit’’ function of Crystal Ball, a h distribution was identified

as the best fit (values see Table III). h distributions are

often used to describe empirical data. For phenoxyacetic

acid, an average price is chosen that is realistic for the

annual demand of 1,600 tons.

The energy costs are dominated by the costs for

electricity. Mean value and probability distribution for this

parameter are derived from monthly average prices for the

United States from 1995 to 2003. (Weibull distribution,

values see Table III).

The price for penicillin V and penicillin in general has

varied dramatically over the last few years as noted earlier.

As the mean value, the current price stated by Milmo (2003)

is used, and a coefficient of variation of 10% is assumed.

Best-Case and Worst-Case Scenario

Based on the parameters chosen, a best-case and a worst-

case scenario are calculated. For those parameters where a

standard deviation is defined, 2 times the standard devi-

Table III. Parameters used for Monte Carlo simulation and their variation and probability distribution chosen.*

Parameter

Base case

value Source

Probability

distribution Variation data Source

1. Technical Parameters

Yield biomass on

glucose (g/g)

0.45 Internal estimate, based

on fermentation data

Normal V = 17.5%; min: 0.2 Industry data

Maintenance coefficient

(mg glucose/g dcw h)

22 Internal estimate, based


Normal V = 17.5%; min: 10 Industry data

Precursor utilization

efficiency (%)

92 De Tilly et al., 1982 Normal V = 15.0; 70–100 (min, max) Industry data

Final biomass

concentration (g/L)

45.0 Internal estimate, based


Normal V = 17.5%; min: 25 Industry data

Final product

concentration (g/L)

63.6 Demain and Elander,

1999; Van Nistelrooij

et al., 1998

Normal V = 10%; 20–100 (min, max) Industry data

Aeration rate (vvm) 0.8 Perry et al., 1997;

Lowe, 2001

Normal V = 10%; 0.5–1.0 (min, max) Perry et al., 1997;

internal estimate

Agitator power (kW/m3) 2.5 Perry et al., 1997;

Lowe, 2001

Normal V = 20%; 1.5–3.5 (min, max) Perry et al., 1997;

internal estimate

Yield downstream recovery (%) 90 Lowe, 2001;

Van Nistelrooij

et al., 1998

Normal Calculated for single step yields

Yield biomass removal (%) 97 Internal estimate Normal F2 (SD)

Industry data

(overall yield)

Kj extraction 60 McCabe et al., 2001 Uniform 60–80

Yield crystallization (%) 97 Internal estimate Normal F2 (SD)

Yield basket centrifuge (%) 99 Internal estimate Normal F1 (SD)

Yield fluid bed dryer (%) 99 Internal estimate Normal F1 (SD)

Yield butyl acetate

recycling (%)

80 Internal estimate Normal F5 (SD) Internal estimate

Yield acetone recycling (%) 70 Internal estimate Normal F5 (SD) Internal estimate

2. Supply chain parameters

Price glucose [$/kg] 0.216 USDA Foreign

Agricultural Service,

2001a

h a = 3.49; h = 1.2;

scale = 29.1 (for a normal

distribution: V = 25%)

USDA Foreign

Agricultural Service, 2001a

Price phenoxyacetic

acid ($/kg)

3.80 Internal estimate;

supplier data

Normal V = F10% Internal estimate

Electricity cost ($/kWh) 0.0468 U.S. Energy Information

Administration, 2004b;

Peters et al., 2003

Weibull Loc: 4.13; Scale: 0.61;

Shape: 1.96

(for a normal distr.: V = 6%)

U.S. Energy Information

Administration, 2004b

3. Market parameters

Selling price final

product ($/kg)

17.30 Milmo, 2003 Normal V = F10% Internal estimate

*SD, Standard deviation; V, coefficient of variance.aForeign Agricultural Service. 2001. World and U.S. raw and defined sugar prices. Available at U.S. Department of Agriculture, Foreign Agricultural

Services: http://www.fas.usda.gov/htp/sugar/2000/November/prices.pdf.bU.S. Energy Information Administration. 2004. February 2004 Monthly Energy Review. Available at http://www.eia.doe.gov.


ation is used to increase and respectively decrease the

base case value. When the values are higher than the

highest possible value, the highest possible value is used

(e.g., recovery yield basket centrifuge: 100%). When a

certain range is defined for a parameter, the maximum and

minimum values set the worst-case and best-case values.

For instance, the lowest and highest prices in the real data

for glucose and electricity are used.

Table IV shows the values of the objective functions for

the three cases. These values define, based on variation

known today, the range over which the objective function

will vary in the future. However, they do not give any

information about the probability distribution of the values

within this range.

RESULTS AND DISCUSSION:MONTE CARLO SIMULATIONS

To enable the Monte Carlo simulations, the process model

has to be transferred from SuperPro Designer to MS Excel.

The software Crystal Ball 2000 is used as the random

number generator to perform the MCS. For a large number

of trials (or iterations), random numbers are generated

for the set of uncertain input parameters based on the

probability distribution for these parameters (see Table III).

The entire model is recalculated for each trial, and the

resulting values of the objective functions are saved.

In the first MCS, only the technical parameters are varied

(MCS-TP), followed by a variation of the supply chain and

market parameters (MCS-S/MP). In the next step, Monte

Carlo simulations are done for all parameters defined in

Table III (MCS-AP). In these simulations, the final peni-

cillin concentration of the fermentation is identified as

the dominant technical parameter (see following sections).

To examine the influence of final penicillin concentra-

tion and other technical parameters on objective func-

tions, additional MCS are run, one simulation varying the

technical parameters without the final penicillin concen-

tration (MCS-TPW) and another only varying the final

penicillin concentration (MCS-Pen). For all parameter

sets, 100,000 trials are run to ensure a low mean standard

error for all objective functions (<1%). A detailed docu-

mentation of the MCS results is given in the online sup-

plementary material.

Unit Production Cost

Figure 3 shows as an example of the probability distribu-

tion of the UPC on a batch-to-batch basis for the MCS-TP.

All UPC distribution curves are more or less normally

distributed. Since the supply chain variables have distribu-

tions balanced around their mean (mean = base case)

values, the mean value of the MCS-SC/MP is equal to the

UPC of the base case. The mean values of the MCS-TP,

MCS-TPW, and MCS-Pen are significantly higher than the

base UPC. For several technical parameters, a minimum or

maximum value is defined resulting in an unbalanced

distribution, e.g., the downstream yield and the precursor

utilization efficiency are truncated at 100%. The average

of these parameters in the MCS is therefore less then

their base case values. This leads to a higher mean UPC

in the MCS. Since the supply chain parameters do not

have such an effect, the MCS-AP also shows a higher mean

UPC of $16.7/kg.

As expected, all values lie within the range defined by the

worst/best case scenarios. The supply chain parameters

cover a much smaller range of values than the technical

parameters. The same tendency is shown by the standard

deviation. The MCS-TP has a standard deviation of

$1.6/kg, equal to a coefficient of variation (V) of 9.5%.

The coefficient of variation of the MCS-S/MP is more than

four times lower with V = 2%. Thus, the variance of the

MCS-AP is dominated by the technical parameters and its

coefficient of variation (10%) is almost identical to the

value of the MCS-TP. In the MCS-AP, the UPC is less than

$18.8/kg with a probability of 90% and less than $17.4/kg

with a probability of 70%.

Figure 4 shows the parameters that drive the variance

of the UPC. The final penicillin concentration dominates

the variation in MCS-TP. The concentration defines the

amount of final product per batch and thus the percentage

of raw materials converted to biomass and carbon dioxide.

Furthermore, the relative amount (and cost) of butyl acetate

necessary in the extraction stage decreases as product

concentration increases (as long as the solvent/broth ratio

remains unchanged). The second driver is the final biomass

Figure 3. Probability distribution of the unit production costs (UPC) in

the MCS-TP, defined in Table III (100,000 trials, 100 groups in the graph).

Table IV. Objective functions in the base case, worst-case, and best-

case scenario.

Objective function Worst case Base case Best case

UPC ($/kg) 28.0 16.0 10.5

EBITDA ($ million) –18 4.0 31

EBIT ($ million) –22 –0.35 26

ROI (%) –32 –0.5 39

EI input (IP/kg P) 0.69 0.45 0.32

EI output (IP/kg P) 1.65 0.72 0.36


concentration. Higher biomass concentration increases the

diversion of C-atoms to cell growth and respiration (i.e.,

CO2) and increases the raw materials requirements to pro-

duce a specific amount of penicillin. Besides these factors,

the different recovery yields in the downstream process play

an important role since they determine the amount of final

product that is ultimately recovered. Finally, the precursor

utilization efficiency affects the phenoxyacetic acid demand.

In the MCS-S/MP, the variance is mostly caused by the

variation of the glucose and phenoxyacetic acid prices.

With the probability distribution used in the MCS, the im-

pact of the electricity cost is small.

The sensitivity chart explains why the additional MCS-

TPW and MCS-Pen simulations were performed. The high

impact of the final penicillin concentration is reaffirmed

in the MCS-Pen. The penicillin concentration alone causes

a variation of V = 8.5%, while all other technical param-

eters (MCS-TPW) result in a coefficient of variation of

V = 5%.

Figure 5 compares the different probability distributions

for the UPC. The MCS-S/MP shows the smallest variation

and has a coefficient of variation of only 2%. As one might

expect, the MCS-AP displays the broadest variation. The

MCS-Pen, which includes substantial variation contributed

by penicillin concentration, is only slightly smaller; the

MCS-TPW distribution lies between those of MCS-S/MP

and MCS-Pen.

ROI, EBITDA, and EBIT

To look at the ROI, EBIT, and EBITDA of a process

retrospectively, only the mean values of the process

parameters are relevant, since batch-to-batch variations

should center on the mean in the long run. However, if one

wants to predict future performance when process param-

eters with uncertain means propagate through the process,

the variation of the process variables influences long-term

economic objective functions.

In the MCS-S/MP and the MCS-Pen, all input variables

have symmetrical distributions. Hence, these MCS show

the same mean ROI as the base case ROI. For the same

reason discussed earlier, in the section UPC, the other MCS

have a lower mean ROI of �1.5%. For all five parameter

sets, the distribution curves of the ROI are symmetrical

(skewness c0) and show the peakedness of a normal

distribution (kurtosis c3.0). Including all input variables,

the values of MCS-AP vary between a minimum of ROI =

�28% and a maximum of ROI = +29%. Thus, they cover a

range of 57%. As expected, the other MCS show a smaller

range width. In contrast, the worst/best case scenario ranges

from �32% to +39% and has a range width of 71%. Thus,

both lie outside the feasible range for the base case and so

actually have a zero probability of occurrence. This shows

the limited value of worst/best case scenarios, if their actual

probabilities are not taken into account.

While the UPC is only defined by the process costs, the

ROI is also affected by the revenues. Therefore, the selling

price of the final product plays a crucial role for the ROI

and causes 50% of the variation in the MCS-AP, while the

penicillin concentration contributes only 35%. Addition-

ally, the biomass concentration, the crystallization yield,

Figure 5. Probability distribution of the unit production costs in MCS-

AP, MCS-TPW, MCS-Pen, and MCS-S/MP (100,000 trials, 100 groups in

each graph). The curve of MCS-TP is very similar to the curve of MCS-AP

(not shown). The area under curves is always the same.

Figure 4. Contribution of the parameters to the variance of the unit pro-

duction costs in the MCS-TP (a), MCS-S/MP (b), and MCS-AP (c). Only

parameters with more than 1% contribution to the variance are shown.


the yield of the biomass removal, and the prices for glucose

and phenoxyacetic acid contribute to a certain extent.

Compared with the UPC, the additional impact of the

selling price to the ROI changes the standard deviations and

the probability distributions of the different parameter

sets (see Fig. 6). The MCS-TPW is not affected by the two

most sensitive parameters (penicillin concentration, selling

prices) and therefore has the smallest standard deviation

(2.3%). The MCS-AP includes both penicillin concentra-

tion and selling prices and thus exhibits the largest standard

deviation (6.5%). The other curves lie in between these two

extremes. Here, the MCS-S/MP with the most sensible

penicillin selling price has a larger variance (SD = 5.2%)

than the MCS-TP with the second most sensible parameter

(SD = 4.8%). As expected, the MCS-Pen lies between the

MCS-TP, which it dominates, and the MCS-TPW.

The EBIT and the EBITDA are influenced by the input

variables in the same way as the ROI. For the MCS-AP the

mean EBITDA is $3.3 million, with a standard deviation of

$4.8 million. Thus, the EBITDA is not positive for all

possible scenarios. It is positive with a probability of 75%

and above $2 million with a probability of 60%. In the

MCS-AP the mean EBIT is �$1 million. This means that

when depreciation and today’s selling price are accounted

for, the process is not capable of realizing a profit on

average. Besides the existing overcapacity in the market,

this explains why new penicillin production facilities have

not been built in recent years. However, with an existing

and already completely depreciated plant, profitability can

be achieved.

For those indicators that are affected by market con-

ditions (ROI, EBIT, EBITDA), the selling price drives the

uncertainty and this allows us to understand the difficult

situation faced by many penicillin manufacturer faced

with a volatile penicillin market. Beside the selling price,

the most relevant parameter for the uncertainty of the

economic indicators is the penicillin concentration. Hence,

key to process control is the ability to achieve a high

penicillin concentration quickly and reproducibility. This is

one of the most promising means of cost reduction and

improved profitability.

Environmental Index Input and Output

The variation of the EIs is determined only by the technical

parameters. Hence, the results of the MCS-TP and MCS-AP

are identical. Figure 7 shows the probability distribution of

the EI input and the EI output. It is clearly shown that even

considering the existing uncertainty the EI input is sig-

nificantly lower than the EI output. This means the output

components are environmentally more relevant than the

input components. The mean values are for all parameter

sets only slightly higher than in the base case. The EI varies

between 0.34 and 0.68 IP/kg P, the EI output between

0.42 and 1.55 IP/kg P. Thus, in contrast to the ROI, they

show almost exactly the same range as the worst/best-case

scenarios. The specific amount of carbon dioxide, environ-

mentally the most relevant output component, varies more

than the specific amount of phenoxyacetic acid, the most

relevant input component.

Figure 8b shows the contribution of the technical param-

eters to the variance of the EI input (MCS-AP). The media,

butyl acetate, acetone, and phenoxyacetic acid have the

highest EFs and input EIs, and this influences the variance.

The final biomass concentration has the highest impact.

It determines the amount of media that must be added to the

fermenter. In contrast to the UPC, the penicillin concen-

tration is only the second relevant factor. It defines the total

amount of final product and the specific consumption of

raw materials and solvents. Furthermore, the butyl acetate

recycling rate, and to a smaller extent the acetone recycling,

contribute to the variation by defining the amount of butyl

acetate, respectively acetone in the waste. However, they do

not contribute significantly to the economic uncertainty.

Similar to the UPC, the precursor (phenoxyacetic acid)

utilization efficiency and the recovery yields (amount of

final product) contribute substantially to the EI variance.

Figure 8a shows the contribution of the parameters to

the variance of the EI output. Carbon dioxide, biomass, and

butyl acetate have the highest output EIs, which again in-

fluences the EI variance. The final biomass concentra-

tion defines the amount of biomass in the waste and by

association the amount of CO2 formed. The maintenance

coefficient for glucose and the yield coefficient of bio-

Figure 7. Probability distribution of the environmental index input

(V = 8%) and Output (V = 15%) in the MCS-TP as defined in Table III

(100,000 trials, 100 groups in each graph). The area under the curves is the

same. [IP/kg P] = index points/kg final product.

Figure 6. Probability distributions of the return on investment (ROI) for

the five different sets of parameters (100,000 trials, 100 groups in each

graph). The area under the curves is always the same.


mass on glucose also affect the amount of carbon dioxide.

Both parameters have no significant impact on the eco-

nomic uncertainty.

The reduced impact of the final penicillin concentration

compared with the economic objective function is clearly

shown in Figure 9 by a smaller variance of the MCS-Pen

curve. The MCS-TPW is wider and lies nearer to the MCS-

AP distribution curve.

These results show that the relevant parameters and how

strongly they contribute to the uncertainty differ to some

extent between the economic and environmental indica-

tors. However, the direction of change is the same for all

relevant parameters. The contributions of the variables to

the overall uncertainty indicate the sensitivity of the pro-

cess to these variables. Thus, there are parameters that can

be changed to improve the economic performance without

affecting the environmental performance. While for other

parameters, an economic improvement leads directly to an

environmental improvement. This represents an economic

and environmental (eco-efficiency) win-win scenario that is

contrary to the use of end-of-pipe technologies for en-

vironmental pollution control that lead to additional costs.

Sensitivity Analysis for Final Penicillin Concentration

The final penicillin concentration is the most important

technical parameter in the model. Therefore, it is inter-

esting to see how the objective function changes when

either the mean or the coefficient of variation of the peni-

cillin concentration changes.

In general, it can be expected that the higher the coef-

ficient of variation of penicillin concentration, the higher is

the variation of the objective function since each draw of the

MCS will assess a different long-run mean concentration.

Figure 10a shows the probability distribution of the UPC at

different coefficients of variation of the penicillin concen-

tration. The strong impact of this variable on the UPC

Figure 9. Probability distribution of the environmental index output

in the MCS-AP, MCS-TPW, and the MCS-Pen (100,000 trials, 100 groups

in each graph). The variation of each parameter is defined in Table III.

[IP/kg P] = index points/kg final product.

Figure 10. Probability distribution of the unit production costs (UPC) (a)

and the EI input (b) at different coefficients of variance of the final

penicillin concentration (100,000 trials).

Figure 8. Contribution of the technical parameters to the variance of (a)

the environmental index input (EI input), and (b) the environmental index

output (EI output) in the MCS-AP (as defined in Table III).


results in significant change of the curve shape and a higher

standard deviation. Figure 10b shows the EI Input for the

same sets of different coefficients of variation. Here, the

variation of the penicillin concentration also leads to a

broader variance of the EI input. However, the effect is

much smaller than for the UPC, based on the smaller impact

of the penicillin concentration shown in Figure 8.

The differences described are illustrated by the relation

of the coefficients of variation of the objective functions to

an increasing coefficient of variation of the penicillin

concentration (VPen). The values at VPen = 0% are identical

to an MCS of all parameters without the penicillin con-

centration. From these base lines, the coefficients of the

objective function increase with increasing VPen. The

coefficient of the EI input increases relatively slowly and

stays clearly smaller than the coefficient of the penicillin

concentration. The EI output starts at a higher coefficient

(broader variance in MCS-TPW). It also increases rela-

tively slowly and runs from VPen = 15% upward in parallel

with the increasing VPen. The UPC increases more quickly

and reaches at about 8% the value of VPen. For the range

VPen = 8–20% the coefficient of the UPC is more or less

identical to the coefficient of the penicillin concentration.

At lower values, the other input variables contribute to the

variation of the UPC to a greater extent. These results

illustrate the fact that an exact definition of the probability

distribution of the main uncertainty drivers is crucial to

obtaining realistic results.

Final penicillin concentration was varied between 40 g/L

and 70 g/L with a constant coefficient of variation to further

explore the impact of uncertain long-run strain performance

that is confined to specific ranges. Figure 11 shows the

change of the UPC probability distribution. The mean

moves to the right with decreasing penicillin concentration.

The constant coefficient of variation of the penicillin

concentration propagates through the model resulting in a

more or less constant coefficient for UPC. Since the UPC

increases with decreasing penicillin concentration, the

standard deviation must also increase and leads to the

broader shape of the distribution curves that is observed.

The distributions of the other objective functions look

similar. The parameters that drive the uncertainty remain

the same. Thus, the results derived are applicable to all

penicillin processes independent from the penicillin con-

centration that is reached.

Figure 12 shows EBITDA as a function of different

penicillin concentration. The penicillin concentration for

which EBITDA = 0 can be graphically identified (56 g/L); a

positive EBITDA is reached at higher concentrations. A

MCS was run with the identified concentration. From the

resulting EBITDA standard deviation at this concentration,

the standard deviation for the penicillin concentration

EBITDA = 0 can also be derived graphically (see Fig. 12).

The obtained standard deviation is 9.5 g/L, documenting

a relative high uncertainty. The variation of the mean

penicillin concentration shows its importance for the eco-

nomic success of the process when assessed from a devel-

opment perspective.

CONCLUSIONS

The development of the base model and the use of Monte

Carlo simulations have led to a better understanding of

penicillin V production and the impact of both technical

and market variance. As such, the most relevant stochastic

variables are identified and proposed as parameters that are

critical to an efficient process control strategy, as well as

starting points for potential process improvements.

From a computational perspective, this work demon-

strates a general methodology for decision analysis that

allows one to understand the impact of uncertainty on

key process metrics. This is of significant value, since it

allows decision makers to more clearly understand process

and economic risks. The construction of a spreadsheet

model that allows for such stochastic analysis is fairly

straightforward, since most bioprocess material and energy

balances have analytical solutions that are amenable to

spreadsheet formulation, and the results of such formula-

tions are readily verified using a simulation tool such as

SuperPro Designer.

Final penicillin and biomass concentrations in the fer-

menter have the highest contribution to the uncertainty

Figure 11. Probability distribution of the unit production costs (UPC)

at different final penicillin concentrations (100,000 trials, 100 groups in

each graph).

Figure 12. Earnings before interest, taxes, depreciation, and amortiza-

tion (EBITDA) at different penicillin concentrations and graphical

derivation of the standard deviation of the penicillin concentration for

which EBITDA = 0.


of UPC and EI. Fermentation parameters such as yield,

maintenance coefficient, and precursor utilization also

have a high impact on the variance of the environmental

impact, as well as the recycling rate of the organic sol-

vents. The production costs are significantly affected by

downstream yield and raw material costs. The selling

price dominates the variation of ROI and other revenue-

dependent parameters.

The additional use of an environmental assessment

method that aggregates the environmental performance of

the process to two indicators allows one to understand

how the uncertainty of the input variables affects not only

economic performance, but also impact on the environ-

ment and the differences between these two metrics. This

approach has been used infrequently so far in the evalua-

tion of chemical and pharmaceutical processes.

The sensitivity analysis shows how important it is to

define exactly the variance of key input parameters. The

threshold for positive EBITDA has been graphically

derived and used to show that decreasing selling prices

over the past few years have drastically increased the

pressure for further strain improvements and cost reduction.

We note, however, that the case presented is limited by the

fact that the base model is a generalized model of the

penicillin V product process. Depending on the location,

the cost structure of a manufacturer might vary.

This article presents the penicillin V production as a case

study. It proves that combining calculation-based modeling

with Monte Carlo simulations can be used as a general

methodology for multi-parameter uncertainty analysis.

Thus, it goes beyond the usual case of economic assessment

based on average value analysis that is standard practice

in process development using commercial simulation soft-

ware. The methodology presented is generally applicable

to the analysis of any process where stochastic variables

influence both within-batch and between-batch process

capability and the long-run economic performance upon

which development decisions are based.

The authors thank Intelligen, Inc., for their support and helpful

discussions. This work was supported by a fellowship within the

Postdoctorate Program of the German Academic Exchange Service

(DAAD).

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