Biotechnology : Measuring, Modelling, and Control / Karl Schugerl

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Library of Congress Card No.: 91-16462 British Library Cataloguing-in-Publication Data: Biotechnology Second Edition

Biotechnology: Vol 4 Measuring, modelling and control

Vol Ed Schiigerl, K 620.8

ISBN 3-527-28314-5

Die Deutsche Bibliothek - CIP-Einheitsaufnahme

Biotechnology : a multi volume comprehensive treatise / ed by H.-J Rehm and G Reed In cooperation with A Piihler and P Stadler - 2., completely rev ed - Weinheim; New York; Basel; Cambridge: VCH

NE: Rehm, Hans J [Hrsg.] 2., completely rev ed

Vol 4 Measuring, modelling, and control / ed by K Schiigerl

- 1991

ISBN 3-527-28314-5 (Weinheim) ISBN 1-56081-154-4 (New York) NE: Schiigerl, Karl [Hrsg.]

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Preface

In recognition of the enormous advances in biotechnology in recent years, we are pleased to present this Second Edition of “Biotech- nology” relatively soon after the introduction of the First Edition of this multi-volume com- prehensive treatise Since this series was ex- tremely well accepted by the scientific commu- nity, we have maintained the overall goal of creating a number of volumes, each devoted to a certain topic, which provide scientists in academia, industry, and public institutions with a well-balanced and comprehensive over- view of this growing field We have fully re- vised the Second Edition and expanded it from ten to twelve volumes in order to take all re- cent developments into account

These twelve volumes are organized into three sections The first four volumes consider the fundamentals of biotechnology from bio- logical, biochemical, molecular biological, and chemical engineering perspectives The next four volumes are devoted to products of indus- trial relevance Special attention is given here to products derived from genetically engi- neered microorganisms and mammalian cells The last four volumes are dedicated to the de- scription of special topics

The new “Biotechnology” is a reference work, a comprehensive description of the state-of-the-art, and a guide to the original literature It is specifically directed to micro- biologists, biochemists, molecular biologists, bioengineers, chemical engineers, and food and pharmaceutical chemists working in indus- try, at universities or at public institutions

A carefully selected and distinguished Scien- tific Advisory Board stands behind the series Its members come from key institutions repre- senting scientific input from about twenty countries

The present volume, fourth in the series, re- flects the enormous impact of computer tech- nology on biotechnology, especially in the areas of measurement and control It describes monitoring of the biotechnological process with sophisticated analytical techniques, use of the resulting data by means of mathematical models, and computer-aided closed loop con- trol for improvement of the productivity of biotechnological processes While Volume 4

can be used independently, Volume 3 “Bio-

processing” is recommended as a companion volume

The volume editors and the authors of the individual chapters have been chosen for their recognized expertise and their contributions to the various fields of biotechnology Their will- ingness to impart this knowledge to their col- leagues forms the basis of “Biotechnology” and is gratefully acknowledged Moreover, this work could not have been brought to fru- ition without the foresight and the constant and diligent support of the publisher We are grateful to VCH for publishing “Biotechnolo- gy” with their customary excellence Special thanks are due Dr Hans-Joachim Kraus and Christa Schultz, without whose constant ef- forts the series could not be published Finally, the editors wish to thank the members of the Scientific Advisory Board for their encourage- ment, their helpful suggestions, and their con-

Scientific Advisory Board

August Kirchenstein Institute of Microbiology Latvian Academy of Sciences

Biochemical Engineering Research Centre Indian Institute of Technology

Weizmann Microbial Chemistry Laboratory Department of Chemistry

Manchester, UK

Prof Dr C L Cooney

Department of Chemical Engineering

Massachusetts Institute of Technology Alimentaire Cambridge, MA, USA

Department of Applied Microbiology The Hebrew University

Prof Dr G Goma

Departement de Genie Biochimique et Institut National des Sciences Appliquees

Institut fur Biotechnologie

Eidgenossische Technische Hochschule Scientific Development Group Oss The Netherlands

Department of Plant Sciences University of Western Ontario London, Ontario, Canada

Chair of Fermentation Chemistry and Industrial Microbiology Lepetit Research Center Gerenzano, Italy

Institute of Molecular and Cell Biology National University of Singapore

Laboratory of Microbial Ecology Rij ksuniversiteit Gent

Gent, Belgium

Prof Dr E.-L Winnacker

Institut fur Biochemie

Contents

1 Common Instruments for Process 12 Analysis and Control 5

6 Determination of Cell Concentration and Characterization of Cells 179

Process Models: Optimization of Yeast Production - A Case Study

IV Control and Automation

16 Control of Bioreactor Systems 509

S Shioya, K.-I Suga

19 Expert Systems for Biotechnology 625

A Halme, N Karim

Index 637

9 Cell Models 267

K -H Bellgardt

Contributors

Dr Graham F Andrews

E G & G

Idaho National Engineering Laboratory Idaho Falls, ID 83415, USA

Prof Dr Aarne Halme

Automation Technology Laboratory Helsinki University of Technology Electrical Engineering Building Otakaari 5A

SF-02150 ESPOO, Finland

Chapter 19

Dr Elmar Heinzle

Biological Reaction Engineering Group Chemical Engineering Department

Eidgenossische Technische Hochschule (ETH) Universitatsstrane 6

CH-8092 Zurich, Switzerland

Chapter 2

Prof Dr Karl-Heinz Bellgardt

Institut fur Technische Chemie

D-3000 Hannover 1, FRG

Chapters 9 and 12

Prof Dr Nazmul Karim

Department of Agricultural and

Fort Collins, CO 80523, USA

Chapter 19

Dr Irving J Dunn

Biological Reaction Engineering Group Chemical Engineering Department

Eidgenossische Technische Hochschule (ETH)

Dr Sun Bok Lee

Pohang Institute of Technology Pohang, Korea

Chapter 15

Prof Dr Henry C Lim

Biochemical Engineering Program University of California

Irvine, CA 92717, USA

Chapter 16

Priv.-Doz Dr Andreas Liibbert

Institut fur Technische Chemie

Prof Dr Jose C Merchuk

Department of Chemical Engineering Program of Biotechnology

Ben-Gurion University of the Negev Beer Sheva, Israel

Chapter I 1

Prof Dr Axel Munack

Institut fur Biosystemtechnik

Bundesforschungsanstalt fur Landwirtschaft Bundesallee 50

D-3300 Braunschweig-Volkenrode, FRG

Chapter 8

Dr Seujeung Park

Department of Chemical Engineering Massachusetts Institute of Technology Cambridge, MA 02139, USA

Chapter 7

Dr Kenneth F Reardon

Colorado State University Fort Collins, CO 80523, USA

Chapter 6

Prof Dr Matthias Reuss

Institut fur Bioverfahrenstechnik Universitat Stuttgart

Boblinger StraRe 72 D-7000 Stuttgart 1, FRG

Chapter I0

Prof Dr Dewey D Y Ryu

Department of Chemical Engineering University of California

Davis, CA 95616, USA

Chapter I5

Priv.-Doz Dr Thomas H Scheper

Institut fur Technische Chemie Universitat Hannover

CallinstraRe 3

D-3000 Hannover 1, FRG

Chapter 6

Prof Dr Karl Schiigerl

Institut fur Technische Chemie

Prof Dr Suteaki Shioya

Department of Fermentation Technology Faculty of Engineering

Osaka University, Suita Osaka 565, Japan

Prof Dr Gregory Stephanopoulos

Department of Chemical Engineering Massachusetts Institute of Technology Cambridge, MA 02139, USA

Chapter 7

Prof Dr Ken-ichi Suga

Department of Fermentation Technology Faculty of Engineering

Osaka University, Suita Osaka 565, Japan

Prof Dr Christian Wandrey

Institut fur Biotechnologie 2

Institute for Automatic Control East China University

of Chemical Technology 130 Meilong Lu

Shanghai, People’s Republic of China

Chapter 12

Introduction

Hannover, Federal Republic of Germany

The fourth volume of the second edition of “Biotechnology” presents a survey on an in- creasingly important field of biotechnology: monitoring of the biotechnological process with sophisticated analysis techniques, use of the resulting data by means of mathematical models, and (computer-aided) closed loop con- trol for improvement of the productivity of biotechnological processes

The bottleneck in biotechnological process control is the on-line measurement of con- trolled process variables Except for tempera- ture, impeller speed (for stirred tank reactors), aeration rate (for aerobic microorganisms),

pH, po,, which are usually controlled process

variables, and the composition of the outlet gas (0, and C 0 2 content), which sometimes is

a controlled process variable (respiration quo- tient, RQ, C 0 2 production rate, O2 consump- tion rate), no other process variables are usual- ly measured on-line in commercial equip- ment

However, manufacturers have recently made great efforts to improve process analysis and control In several laboratories, on-line systems for the analysis of the chemical me- dium composition are used to gain more infor- mation about the process and to control the concentrations of key components Further- more, mathematical models have been devel- oped in order to describe the production proc-

ess and to effect process optimization and con- trol Therefore, the Series Editors decided to add to Biotechnology a separate volume with

the title “Measuring, Modelling, and Con- trol”, and they asked the Volume Editor to or-

Cell growth and product formation/sub- strate conversion is at the focus of attention, and here the measuring and control techniques are well-developed and generally applicable

“Modelling, design, and control” of down- stream processes are also considered because of the great importance of downstream proc- essing However, because of their broad scope, they are too heterogeneous and not yet suffi- ciently developed for treatment in the same way as processes for growth and product for-

0 instruments for gas analysis, and

0 biosensors

The last group of instruments is still being de- veloped

Only instruments that are (or can be) used for process control are considered in detail However, modern off-line techniques (e.g., NMR) are also taken into account

The measuring techniques are subdivided into four groups:

0 physical techniques for the characteriza- tion of fluid dynamics,

0 chemical methods for the analysis of broth composition,

0 physical methods for the determination of cell concentration, and

0 physical/biochemical methods for the characterization of the biological state of the cells

Most of these are on-line techniques; others can only be carried out in a quasi on-line mode All of them are used to characterize the reactor/medium/cell system

There are interesting new developments in the characterization of such systems by mod- ern mathematical methods, with optimization of sampling to gain maximal possible informa- tion These new techniques are also included in

0 aerobic wastewater treatment,

0 anaerobic wastewater treatment, and

0 models for recombinant microorgan- isms

Models for animal and plant tissue cultures have not yet been included because no reliable kinetic data are available for mathematical modelling of these cultures

Modern control techniques are increasingly applied to closed loop control of bioreactor systems Therefore, different types of closed loop control techniques, including computer- aided control, are considered in detail

Instrumental control is much more reliable than control by a human operator Further- more, long-range (many weeks or months) runs are only possible in the laboratories of re- search institutes and universities if automated equipment is used Thus, automation of bio- reactors is also taken into account

Chapter 18 on modelling, design, and con-

trol of downstream processing covers only the most important downstream processes Devel- opment in this field is still limited, so this chapter is not as extensive as the potential im- portance of downstream processing would warrant

Expert systems are being developed in dif- ferent aspects of technology, medicine, and the natural sciences Their use in biotechnolo- gy is desirable, since they would permit the identification of equipment failures and their eventual elimination Furthermore, by means of expert systems, large amounts of informa- tion from on-line and off-line measurements as well as from the literature and from heuris- tic knowledge can be used with high efficiency

The reviews consider only the most impor- tant techniques and omit some detail because of limited space Further information can be gained through the reference notations

It is hoped that information given in this volume will help students, engineers, and scientists at universities, members of research institutes, and those in industry to increase their knowledge of this important and fast- growing field

Hannover, March 1991 K Schiigerl

I Instruments

2.2 Dissolved Oxygen Partial Pressure, po, 7

2.3 Redox Potential, Eh, and Dissolved C 0 2 Partial Pressure, pcO2 9

4.4 Dissolved COz Partial Pressure, pCo2

3 Instruments for Determination of Physical System Properties 10

6 I Common Instruments f o r Process Analysis and Control

1 Introduction

Biological processes are influenced by sev- eral control variables: temperature, pH, dis-

solved oxygen partial pressure p o 2 , as well as

by state variables such as redox potential, Eh,

and dissolved C 0 2 partial pressure, pco2,

which have a direct influence on cell metabo- lism (FORAGE et al., 1985)

Other control variables (power input, aera- tion rate) and state variables (liquid viscosity) have an indirect effect on cell growth and product formation They influence gas disper- sion (bubble size, gas holdup, and specific in- terfacial area) and the transport processes in the broth The broth volume can be deter- mined by means of the liquid level and the holdup In continuous cultivation, the residence time of the broth or its dilution rate, which equals the specific growth rate of the cells, is determined by the liquid throughput and broth volume

With highly foaming broth the cells are sometimes enriched in the foam by flotation The diminution of the cell concentration in the broth reduces cell growth and product forma- tion rates Foam may be carried out of the reactor by the air flow and then may clog the gas analysis instruments and cause infection of the broth Therefore, the foam detector be- longs to the standard equipment of bioreac- tors First, the use of these instruments for process analysis, optimization, and control is considered

2 Use of the Variables

Temperature, pH, po2, Eh,

andpc02 for Process Analysis, Optimization, and Control

2.1 Temperature and pH

Cells have an optimum temperature and p H for growth and frequently another optimum for product formation Several authors have considered the calculation of the optimum temperature and p H profiles for product for- mation

FAN and WAN (1963) used the discrete maximum principle to calculate the optimum temperature and p H profiles for a continuous multistage enzymatic reactor to maximize product concentration

BOURDARD and FOULARD (1 973) consid- ered the optimization of yeast production in a batch process by means of optimum tempera- ture and p H profiles using the continuous maximum principle

SPITZER (1976) used a grid search method with subsequent steepest descent to maximize biomass productivity in a continuously oper- ated bioreactor by optimizing pH and sub- strate profiles

RAI and CONSTANTINIDES (1973) and CON-

STANTINIDES and RAI (1974) investigated the

production of gluconic acid with Pseudomo-

nus ovalis and of penicillin G by Penicillium

chrysogenum in batch operation and used the

continuous maximum principle to maximize the productivity by means of optimal tempera- ture and pH profiles

CONSTANTINIDES et al (1970) and KING et al (1974) studied the production of penicillin

G by P chrysogenum in batch operation and

used the continuous maximum principle and/ or a specific optimal control to evaluate the optimum temperature profile for achieving maximum productivity ANDREYEVA and BIRYUKOV (1973) also investigated the batch production of penicillin G and used the contin- uous maximum principle to find the optimum p H profile for maximum productivity

BLANCH and ROGERS (1972) maximized profit in gramicidin S production by Bacillus brevis by evaluating the optimum temperature

and pH as well as the number of stages using the discrete maximum principle

Erythromycin biosynthesis in batch opera- tion was maximized by CHERUY and DURAND (1979) by evaluating optimal temperature and pH profiles

On the other hand, the pH variation can be used to control the production process PAN et al (1972) reported on penicillin production where carbohydrate and nitrogen source feed rates were controlled by measurement of the pH The nitrogen source was metabolized to basic cations and the carbohydrate source to CO, and organic acids The balance of the two ingredients provided a basis for the pH con- trol

ANDREYEVA and BIRYUKOV (1973) pro- posed a model for this pH effect and its use for calculating optimal fermentation condi- tions CONSTANTINIDES (1979) reviewed these publications SAN and STEPHANOPOULOS (1984) also proposed a relationship between the total rate of biomass growth and ammonia addition to the reactor for pH control

ROSEN and SCHOGERL (1984) used the con- sumption of sodium hydroxide solution at a constant pH to calculate the cell mass produc- tion rate of Chaetomium cellulolyticum and to

control the substrate feed by means of a mi- croprocessor in a fed-batch biomass produc- tion process SHIOYA (1988) developed an ad- vanced pH control system for the measure- ment of biological reaction rates

In many microbial or cell culture systems the pH varies during growth Acid or base must be added to the broth to keep the pH at the optimal value In some enzymatic hydro- lytic reactions acid or base must also be used to keep the pH constant by neutralizing the produced acid or base From the amount of acid or base required for keeping the pH con- stant, the growth rate or enzyme reaction rate can be calculated

If ApH(k+ 1) and ApH(k) are the differ- ences of pH from the set point at times k + 1 and k, F(k ) is the feeding rate of acid or base for pH control, and R(k) is acid or base pro-

duction or consumption rate, then Eq (1) can be used to calculate R(k):

A pH(k + 1) = A pH(k) + aF(k) - bR(k) (1)

where a is a coefficient corresponding to the

pH deviation caused by adding a unit amount of acid or base to the broth, and b is a coeffi- cient that corresponds to the pH deviation caused by the formation of a unit amount of cell mass or product

If the pH is kept constant, i.e., A pH(k + 1) = A pH(k) = 0, then the acid or base production or consumption rate R(k) can

be evaluated from

This principle was applied to

0 baker’s yeast production using a distur- bance predictive controller to determine the growth rate of the yeast,

0 determination of the reaction rate of N- acetyltyrosine ethyl ester (ATEE) with a-

chymotripsin to give ethanol and N-ace- tyltyrosine (AT) in a pH stat using a re- peated feedforwardlfeedback controller (repeated P F system),

0 determination of the overall production rate of (lactic) acid in hybridoma culture by an on-off controller

The excretion of enzymes can sometimes be controlled by the pH value For instance, LEE-

LASART and BONALY (1988) reported on con- trolling the excretion of acid phosphatase by

Rhodotorula glutinis by means of the pH of

the medium The enzyme was excreted only in the pH range 4.5 to 6.5

Several microorganisms produce different

metabolites depending on the pH Thus, As-

pergillus niger produces citric acid in the pH

range from 2.5 to 3.5, whereas gluconic acid is produced at a higher pH and oxalic acid in the neutral pH range (SCHLEGEL, 1974)

Pressure, p o ,

Dissolved oxygen pressure or concentration is a state variable widely used to calculate the biomass concentration by 0,-balancing and to

8 I Common Instruments for Process Analysis and Control

control the growth or production process of aerobic microorganisms

Furthermore, Po,-electrodes are used as re- search tools for determining oxygen transfer rates (OTR) in pioreactors, biofilms, pellets, and cells immobilized in beads

The use of oxygen balancing for real-time estimation of the biomass concentration was recommended first by HOSPODKA (1966) ZA-

BRISKIE and HUMPHREY (1978) worked out this technique of observation in detail Using the relationship between oxygen uptake rate (OUR), the yield coefficient of the cell growth with regard to the oxygen consumption, Yx/02, the maintenance coefficient with regard to the oxygen consumption, moZ/X, and the

where X, is the initial biomass concentration Eq (4) forms the basis for estimating the biomass concentration X(t) from the oxygen uptake rate

The growth rate may be approximated using Eqs (3) and (4):

With this method the biomass concentration of Saccharomyces cerevisiae was estimated

Several other authors used this technique in combination with the respiration coefficient, RQ, to estimate the biomass (e.g., COONEY et al., 1977; WANG et al., 1977; PERINGER and BLACHERE, 1979; TAKAMATSU et al., 1981) SQUIRES (1972) reported that po2 was used to control the sugar addition to the broth of

Penicillium chrysogenum during penicillin pro-

duction The sugar feed was increased at a high po2 value; at a low po2 it was reduced Since a close relationship exists between oxy-

gen and substrate uptake rates, this control of the substrate feed is very popular

Under steady-state conditions, the oxygen uptake rate, OUR, and the oxygen transfer rate, OTR, are identical Knowing the driving force for the oxygen transfer, (0, - OZ), the volumetric mass transfer coefficient, KLa, can

be calculated: 0 TR

KLa =

(02 - 02)

where 0, and 03 are the concentrations of the

dissolved oxygen in the bulk and at the inter- face (in equilibrium with the gas phase) By measuring the oxygen balance during cell culti- vation, the volumetric mass transfer coeffi- cient can be calculated in real time

In cell-free systems, KLa can be determined

by non-stationary or stationary measurements The non-stationary method is based on the re-

By measuring the variation of the dissolved oxygen concentration in the bulk as a function of time, and calculating the dissolved oxygen concentration at the interface from the oxygen concentration in the gas phase, KLa can be

evaluated from Eq (7) However, the interre- lationships between sorption rate and driving force are in practice more complex Several re- lationships have been recommended for this calculation

A good review of these methods is given in a ‘Report of a Working Party on Mixing’ of the European Federation of Chemical Engineering (LINEK and VACEK, 1986) and in the review article of LINEK et al (1987)

Several papers consider the mass transfer of dissolved oxygen into biofilms, pellets, and cells immobilized in beads The dissolved oxygen concentration profiles are determined by means of micro-oxygen electrodes (BUN-

GAY and HAROLD, 197 1 ; CHEN and BUNGAY, 1981; BUNGAY and CHEN, 1981; BUNGAY et al., 1969, 1983; WITTLER et al., 1986)

The combination of Eqs (10) and (11) gives

2.3 Redox Potential, Eh, and Dissolved C 0 2 Partial Pressure,

Pcoz

The oxidation and reduction of a compound is controlled by the redox potential of its envi- ronment

The oxidation-reduction potential of a pair of reversible, oxidizable-reducible compounds is related to the equilibrium between the oxi- dized (ox) and reduced forms (red) and the number of electrons involved in the reaction

(ne-) (KJAERGAARD, 1977; KJAERGAARD

and JOERGENSEN, 1979; THOMPSON and GER- SON, in KJAERGAARD, 1977):

The redox potential of this reaction is given by the Nernst equation:

R T activity of ox

E h = E o + - In

n F activity of red

where Eh is the redox potential referred to the normal hydrogen electrode,

Eo is the standard potential of the sys- tem at 25 "C, when all activities of any reactants are at unity,

R the gas constant,

T the absolute temperature,

n the number of electrons involved in the reaction,

F the Faraday constant

(9)

JOERGENSEN (1941) introduced a concept ana-

logous to the pH, namely the rH, which is de- fined as

where aH2 is the activity of hydrogen in the hy- drogen-hydrogen ion redox system according to Nernst For hydrogen

This rH value may vary from rH = 0, corre- sponding to a solution in which pH2 = 1 bar

and pH = 0, to rH >42, corresponding to a so- lution with po, = l bar and pH = 0 The rH val- ue is a function of the pH value Therefore, for the measurement of the redox potential, both rH and pH values are needed

The redox potential is used in practice for microaerobic cultivations, i.e., at very low dis- solved oxygen concentrations, which cannot be measured by standard oxygen electrodes An

example is the production of exoenzymes by Bacillus amyloliquefaciens in continuous cul- ture at 0.5% oxygen saturation by means of

redox-potential control (MEMMERT and WAN- DREY, 1987)

In small stirred tank reactors, the dissolved

COz concentration in the broth can be calcu- lated from the gas composition by assuming an equilibrium between the phases In tower reac- tors and large commercial units, no equili- brium distribution of COz exists between the

phases; therefore, the direct measurement of

pco2 can be useful

The driving force, (Pco2-pEo2), can be evaluated from the calculated pEo, at the in- terface and the measuredpco2 in the bulk The

CO, production rate, CPR, can be determined

from the evolved gas stream and the gas com- position

The volumetric mass transfer coefficient of the C 0 2 desorption is given by

CPR (KLa)co2 =

(Pco2-PEo2)

CPR can also be used for the calculation of the cell mass concentration and the specific growth rate, ,u The instantaneous specific growth rate of Penicillium chrysogenum was

calculated by Mou and COONEY (1983) by

measuring the CPR during the growth phase

By monitoring the O2 and/or COz concen-

trations in the outlet gas and its flow rate, O2

and/or CO, balances can be calculated and

used for state estimation of biochemical reac-

10 I Common Instruments for Process Analysis and Control

tors (e.g., STEPHANOPOULOS and SAN, 1982) However, because this state estimation method is based on measurements of the gas composi- tion, it will be discussed in Chapter 2

3 Instruments for

Determination of Physical System Properties

3.1 Temperature

Temperature is the most important control variable for most biotechnological processes, including sterilization as well as cell growth and product formation In general, a precision

of f0.5 "C is necessary in the temperature

range from +20 to + 130 "C Only a few types of the various industrial thermometers are suitable because of this prerequisite (BUSING and ARNOLD, 1980) Most popular are the Pt- 100 (100 ohm at 0 "C and 123.2 ohm at 60 "C) resistance thermometers which are encased in a protective steel tube fixed with a sealing com- pound of high heat conductivity

According to DIN 43 760 (German Stand- ard) the resistance of these instruments is guar- anteed with the following precision: 1OOf 0.1 ohm at 0 "C, which corresponds to an error of k 0.26 "C Therefore, these resistance ther- mometers can be used without calibration However, the resistances of all electrical con- nections must be controlled These instruments are steam-sterilizable at 121 "C Thermometers with short response times for fluid dynamical measurements are described in Chapter 4

3.2 Pressure

The absolute pressure is measured with re- spect to zero pressure Gauge pressure is meas- ured with respect to that of the atmosphere The SI unit of the pressure is Newton per square meter (N/m2) called Pascal (Pa) (1 bar=0.1 M P a = 10' N/m2; 1 mbar = 100

P a = 100 N/m2.) Bar and millibar deviate with

less than 2% from the technical and physical atmosphere

Pressure measurements are necessary for the control of the sterilization and the state of the outlet gas filter as well as for the evaluation of the holdup and the partial pressures of the ga- seous components in the gas and liquid phases Membrane pressure gauges are commonly used in biotechnology, because they are particularly suited to aseptic operations Numerous pres- sure gauges are used in the chemical industry (HIRTE, 1980; ANDREW and MILLER, 1979) In biotechnology, the commonly employed pressure gauges are based on strain and/or capacitance measurements The capacitance pressure gauges can measure very small pres- sure differences; therefore, they are used for liquid level measurements For the construction of the different pressure meters, see HIRTE (1980) and ANDREW and MILLER (1979)

3.3 Liquid Level and Holdup

Measurement of the liquid volume is impor- tant for filling bioreactors with nutrient solu- tions, for continuous and for fed-batch culti- vations It can be performed (OEDEKOVEN, 1980; ELFERS, 1964; ANDREW and RHEA, 1970) as follows:

0 by measuring the hydrostatic pressure difference between the bottom of the reactor, P b , and the head space, P h , by means of pressure gauges The pressure difference is proportional to the weight of the liquid in the reactor:

where h is the liquid height above the

p the density of the broth, and

g the acceleration of gravity,

0 by measuring the total weight of the bottom,

reactor by load cells The accuracy of the volume measurement is +0.2% for large reactors and + 1% for laboratory reactors

The measurement of the volume of an aer- ated broth is accomplished with a level con-

troller The common liquid level meters are based on the variation of the capacitance C of the sensor with the composition of the dielec- tricum For plate condensers, the capacitance is given by

A

C= E O E , -

d

where A is the area of the plates,

d the distance between the plates,

E o the absolute dielectric constant of vacuum, and

E, the relative dielectric constant of the

aerated broth between the plates

The value of E, of the broth and of the air dif-

fer by a factor of about 80 In the case of non- aerated broth the capacitance of the condens- er, C, is given by

where Co is the capacity of the condenser with air,

AC the capacity difference due to

broth per unit height, and

h the height of the liquid in the ca- pacitor

The capacity of the condenser with aerated broth is given by

where E is the gas holdup in the aerated broth Analogous relationships hold true for cylindri- cal condensers (OEDEKOVEN, 1980)

The accuracy of the level control amounts to * 2-4% depending on the uniformity of the

liquid level In the case of large reactors, the level variation can be extremely large There- fore, only the level of the broth can be meas- ured in the reactor, not that of the aerated broth, which is measured outside of the reac- tor, e.g., in a non-aerated section Also in the case of foam formation, the measurement of the aerated broth level by capacitance instru- ments becomes difficult Under these condi- tions floating bodies can be used as level con- trollers

Since cultivation broths have adequate elec- trical conductivity, the liquid level can also be measured by inexpensive electrical conductivi- ty probes Their application is restricted to aqueous broths In the presence of a second (organic) liquid phase, their application cannot be recommended

For other level control instruments, see, e.g., OEDEKOVEN (1980), ELFERS (1964), AN-

DREW and RHEA (1970)

Gas and liquid flow rates are important con- trol variables for biotechnological processes; they must be known for reactor operation and for component balancing In this chapter, only instruments for liquid throughput measure- ment are taken into account Instruments for gas throughput measurements are considered

in Chapter 2 Special techniques for measure-

ments of local liquid velocities are treated in

Chapter 4

Of the large number of available instru- ments ( S C H R ~ D E R , 1980; ANDREW et al., 1979; ERICSON, 1979) only three types are im-

portant in biotechnological practice: - floating body flowmeters,

- differential pressure flowmeters, and

- magnetic-inductive flowmeters

The floating body flowmeter or rotameter consists of a conical tube and a floating body with the upper diameter D,, mass M,, and den-

sity ps (Fig 1) In the upstreaming fluid, the lifting force, which is produced by the differ- ential pressure across the slot between the tube wall and the floating body, is balanced by the weight of the floating body minus its buoyan- cy The position of the float is a function of the flow rate and the density of the fluid, p

The volumetric throughput q v is given by

The flow coefficient a is a function of the Rey-

nolds number and the diameter ratio Dk/D,,

where Dk is the diameter of the tube at the up-

per edge of the floating body

12 I Common Instruments for Process Analy> pis and Control

Calibration of q v is necessary because of the nonlinear relationship between the position of the floating body and the throughput It can be carried out with water or air and recalcu- lated for the nutrient medium with known den- sity by means of the a-Ru diagram, where

the Ruppel number

depends only on the instrument constants and fluid properties, but not on the throughput

The accuracy of rotameters is between k 1 and k 3 % depending on the ratio qv/qV,max

( S C H R ~ D E R , 1980)

Differential pressure flowmeters consist of a tube with a restriction (usually an orifice plate) The pressures p 1 and p z upstream and

downstream of the orifice are measured The

p the density of the fluid,

D the tube diameter,

q the dynamic viscosity of the fluid, and

w the mean flow rate of the fluid

the orifice-to-tube diameter ratio d / D for

smooth tubes

In practice, standardized orifices are used for which the flow coefficients are given in diagrams The accuracy of calibrated orifice

flowmeters is f0.5'70 of qv,max

According to the induction law of Faraday, an electrically conductive liquid passing a mag- netic field induces a voltage between two elec- trodes positioned perpendicular to the direc- tion of the flow The voltage is proportional to the flow velocity:

where U is the induced voltage,

B the magnetic induction, D the tube diameter, and

w the mean liquid velocity

The volumetric throughput q v is given by

(SCHRODER, 1980):

rcD U q v - - - U - -

4 B B

Cultivation broths are electrically conductive, because they contain nutrient salts Therefore, magnetic-inductive flowmeters can be em- ployed for the measurement of nutrient me- dium throughputs For the description of these instruments, see S C H R ~ D E R (1980)

Magnetic-inductive flowmeters are fairly ex- pensive However, they have important advan- tages:

- the voltage U is proportional to qv,

- they are independent of the density and viscosity of the fluid as well as of the velocity profile of the fluidin tubes,

- they d o not produce a pressure drop,

- they do not have moving parts, - they can be used for suspensions,

- they can be steam-sterilized

Their accuracy is k 1% at qv,max, and k 1.5% at 0.5 qv.max

The flow coefficient a is usually given as a

function of the orifice Reynolds number and

3.5 Power Input

In an agitated reactor, the power input, P,

can be calculated by Eq (23) by measuring the torque on the shaft, MN, and the speed of ro-

tation, N

The torque is measured by torsion dynamome- ters or strain gauges and the impeller speed by an electronic tachometer In large-scale reac- tors, the consumed electrical energy, as meas- ured by the wattmeter, yields useful data on power input, if the mechanical losses in gear, seals, etc., are taken into account

In small laboratory reactors, the mechanical losses are considerable in comparison with the power input into the broth Therefore, power input measurements are inaccurate and are not recommended

In bubble columns, P can be calculated by

where MG is the gas mass flow,

R the gas constant,

T the absolute temperature,

pin the gas pressure at the column

However, since the second and third terms to- gether make up only 0.2% of the overall pow- er input, the power input due to the gas expan- sion dominates:

P i n

Pout

In the power inputs, Eqs (24) and (25), the en- ergy losses due to mechanical energy (e.g., due to gas compression) are not considered

3.6 Liquid Viscosity

The viscosity of the broth influences the op- eration of bioreactors considerably At a high viscosity, a high specific power input is neces- sary to increase the intensity of transfer proc- esses: oxygen transfer (into the broth of aero- bic microorganisms) and mixing Since at high specific power input the energy dissipation rate in the reactor is high, improvement of heat transfer is also important to keep the tempera- ture constant

High viscosity can be caused by high sub- strate concentration (e.g., starch), high prod- uct concentration (e.g., xanthan), high cell concentration (e.g., penicillin), high solid con- tent (e.g., peanut flour), or by their combina- tion The most general description of the rheo- logical properties of fluids is given by the rela- tionship between the velocity gradient dv/dx and the stress, T, the so-called flow equation: dv

- = f (7)

dx

as long as viscoelastic behavior is not present or very slight This flow equation can be calcu- lated from the experimentally measured shear diagrams (shear rate versus shearing stress) It should be noted, however, that such a calcula- tion is not always possible In contrast to the shear diagram, the flow equation is indepen- dent of the experimental conditions (e.g., the type of viscosimeter) used for the determina- tion of the viscosity

There are many methods available to esti- mate the rheological behavior of fluids, but there are only a few that furnish true fluidity values These include the capillary, the falling sphere, the Couette, the Searle, and the tor- sional pendulum methods Until now, the eval- uation of the flow equation from the shear diagram has only been possible for the capil- lary, Couette, and Searle methods (MUSCHEL-

KNAUTZ and HECKENBACH, 1980)

The capillary viscosimeter cannot be em- ployed for cultivation broths because of ad-

14 1 Common Instruments for Process Analysis and Control

verse wall effects in the capillary As for the

falling sphere and torsional pendulum viscosi- meters, the flow equation cannot be calculated from the shear diagram (only partial solutions are known)

The Couette and Searle viscosimeters can only be used if the following conditions are fulfilled: the annular slit between inner and outer cylinders must be large enough to reduce the wall effects, and measurements must be made using different cylinder lengths to elimi- nate the end effects In a Searle viscosimeter, the speed of rotation is limited by the occur- rence of Taylor instabilities

By measuring the torque MN on the shaft of different types of stirrers at differing stirrer speeds, N is suited for the evaluation of the power input but not for the viscosity These techniques, which are commonly used accord- ing to the literature, are not suitable for the evaluation of the shear diagram and the abso- lute viscosity

Only the coaxial cylinder viscosimeters, Couette with rotation outer cylinder and Searle with rotation inner cylinder, are consid- ered here, since they are the most popular

where w is the angular speed,

Mi the torque exerted on the inner cy- linder, and

L the length of the inner cylinder

From Eqs (27) and (28) it follows that

ti and t, are the shear stresses at the in- ner and outer cylinders

The relationship between the angular velocity

of the rotating cylinder SZ and t is experimen- tally determined to obtain the shear diagram The relationship dv/dx=f(z) (flow equation) can be calculated from Eq (30) For this eval- uation, see MUSCHELKNAUTZ and HECKEN-

BACH (1980) and DINSDALE and MOORE

where q is the dynamical viscosity

In practice, relative viscosities are frequent- ly determined The shear stress is measured for different shear rates with fluids of known (oils) and unknown (broth) viscosities, and the relative viscosity of the broth can be calculated from the ratio of their shear stresses at the same shear velocity, if the broth has Newton- ian behavior

On-line determination of the broth viscosity is sometimes useful for controlling a process The on-line techniques only yield relative vis- cosities The viscosity of the Aspergillus niger

broth was measured on-line by means of a tube viscosimeter by BLAKEBROUGH et al (1978) PERLEY et al (1979) used an on-line capillary technique for the measurement of the viscosity of the Hansenula polymorpha broth

LANGER and WERNER (1981) and NEUHAUS et al (1983) developed an on-line slot-type vis- cosimeter and measured the viscosity of the

Penicillium chrysogenum broth KEMBLOWSKI

et al (1985) used an on-line impeller type vis- cosimeter to determine the viscosity of the

A ureobasidium pullulans broth

3.7 Foaminess

Integration of Eq (29) with s2 = R?/Ri = tilta

cially a combination of different surfactants with proteins, may cause stable foams in aer- ated bioreactors Foam control is necessary to

avoid the loss of broth, the clogging of the gas analyzers, and infections caused by foam carry-out

Foam can be suppressed by antifoam agents (BEROVIC and CIMERMAN, 1979; SIE and SCHOGERL, 1983; SCHUGERL, 1986; PRINS and VAN'T RIET, 1987; VIESTURS et al., 1982) or destroyed with mechanical foam breakers (VIESTURS et al., 1982) Foam can be detected by an electrical conductivity probe, capaci- tance probe, heat conductivity probe, or light scattering probe (HALL et al., 1973; VIESTURS et al., 1982) Antifoam and mechanical foam breakers are frequently combined, if the foam is very stable

The presence of an antifoam agent in the broth may influence cell growth and product formation as well as downstream processing Mechanical foam breaking may exert stress and selection pressure on the cells

4 Instruments for

Determination of Chemical System Properties

4.1 pH Value

The dissociation constant K, of the purest water is very low (10-'5.74 at 25 "C) The con- centration of water can be considered as con- stant because of the low K, value Thus, only the ion product K, is taken into account: [ H + ] * [OH-] =K,= 1.008 at 25 "C (32a) Forming the logarithm of Eq (32a)

log [H '1 + log [OH -1 = log K, (32b) and by multiplication with - 1,

-log [ H + ] = p H -log [OH-] =POH

-log K, = PK, and pH fpoH = pK,

At [H '1 = [OH-], the hydrogen ion con- centration is [ H + ] = lo-', therefore, at the neutral point pH =pOH = 7

The pH can be measured with a galvanic cell

(chain) The potential E of the cell is given by

the Nernst equation:

R T F

where Eo is the standard potential and F the Faraday constant

In this definition the thermodynamic activities of the ions were replaced by their concentra- tions since the activities cannot be measured The absolute potential cannot be measured either, only the potential difference U between the indicator electrode and a reference elec- trode

Silver-silver chloride electrodes are used in the galvanic chain for sterilizable electrodes Fig 2 shows the schematic assembly of a pH electrode (INGOLD I) In this figure E l is the

potential on the outer surface of the glass membrane, which depends on the pH value of

the sample solution E2 is the asymmetry (bias)

potential, i.e., the potential of the glass mem- brane with the same solutions on both sides

E3 is the potential on the inner surface of the

glass membrane, which is a function of the pH

value of the internal buffer solution E4 is the

potential of the internal Ag/AgCl lead-out electrode, dependent on the KCl concentration in the internal buffer solution E5 is the poten-

tial of the reference AgCl/Ag electrode, which

reference

elect rulyt

internal buffer solution

Fig 2 Schematic assembly of a pH-electrode (Dr

W Ingold AG, Brochure I, with permission) For details see text

are obtained

16 I Common Instruments f o r Process Analysis and Control

depends on the KC1 concentration in the refer-

ence buffer solution, E6 is the diaphragm or

diffusion potential

Since El is the potential which we want to measure, the individual potentials E2-E6

should be kept constant These are included in the standard potential U", which has to be de- termined by calibration

In modern pH electrodes, U" varies only in a narrow range (e.g., Type U 402-K7 elec- trodes of Ingold AG have a potential of

- 10.4k3.8 mV at pH 7.02 and 20 "C) The potential difference between the indica- tor and reference electrodes U is also given by

the Nernst equation:

-

2.3R T

F

where the Nernst potential UN = - -

59.2 mV at 25 "C However, in real pH elec- trodes, the Nernst potential is not attained, but only approached to 97.5% (in the case of new electrodes) Furthermore, UN is reduced with

increasing age of the electrode The aging causes sluggish response, increasing electrical resistance, a smaller slope, and zero point (U")

drift During steam sterilization, a pressure difference builds up on both sides of the glass membrane Therefore, a counter pressure is imposed to avoid the destruction of the elec- trode Frequent steam sterilization has a con- siderable aging effect Therefore, pH elec- trodes must be recalibrated frequently with buffer solutions

During in situ steam sterilization a consider-

able, irreversible signal drift of the pH electro- des occurs Therefore, it is advisable to meas- ure the pH value of the broth in the reactor after each steam sterilization by an indepen- dent method and correct the reading of the pH meter

Since the potential U depends on the tem-

perature, pH-meters have a temperature com- pensation, which is usually calculated by the relationship

UN( T ) = UN(25 "C) (1 + CY t ) (35)

where ~ ~ = 3 2 1 f O 5 3 1 0 - ~ / " C ,

t = T - standard temperature (25 "C)

For more information on pH electrodes, their use, storage, aging, etc., see INGOLD I, PE-

TERSEN (1 980), MELZNER and JAENICKE (1980), and MCCULLOUGH and ANDREW (1979)

4.2 Dissolved Oxygen Partial

Pressure, po,

The dissolved oxygen concentration is also measured by electrochemical methods Two types of electrodes are in use:

- polarographic electrodes

- galvanic electrodes

In polarographic or amperometric elec- trodes the dissolved oxygen is reduced at the surface of the noble metal cathode in a neutral potassium chloride solution, provided it reaches 0.6-0.8V negative with respect to a suitable reference electrode (calomel or Ag/ AgC1) The current-voltage diagram is called the polarogram of the electrode (Fig 3)

1

Negative bias voltage Oxygen

Fig 3 Polarogram and calibration curve for a po,-

electrode (LEE and TSAO, 1979)

At the plateau of the polarogram, the reac- tion rate of oxygen at the cathode is limited by the diffusion of oxygen to the cathode Above this voltage the water is electrolyzed into oxy- gen and hydrogen In the plateau region (0.6-

0.8 V), the current is proportional to the par- tial pressure of the dissolved oxygen (Fig 3)

In this probe, the cathode, the anode, and the electrolyte are separated from the measur-

ing liquid by a membrane which is permeable to gaseous oxygen In the electrolyte, the fol- lowing reactions occur: Since hydroxyl ions are constantly being sub- stituted for the chloride ions as reaction pro- ceeds, KCl or NaCl must be used as an electro- lyte When the electrolyte becomes depleted of C1-, it has to be replenished

The dissolved oxygen concentration is meas- ured by the galvanic electrode which does not require an external voltage source for the re- duction of oxygen at the cathode Using a basic metal such as zinc or lead as anode and a nobler metal such as silver or gold as cathode, the voltage is generated by the electric pair and is sufficient for a spontaneous reduction of oxygen at the cathode surface The reaction of the silver-lead galvanic electrode is given by:

During the reduction of oxygen, the anode sur- face is gradually oxidized Therefore, occa- sional replacement of the anode is necessary

The polarographic or amperometric elec- trode is in greater demand in biotechnological practice than the galvanic electrode Fig 4 shows a schematic view of a steam-sterilizable polarographic or amperometric oxygen elec- trode

A constant voltage (ca 650 mV) is applied

between cathode (Pt) and anode (AgIAgCl) A

regular control of this voltage is necessary in order to avoid incorrect measurements The Gas permeable mernbr 'ane

Sterilizable po,-electrode (Dr W Ingold

AG, Brochure 11, with permission)

control is carried out by measuring the polaro- gram and adjusting the bias voltage to main- tain a voltage-independent current in the pla- teau region of the polarogram

The current ip,02 is proportional to po2 only in the plateau region:

where K is a constant,

A the surface area of the cathode,

P the membrane permeability,

d the membrane thickness

The response time is proportional to d 2 / P

Therefore, thin membranes with high gas 02-

permeability are used Two membranes are used for the p o , electrodes for sterile opera- tion The inner membrane consists of a 25 pm teflon foil, the outer one of a 150 wm silicone membrane reinforced by thin steel mesh This type of electrode was developed by the Instru-

18 1 Common Instruments for Process AnalyJ :is and Control

mentation Laboratory Inc., Lexington, Mass., USA, and also produced by Dr W Ingold AG, Urdorf, Switzerland (INGOLD 11) This type of electrode has a fairly long response time (45 to 90 s to attain 98% of the final sig- nal)

During steam sterilization, the membrane thickness and shape change irreversibly An improved construction of BAUERMEISTER (1981) enables the electrodes to endure many (ca 20) sterilizations without any change in the membranes

The temperature of the calibrations and measurements must be controlled closely (k 0.1 "C) because of the temperature sensitivi-

ty of the signal (temperature coefficient 3%/ "C) Since the electrode measures the partial pressure of oxygen, the signal is independent of the 02-solubility in the broth The calibra- tion should be performed in the reactor under the same fluid dynamic conditions (stirrer speed) as those that prevail during cultivation to avoid errors due to differences in diffusion resistance at the surface of the membrane

The calibration is carried out with nitrogen- and air-saturated broth by setting these values at 0 and 100% The partial pressure of oxygen is expressed as follows:

p o 2 = [PB-p(HzO)] x 0.2095 (37) where pB is the temperature-corrected

(barometric) pressure in the react or,

p(H20) the vapor pressure of the broth at the temperature of the calibration,

0.2095 the fraction of oxygen in at- mospheric air

The sources of error in the measurement of

po2 are numerous: errors in reading of temper- ature and pressure, drift due to membrane fouling, change in membrane shape, variation of bias voltage and electrical resistance as well as capture of bubbles, etc With sufficient ac- curacy of temperature and pressure measure- ments, and with bias voltage in the plateau re- gion, the precision of the measurements is on the average f 5 % Below 5 % of the 02-satura- tion, the error increases with decreasing po,

The dissolved oxygen concentration [O,] is calculated by the relationship:

and CY is the Bunsen coefficient

Bunsen coefficients CY of oxygen for some simple aqueous solutions and a few cultivation broths have been given by SCHUMPE (1985) For more details, see MELZNER and JAENICKE (1980), INGOLD 11, LEE and TSAO (1979), FRITZE (1980), BUEHLER and INGOLD (1976), and SCHINDLER and SCHINDLER (1983)

4.3 Redox Potential, Eh

The definition of the redox potential is given by Eq (9) To determine E , the potential be- tween the redox electrode and a standard refer- ence electrode is measured The universal ref- erence reaction is the oxidation of hydrogen: H 2 - + 2 H + + 2 e -

(39) The standard potential Eo(H+/H2) is by defi- nition equal to zero at all temperatures The universal reference electrode is known as the Standard Hydrogen Electrode (SHE), which consists of a platinum-coated platinum foil that is immersed in a solution containing 1 mol L - ' H + , and over which flows hydrogen gas at a pressure of 1 bar The reference electrodes (Hg/calomel/sat KC1, or Ag/AgCl/KCl) used in practice are referred to the SHE:

where Eh is the redox potential against the

The sterilizable redox meter consists of a Pt electrode and an Ag/AgCl reference electrode The electrodes are calibrated with redox buf- fers in the range of Eh = + 200 mV to 600 mV (INGOLD 111) Since the redox potentials have a high temperature coefficient, knowing the temperature of the broth is necessary for cal- culating the correct standard potential for the reference electrode For example, standard po- tentials of Ingold reference electrodes are giv- en in INGOLD I11 for different temperatures

Redox potentials occur in a range of - 1200 to + 1200 mV Measurement precision is + 5

mV A simple pH meter with a mV scale is an adequate measuring instrument The redox po- tential depends on the po, and pH in the broth However, since both are measured in bioreactors, these effects can be taken into ac- count In aerobic cultivations the po, and re- dox meters give nearly the same information at a constant pH value In microaerobic and anaerobic cultivations the redox potential gives additional information about the state of the broth components However, because of the complex composition of the broth this infor- mation is only qualitative

For more information on the redox poten- tial, see MELZNER and JAENICKE (1980), KJAERGAARD (1977), KJAERGAARD and JOERGENSEN (1979), INGOLD 111, and FRITZE (1980a, b)

4.4 Dissolved C 0 2 Partial Pressure,

Pco,

The presence of dissolved C 0 2 in the broth

influences cell growth and product formation (Ho et al., 1987) Therefore, thepco2 can be an important variable The pco, can be meas- ured in-line using thepcoz meter of Dr W In-

gold AG (INGOLD IV) The instrument con-

sists of a pH meter and a hydrogen carbonate solution, which is separated from the broth by a gas-permeable membrane Fig 5 illustrates the main features of the electrode

The dissolved Cot diffuses through the membrane into the hydrogen carbonate solu- tion The equilibrium of the reaction

CO,+H,O + HCO, + H +

Measu

Fig 5 Sterilizable pco,-electrode (Dr W Ingold AG, Brochure IV, with permission)

Construction of a C0,-sensor: (1) 20 mL syringe, (2)

high-temperature coaxial cable, (3) cable screw con-

nection, (4) adjustment nut, ( 5 ) locking plug, (6) supply duct, (7) welding socket, (8) bore hole con- ductor, (9) draw tube, (10) pH-electrode, (11) refer-

ence electrode, (12) C0,-electrode, (13) membrane body, (14) calibration buffer, (15) glass membrane, (16) reinforced silicon membrane

is determined by the dissociation constant K

where H is the Henry coefficient

Since the hydrogen carbonate concentration in the electrolyte is high, it can be assumed to be constant Thus, Eq (41) can be simplified to

The potential of the inner pH electrode is a function of [H'I:

20 I Common Instruments f o r Process Analysis and Control R T

F

E = Eo + 2.3 ~ log [H '1 (44)

where 2.3 R T/F=59.16 mV at 25 "C,

E is the measured potential, and Eo is the standard potential

From relationships (43) and (44)

The response time is fairly long (one to sev- eral minutes) and is influenced by the thickness of the membrane and by the electrolyte solu- tion as well as by the response time of the pH electrode

The measuring range of the electrode is 1 to 1000 mbar COz The deviation is f 2 % , if the electrode is calibrated with gas mixtures If the inner pH electrode is calibrated by buffer solu- tions, the deviation is f 10% To avoid errors due to the complex temperature dependence of the reading, the calibration should be carried out at broth temperature

The electrode is sterilizable The steriliza- tion is performed after the reduction of the pressure of the p H electrode on the stainless- steel reinforced plastic membrane The p H electrode is calibrated by buffer solutions after sterilization Then the electrode is filled with the electrolyte and put into the measuring posi- tion Fig 5 shows the electrode during calibra- tion and measurement For more information, see INGOLD IV

5 Performance of Instruments

for Process Control

According to FLY" (1982) the relevance, accuracy, and precision of the measured data and the reliability, accuracy, precision, resolu- tion, specificity, response, sensitivity, availa- bility, and costs of the sensors/instruments are important for their use in process control All

data which influence the productivity and the yield of the process and the quality of the product are relevant Accuracy of the meas- ured data is expressed as the difference be- tween the observed value of the variable and its true value, which is usually determined by calibration

The precision of the data relates to the probability that repeated measurements of the same system will produce the same values The distribution of the values around their mean is usually characterized by the variance and/or standard deviation, or, e.g., the 95% confi- dence interval

The most important property of a sensor is its reliability, which is made up of factors such as failure rate, failure mode, ease of preventive maintenance, ease of breakdown maintenance, physical robustness, and its credibility in the mind of process operators (FLY", 1982) The latter plays a role only if the data are used by the operator and not by a n automated sys- tem

Based on information from three chemical works, LEES (1976) published data on the re- liability of the instruments important in the fermentation industry (Tab 1)

One can observe that at the time of investi- gation (1970-1975) the pH meter and the 0,

and COz analyzers were the least reliable in- struments During the last ten years, the relia- bility of these instruments has been improved considerably, provided an accurate flowmeter is used for the 0, and CO, instruments

FLY" (1982) gave detailed results on the

performance of the instruments in a 1 m 3 pilot plant bioreactor (Tab 2)

One can see that the po2 measurement had

the lowest accuracy, the po2 and air flow con- trol the lowest precision, and the volume meas- urement the lowest resolution In the mean- time, the air-flow control should have attained a much higher accuracy and precision, pro- vided the right instrument is used (e.g., mass flowmeter) In recent years, the accuracy of the po2 measurement has not been improved markedly, it can, however, be achieved by fre- quent calibration The accuracy and precision

of the po2 control is much better if one uses

three sensors and parameter-adaptive control

Tab 1 Instrument Reliability (LEES, 1976)

Notes: W , weekly; H, hourly; R, per run, which relates to the frequency with which the measuring instru- ments are recalibrated

22 1 Common Instruments f o r Process Analysis and Control

In this chapter, only H +-selective electrodes are considered However, using ion-selective membranes, in principle the concentration of an arbitrary ion can be determined by means of the Nernst equation:

IM the concentration of the measured ion in the broth

The production of ion-selective carrier-mem- brane-electrodes is very easy A standard pH- electrode is combined with an ion-selective membrane consisting of an ionophore in a polymer matrix

The ionophore and the softener are usually dissolved in a PVC solution, put on the sur- face of the pH-electrode, and dried Fig 6

shows several constructions of such elec- trodes

Ion-selective membranes may be prepared by ionophore antibiotics (valinomycin, nonac- tin, etc.) (SCHINDLER and SCHINDLER, 1983) and synthetic carriers (crown ethers and cryp- tates, cyclodextrins, cyclotriveratrylene, perhy- drotriphenylene, etc.) (ATWOOD et al., 1984; V ~ G T L E , 1975, 1981) Chiroselective transport molecules are particularly interesting for the more detailed analysis of broth components (LEHN, 1988)

At present, reliability and selectivity of ion- selective membranes are not always satisfacto- ry However, host-guest-complex chemistry is developing rapidly Therefore, it is expected that some years from now reliable, ion-selec- tive electrodes will be available

The combination of pH, po,-, pco,-, and NH: -selective transducers with biochemical receptors (enzymes, antibodies, lectins, etc.) is considered in Chapter 3 (Biosensors)

Fig 6 Different types of ion-selective carrier mem- brane electrodes with liquid- and solid-lead-offs (SCHINDLER and SCHINDLER, 1983, with permis- sion)

(a) Glass membrane electrode (1) ion-selective glass membrane, (2) non-specific glass shaft, (3) Ag/

AgC1-lead-off electrode, (4) lead-off electrode (liq- uid), ( 5 ) cable

(b) Liquid membrane electrode with ion-exchanger reservoir (1) porous membrane, (2) ion-exchanger

reservoir, (3) lead-off electrolyte (liquid), (4) Ag/

AgC1-lead-off electrode

(c) PVC ion-exchanger membrane electrode (1) PVC ion-exchanger membrane, (2) PVC tube, (3)

lead-off electrolyte (liquid), (4) Ag/AgCl-lead-off electrode

(d) Coated wire-electrode (1) Pt-wire, (2) PVC ion-

exchanger membrane, (3) cable

(e) Disc electrode without O2 reaction barrier (1) carrier-PVC-membrane, (2) Pt-wire, (3) acryl/glass mantle, (4) PTFE-insulated, silver-coated Cu-wire,

( 5 ) PTFE or acryl glass

(f) Coated glass electrode (1) carrier-PVC-mem- brane, (2) ion-selective glass membrane, (3) acryl glass mantle, (4) Ag/AgCl-lead-off electrode, ( 5 ) in- ner electrolyte or cement lead-off, e.g., Ag/AgCl/

Harvard cement, (6) non-specific glass shaft, (7)

acryl glass or PTFE

(9) Disc electrode with O2 reaction barrier (1) car- rier-PVC-membrane, (2) Ag/AgCl (melt), (3) Pt- wire, (4) acryl glass mantle, ( 5 ) PTFE-insulated,

silver-coated Cu-wire, (6) PTFE or acryl glass with

Ag/AgCl/Pt-solid contact

M (1983), Dissolved oxygen contours in Pseudo-

chemical Engineering: Kinetics and Thermody-

ANDREW, W G., RHEA, K G (1970), Level meas- namics of Biological Systems (BLANCH, H W., urement, in: Applied Instrumentation in the PAPOUTSAKIS, E T., STEPHANOPOULOS, G.,

Process Industries (ANDREW, w G., WILLIAMS, Eds.), ACS Symp Ser 207, 395-401

B., Eds.), 2nd Ed., vole 1, PP 99-141 Houston: BUSING, W., ARNOLD, J U (1980), Temperatur-

Gulf Publishing Co messung, in: Messen, Steuern und Regeln in der ANDREW, W G., MILLER, W F (19791, Pressure Chemischen Technik (HENGSTENBERG, J., measurement, in: Applied Instrumentation in the sTURM, B., WINKLER, o., Eds.), 3rd Ed., vol

PrOCeSS Industries (ANDREW, w G , WILLIAMS, 1, pp 1-100 Berlin-Heidelberg-New York: B., Eds.), 2nd Ed., Vol 1, pp 142-167 HOW-

ton: Gulf Publishing Co CHEN, Y S., BUNGAY, H R., I11 (1981), Micro-

G * p B EDMoNSoNt F electrode studies of oxygen transfer in trickling E (19791, Flow measurement, in Applied Instru- filter slimes, Biotechnol Bioeng 23, 781-792

mentation in the Process Industries (ANDREW, CHERUY, A., DURAND, A (1979), Optimization of

w G.9 B.* Eds.)y 2nd Ed., 1, erythromycin biosynthesis by controlling pH and pp 46-98 Houston: Gulf Publishing Co temperature: Theoretical aspects and practical

A N D R E Y E V A y L N * j BIRYUKoV, v v (1973)* application, Biotechnol Bioeng Symp 9, 303-

Analysis of mathematical models of the effect of 320

calculating optimal fermentation conditions, Bio- ous optimization methods to the control and op- eration of fermentation processes, in: Biochemi- technol Bioeng Symp Ser 4, 61-76

Springer Verlag

pH on fermentation processes and their use for CONSTANTINIDES, A (1979), Application of rigor-

ATWOOD, J L.9 DAVIES, J E.9 MACNICOL, D D (Eds.1 (1984)? Inclusion Compounds, vO1 1-3* BAUERMEISTER* '* D* (1981)9 Elektrodenanord-

cal Engineering (VIETH, R., VENKATASUBRA- MANIAN, U., CONSTANTINIDES, A., Eds.) Ann

CONSTANTINIDES, A., UI, V R e (1974), Applica-

N Y Acad Sci 326, 193-221

tion of the continuous maximum principle to fer- 223.9S2G O1 27'28, Int (24 4 1980)' mentation processes, Biotechnol Bioeng Symp

submerged citric acid fermentation on beet mo- London: Academic Press

Ger Patent 2801 223y A* '* 2801

Electrode Device, US Patent 4248712 4, 663-680

BERoVIC, M., A* (1979)9 Foaming in cONSTANTINIDES, A., SPENCER, J L., GADEN, E., Jr (1970), Optimization of batch fermentation batch penicillin fermentations, Biotechnol

BLAKEBROUGH, N., MCMANAMEY, W J., TART,

Bioeng 12, 1081-1098 K R (1978), Rheological measurements on As-

COONEY, C L., WANG, H Y., WANG, D I C

pergillus niger fermentation systems, J Appl

(1977), Computer-aided material balancing for

Chem Biotechnol 28, 453-461

BLANCH, H w., ROGERS, p L (1972), Optimal prediction of fermentation parameters, Biotech- conditions for gramicidin S production in contin-

uous culture, Biotechnol Bioeng 14, 151-171 DINSDALE, A., MOORE, F (19621, in: viscosity and

Eur Conf Computer Control in Fermentation, ' New Reinhold

Dijon, France ELFERS, P A (1964), Liquid level, in: Handbook

BUEHLER, H., INGOLD, W (1976), Measuring pH of Applied Instrumentation (CONSIDINE, D M., and oxygen in fermenters, ProcessBiochem., 19-24 Ross, s D*f Eds.), Sect 5 * pp 55-67 New BUNGAY, H R., 111, CHEN, Y S (1981), Dissolved York: McGraw-Hill

oxygen profiles in photosynthetic microbial ERICSON, F A (197% Pumps and flow measure-

slimes, BiotechnoL Bioeng 23, 1893-1895 ment, in: Laboratory Engineering and Manipula-

tions (PERRY, E- s., WEISSBERGER, A., Ed$.), Simulation of oxygen transfer in microbial 3rd Ed., PP 182-220 New York: John Wiley &

slimes, Biotechnol Bioeng 13, 569-579 Sons

W M (1969), Microprobe techniques for deter- the discrete maximum principle to a stagewise mining diffusivities and respiration rates in mi- biochemical reactor system, Biotechnol Bioeng

crobial slime systems, Biotechnol Bioeng 11, 5 , 201-209

BUNGAY, H R., 111, PETTIT, P M., DRISLANE, A tion processes, in: Modelling and Control ofBio-

lasses, Eur J APPl Microbial BiotechnoI 7,

processes* 11 Optimum temperature profiles for

24 I Common Instruments f o r Process Anal) wis and Control technological Processes, pp 5-12 Helsinki:

IFAC

FORAGE, D E., HARRISON, D E F., PITT, D E (1985), Effect of environment on microbial activ-

ity, in: Comprehensive Biotechnology (BULL, A

T., DALTON, H., Eds.), Vol 1, pp 251-280 Oxford-Toronto-Sydney-Frankfurt: Pergamon Press

FRITZE, U (1980a), Die Technische Messung der

Redoxspannung, in: Messen, Steuern und Regeln

in der Chemischen Technik (HENGSTENBERG, J., STURM, B., WINKLER, O., Eds.), 3rd Ed., Vol 2, pp 367-385 Berlin-Heidelberg-New York: Springer Verlag

FRITZE, U (1980b), Weitere potentiometrische und amperometrische ProzeRanalysenmethoden, in:

Messen, Steuern und Regeln in der Chemischen Technik (HENGSTENBERG, J., STURM, B., WINKLER, O., Eds.), 3rd Ed., Vol 2, pp 383-402 Berlin-Heidelberg-New York: Springer Verlag HALL, M J., DICKINSON, S D., PRITCHARD, R.,

EVENS, J I (1973), Foams and foam control in

fermentation processes, Prog Ind Microbiol HIRTE, W (1980), Druckmessung, in: Messen,

Steuern und Regeln in der Chemischen Technik

(HENGSTENBERG, J., STURM, B., WINKLER, O., Eds.), 3rd Ed., Vol 1, pp 101-190 Berlin-Hei- delberg-New York: Springer Verlag

H o , C H S., SMITH, M D., SHANAHAN, J F (1987), Carbon dioxide transfer in biochemical

reactors, Adv Biochem Eng Biotechnol 35,

HOSPODKA, J (1966), Oxygen-absorption rate-con- trolled feeding of substrate into aerobic microbial

cultures, Biotechnol Bioeng 8, 117-134

INGOLD I, Brochure I: p H Electrodes Dr W In- gold AG, Urdorf, Switzerland

INGOLD 11, Brochure 11: 0, Measurement Systems;

p H and 0, Measurement in Fermentors Dr W Ingold AG, Urdorf, Switzerland

INGOLD 111, Brochure 111: Redox Measurement Dr

W Ingold AG, Urdorf, Switzerland

INGOLD IV, Brochure IV: Sterilizable CO, Probe

Dr W Ingold AG, Urdorf, Switzerland JOERGENSEN, H (1941), Studies on the Nature o j

Bromate effect Thesis, Copenhagen, Munks- gaard

KEMBLOWSKI, Z., KRISTIANSEN, B., ALAYI, 0

(1985), On-line rheometer for fermentation liq-

uids, Biotechnol Lett 7, 803-808

KING, R E., ARAGONA, J., CONSTANTINIDES, A (1974), Special optimal control of batch fermen-

tor, Int J Control 20, 869-879

KJAERGAARD, L (1977), The redox potential: Its

use and control in biotechnology, Adv Biochem

Eng 7, 131-150

12, 170-234

83- 126

KJAERGAARD, L., JOERGENSEN, B B (1979), Re- dox potential as a state variable in fermentation

systems, Biotechnol Bioeng Symp 9, 85-94

LANGER, G., WERNER, U (1981), Measurements of viscosity of suspensions in different viscometer

flows and stirring systems, Ger Chem Eng 4,

LEE, Y H., TSAO, G T (1979), Dissolved oxygen

electrodes, Adv Biochem Eng 13, 35-86

LEELASART, B., BONALY, R (1988), Effect of con- trol of pH on the excretion of acid phosphatase

by Rhodotorula glutinis, Appl Microbiol Bio-

technol 29, 579-585

LEES, F P (1976), The reliability of instrumenta-

tion, Chem Ind (9, 195-205

LEHN, J M (1988), Supramolekulare Chemie -

Molekiile, Ubermolekiile und molekulare Funk-

tionseinheiten, Angew Chem 100, 91-1 16

LINEK, V., VACEK, V (1986), Recommended proce- dure for the measurement of the volumetric mass

transfer coefficient kLa in aerated agitated ves- sels Report of a Working Party on Mixing of the European Federation of Chemical Engineering,

Prague

LINEK, V., VACEK, V., BENES, P (1987), A critical review and experimental verification of the cor- rect use of the dynamic method for the determi- nation of oxygen transfer in aerated agitated ves- sels to water, electrolyte solutions and viscous

liquids, Chem Eng J 34, 11-34

MCCULLOUGH, R L., ANDREW, W G (1979),

Analytical instruments, in: Applied Instrumenta-

tion in the Process Industries (ANDREW, W G., WILLIAMS, B., Eds.), 2nd Ed., Vol 1, p 209 Houston: Gulf Publishing Co

MELZNER, W., JAENICKE, D (1980), Prozefianaly-

tik, in: Ullmanns Encyklopadie der technischen

Chemie, 4th Ed., Vol 5 , pp 891-944 Wein- heim-Deerfield Beach, Florida-Basel: Verlag Chemie

MEMMERT, K., WANDREY, C (1987), Concept of redox-regulation for continuous production of

Bacillus exoenzymes, Proc 4th Eur Congr Bio-

t e c h n o l o g y ( N ~ ~ s s ~ ~ , O M.,VANDERMEER, R R., LUYBEN, K CH A M., Eds.), Vol 3, pp 153- 154 Amsterdam: Elsevier Science Publisher B V M o u , D G., COONEY, C L (1983), Growth moni- toring and control in complex medium: A case study employing fed-batch penicillin fermenta- tion and computer-aided on-line mass balancing,

Biotechnol Bioeng 25, 257-269

MUSCHELKNAUTZ, E., HECKENBACH, M (1980),

Rheologische BetriebsmeBverfahren, in: Messen,

Steuern und Regeln in der Chemischen Technik

(HENGSTENBERG, J , STURM, B., WINKLER, O., Eds.) 3rd Ed., Vol 2, pp 431-512 Berlin-Hei- delberg-New York: Springer Verlag

226-241

NEUHAUS, O., LANGER, G., WERNER, U (1983), On-line Betriebsviskosimeter fur Fermentations- prozesse, in: Biotechnologie-Projekt.forderung

Projekte 1978-1984, pp 39-53 Bonn: BMFT

(Bundesministerium fur Forschung und Techno- logie)

OEDEKOVEN, G (1980), Standmessung, in: Messen,

Steuern und Regeln in der Chemischen Technik

(HENGSTENBERG, J., STURM, B., WINKLER, O., Eds.), 3rd Ed., Vol 1, pp 589-640 Berlin-Hei- delberg-New York: Springer Verlag

PAN, C H., HEPLER, L., ERLANDER, A P (1972), Control of pH and carbohydrate addition in the

penicillin fermentation, Dev Ind Microbiol 13, PERINGER, P., B L A C H ~ R E , H T (1979), Modeling and optimal control of bakers’ yeast production in repeated fed-batch culture, Biotechnol

Bioeng Symp 9, 205-213

PERLEY, C R., SWARTZ, J R., COONEY, C L (1979), Measurement of cell mass concentration

with a continuous viscosimeter, Biotechnol,

Bioeng 21, 519-523

PETERSEN, 0 (1980), pH-Messung in: Messen,

Steuern und Regeln in der Chemischen Technik

(HENGSTENBERG, J., STURM, B., WINKLER, O., Eds.), 3rd Ed., Vol 2, pp 305-333 Berlin-Hei- delberg-New York: Springer Verlag

PRINS, A., VAN? RIET, K (1987), Proteins and surface effects in fermentation: Foam, antifoam

and mass transfer, TIBTECH, November 5, 296-

301

RAI, V R., CONSTANTINIDES, A (1973), Mathe- matical modeling and optimization of the glu-

conic acid fermentation, AIChE Symp Ser 132

ROSEN, W., SCHOGERL, K (1984), Microprocessor

controlled fed-batch cultivation of Chaetomium

cellulolyticum on cellulose, Third Eur Congr

Biotechnology, Munchen, 10-14 Sept., Vol 11,

pp 617-619 Weinheim: Verlag Chemie SAN, K.-Y., STEPHANOPOULOS, G (1984), Studies

on on-line bioreactor identification IV Utiliza- tion of p H measurements for product estimation,

Biotechnol, Bioeng 26, 1209-1218

SCHINDLER, J G., SCHINDLER, M M (1983),

Bioelektrochemische Membranelektroden, Ber-

lin-New York: Walter de Gruyter

SCHLEGEL, H G (1974), Allgemeine Mikrobiolo-

gie, 3rd Ed Stuttgart: Georg Thieme Verlag

S C H R ~ D E R , A (1980), DurchfluBmeBtechnik, in:

Messen, Steuern und Regeln in der Chemischen Technik (HENGSTENBERG, J., STURM, B., WINKLER, O., Eds.), 3rd Ed., Vol 1, pp 191- 364 Berlin-Heidelberg-New York: Springer Ver- lag

103- 1 12

(69), 114-122

pression, and the effect of foam on growth,

Process Biochem (August) 122-123

SCHUMPE, A (1985), Gas solubilities in biomedia,

in: Biotechnology (REHM, H.-J., REED, G.,

Eds.) Vol 2, pp 159-170 Weinheim-Deerfield Beach, Florida-Basel: VCH Verlagsgesellschaft SHIOYA, S (1988), Measurement of biological reac-

tion rates using advanced pH control, in: Fourth

Int Congr Computer Applications in Fermenta- tion Technology, IFAC, Sept 25-29, University

of Cambridge, UK (FISH, N M., F o x , R I., Eds.) Chichester: Society of Chemical Industry and Ellis Horwood Publ

SIE, T.-L., SCHOGERL, K (1983), Foam behavior of biological media IX Efficiency of antifoam

agents with regard to their foam suppression ef- fect on BSA solutions, Eur J Appl Microbiol Biotechnol 17, 221-226

SPITZER, D W (1976), Maximization of steady- state bacterial production in a chemostat with pH

and substrate control, Biotechnol, Bioeng 18,

SQUIRES, R W (1972), Regulation of the penicillin fermentation by means of a submerged oxygen-

sensitiveelectrode, Dev Znd Microbiol 13,128-135

STEPHANOPOULOS, G., SAN, K.-Y (1982), On-line

estimation of the state of biochemical reactors,

in: Chemical Reaction Engineering, Boston 1982

(WEI, J., GEORGAKIS, C., Eds.) ACS Symp

Ser 196, 155-164

TAKAMATSU, T., SHIOYA, S., YOKOYAMA, K., IHARA, D (1981), State estimation and control of a biochemical reaction process, in: Biochemi-

cal Engineering ZI (CONSTANTINIDES, A ,

VIETH, W R., VENKATASUBRAMANIAN, K.,

Eds.) Ann N Y Acad Sci 369, 147-158

VIESTURS, U E., KRISTAPSONS, M Z., LEVITANS, E S (1982), Foam in microbiological processes,

Adv Biochem Eng 21, 169-224

VOGTLE, F., Ed (1975), Host guest complex chem-

istry I, Topics in Current Chemistry 101 Berlin-

Heidelberg-New York: Springer Verlag

VOGTLE, F., Ed (1981), Host guest complex chem-

istry 11, Topics in Current Chemistry 98 Berlin-

Heidelberg-New York: Springer Verlag WANG, H Y., COONEY, C L., WANG, D I C

(1977), Computer aided baker’s yeast fermenta-

tions, Biotechnol Bioeng 19, 69-89

WITTLER, R., BAUMGARTL, H., LUBBERS, D W., SCHOGERL, K (1986), Investigations of oxygen

transfer into Penicillium chrysogenum pellets by microprobe measurements, Biotechnol Bioeng

ZABRISKIE, D W., HUMPHREY, A E (1978), Real- time estimation of aerobic batch fermentation biomass concentration by component balancing,

167- 178,

28, 1024-1036

SCHUGERL, K (1986), Foam formation, foam sup- AIChE J 24, 138-146

2 Methods and Instruments in Fermentation Gas Analysis

E LMAR HE I N Z LE IRVING J D U N N

Zurich, Switzerland

1 Introduction 30

2 Mass Balancing for Gas Analysis 31 2.1 Basic Gas Balance Equations 31

2.2 Inert Gas Balance to Calculate Flow Rates 33

2.3 Steady-State Gas Balance to Determine the Biological Reaction Rate 33 2.4 Determination of CPR with Accumulation of CO, in the Liquid Phase 34 2.5 Determination of KLa by Steady-State Gas Balancing with Well-Mixed Gas and

Liquid Phases 35

2.6 Determination of KLa by the Dynamic Method 35

2.7 Determination of Oxygen Uptake Rates by a Dynamic Method 36 2.8 Loop Reactors with External Aeration to Determine OUR 36 2.9 Methods to Measure Low Oxygen Uptake Rates 37

2.10 Oxygen Transfer in Large-Scale Bioreactors 38 3.1 Systematics of Elemental Balancing 41

3.2 Elemental Balancing for Monitoring a Poly-P-Hydroxybutyric Acid (PHB) Producing Culture 42

4.1 Objectives of On-Line Gas Analysis and Requirements for Accuracy and Reliability 45 4.2 Definition of Measurement Requirements 45

4.3 Errors Caused by Simplification of Balancing 46

3 Application of Gas Analysis Results to Elemental Balancing Methods 41

4 Error Analysis for Gas Balancing 44

4.3.1 Simplifications Concerning Pressure, Temperature, Humidity, and Gas Flow 4.3.2 Errors Caused by Steady-State Assumption 47

4.4 Erroneous Estimation of Reaction Rates Caused by Measurement Errors 49 4.4.1 Errors in the Measurement of Gas Flow 49

4.4.2 Statistical Error Propagation 49 4.4.3 Errors in Oxygen Gas Analysis 50

4.4.4 Instantaneous Error Analysis for the Elemental Balancing Example PHB 4.4.5 Dynamic Error Analysis for Reaction Rates 54

5.1 System without Removal of Condensable Volatiles 56 Rates 46

51

5 Sample Pretreatment and Multiplexing 56

5.2 Application of Paramagnetic and Infrared Analyzers to the Measurement of Oxygen

and Carbon Dioxide 56

5.3 Special Valve Manifolds for Mass Spectrometers 57 6.1 Positive Displacement Devices 58

6 2 Rotameters 59

6.3 Thermal Mass Flow Monitors (MFM) 59

7 Instruments for Analysis of Gas Composition 60 7.1 Paramagnetic Oxygen Analyzers 60

List of Symbols and Abbreviations 29

List of Symbols and Abbreviations

C concentration (kg m-3)

CPR carbon dioxide production rate (mol s - ')

CTR carbon dioxide transfer rate (mol s - ') G gas flow rate (m3 s-')

H Henry coefficient (L bar mol-')

I ion current (A)

K equilibrium constant

K L a mass transfer coefficient (s-')

L liquid flow rate (m3 s - ' )

m/z mass-to-charge ratio

M total mass flow (kg s - ' )

n number of moles

N molar gas flow rate (mol SKI)

OUR oxygen uptake rate (mol s-')

OTR oxygen transfer rate (mol s-')

p pressure (bar)

PHB poly-P-hydroxybutyric acid

Q specific reaction rate (mol kg -' s - ')

r reaction rate (mol L -' s - ')

R gas constant (=0.08314bar L mol-' K - I )

6, 6 molar flux (=specific reaction rate) (mol k g-ls- ') Subscripts and Superscripts

E electrode G gas phase

i index for component inert inert gas

L liquid phase re1 relative

X biomass

0 input into the reactor 1 output from the reactor

* refers to gas-liquid equilibrium ' relative value ( - )

biomass concentration (g L - I )

gas phase molar fraction ( - )

1 Introduction

It is evident from Chapter 1 of this volume of “Biotechnology” that on-line fermentation analysis is of increasing importance because precise control of environmental variables is necessary to optimize process yield and selec- tivity Most biological products are not vola- tile and are either dissolved in the fermentation fluid, precipitated, or enclosed within the cell membrane boundary These products are usually difficult or presently impossible to measure on-line in a process environment This is also true for the biocatalyst itself (cell or enzyme)

In industrial processes each sensor causes risks of infection, whether located in the sterile region or connected to the process with a liq- uid sampling device This risk does not exist if measurements are made in the effluent gas stream outside the sterile region

On-line gas analysis is of general interest be- cause almost any biological process using liv- ing organisms involves consumption and pro- duction of gases and volatile compounds Es- pecially oxygen consumption and carbon dioxide production occur in any aerobic fer- mentation process Measurement of these reac- tion rates gives direct information about the culture activity Oxygen consumption rate usually is directly proportional to the heat evo- lution of any aerobic process (COONEY et al., 1969)

Historically, one of the first instruments for gas analysis was the Orsat apparatus (HERON and WILSON, 1959) In this apparatus CO, and

O2 are subsequently absorbed in sodium hy-

droxide and pyrogallol solutions, and volume changes are detected Inert gases are deter- mined by difference CO, production was one of the first biological activities to be quantified in yeast alcohol production Traditionally, the measurements were made using volumetric methods

Under normal conditions, where the ideal gas law is valid, gas volume, pressure, and mo- lar amount are directly linked with each other This makes barometric and volumetric meas- urements very useful In microbiology the Warburg apparatus is still a very popular method of measuring gas reaction rates Oxy-

gen and CO, production can be measured si- multaneously by first measuring pressure change and subsequently absorbing CO, in an alkaline solution, then making a final pressure measurement Volumetric and barometric methods were also further developed to give on-line readings of gas composition (VANA,

1982)

Historically, the results of on-line gas analy- sis have almost exclusively been used to moni- tor fermentations Since more reliable analyti- cal instruments and on-line data acquisition and computing hard- and software have been developed, it is now possible to use gas analy- sis data together with other measurements to quantitatively characterize fermentation kinet- ics Cheap and reliable process computer sys- tems, together with increasingly powerful and easy to use software, have dramatically im- proved capabilities

Gas analysis usually involves measurement of gas flow rates and gas composition Setting up appropriate mass balances allows evalua- tion of actual production and consumption rates Today, gas flow rates can be measured with mass flow meters which directly give an electric signal This facilitates automatic data

evaluation using computers A whole series of instruments to measure gas composition on- line has been developed The instruments in- clude paramagnetic oxygen analyzers, infrared absorption photometers, gas chromatographs (GC), mass spectrometers (MS), flame ioniza- tion detectors (FID), amperometric and poten- tiometric sensors, and semiconductor devices Generally speaking, excluding pH measure- ment, gas analysis is the most widespread and most reliable on-line analysis in industrial fer- mentation processes It has been applied to the on-line analysis of bacterial, fungal, and high- er cell culture systems Its potential in animal and plant cell culture has not yet been fully ex- ploited This is clearly seen by the fact that in a recent review of on-line analysis of animal cell culture the possibility of oxygen uptake rate measurements has not even been mentioned (MERTEN et al., 1986)

Mass Balancing for Gas Analysis 31

ficient; V, and VL (L3), gas and liquid volume;

r (MT-'L-3), reaction rate

The above equations have been written to apply to any component (oxygen, carbon dioxide, ethanol, etc.) They include accumu- lation, convective flow, inter-phase transfer, and reaction terms Usually there is only one biological reaction term, but a special excep- tion is the case of COz dissociation to yield bi- carbonate In a batch reactor the liquid flow terms are L 1 =Lo = 0 In a fed-batch culture

L o # L 1 , and in a continuous culture Lo= L,>O

Here Ct, is the liquid phase concentration

in equilibrium with CG,, and it is calculated by Henry's law

C G I R T = C t , H (3)

2 Mass Balancing

for Gas Analysis

2.1 Basic Gas Balance Equations

Balances which consider gas transfer and gas reaction rates are necessary to characterize the aeration efficiency and to follow biological activity The same equations can be applied to any component Well-mixed phases, whose concentrations can be assumed to be uniform, can be described simply, while situations with spatial variation require more complex mod- els The following general gas balance equa- tions can be written for a well-mixed (tank geometry) system (Fig 1):

are: Ho, = 856.9 L bar/mol; Hco, = 34.01

L bar/mol; HN,= 1484 L bar/mol The solu-

bility of pure gases in water can also be ex- pressed in liters of gas per liter of water At 30°C the values are: Nz, 0.0134; 02, 0.0261;

v, - dCG1 - GoCt.-jo-GICG,-

dt

(1)

-K,a(Ct, CLJ VL

Pressure and Temperature Effects

+ KLa (Ct , - C L , ) v L + z r VL (2) The variables and their dimensions are as fol- lows:

concentrations; G and L (L3T-'), gas and liq-

uid flow rates; KLa (T-l), mass transfer coef-

It is often convenient to write gas balances in terms of partial pressures instead of concen- trations Using the ideal gas law

where R = 0.08205 atm L/mol K = 0.08314

(bar L/mol K) = 8314 (Pa L/mol K) or its equi-

valent for a flowing system,

where N is moledtime and G is volume/time

Thus, useful expressions are:

Fig 1 Gas transfer in a stirred tank reactor with ni = cGi v = ~ ~